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.util.Scanner;

public class trial_2 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        for(int it=0; it<t; it++) {
            int n = in.nextInt();
            if(n<2020) {
                System.out.println("NO");
                continue;
            }
            else if(n%2020 == 0 || n%2021 == 0) {
                System.out.println("YES");
                continue;
            }

            int rem = n%2020;
            if(rem*2021 > n) {
                System.out.println("NO");
                continue;
            }
            else{
                int formed = rem * 2021;
                boolean isHappy = false;
                for(int i=0; i<=n; i++) {
                    formed = formed + 2020;
                    if(formed == n) {
                        isHappy = true;
                        break;
                    }
                }
                if(isHappy) System.out.println("YES");
                else System.out.println("NO");
            }
            /*System.out.println("n = " + n);
            System.out.println("n%2020 = " + n%2020);
            System.out.println("n%2021 = " + n%2021);
            System.out.println();*/
        }
    }
}
