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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣤⣤⣶⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡍⠛⠿⣿⣿⠿⠛⢩⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠘⣿⣿⣧⣼⣿⣿⠃⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠘⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⣀⠀⠀⣀⠀⠘⠛⠛⠁⠀⢀⣾⣿⣿⣿⡿⠟⠋⠉⠀⣀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠉⠁⠀⣀⣤⣴⣾⣿⣿⠀⠀⣿⣿⣶⣦⣄⡀⠀⠈⠛⠛⠋⠁⠀⣀⣤⣶⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠿⠟⠋⠉⠀⢀⡀⠀⠉⠛⠻⠿⣿⣿⣿⠀⠀⣿⣿⣿⠿⠟⠛⠉⠀⢀⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠛⠉⠀⢀⣠⣤⣶⣿⣿⣿⣿⣶⣤⣄⡀⠀⠉⠛⠀⠀⠋⠉⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠾⠿⠿⠷⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠙⠛⠿⣶⣤⣀⣀⠀⠀⣠⡾⠛⠉⢰⡀⠀⢸⡇⠀⢀⡆⠉⠛⢷⣄⠀⠀⣀⣀⣤⣶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣾⠋⠰⣤⡀⠈⠁⠀⣾⣷⠀⠈⠁⢀⣤⠆⠙⣷⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢣⣀⡀⠙⢏⡱⠂⢸⣏⣻⡇⠐⢮⡹⠋⢀⣀⡜⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⠁⠀⡈⣀⠀⠀⣀⣀⠀⠀⣀⢁⠀⠈⠁⠀⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠴⢶⣾⣿⣋⣽⠀⢸⠁⠈⡇⠀⣏⣙⣿⣶⡶⠦⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢀⠀⠀⢉⠉⠀⠈⠙⠋⠁⠀⠉⡉⠀⠀⡀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡐⠋⠁⣀⢎⡳⠄⢸⣏⣹⡇⠠⢞⠱⡀⠈⠙⢂⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⠠⠟⠋⢀⠀⠀⢿⡿⠀⠀⡀⠙⠻⠄⣠⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣠⣤⣴⡿⠟⠋⠉⠁⠀⠙⢷⣤⡀⠸⠃⠀⢸⡏⠀⠘⠇⢀⣤⡾⠋⠀⠈⠉⠙⠻⢿⣦⣤⣄
⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣶⣤⣤⣶⡶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⡟⠉⣿⣿⣻⣛⣻⣟⣟⣛⡿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⢀⣠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⠀⠈⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿⣷⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠈⢿⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠈⢿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣶⣦⣄⠀⠀⠙⠿⣿⣿⣿⡿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣤⣄⡀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢍⣁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠄⣀⠌⡇⠀⢀⣀⠤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⢄⣈⣁⣡⣼⠗⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢻⠀⠀⠛⣏⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢴⣒⣒⢲⡆⠀⠀⠀⠀⠀⠀⠈⠙⢦⡿⠀⡠⠎⡼⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠒⠉⠉⠁⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠛⢳⠈⠦⠔⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⡷⠦⠤⠖⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⠀⠰⠋⠀⠀⠀⣀⣀⣀⣷⠬⢿
⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⠔⠒⢒⡂⠩⡅⡄⠀⠀⠐⠒⡆⢰⠀⠀⠀⢀⡀⣀⣀⡀⠤⠤⠵⠀⠐⠓⠛⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠈⠐⠒⠀⠈⠁⢡⣋⣀⣀⣀⡀⠤⠧⠄⠀⠒⠒⠓⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⢠⠘⠚⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢂⠀⠀⢀⠎
⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⠒⠄⠸⣍⣢⢀⠀⣑⠺⠄⢀⡾⢢⣀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠖⠫⡐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣡⠀⠁⡀⠀⡌⠶⠌⠱⣄⡜⣤⣁⡼⠁
⠀⡀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠃⠀⠈⠢⣄⠀⠀⠀⠀⢀⡠⠃⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠘⠦⣈⣑⠲⣄⢘⣤⠎⠈⢆⣀⣀⡰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠀⠀⠰⢦⠐⠆⠀⠀⠉⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠒⠀⠉⠸⠀⠳⠀⠉⠀⠒⠀⠄⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⢄⡀⠊⠀⠀⡀⠐⠀⢡⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡎⠁⠂⢀⠀⠀⠐⢀⡠⠊⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡀⠈⠑⢀⠀⠀⠀⢀⠀⠈⣿⢄⠀⣶⠀⡾⢳⠀⣶⠀⣠⠟⠀⠀⡀⠀⠀⠂⡀⠊⠑⢄⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠐⠀⠳⣦⣀⠀⢳⡄⢹⣆⠢⠈⢠⠏⠩⡄⠀⡴⡏⡈⢀⡞⠀⢀⣴⠎⠀⠂⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠀⢀⠈⠠⢀⠀⠘⢯⢓⠤⡑⠈⣾⣄⡰⣾⢆⡴⣷⢾⡝⠀⠁⢊⠤⡚⡽⠃⠀⠀⠄⠁⡀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡀⠀⢀⢄⣀⠀⠀⠙⠦⢈⢣⡄⠍⠻⠯⡉⢀⣟⢀⡀⣻⡀⢋⠼⠟⠩⢠⡜⡁⠴⠋⠀⠀⣀⡰⠀⠀⢀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⠀⠀⠀⠀⠉⠻⢮⣄⡀⠀⠠⡿⡄⢀⠐⣹⣿⡇⠦⠐⢨⣿⡍⠂⡀⢠⢿⡬⣄⡶⠖⠛⠛⠉⠀⠀⠀⠀⡄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠀⠀⠀⠀⠀⢤⣄⣉⠲⢭⡶⠃⠈⣧⣶⣁⡼⠟⠛⠛⠻⢧⣀⣴⣴⠃⠺⢏⡀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠠⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣿⢰⢠⡆⠲⠀⠀⣀⣀⣠⡤⡤⢔⠺⣛⠛⡛⠩⡅⣿⢁⡾⠉⠉⢷⡈⣿⠨⠭⢛⠛⣛⠖⡢⢤⢤⣄⣀⣀⠀⠀⠀⢶⠒⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠈⠇⠸⠆⠈⠉⠉⠙⠛⠛⠲⠦⣴⣬⣥⣈⠐⡠⣿⡈⢧⣀⣀⡼⢁⣿⢀⢂⣁⣬⣥⡦⠰⠖⠛⠛⠋⠉⠉⠁⠀⠽⠉⠄⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠆⠀⠀⠄⠀⠐⠒⠛⠁⠄⠈⣡⡄⢈⡟⢟⡉⢳⣤⣍⣡⣤⡞⢉⣻⢻⡁⢠⣼⣳⣄⡈⠛⠒⠂⠀⠠⠀⠀⠐⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠐⠀⠀⠀⠀⣀⣤⣢⣴⠶⠿⠝⣷⠟⡘⠠⣑⣿⡇⡔⢢⢰⣿⡋⠄⢑⠙⣾⠤⠀⠉⡋⠷⣄⣀⠀⠀⠀⠀⠂⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠊⠉⠁⠀⣠⠴⢊⡔⠃⣂⣠⣖⢉⠈⣷⠀⠀⣿⠁⣉⢲⣤⣐⠘⢢⠑⠦⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢀⠀⠈⠀⢠⢞⡠⠖⠩⢀⠁⡝⡶⢯⠜⠣⡿⠆⠹⡻⡀⠍⠲⢥⡳⡄⠀⠁⠂⡠⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠢⠀⣰⠟⠉⠀⡴⠃⠀⣸⡞⠁⠘⣎⣰⠇⠀⢀⠹⣇⠘⢦⠀⠉⠻⣆⠀⠔⠁⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠑⢀⡠⠈⠠⡀⠀⠌⠀⠀⣴⠎⠀⠿⠀⣷⣾⠀⠿⠀⠡⣿⠀⠀⠡⠀⢀⠀⠁⢄⡠⠊⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡠⠊⠁⢄⠀⠈⠑⠀⠀⡸⠃⠀⠀⠂⠀⢸⡇⠀⠀⠀⠀⠘⢇⢀⠠⠊⠁⠀⡠⠈⠑⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠠⠨⠅⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠈⠀⠀⠄⠀⠀⠀⠀⣴⡒⠀⠀⢀⠀⠀⠐⠀⠁⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣄⣀⠀⠀⠀⠀⠦⠽⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠒⠚⠛⠉⠉⠉



⣶⣶⣶⣶⣶⣾⢶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣾⣷⣿⡾⣿⡿⢿⡾⠶⣶⣶⠾⠶⠿⠾⢿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣍⣙⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠯⠘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠋⠉⠉⠉⢙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣷⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠰⠿⠟⠻⣿⠻⠋⠉⠙⣿
⣾⣶⣿⣿⣷⣤⣄⣐⣻⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⠀⠀⠀⠀⠹⣿⣿⣿⣿⠛⠻⠿⠟⠉⠀⠀⠘⣿⣿⡟⠛⠁⠀⢠⣾⣿⣥⣀⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⢀⣽⡇⠀⠀⠀⠀⠹⠿⠛⣯⣠⡀⠀⠀⠀⠀⠀⢠⣿⠇⠈⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⠸⣿⣆⠀⢛⣁⣀⣀⠀⠀⠀⠀⠀⣿⣶⣿⠟⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⠀⠀⠀⠀⠙⢿⡄⣛⣡⡿⠋⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠠⠤⠾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⡀⠀⠀⠀⠀⠀⠘⢫⣏⣀⣀⣀⣤⣴⡾⠿⠛⠀⠀⠀⠀⠀⠀⣒⣾⣿⣿⣿⣿⣿⣿⣿
⠿⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⢿⣿⣿⣿⣿⣿⣿
⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣴⡒⢶⣤⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠃⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠛⠋⠉⠉⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠉⠻⠙⠛⠟⠛⠛⠛⠋⠛⠛⠉⠙⠻⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⠖⢉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⢠⡇⠀⠀⠀⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣧⠀⣀⣀⣂⡀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⢿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⠯⠿⠯⠭⠭⠿⣒⡲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⣠⣶⡿⠟⠋⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠑⠒⢍⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠠⠀⠀⠀⠀⢻⡄⠀⠀⠀⠠⠀⠀⠀⠈⠲⢌⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣿⠟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠑⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣴⣿⠃⠀⠀⠀⠙⠂⠀⠀⠀⠀⡀⠀⠀⣾⠀⠀⣀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⢆⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⣿⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠁⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⣼⣿⠰⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠁⠀⠈⡞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⡽⠶⣦⣤⠄⠹⣿⣿⡰⣤⣤⣶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢱⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣹⣏⠀⠀⢻⣸⡄⠤⠤⣤⣤⣤⣤⣬⣴⣦⣟⠉⢹⡿⡿⠿⠿⠿⠶⠶⠶⠤⠀⢸⠌⠁⠀⢸⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢸⣧⠀⠀⠈⠋⠋⠀⠀⠀⠃⣊⣭⣽⡿⠿⠛⣿⣿⣦⠀⠺⠷⢦⣀⡀⠀⠀⠀⠘⠈⠁⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡵⡃⠀⠀⠀⠀⠀⠀⠀⠙⣩⡑⣰⡒⢰⡶⢸⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢷⠁⣾⠇⢸⣿⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣀⣤⣤⠷⠷⠶⠶⠶⠦⠤⣤⣀⡀⠀⠈⠘⠋⠒⢸⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⢰⣄⠀⣿⠀⠀⢠⣶⡄⠈⡉⠙⠒⠲⠶⠶⢶⡶⠶⠖⢚⠛⠛⣻⣿⠛⢛⠛⢒⣶⠿⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡟⢷⣼⡆⠀⣾⣛⣧⠘⡇⢠⡟⢸⡇⢰⠋⢙⣃⠀⣿⣧⡀⠈⡇⠀⣼⠀⡏⠉⡇⢠⡌⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⣇⠈⡧⠀⠹⠇⠸⠏⠉⠻⠆⢿⡟⠀⢸⡇⠘⢧⣬⠏⢰⣟⣉⣷⣤⣿⣤⣿⣤⣭⣋⣁⠎⢵⠁⢠⠋
⠀⠀⠀⠀⠀⠀⠀⡐⣀⣴⣶⣼⣤⣴⣶⣶⣶⣶⠶⠶⠤⣤⣤⣤⣠⣬⣥⣤⢶⣶⣛⣿⣯⣿⠶⠗⠛⠁⠀⠀⣴⣿⣿⣷⣦⠀⡏⠁⠀⡀
⠀⠀⠀⠀⠀⢀⠂⠀⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠶⣤⣶⣤⣈⣻⠻⣶⣶⣤⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣽⣻⣷⣾⡿⢿⣿⣏⡁⠈⢀⣿⠇⢻⣿⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢋⡤⣿⣟⠋⣴⣶⣿⣿⣿⢿⣶⠴⢋⣀⢬⣿⣿⣿⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣕⣼⣿⣿⣿⣋⣠⣾⣷⠟⠁⠀⢰⣿⣶⠿⠿⠛⡽⢿⣿⣿⠷⣆⣩⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣹⣿⣾⣿⣻⠛⠉⠉⠁⠀⠀⣀⣀⣸⡿⡟⠀⠀⠀⠀⠀⠉⠻⣷⣽⣏⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣿⣿⢯⣻⣿⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⢿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣤⣥⣿⡿⣿⣃⡐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠆⢹⣿⣍⣥⢠⡆
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⣿⣟⢉⣧⣽⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣼⣿⣿⣷⣾⡇
⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠃⠀⠀⣀⠴⠶⠾⣿⣶⣄⢀⡄⠀⠀⡀⢀⣴⣴⣟⣿⣿⣿⣛⡋
⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠏⡉⠻⡟⣸⠏⠀⠀⠀⠀⢀⣒⣚⣿⣟⣻⠟⠁⠀⢰⣿⡿⠅⠍⢹⣾⣿⣿⣧⡴⠂
⠀⠀⠀⠈⠳⣿⣿⣿⣿⣷⠘⠻⢾⣿⡇⠀⠀⠀⠁⠀⠊⢩⣟⡛⠿⠛⠀⠀⠀⠘⣿⢲⣿⢶⣿⣿⣿⣿⠟⢡
⠀⠀⠀⠀⠀⠺⣧⣿⣿⣿⠀⣿⢾⣿⠃⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⢸⡎⠹⠾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣇⢉⣺⣿⡿⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⣼⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠁⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡴⠿⠀⢤⡀⠀⣠⣿⣆⣤⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠉⠠⣿⣾⣀⣿⡀⠀⠀⠀⠀⠀⠚⠁⠀⡀⠀⠐⠈⠿⢏⠈⢻⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⣀⣀⣸⣿⡻⣿⣄⠀⠰⠀⠀⠀⣠⣾⣿⠷⣶⣾⣶⣿⣿⣶⡤⣿⣛⣿⣿⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⣿⠁⠹⣿⣁⠇⣿⠀⣦⠀⢀⠸⡟⣿⠁⠀⠈⢡⣤⠶⢉⠹⣷⣙⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡧⢰⣄⢸⣇⢠⣿⣸⣿⠀⣬⡿⢃⠉⠀⢀⣰⣸⣷⣾⣷⡶⢤⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋⢹⡇⣻⣿⠟⡇⢸⣟⣻⣗⢶⣿⠀⠘⠀⠠⣿⠟⢉⠃⠈⠳⡆⢠⡍⣿⣿⠛⢿⠉⠁
⠀⠀⠀⠀⠰⢟⢙⣧⣤⣾⣿⣿⣿⠏⠀⣷⠜⢿⡉⠛⠆⠀⠰⠃⠀⠚⠏⠀⠸⢀⠀⠀⡤⠞⢡⡏⢿⣶⣼⣷⣄⡀
⠀⠀⠀⠰⠟⣦⠟⠛⠛⠛⣠⠙⣿⡀⠀⢻⢄⣾⡇⠈⢿⠀⠀⠀⠀⠀⠀⢀⣾⣾⣶⣠⣿⢠⡏⣽⠀⣿⣈⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⠀⠉⢻⣿⡆⣸⣿⡷⠀⣄⠀⠛⢼⣀⣄⣼⣟⡻⢿⠿⠿⢁⠞⠻⡇⡀⢙⣿⣿⣿⣿⣏⣿⢿⣿⢦⣀
⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⠸⠂⢾⠈⠙⢁⡞⠛⢊⠆⢳⠀⠀⠸⡇⠀⠉⠸⠁⡌⠀⠀⢸⠀⠀⠀⢱⣾⣿⢿⣿⣿⣿⣏⢰⣻⠂⣽⠳⡀⢀⣄
⠀⠀⠀⠀⠉⠛⢶⣶⣆⡀⢀⠐⢀⡆⠀⢹⣀⡄⠛⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣷⣤⡦⢾⣶⠈⢠⣿⣾⣿⣿⣿⣿⠞⡛⢶⡆⠈⠁⣠⠁
⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⣮⡀⡷⢠⡇⢸⣿⣀⡀⢸⣁⠀⢊⠀⠀⠀⠀⠀⠀⠸⢸⠇⣉⠛⠚⠛⣰⠏⣿⣿⣿⢯⠹⣻⣞⢾⣾⣱⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢴⣶⣾⣿⣇⣧⡀⡧⢹⣿⣟⣷⠘⣟⠀⠀⠀⢀⠀⠀⢈⡇⠀⠀⠀⠈⢀⡀⡀⢿⣿⣿⣿⣿⡅⣺⣟⣡⣾⠿⢟⣯⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣿⣛⢈⠷⢀⣿⣼⣿⣇⣠⠉⣭⣤⡄⠀⠀⠀⠾⠀⡇⠀⠀⣤⢸⣟⠳⣾⣿⣿⣻⣟⢶⠟⣿⠏⠣⠢⠋⠕⠁
⠀⠀⠀⠀⠀⠀⠀⡰⢿⣮⡷⠀⠈⢄⣸⡟⣿⠏⠙⢻⣶⣿⠛⠻⠆⢸⡄⢀⠸⡇⠀⠲⢻⡀⣥⢾⣻⣏⠻⣿⠿⠇⢘⣽⠓⠁⣀⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠀⣀⣌⠻⣿⣿⣷⣿⠹⣿⣿⠾⣷⣀⣬⣁⢺⡅⠘⣠⡴⣿⣿⡿⣣⡿⣯⠑⣀⡿⢮⡿⠁⠈⠐⢻⠛⡔
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢉⠉⠰⠌⠙⣣⣿⣴⣿⠟⢶⣿⣅⡙⣾⠀⢧⣸⣾⣿⠋⣿⣄⢿⢹⠏⡞⣽⠇⢈⠀⠈⠀⠀⠀⠛⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⢣⣿⣏⢿⣷⣤⣿⣿⡇⠁⠘⢻⣿⣿⣏⣰⡿⣿⣽⡇⢾⠸⡋⢠⣤⠀⠠⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⡿⠀⠙⠛⠛⠛⢁⡇⢀⣘⣛⢿⠛⢩⣿⣿⣿⡏⠀⢠⠎⢜⠁⠰⠁⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⡟⠀⣀⣉⢀⣀⠀⠀⠤⢀⣠⣌⠁⢸⣿⣇⣾⡷⠀⠎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⢻⠿⣿⣿⠀⠀⠀⡹⠿⣟⢷⡞⢱⣿⡟⠁⠈⡰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⡇⠀⠀⠀⠀⡿⠉⠀⠀⠈⠁⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢧⡀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠃⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⢀⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣧⡀⠀⠀⠸⣿⣿⣶⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣋⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣽⠆⢀⡀⣹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡽⣻⣾⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣵⣿⣿⣿⡋⠙⠛⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣮⣿⢿⣵⢷⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⢯⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠋⠀⠺⣯⡽⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⡗⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣶⣽⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⣷⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢛⣩⣿⣿⣿⣽⣿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⡻⠿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠛⠻⢤⣽⣿⣿⣿⣿⡧⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣾⡟⠉⠛⠀⠀⢸⡿⠛⠁⠈⠛⠿⣷⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣷⣯⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⢠⣤⣀⣀⡀⠀⠀⣀⣬⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡀⢤⣿⣿⡟⠛⠀⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡍⢿⢿⣿⣤⠀⠀⠀⠈⠓⠊⠀⠀⠀⠘⣿⡿⢻⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⡘⢦⣟⡃⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣿⣀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⢷⣾⣿⣿⢿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⣟⠏⠀⠀⠀⠀⠀⠀⣴⠷⠶⢾⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣽⡷⠀⠀⢀⠀⣠⠾⠃⠀⣰⣿⡿⢿⣿⣷⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣄⣄⢊⣇⠀⠀⠁⠰⠁⠀⠀⠀⡇⠀⡈⢺⡻⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠫⠊⢻⣆⠀⠀⠀⠀⡄⡔⠀⢠⣴⣧⡌⠜⢿⣟⣳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⢴⣶⣴⣿⣿⣿⣿⣿⣿⣿⡦⢠⡍⢃⡀⠀⠀⠀⠀⠀⠀⠈⡆⠋⢤⣨⣷⣼⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⣠⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡅⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⡀
⠀⠀⠀⡠⠈⠁⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠂⠀⠀⠀⠀⠀⠄⠠⠀⠀⠡⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢼⣵⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠐⠀⠀⠀⠀⠀⠀⢰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢰⢀⣄⠀⢠⢤⡁⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⡟⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡙⠀⠠⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢿⡿⠿⠿⢟⡷⣿⣿⣿⣿⡟⠯⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢭⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣄⡀⣀⠠⣰⠇⣿⣿⡟⠩⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠿⢿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣟⣃⠀⠒⣿⣿⣿⣿⣄⣾⢛⠿⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠻⠿⡟⠻⠿⠿⣿⡇⠀⠳⡟⠋⠘⠓⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⣷⠀⢠⠀⠀⢀⣀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠘⣇⠸⣆⠀⠟⠁⠀⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠸⡦⠶⠴⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠊⠛⠉⠳⣌⠳⡄⠀⠀⠀⠀⠀⠀⢀⣾⣉⡛⠒⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣢⡈⢦⡀⠀⠀⠀⣴⠋⠀⠉⠉⠙⠲⠦⣄⠈⠙⠲⣄
⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠉⠙⢆⠀⠀⣠⠎⠉⠉⠛⠦⣀⠀⠀⠀⠈⠙⢦⡀⠀⠱⣄
⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠷⠀⠀⢸⡆
⠀⠀⠀⠈⢧⠀⠀⠻⡀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠈⠳⣄⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡉⠓⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⠤⣭⣭⣍⣉⣉⣀⣀⣠⣤⣤⠤⠴⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢀⣀⣀⡀⠀⣀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠿⠟⠁⠸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣿⣿⣿⢿⣙⠃⠀⠀⠀⠀⠀⠀⠀⠰⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢿⣿⣷⣿⣿⠆⠀⠀⠀⠀⠐⠂⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠙⣆⡀⠀⠙⢿⣦⡀⠀⠀⠀⠲⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣮⢑⢂⣀⣤⡈⠻⣦⠀⠈⠳⣄⠀⠛⠿⣷⣜⣿⣿⣷⣴⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢾⣿⠧⢉⣿⣦⣶⣨⣀⢈⠀⠀⠀⠙⣷⣦⣤⣈⣙⡛⣛⣿⣿⣿⣄⠀⡢⡀
⠀⠀⠀⠀⠀⠀⠀⣽⣗⠚⠋⠀⠙⠷⣽⣿⣦⡁⠀⠀⠀⠘⢿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠘⣧⣯⣤⣞⠀⢠⡀⠈⢻⣿⣿⣦⡀⠀⠀⠐⢿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣾⣻⡇⣝⣷⣾⣷⠀⠀⠻⣿⠿⡟⠳⠦⣄⠈⣿⡿⠿⠿⠟⠌⢻⡿⠙⠿⠻⣷
⠀⠀⠀⠀⠀⠀⠘⢿⣼⢗⡊⡸⣿⣿⣾⡇⠀⠈⢢⣌⠂⠤⠆⢸⣿⠇⠀⠢⠄⠀⠀⠣⡀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⡸⠏⠿⢺⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠟⣿⢿⣿⡏⠉⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⢒⣿⡀⠤⠤⡇⠀⠀⠀⢀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣳⣤⣤⣷⣴⣶⣾⣿⣿⣿⠁
⠀⠀⠈⠀⢀⣀⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣋⣯⣟⣿⣆⠀⠀⠀⠀⠐⠦⠄⠐
⠀⠀⠠⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣏⣽⣿⠟⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠉⢉⡉⠁
⠐⠚⠛⠿⠷⠶⠾⣟⠛⠛⠹⠛⠿⣷⣿⠟⢻⣿⣿⡿⠿⠽⠛⠛⢛⣖⣿⢿⣿⡟⠉⠉
⠀⠀⠉⠛⠛⠀⠰⠦⢭⣍⣉⣁⠀⠈⠛⠋⠬⠽⣿⠅⠀⠒⠒⠒⠒⣂⣉⡭⠉⠉⠀⠒⠒⠒⠢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠁⠀⠈⠉⠑⠒⠀⠀⠀⠉⠉⠓⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠑⢄⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣢
⠀⠀⠑⣄⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⢣
⢀⠤⠒⠉⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠁⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠒⠄⡀⠀⠀⠀⠃
⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠉⠒⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡤⠤
⠒⠄⠀⠀⠀⠀⠀⠀⠀⢐⣀⠤⠤⠒⠊⠉⠀⠁⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⡀⠤⠐⠒⠉⠁⠀⠀⠀⠑⡄
⣀⣀⢠⡠⠤⠴⠒⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⢃⠀⠒⠂⠈
⠢⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⠉
⠰⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⢀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠖
⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠈⠁⠀⠐
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢤⠀⠀⢀⠙⡴⠢⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⢰⢒⠒⠂⡂⠠⠄⢠⠐⣒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⡆
⠀⠀⡄⠰⠀⠠⡥⢱⢀⠆⡈⡘⢰⠀⠀⠀⡠⠂⠉⠍⢐⢄⠀⠀⠀⠀⢸⠒⠒⢺⠀⠀⠀⠀⢘⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⣇⡀⠀⢠⠒⠊⠉⠀⠉⢁⡈⠀⠀⢰⠡⠀⡴⣪⠃⠀⡆⠀⠀⠀⢸⣤⣄⡸⠀⠀⠀⠀⢸⠀⠀⠀⣄⠀⠀⠀⠀⡇
⠀⠀⡇⡔⡆⡉⠉⠏⡩⠄⠀⣀⢠⠀⠀⠀⢆⠘⠊⠁⠀⡠⠁⠀⢠⡟⠚⡇⠈⠃⢳⣄⠀⠀⢸⠀⠀⠰⡚⡵⠄⠀⠀⡇
⠀⠀⢠⢁⢡⠡⠀⢠⢹⡸⠈⠈⠘⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠫⢭⣧⣴⣧⠋⠀⠀⠀⢸⠀⠀⠀⠈⠳⠀⠀⠀⡇
⠀⠀⠘⠂⠤⠤⠤⢠⡀⠠⠤⠭⠐⠁⠀⠀⠀⠀⠀⠀⠒⡄⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⢸⠀⠘⠃⠘⠃⠘⠃⢀⡇
⠀⠀⠎⠀⠀⠠⠤⠄⠀⠀⠑⠀⠀⠀⢀⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠒⠒⠒⠒⠒⠒⡌⡆⠀⠀⠐⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⣉⡑⡄
⠀⠀⠀⠀⠠⠂⣉⠐⢄⠀⠀⠀⠀⠀⡇⡇⢀⠔⣀⡒⡄⠀⡇⡇⠀⠀⠀⠀⠴⠾⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠿⠇⡇⡇
⠀⠀⠀⠀⢃⠸⠄⠇⡸⠀⠀⠀⠀⠀⡇⡇⠘⡈⠢⠂⡄⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢃⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⢢⠀⡔⠁⠀⠀⠀⠀⠀⡇⡇⠀⠱⡀⡜⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⡄⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠪⢀⣉⣀⠕⠀⠀⠀⠀⠀⡇⡇⠀⠀⠈⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠑⠒⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣈⠉⣉⠉⢉⡉⢉⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃⡇
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢇⠣⠀⠀⠀⠘⠀⠐⢁⠇⠀⠀⢀⠀⠀⠘⠤⠤⠃⠸⠤⠬⠀⠨⠤⠼⠀⠀⢀⠇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠒⠒⠒⣿⡂⠤⠤⣯⠀⠀⠀⠀⣀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣦⣤⣼⣴⣶⣾⣿⣿⣿⠏
⠀⠀⠈⠁⢀⣀⣀⡀⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣋⣯⣽⣻⣇⠀⠀⠀⠀⠀⠲⠄⠐⠒
⠀⠈⠡⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣟⣽⣿⠟⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠈⠍⣉⠁
⠒⠚⠛⠿⠷⠶⠾⣟⡛⠛⠫⠛⠻⣷⣾⠿⢛⣿⣿⣿⠿⠯⠟⠛⢛⣷⣛⡿⣿⣿⠉⠉⠁
⠀⠀⠉⠛⠛⠀⠐⠦⠭⣍⣉⣁⠀⠈⠛⠋⠥⠽⣿⡧⠀⠐⠒⠒⠒⣒⣀⡭⠉⠉⠀⠐⠒⠒⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠃⠀⠀⠉⠑⠒⠒⠀⠀⠈⠉⠙⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠏
⠀⡀⣀⣰⠀⢀⡀⡀⣄⠀⢀⣰⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⢠⣷⣿⣿⣾⣾⣿⣷⣿⣷⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠠⠄⠀⠀⠀⠀⠀⢬⡧
⠸⠟⠟⠿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⢍⡧⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠀⠳⠪⣽⣷⣂
⢀⣰⣷⣠⣼⣥⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⢠⣿⣀⠛⢭⣽⣯⠶
⠀⣿⣿⣿⣿⣿⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⠀⠰⢬⣿⠔⠂⠰⣬⣷⠞
⠀⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⣷⣄⠨⠽⣿⠭⠄⡼⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣩⣭⣭⣭⣭⣭⣭⢉⣭⣭⡉⣭⣭⣭⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⣡⣿⣿⣿⠰⣿⣿⠇⣿⣿⣿⣦⠹⢿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢋⣾⡇⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⢹⣿⣧⣙⣉⣋⢛⣋⣙⠛⣋⣉⣉⣉⣛⡛⣋⣉⣙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣆⠻⣿⣿⣿⣿⠈⣿⣿⡇⣿⣿⣿⣿⡿⣡⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣝⠻⣿⣿⠀⣿⣿⡇⣿⣿⠿⣋⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣭⣌⣛⣛⣁⣭⣴⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁



⠀⠀⣀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣏⢩⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠐⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣶⠒⢂⠀⠀⠈⣠⡴⠂⡀⠂⠀⠀⢤⠄⠠⠀⠀⠀⠐⠀⠥⠤⠎⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⣦⢠⡀⢸⠀⢸⠀⠀⡀⠓⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⣀⠄⠰⠫⠄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣬⣭⣛⠺⡁⠀⡙⠎⠀⠄⠀⢀⡸⠠⣀⠈⠀⠀⠀⠀⡄⠀⠀⠦⠀⠊⢡⣈⠀⠆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠉⠀⠀⢸⠏⠙⠖⡄⠀⠀⠁⠐⠀⠀⠁⠀⠀⠀⢀⠀⠄⠰⢅⠀⠀⠀⣠⠦⠀⠀⠍⠛⡐
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠄⠘⠵⢦⠋⠀⠀⡀⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠎⠀⠀⠀⠁⠒⣦⠀⣾⢁⠃
⠀⠀⠀⠀⠀⠀⢸⡸⠀⢀⡠⠚⠁⢀⡠⢊⢴⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠋⢊⠃⠄
⠀⠀⠀⠀⠀⠀⡈⠠⣄⡠⠭⠭⠀⢐⣈⢔⣣⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢲⠂⠀⠀⠀⠀⠀⣇⠌⡐
⠀⠀⠀⠀⢀⠎⠘⢆⢤⣉⠭⢿⡯⠭⢀⣻⣹⠄⠐⠂⠀⠁⠀⠀⠀⠀⠀⡐⣱⠒⠒⠚⡆⠀⠀⠰⣿⣆⡼⣰⠃
⠀⠀⢀⠀⠧⠤⢀⣀⣁⠀⠀⠀⠉⠒⡊⢁⠟⡀⠀⠀⠀⠀⠄⠀⠀⡀⣘⠢⣸⣐⣛⣙⣃⠛⠀⡀⣛⣛⢃⠏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⢓⠂⠄⢤⡆⢀⡀⠠⠠⠐⠐⠀⠉⠁⠀⠈⠢⡈⠢⡀⠀⡏⠀⠀⣀⢧⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⠢⡂⠀⠫⢄⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⢀⡜⠁⠀⠀⣀⣀⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠦⣤⣀⣀⣀⠀⠀⠈⢧⡀
⠀⠀⠀⣸⣧⡴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⣦⣸⣇
⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄
⠀⡼⠃⠀⠀⠀⢀⡴⠖⠛⠃⠉⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⠛⠋⠛⠲⢦⡀⠀⠀⠀⠘⣇
⠸⠇⠀⠀⠀⠀⢸⡇⠀⣤⣶⣦⠴⣶⣶⣶⡶⠶⠶⠶⠶⠦⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠤⠴⣶⣶⣤⠀⢸⡇⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢸⡇⠀⣷⠀⢿⡀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⡇
⣇⠀⠀⠀⠀⠀⢸⡇⠀⣇⠀⠀⢻⡆⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⡀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣧⠀⠀⢀⡿⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⢉⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣷⣤⠴⠛⠁⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⠀⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣷⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⣼⣿⣿⠁⠀⠀⢀⣼⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣟⣉⣈⠉⠉⠉⠉⠛⠻⢦⣤⡀⠀⠀⠈⠻⣿⣿⣦⣠⣿⣿⠇⠀⠀⣴⠟⣩⠀⢸⡇
⡟⠀⠀⠀⠀⠀⢸⡇⠀⡟⠋⠉⠛⠳⠶⣤⡀⠀⠀⠈⠙⢦⡀⠀⠀⠘⢿⣿⣿⣿⣿⠀⠀⣴⡏⠀⣾⠀⢸⡇
⣇⠀⠀⠀⠀⠀⢸⡇⠀⣷⠶⢦⣀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠙⣦⡀⠀⠘⣿⣿⣿⡟⠀⠀⣹⡄⠀⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⡷⠀⠀⠙⣧⠀⠀⠀⠘⢷⡀⠀⠀⠀⠘⢧⠀⠀⢸⣿⣿⣷⠀⠀⠘⣧⠀⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣽⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⠀⠀⠀⠙⢷⣼⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣯⠀⠀⢠⡟⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⡆⠀⠀⠀⠈⣻⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢸⡇⠀⣏⣀⡴⠋⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡞⠁⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⣿⠀⢸⡇
⡇⠀⠀⠀⠀⠀⢸⡇⠀⡿⠋⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠀⢸⡇
⢻⠀⠀⠀⠀⠀⢸⡇⠀⣇⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⣮⠀⢸⡇⠀⠀⠀⠀⢠
⢸⡇⠀⠀⠀⠀⢸⡇⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣸⠇⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⢸
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⢳⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⢀⣰⠖⠛⠛⠁⠉⠛⠛⠶⣦⡀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⡄
⠀⢸⡆⠀⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣴⣦⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠀⢸⡇
⠀⠸⣧⣤⣄⠀⠈⠉⠙⠛⠿⠿⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠘⢣⠀⠀⠀⠿⠿⠛⠋⠉⠀⠀⣠⣤⣼⠃
⠀⠀⣿⠀⠈⠙⠛⠶⠶⣄⣀⠀⠀⠀⢸⠇⠀⢀⣤⣄⠀⢠⣶⣶⡄⢀⣀⣄⡀⠀⢸⡇⠀⠀⢀⣀⣠⠶⠶⠛⠋⠀⠀⣿
⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠉⠘⢳⡄⢸⡄⠀⠘⠛⠛⠁⠹⢿⡿⠇⠈⠛⠛⠃⠀⢸⡇⢠⡞⠋⠉⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⣿⠀⢠⣾⣿⣆⠀⠀⠀⠸⡇⠘⢧⡀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⢀⡼⠁⢸⠇⠀⠀⠀⣴⣿⣷⡄⠀⣿
⠀⠀⠀⢸⡆⠈⠻⠿⠋⠀⠀⠀⠀⢻⠀⠈⢳⣄⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⣠⠾⠁⠀⡟⠀⠀⠀⠀⠙⠿⠟⠁⢸⡇
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⠳⢦⣀⣀⣀⣀⣀⣀⡴⠞⠃⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠙⣦⠀⢀⣴⣶⣄⠀⠀⢻⡀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⣶⣤⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠸⣧⡘⠿⣿⠟⠀⠀⠸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⠇⠀⠀⠻⣿⠿⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢣⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡞⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⢸⡇⠀⠀⠀⠻⢿⣿⣿⡿⠛⠀⠀⠀⢸⡇⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⣬⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣤⠴⠶⠋⠁
⣴⣦⣤⣴⣶⣤⣶⣤⣤⣤⣤⣴⣴⣶⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴
⣿⣿⣿⣿⠛⠉⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢲⡴⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀⠀⠀⡇⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢋⣜⠳⣢⠅⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢅⣂⡥⢔⡂⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⡃⠀⠀⠐⠩⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⡌⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠋⠑⠦⡠⢊⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠙⠲⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣹⡷⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⣿⣷⣷⡄⠀⠀⢠⣾⣿⣿⣿⣿⡿⢟⡁⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⠂⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⢿⣿⡏⢐⡎⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡛⢤⣻⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡤⣸⣿⠗⠬⠾⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠈⠭⢕⣩⣶⣿⢏⡆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠰⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠻⠿⢶⣿⣿⢿⡛⣉⠴⡁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⠲⠆⠉⣡⠦⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠲⢄⣀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣡⠖⠒⠒⠒⠒⠒⠒⠒⡐⠰⢇⠀⠀⠀⠠⢆⣐⣒⡆⢰⣿⣿⣿⣿⣿⣿⣷⣐⠚⠤⢙
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⢋⡱⠠⠻⡀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠁⠘⠀⠀⠀⢃⡴⠧⠴⡄⢸⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠉⠀⡋⢉⡄⢛⠃⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⣣⠀⠀⠀⠶⣠⡉⠈⠉⠈⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠇⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠋⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠂⢐⢧⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⢸⡌⢀⣤⡞⠐⠃⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⡂⢀⠔⣸⣿⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⡉⣰⡿⣿⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣤⠾⢂⣾⣿⠀⡟⣧⠀⠀⠀⠈⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⢈⠘⠁⠀⣾⣏⡏⠀⡇⢿⡀⠀⠀⠐⠒⠀⠀⠀⠸⠆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡤⠁⠀⠀⣾⣿⣿⡇⠀⡇⢸⡇⠀⠀⠀⠀⠑⡀⠀⢠⠅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⢎⡀⠀⢀⡿⣿⣿⣿⠄⠠⡇⠀⣿⡂⠀⠀⠀⠀⠈⠆⢀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣤⣉⣀⠀⡀⠀⡇⠀⢻⣏⠀⠀⠀⠀⠀⠀⠸⡷⡶⢦⣤⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣤⣼⣶⣤⣤⣤⣃⣀⣀⣀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⢠⣴⠶⠾⠿⡭⣤⣒⡚⠛⣛⠛⠛⠻⠿⠟⠛⠻⠿⠿⠿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⠁⠤⠤
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠃⠀⠤⠖⠊⠉⠩⠵⠖⠛⢳⡖⢀⣤⡴⠶⠶⢟⣩⠴⠤⣤⣴⣶⡆⠨⢤⡤⠉⠀⢀⢀⡤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠴⠤⠈⠭⢉⣉⡥⠴⠶⠒⠒⠒⠲⠄⠈⠉⠉⠀⠀⠀⠉⠛⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀
⠠⡀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠠⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠑⡆⠂⠉⠀⠒⠒⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠉⠁⠀⠈⠐⠤⡀
⠐⡀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠤⣀
⠀⠐⡄⠀⠀⠀⠈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁
⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠑⢄⡀⠀⠀⢈⣆⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠑⢄⠘⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣠⠦⠆⠐⠐⠒⠒⠒⠒⠒⢄⡀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠁⢀⡔⠉⠉⠂⠆⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⠀⣀⠠⠀⠘⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⣀⠔⠁⠀⠀⠀⡀⣀⠠⠤⠄⠐⠓⢤⡀⠀⢠⢞⠘⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠢⡀
⠀⠉⠉⠁⠀⠀⠀⠒⠂⠤⠔⠠⡀⢀⣣⣤⠮⠤⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⢈⠟⠀⠈⠛⠁⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠎⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢰⠀⢀⡀⠠⠠⠀⠒⠂⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡠⠔⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⠊⠐
⢀⠄⠀⡒⠨⠆⠒⠉⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠃
⠐⠈⠁⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠆
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⣀⠀⠀⢀⠀⡀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠺⣼⡇⠠⠀⠀⠸⣿⡷⠘⡀⠀⠀⢀⠀⣧⠟⢀⡆⠀⠀⠀⠀⠀⢠⠘⠀⢸⡇⠀⣸⢉⡇⢀⠸⠀⡇⠴⡟⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⠀⢂⡈⣷⠀⠖⠁⠀⣿⡇⠋⠁⢀⣦⠸⠀⣇⠄⠂⠀⠀⣠⠀⠀⠀⠀⢻⠀⢸⡇⣄⡏⢈⠥⠀⠣⠠⡇⢀⡅⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣧⢸⡶⠃⠀⠀⣿⣦⠀⢠⠈⠀⠀⢀⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⣸⠿⠏⢠⠂⢀⠀⠠⢤⡧⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡁⠈⣧⠀⠀⠀⣿⣿⡇⡈⠀⠀⠀⢸⣀⣤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡶⢰⠀⠀⠄⠀⠀⠀⣿⠦⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣸⡀⠀⠀⣿⣿⠄⡠⠖⠀⠀⠈⠁⠀⠀⠓⠦⠀⠀⠀⠀⠀⠀⠀⠘⣷⢦⠀⠀⠒⠀⠀⠀⢿⠶⠀⠐⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⡟⠈⡄⠀⠀⠀⠀⠂⠈⢲⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣿⣿⠶⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⣰⠔⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣿⣿⡿⢆⣴⠒⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⡀⣿⢠⣶⣷⣶⣄⡀⠀⢰⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢱⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⣿⣿⣿⣿⡧⠇⠘⠛⠿⠷⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⠏⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠙⢿⣿⣿⣿⣿⣿⣿⡁⢸⣦⣄⠀⠀⠐⢾⡄⣠⠴⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⡀⠸⣿⣿⡏⠀⠘⠁⣀⣴⡾⠟⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠇⣸⣿⣿⣷⣤⡀⢸⡇⡏⢤⣠⣿⣴⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢏⠀⠷⢾⣿⣿⡇⣤⣴⠞⠋⢡⠔⢸⠀⠀⢀⠂⠀⠀⡇⡇⡄⡉⠻⣿⡟⠃⣿⣿⣿⣿⣿⣾⣇⡇⠀⢿⣶⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡚⠀⠁⢀⣿⣿⣧⣿⠀⠀⠀⢦⡴⢤⣤⣶⣅⡰⠃⠀⠡⠃⣧⢸⣄⣿⡷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠡⠊⣉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠆⠈⣁⣴⠞⠋⣿⣿⠀⣼⠀⢀⣴⠟⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠇⢸⡇⣿⡟⣧⠈⠻⣿⣿⣿⣿⣯⢛⣉⣴⣾⠛⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⡴⠟⠉⠀⠀⠟⣿⠟⠀⢈⣴⡏⠁⠳⢎⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠉⠀⠀⣬⣿⣿⢸⣿⢹⣯⣦⣿⡇⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⢟⠁⠀⠀⢦⡀⢠⠀⢸⣿⡟⢾⠋⡇⠀⠀⠀⠀⠀⠃⡾⢰⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃⣠⣾⣿⣿⣿⢿⡗⢸⣿⣸⠛⡇⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⣿⠀⠠⠄⢼⠷⠛⢦⣸⣿⠃⠈⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⢰⣿⣿⣿⣿⣿⢸⣇⠘⡟⢿⠀⢳⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⢰⠀⠀⠈⢹⣿⡏⢀⠀⠀⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⣧⢸⣿⣿⣿⣿⣿⢸⣏⢰⣿⠸⡀⠘⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⠀⠈⠀⠀⠀⢸⣿⠇⠠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣾⣿⡍⠈⣿⣿⣿⣿⣿⢸⣿⢸⣾⢠⣷⢈⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢸⠀⠀⣠⣾⣿⣿⣧⡓⡿⣯⣿⣿⣿⢸⡏⠀⢻⢸⣮⢀⡇⡇
⠀⠀⢀⡀⠀⣠⠤⣴⣀⣿⣶⣾⠀⠀⠀⠘⠀⠀⠀⢸⣿⣿⡅⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠰⠀⢀⣴⣿⣿⣿⣿⡷⠟⢰⣿⣿⣿⣿⢸⡇⢀⠹⢸⣿⢸⡇⡅
⠀⢠⣼⣿⣿⣽⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠇⠀⢸⣾⣷⡧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⠃⣾⣿⣿⣿⡇⣿⣇⣼⡀⢸⡟⢸⡏⡇
⠀⠸⣿⣿⣿⣿⢋⣿⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⢷⡇⠀⠀⠀⠀⠀⠀⡿⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣇⢿⡁⣸⣧⣸⣇⣸⡇⠃
⠀⠀⣿⣿⡿⠏⢿⡿⠿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢿⣿⢯⡈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠛⣛⢻⢛⡟⠛⠛⠛⣿⣷⡊⡘⠛⡿⠻⠛⢸⣯⣾⠻⠛⠟⠟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣇⠀⠀⠀⠻⠛⠃⠁⠀⠅⢰⠀⣾⠛⢳⢠⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠂⡈⠀⠛⠀⠈⠈⠀⠀⢸⣿
⠀⠀⠂⠠⢤⢤⢰⠆⠄⠀⠶⠶⠶⠶⠦⠶⠲⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠈⠩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢠⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠸⣷⠀⡇⣽⠀⠀⢸⡆⠀⠀⣴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠀⡀⠀⢠⢰⣟⣿⡇⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⢀⠀⠀⠀⢀⣿⣼⣷⣴⣷⣾⣴⡔⣹⡇⢴⣧⢿⣾⡖⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣿⡇⡣⠀⣼⣼⣿⣿⣿⡃⠀⠀⠐⣢⣤⣼⣇⣸⣧⣼⡆⠀⠤⠬⢿⣿⡟⠉⢻⣿⣿⡇⣚⢻⣽⣿⣧⡿⢡⡛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⣿⣿⣿⣧⣨⡁⢻⣿⣿⡿⢿⠁⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⡿⠀⠀⠀⠙⣯⣥⢿⣾⣏⣺⣿⢕⣯⡄⠸⣷
⠀⠀⠀⠀⠀⠀⣀⣼⣾⣿⣿⣿⣿⣿⣫⡿⠀⠈⣿⣿⠇⠸⣀⡆⠀⠀⡌⠀⣻⣿⣿⠏⠁⠀⠛⡛⠓⣾⠃⠀⡀⡀⠐⠛⣥⡾⢻⣍⢹⣏⣴⠿⣿⠤⠿
⠀⠀⠀⢀⣷⣿⣿⡟⣿⣿⣿⣯⢿⡏⣼⠇⠀⠀⢹⡟⠄⠀⣿⡼⣷⡿⠄⠀⠂⣿⣿⣀⠀⠀⠈⠉⣠⠼⠃⠁⠀⠈⠒⠠⣿⣇⢈⣿⣿⡏⢿⣿⡉⡷⠄
⠀⠀⠀⣾⣿⣿⣿⣿⡿⠿⠿⠓⠛⠓⠏⠀⠀⠀⢸⠇⢀⡀⠘⣷⣽⢓⣀⣄⠠⠝⠿⠛⠳⠾⣿⢶⡇⠀⠀⢠⣠⣤⣀⣀⡜⢻⡿⣷⡿⡈⢼⣿⠳⢟
⠀⠀⠼⠿⠛⠉⣉⠁⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠋⠉⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠛⠉⠙⠗⠞⠃⠛⢂⠈⢠⣹⠆⠀⠃
⠀⠀⠀⠀⠀⠈⠽⠀⠂⠤⣤⣤⣧⠠⢠⣤⣤⡀⣀⠀⠤⠤⢀⣢⣄⣀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠶⠎⢉⣺⡟⣂⣉⣽⣷⣄⣀⣉⣱⡖⠀⠀⠀⠀⠀⠠⢶⣶⠤⢴⣈⡉⠷⣄⠀⠈⢻⡆
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠐⠺⠶⠶⠦⠶⠴⠶⠒⠛⠀⠠⠾⠷⠒⠒⠋⠉
⠀⠈⠀⠈⠁⢦⣴⣾⣿⣁⣀⣄⠀⣷⡄⠀⠀⣴⡄⠀⠀⠀⣆⠀⡀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣷⣷⡄⠹⣿⣤⣧⢾⡏⣧⣷⢠⢼⣷⡀⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣾⣿⡿⠿⠛⢿⣾⣷⣿⡇⠀⢁⠀⡆⡄⠀⡀⣼⣿⣿⠀⣆⣿⡆⠀⠀⢀⢸⡄⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠐⡻⢿⣿⡟⣿⠿⢿⣭⣥⠀⢘⠂⣻⢻⣧⣷⣿⣿⣿⡄⢸⢸⡇⠀⠀⠈⡄⣿⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠛⠁⠀⠒⠒⠀⠓⠄⠊⠀⡥⠜⠛⢛⠻⣿⣿⡗⡚⠉⢉⡠⠄⢠⣧⣿⡿⠴⠏⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠘⣿⠛⠏⠑⢿⠛⢛⢛⡻⢿⣧⣀⣀⣉⣭⡷⢶⣖⣚⣛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠙⠁⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡼⡓⢿⢷⣶⣴⣢⡄⠀⣠⣄⢠⣴⣶⣿⣿⣧⡄⠀⠐⠒⠶⠓⠲⠶⠶⠒⠲⠤⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡬⢝⠀⢁⠰⣼⣿⣿⣿⣯⣽⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠲⠘⠻⢿⠿⠿⡟⠛⣫⣁⢹⠷⢆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠉⢙⠓⠞⢦⣤⡛⣐⠃⡨⠁⣿⣦⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠿⢘⠳⠖⢾⠿⠛⠁⠉

⠀⠀⠀⠀⣠⣴⣾⣿⢿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠛⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⣼⡿⠋⠁⠀⠀⠀⠈⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣤⣤⣀⠀⠀⣿
⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⡾⠋⠀⠈⠙⣧⠀⣿
⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠸⣇⠀⠀⠀⠀⣿⠁⣿
⠀⠀⠈⢿⣷⣀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⠷⣶⣶⠞⠃⠀⣿
⠀⠀⠀⠀⠙⢿⣷⣶⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠹⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⠿⠿⣿⣿⠿⢿⣿⡿⠿⢿⣿⠿⠿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣶⣶⣿⣷⣶⣾⣿⣷⣶⣾⣿⣶⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡋⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡷⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⠲⣦
⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⠿⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠿⠿⢸
⣿⠀⠀⠀⠀⠀⠀⡔⠙⢦⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡶⠋
⣿⠀⠀⠀⢀⠀⠀⠑⣤⠊⠀⠀⡀⠀⠀⠀⣿⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠷⣦⡀⠀⠀⠀⠀⣠⡶⠟⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⢈⡁
⣿⠀⢀⡴⠋⠀⠀⠀⣶⠀⠀⠀⠙⢦⡀⠀⣿⠀⠀⠀⢻⣧⣼⠇⠘⠃⠶⢆⡀⣾⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⢰⡟⢀⣴⣿⣿⡀⢻⡇⠀⠀⠀⠀⠀⢨⡁
⣿⣴⣟⣀⣀⣀⣀⣰⣿⣆⣀⣀⣀⣀⣻⣦⣿⠀⠀⠀⠀⠈⠁⠀⠀⣀⢠⣜⠃⢿⡄⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⣧⠀⣿⣭⣿⠀⣸⡇⢀⣀⢴⡆⠶⠎⠁
⣿⣿⣿⣿⣿⣿⣿⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣄⠺⠊⠉⠀⠀⠀⠈⠻⣦⣤⣤⣴⠟⠁⠀⠀⠀⠀⠙⢷⣦⣤⣤⡾⠏⠀⠨⣥⢀⣀⣀⡀
⠙⠛⠛⠛⠛⠛⢿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠈⠁⠈⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠓⠺⠇⠾⠆⠶⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠷⠰⠗⠰⠆⠺⠂⠾⠊⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢦⡀⠀⠀⠀⢠⠖⠲⣄⠀⠀⠀⡤⠖⢦⡀⠀⠀⢀⠴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⠇⣿⠀⠀⠀⢻⣀⢀⡼⠀⠀⠘⣇⡀⣠⠇⠀⠀⠻⣀⢀⡼⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣶⠞⠃⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⢠⡾⠋⠉⠉⠻⣦⠀⠀⠀⠀⠀⢸⣿⣿⣏⡀
⠀⣠⡶⠾⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉
⣼⡏⣠⣴⣤⣤⠙⣷⡀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠈⠻⣦⣤⣤⡾⠋⠀⠀⠀⠀⠀⣸⣇
⢿⡄⢿⣿⣿⣿⢀⣿⠃⢀⡀⣤⢠⣤⠛⠀⠀⠀⠀⠀⠀⠘⢓⡀⠀⠀⣰⠞⠋⠛⢦⡀⠀⠀⣘⠇⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⢸⣏⣹⡷
⠈⠿⣦⣄⣠⣤⡾⠋⠀⣹⡁⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠂⣿⠀⠀⠀⢸⡇⠛⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣬⡄⢀⡀⣀⣀⣀⣀⡀⢹⣫⠁
⠀⠀⠈⢿⣿⠃⠀⠀⠀⠈⠁⠉⠁⠉⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃
⣀⣀⣀⣈⣇⣴⣆⣴⣄⣶⣀⣶⣰⣦⣸⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡠⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠱⠄⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⢦⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠂⢾⡷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⠙⠆⢆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠸⢻⡏⠀⡇⠸⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠁⡌⡇⠀⢧⠀⢩⣄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⢸⠇⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢘⡀⠀⡈⢿⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⣇⠀⠦⠈⠟
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⢀⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⡑⢀
⠀⠀⠀⠀⣸⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠷⢀⠀⠀⠀⠀⢀⡹⢦⣶⡀
⠀⠀⠀⢀⣿⣿⣦⠂⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠲⠶⣽⣾⣿⣿⣦⡀
⠀⠀⠀⠈⠛⠛⠷⠾⠷⣤⣤⣤⣀⣀⣸⣻⣰⣀⣀⣠⠀⡀⠀⠀⠈⢂⠀⠀⠀⠀⠈⠉⠙⠛⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣄⣼⣭⣭⣿⣿⣡⣶⠰⣧⣧⣤⠧⣀⣸⣦⣤⣴⠶⠒⠒⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣴⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠙⠹⠟⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⣴
⠀⠀⠀⠀⠀⠀⡘⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠙⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢿⣿⣿⣜⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠋⢶⣄⠀⠀⠀⠹⣿⣿⣿⣣⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡉⢸⣿⣷⣀⡀⠀⠈⢻⣿⣿⣷⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠅⢸⣿⣿⣧⣿⣦⡀⠀⣙⠿⣿⠏⣘⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡻⣏⢸⣿⣷⠁⡼⣿⣷⣝⢿⣿⣿⣿⣦⠀⠀⠀⢈⡟⠃⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣱⣿⡎⠿⣡⣿⣷⣌⠻⣿⣷⣝⢿⣿⣿⣧⠀⠀⢘⣇⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠠⠈⠙⠻⢯⣾⣿⣿⡇⣰⣿⣿⣿⣿⣷⣌⠻⣿⣷⣝⢿⣿⣧⠄⠚⠉⠉⠠⢄⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣷⣌⣿⠿⢿⠉⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠈⣿⣽⣯⠰⣷⣝⢿⣿⣿⣿⡿⠉⠰⠀⠰⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀⠈⠁⢤⠈⠄
⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠙⡷⠎⠀⠉⠉⠁⠈⠉⣡⣶⣿⣶⣶⣦⢶⣾⣿⡟⣧⡄⠀⠀⠀⠀⠀⠀⠀⠈⠺⣄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢶⣿⣶⣇⣶⣶⢸⣦⢦⡜⣿⡖⣯⠉⡶⠀⠂⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠁⢸⣶⣦⣮⣅⠀⠀⠀⠀⢰⣿⣿⣷⠛⠛⠹⢿⣿⢨⣿⣌⣫⠈⢣⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠟⢻⣿⣿⣿⣶⣦⡄⢰⣶⣶⣾⣿⣷⢴⣶⣶⣤⣯⣭⡍⠀⢈⣷⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠋⡙⠻⣿⣿⣿⣶⣶⣾⠷⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡄⢈⣿⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣿⡇⣿⡿⠟⠉⠀⢨⣿⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠛⠛⠻⠓⠉⠀⠀⠀⠀⠐⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠠⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⡀⠀⠀⠈⠐⠂⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣄⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠏⢀⠀⢹⡟⣏⠙⠟⣿⠛⠟⠛⠿⢏⡙⡟⠿⠙⠿⠛⡿⠻⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⢛⠛⠛⠛⠛⣿⢿⠿⠿⠿⠿⠿⠿⣿
⣿⣧⣈⣴⣾⣷⣾⣿⣷⣾⣶⣾⣷⣷⣾⣷⣷⣾⣶⣷⣶⣶⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠉⢩⡍⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⣿⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣤⣀⣈⣁⣀⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⢄⠀⠀⠑⠀⢀⣀⣀⣇⠀⠂⠁⠀⠀⣠⠀⠀⢠⠃⠀⠀⡴⠁⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⡠⠷⡊⠉⠉⠀⠀⣀⣈⣦⣀⣀⡀⡔⠁⠀⢀⠎⠀⢀⠞⠀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣏⡠⠔⠊⠁⠀⠀⠘⡤⠒⠒⠉⠁⠀⠀⠂⠀⠈⢻⠒⡤⣋⠀⣠⠋⠂
⠀⠀⠀⠀⠔⠚⣇⡇⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⡀⠀⠈⠀⠀⢜⣔⠁⢀⡽⠧⣀⡀⢀⢂⠀⢀⣀⡠
⠀⠀⠀⠀⠉⠐⠪⠄⠀⠄⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⢄⢀⡴⠋⠈⣱⠮⣄⡀⠀⠈⢸⠁⠉⠄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣠⠜⠫⡀⢀⡜⠉⢣⠀⠉⠓⢦⣞⣀⣀
⠀⠀⠀⠀⣀⣤⢤⠧⠴⠦⡄⢀⣀⣰⠚⡟⠛⠋⠉⠉⠀⠀⠀⡼⠋⠀⠀⢨⡀⠀⢀⡜⠀⠀⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡏⠉⢇⠀⠀⡇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣸⠈⠑⠼⡀⠀⠀⠀⠀⢀⠢
⠀⠀⠀⠀⡀⠤⡔⢳⢊⣹⣇⣠⡼⡤⠤⢵⠴⠶⠶⠖⠚⠁⠀⠈⠠⠀⢠⠃⠀⡀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣱⠋⠉⠀⠳⡀⠀⢱⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠠⠌⠀⠈⠣⡀
⠀⠀⠀⠀⠀⢠⠟⠦⣀⠀⠀⢘⣤⠔⠇⠀⠀⠀⡜⠀⠉⠒⠤⣀⣠⠃⠀⠀⠀⠐⠀⠁⠀⠀⠀⡀⠘⠢
⠀⠀⠀⠀⢠⠏⠀⠀⠈⢢⡔⠁⠈⠣⡘⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠑⠢⠄⣀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠳⣤⣄⣀⡙⡇⠀⠈⡄⢀⣀⣀⣠⣃⣀⣠⣤⣤⡤⡭⠶⠤⣤⡶⠖⠒⠛⠉
⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠉⢹⠋⠉⠉⢁⠏⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠉⠢⢄⡀

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⡰⠛⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣉⣶⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⣤⠟⣦⡞⣡⠞⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢖⢙⣶⡟⢧⡈⢢⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣁⠟⢧⡔⢁⡼⢳⣄⠀⠀⠀⠀⢠⡞⢳⣤⠟⢅⠙⣦⠜⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣉⡽⢯⣴⠎⣨⠳⠄⢀⡞⢧⣼⠿⡉⠳⣄⠟⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣏⡹⢾⡅⠁⠠⣁⣽⢿⡉⠢⣉⠟⠉⠀⠀⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠊⡹⡆⠰⢿⡅⠀⠙⠖⠁⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⣰⣷⣗⣰⣿⣿⣧⣕⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⠀⠀⠀⠀⠀⠀⢀⡴⢏⠙⣇⣹⢿⣉⠉⠉⠀⣹⣿⣿⡗⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠳⣄⣹⢟⢙⡶⠋⠀⠰⢎⣠⣿⣿⣿⣉⠷⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠦⣈⣶⡞⣷⡴⠋⢈⢀⣤⣦⡈⠑⣿⣿⣿⣛⣶⡋⡱⢄
⣿⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠙⣦⡟⢣⣼⠋⠀⠀⣤⠠⣗⣖⡇⠀⢿⣿⣿⣏⡠⠛⣦⡎⢱⠄
⣿⣀⠀⠀⠀⠀⠀⠀⠳⠉⠈⠀⠀⢷⣴⣶⣶⣤⣤⡀⠀⠀⠀⠛⢅⡽⠋⡸⠀⠀⠀⡖⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⠞⣠⠟⠃
⣿⠀⠉⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠒⠂⠈⠀⢠⠇⠀⠀⢰⣟⡃⠀⠀⠀⠀⢸⣿⣿⣿⡇⠛⠁⢀⣤⣤⣴⣶
⣿⠀⠀⠀⠀⠀⠈⠝⢷⣦⣄⠀⢤⣀⠀⡀⢄⡀⠤⣀⠠⢀⡠⠆⣁⠠⡾⠀⠀⠀⢸⣯⣅⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⠀⠀⡀⠀⠀⠀⠀⠈⠉⡟⣿⣦⣌⠀⠘⠢⣄⡉⠲⣭⠓⠮⠝⠶⠽⠇⠀⠀⣀⣼⣷⣶⡀⠀⡀⠀⠀⣿⣿⣿⣽⣦⣤⣄⣀⣀⣀⣀
⣿⠀⣷⣿⡆⢀⡀⠀⣄⡆⠰⠞⠛⠛⠓⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠙⠋⠟⠻⣾
⣿⣤⢽⡏⣧⢺⡿⣼⢻⣳⣄⠀⣠⡶⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢆⠀⠀⠀⠀⠀⢞⣾⣃⡀⠐⢣⣿
⣿⣿⢸⡇⣿⣿⣷⣿⢸⣧⣫⠄⡿⣿⢟⢀⣿⣷⣶⣷⡆⡠⡄⠀⠠⣾⡦⢠⣺⡄⠀⣺⣿⡆⡞⣽⢝⡃⢠⣷⡄⡎⢹⡯⣚⣡⣬⢸⡇
⣿⣾⢸⣗⣟⡼⣿⣽⣌⣿⡐⣧⡭⣿⢡⣏⣿⢝⣷⣷⢹⣻⡿⡆⡈⣿⡇⡓⣿⡜⣶⢿⣿⢧⡇⣿⡪⣦⡺⡿⣷⠂⣿⠪⣽⣿⡷⣼⡇
⣿⣿⣆⣿⢸⣟⢽⣇⣗⣻⣏⡴⣫⣿⣮⡃⣿⢑⡻⣿⣾⢸⣗⢽⣺⡯⣿⠍⣻⢎⠽⣷⡿⣾⡇⣻⣎⠽⣼⡧⡿⣼⡏⣺⣿⣜⣯⣾⣇
⣿⣿⣿⡏⣾⡇⣻⣿⣿⠸⣿⡘⡵⣟⣿⠢⣿⠴⣷⡟⣿⡸⣧⣫⣿⢿⣟⡃⢽⡧⣺⣏⣷⡹⣇⢺⡇⣫⣿⣿⡁⢾⡫⢒⡞⣿⡻⣼⢿
⣿⣯⣿⠢⣿⡣⠾⣼⢹⣏⡲⣟⣰⡧⣽⢘⣟⠨⢷⠂⣿⡂⢿⠔⣻⣸⣟⡅⣿⠖⡥⢿⢻⣏⠷⣉⣿⣴⡛⣗⢨⣿⣊⣭⡷⣿⢸⣿⣼
⣿⣷⣿⣼⣿⣶⣭⣧⣼⣯⣿⣧⣿⣯⣿⣴⣯⣚⣽⣼⣧⣽⣾⣾⣯⣿⣿⣧⣽⣯⣴⣿⣶⣿⣼⣼⣽⣿⣽⣿⣤⣿⣴⣾⣧⣽⣵⣽⣿
⡿⢿⣿⢿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣠⡤⠼⠗⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠉⠁⠀⠀⠀⠀⠀⢠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⡤⠤⠶⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠖⠛⠋⠉⠁⢸⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣻⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⡏⣄⣀⡠⠤⢲⠚⠀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣤⡤⠶⠒⢺⠏⠁⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡆⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠈⠀⠈⠆⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⢀⣴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⢀⡠⣆⣴⡟⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣠⠴⡶⠛⠭⠠⢠⣏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⡾⡔⠚⠋⡀⠟⢀⣠⣴⣶⣖⣾⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠉⠀⢀⡧⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣗⣊⣥⣴⣾⣿⣿⣿⠿⠛⡿⣿⣿⣿⣋⢀⡀⣀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠈⣛⠛⡛⠋⣋⣯⣍⢓⣻⣷⡎⢿⣻⣯⠙⣿⣿⣿⡟⠛⠶⣶⣿⣷⣞⣉⣀
⠀⠀⠀⠀⠙⠉⠀⠀⡠⠙⣉⣠⣿⣭⣽⣿⣿⡞⢛⣯⣥⣶⣿⣟⡛⠟⢛⣩⣶⡈⠀⣍⣛⣛⠛⠻⣿⣿⡿⢶⣿⣯⣟⡛⠁⡤
⠀⠀⠀⠀⠀⠒⠒⠂⠉⠉⢭⣥⠄⢘⣿⣛⡉⠉⠥⠼⠛⠋⠉⠩⠔⠂⣸⡿⣟⠁⠀⢶⣭⣹⡧⣠⠤⢴⣶⣶⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣦⠄⠀⠉⠁⠀⠀⠀⠉⠙⠉⠀⠀⠒⠬⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠢⠂⠃⠂⠘⠞⠚⠘⠂⢀⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡎⠀⠈⠁⠈⠀⠈⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠼⠔⠀⠉⠁⠈⠀⠀⠐
⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⠀⠂⢄
⠀⢀⠄⠪⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⢸⠀⠀⠀⢀⠄⢀⡀
⠀⠈⢄⠀⠀⠀⠈⠐⠢⠤⡀⡀⠤⠐⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠘⡀⠀⠀⠀⢸⠠⠐⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⣰⡤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠠⠀⠈⠢⡀⠀⠀⠀⠀⢀⠤⠐⠈⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⢢⡤⠐⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠁⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠄⠀⢀⠠⠐⠈⠀⠀⠠⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠁⢙⠁⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠄⠈

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠠⡀⠀⠀⣤⣤⣤⣄⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠒⣀⣀⣀⣀⣠⣶⣤⣤
⠀⠀⠀⠀⢐⣿⣿⣿⣷⣤⣤⡘⣷⣍⢠⢵⣼⠋⠐⢿⣿⣿⣿⣿⡖⠀⠀⠀⠤⠀⠀⠀⠀⢀⠀⠀⢀⣴⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣼⣬⠟⢷⡀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⡀⠀⢂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠁⠀⣤⠛⠁⠀⣿⠟⠉⠠⠤⠀⠀⢀⣼⢿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⡄⠘⣻⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⣿⣿⠿⠉⠂⠀⠀⠀⠀⠀⠀⠉⢹⣾⣿⣿⣿⠿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣟⣁⡈⠈⠛⠶⢶⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣷⣶⡿⣿⣿⣛⡿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⠟⠁⠀⠀⢻⡏⠀⠘⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠘⠻⠛⠛⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠁⠀⠀⢤⡄⢀⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠃⠃⠀⠐⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠃⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⢠⣾⢙⣦⠀⠀⠀⡐⢄⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠣⣄⠀⢀⠄⠀⢶⡋⢬⣿⡁⠈⠀⡃⠈⣢⠔⡇⠀⢠⠒⢠⠀⠀⠀⢠⠖⢁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣾⣥⠠⣿⣤⠈⡷⠁⠀⠀⠀⠙⢞⡷⠍⣄⡨⢽⡠⠇⠀⡇⠀⠁⠀⠘⠀⠀⠀⠚⠀⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠘⠈⠻⠘⠋⠀⠰⢡⠇⠀⠀⢸⠁⠀⠈⠀⡠⢤⣤⠴⡇⠀⠀⠄⠂⠀⠀⠀⢠⠔⣄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⡰⠈⠀⠀⣷⠀⠜⣡⠀⣸⢠⣞⣥⡐⡎⠹⠁⣀⡏⠀⡇⠀⡄⠀⠸⠀⠀⠀⢇⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⡄⠁⠀⢻⠀⠉⣉⡀⠉⠘⠛⣿⢛⡟⢀⡴⠁⠁⠀⡇⠀⠀⣀⠀⠀⠀⣠⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⠗⠑⢄⢸⠉⠈⢹⠉⠉⢹⠁⠁⠀⠉⠀⢹⠁⠀⢙⠈⠉⣀⡜⠁⢸⠀⠘⢋⣿⣿⣿⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⠟⠁⡰⡂⠀⠙⢄⠀⠈⠀⠀⠙⠀⠀⠁⠀⠀⠸⠀⠀⠉⠀⠀⣽⠀⢀⠜⢂⠴⠿⣿⣿⡟⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠁⠀⠀⠭⠭⠃⠀⠀⢻⢸⠀⠀⢸⠀⠀⠓⠀⠁⠙⠀⠀⠉⠀⠀⣿⡠⢣⣾⣿⣷⣾⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠔⢀⠀⠀⠀⢼⢸⠀⠀⢸⠀⠀⠀⠀⠀⠘⠀⠀⠛⠀⠀⣿⢐⣿⣿⣿⡟⠹⢽⡇⠙⠛⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠒⠰⠀⣸⠆⠠⡀⡸⠾⠶⡒⢺⠤⢄⠀⢀⡤⠾⡀⠀⣒⣀⠂⣟⣨⣟⠀⢿⣇⣰⣸⡇⡠⠄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣀⠀⣀⠘⠁⡀⠀⠋⠀⠀⠀⢸⠁⠀⠀⠿⠁⠀⠀⢀⣞⡀⠀⠗⠁⠀⠀⢱⠋⠁⠀⠈⠟⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠅⢙⣿⡦⠶⠀⠀⠀⡂⣾⣿⣴⡈⠙⠻⠞⣀⡄
⠀⠀⠀⠀⠀⠀⠀⣨⣤⣤⠀⣀⠉⠺⡄⠑⣌⡇⠙⢢⡀⠀⠘⠀⠀⠀⠀⠈⣗⣒⣒⣒⡿⠀⠀⠀⡂⢰⣶⣶⠬⣭⣭⡭⠵⠆
⠀⠀⠀⠀⠀⠀⢘⠂⠿⠿⣟⠈⠢⡀⢰⢄⣦⠁⢀⣀⣈⡲⠀⠀⠀⠀⠀⣀⣗⣾⣷⡷⠶⠆⠀⢠⡆⠸⣿⣿⡓⠒⠒⠒⢒⣹
⠀⠀⠀⠀⠀⠀⠈⣍⣉⣩⣭⡖⣲⣾⣚⡀⢓⡅⡪⢱⡀⠉⠉⠉⠉⠉⢙⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠯⣭⣉⣉⡩⠤
⠀⠀⠀⠀⠀⠀⠀⡖⠶⠶⢾⡦⠭⠭⠄⢃⣗⢌⠨⠢⢿⣦⡀⡀⠀⠀⠈⠻⢿⣿⣿⡧⠀⠀⣀⣀⡀⠀⠘⠉⢳⠶⠶⠤⠶⠖⡂
⠀⠀⠀⠀⠀⠀⠀⣏⣻⣿⣿⣍⣛⣋⣁⠽⠛⡵⡨⡢⡀⢘⡧⠍⠉⠉⠙⠓⠻⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⢺⣉⣓⠚⢚⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠲⠼⣿⡿⡗⠤⠤⠆⢂⠀⠈⠨⠲⢌⠑⡧⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⣭⣭⣭⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠉⠋⠭⠝⠉⠁⠀⠀⠀⠀⠀⢑⡏⠩⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠐⠟⠁⠒⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣿⣿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠟⠛⠛⠛⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⢁⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⡏⢹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⣴⣿⣿⣿⣿⣿⠟⢋⣥⣶⣶⣿⠃⠘⣿⣶⣶⣬⡙⠻⣿⣿⣿⣿⣿⣧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣾⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣷⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⣿⣿⣿⣿⠏⣴⣿⣿⣎⠛⢿⣿⡇⣀⢀⢸⣿⡿⠛⣱⣿⣿⣦⠹⣿⣿⣿⣿⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣧⡀⣸⠃⠈⠓⠘⣇⢀⣼⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⠥⠿⠟⠛⠛⠉⣍⡁⠀⡖⣡⣌⠢⠀⡬⠉⠉⠛⠛⠻⠿⠬⣿⣿⣿⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⣿⣷⡒⣶⣤⣤⣄⣀⣉⠉⠀⢦⣛⣛⡴⠀⠓⣀⣀⣠⣤⣤⣶⢲⣾⣿⣿⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡿⠁⢹⡄⢠⡀⢠⡏⠈⢿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⣿⣿⣿⣿⣆⢻⣿⣿⢟⣠⣶⣿⡇⠐⠁⢸⣿⣶⣄⡻⣿⣿⡟⣰⣿⣿⣿⣿⡿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⢿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⠁⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢻⣿⣿⣿⣿⣿⣦⣌⡛⠿⢿⣿⡄⢠⣿⡿⠿⢛⣡⣴⣿⣿⣿⣿⣿⡟⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣇⣸⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⢁⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋⠉



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠐⠒⠒⠀⠀⠂⠀⠀⠀⠀⣀⠄⣀⠀⠀⠀⢀⣞⠻⠾⠗⠈⠱⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠉⠀⠀⠀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⢰⠂⠀⠁⠈⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠌⠁⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠒⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠀⣦⠁⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠠⡀⠀⠀⣀⠤⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣺⠇
⠀⠀⠀⠀⠀⠀⢰⣧⣀⣀⣀⣀⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣼⡏⠁
⠀⠀⠀⠢⠀⠀⠀⠀⠉⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠊⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠰⠈⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠠⠈⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡐⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠘⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⢀⠀⠀⠀⢠⡔⢠⡼⠄⠀⡉⡏⠧
⠀⠀⠀⠀⠀⠠⠀⠀⣤⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣧⣼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⠟⢠⠋⠛⠀⠀⠀⠀⠀⠀⣉⠁⡉⠀⣽⠟⢟⡞
⠀⠀⠸⠀⠀⠀⠈⡉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣩⢇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠰⣄⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⢽⡄
⠀⠀⠀⠑⠄⠀⡀⠀⠀⠀⠀⠀⠘⠦⠦⠐⠋⢁⡀⢀⣀⠀⠀⠉⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣤⣤⣤⡞⠫⠉⠉⠉⠉⠉⠉⠉⠛⠉⠉⠉⠁⠙⣷⣶⣄⡤⣦⣦⣤⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⣿⣿⣿⣦⣾⡟⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠛⠻⠻⠛⠻⠻⣿⣿⣿⣤⣶⣤⣤⠀⢀⠀⠂⠁
⠀⠈⠛⠛⠛⠛⠛⠛⠓⠚⠒⠒⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠲⠶⠶⠾⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠁

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠃⣴⡾⠛⠷⠆⣴⡿⠛⢷⣄⢸⣿⣄⢸⡷⢠⣾⠛⠻⣦⡀⣿⣷⡀⣼⣿⡆⣿⠆⣴⡾⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⡃⢿⣇⣀⣠⡀⣿⣄⣀⣸⡟⢸⡏⠻⣿⣏⢸⣧⣀⣀⣿⠃⣿⠹⣿⠏⣿⡃⣿⡆⣿⣄⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠉⠛⠉⠀⠈⠙⠛⠉⠀⠘⠁⠀⠙⠉⠀⠉⠛⠋⠁⠀⠙⠀⠉⠀⠙⠁⠙⠁⠈⠙⠛⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡆⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣀⠀⢠⣤⡀⠀⠀⣠⣤⣤⣤⡀⠀⠀⣠⣾⠟⠙⠃⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣉⣀⣈⣉⣁⣀⣀⣉⣉⠉⠉⠁⣠⡾⠟⠁⢀⣀⣀⡀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢁⣠⡾⠋⠀⠀⠀⢿⡟⢹⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠛⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠶⠷⠾⠶⠿⠷⠿⠾⠿⠷⠀⠀⠀⢰⣾⠿⣶⠀⢿⡇⢸⣿⠀⣿⠀⣿⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⡶⠆⠶⠀⠰⡶⢶⠶⡶⠶⠀⠀⣶⡶⣶⡆⢸⣿⠀⣿⠀⣸⡇⢸⣧⠀⣿⠀⣿⡇⠻⠷⢿⣧⣤⣴⡄
⠀⠀⠀⠀⠀⠀⣺⣶⠿⠛⠉⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿⠀⢸⡇⢸⣿⠀⣿⠀⢹⡇⢸⣿⠀⣿⠀⣿⡇⠀⠀⠀⠀⠉⠙⠻⢶⣷
⠀⠀⠀⠀⢲⣾⠏⠁⠀⠀⠀⠀⠀⢀⣤⣄⠀⣀⠀⢠⣤⡀⠀⠀⣿⣤⣼⡇⢸⣿⣤⣿⠀⢼⣧⣼⣿⠀⣿⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶
⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣉⣀⣈⣉⣁⣀⣀⣉⣉⣉⣀⢀⣉⣉⣉⣀⣈⣉⣉⣁⣀⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⢿⣿⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⢸⡿⠂
⠀⠀⠀⠀⢛⣤⡾⢿⣿⠟⠉⢹⣿⠉⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠉⢀⡈⠉⠛⢷⣄⠻⠁
⠀⠀⢀⣴⠟⠁⣰⡟⠁⠀⠀⢸⣿⠀⠀⠀⠙⠃⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣾⠟⠛⠛⠀⠀⢻⡆
⠀⢠⡿⠻⢷⣶⣿⣀⣀⠀⠀⢸⣿⠀⠀⠀⠀⠠⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠿⠷⣦⠀⠀⢸⡿
⢠⣿⠁⠀⠀⣿⠋⠉⠛⠛⠛⢻⣿⠛⠛⠛⠁⠀⠙⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡿⣷⡀⠀⢶⣶⡾⠟⠀⢀⣾⡷⢶⣶
⣸⡇⠀⠀⢰⣿⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠶⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠈⠳⣦⣄⣀⣀⣠⣴⠿⠃⠀⠀⣿
⣿⣶⣶⣶⣾⣷⣶⣶⣶⣶⠄⢰⣿⠿⠷⢶⣦⡀⠀⣠⡀⠀⣠⣴⠶⠾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢀⣠⣤⣿⡄
⢿⡆⠀⠀⢸⣯⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⠘⣿⠀⣿⡇⢸⡟⢀⡀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣹⡇
⠸⣧⠀⠀⠀⣿⠀⠀⣀⣀⡀⠀⠹⣧⣄⣹⣿⣿⠀⣿⡇⢘⣿⣿⣁⣤⡿⠃⠀⠘⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡃
⠀⠹⣧⣀⣤⣿⣿⠟⠛⠛⠁⢠⣄⠈⠉⢉⣁⣙⣷⣿⣷⣟⣁⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣄⣤⣄⣀⠀⢀⣴⠟⠛⣷
⠀⠀⠙⢿⣅⠀⢻⣦⠀⠀⠀⢸⣿⠀⣼⡟⠛⠛⠛⠛⠛⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢻⣷⠟⠁⠀⣠⡿
⠀⠀⠀⠀⠙⠿⣦⣽⣷⣄⡀⢸⣿⠀⢻⣿⠛⠛⠛⠛⠿⠻⠻⠻⣿⠃⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠟⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠟⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⡙⠿⣶⠄⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡅⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠶⣶⣤⣤⣤⣴⠾⣿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣥⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⡿⠀⠀⢸⣄⠠⣦⣾⡗⠀⠀⠀⠠
⠒⠊⠁⠀⠀⡆⢸⣿⣼⢹⣿⠲⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢹⣾⣿⢡⣿⠇⠀⠈⢁⡀⣠⣤⣼⡄⠂⡞⡰⢁⠘⡆
⠀⠀⠀⠐⠀⠀⠸⣿⣾⣿⣤⣶⣬⣾⣏⣨⣝⣿⣝⣢⣧⠄⢤⡌⠀⠐
⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠱⣤⠏⠽⣒⠻⣀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠁⠀⠀⠁⠀⡀⠀⠀⠀⠙⠂⠁⠀⢀⡅
⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢠⠀⠀⠀⠀⠑
⠗⠄⠰⠀⠖⣿⣿⡟⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀
⣄⠀⡄⢠⢼⣿⣿⡇⡄⡄⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣬⣿⣵⣼⡘⠁⠀⢰⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠘⠻⣿⠟⠛⠛⠛⠿⠣⠄⢐⠍⠈⠆⢠⣤⠧⠂⠁
⣃⣼⣧⣽⣽⡗⣃⣤⠚⠁⠀⠈⣊⠳⣀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣃⡀⠀⣀⣀⣁⠀⣀⣀⠀⡀
⠁⣼⢩⢻⡷⣧⡿⠏⡤⠊⠀⠀⠉⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠹⠽⠍⠉⠍⡛⠛⠛
⠀⢯⢸⡼⠃⣟⠱⢋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⢢⣮⣆⣇⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠔
⠋⠉⠹⠟⣿⡿⡟⠲⢄⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠒⠡⢬⣿⣿⣶⡿⠯⣭⢻⣿⣆⣠⣦⣴⡄⠀⠀⠀⠀⠀⢠⡱⠃⠀⠷⠄⠀⠀⠀⠀⠀⣿⣅⣀⠰⠄
⠂⡄⣀⠠⠐⠶⣶⡿⣷⠞⢻⣛⣿⣿⣿⣿⣿⣷⣄⣴⣴⣧⠴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣷⣷⣿⣿⣷⣶⣿⠿⠿⢿⣿⣿⢷⣾⣉⣴⣛⣻⣿⣿⣿⣿⠀⢿⣤⡴⠒⠲⠴⠀⠀⣃⣀
⣿⣿⡿⣿⠏⠭⣄⣠⣤⣾⣿⣽⣋⣡⣟⣴⣶⣶⣿⣿⡿⠉⠁⠀⠹⡃⠀⣶⣖⣀⡀⠇⠈⠀⠀⠀⠀⠀⠀⠢⣤⣤⣀
⢿⣿⢿⣥⣄⠀⠘⠫⣤⣤⣿⣿⣿⣿⣿⣭⣀⠉⠻⢿⣷⣶⣶⣶⣶⣿⣿⠿⠋⠁⠀⠀⢀⣠⡤⠔⠂⢀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡤⠖⠚⢹⡇⠉⠒⠦⣄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢷⣄⣀⠤⣾⡇⠠⢄⣀⣴⠟⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢈⠿⣿⣦⣿⡇⢠⣾⡿⢏⠀⠈⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣘⣁⣀⣈⣀⣈⣉⣻⣇⣼⣿⣷⣾⣦⣤⣼⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠹⡉⠛⢻⠛⣻⣿⠋⣿⣦⣠⡀⢠⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢈⣿⡿⠛⠀⣿⡟⠻⣿⣎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢟⠉⠈⠙⠀⣿⠇⠉⠈⢙⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠒⠤⠄⣿⠤⠴⠚⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢⣄⣀⣴⡏⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣌⡗⠊⠀⣼⠣⢤⠖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⢠⠞⣈⠉⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣶⣿⣿⣛⡥⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠚⠛⠳⠿⠿⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀
⠀⠀⠀⠀⠀⠀⠀⢲⠴⠦⠤⣄⠀⡴⣑⠂⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣐⣲⣤⢘⣴⠡⡂⠀⠀⠀⠀⠀⢀⢼⠛⡗⡆⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢠⠺⠥⠤⢤⡜⠋⡇⠭⠄⠀⠀⠀⠀⠀⠙⢺⢶⣇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢹⡨⠭⠭⠜⣆⠀⣇⡩⠥⡀⠀⠀⠀⢠⣀⣸⣸⡼⠃⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢀⡵⠾⠭⠭⣌⡳⣽⡬⢭⣒⠤⡀⢀⡀⠀⠋⠸⠀⠀⠀⣀⣠⣤⠾⣟⣻⣶⣄⣀
⠀⠀⠀⠀⠀⡸⣀⠀⠀⢠⠋⣈⣏⡹⣝⣒⠭⣚⡭⢊⣴⣢⣤⠔⠚⣉⡝⠻⢷⣶⡞⠀⠀⠈⢹⡿⢶⣤⣀
⠀⠀⠀⢠⣾⠿⣟⣿⣿⣿⣷⡁⢀⣼⣮⣣⣭⡵⣾⠟⢋⠭⠨⡷⢤⡘⠻⣶⡆⠈⠙⠢⣟⣯⣾⣷⣾⣿⣾
⠀⠀⣴⡛⠞⢾⢷⣯⣽⣛⠋⣴⣿⡿⢫⠧⣝⢷⣿⡀⠀⠀⢀⠝⠒⣚⣲⣍⡨⠤⢒⢋⠉⣟⣿⣿⣿⣿⣿
⢀⢞⣽⣁⡛⠿⢷⡞⠹⣽⣿⣿⠟⠀⢸⣷⣌⠛⢿⣿⣿⣍⣿⡲⠿⠛⢉⣀⠅⠀⣾⣏⠀⣿⣿⣿⣿⣟⡿
⢸⣾⣷⣿⣿⣳⣷⣫⣷⣻⡿⠃⠀⠀⠘⢿⣿⣿⣦⣙⠿⡋⠥⠔⠒⢉⣁⣤⡆⠀⠘⡿⠃⣿⣿⣿⣿⠿⠃
⠀⠉⠙⠓⠿⣿⣿⣷⣿⠟⠀⠀⠀⠀⠀⠀⠈⠙⢷⣽⣳⣷⣶⣾⣿⣻⣯⣭⣇⣀⠤⠗⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣭⠭⠿⠞⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼
⠀⠀⠀⢸⠉⣉⠉⠉⢹⡇⠀⠀⠀⠀⢸⡏⢉⠩⠭⠉⢉⠉⣿⠀⠀⠀⠀⠀⡇⠀⠾⠽⠆⠀⡇⠀⠀⠀⠀⠀⠀⣼⠷⠶⠿⣦
⠀⠀⠀⢸⢘⣿⣿⣆⢸⡇⠀⠀⠀⠀⢸⡇⠈⠦⠛⠢⢀⠁⣿⠀⠀⠀⠀⠀⣧⠤⣠⣦⡤⢤⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⢸⣶⣿⣿⣿⣾⠇⠀⠀⠀⠀⠸⠿⣿⣿⣯⣿⣿⣿⠿⠀⠀⠀⠀⠀⣿⢽⣿⢽⣯⢽⡇⠀⠀⠀⠀⠀⠀⣿⡶⠶⢶⣿
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠚⠓⠚⠁⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣀⡀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢀⣯⣭⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⢭⡒⠀⠀⠀⠀⠀⠀⠀⢰⠩⡌⢳
⠀⠀⠀⠀⣾⡄⠈⡳⣌⠮⠃⠀⠀⠀⠀⠀⡼⠋⠉⠙⢻⡀⠀⠀⠀⠀⠀⠀⡤⠶⠲⡶⠶⢦⡀⠀⠀⠀⠀⠀⢈⣢⣰⣻⣲⣤⡀
⠀⠀⠀⠀⢿⣿⣦⣀⠈⡆⠀⠀⠀⠀⠀⠐⣇⣠⣀⣀⢨⡿⠀⠀⠀⠀⠀⢴⣧⣤⣤⣴⣾⣦⣷⠀⠀⠀⠀⠀⣾⣇⣤⣾⣿⠋⢳
⠀⠀⠀⠀⣰⣿⡛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⣯⣽⠀⠀⠀⠀⠀⢻⣿⣧⢈⣿⣿⡞
⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠭⠽⠃⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⣰⠚⠉⡉⠙⢦⡀⠀⠀⠀⠀⢰⡞⠛⡛⠛⠛⡛⠛⣶⠀⠀⠀⠀⠀⢸⡁⠀⡀⠀⣷⠀⠀⠀⠀⠀⠀⣤⣶⣦⣀⣄
⠀⠀⢼⡇⠤⣴⣳⡤⠀⣷⠀⠀⠀⠀⢸⣷⣿⡟⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⢺⢿⠀⣿⠀⠀⠀⠀⠀⠀⠿⣫⣏⣾⣿⣧⡀
⠀⠀⠈⢧⡀⠈⠏⠀⣰⠇⠀⠀⠀⠀⢸⣧⣭⣤⡬⣤⣬⣥⣿⠀⠀⠀⠀⠀⠸⢤⣄⢀⣤⠟⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠉⠓⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠠⣬⣯⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣠⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡖⠒⠒⡆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢺⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣴⣧⣠⣶⣶⣆
⠀⢸⣿⡿⣿⠂⠀⠰⣿⣿⣿⡇⠀⠀⡇⠰⠀⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⢠⣶⣾⣶⢿⣿⣟⠙⠋⠉⠁
⠀⠸⢋⡜⠁⠀⣀⠀⠈⢮⡻⡇⠀⠀⠧⣄⡤⠃⠀⢠⠄⠀⠙⠉⠀⠀⠀⠀⢀⡾⢳⣷⢻⣆⠀⠀⠀⠀⠘⠋⠉⠁⠰⠿⠟⠃
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠚⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⢻⣿⠉⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⡵

⠐⣿⡍⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⣤⢤⣴⢶⡤⣤⡄⠀⠀⠀⠀⢀⣤⡞⣗⣦⣀
⠀⢿⡇⠀⣼⡇⠀⠀⠀⠀⠀⢴⣷⣶⣲⣶⣻⠿⢿⠆⠀⠀⠀⡟⡟⣿⢻⢻⡿⠀⠀⠀⠀⠀⢹⣹⡏⢈⡏⣿⠁
⡄⠾⣷⣒⣿⠇⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢧⡇⣿⢸⢸⣧⠃⠀⠀⠀⠀⣸⣹⣇⣈⣇⣿
⠈⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠘⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠋⠁⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠂


⠀⢀⡰⠆⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣾⡿⠴⣶⡎⠁⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⣦⠀⠀⠀⠀⢀⡀⠀⢶⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣅
⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⡎⠑⠀⠀⢸⡜⠀⠀⠀⠀⣴⡧⣴⡟⣷⡠⣷⡄⠀⠀⠀⠀⠀⠀⢈⠛⢁⣠⠤
⢀⣿⣇⣀⣿⡇⠀⠀⠀⠀⠀⠀⠧⣥⣬⣥⣞⠇⠀⠀⠀⠸⣿⣄⣿⣧⣿⢧⣼⡿⠀⠀⠀⠀⡀⠀⠐⠒⠚
⠈⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⡀⠀⠀⠀⠀⠀⣼⠟⠁⢶⠼⠇
⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⢀⡴⣾⣵⣯⡻⣇⡀⠀⠀⠀⠰⣤⣶⣦⣶⣤⡴⠀⠀⠀⠀⠀⠀⢰⡄⠀⣦
⣶⣶⣾⣿⣧⣶⣶⠂⠀⠀⠀⠋⣾⣿⠁⢼⣿⣿⠙⠀⠀⠀⠀⢸⡇⣿⣇⣿⡄⠀⠀⠀⠀⢀⣠⢿⡿⣾⣿⣇⣀
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣍⣴⣿⣿⠀⠀⠀⠀⠀⢸⡇⣿⡇⣿⠁⠀⠀⠀⠀⣿⠅⢸⡇⠈⣿⠀⣿
⠈⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠀⠉⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⠉⠙⠛⠳⠦⣄⠀⠀⠀⣠⠟⠀⠀⠀⣠⣾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⢀⣠⠴⠶⠖⠶⠶⣤⡀⠈⠻⣆⣰⠏⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣿
⢀⣠⡤⠶⠶⠶⠶⠦⣤⣀⡀⠀⠀⢰⠏⠀⣰⠟⠁⢈⣷⣤⡄⠀⠀⠙⢦⡀⠈⣿⠀⠀⠀⠀⢀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⣿
⢿⣁⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡟⠀⢰⠇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⣧⠀⢸⣆⠀⠀⠀⢙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢰⠇
⠀⠈⠉⠛⣻⡶⠆⠀⠀⠀⠀⠀⠸⡇⠀⢸⡀⠀⠀⠈⠛⠲⠶⣤⡀⠀⠀⣿⠀⢠⣿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢰⣏⠀⠀⠀⠀⢀⠀⠀⠀⢿⠀⠘⣧⠀⠀⠀⢠⣄⣀⡼⠃⠀⣰⠏⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⣾⣥⠶⠒⠒⢦
⠀⠀⠀⠀⠉⠛⠛⠛⠛⢿⣀⣠⡴⠛⣷⡀⠈⠳⣤⣀⠀⠈⠙⣇⣠⠞⠃⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⠀⠉⠉⠙⠉⠉⠀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣶⣶⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⠉⠉⠉⠉⠉⠛⠛⠶⢤⣄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣠⡤⠶⠒⠚⠛⠓⠲⠶⣤⣀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠙⣷⡶⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡼⠃⠀⣄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡾⠁⠀⠀⠙⣷⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣸⠃⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠈⢷⣀⣀⣀⣀⣤⠴⠶⠶⢤⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⣰⠇⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠖⠒⠛⠛⠛⠒⠲⠶⢿⡆⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠙⠆⠀⣴⠋⠀⠀⠀⢠⣿⣿⡏
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⣰⣿⣿⡟
⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣄⣠⣤⣤⠶⠚⠋⠀⠀⠀⠀⣠⣾⣿⣿⠟
⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠋
⣿⠀⠀⠀⠀⠀⣀⣠⣤⠴⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⠿⣶⣤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠋
⠈⠛⠛⠛⠛⠉⠉⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢀⡴⠃⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣀⡴⠞⠁⠈⠳⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⢻⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⡻⢏⠰⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⢹⢸⢸⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠚⠝⣸⣡⣯⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣮⣵⡿⠋
⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠉⠀⠉⠉
⠀⠀⠀⠀⠀⣤⣬⣿⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣿⣥⣤
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⣠⡀⠀⠀⣰⣶⣦
⠀⠀⠀⠀⠀⣀⢰⣶⣶⣆⡀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⡁⠀⠀⡳⡄⠀⠀⣘⣛⡋
⠀⠀⠀⠀⠀⣿⢸⣿⣿⡟⣛⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣀⠙⢁⣀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣸⣿⣿⣷⣾⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⠀⠀⠉⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠛⢿⠛⠛⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣠⠾⣄⠀⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣄⠰⢿⣷⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣌⠋⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠤⠀⠠⡀⠀⣀
⠀⠀⠀⠀⢀⡀⠀⠀⢀⣴⣌⠿⣿⣿⣿⣣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⡀
⢀⠀⠐⠀⠀⠀⠀⣴⣾⣻⡿⠃⠈⠉⣿⡿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠿⠋⠀⠀⠀⠀⠋⠀⠈⡶⠂⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠒⠀⠐⠀⠀⠂⠀⠀⠙⢷⡿⢟⣵⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢫⣄
⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣟⠛⢫⣼⣿⣻⣦⡄⠀⢄
⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠊⠙⠿⠀⠈⠻⣶⣿⠟⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠣⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⢄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⡀⠀⣿⠽⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢂⡀⠀⠀⠀⡜⠀⠀⠠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣭⣿⠉⣷⣦⣅⣀⣀⣀⢀⠀⢘⡇⠀⠀⠈⣀⠀⠠⣀⣑⣤⡶⠂
⠀⠀⠀⠀⣀⣒⡒⢶⣶⣦⣤⣤⣦⣄⣸⣿⣿⣿⣿⡶⠶⠿⠤⠿⠤⠬⠥⠼⠷⣶⣾⣟⣛⠉⣛⠽⣁⡀
⠀⠠⠄⠀⢻⡛⠛⣿⣯⣽⠟⢛⣻⣏⣙⠛⠃⣿⣿⣿⣍⣻⣶⠿⠀⣲⣿⢗⠓⠿⠯⠀⠿⢿⡋⠤⠟⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠈⠀⠰⠴⠂⠨⠤⢈⣭⠉⠷⠾⢤⣀⠈⠑⡊⠁⢤⠘⠻⠿⠓⠂⠈⠁⠐⠂⠀⠠⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠄⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠁

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣩⡅⢢⣢⣴⡾⡳⢶⡗⢀⠀⠀⠀⣠⠛⠁⠀⠀⠈⣁⡀⠀⠀⢠⣔⣦⣤⠤⠙⠉⠪⠁⠀⠀⠶⠶⠄⡀
⠀⣀⡜⠛⣁⡀⠀⠀⠀⠀⠈⠉⢀⡝⠚⠿⣧⣜⡛⠅⠠⠖⠃⠁⠀⠀⢀⡴⠋⡠⠀⠹⠋⠉⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠆
⠀⠀⠉⠉⢠⣽⠠⠀⠀⠀⠀⠀⠈⠳⠊⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠸⠃⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣇⣈⣤
⠀⠀⠀⢀⣐⡿⢀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠛⠋⠀⠀⠀⠀⠀⠀⣠⠼⠇⢀⡀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠝⡋⠉
⠀⠀⠐⢻⣿⡌⠂⠀⠀⠀⠀⠀⣠⣟⠋⠀⠀⠀⠀⠀⠀⠀⠐⠒⢛⠆⠀⠈⣝⣁⡋⣦⡤⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠻⠾⢿⠿
⠀⠀⠀⠀⠉⣿⣆⠀⣠⣶⣆⠬⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣘⣾⠋⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠂⠀⠐⠀⢑⠖⠆⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⣰⠉⢚⣗⠀⣠⣾⠦⠀⠐⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⣟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣲⣄⠀⠀⠛⢢⡟⠓⠒⢊⠀⠟⠉⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢸⣏⡀⠀⠀⠀⠀⠈⠉⠉⠠⣴⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠑⢶⣦⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢇⠀⠀⠀⠀⠀⠀⠀⣑⡒⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠓⠀⠸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡑⠀⠀⠀⠀⠀⣯⡍⠁⠀⠀⠀⠀⠀⢲⡏⠀⠀⠀⠀⠼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠞⠃⠘⠟⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⡐⠀⠀⢰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠁⠀⠀⠀⠀⠀⠘⣗⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢛⡇⠀⠀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⢤⡜⠉⠀⠀⠀⠀⣀⡤⢶⠶⢤⣀⠀⠀⢀⠻⠀⠀⣴⣦⠀⣀⣾⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⠋⢄⡈⠁⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⠲⡧⡼⡁⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣉⢂⡗⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙


⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠐⠒⠀⠉⠈⠉⠉⠉⠁⠉⠙⡀
⠙⢿⡿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣐⣀⣀⡑⢀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠉⠉⠀⠀⠀⠀⠀⠤⢀⠀⠀⠈⠙⠋⠀⠀⠈⠛⠻⠾⢯⣍⠈⠉⠁⠀⠠⠈⠉⠉⠐⠐⠒⠒⠀⠘
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠾⠟⠛⠛⠛
⠀⠀⠀⠠⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠄⠖⠛⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣠⣶⠛⠛⠋⠉
⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠈⠈⠀⠈⠀⠐⠒⠒⠀⠒⠆⠀⠈⠁
⣶⣶⠶⠶⠶⣶⣾⣷⣷⣿⣿⣿⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠈⠁⣀
⠀⠀⢀⠀⠀⢶⠀⠀⠀⣀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣯⠀⠀⠀⠀⠀⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠛
⠀⠀⠈⠁⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠒⠀⠀⠶⠶⠶⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⣿⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢸⣿⡇⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⣷⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⣀⣀⡄⠀⠀⠀⣶⣶⠶⠀⠀⠀⠀⠙⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠉⠀⠀⠁⠀⠀⢀⣀⣠⣤⠀⠀⠀⢰⣶⣶⠾⠿⠟⠛⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⡿⠇⠀⠾⢾⠀⠀⠀⠀⣤⣤⣤⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⣠⡤⢀⣠⣤⣤⣶⠾⠘⠟⠛⠛⠀⠀⠒⠀⠀⠀⠛⠀⠀⠀⠀⣿⠍⠈⠀⠀⠀⠁⠀⠀⠀⠀⠶
⠀⢰⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠟⠃⠀⠀⢀⡉⠁⠁⠀⠈⠉⠉⠀⠀⠤⠀⢀⣚⣀⡀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠛⠃⠀⢉⡀⠲⠀⠀⠀⠘⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠛⠛⠛⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⠚⢦⣄⠀⠀⠀⢼⡇⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⢀⠀⠀⠀⠸⠇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠾⠃⠀⠀⠀⠀⠤⠀⠀⠀⡤⠄⠀⠀⠀⠀⠙⠙⠀⠀⠀⣶⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣦⣤⣤⣄⣀⡀⣀⣀⣤⣤⣤⠀⠛⡋⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁
⠀⠐⠆⠰⠆⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠚⠀⠀⠀⠀⣄⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣦⠀⣾⣶⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶
⠀⠀⠀⡀⠀⠀⠀⢩⡄⠀⠀⢸⡧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣈⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⣶⣶⡆⠀⠀⢠⣄⡀
⠀⠀⠀⠁⢰⠂⠀⠀⠀⣐⠄⠸⠇⠀⣿⡷⠀⠀⠀⢠⠀⠀⠀⠀⠛⡟⠛⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⠙⠛⠂⠀⢀
⠀⠀⠀⢶⠀⠀⠀⠀⠀⠉⠘⠂⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⡄⠁⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠠⠄⠀⠀⠀⠰⡆⠈⠶⠐⠂⠝

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⢀⡀⠤⢠⢐⡀⡆⣂⢂⣐⣐⢒⡐⠂⡀⣄⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⡀⠄⢂⣡⡴⠼⠋⠉⢀⣀⠀⠠⠤⠌⠉⣍⠹⢓⠶⠬⣓⢤⡀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡠⠢⣀⠶⠚⠓⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠉⠙⠺⣆⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡰⠎⠡⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠐⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡔⢀⡶⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠎⣿⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠂⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⡬⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⢠⠃⣀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠭⠥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠁⠨⢁⡫⠤⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠨⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣓⠂⠀⠀⠀⠀⠀⠄⠈⠀⠁⠀⠀⢠⠀⡨⠋⠘⢲⡌⢽⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠥⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢌⣡⡞⠫⢽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠱
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣨⡄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢀⠞⠀⠀⠀⠀⡠⠀⠐⠁⠀⠀⠀⠀⠠⢤⠄⠀⠀⢠⠃⡙
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡯⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⠒⠈⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠐⡶⢯⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⢥⠀⠁⠀⠀⠀⠀⠀⠀⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠠⠊⠾⠹⠜⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠢⡀⠀⠀⠑⠀⡀⠀⠀⠀⠀⢠⡧⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠔⢢⠶⠚⠆⡶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠲⢄⡀⠀⠀⠁⠂⠤⢀⣈⡁⠀⠀⠀⢀⣀⠠⠄⠒⠛⠉⠁⠀⠀⠀⢀⡄⢂⠁⠈⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⠙⠂⢀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠡⠐⠀⡢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠈⠉⠒⠢⠠⠄⡄⡀⢀⠄⡤⡤⠤⠒⡈⠡⠀⠀⠣⠀⣠⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣄⣀⡀⠂⠀⠀⠀⠂⠠⠈⠀⢂⠈⣀⣥⠰⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡉⠈⠐⠒⠓⠒⠒⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠄⠊⠠⠂⠀⠐⢀⠄⠂⠡⠀⡠⠀⠀⠔⠀⠠⠂⠈⠄⠂⠀⠐⠀⡠⠒⢁⠔⠈⠄⠀⠔⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⢀⡼⢃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢀⠀⠀⣠⣾⠿⠋⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢠⡟⣀⡾⠋⠁⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⡟⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡜⡿⠁⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡼⠁⠈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⡼⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⡼⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋⣠⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠉⠉⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⢀⣴⢟⣁⣤⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠸⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠂⠀⢀⣴⣿⣿⣿⣭⣤⠴⠶⠖⢻⣿⣯⣤⣤⣤⣀⣀⣀⣀⣤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁
⠀⠀⠲⠿⠻⠭⠉⣡⣀⣀⣀⣀⣴⣁⣀⣀⣠⠤⠤⢤⠤⠤⡌⣿⡓⠒⠂⠀⠤⠠⠤⠀⢀⣠⣤⣤⣤⣤⣤⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣛⡛⠻⠿⣯⣭⣄⣀⡈⠃⠸⠧⣬⣍⣀⣀⣀⣀⣀⣀⣀⣀⣐⠆⠀⢉⡿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⡿⠛⠛⠛⠻⢿⣿⣟⠶⠶⠶⠶⣬⣭⣭⣭⣤⣤⣤⡶⠶⠚⠋⣁⣠⡾⠀⠠⠔⢒⣋⣥⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣾⠁⠀⠀⠀⠙⢿⣷⣤⡀⠀⠚⠁⠀⠉⢻⣿⣿⣿⣿⠿⠛⠛⠉⣀⣤⡶⠾⠛⠉⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠀⠀⠀⠀⠉⠻⢿⣟⣓⠛⠀⢀⣠⡟⠈⠙⠛⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢿⡿⠛⠀⠀⣶⣶⡆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢀⣠⣴⠾⠛⠉⠀⠀⣤⣤⡄⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠈⢳⠃⢀⠀⠀⠀⠀⠠⠒⠉⣀⢴⡪⠟⠋⠀⠀⣾⣿⡇⠀⣿⣿⡇⠀⣿⣿⣧
⠀⠀⠀⠀⢠⢿⣷⠀⢠⠷⣵⠤⠊⠁⡠⢔⡩⠖⠉⠀⢰⣶⣶⠀⣿⣿⡇⠀⢿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⢸⡇⣿⣄⢸⠀⠀⠀⠀⢈⠔⠉⠀⢠⣶⡆⠸⣿⣿⠀⣿⣟⡇⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⠀⣠⣞⣧⡟⢠⠀⠀⠀⠀⠀⠁⠀⣀⡀⢸⣿⡇⠀⠟⣿⠀⣿⠟⡇⠀⢸⢿⣻⠀⣿⠀⣽
⠀⠀⠀⠛⠿⣿⠃⠘⡆⠀⠀⢀⣤⡄⠈⣿⣷⠘⠋⠇⠀⠧⢼⠀⢻⠂⡇⠀⢸⢀⢹⠀⣿⠇⡿
⠀⠀⠀⠀⢀⣯⠀⠀⣃⡀⠀⠸⠿⠧⢴⡗⠚⡚⠛⠛⠛⠋⣉⠉⠉⠉⠉⢛⠛⠛⠛⠲⠿⠤⣥⡀
⠀⠀⠀⠈⠛⠻⠟⠉⠛⠛⠋⠀⠀⠀⠻⣤⢸⢳⣟⣶⡖⢢⡏⠀⢰⢯⣏⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠚⠙⢈⣋⣈⣀⣈⣀⣀⣈⣛⣘⣉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⠫⠍⠓⠒⠒⠉⠽⣒⢤⡀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠠⠈⠑⢆
⠀⠀⠀⠀⠀⠀⣠⢫⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢦⠀⠀⠀⠀⢐⠀⠀⠀⠂⠆⠐⠀⠀⢃
⠀⠀⠀⠀⠀⣸⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢣⢳⠀⠀⠀⢸⠀⠀⠀⠀⣷⠀⠀⠀⡘
⠀⠀⠀⠀⢠⡇⠃⠀⠀⠀⠀⣄⢀⡾⢦⣀⡴⠛⠀⠀⠀⠎⡇⠀⠀⠈⠢⡀⠀⠠⠤⠀⢀⡰⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⡌⢉⢰⡆⣭⢰⡇⠀⠀⠀⡀⡇⠀⠀⠀⠀⠈⠐⠒⠒⠂⠁
⠀⠀⠀⠀⠀⢇⢇⠀⠀⠀⢸⡇⣿⢸⡇⣿⢸⡇⠀⠀⢠⢱⠃⠀⠀⠀⠀⠀⣠⣴⣿
⠀⠀⠀⠀⠀⠘⢮⢢⠀⠠⠬⠥⠍⠌⠥⠍⠌⠁⠤⡠⣣⠏⠀⠀⠀⠀⠀⢀⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠓⢝⡢⢄⡀⠀⠀⠀⢀⡀⢤⣪⠞⠁⠀⠀⠀⣴⣄⣠⣿⠟⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠯⠭⠭⠖⠚⠉⠀⠀⠀⠀⣠⣾⡿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡫⠊⠹⠇⠀⣼⠟⠛⠛⠛⠛⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⠀⠀⠀⢀⣴⣿⠏⠀⠀⢸⡏⡭⠭⠭⠭⠭⠭⡟⢻⠭⠭⠭⠭⠭⢭⢹⡇
⠀⠀⠀⠀⠀⠀⢀⡔⠉⢀⠀⠒⠦⡄⠈⠳⡄⠀⠘⢻⠁⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡀⠀⠀⣄⣀⣠⣤⣼⣧⣧⡤⢤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢌⠁⠁⠈⠀⠀⢘⠇⠀⠀⠈⠳⡤⠴⠦⠻⣿⣿⡟⠉⠉⠉⣀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⡜⠂⠒⡄⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣀⠤⠿⢿⣷⣶⠚⠉⠉⠁⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⣁⣃⣀⠴⠋⠀⠀⠀⠀⠘⠻⡀⡀⠀⣀⣀⣼⣿⠿⠶⠒⢢⣀⣀⣀⣀⣀⣀⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⣿⡿⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠷⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⢀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡟⠀⡀⠀⠠⠴⠀⠀⠀⢀⡀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⢀⣀⣠⡄⠀⠠⢄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⣀⣤⢾⡟⣿⠛⢛⡀⠀⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣩⠿⠼⠓⠋⠻⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠁⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢀⡀⢴⡶⠚⡿⠇⠀⠀⠸⣗⠒⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡨⠀⢀⣤⣾⡯⣶⠚⣿⡾⣤⣼⡦⠴⠶⠾⣶⡿⠦⠴⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⣷⠾⢛⣉⡥⠷⠞⠒⠛⢟⠉⠉⠀⠀⠀⠀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠠⣄⠸⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣶⣿⣿⣿⣿⣛⠿⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣤⠶⢺⡿⢸⣶⣞⢫⣾⢿⣿⣿⣿⣙⡻⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠛⡉⠀⢸⣷⢞⣵⣞⣷⣾⣿⣿⣿⣿⣿⣿⡦⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣟⣷⡿⠺⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⠇⠀⠁⠀⠀⠈⠹⡿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠴⠦⣤⡶⠶⠖⠒⠲⢶⣶⣤⡽⠿⠿⠉⣤⣦⡀⢀⣀⣰⣶⣇⠀⢠⡀⠃⠐⠶⠖⠀⠀⠀⠀⠒⠶⠖⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⡗⣰⡿⣶⣶⣶⣤⠀⠐⠒⣯⣷⡷⠈⣽⣾⣿⡏⣀⡘⠻⣿⣿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠡⣶⣾⣍⠙⣃⣠⡔⢛⡿⠃⠀⠚⠿⣻⣥⠙⢿⣷⣄⠀⠀⠀⠀⠈⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠙⠛⠚⠃

⠈⢆⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠱⠀⠀⠀⠀⠀⣸⡀⠀⠀⠌⠀⠀⠀⢸⡀⠀⠀⠀⡞⠀⠀⠀⢠⠞⠁⠀⢀⠜⢶
⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⢳⣀⠤⠔⠒⠒⠊⠉⠉⠈⢣⡀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡰⠃⠀⠀⣰⠋⠀⠀⠀⠁
⠀⠀⢀⡷⠀⠀⢀⣠⠴⢒⠁⠙⢆⠀⠀⢀⣀⣤⠤⠖⠒⠻⠉⠒⠲⠦⣏⣀⠀⠀⡴⠁⠀⢀⣼⢁⠀⠠⠎⠐
⠀⠀⢸⣠⡴⠚⠉⠀⠀⠀⠀⠀⠈⢷⡊⠉⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢸⡀⢩⠾⢄⡀⢠⡞⠀⠁⢄
⠴⠚⠹⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⠠⠄⣀⠀⠀⡊⠀⠂⠄⣜⣡⠋⠀⠀⡽⠻⢄⡀⠀⠀⠑⠀⠀⠀⠀⢀
⠒⠒⠦⣞⢁⠀⢀⡀⠄⠀⠀⠉⠀⢸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⣠⠞⠉⠙⢦⣞⡁⠀⠀⠉⠉⠉⡏⠉⠙⢉⠉⠁
⠀⠀⠀⠈⢩⠂⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠂⢙⣦⠞⠁⠀⢀⡴⠣⡈⠙⠳⢦⣄⡀⢠⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣀⣠⡤⠖⠋⠀⠱⣄⣠⠟⠀⠀⢱⠀⠀⠀⠈⢙⡿⠶⠦⡧⣤⣄⣀
⣠⣤⠤⠴⠷⠒⠒⠲⣆⠀⣀⣀⣹⠉⢿⢉⢉⠉⠁⠀⠐⠒⢂⠀⢠⡞⠃⠠⠀⠀⢼⣅⠀⠀⢀⡞⠀⠀⢀⠁
⠀⠀⠀⠀⡆⠀⠀⠀⡏⠉⢹⡀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⡵⢏⠀⠀⠀⠀⠀⢸⠀⠑⠢⣞⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⣀⣧⠤⠴⢻⠃⠀⠀⢧⠀⡀⢘⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠑⡀⠀⠀⢀⡇⠀⠀⠈⠈⠑⢦⣠⠀⠀⠀⢠⠃
⠒⠉⠩⣅⣸⡤⠶⠻⡖⠚⠛⠛⡏⠉⠉⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠞⠀⢑⠾⢤⣀⠀⢶⣞⠳⢦⣴⠇⠂
⠀⠀⠀⡼⠀⡆⠀⠀⠘⢦⠀⠀⢱⣀⣀⣇⣀⣤⠤⣤⣀⡀⠀⠀⠀⠀⠠⢠⡍⠠⢤⣉⠀⠠⠈⢹⠾⢄⠙⠦⠙⢦⠨
⠉⠉⣹⠛⠶⣄⠀⠀⠀⠀⣳⡤⠔⢇⠀⠀⠀⠀⢰⠃⠀⠉⠑⠢⢄⣀⢀⠎⠀⠀⡀⠀⢀⠂⠀⠁⠀⠀⠐⠄⡀⠀⠑
⠀⣰⠃⠀⠀⠈⠳⣄⡠⠚⠁⠙⢄⠸⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢈⠟⠒⠤⣄⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⣰⠇⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⠣⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⠉⠛⠢⢤⡀⠀⠀⠀⢀⣀⣀⣤⣤
⣏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠦⢤⣽⣀⣀⣀⣧⣤⣤⡤⠤⢤⡾⠴⠶⠶⠶⠒⠺⡖⠛⠛⠛⠛⠻⢭⡉⠉
⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠉⠰⠇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠑⠦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠍⠭⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠊⠀⠀⠁⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠁⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⠀⢀⠐⣰⠁⠀⠀⠀⠀⠀⠀⢀⡤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡉⢽⣇⠑⠠⠄⠂⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣰⠷⢤⣀⠀⠀⠀⢀⢴⠋⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠫⡐⠁⠀⠈⠘⣧⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⡰⠛⣆⡀⠙⠛⢦⡞⠉⡀⠂⠀⠸⢧
⠀⠀⠀⠀⠀⠀⢠⡖⠙⢌⢀⠀⠈⠆⡑⠤⣎⠬⢷⡞⠘⠏⠻⠓⢶⡤⢤⡴⠋⠉⠉⡑⢦⡼⡿⡜⣁⠠⢳⠄⠃⠀⠀⣇⠀⢀⢠⠠⠎⢾⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⠆⡡⠐⠁⠰⠀⠁⠀⠐⠀⠀⠃⠠⠌⠎⠀⣼⠁⠁⠀⠀⠈⢸⡇⠳⠹⠀⠎⠀⠂⢈⠂⠅⢙⡄⣊⡄⣢⠂⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠕⠉⠘⡀⠀⠈⠀⢼⠤⠀⠄⡀⢜⡔⢙⠢⡈⠸⣇⠐⠄⠤⠊⣼⠁⠈⠑⡑⠀⠀⣀⡀⠀⠐⡨⢿⠁⠈⠠⠑⠄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⡀⠐⡨⠊⠃⠀⢀⣡⠄⣦⠀⠀⠈⠀⡘⣦⠀⠀⡼⠁⣤⢀⢠⢳⠋⠀⠸⣅⢌⣖⠕⡉⣄⠊⠔⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⠅⠡⠊⠀⠀⢀⠀⠀⠁⠃⣀⠀⠀⠀⡌⢀⠈⢣⡞⠁⠀⠳⡦⠐⠆⡀⢄⠄⢃⣀⠈⡆⠬⣳⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢂⠔⠈⠀⢀⠔⠋⢽⡷⡑⠋⠀⠈⡗⢈⠤⠀⠀⢠⠁⠀⠀⠀⡀⢇⠀⡒⣴⠀⣠⠋⠉⠓⠓⠦⣤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⢀⢜⡵⠋⠀⣸⠗⢤⡀⠀⠀⢸⡈⡄⠀⠀⢸⡘⠢⡲⡫⠤⠽⡆⠑⠃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣢⠔⠁⢐⡴⠊⠁⠀⠀⠈⠑⠢⢴⣧⣒⠛⠛⠐⠪⠅⠂⠀⠁⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠓⠚⠚⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠒⠨⠉⠒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢐⡒⠦⡄⣤⣀⣀
⠀⠀⠀⢠⠄⠒⡚⡉⠀⢀⣜⡄⢄⠀⡰⠓⡐⢈⡲⠦⢄⡀⠀⢀⡠⠔⠶⠡⡒⠈⠀⠀⢀⠼⢡⡣⠄⠊⠻⡔⠆
⠀⠀⠀⢐⠀⠀⠱⡐⢌⡀⣀⣀⠾⢶⣀⣀⣐⡀⠇⠀⠀⠈⠉⠀⠤⣸⠀⢧⢊⠲⡀⠀⡆⠀⢼⠁⡠⠐⠒⠁⡇
⠀⠀⠀⠸⠆⢐⠀⠘⢄⠓⢄⠨⠤⠤⠄⠋⠂⢠⢠⡔⠉⠑⡀⢸⠀⢷⣤⡾⠈⣃⠐⠒⠀⡄⢊⣉⠐⠀⠀⠐⠁
⠀⠀⠀⠘⠘⠃⠀⠉⠂⠙⠢⣉⠂⢄⡂⠀⢐⢆⢲⠀⠀⡰⠁⢛⡰⠚⠂⠛⣒⠟⠊⠁⠀⠀⠀⠀⠀⠈⠉⠐⡇
⠀⠀⠀⢀⠀⣀⠀⠛⢠⠋⠲⢄⠉⠢⢌⣰⢎⡎⢇⠠⣪⡲⠍⠲⠤⢍⠢⠊⠀⢀⡠⡐⠤⢌⠙⠔⠃⠐⠂⠤⠁
⠀⠀⠀⢸⣀⠋⠀⣖⠁⠀⠀⠀⢱⠀⠠⢡⠲⢌⠲⡾⢋⠒⠀⢢⢈⠜⠀⠀⡰⠡⠊⠀⠀⠀⠡⠄⢀⠀⡬⢵
⠀⠀⠀⠈⠦⢅⡂⢄⡈⠑⠄⠤⠃⢠⢡⠑⢀⠠⠱⡈⢂⠱⢁⠤⠁⠀⢠⠒⢌⠺⡒⢄⡀⢀⡝⠌⠾⢦⠀⢸
⠀⠀⠀⠀⢞⠉⠊⠶⢌⠢⡤⠐⠒⠇⠈⠉⠀⠒⠚⠼⠂⠑⠁⠀⢀⠔⡕⠀⠪⡒⢌⠂⠍⡩⡟⠠⠀⠰⠀⢸
⠀⠀⠀⠀⢸⣀⣴⠞⠉⢱⢱⣀⡯⠘⡦⢤⠂⣀⡀⡀⣀⡀⢄⠘⢅⢨⠀⠀⠀⠈⢂⠉⠒⠠⢬⣉⣀⢒⡒⡚
⠀⠀⠀⠀⡧⠊⠀⢀⠠⢺⢀⠸⠇⡤⢻⡿⠀⢓⡀⠣⢰⠉⠑⡕⢌⠣⡢⠀⠀⠀⠸⠂⡇⣡⠁⠀⠁⢢⠀⡅
⠀⠀⠀⠀⡇⡠⠒⠅⠀⡘⡸⠾⢻⠳⣦⠛⠒⠚⡞⡌⣀⠣⣀⠈⡢⠱⡈⠳⡤⢀⠀⢱⢁⢸⠤⢐⢜⢫⣍⡇
⠀⠀⠀⠀⠫⠀⠁⠀⡔⡰⣷⡠⠛⠀⡘⠷⡢⠜⡔⠜⠀⠑⠠⡄⠀⠀⠈⡒⢌⠒⠍⡊⠀⡡⡙⢟⢑⠁⠀⡇
⠀⠀⠀⠀⠀⠐⢀⢎⠜⠀⠀⢧⠤⠠⠀⢡⢊⢮⠊⠀⠀⠀⠐⠡⠁⠀⠄⢁⡠⠛⠒⠤⠕⣢⡈⠢⠹⡣⢀⡇
⠀⠀⠀⠀⢸⢔⠕⠁⢀⣁⠤⠘⠒⠒⠴⢥⡃⠣⣀⠀⠀⠀⢘⠀⢂⠠⠂⠁⠀⠀⠀⠀⠀⠀⠉⠁⠓⠶⠭⠇
⠀⠀⠀⠀⠘⠚⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠍⣒⠨⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠷⠾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢦⣄⠀⠀⠠⡇⠀⠀⢹⣦⣀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣯⠑⢦⣀⣇⠀⠀⠸⣿⡷⡑⢢⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡃⠸⠀⠀⣹⣿⠄⠀⢸⠇⡇⠀⠀⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢼⣿⠀⠀⠸⠁⠀⠀⠀⠀⡼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⢇⠀⡚⠀⠀⠀⠀⠀⠀⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣷⢸⠀⠇⠀⠀⠀⠀⠀⠀⢹⣜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣻⡋⡞⠀⠀⠀⠀⠀⠀⠀⢸⣻⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡄⠀⠀⠀⢀⠀⣸⢾⣶⠃⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⣈⢂⠀⠀⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣅⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡅⢣⠀⠀⠀⠀⠀⠈⣀⠚⠉⠃⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⢀⣠⣤⣽⣿⡧⠖⣂⣉⣀⠀⠀⠀⠀⠸⣿⣧⢸⠀⠀⣀⡀⠀⢈⣵⡖
⠀⠀⠀⠀⠀⠀⣰⣿⠁⣀⠔⠀⠀⠀⢀⡈⢻⣷⣶⣭⣿⠭⠍⣡⠄⠀⢀⣈⣿⣿⣬⠁⠀⣁⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠨⠷⠩⠿⣁⣈⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣶⣃⣤⣶⣿⣿⣿⣿⡟⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⡏⠉⣿⣷⠂⢀⣠⣤⣾⣿⣿⣿⣿⠿⠋⠉⠙⠿⢀⠴⠃⠀⠄
⣠⣄⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣴⡿⢓⢀⣷⠀⢸⣿⡇⢀⣆
⣿⣿⣿⠿⢿⠂⠉⠚⠦⡀⣶⣬⣀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣇⠉⢈⣉⣶⣾⣿⣿⣿⡀⣿⡿⠛⢸⣿⣦⣤⣀⣀⣠⠤⢢
⠉⠉⠉⠛⠢⠀⠀⠀⠻⣦⣤⣈⠉⠛⢿⣷⣾⣶⣷⣿⣿⣷⣾⣿⡿⠿⠿⠿⣾⣟⠿⠿⣿⡿⠿⠁⠹⠆⠀⢿⣿⣿⣏⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⡤⠌⠉⠉⠉⠛⠶⡿⠍⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⡯⠀⠘⢷⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣕⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⢀⢀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⢀⡀⣀⣀⣑⣒⢊⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠠⡖⠀⠀⠀⠀⠀⠀⢲⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⡀⢰⠒⠔⠀⠀⠀⠀⠀⡐⠦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⢂⡀⠀⠀⢀⠔⠄⠉⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠈⣀⠀⠀⠑⠀⢄⠆⠈⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡏⠱⠄⠀⠁⠢⡄⠈⠀⠀⠀⠀⠈⠤⣀⠀⠀⠀⣀⡐⠈⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢠⡆⠀⠀⢐
⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⡇⠀⢠⠒⠂⠈⠠⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⣴⠛⠳⡆⠁⡀⠀⠀⡀⡠⠒⠉⠀⡂⠀⠀⠈⠐⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣏⠢⠊⠡⠀⠀⠀⠐⠦⠀⠀⠀⠀⡼⣿⣿⣿⠟⠀⠀⠀⠀⢻⣦⣾⠇⠀⢨⢄⠎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠋⡆⠀⠀⡆⠀⠀⠀⠀⠢⢄⠰⠐⠁⠁⠘⠈⠁⢀⠀⠀⠀⠀⢻⡿⠰⠐⠁⠀⠑⡄⡀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡀⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠅⣀⣤⠶⠋⠁⠀⠀⡠⠠⠐⠁⠐⠆⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⠰⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⢁⠀⠀⡤⠐⠁⠀⠀⠀⠀⠀⠈⢂⠀⠅⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠀⠠⠀⢀⠉⠃⠀⠈⠲⣆⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠈⠈⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⢀⠠⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣁⠀⠑⠀⠙⡀⠀⠀⢀⡟⢷⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⡀⠀⠀⠀⠀⢀⢄⠆⠊⠀⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠑⢄⠀⠈⠃⠀⢸⡇⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⢀⢄⠔⠁⠈⠸⢀⡠⡠⠐⠁⠠⠂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠡⡀⠀⠈⢸⡇⡀⠀⠀⠠⡀⠀⠀⠀⡀⠄⠁⠀⠀⢀⢀⣐⠁⠀⠀⠀⠀⠀⠀⠂⢀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠢⠀⠀⠀⠈⠃⣢⣸⡇⠀⠑⢐⣠⣈⣐⡂⠈⠀⠀⣀⣀⡂⠃⠁⠈⣢⡀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠔





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⢀⠎⠏⣠⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡱⡜⠼⠊⠄⠈
⡄⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠠⠀⢈⠓⢤⠠⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠰⢢
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠘⠚⢸⠃⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢀⠈⠀⢀⣀
⡇⠀⠀⠓⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⣡⠔⠋⠀⠀⠀⢀⣄⢄⣤⠆⠀⠀⡠⢐⡄⠠⠤⠐⢂⡡⠔
⡇⠀⠀⠀⠀⠀⢀⢹⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⡈⢀⢀⣰⣴⣶⠏⠐⠫⠇⠆⠀⢠⠳⠎⠔⠀⠀⢀⠦⡑⠄
⡇⠐⠁⠢⠔⡔⠆⠈⡠⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⢀⣸⣿⡿⠛⠋⠂⠀⠀⠐⢐⠄⠀⠑⣦⣀⣠⠔⠋⠀⠈⠚
⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡃⠀⢊⠟⠲⢄⠀⠀⠒⠀⠀⣩⣇⠀⠀⠈⠢⣌⠑⢄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⢢⡼⢂⢄⠀⠀⠀⠀⠱⡌⠒⠆⡇⠀⠀⣀⠨⠷⢂⣙⡦
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⡆⠀⠈⠀⠜⠆⠀⠀⠀⠀⠀⠀⠀⠠⣴⠅⠒⡡⠔⠚⠉⠁
⡇⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠂⠀⠒⡞⢳⠀⠀⢀⠿⠀⠀⡇⠀⠀⠀⢀⣠⣤⣸⠀⢠⠤⡄⠀⠀⢱⠀⠘⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⢰⠁⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠛⠈⠙⢄⢠⣤⣬⡆⣧⣸⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠆⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠈⢣⠙⠛⣡⣧⠉⡀⠀⠀⠡
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⢄⢶⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠓⢲⢊⠩⠀⢀⠀⠀⠀⢂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠧⢠⠄⠃⠀⠐⠂⠀⠀⠓⠦⠖⠃⡆⢸⠀⡇⠀⠨⠀⠀⠀⠀⡀
⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢁⠀⠀⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠀⠄⠀⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠄⠀⠣⣤⠆⠀⠠⠤⠠⠀⡅⠀⣇⠤⠼⠀⢻⠒⠒⠠⡤⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⠉⠱⣄⠘⠠⠴⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠀⠀⠀⠀⠀⠀⢀⠌⣰⠉⠉⠉⠉⠁⠙⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⡁⠄⢠⠃⡔⠁⠀⠀⠀⠀⢀⠎⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⠀⠀⠀⢣⠈⢦⠀⠀⠀⣰⠃⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡐⢣⠀⢠⣉⠉⠉⠉⠉⠑⢢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣠⡶⣶⡄⠀⠀⣴⡟⠁⠀⣿⡇⠀⠀⠀⣀⣤⡀⠀⠀⣰⡿⠃⠀⠀⢸⣿⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⢹⣿
⠀⠀⠀⠀⣠⡾⠋⠀⢸⣧⢀⣾⠏⠀⠀⠀⣿⣇⣤⣤⣼⠟⠙⢿⣦⣾⠟⠁⠀⠀⠀⢸⣿⣾⡿⣷⣄⠀⣀⣀⣤⡿⠋⠀⠀⠀⠀⢸⣿
⠠⣦⣠⡾⠋⠀⠀⠀⠀⠿⠟⠁⠀⠀⠀⠀⣿⣿⠏⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠈⠻⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⢒⣿⣶⡖⠒⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⢤⣀⣚⣉⣉⣁⣀⣀⣀⡤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣄⣀⡀⠀⠉⠉⠉⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⣍⣛⠛⠟⠛⠛⠛⠛⠛⣉⣽⣆⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠴⢶⠆⡣⣈⠉⠛⠛⠛⠛⠛⠛⠛⠋⣽⢡⡇⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣀⡀⠀⠴⠛⠸⡗⠮⢭⣝⣓⣒⣒⣶⡾⠿⠋⣿⠈⣇⠤⢤⠤⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣎⡳⢬⣉⣉⠉⠉⠀⣵⠢⢤⣤⣀⣀⣀⣠⣤⣤⣶⢿⡄⠘⣆⠀⠀⠾⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢛⡉⠙⠛⠛⠛⢻⠻⡿⣤⣀⣀⣀⠈⠉⠉⣉⣀⣠⣤⣷⡄⠘⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠚⠂⢃⣀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠃⠙⢦⡀⠙⢂⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠛⠋⠁⠀⠀⠀⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣤⣤⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⣽⣿⠋⠲⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣀⠀⠀⠀⢀⣈⣵⣤⠀⠀⠀⢀
⠀⠀⣠⣤⣤⣀⣀⣘⣛⣶⣦⣻⣕⡿⢶⣄⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⣘⣁⣰⣶⣾⣿⣿⣿⣿⣿⣾⣦⣴⣶⣦⣄⣀⣀⣀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣐⡿⠁⠈⢿⠏⠁⠀⠒⠀⠀⠀⣴⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠋⠃
⠀⠀⠈⠁⠀⠈⠻⣿⣿⣿⣿⣿⣦⣄⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⣴⡀⣹⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠍⠃⠀⠀⠀⠀⠀⠀⣐⣿⢿⣿⣿⠟⠻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⣄⡀⡉⠛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣯⡟⠻⣿⣿⡿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆⣀⣄⣀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣷⣟⡉⠀⠀⠸⡏⠀⠈⠻⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⣀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢧⠠⠾⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡌⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠻⣿⠏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠻⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⠀⠘⠟⠁⠀⠀⠀⠹⠿⠿⠿⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠋⢁⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣧⠠⢶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⠦⠸⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡜⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣭⣿⣶⣴⣶⣶⣶⣶⡆⠀⠀⣴⣶⣶⣶⣶⣶⣀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣏⠀⠀⢼⣿⣿⣿⣿⣿⣿⠏⠀⠰⣤⣤⣶⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠻⠿⠿⠿⡦⠀⠈⢻⠿⠿⠿⠿⠋⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⣀⠀⠀⢀⡀⠀⠀⣀⡀
⠀⢸⡟⠉⠉⢉⡉⠉⠀⠈⠁⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠈⠙⣿⡏⠀⠀⠀⠀⠀⡜⠉⠓⢤⡛⢈⡲⣈⠑⣶⣏⠀⠀⣰⠃⠈⢲⡄
⠀⢸⡇⢀⡀⠈⣀⠀⠁⣀⣀⣀⡀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⣀⣸⠀⠀⠀⠀⠈⠳⣬⠞⣻⢧⣌⡙⢲⠧⣄⣀⡾⠉⠳⣄
⠀⢸⣷⣤⣤⣤⣤⣤⣤⣀⠠⣤⡀⠈⠻⢿⡆⢰⣶⣄⣀⣤⣶⠿⠿⠛⡟⠛⠛⡿⠿⣷⣶⣄⣀⡜⢁⡜⠓⢧⡀⢩⠟⠒⠢⢽⡇⠀⠀⢠⠗⢦⡀
⠀⠸⢿⣛⣫⣼⣿⡉⢻⣿⣷⡈⠻⢷⣤⣾⡿⣪⣿⡿⡟⠉⠀⠀⠀⠀⡇⠀⡘⠀⡼⠁⡹⢿⣿⣦⣎⠀⠀⠀⠈⠛⠶⠤⣄⣼⠀⠀⢠⠎⢠⠏⠈⠲⣄
⠀⠸⠿⠯⠷⠋⠘⣷⡀⠹⣿⣷⡀⠸⢟⣿⣼⡟⠁⠀⠱⡄⠀⠀⠀⢰⠇⡐⢀⡞⠀⠜⢠⠋⣸⠻⣿⣷⣤⡀⠀⠀⣀⣠⠾⠋⣷⢠⠏⢀⡏⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⡜⢀⣷⡞⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠙⢦⡀⠀⢸⡜⣡⠟⢄⠎⢠⠋⡼⠁⠀⡴⠋⠻⢿⣷⣋⣁⠀⠀⢀⡾⡏⠀⡞⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⢠⣴⣟⣴⣿⣦⣽⠿⣿⡟⠉⣆⠀⠀⣠⠤⢄⣀⣹⡶⠖⠻⡅⠀⣀⠷⢧⠞⠀⣠⠞⠁⠀⠀⠈⢿⣷⠴⠼⢶⠾⠤⣧⣸⡃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣠⣿⠋⠀⠙⢻⡟⠁⠀⢸⡇⠀⡜⠀⢠⡃⠀⠀⠀⡰⠁⢀⣀⡹⣞⠁⠀⢈⣳⡞⠁⠀⠀⠀⠀⣠⣾⠇⠀⢰⠷⣆⣰⡃⡜⠉⠉⢹⡟⠒⢦⡤⢤⡇
⠀⠀⠀⣴⣿⠹⡆⠀⠀⠀⠀⣀⣀⣤⣿⢤⣇⠀⠀⠓⢤⡀⣼⣄⠀⠘⢆⠀⠈⡦⠖⠉⡇⠙⣆⣀⣤⣶⣿⠟⠳⣄⣀⡞⠀⢀⡟⠙⡆⠀⣠⢾⠀⠈⢺⠤⠤⡇
⠀⠀⣼⡟⠁⠀⢳⣤⠒⠊⠉⠀⢸⣿⣿⣦⡀⠈⢲⡄⠀⡼⠛⢯⡀⠀⠐⣇⠀⠱⣄⣠⣴⣶⣿⢿⠟⠋⠀⠀⠀⠀⠉⣳⠖⠺⢯⣓⣿⡊⠀⠈⢇⠀⢸⠀⠀⡇
⠀⢸⠟⠀⡜⠀⠀⢿⠀⠀⠐⣚⣉⣥⠼⣠⠛⠓⠲⣷⠴⣇⠀⠀⠙⠢⣀⣸⣶⣾⣿⠟⠛⠉⠀⠠⣷⡄⠀⠀⠀⣠⠔⠁⠀⠀⠀⠙⡅⠈⠉⢢⡼⠒⢺⠖⠒⡇
⠀⠈⢀⠈⠀⠀⠀⢸⡗⢺⣋⣉⡡⠴⢎⠁⠀⠀⢀⠇⠀⠀⠙⠲⠶⢶⣿⠟⠋⠁⠘⠦⢦⠀⠀⠀⢀⠽⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⡏⠀⠀⢸⠀⢠⠇
⠀⠐⠁⠀⠀⠀⠀⠈⢻⡀⠁⠀⠀⠀⠈⣧⡤⠖⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣠⣾⣷⣄⣰⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣇⣀⣤⣼⣤⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠃⠀⠀⣀⣴⠋⠁⢀⣀⣤⠤⣤⣤⣶⡖⢋⣹⣿⡇⢀⠔⠋⠙⢿⠃⢈⡏⠀⠀⠀⠙⡆⠀⡀⠀⠀⢀⡠⠴⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣠⠴⠚⠋⠉⠁⠈⢳⡋⠉⡇⣀⣠⡿⢿⠛⠯⠭⠔⡿⣿⣅⣀⣶⣀⠏⠀⢸⠁⠀⠀⠀⣠⣧⣸⠿⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠁⠈⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠀⠀⠈⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠠⢀⡤⠄
⢀⡀⠀⢀⠀⡣⠀⠀⢁⠄
⠀⠀⠒⠀⢠⡇⠀⣄⣁⠠⡀⠀⠠⠄
⠠⠀⠀⠀⠙⠳⠀⠃⠀⡑⢈⡕⡉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠾⡃⠹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡴⡋⠀⠀⠀⠀⠀⠀⠀⠐⠋⠢⠀⠀⠀⠀⣠⣤
⠀⠙⠀⠀⢀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠁
⠀⠀⠀⠀⢨⠀⠀⠀⠨⠈⠐⠂⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠼⠀⠀⠀⠆⠀⠀⠀⠅⠀⠀⠄
⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣤⠀⢀⡀⠀⠀⠀⠀⠠⡀
⠀⠀⠐⠀⠀⢠⣄⣠⣀⣦⣄⢀⡽⠷⠖⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⢀⣰⣶⣤⣤⣼⣶
⠶⠶⠶⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣇⠠⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠀⠀⠀⠀⠀⡀⢀⣀⣧⠜⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠦⠶⠒⠚⡟⠉⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢬⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⡢⠐⠀⠀⠈⠉⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠚⠋⠉⠁⢸⠇⠀⠀⠀⠀⠰⡆⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢻⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡃⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡇⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠷⣾⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⢤⠖⠻⠟⠁⠂⡂⡾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣀⠦⡜⡾⠉⠉⡠⠘⢁⣤⣴⣾⣿⣯⣷⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⡀⠿⠐⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣬⣥⣶⣿⣿⣿⣿⣿⣋⠻⢿⣿⣿⣿⣁⣀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⢀⡖⢮⣙⣛⡛⠉⢩⣽⣭⣙⣋⣿⣶⠳⣿⢿⣯⢙⣿⣿⣿⠝⣛⠷⣴⣶⣶⣾⣍⣀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠠⠌⠋⣁⣬⣿⣭⣿⣿⣿⡞⢛⣯⣥⣶⣿⣿⣛⠛⠛⣉⣵⣆⠁⢨⣉⣛⣛⠙⠻⣿⣿⠿⠶⣿⣯⣟⡛⠁⠠⠄
⠀⠀⠀⠀⠀⠐⠒⠂⠉⠉⠉⣭⣥⠀⢼⡿⠛⠋⠁⠤⠼⠛⠋⠉⠩⠕⠂⢀⣿⠿⡋⠀⠰⣮⣍⣻⠥⠤⠤⢴⣶⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠁⠀⠀⠀⠘⠻⢿⣷⣶⡄⠀⠒⠉⠀⠀⠀⠈⠙⠛⠉⠁⠀⠢⠭⣭⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣒⢖⡢⣦⣶⣲⢴⣴⠲⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⢀⡆⣶⠀⡆⢰⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢠⣤⢸⡇⣿⠸⡽⠘⡇⡄⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⠿⠤⠥⢬⡤⠧⠤⠥⡇⠀⠈⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠐⠦⠤⢴⣴⣦⡤⠤⠴⠃⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠫⣯⠑⣀⣀⠀⠀⢀⡴⣲⢤⢀⣤⣴⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠙⠦⣪⠔⠁⠻⡀⠀⠐⠧⣭⠞⠨⢤⡧⢵⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⣩⣧⣇⣾⣹⠀⠉⡆⠀⠒⠦⡄⠒⠲⡗⠲⠖⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⣁⠀⡠⠖⣍⣀⡈⣉⠆⣹⢐⠛⡏⣺⡢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠈⠓⠃⠀⠀⠈⠡⠤⠶⠃⠈⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⣶⣽⣦⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣀⣀⡠⢴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇⣠⣶⣿⡿⠟⠉⠻⣷⡝⣿⣿⣿⣧⣿⣿⣿⡿⣟⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣦⣝⣿⣿⣿⣿⣥⢿⡯⠓⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⣀⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣀⣤⡶⠟⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⠀⢀⣀⣤⡶⠟⠋⠁⠀⠀⠻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠈⠙⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⢀⣴⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠈⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠋⠀⣀⣀⠀⠀⠀⠀⢸⣿⣦⡀⠀⣠⣴⡦⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠋⠀⠀⢸⣿⣿⡷⠀⠀⠀⠀⠉⠉⠁⠈⠻⠛⠉⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣀⠀⠈⠙⠛⠁⢀⣤⡶⠆⠀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠘⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣀⠀⠀⠈⠀⠀⠀⣼⣿⣶⡀⠀⠈⠻⠛⠋⢀⣠⣄⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⣴⣿⣷⡄⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⣠⣤⣤⣄⠀⠻⠿⠋⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠸⣿⡿⠀⠀⠻⢿⠿⠃⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⣀⣀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢰⣿⣶⣦⡀⠀⠀⠻⣿⣿⠃⠀⣀⣄⣀⠀⠀⢀⡀⠀⠀⠀⠀⣼⣿⣿⡆⠀⣠⣶⣿⡇⠀⠀⠀⠩⠟⠯⠁⠀⠀⢸⣿⣿⡗
⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣦⠀⠀⠀⠈⠛⠛⠁⣾⣿⣿⡏⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⢰⠿⠿⠟⠃⠀⠈⠋⠋⠀⠀⠈⠉⠁⠀⠀⢀⣠⣴⠀⠀⠘⠻⠟⠁⣴⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃

⣿⣿⡟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢳⠀⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡜⣧⠀⢻⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣽⡄⠈⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡀⢨⣿⡄⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠠⠐⠒⠁⠈⠉⠀⠀⠀⢸⣧⣼⠟⢻⡄⠀⠰⡀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⣿⣄⠀⠀⢀⡄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⢿⢸⡆⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⢀⣠⣀⣶⡾⠿⠯⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠉⠛⠃⠒⠶⠶⠦⢤⣤⣴⡇⠀⣠⣾⣦⣴⣯⣀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠉⠙⠻⠿⢯⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⠸⢿⢰⣶⡤⣬⣤⣤⣀⣄⡄⠀⠀⢀⣀⣀⣤⠤⡶⠃
⠀⠀⠀⠀⠀⠰⣬⣵⣾⣿⣿⡏⠉⠉⠀⠀⠀⣀⡀⣀⣒⣒⣴⠺⣥⡿⣿⠶⠞⠛⠫⠉⠑⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⠿⣿⣦⣦⣤⣤⡤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠬⠽⠷⠶⣿⣿⠠⠔⠒⠤⠄⣀⣀⣤⠤⠀⠀⠤⣤⣤⣤⡼⠛⠛⠁⢠⣤⡤⠤⠄
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⣉⡉⠀⢀⣀⣀⣀⣉⣉⣉⣀⠀⠄⠀⠀⠀⣉⡥⣤⣄⣓⡙⠉
⠀⠀⠀⠀⠀⠀⠠⠔⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⣀⡀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⢀⣀⣀⣀⣀⢀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠰⠇⠰⠀⠙⢦⡀⠀⠀⠈⠳⠍⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠈⠀⠀⠈⠀⠀⢁⠔⠀⠀⠙⢦⠔⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡠⠁⠀⠀⣠⡴⠁⠀⠀⢀⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠌⠀⠀⠀⠀⠀⢀⠈⠀⠀⣠⣾⠟⠡⠀⢀⣐⠜⠧⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⡸⠏⠁⡀⠀⢸⠟⠁⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠀⠀⠀⠀⠀⢀⠌⠀⠠⡊⠊⠀⠈⣇⠀⢀⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢦⡀⠀⠀⠀⡠⠂⣠⠂⠉⠀⠀⢀⡰⣜⢢⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠳⣝⢦⡀⠊⣠⠜⠃⠀⠀⠀⡠⠊⠀⠈⠻⣽⢦⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢷⡝⠒⠀⠀⠀⡠⡀⠊⠀⠀⠀⠀⠀⠈⠳⣝⢦⣀⡤⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⢂⡄⠒⠀⠀⠀⢠⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣉⢴⣫⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠚⠁⠀⠀⢠⡾⠮⡑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠳⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡼⠋⠀⠀⠙⢮⡳⣄⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠊⠈⠀⠀⠀⠀⠀⠀⠙⢮⡳⣄⡴⣫⠞⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⣪⡾⣅⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡙⢦⠀⠀⠀⠀⠀⠀⣀⠔⣡⠞⠁⠙⢮⡳⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠈⠢⡑⢄⠀⠀⣠⢞⡡⠊⠀⠀⠀⠀⠀⠙⢾⡳⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠜⢦⡳⢞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡳⣄⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠰⠂⣟⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠛⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠒⠒⡄⠑⢝⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠓⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠈⠠⠇⠀⠀⠁⠝⢮⡳⣄⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⡰⠆⠂⠀⠀⠀⠈⠀⠁⠈⠁⣀⣀⣈⢉⣉⣀⡀⠐⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠸⠇⠀⠉⠉⠉⠉⠉⠉⠉⠀⠿⠿⠿⠘⠿⠿⠟⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠀⠈⠀⠀⠀⠀⠈⠀⠐⢋⡴⣫⠞⠉⠻⣟⢧⡁⠀⠁⠉⠀⡘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠈⠉⠉⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⠀⠀⠀⣀⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡖⠀⠀⠀⣠⠤⠤⠞⠉⢉⠹⣏⠀⠈⢲⢛⡉⢀⠻⡄⢠⣄⠀⢠⣄⠀⠀⠀⡀⢠⠥⠄⠀⠀⠀⢀
⠀⠀⠀⢀⡶⣀⡶⠙⠁⠀⠀⠀⢀⠇⣀⣠⠠⠑⢁⡔⠂⠁⠀⡰⠃⠀⠀⠙⡀⠞⠾⣷⠀⠀⠑⠀⠀⠀⠸⠁⠀⠀⠀⠠
⠀⠀⣤⠟⠀⠉⠀⠀⠀⠀⠀⣴⣏⢀⡋⢡⠤⠴⣾⡤⠴⠖⠚⠃⠀⠀⠀⠀⠁⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠱⠃⠀⠀⠃⠀⠀⠀⠀⠀⢀⣤⡄⢠⣤⡀⡤⢬⡀⠰⡖⡇⠀⠀⠀⢀⠄
⠀⠛⠶⠲⠐⠆⢀⠀⠀⠀⠀⢀⣰⡾⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⢯⡠⣦⣼⣀⡿⡗⠚⠁⠀⠿⠁⠀⠀⠀⠋⠆⠀⠀⠠⠠
⠀⠀⠀⡠⠄⠀⠸⣿⣿⣿⠸⣈⣼⡷⠀⠀⠀⣀⠦⣤⣀⠀⢀⡎⣤⡬⠥⠀⢡⠤⣥⡀⠚⢉⠀⠀⡀⠀⡀⢀⠀⢀⠀⠠
⠀⣠⠞⠁⠀⠀⠀⢿⣿⣿⡟⣣⢼⡇⠈⢀⣰⠍⣘⢢⡬⢁⡎⣼⣧⣬⡄⠀⠀⣤⣼⣿⡀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠸⠿⠃⣰⣻⠄⠀⠸⣿⣿⣧⢵⡆⠀⠀⠈⠋⠲⠀⠯⣣⡟⠀⢻⠤⡼⡄⠀⠀⡏⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⢠⢀
⢀⠀⠀⡛⠡⡴⢾⡁⠻⠿⠿⠈⢀⣀⣀⡀⠀⠀⠀⠀⠛⠀⠀⠘⠉⠉⠃⠀⠀⠋⠉⠉⠀⠀⠀⠀⣾⡧⠀⢸⣿⣿⠀⠉⠁
⠀⢠⠀⠙⠀⠙⠾⢷⣀⣀⡤⠀⣏⢀⡀⠀⣀⠀⢀⣄⠀⣀⠀⢀⡀⣀⣀⣀⠀⡀⣀⡀⣠⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀⣶⡇
⠀⠀⠛⠀⢀⠧⠒⠀⢀⣀⣀⠀⣏⣉⣁⠰⣍⡅⢏⡰⠹⠋⠷⢏⠜⠯⠸⠸⠸⠗⣧⠀⣽⠀⠀⢸⠀⡆⠀⠈⠀⠀⠨⠟⠃
⠀⠀⠀⠀⢰⠀⠂⠐⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⣀⣤⠀⢀⡀⠀⠀⠀⠀⠧⠼⠀⠴⠥⠄⠀⠐⠂
⢰⡇⠀⠀⠞⠀⠀⡒⠀⡛⠑⠀⠀⠀⢀⡀⢲⠠⠠⠠⠚⢸⡍⢠⡄⢠⡿⠇⠀⢸⣿⣤⣶⠀⠜⠀⠀⠀⡆⠀⠒⠛⠃⠀⠃
⠀⠀⠛⠀⠂⠀⠀⠀⠐⠈⠀⠀⠘⠃⠉⠥⠈⠀⠀⠀⣆⠰⠃⣾⠻⠟⠀⠀⢠⣾⣿⣿⠛⠁⠄⠸⡤⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣦⡀⠂⠃⢠⣿⣆⣸⠃⢀⣄⡀⠀⣿⣿⣿⣿⣶⣾⣿⣷⡍⢸⠁⢠⣞⠡⡆⠀⡀
⠀⢀⠀⣀⣀⠤⠠⠔⠐⠂⠀⠛⠿⠋⠀⠀⠙⢦⡀⢸⡇⠘⡏⠀⠀⠈⠀⠀⠈⠛⠛⣿⡟⢻⣿⣿⡷⢸⠀⠈⠛⠋⠀⢀⠃
⠀⠀⠉⠃⡃⠀⠈⣤⣤⡀⣦⢰⠸⣏⡿⢰⡄⠀⠉⠻⠃⠀⠀⠠⠀⠔⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⠃⠘⠒⠀⠀⠀⠊⠁
⠀⢰⣇⣼⡧⣔⡂⢿⣀⡿⠘⡿⠀⠿⠀⠀⠙⢦⡀⠀⠀⠀⡀⠂⠀⠀⠹⣀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⢐⣀⣄⡀⣤⡄
⠀⠹⣽⣹⡿⠿⣢⠘⠉⠀⠀⠀⠀⠷⣌⢻⠀⠀⠉⠲⢤⣀⣋⡀⠀⠀⠀⠉⠁⠀⠸⠟⢻⣧⠀⣿⢇⣾⡍⢻⣿⢿⡆⠙⣦
⠀⢴⡻⣧⣭⣽⡟⠀⠘⠛⠛⠂⠀⡐⢦⠑⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠁⠀⠀⠀⠀⠀⠘⠋⠀⣿⠘⠉⠀⣀⢠⣤⣤⡀⡿
⠀⢸⣗⣳⡞⣯⣾⠀⠀⣤⠀⣤⠀⣷⣌⠃⠀⠀⠀⠀⠀⠀⣲⠒⢶⠂⠀⠀⣀⢠⠀⠀⢂⣲⡦⢿⣀⠀⣴⡿⠏⣿⡿⠁
⠀⠀⠷⠯⠿⠔⠚⠘⠦⠷⠋⠁⠀⠛⠓⠑⠀⠀⠀⠀⠀⠀⠛⠚⠀⠀⠀⠐⠿⠿⠆⠀⠈⠉⠉⠈⠉⠀⠀⠀⠀⠉