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
root=lambda x:x if par[x]==x else root(par[x])
same=lambda x,y:root(x)==root(y)
def unite(*z):
  x,y=map(root,z)
  if x!=y:
    if rank[x]<rank[y]:
      par[x]=y
      size[y]+=size[x]
    else:
      par[y]=x
      size[x]+=size[y]
      if rank[x]==rank[y]:rank[x]+=1
n,*a=map(int,open(0).read().split())
*par,=range(n)
rank=[1]*n
size=[1]*n
b=[0]*n
for i,t in enumerate(a):b[t-1]=i
c=0
for k in b[::-1]:
  l=r=1
  if k>0 and a[k-1]>a[k]:
    l+=size[root(k-1)]
    unite(k-1,k)
  if k+1<n and a[k+1]>a[k]:
    r+=size[root(k+1)]
    unite(k+1,k)
  c+=l*r*a[k]
print(c)