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C. Design Tutorial: Make It Nondeterministic

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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".

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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