cf 题解

Mihai and Slavic were looking at a group of $n$ frogs, numbered from $1$ to $n$, all initially located at point $0$. Frog $i$ has a hop length of $a_i$.

Each second, frog $i$ hops $a_i$ units forward. Before any frogs start hopping, Slavic and Mihai can place exactly one trap in a coordinate in order to catch all frogs that will ever pass through the corresponding coordinate.

However, the children can't go far away from their home so they can only place a trap in the first $n$ points (that is, in a point with a coordinate between $1$ and $n$) and the children can't place a trap in point $0$ since they are scared of frogs.

Can you help Slavic and Mihai find out what is the maximum number of frogs they can catch using a trap?

Input

Input

The first line of the input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the number of frogs, which equals the distance Slavic and Mihai can travel to place a trap.

The second line of each test case contains $n$ integers $a_1, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — the lengths of the hops of the corresponding frogs.

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

Output

Output

For each test case output a single integer — the maximum number of frogs Slavic and Mihai can catch using a trap.

Example

input

7
5
1 2 3 4 5
3
2 2 2
6
3 1 3 4 9 10
9
1 3 2 4 2 3 7 8 5
1
10
8
7 11 6 8 12 4 4 8
10
9 11 9 12 1 7 2 5 8 10

output

3
3
3
5
0
4
4

Note

Note

In the first test case, the frogs will hop as follows:

• Frog 1: $0 \to 1 \to 2 \to 3 \to \mathbf{\color{red}{4}} \to \cdots$
• Frog 2: $0 \to 2 \to \mathbf{\color{red}{4}} \to 6 \to 8 \to \cdots$
• Frog 3: $0 \to 3 \to 6 \to 9 \to 12 \to \cdots$
• Frog 4: $0 \to \mathbf{\color{red}{4}} \to 8 \to 12 \to 16 \to \cdots$
• Frog 5: $0 \to 5 \to 10 \to 15 \to 20 \to \cdots$

Therefore, if Slavic and Mihai put a trap at coordinate $4$, they can catch three frogs: frogs 1, 2, and 4. It can be proven that they can't catch any more frogs.

In the second test case, Slavic and Mihai can put a trap at coordinate $2$ and catch all three frogs instantly.

AC

#include <bits/stdc++.h>
using namespace std;
 
typedef  long long ll;
 
const int N = 200010;
 
int n, m, c, k, a, b;
int s[N], f[N];
 
void solve()
{ 
    cin>>n;
    for(int i=0; i<=n; i++) f[i]=0;
    for(int i=1; i<100; i++) s[i]=0;
    for(int i=0; i<n; i++) 
    {
        int x; cin>>x;
        if(x<100) s[x]++;
        else 
            for(int j=1; j*x<=n; j++)
                f[j*x]++;
    }
    
    int ans=0;
    for(int i=1; i<=n; i++)
    {
        int res=f[i];
        for(int k=1; k<100; k++)
        {
            if(i%k==0) res+=s[k];
        }
        ans=max(ans, res);
    }
        
    cout<<ans<<endl;
}
 
int main()
{
    int t; cin>>t;
    while(t--) solve();
    return 0;
}