#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define mod 1000000007
#define mod2 998244353
#define pi pair<ll,ll>
#define pii pair<ll,pair<ll,ll>>
#define vi vector<ll>
#define pb push_back
#define ld long double
#define vpi vector<pair<ll,ll>>
#define vvi vector<vector<ll>>

#define debug(a) { cout << #a << " = " << a << endl;}

void sep(string SS = "BLOCK") {
    cout << "-------------" << SS << "-----------------\n";
}

template<typename t>
void pr(t a) {
    cout << a << endl;
}

template<typename t>
void prs(t a) {
    cout << a <<  " ";
}

template<typename T>
void debugv(vector<T> arr) {
    for (auto t: arr)
        cout << t << " ";
    cout << "\n";
}

template<typename T>
void debugarr(T arr, int n) {
    for (int i=0;i<n;i++) cout << arr[i] << " ";
    cout << "\n";
}

template<typename T>
void chmax(T& a, T b) {
    if (a < b)
        a = b;
}

template<typename T>
void chmin(T& a, T b) {
    if (a > b)
        a = b;
}

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

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

const int maxn = 4e6+100;
const ll INF = 1e18;
ll a[maxn], n, m, t, k, q;
set<ll> s;

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    cin>>t;
    while (t--) {
        cin>>n;
        map<ll,ll> u;
        for (ll i=0;i<n;i++) {
            cin>>a[i]; ++u[a[i]];
        }
        set<ll> s;
        for (pi p: u) s.insert(p.second);
        ll res = INF;
        for (ll x: s) {
            ll tot = 0;
            for (pi p: u) {
                if (p.second < x) tot += p.second;
                else tot += p.second - x;
            }
            chmin(res, tot);
        }
        pr(res);
    }
}


### Prompt

Develop a solution in CPP to the problem described below:

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
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define mod 1000000007
#define mod2 998244353
#define pi pair<ll,ll>
#define pii pair<ll,pair<ll,ll>>
#define vi vector<ll>
#define pb push_back
#define ld long double
#define vpi vector<pair<ll,ll>>
#define vvi vector<vector<ll>>

#define debug(a) { cout << #a << " = " << a << endl;}

void sep(string SS = "BLOCK") {
    cout << "-------------" << SS << "-----------------\n";
}

template<typename t>
void pr(t a) {
    cout << a << endl;
}

template<typename t>
void prs(t a) {
    cout << a <<  " ";
}

template<typename T>
void debugv(vector<T> arr) {
    for (auto t: arr)
        cout << t << " ";
    cout << "\n";
}

template<typename T>
void debugarr(T arr, int n) {
    for (int i=0;i<n;i++) cout << arr[i] << " ";
    cout << "\n";
}

template<typename T>
void chmax(T& a, T b) {
    if (a < b)
        a = b;
}

template<typename T>
void chmin(T& a, T b) {
    if (a > b)
        a = b;
}

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

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

const int maxn = 4e6+100;
const ll INF = 1e18;
ll a[maxn], n, m, t, k, q;
set<ll> s;

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    cin>>t;
    while (t--) {
        cin>>n;
        map<ll,ll> u;
        for (ll i=0;i<n;i++) {
            cin>>a[i]; ++u[a[i]];
        }
        set<ll> s;
        for (pi p: u) s.insert(p.second);
        ll res = INF;
        for (ll x: s) {
            ll tot = 0;
            for (pi p: u) {
                if (p.second < x) tot += p.second;
                else tot += p.second - x;
            }
            chmin(res, tot);
        }
        pr(res);
    }
}


```