#include <bits/stdc++.h>
int dx[4] = {0, -1, 0, 1};
int dy[4] = {1, 0, -1, 0};
using namespace std;
class pa3 {
 public:
  int x, y, z;
  pa3(int x = 0, int y = 0, int z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3 &p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    return z < p.z;
  }
  bool operator>(const pa3 &p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    return z > p.z;
  }
  bool operator==(const pa3 &p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3 &p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};
class pa4 {
 public:
  double x;
  int y, z, w;
  pa4(double x = 0, int y = 0, int z = 0, int w = 0) : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4 &p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    if (z != p.z) return z < p.z;
    return w < p.w;
  }
  bool operator>(const pa4 &p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    if (z != p.z) return z > p.z;
    return w > p.w;
  }
  bool operator==(const pa4 &p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
 public:
  int x, y;
  pa2(int x = 0, int y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  pa2 operator*(int a) { return pa2(x * a, y * a); }
  bool operator<(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator>(const pa2 &p) const { return x != p.x ? x > p.x : y > p.y; }
  bool operator==(const pa2 &p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2 &p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};
class Point {
 public:
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(x * a, y * a); }
  Point operator/(double a) { return Point(x / a, y / a); }
  double absv() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  bool operator<(const Point &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const Point &p) const {
    return fabs(x - p.x) < (1e-10) && fabs(y - p.y) < (1e-10);
  }
};
struct Segment {
  Point p1, p2;
};
double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
bool parareru(Point a, Point b, Point c, Point d) {
  return abs(cross(a - b, d - c)) < (1e-10);
}
double distance_ls_p(Point a, Point b, Point c) {
  if (dot(b - a, c - a) < (1e-10)) return (c - a).absv();
  if (dot(a - b, c - b) < (1e-10)) return (c - b).absv();
  return abs(cross(b - a, c - a)) / (b - a).absv();
}
bool is_intersected_ls(Segment a, Segment b) {
  if (a.p1 == b.p1 || a.p2 == b.p1 || a.p1 == b.p2 || a.p2 == b.p2)
    return false;
  if (parareru((a.p2), (a.p1), (a.p1), (b.p2)) &&
      parareru((a.p2), (a.p1), (a.p1), (b.p1))) {
    if (dot(a.p1 - b.p1, a.p1 - b.p2) < (1e-10)) return true;
    if (dot(a.p2 - b.p1, a.p2 - b.p2) < (1e-10)) return true;
    if (dot(a.p1 - b.p1, a.p2 - b.p1) < (1e-10)) return true;
    if (dot(a.p1 - b.p2, a.p2 - b.p2) < (1e-10)) return true;
    return false;
  } else
    return (cross(a.p2 - a.p1, b.p1 - a.p1) * cross(a.p2 - a.p1, b.p2 - a.p1) <
            (1e-10)) &&
           (cross(b.p2 - b.p1, a.p1 - b.p1) * cross(b.p2 - b.p1, a.p2 - b.p1) <
            (1e-10));
}
double segment_dis(Segment a, Segment b) {
  if (is_intersected_ls(a, b)) return 0;
  double r = distance_ls_p(a.p1, a.p2, b.p1);
  r = min(r, distance_ls_p(a.p1, a.p2, b.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p1));
  return r;
}
Point intersection_ls(Segment a, Segment b) {
  Point ba = b.p2 - b.p1;
  double d1 = abs(cross(ba, a.p1 - b.p1));
  double d2 = abs(cross(ba, a.p2 - b.p1));
  double t = d1 / (d1 + d2);
  return a.p1 + (a.p2 - a.p1) * t;
}
string itos(int i) {
  ostringstream s;
  s << i;
  return s.str();
}
int gcd(int v, int b) {
  if (v > b) return gcd(b, v);
  if (v == b) return b;
  if (b % v == 0) return v;
  return gcd(v, b % v);
}
double distans(double x1, double y1, double x2, double y2) {
  double rr = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  return sqrt(rr);
}
int beki(int wa, int rr, int warukazu) {
  if (rr == 0) return 1 % warukazu;
  if (rr == 1) return wa % warukazu;
  if (rr % 2 == 1) return (beki(wa, rr - 1, warukazu) * wa) % warukazu;
  int zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
double bekid(double w, int r) {
  if (r == 0) return 1.0;
  if (r == 1) return w;
  if (r % 2) return bekid(w, r - 1) * w;
  double f = bekid(w, r / 2);
  return f * f;
}
struct Segmin {
 private:
 public:
  int cor = (1 << 20);
  vector<pair<int, int> > vec;
  void shoki1() {
    vec.resize(2 * cor + 3, make_pair(0, 0));
    for (int i = cor; i < 2 * cor; i++) vec[i].second = i - cor;
  }
  void shoki2() {
    for (int i = cor - 1; i > 0; i--) {
      if (vec[2 * i].first <= vec[2 * i + 1].first)
        vec[i] = vec[2 * i];
      else
        vec[i] = vec[2 * i + 1];
    }
  }
  void updadd(int x, int w) {
    x += cor;
    vec[x].first += w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first <= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  void updchan(int x, int w) {
    x += cor;
    vec[x].first = w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first <= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  pair<int, int> segmin(int a, int b, int k = 1, int l = 0, int r = -10) {
    if (r < 0) r = cor;
    if (a <= l && r <= b) {
      return vec[k];
    }
    if (r <= a || b <= l) {
      return make_pair((1ll << 31) - 1, -1);
    }
    pair<int, int> v1 = segmin(a, b, k * 2, l, (l + r) / 2),
                   v2 = segmin(a, b, k * 2 + 1, (l + r) / 2, r);
    if (v1.first <= v2.first)
      return v1;
    else
      return v2;
  }
};
struct Segmax {
 private:
 public:
  int cor = (1 << 20);
  vector<pair<int, int> > vec;
  void shoki1() {
    vec.resize(2 * cor + 3, make_pair(0, 0));
    for (int i = cor; i < 2 * cor; i++) vec[i].second = i - cor;
  }
  void shoki2() {
    for (int i = cor - 1; i > 0; i--) {
      if (vec[2 * i].first >= vec[2 * i + 1].first)
        vec[i] = vec[2 * i];
      else
        vec[i] = vec[2 * i + 1];
    }
  }
  void updadd(int x, int w) {
    x += cor;
    vec[x].first += w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first >= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  void updchan(int x, int w) {
    x += cor;
    vec[x].first = w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first >= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  pair<int, int> segmax(int a, int b, int k = 1, int l = 0, int r = -10) {
    if (r < 0) r = cor;
    if (a <= l && r <= b) {
      return vec[k];
    }
    if (r <= a || b <= l) {
      return make_pair(-(1ll << 31), -1);
    }
    pair<int, int> v1 = segmax(a, b, k * 2, l, (l + r) / 2),
                   v2 = segmax(a, b, k * 2 + 1, (l + r) / 2, r);
    if (v1.first >= v2.first)
      return v1;
    else
      return v2;
  }
};
Segmax segmax;
Segmin segmin;
long long ans1 = 0ll, ans2 = 0ll;
void dfs1(int l, int r) {
  if (l >= r) return;
  if (r == l + 1) {
    ans1 += segmin.vec[segmin.cor + l].first;
    return;
  }
  pair<int, int> z = segmax.segmax(l, r);
  long long g = z.second - l;
  long long gg = r - z.second - 1;
  ans1 += (long long)z.first * (g * gg);
  ans1 += (long long)z.first * (g + gg + 1ll);
  dfs1(l, z.second);
  dfs1(z.second + 1, r);
}
void dfs2(int l, int r) {
  if (l >= r) return;
  if (r == l + 1) {
    ans2 += segmin.vec[segmin.cor + l].first;
    return;
  }
  pair<int, int> z = segmin.segmin(l, r);
  long long g = z.second - l;
  long long gg = r - z.second - 1;
  ans2 += (long long)z.first * (g * gg);
  ans2 += (long long)z.first * (g + gg + 1ll);
  dfs2(l, z.second);
  dfs2(z.second + 1, r);
}
signed main() {
  int n;
  segmax.shoki1();
  segmin.shoki1();
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int y;
    scanf("%d", &y);
    segmax.vec[segmax.cor + i].first = y;
    segmin.vec[segmin.cor + i].first = y;
  }
  segmax.shoki2();
  segmin.shoki2();
  dfs1(1, n + 1);
  dfs2(1, n + 1);
  cout << ans1 - ans2 << endl;
  return 0;
}

### Prompt

Your task is to create a CPP solution to 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>
int dx[4] = {0, -1, 0, 1};
int dy[4] = {1, 0, -1, 0};
using namespace std;
class pa3 {
 public:
  int x, y, z;
  pa3(int x = 0, int y = 0, int z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3 &p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    return z < p.z;
  }
  bool operator>(const pa3 &p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    return z > p.z;
  }
  bool operator==(const pa3 &p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3 &p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};
class pa4 {
 public:
  double x;
  int y, z, w;
  pa4(double x = 0, int y = 0, int z = 0, int w = 0) : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4 &p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    if (z != p.z) return z < p.z;
    return w < p.w;
  }
  bool operator>(const pa4 &p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    if (z != p.z) return z > p.z;
    return w > p.w;
  }
  bool operator==(const pa4 &p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
 public:
  int x, y;
  pa2(int x = 0, int y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  pa2 operator*(int a) { return pa2(x * a, y * a); }
  bool operator<(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator>(const pa2 &p) const { return x != p.x ? x > p.x : y > p.y; }
  bool operator==(const pa2 &p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2 &p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};
class Point {
 public:
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(x * a, y * a); }
  Point operator/(double a) { return Point(x / a, y / a); }
  double absv() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  bool operator<(const Point &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const Point &p) const {
    return fabs(x - p.x) < (1e-10) && fabs(y - p.y) < (1e-10);
  }
};
struct Segment {
  Point p1, p2;
};
double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
bool parareru(Point a, Point b, Point c, Point d) {
  return abs(cross(a - b, d - c)) < (1e-10);
}
double distance_ls_p(Point a, Point b, Point c) {
  if (dot(b - a, c - a) < (1e-10)) return (c - a).absv();
  if (dot(a - b, c - b) < (1e-10)) return (c - b).absv();
  return abs(cross(b - a, c - a)) / (b - a).absv();
}
bool is_intersected_ls(Segment a, Segment b) {
  if (a.p1 == b.p1 || a.p2 == b.p1 || a.p1 == b.p2 || a.p2 == b.p2)
    return false;
  if (parareru((a.p2), (a.p1), (a.p1), (b.p2)) &&
      parareru((a.p2), (a.p1), (a.p1), (b.p1))) {
    if (dot(a.p1 - b.p1, a.p1 - b.p2) < (1e-10)) return true;
    if (dot(a.p2 - b.p1, a.p2 - b.p2) < (1e-10)) return true;
    if (dot(a.p1 - b.p1, a.p2 - b.p1) < (1e-10)) return true;
    if (dot(a.p1 - b.p2, a.p2 - b.p2) < (1e-10)) return true;
    return false;
  } else
    return (cross(a.p2 - a.p1, b.p1 - a.p1) * cross(a.p2 - a.p1, b.p2 - a.p1) <
            (1e-10)) &&
           (cross(b.p2 - b.p1, a.p1 - b.p1) * cross(b.p2 - b.p1, a.p2 - b.p1) <
            (1e-10));
}
double segment_dis(Segment a, Segment b) {
  if (is_intersected_ls(a, b)) return 0;
  double r = distance_ls_p(a.p1, a.p2, b.p1);
  r = min(r, distance_ls_p(a.p1, a.p2, b.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p1));
  return r;
}
Point intersection_ls(Segment a, Segment b) {
  Point ba = b.p2 - b.p1;
  double d1 = abs(cross(ba, a.p1 - b.p1));
  double d2 = abs(cross(ba, a.p2 - b.p1));
  double t = d1 / (d1 + d2);
  return a.p1 + (a.p2 - a.p1) * t;
}
string itos(int i) {
  ostringstream s;
  s << i;
  return s.str();
}
int gcd(int v, int b) {
  if (v > b) return gcd(b, v);
  if (v == b) return b;
  if (b % v == 0) return v;
  return gcd(v, b % v);
}
double distans(double x1, double y1, double x2, double y2) {
  double rr = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  return sqrt(rr);
}
int beki(int wa, int rr, int warukazu) {
  if (rr == 0) return 1 % warukazu;
  if (rr == 1) return wa % warukazu;
  if (rr % 2 == 1) return (beki(wa, rr - 1, warukazu) * wa) % warukazu;
  int zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
double bekid(double w, int r) {
  if (r == 0) return 1.0;
  if (r == 1) return w;
  if (r % 2) return bekid(w, r - 1) * w;
  double f = bekid(w, r / 2);
  return f * f;
}
struct Segmin {
 private:
 public:
  int cor = (1 << 20);
  vector<pair<int, int> > vec;
  void shoki1() {
    vec.resize(2 * cor + 3, make_pair(0, 0));
    for (int i = cor; i < 2 * cor; i++) vec[i].second = i - cor;
  }
  void shoki2() {
    for (int i = cor - 1; i > 0; i--) {
      if (vec[2 * i].first <= vec[2 * i + 1].first)
        vec[i] = vec[2 * i];
      else
        vec[i] = vec[2 * i + 1];
    }
  }
  void updadd(int x, int w) {
    x += cor;
    vec[x].first += w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first <= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  void updchan(int x, int w) {
    x += cor;
    vec[x].first = w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first <= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  pair<int, int> segmin(int a, int b, int k = 1, int l = 0, int r = -10) {
    if (r < 0) r = cor;
    if (a <= l && r <= b) {
      return vec[k];
    }
    if (r <= a || b <= l) {
      return make_pair((1ll << 31) - 1, -1);
    }
    pair<int, int> v1 = segmin(a, b, k * 2, l, (l + r) / 2),
                   v2 = segmin(a, b, k * 2 + 1, (l + r) / 2, r);
    if (v1.first <= v2.first)
      return v1;
    else
      return v2;
  }
};
struct Segmax {
 private:
 public:
  int cor = (1 << 20);
  vector<pair<int, int> > vec;
  void shoki1() {
    vec.resize(2 * cor + 3, make_pair(0, 0));
    for (int i = cor; i < 2 * cor; i++) vec[i].second = i - cor;
  }
  void shoki2() {
    for (int i = cor - 1; i > 0; i--) {
      if (vec[2 * i].first >= vec[2 * i + 1].first)
        vec[i] = vec[2 * i];
      else
        vec[i] = vec[2 * i + 1];
    }
  }
  void updadd(int x, int w) {
    x += cor;
    vec[x].first += w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first >= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  void updchan(int x, int w) {
    x += cor;
    vec[x].first = w;
    while (1) {
      x /= 2;
      if (x == 0) break;
      if (vec[2 * x].first >= vec[2 * x + 1].first)
        vec[x] = vec[2 * x];
      else
        vec[x] = vec[2 * x + 1];
    }
  }
  pair<int, int> segmax(int a, int b, int k = 1, int l = 0, int r = -10) {
    if (r < 0) r = cor;
    if (a <= l && r <= b) {
      return vec[k];
    }
    if (r <= a || b <= l) {
      return make_pair(-(1ll << 31), -1);
    }
    pair<int, int> v1 = segmax(a, b, k * 2, l, (l + r) / 2),
                   v2 = segmax(a, b, k * 2 + 1, (l + r) / 2, r);
    if (v1.first >= v2.first)
      return v1;
    else
      return v2;
  }
};
Segmax segmax;
Segmin segmin;
long long ans1 = 0ll, ans2 = 0ll;
void dfs1(int l, int r) {
  if (l >= r) return;
  if (r == l + 1) {
    ans1 += segmin.vec[segmin.cor + l].first;
    return;
  }
  pair<int, int> z = segmax.segmax(l, r);
  long long g = z.second - l;
  long long gg = r - z.second - 1;
  ans1 += (long long)z.first * (g * gg);
  ans1 += (long long)z.first * (g + gg + 1ll);
  dfs1(l, z.second);
  dfs1(z.second + 1, r);
}
void dfs2(int l, int r) {
  if (l >= r) return;
  if (r == l + 1) {
    ans2 += segmin.vec[segmin.cor + l].first;
    return;
  }
  pair<int, int> z = segmin.segmin(l, r);
  long long g = z.second - l;
  long long gg = r - z.second - 1;
  ans2 += (long long)z.first * (g * gg);
  ans2 += (long long)z.first * (g + gg + 1ll);
  dfs2(l, z.second);
  dfs2(z.second + 1, r);
}
signed main() {
  int n;
  segmax.shoki1();
  segmin.shoki1();
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int y;
    scanf("%d", &y);
    segmax.vec[segmax.cor + i].first = y;
    segmin.vec[segmin.cor + i].first = y;
  }
  segmax.shoki2();
  segmin.shoki2();
  dfs1(1, n + 1);
  dfs2(1, n + 1);
  cout << ans1 - ans2 << endl;
  return 0;
}

```