Problem

Bleatrix Trotter the sheep has devised a strategy that helps her fall asleep faster. First, she picks a numberN. Then she starts namingN, 2 ×N, 3 ×N, and so on. Whenever she names a number, she thinks about all of the digits in that number. She keeps track of which digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) she has seen at least once so far as part of any number she has named. Once she has seen each of the ten digits at least once, she will fall asleep.

Bleatrix must start withNand must always name (i+ 1) ×Ndirectly afteri×N. For example, suppose that Bleatrix picksN= 1692. She would count as follows:

• N= 1692. Now she has seen the digits 1, 2, 6, and 9.
• 2N= 3384. Now she has seen the digits 1, 2, 3, 4, 6, 8, and 9.
• 3N= 5076. Now she has seen all ten digits, and falls asleep.

What is the last number that she will name before falling asleep? If she will count forever, printINSOMNIAinstead.

Input

The first line of the input gives the number of test cases,T.Ttest cases follow. Each consists of one line with a single integerN, the number Bleatrix has chosen.

Output

For each test case, output one line containingCase #x: y

Limits

1 ≤T≤ 100.

Small dataset

0 ≤N≤ 200.

Large dataset

0 ≤N≤ 10⁶.

Sample

5
0
1
2
11
1692

Case #1: INSOMNIA
Case #2: 10
Case #3: 90
Case #4: 110
Case #5: 5076

In Case #1, since 2 × 0 = 0, 3 × 0 = 0, and so on, Bleatrix will never see any digit other than 0, and so she will count forever and never fall asleep. Poor sheep!

In Case #2, Bleatrix will name 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The 0 will be the last digit needed, and so she will fall asleep after 10.

In Case #3, Bleatrix will name 2, 4, 6... and so on. She will not see the digit 9 in any number until 90, at which point she will fall asleep. By that point, she will have already seen the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8, which will have appeared for the first time in the numbers 10, 10, 2, 30, 4, 50, 6, 70, and 8, respectively.

In Case #4, Bleatrix will name 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 and then fall asleep.

Case #5 is the one described in the problem statement. Note that it would only show up in the Large dataset, and not in the Small dataset.