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 heapq import heappush, heappop

N = int(input())
a = [int(i) for i in input().split()]

b = [N] * N
c = [-1] * N

h = []
for i in range(N) :
    while len(h) > 0 and -h[0][0] > a[i] :
        b[h[0][1]] = i
        heappop(h)
    heappush(h, (-a[i], i))

h = []
for i in range(N - 1, -1, -1) :
    while len(h) > 0 and -h[0][0] > a[i] :
        c[h[0][1]] = i
        heappop(h)
    heappush(h, (-a[i], i))

ret = 0
for i in range(N) :
    ret += a[i] * (b[i] - i) * (i - c[i])
print(ret)