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 collections import deque

N = int(input())

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

l = [N - 1 - i for i in range(N)]

st = deque([])

for i in range(N):


    while len(st) > 0 and st[-1][0] > a[i]:

        p = st.pop()
        l[p[1]] = i - p[1] - 1

    st.append([a[i],i])


a.reverse()
r = [N - 1 - i for i in range(N)]

st = deque([])

for i in range(N):


    while len(st) > 0 and st[-1][0] > a[i]:

        p = st.pop()
        r[p[1]] = i - p[1] - 1

    st.append([a[i],i])

r.reverse()
a.reverse()


ans = 0

for i in range(N):

    ans += (1 + (l[i]+r[i]) + (l[i] * r[i])) * a[i]

print (ans)    
