Softville Initiation Program

In the village of Softville, software is written one way. On the first day a programmer writes at least one line of code, and on every day after that the programmer writes exactly one line more than on the day before.

Once a citizen of Softville turns ten, the citizen has to pass an initiation: writing one very complicated program from scratch. The code of that program is the same for everyone and has exactly $N$ lines. The number of days needed to finish it can differ from citizen to citizen, but the rule always holds: every day a programmer writes one line more than the day before.

You are given how many days each citizen spent writing the initiation program. Find the smallest possible value of $N$. The program is not empty, so $N$ is at least 1.

The first line contains the number of citizens $m$ ($0 \le m \le 1000$). The second line contains $m$ integers separated by spaces, the number of days each citizen spent writing the initiation program. Each of those numbers is positive and smaller than $2^{63}$. When $m = 0$, the second line is empty.

Print the smallest possible value of $N$ on one line. If no value of $N$ agrees with all of the given day counts, print 0. When an answer exists, it is smaller than $2^{63}$. When $m = 0$, print 1.