Transfer Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠁⠀⣠⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣶⠄⣩⠁⠀⠠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡀⠉⢻⡆⣀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣧⣀⣼⠃⠁⠀⠀⠀⠈⠏⠀⠀⠀⠒⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢙⡿⠁⠁⡰⡇⠈⠀⠀⠀⠀⠀⠀⠀⢤⠱⢄⠶⡂⠀⠀⠀⠀⠀⠀⠡⡀⡀
⠀⠀⠀⠐⠉⠀⠀⠀⢁⠀⠀⠀⠙⢀⡀⣷⣽⣤⡤⠐⠂⠀⠀⠀⠄⠈⢻⠉⠀⠈⠀⠀⢻⣤⠀⠀⠀⢛⡟
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠀⢸⠆⠀⢡⡌⢧⠀⠀⠀⢀⠀⠀⠀⠀⣠⢗⡰⠀⠂⣀⣠⡼⠖⢲⠖⠈⡿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⢳⣴⢸⣠⡴⠎⠀⣸⡇⠀⠀⠙⠳⠀⠀⠀⢺⠀⢳⠀⡺⠋⠀⠀⠀⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢱⣼⢠⠂⠀⣰⣿⠃⠀⢀⡶⣶⠒⠖⠒⢘⡇⣶⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⣿⠂⢻⡌⠀⠸⣹⣏⠄⠀⢸⡇⣿⠀⢰⡄⠀⡀⠁⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⢻⢷⣾⡇⢀⣶⣿⣇⠀⠀⢸⡇⣿⠀⢸⡇⢠⣁⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⣿⣿⠿⣶⣿⣽⣷⡆⠀⢰⣿⣿⢯⡀⣼⣿⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠽⢿⣦⣾⣿⣿⡏⠀⠀⠘⣿⣿⢸⣇⣽⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣦⡋⣿⣾⣿⣿⡷⠀⠀⠀⣿⡏⢸⡿⣉⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⡁⡷⣮⣹⣿⠁⠀⠀⠀⣿⡏⢲⣟⣫⣻⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⢰⣟⣻⡿⢿⣇⠀⠀⠀⢸⠇⣸⣿⣿⠿⠆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⣟⣻⣷⡄⢿⡄⠀⠀⣼⢡⣾⡯⣽⠿⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡼⠋⠀⠀⠀⠉⠻⣧⠀⢠⡷⢻⡿⠒⠾⡇⠄⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠙⠀⠀⠀⠀⠒⢶⣿⡄⣸⣡⡿⠀⠀⠀⠙⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣀⠀⢀⣀⣈⣿⣷⣿⠇⠀⠀⠀⠀⠀⢀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣿⡥⠶⢦⣽⣿⣿⣿⣿⣤⣄⠀⡀⠀⠀⠈⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣿⣿⠶⠾⠿⠿⣿⣿⣿⣿⣦⣤⣤⣭⣿⣷⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠋⠉⠛⠛⠂⠀⠀⠈⠀⠀⠀⠛⠁

⠀⠀⠀⢀⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣦⣤⣶⠶⠶⠶⢶⣦⡀
⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠰⠶⠶⠶⠆⢹⣷
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠰⠿⠿⠿⠇⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠿⠿⠿⠇⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠀⠀⢸⣿
⠀⠀⠀⠻⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⠀⠀⠛⠁⠀⢸⣿
⠀⠀⠀⠀⠈⠙⠉⠙⠙⣿⠋⢹⣿⠋⠛⠉⠉⢹⣿⡀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠙⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⣂⣐⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡂⡾⠭⢭⣭⣵⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⢠⡀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢉⡉⠛⠻⣿⣶⡓⠒⠒⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⣿⣶⣄⠀⢀⣾⠟⠁⢠⣾⢿⣿⣷⡄⠈⠻⣿⣉⣈⣉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⠿⠟⠓⢸⡿⠀⠀⠸⣷⣾⣧⣈⠁⠀⠀⢻⣧⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡤⠠⠾⢷⡀⠀⢀⡀⢽⡟⢻⣧⠀⠀⣾⡇⠀⠐⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣽⣛⠛⣓⣤⠘⢿⣿⣷⡾⠃⢀⣴⡿⠁⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⡧⢤⠾⢉⡉⠰⣦⣈⣁⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡗⠲⠆⠤⠤⠐⡎⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣁⠒⠒⣊⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣬⣤⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠰⣶⣶⣶⠦⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠰⠶⠶⠶⠖⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠐⠿⠿⠿⠗⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⢀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⠀⠀⠛⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⣿⠛⢻⣿⠛⠛⠛⠛⢹⣿⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠷⠾⠿⠷⠾⠿⠷⠶⠶⠀⠀⠛⠿⠶⠶⠶⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠄⠐⠒⠒⠒⢀⡈⠉⢈⠏⠋⣙⣏⣟⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⢉⡠⠤⠤⠤⠀⣐⠒⠒⠒⠒⠒⠒⢻⡯⠉⠉⠝⡏⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⡀⡆⠰⠤⠤⠈⠛⠂⠀⠒⠂⠀⢹⠉⠍⠩⡍⠁⢿⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠰⠀⠠⠀⢀⠆⠀⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣳⢠⢃⢂⠎⠄⠀⣿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠃⠀⠀⠀⠀⠀⠀⡠⠔⠋⣉⣉⡉⠚⠾⣄⣘⡼⠸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠰⠀⠀⠀⠀⠀⡠⠊⣠⣔⢫⡇⢏⠉⠟⢦⡈⠁⣻⠰⣻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡈⡀⠀⠀⠀⠙⠒⠀⡎⡼⢀⠆⠂⡜⠿⡶⣶⠿⢀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢃⠀⠀⡏⠉⠩⣷⣰⡙⡜⡌⡼⡌⣸⠞⠛⢷⢼⠡⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠘⡀⠀⠰⠔⠢⣄⡉⠙⠛⠒⠛⠋⠁⣠⣴⣀⢃⢁⢿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠃⠀⠀⠀⡳⠰⡙⠱⠒⠲⢶⣶⣋⣭⣯⣧⣮⣞⠵⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠸⠀⠀⣴⠶⠟⠋⠉⢉⢉⢉⣠⡄⣀⢠⢤⠄⢹⡆⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠄⢠⠇⠸⠃⠿⠌⠃⠘⠛⠛⠓⠊⠙⣈⣀⢿⡧⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢠⠞⢹⣤⠤⣤⣤⣤⡴⡶⡾⡿⡗⡺⠈⡅⠀⡰⠱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡽⠚⣁⢏⢗⠀⣎⠄⣌⡰⡞⡰⠿⣘⣘⡘⢘⢰⣁⣣⣻⣇⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣿⣧⣿⣿⢯⡽⢏⡉⠉⠉⠉⠁⠛⠛⠏⢓⣂⠚⢫⣏⣝⣩⣽⣫⣍⣭⣿⣿⣃⣐⣶⣶⣄
⠀⠀⠀⠀⠀⣿⣅⡂⠄⣀⣿⡿⣋⠭⢉⣉⣁⠍⢁⣚⣦⣤⡤⠬⡟⣿⣲⣦⣄⠀⠀⡀⠀⠀⣈⠻⣿⣿⣿⣿⣿⡿⠿⢾⣿⣿⢿⣟⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠽⠦⣴⣤⣌⡉⠛⠫⠥⢹⣟⣻⣻⣿⣯⣿⣽⣿⣿⣿⣿⣿⣄⠏⣜⣄⣤⣼⣀⣿⢷⣿⠾⢯⣿⢽⣻⣻⣻⣿⣟⣿⣿⠂
⠀⠀⠀⠀⠀⢸⡯⢖⣶⣦⣨⣝⣪⣍⡓⠂⠭⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⡟⠛⠤⠤⠀⣉⣉⣩⣏⣹⣿⣧⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣷⠦⡀⢄⡀
⠀⠀⠀⠀⠀⣸⡷⢶⣄⡈⠭⢙⠳⣯⣝⡋⢸⣽⣿⡿⣯⣿⠿⠟⢯⠿⢿⢷⣤⡀⠀⣀⣤⣸⣰⣬⣾⣿⣿⠿⡿⠿⣿⣿⣿⡿⢿⣿⣿⠿⠟⠡⢀⠠⠁
⠀⠀⠀⠀⠀⠈⠙⠒⠬⣉⡛⠲⢯⣽⢛⡻⣭⣷⣻⣽⡣⠣⠤⠤⢀⣀⢈⣀⢽⣬⣦⡄⢈⢨⣉⣃⣶⡷⠍⣿⠩⢇⣀⣀⣉⣉⣘⣯⣷⢽⠒⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠾⣵⣞⠭⣿⣿⣿⠧⡤⠀⠀⢠⣁⣸⣨⣭⣼⣏⠉⢹⢻⢉⣍⣼⢃⡀⢳⣀⠀⠀⠈⠉⠁⡏⣸⡿⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠹⢧⣀⡀⠀⠀⠁⠈⢹⣀⣾⡟⠛⠛⡛⠹⠯⠍⠛⠀⠀⠉⠈⠉⠋⠙⠋⠙⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠋⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣛⣛⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⣫⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣍⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡞⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣿⣿⣿⣿⡿⣡⣾⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿
⠀⠀⠀⢠⡏⠀⠀⣰⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⢹⡄⠀⠀⠀⣿⣿⣿⡟⣰⣿⣿⠟⠁⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣆⢻⣿⣿
⠀⠀⠀⣿⠀⠀⠈⠻⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⣿⠀⠀⠀⣿⣿⣿⢁⣿⣿⣿⣦⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⡈⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⣿⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣦⡀⠀⠀⣿⠀⠀⠀⣿⣿⣿⡈⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠻⣿⣿⣿⢁⣿⣿
⠀⠀⠀⠘⣇⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠟⠀⠀⣸⠃⠀⠀⠀⣿⣿⣿⣧⠹⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢀⣴⣿⣿⠏⣼⣿⣿
⠀⠁⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⡼⠃⠀⠀⠀⠀⣿⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⢋⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⣫⣴⣿⣿⣿⣿⣿
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣭⣭⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡟⣿⣿⣶⣦⣤⣀⡀⠀⠀⢀⣀⣤⣴⣶⣿⣿⢻⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠹⢿⣿⣿⡏⡉⠉⣉⠙⣿⣿⣿⠿⠁⠀⠀⠈⠿⣿⣿⣿⢫⠉⠉⣉⢹⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⣿⡏⢹⣿⠉⣿⡏⢻⣟⠙⣿⠀⠀⠀⠀⠀⠀⣿⠋⣿⡏⢹⣿⠉⣿⡏⢹⣿
⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⣻⡇⢸⣿⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⣰⣿⣷⣶⣿⣶⣿⣶⣾⣷⣶⣿⣦⡀⠀⠀⢀⣴⣿⣶⣾⣷⣶⣿⣶⣿⣶⣾⣿⣆
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣤⣤⡤⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⡀⠀⣀⣀⡀⠀⢀⣀⣀⠀⢀⣀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠘⠛⠛⠃⠀⠛⠛⠋⠀⠘⠛⠛⠁⠸⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣉⣉⣉⣉⣉⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⡀⠀⣤⣤⣄⠀⢠⣤⣤⡀⢠⣦⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠈⠛⠛⠁⠀⠉⠉⠉⠀⠈⠉⠉⠁⠐⠋⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⡄⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠂⡇⠿⢾⡽⠀⠘⡇⠾⠡⣿⡇⡏⠷⢸⡧⢿⠸⣿⠃⡏


⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢃⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⡏⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣉⣉⣉⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⢠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠂⠿⢸⠸⣿⠂⠀⣯⢸⠃⣜⡧⠿⢹⢘⣧⢸⠑⣯⡗⢿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣀⣀⣀⡀
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⣉⣉⡉⠉⢻⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣶⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣷⣄
⢻⣿⣿⣿⣿⣿⡿⠋⢀⣾⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿
⠈⢿⣿⣿⣿⠟⠁⠰⠿⠿⠿⠿⠿⠿⠿⠄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⢿⣷⣶⣶⡆⠀⣶⣶⣶⣶⣶⠀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠉⠉⠁⠀⣿⣿⣿⣿⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⣿⣿⣿⡇⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣴⣶⣤⣤⣴⣶⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡏⣼⣿⢸⠹⡇⣿⠜⡇⢿⡟⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⢸⣇⠠⣌⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠙⣿⣯⠀⠀⠱⣬⡻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣼⣿⡟⠀⠀⠀⢼⣿⣮⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠛⠹⣿⣮⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣘⣧⠔⠱⣶⢷⣶⠁⠄⠺⠿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡀⢾⡿⡤⣿⡆⢀⣴⣤⣾⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⢽⣿⡇⠰⠁⠀⢹⣷⣿⣿⣾⠃⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡿⢄⡀⠀⠀⠀⠈⠻⣇⠀⠀⠀⢸⣿⡿⠛⠁⠈⠀⣸⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⣀⡑⠲⣄⡀⠀⢐⠈⠀⠠⠤⠿⣿⣿⠀⠀⢀⣴⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠉⠛⢧⣈⠙⠂⣼⠀⠀⠀⠀⢳⣿⣿⠖⠚⢉⣠⣤⡤⠶⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣄⣀⠉⠒⠺⡇⠀⢀⣀⣿⣿⣿⢛⡋⠉⣀⣀⣠⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣙⣉⣻⠯⠄⠨⢿⣿⣋⣉⣉⣉⣉⠉⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠊⠉⠁⠀⠀⢈⠈⠁⢉⣿⣿⡇⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⣀⣨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣀⣤⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣶⣰⢶⣾⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱⡟⢻⣿⣷⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠊⠛⠟⠋⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠰⢷⣤⡀⠻⣝⠏⢰⢻⣍⠛⡀⠶⠍⢻⡇⢷⠀⠀⠑⠒⠒⠤⡀
⠀⢀⢤⢦⡄⠀⢀⡞⢠⡁⠀⡿⡄⠀⠠⠙⣦⠀⠀⠢⠤⠀⠀⠀⠀⠀⠽⡆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈
⠀⢨⣸⣘⣷⠄⠘⠧⠀⠀⠤⠁⡅⠄⠀⠀⠈⠀⠀⢀⠀⠀⡀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠
⢶⣾⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠠⠀⢘⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⢠⣂⠀⣤⣦⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⢀⣀⢘⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢶⠋⢠⠚⣠⢀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠘⠲⠟⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⠈⠀⠀⠀⠀⠀⠉⠟⠛⠀⠐⡃⠦⠘⣃⣀⣦
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⢝⡀⠀⠀⢶⣾⣖⣤⣤⠄⡂⣀⠋⣐⠦⣭⡙⢋⡀
⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠈⠙⠃⠘⢿⣿⣿⢿⠁⠐⠟⣛⣹⣷⠆⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⠀⠀⠀⠛⠫⠴⢆⠒⠒⢻⠟⠟⠐⠘⠀⠀⠀⠀⠒
⠀⠀⣠⣾⠿⠺⠿⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣈⣤⡅⠭⡤⢤⢀⣀⣤
⠀⢰⣿⠁⣴⣴⣧⠘⣿⡆⠀⠀⠀⠀⢀⡀⢤⠀⠖⣃⠔⠛⠀⠀⠀⠀⠀⠀⡰⠲⡆⣀⣀⠿⣋⣱⣦⠁⣿⡎⢠⣾⢙⡿⠀⣀⢰⡒⢂
⠀⠘⣿⡄⠿⢿⡿⣢⡿⠂⢀⠀⢻⣦⡷⠃⠀⠀⠀⣈⢂⡀⠞⢀⠀⠀⠀⠀⠁⠸⠧⡋⠀⠀⠙⢿⣿⣾⣿⣿⣾⣷⠎⠁⠀⠘⡾⠃⡀
⠀⠀⠀⢚⢳⣶⠞⠏⠁⠐⠊⠀⠉⢹⣮⡏⠀⠀⠀⢁⣬⣄⣻⣿⣇⠀⠀⠀⡘⢠⣶⠄⠀⠀⠀⠸⠿⠷⢿⠽⠻⠿⠀⠀⠀⠀⣷⣲⠋
⠀⢠⡄⠳⠦⠲⠃⣄⠀⠀⠀⠀⢿⡿⣿⣇⠀⠀⠀⠏⣹⣛⣿⣿⣧⠀⠀⠘⠀⢾⣏⣳⡄⠀⠀⠀⠂⠤⠠⠀⠀⠀⠀⠀⠀⠂⠈⠸⠂
⠀⣸⠃⠀⠀⠀⠀⢻⠀⠀⣴⠀⠀⣀⢻⡿⠀⣤⡀⠛⠛⢉⣿⣿⣿⡆⠀⠀⠘⠀⣷⣠⠓⣶⡄⠀⠀⠐⠐⠐⠀⠀⣠⣶⠐⡕⢘
⢸⠇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠓⢒⣺⣿⡁⠄⠀⢩⡻⢿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠈⠿⠆⠙⠋⢰⣶⠒⠶⠖⢶⡶⠌⠋⠀⠿
⢸⡇⠀⠀⠀⠀⠀⢀⡏⠀⠀⠘⣿⣿⣿⠀⢠⣀⠀⣴⠌⣿⣿⣿⣿⣟
⠀⠻⣄⡀⠀⢀⣠⡾⠁⠀⠀⢠⠭⡿⣿⣤⣌⣿⣳⣿⣾⣿⣷⣰⣿⡗
⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠌⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠠⣤⢠
⠀⢠⣾⢈⡌⢠⡈⢡⠘⣶⣧⠀⢰⣿⣿⣿⢿⡿⡿⠿⠼⠾⠍⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣺⢘⠇⡴⠲⠾⠃⣴⡴⠶⠿⠓⢶⣶⠦
⠀⠺⠿⠦⠤⠦⠴⠤⠴⠷⠇⠀⠈⠛⠁⠒⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠠⡷⠀⠀⠐⠘⠍⠀⠐⠂⠘⠣⢼⡷
⠀⠀⠀⠐⠶⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠄⠤⠄⠤⠤⠄⠀⠈⠉⣸⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⡤⣤⡻
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣼⣧⣧⣌⠀⠀⠀⣀⠀⢀⡀⠀⠀⡀⠁⠁⠀⠀⠀⠀⢀⣿⣆⣀⡀⢻⠈⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠉⠀⠀⠙⠛⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠁⠀⣶⠀⠀⣶⣄⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣄⠀⠙⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⡀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠛⠻⢿⠀⠀⠿⠀⢀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⣄⣀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢐⡆⠰⢆⢲⣖⠊⠴⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠐⠀⢨⡏⠂⠀⠐⠀⢹⣨⡷⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡀⠐⢀⠀⢁⠀⡈⠀⢀⡱⠓⠁⠁⠪⢆
⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⠄⣘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡐⣥⣼⣷⢨⢬⡣⠸⣇⠀⠂⠀⢀⡕⢣
⠀⠀⠀⢠⠊⡠⠂⠉⡀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢏⠌⠸⠺⡼⠶⠚⢸⣦⡇⡠⡪⠊⠉⠈
⠀⠀⠀⡆⠐⠀⠀⢏⣈⠂⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠟⠛⠚⠛⠚⠢⣮⢏⢴⠎
⠀⠀⠀⢃⠘⡀⠀⠢⡤⠃⢀⠄⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠁⡠⠊⠉⠉⠉⠢⡈⢻⠁
⠀⠀⠀⠈⠢⡈⠒⠄⠀⠔⢉⢠⠁⠉⠉⠉⡩⠭⠭⠭⠭⡉⠉⢉⢟⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠑⢄
⠀⠀⢰⠉⠅⠭⠩⠩⠉⠉⠉⠉⠉⢢⠤⠤⠭⠬⠭⠬⠭⠥⠤⡎⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠊⠛⠻⠛⠛⠋⠉⠉⠉⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢆
⠀⠀⢱⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠈⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠒⠒⠂⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⠛⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣽⣉⣉⣋⡦⢰⠒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠋⠑⠛⠀⢸⣀⡠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢀⡠⠄⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡇⠀⠠⠔⠁⠀⠰⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣐⣀⣀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠥⠚⢧⠀⢀⠗⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂⠈⠓⡴⠡⠤⠀⠓⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠠⠀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠀⠀⠀⣄⢋⣰⠈⢢⠠⠤⠤⠤⠼⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠨⠈⠂⠀⠀⡀⡀⠀⠈⠁⠆⡈⢸⣀⡀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡘⠂⠀⠀⠀⠀⠈⠧⡟⢱⠒⡦⢄⡡⠂⠀⠀⠉⠉⠁⠐⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣧⡠⠊⠀⠀⢀
⠀⠀⠀⠀⠀⢀⢤⠖⡫⠉⠉⡐⠠⢍⡁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⡠⠊
⠀⠀⠀⡠⠚⡱⠃⠀⠀⠀⡠⠃⢠⢄⡌⢝⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⢀⣠⠴⡁⠑⡄⢀⡠⠖⠉
⠀⠀⡜⠀⠘⠂⠤⢀⣠⠌⠀⣐⠣⠆⣠⠋⠲⡑⢨⠃⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⢇⠀⠘⣄⠜⠉
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠉⠒⠠⢉⡒⠦⢌⠔⢀⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡆⠀⠀⠀⠑⢄⡇⠀⠀⠃
⠀⠙⠒⠠⠤⠤⠤⠀⠀⠀⣀⣀⡀⠈⠑⠢⣤⠎⠀⠀⠰⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠢⠄⣀⢤⣀⠀⡀⠀⢀⡁⠤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠤⠤⠤⠄⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡤⠤⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠴⠶⠖⠒⠛⠛⠉⠉⠉⠉⠀⠀⠈⢧⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠉⢹⡏⠁⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠲⣄⠀⠀⠀⠀⠀⠀⠉⠓⠚⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣠⠟⠀⠀⠀⠀⠀⣰⠏⠀⢀⣼⣷⣤⠀⠈⢳⡄⠀⠀⣠⣤⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠁⠀⢀⣀⠀⠀⠀⡏⠀⠀⢿⣯⣤⣀⠀⠀⠀⣷⠀⠐⣇⣀⡽⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡇⠀⠠⡏⠉⣳⠀⠀⣧⠀⠀⠀⠉⠙⣿⡷⠀⠀⣿⠀⠀⠈⠉⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠀⠀⣇⠀⠀⠙⢛⡥⠖⠒⢻⣆⠀⠘⠛⢿⡟⠁⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢿⠤⣤⠞⠉⠀⠀⠀⣸⠋⠛⠦⣤⣤⣤⠴⠚⠁⠀⠀⠀⠀⢀⣸⣇⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⣀⣠⡼⠞⠁⠀⠀⢀⣠⠞⢁⣀⣀⣀⣤⡤⠤⠴⠶⠖⠒⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⢀⡴⠛⠋⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣤⢾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⣩⣴⡏
⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠘⢧⣤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⢸⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⢠⡜⢛⠛⠀⠀⠀⠀⠀⢸⡗⣿⢺⡇⠀⠀⠀⠀⠀⠀⢀⡞⠉⢻
⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣟⠀⠀⠀⠀⠀⠀⢀⣿⡧⠄⠀⠀⠀⠀⠀⠀⢘⡋⣿⣙⠃⠀⠀⠀⠀⠀⢀⣿⡗⠓⢺
⠀⠀⠀⣨⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⡿⠛⠀⠀⠀⠀⠀⠈⠱⣿⣿⡇⠀⠀⠀⠀⠀⣨⣿⣷⡶⠚
⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠅⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠄⠀⠀⠀⠀⠀⠙⠻⠟

⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠿⠿⣿⣯⣽⠿⠿⠃⠀⠀⠿⠿⣿⣿⣽⠿⠿⠃⠀⠀⠿⣿⣿⣿⣿⣿⠿⠃⠀⠘⠿⠟⡍⣉⡩⠻⠿⠃⠀⠀⠿⠟⠍⣉⡩⠻⠿⠃
⠀⠀⠀⠀⣿⣿⣿⠀⡶⠀⠀⠀⠀⠀⣿⣿⣿⠀⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣏⠉⢱⠀⡶⠀⠀⠀⠀⠀⣊⠉⢱⢀⣆
⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢄
⠀⠀⠀⠀⢸⣿⡇⢜⢦⠀⠀⠀⢀⠞⠛⢷⣦⣄⠀⠀⠀⠀⠀⢸⣶⣶⣶⡇⠀⠀⠀⠀⠀⢸⠛⠛⠛⡏⠀⠀⠀⠀⠀⠀⣤⣴⣦⣾⣧
⠀⠀⠀⠰⢁⣀⠀⣇⠀⠀⠀⠀⡜⠠⠸⡋⠉⠈⡄⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠘⢤⣀⡠⠃⠀⠀⠀⠰⢶⣤⣠⢣⠀⠀⠸⡀⠀⠀⠀⠘⢻⣿⡿⠃⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⠀⣶⣿⣿⣿⣯⣤⣤⡀
⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠷⠶⠛⠃⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠸⠶⠿⠷⠇⠀⠀⠀⠀⠿⠛⠛⠛⠻⠿⠿

⠀⠀⠀⠀⣤⣿⣤⣀⣤⡀⠀⠀⠀⠀⣤⣿⣦⡀⠀⠀⠀⠀⠀⠀⣤⣿⣤⡀⠀⠀⠀⠀⠀⠀⣤⣿⣤⣀⡀⠀⠀⠀⠀⠀⣤⣿⣤⣠⡀
⠀⠀⠀⠀⣇⣀⣸⠉⠄⢣⠀⠀⠀⠀⣇⣀⣸⣿⣿⡇⠀⠀⠀⠀⣇⣀⣨⣿⣷⠄⠀⠀⠀⠀⣇⣀⡰⠛⡑⢄⠀⠀⠀⠀⣇⣀⣹⣿⣷⡀
⠀⠀⠀⠀⣿⣿⣿⢗⢂⣀⡆⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠍⠉⠀⠀⠀⠀⠀⣿⣿⣿⠆⣤⡄⠀⠀⠀⠀⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠻⠿⠟⠈⠋⠉⠀⠀⠀⠀⠻⠿⠟⠈⠉⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠈⠁⠀⠀⠀⠀⠻⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⣤⠀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠶⠶⠶⠆⠠⠶⠶⠄⠀⠀⠀⠀⠀⢀⡴⠖⠛⡛⠳⢦⣄⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⣈⣁⡄⠀⠙⣧⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠴⠤⠦⠤⠤⠴⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠦⠤⣤⠀⠀⢹⠆⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡄⠀⣤⠀⢠⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⢷⠹⣄⠀⠐⠒⡒⠋⠀⢀⡿⠀⠀⠀⢸⡇⠛
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣌⠳⣝⠶⣤⣈⣁⣤⠴⢋⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⣙⣛⣛⣋⣉⣉⣉⣉⣉⣙⣙⣛⣋⣸⡇⠀⠀⣤⣤⡄⠀⠀⠈⠳⣬⣛⡲⠶⠶⠶⠚⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡴⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⢷⡘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣡⠟⣀⣀⣈⠉⠉⣁⣀⡈⠉⠉⣁⣀⡉⠉⠉⣀⣀⡉⠉⢉⣀⣀⡉⠉⢉⣀⣀⠉⠉⢉⣀⣀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠉⠉⢁⣀⣈⣉⣉⣁⣀⣈⠉⠉⠁⠀⠈⠉⠉⠀⠀⠈⠉⠉⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣏⣉⣉⣉⣉⣉⣉⣙⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠖⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠐⠛⠛





⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠂⠀⠀⠀⢒⠤⢹⡶⡖⠒⠒⠒⠀⠂⠀⠀⠐⠒⢒⡊⢳
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⡦⡸⢹⡄⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠇⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠄⠀⠉⠁⠀⠘⣡⣿⡞⠃⠀⠀⠀⠀⠀⠈⠀⠈⢉⡀⠀⠀⠇⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⣽⡏⢡⡀⠀⠀⠀⠀⠀⡤⠀⠀⠻⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣀⠀⡈⠀⠀⠻⢣⣸⡇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣯⠘⠋⠁⠀⠀⠀⢀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⢘⡫⠀⠀⠀⠀⠐⠂⠎⠸⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣯⠀⡀⠈⢉⣭⣿⣶⠆⡖⠰⣦⠴⠆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⣿⣯⣿⣟⢚⠸⡱⠿⢿⣻⣖⠀⠀⠀⠀⡀⠀⠀⠐⠛⠆⣳⣾⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣯⣭⣭⣟⣻⣿⠏⠁⣀⡀⠙⠛⠳⠶⠶⣤⣤⣄⣀⣀⠚⠛⠉⠀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠤⠤⣈⣀⣐⠶⠯⢥⡀⠉⢟⣛⠿⢿⣶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⠛⠛⠙⠒⠚⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣄⣀⣄⣀⢀⣀⣀⣀⣠⡀⣼⠀⡓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢸⠀⡇⠀⡉⢉⠉⢉⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣀⠀⠁⠀⠀⠀⢸⠀⠱⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠈⠑⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⠚⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⢤⡀⠀⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡷⠀⠄⠘⠦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⢒⡒⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀⠀⠸⣆⠀⠘⠒⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢒⠒⠒⣒⠒⣐⢒⠒⡒⡒⠒⡒⠒⢲⠀⠀⠀⡠⠶⠉⠋⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠋⠀⠀⢠⠟⣡⠌⠻⡄⠀⠀⠙⡆⢸⠀⠀⣜⠃⠀⢰⠛⠄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⢸⡀⢈⡦⢀⡇⠀⠀⠀⡇⢸⠀⠀⢏⡀⠀⢀⣙⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⠤⠤⠤⠷⠦⠴⠾⠤⠤⠤⠖⠁⢸⠀⠀⠈⠣⣤⠀⡁⢀⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢀⣉⣍⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠨⢉⢉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢘⠆⠀⠀⠆⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠀⣀⠒⠈⢌⡐⠂⠤⢀⣀⠠⣤⠼⠉⠠⠶⠏⣤⣀⡀⢐⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠉⠉⠅⢘⡂⠸⠁⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⣤⣠⠀⠐⢊⠓⠟⠇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠂⠀⠐⠢⠖⠚⡇⠀⠀⠀⠀⠀⠀⢀⠂⣅⡉⠉⢙⠃⠀⠀⠐⠛⠛⠉⠲⠦⠤⠀⡠⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠖⠒⠒⠠⠴⠀⡄⠸⠂⠀⠀⠀⠰⠤⠜⢃⣀⡀⠄⠤⣄⢰⢒⣋⡕⣒⠷⠶⣣⣅⣒⡦⠤⡁⠀⠉⠓⢈⡉⢄⠔⢒⠉⠉⡅
⠀⠀⠀⠀⠀⠃⠤⠀⠠⠼⠁⡅⠰⠦⣀⣀⣀⣀⣀⡠⢞⠈⠉⢈⠢⣿⠸⠀⠒⠨⠍⠛⠁⠀⠬⣁⡈⠉⠀⠍⠐⠽⢒⠉⢉⠩⢀⠀⠀⡇⡀⣠⢀
⠀⠀⠀⠀⠐⠣⠤⢤⡗⠟⠋⠭⣝⠄⠀⠀⠀⠀⠀⢀⡼⢄⠀⠀⡥⣴⠶⢄⠤⣠⣤⣀⣤⣄⣤⣄⡀⠀⠀⢀⣤⠤⠶⠎⣒⣩⡅⠖⠓⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣐⣀⣠⣆⣀⠀⠀⠀⣙⣰⠞⠓⠲⠒⢚⢭⢆⢲⠂⠀⠀⠀⠀⠈⠙⠙⠻⠽⠀⡠⠤⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⢪⡁⠒⠀⠐⡒⠂⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠐⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⣤⠖⠉⠀⠀⠀⠀⠉⠲⢤⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⣀⡤⠖⠋⠁⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⣀⡤⠚⠉⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠛⠧⣄⡀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠶⠾⣁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⣉⠶⠦⣖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡤⠞⠁⠀⠀⠀⠀⠀⢀⡤⠴⢏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⢀⣿⣓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠘⠯⣝⡻⢖⡪⢷⣦⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠔⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠓⢽⣦⣙⢾⡷⠞⠁⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠋⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⢀⡴⠋⠈⠓⢦⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⣠⣾⣛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡴⠋⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁⠈⠙⠻⣦⣝⡻⢿⣶⣤⣀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠙⠲⢤⣀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣮⣙⡻⢷⣆⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠈⠙⠲⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠐⠖⠒⠒⠒⠒⠒⠲⠖⠒⠀⠀⢰⠄⠀⠀⢀⡀⠀⠀⠀⣴
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠰⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⡇⠀⠀⠀⣀⠀⠀⠐⠂⠀⠀⠀⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡇⠀⠀⠀⠉⠈⠀⡀⠀⣀⠀⠀⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣇⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣸
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⣄
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣵⣿⣿⣿⣿⢿⣾⣙⣻⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣽⣿⣿⣿⢿⣵⣿⣿⣾⣿⣿⣿⣭⣭⣝⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠈⠿⠋⠈⠋⠁⠉⠉⠛⠛⠋⠉⠉⠉⠛⠛⠻⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⠀⠀⣀⣠⣤⣶⠿⠛⣉⣠⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣶⡿⠟⢋⣁⣤⣴⡶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣶⡿⠿⠛⠋⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣏⣿⣿⣿⣿⣿⣏⣀⣤⣤⣶⡶⠶⠂
⠀⠀⠀⠀⠨⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⢻⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁







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

⠀⠀⢂⠨⠭⠅⣒⢤⡀⠐⡊⠉⠉⠩⠭⡒⢄
⠀⠈⠀⠀⠀⠀⠈⡇⢱⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⢸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⡰⠊⠁⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠈⠢⢄
⡇⢀⠤⠐⠒⠒⠒⠤⢄⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠑⢄
⡇⢸⠀⠠⠤⠤⠤⠤⠬⠍⠲⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠱⡄
⡇⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠇⢸⠀⠀⠤⠤⠤⠤⠬⠕⠀⠀⠀⠈⠳⡄⠐⠀⠀⠀⠀⠀⠈
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠐⠒⠒⠒⢒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠳⡀⠣⡀
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠈⢢⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⠦⣀
⠀⠀⠀⠀⠠⠤⠤⠤⠨⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠉⡉⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢠⠏⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⢣⣷⣄
⠀⠀⠀⠀⠀⡠⠊⠁⢀⡴⠚⡿⠀⠀⠀⡈⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⢉⣿⣿⣿⠣⣿⣿⣿⣦⡀
⠀⠀⠀⣠⠞⠀⢀⡴⠋⣠⠞⠁⢀⡤⠚⠙⢦⡀⠀⢀⡇⠀⠀⠀⣠⣾⣿⡟⠁⢀⣠⣿⣿⢟⣡⣶⣝⢿⣿⣿⠁
⠀⠀⣰⠃⠀⠀⠸⠖⠋⠁⢀⡴⠋⠀⠀⠀⠀⠻⣄⠘⠀⠀⠀⣴⣿⣿⣿⣤⣶⣿⣿⢟⣵⣿⣿⣿⣿⣷⡙⠇
⠀⢠⡇⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢰⣿⣿⣿⣿⣿⢿⣫⣷⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠈⠳⣤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠛⣛⣯⣭⣶⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⣄⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠉⠙⢿⡆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠠⠤⠞⠁
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠸⣿⣿⡇⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣁⣴⣾⠿⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣤⠀⢻⣿⡇⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠤⠴⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣿⡄⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⢶⣦⣄⡀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⣿⣷⡀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠉⠻⣿⣶⡄⢻⣿⣿⡟⣦
⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠈⢻⣿⣎⣿⣿⡇⢹⣆
⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠤⠤⠶⡶⠶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢻⣿⣿⣿⡇⠈⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⡆⠀⠈⣿⣿⣿⠃⠀⣿⣷
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠀⠀⣿⣿⠃⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢠⡿⠁⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢡⣿⠏
⠀⠀⠀⠀⠀⠀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠑⠦⣤⠀⠀⠀⠀⠀⣤⡶⠞⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⢿⣦⣈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⣶⡤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡄⠀⢠⡾⠷⠿⠶⣤⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣆⠈⠷⢷⡤⠤⠀⠀⠀⠀⠀⠀⣀⢴⡟⢁⡞⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⣤⠃⢨⡅⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠘⢷⣤⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢰⡞⣩⡙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣄⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣤⠀⠈⠁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⠁⠈⠻⣿⣿⡿⠿⣿⠃⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⣼⡏⢠⣿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⢹⣿⡄⢀⡿⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢸⡟⠀⣸⡟⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢢⢘⣾⣿⣦⠞⠁⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣀⡀⣤⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢰⣿⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠛⡿⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⠛⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣾⡇⠀⠠⠀⠄⠀⠠⠤⠤⠄⠀⠀⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠀⠀⠐⠀⠒⠀⠱⠖⠀⠊⠓⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠌⠀⠤⠤⠤⠤⠬⠠⠤⠈⠁⠀⠤⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⢤⢤⠤⠤⣄⢀⡤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠚⠚⠚⠒⠒⣿⢸⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣄⠀⠀⣿⢸⢐⠶⡶⡶⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠘⠧⣌⠠⠄⣹⠘⠒⠖⠒⠶⢒⣲⣒⠲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠶⠟⠀⠀⣿⠀⠀⠀⢀⡼⠋⣭⡙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣠⣀⣄⣿⠀⠀⠀⠸⣇⠀⣽⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠿⠧⠤⠤⠟⠀⠀⠀⠀⠙⠳⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⡿⠿⣿⣿⣿⡿⠿⢿⣛⡇⠀⣰⠞⣛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣏⢺⡇⡷⠀⠀⣿⡇⢸⡇⠀⣻⡅⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⣶⣶⣾⣿⣿⣷⣶⣾⣉⡇⠀⠻⣦⣭⣥⠾⠁





⠀⠀⠀⠀⠀⠀⠀⢰⣖⡆⣴⡄⢦⡴⢰⣄⣶⢰⣒⢰⣆⣴⢲⡖⠀⣦⣠⡆⣶⡒⢲⡖⢰⣀⣆⡔⢲⣰⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⠙⠘⠁⠘⠉⠘⠘⠒⠘⠈⠋⠈⠁⠀⠃⠁⠃⠛⠒⠈⠃⠘⠀⠃⠑⠚⠘⠓⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣋⣭⣭⣍⠳⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠏⠀⠀⠀⢸⡇⡇⠀⠀⠀⣠⢞⡭⠥⠤⢤⡉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⢀⣀⣀⠤⠜⠓⠧⢄⡀⢸⢃⡏⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⢍⣀⠀⠀⠀⠀⠀⠀⠈⡿⣸⠦⢤⣀⡀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠉⠓⠦⣤⣀⠀⠀⡇⡏⠀⠀⢀⣩⠷⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡇⣧⣖⡮⠽⠚⠁⣿⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⣯⣙⡲⠤⣤⣀⣿⣿⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⠀⠀⠉⠙⠒⠮⣿⣿⣆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⢸⣓⠦⢤⣀⡀⠀⣿⣿⢹⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⣿⢸⣹⡙⠒⠶⠭⣙⡇⣿⣄⣷⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡽⠓⠯⡟⣼⢧⣷⠀⠀⠀⠀⡇⣿⠲⠽⣆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡽⠁⠀⠀⡇⡏⠙⣾⢭⣗⡦⢤⡇⣿⠀⠀⢹⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⠳⢤⣀⠀⡇⡇⢀⣸⣾⠦⢝⣳⡇⣿⢑⡒⠤⣷⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠉⠒⠮⣭⡇⣯⠭⠖⠒⠋⠉⠀⣇⣿⠀⠈⠑⠺⣧⢻
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠞⠀⠀⠀⠀⠀⢠⠁⡇⠀⠀⠀⠀⠀⠀⡟⠃⠀⠀⠀⠀⠈⠋
⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠋⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠾⠃
⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⠋
⠀⠀⠀⠀⠈⠻⢽⣲⡤⣄⣀⣀⣀⣀⣠⣴⡾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢠⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⡴⠋⠀⢸⢸⠀⣨⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡇⢸⢸⠀⡇⠀⠀⠀⡼⠁⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⢳⠀⠀⢰⠃⠀⠀⢸⠈⣫⠴⠊⢹
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢠⢣⡄⠀⠀⡿⡄⢶⣄⠈⢇⠀⠀⡀⡇⠀⠘⣆⣤⡀⠘⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢸⢸⠁⠀⢸⣷⣟⢼⣎⣗⣾⡄⠀⡇⢸⠀⠀⢿⠀⣗⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠴⠧⠾⠼⠴⠷⠧⠼⠾⠤⠧⠄⠀⢸⢸⡀⢀⣇⣘⣠⠋⢧⣘⣀⣇⠀⡇⢸⠀⣴⣚⣈⣓⡍⠉⠁⠀⠀⠀⠀⢰⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⢧⣸⣆⠀⢀⣐⣀⠀⢀⠿⡀⣇⡞⠀⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⡷⣄⠀⠀⠀⠀⠘⢮⡟⣨⡳⡤⣉⡡⡴⢋⣤⣱⡟⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠓⣤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣛⣀⡉⠙⡇⠀⠀⠀⠀⠀⠈⠁⣹⠇⠀⠀⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠯⠇⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⡠⠖⠒⠦⣼⠀⠶⠶⠆⠀⡇⠀⠀⣠⠖⠚⠻⣋⢷⠀⠀⠊⢱⢋⡻⠒⠲⠤⣀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⣀⣈⣉⣁⣀⡇⠀⡜⠁⠀⠀⠀⠈⠹⡖⠦⠶⡞⠉⠀⠀⠀⠀⠘⡆⠀⠀⢸⣉⣉⣉⣉⣉⣉⣿⣏⣹
⠀⠀⠀⠀⢀⡹⠀⠀⠀⡆⠀⠀⠈⣇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢃⠀⢀⠃⠀⠀⠀⣤⠀⠀⢹⠀⠀⢸⠀⠀⠀⡴⠦⡄⠀⠀⢸
⠀⠀⠀⠀⡎⠀⠀⠈⠳⡷⠊⠀⠀⠈⢧⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠸⡄⡼⠀⠀⠀⠀⣇⠀⠀⠀⣇⠀⢸⠀⠀⠀⠳⠶⠧⠀⠀⢸
⠀⠀⠀⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⡠⠏⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⣿⠀⠀⠀⢹⡀⢸⠀⣒⣒⣒⣒⡒⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠸⣤⣤⣤⣤⣤⣤⣤⣤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠒⠦⣾⠀⠀⠀⠀⠀⠷⠇⠀⠀⠀⠀⣯⡤⠤⠶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣲⣿⠭⢬⣣⣴⠃⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣼⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠈⠉⣽⣷⡾⠋⠀⠀⠀⡵⣝⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠧⠤⠤⠴⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⢠⡄⠂⠀⠀⠤⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⢀⣼⡅⠀⠀⠀⠀⠀⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣮⣽⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⣾⡇⣧⡄⠀⠀⠀⠀⠀⠀⡛⠛⠛⠒⠢
⢸⡇⢄⢸⡇⢠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⢀⣿⠠⣿⠇⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠄


⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣰⡾⠛⠙⠻⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⣽⠖⠲⡿⢦⠀⠀⠀⠀⠀⢀⣞⣉⡇⢹⠱
⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣟⣽⣿⣿⠅⠀⠀⠀⠀⢸⣸⡅⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣲⢖⡃⡺⢄
⠘⢿⣶⣴⣾⠗⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⢯⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢩⣷⣻⠗


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⣤⣤⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣼⡆⢀⢈⣿⢀⠄⠀⠀⠀⠀⣠⡀⢁⢂⣠⣶⡤⠢⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢
⣿⣿⣧⣤⣾⣿⡇⠀⠀⠀⠀⠀⢻⡇⠈⠘⡿⢀⠀⠀⠀⠀⠀⠸⠱⣦⡦⢫⢔⠔⠳⠄⠀⠀⠀⣯⣱⣾⣿⣶⣶
⠛⠛⠛⠻⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠛


⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢀⣀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⡇⣠⠿⢿⡃⠀⠀⠀⠀⢨⣭⢨⣭⠈⠉⠁⠀⠀⠀⠀⠀⢀⡀⣴⢰⣿⢸
⢿⣿⣯⣽⣿⣿⠇⠀⠀⠀⠀⠀⡿⠛⢾⣿⣦⣾⡇⠀⠀⠀⠀⠰⠶⠰⠶⠰⠶⠲⠶⠆⠀⠀⠀⢸⡇⣿⠨⣿⢸
⠀⠏⢀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠿⠶⠿⠿⠿⠿⠃⠀⠀⠀⠀⠘⠛⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠀⠋⠘
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⢀⣲⢶⡶⠒⠆⠬⠀⣁⠈⠁⠒⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠀⢉⣀⡤⠔⡖⠋⢉⢃⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠐⢠⣤⠄⠈⠁⠰⠦⠄
⢀⡀⠀⠂⠀⢁⣀⡤⠴⠒⡿⢋⠎⠏⣈⠂⢀⡆⢓⡾⡇⠀⠀⠀⠀⠀⡀⠤⠒⠈⠀⠀⠑⡄
⠈⠀⠀⢀⠔⠉⠉⠑⠒⠾⢴⣌⡰⠃⠉⠄⠢⢃⡏⠞⣥⢀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢧⣴⡿⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠃
⠀⠀⠀⠁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠆⠁
⠀⠀⠀⠀⠀⢸⠉⠛⠒⣤⢤⣀⡀⢀⣼⠟⢽⠇⣹⣄⠀⠀⠀⠀⠀⣀⢤⠖⢫⠏⡸⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠁⠹⠛⠉⠂⠸⢠⠁⣹⡧⣀⣤⣖⠟⢣⠎⠀⡈⡜⣸⡖⠂⠤⠀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡶⠁⠙⠉⡔⠡⠀⠎⢀⡊⠄⣰⣽⡆⠀⠉⠥⠤⠀⠐
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡜⠀⠀⢄⡾⢀⠣⠞⣌⣞⣤⡶⠟⣯⠭⠭⠅⠀⠀⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⢸⣉⣄⡴⡛⣢⣯⣤⡶⠛⠉⠩⠭⠭⠭⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⣸⣫⣽⠿⠟⣻⣷⣶⣄⣀⣀⣀⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠎⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⢠⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⡎⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢄⣤⣀⣀⡈⠉⠛⠛⠛⠿⠶⠶⢦⣿⣤⡤⡶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠈⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⣉⣉⣛⣶⡒⠦⢤⣼⣧⢤⣤⠤⠤⠴⠶⠒⠒⠒⠒⠒⠚⢰⡟⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⠿⠻⢿⣿⣿⣦⠀⣧⣼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣸⠀⠀⠀⣉⣿⣃⣠⡇⢸⣼⣧⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣉⡿⠶⠆⠙⠻⠿⢿⡇⣼⣼⡏⢹⡉⣿⢹⡟⣿⠛⢷⡿⣶⢾⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⡇⠀⠀⠈⢑⣮⢭⡏⢻⡼⢧⣈⣁⡋⠘⠃⠿⠀⢸⡇⣿⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠖⣒⣻⡏⢀⣀⣙⠦⣀⣰⣆⠀⠀⡟⢸⠀⠀⠀⢈⣽⣿⣿⣿⣶⣤⣤⣌⣀⡇⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⣛⣩⣭⣶⣶⣿⣿⣿⠿⢿⣤⣿⠿⡆⠈⣽⡅⣴⣶⡷⢸⠀⠀⠀⣈⠉⠛⢿⣿⣿⣿⣶⣄⢨⣇⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣉⣤⣶⣿⣿⣿⠿⠛⠛⠉⠀⠀⠀⠛⠛⠉⢀⣷⡤⠶⠚⣉⣉⡧⢸⠀⠀⠀⢯⠀⠀⠀⢉⣿⣿⣿⣿⠄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣡⣴⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⣉⣤⣶⣶⣿⣿⣿⣇⣸⠀⣀⠀⣀⡵⠖⠉⠁⠉⠛⠛⠋⠀⣹⣿
⠀⠀⠀⠀⠀⣠⠞⢁⣴⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢋⣠⣶⣿⣿⠿⠛⠉⠉⠀⠀⣧⢸⠋⢉⣽⠟⠁⢠⡔⠀⠀⢱⡤⠶⠛⡇⣿
⠀⠀⠀⢠⡞⠁⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣡⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠠⣿⣿⡶⠋⠀⢀⣴⠋⠀⠀⠀⠸⡟⠛⠀⣷⣿
⠀⠀⣰⠏⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣾⣿⠟⠁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣟⢻⠉⣠⡤⠶⠿⣄⠀⠀⠀⠀⢻⡀⠀⣷⣼
⠀⢠⠏⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⠏⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⢀⣿⠀⠀⠀⠈⢓⣦⣤⣤⡼⠟⠁⣿⢸
⠀⡞⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⣿⠃⠀⠀⠀⠀⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⣻⡀⢀⠈⢻⡟⠉⠀⡟⠀⠀⠀⣿⢸
⢰⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣙⠃⠀⠀⠀⠀⠀⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣿⣿⣿⣤⢼⡇⠀⢸⠛⠛⠃⠀⣿⢸
⣾⠁⠼⢀⡀⣄⠀⠀⢀⣠⣤⠶⠶⠶⣶⣄⡹⢿⣿⢟⡀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⠀⠀⠀⠀⠀⠘⡇⠀⢸⡀⠀⠀⠀⣿⢸⡄
⣿⠀⠀⣿⣿⣿⠆⣴⣿⡟⢡⡄⠀⣀⠐⠛⣿⣦⠀⡼⣧⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣀⣀⣀⣠⣴⣿⣦⣴⡷⠶⠓⠀⣿⢸⡀
⣿⡂⢸⡎⠛⣿⣾⣿⣿⠄⠀⠀⢨⣵⡦⠀⢸⣿⡇⣷⠘⣆⠀⠀⠀⠀⢽⣯⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠉⠉⠉⠉⠀⠈⠛⠛⠀⠀⠀⠀⣿⢸⡁
⣿⡇⠀⢷⠹⡄⠈⠻⣿⣶⣦⠀⢀⠈⢀⣤⣿⡿⢰⣿⣆⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡴⠶⠄⣿⢸⡇
⢹⣷⠀⠸⣇⠙⣄⠀⠈⠛⠛⠁⢉⣉⡹⠁⠉⠱⡏⢻⣿⣷⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠗⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠘⣿⣧⠀⠹⣆⠈⠳⣄⡀⠀⠀⠀⠉⠁⠀⠀⠀⠙⣆⢻⣿⣿⣄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇
⠀⢹⣿⣆⠀⠹⣄⠀⠈⢻⣿⣀⡀⠀⠀⠀⠀⠀⠀⠘⠇⢻⣿⣿⣧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃
⠀⠈⣿⣿⣆⠀⠙⣆⠀⠀⢿⣯⡁⠀⣠⡠⠤⢄⣀⠒⠀⠒⠛⠿⣿⣷⣄⠀⠻⣄⠀⠀⠀⠀⠀⠀⠛⠘⠁
⠀⠀⠸⣿⣿⣆⠀⠘⣇⠀⢸⢃⡴⠋⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠙⢿⣦⠀⠈⣧
⠀⠀⠀⢻⣿⣿⣆⠀⠘⣧⠸⠟⠀⠀⢠⠃⠀⠀⠀⣿⣦⣤⣄⡀⠀⠀⠀⠹⣧⠀⠈⣇
⠀⠀⠀⠈⢿⣿⣿⡆⠀⠈⣧⠀⢤⣤⣼⣾⠷⠶⣦⣾⠄⠀⠈⠛⣆⠀⠀⢀⣹⡧⠀⢸
⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠸⣇⠀⠀⠘⢷⡀⠀⣼⣁⡀⠀⡀⠀⠈⠣⣶⠉⢿⡇⠀⢸
⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⢳⣾⠟⣥⣾⠟⠀⠀⠀⠀⠈⣷⣀⣙⣶⣾⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣃⠀⢀⣼⠰⠶⠶⠶⠞⠁⠾⠋⠱⠒⠛⠚⠛⠛⠃⢸⣿⣿⠿⣛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⢿⠿⣿⠿⣿⡏⣀⡀⣀⣠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⣴⣼⣤⠏⠀⠀⠃⠛⠙⠃⠛⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⡰⠫⠍⡒⠤⣀
⠀⠀⠀⠀⡰⠑⠀⢠⣀⠁⠀⠉⠒⠤⣀
⠀⠀⠀⡰⠁⠀⢠⡏⠻⠿⣶⣤⣀⠀⠀⠉⠒⠤⣀
⠀⠀⡰⠑⠀⢠⣿⡃⠀⠀⠈⠉⢿⣓⡄⠀⠀⠁⠂⠍⡒⠤⣀
⠀⠠⠀⠀⢠⡿⠷⠹⠦⣄⡀⠀⣼⡟⠃⠀⠀⠀⢀⣤⣀⠀⠀⠁⠀⠄
⠰⠀⠀⢀⡻⣏⠀⠀⠀⠈⠐⠂⠚⠃⠀⠀⣀⣄⢻⢿⣿⡇⠀⠀⠀⠁⠂⠅⡢⢄⡀
⠡⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠾⡿⠛⠁⢸⣿⡇⠀⠀⠀⠀⠀⣄⣀⠁⠀⠕⡢⢄⡀
⠀⠀⠁⠒⠤⡀⠀⠀⠀⠀⠀⢀⣴⣶⡍⠿⢳⣦⣀⣨⣿⡇⠀⠀⠀⠀⣼⡿⠏⠀⠀⣤⣀⠁⠊⠕⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⢻⣿⡇⠀⠀⠀⢸⣾⠏⠀⠀⠰⣿⡿⢿⣶⣤⡀⠁⠊⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠤⣄⠉⠀⠀⠐⣿⡟⠀⠀⠈⠙⣿⣷⡀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢐⣄⡟⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⠂⠀⠀⠈⠀⠀⢀⠂⣌⡀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠳⢗⣦⣠⣶⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠉⠉⠉⠉⠉⠁⢀⡀⠀⠀⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⣁⣴⡶⠚⠓⠢⡄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠠⠤⠤⠤⠀⢠⢀⡴⠾⢿⠿⠄⢄⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠸⡈⢿⣶⣾⠾⡻⢸⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣲⡶⠶⠤⠤⢤⣤⣵⣬⣀⣈⣡⠜⢐⣲⠞⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡉⠉⡨⠉⠉⠉⣀⠐⠒⠂⠤⢀⡀⠄⠂⠀⠉⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⣅⡰⠆⠀⠾⠤⠄⠀⢾⣁⣠⠞⠁⣠⠒⠮⡑⠠⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠁⠀⠀⠀⠀⠉⠀⠀⠒⢒⣤⢶⡁⢮⣉⠑⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠉⠀⠀⠈⠒⣬⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠂⠀⠀⠀⠀⠀⠀⠐⠒⢄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢣⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠀⠀⠤⡀⠀⢢⠀⠀⠀⠀⠸⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⣍⡙⠆⠐⡜⡆⠀⡇⠀⠀⠀⢰⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡹⠀⣷⠀⣸⣵⣞⣁⣀⣀⣠⣼⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢀⡴⠿⠞⠉⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢈⠁
⠀⠀⢀⣀⡀⠀⠤⠃⠀⠀⠀⢈
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡬
⠀⠸⢓⣶⢤⣤⣀⣀⣤⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢉⣉⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⣥⡀⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢌⡄⢈⣤⢉⣃
⠀⠀⠀⢀⠄⠠⠄⠀⠀⠀⠀⠀⢀⠎⠀⠀⢿⡂⢘⡟⠀⠑⡄
⠀⠀⠀⡵⠉⠈⡊⡄⠀⠀⠀⠀⡜⠷⣤⠎⠀⠙⠛⠁⣴⠞⢃
⠀⠀⢀⡇⠰⠥⢅⠙⠣⡁⠀⢸⠀⠘⠃⠀⠀⠀⠀⠀⡆⡂⠈⡄
⠀⠀⢸⠷⠶⠶⢾⠸⠦⡈⢢⠈⡀⠀⡀⠀⠀⠀⠀⠀⡗⢽⠀⢁
⠀⠀⡾⠀⠀⠀⠈⠀⠀⠈⠢⠁⣅⠸⢉⠁⠤⠀⢄⠉⠈⢪⠃⠸
⠀⠀⠓⠀⠀⠀⠀⢰⠀⠀⠀⠑⡌⢠⠽⡔⠈⠉⠑⠳⡤⠰⡶⡖⢿⡆
⠀⠐⠾⠿⠶⠶⠾⡏⠗⠒⠒⠓⠳⢦⠱⡈⠐⠤⡀⠀⠐⡀⠡⠀⠈⢕⠄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢢⠱⡀⠀⠱⡀⠀⠡⠀⠱⠀⠀⢫⢄
⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠃⠀⢂⠱⡀⠀⠑⡄⠀⢆⠀⠆⠀⠀⠩⢂
⠀⣾⠀⠀⠀⠀⠀⣐⢁⠀⠀⠀⣰⠀⠀⠀⢂⠱⡀⠀⠈⢆⠀⠣⡈⠢⣀⡀⠡⡡
⠀⠻⠋⠉⠉⠉⠉⠻⠸⠙⠉⠹⡅⠀⠀⠀⠀⢆⠱⡀⠀⠀⢣⡖⠝⠒⠛⠉⠀⠑⡑⡀
⠸⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⢸⠁⠀⠀⠀⠀⠀⢆⠰⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⡔⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠈⢆⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⢄
⢰⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢂
⠾⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠢⢄⠑⠢⠄⢀⢀⣀⡀⠀⠀⠔⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠐⠀⠄⠀⠀⠀⠠⠆⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣉⡭⠷⡄⠀⠀⠀⠀⢠⡏⠗⡦⣄⣀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣉⡡⠴⢚⡉⠀⠀⠀⢹⠀⠀⠀⠀⡼⠛⠲⢤⣈⠈⠟⢲⢤⣀⡀⠈⠙⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⡤⠖⢋⡥⠖⣚⣨⠵⠚⠛⣆⢸⠀⠀⠀⢠⠇⢀⠀⠀⠈⠙⠓⠦⣌⡁⠿⢳⠦⣄⣀⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⡞⢀⡜⠁⢀⣠⠤⠒⠋⠁⠀⠀⠀⠀⣿⢸⠀⠀⠀⢾⡀⠈⠁⠲⠄⣀⠀⠀⠀⠉⠛⠲⢤⣁⠛⠹⠖⢾
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠉⠓⠦⢄⣀⠈⠁⠲⠄⣀⠀⠀⠀⠈⠉⠓⠦⣼
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⡇⠀⠀⣠⠖⢋⣉⣉⠙⠲⠄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣿⣨⠀⡀⢠⠞⣡⠚⣉⣤⣍⠙⠂⠀⢺⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⡏⡼⠁⡴⠁⡠⠄⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡋
⠀⠀⠀⠀⠀⠀⠀⣧⣽⠘⡇⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⣚⣩⠷⠒⣿⡉⣿
⠀⠀⠀⠀⠀⠀⠀⡿⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣀⣠⠤⠖⠚⣉⣡⠤⠖⠋⠁⠀⢀⣀⣻⡧⠿⢤
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⢀⣠⠴⢺⡇⢸⢸⠀⠀⣴⣋⣁⣠⣤⣖⣋⣭⡤⠤⠴⠖⠚⠋⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⡇⠀⢀⣠⢴⢚⣭⠰⣼⠀⡇⢸⢸⠀⠀⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⢚⣹
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⣿⣾⢉⣿⣯⡇⢹⢸⡇⢸⢸⠀⠀⡗⠶⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢹
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⣿⣿⠉⠸⠇⢃⣨⠼⠃⢸⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⢺
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⡏⠋⣀⠴⠚⠉⠀⠀⠀⣼⢸⠀⠀⡷⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⢾
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⠀⠛⠉⠁⠀⠀⠀⠀⣠⠞⠁⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡃⡇⠀⠀⠀⢀⣠⠤⠖⠋⠀⢀⡴⠋⠀⠀⣟⠒⠒⠚⠉⠉⠀⠀⠀⠀⣀⣀⣠⠤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠙⠒⠚⠋⠉⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠙⠶⠶⠒⠒⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠾⣇⡀⣀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠻⢿⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣠⡴⠟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡏⠁⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⡗⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠶⠄⠀⠀⠀⡽⠶⣤⣄⣀⣀⣀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣿⠀⢀⣠⡴⠋⣠⠞⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⠙⢦⣿⣄⠙⠳⠦⠤⠤⠶⠒⠀⢀⣴⣛⣻⡿⠟⢧⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣼⠋⠙⠳⢶⡄⠀⣶⡶⠟⠛⢿⠉⣁⣤⠶⠋⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣤⡄⠘⣧⣠⠟⠀⠀⣀⣼⣿⣭⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⡀⠀⠀⣴⣃⣀⣀⣀⣀⣀⣀⣀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣼⣧⣀⡀⠀⠀⠸⣇⠀⠀⠀⡼⠁⠀⡼⠋⠉⠉⠉⠉⠉⢹⠉⠉⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠋⠁⠀⠉⠉⠀⠀⠀⠈⢷⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⢙⡶⢦⣤⣀⣀⣀⠀⣀⣀⣀⣤⠾⢣⡞⠀⠀⠀⠚⠛⠛⠛⠛⠛⢻⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠞⠛⠻⣤⡤⠞⠉⣹⠏⠉⣹⠋⠁⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠙⠓⠶⠞⠉⣴⡋⠉⠙⣷⠞⠁⠀⠀⣰⠏⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⣰⠋⠀⣿⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣼⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⢻⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠲⠒⠒⠒⠒⠒⠒⠒⠒⠲⠂⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠾⠀⠀⠀⠸⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢀⡬⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢸⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⡄⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣚⠧⠖⠒⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⠤⠤⠐⠒⠋⠉⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠤⠤⢤⡀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢀⣠⠤⠖⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⢀⠀⢠⡀⠠⣶⠶⠖⠀⠀⢇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡎⠀⠀⢀⣀⠀⠀⣶⡄⠀⢸⣇⠸⣿⠀⣿⡄⠀⠀⠀⠸⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⣿⡟⣷⠀⢸⣧⠀⠀⣿⡀⢻⣇⠸⣷⣶⠶⠀⠀⢣⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡄⠀⢻⡇⠀⠀⠈⣿⡀⠀⢸⣇⠘⣿⠀⢿⡇⠀⠀⠀⠘⡆⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠀⠸⣿⢠⣤⣄⢹⣧⣀⡀⢿⣄⣿⡇⠸⣷⣶⠿⠇⠀⢳⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡄⠀⢻⣇⣈⣿⠈⢿⠿⠛⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠰⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠒⠒⠊⠉⠉⠉⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠸⡀⠀⣀⠤⠖⠊⠉⠀⠀⢀⣀⡠⠤⠴⠶⠔⠒⠒⠂⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⠈⠀⢀⣠⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠑⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢄⣀⣀⣀⣀⣀⠀⢀⣈⡉⠤⠔⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⢒⡒⠒⠒⠒⠆⠀⠀⠀⢠⠒⠒⠒⠒⠒⢦⠀⠀⠀⠀⠀⡴⠲⠿⠖⢢⠀⠀⠀⠀⠀⢠⣶⣿⡷⠐⠄
⠀⠀⠀⠻⠷⠀⠀⠀⡆⠀⠀⠀⢸⠀⠤⠤⢾⠉⣛⠀⠀⠀⠀⠀⡟⠿⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣣⣄⣈
⠀⠀⠼⠿⠿⠽⠿⠿⠧⠀⠀⠀⠈⠉⠩⠿⠏⠉⠙⠂⠀⠀⠀⠀⣧⣤⣤⣶⣸⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⠶⡶⢦⡀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠆
⠀⠀⡇⠀⣄⢀⣄⡀⣿⠀⠀⠀⠀⣿⠒⣿⢚⡇⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣤
⠀⠀⣇⣺⣛⣟⣟⣇⡿⠀⠀⠀⠀⠈⠓⠛⠛⢧⡀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠋⠀⠀⠀⠀⠀⠀⠺⠛⠒⠛⠻
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣤⣀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣠⡀
⠀⠀⣀⣰⣋⡠⠿⣶⡶⠀⠀⠀⠀⣰⠏⠁⠀⢛⢳⡄⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠴⢒⣄
⠀⠀⠉⠉⠻⠥⠴⢇⠀⠀⠀⠀⠀⢿⡠⠶⠴⠿⣸⠇⠀⠀⠀⠀⠸⠴⢤⡤⠦⠄⠀⠀⠀⠀⠀⡟⢖⣛⣜
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠈⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠰⠾⠷⠀⠀⠀⠀⠀⠀⠀⠳⠶⠴⠶⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡿⠿⠿⠿⠿⠿⣟⠀⠀⠀⠀⡞⠉⣩⡿⡆⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⠀⠀⠀⠀⠀⡠⡼⠩⠍⢧⢄
⠀⠀⡤⣤⣤⣔⣩⣕⣾⠀⠀⠀⠀⢷⣛⣛⣳⡃⠀⠀⠀⠀⠀⠀⣿⣁⣉⣀⣿⠀⠀⠀⠀⠀⠂⡇⠐⡂⡰⠐
⠀⠀⠦⠤⠤⠬⠵⠭⠮⠀⠀⠀⠀⠀⠈⠉⠀⠹⣦⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⠭⣈⣣⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠊⠉⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢆⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠈⠉⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠀⠌⢆⠀⠀⢀⡤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⡄⠀⠐⢣⣔⠊⠺⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⢀⡁⠄⠓⠔⠋⡡⡟⠉⠉⠐⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢀⣠⣤⠒⠊⢉⠀⢂⢆⠀⠄⡀⢠⡷⠂⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠀⣀⠀⢀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⢆⣩⢢⠖⡑⡐⠡⡠⠡⠣⢂⢂⠌⡐⣱⣏⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣩⠷⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠢⠤⠉⠓⠷⣔⡐⡑⡐⡐⡡⢡⢂⠌⡔⡰⠇⠠⠉⠢⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢵⣡⠡⢂⢎⢜⠜⡧⠡⡐⡑⡀⢀⡠⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⢰⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⣎⣊⣗⣱⠼⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⢇⠠⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⢀⠀⠈⢢
⠀⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢙⢸⡩⢳⡀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢀⠀⠃⠄⠰⠘⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⠪⡢⠘⡤⠕⠝⡢⡀⠀⠀⠀⠀⠀⠈⡄⠐⠸⠈⣀⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠲⢤⣑⠒⢴⠖⣡⠊⠢⡑⢕⠨⠀⣖⠊⢊⠜⡝⣦⡀⠂⠀⠀⠀⣀⡤⡶⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⡻⡢⢞⠥⡑⠐⢌⠢⡑⢈⡵⡡⢂⢎⠜⡔⡹⢆⣤⠲⢋⢫⡛⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⡀⠀⠀⢑⠌⢆⠙⡢⠂⠢⡐⠌⠀⠔⠁⠁⠢⢊⠔⡐⡡⡑⡡⠣⠝⡐⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣑⢕⠱⣌⠳⢈⢈⠢⢰⠚⡐⡁⡡⢃⠎⠔⠜⡔⡔⡘⠈⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠣⢙⠦⡑⠁⢔⢸⢊⢌⠔⡠⢁⢎⠎⣜⡨⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠦⣠⣸⠩⠂⢘⠠⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠃⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠅⣀⠤⠀⠁⠂⠡⠂⠡⠂⠥⢊⠡⢂⡡⠐⡩⠐⡉⠄⢂⠁⠐⠁⠂⠥⠂⠅⠊⠥⡊⠕⣊⠔⣂⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠤⠀⠠⠀⠡⠊⠠⠀⡡⠂⡡⠐⡩⠔⢉⠤⢊⡡⠀⠠⠂⠄⠀⠀⠀⠀⠊⠀⠊⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠤⠄⠀⠀⠀⠀⠀⠠⠀⠠⠈⢱⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡠⠐⠈⠈⠈⠐⠠⡀⠀⠈⢚⠀⢸⡁⡀⠉⠉⠑⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⡐⣊⢅⠉⠢⠀⠘⢄⠀⠉⠀⣜⠂⠀⢕⢄⠀⠈⠀⢀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣏⡀⣘⢻⠘⠓⡴⠁⣰⣛⡇⠘⠀⢸⠀⠀⠁⡀⣥⠀⠀⠈⠂⠐⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠴⠵⠒⠿⢡⠎⢤⠈⣡⠁⠀⢀⠀⢸⠀⠀⠀⠈⢪⡲⡄⠀⠀⠀⠀⠑⢕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⠉⠉⠃⠈⠁⠠⠜⠃⠛⣀⠀⠰⢀⣸⡀⡀⠀⠀⢀⠘⢮⠢⣀⠀⠀⠀⠀⠑⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠉⠉⡆⣰⠀⠠⠐⠀⠄⡠⠃⠀⢀⠈⢰⠀⠪⡂⡠⠂⠀⠈⠙⢜⢧⣄⠀⠀⠀⠀⠪⡢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⣀⠔⣋⢉⣱⠆⠀⠀⠀⠘⠀⠀⢀⠶⠀⢸⡀⠤⠚⢕⢄⠀⠀⠀⠀⠑⢝⢷⣄⠀⠀⠀⠈⠪⡂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⣝⠧⠊⢉⣸⢩⠀⢀⣀⣀⣤⣠⠔⠺⢶⠀⢸⠤⠤⠤⢤⣕⣅⢄⠀⡀⠀⠀⠑⢝⢶⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡎⠈⠁⠀⠘⣹⠊⢹⡖⠁⠀⠀⠀⠀⠀⠀⢨⠀⢸⠉⠀⠢⡀⠉⠉⠙⠫⡉⠓⢄⠀⠀⠁⡙⢦⡀⠀⠀⠀⠑⢕⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠙⡀⠀⠀⠈⠀⠀⢰⠱⡆⠠⠤⠤⠀⠀⠀⣠⠀⢸⠀⠀⠀⠘⢤⠀⠠⠬⢮⡣⣄⣡⡀⠀⠈⠪⡻⣄⠀⠀⠀⠀⠑⠕
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⠢⠄⣀⠀⠘⡀⠈⠠⢀⠀⠀⠀⠀⢈⠀⢸⠉⠑⡄⠀⠀⠙⡍⠀⠀⠈⢳⢄⡏⠢⠀⠀⠘⢘⠷⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠁⠉⠐⠒⠀⠄⡈⠉⠈⠘⠠⢼⠀⠀⠈⢂⠀⠀⠈⠢⠄⠀⠐⡳⣕⢤⣵⣄⠀⢨⣴⠛⢧⣀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠈⠣⠀⠀⠓⡀⠀⠀⠘⢍⢨⡝⠀⠑⠔⣚⢋⣜⡇⠀⠀⠁⠒⠈
⠀⠀⠀⢀⠠⠄⠂⢸⡍⠀⠈⠒⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠱⠀⠀⠈⢂⠀⠀⠀⢻⣇⠠⠄⠐⢓⡂⠬⠷⠤⢀
⢀⠔⠈⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠃⠀⠀⠀⠱⡀⠀⢸⣿⠂⠉⠁⠀⠀⠀⠀⠀⠀⠈⠐⢄
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠦⣸⣟⡀⣀⠠⠄⠀⠒⠈
⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⡨⠁⣥⣀⣀⠀⠀⠀⡓⠀⠐⠀⠘⠂⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠁⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⠩⠙⠒⡢⢄⣄⠲⠜⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠁⠒⠀⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠄⠀⠐⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠿⠿⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠘⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠁⠀⠀⠀⠉⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⢀⣤⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣇⠀⠉⠁
⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⡀
⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠈⢿⣷⣦⣤⣤⣤⣤⣤⣶⣶⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣿⡟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⣶⣶⣶⣿⣿⠿⠟⠛⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⢋⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⢀⠀⢈⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠈⠛⠿⠿⠟⠶⣄⠀⠀⡄⠀⠀⣴⣿⡿⡢⢛⣥⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⣝⠁⠀⠀⠡⠝⢿⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣶⠁⠉⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠄⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠋⠁⣎⠉⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠁⠐⠀⠀⠘⠢⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⡿⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢺⣤⣬⠀⢿⠿⠿⠿⠿⢿⣿⣿⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠸⣿⣟⠀⢀⠀⠀⠀⠀⠀⠈⠻⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠚⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⢰⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⣇⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⣀⡄⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠐⠁⠠
⣿⠀⠘⡀⠀⠀⠀⠀⠀⠤⠀⡄⠀⠀⠀⠸⡈⠑⢦⣀⠀⠁⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⢠⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡀⠠⠀⠀⠀⠉⠀⠀⠀⠀⠩⠀⠀⢈⠖⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⠘⠛⠢⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿
⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠸⠀⢀⠀⠀⢻⣿⣿⣿
⣿⣿⡿⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⡛⢛⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡇⠀⣀⡀⠀⠁⠀⠀⠄⠀⠀⢹⣿⣿
⣿⣦⣆⣠⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣉⣲⡀⠐⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠰⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣤⣬⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⢢⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣶⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣄⢀⣶⡄⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠛⠻⠀⣸⠈⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣀⣹⣤⣤⣤⣤⣴⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠇⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⡆⠀⣿⠀⠀⠀⠀⣠⣾⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣠⣾⠟⣳⠀⠀⣰⡾⣛⣭⣽⡻⣷⡄
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡄⠀⣿⡇⠀⣿⠀⠀⠀⣸⣿⣿⣿⢟⣭⡻⣿⣿⡄⠀⠀⠀⣿⡿⠿⠿⠿⣿⣫⣾⠟⠁⠚⠁⠀⢰⣿⣸⣿⣿⣿⣿⡞⣿
⠀⠀⠀⢰⡆⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠀⠀⢻⣿⣿⣿⠻⠿⢇⣼⣿⣶⠀⠀⠀⣿⡿⠿⠿⣿⣣⣬⣷⠀⠀⠀⠀⠀⠘⣿⡜⣿⣿⣿⡿⣳⡿
⠀⠀⠀⢸⠇⠀⢿⠀⠸⡇⠀⢿⠇⠀⠿⠀⠀⠀⠈⢿⢟⣵⣿⣿⣿⢟⣱⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣷⠾⢛⣵⣤⡀
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠈⠙⠓⠲⠚⠋⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⣿⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠻⢿⣿⣿⣿⠀⠀⠀⠋⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣌⣉⣉⣀⣤⡴⠟⠉⢳⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣤⣤⣉⣉⡁⠀⢠⣾⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣦⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠘⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠃⠀⠈⠛⠛⠛⠛




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⣀⣴⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣙⣛⣉⣠⣴⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣿⣿⣿⣿⣿⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⣶⠈⢻⣿⣿⣿⣿⣿⡿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠻⣷⣤⣿⣿⣿⣿⣯⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡲⣶⣺⣿⢿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡞⠁⢸⢱⢪⣴⣴⠶⢥⣟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠇⠀⢸⢸⣺⣿⣾⡀⢸⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣄⡿⣆⣰⣾⣸⣿⣾⣿⢏⢺⢸⣹⣆⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⠶⢻⠙⣽⢲⡼⣔⣿⡟⠻⠽⢿⠬⡹⢾⢸⠚⠚⠢⣟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡜⠑⠘⠂⠈⡹⢫⡞⢁⠄⡿⠊⠀⠁⠀⠀⠋⢼⡢⢤⣔⢻⣏⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡞⠨⠀⠀⠀⡼⣱⠁⠂⣌⣼⣋⣠⢀⣀⣰⣪⣈⣾⠅⢠⡼⡏⠞⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡺⠕⠀⠀⠀⡜⡰⠃⢀⢂⠎⠀⠀⠈⣿⣿⣟⣷⣻⡼⣾⣉⣙⣥⠠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢡⢏⠊⠀⠀⠀⡜⣰⠁⠈⢠⡎⠀⠀⠀⠀⣿⣿⣩⣿⣹⡇⢹⣫⠿⣽⣦⣻⣗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡠⡋⠖⠀⠀⢀⡜⣰⠇⠀⢀⠌⠀⠀⠀⠀⠀⠇⣧⠴⣶⣶⣷⠈⣟⡛⠚⢽⠙⣷⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣰⡍⠊⠀⠀⢀⠞⢰⠏⠄⢠⠏⠀⠀⠀⠀⠀⠀⠀⢹⠶⠷⠾⠾⡇⠸⡴⠒⢼⡀⠔⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⢅⠌⠀⠀⢀⠎⣠⠋⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣦⣿⣷⠀⣯⡩⡁⣧⣸⡿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣜⠈⠂⠀⠀⢀⠎⣰⢫⡧⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣟⠛⢾⠭⠽⡆⢹⡤⠃⣾⠛⣿⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠾⡂⠁⠀⠀⡰⠃⡐⢇⡞⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢤⣤⣬⡍⣿⣥⠨⣿⣿⣿⡇⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢡⡏⠑⠀⠀⠀⡰⠃⡼⠁⡎⢈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢸⠀⠀⠓⠲⠶⡄⣴⠴⠤⣴⣼⡿⡟⣇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⢴⠋⡊⠀⠀⢀⡔⢡⡎⠃⡸⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣏⣉⣙⣥⡼⡇⢨⢒⢚⢝⣾⣯⣯⡿⠷⢓⡲⠶⠖⠒
⠀⠀⠀⠀⡠⠔⣊⢥⢞⠡⡢⠑⠀⠀⣠⠊⡠⠋⡄⢀⡼⠁⠀⠀⠀⠀⠀⠀⣤⣀⣀⠐⠒⡄⠛⣋⣛⣓⣚⣲⣤⠬⠽⠼⠶⠾⠷⠓⠐⠂
⢀⠤⢂⠥⠂⢏⢄⠪⠒⠁⣀⠠⠔⣊⣥⡚⠀⣠⢀⡼⠄⠀⠓⠒⠚⠓⠒⠋⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠈
⢀⠨⣦⡲⠎⠀⠀⣠⢒⠬⠐⠒⠋⠁⠀⡀⣴⣥⠟⡓⠖⠒⠛⠋⠉⠉⠉
⠚⠶⠦⠭⣤⣴⣟⣁⣸⡀⣀⣴⣤⣶⡖⠛⠉⠉⠈⠁

⠀⠀⣶⠢⢤⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⢈⣽⣲⣦⢀⣁⠐⢩⣢⣀⡀⠀⠀⠀⠀⠀⠈⠶⠛⠀⠀⠀⠀⠀⢠⠆⠀⠀⡠⠏⠀⠘⠁⠔⠰⠉
⠀⠀⠈⠳⡁⠁⠙⢄⠀⠀⠀⠀⠀⠀⠂⢀⡉⠘⠛⣩⠉⣩⠴⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⡀⢀⠋⠀⢀⠌
⠀⠀⠀⠀⠈⠁⠠⠾⠆⠂⠁⠀⠀⢀⢐⡁⠀⢠⠞⢡⠞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠔⠕⠀⠀⠀⠀⠾⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⠝⠁⣀⠔⠁⣠⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠡⠖⠉⠁⠀⣼⠵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⢤⠔⠦⣀⠀⠙⠖⠉⠉⠋⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠦⡂⠈⠳⠦⣄⠉⠁⠀⠀⠀⠉⢓⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⣶
⠺⣦⠐⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠈⠓⠴⣄⡀⠀⠀⠂⠽⣦⣀⣤⠄⠂⠉⠀⠀⠀⠀⠀⠘⢆
⣀⠀⠲⡆⠀⠈⢙⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠀⠤⠀⣀⡀⠀⠀⠈⠐⠓⢒⣿⣿⣷⠶⠒⠸⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢠
⠈⠷⣔⢄⠀⠂⠐⢈⣙⣇⠀⠀⠀⣀⠠⠔⠂⢁⠄⠁⠀⣸⠀⠀⠀⡠⠀⢼⢟⠟⠁⡠⢂⠼⡩⠢⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⣾
⠄⢤⣤⣭⣷⣤⣀⡠⢬⣽⣿⡟⠁⠀⠀⢀⢔⡃⢀⡀⠚⠁⠀⡀⠤⠀⣀⡬⢈⠔⠪⠆⠁⠎⢢⣷⠟⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿
⠀⠀⢰⠟⢛⡟⠁⡠⡿⢋⡟⠀⠀⠀⢀⣿⠏⠚⠉⠀⠀⣠⠀⡘⡁⠘⠁⣰⠁⠀⠠⠺⠰⢠⢰⠏⠀⡰⡩⢳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣻⣿⣿
⠁⡂⢀⡵⠋⣰⠂⠞⣱⠏⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣷⠜⢁⠐⠃⠓⠻⣆⠀⣇⠃⡆⣶⢛⠀⢠⣿⢡⢃⣿⡆⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠟⠋
⡢⢀⠄⠁⣼⠖⣪⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⣀⠠⠬⣁⡒⢦⡘⣆⢻⣸⣸⣯⠎⢰⢣⡇⣮⣿⣿⠃⠀⢀⣀⣰⣾⣿⣿⣿⣿⡛⠋⠁
⠂⠁⣀⣴⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⢌⡒⠦⣍⣒⠢⢭⡒⠽⣾⣾⣿⣿⠏⢀⣾⡟⣼⣿⡿⢁⢴⣡⣯⣿⣿⣿⣿⠿⣿⣿⣛⢷⣦⣄⠈⢿
⠀⠸⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠬⠭⣶⣬⣳⣾⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣷⣿⡿⠟⠋⠁⠈⠻⢿⣖⠫⢑⡪⢉⠓⢟⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣶⣞⣒⢄⠀⠀⠐⢿⣿⣶⣤⣤⣤⣤⣤⣤⣭⣉⡉⣙⢻⣧⣸⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠮⡅⢻⣔⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣝⢮⡑⠆⠀⠀⠀⠙⢿⣿⣿⣟⣻⣯⣭⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢻⣯⡻⢕⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠚⢛
⠀⢯⡲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠲⢌⠲⠤⠀⣦⡀⠀⠈⣉⣛⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⠙⠻⣶⣅⡪⣽⡆⠀⢀⡠⠴⠚⠉⠀⠀⣠⢔⡭⢪
⠀⠘⣯⡪⡻⢿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠒⠾⢿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣛⣛⡿⣿⣦⣀⠀⠀⠀⢀⣀⣀⣀⣉⡽⠿⠛⠊⠁⠀⠀⠀⠀⠀⣰⠗⣁⠔⡡
⠀⠀⠈⢗⣌⠢⡑⢽⣆⠀⠀⠀⠀⢀⣠⠤⠖⠚⠋⢻⣿⣿⣿⣿⡿⠟⢋⣩⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⢞⡵⣫⣴
⠀⠀⠀⠈⠻⢗⠬⡳⢽⠄⢀⡠⠖⠉⠀⠀⠀⢀⡔⡫⢋⠜⣡⣾⠁⣴⡿⡹⡫⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣜⢎⡜⡱⠁
⠀⢀⣀⣀⣀⡠⠭⠟⠛⠋⠁⠀⠀⠀⠀⠀⣠⢎⣼⠔⡵⣫⡟⠃⣾⡟⣱⡱⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⢴⡿⣫⣋⠜⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⣿⠞⡡⢎⡴⠋⠀⣼⢞⢼⢋⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡫⣴⢟⢕⣫⣴⠟⠁⢀⡞⡥⣫⢊⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢵⣺⣋⡽⠟⠊⠁⠀⠀⣾⣫⡾⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠁⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⣖⠶⣤⡀⠀⠈⠻⡷⡺⢝⠻⡟⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⡪⡑⢝⠪⣻⣷⣄⠀⠑⢬⣦⣙⠪⢍⡺⣷⢦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣊⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡵⠚⠉⠳⣝⢆⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⡥⠚⠁⠀⠀⠀⣠⠼⣮⠷⣋⠵⣌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡥⠚⠁⠀⠀⠀⣀⠴⣋⠵⣋⡵⠚⣝⣆⠈⠳⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡻⡄⠀⠀⢀⡴⣚⠵⣊⡵⠚⠁⣠⠴⠛⠉⠙⢓⡼⠞⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⢦⡖⢹⡊⣥⠚⠁⣠⠴⠋⠁⠀⠀⣠⠖⠋⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢣⡙⣄⠙⣌⢶⡋⠁⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢙⡾⠛⠉⠳⡙⢆⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠖⠉⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡤⠚⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⣤⣼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡷⠒⠶⢼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣰⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡇⠀⣇⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡞⠁⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡇⠀⣯⣉⣉⣻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢠⠏⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇⠀⡇⠀⠈⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣠⠏⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⡇⠀⡟⠒⠲⢾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⠃⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⡇⠀⡟⠙⠛⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡴⠃⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⣀⣀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⡼⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⠤⣬⣽⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⡞⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢠⠏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣟⠒⠒⢾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠉⠛⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⢤⣀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡷⠦⠤⢼⠀⢸
⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⢀⠀⢸⠀⢸
⣴⠚⠉⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣯⣉⣉⣹⠀⢸
⠘⣆⠀⠀⠀⢀⣠⠴⠚⠉⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣟⠀⠀⢹⠀⢸
⠀⠘⢦⡖⠛⠉⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣟⠛⠓⢺⠀⢸
⠀⠀⠀⠉⠳⣤⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣏⠉⠉⢹⠀⢸
⠀⠀⠀⠀⠀⣿⠉⠓⣬⣦⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⠤⠤⣼⠀⢸
⠀⠀⠀⠀⠀⠙⠒⠚⠃⠈⠓⡶⠚⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠒⠶⢾⠀⢸

⠀⠀⠀⠀⠀⠀⡖⠒⢲⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠂⢐⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⢰⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢠⢁⠞⠁⡠⠄⠈⠢⠑⡄⠀⠀⠀⠀⠀⡀⠤⡀⡀⠿⠸⠸⢂⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠠⢤
⠀⠀⠀⠀⠀⡂⡯⠭⢽⠀⠒⠒⡆⠀⠀⠀⠀⢘⠁⡆⠀⡠⠄⡇⠀⠀⠀⠀⠀⡼⠤⠂⠘⡈⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠠⠠⠤⠠⠤
⠀⠀⠀⠀⠀⠄⣏⠉⣿⢰⣄⣠⡇⠀⠀⠐⡈⢮⡀⠅⠀⣇⡴⢠⠂⠀⠀⠀⠀⠈⣄⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠑⠂⠠⣄⠔⡱
⠀⠀⢸⠈⢹⠅⠏⠉⡿⠸⡏⢀⠇⠀⠀⠀⠈⠢⠍⣁⡉⠡⠴⡣⠑⠄⠀⠀⡔⠁⠀⠎⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠗⠠⠀⣈⣀⠠⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠈⠀⠈⠈
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠔⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⡒⠀⠀⠀⠠⠂⠀⠀⠀⡠⡀⠈⠆⠀⠀⠀⠀⠀⠀⢀⠄⣒⣂⠠⣀⠆⠸
⠀⠀⠀⠋⠀⠊⠀⡄⡂⣀⢇⠀⠀⠀⠀⠀⠀⢀⠔⣉⠢⠔⡠⠲⠁⠀⠀⠀⠀⢄⡀⠀⠀⠀⣇⣠⠃⠀⠀⠀⠀⠀⡐⡐⢁⢄⢀⠐⡌⠎⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡆⠆⠀⠀⠀⠀⠴⡡⠊⠀⠑⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠜⢌⠀⠃⠁⠗⠀⠀⠀⠀⠀⡁⢇⠔⠢⡥⠊⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠊⠤⠌⣜⢀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡂⠀⠀⠀⢄⠙⠪⣂⠀⠀⣊⡔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠤⠤⠧⠠⠤⠸⠤⠤⠧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⠁

⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢩⢩⡍⣭⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⠐⠂⠐⠒⡄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣔⡄⢀⡢⠈⠀⠀⠀⠀⠰⠒⠒⠒⠒⠖⠶⠲⠖⠲⡁⠀⠀⠀⠀⠀⣀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠰⠳⠣⠇⠶⢰⠐⠞⢆
⠀⠀⠀⠀⠀⠙⠀⠘⠝⠀⢀⠀⠀⠀⠀⢀⣘⣈⣃⣛⠄⠀⠠⡐⣄⠇⠀⠀⠀⢀⣀⣀⡀⠁⣀⣀⣀⠀⠀⠀⠀⠆⠤⠴⠤⢤⢔⠢⢑⠾
⠀⠀⠀⢆⣀⣀⣀⣄⣀⣄⣀⠲⠀⠀⠀⠀⢤⠠⠄⠈⠀⡀⠀⠐⡈⡆⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠡⡴⡤⡄⣼⢀⠀⠀⡁⠁
⠀⠀⢘⠘⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠈⠀⠀⠀⠓⠉⠒⠐⠚⢝⠇⠀⠀⡏⠉⠈⢰⠁⠀⠁⠈⠀⠈⠀⠀⠀⠀⠈⠳⠥⠬⠶⠥⠄⠪⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠁⠁⠈⠁⠈
⠀⠀⠀⢀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠈⠔⠈⠉⠁⢢⠀⠀⠀⠀⠀⠀⠱⠆⠒⠀⠂⠒⠀⠐⠂⠶⠃⠀⠀⠈⡤⠤⠄⠠⠤⠤⢬⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⢀
⠀⠀⢠⠤⠥⠔⠠⡀⢰⠠⠖⢄⡀⠀⠀⠀⠀⣀⣀⠉⠀⠀⠔⡄⠀⠀⠀⠀⠀⠀⠀⡄⢀⢄⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⣽⢛⣙⣫
⠀⠀⠘⠒⠒⠢⠐⠁⢠⠒⠦⠊⠁⠀⠀⠀⠀⣃⣸⣀⣖⣲⣀⡇⠀⠀⠀⠀⠀⠔⡆⡇⠀⣄⡀⢌⠘⠀⠀⠀⠀⡄⠀⠀⢤⠀⠀⠠⠠⠀⠠
⠀⠀⠀⠀⠢⠠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠤⠤⠤⠤⠎⠀⠀⠀⠀⠈⠁⠁⠘⠝⠛⠫⡞⢄⠀⠀⠀⣇⣋⣀⣸⠈⠁⢃⣉⣀⣀
⠀⠀⠀⠠⠄⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠤⠈⠤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠎⠁⠉⠱⠀⠀⠰⠉⠈⠱

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠾⠛⠋⠉⠁⣿⡇⠉⠉⠛⠻⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⣷⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⣿⡇⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⢻⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⡇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠈⠙⠻⢦⣄⡀⠀⠀⢀⡿⠁⠀⠀⣿⡇⠀⠀⠹⣆⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣾⠃⠀⠀⠀⣿⡇⠀⠀⠀⢻⣦⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⠀⠀⠀⣿⡇⠀⠀⢀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣿⣧⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣀⣀⣀⣀⡐⠂
⠀⠀⠀⠀⡠⣤⡤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣬⣈⠬⠄⠁⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠉⠉⠉⠉⠈⡇
⠀⠀⠀⠀⡇⣿⡇⠀⣠⣄⡋⠀⢂⠀⠀⠀⠀⠀⠀⠀⢰⣀⣂⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⢨⢐⢒⢒⢒⢒⢊⠠⠀⠀⠀⠀⢀⣈⣀⡠⠀⠀⠀⣠⠀⠀⠇
⠀⠀⠀⠀⡇⣿⣿⡈⠷⠊⠑⠄⠀⠣⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⠂⠐⠲⢰⡆⠀⠀⠀⠀⢸⠨⢎⡨⢌⡨⢌⠀⠀⠀⠀⠀⡆⠀⢾⣵⠔⣁⣈⡀⠇
⠀⠀⠀⠀⡇⣿⣿⡇⡄⢑⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⢸⢨⣣⢠⡣⢘⡣⢐⠀⠀⠀⢀⣥⣤⣤⣶⣾⣿⣿⣶⣧⣤⡀
⠀⠀⠀⠀⡇⣿⣿⠇⠃⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣐⠆⣂⠆⢆⡒⢸⡇⠀⠀⠀⠀⢸⠐⡱⠔⡁⠄⠡⠈⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠤⠒⡠⡃⠢⠔⢸⠇⠀⠀⠀⠀⠘⢴⢲⣶⠒⠒⡦⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠊⡒⠉⠒⠉⠑⡀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠭⠤⠂⠀⠀⠀⠀⠀⠀⢸⣭⣭⣭⣭⣭⣷
⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⢁⣀⣸⣀⡀
⠀⠀⠀⠀⠀⣾⣒⣛⠃⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠓⠠⣤⠄⠃
⠀⠀⠀⠀⢨⣝⠩⣫⢡⡢⢙⣥⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣄⣰⣖⣲⢰⡦⣑⡀⠀⠀⠀⠀⠀⠀⠠⡏⠉⠉⡹⠋⣹⡂
⠀⠀⠀⠀⠀⣆⣀⣀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠄⠀⢽⢹⣿⡆⠉⠀⣯⠀⠠⠀⠀⠀⠁⠀⢀⣠⡀⡠⢊⣼⡶⠀⠀⠀⠀⠀⠀⣇⠠⠊⡠⠊⢸⡁
⠀⠀⠀⠀⠀⠥⠤⠤⠤⠥⠤⠄⡠⣪⣾⠗⢄⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡹⢊⣴⣿⠋⠀⠀⠠⠀⠀⠀⠀⡇⡠⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡴⠀⡠⣪⣾⣿⠁⠀⡠⠃⠀⠀⠀⠀⢸⣿⠿⠇⠀⡇⠀⠀⠀⠀⠀⠖⠖⣪⣴⡿⣫⠇⠀⢀⠔⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠰⢀⣀⣀⣁⣀⣘⠿⡻⠁⡠⠊⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠐⠀⠛⢌⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠇⠀⢀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠃⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠉⠙⢿⣷⣤⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢹⠀⠀⠀⢺⣯⣽⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⡇⢸⠂⠀⠀⣛⣗⡒⢫⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⣷⢾⣇⠄⣀⡏⡧⠖⠠⣸⣿⣇⠈⠉⠙⠛⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⡿⢸⡄⠁⢸⡿⣧⡤⠤⣩⣿⣿⣤⣶⣶⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⡇⢸⡁⢆⣵⣷⣧⣤⣴⣿⣿⣿⣿⣯⣭⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⡇⢸⡅⠈⢻⠛⣟⣻⣿⢛⠛⢻⣿⣿⠛⠿⠿⠿⢿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣶⣶⣶⣶⣶⣶⣷⣾⣷⣾⣿⣿⡿⠛⠁⢸⡄⠈⣿⣿⣇⠀⠀⠀⠀⠀⠉⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣭⣭⣭⣍⣭⣽⣏⣹⣅⣀⠘⠀⣃⣤⣤⣶⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠉⠉⠛⠛⠛⠛⠛⠛⢻⡟⢿⢿⣯⣿⣿⣿⣿⣟⣋⡉⠁⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⣿⣿⠟⠉⠙⢿⣿⣿⣄⠀⠸⣿⣿⣷⡀
⠀⢀⣀⣀⣀⣤⣤⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⠟⠁⠀⠀⠀⠀⢿⣿⡿⣦⡀⢿⣿⣿⣧
⠀⠿⣿⣿⠟⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠁⠸⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣴⣿⣄⡈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠶⣶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⠆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⠀⠀⣿⠀⠈⢻⡀⠀⠀⠀⣤⠀⠀⠀⠉⠙⢧⡀⠀⠀⠀⣸⣏⣹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⣴⠟⠳⢦⣼⠇⠀⠀⠀⣿⠀⣤⣤⣤⠀⢨⡟⢳⡶⠛⠉⠈⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢾⣅⣀⣠⡴⠋⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⢀⣛⡛⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⣿⠀⡿⠀⣿⠀⣿⠀⣿⠀⣾⠛⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣤⣤⣤⡤⠠⣤⣤⣤⡄⠀⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡽⠋⠉⠉⠉⠉⠉⠉⢿⡍⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⠴⣶⠤⣄⣠⠞⠛⠛⠛⠨⠛⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡞⠁⠀⣿⠀⠞⢳⡀⠀⠀⠀⠈⠉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠛⠒⠒⢺⠇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⣄⡈⠳⣄⣠⠞⠀⠀⠀⣶⣶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠛⠚⠛⠛⠂⣦⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣽⡉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⡀
⢠⣾⢟⣩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡂⠀⠀⠀⠀⣀
⠿⠣⠯⡞⣣⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠛⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠑⠋⡶⠶⠶⠂⠀⠹⡆
⠀⠀⠀⠀⣿⠀⣀⣒⣶⣾⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣶⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣻⡜⣷⡄
⠀⠀⠀⠀⣿⠀⣿⣾⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠾⡚⢹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣗⣖⣖⣖⣇⢹⣿⣿⣿⣷
⠀⠀⠀⠀⣿⠀⠈⠉⠉⣽⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⡀⣿⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣷⣿⡆⢿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣏⣹⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢞⠕⢁⣴⣿⣿⠟⢁⢔⡵⡫⠚⣠⢞⡵⡫⠊⡠⣞⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⡴⣿⢿⠗⢁⠔⡵⢫⠎⢠⢾⡵⡫⠊⢠⢾⡿⡯⠀⠀⢴⡿⣿⣿⡿⣿⢿⡿⣿⢿⡿⣿⣿⣿⣿⣿⡿⣿⢿⠃
⠀⠀⢄⠠⡀⢠⡀⣄⠠⡀⢀⠀⣄⠠⡀⢄⠀⣄⢠⡀⢄
⠀⠀⢦⡑⢌⠢⡙⢮⡳⣌⠢⡑⢌⠳⣌⠢⡑⢌⠳⣝⠦
⠀⠈⠂⠙⠂⠑⠈⠂⠙⠊⠓⠈⠂⠑⠈⠓⠈⠂⠑⠈⠓
⠀⠀⢢⣶⣶⣶⣶⣶⣶⣶⣶⣲⣦⣶⣶⣶⣶⣶⣦⣶⡆⠀⠀⣠⢦⡐⢂⡴⣄⢒⡠⢦⡐⣢⠴⣔⢖⡴⢤⡲⣂
⠀⠀⠈⣽⡿⣿⣧⣿⣿⣿⣿⡟⢻⣿⢿⣿⡛⣿⣭⣿⣏⠀⠀⠰⡳⢌⡩⢞⢮⣉⠔⡳⣍⡵⢚⢮⣩⢞⠲⣍⡵⡃
⠀⠀⠀⠉⠉⠈⠉⠉⠈⠁⠈⠉⠉⠉⠈⠉⠈⠉⠁⠀⠉⠀⠀⠈⠉⠀⠀⠉⠁⠀⠈⠉⠀⠀⠉⠁⠁⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⢞⣵⣿⡿⣫⢞⡵⣫⢞⣵⢟⡽⣫⢞⡵⣫⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣵⢿⡿⣫⢞⡵⢫⠞⣵⢿⡵⣫⢞⡵⢫⡾⣿⢿⡄
⠀⠀⣤⣤⣄⣤⣠⣄⣤⣤⣀⣄⣤⣠⣤⣄⣤⣠⡄
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃
⠀⠀⠘⠿⠻⠿⠿⠿⠻⠿⠿⠿⠻⠟⠿⠻⠿⠿⠿⠿⠇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠿⠿⠭⠷⠧⠽⠧⠿⠾⠧⠿⠿⠾⠾⠿⠿⠮⠿
⠀⢀⡰⢢⣠⠄⠀⠀⢠⠶⠶⡄⢀⣀⡠⠀⠀⠀⠀⠀⠂⣐⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⣴⣶⣿⣦
⠀⠀⡅⣇⣆⡇⠀⠀⠻⣄⣠⣏⠘⠿⠳⣅⠀⠀⠀⠈⠸⠤⠇⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠘⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⢀⡐⠆⠐⠇⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢴⣷⠀⠀⠀⠀⠀⢠⣾⠿⣷⣄⠀⠀⠀⠀⠀⣠⡄⣿⡇
⠀⠈⢁⠻⠿⡀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠷⢠⣤⠾⠆⠀⠀⠀⢹⣧⣀⣼⡿⠀⠀⠀⣿⡇⣿⡇⣿⡇
⠀⠀⠙⠀⠀⠉⠀⠀⠀⠀⠃⠈⠃⠘⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢠⠤⠤⡄⠀⠀⠀⠀⢰⣶⢀⣀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⣠⣲⣂⠄
⠀⠀⢉⡏⢥⡄⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⣿⢸⣿⢸⣷⠀⠀⠀⠸⠿⣿⠿⠇⠀⠀⠀⠈⣹⣿⣿⣮
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠚⠛⠚⠛⠚⠛⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠚⠂⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠘⠛⠛⡷⠤⠀⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⠀⢠⣋⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠖⢂⡐⠶
⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠣⠤⠴⣅⠀⠀⠀⠀⠀⣐⣖⣯⡇⠀⠀⠀⠀⣆⡘⢃⣤
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡷⡧⠘⡆⠀⠀⠀⠀⢀⡄⠀⠠⠆⠀⠀⠀⠀⡔⢉⡙⢆⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⡐⢈⡐⠂
⠀⠀⣇⣄⣼⡃⠀⠀⠀⠘⠃⠁⠶⠀⠀⠀⠀⠀⠀⠣⣄⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠡⢈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠠⠔⣒⣊⣙⣒⡒⢤⡀⠠⠒⡊⠭⠭⠭⠭⣓⠢⡀
⠈⡐⠁⠀⠀⠀⠀⠉⢢⠹⡄⠈⠀⠀⠀⠀⠀⠈⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇
⠀⢀⡠⠤⠤⠀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠉⠐⠦⢄
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⡇⢀⡴⠒⠒⠒⠒⠒⠒⠦⣄⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⡇⠘⡅⠀⠤⠤⠤⠤⠤⠤⡭⠙⠦⡀⠈⠢⡀⠀⠀⠀⠀⠀⠐⠀⠙⢦
⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠢⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠒⡄⠀⠀⠀⠈⢢⡀⠐⢄⠀⠀⠀⠀⠀⠀⠢⡀⠁
⠘⠀⡇⠀⠀⠉⠉⠉⠉⠉⣭⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⠄⠀⠀⠀⠀⠀⠈⢂
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⡇⠀⣀⣀⣀⣀⣀⣀⣑⠆⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⢐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⡅⠀⠀⠀⠀⠀⠀⢀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠂⠀⠀⠐⠒⠒⠒⠒⣖⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠣⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠉⠲⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⠤⠈⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡍⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⢩⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠾⢿⡟⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣠⡶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⠛⠋⠁⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⣶⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣄⠀⠀⠀⠈⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠉⠁⠀⠀⠀⠉⠉⠉⠛⠒⠒⠻⣧⠀⠀⠀⢀⣴⠟⣀⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣄⢹⡄⠠⣦⣀⡀⠀⠀⢀⣀⠀⠀⠀⣠⣶⣏⣤⣴⡞⠋⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡉⠛⢿⣦⣄⣉⠙⠛⠛⠉⢉⣀⣠⣾⣯⠼⠿⠛⢉⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣟⡀⠈⠙⢻⡇⠀⣿⠟⠋⠁⠘⣧⣠⡴⠞⠋⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢶⡆⠈⠷⠴⠟⠀⢀⣤⡴⠿⠷⠶⠶⠶⠶⠶⣾⠷⠶⠶⠶⠶⠶⠶⢶⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡇⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⡄⠀⢀⣼⣧⣤⣤⣤⣤⣤⣤⣤⣼⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⣠⡼⢧⣄⣀⠀⠀⠀⢿⡀⠀⠀⢠⡟⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⡾⠉⠀⠀⠈⠉⠀⠀⠀⠀⠹⣦⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠙⢳⣶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⠟⣰⠏⠀⠀⠀⠚⠒⠒⠒⠒⠒⠚⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⡶⠶⠶⣯⣀⣤⠿⠋⣹⡟⠛⢻⡟⠉⠉⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠻⠶⢦⣤⠾⠋⣴⠞⠛⠻⣦⣴⠏⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠋⠀⠀⠀⢀⣼⠃⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠏⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⡔⠉⠉⠐⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠁⠢⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠁⠢⢀⣀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠃⠈⠓⠦⠴⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠉⠲⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠉⠲⠤⠖
⠀⠀⠀⠀⢠⢺⣀⣀⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⣀⣸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⣀⣸⣶
⠀⠀⠀⠀⢸⠃⠉⢉⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⡡⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⡁⢼
⠀⣀⠤⠔⠚⢄⣀⣀⡼⠓⠢⢤⡀⠀⠀⠀⢀⣠⠤⠒⠣⣀⣀⣠⠟⠒⠤⣄⠀⠀⠀⠀⢀⣠⠤⠒⠣⣀⣀⣠⠟⠒⠤⣄
⡮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⢰⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⢰⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡇
⡇⠈⠙⠒⠲⠶⠤⠴⠖⠒⠋⡱⣿⠀⠀⢸⠀⠉⠓⠒⠶⠦⠤⠶⠒⠚⢉⢼⡇⠀⠀⢸⠀⠉⠓⠒⠶⠤⠤⠶⠒⠚⢉⢼⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠱⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢼⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢼⠁
⢡⠀⠀⠀⠀⠀⠀⢀⠔⢁⠀⢸⡇⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⣠⠎⠠⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠞⠠⠀⣾
⢸⠀⠀⠀⠀⢀⠔⠁⠐⠁⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⡏⠀⠀⠀⠀⣧⠶⠂⠀⠀⡠⠞⠁⠛⠷⣦⡟
⢸⡀⣀⠤⠒⡁⠐⡠⠀⠀⠀⣸⠀⠀⠀⠀⣇⢀⡠⠔⠊⠠⠀⠄⠀⠀⠀⡇⠀⠀⠀⠀⣧⠤⠤⢴⣊⠠⢂⡤⠦⠤⣈⡇
⢸⡅⠀⢐⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⢤⠲⡀⠵⣸⡇⠀⠀⠀⣼⠁⢀⣤⡄⠘⣶⠏⢠⣤⠄⠈⢣
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢹⠀⠀⢰⡀⠀⡈⠂⠁⠀⣼⠀⠀⠀⠀⢿⠀⠸⣿⡶⢂⣿⡄⠻⣷⡾⠀⡼
⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⡇⠀⠀⠀⠀⢸⠀⠀⠁⢱⠠⠈⠀⡠⠊⢸⠀⠀⠀⠀⠈⢳⠦⠤⠴⠋⠀⠙⠶⣤⠴⢾⠁
⠀⡇⠀⠀⠀⠀⡠⠔⠁⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠂⠁⢀⠀⠊⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠠⠊⡤⠄⢸
⠀⡷⠀⠐⠈⠁⠀⠀⢸⣿⡀⡇⠀⠀⠀⠀⢸⠆⠐⠒⠉⠀⠀⠀⣻⣇⢸⠀⠀⠀⠀⠀⢸⠆⠐⠒⠉⠀⠀⢀⡇⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠸⠿⠃⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠿⠟⢸⠀⠀⠀⠀⠀⢸⠄⠀⡀⢀⣀⡴⠋⠀⡄⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨⡁⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣍⢸⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠤⠖⠀⠀⠷⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠄⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢐⢸⡇
⣸⠁⠐⠒⠒⠒⠒⠒⠒⠒⠀⠘⡆⠀⠀⢀⡏⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⢳⠀⠀⠀⢀⡞⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⢳
⠙⣦⣤⣤⣤⣤⠶⠶⢶⣶⠶⠞⠁⠀⠀⠈⢳⣤⣤⣤⣤⡶⠶⢶⣶⣶⠶⠊⠀⠀⠀⠀⢳⣤⣤⣤⣤⡶⠶⠶⢶⣶⠶⢚⡀
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢣⡀⠀⠀⠀⠀⠀⡼⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠒⠒⠒⠒⠊⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠁⠀⠀⠤⠢⠄⠀⠀⠀⠤⠤⠀⠀⣸⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠑⠂⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢊⣀⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡏⠉⠀⠀⢢⡀⠀⣠⠣⡀⠀⡠⠃⣀⡀⡧⠤⠤⠤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⡇⠀⢒⠋⠉⠀⠀⠀⠉⠉⠁⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⡠⠊⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢀⡴⠊⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠀⠀⠀⠀⠈⡋⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠮⢩⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡁⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠊⠓⠤⠒⠲⠔⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠢⡤⠞⠉⠒⠂⠀⠀⠀⠀⡠⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠁⠈⠉⠁
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⢩⡈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠇⠀⠒⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⢄⠈⠀⣀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡄⠀⠀⡴⠀⠀⠰⠂⠀⠘⣧
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠶⠀⠀⠈⠁⠀⠈⠁⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣼⠁⠆⠀⠀⠀⠀⠀⣄⠀⠀⢠⡄⠀⠐⠂⠈⠙⠲⣄⣠⠞⠁⡴⠀⠀⠚⠁⠀⠐⠋⠀⠀⠘⠁⠀⠚⢀⡇
⠀⠀⠀⠀⠀⣿⠀⠠⡄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠲⢄⡀⠙⠲⣄⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⣠⠄⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⢤⠄⠀⢠⡄⠀⠐⠆⠀⡴⠁⢀⠈⢀⡬⠲⢄⠀⠙⢦⡄⠉⠀⠀⠀⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣀⠈⠳⢄⠀⢠⡄⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠛⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠱⢄⠀⠑⢤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⣈⠑⠦⣀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠂⠕⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠸⡓⢦⣀⠑⢤⡀⢀⡄⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⠃⠈⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠛⠀⠀⠈⠢⣌⠻⢦⣈⠲⢄⠀⠀⡀⠀⣠⠃⠀⣀⠀⠀⠠⣄⠀⠰⡄⠉⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣀⠀⠀⢠⠄⠀⠀⣀⠈⠳⣄⠉⠳⣄⡑⠤⣀⡰⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡈⠙⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠓⠔⢁⡽⣦⡀⠀⢀⡀⠀⢀⡀⠀⠀⠲⠆⠀⠐⠂⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠚⠀⠰⠆⠀⠀⠶⠀⠀⠠⠆⠀⠀⠖⠀⣰⠟⠁⠀⠙⢦⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢷⡐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⢦⡀⠐⠶⠀⠀⠛⠀⠀⠈⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡐⠁⠋⠀⠀⠚⠁⠀⠈⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠦⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠛⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠛⠁



⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⢈⠠⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠈⠁⡐⠀⠄⠀⢀⠀⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⣀⣀⡈⠀⢠⠂⠀⡀⠈⠤⠀⠀⠀⠎⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠲⠀⢸⡆⠚⠒⠓⠂⠀⠈⠀⠂⠘⡀⡀⠂⠀⠠⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠸⠆⠭⠭⠅⠀⠀⠐⠀⠁⠈⠂⡀⠁⠈⠀⠆⠀⠢⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠊⠀⠀⠴⠄⠠⠤
⠀⠀⠀⠀⠀⠀⡄⠀⠨⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡍⠉⠉⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⡇⢈⣉⠀⢘⡁⣉⡁⠀⠐⠀⣀⢠⣄⠁⠀⠀⠀⠀⠣⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠂⡃⠀⠀⠰⠀⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢈⠑⠀⠀⠀⠀⠀⠀⠀⢠⠍⠈⢅⠀⠀⠀⠀⠀⠀⠄⢄⣀⠂⡀⠀⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠌⠀⠠⠀⠆⠰⠀⠀⠰⠀⠀⠦⠆⠆⠆⠀⠠⠀⠐⠀⠈⠂⠠⠊⠊⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⡆⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠆⠐⠀⠀⡀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠄⠀⠉⠈⢀⣄⠀⣀⠀⢀⡀⠀⣀⡀⠠⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠈⠙⠦⣄⠀⠀⢀⣠⠖⠋⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡇⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠃⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠙⢲⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠷⣏
⠀⠀⠀⠀⠀⢀⡴⠋⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠙⢦⣀
⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠈⠒⢄⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠺⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠉⠳⢤⡀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠈⠓⢦⡀⠀⢀⡴⠋⠀⠀⢸⠀⠀⠀⠙⠲⣄⡴⠋⠁⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⢸⡇⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠋⠉⡍⠂⣠⢆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠖⠛⠒⠶⢤⡀⠀⢀⣼⣶⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠒⠦⠤⣀⣀⠀⠀⠀⠉⣻⣿⣿⣿⠇⢤
⠀⠀⠀⠀⠀⠀⠀⢀⠦⡄⠁⠀⠀⠐⠄⣤⠠⠍⣟⣷⠠⢠⣿⡿⠏⣸⣾⣿⡆
⠀⠀⠀⠀⣾⠤⣚⣡⠀⡐⠀⠀⣀⣀⢀⣠⣴⣿⣿⣿⢀⣿⠟⠒⠺⣿⡿⡗⠁
⠀⠀⠀⠀⡇⠙⠶⢬⣝⢶⣵⣡⢞⣥⣮⣿⣿⣿⣿⠟⢋⡁⢀⣠⠢⣿⡾⢄⠓⠦⠠⢀⡀
⠀⠀⠀⠀⠑⠂⠠⢒⡪⠅⣉⠛⡛⣿⣿⣿⡟⠁⠡⠄⢒⣿⡟⡗⣹⠟⠚⠉⠆⢦⣈⣵⣿⡀
⠀⠀⠀⠀⠀⠀⡠⢴⠏⠙⠂⠭⠴⠟⠋⠐⠀⠀⢀⣤⣿⣿⣏⡼⠁⡠⠀⠀⠀⠈⠌⠙⡟⠃⠄⣀
⠀⠀⠀⠀⢰⡇⠀⠀⡈⠂⠠⠵⢄⣀⠀⢂⠔⣠⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠡⠀⠀⣄⣀⠥⡺⣇
⠀⠀⠀⠀⠈⣧⣀⠤⠐⠀⡀⠀⣀⡤⠄⣬⣀⣿⣿⣿⣧⣄⠠⣤⢀⡀⠀⠀⠀⣀⢂⣑⣥⣶⣿⢾⠃
⠀⠀⠀⠀⠀⢹⡆⡲⡺⠥⠤⠤⠴⠶⠾⠴⠮⠽⣟⢅⠀⠙⢳⣢⡭⣬⡵⣶⣿⣿⡿⠟⢛⠩⣐⠼
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠑⠠⢤⡀⠠⢀⣀⣈⣤⣼⣿⣄⡀⠀⠀⢰⣿⡿⣛⣭⣕⠲⠒⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⡗⠮⢭⣴⣿⣿⣿⠿⠋⠁⠐⠀⠼⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠈⠂⢸⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣁⢀⣀⣀⣀⣀⣠⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣉⣙⣛⣉⣉⠉⠭⠥⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣥⣤⣤⣶⡦⢤⠭⠵⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣀⣀⡠⠤⠤⡄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⢠⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⢰⠀⠀⠀⠀⣹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡈⡀⠀⠀⠀⢿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠁⢀⣀⠀⠸⠇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣇⠀⠘⠒⠒⠲⠖⠚⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠿⠿⠭⣭⡭⠽⠟⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢸⣦⣤⣤⣤⣤⣶⡶⢶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⡀⠂⠁⠈⠀⠀⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣠⡤⠄⢀⣀⣲⡟⠀⠀⠀⠀⡇⡁⠀⢸⠀⠄⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠳⢶⣶⣼⣦⡶⠷⠾⠿⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⡀⡄⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⡀⠁⡈⢥⠀⢈⡄⢀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡘⠀⢁⢀⠇⠀⠤⢈⠄⡠
⠀⠀⠀⠀⠰⡀⠄⡂⠀⠈⠋⠀⠀⠀⢀⢄⡄⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠂⠀⠠⠀⠸⠀⠀⠀⠀⠒⣃⠜⢁⡂⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈
⠀⠀⠞⠃⠑⠀⠀⠀⠘⠠⢀⠐⠀⣀⢀⠤⠁⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠄⠐⠉⠀⠀⠀⠀⢀⢀⠤⠂
⠀⠀⠀⠄⠀⢸⣿⠀⠂⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢠⡠⠁⠀⠂⠀⠀⠉⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠠⡏⠀⠀⠉⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠈⠀⡉⠀⠽⠦⠀⣀⣤⠹⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⡄⠤⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠀⣄⠤⠃
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠂⠐⠒⠀⠈⠁
⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⡶⣶⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡏⡠⡦⣶⠈⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣿⠈⠙⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡙⠗⠟⣠⣿⣿⣿⢟⡵⠚⠉⠛⠒⢭⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣿⣿⣿⣿⢇⡏⢀⣀⣀⣀⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢰⣦⣶⠖⣶⣰⡖⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢐⣿⣹⣉⣹⣹⣿⣉⣉⡘⡇⠘⠛⠛⠛⠛⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠀⠿⠿⠀⠻⠿⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠙⢦⣀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠲⠾⠶⠷⠷⠾⠶⠇⠀⠤⠤⠤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⣿⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣟⠋⠀⣘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⡿⠿⢿⠿⠿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡔⠓⠚⠓⠒⠛⠛⠛⠒⠛⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⡧⠤⢼⠤⠤⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⡧⠤⢼⡤⠤⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⡧⠤⢼⡤⠤⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣧⣤⣼⣤⣤⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠉⠈⢦⡀⠀⠀⠀⢠⠎⠉⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⡟⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠚⠉⠀⠀⠀⡇⠀⠀⠈⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⣀⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⡇⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣇⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⢠⠞⡟⢦⡀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⢀⡴⠁⠀⡇⠀⠑⣄⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣄⡀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⣠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠖⢉⡤⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⡇⠀⠐⠊⢁⡠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⣇⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉