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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	N,i:Longint;
	A,B:Array[1..100000]of int64;
	sum,all,k:int64;
begin
	read(N);
	for i:=1 to N do begin
		read(A[i]);
		inc(sum,A[i]);
		if i>1 then B[i-1]:=A[i]-A[i-1];
	end;
	B[N]:=A[1]-A[N];
	all:=(N+1)*N div 2;
	if sum mod all<>0 then begin
		writeln('NO');
		exit;
	end;
	K:=sum div all;
	for i:=1 to N do begin
		dec(B[i],K);
		if(B[i]>0)or(B[i]mod N<>0)then begin
			writeln('NO');
			exit;
		end;
	end;
	writeln('YES');
end.