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
sys.setrecursionlimit(1000000)

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

b=[i for i in range(1,N+1)]

A=[]
for i in range(N):
    A.append([a[i],b[i]])
A.sort(reverse=True)
#print(A)
PL=[i for i in range(N+1)]+[N+1]
PR=[i for i in range(N+1)]+[N+1]

def findL(x):
    if x==PL[x]:
        return x
    else:
        return findL(PL[x])
        
def findR(x):
    if x==PR[x]:
        return x
    else:
        return findR(PR[x])
#print(PR)
ans=0
for i in range(N):
    ans+=A[i][0]*(A[i][1]-findL(A[i][1]-1))*(findR(A[i][1]+1)-A[i][1])
    #print(ans,A[i][1],(A[i][1]-findL(A[i][1])+1),findR(A[i][1])-A[i][1]+1)
    #print(PR)
    PL[A[i][1]]=findL(A[i][1]-1)
    PR[A[i][1]]=findR(A[i][1]+1)
print(ans)