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 Data.Int (Int64)

judge :: Integral a => a -> [a] -> Bool
judge 1 _ = True
judge n xs = all f ys
    where
        k = sum xs `div` (n * (n + 1) `div` 2)
        ds = diff $ last xs : xs
        ys = fmap (k -) ds
        f x = x >= 0 && mod x n == 0

diff :: Num a => [a] -> [a]
diff xs = zipWith (-) (tail xs) (init xs)

main :: IO ()
main = do
    n <- readLn :: IO Int64
    xs <- fmap read . words <$> getLine :: IO [Int64]
    putStrLn $ if judge n xs then "YES" else "NO"