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
import sys
from operator import itemgetter

n, *aaa = map(int, sys.stdin.buffer.read().split())
aaa_with_index = list(enumerate(aaa, start=1))
aaa_with_index.sort(key=itemgetter(1), reverse=True)
left = list(range(-1, n + 1))
right = list(range(1, n + 3))
ans = 0
for i, a in aaa_with_index:
    li = left[i]
    ri = right[i]
    ans += a * (i - li) * (ri - i)
    left[ri] = li
    right[li] = ri

print(ans)
