A15353 | Add Modulo 10

You are given an array of $n$ integers $a_1, a_2, \dots, a_n$

You can apply the following operation an arbitrary number of times:

- select an index $i$ ( $1 \le i \le n$ ) and replace the value of the element $a_i$ with the value $a_i + (a_i \bmod 10)$ , where $a_i \bmod 10$ is the remainder of the integer dividing $a_i$ by $10$ .

For a single index (value $i$ ), this operation can be applied multiple times. If the operation is applied repeatedly to the same index, then the current value of $a_i$ is taken into account each time. For example, if $a_i=47$ then after the first operation we get $a_i=47+7=54$ , and after the second operation we get $a_i=54+4=58$ .

Check if it is possible to make all array elements equal by applying multiple (possibly zero) operations.

For example, you have an array $[6, 11]$ .

- Let's apply this operation to the first element of the array. Let's replace $a_1 = 6$ with $a_1 + (a_1 \bmod 10) = 6 + (6 \bmod 10) = 6 + 6 = 12$ . We get the array $[12, 11]$ .
- Then apply this operation to the second element of the array. Let's replace $a_2 = 11$ with $a_2 + (a_2 \bmod 10) = 11 + (11 \bmod 10) = 11 + 1 = 12$ . We get the array $[12, 12]$ .

Thus, by applying $2$ operations, you can make all elements of an array equal.

The first line contains one integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. What follows is a description of each test case.

The first line of each test case contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the size of the array.

The second line of each test case contains $n$ integers $a_i$ ( $0 \le a_i \le 10^9$ ) — array elements.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case print:

- YES if it is possible to make all array elements equal;
- NO otherwise.

You can print YES and NO in any case (for example, the strings yEs, yes, Yes and YES will be recognized as a positive answer) .