Photo to Remember

题面翻译

某一天，n个朋友在一起聚会，他们已经很久没见了，于是他们决定拍照留念。

简单的说，拍照的时候，每个人有一个高度和宽度，第i个的高度和宽度分别是hi和wi。这些人排成一条直线，照片的最小的面积必须包含所有的的人，所以照片的面积是W*H，W是所有人的宽度之和，H是所有人中高度最高的那个人的高度。现在想要知道当第i个人不在照片中的时候，照片的最小面积是多少。

输入

第一行是一个正整数N，表示人的数量。

接下来N行，每行两个整数wi和hi，分别表示每个人的宽度和高度。

数据范围：2<=N<=200000,1<=wi<=10,1<=hi<=1000。

输出

包含b1，b2，b3。。Bn，bi表示第i个人不在照片中的时候，照片的最小面积。

题目描述

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.

输入格式

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.

输出格式

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.

样例 #1

样例输入 #1

3
1 10
5 5
10 1

样例输出 #1

75 110 60

样例 #2

样例输入 #2

3
2 1
1 2
2 1

样例输出 #2

6 4 6