CF - 472C. Design Tutorial: Make It Nondeterministic 贪心

1.题目描述：

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".

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.

2.题意概述：

有n个人,每个人可以选择两种签名,问是否给定的顺序能否构成一个字典序排序的签名

3.解题思路：

照指定的顺序,每次贪心地选择符合条件的字典序的最小的字符串,若当前的字符串比下一个人的两个签名的字典序都大,则无法满足

4.AC代码：

#include <iostream>
#include <algorithm>
#include <string>
#define maxn 101000
using namespace std;
struct node
{int id;string fst, snd;
}p[maxn];int main()
{int n;scanf("%d", &n);for (int i = 1; i <= n; i++)cin >> p[i].fst >> p[i].snd;int temp, flag = 1;cin >> temp;string last = min(p[temp].fst, p[temp].snd);for (int i = 2; i <= n; i++){if (!flag)break;cin >> temp;string cur = min(p[temp].fst, p[temp].snd);if (last >= cur){cur = max(p[temp].fst, p[temp].snd);if (last >= cur)flag = 0;}last = cur;}if (flag)puts("YES");elseputs("NO");return 0;
}

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