#P472C. Design Tutorial: Make It Nondeterministic
Design Tutorial: Make It Nondeterministic
Description
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 hi, then the following condition must hold: 
.
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 fi and si (1 ≤ |fi|, |si| ≤ 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: p1, p2, ..., pn (1 ≤ pi ≤ n).
If it is possible, output "YES", otherwise output "NO".
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 fi and si (1 ≤ |fi|, |si| ≤ 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: p1, p2, ..., pn (1 ≤ pi ≤ n).
Output
If it is possible, output "YES", otherwise output "NO".
3<br>gennady korotkevich<br>petr mitrichev<br>gaoyuan chen<br>1 2 3<br>
3<br>gennady korotkevich<br>petr mitrichev<br>gaoyuan chen<br>3 1 2<br>
2<br>galileo galilei<br>nicolaus copernicus<br>2 1<br>
10<br>rean schwarzer<br>fei claussell<br>alisa reinford<br>eliot craig<br>laura arseid<br>jusis albarea<br>machias regnitz<br>sara valestin<br>emma millstein<br>gaius worzel<br>1 2 3 4 5 6 7 8 9 10<br>
10<br>rean schwarzer<br>fei claussell<br>alisa reinford<br>eliot craig<br>laura arseid<br>jusis albarea<br>machias regnitz<br>sara valestin<br>emma millstein<br>gaius worzel<br>2 4 9 6 5 7 1 3 8 10<br>
NO<br>
YES<br>
YES<br>
NO<br>
YES<br>
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.