Problem Statement

There are $N$ people on a number line.

Person $i$ $(1\le i\le N)$ is initially at coordinate $S_i$, and wants to eventually move to coordinate $T_i$. It is guaranteed that $S_1,S_2,\ldots,S_N,T_1,T_2,\ldots,T_N$ are all distinct.

You fix one permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$ and perform $N$ operations in order. In the $i$-th operation $(1\le i\le N)$, you move person $P_i$ from coordinate $S_{P_i}$ to coordinate $T_{P_i}$ along the shortest path on the number line. However, if there is another person on the movement path, a fight occurs.

Determine if there exists a $P$ such that no fight occurs, and if it exists, find one.

Constraints

• $1\le N\le 2\times 10^5$
• $1\le S_i, T_i \le 10^9$
• $S_1,S_2,\ldots,S_N,T_1,T_2,\ldots,T_N$ are all distinct.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
S_1 T_1
S_2 T_2
\vdots
S_N T_N

Output

If there is no $P$ such that no fight occurs, output No.

Otherwise, output a $P$ such that no fight occurs in the following format.

Yes
P_1 P_2 \ldots P_N

If there are multiple $P$ that satisfy the condition, any of them will be accepted.