Design Tutorial: Make It Nondeterministic

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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 h_i, then the following condition must hold: $\text{[math]}$ .

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: p₁, p₂, ..., p_n (1 ≤ p_i ≤ n).

Output:

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

Sample Input:

3
gennady korotkevich
petr mitrichev
gaoyuan chen
1 2 3

Sample Output:

NO

Sample Input:

3
gennady korotkevich
petr mitrichev
gaoyuan chen
3 1 2

Sample Output:

YES

Sample Input:

2
galileo galilei
nicolaus copernicus
2 1

Sample Output:

YES

Sample 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

Sample Output:

NO

Sample 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

Sample 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.

Informação

Provedor Codeforces

Código CF472C