Chemical Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀
⠀⠀⠀⢀⡬⠀⠀⠀⠀⡤⠤⢤⣀⣤⠋⠉⢧⠀⠀⠀⠀⠀⠀⠀⢀⡬⠿⠓⠒⠒⠀⢶⠠⠦⠀⠒⠒⠒⠂⠸⠚⠰⠔⠓⠀⠈⠐⠥⠾⠃⠆
⠀⠀⢰⣡⣷⡄⠀⠌⠀⡇⠀⠀⢸⠛⢤⡀⢈⡄⠀⠀⠀⠀⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⢠⣤⣤⣤⡄
⠀⠀⠀⠀⡟⠾⠀⠀⠀⣸⣤⠒⡛⠉⠉⠉⢫⡏⠉⠒⢄⠀⠀⠀⠀⠀⠀⣀⠤⠄⣀⠀⠀⣠⠀⢱⠚⠛⡋⠀⠀⡟⠑⢲⠁⢰⡄⠀⢀⡀⢀
⠀⠀⠀⡘⣇⠀⠀⢠⠎⠀⠈⠲⡇⠀⠺⠂⠀⡗⡄⢀⠜⠀⠀⠠⠈⠀⠀⣷⣖⣚⡿⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⡇⠀⡺⠀⠀⠀⠀⣈⠟⠁
⠀⠀⠀⠙⢡⣀⠀⠈⠢⣤⣀⣀⡏⢢⣄⣀⣸⠴⠚⡇⣀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡇⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⡇⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⡿⣥⠀⠀⠈⠀⠈⡏⠁⠀⢉⡗⠤⠴⠃⠁⠀⠀⠀⠀⠀⠀⡶⡀⠀⢃⠀⠀⠀⠀⠀⣷⣦⡇⠀⠀⣷⣶⡇⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⡄⠹⡀⣀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠂⠀⠈⠳⡄⠀⠀⢰⣿⣿⡇⠀⠀⣿⣿⣧⠀⠀⣠⡀⣿⡄
⠀⠀⠀⠀⠀⠯⢣⡀⠀⠀⠀⠁⠀⠈⠁⠀⣀⣀⡤⠖⢆⠀⠀⠀⠀⡜⠀⠀⡀⠀⠀⠀⢸⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡗⡄⠀⠀⠀⢠⠚⠛⠋⠉⠁⠀⠀⠘⡄⠀⠀⠀⠙⠲⠤⠶⠖⠒⠚⠉⠀⠀⠘⣿⣿⡇⠀⠀⣿⣿⣟⠀⠀⡀⣨⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⣄⣀⣠⣄⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠙⠛⠁⠀⠀⠁⠉⢾
⠀⠀⠀⠀⠀⣀⠄⠀⢀⣦⠴⠶⠟⠋⠉⠀⠈⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀⡀⢀⣠⠀⠀⣠⡀⠀⠀⣠⣿⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠘⡀⠀⠀⠀⠀⠀⠂⠀⢳⠀⠀⠀⠀⢱⠀⠀⣦⣰⢴⢀⡀⠐⠘⠟⠢⠀⠀⠁⠈⠓⠘⠙⠘⠁⠈⠁⠀⠀⠈⠿⠁
⠀⠀⠀⢀⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆⠀⠀⠀⠀⠀⢰⢴⣔⠀⡠
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠁⠃⠀⠀⠀⠀⢸⠁⠈⠁⠐
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠋⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠊⠑⠦⡀⠀⠀⢀⠔⠉⠑⢄
⠀⠀⢀⢀⣧⣀⠀⡆⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡀⠀⠈⠋⣀⣀⡠⠊⠀⠀⠀⠀⠈⠲⡔⠁⠀⠀⠀⠀⠑⠂
⠀⠀⠘⠈⡇⠀⠀⠱⡀⠀⠀⠘⡀⢀⣠⠤⠒⠒⠒⠉⠁⠀⡔⠐⢠⠉⠀⡂⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢰⢳⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⡗⠀⠀⠀⠙⢆⡀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠈⢃⢠⠆⠐⢆⠛⠐⠄⠀⠀⠈⢆⠀⠀⠀⠀⠀⡄⠀⢇
⠀⠀⢠⠄⡷⠴⠀⠀⠀⠀⠉⠒⠦⠤⠤⢠⡄⠀⠀⠀⠀⠐⠉⢤⠀⠂⢸⣦⠊⠀⠀⠀⠀⢈⠶⠶⠤⠤⠴⠀⠀⡼⠒⠂⢉⣭⣤⡀
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠢⠤⢸⠲⣐⠃⠀⠀⠀⢀⠀⠠⠋⠀⣔⣭⡱⠀⠀⠜⠁⠀⠀⠨⣿⣺⡟
⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⠀⠀⢘⠃⠀⠀⠈⠒⠉⠁⠀⠀⠠⠀⠀⠀⠀⠀⠣⣛⣛⠀⠀⠀⠀⠿⠀⠀⠈⠉
⠀⠀⠀⣉⡟⠉⠉⠉⠉⢉⣉⠉⠉⠉⠉⢉⡉⡍⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠠⠆
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣒⣛⣩⠭⠭⠭⠭⠭⣝⣓⣲⣶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡐⠫⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠨⠿⢈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡇⠀⠀⠀⠉⠉⠉⠉⠉⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠁⣀⠀⠀⡀⢀⠀⠀⢀⠀⡀⠙⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣵⠋⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢱⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡜⠙⠠⠤⢤⣤⣤⣠⣄⣤⠤⠤⠤⠄⠀⠀⠘⣎⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠎⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢣⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣣⠋⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠳⡀
⠀⠀⠀⠀⠀⠀⡴⡱⠃⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⡄
⠀⠀⠀⠀⢀⡜⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⣄
⠀⠀⠀⢀⢎⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⢆
⠀⠀⣠⢫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢦
⠀⡰⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢣⡀
⠘⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡁
⣷⣵⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣱
⠱⢌⡓⠪⠭⣵⣒⣂⡤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠴⣒⣒⣫⠭⠕⢋⡵
⠀⠀⠉⠓⠢⠤⠤⣌⣉⣉⣉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢋⣉⣉⣩⡥⠤⠐⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣯⣭⣤⣤⣦⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⢸⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⣧
⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢾⣷⣿⠟⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡙⢿⠗⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⣠⠞⠁⢠⣤⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠂⠀⠀⠀⠀⢀⣴⣁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠹⡄
⠀⢰⠃⠀⠀⠈⠉⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠒⢀⡀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡀⠀⣀⣀⡀⠀⠘⣆
⠀⢸⣿⣿⡿⢶⣤⣄⣀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠉⢹⠅⠀⢉⣓⠋⠙⣆
⠀⠘⢿⣿⣷⡾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠐⠿⠇⠀⠀⠀⢿⣿⠆⠀⠘
⠀⠀⠀⠙⠿⢿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⢹
⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠭⠭⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⢸⣿⡟⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣂⡃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠘⠻⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠒⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⢼
⠀⠀⢀⣀⣀⣀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠤⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣹⣿
⠀⠀⠀⣰⣿⣖⣚⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠍⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣹
⠀⠀⠾⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣂⣀⣀⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣛⣛⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⣀
⢇⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠑⡧⣄⡼⡗⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣼⠁⠀⣈⡦
⠈⠑⢄⠀⠀⢀⢔⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢶⢺⠟⠛⠛⢿⢲⠾⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⣌⡦⠤⢽⠥⠤
⠀⠀⠀⢱⢰⠁⠈⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠣⣄⣰⢻⣄⠛⢁⣼⢳⣀⡤⠛⠀⠀⠀⠀⠀⠀⠀⠒⢺⠖⠒⢾⠀⠀⡤⡇
⠀⠀⠀⢸⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⣍⠿⢏⡏⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⢀⠗⠒⠚
⠀⠀⠀⠘⠟⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠱⣀⡰⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⠀⡀⠀⠒⠒⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠉⠁⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⣄⡀⠘⠛⠒⠢⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠸⠧⠀⠀⠛⠁⠅⠀⠀⠀⠀⠀⠀⠐⡞⠯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠂⠃⠈⠀⠀⡀⠈⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⡀⠒⠚⠀⠀⠀⠀⠀⠀⡑⠀⠈⢁⣒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢍⠉⣀⣀⣤
⠀⠀⠀⠀⠠⠀⠀⠀⣀⠄⠀⠂⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⢰⡏⡐⠀⢀⡁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠹⣭⠤⢤⣤⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠹⢦⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠘⣇⢀
⠀⠀⠀⡠⡿⢀⠋⠘⠓⠒⠛⠛⠛⠚⢛⠳⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠀⠀⠀⠀⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠈⠉⠉⠉⢾
⠀⠀⠀⠃⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢
⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠀⠐⠀⠀⠀⠀⠚⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠸⠇⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⣧⣀
⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⢸⣶⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⠗⠀⠀⠉⠉⠀⠀⠀⠀⠑⠄⣀
⠀⠀⠀⠀⢀⠻⡶⠄⠀⠀⠙⡿⠉⠀⠀⣀⣀⣉⣣⡀⠀⠀⠀⠀⠀⢀⠎⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⠖⢲⡶⣲⣦⣄⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠡⠌⠡⠈⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠘⢠⣦⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⢀⠿⠀⠀⠀⠀⠀⠈⠫⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣄⢀⡀⠀⠀⠀⠀⠀⠀⡎⠨⡆⠀⢀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⢙⡋⠉⠙⣯⠀⠀⠀⠀⠀⠀⠀⠓⠰⡛⣀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠇⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⢀⠔⢺⣼⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣀⠀⠒⠘⠀⢄⡀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠐⠿⠶⠶⠶⠶⠶⠶⠿⠖⠀⠀⠀⠀⠈⠀⠐⠂⢤⣄⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠂⣨⡤⠖⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣧⣤⣚⣡⠤⢀⣀⣀⠀⠀⠀⠀⢀⣠⢴⡶⠾⠗
⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⠘⣿⡟⠋⠀⠀⠀⠈⠉⠉⠈⠛⠒⢶⣖⣾⣿⡿⠊⠀⠀⠀⠀⠀⠀⣏⢈⡧
⠀⠀⠀⠀⠀⣠⣾⣤⠀⠀⠀⠙⢧⡀⠀⠀⣰⠟⣦⠀⠀⠀⠀⠀⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉
⠀⠀⠀⠀⣠⣿⣿⡿⣧⡀⠀⠀⠀⠉⠙⠛⠁⠀⠘⢧⣄⣀⣀⠼⠛⠁⠀⢠⠔⢦⣀⣀⡔⠈⣯
⠀⠀⣴⣾⣡⣁⣘⡆⢈⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠦⠜⠁⠀⣸⠖⠛⢢⠎⢳⡄
⠀⠀⣿⣳⣷⣾⡿⣥⠄⢸⣿⠇⠀⠀⠀⠀⠙⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣹⡆⠀⠈⠓⠚⠁
⠀⠀⠈⠛⠻⠿⠿⠿⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⣶⠶⣶⠆
⠀⠀⠀⠀⢿⠿⠟⠘⡿⠿⡇⢻⢿⣿⠀⡟⠋⡗⢘⣿⣿⠃⠀⠀⠀⠀⠀⣨⣤⣤⣀⠀⠀⡇⠀⢸
⠀⠀⣠⣆⣺⣶⣇⢀⡇⠀⡇⢸⣿⢉⠀⡧⣤⡇⢸⡏⠉⢰⣦⠀⠀⠀⠀⠹⠓⠛⡏⠀⠀⡇⠀⠰
⠀⠀⠺⣿⢻⣟⣃⡴⣷⢶⣣⡾⠿⡞⠀⠓⡶⣃⠘⣷⣾⣋⡇⠀⠀⠀⠀⠸⠀⠀⡇⠀⡰⠀⠀⠀⢀
⠀⠀⢚⡏⣿⠟⡏⠈⡟⠛⡇⢸⣿⠉⠀⡟⠉⡏⢸⠋⠙⢹⡇⠀⠀⠀⠀⢠⠀⠀⡇⢠⠁⢀⠀⠀⠈⠄
⠀⠀⠀⡗⢸⠀⡇⠀⡇⠀⡇⢸⣿⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⢀⡼⠀⠀⢧⣾⠛⠛⠠⠒⠟⢳
⠀⠀⡄⡇⣀⠀⡇⢀⡇⠀⡇⢸⡿⢠⠀⡇⠀⡆⢸⠀⢰⢸⣇⠀⠀⣔⣁⣀⡀⠀⠀⡈⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠥⣧⣤⢀⣇⢀⣇⣠⡇⢸⠇⢘⠀⣧⢀⡇⢸⡇⢸⣸⡇⠀⢸⣿⡖⠒⠂⠐⠒⢲⣿⣧⣤⣤⣜⣿⡗
⠀⠀⠴⣏⣹⣿⣷⣀⣙⣛⣛⣈⣻⣏⣀⣙⣿⣓⣈⣻⣿⣎⣧⠀⠈⢿⣧⣠⠀⠀⢰⣴⡟⠉⠉⠉⠁
⠀⠀⠰⠋⠉⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠻⠄⠀⠀⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠢⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⡤
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠄⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠷⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳
⠀⠀⠈⠀⠀⠀⠈⠀⠼⠀⡁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢼⠉⣧
⠀⠀⠈⠐⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡍⠃
⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⣀⢄
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀

⠀⠀⠀⠀⣀⡀⠀⠐⠂⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣂⠀⠀⠀⣴⣀⡆
⠀⠀⠀⢸⠀⠘⠛⠛⠛⠛⠀⢸⠀⠀⠀⠀⠀⠀⡦⢄⣀⡀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠉⣉⢹⠄⢶⠀⣏⣷⢃
⠀⠀⠀⢸⠠⣤⣤⣤⣤⣄⣠⢸⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⢸⠀⢸⠀⠈⡒⠏
⠀⠀⠀⢸⠘⠛⠛⠛⠛⢉⠉⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⢉⢸⠀⠰⠀⠀⠘⡿
⠀⠀⠀⢸⠀⢘⣛⣛⣛⣉⣀⢸⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢸⠀⢸⠀⡆⢸⠷⡃
⠀⠀⠀⢸⣀⣈⣉⣉⣉⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠿⠿⢿⡀⣼⠀⡀⠸⡟⢻

⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⣟⣟⣻

⠀⠀⠀⢰⠒⠒⠒⢢⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠈⠋⠉⠉⠁⡇⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠄⣤⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡤⠚⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢠⣤⣄⣠⣤⡄⢠⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣷⡾⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⢀⠔⠁⠀⠀⠁⠢⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠸⣿⣿⡟⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⢠⣿⣿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⡟⣸⣿⣿⠀⠀⠀⢻⣿⣿⣯⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⣴⣿⣿⣿⣿⣄⠀⠀⠀⠱⢽⣛⣛⣛⣛⣛⣛⣛⡫⠊⠀⠀⠀⠹⢿⣿⣿⣧⣿⣿⠟⠀⠀⠀⠀⠛⠿⢷⡿⠟⠋⠀⠀⠈⠾⣿⣿⣿⣿⣿⣿⣿⣿⠫⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡿⡏⠀⠻⣿⣿⡃⠈⡿⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢐⡇⠀⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠃⠀⠐⡇⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣥⣤⣼⣧⣤⣧⣤⣼⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡇⠀⢳⣶⣾⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⡟⠛⢻⡟⠛⡟⠛⢻⡟⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣷⡇⠀⣿⣿⣷⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣷⣿⡇⠀⣿⣾⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡇⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⠇⠀⢿⣿⣿⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⠇⠀⠸⣿⣿⠃⠀⢿⣿⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣷⣶⣶⣶⣿⣷⣶⣶⣾⣿⣶⣶⣾⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⣠⠖⢉⠗⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡇⠀⠀⠀⣠⠞⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣇⣸⠓⠒⢦⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠉⠉⢀⡴⢁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢳
⠀⠀⠀⡴⠒⠲⢄⣀⣀⣀⣀⣀⣀⣀⣞⡀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢶⠋
⠀⠀⢸⠀⠀⠀⣸⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⠆⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠑⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠖⢺⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡉⠀⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⣻⠆⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣦⠤⠤⣄⡀⢀⡴⢋⡴⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢳⣼⡆⠀⠀⠙⣯⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⡟⣷⣤⠴⠋
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴
⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠈⠀⠴⠂⠉⠒⢊⡉⠕⠀⠢⠢⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⠀⠀⠀⡀
⠀⠀⠀⠈⠈⠀⠀⠀⠄⠤⠠⠀⠄⡄⠠⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠠⠀⠀⢀⡀⡀⣀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣍⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠠⡐
⠀⠀⢿⣿⣿⣿⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠥⠎⠃
⠀⠀⠀⠉⠉⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡄⢦⠦⡖⢲⣆⠔⠀⡖⠐⠖⠂⠠⢰⠀⠐⢦⠀⠒⠀⠀⠀⠐⠠
⠀⠀⠠⣶⠒⣲⠆⢲⡶⢶⠄⣶⠀⠀⠀⠀⠸⡀⣸⡄⡆⡞⠸⠀⡧⡏⣬⢩⠁⢼⡬⠀⠀⠸⠄⠘⠃⡀⠀⠀⠠
⠀⠀⠂⠘⠃⠋⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠈⠀⠈⠉⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⢀⠀⠄⠀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣾⣻⣷⣄⠀⠀⠍⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⡉⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠠⠀⠀⡄⠀⡇
⠀⠴⠾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠰⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡂⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⡠⠁⠀⠀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠴⣄⡀⠀⠐⠂⠀⠈⠁⠡⠐⠤⡀⠀⠀⠀⠀⠠⢀⣀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⣀⡠⠤⠐⠊⠁⢊⠀⠠⣂⠉⢐⠄⠀⠉⠑⠦⣄⡀⠀⠁⠂⠀⠀⠉⠑⠢⠀⠀⠈⠀⡀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠂⠂
⠀⠀⠘⢧⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀⠀⡀⠀⠀⢀⠇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢀⣀
⠀⠀⠀⠀⠙⠆⠀⠀⠈⠀⠀⠄⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠊⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡤⢀⡄⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡇⢠⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠄⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣒⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠒⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠈⠤⠤⠤⠬⠥⠁⠠⠤⠤⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⢀⠈⠐⢀⠀⠀⡄⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠤⠄⠈⠀⠐⠂⠄⠆⠐⠀⠀⠀⠀⠀⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠂⠀⠀⠰⠀⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢈⡔⠘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠜⠀⠁⠉⠉⠉⠜⠀⠉⠉⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⢤⠀⠀⢠⠤⠄⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡀⠀⢀⠀⠀⢀⡀⠀⢀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠈⡁⠁⠀⠀⡆⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢘⠀⠀⢐⡃⠀⢘⡀⠀⢘⡃⠀⣚⠀⠀⢘⡂⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⠀⠠⠀⡀⠀⠁⠀⠀⠀⠁⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠈⠇⠀⢸⠀⠀⠀⡇⠀⢹⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠁⠙⠀⠀⠀⢤⠀⠀⠙⠀⠀⠀⠀⡇⢸⠀⠀⢀⠀⠀⢈⢈⠁⠀⡆⠀⢸⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⢀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⡀⠂⠁⠀⠀⡇⢸⠀⠒⠐⡄⠀⢸⠀⠀⠀⡇⠀⢸⠀⠒⢂⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠈⠉⠉⠉⠀⠐⠀⠀⠀⠀⡄⠀⠚⠀⠀⠀⡇⠈⠧⠤⠤⠁⠀⠀⠦⠤⠔⠁⠀⠀⠦⠤⠜⠀⢸
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢂⡀⠀⠀⠀⠀⢀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠁⠤⠤⠠⠄⠤⠤⠤⠤⠤⠠⠄⠄⠀⠤⠀⠀⠀⠈⠤

⣾⣿⣷⣾⣶⡷⢿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣷⣶⢷⡶⠶⣶⠶⠶⣶⡿⠶⠷⢾⠷⠶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢤⠤⢷⢶⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢳⠘⡸⡆⠀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⡇⠀⠀⠀⢤⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⢾⢾⠶⠶⠶⠶⠿⢶⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⡅⡆⠀⠀⠲⣗⢸⣿⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⣧⡶⠿⠶⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢃⢰⠀⢀⣀⢒⢸⣿⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠶⠆⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣿⡇⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⡸⡄⠀⠤⣤⢸⣿⠀⠀⠀⠀⠀⢸⣠⠤⠤⢤⣤⠤⢤⠤⢤⣼⠀⠀⠀⠀⠀⠀⠀⣿⡇⠒⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠇⣇⠀⠀⠭⢸⣿⠀⠀⠀⠀⠀⠈⢿⢦⡀⠈⠚⣤⡘⢃⢞⡟⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣲⣤⣼⣧⣬⣤⣴⣫⠞⠀⠀⠀⠀⠀⠀⠈⠓⢿⣶⣦⣿⣾⠵⠋⠀⠀⠀⠀⠀⠀⢠⣾⣻⣧⣤⣴⣿⣳⣄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⠶⠖⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣉⣉⣉⣉⣉⣉⣉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠒⠒⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⠉⠉⠉⠉⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠦⠤⠤⠤⠞⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠤⠤⢤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣎⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠈⣉⣿⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢀⣐⣳⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢀⡚⣧⢿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠤⠼⡜⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠰⣏⡷⠀⢾⠆⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠠⠬⢿⣹⣧⠀⠀⠀⠀⠀⠀⠈⣯⢧⠀⠀⠀⢶⡦⢰⣦⠀⠀⠀⠀⠀⣠⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣹⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⠤⣀⣀⣀⣀⣀⣀⣀⣀⡠⠔⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⡤
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠀⠀⣀⣀⡀⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⠇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠐⠂⠣⢄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⡇⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡷⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣷⣿⡿⠫⠊
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢻⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣟⠉⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⣿⣿⣏⣿⣏⣿⣿⣿⣿⣿⣿⢯⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⡣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢄⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠀⡀⡼⠿⠄⠀⠀⠀⣠⠤⡤
⠀⠀⠀⠀⠀⠘⢶⢿⣿⡽⠿⣿⣿⠀⢠⠀⠀⠀⠀⣠⡞⡇⠀⣠⣶⣴⣾⡟⢦⡀⠀⠀⠈⠻⡵⠃⠀⠀⠀⠈⣁⣨⣦⠤⠤⠤⠴⠶⠒⠊
⠀⠀⠀⠗⠀⠀⢸⢷⠀⠀⠀⢽⣿⠀⠀⠀⠀⠀⣰⡷⠛⡄⠀⣻⣿⢟⣽⡓⡆⢳⠘⠤⡀⠀⠀⠀⠀⠀⠀⡎⢉⠁⠈⠲⣄⠀⣎⠀⡶⢀
⠀⠀⠀⠀⠀⢀⠎⢌⠀⠀⠀⣼⢺⠀⠀⠀⠀⠀⡷⠒⠚⣃⣀⠈⠉⠛⠶⠞⣁⣸⠀⠀⠀⠀⠀⢰⠶⠰⡶⠙⢄⠀⠀⠀⠀⠳⡀⠀⠀⠉
⠀⠀⠀⠀⠀⡜⣀⣬⣅⣤⣴⣶⣼⡆⠀⠀⠀⠀⢱⡀⣾⢋⣩⣳⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⡰⠚⠋⠑⠒⢿⣄⡐⣈⢀⡧⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠐⠅⠑⢌⡻⡿⠟⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⢀⡀⣧⡀⠐⠊⠀⠁⠀⠻⡉⠉⠀⠈
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡠⣒⢦⡀⠀⠀⣈⠉⠉⠉⠉⢁⡤⣄⠀⠀⠀⠘⠛⣈⡶⠟⢛⡓⢶⡒⠒⠒⠚
⠀⠀⠀⠀⠘⢿⣿⣛⣿⣿⣿⣿⠿⠟⢱⢹⠧⢗⡇⠀⠸⣱⠗⠀⠀⠀⠘⠢⠚⠀⢰⣲⡀⠘⠉⠀⠐⠀⠀⠀⢱⠀⠀⠀⠖⠫⠰⠄⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠉⠀⣀⠀⢀⣀⡀⢀⣤⡘⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⢀⡞⠉⠀⢸⡄⠴⡀⢸⠤⠄⡰⣆⠶⡀⢸⠀⠸⢄⠀⠀⣏⠀⣤⢴⡁⠀⡏⠁⠀⠈⠉⢿⣾⡟
⠀⠀⠀⠀⣦⢴⢠⡆⣶⢠⠀⡄⣄⡄⣀⠈⠦⠤⠄⠘⠀⠀⠃⠘⠒⠀⠁⠉⠀⠁⠘⠀⠐⠋⠀⠀⠁⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠃⠈⠈⠀⠁⠈⠀⠀⠋⠃⠛⠰⠀⠀⠀⠀⢀⡀⢀⣤⣤⠀⠀⢀⣤⡀⢀⠀⢀⣤⣤⡄⣀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠲⠲⠶⢤⣀⣀⣀⠀⠀⠀⠀⢼⠀⢸⠀⠀⢸⠉⣿⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠘⠁⢸⠿⡏⠉⠉⢩⠉⡇⠈
⠀⠀⠀⠀⢀⠠⠄⣰⠋⠀⠀⠀⠈⠁⣀⢹⣇⠜⠁⠀⠀⠀⢹⢶⣾⠀⠀⢸⠀⣿⠀⠀⠀⣿⣿⡇⢸⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠠⡇⡇
⠀⠀⠀⠀⠀⠁⢠⠃⠀⠀⢀⠀⠀⣪⡽⠟⡇⠀⠀⠰⢶⡶⢾⣾⣿⠶⠶⢾⣷⣿⠶⠶⠶⣿⣿⡷⢾⠖⠀⢻⡟⠀⠸⢉⣇⣀⣄⣼⣥⡇
⠀⠀⠀⠀⠀⡴⣻⣄⣐⠬⠔⠚⠉⠀⡴⢡⠇⠀⠀⠀⠀⡇⢸⣿⣿⠀⠀⠸⣿⡇⠀⢀⣀⣿⣿⣇⣸⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠛⠉⠙⠦⣀⣀⢀⣀⡠⠞⢁⣤⣤⠀⠠⢼⡷⠾⠿⠿⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⣦⠀⠀⠈⠻⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣭⣥⠀⠀⢸⠸⡮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣉⠇⠀⣀⣸⡋⠙⣳⠀⠀⢄⢀⠤⠒⢤⣌⣀
⠀⠀⠀⠀⠬⠁⠀⠴⢒⡚⠿⢍⣹⠋⢹⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⡷⠀⡀⠀⣡⠶⠛⠉⣂⠝⣀⡇⠀⠀⢰⠃⣠⣀⣀⠺⣗⠂
⠀⠀⠀⠀⠀⢠⠲⡛⠛⣻⠉⣇⠀⠐⠸⠀⠀⠀⢚⢠⠒⠁⢢⣴⠶⠺⣄⣀⠜⠀⠈⠉⡼⠋⡠⠞⠉⡝⢀⣽⠀⠀⠐⢸⠀⣧⡄⡞⣶⡟⠂
⠀⠀⠀⠀⠀⢸⠀⣉⠁⠀⠀⡇⠀⣀⢀⡇⢠⠀⠀⠉⠦⠤⠞⠀⠀⠀⠀⠀⠀⠀⠠⢸⠁⡼⠁⠀⣶⡇⢸⣧⣄⠀⠀⠁⠳⣼⡕⣷⢟⠑
⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⢇⠀⠀⠀⡇⠀⠿⠃⠀⣀⣤⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⠀⢇⡀⠀⠙⣤⡿⠜⠁⠀⠀⠀⠀⣸⢳⣇
⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⢸⣀⣀⡡⠜⠀⠀⢀⣼⣿⣏⣀⣰⣿⣃⣴⣮⣱⠀⠀⢿⠀⣶⣯⠙⠓⢻⡖⢢⡀⠀⠀⠀⠀⣿⣿⣿⢀⢀
⠀⠀⠀⠀⠀⢸⣀⡠⠤⠤⠤⠼⠁⠀⠀⠀⠀⠚⢻⣷⣆⠀⠀⢹⣷⡄⠉⠉⠁⠀⠀⠈⢷⣬⣅⣀⣀⣀⣱⠞⠀⠀⠀⠐⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⡷⣧⣤⣝⣶⠃⠀⠀⠀⠀⠀⠀⠀⣀⠛⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠰⠀⣰⣁
⢀⡜⠁⢰⣿⣞⠈⢦⡀⠀⠀⠀⠀⢐⣶⡿⠁⠀⠀⠀⠀⠈⠉⠙⢿⣷⣼⣿⡆⠀⠀⠀⠀⠀⠀⡼⡿⢿⠃⠀⠆
⠮⢴⣎⣀⣉⣀⣱⣆⣳⠀⠀⠀⢦⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢴⠦⠄
⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡀⠀⠀⢆⠀⠀⠀⣄⠀⠀⠀⡠⠋⢹⣿⡟⠑⢄⠀⠀⠀⠀⠀⢀
⠘⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠁⠀⠀⡇⠀⡱⠀⠀⣀⠀⠀⠀⢁⣤⣄⣽⣡⣤⣌⡀⠀⠀⠀⠀⠸⣷⠆
⠀⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠈⠑⠁⠈⠲⠀⠀⠁⠉⠀⠀⠀⠺⡿⠋⠀⠙⠿⡟⠀⠀⠀⠀⢀⣤⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐⠊⠁⠀⠀⠀⠀⠸⠿⣿⡿⠗
⠀⠀⠀⠀⡄
⠀⠀⣶⠀⡄⠀⠔⡀⠀⠀⠀⢀⣘⠁⣤⠀⠀⠀⠴⠀⠀⠀⠀⠀⠐⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣷⠀⡇⠀⠰⠇⠀⠀⠀⠘⠛⢄⣀⠶⠀⡶⠀⡀⠀⠀⠀⠀⠰⠿⠿⢆⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣶⠦
⠀⠐⠛⠂⡃⠀⢰⡆⠀⠀⠀⢀⣤⠜⢻⠂⠘⠛⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣰⣄⣀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠉⢀⡘⠗⠀⠀⠁⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⡆
⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢶⣤⣴⣧⣄⠀⠀⠀⠀⠀⠀⢀⠉⢁⡘⠙⣀⠛⢃⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣆⠀⠀⠀⢀⢞⡟⠉⠉⢙⠲
⠀⢰⣏⣠⣟⣀⡀⠀⠀⠀⠀⠸⠉⠉⠉⠈⠉⠁⠘⡃⠀⠀⠀⠠⣾⣷⡇⠀⣸⣿⠀⠀⠀⣤⠞⠳⠄⠰⠚⠳⡇
⠀⠀⢉⣿⡋⢉⢹⠆⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠂⠂⢿⣿⣿⠿⠃⠀⠀⠀⠠⡀⡀⢸⡀⣠⠀⠄
⠀⠀⠀⠙⠛⢻⡟⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣠⣶⣾⣿⣿⣶⣶⠀⠀⠀⠀⠈⠛⠋⠉⠑⠈

⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠒⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣞⣀⣈⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄
⠀⠀⢠⡞⠙⠉⠉⠉⠉⠀⠈⠉⠉⠉⢏⠃⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠒⠢⠴⠦⢄⣀⣀
⠀⠀⠠⡟⡀⠀⠤⠀⠀⠀⠀⠠⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠑⠒⡄
⠀⠀⠐⠑⡀⠀⠀⠀⠀⠀⠀⠉⠉⢁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⣠⡇
⠀⠀⠀⠈⠊⠢⠄⢀⡀⢀⣀⠀⠀⠁⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠉⢇⠀⢀⠠⠂⢈⠢⠀⢃⠀⢀⠀⠀⠰⣗⠀⠀⡠⠀⠀⠀⢪⡆⠀⠀⢀⡄⠀⢠⡄
⠀⠀⠇⡀⠁⢀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠑⠐⢤⡚⡤⠀⠀⠀⠂⣧⢀⠄⢠⠄⠁⠰⡈⠠
⠀⠀⠀⠀⠀⠈⠈⠁⡇⠈⠀⠀⠁⠐⠈⠐⠀⣀⣉⣃⡄⡀⡞⠀⠈⢇⡀⢸⠈⠀⠸⠁⠸
⠀⠁⠀⡀⠀⠀⠠⠤⠅⠤⢄⠀⡄⠂⠢⠀⠀⠐⠒⠄⠋⠇⠑⠀⠀⠁⠀⠈⠀⠂
⠚⠓⠚⠓⠚⠒⠒⠒⠒⠒⠚⠒⠛⠒⠚⠒⠚⠒⠒⠒⠒⠚⠒⠂⠀⠀⠄⠀⠆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠢⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⢂⣔⣒⣄⣀⠒⢒⠒⠒⡒⠒⠶⣤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢒⣡⣄⠊⠁⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠁⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠛⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠀⠛⢋⠉⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠹⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⡽⢁⡾⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⢧⠀⠀⠁⠀⠀⠀⠀⠀⠸⡎⣧⢸⡷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡇⠀⢠⣴⣾⡇⠀⡞⠀⠀⠀⠀⢀⣄⡀⠀⣤⣴⢂⣼⠃⠀⠀⠀⠈⠘⣆⣴⣿⣀⡰⠄⠀⠀⣿⣿⠈⠁⠀⠉⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣾⠸⣿⡏⠀⢿⣿⣿⡇⠀⡇⠀⠀⠀⣠⡿⣽⣹⣿⣿⣿⡜⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⣿⠦⠄⠀⢸⣼⡆⠀⠀⠀⠸⠿⣇
⠀⠀⠀⠀⠀⠀⠀⢻⣆⢻⣇⠀⠘⣿⣿⡇⠀⣿⠀⠈⠈⠉⠁⣽⣿⠋⢿⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⢎⠻⠆⠀⠀⡀⠀⢸⡏⡇⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⠀⠀⠘⣿⣧⠀⣿⡆⠀⠀⣄⠀⠀⠀⠀⣻⣯⠀⠀⠀⠀⢀⢿⠷⠀⠀⠀⠁⢰⣶⠟⠁⠀⢸⣿⠇⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢻⣿⠀⣿⠘⠀⠀⠘⠳⣶⡆⠀⢻⠃⠀⣠⠶⠛⠉⣉⠀⠀⣤⣤⡈⠳⣅⠀⠀⠀⢸⣿⡇⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⢸⣿⡆⣿⠀⠀⠀⠀⠀⡼⠃⠀⡙⠀⡾⠃⠀⠀⠾⣿⡛⠃⠀⣻⡷⠀⢹⡄⠀⠀⢸⣿⣷⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣸⡟⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠳⠿⠇⢠⣦⣙⣿⠃⠀⠃⢀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣴⣿⣿⡇⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⠿⡿⠛⠁⠀⠀⢀⢺⠄⠀⡟⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡍⢿⣿⣧⠀⠘⠁⠙⣾⣧⠀⠀⠀⠀⢀⡁⡅⠩⢿⣿⡇⣸⣿⡒⠂⠀⢸⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⢿⣆⠀⠀⠀⠻⣿⣧⡀⠀⢠⢠⡄⣴⠶⢿⠟⣿⣿⣝⣧⣉⣀⡌⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠸⡆⠹⣆⠀⠀⠀⠈⡿⢿⣶⣤⣠⣤⡤⢲⠛⢷⠽⠉⠈⢿⠻⠋⡴⠁⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⡄⠀⢷⠀⠈⠓⢦⣄⠀⠙⠚⠿⠻⣿⡏⣳⠸⣆⠀⠀⠀⠀⠸⢳⠏⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠁⠀⠈⢧⠀⠀⠀⠙⠦⣀⣀⣀⠀⠈⠿⣿⣷⣤⣉⣁⣠⣤⣠⡟⠀⠀⠀⢀⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⣀⣀⣉⣡⠀⠤⠖⠉⠀⠀⠀⠀⠈⣿⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⢰⣠⠃⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⠇⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⡟⡀⠀⠀⠀⠀⡰⠟⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠆⠀⡿⠀⢸⡏⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠈⢰⡇⢀⠀⠀⠀⠀⠀⠈⠻⣿⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⢿⣇⣴⡄⠀⠀⠀⠀⠀⢸⣿⣿⠀⢠⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⠀⠀⠀⠈⠻⡿⣧⠀⠀⠀⠀⠀⠈⠃⢻⣶⣿⡀⡄⠀⢀⣤⣄⠀⢀⠀⠀⠀⠀⠀⡘⣧⠀⠀⠀⠀⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠙⠎⠻⢿⣴⡿⠁⠙⠻⣾⠉⠙⠂⠀⠀⠹⡿⠀⠀⠀⣸⠇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠋⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠘⠋⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠘⠧⠀⣤⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⡀⠀⠀⠀⠀⠈⠻⢿⣾⣷⣤⣘⣦⡀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⡷⠒⠛⠁

⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢀⡀⢀⠀⡀⠀⠀⠀⢀
⠀⠉⠀⠀⠀⠀⠰⠶⠀⠀⠀⠘⠄⠺⠃⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠉⠀⠀⠀⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠘⢂⡀
⠀⠛⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⠀⠀⠀⠀⠀⠉⠀⠁⠈⠀⠁⠀⠉⠀⠀⠠⡰⢤⡞⠁⠀⢦
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠈⠁⠈⠀⠀⠀⠀⠀⢠⠀⠀⠉⠂
⠀⠐⠲⢀⠈⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠈⠃⢀⠘⢤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⣠
⠀⠀⠀⠀⠤⠀⡄⠀⠄⠀⠀⠀⠺⠗⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⠂⠀⠐⠂⠓⠀⠀⠻⠉
⠀⠀⠀⣀⣀⠀⠀⠀⠤⠀⠃⠀⠀⡀⠀⠀⠘⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉
⠀⠀⠀⠋⠉⠀⢸⣄⠀⠉⠒⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡂⠀⢔⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠏⠙⠀⠒⠀⠀⠀⠀⠀⠀⠦⠀⠁⠀⡀⠀⠃⠀⠀⠀⠀⣠⠰⢶⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠐⢄⡀⠈⠉⢁⠀⣀⡆⢠⣤⣶⡄⠀⡁⠀⠀⠈⠁⠀⣤⠹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠈⠷⠶⣶⡦⠇⠀⠀⠙⠑⠀⠀⠘⠋⠉⠁⠀⠁⠀⠐⣄⢛⡆⠘⠂⠀⠠⠆⠒⠚⠲⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠢⠀⢀⠀⠀⢠⡀⠀⠈⡄⠀⡀⠀⣰⠃⣹⠶⢤⡦⢸⣿⠷⠈⠁⠀⠀⠀⠀⡀⠐⠂⠐⠒⠓⠂⠀⠰⢀⠸⠂⠘
⠀⠀⠀⠁⠀⠀⠛⠁⠀⠀⠹⢼⡈⠀⠈⠉⡀⠀⠘⠓⢁⡁⠀⠀⠂⠀⠀⠁
⠀⠀⠐⠁⠀⢀⠀⠰⠄⡀⠄⠈⢠⠀⠀⠘⠕⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠰⠁⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠶⠀⠀⠀⠉⠀⡀⠀⢀⡤⠞⠁⠐⠆⠀⣀⠀⡀⠀⠈⠀⠀⠘⠙⠁⠀⠀⠀⠀⠀⠀⠀⢚⢲⡀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠉⠁⠠⠖⠁⡠⠀⠀⠂⡀⠀⠁⠀⠁⠀⠀⠤⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠈⠂⠉⠀⢰⠐⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠐⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠁⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢸⣖⡇⠀⢀⠀⠐
⠀⠀⡀⠁⠀⠀⠀⡏⢧⠄⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⠈⠀⠀⠉⠀⠀⠠⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁
⠈⠠⣄⠀⠀⠀⠀⠠⠐⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠐⠀⠀⠟⠀⠀⠀⠈⠀⢀⡀
⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠘⠀⠒⠀⠀⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠀⣄⡴⠆⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣽⣤⣴⣊⡤⠄⢀⣀⣀⠀⠀⠀⠀⣀⡤⣴⠶⠿⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠸⣿⡟⠉⠀⠀⠀⠈⠁⠁⠘⠓⠲⢶⡖⣿⣿⡗⠁⠀⠀⠀⠀⠀⢸⡁⣹⠄
⠀⠀⠀⠀⠀⣠⣿⣄⠀⠀⠀⠙⢦⡀⠀⠀⡴⠻⣆⠀⠀⠀⠀⢨⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁
⠀⠀⠀⠀⣠⣿⣿⡿⣇⡀⠀⠀⠀⠉⠛⠛⠁⠀⠻⢦⣀⣀⣠⠾⠋⠀⠀⡠⠒⣤⣀⣠⠂⠹⡇
⠀⠀⣴⣾⣁⣁⣘⡄⣈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠐⠤⠊⠀⢀⡷⠚⠓⡴⠙⣦
⠀⠀⣿⣳⣷⣾⡿⡥⠄⢸⣿⠆⠀⠀⠀⠀⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣷⠀⠀⠘⠒⠋
⠀⠀⠈⠛⠻⠿⠿⠭⠶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢶⡶⠶⡶
⠀⠀⠀⠀⠿⠿⡟⠘⠟⠿⡇⢻⢿⣿⠘⠟⠙⡇⢸⣿⣿⠀⠀⠀⠀⠀⢀⣡⣤⣄⡀⠀⢸⠀⠀⡇
⠀⠀⣀⣆⣿⣶⣇⢨⡆⠠⡇⣸⣿⢁⠀⡧⣠⡇⢸⠉⠁⣺⣤⠀⠀⠀⠈⡟⠚⢻⠁⠀⢸⠀⠀⠆
⠀⠀⠺⣿⢻⣟⣃⠼⡷⢞⣡⡾⠿⡞⠀⠓⡞⡃⠘⣶⣞⣸⡇⠀⠀⠀⠀⠇⠀⢸⠀⢀⠆
⠀⠀⢚⡏⣿⠟⡏⢸⠟⠛⡁⢹⡿⠉⠈⡟⠉⡇⢹⠉⠙⢹⡇⠀⠀⠀⠀⡄⠀⢸⠀⡈⠀⡀
⠀⠀⠀⡇⠸⠀⡇⢸⡄⠀⡇⢸⡇⠀⠀⡇⠀⡅⢸⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠸⣤⡟⠛⠃⠔⠺⠛⡆
⠀⠀⠀⡇⡀⠀⡇⢸⡇⠀⠃⢸⡇⠀⠀⡇⠀⡇⢸⠀⢸⢸⡇⠀⢀⣎⣁⢀⠀⠀⠀⢉⡀⠀⠀⠀⠀⣿
⠀⠀⠥⣇⣄⢠⡇⢸⣇⣰⡄⣸⠃⣀⢀⡇⢠⡇⣸⠀⣨⣸⡇⠀⢸⣷⠖⠒⠀⠂⠒⣶⣿⣤⣤⣤⣺⣿⠂
⠀⠀⠴⣏⣹⣿⣧⣀⣛⣛⣓⣈⣻⣇⣀⡛⣟⣃⣘⣿⣿⣼⣧⠀⠘⣿⣆⣀⠀⠀⣤⣼⠋⠉⠉⠉⠁
⠀⠀⠰⠋⠉⠉⠈⠉⠁⠉⠁⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠯⠀⠀⠈⠙⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⢈⣉⡱⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⡇⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⢀⢃⠀⠀⠀⡠⠐⠉⠀⡀⠀⠀⢤⠀⠉⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢆⡔⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠠⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⢈⠀⠀⠘⡄⠁⠀⠒⠀⠀⠀⠀⠀⠆⠈⡂⡽⠒⢄⠐⠕⡠⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡸⢃⡀⠅⠹⣄⡔⣉⣂⣄⣢⣠⣠⣄⣱⣤⣇⣁⣀⢑⢿⣋⣡⣴
⠀⠀⠀⠀⠀⠀⡐⠠⠊⠬⠾⠤⠲⢵⢬⣔⠷⢦⢹⡉⠑⢁⡬⠆⠄⠀⠀⠸⡬⠐⠒⢔⠀⠀⣊⡴⠇⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠀⢀⡴⢻⠜⠣⡪⡧⢯⡁⢕⣙⠒⠲⣶⠀⢐⣌⡪⣐⣗⡡⠪⠂⢕⢇⠁
⠀⠀⠀⠀⡰⠀⠀⠀⠈⠂⠊⡤⣨⡂⢕⣕⣄⡪⢐⣎⡗⠻⣕⠀⠀⣀⠀⡋⠀⠉⠖⡡⢈⢔⢕⡽⠸
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⢍⠪⣺⣇⢠⡿⡊⣽⡿⣤⣷⡑⠉⢊⠤⡱⢂⢖⠭⡪⡱⢗⠵⡡⠁
⠀⠀⢠⠁⠀⠀⠀⠀⢅⠌⠀⠸⣋⣌⠞⡊⣕⠄⡪⢐⢡⣱⣹⡶⡋⢕⠅⡪⢚⢕⠈⣊⡔⢁⠔⠁
⠀⠀⠈⢔⠄⡀⠀⠀⠀⠀⠀⢨⠢⠐⠍⡪⠐⢅⢨⣲⡋⢇⡗⣬⣪⣕⡥⢪⠄⠵⠊⣉⠔⠁
⠀⠀⠀⠀⠈⠉⠀⠘⠁⠰⠶⠷⠾⠶⠿⠾⠿⠥⠉⠐⠊⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠠⡀⢀⠄⡀⢄⢠⠠⢀⠀⡀⡀⠄⠠⡀⢀⢀⠀⠀⠄⡀⠄⠀⡀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⣀
⠀⠀⠀⠀⠁⠈⠀⠀⠁⠈⠐⠁⠊⠀⠑⠁⠊⠂⠅⠊⠐⠀⠐⠑⠨⠀⠅⠊⠔⡩⠂⠕⠨⢂⠕⠪⠐⠡⡪⠠⠃⠔⠔

⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⢠⣿⠷⠀⠀⣄⡀⢀⣠⠤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠐⠚⠀⡀⠀⠀⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⢀⣀⣀⣠⣤⣄⣀⣀⣠⣤⣠⣤⣤⣤⣄⠄⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⢠⡏⣶⡟⡙⢹⠼⡇⡁⡇⠦⢗⣧⣰⣲⡏⠒⡀⢀⢀⡀⠠⢶⠶⠀⠀⠀⢀
⠀⠀⢲⡄⠀⠀⠀⠀⠰⠁⠀⠐⠊⠛⠶⠿⠛⠿⠾⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡀⠀⠸
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠠
⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⡳⣇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⣰⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠂⢀
⠀⡄⢁⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⡆⠀⠁
⠀⠀⡄⠠⠌⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⢄⣴⣢⠀⠀⠀⠀⠀⠘⠢⠐⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡄⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠘⠻⠟⠁
⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⡀
⠀⠀⠀⠀⠉⠉

⠀⢀⣴⣾⣿⣷⣤⣤⣤⣤⣤⣴⣤⣦⣶⣶⠄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠂⠠⠀⠀⡂⠀⠀⠤⠀⡂⠀⡇⠀⠂⠀⡆⠀⠂⢠⠀⠀⠀⠀⠀⠀⢰⠀⠰
⠀⠻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣯⡀⠀⠐⠃⠐⠐⠀⠂⠂⠂⠐⠀⠒⠀⠐⠂⠂⠒⠃⠐⠃⠘⠐⠂⠂⠒⠀⠂⠐⠂⠚
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢂⡀⠀⢀⡐⢄⠀⠀⠠⢀⡁⠀⠀⣁⠢⠀⠀⢀⠔⠈⢠⣄⠈⠂⡀⠀⠀⡄⠊⠀⠀⢈⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠠⡀
⠀⠈⢀⣼⣶⣒⣾⣧⡀⠄⠠⢡⣿⣷⣀⣰⣿⣧⠀⠀⠀⠀⣠⣼⣿⣆⡀⠈⠀⡐⠀⠀⣴⠟⣦⡀⠀⠂⢀⣀⡤⠀⠤⠄⠀⢄⣡
⠀⢀⠈⠈⠧⣶⠼⠀⠁⠀⠐⠀⠀⠀⣽⣅⠀⠀⠀⠀⡀⢸⣟⠁⠋⢿⡇⠀⠀⢡⠀⢠⠿⠾⠋⠁⠀⡄⠈⠹⣀⣀⠞⢆⣀⠼⠘
⠀⠀⠁⢐⠚⠛⠓⡂⠐⠀⠀⠐⠄⡘⠛⠛⠀⠔⠁⠀⠈⠨⡉⠉⠉⠉⠡⠂⠀⠀⠲⠼⠀⠀⠀⡀⠈⠀⠀⠑⠄⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⢀⠀⠁⠀⠀⠀⠈⢠⠀⠀⡐⠁⢰⣆⢠⠎⠐⠀⠀⠠⠊⣼⣷⣠⣶⣶⡄⠀⢀⠀⠀⠀⣦⠀⠀⠢⠀⠀⠔⠁⠐⣺⡀⠀⠀⡀
⠀⠀⢠⣶⣤⣶⣤⣤⣄⠇⠰⢰⣧⠀⡁⠀⣤⡄⠐⠀⣤⣶⣿⣿⣿⣿⡿⠃⠀⠂⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠠⠀⠀⠐⠀⠁
⠀⠠⡴⣿⣿⡿⢿⣿⠟⠀⠈⠀⠉⠤⠀⣠⣀⠀⡐⠀⠟⢿⠿⠟⠛⠉⠀⠀⠀⠃⠀⠀⠀⣇⠀⠀⢀⠂⠈⡀⠀⣶⣷⣦⡄⠀⡀
⠀⠀⠐⠠⠀⠀⠀⠄⠀⠀⠀⠈⠢⠇⠈⠉⠩⠀⠀⠀⠀⠀⠄⠀⠀⠠⠐⠁⠀⠀⠑⠠⠴⠿⠦⠄⠁⠀⠀⠈⠠⠿⣿⡿⠇⠊

⠀⠀⡠⢢⣶⣿⣷⡄⠢⠀⠀⢠⣾⣿⠀⠀⠈⠂⡀⠀⢀⢀⡵⠒⠒⠢⣔⠄⠀⠀⣤⠀⠀⠀⠀⠑⢀⠀⠀⡠⠂⠀⠀⠤⠀⠢⡀
⠀⠀⢀⣼⣏⣩⣹⣣⡄⠁⢀⠁⠀⠠⠀⣀⠀⠀⠀⠀⢠⡏⢰⣿⣿⡟⠛⡆⠀⡈⠹⣿⣦⣄⠀⠀⠀⠀⠀⠂⢸⣷⣦⠀⠀⠀⢠
⠀⠠⢀⣠⠽⣿⡿⣄⡀⡀⠈⡀⢠⣶⣶⣿⣿⣶⡶⠀⠘⣧⡴⣿⣿⡇⢠⢇⠀⢁⠀⠈⠙⠛⠳⠀⠀⠀⠀⠀⣼⣿⣿⣶⠀⠉
⠀⠀⠙⠅⢀⠀⢀⠨⠋⠀⠀⠐⠀⢙⠛⢛⠛⠉⠁⠀⠈⠪⠓⠦⠤⠒⠅⠀⠀⠀⠀⠄⡀⠀⢀⠲⠊⠀⠀⠑⢾⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠐⠂⢩⣷⣶⣄⠀⠀⠀⠐⠊⣇⠀⠗⠢⡀⠀⠀⠄⠂⠈⣩⠁⠢⡀⠀⠀⠀⠊⢀⠀⠈⠐⢄⠀⡀⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠾⠿⠿⠋⠃⠀⠛⠲⣀⡼⠦⣄⣀⣀⠀⠈⣰⣆⠀⣿⠀⣿⠀⡀⠀⠀⠀⣤⠷⣏⠀⠀⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡄⢀⣼⣁⡃⣸⡋⢉⠀⢸⣿⣿⣿⣿⣧⣿⠀⠃⢀⠀⢸⡄⠒⠨⠅⠀⠀⠀⠀⠀⠄
⠀⠀⠻⠛⠛⠒⠛⢃⠐⠁⠀⠘⠣⡎⠁⠉⢻⠄⠃⠀⠈⠻⣿⣿⣿⣿⡿⠊⠀⠀⠢⢀⢷⣤⡶⠡⠊⠄⠀⠀⠀⠀⠄⠠⠄⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠠⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣁⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⠉⠉⠉⠉⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠛⠛⠛⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⢿⣄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⠛⢦⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡟⠛⢳⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣉⡛⢶⣌⡛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠷⣤⠾⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣿⠉⣻⡆⠈⢛⣶⣬⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠙⠛⠋⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣴⠏⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢻⡆⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⣠⣤⣄⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠃⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠻⢦⠟⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠶⢤⣤⣼⣧
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡀⠀⠀⢻⣄⠀⠀⠀⠀⢀⣀⣠⣤⠶⠞⠛⠉⠁⠀⢰⡟⢷⡄⠀⠀⣿
⠀⠀⠀⠀⠀⣠⡿⠶⠶⠚⠛⠛⠓⠶⠶⠶⢦⣤⣤⣤⠶⠶⠛⠋⠉⢷⡀⠀⢸⣏⠛⠛⣻⣿⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢸⡇
⠀⠀⠀⠀⣰⡟⠀⠀⣴⠶⣦⠀⠀⣶⠛⣶⠀⠀⣠⣤⣤⡀⠀⠀⠀⠈⢿⡄⠀⢻⡄⠀⢿⣼⠟⠀⠀⢀⡴⠶⢶⡄⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣰⠏⠀⠀⠀⠙⠷⠋⠀⠀⠘⠛⠃⠀⢰⣏⠀⠀⣿⠀⠀⠀⠀⠈⢻⡄⠀⠻⣦⠀⠀⠀⠀⠀⠸⣇⣀⣠⡟⠀⠀⠀⠀⢀⣰⠟
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⣀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠈⠿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠟⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠶⠞⠛⠉


⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣫⠄⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⢛⡀⠀⠀⠀⢀⠀⣑⠠⠵⠕⠃⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⠁⠀⠀⠀⠀⠘⠘⢀⡀⠈⠁⠀⡄⠀⠈⠈⠀⠀⢸⠀⠀⠀⢠⢫
⠀⠀⠀⠀⠀⠀⠀⣰⣻⠀⡀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠿⠢⠀⠀⡀⠀⠀⠀⣀⢼⣆⠉⠁⢸⡑
⠀⠀⠀⠀⠀⠀⣰⠿⢹⠉⣃⡁⠅⢀⡀⠈⠠⢠⣤⠄⠈⠈⠀⡴⠇⠀⠰⠊⠀⢸⠀⠀⢒⡞
⠀⠀⠀⠀⠀⣰⡝⠃⠀⠀⠀⠁⠀⠀⠉⢣⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡴⠿⣶⣷⣴⣤⣤⡄⡆
⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠂⣖⠀⠐⠞⠁⠆⠀⠀⠀⠰⠀⠈⠃⠣⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠈⠁⠉⠀⠀⠘⠁⠉⠉⠉⢻⠆
⠀⠀⠠⠤⠜⠗⢠⣄⢠⣐⣛⠻⠅⠀⠀⢠⠀⠀⠀⠀⠠⠷⠆
⠀⠀⠀⠀⠈⠉⠛⠙⠻⠉⣹⣿⣯⢭⣿⠩⢥⡦⠄⢦⠽⠿⠶⠶⠮⠷⠖⠒⠺⠥⠟⠿⠷⠮⠥⠆

⠀⠄⠀⠐⠀⠀⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡂⠀⠀⡀⢴⣾⢼⠄⠀⠄⠀⠀⠀⠀⠀⡀⠠⠄⠐⠂⠄⠐⢀⡆⣀
⠀⠀⠠⠐⢁⣜⣹⣸⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡸⠆⠙⠃⣰⠇⢆
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠋⠈⠉⠉⠐⠂
⠀⠀⠀⠐⠈⠙⠛⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠂⠐⠂⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⢀⡈
⠀⢀⠀⠂⠀⠀⠀⠐⠀⡀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠖⠂⢸⠃⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣏⣀⣾⣆⣀⣇⣇⣀⣰⣋⡃⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⡖⠈⣿⡟⠋⡏⡏⢹⣏⠟⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⣿⠀⣿⡇⠀⣧⣇⣿⡟
⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⢀⣧⣿⣤⣿⡧⡤⠿⣿⣿⣤⢤⢤⡄⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠀⢀⣄⠠⢾⠋⠀⠀⠀⠀⠀⠀⢨⡀⠤⢆⡵⣠⠀⠀⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠁⠀⠀⠀⠀⠀⠀⡅⠀⠀⢘⣄⠀⠀⢀⠀⠠⢀⡴⠇⠚⢌⠅⠀⠀⠀⡖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠀⠀⠀⠀⠀⠘⠂⠁⢀⠀⣐⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⢸⠀⠀⠀⠀⠔⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣻⠀⡐⠀⢀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢻⠲⠄⠀⠀⡀⠠⠂⠀⠀⣀⣼⣖⠈⠀⠘⠼⠱
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⠘⠏⡋⢘⠀⡀⠀⠈⢀⡀⡀⣀⡀⠸⠀⠃⢠⣠⠇⠀⠀⠔⠊⠀⢸⠀⠀⠠⠤⡎⠁
⠀⠀⠀⠀⠀⠀⢠⢾⡿⠁⢁⠀⠐⠓⠀⠀⠳⠷⢤⠀⠀⠉⠉⢐⡀⠨⠀⠀⠁⠀⠀⢀⣄⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⢂⡀⠊⢐⣠⠄⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠂⠈⠠⠀⡸⣇⣠⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠠⠀⠀⠀⢴⡤⠁⠩⢬⠥⣾⡦⠄
⠀⠀⠀⢀⣀⡠⠀⠀⡀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢭⠀⠀⠉⠁⠈⠃⠀⠀⠀⠀⢸⠁⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠑⠀⡠⠊⠀⠀⠀⠀⣩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⡀⢘⡆
⠀⠀⠀⣠⠤⠼⠷⠀⢠⠀⢀⠲⠷⡽⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠤⠤⠾⠷⠿⠗⠳⣷⣶⡲⠶⣶⠒⠲⢰⠀⢀⡀⢰⣾⣠⣤⣤⠴⣤⣄⢀⣰⣶⣚⣶⣶⣶⣤⣤⣤⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠘⠋⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣯⣿⣿⣽⣯⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣼⣿⡟⠀⠀⠀⣀⠀⢀⣠⣤⣴⣄⡀⣀⡀⠀⠀⠘⣿⣷⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣸⣿⡿⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣄⠀⢹⣿⣧⠀⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣿⣿⣧⣠⣿⣶⣿⢿⣿⣿⣿⠟⢿⣿⣿⣿⣟⣷⣾⣧⣸⣿⣿⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⣿⣿⣿⠙⣿⣮⣽⡿⢋⣿⠋⠀⠀⠻⣿⡿⣿⡯⣾⡛⢿⡿⣿⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣴⣿⣿⣿⡄⢸⣿⣿⠀⡼⠁⠀⠀⠀⠀⠘⠧⣼⣿⣿⢀⣼⡇⣿⢠⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣟⣿⣿⣼⣿⡧⠚⠀⣀⣤⣾⣿⣶⣤⠀⠹⢿⣟⣼⣿⡇⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⢻⣿⣟⣿⡁⡀⢰⡟⣉⣙⣛⣩⣹⣧⠀⠸⣿⣿⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣜⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⡂⢸⣿⣿⡿⠻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⡿⣿⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢸⢿⣿⣇⠑⣽⣿⣿⣿⣿⣾⣽⣿⡿⣿⠿⣡⣿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣶⣤⣾⣿⣿⣛⣛⣿⣿⣿⣷⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣄⢸⣿⣛⣛⣛⣛⡙⢳⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⡾⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣮⣿⣿⣿⣿⣹⣿⣿⠻⠇⣿⣷⣿⣿⡏⣱⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠰⣄⢹⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣷⣙⣾⣿⣿⣿⣿⣿⣣⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣤⣴⣾⠏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠔⠋⠁⠙⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡤⠶⢽⡆⠀⠀⠀⠀⠀⠀⢠⣾⠓⠒⠒⠒⠦⢌⡳⣄⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⡴⢋⡽⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠶⢠⠀⠀⣀⠉⣮⣱⠞⠳⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⢸⣻⣧⠀⠀⠀⠀⠀⠀⠸⡏⠓⠾⠲⢄⣉⣠⠃⠀⠀⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⢱⣻⡀⠀⠀⠀⠀⠀⠀⣷⡀⢠⣄⡠⠀⠀⠀⣼⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣷⣳⡀⠀⠀⠀⠀⢀⣇⣙⣢⣤⡤⠤⠔⠋⢸⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⠓⣒⡩⡇⠙⠁⠀⠀⠀⢀⡴⢚⠟⢩⠟⢢⡀⣠⠴⢚⡆⢹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠁⠀⣿⢠⣖⣲⣄⠔⠁⠰⣅⡀⢸⣄⣾⢿⠀⢀⡜⠀⠈⡏⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢼⡅⢸⡇⡀⠀⢠⡞⠁⢸⠈⣸⠀⢓⠟⢀⣀⣀⡧⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢀⣷⡾⠍⠉⠉⠒⠷⣄⣸⠀⡇⢠⠏⠀⠈⢣⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⡯⣒⣂⠀⠀⠀⠀⠀⠹⣄⡷⠃⠀⢀⠔⠉⠀⣠⠞⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⢀⣀⣠⣼⠛⠓⢶⠶⢶⠶⢦⡀⠀⠈⡳⣄⡐⠁⠀⠀⡴⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣰⠃⠀⠀⠀⠳⣼⠀⠀⠙⢦⠚⢁⠎⠉⠳⣄⡼⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣀⣀⣀⡀⢹⠀⠀⠀⣸⢳⠎⠀⠀⠀⠈⠳⡄⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠥⠤⠤⠤⠭⢾⡇⠀⠰⡇⠋⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⣠⠞⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⣉⡁⣤⢀⡀⠉⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⣠⡍⡿⠀⣾⠋⣄⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠈⠐⠁⠆⠘⠄⠉⣨⢷⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⢠⡿⣷⠀⠰⠻⠻⠳⠀⢰⣿⢽⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢃⣿⡀⡶⢠⣇⢠⠀⢸⣿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠷⡴⢫⣝⢦⡤⣼⢯⣿⡆⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⠁⢻⣿⠟⠃⠈⣱⣿⣿⠇⠘⠆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⢈⡇⠀⠀⢠⣿⣿⡿⠀⠀⠀⢻⡇⠀⠀⢀⠀⠀⠀⠀⠀⠰⣄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣾⣿⣆⣴⣿⣿⣿⠁⠀⠀⠀⣾⠀⢠⠀⢸⣤⣦⣴⠀⠀⠀⠛⠇⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⣸⣿⠀⣾⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠀⠀⢀⠈⠙⢿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⢀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⡸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⣠⠤⠸⢧⣤⣄⣀⣀⣤⣤⣤⣴⡾⠃⠀⢸⣿⣿⣿⠿⠋⠙⠛⢛⡁⠈⠻⡷⣷⡀⠐⡀⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⢀⣠⠞⠀⠀⠀⠀⠙⠻⠿⢿⠿⠟⠛⠉⠀⣀⠀⠀⠋⠁⠀⠀⢀⠀⢀⣼⣿⠦⠚⣡⠾⠃⠀⠀⠀⠙⢿⣿⣿⣷
⠀⠀⠀⠀⢀⡴⠉⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⣰⡤⠞⠉⠀⠀⠀⠀⠀⠀⠈⠤⠉⠛⠁⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿
⠀⠀⠀⠈⠉⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠈
⡴⢠⢀⣄⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁
⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠧

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠤⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⠶⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⢠⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠈⠁⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⢰⠒⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣛⣢⠀⠀⠀⠀⢀⣠⠖⢁⣤⠖⠃⠀⠀⠀⠀⠀⠈⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡀⠈⠉⠉⠒⠤⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡟⡩⠳⠀⣀⣴⣯⠵⠚⠉⡗⠒⠒⠒⠒⢲⠒⢲⠐⠏⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠉⠀⠒⠤⠀⣐⣿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡵⢀⣴⡾⠟⠋⠁⠀⠀⠐⢟⠓⠒⠒⠒⢲⡓⠒⢚⠟⢠
⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠷⢛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⠀⢀⡀⠤⠂⣠⡞
⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠳⡀⠀⠀⠀⢀⠼⠞⠒⢿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢴⠶⠞⠉
⠀⠀⠀⣀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠐⠆⠘⡄⠀⠀⡎⠀⠀⡀⣼⠱⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠣⣸⢄
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠘⠏⠁⠀⠀⠈⠦⣐⠃⠀⢰⠋⡟⢀⡾⠁⣀⣀⣿⣿⣿⠀⠀⠀⠀⠉⠙⠉⢹⠈⠁
⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⢀⢤⠙⠀⡤⠃⠉⠉⣼⣅⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣸⣿⡇⣿⣇⡀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⣆⠠⠋⠀⠀⠇⠀⡀⠀⠀⢰⣿⢿⣾⣿⣻⣿⣿⣿⠀⠀⠀⢀⣼⡇⠀⢸⡇
⢠⣿⣟⣷⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠣⡀⠀⣀⠠⠚⠁⠀⠀⠀⠀⠈⣈⠖⠦⠀⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⠟⡀⠀⢸⡇
⢸⣿⣯⣿⣿⣿⣿⡜⠆⠀⠀⠀⠀⠀⢺⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣗⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣾⣏⡼⡇⠀⣸⣧
⣘⣛⣛⣛⣽⣿⣿⣇⠀⠳⣄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⠴⠾⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⢲⣿⠟⠒⠒⠾⠒⢻⣿⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠈⠳⣄⠀⠀⠀⠀⢀⣀⠠⢰⡋⠀⡄⠀⠀⢀⠀⠀⣠⣤⡤⠤⠤⠠⠀⠀⠄⠀⠾⠃⠀⠀⣰⠰⠄⢾⣿
⠀⠠⠤⠤⠴⡌⡃⠀⢻⠀⠀⠀⠀⠑⠀⠄⠒⠉⠀⠀⠈⠁⠀⠇⠀⠐⠘⣀⡀⣡⣎⢰⣶⠌⢻⣏⣠⣤⠀⣠⣀⣠⠆⠈⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⡇⡃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣐⣈⣻⣡⣭⡷⠶⠻⠋⠋⣿⣽⠃⠈⣩⡹⣇⠀⣹⡇⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠇⡇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣯⡿⢩⠀⣄⡄⠀⠀⡀⠀⣿⣿⡆⠒⡇⢠⠙⠛⣻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⣇⣼⡄⣽⡷⠘⣤⡃⡀⢸⣛⣇⡞⠁⠈⢢⣴⣿⣿⣟⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⢚⣿⡏⣿⡇⣼⡷⢶⣿⣿⣿⠿⠿⢿⡗⢲⣶⣼⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⣀⣠⠤⠄⠒⠊⠉⠀⠀⠀⠀⣠⣼⣿⣿⣿⣷⡿⠟⠛⠉⠁⠀⠀⠀⠘⣟⠀⣿⠃⠠⠦⠄⢳⠈⠋
⠀⠀⠀⠀⣀⣀⠾⠤⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣻⣤⣤⣤⣤⡇
⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣻⣿⣿⣿⢟⣫⣷⣿⣿⣿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⣿⣿⣿⠿⠋⣾⠏⠛⠙⠛⠷⣤⣀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣩⣾⣿⣿⣿⣿⣯⣿⣿⣶⣼⣿⣴⣷⣦⠀⠀⢀⢙⣇⣀⢀⡀
⠀⠀⠀⠀⢻⣿⣿⣿⣋⣾⣿⣿⣋⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⡀⢸⣿⣿⣿⣾⣿⣷⣤⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⡟⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠻⣽⣿⢻⣿⣿⣿⡿⢏⣼⣣⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣉⠀⣠⣿⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢠⣿⣿⠛⣿⣿⣿⣿⠿⠿⠿⠟⢻⣿⣻⣿⠿⣿⣿⢳⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢸⣿⠏⢠⡿⠋⠉⠀⠀⠀⠀⣺⣿⣿⣿⣿⣷⣿⣿⣶⣾⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣶⣴⣦⡀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿
⠀⠀⠀⠀⠀⢰⡏⢸⣿⣿⣦⣌⡙⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿
⠀⠀⠀⠀⠀⣼⠇⢸⣿⣿⣿⣿⣿⣾⡇⢿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣶⣶⡄⠻⣿⣿⣿⣿⡿⠃⢨⣇⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢿⢿⣿⣧⣽⣉⣭⣷⣶⣖⣛⣛⣣⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⢠⢗⡜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠘⣷⣝⣓⢤⣍⠛⢱⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠨⣿⣛⣿⣿⣷⢾⣛⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢈⡿⠛⠻⠛⠄⠺⠟⠛⠛⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⡇⣾⣯⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⢀⣼⣷⣿⣿⣿⣿⣯⣸⣶⣀⡰⡶⠈⢻⣿⣿⣿⣿⡿⠿⠟⢛⢛⡡⠀⠀⣀⣀⡀
⠀⠀⠀⢀⣾⣿⣿⣿⣷⣿⠟⠿⢿⣯⣿⣿⣿⡷⣾⡟⣿⡛⠛⠁⣚⣀⣩⣤⣶⣾⣿⣿⣿⣿⣧⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⡏⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠤⠀⠠

⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢀⣆⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠰⢸⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡢⠀⠈⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡠⠞⠁
⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠁⠂⠈⠀⠀⠀⠀⠘⡂⠀⠂⡀⠤⠄⠀⠀⠠⠄⠀⠀⠤⠁⠪⠀⢀⠃⠀⠀⠃⠀⢨⠀⣠⠾⠀⠄
⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠚⠁⠀⠀⢀⠀⠀⠈⠂⠀⠀⡈⢀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠡⠤
⠀⠀⠀⠠⡀⠀⢀⡀⠀⠐⠒⠒⠒⠒⠚⠂⠧⠀⠀⠂⠀⠁⠀⠀⠀⠄⠀⠐⠂⠀⢀⠀⠀⢀⡇⡤⠄⠀⠀⠀⠀⠀⠀⠰⠐⠂⠖⠒
⠀⠀⠠⠤⠤⠜⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠂⠀⠙⠈⠀⠀⠘⠁⠈⠀⠀⠑⠂⠀⠀⠀⡄⡆⠀⠀⠀⠀⢈⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⠑⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⠘⠂⠀⠀⠀⠠⡀⠀⡈⠀⠀⠀⠀⠐
⠀⠠⠐⠐⢊⠁⠀⠂⠐⠀⠘⠋⠉⢩⢍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠑⠂⠀⠀⠀⠀⠠⠍⠀⠀⢀⡀⠀⠀⠀⠄⢂⡠
⠀⠀⠀⢀⠄⠀⠀⠀⡤⠠⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠒⠀⠀⠂⠀⠀⠀⠀⣡⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠔
⠀⠀⠀⡀⠀⢀⠀⠀⠙⣾⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠒⠚⠀⠠⠀⡤⠀⡐⠁⢨⠓⠀⡉⠂⠀⠀⠀⠀⢀⡄
⠀⠰⡠⠀⠁⣌⠁⠀⡴⠀⠐⠻⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠐⠓⠀⠀⠁⠀⠀⠀⠀⠒⡒⠂⠈⢢
⠀⠀⢉⠠⢄⠊⢀⡄⠀⠀⠀⠀⠠⠟⠣⠤⠤⠤⢤⡦⠀⢠⣖⡀⣔⣂⠀⠀⠀⠀⠀⠠⠀⠀⡦⠄⠄⠀⡇⠀⠀⠀⢨⠉⠀⠀⠊
⠀⠀⠀⠀⠉⠀⠈⠀⠂⠀⠂⢀⣀⠀⠀⠠⠀⠀⠀⠠⠀⢨⠉⡄⡍⠡⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠁
⠀⠀⠉⠀⠉⠀⠀⠀⡀⠀⠰⠥⠤⠤⠤⠤⠕⠀⠀⠀⠀⠀⣄⠇⢘⡀⠀⠀⠀⢋⠋⠀⠀⠀⠀⠀⠄⢂⠀⠃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣈⡁⠁⠀⠀⠀⠀⠀⢸⠀⠁⢰⠀⡆⠈⠀⡀
⠀⠀⠀⠀⠀⡘⠀⠀⠁⠀⠀⠀⠒⠒⠐⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣀⣄⣈⣀⣀⠈⠉⠁⠀⠉⠁⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀
⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣆
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣦⣤⣄⠀⠙⠃⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠈⢿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠘⢿⣦⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣿⣿⣷⡆
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⣀⣠⡼⠿⣟⠋⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⣿⡿⠋⠉⠀⠀⠈⠉⠻⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣾⣿⠿⠋⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣿⣤⣀⣀⣀⣀⣠⡴⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡿⠾⠿⠿⠿⠿⠷⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠴⠀⠀⠉⠒⠂⠀⠀⠛⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⠀⠀⠀⣸⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⢛⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡸⠀⠀⠀⠀⣤⣴⣶⣶⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠿⠂⠀⠀⠀⠀⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠃⠀⠸⡿⠿⠿⠿⠛⠁

⠀⣁⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⣤⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣨⠽⠛⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢶⣶⣾⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄⢐⣶⣀⠀⠀⠀⠀⠀⠀⠘⠳⡌⣿⣿⣿⣟⣛⣥⡀⠀⠀⠀⠀⢶⠒⣶⣶⣶⣶⣶⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢀⣀⣀⣠⢮⢿⡟⠁⠀⠀⠀⠀⠀⠈⠑⠀⠈⠛⠛⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢻⣶⣶⣶⣦⡆⢸⣧⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⣿⣿⣷⣾⡇⣻⣿⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣿⣿⣿⠇⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⣀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⡿⠛⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣆⣿⣻⣿⣿⠁⠀⠀⠀⣿⣿⣿⣶⣶⣦⣶⣶⣶⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⢀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣥⣄⣽⣿⣟⣴⠟⣛⣟⣟⣛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁⣿⠃
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡏
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟


⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⣀⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢸⡿⡘⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⣛⣢⣤⠀⠀⡇⢧⣠⠿⠭⢭⡱⡄⠀⠀⠀⠀⣿⣿⣿⡿⠿⠥⠝⠟⣿⣿⢸⣜⠿⣀⣛⣓⢮⢻⣿⣿⣿
⠀⠀⠀⠉⠓⡼⠁⠀⠀⠀⣇⣀⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⣿⣿⣿⣶⣼⢛⣿⣿⣿⣿⠸⠿⢸⣿⣿⣿⢸⢸⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠚⠛⠂⠀⠀⢀⡇⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣥⣤⣽⣿⣿⡿⢸⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢲⡶⠶⢶⢞⡩⠞⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⢉⣉⡉⡭⢖⣡⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠛⠘⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣤⣧⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠷⠶⠶⠶⠷⠶⠶⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣬⣭⣭⣭⣬⣭⣭⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⠉⡆⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠵⡒⠁⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢦⣀⡼⠀⠀⠸⡯⠀⠁⠀⠀⢀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠓⠀⠀⠠⠄⠀⠈⠛⢇⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣼⠁⠀⠁⠀⠀⢸⠀⠀⠘⡏⡇⠀⢀⣤⡈⠀⠑⠀⠀⠀⡀⠀⠀⠀⢱⠀⣸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠘⠻⢤⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⢀⠊⠈⠁⠀⠀⠃⠀⠀⠙⠿⠿⠿⠋⠀⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡖⠀⠀⡀⠀⠹⡆⠀⠀⡇⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣⠀⠀⠅⠀⣠⠇⠀⠀⡇⠀⠀⠀⠀⠀⣸⠘⣦⠀⠀⠀⠀⡄⠀⠈⢩⠉⠉⡇⠀⠀⢠⡮⡀⠀⠀⢘
⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠈⠟⠛⠟⠛⠏⠀⠀⠀⡇⠀⠀⠀⠀⠉⢻⠀⠉⠻⠉⠉⠋⠁⠀⠀⢸⠀⣗⡇⠀⡖⠉⠀⠀⢀
⠀⠀⣠⣤⣿⣀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣶⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣷⣧⣤⣷⣤⣤⣤⣼⣤⣬⣤⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡤⠒⠉⠀⠀⠉⠺⢝⡢⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣌⠀⠀⠀⠀⠀⠀⣀⣄⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡤⠒⠉⠀⠢⣝⡲⢄⡀⣴⡾⠛⠉⠀⠮⣕⠢⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⠀⠉⠒⢹⢡⠀⠀⠀⠀⠀⠀⠙⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⠀⡀⢸⠸⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠲⢄⡀⠀⣠⣖⡯⠚⠉⠑⠢⣄⡀⠀⡠⣖⡯⠒⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠊⠁⠀⠀⠀⠀⠀⠀⠉⢲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢤⡀⡤⠤⡄⣠⠴⢤⠀⢠⡀⢠⡄⢠⡄⡄⣠⠴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣠⠇⡟⠻⡅⢧⣀⣲⢠⠇⢳⣸⠈⢾⡃⡇⢧⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⡀⠀⡀⢀⣀⡀⣀⠀⢀⡀⡀⢀⢀⡀⠀⣀⡀⣀⢀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⡁⡗⠒⡇⠰⠒⠂⡜⢆⡘⡇⡇⡙⠲⣄⠀⡇⠀⡗⢶⡃⠘⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠁⠀⠁⠈⠉⠁⠁⠈⠀⠁⠁⠈⠉⠁⠀⠁⠀⠁⠀⠁⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠉⠉⠉⠁⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⡀⠀⠁⠂⠀⠀⢄⠀⠀⠀⠀⠀⠈⢀⡠⠀⠺⠠⠤⠀⠀⠀⠀⠂⠂⠉⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠘⠆⠔⠀⠂⠀⠀⠀⠠⠂⠀⠲⠀⠘⣲⠎⢥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠲⣆⠀⣶⡄⠀⣀⡀⠀⣶⡄⢀⠠⠊⠀⠀⡘⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠈⠐⢨⠁⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠁⠈⠉⠁⠀⠉⠁⠈⠉⠉⡃⠀⠀⠀⡄⠈⠢⡀⠀⠈⠀⠀⠀⠀⢀⢔⠕⠄⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡆⠀⠀⠄⠂⠁⢢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠁⡀⢁⠀⣁⠈⢀⠀⡀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢋⡃⠀⠀⠀⡠⠁⠈⠀⠀⠀⠀⡈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⠁⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣉⡀⠀⠀⠀⠐⡀⠀⠀⠈⠈⠢⣀⡌⠀⠀⠁⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠀⠀⠀⠀⠍⣉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⠀⠈⡀⠀⡐⠀⠀⠀⢀⠁⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢰⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠡⠀⠡⡀⠀⠀⠀⢀⠒⠂⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠛⢶⠇⡇⠀⠀⠀⡖⠈⠀⠉⠐⠀⠀⠀⠸⠐⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⢀⠘⠀⠄
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⣀⣀⣀⣀⠀⢢⠀⠀⠢⡀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠈⠂
⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠧⠄⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢪⠟⠁⠀⠀⠀⠀⢠⠋⠳⢄⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⣰⠃⠀⢠⡖⠒⠒⠢⡏⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⣆⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢠⠃⠀⠀⠀⢣⠀⠠⣄⣸⠦⣤⠔⠁⣀⣀⠀⠀⠀⠀⠘⡄⠀⠙⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠀⠀⠀⠀⠀⠑⠒⠚⠓⢄⣸⡴⠋⠁⠉⠉⠓⢦⡀⠀⡇⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡠⠤⠤⣄⣹⢁⠴⠊⠉⠀⡠⠋⠀⠀⡇⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡄⠀⠀⠠⠾⣅⣀⣀⡀⠀⢹⢧⣀⡠⠴⠊⠀⠀⠀⢠⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠈⠙⢺⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠤⣀⠀⠉⠲⣤⣤⣄⡀⠀⠀⢀⡠⠤⣄⠀⠈⠀⣀⠤⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠙⠒⠋⠀⠀⠉⢹⡖⢲⡏⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠊⠉⠁⠈⠉⠙⠒⠒⠂

⠀⠀⠀⡆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢲⢰⠖⠆⠴⠲⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠲
⠀⠀⠀⡏⠀⡙⢙⠀⠀⣀⡀⠀⠀⠀⠀⢠⡦⡧⢼⢼⠤⠦⠤⠴⢴⡆⠀⠀⠀⠀⠀⠀⡏⠀⡙⢙⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⠀⡸⠀⢨⡀
⠀⠀⠀⡧⠰⣧⣤⠇⠀⠀⠂⠀⠀⠀⠀⢸⡇⡇⢸⢸⠀⡂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡧⠰⣧⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⣀⡀⢀⣈⡆
⠀⠀⢀⣇⣀⣈⣁⣀⣰⣶⣾⡀⠀⠀⠀⠸⡇⠓⠚⠘⠒⠃⠒⠚⢸⡇⠀⠀⠀⠀⠀⢀⣇⣀⣈⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⢀⡴⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠒⡆⠸⠛⣷⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣋⡓⠢⣄
⠀⠀⠀⠀⠀⠸⣇⠀⠀⣸⠇⠀⠀⠀⠀⢠⡞⠉⠉⢉⣉⠉⠉⠑⣦⠀⠀⠀⠀⠀⠀⢧⣤⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⡞⣤⣄⠛⠁⣶⡜⡆
⠀⠀⠀⢀⣠⡾⠋⠛⠛⠁⠀⠀⠀⠀⠀⠘⠧⣀⡠⠋⠈⠆⣀⡠⠛⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⣦⠀⣴⣬⢁⠇
⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣄⡠⠴⠋



⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⢃⡀
⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢯⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢴⣷⣮⡤⠀⡀
⠀⠀⠀⢐⣯⡫⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣬⣥⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠊⡿⣿⠑⠈⠁
⠀⠀⠐⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠾⠿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠳⠀⠀⠁


⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣬⡀⠛⠛⢩⣥⠀⠀⠀⠀⠀⠀⢀⢀⡠⠦⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⡀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⣀⠰⠆⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢠⣤⣀⣈⡄⢀⣦⣤⣆⠀⠀⠀⠀⠀⠀⠀⠃⠀⢨⡄⣀⠰⠦⡄⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⡟⠁
⠀⠀⠈⠛⠿⠛⠁⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠠⠒⠀⠉⠉⠉⠉⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⡀⠀⠘⠉⠀⠀⠀⠐⠦⠀⠀⢀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢠⠀⠰⡿⠃⠀⠀⠀⢐⢖⠀⠀⠈⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡌⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡁⣇⠠⡄⠀⠙⠤⠒⠀⠀⢀⡴⠀⢸⡄⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡹⢦⠙⣀⡖⠋⠒⢲⢚⠝⢁⠔⢻⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠱⣼⠀⠀⠀⢸⢁⠔⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⡀⠀⠀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢣⠀⠀⠱⣄⣀⡠⠊⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡈⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢠⠇⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠟⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢄⠀⠀⠀⠀⢠⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡜⢇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⣠⠞⠀⠘⣆⠀⠀⠀⢱
⢠⢶⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⡇⠀⠀⡰⡇⠀⠀⠀⠈⢧⠀⠀⠸⡆
⡇⢘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢧⠀⡰⠁⣷⠀⠀⠀⠀⠀⢣⠀⠀⢇
⡇⠸⡄⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠸⡄⠀⣠⠇⠀⠀⠀⠀⠀⠀⢧⠀⠘⡄
⠹⣄⠙⠦⣄⣀⣀⣀⡼⡆⠀⠁⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢻⣫⠥⠤⡀⠀⠀⠀⠀⠀⠈⢦⠀⢳⡀
⠀⠈⠳⢤⣀⡈⠉⠀⢀⣹⡆⠀⡀⠈⠘⢤⣄⣀⣀⣀⣀⣀⣀⣀⣽⠀⠀⠀⢧⣀⣀⣪⡇⠀⠀⠀⠀⠀⠀⢳⠀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠓⠦⠷⠤⠷⠼⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⡆⠀⣌⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣈⣆⣈
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⡷⣥⣦⣵⡞⠁⠀⠀⠀⠀⠀⠀⢠⡉⠟⠀⠀⠀⢰⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠘⠆⣠⣃
⢀⠎⢀⢹⣿⢇⠘⢆⠀⠀⠀⠀⠈⣷⣿⠉⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⣿⡀⠀⠀⠀⠀⠀⠰⠿⠻⠃⠄⠒
⠳⠼⠧⠤⠤⠤⠽⣮⠇⠀⠀⠐⢾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣷⡄⠀⠀⠀⢀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣀⡀⠀⠀⠀⠀⠐⠛⠂
⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠄⠀⡄⠓⢄⡀⠀⠶⠀⠀⠀⠎⠀⢹⣿⠃⠉⢄⠀⠀⠀⠀⠀⣤⡀
⠀⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠤⡀⠥⢀⠘⠁⠀⠦⠀⠀⠘⢰⣶⠖⠓⣶⣶⡎⠀⠀⠀⠀⠀⣻⡃
⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⣀⠀⢈⠻⠁⠀⠀⠀⠀⣶⣿⣿⣦
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⣀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣠
⠀⠀⡏⠈⡇⠀⣼⠀⠀⠀⠐⠿⡂⠉⢠⡀⢠⠈⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣤⣀
⠀⠠⠿⠄⡇⠀⣤⠀⠀⠀⠀⢀⣈⢶⠎⠀⢶⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁
⢀⡀⠀⢀⡇⠀⠋⠀⠀⠀⠀⠙⠁⠀⣦⠀⠀⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢻⡆
⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⢶⣤⣴⣧⡀⠀⠀⠀⠀⠀⠀⠘⠛⣀⠛⠃⠘⠓⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⡰⡺⠉⠉⢓⠢
⠀⢰⣋⣰⣏⣀⡀⠀⠀⠀⠐⠋⠈⠉⠀⠉⠑⠚⠃⠀⠀⠀⠠⣶⣾⡄⠀⣿⡇⠀⠀⢀⡴⠻⠦⠠⠞⠳⡆
⠀⠀⢩⣟⠉⡉⣿⠀⠀⠀⠀⣀⢀⠀⡀⢀⡀⢀⡃⠀⠀⠀⠀⠠⣿⣿⡿⠟⠁⠀⠀⠀⠄⢀⢀⣇⣠⠀⠄
⠀⠀⠀⠉⠛⣻⠋⠁⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣴⣿⣾⣿⣷⣶⣆⠀⠀⠀⠀⠉⠋⠈⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡄⠀⠞⠒⠤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣾⣿⣿⣶⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⡴⠛⠁⠀⣆⣇⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀⡎⠉⠉⠉⠉⠉⠁⠀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠃⢀⠴⠊⢁⡤⠛⠁⠀⠀⠀⠀⠈⠁⠀⢴⢿⠆⠀⠀⣠⠀⡀⠀⠱⡀⠀⠀⠀⠀⢀⠜⠀⠀⠠⣳
⠀⠀⠀⠐⠈⠀⢿⣅⣠⠖⠉⠀⠀⣤⡄⠀⢠⠆⠀⡇⠀⠈⠉⠉⠀⠀⠁⠀⠇⠀⠀⠈⠒⣤⣴⠶⠁⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢠⡄⠈⠀⠀⢺⣀⣞⣀⣀⠀⠀⡄⢀⡀⠀⢠⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀
⠀⠀⠀⠀⠀⠘⠁⢰⣖⠤⣀⠀⢀⢀⠀⠀⠀⡟⢉⣁⣹⠃⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠈⡕⠂⠉⠰⠦⠀⣀⢠⡯⠚
⠀⠀⠀⠀⠀⠀⢀⡮⠉⣻⠚⢁⠀⠂⠂⠀⠀⠙⠋⡼⢉⣹⠂⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⡎
⠀⠀⠀⢀⡤⠒⠊⠁⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠉⢱⠄⠀⠀⠑⢄⠀⠀⠀⣀⠇⠀⠀⠀⢠⠀⣽⢒⡲
⠀⠀⠀⣿⣿⣶⣦⣄⠘⡆⠀⢰⡠⡇⡀⢰⠆⠀⠀⠀⢧⠄⠀⠉⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⣀⡀⠀⠸⡟⠉⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣷⠇⠀⠘⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠘⣄⡜⠀⠊⠀⢀⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⠤⣶⣶⣶⣐⡦⠀⠟⠳⠄⠇⠀⠀⠀⢹⡀⠀⢀⣴⠷⣴⠁
⠀⠀⠀⢀⠠⡞⢶⠀⠀⠀⠀⢾⣁⣀⣀⡤⠆⠀⠀⠈⢺⢻⠟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣴⠛⠁⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠚⠋⠿⣅⠀⠀⠀⠀⠀⠀⠀⡞⣷⡏⢹⡄⠀⠀⠀⠀⠀⣤⠀⠀⠘⠂⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠠⠚⢧⠀⠀⠈⢛⣦⣄⣼⠆⠀⡀⠀⠀⠀⠀⢹⢻⣷⠘⣇⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣉⣁⣹⠀⠀⠘⠉⠈⠀⠀⠠⠈⡼⣿⡄⢿⠀⠋⠉⠹⡇⢱⠆⠀⠀⠀⠀⠀⠀⠘⠬⠜
⠀⠀⠀⢠⣄⠀⠀⢠⠖⠊⠛⢿⡉⠀⠀⠀⡤⠄⢤⠀⡀⠀⢣⢿⣷⣸⡇⠀⠀⠀⡸⢧⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠈⣁⠀⠀⠙⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠯⠚⠀⠀⠀⠘⠃⠀⢱⡄⠀⠰⣮⣭⣭⣵⠂
⠀⠀⠀⠘⠖⢃⣘⡛⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠇⡇⣀⡤⠒⠁⣠⣀⠀⢸⠀⠉⡇
⠀⠀⠀⠀⢐⠛⠉⠉⢹⠛⠉⡇⠀⠀⠀⠀⠀⠀⣀⡀⠤⠶⠶⠤⠤⣀⣀⣀⣀⣩⣤⡄⠀⠑⠋⣠⠜⠀⠀⠡⡀
⠀⠀⠀⠀⠈⡄⠀⠀⢸⠇⠀⢰⠀⠀⠛⠋⠉⠉⠙⠓⠤⠤⠤⠤⠜⠋⠉⠁⠀⠀⠀⠠⣶⠀⠀⣷⣶⣿⣿⣿⡟⢄
⠀⠀⠀⠌⠀⠉⠉⠹⠥⠤⠔⠚⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⡀
⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡁⢀⠀⣁⣠⢀⡅⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠤⠀⠤⠤⠤⠤⠜⡀⡀
⠀⠌⠀⡄⢠⠆⢀⡀⢠⠀⠀⢹⠁⠀⠉⠈⠀⠀⠀⠀⠈⡇⠀⠆⠰⠀⠠⠤⠄⠂⠁⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁
⠀⠉⠀⠁⠈⡏⢈⠀⠠⡀⠀⣸⠀⣀⠀⠀⡀⠀⠀⠤⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⡀⠠⣈⠃⠀⠀⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⢀⠀⠀⠠⠀⠂⣀⠐
⠀⠀⠀⠀⠠⠆⠀⠀⠀⢀⡀⠀⢁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠒⠂⡑⡄⡅⠀⠀⠀⠐⠠⡤⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣁⡒⠀⠠⠀⠒⠈⣀⠀⠐⠀⠀⠀⠀⠈⠀⠐⠄⠀⠀⠠⠄⠀⠆⡄⢀⠀⡆⠀⠑⠁⠀⠀⠀⢎⠀⠀⠀⣀⠘⠀⢀⡂⠶⡅
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠐⡱⠦⠤⠔⠊⠀⠀⠀⣇⢀⠙⣠⠀⢀⠠⠦⠀⢰⠀⠭⠃⢠⠠⡄⠀⠁⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⠁⠀⠀⠐⠀⠀⠀⠀⠘⢦⡀⠈⠁⠉⠁⢂⡠⠬⠀⠀⠉⠀⠋⠀⠠⡀⠀⠀⠐⠈⠐⠉⠐
⠀⠂⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠰⠀⠀⠀⠀⠀⠀⠉⡁⠒⠒⠊⠉⠀⢠⠀⠀⢰⠀⠑⠀⠠⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠔⠀⠈⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡊⠐⠀⠄⠀⠘⠀⠑⠁⠦⠀⠀⢀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠂⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣄⡀⢀⣀⣀⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠈⠉⠉⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⡀⢸⣿⠀⠀⢸⠟⠉⢻⡇⣿⡇⢹⡇⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠍⠀⠁
⠀⠀⠀⠀⢨⠈⡅⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠃⢸⣿⠀⠀⢸⣆⣀⣸⡇⢸⣧⣾⠇⠀⠀⢀⣀⣀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠆⠺⠀⠆⡀⠠⡄⠀⠀⠀⠀⠱⡀⢀⠔⠀⢸⣿⠀⠀⢸⡇⠀⢸⡇⢸⡏⣹⡇⠀⠀⢸⠉⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠘⠃⠀⠘⠁⠘⠛⠛⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠂
⢀⠀⠐⠉⠀⠀⠀⡆⠀⠂⠀⠀⠀⢠⢀⠀⠀⣀⠀⠀⢸⡛⡟⣻⠻⢿⠛⢟⣿⢻⡇⠀⠀⠀⡄⠀⠆⠐⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠈
⠀⠉⠀⠀⠒⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣷⣷⢾⡾⣾⡷⣷⡿⡾⡇⠀⠀⠀⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠑⠀⠀⢸⠀⠠⠀⠀⠀⣀⠀⠀⠠⠀⠀⠐⢀⠀⠌⠐⢆⡃⠂⠀⠡⠠⢀⡐⠀⠀⠀⠀⠀⠠⡀⠠⠂
⠀⢀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠵⠀⠀⠀⠀⠊⢔⠀⠀⠀⠀⠀⠙⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠀⠀⠁⠀⠂⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠂
⠀⠀⢰⡆⢰⡆⠀⠀⢠⡾⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠐⠁⠊⠁⡐⠀⠀⠀⠉
⠀⠀⢸⣧⣼⡇⡶⣦⠸⣧⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠈⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⢸⡇⢀⡿⠀⣿⣸⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⡄⣡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠈⠛⠘⠁⠙⠛⠀⠙⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡠⠶⠊⠻⠟⠃⠶⡄⣠⣤⡀⡴⠆⠻⠿⠃⠲⡤⣠⣤⡀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⠀⠀⠀⠐⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣥⡀⠀⠀⠀⠀⠀⠀⠀⣤⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢣⣄⠀⢀⣀⠀⣀⡌⠿⠿⢇⣄⡀⢀⣀⠀⢀⣤⠄⠀⠙⠛⣛⣛⣛⣛⣛⣛⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣿⣿⡇⠉⠀⠀⠀⠀⠈⠁⣿⣿⡇⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠈⠙⠃⣾⣿⡆⠀⠰⠶⠶⠶⠶⠶⠶⠶⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⣙⡛⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡆⠛⣛⣛⣛⣛⣛⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⢿⣶⣶⣬⣭⣭⣤⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠿⢿⣿⣅⣢⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⠾⢈⣿⣿⣿⣿⣿⢋⣭⡻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣛⣡⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠈⠙⠛⠛⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠖⠒⠒⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⠒⢲⠂⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣶⣶⠆⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠄⢄
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠑
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢣⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⣿⣿⠿⠁
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠛⠛⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⣿⣿⡟⣻⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣯⣿⣽⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠯⠭⠽⠽⠽⠭⠊⠀⠀⠀⠀⠀⠀⠀⠑⠽⠿⠿⠿⠿⠿⠿⠿⠑

⠀⠀⠀⠀⠀⠀⠀⠖⠈⠐⢦⡄⠀⠀⠀⢀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠘⠙⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⢎⣴⡆⠀⠀⠀⠀⠀⠿⣶⣲⠀⠀⠀⠀⠀⠀⣢⠀⠀⣄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⡜⠀⠀⡠⠀⠤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢠⡋⠉⠐⣄⠀⠀⠀⠀⣀⣿⣄⡠⣪⡗⠀⢦⡤
⠀⠀⠀⠀⠺⡇⠀⠀⣀⠀⢀⣀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣤⣤⡜⠁⠀⠀⠀⠀⠈⠻⡟⠛⠃⠐⠂⠁
⠀⠀⠀⠀⠀⠡⠀⠀⠏⠀⠈⠉⠉⠁⠀⠀⠇⠌⠀⠀⢨⠘⠀⠀⠀⠀⠘⠾⠛⠉⠀⠑⢇⣴⠇⠀⣇⠀⠀⠀⡇⠀⠀⠀⠂⢤⠁⠀⠐⠄
⠀⠀⠀⠘⠃⠂⠀⠀⡀⠀⣦⠀⠀⠀⠀⠀⣆⠐⢀⠈⠖⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⡏⠀⠀⠆⢣
⠀⠀⠐⠦⠀⠂⠀⠀⣄⠤⢚⣦⣄⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⣐⠀⠀⠸⣧⣀⣀⣀⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠊⠀⠀⠈⠉⢁⡆⡄⠀⠀⠀⠘⢃⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣼⡶
⠀⠀⠀⠀⠒⠋⠤⠼⠂⠀⠀⠀⠀⡌⠀⠀⠀⠀⡀⠠⡤⠔⠚⠉⠈⡁⠀⠀⠐⠒⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⡾⠛⠀⠐⠂⠐⠒⢒⣦⠀⠰⣔⣴⠶⠚⠋⠀⢀⠤⡄⠀⣀⡠⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠆⢸⣠⡄
⠀⠀⠀⠀⢓⠀⣠⠄⠉⠉⠉⠀⠀⠋⢿⡀⠀⣀⡠⠜⠀⠈⠉⠁⢠⠤⠀⠀⡔⠀⢠⣤⡄⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⠀⢠⠞⠓⠀⠀⢸⠀⢛⡀⠁
⠀⠀⠀⣀⠀⠀⠀⠐⠾⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⣠⣌⣩⣛⠝⠁⡀⢈⠋⢠⡇⢈⣌⠇⠀⠀⠀⣠⠀⠁⢀⠀⠸⠀⠀⠁
⠀⠀⠺⢫⠁⢀⣈⣉⣉⣉⠿⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⠸⢤⣬⣯⠄⠀⠀⢠⡏⠉⣾⠉⠂⠈⠂⠐⠂
⠀⠀⠀⠀⢙⠢⠤⠖⢂⠀⠀⠀⠀⢮⠤⠴⠶⠖⠂⠂⠐⠂⡗⠂⠀⠀⠀⠀⢀⣴⣺⣠⣤⣵⡷⠃⠄⠀⠀⠀⠀⠀⠀⢾⣀⣀⣻⣷⡀
⠀⠀⠤⢀⣀⠀⠐⣊⡁⠀⠀⠀⠀⢰⡖⠂⠒⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⣛⣯⢿⠋⠼⣽⡄⠨
⠀⠀⡶⠂⠀⠐⠂⠀⠀⢲⠠⠀⠀⠘⡇⠀⠹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣄⠀⠁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠟⢳⢂⡦⣠⠜⣡⡔⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢈⡇⠀⠀⠓⠢⠖⠓⢪⣌⠀⠘⢖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠀⠠⣤⣤⣄⠸⣷⣶⠆⠀⠀⢠⣅⣂⣙⣖⢚⣫⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣠⡎
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⢦⣯
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⣀⠄⠀⠀⠀⠉⢉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠐⡼⠃⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠹⣿⡀⠔⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠐⡸⠆⠒⠄⠐⡆⠀⠗⠀⠶⠀⠴⠀⠂⠀⢸⡇⢸⣿
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⡇⢸⠀⠀⠀⠀⡇⠀⠘⠀⡀⢰⠀⠀⠰⡃⢸⡟
⠀⠀⠀⡀⠀⣠⡤⠀⠒⠦⠾⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠃⠈⠀⠀⠀⠀⠃⠀⠐⠀⠃⢸
⠀⠀⠀⠈⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠐⢝⣁⣉⣀⣉⠐⠀⠀⠀⠐⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠁⠀⠈⠈⠩⢿⣿⣿⣿⣿⠀⣾⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣻⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⣿⣿⠀⣿⣿⣿⠿⣿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⣿⡟⣷⣿⣿⠿⠿⠯⠀⠘⢷⣦⣭⣙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠘⠛⠀⣥⣤⠄⢴⣿⣷⣿⣿⢿⣿⣿⣿
⣿⣿⣿⡿⣡⠆⢀⣿⣿⣿⣿⠷⠁⢦⠀⠰⠀⢀⣿⣿⣿⡛⠛⣻⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⡄⢰⣿⢀⣿⣿⣐⠱⣿⣿⣿⣿⡿⣹⣿⣿
⣿⣿⢣⣾⡟⠀⣾⣿⣿⣿⣿⡇⠀⡳⣶⢓⠶⣟⣻⣿⣿⡇⠠⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠃⢀⣉⣾⣿⣯⣧⡴⣿⣿⣿⣿⣇⣿⣿⣿
⣿⣡⣿⣿⠇⢰⣿⣿⣿⣿⣿⡇⠀⣿⠿⠞⠓⠛⢋⣁⣤⡄⠐⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠌⠿⢿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠏⡾⣾⣿⣿⡿⠛⣛⡁⠀⣤⢶⣶⣿⣿⢹⡟⢷⡧⠠⢽⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠶⣾⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣟⣿⣿
⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⢆⠀⣆⣄⢌⡍⡛⢻⢾⡆⡇⠀⠈⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠰⣈⣃⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⣹⡎⠀⢻⣿⢿⢾⣆⠄⠀⠈⠀⠀⠀⠀⢠⣮⣧⡤⠯⠏⠙⠛⠀⢈⣄⠀⠈⢛⢻⠏⠫⠿⠉⠙⣿⣿⣿⣿⣿⣿⣧⣻
⣿⣟⣵⣿⣿⣿⣿⣿⣿⣹⣿⡆⠀⣿⣿⣿⣿⣿⣧⠒⠄⠀⠀⠀⠀⡟⠛⠀⣄⢤⡄⢀⠀⠀⠀⡿⢦⠀⠀⢰⣦⢰⡶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠇⠀⣿⣿⡏⠙⣿⣏⡅⠀⠀⠀⡐⣼⣅⣴⣀⠁⠉⡁⠀⢤⣆⡀⠹⣿⣦⡀⢰⡄⠸⠕⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⡃⠀⣿⣿⡷⠀⢛⠛⠂⠀⢀⢌⡜⣡⣌⠃⡩⣷⡶⠂⠀⡽⣿⣁⡀⠛⡼⢷⡄⠀⠐⠈⠌⠩⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣥⣠⠏⠟⠃⢀⡉⠁⠀⢠⣿⣿⠁⣿⡿⢸⣆⣿⣿⣦⡀⣿⣋⣙⣷⠠⣞⣾⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⡗⠀⠀⢸⡉⠙⣧⣉⣡⡾⣽⣿⣿⣿⣿⡿⢿⣿⡶⡦⠠⢾⣿⡿⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿
⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣏⣯⣿⣿⣶⡛⣷⣶⣶⣾⠿⠃⠀⠀⣀⣘⣿⣿⣿⣿⣿⡟⠛⠛
⠀⠀⠀⠉⠹⠟⠟⣻⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣌⠴⣏⣽⣿⣿⣟⣿⣿⣾⣾⣿⠏⠀⠀⠀⠀⠃⠘⠿⠍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣝⣻⣿⣽⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠄⣀⢀⡀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠈⠋⢀⣠⣀⡀⢢⡙⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡿⠋⣀⣶⣶⣄⣠⣾⣻⣿⣯⣥⣄⡁⠸⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣠⣧⣾⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⢯⣲⡌⣿⣿⢿⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢿⣿⣿⣋⠧⣼⡟⣿⣿⣿⣅⠀⠼⠿⣿⡗⣯⢞⣿⣛⣿⣿⢨⠰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⣸⣿⣾⣿⣅⠉⢻⣿⣿⡟⠁⢠⡄⢠⣾⣿⠋⣡⣿⣻⣿⡏⢠⠀⡿⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡄⠛⢠⡿⣿⣿⣿⣿⡇⡼⢏⣼⠟⠱⠚⣿⣦⡧⠛⢺⣿⣿⣿⣿⡏⢸⠈⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡃⠀⠇⣻⣿⣿⡿⣿⣧⡿⢋⡤⠤⠄⠈⢻⣿⢰⣿⣿⣿⣿⣿⣷⡇⣰⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣀⠰⢸⣿⣿⣶⣿⢿⣇⣾⣶⣿⢶⡶⣺⣿⡘⣿⣿⣿⣿⣿⣿⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⢻⡿⢻⣿⣿⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⣿⣻⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣿⣄⠘⠻⢿⡿⣯⣽⢿⣿⢣⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⢉⣽⣿⣿⠛⠻⠿⢿⣿⣿⣿⣯⣭⠟⠻⣿⣿⣿⣿⡀⠀⣸⣏⣠⣤⠀⢡⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠰⡥⢶⡶⠾⢍⡀⡿⠃⠀⠀⠀⠙⠻⣿⣿⡗⠀⠀⠀⠻⢿⣿⡟⣰⣷⣿⣿⠿⠀⡙⢰⡟⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠀⠉⠙⠛⣿⠁⠀⠀⠀⠀⠸⠁⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⠿⢿⠿⣿⠟⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡄⠀⡞⠒⠤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣾⣿⣿⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⡴⠛⠁⠀⣇⣇⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀⣎⠉⠉⠉⠉⠉⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠛⢀⠴⠊⢁⡤⠟⠁⠀⠀⠀⠀⠈⠁⠀⢸⣿⠇⠀⠀⣠⠀⡀⠀⠹⡀⠀⠀⠀⠀⢀⠜⠀⠀⠰⣳
⠀⠀⠀⠐⠈⠀⢿⣅⣠⠖⠉⠀⠀⣤⡄⠀⢠⠦⢐⡇⠀⠈⠉⠉⠀⠀⠁⠀⢇⠀⠀⠈⠓⣤⣦⠶⠁⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢠⡄⠈⠀⠀⢾⣠⣞⣀⣀⠀⠀⡄⢀⡀⠀⢠⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀
⠀⠀⠀⠀⠀⠘⠁⢰⣖⠤⣀⠀⢀⢀⠀⠀⠀⡟⢉⣉⣹⠃⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠈⡕⠊⠉⠰⠦⡄⣀⢠⡯⠚
⠀⠀⠀⠀⠀⠀⢀⡾⠉⣻⠞⢁⠀⠂⠂⠀⠈⠙⠋⡽⢉⣽⠂⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⡎
⠀⠀⠀⢀⡤⠒⠛⠁⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠉⢻⠄⠀⠀⠑⢄⠀⠀⠀⣀⠇⠀⠀⠀⢠⡀⣹⢖⡲
⠀⠀⠀⣿⣿⣶⣦⣄⠘⡆⠀⢸⡠⡇⡀⢰⠆⠀⠀⠀⢧⠄⠀⠉⠀⠀⠀⠀⠀⡅⠈⠁⠀⠀⣀⡀⠀⠸⡟⠉⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣷⠇⠀⠘⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠸⣔⡝⠀⠊⠀⢀⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⠤⣶⣶⣶⣒⡦⠀⠟⠳⠄⠇⠀⠀⠀⢹⡀⠀⢀⣴⠷⣴⠁
⠀⠀⠀⢀⠤⡞⢶⠀⠀⠀⠀⢾⣁⣀⣠⡴⠂⠀⠀⠈⢺⢻⠟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣴⠟⠁⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠚⠋⠿⣍⠀⠀⠀⠀⠀⠀⠀⡞⣷⡏⢹⡆⠀⠀⠀⠀⠀⣤⠀⠀⠘⠒⠃⠀⠀⠀⣿
⠀⠀⠀⠀⢠⡚⢧⠀⠀⠘⣛⣦⣄⣼⠇⠀⣀⠀⠀⠀⠀⢱⢻⣷⠸⣇⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣉⡁⣻⠀⠀⠘⠉⠀⠀⠀⠠⠈⡜⣿⡄⢿⠀⠋⠉⠹⡇⢱⠆⠀⠀⠀⠀⠀⠀⠘⠬⠜
⠀⠀⠀⢠⣄⠀⠀⢨⠖⠊⠛⢿⡉⠀⠀⠀⡤⠄⢤⠀⡀⠀⢣⢿⣷⣸⡇⠀⠀⠀⡸⢧⠀⠀⠀⠈⠈⠈
⠀⠀⠀⠈⣁⠀⠀⠙⠀⠀⢐⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠯⠚⠀⠀⠀⠘⠃⠀⢱⡄⠀⠰⣮⣭⣭⣵⠂
⠀⠀⠀⠘⠒⢃⣘⡟⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡆⡇⣀⡤⠒⠁⣠⣀⠀⢸⠈⢩⡇
⠀⠀⠀⠀⢐⠛⠉⠉⢹⠛⠉⡆⠀⠀⠀⠀⠈⠀⣀⡀⠴⠶⠶⠦⠤⣀⣀⣀⣀⣩⣤⡄⠀⠑⠋⣠⠜⠀⠀⠡⡀
⠀⠀⠀⠀⠈⡄⠀⠀⢸⠇⠀⢸⠀⠀⠛⠉⠉⠉⠙⠳⠦⠤⠥⠤⠼⠋⠉⠀⠀⠀⠀⠠⣶⠀⠀⣷⣶⣿⣿⣿⡟⣄
⠀⠀⠀⠌⠀⠉⠉⠹⠥⠤⠖⠚⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⡒⢲⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⢒⠒⣦⠀⠀⠀⠀⠀⣴⠒⠒⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠉⢹⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡇⢀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣀⣴⣶⣶⣦⣀⢀⡀⢻⠀⠀⠀⠀⣰⠃⣤⣶⣦⣤⡈⢧⠀⠀⠀⠀⠀⡇⢸⣹⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⣿⡁⣹⣿⣿⣿⡇⢸⠀⠀⠀⢰⠇⣼⣿⣀⣸⣿⣷⡈⢧⠀⠀⠀⠀⡇⢸⡿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠹⢿⣿⣿⣿⣤⠟⣠⠎⠀⠀⠀⡏⢸⣿⣿⣿⣿⣏⣿⣷⠘⡇⠀⠀⠀⡇⢸⣷⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣬⣭⣭⠴⠞⠁⠀⠀⠀⠀⠳⢬⣭⣭⣭⣭⣭⣭⣥⠾⠁⠀⠀⠀⠹⢤⣭⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡉⠩⣭⡽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⢩⣭⠗⠀⠀⠀⠀⠀⠺⡍⠉⠉⣭⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠃⠀⠀⠓⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣀⡀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡇⢰⣦⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣴⣿⣿⣿⣷⣤⣤⡄⢹⠀⠀⠀⠀⡼⢁⣶⣿⣷⣶⣆⢹⡄⠀⠀⠀⠀⡅⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣿⣿⣿⣿⣿⣿⣿⠇⣼⠀⠀⠀⣼⢁⣾⣿⣿⣿⣿⣿⣆⢳⡀⠀⠀⠀⡇⢸⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⠿⢿⠿⠟⣃⡼⠁⠀⠀⠀⣇⠺⣿⣿⣿⣿⢿⡿⠿⢀⡇⠀⠀⠀⣇⠸⠿⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠒⠚⠁⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠶⠶⠒⠋⠀⠀⠀⠀⠈⠓⠖⠛⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠶⠶⠶⠶⠶⠶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡖⠀⠀⠀⠀⢦⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⢀⡞⢠⠟⠀⠀⠀⠀⠀⠈⢳⡈⢧⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⠛⠻⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠛⠛⠛⠛⠛⠛⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⡾⠁⠀⠀⠀⠘⣆⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡼⠃⠀⠀⠀⠘⢧⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡾⢁⡞⠀⠀⠀⠀⠀⠀⠘⢦⠘⣆⣘⣛⣛⣛⣛⣁⡼⢁⡼⠁⠀⠀⠀⠀⠀⠈⢧⡘⢧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠏⣉⠉⠉⠉⠉⡉⢳⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣀⣀⣀⣀⣀⠀⣰⠏⣰⠃⠀⠀⠀⠀⠹⣄⠻⡄⠀⣀⣀⣀⣀⣀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣭⣩⣭⣭⣥⣴⠃⡼⠃⠀⠀⠀⠀⠀⠀⠘⡆⠹⣤⣭⣭⣭⣭⣍⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢠⠄⠀⠀⠀⢠⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡄⠀⠀⠀⢠⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠏⠀⠀⠀⠀⠀⢳⡈⢷⡀⢠⣤⣤⣤⣤⡄⢠⡞⢠⠏⠀⠀⠀⠀⠀⠻⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠴⡏⠰⠃⠀⠀⠀⠀⠀⠀⠀⠻⠀⣷⠴⠶⠶⠶⠶⠶⣏⠰⠏⠀⠀⠀⠀⠀⠀⠀⠹⠄⣹⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡶⠀⠀⠀⠀⢦⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠶⠶⠶⠶⠦⢀⡞⢡⡞⠀⠀⠀⠀⠀⠈⢷⡈⢧⠀⠶⠶⠶⠶⠶⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠒⠒⠒⠓⠒⢻⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⣨⠗⠒⠒⠒⠒⠓⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⠛⠛⠛⠛⢂⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠉⠉⠳⡄





⠀⠀⠀⢀⠴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⠴⠦⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⡀
⠀⠀⠀⣟⠀⠀⢸⡇⣷⠃⣴⠋⢳⡆⢘⣙⡆⢸⡞⠻⡆⢰⠀⡾⠋⠁⠀⢸⡃⠀⠀⢸⡗⠙⣦⢠⣋⣹⡆⣶⠋⢳⠋⢳⠀⣷⠰⣏⠁⢸⡏⢰⡟⠃⢷⢀⡖
⠀⠀⠀⠙⠦⡤⠞⠀⠟⠀⠻⠤⢾⠇⠯⡤⠇⠸⠇⠀⠇⠸⠀⠳⢤⠄⠀⠈⠳⢤⠤⠘⠇⠀⠿⠘⠦⡤⠀⠿⠀⠸⠀⠸⠀⠇⠠⡬⠇⠸⢧⠸⠇⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠉⠉⠉⠉⠐⠤⡀
⠀⠀⠀⠀⠀⡠⠊⠁⡠⠄⠒⠈⠁⠀⠈⠁⠒⢄⠈⠳⡀
⠀⠀⠀⠀⡜⢀⠔⠁⠀⡀⠤⠀⠒⠂⠠⢄⠀⠀⠑⡄⠘⡄
⠀⠀⠀⡜⠀⠏⠀⢠⠊⢀⠔⠈⠉⠉⠢⡀⠱⡄⠀⠘⡀⠰
⠀⠀⠀⡇⠀⠀⠀⡎⠀⠎⠀⠀⠀⠀⠀⠰⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⢇⠀⢁⠀⠱⡀⠰⡄⠀⠀⠀⡠⠃⢠⠃⠀⠀⢀⠀⠃
⠀⠀⠀⠈⢆⠀⠀⢄⡑⣄⠈⢦⠒⠉⣀⠔⠁⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠑⠢⠄⣀⠘⡄⠀⡗⠉⠀⠀⠀⠀⠀⠀⠘⡀⠈⠄⠀⠀⢠⠤⠤⠤⣤⠀⠀⠀⠀⠀⡤⠤⠤⢤⡀⠀⠀⠀⠀⢠⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⠒⠲⠻⠀⠀⠀⠘⡓⠐⠒⠐⠚⠃⠀⠀⠀⡟⠒⠐⠒⠚⠃⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⢀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⢤⣤⣤⣀⣰⠤⠀⠀⠀⠤⣧⣤⣄⣠⡧⠄⠀⠀⠤⢼⣤⣄⣀⡮⠄
⠀⠀⠊⠀⡄⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡄⠀⢀
⠀⠀⠀⠀⠇⠀⠀⠀⠲⡉⠠⠆⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠐⠺⡄
⠀⠀⠤⠠⠄⠀⠀⠀⠀⠸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠠⡇⠀⠀⠀⠀⠀⠸⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⡇⠀⠀⢈⠁⠀⠤⢘⣋⠒⠂⣙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢣⠀⠈⠀⠀⠀⠀⠀⠀⠢⡀⠠
⠘⠉⡀⠂⡜⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠴⠃⡀⠂⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡎⠀⠠⠄⠀⠀⠐⠀⠊⠢
⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠂⠀⠤⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠂⠐⡄⠀⠀⠀⠀⡀⠀⠀⠐⡠⠀⠀⠀⠀⢀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠐⢧⡀⠠⠀⠀⠀⠤⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠈⡀⠀⠀⠀⠀⢰⠄⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠰⠄⠬⠄⠀⠩⠀⠤⠬⠥⠤⠤⠤⠤⠬⠤⠤⢤⡥⠤⠤⠤⠤⠤⡥⠤⠤⣬⠤⠤⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠇⠀⠀⠀⠀⠀⣿⡄⠀⣾⠀⠀⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠀⠀⠆⠀⠀⠀⠀⠀⠿⠃⠀⠸⠀⠀⠸⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⡅⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠀⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢸⠂⠀⠠⠃⠀⠀⠀⠀⠀⡇⠀⠂⡇⠀⠀⠀⠀⠀⢰⠂⠀⠆
⠀⠀⠀⠀⠀⠀⢀⡤⢒⣪⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣸⠆⠀⠀⠀⠀⠀⣥⠀⣀⠇⠀⠀⠀⠀⠀⢸⡀⠀⣄
⠀⠀⠀⠀⠀⣰⠞⡼⠋⠀⠙⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⡀⠀⣀⣿⣼⡁⠀⡠⠈⠉⠉⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠠⠉⠉⠄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠠⠂⠤⠤⠐⠕⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠍⠉⠉⠅⠀⠀⠀⠀⠀⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠆⠀⠀⠀⠀⠀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠉⣀⠀⠁⠂⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⢠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠊⠀⡐⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢑⠂⠉⠀⠀⠀⠤⠉⠒⠉⢁⡀⡇⠀⠀⠀⠀⠀⢀⡅⢀⡰⢘⠁⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠰⠀⠀⠀⢠⠒⠀⠀⠀⡇⠀⠀⠀⠀⡠⠁⠈⠐⠖⠁⠈⠀⠂⠄⠈⠂⡀
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠑⢕⠄⡀⠀⢀⡠⠀⡀⢐⠅⠀⠀⡇⠀⠀⠀⣔⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⠄⠈⠄
⠀⠀⠀⠀⠡⠀⠀⠠⠃⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠗⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢠⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠶⠚⠠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡐⢒⠓⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡐
⠀⠀⠀⢀⠀⠀⠘⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠠⣤⠙⠠⡀⠀⡠⠊⠁⠀⠈⠀⡤⠊⢀⠔
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠄⡀⠙⠀⠀⠀⠀⡄⠀⠈⡔⠁
⠀⠐⠂⣀⠀⠀⠈⠕⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠀⠀⠠⠀⠀⠉⠀⠀⠈⠀⠁⠀⠀⡇
⡀⠄⡀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠇
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⠤⢤⡀⠀⠀⢀⣀⡤⣴⣂⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠤⢴⣆⡈⠉⠉⠁⠀⢤⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣿⠀⠀⠀⠙⣶⢤⡴⠖⠲⠤⢤⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⠀⠀⢉⡴⠃⠸⡇⠀⠀⣀⠀⢹⠟⡷⠄⠀⠀⣠⣴⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠉⢄⠀⢀⣳⣤⣀⣁⡴⠋⠀⢇⣠⠴⠋⣨⢼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡄⠀⠀⠀⠀⠙⠢⣌⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢊⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⡻⣄⡀⠀⠀⠀⠀⠀⡴⠛⢳⡶⢶⠶⢶⠖⢻⠯⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣯⠹⡄⢙⠒⠦⣀⣠⠔⢣⠀⢰⠈⠁⢈⠋⣴⠋⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠗⠠⣄⡜⠀⠀⠀⠁⠀⢸⠀⡌⠀⠀⠈⢰⠹⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⣣⡀⠀⠀⠀⠀⠏⣤⠃⠀⠀⢠⡇⠀⡆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡏⠈⠁⠒⠒⢸⢠⠃⠀⠀⠀⠀⠇⠀⣥⣀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉⠀⠀⠀⠀⠀⠆⠎⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⢰⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⢠⠴⠚⠒⢄⠀⠀⠀⢠⠎⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡹⠢⠄⣨⠖⠀⠀⠀⡱⠤⠚⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠃⠀⠀⠈⡿⠤⠶⢊⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⠏⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⡠⠀⠀⠀⡀⠀⠀⠀⢔⠒⠒⣒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠁⠂⠄⢀⢀⠃⠀⠀⠈⠉⠉⠀⠉⠉⢫⠀⠀⠀⢘⠉⠁⡛⠀⠀⠀⠀⢨⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠑⠲⠤⠤⣀⡸⠂⠠⠀⡀⠀⠀⠀⠀⠀⢘⡄⠀⠀⢸⠀⠀⠇⠀⠀⠀⠀⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠈⠁⠀⠂⠀⠀⡇⠀⠀⡸⠀⠀⠠⡀⠀⠀⠀⠰⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠙⠦⠤⣄⣀⣀⢸⠂⠈⠉⠑⠒⠠⠤⢤⣀⣀⣀⡇⢠⠊⠀⠀⠀⠀⠈⢢⠀⢠⠃⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇⠀⡆⠁⠀⠈⠉⠀⡆⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠀⢰⠂⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⡃⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠣⣀⠀⠀⢀⡠⠃⠠⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠇⠰⠘⢻⠰⠘⠃⠋⠀⠈⠈⠃⠃⠀⢀⠠⣦⣠⠄⠀⠀⣀⠳⣄⠀⡜⠁⠀⠀⠀⢠⠀⢠⣜
⠀⠀⢣⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠸⠧⠎⠀⠀⠀⠀⠁⠀⠈⠀⢧⠀⣀⣀⡤⠎⠀⡇⡟⠀⠀⢀⡀
⠀⢠⡈⢧⠃⠀⠀⡰⠢⣎⠀⠀⠈⠓⠀⠢⣀⣀⣀⠀⢀⠀⣠⠀⠀⢠⠞⠉⠉⠈⠉⠻⡉⠀⠀⠀⠀⢇⠣⠤⠚⣻⠄
⠀⠀⠘⢼⠄⠀⢛⡀⠀⢹⠀⠀⢀⡀⡠⠊⠁⠀⠀⠈⠙⠁⠉⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⢀⣀⡀⠀⠈⠓⠒⠊⠁
⠀⠀⠀⠈⡇⠀⠁⠘⠛⡍⠀⠀⠈⠁⠀⠀⡄⠀⠀⠀⣠⡼⢀⡤⠤⠤⠵⢤⠐⠤⠒⠋⡰⡟⠉⢠⢪⢂⢆⠀⣀
⠀⠀⢀⡀⢡⠟⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠚⠋⠀⢯⠀⠀⠀⠀⠀⢳⠀⠀⠀⢧⣉⠷⣇⡈⢁⠆⠸⣿⡇
⠀⠀⠀⠱⣾⠀⢰⠉⠉⡱⠚⢄⣸⠀⠄⠤⠶⠋⠉⠉⠓⠒⠶⢷⠤⠤⠴⠖⠚⠀⠀⠀⠀⠀⠈⠁⠘⢪⡤⡄
⠀⠀⠀⠀⠹⠀⠀⠳⣔⠁⠲⢀⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⣤⡄⠠⣤⡄⢠⣤⠀⠀⢸⡂⡄
⠀⠀⠀⠀⠘⠀⠈⢀⡃⢑⡲⠮⠀⠴⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⢰⡆⠀⣶⠀⢸⢷⠀⠀⢸⠄⡇
⠀⠀⠀⠀⢀⣀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠐⠆⠀⠀⡔⡲⡀⠀⢸⡇⠀⣿⠀⢸⣾⠀⠀⢸⠀⡇
⠀⠀⠀⠠⠘⡍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢓⠃⢀⠀⠀⡯⣹⡁⠀⠘⠃⠀⠛⠀⠘⠛⠀⠀⠸⠤⠇⠆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡟⠻⡃⠀⠀⣐⠃⢱⡆⢐⠆⠣⠔⠁⠀⠀⡸⠁⠀⠀⢀⣄⠀⢀⠴⢆
⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⡰⠀⠀⢡⠀⠀⠉⠀⠀⠀⠀⣀⡀⢀⠀⠀⠘⠓⠠⣶⠊⠀⠀⠱⠃⢀⠀⠙⠆
⠀⠀⠀⢠⡪⢌⡆⠀⠀⠀⠀⢠⠃⣠⡀⡀⣆⠀⠀⠛⢸⠂⠀⠀⡄⠸⠄⠀⠀⠀⢀⡀⠳
⠀⠀⠀⡏⠀⠉⢹⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⡀⠀⠀⣷⠀⣦⠀⣺⠀⠀⠑⠂⠀⡤⠤⢴⠀⠀⠴
⠀⠀⠀⠙⠲⠶⠊⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⠀⠀⠀⣿⠀⠻⠀⣿⠀⢸⡇⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢰⣄⣀⡘⣧⣀⠬⢿⡬⠤⠄⠀⠀⠀⠠⢸⠄⠀⠀⣟⠀⠀⠀⢿⠀⢸⠁⠀⠀⣿⠀⢸⡇⠀⢴⡄
⠀⠀⠀⣶⠖⠈⠉⠟⠀⠘⠋⠀⠘⠁⠀⠀⠀⠐⡆⠒⠺⠓⠒⠚⡛⠚⠛⠒⠛⠒⠚⠞⠒⠲⠛⠃⠛⠃⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠉⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢎⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⡘⠶⠶⠦⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⡠⠊⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠁⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠠⢀⡇⠀⠀⢀⠄⢲⣿⡤⢄⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠱⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠘⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⡠⠀⠀⠈⠢⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⢠⣤⡄⠤⡀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡏
⠀⡇⠀⠀⡜⠀⠀⠀⠀⠀⢘⠢⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡖⠁⠀⠀⠀⠀⠱⠦⠤⠖⢏⣢⣀⠀⠀⠀⠀⡎⠀⠀⡵⠀⠀⠀⠀⢰⠁
⡰⠁⠀⠀⠐⠂⠤⠤⠀⠀⣤⠀⠤⠑⠒⢌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡰⠚⠓⣄⠀⡎⠀⠉⢳⠀⠀⠀⠙⠢⠾⠁⠀⠀⠀⠀⠘⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠳⠄⡤⠃⠀⠙⠒⠒⠁⠀⠀⠀⠀⠀⡼⠋⠉⢢
⢀⡞⠉⢳⡀⠀⠀⠀⠀⠈⠻⡁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⡜
⠈⠧⡤⠞⢣⡶⠒⠒⢄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠤⠤⣄⠀⡏⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠠⠄⠀⠀⠄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⡼⠌⢧⡀⠀⣠⠞⠀⠀⠀⠀⡞⠉⢲⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢠⣶⡄⣠⠀⠀⠀⠀⠐⠀⠀⠀⢈⡀
⠙⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠀⠈⠀⡀⠛⠀⠄⡀⠀⠀⠻⠃
⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠁⡰⠄⡀
⠶⠋⠀⠺⡀⠀⠀⢰⠉⠙⣦⣀⠄⡴⠋⠉⠳⡄⠀⠀⠀⠈⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠌⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢠⠀⠀⠀⠑⠄⠀⠈⠑⠚⠁⠀⠈⢧⡀⠀⢀⡧⠀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⣤⡤⢤
⠀⠡⡀⠀⠀⠈⠂⣀⡀⡀⠀⠀⠀⠀⠉⠉⠉⠀⡟⠁⠀⠙⣦⠀⢐⡎⠀⢹⠀⠀⠀⠣⡄⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠳⢄⣀⣠⠏⠀⠀⠈⠐⠁⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷
⠀⠀⢀⠃⠀⠀⠀⠀⠀⡀⠀⠐⠈⡆⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⢸⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠗⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⡇
⠀⠀⠘⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠱⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢡⠀⠀⠀⡠⠂⠉⠉⠙⢢⡀⠀⠀⠀⠀⡠⢤⡜⠓⠉
⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢧⡀⠀⠀⠀⣰⠃⠀⠀⠀⠸⡀⢀⡸
⠀⠀⠀⠀⠀⠉⠒⠒⠐⠒⠈⠀⠀⠀⠀⠀⠀⢀⡖⠋⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠⠀⠀⠀⠀⣟⠒⠒⠛⣥⢦⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⢤⡜⠷⢄⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡎⠉⠙⡄⠰⡂⠀⢀⡇
⠀⠀⠀⠀⠀⢠⠖⢠⡀⠀⠀⠀⠀⢺⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠚⠁⠀⠉⠛⠉
⠀⠀⠀⠀⠀⢃⠀⣀⠇⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⢀
⠀⠖⠲⠀⢸⠀⠀⠀⠀⠀⢀⢀⣀⣄⣨⣀⣄⣸⣀⡇⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⢀⠤⠀⠀⠀⠀⠀⢛⡀⡀⠀⠀⡀⢀
⠀⣍⢈⡄⡜⣄⣸⠉⡄⠀⠈⠉⠉⠉⢉⠉⠉⢩⠀⠁⡇⠀⠖⠰⠠⠄⠐⠒⠈⠀⠀⠤⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈
⠀⠁⢀⠀⠸⠁⡜⠀⠣⠀⠠⠄⠠⠀⠈⠠⠀⠈⠤⠀⠇⠀⢀⠀⠠⠄⠀⠀⢀⠎⠀⠀⠀⠀⠀⠠⠠⠤⣏⡁⠀⠀⠌⠁⠐⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠈⠁⠀⢀⠈⠀⠀⠀⠀⠀⢀⡀⠂⢀⠀⠀⠈⠁⠸⠀⠀⡨⠀⠀⡆⠈⠣⠀⠁⠰
⠀⠀⠀⡀⠰⠈⠀⠂⠀⡤⠀⠠⠄⠀⠀⠀⠠⡀⠀⠀⠀⠂⠀⢁⠑⠘⠦⠀⠀⠀⠀⣠⠲⠆⠦⠀⡂⠀⠀⠀⠀⠀⠀⠊⢢
⠀⠀⢀⡉⡁⠒⠒⠂⠁⠠⠄⠈⠀⠀⠀⠀⠀⠀⠈⠡⠀⡀⠀⠂⠀⢠⠆⠀⢠⠐⢈⡅⠀⠀⠀⢘⠂⠀⡄⣤⣈⠀⠀⠗⠳⡆⠀⡀
⠀⠀⠀⠀⡆⢀⠤⡀⠀⠀⠀⠀⢠⠄⢐⠀⠀⠀⠂⠀⢈⡞⠓⠒⠈⠀⠀⠀⠘⡆⠈⠱⣦⢠⣄⠛⠁⢰⠃⠒⢇⡸⣐⠂⠀⠀⠀⠀⠀⢠⠰
⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⢀⣀⡒⠀⠀⠀⠀⠠⠋⠀⠀⡀⠀⠐⠀⠀⠀⠈⠢⣄⣐⠀⣀⣡⠔⠚⠀⠀⠀⣐⢁⠀⠐⡤⠀⠂⡀⠀⠁⠀⡁
⠀⠁⠀⠀⠀⠈⡆⠀⠂⢐⠀⠀⠠⠠⠀⠀⠀⠀⠀⠔⠈⠉⡉⠀⠜⠠⠀⠀⠀⠀⠀⠢⠉⠉⠁⠀⠀⠠⠀⠀⠘⠀⠈⠀⠐⢠⡀
⠀⠀⠀⠀⠀⠔⠀⠀⡀⠈⠠⠀⠠⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⢀⢀⠀⠀⡀⢦⠀⢄⠔⡙⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠔⡈⠁⠐⠀⠀⢀⡀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠄⠀⠀⠀⠀⠀⠘⠀⠀⠉⠉⠀⠙⠁⠀⢠⠀⠀⠀⠢⠒
⠀⠀⠂⠀⠀⣀⣀⣀⣈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⣰⣶⠶⣶⡆⣶⠶⣶⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠁⠠
⠀⠀⡀⠀⠄⠳⠄⠀⢸⠀⠀⠀⠀⢐⠀⣀⣀⡢⢸⣿⠀⠀⢿⡅⠀⢻⡇⣿⡀⣼⠇⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡁
⠀⠀⢧⠀⡝⢻⠀⠀⢸⠀⠀⠀⠀⢠⡀⠀⢠⠅⢸⣿⠀⠀⢸⡗⠒⢻⡇⣿⠿⣿⡄⠀⠀⡶⠶⠒⠒⢶
⠀⠀⠚⠁⠍⠈⠀⠂⢘⠃⠒⠀⠀⢀⠑⠐⠁⠀⠸⣿⣶⡆⣽⠇⠀⠸⠇⠿⣴⠿⠁⠀⠀⠃⠀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠀⠠⠀⠀⠃⠩⠁⠉⠀⠀⡂⠀⠀⢀⠀⠀⢠⡤⣤⣤⣶⣶⣶⣶⣶⣶⡄⠀⠀⢀⠀⢀⣐⡀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑
⠘⠒⠤⠠⠤⠔⠂⠁⠀⡀⠀⠀⠘⠉⠑⠒⠚⠀⠀⢸⣧⣧⣿⣦⣿⣤⣿⣧⣾⡇⠀⠀⠸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠉⠉⢉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠁
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠘⢘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⢀⠃⠄⠀⠀⠀⢀⢂⠀⣠⠀⠀⠀⠀⠀⣁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠖⠀⠀⠀⠀⠀⠁⡌⠀⠀⣑⡄⠂⠀⠐⠜⡡⠀⠀⠀⠀⠀⠂⠁⠀⠐⠁
⠀⠈⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⡐⠀⠀⢀⠈⠀⠈⠀⠀⠀⠀⠂⠑⠢⠁⡀⠀⠀⠀⠜⠁⠁⠀⠈⠀⠀⠄
⠀⠈⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠃⠠⠄⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠄⠠⠀⠠⠀⠀⠀⠘⠀⠀⠀⠀⠆⠀⠀⠡
⠀⠀⢠⡄⣴⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⡀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠆⠰⠀⢀⠠⢀⠒⠂⠐⠀⠀⠀⠉
⠀⠀⢸⣇⣿⢠⣶⡄⢸⡆⣿⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢂⠀⠱⠚⠀⠀⠁⠀⠀⡌⠀⠀⠘⠀⡀
⠀⠀⢸⡇⢹⠀⢰⡇⢸⣇⣿⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠂⠁⢁⢈⡀⡄⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠀⠂⠀⠐
⠀⠀⠘⠃⠘⠀⠛⠓⠈⠛⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠈
⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡠⠊⠀⠀⠀⠀⠐⠀⡵⠂⢓⠉⠂⠀⠀⠀⠀⠉⢩⠁⠁⡀
⠀⠀⠀⠄⠀⢉⠄⠀⠀⠀⠀⠀⢀⠀⡀⠁⠈⠀⠀⠀⠀⠀⢐⠡⠊⠀⠀⠀⠀⠀⠀⢠⠑⡆⢀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠂⠈⠂⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠜⠢

⠀⠀⠁⡅⠁⡄⠀⠄⠀⠀⠀⠀⠀⡀⠀⢠⡄⠀⠀⠀⠀⠁⣂⠄⠙⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡠⠘⠑⠀⡄⡄
⠀⠠⠄⠇⠄⠣⠄⠳⠄⠀⠀⠀⠀⢯⠐⢨⠇⠀⠀⠀⠀⠀⠁⠀⠐⢢⢀⠀⠀⠀⠀⠐⠢⠁⠈⠤⡖⠢⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⠷⠟⡂⠄⠀⠀⠀⠀⠀⠀⣨⠉⠀⠁⠀⠀⠀⡔⠐⠁⢇⠀⠀⠀⠀⠀⢀⠈⠂⢀⢀⠠⠊⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠉⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⡴⡄⠀⠀⠀⠀⠀⠀⡄⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠠⢀⢀⡠⢄
⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡠⢁⠁⡀⠀⠀⠀⠀⡊⠀⠲⣀⠑⢄⠀⠀⠀⠀⠀⠀⢰⣤⡂⠀⠀⠀⠀⠐⢅⠀⢀⢵⡀⢀⠕
⠀⠀⠠⡄⢠⠀⡇⠀⠀⠀⠀⠀⠀⢰⢤⠤⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⢠⠌⡀⠀⡀⠀⠀⠀⠀⠀⠈⠇⠉⢈⠅
⠀⠀⠐⠤⠀⠀⠃⠀⠀⠀⠀⠀⠈⠄⠑⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⠉⠄⠀⠀⠀⠀⠀⠀⠡⠒⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⡆⠀⢁⠀⠀⠀⠀⠐⠀⠢⠄⠨⠢⠀⠀⠀⠀⠀⠀⠀⠉⣆⠀⠀⠀⠀⠀⠀⠈⢆⠀⡐⠁⠀⠀⠀⠀⢈⠔⠠
⠀⠀⡠⠂⠁⠀⠈⡇⠀⠀⠀⠈⢀⣙⠷⡟⣁⠈⠀⠀⠀⠀⠰⣠⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠉⠀⠀⡂
⠀⠀⠁⠈⠁⠁⠀⠃⠀⠀⠀⢀⣀⡀⠿⠃⡀⣀⠀⠀⠀⠠⠒⠒⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠈⠠⠠⠄⠠⠄

⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠂⠓⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⢀⢠⡤⠤⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠏⠉⢙⠇
⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢆⠀⠀⠀⠀⠀⠀⡰⠀⠀⠳⡀
⠀⠀⠀⠁⠀⠀⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠁⠈⠀⠁⠀⠉⠁⠀⠀⠀⣱
⠀⠤⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠠⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⡀⣰⣾⠤⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂
⠀⠀⢣⠁⠀⠀⠀⡼⠁⠀⠛⠙⣄⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠄⠀⣀⢀⣀⠠⠒⠁
⠀⠀⠀⠀⠀⢀⣀⡤⢐⣒⠚⠷⠊⠧⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲⠒⠾⠼⠟⣲⠀⠀⠀⠀⠀⠠⠶
⠀⠀⣀⠀⠀⠘⠀⡀⢰⢛⡾⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠥⠦⣀⣩⡗⠒⠄
⠀⠠⠀⠀⠀⠰⢄⠀⠀⠘⡇⢉⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠰⣷⠀⠀⠐⠂⠀⠀⠀⡏⠉⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣍⣉⡗
⠀⠀⠛⠀⠀⠀⠀⠀⠢⠤⠇⠀⠀⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠠
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⣀⡀⠀⠄⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠈⡀⠀⠀⠀⠀⢠⣄⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠿⠿⠿
⠀⠀⢾⣶⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠑⡒⠂⠘⢢⡄⡔⠁⠀⠑⠊⠂⠘
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⡄⢀⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢼⡿⡷⡶
⠀⠀⠀⠰⠰⠂⠴⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⠃⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠃⠘⠂⠛⠀⠓⢘⡃⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⢀
⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠄⢀⢠⠄⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⠘⠃⠁⠉⠈⠀⠀⠀⠀⡀⡀⠀⠘⠶⠤⠤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠈⠀⠀⡀⢄
⠀⠀⠰⣶⣶⣶⣶⡆⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡏⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⢐⠆⣀⢷⡄
⠀⠀⠐⠻⣿⣿⡿⠛⡀⠀⠠⠀⠀⠐⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢳⡜⢆⠏⠛⡾⣠⠈⠀⡜⠀⢸⣼⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢠⣴⠶⠶⣶⠄⠴⣦⢴⣦⡀⢴⡆⠀⠀⠀⠁⠀⢸⠀⢀⣇⣸⡄⢸⠁⡇⠐⡇⡜⠀⡯⢻⠃⠀⣶⡆
⠀⠀⢀⠄⠹⡇⠸⠏⠘⠀⠿⢀⠉⣀⢸⠇⠀⠀⠀⠀⠀⠈⠁⠚⠚⠁⠧⠞⠀⠈⠜⠁⠁⠒⠃⠘⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠀⠄⠀⠀⠀⠀⠀⠀⢀⣻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣤⡀⠀⠀⠀⢠⢀⡒⡁⠀⠀⢠
⠀⠀⢀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣻⣻⣦⡀⠀⠀⠠⠖⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠂⠀⠀⠀⢀⠀⢀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⢀⣶⡄⠀⢀⠀⢀⣀⠀⠀⢰
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢼⣿⣿⠀⠘⠒⠂⠂⠇⠀⠸
⠀⠐⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠐⠂⠀⠀⠀⠐⠐⠀⠐⠀⠀⠃⠀⠀⠃⠀⠐⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠧⠤⢩⠆⠀⠀⠀⠈⠀⠀⣠⢶⢆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠊⠀⠡⠀⠨⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠆⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠋⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠄⠈⠀⠀⠀⠀⠠⠀⢁⠀⠄⡉⠀⠀⠀⠀⠀⠀⠨⠀⠀⠂⠍
⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠑
⠀⠀⠀⠀⠀⡀⠃⠀⠘⢀⠀⠀⠀⠀⠀⢀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡐⡀
⠀⠀⠀⠀⠀⡀⠀⠘⠀⡈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠄⠈⠀⠀⠀⠀⠐⡊⢀⡀⠀⠀⡁⠂⠀⠀⠀⠀⠀⠂⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⡀⠈⠁⠀⠀⠀⠁⢀⠀⠀⠀⠀⣐⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠠⠀⠂⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠄⠀⠀⠀⠀⠈⡐⠠⠄⠘⠑⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠔⠀⠢⢄⠀⠀⠀⠀⠀⠀⠤⠂⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⡀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢐⠀⠠⠂⠠
⠀⠀⠀⠀⡈⠀⠐⠀⠀⠀⢁⠀⠀⠀⠀⠄⠈⠐⡁⠂⠀⠀⠀⠀⠀⠀⠒⠁⢉⠊⢀⠐⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠈
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⢀⠀⠀⠓⠀⢠⠀⠀⠀⠀⠀⠂⠀⠃⠘⠀⢡⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠁⠂⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠁⠈⠂⠊

⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠒⠶⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡤⠖⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡞⣉⡀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣰⠖⠒⠦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⠉⠉⠉⠉⠛⠓⠦⣌⡳⣄⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣾⠼⢁⡴⠛⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣶⠀⡀⠀⠀⠀⠀⠙⢦⣙⣦⡶⠓⣦⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠀⠚⢡⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠤⣭⣤⣿⡀⠀⠸⠿⠀⡼⠉⠉⠀⠀⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠘⢧⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠘⠃⠉⠓⠦⠤⠞⠁⠀⢠⣀⣰⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⠈⢧⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⣤⣀⣠⠄⠀⠀⠀⣠⣏⠈⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⣧⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠙⢦⣄⣀⣀⣀⣀⡤⠞⠁⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣠⢼⡏⢧⡷⠀⠀⠀⠀⠀⠀⠀⢉⣳⣶⡶⠶⣿⡉⠉⠀⠀⠀⣀⣿⠙⢦⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⣇⣀⣤⠴⠾⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡴⠋⠀⣿⠁⠙⣦⣠⠴⠚⠁⢸⠃⠀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡍⠉⠁⠀⠀⠀⠀⡇⠀⣴⠶⢶⡄⣠⠞⠁⠀⢾⣀⠀⠀⣧⣀⣼⡟⣇⠀⠀⢠⠏⠀⠀⢸⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⢀⣿⠉⠙⡟⠁⠀⠀⠀⣀⠼⠃⠀⡏⠙⢹⠃⠘⡦⣾⠋⠀⠀⠀⠸⡇⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟⠉⣿⠀⣀⡧⠴⠤⣤⣀⣻⡄⠀⢸⡇⠀⣼⠀⠀⡼⠃⠀⢶⡒⠛⠛⠃⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⣽⣫⠵⠖⠀⠀⠀⠈⠉⠛⢦⣘⡇⠀⡟⢀⡾⠁⠀⠀⠀⣻⠄⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢠⣟⡵⠖⠒⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⣧⠟⠀⠀⠀⣠⠞⠁⠀⠀⣠⠞⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢈⣿⠾⣏⣉⣁⣀⣀⣀⣀⣀⠀⠀⠀⠙⢧⡀⠀⣠⠞⠁⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠶⠒⠋⡿⠁⠀⠀⠙⢧⡀⢸⠅⠀⠙⢦⠀⠀⣠⡞⢙⡶⢤⡀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢳⣼⡀⠀⠀⠈⠳⣞⠉⢀⡾⠀⠀⠉⠳⣄⡾⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⡞⢣⡞⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣐⣛⠉⢉⢉⡉⠛⢒⣸⡇⠀⠀⠀⡼⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⡇⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠶⠋⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡠⠶⠙⠿⠃⠶⢄⣤⡀⠴⠊⠻⠛⠲⠄⣠⣄⠠⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠈⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣆⠀⠀⠀⠀⠀⢸⣿⡷⡀⠀⠀⠀⠀⢀⡀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢼⣿⡆⠋⠁⠀⠀⠙⢲⣿⣷⠚⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠙⠛⠳⢦⢀⣤⣄⠀⣀⣀⣀⣀⣀⣀⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠈⣭⣭⣭⣭⣭⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢘⣻⣭⣭⣭⣝⣛⠿⠿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⡛⣿⣿⣷⣶⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡟⣭⢻⣿⣾⣿⣿⠿⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣷⣶⣿⣿⣿⣿⣇⡻⢃⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠈⠉⠙⠛⠛⠋⠉