402049: GYM100633 G Nano alarm-clocks

An old watchmaker has n stopped nano alarm-clocks numbered with integers from 1 to n. Nano alarm-clocks count time in hours, and in one hour there are million minutes, each minute lasting a million seconds. In order to repair them all the watchmaker should synchronize the time on all nano alarm-clocks. In order to do this he moves clock hands a certain time forward (may be zero time). Let’s name this time shift a transfer time.

Your task is to calculate the minimal total transfer time required for all nano alarm-clocks to show the same time.

The first line contains a single integer n — the number of nano alarm-clocks (2 ≤ n ≤ 10⁵). In each i-th of the next n lines the time h, m, s, shown on the i-th clock. Integers h, m and s show the number of hours, minutes and seconds respectively. (0 ≤ h < 12, 0 ≤ m < 10⁶, 0 ≤ s < 10⁶).

Output three integers separated with spaces h, m and s — total minimal transfer time, where h, m and s — number of hours, minutes and seconds respectively (0 ≤ m < 10⁶, 0 ≤ s < 10⁶).

2
10 0 0
3 0 0

5 0 0

3
11 999999 999999
0 0 0
11 999999 999999

0 0 2