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())
d=list(map(int,input().split()))
c=[0]*n
ans=0
for i in range(0,n):
  c[d[i]]+=1

if d[0]!=0 or c[0]!=1:
  print(0)
  
else:
  for j in range(2,n-1):
    if c[j+1]!=0 and c[j]==0:
      ans=0
      break      
    elif c[j]==0 and c[j+1]==0:
      ans+=0
    else:
      ans*=c[j]**c[j-1]
      
  if c[n-2]==0　and c[n-1]!=0:
      ans=0
  elif c[n-2]==0 and c[n-1]==0:
    ans+=0
  elif:c[n-1]==0:
    ans+=0
  else:
    ans*=c[n-1]**c[n-2]
      
  print(int(ans%998244353))