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
#include<bits/stdc++.h>
#define IOS ios_base::sync_with_stdio(false);cin.tie(NULL);
using namespace std;
#define ll long long
template<typename KeyType, typename ValueType> 
std::pair<KeyType,ValueType> get_max( const std::map<KeyType,ValueType>& x ) {
  using pairtype=std::pair<KeyType,ValueType>; 
  return *std::max_element(x.begin(), x.end(), [] (const pairtype & p1, const pairtype & p2) {
        return p1.second < p2.second;
  }); 
}
const int mod=1e9+7;
void solve()
{
	int n;
	cin>>n;
	if(!(n%2021)||!(n%2020))
	{
		cout<<"YES";
		return;
	}
	else
	{
		int chk=n;
		while(chk>=2021)
		{
			
			chk-=2020;
			if(chk%2021==0)
			{
				cout<<"YES";
				return;
			}
		}
	}
	cout<<"NO";
	return;
}
int main()
{
	int t;
	cin>>t;
	while(t--)
	{
		solve();
		cout<<"\n";
	}
}


