Description

Our esteemed Guo Jia is living a carefree life under Cao Cao's patronage. However, one day Cao Cao assigned him a mission: within Jianye City, there are $N$ spies of Yuan Shao, numbered from $1$ to $N$. There exists a transmission relationship among them—if $C_{i,j}=1$, then spy $i$ can directly pass a message to spy $j$.

Now, Cao Cao wants to spread a false message to all the spies. Our task is to determine the minimum number of spies Guo Jia needs to inform initially so that the message reaches every spy.

Input Format

The first line of the input contains $N$. The next $N$ lines form an $N \times N$ matrix (where the $I$-th row and $J$-th column being $1$ means spy $I$ can directly pass a message to spy $J$, and $0$ means spy $I$ cannot directly pass a message to spy $J$).

Output Format

The output consists of a single line: the minimum number of spies Guo Jia needs to inform initially.

Sample 1

8
0 0 1 0 0 0 0 0
1 0 0 1 0 0 0 0
0 1 0 1 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 1 0 0 0 1
0 0 0 0 0 0 1 0

2

Constraints & Hints

$N \le 1000$