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 $*n*$ $(1 ≤ *n* ≤ 10^{5})$ — 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 $2*n*$ 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".

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.