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: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <algorithm>
#include <iomanip>
#include <math.h>
using namespace std;
using ll = long long;
using pll = pair<ll, ll>;
using vl = vector<ll>;
using vll = vector<vl>;
#define REP(i,n) for(int i=0; i<(int)(n); i++)
#define REPR(i,n) for(int i=n-1; i>=(int)(0); i--)
#define FOR(i,a,b) for(int i=(int)(a); i<(int)(b); i++)
#define FORR(i,a,b) for(int i=(int)(b)-1; i>=(int)(a); i--)
#define CHMIN(a,b) (a)=min((a),(b))
#define CHMAX(a,b) (a)=max((a),(b))
#define ALL(v) (v).begin(),(v).end()
//**関数リスト**//
int ctoi(char c) {
	switch (c) {
	case '0': return 0;
	case '1': return 1;
	case '2': return 2;
	case '3': return 3;
	case '4': return 4;
	case '5': return 5;
	case '6': return 6;
	case '7': return 7;
	case '8': return 8;
	case '9': return 9;
	default: return 0;
	}
}
bool pairCompare(const pll firstElof, pll secondElof)
{
	return firstElof.second < secondElof.second;
}
ll nod(ll F) {
	ll keta = 1;
	while (F / 10 > 0) {
		keta++;
		F /= 10;
	}
	return keta;
}
ll gcd(ll x, ll y) {
	ll r;
	if (x < y) {
		swap(x, y);
	}
	while (y > 0) {
		r = x % y;
		x = y;
		y = r;
	}
	return x;
}
ll lcm(ll x, ll y) {
	return x * y / gcd(x, y);
}
ll isPrime(ll x) {
	ll i;
	if (x < 2) {
		return 0;
	}
	else if (x == 2) {
		return 1;
	}
	else if (x % 2 == 0) {
		return 0;
	}
	else {
		for (i = 3; i * i <= x; i += 2) {
			if (x % 1 == 0) {
				return 0;
			}
		}
		return 1;
	}
}
void eratos(vl isPrime) {
	//(注)isPrimeのサイズはN+1にする！実際にはmain内に配置して使用
	ll i, j;
	REP(i, isPrime.size()) {
		isPrime[i] = 1;
	}
	isPrime[0] = 0; isPrime[1] = 0;
	for (i = 2; i * i <= isPrime.size() - 1; i++) {
		if (isPrime[i] == 1) {
			j = i * 2;
			while (j <= isPrime.size() - 1) {
				isPrime[j] = 0;
				j = j + i;
			}
		}
	}
}
ll modinv(ll a, ll m) {
	ll b = m, u = 1, v = 0;
	while (b) {
		ll t = a / b;
		a -= t * b; swap(a, b);
		u -= t * v; swap(u, v);
	}
	u %= m;
	if (u < 0) u += m;
	return u;
}
void bitSearch(ll n) {
	//実際にはコピーして中身を改変して使う
	ll i;
	REP(i, pow(2, n)) {
		ll p = i;
		REP(i, n) {
			cout << p % 2;
			p /= 2;
		}
		cout << endl;
	}
}
void dfs(ll now) {
	//中身は毎回書き換えて使用
	stack <ll> S;
	//flagは初期値0
	S.push(now);
	//flag[now]=1;
	while (!S.empty()) {
		ll u = S.top();
		//ll v = ;
		//if(flag[v]==0){flag[v]=1;S.push[v];}else{S.pop();}
	}
}
void bfs(ll now) {
	//中身は毎回書き換えて使用
	queue<ll> Q;
	Q.push(now);
	ll u;
	while (!Q.empty()) {
		u = Q.front();
		Q.pop();
		//ll v=;
		//Q.push(v);
	}
}
//**定義場所**//
ll i, j, k, l, m, n;
ll N, M, K, H, W;
ll MOD = 1000000007;
ll ans = 0;
//***********//
int main() {
	cin >> N;
	vl P(N);
	for (i = 0; i < N; i++) {
		cin >> P[i];
	}
	ll key = 1;
	for (i = 0; i < N; i++) {
		if (P[i] == key) {
			key++;
		}
	}
	ans = N-(key - 1);
	key = N;
	for (i = N - 1; i >= 0; i--) {
		if (P[i] == key) {
			key--;
		}
	}
	ans = min(ans, key);
	cout << ans;
}