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.