#include <bits/stdc++.h>
using namespace std;
long long GCD(long long a, long long b) {
  if (b == 0) return a;
  return (a % b == 0 ? b : GCD(b, a % b));
}
long long POW(long long base, long long exp) {
  long long val;
  val = 1;
  while (exp > 0) {
    if (exp % 2 == 1) {
      val = (val * base) % 1000000007;
    }
    base = (base * base) % 1000000007;
    exp = exp / 2;
  }
  return val;
}
int a[100005];
int pos[100005];
int main() {
  int n, i, c, mx;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  for (i = 1; i <= n; i++) {
    pos[a[i]] = i;
  }
  mx = 0;
  for (i = 1; i <= n; i++) {
    c = 1;
    while (i < n && pos[i + 1] > pos[i]) {
      i++;
      c++;
    }
    mx = max(mx, c);
  }
  printf("%d\n", n - mx);
  return 0;
}
