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)

#ifdef LOCAL111
	#define _GLIBCXX_DEBUG
#else
	#define NDEBUG
#endif
#define _USE_MATH_DEFINES
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif
const int INF = 1e9;
using namespace std;
template<typename T, typename U> ostream& operator<< (ostream& os, const pair<T,U>& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; }

#define endl '\n'
#define ALL(a)  (a).begin(),(a).end()
#define SZ(a) int((a).size())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#ifdef LOCAL111
	#define DEBUG(x) cout<<#x<<": "<<(x)<<endl
	template<typename T> void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
#else
	#define DEBUG(x) true
	template<typename T> void dpite(T a, T b){ return; }
#endif
#define F first
#define S second
#define SNP string::npos
#define WRC(hoge) cout << "Case #" << (hoge)+1 << ": "
template<typename T> void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}

typedef long long int LL;
typedef unsigned long long ULL;
typedef pair<int,int> P;

void ios_init(){
	//cout.setf(ios::fixed);
	//cout.precision(12);
#ifdef LOCAL111
	return;
#endif
	ios::sync_with_stdio(false); cin.tie(0);
}

int getLIS(vector<int> a){
	vector<int> dp(a.size(),INF);
	for(int i = 0; i < a.size(); i++){
		*lower_bound(ALL(dp),a[i]) = a[i];
	}
	return lower_bound(ALL(dp),INF)-dp.begin();
}


int main()
{
	ios_init();
	int n;
    while(cin >> n) {
        vector<int> p(n);
        REP(i, n) {
            cin >> p[i];
            p[i]--;
        }
        vector<int> dp(n);
        REP(i, n) {
            if(p[i] == 0) {
                dp[0] = 1;
            } else {
                dp[p[i]] = dp[p[i]-1]+1;
            }
        }
        dpite(ALL(dp));
        int ma = 0;
        REP(i, n) {
            chmax(ma, dp[i]);
        }
        cout << n-ma << endl;
    }
	return 0;
}