Problem:
Score : 500 points

Problem Statement

There are N boxes arranged in a circle. The i-th box contains A_i stones.

Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:

Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.

Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.

Constraints

1 ≦ N ≦ 10^5

1 ≦ A_i ≦ 10^9

Input

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

N
A_1 A_2 … A_N

Output

If it is possible to remove all the stones from the boxes, print YES. Otherwise, print NO.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <queue>
#include <functional>
using namespace std;

int main() {
	long long N; cin >> N;

	vector<int>A(N);
	for (int i = 0; i < N; i++)cin >> A[i];

	long long z = N * (N + 1) / 2;
	int cnt = 1e9;
	for (int i = 0; i < N; i++)cnt = min<long long>((A[i] - 1)/z, cnt);
	if (cnt)for (int i = 0; i < N; i++)A[i] -= z*cnt;

	int min_value = 1e9 + 1;
	int target = -1;
	for (int i = 0; i < N; i++) {
		if (min_value > A[i]) {
			min_value = A[i];
			target = i;
		}
	}

	int x = 0;
	int y = 0;
	while (x < A[target]) {
		x += y + 1;
		y = (y + 1) % N;
	}
	vector<int>B(N);
	for (int i = 0; i < N; i++) {
		int target2 = (target + i) % N;
		B[target2] = x;

		x += y - i;
		y = (y + 1) % N;
	}

	bool flag = true;
	for (int i = 0; i < N; i++) {
		//cerr << A[i] << " " << B[i] << endl;
		if (A[i] != B[i])flag = false;
	}

	if (flag)cout << "YES" << endl;
	else cout << "NO" << endl;

	return 0;
}