There are $n$ events, where each event $(t_i, x_i)$ indicates that a ball will land at position $x_i$ at time $t_i$.

Little F starts at $x_0 = 0$ at time $t_0 = 0$. Little F needs to catch all these balls, meaning that at each time $t_i$, either Little F or one of Little F's clones must be at position $x_i$.

If Little F is at position $x$ at the current time, they can move to $x-1$, $x$, or $x+1$ at the next time step.

Little F can place an immobile clone at their current position at any time. This clone can be used to catch a ball. However, when a new clone is placed, any previously existing clone will disappear after $0.01$ time units.

Determine if Little F can catch all the balls. If they can, output YES; otherwise, output NO.

Input

The first line contains a positive integer $n$.

The next $n$ lines each contain two numbers, where the $(i+1)$-th line represents $t_i$ and $x_i$.

Output

Output a single string, YES or NO, representing the answer.

Examples

Input 1

5
2 1
3 2 
9 6
10 5
13 0

Output 1

YES

Input 2

5
30 10
40 -10
51 9
52 8
53 20

Output 2

YES

Input 3

6
2 1
3 1
5 5
6 1
8 7
8 6

Output 3

YES

Input 4

10
1 -1
2 -1
3 1
4 2
4 -1
5 3
7 2
8 3
10 -2
11 1

Output 4

NO

Input 5

3
2 2
5 5
6 1

Output 5

YES

Constraints

There are 8 subtasks.

Subtask 1 ($5\%$): $n \le 20$, special properties.

Subtask 2 ($5\%$): $n \le 100$, depends on Subtask 1, special properties.

Subtask 3 ($10\%$): $n \le 5000$, depends on Subtask 2, special properties.

Subtask 4 ($20\%$): $n \le 5000$.

Subtask 5 ($20\%$): $n \le 10^5$, depends on Subtask 3, special properties.

Subtask 6 ($10\%$): $n \le 3 \times 10^5$, depends on Subtask 5, special properties.

Subtask 7 ($20\%$): $n \le 3 \times 10^5$, depends on Subtasks 4 and 6.

Subtask 8 ($10\%$): $n \le 10^6$, depends on Subtask 7.

For all data, $n \le 10^6$, $\forall i > 1, t_i \ge t_{i-1}$, and $\forall 1 \le i \le n, |x_i| \le 10^9, 0 \le t_i \le 10^9$.

Special properties: All $x_i$ are distinct.