Given two permutations , you should construct an unrooted tree , which satisfies that is a possible topological order of if is made the root, and that is a possible dfs order of if is made the root.

Here, a permutation of size is a valid topological order of a rooted tree of size iff that for all edges in , the parent nodes are at front of the child nodes in permutation .

输入描述:

The first line contains one integer , denoting the size of permutations.

The second line contains  integers , denoting permutation .

The third line contains  integers , denoting permutation .

输出描述:

If solution exists, print "YES" in one line, and following  lines each contains two integers , denoting one edge in . If multiple solutions exist, print any one of them. If no solution, print "NO" in one line.

5
2 1 4 3 5
4 2 5 1 3

YES
1 2
1 3
2 4
2 5