472_C. Design Tutorial: Make It Nondeterministic
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: <image>.

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.
```python
# itne me hi thakk gaye?
n = int(input())
arr = []
for i in range(n):
    arr.append(sorted(input().split()))
to_get = [i-1 for i in list(map(int, input().split()))]
# print(arr)
# print(to_get)
ok = True
checked = ""
for i in to_get:
    if(arr[i][0] > checked):
        curr = arr[i][0]
    else:
        curr = arr[i][1]
    # print(curr, checked)
    if (curr < checked):
        ok = False
        break
    checked = curr
if ok:
    print("YES")
else:
    print("NO")
```