Tolerant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣦⣴⠶⣤⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠶⣤⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣤⠶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⣴⠟⠁⣠⠿⣦⣀⣀⠀⠀⠙⢷⣄⣠⡾⠋⠀⠀⣀⣀⣴⠿⣆⠈⠻⣦⣠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⡾⠃⠀⢀⡉⠙⡻⣦⡀⠀⠙⠋⠀⢀⣴⢟⠋⢉⡁⠀⠘⢳⣤⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠉⠛⢻⣏⣾⢷⣄⠀⠀⣠⡾⣷⣹⡟⠛⠁⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣴⣦⠈⠛⣁⣶⠟⠀⠀⠻⣶⣈⠛⠁⣴⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣦⣄⠀⠀⠈⠻⣤⡶⠾⠋⢁⣤⡶⢶⣤⡈⠙⠷⢶⣤⠟⠁⠀⠀⣠⣴⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢠⡿⠁⢀⡀⠈⢻⡄⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠘⣷⡀⠈⠁⢀⣾⠃⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠟⠋⠀⠀⢀⣴⠟⠷⢶⣄⡈⠛⠷⠾⠛⢁⣠⡶⠾⠛⣦⡀⠀⠀⠙⠻⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⠟⢀⣤⡉⠿⣦⠀⠀⣴⠿⢉⣤⡀⠻⠟⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣀⣤⣼⣏⢿⡾⠋⠀⠀⠙⢷⡿⣹⣧⣤⣀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠛⢷⣀⠀⢈⣁⣠⣵⠟⠁⠀⣠⣄⠀⠈⠻⣮⣄⣈⡁⠀⢠⡾⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠻⣦⡀⠹⣶⠟⠉⠉⠀⠀⣠⡾⠋⠙⢷⣄⠀⠀⠉⠉⠻⣶⠋⢀⣴⠟⠙⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠶⠛⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠛⠶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠛⠶⠟⠻⠶⠛⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡴⠶⠶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢳⣄⣘⣷⣄⣀⣀⣀⣀⣀⣀⣠⣾⣁⣰⡟⠛⣷
⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠈⠳⠶⠞⢉⡽⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⢯⠙⠷⠶⠟
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠹⣆
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⣀⡴⠟⠈⢿⡀⠀⠀⠀⠀⢹⡆
⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋⠈⢷⡀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣤⠶⠟⠋⠉⠀⠀⠀⠈⢻⣄⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡄⠀⠀⢀⡴⠞⠋⡉⠀⠀⠀⠀⡈⢳⣄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡄⠀⣾⠁⢀⡀⠀⠀⠀⠀⠀⠀⢀⡙⢷⡄⠀⢸⡇
⠀⠀⠀⠀⠙⢶⡄⢸⡇⠀⠈⠋⠀⠀⠀⠈⠉⠀⠙⣷⠀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢻⡀⠈⠙⠳⡄⠀⠀⣴⠟⠋⠁⢨⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠻⣾⣇⠀⠀⠀⣠⣄⣤⡀⠀⠀⠀⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠰⣾⡋⠈⠈⣻⡶⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠻⠶⠶⠛⠀⣠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠙⠛⠋⢉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣀⣠⡰⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠏⠛⠳⠛⠋⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠛⠁⠀⠉⠁⠀⠈⠳⠶⣤⣄⡀
⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠉⠛⢶⣄⡀⠀⠀⠀⠀⢀⡀⠀⠈⠙⠻⠶⣤⡀
⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⣴⠋⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⠶⠿⠿⠿⠿⠿⠿⠿⠷⢶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⣶⣤⣼⡟⠉⠀⠉⠻⣷⣾⠟⠉⠉⠙⢿⣄⣤⣶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⣼⣇⣴⡾⠿⢷⣾⣿⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⡟⠻⣶⣄⠀⠀⠀⠀⠀⠀⠉⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⣤⣾⣿⡄⠀⠀⠀⢀⣿⣇⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠛⠉⠀⠘⠿⣶⣤⣴⠾⠋⠛⠷⣦⣤⣾⠿⣿⣦⣄⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣶⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣿⣿⣷⣶⣶⣶⣶⣿⣿⣟⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣁⣼⡏⠀⠈⣿⣌⣙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠉⢹⣿⠛⠛⠛⢻⣟⠉⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⣀⣀⣸⣇⣀⣀⣀⣈⣿⣀⣀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⠛⢻⡟⠛⠛⠛⢙⣿⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠀⠀⠸⣿⠀⠀⠀⢸⡟⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡟⠛⠛⠛⢻⣿⠋⠀⠀⠀⠀⠀⠉⠛⠷⣿⡏⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⣴⠟⠁⣠⡶⠶⢶⣤⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠻⣦⡾⠋⠀⠀⠀⠹⣧⡀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣭⡅⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣶⣿⠏⠙⣷⡀⠀⣀⠀⢤⡄⠀⣷⡄⢸⣿⠛⣿⣆⣀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠹⣧⡈⣿⣆⣸⡿⠛⠃⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⣿⣏⣹⣿⣧⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⢿⣿⡿⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⠆⠀⠀⠀⠀⠀⠀⣴⣿⠟⢿⣿⡄⠀⠀⠀⠀⢠⣿⡿⠻⣿⣦⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⠀⠀⢀⣀⣴⣄⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣼⣿⡇⠀⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠁⠀⠈⠉⠉⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⡄⠀⣴⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡇⠀⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣶⣿⡿⠋⠀⣀⣴⣶⣿⣿⣿⣷⣦⣄⠀⠀⣠⣴⣾⣿⣿⣿⣶⣦⣀⠀⠀⠀⢸⣿⣧⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠈⠛⢿⣷⣾⡿⠋⠁⠀⠀⠀⠉⠻⣿⣷⡀⠀⠈⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣷⡄⠀⠀⠀⣠⣾⠿⠛⠻⢿⣦⡀⠀⠀⠀⣴⡿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⣸⣿⠿⠿⣿⣿⣷⣶⣶⣶⣶⣿⣿⡿⠿⢿⣿⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⢁⣴⡾⠟⣿⡟⠁⣿⡇⠙⣿⡟⠿⣶⣄⠙⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣾⣿⣤⣼⣟⣀⣀⣿⣇⣀⣘⣿⣤⣼⣿⣦⣾⡇
⠀⠀⠀⠀⠀⢀⣀⡀⣠⣾⢿⣿⠇⠀⢩⣿⠛⠛⠛⣿⡟⠛⠛⢻⣏⠁⠀⢿⣿⢿⣦⡀⣀⣀
⠀⠀⠀⠀⣾⠟⠛⢻⣿⠁⢸⣿⣤⣤⣼⣿⣤⣤⣤⣿⣧⣤⣤⣼⣿⣤⣤⣼⣿⠀⢹⣿⠛⠛⢿⡆
⠀⠀⠀⠀⠻⣷⣤⣾⣿⡄⢸⣿⠉⠉⢹⣿⠉⠉⠉⣿⡏⠉⠉⢹⣿⠉⠉⢹⣿⠀⣼⣿⣦⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠙⠿⣾⣿⣆⢀⣈⣿⣤⣤⣤⣿⣧⣤⣤⣼⣏⣀⢀⣾⣿⡾⠟⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⣿⡛⢻⣿⠉⠉⣿⡏⠉⢹⣿⠛⣻⣿⠏⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣧⡀⠙⢿⣦⣿⣷⣄⣿⣇⣴⣿⣧⣾⠟⠁⣠⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⣹⣿⢷⣶⠿⣿⡟⠛⠿⠟⠛⣿⡿⢷⣶⢿⣿⡉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⠿⠃⠀⠀⠀⠙⢿⣶⣶⣶⣾⠟⠁⠀⠀⠀⠻⢿⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⡾⠏


⣏⣈⣯⣍⣟⣯⣿⣹⣽⣽⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⣉⣉⣉⣉⡉⠛⠂⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢁⣤⠶⣻⠿⠋⠉⡏⠙⠻⣿⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⡼⠃⠀⠀⠀⡇⠀⠀⠈⢷⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣤⣄⣘⣁⠀⠀⠀⠀⡇⠀⠀⠀⡀⢷⠀⣤⠾⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⡉⠉⠉⠛⠛⠛⡟⠛⠛⠋⠉⠘⣇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢦⣀⠀⣸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⢀⣴⠞⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠙⣷⣿⣤⡤⠶⠶⠶⣤⣠⡴⠶⠶⠦⣤⣿⣶⡋⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⣴⡄⢀⡾⠋⠀⠀⠀⠀⢀⣴⠞⠁⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢠⣦⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣴⠋⠀⠀⠀⠀⠀⠀⢾⡁⢀⣴⠟⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣦⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡾⠛⢶⣤⡤⣄⠀⠀⠀⠀⠀⡀⠀⠙⢦⡀⠈⠻⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⡞⠁⠀⣸⠷⢶⡄⠀⠀⠙⢦⡀⠀⢹⣦⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⠞⠁⠀⣰⠟⠛⣦⡀⠀⢹⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⠾⣇⣀⣴⠏⠙⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣭⣭⣭⣭⣭⡻⣿⣿⣿⣿⣿⣷⠦⠀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣸⣿⣿⣿⢣⣶⣿⡟⣭⡍⣩⣭⢻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣛⣛⣛⣛⣛⣛⣛⣋⣵⣿⣿⣿⣿⣦⡙⣿⣷⡙⣿⣿⢏⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣌⣡⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣌⡛⠿⠿⢫⣭⣝⢿⡟⣩⣭⡛⣿⣿⣿⣧⡻⠿⢛⣩⣙⡻⠿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢋⣥⡙⢿⣿⣦⡸⣿⣿⠟⣨⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢃⠹⣿⣿⣮⠻⣿⣿⣌⢣⣾⣿⣿⠃⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⠶⠸⣿⣿⣌⢻⣿⣷⣜⠿⠿⣡⣿⠟⣱⣿⣿⡆⣿⣿⡿⣡⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣷⣌⢻⣿⣷⡙⠿⠿⣰⣿⡿⢫⣾⣿⣿⢋⣴⣶⡎⣧⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡌⢻⣿⣷⡙⠿⠟⣰⣿⣿⣟⣴⣿⣿⡟⣱⣿⣿⡿⢡⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⣶⡙⠿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣋⣾⣿⡿⢋⣶⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⡿⣡⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣾⣯⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⠉⠛⠉⠰⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠙⠿⠋⠁


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣟⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡦⢴⡆⠀⢠⣶⡄⠀⠀⠀⢄⣶⡂⠀⢰⣶⣶⣀⠀⠀⠀⢀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠠⠀⡀⠀⠀⣀⣰⡆⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⢈⠣⠎⠀⠀⠈⢉⣽⣄⠀⠀⣻⡿⠇⠀⠈⠉⠯⣿⠀⠀⠀⠐⠀⠀⠀⢰⣿⡿⠀⠀⠀⢶⠖⠀⠀⢰⡿⠋⡀⠀⠀⠠⢴⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐
⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣶⢶⣶⣶⣾⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣤⡾⠁⣴⣤⡈⢻⠀⢸⣿⣿⠀⡤⢴⡇⢠⣤⠈⣿⡟⢀⠈⣿⡏⠀⠘⣿⠀⣿⠁⣤⣦⣼⡇⢰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣧⠈⢿⡿⠃⣸⠀⠸⢿⣿⠠⣶⢾⡇⢀⡀⠰⣿⠁⣈⡀⠸⡇⠈⣧⠘⠀⣿⠀⢿⡿⢿⡇⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣦⣴⣾⣿⣶⣶⣶⣿⣶⣶⣶⣷⣾⣿⣶⣷⣾⣿⣿⣦⣿⣼⣿⣷⣶⣿⣷⣦⣴⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠈⢁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⢀⣉⡀⠀⠀⠀⣉⠀⠀⠀⢀⠈⠀⠀⠀⠀⢈⠁⠀⠀⠀⡈⢁⡀⠀⠀⣀⣁⡀
⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠛⠓⠛⠃⠀⢸⡇⠸⡟⠀⢠⣤⣤⣤⠀⠠⣿⡟⡛⠀⠀⣶⣿⣦⠀⠀⢻⣿⡿⠃⠀⣀⣿⣀⡄⠀⠘⣿⣟⠃⠀⠐⣿⣻⡇
⠀⠀⠀⠀⠀⠚⠓⠛⠂⠀⠐⠒⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠉⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠘⠛⠛⠀⠀⠈⠀⠑⠀⠀⠀⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢄⣀⣬⣡⡿⢿⡟⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣤⣚⣿⣿⣟⣻⣿⣿⡿⣿⣿⣿⣿⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀
⠀⠀⠀⠀⢀⣴⣿⢿⣿⣾⠿⣻⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈
⠀⠀⣾⣷⣮⡕⣿⣿⢽⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠈⠉⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠙⢻⣿⣽⣿⡿⢡⣟⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠋⠀⠀⠀⠈⡹⣿⡿⢡⣿⣿⣿⣿⣿⣾⡿⣡⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⣨⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢃⠹⢡⣿⣿⣿⣿⣿⡿⢋⣼⣿⡿⠋⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠈⠙⠻⠿⢿⣿⣧⠀⠀⠀⠀⠀⢸⠀⣾⣿⣿⣿⣿⡟⠁⠛⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠐⠀⠀⡘⠀⠀⠀⠰⡀⠀⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡅⠀⠀⠀⠀⡠⠖⠒⠓⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣻⠲⠃⠀⠀⠀⠀⠀⠀⠀⢀⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣼⡧⠀⢀⠇⠀⠃⠀⠀⠀⠀⠀⢠⡃⣤⣴⠫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⠻⢇⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢼⣟⡿⠿⣦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⡯⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠋⠀⢀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠁
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠙⣆⠀⡐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠘⠛⠃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⣤⣹⣦⣄⠀⠀⠀⠀⠀⠲⢯⡀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣿⣿⣿⡿⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣫⣾⣿⡿⢢⣶⣤⡀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣷⡿⣾⢠⣿⣿⣿⡇⠀⠀⠀⡀⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣷⣤⣶⣄⣬⣪⣀⣤⣙⠿⣿⣿⣿⣿⡿⣻⣿⠉⢩⣿⣾⣿⡝
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠛⠛⠻⠛⠻⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⢷⣿⠃⣠⣾⣿⣿⣿⣏⡅
⠀⠀⠀⠀⠀⣠⡴⠿⠛⠉⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠃⣿⣿⣾⣷⣿⣿⣿⣿⡟⣷⡄
⠀⠀⠀⠐⠻⠿⣿⣿⣶⣄⣀⣀⡀⠁⠀⢀⣀⣀⣀⣀⠀⠀⢀⣀⠀⢠⣟⣛⣛⠻⡆⠀⠐⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⢟⣻⣿⣿⡇
⠀⢰⣄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣩⣿⣻⡇⢿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣟⡵⠋⠈⢉⣿⠇
⠀⠈⢊⡓⡆⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡘⢬⣭⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣾⠏
⠀⠀⢸⢸⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⠿⢿⣿⡿⠶⣤⡁⠀⠙⠿⡧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠦⠞⠛⠁
⠀⠀⠀⢟⣯⡣⢤⣀⠀⠀⢀⣠⢔⡋⢍⠉⠉⢁⠠⢶⣲⣭⣿⠁⠈⢿⠳⣤⡀⢠⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠿
⠀⠀⠀⠘⠮⡍⢲⣆⣭⣭⣽⣿⣿⣿⣶⣮⣭⣶⣿⣿⡿⡿⡌⠀⠀⢼⡇⢀⠋⠋⢿⣿⣿⡿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣾⡒⡄
⠀⠀⠀⠀⠀⠈⢮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡇⠃⠈⡄⠈⣷⠀⠀⠸⡿⢿⠟⠻⣾⣷⣿⣿⣿⣿⣿⣿⣿⠿⢟⠵⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢻⡈⠀⠈⠁⠈⣧⡀⢠⠀⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⠂⠙⢧⣀⠴⠆⠀⠈⡷⠶⠶⣿⣿⣿⣿⣿⣿⣿⠟⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⣿⣿⣿⣿⣿⣿⣿⣿⡏⡆⣿⠇⠀⠓⢢⣄⡀⡼⣷⣶⣿⣿⣿⣿⣿⡿⢟⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⠿⣿⣿⣿⣿⣿⣿⣧⠃⢸⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠬⠍⢩⣙⡻⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⡿⣿⢟⡫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⣰⠟⠀⠀⢻⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⣤⣾⣿⣃⡀⣠⣶⣶⣶⣶⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠛⠻⣿⣿⡏
⠀⣠⣾⡿⠿⢿⣷⣴⣾⠿⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⡀⠀⠈⢿⣷⣄
⢸⣿⠃⠀⠀⠀⠘⠛⠁⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠻⢿⣦⣄⠀⠙⢿⣧⡀
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠙⢿⣷⣄⠈⠻⣿⡄
⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣰⣿⠏⠀⣠⣿⠇
⠀⠀⠈⠻⣿⣦⡀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⠿⢿⣿⡟⠀⣰⣿⣏
⠀⠀⠀⠀⠈⠻⣿⣶⣿⠏⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⣶⣶⣿⠟⠋⠁⣀⣠⣾⡟⠀⣰⣿⠟⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⢠⣿⠟⠛⠉⠉⢩⣿⡟⠁⣠⣶⣿⠟⠻⣿⣧⣴⣿⣿⣦⡀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢀⣿⡟⠀⣰⣿⠏⠀⠀⠀⠈⠙⠋⠁⠈⠻⣿⣆⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣿⣿⠁⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣿⣿⣿⡆⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢁⣀⣠⣿⡇⢻⣿⣄⠈⠻⣷⣦⣀⠀⠀⠀⠀⣀⣴⣿⠟⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣿⠟⠛⢿⣷⠀⠙⣿⣦⣀⠈⠛⠿⠿⣿⡿⠿⠟⠋⠁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣦⣠⣼⡿⠀⠀⠈⠙⠿⣷⣦⣤⣄⣀⣀⣤⣤⣶⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠒⠲⠤⣄⡀⠀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠉⠉⠙⢦⠀⠀⠀⣀⠭⠷⣃⡀⣈⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⣀⣀⣀⣀⣀⣀⠞⠀⠀⠀⢇⠀⠸⡁⠙⢁⡗⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠙⣦⠎⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠦⣤⣤⠖⠲⣄⡠⠒⠢⡀⠀⠀⠣⣀⠤⠲⢤⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡖⠛⢦⡀⠈⢣⡀⡠⠛⠓⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⢶⠚⠳⣄⠀⠑⣄⠀⢹⡅⠀⡴⠛⠲⡀⠀⢀⡤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡔⠉⠳⡀⠈⢣⡀⢈⡟⠉⣠⠞⠀⢀⡼⠓⢦⢺⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠘⣦⡀⠙⢦⣀⡽⠉⠀⠴⠁⠀⣠⠋⠀⢠⡞⠀⢙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢯⠑⠤⠼⠃⠀⠀⠀⠀⠀⠘⠁⢀⡴⢁⡇⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡴⢯⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⢀⠴⠤⢶⡁⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠴⠋⠀⠀⠀⠙⠦⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠰⠰⠀⠀⠀⠀⠂⠐⠀⠄⠀⠀⠄⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠟⠋⠛⠿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣠
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⢀⣀⣀⡀⢠⡶⠿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⢿⡏⠀⣹⣿⣿⣿⣿⣿⣿⣅⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠤⠤⢤⣸⠛⣶⣿⠿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣆⡀
⠀⠀⠀⠀⢀⡤⠤⠤⠋⠀⠀⠀⠀⠈⠙⣿⣿⣿⣾⣟⢛⣷⣿⣿⠟⠉⠁⠀⠀⠈⠑⢤⣶⢿⣷⣄
⠀⠀⠀⠀⡏⢰⣾⡦⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡅⠈⣿⣿⣏⡀⠀⠀⢀⡀⠀⠀⠀⣁⠀⣹⡟
⠀⠀⠀⠀⠙⠦⠭⠅⠀⠀⠀⠀⢠⣄⠀⠀⠻⣟⡿⢷⣾⠿⣟⣹⠏⠀⢠⣿⣿⡆⠀⠀⢙⠛⠉
⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠉⠀⠀⢲⣾⣿⣿⣿⣿⣿⡥⠀⠀⠈⠛⠛⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⢾⣿⣿⠓⠢⠤⢤⣬⣶⡶⠿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣶⢻⣿⡇
⠀⠀⠀⠀⠀⠀⢸⢿⣿⠀⠀⠀⠀⠀⠉⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣦⣉⣿⡄
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣚⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⢻⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⠙⣿⣿⢧⣤⣄⣀⣀⠀⠀⣀⣀⣠⣤⣾⠃
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠⠶⡍⠀⠀⠀⢿⠿⠇⠀⠀⣽⣿⣿⣿⣿⡿⠋⣻⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⣏⠀⠙⠦⣀⡀⠈⣣⡀⠀⠀⠉⠛⠛⠉⠁⠀⣠⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣈⣦⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠂⠀⠿⠂⠐⠿⠿⢿⣶⣶⣤⣶⡾⠿⠿⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⢀⣤⣤⣄⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⢠⣿⠋⠉⣿⡇⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢈⣿⣦⣤⣿⣇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣀⣀⣴⡿⠋⠉⠉⠙⢻⣷⡀⠀⣸⡿
⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠿⣷⣄⣠⣾⠿⠛⠛⠻⢿⣦⡀⠀⠀⠀⠻⠃⣠⣿⠃
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠹⣿⡄⠀⢀⣠⣾⠿⣿⡇
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠟⠛⠁⠀⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣇⠀⢀⣤⣴⣶⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⢸⣿⣶⡿⠋⠁⢀⣠⣄⡀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⢠⣿⠋⠀⠀⢰⣿⠛⠻⣿⡀⠀⠙⢿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⣾⡏⠀⠀⠀⢸⣿⣄⣰⣿⠃⠀⠀⠈⣿⣿⣦⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⣿⡇⠀⠀⣴⡿⠛⠛⠛⠻⣿⣆⠀⠀⣿⡏⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾⡆⣠⣾⠟
⠀⠀⠀⠀⠸⣿⡄⠸⠿⠀⠀⠀⠀⠀⠸⠿⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣶⣶⡾⠿⠛⠿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⠀⠀⠀⢀⠄⠰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡟⠀⠀⢠⡇⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡀⠅⠀⠀⡼⠀⢳⡜⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡕⢿⡷⠀⠀⠘⠀⠡⠈⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢤⣅⣀⠀⢀⣆⠞
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢲⣳⣏⠣⡎⠁⠒⠃⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠐⠁⣀⠀⡜⠉⠀⢹⡓⡇⡀⣴⠀⠀⠀⡟⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠲⣈⣯⠂⡈⣃⡏⣇⢀⠀⡠⠞⠼⠒⢌⡓⠄
⠀⠀⠀⠀⠀⠈⡁⡀⣷⣿⠛⠃⠐⠀⠹⣄⠘⠆⡈⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⢀⠇⡸⠟⠁⠀⠀⠀⠀⠀⠘⠈⠀⡄⠀⠀⠀⠀⠡⠂
⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⢀⡴⢦⡀⠀⠀⣴⠲⠀⠸⣷⣿⡆⠀⠀⣿⣷⣄⠀⠀⢰⣿⣦⠀⠰⠀⣄⠀⠃⢀⣤⡖
⠘⠐⠀⠀⢠⠁⠀⠙⡠⢄⡧⠀⠀⣯⣴⠀⠀⣿⡛⠁⠀⠀⢹⢿⠇⠀⣦⢾⣿⠏⠀⠀⠀⣿⣷⡄⢈⣷⣿
⠀⠀⠀⠠⠀⠀⠀⠀⣠⢋⠀⠀⢀⡟⢣⠀⠀⠀⡀⠀⠀⠀⠛⠆⠀⠀⣧⢀⣽⣦⠀⠀⠀⢿⡿⠁⠀⠩⠶
⠀⠀⠄⠰⢀⠀⠀⠈⢹⠐⡄⠀⢸⡓⠈⠀⢀⢀⡀⠀⠀⠀⡆⢡⠀⠀⣿⠘⡇⢸⡆⠀⠀⡟⠙⡀⠀⢐
⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠘⡇⠀⠀⢰⡟⠁⠀⠀⠀⡇⠘⠄⠀⣿⠀⠃⠘⠇⠀⢰⡃⠀⠇⠀⡟
⠀⠀⢠⠀⢁⠀⠀⠈⠈⣦⣰⠀⠀⡇⠀⠀⠀⠃⠀⠀⠀⠀⣥⠀⠀⠀⠘⢠⠀⠠⠀⠀⠀⠁⠀⠀⠠⠃
⠀⠀⡈⠀⠈⠀⠀⠀⠀⢹⠉⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠃⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⡙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⡿⢩⣤⣴⣶⡾⢛⡛⠿⢛⡛⠳⣦⣤⣄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⠐⣿⣿⣤⣿⣿⠆⣿⣿⣿
⠀⠀⢀⣾⣿⣿⣿⡿⢋⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣴⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣷⡘⢿⣿⡿⢃⣾⣿⡟⠁
⠀⢀⣾⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣿⣿⣌⠛⣡⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⠿⠟⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣦⣭⣭⣭⢁⣾⣿⣷⣌⠻⠏⣴⣿⣿⣦⡙⣿⣿⣿⣿⣿⣬⣉⣉⣥⣶⣷⣦⣍⣙⡉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣥⣤⠙⣿⣿⣿⣷⡘⢿⣿⣿⡟⣁⣭⣍⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣷⡌⠻⣿⣿⣿⣆⠙⠋⣴⣿⣿⣿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣉⣉⣉⣉⢉⣴⣶⣤⠙⣿⣿⣿⣦⡈⢻⣿⣿⣷⠀⣿⣿⣿⠏⢠⣤⣤⡌⢿⣿⣿⣿⣿⠟⣋⣉⡉
⢻⣿⣿⣿⣿⠟⢛⡀⠻⣿⣿⣷⣌⠻⣿⣿⣷⣄⠙⠋⣉⣰⣿⠿⢁⣴⣿⣿⣿⠏⠸⠿⣿⣿⢁⣾⣿⣿⡇
⠘⣿⣿⣿⡇⢸⣿⣿⣧⡙⢿⣿⣿⣦⡘⢿⣿⡿⢁⣿⣿⣿⠋⣴⣿⣿⣿⡟⢋⣴⣶⣷⡆⢻⡈⢿⣿⣿⠁
⠀⠹⣿⣿⣿⣦⠹⣿⣿⣿⣆⠻⣿⣿⣿⠄⣴⣶⣿⣿⠟⣡⣾⣿⣿⣿⠟⣱⣿⣿⣿⡿⢃⣾⣿⣦⣍⠁
⠀⠀⠹⣿⣿⣿⡇⣈⢻⣿⣿⣷⡌⢉⣩⣼⣿⣿⣿⣿⣶⣿⣿⣿⡿⢃⣾⣿⣿⣿⠟⡁⢸⣿⣿⣿⠏
⠀⠀⠀⠙⣿⣿⡇⣿⣦⡙⠿⠟⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⡿⢁⣾⡇⣸⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⠟⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⠟⣡⡘⠋
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⣿⣿⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠋⣥⣾⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⠛⠛⠛⠛⠲⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄⠀⠀⢀⡾⠋⠁⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⡾⠁⠀⠀⠀⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠉⢀⣠⣀⡀⢀⣀⣤⡈⠛⠛⠳⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢰⡏⠀⠀⢻⡏⠀⠀⢻⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢀⡶⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠈⠻⣄⠀⠀⣰⠟⠀⠀⢀⣾⠋
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⣧⣼⠋⠀⠀⠀⠸⣇
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣤⣤⣤⣴⠛⠉⠉⠻⣦⡀⢀⣴⠟⠋⠙⠻⢦⡀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣤⡶⠟⠛⠻⢶⣤⣀⣀⣴⠏
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣧⡀⠀⠀⠀⠈⢳⣾⠁⠀⠀⠀⠀⢈⣿⣀⣀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⣿
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠉⢷⣄⠀⠀⠀⠀⠙⢷⡀⠀⠀⣠⡞⠋⠉⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣄⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠈⠻⣦⣴⠏⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠸⡷⠶⠶⠶⠶⠶⠶⠶⠶⣶⡾⠛⠉⠛⢷⡀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⡾⠟⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⣠⣤⡴⡤⣾⠇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠙⢷⣄⠀⣀⣠⡟⠀⠀⠀⣴⠟⠁⠀⠀⠀⢀⡿⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⣸
⠀⠀⠀⢻⡄⠀⠀⠀⠀⢠⡞⠋⠉⠙⢧⡀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⢻⡟⠉⠁⠀⠀⣠⡾⠃⠀⠀⠀⠀⢀⣾⠷⠶⠶⣤⠀⣾⡁⠀⠀⠀⢰⡟
⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠹⣦⣀⣀⣤⡾⠁⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢸⡇⠘⢧⡀⠀⠀⣾⠁
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠘⢷⣄⠀⠀⠀⢘⡿⠉⠁⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⢀⡾⠁⠀⠀⠙⠻⣾⠇
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⠀⠙⣶⣤⡴⠟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢸⡇⠘⢷⣄⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣠⡞⠁⢸⡇⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠘⣧⠀⠀⠙⠛⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⡿⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⢀⣴⠟⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣠⠟⠻⣦⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠈⠉⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠶⠶⠞⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠞⠋


⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⡷⠴⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⢾
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⡴⠐⢦⠀⡄⠰⡖⠀⠰⡄⠀⠴⠐⡄⡄⠀⠀⡖⠒⠀⠀⡔⠀⠀⠲⠆⢠⠐⢢⢀⠔⠐⢄⢠⠀⠄⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⢗⠀⣠⠀⡁⠀⡇⢀⠧⠰⠄⠚⠘⡆⠃⠀⠀⡗⠀⠀⠀⠈⢲⠀⢨⠀⢸⠒⠇⠸⡀⠀⡸⢸⠛⣄⠀⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣿⣷⣶⣷⣶⣷⣾⣶⣶⣷⣿⣿⣶⣿⣿⣷⣿⣿⣶⣶⣿⣷⣶⣾⣶⣾⣶⣾⣶⣿⣿⣶⣾⣶⣾⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⣀⣀⣀⡀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡾⠿⠿⠿⠿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣼⡟⠈⠉⠛⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠋⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⠿⠃⠀⠀⠀⠈⣿⡟⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣶⣶⣄⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢻⣷⡀
⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⣿⡇⠘⢿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⣾⡟⢿⣦⡀⠀⠘⢿⣦⣄⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣻⡧⠀⠀⠀⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠙⢿⣶⣄⡀⠉⠛⠛⠛⠛⠛⠛⠀⢰⣶⠶⠶⠶⠶⠾⠿⠇⠀⠰⠿⠿⠶⠶⠶⠿⠿
⠀⠀⠀⠀⢿⣇⠀⠀⠀⠈⢛⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⣶⣶⣦⣄⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢷⣿⠏⠁⠀⠉⠻⠟⠁⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣷⣶⣾⠿⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢸⣿⠀⠀⠀⡀⠀⢸⡏⠀⠀⠀⠀⠙⢿⣦⡀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣿⣀⣀⣾⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠢⣀⣰⣀⣀⠄⠀⢠⡆⠀⠀⠀⣀⣰⣀⡀⠀⠀⢀⠂⣀⠀⠀⢠⠀⠀⠀⢰⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⣄⠀⠀⢀⣀⣠⢀⡀⠀⢸
⠀⠀⠈⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠈⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠉⣿⡏⠀⠀⢸
⠀⠀⠀⣿⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⢸
⠀⠀⠀⡇⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠂⠐⠂⠠⠀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⣶⣦⣤⡀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠁⠀⠰⠈⠑⠒⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⣻⣿⣏⣿⣿⣯⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠌⠀⢌⠀⠀⡀⠀⣀⠀⠀⠀⠈⠒⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣽⣾⡇
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡁⠣⡀⠪⣀⠕⢀⠈⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢷⣜⢿⣜⠿⣫⡿⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠾⡉⠂⠈⢢⠘⡠⠊⢡⢄⡐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣱⣾⣻⣿⡟⣿⣟⣵⡞⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢂⠀⣦⠀⢄⠙⠁⠀⠀⠔⠁⡜⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⣮⡻⣪⣾⣿⣿⣫⣿⢻⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠈⠁⠀⠀⠀⠀⡠⢠⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣾⣿⣿⣿⣿⣟⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⣀⠊⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠈⠻⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠤⡠⢀⠰⡩⠋⠿⡏⢹⠽⠿⡿⠿⠿⠟⠻⡏⣿⠿⠿⣿⠿⠿⣿⣿⠛⣉⣹⡏⣿⢿⢻⠉⡏⣿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠂⢴⠀⠁⠸⠀⡂⢰⠀⠁⠀⠰⠶⠀⠶⠄⡆⢰⠆⡁⠰⠆⡀⢰⡆⢸⣿⠷⢦⠙⡇⡁⢾⠸⠀⡇⡷⢌⠺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⢄⠒⠚⠵⣾⢦⢶⡾⣶⣶⣿⣶⣶⣿⣶⣷⣿⣶⣾⣷⣿⣷⣿⣿⣷⣶⣾⣷⣿⣾⣿⣿⣿⣿⣶⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⠤⢄⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⡣⠀⢰⠊⡡⣤⣦⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⢔⠉⢉⡉⠉⣀⠀⠈⡇⠘⠿⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢟⣽⣶⣾⣿⣿⣿⣍⣛⣹⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠉⠫⡈⠻⣉⠵⢤⠘⠛⠛⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⠿⣻⢿⡻⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⠖⢒⠶⠙⢄⠙⢤⠝⢀⠊⢱⣄⡔⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⢫⡿⣟⢯⡽⣪⢿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢣⠙⣄⠑⣄⠕⠋⠐⠁⡔⠁⣼⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡻⣝⣮⣿⣿⣷⢏⣾⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡧⠑⠃⠀⠀⠀⠀⣠⢪⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⡤⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⠜⠁⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣽⣿⣷⣟⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⠁⠙⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠴⠒⢻⡟⠒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⣠⠇⢧⡀⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠏⢇⠀⢸⡇⠀⡼⠹⡀⠀⠀⠀⠀⠀⠀⣰⡱⠗⣡⢤⢤⡑⠷⣱⡀⠀⠀⠀⠀⠀⠀⣏⢐⠂⡉⠛⢉⠑⢏⡽
⠀⠀⠀⠀⠀⠈⣔⡎⠀⢸⡇⠀⢱⣦⠁⠀⠀⠀⠀⠀⠀⠹⡱⡦⡉⠘⠈⡡⡶⡹⠁⠀⠀⠀⠀⠀⠀⠀⠁⡈⠈⠉⠁⢱⠈⠁
⠀⠀⠀⠀⠀⠈⠀⠈⣴⣯⣽⣦⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠳⡅⠈⡆⡎⠀⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⢠⢤
⠀⠀⠀⠀⠀⢰⡋⢀⣠⠟⠃⢎⠥⠟⡆⠀⠀⠀⠀⠀⠀⠐⠐⠒⠒⡖⡖⠁⠛⢲⡀⠀⠀⠀⠀⠀⠀⡴⠛⠚⢢⠀⡰⠛⠚⢢
⠀⠀⠀⠀⠀⠸⣵⡿⠥⡄⠀⢐⠉⣱⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣧⢦⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⣸⠀⣟⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠣⡀⢈⠆⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣰⣆⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠶⢯⣀⡼⠷⠶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⡼⢧⠿⢧⠿⢇⠀⠀⠀⠀⠀⠀⠀⢀⣬⣟⣓⣐⣚⣫⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠞⠛⠛⠲⠶⠶⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⣁⣤⣴⣶⠶⢶⡶⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢉⣴⠋⠁⠀⢸⡇⠀⠈⠻⣌⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⡾⠁⠀⠀⠀⢸⡇⠀⠀⠀⠙⣧⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠓⠶⢦⣤⣤⣄⣀⣀⣸⣇⣀⣀⣤⣤⢹⡆⠲⠛⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢠⡆⠀⠀⠀⠈⠉⢹⡏⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠳⣄⡀⢸⡇⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢹⡄⢀⣴⠟⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠈⣿⣾⣧⠴⠶⠒⠲⠶⣤⣤⠶⠖⠒⠶⠶⠾⢷⣏⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⣴⡄⢀⡾⠋⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⢠⣦⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢉⣴⠏⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣴⠟⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⡴⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠐⢲⡄⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣨⡿⠋⠙⣧⣄⡀⠀⠀⠐⢦⡀⠀⠙⢷⣄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡏⠀⢀⡴⠋⠈⢹⣦⣤⡀⠀⠙⢦⣀⣠⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⡏⠀⢀⣴⠟⠁⢈⣿⢦⣀⣸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠛⠙⢦⡴⠟⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣭⣭⣭⣭⣭⡻⣿⣿⣿⣿⣿⣷⠦⠀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣸⣿⣿⣿⢣⣶⣾⡟⣭⡍⣩⣭⢻⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣛⣛⣛⣛⣛⣛⣛⣫⣵⣿⣿⣿⣿⣦⡙⣿⣷⡙⣿⣿⢋⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣌⣡⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣌⣛⠛⠿⣫⣭⣝⢿⡟⣩⣭⡙⢿⣿⣿⣧⡹⠿⣛⣭⣝⡻⠿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢋⣥⡙⢿⣿⣧⡘⣿⣿⢟⣨⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⣃⠹⣿⣿⣮⠻⣿⣿⣎⢡⣾⣿⣿⠃⡻⢿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⠶⠸⣿⣿⣌⢻⣿⣷⣜⠿⠟⣡⣿⠟⣱⣿⣿⡇⣿⣿⡿⣡⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⣿⣿⣌⢻⣿⣷⡙⠿⠿⣰⣿⡿⣫⣾⣿⣿⢋⣴⣶⡎⣧⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡌⢻⣿⣷⡙⠿⠟⣰⣿⣿⣟⣴⣿⣿⠟⣵⣿⣿⡟⢡⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⣷⣝⠿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⡿⢫⣾⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⡟⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣾⣯⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠟⠉⠉⠉⠰⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠈⠛⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⠿⠿⡿⢿⡿⠿⠿⠿⠿⢿⡿⠿⢿⠿⢿⠿⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⠿⣿⣿⣿⣿⣿⣿⣶⠀⠐⠀⢶⠀⠀⠸⡇⠀⣀⠀⠀⢀⠃⠀⠘⠀⠀⠀⠀⠰⡶⠄⢀⣰⣿⣿⣿⣿⣿⡿⠟⠿
⣤⣼⣤⣽⣿⣿⣿⣿⣿⣿⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣶⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣧⣥⣤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠔⠢⢠⣔⠢⡀⠀⡠⠐⢠⡄⠀⠀⠀⠀⢀⡀⢄⠀⢀⠄⠀⠐⠒⡐⢂
⠀⠀⠀⠀⡐⡀⢸⠁⢈⠃⠀⢀⢀⣥⣾⣧⢘⡄⠀⣀⠀⡀⣐⣤⡀⠀⠀⣝⣛⡁⠀⠝⡄⠀⠀⠖⠀⢚⣒⠒⠄
⠀⠀⠀⠀⣴⡁⢸⡀⢀⢆⠀⢀⢭⢼⣟⣋⠋⠀⠀⣈⡐⡈⠵⡴⢀⠀⠀⠀⡡⠈⣆⣥⡁⠀⠐⠒⡃⠧⡦⠅
⠀⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⠐⠙⠀⠉⠀⠀⠀⠀⠉⠘⠒⠀⠀⠀⠀⠀⠊⠀⠐⠂⠁⠀⠀⠀⠀⠈⠀⠐⠊
⠀⠀⠀⠀⢠⣄⣰⣆⣠⠀⠀⠀⢀⡔⠒⠂⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠤⠀⠈⢂⣇⠂⠀⠀⠀⠀⢈⣄
⠀⠀⠀⠀⣤⣿⣷⣿⣿⣤⠀⠀⠀⡒⢒⠐⠀⠀⠀⠅⠂⢙⡋⡐⠽⠀⠈⢰⡉⠉⢉⠆⠃⠀⢇⡸⢀⣠⣴⣆
⠀⠀⠀⠀⢠⡿⢿⡿⢿⠄⠀⠀⠀⠈⠐⢀⠄⠀⠀⠀⠠⡀⢀⠜⠀⠀⢈⠼⢍⠆⠊⣀⠂⠀⠀⢀⣰⣏⠈⣹
⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁
⠀⠀⠀⠀⢀⠊⢀⡀⠁⡀⠀⠐⠒⠒⣦⠊⠓⡄⠀⠔⠚⠄⢠⠒⠣⠀⠀⠰⠆⠪⠃⠖⠄⠀⠐⣈⠔⠊⠙⢦
⠀⠀⠀⠀⠈⣚⠁⠁⡁⡄⠀⠠⠄⡀⠛⠠⠤⠃⠀⣇⢀⡇⢸⡄⣸⠀⠀⢰⢂⡢⣄⠂⠀⠀⠃⡒⠂⠄⠊⠒⠂
⠀⠀⠀⢀⠔⠈⠳⠞⠑⠣⠀⠀⣴⣳⣟⢞⣷⡀⠀⢃⡲⠗⠺⢖⡈⠀⠀⠲⣶⣤⡼⠛⠀⠀⠀⢴⣀⠙⠠⠌
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⠀⠀⠈⢀⣀⡀⠀⠁⠀⠀⡀⠄⠀⠠⢀⠀⠀⠀⡀⢀⡀⢀
⠀⠀⠀⠀⣤⣬⠢⠔⣤⡄⠀⢼⢠⠔⠋⠸⣌⡃⠀⠀⡸⠛⡧⣠⣠⠀⢨⡀⠀⢒⡀⢠⡅⠀⢰⡠⢊⡑⢄⡡
⠀⠀⠀⠀⡳⡞⠀⠀⣞⢳⠀⠈⢿⠉⢠⢐⠔⠁⠀⠿⡿⡦⡼⢿⢿⠀⢀⢹⡈⠁⢉⡏⠀⠀⠿⣄⠋⠝⡠⢿⠁
⠀⠀⠀⠀⠈⠉⠇⠟⠉⠁⠀⠀⠀⠙⠡⠂⠀⠀⠀⠆⠰⠀⠰⠀⠆⠀⠈⠈⠁⠉⠹⠀⠀⠀⠐⠄⠱⠎⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠲⣄⣀⣀⣀⣀⣀⣀⣀⣀⡴⠚⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⠏⢀⣠⠴⠛⠉⠉⠉⠈⠳⣄⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⡄⠀⡴⠃⢰⡋⠀⣀⡤⠖⠓⢦⣀⠀⠘⢦⡀⠠⡄⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡼⠁⣀⡀⠙⠋⠁⠀⠀⠀⠀⠈⠓⢦⣀⠙⣆⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠞⠁⣹⠦⣄⠀⠀⠀⠀⠀⠲⢤⡀⠈⡷⠋⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡼⠁⢠⡞⠛⣷⣀⠀⠲⣄⡀⢙⡏⢡⣼⣧⣤⣤⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⣏⢀⡴⠃⣸⠷⣄⣠⡟⠉⠀⠀⠀⢸⡄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠞⠓⠖⠃⠀⠀⡆⠀⠀⠀⠘⡇⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⡀⠘⠛⡟⠛⠛⠛⠛⡟⠛⠛⠛⠛⡟⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⢷⠋⠀⠀⠈⢦⠀⣷⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢼⡤⠤⠤⢤⡧⠤⠤⠤⣾⠤⠤⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡴⠋⢀⡀⠀⢳⡀⠀⠀⡇⠀⠀⡼⠃⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠋⠀⠀⠀⠙⠳⢤⣽⣦⣀⣇⣠⣞⣥⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁




⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣛⣿⣟⣛⣟⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⢉⣡⣤⡴⢶⡶⣤⣤⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⡞⠉⠀⢸⡇⠀⠙⢮⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠠⠟⠀⠀⠀⢸⡇⠀⠀⠈⢷⠀⢈⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⠙⠛⠒⠶⠶⠶⢾⡷⠶⠶⠖⠘⣇⠉⠁⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⣀⠀⢰⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⠀⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠉⢳⣼⣇⣤⡤⠤⣤⣌⣠⡤⠤⢤⣤⣼⣴⠟⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⣴⠋⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠐⠋⠀⢴⡄⣠⠞⠁⠀⠀⠀⢀⣴⠟⠁⢀⡤⣄⠀⠀⠀⠀⠀⠀⠈⢷⡄⢴⡄⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡞⠁⠀⠀⠀⠀⠀⢸⣅⣠⡶⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⢦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠈⠡⣄⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⢙⡷⠛⢳⣄⡀⠀⠀⠰⣄⠀⠙⢦⡀⠘⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⠀⣠⠞⠉⢙⣦⣄⡀⠈⢳⣄⣨⠟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⢀⣴⡏⠀⣨⠿⢦⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠚⠁