Score: $300$ points

问题陈述

有 $N$ 个巨人，编号为 $1$ 到 $N$。当第 $i$ 个巨人站立在地面上时，他们的肩膀高度是 $A_i$，头部高度是 $B_i$。

你可以选择一个排列 $(P_1, P_2, \ldots, P_N)$，它是 $(1, 2, \ldots, N)$ 的一个排列，并根据以下规则堆叠这 $N$ 个巨人：

• 首先，将巨人 $P_1$ 放在地上。巨人 $P_1$ 的肩膀将离地面 $A_{P_1}$ 的高度，他们的头部将离地面 $B_{P_1}$ 的高度。

• 对于 $i = 1, 2, \ldots, N - 1$，按顺序将巨人 $P_{i + 1}$ 放在巨人 $P_i$ 的肩膀上。如果巨人 $P_i$ 的肩膀离地面的高度是 $t$，那么巨人 $P_{i + 1}$ 的肩膀将离地面 $t + A_{P_{i + 1}}$ 的高度，他们的头部将离地面 $t + B_{P_{i + 1}}$ 的高度。

找出顶部巨人 $P_N$ 的头部离地面的最大可能高度。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There are $N$ giants, named $1$ to $N$. When giant $i$ stands on the ground, their shoulder height is $A_i$, and their head height is $B_i$.

You can choose a permutation $(P_1, P_2, \ldots, P_N)$ of $(1, 2, \ldots, N)$ and stack the $N$ giants according to the following rules:

• First, place giant $P_1$ on the ground. The giant $P_1$'s shoulder will be at a height of $A_{P_1}$ from the ground, and their head will be at a height of $B_{P_1}$ from the ground.

• For $i = 1, 2, \ldots, N - 1$ in order, place giant $P_{i + 1}$ on the shoulders of giant $P_i$. If giant $P_i$'s shoulders are at a height of $t$ from the ground, then giant $P_{i + 1}$'s shoulders will be at a height of $t + A_{P_{i + 1}}$ from the ground, and their head will be at a height of $t + B_{P_{i + 1}}$ from the ground.

Find the maximum possible height of the head of the topmost giant $P_N$ from the ground.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq B_i \leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$

$A_1$ $B_1$

$A_2$ $B_2$

$\vdots$

$A_N$ $B_N$

Output

Print the answer.

Sample Input 1

3
4 10
5 8
2 9

Sample Output 1

18

If $(P_1, P_2, P_3) = (2, 1, 3)$, then measuring from the ground, giant $2$ has a shoulder height of $5$ and a head height of $8$, giant $1$ has a shoulder height of $9$ and a head height of $15$, and giant $3$ has a shoulder height of $11$ and a head height of $18$.

The head height of the topmost giant from the ground cannot be greater than $18$, so print $18$.

Sample Input 2

5
1 1
1 1
1 1
1 1
1 1

Sample Output 2

5

Sample Input 3

10
690830957 868532399
741145463 930111470
612846445 948344128
540375785 925723427
723092548 925021315
928915367 973970164
563314352 832796216
562681294 868338948
923012648 954764623
691107436 891127278

Sample Output 3

7362669937