Happy Birthday, Polycarp!

Hooray! Polycarp turned n years old! The Technocup Team sincerely congratulates Polycarp!

Polycarp celebrated all of his n birthdays: from the 1-th to the n-th. At the moment, he is wondering: how many times he turned beautiful number of years?

According to Polycarp, a positive integer is beautiful if it consists of only one digit repeated one or more times. For example, the following numbers are beautiful: 1, 77, 777, 44 and 999999. The following numbers are not beautiful: 12, 11110, 6969 and 987654321.

Of course, Polycarpus uses the decimal numeral system (i.e. radix is 10).

Help Polycarpus to find the number of numbers from 1 to n (inclusive) that are beautiful.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

Each test case consists of one line, which contains a positive integer n (1 ≤ n ≤ 10^9) — how many years Polycarp has turned.

Output

Print t integers — the answers to the given test cases in the order they are written in the test. Each answer is an integer: the number of beautiful years between 1 and n, inclusive.

Example

Input

6 18 1 9 100500 33 1000000000

Output

10 1 9 45 12 81

Note

In the first test case of the example beautiful years are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 11.

inputFormat

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

Each test case consists of one line, which contains a positive integer n (1 ≤ n ≤ 10^9) — how many years Polycarp has turned.

outputFormat

Output

Print t integers — the answers to the given test cases in the order they are written in the test. Each answer is an integer: the number of beautiful years between 1 and n, inclusive.

Example

Input

6 18 1 9 100500 33 1000000000

Output

10 1 9 45 12 81

Note

In the first test case of the example beautiful years are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 11.

样例

6
18
1
9
100500
33
1000000000

10
1
9
45
12
81

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