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: Wrong Answer)

def mergecount(A):
    cnt = 0
    n = len(A)
    if n>1:
        A1 = A[:n>>1]
        A2 = A[n>>1:]
        cnt += mergecount(A1)
        cnt += mergecount(A2)
        i1=0
        i2=0
        for i in range(n):
            if i2 == len(A2):
                A[i] = A1[i1]
                i1 += 1
            elif i1 == len(A1):
                A[i] = A2[i2]
                i2 += 1
            elif A1[i1] <= A2[i2]:
                A[i] = A1[i1]
                i1 += 1
            else:
                A[i] = A2[i2]
                i2 += 1
                cnt += n//2 - i1
    return cnt


n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))



ab=[[a[i],b[i]] for i in range(n)]

a.sort()
b.sort()


for i in range(n):
    if b[i]<a[i]:
        s="No"
        break
else:
    s="Yes"

ab.sort(key=lambda x:x[1])
for i in range(n-1):
    a[-1-i],a[-2-i]=a[-2-i],a[-1-i]


a2=[]
for i in range(n):
    a2.append(ab[0])

if a2==a:
    s="No"

print(s)