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: $\forall i, j(i < j) : h_{p_{i}} < h_{p_{j}}$.

-----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 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 3 gennady korotkevich petr mitrichev gaoyuan chen 1 2 3

Output NO

Input 3 gennady korotkevich petr mitrichev gaoyuan chen 3 1 2

Output YES

Input 2 galileo galilei nicolaus copernicus 2 1

Output YES

Input 10 rean schwarzer fei claussell alisa reinford eliot craig laura arseid jusis albarea machias regnitz sara valestin emma millstein gaius worzel 1 2 3 4 5 6 7 8 9 10

Output NO

Input 10 rean schwarzer fei claussell alisa reinford eliot craig laura arseid jusis albarea machias regnitz sara valestin emma millstein gaius worzel 2 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.