//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
//* vamsicool007      Nothing is IMPOSSIBLE as the word itself says I'M POSSIBLE!!       vamsicool007 *
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

#include<bits/stdc++.h>
using namespace std;
#define flash ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define F first
#define S second
#define pb push_back
#define all(v) (v).begin(),(v).end() 
#define endl "\n"
#define int long long int
#define ll long long
#define ld long double
const int mod = 1000000007;
const int N=200005;
const int inf=1e18;
vector<int>vis(N);
vector<vector<int>>adj(N);

//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

bool isPrime(ll n){if(n<2)return false;for(ll i=2;i*i<=n;++i){if(n%i==0){return false;}}return true;}
ll power(ll x,ll y){ll res=1;x=x;while(y>0){if(y&1)res=(res*x)%mod;y=y>>1;x=(x*x)%mod;}return res%mod;}
ll gcd(ll a,ll b){if (a==0)return b;return gcd(b%a,a);}
ll lcm(ll a,ll b){return (a/gcd(a,b)*b);}
ll max(ll a,ll b){ll ans=a>b?a:b;return ans;}
ll min(ll a,ll b){ll ans=a<b?a:b;return ans;}

//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

void fun()
{
    #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
}

//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

signed main()
{
    flash;
    fun();
    int tt=1;
    cin>>tt;
    while(tt--)
    {
        int n;
        cin>>n;
        int a[n];
        map<int,int>m;
        int maxx=-inf;
        for(int i=0;i<n;i++)
        {
            cin>>a[i];
            m[a[i]]++;
            maxx=max(maxx,m[a[i]]);
        }
        map<int,int>h;
        for(auto i:m)
            h[i.S]++;
        int s=0,ans=inf;
        for(int i=maxx;i>=1;i--)
        {
            s+=h[i];
            ans=min(ans,n-(i*s));
        }
        cout<<ans<<endl;
    }
    return 0;
}
### Prompt

In Cpp, your task is to solve the following problem:

Polycarp was gifted an array a of length n. Polycarp considers an array beautiful if there exists a number C, such that each number in the array occurs either zero or C times. Polycarp wants to remove some elements from the array a to make it beautiful.

For example, if n=6 and a = [1, 3, 2, 1, 4, 2], then the following options are possible to make the array a array beautiful: 

  * Polycarp removes elements at positions 2 and 5, array a becomes equal to [1, 2, 1, 2]; 
  * Polycarp removes elements at positions 1 and 6, array a becomes equal to [3, 2, 1, 4]; 
  * Polycarp removes elements at positions 1, 2 and 6, array a becomes equal to [2, 1, 4]; 



Help Polycarp determine the minimum number of elements to remove from the array a to make it beautiful.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case consists of one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array a.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — array a.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output one integer — the minimum number of elements that Polycarp has to remove from the array a to make it beautiful.

Example

Input


3
6
1 3 2 1 4 2
4
100 100 4 100
8
1 2 3 3 3 2 6 6


Output


2
1
2

### Response

```cpp
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
//* vamsicool007      Nothing is IMPOSSIBLE as the word itself says I'M POSSIBLE!!       vamsicool007 *
//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

#include<bits/stdc++.h>
using namespace std;
#define flash ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define F first
#define S second
#define pb push_back
#define all(v) (v).begin(),(v).end() 
#define endl "\n"
#define int long long int
#define ll long long
#define ld long double
const int mod = 1000000007;
const int N=200005;
const int inf=1e18;
vector<int>vis(N);
vector<vector<int>>adj(N);

//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

bool isPrime(ll n){if(n<2)return false;for(ll i=2;i*i<=n;++i){if(n%i==0){return false;}}return true;}
ll power(ll x,ll y){ll res=1;x=x;while(y>0){if(y&1)res=(res*x)%mod;y=y>>1;x=(x*x)%mod;}return res%mod;}
ll gcd(ll a,ll b){if (a==0)return b;return gcd(b%a,a);}
ll lcm(ll a,ll b){return (a/gcd(a,b)*b);}
ll max(ll a,ll b){ll ans=a>b?a:b;return ans;}
ll min(ll a,ll b){ll ans=a<b?a:b;return ans;}

//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

void fun()
{
    #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
}

//* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

signed main()
{
    flash;
    fun();
    int tt=1;
    cin>>tt;
    while(tt--)
    {
        int n;
        cin>>n;
        int a[n];
        map<int,int>m;
        int maxx=-inf;
        for(int i=0;i<n;i++)
        {
            cin>>a[i];
            m[a[i]]++;
            maxx=max(maxx,m[a[i]]);
        }
        map<int,int>h;
        for(auto i:m)
            h[i.S]++;
        int s=0,ans=inf;
        for(int i=maxx;i>=1;i--)
        {
            s+=h[i];
            ans=min(ans,n-(i*s));
        }
        cout<<ans<<endl;
    }
    return 0;
}
```