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.BufferedReader;
import java.io.InputStreamReader;
public class Main {
    public static void count(int val,long year)
    {
        int i=0;
        String ans="NO";
        while (val>=0)
        {
            if(2020*val+2021*i==year)
            {
                ans="YES";
                break;
            }
            i++;
            val--;
        }
        System.out.println(ans);
    }
    public static void main(String[] args)
    {
        try
        {
            BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
            int t=Integer.parseInt(in.readLine());
            for (int i = 0; i <t; i++) {
                long year=Long.parseLong(in.readLine());
                if(year<2020)
                {
                    System.out.println("NO");
                }
                else
                {
                    if(year%2020==0 && year%2021==0)
                    {
                        System.out.println("YES");
                    }
                    else
                    {
                        int times=(int)(year/2020);
                        count(times,year);
                    }
                }
            }
        }
        catch (Exception e)
        {
            e.printStackTrace();
        }
    }
}
