Problem:
Score : 500 points

Problem Statement

You are given a sequence (P_1,P_2,...,P_N) which is a permutation of the integers from 1 through N.
You would like to sort this sequence in ascending order by repeating the following operation:

Choose an element in the sequence and move it to the beginning or the end of the sequence.

Find the minimum number of operations required.
It can be proved that it is actually possible to sort the sequence using this operation.

Constraints

1 \leq N \leq 2\times 10^5

(P_1,P_2,...,P_N) is a permutation of (1,2,...,N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1
:
P_N

Output

Print the minimum number of operations required.

Sample Input 1

4
1
3
2
4

Sample Output 1

2

For example, the sequence can be sorted in ascending order as follows:

Move 2 to the beginning. The sequence is now (2,1,3,4).

Move 1 to the beginning. The sequence is now (1,2,3,4).

Sample Input 2

6
3
2
5
1
4
6

Sample Output 2

4

Sample Input 3

8
6
3
1
2
7
4
8
5

Sample Output 3

5

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define inf 2000000000
#define eb emplace_back
#define pb push_back
#define fi first
#define se second
#define fastread ios::sync_with_stdio(false);cin.tie(NULL)
#define rng_23 mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<pair<int,int>> vii;
typedef set<int> si;
typedef multiset<int> msi;
typedef map<int,int> mii;
int ara[200001],pos[200001];
int main()
{
    int i,j,k;
    int n;
    cin>>n;
    for(i=1;i<=n;i++){
        cin>>ara[i];
        pos[ara[i]]=i;
    }
    int mx=0;
    i=1,j=2;
    while(i<=n){
        while(pos[j]>pos[j-1] && j<=n)
            j++;
        mx=max(mx,j-i);
        i=j;
        j++;
        //cout<<i<<endl;
    }
    cout<<n-mx;
}