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
#include <cstdio>
#include <set>
#define repi(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,a) repi(i,0,a)

constexpr int MAX_N = 200000;

using ll = long long;

int N;
ll a[MAX_N];
ll p[MAX_N+1];
std::set<ll> S;

int main()
{
  scanf( "%d", &N );
  rep( i, N )
    scanf( "%lld", a+i ), p[a[i]] = i+1;

  S.insert( 0 );
  S.insert( N+1 );

  ll ans = 0;
  repi( i, 1, N+1 )
  {
    auto it = S.lower_bound( p[i] );
    ll r = *it;
    --it;
    ll l = *it;
    ans += (r-p[i])*(p[i]-l)*(ll)i;
    S.insert( p[i] );
  }

  printf( "%lld\n", ans );

  return 0;
}