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

N=int(input())
A=list(map(int,input().split()))
oneton=(N*(N+1))//2
flag=1
allsum=sum(A)
dif=[]
for i in range(N):
    dif.append(A[(i+1)%N]-A[i%N])
#print(dif)
#print(allsum,oneton)
if allsum%oneton!=0:
    flag=0
else:
    opnum=allsum//oneton        
    l=[opnum]*N                 
    #print(l)
    for i in range(N):
        if l[i]<dif[i]:         
            flag=0
            break
        else:                   
            diff=l[i]-dif[i]    
            useminus=diff//N    
            opnum=opnum-useminus
            l[i]=l[i]-(useminus*N)
    if opnum!=0:                    
        flag=0
    for i in range(N):              
        if l[i]!=dif[i]:
            flag=0
if flag==0:
    print("NO")
else:
    print("YES")


