Flip Sorting

 Chef has a binary string 

S of length N. Chef can perform the following operation on S

any number of times (possibly zero):

• Choose a number X

(1≤X≤N) that hasn't been chosen in any previous operation and flip any substring of S having length X (i.e. change all 0s to 1s and all 1s to 0s in any substring of S having length X

• ).

Chef wants to sort S

in non-decreasing order using any sequence of operations. Can you help Chef find such a sequence of operations?

If there are multiple answers, print any.

Input Format

• The first line contains a single integer T

- the number of test cases. Then the test cases follow.

The first line of each test case contains an integer N

- the length of the binary string S

.

The second line of each test case contains a binary string S

of length N containing 0s and 1

• s only.

Output Format

For each test case,

• Output in the first line K

- the number of operations applied.

In each of the following K

lines, output two integers i and X - the starting index of the substring selected and the length of the substring. (Note that X

• selected should not be used in any of the previous operations)

Constraints

• 1≤T≤100

1≤N≤1000

Sample Input 1

3
6
110111
9
110110111
5
00111

Sample Output 1

1
1 2
2
1 2
4 3
0

Explanation

Test Case 1: The operations applied are as follows: 11–––0111→000111

.

Test Case 2: The operations applied are as follows: 11–––0110111→000110––––111→000001111

.