## 2009-09-18

### Power Analysis for mixed-effect models in R

The power of a statistical test is the probability that a null hypothesis will be rejected when the alternative hypothesis is true. In lay terms, power is your ability to refine or "prove" your expectations from the data you collect. The most frequent motivation for estimating the power of a study is to figure out what sample size will be needed to observe a treatment effect. Given a set of pilot data or some other estimate of the variation in a sample, we can use power analysis to inform how much additional data we should collect.

I recently did a power analysis on a set of pilot data for a long-term monitoring study of the US National Park Service. I thought I would share some of the things I learned and a bit of R code for others that might need to do something like this. If you aren't into power analysis, the code below may still be useful as examples of how to use the error handling functions in R (`withCallingHandlers`, `withRestarts`), parallel programming using the `snow` package, and linear mixed effect regression using `nlme`. If you have any suggestions for improvement or if I got something wrong on the analysis, I'd love to hear from you.

## 1 The Study

The study system was cobblebars along the Cumberland river in Big South Fork National Park (Kentucky and Tennessee, United States). Cobblebars are typically dominated by grassy vegetation that include disjunct tall-grass prairie species. It is hypothesized that woody species will encroach onto cobblebars if they are not seasonally scoured by floods. The purpose of the NPS sampling was to observe changes in woody cover through time. The study design consisted of two-stages of clustering: the first being cobblebars, and the second being transects within cobblebars. The response variable was the percentage of the transect that was woody vegetation. Because of the clustered design, the inferential model for this study design has mixed-effects. I used a simple varying intercept model:

where y is the percent of each transect in woody vegetation sampled n times within J cobblebars, each with K transects. The parameter of inference for the purpose of monitoring change in woody vegetation through time is β, the rate at which cover changes as a function of time. α, γ, σ2γ, and σ2y are hyper-parameters that describe the hierarchical variance structure inherent in the clustered sampling design.

Below is the function code used I used to regress the pilot data. It should be noted that with this function you can log or logit transform the response variable (percentage of transect that is woody). I put this in because the responses are proportions (0,1) and errors should technically follow a beta-distribution. Log and logit transforms with Gaussian errors could approximate this. I ran all the models with transformed and untransformed response, and the results did not vary at all. So, I stuck with untransformed responses:

```Model <- function(x = cobblebars,
type = c("normal","log","logit")){
## Transforms
if (type[1] == "log")
x\$prop.woody <- log(x\$prop.woody)
else if (type[1] == "logit")
x\$prop.woody <- log(x\$prop.woody / (1 - x\$prop.woody))

mod <- lme(prop.woody ~ year,
data = x,
random = ~ 1 | cobblebar/transect,
na.action = na.omit,
control = lmeControl(opt = "optim",
maxIter = 800, msMaxIter = 800)
)
mod\$type <- type[1]

return(mod)
}
```

Here are the results from this regression of the pilot data:

```Linear mixed-effects model fit by REML
Data: x
AIC       BIC   logLik
-134.4319 -124.1297 72.21595

Random effects:
Formula: ~1 | cobblebar
(Intercept)
StdDev:  0.03668416

Formula: ~1 | transect %in% cobblebar
(Intercept)   Residual
StdDev:  0.02625062 0.05663784

Fixed effects: prop.woody ~ year
Value  Std.Error DF   t-value p-value
(Intercept)  0.12966667 0.01881983 29  6.889896  0.0000
year        -0.00704598 0.01462383 29 -0.481815  0.6336
Correlation:
(Intr)
year -0.389

Number of Observations: 60
Number of Groups:
cobblebar transect %in% cobblebar
6                      30
```

## 2 We don't learn about power analysis and complex models

When I decided upon the inferential model the first thing that occurred to me was that I never learned in any statistics course I had taken how to do such a power analysis on a multi-level model. I've taken more statistics courses than I'd like to count and taught my own statistics courses for undergrads and graduate students, and the only exposure to power analysis that I had was in the context of simple t-tests or ANOVA. You learn about it in your first 2 statistics courses, then it rarely if ever comes up again until you actually need it.

I was, however, able to find a great resource on power analysis from a Bayesian perspective in the excellent book "Data Analysis Using Regression and Multilevel/Hierarchical Models" by Andrew Gelman and Jennifer Hill. Andrew Gelman has thought and debated about power analysis and you can get more from his blog. The approach in the book is a simulation-based one and I have adopted it for this analysis.

## 3 Analysis Procedure

For the current analysis we needed to know three things: effect size, sample size, and estimates of population variance. We set effect size beforehand. In this context, the parameter of interest is the rate of change in woody cover through time β, and effect size is simply how large or small a value of β you want to distinguish with a regression. Sample size is also set a priori. In the analysis we want to vary sample size by varying the number of cobblebars, the number of transects per cobblebar or the number of years the study is conducted.

The population variance cannot be known precisely, and this is where the pilot data come in. By regressing the pilot data using the model we can obtain estimates of all the different components of the variance (cobblebars, transects within cobblebars, and the residual variance). Below is the R function that will return all the hyperparameters (and β) from the regression:

```GetHyperparam<-function(x,b=NULL){
## Get the hyperparameters from the mixed effect model
fe <- fixef(x)

if(is.null(b))
b<-fe[2] # use the data effect size if not supplied

mu.a <- fe[1]

vc <- VarCorr(x)
sigma.y <- as.numeric(vc[5, 2]) # Residual StdDev
sigma.a <- as.numeric(vc[2, 2]) # Cobblebar StdDev
sigma.g <- as.numeric(vc[4, 2]) # Cobblebar:transect StdDev

hp<-c(b, mu.a, sigma.y, sigma.a, sigma.g)
names(hp)<-c("b", "mu.a", "sigma.y", "sigma.a", "sigma.g")
return(hp)
}
```

To calculate power we to regress the simulated data in the same way we did the pilot data, and check for a significant β. Since optimization is done using numeric methods there is always the chance that the optimization will not work. So, we make sure the regression on the fake data catches and recovers from all errors. The solution for error recovery is to simply try the regression on a new set of fake data. This function is a pretty good example of using the R error handling function `withCallingHandlers` and `withRestarts`.

```fakeModWithRestarts <- function(m.o, n = 100,  ...){
## A Fake Model
withCallingHandlers({
i <- 0
mod <- NULL
while (i < n & is.null(mod)){
mod <- withRestarts({
f <- fake(m.orig = m.o, transform = F, ...)
return(update(m.o, data = f))
},
rs = function(){
i <<- i + 1
return(NULL)
})
}
if(is.null(mod))
warning("ExceededIterations")
return(mod)
},
error = function(e){
invokeRestart("rs")
},
warning = function(w){
if(w\$message == "ExceededIterations")
cat("\n", w\$message, "\n")
else
invokeRestart("rs")
})
}
```

To calculate the power of a particular design we run `fakeModWithRestarts` 1000 times and look at the proportion of significant β values:

```dt.power <- function (m, n.sims = 1000, alpha=0.05, ...){
## Calculate power for a particular sampling design
signif<-rep(NA, n.sims)
for(i in 1:n.sims){
lme.power <- fakeModWithRestarts(m.o = m, ...)
if(!is.null(lme.power))
signif[i] <- summary(lme.power)\$tTable[2, 5] < alpha
}
power <- mean(signif, na.rm = T)
return(power)
}
```

Finally, we want to perform this analysis on many different sampling designs. In my case I did all combinations of set of effect sizes, cobblebars, transects, and years. So, I generated the appropriate designs:

```factoredDesign <- function(Elevs = 0.2/c(1,5,10,20),
Nlevs = seq(2, 10, by = 2),
Jlevs = seq(4, 10, by = 2),
Klevs = c(3, 5, 7), ...){
## Generates factored series of sampling designs for simulation
## of data that follow a particular model.
## Inputs:
##   Elevs - vector of effect sizes for the slope parameter.
##   Nlevs - vector of number of years to sample.
##   Jlevs - vector of number of cobblebars to sample.
##   Klevs - vector of number of transects to sample.
## Results:
##   Data frame with where columns are the factors and
##   rows are the designs.

# Level lengths
lE <- length(Elevs)
lN <- length(Nlevs)
lJ <- length(Jlevs)
lK <- length(Klevs)

# Generate repeated vectors for each factor
E <- rep(Elevs, each = lN*lJ*lK)
N <- rep(rep(Nlevs, each = lJ*lK), times = lE)
J <- rep(rep(Jlevs, each = lK), times = lE*lN)
K <- rep(Klevs, times = lE*lN*lJ)

return(data.frame(E, N, J, K))
}
```

Once we know our effect sizes, the different sample sizes we want, and the estimates of population variance we can generate simulated dataset that are similar to the pilot data. To calculate power we simply simulate a large number of dataset and calculate the proportion of slopes, β that are significantly different from zero (p-value < 0.05). This procedure is repeated for all the effect sizes and sample sizes of interest. Here is the code for generating a simulated dataset. It also does the work of doing the inverse transform of the response variables if necessary.

```fake <- function(N = 2, J = 6, K = 5, b = NULL, m.orig = mod,
transform = TRUE, ...){
## Simulated Data for power analysis
## N = Number of years
## J = Number of cobblebars
## K = Number of transects within cobblebars
year <- rep(0:(N-1), each = J*K)
cobblebar <- factor(rep(rep(1:J, each = K), times = N))
transect <- factor(rep(1:K, times = N*J))

## Simulated parameters
hp<-GetHyperparam(x=m.orig)
if(is.null(b))
b <- hp['b']
g <- rnorm(J*K, 0, hp['sigma.g'])
a <- rnorm(J*K, hp['mu.a'] + g, hp['sigma.a'])

## Simulated responses
eta <- rnorm(J*K*N, a + b * year, hp['sigma.y'])
if (transform){
if (m.orig\$type == "normal"){
y <- eta
y[y > 1] <- 1 # Fix any boundary problems.
y[y < 0] <- 0
}
else if (m.orig\$type == "log"){
y <- exp(eta)
y[y > 1] <- 1
}
else if (m.orig\$type == "logit")
y <- exp(eta) / (1 + exp(eta))
}
else{
y <- eta
}

return(data.frame(prop.woody = y, year, transect, cobblebar))
}
```

Then I performed the power calculations on each of these designs. This could take a long time, so I set this procedure to use parallel processing if needed. Note that I had to re-~source~ the file with all the necessary functions for each processor.

```powerAnalysis <- function(parallel = T, ...){
## Full Power Analysis

## Parallel
if(parallel){
closeAllConnections()
cl <- makeCluster(7, type = "SOCK")
on.exit(closeAllConnections())
clusterEvalQ(cl, source("cobblebars2.r"))
}

## The simulations
dat <- factoredDesign(...)

if (parallel){
dat\$power <- parRapply(cl, dat, function(x,...){
dt.power(N = x[2], J = x[3], K = x[4], b = x[1], ...)
}, ...)
} else {
dat\$power <- apply(dat, 1, function(x, ...){
dt.power(N = x[2], J = x[3], K = x[4], b = x[1], ...)
}, ...)
}

return(dat)
}
```

The output of the `powerAnalysis` function is a data frame with columns for the power and all the sample design settings. So, I wrote a custom plotting function for this data frame:

```plotPower <- function(dt){
xyplot(power~N|J*K, data = dt, groups = E,
panel = function(...){panel.xyplot(...)
panel.abline(h = 0.8, lty = 2)},
type = c("p", "l"),
xlab = "sampling years",
ylab = "power",
strip = strip.custom(var.name = c("C", "T"),
strip.levels = c(T, T)),
auto.key = T
)
}
```

Below is the figure for the cobblebar power analysis. I won't go into detail on what the results mean since I am concerned here with illustrating the technique and the R code. Obviously, as the number of cobblebars and transects per year increase, so does power. And, as the effect size increases, observing it with a test is easier.

Date: 2009-09-18 Fri

HTML generated by org-mode 6.30trans in emacs 22

#### 234 Comments:

1 – 200 of 234 Newer› Newest»
Unknown said...

This is awesome Todd! I'm trying to adapt your parallel processing code for a randomization procedure I'd like to speed up.
Thanks!
Dan McGlinn

October 26, 2009 at 12:25 PM
Anonymous said...

this is really complex

Online Tutoring

August 15, 2010 at 12:02 AM
Anonymous said...

This is remarkable work

Online Tutoring,Home Tutor,Private Tutor

August 23, 2010 at 12:02 PM
Unknown said...

This is really very complicated and comlex, I don't how people can solve this.

bioinformatics training india

September 22, 2010 at 5:36 AM
Shagor said...

This blog is nice and amazing. I love your post! It's also nice to see someone who does a lot of research and has a great knack for ting, which is pretty rare from bloggers these days.
Thanks a lot!
Pilot license

January 29, 2012 at 1:54 PM
Anonymous said...

Thanks for sharing very nice info. your post is very informative and awesome and

its very helpful for the reader.I like your post.Keep it

up.http://www.technologyexplores.com

June 18, 2013 at 10:39 AM
Unknown said...

You have some really good ideas in this article . I am glad I read this. I agree with much of what you state in this article. Your information is thought-provoking, interesting and well-written. Thank you.

Term Papers Essay Services

July 10, 2013 at 3:16 AM
Unknown said...

I would like to thank for the efforts you have put in writing this blog. I am hoping the same high-grade blog post from you in the upcoming as well. In fact your creative writing abilities has inspired me to get my own blog now. Really the blogging is spreading its wings quickly. Your write up is a good example of it.
Best security system for home in Bangalore

August 6, 2013 at 9:06 AM
Unknown said...

great blog man, really helped with some of my research.

See secret documents about Nikola Tesla
http://fbi-about-tesla.blogspot.com

August 17, 2013 at 3:37 PM
Unknown said...

I love the way you are teaching us. Waiting to read more from you. I love to design websites.

August 30, 2013 at 4:06 AM
Anonymous said...

http://electricfireplaceheater.org/component/k2/item/66-10-best-electric-fireplace-heaters-by-user-reviews.html - find best electric fireplace heaters ...

October 29, 2013 at 2:49 PM
romunov said...

This is not spam. :) Unfortunately links to figures don't work any more. Can you look at this?

November 6, 2013 at 8:38 AM
laurawkelly said...

The Apache® Hadoop project is a framework enabling distributed processing of Hadoop Online Training large data sets through a network of computers using simple programming models.
It is born to scale single servers up to thousands of machines, each that can offer local computation and storage. Hadoop Online Training To deliver high availability and uptime of 99% and more rather than relying on hardware, the library can itself detect and handle failures at the application layer.
So delivering a value based service on top of a network of computers Hadoop Online Training which may be prone to failures is the objective that is attained with the Hadoop project.

February 21, 2014 at 11:53 PM
Richard C. Lambert said...

Collect and learn them". William Penn, founder of the State of Pennsylvania.makita impact driver

November 3, 2015 at 1:34 AM
Richard C. Lambert said...

Given a set of pilot
data or some other estimate of the variation in a sample, we can use
power analysis to inform how much additional data we should collectc10fce2 review

November 29, 2015 at 6:02 AM
henris said...

Thank you for posting it will be helpful by knowing more about GDAL. Thank you and please keep update like this with this site. Definitely it will be useful for all.

SQL DBA Training in Chennai

March 2, 2016 at 7:50 AM
Unknown said...

Hi Todd,

Thanks for this post, it's very helpful. A couple of the images are currently unavailable though. I was wondering if you could possibly fix them?

March 5, 2016 at 3:01 PM
Unknown said...

Excellent info here, I am currently doing some research and found exactly what I was looing for. my review here

March 10, 2016 at 6:54 PM
Unknown said...

Really good job on the site, Thanks for guide! best 14 bandsaw

March 12, 2016 at 3:33 AM
Unknown said...

All are saying the same thing repeatedly, but in your blog I had a chance to get some useful and unique information, I love your writing style very much, I would like to suggest your blog in my dude circle, so keep on updates.

Peridot Systems Adyar Contact Number

March 22, 2016 at 8:14 AM
Jubaer said...

Really Nice post Todd, you just made my problem solved. Thanks again. web design

April 13, 2016 at 3:35 PM
Karis said...

The image with your model structure doesn't load in my browser. I am not sure if this is a problem with my firewall or a broken link.

May 24, 2016 at 4:18 PM
franklin said...
June 22, 2016 at 11:33 AM
Prashanthi said...

Your post is really great. Thank you for taking time to provide us some of the useful and exclusive information with us. Keep on blogging!!
Best SharePoint Training Institute in Chennai

August 16, 2016 at 6:07 AM
Unknown said...
May 10, 2017 at 1:14 AM
Unknown said...
June 4, 2017 at 10:58 AM
Unknown said...

Telangana DSC Recruitment 2017 Notification is announced in last week of December with District wise Vacancies lists TS DSC 2017 , Telangana DSC 2017, TS DSC Notification 2017, TS DSC Model Papers 2017, Sakshi TS DSC Model Papers 2017, Namasthe Telangana TS DSC Model Papers 2017, TS DSC District wise Vacancies list 2017 Government Primary and Secondary Schools for Secondary Grade Teacher (SGT),Language Pandit (LP),School Assistant(SA)and Physical Education Teacher (PET) Posts with the TS DSC 2017.

June 26, 2017 at 1:45 PM
Anonymous said...

Really Good blog post.provided a helpful information about power analysis of mixed model.keep updating...
Digital marketing company in Chennai

July 3, 2017 at 6:30 AM
Unknown said...

All the board students can Download Subject wise new Syllabus for all state and central board schools with model papers 2018 for all board of secondary education boards and students can apply scholarship 2018 for ekalyan epass to online application and status check

July 3, 2017 at 11:35 AM
kingrani said...
August 8, 2017 at 6:35 AM
Unknown said...

Best Dyson Vacuums

August 15, 2017 at 9:37 AM
Unknown said...

Its a wonderful post and very helpful, thanks for all this information. You are including better information regarding this topic in an effective way.Thank you so much

Personal Installment Loans
Title Car loan
Cash Advance Loan

August 28, 2017 at 12:22 PM
Karthik Jessie said...
September 5, 2017 at 8:25 AM
kingrani said...
September 5, 2017 at 8:41 AM
Unknown said...

Find best vacuum for pet hairs.

October 29, 2017 at 5:35 PM
sophia sophia said...

Thanks for this wonderful post. The information in this article is very helpful to me. Thanks a lot for sharing. Keep blogging.
Truth or Dare Questions
Best questions to ask your girlfriend over text

November 9, 2017 at 12:27 AM
Unknown said...

amazing !!! good work. keep it up. find shredder

November 11, 2017 at 1:24 AM
David Smith said...

Hi, Great.. Tutorial is just awesome..It is really helpful for a newbie like me.. I am a regular follower of your blog. Really very informative post you shared here. Kindly keep blogging. If anyone wants to become a Java developer learn from Java Training in Chennai. or learn thru Java Online Training in India . Nowadays Java has tons of job opportunities on various vertical industry.

December 7, 2017 at 11:48 PM
Anthony Paul said...
December 20, 2017 at 12:33 AM
kingrani said...

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it.

CashbackoffersCoupons.in
Tatacliq Cashback

January 11, 2018 at 7:20 AM
sophia sophia said...

Thanks for this wonderful post. Keep blogging.
If you want to know latest technical news click link below.
Interestwaypoint

January 25, 2018 at 8:13 AM
sophia sophia said...

Thanks for this wonderful post. Keep blogging.
If you want to know latest technical news click link below.
Interestwaypoint

January 25, 2018 at 8:13 AM
Cricket Fan said...

Thank you facebook data saver

March 1, 2018 at 9:39 PM
Cricket Fan said...

samsung j7 update nougat

March 1, 2018 at 9:50 PM
Cricket Fan said...
March 4, 2018 at 9:49 PM
Unknown said...

Thanks for sharing this amazing information
See this

March 30, 2018 at 6:19 AM
Unknown said...

Thanks for sharing this amazing information
See this

April 2, 2018 at 2:19 PM
Unknown said...

Thanks for sharing this amazing information. Keep it up Really appreciated
see this

April 3, 2018 at 9:32 AM
Unknown said...

nice to see this have a look

April 4, 2018 at 6:27 AM
Unknown said...

Thanks for shring this amazing article. It help a lot.. Thanks once again
see this

April 4, 2018 at 2:25 PM
Unknown said...

nice to see this have a look

April 5, 2018 at 4:13 AM
Unknown said...

Thanks for sharing this amazing information. Keep it Really appreciated
see this

April 5, 2018 at 6:52 AM
andrew said...

Graet post i love this very much.
Best dyson vacuum

April 5, 2018 at 9:48 AM
andrew said...

Thanks for sharing this great article.

Best vacuum cleaner

April 6, 2018 at 8:08 AM
Unknown said...

Nice Informative Post. Great work Really Appreciated
See this

April 7, 2018 at 4:49 AM
Unknown said...

I really enjoyed that post
see this

April 8, 2018 at 8:40 AM
Unknown said...

nice to see this have a look

April 9, 2018 at 2:21 AM
Unknown said...

Nice work really appreciated
see this

April 9, 2018 at 5:19 AM
Unknown said...

Nice to see this Have a Look

April 11, 2018 at 3:45 AM
Unknown said...

What a great platform that for such nice information Have a Look

April 12, 2018 at 6:58 AM
Unknown said...

Really amazing post..much helpful see this
check this

April 16, 2018 at 7:25 AM
Unknown said...

check this
Really amazing post..much helpful see this

April 16, 2018 at 11:56 PM
Unknown said...

Amazing post really appreciated Check here

April 17, 2018 at 2:20 AM
Unknown said...

I was surfing to find something amazing and found that excellent post

April 17, 2018 at 6:57 AM
Unknown said...
April 21, 2018 at 1:32 AM
Unknown said...
April 21, 2018 at 1:34 AM
Unknown said...
April 21, 2018 at 1:35 AM
Unknown said...
April 21, 2018 at 1:35 AM
Unknown said...

After searching for hours finally i found something that I can say helpful

April 24, 2018 at 7:07 AM
Unknown said...

The Information I found is quite nice and helped me alot. Thanks for this

April 25, 2018 at 11:30 PM
Unknown said...

I was looking for something amazing and finally found it

April 26, 2018 at 6:29 AM
Unknown said...

What a great platform that for such nice information Have a Look

April 27, 2018 at 11:49 AM
Unknown said...

What a great platform that for such nice information Have a Look keep up the good work

April 30, 2018 at 8:13 AM
Unknown said...

What a great platform that for such nice information Have a Look keep up the good work

May 20, 2018 at 5:46 AM
Unknown said...

What a great platform that for such nice information Have a Look keep up the good work

May 21, 2018 at 5:52 AM
flipkart cashback offers said...
May 23, 2018 at 8:22 AM
flipkart cashback offers said...

flipkart is Offering Cashback Offers Flipkart hdfc cashback offers You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart SBI Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart AXIS Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart YES Cashback Offer You will get upto 75% Discount

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart big billion day offers

Flipkart is one of the biggest world wide eCommerce Site so here you will getflipkart bank cashback offersso

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart big billion day offer

Flipkart is one of the biggest world wide eCommerce Site so here you will getflipkart bank cashback offersso

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart bank offersso

Flipkart is Offering Cashback Offers Flipkart Today Offers You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart offers today You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart Today saree offers You will get upto 75% Discount

May 23, 2018 at 8:22 AM
flipkart cashback offers said...

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it.

flipkart is Offering Cashback Offers Flipkart hdfc cashback offers You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart SBI Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart AXIS Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart YES Cashback Offer You will get upto 75% Discount

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart big billion day offers

Flipkart is one of the biggest world wide eCommerce Site so here you will getflipkart bank cashback offersso

Flipkart cashback offers on mobiles,
Flipkart cashback offers,
Flipkart cashback coupons,
Flipkart upcoming offers on mobiles,
Flipkart HDFC cashback offers,
Flipkart SBI cashback offers,
Flipkart AXIS cashback offers,
Flipkart Citibank cashback offers,
Flipkart cashback on mobiles,
Flipkart cashback offers today,
Flipkart big billion day cashback offers,
Flipkart big billion days cashback offers,
big billion day cashback offers,
Flipkart big billion days offers,
flipkart cashback on mobiles,
flipkart citibank offer,
sbi credit card offers on flipkart today,
flipkart upcoming offers on mobiles,
hdfc credit card offers on flipkart,
flipkart upcoming big billion day,
flipkart upcoming sale,
sbi credit card offers on mobiles,
flipkart offers today,
flipkart offers on mobiles,
flipkart offers today mobile phones,
flipkart cashback offers,
flipkart cashback coupons,
flipkart sale today offer,
flipkart cashback offers today,
cashback offers,
flipkart cashback offer today

May 23, 2018 at 8:22 AM
flipkart cashback offers said...

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it.

flipkart is Offering Cashback Offers Flipkart hdfc cashback offers You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart SBI Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart AXIS Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart YES Cashback Offer You will get upto 75% Discount

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart big billion day offers

Flipkart is one of the biggest world wide eCommerce Site so here you will getflipkart bank cashback offersso

Flipkart cashback offers on mobiles,
Flipkart cashback offers,
Flipkart cashback coupons,
Flipkart upcoming offers on mobiles,
Flipkart HDFC cashback offers,
Flipkart SBI cashback offers,
Flipkart AXIS cashback offers,
Flipkart Citibank cashback offers,
Flipkart cashback on mobiles,
Flipkart cashback offers today,
Flipkart big billion day cashback offers,
Flipkart big billion days cashback offers,
big billion day cashback offers,
Flipkart big billion days offers,
flipkart cashback on mobiles,
flipkart citibank offer,
sbi credit card offers on flipkart today,
flipkart upcoming offers on mobiles,
hdfc credit card offers on flipkart,
flipkart upcoming big billion day,
flipkart upcoming sale,
sbi credit card offers on mobiles,
flipkart offers today,
flipkart offers on mobiles,
flipkart offers today mobile phones,
flipkart cashback offers,
flipkart cashback coupons,
flipkart sale today offer,
flipkart cashback offers today,
cashback offers,
flipkart cashback offer today

May 23, 2018 at 8:23 AM
flipkart cashback offers said...

flipkart is Offering Cashback Offers Flipkart hdfc cashback offers You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart SBI Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart AXIS Cashback Offer You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart YES Cashback Offer You will get upto 75% Discount

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart big billion day offers

Flipkart is one of the biggest world wide eCommerce Site so here you will getflipkart bank cashback offersso

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart big billion day offer

Flipkart is one of the biggest world wide eCommerce Site so here you will getflipkart bank cashback offersso

Flipkart is one of the biggest world wide eCommerce Site so here you will getFlipkart bank offersso

Flipkart is Offering Cashback Offers Flipkart Today Offers You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart offers today You will get upto 75% Discount

Flipkart is Offering Cashback Offers Flipkart Today saree offers You will get upto 75% Discount

May 23, 2018 at 8:23 AM
flipkart cashback offers said...
May 23, 2018 at 8:23 AM
Unknown said...

What a great platform that for such nice information website

June 22, 2018 at 5:12 PM
Unknown said...

What a great platform that for such nice information website

June 25, 2018 at 5:46 PM
Unknown said...

Good work keep it up website

June 28, 2018 at 12:04 PM
Unknown said...

Keep up the good work thanx website

July 1, 2018 at 4:35 AM
Anthony Paul said...

Thank you very much for this excellent information.!!!
i really appreciated, keep it up !
check list of best vacumm for 2018

July 7, 2018 at 7:18 AM
Unknown said...

Thanks for sharing this amazing information
Know more
check here
click here
see this
amazing information

August 7, 2018 at 6:06 AM
Unknown said...

thanks for posting this blog
machine learning training in bangalore
hadoop training in bangalore

August 7, 2018 at 8:51 AM
Unknown said...

Hadoop concepts, Applying modelling through R programming using Machine learning algorithms and illustrate impeccable Data Visualization by leveraging on 'R' capabilities.With companies across industries striving to bring their research and analysis (R&A) departments up to speed, the demand for qualified data scientists is rising.
data science training in bangalore

August 7, 2018 at 8:51 AM
Anthony Paul said...

Thanks for every other informative blog. The place
else may just I am getting that kind of information written in such a perfect way.
Keep it up. please visit our blog
for more info
click here
have a look
get info
more information

August 7, 2018 at 10:15 PM
anosh said...
August 12, 2018 at 4:45 PM
Unknown said...

Thanks for sharing this excellent information
See

More

Click

Here

che

ck this

know

more

see

this

August 13, 2018 at 4:38 AM
Chaudhry said...

That's a well managed & informative
blog it's really nice to read it keep
bringing more value into your blog.
External Hard drive

August 20, 2018 at 2:57 AM
Chaudhry said...

Your blog really helps visitor all the time.
Check this one too.

August 29, 2018 at 3:53 AM
shaban ali said...

Thanks for sharing this amazing information.
liftmaster 8550w review

August 30, 2018 at 2:07 PM
Unknown said...

Thanks for sharing this amazing information
see this
check this

September 4, 2018 at 11:26 AM
shaban ali said...

Thanks for sharing this best information.
liftmaster csl24u review

September 6, 2018 at 12:20 PM
shaban ali said...

Thanks for sharing this Nice article.
See this

September 7, 2018 at 6:49 AM
shaban ali said...

Thanks i really like that.
See this

September 7, 2018 at 11:02 AM
shaban ali said...

very appreciated great post! Keep it up.
See this

September 7, 2018 at 1:59 PM
shaban ali said...

Thanks for this informative post.
check this

September 8, 2018 at 7:27 AM
shaban ali said...

thanks for sharing this amazing information.
Dyson 360 Eye Review - allofvacuums

September 10, 2018 at 5:57 AM
shaban ali said...

Great really nice information.
Neato Botvac D7 Review - allofvacuums

September 11, 2018 at 5:01 AM
shaban ali said...

Great post Keep it up.
Electrolux Pure i9 Review- allofvacuums

September 11, 2018 at 7:24 AM
shaban ali said...

Great really nice information.
iLife V5S Pro Review - allofvacuums

September 11, 2018 at 12:43 PM
shaban ali said...

Thanks again for this amazing post.
See this

September 20, 2018 at 4:17 PM
shaban ali said...

Great post and I hope this is best for all visitors.
See this

September 21, 2018 at 11:45 AM
shaban ali said...

Really amazing information.
See this

September 21, 2018 at 2:02 PM
Chaudhry said...

I think you have the best understanding of blogs.Do help me
Here's my site Check it out and give suggestions.

October 1, 2018 at 7:54 AM
shaban ali said...

Great post and I hope this is best for all visitors.
See this

October 2, 2018 at 12:41 PM
Chaudhry said...

I think you have the best understanding of blogs.Do help me
Here's my site Check it out and give suggestions.

October 3, 2018 at 2:58 AM
shaban ali said...

Really amazing and nice information.
See this

October 3, 2018 at 5:19 AM
Chaudhry said...

Thanks for this amazing post
Click here

October 4, 2018 at 1:39 AM
shaban ali said...

Thank you for the interesting history really great.
Click here

October 8, 2018 at 5:12 AM
shaban ali said...

Thanks for every other informative blog.
Click here

October 8, 2018 at 6:32 AM
Unknown said...

A great platform for such a nice information have a look keep up the good work

October 18, 2018 at 7:06 PM
Unknown said...

Nice platform Visit website!

October 24, 2018 at 8:04 PM
Chaudhry said...

I think you have the best understanding of blogs.Do help me
Here's my site Check it out and give suggestions.

October 25, 2018 at 6:31 AM
shaban ali said...

I like this post very much.
Click Here

October 25, 2018 at 8:51 AM
Chaudhry said...

I think you have the best understanding of blogs.Do help me
Here's my site Check it out and give suggestions.

October 25, 2018 at 8:58 AM
shaban ali said...

Great post i hope this is best for all visitors.
Click Here

October 27, 2018 at 1:59 PM
Unknown said...
October 29, 2018 at 8:21 AM
Unknown said...
October 31, 2018 at 3:40 PM
shaban ali said...

The nice information I really like this keep it up!
Click Here

November 3, 2018 at 8:45 AM
Anthony Paul said...

Thanks for sharing your thought with us!
please see this

November 4, 2018 at 1:46 PM
Umair said...

It's best knowledge shared on this topic. I have never seen such accurate post
read more..

November 5, 2018 at 8:33 AM
johnroy said...

Thanks alot for this beautiful information!
please click here

November 6, 2018 at 11:15 PM
assad said...

its nice to be here.keep posting such content
click here

November 7, 2018 at 2:07 AM
Umair said...

What a great piece of content. Exactly to the point and concise with all the information.
read more..

November 7, 2018 at 9:44 AM
assad said...

very good information given by your blog.
thanks! see more

November 7, 2018 at 3:42 PM
Unknown said...
November 8, 2018 at 1:07 AM
assad said...

Thanks for sharing this amazing post.
see more

November 8, 2018 at 7:03 AM
Umair said...

maybe you have to enter some more info but not bad. Nice work
Keep improving it.
Click Here

November 9, 2018 at 6:27 AM
assad said...

Thanks for sharing this amazing post.
see more

November 10, 2018 at 3:43 PM
johnroy said...

Thanks for sharing your thought with us!
please see this

November 10, 2018 at 8:31 PM
David zen said...

Thanks for sharing your thought with us!
see this

November 13, 2018 at 7:01 AM
Davin Smith said...

nice to see this post! keep sharing such type of post.
please have a look

November 15, 2018 at 3:44 AM
mohit said...

nice post
hotmail sign up login

November 15, 2018 at 5:47 AM
assad said...

its nice to be here.keep posting such content
click here

November 16, 2018 at 5:29 AM
assad said...

its nice to be here.keep posting such content
click here

November 17, 2018 at 3:07 AM
Rithi Rawat said...

Very nice post here thanks for it .I always like and such a super contents of these post.Excellent and very cool idea and great content of different kinds of the valuable information's. Machine learning training in chennai
machine learning with python course in Chennai

November 17, 2018 at 8:44 AM
David zen said...

Thanks alot for this beautiful information!
click here

November 19, 2018 at 9:31 AM
assad said...

very good information given by your blog.
thanks! see more

November 23, 2018 at 8:12 AM
elbert said...

Thanks for sharing this amazing post.
see more

November 23, 2018 at 8:09 PM
elbert said...

Thanks for sharing this amazing post.
see more

December 3, 2018 at 3:12 AM
Fashioner said...

Amazing article. keep posting such great content on daily basis it literally attracts us all the time to your blog
See more..

December 3, 2018 at 10:42 PM
asad said...

Thanks for sharing this amazing post.
see more

December 5, 2018 at 3:24 PM
Chaudhry said...

Keep posting such content
Read more

December 6, 2018 at 9:07 AM
Chaudhry said...

Thanks a lot for sharing that article with your audience.
see more..

December 7, 2018 at 8:22 AM
Chaudhry said...

Thanks a lot for sharing that article with your audience.
see more..

December 8, 2018 at 7:57 AM
Umair said...

you have covered all the aspects so accurately. Keep going on!
Read more..

December 9, 2018 at 1:42 PM
asad said...

its nice to be here.keep posting such content
click here

December 10, 2018 at 3:26 AM
jhon miller said...

very good information given by your blog.
thanks! visit our website

December 11, 2018 at 8:24 AM
Chaudhry said...

Thanks a lot for sharing that article with your audience.
see more..

December 11, 2018 at 9:24 AM
jhon miller said...

its nice to be here.keep posting such content
click here

December 12, 2018 at 2:20 AM
asad said...

its nice to be here.keep posting such content
lock here

December 12, 2018 at 3:26 AM
jhon miller said...

very good information given by your blog.
thanks! visit our website

December 12, 2018 at 5:24 AM
asad said...

very good information given by your blog.
thanks! see more

December 13, 2018 at 3:38 AM
asad said...

Nice info see this keep up the good work.
thanks! svisit website

December 14, 2018 at 5:41 AM
asad said...

What a great platform that for such nice information Have a Look keep up the good work.
thanks! web page

December 14, 2018 at 3:15 PM
Unknown said...

Love this idea! Thanks for sharing!!
visit website

December 15, 2018 at 6:28 AM
asad said...

very good information given by your blog.
thanks! see more

December 15, 2018 at 3:02 PM
johnroy said...

Amazing work.
keep it up. for more information visit this link

December 15, 2018 at 11:24 PM
jhon miller said...

Thanks very informative. Do check out more info at:
thanks! our website

December 17, 2018 at 2:23 AM
jhon miller said...

I wanted to thank you for this great read! keep positing here...
click here

December 17, 2018 at 3:56 AM
jhon miller said...

It's worth reading your content all the time.
Hope to see you in top positions of internet our website

December 18, 2018 at 1:47 AM
asad said...

What a great platform that for such nice information Have a Look keep up the good work.
thanks! web page

December 18, 2018 at 2:55 AM
asad said...

it is nice content keep improve thanks for this
thanks! look website

December 20, 2018 at 2:15 AM
johnroy said...

Thanks for every other informative blog. The place
else may just I am getting that kind of information written in such a perfect way.
check more information

December 20, 2018 at 1:14 PM
asad said...

it is nice content keep improve thanks for this
thanks! look website

December 21, 2018 at 3:11 AM
johnroy said...

Amazing work.
keep it up. for more information visit this link

December 25, 2018 at 10:51 PM
asad said...

thanks for amazaing information.
robert

December 31, 2018 at 5:29 AM
elbert said...

Very beautiful makeover! This just inspired me.thanks!
visit here

January 1, 2019 at 3:01 AM
Unknown said...

It would be better, amazing work . Click here for this url

January 9, 2019 at 8:11 AM
Ben Myers said...

Hey, I read the post entirely and couldn’t help thanking you for sharing with us this piece of informative resource. Could you please explain the Best Paints a little more, so I can enhance the knowledgebase of our community website Sandersreview. Of course, you can do it in another post! Any effort appreciated!

January 12, 2019 at 6:22 AM
Erik Himmel said...

Good job! Some might find your information to be lacking in-depth analyses. But I’m certainly not one of them. I’m thinking about using some of your information for a whitepaper that I would share via Spottingpro, our website for our community.

January 13, 2019 at 3:46 AM
flipkart cashback offers said...

flipkart mobiles all android phones,
flipkart mobiles all android phones offers,
flipkart mobiles all smartphones,
flipkart mobiles all smartphones offers,
flipkart money offers,
flipkart netbanking offers,
flipkart new arrival mobiles,
flipkart new customer offer,
flipkart new deals,
flipkart new mobile,
flipkart new mobile offer,
flipkart new mobile phone,
flipkart new offer,
flipkart new offer mobile,
flipkart new offers today,,
flipkart new phone,
flipkart new user offer,
flipkart offer 2017,
flipkart offer citibank,
flipkart offer code
flipkart offer code for mobile,
flipkart offer code today,
flipkart offer coupon code,
flipkart offer for citibank credit card,
flipkart offer for sbi cards,
flipkart offer for sbi debit card,
flipkart offer hdfc card,
flipkart offer in may 2016,
flipkart offer now,
flipkart offer of the day mobile,
flipkart offer of the today,
flipkart offer on 15th august,,
flipkart offer on icici bank credit card,
flipkart offer on sbi debit card,
flipkart offer price,
flipkart offer with citibank,
flipkart offer with sbi debit card,
flipkart offers,
flipkart offers 2016,
flipkart offers and coupons,
flipkart offers coupons 2016,
flipkart offers coupons on mobiles,
flipkart offers for icici debit card,
flipkart offers for today on mobiles,
flipkart offers in 2016,
flipkart offers latest,
flipkart offers memory card,
flipkart offers on bank cards,
flipkart offers on citibank,
flipkart offers on credit cards today,
flipkart offers on electronics,
flipkart offers on hdfc debit card,
flipkart offers on mobiles 2016,
flipkart offers on mobiles april 2015,
flipkart offers on mobiles low price,
flipkart offers this month,
flipkart offers today,
flipkart offers today for mobiles,
flipkart offers today mobile phone
flipkart offers watches,
flipkart offers with banks,
flipkart old mobile sale,
flipkart on,
flipkart online,
flipkart online coupons,
flipkart online deals,
flipkart online mobile,
flipkart online mobile booking,
flipkart online mobile offers,
flipkart online mobile purchase,
flipkart online mobile sale,
flipkart online mobile shop,
flipkart online mobile store,
flipkart online offers today
flipkart online payment offer,
flipkart online payment offers,
flipkart online phone,
flipkart online purchase,
flipkart online shop todays offers,
flipkart online shopping discount
flipkart online shopping discount coupons
flipkart online shopping diwali offers
flipkart online shopping dresses
flipkart online shopping electronics
flipkart online shopping memory card
flipkart online shopping mobile
flipkart online shopping mobile accessories
flipkart online shopping mobile offers
flipkart online shopping mobile phones
flipkart online shopping mobile samsung
flipkart online shopping offers
flipkart online shopping offers today
flipkart online shopping phone,
flipkart online shopping site,
flipkart online shopping smartphone,
flipkart online shopping watches,
flipkart online store,
flipkart online watch,
flipkart payment offer,
flipkart payment offers

February 27, 2019 at 6:16 AM
flipkart cashback offers said...
February 27, 2019 at 6:16 AM
flipkart cashback offers said...
March 31, 2019 at 6:26 AM
flipkart cashback offers said...
March 31, 2019 at 6:26 AM
flipkart cashback offers said...
April 18, 2019 at 4:37 AM
flipkart cashback offers said...
April 18, 2019 at 4:38 AM
vinith said...

This is an excellent post I seen thanks to share it. It is really what I wanted to see hope in future you will continue for sharing such a excellent post.
machine learning course in bangalore

May 24, 2019 at 6:00 AM
Anonymous said...

Excellent Blog! I would like to thank for the efforts you have made in writing this post. I am hoping the same best work from you in the future as well. I wanted to thank you for this websites! Thanks for sharing. Great websites! Now please do visit our website which will be very helpful.
machine learning course bangalore

June 4, 2019 at 4:52 AM
flipkart offers said...
June 9, 2019 at 5:34 AM
flipkart offers said...

Grab Cashback - Up to 50% Off at Flipkart SHOP NOW,
ICICI debit card EMI offers - Flipkart,
Debit card EMI facility - Flipkart,
ICICI debit card EMI offers - Flipkart,
Flipkart HDFC EMI offers,
Grab Cashback - Up to 50% Off at Flipkart SHOP NOW,
10% Instant Discount on SBI Credit Cards at Flipkart,
10% Instant Discount on SBI Credit Cards - Flipkart
10% Instant Discount with HDFC Bank Debit and Credit at Flipkart
10% Instant Discount on SBI Credit Cards - Flipkart,
10% Instant Discount on SBI Credit Cards at Flipkart
Monsoon Offers on Home Appliances - Flipkart,
Flipkart SBI Offer 2019: 10% Instant Cashback,
Flipkart HDFC Offer 2019: 10% Instant Offer,
Flipkart Cashback offer 2019: 10% Cashback,
Cashless Pay Store - Flipkart,
Flat Rs. 4000 instant discount on transactions made using at Flipkart,
No Cost EMI available on Credit Cards Valid till 10 January at Flipkart
Diwali Festive Sale - Flipkart
10% Off on All Cards on Home Appliances - Flipkart
10% Off on Cooling Days at Flipkart on SBI Credit Cards | SBI Card
flipkart samsung carnival,
flipkart mobiles,
TV & appliances Sale (Axis Bank Offer) at Flipkart,
10% Off on purchase of Fashion, Home & Furniture and at Flipkart,

Air purifiers Offers - Flipkart,
Offer Details - Flipkart,
SBI Debit Card Offer at Flipkart,
Extended Warranty on Appliances - Flipkart,
Ganesh Chaturthi Festive Offers - Flipkart,
EMI on Debit Cards - Flipkart,
Top selling Latest Mobiles - Flipkart,
Honor Mobiles Day - Flipkart
Axis Bank Debit Card - Flipkart,
HDFC Debit Cards - Flipkart,
ICICI Debit Cards - Flipkart,
Top selling Latest Mobiles - Flipkart,
Explore New & Latest Mobiles of this season - Flipkart
Republic Day Sale - 10% Instant Discount on SBI Credit Cards - Flipkart
Flipkart cashback offers coupons-Daily discount Coupons
Flipkart Bank offers,
Flipkart Cashback Offers Coupons Electronics ,
Flipkart Cashback offers Lifestyle ,
Flipkart Cashback offers on Music,
Flipkart Cashback offers on Computers devices,
Flipkart Cashback offers on Furniture ,
Flipkart Cashback offers on Footwear ,
Flipkart Cashback offers on Accessories,
Flipkart Cashback offers on Other Products ,
Microwave oven – Get 20% to 55% offer,
Flipkart Cashback offers on Watches,Flipkart Mobile Offers
flipkart Credit card offers
flipkart offers
Flipkart cashback offer
Flipkart Cashback
Flipkart offers 2017
Flipkart SBI Offer
flipkart cashback offers
Flipkart Vouchers
flipkart laptop offers
flipkart mobile Offers
Flipkart cashback Coupons
flipkart offers
flipkart electronics offers
flipkart Clothing Offers
flipkart Air Conditioners

Flipkart Bank Cashback,Cashback Offers
AXIS Bank:10% discount Cashback
ICICI Bank :15% Cashback Discount
Yes bank:10% Cashback Discount
State Bank of India:10% Cashback Discount
HDFC Bank:10% Cashback Discounts
CITI Bank:10% Cashback Discounts
flipkart cashless payday sale
flipkart pay day sale
flipkart cashless payday sale 2018

June 9, 2019 at 5:35 AM
Unknown said...
June 9, 2019 at 4:51 PM
flipkart cashback offers said...
August 14, 2019 at 6:13 AM
flipkart cashback offers said...
August 14, 2019 at 11:26 PM
flipkart cashback offers said...
August 14, 2019 at 11:26 PM
BBG India plots said...

Hi nice information thank you so much.
Flipkart Hdfc offer : %10 Cascback offer
Flipkart Cashback Offer

June 30, 2020 at 1:57 PM
SitJobs said...

MP Board 12th Blue Print
MPBSE 12th Model Papers
MPBSE 10th Model Papers 2021
MP Board Ruk Jana Nahi Result

BIEAP Intermediate Second Year Model Question Papers 2021, AP Senior Inter Test Papers, Chapter wise important Questions download.
AP Inter MPC, Bi.PC, CEC Blue Print
AP Inter 1st / 2nd Year Model Papers
AP 2nd year inter Test Papers

Kar 1st / 2nd PUC Blue Print
UP Board 12th Blueprint 2021
Bihar Board 12th Model Papers

July 1, 2020 at 6:23 AM
Flipkart SBI Offer , Flipkart SBI Offers said...

Hi, nice post great offers here. Great information Thank you so much.
Hi,Very interesting post.this is my first time visit here. I found so many interesting stuff in your blog especially its discussion..thanks for the post!
Flipkart SBI Offer,
Flipkart HDFC OfferHi, very good article thanks for sharing keep up the good work!
Flipkart SBI Offer
Hello
Such a great and informative article.
Thanks for sharing

Nice post. You covered a lot of points in your post . Thanks For sharing this with us.

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it.

January 2, 2021 at 5:57 AM
jhon miller said...

"In today's security industry there are many Opitions related with system to upkeep.
youthmarketingacademy
hopenowmod
cash2day4u
enforma2000
newhopemodifications
fedhomeaffordableplan
fedmortgageloans
divbits"

June 10, 2021 at 3:53 AM
Jhonson said...

"So it has consistently been, and tragically consistently, that we who have the most exceedingly terrible get the most paid.
cleanfuncomedy
wonkologist
icomparestudy
campaignsite-hk
autoquicktrade
digitalimperative-bcgdv
kvtakeout
helpingyoufindyourplace
sengkangrandsresidences
the-ola-ec-sg
parccanberra-ec-sg
ambers-park
wifikillandroid
theparcbotannias
treasureattampines-officialsales
howmuchdoyouheartme
flaglercomputerclub"

June 18, 2021 at 3:36 AM
jhon miller said...

"You have a cunning yet alluring method for composing blog posts or articles on the off chance that you utilize valid informations in it.
wonkologist
icomparestudy
campaignsite-hk
autoquicktrade
digitalimperative-bcgdv
kvtakeout
helpingyoufindyourplace"

July 5, 2021 at 7:41 AM
Unknown said...
July 16, 2021 at 1:17 AM
Unknown said...
July 23, 2021 at 8:18 PM
Pixel Studios said...

Great post. It is very useful and informative. Thanks for the sharing.
Ecommerce Web Development In Chennai
Digital Marketing Company
Digital Marketing agency
Digital Marketing for healthcare

July 28, 2021 at 1:55 AM
James said...

Short time intervals of concentration are strongly linked to improved memory and learning.for more infosee morevisit here

August 2, 2021 at 3:55 AM
1 – 200 of 234 Newer› Newest»

#### Post a Comment

Subscribe to Post Comments [Atom]