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 main():
    n = int(input())
    a = list(map(int, input().split()))
    a = sorted(list(enumerate(a)), key=lambda x: -x[1])
    L = [i for i in range(n+2)]  # 連結成分のうち一番左のindex
    R = [i for i in range(n+2)]  # 連結成分のうち一番右のindex
    ans = 0
    for i, j in a:  # 1-indexなので1ずれる
        M = R[i+1]  # 連結成分の最大値
        m = L[i+1]  # 連結成分の最小値
        ans += j*(M-i)*(i+2-m)  # 計算
        R[m-1] = M  # 連結成分の左端の更新
        L[M+1] = m  # 連結成分の右端の更新
    print(ans)


main()