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.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
//-------------------------------------------------- X --------------------------------------------------------------\\
//-------------------------------------------------- XX -------------------------------------------------------------\\
//-------------------------------------------------- XXX ------------------------------------------------------------\\

public class CAGE_CODE {

    public static void main(String[] args) throws Exception{
        Scanner input = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        long tests = input.nextLong();
        while (tests-- > 0) {
            completeContract(input, out);
        }

        out.close();
    }

    private static void completeContract(Scanner sc, PrintWriter out) throws Exception {


        int n = sc.nextInt();
        if(n % 2020 == 0 || n % 2021 == 0){
            out.println("YES");
        }
        else{
            while(n > 0){
                n -= 2020;
                if(n % 2021 == 0){out.println("YES");return;}
            }
            out.println("NO");
        }



    }

}