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
import sys
input = sys.stdin.buffer.readline

N = int(input())
A = list(map(int, input().split()))

left = [0] * N
tmp = []
for i, a in enumerate(A):
    cnt = 1
    while tmp:
        aa, c = tmp.pop()
        if aa < a:
            tmp.append((aa, c))
            break
        else:
            cnt += c
    tmp.append((a, cnt))
    left[i] = cnt
A =A [::-1]
right = [0] * N
tmp = []
for i, a in enumerate(A):
    cnt = 1
    while tmp:
        aa, c = tmp.pop()
        if aa < a:
            tmp.append((aa, c))
            break
        else:
            cnt += c
    tmp.append((a, cnt))
    right[i] = cnt
right = right[::-1]

A = A[::-1]
answer = 0
for i in range(N):
    answer += left[i] * right[i] * A[i]
    
print(answer)