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 <bits/stdc++.h>
 
using namespace std;
 
const int MOD=1e9+7;

//const int MOD=998244353;


int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    long long n=100000;
    //cin>>n;
    
    vector<int> v(n,1000000000);
    
    long long sum=0, d=n*(n+1)/2;
    
    for(int &i:v)cin>>i, sum+=i;
    
    if(sum%d){
        cout<<"NO";
        return 0;
    }
    
    for(int &i:v){
        if(i>d){
            i%=d;
        }
    }
    
    int mp=max_element(v.begin(),v.end())-v.begin();
    bool stop=0;
    while(!stop){
        int mp2=-1;
        for(int i=1; i<=n; i++){
            int pcur=(mp+i)%n;
            if(v[pcur]>=i){
                v[pcur]-=i;
                if(mp2==-1 || v[pcur]>v[mp2]) mp2=pcur;
                if(!v[pcur]) stop=1;
            }
            else{
                cout<<"NO";
                return 0;
            }
        }
        mp=mp2;
    }
    
    for(int i:v){
        if(i){
            cout<<"NO";
            return 0;
        }
    }
    
    cout<<"YES";
    return 0;
}