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 Perl (v5.18.2) (judge verdict: Wrong Answer)

#!/usr/bin/perl
my ($n) = map { $_ - 0 } split(/\s+/,<STDIN>);
my @A = map { $_ - 0 } split(/\s+/,<STDIN>);
my @B = map { $_ - 0 } split(/\s+/,<STDIN>);

my @sA = sort { $a <=> $b } @A;
my @sB = sort { $a <=> $b } @B;

for(my $i=0;$i<$n;$i++){
  if( $sA[$i] > $sB[$i] ){
    print "No\n"; exit(0);
  }
}

my $j = $n - 1;
my $c = 0;
for(my $i=0;$i<$n;$i++){
  my $k = $sA[$n-1-$i];
  while( $sB[$j] >= $k and $j>=0 ){
    $c ++;
    $j --;
  }
  if( ( 1 + $i ) < $k ){
    print "Yes\n"; exit(0);
  }
}

print "No\n"; exit(0);