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)

#include <bits/stdc++.h>
using namespace std;

#define LL long long
#define LD long double
#define SC(t,x) static_cast<t>(x)
#define AR(t) vector < t >
#define PII pair < int, int >
#define PLL pair < LL, LL >
#define PIL pair < int, LL >
#define PLI pair < LL, int >
#define MP make_pair
#define PB push_back
#define PF push_front
#define POB pop_back
#define POF pop_front
#define PRF first
#define PRS second
#define INIT(ar,val) memset ( ar, val, sizeof ( ar ) )
#define lp(loop,start,end) for ( int loop = start; loop < end; ++loop )
#define lpd(loop,start,end) for ( int loop = start; loop > end; --loop )
#define lpi(loop,start,end) for ( int loop = start; loop <= end; ++loop )
#define lpdi(loop,start,end) for ( int loop = start; loop >= end; --loop )
#define qmax(a,b) (((a)>(b))?(a):(b))
#define qmin(a,b) (((a)<(b))?(a):(b))
#define qabs(a) (((a)>=0)?(a):(-(a)))

const int INF = 0x3fffffff;
const int SINF = 0x7fffffff;
const long long LINF = 0x3fffffffffffffff;
const long long SLINF = 0x7fffffffffffffff;
const int MAXN = 100007;

int n;
int a[MAXN];
int d[MAXN];
LL cc[MAXN];

void init ();
void input ();
void work ();

void NO ()
{
	cout << "NO" << endl;
	exit ( 0 );
}



int main()
{
	init();
	input();
	work();
}



void init ()
{
	// Init Everything Here
	
	ios::sync_with_stdio ( false );
}

void input ()
{
	// input method
	
	scanf ( "%d", &n );
	lpi ( i, 1, n ) scanf ( "%d", &a[i] );
}

void work ()
{
	// main work
	
	lpi ( i, 1, n ){
		d[i] = ( a[i%n+1] << 1 ) - a[i] - a[(i+1)%n+1];
		if ( d[i] % n ) NO ();
		d[i] /= n;
	}
	
	LL sum = 0;
	lpi ( i, 1, n ) sum += d[i];
	if ( sum ) NO ();
	
	sum = 0;
	lpi ( i, 1, n ) sum += a[i];
	if ( sum % ( SC ( LL, n ) * ( n + 1 ) >> 1 ) ) NO ();
	
	cc[n] = 0;
	lpd ( i, n-1, 0 ) cc[i] = cc[i+1] + d[i];
	LL mini = *min_element ( cc+1, cc+1+n );
	lpi ( i, 1, n ) cc[i] += mini;
	sum = 0;
	lpi ( i, 1, n ) sum += i * cc[i];
	
	if ( sum > a[1] ) NO ();
	
	cout << "YES" << endl;
}