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
def getNums(As):
    nums = [0] * N
    stack = [(-1, 0)]
    for iA, A in enumerate(As):
        while stack[-1][1] > A:
            stack.pop()
        nums[iA] = iA - stack[-1][0]
        stack.append((iA, A))

    return nums


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

numLs = getNums(As)
numRs = getNums(reversed(As))
print(sum([A * numL * numR for A, numL, numR in zip(As, numLs, reversed(numRs))]))
