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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Control.Applicative ((<$>))
import Data.List (sort)

main = do
  n <- read <$> getLine :: IO Int
  as <- map read.words <$> getLine :: IO [Int]
  let m = n*(n+1)`div`2
      s = sum as
      diffs = zipWith (-) (tail as++[head as]) as
  case s `divMod` m of
    (d,0) -> putStrLn $
      if any (\x->if x > 0 then x==d else or [x==d-y*n|y<-[1..d]]) diffs
        then "YES"
        else if sum diffs == 0
          then "YES"
          else "NO"
    _ -> putStrLn "NO"