Problem:
Score : 600 points

Problem Statement

Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N.
Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:

Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.

Constraints

2 \leq N \leq 10^5

1 \leq A_i,B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

3
1 3 2
1 2 3

Sample Output 1

Yes

We should swap the values of A_2 and A_3.

Sample Input 2

3
1 2 3
2 2 2

Sample Output 2

No

Sample Input 3

6
3 1 2 6 3 4
2 2 8 3 4 3

Sample Output 3

Yes

Solution in Python (3.4.3) (judge verdict: Runtime Error)

N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
sA,sB=sorted(A),sorted(B)
data=[[a,b] for a,b in zip(sA,sB) if b>=a]
if  len(data)!=N:
    print("No")
    exit()
flag=[[a,b] for a,b in zip(A,B) if b>=a]




        exit()

A=sorted(A,reverse=True)
B=sorted(B,reverse=True)
for i in range(N):
    for m in range(m,N-i-1):
        if B[i+m]>=A[i]:
            for a1,b1 in flag:
                if B[i+m]==b,A[i]==a1:
                    print("Yes")
                    exit()
print("No")