## 1035 - Artificial Lake

Time Limit : 2 Second

Memory Limit : 128 MB

Submission: 8

Solved: 4

Description
The oppressively hot summer days have raised the cows' clamoring
to its highest level. Farmer John has finally decided to build an
artificial lake. For his engineering studies, he is modeling the
lake as a two-dimensional landscape consisting of a contiguous
sequence of N soon-to-be-submerged levels (1 <= N <= 100,000)
conveniently numbered 1..N from left to right.

Each level i is described by two integers, its width W_i (1 <= W_i
<= 1,000) and height (like a relative elevation) H_i (1 <= H_i <=
1,000,000). The heights of FJ's levels are unique. An infinitely
tall barrier encloses the lake's model on the left and right. One
example lake profile is shown below.
```
*             *  :
*             *  :
*             *  8
*    ***      *  7
*    ***      *  6
*    ***      *  5
*    **********  4 <- height
*    **********  3
***************  2
***************  1
Level    |  1 |2|  3   |
```

In FJ's model, he starts filling his lake at sunrise by flowing
water into the bottom of the lowest elevation at a rate of 1 square
unit of water per minute. The water falls directly downward until
it hits something, and then it flows and spreads as room-temperature
water always does. As in all good models, assume that falling and
flowing happen instantly. Determine the time at which each elevation's
becomes submerged by a single unit of water.
```
WATER              WATER OVERFLOWS
|                       |
* |          *      *     |      *      *            *
* V          *      *     V      *      *            *
*            *      *    ....    *      *~~~~~~~~~~~~*
*    **      *      *~~~~** :    *      *~~~~**~~~~~~*
*    **      *      *~~~~** :    *      *~~~~**~~~~~~*
*    **      *      *~~~~**~~~~~~*      *~~~~**~~~~~~*
*    *********      *~~~~*********      *~~~~*********
*~~~~*********      *~~~~*********      *~~~~*********
**************      **************      **************
**************      **************      **************

After 4 mins        After 26 mins       After 50 mins
Lvl 1 submerged     Lvl 3 submerged     Lvl 2 submerged
```

Warning: The answer will not always fit in 32 bits.
Input
* Line 1: A single integer: N
* Lines 2..N+1: Line i+1 describes level i with two space-separated integers: W_i and H_i

Output
* Lines 1..N: Line i contains a single integer that is the number of
minutes that since sunrise when level #i is covered by water
of height 1.
sample input
```3
4 2
2 7
6 4
```
sample output
```4
50
26
```
hint
source
USACO JAN08
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