103522: [Atcoder]ABC352 C - Standing On The Shoulders

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

问题描述

有$N$个巨人，分别名为1到$N$。当巨人$i$站在地面上时，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$(P_1, P_2, \ldots, P_N)$，其中$(1, 2, \ldots, N)$，并按照以下规则将$N$个巨人堆叠起来：

• 首先，将巨人$P_1$放在地面上。巨人$P_1$的肩膀离地面的高度为$A_{P_1}$，头部离地面的高度为$B_{P_1}$。

• 然后，按顺序$i = 1, 2, \ldots, N - 1$，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为$t$，那么巨人$P_{i + 1}$的肩膀离地面的高度为$t + A_{P_{i + 1}}$，头部离地面的高度为$t + B_{P_{i + 1}}$。

找出最上面的巨人$P_N$头部离地面的最大可能高度。

限制条件

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq B_i \leq 10^9$
• 所有输入值都是整数。

输入

输入从标准输入以以下格式给出：

$N$
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_N$ $B_N$

输出

打印答案。

样例输入1

3
4 10
5 8
2 9

样例输出1

18

如果$(P_1, P_2, P_3) = (2, 1, 3)$，那么从地面测量，巨人$2$的肩膀高度为$5$，头部高度为$8$，巨人$1$的肩膀高度为$9$，头部高度为$15$，巨人$3$的肩膀高度为$11$，头部高度为$18$。

最上面的巨人头部离地面的高度无法超过$18$，所以打印$18$。

样例输入2

5
1 1
1 1
1 1
1 1
1 1

样例输出2

5

样例输入3

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

样例输出3

7362669937