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: Accepted)

#define _CRT_SECURE_NO_WARNINGS
#include <vector>
#include <iostream>
#include <string.h>
#include <string>
#include <algorithm>
using namespace std;

typedef double LD;
typedef long long LL;
typedef pair<int, int> PII;
#define MP make_pair
#define PB push_back
#define FOR(i,a,b) for(int i = (a); i < (b); ++i)
#define RFOR(i,b,a) for(int i = (b) - 1; i >= (a); --i)
#define REP(i, t) FOR(i,0,t)
#define ALL(a) a.begin(), a.end()
#define SZ(a) (int)((a).size())

const LL MOD = 1000000007;
const int INF = 1e9;
const int MAXN = 100007;
const LD EPS = 1e-7;

int n, A[MAXN];

bool possible()
{
	LL s = 0, c;
	REP(i, n) s += A[i];
	if ((2 * s) % (n * (n + 1LL))) return false;
	c = (2 * s) / (n * (n + 1LL));
	REP(i, n)
	{
		if (c + A[i] - A[i + 1] < 0) return false;
		if ((c + A[i] - A[i + 1]) % n) return false;
	}
	return true;
}

int main()
{
	ios_base::sync_with_stdio(0);
	//freopen("In.txt", "r", stdin);
	cin >> n;
	REP(i, n) cin >> A[i];
	A[n] = A[0];
	if (possible()) cout << "YES";
	else cout << "NO";
	//cout << endl; system("pause");
	return 0;
}