Contest Duration: - (local time) (100 minutes) Back to Home
H - Candles /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 1 \leq N \leq 300
• -10^9 \leq X_i \leq 10^9
• 1 \leq A_i \leq 10^9
• 入力は全て整数である。

### 入力

N
X_1 A_1
X_2 A_2
:
X_N A_N


### 入力例 1

3
-2 10
3 10
12 10


### 出力例 1

11


3 番目のろうそくは座標 12 にあるため、高橋君の行動に関わらず火を消すより先に燃え尽きてしまいます。

### 入力例 2

5
0 1000000000
0 1000000000
1 1000000000
2 1000000000
3 1000000000


### 出力例 2

4999999994


Score : 600 points

### Problem Statement

There are N candles on an infinite number line. The i-th candle is at the coordinate X_i. At time 0, it has a length of A_i and is lit. Each minute, the length of a lit candle decreases by 1. When the length becomes 0, it burns out, and its length does not change after that. Additionally, the length of an unlit candle does not change.

Takahashi is at the coordinate 0 at time 0. Each minute, he can move a distance of at most 1. If there is a candle at his current coordinate, he can put out that candle. (If there are multiple candles there, he can put out all of them.) The time it takes to put out a candle is negligible.

Find the maximum possible total length of the candles remaining at 10^{100} minutes after time 0, achieved by Takahashi's optimal course of actions.

### Constraints

• 1 \leq N \leq 300
• -10^9 \leq X_i \leq 10^9
• 1 \leq A_i \leq 10^9
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N
X_1 A_1
X_2 A_2
:
X_N A_N


### Sample Input 1

3
-2 10
3 10
12 10


### Sample Output 1

11


The third candle, which is at coordinate 12, will burn out before Takahashi puts it out, regardless of Takahashi's behavior.
For the other two candles, if he goes to coordinate -2 in two minutes to put out the first and then goes to coordinate 3 in five minutes to put out the second, the lengths of those candles will not change after that. The lengths of those candles remaining are 10-2=8 and 10-2-5=3, for a total of 8+3=11, which is the maximum that can be achieved. Thus, print 11.

### Sample Input 2

5
0 1000000000
0 1000000000
1 1000000000
2 1000000000
3 1000000000


### Sample Output 2

4999999994


Note that two or more candles may occupy the same coordinate and that the answer may not fit into a 32-bit integer.