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.*;
import java.io.*;
import java.lang.*;

public class NewYear {
  public static void main(String[] args) throws Exception {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int t = Integer.parseInt(br.readLine());

    String[] ans = new String[t];
    HashMap<Integer, Boolean> hmap = new HashMap<>();
    for(int i = 0; i < t; i++) {
      int n = Integer.parseInt(br.readLine());
      if(sumPossible(n, hmap))
        ans[i] = "YES";
      else
        ans[i] = "NO";
    }
    for(int i = 0; i < t; i++) {
      System.out.println(ans[i]);
    }
    br.close();
  }

  static boolean sumPossible(int n, HashMap<Integer, Boolean> hmap) {
    if(hmap.containsKey(n)) return hmap.get(n);
    if(n < 2020) return false;
    if(n == 2020 || n == 2021) return true;
    hmap.put(n, (sumPossible(n - 2020, hmap) || sumPossible(n - 2021, hmap)));
    return hmap.get(n);
  }
}
