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
# https://atcoder.jp/contests/abc140/submissions/7411285

def main():
    N = int(input())
    *a, = map(int, input().split())

    xtoi = [-1] * (N + 1)
    for i, x in enumerate(a):
        xtoi[x] = i

    L = [-1] * (N + 2)
    R = [N] * (N + 2)
    for i in range(N):
        L[i] = i - 1
        R[i] = i + 1

    ans = 0
    for x, ind in zip(range(N, 0, -1), reversed(xtoi)):
        # l1, ..., x, ..., r1
        # (ll,r1)
        l1 = L[ind]
        r1 = R[ind]
        ans += x * (ind - l1) * (r1 - ind)
        L[r1] = l1
        R[l1] = r1
    print(ans)


if __name__ == '__main__':
    main()
