⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⡤⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣽⣻⢷⡬⠦⣄⠀⠀⠀⠀⠀⠀⡀⠤⣟⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⢹⣏⡟⡳⣌⠳⡤⢤⠄⡄⢎⣥⣛⣯⢿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣧⣷⣼⠿⡍⢉⣡⣦⣭⠔⡊⠵⡝⣮⣟⡿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣆⢣⣭⣭⡍⢁⠐⢠⠀⠩⠍⡿⠿⡿⢇⠧⣏⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣸⢣⣤⣽⣿⣿⡇⢐⡈⠄⢨⣜⠷⠏⣿⣥⡇⡚⡵⣯⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⡆
⠀⠀⠀⠀⠀⠀⢀⣸⠆⣿⣯⣹⠿⡍⡐⢠⢐⡈⢼⣿⣶⣶⣿⣿⡧⣃⠷⣗⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣺⣇
⠀⠀⠀⠀⠀⠀⢸⡦⡙⡬⣍⣋⠒⡰⢉⠖⢪⠐⠮⡿⣿⣿⣉⡿⢧⢏⠺⣵⣻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢆⡾⠯⠉
⠀⠀⠀⠀⠀⠀⠸⢵⡳⡰⣡⢆⡹⢰⣩⣼⠡⢎⡱⡘⢯⡝⠯⣝⢣⣎⣟⣯⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢂⠐⠠⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡰⢞⣹⡾⠧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢷⡷⡱⢎⠶⣿⡏⢿⣿⣦⡓⡝⢶⣘⡳⣌⣷⣞⢿⣼⢻⢲⢲⣀⣀⣀⣀⡀⢀⠀⣄⢂⠣⡔⢢⠜⡰⠓⡄⣀⡒⣖⣲⢒⡖⣎⣡⣑⡾⠯⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢷⣿⣛⣶⣙⣶⣜⣯⣟⣼⣳⡝⣞⡯⢷⡺⣝⠾⣩⠾⡱⣐⠲⡐⢦⠐⣂⠲⢠⠎⡱⢌⢣⡘⣡⢓⡬⢱⡉⢖⡥⠯⠾⠶⠷⠏⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠷⢿⣞⣽⣾⣹⢎⣷⡹⢯⡝⢧⠻⣌⠻⠴⢣⡱⢌⡒⢍⢢⡉⢦⡉⢖⡬⡑⣎⠲⣑⢎⠲⣌⢣⡜⣭⢓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠮⢧⠹⣍⠾⣡⠟⣬⢋⡝⢢⠱⡊⠜⣌⠢⡜⢢⡙⢦⣘⡱⣌⢳⡜⣌⠳⣌⠲⣌⢧⣋⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡓⣌⠲⡡⠞⢤⠣⡜⢣⢡⠙⡌⢆⠳⣌⠳⣜⡱⢎⡱⢎⡷⢪⣜⢣⡜⣱⢒⠮⣌⣳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢆⡳⢌⡱⢢⠱⡘⢢⢊⡑⢎⡌⢧⡍⡳⡜⣬⢳⡹⣎⣟⡷⣎⢷⡸⢥⣋⠞⣼⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⣮⠱⣍⠶⡑⢦⢡⠃⡆⡝⣦⡙⣦⢓⣧⠳⣖⣫⢷⡻⣞⡵⣯⢷⣹⢶⣩⠞⣧⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡇⢻⡜⣼⢩⣶⢡⠙⡄⡇⣧⡟⣶⣯⣶⢻⣼⣯⢻⣵⡏⣷⢫⡏⣿⢲⣭⢫⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢏⠶⣱⣧⠫⣼⣹⠂⡵⡘⣷⠻⠶⠽⠮⠯⠷⣯⣞⡿⣿⠿⣿⣞⣭⠷⣏⡾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡏⣞⣧⣿⠀⠉⣿⡘⡔⣯⣿⠀⠀⠀⠀⠀⠀⠿⣌⠟⣿⡀⠉⣯⢎⡟⡽⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣧⠳⣿⠀⠀⠉⡷⢡⡗⣿⠀⠀⠀⠀⠀⠀⠀⡯⡞⣽⠀⠀⠈⡷⡜⣭⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢢⣛⣿⠀⠀⠀⡯⡅⣟⣿⠀⠀⠀⠀⠀⡀⣄⢣⣏⠿⠆⠀⣀⠳⡙⢦