Polycarp has n friends, the i-th of his friends has a_i candies. Polycarp's friends do not like when they have different numbers of candies. In other words they want all a_i to be the same. To solve this, Polycarp performs the following set of actions exactly once: 

  * Polycarp chooses k (0 ≤ k ≤ n) arbitrary friends (let's say he chooses friends with indices i_1, i_2, …, i_k); 
  * Polycarp distributes their a_{i_1} + a_{i_2} + … + a_{i_k} candies among all n friends. During distribution for each of a_{i_1} + a_{i_2} + … + a_{i_k} candies he chooses new owner. That can be any of n friends. Note, that any candy can be given to the person, who has owned that candy before the distribution process. 



Note that the number k is not fixed in advance and can be arbitrary. Your task is to find the minimum value of k.

For example, if n=4 and a=[4, 5, 2, 5], then Polycarp could make the following distribution of the candies: 

  * Polycarp chooses k=2 friends with indices i=[2, 4] and distributes a_2 + a_4 = 10 candies to make a=[4, 4, 4, 4] (two candies go to person 3). 



Note that in this example Polycarp cannot choose k=1 friend so that he can redistribute candies so that in the end all a_i are equal.

For the data n and a, determine the minimum value k. With this value k, Polycarp should be able to select k friends and redistribute their candies so that everyone will end up with the same number of candies.

Input

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

The first line of each test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^4).

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

Output

For each test case output: 

  * the minimum value of k, such that Polycarp can choose exactly k friends so that he can redistribute the candies in the desired way; 
  * "-1" if no such value k exists. 

Example

Input


5
4
4 5 2 5
2
0 4
5
10 8 5 1 4
1
10000
7
1 1 1 1 1 1 1


Output


2
1
-1
0
0
import java.util.*;
import java.io.*;
//import java.math.*;

public class Task{
        //..............code begins here..............
static long mod=(long)1e9+7,mod1=998244353l,inf=(long)1e17;

static void solve() throws IOException {
        int n=int_v(read());
        int[] a=int_arr();
        sort(a);
        int[] f=new int[10002];
        int[] s=new int[10002];
        int tot=0;
        for(int i=0;i<n;i++){
            f[a[i]]++;tot+=a[i];
            s[a[i]]+=a[i];
        }
        for(int i=1;i<10001;i++){
            f[i]+=f[i-1];
            s[i]+=s[i-1];
        }
        if(tot==0||(a[0]==a[n-1])){out.write("0\n");return;}
        int res=n+10;
        for(int i=1;i<=10000;i++){
            int lessf=f[i-1],moref=n-f[i],curr=f[i]-f[i-1];
            int extra=tot-s[i]-i*moref;
            if(f[i-1]==0||f[i+1]==0) continue;
            if((s[i-1]+extra)%f[i-1]==0&&(s[i-1]+extra)/f[i-1]==i){
                res=Math.min(res,moref);
                //out.write(i+" "+f[i+1]+", ");
            }
        }
        if(res>=n)res=-1;
        out.write(res+"\n");
}
public static void main(String[] args) throws  IOException{
        assign();
        int t=int_v(read());
        int cn=1;
        while(t--!=0){
            //out.write("Case #"+cn+": ");
            solve();
            cn++;
        }
        out.flush();
}

// taking inputs
static BufferedReader s1;
static BufferedWriter out;
static String read() throws IOException{String line="";while(line.length()==0){line=s1.readLine();continue;}return line;}
static int int_v (String s1){return Integer.parseInt(s1);}
static long long_v(String s1){return Long.parseLong(s1);}
static void sort(int[] a){List<Integer> l=new ArrayList<>();for(int x:a){l.add(x);}Collections.sort(l);for(int i=0;i<a.length;i++){a[i]=l.get(i);}}
static int[] int_arr() throws IOException{String[] a=read().split(" ");int[] b=new int[a.length];for(int i=0;i<a.length;i++){b[i]=int_v(a[i]);}return b;}
static long[] long_arr() throws IOException{String[] a=read().split(" ");long[] b=new long[a.length];for(int i=0;i<a.length;i++){b[i]=long_v(a[i]);}return b;}
static void assign(){s1=new BufferedReader(new InputStreamReader(System.in));out=new BufferedWriter(new OutputStreamWriter(System.out));}
//static String setpreciosion(double d,int k){BigDecimal d1 = new BigDecimal(Double.toString(d));return d1.setScale(k,RoundingMode.HALF_UP).toString();}//UP DOWN HALF_UP
static int add(int a,int b){int z=a+b;if(z>=mod)z-=mod;return z;}
static long gcd(long a,long b){if(b==0){return a;}return gcd(b,a%b);}
static long Modpow(long a,long p,long m){long res=1;while(p>0){if((p&1)!=0){res=(res*a)%m;}p >>=1;a=(a*a)%m;}return res%m;}
static long Modmul(long a,long b,long m){return ((a%m)*(b%m))%m;}
static long ModInv(long a,long m){return Modpow(a,m-2,m);}
//static long nck(int n,int r,long m){if(r>n){return 0l;}return Modmul(f[n],ModInv(Modmul(f[n-r],f[r],m),m),m);}
//static long[] f;
}