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 heapq

N = int(input())
A = list(map(int,input().split()))

pos = [-1] * N
for i,a in enumerate(A):
    pos[a-1] = i

q = []
heapq.heapify(q)
right = [N] * N
for i,a in enumerate(A):
    while q and -q[0] > a:
        v = -heapq.heappop(q)
        right[v-1] = i
    heapq.heappush(q,-a)

q = []
heapq.heapify(q)
left = [0] * N
for i,a in reversed(list(enumerate(A))):
    while q and -q[0] > a:
        v = -heapq.heappop(q)
        left[v-1] = i+1
    heapq.heappush(q,-a)

ans = 0
for i,(p,l,r) in enumerate(zip(pos,left,right)):
    ans += (p-l+1) * (r-p) * (i+1)
print(ans)