#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"
#include <random>
#include <unordered_map>
#include <unordered_set>
//#include <opencv2/core.hpp>
//#include <opencv2/highgui.hpp>
//#include <opencv2/imgproc.hpp>

using namespace std;

//呪文
#define DUMPOUT cerr
#define dump(...) DUMPOUT<<"  ";DUMPOUT<<#__VA_ARGS__<<" :["<<__LINE__<<":"<<__FUNCTION__<<"]"<<endl;DUMPOUT<<"    ";dump_func(__VA_ARGS__)

typedef unsigned uint; typedef long long ll; typedef unsigned long long ull; typedef pair<int, int> pii; typedef pair<ll, ll> pll; typedef pair<double, double> pdd; typedef pair<string, string> pss;
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const pair<_KTy, _Ty>& m) { o << "{" << m.first << ", " << m.second << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> ostream& operator << (ostream& o, const unordered_map<_KTy, _Ty>& m) { if (m.empty()) { o << "{ }"; return o; } o << "{" << *m.begin(); for (auto itr = ++m.begin(); itr != m.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const vector<_Ty>& v) { if (v.empty()) { o << "{ }"; return o; } o << "{" << v.front(); for (auto itr = ++v.begin(); itr != v.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; } o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const unordered_set<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } o << "{" << *(s.begin()); for (auto itr = ++s.begin(); itr != s.end(); itr++) { o << ", " << *itr; }	o << "}"; return o; }
template <typename _Ty> ostream& operator << (ostream& o, const stack<_Ty>& s) { if (s.empty()) { o << "{ }"; return o; } stack<_Ty> t(s); o << "{" << t.top(); t.pop(); while (!t.empty()) { o << ", " << t.top(); t.pop(); } o << "}";	return o; }
template <typename _Ty> ostream& operator << (ostream& o, const list<_Ty>& l) { if (l.empty()) { o << "{ }"; return o; } o << "{" << l.front(); for (auto itr = ++l.begin(); itr != l.end(); ++itr) { o << ", " << *itr; } o << "}"; return o; }
template <typename _KTy, typename _Ty> istream& operator >> (istream& is, pair<_KTy, _Ty>& m) { is >> m.first >> m.second; return is; }
template <typename _Ty> istream& operator >> (istream& is, vector<_Ty>& v) { for (size_t i = 0; i < v.size(); i++) is >> v[i]; return is; }
namespace aux { // print tuple
	template<typename Ty, unsigned N, unsigned L> struct tp { static void print(ostream& os, const Ty& v) { os << get<N>(v) << ", "; tp<Ty, N + 1, L>::print(os, v); } };
	template<typename Ty, unsigned N> struct tp<Ty, N, N> { static void print(ostream& os, const Ty& v) { os << get<N>(v); } };
}
template<typename... Tys> ostream& operator<<(ostream& os, const tuple<Tys...>& t) { os << "{"; aux::tp<tuple<Tys...>, 0, sizeof...(Tys)-1>::print(os, t); os << "}"; return os; }

template<typename A, size_t N, typename T> inline void Fill(A(&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }

void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) { DUMPOUT << head; if (sizeof...(Tail) == 0) { DUMPOUT << " "; } else { DUMPOUT << ", "; } dump_func(std::move(tail)...); }

#define PI 3.14159265358979323846
#define EPS 1e-10
#define FOR(is,a,n) for(int is=(a);is<(n);++is)
#define REP(is,n)  FOR(is,0,n)
#define all(j) (j).begin(), (j).end()
#define SZ(j) ((int)(j).size())
#define fake false




class DisjointSet {
public:
	vector<unsigned> par;
	vector<unsigned> rank;
	vector<unsigned> numElems;	// 要素の個数
	size_t numSets;			// 集合の個数

	DisjointSet() : numSets(0) { }

	DisjointSet(size_t n) :
		par(n), rank(n, 0), numElems(n, 1), numSets(n) {
		for (size_t i = 0; i < n; i++) par[i] = i;
	}

	size_t set_size() { return numSets; }
	size_t size(size_t v) { return numElems[find(v)]; }

	void makeset() {
		par.push_back(par.size());
		rank.push_back(0);
		numElems.push_back(1);
		numSets++;
	}
	void makeset(size_t n) {
		for (size_t i = 0; i < n; i++) makeset();
	}

	size_t find(size_t x) {
		if (par[x] == x)
			return x;
		else
			return par[x] = find(par[x]);
	}

	void unite(size_t x, size_t y) {
		x = find(x);
		y = find(y);
		if (x == y) return;

		if (rank[x] < rank[y])
			par[x] = y;
		else {
			par[y] = x;
			if (rank[x] == rank[y]) rank[x]++;
		}
		numElems[x] += numElems[y];
		numElems[y] = numElems[x];
		numSets--;
	}

	bool same(size_t x, size_t y) {
		return find(x) == find(y);
	}

	friend ostream& operator<<(ostream& ostr, const DisjointSet& ds) {
		ostr << endl << "parent : " << ds.par << endl << "rank : " << ds.rank << endl << "size : " << ds.numElems << endl << "size of set : " << ds.numSets << endl;
		return ostr;
	}
};


int main() {

	cin.tie(0);
	ios::sync_with_stdio(false);

	int N;
	cin >> N;
	vector<int> P(N);
	for (int i = 0; i < N; i++) {
		cin >> P[i];
		P[i]--;
	}

	DisjointSet ds(N);

	vector<bool> appeared(N, false);
	// P[i] + 1 が i < j なる P[j] に存在するか調べる
	for (int i = 0; i < N; i++) {
		int p = P[i];
		appeared[p] = true;
		if (p == N - 1)
			continue;
		if (!appeared[p + 1])
			ds.unite(p, p + 1);
	}

	cout << N - *max_element(all(ds.numElems)) << endl;

	return 0;
}


Measured memory_bytes: 3456