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
import java.io.*;
import java.util.*;

public class Solution {
    
    static int sum = 4041;
    
    static boolean isDivisible(int n){
        int count = 0;
        while(n >= 2020) {
            n -= 2020;
            count++;
        }
        if(n <= count)
            return true;
        else
            return false;
        // if(n%2020==0 || n%2021==0 || (n>=sum && n%sum==0))
        //     return true;
        // if(n>sum){
        //     n=n-(sum*(n/sum));
        //     // System.out.println(n+"===");
        //     return isDivisible(n);
        // }//else if(n>2021 && n<4041){
        // //     return false;
        // // }
        // return false;
    }

    public static void main(String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        
        int T = Integer.parseInt(br.readLine());
        for(int t=0; t<T; t++){
            int n = Integer.parseInt(br.readLine());
            boolean f = false;
            if(n<2020)
                f=false;
            // else if(n>2021 && n<4041)
            //     f=false;
            else
                f=isDivisible(n);
            if(f)
                bw.write("YES\n");
            else
                bw.write("NO\n");
            
        }
        bw.flush();
    }
}