⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⠔⠁⠀⠈⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⠔⠀⠒⠤⠒⠛⠳⢄⠀⠀⣀⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⡤⠐⣁⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠙⡆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠠⠞⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣾⠀⠀⠠⠀⠀⠀⣶⠀⠀⠀⠀⠀⡢⠠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡔⠁⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⠀⠀⠉⠀⠀⠀⠀⠐⠌⠀⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡗⠀⠀⠀⠀⠀⠀⢈⢻⠄⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠤⠤⠤⣼⣀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠑⢒⡒⠒⠈⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠁⠀⠀⠀⠀⠀⠉⠢⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡶⠒⠒⠒⠶⠤⣀⣀⡄⠀⠀⠉⡗⢦⣄⣀⣀⡀⠀⢀⣀⣤⠔⠋⠒⢤⣀⠀⠀⠀⠀⠀⣡⠏⠀⢈⡗⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀⠃⣜⠣⢎⡭⢭⡙⠯⣍⠳⢬⡙⣄⠀⠀⠙⠻⠶⠶⠒⠋⠁⠀⠀⣼⡘⠧⡜⣩⢓⣦⣀⠀⠀⠀⠀⠀⠀
⠀⡝⠋⠉⠉⠑⠒⠦⣤⠆⠐⠋⠀⣏⡙⠶⣘⠦⡹⢜⢢⠛⢦⡙⣬⠛⡶⣤⣀⡀⠀⠀⠀⢠⡴⣞⢣⡹⢜⡡⢇⡣⢖⡩⠷⣄⠀⠀⠀⠀
⠀⢆⠀⠐⢄⣀⠀⣀⡰⠀⡰⠁⣸⢥⢋⡎⡕⢮⠱⢎⢣⠛⢦⡙⣤⠛⣔⠣⣍⠇⠀⠀⠀⠈⡖⡱⢎⡴⢋⡼⢌⡵⢊⡵⢣⢍⡳⣄⠀⠀
⠀⠀⠉⠒⠤⠤⠭⠭⣴⠋⠀⣰⢏⠦⣋⠴⡙⢦⠛⣬⣧⣿⠷⣉⠦⡛⣌⠳⣌⢻⠀⠀⠀⠀⠸⣑⠮⡔⣻⡜⡬⠲⣍⠲⣍⢲⠱⣙⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠺⠾⠥⠯⠝⠒⠛⠉⢹⢆⡣⣍⠶⡙⡴⢋⡴⢋⡆⠀⠀⠀⠀⡇⢞⡱⣌⡷⡑⢯⡶⣩⢒⡍⢞⡡⢏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢎⡱⢜⠲⣉⠶⣉⠶⣉⠇⠀⠀⠀⠀⢘⡣⢖⠬⣻⣹⡟⡱⢆⡫⢜⢪⡱⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡹⢌⡳⣉⠶⣉⠶⣉⠆⠀⠀⠀⠀⢸⡔⢫⡜⣼⡟⡜⢥⢣⢣⢋⡖⣱⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣥⠫⣔⢣⢣⡍⠶⣉⠾⠀⠀⠀⠀⢸⡜⣥⡾⠛⢧⣙⣎⠲⣍⢲⣩⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⠺⠶⣧⣼⣣⣍⣾⠀⠀⠀⠀⠀⠋⠁⠀⠀⠈⠉⠉⠛⣴⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣟⣹⠀⢠⡔⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠢⢏⣛⠶⣦⣤⣤⣄⣤⣤⣤⣤⡶⢶⡛⢯⣙⠲⣡⠾⡄⠀⠜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢳⣉⠦⣋⠴⣊⠖⣩⢆⢳⡘⢦⡙⢦⣙⠲⣌⠳⣡⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⡲⢌⡣⣍⠶⣉⠞⣡⠞⣢⣿⢣⢚⢥⠪⣕⠪⡕⢣⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣘⠲⡍⡖⡜⡲⣉⢮⡑⣎⡿⣑⠮⡱⢪⢕⠪⣕⡩⢇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢎⠵⡚⡜⡴⢣⢍⠦⣓⡾⢿⣘⠲⣍⢣⢎⠳⣌⠶⡩⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡱⢎⢣⡕⠳⣌⡓⢎⡵⣺⠁⢸⣌⢳⡘⢦⡙⠮⡔⣣⠝⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡖⢭⢲⡘⡳⠬⡜⢣⢲⠇⠀⢸⡎⣕⠪⣕⠪⢇⡳⢌⢞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠱⢎⡣⢖⡩⢖⡹⣘⢣⡟⠀⠀⢸⡳⢌⡳⢬⡙⢦⢃⡏⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠫⢖⡩⢖⡩⢖⣡⠓⣾⠁⠀⠀⢸⡣⣍⠶⡑⢮⡡⢏⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣌⠳⣉⠶⣉⠶⣉⠦⣻⠃⠀⠀⠀⢸⡱⢜⠲⣙⠦⡱⢎⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢌⡳⣉⠶⣉⠶⣉⣶⠏⠀⠀⠀⠀⢺⣵⣍⣞⣡⣞⣱⣎⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣥⣷⣭⡶⠛⠁⠀⠀⠀⠀⠀⠘⠿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ si

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⠔⠁⠀⠈⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⠔⠀⠒⠤⠒⠛⠳⢄⠀⠀⣀⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⡤⠐⣁⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠙⡆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠠⠞⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣾⠀⠀⠠⠀⠀⠀⣶⠀⠀⠀⠀⠀⡢⠠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⠀⠀⠉⠀⠀⠀⠀⠐⠌⠀⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡗⠀⠀⠀⠀⠀⠀⢈⢻⠄⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠤⠤⠤⣼⣀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠑⢒⡒⠒⠈⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⠀⠀⠀⠀⠀⠉⠢⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡶⠒⠒⠒⠶⠤⣀⣀⡄⠀⠀⠉⡗⢦⣄⣀⣀⡀⠀⢀⣀⣤⠔⠋⠒⢤⣀⠀⠀⠀⠀⠀⣡⠏⠀⢈⡗⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀⠃⣜⠣⢎⡭⢭⡙⠯⣍⠳⢬⡙⣄⠀⠀⠙⠻⠶⠶⠒⠋⠁⠀⠀⣼⡘⠧⡜⣩⢓⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⡝⠋⠉⠉⠑⠒⠦⣤⠆⠐⠋⠀⣏⡙⠶⣘⠦⡹⢜⢢⠛⢦⡙⣬⠛⡶⣤⣀⡀⠀⠀⠀⢠⡴⣞⢣⡹⢜⡡⢇⡣⢖⡩⠷⣄⠀⠀⠀⠀ ⠀⢆⠀⠐⢄⣀⠀⣀⡰⠀⡰⠁⣸⢥⢋⡎⡕⢮⠱⢎⢣⠛⢦⡙⣤⠛⣔⠣⣍⠇⠀⠀⠀⠈⡖⡱⢎⡴⢋⡼⢌⡵⢊⡵⢣⢍⡳⣄⠀⠀ ⠀⠀⠉⠒⠤⠤⠭⠭⣴⠋⠀⣰⢏⠦⣋⠴⡙⢦⠛⣬⣧⣿⠷⣉⠦⡛⣌⠳⣌⢻⠀⠀⠀⠀⠸⣑⠮⡔⣻⡜⡬⠲⣍⠲⣍⢲⠱⣙⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠺⠾⠥⠯⠝⠒⠛⠉⢹⢆⡣⣍⠶⡙⡴⢋⡴⢋⡆⠀⠀⠀⠀⡇⢞⡱⣌⡷⡑⢯⡶⣩⢒⡍⢞⡡⢏⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢎⡱⢜⠲⣉⠶⣉⠶⣉⠇⠀⠀⠀⠀⢘⡣⢖⠬⣻⣹⡟⡱⢆⡫⢜⢪⡱⢺⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡹⢌⡳⣉⠶⣉⠶⣉⠆⠀⠀⠀⠀⢸⡔⢫⡜⣼⡟⡜⢥⢣⢣⢋⡖⣱⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣥⠫⣔⢣⢣⡍⠶⣉⠾⠀⠀⠀⠀⢸⡜⣥⡾⠛⢧⣙⣎⠲⣍⢲⣩⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⠺⠶⣧⣼⣣⣍⣾⠀⠀⠀⠀⠀⠋⠁⠀⠀⠈⠉⠉⠛⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣟⣹⠀⢠⡔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠢⢏⣛⠶⣦⣤⣤⣄⣤⣤⣤⣤⡶⢶⡛⢯⣙⠲⣡⠾⡄⠀⠜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢳⣉⠦⣋⠴⣊⠖⣩⢆⢳⡘⢦⡙⢦⣙⠲⣌⠳⣡⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⡲⢌⡣⣍⠶⣉⠞⣡⠞⣢⣿⢣⢚⢥⠪⣕⠪⡕⢣⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣘⠲⡍⡖⡜⡲⣉⢮⡑⣎⡿⣑⠮⡱⢪⢕⠪⣕⡩⢇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢎⠵⡚⡜⡴⢣⢍⠦⣓⡾⢿⣘⠲⣍⢣⢎⠳⣌⠶⡩⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡱⢎⢣⡕⠳⣌⡓⢎⡵⣺⠁⢸⣌⢳⡘⢦⡙⠮⡔⣣⠝⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡖⢭⢲⡘⡳⠬⡜⢣⢲⠇⠀⢸⡎⣕⠪⣕⠪⢇⡳⢌⢞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠱⢎⡣⢖⡩⢖⡹⣘⢣⡟⠀⠀⢸⡳⢌⡳⢬⡙⢦⢃⡏⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠫⢖⡩⢖⡩⢖⣡⠓⣾⠁⠀⠀⢸⡣⣍⠶⡑⢮⡡⢏⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣌⠳⣉⠶⣉⠶⣉⠦⣻⠃⠀⠀⠀⢸⡱⢜⠲⣙⠦⡱⢎⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢌⡳⣉⠶⣉⠶⣉⣶⠏⠀⠀⠀⠀⢺⣵⣍⣞⣡⣞⣱⣎⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣥⣷⣭⡶⠛⠁⠀⠀⠀⠀⠀⠘⠿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ si