#include <bits/stdc++.h>
typedef long long ll;
const int INF = 1e9;
const int MOD = 1e9+7;
const ll LINF = 1e18;
using namespace std;
 
#define dump(x)  cout << #x << " = " << (x) << endl;
#define YES(n) cout << ((n) ? "YES" : "NO"  ) << endl
#define Yes(n) cout << ((n) ? "Yes" : "No"  ) << endl
#define POSSIBLE(n) cout << ((n) ? "POSSIBLE" : "IMPOSSIBLE"  ) << endl
#define Possible(n) cout << ((n) ? "Possible" : "Impossible"  ) << endl
#define possible(n) cout << ((n) ? "possible" : "impossible"  ) << endl
 
#define SANKOU(n,a,b) cout << ((n) ? (#a) : (#b) ) << endl
 
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) for(int i=0;i<(n);++i)
#define REPR(i,n) for(int i=n;i>=0;i--)
 
#define FOREACH(x,a) for(auto& (x) : (a) )
 
#define WFA(d,v) REP(k,v)REP(i,v)REP(j,v)d[i][j]=min(d[i][j],d[i][k]+d[k][j])
 
#define SCOUT(x) cout<<(x)<<" "
#define ENDL cout<<endl
 
#define VECCIN(x) for(auto&youso_: (x) )cin>>youso_
#define VECIN2(x,y) REP(i,x.size())cin>>x[i]>>y[i]
#define VECCOUT(x) if(1){for(auto tt=x.begin();tt!=x.end();tt++){if(tt!=x.begin())cout<<" ";cout<<(*tt);}cout<<endl;}
 
#define ALL(obj) (obj).begin(),(obj).end()
 
#define EXIST(n,x) (find(ALL(n),x)!=n.end())
#define UNIQUE(obj) sort(ALL( obj )); obj.erase(unique(ALL(obj)),obj.end())
#define EN(x) if(1){cout<<#x<<endl;return 0;}
#define COUT(x) cout<<(x)<<endl
void CINT(){}
template <class Head,class... Tail>
void CINT(Head&& head,Tail&&... tail){
    cin>>head;
    CINT(move(tail)...);
}
#define CIN(...) int __VA_ARGS__;CINT(__VA_ARGS__)
#define LCIN(...) ll __VA_ARGS__;CINT(__VA_ARGS__)
#define SCIN(...) string __VA_ARGS__;CINT(__VA_ARGS__)
 
template <class T = ll>
T IN(){T x;cin>>x;return (x);}
 
template <class Head>
void VT(Head head){}
template <class Head,class Seco,class... Tail>
void VT(Head&& head,Seco&& seco,Tail&&... tail){
    seco.resize(head);
    VT(head,move(tail)...);
}
void VT2(){}
template <class Head,class... Tail>
void VT2(Head&& head,Tail&&... tail){
    VECCIN(head);
    VT2(move(tail)...);
}
 
template <class Head>
void VT3(Head&& head){}
template <class Head,class Seco,class... Tail>
void VT3(Head&& head,Seco&& seco,Tail&&... tail){
    seco[head]=IN();
    VT3(head,move(tail)...);
}
 
#define VC1(n,...) V __VA_ARGS__;VT(n,__VA_ARGS__);VT2(__VA_ARGS__); //aaabbbccc
#define VC2(n,...) V __VA_ARGS__;VT(n,__VA_ARGS__);REP(i,n)VT3(i,__VA_ARGS__); //abcabcabc
 
//#include <boost/multiprecision/cpp_int.hpp>
//using namespace boost::multiprecision; // cpp_int
 
#define P pair<ll,ll>
#define V vector<ll>
#define M map<ll,ll>
#define S set<ll>
 
#define pb(a) push_back(a)
#define mp make_pair

int main(){
    CIN(n);VC1(n,a);
    REP(i,n)a[i]--;
    //順列ソート
    //順列の部分列になっているような最大の長さ
    //最長連続(増加,減少)部分列
    //1-7の順列の4,5,6みたいな感じで、隣接2要素に対してv[i]<v[i+1]みたいな

    //先頭要素が0でないなら不可能
    //前から貪欲をする
    //a[i]-a[i-1]が1以上なら不可能
    //a[i]の値は必ずa[i+1]-1になっていなければならない
    
    V v(n);
    REP(i,n)v[a[i]]=i;

    V flag(n-1,0);
    REP(i,n-1)flag[i]=(v[i+1]>v[i]);//増加かどうか
//    VECCOUT(flag);
    V vv(1,1);
    REP(i,n-1){
        if(flag[i]){
            ++vv.back();
        }else{
            vv.pb(1);
        }
    }
    COUT(n-*max_element(ALL(vv)));

    /*
    ll ans = INF;
    ll pos = v[0];
    bool flag = true;
    FOR(i,1,n){
        if(pos>v[i]){
            ans=n-i;
            flag=false;
            break;
        }
        else pos = v[i];
    }
    if(flag)EN(0);

    pos = v[n-1];
    flag=true;
    REPR(i,n-2){
        if(pos<v[i]){
            ans=min(ans,1LL*i+1);
            flag=false;
            break;
        }
        else pos = v[i];

    }
    if(flag)EN(0);
    COUT(ans);
    */
    

    return 0;
}

Measured memory_bytes: 7156