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)

#pragma warning(disable:4996)
#include <bits/stdc++.h>

using namespace std;

#define FOR(i, a, b) for (ll i = (ll)(a); i<(ll)(b); i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(a) begin(a), end(a)
#define TPL template
#define TNM typename

using ll = long long;
using ull = unsigned long long;
TPL<TNM T> using vec = vector<T>;
TPL<TNM T> using vec2 = vec<vec<T>>;
TPL<TNM T> using vec3 = vec<vec2<T>>;
TPL<TNM T> using vec4 = vec<vec3<T>>;
TPL<TNM T> using vec5 = vec<vec4<T>>;

TPL<TNM K, TNM V> using umap = unordered_map<K, V>;
TPL<TNM K, TNM V> using uset = unordered_set<K, V>;

TPL<class T> inline void OUT(const T &x) { cout << x << "\n"; }
void YESNO(bool c) { OUT(c ? "YES" : "NO"); };
void YesNo(bool c) { OUT(c ? "Yes" : "No"); };
void bOUT(bool c, string s, string t) { OUT(c ? s : t); }
struct pre_ { pre_() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(6); } } pre__;

TPL<TNM V, TNM H> void resize(vector<V>& v, const H h) { v.resize(h); }
TPL<TNM V, TNM H, TNM ... T> void resize(vector<V>& v, const H& h, const T ... t) { v.resize(h); for (auto& _v : v) resize(_v, t ...); }
TPL<TNM V, TNM T> void fill(V& x, const T& val) { x = val; }
TPL<TNM V, TNM T> void fill(vector<V>& vec, const T& val) { for (auto& v : vec) fill(v, val); }

template< typename Monoid >
struct SegmentTree {
	using F = function< Monoid(Monoid, Monoid) >;

	int sz;
	vector< Monoid > seg;

	const F f;
	const Monoid M1;

	SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
		sz = 1;
		while (sz < n) sz <<= 1;
		seg.assign(2 * sz, M1);
	}

	void set(int k, const Monoid &x) {
		seg[k + sz] = x;
	}

	void build() {
		for (int k = sz - 1; k > 0; k--) {
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	void update(int k, const Monoid &x) {
		k += sz;
		seg[k] = x;
		while (k >>= 1) {
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	Monoid query(int a, int b) {
		Monoid L = M1, R = M1;
		for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
			if (a & 1) L = f(L, seg[a++]);
			if (b & 1) R = f(seg[--b], R);
		}
		return f(L, R);
	}

	Monoid operator[](const int &k) const {
		return seg[k + sz];
	}
};

int main(void) {
	int N;
	cin >> N;
	vec<int> P(N);
	REP(i, N)cin >> P[i];

	SegmentTree< int > seg(N, [](int a, int b) { return min(a, b); }, INT_MAX);
	REP(i, N) {
		seg.update(i, P[i]);
	}


	int ans = 0;

	REP(i, N - 1) {
		int l = i + 1;
		int r = N;
		//cout << P[i] << " " << seg.query(i + 1, N) << endl;
		/*
		if (P[i] < seg.query(i + 1, N)) {
			cout << "T" << endl;
		}
		else {
			cout << "F" << endl;
		}
		*/
		if (P[i] >= seg.query(i + 1, N))ans++;
	}

	OUT(ans+1);

	return 0;
}