C. Design Tutorial: Make It Nondeterministic
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A way to make a new task is to make it nondeterministic or probabilistic. For example, the hard task of Topcoder SRM 595, Constellation, is the probabilistic version of a convex hull.

Let's try to make a new task. Firstly we will use the following task. There are n people, sort them by their name. It is just an ordinary sorting problem, but we can make it more interesting by adding nondeterministic element. There are n people, each person will use either his/her first name or last name as a handle. Can the lexicographical order of the handles be exactly equal to the given permutation p?

More formally, if we denote the handle of the i-th person as h i, then the following condition must hold: .

Input

The first line contains an integer n (1 ≤ n ≤ 105) — the number of people.

The next n lines each contains two strings. The i-th line contains strings f i and s i (1 ≤ |f i|, |s i| ≤ 50) — the first name and last name of the i-th person. Each string consists only of lowercase English letters. All of the given 2n strings will be distinct.

The next line contains n distinct integers: p 1, p 2, ..., p n (1 ≤ p i ≤ n).

Output

If it is possible, output "YES", otherwise output "NO".

Examples
Input
3gennady korotkevichpetr mitrichevgaoyuan chen1 2 3
Output
NO
Input
3gennady korotkevichpetr mitrichevgaoyuan chen3 1 2
Output
YES
Input
2galileo galileinicolaus copernicus2 1
Output
YES
Input
10rean schwarzerfei claussellalisa reinfordeliot craiglaura arseidjusis albareamachias regnitzsara valestinemma millsteingaius worzel1 2 3 4 5 6 7 8 9 10
Output
NO
Input
10rean schwarzerfei claussellalisa reinfordeliot craiglaura arseidjusis albareamachias regnitzsara valestinemma millsteingaius worzel2 4 9 6 5 7 1 3 8 10
Output
YES
Note

In example 1 and 2, we have 3 people: tourist, Petr and me (cgy4ever). You can see that whatever handle is chosen, I must be the first, then tourist and Petr must be the last.

In example 3, if Copernicus uses "copernicus" as his handle, everything will be alright.