One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

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Constraints

* 1 ≦ N ≦ 200,000
* (a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3
2 1 3


Output

9


Input

4
1 3 2 4


Output

19


Input

8
5 4 8 1 2 6 7 3


Output

85
N = int(input())
A = list(enumerate(list(map(int, input().split()))))
A = sorted(A, key=lambda x:x[1], reverse=True)

before_idx = list(range(-1, N-1)) + [-1]
next_idx = list(range(1, N+1)) + [N]

ans = 0
for i, a in A:
  il = before_idx[i]
  ir = next_idx[i]
  ans += (i - il) * (ir - i) * a
  before_idx[ir] = il
  next_idx[il] = ir

print (ans)