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
# B - Minimum Sum
N = int(input())
A = list(enumerate(list(map(int,input().split()))))
left = [i-1 for i in range(N)]
right = [i+1 for i in range(N)]
A.sort(key=lambda x:x[1],reverse=True)
ans = 0
for i,a in A:
    il,ir = left[i],right[i]
    ans += a*(i-il)*(ir-i)
    if ir<N:
        left[ir] = il
    if il>-1:
        right[il] = ir
print(ans)