Problem Description

It is a well known fact that a number is divisible by $11$ if and only if the alternating sum of its digits is equal to $0$ modulo $11$. For example, $8174958$ is a multiple of $11$, since $8 - 1 + 7 - 4 + 9 - 5 + 8 = 22$.

Given a number that consists of digits from $1$-$9$, can you rearrange the digits to create a number that is divisible by $11$?

Since the number might be quite large, you are given integers $A_1, A_2, ..., A_9$. There are $A_i$ digits i in the number, for all i.

Input Format

The first line of the input gives the number of test cases, $T$. $T$ lines follow. Each line contains the nine integers $A_1, A_2, ..., A_9$.

Output Format

For each test case, output one line containing Case #x: y, where x is the test case number (starting from $1$) and y is YES if the digits can be rearranged to create a multiple of $11$, and NO otherwise.

6
0 0 2 0 0 1 0 0 0
0 0 0 0 0 0 0 0 12
0 0 0 0 2 0 1 1 0
3 1 1 1 0 0 0 0 0
3 0 0 0 0 0 3 0 2
0 0 0 0 0 0 0 1 0

Case #1: YES
Case #2: YES
Case #3: NO
Case #4: YES
Case #5: YES
Case #6: NO

Hint

• In Sample Case #1, the digits are $336$, which can be rearranged to $363$. This is a multiple of $11$ since $3 - 6 + 3 = 0$.
• In Sample Case #2, the digits are $999999999999$, which is already a multiple of $11$, since $9 - 9 + 9 - 9 + ... - 9 = 0$.
• In Sample Case #3, the digits are $5578$, which cannot be rearranged to form a multiple of $11$.
• In Sample Case #4, the digits are $111234$, which can be rearranged to $142131$. This is a multiple of $11$ since $1 - 4 + 2 - 1 + 3 - 1 = 0$.
• In Sample Case #5, the digits are $11177799$, which can be rearranged to $19191777$. This is a multiple of $11$ since $1 - 9 + 1 - 9 + 1 - 7 + 7 - 7 = -22$ (which is $0$ modulo $11$).
• In Sample Case #6, the only digit is $8$, which cannot be rearranged to form a multiple of $11$.

Limits

$1 \le T \le 100$.

$1 \le A_1 + A_2 + ... + A_9$.

Test set 1 (Visible)

$0 \le A_i \le 20$, for all i.

Test set 2 (Hidden)

$0 \le A_i \le 10^9$, for all i.