问题 C: Ama no Jaku

Let me tell you the things that I have been thinking for a long time.
You are given an $n\times n$ matrix $A$ with each number in $A$ either $0$ or $1$.
You can do the following operation on $A$ any number of times (possibly zero):

• Choose a row or a column from $A$, and flip it (i.e. all the $0$s in that row or column become $1$s, and all the $1$s become $0$s).
  

Define rir_iri as (Ai1Ai2…Ain‾)2(\overline{A_{i1}A_{i2}\dots A_{in}})_2(Ai1Ai2…Ain)2, which means writing all the number in the $i$-th row from left to right, forming a binary number rir_iri.
Define cjc_jcj as (A1jA2j…Anj‾)2(\overline{A_{1j}A_{2j}\dots A_{nj}})_2(A1jA2j…Anj)2, which means writing all the number in the $j$-th column from top to bottom, forming a binary number cjc_jcj.
Note that rir_iri and cjc_jcj may change after operations.
Determine whether you can achieve min⁡(ri)≥max⁡(cj)\min(r_i)\geq \max(c_j)min(ri)≥max(cj) by operations. If so, find out the minimal number of operations needed.

The first line contains a positive integer $n$ ($1\le n\le 2000$), denoting the size of matrix $A$.
Each of the following $n$ lines contains a string consisting of $n$ 0and1s, denoting each row of matrix $A$.

If it is possible to achieve min⁡(ri)≥max⁡(cj)\min(r_i)\geq \max(c_j)min(ri)≥max(cj), print the minimal number of operations in a single line. Otherwise, print $-1$.

3
100
010
001

-1