Contest Duration: ~ (local time) (100 minutes) Back to Home
E - Tozan and Gezan /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

とざん君とげざん君は、以下の操作を繰り返します。

• もし A,B が列として等しいなら、繰り返しを終了する
• そうでない場合、まずとざん君が A の正の要素を 1 つ選び、1 減らす
• その後、げざん君が B の正の要素を 1 つ選び、1 減らす
• その後、ペットの高橋君に飴を 1 つ食べさせる

とざん君は繰り返しが終了するまでに高橋君に食べさせる飴の個数を最大に、げざん君は最小にしたいです。 両者最適に操作を行ったとき、高橋君に食べさせる飴の個数を求めてください。

### 制約

• 1 \leq N \leq 2 × 10^5
• 0 \leq A_i,B_i \leq 10^9(1\leq i\leq N)
• A,B の値の総和は等しい
• 入力はすべて整数である

### 入力

N
A_1 B_1
:
A_N B_N


### 入力例 1

2
1 2
3 2


### 出力例 1

2


• とざん君は A_11 減らす。
• げざん君は B_11 減らす。
• 高橋君に飴を 1 つ食べさせる。
• とざん君は A_21 減らす。
• げざん君は B_11 減らす。
• 高橋君に飴を 1 つ食べさせる。
• A,B が等しくなったので終了する。

### 入力例 2

3
8 3
0 1
4 8


### 出力例 2

9


### 入力例 3

1
1 1


### 出力例 3

0


Score : 700 points

### Problem Statement

You are given sequences A and B consisting of non-negative integers. The lengths of both A and B are N, and the sums of the elements in A and B are equal. The i-th element in A is A_i, and the i-th element in B is B_i.

Tozan and Gezan repeats the following sequence of operations:

• If A and B are equal sequences, terminate the process.
• Otherwise, first Tozan chooses a positive element in A and decrease it by 1.
• Then, Gezan chooses a positive element in B and decrease it by 1.
• Then, give one candy to Takahashi, their pet.

Tozan wants the number of candies given to Takahashi until the process is terminated to be as large as possible, while Gezan wants it to be as small as possible. Find the number of candies given to Takahashi when both of them perform the operations optimally.

### Constraints

• 1 \leq N \leq 2 × 10^5
• 0 \leq A_i,B_i \leq 10^9(1\leq i\leq N)
• The sums of the elements in A and B are equal.
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N
A_1 B_1
:
A_N B_N


### Output

Print the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.

### Sample Input 1

2
1 2
3 2


### Sample Output 1

2


When both Tozan and Gezan perform the operations optimally, the process will proceed as follows:

• Tozan decreases A_1 by 1.
• Gezan decreases B_1 by 1.
• One candy is given to Takahashi.
• Tozan decreases A_2 by 1.
• Gezan decreases B_1 by 1.
• One candy is given to Takahashi.
• As A and B are equal, the process is terminated.

### Sample Input 2

3
8 3
0 1
4 8


### Sample Output 2

9


### Sample Input 3

1
1 1


### Sample Output 3

0