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

iAs = [0] * (N + 1)
for i, A in enumerate(As):
    iAs[A] = i

ans = 0
iLs = list(range(N + 1))
iRs = list(range(N + 1))
for A in reversed(range(1, N + 1)):
    iA = iAs[A]
    iL, iR = iLs[iA], iRs[iA]
    ans += A * (iA - iL + 1) * (iR - iA + 1)
    iLs[iR + 1] = iL
    iRs[iL - 1] = iR

print(ans)
