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 Lua (5.3.2) (judge verdict: Accepted)

local n = io.read("*n")
local t = {}
local sum = 0
for i = 1, n do
  t[i] = io.read("*n")
  sum = sum + t[i]
end
if (sum * 2) % (n * (n + 1)) ~= 0 then
  print("NO")
else
  local mul = (sum * 2) // (n * (n + 1))
  local isok = true
  local c = 0
  for i = 1, n do
    local sub = i == 1 and t[1] - t[n] or t[i] - t[i - 1]
    if (mul - sub) % n == 0 and 0 <= mul - sub then
      c = c + (mul - sub) // n
    else
      isok = false
      break
    end
  end
  isok = isok and c == mul
  print(isok and "YES" or "NO")
end