New Year's Number

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

inputFormat

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.

outputFormat

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

样例

5
1
4041
4042
8081
8079

NO
YES
YES
YES
NO

</p>