# Palindrome Partition Codechef Solution

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Palindrome Partition Codechef Solution

## Palindrome Partition Codechef Solution

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## Problem

JJ has a binary string S of length 2 \cdot N. He wants to partition it into M substrings such that:

• 1 \le M \le 2 \cdot N
• Each S_i belongs to exactly one partition
• None of the partitioned substrings is a palindrome

For example: One of the valid partitions of 10010011 is \underline{100}\ \underline{10}\ \underline{011}.

Can you find any partition satisfying the above conditions? If no such partition exists, output -1.

A string is called palindrome if it reads the same backwards and forwards, for e.g. 1001 and 00100 are palindromic strings.

### 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 — half the length of the binary string S.
• The second line of each test case contains a binary string S of length 2 \cdot N containing 0s and 1s only.

### Output Format

For each test case,

• In the first line, output: M (1 \le M \le 2 \cdot N) – the number of partitions
• In the second line, output M integers: L_1, L_2, \dots, L_M – where L_i denotes the length of the i^{th} partitioned substring. (Note that L_1 + L_2 + \dots + L_M = 2 \cdot N and L_i \ge 1 for all i)

### Constraints

• 1 \leq T \leq 10^5
• 1 \leq N \leq 10^5
• The sum of N over all test cases won’t exceed 2 \cdot 10^5.

### Sample 1:

Input

Output

3
4
10010011
1
00
3
101101

3
3 2 3
-1
2
2 4


### Explanation:

Test Case 1: Explained in the problem statement.

Test Case 2: It can be proven that no valid partition of 00 exists.

Test Case 3: One of the valid partitions of 101101 is \underline{10}\ \underline{1101}.

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## Palindrome Partition Codechef Solution

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