Score : $1000$ points

Problem Statement

We will host a rock-paper-scissors tournament with $N$ people. The participants are called Person $1$, Person $2$, $\ldots$, Person $N$. For any two participants, the result of the match between them is determined in advance. This information is represented by positive integers $A_{i,j}$ ( $1 \leq j < i \leq N$ ) as follows:

• If $A_{i,j} = 0$, Person $j$ defeats Person $i$.
• If $A_{i,j} = 1$, Person $i$ defeats Person $j$.

The tournament proceeds as follows:

• We will arrange the $N$ participants in a row, in the order Person $1$, Person $2$, $\ldots$, Person $N$ from left to right.
• We will randomly choose two consecutive persons in the row. They will play a match against each other, and we will remove the loser from the row. We will repeat this process $N-1$ times, and the last person remaining will be declared the champion.

Find the number of persons with the possibility of becoming the champion.

Constraints

• $1 \leq N \leq 2000$
• $A_{i,j}$ is $0$ or $1$.

Input

Input is given from Standard Input in the following format:

$N$

$A_{2,1}$

$A_{3,1}$$A_{3,2}$

$:$

$A_{N,1}$$\ldots$$A_{N,N-1}$

Output

Print the number of persons with the possibility of becoming the champion.

3
0
10

2

Person $1$ defeats Person $2$, Person $2$ defeats Person $3$ and Person $3$ defeats Person $1$. If Person $1$ and Person $2$ play the first match, Person $3$ will become the champion. If Person $2$ and Person $3$ play the first match, Person $1$ will become the champion.

6
0
11
111
1111
11001

3