946A split

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原创最新推荐文章于 2026-06-21 10:58:37 发布 328 阅读 AI 写同款· GEO 优化 ›

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Let's define a split of n as a nonincreasing sequence of positive integers, the sum of which is n.

For example, the following sequences are splits of 8: [4, 4], [3, 3, 2], [2, 2, 1, 1, 1, 1], [5, 2, 1].

The following sequences aren't splits of 8: [1, 7], [5, 4], [11, - 3], [1, 1, 4, 1, 1].

The weight of a split is the number of elements in the split that are equal to the first element. For example, the weight of the split [1, 1, 1, 1, 1] is 5, the weight of the split [5, 5, 3, 3, 3] is 2 and the weight of the split [9] equals 1.

For a given n, find out the number of different weights of its splits.

Input

The first line contains one integer n (1 ≤ n ≤ 109).

Output

Output one integer — the answer to the problem.

Examples
inputCopy
7
outputCopy
4
inputCopy
8
outputCopy
5
inputCopy
9
outputCopy
5

简单的想。。。全是1的时候weight是n；当变成2之后可以取遍n/2之内的所有权值，而且易证，所有开头元素比2大的split的weight一定被2的取过了，所以说只用看1和2开头的就能做到“不重不漏”，又因为是非增的，所以1打头的就是全为1，weight自然就是n啦！

#include<stdio.h>
#include<iostream>
using namespace std;
int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        int weight=n/2+1;            //加的1就是全为1的情况
        cout<<weight<<endl;
    }
    return 0;
}