如何用pycharm提取两个固定字符之间的行写入其他文本？

比如有1.txt
内容是:
123456
2222
11
33
44
5555
77777777
怎么用Pycharm提取2222到5555之间的内容？并写入2.txt理想结果:11(换行)33(换行)44

# !/usr/bin/python
# -*- coding: UTF-8 -*-
"""
@author: Roc-xb
"""

if __name__ == '__main__':
    with open("1.txt", 'r') as f1:
        lines = f1.readlines()
    print(lines)
    start_index = lines.index("2222\n")
    end_index = lines.index("5555\n")
    print(start_index)
    print(end_index)
    with open("2.txt", 'w') as f2:
        f2.writelines(lines[start_index + 1:end_index])

读取1.txt的每一行，首次读取到2222时开始将后续内容开始追加到2.txt，当读取1.txt遇到5555时，停止对2.txt的写入