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-----
3
1 -1
-1 4
-1 6

-----Sample Output-----
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.

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