#include <bits/stdc++.h>
using namespace std;
inline void R(int &v) {
  v = 0;
  char c = 0;
  int p = 1;
  while (c < '0' || c > '9') {
    if (c == '-') p = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    v = (v << 3) + (v << 1) + c - '0';
    c = getchar();
  }
  v *= p;
}
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
inline int getint() {
  int _b = 0;
  char _c;
  for (_c = getchar(); _c < '0' || _c > '9'; _c = getchar())
    ;
  for (; _c >= '0' && _c <= '9'; _c = getchar()) {
    _b = (_b << 3) + (_b << 1);
    _b += _c - '0';
  }
  return _b;
}
inline int exgetint() {
  int _b = 0;
  char _c;
  int _p = 1;
  for (_c = getchar(); (_c < '0' || _c > '9') && _c != '-'; _c = getchar())
    ;
  if (_c == '-') {
    _c = getchar();
    _p = -1;
  }
  for (; _c >= '0' && _c <= '9'; _c = getchar()) {
    _b = (_b << 3) + (_b << 1);
    _b += _c - '0';
  }
  return _p * _b;
}
inline int Read() {
  int p = 1, x;
  char c;
  while ((c = getchar()) < '0' || c > '9')
    if (c == '-') p = -1;
  x = c - '0';
  while ((c = getchar()) > '0' && c <= '9') x = x * 10 + c - '0';
  x *= p;
  return x;
}
inline int READ() {
  char ch;
  bool flag = false;
  int a = 0;
  while (!((((ch = getchar()) >= '0') && (ch <= '9')) || (ch == '-')))
    ;
  if (ch != '-') {
    a *= 10;
    a += ch - '0';
  } else {
    flag = true;
  }
  while (((ch = getchar()) >= '0') && (ch <= '9')) {
    a *= 10;
    a += ch - '0';
  }
  if (flag) {
    a = -a;
  }
  return a;
}
void WRITE(int a) {
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  if (a >= 10) {
    WRITE(a / 10);
  }
  putchar(a % 10 + '0');
}
template <typename T>
class Treap {
 public:
  int tot;
  int root;
  int ls[300010], rs[300010], fa[300010], priority[300010], size[300010],
      num[300010];
  T val[300010];
  Treap() {
    tot = 2;
    root = 1;
    val[1] = 1000000000 + 1;
    val[2] = -1000000000 - 1;
    ls[1] = 2;
    fa[2] = 1;
    size[1] = 2;
    size[2] = 1;
    priority[1] = priority[2] = 1000000000 + 1;
    num[1] = num[2] = 1;
  }
  int newnode() {
    ++tot;
    priority[tot] = rand();
    size[tot] = 1;
    num[tot] = 1;
    return tot;
  }
  int begin() { return 2; }
  int end() { return 1; }
  int next(int now) {
    if (rs[now] != 0) {
      int x = rs[now];
      while (ls[x] != 0) x = ls[x];
      return x;
    }
    while (rs[fa[now]] == now) now = fa[now];
    return fa[now];
  }
  int prev(int now) {
    if (ls[now] != 0) {
      int x = ls[now];
      while (rs[x] != 0) x = rs[x];
      return x;
    }
    while (ls[fa[now]] == now) now = fa[now];
    return fa[now];
  }
  void _dfs(int now) {
    if (ls[now] != 0) _dfs(ls[now]);
    cout << val[now] << endl;
    if (rs[now] != 0) _dfs(rs[now]);
  }
  void update(int now) { size[now] = size[ls[now]] + size[rs[now]] + num[now]; }
  void left_rotate(int now) {
    if (now == root) return;
    int f = fa[now], ff = fa[fa[now]], b = ls[now];
    if (f == root) {
      root = now;
      ls[now] = f;
      fa[f] = now;
      rs[f] = b;
      if (b != 0) fa[b] = f;
    } else {
      fa[now] = ff;
      if (ls[ff] == f)
        ls[ff] = now;
      else
        rs[ff] = now;
      ls[now] = f;
      fa[f] = now;
      rs[f] = b;
      if (b != 0) fa[b] = f;
    }
    update(f), update(now);
  }
  void right_rotate(int now) {
    if (now == root) return;
    int f = fa[now], ff = fa[fa[now]], b = rs[now];
    if (f == root) {
      root = now;
      rs[now] = f;
      fa[f] = now;
      ls[f] = b;
      if (b != 0) fa[b] = f;
    } else {
      fa[now] = ff;
      if (ls[ff] == f)
        ls[ff] = now;
      else
        rs[ff] = now;
      rs[now] = f;
      fa[f] = now;
      ls[f] = b;
      if (b != 0) fa[b] = f;
    }
    update(f), update(now);
  }
  void _insert(int now, T x) {
    if (x == val[now]) {
      num[now]++;
      update(now);
      return;
    }
    if (x < val[now]) {
      if (ls[now] != 0)
        _insert(ls[now], x);
      else {
        ls[now] = newnode();
        fa[tot] = now;
        val[tot] = x;
      }
      if (priority[now] > priority[ls[now]]) right_rotate(ls[now]);
    } else {
      if (rs[now] != 0)
        _insert(rs[now], x);
      else {
        rs[now] = newnode();
        fa[tot] = now;
        val[tot] = x;
      }
      if (priority[now] > priority[rs[now]]) left_rotate(rs[now]);
    }
    update(now);
  }
  void down(int now) {
    while (ls[now] != 0 || rs[now] != 0) {
      if (ls[now] == 0)
        left_rotate(rs[now]);
      else if (rs[now] == 0)
        right_rotate(ls[now]);
      else {
        if (priority[ls[now]] < priority[rs[now]])
          right_rotate(ls[now]);
        else
          left_rotate(rs[now]);
      }
    }
    int f = fa[now];
    if (ls[f] == now) ls[f] = 0;
    if (rs[f] == now) rs[f] = 0;
    while (f != root) update(f), f = fa[f];
  }
  void _erase(int now, T x) {
    if (now == 0) return;
    if (val[now] == x) {
      num[now]--;
      if (num[now] == 0)
        down(now);
      else
        update(now);
      return;
    }
    if (x < val[now])
      _erase(ls[now], x);
    else
      _erase(rs[now], x);
    update(now);
  }
  T _findkth(int now, int kth) {
    if (size[ls[now]] >= kth) return _findkth(ls[now], kth);
    int s = kth - size[ls[now]] - num[now];
    if (s <= 0) return val[now];
    return _findkth(rs[now], s);
  }
  int _calc(int now, T x) {
    if (now == 0) return 0;
    if (x < val[now]) return _calc(ls[now], x);
    if (x == val[now]) return size[ls[now]];
    return _calc(rs[now], x) + size[ls[now]] + num[now];
  }
  int _find(int now, T x) {
    if (now == 0) return -1;
    if (x < val[now]) {
      int ret = _find(ls[now], x);
      if (ret == -1) return prev(now);
      return ret;
    }
    if (x == val[now]) return now;
    if (x > val[now]) {
      int ret = _find(rs[now], x);
      if (ret == -1) return now;
      return ret;
    }
  }
  void insert(T x) { _insert(root, x); }
  void erase(T x) { _erase(root, x); }
  T findkth(int x) {
    if (x < 0) return -1;
    if (x > size[root] - 2) return -1;
    return _findkth(root, x + 1);
  }
  int calc(T x) { return _calc(root, x) - 1; }
  T findmin(T x) {
    int s = _find(root, x);
    if (val[s] == x) s = prev(s);
    if (val[s] <= -1000000000) return -1;
    return val[s];
  }
  T findmax(T x) {
    int s = _find(root, x);
    if (val[s] <= x) s = next(s);
    if (val[s] >= 1000000000) return -1;
    return val[s];
  }
  int find(T x) { return _find(root, x); }
  void sort() { _dfs(root); }
};
int ans = 1, p[100010], dp[100010], a[100010];
int n;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    dp[i] = 1;
    a[i] = getint();
    p[a[i]] = i;
  }
  for (int i = 2; i <= n; i++) {
    if (p[i - 1] < p[i]) {
      dp[i] = dp[i - 1] + 1;
      ans = max(ans, dp[i]);
    }
  }
  cout << n - ans << endl;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

An infinitely long railway has a train consisting of n cars, numbered from 1 to n (the numbers of all the cars are distinct) and positioned in arbitrary order. David Blaine wants to sort the railway cars in the order of increasing numbers. In one move he can make one of the cars disappear from its place and teleport it either to the beginning of the train, or to the end of the train, at his desire. What is the minimum number of actions David Blaine needs to perform in order to sort the train?

Input

The first line of the input contains integer n (1 ≤ n ≤ 100 000) — the number of cars in the train. 

The second line contains n integers pi (1 ≤ pi ≤ n, pi ≠ pj if i ≠ j) — the sequence of the numbers of the cars in the train.

Output

Print a single integer — the minimum number of actions needed to sort the railway cars.

Examples

Input

5
4 1 2 5 3


Output

2


Input

4
4 1 3 2


Output

2

Note

In the first sample you need first to teleport the 4-th car, and then the 5-th car to the end of the train.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline void R(int &v) {
  v = 0;
  char c = 0;
  int p = 1;
  while (c < '0' || c > '9') {
    if (c == '-') p = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    v = (v << 3) + (v << 1) + c - '0';
    c = getchar();
  }
  v *= p;
}
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
inline int getint() {
  int _b = 0;
  char _c;
  for (_c = getchar(); _c < '0' || _c > '9'; _c = getchar())
    ;
  for (; _c >= '0' && _c <= '9'; _c = getchar()) {
    _b = (_b << 3) + (_b << 1);
    _b += _c - '0';
  }
  return _b;
}
inline int exgetint() {
  int _b = 0;
  char _c;
  int _p = 1;
  for (_c = getchar(); (_c < '0' || _c > '9') && _c != '-'; _c = getchar())
    ;
  if (_c == '-') {
    _c = getchar();
    _p = -1;
  }
  for (; _c >= '0' && _c <= '9'; _c = getchar()) {
    _b = (_b << 3) + (_b << 1);
    _b += _c - '0';
  }
  return _p * _b;
}
inline int Read() {
  int p = 1, x;
  char c;
  while ((c = getchar()) < '0' || c > '9')
    if (c == '-') p = -1;
  x = c - '0';
  while ((c = getchar()) > '0' && c <= '9') x = x * 10 + c - '0';
  x *= p;
  return x;
}
inline int READ() {
  char ch;
  bool flag = false;
  int a = 0;
  while (!((((ch = getchar()) >= '0') && (ch <= '9')) || (ch == '-')))
    ;
  if (ch != '-') {
    a *= 10;
    a += ch - '0';
  } else {
    flag = true;
  }
  while (((ch = getchar()) >= '0') && (ch <= '9')) {
    a *= 10;
    a += ch - '0';
  }
  if (flag) {
    a = -a;
  }
  return a;
}
void WRITE(int a) {
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  if (a >= 10) {
    WRITE(a / 10);
  }
  putchar(a % 10 + '0');
}
template <typename T>
class Treap {
 public:
  int tot;
  int root;
  int ls[300010], rs[300010], fa[300010], priority[300010], size[300010],
      num[300010];
  T val[300010];
  Treap() {
    tot = 2;
    root = 1;
    val[1] = 1000000000 + 1;
    val[2] = -1000000000 - 1;
    ls[1] = 2;
    fa[2] = 1;
    size[1] = 2;
    size[2] = 1;
    priority[1] = priority[2] = 1000000000 + 1;
    num[1] = num[2] = 1;
  }
  int newnode() {
    ++tot;
    priority[tot] = rand();
    size[tot] = 1;
    num[tot] = 1;
    return tot;
  }
  int begin() { return 2; }
  int end() { return 1; }
  int next(int now) {
    if (rs[now] != 0) {
      int x = rs[now];
      while (ls[x] != 0) x = ls[x];
      return x;
    }
    while (rs[fa[now]] == now) now = fa[now];
    return fa[now];
  }
  int prev(int now) {
    if (ls[now] != 0) {
      int x = ls[now];
      while (rs[x] != 0) x = rs[x];
      return x;
    }
    while (ls[fa[now]] == now) now = fa[now];
    return fa[now];
  }
  void _dfs(int now) {
    if (ls[now] != 0) _dfs(ls[now]);
    cout << val[now] << endl;
    if (rs[now] != 0) _dfs(rs[now]);
  }
  void update(int now) { size[now] = size[ls[now]] + size[rs[now]] + num[now]; }
  void left_rotate(int now) {
    if (now == root) return;
    int f = fa[now], ff = fa[fa[now]], b = ls[now];
    if (f == root) {
      root = now;
      ls[now] = f;
      fa[f] = now;
      rs[f] = b;
      if (b != 0) fa[b] = f;
    } else {
      fa[now] = ff;
      if (ls[ff] == f)
        ls[ff] = now;
      else
        rs[ff] = now;
      ls[now] = f;
      fa[f] = now;
      rs[f] = b;
      if (b != 0) fa[b] = f;
    }
    update(f), update(now);
  }
  void right_rotate(int now) {
    if (now == root) return;
    int f = fa[now], ff = fa[fa[now]], b = rs[now];
    if (f == root) {
      root = now;
      rs[now] = f;
      fa[f] = now;
      ls[f] = b;
      if (b != 0) fa[b] = f;
    } else {
      fa[now] = ff;
      if (ls[ff] == f)
        ls[ff] = now;
      else
        rs[ff] = now;
      rs[now] = f;
      fa[f] = now;
      ls[f] = b;
      if (b != 0) fa[b] = f;
    }
    update(f), update(now);
  }
  void _insert(int now, T x) {
    if (x == val[now]) {
      num[now]++;
      update(now);
      return;
    }
    if (x < val[now]) {
      if (ls[now] != 0)
        _insert(ls[now], x);
      else {
        ls[now] = newnode();
        fa[tot] = now;
        val[tot] = x;
      }
      if (priority[now] > priority[ls[now]]) right_rotate(ls[now]);
    } else {
      if (rs[now] != 0)
        _insert(rs[now], x);
      else {
        rs[now] = newnode();
        fa[tot] = now;
        val[tot] = x;
      }
      if (priority[now] > priority[rs[now]]) left_rotate(rs[now]);
    }
    update(now);
  }
  void down(int now) {
    while (ls[now] != 0 || rs[now] != 0) {
      if (ls[now] == 0)
        left_rotate(rs[now]);
      else if (rs[now] == 0)
        right_rotate(ls[now]);
      else {
        if (priority[ls[now]] < priority[rs[now]])
          right_rotate(ls[now]);
        else
          left_rotate(rs[now]);
      }
    }
    int f = fa[now];
    if (ls[f] == now) ls[f] = 0;
    if (rs[f] == now) rs[f] = 0;
    while (f != root) update(f), f = fa[f];
  }
  void _erase(int now, T x) {
    if (now == 0) return;
    if (val[now] == x) {
      num[now]--;
      if (num[now] == 0)
        down(now);
      else
        update(now);
      return;
    }
    if (x < val[now])
      _erase(ls[now], x);
    else
      _erase(rs[now], x);
    update(now);
  }
  T _findkth(int now, int kth) {
    if (size[ls[now]] >= kth) return _findkth(ls[now], kth);
    int s = kth - size[ls[now]] - num[now];
    if (s <= 0) return val[now];
    return _findkth(rs[now], s);
  }
  int _calc(int now, T x) {
    if (now == 0) return 0;
    if (x < val[now]) return _calc(ls[now], x);
    if (x == val[now]) return size[ls[now]];
    return _calc(rs[now], x) + size[ls[now]] + num[now];
  }
  int _find(int now, T x) {
    if (now == 0) return -1;
    if (x < val[now]) {
      int ret = _find(ls[now], x);
      if (ret == -1) return prev(now);
      return ret;
    }
    if (x == val[now]) return now;
    if (x > val[now]) {
      int ret = _find(rs[now], x);
      if (ret == -1) return now;
      return ret;
    }
  }
  void insert(T x) { _insert(root, x); }
  void erase(T x) { _erase(root, x); }
  T findkth(int x) {
    if (x < 0) return -1;
    if (x > size[root] - 2) return -1;
    return _findkth(root, x + 1);
  }
  int calc(T x) { return _calc(root, x) - 1; }
  T findmin(T x) {
    int s = _find(root, x);
    if (val[s] == x) s = prev(s);
    if (val[s] <= -1000000000) return -1;
    return val[s];
  }
  T findmax(T x) {
    int s = _find(root, x);
    if (val[s] <= x) s = next(s);
    if (val[s] >= 1000000000) return -1;
    return val[s];
  }
  int find(T x) { return _find(root, x); }
  void sort() { _dfs(root); }
};
int ans = 1, p[100010], dp[100010], a[100010];
int n;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    dp[i] = 1;
    a[i] = getint();
    p[a[i]] = i;
  }
  for (int i = 2; i <= n; i++) {
    if (p[i - 1] < p[i]) {
      dp[i] = dp[i - 1] + 1;
      ans = max(ans, dp[i]);
    }
  }
  cout << n - ans << endl;
}

```