def rollback(output_sequence):
    import re

    before_python_idx = output_sequence.rfind("<python>")
    if before_python_idx == -1:
        return output_sequence  

    i = before_python_idx - 1
    while i >= 0 and output_sequence[i] in {' ', '\n'}:
        i -= 1
    before_python_idx = i

    if output_sequence[max(0, before_python_idx - len('</think>') + 1):before_python_idx + 1] == "</think>":
        before_python_idx -= len('</think>')  
    
    while before_python_idx >= 0 and output_sequence[before_python_idx] in {' ', '\n'}:
        before_python_idx -= 1

    newline_idx = output_sequence.rfind("\n", 0, before_python_idx + 1)

    if newline_idx != -1:
        return output_sequence[:newline_idx + 1]
    else:
        return "" 
    
    
if __name__ == "__main__":
    print(len('</think>'))
    str1 = """
<think> To solve the problem, we need to find all integer bases \\( b > 9 \\) for which \\( 17_b \\) is a divisor of \\( 97_b \\). We will convert the numbers from base \\( b \\) to base 10 and then determine the conditions under which \\( 17_b \\) divides \\( 97_b \\).\n\n1. Convert \\( 17_b \\) to base 10:\n\\[ 17_b = 1 \\cdot b + 7 = b + 7 \\]\n\n2. Convert \\( 97_b \\) to base 10:\n\\[ 97_b = 9 \\cdot b + 7 = 9b + 7 \\]\n\nFor \\( 17_b \\) to be a divisor of \\( 97_b \\), \\( b + 7 \\) must divide \\( 9b + 7 \\). This means there exists an integer \\( k \\) such that:\n\\[ 9b + 7 = k(b + 7) \\]\nRearranging this equation, we get:\n\\[ 9b + 7 = kb + 7k \\]\n\\[ 9b - kb = 7k - 7 \\]\n\\[ b(9 - k) = 7(k - 1) \\]\n\\[ b = \\frac{7(k - 1)}{9 - k} \\]\n\nSince \\( b \\) must be an integer greater than 9, we need to find values of \\( k \\) such that \\( b = \\frac{7(k - 1)}{9 - k} > 9 \\). Let's iterate over possible values of \\( k \\) to find valid \\( b \\).\n\nWe will use Python to find these values.\n </think><python>\n# Iterate over possible values of k to find valid bases b\nvalid_bases = []\n\nfor k in range(1, 100):  # We start with a reasonable range for k\n    if (9 - k) != 0:  # Avoid division by zero\n        b = 7 * (k - 1) / (9 - k)\n        if b.is_integer() and b > 9:\n            valid_bases.append(int(b))\n\n# Sum of all valid bases\nsum_of_valid_bases = sum(valid_bases)\nprint((valid_bases, sum_of_valid_bases))\n</python><result>\n([21, 49], 70)\n</result> <think>\nThe valid bases \\( b > 9 \\) for which \\( 17_b \\) is a divisor of \\( 97_b \\) are \\( 21 \\) and \\( 49 \\). The sum of these bases is \\( 21 + 49 = 70 \\).\n\nThus, the final answer is:\n</think><answer>\\$$ \\boxed{70}\n\\ $$</answer>
"""
    str1_ = rollback(str1)
    print(f'----------------- init str1 -----------------')
    print(str1)
    print(f'----------------- rollback str1 -----------------')
    print(str1_)
    print("===" * 20)
    str2 = """<think> To solve this problem, we need to understand how the line segments divide the disk. When we draw a line segment between two randomly chosen points on the perimeter of the disk, it will intersect all the previously drawn line segments. The number of regions created by the line segments in a disk is related to the number of intersections of these line segments.\n\nFor a disk divided by \\( n \\) line segments, the maximum number of regions \\( R(n) \\) that can be formed is given by the formula:\n\\[ R(n) = n + 1 + \\text{number of intersections} \\]\n\nHowever, since we are asked for the expected number of regions, we need to consider the average number of intersections per new line segment added. Each new line segment will intersect all the previous \\( n \\) line segments. If there are \\( n \\) line segments already drawn, each new line segment will intersect each of the existing \\( n \\) line segments. Therefore, each new line segment will intersect \\( n \\) times, but we have to avoid double-counting the intersections.\n\nThe expected number of regions formed by \\( n \\) line segments in a disk is not straightforward to compute directly without simulation or a more complex combinatorial argument. However, we can use a known result from geometric probability theory for this type of problem.\n\nFor a disk divided by \\( n \\) line segments, the expected number of regions \\( E(R(n)) \\) is approximately \\( 2n + 1 \\). This result comes from the fact that each new line segment intersects all the previous ones, creating an additional region for each intersection plus one more.\n\nGiven that we start with 4 quadrants and draw 27 line segments (including the original 4), the expected number of regions can be approximated using the formula above. Let's calculate it using Python to ensure accuracy.\n\nWe'll simulate the process to find the expected number of regions. Here's the Python code to do that:\n\n </think>\n\n   \n\n<python>\nimport numpy as np\n\ndef expected_regions(n):\n    # The expected number of regions for n line segments in a disk\n    return 2 * n + 1\n\n# Number of line segments\nn = 27\n\n# Calculate the expected number of regions\nexpected_regions_27 = expected_regions(n)\nprint(expected_regions_27)\n</python><result>\n55\n</result> <answer>The expected number of regions into which the 27 line segments divide the disk is \\(\\boxed{55}\\).</answer>"""
    str2_ = rollback(str2)
    print(f'----------------- init str2 -----------------')
    print(str2)
    print(f'----------------- rollback str2 -----------------')
    print(str2_)