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
n = int(input())
A = list(map(int,input().split()))
l = [i-1 for i in range(n+2)]
r = [i+1 for i in range(n+2)]
ind = [0]*n

for i,a in enumerate(A):
    ind[a-1] = i

ans = 0
for i in range(n-1,-1,-1):
    x = ind[i]
    ans += (i+1)*(r[x]-x)*(x-l[x])
    l[r[x]],r[l[x]], = l[x],r[x]
print(ans)