Problem Statement

The Kingdom of AtCoder has 2N intersections labeled with numbers from 1 to 2N. Additionally, there are three types of one-way roads in the kingdom:

• Type A: For each $2 \leq i \leq N,$ there is a road from intersection 2i-3 to intersection 2i-1.
• Type B: For each $2 \leq i \leq N,$ there is a road from intersection 2i-2 to intersection 2i.
• Type C: For each $1 \leq i \leq N,$ there is a road connecting intersection 2i-1 and intersection 2i with direction s_i.

Here, s_i is X or Y, where direction X means the road goes from intersection 2i-1 to intersection 2i, and direction Y means it goes from intersection 2i to intersection 2i-1.
Takahashi wants to walk several times so that for each $1 \leq i \leq N$, the direction of Type-C road connecting intersections 2i-1 and 2i will be t_i.

What is a walk?
Start at any intersection and repeat the following action zero or more times:

• If it is possible to proceed to a Type-C road from the current intersection, walk along the Type-C road to the next intersection.
• Otherwise, if it is possible to proceed to a Type-A or B road from the current intersection, walk along that road to the next intersection.

Then, reverse the directions of all Type-C roads that were passed.

Calculate the minimum number of walks needed to achieve the goal and provide one method to achieve the goal in the minimum number of walks. Under the constraints of this problem, it can be proved that the goal can be achieved in a finite number of walks.

Input

The input is given from Standard Input in the following format:
N
$s_1 s_2 \cdots s_N$
$t_1 t_2 \cdots t_N$

Output

Print your solution in the following format, where X is the number of walks, and the $i-th walk (1 \leq i \leq X) starts at intersection a_i$ and finishes at intersection b_i.
X
a_1 b_1
a_2 b_2
$\vdots$
a_X b_X

Constraints

• N is an integer such that $1 \leq N \leq 4000$.
• Each of $s_1, s_2, \dots, s_N$ is X or Y.
• Each of $t_1, t_2, \dots, t_N$ is X or Y.

Sample Input 1

5
XYXYX
XXYXX

Sample Output 1

1
2 7

In this sample input, Takahashi will walk as follows:

• Start at intersection 2.
• Since there is no Type-C road to proceed from intersection 2, walk along the Type-B road to intersection 4.
• Since there is a Type-C road to proceed from intersection 4, walk along the Type-C road to intersection 3.
• Since there is no Type-C road to proceed from intersection 3, walk along the Type-A road to intersection 5.
• Since there is a Type-C road to proceed from intersection 5, walk along the Type-C road to intersection 6.
• Since there is no Type-C road to proceed from intersection 6, walk along the Type-B road to intersection 8.
• Since there is a Type-C road to proceed from intersection 8, walk along the Type-C road to intersection 7.
• Finish at intersection 7.

This walk passes through the following three Type-C roads:

• The road connecting intersection 3 and intersection 4.
• The road connecting intersection 5 and intersection 6.
• The road connecting intersection 7 and intersection 8.

The directions of these roads are reversed, so the directions of the roads connecting intersections 2i-1 and 2i for i = 1, 2, 3, 4, 5 are now X, X, Y, X, X, respectively, achieving the goal.

Sample Input 2

5
XXYYX
XXYYX

Sample Output 2

0

Note that the goal is already achieved at the beginning, so there is no need to walk even once.

Sample Input 3

5
XXXXX
YYYYY

Sample Output 3

5
1 2
3 4
5 6
7 8
9 10

Sample Input 4

20
XXXYXYYXXXYXXXXYYXXY
XXYXYYXXYXXYXYXYXYXY

Sample Output 4

5
14 18
29 38
14 26
5 10
27 35

Sample Input 5

20
YXYXYXYYYXYYXYYXYXXX
XXXXXYXYYYXYYXXYYYXY

Sample Output 5

5
29 36
10 38
2 3
4 7
28 40

见题面 Input 部分

见题面 Output 部分