You are given a number $$$n$$$ with a length of no more than $$$10^5$$$.

You can perform the following operation any number of times: choose one of its digits, square it, and replace the original digit with the result. The result must be a digit (that is, if you choose the digit $$$x$$$, then the value of $$$x^2$$$ must be less than $$$10$$$).

Is it possible to obtain a number that is divisible by $$$9$$$ through these operations?

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The only line of each test case contains the number $$$n$$$, without leading zeros. The length of the number does not exceed $$$10^5$$$.

It is guaranteed that the sum of the lengths of the numbers across all test cases does not exceed $$$10^5$$$.

Output

For each test case, output "YES" if it is possible to obtain a number divisible by $$$9$$$ using the described operations, and "NO" otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Note

In the first example, from the integer $$$123$$$, it is possible to obtain only $$$123$$$, $$$143$$$, $$$129$$$, and $$$149$$$, none of which are divisible by $$$9$$$.

In the second example, you need to replace the second digit with its square; then $$$n$$$ will equal $$$342 = 38 \cdot 9$$$.

In the third example, the integer is already divisible by $$$9$$$.

Uninteresting Number

Examples