Connected Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠣⠠⠟⠀⠀⠀⣀⠀⢀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⡠⠤⡀⠀⠀⠀⠘⠿⠃
⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠉⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠣⠤⠃⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⢄⠤⠀⠀⠀⠀⠘⠟⠁⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡆⠀⠀⠀⠀⠘⠃
⠀⠀⢀⣤⡀⠀⠀⢠⡄⠀⠀⠀⠀⠑⠒⠁⠀⡀⠀⠀⢀⡀⠀⠀⢠⣤
⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⡁⣈⠀⠀⠈⠛⠀⠀⠰⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡱⠀⠀⠀⢀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢾⡷⠀⢀⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠜⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣨⠂⠀⠀⠀⠀⠀⠀⠀⢿⠗⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⢀⡀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠁⡀⠀⠐⠈⠁⠠⡄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈
⠀⠠⠈⠁⠐⠚⢷⣤⣀⣤
⠀⠀⠂⠀⠀⠀⣨⣿⢿⠷⣦⣤⡾⠗⠖⠀⣴⢀⣄⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠐⠀⠀⢰⡿⠀⢳⠆⣽⣶⡆⠀⡰⢿⣭⠀⠹⠤⠤⠄⠤⠀⠀⠀⠀⠀⠀⣠⣤⡶
⢠⠐⠁⠄⡀⠀⠀⠀⠠⣾⠷⣤⠈⢛⣀⡀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⣾⠛⠿⠄⠀⡀
⠀⠐⠂⠀⠉⠀⠀⠀⠀⣾⣀⠀⠉⠚⢳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⢀⠀⠀⠀⠙⠃
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢀⣦⣤⣀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣏⣁⣈⣙⣉⣀⣉⡓⣦⡀⢀⣀⣠⣼⣿⢟⣋⣩⣭⣭⣉⣈⡙⣆⠀⠀⠀⠀⣠⡴⠶⠶⢾⡷⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠯⢍⣉⣉⣉⣉⣉⠉⠩⠽⠟⣿⠟⠉⠉⢻⣿⣟⠛⠋⠛⠉⢉⣹⣿⣿⠀⠀⠀⠞⠁⣠⡶⠶⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⣍⣩⡿⠀⠀⠀⠀⣿⠀⠀⠀⢸⠉⠙⠛⠿⠿⢿⠿⠛⠉⢸⠀⠀⠘⠀⠀⠈⠉⠓⢺⡟⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣀⡀⠀⠀⢀⣀⣠⡟⠀⠀⠀⢸⠀⠀⠀⠀⢀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⢀⣠⠶⠚⡗⠒⠒⠒⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣨⡷⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠁⠤⣀⣀⡀⠀⠀⠀⠀⠈⠓⡄⠻⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡜⠋⠀⣇⠀⠀⠀⠙⣦⠀⠀⠀⣠⠔⣚⣻⣏⣶⣄⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠶⣛⢿⣿⠿⠉⠙⠶⢾⡆⠀⢰⠁⠿⠉⢹⡯⠶⠘⡇⠀⠀⠀⠀⠀⠀⣠⢠⡶⠛⠓⣶⣒⣓⠢⣀⣀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⣾⠀⠀⠀⠀⡄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠘⠿⠶⢿⡿⠭⣭⠛⠛⢩⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠀⢀⡇⠀⢀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⢠⣷⣚⣉⣽⣉⣉⣉⠛⠢⡀⠀⠀⠀⡾⢧⣀⣀⣠⣴⣇⣀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣇⠀⠀⠳⡤⢶⠇⠀⠀⠸⠻⠭⣯⣯⣯⣽⠿⠟⠀⢹⠀⠀⢰⠗⠋⣉⢻⣉⠛⣉⣋⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡴⠖⠁⡠⠤⠀⠀⢠⣠⠤⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⢹⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡾⠤⠤⠤⠤⠤⠤⠔⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠀⠀⠀⠠⢄⣤⣀⣀⠤⠖⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠘⡄⠀⠀⢸⣇⣀⣀⣤⠾⠁
⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀⣀⣠⣤⡾⠀⠑⠒⠂⠠⢄⡀⠀⠀⠈⡿⠈⡷⠃⢀⡾⢹⡏⠁
⠀⠀⠀⠀⠈⡟⠳⣄⠀⠀⠀⢠⣶⡿⠟⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⠾⠿⣶⠟⠷⣼⡇⠀⠳⠤⢀⡀
⠀⠀⠀⠀⢀⣷⣤⣼⡆⠀⠀⣾⡏⢠⣶⠾⠿⠿⠿⠿⠿⣶⣤⠶⠖⠒⠒⠒⢻⣇⣀⠶⠶⠦⢄⣽⡇⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠘⠋⠉⠉⢱⠀⠀⣿⡇⠀⠁⠀⠀⡄⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⡄⠉⠉⠉⠙⠋⢻⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⣿⡇⠀⠀⠀⠀⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠢⠴⠞⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢹⡇⠀⠀⠀⠀⠻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣄⠈⠓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡿⠃⠀⠀⠀⢀⣩⣤⣤⣼⠏⠀⣠⠤⠒⠒⠒⠀⠀⢀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⢣⣤⣤⣄⣸⡟⠹⠁⠀⠀⠀⠀⢷⣴⣶⣖⣶⣶⢦⣼⡄⠀⢸⡶⠖⠷⢶⡶⣤⣄⣸⡇
⠀⠀⠀⠀⠀⠀⣰⡟⠉⠉⠉⠛⠁⠀⠈⣿⣄⠀⠀⠢⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠉⠉⠁⠀⠀⠉⣹⡷
⠀⠀⠀⠀⠀⢰⣏⣤⠶⠛⠓⠶⠛⠓⠒⣿⣮⠷⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⡀⠀⠀⡇⠀⢸⠀⠀⠀⣀⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠳⠶⠦⠤⠤⠤⠶⠶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠓⢴⡞⠀⠀⢰⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠙⠂⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣶⣤⠄⠀⠰⢠⢤⣀⠔⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡿⠟⠛⠿⣧⣠⡀⠀⠀⠀⢴⣦⠀⣹⣇⠀⣹⡗⣠⠦⠎⣀⡤⢤⣈⠉⢹⠀⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣸⡏⠀⠀⠀⠀⠘⣿⠁⠀⠀⢠⠤⡀⡰⢄⠛⣛⠋⢁⡼⠀⡜⠁⠀⠀⠈⢣⠈⢉⠆⠉⣀⣦⣷⣧⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⣷⡀⠀⠀⠀⣰⠿⡇⠪⡑⠼⣀⡑⣁⣑⠚⡸⢀⣘⢢⠀⢇⠀⠀⠀⠀⡸⠀⠑⡄⠀⣾⣿⠉⢙⣿⣖
⠀⠀⠀⠀⠀⢀⣲⡾⠷⣾⣘⠿⠛⣷⡶⠻⠿⠚⢍⠙⡕⠉⠀⠀⠀⠀⠙⢎⢡⠞⣻⠤⡌⠑⠲⠖⠊⠁⢸⠉⠀⠀⠹⣿⣷⣿⣟⠃
⠀⠀⠀⠀⠀⢈⣿⣄⣀⣿⡏⠀⢄⡨⣁⡀⠰⢉⡈⡜⠀⠀⠀⠀⠀⠀⠀⠀⡇⡩⠝⠀⠳⠔⠙⢤⠎⢉⣉⣰⣦⣴⡆⢀⠁⠈
⠀⠀⠀⠀⠀⠀⠈⠛⡙⠃⣀⠍⠀⠠⠄⢁⢦⡔⡃⢣⠀⠀⠀⠀⠀⠀⠀⠀⠇⣉⣐⢠⡟⠛⣦⠀⣤⣼⠟⠉⠉⠉⠙⢿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢨⣀⠑⠤⠂⢠⠈⢁⡼⢀⡣⣀⠀⠀⠀⠀⣠⢞⣈⣳⡄⠀⠻⠛⠃⢤⡾⠇⠀⠀⠀⠀⠀⠈⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠔⠒⢠⣦⠀⠉⢡⠇⡤⡍⢐⣌⢩⠦⣘⡆⠈⠀⠀⠀⠰⠶⠀⣶⡆⠀⠀⠀⠀⠀⢰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠉⠀⠣⠊⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⢷⣦⣤⣤⣾⣿⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠊⠉⠉⠉⠉⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⢤⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣄⠐⠄⠀⠀⠀⠀⠘⣧⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣯⣉⣯⢤⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡻⠶⠟⠷⠞⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣌⡀⣈⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠐⢃⠀⠀⠀⠀⠀⠀⠀⢠⣋⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠈⢁⠉⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⢀⣠⠶⠦⢤⣤⣠⡴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣀⡀⣀⠀⢀⡤⠋⠓⢦⣄⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⡏⢻⠒⡖⠲⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣈⢁⡼⠀⡇⠈⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣀⡀⠀⠀⠀⢠⣀⠀⠐⠒⠲⠒⠒⠒⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⡄⠈⠉⠉⠉⠀⠐⠒⠂⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠐⣆⠀⠀⠀⢸⡇⠀⠀⠀⠤⠶⠀⠀⢰⣷⠀⠀⠀⠀⢰⠀⠀⠀⠐⠂⠀⠒⡖⠀⢸⡃⠀⠀⠀⠚⠚⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⢸⠀⠀⠀⠐⠃⠀⠀⡇⠀⠸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡇⠀⠀⠀⢸⠐⣠⡤⢤⣀⣀⣀⣀⣘⣱⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣗⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠁⠀⢀⣴⣙⣛⣻⣻⣛⣛⣛⣟⣛⣛⣛⣑⣄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⠀⢟⣹⠅⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⢸⠇⠀⠀⠀⠀⠀⠿⣿⠇⠀⠀⠀⢰⠋⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠈⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡆⠀⢠⣶⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠘⢧⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⡀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⢀⣀⡀⠄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠨⣀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⢦⠀⠀⠸⢿⠿⣴⠋⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠀⠀⠀⠀⠐⠧⠽
⠀⠀⡰⠲⡄⠀⠀⠀⠀⠀⠘⢄⣀⡼⠀⠀⠀⠀⠀⠈⠲⠖⠃
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⢠⣶⣶⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡷⠀⠀⠸⣄⣠⠞⠀⠀⠀⣶⣶⡆⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⢠⢮⣶⣤
⠀⠀⠙⠋⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠛⠋
⠀⠀⠀⡠⠶⢦⡀⠀⠀⡀⠀⠀⠀⣠⣀⠐⣇⡀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣏⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⢧⣀⣠⠇⠀⠀⠀⠀⠀⠸⢿⠿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡞⠁⠈⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠻⣤⠟
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠸⠿⠀⠀⠀⠘⠲⠞⠁⠀⠀⡜⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠙⠦⠖⠁⠀⠀⠀⠀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⡀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠘⠲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣶⣿⡆⠀⠀⢧⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠈⡆⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠒⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢲⡄⠀⠀⡼⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡠⠞⠉⠉⠉⠉⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠚⠉⠀⠀⠀⢠⠃⠀⡼⣦⣏⢧⠫⠻⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢒⣒⣛⣷⣣⢃⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢨⢳⡀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠉⣔⣺⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⡚⣧⡀⢀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⢻⢲⡲⠲⡲⠶⠶⠲⡻⠁
⠀⠀⠀⠀⠀⢀⠒⣒⣚⢻⣬⣊⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣣⣁⣱⢠⢡⢃⣶⠁
⠀⠀⠀⠀⠀⡽⠋⠉⠁⠀⠈⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⠛⠛⢻⣛⠿⠄
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠥⠞⠋
⠀⠀⠀⡘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⢟⢫⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠀⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⡟⠸⡷⣤⣀⠀⣀⣀⣤⢞⢧⣏⣀⢆⢛⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢀⣠⣴⡷⠲⢄
⢠⡥⠹⣧⡐⡑⡙⡙⠏⠍⣍⠆⣌⡟⠻⣿⠌⢌⠞⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⢸⡟⠀⠀⢀⣀⣤⣶⠿⠛⠁⠀⠀⠀⠑⣄
⢘⣃⣀⠘⣳⣝⣐⡀⡀⣈⣏⣼⣏⣉⣩⣿⡜⡞⡜⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡄⠀⠀⠹⣷⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠐⠠⠤⠀⠉⠛⠿⠿⠿⠯⠽⢦⡴⠒⢺⡷⡐⠠⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠈⠉⠀⠂⠩⡥⡭⠏⠉⠀⠂⠈⠉⣷⡱⡑⣱⣿⣦⣤⣤⣤⣶⣶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡹⠳⡶⡤⣤⡤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠠⠀⣻⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡬⢵⣡⡝⡐⡀⡃⣼⠃⣤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡭⠩⠍⠿⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣊⣽⠿⢶⣿⣼⡟⣼⠇⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⠨⢽⣿⢪⠻⣇⠀⠀⠀⠀⢠⡾⡫⡀⡡⢀⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⡁⠉⠙⠛⡿⠩⠭⣰⠏⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⣿⣣⠑⠹⣆⠀⠀⠀⣾⣴⣷⣥⣵⣧⣡⠆⢌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣒⣂⠘⣷⣠⠌⠜⠷⣄⣰⠯⠅⣶⠾⠿⠿⢿⣆⣾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣠⡖⠛⣷⣎⢊⢎⣾⠃⠀⠀⠀⠀⠉⣉⣭⣿⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠛⠋⠁⢠⡞⠉⠙⠃⠒⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢴⢶⠶⠾⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢶⡶⠆⢠⠎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣻⡙⡀⠂⢂⠂⠆⠌⢄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣾⠂⢀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⡀⠀⠀⠈⠉⠙⠛⠶⣾⠞⡚⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⢂⠹⣆⢎⠎⠙⣦⡀⠀⠀⠀⠀⠀⠀⣀⢴⠞⠋⢡⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣥⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠹⢯⡞⠀⠈⠟⣦⡀⠀⣠⡴⠛⡉⠀⡀⣦⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠠⠬⢿⣆⠎⡜⡜⡙⠛⡹⠐⣐⣴⣾⣛⣛⣹⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢙⣾⣜⣜⣆⣠⣤⡷⢛⡉⢭⠤⠕⣿⢃⢟⢳⣤⣀⣀⣀⣀⣤⠴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⡠⠀⠚⠛⠛⠉⠙⠋⠉⠈⠙⠛⢛⣛⣿⣧⣧⢡⠩⢉⢉⢁⣦⣾⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠤⠶⠖⠒⠊⠀⠀⠀⠀⠀⠀⢐⣒⣛⣛⣻⣷⠷⠞⠋⣉⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠡⠭⠥⠤⠤⠖⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠶⠶⠶⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⣀⣤⣤⣴⣶⣶⣤⣤⣄⡀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢰⣟⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣷⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⡶⠟⠛⠉⠉⠉⠉⠉⠉⠙⠛⠷⢶⣤⣴⠾⠟⠛⠉⠉⠉⠉⠉⠉⣿⡆⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣿⡇⠀⠀⢸⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣶⢾⣟⠛⠉⠉⠙⢛⣿⠏⠁⠀⠀⢀⣤⡶⢾⣟⠛⠉⠉⠙⢛⣿⠀⠀⠀⣼⡇⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣴⣿⠉⠀⠀⢿⣆⠀⠀⣰⡿⠁⠀⠀⢠⣶⣿⠁⠀⠀⠙⣷⡀⠀⢀⣾⠇⠀⠀⢠⣿⣄⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣰⡟⠁⢻⣆⠀⠀⠀⠻⣦⣰⡟⠀⠀⠀⣰⡟⠀⠘⢷⡀⠀⠀⠘⣷⣠⡾⠃⠀⠀⢀⣿⠃⠙⣷⡀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣰⡟⠀⠀⠀⠹⣧⡀⠀⠀⠙⠻⣧⣄⠀⣸⡏⠀⠀⠀⠈⣿⡀⠀⠀⢹⣟⠀⠀⠀⣠⡿⠁⠀⠀⠘⣷⡀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⣿⠁⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠙⠛⠿⠶⣦⣤⣤⡶⢾⣧⠀⠀⠀⣿⠀⣠⣾⠏⠀⠀⠀⠀⠀⢹⡇⠀⠀⠘⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠻⢶⣦⣤⣤⣤⣤⣤⣴⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢻⣆⠀⠉⠀⢀⣾⠃⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠈⢻⣆⠀⢀⣾⠋⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠙⢷⣿⠁⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣹⣷⣄⠀⠀⠀⠙⠻⢶⣴⣟⣁⣀⣀⣀⣀⣤⣴⠾⠛⠁⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉⠛⢷⣄⡀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⡿⠿⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠉⠀⠈⠙⠻⣿⣶⣄⡀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠙⠿⣿⣦⣴⣿⠟⠋⠁⠀⠀⣠⣶⣦⡀⠀⠀⠉⠛⢿⣷⣴⣾⡿⠛⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣤⣤⣼⣿⣿⣤⣤⣄⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣠⣶⣿⠟⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⢿⣷⣦⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠉⠛⢿⣷⣤⣀⠀⢀⣠⣴⣿⠟⠋⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⠶⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣠⠏⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣸⠆⠀⠀⠀⣠⠴⠶⢦⣄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠿⠛⠓⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠀⠀⠀⣼⠁⠀⠀⠀⠈⢧⣀⣀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⢀⡾⠉⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⡏⠀⣹⡂⠀⣠⠖⠋⠉⠉⠉⠙⠲⣄⣀⣤⡾⠟⠋⠛⠶⠦⠶⠋⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠙⠊⠉⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢰⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠁⠀⠀⠀⠀⠉⠙⠛⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⡁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣦⣀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡴⠋⠀⠉⠻⣗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣶⠛⠉⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡴⠋⠁⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣤⣤⡾⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠹⣄⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⢦⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⠤⠞⠁⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠓⠦⠤⠤⠤⠤⠤⠤⠤⠖⠚⠉⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⢱⣤⡶⠶⢷⡀⠀⠀⠀⠀⢀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠋⠀⠀⠀⠀⠙⠲⠦⠤⠖⠋⠀⠙⠿⣦⡤⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡰⠃

⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠝⠁
⠀⠀⠀⢰⣷⠄⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠀⢀⡀⠀⠀⠠⠆⠀⠈⠛⠋⠀⠀⠿⠇⠀⠀⠀⠀⠀⠈⠛⠁⠀⢰⣶⠄
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣴⠀⠀⠀⠰⢀⠀⠀⠀⢈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⣒⠀⠀⢰⣘⢗⣀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠂
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⡀⠀⣾⣤⣼⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠞⠛⢠⣿⣻⠆⠰⠄⠘⣻⣶⣶⠠⠂⠀⠴⡂⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣧⣤⣾⣧⣾⣭⣯⣥⣦⣬⣽⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡼⣅⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣀⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠁⠀⡇⠀⣸⣙⣞⡷⢤⠀⠀⠀⠀⠀⠈⡆⠀⢠⠎⠁⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠠⠄⠴⣘⣛⣿⡀⢨⡇⠀⠀⠀⠀⠀⠘⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⣸⠸⠳⡀⠀⠀⠀⠀⠀⠣⣀⣈⣀⣼⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠠⡌⠙⣦⠠⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⡙⠩⠉⠉⠛⡉⡽⠁
⠀⠀⠀⠀⣲⠒⠒⠘⠛⠶⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣟⠻⠼⡶⠾⡇
⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣦⣤⡀⠀⠀⠀⠀⠈⠳⣾⠮⠕
⠀⠀⢠⠳⡀⠀⠀⠀⠀⠀⣠⠪⢫⢳⡄⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠄⣯⢀⢟⠶⢤⠤⠶⠚⣿⣶⣴⠃⣽⡄⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣠⣴⠞⠋⠑⢄
⠺⠀⠙⢧⣦⠀⠂⠀⠗⣴⠟⠄⣿⢠⢂⢷⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⢺⣅⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠑⡄
⠈⠋⠥⠉⠙⠻⠿⠿⠿⠭⡥⠄⢿⡇⢀⢺⡆⠀⠀⠀⠀⠀⠀⢀⣠⣿⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠐⠀⠤⠶⠋⠁⢀⠀⢸⡇⢂⣸⡷⠶⠶⠶⠶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠉⡓⠖⡦⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢿⣾⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⠾⣮⣅⣀⣡⡏⣰⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣈⣿⢱⢿⡀⠀⠀⠀⢀⡴⠚⠋⠙⠓⢦⡀⠀⠀⠀⠀⠀⠸⠓⠒⠿⢿⢛⡛⣱⠇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢻⣏⠘⢷⡀⠀⢀⣯⣼⣤⣥⣄⡤⢀⢷⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢀⡴⠃⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⡀⣿⡤⠀⠙⢦⡼⠓⠰⠞⡛⣻⣷⣅⢺⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈⠛⢦⣼⠞⠀⡄⠄⠀⣀⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⢀⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠒⠛⠋⠉⠈⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡄⠀⠈⠉⠛⠲⢦⣶⡖⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⣦⡌⠉⢳⡀⠀⠀⠀⠀⣠⡴⠞⠉⣁⣼⠃⠀⠀⠀⠀⠀⠀⠈⢶⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⢿⡄⠀⢉⡷⣤⢴⠋⠁⣀⣦⠿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡻⢧⣢⢈⠀⣀⡤⠞⢛⣒⡲⣿⢹⢦⣀⠀⠀⠀⣀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠉⠙⠛⠛⠙⠋⠉⠐⠒⢚⣻⣷⣮⢈⠉⡉⢉⣥⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠉⠀⠀⠀⠀⠀⢴⣎⢽⠽⠿⠞⠋⠭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⢙⡯⠛⠂⠀⠂⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣀⠀⠀⠀⠀⠀⢠⠊⠄⠐⠆⠘⡅⣄⠀⠀⠀⠠⠀⡼⠀⠄⠀⢀⡀⠀⠀⠀⠈⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡄⠀⠈⡶⠉⠀⠐⠒⠲⢸⡀⢀⣤⠀⢀⣼⠁⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠈⠉⠐⠂⢲⠀⠀⢙⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠁⡼⣤⠄⠀⢐⠀⠀⠀⢀⠀⠀⢗⣠⣦⣔⡺⠃⠀⠀⠀⢀⣀⠤⠤⠤⢄⡀⠀⠀⠀⢻⡾⠛⠆⡀⠈
⠀⠀⠀⢀⠀⠀⠁⠜⠶⣶⠃⠀⠀⠈⢃⡀⠀⠀⠀⠀⠜⡹⠷⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠘⢆⢀⡀⡀⠁⠀⢠⡜
⠀⠀⠀⠁⠀⡐⠁⠀⠀⠈⠀⠀⠀⠀⢀⠔⠊⠉⠁⠀⠢⡀⢀⠀⠀⠀⠂⠀⠃⠀⠞⠀⠙⠒⠀⠀⠠⢸⠋⠀⢰⣚⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⡆⠀⠄⠀⠁⡤⠀⠀⠀⢆⣀⠀⡄⠀⡆⠀⠘⣤⣤⡇⠀⠀⠀⣸⠛⠁⠀⠈⣠⠠⢤⡀
⠀⠸⠁⠀⠀⠀⠀⠀⠀⠊⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⢄⡘⠤⡲⠃⣈⡙⠢⠔⠃⠾⠁⠀⠀⠀⢆⣀⢀⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢇⣀⠀⠲⠆⠀⠀⠀⢠⠾⠅⠀⠀⠘⠉⠑⠠⠥⠥⠤⠴⠒⠁⣀⣤⣀⡀⢄⠙⠛⠛⠇
⠀⠀⠀⠠⢃⡀⠀⠀⢀⠔⠊⠉⠉⠳⣤⡑⠒⠶⠦⠴⠂⡠⣞⠀⠀⠸⠶⠢⠤⢀⡀⠀⠀⠀⢀⠀⡜⠠⠘⠲⠈⢢⣣⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠁⠠⠀⡎⠀⠀⠈⢺⡆⠈⣏⠋⠒⠒⢿⠁⠀⠀⠠⠀⡠⠂⠅⠈⣐⠋⠛⠀⠐⠚⠘⠂⠐⣶⣶⠀⢰⣿⡶⠴⠂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣸⠤⡟⠂⠀⠡⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠚⠓⠦⢺⠇⠈⢯⡅⠈⢌⠧⡔⣿⣯⣦⢾⡿⠀⠜⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣑⡐⠒⠒⣠⠔⠓⠒⡄⠀⢹⣄⡀⠀⡀⢸⠀⠀⢀⣀⠀⠀⠀⠀⣆⠀⠀⠑⠒⢡⣭⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠈⠁⠉⠋⠀⠀⠀⠚⠏⠛⠀⠀⠀⢠⣀⠢⡄⡈⠏⣀⣀⠼⡵⠓⠁⠀⢀⠐⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠎⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈⠥⠤⠖⠺⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⣨⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢚⡀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠈⠉⠁⠀⠀⠰⠾⠭⠭⣄⣸⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢃⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠨⣁⠠⠀⠉⠀⠀⠐⠡⠀⠀⢤⣶⣚⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠒⠀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠋⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠼⠇
⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⢤⠟⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠖⠓⠒⠒⠠⡀
⠀⠀⠀⠀⢐⡂⠉⠀⠐⠀⠰⡃⠀⠀⣴⠒⠉⠀⠀⠀⠀⢀⠔⠁⠀⠈⠢⡀⠀⢊⡠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠪⡇⠈⠉⠀⠐⠂⠰⠅⣀⡂⠠⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⢄⠀⠀⠀⠀⠀⢈⡄⡽⠍⠍⠉⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠅⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠒⠂⠤⡀⠔⠀⠀⠐⠀⠀⢀⠀⣠⠎⠀⣹⠄⠉⠁⠀⠋⢋⢀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠁⠀⠀⠀⠀⢸⠉⠐⠂⠀⣞⠇⠐⠀⣸⠁⠀⠀⠀⠐⠁⠑⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⣾⠀⠀⠀⠀⡇⡈⠀⠀⣼⠕⠀⠀⠀⠨⠀⠀⠨⡏⠁
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠠⠊⠀⣠⠞⢽⠀⠀⠀⢠⠷⠤⠴⠤⣼⢔⢥⠀⠀⡠⡢⢤⣼⣇⡀⠠⠤⠄
⠀⠀⠀⠀⠈⠐⠠⠀⠐⠀⠰⢸⡶⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒⠒⡛⠫⠀⠠⢺⢀⠀⠀⠠⠤⠠⠄⠤⢾⢤⣤⡀⠀⢝⣵⢟⣾⡷⡾⠿⣛⣒⣂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠣⢀⡀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠄⠄⠐⡀⣸⠅⠄⠀⠸⡓⠚⠐⢶⠟⣿⣛⠗⠐⠑⢑⣿⠟⠉⠉⠑⠤⠀⠀⠒⢓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠃⠥⠄⠀⢈⠠⠀⡠⠀⢀⠀⣼⢄⠀⡀⠸⠀⠀⡼⠃⠀⠀⠉⠁⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠔⠁⣡⠅⣜⠁⡈⠄⠘⣠⠜⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⠀⡀⠊⠨⠁⣠⠏⠙⠛⠳⠼⠯⠀⠀⠀⢀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂⢈⠀⢄⢄⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠆⠀⣀⠀⠂⠀⠀⠈⢀⡤⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠻⣥⠓
⠀⠀⠀⠐⠀⠀⠠⠄⠈⠁⠄⠀⠀⠐⠹⠀⠀⠀⠀⣀⢀⠂⠐⠲⠀⡠⠀⠁⠀⠀⠀⠀⠝⠀⠍⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⣀⡀⠀⠘⠚⠉⠀⠀⠐⢬⠇⠈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠘⠀⠉⠀⠀⠰⠄⠀⡀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠗
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⢴⠇⠁
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠛⠛⢯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣊⠭⣔⠃⠱⡀⠀⠀⠀⠀⠀⡇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠖⠉⠀⠀⡮⠤⠴⢃⠔⡐⡄⠀⠀⡇⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣀⣠⠊⣠⣗⣶⢆⢦⣀⣀⢐⡒⡂⠳⢾⢿⣶⣴⡱⠁⠘⡉⠉⢉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⢊⢗⣵⠆⡰⠋⠀⠀⠀⠀⡶⢄⠀⠀⠴⢥⣅⣑⣾⡿⣎⠢⣄⣣⠴⣄⠑⢄
⠀⠀⠀⠀⠀⡔⡁⡲⠸⢸⢁⣚⡏⢀⠇⠀⠀⡠⢖⣉⡁⠈⣳⠄⠀⠀⢠⢋⠼⢄⠈⢷⡘⢿⢶⢬⢢⡈⠳⠤⢄⣀
⠀⠀⠀⢀⢊⠕⠈⢁⡆⣸⠨⢸⠀⡌⢠⠄⡰⢱⣋⠼⠷⠚⠱⠄⢀⡔⣡⢊⣀⣀⠹⡄⠻⡌⣟⣷⣿⣧⡀⢙⠑⠦⡙⢆
⠀⠀⢀⠇⡎⠀⢠⢏⡆⢽⠥⡍⢠⣷⡋⢀⠃⡎⠀⠀⣰⢄⢀⡴⢋⠜⠁⠘⠀⠈⢉⡝⠈⣷⢸⣷⣽⣿⣷⠀⢆⣀⠜⡼
⠀⠀⢸⠀⡇⠀⡮⢄⡇⢹⡒⠛⠚⡆⠀⠸⠀⠇⠀⢠⠇⠀⠉⡖⠁⣠⡞⠀⣄⠴⢦⠑⢝⡿⢸⣵⠏⠻⣿⣇⢸⠔⠊
⠀⠀⠘⡄⢱⣸⢉⠕⣃⢸⡱⠼⠗⠁⠀⠀⠀⠀⠀⠘⠒⠤⣤⣹⠄⠁⠀⠀⠉⠀⢀⣵⣬⠇⣼⣿⣤⣀⣿⢸⢸⣷⣦⡀
⠀⠀⠀⠐⡄⠻⡔⡺⡉⠀⣹⢗⢀⠀⠀⢠⠘⠀⠀⠀⢰⠯⣅⡀⠀⠀⠀⠀⠀⠘⡎⣮⠏⣴⡿⢿⢰⢻⠿⠛⠺⡄⠱⡉⢆
⠀⠀⠀⠀⢈⣦⡈⠳⢽⣺⢖⠕⡁⡡⢢⢼⠀⡄⠀⠀⢸⠀⠀⠉⠓⢲⢀⡴⣞⣸⠞⡡⡞⠎⡷⡌⢿⢸⣄⠤⢤⡞⠀⡇⢸⠄
⢀⡤⣂⠿⠛⡏⢌⢗⠦⣌⣉⡚⠚⠓⠓⠛⠒⠛⠓⠊⣉⣄⠀⠀⡐⠷⢯⡀⢩⠲⡏⢡⢠⢰⣵⢙⢆⢻⢸⣿⠁⡶⠴⢃⠞
⡆⢼⡁⡦⣄⢣⠊⡮⠞⢴⢠⢋⢟⢟⡖⡶⣶⣲⡞⡝⡝⠼⣀⡞⢹⢸⢸⢸⢻⠀⢸⢸⢸⠎⠈⣶⠘⣆⢿⠃⣸⠀⠀⢫⡀
⠘⠢⠭⣅⡼⠋⢏⡣⣐⣾⡓⠮⣎⡎⡜⡜⢘⣗⠻⣰⢠⡀⣹⡇⢸⢸⢸⢘⡸⢸⢸⢸⢧⣄⢀⣘⣇⣿⡌⡄⠈⠉⠉⠉⠁
⠀⠀⠀⠉⠀⠀⠈⢣⠁⠂⡌⡗⡮⡭⣽⣓⡾⠾⢆⠱⣶⣥⠧⠥⠧⠬⠤⠜⠑⢾⣘⡞⢸⡏⣼⣽⣵⡇⠇⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢤⢸⢘⢱⢣⢣⢣⠃⣯⡽⢣⡙⢽⣹⠐⢖⢶⢢⢸⣇⡠⢺⡇⣼⠀⣿⡽⢽⣧⠄⡆
⠀⠀⠀⠀⠀⠀⣄⠸⠿⣀⣙⢼⣸⢸⠸⢼⣉⠀⢇⡆⡽⣁⢠⡽⡸⡐⡌⠂⠋⡅⢿⣰⡇⡼⠁⢩⣶⠖⠊
⠀⠀⠀⠀⠀⠀⠈⠢⡀⢠⠋⠀⢸⣷⠤⣃⡎⡸⡛⢇⣇⢋⢣⢠⠑⠰⡘⡜⡜⢜⣨⡼⢰⢁⠤⢯⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡙⠦⠊⡰⠋⠒⠚⠤⠬⠦⠿⣧⣧⠷⠗⠊⣿⡷⣡⠃⠸⠴⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠀⠀⠀⠀⢈⣉⡉⢟⠉⠻⣗⣶⣒⣫⡞⠁
⠀⠀⡀⢀⠄⡠⡠⢀⢄⠄⡠⣢⢄⢔⡠⢀⠔⡠⢂⠄⠈⠁⡘⢦⣙⠢⠤⠤⠞⡹⠣⠠⢀⢀⠄⡄⣠⢀⠄⠀⡀⠀⡀
⠀⠀⠀⠁⠁⠉⠘⠑⠑⠈⠊⠔⠕⠫⢊⠔⠠⢂⠔⡡⢀⠘⡵⡣⠊⡙⡲⣲⢊⢔⠕⡕⡅⡡⢊⠔⡕⠡⢪⠊⡾⠡⠾⠣⠣⠶⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣼⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣼⣤⣤⣤⣤
⠀⠀⠀⠀⠀⢰⠋⠸⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⢠⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠉⢩⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡀⢠⣤⣤⣤⣬⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠈⠉⠸⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⡏⠀⠀⢹
⠀⠀⠀⠀⢙⠶⠶⡫⠂⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠠⣀⣀⠄⠀⡴⠒⠣⡖⠶⢭⡲⡀
⡀⠀⠀⠀⢸⣿⣿⡇⠡⢧⣀⣠⣿⣦⠀⢳⠘⡀
⣷⠀⠀⠀⠐⠨⠍⠊⢱⠸⡍⠙⠿⠟⢀⡼⢠⠃
⠣⢀⣀⣐⢄⠀⠀⠀⠀⠳⣝⢷⣶⡶⢛⢕⢁⡤⠂⢄
⠆⣿⣿⣿⢎⠆⠀⠀⣀⡠⡈⠂⠠⠚⡅⣿⣿⡀⠀⣸
⡘⣮⢍⡥⡊⠀⠀⠀⠛⠃⠃⠀⠀⠀⠇⠻⣿⠿⡩⠓⣄
⠳⣌⣉⠼⢄⢀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢷⡔⠂⠑⠶⠋
⢠⠑⢃⣶⡀⣯⡙⣆⢀⠀⠀⢀⣠⣿⣶⡟⣱⢀⢀⡠⢤⣀⢀⡴⠒⢦⡀
⢿⡀⣿⣿⠗⠳⣌⢫⠈⣹⢚⣭⣤⣄⠹⡄⢿⣦⡙⢶⣶⣌⠙⣦⠔⣚⡛⢷⡄
⢠⢸⡇⠀⣴⣶⠤⣕⣛⡃⣿⠁⠀⢹⡇⡿⣸⠟⣡⢇⠽⢋⡜⣱⠟⠉⠙⢷⡹
⠋⣠⡙⢆⢹⡓⣮⣉⣉⠱⣝⠷⠶⢟⣵⣧⡡⡏⠀⠉⠈⠁⢇⢻⣄⠀⢀⣼⢣⡁
⢛⣕⡽⢊⣨⠏⠙⠿⠟⢀⡿⠉⣿⡍⠳⣅⡣⡠⣄⡢⡀⠀⢨⣓⣍⣛⢫⠕⠁⠙⣆
⡸⣾⢔⠭⠖⠶⣷⡀⡴⣫⠴⣾⣿⣿⣷⡄⢳⡜⡀⢓⣨⣭⡛⡏⢱⡞⣙⠀⢨⢒⡥⠤⣅⡆⣥⡀
⠁⠥⡥⠒⢮⢱⡌⡇⠱⣣⣤⠘⢿⣿⣿⡟⢸⢇⡇⣿⠁⠈⣿⠸⠞⢴⡿⢠⠃⡏⠀⠀⠈⣧⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⣠⡴⠞⠋⠁⠒⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡴⠯⢀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⣧⡀
⠀⠀⠀⠐⠂⠀⠀⢀⣼⣯⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⢀⡴⠋⠀⠈⠿⢦⣄⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠈⠀⠙⠳⣄⡀⠠⠖⠁
⣀⣤⠶⢚⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠳⢦⡀⠀⠀⠀⠂
⣍⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⡹⢶⣄
⡼⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠈⠳⣄⡀⢀
⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢀⠀⠀⠀⠀⢈⡿⢯
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠳⢦⣄⡀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢈⠀⠀⢀⣴⠏⠠
⠀⠀⠀⠀⠀⢄⡠⠐⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⣷⠟⠁
⢀⠠⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⠞⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣠⠞⣅⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡦⣄⡀⠀⠀⠂⢠⡆⠀⠀⠀⠀⠀⠀⠰⣦⣤⡄⠠⠤⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠐⠂
⡀⠀⠀⠀⢀⣀⠀⠀⠠⠴⢢⠋⠀⠀⠀⠄⢀⡶⠋⠀⠀⠀⠀⠀⠀⢠⠄⠈⠉⢙⠳⢦⣄⡀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠒
⠙⠛⠶⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠠⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠂⠀⢀⡼⠛⠳⢦⣄⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⣴⠋⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⣀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⡀⠀⠸⡿⠀⠀⠀⡀⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⣴⣀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⢹⠆⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣠⣤⠔⠉⠛⠚⠫⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠟⠀⠙⠋⠉⠀⠒⠀⢰⡏⠉⢻⣄⠀⣀⡀⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣤⣤⠊⠛⠖⠋⠀⠀⠛⠃⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢄⠀⣰⣤⡀⠀⠀⢀⣌⠁⠀⠈⠀⠀⠀⠺⠷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢹⠖⠂⡹⠛⠀⣴⣷⡄⠀⠀⠀⣀⡽⠋⠻⣆⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠒⠀⠉⢀⣄⠈⠳⠶⠋⠀⠔⠀⠀⠀⠙⠋⠣⣀⣤⣄⡀⠛⢦⠾⠃⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠋⠂⢤⡴⠦⣎⠀⣠⣦⠀⠀⠀⢰⡏⠀⠈⣷⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡿⠀⠈⠉⠀⠀⢀⡤⠛⠶⠚⠣⡈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠉⠉⠀⠈⠒⣤⣦⡔⠁⠀⢀⣴⡄⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠈⠛⠁⠀⠀⠀⣵⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⣀⡤⠶⠶⢦⣄⠀⠀⠀⠀⢰⡟⠛⠛⢳⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡴⠲⢤⠀⠀⠀⠀⠀⢰⠛⠛⣷⣄
⠀⠀⠀⠩⠖⣛⣙⡳⠌⠁⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⡴⠚⠉⢤⡄⠘⠳⡄⠀⠀⠀⡖⠋⠁⢰⠀⠘⢳⡄⠀⠀⠀⢸⠀⠀⠈⠈
⠀⠀⠀⠀⠈⢡⣦⠁⠀⠀⠀⠀⠀⢸⣧⣤⣤⣼⠀⠀⠀⠀⠀⠙⠒⠒⢸⡇⠒⠚⠁⠀⠀⠀⠉⠉⠋⣼⡌⠛⠉⠀⠀⠀⠀⢸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣿⠁⠈⢻⡆⠀⠀⠀⢠⡿⣍⠉⢉⡩⢿⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠤⠤⠤⢼⡂⠀⠀⠀⢀⣴⠋⡑⡉⢳⣄
⠀⠀⠀⠀⠻⣷⣶⡿⠁⠀⠀⠀⢸⡇⠈⠙⠋⠀⢸⠀⠀⠀⠀⠀⠈⠻⣷⣤⣦⡀⠀⠀⠀⠀⠀⡯⣙⣛⣛⢹⠄⠀⠀⠀⢸⢈⠗⠬⠖⢏⢸
⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠑⠒⠒⠒⠚⠀⠀⠀⠀⠈⠛⠒⠒⠒⠒⠋


⠀⠀⠀⡰⢊⣉⣌⠙⢢⡀⠀⠀⢠⠄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡆⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇⠀⠀⠀⠀⠀⢠⢾⠦
⠀⠀⠀⡇⠀⣿⠼⣇⠀⡇⠀⠀⢸⠋⣙⠙⠙⠙⠛⡇⠀⠀⠀⠀⡇⣠⠦⡴⠃⠀⠀⠀⠀⠀⠀⠀⢠⡌⣿⢸⡇⠀⠀⠀⠀⠀⠘⢻⢦⡀
⠀⠀⠀⠳⣀⠛⠟⢁⡴⠁⠀⠀⠘⠤⠤⠤⠤⠴⠶⠁⠀⠀⠀⠀⡗⣁⣀⣀⣀⡀⠀⠀⠀⠀⠰⡷⢸⠇⣿⢸⡇⠀⠀⠀⠀⠀⠘⢻⠋
⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣴⣾⣿⡿⠇⠀⠀⠀⠀⣿⡿⣫⡝⣿⣷⠀⠀⠀⠠⠿⣶⣶⣶⣶⣶⡾⠧⠀⠀⠀⠀⣼⠉⣀⠈⣷⠀⠀⠀⠀⢸⠁⠠⣤⣄⠀⢹
⠀⠀⠀⠘⠋⠋⠉⢧⣄⠀⠀⠀⠀⠿⠿⠭⠵⠿⠿⠀⠀⠀⠀⠀⠏⠀⠐⠀⠈⠇⠀⠀⠀⠀⠀⠙⠆⣿⠠⠟⠀⠀⠀⠀⠸⣄⣈⣋⣁⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⢠⣤⣀⣤⣄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⢻⣿⣿⣿⣿⡾⠁⠀⠀⠀⠀⠈⣻⣟⠀⠀⠀⠀⠀⠀⣬⣿⡜⢿⠟⣼⣯⡄⠀⠀⠀⠰⢶⣾⣿⣿⡶⠆⠀⠀⠀⠀⢀⣏⣀⣈⣇
⠀⠀⠀⠀⣿⠿⢿⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠸⢿⣿⡿⠗⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣛⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠰⣿⣿⠇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣤⣤⡀
⠀⠀⠀⠀⠻⠟⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠇⢀⢀⣤⡀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⣠⣄⠀⠀⠀⠛⠂⠀⠀⠉⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⠀⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠘⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⢀⣴⣶⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⢠⣤⣽⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣤⣽⣯⣤⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣯⣤⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠘⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃

⣿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡛⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⣄⣰⢐⣀⠀⢆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⢀⡼⠞⠉⠀⠀⠈⠳⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣀⠜⠋⠀⠀⠀⠀⠀⠀⢠⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⡹⠁⢪⣾⠦⢄⠀⠀⠀⠀⠀⢀⠔⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠤⡰⠴⡆⡀⠘⣿⡇⠀⡇⠀⢀⠴⢊⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⠔⠋⠀⠀⠘⢌⣶⡼⠀⢀⡿⣩⢁⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠒⠋⡉⡐⠢⣄⠀⢀⡠⠚⠀⢀⠞⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⡠⣢⡿⣞⡻⡿⠾⠒⠉⢀⢔⡤⠊
⠀⠀⠀⠀⠀⠀⡠⠒⠁⡀⢐⠵⠊⠳⢯⣕⡆⠀⢀⣊⠬⠒⠁
⠀⠀⠀⠀⡠⠊⠀⡄⡸⠖⠁⠀⠀⠀⠀⠀⢩⠟⣏⡝
⠀⠀⠀⠰⠀⠀⢈⠎⠀⠀⠀⠀⠀⠀⡠⠒⠁⢎⠜
⠀⠀⠀⡇⠀⠘⠸⡀⠀⠀⠀⢀⠴⠊⣠⡴⠚⠁
⠀⠀⠀⠹⡙⣇⢀⠈⠒⠒⠊⢁⢰⡤⠊
⠀⠀⠀⠀⠈⠒⠥⣱⣒⣰⠤⠖⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡀⢀
⠀⠀⠀⠒⠱⠪⠖⠅⠢⢒⠔⡩⢊⠕⡪⢊⠕⠥⢪⠔⠥⠪⠊⠕⠪⠚⠕⠫⠪⢊⠔⠕⠕⠱⠩⠪⠪⠲⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣁⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣷⣦⣄⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢠⣠⣤⡿⠋⠀⠀⠀⠀⠀⣀⠔⢩⣿⣿⣿⣄
⠀⢀⣀⣀⣿⣿⣟⡁⠀⠀⠀⠀⠀⢰⡎⣀⡈⣿⣿⣿⣿⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠈⠉⠙⣿⣿⣟⡃⠀⠀⢀⣀⣠⣿⣏⣝⠃⣿⣿⣿⣿⠛⠛⢻⠛⠛⠛⠋⠃⠉⠃⠋⠙⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠸⠙⠹⣷⡀⠔⠁⠉⠋⠱⠋⢀⣼⣿⣿⣿⡟⠀⡆⢸
⠀⠀⠀⠀⠀⠀⢀⠜⠻⣶⣤⣰⣿⣤⣶⣿⣿⣿⡿⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢰⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠉⠉⠉⠀⠀⠀⡄⢈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⡆⠰⠀⠀⠀⠀⠀⡄⠀⠀⠲⠀⠀⠁⠀⠄⠀⢀⠄