L - Competition

Languages: C, C++, Java, Python, ... (details)

There are $n$ contestants participating in a round robin competition. Each pair of contestants face each other only once. In each match there is only one winner, (there are no ties).

Given a subset of contestants $X$  and the winners of the matches between these contestants, it is said that the best player of $X$ cannot be determined if there is no contestant with more wins than the rest.

It is desired to find, given the results of all the matches made in the competition, a set of $3$ contestants where the best contestant cannot be determined.

Input

The first line contains an integer $1 \le n \le 2000$. The amount of contestants in the competition.

The next $n$ lines represent the results of player $i$-th against the other contestants.

If the $j$-th character in the $i$-th line is $1$, it means that the contestant $i$ defeated the contestant $j$, if it is a $0$ it means he lost. For each pair of distinct contestants $i$ and $j$, it is guaranteed that either $i$ defeats $j$ or $j$ defeats $i$ (but not both).

Output

Print three integers $a,b,c$ ($1 \le a, b, c \le n$), the indices of the players that satisfy that a better player cannot be selected among them.  If there are multiple answers, print any. If there is no solution to the problem, print $-1$.

Sample test(s)

Input
4 0110 0000 0101 1100
Output
1 3 4
Input
4 0111 0000 0101 0100
Output
-1