201042: [AtCoder]ARC104 C - Fair Elevator

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.

Sample Input 1

3
1 -1
-1 4
-1 6

Sample Output 1

Yes

For example, if $B_1 = 3, A_2 = 2$, and $A_3 = 5$, 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 $C_1 = C_2 = 1$.

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 $C_1 = 2, C_2 = 0$, 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.