Algorithm

A. Splits
time limit per test
1 second
memory limit per test
256 megabytes
Problem link- https://codeforces.com/contest/964/problem/A
input
standard input
output
standard output

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 88: [4,4][4,4], [3,3,2][3,3,2], [2,2,1,1,1,1][2,2,1,1,1,1], [5,2,1][5,2,1].

The following sequences aren't splits of 88: [1,7][1,7], [5,4][5,4], [11,−3][11,−3], [1,1,4,1,1][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][1,1,1,1,1] is 55, the weight of the split [5,5,3,3,3][5,5,3,3,3] is 22 and the weight of the split [9][9] equals 11.

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

Input

The first line contains one integer n� (1≤n≤1091≤�≤109).

Output

Output one integer — the answer to the problem.

Examples
input
Copy
7
output
Copy
4
input
Copy
8
output
Copy
5
input
Copy
9
output
Copy
5
Note

In the first sample, there are following possible weights of splits of 77:

Weight 1: [77]

Weight 2: [33, 33, 1]

Weight 3: [22, 22, 22, 1]

Weight 7: [11, 11, 11, 11, 11, 11, 11]

 



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <bits/stdc++.h>

using namespace std;

int main() {
	int n;
	cin >> n;

	if(n == 1) {
		cout << 1 << endl;
	} else if(n % 2 == 0) {
		cout << n - (n / 2 - 1) << endl;
	} else {
		cout << n - (n / 2) << endl;
	}

  return 0;
}
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Input

x
–
+
cmd
7

Output

x
–
+
cmd
4
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Demonstration

Codeforces Solution-A. Splits-Solution in C, C++, Java, Python

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