Booze Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠰⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠈⠀⠐⡏⠁⠀⠀⠀⠰⠀⠀⣀⠀⠀⠀⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⡄⠀⢤⡄⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠃⠀⢛⠁⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠂⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡖⠀⠀⢀⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⡀⡀⣰
⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠴⣀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡾⠟⠛⠻⢷⡄⠀⠀⠀⠀⢀⡾⠟⢿⡀
⠀⠀⠀⠀⠀⣀⠜⠛⠙⣄⡀⠀⠀⢀⣤⣇⣿⣿⣦⠀⠀⠀⢀⣀⠀⢀⣠⣰⠀⢐⠀⠀⠀⢰⠆⠀⣎⠀⣀⡀⡀⠀⣿⠀⠀⠀⢀⣤⣤⣤⣤⣽⣶⡄
⠀⠀⠀⣶⣿⣷⣴⡶⠶⢿⣿⣷⡆⢀⠺⠟⠛⠻⢿⡇⠀⠐⠿⠲⠟⠋⠀⣿⠀⠐⠀⠀⠀⠀⠁⠀⣿⠾⠛⠛⠿⠷⣿⠀⠀⠀⣜⠋⠀⠉⠉⠙⠿⠃
⠀⠀⠀⣀⠤⠀⠠⠤⠰⢰⣀⢸⠇⠈⣤⡀⠠⠀⣼⡇⠀⠀⣀⢤⣠⠄⡀⢹⠀⠀⠀⠀⠀⢀⡁⠀⡏⠀⠀⠀⠀⠀⣿⠀⣾⢸⠃⠀⠠⠀⠄⠤⠈⣿⡆
⠀⠀⠀⠹⣶⡍⠛⠋⢰⣿⣿⣿⠀⢀⡇⠀⠀⠀⢸⡁⠀⠀⠈⠀⠀⠈⠁⠀⠀⠸⠀⠀⠀⠸⠇⠀⣧⣀⣀⣀⣀⣀⣿⠀⢩⣼⣧⣀⠀⠀⢀⣀⣴⣿⡇
⠀⠀⠀⣼⣿⣿⠟⠓⢬⣯⣾⣿⡄⠀⠗⠶⠶⠶⠾⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠤⠀⠻⠿⠿⢿⠿⠿⠏⠀⠀⠙⠻⠟⠏⠀⣽⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠚⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠍⠁⠀⢀⠀⠀⢀⠀⠀⣠⡀⠀⠀⠀⡀⢈⣈⠃⠀⠀⠀⠙⠛⠆⢀⡴⠶⠀⠀⠀⠀⠀⣥⣾⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣤⡄⡤⠀⣿⡏⡀⠀⠀⠀⡧⠀⠉⠑⠀⢹⣿⣿⡇⠀⢹⣿⡇⠀⠀⢰⣄⡐⡆⠀⠀⣀⣀⣀⣄⠀⠀⠀⡟⢛
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠹⣿⠎⠀⠀⣿⣷⢁⠀⠀⢲⣶⣶⣶⠀⠀⢺⣿⣿⡰⠀⢸⣿⠀⠀⠀⢸⡛⡃⡇⠀⣰⣿⣿⣿⣿⣧⠀⢰⡏⣻⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠂⠀⠀⢸⣿⣿⣿⠀⠀⠀⠙⠋⠁⠀⢨⣿⠀⠀⠀⢸⣉⡇⡇⠀⢺⣿⣿⣿⣟⡿⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠠⠀⠀⠀⠘⠻⠿⠓⠁⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠸⠿⠇⠇⠀⠈⠻⠿⠿⠟⠁⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣀⣀⣤⡄⠀⠀⢀⣄⠀⠈⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⡀⢰⣿⣿⣿⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⢹⠀⠀⢸⣿⣿⡟⠄⢾⣿⡿⠀⢠⣤⣤⣤⡉⠀⠴⠋⣷⢿⣿⠆
⠀⠀⢸⣿⣿⣏⡇⠘⣿⣿⣿⢸⠀⣤⣤⣤⣀⠀⢰⡦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⠀⠀⢸⣿⣿⡇⠀⢸⣿⡯⠁⢸⣿⣿⡏⠀⠀⢹⡾⢽⢸
⠀⠀⠀⠉⠙⠉⠀⠀⣿⣿⣿⢸⠀⠉⠛⠛⠉⠀⠈⡃⠀⢸⣧⣌⣍⡇⢸⣿⣿⣿⢸⠀⠀⢸⣿⣿⡇⡄⠀⠻⠇⠀⢸⣿⣿⣇⠀⠀⢸⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠘⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⢠⣶⡶⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⢀⣴⣷⣿⠁⣘⠛⠛⠛⢛⣛⠈⢛⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠘⣿⣿⣿⠃⠿⠿⠿⠿⠿⠿⠇⠻⠇⠀⠀⠀⠀⠀⣾⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⣤⡄⠀⠀⡄⠀⠀⣾⣧
⠀⠀⠀⠈⠛⠁⢠⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⣠⣤⡤⡄⠀⠀⣠⠀⠀⠀⠀⡇⠀⣿⡇⠀⠀⡇⠀⣸⡟⢻⡆⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠃⠠⡈⣛⣛⣛⣛⣛⣛⡃⢘⡃⠸⣿⣿⡿⠃⣿⣿⡇⠂⠹⣿⡷⠁⠀⠀⠘⠀⠀⠀⠀⡇⠀⢿⠇⠀⠀⠀⠀⣿⣷⣿⡇⠀⠻⠿⡿⠟⠁
⠀⠀⠀⠀⠀⢠⠈⢛⠛⠛⠛⣛⣛⠃⣛⠃⠀⠈⠉⠀⠀⣿⣿⡇⡄⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠘⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠁⠀⠘⠛⠛⠛⠟⠛⠐⠟⠀⠀⠀⠀⠀⠀⠛⠛⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⡊⠉⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⡄⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠶⠶⠶⢾
⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠚⠛⠋⠉⠉⣉⣠⠴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⡎⠀⠀⡀⠄⠘⠓⠀⢀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⢀⣀⣠⠴⠖⠛⠉⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡇
⠈⠉⠉⠀⠀⢀⡴⠛⡏⠀⠠⣯⠤⠤⠤⠤⠶⠶⠚⠛⢉⠡⠄⠀⠀⠀⢈⢭⣭⡙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣇
⠀⠀⠀⠀⢰⠋⠀⣸⠃⠀⠀⠹⣦⡀⠀⠀⣀⣤⡶⣯⡀⢀⣤⠴⠶⣦⢀⣀⣬⢿⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢻⡀
⠀⠀⠀⠀⢿⣄⣴⠏⠀⠀⠀⠀⠘⢿⣤⣾⣟⣁⣀⣨⣵⣯⡴⠶⠖⢛⣩⢥⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣯⠉⠉⢉⣵⠞⠛⠶⠶⣆⢻⠀⠀⢹⡧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠋⡏⠀⠀⠀⠀⣿⠀⠀⣐⡚⠁⠀⣿⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠰⠶⢶⠇⣴⠋⠉⠉⣋⡴⣿⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣁⣤⣥⡴⠶⠛⢉⣠⠟⠀⠀⠀⠀⣼⠵⠒⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⢉⣀⣠⡤⠔⠚⠉⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠒⠒⠒⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣤⡾⠚⠛⠻⢦⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢹⡄⠀⣀⣀⣀⡴⠞⠉⠀⠈⣷⠀⠀⠀⣠⠞⠻⠷⠊⠀⣿⠀⣠⠤⣄⠀⢻⡄⠀⠀⡇
⠀⠀⠀⢠⣶⢨⡇⢸⡏⠉⠉⠀⠀⠀⠀⠀⠘⠷⠤⠖⠁⠀⠀⠀⠀⠀⣿⠎⠀⠀⠘⡆⠀⡇⠀⠀⡇
⠀⠀⠀⠛⢋⡜⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇⠀⡏⠀⠀⢻
⠀⠀⠀⢠⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠀⣸⠁⠀⠀⢸
⠀⠀⠀⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡼⠁⡴⠃⠀⠀⠀⢸
⠀⠀⠈⢧⣤⣤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠋⣠⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠠⠖⠀⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⡷⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠶⠛⠋⠁
⠀⠀⠀⣠⣤⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠿⠋⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠸⣧⠈⠙⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⠶⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⠀⣴⣦⠀⢠⣶⣦⣄⢰⣦⣶⡦⣤⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⢄⠠⠤⠤⣤⡴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⣿⠀⣿⢻⡆⢸⣇⢀⣿⠀⢸⡇⠀⠸⣇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠆⠀⠀⠲⡶⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠋⢰⣇⣸⡇⢸⡟⠻⣧⠀⢸⡇⠀⠀⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢼⠏⠙⣿⠸⡇⠀⣿⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠒⠒⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⣤⡄⢠⣤⡄⠀⢠⣤⡄⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠉⠀⣿⡇⢸⣿⣷⠀⣼⣿⡇⢸⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠤⠶⠶⠾⣮⠿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⡇⢹⣷⡏⢸⡇⢸⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠉⢀⠀⢀⣀⣀⠐⢷⠶⠤⠭⢒⠒⠤⣀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⡇⢸⡇⢸⣿⡇⣿⡇⢸⣿⣤⣤⡄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠑⣄⠀⠀⠀⠈⠁⠀⠀⠉⠁⠈⠁⠀⠉⠀⠈⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⡆
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠠⡆⠀⠀⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⠀⠀⢀⠀⠀⢠⠜⠛⠀⠁⠐⠄⠀⠀⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡏⠀⠀⠀⠀⠀⠈⡶⠀⠀⢀⡠⠂⠠⠴⠃
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡼⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠂⠊⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⣠⢷⣇
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢹⣀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀⠐⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠉⢤⢐⣲⣦⣶⡔⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣾⠙⠛⢻⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠐⢾⣿⣏⠟⣟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠃⢉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠅⠀⢨⣞⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⢠⣼⣷⠦⡄⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⣈⠛⠿⢿⣷⣾⡿⢟⣱⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⡷⠀⠀⠀⠠⡀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⢤⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠖⠦⠤⠴⠿⠿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⠠⠤⠤⠤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠸⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠐⠄
⠀⠀⠀⠀⠀⠠⡦⠠⣦⣤⣶⣤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⢀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠰⡇⠀⠙⠿⡿⠋⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠹⠶⠦⢤⠀⢰⠆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⠉⠉⠉⠛⠛⠒⣚⣛⣺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠰⣾⣿⢄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠶⣿⠋⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠋
⠀⠀⠀⠀⠀⠀⠀⡆⡄⠐⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⣟⠂⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡭⠉
⠀⠀⠀⠀⠀⠀⠀⣷⣞⡃⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣆⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣴⣶⠞⠠⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⣯⣽⣭⣭⣉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠈⠁⠀⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠢⣨⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢳
⠀⠀⠌⠂⠶⠀⠒⡀⠀⡀⠖⠀⠀⠀⠀⢀⠶⠂⠀⠂⠀⠘⡅⠛⠀⢹⠈⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠎
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠬⠰⠀⠀⠁⠀⡀⠀⠀⢠⠚⠀⠀⠀⠄⠰⠈⠀⠀⠀⠇⠀⠶⠀⠀⠀⠀⡠⠑⠀⠔⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠉⠉⡁⠀⠀⠀⠁⠀⡀⠀⠐⢢⢤⡀⠀⠀⢠⢀⣀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠁⠀⢀⠀⠀⠀⠁⠀⣀⠒⠀⠃⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠂
⠀⠀⠀⡀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡁⢸⠀⠀⠀⡁⠀⠀⠀⠀⠶⠆⠀⠀⢀⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠁⠒⠂
⠀⠀⡰⠁⠈⠄⠀⡔⠀⠐⡄⠀⠀⠄⠀⠀⠀⠘⠈⠁⠈⠕⠐⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄
⠀⠀⡄⠀⠀⢸⢀⡄⠀⠀⡄⠀⡌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡮⠆⠠⢥⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⠀⢁
⠀⠀⡷⠤⠦⠎⠀⡅⢉⢀⠀⠀⠅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠒⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠐⠐⠀⠀⠀⠈
⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣛⡃⠀⠠⠙⠀⠈⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠜⠀⠀⢆⠀⡤⠀⢤⠀⠀⢀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⠀⠀⠀⡠⠀⠀⠀⢀⡄⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠁⠀⠀⠀⠀⢠⠚⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠈⠀⡀⠀⠁
⠀⠀⠰⠄⠤⠤⠀⠐⢀⠀⠀⠀⡀⣀⣀⡀⠀⠀⢿⡀⠀⡘⠀⠀⠀⠰⠤⠤⠆⠘⠨⠅⡈⠁⠆⠀⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠘⠀⠁⠀⠀⠠⠄⠀⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⡔⠄⠚⠂⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⣶⠖⢢⣀⣠⣀⢸⡇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡚⣿⣿⣾⡿⢀⡭⠓⠊⢷⡄⢰⡏⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⣈⠛⠔⠉⠛⠁⢀⣠⣇⣽⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣴⡀⠀⠒⠛⠋⠉⠋⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠒⠂⠈⠉⣠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠦⠠⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡈⠛⠷⢶⣦⣶⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣷⣤⣄⣀⣀⣀⣤⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢧⣄
⠀⠀⠀⠀⢠⡞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡭⣭⣭⣭⣽⡇
⠀⠀⠀⠀⢿⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡼⠀⠀⠀⡠⠓⠀⠀⠀⠀⠀⠀⠀⢀⡼⡡⠀⠀⠀⡀⢀⠳⣄
⠀⠀⠀⠀⢀⡭⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣛⡓⠛⠖⠲⡄⣀⣳⣞⣀⡀⠀⠀⠀⠀⠀⠈⢳⡑⠀⠀⠀⠃⠌⡴⠋
⢠⡶⠶⠚⠋⠀⠀⠙⠓⠶⢶⡄⠀⠀⠀⠀⠘⣏⠙⠒⠲⠶⠶⠶⠾⠛⢺⡷⠄⠀⠀⠀⠘⡏⣿⣤⠏⢻⠛⣯⢯⢩⠷⡟⠀⠀⠀⠀⠀⠀⠀⣿⣓⣚⣚⣛⣻⡇
⠈⢷⣐⡒⠰⠆⠲⠂⣒⣢⡞⠁⠀⠀⠀⠀⠀⠹⣆⡻⠒⠗⠐⠆⠲⢂⡿⠁⠀⠀⠀⠀⢰⡇⡇⠀⠀⢸⠀⡗⠈⠉⢠⡇⠀⠀⠀⠀⠀⠀⠀⠏⠉⡹⢩⡙⠹
⠀⠀⠉⠛⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠶⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠶⠚⠀⠛⠲⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠂⠆⣁⣎⢰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠺⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⣰⣳⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠋⠙⠑⣦⡀
⠀⣠⠞⠓⢦⣈⣁⡴⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⠔⠗⢤⡴⠾⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⣿⣭⣭⣽⣋⣿⠀⠀⠀⠀⠀⠀⠀⠤⠈⡟⡏⠉⠉⢹⢻⠃⠤
⣞⠡⠈⡴⠋⠁⠉⠳⣄⠡⢜⡆⠀⠀⠀⠀⠀⡤⣿⢤⣠⢼⠧⣄⡤⡷⢄⠀⠀⠀⠀⠀⠀⠀⠻⠂⠈⢳⡷⠁⠐⠾⠁⠀⠀⠀⠀⠀⠤⠤⠀⡇⠀⡜⢣⠀⢸⠆⠠
⠈⢩⠟⠁⠀⠀⢀⡀⠈⢳⡉⠀⠀⠀⠀⠀⢸⣅⣀⣠⣧⣀⣀⣼⣀⣀⣠⡃⠀⠀⠀⠀⠀⠀⣰⣛⡀⠈⡇⢀⣜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡔⠻⣄⢸⡀⠦
⠀⢯⡀⠀⠀⠀⠨⠅⠛⣀⡗⠀⠀⠀⠀⠀⠘⠯⣭⢭⣭⡭⠍⠉⢭⣭⠽⠃⠀⠀⠀⠀⢀⡽⢭⣭⣽⣧⢧⣯⣭⣭⢿⡀⠀⠀⠀⠀⠀⠀⠘⢿⡉⡀⡉⢋⡽⠃
⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠗⠀⠘⠚⠀⠀⠙⠂⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠿⠭⠭⠥⠭⠽⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠧⢸⡇⠸⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⡑⠘⠁⣋⠴⢆⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣄⣄⡤⢄⣀⡀
⠀⠀⣏⠀⣠⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠙⢦⠘⠃⡰⠛⠡⠦⠀⠀⠀⠀⠀⠀⠉⡥⠶⠌⠀⠀⠡⢒⠲⠆⠀⠀⠀⠀⠀⠀⣯⡧⠄⢒⣿⢾⡗⠲⠶⣭
⠀⠀⠈⠓⠿⠿⠀⡏⠉⠉⢣⠀⠀⠀⠀⠀⠀⠲⠶⠶⠀⢮⡵⠀⠶⠶⠶⠀⠀⠀⠀⠀⠘⠃⣰⠊⣱⣄⠀⣠⣈⠙⠈⠃⠀⠀⠀⠀⠀⡷⣗⣋⣩⣿⣻⣏⣙⣛⠶
⠀⣠⠤⠴⢶⡄⢰⣶⡮⢀⣠⠃⠀⠀⠀⠀⠀⠘⢋⣴⠎⢠⡄⠙⣦⡘⠒⠀⠀⠀⠀⠀⠙⠀⢹⠟⣛⡏⢺⠧⣼⡇⠙⡁⠀⠀⠀⠀⠀⣏⡯⠤⠴⣿⣽⡷⠤⢭⣛
⠠⠋⠀⢀⣀⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⢘⡃⠰⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⢴⡇⢸⣓⣺⡇⠀⠁⠀⠀⠀⠀⠀⠧⠗⠒⠪⠉⠏⠙⠒⠲⠾
⠘⠦⣄⣘⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢹⠀⠈⡛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠡⠂⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⢺⣏⡽⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄⢀⢀
⠀⡔⠲⢅⣿⣅⣸⡷⡬⠒⢢⠀⠀⠀⠀⠀⠀⠀⢰⢤⠈⡵⢶⡄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡦⡴⠠⠀⠓⡤⢢⡔⠀⠀⠀⠀⠀⠀⠀⢀⣲⣡⠖⣧⣬⠳⣄⣗⡀
⠀⢇⢈⡏⡀⢠⠄⣁⢻⠀⡘⠀⠀⠀⠀⠀⢰⠲⢎⢹⣲⢰⢁⢤⢉⡃⡄⠀⠀⠀⠀⠀⠈⠒⠰⢤⡴⠁⠈⠣⡤⠥⡐⠁⠀⠀⠀⠀⠀⡭⣧⣾⠚⠧⠸⠓⢻⣤⠯
⠀⠘⠀⠇⠈⢈⡀⠁⡸⢠⠁⠀⠀⠀⠀⠀⠀⣙⡙⢶⣿⢸⠫⢭⣴⠉⣗⢺⠀⠀⠀⠀⠘⠹⢃⡠⣃⠀⠀⢀⢇⣈⠃⠃⠀⠀⠀⠀⠀⣄⡷⣼⠋⣀⢠⡈⣻⡼⣁
⠀⠀⠷⢚⣿⠀⠀⣿⡓⠜⠀⠀⠀⠀⠀⠀⠑⢬⠿⢢⡻⣌⠓⠄⣱⣚⠍⠁⠀⠀⠀⠀⠘⠉⡈⣄⢠⠃⠐⣇⢠⣄⠈⠃⠀⠀⠀⠀⠀⠐⠣⠾⣍⣳⣴⣋⡽⠴⡗
⠀⠀⠀⠀⠘⢆⠀⠛⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠄⢢⡋⠠⡥⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠳⠞⠣⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⣀⠀⣀⠁⢂⠀⠀⠀⠀⠀⢸⠀⠐⠐⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⡈⠀⠀⠋⠀⠉⠀⠀⠃⠀⠀⠈⠉⢨⡦⡄⠊⠉⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠛⠢⢀⠀⠠⠀⠐⠤⠀⠠⠀⢀⠂⠀⠀⠁⠈⠘⠀⠀⢤⠀⠶⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢠⠂⡀⣀⣀⣀⠀⢢⠁⠁⠢⠀⠀⠠⠔⢙⠁⢙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠒⠀⠒⠐⢀⡒⠂⠑⡀
⠀⠀⠀⠀⠀⠰⠀⠈⠉⠈⠁⠀⠠⠀⠈⠙⢢⠀⢰⠀⠀⠈⠀⠀⠐⠀⡀⠁⠈⠒⡄⠀⡆⠈⠱⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠔⠁⠣⡀⠀⡠⠀⠀⠄⠀⠀⠀⠀⠁⠀⠐⠨⠤⠀⢱⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⣀⣠⣀⠐⠀⣇⡀⣸⠀⠠⡀⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠦⣀⣀⢀⣀⡠⡆⢠
⠀⠠⢤⠊⡀⠁⠀⠑⠐⠃⠀⠈⠀⠀⠈⠢⡀⠀⠀⠀⡀⠤⠠⣄⠀⠀⠈⠀⠀⠦⠀⠀⠀⠐⠀⠄⢘⠀⠀⠖⠼⠍⠂
⡀⠄⡀⠤⠀⠀⢀⡀⠀⠀⠄⢐⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠂⠀⠳⠌⡀⠠⠊⠀⠀⠠⠀⢠⠀⡀
⠁⠀⠀⠀⠐⠊⠁⡈⠐⣄⠁⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢱⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠆⠀⠁⠀⠘⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠸⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠁⠀⢀⡀⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠂⠄⠀⠀⠀⠰⡀⠀⠤⢀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠑⠀⡲⠃⠉⠀⠉⠙⠦⡀
⢠⠂⢀⢄⠀⠀⠀⢀⠔⠣⡀⠄⠀⠀⠀⠀⠀⠈⠲⠄⣀⢀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡴⠀⠰⠆⢠⠄⠀⠀⠘⡀
⠠⡁⠈⡠⢩⠉⠀⠄⠰⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⡀⠀⠀⠐⢄⠀⠀⠀⠀⢸⠤⠐⢇⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠠⠀⠀⠌⢄⠒⠦⠘⠁⠔⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠⠤⠬⠲⢄⠀⠀⠑⢄⡀⠀⠀⠀⠀⠈⠢⠈⠁⠀⠀⠀⡠⢎⡀
⠀⠀⡀⠴⠦⡀⠉⠐⠂⠁⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠛⠀⠀⠠⠀⡀⠑⢄⠀⠀⠈⠂⠀⠀⠀⠠⡀⢤⡀⡈⢊⡁⢠⠀⠙
⠀⡌⠀⠂⠂⠈⠦⠒⠋⠙⠢⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢤⠄⠁⠀⠀⠀⠀⠄⠀⡆⠀⠀⠸⠄⢨⠐⠈⠀⠀⠀⠀⢀
⠀⠡⣀⠀⠀⡈⠀⠴⠀⠦⠀⠈⡄⠠⡀⠀⠀⠀⢀⠀⠂⠀⠀⠐⠀⡀⠀⠂⠈⠀⠀⡠⠁⠀⠀⢀⠀⠀⠀⠀⠰⠠⠤⠔
⠀⠀⢀⣈⠁⢁⠀⠀⠀⠀⠀⢀⠃⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⠀⠡⢺⠀⠒⠄⠠⠤⠴⠃⠁
⠀⠀⠀⠀⠀⠀⠐⠤⠀⠠⠔⠋⠀⠀⠈⠀⠀⠀⠀⠀⢀⠌⡅⡍⡢⠐⠊⠒⠢⡁⠀⠀⢀⠀⠒⠲⣤⠀⠢⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡉⡉⢂⠀⠆⠘⠀⠁⠈⠢⢀⢠⠀⠐⠀⠒⠀⢱⠀⠀⠃⠐⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠐⠀⠲⢄⣄⠴⡆⠀⠀⠘⣄⠀⠒⠂⢀⠜⠀⠀⠁⢅⣀⡠⠜
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠤⠒⠒⠉⠉⠉⠉⠛⠒⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⢀⡀⠰⠶⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡫⠒⠁⠠⠚⣫⡽⠭⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠈⢀⡤⠖⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⣀⠀⠀⠀⠀⣈⡿⠋⠀⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡾⠁⠀⠀⠀⢸⣿⣦
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⠄⢻⣇⠀⡴⠁⣀⠼⠿⣿⣇
⠀⠀⠀⠀⠀⢀⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⣠⣿⢶⣤⢋⣀⠀⠀⠀⠈⡀⢀
⠀⠀⠀⠀⠀⢸⠃⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠠⠤⠄⣿⣿⣷⣼⣯⣀⣀⣀⣤⡾⣿⢰⡄
⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠚⠛⠂⠀⠐⠚⠳⣄⡀⣀⠜⠛⠻⠟⠳⠤⡈⠙⢇⣿⠹⡄⣇
⠀⠀⠀⠀⠀⢸⠀⢸⠷⠚⠛⠛⠁⠀⠀⠀⠀⠁⠀⢀⣠⠤⡤⠀⠀⠀⡀⠈⠙⠀⠀⠘⠀⢀⡀⠀⠀⣀⠀⢹⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⠈⠀⣠⣶⣂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⠂⠀⠀⣧⠀⠀⠀⠀⠀⣠⠎⠉⠛⠋⠉⢹⡎⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠐⠹⠿⠃⢠⠂⠀⠀⠀⠀⠀⠚⣉⠉⠉⠁⠀⠀⠘⣧⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣿⠀⡇⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡇
⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠑⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡠⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿
⠀⠀⠀⣾⠏⠀⠀⠀⢰⡇⠀⣧⠄⠐⠒⠢⠤⠤⣤⡤⠀⠄⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡆
⠀⠀⣸⡟⠀⠀⠀⠀⣼⡇⠀⠈⠲⠶⠶⠶⠒⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠀⡏⠀⠀⠀⠈⣷⠀⠀⠀⠀⢸⣧
⠀⢠⡿⠀⠀⠀⠐⢀⣿⠃⠀⠀⠐⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢰⡇⢀⡇⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⣿⡄
⠀⣾⠃⠀⠀⠠⠀⣸⡿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⡀⠀⣼⠀⢸⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠸⣧
⢰⡟⠀⠀⢀⠂⢀⣿⠃⠀⡐⣼⣦⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠸⠿⠁⢘⠋⠀⣿⠀⠀⠨⠀⠀⠀⢿⣧⠀⠀⠀⠀⢻⣧
⣼⠇⠀⠀⠀⠀⣾⠃⠀⠠⢰⣿⡟⣿⣦⣤⣤⡤⠒⠋⠁⠀⠀⠀⠀⠀⠾⠆⠀⠶⠀⠀⠟⠀⠀⢰⡀⠀⠀⠈⣿⣆⠀⠀⠀⠀⢿⣧
⣿⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⣿⡇⢹⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣷⠂⣴⠇⠀⠰⡷⠀⠀⠀⠅⠀⠀⠀⠸⣿⡆⠀⠀⠀⠈⢿⡆
⣿⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⣿⡇⢸⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⢳
⢻⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⣿⠀⠘⣿⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈
⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⢼⣿⠀⢐⣿⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣾⡿⠀⣸⣿⣸⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠿⠓⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⢷⡀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⢀⡠⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢀⡔⣂⠀⠀⠀⠀⣶⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠙⠟⠀⠀⠀⣠⠛⠦⠀⠀⠀⠀⠉⠻⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⢀⠼⠑⠆⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠛⠙⠂⠀⠀⠀⠄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠁⠀⠀⠀⠀⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⣦⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⣰⢚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣤⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠗⡀⠀⠁⠀⡀⠀⠀⡠⠀⢓⠴⠊⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠈⣠⠀⠈⠑⢤⢠⣩⠚⠋⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⡖⠰⠿⠁⠛⠁
⠀⠀⠀⠀⠀⢠⣿⠋⠀⢀⣾⣿⣷⡤⠀⠶⠚⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⠏⠀⠉
⠀⠀⠀⠀⢀⣾⠃⢀⣴⣿⣿⠿⠋⠀⠈⣠⣄⡈
⠀⠀⠀⠀⣼⠃⣠⣾⡿⠛⠁⣀⣤⣶⣿⠿⠛⠋⠁
⠀⠀⠀⣸⢃⣾⠿⢋⣠⣴⠾⠟⠋⠁
⠀⠀⢰⣷⣿⠵⠞⠋⠉
⠀⠀⠛⠉

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⡾⠟⠉⠀⠙⠿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⡈⣐⡒⠀⠀⠀⢒⣉⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠁⠉⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⡀⠀⢀⣼⣿⣿⡇⣿⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⣾⣿⣿⣿⣧⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⣿⣿⡇⣿⣿⣿⣧⢿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢸⣿⣿⣿⢸⣿⣇⣿⣿⣏⢿⣿⣿⣧⡲⣤⣀⣀⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⡼⣿⣿⣯⡻⣿⣿⣿⣷⣯⣿⣿⣟⡝
⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⡽⣿⣿⣿⣮⣟⣿⠿⠿⣿⡿⠋
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⢿⣿⣿⣿⣾⡻⣿⣿⣿⣿⣿⣿⡽⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣮⡻⣿⣿⣿⣿⣾⣯⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣭⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀⡀⠀⠂⢀⡀⠀⢀⡆⠀⠀⢀⡀⠀⢀⣀⠀⢀⡎⢀⠀⠀⣀⠀⣀⡀⠀⣀⡀⣰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡆⢺⡵⠁⣏⡀⠜⢰⣫⣏⡀⡼⠀⠀⢠⠟⠹⠰⣿⡋⠘⡿⠉⢼⢾⣠⠇⢸⡥⠃⡟⠁⡴⠿⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣏⡀⠀⠀⠀⠀⠁⠀⡀⠘⠙⠋⠀⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⢛⠁⠀⠀⠀⠀⡠⠊⠀⠀⢀⣰⣤⡄⡀⠀⠈⠑⠠⡄⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢂⡀⢀⡀⠊⠀⠀⠀⠀⡆⢿⣉⠗⠈⠄⠀⠀⠀⢆⣥⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⢐⣥⣤⣤⠈⠢⡀⠄⠀⠒⠙⠺⡿⠷⢊⠀⠀⠀⠀⠀⡅⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⢻⡟⢉⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢀⡀⠔⢄⡠⠅⡿⢀⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢑⠄⠒⠈⡀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡶⢮⠡⡤⠐⠂⠁⠀⠀⠀⢀⠁⠁⠀⠙⡤⠔⠀⢀⣀⠐⠢⡀⠀⠀⢠⠁⢸⠛⣧⠈⢆⠀⠀⠀⡐⣼⢿⠱
⠀⠀⠀⠀⠀⠀⠀⢬⣷⠆⣀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠌⠀⠀⡾⠟⠻⣇⠀⠈⠢⡀⠸⢄⠠⠆⠧⣀⠆⠀⠀⠀⠀⠻⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠈⠢⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⡇⠂⠂⣻⠀⠀⠀⠇⠀⠈⠑⠖⠂⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠖⡟⠹⠑⡀⢀⡀⠀⠴⠀⠀⠀⢰⠬⠥⡃⠀⠀⠀⠇⠀⠀⠰⠀⠀⢢⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠣⣼⣾⡤⠁⠀⠀⠀⠀⠱⣤⣶⣿⣴⣏⣽⣿⡶⠊⠀⠀⢀⠁⠀⠀⠀⢂⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠢⠀⠀⠀⠀⠀⡨⠛⠛⠛⠛⠛⠉⠑⡀⠀⠀⠄⠀⠀⠀⠀⠈⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⣠⠁⠀⠀⠀⠀⡐⢠⣶⣶⣌⠢⠀⠀⠀⠀⠀⠀⠀⠘⢢⡞⠄⠀⠀⠀⠔⠁⡴⠿⢦⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⡏⠂⠀⠀⠀⢀⠀⠸⡿⢏⡿⠀⡇⠠⠄⠀⠐⠒⠂⠃⢾⠷⠋⠀⠀⠘⠀⠐⡏⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣧⠊⠉⠉⠀⠈⠢⡤⠚⠁⢃⠶⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠡⣀⣼⣤⣧⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⢄⠀⠀⠀⠀⢀⠁⠀⠀⠀⡠⠐⠈⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⣀⣄⡀⠀⠀⠀⠀⠈⠂⠔⡠⢌⠂⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⣼⠀⠤⠤⠄⠀⠰⣀⣷⣎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠉⠈⠛⠁⠉⠋⢹⠙⠋⠈⠙⠉⠉⠁⠀⠀⢸⣿⣿⣿⣷⣾⣷⣴⣿⣶⣴⣶⣦⣾⣷⣦⣾⣷⣿⣿⣿
⠀⠀⠀⠀⢠⣦⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣧⣿⢿⣦⣄⣬⡴⠶⢦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⢠⣈⠉⠻⠟⣋⣉⣛⠿⢿⣿⣿⣿⣿
⠀⠀⢀⣀⣞⣀⣉⣛⣾⣭⣵⣞⣛⣛⣾⣯⡀⠀⠀⠀⢸⣿⣿⣿⠿⢱⠿⡶⣬⠑⠒⠋⣡⢶⣬⡉⠚⢿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡰⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⠤⠖⠉⠀⠠⠜⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⣅⠈⠁⢠⠀⠈⠁⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣄⠀⠠⠄⠀⣠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⢗⠂⠐⡿⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠄⣡⣌⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡴⣹⡠⠊⠉⠉⠙⠉⠉⠉⠑⠄⠏⢆⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠂⢄⠀⢀⡼⠥⠛⠂⠄⡀⠀⠀⠀⠀⢀⠠⠒⠚⠬⢧⡀⠀⠠⠐⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢢⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠒⢄⡔⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡑⡐⣠⢠⠁⠈⠒⠒⠒⠒⠒⠒⠒⠂⢤⠄⠒⠒⠂⠒⠒⠒⠒⠒⠁⠈⡄⣄⢂⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⠂⠁⠢⢄⠀⠀⠀⠀⠘⠁⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣈⣐⣤⣀⣀⠤⠔⠁



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣷⠀⠀⠀⠀⠀⢀⣀⣀⣼⣄⣀⣀⠀⠀⠀⠀⠀⢰⡏⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣦⠀⣠⡴⠚⠋⠉⢀⣀⣀⡉⠉⠛⠲⣤⡀⢀⡾⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⢀⡴⣺⠟⣹⠋⢻⡛⢿⡲⣄⠀⠙⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡴⢯⣴⣃⣀⡏⠀⠈⣇⣀⣳⣬⠷⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡾⠀⢰⡏⠉⢹⠋⠙⠉⢻⠉⠉⣷⠀⠸⡆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠳⣆⣀⣀⣼⠀⢸⣇⣀⣼⣀⣀⣸⣀⣀⣀⣸⣀⣀⣸⣀⣀⣿⠀⢹⣄⣀⣀⡶⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠶⠃⠀⠀⢹⡀⠸⡇⠀⢹⡀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠁⠀⡿⠀⣼⠁⠀⠀⠻⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⡀⢘⣇⣠⣼⡦⠤⠤⣾⣤⣀⣟⠀⣸⠃⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠹⣏⡹⣆⠈⣧⠀⢀⡏⢀⡾⣉⡿⠁⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣄⡀⠙⠺⠷⣼⣦⣾⡴⠿⠚⠁⣀⡴⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣾⠋⠀⠈⠙⠶⢤⣤⣀⣀⣀⣠⣤⠴⠚⠉⠀⠈⢳⡶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⠿⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⠢
⠀⠀⠀⠀⣰⣀⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠩⠦⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡃⢐⡃⢘⡀⣓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠈⣠⠤⢀
⠀⠀⠀⠐⠀⠀⠀⠚⠘⠁⡇⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣠⡜⠀⠀⠀⠀⠀⠀⠀⠎⠁⣈⠄⠁⠄⠈
⠀⠀⠀⢸⢠⡥⢹⠀⣀⠖⠆⠀⠀⠀⠀⠀⠀⠀⠁⠰⠟⢀⠂⠀⠀⠀⠀⠀⠀⠀⡧⠶⠶⠶⠀⢠⢤⣾⠀⠀⠀⠀⠀⠀⠀⢀⣾⠡
⠀⠀⠀⢸⡀⠀⡘⠠⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠓⠓⠚⠚⠓⠁⠉⠈⠃⠀⠀⠀⠀⠀⠒⠁⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠐⠆⠻⠉

⠀⠀⠀⠀⠀⠀⡁⢁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠁⠀⠁⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠖⢤⠔⠂⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠂⢤⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠚⢁⠱⠦⠰⠏⠈⠁⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠄⠀⡆⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠺⡏⠶⠒⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠃⠀⣤⣄⡀
⠀⠀⠀⠐⡨⠁⢀⡀⠈⠭⠀⠀⠀⠀⠀⢀⢠⠄⠊⠀⠀⠈⠣⢆⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠚⢠⠤⡔⠤⣌⣈⢭⡈⠆
⠀⠀⠀⠘⢀⡠⠃⠘⠄⠀⠁⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠂⠒⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⢄
⠀⠀⠀⠀⢀⠂⠡⠄⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢎⠃⠀⠈⠆
⠀⠀⠀⠀⠤⠄⠤⢠⠠⡤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠓⣆⠃⠀⠀⠀⠀⠀⠐⢀⢰⠂⠐⠆⠒⠓⡀⡂⠀⠀⠀⠀⠀⠀⠆⡈⡁⠯⠘⠡⠄
⠀⠀⠀⠀⠠⠄⢀⡰⠠⠇⠀⠀⠀⠀⠀⢀⣠⣄⣀⣄⣀⣄⣡⣄⠀⠀⠀⠀⠀⠀⠘⢈⠘⠁⣆⠨⢳⡟⠁⠀⠀⠀⠀⡀⡡⠊

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⠈⢰⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡣⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡐⠛⠘⠂⢁⠒
⠀⠀⠀⠉⠘⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠰⡁⠀⢼⡱⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠘⢁⠐⠃⡚
⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠓⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠄⠁⠄⠌

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠗
⠀⠀⠘⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡟⠙⡆⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⣼⠿⡄
⠀⠀⢠⠿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠟⠀⠐⠀⠀⠀⠀⠀⠀⠃⣰⡏⣰⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⡾
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠙⢿⣿⡆
⠀⠀⠀⠀⠀⣿⡇⠘⣿⡇⠀⠀⠀⠀⠀⠙⠛⠿⠿⠆⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻
⠀⠀⠀⠀⠀⣿⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⡏⠀⠰⠟
⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣙⢿⣾⣿⣿⣿⣶
⣿⣟⣴⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⡷⣿⡿⢶⣿⣷⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠁⡀⠰⣿⣍⢛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠈⠆⠙⠿⠿⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡠⠿⠛⠛⢻⡿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡴⢠⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠀⠒⠂⠚⠉⠁⠂⢀⣿⣿⡆⠀⡏⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⠤⠶⠒⢂⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣠⠤⠤⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⠀⡠⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⠈⣭⣿⣥⣤⠀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠛⠂⠙⠉⠉⠀⠠⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢤⣤⣰⣾⠃

⠀⠀⠀⠀⠀⢀⣤⡶⠾⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣷⢶⣦⣤⣤⣤⣤⣄
⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠙⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣁⣀⣀⣀⣀⣀⡈⢻⡇
⠀⠀⠀⣼⣿⠟⠻⠿⠿⠿⠟⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣽⡉⠉⣹⣏⣿⡟⠃
⠀⠀⠀⣿⡇⠰⡷⠀⠀⠰⡷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣉⠀⠀⢈⡁⣿⡇
⠀⠀⠀⠸⣧⡀⢴⣄⣀⣴⡆⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣙⠿⠶⠟⣡⡿⠁
⠀⠀⠀⠀⠘⠻⣶⣽⣿⣭⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣬⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣀
⣠⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠
⠈⠉⠉⠉⠉⠉⠙⣿⢹⡟⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣿⠛⣿⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣼⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣤⣿⣀⡀
⠀⠀⠀⠀⢠⣶⠟⠋⠉⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠉⠉⠉⠉⠛⠷⣦⡀
⠀⠀⠀⢰⣿⣥⣤⣤⣤⣤⣤⣀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣠⡶⠶⠶⠿⠿⠷⢶⣄⠈⢿⡄
⠀⠀⠀⣿⡏⢀⣤⠀⠀⢀⣭⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡟⢀⣤⡀⠀⠀⡤⡄⠹⣧⢸⡇
⠀⠀⠀⢻⡇⠈⣉⠀⠀⢈⡉⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⢉⡀⠀⠀⣈⠁⢠⣿⢸⡇
⠀⠀⠀⠈⠻⣦⣙⣷⣶⢟⣣⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡌⢿⣦⡘⠿⠶⠾⠋⣠⡾⢃⣼⠇
⢀⣠⣤⣤⣤⣬⣿⣿⣿⣿⣯⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠙⠛⠷⠶⠶⠟⠋⠀⣸⡇
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢶⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠂⠀⣀⡀⠀⠐⠀⢀⣀⠀⠀⠘⣷⣤⡴⡿⠀⠀⢀⠀⠄⡀⠘⠂⠀⣀⡀⠀⠐⠀⠁⣀⠀⠀⠘⣷⣤⡴⡿⠀⠀⢀⠀⠄⡀
⠀⢸⠉⠀⠘⠀⠀⡴⠪⣥⠆⠀⠀⠉⡁⠀⠀⢰⠦⣴⡟⢡⠂⠀⢸⠋⠀⠘⠀⠀⡴⠪⣅⠆⠄⠀⠈⡁⠀⠀⢰⠦⣴⡞⢡
⠀⠀⠀⣀⠀⠀⡏⠁⠃⠀⠀⠀⠀⠀⠠⠺⠀⡹⢟⣿⢹⠆⠀⠀⠘⠀⢀⠀⠀⡎⠀⠂⠐⠀⠀⠀⠀⠠⠺⠂⡹⢟⣿⢹⠆
⠀⠰⠆⠈⠋⠀⠈⠠⠀⠀⠀⡴⠈⠀⡠⠾⠁⣤⡶⠤⠀⠀⢠⠀⠰⠆⠈⠋⠀⠈⠠⠀⠀⠀⡴⠈⠀⡠⠾⠁⣤⡶⢤⠀⡀
⡶⠂⠀⠀⠀⠺⠃⠀⠀⠂⠀⡀⠀⢄⠀⠀⠈⢟⠓⠚⢀⣿⣿⡶⠂⠀⠀⠀⠺⠃⠀⠀⠂⠀⡀⠀⢄⠀⠀⠈⢟⠓⠚⢀⣿
⠙⠀⠀⠀⠀⠀⡠⠀⣀⡀⠀⠉⠀⠀⡀⠄⠀⠘⠃⠀⣀⡘⠋⠙⠀⠀⠀⠀⠀⠠⠀⣀⡀⠀⠉⠀⠀⠀⠄⠀⠘⠃⠀⣀⡘
⠀⠀⠀⠂⢡⣂⠀⠀⠈⠁⠀⠀⡄⠀⢀⠀⠐⠦⠀⠈⠛⠃⠀⠀⠀⠂⠢⢤⣂⠀⠀⠈⠁⠀⠀⡄⠀⢀⠀⠰⠤⠀⠀⠛⠃
⠈⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⡛⠑⣀⠀⠀⠀⠀⠈⠀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⡟⠃⣀
⣢⣀⡀⠀⠀⠀⠀⣅⠀⠀⠀⠀⣈⣀⠱⣶⣇⡀⠉⠀⠀⠀⠰⣢⣀⡀⠀⠀⠀⠀⣍⠀⠀⠀⠀⣘⣀⠱⣴⣆⡀⠁
⢀⠁⠀⢸⣧⠀⠀⢻⣷⡶⠾⠛⠁⠀⠀⠈⠉⠀⣠⣶⣶⣄⠀⢀⠁⠀⢸⣧⠀⠀⢻⣶⡶⠾⠛⠁⠀⠀⠉⠉⠁⣠⣶⣶⣤
⠘⣄⣦⣼⠟⠀⠀⠘⠉⠀⣤⠀⣀⠤⠴⣿⠀⢠⠘⠋⠑⡿⠀⠘⣄⣦⡼⠟⠀⠀⠘⠁⠀⣤⠀⣀⠤⠴⡟⠀⢠⠙⠋⠑⡿
⡀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢸⣅⠀⢀⣬⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⢸⣄⠀⣀⣼
⠀⢠⡖⠒⢠⠀⠀⢐⡲⠀⡀⠀⠛⠿⠯⠉⠀⢀⡀⢀⣡⠆⡀⠀⢠⡶⠂⢠⠀⠀⢀⡲⠀⡀⠀⠛⠿⠏⠉⠀⢀⡀⢀⣡⠆
⠀⢘⠀⠀⠀⠀⡠⠋⠈⢛⠁⠁⠀⠀⠂⣠⡀⢼⣭⣿⢧⡘⠀⠀⢘⠀⠀⠀⠀⡠⠋⠈⢛⠁⠀⠀⠀⠂⣠⡀⢼⣭⣿⢧⡘
⠀⢀⡀⠰⡤⠀⠣⠀⠀⠀⠐⢀⠀⠀⠉⣨⠄⠊⣑⠛⠘⠁⠀⠀⢀⡀⠰⡤⠀⠡⠀⠀⠀⠐⢀⠠⠀⠈⣨⠄⠊⣑⠛⠘⠁
⣀⡈⠁⠀⠀⣠⡄⠈⠀⡀⠀⠋⠀⠀⠊⠉⠠⣿⣏⣩⠀⣦⣸⣀⡈⠁⠀⠀⣠⡄⠈⠀⡀⠀⠊⠀⠀⠊⠉⠠⣿⣏⣩⠀⣦
⢯⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠦⠀⠐⠈⠀⠀⢱⡄⠀⠐⢻⡿⢯⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠦⠀⠑⠀⠀⠀⢱⡤⠀⠐⢻
⠀⠀⠀⡀⠀⠀⠈⠀⠲⠆⠀⠀⠀⠀⠂⠁⢀⣀⠀⠠⣶⡆⠀⠀⠀⠀⡀⠀⠀⠈⠀⠲⠆⠀⠀⠀⠀⠂⠁⢀⣀⠀⠠⣶⡆
⠠⠀⢀⠄⠉⠒⠀⠀⠀⠀⠀⠀⠃⠀⢰⢤⣤⢍⠀⠀⠀⠀⠀⠠⠀⢀⠄⠉⠒⠀⠀⠀⠀⠀⠀⠃⠀⢰⢤⣤⢁
⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢆⣀⡆⠀⠦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢆⣀⡃⠀⠶
⠚⠖⠂⢠⡄⠀⠀⣷⣀⣀⣤⣤⠖⠒⠈⠿⠷⠂⠀⣀⣀⠀⠈⠚⠒⠂⢠⡄⠀⠀⣷⣄⣀⣤⣤⠖⠒⠈⠿⠿⠂⠀⣀⣀
⢰⠀⡀⢸⡿⠀⠀⢸⠿⠋⠉⠀⠀⠀⢀⣤⠀⠀⢺⡿⢻⣿⠀⢰⠀⡀⢸⡿⠀⠀⢸⠟⠋⠁⠀⠀⠀⢀⣤⠀⠀⢺⡿⠻⣿
⠀⠓⠻⠛⠁⠀⠀⠀⠀⠀⠛⢠⠖⠁⠉⠫⠀⠘⠀⠀⠀⠋⠀⠀⠓⠻⠛⠁⠀⠀⠀⠀⠀⠛⢠⠖⠉⠉⠻⠀⠘⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⡀⡀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⣰⣶⣶⣦⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢘⣿⣿⡁⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣾⣿⣿⣿⣿⣷⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⢉⣉⡉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠳⣬⡛⠛⠛⠛⠛⢛⣤⠞⠀⠀⠀⠀⠀⠀⣠⠖⠛⢉⣉⣉⡙⠓⢦⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⣼⣿⣿⣿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⡖⠛⠉⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢰⣿⣿⣿⡧⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡟⠀⠀⠀⢻⣿⣿⡿⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⢿⣿⣿⠗⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣷⠀⠀⢀⣤⣿⣿⣧⣄⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣠⣤⣿⣯⣤⡀⠀⠀⣾
⠀⠀⠀⠀⠀⠘⢦⡀⣿⣿⣿⣿⣿⣿⡇⣠⠿⣄⡀⠀⠀⠀⠀⢀⣠⡤⠾⠧⢤⣄⡀⠀⠀⠀⠀⢀⣤⠷⣄⢸⣿⣿⣿⣿⣿⣿⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⣠⡤⠞⠁⠀⠀⠉⠳⢦⣀⡴⠋⠀⣴⣶⣶⣦⠀⠙⢦⣀⡴⠞⠉⠀⠀⠉⠳⢤⣄⣀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣈⣿⣿⣁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⡼
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⣉⠙⠓⢦⡀⠀⠀⣀⡴⠞⠉⠳⣜⠛⠛⠛⠛⠛⠛⣣⠞⠉⠳⢤⣀⠀⠀⢀⡴⠚⠋⠉⠉⠙⠲⣤⡀
⠀⠀⠀⠀⠀⢠⠞⠀⠀⣾⣿⣿⣿⡄⠀⠙⣶⠛⠁⠀⠀⠀⠀⠈⠙⠓⢶⡶⠚⠋⠁⠀⠀⠀⠀⠈⠛⡶⠋⠀⠀⣿⣿⣿⡦⠀⠀⠳⡄
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠰⣿⣿⣿⡷⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣧⠀⠀⢀⣤⣼⣿⣥⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣀⣬⣿⣯⣄⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠘⣆⠀⣿⣿⣿⣿⣿⣿⡇⢀⡞⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠧⣤⣀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⣿⣿⣿⣿⣿⣿⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠳⢭⣉⣉⣉⣉⣭⠷⠋⠀⠀⠀⠀⠀⠀⡴⠋⠁⢠⣤⣤⣀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠙⠶⣭⣉⣉⣉⣩⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣿⣿⣿⣿⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣴⣾⣿⣿⣷⣦⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠿⠿⠿⠿⠿⠿⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠰⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠐⡀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣅⡀⠀⠀⠀⠀⠐⢤⣿⡬⠀⠀⠀⠀⠀⠀⠀⠐⢹⣟⠡
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⣴⣿⡦⠃⠀⠀⡠⣠⠤⠀⠀⠉⠛⢯⣤⡄⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⢰⡔⠄⠀⠀⠀⠀⠀⠀⠐⢢⣿⣆⠂⠀⠀⠀⠀⡠⢀⣀⡂⢌⢣⣿⡦⠃⠀⠀⠁⢾⣿⡗⠈⠂⠀⠀⢀⣠⢄⠀⠀⠔⣶⠢⡀
⠀⠐⠿⠷⠀⠀⢀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⠀⡄⠀⢸⣿⡇⠀⠱⠁⠀⠀⠀⢦⠀⣼⣿⣧⠀⡀⡀⠀⢆⣿⣅⠆⠈⠲⠿⠖
⠀⠀⠀⠀⠀⠐⠁⢸⣿⡇⠀⠃⠀⠀⡎⣾⠁⡂⠀⠠⡘⣿⣿⣿⣇⠄⢀⠀⢀⣠⣀⠁⠻⠛⢟⠈⠀⠀⠀⠀⠉⠁⡠⢀⣶⣆⢄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠠⠀⣼⣿⣷⡄⠀⠀⠀⠙⠻⠛⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⢃⣿⣇⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠀⠻⣿⡿⠀⠁⢈⣰⣇⡁
⠀⠀⠀⠀⠀⡀⠉⠛⠿⠛⠁⠀⠀⠀⠀⢀⣀⡀⠀⠉⠀⠀⠔⣶⠢⠀⠀⠀⠈⠙⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠐⠀⣾⣿⣿⣆⠔⠀⠙⠋⠁
⠀⠀⠀⠊⣿⠑⠀⠠⣄⢄⠀⠀⠀⣀⠊⣰⣶⡄⠑⡄⠀⠀⢲⠿⠖⠀⠀⢀⠔⠀⣥⡄⠐⠈⠀⠀⠀⠀⠀⣌⣿⡉⠄⠛⠛⠋⠁⠀⠀⠀⡀
⠀⠀⠀⠙⠿⠋⠀⢇⣿⡀⠁⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢀⣀⡀⠀⠀⢈⠀⣈⣿⣏⠀⠰⠀⠀⠀⠀⠀⢈⡛⡋⠀⠀⠀⠀⠀⡔⢈⣤⣤⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⡠⡀⠠⠿⣿⡿⠀⠀⢀⠊⣴⣿⣷⠀⠀⠀⠦⣿⣿⣿⡧⠀⠀⠀⠀⠠⠊⢶⣿⡦⠑⠄⠀⠀⠐⠀⣈⣿⣟⡀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⡸⠀⠀⠀⢴⡤⠀⢀⠀⣩⣿⣏⡀⠰⠀⠀⠀⠀⠁⣤⣀⠀⠀⠀⠀⢀⣸⣿⣅⡀⡀⠀⠀⠀⠡⢿⣿⣿⡯⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣉⣉⠀⠀⠀⠁⣼⣧⠀⠀⠁⠿⠿⡿⠆⠁⠀⠀⠀⠀⢠⣼⣧⣁⠔⣿⠂⡸⠿⠿⠿⠃⠀⠀⠀⠀⠀⢀⢴⣧⠄
⠀⠀⠀⠠⠊⢠⣶⡄⠑⠀⠀⣸⣇⡡⠀⠀⠀⠀⠠⣲⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠲⢿⠖⠀⠀⠀⠀⢠⠺⣿⡇⢀⠀⠰⣼⣧⠄
⠀⠀⠀⠀⠀⣸⣿⣇⠀⣠⠀⠉⠛⠀⠀⠀⠀⠀⢡⣿⡦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⣿⠃⠀⠀⠀⠠⣦⠄⠀⠀⠀⠈⣴⣿⡧⠈⠀⠀⠈
⠀⠀⠀⠈⠺⢿⣿⡿⠆⠁⠀⠀⡠⢒⣀⡐⠢⡀⠀⠀⠂⠀⠀⠀⠀⠔⠉⣶⣦⠁⢿⠿⠛⠀⠀⠐⢤⣿⡜⠂⠀⠀⠀⠀⠀⡠⢀⣂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢸⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠸⠀⣤⣿⣿⣤⢨⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⡇
⠀⠀⠀⢸⣿⡗⠄⠀⠀⠀⠀⠈⠀⣾⣿⣿⡆⠄⠀⡠⢶⣶⢄⠀⠀⠁⢿⣿⣿⡧⠂⠀⣀⡀⠀⠘⢹⣿⠀⡄⠀⠀⠀⠀⠀⠨⣿⣿⣿⠄
⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⢇⣼⣧⡠⠀⠀⠠⣴⠄⠀⠀⠀⠎⣺⡆⡂⠐⠿⠿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣄⢀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢡⣿⣧⠇⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣿⡜
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⡆⣾⣿⣴⣿⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⣿⣦⣿⣷⢸⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⡹⠟⣼⣫⠟⠁⠀⠀⠈⠻⣿⣯⣽⣿⠟⠀⠀⠀⠈⢿⣝⣧⠻⢏⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢀⣠⣤⣤⣤⣭⣭⣤⣤⣤⣄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⣠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣄⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣾⣿⣿⠗⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠸⣿⣿⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣦⣌⣛⠿⢿⣿⣿⡿⠿⣛⣡⣴⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣚⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢻⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠒⠉⠙⠛⠿⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠠

⠀⠀⠀⠀⡀⠀⠀⡀⠀⣀⠀⠀⡀
⠀⠀⢀⡾⠙⣄⢿⣿⣷⣶⣶⡤⠠⠥
⠀⣠⠎⠀⠀⠈⢿⣿⣿⣿⣿⣇⢀⡤⡄
⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠟⠋⡀
⠀⠀⠀⢀⠀⠀⠀⢈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⡀⠈⠋⠉⠀⠀⠄⠂⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⡟⢺⡟⠀⠌
⠀⠠⡀⠀⠀⠀⢸⠀⠀⠀⢤⡀⠀⢨⡄⢠⡄⠼⠀⠀⠂⢀⠆⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣠⣄⡼⢀⣿⣿⣦⡄
⢠⠦⠁⠀⠀⢀⣹⠀⠀⢐⡋⠀⢀⣿⡷⢃⣀⠐⠀⠀⠈⠁⠀⠀⣺⣟⠁⠀⠀⠀⠀⠀⠈⠛⠛⣧⣾⣻⣿⡟⠄
⠀⠀⣀⡤⠔⠊⠻⢦⠀⠀⢹⡆⢠⢬⡅⠀⢈⡇⠀⣶⠀⠀⠀⢪⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⣿⠒
⠀⣈⠍⠀⠀⠀⠀⠀⠀⠂⣼⡇⢰⣌⣿⠀⢘⠓⠀⢨⡅⠀⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⢠⡽⠀⠀⠀⠀⠀⠀⠀⠙⡿⢿⣞⢻⠁⠀⠸⠀⠈⢛⡅⣀⢹⣿⢛⣷⣿⣏⠀⠀⠀⠀⠀⢀⡀⡠⠀⠀⠀⡹
⠸⠀⠸⣷⣞⡿⠆⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⢘⣼⡇⢡⠀⡀⡀⠈⣿⣿⡄⠄⠠⠀⢀⠘⠤⠷⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⢰⣾⣿⣷⠀⢀⠀⠀⠈⢫⣵⣾⣦⣷⣷⣟⣿⣿⣷⠄⠀⠠⠿⢿⠂⠀⠀⠀⠀⠀⢠
⠰⣶⣷⣄⣀⠀⠀⠀⠇⡀⠈⣿⡿⠙⠀⠈⠷⣾⣠⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣻⠀⠀⣴⣿⣿⣦⣀⡀⠀⠀⠈
⢰⣶⣤⣭⣿⡏⣵⣤⣀⣥⣀⣙⣄⣀⡠⠤⠤⠀⢻⣿⠛⢻⣿⣿⡿⣿⣿⡿⣿⣿⡀⣴⣿⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠉⠉⠛⠿⠿⠶⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠛⠋⠀⢀⢝⠂⢾⣇⣀⠈⠉⠉⠿⠿⠿⠿⠿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⠀⠀⠈⠃⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠫⡐⠄⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⢀⠤⣤⣴⣶⣶⠦
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣤⣶⠀⠉⠒⠁⠀⠰⠚⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀⠸⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⢸⡆⠀⠀⢀⠁⠀⠀⠀⠀⡆⡆⣰⢰⠰⡆⠐⢰⠀⡆⠀⠀⡀⠁⢠⠀⠑⠂⠀⠀⠀⣤⠀⠀⣠⣶
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⠏⠸⠁⠃⠨⠀⠃⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣆⠰⠀⡇⡖⣖⣰⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠃⠃⠇⠛⠏⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠀⠀⢀⣤⣁⣶⡀⠀⣰⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⢀⠤⢠⠀⢀⠠⠄
⠀⠀⠠⠀⠀⠀⢾⣿⡗⠀⠀⠀⠀⡀⠘⠿⢿⠟⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⡄⠄
⠀⠀⢿⠓⠀⠀⠀⠉⠀⠀⠀⠀⢴⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⡏⡉⠀⠀⢠⠂
⠀⢸⣼⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠄⠀⠀⢀⢀⠀⢠⣷⠁⠀⠀⠸⡀⣀⡤⣤
⠀⠘⠷⠿⠀⠀⠞⠃⠀⡀⠈⠂⠀⠀⠄⠀⠀⠀⠀⢰⣿⠂⠘⠇⠀⢄⠀⠰⣭⣾⣹⡿⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⢠⢾⡟⠀⠀⠀⡶⢶⠀⠀⠈⠛⠉⢠⠀⢢⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⢀⣟⡿⠁⠀⠀⠀⣿⡜⡆⠀⠀⠀⠀⡇⠀⡉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠰⡀⠀⠀⠁⠈⠁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣄⣠⣶⣶⣷⣶⣶⣦⡀⠀⠀⠙⠒⠀⠂⠁⠤⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⡿⠃⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠋⠀⠀⢿⠆⣤⢸⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣰⣿⣤⡄⠀⠀⠀⠀⠘⣿⣿⣷⣶⡀
⢠⡶⠂⠀⠀⠀⠀⠀⠻⠃⡠⠀⢀⢀⣤⣤⣀⠀⢠⣿⣿⣵⣶⣾⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣣⠀⠀⠀⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠉⠉⢰⣶⣶⣴⣶⣤⠀⣉⠋⠀⠀⠀⠀⠀⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣴⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⢿⣿⣿⣿⡦⡤⢤⣀⡀⠀⠀⠀⢀⣸⣿⣶⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠒⠒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠏⠉⠉⠉⠉⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠻⣿⣿⣇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣸⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢋⣥⣴⣶⣾⡿⠿⠟⠛⠻⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣦⢹⡿⣰⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠋⣠⣭⡙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢟⣽⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣸⣿⢿⣿⠁⣠⠤⣤⣀⡀⠀⠀⠀⢀⣀⣤⣤⣄⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢿⣿⢸⣿⡀⢀⣀⣀⣉⠉⠀⠀⠀⠋⣉⣀⣀⠀⠀⢸⠏⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣦⣿⡇⠈⠋⠛⠋⠀⠀⠀⠀⠀⠛⠟⠙⠁⠀⠈⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⣵⣃⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⢰⣶⣿⣿⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡆⠀⠀⠀⣠⣴⣤⣦⣄⠀⠀⠀⢠⣟⡿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⣰⣿⣿⣾⣿⣿⢃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢹⣿⣿⣿⣿⣣⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠛⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠉

⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⢸⣿⣶⠶⠦⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠤⣤⡍⠀⢻⠀⠀⠀⣠⣄⡀
⠈⠛⠁⠀⠀⠀⠀⢠⣴⣿⠀⠀⠀⠀⠐⠞⢆⠀⠀⠀⠘⠀⠀⠀⠲⢶⡏⠉⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠠⠀⢤⠄⠀⢰⣘⣦⠀⠀⠀⠀⠀⠀⣤⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢐⣀
⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣠⣴⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠂⠀⠀⠉⣤⠆⠀⠀⠀⠀⠐⠩
⢸⣿⠀⠀⠐⠾⣿⣷⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄
⢠⣤⣠⡄⠀⠀⠻⠿⣦⣤⡄⠀⠀⠸⠏⠀⠀⢀⣀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢠⣌⠙⠃⡀⠀⠀⠀⠀⠀⠻⠠⣤⢀⣀⡀⠀⠘⠛⣷⣤⣦⠀⠀⠘⠛⠂⠀⠀⠀⠀⢀⠀⢠⡋⠇⠀⣴⡆⠀⠀⠀⠀⠀⣦
⠈⠛⣷⣶⡷⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⢀⡀⠀⣼⠏⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠿⠊⠗⠀⠱⠂⠀⣹⣇
⠀⠀⠉⠰⠿⠦⣀⣠⣄⣈⠛⡶⠀⡀⠀⡏⠉⠳⡽⣤⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠁⢠⣤⣤⣥⡀⠀⠀⠀⠀⠀⢠
⢀⣄⣀⠀⠉⠛⠋⠀⠉⢻⣷⠤⠀⠃⠀⠓⠿⢷⡅⠀⣤⠀⠀⠀⢴⣶⡔⢿⡃⠙⠆⠈⣿⣦⠀⠛⠿⠟⢷⡄⠀⠀⠀⠀⠈
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⡄⢀⡀⠀⠀⠀⠈⠇⠀⠉⡄⠀⠀⠀⠀⢻⣀⣷⣶⠀⠀⠁⢨⣷⢺⡀⠀⠠⠅
⢸⣿⣿⠀⠀⠶⡄⠀⢀⣾⣿⣧⣾⣳⣷⣄⡠⡤⠀⠀⢀⣵⠀⠀⣼⣿⣭⣿⣿⣷⣴⡗⢠⡄⠃⠘⢳⡆⠐⢶⡀⠀⠀⠀⢀
⢸⣿⣿⡀⠀⢰⣿⡿⠛⠛⢍⠛⠿⣿⠛⠻⠿⠇⠀⠀⠼⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠻⠿⢤⡟⠃⠀⠀⣴⡟
⠘⠛⠋⠁⠀⠀⠈⠃⠀⠀⢘⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⠿⠋⠀⠀⠈⠛⠛⢿⡄⢠⡀⠀⠙⢧⡀⠀⢀⠈⣿⣷
⢰⣶⣶⣶⣤⡄⠀⠲⣄⣀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣀⣤⠑⠀⢀⡀⠸⢃⣿⣷⡄⠀⢸⣇⠀⠿⠀⠻⢿
⢸⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠈⠰⡾⢭⣽⢷⡄⠀⠂⠀⣼⣿⣿⣿⣶⣌⢿⠀⠀⠀⠀⠈
⠘⢿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣇⣴⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⡜⠁⣠⣍⡈⠙⠟⢡⡄⣨⣿⣿⣶⡶⡀⠀⣀
⠀⠀⠈⠉⠉⣿⣿⡟⠀⠀⠹⠷⠶⠶⠈⣽⣿⣿⣿⡟⣹⠟⠋⠹⠀⠀⠀⠀⠀⠛⠏⠉⠙⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀⢈
⠀⡤⢠⡤⠀⠙⠋⠁⠀⢀⣀⠀⢀⠀⠠⣿⣿⣿⡇⠀⠀⡀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⣀⣤⡉⢛⠿⣿⣿⣿⣇
⢰⣇⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⣷⣶⡿⠛⠓⠒⠀⠀⢁⢀⣤⡀⣀⡀⠐⠀⠀⠀⠀⠀⠿⠟⢡⣿⣄⠠⣤⣠⣾⣿⣶⠶
⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⢿⠃⠀⠀⢠⡏⠙⢿⠟⣴⣿⠋⠙⠞⠀⣀⣤⣤⡀⠀⠀⢺⣟⣿⠀⢿⠿⣿⣿⢀⣠
⢀⡌⠙⢿⡄⠀⠀⠀⠀⠀⠸⢿⣧⠀⠸⠇⠀⠀⠘⠃⠀⠘⠀⠉⡈⠁⣀⣴⣶⣿⡿⠀⣧⢀⣴⣿⣿⢿⣄⣴⣾⣿⣿⣿⣿
⢠⣶⣶⣿⣧⠀⢀⣀⠀⠀⠀⣿⡟⠀⢀⣀⣰⠶⢿⣶⣄⣤⣶⠀⢿⣿⠟⢃⣿⣿⣷⣾⣿⠁⣸⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿
⢸⣿⣿⢿⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠄⠨⢿⣿⣿⣧⣾⡿⣤⠈⠻⣿⣿⠶⣤⡄⠘⢦⠤⡼⠤⠿⠿⠿⡿⠻⡿

⠀⠀⢀⣤⣦⣠⡄⠀⠀⠀⢠⣾⣿⣆⠀⠀⠀⠀⣀⠠⡄⢀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢠⣷
⣠⡴⣫⣵⣾⣝⢷⣄⠀⠀⠈⠻⡿⠋⠀⠀⠀⠠⣿⣾⣿⣼⣆⠀⠀⠀⠀⠺⡿⠗⠀⠀⠀⠀⣴⣿⣧⣤⣄
⠉⢸⣿⡟⢻⣿⣷⠉⠀⣰⣾⣿⣿⣿⣦⡀⢰⡇⠿⢸⡿⠸⢇⣷⠀⣸⣟⠰⠿⠄⣻⡇⠀⢸⣿⣿⣿⣿⡿
⠀⠘⠛⠃⠈⠛⠋⠀⠀⠛⠛⠛⠛⠛⠛⠁⠈⠛⠳⠶⠶⠶⠛⠉⠀⠛⠛⠃⠀⠘⠛⠛⠀⠈⠛⠛⠛⠛⠁
⠀⢀⣤⢶⠖⢤⡀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⣠⢀⣀⡀⣄⡀⠀⢀⡀⡀⢀⣤⣄
⠀⣿⠟⠁⠀⣼⣻⡀⠀⣿⣝⠻⡿⣋⣽⡇⠀⣾⣿⣏⣯⣿⣿⡆⠀⢸⠓⣛⠛⣛⠚⡇⠀⢸⣷⣯⣿⣿⣿
⠀⢇⢺⡦⠀⠙⡿⠁⠀⣿⣫⣿⣾⣯⣻⡇⠀⠹⢿⣷⠶⠿⠟⠁⠀⢸⠀⠼⠡⠿⠀⡇⠐⠶⣿⣿⣿⡿⠃
⠀⠀⠙⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⢠⣤⣤⣤⣤⣄⠀⠀⠀⢀⣠⣴⣤⡀⠀⠀⠀⠀⠠⢤⣤⣄⣀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢠⢢⢠⣤⡠⢰
⠀⢸⣿⡇⢹⣿⣟⠀⠀⣶⣿⣿⣿⣿⣿⡆⠀⣿⠉⣽⡍⢹⠀⣼⠀⠸⢿⠟⣛⠻⣿⡇⠀⠘⠌⢈⣿⠀⠸
⠀⢸⣏⣀⣀⣹⣯⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⣿⣠⣿⣦⣸⢀⡇⠀⢸⣿⣦⣛⣴⣿⡇⠀⠀⠀⣼⠽⡇
⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠙⠛⠛⠛⠋⠈⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⡠⠖⡒⢦⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⢠⠶⢦⢠⡶⢦
⠀⠀⠐⢾⣿⣿⠃⠀⠀⠀⠀⣇⠺⠗⣸⠇⠀⢸⡟⠛⠛⠛⣿⠀⠀⢰⣶⣆⠛⠛⠛⠀⠀⠘⣶⡟⠘⢷⡞
⠀⢀⣴⠟⠙⠏⠀⠀⠀⢠⣾⠏⠛⠚⠁⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠈⠉⠉⠛⣾⣷⠄⠀⢸⣿⣿⢸⣍⣹

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣆⡀
⠀⠀⠀⢀⡶⣄⡀⠀⣀⣴⣾⣿⡿⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠿⣿⣿⣦⣄⠀⠀⣀⡴⡆
⠀⠀⢙⣺⣷⣿⢿⣿⣿⣟⣉⣁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣉⣙⣿⣿⣿⢿⣷⣷⡊
⠀⠀⠀⠀⠈⠁⢾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠆⠉
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⣿⣿⣿⣿⣟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁⠀⠀⠀⠀⠻⠿⠿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣀⡄⢉⣩⣴⣾⡿⠿⠿⠗⢙⠋⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⡀⠉⣩⣽⣿⣿⣿⣦⣶⣷⣶⣼⣿⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢻⣿⣿⣿⢾⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣟⣿⣉⣭⣷⣦⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠘⣿⡿⠁⣼⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣌⡛⠿⢾⣧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣧⣴⣴⣜⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡦⡀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣠⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣠⣬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣺⣿⣿⣿⣭⣿⣿⣿⣿⣶⣦⣤⠀⠀⠀⠀⣤⣴⣶⣿⣷⣶⣬⣯⣽⣶⣽⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡙⠲⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣄⠀⠰⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣀⡀⡀⠘⠛⠻⠿⣿⣿⠿⠟⠋⠀⠀⠈⠛⠿⢿⣿⡿⠿⠛⠋⠀⠼⣿⣧⡀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣼⣿⣿⠀⠀⠀⠀⠀⠘⠐⠂⠀⠒⠂⠀⠀⠀⠀⠀⢸⣿⣿⠀⠘⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⣼⣿⠋⣤⣼⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⡀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⣰⣿⣿⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠻⢷⡄⠀⠀⠀⠓⠶⠶⠚⠁⠀⠀⢀⡀⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠙⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⠻⢷⣶⣤⣤⣶⣾⠿⠋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠉⠉⠁⠀⢀⠄
⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣠⠎⠀⠀⠀⢤⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣰⠋⠀⠀⠀⠀⠈⢷⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣍⠂⢀⡴⠁⣀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡘⡆⠰⢋⡤⠶⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⡠⠤⠀⠈⢐⣂⣀⠀⠀⠀⢠⣤⣄⣛⠳⣄⠳⠀⠐⣫⠶⢂⣀⣤⣤⣀
⠀⠀⠀⠠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⠆⣿⠀⠀⠉⠖⡁⠀⠀⠠⡉⣀⠀⠀⠖⠒⠀⢀⣉⣑⠂⠳⠀⠞⣁⣤⡴⠆⠀⠀⠁
⠀⠀⠀⢀⣭⣭⣶⣤⣄⣀⣠⠆⠀⢠⢿⣡⣾⣷⣾⠏⠀⠀⠀⠘⡀⠇⠆⠃⠉⠈⠀⣠⠔⣂⣠⡬⠭⠭⠉⠀⠀⠈⢁⣐⣒⠶⢤⣬⡑⠦
⠀⠀⠀⣿⣻⣿⣿⣧⠞⠋⠁⠀⠀⠀⠀⠁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠘⡋⠁⣠⠴⢋⡥⠀⠀⠀⠠⣀⠉⡙⠓⠈⠉
⠀⠀⢰⣿⣿⣥⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢇⠀⢠⠎⠀⢘⠁⣠⠏⠀⡆⢸⡈⣆⠈⢳⡌⠳⣤⡀
⠀⠀⠀⠛⠿⢻⣿⠉⣿⣇⠀⠀⠀⠀⠀⣾⡟⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⠀⠀⠀⣰⠃⣴⠏⡰⢰⡇⢸⡇⢸⡆⢠⠛⠀⠈⠃
⠀⠀⠀⠀⣴⣿⠋⠀⣾⡟⠀⠀⠀⠀⠀⣿⣇⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠉⢀⡇⠘⠃⢸⡇⠈⠃⡀⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⠂⢷⡀
⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣾⣿⡀⠀⠀⣠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢸⡇⢾⣿⡇⠀⠀⠀⠀⣤⣦⡀⠀⣀⡀⠀⠀⠀⠙⢷⣄⠀⢿⣿⠇⣠⡴⠋⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠈⢷⣶⣿⣦⣰⠇⠀⡀⠛⠟⣱⣾⣏⢻⡆⠀⠀⠀⠀⠉⢻⣾⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⢸⣿⣿⡏⠁⠀⠀⠻⠶⠞⠻⣿⣿⣧⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⣿⠀⣄
⠀⠀⠀⠀⢸⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢹⠀⣿
⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⣼⡟⠁⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠐⠢⢄⠀⠁⠸⠀⠀⠀⠀⢀⣭⠇⠀⠀⠀⢸⡄⣿
⠀⠀⠀⢠⣿⠇⢸⣿⠀⠀⠀⠀⠀⠀⢻⣧⠀⠘⣿⡄⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣄⡉⠂⠀⠆⠀⠀⠀⠲⠄⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠈⢑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⠃⣿
⠀⠀⣤⡀⠀⠀⣠⣄⠀⣀⣤⠀⠀⠀⠀⠀⣀⣀⠸⡆⠀⠀⠀⠀⣀⡀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⣀⠀⠀⠀⠀⢸⠀⡏
⠀⠀⠈⠙⢶⡜⢿⡿⠃⣨⡟⠀⠀⠀⠀⠘⢿⡿⢠⡇⠀⠀⠀⠸⣿⡿⠙⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⢺⣿⡗⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⢹⣿⣿⡟⠉⠀⠀⠀⠀⢀⡴⣾⣿⣿⠀⠀⠀⠀⠀⣴⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⣿⣦⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠠⡟⢰⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣇⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠁⡏
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡧⠀⠀⠀⠀⠈⠻⣿⡋⠉⠙⠿⠂⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⣿⠹⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⡆⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠚⠛⠛⢀⠀⠘⠛⠛⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠲⠶⠖⠈⡇⠀⠳⠶⠃⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠓⠒⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣥⣀⣀⣀⣬⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⢷⡀⠀⠀⠈⠓⠦⣖⣒⠒⠶⣤⠶⠋⠀⠀⢀⡴⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⣀⠀⠙⠳⢤⣀⣠⡶⠤⠭⠇⠀⠀⠀⢀⣠⡴⠋⠀⠀⢀⣀⡈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣈⡉⠓⠲⠶⠶⠶⠒⢛⣉⣥⠴⠖⠚⠋⠉⠉⠉⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠓⠶⠶⠒⠒⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⠀⠀⢀⢀⣀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣰⣄⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣟⠡⡨⣻⣦⣀
⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⣾⠁⣄⢹⢊⠂⡏⣰⣉⣷⡦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆
⠀⠀⠀⠀⢿⣿⡿⣛⡶⠲⠶⣶⣶⠶⡛⡟⠋⣽⡵⣎⢿⣧⡈⢓⡄⢠⠚⢁⣼⡿⣱⢮⣯⠙⢛⣛⠶⣶⣶⠶⠖⢶⣛⣿⣿⡿
⠀⠀⠀⠀⠈⢿⣷⢳⣷⠄⣈⠃⠹⠀⢸⣥⡾⢹⣇⣸⢄⣉⡻⢶⣄⣠⡶⢟⣉⢰⣇⣸⡏⢷⣤⠇⠀⠇⠼⣁⠠⣾⡞⣾⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⠟⣿⣷⣿⣕⢄⠙⠾⣄⣬⠷⠁⣿⣿⡗⠀⠹⠯⠀⢺⣿⣿⡈⢾⣅⣠⠓⠏⠠⣪⣷⣾⣿⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣾⣯⢏⠹⣿⡆⠄⣉⠂⠀⠀⣀⠻⣿⡇⣀⢀⡀⣀⢸⣿⠟⢀⠀⠈⠀⣍⠰⢰⡿⠏⡹⣽⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠀⣹⣽⠈⠛⣰⣿⢀⡤⢴⢏⠳⣽⢏⡹⣯⠞⡹⡦⢤⡀⣿⣆⠛⠀⣽⣇⠀⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⢽⠀⠀⢱⠁⡈⠒⠁⣾⢰⠿⠆⠰⠿⡆⣷⠈⠒⢁⠈⡏⠀⠀⡏⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠈⢸⠣⣤⣼⣿⣾⠀⠀⠀⠀⡧⣿⣧⣤⠼⡆⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢼⣿⣙⡏⢉⣿⣧⡀⢀⣼⣿⡉⢹⣋⣿⡧⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠳⠿⠿⠟⠓⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⠀⠀⡷⣠⣆⠠⠔⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣒⠀⠀⠘⠻⣿⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡭⠶⣷⢀⡘⠓⣀⠘⠁⠈⢠⠰⠘⠀⢠⡀
⠀⠀⠀⠀⠀⢙⠀⣿⠀⠀⠀⣸⣿⡆⠡⠅⣎⠀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠚⢀⡈⠡⡄⠉⠶⡀⠴⠦⠰⢆⢁⡀⠖⣈⠠⠌⣁⠈
⠀⠀⠀⠀⠒⡰⣴⣿⣧⣤⣴⣿⣿⡞⠈⠁⠀⠀⠀⠉⠒⠀⠀⠠⠄⢤⡤⠶⢀⡐⢃⡀⠛⠄⡤⠘⠀⠀⠀⠙⠳⠴⠮⠰⠦⠁
⠀⠈⠁⠀⡰⠉⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠘⠓⢠⠐⢢⠀⠅⢀⠐⡦⡀
⠀⠀⠐⠈⠀⠀⠀⠀⠹⣿⠿⢿⣻⠅⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠠⣌⣀⢚⡀⠈⣀⠘⠠⡆
⠀⠀⠀⠀⠀⠀⠠⠅⠀⡜⠀⡀⣶⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣶⣾⣶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠅⣁⠀⠠⠀⠀⠘⠀⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⢀⠒⠠⠟⠀⠁⠒⠩⢀⡀⠀⠒⠉⢈⡁⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣶⠉⡀⢤⣄⡓⢠⡅⠨⠒⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠉⠁⠀⠑⠄⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠂

⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠐⠀⠀⠐⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢰⡞⠃⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢀⡀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠙⠄⠆⠀⠀⣀⠀⠀⠀⠀⠘⠋⠁⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣶⠾⣹⣅
⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡋⢀⠀⠂⠓⠀⠀⣠⡦⠀⠁⠀⠀⠠⠄⠀⠀⠒⠋⢀⠀⠀⠀⠔⠀⠄⢤⢀⠘⠀⠀⠀⠀⠀⣀⠀⣀⢭⢟⡁
⠀⠀⠀⠄⠀⠙⠁⠀⠀⠠⡆⠀⢀⠀⠀⣖⠀⠀⠀⠐⡂⠶⠀⠈⠁⠠⠄⠀⣀⢀⡘⠃⠈⠉⠟⠁⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠠⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠰⣆⠞⢛⠀⠀⠀⠠⠂⡐⡆⠈⠸⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⢀⢀⡶⠴⠂⠀⠀⠀⠁⡀⠀⢠⣀⠀⠀⠀⠛⠀⠈⠓⠠⡀⢀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠘⠂⠀⠀⠠⠁⢀⠀⠀⠀⠀⠀⠸⠆⠀⠀⣀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠸⠊⠀⠠
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠰⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⣠⡄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠁⢠⡀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠁⣤⡟⠘
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⣶⡶⢳⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣷⣶⣶⣶⣶⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⢰⣿⣇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⠀⢰⣏⣽⢆⠀⣿⣿⡆⢸⢀⡇⢀⣀⡾⠁⠀⠀⢢⠀⠀⣼⣿⣿⣿⣿⣀⣤⠤⠀⠀⠸⣿⡿⠀⠔⣈⣀⡪⣄⢀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⠐⠆⠀⠚⠊⠁⢀⠈⠻⠇⠈⢼⠃⠘⠉⠀⠀⠀⠀⠚⠂⠀⠈⠙⠛⠿⠿⠿⠀⠀⠀⠄⠀⠀⠁⠈⢸⣝⣷⠿⢾⡆⠆
⠀⠀⠀⠀⠀⠀⠸⣾⣿⡇⠀⣰⡦⠸⠿⠿⠯⠿⣤⣄⠀⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠄⠀⢷⣄⣀⣠⠄⠐⠜⢿⣶⠗⠾⢃⠂
⠀⠀⠀⠀⠀⠀⡈⠙⠛⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡠⠁⡀⡀⠀⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠁⣄
⠀⠀⠀⠰⣤⣦⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⡄⠘⢤⣄⣄⡤⢀⠐⠆⢤⡀⢀⠀⡙⠟⠁⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠒⣿
⠀⠀⠀⠀⣛⣿⣿⡿⠁⠠⠆⠀⠀⠀⠙⢖⠀⠁⠀⠁⢄⠀⠠⢤⡈⠛⠀⢠⠉⣉⢳⣈⠱⣄⡀⣀⠀⠹⠋⠀⠀⠀⣀⠐⣆⠐⡄⠐⡄⢤⡀⠀⠋
⠀⠀⠀⠈⠉⠙⠋⢀⡀⠐⠀⢠⣴⡀⠀⠈⠀⣰⣃⠀⠸⠀⠀⡄⠉⠋⠓⠀⠃⠘⢃⣻⠘⣅⠂⣜⢂⠀⠀⠄⢒⢀⡉⠀⠱⠀⠰⠆⠰⠆⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠠⠛⡟⣦⣤⣴⠏⢙⣁⡀⠀⠀⠀⠛⡜⣧⠷⣦⡼⠿⠿⢒⠋⠁⠀⢸⠀⠀⠈⠽⠆⢰⡀⠀⠂⠐⣲⠀⠲⠈⢟⡅⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣷⡀⠰⣾⡧⠖⠽⠻⣗⠤⠻⠟⠀⠀⠀⠀⠙⠋⠞⠀⠶⠀⢤⠀⢦⠉⠀⠀⢀⠤⠀⠀⠻⣶⣭⣯⣤⣻⣄⣝⣧⣶⡶⠋⣀⢾⣸⡅
⠀⠀⠀⠀⠀⠀⠸⠛⠛⠇⠀⢈⣀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢉⣁⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠀⠦⠦⠀⠀⢀⠀⠉⠛⠛⠛⠛⠛⠋⠁⠰⣎⣙⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢰⣿⣿⣿⠀⠴⠖⠀⢤⣾⠀⢠⣤⡄⠁⠀⠆⠘⠇⠙⠂⠉⠀⠉⠈⠉⢀⠀⠀⠂⡈⠀⠉⠐⠂⠠⠂⡀⠀⠀⢶⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠾⡿⠂⢸⣿⣿⣿⠀⠀⠀⠀⠋⠛⠆⠀⠈⠑⠀⠀⢠⣴⣶⠄⠀⣠⣤⣶⣶⣦⡈⠀⠀⠀⠆⠀⠁⠈⠀⠆⢠⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⠈⠻⡿⢛⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣠⡄⢾⣿⣿⣿⡿⠟⠁⡀⠐⠠⠀⠀⠀⡅⠀⠀⠰⠀⠸⡧⢯⣍⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⣤⣤⣤⣤⠀⠤⠤⠤⠤⠤⠤⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⠀⠒⠒⠒⠒⠒⠒⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⠀⣉⣉⣉⣉⣉⣉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠿⠿⠥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣰⣆⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⣉⡉⢻⠀⠀⡟⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⠠⠭⠭⠭⠭⠭⠭⠭⠄⢸⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠛⠛⠛⠐⠒⠒⠒⠒⠒⠒⠒⠂⢸⠀⠀⡇⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣼⠀⠀⣧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣻⣿⣟⣉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⣉⣻⣿⣟⣉⠉⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿