C. Design Tutorial: Make It Nondeterministic

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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: .

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".

Sample test(s)

input

3gennady korotkevichpetr mitrichevgaoyuan chen1 2 3

output

NO

input

3gennady korotkevichpetr mitrichevgaoyuan chen3 1 2

output

YES

input

2galileo galileinicolaus copernicus2 1

output

YES

input

10rean schwarzerfei claussellalisa reinfordeliot craiglaura arseidjusis albareamachias regnitzsara valestinemma millsteingaius worzel1 2 3 4 5 6 7 8 9 10

output

NO

input

10rean schwarzerfei claussellalisa reinfordeliot craiglaura arseidjusis albareamachias regnitzsara valestinemma millsteingaius worzel2 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.

解题说明：题目的意思是每一个人 都有frist name 和 last name。 从每一个人的名字中任意选择first name 或者 last name 作为这个人的编号，通过对编号的排序，得到每一个人的最终顺序，比较中的序列能否得到给定输出的序列一致。字符串处理题，对字符串进行排序即可。

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<string>#include<cmath>#include<cstdlib>using namespace std;int N;string a[100100],b[100100];string cur="";int p[100100];int main(){int i,x;cin>>N;for(i=0;i<N;i++) {cin>>a[i]>>b[i];}for(i=0;i<N;i++){cin>>p[i];p[i]--;}for(i=0;i<N;i++){x=p[i];if(a[x]>b[x]){swap(a[x],b[x]);}if(cur<a[x]){cur=a[x];}else if(cur<b[x]) {cur=b[x];}else{cout<<"NO"<<endl;return 0;}}cout<<"YES"<<endl;return 0;}