Problem Statement

There is a building with $2N$ floors, numbered $1,2,\dots ,2N$ 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 $i$ $(1\le i\le N)$ got on at Floor Ai​ and off at Floor Bi​. Here, 1≤Ai​<Bi​≤2N, and just one person got on or off at each floor.

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

• Let Ci​(=Bi​−Ai​−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, Ci​=Cj​.

We recorded the sequences $A$ and $B$, but unfortunately, we have lost some of the records. If the record of Ai​ or Bi​ 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

• $1\le N\le 100$
• Ai​=−1 or 1≤Ai​≤2N.
• Bi​=−1 or 1≤Bi​≤2N.
• All values in input are integers.

Sample Input 1

3
1 -1
-1 4
-1 6

Sample Output 1

Yes

For example, if B1​=3,A2​=2, and A3​=5, all the requirements are met.

In this case, there is a moment when both Person $1$ and Person $2$ were on the elevator, which is fine since C1​=C2​=1.

Sample Input 2

2
1 4
2 3

Sample Output 2

No

There is a moment when both Person $1$ and Person $2$ were on the elevator. Since C1​=2,C2​=0, some of the information is incorrect.

Sample Input 3

2
4 1
2 4

Sample Output 3

No

The records are seemingly intact but clearly are incorrect.