CF1060B.Maximum Sum of Digits

普及-

通过率:0%

时间限制:2.00s

内存限制:512MB

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题目描述

You are given a positive integer nn.

Let S(x)S(x) be sum of digits in base 10 representation of xx, for example, S(123)=1+2+3=6S(123) = 1 + 2 + 3 = 6, S(0)=0S(0) = 0.

Your task is to find two integers a,ba, b, such that 0≤a,b≤n0 \leq a, b \leq n, a+b=na + b = n and S(a)+S(b)S(a) + S(b) is the largest possible among all such pairs.

给定一个正整数 nn。

令 S(x)S(x) 表示 xx 的十进制表示中各位数字之和,例如,S(123)=1+2+3=6S(123) = 1 + 2 + 3 = 6,S(0)=0S(0) = 0。

你的任务是找出两个整数 a,ba, b,满足 0≤a,b≤n0 \leq a, b \leq n,a+b=na + b = n,且在所有满足条件的数对中,S(a)+S(b)S(a) + S(b) 的值尽可能大。

输入格式

The only line of input contains an integer nn (1≤n≤1012)(1 \leq n \leq 10^{12}).

输入仅包含一个整数 nn (1≤n≤1012)(1 \leq n \leq 10^{12})。

输出格式

Print largest S(a)+S(b)S(a) + S(b) among all pairs of integers a,ba, b, such that 0≤a,b≤n0 \leq a, b \leq n and a+b=na + b = n.

在所有满足 0≤a,b≤n0 \leq a, b \leq n 且 a+b=na + b = n 的整数对 (a,b)(a, b) 中,求 S(a)+S(b)S(a) + S(b) 的最大值。

输入输出样例

  • 输入#1

    35

    输出#1

    17
  • 输入#2

    10000000000

    输出#2

    91

说明/提示

In the first example, you can choose, for example, a=17a = 17 and b=18b = 18, so that S(17)+S(18)=1+7+1+8=17S(17) + S(18) = 1 + 7 + 1 + 8 = 17. It can be shown that it is impossible to get a larger answer.

In the second test example, you can choose, for example, a=5000000001a = 5000000001 and b=4999999999b = 4999999999, with S(5000000001)+S(4999999999)=91S(5000000001) + S(4999999999) = 91. It can be shown that it is impossible to get a larger answer.

在第一个例子中,你可以选择,例如,a=17a = 17 和 b=18b = 18,使得 S(17)+S(18)=1+7+1+8=17S(17) + S(18) = 1 + 7 + 1 + 8 = 17。可以证明,无法得到更大的答案。

在第二个测试样例中,你可以选择,例如,a=5000000001a = 5000000001 和 b=4999999999b = 4999999999,满足 S(5000000001)+S(4999999999)=91S(5000000001) + S(4999999999) = 91。可以证明,无法得到更大的答案。

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