We have an analog clock whose three hands (the second hand, the minute hand and the hour hand) rotate quite smoothly. You can measure two angles between the second hand and two other hands. Write a program to find the time at which "No two hands overlap each other" and "Two angles between the second hand and two other hands are equal" for the first time on or after a given time. \includegraphics{https://static.e-olymp.com/content/69/6937b06843081dea07653fb1c7893379b729906e.jpg} \textit{\textbf{Figure 1}}. Angles between the second hand and two other hands Clocks are not limited to \textbf{12}-hour clocks. The hour hand of an \textbf{H}-hour clock goes around once in \textbf{H} hours. The minute hand still goes around once every hour, and the second hand goes around once every minute. At \textbf{0:0:0} (midnight), all the hands are at the upright position. \InputFile The input consists of multiple datasets. Each of the dataset has four integers \textbf{H}, \textbf{h}, \textbf{m} and \textbf{s} in one line, separated by a space. \textbf{H} means that the clock is an \textbf{H}-hour clock. \textbf{h}, \textbf{m} and \textbf{s} mean hour, minute and second of the specified time, respectively. You may assume \textbf{2} ≤ \textbf{H} ≤ \textbf{100}, \textbf{0} ≤ \textbf{h} < \textbf{H}, \textbf{0} ≤ \textbf{m} < \textbf{60}, and \textbf{0} ≤ \textbf{s} < \textbf{60}. The end of the input is indicated by a line containing four zeros. \includegraphics{https://static.e-olymp.com/content/89/8935ee37475deea03777346303e153669c58c9d9.jpg} \textit{\textbf{Figure 2}}. Examples of \textbf{H}-hour clock (\textbf{6}-hour clock and \textbf{15}-hour clock) \OutputFile Output the time \textbf{T} at which "No two hands overlap each other" and "Two angles between the second hand and two other hands are equal" for the first time on and after the specified time. For \textbf{T} being \textbf{h_o:m_o:s_o} (\textbf{s_o} seconds past \textbf{m_o} minutes past \textbf{h_o} o’clock), output four non-negative integers \textbf{h_o}, \textbf{m_o}, \textbf{n}, and \textbf{d} in one line, separated by a space, where \textbf{n/d} is the irreducible fraction representing \textbf{s_o}. For integer \textbf{s_o} including \textbf{0}, let \textbf{d} be \textbf{1}. The time should be expressed in the remainder of \textbf{H} hours. In other words, one second after \textbf{(H−1):59:59} is \textbf{0:0:0}, not \textbf{H:0:0}.