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 <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main(void) {
  ll n;
  cin >> n;
  
  vector<ll> a(n), b(n + 1);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[a[i]] = i + 1;
  }

  ll ans = 0;
  set<ll> st;
  st.insert(0);
  st.insert(n + 1);
  for (int i = 1; i <= n; i++) {
    ll l = *(--st.lower_bound(b[i])), r = *(st.upper_bound(b[i]));
    ans += (b[i] - l) * (r - b[i]) * (ll)i;
    st.insert(b[i]);
  }
  cout << ans << endl;

  return 0;
}