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 hisher 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: .
输入描述:
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).
输出描述:
If it is possible, output "YES", otherwise output "NO".
示例1
输入
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 />
输出
NO<br />YES<br />YES<br />NO<br />YES<br />
备注:
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.
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