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: Time Limit Exceeded)

import Control.Applicative ((<$>), (<*>))
import Control.Monad
import Data.List

main :: IO ()
main = do
  solve <$> getl read <*> getl (map read . words) >>= putStrLn

solve :: Int -> [Int] -> String
solve n as = g as
  where
    f xs = zipWith (-) xs (rot (n - i) [1..n])
      where
        (Just i) = findIndex (== (minimum xs)) xs
    g xs = if all (== 0) ys then "YES" else if any (< 0) ys then "NO" else g ys
      where
        ys = f xs

rot :: Int -> [Int] -> [Int]
rot n xs = (drop n xs) ++ (take n xs)

getl :: (String -> a) -> IO a
getl f = f <$> getLine