Food processing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣾⣛⠲⣤⡀
⠀⠀⠀⠀⢠⡶⠋⡍⠉⡍⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⣴⠶⠾⠷⠶⣦⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⢞⣩⣭⡇⡿⢞⡙⢦⣻⡄
⠀⠀⠀⠠⣏⣀⣃⣀⣃⣀⣀⣈⣀⣸⡆⠀⠀⠀⠀⣾⣉⣉⣉⣉⣉⣉⡇⠀⠀⠀⠀⠀⢠⡟⠒⠻⡆⠀⠀⠀⠀⢠⡟⣰⢋⣑⢲⡇⣿⡯⢟⣫⣍
⠀⠀⠀⠀⣯⡤⢤⣤⡤⢤⣤⡤⠤⣽⠇⠀⠀⠀⠀⠈⣯⠈⠉⠉⠉⡿⠀⠀⠀⠀⠀⠀⣼⠛⢶⡀⣿⠀⠀⠀⠀⣾⢰⡇⢯⡽⢺⣥⠵⣚⠛⡇⢻
⠀⠀⠀⠀⢷⠶⣶⠒⠒⠒⠒⣶⡶⣾⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡶⠟⠀⡏⠀⠀⠀⠀⢹⡈⣇⢰⣷⡌⠄⠺⠿⣰⠇⡿
⠀⠀⠀⠀⠘⠳⠾⠷⣄⣠⡾⠿⠶⠋⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡇⠀⠀⠀⠀⠀⠳⣌⠳⢭⣴⣛⣷⠞⣣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠺⠤⠤⠤⠟⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⣀⣠⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣤⠻⡍⢿⢸⡟⣹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡍⠻⣜⣳
⠀⠀⠀⠈⡏⠛⠛⠾⠿⠗⠛⠛⣿⠀⠀⠀⠀⠀⠀⢠⠶⠮⠶⠵⠶⣦⣀⡀⠀⠀⠀⢠⡞⠋⠠⠈⠠⠈⠤⠉⢳⡄⠀⠀⠀⠀⢀⡞⠠⠀⠄⠠⠈⣿
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡿⢉⡿⠀⠀⠀⠀⠻⡏⠙⡟⠉⢻⡟⢙⡟⠁⠀⠀⠀⠀⣸⣅⠰⠀⢂⣠⠞⠁
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⣀⣸⣇⣀⣀⣀⣠⣟⣉⣀⠀⠀⠀⠀⠀⢳⠀⣷⠀⣸⠃⣼⠁⠀⠀⢀⣤⡴⢃⡼⠓⠛⠋⠁
⠀⠀⠀⠀⠈⢧⣤⣤⣤⣤⣤⡾⠀⠀⠀⠀⠀⠹⣤⣀⣀⣀⣀⣀⣀⣀⣤⠞⠀⠀⠀⠀⠀⠘⢧⣼⣤⣿⡴⠃⠀⠀⠀⠈⠳⣬⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⢉⣳⣄
⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠳⣄⠀⠀⠀⠀⣾⣉⣉⣻⣍⣙⣦
⠀⠀⠀⠀⠀⣾⣉⣉⣀⣀⣙⣧⠀⠀⠀⠀⢀⡾⠋⠉⢹⠏⠉⠉⡟⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠓⠦⢿⡀⠀⠀⠘⢷⠷⠷⠷⣾⣷⡟⠁
⠀⠀⠀⠀⢾⣡⣀⣀⣄⣀⣠⣨⡇⠀⠀⠀⣼⢦⡤⠤⡤⠤⠤⠤⠤⡤⠤⢤⢼⡄⠀⠀⠀⠀⠀⢀⡴⠛⠳⣄⡀⢸⡇⠀⠀⠀⠘⣧⠶⠛⣁⣼⠁
⠀⠀⠀⠀⢸⡄⠈⡇⠀⣿⠁⣸⠃⠀⠀⠀⣿⣏⣓⠺⣟⣒⡋⣓⣚⣿⢒⣋⣿⡇⠀⠀⠀⢀⡴⠚⢳⡄⠀⠀⠙⣿⠀⠀⠀⠀⠀⢹⡖⢋⣩⡇
⠀⠀⠀⠀⠀⣷⠀⣷⠀⡿⢀⡏⠀⠀⠀⠀⠘⠶⠭⢭⣭⣭⣍⣭⣭⣭⠭⠵⠞⠁⠀⠀⣾⡋⠻⡄⠀⠙⣦⣀⡴⠋⠀⠀⠀⠀⠀⠈⣿⠋⡽
⠀⠀⠀⠀⠀⠘⠷⠿⠶⠷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢻⠛⠶⡦⠀⠀⠀⠀⢀⡾⠳⣄⢀⡴⠳⣄⠀⠀⠀⠀⠀⣿⣿⣿⡇⣠⠟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡞⣽⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⣷⠛⣯⣷⣻⠆⠀⠀⣰⠋⠐⣆⠙⣿⠀⢦⠈⢷⠀⠀⠀⠀⢸⠀⢸⠀⣹⡟⢻⡇⠀⠀⠀⠀⠀⠀⣠⠞⣱⣏⡾⠁⠀⠈⡇
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡟⠓⢻⡼⠃⠀⠀⠀⢿⠀⣰⠃⠀⣽⢠⡟⠀⢸⠇⠀⠀⢀⡼⠀⠸⣾⠉⠀⠀⠙⡇⠀⠀⢀⡴⢚⡵⢞⡵⠋⠀⠀⢀⡼⠃
⠀⠀⠀⢰⠋⠀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠘⢦⡘⢂⣴⢿⡈⠃⣠⠟⠀⠀⠀⢸⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⠸⡟⣽⠞⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠳⣄⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠞⠁⠀⠙⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠙⢧⡀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠈⠻⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠾⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠉⠉⠉

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⠶⣶⡶⠶⣶⡶⠶⣶

⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠢⡀⠀⣀
⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⡉⠍
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⠀⢀⠀⢀⠀⢀⠀⣤⠀⢘⡇⠀⢀⠀⢀⠀⠀⠀⢠⡄⠀⣉⠀⡀⠀⢀⠀⠀⠀⡁⠖⠀⠁
⣿⡿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠃⠈⠲⢄⠀⣿⠀⢸⡇⠀⢸⡆⢾⠀⠀⠃⢸⡆⠀⣿⠸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠂⠀⠈⠀⠈⠀⠈⠀⠈⠁⠀⠈⠁⠈⠑⠀⠀⠀⠁⠀⠉⠀⠉⠒⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠀⠀⠿⠀⠀⣟⠀⠈⡇⢠⠁⠀⢹⠄⢻⠀⡇⠀⠣⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠛⠀⠀⠛⠀⠀⠛⠈⠃⠀⠘⠀⢻⠀⠓⠀⠂⠀⠃⠀⠀⠰⣶⣿⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠸⣶⣝⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⡀⣀⣿⣿
⠀⢠⣀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠌⠳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⡾⢷
⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⢀⣸⡇⢸⡤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣀
⠀⠀⠀⣴⠋⢭⣾⣇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⡀
⠀⣀⣴⠉⠑⠒⠮⠭⠭⢭⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠖⠚⠉⢧⣄⡀
⣎⡀⠳⠤⢤⣀⣀⣀⣀⡀⠀⣀⣀⠀⣀⠀⠀⣀⣀⣀⣀⡠⠤⠜⠀⣹⡆
⡧⢭⣓⡲⠦⠤⠤⠤⢌⣉⣉⣉⣉⣉⣉⣉⣉⣁⠤⠤⠤⠴⠒⣚⣫⢽⠃
⢸⠀⠀⠉⠉⠑⠒⠒⠒⠒⠲⠶⠶⠶⠖⠖⠒⠒⠒⠒⠊⠉⠉⠁⠀⢸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠶⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡾
⠀⠸⡇⠀⠀⠀⠈⠉⣉⠙⠓⠒⠒⠒⠒⠒⠒⢚⡉⠉⠉⠀⠀⠀⡇⠀⠀⠀⣠⠴⠶⠦⣄
⠀⠀⡇⠀⠀⠀⠀⣼⠿⣦⠀⠀⠀⠀⠀⠀⢠⡿⢿⡄⠀⠀⠀⣠⣧⠤⠴⢮⣁⣀⣀⡀⠀⠳⣄⣀⣠⠤⣴⡤⠤⠶⠲⠤⠤⣄⡀
⠀⠀⢳⠀⠀⠀⠺⠃⠀⠹⠇⢀⣀⣀⣀⠐⠟⠁⠈⠿⣠⠖⠋⠁⢀⣀⣤⡴⠞⠉⠉⠉⠻⣍⠉⠉⠉⠉⠙⠓⠒⠲⠤⢤⣀⠀⠉⠓⢦⡤⣀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡧⠀⠀⢠⠞⢁⣠⢔⡾⠟⠚⠉⠀⠀⠀⢀⣀⣀⣬⣷⣶⣮⣉⣉⣉⠉⠒⠲⠤⢤⣍⣓⣦⣄⠳⡈⠳⡄
⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⣿⣿⠉⢻⠇⠀⢀⣏⠔⣫⠖⠉⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠓⠦⣄⡀⠀⠀⠈⠉⠙⠳⡄⣙
⠀⠀⠀⡷⠤⢄⣀⣀⠀⠀⠀⠈⠻⠶⠋⠀⠀⡼⢣⠞⠁⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⣇
⠀⠀⠀⢱⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠋⠉⢹⠁⡏⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⡿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠄⣼⠋⠀⠀⠀⠀⠀⠈⢓⢦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠚⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⠋⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷⡸⣴
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢹
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠎
⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠦⠤⠤⠤⠤⠴⠶⠶⠚⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠦⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠴⠶⠖⠛⠋⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠿⠿⢿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣶⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠈⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣠⣤⣤⣤⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⢿⣿⣄⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⡿⠛⠋⠙⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣿⣿⡄⠀⠸⠿⠿⠿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⡿⠛⠃⠀⣀⡀⠀⣀⣸⣿⡇⠈⠉⠛⠛⠛⠛⠉⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⣿⡀⠀⣀⣼⣿⣿⣿⣿⠿⠋⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠉⠛⠻⠿⠿⠛⠋⠀⠀⠀⠘⠿⢿⣿⠿⠟⠁⠀⣀⣠⣤⣶⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⢠⣿⣿⠁⠀⣾⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⣠⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠈⠀⠀⢀⣤⣤⣤⣄⣀⣀⣴⣿⣿⠿⠿⠿⣿⣿⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣰⣿⡿⠿⠿⢿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡌⢿⡀⠀⠀⠀⢀⡔⠂⠁⠀⠀⠀⠀⠀⠀⢠⡾⣣⠶⣤⡀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣠⣄⠁⣤⢀⡀⡄⠀⠀⠂⣤⠤⠄⠐⠀⠀⠀⠀⢸⡀⢸⡧⠈⠣⡄⠀⠠⠉⠶⠀⠀⠀⠂⠀⠀⢀⡰⢿⣜⡱⢶⡌⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤
⠀⠀⠉⠉⠉⠀⠸⠼⠃⠇⠀⠀⠺⠶⠒⠺⠛⠁⠀⠀⠀⠘⡗⠈⠡⠀⣰⠇⠀⠀⠤⠼⠒⠈⠤⠀⠀⠀⠚⢵⢏⣺⡷⠋⠀⠀⠀⠀⠀⠂⠀⢺⣗⣤⠟
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠛⠁⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠰⣦⠙⠃⢰⠀⠀⠀⠛⠿⣿⡿⠛⠁⠀⠀⠀⠃⣀⠈⠓⢄⣤⠀⠀⠀⢠⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢞⠁⣽⠆⠉⠀⠀⠀⠀⠛⠇⠀⢀⠴⠋⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⣴⠏⢠⣤⠀⠙⠃⠀⠀⠀⠀⢠⠙⠃
⠀⠀⠀⠀⡀⠻⠀⠀⠀⠀⠀⠧⠀⢠⣠⡤⠀⠁⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠙⣁⣠⣤⣤⣤⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⣦⠤⡤⠀⠀⠀⠀⠀⠙⠇⢠⣄⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢘⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡉⠀⠀⠈⠀⣀⠀⠐⢦⡀⠀⠛⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡷
⠀⠀⠀⠀⠀⢾⡧⣴⠄⠀⠀⠧⠀⠁⠀⠈⠀⠀⠛⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡆⠀⠀⠀⠒⠃⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠘⢷⠜⠃⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⢀⣴⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠉⠟⡄⠀⠀⠀⠀⢰⠄⠸⣀⡴⠆⠀⡀⠀⠀⢄⠀⢰⠀⠀⠀⢠⣴⣶⣶⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡇⠀⠠⣠⡁⣠⡤⠘⠋⠀⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠉⢀⡰⠶⠃
⠀⠀⠆⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠈⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⣩⡁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡗⠀⠀⠰⠟⠆⠀⠀⢀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⠄⢨⠀⡀⠚⠁⠀⠀⢀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠈⠀⢀⠟⠀⠀⠀⠂⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣟⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠐⢣⠀⠈⠒⠂⠀⠀⠀⠀⠠⢠⡄⢠⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠟⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⠜⠃
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣴⠶⠿⣷⣶⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣦⠀⠀⢠⣶⡄⠀⠀⠀⢦⠀⠘⢇⠀⠀⠀⠀⠀⢀⣤⣤⣠⡄⠠⠶
⠀⠱⣤⣤⣄⣄⣰⣤⠆⠀⠀⠙⢿⣤⣿⣦⡼⠇⠀⠀⡀⠀⠋⠉⠃⠀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠰⠀⠀⠸⠃⡰⣿⡟⢶⡏⠓⣤⠀⢿⠯⣍⡼⠇
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠴⠶⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠈⢱⣏⣠⠼⠷⠞⠁⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⣤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⣄⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠆⣠⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢲⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠺⠀⠀⠠⠀⠀⠀⠈⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠠⠀⠀⢑⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠀⠀⠀⢠⣬⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠄⠀⠄
⠀⠀⠀⠼⠃⣀⠴⢟⠀⠀⠠⠖⠐⠒⠀⠈⠆⠀⠀⠀⢴⣬⣿⣷⣤⡈⠀⠀⠀⠀⠀⣰⡀⠊⣱⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠒⠶⠐⠿
⠀⠀⠀⠲⠀⠙⢄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠋⣹⡄⢣⡷⠀⠀⠀⠀⠂⠙⠁⡟⠁⠀⠀⠀⠘⠛⢃⣀⡄⢶⡄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⢠⣤⣤⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠐⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡄⠀⠀⠀⠀⣀⣤⣴⠾⠟⠂⢀⠀⠀⡤⠈⠀⡀⠺⠆⠀⠀⠀⠀⠘⠛⠛⠂⠀⡄⠀⠀⠀⢈⠛⡀⠀⠰⣺⠉⣧
⠀⠀⠀⢶⣿⠿⠃⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⣶⠟⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠦⣿⡶⠀⠀⠀⢄⣠⡀⣀⣸⣀⡲⠐⠀⠀⠀⠀⢀⡀⠀⠀⢑⠊⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠐⠋⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠺⢀⢈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡛⠏⠙⢻⡋⠉⡟⠛⢻⡙⠏⣙⡿⢛⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤
⠀⢀⣀⡀⡀⢙⠁⠀⠄⣀⡀⠀⠀⠀⢰⡁⣷⠘⢆⠀⠀⠮⠀⠀⠀⠀⠀⣤⣿⣮⡟⠀⠀⠀⠀⢀⣠⣄
⠀⠉⠉⠁⠐⠋⠓⠀⠐⠓⠒⠋⠀⠀⠈⣇⠈⣀⡜⠀⠀⠐⠒⢐⠀⠀⠘⠿⣽⠟⠀⠀⠀⠀⠀⠺⠷⠟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢞⠉⠀⠀⠀⠀⢀⠀⡠⡄⠀⠀⢀⡰⡖⠃⡄⠀⠘⠚⠿⠟⠃⠀⠀⢀⡁⠀⢤⡀⠀⠰⠷⣾⠿⠄
⠀⠀⠀⢠⠆⠀⠀⢠⠐⠐⢋⠀⠀⠀⢈⠁⠄⠊⠀⠀⠀⠀⠀⠀⣠⠄⠰⠋⣐⣂⠀⠁⠀⠀⠐⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠄⠀⠀⢈⠁⠶⠄⡀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠉⢳⡄
⠀⠀⠀⠰⣦⣤⠀⠰⠁⠀⠀⠀⠚⠀⠈⠁⠀⠀⠁⠀⢠⣤⣀⣤⡄⠀⠀⠘⢀⣀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⢠⠐⣀⡤⠀⠀⠀⡀⢠⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⡀⡀⣤⡈⠀⠠⠤⠴⠊⠁⠀⠀⠤⠄⢀⡀⠀⠀⠘⠄⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠐⠒⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠈⠀⠀⠈⢀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠲⡀⠀⠀⠀⠐⠀⠀⡀⣂⢢⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠿⠞
⠀⠀⠀⠓⠄⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⡀⠰⡆⠀⠀⠀⠀⣀⠀⠀⣀
⠀⢦⣤⣤⣤⡴⠀⠐⠿⣽⣦⠿⠀⠀⡀⠊⠑⢀⠀⠀⠉⠁⠀⠉⠡⠀⠰⢁⢶⠦⣔⢢⡀⠾⢏⡽⠃
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉
⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠰⡆
⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠀⠘⢻⡙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠿⠄⠀⠀⠀⠀⢦⣤⡤⠟⠁
⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠁⣠⡆⠀⠠⠄⠂⠴⠈⠀⠀⣀⣿⣄⡑⠀⠀⠀⢀⠀⢢⠀⠀⠀⠀⠀⠛⠃⠈⠀⢠⡤⡤⢤⡄
⠀⠀⠀⠈⠂⠀⠀⠀⢀⣀⠀⠀⠀⠤⠟⠽⠑⠷⠀⠀⢀⡘⢑⡎⠀⠀⠘⠋⣤⠀⠆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⠂
⠀⠀⠂⣀⡀⠀⠀⠀⠀⠉⡄⠀⠀⢀⣠⡴⠶⠂⠀⠀⠀⠀⡀⠒⠀⠀⠀⠒⠒⠂⠤⠀⠀⠘⠃⠀⢴⢓⡄
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣀⠀⠿⠁⠀⢀⣶⡤⠼⠶⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣷⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣠⣈⣡⡘⠋⠀⠀⠀⠀⠀⢀⡀⠄⢀⡀⠴⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠑⠀⠐⠈⠀⠀⠀⠈⣅⣀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡠⠃⠀⠀⢀⠀⠀⠀⠀⠀⠁⡀⠐⠁⠀⡀⢀⠀⠀⠁⠀⠠⠀⠀⠠⠀⠊⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂⠠⢐⠡⠂⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠋⢉⠡⡉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡆⢠⠋⠀⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢋⠀⠂⠀⠐⠖⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁⠀⠀⢀
⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠰⢄⠰⠄⠤⠂⠀⢀⡤⠠⠀⠆⠆⠰⠀⠀⠀⠀⠜⠢⢀⡠⠄⠤⠄⢠⡤⠀⠰⠄⠠⠀⠀⡠⠄⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠰⠂⠸⠀⠀⠀⠀⠀⠀⠠⠤⠥⠀⠐⠀⣈⢐⠂⠀⠀⠃⠠⠄⠆⢀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠙⠂⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠐⠒⠀⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠠⠄⠀⠂⠀⠀⠀⠠⢉⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢉⠁⠀⠂
⠇⠀⠈⠀⠑⠦⠠⠄⠀⠈⡄⠀⢀⠤⠆⠀⠈⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠒⠀⠀⠸⡀⠀⡇⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠥⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠒⠈⠀⠄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⡀⠀⢠⡴⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠬⢉⠡⡐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠈⠁⠀⢠⣰⡀⠀⠀⠀⠠⠀⢀⠀⠀⢀
⠀⠀⠀⠂⠐⢊⠢⠀⠀⠀⠀⠀⣈⠀⠤⣴⠁⠀⠀⠀⠀⠁⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂⠀⠂⠀⠀⠐⠂⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⣛⣿⣍⣉⣿⠛⢛⣻⣿⣭⣿⣷⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣡⣶⡿⠛⣿⠟⢉⣵⠾⠛⠉⠉⠁⠀⠀⠉⠉⠛⠻⣧⣄
⠀⠀⠀⠀⠀⠀⢠⡾⠋⣤⣾⠿⣶⣴⠶⢟⣴⠟⠁⠀⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢠⡿⢁⣾⠟⠀⢀⣸⡏⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠠⡄⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣾⠃⣰⡿⠶⢾⡟⠉⣰⡟⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢰⡟⢸⣏⠀⢠⣼⠇⣴⠟⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠰⠂⠀⠀⢹⡇
⠀⠀⠀⠀⢸⡇⣿⡅⠀⢻⡇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢸⣿⡏⠁⣴⠟⣽⠏⠀⠀⠘⠃⠀⠀⠐⠇⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⣇⣀⣿⣾⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠾⠏
⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⢀⣼⣀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠉⠀⠒⠂⠀⠀⠀⠀⠒⠂⠈⠉⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⢺⠤⣄⣀⣀⣀⣀⣀⠀⠀⠠⠐⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⠚⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣀⡠⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠒⠋⠍⢀⡠⠚⣳⢦⡀
⢀⣀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡀⠀⠀⠁⠀⠉⠀⠉⠙⠳⢄⡀
⠀⢆⣿⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠤⢀⣀
⠀⢌⠛⡙⢷⣦⣤⣠⡤⠄⠀⠀⠀⠀⢀⣀⣀⣬⢴⣯⢠⣼⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⡷⠤⠒⣟
⠀⢀⣷⡊⠐⠶⠒⠿⣏⣹⣛⣻⠋⢭⣍⣡⣤⣀⣉⢩⣾⠁⠀⠈⠐⢄⠀⣠⠶⣾⡿⠋⣹⣏⣉⣉⡤⣤⡴⣞⣋
⠀⢸⠩⡓⠶⣄⣀⠀⠀⠀⠈⣑⠀⢀⡰⠀⠈⠭⠤⠎⣿⡀⡀⡄⠀⠀⣼⠉⠲⡌⠀⢮⡌⢿⠑⢺⢥⡂⠌⣓⡽
⠀⠈⠳⠄⠀⣄⡈⠛⠀⠤⡄⠀⣄⠉⣀⠀⠀⡀⢠⠞⢱⠙⢤⢣⠆⢸⣿⡇⢸⣌⣵⠪⠷⣘⡆⢘⠶⠼⠷⣧⡂
⠀⠐⡀⠀⠈⠉⠉⠉⠁⠒⠚⠃⠈⠛⠁⠀⠁⠈⠁⡀⠎⠀⠀⠙⢄⣋⠹⣧⠀⢿⠮⣉⡛⢒⠯⡴⣷⠒⠒⠓⠁
⠀⠀⠈⠁⠐⠒⠒⠂⠤⠤⠤⠤⠤⠤⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠙⡄⠹⡦⡞⢡⣈⢙⠆⠑⢌⣻⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⡐⡴⢳⠀⠀⠀⠀⠀⠁

⠀⠑⠶⠕⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠁⠓⠁⠐⠁⠀⠀⠀⠰⠈⠀⠄⠀⠀⠀⢠⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚

⣰⣖⠀⣺⡂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠰⢀⡁⠀⠀⠀⠀⠀⢀⠄
⢨⠇⠀⢹⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⢡⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡤⣀⠀⡄⠀⠀⠀⠄⢘⠀⠢⠀⠀⠀⠀⡁⠀⠀⡀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠉⠉⠃⠀⠀⠀⠀⠦⢀⡁⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠈⠀⠀⠀⠆⠀⠀⠀⠘⠙⢐⠂⡀⠀⠀⠀⠀⡬⢁⡃⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⢀⣤⣦⢄⡀⠀⠀⠀⢈⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⢵⡅⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠋⠃⠃⠀⠀⠀⠀⠀⢐⡀
⣿⣿⠿⠿⠻⠿⡿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠐⣀⣴⣿⣿⠏⠀⠀⠀⠈⠋⡀⠀⠡⠁⡀⠀⠤⠀⠔⠀⢀⠀⠀⡀⡀⠁⢀⠄⠀⠀⢼⠿⠟⠻⠿⠿⣷⡀
⠀⡀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘⠟⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠐⠆⠉⠛⠁⠉⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⣜⣠⡖⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⡐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣐⢎⠗⣼⣷⡱⡀
⠀⠀⠉⣠⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡿⢷⣮⠡⠊⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⢯⣠⣴⣾⠫
⠀⠀⠀⡆⢀⠀⠀⠀⢀⡴⠖⣢⡶⢶⡄⠀⠘⠀⠀⠀⠸⢛⠿⠟⠀⠀⢀⠂⣵⠁⠀⡱⢍⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⢰⠀⢠⡿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⠀⠇⠀⠐⠀⢀⠀⠀⢶⡷⣷⠆
⠀⡄⠰⠔⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⢄⠀⠀⠠⠀⠀⠀⡀⠔⠃
⠀⠀⠀⠀⠀⠈⠊⠀⡄⠄⠀⠀⠀⠀⠀⣥⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢇⠀⠀⠠⠀⠢
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠈⠂⠀⠀⡀⠀⠀⠘⠒⠂⠀⠐⠂⠈⠀⠀⠀⠀⠈⠊⠠⠀⣀⣀⠁⠎⠀⠄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠘⣇⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⣷⣀⠤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠰
⠀⠀⠀⠀⠳⠄⠔⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠂⠀⠀⡠⠄⠒⠂⠐⠀⠄⠀⠀⠀⠁⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⢀⡧⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⢈⢘⡀⠀⠀⠆⢀⠀⡄⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠱⡀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⠰
⠀⠀⠀⠿⢤⣀⣀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⢰⡀⢀⠄⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⣉⠉⠉⠉⠉⠉⠀⠀⢠⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡂⡒⠠⡀⠀⠄
⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⢦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠄⠠⠀⠈⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡉⠀⠀⠀⠈⣆⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⡀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠂⠀⠃⠀⠀⠀⠆⠀⠀⡀⣀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣝⠠⠐⠓⠀⠒⠒⠊⠁
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⡀⠄⠊⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⡈
⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠉⠑⠚⠒⠋
⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠤⠤⠀⠀⠉⠀⠀⠐⠦⡀⠀⠀⢎⠀⣈⡀⠠⢀⣠⠀⠀⠀⠀⠤
⠀⠀⠀⡡⣈⢹⡒⠒⡢⡄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⠙⠃⠀⠠⢠⠈⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠒⠚⠀⠈⠉⠉
⠀⠀⠀⠣⠈⠀⠂⠀⠤⠢⠌⡀⠁⠀⠀⢰⣀⠀⠀⡄⠀⠀⠀⠠⠀⠰⠀⠀⢉⢀⡘⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠳⢄⣇⡀⠐⠂⠂⢀⣆⠀⠄⠐⠁⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣰⠛⠻⡆
⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⢻⡏⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⣏⡸⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠦⠶⠛⢻⠶⣤⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠓⠲⢤⣤⠶⠛⠉⠀⢹⡆
⠀⢀⡾⣧⣀⣈⣇⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡿⢀⣴⣋⣙⣦⣭⣹⡟⢷⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠘⣇
⣴⣯⣤⡟⠁⠈⠙⢷⣄⠀⠀⠀⠈⠉⠛⠲⢶⢺⠀⠀⠀⠀⣾⣼⣶⣫⡟⠉⠉⢳⣤⠏⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢰⡏⠀⠀⠀⠙⣧⠀⠈⠛⢦⡀
⠀⠀⠘⣇⠀⠀⠀⠀⠉⠻⢶⣤⣤⣤⣤⠤⠚⠾⠅⠀⠀⠀⢹⡀⠈⠉⣉⠛⠋⡿⠃⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⠟⠀⢸⡆⠀⠀⠀⠀⡿⠀⠀⠀⠈⣷
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠉⠉⠙⢲⡴⣷⠀⠀⠀⠀⠀⢳⡀⠀⠉⢀⡼⠁⠈⠁⠀⠀⠀⢷⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙⠶⠤⠶⠚⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣤⣤⣤⠴⠿⣄⡇⠀⠀⠀⠀⠀⠀⠳⣄⢀⡞⠁⠀⠀⠘⠃⠀⠄⠘⡆⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⠀⠈⠉⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠘⠃⠀⠐⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠁⠀⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⡛⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄⠀⠈⠛⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣧⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⢳⣤⡏⢻⣆⣠⣯⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠘⢧⣄⠀⠀⠀⣿⢠⡆⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⣀⡈⢳⡏⠉⣻⣾⠙⣧⠈⢿⣹⠆
⠀⢀⡶⠒⠒⠒⠒⠚⠛⠛⠛⢛⣛⣛⣻⣆⠀⠀⠀⠀⠀⠀⣟⣉⣉⣉⣉⣹⠂⠀⠀⢿⠘⡇⣠⡤⣤⣴⣿⠟⠁⠀⠀⢸⣏⣉⡙⠳⢴⡃⣿⢰⡿⣧⠀⠻⡄
⠀⠘⠹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠀⠀⠀⠀⠀⡴⠟⠉⠉⠉⠉⠉⠲⣄⠀⠸⠀⠀⣿⡀⠁⢹⡇⠀⠀⠀⠀⠀⢀⣀⡿⢦⠀⠙⢧⣸⠃⣼⣆⣀⣽⡦
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠆⣰⠛⠛⠻⣿⢦⡼⠃⠀⠀⠀⠀⠀⠈⢿⠙⠛⠓⠒⠚⠛⠚⠛⠉⠁⣼⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣄⣹⣦⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡏⠀⠉⢻⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣠⠶⠛⠶⣿⣶⣦⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡀⠀⢸⡇
⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⢁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣿⣿⠷⠮⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠲⠶⢤⣄⡀
⠀⠀⠀⢀⣾⡭⠽⠧⠬⣍⡉⣿⣋⣽⣇⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⡴⠶⠶⢶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⡀⠀⠀⣤⠀⠈⠙⠳⢦⡀
⠀⠀⣠⠞⠁⡀⠘⠀⡀⠈⠙⢦⡀⣽⡛⢯⡉⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋⠰⢦⠀⣤⠈⠁⣠⠌⠛⢦⡀⠀⠀⠀⠀⠀⠀⢸⣧⣌⠉⠛⠻⢧⣄⣀⡄⠀⠀⠙⢦⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠉⠀⢠⠀⠙⣦⠙⣿⢛⣷⠘⡆⠀⠀⠀⠀⢾⠀⠞⠀⠀⠀⠈⣠⠄⠀⠴⠖⠈⢷⠀⠀⠀⠀⠀⠀⢸⣇⠊⣷⠀⠀⠦⠈⠙⠳⣄⣠⠆⠀⠹
⠀⠀⠹⣄⠉⠀⠠⠄⠀⠀⠀⠀⢠⠌⣧⠉⢻⣽⡆⡇⠀⠀⠀⠀⠈⡿⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⣾⠇⠀⠀⠀⠀⠀⢸⣏⡴⠏⢠⠖⣛⣉⣽⡳⣬⣻⣦⡤⠶
⠀⠀⠀⠈⠳⢦⣀⠀⠀⠰⠆⠀⠀⠀⠘⡇⢸⢉⣷⠇⠀⠀⠀⠀⢰⡟⠖⠛⠛⠳⢶⠶⠛⠉⠳⠶⠞⣩⡷⠀⠀⠀⠀⠀⢸⡁⠀⠀⣟⢾⣙⣧⣷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠐⠀⠀⢻⠟⢫⠏⠀⠀⠀⠀⠀⠀⢻⡗⠛⠛⠛⠛⠻⢿⣝⡛⠛⠋⣹⠃⠀⠀⠀⠀⠀⣾⠛⢳⣀⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣸⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣀⣨⡿⢦⠾⠃⠀⠀⠀⠀⠀⠀⠿⠖⠋⠁
⣶⣶⣶⠶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢰⣿⣿⠂⠀⠀⢀⡄⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡧⠛⢞⢩⢿⣿⣿⣏⣓⣶⡶⠓⣇⣀⣈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣤⣾⠛⣭⣀⠇⢀⣠⡁⢸⣿⣿⣓⣁⣾⣄⣠⣋⡉⣓⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠿⣿⣷⣴⠒⣿⣷⢲⣷⡾⠟⢛⣛⡭⠁⠄⠖⢀⠐⠛⠻⣿⣿⡿⣧⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⡄⢸⢿⣿⣷⡽⠟⠉⠙⠃⠄⠘⠚⠀⠀⠂⠐⠀⠀⠻⠀⢉⠛⢿⠺⣝⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡛⠓⠒⠷⣏⣧⣿⡏⠒⠀⠀⠀⠁⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠐⠀⡈⠀⠂⠈⡳⣽⣄
⠀⠀⠀⠀⢰⠿⢆⣾⣳⡤⢤⣦⠞⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣸⣶⣤⠀⢘⡆
⠀⠀⠀⠀⠈⠓⡾⠋⢽⣶⣶⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⠀⠀⠐⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⣠⣾⣥⣤⣬⣿⣿⡄⠀⠈⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢀⣼⠵⠚⠉⠁
⠀⠀⣠⣾⣿⣿⠿⠟⣿⣿⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣀⣤⠶⠚⠉
⠀⠐⣿⣿⣟⠁⢾⣿⣿⠉⡤⢀⠀⠀⠀⠀⠁⠀⠄⠀⣀⡤⠖⣻⡿⠖⠋⠁
⠀⢠⣴⢧⢨⣟⡥⢾⣿⡄⠀⠄⠀⠀⢀⣯⣯⠀⢒⣫⡵⠞⠋⠁
⠀⠘⠮⠥⠜⢣⢠⣿⢹⠃⠀⠀⠀⠠⢀⣨⠴⠚⠉
⠀⠀⠀⠀⢀⣧⣿⣿⣿⣖⣶⡤⠷⠛⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣈⠫⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠨⣥⠀⠙⣃⠀⠐⠀⠀⠀⠀⠐⠈⠁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⢰⣋⠰⠿⠀⠺⠽⡀⠀⡀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡦⠁⣤⠠⢞⡇⠠⡇⠀⡀⠀⠀⠀⠀⢤⢆⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⡇⢸⠅⣐⡋⢈⠧⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠄⠐⠀⠂⠒⠸⢎⣀⡚⣠⢀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⣫⣑⠂⢦⡀⠀⠀⠀⢠⣴⣶⣤⣤⣤⠒⠀⠀⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣙⣤⠤⢤⡃⠀⠐⠿⣿⣿⣿⣿⣿⡓
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⡋⢈⡂⡁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⡷⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⢄⡀⠀⠹⣿⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠉⠀⠀⣀⣄⠀⢀
⠀⠀⠀⠀⠘⢷⣤⣄⣀⠀⣀⣠⠜⠁⠀⠀⠀⢀⠀⠘⣄⠀⠤⠂⠀⡅⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠰⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠠⢒⠀⠀⠀⠀⠀⠀⢀⣞⠁
⠀⠖⠶⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡜⠁⠀⠐⢤⡹⠀⠈⡀⠀⠀⠼⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⠀⠀⢠⡄⠀⡠⠀⠀⠀⠀⠀⠉⠡⠀⢁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⠀⠀⠀⡀⢤⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣭⡢⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀
⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡀⠠⠀⠤⢠⠀⠀⠀⣀⡀⢠⣠⠄⠀⠀⠀⠀⠀⡀
⠈⢀⠰⢒⣶⠀⠀⠀⠀⢘⠓⢀⠿⡅⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠐⠻⠋
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⣠⡄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⢀⣀⣀⠀⡀⠀⠀⠀⢀⠁⠈⠀⠀⠀⣼⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠂⠀⢀⠁⡀
⠀⠢⠀⠀⠀⠀⠘⠁⠀⠰⡄⡀⠁⠀⠀⠀⠀⢉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠔⠈⠀⠈⠐⠠

⠀⠀⢀⣀
⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠆
⠀⢰⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠉⠀⠀⠀⠂⠀⠀⢠⣄
⠀⠸⠀⢸⠀⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⢀⡴⠒⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠀⠀⠠⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠄
⠀⠀⠀⡎⠤⠠⠂⠲⠅⠀⣧⠀⠀⠀⠀⠐⣿⠽⠯⠿⠽⢿⡇⠀⠀⠀⠀⠀⠐⣏⠴⣠⣄⣰⡿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠘⠢⢴⡁⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⠡⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣰⠁
⠀⠀⠀⠈⠓⠧⣤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⠖⡛⠉⠉⢉⡉⡙⢦⠀⠀⠀⠀⠀⠀⢀⣖⢒⣆⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠓⠲⣄⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⡶⡄
⠀⠀⠘⣎⡔⠜⠓⢼⠵⢈⠟⠀⠀⠀⠀⠀⢰⡉⠤⡠⠭⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⢿⣯⢿⢹⢻⣽⠇
⠀⠀⠀⠘⣄⣸⡃⣭⣰⠏⠀⠀⠀⠀⠀⠀⢸⠄⣀⡼⡀⣼⠂⠀⠀⠀⠀⠀⣷⣦⣤⣼⣧⣤⣴⡇⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡗
⠀⠀⠀⠀⠘⣏⡵⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠜⠁⠀⠀⠀⠀⠀⠈⠲⣀⣓⠉⢀⢛⡸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠂⠀⠀⠀⠀⢠⠋⣿⢁⣾⡇⢳⠀⠀⠀⠀⠀⡶⢷⣾⡶⣄
⠀⠀⢠⢴⠞⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟⠻⣴⡇⠘⡇⠀⠀⠀⠀⡏⢦⢻⣿⣿⣆
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢴⡖⠚⣛⣛⡒⢲⡆⠀⠀⠀⠀⠀⣧⠀⣫⡴⢛⡆⠀⡇⠀⠀⠀⠀⡇⠀⠱⡻⣿⣿⣄
⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⣤⣀⣀⡀⣀⣸⠃⠀⠀⠀⠀⠀⢣⠀⢿⠙⢺⡇⢠⠃⠀⠀⠀⠀⡇⠀⠀⠙⢝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡏⠛⠛⠻⠟⢻⠀⠀⠀⠀⠀⠀⠘⣄⣸⣞⢋⣧⡼⠀⠀⠀⠀⠀⠧⠤⣤⣄⣈⣮⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡏⠉⢳⠏⠉⢷⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢱
⠀⠀⠀⢠⣇⡀⣀⢆⣀⣾⠀⠀⠀⠀⢀⡤⠚⠉⠁⠆⠉⠑⢦⡀⠀⠀⠀⠀⣀⢔⠚⠿⠟⢷⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡾⡛⠁⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⣸
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠀⠀⠀⠸⣽⡀⠀⠀⠀⠀⠀⠀⢀⣞⡶⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠸⡀⠀⡸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⣖⡒⠒⣲⠾⠛⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠓⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠤⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢇⣀⣬⠗⠒⠐⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠂⠈⠀⠀⠀⢀⠀⠀⡁⠠⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠈⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⢠⡀⠀⠐⠄⠀⠇⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠁⣀⣠⢰⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠂⠀⠁
⠀⠀⠒⠁⠦⢀⢀⡀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠎⠋⠉⢁⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⡠⣄⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠐⠂⠀⠀⣀⠄⠐⠆⠁⠀⠉⢁⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠈
⠀⠀⠀⠀⡀⠀⢄⡤⠴⠀⠐⠚⠁⣀⠀⠤⠀⠒⠀⠛⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⠃
⠀⣀⠀⠀⠀⠐⠀⠀⠀⠐⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⢀⠀⠀⢐⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠂⢈⠃⠀⠀⢀⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔⠉⢀⡂⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⡤⢀⠀⠄⠈⠁
⠀⠀⠃⠀⠑⠀⠐⠒⢐⡋⠁⠀⠀⠆⠤⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠁⠀⠶⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠀⡀⠀⠐
⠀⠀⠀⠈⠉⠂⠀⠠⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⢀⠆⠁⠔⠁⠀⢸⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠈⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠥⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠈⠁⠀⠀⠀⠀⠀⢰⠀⠸⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠰⠀⠀⠘⠀⠐⠚⠉⠂⠀⠀⠤⠤⠄⠂⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⡄⠐⠾⠒⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡄⠀⠀⢀⢰⠘⠀⣅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠐⠠⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⠐⠒⠀⠈⠒⠀⠛⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠉⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣌⢀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀
⠀⠀⠜⠁⠉⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢤⠀⠂⠀⠉⠁⠀⠀⠀⠂⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢃⠀⠀⠀⠰⡄⢈⢉⠉⠁⠀⠀⢀⠈⠠⠦
⠀⠈⠀⠀⠀⠀⢒⠀⠀⠀⠀⢸⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⡀⠈⢁⠀⠀⠈⠠⡀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⢲⣄⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣀⡀⡀⣰⣆⡈⢠
⠀⠀⠻⠀⠘⠉⠉⠈⢡⠃⠀⢸⠀⠀⠀⠀⠐⠤⠄⢩⣈⣁⣭⡥⠤⠶⢦⠀⠀⠀⠀⠀⠀⡄⠀⡀⠁⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠐⠒⠤⠄⡀
⠀⠀⠀⠈⠁⢀⠀⡉⠁⠀⠀⠈⠀⠀⠀⠘⡇⠠⠀⠀⣄⠰⡆⠠⠄⠀⢸⠀⠀⠀⠀⠀⠀⡧⢠⠂⠁⠑⠦⠆⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠂⠘⠐⠁⠀⢀⠈⢤
⠀⠀⠀⠀⠐⣶⢄⡀⠀⠀⠀⢨⠀⠀⠀⠀⠳⡀⠉⠈⠉⠀⠂⠐⠈⠀⠟⠀⠀⠀⠀⠀⠀⠂⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⢘⣋⠉⢀⠘⠃⠙⠈⠀⡼
⠀⢰⠀⠀⠀⠄⠀⠀⢄⠀⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠤⣀⡈⠉⣉⡈⣀⡤⠊
⠀⠀⢄⡀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠚⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⠉⠁⠀⠀⡀⠂⠀⠀⠀⠀⠰⣤⡀⡀⠉⠉⠉⠉⠀⣀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠤⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠁⠀⠀⠀⠀⠉⠈⣆⠈⠁⡎⠀⠂⠀⠑⡄⠀⠀⠠⠁⡠⠖⢄⠠⠕⠌⠀⠀⠀⠀⠀⠃⠠⠀⡠⠂⠀⠂⠁⠀⢅⢜⠀⢀⠄⠒⣄⢤
⠀⠀⠀⡀⠀⠤⠀⢐⠊⢮⡀⠀⠳⡀⠈⠆⢄⠀⡆⠀⢇⣀⡠⢀⠔⠀⠀⠀⠠⠀⠀⢀⠀⡀⢀⠊⠀⠀⠈⡰⠁⢠⣤⡉⠀⠓⠒⠂⠌⠉
⠀⠀⠐⡲⠤⠁⠀⡀⢈⠠⠃⠀⠀⠑⠢⣈⠠⡑⠘⠀⡀⢒⢝⣱⠀⠀⠀⢠⢁⣄⡀⡈⠀⠃⠂⠀⠀⢀⠜⢡⠀⠀⠀⠀⠄
⠀⢰⡀⠐⢒⠂⠀⠀⣠⠄⡒⢢⢂⠒⠠⣀⠀⠁⢀⣾⠅⠘⡮⡞⠀⠀⢢⡐⠁⠀⠰⠀⠀⢈⠐⢄⠔⠁⠀⠀⠏⠑⠒⠂⠀⠀⠀⠈⠁⢄
⠀⠀⠁⠀⠘⠀⠠⠊⠄⠄⢀⢁⠂⣬⠤⣂⡗⠀⠈⠁⢀⠀⢹⠃⠀⠈⠙⠥⢀⣀⢾⡢⠄⠈⠀⠁⠠⢁⠂⠀⠑⠒⠊⠀⡄⡘⠂⡄⠀⠈
⠀⠀⡏⠙⡆⠀⢡⠬⢉⠭⠆⠤⠔⠊⣉⡴⠀⢸⠉⠉⠑⢢⠈⠁⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⣀⣀⣀⠁⠐⠗⠀⠐⠀⠀⠀⠀⠐⡀⠠
⠀⠀⡷⢀⠘⢄⠀⠐⠒⠒⠒⠒⠋⠉⠀⠀⠀⡌⠀⠀⠀⡷⠀⢀⠠⠀⠠⡊⠘⠀⠀⢠⣾⣿⣻⣟⣙⣷⠀⢠⠀⠀⢠⡀⠀⣰⠃⢀⠋
⠀⠀⢧⠐⠂⡸⠀⠀⠀⢖⠒⠂⠠⠤⠐⠲⠂⠙⠀⠒⠊⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⡀⢀⠿⠁⠀⠀⠀⢃⠐⢀⡀⠐⠀⠀⠈⠉⠁
⠀⠀⠈⠉⠉⢁⠔⣄⡀⣄⠉⠀⠒⠒⠈⠁⠀⠀⣀⢒⣂⠀⠀⡠⢀⡀⠀⠒⡲⢲⠀⢡⠀⠀⠀⡙⠅⠨⠀⢀⡀⢇⠀⠀⣠⠈⠣⠈⠀⡆
⠀⢌⡀⠅⠀⠂⠀⠈⠀⠈⠀⠀⠀⠊⠖⣂⡎⠧⠓⢃⠜⣠⡄⢰⠀⣀⣀⡀⠁⠁⠀⠀⠐⠂⠀⠐⠀⠁⠰⠀⠀⠉⠀⢐⠁⠀⡠⠋⠑⠕
⠀⠀⠀⠀⠌⠀⠀⠄⠠⠀⢸⠆⠈⢉⡀⢁⠀⠄⠂⢁⠬⠐⡁⢀⡮⠞⠁⠀⠀⠀⠈⡄⠀⠋⠀⢠⠦⠄⠰⠢⠄⣤⠀⢇⡀⠼⡀
⠀⠀⠀⡈⠠⢄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠄⠰⠗⠚⠓⠉⠀⣠⠾⠆⠀⠀⠠⡠⠁⠀⠀⠃⠌⠀⠁⠉⠀⠃⠀⠱⠀⠐⠊⢁⠔⠂
⠀⢰⡀⠁⠀⠠⠒⠀⠀⠀⣐⣥⡌⠁⠄⠀⣀⣀⣤⡄⣸⣆⠀⠀⠲⠉⢀⠳⠒⠀⠠⠲⠀⢀⠠⠀⠁⠀⠠⠀⠀⠀⠴⠀⠀⠀⡄⢀
⠀⠀⠉⢀⡄⢢⠞⠁⠀⠀⠀⠘⢄⠁⠀⠜⠉⠀⠀⠠⠀⠚⠛⠂⠠⢒⠁⡀⠀⠀⡀⠀⡀⠸⠂⠀⢀⣀⣀⣀⣀⠤⠶⡀⠀⢀⠁⠀⠘⡆
⠀⢐⠁⠖⠀⠠⠀⢈⠀⣀⢀⣀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠠⠀⠒⠄⠀⠑⠁⠅⡀⠤⠊⠁⠀⢀⢀⠀⠀⠀⠀⠀⠂⠈⠐⢂⠈⢤⣀⠠
⠀⠈⡄⠀⢀⠤⠂⠀⡊⡴⠀⡄⠡⡀⠐⠀⠀⠐⠒⠛⠠⠁⠀⠀⢰⠀⠠⠀⠤⠃⠔⠐⠄⠰⠯⢀⡀⠀⠀⣀⠔⠆⠀⠙⠗⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢱⠈⠈⣀⠀⠄⢰⠁⠂⠒⠀⠐⠀⠀⠀⠄⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠒⠺⡀⡀⢀⠱⠀⠀⠀⠀⡀
⠀⢠⠄⠅⠋⢇⢸⡄⠈⠒⣊⡀⠀⠠⣁⢠⢔⠁⠐⠀⠀⠙⠀⠀⠱⠀⠐⠈⣉⠀⠀⠠⠒⠉⠀⠀⢀⠔⠂⠁⢁⡟⠁⠀⠀⢺⣿⡤⠐
⠀⠀⢀⠀⣂⢀⠠⠄⠀⠈⡤⠌⠂⠀⠀⠈⠈⡄⠀⠢⠁⢀⡠⠴⠁⠀⠀⡀⠀⢠⠂⠣⣀⡀⢐⣢⠄⣀⣀⡠⠎⡐⠇
⠀⠀⠨⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⡀⠔⠀⠀⠀⢀⡠⢤⣄⠀⠠⢀⠀⢀⠊⠐⠠⠑⠂⠀⠀⠀⠑⠊⠈⠁⠒⠉⠀⠰⠅⠀⠀⠈⠀⠰⡀
⠀⠀⠀⠁⠀⠀⠀⠄⠀⡀⢆⠀⠀⠁⠀⢔⠒⡂⢹⠀⠀⡜⠂⠀⠌⠀⢀⠀⠀⢀⠄⠀⠀⢰⢩⠇⠔⢉⠆⠆⠙⠄⠀⠀⠀⢠⡠⡀⡀
⠀⠘⠜⠀⠀⣀⠀⠀⠀⠈⣉⠀⠀⡀⢀⠀⠋⠀⠘⠤⠤⠧⠀⠠⠀⣠⡀⠁⠈⠋⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢰⠉⠀⠒⠀⠀⠐⣺
⠀⠀⡴⡝⠃⣴⠓⠀⡠⡈⢂⠄⠂⠀⠀⡅⠀⢀⠄⠂⣀⣂⡄⠀⠀⢀⠠⠠⠆⠀⠀⠀⠠⠀⠐⢢⠴⣶⣖⠀⠐⠀⠀⢣⠄⣀⣀⣀⡐⠃
⠀⠀⣧⠤⠙⠀⠀⡄⠀⠀⢀⠀⠀⣀⠔⣁⠀⡂⡰⠋⠀⠤⠈⠂⠤⠤⠄⠊⠀⠠⠂⠀⠀⡀⡀⠜⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢰
⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠲⡄⠀⠀⢰⡷⠂⠁⠀⠀⠀⠀⠀⠀⠚⠈⡀⠀⠀⠀⠀⠀⢰⠒⢦⣤⣤⡴⠖⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢠⠀⠀⠀⢀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⠲⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡒⠀⢠⠀⠀⠀⡠⠘⢩⢃⠀⠀⠀⠀⠀⠄⠀⠈⠉⠂⠀⠀⠀⠀⠀⠔⠇⢘⢁⠀⠀⠘⠢⠰⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠘⠠⠸⠁⠀⠀⠱⠀⢐⠄⠀⠀⠀⠀⠀⢄⠀⠀⣁⠎⠀⠀⠀⠀⠠⢆⢨⡉⠡⠀⠀⠀⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠰⢦⣤⣤⡶⠂⠂⠀⠀⠀⠀⠉⡙⠃⠀⢠⠊⠀⡰⠀⠀⠀⠀⣠⣤⣄⠀⠀⠘⠣⣄⣀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠶⠛⠀⠀⠀⠀⠀⠀⢀⠀⢠⠇⠰⠋⠀⠀⠀⠀⢼⠁⡠⢸⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⡄⠀⠀⠀⠁⠈⠀⠀⢠⡀⢈⣶⠀⠈⠃⠒⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⢀⠇⠀⠐⠂⠀⠀⠀⠀⠀⢡⡸⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⢀⣠⣶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡠⠀⡟⠀⠀⠰⣵⣷⢿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠁⡀⠀⠀⠀⡂⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠆⠀⠀⠁⠴⠊⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣂⠀⠀⣠⠃⠀⠀⠀⢃⡀⢺⠀⠀⠈⠻⠷⠴⠞⠋⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⢡⠆⠩⠄⠀⠀⠀⠀⠀⠀⠀⠓⠂⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡠⠤⣀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⡆⢀⣲⢺⡿⣦⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠀⢶⡁⠀⠀⠀⡙⠆⠀⢀⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣵⣿⣿⣿⠋⠀⠀⠠⣶⣶⡶⠀⠀⠙⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⢀⡠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⡤⠠⠤⠠⡀⠐⠴⣔⡶⠤⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠠⠤⠤⠆⡒⠚⠛⠁⠤⠤⠤⠄⠀⠠⠤⠤⣄⣀
⠀⠀⠀⠀⠤⢀⠠⣄⠀⠀⢠⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉
⠀⢀⠠⠒⠂⢠⠄⠄⠀⣰⡟⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⣀⡀⠊⢀⡘⠈⠢
⠀⠈⣀⠀⣤⠄⢈⡑⢊⣀⡀⢡⣤⡀⠀⠠⠀⢀⠄⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠐⠤⡞⣀⣌⡉⠉⠑⠀⠀⠀⠀⠐
⠀⠀⢋⢳⡆⠀⠈⠉⠉⠁⠠⠄⡁⢀⠠⢒⢀⠦⣨⠀⠀⠁⠀⠀⠀⠠⠀⡄⠀⠀⢀⡀⠌⡆⠂⠀⠀⠀⠈⠉⠑⢒⢚⡀⠀⡾⡁⠀⣤
⠀⠀⠀⣑⣌⠱⠂⢰⡂⢀⠈⣰⠀⠕⣤⠥⢮⣖⠆⠀⠀⠀⣤⠖⠂⠀⡸⠤⠀⠁⠣⣹⢶⡶⠤⠄⠀⠀⠀⠀⠀⢀⠞⠐⡰⠐⡇⠀⠠⠁
⠀⠀⠀⠈⠙⠷⢾⡤⡤⠄⠰⢩⠿⡛⠛⠋⠉⠀⠀⠀⠀⠀⡎⢀⡴⠡⡇⠚⠹⠤⠄⢤⠼⠁⠀⠀⠤⠀⠀⠀⣠⠎⣠⠖⠁⣸⠃⠀⠰⠂
⠀⠀⠀⠀⠆⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⡄⢸⡀⢲⠀⠀⠀⠀⠠⠀⠈⠀⠀⠡⠄⠀⣤⡞⢁⡴⠀⢀⡴⠃⠀⢀⠒
⠀⠀⠀⠀⠀⠤⠖⢴⣞⣁⣄⣚⣂⡠⠀⠀⠀⠀⠀⠀⠀⠂⠈⢺⠙⣏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠞⠁⠔⣻⣥⠔⠋⠀⣀⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠉⠛⢶⠖⠈⣛⢅⢀⠀⠈⠀⠀⠘⣀⠘⡔⠋⠁⡐⠒⠛⠛⢋⠍⡩⠇⠊⠤⢀⠀⠤⠄⠒⠒⠚⠁⡸
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⢠⡀⠹⡤⠤⣴⣎⠀⠀⠀⠀⠀⠻⠉⣇⠀⠘⠤⣤⠤⠒⠁⠀⣀⣴⣊⠀⠀⠀⠀⠤⠀⡀⠠⠊⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢥⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠦⢤⣤⠖⢞⠁⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢤⡀⠀⠀⣠⠈⣆⢉⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠑⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠀⠘⠌⠦⣼⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠳⢆⣀⣄⣀⠞
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀
⠀⠀⢠⢴⡧⠖⠚⡛⣷⠀⠀⠀⢀⠌⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⢀⠔⣄⠀⢠⣄⣀⡀⠀⠀⣤⢤⡤
⠀⠀⢸⡄⠁⢁⡀⠤⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠱⠑⡀⠀⢀⠔⠲⡒⡀⠀⠀⡆⢹⠀⢇⠀⢸⠀⢘⠿⢿⠂⠀⠀⡆⠀⡆
⠀⠀⠀⡧⠠⠀⢒⣂⠁⣳⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠁⡠⠃⢄⡄⠈⢶⡀⠀⢁⠸⡆⠀⡕⡅⠀⢀⢳⠁⠀⠀⢀⠇⠀⢇
⠀⠀⠀⢳⡈⠭⢄⡐⠦⠝⠀⠀⠀⠍⠹⠹⠉⠍⡇⠀⣰⢁⣀⡈⠀⠀⣀⢳⠀⠈⢸⠃⠀⠀⡇⠀⠈⢠⠀⠀⢠⡋⠀⠀⠘⢷
⠀⠀⠀⠈⠊⠀⠒⠂⠁⠁⠀⠀⠀⠺⠈⠙⠛⠋⠇⠀⠈⠉⠉⠉⠉⠉⣉⣁⣀⣀⣀⣋⣀⣉⣁⣀⣈⣁⠀⠀⢠⠀⣉⡀⠈⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠒⢲⣲⡒⠒⠒⢒⣖⡖⠒⠒⠒⠁⠀⢸⡀⣊⣈⣀⢀
⠀⠀⠀⡔⣡⠔⠂⠁⠐⢌⠢⡀⠀⠀⠀⢀⡔⢈⠉⠈⠉⠒⢄⠀⠀⠀⠸⠘⠉⣠⠖⠒⢦⡉⠙⣮⠀⠀⠀⠀⠨⣀⡀⠀⢀⡰
⠀⠀⠈⠘⠔⠒⡄⣀⢀⣀⢡⠡⠀⠀⠐⠑⠁⡎⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⣶⢠⣴⡇⠀⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⢀⢸⡀⢀⠇⡣⠿⢝⡜⠠⠀⡤⣦⣤⣤⡄⠐⠒⠒⠒⠒⠚⠢⡄⢰⢀⠀⠈⡷⠒⡏⠁⠀⠿⠀⠸⠼⡆⣷⠲⢷⢸⢈⢼⢃
⠀⠀⠀⠢⠋⠅⣀⣈⡒⢛⠔⢁⣀⡈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠈⠈⠉⢀⠀⠀⠀⠈⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠒⠊⠁
⠀⠀⠀⢸⡸⠁⠐⠀⠀⠀⠠⣟⣒⡨⡆⠀⢀⠔⡒⡒⠒⠈⢕⠌⣇⠀⠀⡏⠀⠤⠀⠐⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠌⠃⠹⠁⠀⣤⠰⠀⠃⠆⠃⣀⠴⡍⠀⠀⢳⠛⠉⣽⣟⡇⠀⠀⢹⠓⣛⡛⣛⠛⡛⢛⢛⠻⣻
⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠙⠦⠦⠄⠀⠀⠘⠵⣲⣖⡆⠽⠚⠉⠀⠀⠀⢸⡴⣶⠏⢹⠇⠀⠀⢧⠘⣅⠗⠟⠹⡇⠟⠾⢀⢿
⠀⠀⢰⠧⠤⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠛⠀⠀⠀⠂⠁⠀⠈⠈⠀⠀⠀⠀⠁⠘
⠀⠀⢈⡺⠡⠀⠘⡂⠀⠀⢰⢑⡠⠤⠤⠤⠴⠥⠯⠮⠬⠤⠤⠤⠤⡄⡏⡇⠀⢀⠤⠐⣑⣒⣑⡒⠠⠤⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠘⡔⢄⣀⠰⡱⠀⠀⢸⢸⣈⣉⣉⠉⠉⠉⠋⢹⠉⠉⠉⣉⣉⣁⡇⡇⠀⢨⠢⠉⡇⠆⠀⡂⢉⠢⣤⠛⡂⢠⠇⠀⠘⡆
⠀⠀⠀⠈⠑⣲⠉⠀⠀⠀⢸⢰⠒⠒⡆⡇⠀⠀⡀⢸⠀⠀⢸⢰⠀⠀⡆⡇⠀⢸⡤⣀⡃⠂⠀⠃⡈⠴⠙⢄⡀⠀⢙⠉⠉⡅
⠀⠀⠀⠀⠰⠾⠄⠀⠀⠀⠸⡸⠀⠀⡇⠇⠀⠀⣅⡸⠀⠀⠸⡸⠀⠀⠇⠇⠀⠀⠘⠚⠩⠉⠍⠃⠊⠁⠀⠀⠀⠈⢤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⣀⣀⡀⣀⡠⢜⠵⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⡢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠁⠑⠋⠭⠝⠋⠁⠀⠀⠀⢀⠔⡩⠢⠀⠰⠉⠀⠠⢆⠀⠀⠀⠀⠀⠀⠹⣿⣧⠎⠉⠀⠀⠀⠀⠀⠀⡔⢮⣹⠖⢤⡀
⠀⠸⡡⡁⠁⠁⠀⠀⠀⡇⠀⠀⠀⠈⠰⡁⢣⡄⠈⠂⠒⡡⡸⠀⠀⠀⠀⣠⡤⢦⣽⣦⢦⣤⡀⠀⠀⠀⠀⢸⡠⠤⠒⣊⡩⠇
⠀⠀⡱⠕⣂⣀⢀⡠⢮⡀⠀⠀⢄⠘⠂⠘⠒⠃⠀⠀⠁⠚⢁⠄⢠⡤⠼⠿⠿⠿⠿⠿⠿⠿⠷⠤⢤⠀⠀⡗⠐⣋⡉⠥⠔⠃
⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉

⠀⠀⠀⠀⠠⠀⠀⠠⢄⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠻⣷⡶⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⢆⣂⡠⠧⠄⢀⡀⠀⠀⠀⠀⠈⠐⠨⠻⣭⣑⢲⣤⡀⠀⠀⠀⢰⣿⡒⢂⡀⠀⢀⣴⡿⡀⠀⠀⠀⠀⡄⠐⠀⡀
⠀⠀⢹⡀⢙⢴⣤⣾⣾⣿⣽⡁⠀⠀⠀⠫⡇⣰⠶⡧⢢⣜⣰⠂⠀⠀⠐⣭⣛⡻⢟⠶⠗⠚⣡⠀⠀⠀⢀⡀⡀⠁⠠⠁⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠍⠋⠀⠠⠀⠀⠀⠀⠀⠚⢦⣄⡔⢌⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠒⠆⠀⠐⠂⡀⠀⠀⠀⠀⢠⣶⣦⣄⡔⠦⢤
⠀⠀⢀⣄⡟⠛⠂⣸⢻⣵⠦⡀⠀⠀⡀⢂⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⢻⢿⢿⣷⣞⠨⣧⡄⠀⠀⠈
⠀⠀⠿⣀⠀⠀⠰⣿⢲⢵⣡⡶⠀⠀⠀⠀⡈⠐⠀⠀⠚⠈⢠⠀⠀⠀⠀⠀⠀⠐⠯⠷⠏⠉⠛⢳
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠲⠤⠠⠠⠤⠶⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡐⠀⢄⠀⠂⠈⠁⣀⠀⠀⠀⠠⡚⠢⠈⠙⠴⠿⠆⠀⠀⠀⠀⢀⠀⢔⠂⠀⠂⠀⠀⠀⢰⡎⣻⣷⢿⣯⣗⣦⣄⡀
⠀⠀⠀⠣⠩⠄⢄⢠⣤⠔⠀⠛⠀⠀⠀⢷⡖⢂⣂⠀⠀⡀⠢⠂⠀⠀⠆⡀⢀⠀⠐⠀⡀⠀⠀⡀⠀⠉⠉⠦⢤⠿⠒⠣⣴⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠁⠀⠀⠀⠈⠑⠦⢄⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠤⣀⠀⢠⣄⣰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠳⣀⢂⣝⡅⠀⠠⢚⣩⣥⠶⣶⠶⠾⠶⠶⣦⠌⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⣧⠂⢉⢃⠮⢎⡤⣲⠜⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⠁⠲⠛⠒⠠⣠⢆⣲⢞⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡈⠄⠒⠒⡆⢤⣨⢞⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡐⠀⡠⠔⠠⠀⢔⠔⡱⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⢰⠒⠰⠀⠀⣇⡤⠂⢜⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠏⡀⠃⡴⠋⡇⢀⢪⠞⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⡠⢤⣄⠂⠀⠄⣀⣀⣠⣤⠤⠤⠖⠚⠁
⠀⠀⠀⠀⠀⡸⠅⠠⠎⠀⠥⡠⣣⠋⠀⠀⠀⠀⠀⢀⡠⠄⣒⠢⠍⣒⣂⡭⠥⠖⠒⠛⠉⠉
⠀⠀⠀⠀⢀⠗⠀⢄⣀⠚⡴⡵⠃⠀⠀⠀⠀⠀⠀⣀⣨⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠈⣆⠈⣀⣊⢌⠞⠁⠀⣀⣠⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠘⣝⣒⣵⡥⠴⠚⠋⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⢠⡌⠀⠀⠀⠀⠀⣾⠶⡀⠴⢄⠠⠐⡆
⠀⢀⡈⣿⠀⠀⠀⢨⡙⡐⢈⠰⠚⣶⠖⢲⠁
⠀⠀⠐⠘⡾⢱⢄⠃⠅⢐⠨⠀⢁⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢋⢉⠤⢝⢤⡛⠀⠈⡀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠑⠄
⠀⠀⠀⠈⣻⡣⣋⠓⢠⣈⣲⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠂⠀⢀
⠀⠀⠀⠘⠂⢈⠖⠨⠌⠀⠾⢀⠄⠓⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠐⠒⠂⠒⠀⠇⠘⡀⠀⡐⠃⠤⢀
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⡀⠁⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⢀⣁⠀⠀⡐⠀⡜⠀⠀⡷⠎⡀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⡀⠀⢠⣾⡟⢨⢤⣴⠎⠀⠀⠀⢠⠆⠀⠀⡔⠔⡀⢀⠊⡄⢀⡜⠀⠈⠀⠀⠀⠁⠀⠈⢃⠠⠊⠀⠀⡀
⠀⠀⣘⣖⠒⠦⠙⡒⢿⡟⣑⠭⣄⣀⡀⠀⠒⠁⠈⠄⠀⠢⠐⠀⢀⠎⠀⠊⠀⣀⡠⠄⠀⠀⠀⠀⢠⠂⠀⠀⠀⠔⠑
⠀⠌⠀⠈⠀⠈⠀⠬⠰⠎⠄⠀⠀⠀⠈⠢⡠⠄⠀⠘⡞⠀⠀⠀⣀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠄
⠈⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠖⠁⣤⠶⠛⠉⠀⠐⠒⠂⠉⠀⠒⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠠
⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⡀⠀⢀⠙⢉⠉⠥⠀⠀⠀⠀⠔⠂⠄⠀⠀⡤⠆⠐⠄⢀⠔⠀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⠉⠉⣚⡁⠀⠃⠀⠀⠁⠐⠀⣀⠀⠀⢀⠀⣀⠄⠀⠀⠀⠁
⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⢈⡄⠀⠠⠐⠀⠀⠑⠀⠂
⣶⣶⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠣⠀⠀⠀⢀⡴⠊⠉⠀⠀⠁⠐⢄⠀⢈⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠠⠀⠣⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠂⠑⠀⠀⠸⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠻⢦⣀⣀⣀⣤⠞⠀⠀⡀⠀⢸
⠀⠄⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠈⠂⢄⠀⠀⠈⠒⠢⠄⠀⠀⠐⡩⠂⠈⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠄⣠⠔⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⡇
⠘⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠈⠐⠂⠦⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠑⠒⡄⠀⡔⠉
⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠇⢀
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠼⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣉⢰⠟⠉⢻⡆⣼⠋⠉⢳⡀⡟⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠸⢦⣤⡼⠃⠻⣤⣠⡾⠁⣧⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢀⡄⠀⣠⣤⡀⣀⣠⠀⣠⣄⡀⣠⣄⠀⣠⣄⠀⡄⢀⢀⡄⢀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⠆⡾⠻⡀⢧⣀⠄⡿⢧⠘⣇⣲⠆⡷⢎⠸⣄⣸⠃⢇⡼⢸⠙⣾⢸⣇⡿


⢀⠰⣉⡝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⡀
⡀⠀⢡⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠁⠀⢠⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⢄⡀⠁⠂⢄⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠋⡀⠀⠀⠀⠈
⠤⠒⠁⠀⠀⠈⠉⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠁⠀⠀⢈⡀⠀⠀⠀⠀⠁⡄⠀⠀⠁⠀⠀⠀⠈⠂⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠑⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠂⢀⡀⡀⢜⠤⠐⠀⠐⠲⠠⢀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈
⠆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠀⠀⢀⡴⠖⠛⠓⠶⣄⠀⠀⢥⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠠⣤⠀⠐⠀⠀⠀⠀⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢷⡀⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠄⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⢀⠃⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢁⠀⠑⠤⢀⠀⠀⢀⡀⠔⠃⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⡤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⡞⡸⠿⣷⠂⠀⠀⠒⠒⠾⠤⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠴⣋⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠫⠘⢣⢤⠃⠖⡠⢼⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣰⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡾⡨⠝⣀⡅⢄⠑⢼⣁⣌⣺⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⢄⣹⣦⣀⣉⠶⠖⠚⣠⠉⡀⢇⡇⠀⠀⠀⡀⢀⠂⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⠋⠙⢩⣧⣤⢘⣟⠋⣷⣹⠇⠀⠄⠐⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡋⠀⠈⣤⠝⠈⢉⡏⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠼⡯⠴⠶⠟⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⡿⠀⣠⠀⢀⡀⣴⡄⣀⢀⡀⣀⠀⢘⠃⣾⡧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⡏⠈⣿⡄⣿⠀⢸⡇⢈⠋⣿⠀⡏⣽⠁⣿⠀⣿⠁⣼⠁⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⣇⣠⡿⠀⣿⣀⢾⡇⠌⠐⡇⢠⠁⣿⢀⣿⠀⣿⡀⢿⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠈⠁⠀⠈⠁⠈⠁⠈⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠓⠚⠉⠀⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢀⣀⡄⠖⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠀⠑⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠂⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⡀⣀⢀
⠀⠀⠀⠀⠐⠒⠂⣀⡩⠀⠀⠂⠀⠀⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡀⡀⡀
⠀⠘⢀⡃⠀⠀⠰⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⢉⡀⠉⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠐⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠂⠀⠀⠀⠋⠉⠀⠀⠀⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⠠⠄⠧⠄⣶
⠀⠀⢀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠆
⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠐⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⢠
⠀⠁⢀⠀⢐⣀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠈
⠀⢠⠀⠴⠠⠠⠀⠀⠀⠀⠀⠀⡀⠀⠞⠉⠱⠆⢀⡀⠀⠀⠀⠀⠀⠖⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠑⠂⠀⠐⠁⠀⠀⠀⠀⢰⠈⠁⢉⠉⡉⢉⠀⢱⠀⠀⠀⠀⢀⣠⠀⠨⡤⠀⠀⠂⠀⠀⠀⠐⠈⠁⠰⠐⠈⠙⢢
⠀⠀⠀⠐⠆⠀⠀⠀⠠⠀⠀⠈⠂⠈⠉⠁⠀⠀⠁⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⣀⡉⠈⠈⡰
⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⡈⠑⠢⠤⠤⠔⠊⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠉

⠀⠀⠀⠀⠀⢠⡀⠀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠀⠀⢀
⠀⠀⠀⠲⡄⠈⢧⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⡠⢀⠀⠀⡠⢦⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡠⠋⠀⣀
⠀⠀⣄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⢄⡠⠁⠈⠳⠔⠁⠀⠣⠐⠉⠀⠸⠀⢀⡠⢦⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⢀
⠀⡀⠈⠃⠀⠀⠀⠀⢰⠆⠠⢄⣠⡀⢄⠀⠀⠀⠀⠀⡠⠄⠒⠀⠀⡂⠀⠀⠃⢁⡀⠼⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠈⠁⠀⣀⡀⠤⢤⠀⠀⠊⠁⠀⠀⠀⢂⠀⠀⢀⠎⠀⠀⢀⡀⠀⠇⢀⡴⠋⠀⠀⠀⠀⠈⢫⡇⠀⠀⡤⠠⢀⠀⠚
⡠⠄⠂⠉⠀⠀⠀⠈⡜⡀⠀⠀⠀⣇⠀⠈⠆⠀⣼⠀⠀⠀⣿⠀⡴⢀⢺⠁⠀⢠⠎⠑⢆⠀⠀⢣⣀⡾⠀⠀⠀⡹⠈
⠘⡀⠀⠀⠀⠀⢰⠂⠑⣴⡄⠀⠀⠉⠀⠀⠘⣄⠿⡀⠀⠀⠓⠀⢰⡇⢸⠀⠀⠈⠈⢂⡘⠀⠀⣸⣱⠁⠀⠀⡐⠁
⠀⠑⠮⣉⡄⠀⠈⡇⡆⠀⡇⠀⠀⢲⠳⡄⠀⠘⣇⠑⢄⡀⠀⠀⠈⡇⠘⡄⠀⠈⠒⠋⠀⠀⣠⢧⠃⠀⢀⡜
⠀⠀⣀⠠⠴⠀⠀⠸⡰⠀⠇⠀⢀⣸⠦⢗⠔⠂⢹⣄⣀⣈⣉⠉⣹⢣⡀⠈⠢⢤⣤⣤⢤⠞⣿⠵⠬⡕⢀⡽⠃
⠀⠉⠢⡀⠀⢧⢀⣀⠵⢇⠘⢉⡁⣠⣶⢾⡓⣛⠿⢉⠟⣻⣅⣛⢿⣽⣍⡳⢤⡄⠐⠀⠀⡼⠙⢤⡤⠾⢉⡀
⠀⠀⠀⡈⠓⠈⠉⠂⠐⡈⣠⣮⣵⠷⠾⠷⠶⠿⠶⢾⣮⣜⡡⡯⠹⠿⣶⢻⣶⣬⠷⣄⡀⠈⠀⠈⠀⠀⠀⢈⡳⠂
⠀⠤⣊⠀⠀⠀⠀⢀⡾⠛⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠩⢈⠙⠶⣄⣀⠻⡐⢻⠰⣇⠘⣿⢦⡀⠀⠀⢠⠖⠉
⠀⠀⠀⠈⡑⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠪⡳⣌⠺⢟⡓⢾⠦⡛⢛⣿⣦⠀⠀⠉⠢⡀
⠀⠀⢠⠎⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠳⣍⢙⣧⢴⣽⣈⣆⣻⣳⣀⠤⠒⠁
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢊⢷⡇⣤⢜⣽⠋⣃⣿⣷⢄
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⡼⢑⠶⠞⠉⢿⡎⡏⠁
⠀⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠻⣆⠀⠉⢀⣰⢇⡇
⠀⣀⠀⠀⠉⠓⠲⠦⠤⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⢳⡾⢟⣫⡾⠁⠀⠀⠀⣄
⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠤⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⡖⠒⠲⠶⠞⠛⠉⠁⠀⠀⠀⠰⣄
⠀⠉⠀⣠⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢇⠀⡠⠖⢀⠀⠀⡰⠀⡀⠀⢰⠁⠢⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⠁
⠀⠀⠘⠁⢀⡔⠀⢀⡄⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠢⠊⠀⠀⠙⢦⠃⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠸⣄⠀⠳
⠀⠀⠀⠀⠉⠀⠀⠛⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⠀⣤⣤⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣶⠶⠦⠤⠤⣤⣤⣀⣀⡀
⠀⢀⡤⠚⣷⠒⠒⠛⠛⠛⠛⠛⠓⠒⠒⠒⠀⠈⠀⠀⠀⠀⠀⠈⠉⠋⠙⣛⣳⣶⣤⣀⡤⠖⢦⡀
⢠⠟⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣯⣡⢴⡏⠸⠧⣤⡀
⣿⣕⠄⠀⠀⠙⢷⣄⣀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⠿⠿⠟⠋⠉⣴⠟⡗⢰⣼⣾⣧⣀⠉⢀⡀⠈⣿
⣿⣷⣯⡂⠄⡀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣾⣗⢳⠭⡱⢟⠯⡎⠝⣷⠉⠀⢀⠙⢷
⠙⠿⣿⣷⠥⣂⠥⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣈⠨⠓⡁⠯⣘⣡⠀⢹⡖⠒⠛⠂⣼
⠀⠀⠈⠙⠻⢶⣭⣐⠂⠥⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⡎⢈⠆⣖⠆⠁⢓⣸⣇⣠⠤⢸⡁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢤⣬⣥⣀⣒⣒⠢⠤⠤⠤⠤⠀⢸⣦⣤⣬⣅⣂⣤⣞⣉⣉⣉⠉⣙⣢⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠿⣌⠉⠻⣅⣀⣈⣙⣢⣾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠉⠀⠉⠉⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⢰⡤⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢵⡖⠱⢽⣷⡖⠒⠂⠠⠤⠤⠼⢄⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠶⢋⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠋⠿⣀⡠⠇⣅⢄⣀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢈⡀⠉⢉⠩⣤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⠄⢰⠁⠁⢢⣠⠏⠈⠃⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣈⠁⣠⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡏⠁⢐⢞⡊⠁⣠⠉⠶⠒⢳⢻⠐⠀⠄⠀⠀⢀⡀⠀⠀⠀⣨⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢼⣹⠦⢴⢞⡉⠃⢠⢦⡡⢶⣩⣼⠃⠀⠀⢀⡶⠸⣂⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣈⣱⡼⠺⡧⣤⣯⢁⣭⣧⡟⠀⠀⠃⣪⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣏⠀⠀⠀⡶⠒⠁⢠⡸⠀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠿⠥⠾⠿⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠶⣯⠀⣼⡇⠀⣷⠀⢿⡧⣶⠄⢷⢴⣦⠀⣶⠀⣿⡏⢉⡶⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢸⡇⠀⣿⡇⣿⡇⢀⣿⠀⢠⠀⣿⠀⡘⢸⡇⢸⡏⠀⣿⠀⢸⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⣧⠴⠟⠀⢻⣧⠞⢿⡤⠃⠀⣯⣠⠃⠸⣇⡸⣇⠀⢿⣄⠸⣇⣰⠇


⣿⢿⢿⢿⡿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡴⠒⣒⠒⣆⣀⣴⢲⣟⣿⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣳⡯⣽⢋⣭⠭⣟⣾⡋⣥⣴⣿⣶⣮⣹⢯⢵⡚⠳⣶⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣚⠽⠖⠻⠵⠋⠠⠾⠽⠛⠧⣑⠦⣽⣟⡚⠻⢿⡇⢠⣠⢰⣶⡇⣠⢜⣴⡫⠿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣞⣽⣷⡶⠬⣟⢿⡼⡿⢚⣠⣴⣿⡇⠀⠀⡈⣽⣂⣤
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⣿⢿⣩⢤⡖⢲⡛⠀⠹⡍⠉⢭⣏⣿⢻⡚⠘⢩⢟⡿⡗⡶⠂
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣀⣀⣀⣹⣦⡙⠻⣖⡓⠚⠾⠶⠿⠮⡭⣝⢯⣱⠹⣽⣳⣆⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠛⠋⠉⢿⡶⣤⣍⡛⢿⣖⣒⡚⣅⣞⢿⡛⠃⣮⠔⢻⡽⠻⣦⡀
⠀⠀⠀⠀⡼⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢧⣷⣏⡛⠛⢷⡦⣏⠘⣎⢦⡑⢄⠪⣵⡌⢩⣭⠴⠃
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠕⠛⢿⡯⣗⣌⠢⡱⣿⣞⠙⢲⣧⣮⡛⡶⣾⢵⡆
⠀⠀⠀⢰⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠷⢻⠳⣭⣒⣿⣮⡪⣴⣷⡛⣿⡙⣟⡟⣆
⠀⠀⠀⠸⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣝⣒⣶⠀⢩⠍⣤⠣⣬⣟⡻⣷⢿⡀
⠀⠀⠀⢠⠇⡆⡆⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣹⣜⡶⢃⣜⣁⠹⢼⡼⣩⠏⣩⡛
⠀⠀⠀⢸⡄⡇⡇⡇⢸⢸⢸⠰⡄⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⢹⠘⠲⣟⢮⡛⣟⣫⡞⢧⣀⡞⡇
⠀⠀⠀⢸⠛⢇⠇⡇⣸⢸⢸⠀⡗⢇⢸⠘⡆⢰⢰⢠⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠙⠚⣧⣳⣬⣿⡠⠄⠊⢹⣸⣍⠦⣹
⠀⠀⠀⠈⢧⡀⠀⠁⠙⠈⠘⠃⢧⢸⣸⠀⡇⢸⠘⣬⡆⡇⢸⠀⡏⠘⡆⡆⢠⠀⡄⡀⢀⠀⠀⠀⠀⠀⢸⡉⠙⢯⡷⢀⣤⣎⠙⢺⢳⢺⠃
⠀⠀⠀⠀⠀⠉⠓⠲⠮⠤⢤⣀⣀⠀⠉⠃⠳⠈⠇⢧⢧⢻⠘⡆⢳⠀⢇⢹⠸⡄⡇⢳⠸⡄⡇⡄⠀⠀⠀⢿⢳⠦⠽⢤⡞⣽⣇⣨⣿⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢤⣀⡀⠀⠈⠘⠂⠳⠘⡆⢸⡸⡄⣇⢱⢸⡀⡇⢹⢹⠈⡆⢧⠘⡿⣰⣆⠈⢷⣖⠥⣌⠻⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣤⣀⠀⠀⡀⠁⠓⠸⠜⡆⡇⢹⡈⡇⣇⢻⢸⡀⢳⣈⢻⠀⢳⡙⢄⠨⣝⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣀⡀⠀⠃⠀⠃⠹⠘⡌⣆⣇⠀⢷⡀⢾⢨⣇⢸⡀⠹⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⣀⠀⠀⠀⢘⠀⠸⣷⡎⡃⢹⣾⣟⡸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠬⣄⠀⠹⣧⣿⡦⣽⡿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣉⡭⠥⠚⠁

⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣖⡀⠢⢗⣦⣀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢠⡀⠀⠀⠀⢀⠀⢀⠀⠀⢠
⠀⠠⢌⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣡⣮⣿⢶⡇⠀⠀⠀⡀⠀⢀⣉⠿⠇⠁⠘⠀⠀⠀⠀⢀⠈⠀⡄
⠀⠀⠘⠀⠂⠀⠰⠔⠁⠀⠀⠀⠀⠀⢠⡆⡆⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠘⠓⡚⢁⣀⠠⠄⢂⠀⠰⠣⡀⠀⠀⠀⡀⠀⣀
⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣉⢸⠗⠤⠔⠂⠁⣰⠳⡀
⠀⠐⡀⠠⠀⠀⠈⠢⠤⠄⣤⣤⡄⠍⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣅⠄⠀⠀⠈⢴⣰⠂⠀⡀⠀⠈
⠀⠃⢀⠰⠦⠀⠀⠀⠀⠀⠁⠀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠖⠚⠉⠉⠀⠀⠘⠟
⠐⠀⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⠆
⠀⠀⢀⠀⠀⠀⢀⠄⡄⠓⣴⡄⠀⠀⠀⢀⠠⢠⠀⠀⣠⢠⡀⠠⠠⠀⠠⢀⢠⢀⠄⠀⠀⠀⠀⠀⣠⠄⠀⠀⢠⡀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⠀⡌⡿⣿⣿⡧⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠀⠈⠁⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⣄⠀⠑⠆⠈⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⣤⣖⡢⠐⠋⠀⠀⢤
⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣴⡽⠟⠿⠑⠺⠫⠈⠂⠀⠠⠒
⠀⠀⠠⡀⠀⠁⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⢀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠐⠀⠉⢉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣩⡭⢎⠉⠿⠀⠀⠠⠒⠀⠀⠀⠸⠣⠀⠀⠀⠀⣀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢒⡯⢉⣶⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⡤⠦⠠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠐⠀⢀⠀⠀⠀⠀⡄⡀⠀⠀⢀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠃
⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢓⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠱⡀⠀⢀⣀⠀⣴⠂⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⢡⠶⠂⢠⠆⠀⠀⠀⠀⠜⡁⣈⡈⠀⠀⣀⢠⡀⡀⣄⣀⡠⠀⠀⠀⢰⡆⠀⠄⠈⠀⠉⠁⠈⠀⠀⢻⣄⡀⠀⢀
⢀⠀⠀⠀⠀⠂⠀⣄⠀⠀⠀⠡⠆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠈⠀⠀⢠⡄⡒⠚⠀⠀⠀⠉⠁⠄
⣄⠀⡆⠀⠀⢀⡀⠀⠶⠀⡠⠐⠁⣀⣄⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠸⠛⠓⠲⡀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠀⠀⠛⣠⠄⠠⠆⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⢰⡀⢠⣰⡀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡘
⠀⠀⠠⠤⣭⣿⣿⢿⣤⡤⠀⠀⠻⡏⠀⠀⠀⣷⡞⠀⠠⠰⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⡾⢠⣉⠅⣿⡀⠀⠙
⠀⠀⠀⠰⠤⠞⠸⠦⠤⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠐⠀⠠⠁⠰⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⠉⠐⠤⠗⠹⠇⠀⠈⠡

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⡄⢀⠐⠁⠔⢸⡄⠀⠀⠀⠀⠀⠀⠁⠀⣵
⠀⠀⠀⢀⡠⠈⠋⠆⢰⠆⣝⠀⠀⠀⠐⠐⠶⠚⠙⠿⠿⣖⡂⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡼⠎⠀⠀⡀
⠀⠀⠈⠐⠂⠀⡧⠐⠒⡠⠡⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠚⣿⡷⠀⣤⢠⠌⣍⢀⣀⣈⣉⡀⢀⡀⠀⠀⠈⠙⠒⠒
⠀⠀⠀⠤⡀⢶⠸⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣴⣿⡇⠀⠈⠻⠴⣧⣰⣄⣤⣠⡷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠃⠀⢰⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣷⣄⣤⣾⣿⣿⡿⠀⠀⢀⡀⠡⠔⠤⠀⠀⠀⡇⠀⠀⠀⠐⠒⠀⠡⡀
⠀⠀⠀⠀⠀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠙⠁⠀⠀⠀⢀⣀⠀⢐⠇⠀⢠⠃⠀⣄⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠸⠀⠀⠹⡇⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⣀⣴⠋⠀⠀⠘⢄⣀⢀⣠⣠⣶⡞
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⢘⣁⠀⠀⠀⠀⠻⣷⣶⣾⣿⢃⡖⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠨⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠖⠋⠀⠀⠀⠔⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡀⠀⠀⠀⠀⠀⠀⢂⣿
⠀⠀⠀⠀⠀⠑⠀⡾⠀⠀⠐⢦⣀⣧⣀⣴⡷⠃⠠⢂⣱⣯⢧⠷⠾⣷⣄⠀⢐⠀⣏⠀⠀⠈⠻⣤⣀⣀⣀⣰⣦⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠃⠁⠈⠉⠆⠀⠀⠈⢻⡆⠀⠀⢹⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠡⠀⠀⠀⢴⡇⠀⠈⠒⢤⣄⣠⣼⣶⠿⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣤⣀⣠⡶⡀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣾⣎⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣄⠀⠀⠏⠀⠀⠀⠀⠠⠟⠃⠙⠁⡧⠠⠄
⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣟⠓⠀⠈⠳⣦⣄⣀⣀⣀⣀⣀⣴⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠿⠿⠿⠿⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣋⣡⣶⣷⠾⠻⣾⠿⣦⣤⣤⣌⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⣿⣋⣁⣈⣛⡋⠉⠻⣦⣤⣤⣾⠋⠈⠉⠻⢿⣦⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣶⠿⠛⠛⠉⠉⠙⠛⠻⠷⣾⣥⡀⠹⣷⣴⣶⣴⠾⠻⠿⣶⡌⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⠁⠈⠁⠀⠀⠈⢁⣀⣀⣀⣂⡀⠉⠛⢷⣦⡀⠈⢿⣤⣄⠀⠘⠿⣦⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⣀⣤⣴⠾⡟⢛⣛⠛⣛⠛⠛⠿⢶⣤⣈⠙⢷⣦⣉⠹⣷⣀⠀⠛⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢀⣣⣴⡿⢿⣭⣴⣿⣿⠛⠛⠿⢛⣷⢶⣶⣦⣈⠛⢷⣦⡈⠛⢷⣿⡛⢿⣄⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢻⣿⣥⣤⣤⣭⣥⣀⡙⢷⣶⠶⣿⡁⠀⠀⠙⢻⣷⣀⠙⢿⣦⢀⡍⠻⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⠿⠛⠉⠉⠀⠀⠈⠉⠉⠛⠷⣦⣄⡘⠿⠶⢷⣾⠟⠛⠛⢿⣆⠙⣷⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠋⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠻⣶⣤⡀⠈⠛⣷⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡘⣿⣄⡀⠉⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠉⠻⣾⣍⣻⣧⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣴⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠙⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰⠆⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠶⠂⠀⠀⠀⢀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⡶⠟⠋⠉









⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⣿⣿⣿⢿⣿⠿⢻⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣀⣀⡀⣀⣤⠤⠤⠤⠶⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠒⠉⠀⠤⠠⠤⠤⢀⠀⡀⠤⠐⠒⠒⠀⠐⠂⠷⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠁⠀⡸⠀⣀⣠⡎⣁⣀⠀⣀⡀⡠⠋⠀⣀⠤⠒⡒⠶⠶⢦⣄⠀⠙⢕⠦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡡⠔⠋⠀⠂⢛⠣⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⢤⡖⠀⠒⠾⠀⠀⠀⠀⠈⠥⣤⣀⣳⠉⠉⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡨⣠⠔⠊⢁⠞⠁⠀⡤⣖⣉⡍⠄⠠⡜⠋⠐⠂⠔⠊⠀⢀⣠⣀⠀⠄⠄⠤⠤⠤⠈⣁⣀⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡅⠂⠁⠘⠡⡡⠀⢀⠂⠀⠠⠺⣜⠁⠀⠁⠲⢞⠀⠀⢀⣠⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠐⠠⡄⠘⢣⡀
⠀⠀⠀⠀⠀⠀⢠⠋⢸⠀⠀⠀⣠⠐⣇⠀⠆⠀⠀⠛⣆⠉⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣱
⠀⠀⠀⠀⠀⢀⠃⢀⡸⢄⡀⠴⠃⠀⢛⢸⠀⠀⠀⡎⠈⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⢇
⠀⠀⠀⠀⢀⠆⠀⡙⠀⡎⠀⠀⠀⠀⠈⠾⡄⠀⠀⡀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⡜⠀⣺⠄⠒⠛⠒⠒⠀⠀⢠⣀⠇⣀⡧⠂⢀⠎⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠱
⠀⠀⠀⢰⠁⠀⠃⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢀⠔⠁⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⡎⠀⠀⡄⠀⠀⠀⠀⡠⠤⠷⠀⠤⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⢠⡔⠁⠀⠀⠀⠀⡇⠀⠀⠀⣀⠞⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢱⠀⢆⠀⠀⠀⠀⢠⠄⠀⣀⠞⠁⢀⡴⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠘⣆⠈⠳⢄⣀⣤⡩⠴⠛⠁⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡼⠁
⠀⠀⠀⠀⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠤⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠳⣄⠁⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠴⠖⠒⠒⠒⠚⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠖⠒⠒⠊⠋⠉






⣿⣿⡿⠿⣿⡿⢿⠿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠰⠏⢀⠀⠀⠀⠈⠉⠑⡄⠈⠁⡜⠀⠤⠀⠘⢂⠀⠀⠀⢰⠉⣀⠴⢄⠀⡼⠮⠑⠀⠀⠀⠀⠀⠁⠰⠀⢀⢄⠈⠀⠈⡆⠸⣡⠑⠀⢀⡠⠤⣤⣤⡀
⠀⠀⠀⡀⠀⢀⣀⠠⠄⠊⡍⠀⠀⢱⠀⠈⢠⢄⠀⠡⠀⠠⡁⠀⣁⠀⡈⠀⠀⠀⠀⡄⠁⠀⠐⠀⠀⠀⠐⠅⠀⠁⠂⡜⠀⢀⡈⠙⠀⠷⠦⠄⡸⢺⠁
⠀⠀⠀⢥⣁⡐⠠⠀⠀⠐⢈⠇⠀⠀⠑⢄⠀⠢⡑⢄⠇⠀⠈⠍⡹⢪⠅⠀⠀⡀⡰⠀⠀⠀⠇⠀⠂⠨⠀⠀⠀⢢⠎⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢰
⠀⢠⡄⠸⠄⠤⠀⠈⠑⠈⣀⣤⡀⠄⡤⢀⠉⠁⠐⠀⢠⣞⡃⢸⡞⣵⠀⠀⢀⠀⡕⠉⠈⣄⠣⠂⠰⢀⡈⢈⠔⠁⠀⢱⠶⠤⢤⡄⠀⠐⠀⠀⠒
⠀⠈⠃⠀⠠⡆⠀⢀⠖⠍⡀⠀⠌⡐⠠⠄⣘⢦⡀⠀⠸⠋⠀⠀⢯⡖⠀⠀⠀⡟⠀⠀⠀⣦⠀⠄⠐⠄⠐⠁⡐⠀⠀⠸⣄⣀⠀⠀⡀⠈⡅⠀⠀⠋⠂
⠀⠀⣠⠦⡄⠀⡠⢁⡨⠴⢤⡸⣒⣒⣫⠭⠒⡏⠀⡤⠴⠦⡐⡀⠸⠇⠀⠀⠀⠈⠉⢁⠊⠙⠊⠁⠀⠀⠀⠐⡠⠁⣤⠀⠀⠀⠀⠀⠁⠂⠂⠁
⠀⠀⢷⠀⠸⡄⠈⠣⣉⢈⢉⣉⣍⣍⠤⠴⠚⠀⠀⡇⠀⠀⢀⡜⠀⠠⠈⠐⠀⢀⣀⡀⠀⠀⠀⣀⣴⣶⣶⢾⣄⠀⠈⠀⠈⠀⠁⠀⠀⠀⡠⠆⢤
⠀⠀⡯⢀⢢⠘⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡀⠻⣀⠀⡀⡠⠗⠀⠘⢜⡥⠀⠃⠀⠈⠀⢀⠚⠿⣶⠽⠿⠿⠿⢧⠀⡂⠀⠀⣐⠀⠀⠶⠤⠠⠂
⠀⠀⠹⣄⣉⡰⠃⢀⠀⠈⠣⢀⡉⠀⠒⢉⡹⠋⠀⠀⠈⠉⠁⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠰⡤⠤⠙⠄⣀⡀⠠⡤⠀⠁⢠⠐⠂⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠄⠑⡤⠀⢆⠀⠀⠈⠉⠀⠀⣀⣠⢴⢮⡫⢆⠀⢀⡔⠠⠀⣀⡈⣩⢋⠕⠀⢀⠀⠀⠀⠀⠁⢰⠀⠀⠤⠘⠠⠀⢀⡜⠀⠘⡄⡅⢰
⠀⠪⡤⠔⠀⡌⠀⠀⠀⠀⡔⠀⠀⢠⠉⡈⣷⡼⠽⠞⠉⡠⢊⠴⣎⠨⢅⡠⣥⡤⠀⢀⢀⡀⠀⠀⣉⠉⠀⠉⠁⠀⠃⠀⠀⠀⠀⠬⡀⢀⡴⠃⠈⠓⠁
⠀⠀⠀⠀⡘⠀⠠⠠⠁⠈⠀⠪⠇⠀⠅⣀⡀⠤⠄⠂⠉⡠⡦⢂⣀⣠⡮⠞⠁⢀⠢⠂⠀⠈⡆⠈⠉⢀⣀⠖⡆⠐⠚⠠⠠⡆⠀⢦⠤⠸⡀
⠀⠀⠀⢀⠠⢤⡐⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡦⠀⠾⠒⠋⠉⠉⠀⢠⡺⡷⠀⠀⠀⢄⠜⠀⠀⢠⠛⠘⠁⠭⠬⠁⠨⠤⠌⠶⠀⠀⠈⢉⠔⠀⢄
⠀⢰⠀⠈⠀⠀⠱⠂⠀⠀⠠⡐⣥⣬⠁⠠⠀⢀⣀⣀⣠⠀⣿⣆⠀⠀⠹⠏⠁⡐⠦⠂⠁⢰⠦⠀⢘⢂⠀⠀⠀⠤⠄⠤⠐⢠⡄⠀⠀⠀⣌⠀⠀⢸
⠀⠀⠉⢀⣀⠀⣰⠚⡀⠀⠀⠀⠼⠁⠡⠀⠠⠟⠋⠁⠀⠈⠱⠿⠿⠃⠀⡄⠊⠀⠀⠀⠀⠀⢠⠀⡸⢄⣂⡈⠀⠀⠀⠀⣀⣠⠦⠀⠀⢠⠁⠀⠔⠺
⠀⠰⠢⠤⠤⠊⡀⠀⢁⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠃⢀⠄⠠⠀⠀⠑⠀⢠⠀⣉⡠⠖⠂⠀⠀⠀⠀⠩⠉⠭⠭⠀⠐⠈⠠⠄⠠⡀⠀⢀⠇
⠀⠘⡆⠠⠀⣀⡠⠈⢁⠊⡥⠀⡁⢱⠀⠢⢄⣀⡀⠤⠶⠗⢠⠃⠀⠀⢀⡀⢠⠀⠀⡘⠀⠀⢠⠀⢠⡟⠩⠀⠀⠀⠀⢀⠠⠀⠀⠳⡟⠀⠈⢸⠁
⠀⠀⠑⠐⠀⠁⠀⠀⠘⡄⠃⠐⠁⠀⡃⢀⠄⠄⠠⡀⠀⠀⠁⠂⠀⠀⢨⠇⠀⡁⠀⠀⠀⠠⠀⠁⠀⢀⡄⠭⠈⠡⢬⡇⠀⠀⠐⢄⠀⠀⠐⠂
⠀⠠⠂⡐⡢⢲⠁⠄⠀⠡⣀⠔⠂⠈⠀⡘⠁⢀⠠⠀⠈⠀⢀⠶⠀⠀⢹⠀⠐⡀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠈⢀⠤⠤⠜⠒⡥⠂⠉⠀⢤⡔⠀⡈⠄
⠀⠐⠃⠈⢰⠈⠃⠚⠁⠀⡔⠀⠒⡄⠀⠒⠉⡯⠆⠀⠠⡀⠀⠉⠐⢀⡘⠀⠀⠀⠸⠆⠀⡠⠏⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⢰⠀⠀⢀⠘⠛⠉
⠀⠀⠠⠤⠘⠒⠐⠉⠃⠀⠈⠃⠁⠀⠀⠀⠀⠇⡈⠀⠀⠈⠐⠒⠒⠉⠀⠀⠀⢒⣄⠀⠪⣁⠌⠒⠠⠄⠶⡉⠐⠶⢚⣁⠤⠊⢀⡀⠐⡀⠀⠠⠂⣀
⠀⠀⠀⠀⠀⠉⠑⠀⠀⢀⢀⡀⠀⠣⢄⡊⠀⣀⡀⢀⡖⠒⠚⢳⠀⠀⢠⠀⠀⡄⠀⠀⠑⡄⠀⠉⠁⡠⡀⠀⣠⠄⠀⡠⡀⠀⠈⠀⠀⠀⠀⠀⠘⠐
⠀⠀⠀⡀⠠⠀⠁⠐⠀⠘⢄⣢⠐⠂⠀⠀⠈⠥⡬⠂⠹⠀⠀⡏⠀⠀⡁⠀⠀⢄⣀⣀⡔⠀⠀⠀⠸⠬⠋⠋⠰⠋⢸⢠⡘⠀⢁⣀⠔⠐⠒⠂⠄⠀⡀
⠀⠀⠒⢀⡠⠤⢄⡀⠀⡀⡄⠄⠀⢀⠄⠂⢄⠈⠀⠀⠙⠒⠚⠓⠒⠒⠁⠠⠄⠀⠀⠈⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡉⠈⠉⠉⢩⠃
⠀⠀⡴⢯⣗⢸⠎⢁⠀⡷⠄⡠⠐⠁⠈⠀⢸⠀⠀⡴⠊⣀⡀⠱⠆⠀⠀⠀⠠⠐⡖⠀⠀⠀⡠⠔⠈⠉⠑⡾⠿⠷⣂⠉⠁⠀⠀⢱⠤⠀⠀⠀⡔⠃
⠀⠀⢿⠷⠑⠁⠀⢸⠀⠀⠀⢀⡀⠀⣀⠔⢡⡀⢸⢠⠎⠁⠀⢤⠈⠐⠂⠀⠐⠊⠁⠀⠐⠀⡀⣀⡄⠤⠔⠀⠀⠑⢄⠀⠀⠀⠠⠄⠀⠀⠀⢈⣁⣰⠆
⠀⠀⠀⠁⠀⠀⠂⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠞⣉⠻⣟⠲⢶⣒⣲⣦⠄⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣤⣿⣿⣭⣭⣝⣛⣳⠮⠤⠬⢭⠷⠞⣛⠉⠉⠛⢦⡇⣸⠗⢦⡀⠀⠀⠀⢀⡀
⠀⠀⠀⢤⢤⣀⣀⣠⡿⢒⡭⢕⣚⡽⢖⣛⡭⣤⢶⡶⠖⣫⣴⠞⢉⣍⡛⣯⣡⡬⢇⡿⢋⣝⣿⣶⣶⠿⡟⣀⡀⣠⡤
⠀⠀⠀⠘⠒⣦⣬⠭⠿⠟⣛⣓⣛⡚⡓⠢⠬⣴⣉⣴⣞⡓⣻⠟⠁⠳⡙⠿⡏⢸⢹⡶⣿⠿⠟⣛⣻⣤⣭⢁⡖⠁
⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠍⣛⠻⢅⡀⠀⠀⢧⠀⡏⡞⢸⡼⠃⡼⢋⡡⠒⠉⣼⣛⣓⣒⣒⡒⢲⠆
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⡓⢦⣼⣷⡿⠁⠛⠳⠦⠿⣟⣲⣿⣿⣿⣿⡷⠼⠬⣍⣁⣀
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢌⠻⣥⡠⠤⠄⠒⠂⢠⣿⣿⣷⣶⣶⣶⣶⣦⢤⡤⡜
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡙⢦⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢣
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢧
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡆
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿
⠀⠈⠓⠲⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠢⠻⣿⣿⣿⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⢦⣤⣄⣈⣙⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠂
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⡠⠀⠰⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢣⡀⠀⢀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢷⡀⠘⢇⠀⠀⠀⠲⠆⠶⠄⠀⠉⠑⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠑⣤⣀⠀⠀⠀⣀⣀⡤⠴⠒⣻⣿⣶⣿⣿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠛⠉⠛⠉⠁⠀⣠⣾⣿⣧⣟⣍⣫⡞⣽⣿⡄
⠀⠀⠀⠀⡠⠐⢉⣀⣽⠀⠠⠸⢷⠖⠉⠉⠀⠀⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢰⣿⣻⣖⡷⡾⣶⣳⣏⡼⢯⢿
⠀⠀⠀⠠⡟⣿⣽⣿⣿⠐⠀⡠⣿⠰⣰⣶⢶⣾⡎⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⣽⢿⣹⣛⡯⠓⢊⣧⣄⣀⢺⣶
⠀⠀⠀⢀⣿⣿⢿⣿⣿⠐⠀⣴⠿⠃⢉⡣⢹⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣿⣿⣨⣭⣿⣿⣿⣿⣿⣿⣿⡟
⠀⣀⡄⢤⣿⠛⢿⣿⣿⣦⠟⠁⠀⠄⠀⠸⣼⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠊⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⢻⣿⠿⣿⣭⣿⣶⣾⣿⡟
⠸⡿⣷⠄⣿⠀⠀⠙⠻⣿⠀⠀⠀⠀⢀⡴⣋⡏⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣀⢒⡻⠟⠁⠀⢀⣾⣿⡤⠔⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠟⠛⠉
⣼⣾⡿⠦⣽⠂⠁⠀⠀⠹⣦⣀⣠⣴⣟⣵⢩⠁⠀⠀⠀⠀⡠⢀⠀⠀⠐⠎⢉⣉⠿⡧⢀⡀⣼⣿⣿⣆⣠⣶⣰⣤⣦⠀⣀
⠀⢸⡟⠢⣵⠀⠀⠀⠀⢀⣽⣿⡿⣽⣿⠃⢸⠀⠀⠀⠀⠸⠦⣼⣳⣦⠠⠤⠤⠤⠤⢒⣾⢧⣿⠯⠇⠈⠙⠿⣿⣿⡿⠁⢈⣁⣤⡀
⠀⢰⡇⠀⠀⠳⣄⣴⣴⣿⣿⣯⣾⣿⣯⠂⢨⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⠶⠶⣶⣿⣿⣿⣾⠟⠛⠒⠶⠶⠾⠿⠟⠛⠋⠉⠁⠈⠁
⠀⢸⡇⠀⠀⠀⠈⠻⠿⠽⠾⣿⣿⣿⣿⠄⢸
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣀⡠⠄
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⢼⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⣶⣇⣀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⡀⣼⣷⠌⠟⠽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠
⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⢷⢸⣟⣷⣶⠆⢺⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⢰⠆⠁
⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠂⣳⠄⠚⠋⠉⠉⡳⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣔⢠⡔⠀⠀⠀⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡴⠋
⠀⠀⢸⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠠⣿⠊⠀⠁⢰⣾⡿⣻⣿⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⣠⣇⣰⠿⠋
⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣜⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⣶⠃⠀⠀⠀⢈⡿⢛⠫⡉⢉⡇⠀⠀⠀⠀⠀⢸⣗⣰⠿⠛⠁
⠀⠀⠀⢿⣷⠀⠀⠀⠀⢀⣐⣀⡾⣟⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠒⢬⣾⠻⠜⠿⠁⣼⠁⠠⣶⣄⣀⡶⠟⠋
⠀⠀⠀⠀⢻⣿⣴⣆⣤⣿⣿⣿⣿⠟⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠑⠀⠀⠀⠀⠀⠀⠀⣠⡏⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⣀⣤⡤⠴⠟⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⢘⠦⠀⠀⠀⠀⠀⠐⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠀⠀⠀⢰⡁⢀⡠⣀⠀⠀⠆⠀⠀⠀⠀⠀⡄⠠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢢⣴⡆⢧⡸⠁⠈⣴⠖⡀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣬⠟⢋⣉⠁⠢⡜⠁⣨⠁⠠⢂⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⠀⣴⠏⣴⢻⡀⢹⠦⠃⣴⠇⠆⢀⢎⣠⡔⠢⣴⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⡟⣡⡤⠛⣸⣄⡘⠃⣰⡏⢠⡖⠙⢏⠀⣀⠔⠉⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢛⠹⠀⡿⠑⣾⠻⠝⣻⡞⠉⢹⣾⣛⡄⢸⣶⠋⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠸⣴⣄⠵⣤⣿⠃⣸⡿⣷⣶⣻⣆⡸⡡⠞⠛⣦⠴⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢻⡆⢐⣳⣮⡻⠇⢡⣿⠁⠀⣿⠟⠁⠀⠀⣤⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡇⠈⢹⣿⡟⡰⠯⠧⠀⠀⠀⢀⣠⠞⠋⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡐⣯⠏⣷⠿⣦⣤⢤⡐⠛⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠹⣞⣹⠷⠚⠉⠀⠀⠁⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣜⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⣀⣀⣀⣤⣴⣷⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁



⣶⣶⣶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣴⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⣀⢸⣇⡀⠀⣿⡇⣿⣿⣿⢻⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡟⢿⢻⣿⢸⣿⣿⡇⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⣿⡇⠀⣿⣿⣿⡇⠀⣿⡇⣿⣿⡟⠀⢿⡇⠈⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢠⣤⣤⣤⡀⢸⣿⠀⣿⣿⣷⣿⣾⣿⣼⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⣿⡇⠀⠙⢻⡟⠃⠀⣿⡇⣿⣿⣧⣤⣿⣧⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣾⣿⠀⣿⣶⣶⣶⣶⣶⣶⣶⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣷⣶⣶⣾⣷⣶⣶⣿⡇⢿⣷⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⠤⡤⠤⠤⠤⠀⠀⠀⣄⣠⣠⣄⣄⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣇⢠⣷⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢦⣭⣭⣬⣥⣭⣭⡤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠛⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⢶⡶⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢦⡀⠀⠀⠀⢀⣀⣐⣀⡀⠀⣰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠿⠷⠾⠀⠠⠿⠿⠿⠆⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠾⠿⠇
⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣩⣭⣭⣭⣭⣭⣭⣭⣭⡍
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⣿⣛⣛⣛⣿⣿⣿⡇⣿⡷⠷⠾⠶⠾⠶⠷⣿⡇⣿⡇⠀⣠⣤⣤⣄⠀⢽⡇⣿⡇⠀⠴⠶⠶⠦⠀⢸⡏
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⠋⢻⣋⣟⠙⠋⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⡟⠛⣛⣛⣛⣛⠛⢻⡯
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⣿⣿⣿⠀⠀⣿⡇⣿⡇⠀⣤⣤⣤⣄⠀⢹⡇⣿⡷⠶⠶⠾⠿⠶⠶⢾⡯
⠀⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣴⣾⣿⣷⣦⣤⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⣇⣀⣛⣛⣛⣋⣀⣸⡧
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⡀⠀⠘⣧⠀⠀⠻⠀⠀⠓⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡾⠃⠀⠀⣰⠗
⠀⠀⠀⠀⠈⢻⡄⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠓⢄⠀⠀⢀⠞⠙⣆⠀⠀⢀⡠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠞⠁⠀⢀⡶⠄
⠀⠀⢠⣄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠑⠦⣄⢠⠁⠀⠀⠑⠶⠁⠀⠀⠘⠦⠐⠁⠀⠀⠸⡆⠀⢀⣠⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⡀
⠀⠀⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠂⢠⠀⠀⠀⠷⠒⠉⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠽⠓⠋⠉⠉⢆⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠑⠢⣤⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⢀⣠⠤⠖⠒⠙⢦⢀⡇⠏⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢠⠃⠀⠀⠀⢀⡤⠒⠒⠎⠀⣠⡾⠁⠀⠀⠀⡀⠀⠀⠀⠈⢻⠁⠀⠀⢠⡞⠙⠲⢤⡀⠀⢀
⢀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠘⡌⠃⠀⠀⠀⠀⢸⣇⠀⠀⠘⡆⠀⠀⡎⠀⠀⠀⢠⠇⡀⠀⡸⠀⡌⣽⠁⠀⠀⢠⠞⠉⠑⡆⠀⠀⠀⢧⢀⡴⡟⠀⠀⠀⠀⢨⠃⠉
⠘⡄⠀⠀⠀⠀⠀⠀⢀⡤⠔⠳⣸⢴⠀⠀⠀⠘⠛⠀⠀⠀⠘⡄⢘⣧⠀⠀⠀⠈⠯⣁⣀⣁⡜⠁⡎⠀⠀⠀⡏⠘⢢⠀⣸⠀⠀⠀⣸⠋⡼⠁⠀⠀⠀⡰⠃
⠀⢹⡀⣀⠤⠄⠀⠀⠈⡷⢄⡀⠜⢻⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⣼⠘⢆⠀⠀⠀⠀⠀⠀⠸⡇⠀⣥⠀⠀⠀⢇⠀⣰⡧⠃⠀⠀⢀⡟⡸⠁⠀⠀⠀⡰⠁
⠀⠀⠙⠠⢤⢸⡀⠀⠀⠸⡀⢅⠀⠸⡀⠀⠀⠀⣻⠈⢧⠀⠀⠀⠙⣄⠈⠳⣤⣀⠀⠀⠀⢀⡇⠀⠘⣆⠀⠀⠀⠉⠁⠀⠀⠀⢀⡞⣱⣃⠀⠀⢀⣜⡀
⠀⠀⠀⠀⣀⡠⢵⠀⠀⠀⢳⠘⡀⠀⡂⠀⠀⠀⣙⢣⣸⡧⠐⠂⠚⣻⡀⠀⠀⢉⠙⢙⠉⢩⢣⡀⠀⠈⠳⢄⣀⣀⣀⣀⣤⡶⢻⣽⠤⠬⣉⠗⠁⢈⠝
⠀⠐⢎⡉⠀⠀⠈⡆⠀⠀⠈⢧⢁⠀⠧⠄⠒⠊⢡⣠⣀⣻⣤⢤⣤⢟⠿⢟⣻⣿⡎⢠⢽⣿⠶⠗⠦⣤⠀⠀⠀⠀⣁⠕⠈⢠⠛⢇⠀⠀⢈⣦⠞⠁
⠀⠀⠀⠈⠲⣄⠀⢹⣤⠴⠒⠉⠀⡦⠈⢢⣴⠀⣾⢿⣋⠷⠀⢵⠖⠋⢲⡈⡠⢾⠿⠭⣦⣽⡿⠿⠚⣍⢛⠳⣬⡉⠀⠀⠀⠺⣀⠈⢙⠟⠉⠙⠒⠦⣄
⠀⠀⠀⠀⣀⠜⠁⠀⠀⠉⠐⠀⠡⢒⣲⣥⣶⡿⠿⠿⠛⠛⠛⠛⠻⠛⢺⠿⣤⣉⡀⢾⠧⠉⠾⢟⡛⢙⠷⢶⣤⠛⢶⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣈⠽⠃
⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⢀⣦⡿⠟⠉⠈⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠈⠐⠨⠛⠶⣤⠐⠂⠚⣧⠲⠞⡅⢠⡃⡀⢿⡗⢦⡀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠁⠙⠒⠢⠄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡔⠈⡻⢦⡃⢤⣦⣤⣧⣄⢹⡄⢘⣿⡲⡙⣆⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⡠⠂⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠦⡙⢧⡀⢹⣤⡈⣯⠛⢣⡂⢄⡼⢮⣷⡄⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢠⠞⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⡢⠹⣧⡀⢈⣧⡤⣮⣽⣀⣘⣂⣷⡹⣄⣠⠴⠚⠁
⠀⠀⠀⠉⠐⠒⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠑⢌⢻⣍⠏⢀⣀⠹⣋⡷⠛⡏⢳⢹⣦⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠹⣧⡨⠥⢖⢊⣃⣴⠲⡿⣇⢻⡝⠦
⠀⠀⠀⠀⠀⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⣧⡃⢨⠏⢛⡠⠀⠸⢿⢸⡇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠱⡘⣿⣄⡀⢡⡀⠄⣀⣿⢸⡇
⠀⠘⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⢌⡻⣤⣤⣰⣼⠿⢣⣾⠁
⠀⠰⠖⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠛⠛⠓⠒⠒⠲⠶⠶⠶⠶⠴⠤⢤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣈⣐⣪⣭⣴⡾⠟⠁⠀⠀⠀⠀⠀⠙⠶
⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠤⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠉⣹⠉⠉⠙⠛⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀
⠀⠈⠋⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⢧⠀⠀⢀⡴⠂⡀⠀⠀⠀⡴⢄⠀⠀⠀⠀⡌⠑⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠛
⠀⠀⠀⢴⠟⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠔⠉⠀⠀⠑⡄⢀⠞⠀⠀⠑⢄⠀⡸⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢻⣄
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣴⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢰⡄⠀⢱⡄⠀⠸⣧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣷⣾⣷⣶⣾⣷⢷⣿⣶⣿⣾⣷⣷⣾⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡷⡷⢾⡷⠾⢶⣶⠶⠿⠶⠾⢿

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⠀⠐⠚⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠁⢀⡀⠓⠒⠒⠒⠒⠒⠒⢀⡀⠀⠀⠀⣶⡷⣿⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡠⢺⢀⣁⠆⠁⠀⡂⡾⡀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡟⣰⠋⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⢠⡌
⠀⠀⠀⠀⠰⣀⠀⠇⢐⠈⠼⠀⠀⢻⡥⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠤⠲⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢨⣉⢿⡇⠄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠰⠒⠀⠀⢸⠀⠆
⠀⠀⠀⡠⠀⠰⢂⠛⢺⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠡⠄⠄
⠀⠀⠀⢉⣀⠀⠀⠌⠀⠨⠌⢻⠍⠀⠀⠀⠠⠄⠐⠀⠀⠁⠀⠀⠀⠈⠀⠀⢣⠀⠀⠀⢀⢀⠀⠠⠄⠤⣀⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠰⢤⢀⠀⠈⠓⠂⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠰⡁⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠭⠙⢲⡄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠊⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⢀⣀⣄⣀⣀⡀⡀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠄⠀⠀⠠⠶⠀⠀⢂⠀⠀⠠⠄⠀⠀⠈⢀⠠⢀⣀⠀⠒⣤⡀
⠀⠀⠀⠀⠨⡉⠁⠙⠀⠛⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⠆⠀⢀⡀⠀⠀⠀⢀⠀⡡⠀⣁⢀⡴⠎⠁⡱
⠀⠀⠀⠀⠀⠱⡒⠲⠲⠒⠒⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣀⢠⠴⠙⠘⠀⠀⠀⡀⠋⢸⠅⠀⡀⡤⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠀⢀⠉⠃⠀⠀⢒⠈⢡⠀⠠⠇⠀⠘⠀⠂⠁⠑⠀⠀⠀⢀⠀⠈⠀⠀⡀⡁⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⢠⠀⢀⣄⠀⠀⠀⠉⠁⠀⢀⠐⢉⡀⠀⠀⠀⠀⢀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⠀⡘⠀⠀⠠⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⢀⣠⠰⠃⣀⢶⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡘⡷⠀⢠⣄⠀⠀⠀⠀⢀⠨⠁⠀⠄⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠾⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢂⢀⣔⢴⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠈⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠁⠀⠛⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠒⢀⠀⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠀⠉⠀⠀⠀⠈⠀⠀⠄⠀⠠⠠⠔⠲⢖⠒⠀⠥⠀⠀⠀⢢⢢⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠅⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢴⡡⠠⠤⠄⠄⠤⠤⠠⠄⠡⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠊⢁⠉⢀⡀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠄⠀⢀⡀⠀⠁⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠤⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠠⠄⠠⠶⠶⠒⠐⠂⠒⠀⠒⠖⠂⠤⠤⢀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⢀⠔⠉⠂⡀⠈⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠊⡀⠀⠁⠀⠀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠸⠀⠐⢀⠂⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡖⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠁⠂⠠⠄⠀⠁⠀⠁⢁⡉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⠉⠐⢄⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠁⠂⠰⢁⡀⠤⡀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢤⡀⡀⠀⠐⠀⢠⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⢂⠙⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⠜⠀⢸⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠺⠃⠀⠀⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⠀⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢂⣀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠅⡀⠉⠀⠈⠀⠀⠀⠀⠆⠀⠰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡤⠀⠀⠀⠀⠀⠉⢠⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⢀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠂⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠂


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

⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠸⣇⠀⠠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⢠⡶⠀⠀⠀⣠
⠀⠀⠀⠀⢾⣄⠀⠈⢷⡀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⢶⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠞⠁⠀⢀⡾⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠂⢄⠀⠀⠀⠎⠀⠑⢄⣀⡔⠁⠀⢳⡀⢀⠴⠊⠁⢰⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣴⠟⠁
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠢⠜⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣇⢀⡤⠚⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⡤
⠀⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢐⡗⠒⠢⢤⣀⡧⡤⢤⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠉⠉⠉⢸⠀⠀⠀⠈⠁⣀⢠⡤⠧⢤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠈⠓⠀⠀⠀⠀⢀⣀⣤⡀⠀⠁⡔⠊⠉⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠈⠳⣏⡇⠀⠀⠀⢀⢀⣀⠀⠀⠀⠚
⠀⠀⢀⡠⠴⠒⠉⠉⠀⠀⢧⢠⡄⡇⠀⠀⠀⢠⡀⠀⠀⢣⠀⠀⠀⣼⠀⠀⠀⠀⡴⠛⡉⢉⠁⢀⢼⡏⠀⠀⠀⣠⠤⢄⡀⠀⠀⠈⢇⠀⠀⣰⠏⠀⠀⠉⠲⣄⠠
⢖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢅⠁⠀⠀⠀⢸⣧⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀⠀⣇⠧⠤⠞⢀⡎⣾⠀⠀⠀⣰⢃⠀⠀⢱⠀⠀⠀⢸⣤⢞⡟⠀⠀⠀⠀⣠⠃
⠘⡄⠀⠀⠀⠀⠀⠀⢰⡃⠁⠘⢴⣰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢰⢿⡀⠀⠀⠀⠑⠒⠒⢲⡎⠀⢿⠀⠀⠀⠂⠀⠘⡆⡸⠀⠀⠀⢸⠁⡼⠀⠀⠀⠀⡰⠁
⠀⠻⡤⠖⠚⡀⠀⠀⠈⣯⠢⠄⠊⢸⠀⠀⠀⠀⣤⢶⡄⠀⠀⠈⢾⠀⠳⣄⠀⠀⠀⠀⠀⠈⡇⠀⢹⡀⠀⠀⠰⠄⠴⠟⠁⠀⠀⢀⡏⡼⠁⠀⠀⢀⡜⠁
⠀⠀⠀⠈⠓⠸⡀⠀⠀⠘⡄⢃⠀⢸⠀⠀⠀⠀⢫⠂⢻⡀⠀⠀⣈⣧⠀⠈⠓⠦⢤⣀⣀⣠⡗⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⣠⣟⠔⠣⠤⣀⡠⠾⢤⡀
⠀⢀⣀⡤⠤⠒⢣⠀⠀⠀⢳⠸⡀⠈⡄⠀⣀⣠⡤⠳⠘⣅⠉⠁⠀⣼⣤⣠⣤⡰⠀⡠⢄⣰⡁⣄⠀⠀⠈⠒⠦⠤⠤⠴⣒⠟⢹⡾⠚⠓⠲⡌⢀⣠⠊
⠀⠈⠓⢄⠀⠀⠈⡆⠀⠀⢀⣷⢠⠀⠣⠋⠁⠀⢠⣼⣤⡼⠶⠞⠻⣯⡋⠱⠞⢛⡏⠹⣛⣿⣛⣉⡉⢶⣇⣀⠀⠠⠔⠊⠁⢠⠇⠳⢄⣀⣠⣿⡋
⠀⠀⠀⠀⠑⢦⡀⠸⠖⢊⡁⢀⠌⠃⢀⡵⠺⣬⣟⣻⣬⣩⣥⣹⣃⣀⣸⣄⠔⣹⠛⢛⡿⢶⣞⣻⣭⣦⣄⠈⠒⢦⡀⠀⠀⠘⠢⠠⠤⠊⠀⠀⠈⠙⠲⣤⣀
⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⣀⣼⣭⣷⠞⠟⠛⠋⠛⠉⡉⢉⠉⠉⠉⠹⣟⠳⢦⣌⡙⠛⢒⡋⢻⡌⢈⢟⣿⠿⣍⠹⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠰⢚⣁⠀⠀⠀⠀⠀⠀⣸⡾⠛⠋⠀⠄⠀⠀⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠄⠁⠪⠙⢶⣍⠁⡈⠷⡙⢫⡵⠀⢧⡤⠘⣿⡻⣆⠀⠀⠀⠀⢠⡞⠋
⠀⠀⠀⠀⠉⠒⡂⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠎⢰⢌⠳⣄⡐⠴⣾⠷⢶⣤⣧⡀⠿⢝⢮⡳⣄⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⣠⠎⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠑⢈⠳⣆⡠⠖⢦⡰⠋⠑⣦⠠⢦⡙⣟⣦⠀⠀⠀⠀⣈⠦
⠀⠀⠀⡔⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⢈⢳⣄⣠⣣⠖⠿⢼⣤⣬⢇⣸⣎⢷⡤⠒⠉
⠀⠀⠀⠀⠀⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⡙⣧⡟⢀⡤⠜⢣⡿⠉⠳⢸⡎⣷⣄
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⡌⢿⡄⢖⢈⣅⣧⡼⠙⢟⣻⡘⡧⠓
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡌⢿⣝⠀⠊⢩⡄⠀⠀⢻⡇⣿
⠀⣀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⢄⢻⣇⠄⠐⠄⠀⣤⣿⢃⡟
⠀⠉⠀⠀⠀⠈⠛⠲⢦⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢝⠳⢤⣮⣷⠟⣡⣾⠃⠀⠀⠀⠀⢀
⠀⠚⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⢹⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣉⣺⣦⡶⠾⠛⠁⠀⠀⠀⢀⠀⠈⠛
⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡠⠔⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⠁⠀⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡀
⠀⠈⠁⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢷⠀⠀⣠⠔⠐⡄⠀⠀⢀⡴⠢⡀⠀⠀⠀⡎⠉⠢⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠁
⠀⠀⠀⠾⠋⠀⢀⡴⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠚⠁⠀⠀⠘⣄⣠⠎⠀⠀⠈⢦⡀⡸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⣧⡀
⠀⠀⠀⠀⠀⢰⡟⠁⠀⢀⣾⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡦⠀⠘⣆⠀⠈⢿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢂⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠒⠋⠀⠀⠀⠀⢠
⠀⠑⢀⡀⠈⠐⠠⠀⠀⠀⢐⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠁
⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣴⠋⠙⣆⡞⠉⢹⡄⡏⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠲⠞⠁⠙⠲⠚⠁⠳⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⣰⣇⢰⠋⡂⣶⡃⣞⢹⡀⣿⠢⡎⢱⢸⢰⢰⢦⡆⣞⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠉⠀⠀⠁⠈⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠁⠈⠁
⠀⢀⢀
⠀⠰⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠠⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠂⠤⡀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠋⠁⠀⠈⠙⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⢀⠠⠊⠀⠀⠘

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠠⡏⠀⠀⠀⠀⠈⠉⠑⢆⠀⠋⢰⠋⡠⠄⠀⠓⣄⠀⠀⠀⢘⠁⣀⠥⠀⠀⣌⢮⠑⠁⢀⠀⠀⠀⠊⢄⡊⠀⠠⠀⠁⠄⢱⠀⢛⣌⠂⠀⢀⡠⠤⣤⣄⡁
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢤⣋⠃⠀⠘⡄⠈⠂⡄⡀⠈⠆⠀⢠⠁⠀⣁⠀⡸⠀⠀⠀⠐⡂⠀⠐⠀⠠⠀⠀⠀⠆⠀⠀⠐⢀⠆⠀⣀⠑⠃⠰⡯⡤⠄⡹⢺⠁
⠀⠀⠀⠌⡄⠡⠀⠀⠔⡠⠌⡳⠀⠀⠘⢆⡀⠠⣈⠢⣘⠀⠀⠙⡝⡣⢬⠁⠀⠀⠀⠠⠅⠀⠀⠸⠀⠀⠠⠁⠀⠀⠑⡠⠋⠀⠀⠉⠓⢄⠀⡄⠀⠀⠀⢸
⠀⢀⡀⠰⣉⣉⡀⠤⠂⠂⠉⣀⣀⢀⣀⡀⠈⠒⠈⠔⠀⢠⢶⠀⢛⠽⣳⠀⠀⠀⠡⡡⠊⠘⢄⢀⠰⢀⠅⡀⠀⢂⠜⠁⠈⠦⢇⣀⣀⡘⠀⠃⠠⠤⠔⠈
⠀⠈⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⠃⠌⠠⠉⢲⡀⠀⠀⣿⠙⠀⠈⣞⡜⠀⠠⠬⡶⠁⠀⠀⣸⡀⢀⠐⢄⡩⠔⢁⠄⡀⠀⣀⠀⣀⠌⠀⠄⢠⡀⠀⠀⢒⠄
⠀⠀⢀⣄⡀⠁⠀⡈⢁⣀⣎⡀⠦⠬⠐⡦⣮⠵⡎⠀⣀⣤⣄⢀⠀⢻⡃⠀⠀⠀⠙⡂⠐⡦⠛⠬⠂⠀⠀⠀⠀⠌⡔⢀⣀⠀⠉⠉⠀⠐⠂⠁⠀⠆
⠀⠀⢿⠀⢹⡄⠘⠰⠒⠠⠐⠚⠒⠒⣉⣀⡤⠞⠀⢘⠇⠀⠀⢉⡗⠀⢠⠄⢠⠀⠀⡀⠼⠀⠀⠀⠀⢀⣤⣄⣤⣎⠀⠈⠋⠀⠊⠑⠀⠀⠈⠀⣀⡀⣀⠂
⠀⠀⢸⢀⠤⠑⡄⠀⠉⠓⠃⠉⠉⠉⠉⠀⠀⠀⠐⡼⠀⠀⠀⢸⡇⠀⢠⠰⠀⠀⠎⠁⠃⠀⠀⠠⣿⣿⣝⣿⣵⣿⣷⠀⢠⠄⠀⠀⡆⠀⠤⣼⡁⢠⠍
⠀⠀⢱⡈⠒⢀⡇⠀⠀⠀⢳⠚⠒⠀⠤⠄⠒⢶⠂⠈⠃⠒⠶⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡼⡅⠀⠀⠀⠀⢃⠀⢄⣀⡠⠃⠀⠀⠉⠉
⠀⠀⠀⠙⠙⠋⢀⠴⡀⡀⢄⠉⠀⠐⠒⠒⠊⠁⠀⢀⢠⡠⢂⡀⠀⠀⣀⠁⠀⠀⠒⠒⡶⢦⠀⠉⠉⠀⠀⢘⠻⠀⠉⠁⠀⢀⠇⠀⠀⠀⡀⠀⢣⠈⠂⢢
⠀⣰⠂⢐⠀⢠⠃⠀⠉⠁⢈⠀⠀⠀⠠⠄⠤⡄⡖⣆⡿⠿⢉⡕⢀⡔⢱⠊⠉⠌⠉⠉⠐⠁⠀⠈⠒⠀⠤⠀⠀⠐⠀⢠⠌⠁⠀⠁⠀⠞⠁⠀⢀⠗⠲⣎⠄
⠀⠈⠉⠀⢀⠆⠀⠀⠀⠀⠄⢠⢤⠀⢲⠒⠀⠛⠁⣀⠠⠔⢋⡔⠹⠃⠈⣰⣹⠟⠉⠀⠒⠀⠒⡄⠀⠶⠀⠀⣠⣀⡀⣠⡄⠀⣀⠀⢰⠁⠂⣰⠁
⠀⠀⠀⢀⠎⠀⠀⠐⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⢉⡀⠀⣠⣈⡥⠴⠖⠚⠋⣡⣄⢠⠀⠀⠀⢀⠇⠀⠀⣤⢒⠇⠨⠄⠤⠀⠅⠘⠠⡀⠙⢁⠼⠂⡀⣀
⠀⢀⠀⠰⢈⠋⠣⣀⠄⠀⠀⢀⡂⠀⠤⠄⠀⠀⠙⠁⠀⠁⠀⣤⠀⠀⠀⢞⣭⠍⢸⡀⣀⠔⠁⣀⠀⠀⡀⠀⠠⡈⠉⠉⠁⠉⠉⠁⡁⠀⠀⠀⡘⠀⠀⢁
⠀⠘⢤⡀⠀⠈⠁⣁⡀⠀⠀⠰⠺⣾⠪⠀⠁⢠⣶⠶⠒⠒⠠⢟⡦⣄⡀⠘⠁⡠⠀⠉⠀⠀⠈⠊⠀⠀⡆⠁⠀⠀⠀⠉⠀⠁⠀⢹⠁⠀⠀⠀⠇⠀⢀⡘
⠀⠀⡀⠄⠲⢈⠜⠁⢀⠀⠀⠀⠀⠑⠄⠀⠠⠋⠀⠀⠀⠀⠂⡈⠉⠉⠀⠐⠏⠄⢀⠀⠄⠠⠔⢈⣆⠈⠑⠂⠠⠤⠤⠤⠤⠤⠔⢚⠳⠀⠀⠰⠈⠀⠁⡇
⠀⢨⠁⠙⠀⡁⠆⠀⡠⢀⡠⠄⠤⢄⠀⠀⠁⠀⠀⠀⠀⢈⡄⠀⠔⠈⠉⢂⠀⠈⠁⠐⠀⠄⠂⠉⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠈⠀⢀⣎⡆⠐⠤⢤⠰
⠀⠀⢅⢐⡂⠠⠔⠁⠠⡃⣰⠉⢱⠀⢧⠀⠛⠀⠀⠐⠚⠛⠁⠜⠀⠀⠐⠸⡄⠐⡄⠠⠜⠀⢂⠉⠆⠀⠏⠐⡀⠄⠀⠀⣀⠐⠠⠀⠀⠓⠇⠀⡇⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢁⢀⡠⠃⣾⠑⠒⠒⠄⠠⠊⠈⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠼⠒⠀⠀⠒⠺⡀⠀⠀⣈⡆⠀⠀⠀⠀⡀
⠀⠀⡁⢨⠽⢹⣀⢓⡀⠈⠢⠚⠁⠀⠀⢰⠁⣀⡤⠊⠀⡇⡀⠰⠿⠀⠃⢸⠀⠈⠄⠉⡁⠀⠀⢀⠴⠊⠁⠀⠀⢀⠔⠂⠀⠉⡹⠊⠀⠀⠀⢾⣟⣀⠤⠂
⠀⠈⠁⠀⠠⡀⠸⢘⡀⠀⠰⣉⣈⡳⠀⠀⠁⠘⠘⡄⠀⠡⡐⠀⠀⢈⣠⠎⠀⠀⠀⠈⠁⢀⠄⢃⠀⠀⠀⠤⢀⠀⠀⠀⢀⡼⠡⡮⠀⠀⠒⠊⠉
⠀⠀⠀⠓⠀⠃⣉⠉⠁⠀⠀⠁⠀⢠⠄⠀⡄⠀⠤⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠨⠦⠀⣑⠬⠤⣉⣒⣒⠚⣥⢊⡛⠋⠥⠐⠊⠁⡄⠄⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠁⢈⠀⠀⠀⡉⡕⢀⠈⠒⠬⠀⢀⣤⡀⢰⡋⠉⠉⣷⠀⠉⢱⠀⠀⠃⠀⠀⠀⡀⠀⠀⢀⡠⣤⠀⡠⢦⡀⣀⠤⡀⢀⠉⠀⠀⠀⠀⠀⠈⠖
⠀⢠⠀⡀⠢⠀⠠⠐⠀⠀⠱⢡⠞⠁⠀⠀⠀⠱⡤⠜⠀⠇⠀⢸⠇⠀⠀⡆⠀⠈⠢⠀⣠⡔⠁⠀⠀⠈⠠⠋⠈⠄⠎⠀⠅⠠⠁⠀⣴⣤⢂⡘⠃⠁⢆⣀⡄
⠀⠀⠉⣀⣤⠐⠤⡀⠀⠀⢀⢰⠀⠀⡠⠒⠒⡄⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⠠⠤⠀⠀⠀⠀⣠⠃
⠀⠀⣼⢳⣽⣐⡟⠉⠀⠼⠄⢈⠔⠉⠀⠀⠂⡄⠀⢀⠔⢁⡀⠤⠵⠆⠀⠄⠠⠄⠂⡚⠀⠀⠀⡀⠔⠈⠈⠉⡶⠻⡿⠥⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠔⠁
⠀⠂⢻⡶⠒⠉⠀⠀⡄⠀⠀⠸⢀⠀⣀⡠⠊⣤⠀⡇⡰⠋⠀⢠⢤⠀⠑⠒⠒⠒⠊⠀⠀⠐⠀⣀⣀⠤⠤⠔⠁⠀⠈⠢⣀⠀⡀⠀⠠⠄⠁⠀⠀⣀⣀⢺⠃
⠀⠀⠀⠈⠐⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡤⠤⢄⡀⢀⡠⢎⠉⠳⣄⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠁⠈⢳⢤⡤⠃⡠⠴⡌⠭⠀⠈⠂⠀⢈⠭⣓⣂⣚⢳⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠉⠉⢆⠀⠀⢦⠃⠀⠘⡀⣀⣱⠰⡶⠧⠴⢊⡵⠮⢭⢤⣍⣿⢀⠎⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠲⠤⣀⠀⢦⡱⣀⠮⠁⠀⣊⣉⠭⢵⣿⣭⠥⠤⠽⢊⣉⣠⠤⢾⠋⠉⠑⢤⣀⣠⢷⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣇⠀⠀⢲⠤⠞⣓⡩⠭⠭⠝⣒⣦⣀⣹⡀⣁⣠⠤⠔⠚⠛⢛⣛⣛⣛⣛⣒⠲⠦⢄⡀⠀⢃⠄⢀⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠤⠤⢩⠖⣡⣶⠋⣠⡂⠤⠔⡺⠉⢉⡥⠖⠉⢁⣠⠴⠒⠚⠉⠉⠁⠀⠀⠀⠉⠉⠙⠒⠮⣕⡺⡀⠁⠈⠉⡧
⠀⠀⠀⠀⢀⡖⠉⢱⠀⠙⠲⢡⢞⣥⣶⠦⢤⣛⡏⢈⡱⠚⠁⣠⠴⣚⠥⠂⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠲⢍⠻⣦⡀⠘⢑
⠀⠀⠀⠀⠀⡇⢀⡴⣒⣤⢣⣣⠟⠋⠘⡄⠀⢜⡵⠋⢀⡴⢋⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢷⡔⠋
⠀⠀⠀⣠⠚⠉⡰⡪⠃⣟⢿⣧⠀⠀⡠⣇⡴⠋⢀⠔⢩⠞⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢷
⠀⠀⠀⢇⠀⡰⠃⠀⣸⡟⢀⡾⣖⠊⢠⠎⢀⡴⠃⠔⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡆
⠀⠀⠀⣸⠙⠁⢅⠮⠊⡠⢪⡄⠀⡴⠃⣠⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢰⠃⢠⡌⡆⠠⡪⡾⠛⠃⡜⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⢀⡏⠀⢾⡀⠀⡇⡇⠳⢄⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤
⠀⡼⠀⠖⠀⢨⠂⢄⠀⠀⡜⢀⡞⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⠁
⢠⠇⡆⠠⣀⡴⠒⢲⠁⡼⢀⡞⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠤⢒⣊⠭⠐⣂⡥⠴⠒⠉⠁
⣸⢰⠉⡀⢀⠀⠐⠊⡼⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢒⣊⠥⠖⠊⠉
⡇⠘⢀⠀⠘⢰⠄⡰⠁⣰⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀
⡇⡇⠈⠓⢚⣜⡼⠁⣰⠃⠀⠀⢀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠉⢻⡏⠉⠀⣸⣧⠀⠀⣴⠟⠋⠙⠁⣴⠟⠉⠛⢷⡄⢼⡏⠉⠋
⢻⡿⣌⣩⠥⠊⢀⣜⣡⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⣯⣼⣇⠀⣿⡀⠀⠀⠐⣿⠀⠀⠀⢸⡇⠈⠙⠻⣦
⠀⠙⠒⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠠⠟⠀⠀⠹⠆⠘⠻⠶⠶⠆⠙⠳⠶⠶⠋⠀⠲⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀⠀⣐⠀⠀⠀⢀⠀⢠⠂⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢰⠚⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡞⠘⠗⠦⠜⢜⢷⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⡠⡧⢠⣼⢑⣄⡓⠠⡄⡜⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⠀⠀⠀⠀⣿⣸⢿⢿⡨⣥⡠⡃⠝⠉⠸⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠀⠈⠊⠉⠀⢀⠀⡏⠀⣡⠎⣑⡈⡶⢛⣩⣧⡀⠡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⡝⠁⠀⠀⠀⠀⠀⠀⠎⢸⢛⡿⣧⠶⣂⣟⢉⡏⠀⠀⢃⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣁⠀⠈⠀⠀⠀⠀⠀⠒⠀⠀⢠⣏⢠⣀⡇⢑⢸⣩⡥⣤⠔⢚⣽⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠐⠪⠍⠓⠂⠀⠀⠀⠀⡠⢀⡴⠛⢌⠻⣄⢟⠟⢋⠔⡬⡃⣶⡙⠓⠻⡡⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢚⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢀⡴⠋⠀⠀⠀⠀⢈⡻⢤⡯⠀⣿⠛⣦⠤⠃⣔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠁⠀⠤⢔⡲⠤⠀⠀⠀⠀⠀⠀⣠⠴⡋⢀⣀⠀⠀⠀⠀⠀⠉⠢⢍⠛⠿⣴⣴⣬⣘⢧⡀
⠀⠀⠀⠀⢀⡴⠊⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣠⠴⠋⠁⠀⠈⠙⠚⠍⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠈⠉
⠀⠀⠀⢠⡏⢀⡀⠀⠉⠀⢀⣀⣀⡤⠄⣐⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣉⡤⠖⠋⠁
⠀⠀⠀⢸⠹⡖⠭⠭⠭⠭⠥⠴⠒⠚⠉⠉⠀⠀⠈⠒⠮⢝⡒⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣠⣶⠵⠚⠉
⠀⠀⠀⠈⣇⠀⣄⠀⠀⠨⣕⡢⠄⠘⠛⠀⠀⠀⠀⠀⣠⡴⠟⠉
⠀⠀⠀⠀⠈⢦⡈⠣⣄⠀⠀⠈⠁⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣀⣠⡤⠴⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣭⣶⣖⣒⣀⣀⣀⣚⣒⡒⠲⠂⠨⡍⠙⠻⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠟⠛⣉⣉⣉⣉⣉⣉⡙⠛⠻⠿⣿⣟⡛⠛⠿⠶⣦⣤⣈⠳⢦⣍⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⣩⣴⡶⠿⠛⠛⠉⠉⠉⠉⠛⠛⠻⠶⣦⣤⣉⠛⠷⣦⣀⠀⢉⡙⠻⢶⣬⡙⠦⣍⠻⣷⣦⡀
⠀⠀⠀⠀⠀⣰⡿⣫⣴⠟⠋⠁⢀⣠⣤⣤⣶⠶⠶⣶⣤⣤⣄⣀⠀⠉⠛⠷⣦⣈⠙⢿⣟⠛⢻⣆⠉⠻⢷⣌⣷⠈⠻⣿⣆
⠀⠀⠀⠀⣼⣿⡿⠋⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄⡀⠈⠙⢷⣄⠙⢷⣬⣿⣀⡀⠀⠙⢿⠳⠦⣌⠻⣷⡄
⠀⠀⠀⣼⣿⠟⠀⣠⡾⠋⠁⠀⠀⠀⠈⠀⠀⠀⠞⠋⠀⠀⠀⠀⢠⡄⠉⠻⣶⣄⠀⠙⢷⣄⠙⣿⡍⠻⣧⠀⢸⡄⣼⣟⡇⠙⣿⣆
⠀⠀⣰⣿⠋⢠⣾⠋⠀⠀⢀⡄⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠈⠙⣷⣄⠀⠹⣷⡈⢻⣆⣿⣦⣤⡙⢦⣽⣇⢠⡈⢿⣧
⠀⢠⣿⠇⢠⡿⠁⠀⠀⠀⠈⠓⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠻⣦⡀⠘⢿⡄⠹⣯⠁⠈⠻⣦⠈⢻⣆⠻⡌⢿⣧
⠀⣿⡏⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⣷⡄⠈⢿⣆⠹⣧⣀⠀⣿⠀⠀⢻⣇⢻⡌⢿⣧
⢸⣿⠁⣾⠃⠐⠖⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠈⠋⠀⠀⠠⠄⠀⠈⢿⡄⠈⢿⡄⢹⣿⢿⣿⡀⠀⠀⢻⣆⠁⠘⣿⡆
⣾⡟⢸⡟⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⣿⡄⢻⣆⢹⣿⣆⣀⡀⢿⡄⠇⢸⣿⡀
⣿⡇⢸⡇⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠳⠀⠘⣷⡀⠘⣷⡈⢿⡾⠿⠛⢻⣧⠸⣷⠀⡄⢿⣇
⣿⡇⢸⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡆⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠹⣧⠘⣷⣖⣛⣩⣿⠆⢻⡇⣷⢸⣿
⣿⣇⢸⡇⠀⠋⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣇⠀⢻⣆⠸⣿⠿⢹⡇⠀⢸⣧⢸⡈⣿
⠘⣿⣾⣿⠀⠤⣤⣄⠀⢀⡀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠄⠀⠛⠋⠀⠀⡄⠀⠀⢿⡆⠀⢿⡄⢻⣿⠽⣷⠀⠈⣿⠈⠁⣿
⠀⠈⠛⠿⣿⣶⣶⣶⣤⣬⣥⣀⣘⣛⡒⠲⠶⠦⠄⠀⠀⣀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠘⣿⡀⢿⣞⣿⠀⢰⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣷⣶⣶⣦⣤⣭⣭⣁⣈⣓⡀⠀⠶⠤⢤⣤⣄⣀⣀⡀⠀⠀⠘⣷⡀⠘⢷⣄⠻⢿⣴⠿⠁⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣷⣶⣶⣶⣤⣭⣭⣉⣁⣀⡈⢿⣦⡈⠻⢷⣤⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣷⣶⣾⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡗⠐⠂⢲⠀⠄⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⢇⠸⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠐⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠛⠠⡘⠳⠀⠒⡦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⡀⡀⠀⠀⠀⠆⠀⣆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠈⣶⡦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣄⣤⣤⣤⣤⣶⠁⠀⠀⠀⠀⠀⠈⠙⠛⠒⠓⠻⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠰⣿⣷⣿⡿⢽⣿⣿⣯⣿⣿⠷⢾⣿⣷⠾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢸⠂⢉⡛⢛⠓⡻⠿⡿⠿⠿⣿⣏⣀⣦⣜⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢸⣿⣭⠟⠾⠃⠐⠊⠙⠁⠉⠉⠉⠉⠉⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡁
⠀⠀⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣥⠨⠟




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⢠⠞⠃⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⣼⠀⣀⣀⣀⠳⠶⢶⠤⣤⡤⣀⢄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⢲⡀⠀⢀⡄⢰⠃⠐⢄
⠀⠀⠀⠀⢠⠛⣼⣯⣢⡿⢥⠑⢀⠙⠾⠟⣓⡛⠐⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠁⠈⠨⠟⢮⠁⣨⠠⠴⠚⣦⢤⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠜⢲⡈⣥⠤⢤⡴⠎⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⡘⠲⠒⠲⠋⠃⠀⡆⢰⣅⠀⠂⡴⠃
⠀⠀⠀⠀⠀⠀⠻⣄⡤⠤⠀⠻⢆⣠⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣆⣀⠀⢸⣷⡷⣌⣉⣾⣿⣠⣼⢀⣰
⠀⠀⠀⠀⠀⠀⠀⣟⠀⠐⢃⣴⠞⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣧⠈⢻⣏⣢⣄⡹⢷⠀⢸⣿⣤⣠⣟⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⢙⢷⠾⠓⣾⣠⣽⣿⣦⣭⣵⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡳⠶⠶⠞⢁⠞⢬⠭⠫⠤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠐⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⢰⣶⠁⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐
⠂⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠐⠀⠈⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠂⠀⠀⠀⢂⠀⡈⠀⠀⠄
⠀⠐⡆⠀⠀⠀⢀⠀⠈⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⠀⠀⠀⢈⡰⠀⠀⠀⠄⠄⠀⠀⠂⠀⠀⠀⠀⢀⣀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄
⢄⡄⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢠⣀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⡘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠃
⠰⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡄⠒⢢⠀⠿⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠖⠄⠀⠀⠁⠀⠀⠀⠆⠆⠀⠀⠀⢀⠀⠈⠀⠠⠀⢠⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡀⠀⢄⡰⠀⠀⠀⠄⠄⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠠⠴⠀⠀⠀⠂⠂⠀⠀⠈⠀⠀⠀⠀⠠⡠⠀⠀⣖⣀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠀⠀⠐⠀⠠
⠀⠀⠀⠀⢀⠀⠀⢀⠂⠀⠀⡀⠌⠀⠀⠀⠀⡀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢀⠀⠀⠈⠀⠐⠤⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⣌⡅
⠀⠀⠈⠐⠂⠀⣀⣀⠀⠀⠠⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣖⠑⡢⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⡔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠮⠁⠽⠀⠉⠁⠀⠀⠀⢀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠋⠂

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠌⠁⠀⠀⠈⠂⠤⠀⡖⡂⢆⡔⣀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⡐⢂⠀⠀⠀⠠⠁⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠪⠄⠀⡀⡆⠐⢀⠴⢀⠀⠀⠀⠀⠐⠁
⠀⢀⠐⠂⠀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢐⠁⡄⠔⢒⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠀⢠⠀⡶⠡⣤⡔
⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡶⠀⠠⡧⠟⠄⡆
⠀⠀⠡⡄⠀⠐⠂⠀⠀⠀⠀⢉⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠘⠁⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐
⠀⠠⠀⠉⠘⠶⠆⠉⠐⠄⠀⠄⠀⠀⠐⠀⡡⡈⠟⣰⡆⠀⠦⠀⠀⠁⣀⡀⢠⣴⡀⠀⠀⠀⠉⠀⠀⠐⢀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⠂⠀⠀⢺⣆⣬⠗⣢⡁⠢⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢸⠇⠠⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂⠀⠀⠏⠁⠙⠜⠅