⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠙⣶⡏⢠⡞⠉⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠉⠛⠶⣦⣤⣤⣤⣾⡀⠀⠀⠀⠀⠀⢸⢠⣯⢶⣾⠟⢁⣽⠷⣾⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣛⣥⡤⠦⣄⠀⠀⠀⠈⠻⣦⣬⠭⠽⠿⢶⣤⣀⠀⢻⡟⣷⡟⢁⡴⢋⣁⣰⡽⠿⠷⠒⠒⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠋⢉⣩⡿⠛⠉⠁⠉⠈⠉⡛⠳⢦⣼⣿⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠛⢾⣟⠉⢙⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⢋⠁⠀⠀⠀⠀⠀⠀⠙⠻⣍⠐⢮⡙⠿⣦⠀⠀⠀⠀⠈⢷⡀⣀⣠⣤⠴⠶⠿⠷⣾⣀⡤⠴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⣴⠋⠀⠀⠀⠀⠀⠀⠀⠠⢤⣌⣳⡀⠀⠱⡝⢷⡀⠀⠀⠀⠀⠹⣟⠋⠀⠀⠀⠀⠀⣸⣿⣤⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠵⣫⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⢦⡀⠀⠈⢳⡄⠀⠀⠀⠀⠹⣆⠀⠀⢀⣠⢞⣿⠟⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠞⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡋⠀⠀⠙⢷⣄⠈⢿⡀⠀⠀⠀⠀⠹⡶⠞⠋⠷⠋⠁⠀⠀⡿⣆⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀
⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⠀⠀⠀⠈⠻⣆⠀⢀⡀⠛⢷⡼⣿⡀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡇⢻⡄⠀⠀⠀⢀⣴⠟⠁⢹⡄
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢀⡨⠟⠉⠀⠀⠀⠙⣿⣧⠀⠀⠀⡀⠀⢷⠀⠀⠀⠀⠀⢀⡇⢸⡇⢀⣤⣾⠋⠀⠀⠀⠀⣷
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢳⠀⠘⣇⠀⠀⠀⢀⣸⠇⢸⣿⠉⠀⠙⢿⣆⡀⠀⠀⠙
⠀⠀⠀⢠⡇⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⠀⠘⢦⡀⠀⣿⣇⠀⠀⠸⡆⠀⢻⡀⢀⣠⣟⡟⠀⣼⢿⠠⠀⠠⠤⢿⣷⣄⠀⠀
⠀⠀⠀⣼⠀⠀⠀⠀⣷⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠠⡄⠀⠀⢸⣧⠀⠀⠀⠸⣦⠀⠀⠹⣦⢹⢿⠀⠀⠀⡇⠀⠘⣷⣻⢟⡾⠁⢠⣿⣿⠀⠀⠀⠀⠀⠈⢻⣦⠀
⠀⠀⢠⢏⡄⠀⠀⠀⣿⡆⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣿⣷⣤⡤⠤⢽⣧⡀⠀⠈⢻⣼⡇⠀⠀⡇⠀⠀⢿⣱⠟⠀⢀⣾⣯⣿⠀⠀⠀⠀⠀⠀⣠⡿⠀
⠀⣠⣯⣾⠃⠀⠀⠀⣿⢿⡀⠀⢸⢹⣆⠀⠸⣆⠀⠀⠘⣟⠷⣄⢿⠹⣟⠳⣄⣈⢿⣿⣦⣀⠀⢹⣧⠀⢰⡇⠀⠀⢸⡅⠀⣠⣾⣿⣾⣿⡇⠀⠀⠀⣠⡾⠋⠀⠀
⠰⠛⠉⢸⠀⠀⠀⠀⢹⡜⣷⡴⢶⡾⣿⣦⡀⢿⡷⣄⡀⠘⣦⠛⠛⠲⠾⠷⣄⣉⣉⣻⣟⣉⠙⢲⣿⠀⣼⡇⠀⠀⠈⣧⡴⢋⡼⢻⣿⣿⣇⠀⣠⡾⠋⠀⠀⠀⠀
⠀⠀⠀⠘⡇⢀⠀⠀⠈⣿⡇⢹⠾⢧⣽⣍⠳⣼⣟⠾⠿⣶⣼⣷⣄⠀⣴⣾⣿⣿⣿⠿⣿⣿⣿⣶⣾⢀⣿⠀⠀⠀⡄⣿⣡⣾⣡⡟⠀⣿⢿⣿⠇⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⢻⡌⣧⡀⠀⠸⣧⣸⣷⣶⣧⣿⣶⣀⠉⠀⠀⠀⠀⠀⠀⣼⠟⢻⠁⢸⡅⠀⣽⢸⢋⡿⢻⡀⣿⠀⠀⠀⣻⢸⠞⣿⣯⠀⠀⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢳⣿⡻⣦⡀⠹⣿⣿⠋⣯⠹⣏⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡠⣙⣺⣧⡾⠚⠁⣿⢿⡇⠀⠀⠀⣿⣸⡄⣼⣽⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠙⠧⠀⠙⢷⣿⣿⣦⡸⣆⠙⣓⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣽⣿⠁⠀⠀⠀⣿⣿⣟⡽⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⣿⡍⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢰⡿⣿⡏⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣼⠁⣿⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⡿⣇⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⠀⠀⠀⢠⡏⢰⡿⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣟⠀⠙⢷⣴⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⣿⠃⠀⠀⠀⠀⡾⢀⣿⠃⠀⢀⡾⢻⠇⠀⠀⠀⠀⠀⠀⠀⣸⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠃⠀⣀⣾⣿⣾⠛⠲⠦⣤⣄⣀⣠⣤⣤⣴⣶⣟⣭⣿⠻⣿⠇⠀⠀⠀⠀⣼⣡⣾⠏⠀⣠⣿⢁⡿⠀⠀⠀⠀⠀⠀⠀⢰⠇⣰⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠙⣴⠿⢶⣿⣏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣯⣽⡿⠷⢶⡟⠀⠀⠀⠀⣾⣟⡿⠋⢀⡼⢋⡟⡾⠁⠀⠀⠀⠀⠀⠀⢠⡟⢠⢟⡟
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣠⡿⢤⣿⢏⡟⠀⣠⡾⢿⣿⣻⠿⣿⣃⣿⣯⠉⢀⣀⡿⠀⠀⠀⠀⣼⡿⢿⡄⣠⠟⠁⣾⡿⠃⠀⠀⠀⠀⠀⣠⣤⡟⣠⠏⡾⠁
⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⣴⠋⡇⣿⠟⣸⣧⣶⠏⢡⡿⣿⠋⢰⣿⠟⠀⠉⢘⣻⣿⠃⠀⠀⠀⣾⠇⠀⠀⠻⣏⠀⣼⠟⠁⠀⠀⢀⣠⠶⠋⢡⣟⡴⢋⡼⠁⠀
⠀⠀⠀⠀⠀⣼⢋⠀⠀⠀⡼⠃⠀⣿⡦⠴⣻⣿⣷⠀⢸⡇⢻⡄⢸⠃⣀⡴⠞⠋⠉⣽⢰⠀⠀⢸⣏⠀⣠⠤⢤⣹⣾⠋⠀⠀⢀⡴⠛⠁⠀⣴⣻⠞⢠⡞⠁⠀⠀
⠀⠀⠀⠀⠀⡇⣿⠀⠀⣼⠃⠀⠀⠻⣿⣻⣽⡿⢹⠀⢀⣿⣍⢳⣼⣴⠯⡤⠤⠤⠀⣿⣿⠀⠀⢸⣉⣿⣁⡀⠀⠘⣿⡆⠀⠴⠋⠀⠀⣠⣾⠿⠁⣠⠟⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣹⢞⣩⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠳⣦⡀⢨⢛⣦⡸⡻⡅⠒⢍⣷⣄⡈⠉⣶⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⡡⣫⢮⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢷⡄⢣⢣⠘⢮⢿⣤⣈⢪⠻⣏⣙⠚⠧⣀⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⣠⡴⢿⡿⢁⡚⢠⠃⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢦⡈⠹⡜⡏⡇⠀⢳⣿⡌⠑⠢⣌⣏⠓⢄⠀⠙⠢⢄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣡⡴⢟⣩⢞⢟⣤⠊⢑⢋⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠤⡑⢆⡀⠀⠈⢯⢦⢡⢰⢸⠀⠀⢿⣵⣤⣀⣈⠙⡄⠈⠙⢢⣀⠀⠈⠐⠤⡀⠀
⠀⠀⠀⠀⠀⢀⣴⠟⣋⢔⠟⠁⣎⣎⠆⠀⡞⡎⠢⡆⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⣄⠀⠀⢳⡉⡏⡎⠃⠀⠘⣻⠀⠰⠀⡀⣇⠀⠀⠀⠈⠳⢦⣀⠀⠈⠀
⠀⠀⠀⠀⢰⠛⠓⠉⠀⠈⠀⡸⣼⡟⠀⢱⠋⠈⠀⢠⠀⠀⠀⠀⠱⡀⠀⠀⠘⣦⠀⠀⠀⠀⠹⣮⠣⡑⠀⠣⢰⠃⡇⠀⠀⣿⠃⠠⠉⠀⣿⣢⡀⠀⠀⠀⠀⠈⠓⠤⣀
⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢠⡱⢸⡇⠀⡘⠀⠀⠀⠸⡄⠀⠀⠀⠀⢳⡀⠀⠀⠈⢳⡀⠀⠀⠀⠙⢗⣕⡄⠀⢸⣷⠀⠀⠀⢿⡇⠀⢀⣼⢏⡌⠻⢦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣜⠃⠀⠀⠀⡇⠀⠀⠀⡀⢣⠀⠀⠀⠀⠀⠣⡀⠠⡀⠀⠻⣆⠀⠀⠀⠀⠨⢾⢆⢸⣿⠀⠀⠀⠈⡇⢠⣾⠏⣾⠙⢄⠀⠉⠒⠤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠼⡖⠚⡿⠀⠀⠀⠀⡇⡇⠀⠀⢣⠸⡇⠀⠀⠀⠀⠠⡝⣄⠉⢦⡀⠙⢗⢄⠀⠠⠀⠁⠸⡿⣿⡄⠀⠀⠀⣗⠟⠁⣰⢹⠀⠉⠁⠒⠤⠀⢈⠴⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢑⢤⣿⡆⠀⠀⠀⣇⢹⠀⠀⢸⡆⢹⡄⠀⣄⠀⠀⢳⡈⣷⣄⠙⠢⠈⠃⠑⢄⡀⠀⠀⠀⣧⠇⠀⠀⠀⠁⠀⣴⠃⡼⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀
⠤⠤⠤⠤⠤⠤⠀⠀⠀⢼⡇⣇⠀⡀⠀⢸⡈⣇⠀⠘⣷⡀⢿⣤⠈⣦⡀⠈⣿⣮⡿⣷⣄⠀⠀⠀⣀⣙⣀⢀⠀⣿⠀⠀⠀⠀⡄⢀⡜⣠⡁⠀⠀⠀⢠⠾⠦⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⠀⡇⠀⢸⣷⣹⣦⠦⢯⢿⢾⣿⢷⣜⡎⢢⡸⢣⣙⠺⣦⡙⠫⢅⡀⠉⠉⠁⠀⣿⠃⠀⠀⠀⣧⡾⠁⡞⠑⢤⣀⣴⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡆⢸⡄⠀⣿⣻⢿⣷⣮⣎⣶⡬⠞⢿⡗⢼⣿⡁⠳⣧⠀⠙⢶⣬⣾⣿⣶⣦⣤⣿⡀⠀⠀⠀⣿⣣⣰⣿⣦⠉⠀⢳⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢿⡸⣧⠀⢹⡽⡿⢿⣿⡻⢿⣿⡶⡄⠈⠀⠉⠉⠲⣹⣆⠀⠘⠻⡻⣿⣯⣿⡟⣹⡃⡀⠀⡄⣿⡭⣿⠿⣿⣧⠀⠀⢳⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠘⢷⢏⣆⠈⣷⡝⠍⢿⣟⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠙⠋⠈⠏⠉⠰⡇⡇⠀⡇⣏⣷⣿⠀⢿⣏⢢⡀⠀⠱⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⠀⠀⠈⠿⣿⣷⣽⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠁⠀⡇⣿⢻⣿⡇⠈⣿⠀⠱⡄⠀⠹⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠃⠀⢠⠃⠙⢿⣾⣿⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⣿⡄⠻⣿⣆⠘⡆⠀⠘⢆⠀⠈⢦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢠⠏⡟⣆⢣⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⠀⠀⢺⢸⣷⡀⠉⠉⠀⠱⡀⠀⠸⣧⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⢏⡄⡇⡏⣢⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⡀⠀⠀⠘⡾⡏⠳⡀⠀⠀⠀⠁⡀⠀⢻⣷⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡜⠀⠀⢠⠎⡼⡇⡇⡇⣇⢱⣕⣄⠀⠀⠀⠘⠂⠤⠤⠤⠐⠋⠀⠀⠀⠀⣠⠞⠁⠀⡇⠀⠀⠀⢧⣧⡀⠙⣄⠀⠀⠀⠰⠀⠀⠛⣿⢢⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠜⠀⠀⡰⠃⢠⡽⣹⠇⠀⠃⢸⡏⠓⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠁⠀⠀⠀⡇⠀⠀⠀⣿⣿⣇⠀⠘⢦⠀⠁⠀⠀⡀⠈⡞⣇⠑
⠀⠀⠀⠀⠀⠀⠀⡇⢀⠎⠀⠀⡜⠁⠀⣾⠁⡿⠀⠘⠀⢸⡇⠀⠀⣼⣟⣶⣤⣀⠀⠀⢀⣠⣶⢛⣦⣠⠊⡆⠀⠀⡇⠀⠀⠀⣹⣿⣿⣆⠀⠀⢳⡀⠀⠀⠈⠀⠹⡿⡆
⠀⠀⠀⠀⠀⠀⠀⣧⠋⠀⢠⠎⠀⠀⣜⠃⠀⡇⢡⠇⠀⢸⣇⣴⣾⣮⢟⡻⣿⢝⣶⣖⡋⣡⣴⡤⠀⢉⣉⣺⣦⢄⡇⠀⠀⢸⠸⣿⣿⣿⣆⠀⠀⠹⣆⡀⠀⠀⠂⢹⣿
⠀⠀⠀⠀⠀⠀⡰⠃⠀⡴⠁⠀⢀⣼⠏⠀⢀⣧⡤⠔⡒⠝⠋⠓⠊⢩⡤⡤⠌⠛⠚⣉⣇⣠⣀⡉⠑⠂⢤⣄⠀⠙⠻⡢⣄⠘⠠⢯⣽⣏⢿⣷⠀⠀⠘⣷⣄⠀⠀⠀⢁
⠀⠀⠀⠀⢀⠜⠀⣠⠊⠀⣀⣤⣺⠷⠙⢻⠛⣡⠔⠋⠀⠀⠀⢀⣤⡌⠅⠐⠚⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠈⠙⠻⣧⣠⡀⠈⢻⡳⢄⠀⠘
⠀⠀⠀⡰⠃⡠⣪⡷⠟⠓⠉⠁⠀⠀⠀⡇⡜⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠉⠛⠒⣻⢯⣫⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢇⠀⠀⠀⠀⠈⠙⠳⠦⢝⣮⠱⣄
⠀⡠⢊⡠⢊⢾⠿⢷⡄⠀⠀⠀⠀⠀⢠⢣⠀⠀⠐⠢⣤⡤⠤⣤⣤⠤⠒⠒⠒⢢⣶⣓⣤⣈⠓⢇⡀⠈⠁⣲⡤⢀⣀⡀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡳⠈
⢄⡵⠋⢀⢾⠋⠀⠀⠻⡄⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⠀⠀⠈⠙⣦⡀⠀⢠⠋⣠⣿⣿⡿⣯⡏⠉⠀⣴⠏⠀⡆⣏⡇⠀⠀⠀⠀⠇⡆⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡀
⠁⠀⠀⡌⡎⠀⠀⠀⠀⠙⡄⠀⢶⡄⡌⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡵⣤⢏⣴⢟⣿⣿⣷⠘⢿⣄⠞⣾⠀⢠⣿⢇⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀
⠀⠀⠀⢃⠁⠀⠀⠀⠀⠀⠹⡄⢀⣷⡇⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⣷⣾⠿⣿⣿⣿⣿⣖⡺⣿⣾⠃⠀⢸⡇⣸⡇⠀⠀⠀⠀⢰⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠰⣀⢻⣩⢏⢗⢄⠀⠀⠀⠀⢸⢄⡀⠀⠀⠀⣰⣿⡏⢱⣿⣽⣧⣿⣷⠋⣹⣿⡆⢀⡟⣡⠷⡇⠀⠀⠀⠀⣸⡜⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢲⣿⡌⢪⡣⡉⠀⠀⠀⢸⠑⢍⢲⢤⣀⡹⣇⣿⣾⣟⣿⡿⣽⣿⡞⡟⣹⠟⣼⣔⣵⠞⡇⠀⠀⠀⢉⢿⢼⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢨⠉⠘⠆⢑⣬⣓⠠⢄⣸⡀⠤⠽⡵⡬⠟⠛⢿⣿⣿⢿⣶⣫⣿⣿⠿⠟⣲⣿⡿⠧⠀⠇⠠⠔⣊⠕⢃⣘⣀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠈⠛⢝⣫⣷⡷⢶⣿⡟⠀⠇⠀⠀⢰⣿⣦⡴⠊⢳⣯⡏⠀⢠⢻⡌⠉⠉⠒⠒⠊⠉⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⢻
⠀⠀⠀⠀⣹⢄⡀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠨⣝⣻⣽⡿⠃⡸⠀⠀⠀⠘⠇⢿⣽⠿⣥⡼⠂⢠⠋⠈⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢹⠆⠉⠢⢄⡀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⢠⠃⠀⠀⠀⠀⠀⠘⣶⣶⣾⠋⢀⣿⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣸⢻
⠀⠀⠀⠀⠀⣼⢠⡀⠀⠉⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠑⣄⠀⠀⠀⠀⠀⢻⣯⡏⢀⡾⡟⠀⢸⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠀⠀⠀⠀⡔⢸⠃
⠀⠀⠀⠔⡤⠙⡇⠙⢆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⡄⠀⠀⠀⠈⡟⠀⢸⠃⣧⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠊⡰⢻⠃⠀⠀⠱⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠸⠀⡉⠀⡿⢤⢿⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⡼⠀⠀⠀
⠀⠀⡴⢋⡴⢉⣿⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠄⠀⡰⠂⢹⠀⣇⢸⣼⡇⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠃⠀⠀⠸
⠀⠀⠀⠊⠀⠋⢹⠄⠀⢀⣿⢫⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡰⠁⠀⠈⢦⢹⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠱⣄⠀⠐
⠀⠀⠀⠀⠀⠀⢸⡈⠤⡼⠃⢸⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡇⠀⠀⠀⠀⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀
⠀⠀⠀⣀⠀⣠⠶⣧⠐⠁⠀⠈⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡀⠀⠀⠀
⠀⠀⡾⠁⣴⠃⠀⢩⡆⠀⠀⠀⠀⠀⠊