Frypan Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣉⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣍⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣋⣥⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣤⣭⣭⣉⣉⣉⣉⣉⣭⣭⣥⣴⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⣻⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⢉⡩⢖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⣠⠖⣩⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⢀⡴⣋⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠶⠶⠶⠦⠤⠤⢤⣤⣀⣀⡀⢀⣀⣤⠾⠋⠀⠀⣰⢋⡼⠋
⠀⠀⠀⠀⠀⣀⡤⢶⣚⣯⠭⠷⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠿⠭⣟⣻⠦⣄⡀⠀⢠⢇⡾
⠀⠀⣠⡶⣻⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢭⡳⣾⣸⠇
⢀⡾⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⡄
⡿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻
⣧⢻⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⢀⡟⣼
⢻⣮⢧⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⣠⠞⣱⡏
⠸⣟⠳⣿⣶⣤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⢞⡥⢞⡿
⠀⠹⣦⠈⠙⠳⢯⣷⣢⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢴⣒⣭⠷⠞⠋⢠⡾⠁
⠀⠀⠘⢷⣄⠀⠀⠈⠉⠛⠛⠶⠿⠿⣿⣿⣿⣿⣿⣿⣭⣭⣭⠿⠶⠞⠛⠋⠉⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣍⣓⠲⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣤⡤⠤⠖⣚⣩⣵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠄⠀⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠠⠤⠄⢀⣀
⠀⣀⠤⠒⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣀⢒⡀⠀⠤⠤⠤⠭⠭⠉⠬⠷
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣓⣦⠀⠖⣒⡢⠭⠇⠒⠈⠉⣀⣀⡠⠤⠤⠴⠶⠶⠶⠤⢤⣀⣀
⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡆⢹⠀⠁⠀⣀⡤⠔⠒⠋⠉
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡄⣨⡤⠒⠉
⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠴⠚⠁
⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⡿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⣾⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⢀⣀⣤⣤⣤⡶⠶⠶⠶⠶⠶⠶⣦⣤⣤⣄⣀
⣠⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣦
⣿⣄⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⢀⣼⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⡟⠷⢾⣿⣍⣉⣀⣀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣽⣿⠾⠟⣿⣹⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠘⣷⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⢰⡟⠋⠁
⠀⠘⠻⠶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣔⣒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠋⠁⣋⣩⡾
⠀⠀⠀⢀⣠⣤⠴⠖⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⣶⣤⣀⣀⣀⡤⠴⠒⢉⣁⣤⡤⠶⠚⠛⠉⠁
⢀⣴⣾⣿⣿⣿⠏⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⣤⣀⡀⠙⢯⣿⣧⣴⠶⠛⠋⠉
⣿⣹⡿⣻⠵⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡾⣿⠃
⢻⣽⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⣩⣳⠃
⠈⢿⣿⣿⣿⣿⣗⣲⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠉⠁⠀⠀⢐⡵⠃
⠀⠀⠙⠛⠿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡿⢁⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠟⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡃⠄⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣶⣶⣶⣮⣽⣿⣿⣿⣿⣿⣯⣭⣭⣝⣛⣘⠷⣀
⠀⠀⠀⠀⠀⠀⡀⣔⡮⠟⢚⠉⠭⠁⡄⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⡀
⠀⠀⠀⠀⢀⢮⣾⣫⠀⣠⠸⢀⣈⠁⢁⣛⠫⠭⠭⠭⠭⠭⠽⠿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣿⣿⣟⣡⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠏⢻⣳
⠀⠀⠀⠀⠸⣟⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣔⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣾⣯⣶⣴⣠⣤⡀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣽⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢿⣟⡿⣻⣿⣿⠿⠿⡿⡿⣻⣿⣿⣿⣿⣟⣿⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣴⡾⠿⢶⣿⣻⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣼⠃⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠐⡏⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣭⣍⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣩⣭⣿⣿⡇
⠀⠀⠀⠀⠀⣿⠉⠈⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⣻⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⣼⠇
⠀⠀⠀⠀⠀⠙⠷⠶⠶⠶⠶⠾⠿⠛⠛⠛⠛⠛⠛⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⣴⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢩⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠠⠔⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣾⡛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢤⣶⠴⠋⠉
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⣀⢀⠀⠀⠀⠀⡆⠀⣱⡆⡀
⠀⠀⠀⠐⣿⣿⣿⣿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡻⣷⣿⣿⡵⠁
⠀⠀⠀⠀⠘⢿⡛⠟⠒⠚⠷⠶⠶⠤⠤⠤⠤⠤⠤⠴⣶⣶⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠛⠒⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠛⠛⠛⠉⠉⠁
⠀⠀⠘⣶⣶⡖⠒⠚⠛⠛⠛⠛⠛⠒⠓⣶⣾⣿⣿⣿⣿⣿⣿⡷⠛⠉
⠀⠀⠀⠻⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠷⠶⠶⠿⠿⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⣀⠠⠀⠐⠀⠁⠀⠉⠉⠉⠉⠁⠉⠁⠒⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⢄⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠠⠤
⡇⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⣇⡠
⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠉⢼⡝
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠒⠒⠒⠂⠀⠁⠉⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠉⠒⠢⠤⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠲⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⡿⠿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⠋⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣂⣤⣾⣿⡿⠿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⠶⠿⠟⠛⠉⠀⢀⣠⣴⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠾⢿⣿⣛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠒⠲⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣄⣀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣀⣤⠀⠀⢠⠀⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⡾⠀⠐⠢⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⡇⠀⠀⠀⡷⠀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⠷⠤⠤⠞⠁⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣿⣦⣤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⣀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣶⣤⣤⣤⣴⣶⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣀⣰⣠⣀⢀⣀
⠀⠀⠀⣰⠊⠀⠐⠃⠀⢀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢹⣿⣿⡿⠿⠟⠛⣿⣿⠀⢠⣤⡄⣀⣀⣀⣀⡻⠿⠿⣿⣿⢀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⣤⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢸⣿⡇⠀⣀⣤⠀⠘⣿⡀⢸⣿⠇⠻⠿⢿⣿⡗⠀⣸⣿⠃⢸⣿⠁⠘⣿⡇⠀⣿⣿⣧⠀⠀⣿⡇⢀⣴⣿⠟⢻⣿⡇
⠀⠀⠀⠈⣿⡇⠀⢻⣿⣶⣾⣿⡇⢸⣿⠀⠀⢀⣿⡟⠀⣰⣿⠃⠀⢸⣿⠀⠀⣿⡇⠀⣿⣿⣿⣆⢰⣿⡇⣼⣿⠃⠀⠀⠉⠁
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠈⢻⡇⣸⣿⠀⠀⣾⡟⠀⢠⣿⠃⠀⠀⢸⣿⠀⠀⣿⡇⠀⣿⡏⢻⣿⣼⣿⢣⣿⡇⢰⣿⣿⣿⡟
⠀⠀⠀⠀⢸⡿⠗⢲⣿⣧⠀⢸⣿⣿⡏⠀⣼⡟⠀⠀⣿⣷⣶⣶⡄⢸⣿⠀⠀⣿⡇⠀⣿⡇⠀⢿⣿⣿⠸⣿⣇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡀⠈⠋⠉⠀⣸⣿⣿⡇⢸⣿⣶⣶⣶⡎⠉⠉⠉⠀⢸⣿⣤⣤⣭⣄⠀⣿⡇⠀⠘⣿⣿⠀⢿⣿⣄⢀⣼⣿⠃
⠀⠀⠀⠀⠀⣿⣷⣦⣤⣶⣶⣿⡿⠃⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⠛⠛⠁⠀⠉⠀⠀⠀⠈⠉⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠫⠙⠉⠉⠀⠀⠀⠈⠀⠀⠀⠈⠙⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⠛⠳⠁⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣶⣃⣀⠀⠀⣀⣠⣎⠀⠀⠀⠀⡱⠄⠀⠤⡀⠀⠠⡀⠀⠉⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠟⠈⢛⠟⠣⡴⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠒⠂⡐⢀⣘⠈⠙⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣻⠀⢀⡎⠀⠀⢸⡇⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⡮⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⣉⣄⠘⣇⡀⠰⣾⣿⣦⣀⣳⣄⢈⣿⣆⡀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠅⠀⢈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢶⣶⣶⣅⣄⣀⣀⡀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⡻⣿⡿⠻⣯⣽⣟⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⣛⣿⣿⣿⣿⣯⣭⣭⣿⡿⣛⣴⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠁⠹⣿⣿⣿⣮⣹⣿⠿⢿⣿⣿⣿⡖⢤⠴⠒⠢⣼⡟⣻⣿⠿⢿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠀⠀⠀⠀⠋⠙⡿⢿⣿⣿⣆⠀⠹⠉⣿⡇⠀⠀⠀⢠⠉⢠⡿⠁⣠⣾⣿⡿⣋⣵⠟⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡿⢷⣝⠳⡈⠻⣦⠀⢀⣿⡇⠀⠀⠀⢸⡀⠘⠁⣴⣿⠟⣡⠞⡛⠛⠀⠀⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⠿⣷⣬⡑⠮⡂⠈⠷⢸⣿⡇⠀⠀⠀⠈⡇⢀⡼⠋⠠⣪⠥⠬⣡⣤⣤⣤⣤⣤⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠁⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⢹⡄⠀⠀⠈⠁⢀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣾⣭⣭⣁⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⣉⣩⣭⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠀⠀⡀⢰⣿⣿⣿⣿⣄⠋⠁⡤⠄⠊⠃⠄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠀⠠⣀⣀⡀⠀⠻⠟⠉⠉⠙⢿⣷⣿⣤⣄⢀⣀⣄⣡⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢾⣥⣤⣤⣤⣤⣤⡽⠿⠿⠧⣤⣤⣤⡄⠈⠉⠀⠉⡙⢻⣿⣤⣬⣭⣽⣿⣶⣶⣶⣾⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣟⣹⢛⣟⢋⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⣀⣤⣄⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⢿⣧⢰⣿⡏⢻⣷⡀⣿⡟⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠘⣿⡆⢻⣿⠈⣿⡇⢹⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⣸⣿⢣⣿⠏⢰⣿⢃⣾⡟⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⠃⣿⡏⢰⣿⠏⣾⡟⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠘⣿⡆⢿⣧⠘⣿⣆⢻⣿⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡿⠃⠈⠿⣷⡿⠏⠈⠻⣷⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠋⣉⣠⣤⠴⠶⠶⠶⠒⠲⠶⠶⠶⢤⣤⣈⡉⠛⠻⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠁⢀⣠⠶⠛⢉⣡⣤⠶⠶⠖⠒⠒⠒⠒⠲⠶⠶⢤⣌⠙⠳⢦⣀⠀⠉⠛⢿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋⠀⠀⢀⡴⠋⠁⣠⡶⠋⠁⠀⠀⢶⣴⠂⠀⠀⠻⣦⡖⠀⠀⠈⢳⣄⠀⠉⠳⣄⠀⠀⠈⠙⠿⣷⣄⡀
⠀⠀⠀⠀⠀⢸⣿⠋⠀⢀⣀⣀⣴⠏⠀⣠⣾⣿⠁⠀⢦⣀⡴⠋⠙⢷⣄⣠⠞⠉⠻⣦⣠⡴⠈⡏⠻⣦⡀⠈⢷⣤⣄⣀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⢸⣿⠀⣰⠟⠁⣸⠃⠀⣴⢻⡏⢿⠀⢀⡴⠛⢦⡀⠀⣠⠟⢷⣄⠀⢀⡼⠻⣦⠀⡇⠀⠈⢳⡄⠀⢻⡀⠙⢷⡀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⡟⠀⢰⡇⠘⣇⠘⣧⡀⠀⠀⠀⣹⣾⡁⠀⠀⢙⣷⣏⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠘⡇⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⣇⠀⢸⡇⠀⠻⣄⠈⠛⢦⣀⠀⠁⠀⠙⣦⡴⠋⠀⠙⠃⠀⠀⣼⠀⠀⠀⠀⣿⠀⢀⡇⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⢻⡀⠀⢻⡀⠀⢷⡀⠀⠉⠳⣤⡀⠉⠳⣤⠀⠐⠋⢙⣤⣀⠀⠀⠀⢠⡏⠀⠀⠀⣰⠏⠀⣸⠃⠀⣼⠃⢸⣿
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠙⠳⠾⢷⡀⠈⠳⣄⠀⠀⠀⠙⠷⣄⠘⣇⠀⠠⣏⠀⢸⡇⠀⣠⡟⠀⠀⣀⡼⠋⠀⣰⠿⠶⠚⠁⠀⣸⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠹⣦⡀⠈⠛⢦⣄⣀⠀⢻⡄⠙⢦⣀⠉⠛⢋⣠⣴⠟⣀⣤⠞⠋⠀⣠⡾⠁⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠙⠶⣄⡀⠈⠉⠛⠚⠷⣤⣀⠉⠙⣛⣿⠟⠛⠋⠉⠀⣀⡴⠞⠁⠀⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⣈⠉⠛⠶⠦⣤⣄⣀⣉⣙⣋⣉⣀⣤⡤⠶⠞⠛⢉⣀⣤⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣷⣶⣦⣤⣤⣬⣭⣉⣉⣥⣤⣤⣤⣶⣶⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁


⣿⠿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠂⠐⠀⠀⠁⠈⠀⠁⠉
⠀⠀⠀⠀⠀⣿⣿⣿⡿⠻⣿⡟⢻⣿⡛⣻⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢀⣄⠀⢠⡄⠀⣴⠄⠠⠦
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⡀⠀⣀⣄⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⡿⢿⠈⡏⣰⣷⡄⢻⣿⠈⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⢀⣈⣿⢰⡏⠉⢻⡆⠀⣿⠀⠀⠀⠀⢒
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣶⣾⠀⣧⡘⢿⢃⣼⣿⣄⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⠉⠉⣿⠘⢧⣄⡼⠃⠀⠿⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡷⠟⢿⢛⡛⠟⢻⢛⣝⣿⢩⢽⣿⣿⣿⣿⠀⠀⠀⠀⠀⢘⠀⠀⠀⢈⣠⡀⣬⢤⣠⣄⡴⠶⠄⣖⣒⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣩⣼⠨⣅⢻⢸⣘⣟⣿⣘⣛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⠶⠋⣷⠺⣝⡏⠧⠠⠆⠧⠤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⡿⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢀⣄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣠⣿⣧⣼⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠄⠀⠀⠐⠟⠀⠘⠃⠀⠙⠁⠀⠉⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⢀⢀⠀⠄⠠⠠⠀⠀⠀⠐⠀⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡋⠀⠀⠀⢼⣿⡏⠀⠀⠀⢸⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⣻⣿⡆⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⠀⣸⣿⡟⠀⠀⠀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠘⢿⣿⡄⠀⠀⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀⢰⣿⡿⠁⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⣄
⠀⠀⠀⢀⣾⣿⠏⠁⠀⢀⣠⣴⣶⣶⡆⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⢀⣿⣿⠃⠀⢀⣴⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⣸⣿⡇⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣄
⠀⠀⣿⣿⠁⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣶⣶⣶⣿⡿⠛⠙⠻⣿⣧
⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⣿⣿
⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠿⠿⠿⠿⠿⠿⣿⣷⣄⠀⠀⠀⣻⣿⡆
⣠⣤⣤⣤⣤⣽⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣶⣤⣴⣿⣿⣤⣤⣤⣤⣤
⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿
⢹⣿⣇⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣰⣿
⠀⢻⣿⣦⡀⠙⠻⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⠿⠋⢀⣴⣿⡟
⠀⠀⠙⢿⣿⣦⣄⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⡿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⢻⣿⣿⣿⣸⣿⢿⣿⢣⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣥⣶⣾⣆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠈⢿⡿⠿⠇⡿⠋⠉⠙⠻⣿⣿⡿⠟⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⣛⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠈⣿⣶⣿⠿⠿⢛⣛⣭⣭⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠶⢦⡿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⠀⠀⠀⠀⢹⣆⣀⣀⣤⣄⣀⣴⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣴⣦⣤⣤⣽⣿⣿⣶⣤⣤⣴⣿⣿⡿⠿⠛⣿⡟⠛⢉⣠⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⣽⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣦⣤⣾⣿⢹⠉⢹⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⡁⠀⠀⠀⠀⠀⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⠃⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⣟⣉⡉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⣭⣭⣭⡿⠀⠀⠀⠀⢸⡇⣿⣿⣯⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡆⢸⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⣀⣤⣄⣀⡀
⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠁⠀⠀⠸⠇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⢦⣄⠀⠀⣼⠀⠀⠀⠈⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢤⣠⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⣿⣵⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢂⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⣀⠀⠀⠀⢀⠐⠢⣄⠀⠠⠈⠠⣄⠀⠀⠀⠊⠁⣾⡏⠀⠀⠀⠀⢠⡄⢀⣀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣈⡀⠀⠈⠙⠀⠀⠀⠙⠃⡀⠀⠀⣸⡿⠂⠀⠴⠃⠀⠹⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠤⠂⠂⠉⠉⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠠⠶⣎⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣼⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⢀⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠉⠉⠁⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠶⢶⣯⡴⠇⠀⠀⠤⠤⣿⣟⣠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠒⢄⡈⠳⣌⢀⠠⣼⠓⠀⢀⣿⠃⠀⠀⠀⠘⣧⡀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈⢳⡄⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠈⠓⠀⠀⢹⣿⡟⠛⠛⠛⠓⠒⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣿⡀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣷⣿⠿⠆⠀⠀⠀⣴⣿⡷⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣿⡟⠁⠀⠈⡄⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⣾⣿⠇⠀⠀⠀⠹⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉


⣿⠿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣻⣟⣻⣟⣿⣿⣿⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠐⠀⠀⠀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢿⠧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⣀⣀⣀⣀⡀⢁⠶⠭⣓⠦⡀⠀⠙⠔⢅⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠖⠀⠠⠖⠛⠉⢉⡔⠣⢌⢙⠣⣍⡒⢌⠳⡄⣄⠀⠀⡀⡀⡢⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠴⠐⠁⠀⠀⠀⠀⠀⠑⠰⢯⡈⠑⠠⣁⠡⡄⢉⠀⢣⠙⣌⠳⣄⠀⠘⠄⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠑⠈⠢⠑⡇⠘⡄⠠⡀⠑⢬⣑⠲⣄⠀⠂⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⡀⠀⠘⡀⠡⡘⢤⡘⠂⡀⡀⠂⢤⡑⣌⢣⠁⡀⠈⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡁⠑⣄⠳⡜⢆⠱⢌⠢⢤⡂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⡙⢅⠈⢢⠙⠀⡑⠦⡽⠊⠀⢦⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⡀⢡⠈⠢⢌⡀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⡐⠀⠌⠀⠀⠀⠈⠃⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢆⡈⠑⢢⠍⠀⠀⠀⠀⠐⠀⠑⡀
⠀⠀⠀⠀⠀⠌⠀⠘⠄⠀⠀⠀⠀⠠⠀⢳⡀⢀⠀⠤⢤⠤⠂⠀⠲⠂⠰⠂⠐⠢⠄⢀⣀⠀⠀⠀⢠⠏⠢⠌⠛⠀⠀⠀⡀⠀⠀⠀⠀⠄⠈⠄
⠀⠀⠀⠀⠌⠀⡐⠀⠘⡀⠀⠀⠀⠀⡡⠤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠰⣏⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⢂⠈⠂
⠀⠀⠀⠐⠀⡐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠈⢄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡃⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⢤⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠀⠐⠃⡀
⠀⢀⣀⠀⠐⣬⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠐⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⣠⠏⠀⠀⠀⢀⠴⠀⠀⣁⠈⠀⠀⠀⢀⠀⠀⡴⠋
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⢀⣀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⢀⡈⢉⠀⠀⠉⡠⠆⠀⠃
⠀⠀⠀⣀⠀⠀⠀⠋⠀⠈⠛⠂⠴⠓⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠃⠀⠀⡄
⠀⠀⠂⠌⠀⠀⣀⢀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠛⡒⠤⠀⠀⢸⠀⠀⠀⠀⠂⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⡀⢀⡠⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠄⠄⠀⠀⠀⠀⡀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⠀⢀⠌⠀⠠⠒⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠱⠄⠀⠣⡀⠐⠁⠿⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⠀⣀⠀⡀⠀⠀⠀⠀⠋⠒⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⡴⠒⠀⠀⠀⠀⠀⠐⡌⠓⠀⠃⠀⠀⠀⠀⠀⠁⠂⠀⠀⠐⢢⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⡄⠐⠀⣠⠞
⠀⠀⠤⠀⠀⠓⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣴⢟⣉⡁⢀⠀⡀⠀⠀⠀⠀⣉⡡⠤⠔⠋
⠀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠷⠀⠀⠀⢀⡤⠀⡆⠀⠔⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠒⠋⠁⠐⢀⣡⣌⠢⣀⡤⠟
⠀⠉⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠋⠉⠉⠈⠉⠈⡧⣈⠂
⠀⠀⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⣠⡄⠀⠹⡀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⡰⠃⠀⠀⠀⠄⠚⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⡀⠀⠈⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠋⠀⠀⠀⠀⠀⠀⠀⡀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠢⢌⠙⢤⠀⠀⠀⠀⠀⠁⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⢇⠀⠀⠀⠀⢤⣀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠒⠒⠀⠀⠀⠀⠀⠐⢄⠀⠈⠀⠀⠀⠀⠀⢀⠀⡸⠁⠀⠀⠀⠀⠈⠗⢠⡎⠀⠀⠀⡀⠀⠀⠀⠀⠈⡦⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡤⠒⢀⠀⠄⢀⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢀⠤⠀⠀⠀⠀⠃⠀⠀⠠⠀⠸
⠀⠀⠀⠀⠁⠊⠀⠀⠀⠈⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⠀⢀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠐⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⠀⡀⠀⢀⠢⢤⡀⠀⠀⡏⠀⢻⢀⡤⣠⠊⠉⠀⣀⠤⠄⠀⢞⢡⠀⠑⢆⠀⠐⠤⡀⠀⠀⡞⢳⡄⠀⢠⠟⠓⠦⣔⠒⠓⠦⣄⣀
⠀⠀⢀⠰⢀⠑⣄⢻⠀⡠⠓⠀⠀⠈⠓⠁⠸⡀⣀⠇⠀⢸⣇⠀⠀⠀⠈⠉⠁⠉⠁⠤⠤⠒⠳⡄⠀⣧⣸⠃⢀⡟⠀⠀⠀⠈⠙⠒⠶⢤⡈⠉⠉⢱⡀
⠀⠀⠀⠂⢢⣽⣿⡻⠋⡠⠔⠒⠉⠉⠓⠦⣀⠀⠀⠀⠀⢸⣧⠤⢄⣀⡀⠀⠀⠀⠈⢉⣀⡈⢽⡃⠀⠼⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢀⡟⡄
⠀⠀⠀⢊⢀⠔⠁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡅⢀⡀⠀⠈⣈⡉⢉⣉⣀⠀⠀⣰⠇⠀⠀⣠⠞⠀⠀⠀⠀⠁⠀⠀⣠⢎⡵⠁⠀⡼⡸
⠀⠀⠀⠀⠁⢀⡎⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⣇⠀⠙⠒⠦⠬⠤⠤⠄⠀⢀⣀⠠⠤⠘⠁⠀⠀⣧⣀⠀⠀⠐⠀⠀⠀⣰⢣⠏⠀⠀⢠⢇⡇
⠀⠀⠀⠀⠀⠸⣇⠠⡀⠀⠀⢀⡞⠁⠀⠀⠙⢦⠀⠀⡿⠀⡴⠾⠶⡆⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠀⠀⠘⠫⢽⣲⡦⣄⠀⢠⠇⣾⣀⣀⣠⡼⢸⠁
⠀⠀⢀⣤⣄⠀⠙⢦⡀⠀⠀⠘⣇⠀⡀⢀⡄⣸⠀⢠⠇⢸⠁⠀⣰⠏⠀⢠⠒⠒⢦⡀⠀⠀⠈⣧⣀⣀⣀⣀⣀⡈⠙⠲⣝⣫⠞⠓⠶⠶⠶⠖⠋
⠀⠀⣾⠁⠈⠳⣄⠀⠉⢦⡀⠀⠈⠳⠬⠵⠞⠁⢠⠟⠀⠘⠒⠚⠁⠀⠀⠘⢮⣀⣠⡇⠀⢰⣯⣽⣏⣀⣠⣤⠤⠽⠇⠀⠀⠀⠀⠀⢠⠖⠒⠲⡄
⠀⠀⣿⡄⠀⠀⠈⠑⢤⣀⠑⢄⡀⠀⠀⢀⣠⡴⢋⣠⠴⠖⠒⢛⡓⠒⠲⢦⡀⠀⠀⠁⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⠀⠀⠠⢹⡀
⠀⠀⠸⣷⡀⠀⢀⣤⣤⡈⠑⢦⡈⠉⠉⠉⠁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠲⢄⡀⠀⠸⣄⠤⠤⢷⡤⠤⠤⣤⡇⠀⠀⠀⢠⣾⠀⠀⠀⠀⠃⢦⡀
⠀⠀⠀⡟⣧⠀⢻⠀⠀⡝⣦⠀⢹⡄⠀⠀⡞⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⢙⡆⠀⣟⠒⠒⠚⣷⠚⠛⢉⡇⠀⠀⠀⠸⡍⢙⠋⠙⠉⠉⣩⠁
⠀⠀⠀⢿⠘⣇⠀⠳⢤⣤⠟⠀⢰⠇⠀⢰⠳⣕⠀⠘⣆⢀⣒⣒⣀⣀⣸⣇⣀⠐⣡⠞⢳⠀⢻⠀⠀⠀⠸⣆⠀⢸⠃⠀⣀⡀⠀⠙⠾⣷⣤⡤⠞⠁
⠀⠀⠀⠈⢧⣈⠳⢤⣀⣀⣠⣴⠟⠀⠀⢿⣐⣨⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⢧⣀⣸⠇⠈⢧⣀⣀⣀⣉⣠⠜⠀⢯⠉⢧⠀⢀⣠⡴⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠋⣁⣀⣀⡀⠀⢉⣁⡀⠀⠀⠀⠸⡳⣶⣄⡇⠀⠀⠀⠀⠈⠁⢀⣴⣦⣍⡉⠉⠀⠀⠀⠀⠈⠓⠻⣄⣈⡓⠶⠴⠶⠞⠃
⠀⠀⠀⢰⡒⠦⣴⡒⠋⢉⣉⣀⠠⠀⠉⢶⡁⠀⡝⠀⠀⠀⣠⠽⠾⢿⣧⣠⠤⠤⣄⡀⠀⢸⣝⡻⠷⣯⣭⣍⣉⣉⣉⣛⠲⢤⣀⠈⠉⠓⠦⣄
⠀⠀⠀⠘⣧⠀⠱⢭⣒⣤⣀⠀⠠⠄⠀⠀⠱⡀⢨⠆⠀⣼⢡⠊⠈⠀⠈⠁⠀⠀⢠⠹⡄⠈⠻⢿⣷⣶⣶⣯⣭⣭⣽⣛⡻⠶⣌⢳⡄⠀⠀⠘⣆
⠀⠀⠀⢰⡿⡦⢤⡘⣿⣭⢻⢷⣦⣄⡀⠀⠀⠑⣌⠆⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠶⠤⢤⣉⣉⣉⣉⡉⠛⠻⢷⣼⠋⠀⠀⠀⠀⣿
⠀⠀⢀⣀⠓⢬⣒⢵⡀⠛⠉⣟⠀⠛⢿⢗⠦⣄⡈⣧⠀⠸⡆⠀⠀⠀⠏⠘⠆⠀⠀⢰⠁⠀⢸⠭⠶⠶⠶⠶⠶⠦⣭⣍⡓⠤⡉⠀⠀⢰⠋⠉⠉⣹⠂
⠀⠀⠀⠈⣳⡀⠈⠑⠮⣓⢦⣈⠉⠳⡀⢀⡙⠲⠽⠇⠀⠀⠹⣔⠤⡀⠀⠀⠀⠄⣠⠏⠀⠀⠘⠿⢿⣒⣒⣒⣒⣒⠢⠌⡙⣾⠀⠀⢠⡟⡶⠒⢲⣿
⠀⠀⠀⠑⢿⣧⣤⡠⠴⡌⠑⢬⡓⢦⣉⣁⡸⠂⠁⢀⣀⠀⠀⠈⠓⠒⠛⠓⠒⠛⠁⠀⣀⣤⠴⠶⠲⠶⠦⣄⡀⠈⠙⢦⣄⣷⠀⠀⠸⠶⢷⣬⣿⣸
⠀⠀⣠⢾⡿⠋⠛⠒⠋⠀⠀⠀⠈⠓⠖⠋⢀⡠⠞⠉⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢉⢳⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠉⢁⡤⠤⠤⠄⢤⣄⣤⠤⠤⡀⠀⠀⡿⠤⠤⠤⠤⢤⡴⢦⣄⣈⣓⠲⢄⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⡰⡠⠃⢀⡴⠞⣻⠋⠉⠉⠉⠓⢦
⠀⠀⡎⢹⠉⣿⠛⠛⠛⠛⠛⠛⠛⡏⠀⠀⣛⣷⠀⠀⣀⠀⠙⠋⠀⠀⠉⠉⢻⠀⠈⢧⡳⢤⡀⠀⠀⠀⠀⠀⢸⠁⢀⡞⠀⢎⠉⣠⠶⢶⣄⠀⠈⢧
⠀⠀⠹⣼⣧⠘⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣯⡀⠀⠸⠽⠂⠀⣠⣤⣄⠀⠀⢳⠀⠀⠀⠙⣆⢷⠀⠀⠀⠀⠀⠘⡇⠸⡇⣠⠊⠘⣇⠀⣸⣽⠀⠀⣸
⠀⠀⠀⢠⡛⣦⣀⡀⠀⠀⠀⣠⠗⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠛⠶⠟⠀⠀⢸⠀⠀⠀⠀⢿⢸⡆⠀⠀⠀⠀⠀⢹⠀⢷⡸⢄⣠⣌⢉⣩⣁⡖⣲⠏
⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠙⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠳⣧⣄⣀⣠⣤⡤⠞⠀⠀⠙⠶⣤⣈⣉⣠⡭⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣠⠴⠃
⠀⠀⠀⢀⡔⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠈⠧⣤⣀⣱⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢦⣀⠀⠀⠀⠀⣠⠶⠒⣦
⣰⠒⠒⣦⡀⠀⠀⠉⠃⢀⣤⠶⠛⠉⠉⠁⠀⠀⠉⠉⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⢉⣠⠴⢊⠩⠷⣄⠀⠀⠷⠶⠖⠋
⠙⠶⠚⠉⠁⠀⠀⢀⠖⠋⢀⡠⠤⠒⠒⠒⠒⠒⠂⠤⢄⣀⡀⠈⠉⠓⠲⠶⠦⠴⠶⠒⠛⢉⣁⠠⠐⠊⠁⢰⠊⠁⡠⢖⡩⢷⡀
⠀⠀⠀⠀⠀⠀⣰⠋⡠⠊⠁⢀⡠⠤⠄⠒⠒⠒⠒⠂⠤⠤⣈⠉⠓⠒⠒⠒⠒⠒⠒⡋⢉⣤⠤⠖⠊⠉⢀⣡⣴⡿⢊⣥⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⢧⣤⠞⠁⠀⠀⠀⢀⠤⠤⣄⠀⠀⠀⠈⠳⠤⠚⠁⠉⠉⠀⠀⡀⠀⡠⠤⠆⠉⠉⠩⠟⠁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⡠⠗⠀⠀⠀⢁⣀⣀⢉⣉⣁⣒⣒⣒⣂⠀⢉⣁⡠⠴⠒⠒⠋⠁⢀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠊⠁⠀⣀⠤⢒⣩⠵⠶⠒⠒⠛⠓⠶⠦⢤⣤⣀⣀⣀⣀⣀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣊⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢀⣤⣀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣴⣿⣿⣿⡆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠒⠤⣀⣀⣀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡼⠀⠀⠀⣀⣤⡤⠤⠶⠤⣄⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⢺⡆⠀⠀⠀⠀⠀⢨⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠒⠒⠒⠒⢠⡀⠀⠀⠀⠀⠀⢀⡤⠼⠧⠤⠤⠤⠤⠤⠼⠼⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃
⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⢀⣀⡠⠤⠔⣊⡅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠐⢬⠭⠉⠉⠭⠭⠁⠤⠐⠂⠉⠀⡂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠘⡄⢀⣀⣀⡀⠤⠤⠀⠐⠒⠈⢹⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⢀⣀⣀⣀⠀⠻⣃⣟⠘⠃⠀⣠⠒⠢⠤⠭⠍⠉⠐⢲⠋⡇
⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⣤⣦⣄⠀⠀⠀⢸⠀⠀⠀⠀⠓⠐⠒⠀⠀⠀⠐⠒⠒⠒⠒⠒⠐⠀⠐⠃⠀⠀⡇⠀⠀⠢⠠⠐⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⢱⠀⠀⠰⣿⢿⣽⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⢀⡀⠀⠠⠤⠤⠄⠚⠃⢰
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠻⠟⠋⢀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣔⡉⣑⢏⡠⢶⠀⠀⠀⠀⠘⠁⢠⢰⡴⠄⠶⠦⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠐⢖⠒⠒⠂⠈⠉⠀⠀⠀⡄⠀⠀⠀⡠⠠⠤⢊⠭⠠⠕⠀⣈⠔⠨⠥⠄⠒⠤⠀⠀⠀⠀⢰⣈⡡⡀⠤⠤⠤⠤⠒⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⣀⡠⠄⠊⠀⠀⠀⠀⡗⢒⡒⢁⠔⠒⠊⠀⠀⠀⠀⣀⠀⠀⡀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢰⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⠂⠑⢊⣐⢂⡮⠭⠱⢞⢄⡨⠮⡀⢴⠀⠀⠀⠀⠆⠀⠐⠒⠂⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠐⠠⣀⠀⠀⠀⠀⠀⢸⣁⢉⡈⡡⠤⠤⠊⠑⠒⠉⠑⠀⠒⠢⠼⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠤⡐⠜⠋⠁
⠀⠀⠀⠀⢀⠴⠈⠠⠤⠤⠄⠤⠤⠤⠤⠄⠤⠤⠤⠬⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠧⠤⠶⡈⢁⡀
⠀⠀⠀⠀⠘⣷⣮⡴⡤⠰⢶⣤⣤⣄⣄⣠⣡⣤⣐⣲⣶⠃⠀⠀⠀⠀⠀⠀⠀⣔⠈⡡⠄⠰⡀⠠⡤⢀⣐⠢⠤⣄⡉⢲⡄
⠀⠀⠀⠀⠀⢏⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⢋⡁⠃⠀⠀⠀⠀⠀⠀⠀⢙⠛⠠⠬⢵⣏⣘⣏⣁⣬⣡⠦⠶⠚⢛⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⣸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠙⡄⠀⢠⠤⠜⠁
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠸⡀⡏
⠀⠀⠀⠀⠀⠀⠈⢤⣈⣂⠜⢆⠀⢿⡇⢰⢁⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⡇⠸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠎
⠀⠀⠀⠀⠀⠘⢠⡀⠀⠀⠀⢠⠇⠀⡜⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠸⡀⢰⠁⣀⠀⠀⢠⠎⠁⠀⠀⡔⠁⢨
⠀⠀⠀⢶⠒⠂⠤⢄⡀⠀⠀⠀⡇⡘⠀⠀⠀⠀⠋⠀⠀⠀⢀⡇⠀⣸⠤⠤⢒⡰⠖
⠀⠀⠀⢳⠀⠀⠘⠁⠘⢤⠀⠐⢳⣹⠀⠀⠉⠉⠉⢉⡩⠚⠁⢀⡴⠡⠔⠚⠉
⡠⠐⠈⠉⠁⠀⠀⠀⠤⠋⠁⠒⠀⠋⡰⠆⠠⠆⠀⠈⢀⠀⢠⠋⠀⠈⡱⡶⠤⠤⠤⠤⠤⠀⠀⠀⠒⠒⠚⠋⠉⠉⠉⠉⠉⠑⠒
⠑⡄⠀⠠⡄⠐⠦⡁⠀⠠⠐⠁⠀⢀⠆⠀⠀⠀⠀⠀⡠⠖⠁⡠⠖⠁⢠⠣⢀⣀⡀⡀⠀⠀⠤⠤⠀⢀⣀⣀⣀⣀⣀⣀⡀⠠⠔
⠀⢱⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠐⠒⠀⠀⠀⠚⠤⠁⠐⠈⠀⠀⠀⢀⠴⠋⠁
⠀⠀⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁
⣀⣀⣀⣀⣈⣁⣒⣢⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣄⣒⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡔⣍⣁⣀⣀⣈⣹⡵⣄⣤⣤⣤⣤⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠓⢸⣿⣿⣿⡟⣳⣾⣤⣠⡈⢀⠀⠀⣀⣱⣧⣼⢻⣿⣿⣿⡆⠈⠘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⢠⡟⠀⣹⢟⣣⣹⣏⣘⣿⣯⡉⢹⡄⣿⣿⣿⣧⠀⠀⠀⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡀⢤⣿⣿⣿⣿⡶⣟⣽⣿⡿⠟⢛⡛⠿⢿⣿⣿⣿⣇⣿⣿⣿⣿⡄⠠⢀⣯⣉⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢸⣿⣿⣿⡇⢠⣿⡟⠁⠐⠀⢸⠃⠀⠂⠉⢿⣷⡌⢸⣿⣿⣿⡇⠀⠀⠀⠸⡗⢻⣿⣷⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢸⣿⣿⣿⡇⣿⡟⠀⠛⠀⠀⢸⡀⠀⠀⠚⠈⢿⣷⢸⣿⣿⣿⡇⠀⠀⠀⢀⠟⣫⡿⠿⢿⡃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠱⢤⠤⢼⣿⣿⣿⡿⣿⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣾⣿⣿⣿⡷⢤⡤⣤⣼⡼⡿⠁⠰⣟⣙⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇⢻⣿⡄⠿⠀⡀⠀⠀⢀⡀⠚⣰⣿⠇⣿⣿⣿⣿⠀⠀⠀⢸⣩⠼⠃⠠⣖⠻⣏⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢹⣿⣿⣿⡄⠻⣿⣶⣄⣁⠐⠂⣀⣥⣾⣿⠋⣸⣿⣿⣿⠇⠀⠀⠀⡘⠁⠀⣴⠲⣎⠛⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠹⠅⠛⠻⢿⡿⠿⠿⣛⡫⣹⠙⠛⠛⠛⠛⠉⠉⢉⡉⠁⣴⠶⡜⠓⢾⡗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣾⣽⢷⡞⣷⢠⡶⣦⢠⢶⡄⣿⢹⡆⠹⢦⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠼⣿⡁⢸⣧⠟⠸⣠⡇⢙⣿⣇⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠋⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠀⣰⠂⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡇⡠⠉⣀⠄⠤
⠀⠈⠀⠀⠐⠀⠀⠀⢄⠀⠀⠢⠀⠠⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢵⡆⡄⣏⣤⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠀⠀⠀⢈⡙⠾⣄⠀⠀⠀⠀⠌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠨⠉⠀⠉⠀⢐⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⡀⠀⠀⠈⠂⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⣀⠀⠀⡀⠂⠀⠀⠆⢠⠀⠩⠑⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡤⠉⠙⠒⠺⢦⣁⣢⡀⢾⠀⢠⠐⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠖⠋⠁⠘⠂⠈⣃⠈⠠⠀⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠀⠀⠀⣀⠤⢤⣄⣢⢄⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠉⠀⠒⠠⠀⠐⠂⠀⠀⠙⠒⢛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⠙⠋⠉⠑⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣠⢰⢠⠀⣀⠄⡄⢠⠄⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠉⠘⠘⠐⠙⠐⠁⠘⡘⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠉⠙⠳⡤⠶⠠⠀⡀⠀⠀⢀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⣼⣿⣓⠦⣄⡀⠀⢀⣀⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠳⣄⠉⠉⠀⠀⠉⠻⠋⠉⠩⠋⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠴⣚⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⠷⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣥⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⡀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠳⢦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠁⠀⠀⠀⠀⠁⢐⡟⠀⠀⢀⣀⣠⡴⠖⠋⠁⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠈⠛⠻⢯⣍⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⣻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠷⠶⠤⠄⠀⠀⠀⠀⠀⠀⢾⡛⠉⠋⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠃⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⢰⣴⣮⡀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡼⠃⢿⠹⣿⡏⠇⠙⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣠⢤⡖⠒⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠛⠉⠁⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣆⠀⡤⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠲⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡏⢸⡄⠀⠀⠀⠀⢀⣄⠀⠀⠀⢘⡆⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠀⠀⠙⠶⣤⣤⠶⠋⠹⣄⣀⣠⡾⠁⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠐⡐⢠⠀⣀⠀⠈⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠀⠀⠄⠀⡀⠐⠆⠀⠀⣄⠀⣠⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠀⠁⢀⠀⠀⠀⠆⠀⠄⠈⠃⠈⠀⡄⠀⠈⡄⠀⢀⡄⠈⠀⠒⠰⠃⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠠⠐⠀⠀⣀⠐⠈⠀⡀⠐⠄⠀⠀⠈⠀⡀⠄⠃⠀⡀⠠⠆⢢⠄
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠆⠀⠀⠘⠈⠀⠀⠀⠈⡀⠀⣀⠀⢈⠈⡇⠙⢁⠀⠁⠈⡡⡯⡻⢀⠀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠰⠀⠂⠂⠄⢀⢌⠁⠀⠀⡀⣀⣰⢨⣄⠀⣅⠊⠀⠃⠀⣂⣀
⠀⠀⠀⡀⢀⠄⠠⠘⢀⠀⠀⢐⠂⡠⠌⢠⡶⠐⣐⡃⡄⠁⠠⠃⠄⠊⡄⠀⢍⡀⡄⡏⠿⡄⠤⣵⢌⢡⠆
⠀⠀⠀⠀⠀⠃⢠⠑⠈⠀⠰⢤⠀⠄⡀⠀⠁⠠⠈⣅⠀⣬⠠⢏⠌⠀⣻⡀⢘⢿⡍⠁⡌⠃⠃⡀⢠⡃
⠀⠀⠈⠋⠀⢠⠀⠄⠀⢠⠤⡐⠘⢠⡉⣀⣤⠳⠗⠂⣡⠉⠐⡄⣯⠈⡠⢶⢤⠈⣛⠛⡶⠀⢹⠿⠚⢁⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⡈⠁⠀⠀⠀⠀⠀⠀⡞⠠⡊⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢽⠀⠀⠀⠀⠀⠀⢀⣇⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡄⠀⠀⠀⠀⠀⢸⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣾⡆⠀⠀⢀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢃⠀⠀⠸⠀⠀⠰⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⡆⠀⠀⠇⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⠀⠀⠀⡴⠀⠀⠀⠀⡇⠀⣼⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢤⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠃⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⡤⠀⠄⡀⠠⠀⠀⠀⠘⠀⢸⣆⠄⢼⠀⠀⣀⠄⠂⠲⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢈⠁⡄⠀⣄⠀⠈⡢⣀⡀⠀⢀⠆⠀⠀⠀⢀⠱⡊⠠⠒⢁⠀⠱⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡠
⠀⠀⠀⠀⠀⢠⡕⠀⠀⡇⠀⠘⢄⠀⡈⠪⣻⡦⠉⠀⠀⠀⢰⠀⡄⢇⡀⠈⠁⠔⠀⣱⠔⠂⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⠁
⠀⠀⠀⠀⠀⡞⠈⡓⠦⡘⡄⠀⠈⠳⡈⠂⠀⠙⣇⠀⠀⡀⠀⠀⡀⢸⠂⠉⠐⢂⡠⣤⠀⠈⠓⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠐⠬⠒⠤⠉⠒⢤⣀⡈⠢⣄⠀⠸⣆⠀⠡⡀⠀⠁⣼⠋⠩⠭⠅⠉⢀⡑⢦⣠⠔⠉⠀⠀⠈⢢⡀⠀⠀⠀⣀⠄⠀⢀⠜
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠀⢨⠃⠀⠱⠾⢋⡳⠢⢼⠶⢞⠡⠔⣒⣉⠩⠠⡨⢉⠓⠨⡀⢄⠀⠠⠖⠀⠧⣀⠤⠊⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢠⠃⠀⡞⠀⠀⠀⠀⠀⠀⢹⠃⠒⠴⠲⠅⢀⣀⢁⡀⡁⣁⡀⠁⠜⢦⡙⠄⣀⡈⢂⡡⠤⠂⠉
⠀⠀⠀⠀⠀⠀⠰⡉⠉⠢⣄⡎⠀⢰⠁⠀⠀⠀⠀⠀⠀⡆⠀⢀⠇⠀⠀⢀⡀⠈⠉⠉⢨⣞⠁⡤⠂⠂⠒⠁⠰⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢣⠈⠳⢬⠁⠀⡧⣀⡀⢀⣀⣀⣀⣸⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡌⠛⢠⠃⠈⠉⠉⠉⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠫⡑⢾⠀⢸⢦⣀⣀⣀⣀⣀⢀⡏⠀⢠⣧⡀⠀⠀⠀⠀⠀⣀⣠⠃⠀⡜⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⠀⡞⠠⢀⣀⣀⣀⣀⢸⢁⠀⣼⣀⠈⠑⠒⠂⠒⠉⠀⣼⡀⢠⠃⠒⢄⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⡟⡌⢠⣇⠈⠙⠒⠶⠶⠖⠒⢐⢇⠁⡼⢢⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⡀⢰⠇⠁⢸⠀⠉⠓⠶⠶⠖⠒⠀⣸⣠⠴⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠚⠶⠶⠶⠶⠖⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⠚⢹⣟⡝
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣦⣤⣤⣤⣴⣦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣫⣥⣶⣾⠿⠿⠟⠋
⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡻⣿⡭⠉⠀⠀⠀⠀⠀⠁⠉⠉⠋⠳⢦⡄⣀⣤⣴⡾⠉⣠⣾⠿⠋⠁
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢙⣷⣿⠟⠁
⣿⣿⢿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⠏⠁
⣏⢿⣎⢋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⣬⡿⣸
⠙⢦⣅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣛⣵⠏
⠀⠈⢿⣷⣦⡄⠀⠠⠤⠀⣀⣀⣀⣀⣀⣀⣀⡀⣀⡀⠤⠐⣒⣠⣵⣾⣿⠃
⠀⠀⠈⠻⣿⡙⠛⠻⠶⣦⣤⣤⣤⣤⣤⣴⣶⣴⣶⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠙⠳⠶⢶⣦⣤⣤⣤⣉⣁⣀⣨⣿⣿⣿⣿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢨⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠊⠀⠀⠀⠀⠀⠀⠙⠙⠂⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠋⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠀⠐⣂⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⡖⠀⠀⠀⠀⠀⣼⡆⠀⠀⠰⡀⠁⠋⠀⢹⡵⠋⠀⠰⢀⠀⢀⡁⢀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡭⠁⠀⠃⠀⠈⠓⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠊⠰⠄⠀⠀⠀⠀⠊⣭⢤⡼⢃⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠸⣦⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠒⠒⢿⡣⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢴⡾⠛⠓⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡄⢸⣷⠀⣿⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⣀⡏⠉⠁⠐⠘⠀⠀⠀⣤⠠⠞⠃⠰⠆⢠⣤⣌⡶⡚⠀⡆⠀⢩⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⣼⠃⠁⠀⢰⠆⡴⠃⠰⠦⠐⠤⠄⠀⠃⠀⣀⣀⣤⢅⡆⠇⢴⡀⢈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣾⠗⠀⢠⡖⠐⠺⢦⡀⡦⠤⢿⣷⣶⣶⣦⣭⣥⣴⣾⣿⣷⣆⣀⠘⣿⣯⡴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠻⣦⣒⠲⣽⣮⣻⣯⣙⣭⢙⠉⢻⣭⣿⣤⣯⣛⣛⡛⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠛⠉⠀⣯⣽⠙⣈⣁⢉⡞⠂⠨⣻⣿⡃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢊⠉⠹⠻⡇⠳⢷⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠉⡛⣻⡆⢀⠤⡆⢄⢟⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⢸⠀⣘⡇⠸⡀⣴⣿⣨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⣼⣿⡏⠗⢀⣀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠃⠿⠿⠁⠶⠌⠁⠀⠙⠋⢹⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠰⠀⣀⠀⠀⠉⠙⠃⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⣲⣿⣠⣄⢲⣴⣤⣤⣦⣬⣿⣟⡾⣠⣤⣀⣰⣽⣿⣵⣆⣀⠀⠠⠤⠶⡤⣦⣤⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠠⠤⠤⠬⠿⠿⠶⠌⠐⠂⠒⠚⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣤⣤⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⣀⣀⠤⠄⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡔⢲⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠓⠲⢄⠀⡀⠤⠒⠒⡲⠦⣀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠋⠀⠑⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠁⠀⠀⠀⠀⠀⠘⣦⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢠⠀⠀⠀⢻⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠠⠀⠛⠺⡄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣽⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣀⡀⣀⡀⠻⠗⠀⣣⠈⠀⠀⠀⠑⠄⣀⢀⠀⠀⠀⠀⠀⣴⠋⠊⢉⠉⠣⣀⠀⠀⡀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠁⣠⢄⠹⢶⠤⠾⠃⠦⡀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣰⣾⡀⠀⠀⠈⠀⠀⡤⠑⠛⠀⠀⠀⠀⠀⠀⠈⠓⠄⣀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⣀⡩⠞⣼⠁⠀⣠⠀⠘⢂⡤⠐⠒⠀⠐⠒⠠⢄⣹⡞⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡠⠄⠠⣄⠸⡀⣶⢌⢁⣠⡞⠉⣠⠀⠐⠀⡒⠀⠀⠀⠉⢧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢸⡆⢧⣅⣀⢀⡀⠀⠀⠈⠣⠈⠀⠁⠔⠁⠀⠀⠈⣳⣦⠤⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠥⠎⠀⡟⠁⠀⠈⡇⠀⣀⡈⠁⠀⠀⠀⠐⢂⠨⠓⠝⠋⠀⠀⠀⠀⢘⠀⡠⠂⠀⠀⠉⠒⠤⠤⣀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣇⠸⠖⠀⣣⠀⠀⠤⠂⠀⡐⠠⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠾⠀⠓⠒⠒⠙⢄⠀⢂⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣡⠀⠀⠀⠤⠐⢞⠈⠑⠤⣀⣀⠀⣀⣳⡀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢿⠁⠁⠀⠠⣄⠀⠀⠀⠀⠀⢨⠀⠀⠈⠢⠵⠀⣠⣄⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⡀⠀⠉⠉⠳⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⠐⠂⢤⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⢀⣀⠤⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠐⢄⣀⣀⣀⠠⠜⢗⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣁⠠⠊⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⣠⠴⠖⠒⠉⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠁



⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣴⣿⣷⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠟
⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣴⣾⣿⠟⠋⠁
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣦
⠀⠀⠀⠸⣝⢷⣽⣹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢿⠃⠀⠈
⠀⠀⠀⠀⠘⢦⣙⢧⠝⠻⠜⠿⠏⠛⠿⠆⠻⠏⠛⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⡠⠂⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⡔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢠⠊⠀⠀⠀⠀⠀⠀⢰⢡⣄⠸⡇⠀⢇⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡘⢤⡀⠀⠀⠀⠀⠀⡇⢯⡔⢘⡇⠀⠀⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠆⠀⠀⠀⠈⢆⠱⠀⠀⠀⠀⠀⢸⢠⣬⠞⠀⢀⣴⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡡⠂⠀⣤⠀⡠⣣⠆⠘⠃⠀⠀⠀⡎⢼⠁⠀⠀⡇⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡑⡄⣤⠀⢸⢱⠁⠀⣤⠀⠙⠀⢸⢨⡽⠀⠀⠀⢱⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠤⡇⣼⣇⣀⣀⣀⣈⡋
⠀⠀⠀⠀⡠⠔⣚⡭⡵⢶⠶⢶⠳⡳⣚⡛⡚⡛⣚⠉⠉⢹⢱⡟⣒⣶⢒⠒⠒⠭⢭⡁⠒⢄
⠀⣀⠴⡺⣄⡀⠳⢼⣜⣺⠾⠷⠓⠛⠛⣻⠛⠻⠟⡻⣟⠻⠰⠟⠍⠛⢹⡏⠛⣓⣤⠼⠀⣸⠄
⡞⠁⡾⠛⣟⢝⡲⢴⣤⣨⣩⣉⣉⡉⣉⣉⡉⡉⡉⡉⢉⣉⣉⣉⣉⣉⣉⣉⣭⣤⠦⠾⣚⣽⠀⠀⣰⢒⡆
⠹⣶⡙⢤⡟⠭⡂⠀⠙⠋⠊⠉⠉⠻⢿⣛⣟⣉⢉⣙⡋⠉⠛⠛⠛⠒⣒⣒⣒⣋⢭⣭⣷⡟⣳⢞⢡⡿⠃
⠀⠈⠛⠓⣿⡷⣢⠀⠀⠀⠀⠀⠀⠨⠭⠀⣐⣒⣒⡒⠂⠀⠀⠀⠀⠀⢐⣒⣒⡦⣭⣰⡾⡋⣅⠾⠋
⠀⠀⠀⠀⣗⠬⣒⠀⠀⠀⠀⠀⠀⢈⡻⠥⠶⠲⠄⠒⠂⠀⠀⠀⠀⠀⢀⣒⣾⠋⣬⣠⣴⡟⠁
⠀⠀⠀⠀⢳⡭⡒⠅⠀⠀⠀⠀⠀⠀⠨⠭⠄⣐⣒⣒⠂⠀⠀⠀⠀⠀⢐⣒⣛⣿⣯⣒⢽⡇
⠀⠀⠀⠀⢸⠭⣒⠅⠀⠀⠀⠀⠀⠠⠭⠍⢂⣒⣒⠶⠆⠀⠀⠀⠀⠀⢀⣛⡒⠭⠝⣊⢽⠁
⠀⠀⠀⠀⢸⡪⢐⠅⠀⠀⠀⠀⠀⠨⠭⣒⣒⣒⣒⡒⠀⠀⠀⠀⠀⠀⢐⣒⡀⠭⢕⣊⢽
⠀⠀⠀⠀⢸⡫⢖⠭⠀⠀⠀⠀⠀⠀⡯⠴⢒⣂⣀⣐⠂⠀⠀⠀⠀⠀⢒⣒⣒⠩⠕⣒⣽
⠀⠀⠀⠀⠘⣟⢕⠭⠀⠀⠀⠀⠀⠀⣪⠭⠒⣒⣒⣒⠀⠀⠀⠀⠀⠀⠂⠒⣒⡂⠭⣂⣿⠶⢶⣀⣀⣀
⠀⠀⠀⢠⢾⣟⢵⡭⡀⠀⠀⠀⠀⠀⡨⢭⣐⣒⣂⣀⠂⠀⠀⠀⠀⠀⠭⠅⣐⠢⢭⠺⣗⣒⠒⢒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠸⡝⢭⠷⢯⣒⠀⠀⠀⠀⠀⣻⣭⣉⣉⣂⣈⠀⠀⠀⠀⢀⣀⣵⣶⣶⡿⢷⡿⠳⣏⢷⡀⠀⣀⣈⣉⣉⣉⣉⣉⣁⣐
⠀⠀⠀⠀⠈⠒⠭⣒⠤⣍⡓⠲⠦⠤⣤⣍⣉⣉⣉⠈⠀⠉⠉⣉⣟⣛⣫⡭⠷⠮⠭⣭⡭⢯⡽⠉⠩⠍⠉⠭⠉⠉⠭⠭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠭⣝⣒⡒⠲⠶⠶⠿⣿⣟⣻⣿⣟⣛⣛⡧⠶⠶⠚⢛⣯⠭⠿⠭⠭⠭⠥⠬⠭⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⡰⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣢⡒⢷⡀⠀⠀⠀⠀⡐⠱⣍⠀⠄⡑⢇⣳⣀⠠⢊⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡊⠉⢲⣀⣀⠹⠁⠑⣄⠴⢾⡽⣿⣣⢟⡠⢡⢄⡏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠱⠘⠃⠀⣤⣋⢌⣛⢻⣷⣟⠋⢠⠁⡼⡀⠘⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⢁⠀⡁⢳⡄⢠⣴⠾⡴⡮⢤⣹⣷⣿⠚⣕⡁⢻⣧⡴⠀⣉⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠁⠀⡡⠉⠠⡜⢁⠰⣦⡀⣋⣿⣼⣄⠑⢾⣟⣾⣫⣭⡽⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠛⡔⠧⠀⠀⡠⠿⣲⣦⣹⣃⣼⠋⣻⣸⣟⢖⠻⣟⢻⣿⣦⡁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⡀⠤⡄⠞⠡⠩⣝⠛⠯⡼⡹⢃⣽⡉⠿⣾⠿⡶⠖⢚⠉⠉⡨⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠶⢄⠧⠰⣴⣤⠐⡟⢗⣼⠏⢷⡀⠛⢻⣒⠶⠲⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⣵⡛⡧⡠⢉⡔⠋⢸⠀⣾⠄⢰⡋⠁⠀⠀⠢⣵⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠠⠀⠀⠠⠜⠿⠆⠰⠯⣱⣤⡼⣶⡅⢩⢸⠗⡠⠐⢈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢻⣠⠿⣷⣿⠈⣟⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠹⠟⣄⣽⣷⠾⠇⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢄⠈⣄⣀⠅⡃⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣤⠾⣧⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠘⠗⢾⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡻⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠀⢄
⠀⠀⠑⠦⣀
⣀⠀⠀⠀⠈⠉⠒⠀⢀
⣿⣷⣦⣄⣀⣤⡀⠀⠀⢱⣄
⠉⠛⠛⠛⢿⣯⠔⠀⠀⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⣾⠀⠀⢠⠀⠢⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣿⢁⡀⠀⣱⠀⠙⣦⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡄⢠⡏⠀⣶⡏⠀⣿⠈⣇
⠀⠀⠀⠀⠀⢸⣿⡿⢀⣿⡁⢠⣿⣇⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⣧⣾⣿⣿⡀⠙⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣍⠓⢆⣻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣹⡇⠈⡇⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠸⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠚⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠅⠀⠀⠀⠙⠲⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠙⢴⡠⠀⢰⠁⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠠⠀⣀⣀⠛⠁⠀⠀⠦⠀⠸⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣆⠀⢰⣶⣄⣀⢤⣤⣤⣦⣴⣥⣀⣀⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⡻⠛⠻⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠓⠒⠛⠛⠛⣛⣿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠦⠤⣤⠤⠤⠤⠴⠾⠿⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢰⠋⢹⢂⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⠒⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠠⠁⣰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠐⠁⣰⢣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠰⠀⡰⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀⡞⠐⠀⡰⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡞⠐⠀⡘⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡔⠋⠘⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣀⡤⠖⡛⠉⠁⠒⠒⠒⠒⣒⣒⠂⠩⠝⣓⠲⢤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⠵⠊⠁⠀⠀⠀⠀⣀⣀⣀⣀⠀⠉⠀⠀⠀⠈⠓⠬⡛⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠞⠋⠉⠉⠉⠙⠙⠛⠇⠀⠈⠉⠓⠲⢤⣀⠀⠑⢌⠂⠙⢦⡀
⠀⠀⠀⠀⠀⢠⠞⠀⠀⡰⠋⠀⠠⠄⠀⠀⢠⠀⠀⠀⠀⠘⣄⠀⠀⢈⣀⣬⣷⣄⠀⠙⢄⠀⠳⡄
⠀⠀⠀⠀⢰⡣⠀⠂⡘⠁⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⢸⣠⠞⠋⠁⡀⠐⠉⠳⡄⠄⠣⠰⡹⡄
⠀⠀⠀⢀⡔⠀⠀⠀⡇⠠⠀⡀⠀⠀⠀⢀⣜⡋⠀⠀⠀⠀⣼⠡⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⠱⡹⡀
⠀⠀⠀⡼⠀⠀⠀⢸⢷⠀⠀⠀⠀⣀⠴⠏⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⡆⠀⠀⢣⢧
⠀⠀⢠⡇⠀⠀⠀⣾⣸⠀⠀⡴⠣⣄⠀⠀⠀⣀⣀⠠⣠⠟⠀⠀⠀⠀⢄⡞⠁⠀⠀⠈⠀⠀⡄⠀⢸⡜
⠀⠀⢸⡇⠀⠀⠀⣿⡃⣀⢐⡇⠀⢈⡿⠛⠉⠉⠉⠉⠙⡒⢦⡀⠀⡑⢾⠃⡄⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠘⡇⠀⠀⠀⢻⡉⠉⣍⠀⣴⠋⠀⢀⠄⠀⠀⠀⠀⠀⠀⠻⣶⢤⣾⡄⠀⠀⠀⠁⠀⢀⡇⠀⢸⢃
⠀⠀⠀⢻⡀⠀⠀⣾⠛⠀⠙⠻⠷⠤⠖⠛⠀⠛⢐⠛⠂⠄⠀⢠⢹⡄⠈⣳⡀⠀⠀⠀⢀⡾⢀⡆⡜⡈
⠀⠀⠀⠘⣧⡀⢂⠈⠻⣦⢄⡀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢧⠀⢹⠁⠀⠈⣤⠞⢀⡞⡐⡱⠁
⠀⠀⠀⠀⠘⢿⠀⠀⡀⠈⢣⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠔⡁⠈⣴⠞⠁⢠⠎⡔⡰⠁
⠀⠀⠀⠀⠀⠈⢳⡀⠘⢦⡀⠙⠮⣗⡤⣀⡀⠀⠀⠀⠀⠀⠐⠀⢠⠟⢺⣥⠞⠁⢀⠔⣡⢎⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠢⢀⠈⠙⠓⠉⠿⢒⣒⣀⣀⡲⠖⠡⠖⣋⠵⠂⠀⡁⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠉⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⣀⠀⠉⠉⠉⠤⠴⣒⣊⠥⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠇⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣀⠉⠈⠦⠄⠃⢥⡤⠀⠄⠐⢀⡜⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⠀⡁⠖⣀⠰⢍⡳⠀⠀⣀⣀⡀⠠⠤⠒⠃⠀⠀⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣠⣾⣛⣫⠍⠐⠁⠀⠉⠉⠀⠀⠀⠀⠀⠖⣦⣿⠁⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠞⠛⠋⠉⠉⠉⣀⣦⠴⣶⡾⡋⢻⣤⢤⣤⣿⣟⣿⣽⣦⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠛⡟⠛⡃⢀⡠⣤⣿⣉⠉⢋⠁⣐⠛⠈⢁⠈⢿⣟⣩⡜⣟⣥⣶⡻⣻⣷
⠀⠀⠀⠀⠀⢠⠗⠋⢓⡆⠲⠛⠿⠧⠜⠉⠉⡠⠆⠈⠁⢀⡴⠇⠤⣀⠙⠛⢿⠷⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠓⠛⠳⠄⠁⠀⠂⠒⢂⡽⢣⠴⠀⠀⠈⠑⠠⠄⠻⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡒⠓⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢸⡴⠒⢲⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡜⢀⠎⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡴⢹⠇⢀⡞⠀⢠⠇⣰⠉⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡜⠀⡘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡼⢱⡇⡀⠺⠤⠤⠋⠀⠓⠚⣁⡤⠤⠤⢴⢀⡞⠋⠉⠉⡉⢰⠁⡸⠁⡌⢉⠇⡰⠋⠃⠒⠲⡄⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠰⡇⠀⠻⣞⡆⠀⠀⡰⠉⡲⠀⠧⣤⠀⢀⠎⢀⡽⠋⡠⠞⢡⠃⢰⠃⡸⠀⡜⢰⠁⡰⢺⠃⣸⢁⠴⠋⣀⣀⠉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠙⠦⣤⡃⠀⠀⢰⠃⢠⠃⢠⠞⢁⠔⠁⡰⠋⠀⠾⢰⠀⡞⢠⠇⢠⠃⡸⢀⠃⣰⢃⡏⢠⠇⡏⠀⣞⡡⠦⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠹⡄⢠⠏⢠⠏⡰⠁⠀⢉⡹⠐⠧⠀⠒⠒⠋⠀⠉⠉⣀⣀⣉⣀⣀⣉⠁⠈⠙⠊⠀⠣⣤⣀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⠀⠀⡇⢼⣀⠞⠀⠗⠒⠋⠉⠀⠀⠀⠀⠀⠀⢠⣎⣉⣉⣭⣄⣤⣤⣤⣍⣉⣉⣙⠓⠒⠤⠤⠃⣰⠁
⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⢠⠟⢤⣸⠁⠀⣴⣶⣶⣶⣦⠀⣶⣶⣶⣶⣶⢰⣶⣶⣿⣶⠄⠀⢀⣶⣶⣦⠀⠀⢠⣾⣿⠙⣲⣶⡖⣡⣶⣶⣶⣦⡄
⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⣠⠏⠀⣸⡧⡄⢰⣿⣿⠋⣿⣿⠀⠛⣻⣿⡟⠋⢸⣿⣿⠛⠛⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣰⣿⡿⠀⣿⣿⡟⢻⣿⡇
⠀⠀⠀⠀⣟⠀⠈⠧⠤⠚⠁⢀⡴⠃⡷⠇⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⢸⣿⣿⣿⡿⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠘⠲⢤⣀⣀⡠⠔⠋⠀⡞⠀⠀⠘⢿⣿⣦⣄⡀⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⢻⣿⣇⠀⢸⣿⣿⣿⣇⠀⠀⠻⣿⣷⣄
⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣤⣤⣤⣤⣽⣿⡿⣿⣤⣤⡿⡿⣧⣤⣼⠿⠿⠿⠿⣦⣴⡿⣿⣼⣿⣿⣤⣼⣿⢿⣿⣿⣤⣤⣤⣬⣿⣿⣿⣦
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⡇⠉⣿⣿⡇⠀⣿⣿⣿⠀⢸⣿⣿⣿⡏⠁⠘⠛⠈⠉⣿⣿⠀⢸⣇⠉⢻⣿⣿⣿⣿⡯⠛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢱⣿⣿⣿⠛⢻⣿⡇⠀⣿⣿⡇⠀⣿⣿⣿⠀⢸⣿⣿⣿⠃⠀⣴⣶⡄⠀⢻⣿⠀⢸⣿⡀⠘⣿⡟⠛⣿⡇⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣮⢻⣿⣿⡀⠈⠉⠀⢀⣿⣿⡇⠀⣿⣿⣿⠀⠈⠉⠉⣿⠀⢰⣿⣿⣿⠀⢸⣿⠀⢸⣿⣇⠀⢻⡇⠀⠉⠁⠀⣼
⣿⣿⣿⡿⠿⠿⠛⡟⢻⣿⠿⠿⠿⠟⠘⢛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣿
⣿⣿⣿⢁⠒⠗⢨⣥⣾⣶⣿⣿⡿⣇⣙⡋⢭⣿⣿⣿⣿⣶⣶⢦⣼⣕⡂⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⡿⠣⢿⡟⣸⣿⣿⣷⡿⢿⡏⠜⣽⣿⣿⣿⣿
⣻⣿⡧⣄⠱⠄⣹⢿⡏⣛⠛⣂⣭⣶⣶⢜⠻⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡧⡪⣳⣿⣿⣿⡿⢛⣉⡉⢀⣶⡏⠸⠉⡿⢱⠏⠼⣋⣴⣌⣵⣿⣿⣿⣿
⣼⡟⢘⡕⣪⣧⡼⢤⡑⢀⣈⣩⣭⣭⣭⣼⣿⣿⢿⣛⣙⠀⣽⣿⣿⠛⠛⠺⡴⠁⢻⣿⣿⣿⣿⡿⢡⣿⣿⣀⣾⣤⣶⣶⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿
⣿⣷⡘⣻⠞⣱⢱⢇⡻⣿⣿⡟⣿⠏⠛⢛⣋⣙⣉⣢⣩⣤⣾⠿⠄⠄⠐⠊⠀⢀⣿⣿⣿⣿⡿⣷⣾⣿⢟⣭⠛⣿⣿⣿⣿⠿⡿⣫⡭⢋⡼⢁⣾⣿
⣿⣿⣿⣦⣙⠾⠈⠺⢇⣉⣉⠉⠉⠉⠉⠉⠉⠘⠛⢛⣻⣿⠷⠁⠀⠀⢀⣠⣴⣿⣿⣿⣿⠣⣶⣾⣿⣇⣼⡏⣰⡏⡼⠱⣋⣸⣤⣭⣾⠶⠂⣘⣻⣿
⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⢁⣾⠍⣽⣿⢟⡋⣰⣿⣷⣿⣿⣿⣿⣿⣟⣰⣫⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣵⣾⣿⡧⢞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀⠀⠀⠀⠀⠀⠀⢿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠀⢬⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣄⠀⠀⠀⠀⠀⢠⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⣻⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠿⡄⠀⠀⣀⠀⠀⠀⠀⣲⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⣿⣴⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠘⣷⡆⠀⠀⠙⠀⠀⡀⠀⠛⠁⠀⠀⠀⣺⣟⠄⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠂⣙⠂⠀⠀⢼⠁⠀⣤⠀⢺⠃⠀⠀⠀⠿⠁⡀⠀⠀⠀⠘⠿⣁⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣺⣀⠐⠢⠿⠓⠀⠀⢿⠄⠀⢤⠀⣿⠃⠀⠀⠠⣤⣠⡆⠀⠀⠀⢀⣶⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⣤⣤⠄⠔⢠⢼⡄⠘⠇⢉⣠⠄⠀⠀⢻⡿⠇⠀⠀⠐⣿⣇⠀⠀⢿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⠀⢩⣇⠀⠙⡿⣩⠆⢱⣿⡴⠀⠀⠱⣤⣿⠀⠀⠀⠀⢻⡞⠀⢠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⣤⡞⢯⡆⠀⠀⣽⠂⢪⣽⣧⠈⠀⠢⣬⡉⠂⠀⠀⢀⣀⠸⢟⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢷⠀⣾⠃⠀⠀⠫⡜⠻⠛⢷⠀⠀⠀⠹⣿⠀⠀⢀⡀⠟⠀⠀⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣷⠉⣶⠀⢿⠆⠻⠦⢙⡟⠀⠀⢳⣤⣈⠃⠀⠘⣵⣏⠀⢀⣿⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣠⠿⠇⠀⠁⣠⣶⣛⠁⢀⠀⣰⣿⡏⠀⠀⠀⢛⣧⡀⢸⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡾⠁⣿⠆⠸⡇⠘⣧⣾⣿⣇⣻⡇⠀⢿⣄⠴⠀⢼⡋⠐⡏⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡀⢈⠀⠳⡆⢁⡌⢻⣩⣟⢀⣹⡇⠤⣼⠋⣤⣈⢈⡡⠤⣘⢯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣾⡃⠂⣩⣾⠀⡌⠱⣿⠗⢹⡏⠁⢿⣦⢆⣡⣬⣦⡐⢾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢜⣷⠄⠶⣁⡖⠀⠛⣴⡶⣿⠀⢁⣸⣇⡿⠘⠛⠛⣷⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡤⢹⡿⠀⠀⢠⡀⢈⠀⠘⡁⠈⣿⣦⠶⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡘⣿⢳⣄⠀⢙⠋⠀⢸⣻⡟⢪⣤⠴⢀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣯⠀⣾⡿⠄⠘⣿⣃⢹⡅⠲⠿⠗⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⢋⡀⠀⠟⣴⣿⣧⣍⠠⠿⠀⣰⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⡀⠛⣽⠋⠈⣤⡀⠆⠈⢿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡌⢷⠀⣀⣾⡀⠛⣶⠀⠱⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣰⡄⢻⡿⡇⢸⠟⣿⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢻⡏⢹⣷⣀⠀⢀⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⣿⣯⣿⣡⢿⣨⡅⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⢿⣿⠃⣶⣿⡅⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⢻⣾⣿⣷⡈⣿⠁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣷⣼⣯⣿⣿⣌⠳⣀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣬⣥⣼⣆⣻⡕⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣾⠿⣿⡗⢈⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢳⡾⣿⣷⡌⠀⣿⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣏⡟⣡⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠇⣼⠘⠃⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⣟⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣻⣿⡟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠘⣃⡬⢚⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⢞⣥⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣠⠞⣩⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⣀⣤⠾⠁⠀⢠⡞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⣀⣠⠤⢖⣚⣫⠭⠥⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠮⠭⣭⣓⣺⠿⣭⣁⠀⠀⠀⡿⣰⠋
⠀⠀⠀⣠⠴⣛⡭⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢬⣙⠦⣼⢃⡏
⠀⣰⢞⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢻⡁
⣼⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢹⡀
⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠒⠚⠋⠉⠉⠒⠒⠒⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⢻⡸⡄⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⣠⠏⣼
⢸⡷⣜⠦⣀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣠⠞⣡⢾⠇
⠈⢷⡈⠻⢮⣟⡦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢖⣫⡵⠞⢡⡟
⠀⠈⢻⣆⡀⠈⠙⠳⠾⣭⣕⣒⣲⠤⠤⢤⣄⣀⣀⣀⣠⡤⠤⠤⠴⣒⣒⣭⣭⠶⠞⠋⠁⠀⣠⠏
⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠳⠶⠶⠚⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⣀⢀⣼⠃
⠀⠀⠀⠀⠀⠙⢷⣄⡰⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣺⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣭⣙⣛⣒⠒⠶⠶⠶⠶⠶⠶⠶⠒⢚⣛⣩⣭⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⡆
⠀⠀⠀⠀⠀⠀⠀⣰⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠒⠛⠒⠶⠶⣤⣀
⣠⠴⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣤⣶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳
⣿⠦⣤⣀⣀⣀⣠⣤⣤⡤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣤⣄⣀⣀⠀⢀⣺⣿⡦⢾⡇⣿
⢿⠀⣀⡈⠉⠉⠛⠛⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠋⠉⠁⠀⠀⣾⠶⠿⠶⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠞
⠸⡇⠈⠉⠙⠓⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠖⠛⠋⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠙⠦⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⣳⣤⠄⢀⣠⣴⡾⠛⠚⠛⢶⣶⣤⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢕⢶⣿⡿⠟⢻⠿⠒⠣⠀⠀⠀⢉⠙⢿⣤⡄⠲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣷⠋⠀⠃⠁⠀⠀⣀⣄⡀⠀⠀⠽⣿⠿⣾⣷⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡿⠖⠀⠀⠀⠔⠉⠀⠀⠈⠁⠀⠀⠈⠀⠈⢻⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⡿⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⢿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣇⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⡢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣫⣷⡁⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡿⠉⠛⠦⣌⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢫⡻⢿⣿⣷⡷⣄⠙⠚⠳⢤⣤⠒⠅⠀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠛⠚⠛⠛⠋⠙⠿⠿⠿⠿⠛⠓⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⠒⠒⠊⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣹⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢿⠀⡥⠁⠀⠀⠀⠀⠀⠀⠀⢹⡣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣸⠃⠀⠀⠀⠀⠘⠀⠀⡀⡀⡑⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⣶⣶⣶⣶⣤⣶⣶⡴⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠈⢿⠁⠀⠊⠀⠀⠀⠀⠀⠀⠉⡷⠁⠈⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡱⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠁⠀⠀⠐⠀⠀⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢹⣣⠞⠂⠊⠀⠀⠀⠀⠈⠉⠀⠺⠿⠿⠿⠿⠿⠿⠛⢛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⢀⠀⢀⠋⠱⡇⢠⠄⡀⠂⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣘⠶⢴⡷⣶⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠐⡌⢡⠀⢀⣹⡇⠰⠁⡈⠀⢀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢠⡆⠂
⠀⠀⠀⠀⠀⠀⠑⢈⣀⠇⠀⡀⢀⠀⢰⡇⠀⢀⠀⡀⢠⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣦⡈⠄⢸⠀⣠⢎⠜⠠⡾⡈⠀⢠⠇⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⢰⡼⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠐⠄⠘⠀⠀⢫⠏⠒⢼⣠⣴⠋⠀⢸⠃⢀⠄⡱⠂⠀⠀⠐⠀⣤⠀⠸⠀⠀⠀⠀⣟⠉⢀⠀⠀⠄⠀⠰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠑⠷⣄⢄⠀⠄⠀⢸⠕⠁⠀⠀⣼⣴⣠⠜⠁⠀⠀⠀⠀⠈⠘⠧⣼⡀⠀⡀⢤⣼⡰⠊⠋⠀⠀⠀⠀⡟⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⠈⠀⡙⠀⠀⠀⠀⠷⠋⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡄⢈⣼⡅⡴⠀⠀⠂⠀⢰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠠⣯⡠⣄⠀⣠⣐⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⠙⠏⢹⡜⠀⠀⠀⢠⠀⠀⠠⠇⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄⠀⢱⡀⡏⠉⢳⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⢸⠀⣄⣠⠂⣰⡧⣀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡇⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡖⠘⠁⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⡏⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⢘⡠⠛⠳⢦⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢈⡏⠁⣠⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⠁⠃⣨⠙⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠶⠀⠸⠇⢀⡾⢡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣱⠄⠀⠀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⡱⣦⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠧⠀⠀⠋⠠⠋⠔⠁⠀⠀⠀⠀⠀⠀⢀⡀⡠⠀⠃⠀⠀⠀⢠⣄⣂⣀⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⡄⠇⠀⠀⠁⠀⠀⠀⠉⠙⠛⠻⠷⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠒⠶⠲⢀⣤⠄⣠⠴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠟⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠰⠀⠐⠂⠘⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠙⢻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⡠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠆⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠞⠢⠄⠀⠤⠊⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⡀⣀⡀⠠⢀⠐⠃
⠀⠀⠀⠀⠀⠀⡬⢀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣷⡾⠷⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣈⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠠⢛⠀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⠀⠀⡄⠐⠃⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⢤⡀⢤⠈⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟
⠀⣠⠀⠀⠀⠀⠈⠀⣀⠒⣀⠀⠂⡐⢂⣤⡄⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡀⣀⠀⡀⣀⡠⠆
⠘⢋⡙⠉⠉⠁⡀⠀⠻⠿⣃⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⠚⠃⠰⠂⠉⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠼⢇⡨⠍⠀⠀⢀⠄⠀⠛⠀⠀⠠⠀⠐⢢⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡃⠐⢀⠀⠀⡁⢠⡤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠛⠂⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡼⠃⠀⠚⠃⠀⠀⠀⠁⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤
⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠁⠀⠀⢠⡀⢃⡰⠐⠶⠀⠑⠲⢄⣠⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡰⠚⠎⠀⣠⣀⠀⠀⠀⠀⣀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀
⠀⠀⠐⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠉⠀⠀⡰⠀⠀⠀⠀⠠⠤⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀
⣀⣀⣀⣀⣈⣉⣉⣁⣀⣘⣢⣄⣀⣀⣐⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡶⣻⣽⣏⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠑


⠀⠀⠀⠀⣀⠠⠄⠐⠂⠀⠉⠉⠉⠀⠁⠈⠀⠈⠉⠉⠁⠒⠒⠠⠄⣠⡄
⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠴⡀
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠁⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠤⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠄⠀⠒⠀⠁

⣶⡾⠳⠛⢷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣷⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠛⠛⠛⠓⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠛⢛⡛⣛⡛⠛⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⢛⣩⣭⣯⣿⠿⣿⣭⡉⠉⠉⠛⠓⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣋⡭⠥⢬⡀⠁⣸⠀⠐⠂⠀⠀⠒⡂⢹⡖⠀⠀⢠⠖⠒⠻⢿⣟⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⠞⠉⠀⠀⠀⣿⠀⢸⠀⠀⠀⠂⢀⠀⠀⢸⡇⣆⠀⣿⠀⠀⠀⠀⠉⠳⣌⠳⣄
⠀⠀⠀⠀⠀⣠⠏⣠⠞⠁⠀⠀⠀⠀⢀⡿⠀⡿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⠀⣛⠀⠀⠀⠀⠀⠀⠈⠳⡌⢷⡀
⠀⠀⠀⠀⣰⠃⣴⠷⠶⠶⠶⠶⠶⠶⣏⠀⠀⡿⠒⠒⠒⠒⠒⠶⠟⠳⢾⠀⠐⣿⠀⢀⠀⠐⠄⠀⠀⠀⠙⣆⢳⡄
⠀⠀⠀⢰⠇⣸⠃⠀⠀⠀⠀⢀⠀⠀⠈⢷⠀⡏⠀⠀⠀⡀⠀⠁⠨⠅⠈⡇⠀⣿⠀⠁⠀⠀⠀⠄⣀⠠⠡⢹⡄⢷
⠀⠀⠀⡾⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠉⠙⠳⢼⡇⠸⡆
⠀⠀⢀⡇⢸⣇⣀⣀⣀⣀⣀⣀⣀⣒⣂⣼⠀⣇⣐⣠⣤⣤⣤⣀⣀⣀⣠⠇⠀⢹⣄⣀⣀⣀⣀⣀⣀⣀⣊⡼⢻⡄⢳⡀
⠀⠰⢯⠤⠬⠭⠭⠭⠭⠭⠭⠭⠭⡭⠭⠥⠤⠬⠭⠭⠭⠭⣭⣭⡭⠭⠥⣤⣤⣤⠭⢭⣭⢭⡭⡭⠭⢭⠍⠠⠤⠥⣤⠷⢀
⣎⣲⠼⡀⠀⠛⠛⠛⠛⠛⠛⠲⠶⣄⠀⠀⣶⡇⠀⠐⡟⠛⠋⠉⠛⠻⢦⠘⠋⠉⢹⠋⠉⠉⢉⠛⠀⠀⠀⠀⢀⣆⢸⠲⣉
⠈⠁⠀⣇⠘⣇⠀⠀⠀⠀⠀⢸⠀⣽⠀⢸⡟⡇⠀⠀⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⣸⣇⡏
⠀⠀⠀⠘⡄⢻⡀⠀⠀⠀⠄⠀⠀⣿⠀⣼⠁⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢹⠀⠀⠀⠀⢠⡿⣼⠁
⠀⠀⠀⠀⢻⡀⢳⣀⣈⣀⡀⠀⣀⡟⢠⡏⠀⣻⠀⢀⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠸⡇⠀⠠⠸⡄⠀⠀⢠⡿⣱⠇
⠀⠀⠀⠀⠀⢳⡄⢻⡉⠉⠉⠉⠉⠀⡼⠛⠋⢻⡀⢸⡷⢶⣖⠶⡶⠒⠋⢀⠀⠀⠀⡇⠀⠀⠀⠘⠶⢶⡞⣱⠏
⠀⠀⠀⠀⠀⠀⠻⣄⠱⣄⠈⠀⠀⢰⠇⠀⠀⠸⡇⢸⡇⠁⠙⢷⡁⠐⠂⠡⠀⡀⠀⡇⠀⠀⠀⢀⡴⢋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣜⢦⠀⠀⡟⠀⠀⠀⠀⣷⢸⡇⠀⠃⠀⠹⡄⠀⠀⠀⠀⠀⡇⠀⣤⠔⢋⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣘⠃⠀⠀⠀⠀⠹⢸⡇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠁⣠⣴⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠗⠲⢦⡤⠤⠌⣁⣀⣀⣠⣠⠤⠤⣤⠶⠒⠺⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅⣀⣀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⣴⣿⣦⡀
⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣛⣛⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠐⠦⢳⡋⠀⠀⠀⠂⠀⢠⠁⠀⠀⢆⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠈⠈⠲⠡⠏⠀⠀⣀⡎⢀⠄⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⡘⠀⢐⢤⠁⠋⠘⢨⡅⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠰⣤⣘⠅⢰⡞⢃⠃⠉⠰⣿⠊⠳⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠤⠀⠋⢛⣸⠐⠀⡁⣻⢜⠘⡋⣠⢆⠎⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣆⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡏⢩⠄⠈⠁⡯⠈⢸⡏⣭⠜⢱⣫⡴⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠃⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠰⠸⣇⠃⠀⢠⡄⠀⣖⢳⡀⣼⡇⡾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣧⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠄⠌⢲⢸⡎⢰⡦⠛⠛⠙⠋⣰⠤⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⣠⢼⡖⢋⡔⢙⡐⠁⠀⠀⠀⠀⠀⢀⣤⡶⢀⠀⠀⠀⠀⣆⡃⠀⡀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣾⣾⡿⢾⣤⣿⡁⠀⠀⠀⠀⠀⢰⠟⠋⠀⠈⠀⠀⠀⠀⣈⣳⠿⠡⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢺⠛⣙⣴⣿⠸⢻⡵⠂⠀⠀⠀⠀⢸⡲⠆⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣹⣸⣿⡀⠛⠀⠀⡀⠀⠈⡅⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠃⠀⠀⠀⠀⢀⡴⠗⢺⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠄⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠋⠀⠠⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⣠⡖⠁⢀⣀⡀
⠀⠀⠀⠀⠀⣷⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋
⠀⠀⠀⠀⠘⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⣠
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠔⠂⠀⠀⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢻⣌⣀⠾⠁
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢦⡔⢀⠎⠀⣤⢀⠄⠀⡱⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠁⠊⠀⢀⠁⠈⠀⢀⠅⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⢤⣡⠎⠀⢀⠀⠄⠀⢀⢎⠜⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡄⠀⢀⡖⠀⠀⠀⡠⠂⠀⢀⠔⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡃⢐⠎⠀⢀⠊⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠐⠀⠀⠀⠀⠁⠀⠠⠔⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⡀⠀⠀⠀⡁⠀⢀⢂⠅⢄⠈⠒⠀⢠⠄⢡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⡀⢖⠁⠄⠀⠀⠁⠀⢨⡌⠓⠃⠀⠀⠀⠈⠡⠂⠀⠀⠇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⠸⠒⢁⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣀⡄⠤⢉⢀⡔⠘⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠈⡀⠀⠀⣰⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⡀⢉⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⢀⠄⠉⠁⠻⣚⠠⠧⠄⣄⠀⠘⢆⠀⠀⠀⠀⣀⠀⠁⠈
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⡠⠇⠀⠀⠀⡁⠀⠀⢄⡀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠴⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡇
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠍
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠎
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⢄⡀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣻⣿⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢙⠀⢀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠛⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣦⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠄⠀⢀⠀⠀⠀⠀⢀⠔⠈⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠿⠛⠁
⠀⠀⠀⡀⠄⠈⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠁⠒⢅⠀⠠⠐⠈⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣴⣿⣿⠿⠛⠉
⠀⢀⠈⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠑⠄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⢍⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢚⠏⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭
⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠄⠀⠀⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣈⠣⣰⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⣄⠀⠀⢱⡀⠠⠋⡀⢹⠛⢢
⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⢱⠀⠃⠀⢳⠀⠂⠁⠀⠸⢀⠈⡘⡜⠐⠀⢀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢠⠿⡇⠀⢠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢢⣆⠀⢠⠈⢷⠃⡎⣠⢆⠌⢰⡇⠀⠀⡶⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⡏⢀⠂⢡⣳⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⣇⠀⢡⠘⣴⠷⢁⡜⠥⢼⠁⠎⠀⡆⣴⠀⣠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡀⠀⠀⠀⢸⠀⠈⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠈⢢⡀⣶⠛⢦⠜⢣⡕⠚⡄⡀⠘⣡⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡆⠘⡆⡿⢀⡆⢠⡿⠃⠀⣀⡤⠖⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠶⡛⡇⢐⠈⠒⢸⠀⡀⠜⠁⡄⢀⠀⡀⢺⠁
⠀⠀⣤⠠⠤⠤⠄⣀⣀⠘⣆⣿⣤⠃⣿⣠⡇⢸⠅⢀⠞⠁⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠱⡀⢀⣰⡇⡞⡟⢀⠜⣠⠏⠐⢀⡜
⠀⠀⠈⠓⠦⣤⣀⡀⠀⣉⢪⣉⠣⣀⢺⣿⣥⠂⢠⣏⢀⡀⠔⢃⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈⣾⢿⡏⠀⣷⣥⣶⠿⠒⠒⠉
⠀⠀⠀⠀⠀⠀⢈⠝⠛⠉⢁⣈⣈⣻⣧⡽⠟⠁⣸⣞⣉⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢍⠹⣿⠁⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢴⣶⠞⢿⡀⡀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢻⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠀⠀⠀⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠀⠈⠡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣴⠥⠀⠰
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠂

⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣆⠄⢀⠀⠀⠀⢰⠀⣰⠀⠀⠀⢰
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠏⠾⠈⠳⠁⠼⠸⠇⠘⠠⠿⠑⠼⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠱⡀⠈⠁⣀⣼⢀⡀⠜⠀⠀⠀⠀⠀⠀⠇⢀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀⠀⠀⠀⠈⠉⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠
⢀⡀⠀⢰⢁⡈⢀⡶⢾⣹⡾⡿⠂⠀⠀⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢐⣒⠀⠂
⠈⠻⠀⠈⠁⠠⢭⣙⣤⣄⣘⣭⡼⠶⠞⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠪⢙⠒⠀⠤⠤⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠉⠂⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣠⡀⣄⢠⡄⣠⣄⠰⢤⣄⢠⡄⣀⣤⣠⠆⣀⠀⡀
⠀⠀⠀⠀⢀⡀⣀⣘⣇⣼⡿⣯⣾⠋⢿⣾⠟⣷⡾⠋⠙⢷⠿⠛⠷⠿⠛⡿⠾⠛⣿⣤⣭⡦
⠀⠀⠀⣀⡈⢃⣼⠿⢿⡿⣤⣤⣤⣤⣠⣤⣤⣴⣶⣤⠄⢰⡲⠤⣶⣶⣢⣶⢖⣶⠿⠀⣾⢁⣀
⠀⠀⠀⠀⠺⠿⣷⣜⢛⣛⡛⢿⣝⠓⢿⣛⣛⠙⣛⣮⣁⠛⣫⣽⣭⣍⣉⣬⣭⣉⢠⠾⡛⠓⠈
⠀⠀⠀⠐⠂⠐⠛⡿⠉⠹⠟⣫⠛⠛⢫⠍⠙⠛⠉⠰⠙⠛⠉⢰⠂⠉⠉⠐⠮⠉⠛⠀⠉⠃
⠀⠀⠀⠀⠦⠲⠖⠤⠶⠶⠂⠓⠂⠘⠒⠒⠓⠒⠂⠀⠐⠒⠂⠂⠚⠀⠐⠓⠀⠀⠓⠀⠑⠋
⠀⠀⠀⠀⠔⠞⠚⠂⠘⠚⠒⠂⠚⠒⠛⠒⠒⠁⠘⠃⠘⠚⠚⠛⠓⣚⣀⠉⠓⠚⠓⠚⠐⠓
⠀⠀⠀⠀⢀⡴⠛⢉⢉⠑⠖⠋⠉⣧⣤⣤⠔⠒⠒⠖⢚⠳⣄⣤⣼⠋⢭⣙⠶⠒⠶⢤
⠀⠀⠀⠀⢿⡈⢂⣛⣭⡆⢟⣁⣤⡤⠜⣇⢰⠶⠶⠿⠈⢀⣉⠉⣦⠒⠄⠈⢙⠓⠶⢆⣟⡛⠲⢄
⠀⠀⠀⠠⣏⠘⢉⣉⠰⠞⠛⢉⣡⢶⠎⠰⠶⠖⠂⠘⠓⠙⣫⢡⡏⠘⡃⠤⣬⣉⡂⢶⣬⣙⡳⢚⠇
⠀⠀⠀⢰⣏⢘⣋⡡⠞⠉⠉⠉⠀⠈⠓⢲⠀⢰⠷⢷⠿⠧⣈⡰⢷⡄⠛⠆⣤⣈⠉⠐⠶⣉⣁⠏
⠀⠀⠀⠀⠉⠉⠁⠀⢻⣎⣉⡉⠉⡉⢉⣉⠉⠛⠙⠒⠒⠚⠉⠉⠉⠉⠛⠒⠒⢥⣘⣠⠾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠙⠙⠀⠁⠈⠩⠭⠥⠌⠩⠭⠭⠄⠑⠘⠙⠊⠁⠀⠀⣇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡤⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⣀⡀⣠⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⢀⡀⠄⠀⠀⠀⠁⠀⠀⠐⢦⡤⠾⠋⠀⠘⣁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡄⠀⠂⠀⠀⣼⠫⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⣠⠌⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠶⠤⠀⢄⣴⠋⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠈⢡⡄⠀⠀⠀⠀⠛⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡧⠀⠀⠄⣼⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠿⠀⠂⠀⢀⠁⠀⠀⠀⠀⠀⠐⠀⠈⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠲⣌⠁⡰⠛⠋⠉⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣦⣀⠀⠈⠀⠀⣼⠀⢄⡀⠀⠀⣀⠀⠐⢦⣶⡾⠋⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⣾⣧⡧⢾⣦⣼⣶⠿⠷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡆⢾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⢺⣿⠓⢶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠂⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣿⠃⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸⣿⠏⠁⣤⠆⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⣛⣿⡿⠀⠀⣾⠠⣤⠀⠀⠀⠀⠀⡄
⠀⠀⢀⣤⣀⠀⠒⠀⠀⠔⠀⠀⠀⠳⠒⠶⠟⠷⢄⡀⣹⠀⠉⠀⠰⠄⠀⢀⣀⠀⠀⠀⠀⠀⠃
⠀⠀⣽⣽⣿⣷⣿⣤⣽⣤⣴⣀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⠇⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠁⠙⠛⠖⠺⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠒⡀⠐⠒⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣌⡙⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠉⠉⠉⠉⠁
⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣶⣶⣶⣦⣾⣦⣾⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠒⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢠⠁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⡷⠦⠤⢾⠧⢴⠚⠻⠛⠶⠤⠤⠤⢤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠠⠀⡸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠳⢤⡤⠃⠀⡎⠠⠀⡤⠄⠰⣄⣠⡀⠀⠙⣆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⡀⣤⠔⢀⣀⢴⠾⠀⠙⠀⠓⡘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡷⡇⠘⠛⠋⡀⢀⠀⢀⠀⠀⣅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⡼⠂⠀⠘⢛⠘⢻⡀⢋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⡇⠳⡄⠀⠈⠈⠁⠉⠉⠉⠁⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠇⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⡀⠀⠀⡇⠘⢄⡀⠀⠀⡠⠻⣀⣀⡠⠏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢄⠀⠀⠑⠢⠄⣀⠀⠀⠀⠀⣾⠈⠭⠍⠩⠍⠁⠀⡇⠀⣀⢀⢉⣉⣀⡀⠀⣀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠠⡀⠀⠀⠀⠉⠁⠐⠾⠿⢀⣟⡀⠘⠓⠀⣠⠀⠀⢩⡄⣬⠩⠉⠁⠁⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣀⣀⡑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠛⠧⠰⠴⠶⠶⠶⣦
⠀⢀⡴⠛⠛⠙⠋⠁⠉⠙⢶⣄⠀⠀⣿⠶⠛⠋⠉⠉⠉⠙⠲⢬⡒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡌⠀⠀⣀⣠⡀⢸
⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠉⠉⠙⠂⠚⠉⠉⢀⠀⢻⠋⠀⠀⠈⢋⣉⡡⠼
⡏⠀⠀⠀⠀⣰⠋⠉⠙⢳⣶⡿⠘⠁⠀⣠⠖⠓⠉⠙⢦⡀⠀⢀⣀⡿⠷⠤⠴⠆⠀⠲⠒⠴⠶⠦⠤⢤⣴⡟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⡀
⠃⠀⠀⠀⠀⠇⠀⠰⠊⣸⡏⠀⠀⠀⠀⠻⣀⡀⣀⡤⠞⠋⠉⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠉⠙⠒⠤⣀⠀⠀⠀⢀⡴⣋⡿⠷⢦⡀
⠰⡄⠀⠀⠀⠈⠓⠲⠟⠛⢧⠀⠀⠀⠀⠀⡼⠛⠁⠀⣀⡤⠖⠊⠉⢈⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠒⠦⢄⡀⠀⠀⠑⠢⣴⣩⡟⣹⠤⠖⣶⠟⢧⣀
⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⢀⡷⢦⣀⡰⠋⠀⠀⡠⠊⡥⢤⣀⡔⠊⠉⠙⣿⠯⢤⣞⣿⡾⣻⣏⢉⡵⣶⢦⣀⠀⠉⠒⣄⠀⠀⠈⠻⣿⡧⣶⠋⢉⣽⠛⢯⣧
⠀⠀⠀⠀⠉⠑⠒⠒⠒⠚⠉⠀⠀⡟⠀⠀⢀⠞⠀⢀⡴⠾⠿⡆⠀⠀⣴⠃⠀⢠⠋⠉⠉⢉⠏⠀⠀⠘⡟⠋⠑⢦⠀⠀⢳⡀⠀⠀⠹⣿⣛⣻⣋⣉⣩⠟⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡎⠀⣰⢻⠀⠀⠀⣸⣏⣉⣽⣇⡴⡞⠀⢀⡰⠛⢳⡤⡤⣾⠥⠤⢄⡠⢳⡄⠀⢷⠀⠀⠀⢋⣸⣏⣋⡽⠉⠙⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⢠⣏⠙⠤⡤⠴⠛⠌⢻⡶⣏⠀⠈⠉⣁⣹⣀⣸⣄⠑⣷⠀⠀⠘⡷⠋⡿⣄⢸⠀⠀⠀⢸⣇⣀⣝⠹⢓⡶⠧⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢯⠹⡏⠹⢶⣿⣻⣦⠀⣀⣽⠛⢋⣩⣿⣏⣿⢯⢤⠀⣑⡛⡶⡖⣾⣁⣼⣾⣇⡎⠀⠀⠀⣾⣻⣏⡉⣹⢿⢦⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣀⣀⣈⣿⣷⡧⠴⢟⡛⣛⣉⠉⣉⡀⠘⠻⠾⠀⠈⠁⣼⣼⣭⡟⠓⢻⣁⠀⠀⣸⠟⠀⠀⠀⣼⠉⠑⣴⡙⠙⢳⣾⣁⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⢉⣩⢭⣭⣵⠶⠒⠛⢿⣍⠁⢽⠁⠀⠈⠛⡿⠟⠉⠒⠒⠚⡄⠀⠀⣷⠤⠿⣯⡷⠛⠁⠀⠀⣠⣞⠛⢳⢶⠋⢉⠟⢧⣀⡝⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠒⢄⡀⠀⠈⠑⠂⠕⣶⣿⠞⢣⣜⠄⠒⠒⢲⣧⣄⡴⠥⠔⠊⠁⠀⢀⣠⣴⠿⡁⢈⠷⣅⢀⡽⠧⢤⣀⠟⠦⣤⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠄⠀⣀⠀⠀⠀⠀⠉⠈⠁⠉⠀⠀⠀⢀⣀⠠⠤⠒⢊⠉⠉⠑⣤⡜⢧⣀⣼⢋⠛⢣⡴⠛⣆⡠⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠒⠒⠀⠉⠉⣁⡀⠀⠀⠀⢮⣋⠆⠀⠈⠣⣤⣏⡽⣻⡔⠛⢧⡠⠚⢷⡤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣈⡼⢟⠻⢳⠀⣡⠦⡄⠀⠀⠀⠀⠟⠉⣀⡡⠋⠉⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣩⠟⠓⠋⠉⠁⠀⠛⠴⠀⠀⠀⠀⠀⠱⣴⠿⠧⣄⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠑⡀⠀⠀⠠⠖⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠒⠁

⠀⠀⢀⣀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠤⠄⣀
⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠤⠄⠀⠀⠀⠒⠀⠒⠂
⡀⠀⢃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠤⠐⠒
⢋⠢⠬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣁⠴⡀
⠈⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣪⠄⠈⠉⣠⡁
⢰⠀⣀⣀⠀⠖⠀⠀⠀⠐⠀⠀⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠂⢂⡉⠅⠃
⠀⠁⠰⢁⠀⠀⠠⠤⠀⠀⠐⡀⠀⠀⢀⠀⠀⠀⢀⠀⣂⣰⠦⠔⠉⠁⠕
⣀⣀⣀⣀⣈⣒⣤⣔⣂⣀⣐⣒⣒⣒⣚⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⢋⣍⢉⡉⠓⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣀⣠⣤⣤⣀⡀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡴⣫⣅⢄⣰⠠⠈⠝⢦⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡞⢼⣊⠊⠜⠇⠁⠈⠁⠦⢹⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠓⠱⡠⠁⡅⠂⡀⠀⠈⢠⠷⠶⣄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠀⣇⠀⠀⠀⢳⡄⠔⠈⣈⢄⠐⠊⠌⣀⣼⠟⠛⠁⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⣤⠤⠴⠶⠶⣶⣶⣶⣤⣄⣀⠀⠀⠉⠒⢤⡀⢸⣄⠀⠀⠀⠙⠶⣼⣂⡪⣁⣮⡵⠛⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⣤⣶⣿⡛⠓⢦⣤⡄⠸⣷⢄⠐⢈⢻⡈⠙⠲⣄⠀⠘⢉⡻⣿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⣠⠊⠀⠀⣠⣶⡏⠀⣹⠛⠻⠶⢿⣤⡇⠀⠙⢮⡧⠄⠁⠑⢦⡀⠀⠙⢦⡈⠁⠈⢻⣿⡶⢄⣀⡀⠰⠆⠖⠀⣀⣠⠔⠋
⠀⠀⡴⠁⠀⢀⣼⠿⣽⡧⢤⣿⠦⣦⡄⢀⡍⠛⢓⢆⠈⢷⡂⢡⡀⠠⠙⡆⠀⠀⠑⣄⠀⠀⠹⡇⠀⠈⠉⠉⠉⠉⠉⠁
⠀⡸⠁⠀⢠⡏⣸⣠⡇⢀⣠⡃⢀⣼⣽⣷⠲⡀⠄⠉⠛⠶⣿⣿⣬⡤⠀⢹⣦⡀⠀⠘⣆⠀⠀⠹⡀
⢰⠃⠀⢀⣿⣧⠋⠉⣹⠁⠀⣿⣏⠀⣼⣃⠀⠈⠻⢧⣙⣶⢤⡘⠻⢦⡀⠀⠀⠻⡄⠀⠘⣆⠀⠀⢧⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠓⠒⠤⣄
⡾⠀⠀⣸⡿⠻⣤⠼⢻⠶⠚⠋⠉⠉⠙⠛⠛⠦⢤⣀⠀⠉⠛⢿⣴⠄⣗⠄⠒⠀⢹⣄⣀⣿⠀⠀⠸⣄⣀⡴⣪⠅⠀⠀⣀⣀⣤⠴⠚⠉⣹⠀⢠⠶⡝⠦⡀
⡇⠀⠀⣿⣇⡀⣸⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⠄⠈⠙⠶⣽⣦⡂⡄⠀⠳⡽⠟⢦⡀⠀⡿⠋⠘⠁⣠⠖⢋⡽⠋⠁⠀⠀⢠⠟⢿⠏⠀⢹⠀⠈⢦
⡇⠀⠀⣿⠉⢿⠋⠀⠀⠀⠀⣠⠴⠖⠒⠒⢦⠀⠀⠂⢸⡙⠂⠀⠀⠀⠀⠈⢷⡘⡆⠀⢻⣿⣫⠇⠀⡇⠀⣠⣾⡵⠚⠁⠀⠀⠀⠀⢀⠏⢠⠏⠀⠀⠸⡇⠀⠀⢳
⢷⠀⠀⢿⠙⣿⡀⠀⠀⠀⡾⢱⠀⠀⠄⢂⢘⣇⡴⠒⠚⡛⠛⠉⠓⢦⠀⠀⠀⢹⡄⠠⠀⣿⠃⠀⢰⠁⢸⡟⠁⠀⠀⠀⠀⠀⠀⢀⡎⢀⠏⠀⠀⠀⠀⣷⡀
⠸⡄⠀⠸⡇⠜⣧⠀⠀⠀⢷⡈⠀⡀⠆⢀⣸⠟⢀⡤⠥⠦⣤⡀⠀⠀⢳⣀⠀⠸⣌⣅⣠⡟⠀⠀⡜⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⡼⢀⡞⠀⠀⠀⠀⠀⢹⣇
⠀⢱⡀⠀⠙⣦⣈⣦⡀⠀⠀⠈⠓⢳⡿⠛⠁⣰⠯⡀⠀⠐⠠⠙⣆⠀⠀⢹⣆⠂⡈⣹⠟⠀⠀⣰⠁⠘⣯⣿⣇⠀⠀⠀⠀⠀⡜⢁⡜⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢳⡀⠀⠘⢖⡐⡛⡄⠀⠀⠀⢸⠀⠀⠀⢿⡣⠐⠠⠐⢀⠂⡿⠀⠀⠈⢷⣬⣶⠋⠀⠀⣰⣷⠀⠀⢹⣽⣿⡀⠀⠀⠀⣰⢗⡾⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠙⢄⢀⡈⠳⣄⠿⢦⣀⣀⣼⣧⠀⠀⠈⠳⣤⣁⣵⣥⠖⠁⠀⠀⠀⠈⢿⠁⠀⢀⠞⠁⠙⡆⠀⠀⢻⣷⣹⡄⠀⢰⡏⡼⠁⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⢰
⠀⠀⠀⠀⠀⠻⢵⡆⠈⠑⠦⣈⠉⠀⠈⠣⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⣀⠔⠁⠀⠀⠀⠘⢆⠀⠀⠙⣧⣇⢠⣯⣥⠃⠀⠀⣀⣀⣠⣴⡾⠟⡡⠆⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠉⠑⠲⠤⠶⢭⣽⠷⠶⠶⠦⠤⠤⠖⠊⣉⡥⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠿⠿⢾⣷⣶⣶⣿⠧⠴⠚⠉⠀⠀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠔⠊⠁

⠑⠀⠈⢠⡀⣧⠛⠾⡓⠀⠀⠀⠀⠀⠀⢀⠸⡃⠀⢀⠀⡀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠐⣠⠄⠀⣠⠊
⢀⣶⣕⠌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠁⠀⠐⠁⠘⢆
⡉⠀⠁⢠⠶⠈⠀⠀⠀⡀⠆⠘⠖⠒⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠈
⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠓⠀⠀⠀⢀⠐⠑⠆⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠐⠂⠁⢀⠀⣀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠁⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠋
⠀⢀⡄⠀⠂⢘⠀⠀⠀⠀⠏⠈⠀⠀⠢⠀⠀⠀⠁⠐⠀⠀⠀⠸⠂⢈⠄⠋⠈⠁⡆⠓⡀⠀⢄⠀⠀⠀⠐
⡈⠀⠀⠀⠀⠠⠛⠈⠁⢐⠀⠊⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠥⠀⠀⠰
⠉⠁⠀⠀⢀⠤⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠂⠠⡄⠀⠀⢨⠥
⠓⠠⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰


⣉⣉⣀⠤
⣉⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⣉⣤⡴⠖⡊
⠉⣥⠶⢃⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠛⢿⣶
⣈⣴⣮⣅⣤⣴⣎⣠⣠⣄⣤⣄⣠⣇⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣀⣤⣤⣈⣤⣌⣵⣦⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠉⠐⠂⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠂⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠂⠀⠠⢼⡄⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠁
⠀⠀⢄⠀⠀⠀⠙⠆⡠⠊
⠀⠀⠈⠢⠴⠂⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠹



⣶⣶⡶⠶⢶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣀⣤⠴⠶⠚⠛⠛⠉⠉⠉⢿⣍⠉⠉⠉⠉⠛⠛⠳⠶⢦⣤⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⢻⠀⠀⣀⣠⣤⠶⠶⠖⠛⠛⠛⠋⠉⠉⠙⠉⠉⠉⠉⠛⠛⠳⠶⢦⣤⣀⠀⠀⢹⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⣠⣼⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢾⣅⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⠾⠛⠁⠀⢀⣠⠄⠀⠀⠀⢀⣀⣠⣤⣄⣀⣀⣤⡴⠶⠛⠛⠛⠷⣦⡀⠀⠀⠙⠓⠶⣤⡀⠉⠛⢶⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⢰⠏⣠⠞⠁⠀⠀⢀⣴⠟⠁⣠⡴⠶⠾⠛⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⢦⣄⡀⠁⠀⠀⠀⠙⢷⡘⣧
⠀⠀⠀⠀⠀⠀⣿⣴⠋⠀⠀⠀⠔⠋⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⠛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⣀⣀⣀⣀⣢⣴⠏⠀⠀⠀⠀⠀⢀⣀⣤⠞⢁⡾⠁⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⢿⡘⢷⡀⠀⠀⠀⠸⣧⣐⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⡿⠋⣡⠶⠋⠁⠀⠀⢀⡼⠋⣾⠁
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠙⠷⣤⣀⠀⠈⠉⠙⡛⠳⢦⡀⠀⠀⠀⠠⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠈⠁⠀⠀⣀⣤⠾⠋⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⠉⠛⠲⠶⣤⣬⣁⣀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⠾⠿⠶⠚⠋⠁⠀⠀⢀⣀⣤⡴⠞⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠟⠉⠉⢻⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⠀⠀⠀⠙⣿⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⡇⠀⠀⠀⠈⡷⠶⠖⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠞⠛⠓⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠒⠛⠙⠛⠢⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⣀⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡟⠁⠉⢻⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠿⠟⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡴⠶⠶⠲⠶⢤⣄⣷
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣹⡟
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⣤⠴⠞⠋
⠀⠘

⠬⠒⠃⠀⠀⠀⠈⠀⠄⠀⠀⠂⠀⠀⢀⠀⠘⠦⠀⠀⡀⠀⠅⠀⠁⢧⡀⢹⠋⢻⣬⢺⣣⣼⣼⡿⠉⡽⠁⡨⢋⠁⠃⠼⢁⠞⠹⠃⢈⡼⠋
⣅⡀⠀⠀⠀⠀⠀⠈⠀⠈⢢⣠⣤⣄⣤⣀⡀⠀⠠⠀⠀⠀⠀⣠⠖⠾⣇⡀⢱⢋⡷⠻⠋⠀⠈⣷⡼⢁⣀⠀⡈⠀⠀⢀⡀⠀⣀⠐⠁⠀⠈⠀⠀⢀⡴
⢤⢉⠁⠤⣀⠀⠀⠀⠀⠀⣾⠉⠀⡀⢀⣉⣻⡖⡦⠥⡀⣀⣴⠧⠁⠀⠙⠉⢨⠮⣤⡀⠀⠀⠰⠟⠗⠛⠉⠙⠉⣹⠋⠁⠹⠏⢉⠷⡄⠀⡀⠔⠊⠉⠉
⣓⠀⠀⡀⠀⠐⠀⠀⠀⠀⢻⡍⠀⠈⠯⡉⠁⠀⠁⠀⠀⠉⠉⠗⠲⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠉⠀⠀⠸⠀⠀⣈⡗⠂⠁⠀⠀⠠⠐
⠦⣠⠀⠁⠉⠒⠀⠀⠀⠀⠻⣆⡄⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⣲⢤⠤⢤⠀⠀⠀⠀⢲⡋⠀⠀⠀⠀⠠⣄⠼
⠂⠀⠅⠀⠂⠀⠀⡀⠀⠀⠀⠈⣟⠁⠀⠀⠀⠀⢀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⡀⠀⠠⠆⠀⠈⠹⠀⢀⣸⠃⠀⠀⣀⣠⠇⠀⠀⠀⠀⠀⠀⢀
⠙⠃⠀⠀⠀⠀⢀⢀⣠⣔⡓⢺⡋⣷⠒⠀⠀⠀⠀⠀⠀⠈⠁⠉⠠⠄⠀⠀⠱⠀⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡰⠞⠁⣴⣃⣠⡀⠀⠀⠀⠀⠄
⠚⠛⠓⠲⠆⠀⢰⣏⡀⠉⠀⠀⠃⠈⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠹⠻⡟⢲⡄⣀
⣛⠖⠃⠀⠀⢀⣿⠉⠀⣀⠴⠚⠁⠀⠙⠂⠀⠀⠀⠒⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⠀⠀⠀⠁⠀⠀⢀⡼⢋⣑
⠻⠍⣠⣶⠋⠙⠇⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶
⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⣀⠀⠀⠀⢠⣤⣄
⠤⠼⢿⣓⣤⣰⠯⠀⠸⣧⣀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠂⢠⠀⢀⡀⠀⠀⠀⠀⠁⠀⠉⠉
⠃⠉⠀⠀⠀⠉⢳⣀⠀⠀⠈⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠘⠆⠀⠀⠁⠢⠄⠀⠀⠀⠀⠀⠀⠀⠈⣠⣸⠇⠀⣠⡼⠟⠂⠒⠠⠤
⣴⡖⠊⠀⠀⠀⠀⠈⠛⠷⠖⢡⡀⠀⠀⠀⠀⠺⢤⠴⠦⠄⠀⠀⠀⠀⠘⡄⠀⡀⠀⠀⠀⠠⠀⠀⠠⠨⠆⠀⢀⠀⠀⠀⣹⡝⠀⢙⠀⠀⢄⣀⠀⠘⠑
⡩⠀⠀⠀⠀⠀⣀⠄⠈⠁⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⢆⣀⡔⠀⠀⠰⣤⠤⡀⠙⠆⠀⠀⢀⣄⠀⠀⡀⠘⠒⠋⢹⣷⣛⠁⢠⣴⡏⠀⠀⠀⠀⠉⠀⠈
⠂⠀⢀⡀⠄⠊⠀⠀⣀⡤⡾⠊⠳⠴⠤⠴⠻⣄⣀⣰⣯⠉⣅⡀⡐⢀⣽⡆⠁⠘⠲⢤⢶⡞⠉⠓⠚⠻⣤⣤⡽⠛⠀⠉⠙⠋⠁⠀⠀⠀⠀⠑⠢⢈⡐
⣪⠕⠉⠀⠀⣀⠔⠛⡉⠈⠁⠀⠀⠀⠀⢀⠀⠀⠁⡰⠃⢠⠻⣤⠶⣞⠈⡻⣆⠀⡀⣀⡾⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠁⠀⢂⡠⠋⣡⡴⡋⢀⣄⣠⠊⡰⢂⠔⣉⡴⠀⣰⠃⣰⣦⣢⠘⣶⡔⣾⣧⣨⣃⢹⡉⡀⠀⡀⠀⠪⠀⠰⣄⠀⠐⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠐⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡜⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠊⠀⠊⠰⠰⠁⠀⠁⠁⠈⠐⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃




⠀⠀⠀⠀⠀⠠⣄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠻⣦⢸⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢰⣧⣆
⠀⠀⠀⠴⠖⠒⢒⣿⢿⠀⣦⣀⡞⠀⠀⢘⣳⢾⣷⣡⠞⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⡅⠚⠛⠻⢥⡀
⠀⠀⠀⠀⠀⢞⠉⠀⠀⠳⣼⠏⠀⠀⠈⠉⢙⡷⢿⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⣀⠞⠉⠙⠓⠲⠤
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠖⠻⠀⠀⡀⠀⠐⠋⠀⠈⢶⣠⡟⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠛⠛⠛⠓⠒⠀⠀⠀⠀⠰⣄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⡼⠀⠀⠤⠤⣤⣄⣸⡟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⣸⠀⠞⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠈⣄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢥⣤⠀⠀⠀⠀⠀⠀⠀⠙⢲⡿⠥⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠱⠀⢀⠀⠀⠐⠲⠶⠒⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢠⠁⡄⣀⣤⠄⠀⠀⠀⠀⠀⡆⢠⡾⠤⠤⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣈⣶⡆⡸⠀⡄⠀⠀⢰⣠⢧⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠘⠻⣅⠀⠀⠀⠀⠀⢀⠀⢱⣦⡤⠤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠾⠿⠻⣿⠗⠚⠁⠀⠴⡺⢟⡾⠄⣼⣀⠞⠀⠀⠀⠀⡀⠀⢸⣄⢀⠄⢀⠀⠀⠀⠀⠀⠀⠲⣄⡀⠈⣷⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠈⢡⠏⣀⠔⢻⠀⠀⠀⢀⡄⠀⠘⡄⠸⠟⠋⠀⡘⢰⠀⡰⠀⠀⠀⠀⠈⠉⠉⡻⠗⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⣴⣴⣃⡄⠀⠀⡀⠀⠀⢠⡀⣿⣦⡼⠉⠀⠀⠀⠙⢢⡄⠀⢀⠃⣸⡾⠁⠀⠀⠀⢆⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠦⣽⣿⡿⠶⠒⠋⠀⢀⣀⢀⣳⣿⠏⠀⠀⠀⠀⠀⠀⠀⠁⢸⡌⢀⠟⠓⠒⠒⠒⠀⠈⢧⣧⣼⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡿⣷⠒⠦⣄⠀⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣇⣬⡴⠚⠁⠀⠀⠀⠀⠈⠻⠿⠷⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃⠈⠁⠀⠈⠇⠀⠀⠀⢄⢈⣠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠤⠬⣿⠿⣯⣄⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢄⣠⣬⣿⡯⠤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣸⠀⣀⣀⣀⣀⡤⠀⠀⠀⠀⢩⠀⠀⠉⠙⠂⠀⠈⠓⣤⣼⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⠛⠉⠉⠉⠻⡛⠉⠛⠛⠛⠛⠋⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⢆⠀⠀⠀⠐⠠⠀⠀⠄⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠰
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠄⠀⠀⠠⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠂⠀⠄⢠⠄⠂⠊⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣊⠠⠁⠀⠀⠀⠐⢘⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠡⢉⠀⢀⡀⠀⠀⠀⡀⠈⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡈⠀⠆⡈⠂⠄⡁⠀⢔⠀⡑⠀⡐⡂⠘⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠒⢄
⠀⠀⠀⠈⡄⣆⢱⠀⠀⠀⠀⠀⠀⡄⠁⠀⢠⠀⠈⠀⠈⠚⠋⠄⠉⢉⠁⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠃⢱⠘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠐⠃⠀⠚⠉⠉⠉⡉⠉⠉⠉⠐⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠀⠀⠌⠀⠀⠀⠊⠀⠀⠀⢀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠤⠒⠂⠀⠀⢠⠏⠉⠉⡁⠀⠀⠀⠠⠀⠈⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡘⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⠰⠀⠒⠂⢀⣶⠚⠈⠉⠉⠉⠉⠉⠉⠂⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⡞⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠠⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢷⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠠⠬⠙⠶⠤⠤⠤⠤⠤⠤⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠉⡙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡀⠬⢥⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⠀⠀⠀⢐⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠄⠀⠈⢁⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⢀⠀⠁⠁⢱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠐⠀⡄⡐⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⠻⢟⡲⣄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠊⠉⠉⠉⠋⠙⠙⢛⠟⠤⢠⣀⠀⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡏⠓⠀⠈⠑⠢⢄⣼
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣀⡤⠄⠤⠶⠶⠷⠦⢤⣀⡁⠀⠀⣤⡀⢀⠞⠙⢦⡀
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⡠⠖⢉⠃⠉⠂⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⠲⢌⡐⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣰⠏⠀⠀⠀⣠⠞⠋⡀⠈⠠⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠉⠢⣀⠀⠀⠀⠀⠳⡄
⠀⠀⣼⣿⠀⠀⣠⠞⢡⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⠀⠸⡄
⠀⣸⣿⠿⠓⠾⢿⣴⢨⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠸⡀
⢠⣿⣇⢹⠄⠒⡉⠈⢧⡀⠀⠁⠀⢐⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡄⠀⠀⠀⢧
⠸⠁⢹⠐⡎⠄⠀⠀⠀⠉⠒⢤⣈⣤⣄⣤⠤⠦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠛⡀⠀⠀⢸⡄
⡇⠂⢀⡇⡄⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣄⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⡁⠀⠀⠀⡇
⡇⠀⢸⣇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢷⣦⠠⠄⠀⠐⠀⠀⠈⢄⡄⠀⠀⠀⡇
⡇⠀⢸⣿⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⢸⠇
⢠⠀⠸⣿⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⡄⠐⡀⠀⠀⠸
⠈⠄⠀⢳⢿⡆⢀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠂⠂⡀⠀⠀⠀⠀⠀⣔⠃⠀⡇⠄⠀⠠⢄⠐⠰⠀⠀⢠⠃
⠀⠠⠀⠈⢷⣱⡈⢢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡀⠀⠀⠀⠀⠀⡽⠀⢀⠇⠀⠀⠀⠀⢰⠃⠀⢀⠂
⠀⠀⠑⡄⠀⢻⣵⣄⠣⣀⠀⠀⠀⠀⠀⠀⠀⣴⣫⣭⣍⢦⠀⢀⣠⠜⠁⢀⠌⠀⠀⠀⠀⠘⠃⠀⢠⠎
⠀⠀⠀⠈⢦⠀⠙⢾⣦⠈⠙⠛⠢⡀⠀⠀⣾⡇⣿⣄⣾⣼⡵⠋⠀⠀⢠⠮⠀⠥⠀⣀⠔⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠙⢆⡀⠙⢷⣤⡀⠀⠉⠛⠛⠻⠷⠶⠛⠊⠉⠀⠀⣀⣾⠣⠄⠀⣰⠖⠅⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠈⠛⠷⣶⣤⣤⣄⣀⣀⣀⣤⡤⠶⣛⣋⣠⡤⠾⠉⡃⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⡎⠉⠙⠛⠟⢛⠛⠛⠟⠉⠉⣁⡀⠦⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣰⢾⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢰⠟⢷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠸⠁⠈⠀⠀⠀⠀⣀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠁⠀⠀⠀⢀⠀⣠⢤⣀⡴
⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠻⢦⡀⠀⡠⠖⣷⠞⠙⠿⠛⠋⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⡀⠀⠒⠉⠟⠁⠈⠉
⠀⠀⠀⠀⢀⣴⡋⠀⠀⠀⠀⠀⣀⣀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⡀
⠀⠀⠀⣰⢿⠋⠉⣷⣠⡴⠞⠋⠉⠁⠀⣹⠀⠉⠻⠷⠄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠉
⠀⠀⠘⢷⡈⢷⣾⠟⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢷⡞⢁⣠⠶⠛⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⢿⣿⠿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠈⠉⠉⠛⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⣠⠔⠛⠳⢶⣖⠒⠲⠶⠦⠤⣤⣀⡀⠀⠉⠓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡠⠊⣱⠋⠙⢦⣀⠉⠓⢦⣄⠀⠀⠀⠀⠉⠓⠦⣄⡀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡠⠋⢠⠞⢡⡶⠒⠶⢬⡙⢆⡀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠞⣁⡴⢋⡤⣤⣍⣒⠶⠶⠗⠀⣹⠀⢠⠞⠉⣷⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣰⢇⣀⠻⠤⢌⡢⣄⡀⠉⢹⡆⡤⠞⢁⡴⠃⡠⣞⣅⣄⣤⣤⣀⣀⣀⣀⣘⣆⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠓⠤⣈⡉⠒⢄⡙⠦⣍⠙⢋⡴⢃⡴⠋⣠⠞⢡⡏⡿⣠⠤⣄⣀⣤⣤⣉⣉⡉⣹⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣭⡓⠦⣈⠓⢮⣛⠋⣰⠋⣠⠞⠁⠀⢸⢠⡇⢹⠀⢠⠖⣲⣦⠀⣼⢁⡟⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢠⠞⣡⡾⠁⢠⣀⠙⠲⢬⣿⣡⠞⠁⠀⠀⠀⡟⢸⠀⡏⠀⠈⠳⠽⠛⠁⣿⢸⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⠸⢹⠃⠀⠸⡄⠙⠶⢤⣉⡉⠀⠀⣀⡀⢀⡇⣿⠀⡇⠀⣠⢶⣦⣄⠀⡇⡿⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⢦⣸⣄⠀⠀⠹⢤⡀⠲⠤⠍⠉⢉⣼⠇⢸⠁⡇⢰⠃⠀⠘⢤⠿⠞⠸⡇⡇⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠙⠉⠳⣦⣀⠀⠉⠓⠒⠚⠋⠉⣀⡄⢸⢀⣇⡘⠒⠲⠤⠴⠦⠤⠴⠇⡇⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠻⣏⠉⠓⠒⠒⡚⠉⡹⠃⠸⠯⢭⣭⣍⣉⣉⣉⣙⣛⡛⢙⡇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠙⠲⠬⠯⠷⠿⠷⠤⠤⠤⠤⠤⠤⠴⠞⠛⠉⠉⢉⣩⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠠⠀⠂⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠠
⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠂⠀⠉
⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠑⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣇⠀⠀⠀⠀⠀⠀⡀⠄⠒⠊⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⣀⠀⠀⠐⠀⠀⠈⠉
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⡝⠗⠃
⠈⢆⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⠀⠤⠤⠄⠒⠂⠉⠀⠀⡼⠝
⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣍⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠯⢴⡾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣙⠓⠶⢾⣉⠁⠀⢀⡤⠚⠉
⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠀⠀⠀⣈⡓⢶⠉
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠧⠟⠈⣷
⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢦⡀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠈⢿⢦⣀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⣀⡴⡿⠁
⠀⠀⠀⠀⠈⠳⣌⠙⠻⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠛⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠈⠉⠉⠙⠛⠛⠓⠒⠒⠛⠛⠋⠉⠉⠁⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⠀⡆⡤⠀⠀⠀⠀⠀⠀⠀⡰⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢸⡆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠳⣾⡽⠁⢠⠀⠀⠀⠀⠀⠀⢠⣠⡲⠀⠆⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⢀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡝⠁⠀⠀⡀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠆⢹⠆⡄⠀⠀⠀⠀⠐⠠⢬⡾⢀⡀⢀⠐⠁⠀⠐⠀⠾⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁
⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⡧⢄⣿⢀⠀⠀⢀⠂⠀⠀⠀⢠⡷⠋⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠀⠂
⠀⠀⠀⠀⠀⠁⠀⣰⣄⢰⢁⠈⡏⣸⡋⠔⠁⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠄⢀⡀⢀⠀⠈⢦⡙⠛⡏⠻⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢄⠠⠀⠃⠐⠂⠠⠖⢃⠈⠀⠀⠀⢰⠀⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢼⣌⠀⢤
⠀⠀⠈⠐⣤⠀⠀⠆⠠⠀⠘⡇⠀⢠⠀⠎⢀⡇⠆⠁⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠹⠀⡘
⢀⠀⠀⠀⢻⡆⠀⣽⣤⡀⠀⠇⠸⣣⠎⡀⣿⠀⠀⠠⠋⠀⠀⢈⠁⠀⠀⠂⡀⠀⠈⠀⢿⣅⠤⠄
⠀⠀⠈⡀⡈⠁⠠⠁⠃⠈⢳⡶⡿⠁⠀⣠⠇⡀⠊⡰⠁⠀⠀⠀⠀⣰⣆⠀⡇⠀⠀⠠⠸⡄⢀⣤⠄⠐⠀⠀⢁⡰
⠀⠀⠀⠀⠙⢧⣰⠀⢀⠀⢸⠋⠁⠀⠀⢠⣾⡡⠊⢀⠀⠀⠀⠀⠀⠀⠉⠒⣧⠀⠢⠀⠖⣵⠋⠈⠀⢀⠀⠀⣸⣁⠐
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠑⢤⠀⠀⠀⠀⠘⠁⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⢦⣄⡴⡷⡰⠃⠀⠘⠀⠀⠛⢁
⠀⠀⠀⠀⡀⠀⠀⠱⡄⠐⢶⣄⣦⠀⣰⣤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡀⠙⠈⡿⠁⠀⠀⠀⡆⡀⠀⠚⠀⠁
⠀⠀⠀⠀⠀⠉⠒⢀⣸⣄⠃⠀⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⡇⠰⣤⠎⢀⣿⣓⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠁⢃⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⠀⡼⢀⣠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡡⠊⠛⠓⠦⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠁⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣾⡟⠁⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⢾⣿⣥⣀⡀
⠀⠀⠀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⡄
⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣄⣀⠀⠀⠀⠀⣸⣿
⠀⠀⠸⣿⣿⣦⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⣤⡾⣿⡟
⠀⠀⠀⢻⣧⠈⠉⠛⠻⠿⢶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⠾⠿⠛⠋⠉⣠⣿⠁
⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣀⠀⠀⠀⢀⣀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠎⡀⠀⠈⢋⢲⠞⠋⠈⠉⠋⠉⠛⠁⠈⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⡞⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣢⠖⢢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡉⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⢀⠆⠀⠀⠀⠀⠀⠀⠘⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⣁⠀⠀⣨⠀⠀⠀⠀⠀⠠⠀⢤⡠⠞⡀⠀⡀⢀⠖⠓⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⣗⠀⠐⠠⠀⠀⠀⠀⢠⣾⡶⣿⣆⠀⠀⠀⠀⠀⠀⠈⢹⣿⣧⣦⣤⡄⠀⠀⠀⠀⠀⠩⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠃⠀⠠⠀⣀⡀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠠⠘⠋⠻⠟⠁⡀⣀⠀⣄⣀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢇⠆⢀⣤⠂⠀⠀⢀⡇⠂⠀⠀⠀⠀⠀⡄⠀⢀⣀⡵⣅⣩⠴⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠓⠋⠛⠉⢷⠀⠀⠀⠀⠀⢸⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄⡴⠊⣿⡁⠀⠀⠀⠀⣿⠦⢤⡤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⠐⡂⢹⡤⢄⡀⠤⣀⣿⢐⠤⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠆⢀⠀⣀⣄⠁⠐⠀⠀⣀⣀⣀⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⡏⠈⠛⠦⢾⡶⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⢧⡀⠀⢀⣠⠊⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠐⠒⢴⡉⠉⠋⡇⠀⣀⢀⣿⡁⠈⠉⠡⠀⠀⠀⠳⢦⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⢀⠐⠋⠁⢀⠀⠊⠙⠞⢄⠁⠀⠁⠀⠁⠀⠀⠀⠈⠁⢀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡃⠆⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠰⢎
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠛⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠉⠑⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠛⠃⠉⠀⠀⠀⠀⠁⠀⠐⠐⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠁⠈⠉⠙⠓⠊⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡦⠀⠰⠆⠀⠷⠀⠘⠂⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⣠⡤⠄⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣠⡬⡇⢾⠁⢉⡇⠀⣗⠀⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠃⡀⠛⣈⡃⠚⣁⠀⣩⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡏⢹⣮⡗⠂⢸⡿⣇⢹⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠋⠀⠉⠉⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠶⠀⠰⠆⠀⠻⠀⠘⠃⠀⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣈⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉