#include <bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void rset();
void init_test();
void solve();
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed;
  cout.precision(20);
  init_test();
  return 0;
}
template <typename T>
void chmin(T& a, T b) {
  if (a > b) a = b;
}
template <typename T>
void chmax(T& a, T b) {
  if (a < b) a = b;
}
template <typename T>
void MACRO_rdv2_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_rdv2_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_rdv2_Init(n, rest...);
}
template <typename T>
void MACRO_rdv2_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_rdv2_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_rdv2_Scan(p, rest...);
}
template <typename T>
void wrv(const vector<T>& v) {
  for (int(__ii) = (0); (__ii) < (((int)v.size())); ++(__ii)) {
    if (__ii) cout << ' ';
    cout << v[__ii];
  }
  cout << '\n';
}
template <typename T>
void wrm(const vector<vector<T>>& v) {
  for (int(__ii) = (0); (__ii) < (((int)v.size())); ++(__ii)) {
    for (int(__jj) = (0); (__jj) < (v[__ii].size()); ++(__jj)) {
      if (__jj) cout << ' ';
      cout << v[__ii][__jj];
    }
    cout << '\n';
  }
}
template <typename T>
void sc(T& x) {
  cin >> x;
}
template <typename Head, typename... Tail>
void sc(Head& head, Tail&... tail) {
  cin >> head;
  sc(tail...);
}
template <typename T>
void wr(const T& x) {
  cout << x << '\n';
}
template <typename Head, typename... Tail>
void wr(const Head& head, const Tail&... tail) {
  cout << head << ' ';
  wr(tail...);
}
template <typename T>
void wrf(const T& x) {
  cout << x << endl;
}
template <typename Head, typename... Tail>
void wrf(const Head& head, const Tail&... tail) {
  cout << head << ' ';
  wrf(tail...);
}
template <typename T>
void debug_out(const T& x) {
  cerr << x << '\n';
}
template <typename Head, typename... Tail>
void debug_out(const Head& head, const Tail&... tail) {
  cerr << head << ' ';
  debug_out(tail...);
}
template <typename... T>
void err(const T&... cod) {
  wr(cod...);
  exit(0);
}
void solve() {
  int n;
  sc(n);
  vector<int> a(n);
  for (int(__ii) = (0); (__ii) < (n); ++(__ii)) cin >> a[__ii];
  const int N = 1e6 + 10;
  vector<vector<int>> pos(N);
  for (int(i) = (0); (i) < (n); ++(i)) pos[a[i]].push_back(i);
  set<int> s;
  s.insert(-1);
  s.insert(n);
  long long ans = 0;
  for (int(i) = (0); (i) < (N); ++(i)) {
    for (auto& x : pos[i]) {
      auto p = s.lower_bound(x);
      ans -= 1LL * i * (x - *prev(p)) * (*p - x);
      s.insert(x);
    }
  }
  s.clear();
  s.insert(-1);
  s.insert(n);
  for (int(i) = (N - 1); (i) >= (0); --(i)) {
    for (auto& x : pos[i]) {
      auto p = s.lower_bound(x);
      ans += 1LL * i * (x - *prev(p)) * (*p - x);
      s.insert(x);
    }
  }
  wr(ans);
}
void init_test() {
  int qq = 1;
  while (qq--) solve();
}

### Prompt

In cpp, your task is to solve the following problem:

You are given an array a consisting of n elements. The imbalance value of some subsegment of this array is the difference between the maximum and minimum element from this segment. The imbalance value of the array is the sum of imbalance values of all subsegments of this array.

For example, the imbalance value of array [1, 4, 1] is 9, because there are 6 different subsegments of this array: 

  * [1] (from index 1 to index 1), imbalance value is 0; 
  * [1, 4] (from index 1 to index 2), imbalance value is 3; 
  * [1, 4, 1] (from index 1 to index 3), imbalance value is 3; 
  * [4] (from index 2 to index 2), imbalance value is 0; 
  * [4, 1] (from index 2 to index 3), imbalance value is 3; 
  * [1] (from index 3 to index 3), imbalance value is 0; 



You have to determine the imbalance value of the array a.

Input

The first line contains one integer n (1 ≤ n ≤ 106) — size of the array a.

The second line contains n integers a1, a2... an (1 ≤ ai ≤ 106) — elements of the array.

Output

Print one integer — the imbalance value of a.

Example

Input

3
1 4 1


Output

9

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void rset();
void init_test();
void solve();
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed;
  cout.precision(20);
  init_test();
  return 0;
}
template <typename T>
void chmin(T& a, T b) {
  if (a > b) a = b;
}
template <typename T>
void chmax(T& a, T b) {
  if (a < b) a = b;
}
template <typename T>
void MACRO_rdv2_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_rdv2_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_rdv2_Init(n, rest...);
}
template <typename T>
void MACRO_rdv2_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_rdv2_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_rdv2_Scan(p, rest...);
}
template <typename T>
void wrv(const vector<T>& v) {
  for (int(__ii) = (0); (__ii) < (((int)v.size())); ++(__ii)) {
    if (__ii) cout << ' ';
    cout << v[__ii];
  }
  cout << '\n';
}
template <typename T>
void wrm(const vector<vector<T>>& v) {
  for (int(__ii) = (0); (__ii) < (((int)v.size())); ++(__ii)) {
    for (int(__jj) = (0); (__jj) < (v[__ii].size()); ++(__jj)) {
      if (__jj) cout << ' ';
      cout << v[__ii][__jj];
    }
    cout << '\n';
  }
}
template <typename T>
void sc(T& x) {
  cin >> x;
}
template <typename Head, typename... Tail>
void sc(Head& head, Tail&... tail) {
  cin >> head;
  sc(tail...);
}
template <typename T>
void wr(const T& x) {
  cout << x << '\n';
}
template <typename Head, typename... Tail>
void wr(const Head& head, const Tail&... tail) {
  cout << head << ' ';
  wr(tail...);
}
template <typename T>
void wrf(const T& x) {
  cout << x << endl;
}
template <typename Head, typename... Tail>
void wrf(const Head& head, const Tail&... tail) {
  cout << head << ' ';
  wrf(tail...);
}
template <typename T>
void debug_out(const T& x) {
  cerr << x << '\n';
}
template <typename Head, typename... Tail>
void debug_out(const Head& head, const Tail&... tail) {
  cerr << head << ' ';
  debug_out(tail...);
}
template <typename... T>
void err(const T&... cod) {
  wr(cod...);
  exit(0);
}
void solve() {
  int n;
  sc(n);
  vector<int> a(n);
  for (int(__ii) = (0); (__ii) < (n); ++(__ii)) cin >> a[__ii];
  const int N = 1e6 + 10;
  vector<vector<int>> pos(N);
  for (int(i) = (0); (i) < (n); ++(i)) pos[a[i]].push_back(i);
  set<int> s;
  s.insert(-1);
  s.insert(n);
  long long ans = 0;
  for (int(i) = (0); (i) < (N); ++(i)) {
    for (auto& x : pos[i]) {
      auto p = s.lower_bound(x);
      ans -= 1LL * i * (x - *prev(p)) * (*p - x);
      s.insert(x);
    }
  }
  s.clear();
  s.insert(-1);
  s.insert(n);
  for (int(i) = (N - 1); (i) >= (0); --(i)) {
    for (auto& x : pos[i]) {
      auto p = s.lower_bound(x);
      ans += 1LL * i * (x - *prev(p)) * (*p - x);
      s.insert(x);
    }
  }
  wr(ans);
}
void init_test() {
  int qq = 1;
  while (qq--) solve();
}

```