Problem Statement

There is a building with $2N$ floors, numbered $1, 2, \ldots, 2N$ from bottom to top.

The elevator in this building moved from Floor $1$ to Floor $2N$ just once.

On the way, $N$ persons got on and off the elevator. Each person $i$ $(1 \leq i \leq N)$ got on at Floor $A_i$ and off at Floor $B_i$. Here, $1 \leq A_i < B_i \leq 2N$, and just one person got on or off at each floor.

Additionally, because of their difficult personalities, the following condition was satisfied:

• Let $C_i (= B_i - A_i - 1)$ be the number of times, while Person $i$ were on the elevator, other persons got on or off. Then, the following holds:
• If there was a moment when both Person $i$ and Person $j$ were on the elevator, $C_i = C_j$.

We recorded the sequences $A$ and $B$, but unfortunately, we have lost some of the records. If the record of $A_i$ or $B_i$ is lost, it will be given to you as $-1$.

Additionally, the remaining records may be incorrect.

Determine whether there is a pair of $A$ and $B$ that is consistent with the remaining records.

Constraints

• $1 \leq N \leq 100$
• $A_i = -1$ or $1 \leq A_i \leq 2N$.
• $B_i = -1$ or $1 \leq B_i \leq 2N$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
:
A_N B_N

Output

If there is a pair of $A$ and $B$ that is consistent with the remaining records, print Yes; otherwise, print No.