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문제

Let A be a sequence of N elements. You can perform two types of operations on this sequence:

1. Select an interval of positions [a, b](1 ≤ a ≤ b ≤ N). Let x be the maximum value on this interval. Replace all the elements in the interval with x.
2. Select an interval of positions [a, b](1 ≤ a ≤ b ≤ N). Let x be the minimum value on this interval. Replace all the elements in the interval with x.

Determine a sequence of operations such that sequence A becomes another given sequence B (of also N elements). The number of operations must be less or equal than 2 ∗ N.

입력

The first line of the input contains a single number N. The second line contains A, a sequence of N elements. The third line contains B, another sequence of N elements.

출력

If there is no solution such that sequence A becomes B, print –1. Otherwise, print on the first line a single number x, the minimum number of operations needed to transform sequence A in B. Each of the next x lines will contain a character (the type of the operation: m if the operation use the minimum and M for the maximum) and an interval (a, b), describing the operations needed for the process. If there are multiple solutions, print any of them.

제한

• 1 ≤ N ≤ 100.000
• All values in A and B are integer numbers from [1, N]

5
1 5 5 3 4
1 1 4 4 4

3
m 1 2
M 4 5
m 3 5

5
1 2 3 4 4
2 2 2 2 5

-1