Cyclist Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠈⠹⣿⣷⣦⣤⣄⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣷⣄⠀⢀⡤⠿⢿⠋⣧
⠀⠀⠀⠀⠀⠀⣤⣴⡖⠛⠀⠀⠈⠻⢿⣿⣿⣆⣘⣧⣠⠞⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⣀⣠⡤⠞⣿⣿⡏⣸⢷⣤⣠⣴⠶⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠉⠀⣴⣾⣿⣿⢡⠏⣨⡿⣿⣄⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠘⢦⣰⣿⠟⢿⣿⡟⢠⡿⠀⠈⠻⢧⣀⡀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⣀⣴⠶⠛⠛⣿⠷⣦⣾⠿⡅⠀⠸⣿⠁⢸⣇⠀⠀⠀⠀⠛⠃⠀⠀⠀⢰⡟
⠀⠀⠀⣴⠟⠁⠀⠀⢠⡏⠀⠙⣿⣦⣽⣿⣽⣷⣄⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣀⣤⣴⠆
⠀⠀⢸⡏⠀⠀⠀⠀⣸⣁⣠⣤⠾⢿⡿⣿⣻⠟⠉⠀⠀⠙⢷⣤⣀⣀⣀⣤⣴⣿⣥⣴⣾⣿⣿⣿⣿⣿⡟
⠀⠀⢸⡇⠀⠀⠀⠀⠙⠉⡤⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⡟⠁
⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣴⣾⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿
⠀⠀⠩⠿⠿⠿⠿⠿⠿⠟⠛⠉⠙⠓⠻⠿⠿⠟⠟⠿⠛⠛⠛⠉⠉⠉⠀⠐⠒⠛⠛⠛⠛⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠈⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠀⠀⢠⣹⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠘⠃⠈⠳⢤⣈⢿⣿⣷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠛⠉⠉⠉⠙⠻⠆⠀⢀⠲⣤⣍⣛⣻⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠟⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡿⠀⠈⠻⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠀⠀⠀⠀⠀⣧⠀⢀⠄⠀⠀⠀⣿⡀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢐⣦⠀⠠⣀⣷⣿⡼⠋⠀⠀⠀⠀⠘⠿⠖⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣲⣾⡟⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠰⣿⣟⡇⠀⠀⢠⣿⣾⣷⣾⣾⣷⣿⣾⠇⠙⣧⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠂⠳⣿⢸⣄⢀⣤⣽⣿⣿⠿⣿⡹⣿⣿⡇⣤⡀⠈⣀⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⢄⣻⣷⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠳⣬⡻⣆⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡀⠈⠻⠀⠀⠉⠉⣭⣝⢿⣿⠦⠀⠠⠴⢾⡿⢷⣤⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⠇⢀⡄⣀⣀⣠⡤⢤⣴⣶⣒⠀⠀⣰⣶⡟⠙⠢⣮⠻⣶⣄⣤⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⢀⡾⠶⠟⠛⠛⠋⠉⠉⣀⠀⢀⣾⣿⡏⠁⠀⠀⠃⢀⣼⣏⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠀⣴⡿⠁⠉⢀⣴⠋⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⣿⣿⠹⠿⠀⠀⠀⠰⣿⣿⣿⢷⡌⠿⣡
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⠀⣸⡟⠀⠀⢰⡟⠁⠀⠀⠀⠀⢀⣠⠞⢁⣴⢿⣿⡟⠟⠀⠘⠿⣶⣦⡀⠈⠉⢹⣿⡥⠺⠟
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⢠⡟⠀⠀⣠⢋⣾⠀⠀⠀⣀⡴⠋⣡⡾⠟⠁⣼⡿⠀⡀⠀⠀⠀⠙⣿⣿⡆⠀⠀⠉
⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⣠⠔⠀⡾⠀⠀⠐⢱⣿⣯⡾⠋⠉⢀⣴⠾⡋⠀⠀⢠⣿⠃⣾⡇⠀⠀⠀⠀⢻⣿⣷
⠀⠀⣠⣿⣿⠋⠀⣀⡴⠋⠁⠀⠀⠁⠀⠀⠀⣿⣿⠁⠙⣠⣴⠟⢁⣾⠁⠀⠀⣸⡟⠀⣿⠇⠀⠀⠀⠀⣸⣿⡟
⠀⣰⣿⡿⠁⢀⣾⣿⣿⣧⡀⡄⠀⠀⣠⣶⣿⣿⣿⣴⣾⠟⠁⢠⣿⠇⠀⠀⢀⣿⠁⠀⣿⠀⠀⠀⠀⠀⣿⣿⠇
⢠⣿⣿⠁⠀⢋⣽⠟⠉⠀⣼⠇⠀⢰⣿⣿⣿⣿⣿⠟⠀⠀⢠⣿⡟⠀⠀⠀⢺⣿⠀⠀⡟⠀⠀⠀⠀⣼⣿⡟
⣼⣿⡇⠀⠀⠻⠇⠀⢀⣼⣟⠂⠀⢸⣿⣿⣿⣿⠋⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠲⠴⠇⠀⠀⠀⣰⣿⡿⠁
⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣤⣀⠀⣈⠛⠋⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⡈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁
⠸⣿⣿⣷⣦⣤⣤⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠈⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣀⠀⢀⣀⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⣀⣸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣽⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢰⠙⠲⠟⠛⣧⣄⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣀⣠⡿⢷⡘⠀⠀⠀⡀⡿⠁⠀⣧⠀⠀⠀⠀⢀⡔⡀⠂⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠔⠋
⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⠀⠉⠀⠀⠀⣿⡇⠀⠀⣿⣧⡀⢠⡴⠋⠀⠀⠀⠀⡾⠃⠀⠀⠈⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⢀⣾⠞⠁⠀⠀⠀⠀⠀⠀⠐⣾⡇⠀⣴⣿⣋⢇⡞⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣰⠞⠋⠀⢀⡤⠂
⠀⠀⠀⣰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡟⠀⣿⣟⣳⠾⠀⢀⠁⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⢠⡤⠞⠁
⠰⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡴⠊⠁⠀⢰⣿⣿⡿⠃⡠⠛⠀⠀⡠⠀⢀⡴⠋⠁⠀⠀⠀⣁
⠀⠀⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠋⢀⣠⡆⢀⣾⠟⠁⠀⠈⠀⠀⠀⢀⠀⠘⠁⠀⠀⢠⣤⠴⠛⠁⠂⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣬⣹⣿⡉⢄⣨⠆⠀⠀⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠠⠛⢁⠀⠀⠀⠄⠀⠉
⠀⠀⠀⠀⠘⢆⡀⡀⠀⡰⠋⣶⣿⡿⣿⣿⣇⠀⠀⠀⣠⠴⠛⠁⡀⠀⠐⠐⠋⠁⠀⡠⠅⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠈⠀⢰⣿⣿⣇⣻⣿⡿⣤⣴⡎⠁⢀⠐⠋⣠⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣿⣉⠛⠓⢲⣿⣿⣿⣼⠁⣾⠏⣊⢻⡆⠀⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣴⣿⣇⡙⠲⣄⣼⣿⣿⣿⣿⡶⢫⡎⠁⢸⣿⡟⠃
⠀⠀⠀⣼⡿⢛⡏⢀⡾⠛⡻⣿⣿⣷⣶⣶⡾⢷⣄⣼⠃
⠀⠀⣼⣿⢁⣼⡷⠿⠤⣼⢷⡾⢿⣿⡿⠚⠀⠈⣰⠃
⠑⣺⣿⣧⣶⡿⣿⣿⢛⢧⣦⣶⡿⢿⣦⣬⣤⠞⠁
⢀⣿⡏⡿⢩⣿⣿⣵⠾⠋⠉⠁⠀⠀⠉⠉
⢸⣿⠏⣡⡿⠿⠋⠑
⣀⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣷⣸⣯⣛⣿⣭⣫⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⠶⢶⣤⣤⣶⣭⣻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣙⢻⣿⣿⡟⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠉⠙⢳⣽⣿⣿⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⠛⠳⣦⡀⢧⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡏⢿⣿⣿⣿⣛⣋⠀⠀⠀⠀⠀⠙⢢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⢻⣿⠿⠟⠛⠆⢀⡤⠋⠀⣠⠞⠁⢳⣤⣀⣀⣈⠁⠐⠒⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⢿⡶⠶⠶⣶⠋⠀⣠⣾⣷⣶⣶⡿⠿⠿⠛⠛⢻⣿⠓⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⠀⠀⠀⢿⡄⠀⢻⡀⣼⠃⠀⠀⠀⠀⠀⢹⣿⣷⡀⣀⣉⣩⣍⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠬⣍⣛⠷⢄⣼⣿⣀⣴⣿⣷⠄⢸⠀⠀⢀⣴⣿⣿⠿⣷⡉⠁⠀⠀⠬⣍⣛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⣿⠻⣿⣿⣿⣿⣿⠀⠏⠀⣠⣿⢿⡟⠁⠀⠙⣷⡀⠀⠀⠀⠀⠉⠳⣌⠻⣄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠈⢧⠹⣿⡟⠻⣿⣿⣤⣾⠟⢡⡟⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠈⢧⠹⡆
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣶⣶⣞⠁⠀⠀⠀⠬⡤⣽⣯⣿⣶⣿⠟⠁⠀⣼⠁⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠈⠃⣿
⠀⠀⠀⠀⠀⠀⢿⡀⡀⠀⠀⠀⢠⡸⢿⣿⠟⠀⠀⠀⠠⠤⢤⣿⣿⣿⣿⣿⡆⠀⠀⢿⠀⡀⠀⠀⠀⠀⠰⠝⠛⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣇⢳⡀⠀⠀⠀⠙⢲⣆⣀⣀⣀⣀⡀⠀⣰⣿⣿⣿⣿⣿⠇⠀⠀⠸⣇⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢩⣿⣿⣿⣷⣤⠄⠀⠀⠙⣦⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣝⡓⠦⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠻⢦⣙⡓⠶⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠾⠿⠿⠷⠾⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠾⠿⠿⠿⠶⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣧⣀⣀⣀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣿⣏⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡄⠀⠀⠛⠁
⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⣶⣦⣤⣾⣿⡏⠉⣿⣿⣿⢸⣿⣿⣷⡿⣿⣷⣶⣾⣿⣶⣶⣤⣀
⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⣽⡿⣿⣿⣷⣼⣿⣿⠇⢸⣿⣿⣿⣿⠟⣿⡆⠀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢠⣾⡟⠁⠈⢿⣿⣿⣿⠏⣴⣿⣿⣿⡿⠁⠀⠸⣿⣄⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⣿⡇⠀⠀⠀⠀⣴⣿⣿⣏⣀⠀⠀⢸⣿⣿⣯⣾⣿⣿⣿⣿⣧⣀⠀⠀⠘⣿⣿⣷⡄⠀⠀⠀⢸⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠻⠿⠿⠛⠛⠿⣿⣿⣿⣿⣿⡧⠀⠀⠸⣿⡍⠉⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⣸⣿
⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⣿⣟⡁⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠘⢿⣦⣄⡀⠀⠀⠀⠀⣀⣴⡿⠏⠀⠈⠉⠀⠀⠀⠀⠀⠹⢿⣦⣀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠙⢒⣤⣤⣤⣤⣤⣤⣄⣰⣿⠛⠀⠀⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⣠⠖⢀⣴⣾⠟⠁⠀⠀⠀⠀⣈⣽⣿⣿⣿⣦⡈⢢⡀⠢⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣽⣿⣿⣧⣤⣤⣤⣀⣀⣾⣿⣿⣇⢻⡙⣿⣷⡄⠙⡆⠙⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣆⠙⠿⣆⢘⣄⠴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣿⣿⣿⣿⠷⢬⣟⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⠑⠀⢈⣤⣿⣿⠟⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⣿⣿⣿⣇⠀⠀⠙⢿⣿⣿⣿⣿⡷⠀⠀⠀⡿⠛⠋⠉⠁⠠⠜⠛⠿⣿⣷⡀⠈⠄
⠀⠀⢀⣴⣾⠿⠿⠿⢿⣶⣌⣻⣿⣿⣿⣿⣷⡀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠘⡀
⠀⣰⣿⠋⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣸⣿⣿⣏⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢧⠀⠐
⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⠟⢻⡁⠀⠀⠙⢿⣷⡌⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⣆⠘⢷⡀⠁⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡤⢄⣀
⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠸⣿⡄⠀⠙⣦⠀⠀⠄⠀⡿⣟⠁⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⢻⣿⣶⡄
⣿⣇⠀⠀⠀⠀⣴⣾⣿⣿⡆⠀⠀⠀⠀⢿⣧⠀⣸⣿⠂⠀⠀⡸⠁⠈⢦⡀⠀⠀⠈⢿⣶⣄⣠⣾⣶⣦⣤⣴⣾⠟⠋⠀⠀⠀⣹⣿⣿
⢸⣿⠀⠀⠀⠀⢿⣿⠿⢿⣍⠲⢄⡀⠀⢸⣿⠀⣿⡟⠀⠀⡰⠁⠀⠀⠀⠀⠂⣀⠀⠀⠙⡛⢿⣷⣦⣾⣿⠟⠁⠀⠀⠀⠠⡾⠛⠎⠛
⠀⢿⣇⠀⠀⠀⠀⢷⣄⠀⠙⠳⣦⣙⠢⣼⣿⢰⣿⠇⠀⡼⠁⠀⢀⣠⣤⣤⣄⠈⠻⢶⣄⠘⣤⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠘⣿⣆⠀⠀⠀⠀⠈⠓⢄⡀⠈⠙⢷⣼⣿⣾⣟⣒⣾⣷⣶⣿⣿⣿⣿⣿⣯⣤⣴⡾⢿⣆⠉⠈⠙⣿⣿⣇
⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠙⠢⡀⢠⣿⣿⣿⠍⢹⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⢙⣆⠀⠀⢻⣿⡿⠿⣷⣦⡀
⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⣀⣼⣿⢏⣿⣿⣄⠈⢻⣿⡟⠉⠀⠀⠀⠀⠀⠀⣶⣄⣠⣾⣧⣤⣴⣿⣿⡇⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠋⠀⠀⢹⣿⣷⣆⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⡏⢸⣿⢿⣧⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠻⢷⣆⣠⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠈⣿⠚⣿⡀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢻⣧⢻⣧⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠈⢿⣦⣿⣷⡄⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠻⠿⠛⠁⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⣠⣤⣾⠿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣭⣥⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣏⢁⣴⣦⣄⡙⢿⡁⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣛⣛⣛⣛⡛⠿⠿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢛⣯⣝⢿⣿⡿⠋⠀⠀⣰⣇⠙⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⣿⣿⣷⣧⠀⠀⠀⠺⢿⣟⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣌⡁⠀⠀⠀⠀⢻⣄⡀⠀⠀⠈⠳⣄⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠙⠷⣄⠀⠀⠀⢘⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠈⠳⣶⣴⣯⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⡌⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣴⣻⡿⠇⠀⠐⠀⠈⠀⠀⡀⢺⣦⣶
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣤⣀⠀⠀⠀⣹⣿⣿⠿⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢹⣸⡠⣤⣤⣤⣄⡀
⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠈⢙⠷⣦⡾⠟⣯⠀⠀⣶⠀⠀⠀⢀⠜⠁⠀⢀⣴⠿⣯⣿⡟⠀⠈⠉⠻⠷⣄
⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⡄⠸⡆⠀⣿⠄⠀⡠⠁⠀⠀⢀⣾⠋⠀⠘⣿⢷⡀⠀⠀⠀⠈⠙⢷⡀
⠀⢰⡟⠀⠀⠀⠀⠀⢀⣠⢀⡀⠀⠈⢿⣿⣿⣿⡀⣣⣀⠉⠀⠊⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣞⣧⠀⠀⠀⠀⠀⠙⣷
⠀⢸⣇⠀⠀⠀⠀⠀⢾⡿⣾⡇⠀⠀⠀⠛⠟⢻⣦⣾⣿⣄⣠⣶⣦⣤⣀⣀⢻⡇⠀⠀⠀⠀⠻⠿⠷⠀⠀⠀⠀⠀⢻⡆
⠀⢸⣧⠀⠀⠀⠀⠀⠈⠀⠛⡷⠀⠀⠀⠀⢠⣿⠉⢿⣿⣿⠿⠿⠿⠿⠟⠉⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⢴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⠀⢀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠤⠙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠫⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⡀⣀⢋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠠⡀⠀⠉⠁⣬⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠒⠳⣄⡀⠀⠀⠀⣾⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠈⢡⠌⠀⣴⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣺⣷⠿⣫⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠯⣅⡀⠀⢀⣀⠤⢤⣤⣾⠎⡰⢋⣡⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠁⠀⠀⠘⠋⠁⠀⠀⠀⣙⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠤⠤⣤⣀⣀⣁⠀⠺⠟⠙⠀⠀⠀⡠⣖⢒⡒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⣄⠀⠀⠀⢈⠉⣀⠀⠈⢿⡷⣄⣿⠟⠉⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⢛⠟⣦⣈⢣⡀⠀⠈⠀⠀⡀⠀⠀⣽⣞⢇⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⢀⡇⠙⣧⠙⢦⡀⠁⠀⠁⠀⣀⣻⡏⠁⠁⣤⡠⠄⠀⢸⡇
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⡆⢸⠁⠀⢹⡇⠀⠙⢦⡀⡀⠀⣹⣿⠇⠀⣬⣿⠿⡜⠀⢸⡇
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣴⢁⡏⠀⠀⢸⡧⠀⠀⣸⣿⣟⡧⠿⢿⡂⠀⠵⠾⠒⠁⠀⣾
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢿⠟⠀⠀⠀⢸⡇⠀⢀⣿⣿⠟⠁⠀⠘⣇⠀⠀⠀⠀⠀⣼⢃⣀⠤⠤⠒⠂⠁⠁
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠑⠀⠀⠀⠀⡼⠁⠰⠿⠛⠁⠀⠀⠀⠀⠘⠷⣤⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠻⠿⠛⠋⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⣸⣿⣿⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣯⣭⣽⣿⡼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⣀⣸⣿⣿⣿⣿⡇⠀⠀⠈⠙⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⣩⣿⣿⠟⢱⣿⣿⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⣶⣿⣿⣿⣵⣿⡟⠁⢠⣿⣿⣿⣿⡟⠛⠛⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣠⣿⣿⣿⣿⣿⣿⡄⢠⣿⠟⣼⣿⠈⢿⡀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡰⠁⢿⣿⣿⢿⣌⣿⣿⣿⠏⣸⡏⢹⣇⠘⣧⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣰⣷⣀⣼⣿⣏⣸⣿⣧⣿⠏⠀⣿⠁⠀⢿⡀⠹⡄⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢺⡟⠷⢽⣿⣿⣿⣿⣿⠏⠀⠀⣿⠀⠀⠘⢧⣤⠷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠇⠀⣸⣿⣿⣿⣿⠏⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠻⣿⣿⣿⡋⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⠾⠛⠿⠟⠛⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣄⣠⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⢹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢀⠐⢲⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⡼⣟⡶⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠭⠎⠃⠀⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⠾⡀⠀⠀⠀⡰⢿⠢⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠜⠁⠀⢱⡀⠀⠈⠐⣦⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⡜⠰⣈⣦⣀⣡⠤⠷⠶⠛⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢼⠖⠉⠙⠿⣧⣹⡤⠤⠤⠄⠐⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡿⣶⣏⢳⡀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣧⣿⡜⠻⣿⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠔⢻⣿⣿⣿⡿⣄⠘⡅⠀⢿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠸⣿⣹⢸⢿⣞⣆⢸⣦⡈⠳⡄⠚⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡀⠀⣷⠹⣾⢿⡞⡞⣦⣿⠓⣤⠽⣄⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⣹⣘⣿⣸⣿⠘⡠⡿⣁⡾⠀⢈⡆⠘⣿⡄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⡀⠉⠀⠀⠀⡟⡗⢧⣣⠈⡃⢲⣭⡈⡇⢩⣧⠀⡀⠀⠀⢄⠜⠀⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢣⠀⠀⠀⠀⡗⡇⠀⠀⠀⠸⡘⡌⠉⠀⢸⣿⠀⠇⡀⠀⢀⢁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡳⣄⠀⡰⣣⠇⠀⠀⠀⠀⠳⡘⠄⠠⢾⠏⠐⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠈⠲⠤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣴⠀⡰⢁⠞⠁⠀⠀⠐⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡟⠀⠀⠀⠀⣠⣿⣿⣿⠇⣜⠵⠋⠀⠀⣀⢀⡷⣫⡤
⠀⠀⠀⢠⣶⣷⠀⣀⠀⠀⠀⠀⠀⠀⢀⢆⡿⣱⢇⢠⣾⣴⣿⣵⣿⣃⠴⠀⠀⠀⢀⠔⣱⣯⡾⠋⣀⡀
⠀⠀⠀⠸⣿⣧⠌⢿⣿⡀⠀⠈⠐⠂⠞⠼⣰⢧⣿⢿⣾⣿⣿⣿⣿⡟⠀⠀⢀⠔⣹⣿⣿⣫⣠⣴⠏⠁
⠀⠀⠀⠀⠈⣿⣶⣿⣿⣿⠀⡄⠀⠁⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢟⢁⣤⠖⣡⣿⣿⣋⣉⢼⣯⠖⠁
⠀⠀⠀⠀⠀⣿⡟⠉⠙⠻⠀⢸⣶⣾⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢃⣴⣾⠟⣻⣿⢿⡥⣚⡡⠄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿⣿⣿⡗⠀⢸⣿⣿⣿⣿⣿⡝⣻⣴⣿⢟⣷⣿⣿⡷⡿⠚⠉⣀⣤⡦
⠀⠀⠀⠀⢏⠀⠀⣴⠳⠀⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣾⣿⣿⢿⣷⣿⣟⡩⠟⠁⢀⣴⣛⣫⣥⠒
⠀⠀⠀⠀⠘⣠⣼⡉⠀⠀⣠⣿⣿⣿⣷⡀⠙⣿⡿⣻⣿⣿⣿⣿⣿⠿⠎⠉⣠⣴⣾⣿⣿⣿⠿⣩⡄
⠀⠀⠀⠀⠙⠃⣿⠦⣄⣠⣹⣿⢿⠻⣿⣿⠀⢘⣴⣿⡿⢷⣾⠋⢛⣠⣶⣿⣿⣿⡿⢛⣉⡤⠖⠋
⠀⠀⠀⠀⠀⠀⣿⠋⣻⣏⣻⡿⠤⣬⣟⣾⣇⠀⢄⣍⡻⣿⣿⡾⢿⣿⣿⣿⣿⣯⣶⠉⠁⠀⢤⣆
⠀⢀⣠⡴⠶⢾⣿⢤⣁⠊⣿⣇⠀⣿⣿⣿⣿⡄⠹⣟⣳⠘⣿⣟⣯⣿⣿⣿⣿⣭⣼⡿⠛⠛⠋⣀
⢠⡿⠁⠀⠀⢸⣿⠀⠉⢻⡿⢋⣳⣯⣿⣟⡻⠇⣼⣿⢑⡆⣿⣿⣿⣿⣟⣿⣿⣿⣿⠴⠔⠞⠁⠁
⣿⠁⠀⠀⠀⣸⣿⠀⠀⠀⢻⣿⣿⣿⡿⣿⡵⢞⣩⣌⣿⠇⣿⣽⡿⠟⠃⠈
⢿⡀⠀⠀⠀⠛⠈⠀⠀⠀⢸⣿⣿⣿⡿⣾⣿⣷⣽⣿⣥⠾⠋⠈
⠘⢷⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⣿⠿⠋⠉
⠀⠀⠙⠷⣶⣤⣤⣴⠾⠋⠀⠈⠉
⣿⡯⣟⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣾⡿⣿⣿⡿⠛⠛⠛⠛⣛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣷⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⣿⣿⣿⣷⣶⣶⣾⣷⣶⣦⣤⢴⣶⢤⣄⣀⣠⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠶⠶⠶⠶⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⣿⠀⠀⠀⠀⣀⣬⣾⣿⣿⣿⣿⣿⣿⣿⡷⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⡿⣵⣿⡿⠏⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣃⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⢀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣻⣿⡿⠿⠟⣿⡇⠀⠀⠸⣿⣿⣿⠉⠀⣘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣏⠀⠀⠀⢠⣿⠟⠛⠛⠋⠛⣿⣿⣏⢷⣿⣿⣿⡿⢻⣿⣄⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣳⣶⣆⢠⠿⣷⡄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣏⠀⣸⠁⠹⣆⢀⣤⣤⣶⣶⣶⣶⣦⣭⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠿⠛⠛⠛⠛⢻⡾⣶⣬⡻⣦⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⠀⣠⣾⢿⠋⠉⠀⠀⠀⠀⠉⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⢠⡿⠀⠀⠙⢿⣮⠳⣄⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠏⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢻⣷⠈⣳⣶⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠹⣄⠀⢀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠈⣿⡆⠛⠿⠿⣿⣍⡤⣼⣿⣿⣿⣷⣆⣀⣀⣠⣽⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡿⣷⣿⣾⣿⣿⣿⣿⡿⠉⠁⠈⠻⣿⣁⡀⠀⠀⠀⠀⢀⣿⣿⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠈⠳⣬⣿⣿⣿⣿⠋⠀⠀⠀⠀⠂⠀⠈⠉⠁⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠷⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣄⣀⣠⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣻⣿⣶⣦⣤⣤⣤⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢦⣥⡄⠀⠀⠀⠀⠀⠀⣀⢀⣠⣄⠈⠛⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠃⣀⣸⡆⠀⠀⠠⣤⣷⡀⣹⣿⣿⣿⣵⡟⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⣿⣿⡟⣿⣿⣴⢾⡿⣿⣿⠿⢿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢿⣿⡿⣿⣵⣾⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣿⠀⣼⣿⣷⣿⣿⠿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⣿⡿⢺⢷⣿⣦⣤⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢿⣿⢿⣭⣿⣿⣿⣏⢿⣿⣿⣿⣯⣧⣼⣷⣾⣗⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣻⠊⣿⣿⣿⣿⣼⣿⣿⣿⡟⢿⠟⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣽⢹⡆⣿⣿⣿⣯⣭⣿⣿⣿⣿⠢⣶⣾⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⠀⠀⣿⡿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠛⠿⣿⣿⣶⣿⣿⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣆⢰⣄⢠⡏⢹⣮⣿⢏⣾⡿⠋⠁⠈⠙⣸⣿⠟⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣹⢿⣶⣯⣭⣴⣿⣿⡟⠂⠀⠲⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣿⣿⣿⣿⠿⠿⡿⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠁⠀⢀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⣴⣿⣿⣿⠿⠋⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠎⣻⠛⡿⣿⣿⣯⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡄⠻⣦⣏⣀⣸⣿⣿⠉⢀⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⠉⠉⣿⣿⡿⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠿⠷⣾⣏⡙⢷⡄⠸⣿⣇⠹⣿⣿⣶⡟⢣⣤⣴⠾⠿⠛⠿⠷⣦⣄
⠀⠀⠀⢠⣾⠋⠁⠀⠀⠀⠀⢀⡟⠙⢿⣎⠻⣦⣻⣿⡀⠀⠙⣿⣿⣾⠛⢧⡀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢿⡆⢈⣿⣿⡿⠀⢰⣯⣿⣿⣦⡀⠑⢄⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⢸⣿⠿⣿⣛⣷⣤⣿⣾⣇⣸⣿⣿⣧⣼⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⠇⠀⠀⠈⢻⣻⠿⣿⣿⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠀⠀⠀⠀⠈⠙⠒⠊⠹⣿⣏⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠈⠙⠿⣶⣤⣤⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣶⠾⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣒⡶⣄⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣾⠏⢻⢻⠴⠚⠛⠛⣫⠟⠻⣯⣯⠰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠈⣾⠖⠛⣩⢟⣥⠶⣿⣿⣯⣣⡻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠈⡷⣮⠵⠾⠧⠾⠏⢭⣿⣿⣿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣳⣴⣶⣤⣄⠘⡗⡟⠀⠀⠀⢀⡴⠋⠀⣸⣿⣿⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣦⣭⣿⣮⣻⣇⠀⠀⣠⣾⣿⣿⣿⡿⠟⢹⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⣈⡉⣹⣷⣤⣼⠧⣧⣽⣟⣋⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⢡⡟⢷⡀⠀⢛⢿⢻⡛⢯⡙⣻⡏⠀⠀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⢩⡿⠷⣄⠙⢦⡈⣯⣾⣷⢮⣿⣿⣷⣶⠛⠉⠁⠀⠉⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢀⡾⠁⠀⠘⢷⡈⠻⣾⣿⣿⠀⢹⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠘⣧⠀⠈⣏⡿⣄⣾⣿⡴⠛⠀⠙⢦⡀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⣿⣠⠞⡉⠛⢻⡍⢿⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠟⠻⣍⣠⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠖⠛⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄⠀⠻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣦⣄⡈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣦⠄
⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠿⠶⠶⢶⣄
⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⣸⣿⡇⣶⠶⢾⣭⣭⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠻⠶⠶⢶⡶⠾⠽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢎⣿⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢋⡾⣫⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠈⣷⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣭⣥⡟⣵⣿⣷⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠘⣷⣀⣤⣴⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⣠⣾⡿⢛⣭⣵⣶⣶⡎⠉⣿⢿⣷⣌⢻⣿⣿⡜⣷⡀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⣠⣾⣿⠛⠉⠉⠀⠀⠉⠙⠻⢿⣷⣄
⠀⠀⠀⣼⣿⢋⣾⣿⣿⣿⣿⠟⢀⣾⠋⠀⠙⢿⣷⡹⣿⣿⡌⢿⡄⠀⠀⢀⣼⠏⠀⠀⠀⠀⣼⣿⠋⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⢰⣿⢇⣾⣿⣿⣿⣿⠏⢠⡾⠁⠀⠀⠀⠘⣿⣇⢿⣿⡇⣠⣿⣶⣶⣾⡁⠀⠀⠀⠀⣸⣿⠃⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⢸⣿⢸⣿⣿⣿⣿⠃⠰⡿⠷⠶⠶⠶⠶⠶⣿⣿⠶⠶⣾⣿⣾⡟⣿⡏⣷⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠛⢶⡦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠸⣿⡎⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣾⣿⡟⣧⣻⠿⢟⣱⠟⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⢠⣦⢻⣿⣌⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣱⣿⣿⡇⠈⢙⣿⡋⠁⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠉⠳⠙⢿⣷⣤⣀⠀⠀⠀⠀⣀⣠⣶⣿⢟⣴⣿⣿⣿⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⣀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⡿⠿⠛⠋⠀⠘⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠳⣄⡈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢳⡀
⠀⠀⠀⣀⡤⠖⠛⠋⠉⠉⠛⢲⣾⣄⠀⠀⠀⠙⠦⣄⠀⠉⠓⠶⢤⣤⣀⣤⡤⠞⡿⠁⠀⠀⠙⣦⣤⠴⠖⠒⠒⠶⠤⣄⡀
⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠳⣄⠀⠀⠀⠈⠓⢦⡀⠀⠀⣀⠀⠀⠀⣸⠃⠀⠀⣠⠞⠉⠳⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠉⠳⣌⡹⣄⣀⣠⠏⠀⠀⣴⠃⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢻
⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠉⠉⢳⡴⢶⡧⢤⣄⣀⠀⠀⠀⢻⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⡼⠁⢸⡄⠀⠀⠈⠙⠓⠲⠬⡇
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢙⣦⠌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⢀⣀⡤⠞⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣊⠩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⣒⣒⣥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠈⠁⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⢌⣉⣀⣒⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⢶⠒⠒⠊⠀⠀⠀⠀⢀⡠⣔⡲⠝⣊⢽⣼
⠀⠀⠀⠀⠀⢀⠤⢔⣒⣒⣒⡠⠦⡃⠀⠀⠀⣀⢤⣲⣯⠓⠉⠀⣠⣾⠟⣁⠯⠦⠤⠤⠄⣀
⠀⠀⠀⡠⢪⠕⠉⠁⠀⠀⢀⣾⠟⠪⡑⣮⠛⠋⠁⠀⣿⠀⡠⡾⢋⢕⡩⠒⢻⢯⠉⠉⢉⠒⢍⡢⡀
⠀⠀⡐⡕⠁⠐⢄⠀⠄⢀⣼⠏⠠⠂⠈⢎⢆⢠⠔⠚⠛⢮⠊⢠⠣⠊⠀⠀⠈⣇⡇⠀⠂⠀⠀⠙⢜⠄
⠀⢠⢱⠀⠀⠐⠀⠁⢀⣾⣟⣈⣀⣀⠀⠨⡜⣇⢀⣖⡄⠀⣧⢇⠋⠐⠀⠀⠀⢸⣧⡀⠀⡀⠀⠐⠘⡜⡀
⠀⢸⢸⠀⠀⠀⠀⠄⠻⢴⠟⠛⢉⠉⠉⠉⣟⠦⡉⢫⣀⡴⢹⢸⠂⠀⠀⠀⠀⢼⣭⡗⢀⠀⠀⠀⠐⡇⡇
⠀⠀⢇⢆⠈⠀⠀⠂⠄⠀⠀⠀⢀⠀⠐⡼⡸⠀⠈⠉⠀⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱
⠀⠀⠈⢪⡲⡀⠀⠀⠀⠀⠀⠀⠀⣁⢞⠕⠁⠀⠀⠀⠀⠀⠀⠘⢌⢦⠀⠀⠐⠀⠀⠀⠀⠀⠀⡴⡣⠃
⠀⠀⠀⠀⠉⠪⠝⣒⡠⠤⢄⣚⠪⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠭⣒⠤⠄⠤⠀⠴⣒⠭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⣒⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠃⠀⠀⠀⠀⠀⠀⠀⠠⣖⡒⠒⠚⠋⠉⢉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠽⠂⢰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠰⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⢀⡈⠢⡀
⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⡉⠉⠓⠲⠞⢀⣄⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⠙⢆⠙⢤⠴⠒⠋⠉⣉⠉⠑⠲⢤⡀
⠀⠀⠀⡴⠋⣠⠔⠊⠉⠉⠉⠉⠙⢲⠀⠈⠢⡳⣄⠑⢄⠀⠀⠀⠀⠀⠀⢀⠇⢰⠃⢀⡴⠃⡀⢰⡊⠉⠁⠈⠉⠉⠒⢤⡈⠳⡄
⠀⢀⠎⢀⠞⠁⠀⠀⠀⠀⠀⠀⢠⠇⡰⠙⣄⠘⡌⠢⡈⠳⡄⠀⠀⠀⠀⡜⠀⡏⢀⡎⢠⠎⠉⢦⠑⣄⠀⠀⠀⠀⠀⠀⠙⢆⠈⢆
⠀⡜⠀⡎⠀⠀⠀⠀⠀⠀⢀⡴⢁⠜⠁⠀⠘⡆⠸⡀⠘⢦⡈⠢⣠⡤⣴⠁⡸⠀⡸⠀⡎⠀⠀⠀⠱⡌⢢⡀⠀⠀⠀⠀⠀⠈⡆⠘⡄
⠀⡇⢸⠀⠀⠀⠀⠀⠀⣞⢁⡔⠁⠀⠀⠀⠀⠃⠀⡇⠀⠀⠑⢄⠙⠇⠃⢠⠃⠀⡇⠀⣇⣀⡠⠤⠤⠞⠂⠙⡆⠀⠀⠀⠀⠀⢸⠀⡇
⠀⡇⠈⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡇⢀⠇⠀⠀⠀⠈⠳⡄⠀⠘⠋⣉⣁⠀⣤⠤⠴⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⡌⠀⡇
⠀⠸⡄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡜⠀⠀⠀⠀⠀⠀⠳⡄⡞⠉⠁⠘⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡼
⠀⠀⠙⢄⠘⠢⣀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣵⢣⡀⠀⠀⠘⢆⠈⠢⣄⠀⠀⠀⠀⠀⠀⢀⡠⠚⢀⠜⠁
⠀⠀⠀⠀⠑⠦⣈⠉⠒⠒⠒⠒⠊⢁⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⠦⣀⠉⠒⠒⠒⠒⠊⢁⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠊⠉⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢒⣈⣹⠖⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠠⠤⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⢴⡴⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠤⢀⡀⠀⠀⠚⢋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡩⢂⠡⠐⣁⢅⠠⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣡⡤⠶⠖⠒⠶⢶⣤⣁⠢⣀⢞⢤⠱⡀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⢊⢕⠨⢊⣹⡜⡶⠲⡶⠶⠶⡣⢄
⠀⠀⠀⠀⠀⠀⣠⢊⡴⠋⠉⢂⠀⠀⠀⠀⡎⠀⢉⢟⣵⠻⡀⠡⡱⡀⠀⠀⣀⠔⡪⠚⢁⢎⠔⡱⢡⣶⠋⠁⢁⢡⠀⡇⠀⠀⠀⠑⣽⢦
⠀⠀⠀⠀⠀⠀⡘⠝⠁⠀⠀⠀⢢⠀⠀⡸⢀⢔⠕⠁⣈⣷⡘⡄⠱⡈⡨⠥⠒⠁⠀⡠⡡⠃⡜⣰⠏⠀⠙⢦⡀⢆⢢⡇⠀⠀⡠⠊⠀⠑⣕⡀
⠀⠀⠀⠀⠀⠠⡘⠃⠂⠤⢀⡀⠀⢣⣠⢗⣵⠡⠒⠉⠀⠘⣇⢰⠀⢱⣴⠤⣤⣠⢊⠔⠀⢰⢀⡟⠀⠀⠀⠀⠉⢺⡜⡇⡠⠊⠀⠀⠀⠀⠘⡤
⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⢉⢾⣁⡛⣁⣄⡀⠀⠀⠀⣉⢈⠁⢗⡅⠠⡈⡟⠁⠀⠀⢀⣸⡗⠒⠒⠒⠒⠒⠒⣳⣽⡐⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠐⣱⠀⣀⠤⠒⠈⠀⡘⠀⢢⠀⠀⠁⠂⠒⢰⡙⠛⠀⠈⠛⠒⠻⡀⠀⡀⠀⠈⠙⡰⠀⠀⠀⠀⡠⠊⠀⡇⠙⢦⡀⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠱⡹⡀⠀⠀⠀⢀⠃⠀⠀⢣⠀⠀⠀⢠⠱⠁⠀⠀⠀⠀⠀⠀⠈⠚⠚⠃⠀⠀⠱⣧⡀⡠⠊⠀⠀⠀⡇⠀⠀⠙⢦⡀⡠⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠮⡢⢀⠀⡌⠀⠀⠀⠀⢃⡠⣂⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⠦⣀⠀⠀⠀⡇⠀⠀⢀⠠⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠫⠵⠒⠒⠒⠬⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠫⠔⠒⠓⠒⠬⠒⠉






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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠆⠠⠀⠀⠃⠀⠑⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⢰⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢀⠀⠐⠂⡰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠐⠚⠁⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠳⠤⢄⠀⢀⠠⠊⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡋⠀⠀⠀⢐⠂⠀⠀⠀⠀⠸⠶⢖⠒⠲⠦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠠⠀⠐⠒⠦⢤⠁⠀⠀⠀⢀⡀⠀⠀⠀⢀⡃⡀⠀⠐⠄⢀⡀⢈⡒⣄⠀⠀⠀⠀⠀⠀⠀⠈⠒⣕⢄
⠀⠠⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠙⠢⡀⠀⣠⡁⠀⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠃⣄⡄⠀⠉⠒⠤⢁⣴⠋⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⡄
⢰⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠹⠂⠀⠀⠘⠭⢶⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⡈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠊⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠱⡐⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠈⠃⡀⠀⠀⠀⠀⠀⢀⠀⡢⠂
⠀⠀⠈⠪⠐⠄⢀⠀⠀⠀⡀⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣭⣿⣯⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣒⠠⠖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⡔⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣷⣄⣀⣀⣤⣤⣶⣶⠿⠿⠛⠛⠛⢿⣿⡆
⠀⠀⣾⡟⠒⣀⣀⣐⣚⣿⠿⠟⠒⠒⢦⣴⣿⣿⠛⠋⠉⠉⠀⠀⠀⠀⠀⡠⣾⠞⢿⠿⣄⠀⠀⠀⠄
⠀⠀⡨⣿⣖⡩⠄⠐⠒⠀⠀⠩⣒⣴⣾⠟⠹⡿⡀⠀⠀⠀⠀⠀⠀⢠⢮⡾⢁⣴⠞⢣⠹⡄⠐⠂
⢠⢎⢞⠔⠙⠄⠀⠀⠀⠀⠀⣀⡾⠛⠉⢂⠀⢻⣇⠀⠀⠀⠀⠀⣔⡵⠋⣰⡿⠑⠁⠀⢠⢳⠀⠀⠀⠀⠀⠀⠊⡂
⣤⣮⣎⣀⡀⠀⠢⡰⠀⣠⢾⠟⠁⠀⠀⠀⠃⠘⣿⡄⠀⠀⡠⣢⠟⠁⢐⡿⣄⣀⠀⠀⠀⢣⣣⡀⠀⠀⠀⠀⠀⠈
⠅⣼⠁⠈⠉⠙⠾⣿⣫⡕⣯⣤⣤⣤⣤⠤⠭⣤⡽⢧⣤⢎⡞⠁⠀⠀⣿⠀⠀⠀⠉⠉⠒⢢⣿⣷⡂⠀⠀⠀⠀⠀⠐
⠀⢿⠀⠀⠀⠀⠰⠙⣿⠿⠛⠓⠛⠛⠩⠿⠿⣟⡀⣹⣏⠔⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠈⠋⠢
⠀⠘⠇⠀⠀⠀⠀⠀⠈⢹⡀⠀⡀⠀⢀⣐⣀⠘⣍⣶⣅⡈⠀⠛⠛⠃⠀⠀⠱⡀
⠀⠀⠀⠰⣀⠀⠀⠀⠀⠈⠉⠋⠉⠭⠉⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠍⡂⠀⠄⠠⠀⠂⠠⠜⠋
⣶⣶⠶⠶⠶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣶⣶⣶⣶⣶⣶

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣰⣧⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡠⠤⠤⠄⣄⣤⣄⡀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠠⢖⣫⣭⣶⣶⣶⣮⣭⣵⡿⣌⢷⡴⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢯⣜⣡⣖⣮⣽⣿⣶⣾⣿⣭⣷⡧⣄
⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠋⠉⠉⠉⢻⡿⣿⣦⡙⣿⣆⠘⢷⡄⠀⠀⠀⠀⠀⠀⣼⠃⣴⣿⣿⡿⠟⠛⠉⠉⠉⠉⢻⠿⣿⣮⡳⣄
⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⢠⡟⠁⠈⠻⣿⣮⢟⢷⣤⠟⣦⡀⠀⠀⢀⣼⢃⣾⣿⣿⠛⠳⣄⠀⠀⠀⠀⢠⠃⠀⠈⠻⣿⣞⢦
⠀⠀⠀⣾⣿⠅⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢹⣿⡇⠀⠻⣆⠠⢽⣭⠉⣹⠃⠘⣿⣿⠁⠀⠀⠈⢳⡄⠀⢠⠇⠀⠀⠀⠀⢻⣿⡎
⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⣴⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⢷⣨⡤⣴⠧⠤⢼⣿⡗⠒⠖⠂⣒⣒⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠘⠻⠟⠁⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⣎⣿⣿⣿⣷⡤⠾⣿⣿⠟⢛⣋⡩⠽⠿⠛⠛⠁⠀⠀⠀⠀⢐⣿⡇
⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠣⣱⢿⣛⡾⠠⠄⢻⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠁
⠀⠀⠀⠀⠙⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠉⣅⡀⠀⠀⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣶⣤⣶⣶⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣶⣴⣦⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣩⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢃⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⣤⡏⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⡀⠀⠀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡈⣿⠈⠁⠀⠀⠀⠀⠀⠈⠁⠂⢦
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠂⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣦
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢻⡀⠈⢷⡀⢣⠀⠀⣠⡶⠋⠀⠀⢀⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⢡⣶⣿⣤⣤⣤⠤⠤⠀⠠⢬⡧⠀⠼⣧⣼⣠⡶⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢷⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠭⡉⡙⠛⠛⠟⠻⠶⡿⠶⣾⣼⣿⠻⡇⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⣺⠅⠀⠻⣥⣏⡳⠃⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣤⣤⣤⣤⣶⣿⣿⣾⣦⡶⠒⢂⠀⡀⠀⡂⠀⢠⡤⢦⣐⠮⠤⠦⣤⡀⢿⣳⣮⣍⣒⣒⣒⣲⣬⣴⣿⣏⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠋⠉⠉⠉⠉⠉⠉⠉⠃⠈⠐⠈⠉⠀⠀⠀⠄⠂⠀⠛⠃⠜⠁⠀⣀⣈⠡⠀⠙⠋⠉⠉⠉⠙⠉⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⡇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠄⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⡄⠀⠀⢀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⠀⠠⠄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⠤⠀⠀⠀⠀⠄⠂⠒⠂⠤⢄⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠔⠂⠉⠉⠡⠂⢀⠑⢄⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠐⠁⠈⠁⠙⡁⠀⠉⠀⠀⠀⠀⠀⠈⡄⠀⠑⠈⠎⠐
⠀⠀⠀⠀⠀⠀⠀⢨⢀⣀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠒⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠤⠌⡀⢰⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠐⡔⠈⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⢁⣀⣤⣤⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⠚⡄⠀⠀⠀⠀⠀⡆⢠⠀⠔⠁⠌⠀⢀⡇⠇⠀⠀⣠⠴⠖⠒⠢⣄⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢁⠀⢀⠠⠠⡀⡇⠈⠁⠀⢂⠀⢀⠞⠁⠸⠀⠚⠁⢸⠆⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠈⠀⡊⠀⠀⠸⡇⠀⠀⠀⠀⢄⡎⠀⠀⣴⡆⢠⠀⠘⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⢆⠀⣷⠀⠀⠀⠀⠰⠀⠀⠀⠀⡟⠀⠀⢰⠁⢱⠈⡐⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠑⠾⠀⠀⠀⠠⠘⠓⠒⠁⠀⠇⠀⠀⣿⠀⠀⡆⢁⠓⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⡜⠀⠀⠀⠀⠀⠀⠘⡆⢸⠀⠀⠀⡏⠀⠀⠛⡀⣀⣁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⢸⠀⠀⢰⡇⠀⠀⠀⠑⠈⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⣁⣠⠇⠀⠀⠘⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢧⡀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠉⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⢀⣀⣠⠴⠚⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠛⠛⠛⣻⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠁⣠⣴⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡴⢤⣤⡀⠀⠀⠀⠀⠀⠉⣿⠀⢠⣿⣿⣁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⢁⣤⣶⠟⠀⠀⣀⠤⢤⣴⠁⠑⣼⣿⣹⣿⣄⡴⠖⠒⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⣾⣯⡀⣀⣠⡎⠀⠀⡾⠉⢳⠀⢈⣿⣻⡖⡟⠁⢠⣤⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣹⠓⠄⣻⣻⣟⠁⣽⠀⠆⠻⠇⠀⢠⠃⠛⠋⠈⠋⢻⡄⠀⠿⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⣉⣠⣄⠁⠀⣜⣦⣤⣷⣇⣠⣀⣤⣿⣦⣤⣤⣦⣶⣶⣿⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤
⠀⠀⠀⠀⣀⣀⣠⣤⣤⠶⠶⠿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠗
⠀⠀⠊⠉⠉⠉⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠘⠛⠛⠋⠉⠉⠉⠉⠁

⣷⣶⠾⠾⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⣶
⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠸⣿⣶⣤⡉⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⢿⣿⡿⠀⣠⣤⡄⣠⡄⠉⣻⣿⠘⣿⡄⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⠿⠿⠁
⠀⠀⠀⣰⣿⣮⣧⣿⣦⠀⠀⠀⢀⣴⣶⣶⣿⣿⣥⣤⠙⠻⣿⡟⠋⠀⠹⠿⢷⣆⣆⣦⣤⣄⡀⠀⠀⣴⣿⣼⣵⣿⣆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⢻⣧⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣹⣿⣿⣿⢿⡇⠀⢠⣿⣿⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣧⠈⠛⠀⢸⡿⣿⣿⣿⡇⣿⡆
⠀⠀⠀⠁⣿⣿⣿⣿⠈⠁⠀⢸⣿⡟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠛⣿⣿⠀⠀⠀⠈⠁⣿⣿⣿⣿⠈
⠀⠀⠀⠀⣿⡿⢹⣿⠀⠀⠀⣸⣿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢿⣿⡀⠀⠀⠀⠀⣿⡇⣿⣿
⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⠻⣿⡄⠀⠀⢀⣿⡇⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢴⠔⢜⣫⠝⣠⠀⠀⠀⠀⠀⠀⠀⠰⣄⠸⠟⣀⡖⠀⠀⠀⠀⠀⠀⠀⣀⣄⢰⡶⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀
⠀⢰⣿⣷⢸⣿⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢦⣯⠜⢳⣶⠻⣼⡵⠋⠀⠀⠀⠀⠐⠿⠿⠏⠺⡾⢒⣕⡏
⠀⠀⣿⣇⡼⠿⡌⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⢠⣶⣶⡆⢴⢶⠀⠨⡪⣇
⠀⢸⠉⠉⡆⠀⡗⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠸⠿⠀⠿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠈⠙⠁
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣶⡶⠖⢶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⡠⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⢰⣶⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⣠⣿⡇⢙⠸⣿⣤⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣤⣤⢧⣤⣬⣥⣄⠀⠀⠀⠀⠀⣠⣼⣧⣤⣿⣄⣀
⠀⠀⣾⡚⠷⣿⡾⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢾⣿⡿⣿⣿⠟⠀⠀⠀⠀⠘⠁⣿⣯⣀⣿⣌
⠀⠀⠘⢷⣤⣿⣦⣾⠏⠀⠀⠀⠀⠀⠀⡞⠛⡇⠀⢸⠀⢠⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⠀⠀⠀⠀⢀⣈⣛⣁⣉⣛⣁⣈⣓⡀
⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠐⠓⠒⠓⠒⠛⠒⠚⠂⠀⠀⠀⠀⠈⠉⠁⠘⠙⠁⠉⠉

⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⢀⡀
⠀⠘⣿⣿⡉⣩⣿⡿⠁⠀⠀⠀⠀⠀⣄⢰⣶⢀⡟⠑⠚⠛⠀⠀⠀⠀⠀⠤⠀⢁⣠⣀⡀⠁⠤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣽⣷⣾⣍⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠘⣧⣼⠃⠀⢠⠄⠀⠀⠀⢰⣶⣾⢷⡆⢠⡾⣷⣶⡆
⠀⠀⣿⣿⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⣧⠀⠀⡄⠀⠀⠀⠀⠈⠉⠙⠛⠁⠈⠙⠋⠉⠁
⠀⠀⠘⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠐⠂

⠀⠀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⢋⢁⣉⢻⠇⢀⠀⠀⠀⠀⠀⠰⡄⢸⡿⠘⡿⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⡆⠐⢼⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠂⢸⣌⣛⣫⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣲⠟⠁⠀⠀⠀⠀⠀⠀⣠⣧⡄⢾⣿⠂⢸⡇⠀⠀⠀⠀⠀⠠⠖⢛⣿⣶⣜⠿⠟
⠀⠀⠀⠈⠙⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⣸⣿⠀⠞⠓⠀⠀⠀⠀⠀⠀⡉⠉⣉⢉⡉⠁
⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⡀⡇⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⢉⡉⠱⠶⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⢂⠀⠙⢃⣤⡀⠺⣦⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⢿⠇⠀⠙⢿⠿⠀⢠⡄⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⣀⠀⢰⣷⡄⠀⣤⡄⠸⣿⠀⠰⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠻⣷⡄⠹⣿⡄⠸⠟⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠃⠤⠈⠛⠀⠈⠁⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠐⠂⠐⠒⠶⠶⠂⠉⣉⡴⠾⠀⠀⠀⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⣄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣀⣀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠙⣦
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢌⠡⠤⠀⠰⠆⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠉⢣⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⡤⠛⠁
⢸⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⢠
⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠈⢠
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠈⢳⣄
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠛⠋⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠙⢷
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠉⢶⡄⠀⠀⠀⠀⠀⠷
⢹⣆⠀⠻⣶⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠂
⠈⢻⣆⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠁
⠀⠀⠻⣆⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⢦⡀
⠀⠀⠀⠙⡆⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠈⠀⢱⡀
⠀⠀⠀⠀⠀⠉⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠁⢀⡀⠰⠆⠉⠉⣀⣀⣀⣀⣀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⢧⠘⢧⠀⠀⠀⠀⠀⠀⠸⠃⠘⠿⢀⡠⠐⠃⠀⠀⠠⠄⠚⠋⠀⠀⠀⠁⠀⠁⠀⠀⠘⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠈⡇⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣿⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⢀⣤⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠘⠀⢀⣠⠴⠶⠶⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠇⠀⠘⢟⠀⠀⠀⣤⣄⠀⠀⠀⡀⠀⡄⠀⠀⢱⡄⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢙⡀⠀⢶⠀⠀⠀⠉⠀⠀⠀⠀⡀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠤⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠂⠀⣼⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⢃⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠷⠶⠶⠖⠀⠰⠾⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⡀⠀⠘⣧⣦⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠃⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⢿⡀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⢿⡄⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠈⢿⣆⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠈⠻⣄⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢻⣄⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠑⠀⠀⠀⢀⣠⡴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⢹⡆⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠂⠀⢻⡄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠐⠀⢀⡀⠐⠒⠀⢿⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠞⠁⠀⣦⠀⠀⠀⢿⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢡⡄⠀⠀⠸⣇⠈⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⠈⠳⠀⠀⠀⢹⡆⠀⠀⢶⠀⢙⣥⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠁⠀⢠⠄⠀⢸⠁⡄⠀⠈⠛⠀⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⡀⠀⠀⠀⠁⠀⢠⡇⠀⠀⠀⠀⠀⠈⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢠⠀⢸⡏⠀⠀⠀⠀⠀⠀⠸⣆⠀⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠼⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢂⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⢀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣆⠀⣠⡄⠀⢀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣾⣿⣶⣿⣿⣿⣿⣿⣆⣴⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⠿⠿⢟⣫⣶⣿⣿⣿⢭⣽⣛⡝⠂⠩⣭⣛⡛⠻⠿⠿⠿⢟⣛⣫⣵⣿⠟⣿⡿⢟⡪⣔⣮⠳⢍⡙⠛⢫⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣑⣃⣀⣠⠄⣐⣬⣽⢟⣋⡭⠷⠦⢶⣢⣤⡉⢔⣲⣭⣿⣿⣷⣮⣭⣿⣿⣿⣯⣙⣶⠾⠫⢾⣿⣿⣭⣖⣿⡶⠿⢛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠙⠋⣉⣉⣭⣭⣅⣛⠻⢭⣛⣫⡴⢮⣽⠷⠾⠿⠿⠶⡾⢿⣿⠿⣭⣷⣶⣮⠭⠽⠿⠛⠛⣒⣙⣫⡵⠾⠛⣉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣼⠻⠷⠶⢖⡫⠽⣛⣴⣬⠭⣿⣛⠤⣶⠾⢝⣟⣭⣝⣿⣿⣾⣷⣽⣍⣋⣙⣀⣈⣊⣛⠽⣵⣒⠴⢞⣋⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⣭⣭⣭⡭⢽⣓⠶⢿⣻⣶⣬⡵⢞⣛⣯⡥⢶⣿⣥⠯⠽⣟⣿⣶⠭⢭⣭⡉⣉⣩⣭⠭⢴⣞⡯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢭⣿⣶⣢⢌⣉⣑⡒⠒⠂⢘⣫⢭⠒⣉⣽⣖⣛⣩⣭⣽⣭⣭⣽⣛⠤⠮⣌⡕⠀⠚⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣭⣛⡻⠿⣙⣻⣤⣤⠈⠶⣯⣝⡻⣛⠭⣑⣻⣧⣶⣾⣿⡿⣛⡿⢾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⢿⣤⣞⠿⠯⠉⣭⣯⣿⡶⠾⠧⣬⣽⣿⢥⣼⣟⡻⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠟⠛⢭⡴⣬⠴⠾⠿⠟⠟⠋⠛⠈⠁




⣶⣶⣶⣶⣶⡾⢶⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣾⢿⡾⠶⡶⠶⢾⣶⡾⠾⠾⠶⠶⢾

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⢷⣄⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠛⠻⠷⣾⣟⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢙⣷⡾⠟⠛⠋⠛⠛⠿⣶⣄
⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⢠⣿⠛⣷⡌⠻⣧⡀⠀⠀⠀⠀⣸⡏⠀⣰⡿⠋⠻⣆⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠘⣿⡀⠈⠻⣦⡀⣀⣠⣿⠁⢠⣿⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⣿⡇⠀⠀⠈⢻⣾⣿⡇⢀⣸⣯⣤⣤⣴⠶⠾⠿⠇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢿⣿⠟⠛⠙⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣶⣶⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠁⣨⡵⠒⠒⠲⢶⣾⣯⡉⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣿⣯⣤⣤⣤⣴⣿⣟⣟⢿⣄⢣⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣂⣃⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠮⠿⣿⣿⣿⣟⠛⠛⣿⣿⣯⠁⣩⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣦⣌⣻⣿⣿⣧⠀⠈⢻⣿⣿⠀⠀⠉⠀⠀⠀⠀⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠈⠻⣿⣿⣿⣦⡤⠤⢿⣿⠤⠤⠆⠀⠀⠀⠀⠀⠈⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠞⢿⡙⢧⠁⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⣀⣤⣶⠁⠀⠘⣧⠀⣷⠀⠀⡸⠫⠀⠈⠢⣄⡀⢀⣄⡀⢀⣤⠾⠋⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢻⡿⢿⣀⢄⠀⣿⢠⡿⠀⡰⠁⠀⠀⠀⣀⠈⠛⢿⣭⣿⠟⠁⠀⠠⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠓⢄⠉⠳⣍⣿⣼⠇⣴⣡⣤⣶⣿⣆⣈⣷⡎⠖⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠢⣸⣿⡿⠹⣿⣿⡿⠿⠛⠋⢉⠀⢹⡄⠀⣿⡟⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣴⠾⠋⠙⣿⣆⠹⠇⠀⠀⠀⠀⠘⢷⣿⣿⢻⣿⡇⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠤⠀⠀⠀⠀⠀⣾⠃⠀⠘⣿⣷⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠻⣼⣧⡀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠙⠉⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣴⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠘⠀⢿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⣤⣤⠐⣲⡿⠁⠁⠀⠀⠀⠀⠀⠈⠻⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠠⢠⣀⣀⠀⢸⣷⣮⣿⡯⣹⠋⠀⢀⢠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⣾⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠢⡤⡘⣿⣿⣷⣌⢻⣿⣿⢽⢿⣤⣌⠁⣈⡿⠆⠀⠀⠀⢨⠁⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠫⣫⡿⣿⣿⣷⣿⣿⡅⠁⠉⠉⠉⠉⠉⠉⠁⠀⠈⢸⠳⢴⢃⡘⠈⠻⠋⠑⠉⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣿⣿⠟⠉⠓⠒⣲⠖⠒⠒⠒⠒⠲⡖⠒⠚⠢⡀⠙⠷⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡁⠀⢀⡴⠞⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⢄⣀⢝⢶⣫⣤⣾⣿⣶⣤⣤⢀⠀⢀⠀⢀⠙⢦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⡇⠄⣩⣵⣶⢻⣻⣷⣾⢣⣿⣿⣿⣷⣷⣷⣷⣾⡏⣽⣿⣶⡆⣴⠀⡦⢤⡄⢠⡶⠀⠀⠀⡀⠀⠘⢿
⣿⣿⣿⣿⣿⣿⣿⣛⠿⠟⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⠁⠺⠦⠻⣅⠠⠔⠈⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⢚⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣒⣓⣖⠒⠒⣒⣲⡶⠶⣞⣉⣩⡤⣶⠒⣿⡹⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠭⢿⢛⣉⡥⠤⢲⡾⣿⣧⢻⣧⣻⣧⠽⠗⣋⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠉⠉⠙⢓⣲⡆⠀⠀⠀⠈⠓⠒⣋⣩⠤⠖⢚⣉⣷⠸⣟⣩⣭⡴⣶⡞⢿⡏⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠉⡏⠉⠀⢀⣀⡤⠤⠖⢛⣉⡥⠴⠒⠋⣩⠞⢉⡷⠻⣿⡸⣿⡘⣿⣘⣿⠼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡷⠒⠋⣉⣠⠤⠖⠚⠉⠀⠀⠀⣠⠞⢁⡴⠋⠹⡴⢿⠷⣛⣛⠭⠵⠒⠋⠉
⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⢤⣀⡀⠀⠀⣠⠞⢹⠀⡗⠚⠉⠁⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⢳⠘⣯⠤⠤⠤⣄⣀
⠀⠀⢀⡴⠊⠁⢀⣀⣤⣤⣄⣀⠀⠉⣲⠞⢁⠔⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠋⠀⠀⢀⡴⠚⠉⣇⢳⣠⣤⣀⣀⠈⠙⠲⣄
⠀⣰⠋⠀⡠⠚⠹⡄⠀⡇⠀⡸⣻⠞⢁⠔⠻⡀⢸⠀⡇⠀⠀⠀⢠⣀⣠⠞⢁⡴⠋⠀⠀⠀⣰⠋⠀⡠⠾⡹⡌⣧⡇⠀⡸⠛⢦⡀⠈⢣⡀
⣰⠃⢀⡾⣄⠀⠀⢳⡀⡇⣼⠟⢁⠔⢙⣆⠀⢹⣸⣀⣷⣀⣀⡤⢽⢲⣭⡷⠋⠀⠀⠀⠀⣰⠃⢀⣞⡁⠀⠙⢷⠸⡇⡼⠁⠀⢀⣹⡆⠀⢳
⡏⠀⢸⣀⣀⠙⡲⣤⡷⠿⣁⣴⠿⠾⠿⠛⠚⠋⠉⠉⠀⠀⣏⢠⣏⡞⡏⠀⠀⠀⠀⠀⠀⡏⠀⣸⠀⠉⠙⠲⣬⡷⠿⡥⠖⠚⠉⠀⢹⠀⠈
⡇⠀⢸⠉⠉⠉⣉⠽⣧⣴⠷⣦⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣬⡷⠿⠚⠁⠀⠀⠀⠀⠀⠀⡇⠀⢹⠛⠉⢉⡭⢟⣷⣴⠛⠯⣍⡉⠉⢹
⢹⡀⠈⢧⡴⠚⠁⣰⠁⡏⢣⡈⠙⠢⣤⠎⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⣦⠚⠉⢀⠎⢸⠉⢧⠀⠀⠉⢲⠏⠀⣸
⠀⠳⡀⠈⠳⣄⣰⠃⠀⣇⠀⠳⣀⡴⠋⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠣⣤⠏⠀⢸⠀⠘⣆⢀⡴⠋⠀⡰⠃
⠀⠀⠘⠢⣄⠀⠉⠓⠒⠛⠒⠋⠁⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠈⠙⠒⠚⠒⠒⠋⠉⢀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣟⣉⣙⣛⣛⣿⠷⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠭⢾⡛⣉⣉⡤⠴⢶⣯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠛⠒⠲⣦⠀⠀⠀⠀⠘⠷⠖⠚⣉⣩⡤⠶⠚⢋⣧⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢶⠒⡞⠛⠉⠁⠀⠀⣀⣠⠤⠖⠚⢋⣉⡤⠴⠒⢋⡽⠛⣦⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⣠⠴⠖⠚⢉⣁⡤⠴⠒⠋⠉⠀⠀⢀⠔⠉⣠⠞⢳⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡴⢿⠀⣯⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁⠀⠀⢧⠘⡆
⠀⠀⠀⠀⣀⡴⠖⠋⠉⠉⠉⠉⠉⠓⠲⣄⡀⣠⠊⢀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁⠀⠀⠀⣠⠼⡆⢻⠉⠉⠉⠉⠓⠲⢤⡀
⠀⠀⣠⠞⠁⢀⣠⣴⠖⠒⡖⠒⠶⣤⣀⣠⠟⢁⡴⠋⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁⠀⠀⢀⡴⠋⠀⢀⣽⡈⣷⢲⠒⠶⢤⣀⠀⠉⠳⣄
⠀⡼⠁⠀⡴⠋⠀⠸⡄⠀⡇⠀⡼⣡⠟⢁⡴⠋⠹⡄⢸⠀⣿⠀⠀⠀⠀⠀⢠⠞⠁⣠⠞⠁⠀⠀⠀⢠⠎⠀⢀⠞⠙⢦⣧⠸⣼⠀⢠⠎⠈⠑⣄⠀⠘⢦
⣸⠁⠀⡼⠧⣄⡀⠀⢳⡀⣇⣼⠟⢁⠴⣋⣹⡆⠀⢹⣸⣀⣿⣤⢤⡴⠒⠚⢧⣠⠞⠁⠀⠀⠀⠀⢀⡏⠀⢠⢯⣀⡀⠈⠻⡆⢿⣠⠏⠀⢀⣀⡬⢧⠀⠘⣇
⡏⠀⢸⣇⣀⣀⣙⣲⣬⠷⠻⣅⣴⠿⠿⠟⠒⠛⠉⠉⠁⠀⠀⠀⢸⡀⢾⠹⣌⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⡟⠀⠀⠉⢓⣲⣽⠞⢿⡖⠚⠉⢁⡀⢸⡆⠀⢻
⣇⠀⢸⡏⠉⠉⠉⣩⠽⣦⣴⠷⣶⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣽⡶⢧⣹⢶⡄⠀⠀⠀⠀⠀⢸⠀⠀⣿⠛⠋⢉⣩⠽⣻⣦⡞⠻⢭⣉⠉⠉⢹⡇⠀⣸
⢹⡀⠀⢧⣀⡴⠋⠁⣼⠙⡏⢣⡈⠙⠢⣄⣠⠇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠿⠖⠋⠁⠀⠀⠀⠀⠀⠘⣇⠀⠸⣤⠖⠋⠀⡼⠁⡟⠹⡄⠀⠈⠙⠲⡼⠀⢀⡟
⠀⢳⡀⠀⠳⣄⠀⣰⠃⠀⣇⠀⢳⡀⢀⡴⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⢦⣀⡼⠁⠀⡇⠀⢳⡀⠀⣠⠞⠁⢀⡞
⠀⠀⠙⢦⡀⠈⠙⠳⠤⣤⣿⡤⠴⠛⠉⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠙⠳⠤⣴⣧⣤⡤⠷⠚⠁⢀⡠⠋
⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣄⣀⡀⠀⠀⣀⣀⡤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⣄⣀⣀⡀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠙⢻⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⢀⣼⠏⠙⣿⡿⠋⠉⢹⣿⣄⡀⠀⢀⣾⢿⡟⠛⠛⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⣬⣿⣿⣿⣿⣦⣴⣿⡋⠙⠛⠻⢿⣿⣦⣰⣾⡛⢡⣄⣠⣿⣿⣤⠀⠀⣀⠈⠉⠛⠟⢃⡿⢁⣤⣶⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠠⠿⢿⠟⢁⣤⣾⣿⣿⣿⡿⠿⢋⣴⣟⠀⣠⣴⣾⣿⣿⣿⣤⣤⣟⣦⣾⣿⣿⣿⠏⣠⣾⣿⣷⠶⠖⠀⢹⣿⣿⣿⡿⠭⣴⣁⣀⡀
⠀⠀⢀⣠⠶⠶⢶⣯⣷⣾⣿⣿⣿⣿⣿⣥⣤⢻⣿⣿⡻⣿⣿⢯⣟⡝⠀⢀⣯⣹⣿⣿⡿⠉⢡⣾⣿⠟⠉⠀⣀⣠⢠⣿⣿⣿⣿⣦⣤⣴⡟⠉⠉⠀⠄
⠀⠀⡞⠁⠀⠀⡌⢈⣿⣿⣿⣿⢛⣩⣤⣬⢁⡛⠈⢿⣷⢌⠁⣛⠟⣉⣷⠚⢂⣾⡿⠟⠛⠛⠹⠛⣿⣆⠀⢼⣿⡷⠟⣻⣿⣿⣿⣿⣿⣀⠈⢆⠀⠀⠀⢑⡀
⠀⠀⡇⠀⠀⠀⣽⣿⣿⣿⣿⢣⣿⣿⣿⡟⣿⣿⣎⢳⡍⠈⣷⠈⢸⣿⣿⣦⣼⢣⣾⣿⣿⢷⣶⡄⢌⠛⠱⣄⠓⣴⣾⣿⣿⣿⡿⠹⣯⠁⠀⢘⡿⠀⠀⣸⣇
⠀⠀⠈⠀⠀⠀⠀⠐⢻⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⢸⣿⢀⣴⡆⢿⣿⣿⣿⣶⢸⣿⣿⣿⣿⣿⣿⢸⣷⢀⣩⡀⣿⣿⣏⢹⣿⣿⣟⣿⣿⣿⣿⣷⣶⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣻⣷⣮⣿⣿⣿⣿⣿⣿⣟⣥⣤⣿⣿⣮⡻⢿⣿⣿⣯⣿⣿⣿⣿⣿⠿⣾⣋⣸⣿⣧⡙⢟⠋⢾⣿⠟⠼⠿⣿⣿⣿⣿⡟⠉⠛⠓
⠀⠀⠀⠀⠀⠘⢛⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⡕⠏⠙⠿⣿⡿⠿⡟⠛⠛⢛⠃⠀⠙⠷⠂⠀⠀⠛⠃⠀⠈⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠛⠛⠉⠉⠉⠻⠷⠀⠀⠀⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⢅⠀⠐⠀⠀⠀⡀⠀⠔⢀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠢⠀⠀⠀⠀⠀⢀⠘⢀⠀⠀⠀⠐⠁⠠⡀⠀⠄⠐⠠⢄⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠄⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠑⣀⠌⠀⠀⠀⠈⢀⣤⣴⣶⣶⣿⡿⣷⣶⡶⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠴⠶⠿⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷⡿⠷⠿⠿⠿⠷⠤⠄⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠀⠀⡐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⢀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⡏⠙⣷⢸⣷⠀⡖⣿⠁⢠⣿⡇⠀⡦⠉⣿⠁⣾⡇⠀⣸⣼⣿⠉⢷⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣷⠀⣿⠈⣿⣴⠇⣿⠀⢸⣿⣿⢸⠇⠀⣿⠀⣿⡇⢀⡇⣿⣿⣠⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⣿⢸⣿⢀⡟⠀⢻⣿⠀⣿⠖⢸⡏⢻⣿⠀⠀⣿⠀⢻⣧⡾⠁⢿⣿⠻⡄⢸⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠋⠉⠀⠀⠈⠉⠀⠙⠃⠈⠁⠈⠁⠀⠀⠉⠀⠈⠉⠁⠀⠈⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⣀⣀⣀⠀⠔⢢⠀⠀⣀⠔⠂⠀⡃⠀⠠⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠈⠑⠑⠀⠁⠊⠁⠀⠊⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡶⣶⣤⣄
⠀⠀⠀⠀⠀⢶⡦⢀⣀⣀⡀⠀⠀⠀⠠⠴⠋⢈⡉⣻⣷⠀⠀⠀⠀⠈⠿⢇⣤⣤⣤⠀⠀⠀⠄⠐⠋⢀⡤⣈⣿⠇
⠀⠀⠀⠀⠀⠀⣰⠿⠛⠙⢻⣦⠀⣀⠀⠐⢒⡿⣾⡋⢀⣀⡀⣀⣀⣀⣠⣟⣋⡉⢉⡟⠀⡒⠒⢢⣉⣹⠻⣯⣄⠀⠠⡄
⠀⠀⠀⣠⠠⠾⠿⠞⢉⡽⠛⠀⢴⣶⡆⢀⣿⣿⡇⣷⣬⣿⣿⢹⣹⣿⣛⠛⠉⠴⠛⢁⣴⣄⢀⠺⠛⠛⠒⠿⡈⠁⠀⢸
⠀⠀⣠⠴⠶⢿⣃⣴⣶⠀⣶⡷⠶⢭⣿⡿⠿⠛⠛⢿⡻⢿⣧⣿⣿⣿⣿⣴⣿⡇⠐⢿⣿⠿⠏⢀⡤⠶⠶⢶⡌⣷⠶⡅
⠀⢰⠃⠀⠀⠀⠙⡆⠀⢹⢇⠁⣠⡾⠋⣇⢀⣀⠀⣡⣿⠀⡞⠀⠀⠀⠀⠘⡆⠀⢄⠀⣀⠶⠛⢀⣇⡤⢖⣀⣾⠇
⠀⠸⡀⠀⠀⠀⢀⠇⠀⠘⢧⠚⠡⠶⣶⡿⣧⣴⡿⠟⠃⠀⠹⣄⠀⠀⠀⠜⠁⠀⠈⣂⣁⡚⢹⡿⠛⣶⣿⡟⢉⣀⣀⣀⡀
⠀⠀⠉⠲⠶⠂⠀⠀⢠⡴⠚⠛⠓⢶⡏⠀⠸⣿⣓⠶⡚⠋⠛⠻⢯⡉⠀⠀⠀⠴⠋⠉⠈⠉⠻⡅⠀⠸⣿⡽⠻⣅⠀⠈⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠹⡆⠀⠙⣏⠀⠈⠂⠀⠀⠀⣧⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⡄⠀⢹⡇⠀⠀⠁⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⢀⠏⠀⠀⠸⣆⠀⠀⠀⠀⠀⡸⠁⠀⠀⠣⡀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⠄⠊⠀⠀⠀⠀⠑⠤⣤⡤⠴⠋⠀⠀⠀⠀⠈⠳⠦⠤⠖⠈⠀⠀⠀⠀⠀⠈⠒⠖⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢁⣿⡿⠙⠿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣤⣾⡿⠁⠀⢀⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣯⣶⠿⠛⠁⣀⣴⣾⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠜⢨⡏⢹⠟⢛⣟⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⠋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠾⠦⣼⡋⠉⠉⠉⠉⠻⣿⣿⣿⣟⠉⣹⢧⡀
⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠖⠲⣶⣿⡙⢦⡀⠀⠀⠘⣿⣿⡿⢿⣷⣯⡀⣳⡤⠶⠒⠒⠒⠶⣤⡀
⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⢀⣿⠁⠙⢦⡳⣄⠀⠀⢹⣿⣧⠀⣿⣿⣿⣯⢣⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢳⡈⠳⣄⠘⣿⣿⣼⣿⣿⠛⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣷⡇⠀⠀⠀⠀⢸⡇⠀⠘⢦⣿⣿⣿⣿⠉⠀⣀⣀⣄⣿⣿⣦⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠇⠀⠀⣸⣿⣿⣿⣿⡛⠉⠉⠁⠀⢸⠿⠃⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠲⣿⣿⠻⠿⠛⠁⢳⡀⠀⠀⠀⠼⠆⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠙⠲⣄⣀⡀⡀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

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

⠀⠀⠀⠀⢠⡤⣤⣄⣠⣤
⠀⠀⠀⠀⠈⠛⠒⠶⣟⣿⡛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⣿⠀⠀⠀⠀⠀⠀⢠⡞⣩⣟⣾⣛⣓⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡙⣶⠶⠶⠦⣄⣠⠞⣸⠃⠉⠁⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡤⣤⣠⡿⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⣺⡃⠀⠀⠀⠀⠀⠀⢠⣶⡖⠒⠒⠲⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣿⣭⣛⣓⡶⢤⣤⣀⡈⠛⠻⢯⣭⣒⣒⠒⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⣼⠟⣆⠻⡍⠉⠛⠲⠮⣭⣝⣳⡟⣸⡋⠉⠉⠁⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⡟⠀⣾⡀⠘⢧⠹⣆⠀⠀⠀⠀⠀⡿⢰⢯⣝⢦⣀⢀⣤⠖⢛⣉⣩⣭⣭⣉⠛⠲⣤⡀
⠀⠀⠀⠀⣠⠶⠋⣁⣠⣤⣼⠇⢀⣏⠙⠳⣬⣷⡘⣆⠀⠀⠀⣼⢃⡟⠀⠈⢳⣝⠻⣤⢾⠋⢹⠀⠀⡇⠈⡟⠲⣤⠙⢦⡀
⠀⠀⢀⡾⠁⣠⠞⠻⡀⢸⡾⠀⢸⣯⠷⣄⠈⢻⣷⡈⢷⡀⢰⠇⡾⠀⠀⢠⡟⢩⣷⣌⠻⣷⡀⡇⢰⠁⡸⠁⠀⡨⢷⡀⠻⡄
⠀⠀⡾⠁⣼⠋⠲⢄⡱⣼⡇⠀⣾⡣⢊⡹⢷⡀⢻⣷⡄⣷⠿⣼⣧⠤⢤⣾⣤⣯⣤⣽⣿⣮⣹⣿⣸⣠⠃⣠⠊⠀⣀⣷⠀⢻⡀
⠀⢰⡇⠀⡟⠉⠓⢒⣽⣿⢡⢠⣿⠿⠓⠒⠚⣧⠸⡇⡟⡵⣒⡢⡙⣦⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣀⡉⠛⣧⠒⠉⠀⢸⡇⢸⡇
⠀⠸⡇⠀⣿⠉⢉⡡⠔⡻⣳⡟⢻⡻⢭⣉⠉⣿⢰⡇⢷⣱⡿⠕⣡⠟⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠋⢀⣼⡉⠒⠒⣾⠃⢸⠇
⠀⠀⢻⡄⠹⣖⠉⢀⠞⠀⡇⢸⠀⠙⢦⠈⣹⠏⣸⣃⣨⠟⠛⠛⠛⠒⠒⠲⣖⠲⣖⢲⠖⢒⡶⠲⡖⢺⡋⢣⠈⠓⣴⠏⢀⡟
⠀⠀⠀⠹⣆⠙⠳⣎⡀⢰⠁⠈⡆⢀⣠⡿⠁⣴⠃⠈⠙⠂⠀⠀⠀⠀⠀⠀⠙⣦⠘⠷⣤⣎⠀⢸⠀⠀⣇⣀⣷⠞⠁⣠⠟
⠀⠀⠀⠀⠈⠳⢦⣈⠙⠛⠒⠒⠛⢋⣡⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡉⠛⠛⠒⠚⠋⢉⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠚⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠷⡄⠀⠀⠀⠤⠠⢤⠴⣬⣃⠄⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢢⡍⡶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⣎⡑⠀⠀⠀⠀⠀⠀⡀⠀⢲⡀⠉⠀⠀⠟⡒⢠⣁⣶⡚⠻⠀⠠⠄⠀⣠⠶⠟⠀⠙⠿⣍⠙⠃⠠⠮⣍⠒⠅
⠀⠀⠀⠀⠀⠀⠰⣅⡀⢀⡞⠿⢦⡳⣆⠘⡃⠋⢀⣀⣠⠀⠀⠁⢀⠀⢀⡈⠙⠈⠀⠀⠙⠂⣌⣰⣖⡯⠀⠀⠀⠀⢀⠔⠸⡁⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠁⠀⠉⣺⠄⠀⠀⠙⢪⡦⠟⠖⠉⠁⠙⠖⠲⡖⠛⠳⣜⠁⢦⠐⣀⣤⠤⣄⣶⣧⣈⡃⠉⢀⣀⣀⡘⠲⡈⡇⠀⣀⣀⡐⠠
⠀⠀⠀⠀⠀⠘⢦⣴⣴⣇⠀⠀⠠⠲⠀⠙⣦⠀⠀⠀⢤⣀⠀⠘⠄⢀⠈⠛⠀⠹⠀⠈⠠⡼⠁⠁⠈⠙⠷⠋⣀⢹⡇⠀⢡⠘⡉⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠞⢹⠇⠈⠙⢻⣧⣀⢀⠀⠈⠳⠄⠁⠀⡹⠓⠀⣿⢦⣷⣦⣄⣰⣿⣔⣻⣷⡔⠀⠀⠀⡀⠀⠈⠙⠻⣦⡀⠁⠈⠑
⠀⠀⠀⠤⠒⠒⠒⠾⢉⡐⠀⢀⣿⣟⣿⢿⣄⠶⠳⣤⣾⣥⣤⣤⣿⣿⣷⠘⣀⡜⣻⣼⠶⣯⢿⣶⣶⣴⣤⣀⣀⣀⡠⠃⠙⢖⠠⣀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⡠⣻⣿⣿⠋⣨⠿⡓⢉⡏⣱⠀⣠⣾⣁⣤⣿⣶⣿⡿⠋⢻⡞⣹⣼⣻⣿⣿⡿⢯⡁⢞⣬⠗⣠⣿⣠⠏⠃⠀⠠⣄⣜⠃⣀
⠀⠀⠀⠀⣀⡶⠖⠒⠚⠳⢶⣯⠻⣿⡟⣠⢈⠕⠁⢀⢈⣶⣿⣿⠋⢳⣿⠋⢿⡟⠦⣚⡿⢗⠿⣰⡿⣿⡆⠊⡻⠏⠶⢠⠟⣸⡏⠁⠀⣢⠞⠫⠀⠀⠀⠙⣆
⠀⠀⣠⠞⠁⠀⠀⠀⢰⠣⠃⠀⠋⣻⣆⣡⠋⠤⢀⣽⣿⢿⢻⣞⠗⣿⠷⠿⠈⣧⠀⣾⣧⣾⢀⣿⠁⢿⡆⠞⠁⢰⠆⡌⡠⢃⣿⠒⠛⠛⠦⣀⠀⠀⠀⠀⠘
⠀⢠⠋⠀⠀⠀⠠⠒⡱⠇⠀⢀⠠⡏⢸⠓⠀⢀⣾⣋⣼⠟⠳⠛⡽⢁⣄⣠⠖⣭⣛⡿⠇⠰⡰⠈⠻⣌⡇⠀⢀⣿⣰⡔⣵⠃⠸⡆⣸⠀⠀⠈⢾⠂
⠀⣿⠀⠀⠀⠀⠀⠄⠁⡤⠠⠬⢦⡈⡇⠀⡈⠚⠁⠀⢸⠂⡀⢠⠁⠀⠀⢀⡾⠉⠳⢤⡌⡰⠧⣤⣀⣸⣧⠄⠉⠦⣽⣶⠃⠀⠀⢃⣸⡁⠀⠉⠀⡀⠀⠀⡘
⠀⢻⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢷⠈⠰⠓⠀⠀⠀⠘⣧⠈⠺⠀⠀⠒⢉⠀⠀⠀⠀⢠⠆⠲⣌⠃⠈⣷⠚⣝⡦⠛⣻⠉⠈⠀⠈⠋⠀⠀⠀⢠⡁⡠⠞
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢃⡀⠀⠈⣆⠀⠀⠀⡤⡰⠂⠙⠫⢲⠛⢶⣿⡧⠔⠻⣆⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⣬⣄⠠⠊⠀⠈⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣇⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣼⣿⣿⡷⣄⡘⣦⠻⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢉⢻⢿⣿⣿⣿⣡⡱⣾⡝⢦⡈⠛⠛⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠈⠫⠳⣄⠻⢿⣿⣝⣾⣿⣷⠙⠲⣴⣷⣦⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣍⣛⠛⠛⠉⣠⣴⣾⣰⣤⡴⠶⣤⣀⠀⠉⠛⠿⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣿⣿⡿⡋⣠⣦⡈⡛⠿⣷⣾⣴⣴⣴⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡛⠉⠉⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⣿⡙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⢿⡿⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣀⣀⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠽⠛⠉⣿⠁⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣹⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡾⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠙⣧⠀⠀⠀⠀⢻⡄⣴⠏⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⣴⠋⠀⠀⠀⡶⠛⢷⡞⠛⣦⠀⠀⢰⡏⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⣷⠀⠀⢸⣇⡀⠘⠁⢀⣿⠀⠀⠀⣹⠆⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠸⣏⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⢸⡇⢀⡀⢸⠀⠀⠀⢠⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⣇⣿⠀⠀⠀⢸⣗⣏⣿⣸⠀⠀⠀⢸⣇⣞⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠹⠏⣿⠀⠀⠀⢸⡿⠿⠿⢹⠀⠀⠀⢸⡯⣭⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣤⣤⣿⣄⠀⢀⣼⣧⣤⣤⣼⣄⠀⢀⣼⣧⣤⣤⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣼⠀⢸⣇⣀⣀⣀⣀⣸⠇⢸⣄⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡫⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡆
⠀⠀⠀⠀⠀⠠⠤⢤⣤⣤⣀⣀⠀⠀⠀⠀⠉⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⡿⣿⡰⠶⠖⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠷⣦⡴⠚⠉⢿⣆⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣴⡿⣋⡤⢿⣿⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠿⢿⣶⣤⣀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠏⢁⣴⡿⣫⣾⠏⠀⣠⣿⣿⡿⠿⠿⢿⣷⣦⣄⡀
⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⢹⣧⣤⡾⠟⢻⡏⣠⡿⢋⡼⠋⠁⣰⣿⠟⠙⣿⡇⠀⠀⠀⠀⠉⠻⣿⣆
⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⡞⠛⣿⡀⠀⢠⣿⣾⠟⠁⠀⠀⠀⣼⡿⠁⠀⢀⠸⣿⡀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⣼⣿⠀⠀⠀⠀⣠⣼⣶⣦⣤⠶⠿⠭⠥⢿⣿⢤⣿⣷⣶⣾⠟⠁⠀⠀⠀⠀⢰⣿⡃⠀⠀⠘⣶⣿⣷⣶⣦⡀⠀⠀⠀⢘⣿⡆
⠀⠀⣿⣯⠀⠀⠀⠀⢿⣿⣿⣿⠿⠷⠿⠿⠷⢿⣿⢾⣟⣿⣿⣿⡶⢶⣶⠄⠀⠀⢸⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⡇
⠀⠀⠸⣿⡄⠀⠀⠀⠀⠿⠛⣿⠀⠀⠀⠀⢀⣿⣏⣈⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠙⣿⣆⡀⠀⠀⠀⠀⠟⠓⠒⠂⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃
⠀⠀⠀⠀⠈⠻⢿⣶⣤⣤⣤⣤⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣤⣤⣤⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣨⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠁⠀⠀⠀⠀⠀⠀⠐⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⡷⠀⠀⠀⠀⡈⠄⠴⠦⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⣁⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣇⢀⡐⠡⠄⠒⡸⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡘⠓⢄⠀⠠⠀⣠⠞⠀⠀⠐⢄⠀⠀⠀⠈⣽⠃⠀⠀⠀⠀⢀⢿
⠀⠀⠀⠠⠂⠀⠀⡼⠁⠑⡇⣇⢀⠎⠀⠈⢃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠨⡇⡄⠜⠁⠀⠀⠀⠀⠀⠇⠀⢀⡼⠁⠙⡄⠰⣠⠔⠁⠀⠂⠀⠈⠂
⠀⠀⠐⠀⠀⠀⠼⠁⠀⠀⢴⡤⠃⠀⠀⠀⡄⢦⠀⠀⠀⠃⠀⠀⠀⠀⠀⠾⠀⠀⠀⢐⣧⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠁⠀⠀⡇⣴⠛⡄⠀⠀⡈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠎⠑⠒⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⠒⠁⠀⠀⠀⠀⠀⢀⠜⠀⡀⠀⢀⣰⠃⠁⠈⠁⠀⠀⠀⡀⠔⠁
⠀⠀⠀⢀⣂⣤⣠⣤⣖⡉⠠⠤⠤⠤⠤⠤⠠⠀⠀⠊⠀⠀⠀⠀⠲⠴⠶⢒⣚⡉⠀⠀⠤⠤⠤⠀⠀⠒⠐⠊⡀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠀⠈⠈⠁






⣷⣶⡶⠶⢾⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⢬⡄⠀⢂⠄⠂⠀⠀⣀⣀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣔⣁⠄⠁⠀⠄⠀⠀⠂⢀⠡⢤⣒⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⠉⠀⠀⠀⠀⠀⣀⠀⠀⢘⡀⠀⠋
⠀⠀⠀⠀⠀⠩⣀⠀⠠⠔⠀⠀⠀⠀⠀⣨⠬⠢⣤⡞⠠⠊⠻⣄⠠⠔⠒⠀⠉⠒⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡤⠖⠒⠀⣬⠐⠢⣄⡀⠀⠀⠀⠠⠐⠂⠀⢠⠎⢳⡀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⡴⠃⠀⠀⠠⠀⠀⠑⠀⠀⠁⠀⡶⠀⠈⢀⣀⣀⣨⢒⣂⢙⠆⠐⣀
⠀⠀⠀⡜⠀⠀⠀⠚⠤⠀⠀⠀⠀⠀⠀⠀⠡⠄⠈⠤⠤⠀⢰⡒⠒⠒⠂⠛⠃
⠀⠀⠀⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⣐⡂⣂⠀⠄

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

⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⣶⣤⣄⡀
⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣶⡄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣤⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⣿⠏⠉⣿⡝⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⣽⡏⠉⢿⡝⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣰⡟⠀⠀⠘⣷⡀⠀⠈⢿⣆⠀⠀⠀⢀⣾⠏⠁⠀⣰⡟⠀⠀⠘⣷⡀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⢀⣿⠃⠀⣠⡾⠋⠀⠀⠀⠀⠈⢿⣦⡀⠀⢻⣇⠀⢀⣿⠃⠀⣠⣾⠏⠀⠀⠀⠀⠈⠻⣦⡀⠀⢻⣇⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠈⠛⠷⢶⣤⣤⣼⡿⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣿⣤⣼⡿⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣿⣤⣤⣴⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⣀⣀⣀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⣀⣀⣀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁




⣄⣀⣀⣀⣀⣄⣠⣀⣀⣠⣤⣠⣀⣀⣀⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣤⣀⣠⣤⣤⣤⣤⣤⣤⣀⣠⣀⣀⣀⣠⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠔⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣴⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠏⢀⣠⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠁⢰⣿⡟⠛⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄⡈⠻⢿⣾⣿⠟⠁⢀⣠⣤⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠈⠙⢿⣆⠀⣿⡇⠀⣰⡿⠋⠁⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⡇⠘⣿⡄⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣀⣠⣴⠿⠁⠀⠘⠃⠀⠘⢿⣦⣄⣀⣀⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠀⠀⠀⠀⠀⠀⠲⣶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠷⢶⣦⣤⣄⣀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⡏⠹⣷⣄⠀⠈⠉⠙⣿⣿⣄⢀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⣹⡟⠻⣦⡈⠻⣧⡀⠀⢸⡿⢀⣿⣿⣏⠉⠉⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣿⠀⠀⢻⣇⠀⠈⢿⣶⣿⡃⢸⡏⠈⠻⣷⣤⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠙⠋⠀⠀⣼⡏⠀⠀⠘⠿⠿⠃⢸⣧⠀⠀⠙⠋⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁

⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠠⠒⠶⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⠀⠀⠀⠀⠀⠀⢀⣵⡼⣶⣿⠀⠀⠀⣤⣤⣀⣀⣀⣄⣀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠒⠲⠶⣾⢟⢭⣴⣶⣿⣏⠁⠒⢶⡟⠀⡫⠅⠉⠛⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢉⠃⣾⣿⠟⠙⠓⠈⠐⢄⢻⡄⠋⠀⠀⠘⠞⣦⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠂⢀⣒⣤⣄⡌⢠⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⡷⡀⢰⠚⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⣉⡠⠤⠐⠛⡭⡙⢀⢎⠎⠀⣦⡀⠀⠀⠀⣼⡟⠛⢻⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⠴⣻⣿⠀⠀⠀⠀⢠⠁⣌⠃⠀⠀⠈⢿⣄⠀⠀⠙⠇⢀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠰⠁⡀⣿⡏⣀⠄⠀⠀⣼⡞⣤⡴⠈⡲⢟⣛⠿⠄⠐⢲⣾⢎
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠇⠀⢸⣿⠏⢁⣀⢠⣤⡿⣿⠩⠔⠁⠀⠉⠉⠀⢢⣄⠀⢧⠸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⣼⣿⠟⠉⠀⠀⠹⢷⡝⣥⠀⠀⠀⢠⣦⠚⠀⠹⣄⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡀⢠⢊⠄⢀⠀⠀⡅⡟⠂⠀⠀⢹⠏⠀⠀⠀⢻⣷⠀⠀⠀⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣿⣿⣧⣤⠁⣠⠎⠀⠀⠀⠀⣤⣼⠿⣦⣀⡀⠀⠈⠓⠤⣀⠀⠀⠉⠻⢶⣖⡈⠒⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢝⠻⣧⣾⣧⣄⣀⣀⢀⣀⠿⢏⡀⠈⠓⢮⣳⠶⢤⣀⠀⠈⠁⠒⠢⢤⣈⠻⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡉⠀⠀⠀⢘⣶⣦⣴⡞⠁⠀⠀⢀⡞⠀⠀⠀⣽⢧⠀⠀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠐⣹⢿⡇⣿⣷⡄⣀⣴⣿⣡⣤⣴⠤⠉⣸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠟⡘⠻⢿⣿⢀⠏⠈⠓⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠃⠇⠀⠀⠈⠁⠀⠀⢶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠟⢿⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣠⡾⢧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡿⢄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠠⣷⣤⣤⣤⣦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠩⠁⢀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠐⣀⣡⢴⠶⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠒⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡿⣷⢸⠀⠀⠈⠹⠷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣀⢠⠆⢀⣀⣀⣴⢨⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠛⠛⠛⠛⠋⠉⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠘⠿⠷⢖⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⣂⣈⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠶⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⡟⠉⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡤⢤⣄⡀⠀⣼⣿⡶⠿⠛⠛⠉⠉⠁⠀⠀⣀⡤⠂⣨⣧⠴⠶⠒⠒⠒⠦⠄⡀
⠀⠀⠀⣠⣾⣿⣿⠿⠓⠒⠀⠒⠒⢤⣴⡿⠟⢳⡄⠀⠀⠀⠀⢀⣴⠞⠁⣴⡾⣫⠽⡞⠉⠉⠉⠉⠁⠂
⠀⢠⣾⣿⣿⢋⡤⠂⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠙⣤⣤⣤⣶⠟⠁⢠⣾⣿⡞⠁⠀⠳⡀
⠀⠈⠙⣿⢡⡟⠀⠀⠀⠀⠀⣴⣿⡤⠶⠒⠋⠀⢸⡟⣿⣿⠇⠀⠀⣾⣿⡟⣴⠀⠀⠀⢑⣤⣶⡆
⠀⠀⢀⣇⣿⠁⠀⠀⢰⠂⣼⣷⣿⠤⠤⠀⠀⠀⠘⢧⣍⣁⠔⠀⠈⠛⢻⣷⣇⠀⠀⠀⢸⣿⡋⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣿⣿⣇⠀⠀⠘⢷⣾⣿⣯⡤⠤⠶⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠹⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠙⢿⣿⡁⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣄⣀⠀⠀⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⣶⣾⣶⣦⡀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠈⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⢿⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢼⢇⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⢻⣿⣿⣿⣿⣿⡿⣿⣿⢃⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢿⣿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡾⠂
⠀⠀⠀⢹⠄⠀⠀⡄⠁⠀⠀⠀⠀⠀⠠⣿⡟⠻⣄⠀⠀⠀⠀⠀⠐⢶⡀⠀⠄⢯⠁⠀⠀⠀⠀⠰⣿⡙⠏⡠⢀
⡔⢁⣨⠳⣆⠀⢰⠛⣀⠙⡆⠀⢀⠔⠠⣌⣿⢀⠄⠢⡀⠀⡰⢋⣻⢪⡄⠠⠊⠼⣏⠓⡆⠀⠀⡠⣼⣽⡄⠌⣠⠖
⠣⣈⣉⡸⠛⠇⠘⢄⣉⡠⠃⠀⠠⡘⢃⠞⠿⠡⡘⢁⠄⠀⠳⣈⣛⠝⠻⠇⠀⢇⣈⣠⠎⠀⠀⠦⣝⡥⠖⠲⠃

⠀⠀⠀⡤⣶⢲⡦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣶⣀⣀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⡀
⠀⠀⢸⣻⣼⣼⣷⣫⡆⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠈⣿⡿⠿⢿⠁
⠀⠀⠹⠋⢙⣛⠉⠹⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣼⡿⠀⠀⠀⢀⠀⠀⡀⢀
⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣙⣾⡇⠀⠀⠀⠀⠀⠀⢛⣯⣾⠟⠁⠀⠀⠀⣶⣦⣑⠲⠟⣵⢆⣤⢀⡀
⠀⠀⠀⠀⠠⡠⠐⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⣿⠇⠀⠀⠀⠀⠀⠀⢨⣿⣿⠇⠀⠀⠀⠀⠹⠿⠿⠷⠶⢤⣥⡥⠴⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⠂⠀⠀⠀⠀⣠⡶⠟⠛⠻⢶⣄⠀⠀⠀⠀⠰⠶⠶⣶⠶⠶⠆
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣤⢰⣿⣄⠀⠀⠀⠀⣾⠋⠀⢀⣀⡀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣿
⠀⠐⣿⠻⠿⠽⠽⢯⡭⣿⠂⠀⠀⣴⠟⠁⠀⠈⠹⣧⠀⠀⠀⣿⠀⠀⢯⣻⡗⠀⢀⣿⠀⠀⠀⠀⠀⠀⣿
⠰⠶⢿⣀⣄⣀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⢰⣿⡀⠀⠀⠹⣧⣀⠀⠀⠀⣠⣬⠋⠀⠀⠀⠀⠀⠀⣿⢀
⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠇⠀⠀⠀⠀⠈⠛⠛⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠴⠿⠿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡛⣿⣛⢷⣄⠀⠀⠀⠈⠀⢐⠁⠉⡁⠢⡀⠀⠀⠀⢀⡆⣄⡄⢀⣰⠀⠂
⠀⠙⢿⣿⣿⣶⣤⣤⣄⡀⠀⠀⢸⡟⡾⣴⠒⡆⠶⢿⡄⠀⠀⠀⡔⠡⠒⠀⠈⢠⠘⡀⠀⠀⢸⡇⣿⠀⣿⡏
⠀⠀⠶⢬⣭⡭⠝⠉⠙⠃⠀⠀⠘⣧⣱⡍⣛⢥⣂⡾⠁⠀⠀⠀⡅⠣⡀⠀⢀⠔⢠⠁⠀⠀⢸⡇⢛⠀⣿⡇⠀⢀
⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠛⠁⠀⠀⠀⠀⠈⠲⠤⠭⠡⠂⠁⠀⠀⠀⠸⠇⠼⠁⠻⠟⠂⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡒⠀⠀⠀⠀⠀⠀⠲⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣰⣿⠿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢰⠟⠁⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⡀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⡄⠀⠀⡇⠀⠀⡄⠹⢿⣿⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡆⣿⣴⠀⣿⣇⠀⢰⣧⠀⣦⣧⠀⢀⠀⠀⠀⢀⣷⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⢀⣿⣿⣿⡴⣋⣠⡕⠺⢿⢀⣿⣿⣤⣿⡄⠀⠀⢸⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⢀⠜⣉⣙⣿⣿⣿⣿⣵⣶⣆⡬⣿⣿⣿⣿⡇⠀⢄⠹⣿⡅⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⡙⡟⢁⣚⡟⢫⣾⣿⣿⣿⣿⣿⣿⡇⠙⣿⡟⢻⣿⡤⠀⠀⢹⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣿⢀⣿⡿⠿⠀⡾⣿⡷⢮⡽⠿⣿⡿⡷⢾⣭⠀⣤⡬⣏⣀⣀⠖⢿⣀⣙⠦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠃⣚⠋⢘⠃⣾⠆⣼⠇⣿⢁⡚⢀⣡⡿⢀⡖⢸⡟⢰⡿⢠⡟⢠⡟⣰⠆⣿⠁⡣⡮⢶
⠀⠀⠀⠀⠀⠀⠀⢀⠏⢸⠁⠇⢾⣦⣵⣤⡵⣦⡴⠃⠑⠬⠭⠦⠞⠣⠬⠲⠬⣴⣬⢥⣬⣴⣿⠬⠕⠤⠭⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠒⠁⠀⠧⠚⠙⢿⣿⣷⣼⢻⣷⡀⠀⠰⡢⢔⠆⠀⣠⣾⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣬⣻⣦⡈⠠⠄⣠⣾⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣍⢻⣶⣾⡿⣯⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣏⣹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠄⠀⣀⡀⠀⢀⣤⡤⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢩⣤⡰⠿⣃⡀⠚⠛⣧⣤⣤⠛⠛⢟⡀⠀⣼⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⡿⠈⠛⣁⢰⡿⣣⣤⠌⠉⠉⢡⣤⣀⢼⣿⡏⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠄⠰⠿⡷⠘⠿⠃⠸⠛⠉⢶⣶⣦⠺⢿⡏⠀⢨⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣧⡄⢴⣾⠟⠓⢀⣿⣰⣾⡿⠋⢿⠏⠀⣰⣶⠄⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠐⠿⠏⠀⣠⣷⣤⣾⡿⠏⣿⠁⢤⣴⡿⠗⠘⢻⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⡃⠀⣸⣷⡦⠻⠿⠷⣀⣤⡆⢠⣶⡄⢾⣶⠆⠚⠿⠟⠁
⠀⠀⠀⠀⠀⠀⣤⣀⢸⣿⡗⠉⠛⢃⣀⣀⡐⠛⢫⣾⠇⢉⣤⡀⣾⣶⠄
⠀⠀⠀⠀⠀⠸⠿⡟⠀⠈⣵⣤⣤⠛⠛⢻⣤⡴⠈⢩⣶⠎⠛⣃⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠚⠛⠁⠀⠈⠉⠀⠐⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⡀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡀⠀⠐⠼⠁⠀⠀⠀⠀⢀⠂
⠀⠈⠄⠀⠰⡄⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⢸⡄⡞⠀⠀⠀⠀⢆⢤⠀⠐⠀⠆⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣦⠘⢄⠒⠲⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⠀⠀⠀⠊⠁⠔⠂⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠐⠀⡀⠀⠀⠈
⠀⠀⠀⡀⠸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⡀⠠⠀⠀⡀⠀⢀⠖⠀⠊⢀⠁
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠄⠀⠀⠀⠀⡦⠃⠀⢠⠀⡇⢀⠀⢰⡁⠀⢸⠀⡰⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠱⠠⠀⠀⠘⠁
⠀⠀⠤⠀⡤⠤⠒⡠⠔⠀⠀⠀⠀⠂⠀⡀⢀⡒⢦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠤⠠⠠⣄
⠐⢀⣠⡀⠄⠀⠀⡀⠀⠀⣀⠐⠁⢀⠔⠁⠠⠉⠋⠁⠀⠀⠀⠀⠀⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠰⠲
⠀⠘⠛⠉⠀⠈⠀⠀⠉⠁⠙⠶⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠢⣄
⠀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠁
⠀⡄⢠⠀⠀⠀⢐⡀⣠⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡾⠋
⠀⠻⠶⠘⡆⠀⠀⡼⠘⠛⠾⠧⠢⠀⠠⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠄⠀⠘⠂⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⡄⠀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠴⠖⠒⠒⠒⠊⠉⠉⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡤⠤⠾⠖⠒⢚⡙⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⠻⠶⣤⣀
⢀⠤⠤⠴⠶⠒⠒⠙⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠐⡖⠒⠒⢤⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤
⡆⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⢠⠀⣴⠴⠶⠶⠆⢶⣄⠀⢸⡀⠀⠘⡇⠀⢸⡄⠀⠸⡄⢻⣠⠴⠚⠀⢸⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢹⢾⡀⠀⠀⢰⣆⠀⠀⠀⣏⠙⢦⠘⣆⠀⡌⠀⢻⣀⣀⣀⠀⢸⡍⢷⡈⣇⠀⠀⢧⠀⠈⢧⡀⢸⠃⢸⡟⢦⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠘⣿⣇⠀⠀⢸⠘⣆⠀⠀⢹⡀⢘⡇⠹⡄⡇⠀⢸⡇⠀⠀⠀⠈⡇⠀⠙⢿⠀⠀⠸⠄⠀⠈⠙⠃⠀⠀⠃⠀⠙⠂⠀⠉⠉⠉⠁⠀⠀⠀⡠⠖⠁
⠀⢿⣿⠀⠀⡷⠖⠘⣆⠀⠈⣇⠜⠁⠀⢻⠁⠀⠀⠷⠶⠶⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠊
⠀⢸⣿⡀⠀⠃⠀⠀⠙⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⠀⠠⢤⣤⣤⣤⣶⣶⣦⣤⣤⣴⠶⠶⠶⠶⠟⠛⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡤⠤⣤⣴⣖⣲⠶⣶⠶⠶⠖⠻⠟⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⢙⣳⣾⣤⣐⠶⠶⠮⠿⠛⠓⠛⠊⠉⠉⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠳⠀⠀⠀⠸⣤⡆⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⡄⢠⠀⠀⠀⢀⡿⠀⠋⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⢆⠘⢆⢇⠀⠀⣼⣷⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠣⠘⡞⠀⡈⣿⢿⣀⠞⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡉⠪⠐⠄⢹⠷⣗⣨⠁⣁⠀⠀⠲⠊⠁⠀⠀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠈⠁⠠⠤⠭⠤⠄⠀⠐⠟⠛⠒⠚⠛⠒⠒⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣿⣭⡷⣦
⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⠷⠒⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⢿⣿⣶⣾⣶⣿⣿⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠚⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣶⣾⣿⠏⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠈⠉⠉⣹⣿⣿⣿⠿⠧⡤⠀⠘⢿⣿⣟⡉⠉⠋⠉⣽⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⣾⡷⠤⠴⠤⠿⣿⣷⡤⠦⣼⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⡟⢿⣦⡀⠀⠀⠈⠻⣷⡀⣿⣿⡿⠛⢧⡀⠀⠀⠀⠀⢀⣀
⠀⠀⢀⣤⣶⠿⠟⠛⠛⣿⣿⣦⣄⠙⣿⣄⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⠻⣦⣴⡾⠿⠛⠛⠻⠿⣶⣦⡀
⠀⣴⡿⠋⠀⠀⠀⠀⢠⡿⠁⠈⠻⣷⡈⠻⣷⣄⠛⠛⡏⢹⣿⡆⠀⢀⣾⠟⢻⣄⠀⠀⠀⠀⠀⠀⠙⢿⣦
⣼⡟⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢹⣷⠀⠈⠻⣷⣤⣷⣼⣿⡇⠀⣾⡏⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠠⣞⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⢩⢹⣿⣥⣴⣿⣤⣤⣤⣤⣤⣿⣲⠄⠀⠀⠀⠀⢸
⢿⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠘⠿⣿⣿⣿⠀⠈⣿⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸
⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⢠⣤⣿⡿⠇⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠈⠻⢷⣦⣄⣀⣀⣀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣀⣠⣴⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡠⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣶⢶⣶⣆⡆⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣋⣬⣴⠺⡿⢷⠛⡉⠉⠉⠉⠛⠳⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠇⠉⢾⣇⣸⣶⠀⠀⠀⢰⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣠⠿⠛⠟⠈⢧⠀⠀⣿⣷⠦⣤⣄⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣀⣶⣶⣾⡆⠀⢹⣿⣷⣶⣶⣶⣶⠦⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠁⠉⠉⣧⠀⢸⡿⣿⣿⡿⠋⠀⠀⠀⣶⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⢀⡞⠀⣸⣇⣾⡿⠁⠀⠀⠀⣼⣿⣷⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⢠⣿⡀⢀⠞⢀⡴⢋⣾⣿⠃⠀⠀⣠⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢷⣶⣶⣴⠗⢋⡴⠋⢠⣿⣿⠇⠀⠀⠞⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⡓⠤⢒⢿⡿⢋⣿⠾⣅⣀⣼⣷⠦⠿⠿⣿⡀⠀⠀⣼⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⢛⣟⡛⠊⢠⠞⠁⢠⡇⠀⢿⡛⣿⣿⣿⣿⣧⡀⠀⠹⣷⡆⠸⡇⠀⢀⡠⢴⣖⣒⣶⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢧⣩⡿⠿⣷⣶⡾⣧⢲⣦⡙⢮⣿⣟⣿⣿⣧⠀⠀⢻⣇⢠⣬⡲⢯⣾⣿⣿⣿⣿⣿⣷⣮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣽⣾⣿⣿⣿⣿⣿⢰⣿⣻⣦⡉⠻⣿⣿⣿⣧⠀⠈⣿⣸⡏⣿⣶⣝⠿⣿⠿⠛⠻⠿⣿⣿⣷⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣾⣿⢟⡵⠞⠛⣿⣿⢸⣿⣿⣿⡽⣷⣌⠛⢿⣿⣧⠀⢸⣿⣽⣿⣿⣿⣷⣮⡓⢄⡀⠀⠀⠙⢿⣿⣞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣿⢣⠎⠀⠀⢠⣿⡏⣿⠙⢿⣿⣿⣞⣟⢷⣄⡙⠻⣷⠈⢿⣿⣿⣿⡏⠻⣿⣝⣶⡝⢢⡀⠀⠀⢻⣿⡼⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⡌⠀⠀⠀⢸⣿⣷⡇⠀⠈⢿⣿⣿⡞⡆⠙⢿⣦⠜⠁⢀⣿⣿⣿⠷⠖⣛⣭⠷⠚⠉⠀⠀⠀⠀⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⣿⠁⠀⠀⠀⢿⡿⠿⠃⠀⠀⠀⠸⣿⣿⢹⠀⢾⣥⣴⣾⣿⣿⣩⣴⡾⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⠀⠀⢿⠛⠿⠿⢻⢯⡹⣿⣮⡳⠀⠀⠀⠀⠀⠀⠀⣰⣿⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⠀⠀⠈⠙⠒⠒⠋⠀⠱⣌⠻⣿⣦⣤⣀⣀⣀⣤⣾⣿⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣿⣿⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣍⣛⠻⠿⠿⢛⣫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠻⢿⣷⣶⣶⣶⣿⣿⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠭⣭⠭⠵⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠈⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢶⡀⠀⠀⠀⢸⠟⠀⠀⢳⣿⣿⣿⣦⡀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣾⣿⣦⠊⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⡀⠀⢶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠠⣤⣹⣿⣿⡆⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣶⠖⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠁⢀⠀⠠⢈⣷⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣇⠀⠐⣿
⣸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠞⠃⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡧⠀⠀⠀⢀⣼⣿⣿⣷⣄⡈⠙⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⠄⢻⣿
⣿⡆⠀⢠⣧⠀⠀⡀⠀⠀⠀⢨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢠⣿⠿⠛⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠈⠛⠉⠙⣿⣿⠉⠉⠉⣽⣿⣿⡤⣾⣿
⣿⡗⠀⣸⣿⡀⢰⡇⠀⠀⢀⣸⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⢾⣿⣿⠶⣿⣿
⣿⣿⡀⣻⣿⡃⣼⣧⠀⠀⠠⣽⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⠀⠘⢿⣿⣿⡿⣿⣿
⣿⣿⣽⣿⣿⣿⣿⣿⠄⠀⠴⣾⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣭⣿⣿⣿⣿⣿⡃⢀⣤⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣦⠸⡦⠀⠀⠃⠚⠃⠀⠰⣉⠆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢⡼⠈⢀⣀⣀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠓⠃⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡙⠂⡀⠀⡏⡏⠀⢀⠀⠀⠀⢺⠆⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠃⠀⡀⠀⠀⠑⠬⠶⠋⠀⣀⡀⠀⠀⠀⠈⠀⣴⠄⠀⠀⢁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢍⠛⠁⠀⠟⢀⣤⠀⠀⠀⠉⣰⢻⢳⡠⠖⡆⠀⠀⢈⡀⠈⠁⠀⢚⣁
⠀⠀⠀⠀⠀⠀⠀⢐⣊⠁⢀⠀⡠⠋⡏⢧⠐⠀⡰⠃⡜⠀⢁⡴⠁⠂⣠⠚⡟⣆⠀⡀⠙⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⠚⠁⠘⣅⡸⠳⡞⠀⠸⠵⠂⡞⣞⠱⠘⠹⣤⠇⢈⠢⠀⠐⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠄⠀⢼⡧⠀⠈⠁⠀⠘⠄⠀⠀⠀⠘⣌⡆⠑⠀⠈⠀⢾⠦⠀⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣺⣟⠀⢠⣿⡄⠀⢰⠒⠦⠤⢦⡈⠇⣰⣷⡀⠐⣿⣗⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⢽⡿⡁⠰⣿⡢⢠⠋⠓⠤⢎⢿⣱⡄⢞⣿⠆⠨⢾⡮⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣻⣏⡂⣪⣿⢝⠀⠭⠍⠑⠚⠉⠥⠀⡻⡿⡅⢐⣽⣝⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠉⢔⣿⡳⠄⣱⣆⢩⠍⣴⡌⠠⢚⣟⡢⠉⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⠌⠂⢽⡷⡀⠨⣾⢮⠘⠵⡷⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣒⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠴⣲⡆⠠⠤⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⢰⡇⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠈⠀⠳⢈⠻⠟⠠⠀⠀⠀⡄⠀⠀⠂⠁⠀⠃⠘⠁⠀⠀⢀⠅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢤⠊⠀⡀⠃⡠⠂⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡇⠀⠀⠀⠁⠀⠰⢅⠀⠀⠔⢀⠎⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠖⠀⠒⢄⣘⡆⠊⠙⠀⠀⠀⡄⠀⠄⡰⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⡆⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠉⠘⡆⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣍⡻⠙⡦⢄⠀⣀⣀⣀⣀⣀⣠⠠⢠⡄⠀⠀⠹⢆⡰⣄⠠⡀⠤⠔⠂⠊⠘⠦⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠉⠙⣰⣠⡖⠬⡉⢽⣟⡢⡀⠀⠀⣔⢲⡀⠀⢀⡌⢡⡌⠳⡀⢀⠀⠀⠀⠀⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠈⢹⡆⠈⠀⠈⠛⠃⠀⠁⠀⠈⠀⠀⠈⢀⣘⣀⣤⣙⣆⠁⠀⣀⡀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠹⢠⠀⠀⠀⠁⠀⠀⠀⠀⠁⠐⠀⢙⠛⠚⠺⠛⠂⢀⡈⠙⢻⡗⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠝⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⣀⣠⠀⠀⢻⡅⠀⠀⠐⢢⣿⣒⣩⡤⠀⠀⠀⠀⡾
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠤⠄⠋⠛⠀⠠⠤⠬⢧⣤⣀⠀⣈⣒⠛⠆⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣤⡄⡈⠉⢀⡀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠖⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡤⠔⠲⠦⢤⣀⣀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠛⠛⠛⠷⠶⠶⢶⣤⣤⣤⣀⣀⣀⡀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠈⢷⣄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠉⠉⠉⣿⠓⠦⣍⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠹⣧⣠⠴⠞⠋⠉⢉⣉⣉⠉⠙⠓⠶⣤⡀
⠀⠀⠀⣠⠞⠉⣠⠴⡞⠉⠉⢹⠉⢹⣿⡖⠤⣀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⡴⠛⢻⣤⠲⡏⠉⠀⢹⠀⠉⣹⠒⠤⣀⠙⢦⡀
⠀⢀⡼⠁⡠⢮⡀⠀⠹⡄⠀⢸⠀⣾⡟⠀⠀⢈⡷⣄⠙⢯⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣠⠟⢀⠴⢧⡙⣧⣳⡀⠀⣸⠀⢠⠏⠀⠀⣨⠷⡄⠙⣆
⢀⡟⠀⡜⠀⠀⠙⢦⡀⠹⡄⢸⣴⡿⠁⢀⡴⠋⠀⠈⣆⠈⢷⠈⠛⢦⣄⠀⠀⣠⠴⠒⠛⠶⠴⠯⠤⣯⣤⣀⣙⣮⣻⣷⡀⣸⢀⡞⠀⣠⠞⠁⠀⢘⡆⠘⣧
⣼⠁⡸⠙⠲⠤⣄⣀⠙⠦⠛⢈⣿⠃⠴⢋⣠⠴⠒⠋⠉⡆⠸⡇⠀⠀⠙⢷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⢦⡞⣁⡤⠖⠋⠉⠸⡀⢸
⣿⠀⣇⣀⣀⣀⣀⣉⣙⠀⠀⢸⡏⠀⠈⣉⣀⣀⣀⣀⣀⡅⠀⣿⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣥⣤⣤⣤⣤⣤⡇⢸
⣿⠀⢇⠀⠀⠀⢀⣠⠴⣄⠀⠄⠀⠂⡰⠦⢤⣀⠀⠀⠀⡇⠀⡟⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢼⡑⠦⢤⣀⡀⠀⢀⠇⢸
⠸⡄⠘⡤⠖⠚⠉⢀⡴⠋⡴⢰⠄⢮⠙⢦⡀⠈⠉⠓⢶⠁⣸⠃⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⢲⡛⢻⡿⠛⠉⠉⣩⠟⢉⠟⢻⠙⣇⠙⢦⡀⠀⠉⠓⡾⠀⡾
⠀⢳⡄⠐⣄⢀⡴⠋⠀⣰⠃⢸⠀⠈⣇⠀⠙⢦⡀⡰⠃⣠⠏⠀⠀⠀⠀⢠⠤⠤⠤⠤⡄⠀⠈⢷⡀⠱⣄⣠⠎⠁⠀⡜⠀⢸⠀⠘⡆⠀⠙⢦⣀⠜⠀⡼⠃
⠀⠀⠹⣦⡈⠻⢄⡀⢠⠇⠀⢸⠀⠀⠘⣆⢀⡠⠋⢀⡴⠋⠀⠀⠀⠀⠀⠈⠂⠀⠀⠒⠃⠀⠀⠀⠻⣄⠈⠣⢄⠀⣸⠁⠀⢸⠀⠀⠹⡄⣀⠔⠉⣠⠞⠁
⠀⠀⠀⠈⠛⢦⣄⡉⠛⠒⠤⠼⠦⠄⠒⠋⢁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡉⠓⠒⠆⠾⠐⠒⠒⠉⣀⡴⠞⠁
⣀⣀⣀⣀⣀⣀⣈⣙⣓⣶⣶⣶⣶⣶⣖⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣲⣶⣶⣶⣖⣚⣋⣁⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⣉⣍⣑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡴⢃⠴⢌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⡱⠀⠀⠀⠀⠀⠀⠀⡜⢰⠃⠀⠀⠱⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢤⢤⡤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⢇⢹⠀⠀⠀⢠⣃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠄⣇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⠎⣀⠰⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢢⠘⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢊⣉⠥⢤⠤⢍⣉⠛⠾⣀⠣⡘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢋⣉⠥⢤⠤⢍⣉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⡰⢋⡤⠊⠁⠀⠀⢸⠀⠀⡎⡹⠲⣌⠳⡕⣌⢢⡀⠀⠀⠀⠀⠀⡴⢋⡴⠊⠙⡄⡇⢸⠀⠀⠀⠉⠢⣌⠳⡀
⠀⠀⠀⠀⠀⡜⢠⠊⠈⠦⡀⠀⠀⢸⠀⡜⡰⣡⠞⠉⢣⡈⢎⢦⠱⡄⠀⠀⢀⡎⣠⠋⠘⢦⡀⢣⠘⣼⠀⠀⠀⣠⠞⠉⢢⠘⡄
⠀⠀⠀⠀⢸⢀⠇⠀⠀⠀⠈⢢⡀⢸⡼⣡⠟⠁⠀⠀⠀⢣⠘⡄⠳⡘⢆⢀⣜⢠⠃⠀⠀⠀⠉⢦⣇⢹⠀⣠⠞⠁⠀⠀⠀⢇⢸
⠀⠀⠀⠀⡆⢸⡤⠤⠤⠤⠤⠤⠬⣾⣿⣷⣶⣶⣶⣖⣒⣺⣒⣗⣒⣛⠞⠁⢀⣿⠤⠤⠤⠤⠤⠤⠭⣾⣾⠥⠤⠤⠤⠤⠤⣼⠀⡆
⠀⠀⠀⠀⢰⠘⡄⠀⠀⠀⠀⣠⠞⢹⠉⠢⡀⠀⠀⠀⠀⡸⢈⠇⠀⠹⡠⠔⢏⠸⡀⠀⠀⠀⠀⣠⠞⢹⠙⢦⡀⠀⠀⠀⠀⡜⢰
⠀⠀⠀⠀⠈⢆⠱⡀⠀⣠⠞⠁⠀⢸⠀⠀⠈⠦⡀⠀⣠⠃⡜⠀⠀⠀⠀⠀⠘⡄⢣⡀⠀⣠⠞⠁⠀⢸⠀⠀⠙⢦⡀⠀⡰⢁⡎
⠀⠀⠀⠀⠀⠈⢦⡙⢾⡁⠀⠀⠀⢸⠀⠀⠀⠀⣈⠖⢁⠞⠀⠀⠀⠀⠀⠀⠀⠘⢆⠑⢎⡁⠀⠀⠀⢸⠀⠀⠀⠀⣩⠞⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⡓⠢⠤⠼⠤⠤⠒⢊⡡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣉⠒⠢⠤⠼⠤⠤⠒⣋⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣦⣤⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡏⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠶⠶⢀⣿⣿⡟⠛⠛⠿⠿⠷⠶⠶⠶⣶⣶⣶⣤⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡏
⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠿⠿⠿⢿⣿⣦⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠻⣦⣠⣴⣶⠿⠿⠿⠿⠿⣶⣦⣄
⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠀⣾⠃⠉⠻⣿⣦⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⣴⣿⢿⣍⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦
⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⢻⣷⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⣾⡏⣾⡟⠁⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠙⢿⣷⣄⣀⣀⣸⡿⣸⣿⠀⠀⠀⠀⠈⢿⣆⣀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢴⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣇⣿⡟⠈⠋⢈⣁⣀⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣷⠞⠛⠛⠉⠉⠩⣾⠟⠛⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠈⢷⣿⣿⡷⠛⣿⣆⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢧⠄⠈⢿⣷⣍⠀⠈⠀⠈⠉⠁⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠉⠻⢷⣶⣤⣤⣤⣤⣤⣶⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣤⣤⣤⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⢀⠀⣀⠀⢀⡀⢀⠀⢀⡀⢀⠀⢀⡀⢀⠀⢀⡀⢀⠀⢀⡀⢀⠀⢀⡀⢀⡀⠀⡀⢀⡀⠀⡀⢀⡀⠀⡀⢀⡀⠀⡀⢀⡀⠀⣀⠀⡀
⠀⠀⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠋⠛⠛⠛⠋⠛⠛⠛⠛⠙⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠋⠛⠛⠛

⠀⠀⠀⠀⠀⢰⣶⣶⠀⠀⠀⠀⡀⠀⠀⣀⣤⠀⠀⠈⠻⠄⠀⠀⢀⣀⠀⠀⠀⣶⣾⣿⣶⣶⡀⠻⡟⠀⠀⢐⣿⡗⠀⠀⣀
⠀⠀⠀⠀⠀⢸⣿⡯⠀⠀⣾⣿⣿⣷⠘⣿⣿⠃⠀⠀⠀⠀⠀⢺⣿⣿⡃⠀⠀⣿⣿⣷⣿⣟⠀⣿⡿⢰⣿⢿⣿⡇⣰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣾⠇⠻⢿⣶⡆⠀⢿⣷⡆⠀⠀⠀⠀⠀⢶⣾⣿⠇⠀⠀⢹⣿⡇⢿⣿⠇⣿⡇⠘⢿⣷⣿⡇⠘⠿⣷⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠙⢦⡐⢾⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣦⣬⣝⣼⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣯⠻⠻⠟⠻⣷⣦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⣤⣀⠀⠈⠡⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠈⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⡄⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣴⠖⠊⠉⠹⣿⣿⣧⣄⡠⠀⠀⠀⠀⠀⠀⢀⣬⠿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⣦⡀⠀⠀⠹⣯⡹⢿⣄⠀⡀⢀⣀⣀⣰⠟⠁⠲⠾⠋⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠁⠀⠀⠀⠈⠳⡿⠯⣭⣥⣼⣶⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⠲⣤⡀⠈⠀⢻⣿⣿⣿⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⣿⣿⣙⠦⣴⠿⣿⡃⣨⣿⡿⠓⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢤⣄⣐⠢⣝⣿⣧⣼⣷⣿⢛⢿⣿⡳⣄⠀⠘⢍⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠿⣍⣉⣁⠘⠃⠈⠳⣜⠲⣄⢠⡗⠀⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⢦⣌⡳⣬⡁⠀⠀⠀⠁⠙⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣦⣤⣄⣀⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⢴⣶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⢀⣼⣷⢶⠖⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣦⠀⣨⠿⣄⠀⠀⠀⠀⠀⢠⣬⡷⠞⠁⣿⠀⠀⠀⠀⠀⠀⢠⣶⣬⡉
⠀⢸⣝⣿⣧⢶⣄⠀⣼⡇⠀⠀⠀⠀⠿⢷⣼⠿⣥⡀⠈⠀⠀⠀⠀⠀⣾⣏⡛⠋⣼⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⠶
⠀⠜⠁⠀⠻⣆⠈⣴⣿⡇⠀⠀⠀⠀⣠⠞⠉⢿⣬⣿⡄⠀⠀⠀⠀⠀⢸⡏⠻⣠⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⢻⡄⡀
⠀⠘⠀⠀⠀⢉⣼⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⢘⣣⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠃⠘⠃⠁

⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⢄⡀
⠀⠀⠀⠀⣴⣷⣤⣄⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⡠⠊⠁⠀⠀⠀⠀⠀⢘⣛⠀⠀⣛⡃⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠐⠠
⠀⢐⡶⣤⣿⣷⣴⡾⠷⠄⠀⠀⠀⠀⠀⣀⡸⠫⣄⣀⠀⠀⠀⠀⣠⣴⣿⣯⣷⣼⣿⣽⣦⡄⠀⠀⠀⠈⢛⣧⡴⠟
⣼⣟⣻⡯⠿⠿⠏⣾⠿⣷⡄⠀⠀⣤⣾⡿⠃⠀⠻⣿⣷⡄⠀⠀⢎⣭⡝⠭⢭⣭⠯⠯⠭⠅⠀⠀⠀⠀⠌⠻⣷⣶⣦⣄
⠈⠛⠛⠁⠀⠀⠀⠛⠿⠛⠀⠀⠀⠙⠋⠀⠀⠀⠀⠈⠛⠁⠀⠀⠘⠋⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠉

⠀⠀⠀⢀⠠⡠⡄⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⡀
⣴⣔⣊⣹⣞⣓⣼⣦⣤⣄⠀⠀⠀⠉⠱⠀⢸⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⡀
⠻⣿⠿⣿⣿⣿⣿⣿⠿⣿⠆⠀⠀⠀⠀⢧⣼⣷⣿⣿⣶⡄⠀⠀⠀⠀⣠⣿⣿⠹⣷⡀⠀⠀⠀⠀⣶⣀⣀⣠⣿⣻⣃⣀⣠
⠀⠻⠶⠟⣁⣀⣈⠻⠶⠟⠀⠀⠀⠀⠀⣿⣿⠉⠀⠈⠉⠀⠀⠀⣀⣼⣿⣿⣿⠀⠙⣿⣄⡀⠀⠀⢙⡛⣛⣛⡛⣛⣛⡛⣛
⠤⠶⠿⠿⠿⠿⠿⠿⠶⠦⠀⠀⠀⠀⠤⠴⠶⠶⠶⠶⠤⠄⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠁⠀⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⢺⠂⠀⣠⣶⠄⠀⠀⠀⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⠋⠀⠀⠀⠀⠀⠀⠀⠀⢾⠆⢠
⢀⣀⣤⣤⣿⣷⣾⣭⣄⣀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣉⠳⠂⠀⠀⠀⠀⣀⣀⣼⣿⣲⣴⣷⣦⡀
⢨⣍⣩⠭⣭⣩⡭⣭⣩⡥⠀⠀⠀⠀⠀⠀⠀⠶⢼⡃⠀⠀⠀⠀⡾⠉⠙⣮⢿⣉⡞⠉⠙⡆⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⡄⠀⠀⠻⠤⠴⠋⠈⠁⠳⠤⠴⠃⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉