#include <bits/stdc++.h>
using namespace std;
//#include "testlib.h"
#define ff first
#define ss second
#define all(v) v.begin(),v.end()
#define int long long
#define ll long long
#define M 1000000007
#define MM 998244353
#define inputarr(a,n) for(int i=0;i<n;++i) cin>>a[i]
#define GCD(m,n) __gcd(m,n)
#define LCM(m,n) m*(n/GCD(m,n))
#define mii  map<ll ,ll >
#define msi  map<string,ll >
#define rep(a,b)    for(ll i=a;i<b;i++)
#define rep0(n)    for(ll i=0;i<n;i++)
#define repi(i,a,b) for(ll i=a;i<b;i++)
#define pb push_back
#define vi vector<ll>
#define vs vector<string>
#define ppb pop_back
#define endl '\n'
#define asdf ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define r0 return 0;
#define FORD(i, a, b) for (int i = (int) (a); i >= (int) (b); --i)
#define inputoutput freopen("input.txt", "r", stdin);freopen("output.txt", "w", stdout);
#define Set(a, s) (a, s, sizeof (a))
#define FOR repi
#define vii vector<pii>
#define pii pair<int,int>
#define REVERSE(v) reverse(all(v))
#define trav(a, x) for(auto& a : x)
#define display(x) trav(a,x) cout<<a<<" ";cout<<endl
#define debug cerr<<"bhau"<<endl
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    std::cerr << name << " : " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');std::cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
template<typename T, typename U> static inline void amin(T &x, U y) 
{ 
    if (y < x) 
        x = y; 
}
template<typename T, typename U> static inline void amax(T &x, U y) 
{ 
    if (x < y) 
        x = y; 
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

ll max(ll a, ll b) { return (a > b)? a : b;}
int min(int a, int b) { return (a < b)? a : b;} 


int solve(){


	int n;
	cin>>n;
	int a[n];
	inputarr(a,n);
	int dp[n+1];
	memset(dp,0,sizeof(dp));

	int l[n+1],r[n+1];
	int f[n+1];
	int cf[n+1];
	memset(r,0,sizeof(r));
	memset(l,-1,sizeof(r));
	memset(f,0,sizeof(f));
	memset(cf,0,sizeof(f));




	for(int i=n-1;i>=0;i--)
		l[a[i]] = i;
	for(int i=0;i<n;i++)
		r[a[i]] = i,f[a[i]]++;

	for(int i = n-1;i>=0;i--){
		dp[i] = dp[i+1];
		cf[a[i]]++;
		if(i==l[a[i]]){
			dp[i] = max(dp[i],f[a[i]] + dp[r[a[i]]+1]);
		}
		else{
			dp[i] =  max(dp[i],cf[a[i]]);
		}
	}

	cout<<n-dp[0]<<endl;


    return 0;
}
signed main(){
    asdf
    int t=1;
    // cin>>t;
    while(t--){
        solve();
    }
    return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

One day you wanted to read something, so you went to your bookshelf to grab some book. But when you saw how messy the bookshelf was you decided to clean it up first.

<image>

There are n books standing in a row on the shelf, the i-th book has color a_i.

You'd like to rearrange the books to make the shelf look beautiful. The shelf is considered beautiful if all books of the same color are next to each other.

In one operation you can take one book from any position on the shelf and move it to the right end of the shelf.

What is the minimum number of operations you need to make the shelf beautiful?

Input

The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the number of books.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — the book colors.

Output

Output the minimum number of operations to make the shelf beautiful.

Examples

Input


5
1 2 2 1 3


Output


2


Input


5
1 2 2 1 1


Output


1

Note

In the first example, we have the bookshelf [1, 2, 2, 1, 3] and can, for example: 

  1. take a book on position 4 and move to the right end: we'll get [1, 2, 2, 3, 1]; 
  2. take a book on position 1 and move to the right end: we'll get [2, 2, 3, 1, 1]. 



In the second example, we can move the first book to the end of the bookshelf and get [2,2,1,1,1].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
//#include "testlib.h"
#define ff first
#define ss second
#define all(v) v.begin(),v.end()
#define int long long
#define ll long long
#define M 1000000007
#define MM 998244353
#define inputarr(a,n) for(int i=0;i<n;++i) cin>>a[i]
#define GCD(m,n) __gcd(m,n)
#define LCM(m,n) m*(n/GCD(m,n))
#define mii  map<ll ,ll >
#define msi  map<string,ll >
#define rep(a,b)    for(ll i=a;i<b;i++)
#define rep0(n)    for(ll i=0;i<n;i++)
#define repi(i,a,b) for(ll i=a;i<b;i++)
#define pb push_back
#define vi vector<ll>
#define vs vector<string>
#define ppb pop_back
#define endl '\n'
#define asdf ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define r0 return 0;
#define FORD(i, a, b) for (int i = (int) (a); i >= (int) (b); --i)
#define inputoutput freopen("input.txt", "r", stdin);freopen("output.txt", "w", stdout);
#define Set(a, s) (a, s, sizeof (a))
#define FOR repi
#define vii vector<pii>
#define pii pair<int,int>
#define REVERSE(v) reverse(all(v))
#define trav(a, x) for(auto& a : x)
#define display(x) trav(a,x) cout<<a<<" ";cout<<endl
#define debug cerr<<"bhau"<<endl
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    std::cerr << name << " : " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');std::cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
template<typename T, typename U> static inline void amin(T &x, U y) 
{ 
    if (y < x) 
        x = y; 
}
template<typename T, typename U> static inline void amax(T &x, U y) 
{ 
    if (x < y) 
        x = y; 
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

ll max(ll a, ll b) { return (a > b)? a : b;}
int min(int a, int b) { return (a < b)? a : b;} 


int solve(){


	int n;
	cin>>n;
	int a[n];
	inputarr(a,n);
	int dp[n+1];
	memset(dp,0,sizeof(dp));

	int l[n+1],r[n+1];
	int f[n+1];
	int cf[n+1];
	memset(r,0,sizeof(r));
	memset(l,-1,sizeof(r));
	memset(f,0,sizeof(f));
	memset(cf,0,sizeof(f));




	for(int i=n-1;i>=0;i--)
		l[a[i]] = i;
	for(int i=0;i<n;i++)
		r[a[i]] = i,f[a[i]]++;

	for(int i = n-1;i>=0;i--){
		dp[i] = dp[i+1];
		cf[a[i]]++;
		if(i==l[a[i]]){
			dp[i] = max(dp[i],f[a[i]] + dp[r[a[i]]+1]);
		}
		else{
			dp[i] =  max(dp[i],cf[a[i]]);
		}
	}

	cout<<n-dp[0]<<endl;


    return 0;
}
signed main(){
    asdf
    int t=1;
    // cin>>t;
    while(t--){
        solve();
    }
    return 0;
}

```