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
from sys import stdin
def main():
    n = int(stdin.readline())
    a = map(int, stdin.readline().split())
    L = range(n + 2)
    R = range(n + 2)
    b = [0] * (n + 2)
    L[n+1] = R[n+1] = n
    L[0] = R[0] = 1
    for i, x in enumerate(a, 1):
        b[x] = i
    s = 0
    for i in xrange(n, 0, -1):
        j = b[i]
        s += i * (R[j] - j + 1) * (j - L[j] + 1)
        R[L[j]-1] = R[j]
        L[R[j]+1] = L[j]
    print s
main()
