Problem Description

Takahashi recorded his recent daily life as a sequence of length $2N$ as follows:

• $a_1, b_1, a_2, b_2, \ldots, a_N, b_N$

This represents that Takahashi started his day at a certain time $T$ and followed a routine where:

• He slept for exactly $a_1$ seconds.
• Then he stayed awake for exactly $b_1$ seconds.
• Then he slept for exactly $a_2$ seconds.
• (omitted)
• Then he slept for exactly $a_N$ seconds.
• Then he stayed awake for exactly $b_N$ seconds.

In this record, Takahashi woke up $N$ times.

Takahashi is curious about how many times he woke up early.

Here, "waking up early" refers to waking up between 4 AM and 7 AM. Waking up exactly at 4 AM or 7 AM also counts as waking up early.

If he wakes up during this time period on the same day more than once, it counts as multiple early risings.

However, Takahashi forgot the time $T$.

Find the maximum number of times he could have woken up early out of the $N$ times.

Note that a day has $86400$ seconds, and the time between 4 AM and 7 AM is $10800$ seconds.

Input Format

The input is given from the standard input in the following format:

$N$ $a_1$ $b_1$ $a_2$ $b_2$ $:$ $a_N$ $b_N$

Output Format

Output the maximum number of times he could have woken up early out of the $N$ times.

Sample Input and Output

Sample Input #1

3
28800 57600
28800 57600
57600 28800

Sample Output #1

2

Sample Input #2

10
28800 57600
4800 9600
6000 1200
600 600
300 600
5400 600
6000 5760
6760 2880
6000 12000
9000 600

Sample Output #2

5

Notes/Hints

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq a_i, b_i \leq 10^5$
• $a_i, b_i$ are both integers.

见题面 Input 部分

见题面 Output 部分