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

Find the following:

<image>

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
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    N = int(input())
    A = list(enumerate(map(int,input().split())))
    A.sort(key = lambda x:-x[1])

    left = list(range(-1,N + 2))
    right = list(range(1,N + 4))
    ans = 0
    for i,a in A:
        L = left[i]
        R = right[i]
        ans += a*(i - L)*(R - i)
        left[R] = L
        right[L] = R
    print(ans)
if __name__ == '__main__':
    main()