Refreshed Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⠤⣤⣤⣤⠶⠖⠛⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢠⠞⠉⠁⢀⣀⣚⣛⣛⠿⠿⡻⠦⠰⣼⡇
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣩⠴⠀⠈⢁⡤⠶⠾⠉⠙⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣾⣁⠀⠀⢰⢧⡀⠀⣀⣠⡀⠀⠀⠀⣀⣤⣀⢸⡆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣟⡵⠞⠀⠀⠀⢉⡩⣷⡿⠃⠀⠀⠼⠋⠀⠈⠀⣧
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠘⣠⠖⠀⠀⠼⣿⣿⡷⠂⠀⠀⠀⠀⣀⡀⣷⡀⢻⣄
⠀⠀⠀⣠⡇⠀⢀⣠⠞⢋⣾⡏⠀⠀⠠⠚⢱⣟⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠉⠳⣤⣴⠷⢦⣀⣠⣄
⠀⢠⡞⣡⠖⣴⡞⢙⠀⠘⠀⠁⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⠉⠷⢾⣭⡷⣦⠀⢀⡴⡄
⠀⢸⡀⠛⠸⠃⠃⠀⠐⢦⣄⡀⠀⠐⢦⣤⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣯⡚
⠀⠀⠙⣦⠀⠀⠀⠠⣄⣀⠈⣙⡿⠟⠛⠛⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⡦
⠀⠀⠀⢹⡄⠀⠀⠈⠳⢭⠭⢩⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣏⣙⠿⠮⣭⣍⣉⠉⠉⠉⢹⠏⣰⠃
⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⣀⡾⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⣆⠀⠘⠀⢉⡽⠓⠶⢬⣴⠃
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠰⢾⡶⠶⢦⣀⣀⡀⢀⣤⢤⣤⣀⣀⣀⣀⣴⠏⠀⠀⠀⢿⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣤⣀⣀⠙⠉⠻⣿⠧⣄⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠈⠉⠛⠲⢤⡀⠀⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠴⠛⠉⠀⠀⢤⡀⠀⠉⠃⠰⡿⢷⣀⣤⢔⡄⠀⠀⠀⢠⡟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣡⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⢿⣰⠏⠐⢾⣦⣤⣀⣀⣸⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢻⠟⠁⠀⠈⠉⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⣖⣒⠋⢤⣄⠀⠀⠀⠀⠀⣠⡤⢀⡞⠀⠀⠀⠈⢿⣯⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠉⣿⢤⣤⡌⠛⢦⡀⣠⠾⢯⡀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠳⢤⣤⡄⢻⡄⠀⠁⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢠⠞⡇⠙⠛⠁⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⡏⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠛⠋⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣠⣶⣋⣤
⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⡶⣫⠞⡩⠛⠁
⠀⠀⠀⠀⢀⠴⠋⡞⣻⠋⠀⣠⣋⡀
⠀⠀⠀⠀⣸⣼⣿⣿⣿⣄⡠⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣀
⠀⠀⠀⠀⡙⣿⣿⣿⣷⣟⠀⠀⠘⣄⠀⠀⢉⣤⣀⠀⠀⢀⠜⠁⠀⢹
⠀⠀⠀⠀⠑⠒⣼⣏⠀⠈⠙⠦⣀⠈⠙⠢⢾⡀⠈⠓⢦⣌⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡌⢫⡣⡀⠀⠀⢙⡲⢤⡀⠀⠳⡄⠀⠀⠙⣶⣚⣁⣀⣀⣀⣀⡤⠤⠴⠒⠋⠉⠉⠉⠉⣷
⠀⠀⠀⠀⠀⠀⢳⣼⡉⢪⡓⢤⡋⠉⠒⢿⣶⣄⠈⠢⣄⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⠒⠛⠀⢀⣀⣉⣿⣧⠀⠀⠉⠨⠃⠀⠙⢶⠒⠢⠤⠤⠤⠤⠐⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠴⠶⢒⣠⠴⡀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⠤⠒⠉⠀⠀⢣⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢤⣿⣒⡒⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠈⣇⠀⠈⠯⣲⣤⣤⢤⡀⠀⠀⣀⣤⣶⠝⠋⣃⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⢱⠱⣖⡾⠟⠉⠀⢰⠒⠉⠉⠉⠉⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⡀⠀⠸⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠙⣦⠀⠀⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⣀⡀⠉⠉⣉⠐⣅⠲⠖⠘⢎⠳⢄⠀⠀⠀⠀⠀⠀⠀⠑⢄⢲⠋⠀⠀⢸⠁⣬⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⢄⠀⠀⢀⡠⢒⡥⠖⠊⠁⠀⠀⠀⢀⡼⡆⢸⠄⠀⠀⠈⠙⡦⣝⠢⣄⠀⣀⣀⠤⠤⣚⣻⡄⠀⠀⠀⢹⡥⣄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣒⢤⡙⠒⠋⢴⣉⣀⠤⢄⠀⠀⠀⠀⠹⣜⠛⠉⠀⠀⠀⠀⠀⠘⣄⠑⠮⣭⠤⠒⠊⠉⠀⠀⠑⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⣀⠭⠅⡶⠀⡠⠖⠒⠦⠤⠊⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣊⣉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⡤⠤⢤⣤⣤⣤⣒⡖⢚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣹⠓⣞⢀⡡⣑⠒⣈⠸⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠤⠁⡠⢻⣿⣿⢏⢙⣿⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⡿⠛⠛⠛⢻⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠤⠜⢸⠁⠀⢀⡠⠋⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣇⠄⢈⣟⣦⣄⣀⡠⡴⠇⣾⢁⠀⠀⢉⣩⣿⣿⡀⢛⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣝⡯⣣⢟⠤⠊⠀⠀⠈⠒⠮⢝⡻⢯⡁⢞⡿⡷⡫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠜⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠷⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠁⢀⠂⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠉⠉⠈⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⠀⠄⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠤⠤⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⠈⡁⠞⢛⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣨⣄⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠂⡂⠄⣐⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡟⠓⠘⣀⠁⠄⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⣈⢁⡈⠤⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠤⠐⢂⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣄⢀⣾⣶⡄⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠶⠶⣟⡛⣿⣿⣶⣿⣿⣿⣾⣿⣿⣷⢺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡡⠀⠠⢴⠾⢶⣿⣿⣿⠛⠠⠤⢬⣙⢿⣿⣿⣿⡆⣿⣿⠑⢦
⠀⠀⠀⠀⠀⠀⠠⠤⡌⡀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠙⠓⠂⠈⢀⡒⠒⠛⠳⢝⢿⡿⠲⠛⣁⡀⣘⡇
⠀⠀⠀⠀⠀⢰⠀⠘⣇⠹⣿⢿⢷⣶⣄⡀⢀⠀⠀⣰⡆⠰⠂⠈⠙⢦⣄⣀⣐⣄⡄⠀⢣⣽⣿⣿⡟
⠀⠀⠀⠀⠀⠘⢷⣤⣌⣳⣶⣤⠦⣉⠻⣿⣮⡟⠛⠟⠀⠀⠀⠀⢶⣄⣬⠉⠉⣿⣿⡄⠞⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠢⠈⠳⣦⣤⠾⠃⡀⠀⠀⠀⠀⠙⠭⠀⡀⢀⣿⣿⣇⠈⣴⣿⡏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣀⠀⠀⠀⠀⠁⠀⢤⡶⠟⠛⠦⠀⠀⠀⠤⠶⠾⠋⡼⢹⣿⣿⠀⣿⣿⠀⢧⣽⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⡞⠁⣼⢿⡏⢤⡘⠿⡷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⣳⡄⠀⠀⠀⠀⢀⠞⣷⣦⡀⠀⠀⠀⠀⠀⢩⡌⢻⡁⣾⠣⣄⣙⠲⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠿⣧⠀⠀⠀⠀⠀⢤⠿⠛⠁⠀⠀⠀⠀⠀⢲⡀⢸⣿⠏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⡁⠀⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢰⡅⢀⠀⠙⠂⠉⠀⠁⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠒⢫⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠠⣴⠶⠶⠤⠤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣦⣀⣠⣾⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⠛⠛⠁⠀⠀⠀⣴⣊⠉⠁⠀⠀⠀⣀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⡹⠀⠉⠉⠉⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠖⠒⠺⣅⠈⠀⠀⠀⠀⠀⢀⡀⡀⠜⠂⢹⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠈⢿⡁⣂⣘⠀⠉⢉⡽⢁⠄⣠⠞⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢩⡆⢀⣒⠚⠇⢹⣿⡗⠀⠉⢘⡿⠋⣠⠔⣡⡾⡄⠀⢀⡤⠚⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⡟⠀⠀⠈⠙⣻⣼⣿⣯⣄⠀⢛⣷⡞⣡⠞⢁⣴⡷⠞⣉⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⠀⢠⡏⢠⡟⠀⠀⠀⠀⠀⢩⣿⣿⣏⡁⢈⡈⢹⡾⣣⠾⠋⣁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣦⡟⠠⣾⣃⠀⠀⠀⠀⠀⠘⣛⣻⣛⠁⠘⠁⡓⢛⠁⣰⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠏⠀⠀⣈⣉⡛⣦⠀⠀⠀⠈⣿⣿⣭⣥⣭⣤⣍⣹⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠈⣍⡉⠙⢧⠀⠀⠀⢻⣿⣂⣠⣤⣤⣶⠟
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠈⠙⠛⠻⣄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠟⠛⠿⢃⣠⠟
⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⣠⡟⠀⠀⠞⠋⠁
⠀⠀⢀⣀⣿⠃⠀⠀⣀⣤⡾⠋
⠀⠀⠘⣩⣿⣄⠀⠀⠈⡷⢀
⠀⠀⠀⠧⠼⢿⡷⣤⣀⠁⡼⢿
⠀⠀⠀⠀⢶⣼⡟⢳⡇⢲⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠶⠒⠒⠒⠒⠒⠒⠦⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣲⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⣀⡜⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡠⣴⠋⢀⣀⡤⠀⠀⢀⣀⣠⡄⠀⣀⡠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⢢⣀⣀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⢠⣣⠖⠋⣾⢴⠚⠋⠉⠀⠘⠓⠉⠁⠀⣉⠉⠉⠉⠉⠉⠉⠉⢷⠄⠀⠀⠀⠈⠲⡇⠀⢱⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⡆⣀⠐⠂⠀⠀⠀⣀⡠⠤⠭⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣠⠟⠀⢸⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠃⠀⣵⠀⠀⢰⣩⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⢸⠃⣠⠔⠚⠉⠀⠀⠀⠸⡄⣆⠀⢰⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠁⠀⠁⠀⠀⠀⠉⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⣾⢸⠁⠀⢀⠀⠀⠀⠀⠀⠈⠛⢦⡀⢿⢦⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢡⠖⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⢄⠀⠀⠀⠀⢿⡸⠓⣉⣁⠘⡆⠀⠀⠀⠀⠀⠀⠉⠛⠃⠈⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠐⢄⣀⣀⠤⠂⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⡴⠁
⠀⠀⠀⠀⠀⢀⡤⢆⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠋⠀⠀⠀⠀⠀⠀⣀⡤⠚⠓⠢⠤⠖⠋
⠀⠀⠀⠀⢰⡏⠀⠈⠦⢄⣀⣄⠀⠳⣄⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠁
⠀⠀⠀⠀⠱⡽⡄⠀⠀⠀⠁⠘⡄⠀⠀⠙⠲⠦⠤⢄⣀⣀⣀⣠⣤⣤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠘⢞⢦⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠋⣉⠿⠸⢧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠣⣷⠤⢶⣛⡤⠒⢦⠀⣀⡀⢀⠤⠻⠐⠋⠉⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣁⣸⣤⡔⠸⠄⠯⢧⢀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡤⢞⢣⡠⠀⠐⡶⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣠⣾⣿⢆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣠⠚⠖⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣇⢘⡇⠈⠁⠈⠳⡄
⠀⠀⠀⠀⠀⡤⡖⠻⣽⣓⣢⡀⢠⠤⠐⠚⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣞⣀⠀⢀⡀⡖⠃
⠀⠀⠀⠀⠀⠙⢝⢤⡘⡿⡈⠣⣬⣷⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢼⠀⠉⠣⠼⠉
⠀⠀⠀⠀⠀⠀⠀⠑⢝⢃⡇⠀⠀⢹⠟⠢⣄⠀⠐⠒⡦⡤⠤⠄⠀⠀⠀⠀⠀⢠⠟⠻⣗⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣝⠄⣀⡇⠀⠀⠀⠑⠢⠼⠁⢧⣀⠀⢀⣀⣀⣤⣶⡏⠁⢀⢋⠖⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠻⠿⢧⣦⣈⣿⠀⢈⡮⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⠛⡶⣚⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⣤⣤⣤⣤⡶⠶⠒⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣠⠞⠋⠉⠁⣐⣒⡒⠾⢿⣿⡶⢦⠠⣤⡇
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣁⡤⠀⠚⢉⣩⣭⠽⠛⠒⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⡞⠉⠀⠀⣴⡋⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠘⣇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢺⢟⣡⠄⠀⠁⠙⠲⢒⣿⣿⠇⠀⠀⣠⠞⠉⠙⠃⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⡞⣁⠄⠀⠀⣴⣾⣽⣻⠅⠀⠀⠀⠁⠀⠀⢶⠀⢻⡄
⠀⠀⠀⠀⣷⠀⠀⠀⣠⡶⢦⣶⠋⠀⠀⢈⡵⢻⡿⠁⠀⠀⠀⠀⠀⠷⠶⠾⠳⠀⠻⢦⡀⠀⣤⣄
⠀⠀⣠⠖⣻⢀⣠⢶⠏⠀⡟⠻⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠈⠛⢶⣛⣷⢶⣄⡀⠀⠀⢀⡀
⠀⢸⠇⣾⠁⡞⣿⠘⠀⣀⠀⠀⠀⠀⣄⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠃⠀⠀⠀⠀⠉⠙⠿⣯⣷⣠⠔⡩⠃
⠀⠘⢧⡀⠀⠁⠀⠀⠀⠈⠛⠶⣤⣤⣬⣿⣟⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⡀
⠀⠀⠀⢻⡀⠀⠀⠀⣝⠶⠤⣤⠾⠋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⡤⠤⠤⠤⠤⣤⣄⣄⣀⡴⢀⡟
⠀⠀⠀⠘⣧⠀⠀⠀⠈⠙⠛⠁⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠶⡎⠋⠛⣖⠶⢤⣄⣀⠀⢼⢁⡞
⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣤⠞⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢹⣦⠀⠀⢀⡴⠋⠉⠙⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⠙⠻⠛⠛⠳⣤⣤⣄⣰⡞⠓⠶⠦⢤⣤⣤⡶⠏⠀⠀⠀⠘⡇⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠰⠶⣤⣤⣀⠀⠙⠿⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣀⡀⠀⠈⠉⠛⠶⠄⠀⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡴⠛⠉⠀⠀⠰⢆⡀⠀⠀⠀⢀⣟⠷⣤⡴⢚⡳⠀⠀⠀⠀⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⡆⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⢭⣤⠉⠀⢻⣷⢤⣤⣄⣠⡿⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡟⠃⠀⠀⠀⠘⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣖⣓⡛⠡⣤⣀⠀⠀⠀⠀⢀⣠⠆⢀⠞⠀⠀⠀⠈⢿⣯⣤⣀⣀⣀⡀⠀⠀⠀⢀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣤⣤⠙⠳⣄⢀⣴⠿⣧⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⠉⠉⠉⠙⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠘⢦⣤⣤⡘⣧⡀⠈⠁⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⢿⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠠⣯⠀⠀⠀⠀⢰⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠸⠶⠃⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣶⣦⣤⣶⣦⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠀⠀⣸⣿⣿⣿⠟⠿⠿⢿⣿⣿⣿⠿⢷⠀⠀⠘⢻⣿⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠈⠙⠛⠋⠈⠛⣿⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⡏⠛⠁⠋⠀⠉⠀⠀⠈⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⠃
⠀⠀⠀⠀⠀⢰⠷⡞⠛⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⢇⡟⠀⠀⠀⠀⠉⠀⢀⠀⡀⠈⠀⠈⡄⠀⠀⠀⠴⠀⠀⠀⠀⠴⠀⠀⠀⠈⠸⠛⠃
⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⡁⡀⠁⠀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠛⠿⠍⠀⠀⠀⠇⠀⡁⠀⠀⢰⡂⢐⠆⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠂⢉⠅⠛⠅⡘⠦⡤⢀⣀⠀⠀⢀⠀⣀⠤⠺⡐⠤⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢢⠀⠠⠂⠰⠊⠀⢀⠔⠁⠀⠀⠀⠀⠉⠋⠂⠀⠃⠀⢃⠀⠀⠀⠀⠀⠑⠄⡉⡗⠄⡓⡄⢠⡊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢎⠐⠩⣤⠂⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⠂⠤⡄⠀⠀⢏⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⢄⡔⢄⢻⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⡷⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠑⢌⡢⢠⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⠀⠀⠀⠀⢡⢂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡔⢮⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠛⠶⡇⠀⠀⠀⠀⠀⢀⠌⠀⢀⡔⠀⠀⠀⠀⠀⢸⣇⣢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⡂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠠⠄⢀⠀⢀⠠⡇⠀⠓⠄⣀⣀⡠⠐⠁⡀⠔⠈⠁⠀⠀⣀⠀⠈⡇⠀⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒⠂⠀⠱⠐⠛⣱⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠠⠄⢀⣀⠠⠊⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠔⠁⠀⠀⠢⡀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡆⠀⡄⢀⡃⠀⠀⠀⠀⠀⠀⡆⠀⠔
⠀⠀⠀⠀⠀⠀⠰⡙⢶⡇⠀⠀⠀⠀⠀⠱⣂⣱⣂⠶⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠇⠀⠧⢠⣇⣀⠀⠀⠰⡉⠻⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠛⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠍⠐⠋⠀⠀⠓⠒⠒⠀⠃⠀⠀⠀⠁⠂⠁


⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⢰⣿⣦⠀⣰⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠚⠛⣿⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠤⠤⠂⠀⠲⣟⠻⣿⡿⠿⣉⠐⠒⢦⣝⢿⣿⣿⣿⢸⣿⠇⠳⡄
⠀⠀⠀⠀⠀⠀⠒⢲⠠⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⡁⠉⠀⢨⣉⠉⠉⠙⠟⠿⠏⢛⢣⣤⣠⣿
⠀⠀⠀⠀⠀⣿⠀⠸⣄⡙⠟⠛⢿⣧⣄⢠⣄⣠⣼⠇⠈⠁⠀⠈⠳⢦⣤⢽⣔⡄⠈⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠶⠾⠻⠛⢋⠲⣌⠻⠿⢞⡉⠉⠀⠀⠀⠈⣿⠶⠖⠀⢸⣿⣷⠈⡽⣹⣿⠇
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⠌⠛⠛⢋⣠⣤⡀⠀⠀⠀⠈⢑⣠⡄⣼⣿⣿⡆⢸⣿⡟⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠘⣤⠲⣦⠀⠀⠀⠀⠀⠘⠛⠁⠈⠉⠀⠀⠀⠉⢉⠉⡰⠃⣽⣿⠇⠸⣿⣧⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢯⣀⣤⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠻⠞⠧⡴⢛⣿⠈⠳⣌⣹⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢱⣿⠀⠀⠀⠀⠀⠁⣿⡿⠆⠀⠀⠀⠀⠀⡟⠁⣿⣾⠇⠙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡽⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠿⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠙⠆⠐⠆⠑⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⢾⣋
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠃⣀⣤⣤⣄⣀⣀⡤⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⣧⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠘⠿⠿⠋⠀⠀⠀⢠⡔⠒⠉⠉⠉⠉⢉⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣹⠉⠙⠛⠛⠛⠋⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠠⠶⠶⣏⠘⠀⠀⠀⠀⠀⣀⠀⠀⠗⠚⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠈⢻⡅⣀⣙⠀⠏⣩⡟⣁⢀⡴⠋⠁⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡆⠀⣖⡚⠇⢹⣿⣇⠀⠁⣛⡟⢃⡴⢊⡴⢧⠀⢀⣠⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡾⠁⠀⠀⠙⣿⣾⣿⣿⡆⠘⣻⣶⣫⡴⢋⣤⡾⠶⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⢀⡾⠁⣿⠀⠀⠀⠀⠀⢨⣿⣿⣭⠀⣀⠀⣻⣟⠶⠋⣡⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⡾⠁⠾⣧⣀⡀⠀⠀⠀⠈⣟⣛⣋⠀⡈⢙⡛⡋⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠠⣬⣭⣿⡄⠀⠀⠈⣿⣿⠾⠿⠓⠾⢷⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠰⢤⣈⣹⠀⠀⠀⠙⠿⠶⠶⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⣀⣀⣈⠉⣳
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣰⡏⠀⢈⣥⠞⠋
⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⣴⠟⠀⠀⠈
⠀⠀⣴⢶⣯⠀⠀⠀⢶⡟⠁
⠀⠀⢰⡞⣻⣷⣀⠀⠘⠃⣶⡄
⠀⠀⠀⠉⣅⣻⡿⣿⢋⣼⣏⠁
⠀⠀⠀⠀⠙⠉⢠⣿⡆⠙⠉

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾
⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⣠⣀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣄⣴⣶⣾⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠾⠟⠟⠁⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⣻⡅⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⠂⠀⢠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⣴⣿⣿⣿⣿⣿⡀⠀⣹⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣆⠂⣼⣿⣿⣿⣿⣿⡯⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡟⣡⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⠻⣿⣿⣿⣿⠟⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠁⠉⠛⠋⠀⠀⠀⠀⠀⠈⡙⢂⠆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣈⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠈⠉⠉⠉⠀⠀⠀⣿⠿⠿⠋⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠂⢐⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⣐⡞⢤⡤⠶⠀⠀⠀⠀⢸⢇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⢄⡀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢱⣦⣄⣀⣠⡴⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠋⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠧⠀⠀⠒⠂⠀⠒⠀⠄⡀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡄⠀⢀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⣠⣿⡿⠀⠀⠸⣿⣿⡇⠀⠀⠀⢤⢾⣧⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠿⣿⡿⠀⢀⣴⣦⡄⠀⣴⣶⡄⢠⣄⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⢣⣤⣄⡀⠀⠀⠀⠈⠻⠿⠟⠀⠻⡿⠇⠘⢿⡇⠀⠐⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⠿⠿⠃⠒⠈⠀⠈⠋⢠⡄⠀⠀⢠⣶⣄⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⣆⣰⡎⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠸⣿⠟⠀⣾⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⢠⣴⣤⠀⠙⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠻⠿⠟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢀⣤⡶⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⣰⡄⠉⠁⠀⠈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠿⠇⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣦⣶⣴⣶⣦⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣉⣉⣉⣛⠲⣶⣤
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⣿⣿⡿⠿⣿⣿⣿⣿⣶⣿⣇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠉⠉⠉⠋⠙⠛⠛⣿⠀⠀⠀⠀⢻⡏⠁⠀⠀⠀⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠙⢫⢵
⠀⠀⠀⠀⠀⠰⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣠⠀⠀⠀⠈⠠⣤⡄⠈⠀⠀⠀⢨⡆⢠⠴⣦
⠀⠀⢠⡟⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠤⠒⢶⠄⠀⠀⠀⠀⠀⠀⣀⣤⡾⢛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡙⠻⠷⠀⢾⠟⢋⣡⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠄⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢰⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⠻⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠢⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠉⠈
⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠊

⣾⡷⠻⠗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠆⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢁⠘⡈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣓⠁⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠦⢀⡈⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠑⡄⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⣀⠠⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠉⠓⠢⣴⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂⣨⠖⠂⠉⠉⠉⠉⠐⠂⢬⡀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠜⠁⠈⢀⡀⠁⠁⠀⠀⠀⠀⠈⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠈⠀⠀⠀⠀⢈⣽⠢⠀⠙⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡇⠀⠠⡄⠤⠤⠤⠄⢀⣠⣾⡏⠀⠀⠀⡄⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠻⣿⣿⡾⠿⠛⢻⡟⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠉⠛⠤⠤⠒⠉⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠶⠤⠤⠤⡤⣤⠤⠒⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢠⠃
⡆⠀⠀⠀⠀⠀⠀⡀⢈⡀⢠⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⡏
⠱⡀⠀⠘⠢⡀⠀⠁⠀⠀⢱⠀⠐⢄⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠘⢎⠠⠀⠈⠒⡷⢤⠀⠈⣀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠑⠦⣀⠆⠀⠀⡄⠀⠀⠉⠒⠤⢀⠈⠲⢄⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠔⠀⢀⠶⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠉⠐⠒⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⡓⠢⠤⣄⠀⠀⠀⠀⠀⠀⠈⢲⠥⣄⠀⠀⠀⠠⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠢⠀⠀⠀⠀⠀⠘⠀⠂⠑⢄⠀⠀⠈⠇⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡸⢁⣀⠀⠀⣁⠜⠀⠀⠈⠣⣀⡘⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡴⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⡂⢀⡴
⠀⠀⠀⢠⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠉⠉⠃⢈⠐
⠀⠀⠀⠀⠣⠀⢀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠚⠤⠈⠉⠒⠒⠄
⠀⠀⠢⡈⠢⣁⡄⠛⠁⢠⠀⠁⠐⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠇
⠀⠀⡀⠈⠓⠀⠀⠖⠉⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠲⠀⠠
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠡
⠀⠀⠀⠀⠀⠀⠈⠉⠐⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠁⠘⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡀⠀⠀⠀⠀⢀⡔⠉⠲⠂⠉⠉⠙⠛⠶⣷⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢠⠁⢠⡤⠄⠠⠤⠤⠒⠒⠉⢀⣠⣾⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⠀⠀⠰⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠗⠠⠄⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠙⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡌⠁
⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠻⣿⠁⠀⠀⠀⠘⣩⠏⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠉⠁⠒⠒⢊⡁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⢾⣅⣀⡀⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⣠⣤⡤⠶⠛⣁⠰⠌⢣⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢹⢄⠀⣤⠀⠈⠐⠃⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠀⣀⣀⠀⠠⠖⠋⠀⠀⠀⠘⣴⠁⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢋⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡄⠀⠀⢸⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⣤⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠓⠒⢁⡖⠀⢀⠇⠀⠀⠀⠀⠀⠀⣀⠩⠴⠚⠉⠈⠳⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⠛⡀⠰⠿⠤⠤⠤⠐⠐⠛⡏⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠓⢤⣀⣀⡴⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠴⠂

⠀⠀⡄⠀⠰⠂⠀⠀⠂⠀⢀⣀⠀⠀⠀⠄⠲⠀⠀⠀⠀⡀⠀⣠⠆⠀⠀⠆⠀⢀⠀⠀⢀⠀⠀⠀⠰⠀⠀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⡀⠁⠀⠀⠁⠓⠀⠀⠁⡄⢀⠆⡰⢡⣷⣊⡄⠀⠔⠀⢀⠀⠀⠀⠄⠈⠀⠐⢤⣄⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠈⣄⡠⠁⠀⠀⠉⠀⠃⠀⡄⠀⡇⢰⠃⠈⢠⣶⡪⠥⠂⠀⠃⠀⠠⠀⠐⠀⠀⠔⠠⠠⠄⠀⠀⠉⠓⠤⡄⠀⠀⠀⠉
⠀⠈⠁⠀⠁⠀⠠⠤⠀⡀⢰⠀⠙⠸⠀⡀⢠⣶⠋⠄⠄⠒⠂⠐⢁⠀⠀⠀⠠⠆⠀⠀⠀⠠⣠⠎⢀⠀⠀⠀⠀⠺⢆⠀⠈
⠈⠀⣄⠀⠀⠀⠀⢰⠀⡇⠈⠀⡆⢸⡰⠷⠇⠀⠀⠀⠒⠒⠀⡀⠀⠀⢀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠀⢠⠂⠘⠃
⠀⠀⠀⢄⠀⡆⠀⢀⡀⠀⢰⠀⣧⣈⣉⠓⠂⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀
⠀⡀⠰⠸⠀⢇⠀⠀⡇⢻⣘⠁⠀⠀⠀⠁⠀⠉⢉⡁⠀⣀⠀⠀⠄⠀⠀⠀⠀⠟⠂⠀⠀⠐⠀⠀⠀⠈⠂⠀⠀⠀⠂⠐⣄
⠀⠓⠀⠀⠀⢸⠀⠀⠣⠤⣬⡉⢀⠁⠒⠦⠄⠀⠞⠙⢦⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⣇⠘⣤⣘⣓⠒⠂⠠⠤⣈⠛⢂⡤⢨⢥⠛⡀⣁⠐⠆⠀⠀⠀⢀⠆⢀⠀⠀⠊⠀⠀⠐⠒⠀⠀⠿⠄⠀⠀⠀⢁
⠀⠀⠀⠀⠐⠓⠒⠀⠠⢄⣈⡑⠂⠀⠀⣉⠝⣇⠈⠆⠁⣨⠀⠘⠃⠈⡡⠄⢀⠀⠀⠈⠀⣀⠄⠀⠀⠀⠛⠀⠑⡄⠀⠀⠈
⠀⡠⠂⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠈⠁⠀⢠⠀⠺⠀⠀⠀⠀⠀⠼⠃⠈⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠘⠀⠘⠀⠀⠀⡠⠚⠀⠀⠀⠀⢀⠠⠋⢀
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣢⡄⠉⠀⠀⠀⠀⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⣰⠦⠤⠄⠀⠀⠀⠤⠀⡀⠄⡀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠈⠁⣀⠜⢏
⠀⠀⠀⢀⣀⠄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⡜⠓⠀⠂⠀⢀⣀⠐⠀⠐⠃⢀⡠⠀⢰⠀⠁⠀⢀⡠⠀⠀⠰⠀⣠⠒⠀⠘
⠠⠤⠒⠊⠉⠀⠀⠈⢀⠀⠈⠀⠐⠄⠀⣴⣋⡁⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⠔⠋⠀⠂⠀⠔⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠂⠀⠀⠰⠯⠀⠀⠀⡀⠀⡋⠀⠀⠂⠀⠀⠱⠀⠀⢠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡲⠄⠀⠰
⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠦⡀⠀⠊⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠜⠊⠀⠀⡀⠀⠀⢀⠔⣴⣾⣿⣿⡿⣿⣿⣿⣿⣷⣦
⠀⠀⠁⡀⠀⣐⠆⠂⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠡⠐⠀⠊⠀⠀⢆⠀⠀⠈⡠⠀⠁⢸⣿⣿⡿⢿⡷⣿⣿⡿⣿⢿⣿
⠀⠀⠃⠀⠀⠀⠿⠰⠙⠀⠒⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⢸⣿⢸⡇⣻⡇⢹⠃⡆⣿⡸⣿
⠀⠀⠀⢀⠠⠊⠀⠄⠀⠀⠀⠀⠀⢠⠀⣤⢀⣀⣐⠀⠀⠀⠀⠀⠀⠈⠁⡠⢐⠊⠔⠃⠀⠘⣿⣼⣧⣻⣴⣾⣴⣇⣿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠉⠁⠀⠀⠈⠁⠒⠤⡀
⠀⠀⠀⢀⣀⡀⠀⡠⠊⣁⣀⣀⠀⠐⠒⠤⠤⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⡥⠄⡶⠉⠀⠢⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢉⠄⠀⠀⠀⠈⠑⢍⠁⠒⠠⣀
⠀⠀⠀⠀⠰⢡⠀⠀⠀⠙⡆⠀⡗⠒⠠⠴⠤⠤⠤⠤⠽⠉⠐⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠖⠠⠃⠀⣴⠂⠀⠀⠀⠀⠑⡀⠀⠈⢳⣄⣀
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣂⢀⡁⢀⡌⡇⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⢯⠉⢆
⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠁⠀⢀⠖⠒⠒⠀⠓⠀⠉⡏⢑⡄⠀⠀⠀⠀⡍⠉⠀⠀⠀⠀⠈⠙⠃⠒⠀⢤⢀⣸⠀⠀⠀⠀⣼⠀⢨
⠀⠀⠀⠀⠈⠆⠀⠀⡜⠉⠱⠉⠀⠀⠀⠀⠀⠀⡀⢼⠀⠐⣆⠀⡤⠴⠾⣏⡁⠁⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠰⢄⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠈⢆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⣆⠬⠁⣰⡇⠙⠢⠴⡖⠁⠀⠀⠀⠘⠈⠀⡄⠀⠀⠀⠓⠀⠀⠀⠀⠘⠤⠀⢄⠀⠀⠀⡌⢰
⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⡩⠋⠉⡆⠀⠸⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠜⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⡄⠀⠀⠲⡒⠉⡇⠀⢀⠜⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⢄⡠⠐⠈⠉⢘⠅⠀⠀⠀⠀⠀⠀⠀⢈⠦⠻⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠀⢤⣿⡦⣤⠴⠋⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠎⠀⡠⠶⣶⢻⠀⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠒⠢⠼⠛⠉⠱⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠈⡎⠉⣿⠁⠀⠀⣸⠦⡀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⠁⠀⠀⠀⠀⠀⡸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⣇⠀⠘⠳⠶⠚⠋⠀⠈⢢⠀⠀⠀⠑⢄⡀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⠄⠀⠀⠒⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣼⠀⠀⠀⠀⣀⣀⠀⠀⢡⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⣂⡀⢰⡀⣀⠤⠚⡅⠀⠀⡠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣟⠀⠁⠀⠀⠀⠀⣀⠬⠦⠞⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡨⠋⠉⠘⠃⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⠶⣐⣂⣙⢲⣖⣖⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠈⠀⠔⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠒⠀⢠⢠⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣉⣉⡉⠈⠉⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠸⠖⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⢀⣀⢀⣀⣀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣈⢉⣉⣀⡀⠬⢥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⢆⡀⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠤⠴⠃⠀⠀⡗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠄⠤⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠢⡀⠀⢀⡜⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡠⠓⠌⣲⠿⠀⢀⠄⠀⠀⠀⠈⠣⡀⠰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣆⠞⢀⡼⠁⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⡄⣀⣸⠿⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠙⡶⠋⠀⣠⣟⣡⣀⣀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⢈⣳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠉⠉⠃⢀⣀⣀⠀⠀⠀⠀⠀⡀⠀⣠⡄⡄⠀⢄⡄⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⢀⣴⠟⠁⣼⡇⠀⠀⠀⣼⠇⠀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣠⣾⢀⣠⠄⠀⢀⣀⣌⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣾⠃⠀⣰⣿⢁⣤⣤⣼⣿⣤⠀⡩⣀⣀⠀⣠⡀⢀⣤⡄⣸⡿⠁⣤⠀⣘⢻⡉⣰⡏⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⣀⣤⣿⢳⡿⢃⣼⣿⣿⡏⡰⣿⡟⡹⢣⣿⡴⢫⡿⢁⡿⠁⣼⠏⣰⡏⣸⣿⠏⣾⢋⡼⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⢸⡏⠁⣼⣿⢾⣣⠏⢸⡏⢿⣣⠁⢿⣉⡔⠹⡿⠁⢿⣁⡼⣇⡴⣯⠜⢿⡼⣿⠏⡸⡏⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠘⠇⠀⢿⡟⠀⠁⠀⠀⠀⠀⣁⠀⣀⠀⣀⢀⣀⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⡯⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⣿⢢⣿⠸⣧⣼⣿⡇⠈⣧⠐⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠶⠤⠤⠶⠶⠚⠛⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⢀⣀⡄⠀⠀⠀⢀⣀⣀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⠞⠁⠀⣀⡤⠭⣭⣝⡛⠫⠛⠂⠰⣾⡀
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣠⠖⠂⠀⣠⠖⠚⠛⠀⠉⠀⠀⠀⠀⠀⠻⡆
⠀⠀⠀⢀⡏⠀⠀⠀⠀⢸⣧⢄⡀⠸⠳⣤⣀⡤⣶⠄⠀⠀⢀⡴⠶⠄⢻
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠾⡵⢋⠀⠀⢀⣠⣖⣿⡛⠁⠀⠀⠋⠀⢠⡀⢸⡆
⠀⠀⠀⢸⡄⠀⠀⢀⣤⣄⣵⠏⠀⠀⢚⡽⣻⠏⠀⠀⠀⠀⠠⣤⣬⠧⠈⠳⣄⠀⠀⣀
⠀⠀⣠⠼⡃⢀⡤⡞⠁⡞⠿⠀⠀⠀⠁⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣾⠋⠙⢶⡖⢶⣤⣄
⠀⣼⠁⡞⢰⢻⡇⠃⣀⠀⠀⠀⢀⡀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠃⠀⠀⠀⠉⠙⠶⣯⣷⣠⢔⡽
⠀⠘⢦⡀⠈⠀⠀⠀⠈⠛⠶⢤⣤⣭⢿⣛⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⡀
⠀⠀⠈⣧⠀⠀⠀⢬⣓⢶⡶⡚⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⠤⣤⣀⡀⠤⠤⠤⠤⠤⢤⠖⣰⠃
⠀⠀⠀⠸⣆⠀⠀⠀⠉⠉⢠⡟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⠻⡎⠉⠹⠛⠒⣦⣤⣀⡞⣰⠃
⠀⠀⠀⠀⠘⠳⠶⠤⠴⠖⠋⠀⣼⣆⣠⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢹⡆⠀⠀⡞⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⣉⠀⠈⠳⠚⢷⣾⣏⠉⠉⠙⠛⠛⠛⠁⠀⠀⠀⢸⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⠉⠛⠲⢦⣀⠉⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⠶⠒⠀⠀⣀⠀⠈⠑⠆⠤⢿⣆⢀⣠⣤⠀⠀⠀⠀⣽⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢘⡅⠀⠀⠀⠀⠈⢷⠀⠀⠀⠸⣷⣽⠉⢠⣭⣀⣀⣀⣠⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⣧⠐⡶⠛⠀⠉⠉⠙⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣴⣒⡚⠣⣄⡀⠀⠀⠀⠀⣀⡤⢀⡞⠀⠀⠀⠸⣿⣥⣀⣀⣀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠈⢹⡧⣤⣤⠙⠳⡀⣠⡾⢿⡀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠙⠦⣤⣄⠹⡄⠀⠁⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⡜⢣⠈⠙⠁⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢾⢀⠟⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠀⢀⡀⠀⠀⠀⠀⠱⠀⠀⠂⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠃⠀⡵⠉⢀⡀⡀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠌⠉⠐⡄⠀⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠄⡉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠥⠈⡤⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⢰⠌⠀⠆⠤⠀⠸⠓⠒⠀⠭⠀⠀⠀⠀⠀⠢
⠀⡀⠠⠀⢤⢄⣀⠀⠤⠐⣂⢀⣀⡇⠠⠇⡀⢀⣀⠀⠀⠄⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠
⢆⢄⡠⠠⠏⢣⡐⡖⠋⠀⠀⠐⠒⣒⠀⡆⠘⠺⠏⠑⠒⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢐⠰
⠀⠀⠈⠁⠀⠁⠐⠌⢄⠀⠀⠀⠀⡈⠌⠁⣘⣾⣄⡀⠀⠀⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠀⠀⠀⠗⠀⢀⠁⢱⠄⠟⢷⣲⠄⠄⣤⠤⠼⠥⠄⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡑⠄⠊⠀⣤⣠⠀⠀⢡⡂⠒⢘⠛⠣⠀⠈⢈⠂⠓⠛⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠔⠀⠀⠀⠀⠀⠀⠀⢃⣉⢨⣀⡍⡄⠂⠁
⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠐⡀⠀⠀⠀⠀⠀⠀⠲⠈⠉
⠀⠀⠀⠀⠀⠀⠁⠐⠂⠉⢈⣳⣂⣠⣠⣤⣀⣀⣀⣑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡘⠫⠬⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⠶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣹⣵⠟⠁⣀⣤⣾⣿⣿⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣴⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⠂⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣾⣿⣿⠟⠉⠀⠈⠉⠱⣿⣆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣟⣄⢠⢾⣿⡿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣺⣯⣞⣷⠋⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡴⣿⣯⡞⠁⣰⣿⢯⣉⡛⠲⠄⠀⠀⢀⣀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⠋⠀⣰⡿⠃⠀⠈⠙⠓⠀⠀⣾⣫⣥⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠘⣶⣾⡏⠁⠀⠀⠀⠀⠀⠀⢰⠇⢀⣾⣿⡟⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⣿⣧⠀⠀⠀⠀⠀⠴⠒⠞⣠⣾⡋⢸⡇⣷⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠋⣼⣿⢏⣿⢆⡀⠘⠳⠷⣶⣶⣶⣿⣏⢳⡀⢿⡘⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣿⣿⠏⠈⡿⠀⢱⣤⣤⡶⠦⠒⠛⠘⠛⠒⠻⠎⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⠤⢤⣀⠀⠀⠀⠀⡇⠀⣀⣨⣤⠶⡀⠄⠒⠒⠒⠒⢒⣮⠉⠉⠉⠑⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠁⠘⠁⠀⢀⠀⣛⡸⠀⠀⠀⠠⡾⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⡴⠚⢙⣓⣒⣙⣤⣀⠀⠀⠀⢛⠲⣼⠀⠀⠀⠀⠀⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⢀⠔⠛⢛⣚⣋⠁⠙⠶⢤⣶⢾⠀⢹⡀⠀⠀⠀⢰⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢀⡔⠁⠀⡰⠃⡴⠾⠓⠲⠶⠶⠀⠀⠀⡝⠋⠀⢸⠃⠀⠀⢠⠇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣠⠋⠠⠤⠊⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠐⠃⠀⠀⢠⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠔⠁⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⡀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⠾⣦⣤⣤⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠉⠑⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠏

⣄⢌⠀⠰⡘⢃⠀⠀⠋⣰⠟⣱⡿⣻⣿⡟⠀⠀⣰⣿⣿⣿⣄⠀⠘⢀⢀⡄⠐⣶⣌⣿⣿⣿⠿⠟⠋⠁⣿
⡮⣑⣇⠀⠀⠈⠀⠀⠘⠃⠀⠋⣈⣼⣿⣀⣀⣀⣿⣿⣿⡻⡿⢷⣦⠀⠳⣿⣶⣾⣝⣿⣿⡇⠀⠀⠀⠀⠻
⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⡿⣿⡝⢿⡄⠈⡯⠳⠀⠀⠉⠛⠿⢿⣿⡏
⠀⠉⠢⠄⣈⢦⡀⠀⠀⠀⠠⠒⠁⠈⣦⣍⠙⠻⣷⠈⢿⡄⠀⠀⠀⠀⠤⠀⠀⣠⣄⠀⠈⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢦⣄⡀⠀⠘⢯⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⢙⣧⣤⣄⣠⣼⣿⡿⢷
⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣐⡽⠃⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠲⢿⣿⣿⡷⢞⡫⠅
⠂⠀⠀⠀⢐⣤⠀⢀⢨⣦⣿⡆⠀⣠⣶⣬⡄⣀⣀⠀⣀⠠⠔⠒⡫⠉⠁⠀⠀⠀⠀⠈⣉⠭⣭⡶⠋⢴⣿
⣴⠋⠀⡄⢹⣿⣦⣇⢿⣿⠟⠀⠀⠒⠂⢀⡬⢔⣈⠝⠀⢀⠀⠎⠀⠀⠀⡀⠀⠀⠸⣿⣿⡿⠋⠀⠀⣰⠟
⠇⣀⣴⣃⢀⡉⠙⠛⠈⠁⠀⠀⠀⠀⠐⠻⠶⠿⠟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠦⡄⠀⠀⣼⡇⣿
⣾⣿⣿⡿⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⢠⢀⢠⣀⡄⠀⢧⡀⠀⣿⠀⠀⠘⠛⠛
⠟⠸⠁⠃⠀⣿⣿⠀⠞⠙⠙⢣⣶⣶⣤⣀⠀⠀⠀⠀⠀⢿⢏⡿⣿⢸⡘⣿⠷⣦⢲⣽⣷⣾⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠍⠁⠀⠤⠤⠞⠫⠪⠫⣾⠇⠀⠀⠀⠀⡀⣤⣾⣷⢿⠜⠗⠀⠀⠘⢷⣗⣽⠇⠀⠀⠀⠈⠻
⠀⢀⠀⠀⠀⢀⡀⠀⠀⠤⣤⣾⠛⠉⣟⢿⡗⣄⡀⣠⡹⡌⣇⣿⣾⣦⠀⠀⠀⠀⠀⠀⣈⣠⠤⠀⠐⠂
⠀⢸⡇⡀⠀⠀⠀⠀⠀⠐⣛⣛⣡⣴⣷⣿⣛⠌⠻⢿⣷⠸⠸⢹⡿⠏⠀⠀⠀⢀⣤⣾⣿⠋⠙
⠀⠀⡇⠈⢢⠀⠐⠶⣬⣴⣒⡶⣶⣖⢰⡀⠉⠳⡄⠈⠁⠀⠀⠈⠃⠀⠀⠀⠸⡿⢏⡝⠁⣀⡍⣀⣠
⠀⠀⢡⠀⠈⠂⠀⠈⢺⣿⣿⠝⠛⠉⠈⠳⠦⠀⠀⠀⠀⠠⠀⠀⠀⡔⠁⠀⣘⢤⠩⠂⡴⢶⣞⣉⡀
⠄⠀⠞⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⠀⠀⠀⠀⠀⠘⣀⠴⠊⠀⠀⠠⢀⣀⣠⡿⠋⣠⢀⣼
⠄⣶⠀⢷⢹⡿⠀⣀⣴⣿⣦⡀⠀⠀⢠⡿⠭⢉⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠛⠻⢿⣵⣾⠷⠟⠁
⢸⡟⡄⠀⠻⢁⣾⡟⢸⣿⣿⣧⣀⣠⣤⣿⣿⣿⡦⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠿⣦⡀
⠎⣿⠡⠄⠠⡿⠘⠁⠼⠿⢻⡿⢿⢿⢿⣿⠛⠻⠿⢿⡕⣠⠞⠀⠀⠀⠀⠀⠀⠻⣦⡈⠿⡿⣷⣶⣶
⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠩⣿⡿⢿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣸⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣼⢇⢼⣷⣇⢸⣀⣀⡀⢥⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠬⠿⠿⠿⠿⠏⢹⣿⣿⠈⡡⣿⣿⠿⠿⠷⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣄⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡋⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠧⠔⠊⣩⠿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠁⣷⡀⠀⢰⡒⠀⠀⡴⠶⠖⡀⠒⠐⠤⠀⠀⠨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⠬⠁⠀⢘⠁⠀⠉⡰⠿⣿⣷⠤⠤⠴⠆⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⣶⣤⡼⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠐⠘⡀⠀⠈⣤⠞⠉⠀⢀⡆⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣧⡀⢰⡀⠀⢀⣾⡷⠋⠀⢋⣄⣀⣰⣆⡠⡯⠀⠀⢿⣥⡴⠞⠋⣷⢀⡟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡛⠳⣀⢹⣉⡝⣉⣤⣨⣿⣞⡏⢀⠜⡡⠂⠈⡿⠉⢖⡘⣿⡃⠀⢻⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⠀⠀⠻⠈⢻⣏⣷⢨⣾⣿⣧⡤⠚⠐⠉⡰⠁⠀⠈⠈⣴⠐⣄⠚⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠿⠀⠒⠒⠚⠒⣲⣿⣿⣿⣿⠟⠁⣤⣰⣦⠔⢲⡤⡤⠀⠀⢋⠁⠉⠉⠓⢦⠀⠶⠄
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⢀⣠⢀⡔⠁⠴⠶⠖⠲⠦⠤⠇⠀⠀⣥⠂⢀⣞⣟⢓⣺⣏⣾⣷⢤⠆⡀⠀⠐⠠⠄⠸⢑⣤⠆⠦
⠀⠀⠀⠀⠀⠴⠉⠁⠀⠀⠀⠈⠀⠢⠤⠤⠤⠤⠤⠀⠀⠤⠤⠠⠤⠤⠤⠄⠀⠉⠉⠉⠀⠀⠒⠊⠀⠀⠀⠐⠒⠛⠉⠉⠁⠰⠠⠤⠤⠔⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⢰⠄⠰⣓⠂⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⡆⠘⣯⠅⠀⠀⠘⠁⠙⠚⠁⠀⠀⢯⣀⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢳⡈⠋⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠸⣤⠞⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢇⡀⠙⠋⠀⢀⡴⣾⠟⠒⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠠⠀⠀⠀⠴⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⡀⠁⢀⡀⠀⣾⠸⡇⠀⠀⢀⠀⠀⠀⠀⠐⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠉⠀⠀⠀⠁⠀⠘⢦⣉⣒⡶⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⢀⣦⡀⠁⠀⠀⠋⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣆⡆⠀⠀⣼⡤⠀⠁⠀⠀⠀⠀⠀⠤⠀⣰⢿⣦⠀⠀⣀⡀⠀⠀⠀⠈⠟⠁⠀⠰⠂⠀⠉⣻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡈⠀⢀⠀⠘⠀⣠⣿⣄⠀⠂⠀⠀⠀⢰⠇⢹⡘⣇⠘⠃⢹⠀⠀⠉⠀⢠⣄⠀⠀⠀⠀⠈⣡⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⡀⠀⢀⡼⠃⣼⠸⡆⠰⠆⠀⣰⠋⢀⡞⠀⠈⢁⡴⠋⠀⠆⠀⡴⠻⡏⢷⠀⠀⠀⠀⠓⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⢹⡆⠀⢁⡴⠋⠀⢰⡇⠀⢹⣄⣠⠞⠁⠀⣾⣁⡠⢀⡞⣠⠶⡄⢠⠾⣇⢀⡟⠈⠳⣄⠛⠀⢘⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠄⠀⠈⢀⡄⠀⠈⢳⣴⠋⠈⠻⡄⠀⠈⠋⠉⠀⠸⡇⢻⡀⠡⡀⠀⠙⣾⠁⠀⣤⠈⠃⠀⢨⣄⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠄⠀⢀⠾⡿⣆⠀⠀⠉⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠹⣄⢳⡀⠙⠀⠀⠀⠀⡴⣿⢧⠀⠀⠛⠚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⢦⠀⠀⢠⣷⡀⠀⠀⢀⣤⣀⣀⣀⣀⡀⠹⢸⠇⢀⣿⡀⠀⢀⡴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⣠⢞⣟⢦⡀⠐⢫⣯⡓⠀⢀⡾⡴⠀⠀⢠⢠⣿⣆⠋⠀⢋⣿⡙⠀⢀⡾⣿⠳⡄⠰⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠀⡴⢛⣟⠢⡀⠐⣫⣯⡛⢀⣞⡁⠙⠓⠒⠋⡼⣻⣘⣦⠐⢫⣿⣝⠂⢠⠞⣿⡳⡄⠘⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡴⢛⣟⠳⡄⠜⣩⣯⡙⠆⢉⣉⣙⠛⠒⠞⠛⢋⣉⡀⠰⣫⣿⣝⠆⡠⢞⣿⡛⢦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣫⣏⠳⢦⢚⣵⣷⣍⠂⠰⠆⣄⠰⠶⠶⠀⣀⠰⠆⠘⣡⣿⣌⠃⡴⢋⣿⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠑⠀⢋⣴⣷⣌⠓⠈⣼⣿⣄⢉⡉⣴⣿⣆⠁⢚⣡⣿⣮⡓⠀⠋⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⡷⣌⠓⢈⡴⡿⣆⠐⢀⡴⣿⢦⠀⠋⡴⣿⢦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠾⡿⢮⠀⠈⡼⡿⠦⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡁⠶⠂⠉⡑⡖⠒⠠⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠋⠈⢄⢣⡀⠇⡇⢀⡠⢊⠦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢰⣀⣀⣀⣈⣧⠙⠠⠖⣩⠖⠁⠀⢱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⠐⠒⠀⢠⡄⢀⡀⢈⡉⣀⣐⣒⣚⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⢤⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⣰⡀⣀⣴⢾⠶⠋⣽⡌⠣⡀⠉⠉⠹⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠣⡉⠔⠀⠀⠀⣿⠈⠣⡹⢄⡰⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠐⠀⠀⠄⣹⡀⡠⠜⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠶⢤⣤⣠⣤⠤⠶⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠦⣄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⠀⠀⠀⠀⢀⡠⠔⠈⠉⠑⡉⠒⠢⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠈⣳⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠐⠁⠀⣠⠴⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠃⠀⠈⠀⠀⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠐⣬⠒⠒⠒⠒⠒⠒⢦⡀⠀⠀⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⠀⠀⠀⠈⢆⢄⡀⠀⢀⡠⠔⢸⠀⠀⢠⠀⠀⠀⠀⠘⢆⠀⠀⠀⣼⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠈⠢⠤⠚⠉⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡄⠀⠀⠀⠀⠀⠀⣠⠒⠢⢄⡘⢠⣀⠈⠀⠀⠀⠀⢀⢸⠀⠀⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣷⠀⠀⠀⠀⠀⡰⠁⠀⢀⠀⠈⠙⠷⠄⠀⠀⠀⠀⠊⠜⠀⠀⢸⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢱⠀⠀⠀⠀⡐⠁⠀⡠⠉⠐⠢⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⢃⠆⠀⠁⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢻⠀⠀⠀⠀⠀⠉⠂⠄⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠦⣈⠉⠙⠛⠛⠛⠛⠛⠋⢉⣁⠴⠖⠋⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⠤⠤⠤⠤⠤⠶⠖⠋⠁


⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣭⣭⣬⣭⣭⣉⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣦⣤⣿⣿⣿⣭⣿⣿⣽⣿⣯⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶
⠀⠀⠀⠀⠀⡀⠛⣍⠈⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⢢⡀⠘⣿⠁⠀⠔⠁
⠀⠀⠀⠀⡀⠀⠀⠸⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣿⠁⠁⠀⠊
⠀⠀⠀⠀⠙⠀⠂⠠⢸⡂⠠⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣿⡤
⠀⠀⠀⠀⠀⠂⣀⠀⠌⣇⢀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠁⢀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠚⠲⠒⠓⠚⠀⠛⠒⠓⠒⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠠⡀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡄⠀⠀⣸⠅⠀⠀⠀⢤⠠⠀⠙⠀⠀⠁⠉⠃⠀⡀
⠀⠀⠂⠀⠀⠀⢲⡆⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠃⠀⠀⠉⠀⠀⠀⠳⢤⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠠⠤⠤⢴⣾⡿⠃⠈⠉⠂⠀⠁⠀⠀⠀⢠⡼⠄⠀⠀⠀⠀⠀⠈⡓⠀⠈⠈⣙⡦⣄⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⠐⠉⠹⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣠⣤⣀⢀⣄⡀
⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠈⠉⠛⠛⠈⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡿⣿⠿⠻⠿⠋⠈⠻⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⢠⡨⡝⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣛⡏
⠀⠀⠈⠀⡑⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠸⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⡀⠀⠀⠐⣾⠛⠐⡀⠀⠀⠀⠀⠀⠀⡂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⢀⠄⠈⠀⠁⠒⠍⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⠀⠒⡀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢈⠀⠀⠡⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠜⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠐⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣠⠀⠀⠔⠁⠀⠀⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠈⢁⡠⠯⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠺⠀⢈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⢳⠀⣀⣀⡀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⢀⡴⠖⠋⠀⠙⠚⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡼⠀⠀⠀⠀⢠⠞⠋⠀⠈⠉⠙⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠙⣛⠉⠀⠳⣄⠀⠀⠸⣄⣀⣀⣀⣀⣀⣹⠆⠀⠀⠙⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⢉⡁⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⡤⠤⣄⠀⠀⣀⠀⠀⠀⠀⢿⠉⢦⢰⡏⠀⠈⡇⢠⠎⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡄⢺⠀⠀⢸⢆⡞⢁⡇⠀⠀⠀⠈⢧⡸⣆⠓⠦⠖⢁⠯⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠿⣄⣙⣛⣁⡼⢤⡼⠀⠀⠀⠀⠀⠘⣆⠈⠉⠉⠉⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡾⡄⠀⠀⠣⠴⠖⠒⡏⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⣦⠀⠀⠘⡆⠀⠀⠀⠀⠀⡇⠀⠀⣞⠀⠹⣄⡀⢀⣀⣠⠤⠿⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣼⠈⢷⡀⠀⠹⡄⠀⠀⠀⠀⠙⣄⠀⠈⠳⡀⠀⠉⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡇⠀⠀⢳⡀⠀⢹⡀⠀⠀⠀⠀⠈⢳⡀⣠⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠀⠀⠀⠀⠳⣀⡤⠷⣄⠀⠀⠀⠀⠀⣟⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣉⣑⡇⠀⠀⠀⠀⠀⢯⡴⠚⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠃⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⡄⡀⠠⡄⢀⡄⠀⡄⡄⡀⠀⡤⠀⠀⠠⠀⠠⡄⢠⠀⡄⡄⠠⡀⡄⡄⠠
⠀⠀⠀⠀⠀⠀⠀⣋⡀⣀⣀⠆⡂⢀⡁⡞⠰⢀⣉⡇⣃⡀⣏⣀⠀⣈⡳⠀⡃⢸⠘⡌⢄⣀⠃⡏⢆⣈⣀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⢹⣶⣦⠀⢻⡆⠈⣿⡄⠠⣄⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠉⠀⡄⠀⠻⠷⠈⠁⢠⡹⣇⠀⠙⣿⡆⠀⠀⣿⡟⠁⢼⣇⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡃⠀⠐⠗⠀⢀⡀⠀⢿⣦⠙⣿⠁⢶⣦⠈⢱⣦⡆⢽⡅⢰⣞⠛⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠛⠓⠀⠙⣷⡾⣷⡠⠀⠻⢄⠈⠄⣨⣟⠀⠀⢿⢥⡀⠁⠀⠿⠆⢰⡦⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠰⣤⡄⠛⠻⣷⣦⠸⣷⣌⠻⣿⣧⡀⠀⣷⣆⢸⣿⠂⠠⡿⠸⠇⠀⣦⠀⡄⠈⠿⢢⠀⢰⡟⠛⠀⢀
⠀⠀⠀⠀⠀⠘⠛⢿⣇⠀⠀⣤⣉⠃⣈⠛⠃⢄⣵⣄⣼⣿⡏⠘⣿⡆⠀⠻⢇⣀⠀⠿⢱⣆⠀⡆⠘⢀⠈⠁⣶⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢧⡈⠛⠷⠈⠳⣤⣀⠙⠻⠇⠙⢃⠀⠀⢤⣄⠀⢸⣿⠏⠀⠀⢙⠀⠓⠀⣿⠇⢠⡇⠀⠉⠀⢀⡀
⠀⠀⠀⠀⠛⠿⣧⣤⣤⣄⠀⣴⣶⣆⠰⣦⠈⢿⣷⢀⢠⣤⡘⠧⣀⡈⢋⡀⠈⣷⠀⣷⣤⡜⠀⠀⠀⢁⣀⠘⠁⣰⡀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠇⠈⠻⣿⣶⡟⣁⣀⡿⢧⣉⡿⠟⠚⠿⠷⠘⠏⢀⢻⣦⣈⢹⡇⠀⣀⠐⠈⠉⠀⠀⠉⣽⠒⠉⢠⡶
⠀⠀⠀⠀⣀⣀⠀⠴⣶⣶⣤⠀⠀⠿⣿⠛⠈⢿⣷⠀⡙⠷⣦⣀⣀⡀⠐⣦⣌⡈⠻⠟⠣⡀⠀⠿⠇⣴⣶⣾⠀⣀⠛⢠⣶⣶⡄
⠀⠀⠀⠀⠉⠛⠿⠂⠀⠈⠁⢰⣶⣆⢀⣠⣴⣄⡀⠾⣿⡄⠠⢼⣿⡁⠀⠹⡻⠿⢤⣾⣦⡉⣶⣄⠀⠻⣿⣭⡾⢃⣠⡦⠠⠟⠃
⠀⠀⠀⣀⣀⣠⣄⠀⢻⠿⠟⠿⠤⣿⡿⠋⠙⣯⣾⣷⣾⢟⣶⣦⣍⠹⢷⠖⠰⣤⣠⣄⣈⣷⣾⡿⢆⣀⣹⣯⡠⠀⡈⢡⡶⠶⠆
⠀⠀⠀⠉⠉⠛⠻⠃⢤⣤⣤⣤⠄⠀⠀⢀⣈⣉⠉⠀⣩⠉⢉⣉⣷⣤⣤⣶⣄⡹⠟⢉⣽⣿⣿⣿⡧⢿⣿⣤⣤⣾⣿⡦⠶⠶⠂
⠀⠀⠀⠀⠠⠶⠿⠷⠂⠉⣁⣀⠀⠀⢶⣿⠟⠁⢀⣾⣏⣴⣈⡉⠁⢀⣀⣉⠉⣀⡈⣍⣻⡿⢿⣿⢿⣿⣿⠿⢠⣷⡄⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⠟⠂⢀⣨⡥⢠⣾⠏⠁⢨⣛⣿⢫⣿⠟⠉⠀⠀⣠⣿⣿⠿⠋⣸⣿⣧⠉⠛⠖⠘⠿⠋⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⣀⡤⢤⡾⠋⣡⡾⠋⠀⠀⣠⣿⣿⠶⠄⠀⢠⣄⠈⠙⢻⣿⣶⡆⢉⣿⢝⢠⣿⣿⣿⣿⣿⡶⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⣠⡾⠃⠀⠈⣁⣴⣿⠏⢠⠿⡿⠃⣠⣦⣿⠟⠁⠐⠛⢋⡁⢰⢿⣿⡌⣷⣤⣀⠀⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣁⠐⢻⣥⠀⣀⣴⠞⢋⣾⠃⢀⢀⡀⢠⡾⢟⣭⠀⠀⡠⠀⣸⣿⡇⠙⣇⠀⣿⠇⣹⡛⢧⡀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠴⠛⠉⠀⠚⠁⢸⡿⢁⣴⠟⠁⣴⠇⣼⠁⠀⠀⣿⡟⠀⠔⠁⢀⣿⠖⢱⣤⡙⠆⣿⡄⠙⡿⠁⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣰⠿⠋⠁⢰⣾⠃⣼⠏⠀⣀⡀⠈⠠⠀⠀⠀⠾⠁⠀⠸⠟⢿⡄⠸⣿⠸⣷⣄⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠀⠀⢠⣾⠟⢉⣷⣾⡇⠀⣾⠛⠃⠀⠀⣾⠿⠃⣠⠖⠁⠀⣰⡎⠁⢀⣄⠀⠉⠁⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⢠⡿⠁⢀⣷⠞⠁⠀⢠⡤⠀⣀⠀⢈⣵⡄⠀⠐⣿⠁⠀⠈⠿⠆⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢁⣼⠋⠉⢠⡄⠀⡾⠃⠼⠏⢰⣿⠛⣷⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⣿⠀⠀⠀⠀⠀⠀⢼⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⢀⢄⢀⠀⠀⠀⠀⠀⠀⡖⠈⣀⢀⢰⡆⠀⠀⠀⠈⠁⠈⠉⠙⡇
⠀⠀⠀⠀⠀⠀⣟⣛⡟⠚⣿⡇⠀⠀⠀⠀⠀⡀⠰⠀⠌⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⡃⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢾⠃⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠓⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠑⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠰⠆⠈⣴⠟⠀⠀⠀⠀⠀⠀⠳⠄⣀⣠⠾⠀⠀⠀⠀⠐⠦⠀⠐⠶⠃⠀⠀⠀⠀⠀⠠⠐⣠⣴⠇⠀⠀⠀⠀⠀⠸⠦⠀⣀⣀⣀⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢀⠀⣀⡀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠰⣾⠀⠀⠨⢷⣩⡗⠀⠀⠀⠀⡋⠀⠀⠀⠁⠀⢹⠀⠀⠘⢆⠀⠀⠀⠀⣼⠃⠀⠀⢸⡛⠀⠒⠒⠒⠛⠻⠂
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠠⠋⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠀⠈⢢⠀⠀⡜⠁⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠰⠀⠀⢠⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⢃⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⣿⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣏⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⣀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠐⠄⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠘⠤⠄⠀⠐⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠂⠀⠀⠀⠀⠛⠀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⡶⠊⠉⠉⣀⣨⣷⠀⠀⠀⠀⢠⣇⣤⣾⣧⣤⡄⠀⠀⠀⢠⠀⠀⠄⠀⣄⠀⠀⠀⠀⢰⠏⠉⠉⢭⣿⠀⠀⠀⠀⢠⣄⣒⣒⢒⢲⣦⡄
⠀⠀⠀⠀⠈⡇⠠⠆⠤⠖⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣁⠀⠀⠈⣿⠀⠀⠀⠀⢰⠂⣠⢿⡴⣣⢰⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠤⠀⠀⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣗⠀⠀⠀⡟⠀⠀⠀⠀⢸⠢⠔⠪⠃⡼⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⡀⠁⠀⢀⡅⠀⠀⠀⠀⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⢘⡀⠈⠉⠉⠁⣐⡀
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠚⠃⠀⠀⠀⠀⠀⠀⠘⠂⠐⠚⠃⠀⠀⠀⠀⠀⠂⠀⠐⠛⠀⠀⠀⠀⠀⠀⠘⠀⠀⠚⠁⠀⠀⠀⠀⠈⠓⠂⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠠⢊⡆⠀⣤⠀⠤⢤⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡶⠚⠁⠀⣴⠠⠁⢸⠀⠀⣿⠀⠀⣼⠃⣼⡁⢹⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⠴⠂⣷⠂⠀⢸⡄⢀⡿⠀⠈⠃⠀⢋⡤⣾⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⢔⠁⠀⠀⠀⠀⠀⠀⡳⢢⠇⠀⠀⠀⡰⠋⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀⡟⠀⠀⠀⠀⠀⠀⡌⠀⡞⠀⠀⠀⢰⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠐⢰⡧⢻⢠⡟⡐⢀⡸⣀⠞⠁⠀⣀⠀⣨⠋⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣀⣘⠃⠸⠯⠁⠀⣾⠁⠀⠊⠉⢩⡏⠙⡟⠀⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⡿⠿⠿⢿⠆⠀⠀⢰⡇⢀⠔⢸⠂⣼⠀⢰⡇⢸⡇⣼⠏⢠⠁
⠀⠀⠀⠀⠀⠠⣾⣿⠿⠛⠉⢁⣿⠁⠀⢠⡖⠀⠀⠀⠀⢸⡧⠂⠀⠸⠀⠿⠀⢸⡇⠘⠇⠻⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡏⠀⠀⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠸⡇⠀⠀⠀⠀⠀⣀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸⠇⡠⠀⣷⠀⠀⠔⣽⠂⢠⣇⠎⢠⡟⠀⢀⣠⡾⣷⠄⠈⠯⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠰⠁⠀⣿⢀⠎⠀⣿⠀⢸⠇⠀⣾⢁⡴⠁⢘⢓⡟⠀⢠⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠈⠁⠀⠀⠙⠊⠀⠀⠉⠀⠀⠀⠀⠻⠋⠀⠠⠁⣼⠃⠀⠧⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣰⣴⣬⣧⠀⠀⣠⣤⣀⡀⣀⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠐⠒⠲⣾⠫⣴⣶⣿⡏⠐⠲⣞⢠⡫⠁⠙⢷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⡀⠀⠀⠀⠌⢸⡿⠋⠉⠉⠀⠱⣸⣆⡁⠀⢈⠋⢳⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠃⠀⣼⠿⠶⢀⢞⠁⡀⠀⠀⠀⢠⣿⣿⡇⠤⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣨⢴⡞⠉⠁⠀⢋⠂⡸⠃⠀⠙⣦⠀⠀⠸⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠂⠜⠀⣿⠇⡀⠀⠀⣸⣴⣥⠄⡠⢶⡻⡧⠀⢠⣴⠎
⠀⠀⠀⠀⠀⠀⣇⡘⠀⢰⣿⢋⣀⠀⣤⡿⣿⠁⠊⠀⠈⠉⠀⢦⡀⠷⠸⡀
⠀⠀⠀⠀⠀⠘⠿⠇⠀⣼⠟⠋⡀⠀⠈⠻⣾⣆⠀⠀⢰⡷⠁⠀⢷⣀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣤⣾⡄⠠⠀⡠⠂⠁⠀⢀⢸⣥⡀⠀⠈⠻⣄⠀⠀⠙⠳⣤⣀⡀⢄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⠿⣿⣣⣾⡁⠀⠀⠀⣼⡿⠉⠻⢗⢦⣄⣀⠉⠒⠠⠤⢄⣉⠳⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠉⠉⠉⢹⣷⣭⡴⠊⠀⠀⢰⠋⠀⠈⣿⡄⠀⠀⠀⠈⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠽⣿⡸⣿⣄⣠⢶⣯⣤⡴⠤⢉⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⢡⠉⠻⢿⠘⠁⢉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡶⣞⠁⠀⠀⠀⠀⠀⠈⢧⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡼⢇⡟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⡾⢇⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣷⡤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⠀⠀⣀⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣶⡏⡏⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠁⡁⠀⣀⣀⡄⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠛⠛⠛⠋⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠛⠛⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠤⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠆⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣐⠀⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠆⠀⠀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠉⠒⠢⣄⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⠖⠒⠉⠉⠉⠁⠒⠢⢌⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠔⠁⠈⢀⡀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣽⠢⠀⠑⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⠀⡤⠀⠀⠤⠄⢀⣠⣾⡇⠀⠀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠻⣿⣶⡶⠿⠛⢻⡟⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠻⠄⠀⠔⠋⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠶⠤⠤⠤⡤⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⢠⠃
⡄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⡎
⠱⡀⠀⠀⠢⡀⠀⠀⠀⠀⠑⠀⠀⢄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠘⢎⠀⠀⠈⠂⡤⢆⠀⠀⣀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠑⠦⡀⠄⠀⠀⡀⠀⠀⠁⠂⠤⣀⠈⠢⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠦⠤⡄⠀⠀⠀⠀⠀⠀⠈⠶⠥⣄⠀⠀⠀⠢⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄⠀⠀⠈⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡸⠁⣀⠀⠀⣀⠜⠀⠀⠈⠢⣀⠌⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⣶⣶⣶⣴⣄⣀⣴⣴⣤⣤⣤⠤⢤⣤⣴⣴⣶⣶⣤⢄⡶⢶⡤⡶⠶⠄⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂
⠀⠀⠀⣿⣿⣿⣿⣿⠿⡇⣹⡟⢋⣽⡶⠾⢿⣻⣿⣽⣿⡛⠒⠒⠿⣶⣿⡟⠀⠀⠅
⠀⠀⠀⣿⣿⣿⣿⣷⣦⣿⣿⡇⢻⣷⣄⣠⣼⣿⡿⢿⣿⣷⣤⣤⣤⣸⣿⣿⠙⠆⢠⠌
⠀⠀⠀⣟⣉⣽⣉⣼⣿⣿⣿⣻⡟⠿⣿⠿⣿⢉⠀⡺⠟⠻⠿⠿⢿⣿⣿⣿⠿⣄⠣⠀⠀⢀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣾⣿⠿⣿⣻⣻⢿⡟⣹⣿⣾⣭⣦⣿⣿⣿⡛⠓⣶⣶⢶⣦⣄⡉⢿⣿⠊⠠⠄
⠀⠀⠀⣼⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⠀⠀⣀⡈⢻⣽⣷⣿⣿⢛⡿⣦⠄
⠀⠀⠀⣼⣿⣿⣿⣿⣟⣫⠛⢻⣿⣺⣿⣿⠟⠛⠉⠀⠓⠦⡽⠲⠟⢿⣿⣿⣟⡈⠉⡚⠃
⠀⠀⠀⢿⣿⣿⣿⢻⣿⣾⣷⣿⣿⡟⠛⠁⣤⠞⠀⠀⠈⠀⠀⣀⡤⠀⣻⣟⠻⠶⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢼⣿⣿⣿⡧⢹⣿⣯⣽⣿⣿⣷⣤⣤⡄⠀⠀⠀⢀⡞⠁⠀⣄⣼⣿⡧⠀⢦⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⣿⣿⠋⢿⣵⣦⣾⡟⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣧⣦⣶⣿⣿⡿⠃⢀⣿⡘⢛⡻⣿⡷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢸⡇
⠀⠀⠀⣼⣿⣿⣿⣿⣌⣭⣥⣼⣏⣀⣹⠁⠈⠀⠀⠀⠀⠈⣿⣿⠿⠟⠋⣀⣴⢿⣿⠟⠙⠛⠛⢛⣫⣾⠆⠴⠂⢰⡦⠀⢀⠋⠀⠀⠀⢀⠀⣦⠸⡇
⠀⠀⠀⣿⡙⢋⣿⣿⢟⣽⣍⠻⣦⣀⡿⠀⢀⠀⠀⠀⠀⠀⠘⠵⠦⢦⢚⠻⠙⣶⣿⡇⢠⣶⣿⣿⣿⣾⡆⠐⠀⠀⠑⠀⠀⠂⠀⠘⠀⠘⠀⢈⠀⡇
⠀⠀⠀⣿⣻⣟⢻⣿⣿⣿⣿⣶⠞⣻⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⢟⠘⠀⠀⠀⠀⢀⡘⡀⠀⠀⠀⠀⠀⠈⠀⡁
⠀⠀⠀⣿⣟⣿⣿⣿⣿⣧⣤⣏⣹⡟⠀⣴⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣏⣁⣤⣽⠛⢿⣿⣿⡷⠏⠀⠀⠀⡠⠀⠈⡀⢣
⠀⠀⠀⣿⣿⣿⠿⠟⣿⠟⣟⠫⡿⠃⣸⣟⡅⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⣛⣛⠛⢻⣿⣷⣤⣤⣀⣀⣀⣀⣀⠼⠛⢀⡴⠃⣼
⠀⠀⠀⣿⣿⠯⠛⠛⢡⡀⠉⢀⠣⣠⣿⣿⠀⠀⢠⡇⠀⠠⠀⠯⢠⣋⣛⡸⠃⠀⣼⠏⢈⡛⣷⣬⣿⣬⣉⠑⠲⠒⢋⣴⣾⣿
⠀⠀⠀⡿⢿⡖⠛⠡⠀⠈⢻⠇⣴⢢⣽⠟⢠⡴⠋⠀⡀⢀⣀⢀⠉⠹⠟⢀⣤⣞⡥⣶⡾⣥⣤⣿⣿⣍⣉⠋⢲⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⣈⢠⣈⡠⣬⡎⢤⡶⠇⢘⣿⡟⢌⠠⡄⠀⠐⣊⠿⡿⠒⢴⠚⣵⣿⡿⣿⣾⣻⣿⣷⣿⣷⣿⣯⣽⣿⣿⣿⣷⣿⣷⠖⣯⣄⡀⠀⠀⠀⠃
⠀⠀⠀⣿⣿⣿⠁⠀⡘⢳⠞⣧⣰⣿⣿⣩⡊⣧⡌⢙⣈⣛⡦⣼⠳⣿⠹⡴⣛⣻⠿⣿⣟⣫⡿⠟⡉⣟⣉⣴⣴⢿⣿⣿⣏⣻⡛⢳⢤⣍⠀⠾⠘⡇
⠀⠀⠀⣿⣿⠾⠿⣿⣯⣾⣾⣿⣿⡿⢿⣇⣀⣶⣯⡘⡟⢿⣦⡄⠀⠉⠀⠀⠤⢼⡧⡶⣶⣶⠾⣿⡟⠻⡘⢀⡀⠠⠷⠼⠂⠛⠃⠄⠜⢃⡈⠀⠀⡇
⠀⠀⠀⣟⣻⣓⢜⠻⠻⣏⢿⣿⡿⣿⣿⣿⣿⣿⢿⠟⡿⢰⣿⣿⣥⣶⣶⣄⣀⠀⠛⠣⠀⠩⠶⡮⢃⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠃⠀⠀⠀⠀⠀⠇
⠀⠀⠀⡏⠉⢁⠈⠓⢀⣤⣄⠉⡽⢿⣿⣿⣿⣿⠶⠿⠖⣻⠿⡿⢫⡟⠿⠥⢉⣻⣤⣀⣤⢄⠀⠀⡁⠀⠠⠀⣀⠀⠀⢀⠀⠀⠀⠀⠐⠂⠂⠀⡀⡆
⠀⠀⠀⡇⠈⠀⠈⣓⡄⢁⠀⠌⠲⣿⣻⣿⣿⣿⣤⣤⢙⠛⠀⠠⠐⠀⠆⡐⠳⠈⡈⡉⢿⠀⣀⠀⠁⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⡇
⠀⠀⠀⡛⣆⠀⠤⠈⠀⠁⠐⠀⢈⣻⡏⡼⠻⢻⣾⡃⣺⠟⠛⠁⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⢄⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣇⠈⠰⠱⠆⠀⠀⠐⠀⢀⠃⠤⠉⠀⠦⠁⢉⠋⢰⡷⠤⠄⠀⢠⣀⣌⠀⠄⠀⠀⠀⡀⡀⠑⠄⡀⠀⠈⠁⠐⠚⠂⢀⢈⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠡⢓⠂⠀⠀⠁⠢⠀⠀⠸⠓⠀⠀⠠⠜⢠⣤⣀⠡⠾⣁⡄⠆⢠⠀⠆⢀⣤⠀⠀⠀⠀⠃⠀⢀⠀⠀⠰⠀⠁⠀⠁⠉⠉⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠈⠀⠃⠼⠋⠀⠀⠐⠆⠈⠀⠉⠘⠏⠀⠀⠀⠆⠐⠤⠎⠀⠀⠐⠀⠀⢀⠘⠂⡠⠤⣄⠀⠀⠀⢠
⠀⠀⠀⠓⠀⠄⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⠀⠈⠀⠀⠀⠀⠀⢐⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡧⣀⢳⡜⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣉⣙⣿⣿⣿⣿⣌⡲⣯⡳⣄⠙⠛⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠟⠟⡁⠀⠑⠑⠄⠙⢿⣿⣕⣿⣿⣌⠑⠴⠿⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣭⣉⣉⣠⣴⣿⣧⣷⠶⠛⢶⣤⣀⡈⡙⠛⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣷⣤⣭⣻⣿⣿⣷⣶⣷⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⢃⡸⢶⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠈⣇⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠰⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⢠⠄⠀⣰⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠘⠀⠀⢠⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⡆⠀⠀⢠⣿⡿⠿⡟⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⣃⣶⣿⣿⣽⢧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⡤⠤⠚⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠊⠘⢷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣸⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⣾⣷⣿⣐⣂⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠦⣼⡄⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢠⡌⠙⠛⠻⠿⠿⠛⢩⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⡇⠀⠀⠀⠀⣇⣀⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠲⡾
⠀⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⣁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠋⠓⠒⠒⠛⠛⣛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠤⠶⠶⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠈⠷⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠤
⠀⠀⠀⠀⠀⠀⣤⠄⢤⣤⣤⣤⣄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⠀⠀⣀⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠠⠤⠤⠤⠀⠀⠐⢢
⠀⠀⠀⠀⠀⠀⡿⠀⠘⢻⣿⡿⠛⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠉⠁⢲⣤⣄⣉⡁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠈⠁⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⡇⠀⠀⠀⠀⠀⠀⣰⣃⠀⠐⠒⠒⠒⠶⠶⠦⠤⠴⡦⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⢠⣤⣶⡆⠀⠀⠀⠀⠀⠀⣿⣷⣶⣴⣶⣶⣦⣤⣶⣶⣶⣶⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣉⣻⣷⠊⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣔⣁⡈⠓⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⢀⣿⣥⠭⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡄⠀⢂⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣛⣆⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠐⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠶⠾⠿⣟⠁⠒⠂⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠿⠦⣷⣶⣒⣄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠀⠀⠈
⡈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢠⡡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣧⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣆⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠳⣻⡵⡃⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐
⠀⠦⡆⠘⢄⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠯⢳⡵⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⡄⠙⠠⠂⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⠀⠀⠁⠘⢃⠉⣀⡀⠛⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⣨⠃⠀⢲⣁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⡴⠂⠈⠈⣌⠁⢋⣠⠆⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⢐⠀⠱⠀⠈⢑⠀⠈⠉⠀⠀⠠⠖⡄⠀⠞⠀⠀⠀⠀⠈⣄⠩⠖⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠾
⠠⠀⡀⠀⠀⣨⠆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢫⣭⣙⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣀⢁⣂⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⠶⣴⡏⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡶⠛⠿⠻⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠟⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⢣⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠰⢠⠅⠀⠀⠀⠐⣷⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢠⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡄⡘⠀⠀⠀⠀⠀⠫⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠁⠀⠀⠀⠀⠀⠸⢁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠘
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢰⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢦⠦⠤⠐⠒⠀⠐⠂⠤⠤⠒⢒⡠⠃⠀⠀⡇⠈⠢⠤⠤⠤⠤⠔⠂⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠚⠚⠀⠀⠁⠉⠀⠀⠀⠈⠀⠀⠋⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⣰⣾⣿⣿⣿
⠉⠿⠛⠋⠙⠋⢹⠿⢿⣿⣿⡿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⢹⣿⣿⡏⠈⠉⠘⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⢳⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡤⠾⠛⠋⠀⠀⠀⠀⠈⠉⠀⠀⢀⠉⠁⢈⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣥⣤⣿⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⢿⣿⠟⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠈⠖⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⡀⢠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠠⢘⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣼⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⠇⠀⠀⢀⣶⣎⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⢿⣟⣉⣛⣻⣿⣿⣿⣆⠀⣠⣶⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣏⣸⡽⠿⣉⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣀⢀⣽⣿⣿⣿⢿⣶⠀⣹⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠄⠀⠀⢀⣤⡄⠀⣠⠀⠄⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⣿⣿⣿⣿⣿⠀⢁⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢁⣈⣀⡀⠊⣀⡀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⣀⣻⣳⣾⣿⣿⣿⣿⢿⠠⣿⣿⢿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⣂⣠⣴⣿⡿⠛⠙⣛⣛⣻⣿⣶⣿⣶⡄⠀⠀⠀⠀⢰⠏⠀⠉⠛⢤⣿⣿⣿⣿⣿⡿⠾⠛⣿⠋⣸⣧⣸⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠓⠻⠿⢻⣿⣿⣿⣿⣿⣤⠀⠈⢠⣴⠏⠀⠀⠀⠀⠈⠉⠛⠁⠉⢹⡄⢀⢀⣘⣷⣿⣿⣿⣿⠁⣭⡟⣿⣿⣿⣿⣿⣿
⠛⢁⣉⣄⣴⣴⣶⣾⣿⣿⣿⣿⣿⣛⠻⠿⣀⠈⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣷⡀⣹⡿⠟⠛⣿⣿⣷⣆⣤⣤⣼⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣙⣾⣃⠀⠀⠀⠀⠀⠀⢺⠓⣶⡆⠋⠉⣹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣶⣶⣶⣦⣤⣄⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠉⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⣄⣤⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢲⣿⣿⣿⣩⣽⢿⠿⠟⣿⣿⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣻⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⡟⢛⣿⣿⣋⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢹⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⡋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠃⣴⡿⣧⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠐⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠚⢉⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠴⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠆⠀⠀⠀⠀⠀⠀⣀⡈⠛⢻⣿⡋⠙⣿⣿⣿⣿⣿⣟⢛⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⢆⡀⠀⠀⠀⠀⠹⣾⢿⣶⣿⣁⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⣷⣤⣘⢢⢀⣠⣿⣿⣇⠀⠉⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣀⣼⡿⠃⠀⠀⠀⡀⠀⠐⢆⡀⠀⠀⠄⠀⠀⠀⠀⢠⢀⠘⠀⠀⠈⢻⣿⣿⣋⠉⠻⠻⡿⠀⠀⠈⠙⣿⣿⣿⣿⣧⠹⠆⠙⠻⢿⡏⠿
⣿⣷⡿⢿⣿⡋⠉⠀⣤⡀⠤⠉⠳⠎⠀⠀⠀⠀⠀⣶⣷⣀⣘⡦⠉⣧⠙⠿⠻⠦⣀⠀⠀⢴⣄⣙⣟⢉⡿⣿⣿⡿⣿⡭⠃⢀⡸⢻⣾
⣷⣿⣀⣼⣿⣿⣿⣿⣾⣷⣦⢈⡀⢻⣯⣿⣶⣤⣤⣿⣿⣿⣿⣿⢻⣾⡀⠀⠈⠃⠀⠀⠀⠀⣈⡿⢻⣤⣄⣿⣿⣿⠉⢁⡂⠀⣧⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⠛⠠⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠿⢿⠋⢹⣷⣼⡇⠠⣽⡖⣿
⣿⣧⣤⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠘⠛⢿⠁⡀⠈⢻⣺
⣿⣿⣿⣍⣿⠟⢿⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣆⣠⣀⣀⣤⣄⣀⣠⣄⠀⠛⣿
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏⣼⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠖⢁⡄⢻⣿⣟⠻⢿⠄⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣷⣿⣶
⣾⣿⣿⣿⣿⣿⣿⣿⣯⣙⣏⠉⠛⠁⠀⠀⢠⡼⡃⠿⡿⠓⠈⣦⢹⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣏⡯⣸⢿⣿⣿⣿⣿⣿⣿⣉⠙⠣⣤⣶⣶⣀⠘⠳⣀⢶⡾⠂⠏⠸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣜⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⡏⣿⠟⠛⠀⠀⠀⠘⠁⠀⢀⠀⣸⡟⢉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠀⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠋⢩⣿⣿⣿⣿⣿⣦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢠⣤⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣾⠋⡉⠻⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠤⠀⢀⣄⠸⠀⠀⠀⣤⣶⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢰⡖⢰⣶⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡽⠟⠛⠘⡅⢆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤
⢀⡌⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠐⠆⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠦⣄⠀⠄
⣿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄
⠋⠀⠘⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢄⠀⠠⠀⡀⠀⠑⠩⣢⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀
⠈⠀⠀⣦⡈⡢⠄⡀⠀⠀⠀⠀⠀⢉⣉⣙⡛⠙⠋⠀⠀⠀⠀⠐⠠⢀⠀⡠⡀⠰⡃⠀⠠⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢶⢶⣦⣃⡀⠀⣤⣀⣉⣩⣭⣍⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠲⣆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹
⠀⠀⠀⡃⠸⣿⢿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠁⠘⣄⠀⠄⠀⢀⡀⠀⠀⠀⢀⠀⠂⠁⠠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⢀⠀⠀⠘⠛⢿⣏⣛⠙⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⡁⠀⢀⡀⠈⠧⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⢤⢀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠐⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠰⠂
⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⣦⡀⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠘⣣⠈⠓⠘⡦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠀⠀⠀⠀⠢⠀⠐⢄⠐⠀⠀⠀⠘⠋⠁⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠄⠘⡀⣄⢀⢃⠀⠀⠀⠀⠁⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢠⠼⠏⡐⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠈⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡈⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠰⣟⣿⣿⣿⡿⠟⡻⠶⠖⠲⢆⣀⣀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃
⠀⠀⠀⠀⠀⠇⠀⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣄⠀⠀⠀⠀⠀⠃⢠
⠀⠀⠂⢄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉
⠀⠀⠀⠀⠀⠙⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢀⠔⣩⠖⠈⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣶⠠⠀⠀⠀⠀⠀⠁⠠⢁⠎⠀⢀⠔⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⢋⠞⡴⠁⢀
⠉⠀⠀⠀⠀⣘⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠐⠀⢠⠃⡠⢀
⠀⠁⠀⠀⠀⠉⠲⠠⠄⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠂⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢁⠂
⠀⠀⠀⠀⠀⢀⡄⣧⠀⠀⠁⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⢸⠇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⡅⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⠈⠂⠑⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠀⠂⠔⠁⠀⠁⠈
⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠁⠀⠀⢀⠀⠈⠢⡂⠀⠘⠀⠀⠢⠀⠀⠀⠀⠀⢁⠀⠐⠀⠀⠀⠀⠀⠊⠀⠀⠀⡠⠊⠀⠠⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠄⠀⠑⠤⡀⠀⠂⠀⠀⠈⠢⠀⢁⠀⠀⠐⠤⠃⣀⠀⠼⠘⠂⠀⠠⢄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇⠀⠀⡈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⠄⠈⠁⠀⠈⠁⠐⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠐⠠⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⡇⢀⠁⠀⠀⠀⠀⢀⠅⠀⠀⠈⠢⡀⠀⠀⠀⠀⡨⠂⠀⢀⣤⠤⠤⢤⣄⡀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⠲⢄⠀⠀⠀⠀⢀⠂⠀⠀⢀
⡇⠀⠉⠁⠈⠉⠁⠉⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠀⠀⠐⠁⠀⠚⢉⣀⠀⠙⠀⠀⠀⢠⠎⠀⣠⣍⡑⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠀⠀⢀⠔⠁⠀⠀⢀⠠
⡇⠀⠀⠀⠘⠢⠀⠀⠂⠀⠤⠀⠀⠀⠀⣑⠂⠠⡠⠀⠀⠀⠀⢰⠋⠉⢷⠀⠀⠄⠀⡜⠀⠸⠁⠈⣷⠀⠀⠀⠀⠀⡴⠄⠐⠀⠀⠀⠀⠐⠀⣀⠠⠒⠈⣀⠠
⡇⠀⠀⠐⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠞⢄⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⢀⠒⠃⠀⡀⠂⠀⠐⠉⠀⠀⠈⠁
⡇⠀⠀⠀⠀⠠⠄⢈⣁⠒⠂⠁⠀⠄⡌⠀⠴⠈⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠙⠁⠀⢀⣠⠔⠋⠈⠀⠀⠀⠀⠀⠀⠁⡖⠀⠑⠀⠀⠒⠥⠁⠀⠀⠀⠀⠴⠂
⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢷⠀⢃⣄⠀⡀⡤⢠⠄⠾⠇⠶⠽⠻⠟⠻⠟⠛⠐⠃⠖⠏⠻⠚⠇⠆⣠⣀⠈⢴⡗⣠⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠱⠐⠃⠔⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠸⠓⡷⢠⢄⢴⡰⠀⡀
⡇⠀⠀⠀⢤⠠⠷⠒⠎⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠴⠀⠀⠀⠉⠁⠀⠀⠐⠁⠀⠀⠀⠀⠄⠆⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠑⣰⣦⠰⣄
⣇⡔⣖⠨⠆⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⢠⠠⠠⠀⠀⢐⣄⢀⣈⠀⠀⠀⠀⠀⠀⠲⢦⠀⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠄⠁⡒⡀⠀⠀⠀⠀⠀⠀⠈⠑
⡧⠉⠀⠀⠀⠠⣂⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠊⠈⠈⠀⠀⠀⠒⠬⢨⠀⠉⢀⠀⢀⣁⠀⣂⠐⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠂⠸⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠋⣀⡉⠁⠀⠄⠂⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣂⣤⡆⡠
⡞⣣⠄⠈⠡⠀⠀⠀⠀⠈⠄⠁⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠢⠀⠀⠩⢄⣀⣀⠀⢠⣀⣠⢖⢀⡀⠀⠀⠀⠀⢼⡦⢀⣀⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢈⡀⡷⢆
⢇⡀⡬⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢠⢰⠆⠀⠀⠀⠀⠘⠷⠅⡼⣉⠛⠋⠉⣷⠕⠊⠀⠀⠀⠀⠀⠝⠳⢺⠗⠂⠀⠀⠔⠂⠪⠐⠀⠀⠀⠀⠠⠘⠂⢀
⡇⠀⠀⠀⠀⠀⠐⠂⠄⡀⠀⠀⠦⠄⠀⠀⡃⠈⠰⠆⠀⠀⠀⠀⠀⠂⢀⠇⡴⠶⠶⠶⠲⡄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠰⠄⠀⠀⢄
⡇⠀⠀⠘⠀⠀⠀⠘⠀⠙⠀⠠⣤⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐⠀⠺⠃⠀⠀⠃⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡈⠦⠂⠀⠀⠀⢄⠀⠉⠀⠈⠒⢄
⡳⣄⠀⠀⠀⠀⠀⢘⠐⢃⠁⢀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢦⡀⠃⠶
⡇⠘⣎⠀⢀⠄⠀⠈⠀⠈⣤⠀⠒⠀⠀⠀⠀⠂⠠⠀⠀⠄⠀⠳⠙⢇⣴⣄⠀⠀⠀⠀⣠⡆⡹⢋⠞⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠨⠀⠀⠠⠀⢛⠳⡈
⠅⠐⠺⣆⠞⠀⣠⠀⣠⠀⠀⠘⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠓⠀⣀⠐⠉⠠⡄⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⣀⣀⣀⣠⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⣾⣿⠿⠿⠿⠿⠿⣯⣍⡑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⣴⣟⡭⠶⠶⠶⣶⣤⣤⣤⣌⣩⡓⠦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣱⠿⠛⠋⣉⣟⠛⠮⣝⣿⠃⠀⣝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡿⠃⢀⠶⢋⣽⣟⠛⠛⠾⣿⣧⠀⠹⣆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠻⠿⠆⢸⠁⠈⢣⣤⡖⣻⣿⣷⣶⡄⠣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⢻⡘⢦⠠⣀⠁⣀⣸⣍⣽⣿⣿⣇⣿⣠⠞⢡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠘⡀⠹⣦⣑⡾⢿⣽⣿⠿⡟⣋⣿⠃⠈⣹⢆⠞⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⢟⠓⠒⠒⠛⠛⠛⢉⣀⣴⡞⣁⣮⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⢤⣄⢒⡶⠶⠶⢞⣫⡤⡾⠁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠅⢸⡇⠉⠉⣏⢙⣄⠼⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣉⣹⡆⠀⠀⢀⣴⣯⣉⣉⣉⣳⣄⠀⠀⠐⣦⠀⠀⣤⡄⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⠙⢯⠁⠀⠰⠏⠉⠉⠛⠛⠛⠛⠙⣆⠀⠀⠘⢧⡼⠻⣧⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⣷⡀⠀⡠⠤⡄⠀⢀⣤⡄⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢀⡼⠃⠀⠳⣖⠃⠀⠿⢶⡇⢸⡇⣴⣄⡞⢠⡄⠀⡏⠳⣦⡀⣼⠃⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠋⠀⠀⠀⠀⠈⠃⠀⠀⠘⠃⠀⠛⠁⠙⠁⠘⠃⠈⠀⠀⠈⠙⠁⠀⠈⠷⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⡀⠠⠀⡀⢀⣀⠀⢀⣀⠀⠀⡄⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠈⠈⠀⠉⠈⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡆⠐⠀⠀⡆⠀⠀⠀⠀⢀⠀⠴⠠⠆⣀⡄⠀⣀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⡦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠁⠀⠏⢀⣴⠞⠋⠉⠁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠲⠶⠦⣄⡉⠀⠀⠀⢛⠃⠠⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⢿⣦⡀
⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⢵⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⣇
⠀⠀⣾⡏⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡆⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⢀⣄⣠⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⡟
⠀⠸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁
⠀⠀⢻⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⡀⠀⢹⡄⠀⠀⠀⢀⡀⡂⠀⠀⠀⣠⡄⠊⠀⠀⠀⡀⠈⢿⣇⠀⠃⢀⣀⠀⠛⠻⣐⠿⢤⠔⠒⠤⠄⣿⡾⠟⠀⢊⣿⣿⣿⠏⠈⣯⡐⢀⠀⠀⠀⠈⠒⠤⣤
⠁⠀⠀⠙⡄⠀⠀⣤⡀⠡⠶⢶⣼⣯⠕⠀⠀⢂⠀⠀⡀⣸⡿⠀⠘⠀⢩⣄⠀⠀⠎⣤⢤⡴⠶⠟⠘⠈⠀⠀⢀⣌⢶⡟⡻⣄⠀⠋⠐⢦⣣⣄⡀⠀⠀⢀⣀
⡀⠀⢀⠀⠙⠂⠒⢿⡈⠳⢤⡈⠛⠻⠀⡀⠠⡤⠀⠀⠀⡿⠃⠐⠀⠀⢾⠋⡥⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠋⠑⠫⡀⠀⠀⠈⠉⠻⠻⠆⠉⠉
⡇⠀⠸⣆⠀⠀⡀⢈⣷⡀⠀⠙⠣⢀⠈⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣇⢀⠀⠘⡆⠀⣇⠀⢿⠛⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠟⡌⠀⠀⠋⠂⠄⠀⢠⡀⠀⠈⠓⢆⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠠
⠀⡀⠀⠀⠠⠀⠀⠀⠀⠈⠒⠄⡀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣘⠀⠀⠀⢀⠀⢂⡐
⠟⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⣦⣤⣀⠉⢷
⠀⠀⠀⠀⠃⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠈⣉⣙⠛⠶⢬
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢠⡤
⢆⠀⠀⠀⣶⣠⣥⡀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⡀
⡛⣷⠀⠀⣮⣽⣷⠞⠁⡀⠀⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠄⠀⠀⠀⢀
⡻⣾⡇⢸⣿⣯⣿⠀⣸⠗⠊⠖⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⠓⠲
⣿⠿⣿⣼⡇⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢹⢶⣽⠙⣷⣿⣥⣄⣤⡴⣆⠀⢰⠴⣦⠠⢄⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠠⡀⢀⣦⠀⠀⠀⠠⠀⣴⣟⠉
⠀⣿⣽⣷⡌⠻⠟⠛⠉⠁⠀⠀⡀⢅⣨⣤⡀⠀⠀⠀⠀⢀⠃⠀⠀⠂⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣃⠀⠀⠀⠀⢀⠀⠈⠻
⠂⢿⡏⠙⠟⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⡜⠀⡠⠀⣼⠏⠀⠀⢀⡤⠤⠎⠀⠀⠀⠀⠀⠁⠀⢀⡅⠀⠀⠀⠀⠀⠀⢰⡖⠒⠁⠊⢄⠈⠐

⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⠴⢖⡲⠦⣄⠀⠀⠀⢀⡴⠚⣉⠉⠓⠢
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⡎⢀⠔⢦⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡈⠃⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠈⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢠⠈⠀⠀⠀⠀⠀⠳⣄⠀⠀⠃⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡄⠀⠤⢠⠀⠶⠠⠭⠛⠗⠺⠛⠑⠂⠒⠛⠂⠃⠆⡄⣀⠠⡆⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠰⠄⠑⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠙⠠⠀⠢⠀⡀
⠀⢀⠀⢀⠀⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠌⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠨⢆
⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠐⠀⠉⠀⠊
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢠
⠘⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⠀⣄⡀⠔⢠⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢄
⠡⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠐⠀⠀⠀⠀⠉⠂⠾⠉⠉⠁⠫⠂⠁⠀⠀⠀⠀⠈⠃⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⡄⠀⠀⠀⠰⠀⠀⠁⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⢀⡦⠀⢀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠅⠀⣀
⢆⠀⠀⠀⠀⠀⠄⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠄⡄
⡀⠱⡀⠀⡄⠀⠃⠈⢡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠺⢠⣄⠀⠀⠀⢀⡄⠘⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢑⢦⡒
⡁⠀⣣⡜⢀⡄⠠⣀⡀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠙⡀⡀⠊⠠⠄⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠚⠛⠛⠛⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡂⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠉⠰⠄⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⠂⠢⠤⢀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱⣀⣀⠀⠀⠠⠤⠤⠤⠄⠈⠒⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⠀⠀⣀⡀⢰⣶⡆⢠⣄⣀⣤⠀⠀⣼⠓⠒⠒⡞⣷⡀⠰⢤⣴⡄⢰⣦⠀⢀⢀⣀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⠆⢠⠏⠲⠟⠀⢥⣾⡁⣸⣟⠧⢸⣇⣼⣀⡀⠿⠙⣷⡿⢋⡉⢿⣾⣍⣧⣜⡏⣹⣧⠀⣠⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡴⣆⣤⣄⣤⡄⢤⣤⢼⣿⣸⣿⠈⠳⡏⠻⡟⢩⡌⢠⣸⡷⠻⣇⠘⠛⠀⠈⠙⠿⢿⣽⣿⣿⣏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣉⣛⠿⠉⢿⣯⣿⣿⡏⠀⠻⠿⠟⢓⠋⢠⣦⡏⢻⡇⠹⠟⠀⠄⠀⠀⠀⣐⡀⠀⠀⡤⣄⣈⢙⣫⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣸⣿⣧⣽⣧⢿⡏⢘⠿⣿⣟⡙⢾⣷⢯⣽⣧⠈⣧⠁⢲⡇⢤⣖⠈⣽⢛⣿⣯⣿⠀⢹⣿⢛⢿⣦⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⣿⣧⣬⣇⣸⣯⣿⣤⣤⣿⣿⣷⣿⣷⣖⠛⠛⢻⣿⣿⣿⣴⣇⣿⣾⣿⣾⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠛⠲⠿⠿⢿⣿⣿⣿⡿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⠟⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠁⠀⠀⠉⠙⠻⣿⣿⣟⣩⣤⣠⣴⠲⢲⣄⢀⠀⣀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡶⠿⠖⠛⠋⠉⠁⠀⠀⠀⠈⠉⣽⠒⣾⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⠈⠝⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣰⠆⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⡋⠹⠉⠻⠃⣤⡐⠿⠛⠷⢤⣄⣀⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⠖⠉⠀⠀⠀⠀⢰⠇⣼⠀⠀⢸⠀⣇⠀⠀⠀⠀⠈⠉⠻⢷⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⣠⡟⠀⣿⠀⠀⠈⣧⠈⢣⡄⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠿⣤⣴⣿⣀⣀⡀⣻⣧⣀⣿⠶⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣶⣤⣶⣦⣶⣖⣀⠀⠀⠀⠀⠀⠀⠀⣒⣛⣉⣉⣛⠲⢶⣤⡀⠀⠀⢀⣠⣤⣶⣶⣤⣄
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣿⣿⣷⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢸⣿⣿⠟⠋⠈⠛⠙⠟⠻⢻⠇⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠈⢿⣿⡟⠀⠀⠈⠉⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠈⢫⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇
⠀⠀⠀⢉⠃⠀⠀⠐⠀⠀⠀⠐⠀⠀⢰⣶⣤⡀⡀⠀⠀⠲⠶⠀⠀⠀⠀⢰⣇⠀⠀⠐⠶⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠛⠀⢠⣄⣀⠀⢀⣠⣤⡶⢛⣩⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡂⠠⠀⠀⠀⠀⠀⠀⠀⠠⣍⠙⠁⠘⠋⣡⣶⣿⡏⠀⠀⢀⠌⠀⠑
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠈⢿⣿⣿⡁⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⢠⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⢀⡀⠘⠚⠂⠀⠀⠀⠐⠈⠚
⠀⠀⠄⡌⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⠀⠀⠲⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠐⠀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠜⠀⠘⠏⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣖⡶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢰⣶⣆⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠠⣄⠀⠀⠀⢸⣻⢶⡠⡀⢹⠄⠀⠘⠇⠀⠀⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠐⠀⠠⡟⠀⣤⠂⠈⡇⠀⠀⠘⣿⡗⠋⠡⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣵⣄⣀⡀⠀⠀⡀⣀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢨⣍⣀⣀⡀⠀⠀⠀⢈⣻⣍⣏⣐⠞⠁⠀⠀⠀⣿⣇⠶⢦⠠⠈⠳⠈⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⠖⠂⣤⠄⠀⢠⠋
⠀⠀⠀⠀⠀⠀⢸⣡⣍⠁⠿⢀⠀⠀⠈⠠⣿⠋⠁⠀⠀⠀⠀⠀⢺⣇⠳⣀⠶⠦⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣌⠁⠖⡔⠁
⠀⠀⠀⠀⠀⠀⠸⣿⢿⡷⠾⠽⠶⢶⠖⠈⣻⠀⠀⠀⠀⠀⠀⠀⣾⣄⢴⣟⡀⢠⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠈⠏
⠀⠀⠀⠀⠀⠀⠀⢿⡟⠓⠂⠀⢶⠀⢠⠋⡏⠀⠀⠀⠀⠀⠀⠀⡿⣟⣟⠋⠀⠻⠄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⢸⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠟⠳⢴⡀⡁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⠸⡏⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⣄⠀⠣⡖⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋⠠⠃⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠄⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡛⠛⠓⠓⠛⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⣀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣀⢀⠠⠐⠀⠀⠡⠄⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡄⠠⠠⠄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠛⠉⠀⠀⠈⢦⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣤⠀⠀⠠⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⠒⢀⡬⠷⣄⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⣀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡛⠳⠖⠉⠙⣣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠿⠛⠋⠉⠁⠿⠀⠀⠀⠀⠀⠀⣄⢦⢀⣠⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠯⢅⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠎⣤⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣧⣄⡰⠂⠁⠈⠣⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⡀⡀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠹⡀⠶⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⡀⠀⠈⢀⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠾⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠶⠄⠸⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠀⠐⠁⠀⠀⠀⠀⠀⠀⠙⠚⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡿⠀⠈⠳⣄⣠⣤⣤⠤⠶⠶⠶⠦⢤⣤⣴⣋⠀⠀⢹⣼⡆
⠀⠀⠀⠀⣠⠶⠚⣛⣿⡟⣁⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⣹⠿⢿⠓⠦⣄
⠀⠀⣠⣞⣡⠤⣶⣿⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡟⢿⣒⠺⢷⡄
⠀⢠⡟⣿⠒⠛⠁⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⢉⡿⢻⡀
⠀⢸⡇⠘⢷⣄⢀⡏⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠟⠁⢸⡇
⠀⠘⣇⠀⠀⢉⡿⠀⠀⠀⠀⠀⢀⡏⠙⠦⣄⣀⣙⣷⣤⣀⡀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠈⢷⣄⡀⣼⠁
⠀⠀⢿⡀⣴⠞⠁⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⣠⡬⠁⠀⠠⣭⡉⠉⠉⠁⠉⠳⢦⣀⣀⠀⢀⣠⡼⢁⡟
⠀⠀⠘⣇⢹⣷⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠁⣴⠀⠀⢠⣦⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⡍⢧⣼⠃
⠀⠀⠀⢻⣯⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⡏
⠀⠀⠀⢸⡏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⣤⣀⣤⠟⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠳⣤⣀
⠘⢯⣄⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣠⡿
⠀⠀⠉⠳⢤⣀⣀⣈⣳⣄⡀⠀⠀⠀⠀⢀⡴⠲⠤⢿⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⢠⡞⠃⠀⠀⠀⠀⠀⠛⣦⠀⠀⣀⣠⡴⠚⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⢿⣿⣶⣶⣶⣶⣶⣿⢻⣟⣻⣯⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢹⡆⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⠃⢸⠀⢀⣀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠿⣤⠾⠛⠋⠹⣆⣀⣀⣀⣼⠋⠓⠶⣤⣽⠇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠈⣩⣭⣿⡁⠀⠀⠀⠈⢷⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⢸⡀⠀⠀⠀⠀⠀⢠⣤⣤⠏⠀⠀⠀⠀⢸⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠾⠷⣤⣄⡀⠀⠀⢤⣤⡽⠂⠀⢀⣀⣤⡿⠶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠙⠛⣶⣴⣯⣤⠶⠛⠋⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠴⠿⠭⠤⠭⠶⠆⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠞⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⢹⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣴⣶⣤⣤⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⣿⣿⣿⣿⣿⣿⣿⠇⣿⡁⣿⣿⣿⣿⣿⣿⣿⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢦⣤⣀⣀⣀⣠⣤⢞⣿⣟⢦⣄⣀⣀⣀⣀⣤⢴⣿⠁

⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⡟⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⣿⡿⢿⣿⡿⠿⠿⠿⠿⣿⣿⠿⣿⡇⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⠀⠀⣿⡇⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⣿⡇⠀⢰⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣿⡇⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⣿⡇⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⠀⣿⣧⣼⣿⣦⣤⣽⣥⣤⣾⣿⣤⣿⡇⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⣦⣤⣤⣦⣤⣤⣤⣤⣦⣤⣦⣦⣤⣶⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠻⣿⣦⣤⣴⣦⣤⣤⣦⣤⣤⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⢸⣿⠉⢉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⠉⢻⣿
⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⢿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣻⣿
⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣤⣄⣀⣀⣠⣾⣿⣁⣀⣀⣹⣿⣦⣀⣀⣀⣤⣴⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢲⠀⠠⢀⠀⠀⠀⢀⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣾⠀⠀⢲⡆⢸⡄⢸⡇⣾⠀⠐⢸⠃⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⣀⠀⢿⠀⠀⠸⠁⢸⡇⢸⡇⠻⠀⠀⠈⠃⠈⣿⠈⠆
⠀⠀⠀⠀⠀⠀⢠⠖⠀⢸⠇⠀⣼⠁⠈⠀⠀⠀⠀⠀⠈⠓⢈⣇⠀⠀⠀⠀⢠⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⢀⡧⠀⠀⠀⢀⡠⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢠⡄⠀⣾⠀⠀⠀⠀⠠⠊⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⣷⠀⣿⠀⠀⠀⠀⢀⣀⣿⠀⣀⡀⠀⢀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⡆⢻⣀⠙⠦⠃⠀⢰⡏⢸⡇⢰⡇⢰⡇⣸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠃⠀⠁⠐⢤⡀⠀⢸⡄⠸⣇⠸⠇⢾⡀⢻⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⢱⠀⠀⠉⠀⠉⠀⠀⠀⢥⡀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠘⠿⠿⠃⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢠⡾⠟⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⡿⠛⠛⠻⣿⣿⡿⠛⠛⢿⣿⡇⠀⠀⢸⡇⢀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⠀⢸⣟⠁⢰⣿⠆⣀⣀⠀⢾⡷⠀⢹⡇⠀⣴⣾⡇⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠘⣿⣷⣦⣤⣴⣿⣿⣷⣤⣤⣾⣿⠁⠀⠻⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣦⣌⠉⠛⠛⠛⠛⠋⣁⣴⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡿⣶⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣿⣿⠿⠟⠁





⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⡶⠶⢶⣶⡶⠶⠶⢶⠶⣶⣶

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠀⠉⠈⠛⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣼⣿⣿⠏⠉⠀⢉⣉⢀⣀⣶⣶⣦⣄⠀⢠⣿⣿⡟⠉⠉⠉⠙⠛⠛⣿
⢠⡿⠏⠋⠀⠀⠀⠈⢙⠋⢋⣀⣡⣬⣿⣷⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⡇
⣸⠃⠀⣀⣤⣤⣿⣦⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣿⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠋⣧⠀⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⣴⣿⠞⠋⠉⠳⣄
⠀⢻⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠚⠉⠛⠁⠀⠀⢠⠞⠁⠀⡠⠊⣹⠈⠓⢄
⠀⠀⠹⣿⣿⡏⢠⠖⠶⣦⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠎⠀⣘⡡⠄⠐⠢⣝⢦⣤⣄⣀
⠀⠀⠀⠹⣿⣇⠈⠀⠠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢠⠁⢠⠞⠁⢀⡤⠒⠊⢁⣴⠈⠳⣄⠉⠲⢄
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠸⠀⠉⠀⠰⠋⠀⡠⠖⠋⣠⠃⠀⠈⠓⢄⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢆⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢶⡄
⠀⠀⠀⠀⠀⠀⢀⣠⠾⣥⣄⡀⠀⠈⠉⠛⠷⢦⣤⣄⣀⡀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⡉⢢⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⢀⣼⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣤⡀⠀⠀⣸⠋⠀⠀⠀⠀⡰⠁⠀⢳⡀
⠀⠀⠀⢀⣾⡷⠞⠋⠉⠓⠂⠀⠀⠀⠈⢙⣶⣤⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠙⣿⣿⣿⣶⣄⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⢳⡀
⠀⠀⠀⣾⠋⢀⡠⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠈⠿⠃⠀⢹⣿⣿⣿⣿⣿⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⢷
⠀⠀⢰⣷⠞⠋⠀⣠⡴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⣟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⢸
⠀⢀⡾⠋⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠘⢿⣦⠀⠀⠀⠀⢸
⢀⡾⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣤⣤⣽⣿⣶⣤⣶⠟
⣾⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠶⠶⠿⠟⠛⠋⠉⠉⠉⠉
⢹⣧⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠙⣧⣿⣿⣿⣷⣤⣀⣀⠀⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⣿⠿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡿⠀⠀⠀⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃

⠀⠀⠀⠀⠀⠀⠀⢰⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⠙⢶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⣴⣀⠀⠀⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢓⠳⣤⠀⡀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⣿⣆⣿⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡘⠷⣧⣴⡂⣀⠻⡇⠀⠀⠀⠀⠘⠠⡀⠀⠘⠶⢦⣴⣿⡧⠔⠁⠀⠀⢳⣸⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠻⣥⣈⣻⣿⣿⡾⠀⢠⠤⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣿⣗⠀⠀⠀⠀⢹⣿⣃⡠⠉⠙⠋
⠀⠀⠀⠀⠀⢠⢁⡤⠴⠆⠶⠶⠿⣿⠿⣿⣧⡠⣷⠀⢀⠀⠀⠁⠀⣠⣤⠶⠋⠀⠀⠛⢆⡀⠀⣤⣾⣿⢻⣍⢛⠠⢄
⠀⠀⠀⠀⠀⠈⠈⠒⠤⠀⢀⣤⠤⠾⣄⠀⠉⠧⢿⣄⡽⠒⠀⠂⠀⠑⢆⠀⠀⠀⠀⠀⠈⠁⠀⠘⠿⠿⠏⠉⠙⠷⠬⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣟⢠⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠄⡄⡄
⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢣⠈⣄⠀⠀⠀⡞⠀⡄
⠀⠀⠀⠀⠁⢀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⣼⡀
⠀⠀⣀⠀⠀⠈⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⠀⠀⠀⢨⣀⣴⣿⠷⣠⠀⣠⠔
⠀⠈⠀⠀⣀⠀⠀⢧⠀⠀⠀⠀⠐⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⢀⣄⠤⣙⣿⣿⣿⣷⣶⡈⠀⠀⠂
⠀⢀⡠⠜⠁⠀⠀⠼⡖⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡇⣆⡏⠀⡀⠀⠀⠀⠐⠂⠀⠉⠿⡿⠟⠿⠿⣿⡂
⠀⠸⠀⠀⣄⠍⠀⠀⠉⠀⡀⠀⠀⠲⠄⠀⠀⠀⢀⡃⢀⠹⣿⣠⣨⣾⡶⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠁⠀⠀⢀⠀⢁⠉⠚⠉⠀⠀⠀⠀⠀⠰⢄⡪⣤⣰⢳⣿⣿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠠⣄⠈⣑⢿⡻⡘⣿⣗⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡇⠀⢸⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⡰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⡀⠘⣿⠇⢇⠘⢻⣃⠌⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⠃⡀
⠀⠀⠀⠀⣤⡀⠆⠸⠀⢐⡤⠂⢐⠀⠀⠀⠀⠀⠠⠄⠉⠙⢳⠄⢧⡘⡵⢊⠤⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠠⣸⣿⣰⠁⡠
⠀⠀⠂⠀⠨⣍⠳⡟⢤⣠⣦⠄⠚⠚⠀⠘⠁⠀⠀⠀⠄⠚⣉⡥⠄⢣⣘⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡟⣿⣇⠎
⠀⠀⠀⠀⢢⣝⣦⣶⠈⣿⣡⣴⣷⡶⠂⢀⠀⡀⠀⠀⠀⠈⠐⠚⠿⠶⣛⠅⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⢈⣻⣷⣿⠃
⠠⠀⠀⠀⠀⢉⡽⠿⠿⣿⡿⠑⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠬⢝⣿⡏
⠀⠀⠀⠀⠀⠨⣀⠀⠠⡿⠛⣦⣤⣴⣶⣍⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⠴⠾⢿⡦⠂
⠀⠀⠀⠀⠀⠀⣦⠀⠀⣏⠉⣡⠋⠯⠙⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⣤⣤⣤⣤⣤⣤⣬⣤⣤⣥⣤⣤⣤⣤⣤⣦⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢰⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡆
⠀⠀⠀⠀⠀⢸⣿⠛⠿⢿⣿⣶⣦⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⡿⠿⠛⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠉⠉⠀⠈⠹⣿⣆⠀⠀⠀⠀⠀⠘⢿⣷⣶⣶⣶⣶⣶⣿⣏
⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣿⡷
⠀⠀⠀⠀⠀⢹⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣶⣶⣶⣶⣾⣿⣿⡿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠐⠒⠒⠂⠀⠤⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠂⠀⠈⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠤⠀⠀⠀⠠⡔⠀⠀⠀⠀⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢈⣓⣖⠂⣤⠄⢀⠀⠀⠀⠀⠀⠀⠈⠦
⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢐⠂⠀⠀⠀⠉⠉⠙⡀⠐⠐⠀⠙⠓⠂⠠⢀⠀⢰⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠄⢀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠘⠀⠀⠀⠀⢀⡤⠤⠀⠠⠤⠀⡀⠀⠀⠈⠖⠐⠀⠀⠀⠀⠀⠀⢀⠈⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⠒⠒⠲⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠈⡄⠀⠀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠐⠓⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⢀⠔⠀⠀⠈⠀⠍⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠐⠆⠐⢄⠀⣶⡀⠀⠀⠰⠄⠠⠀⢀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠢⠐⢠⠘⠉⠃⠀⠀⠀⠀⠁⠀⠼⡀⠀⢀⠂⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⡁⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠈⠢⢄⠀⠀⢀⣀⠀⣠⠴⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣹⣇⠔⢟⠉⠀⠀⡥⠁⠀⠐⢄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠂⠀⠚⠁⠈⠒⠀⠈⠀⠀⠀⠡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣇⠃⡐⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⢰⡇⡐⢀⡌⠀⠀⢸⠀⠀⠀⠀⠁⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣽⡄⢠⠋⡀⠀⠀⠘⠀⠆⠀⠀⠀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠚⠊⠀⠀⠀⠀⡹⠀⣀⠀⢀⡄⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠔⡈⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⢀⣞⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠑⢄⣄⣠⡴⠀⠷⠄⠀⠀⡠⠔⠋⠈⠳⠄⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠦⠿⠀⠸⢿⡷⠶⣶⠐⠂⠈⡄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠌⢸⡏⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠰⠀⢸⡇⠀⠀⠀⠉⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠃⠀⢸⡇⠀⠀⢀⠂⡇⠀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠘⠀⠀⢘⡇⠀⠠⠁⠀⠤⠀⣈⣀⣀⠀⡀⢀⣀⣀⡀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠃⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠠⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠐⠄⡑⠄⡀⢉⡷⠀⠀⠀⠀⡏⠐⢺⠀⠑⢄⠀⠀⠒⠀⠁⡈⡤⠐⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠇⠀⠀⢆⠐⠀⠀⠄⠀⠀⠴⠉⠉⠁⠠⠴⠃⡀⠦⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠱⣀⠀⠀⠀⠀⠀⢀⠠⡰⠚⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠞⠀⠀⢀⠈⠑⢦⡄⠠⠔⠁⡰⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠔⢈⠠⢐⡈⢠⠄⢤⡤⠔⡡⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠊⠀⢀⠕⢈⣀⠠⠊⠀⠀⠮⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡔⠠⠀⢀⢂⠌⠁⢈⠰⠂⢈⠀⠀⠙⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⣠⡆⢸⣄⠀⠀⠀⡆⠀⠈⠀⠈⠁⠀⠀⠈⠀⠐⠠⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣘⡁⡄⠊⠀⠘⢄⣀⠠⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⡀⠀⠀⢪⡘⠂⠀⠀⠀⡰⠋⠀⠀⢑⡲⣄⠜⠹⠿⠀⠈⢠⡞⢄⠀⠀⠁⢦⢀⡀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢾⡁⠭⠄⠀⠀⠤⠀⠤⠐⠀⣀⠀⠂⠁⠀⠈⠰⠠⠊⢀⠄⠸⢇⣀⠑⣄⠀⠘⡆⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠛⣀⣴⢄⠀⢰⣾⠂⠀⡰⠖⣲⡌⠀⠀⠀⠀⢸⡄⠄⠊⠀⠑⢄⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡀⠤⢀⠀⠀⠀⠒⠠
⠀⠃⠀⢸⣀⠀⠹⠉⠁⠀⠰⢈⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⡬⠷⢄⠀⠀⠀⠀⢢⡀⣠⣠⠀⣀⡴⠶⣤⠀⡂⠄⠊⠁⠀⠀⠀⠈⠁⠀⡐⢅⠺
⠀⠀⠁⣤⠤⢀⣀⡀⠀⠀⠐⠀⠈⠁⠤⡀⠀⠀⠀⠀⠀⠀⠈⠲⡶⠤⢵⣄⡀⠀⢸⣱⠛⠋⢈⠓⠚⠀⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⢛⣠⠓⠈⠉⠁⠒⠁⠀⠀⠀⠀⠸⣤⠀⠀⠀⠀⠀⠀⠀⠉⣶⢠⡉⠏⡴⠦⣉⡄⢌⡱⣭⠁⠀⣃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢐⡆⠒⠹⢨⠙⡞⠂⠔⠀⠀⡅⠂⠃⠘⠏⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠦
⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠰⡁⠀⡀⢍⠱⣀⠈⠈⠀⠀⠰⣰⠶⠈⡉⢆⣰⠀⠘⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⢀⡀⠀⠒⠀⢃⠀⣀⠆⠃⠀⠀⠘⣎⣧⣎⠐⢂⡈⠱⠈⠋⠀⠌⣷⠿⢇⠀⠈⠁⠉⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠗⢆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠣⢀⠂⠈⠡⠧⡼⡞⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⠀⠀⠐⣀⠆⠀⠀⠀⢄⣹⣎⡱⠀⡄⠛⠀⣠⡒⡇⠠⣤⢒⠀⠯⠴⠐⢿⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⠃⠀⠻⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠩⠎⠙⣀⢀⣀⠢⠙⠌⠣⠀⠀⠀⣼⡿⢇⣠⣤⢈⢹⠐⡂⠀⡞⠚⢻⣦⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠄⣀⠰⠤⠷⠤⠂⠂⠁⡠⠀⠁⡠⢂⠘⠀⠁⠀⠀⠀⠁⠀⠀⠈⠈⠈⠑⠧⠬
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠂⠀⠀⠀⠀⠀⠘⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠏⡀⠀⠀⠀⠀⠀⠀⢈⠱⢆⡵⠌⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⢀⠀⠒⢿⣿⠶⢁⠑⠈⢆⠀⠀⠀⠀⠀⠀⠂⠐⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡅⢿⠖⠂⠉⢀⡀⠡⠌⢂⡱⣀⠀⠀⠀⠀⠀⣄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⢟⡭⠧⣄⠀⠨⣩⡍⡭⡤⢐⣠⠄⡀⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠁⠄⠓⠄⣿⠿⣦⣈⠄⠀⠀⠀⠘⢷⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠐⠈⠀⠀⢡⣸⠀⣠⠙⠖⠀⠀⢀⠼⠶⠞⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⣀⠘⠐⢦⣹⡀⠄⠀⠀⠈⠓⡲⡥⠔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠳⡄⠀⠀⠀⠀⠐⣷⠴⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠀⠘⠣⢐⣒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⠿⢟⣛⣛⣭⣭⣭⣭⣝⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢗⡲⣶⣿⣿⣿⣿⠫⣵⡤⣶⠝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣵⣿⣿⡿⠿⢿⣿⣮⡃⠫⠾⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⣫⢍⢠⣚⠿⢸⣿⣿⣿⣮⡻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⡋⠾⠇⢟⣣⣿⣿⣿⠿⠿⣿⣿⣿⣀⠀⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢟⣼⣿⣿⣿⡤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⢰⣭⡝⠻⠿⣿⣿⣿⣿⠛⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣣⣿⣿⣌⢵⡞⣴⡹⣶⢎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣥⣶⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠐⣶⣤⡄⠀⠀⣀⢰⡶⣾⣶⠀⠀⠀⢠⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⢀⣆⡀
⠀⠀⠀⠀⠀⠀⣼⡞⠀⠀⠀⠀⡀⢿⣼⢟⣿⣛⡆⠀⣤⢹⣼⣿⣿⡩⠄⣠⣴⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⣿⡿⡃⠀⠀⠐⢿⣷⡄
⠀⠀⠀⠀⠀⠲⣿⠂⠀⠀⠀⠀⠻⣾⣫⣾⠿⢦⠀⢰⣸⣿⣿⣽⣿⡗⠀⣿⣿⣿⣿⣿⣷⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⣯⣴⡶⠂⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡟⢯⠷⠀⠀⠀⠉⠙⠿⠟⠃⠀⠀⠻⢿⣿⣧⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠙⣿⡓⠀⠀⠀⠠⣾⣿⡇
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⡡⠄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠹⢿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⢠⣿⠂⠀⠀⠀⠀⢀⡴⡛⠈⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⡀⣄⣀⠀⠀⢠⣄⠀⠀⠀⠀⣀
⠀⠀⠸⢿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣦⣿⡟⢁⣴⡿⠀⠀⢀⠎⡀⠁⠀⡀⠄⠀⢸⣿⡆⠀⠉⠀⠠⣉⣻⡥⢆⡀⠘⣿⣷⠀⣠⣾⣿⠀⠀⠀⢀
⠀⠀⢻⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⢬⣷⡿⣋⣤⡤⠀⠀⠘⠁⠀⠀⠀⠀⠀⠒⠓⠒⠀⠀⢐⠲⠶⣽⠋⠩⠀⠀⠈⠛⠃⣿⣿⠟
⠀⠀⠻⣿⣿⣿⡗⠀⣤⣤⠀⣼⣷⠀⣠⣤⠸⠿⡶⠦⣿⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠀⠀⠠⠭⢭⣯⠴⠞⣋⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠁
⠀⠀⠈⢿⣿⠆⠀⠀⡻⣿⣷⣿⣿⣾⠿⠋⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠘⠀⠀⡀⠀⠀⢠⠀⠐⣻⡭⠀⠠⣤⣀⡒⣶⣚⣯⠗
⠀⠀⢠⣀⠀⠀⠀⠘⠿⠿⣿⣿⣿⡷⠿⠷⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠐⢢⡤⠙⠀⠄⠀⠀⠀⢻⡯⠀⠲⠦⣤⣄⣋⣡⠴⠚
⠀⠀⠸⣿⣿⣦⠀⠀⠀⠰⠿⠛⠻⠿⠀⣴⣄⢠⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠂⠐⠠⠀⠀⠀⠁⠀⠑⠶⢦⣄⣉⣴⠾⠋⠀⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⢰⠀⠀⠀⣬⣽⠿⡇⠀⠀⠀⠀⠀⠀⣾⡆⠾⠡⡤⠆⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠁⠀⠀⠀⠛⠏
⠀⠀⠀⠀⠈⠉⠁⠀⢠⡀⣴⠀⢁⣀⣠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣦⡘⠳⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⡀⠀⢰⣴⡀⠀⣄⠀⠀⣶⡧
⠀⠀⠀⠀⠀⣀⠸⣆⢸⠇⣯⣴⣿⡉⠁⠀⠀⢀⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠛⠀⢼⣯⠄⠈⠉⠀⠀⠿⢀⡀⠈⠁⠀⢠⡐⣴⢃
⠀⠀⠀⠀⢦⡙⢦⠻⣼⣿⠯⠄⠀⢀⢠⣶⠶⠘⣿⣖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢀⣀⡙⠶⣋⣤⠄⠀⠀⠲⣝⣗⣫⣔
⠀⠀⠀⠳⣮⡻⣦⣍⣛⡛⠁⠀⠠⢜⠛⠁⣀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⡇⠀⢠⣛⠯⢈⠥⠶⡂⠀⣈⡻⢮⡭⢟⡋
⠀⠀⠐⠲⣞⣿⡓⢦⡄⠀⠀⠀⠀⠀⣶⡿⣿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⡿⠇⠀⠀⢭⣍⡀⢚⡋⠁⠀⠠⣭⣹⣛⡭
⠀⠀⠀⠉⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠱⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠑⠋⠁⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣤⣭⣥⣦⣭⣷⣥⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛
⡇⠰
⡇⠸
⠃⠨⠀⠀⠀⠀⠀⢠⡇
⠈⠁⠠⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⣄⠘⣿⣦⠀⣿⣿⡠⠇⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣷⣦⣤⡹⡿⠂
⠴⢴⠭⠦⠍⠉⠉⠹⢿⡇⠀⠀⣠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠸⣧
⢠⣤⣤⡄⠀⠀⠀⠀⡾⣴⢇⠎⠉⠀⡠⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣧
⢀⣉⣀⣀⣀⠀⠀⠀⢿⣋⠀⠀⠀⣶⠃⣴⣷⣾⣿⣿⣿⣿⣿⣿⣇⡀⠈⣿⣧
⣦⣴⣶⣤⣦⣤⡄⢠⣿⣿⠆⣴⣶⣶⠟⣽⣿⡏⠻⣿⣿⣿⣿⡿⠁⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠾⢷
⣿⣿⣿⣿⣿⣿⡇⢸⣿⣃⡶⣿⡛⠁⣾⣿⡓⠂⠀⠸⣿⣿⣿⠁⣠⣬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢠⠀⣤⣤⣤⣤⣶⣶⣾
⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⢴⣷⣦⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠛⣛⣉⡁⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣷⠘⠉⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⠀⣀⣤⢶⣶⣿⣿⣿⣿⣿⣿⣿⠈⠛⠀⠀⣀⣀⣀⣠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠿⠿⠾⢿⣶⣶⣶⣍⣻⣿⣿⣿⣿⣿⣦⠚⢛⣛⣛⣛⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠟⠛⠛⠋⠉⠁⠘⢾⡖⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⡀⣀⣀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣀⣀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⢶⣿⣿⣿⣿⣟⠀⠀⠀⠀⠘⠛⠛⡃⣀⣤⡀⠀⠉⠛⠛⠻⠛⠛⠛⠉⠀⠀⠀⠀⠀⢼⣿⣿⠇⠀⠀⠘⠛⠛⠛⠛⠿
⣾⣿⣿⣿⣿⣿⣦⣀⡀⠀⢰⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣙⣿⣦⡉⢻⣿⣿⣿⣿⣍⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⣒⣯⣽⣵⣒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣷⣾⣿⣿⣿⣿⣿⣿⠿⠗⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠀⠈⠉⠉⠻⡶⣶⣦⣤⣤⣤⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠑⡎⠩⣿⣿⣿⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠰⠖⠂⠀⠀⠀⢞⣁⣘⣿⣿⣿⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠃⠀⠀⠈⠋⠀⠀⠀⢸⣽⡿⣛⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠁⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠈⣠⣶⣅⠀⠀⠀⠀⣠⠏⠀⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⠂⠐⠂⡆⠀⠀⠀⠀⠀⡴⠚⠀⠐⠊⠁⠣⡰⠙⠃⡸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣬⠃⠀⣀⠀⠀⠃⠀⠀⣀⠴⠞⠁⠀⢀⠐⠢⠀⢠⠇⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⢀⣹⣄⣈⣀⣵⠒⠔⠉⠀⠀⠀⠀⠀⠎⠀⢠⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠄⠀⠀⠀⠀⢙⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡉⢻⡏⣾⣿⡇⠊⠀⢠⠎⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠊⠀⣀⣤⠴⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠉⣻⣿⣼⣿⣿⠁⠀⠀⢸⡄⠀⠀⠀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠁⢠⠎⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⢧⠀⠀⢸⠁⠙⠀⠀⠀⠀⠠⢄⡀⠀⠀⠈⢢⠀⠈⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⡴⠁⠀⠀⠀⠀⣰⠏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⢣⡀⠀⠀⢀⠀⢧⠀⠀⢺⡁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣇⣠⣖⣁⣤⡜⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⢀⣧⡴⠖⠒⠒⠒⠢⠤⢀⡀⠀⢸
⠠⣄⣀⡀⠀⠀⠀⢀⣸⣦⣤⣤⡔⠒⠙⠛⠉⠉⠁⢸⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸
⠀⠀⠀⠉⠙⣢⠞⠁⠀⠀⠀⠀⠉⠙⠓⠦⡀⢀⣀⣋⣀⣀⣘⠀⠀⠀⣀⡤⠤⠂⠀⠀⠑⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠀⠀⠀⠳⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⣀⠞
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠳⢦⣤⣀⠀⡠⠤⠀⢸⣅⡧⠠⣤⣾⢿⣛⠛⠋⢉⡉⣉⢉⡟⠛⠛⠋⠉⠁
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠛⠦⡀⣀⣠⠼⠒⠋⠁⠀⢀⣿⢠⣆⣼⣷⠿⣾⠃⢀⠂
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⡠⠖⠋⠉⠀⢀⣀⠤⠶⡞⣹⠏⣾⣿⠻⠏⠀⠁⠀⢸
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣠⠋⠀⢀⡤⠖⠋⠉⠀⢲⡄⣷⠏⠀⠀⠁⠀⠀⠀⠀⠀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⠀⠀⠀⡌⣴⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣶⣴⣿⡆⠀⠀⠀⡇⠀⠀⡟⠀⠀⠀⠀⡇⡇⣘⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⢿⣿⣿⣿⡃⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⡇⡈⠉⠉⠛⣿⣦⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠂⢉⢹⡟⠁⠀⠀⢸⡇⠀⠀⡇⠀⠀⠐⠐⠃⢦⠠⣶⠈⠻⢉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠁⠀⠘⠸⡀⠀⠀⠀⢸⠀⢠⠆⣳⠀⠀⣼⠀⠀⣶⢀⡀⠀⠀⢴⠃⢀⡤⣤⣴⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠂⠀⠀⢠⡆⠁⠀⠀⠀⢸⠀⠀⡇⠈⠀⠀⣿⠀⠀⢙⣋⣁⡤⠀⢾⡄⠀⠀⠛⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡠⢼⠁⠀⠐⡶⡶⠃⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⣈⠤⢴⣾⣏⣭⠆⠀⣿⣿⣷⣶⣤⣄⣈⠛⠟⠁
⠀⠀⠀⠀⣰⣿⡇⡰⠚⠏⠹⡄⠈⢢⠀⠐⡇⢹⠉⢻⠀⠀⠀⢸⠀⠰⢏⢻⣖⠒⣀⣰⣾⣿⣯⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⢧⠃⠀⠀⠀⠹⡄⠀⠳⠺⠇⢸⠀⡟⠀⠀⠀⣿⠀⠘⠦⡽⡃⢸⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⡏⡇⠀⠀⠀⢸⠀⢻⡀⠀⠀⠀⢸⢸⡗⣠⣄⡀⡿⠀⢺⢠⣗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⣏⠀⠸⡇⠀⢀⡄⠸⢸⣷⣿⣿⣇⡇⠀⠘⠘⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⡏⡇⠀⡴⣲⣿⢆⠀⡇⢀⣿⣁⢂⠛⢻⣿⣿⣿⡇⢰⠒⡒⣿⣿⣿⠏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠛⢡⠇⣀⣀⣟⢈⣀⣀⣀⡠⢦⣭⣭⣕⠦⢍⣻⠥⠧⠘⢎⡻⢈⣩⠄⠀⢶⣾⣿⡻⠿⣿⡻⡍⠻⠿⠿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⡏⠁⠈⠉⠉⣉⣀⣠⢴⡸⠰⣆⣍⣤⣤⡤⣄⠀⠀⢸⠀⢸⣽⣶⠳⢆⡛⢩⡶⠞⢀⡵⠐⠺⢦⡀⠹⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⡤⠷⠖⠓⠉⠉⠁⠀⠧⣌⣁⢱⠟⠛⠉⠉⣀⡬⠃⠘⠚⢯⣵⡻⢖⣲⣌⣹⣈⢻⣽⣿⠂⠀⡄⠀⠈⠉⠉⠐⠒⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠘⠘⡛⠛⠛⠁⠀⠈⠐⠛⢯⣿⠻⡶⠻⡥⣿⡏⢳⡿⠧⠴⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⠲⠾⣵⣚⣁⣒⣓⣜⣻⣮⣷⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣰⡦⢴⢴⢄⠴⣴⡦⣶⡄⠀⠀⠀⠀⠀⠀⢀⠀⣀⡠⡤⢀⠀⣤⢄⡀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⣽⣿⣗⠀⢸⠀⢄⡮⣛⡇⠀⠀⠀⠀⠀⢸⣾⢿⣿⢧⣳⣽⢠⣟⡞⣷⡏⡿⡇⠀⠀⠀⠀⣼⡻⠤⠽⠷⢾⣿⠴⠿⠥⠴⣟⡀
⠀⠀⠀⠀⠀⢹⣖⠍⠀⢸⠁⢐⣭⣶⡂⠀⠀⠀⠀⠀⢸⡜⡜⣟⢯⣻⣿⣿⣯⡞⡽⣱⣱⠆⠀⠀⠀⠀⣿⠅⠀⠉⠍⢹⣿⠉⠩⠥⠬⢽⡇
⠀⠀⠀⠀⠀⢿⣛⡫⠁⢸⡄⠉⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡝⣌⢳⡙⣿⣿⣫⢞⡵⢣⢿⠃⠀⠀⠀⠀⣿⡛⣛⣛⣒⣻⣿⣛⣛⣛⡓⣻⡇
⠀⠀⠀⠀⠀⣿⣿⣓⠂⢸⡇⣐⣿⣿⡃⠀⠀⠀⠀⠀⢨⢳⡹⣌⢳⣽⣿⣿⣣⢞⣵⢋⢎⠂⠀⠀⠀⠀⣿⠄⠀⠠⠤⢾⣿⠤⠤⠤⠄⢽⡇
⠀⠀⠀⠀⠀⣲⣿⠿⠗⢸⡇⠾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣧⣳⣌⢷⣽⣿⣿⣫⠟⣡⢟⣾⠇⠀⠀⠀⠀⣿⡍⠉⠩⠭⢽⣿⢭⣭⠍⢩⣽⡇
⠀⠀⠀⠀⠀⣸⡷⢏⠁⢸⡇⠨⣿⣿⡇⠀⠀⠀⠀⠀⢸⣧⠳⣽⣦⡙⢿⡿⣡⣾⣿⢋⢾⠇⠀⠀⠀⠀⣿⣄⣒⣒⣒⣚⣿⣒⣒⣒⣒⣺⡇
⠀⠀⠀⠀⠀⣻⠽⡣⠂⢸⠀⢔⣽⣿⠃⠀⠀⠀⠀⠀⠀⢧⠳⣬⡳⣽⣿⣿⡵⣛⣵⢏⡞⡀⠀⠀⠀⠀⣿⣒⠲⠶⠶⢺⣿⠒⠒⠒⢒⣺⡇
⠀⠀⠀⠀⠀⣼⣭⡶⠀⢸⠂⢨⣒⣿⡇⠀⠀⠀⠀⠀⢸⡘⠷⢮⣽⣿⣿⣿⣞⣯⠵⠟⣡⡇⠀⠀⠀⠀⣿⠧⠤⠭⠭⢭⣿⠭⠭⠭⠴⢿⡃
⠀⠀⠀⠀⠀⣾⣿⣡⣀⡸⣠⣤⣝⣿⡅⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠻⢿⡿⠖⠒⠚⠻⠟⠁⠀⠀⠀⠀⠛⠁⠀⠀⠈⠸⠿⠘⠛⠁⠈⠙⠃
⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠈⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠛⠛⠛⠛⠓⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣋⡽⠟⣁⣀⣀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⢀⣾⡯⠖⢋⡽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠖⠛⠿⠿⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⡬⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢿⣟⡛⠉⠉⠉
⠀⠀⠀⠀⠀⣀⣠⡤⠶⢺⡿⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠶⠶⠶⠒⠒⠛⠉⠁
⠀⠀⣠⡴⠟⠉⠀⠀⠀⠈⠃⠀⠀⠰⠶⢿⡍⠉⠉⢉⣀⡀⠀⠀⠴⠖⠒⣙⣶⣄⣀⡀
⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢠⠞⢋⣭⠤⠤⠤⣄⣀⣾⢩⣤⠀⠈⠙⢶⡀
⠚⠓⣲⡶⠃⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠉⠻⣟⠛⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⢠⡾⠁⠀⠀⠀⠀⠀⠐⠺⠯⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠾⠷⢻⣀⠀⠀⢀⣰⠇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠚⢉⡼
⣿⠁⣴⣿⠀⠀⠀⠀⠀⠐⠶⢾⣁⡀⠀⠀⠀⠀⠀⠰⠮⠷⢦⣄⣀⠀⠀⣸⠋⠙⠋⠉⠁⠀⠀⣴⠛⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠋
⠙⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣿⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⠸⡆
⠀⠀⠀⠳⣤⣀⠀⠀⠀⢀⣠⡤⠤⠤⢤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢀⡴⠟⠁⠀⠳⡄⠀⠀⠀⠀⠀⠀⢻⣄⡀⠈⠉⠻⣷
⠀⠀⠀⠀⠀⠉⠉⠛⢻⡏⠁⢀⣠⠤⢤⣀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠚⠋⠛⣦⠀⠀⠈⠙⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠈⠉⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢾⢀⡟⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠚⠛⠋⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠛⠓⠒⠋⢀⣤⠤⣴⡋⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠊⠉⠉⠉⠉⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠻⠶⠶⢶⡶⡄⠀⠘⣇⢤⣈⣿⢁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢠⡟⠛⠓⠒⠒⠛⠀⠉⢹⣉⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢀⣹⡄⠀⠀⠀⣠⠴⣾⠁⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⢦⣄⢸⣏⡟⠓⠒⠒⠉⠙⠶⢚⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⠶⠋⢀⡴⠚⠛⢧⣹⣀⡴⠋⠁⠀⢿⠂⠀⠀⠀⠤⠤⠤⠀⠀⠐⠀⠀⡈⠻⣏⠋⠀⢀⣠⠤⣤⡖⢉⣽⣿⠟⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⠀⠀⠀⠀⠙⣳⠄⠀⠀⠉⠋⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠖⠋⠀⢠⡞⣷⢋⠾⣁⣉⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣠⠀⠀⣠⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠞⠁⠀⠀⠀⡞⣰⢣⠯⣀⣀⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠲⠶⢤⣤⣤⣀⣠⣤⣤⡴⢯⠀⠀⣀⣤⣀⠀⢰⣷⢣⡿⣤⣀⢈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⠾⠒⠉⠁⠀⠈⣷⣸⡇⡾⠲⠤⣈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡵⣏⢿⡄⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⠷⣤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⣀⣹⣆⢣⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡏⠓⢲⠞⢦⣱⣄⡀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣷⡘⠉⠀⠀⠉⢻⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀⣀

⠀⠀⠀⠀⣀⠤⠒⠂⠉⠉⠉⠉⠉⠁⠒⠢⢄⡀
⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠄⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⢼⡇⠙⠋⣿⢂⡥⡐⡄
⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⠖⣫⣽⠶⠖⠒⠈⣑⣳⣤⡇
⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢀⣼⠋⣡⣴⣿⢧⠀⠀⠐⢮⣽⣿⣿⣿⡀
⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠐⡄⢰⠒⠒⠂⢙⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠋⠀⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣄⠀⠀⢈⣙⠀⠀⠀⠊⠁⢀⠀⠀⠀⢶⣖⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠙⠀⠀⠀⠈⠙⠃⠀⠀⠈⠛⠉⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⠤⠤⠤⣀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠶⠞⠁⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⠈⠀⠀⣴⣄⣠⣶⠟⠁⠀⠘⠆
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠦⣥⠀⠀⠀⠀⢀⡿⠉⠉⠀⠀⠀⠀⢀⠀⠁⡀
⠀⠀⠀⠀⠀⠆⠂⠀⢀⣤⠀⠀⠀⠈⠁⣆⣀⡐⢏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣄⣀
⠀⠀⠀⠀⢠⠀⠀⠀⢸⡇⠀⠀⣠⣶⣿⣿⣿⢡⣿⣧⠁⠀⢀⣠⣴⣶⣦⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣧⡀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡄⠀⠀⣤⣀⣠⣿⣿⣿⣆⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⣾⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⢟⣯⣷⣶⣿⣻⡷⣞⠏⢙⣛⠿⠿⢿⣿⣿⡿⢿⣟⣯⣿⢟⣿⣿⢏⣫⣝⢮⠛⠻⠿⣛⡿⠇
⠀⠀⠀⠀⠀⠀⠈⣓⣊⣉⣭⢅⢂⣱⢿⠟⣫⢽⣥⣞⣭⡈⢐⣥⣽⣿⣷⣦⣶⣶⣾⣿⣿⣛⡵⠾⢽⣾⣿⣯⣧⣲⡭⠷⣒⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠯⠛⠋⣉⣭⣭⣏⣛⠻⢿⣓⣯⠴⣭⡷⠿⡿⠿⣶⡿⢿⡿⣯⣷⣶⣯⠭⠿⠟⠛⣒⣙⣻⡵⠾⢛⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢝⣛⣒⣒⣋⣝⣻⠶⣬⡯⠭⡁⠶⣛⣿⣯⢿⣿⣿⣷⣶⣯⢭⣩⣍⣄⣐⣙⣹⢷⡗⠶⣛⡭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢴⢶⣶⡿⠻⢽⣛⡫⠽⠶⢾⣛⣭⠽⣖⡿⢷⣾⣒⣿⣿⣿⣲⡶⠦⡠⠤⠶⢷⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣿⠧⣔⡦⢬⣍⡉⠀⠤⢖⣋⣶⣿⣯⢵⣶⣶⠶⣖⣺⣷⣈⡲⢶⣄⣈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠦⢊⡅⢒⣶⣶⠦⠭⡿⣶⣙⣠⡑⠶⣾⡿⢿⣿⣧⣒⡫⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠪⠭⣠⢽⠟⣛⠫⣉⣹⣿⣿⡿⠿⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⣶⠶⢶⡄⠀⣴⣆⠀⢠⣶⡄⢠⣶⡄⣴⠶⢶⣄⢰⡶⠶⠶⠀⣶⠶⢶⣄⢠⡶⠶⠶⠀⣶⠶⢶⣄
⠀⠀⠀⠀⣿⠶⠾⠃⣸⣏⣻⡆⢸⡟⣧⣾⢻⡇⣿⡶⠾⠏⢸⡷⠶⠖⠀⣿⠶⣾⠋⢸⡿⠶⠶⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠿⠀⠀⠰⠟⠉⠈⠻⠘⠇⠸⠇⠸⠃⠻⠀⠀⠀⠸⠷⠶⠶⠀⠿⠀⠘⠷⠘⠿⠶⠶⠀⠻⠶⠾⠋
⠀⠀⠀⠀⣶⠶⢶⡄⠀⣶⣆⠀⢰⣶⡆⢰⣶⡆⣶⠖⠶⣆⢰⡶⠒⠶⠀⣶⠲⠶⣦⢰⡶⠒⠶⠀⣶⠶⠶⣄
⠀⠀⠀⠀⣿⠶⠾⠃⣼⣧⣽⣆⢸⡟⣷⡾⢹⡇⣿⠶⠾⠋⢸⡟⠛⠛⠀⣿⠲⣾⡋⢸⡿⠛⠛⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠛⠀⠀⠐⠋⠀⠀⠛⠘⠃⠘⠃⠘⠃⠛⠀⢀⠀⣈⡽⣨⡛⡀⠛⠀⠈⠛⠘⠛⠚⠛⠂⠛⠛⠛⠋
⠀⠀⠀⠀⣿⠛⢻⡆⢀⡾⣧⠀⢰⣿⡆⢰⡿⢂⣠⣾⢢⣾⡿⣱⣿⣷⢹⣆⢙⢻⣦⢰⣟⠛⠛⠀⣿⠛⠻⣦
⠀⠀⠀⠀⣿⠓⠛⠁⣼⣧⣽⣆⢸⡏⡷⣨⣶⠟⢻⠏⠏⠘⢳⠏⠉⢹⡇⣿⣞⣷⣥⢸⡟⠛⠛⠀⣿⠀⢀⣿
⠀⠀⠀⠀⠛⠀⠀⠘⠋⠀⠀⠛⠈⠃⣼⣳⠏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠇⡇⢸⠏⢻⣯⠛⠛⠛⠀⠛⠛⠛⠁
⠀⠀⠀⠀⣿⠛⢻⡆⢀⡿⣧⠀⠈⣼⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣇⠘⢛⣛⠀⣿⠛⠛⣧
⠀⠀⠀⠀⣿⠛⠛⠁⣾⠧⠾⡇⣰⡟⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢌⠉⠀⣿⡀⢀⡿
⠀⠀⠀⠀⢉⣀⡀⠈⠁⢀⠀⡴⠸⠇⢰⡇⠀⠸⢤⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⡇⢸⠉⠁⢉⣉⡉⠁
⠀⠀⠀⠀⣿⠋⢻⡇⢀⡿⢻⡇⠀⠀⡄⠐⡀⠀⠀⠈⠉⠁⠀⠀⠀⠲⠛⠛⠙⢠⡆⢀⡇⢸⠀⠀⣿⠉⠛⣷
⠀⠀⠀⠀⣿⠛⠋⠁⣾⠇⠻⡇⢀⠀⠆⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⢼⣿⢼⣄⠀⣿⣀⣀⡿
⠀⠀⠀⠀⣉⣀⣀⠈⠁⠀⠀⠁⠘⠄⠈⣦⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢁⠀⠀⠀⠉⠘⠛⠀⢉⣉⣉
⠀⠀⠀⠀⣿⣉⣹⡇⢠⡇⠀⠀⠀⢠⠀⢸⡎⢹⡆⠀⠀⠀⠀⠀⢀⡀⡌⢁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷
⠀⠀⠀⠀⣿⠉⠉⢀⣾⠷⠀⠀⣤⣰⣧⣼⡷⠸⠃⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁⣠⣀⢠⡄⢀⡠⠀⠀⠀⢠⡿
⠀⠀⠀⠀⣈⠀⠀⠈⠁⣀⡀⣼⣏⡛⠃⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⣿⣿⣇⣄⣈⠀⠆⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡈⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣶⢹⡏⠈⢹⡟⡀⣄⠀⠀⠀⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠻⡇⠀⢣⣠⣷⠦⣴⠀⠀⠀⠀⠀⠘⣿⡿⢿⡁⢸⡇⠀⠞⠁⠷⣿⡆⢶⡆⡞⠃
⠀⠀⠀⠀⢠⡴⠂⠀⠀⣠⡄⣠⠀⢸⣿⣿⡀⠀⣷⠀⢰⡎⠀⠀⠛⠀⠀⠁⠈⢳⠆⢀⣄⠀⣽⠹⣜⠀⠇
⠀⠀⠀⠀⠀⠀⢀⡄⢰⡏⢿⣿⢀⡈⠁⠀⠛⢨⠩⣿⠛⠓⠆⡐⠀⠀⠀⠀⠀⠐⠟⠉⢻⡀⢻⡄⠹⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠈⠇⢙⠛⠛⠃⠾⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣆⣼⠻⡆⢢⡀⠀⢹
⠀⠀⠀⠠⠄⠀⠀⠀⠈⠐⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠼⣿⡄⠘⡘⣷⡄⡰
⠀⠀⠀⠀⣶⣶⣾⣿⣦⠀⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢸⣷⠶⠾⠛⢄⣀⠿
⠀⠀⠀⠀⠿⠈⠛⠉⠙⠻⣮⡀⣤⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⢿⠆⠸⠷⠶⠶⠄⠮⠿⠷⠃
⠀⠀⠀⠀⣶⠶⢾⣷⠦⠀⠀⠻⣎⠓⢦⣤⠀⠀⠈⠉⢻⣿⣿⣗⠂⠀⠀⠀⠀⠚⠷⢰⡶⠶⠶⠀⣶⠶⢶⣄
⠀⠀⠀⠀⣿⠶⠾⠃⣸⣄⡀⠀⠡⣶⣤⣈⠀⠀⠀⠀⢰⣶⣶⣶⠒⠀⠀⠀⠀⠐⣾⣽⡿⠲⠶⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠻⠀⠀⠐⠏⠉⠈⠻⠐⠇⠸⠇⠈⠀⠀⠀⢨⣿⣿⣯⣥⠀⠀⢠⣴⡶⠍⠻⢄⠰⠶⠂⠻⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣴⣿⣾⣵⣿⣯⠻⣿⠛⠊⠛⢷⣄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢸⡇⣿⣿⣿⣷⠹⣷⣄⠀⠀⠙⢷⣦⣤⣼⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠉⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣤⡾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡇⠀⠀⢠⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠖⠘⠛⠛⠋⠀⠀⠀⠀⣀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠳⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⢀⣀⣤⣶⠾⠿⠋⠉⠁⠀⠀⣀⣤⡔⠓⠂⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠷⠶⣤⣄⡀⠀⠠⣤⣄⠀⠀⠈⠉⠻⢷⣄
⠀⠀⢀⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣆⣀⣀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣯
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⠶⠾⠛⠀⠀⠀⠀⠀⢀⣠⣴⡿⢇
⠀⠀⠻⢿⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣤⣤⣤⣶⣾⡿⠿⠛⠁⠀⠘
⠀⠈⠶⠦⠞⣻⣟⠛⠻⠷⠶⠶⢶⢶⣶⣴⣦⠤⣤⢶⡶⠤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠶⠖⠛⠋⠉⠉⠉⠁⠀⢠⠛⠉
⠀⠀⠀⠀⡆⠉⠉⠛⠛⠲⠶⠶⠆⣠⣴⣦⣤⣤⣤⡤⠤⠠⠄⣀⠴⠦⠤⠄⠀⠀⠀⠀⠀⣀⡴⠦⢀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⣀⣀⣠⡴⣶⠚⠋
⠀⠀⠀⠸⡧⠠⢤⣀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⡶⠾⠛⠛⠉⠉⠁⠀⣾
⠀⠀⠀⠀⠃⠀⠀⠈⠉⠉⠛⠺⠷⠶⠶⠶⠶⣶⣶⣤⣤⣴⣦⣤⣤⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠾⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠒⠚⠒⠂⠀⠋⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡄⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣧⢀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣼⠇
⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠁⠀⠀⠀⠀⢀⡰⠶⠛⠛⠛⠛⠲⠦⣀⡀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⣿⡏⠛⠢⠤⠄⠀⣰⡁⠀⠀⠂⠀⠀⠀⠀⠠⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠒⢦⣤⣾⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠒⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠁⠀⠀⠀⠀⠉⠻⢈⠙⠉⠛⣻⠟⠛⠉⠉⠙⠛⠛⠛⠛⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠻⠇⡀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢠⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠂⣀⠀⠀⠀⠀⠡⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠠⠀⠀⠀⣠⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠻⠀⠀⠀⣻⠄⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠤⠤⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⠢⠀⠀⠈⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢀⣀⡄⠺⠶⠀⠈⠉⢣⣤⣀⣀⣀⣤⠶⠶⠀⠀⠀⠀⡄⢨⠀⠈⠉⠉⠛⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠤⠉⠁⠀⠀⢀⣴⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣀⡀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠋⢀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⠶⣤⣤⣀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠿⠋
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣶⣦⣤⣄⣀⣤⣀⣀⣀⣀⣀⣀⠤⡴⠾⠛⠛⠉
⠀⠀⠀⠀⠀⠙⠻⢦⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣄⣀⣀⣀⣀

⢱⡄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠑⡀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠁⠀⠀⠹⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢂⡀
⠸⣄⠀⠀⠱⡀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠉⠢⣄
⠀⠸⣇⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠡⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠘⢦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠈⢳⡀⠀⢧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂⠀⠀⢒⠆⠙⣦
⡅⠀⠀⠀⠀⠀⠻⣄⠈⣆⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⠈⠀⠀⠀⠀⠀⠂
⠘⢦⠀⠀⠀⠀⠀⠹⣆⠘⡄⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠊⠁⠀⠀⠔
⠀⠀⠳⡀⠀⠀⠀⠀⠘⢆⠹⠀⠀⡂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠿⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀
⠐⠀⠀⢀⠀⠀⠈⢧⡀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠁⠠⠌⢷⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⢀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⡌⣿⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠪⣷⡟⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⢀⠞⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠠⡀⠀⠀⠀⠀⠈⠠⡀⠀⢹⡇⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⢸⡇⠐⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣟⠉⣿⣻⣛⣛⣛⣟⣛⣛⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣻⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⢄⡀⠀⠀⡤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⡇⠀⠀⠘⡂⠀⠀⠀⠆⠒⠠⢄⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠒⠐⠄⠀⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⣘⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⢴⠂⠘⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⠀⠾⠟⢻⠆⢀⡀⣀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣶⣦⣾⡿⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⡀⡅⠀⡇⠀⠀⠀⠀⠀⡀⡀⢄⠀⠀⠀⠀⠈⢌⣀⢷⡿⠖⣄⡄⠃⠀⠀⠀⠀⠀⠀⠉⡙⠻⡟⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠄⠁⢀⠁⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⡄⡄⠀⡌⠉⠁⠑⠄⠈⠁⠃⠀⠀⠀⠀⠀⠤⠐⠀⠀⠡⡀⠀⠀⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠶⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠊⠀⠀⠀⠃⠁⠃⠀⠀⢠⠇⠀⢹⡀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⠀⡉⠆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠇⠀⠀⠀⠃⠘⠀⢠⡜⠐⠠⠚⣇⢀⠀⠈⠦⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣈⠔⢊⠀⠀⠀⢱⡤⠀⠀⠀⠀⠻⠂⠀⠀⠀⠻⢶⡄⠀⡆⠀⠹⠉⠀⠀⠉⠀⠀⠀⠀⢸⠉⠓⠒⠶⠶⢬⠇⠀⠂⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠠⠉⡖⠤⠀⠀⡈⢀⠀⡀⠈⠄⢀⠐⠁⠀⠀⢀⠀⠠⠀⠀⠙⠒⠈⢡⡁⠀⠀⠀⠀⠰⠀⢀⠀⠀⡃⢀
⠀⠀⠀⠀⠀⠀⡠⠠⠀⣀⠐⠀⡜⠈⠉⠠⠀⠀⢣⡀⣍⠀⠂⡀⠀⠀⠀⠀⢀⠀⠀⠈⠛⠣⠀⠀⢂⣺⡄⡀⠀⠀⢀⡴⠶⠦⠐⠛⣦⡀⠄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠤⠤⠄⣀⣊⡁⠐⠀⢀⠄⠐⠀⠀⠀⣤⠑⢶⠇⠀⢠⢀⡎⡀⡀⡀⠽⠦⠤⡘⠁⠀⠀⠀⠀⠉⡓⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠉⢉⠉⠉⠐⠒⠒⠓⠅⠋⠀⠈⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢁⠀⠃⠀⠐⡠
⠀⠀⠀⠀⠰⡇⠀⢀⠀⠀⠀⠀⣀⠉⠂⠐⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⣀⠀⠠⣀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠈⠁
⠀⠀⠀⢀⠀⠁⠢⢄⠀⢰⠀⠠⠄⠀⠐⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠉⠈⡴⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢁⠉⡖⠁⡀⠨⠁⠖⢀⠀⠀⠀⠀⡀⠀⠐⠈⡄⠀⠠⠉⠀⠁⠀⠈⠀⠠⠀⠐⠁⠐⠠⠀⠀⠁⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠸⠀⠚
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠐⠐⢀⠀⠁⠂⠀⠀⠀⠀⢈⠐⠋⠠⠀⠄⠙⡐⠠⠰⠃⠠⠜⢁⡝⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠒⠂⠀⠀⠀⠊⠀⠉⠉⠀⠀⠈⣀⠀⠃⢀⠴⣉⠐⣀⣖⡜⢚⠉⡀⠀⠆⠠⠀⠀⠁⠀⢏⠤⣤⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⡀⣁⡀⠀⠀⠈⠀⠊⠈⠃⡄⡄⢀⠀⢄⠀⠀⠂⠀⠸⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⢄⠀⠰⠀⠅⠀⠀⠀⠀⡄⡀⢂⡀⠴⠁⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠉

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡅⠀⢸⣿⣿⣄⠀⠀⣷⣾⠀⠀⠀⢸⣶⡇⠀⠀⣴⣾⡿⠿⢿⣷⣦⠀⠰⣶⣧⠀⠀⣼⣷⠆
⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⠀⠀⢸⣿⢻⣿⣆⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⣼⣿⡏⠀⠀⠀⢻⣿⣧⠀⠹⣿⣧⣸⣿⠏
⠀⠀⠀⠀⠀⣿⣿⠿⠿⠧⠀⠀⢸⣿⠀⠹⣿⣆⣿⣿⠀⠀⠀⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⡀⠀⢸⣿⠀⠀⠹⣿⣿⣿⠀⢀⣀⣼⣿⡇⠀⠹⣿⣷⣀⣀⣠⣾⣿⠇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠀⠙⠙⠀⠀⠀⠙⠿⠿⠀⠸⠿⠿⠋⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣤⡾⠟⠀⢟⣋⡙⢷⣴⡿⣋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡀
⠀⠀⠀⠀⠀⠀⣹⡿⢃⡴⠋⢸⡇⢸⢏⣼⠇⡼⣡⣶⠾⢶⣠⣶⢶⣶⠶⣦⣤⣀⣤⡶⠶⢶⡶⣶⡶⢶⣴⠿⠁⢾⡆⣿⣶
⠀⠀⠀⠀⣠⡾⢋⠄⡼⠁⠀⣼⡇⢠⢾⡟⢰⣷⠟⢡⣾⢀⡿⠁⢚⡄⢀⠁⣼⡿⠋⢐⣣⡞⠀⣩⢀⣾⠟⢠⣿⢿⡇
⠀⠀⠀⠠⣿⠱⢋⡾⠁⠀⠀⠻⠴⠋⠘⢧⣈⡥⢦⣙⡥⢦⣆⡴⠛⠖⢿⣄⣭⢦⣜⣋⣥⣠⠾⢧⣈⡥⣦⣨⡵⠋
⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⢀⣀⣀⣀⣠⣒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⣭⣭⡦
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣶⣖⢒⡇
⠀⠀⠀⠀⢸⠀⣴⡜⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠿⠯⢼
⠀⠀⠀⠀⠘⠒⠒⠂⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂


⠀⠀⠀⠀⠀⣀⣀⣀⣖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⢠
⠀⠀⠀⠀⢰⠁⠀⠨⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠸⠘⠄
⠀⠀⠀⠀⢇⠀⠀⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢹⠓⡆
⠀⠀⠀⠀⠀⠁⠒⡖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠂


⠀⠀⠀⠀⠀⣀⢠⡄⣀
⠀⠀⠀⠀⣰⣁⣰⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠄
⠀⠀⠀⠀⢸⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⢫⠱⠋⠉⠉⠉⠉⠙⡗⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠘⡀⡄⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⣇⡇⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠞

⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⣾⣿⠟⣛⠫⡿⣆⠀⠀⠈
⠈⠙⠻⠿⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠄⡵⠉⠁⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣦⣀⣀⣄⣤⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⠛⢾⣿⣿⣷⣶⡖⠚⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣶⣦⣀⢀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣦⣤⣶⣦⣶⣦⣤⣀⠀⢀⣠⣤⣀⣀⣀⣀⣿⣟⠀⠀⠀⣀⣤⣄⣀⣀⣀⣀⣤⣴⣶⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠖⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⠿⣿⠿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠛⠁⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⣤⠤⠦⠠⠦⠀⠀⣤⣤⣤⣠⣤⣤⡀⣠⣤⣤⣄⣠⣀⣤⣤⣠⣙⣷⢆⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠘⠛⠋⠉⠉⠙⠿⠟⠛⠿⠟⠹⠛⠛⠉⢻⣿⣿⠿⣿⣿⣿⣿⣿⠿⠛⣿⡿⠻⢿⣯⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠖⠛⠀⠀⠀⠀⠀⠩⠇⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠩⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠇⠀⠀⠐⣭⠂⠀⠀⠀⣀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⣄⣀⡼⠈⢦⡀⠀⢀⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠈⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣑⣦⠀⠧⣦⢄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⠀⡏⢠⠖⠉⠓⢝⢄⢀⣀⡀⣠⠗⠊⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣠⠎⠀⡇⡇⠀⠀⠀⠈⡇⣀⡛⠂⠨⢟⠉⡇⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠀⠀⢱⢣⠀⠀⠸⢷⡏⠀⠈⡆⢀⠏⠀⢣⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⣃⣑⣶⣶⣉⣓⡤⠔⢡⣊⡀⠀⠀⠑⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠰⡏⠁⠀⠀⠀⠀⠀⠉⣢⠀⠀⠈⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠀⠀⡀⠀⠉⠒⠢⢤⠤⠤⠄⠚⠁⠀⠀⢀⣤⠄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⠒⠤⠤⠤⠮⠀⣀⣀⣀⣀⠤⠔⣫⠃⠀⡠⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠚⣁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠄⠤⢤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠤⡇⠀⠀⠀⠀⢸⡤⠔⠒⡆⠀⣀⣄⡠⠔⢋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣄⣀⠃⠀⠀⢀⢰⠀⣀⠀⣰⠗⠊⠀⠁⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⣹⡁⠀⡈⠐⡤⠤⡔⠈⠀⢀⢳⡁⡄⣝⡆⠂⠈⠉⠀⠒⠀⠠⢄⣀⡀
⠀⠀⠀⠀⠀⢺⡽⣦⡀⠀⠀⠀⠀⠀⠈⠈⠑⠈⠀⠀⠈⠐⠋⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⢳⡜
⠀⠀⠀⠀⢀⢶⢆⠈⠻⠶⣞⠶⠶⠶⠰⠶⠶⣶⣤⣤⣤⣤⣤⣀⣠⣤⣤⣤⣴⡶⠶⠛⠋⠁⠀⠀⢀⣷⠮⡀
⠀⠀⠀⠀⠸⡈⡸⡄⠀⢐⣭⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⢀⠇
⠀⠀⠀⠀⠀⠈⠀⠈⠲⡏⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠖⠊⠉⠙⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⣠⣶⣶⡄⠀⠀⠀⣰⣿⠋⢹⡆⠀⣸⣿⡇⣀⠀⠀⢀⡄⢀⡠⢊⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣿⡿⠀⢸⡇⠀⣿⣿⣿⣿⡇⠀⠊⠀⠀⠀⢁⠄⠂⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⡇⠀⡾⠀⠨⢿⣿⣿⣿⠇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⡇⡼⠃⠀⠰⠾⠷⢾⣶⠶⣶⠶⠶⠷⠿⠶⠶⠶⠶⠶⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⢀⣀⡴⠒⢦⡀⠀⢠⣤⣤⠀⣠⣦⡀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣾⣿⣿⠀⠀⣷⠀⣿⣿⣿⠀⣿⢸⡇⠀⣾⣿⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣿⣿⣿⠀⠸⣾⠁⣸⣿⣿⡵⠟⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⠇⠀⠈⢿⣿⡇⠀⢀⡾⣿⣿⡈⢷⣤⣏⡴⢻⣿⣿⠀⢠⡟⠛⠻⣿⣿⡀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡤⠏⠀⠀⠀⠈⠻⠿⠶⠞⠁⠈⠻⠷⠶⠋⠉⠀⠀⠙⠿⠶⠋⠀⠀⠀⠙⠻⠷⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢶⡒⢿⡛⠻⡟⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣿⣤⢿⡦⢿⡶⠶⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⣼⣯⠙⠓⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡾⠀⣾⢁⣼⢁⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢠⣤⡀⠀⢀⣄⠀⠀⣤⠀⠀⣠⣤⡄⠀⣠⣤⠀⠀⣤⢀⣄⣤⣤⣠⠀⣤⠀⢠⡄⢠⣤⣄⡀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⢸⡏⠻⣦⠈⣿⠀⢀⣿⠀⣾⠋⠀⠀⢠⡿⢹⡇⠀⣿⠀⠉⢹⡏⠉⠀⣿⠀⢸⡇⢸⡇⠉⣿⡄⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣨⣿⠀⢸⡇⠀⣿⠀⣿⡄⣸⡇⢸⣧⣤⣤⠀⢸⡇⠘⣿⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⢸⣧⣶⠟⠀⣿⣧⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⢻⡆⣹⡇⣠⡿⠀⢸⣧⣿⠀⠸⣧⠀⢀⣤⢸⡇⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⣼⡟⢷⣄⠀⢻⡄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠸⠇⠻⠿⠛⠀⠀⠈⠿⠃⠀⠀⠙⠷⠟⠁⠸⠇⠀⠙⠿⠋⠀⠀⠸⠇⠀⠀⠙⠷⠟⠀⠻⠃⠀⠹⠃⠈⠻⠾⠛

⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤
⠀⠀⠀⠀⠤⠀⡈⡀⠎⠀⠉⠙⠙⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠲⣤⡀⠈⢇⠇
⠀⠀⠀⢀⠔⡺⠷⠼⠦⣶⣿⣷⣦⢴⣿⣧⡀⠀⠀⠀⠀⠀⠈⠳⡤⢄⠈⠣⡘⠡⡀⠈⣾⣄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠋⢹⢻⣿⣾⠖⠹⣆⠀⠀⣀⡀⠀⠀⢌⠢⡣⣀⢻⡦⣌⢲⣜⣟⠄
⠀⠀⠀⠀⠹⢠⠀⢀⢀⡀⠀⠀⠈⠛⢳⣷⡀⠩⠄⠀⠀⢍⡑⠠⢀⣲⣬⡻⣗⣏⣾⢸⡼⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠘⢸⠷⣶⣤⢄⠀⡘⣿⣏⢸⠧⠀⠀⠀⣀⠭⢛⡟⡟⡇⢸⡏⠸⣈⡁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠐⣽⡈⠐⠀⠀⠀⠈⠀⢀⠄⢀⠇⠀⢠⠱⡄⠙⣷⠀⠸⡄
⠀⠀⠀⢀⣀⡀⠀⢀⡄⣤⣦⣤⣄⡀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠋⠀⠎⢠⢧⠏⠀⠁⠐⠉⠀⠀⠁
⠀⠀⠤⠀⢠⣼⠇⣶⡷⢺⡌⠆⡽⡿⠲⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⣀⠀⡀
⠀⠀⢠⣾⠟⠁⣼⠏⠀⡼⠀⢀⠁⠀⠀⠀⠀⠀⣀⠙⣓⣲⢶⣶⣶⣶⠼⠾⠟⠙⠟⠂⢄⠓⠷⢤⣤⣤
⠀⠔⡝⡏⠀⠸⡟⠀⡰⠃⢰⢸⠀⢱⠀⠘⡄⠀⠈⢱⣎⡙⠿⠷⢶⣶⣶⣴⣦⣤⣶⣯⣷⣤⣶⣶⣶⣿⠂
⠀⠀⠈⠀⠀⠀⠇⠀⠁⠀⠸⢸⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡈⡁⠉⠉⠛⠉⡁⢈⣩⣤⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠡⠁⠞⠁⠘⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⡄⠀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠴⠖⠒⠒⠒⠊⠉⠉⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡤⠤⠾⠖⠒⢚⡙⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⠻⠶⣤⣀
⢀⠤⠤⠴⠶⠒⠒⠙⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠐⡖⠒⠒⢤⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤
⡆⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⢠⠀⣴⠴⠶⠶⠆⢶⣄⠀⢸⡀⠀⠘⡇⠀⢸⡄⠀⠸⡄⢻⣠⠴⠚⠀⢸⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢹⢾⡀⠀⠀⢰⣆⠀⠀⠀⣏⠙⢦⠘⣆⠀⡌⠀⢻⣀⣀⣀⠀⢸⡍⢷⡈⣇⠀⠀⢧⠀⠈⢧⡀⢸⠃⢸⡟⢦⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠘⣿⣇⠀⠀⢸⠘⣆⠀⠀⢹⡀⢘⡇⠹⡄⡇⠀⢸⡇⠀⠀⠀⠈⡇⠀⠙⢿⠀⠀⠸⠄⠀⠈⠙⠃⠀⠀⠃⠀⠙⠂⠀⠉⠉⠉⠁⠀⠀⠀⡠⠖⠁
⠀⢿⣿⠀⠀⡷⠖⠘⣆⠀⠈⣇⠜⠁⠀⢻⠁⠀⠀⠷⠶⠶⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠊
⠀⢸⣿⡀⠀⠃⠀⠀⠙⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⠀⠠⢤⣤⣤⣤⣶⣶⣦⣤⣤⣴⠶⠶⠶⠶⠟⠛⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡤⠤⣤⣴⣖⣲⠶⣶⠶⠶⠖⠻⠟⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⢙⣳⣾⣤⣐⠶⠶⠮⠿⠛⠓⠛⠊⠉⠉⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠳⠀⠀⠀⠸⣤⡆⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⡄⢠⠀⠀⠀⢀⡿⠀⠋⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⢆⠘⢆⢇⠀⠀⣼⣷⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠣⠘⡞⠀⡈⣿⢿⣀⠞⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡉⠪⠐⠄⢹⠷⣗⣨⠁⣁⠀⠀⠲⠊⠁⠀⠀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠈⠁⠠⠤⠭⠤⠄⠀⠐⠟⠛⠒⠚⠛⠒⠒⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿