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 bisect import*
class SqrtSet:
    def __init__(self,block_limit=201):
        self.key=[]
        self.child=[[]]
        self.block_limit=block_limit
    def search_lower(self,key):
        if not key:return None
        ret=None
        i=bisect_left(self.key,key)
        if i:ret=self.key[i-1]
        block=self.child[i]
        i=bisect_left(block,key)
        if i:ret=block[i-1]
        return ret
    def search_higher(self,key):
        if not key:return None
        ret=None
        i=bisect(self.key,key)
        if i<len(self.key):ret=self.key[i]
        block=self.child[i]
        i=bisect(block,key)
        if i<len(block):ret=block[i]
        return ret
    def insert(self,key):
        i=bisect(self.key,key)
        block=self.child[i]
        insort(block,key)
        if len(block)==self.block_limit:
            sep=self.block_limit//2
            self.key.insert(i,block[sep])
            self.child.insert(i+1,block[sep+1:])
            self.child[i]=block[:sep]
def main():
    n,*a=map(int,open(0).read().split())
    l=[0]*n
    for i,v in enumerate(a,1):l[v-1]=i
    t=SqrtSet()
    t.insert(0)
    t.insert(n+1)
    c=0
    for i,v in enumerate(l,1):
        c+=(t.search_higher(v)-v)*(v-t.search_lower(v))*i
        t.insert(v)
    print(c)
main()