jmc

Since $697=12\cdot 58+1$, each Martian year consists of 58 weeks and a day. Therefore, for every year that passes, the first day of the year shifts to the next day of the week. Since year 0 begins on the first day, year 1 begins on the second day, then year 2 begins on the third day, and so on. A week consists of 12 days, so the next year that begins on the first day again will be year $\boxed{12}$.