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())
a = list(map(int,input().split()))

b = [[a[i],i] for i in range(N)]
b.sort(key=lambda x:x[0],reverse=True)

lr = [[0,0] for i in range(N)]
ans = 0
for i in range(N):
    ans+=b[i][0]*(lr[b[i][1]][1]+1)*(lr[b[i][1]][0]+1)
    if b[i][1]+lr[b[i][1]][1]+1<N:
        lr[b[i][1]+lr[b[i][1]][1]+1][0] = lr[b[i][1]][0]+lr[b[i][1]][1]+1
    if b[i][1]-lr[b[i][1]][0]-1>-1:
        lr[b[i][1]-lr[b[i][1]][0]-1][1] = lr[b[i][1]][0]+lr[b[i][1]][1]+1


print(ans)