Fishery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠨⠂⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⣀⣼⣿⢱⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠛⡿⠃⠈⣏⣾⣿⡷⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⠄⠻⠏⡙⠛⢶⣤⡉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠌⠢⢄⠀⢀⠒⠀⡀⣌⢿⣿⣷⣄⠙⢿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣧⠈⢆⠈⠉⣚⠁⠀⠰⠙⣼⡿⣿⣿⣷⣄⠻⣿⣷⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⠄⣑⢢⣤⠤⢚⠑⡿⠟⣶⣿⠟⣿⣿⣧⡙⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡀⠀⠡⠀⠖⣫⣷⣆⢺⡅⣶⢿⢋⣿⣿⣷⡹⣿⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢷⠀⠀⠠⢛⣵⣿⣿⣏⢐⠃⢔⡻⣉⡽⣿⣧⢻⣟⣽⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣳⠀⠀⢘⠿⣿⣿⣿⢈⠏⠠⣴⠟⢾⠾⣿⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢻⣿⣿⣦⠀⠀⠀⠆⠠⠄⣉⢼⠱⡟⡶⢫⣶⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⣿⣿⣷⡀⠀⠃⠠⠀⠉⠤⠰⢟⠱⠞⢉⡯⣿⣿⡿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣿⣿⣦⡀⠀⠐⠀⠁⠂⢐⠘⢧⢍⣿⣾⢿⣿⡻⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⡈⣁⢰⡿⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡤⠀⣉⠄⣤⣘⣬⣹⣿⣗⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⡄⠀⠑⠴⢆⣬⣶⣟⢝⣺⢯⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠿⡟⣌⢮⣻⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠘⣽⣜⣧⣻⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣻⣿⣿⣯⣽⣵⣦⣀⣀
⠀⠀⠀⠀⠀⠀⡞⠁⠂⠄⠀⠀⠀⠀⣀⡀⠀⠀⣐⡐⠈⠙⠟⣉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠈⢉⣁⡖⠐⢒⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣧⢴⢶⠿⢶⠤⢼⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠐⠂⢤⣀⠀⠀⠀⠀⠑⢿⣋⣿⣯⣍⠳⠿⢃⣃⣀
⠀⠀⠀⠀⠀⠀⠘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢀⠀⢠⠀⠘⢇⠀⠀⠛⢋⡄
⠀⠀⠀⠀⢀⣶⣌⣻⣮⠀⠄⠒⠒⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢄⡀⠀⠆⢒⠶⠋⠠⠶⠋
⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⢀⡤⠾⠴⠦⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⣷⠆⠈⠕⠠⣁
⠀⠀⠀⠀⠀⠀⠀⠒⢀⣠⠴⢏⢀⣲⡀⠀⠀⠀⠈⣱⠶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⡜⢰⠿⠟⠊⠀⣰⣂⢈⡿⢤⣀⠐⠂
⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⣘⣰⠼⠟⠂⠀⠀⢤⣌⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠁⡙⣡⠔⠀⠀⠒⠽⠤⣺⡄⠀⠈⠲⢄
⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙⠀⠰⠶⠂⠀⠠⠀⠀⠰⠶⠈⠘⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⢟⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⢀⡀⢢⣼⢱⣴⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠶⢾⡿⠿⠟⠛⠊⠻⣺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⠉⠉⣽⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣻⣿⣿⣿⣿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣇⣼⣿⣿⣟⣁⣀
⣿⣯⣭⣭⣭⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣶⣿⣋⣿⡶⢶⣶⠐⣲⣦⣶⠀⢀⣶⣾⣿⣗⠀⠒⠆⠤⣶⢆⢺⡟⢿⢸⣴⣶⣿⠾⢻⡏⣷⡷⣶⢀⣄⠀⢀⣤⡄⣀⡀⡀⠀⠀⠐⠆⢩⣀⣦
⠀⠀⠀⠀⠹⠿⠿⠿⠟⠿⠷⠾⠳⠿⠷⠚⠋⠯⢼⣯⣭⣴⣿⠿⣤⣞⠉⢼⡧⢸⡟⢻⡅⣿⢾⣿⣏⣹⡇⢿⠌⡭⠡⢺⠗⣞⢨⣿⢿⡯⣾⡤⣠⣸⡟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⠉⠃⠈⠻⣶⣤⣁⡐⠶⠾⣽⣩⢿⣻⢿⢿⣧⢾⣿⡆⠈⠠⢒⣲⣌⣽⣾⠃⠼⠀⡸⡞⣜⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⠏⠉⣠⣴⣾⣲⣿⣿⣿⣧⣀⡀⠳⠴⠾⠬⠤⠸⠟⠛⠚⠇⠠⠤⠌⠑⣾⣿⠿⠀⢠⣾⣏⡗⢻⡷⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣤⢞⣥⠈⢈⣿⡇⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⣻⣿⣿⣿⣿⡿⠿⣿⣿⣿⣯⣝⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣌⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣟⣻⣛⣿⠻⢿⣠⡛⢻⡊⡱⠟⠾⠿⣟⠻⠥⣾⠛⣿⣿⡿⢿⠻⢿⣿⣳⢄⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⢡⠅
⠀⠀⠀⠀⢀⣠⣖⣸⣯⣿⣿⣿⣿⣿⣿⣿⡿⠷⠁⠘⠟⠃⠀⠈⠁⠀⠀⠀⠀⠈⡿⡜⠀⠈⣸⣿⡟⠲⠮⡈⣚⠿⢷⣿⣦⡀⠀⠀⠀⠀⢀⡤⢀⣼⣿⠋⠁
⠀⠀⠀⢾⠒⣦⣽⢋⣽⣿⣿⡟⢹⣿⣽⣿⡇⠊⠀⠀⠀⢠⣄⡀⠐⠀⠀⠀⠀⢰⡓⡀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠚⠶⠈⠛⣦⡀⠀⠀⠀⠉⠒⠿⠆⠹⠄⠄
⠀⢀⣬⣈⣧⡹⣇⣿⣿⣿⣿⡅⣿⣿⡿⠉⠀⠀⠀⠀⠀⡈⢿⣿⣄⠙⣷⣤⣀⣿⣧⠳⢄⡃⠀⠀⠀⡀⣠⠒⠀⣀⣀⡤⠴⠂⣬⣳⡄
⠀⢸⣇⠹⣿⣷⣿⣿⣿⣿⣿⡏⣿⣿⡇⠀⠀⠀⠶⠻⠋⠘⠒⠙⠿⣆⡘⣿⣿⣗⠙⢷⡀⠀⠳⣤⣐⡁⠛⠀⠘⠻⡏⢀⣴⠟⠉⠉
⠀⠐⣿⣦⡙⠿⣿⣻⣿⣿⣿⣿⣼⣿⡇⠀⣀⣀⣀⣰⣷⣶⣦⣤⣤⣤⣄⣀⡀⠈⠁⠈⠹⣦⣥⡀⠀⠀⠐⠦⣄⠐⠄⠛⠧⣶⣄⡀⡀⠀⠀⠀⠀⢰⣥⡶⡧
⠀⠀⢘⣿⣿⠀⢹⣷⣿⣿⣿⣿⣿⡿⢿⡿⠙⣹⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣻⡿⣿⣿⣿⠶⢿⣿⣿⣿⠛⠷⢶⣶⣦⣾⢛⡟⠀⠀⠀⠀⠻⣿⡷
⠀⠀⣸⣿⣿⡀⠘⠛⢿⣧⠙⢿⣿⡿⣾⣷⣁⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⡿⢿⣿⣿⣿⡗⣛⣭⣵⣶⣾⣿⢛⡿⠷⢄⡀⠨⢤⡽⠋
⠀⠈⢉⣼⣿⣧⢀⣀⡄⠙⢷⣌⠋⠟⠺⣿⣿⣿⣿⠅⣿⡾⣿⡿⠷⠾⢋⣴⣿⣿⣿⣿⣿⣽⠿⠋⠁⣹⣿⣿⠀⠀⠀⠀⠠⠄
⠀⠀⠈⣿⢿⣿⣦⡈⠙⠆⠻⢿⣶⡀⠀⠘⠙⠻⣿⡆⢩⣿⣿⢳⣶⡾⢋⣿⣿⣿⠋⣩⣤⣤⣴⠖⠚⢻⠟⠁
⠀⠀⠀⠉⢾⣿⣿⣿⣦⡘⢶⡆⠈⠻⠶⣤⠀⠀⢹⠇⢸⣿⣿⠟⠁⢀⣏⣽⣿⣣⠾⠛⣹⣿⠏⠀⠐
⠀⠀⠀⠀⠉⠻⠍⠩⣭⣹⣷⡕⡄⠀⠐⠈⠷⣴⣿⠧⣽⡟⠋⠀⠴⠾⠿⠷⠛⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠈⠁⠘⢄⠻⣟⠻⠿⢿⡇⢿⡇⠀⠠⣾⣿⠿⠶⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠈⣷⣬⡛⠋⠁⠑⢾⣇⠀⠀⠀⢀⡠⠄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠃
⣀⣤⢶⣾⣿⠿⠿⣻⠟⣡⡏⠀⠀⠀⠀⣀⠉⠉⠀⢉⠈⠀⢀⠀⡁⠀⠈⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣶⣿⣿⡽⠃
⠙⢿⡀⠋⠤⠤⠊⠉⠺⡿⠯⠐⠒⠒⠀⠀⠉⠈⠀⠀⠐⠀⠂⠈⠂⠀⠀⠀⠀⠈⠉⠀⠒⠢⠂⣒⠶⢾⣿⣇
⠀⠀⠙⠲⠴⣂⡐⠻⣖⡀⠁⠀⠀⠠⠄⠀⠈⢈⡀⠉⠁⠡⠤⠀⠄⠀⠉⠉⠀⠁⢀⣠⢴⡾⠛⠉⠙⠻⣿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⣾⣾⣷⡶⠶⠶⠤⠤⠴⣶⣶⡶⠒⠒⠒⠒⠒⠶⣟⢍⣥⣶⠟⠀⠀⠀⠀⠀⠈⠳⣭⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷

⠀⠀⠀⠀⠀⠀⠠⠂⠀⠉⠉⠁⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠦⣤⣁⣀⣀⣀⣀⣀⣀⣀⣀⡭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡙⠢⢈⣻⡄⡀⢠⢞⣽⣛⠲⣤⣄⣤⢤⡤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⣸⣿⣿⣧⠈⣿⣿⣻⣿⣿⣦⡴⣬⣍⣑⠲⢶⣭⢔⡒⠰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡟⢿⣿⣿⡇⢳⡈⢻⣦⡈⣌⢿⡎⣿⣿⣷⣦⡉⠻⣿⣅⣀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢁⡼⣹⣿⣿⡈⡑⢄⡅⢸⠚⢸⢾⢸⣇⢻⡿⣿⣾⣾⡙⣧⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡕⠚⠿⠴⠷⠶⠿⠷⣴⣾⣷⣀⢘⡸⠬⠘⣟⣬⡅⠾⠿⢿⣿⣮⣻⣞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣩⠉⣉⠉⠓⠊⠉⢛⡛⠋⠀⢀⣴⣿⣿⠏⠀⠀⡠⣿⣿⣷⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣍⠢⢔⣌⡒⢌⣉⠵⠃⠘⢿⣁⣀⣠⠾⠇⠟⢹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠦⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠿⢃⣿⣿⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣵⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢦⣤⣤⠀⣀⠀⠀⠀⠀⠀⠁⠋⠺⢡⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⡄⠳⣜⢿⣷⡲⢤⣀⠀⠀⠃⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢶⣤⡀⢸⢁⣿⣦⣌⠳⣬⣇⢈⣿⣷⡀⠐⢺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠋⢻⣿⣾⣿⣿⣿⣾⣿⣦⣽⣷⢿⠟⣿⡀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠐⢦⡉⢿⣿⡽⢿⣿⡏⠛⠙⠂⢨⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⣬⣆⠀⠀⣶⣿⣿⣿⡏⠚⢻⢿⣦⡤⠔⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣼⣿⠰⣶⣿⣿⣿⣿⠇⣴⡿⣿⢟⣀⣀⣧⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣼⣿⣿⣿⠏⣶⣿⢿⣿⢏⣟⣀⠥⣺⠿⣿⣿⣿⠿⣿⣿⠋⠑⢆
⠀⠀⠀⠰⣶⣶⣶⣶⣶⣾⣿⣿⣾⣿⣿⣶⣶⣶⣶⡤⠀⠀⠀⢀⣤⣤⣿⣿⣿⠋⣰⣿⢋⣾⢏⡞⠉⠀⣺⣵⢿⣿⣿⠿⠛⠎⠛⣷⡄
⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠆⣴⡿⢟⣯⣿⣿⠁⠘⠋⣴⡿⠁⠈⠀⢀⣴⢋⣾⠿⠋⠁⠀⠀⠀⠐⢃⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⣵⣿⡿⠛⠛⠛⠁⠸⠋⠀⠀⠀⠀⠋⠁⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣯⣿⣿⡇⢸⣶⣿⠞⣩⣿⡇⠀⠘⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢿⣷⣄⣽⣻⣶⠟⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠋⣩⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠁⢈⣉⠭⠤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡉⣀⠴⠊⠁⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢋⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⢀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣺⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡘⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣄⣵⣺⣷⣦⣤⣄⡀⠀⠀⢀⣠⠶⠋⣠⠞⠁
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣾⣁⣠⣤⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⢀⣠⣴⣶⢿⡿⠿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣾⢿⡿⣽⠟⣽⢟⣽⢟⣿⢿⡟⣿⠿⣿⣿⣿⣥⣤⣠⡄⣀⠀⠀⠀⠀⣠⠟
⠛⢋⣫⣿⣯⠇⠈⠉⢻⣦⣤⣴⣶⣶⣾⣶⣶⡶⠷⢯⣴⣧⣬⠁⠈⠁⠉⠸⠛⠀⠛⠁⠿⠯⠿⠿⠿⠿⠿⢷⣶⣶⣿⣿⣿
⡄⢤⡙⠛⠃⠀⠀⠂⢈⣿⢻⠉⠁⠁⢀⣀⣨⡤⠤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⣶⠻⠛⠛⢿⣿⣯⣿
⠿⣯⣅⣀⢀⠀⣰⣿⣼⣯⣿⣷⣶⣯⣤⣤⣄⠤⠤⣾⣂⡀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠻⣎⠉
⠀⠀⠈⠉⠛⠻⢾⣿⣿⣽⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠻⢿⡟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠙⢯⣍⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⣦⣀⠀⠀⠀⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⢀⣠⣴⡻⠿⠿⠛⠋⠉⢉⣉⣉⣍⣭⣭⣭⡉⠉⠛⠛⠛⠿⠿⠶⣤⣤⣄⠀⠀⠀⠀⣠⠏⡾⠁
⠀⠀⠀⢫⡀⠺⠟⠀⠀⠀⠀⠀⠈⠉⢩⣽⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢒⣒⣃⠄⡇
⠀⠀⠈⠣⣉⣀⣀⠀⡰⠀⡄⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠋⠉⠈⢇⡀⡇
⠀⠀⠀⠀⠀⠉⠒⠲⠴⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣻⣿⠛⠛⠛⠛⠋⠉⠉⠉⠺⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡡⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠵⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠉⠉⠉⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⣤⡶⢿⣿⣿⣿⣿⣿⣶⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡠⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣠⣴⣾⡟⠁⠀⠈⣉⡁⠉⠉⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠴⠊⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠁⠀⠀⠀⠰⠀⠀⠌⢃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠃⠀⠀⠀⠀⠀⢀⣐⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠕⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠂⠀⠀⠀⢒⠲⠤⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⡠⣄⣀⠀⢀⣒⣡⠔⠁⠀⠀⠀⠀⠀⠀⡀⠉⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠒⠒⣬⣇⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣠⢴⡅⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⠒⠚⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠁⢠⡀⠀⠀⠀⠀⠈⠉⠉⠉⡝⠀⠀⣤⣳⣾⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⣄⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢔⠻⠶⣶⣤⣤⣤⣤⣤⡴⣫⣿⠶⡟⢁⣈⠥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡇⠀⠀⠉⣩⢋⣽⢭⡭⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢔⣒⠒⢤⠀⠀⢀⡤⡇⠀⠀⢾⡕⠀⠧⠴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠁⠈⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⢳⡦⣤⣤⣄⣀⣀⣼⣀⡤⡇⠀⠀⠀⠀⠀⠀⠤⣄⣀⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠒⠒⠋⠀⠀⠀⠀⢀⠊⠀⢀⠀⠀⠀⠈⠁⢧⠀⢸⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠒
⠀⠀⠀⡀⠀⡀⠀⠀⠀⢠⣏⣀⡠⠃⠀⠀⡄⠀⠀⠘⣆⣨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠁⠀⠀⠉⢀⣶⣿⡆⠀⠢
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⠀⠀⠀⠀⠐⠈⠉⠙⠓⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⡿⠋⣉⡅⠀⠈⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡿⠣⠾⠋⠁⠀⠈⠁⣉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣠⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣷⡀⠀⠀⣲⣿⣧⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⢳⣄⣀⠀⠀⠉⠉⠙⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⢻⡿⠃⠀⠀⢠⣶⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠶⣄⡀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠷⢶⣤⣤⣤⣤⣤⣤⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⣛⣉⣩⣤⣦⣤⡴⠚⣭⣢⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣄⡀⢸⣿⣿⢫⣴⣿⣿⣿⣿⣿⣿⡿⢡⡜⡎⣿⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣽⢡⣿⡿⣿⣿⢿⣿⣿⠛⠁⠟⠹⡿⡇⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡜⢿⡗⢿⣿⣬⡭⣙⡿⣷⣦⣤⣀⣸⡦⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣷⣝⠶⣶⣶⣶⠾⣿⣿⣶⣭⣿⡟⠉⠁⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠉⠉⠓⠒⠒⣠⡞⠓⠋⠻⠋⠀⠀⠠⢤⣤⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣾⠏⠀⣦⠀⠀⠀⠀⠀⠀⠈⢫⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢠⣿⡟⠀⠀⣿⣆⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠛⠋⠁⠀⠀⠟⣿⠀⠀⠀⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⡀⢀⣀⣀⡀⣀⡀⣀⡀⢀⣀⢀⣀⠀⣀⡀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣉⠋⢹⡏⢿⣯⣝⡃⣿⣧⣽⡏⢹⡏⢸⣿⣦⣿⢱⣿⠋⣻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠆⠀⠾⠧⠿⠶⠿⠃⠿⠇⠾⠧⠼⠷⠼⠧⠹⠿⠈⠻⠶⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⠀⡀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣯⣿⣷⡿⢛⣿⣦⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⣩⣶⣿⣿⡿⠋⠁⠋⠀⢀⠟⠻⠿⠛⠃⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣡⣿⣿⡿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⠛⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠏⣼⣿⡟⢿⡇⠀⠀⢰⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⣿⣇⣀⣼⣵⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⠗⢻⣿⣿⣿⣼⣿⠻⠧⠀⠀⠀⢀⣼⣆⠀⠀⠘⠦⠤⠤⣄⣙⣛⣁⣤⡤⠶⣶⡶⢾⣻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡍⠀⠀⢾⣿⣿⣧⣿⠿⠄⠀⣀⣤⣶⣿⡿⠈⠓⠦⣤⣀⣀⡤⠞⣋⣉⡥⠤⠶⢚⡉⠀⠀⢉⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⣤⠛⢿⣿⣿⣦⡀⠺⣿⣿⣿⣿⠇⠀⠀⠀⢀⣩⠿⠦⠼⠋⠀⢠⡄⠀⣼⣷⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡆⢠⣿⡆⠈⣿⣿⣧⡄⠀⠀⠀⠀⢀⡀⠀⣠⡄⡘⢁⣶⠀⢠⣿⡀⣾⣷⢐⣿⣿⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡼⣿⠇⣀⣿⣿⣿⣶⣤⣤⣤⣶⣿⣶⣾⣿⣿⣷⣾⣿⣧⣾⣿⣧⣿⣟⣈⠻⡟⠃⣾⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⡿⠿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠠⣿⣿⡟⢻⡿⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠻⠿⢿⣿⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⡶⠶⠶⠿⢿⡶⢶⣶⠶⢶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⣠⡾⢻⣧⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⢯⡀⠀⠈⢻⣿⣷⣀⠀⣀⣼⣿⣿⣿⣿⣷⣦⡀⠀⣽⣻⣿⣿⣿⣿⣿⣷⣶⣤⣤⣰⡿⢿⣦⡀
⠀⠀⠀⠀⢀⣾⠟⠀⠀⠛⠉⠉⠉⢀⣠⣤⣼⡿⠿⠿⣯⣳⡄⠀⠀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⣽⡿⠿⠿⣧⣤⣄⣀⠈⠉⠉⠛⠁⠀⠙⣷⡄
⠀⠀⠀⠀⣾⠏⠀⠀⢀⣠⣤⡶⠿⠛⠋⠁⠀⠀⠀⠀⢹⣿⣟⣿⠀⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠀⣾⢟⣿⡏⠀⠀⠀⠀⠈⠉⠛⠻⢶⣦⣄⡀⠀⠀⠘⣿⡀
⠀⠀⠀⣸⣟⣠⣴⠾⠛⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠿⢿⣮⣳⣹⣿⣿⣿⣿⠃⠀⠀⠀⢀⡼⣿⡿⠿⣇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠛⠿⣶⣄⣹⣧
⠀⠀⠀⡿⠟⠋⠀⠀⠀⠀⠀⣠⡮⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠙⢿⣟⢿⡿⠟⠁⠀⠀⢀⣴⣫⡾⠋⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢡⣄⠀⠀⠀⠀⠀⠉⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣝⢦⡀⢀⡴⣫⣾⠟⠁⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠈⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣠⣾⠟⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣿⡾⠋⠁⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⣷⣄⡀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡇⠀⣰⠾⠁⢀⡴⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠲⡄⠈⠳⣆⡀⠘⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣏⣁⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣈⣙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠆⠀⡇
⠀⠀⠀⠀⠀⠰⣼⠇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣄⣀
⠀⠀⠀⢸⠂⠀⢿⠀⠀⡠⠆⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠠⡇⠀⠀⢾⠀⢰⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⡁⠀⠀⢸⠀⠀⠁⢼⣿⣿⣿⣿⡿⢿⠛⠿⠙⠛⢋⠙⠛⠛⣛⡿⢿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⠃⡁⠀⠀⠀⠀⢴⠿⠶⠴⠟⠉⠈⢠⠊⣴⣿
⣀⣠⣤⣐⢠⣤⣿⣸⣠⣤⣼⣿⣿⣿⣿⣿⣀⠀⡀⣀⠀⠀⠀⠀⠒⠀⣀⣿⣶⣷⣿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⣿⣿⡿⠿⠸⠿⣟⢿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣄⣤⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣩⣤⣺⣦⣽⣯⣷⣿⣿⣿
⠉⢀⣘⣿⣿⣦⣭⠀⠉⠙⠁⠀⠉⢯⡉⠉⠁⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣠⣾⣿⡿⠟⠛⠛⠛⠛⠛⠉⠉⠉
⣾⣿⣿⡻⣿⡍⠻⣿⣷⡄⠀⠀⠀⠠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⣿⣿⡿⣿⡙⡷⣶⡈⣿⣿⣷⣤⡀⠤⣘⡇⠀⠀⣤⣤⣤⣤⡀⣄⠀⠀⠀⢀⣀⣴⣿⣾⣿⡿⠃
⠟⠉⠐⢜⣿⣿⣿⠙⢿⡀⢻⣿⣭⣻⣦⣻⣦⣄⣾⣿⣿⠿⢿⣿⣿⠶⢶⣆⣛⠛⠛⠛⠛⢡⡒⠩⠀⠒⠶⠦⠤⠄
⠀⠀⢀⣼⣿⣿⣿⣧⠀⠉⡀⣿⣿⣋⠱⠝⠿⣿⣿⣿⣿⣷⡀⠈⠀⠺⢍⡉⢋⣁⠀⣀⣀⣀⣀⣀⣀⣀⣐⣖⣖⣶⣤⣤⣤⣤
⠀⠀⠸⠛⢿⣿⣿⣿⣿⣧⠀⠉⠋⠻⡗⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⢀⣀⣭⣭⣭⣍⡩⠻⠿⠿⠿⢿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⠀⡀⢀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠦⢼⢸⢱⢸⡞⢰⡎⠀⠀⠀⠀⠀⠀⠀⡇⣾⣦
⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠗⠀⠸⠈⠙⠸⠙⠸⠑⠀⠀⠀⠀⠀⠀⠀⡿⠃⠈⢃
⠀⠀⠀⠀⢹⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠀⠀⠿⠄⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⢻⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠉⠐⠂⠀⠄
⠀⠀⠀⠀⠀⠀⢣⠀⣦⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⣊⠉⠐⠂⠀⠀⠀⠀⠀⠀⠄⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠒⢠
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠤⠤⠤⠤⠶⠀⠀⠈⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠄⡾⢰⠀⡇⡈⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⣠⢠⢤⠘⠑⠒⠤⣄⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣔⣀⡔⡆⠈⠀⠈⠀⠄⠐⠘⠇⠇⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠂
⠀⠀⠀⠀⠀⠀⢠⠁⡲⠃⠀⠀⠀⠀⠟⠋⠉⠉⠓⢛⡿⠿⣿⣿⣛⣟⣛⡶⠁⠛⠃⣠⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⢀⡾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠐⠂⣿⠟⠁⠀⠈⠀⠀⡠⠖⠛⠛⠛⠋⠋⠲⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢏⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢒⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡿⢤⡀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢼⣆⣀⠀⣀⣤⣶⣿⣟⣛⣿⣿⣿⣿⣿⡟⢿⣷⣶⡅⠀⠀⠀⠀⢀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⣼⣷⡘⢷⣽⡿⠿⠿⣛⡋⡉⠛⠛⠻⣾⣿⠏⣴⣿⣶⣄⠀⠀⠓⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣞⠉⠀⣴⣿⣿⣿⡿⠈⠁⠀⠀⠀⠀⠀⠈⣉⣉⣉⣡⣄⣜⣷⣿⣿⣿⣷⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡁⢈⣧⣾⣷⣾⣿⡯⣄⡀⠀⠀⣠⠴⡒⡋⠉⠉⠀⠈⠠⠀⠀⣉⣻⣿⠿⢿⡿⢿⡿⣿⡿⢟⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢍⣉⣿⣿⡿⠋⠀⠀⠉⣽⠟⠉⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠞⠐⣛⠛⠈⢀⡼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⢠⠀⣱⠟⠇⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⠀⠠⣄⡈⣿⣦⣾⣥⣇⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢫⠀⣒⠿⡈⠠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⣛⠶⣄⠈⠁⠉⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢦⣄⡠⠀⠀⠀⣤⠀⠀⣰⡦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⢖⣛⣿⡦⠖⢻⣿⣿⣿⠦⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡿⠉⣹⠃⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⡀⢰⢖⡓⢲⠶⠚⠁⠀⢰⠇⣰⠏⢇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿⣿⣷⣀⠀⡀⡠⠚⠙⡟⡇⡿⠀⠀⠀⠀⢸⢞⣅⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢻⣿⣿⣿⣷⣾⣄⡜⡇⢀⣿⠇⠠⣀⠀⣀⡄⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⡱⢄⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣆⠀⢹⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡐⠀⡄⡌⠙⢻⣶⣯⣿⠿⢿⣿⡿⠿⠿⣿⣿⣿⠿⠛⡿⠲⠁⠀⡠⡀⠡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢳⠮⠥⡘⠃⠀⠀⠀⠙⢿⣷⣆⠈⠚⢿⣿⣿⣿⡿⠁⠀⡰⠃⠀⠀⠀⠈⠛⣀⠭⢶⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⣤⠀⠀⠀⠀⠙⢻⡄⠀⠈⠹⣿⣿⠀⠐⡏⠀⠀⠀⠀⢀⡔⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣥⠀⠀⠀⠀⠀⠀⠿⠒⠦⣤⣿⢟⠁⠀⣧⠀⠀⠀⠀⢤⡁⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠻⣄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⡻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⠀⠀⠈⠈⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣦⠤⣀⠀⠿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣿⣿⣿⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠙⣷⣌⠑⢄⠀⠀⠀⠃⢀⠆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠘⠛⠣⣨⠂⠀⠀⢀⠞⣀⣿⣿⣿⣿⣷⡶⠀⠀⠙⢿⣧⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄⣀⣲⢦⡤⠗⠋⠀⠉⠛⠋⠛⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡑⠂⠤⣤⣀⠀⠀⢰⣶⣶⣿⣦⣄⠈⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠦⠀⢹⣿⣷⠀⠀⠈⡙⠻⢿⣿⣧⡀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢸⣿⡿⠀⠀⢠⣿⡀⠀⠈⠉⠉⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠉⠀⣀⣴⣿⣿⠃⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣃⣀⠀⢀⡤⠚⢡⡿⠟⠋⠀⠀⠀⢀⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠭⠭⠵⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡤⠴⠈⠙⢗⣶⣄
⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠉⠚⢷⡦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠙⢦⣄⠉⠲⢄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡔⠁⣴⣾⣷⣦⣤⠀⠀⠙⠛⢷⣦⣿⣧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⡻⡠⠀⢀⠀⠀⢉⣿⣿⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡭⠓⠈⠀⢁⡴⠃⠀⠀⠺⢻⣟⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠠⣈⠁⠀⡀⠀⠀⠀⣾⣿⣿⣷⣤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠙⢦⣿⣿⣤⡀⠈⢶⠈⠋⠙⠛⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡠⠒⠉⠉⠁⠀⠉⠛⠷⣼⣤⣭⣭⣍⣽⠖⠂⠤⣀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣟⠋⠙⠆⠀⠀⠀⠈⠑⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⢡⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠎⡐⢁⠞⡠⣊⢔⡁⢒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣰⣘⣃⣃⣊⣐⣡⣊⣊⠕⡰⠲⠕⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣲⠟⢹⣿⡿⡪⠋⠛⣽⣽⡝⡟⠹⣷⣷⣯⣀⣠⡾⠪⣂⢐⢌⢂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⢀⣤⠔⠛⠿⠱⠑⡀⡢⠙⣿⡇⡄⠜⣾⣿⣟⣄⣜⣿⣿⣻⡟⠊⠻⣿⣷⡶⢵⣯⡇⠀⠀⠀⠀⠀⠀⣠⣶⣫⡂
⢀⣠⠖⣁⠣⠖⠇⠀⠀⠀⠀⠍⠉⠎⢅⢄⠌⢜⣿⣞⢀⠈⠜⣿⣽⡟⠔⠴⣽⣽⣟⣔⢜⣿⣿⢁⣦⣿⣷⣘⡮⣿⣥⠂⢀
⠫⣁⠑⢬⡁⣧⢠⠆⠀⠂⡙⠂⠃⣀⢂⡎⠊⠊⠻⠏⠔⠐⡠⣻⣿⠏⡊⡀⣾⡿⣫⠎⠨⠛⠋⠉⣉⢉⢩⣉⡡⣿⣆⠡
⢀⠈⣢⢤⠳⡈⠜⣠⠤⠈⠀⡠⢠⡾⠛⠇⠀⠀⡐⠄⡸⡈⢀⡿⠋⠈⢁⠁⠙⠈⢄⢠⣢⣥⢾⣉⠀⠀⠀⠀⠙⠯⣍⠒⡠
⠀⠀⠈⠁⠉⠐⠲⠤⢤⡄⠀⠐⠰⡋⠅⠲⡀⠄⡠⢑⠀⠀⠎⡈⣖⣱⣕⡤⠴⠚⠻⠛⠈⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢺⣷⠖⣚⣒⠛⠒⠓⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣲⡽⡟⢌⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣳⠝⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⡭⢍⡻⣿⣟⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⣠⣴⣶⣷⣿⣿⣭⣷⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⣟⣼⣽⣷⣦⡀⣠⣾⣿⣿⣿⣿⣟⣿⣿⣿⢃⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣧⡾⢋⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣒⢻⣿⣿⣿⣿⣟⣛⣥⣾⡿⠇
⠀⠀⠀⠀⠀⢀⡀⠀⣀⣠⡤⢴⣶⣿⣿⢛⢛⣋⣉⣹⣷⣿⣿⣿⣿⣷⣿⣾⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⣾⣯⡋⡙⢿⣛⣿⢿⣿⣿⣿⣯⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢹⡆
⠀⠀⠀⠀⠀⠘⢿⣿⡶⠰⠈⠻⣄⠈⠁⢤⠀⠉⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢟⡯⢭⣀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⠀⣄⣻⠃⠀⠀⠹⣮⡄⣿⣥⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠂⡻⠃⣨⣾⠙⠃
⠀⠀⠀⠀⠀⠀⠾⢛⣿⣿⠀⢿⡿⠀⠀⠀⠀⠈⣧⠟⠁⣼⣭⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠇⠛⣠⠿⠿⠟⠁
⠀⠀⠀⠾⠆⣀⠚⠛⠛⣉⠀⣼⣇⣴⣶⡶⠶⠀⠀⠀⣰⡟⠉⠉⠉⠉⠉⠋⠁⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠭⠁⠀⠀⠀⠠⢾⣿⣦⣿⣿⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠻⠿⡯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⡄⠙⣿⣿⣿⡟⢁⡶⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⣾⣿⡿⢇⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠡⡀⠛⢻⡿⢿⣿⠁⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠙⠻⠗⠛⠃⠀⠛⡇
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠈⠀⠈⠁⠘⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣦
⠀⠀⠀⠀⣠⡖⠁⠀⠾⠆⠀⠀⠀⠀⠐⠄⠀⢀⣀⡈⢻⡀⠀⠀⢠⢢⡉⠀⠀⡀⢀⠌⡟⠀⠀⠀⠀⠀⣄⠀⠀⠀⠉⢻⡇
⠀⠄⠀⢰⠃⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣌⠰⢦⡁⠀⠀⠀⠀⠑⠆⠈⢠⣄⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⢙⠋⣄⡑
⠀⠀⠀⠰⣄⠚⠃⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠼⠃⣤⠀⠀⠀⠰⣇⠀⠠⠞⢉⣀⡔⠁⠀⠀⠀⠀⠀⠶⣴⣾⣧⣬⡽⠈
⠀⠀⠸⠦⢌⣀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠖⠉⠉⠀⠀⠀⠀⠘⠾⠀⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠲⠖⠛⠛⠃
⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢻⡟⠉⠉⠉⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⡄⠀⢈⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⡶⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⡠⠐⡞⢉⡿⣠⣶⠇⣠⣼⠃⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢀⣤⣆⣼⣣⠞⣷⢟⡿⠋⣿⠟⣿⣧⣶⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣶⣿⠿⠃⠙⠁⠊⠉⠉⠛⠒⠦⣔⢋⡾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡌⢿⡟⠁⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⢿⣿⣿⠶⣦⡀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣙⣃⠀⠀⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⠇⠉⠛⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡤⠶⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠀⠀⠀⠀⠀⣀⣤⣶⠟⠁
⠀⠀⠀⢀⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁
⠀⠀⢀⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠁
⠀⠀⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⣿⠋⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠐⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡜⣲⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢲⠡⢑⢳⠭⢇⣳⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢎⣂⠎⠍⣒⡂⠌⡘⡺⡿⣿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⢀⣔⣞⡿⣝⡚⡬⠼⡐⡨⢩⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⣀⣾⣽⡻⠻⠽⢓⠳⢡⢁⣂⠥⢧⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⢠⣼⣿⣿⣿⣶⣦⣧⣖⡂⡯⣖⣞⡼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⣲⢡⢀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟
⠀⣠⣯⣟⣿⠟⣿⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣯⣗⣮⡽⡄⠀⠀⠀⠀⡀⣤⡺⠋
⢐⣾⢿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠴⠷⠷⠋⠃
⣼⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣤⣠⣴⣿⣿⣿⣿⣿⣛⣥⣶⣾⠿⠃
⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⢻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣡⣶⣿⣿⣿⣷⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠘⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⡿⠁⠀⠀⠈⠙⠛⠛⠟⠛⠛⠋⠁
⠀⠘⢷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣄⠈⠙⠛⠉
⠀⠀⠈⠁⠀⠻⡿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠳⣿⢿⣷⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠈⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠢⢡⢀⣀⢀⣀⣤⣶⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣟⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⡀
⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠠⠄
⠀⠀⠀⠀⠀⣀⠠⠤⠰⠒⠒⠒⠘⠋⠉⢀⣈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⡊⠁⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠑⣄⠈⠂⠂⠀⠀⠀⠀⠀⡀⠐⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⠠⣤⠜⠁
⠀⠀⠀⠀⠈⠳⣤⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠙⢟⢿⣾⣕⠹⠇⠙⠂⠉⠘⠉⠛⠳⢤⡀⠀⠀⠀⠀⡀⠀⢸⡄⡾⢀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠭⣄⢀⣠⣦⠲⠂⠓⠛⠚⠓⠋⠓⠀⠀⠀⠀⠠⠋⢠⠗⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣮⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠉⢠⠃⠀⣠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠂⠀⡀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠑⠠⡀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠉⠉⠛⠙⣇⣰⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⡀⠀⠈⠢⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⣾⣿⡿⡪⠟⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣻⢶⣀⠀⠈⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣫⢿⡿⠛⠉⠀⠀⠀⠀⠉⠉⠙⠛⠿⠶⣶⢤⣄⠀⠀⠀⠉⠻⣯⣗⢤⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⡫⢷⡉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢳⡄⠀⠀⠀⢹⣿⣿⢿⣷⣄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡠⡾⠕⠉⠀⠀⠈⠂⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⡴⠋⠰⠀⠀⢀⣾⣿⠟⠁⠈⠙⢷⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⡰⠒⠁⠀⠠⠁⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢈⡱⠖⠁⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⠁⠀⠀⠀⣀⡠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⢴⣾⣿⣿⣿⠏
⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠈⠻⡉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⢀⣀⣀⡤⠀⠀⠀⠀⠉⠙⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡿⣹⢿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡛⠿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢿⣶⣭⣝⣛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡽⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣍⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⣸⣰⣿⠟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉

⠀⠀⠑⢄
⠀⠀⠀⠐⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⢀⡄⠀⢀⠠⠄⡀
⠀⠀⠀⠀⠀⢀⠑⢄⡀⠀⠀⠀⠀⡀⠔⡒⢤⣀⠄⠂⠁⠀⠀⠀⠀⠀⠈⠐⠠⡎⠱⢸
⠀⠀⠀⠀⠀⠀⠘⠉⠙⠄⠀⠀⠀⡁⢌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⢀⠈⢤⡀⠀⠙⢄⡀⠑⠠⠍⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠉⠋⠑⠱
⠀⠀⠀⠀⠰⠁⢀⠀⠀⠀⠂⠤⠽⠆⣸⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡐⠆⠘
⠀⠀⠀⠀⠋⠈⠁⠀⠀⠀⠀⠀⢄⠀⢉⠀⠀⠀⢄⠀⠸⣯⣔⠀⠀⣠⠤⠤⢸⡿⠤⡜
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠄⡀⠀⠁⠺⣄⠀⠀⠀⠀⠀⠛⠋⠐⡀⠀⠘⠛⣡⡀⠀⡀⢀⠤⠐⢶
⠀⠀⠀⠀⠀⠀⠜⢁⡀⠂⣀⠈⠱⡄⠀⠈⠢⣄⠀⠀⠀⠄⠂⠈⠙⠛⡥⣈⠤⢓⡪⠔⠁⠀⠁
⠀⠀⠀⠀⠀⡘⠐⢂⡰⠢⣀⠒⢅⡘⡀⠀⠀⠀⠉⠒⠢⢤⣀⡀⢒⠡⠒⠉⠀⠀⠀⠀⠀⡴⠛⠁
⠀⠀⠀⠀⠀⡇⠰⢎⡀⠒⢀⠑⢂⡀⢇⠀⠀⠀⠀⢀⠔⠈⠑⠛⣄⣃⠀⠁⠰⠀⣠⠖⠉⠀⡀
⠀⠀⠀⠀⠀⠆⠁⠄⢁⠶⢁⡐⠂⡄⢸⠀⠀⠀⢠⠁⠀⠀⠀⠀⠘⠿⢦⣤⣤⣏⠀⠀⠀⠀⡈⢆
⠀⠀⠀⠀⠀⡆⠃⢤⠋⡰⢈⡀⠂⢀⢸⠀⠀⢀⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⣆⠈⠇
⠀⠀⠀⠀⠀⠠⡰⢀⡌⢠⠮⢈⡒⠡⢸⠀⡰⠋⠀⠀⠀⠑⠲⠶⠶⠶⠒⠾⠛⠳⡶⣾⡀⠀⠙⡦⣟
⠀⠀⠀⠀⠀⠀⢣⠂⢀⠃⢠⢊⡠⠃⣼⠊⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠆⠃⠴⠟⠮⡿⣦⡰⠟⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⠓⠤⢁⠓⡇⠀⠀⠀⠀⠀⠀⠈⠳⡆⠀⠀⠀⠀⠀⠟⠘⠓⢟⠻⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡈⠃⠆⠠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡠⠚⠀⠀⠀⢸⢀⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠬⣆⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣊⠀⠀⠀⠀⢠⠜⠉⡠⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠋⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⠉⠛⢦⡀⠀⢀⠊⢰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠒⠒⢿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠳⠤⠬⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢀⣱⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣿⡄⠀⠀⠀⢀⣀⡤⠤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⣿⣿⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣨⠟⣫⣿⡿⠿⠛⣉⣩⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⠄⢀⠞⠁⢠⡞⢡⡾⠋⢁⢀⣿⣿⣿⠿⣋⣽⠿⠛⢉⣤⣶⣶⣶⣶⢤⣤⣀⠀⠞⠁
⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⢤⠏⠐⡉⢀⣦⣾⣿⠛⠋⠁⢉⡤⠔⠒⠀⠀⠀⠀⠙⠿⣿⡏⠉⠁
⠀⠀⠀⠀⢠⡏⠀⠀⣴⠁⠈⣰⡿⢷⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡤⠏
⠀⠀⠀⠀⡼⠀⢀⡞⠁⢀⣼⣋⣬⣿⠿⠓⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠶⠛⠉
⠀⠀⠀⠀⠇⠀⠈⠀⢀⣬⡿⢟⡩⠊⠀⠀⢀⣤⣀⣤⡭⢿⠿⡿⠿⠿⣄
⠀⠀⠀⠀⡄⠀⢀⣴⢟⡩⢶⡯⠀⠐⢾⠛⠉⠉⠁⠀⣀⠓⠲⢦⣀⠀⠘⣧
⠀⠀⠀⠀⢀⣴⠿⠚⠁⠀⢰⣵⣾⠙⣾⡄⣴⠃⠀⠈⠀⠀⠀⠊⠉⣑⢆⣸
⠀⠀⠀⠠⠟⢡⠀⠀⠀⠀⠀⠀⠙⢦⣸⣼⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⠀⢸⡀⢠⠀⠀⠀⠀⠈⢻⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⢧⣦⠀⢦⡀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠣⠑⢄⠑⢄⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣆⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣟⠿⣿⡿⠿⠿⢯⣭⣿⣿⣾⣿⣮⣜⡿⣆⠀⢉⣦⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣒⠚⠓⠈⢀⣀⣀⡼⢥⣿⣿⠼⠋⠛⠻⢿⣼⡄⠀⢀⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢠⣾⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠒⠒⠒⠢⣤⣤⠰⢿⣿⡦⠌⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣤⣤⣤⡾⠙⠏⢀⣼⠅⠀⠀⠒⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣀⡔⢿⣿⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⢶⠂⣦⡄⢠⣴⣾⢶⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣀⣴⣶⡶⣷⣟⣚⣯⣾⣿⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⡀⠀⢀⣊⠉⠛⠛⢒⣿⣿⣯⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⠟⢒⣛⣷⣶⢶⣶⣿⣿⣋⣇⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣽⣧⣽⠋⠻⣍⡽⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⢿⣿⣋⣿⠽⠋⣙⣶⣿⣿⣿⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣟⣿⣬⣶⣧⣿⣿⣻⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣗⣀⣤⣤⣦⡾⢶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡻⣾⣦⠴⣶⡽⣾⣷⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠙⠻⠿⠿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⢾⡿⠟⠻⠿⠿⢿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡄⠈⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⡀⠘⣀⣠⣦⣤⢀⣤⠄⠠⠶⣆⢼⡟⠘⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢑⠤⣖⣿⡿⣛⣋⣽⣿⡷⢀⢾⡀⡉⠘⠙⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣪⡵⢚⣩⣶⣾⣿⣻⡅⢻⠇⠀⠀⠂⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣼⣞⣹⣶⣿⣿⣿⣟⣷⠣⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠦⢄⣠⡄
⠀⠀⠀⠀⠚⢁⡈⣻⣻⣿⣡⡾⢿⣯⡜⠙⠎⠥⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠉⠁⢀⠤⠊
⠀⠀⠀⠀⠀⠈⣽⣽⢏⣾⣿⣶⡌⠈⠈⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⣸⣿⢃⣾⣯⣄⠉⠀⠐⠀⠀⠀⠀⠘⠿⠂⠀⠱⣄⡤⠂⠀⠐
⠀⠀⠀⠀⠀⣿⣏⣾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁
⠀⠀⠀⠀⠀⣿⣿⣍⡁
⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠹⣿⡁⠀⠀⠐⠋⠀⠁⠇⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠘⢖⠀⠀⠀⠀⠀⠀⠂⠀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⠳⢦⣄⣀⣠⡾⠟⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣟⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣾⡆⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣟⠓⢀⣠⣴⣿⣿⡀⠀⠀⠀⠀⣌⣹⣧⡼⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⢿⡄⠀⠀⠐⢿⣹⡟⢳⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡬⠈⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁
⣶⣶⣶⣶⠶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣶⢶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣖⣤⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⣿⣿⣿⡿⠶⠊⣛⣉⣴⣿⣿⣿⣿⣿⠟⠛⠙⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢝⣫⣵⣾⣿⣿⣿⣿⢻⠻⠛⠋⠀⠤⠶⠚⠛⠛⢷⣆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠿⠿⠛⠛⠛⠛⠛⠨⠄⠀⠀⠀⠀⠀⠀⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣉⣁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⠟⠋⠉⠁⠀⠀⠀⠀⢀⣀⠄⠒⠒⠉⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⠠⠐⡎⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⢈⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠢⡏⠀⠀⠀⠀⠀⠀⠢⠴⠾⠋⢠⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠛⠻⠷⠶⠶⠀⠴⣦⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢷⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡎⢠⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠀⠀⠀⠀⢀⠀⠀⠐⠀⣀⠤⠀⠀⢀⠀⠀⠀⠘⠄⠀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠉⠠⠀⠘⠓⠁⠀⠀⡐⠂⠾⡐⢄⡀⠀⢠⡘⠀⠄⢼⣷⡤⠅⢷
⠀⠀⠀⠀⠀⠠⠄⢰⡀⠀⠂⠠⠀⠀⠀⠀⣰⡿⣣⣾⣧⣁⣈⠀⣇⠉⠀⠀⠀⡀⠱⡄⠈
⠀⠀⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⠀⠈⠆⠠⠄
⠀⠀⢳⡀⠀⠈⠛⠿⠿⠷⠾⠲⠶⠶⠶⢶⣶⣒⣛⣛⣛⣛⣛⣉⠉⣿⠀⡸⠃⠀⠀⠀⠀⠂
⠙⠛⣉⣉⣐⣛⣛⣛⣋⣁⠀⠀⠈⠛⠿⠯⠭⢥⣤⠀⠀⠀⠀⠀⠀⢹⡗⠰⠀⠀⠀⢱⠀⠀⠁⠀⠀⣠⡀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣦⣬⣭⠉⠁⠀⡀⢠⠀⠀⠀⠬⣤⣴⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⡉⠀⡀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠀⣿⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⢰⡀⠀⠀⠛⠁⠀⠀⢰⡀⠐⠠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼⠁⠠⠄⠀⠀⠀⠀⠀⠀⠁⠐⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡓⠀⠀⠀⠄⠈⠛⠉⠓⠄⠀⠠⠀⠀⠐⠊⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠽⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣀⣀⣤⣤⣶⣦⣀⣀⣀⣓⣠⣤⣤⣤⡀⠀⠀⠶⠿⠿⠛⠛⠉⣉⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠉⠉⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠶⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠈⢉⣓⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣀⣀⣀⡈⠙⢳⡅
⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠤⠤⣄⠈⠙⡆⠀⣿
⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⣷⠸⠃⣰⠃⠀⠛⠀⠀⣾
⠀⠀⣸⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣿⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⢀⣀⠄⠀⠀⠀⢀⣠⡤⠖⢊⡉⠀⠀⣀⡠⠄
⠀⠀⣿⠀⠀⠀⠉⠳⢤⣄⣀⠀⠀⠀⠀⣠⠞⠁⢀⡤⢞⣩⠤⢂⣤⠶⣛⣩⠴⠖⢋⣁⡤⠖⣋⡥⠔⠂
⠀⠀⣿⠀⠀⠀⠑⠲⠤⠤⣭⣽⣿⣷⠚⠁⢀⡴⣫⠖⠋⢠⢞⣩⠴⠛⠉⠀⠀⠀⣩⡥⠖⠋⠁⠀⠀⢀⠀⠀⠠⣶⣶⣶⠄
⠀⠀⢿⡄⠀⠀⠀⠤⠶⠶⢶⣖⠒⠂⠀⠀⣨⠞⠁⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⠀⠀⠀⠘⠿⠟
⠀⠀⢸⣧⠀⠀⠀⠉⠉⢉⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⣷⢹⡀
⠀⠀⠀⢿⣦⠀⠀⠐⠛⠉⣉⣡⣤⠄⠀⠀⢦⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⣿⡲⠤⠄⠀⠀⠈⡇⢹⠘⡇⠀⠀⠀⠀⠀⠀⢠⣤⣴
⠀⠀⢀⡼⠁⢀⣠⠴⠖⠋⣉⣤⠤⠆⠀⠀⠸⣷⣄⡀⠙⠿⣝⡲⠦⣤⣀⣀⠈⠉⠛⠂⠀⠀⠀⢹⠀⢇⠘⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⢠⠞⠀⠀⠀⣀⡤⠖⠋⠉⡀⠤⠒⠛⢿⣦⣘⠳⢭⣓⠶⢤⣍⣛⡲⠦⠭⣭⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⢀⡏⠀⠀⠀⠈⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠙⠿⣷⣦⣌⡙⠓⠶⠤⠭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋
⣸⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⡖⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⠀⢤⣤⣤⣶⠶⠟⠛⠉
⢻⡀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠠⠴⠃⢀⣨⠇⠀⠉⠙⣦⠀⠈⠉⠁
⠘⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠚⠉⠁⣀⣤⠶⣚⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⢄⣒⣫⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣥⣴⣶⠶⠾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆
⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠙⣧
⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠁⠀⠀⠘⣧
⠀⠀⠀⠈⣿⣿⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠞⠛⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⢶⣦⣄⡀
⠀⠀⠀⢸⣿⢸⣷⣤⣴⡿⠿⠿⠶⠒⣛⣛⣋⡭⢅⣀⣤⠖⢀⣤⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠍⠳⢦⣀
⠀⠀⠀⣼⣿⣌⠛⠛⠛⠻⠿⠿⠿⠭⠿⠶⢶⣿⣿⣿⠏⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠠⠬⠷⣦⣄⡀
⠀⠀⣼⣿⡿⠋⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠀⡿⠁⠀⠀⠀⡴⢠⠄⠀⠀⠐⠶⣶⣗⠋⠑⠉⠁⠀⠀⠀⠀⠒⠪⢝⡛⠶⣤⣀
⢠⠾⠟⠉⠀⠀⠀⠐⠶⠛⠛⠓⠶⢤⣀⡀⠀⠀⠀⠇⠘⠃⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠉⠓⢺⣿⣔⣀⣀⡀⠀⢀⣀⣀⡀⠀⠈⠓⠈⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⢉⠛⠛⠛⠛⡛⢿⡿⠶⣶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⠟⠀⣠⣶⠀⠀⠀⠀⠀⠀⠈⠳⢶⣶⡱⠎⢦⢦⣤⣤⣭⣤⣤⡴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⢋⣠⣴⠞⠻⠷⣤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠢⠤⠤⣴⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣛⣭⠴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠒⠲⠶⠶⠶⠶⠒⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠳⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⢱⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⡀
⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠁
⠀⠀⠀⠀⣿⠃⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⢀⣄⠀⢁⣤⣄⡀⠀⣤⡀⢠⣄⠀⣤⡀⢠⣄⠈⢩⡍⠁⢀⣤⣀⡀
⠀⠀⠀⢰⡟⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠋⠀⣿⠀⣿⠀⠘⠇⠀⣿⠀⢸⡇⠀⣿⠁⠸⣿⡄⢸⡅⢠⡟⠀⠘⠇
⠀⠀⠀⠸⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣴⠀⠀⣿⠀⢿⣦⣀⠀⠀⣿⣀⣸⡇⠀⣿⠀⢀⡻⣇⢸⠇⣾⡷⣆⣀⣀
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠛⠀⠀⣿⠀⠈⠙⢻⣷⠘⣿⠉⢹⡇⠀⣿⠀⠰⡆⢻⣼⡅⢿⡇⠀⢸⡏
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣆⠀⠀⣿⠀⣿⠀⢸⡇⠀⣿⠀⢰⡇⠘⣿⠀⠸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣃⡀⠀⢐⣟⣀⠛⣳⣖⠁⢀⣿⣆⢸⣷⡀⣿⣇⣸⣧⡀⢹⡀⠀⠙⣳⣞⢿
⣿⣿⡿⠿⣿⡿⠿⠿⡿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡖⠀⠀⠀⡠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠈⠀⠄⢀⠜⢁⠔⣁⠀⣀⠄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⣦⣤⣆⣶⣿⣤⣮⣾⣁⣞⣡⢂⡡⠄⠀⢀⡴⠋⠉⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠛⢛⠭⠻⣿⣶⣿⣯⠝⣋⠻⡟⣿⣿⡟⢶⢿⣶⣷⣤⣤⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⣺⣭⢞⡏⢓⠈⢿⣿⣿⡤⠡⠑⠻⣾⣿⣯⡄⠀⢻⣿⣿⡙⠿⣷⣄⡙⠆⠀⠀⠀⠀⠀⢀⣠⣴⠛⠁⢰⠇
⠀⠀⠀⢀⣤⣶⡾⣯⠉⠈⠁⠉⠛⠮⣯⣿⠍⠗⠂⠻⣿⣿⣧⠀⠀⠀⣻⣿⣿⠃⠀⠈⣯⣾⣗⠀⠀⠈⠙⠛⠦⠤⠤⠶⠾⢿⡿⠁⠀⣡⠏
⠀⠀⢰⡟⠋⠳⠙⠋⠀⠀⡄⠀⠀⠀⡜⠛⠁⣀⡀⠀⢸⣿⡯⠀⠀⠀⢘⣷⣿⠇⠀⠀⢿⣽⠇⠀⠀⠀⠀⠀⠂⠀⠀⠈⠊⢺⡇⠀⠸⢯
⠀⠀⠈⠉⠋⠀⢀⠄⠀⣠⡿⠀⢸⡞⠱⣮⠉⠉⠉⠙⠶⡟⠁⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠁⣀⣠⡴⠶⣖⠒⠒⠒⠒⠶⢶⣾⣿⡀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠴⠋⠀⠀⠿⣁⣀⡀⢀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⡿⢟⢏⡲⠔⡜⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠠⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠁⠀⠈⠳⣴⣕⠪⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⢮⣀⣙⡅⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡍⠛⢦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⡢⡀⠀⠀⠀⠀⠄⣐⣠⣤⣤⣶⣿⣶⣾⣿⠿⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢜⣢⣤⣶⣾⣿⣿⣿⣿⠿⠛⠋⠁⠀⠁⢀
⠀⠲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣵⣾⣿⣿⣿⣿⣿⣿⠿⠟⠡⠶⠾⠿⠿⠟⡐⠁
⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣶⣿⣿⣿⣿⣿⡿⠝⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠈⢻⣿⣿⣶⣄⠀⠀⢠⣄⣀⣴⣴⣾⣿⣿⣿⣿⢿⣛⡭⠵⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⡷⠾⠿⠿⠟⠛⢻⠿⠛⠝⠊⢉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⢢
⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⢀⣤⣤⣊⡉⠤⢤⠶⠖⠮⢤⠤⠤⠤⠄⠒⠂⠙⠥⠄⣀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣤⣰
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⢦⣀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣄⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⣟⣷⣼⣿⣿⣿⡿⢟⣯⣽⡟⠟⡴⢋⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⢷⣶⣿⣿⣿⣿⡿⠋⠑⢋⡽⢛⡅⣠⢿⠟⡉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠻⠿⣿⡘⣿⡇⡄⠀⠀⠀⢉⡞⠟⢸⣴⣷⣦⣿⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⠀⣘⣶⣶⣝⠻⡧⢳⣄⣀⢀⣼⣤⡄⣨⡭⠭⣂⣀⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠽⣿⣿⠀⢷⣆⠛⠛⠛⢛⡭⠀⢰⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣷⣤⠙⠿⠶⣟⣫⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠩⢭⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⣠⠴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣣⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⡏⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢿⣿⣧⠀⠀⠀⠀⠀⠈⣿⡇⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡇⠀⠈⢻⣷⣄⠀⠀⠰⠿⣧⣀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⡇⠀⠀⠀⢿⣿⣷⣦⡀⠀⠀⠉⢿⣿⡟⠋⣉⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡇⠀⣦⡄⠈⠿⠟⠙⠻⣷⣤⣤⣾⣟⠳⣌⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣧⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⢻⡝⢳⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⣾⣿
⠀⠀⠀⣦⣹⣿⣰⣷
⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠄⠀⠀⢀⡤⣶⣶⣟⣁⣀⣤⣤⡶⠂
⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣾⣿⣿⣿⣿⣟⣉⣩⣽⣿⡛⠉⣀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣟⡋⠉
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢼⣿⡿⢿⣿⣷⣖⣂⣈⣉⣹⣿⣿⡋⠁
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠡⢿⣿⣿⣿⣿⡿⢿⣿⣿⡯⠭⠭⣭⣿⠿⠉
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢭⣿⣿⣿⣶⣶⣿⣿⣯⣤⣤⡽⠛⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣧⠀⣺⡫⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠏⠘⠁⠀⣼⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⣀⣀⣨⣡⣾⣿⣿⣿⠆
⠀⠀⠀⠀⢀⣾⣿⣿⣯⡍⠛⡿⠙⣿⠉⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠸⠿⢿⣾⠿⢛⡎⢀⣾⠇⠰⣦⡀⣴⠂⠂⠀⢤⣤⣀⠙⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠽⠟⠷⠚⢷⣿⣿⣿⣿⡷⢿⠐⢦⣄⠉⠑⠂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠷⢿⣇⢸⠀⠈⠃⠘⣦⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣻⣥⣤⣾⣿⠟⠀⠀⠀⢀⣿⡇⣿
⠀⢀⣀⣤⡤⠤⠶⣚⣿⣿⣿⣻⣿⣿⣿⣄⡾⠛⠁⠀⢀⣠⣴⣿⣿⡇⠁
⣉⣭⣥⣶⣶⣾⠷⠾⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣏⡉⢸
⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢄⠁⣄⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡻⠟⢿⠟⡤⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣶⣶⣾⣷⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⢋⡄⠀⠀⠀⠀⢲⡴⠋⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠘⢃⠀⠿⢿⣿⣿⣦⡾⠁⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠻⣿⣿⡥⢾⠀⢠⣶⡇
⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠈⠳⠀⠘⠟⠁⣿⠇⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠙⠻⢿⣧⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣷
⠀⠀⠀⠀⣰⠿⠁⠀⠈⠉⠀⠀⠀⠀⠈⠈⠓⢀⡀⠤⠤⠄⠻⠀⠀⠀⠸⠹⡤⠀⠀⡐⠀⠔⠈⡇⠀⠀⠀⠀⠀⠲⠈⠀⢀⣀⡀⢻⡆
⠀⠀⠀⢠⠏⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢰⡆⢛⠶⠄⠀⠀⠀⠀⢀⠑⠀⠀⣶⣄⠀⠁⡠⠂⠀⠀⠀⠀⠀⠀⠠⣍⠡⣦⡁⣀
⠀⠀⠂⠈⢢⡈⠛⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠰⠋⣠⡎⠀⠀⠀⠘⢿⡀⡠⠖⣁⡠⣴⠊⠀⠀⠀⠀⠀⠀⠙⢶⣾⣿⣶⣶⠟
⠀⠀⠐⠗⠤⣅⣀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠛
⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣯⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿

⠀⣀⣤⢤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢄⠀⠀⠀⣀
⠀⠸⣿⠀⢿⣇⢠⡄⠀⠀⣠⣄⡠⠤⣤⣤⣤⣀⢀⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⣺⣷⣶⣾⢿⡆
⠀⢀⢻⡇⠘⡏⢸⣷⣤⣿⣟⠟⠋⢀⣸⣿⢿⣿⠿⢛⢉⡀⡀⡸⠦⣤⡤⠀⢀⣴⣿⡟⢦⠁⢀⡙⣿⣿⠀⣿
⠀⡀⠸⣿⠀⠃⠈⣿⡿⠋⢁⣴⣴⣿⣿⣿⠿⡿⠿⠿⣿⣷⣷⣦⣼⣿⡿⠯⣝⣍⣸⣥⣶⠀⢨⣬⣿⣿⠀⣿
⠀⠱⠈⣻⡧⢸⠀⣼⣥⣾⣿⠟⢋⣡⡤⠤⠶⠒⠒⠒⠆⠐⢤⣬⣉⠛⠿⣷⣶⣍⠻⣿⣉⠁⢶⣿⣿⣿⠀⣿
⠀⢠⠀⣿⣷⡞⢠⡿⣿⣿⠗⣋⡍⢷⡆⣿⡇⢾⣇⣰⡧⢠⣷⢈⣹⠙⣗⠤⣈⠛⣷⣤⣛⡷⣬⣿⡿⢻⣤⡟
⠀⣈⡇⢹⣿⠃⠘⢱⡟⢡⣼⡏⡧⢼⡇⣿⡇⣿⠃⣾⠇⣺⡧⠋⠀⠀⠈⠁⠀⠀⢶⠟⠙⢳⣄⠛⠇⢸⠻⠁
⠘⣾⣧⣼⡇⡆⠀⣿⢸⣿⢯⡽⣇⢀⠀⣄⢠⣄⠀⠉⠈⢻⠁⠀⠀⢀⠀⠛⠳⠶⡦⠁⠚⠋⠝⣻⣦⣙⣸⠀⡇
⠀⣿⠛⣿⡗⡇⢸⣿⣈⠟⠙⡠⣻⠀⠀⢹⣿⡇⠀⣴⣤⢸⠀⠀⠀⠎⠘⠓⠒⠖⠋⠀⠀⢀⡄⣡⠔⢢⡟⠰
⠀⣼⣆⠸⡇⢡⡀⠻⣿⣄⠈⡪⣹⣷⣄⣀⠹⣷⣌⣿⠿⠂⢁⠀⠀⠈⠢⠀⠘⢠⠞⠁⠀⣨⡾⠁⣠⣿⠁⠆
⠀⢻⣿⡆⢿⣼⠣⠀⠍⢻⡄⢼⣿⣿⢭⣍⣛⣶⡶⠤⣤⣀⣰⣧⣀⠀⠀⠀⠀⠻⠀⠀⠐⢻⡀⣼⣿⠃
⠀⠘⢾⣿⡌⢿⡀⠁⠀⢸⡇⢸⣷⣾⡞⠻⣿⣿⣇⠀⢉⡿⣫⡿⠫⣟⢶⣤⣤⣄⣈⡀⠂⠀⠑⠨⠁
⠀⠀⡼⣿⣿⡌⠻⣦⡤⣩⡄⢘⣿⠛⠀⠀⠈⣻⣍⣴⣯⡾⠋⠀⠀⠀⠀⠦⢛⣿⣿⣿⣿⣿⣶⣷⣆⣴⣄
⠀⠀⠀⠤⣄⣀⣀⣀⣉⣻⠅⠈⣻⡷⠤⠤⠔⠀⠘⠛⠁⠒⠀⢦⡤⠴⠊⠀⣈⣉⠅⠒⠲⠦⢄⠽⠛⠏⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠀⠂⢉⠳⢤⣀⡠⠄⠚⠉⠁⠀⠀⠠⢤⣴⠶⠋⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛
⣿⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⣶⢶⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣦⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡿⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠛⠛⢇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⣀⣶⠞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡟⣅⣠⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣤⠀⣼⣿⢋⣾⣿⡍⠁⠘⣛⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣧⣉⣉⣱⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠀⢿⡇⣸⣿⠋⡀⣬⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠹⣿⡸⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⣶⣶⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣸⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠢⣶⣿⠇⢼⡿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠋⠀⠰⣿⠿⢿⣬⡙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡐⢅⠋⠀⠀⠄⠀⠀⢿⣷⣦⡉⠳⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠐⡄⠉⠂⠔⠀⠀⡼⢆⣿⣿⣿⣦⡈⢿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡦⢈⠂⠨⣅⠤⠊⢶⡞⢡⣞⡿⣿⣿⣆⢻⣿⣿⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡀⠈⠁⢠⠖⢱⣦⠰⡏⣴⣼⢛⣿⣿⣧⢻⣾⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠸⣿⣿⣿⣿⢑⡋⢰⡺⣩⠽⣿⣏⣿⣻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⠀⠀⡻⠿⣿⣿⢠⡿⡸⠶⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⣻⣿⣿⣧⠀⠀⢐⠀⠄⢨⠘⠅⠟⡞⠱⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⣿⢿⣷⡄⠈⠀⠂⠀⢐⠈⠫⢹⡉⣼⡾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠠⠁⠀⠈⠳⢣⠟⢟⣿⣯⡙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠆⠹⢃⡿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠢⡀⢗⠚⢗⣿⢿⣺⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠈⢲⣼⣟⢟⢮⣶⣯⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⢞⣞⣮⡻⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢤⡤⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣇⣀⠀⠀⠀⠀⠀⠻⣿⣯⢯⢿⣽⣾⣞⡿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠻⢦⣚⣿⣦⡀⠰⣆
⠀⠀⠀⣶⣦⡀⠀⠀⠀⢿⣻⣿⣷⣄⠐⣀⠀⠀⢹⣟⣯⣯⣯⣿⣿⣽⣽⡿⡽⣿⡿⣆⠀⠀⠀⠀⠀⠟⠋⠉⠳⠀⠙
⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⢹⡶⠏⢻⡄⢙⡆⠀⠀⢻⣾⣾⣾⣶⣷⣷⣿⣿⣿⣿⣿⣿⣧⣄⣀⡀⠀⠀⠰⠦⠞
⠀⠀⢸⣿⢿⣿⣿⣷⡀⠀⠀⠀⣀⡸⠀⠀⢀⣠⣴⣾⣿⣿⡏⣿⣟⣻⣟⣹⣟⣹⣿⣫⣿⣻⣿⣿⣿⣶⣤⣀⠀⠠
⠀⠀⢸⣿⣿⡿⣮⠿⣿⡄⠀⠀⠈⢀⣤⢾⣿⡿⢻⣿⢴⣿⢥⣿⣟⣹⣏⣿⣋⣿⣥⣿⣫⢳⣿⣿⡿⠛⠛⢿⣷⣄
⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⡄⢀⡴⢿⡷⢰⣿⢧⣿⣋⣿⠿⢸⣿⢶⣿⢭⣿⢬⣿⣥⣿⣽⣾⣿⣿⡇⠸⠿⠀⣿⣿⣷⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⠟⡦⢾⡟⣹⣟⣹⣟⣨⣿⡟⣻⡿⢚⣷⣺⡿⣾⣿⣼⣧⣶⢿⣿⣿⣿⣶⣶⣾⣿⢏⣭⠅
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣖⣻⣋⣿⣘⣿⢛⣿⣹⣟⣨⣿⣛⣹⡿⢻⡿⣹⡿⣵⣟⣿⣿⣿⢸⣿⣿⣿⣿⢻⣿⣧⣭⣵⠂
⠀⠀⠸⣿⣿⣵⣾⣿⣿⣿⠿⣧⣟⣩⣟⣹⣻⣹⣿⢏⣿⠏⣻⡏⣻⡟⢻⣼⣿⣿⣿⣻⣿⡆⠻⣿⣿⣿⣷⣿⣿⡿⠁
⠀⠀⠀⣿⣿⣿⣿⣟⣿⡟⠀⠈⠻⣿⣅⣿⡿⢙⣿⠏⣻⣛⣹⣏⣿⣛⣿⣿⣿⣟⣯⢷⣻⣷⡀⠪⠻⡿⢿⡿⠋
⠀⠀⠀⣿⣿⣿⣿⣿⣾⠁⠂⠀⠀⠈⠙⠿⣿⣿⣟⣹⣟⣉⣿⡻⣹⣇⣽⡽⣿⣿⣾⣽⣾⣿⣿⣷⣥⠶⠋⢀⠀⠄⡄
⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠰⡆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣥⣿⣟⣣⣿⣾⣙⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⢦⡀
⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡀⠂⠀⢀⡤⠤⡄⠀⠀⠹⡆
⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠉⢙⡄⠀⢠⣿⣿⣿⡿⠟⠋⣼⣿⣿⣿⣿⣿⣿⡿⠃⠀⢽⠃⠀⠀⠀⠀⢀⣽⠀⠀⠀⠈
⠀⠀⠀⠀⡿⠃⠀⠀⢀⣀⣴⢾⠀⠀⠉⠉⠉⠁⠀⢀⣾⣿⣿⢟⣿⣵⣽⠟⠁⠀⠀⠀⠀⣠⣴⣶⡟⣽⡏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⣱⠟⠀⠀⢠⡄⠁⠀⢠⣾⣿⣿⣷⣿⠿⠛⠁⠀⢠⡤⠀⠀⣼⣿⡿⣋⣼⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠾⠿⣶⡟⠋⠀⠀⠀⠸⠃⠀⠰⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠛⠀⠀⠈⠉⠉⠻⡟⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠠⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠒⢤⠄⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠠⡴⠄
⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⣀⣴⠁⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠙⠋⠁⠀⠀⠀⠀⠼⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣤⣀⠀⣤⣶⣧⣿⣿⣿⣶⠀⣀⣤⣤⣶⣶⣾⣶⣦⣴⣄⡁⣂⠀⠠⠄
⠀⠀⠀⠀⠀⢘⣳⣴⣴⣶⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣷
⠀⠀⠀⣴⠟⠛⠙⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣿⣿⠿⠟⠛⢉⣩⣤⣈⣉⣡⣤⣵⣾⣿⣿⠿⠃
⠀⠀⠀⠸⢿⡿⠿⠿⢿⣿⣿⣿⣿⣥⣶⡾⠟⣋⣭⣽⣿⣦⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠈⠙⠛⣿⢻⢿⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⢈⣉⠥⠶⠚⠍⣁⣀⣖⢂⣀⡀⠀⣀⠀⠀⠀⣀⣠⣤⣀⣀⣂⣾⡿⠶⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⢐⠒⠠⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠓⠒⠛⠛⠛⠻⠿⠛⠛⣷⡄
⠀⠀⠐⠐⠒⠚⠋⠁⠀⠀⡔⠀⠺⠗⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣧⠤⠤⢤⡀⡆⡀⠀⣤⣶⣴⣶⣿⣷⣶⡄⠀⠀⠀⠀⠰⠐⠲⠤⠀⠀⠳⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠈⠛⠿⢿⣟⣿⣶⢾⣿⣯⡿⠿⢿⡿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣤⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⢾⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠉⠀⠀⠁⠀⠋⠙⠛⢻⣿⣷⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠂⠉⠋⠻⣿⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢿⣮⡓⢢⡀⠉⠁⠀⠀⢰⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠙⢿⣦⡈⠢⡀⠀⠀⠈⠀⢰⠁⣀⣀⣀⣀⣀⡀⠀⠀⠸⢿⣿⣧⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⡁⠈⠉⠱⠤⠃⠀⠀⠀⡰⢃⣠⣿⣿⣿⣿⣿⡿⠗⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠄⣒⣶⣦⠵⠚⠁⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠤⣄⣀⠀⠀⠀⣶⣶⣶⣿⣦⣄⠀⠃⠖⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠄⠀⠀⠀⠀⠀⠰⡅⢸⣿⣿⡆⠀⠀⠙⠻⢿⣿⣿⣧⡀⠀⣠⡿⣠⣤
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣷⣇⠘⠮⣄⣠⡄⢸⣼⣿⣿⠁⠀⢸⡇⠀⠀⠈⠙⣻⢛⡾⠁⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣴⣿⣿⣿⣟⣇⠿⠛⣸⣷⣾⣿⣷⣦⣤⣼⣿⣿⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⡟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣶⣶⣶⡶⠾⠛⠋⠹⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⠉⠉⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣟⣹⣆
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⡌⡀⡀⢀⠂⠀⡀⠀⠀⠀⠀⢸⡿⠑⣮⢿⣧⣚⠵⡶⢖⣫⠃
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢤⡴⣿⣯⣿⡿⣥⡡⢎⣉⠀⠀⠀⠀⡠⢜⡷⢶⣗⡌⣩⣽⡶⠖⠋
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣷⣄⠀⠀⠀⠀⠐⡀⣝⣾⣯⣯⣷⡾⡼⢯⡅⢲⡒⢦⣥⣠⣿⡽⣾⠟⠉⠉
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⡈⢠⠑⠣⢅⡼⣹⡰⢂⡴⢠⡋⣼⠃⠞⠑⣻⣯⣷⡏
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⠷⣶⣿⣬⣧⣵⣿⣾⢡⠇⣼⢓⠈⣿⢏⢂⠟⢁⣿⣿⡿
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣳⢃⡿⠛⠗⢛⣿⣼⣿⣿⡟⣋⣟⠘⣿⡇⣨⢊⢠⢁⡘⣿⡏
⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡯⠿⣾⣇⠀⠀⣸⣿⣻⣿⣟⣽⣿⣿⣿⣿⣽⢯⠃⣾⢻⡇⣾⣷⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⣿⣿⣾⣿⣿⡿⣇⣧⣿⣿⣿⣿⣿⠇⣾⣰⣏⡞⡱⣿⣵⣻⣿⣿⢿⡿⣟⣓⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⣿⡟⣿⡹⣿⣿⣿⣿⣿⣿⣿⡿⡎⣿⢻⡪⡂⣿⣿⣿⣿⣿⣭⣻⣾⣿⣭⠶⡇⢨⣦
⠀⠀⠸⠾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢏⣿⣿⣸⣷⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⢷⡅⡌⣯⢸⣿⣽⣷⣒⣷⢶⣿⣿⣿⣮⡿⠛⣩⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⠌⢰⣿⡉⣇⢿⣿⣿⠈⠈⠙⠓⠋⠙⠛⠓⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣯⣣⣿⣿⣿⣿⣿⣿⣿⣿⢷⣯⣿⡟⠈⡚⡙⠟⠡⢷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠈⢹⡿⠿⣿⣿⣿⣿⣿⣿⣷⣾⢻⢃⣼⡾⠃⢡⢡⠚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣌⣘⠂⢸⠁⢀⣾⣯⡛⠿⣿⣽⣿⣧⣏⢺⡧⡃⡗⠋⣆⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⢳⡈⣿⡀⣨⣁⠺⢿⣯⣛⢷⡶⣹⣿⣿⡇⣾⢱⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣕⠦⣭⢽⡶⣮⢭⣛⣶⣾⣿⣯⣼⣿⣧⣿⣾⠿⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⣷⡿⣿⣟⢏⣿⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠁

⢠⡾⠛⠛⠻⠿⣿⣿⣶⠶⠶⠤⣤⣤⣄⣀⡀
⣼⠁⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⠀⠀⠀⠉⠙⠛⠶⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣠⣍⠛⠶⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢷⡀⠀⢰⣿⡷⢾⡄⠀⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢦⡄
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠻⣆⠘⣿⠷⠾⠃⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⢀⡴⠋⠁⠀⣴⠋
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣠⠟⠁⠀⠀⢸⡇
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⢸⠃
⠀⠀⠀⠹⣆⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣿
⠀⠀⠀⠀⢻⣤⣾⣿⠟⢶⢻⡶⠻⣴⢷⡼⢧⣽⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠈⣯⠙⠛⠛⠛⠛⠛⠛⠛⠒⠒⠚⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⣷
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣨⡿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢻
⠀⠀⠀⠀⠀⡿⣦⣤⠶⠋⠁⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⠶⣼⣆
⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⠄⠉⠛⠶⣤⣀
⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠒⠒⠒⠶⠶⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀
⠀⣾⠁⠀⠀⠀⠀⣀⣤⠶⠞⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢶⡶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⢿⣤⣤⡴⠞⣿⠉⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡴⠟⠀⠀⠀⠀⠈⠉⠙⠛⠶⢦⣤⣀⡀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠾
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠙⠳⠞⠛⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣆⣴⡿⠴⠶⢶⡆⢉⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠀⠈⠛⠁⠀⠀⠀⢸⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠞⠁⢀⠄⢐⢠⡀⡄⢠⢀⣄⡠⣀⡤⣀⣤⡤⣀⠄⡖⢀⡤⡄⢠⣀⡄⡤⠀⡠⢀⢤⣠⢤⢤⠀⠀⡀⠀⠀⢒⢤⢲⠀⡆⠐⡆
⠀⠀⠀⠀⠀⠀⢸⣇⡴⠟⠁⠀⠀⠈⠁⠈⠉⠁⠉⠈⠉⠀⠁⠁⠁⠉⠀⠁⠉⠁⠉⠉⠃⠉⠉⠉⠀⠁⠀⠑⠈⠈⠈⠈⠈⠀⠀⠀⠀⠀⠋⠈⠉⠀⠁⠀⠁
⠀⠀⠀⠀⠀⣴⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢳⣄⠀⠀⠀⠀⠀⠀⢀⡤⢚⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣾⣾⣿⣿⣿⣶⣤⣤⣾⣍⣴⠋⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡱
⠀⠀⢀⣠⣤⣶⡾⢿⣿⢿⣿⠿⠿⣿⡿⡿⢿⢿⡟⣻⣿⡿⣿⢿⢿⡿⣿⣿⣷⣤⣄⣀⣀⠀⠀⠀⣰⠋⣰⠁
⠰⢾⠋⠩⣽⣿⠃⠀⠉⢷⣶⣶⠶⠾⠿⠷⠚⠳⢶⣷⡌⠀⠁⠉⠚⠁⠉⠁⠋⠙⠛⠛⢛⣿⣾⣾⣿⣿⠃
⠲⢦⣧⡶⠈⠁⠀⢀⡄⣾⣸⣄⣀⠄⠒⠒⠒⣈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠋⠋⠉⠉⠙⣿⠿⢇
⠀⠀⠈⠉⠛⠲⢦⣼⣿⣟⣻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣶⣶⣶⣾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠿⡿⠛⠛⠛⠛⠋⠉⠉⠉⠙⠯⣉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢬⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠰⠙⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⠷⠄⠀⠀⣤⠘⠃⠊⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠠⢀⠐⢄⠀⠑⢄⠀⠀⠀⠀⠐⠲⢆⣀⠨⠀⠠⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠠⠐⠀⢂⠀⠀⠈⠀⠢⣤⣀⠂⠐⠉⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠡⢌⡠⢈⡐⠈⠀⠀⠀⠀⠀⠀⠉⢦⡄⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⡔⠢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠃⠄⠀⢠⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⢁⠂⠀⢀⠔⠁⠀⠀⢀⠖⠒⠂⠐⠒⢦⢤⡀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⢐⠂⠌⡸⠁⠀⠀⠀⠀⢀⡀⠀⠀⠐⢠⡊⡵⣝⢦⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡂⠄⠀⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠜⠀⠀⠡⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⢆⡀⠀⠀⠀⠀⠀⣧⣄⡀⠀⠀⠀⠘⠉⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠁⢀⣀⣀⡠⠜⠁⠀⠀⠙⢦⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡈⢈⡹⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡈⠙⠻⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠉⠻⢿⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡿⠿⢿⣶⣦⣄
⠀⠀⠀⠀⠈⢿⣧⠉⠛⠻⢿⣶⣄⡀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠈⠙⠻⣿⣦⣀
⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠉⠻⢿⣦⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⢀⣠⣴⡿⠟⠛⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⢀⣿⣟⣠⣴⣾⡿⠟⠋⠀⠀⠀⠀⠈⠙⠿⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⢾⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⣀⣤⣾⡿⠛⠛⠛⠿⠿⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⣀⡀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠊⢑⡀⠀⠈⠀⠀⢄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠐⠂⠿⠹⠂⠈⠂⠀⠀⢳⠤⡀⡠⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⠷⣶⡄⢀⡀⠀⠀⠀⠀⠀⡌⠀⠀⡘⠀⠀⠈⡀⢀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⢶⣶⣦⣀⣀⣿⣿⣿⣯⣿⣶⣦⡀⠀⠈⠀⡄⠀⠐⡊⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠠⠀⠂⠸⠙⠂⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⢠
⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⢻⣿⣿⣇⣀⣠⣼⣿⣶⣤⣀⠀⠀⠀⠀⣉⣀⠀⠀⠀⠀⠀⠘
⢾⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⢟⠉⢡⣴⠞⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠤⢄⡀⠹⡀⠀⠆⠀⢰⠇⠀⠀⠀⠀⢀⣀⣴
⠘⠁⠀⠀⠈⠛⢛⣡⠔⠚⠁⠞⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⣿⣿⣶⣿⣿⣦⠀⠁⠂⠀⣼⣶⣞⣿⣿⣿⣯⣿⠁
⠀⠀⠀⣼⡟⠀⠐⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣆⢽⢿⠏⡛⣿⡿⠀⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡷⠐⠘⠋⢀⣤⣸⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠛⠀⠰⠾⣿⣿⣿⣿⡿⢾⣫⠏⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡻⠟⠛⠉⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠒⠂⠀⠀⠀⢀⠀⠀⠀⠀⡀⠉⣉⠑⢤⢤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠲⠊⢀⣠⡶⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⣉⢀⣀⢀⣠⠠⣤⢤⣤⣈⡓⠄⠰⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠫⣿⠲⡮⣹⠣⣽⡑⣿⣺⠿⠿⢿⡆⠀⠆⢀⢠⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣽⣳⣼⠱⠶⠙⣓⣯⠕⠈⠀⠀⠀⠀⠹⠀⠀⠚⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣵⣾⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣯⣅⡢⢭⣉⢿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣠⣴⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⢀⠔⣡⣾⡽⠟⠉⠉⠀⠐⠚⠛⠛⠓⠲⢶⣿⣭⣭⣭⣿⣿⣿⣿⣿⠿⠿⠿⣻⣿⣶⣤⣀
⠀⠀⠀⠀⢐⣵⡿⠟⡉⠀⠤⠄⠖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⠻⣿⣿⣿⣇⠀⠀⠀⠀⠉⠉⠛⠳⠥⡀
⠀⠀⠀⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡸⣿⣿⣿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠑⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠠⠀⠀⠂⡀⠙⢇⣿⣿⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠚⠁⣠⣾⣿⡇⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣆⣀⣠⡴⠞⠛⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣾⡿⠉⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠛⠒⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠶⠒⠚⠛⠛⠛⠒⠒⠦⣄⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⣀⣠⣤⠤⠤⢤⣤⣀⡈⢳⡄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⡴⠋⠁⣀⡀⠀⠀⠀⠀⣀⢍⡛⢷⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠻⣦⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣧⠀⠀⣶⡄⠀⠀⠀⠀⢰⣦⠀⠀⠀⠣⣼⠙⡇
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣽⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠃
⠀⠀⠀⡯⠭⢍⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢰⠤⠤⠤⠤⢴⠀⠀⠀⠀⣼⠓⠋
⠀⠀⠀⢧⣀⣠⠾⣟⢦⡀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠢⣀⣀⡠⠊⠀⠀⠀⡴⠃
⠀⠀⠀⠀⡀⣁⠀⠘⢧⡙⣄⠀⠀⠀⠀⠀⢀⣈⣷⣄⡀⠀⠀⠀⠀⣀⡤⠾⣥⡀
⠀⠀⠀⡰⠿⠿⢦⠀⠀⠙⢾⣆⣀⣀⣀⣾⠉⠁⠀⠀⢹⣛⢛⣛⡿⠉⠀⠀⠀⠉⢳⡄
⠀⠀⡞⠁⠰⣿⡎⢷⠀⠀⠀⠸⡉⠉⠉⠹⣄⣀⣼⠃⠀⠉⠉⠉⠀⠀⠓⣦⣄⣠⠞⠛⢦⡀
⠀⣸⠃⠀⡀⢀⠀⠘⡷⢄⠀⠀⡇⠀⠀⠀⠉⠀⣾⠀⢀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⢻⡄⠀⠀⣀⡀
⠸⣸⡇⡜⠅⠀⢑⢀⡇⡰⠃⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠑⢄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⢃⡤⠚⢣⡹
⠀⢺⣇⠁⠀⠀⠁⣸⢣⠁⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠃⠀⠀⣧⠀⠀⢀⡤⠴⣟⢉⡵⠚⠁
⠀⠀⠹⡄⠀⠀⢠⡯⠂⠀⠀⠀⡌⠀⠀⠀⠀⠀⢳⠤⣤⣤⣤⣤⣤⣤⠤⣾⢀⠠⢚⣷⣀⡼⠁
⠀⠀⠀⢹⣄⣤⡏⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣸⠀⠀⠘⡔⠀⠀⡀⠔⣋⠄⠒⠇
⠀⠀⣰⠋⠁⠀⠉⢳⡄⠀⠀⣸⠀⠀⠀⠀⠀⠀⣿⠀⣀⠄⣛⡃⡄⠀⠀⢽
⠀⠀⠷⠴⠖⠒⠲⠶⠇⠀⠀⡇⠀⠀⠀⣠⣤⡰⣿⠙⠈⢉⡟⡇⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡴⠁⠀⠀⢸⠀⠀⢸⠁⢿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⣼⠀⠸⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⣀⣤⣬⣇⡀⡇⠀⠀⢷⠀⢸⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⡇⢼⣅⣀⣈⣀⣽⠇⠀⠀⠸⣖⠛⠙⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⡼⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠒⠖⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠠⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠰⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠁⣴⠞⠁⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣧⣤⣠⠄⠀⠀⠀⠀⠰⡖⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⢁⠀⣸⠀⠀⠀⠀⠀⢸⣇⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⢉⣧⠀⠀⠀⠀⠀⣸⠟⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣿⠀⠘⢀⠀⠈⣿⠃⠀⠀⠈⢻⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⣿⠀⠀⠋⠉⠑⣏⠀⠀⠀⠀⠘⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⠀⠀⠀⠀⠀⠈⣶⣄⠀⠀⠀⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣮⠟⠑⠛⠣⠙⢿⡛⠛⠓⠛⠛⠛⠒⠈⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣀⠀⠀⠀⣀⠈⣷⣄⠀⣀⡀⠂⢀⠁⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⠿⢿⣿⣿⣿⠭⠿⣿⣿⠿⠿⠿⠿⣷⠘⣷⠀⠀⠀⠀⠀⠀⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⢠⡏⢀⡿⠀⠀⠀⠀⠀⠀⣿⣤⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣋⣁⣀⣒⣂⣀⣄⠀⠀⠀⠀⣀⠞⠋⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢘⡏
⠀⠀⠀⠀⠀⡀⣠⡤⠶⢿⣉⣉⣉⡉⠤⠉⡉⠉⠙⠛⠒⠒⠛⣿⡀⠘⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢸⠀⠀⠀⠀⠀⢀⣤⣴⣤⣼⡃⠰⣷
⠀⣀⠀⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠷⢦⣀⣀⣀⣠⡴⠛⢩⡍⢀⣀⠀⠀⡟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡃⢸⠀⠀⠀⠀⢰⠏⠀⢀⡀⠈⠟⠒⣼
⢆⠉⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠹⠃⠀⠂⠀⠀⠀⠀⠀⢇⠀⠀⠘⠃⠈⡿⠿⠃⠀⠠⠀⠉⠀⢸⠀⠀⠀⠀⠘⣄⠀⠉⠁⠀⣆⢸⣿⡄
⠀⠈⠛⠴⠤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⠦⠈⠛⠋⠺⠆⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠳⠶⠶⠛⣧⠈⢛⡅
⠀⠀⠀⠀⠀⠀⠈⠻⠛⡿⠛⠛⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠴⠤⠄⠀⠀⠀⠠⠤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢻⡄
⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⣾⣯⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢞⣳⣽⣯⣽⣇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠂⠄⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣞⠁⠁⠢⠉⠂⠄⠢⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⢳⣄⠐⢀⠀⠄⠠⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⢆⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⢑⣦⡤⠶⡷⠿⡷⠟⢺⠛⠳⠶⢶⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⣴⠞⠋⠉⠀⠘⠀⠀⠀⠀⣼⠃⢱⠤⢯⠀⣸⡟⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⣩⣳⡈⠀⠀⠀⣠⠊⠳⠄⣸⡷⢤⣵⣤⣶⠟⠉⢷⠀⠀⠉⠲⡀
⠀⠀⠀⠀⠀⢠⣟⢀⣐⣬⣳⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⣤⠟⢷⡀⠀⠀⠀⠀⣾⣾⣍⠀⣘⣇⢠⡏⠐⠒⣼⠃⣠⣤⡄⠹⡆
⠀⠀⠀⠀⢀⡿⠀⢀⡀⠈⠙⢷⣄⡀⠀⠀⢀⡴⣏⢧⡖⣋⡤⠞⠛⣧⠀⣀⣨⢥⡟⠀⠌⠹⣄⣸⡾⠷⣄⣰⠏⠘⣡⠶⠶⢤⡹⣄
⠀⠀⠀⠀⣸⠃⠀⠀⠀⡀⠀⠈⣹⠋⡾⢻⠃⠱⡜⢆⢻⣡⠴⠖⠋⢹⡇⡿⢀⢀⠙⣦⡠⢢⣻⣉⢱⣤⠌⢳⠀⠀⣷⣦⡀⠀⣷⠈⠙⠦⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⡇⢸⡀⠀⢱⠘⡆⢷⠶⠖⠛⠛⣧⢘⣦⣅⣳⣮⣻⣮⣿⣿⠶⢷⣌⡿⠀⠀⣿⣿⠇⣠⠏⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⡀⠄⠘⣧⢹⡀⢳⡀⢸⢇⡇⢸⠖⠒⠒⠺⣿⡏⠀⠀⠈⢉⠭⠿⢛⣗⠸⠂⣘⣷⣀⠀⠈⠛⠚⠁⣤⡀⠀⠀⣸⠇
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣳⣜⡇⡞⡼⠀⡼⠒⠲⠦⣖⡏⢷⡀⠀⠤⠀⡠⠂⣼⠉⠻⣶⣁⣸⡏⢳⢦⡀⠀⠀⠈⢿⠛⠋⠁
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠙⠻⣾⡁⣴⡛⠒⠦⣤⣼⠃⠈⠳⣤⣔⣀⡤⣾⡃⠳⠊⢸⣯⠛⢷⡎⠈⢳⡄⠀⢀⣨⠧
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠙⠧⣝⠲⣤⣼⠏⠘⢁⣀⣹⡦⠬⣀⣿⠷⣦⣁⢀⡟⢰⡈⢿⢉⣩⡷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣴⣀⣀⣀⣸⣧⡶⠟⡁⠠⠄⠙⣏⣁⣬⠵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠛⠻⠲⠶⠶⠷⠶⠛⠚⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠞⠳⠦⠤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣅⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠻⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠂⠀⠀⠀⣠⠔⠋⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⣴⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢡⢾⠉⠉⢁⣲⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠦⣔⡏⠀⠀⠈⢛⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣱⣽⠃⠀⠀⠀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠐⠀⠀⠀⢰⣶⣿⠃⠀⠀⠀⢸⡿⠿⢿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡗⠒⡖⠀⠀⠀⠀⠀⢀⢨⠟⠁⠀⠀⣀⣐⣺⣿⣶⣿⣿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢿⣿⣿⣶⣤⣄⣠⡾⠋⠀⠀⠀⠰⢠⣿⣿⣿⣿⣿⡟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⣜⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⡟⠀⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠫⠿⣿⠁⠀⠀⠀⠀⢀⢢⣷⣿⣿⣿⣿⣿⣿⡿⣛⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⡂⠀⣴⠃⠀⠀⠀⠀⣤⣾⣼⣿⣿⣿⣿⣿⡿⢫⠾⠛⠈⢀⡄⠀⠂⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡟⡿⠀⠀⣿⠀⠀⢀⣰⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⠣⢀⣀⠀⠈⠂⢀⣾⣿⣿⣿⣿⡿⢟⣛⡳⣿⠃⠀⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⣾⠟⠋⠙⢿⡿⢐⣛⣻⣏⣼⠀⢠⡿⠟⠛⡄⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢻⠀⢀⣐⡄⢠⣿⣷⠀⣇⠚⣽⢿⣿⣿⡄⠈⠃⢾⡷⠀⣴⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢪⣾⣿⣧⠈⠋⠁⣀⣜⣦⡻⠟⡫⠤⠀⠀⠀⡀⡀⣄⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠐⠙⢿⣦⣽⣿⣿⣷⣦⣤⣈⠻⠿⠇⣈⣡⣤⣶⣦⣄⣘⢿⣿⣿⣿⣿⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠦⣝⣿⣿⣿⣿⣽⣿⣿⣿⡟⠛⢉⣁⣤⣿⣿⣿⣿⣿⠋⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠾⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠛⠛⠛⠛⠿⠯⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿