Score : $100$ points

Problem Statement

Takahashi recorded his daily life for the last few days as a integer sequence of length $2N$, as follows:

• $a_1, b_1, a_2, b_2, ... , a_N, b_N$

This means that, starting from a certain time $T$, he was:

• sleeping for exactly $a_1$ seconds
• then awake for exactly $b_1$ seconds
• then sleeping for exactly $a_2$ seconds
• :
• then sleeping for exactly $a_N$ seconds
• then awake for exactly $b_N$ seconds

In this record, he waked up $N$ times.

Takahashi is wondering how many times he waked up early during the recorded period.

Here, he is said to wake up early if he wakes up between $4:00$ AM and $7:00$ AM, inclusive.

If he wakes up more than once during this period, each of these awakenings is counted as waking up early.

Unfortunately, he forgot the time $T$.

Find the maximum possible number of times he waked up early during the recorded period.

For your information, a day consists of $86400$ seconds, and the length of the period between $4:00$ AM and $7:00$ AM is $10800$ seconds.

Constraints

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

Input

The input is given from Standard Input in the following format:

$N$

$a_1$ $b_1$

$a_2$ $b_2$

:

$a_N$ $b_N$

Output

Print the maximum possible number of times he waked up early during the recorded period.

3
28800 57600
28800 57600
57600 28800

2

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

5