You’re given a complete directed graph $G$ with $n$ vertices. We call a vertex $u$ dominating if for every $v \neq u$, there either exists an edge $(u \to v)$ or there exists a vertex $w$ satisfying $(u \to w)$ and $(w \to v)$.

You now need to find 3 distinct dominating vertices of the given graph. If there are less than 3 dominating vertices, output NOT FOUND.

Input

The first line of input contains one integer $n$ ($1 \le n \le 5000$).

The next $n$ lines of input contain a binary string $s_i$ each. There exists edge $(u \to v)$ if the $v$-th character of $s_u$ is $1$; otherwise, there is no such edge. It is guaranteed that exactly one of $s_{i,j} = 1$ and $s_{j,i} = 1$ holds for every $1 \le i < j \le n$ and $s_{i,i} = 0$ for every $1 \le i \le n$.

Output

The first line of output contains three integers $a, b, c$, denoting the answer you’ve found, or NOT FOUND, if there are not enough dominating vertices.

Examples

Input 1

6
011010
000101
010111
100001
010100
100010

Output 1

3 1 4

Input 2

3
011
001
000

Output 2

NOT FOUND

Input 3

3
010
001
100

Output 3

1 3 2