Sifid and Strange Subsequences（思维）

A sequence (b1,b2,…,bk) is called strange, if the absolute difference between any pair of its elements is greater than or equal to the maximum element in the sequence. Formally speaking, it’s strange if for every pair (i,j) with 1≤i<j≤k, we have |ai−aj|≥MAX, where MAX is the largest element of the sequence. In particular, any sequence of length at most 1 is strange.

For example, the sequences (−2021,−1,−1,−1) and (−1,0,1) are strange, but (3,0,1) is not, because |0−1|<3.

Sifid has an array a of n integers. Sifid likes everything big, so among all the strange subsequences of a, he wants to find the length of the longest one. Can you help him?

A sequence c is a subsequence of an array d if c can be obtained from d by deletion of several (possibly, zero or all) elements.

Input

The first line contains an integer t (1≤t≤104) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer n (1≤n≤105) — the length of the array a.

The second line of each test case contains n integers a1,a2,…,an (−109≤ai≤109) — the elements of the array a.

It is guaranteed that the sum of n over all test cases doesn’t exceed 105.

Output

For each test case output a single integer — the length of the longest strange subsequence of a.

Example Input

6
4
-1 -2 0 0
7
-3 4 -2 0 -4 6 1
5
0 5 -3 2 -5
3
2 3 1
4
-3 0 2 0
6
-3 -2 -1 1 1 1

Output

4
5
4
1
3
4

Note

In the first test case, one of the longest strange subsequences is (a1,a2,a3,a4)
In the second test case, one of the longest strange subsequences is (a1,a3,a4,a5,a7).

In the third test case, one of the longest strange subsequences is (a1,a3,a4,a5).

In the fourth test case, one of the longest strange subsequences is (a2).

In the fifth test case, one of the longest strange subsequences is (a1,a2,a4).

题意：给你n个数，让你从这n个数中找m个数，保证这m个数中任意两个数的差的绝对值大于等于这m个数中最大值。求一个最大的m。

题解：这m个数中最多只能有一个正数，因为如果有两个正数，这两个正数的差的绝对值一定小于最大值。所以我们只需要判断当有正数的时候，我们判断这个序列中的差的绝对值的最小值是否大于等于这个最小的正数，符合就加一。

AC代码：

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<stdlib.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
const int maxn=1e5+10;
const ll inf=0x7fffffff;//ll中的最大值
const int inf1=0x3f3f3f3f;//int中的最大值
int a[maxn];
int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		int n,i,j,k;
		scanf("%d",&n);
		for(i=1; i<=n; i++)
			scanf("%d",&a[i]);
		sort(a+1,a+1+n);
		int minn=inf1;
		k=0;
		int f=0;
		for(i=1; i<=n; i++)
		{
			if(a[i]>0)
			{
				f=1;
				break;
			}
			k++;
			minn=min(minn,abs(a[i]-a[i+1]));
		}
		if(minn>=a[i]&&f)
			k++;
		printf("%d\n",k);
	}
	return 0;
}