Trinity

C. Trinity

You are given an array $a$ of $n$ elements $a_1,a_2,\dots ,a_n$.

You can perform the following operation any number (possibly $0$) of times:

• Choose two integers $i$ and $j$, where $1\le i,j\le n$, and assign $a_i:=a_j$.

Find the minimum number of operations required to make the array $a$ satisfy the condition:

• For every pairwise distinct triplet of indices $(x,y,z)$ ($1\le x,y,z\le n$, $x\ne y$, $y\ne z$, $x\ne z$), there exists a non-degenerate triangle with side lengths $a_x$, $a_y$ and $a_z$, i.e. $a_x+a_y>a_z$, $a_y+a_z>a_x$ and $a_z+a_x>a_y$.

Input

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($3\le n\le 2\cdot 10^5$) — the number of elements in the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\dots ,a_n$ ($1\le a_i\le 10^9$) — the elements of the array $a$.

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

Output

For each test case, output a single integer — the minimum number of operations required.

Example

Input

4
7
1 2 3 4 5 6 7
3
1 3 2
3
4 5 3
15
9 3 8 1 6 5 3 8 2 1 4 2 9 4 7

Output

3
1
0
8

Note

In the first test case, one of the possible series of operations would be:

• Assign $a_1:=a_4=4$. The array will become $[4,2,3,4,5,6,7]$.
• Assign $a_2:=a_5=5$. The array will become $[4,5,3,4,5,6,7]$.
• Assign $a_7:=a_1=4$. The array will become $[4,5,3,4,5,6,4]$.

It can be proven that any triplet of elements with pairwise distinct indices in the final array forms a non-degenerate triangle, and there is no possible answer using less than $3$ operations.

In the second test case, we can assign $a_1:=a_2=3$ to make the array $a=[3,3,2]$.

In the third test case, since $3$, $4$ and $5$ are valid side lengths of a triangle, we don’t need to perform any operation to the array.

code

#include<bits/stdc++.h>
#define int long long
#define endl '\n'
 
using namespace std;


const int N = 2e5+10,INF=0x3f3f3f3f,mod=1e9+7;
 
typedef pair<int,int> PII;

int T=1;

void solve(){
	int n;
	cin>>n;
	vector<int> a(n);
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	sort(a.begin(),a.end());
	int l=0,ans=INF;
	for(int r=2;r<n;r++){
		while(a[l]+a[l+1]<=a[r]){
			l++;
		}
		ans=min(ans,l+n-r-1);
	}
	cout<<ans<<endl;
}

signed main(){
	cin>>T; 
    while(T--){
        solve();
    }
    return 0;
}