⠀⠀⠀⠠⠒⡐⢡⡏⢌⡒⢍⠣⢠⣷⢈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡘⠷⢋⣿⣜⡺⣝⡣⣝⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢆⡉⠲⣉⡰⢻⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡳⢎⣍⠿⣵⢎⡵⢎⡳⢥⡳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⠢⡜⠆⡩⡔⠸⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣮⣍⠳⢯⣼⣛⡲⣝⡳⣎⡱⣹⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠒⣉⢤⡙⠦⣉⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⡹⢳⢯⣏⡹⢷⣏⠝⣮⡝⡹⢽⣻⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⢃⣌⠓⢣⡑⢈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠞⡿⢭⣳⣹⢶⣻⣜⣻⢮⣹⣿⣟⡾⣿⣿⣶⣽⣳⣧⣊⢵⠮⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢡⡜⠣⢡⡰⡜⡌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢢⢣⣕⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠧⡤⣜⢣⣜⡳⢬⢻⣭⡶⡝⣮⠽⣻⢿⣿⣿⣾⣻⣼⢾⣻⣭⡳⢬⢳⣌⠳⢦⡙⣣⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⡙⢣⡰⡜⠎⢈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢃⡱⢞⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢠⡄⠀⣀⡄⣄⣦⡟⣿⣿⣿⣷⣞⣯⣜⢻⣧⣜⠾⣋⠵⣎⠳⣌⡹⢦⡘⢹⡱⣜⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡤⠚⢡⡴⠎⢃⢤⡘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠍⢢⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣷⣞⣫⡵⢞⣭⡞⢭⡶⢏⢥⡳⢎⢣⣖⡙⢦⣙⠴⡹⠖⢋⣤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⣈⡵⢊⢱⣎⠑⣦⠀⠀⠀⠀⠀⠠⠄⠣⠑⠀⠃⢮⡍⠆⢣⡔⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣵⣟⣳⣬⡞⢣⢧⣜⡻⢧⣛⢧⣓⣮⢓⣣⠴⣋⢡⡴⡙⢦⡙⡴⡓⠴⢏⣃⡤⠹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢓⣌⠳⣔⠪⢝⡡⡜⢱⠀⠀⠀⠀⠀⠀⠀⣹⢿⢥⢌⠲⣄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢖⣤⣀⠀⠀⠀⠀⠀⡅⡒⢯⡒⣹⡷⢏⣡⠲⣌⠐⡰⡌⠑⢦⠃⣡⠲⣍⠢⢱⣎⡉⢳⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠲⣌⡱⡞⢇⡌⠳⡜⡇⠘⠀⠀⠀⠀⠀⠀⡇⢡⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⢋⣴⡻⢭⡱⡔⠀⠀⠀⠀⠀⡀⠀⢠⡐⠢⢑⣨⠳⢆⡙⡠⢻⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢏⣉⡼⡙⢻⣌⠻⡜⡘⢻⠀⠀⠀⠀⠀⠃⢻⣀⠀⠀⠀⠀⠀⠀⠀⠁⠃⡀⠘⠃⠡⠃⠄⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣩⡿⢏⡹⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡛⠅⢣⡘⢣⣌⠹⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣖⠎⣎⡙⢦⡙⠴⢏⡆⠈⠀⠀⠀⠀⡆⡑⠀⠀⠀⠀⠀⠀⠀⠂⡡⠄⠊⢁⠰⡌⠃⠠⢐⡉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡄⣎⡙⢦⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠰⢎⡡⢜⡎⠘⠀⠀⠀⠀
⠀⠀⠀⠁⠉⠛⠴⣠⣀⠠⠀⣾⢃⡰⢞⢎⡱⢮⡙⣦⠚⣍⢱⠀⠀⠉⠒⣽⠨⠀⠀⠀⠁⠂⠌⠣⢌⠣⣂⠑⢢⡌⠒⢁⡠⠔⠈⡐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡟⣀⠀⠀⣓⢬⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⢢⡌⠜⢧⠈⠀⠀⠀
⠛⠯⣲⣽⡴⣤⣤⣤⠤⠐⠀⣻⢌⡳⢎⣇⡙⢦⡙⢳⢬⡞⡇⠞⣡⠋⡗⠸⢘⠣⣀⠜⢃⠤⢃⠥⠆⢈⡰⠚⢠⡜⠃⢠⡔⠊⢀⡐⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡏⢁⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢆⡉⡰⢱⠀⠀⠀
⢠⢋⡼⢀⠀⠀⠀⠀⠀⠀⠀⢽⡣⢆⡜⢫⡱⢮⡜⠳⡵⢎⣣⣾⡞⡛⣿⠆⣈⠱⢢⡑⢊⣐⠬⡑⠣⢄⡩⠆⢂⠠⢑⡠⠌⠂⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢡⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⡱⡆⠸⠀⠀
⡝⡾⢀⠀⠀⠀⠀⠀⠀⠊⠠⣻⠥⣪⡝⢎⡱⢞⣍⡱⡳⢎⢣⣾⢶⣿⠱⢣⢆⡉⠥⠢⢆⡉⢆⡈⠐⠤⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡉⠠⢷⠀⠀
⡽⢸⠀⠀⠀⠀⠀⠁⡐⠁⠖⣿⢋⢦⡙⢦⣙⠶⣋⡴⠻⣌⢳⢾⠿⣽⠣⢡⢒⠤⡒⢉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⡆⠘⠀
⡿⢀⠁⠉⠓⠛⠟⢶⠿⣳⣼⣆⢛⢦⣙⢦⡹⢶⢫⣵⠮⣝⡯⣞⡿⢡⡰⡙⠦⣁⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢰⠀
⣿⡿⣞⣪⣤⢀⠠⠏⣗⡯⢋⡾⢻⣣⡜⢮⣙⡶⢎⡳⣏⠧⣟⣯⢾⣉⡰⠙⢢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡⠀
⣾⢃⡠⠀⠀⡄⠏⣽⡿⣞⣫⠟⣷⢺⡵⢚⣱⡼⣛⢧⡱⢿⣿⣿⢎⢑⡬⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⠃⣞⠸⠀⠀⢣⢯⣹⢷⣾⢳⣻⣷⢽⣣⡜⣳⡜⢻⣭⡿⣿⣮⢷⣈⠳⣅⠢⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⠷⣮⢟⠀⠀⣿⢳⣭⡿⣯⣵⣟⣯⡲⢹⣳⢮⣝⠯⣿⣵⢪⣜⠳⣄⠳⣈⠱⠀⠀⠀⠀⠀⠀⡔⣴⣶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣯
⣟⣭⣞⠸⠀⣼⢻⣴⣿⣽⣯⡞⣿⣧⡜⢻⣧⡟⣶⢋⢱⢪⣕⠣⣄⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡽⢟⣮⣟⡏⣽⣸⠇⣼⡟⢳⣯⢾⣹⡷⢏⣾⣹⢧⢃⡱⢎⡡⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱
⡷⢏⣳⢯⣶⣿⠀⡽⣾⢳⣯⣟⣵⡞⢫⣾⢞⡡⠶⣀⠦⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀
⡽⣳⢯⣱⣾⣟⠹⣳⣿⣛⢾⡿⣧⡜⢿⣼⢛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀
⣞⣺⡽⣞⡯⢗⣮⣿⣌⠾⣟⣼⢻⣧⣟⣸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀
⣽⣾⣛⢧⣝⡳⢯⣟⢦⣽⣣⣤⣶⣬⣿⢿⣎⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⣒⢽⠿⣹⣾⣝⣻⢶⣟⡾⣠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠋⡾
⣎⡽⢞⣳⡿⣣⣔⠋⢤⡘⠲⣉⠴⢎⡑⣦⢿⣜⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠖⡵⢢⣿⡽⢟⣫⡽⣿⣩⠛⡿⣞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⡾⢀
⣿⣶⣏⣾⣉⠱⢢⢑⣨⠜⢢⡒⡍⠆⡐⢜⡩⣶⡼⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠴⣟⡽⢿⣿⣾⣥⣋⠷⣭⣞⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢯⡴⠋⡟
⣭⣷⣟⢬⡑⠢⣄⠒⢄⡐⢣⢄⠸⣍⡆⠌⡓⢃⣄⣳⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣢⡜⡟⣿⣤⢋⢿⣳⢼⣻⢯⣾⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⣿⣴⢀
⣏⡱⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠢⣐⠸⣇⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠚⠗⠵⣣⣜⢋⢦⣙⡷⢔⡿⣞⢫⣼⡟⢯⣿⢶⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢷⣴⢀⠀⠀
⣏⡱⣿⢬⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⡙⢦⠙⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠝⡪⣵⢎⢣⡕⢩⡻⢍⡻⢛⣭⡝⣯⡾⣹⡷⢏⣳⢯⣿⣚⣼⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀
⢧⡹⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡳⠻⠀⡀⠘⠀⠀⠀⠀⠉⠛⠟⡶⣞⡵⠶⠮⣥⡴⣎⣡⣰⣎⡑⣌⠲⣌⣌⣮⣷⣽⡹⢺⣿⡿⣽⢻⣾⣵⣲⡤⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀
⢿⡿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠁⠿⣰⣸⢇⡀⠸⢇⡀⠶⢁⡰⡏⠀⢰⡶⠇⠆⡈⠾⢁⢈⢷⡀⣶⡿⢇⣸⢿⣿⢿⠿⢿⠾⣶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⡏
⣽⢯⢿⡓⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠎⣤⢀⡠⠄⢀⡰⠆⢈⡱⢌⡘⠬⠓⣂⡑⢊⢡⢎⡄⠓⢢⡌⠒⣡⡜⡆⣽⡾⢏⡹⣿⣯⠽⠿⠽⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠁⠋⠖⡰
⣌⠷⣝⡻⣆⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⡠⠐⢠⠤⣀⠠⢄⡀⢀⠠⡀⢆⣏⡾⣛⡶⣟⢷⣯⢻⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣷⣍⣿⣏⣿⣴⡁⠊
⢿⠈⡢⣬⢷⡍⣵⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠷⣙⣼⡿⣻⢯⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⡻⣞⡧⣭⢄⠦⢳⠛
⡽⢿⠻⢌⠱⣄⡳⣿⣌⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡵⡟⣎⡿⣹⢿⣿⣿⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⡀⣀⠀⠤⠒⠑⠂⠀
⡷⣞⣽⣿⢿⠿⠚⣯⠉⠈⢦⢌⠳⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣻⡵⠻⣿⢿⣿⣵⣞⢾⣏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⡇⢳⠀
⠀⣳⣥⣤⣖⣖⣯⣯⢿⣳⣽⣟⢯⢷⣛⠼⠲⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠟⢯⣾⣻⣿⣶⣱⢭⣾⣟⢷⣮⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢲⠒⠁⠈⠀⠀⠀⠁⡟⡴⠀
⠑⡄⢹⢄⠺⠙⡀⢧⣸⣖⡙⣄⣕⣬⣲⣶⢷⡛⣝⣦⠒⠽⠚⠈⠀⠀⠀⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠋⠛⠟⠿⠀⠁⡔⠀⠀⠀⠟⡿⣿⢾⣴⣫⢟⣪⣷⣎⣝⠯⢻⣶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡀⠄⠋⠖⣠⢀⠀⠀
⠀⢄⡗⠹⡀⠷⣌⠳⣏⠈⡄⠢⠈⣀⠢⠈⠀⠀⡀⣂⢿⠿⡙⣮⢗⠐⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⡀⠤⠀⡖⡲⢴⢄⡠⠀⠁⠊⠟⣴⣯⣳⢟⡾⣷⣥⣮⣬⢷⣲⣙⢉⠢⠐⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡀⣁⠎⣐⣤⢀⠀⠀⠀⠀⠀
⢀⠒⠈⣄⣳⣭⣳⣍⡱⢿⠑⠀⣆⠻⠛⡐⢣⠈⠀⠀⡀⣕⡳⣼⢼⠓⠈⠀⠉⠉⠉⠀⠀⡀⠠⠑⠀⠀⠀⠀⠀⠁⠉⠉⠛⠞⡰⢤⣪⢃⡴⢣⣿⢣⡤⠚⢡⠦⢍⡡⢎⡃⢃⣡⠦⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢴⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢄⠑⣌⡵⢦⡹⡜⢻⣇⣬⣿⢷⣯⠷⡯⠻⠈⠀⡀⡱⢸⣽⠩⣩⢍⣋⠛⢃⣙⢬⠒⠙⠉⠠⣹⣛⣽⣀⣞⣾⣠⢀⠁⠜⣠⠎⢀⡇⡆⣽⠡⢠⠴⣊⠥⡑⠢⢘⢣⡑⠢⢌⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⣷⡄⠹⢆⣮⡟⢹⣧⣟⡜⢻⣼⢿⣯⣿⠻⠀⡄⠁⣿⣿⡽⣎⡇⠳⢆⡘⢮⢚⢏⠉⣭⡉⡦⢵⣿⠇⢻⠜⠎⢠⠀⠏⢈⠀⠀⢦⣏⠈⣀⢀⠦⡑⠩⢌⡡⠰⠬⡓⢇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢧⡈⠢⡈⡑⣦⠸⣇⢸⣏⡿⢣⣿⣾⢿⢧⠈⡏⣿⣻⣷⢚⣌⠱⢨⠵⢊⡕⢋⣳⡜⣿⣿⣿⣧⡻⣎⣿⠀⠀⠃⢻⢦⠈⠀⠀⣄⢳⠈⠀⠀⠀⠀⣀⢇⡠⡜⠆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢆⠨⠆⡘⠡⠆⠈⣯⢃⢷⣭⡿⢼⣸⠀⢷⣿⡿⣿⣿⢾⢎⡡⡔⠫⢞⣶⡖⢻⣻⣿⣏⣧⣛⣷⣿⢿⢝⠲⡄⣶⢿⡙⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡐⢎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⣆⠘⢃⢡⠇⡆⣿⢻⣿⢧⣀⢦⡟⣽⣿⣟⣿⢺⢆⣋⡴⢀⠀⠀⠀⠀⠀⣀⣄⣤⡖⣻⣿⣿⣿⣻⠿⡗⠿⡳⣹⣍⠬⠫⠓⠛⠋⠚⠙⠉⠀⡄⡹⠄⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⡇⢼⣈⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⣿⠀⣆⠘⢱⢳⣿⣨⢸⠁⠄⣿⣿⣿⣿⣿⢿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣾⣿⢿⣌⡻⣍⣷⣿⣶⢿⡈⣦⣻⣰⢟⣦⠿⡠⠲⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢺⣧⢻⢁⢢⡈⢖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣥⠐⠀⢃⡆⡿⣿⢇⠀⠀⣇⣼⣷⣿⣿⣼⢀⠀⠀⠀⠀⠀⠉⠒⠐⠒⠂⠙⠀⠀⠀⠀⠀⡀⣷⢿⣿⢿⡀⣷⡻⣯⣿⣿⢻⣆⣟⡏⢹⠀⠏⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠐⠠⠈⠀⠄⡀⠌⡐⣷⡥⢺⠱⢌⡐⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠱⠀⡀⠘⣧⣿⡆⠀⠁⣿⣿⠸⣇⣿⢸⠀⠀⠀⠀⠞⡀⠁⠈⠒⠄⡠⣀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⠾⡈⡥⠵⣿⣿⣷⠸⣇⣿⣄⠟⢠⠀⠀⠀⢱⠀⠀⠀⠀⠀⠂⡁⢂⠀⢀⡀⠀⠂⣁⡆⣹⢾⠘⢣⣃⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠰⠀⢇⡄⣿⠀⠀⡿⣿⣿⣿⠈⣷⢹⠀⠀⠀⡄⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠈⣆⣿⢻⢃⡀⡶⡟⣿⣻⣽⡇⢸⠏⢸⠀⠀⠀⠀⡆⠈⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⠰⣇⢿⣂⠜⠩⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡄⠘⠀⠰⣿⠀⠀⣿⣴⢡⡀⢱⡆⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠋⠽⣤⣧⢿⣿⣿⡨⠸⠆⣟⢺⢳⣷⡟⣿⢠⢰⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠠⣯⠱⢎⡁⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢃⠀⠀⣧⠀⡇⣰⠟⣾⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⠀⠀⠀⠷⣾⣿⣿⠿⣿⣿⣿⣿⢿⡇⠀⣧⢼⡇⡾⣃⣸⡎⠄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣇⡸⠜⣊⠠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⡄⠸⡇⠸⢧⢺⠙⡄⢸⡆⢸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠋⡟⣾⣿⣷⣼⣼⣿⢰⣿⣼⣏⠈⢱⡀⢸⡇⢸⡏⠃⢀⠠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⣸⠝⢂⢨⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⢸⡄⣿⢿⢿⣿⠈⢸⠃⣾⣤⣿⣿⣿⣿⠟⢹⠃⠉⡿⣾⣿⣴⢻⣷⡼⠀⡿⣾⠀⣿⢠⣇⢸⡇⠀⢸⡆⢇⡏⣸⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢩⣷⠑⢢⡔⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢇⠀⣧⡿⣽⣿⢿⢾⢿⣿⠿⣿⣿⣶⣶⣶⢠⣿⡇⣿⢑⣿⠀⣿⡇⢡⠉⣿⢼⣀⣿⠀⡆⢹⠀⢰⠄⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡧⡜⡉⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡆⠀⡄⣿⣿⣧⣷⢸⣀⣇⣤⣠⣀⠀⠀⠀⡎⣸⡞⣼⡀⣿⠀⣇⡇⡀⣀⣿⢀⠀⣰⠀⠀⣿⠀⠀⡄⠀⢚⢸⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢚⣠⡜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⣧⢸⢣⢆⢸⢘⡆⢸⠀⠀⠀⠄⣀⡅⠛⢼⢠⠀⢼⢣⡆⡇⠀⠀⣇⠀⠀⠀⠀⠀⡇⠀⠀⡈⠁⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣍⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡀⣇⡀⡰⢰⠀⠀⣿⠪⠈⠀⣀⣀⡀⠈⢱⠀⠀⣄⠀⢫⡀⠀⠀⡂⠀⠀⠀⠀⠀⡃⠀⠀⢰⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠰⣘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢡⡀⠗⠀⠀⡆⡘⣄⠰⠉⠀⠀⢸⡆⠀⠀⡄⠀⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢦⡉⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⡀⠡⡄⠘⠀⠀⢣⠀⠀⠀⢄⠙⡆⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠀⠊⡰⠀⠃⢀⠁⠰⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⡈⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠀⠢⠆⠈⠀⠀⢣⠀⠀⠀⠄⠧⠸⠀⠀⠀⠀⠀⠀⠀⠁⢘⠀⠁⠀⠁⡸⠀⡘⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠥⢈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠑⠀⠀⢂⠈⠀⠀⢢⠈⠀⠀⠀⣤⠈⠀⠉⠈⠐⠠⠄⢀⠰⠀⡰⠁⡼⠀⡐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⠂⢢⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⢈⠑⠀⠄⠐⠀⠀⣄⠑⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⡆⠀⠀⠃⡼⠀⠀⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠌⡱⢆⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠁⠀⠀⠠⠀⠀⠀⢄⠳⠈⠀⡄⠑⠀⠀⠀⠃⢠⠁⠞⣠⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠜⠪⢆⠈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠌⠀⠀⠀⠀⡀⢤⠲⠒⢐⠀⠄⢤⡤⣡⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣤⠚⢆⢃⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⠀⠒⠐⠀⠄⡀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣻⣱⠆⣈⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣇⢾⡱⢆⡌⠒⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀