A9817 | Photo to Remember

One day $n$ friends met at a party, they hadn't seen each other for a long time and so they decided to make a group photo together.

Simply speaking, the process of taking photos can be described as follows. On the photo, each photographed friend occupies a rectangle of pixels: the $i$ -th of them occupies the rectangle of width $w_{i}$ pixels and height $h_{i}$ pixels. On the group photo everybody stands in a line, thus the minimum pixel size of the photo including all the photographed friends, is $W×H$ , where $W$ is the total sum of all widths and $H$ is the maximum height of all the photographed friends.

As is usually the case, the friends made $n$ photos — the $j$ -th ( $1<=j<=n$ ) photo had everybody except for the $j$ -th friend as he was the photographer.

Print the minimum size of each made photo in pixels.

The first line contains integer $n$ ( $2<=n<=200000$ ) — the number of friends.

Then $n$ lines follow: the $i$ -th line contains information about the $i$ -th friend. The line contains a pair of integers $w_{i},h_{i}$ ( $1<=w_{i}<=10,1<=h_{i}<=1000$ ) — the width and height in pixels of the corresponding rectangle.

Print $n$ space-separated numbers $b_{1},b_{2},...,b_{n}$ , where $b_{i}$ — the total number of pixels on the minimum photo containing all friends expect for the $i$ -th one.