Problem Statement

You are given a character table with $1$ of its values hidden. Find the hidden value.

Detailed Problem Statement

Suppose that a finite group $G$ has exactly $N$ irreducible characters, and let them be $\chi_1,\ldots,\chi_N$. Then $G$ has $N$ conjugacy classes. Choose one element from each of the $N$ conjugacy classes, $1$ element per class, and let them be $g_1,\ldots,g_N$. With $A_{ij}=\chi_i(g_j)$, the square matrix $A$ of order $N$ is called the character table.

You are now given a square matrix $A$ of order $N$. In this $A$, $A_{ij}$ is ? for exactly $1$ pair $(i,j)$, and replacing it with an appropriate integer yields the character table of some group. Find this integer.

Constraints

• $N$ is an integer between $1$ and $10$, inclusive
• For exactly $1$ pair $(i,j)$, $A_{ij}$ is ?; for all other $(i,j)$, $A_{ij}$ is an integer
• Only inputs that can be a character table are given

Input

$N$
$A_{11}$ $\ldots$ $A_{1N}$
$\vdots$
$A_{N1}$ $\ldots$ $A_{NN}$

Output

Output the appropriate integer.

Sample

3
1 1 1
1 -1 1
? 0 -1

2

5
1 1 1 1 1
1 -1 1 -1 1
2 0 ? 0 -2
1 1 -1 -1 1
1 -1 -1 1 1

0

1
?

1