#include <cstdio>
#include <cstdlib>
#include <string>
using namespace std;

int n, a[100000];

void exit(string str){
	puts(str.c_str());
	exit(0);
}

int main(){
	scanf("%d", &n);

	long long sum=0;
	for(int i=0; i<n; i++){
		scanf("%d", &a[i]);
		sum+=a[i];
	}
	if(n==1) exit("YES");

	long long p = n*1ll*(n+1)/2;
	if(sum%p!=0) exit("NO");
	int x = sum/p;

	for(int i=0, j=1; i<n; i++, j++){
		if(a[i]<x || a[i]>x*1ll*n) exit("NO");
		j%=n;
		int diff = a[j]-a[i];
        int dmn = diff%n;
        if(dmn<0) dmn+=n;
        if(dmn != x%n) exit("NO");
	}
	exit("YES");
	return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

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`.

Examples

Input

5
4 5 1 2 3


Output

YES


Input

5
6 9 12 10 8


Output

YES


Input

4
1 2 3 1


Output

NO

### Response

```cpp
#include <cstdio>
#include <cstdlib>
#include <string>
using namespace std;

int n, a[100000];

void exit(string str){
	puts(str.c_str());
	exit(0);
}

int main(){
	scanf("%d", &n);

	long long sum=0;
	for(int i=0; i<n; i++){
		scanf("%d", &a[i]);
		sum+=a[i];
	}
	if(n==1) exit("YES");

	long long p = n*1ll*(n+1)/2;
	if(sum%p!=0) exit("NO");
	int x = sum/p;

	for(int i=0, j=1; i<n; i++, j++){
		if(a[i]<x || a[i]>x*1ll*n) exit("NO");
		j%=n;
		int diff = a[j]-a[i];
        int dmn = diff%n;
        if(dmn<0) dmn+=n;
        if(dmn != x%n) exit("NO");
	}
	exit("YES");
	return 0;
}

```