Polycarp remembered the 2020-th year, and he is happy with the arrival of the new 2021-th year. To remember such a wonderful moment, Polycarp wants to represent the number n as the sum of a certain number of 2020 and a certain number of 2021.

For example, if: 

  * n=4041, then the number n can be represented as the sum 2020 + 2021; 
  * n=4042, then the number n can be represented as the sum 2021 + 2021; 
  * n=8081, then the number n can be represented as the sum 2020 + 2020 + 2020 + 2021; 
  * n=8079, then the number n cannot be represented as the sum of the numbers 2020 and 2021. 



Help Polycarp to find out whether the number n can be represented as the sum of a certain number of numbers 2020 and a certain number of numbers 2021.

Input

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

Each test case contains one integer n (1 ≤ n ≤ 10^6) — the number that Polycarp wants to represent as the sum of the numbers 2020 and 2021.

Output

For each test case, output on a separate line: 

  * "YES" if the number n is representable as the sum of a certain number of 2020 and a certain number of 2021; 
  * "NO" otherwise. 



You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).

Example

Input


5
1
4041
4042
8081
8079


Output


NO
YES
YES
YES
NO
#include<iostream>
#include<bits/stdc++.h>
using namespace std;
int main()
{
    int t,x,y,z;
    cin>>t;
    while(t--)
    {
        int flag =0;
        cin>>x;
        if(x%(2020)==0)
        {
            cout<<"YES\n";
            flag=1;
        }
        else if(x%(2021)==0)
        {
            cout<<"YES\n";
            flag=1;
        }
        else
        {
            y=0;
            while(y<x)
            {
                z=x;
                y+=2020;
                if((z-y)%(2021)==0)
                {cout<<"YES\n";
                flag=1;
                break;}
            
            }
        }
        if(flag==0)
        {
           // cout<<"hi";
            cout<<"No\n";
        }
    }
    return 0;
}