/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author champon
 */

#include <iostream>
#include <fstream>

#include <bits/stdc++.h>
#define ok cout << "ok" << endl;
#define sp << " " <<
using namespace std;
typedef long long ll;
const ll mod = 1e9+7;
const ll inf = 9e18;
template<typename T1, typename T2> ll ceill(T1 a, T2 b){ return (a+b-1)/b; }
void ans(bool b, ostream& out=cout){ out << (b ? "Yes" : "No") << endl; }
void ans2(bool b, ostream& out=cout){ out << (b ? "YES" : "NO") << endl; }
template<typename T> inline bool chmax(T &a, T b){ if(a<b){a=b; return true;} return false; }
template<typename T> inline bool chmin(T &a, T b){ if(a>b){a=b; return true;} return false; }
template<typename A, size_t N, typename T> void Fill(A (&array)[N], const T &val){ fill((T*)array, (T*)(array+N), val); }
int dx[] = {1, 0, -1, 0, 1, -1, 1, -1};
int dy[] = {0, 1, 0, -1, 1, -1, -1, 1};

#ifndef INCLUDE_DEBUG_HPP
#define INCLUDE_DEBUG_HPP

#include <iostream>
#include <vector>
#include <map>
using namespace std;

class debug
{
public:
    typedef long long ll;
    template<typename T> void vd(vector<T> vec);
    template<typename T> void vd2(vector<vector<T>> vec);
    template<typename T> void vpd(vector<pair<int, int>> vec);
    template<typename T> void ad(T *arr, ll n);
    template<typename T, size_t N> void ad2(T (&arr)[N], ll n);
    template<typename T> void md(T mp);
};

#endif //INCLUDE_DEBUG_HPP

template<typename T> void debug::vd(vector<T> vec)
{
    for(auto vv : vec) cout << vv << " ";
    cout << endl;
}

template<typename T> void debug::vd2(vector<vector<T>> vec)
{
    for(auto vv : vec) for(auto vvv : vv) cout << vvv << " ";
    cout << endl;
}

template<typename T> void debug::vpd(vector<pair<int, int>> vec) {
    for(auto const& vv : vec) {
        cout << vv.first << " " << vv.second << endl;
    }
    cout << endl;
}

template<typename T> void debug::ad(T *arr, ll n)
{
    for(int i=0; i<=n; i++) cout << arr[i] << " ";
    cout << endl;
}

template<typename T, size_t N> void debug::ad2(T (&arr)[N], ll n)
{
    for(int i=0; i<=N; i++) for(int j=0; j<=n; j++) cout << arr[i][j] << " ";
    cout << endl;
}

template<typename T> void debug::md(T mp)
{
    cout << "key : value" << endl;
    for(auto const& m : mp) cout << m.first << " : " << m.second << endl;
    cout << endl;
}
debug debug;

class BBackfront {
public:
	void solve(std::istream& in, std::ostream& out)
	{
        int n;
        in >> n;
        vector<int> p(n);
        for(int i=0; i<n; i++){
            in >> p[i];
        }

        vector<int> mp(n);
        for(int i=0; i<n; i++){
            mp[p[i]-1] = i;
        }

        vector<int> cnt(n), visit(n, 0);
        for(int i=0; i<n; i++){
            if(visit[p[i]-2]){
                cnt[i] = cnt[mp[p[i]-2]] + 1;
            }else{
                cnt[i] = 1;
            }
            visit[p[i]-1] = 1;
        }

        int mx = 0;
        for(int i=0; i<n; i++){
            chmax(mx, cnt[i]);
        }

        out << n-mx << endl;
	}
};


int main() {
	BBackfront solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}


Measured memory_bytes: 3328