Gate Opening Time

Given a day number n (1-indexed), compute the time at which a gate opens. The gate opens exactly n - 1 seconds after midnight. The output should be in the format HH:MM:SS, where:

\(\text{hours} = \lfloor \frac{n-1}{3600} \rfloor\),

\(\text{minutes} = \lfloor \frac{(n-1) \bmod 3600}{60} \rfloor\),

\(\text{seconds} = (n-1) \bmod 60\).

For example, if n = 1, the gate opens at "00:00:00"; if n = 86400, the gate opens at "23:59:59".

inputFormat

The first line contains a single integer T, the number of test cases. Each of the following T lines contains an integer n (where n ≥ 1), representing the day number.

outputFormat

For each test case, output the gate opening time in the format HH:MM:SS on a separate line.

## sample

3
1
2
3

00:00:00
00:00:01
00:00:02

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