Leafe Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢓⣄⡀⠀⠀⠀⠀⢀⣔⠀⡀⠀⠀⠀⡐⠁⣼⢡⣯⠤⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⣷⠀⣟⠀⢁⠀⠀⠀⠀⠀⠀⢀⠷⠀⠀⠀⠀⠀⠀⠀⠹⣦⠄⠠⠾⡿⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢲⠃⠁⠀⠁⠀⢸⡄⠙⣴⠋⠉⠁⠀⡎⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠷⣤⡙⠖⠂⠈⠀⠀⢙⠁⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⡿⠷⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠗⠀⠀⠀⠀⠀⠐
⡐⠒⠲⠄⣀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⡰⠊⠀⠀⠀⠀⢠⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠳⠊⠀⠀⠀⠀⠀⠀⠀⠙⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⡄⣠⠜⠀⠀⠰⠀⠀⠀⢠⣿⠆⢀⠈⠀⠀⠀⠈⢦⡑⠙⢁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣄⣠⡄⠀⠀⢃⢀⠀⣧⡍⠀⠀⠀⠀⠀⣀⣾⣿⣿⠆⠀⠀⠀⠀⠀⡈⠄⢿⣧⠴⢊⠀⠀⠀⠀⠀⠀⢹⡔⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠤⠀⠬⠹⡄⠀⠀⠀⣾⢆⠋⠀⠀⠀⠀⠀⠀⠈⡻⠛⠁⠀⠀⠀⠀⠀⠀⢛⣄⣞⠠⢀⡀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠊⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠉
⠀⠀⠀⠀⠐⣷⠀⢂⡀⢀⠉⠀⠀⡋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠹⠈⢻⡇⢈⡇⠀⢠⠁⢀⡀⠀⠀⢀⣀⡤⠀⡰⠀⠀⡠⢾⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣿⣟⡴⡾⠿⡏⠀⠔⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡸⢁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⢀⠀⠈⠄⠀⠀⢀⡤⠂
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠛⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠷⣬⠀⡄⡰⠋⢀⠀⠁
⠀⠙⢛⢷⡶⠂⠀⢀⠀⠀⠀⠀⠀⡏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⣶⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⢄⠠⠀⢂⠙⠛⠂⠂
⠀⠀⠀⠉⠋⠐⠂⢀⡻⢦⡀⠀⠀⠄⠐⣾⡋⢻⡄⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⣀⣠⠀⠉⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡀⠙⡆⠀⠙⢛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣁⣈⣠⣉⡛⠍⠉⡋⠉⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠇⠸⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⡉⠳⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣤⡀
⠀⠀⢠⡆⠀⢠⡶⠀⠀⠀⣦⡄⠀⢀⣀⠀⠀⠸⡄⡏⡄⠀⠀⠀⠿⣿⣤⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠘⢷⡀⣼⠟
⠀⢀⠘⡇⡴⢋⡀⠀⣀⡀⠹⠿⣾⡿⠟⠀⢀⠳⣜⢊⡴⢀⠀⢀⣠⡛⠁⠀⠀⠀⣴⣿⣷⣦⡄⠀⠀⠀⠀⠈⠳⢁⣴
⠀⠘⣧⡈⢠⠾⠁⡄⠻⣷⣄⠀⣠⣴⡦⠀⣬⢷⡈⡡⠴⢋⡄⠘⠿⣿⣿⠀⢠⣷⣹⣯⣿⣾⣽⣷⡄⠀⠀⣈⢣⡿⠋
⠀⠀⢨⠛⠆⣠⡾⠃⠀⣨⡍⡀⠛⢋⠀⢀⡙⢇⢹⣠⠶⢟⠀⠀⢀⠀⡀⠀⣼⡛⣿⣿⣿⣿⣿⣻⣥⠀⠈⣿⢿⠁
⠀⠀⠸⣦⡀⠋⠀⠀⠀⠘⠿⣧⣾⡿⠃⠀⡳⡌⣯⣶⠞⠁⠀⢾⡿⣿⣿⠀⣻⠿⣯⣿⣿⣿⣿⢿⣿⢃⣀⠈⢿⢋⣤⡄
⠀⠀⠀⠈⠳⣠⡄⠀⠀⢿⣦⣏⣴⣶⠀⠀⠳⣘⣡⠆⠀⠀⠀⢀⣀⠀⣀⠀⢿⣋⣿⡟⢻⣏⣹⣿⣦⠈⠿⡀⡸⠚⡋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⠟⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢿⠿⠿⠂⠀⠉⠉⠀⠀⠻⠿⠿⠃⠀⠀⠰⢡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⣶⣄⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣆⢀⣤⣤⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⢸⣧⠀⠀⡀
⠀⠀⠀⢻⣿⠆⠃⣀⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠈⢁⣈⠛⠋⠀⠀⠀⠺⣦⡀⢹⡿⠃⠀⠀⠙⠀⣾⠇
⠀⠀⠀⠀⠉⣥⣾⣿⠇⠀⠀⠀⠘⢿⡇⣠⣴⣶⠀⣤⡄⠸⡟⢷⡶⠀⢀⣤⣤⡬⢥⡄⣀⣀⣄⠻⣶⡤⡄⠀⣰⣿⠂
⠀⠀⣀⣤⣀⠘⠋⠀⣀⣀⠀⢀⣄⠀⡀⣿⡿⠃⠀⢙⣥⡄⠀⢰⣶⡆⠈⠛⣡⡀⠀⠱⠀⢉⡋⠀⠀⠀⠬⣀⠛⢁
⠀⠀⠻⣿⡿⠿⡇⣾⣿⡿⠂⠸⣿⣷⠸⡇⢀⣴⡆⠈⠻⠓⢤⠘⠛⡁⠀⠘⢿⣧⠀⢆⣾⡿⠃⠀⢀⣤⣀⢸⠐⠁
⠀⠀⠀⠀⠀⣀⣸⠈⠉⠀⠀⠀⠉⠻⡄⣶⣿⣿⠟⠀⠀⠐⣄⢀⠞⠀⠀⠀⠀⠉⢠⠋⠁⠀⠀⠀⠀⠙⢻⠘
⠀⠀⠀⠰⣾⣿⡿⣠⣴⣆⢸⣿⣷⡄⢸⠛⠋⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡄⡞
⠀⠀⠀⠀⠈⠁⠀⠟⠛⠁⠀⠙⠛⠓⠷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠏⠀⠀⠀⠀⠀⢠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⣛⣭⣿⣿⣿⠏
⠀⠀⠀⢠⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠻⠷⣶⣤⣤⣤⣤⣠⣤⣤⣴⡶⠿⠛⣩⢖⣴⠞⣹⡿⠋⠉
⠀⠀⠀⢸⣿⣝⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⢉⡴⠂⠀⠀⠀⠀⠀⠀⣀⣠⠤⠂⠀⡉⠉⠉⠉⢉⡭⠀⠀⠀⣼⡵⠋⠀⣰⡿⠁
⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣴⡿⠋⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⣠⡾⠋⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣶⣴⣶⠿⠛⣁⠴⠊⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⣀⡴⠿⠧⠦⠔⠒⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠳⠶⢶⣮⣅⣀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⣀⠴⠋⢀⣀⣤⡴⠞⠉⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠈⢫⡙⠓⠶⠾⣭⣤⣤⣤⡤⠴⠶⠖⠚⠛⠛⠛⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠠⡀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⢀⣀⣠⣭⣦⣤⣤⣤⣴⡾⠟⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⡀⠀⠀⠀⠀⠉⠓⢀⣠⣶⠾⠟⠛⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠶⠶⠿⠿⠛⠉


⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⣠⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠁⠀⣠⣾⣿⣿⣏⣉⣀⣀⣠⣴⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢥⣄⢵⠄⠀⠈⠠
⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⢸⣿⡴⠚⠉⠉⢿⣿⣶⣦⣄⠉⠙⠻⢿⣿⡿⠿⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⢁⠀⠀⠬⢩⣇⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⠞⠻⣷⣶⣶⡄⠀⠙⠻⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠶⠄⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣦⣠⠏⠀⠀⠘⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⣛⡄⠀⠀⠀⠀⠊⡀
⠀⠀⠀⠰⣶⣤⣄⠀⠈⡿⠀⠀⢀⣤⣤⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠤⠼⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠘⣿⣿⣄⠀⢧⢀⣴⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠈⢛⡀⠀⠀⠀⠀⠈⡠
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⡟⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⡥⠀⠀⠀⠀⠊⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣬⣷⣤⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠓⠦⠤⠄⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡀⡀⢡⡼⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠈⠢⣘⣄⣷⣀⠰⣡⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⢿⡇⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠊⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠊⡁⠢⡈⣿⠡⠋⡠⠁⠀⠀⠀⠀⠀⠀⠻⣷⡄⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢻⡄⠀⢠⡇⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢠⠒⠨⡁⠚⠿⢀⠥⠒⡂⠀⠀⠀⠀⠀⠀⠀⠙⢿⡌⣇⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢻⠀⢸⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠈⠲⣿⠦⢄⠊⢤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⢀⡿⠋⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣢⡀⠑⢀⣿⠔⠁⠠⠚⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢹⡇⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⢀⡶⣄⠀⠀⠹⣤⣧⢋⡤⠚⠉⠉⢉⡽⠋⠀⠀⠀⠀⠀⠑⠄⠀⠠⣀⣯⡠⠒⢋⠠⠋⠀⠀⠀⠀⠀⠀⠙⢧⡀⢸⡇⠀⣿⠟
⠀⠀⠀⠀⠀⠀⢸⠀⠘⢧⡀⠀⣸⠿⠿⠤⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⡂⠀⠐⠠⢈⣿⡀⠤⠐⠘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⡇⣼⠋
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⣷⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠠⣀⠈⣿⠁⠐⣀⠠⢀⠀⠀⠀⠀⠀⢺⣦⡀⠀⢹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⣿⣡⠖⠋⠉⠉⢛⡿⠆⠀⠀⠀⠀⠀⠀⠀⢀⠱⠤⠀⠀⠙⠟⠈⠁⠀⠀⠜⠀⠀⠀⠀⠀⠈⠻⣧⡀⢸⡇⠀⢀⣴⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠷⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⠒⢤⣥⣀⠀⠀⠒⡢⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⠀⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠤⢀⣿⣀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⣿⠉⠀⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠴⠒⠊⠉⠉⠉⠍⣉⠉⠉⠂⠒⠈⠉⡀⠀⠀⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠉⠅⠒⠒⠒⠒⠒⠲⠤⢀⡀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠈⠂⠒⢄⣀⣀⠑⢂⡀⠮⠭⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠠⠤⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠒⠄⡀⠀⠀⠈⢓⡤⢤⠖⠊⡩⠋⠁⡜⠁
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⣀⠀⠀⠀⠀⢀⡨⠕⡲⠉⠁⢀⠎⠀⢠⠁⠀⡼⠁
⠀⠀⠀⠀⠀⡔⣁⡤⠤⠤⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣩⠝⡶⠊⠁⠀⢀⠁⠀⢀⠎⠀⢠⠃⢀⠞
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡠⣴⠚⠉⠀⢠⠁⠀⠀⠀⡎⠀⠀⡎⠀⠀⠁⡠⠋
⠀⠀⢠⢃⠀⠠⠄⠀⠠⠤⠤⢀⡀⠀⠀⣀⡤⠚⠁⢠⠁⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⡰⠁⠀⢡⠎
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠋⡝⠀⠀⠀⡘⠀⠀⠀⢰⠃⠀⠀⢀⠇⠀⠠⠁⠀⡰⠁
⠀⡜⠀⠀⠀⠀⠀⠄⠠⣤⢴⠋⠀⠀⢸⠁⠀⠀⢠⠃⠀⠀⠀⡎⠀⠀⠀⠎⠀⠠⠃⢠⠞⠁
⡜⠀⠀⠀⠀⠀⢀⠴⠊⢠⠇⠀⠀⠀⡌⠀⠀⠀⡎⠀⠀⠀⡜⠀⠀⢀⠎⠀⠐⣀⠔⠁
⡇⠒⠉⢉⠩⠟⠁⠀⠀⠎⠀⠀⡠⠊⠀⠀⠀⡼⠀⠀⢀⠎⠀⠀⠐⢁⡤⠖⠉
⡇⡠⠂⠁⡄⠀⠀⣠⠎⠀⠀⡔⠁⠀⢀⠤⠊⢀⡠⢖⣁⣠⠤⠖⠊⠁
⠛⠒⠲⠤⠤⠤⠬⣅⣀⣀⣈⣀⣀⣠⠥⠤⠖⠊⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢁⠀⠀⠀⠀⡈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⡀⢠⠀⠘⡀⠀⠀⢠⠁⠀⡀⢀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠁⠀⠀⠱⡀⢀⠆⠀⠀⠈⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡀⠀⠀⠀⠙⠃⠀⠀⠀⢀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠴⠠⠄⡀⡀⠀⠀⡌⠑⣄⠀⠀⠀⠀⠀⢸⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡇⠀⠀⠀⠀⠀⡠⠊⢁⠀⠀⢀⢀⠄⠄⠦
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⢄⡉⠑⠘⠀⠀⡀⠑⢄⡀⠀⠀⢸⠀⠀⠀⠑⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⢀⡤⠊⢀⠀⠈⠓⠃⢁⡠⠄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠉⠢⣀⠀⠀⠰⠀⠀⠈⠐⠂⠊⠀⠀⠀⠀⠘⡄⠀⠀⡠⠃⠀⠀⠀⠀⠑⠐⠂⠁⠀⠀⠂⠀⠀⡠⠔⠉⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⠓⢄⠀⡆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⢦⡔⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢐⠀⡠⠊⠁⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠃⠀⠀⠀⠀⠈⠱⡅⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠐⠠⢀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢡⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡌⠀⠀⡔⠁⠀⠀⠀⠀⢀⡀⠔⠂⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⠉⠐⠂⠤⠄⣀⣱⡄⠘⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠃⢠⣎⣀⠠⠤⠐⠂⠉⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⢦⡔⠁⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⠆⠀⠉⠀⠒⠒⠒⠀⠠⠤⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⠄⠀⠒⠒⠒⠈⠁⠀⠰⠅⢀
⠀⠀⠀⠀⠀⢀⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢀⡀
⠀⠀⠀⠀⠻⢄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠛
⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠉⠒⠒⠂⠹⢤⡤⠤⠄⠀⠀⢀⣀⣀⣀⣀⣀⣑⣤⣤⣊⣀⣀⣀⣀⣀⡀⠀⠀⠠⠤⢤⡴⠃⠒⠒⠂⠉⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢉⡉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠋⡟⢢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀⡴⠋⣀⠔⠁⠀⠀⡇⠀⠉⠢⣀⠑⢤⡀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠔⡡⠔⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⠢⢍⢢⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⢀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠙⡄⠀⢀⠠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⠀⠀⠀⠀⢃⠀⡇⡐⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢃⠀⣀⠤⡌⠫⣲⣷⡤⢓⡂⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡜⠘⠀⢀⠆⠀⡠⠚⠪⡁⠀⠀⢈⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠈⠉⠐⡌⣶⠔⢊⣴⡉⢤⠔⠂⠒⢍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠙⢶⡠⠊⡉⠉⠢⠁⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠢⡀⠀⠀⢈⠘⢀⣎⠤⠤⡕⠤⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⢰⢀⠔⠂⢹⠿⢀⠠⢊⠠⠄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡂⠐⠦⣙⣼⠀⠇⠎⢀⢈⣣⣊⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠺⠲⢽⡦⢀⠀⡎⢣⠹⣁⠞⠉⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠛⢷⢤⡀⢇⢠⡾⢉⡁⢒⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠤⢐⣁⠀⢣⠈⣾⡵⠁⠀⠀⡨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⢀⡨⠚⢶⠉⠑⠒⣐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠙⡄⠳⡀⢘⠀⠆⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠐⠬⣢⡄⣴⣹⠓⣶⡿⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣒⣒⣈⠩⣏⠁⠀⡠⠤⠬⡴⠒⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠁⠘⠈⢣⢸⡄⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⠀⠀⠈⠢⡜

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿

⠛⣁⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⢬⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⡋⠀⠈⠑⠓⠄⠀⠀⠀⠀⠰
⠈⠋⠉⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡔⠀⡄⠀⠀⠀⠣⠄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠳⠀⠀⠐⡄⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠐⣆⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡁⠠⠤⠄⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄⡀⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣵⣤⢄⠐⠂
⠀⠀⠁⠀⠀⢐⣀⣠⡀⠐⠲⠶⣶⡶⠀⠈⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠋⠁⢠⠆⠀⠀⠀⢘⠀⠀⠀⢠⣤⣴
⠀⠐⠁⠀⠀⠀⠉⠁⣀⠀⠀⡄⠁⢐⡆⠀⠀⠀⠀⠀⠐⠈⠆⠶⣄⣀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠉⠑⠦⠀⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠀⠀⠀⠀⠀⠀⣴⢀⠀⢰⠁
⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠧⠠⠀⠃⠀⠀⠠⢄⡂⠐⢦⠘⠱⡀⢧⠇⢀⡠⠤
⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡓⠦⢙⣦⣁⣆⢀⡡⠀⡨
⠀⠀⠈⢀⠀⠠⡄⠁⠈⠀⠀⠀⠀⠀⡘⠖⠉⣠⡼⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⠛⠙⠻⢿⣿⣿⡶⠒⠛⠁
⠀⠀⠀⠈⠷⠢⣤⠀⡀⠀⠀⠀⢀⠐⢁⣦⠟⡉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⢰⣥⠴⡺⠋⢁⠞⡿⢹⢟⢣⣀⠀⠁⠁⠀⠐
⠀⠀⠀⠀⠤⠒⠄⠁⠀⠀⠀⠀⠀⣴⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠤⠂⠁⠐⠀⣰⠈⣥⠜⢆⠉⠁
⢄⠀⡄⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠀⠀⢠⡄
⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢐⡀⠀⠀⠀⠴⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠃⠀⠈⠸⠀⣴⡃⡀⠄⡠⠀⠀⠀⠀⠐⣡⠾⠀⠀⠀⠀⠐⠀⠂⡨⠿⢧⡀
⠠⠄⠀⠀⡀⠀⡐⠀⠀⠃⠀⠈⠁⠀⠊⠀⠀⠀⠀⢸⣿⣁⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⢸⠀⠀⠁⠈⠁⠀⠀⡠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⢀
⠅⠊⡀⠌⠀⠀⠠⠄⢀⠠⣈⣉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠁⣀⣒⠒⠂⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣈⠄⡤⠈⠓⠒⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⠊⠉⠄⠘⠉⠉⠐⡄⠀⠀⠀⠤⢀⡐⠠⠀⠠⣄⠉⣠
⠀⠀⠒⠀⠂⠉⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠰⢄⡙⣳⣄⡀⠁⠘⠛⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠱⣤⠉⠛⠶⣶⣸⠀⠋⠃⡀
⣉⣯⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡠⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠐⢒⡀⠙⢛⢃⣀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣤⡀
⠀⠀⢠⡆⠀⢠⡶⠀⠀⠀⣦⡄⠀⢀⣀⠀⠀⠸⡄⡏⡄⠀⠀⠀⠿⣿⣤⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠘⢷⡀⣼⠟
⠀⢀⠘⡇⡴⢋⡀⠀⣀⡀⠹⠿⣾⡿⠟⠀⢀⠳⣜⢊⡴⢀⠀⢀⣠⡛⠁⠀⠀⠀⣴⣿⣷⣦⡄⠀⠀⠀⠀⠈⠳⢁⣴
⠀⠘⣧⡈⢠⠾⠁⡄⠻⣷⣄⠀⣠⣴⡦⠀⣬⢷⡈⡡⠴⢋⡄⠘⠿⣿⣿⠀⢠⣷⣹⣯⣿⣾⣽⣷⡄⠀⠀⣈⢣⡿⠋
⠀⠀⢨⠛⠆⣠⡾⠃⠀⣨⡍⡀⠛⢋⠀⢀⡙⢇⢹⣠⠶⢟⠀⠀⢀⠀⡀⠀⣼⡛⣿⣿⣿⣿⣿⣻⣥⠀⠈⣿⢿⠁
⠀⠀⠸⣦⡀⠋⠀⠀⠀⠘⠿⣧⣾⡿⠃⠀⡳⡌⣯⣶⠞⠁⠀⢾⡿⣿⣿⠀⣻⠿⣯⣿⣿⣿⣿⢿⣿⢃⣀⠈⢿⢋⣤⡄
⠀⠀⠀⠈⠳⣠⡄⠀⠀⢿⣦⣏⣴⣶⠀⠀⠳⣘⣡⠆⠀⠀⠀⢀⣀⠀⣀⠀⢿⣋⣿⡟⢻⣏⣹⣿⣦⠈⠿⡀⡸⠚⡋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⠟⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢿⠿⠿⠂⠀⠉⠉⠀⠀⠻⠿⠿⠃⠀⠀⠰⢡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⣶⣄⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣆⢀⣤⣤⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⢸⣧⠀⠀⡀
⠀⠀⠀⢻⣿⠆⠃⣀⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠈⢁⣈⠛⠋⠀⠀⠀⠺⣦⡀⢹⡿⠃⠀⠀⠙⠀⣾⠇
⠀⠀⠀⠀⠉⣥⣾⣿⠇⠀⠀⠀⠘⢿⡇⣠⣴⣶⠀⣤⡄⠸⡟⢷⡶⠀⢀⣤⣤⡬⢥⡄⣀⣀⣄⠻⣶⡤⡄⠀⣰⣿⠂
⠀⠀⣀⣤⣀⠘⠋⠀⣀⣀⠀⢀⣄⠀⡀⣿⡿⠃⠀⢙⣥⡄⠀⢰⣶⡆⠈⠛⣡⡀⠀⠱⠀⢉⡋⠀⠀⠀⠬⣀⠛⢁
⠀⠀⠻⣿⡿⠿⡇⣾⣿⡿⠂⠸⣿⣷⠸⡇⢀⣴⡆⠈⠻⠓⢤⠘⠛⡁⠀⠘⢿⣧⠀⢆⣾⡿⠃⠀⢀⣤⣀⢸⠐⠁
⠀⠀⠀⠀⠀⣀⣸⠈⠉⠀⠀⠀⠉⠻⡄⣶⣿⣿⠟⠀⠀⠐⣄⢀⠞⠀⠀⠀⠀⠉⢠⠋⠁⠀⠀⠀⠀⠙⢻⠘
⠀⠀⠀⠰⣾⣿⡿⣠⣴⣆⢸⣿⣷⡄⢸⠛⠋⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡄⡞
⠀⠀⠀⠀⠈⠁⠀⠟⠛⠁⠀⠙⠛⠓⠷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠏⠀⠀⠀⠀⠀⢠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡇⣿⡇⢸⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠉⠙⠀⠀⢸⢾⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⣾⣹⣿⠀⢿⣷⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠻⣵⣿⡟⠀⠈⢿⣿⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠈⠛⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⢻⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡄⢳⣸⣶⣾⢀⠂⣼⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣠⠀⠀⠀⠀⠀⢸⡇⢰⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⡛⢊⣽⠉⣽⢯⡐⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠆⠀⠐⠀⠄⠐⠃⡈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣡⡉⢛⠡⠜⠓⢠⠾⢗⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠠⢔⠂⠚⢙⡀⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠙⠋⣸⣧⢘⡇⠻⠉⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⢀⠁⠂⠛⣡⢁⡀⢭⠘⠀⠟⡴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠁⠿⣷⠸⠃⠸⠃⣶⠀⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⢌⡘⢃⡁⠲⢂⣁⠷⠈⠱⠗⡉⡠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣜⠷⢴⣶⠆⢰⢶⡀⡴⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡑⠦⣤⠉⡈⢏⡈⠴⠢⢆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠀⢠⠶⡶⠦⠤⠀⣶⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠡⠆⡰⠄⣡⢨⠰⠶⣀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⡇⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢁⡦⠀⠶⢈⣤⢠⣦⣿⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡷⠀⠀⠀⠀⠀⠀⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⢾⠐⣿⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠐⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⣾⠀⠀⡀⢸⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠃⠀⡁⠀⠀⠁⠀⣀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢠⠄⠈⠀⢀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠏

⠀⠀⠀⢀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠉⠁⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠠⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠂⠉⠀⠈⢈⡻⢶⡀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠢
⠀⠀⠀⠀⠀⠀⠀⡀⢁⠐⠂⠈⠀⠀⠀⠉⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠤⠈⠁⠀⠀⠀⠀⡀⢀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠤⠉⠀⠀⠀⡀⠀⣤⢵⡤⠟⠛⠉
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⠠⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢆⢰⡤⠋⣡⠀⠀⠀⠄
⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠠⡀⠠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠠⠀⢀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡽⡑⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠠⠐
⠀⠀⠈⠠⠀⠀⣀⠔⠑⠀⠐⠱⠀⠀⠀⠀⠀⠀⠀⠈⠈⠡⡀⠈⠀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⡾⡀⠦⡀⠀⠀⠁⢆
⠀⠀⠀⠀⠘⠂⠀⠀⠠⠐⠁⠀⠴⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠃⠀⠘⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⡆⠠⢀⠀⠄⠁⠠⠀⠀⠄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⢀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠘⢄⠀⠉⠉⠀⢀⡀⠁⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⢰⣦⠸⣿⢠⣤⡀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⠶⠤⣀⢿⠇⠿⡏⠛⣤⠁⠀⠛⣿⠛⠁⣴⡿⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⢶⣶⣌⢻⡀⢠⣌⢦⡘⡄⠀⣰⡧⠶⠾⠤⣄⡜⣫⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠹⡟⢠⣷⠀⠰⣤⡈⠙⣇⠘⡿⠘⡇⣿⡾⠁⢀⣄⠀⣠⡄⠈⢉⣩⠄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⠻⣿⠀⠘⢤⣻⡀⠀⠛⠿⡀⠸⣶⡅⢸⣷⡏⢰⣷⢸⡿⠀⡹⠃⣠⠟⠋⠀⣿⡟⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠙⠻⠦⢸⡀⠀⠀⣀⣉⠛⢶⡀⢹⠀⠘⣿⣿⣿⡇⠈⢋⣰⠀⣸⠟⢉⣀⠀⠀⣀⣯⠔⠛⠋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠿⣄⠀⠰⣶⣦⣝⣦⣈⠛⠿⠛⠙⠻⣿⡀⠀⢹⣿⣿⣧⢀⡾⣡⠞⠉⠉⠛⠟⢃⡼⠋⢰⡿⠃⠀⠀⣿⢿⣃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠿⠷⠄⣚⡋⠛⠛⢧⡀⠀⠈⢻⣆⠀⠀⠀⠙⠷⣦⣿⣿⣿⣽⣿⠿⠃⠀⠀⠀⣰⠞⠉⠀⣀⡼⠔⣾⡟⠛⠒⠿⠿⠟⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣈⣻⣟⣆⠀⠀⠉⠻⣆⠀⠙⠳⣤⡀⠀⠀⠸⣯⣿⣿⣿⠁⠀⠀⢀⣠⠾⠋⢀⡴⠛⠋⠀⣸⣛⣥⣤⣾⣓⡒⠾⣿⡷⠆⠀⠀⡇
⠀⠀⠐⠿⠿⠛⣰⢚⣽⠉⣠⣤⣤⡭⠷⢦⣄⡀⠈⢷⣄⣀⣹⣿⣦⣄⣸⣯⣿⣿⣿⣀⣠⣶⣿⣃⣀⣠⡾⠁⢀⣠⠴⠿⣵⣶⣤⡀⠙⣯⣍⠳⣄⠀⠀⠀⡇
⠀⠀⠀⢀⣤⠎⠁⠾⠛⣀⡉⠉⠉⠀⠀⠀⠘⣷⠀⠀⠉⠉⠉⠛⠿⠻⣯⣾⣿⣧⣿⣽⠿⠟⠋⠉⠉⠉⠀⠀⣼⠃⠀⠀⠈⠙⠉⣁⣀⣙⢿⠆⢸⣷⡄⠀⡇
⠀⠀⠀⣿⠟⠀⠀⠀⠘⠿⠿⢦⠀⠀⣀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣼⡏⢀⠀⣀⡀⢀⡾⠿⠟⠉⠀⠀⠈⠻⡇⠀⡇
⠀⠀⠀⠁⠀⣴⣶⡶⢲⣶⠶⠾⢿⣿⢽⣿⣿⣷⣿⡻⣟⣿⣦⣤⣄⡀⢰⣿⣫⣿⣿⡇⣀⣀⣠⣤⣶⣾⣿⣿⣾⣿⣿⢿⣿⡛⠛⠶⢿⣛⠻⣿⣷⡄⠀⠀⡇
⠀⠀⠀⠀⠘⠛⣫⣶⠋⠀⠀⣰⡏⠀⠀⠀⠀⠀⠈⠉⠉⠉⠽⣾⣿⣿⣦⣟⢿⣿⣿⡿⣫⣿⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⣿⣄⠀⠀⠉⣷⣌⠉⠋⠀⠀⡇
⠀⠀⠀⠀⠀⡜⢡⣿⡄⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⢿⣦⣻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢰⣿⡎⢧⠀⠀⠀⡇
⠀⠀⠀⠀⢠⣇⠀⠻⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠟⠁⣼⡆⠀⠀⡇
⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⢏⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢟⣫⡽⣿⣿⢟⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣧⡀⠀⠀⠀⠀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣛⣛⣿⣷⡴⣶⢾⣿⡿⣻⣽⣾⡿⣛⣝⡿⣿⣟⡿⣮⣟⣷⣶⣦⣾⣿⣛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣭⣽⣿⣰⣿⣿⣸⣿⡟⣵⡿⣫⣾⡹⣿⡽⣿⣿⣻⣿⣇⣿⣯⣭⡽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢻⣷⣝⢿⣿⣿⣧⣻⣿⣯⣼⣧⡿⣳⣿⡿⢼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣭⣛⢿⣟⣻⣿⣿⣿⣯⣶⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣎⣫⣿⣿⡿⠟⠛⠉⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠁⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣌⠻⣿⣧⡀⠀⠀⠀⠀⢀⣾⡿⢱⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡙⣿⣷⡀⠀⠀⠀⣾⣿⢃⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣌⢿⣇⠀⠀⢰⣿⡟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠈⠻⣿⣦⢿⡄⠀⢸⣿⠇⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣮⣭⣛⠻⠿⣿⣷⣦⡀⠀⠙⠿⣧⠀⠘⣿⢸⣿⡏⠀⠀⠀⠀⣠⣴⡿⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣦⣍⡛⢿⣦⡀⠀⠘⣷⡀⡿⣾⠟⠀⠀⠀⣠⣾⡿⢋⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣷⣮⣿⣦⡀⠘⣧⣼⠋⠀⠀⠀⣴⣿⠟⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⠉⠓⢾⡏⠀⠀⠀⣼⣿⠏⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣝⡻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢿⡀⠀⢠⣿⢏⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣌⡻⢿⣿⣦⡀⠀⠀⠀⢸⡇⠀⢸⣏⣾⡿⠋⠀⠀⠀⢀⣀⣤⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⣿⠀⣬⡿⠋⠀⠀⢀⣠⣶⡿⢛⣵⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣙⢿⡄⠀⠀⢻⡾⠋⠀⠀⠀⣴⣿⡿⢋⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠉⠛⠿⣦⣿⡄⠀⢸⡇⠀⠀⢠⣾⣿⢋⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣙⠿⣿⣦⣄⠀⠀⠀⠀⠉⠛⢦⣸⡇⠀⢀⣿⡟⣡⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣮⡛⢿⣷⣦⠀⠀⠀⠀⠀⢹⡇⠀⣸⢟⣼⣿⠟⠋⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⢸⡇⢠⣿⡾⠟⠁⣀⣴⣾⢟⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡻⣿⡀⠀⠀⢸⣷⠟⠁⠀⣠⣾⡿⢋⣵⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⢦⣄⡀⠀⠈⠛⠿⣷⣜⢷⡀⠀⢸⡇⠀⢀⣾⣿⠟⣵⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡝⢿⣶⣄⠀⠀⠈⠙⠻⢧⡀⢸⡇⢀⣾⡿⣡⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡹⣿⣷⡄⠀⠀⠀⠀⠙⣿⠁⣸⡟⣴⣿⡿⠋⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡌⢿⣿⡄⠀⠀⠀⠀⣿⢀⣿⣾⠟⠋⢀⣤⣶⣾⠿⣻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣎⢻⣿⡄⠀⠀⢠⣿⠞⠋⠁⣠⣶⣿⠿⣋⣵⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢻⡇⠀⠀⢸⡏⠀⢀⣼⣿⠟⣡⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⣿⠀⠀⣿⠀⢀⣾⢟⣥⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⢠⡏⢀⣾⣣⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣡⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡟⠄⣠⡄⠀⠀⠀⠀⣄⠀⢀⣠⡶⠔⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠁⠀⠀⣇⣴⡇⠀⢰⣿⠋⠉⠘⠁⠀⠀⠘⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢇⠀⠀⠀⠀⠀⠈⡇⣰⠏⡇⠀⠀⡇⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢜⠀⠀⠀⠀⢱⡏⠀⠃⠀⠀⠃⠈⠀⢀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⠘⠀⠀⠀⠀⠘⠁⠀⣸⠂⠀⠀⠀⠠⢶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠖⠶⠞⠀⠀⠀⠈⡇⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣀⠔⢋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⢄⠀⠀⠀⠐⢦⣀⠀⢰⢁⡔⠄⠀⠀⠀⠀⠉⠉⠉⠁⠀⠹⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠢⣄⡀⡀⠙⣄⡷⠋⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠚⠋⣻⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣈⣉⣙⣷⣿⣷⠶⠶⠒⠐⢦⡀⠀⠚⠒⠄⠀⠀⠀⠀⢈⠍⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⡎⠢⣄⡀⠀⠀⠉⠓⠒⠂⠀⠀⡠⠀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢿⣀⠀⠉⢢⣄⠀⢸⡉⠉⠒⠒⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠙⠲⢦⣪⢿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣲⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣰⣿⣿⣿⣟⣯⡶⠀⠀⠀⠀⠀⠀⠀⢲⣿⣻⣿⣿⣿⣆⠀⠀⠀⠀⢀⡀⣿⣤⣿⣴⡾⠀⠀⠀⠀⠀⠀⠀⢷⣦⢿⣤⣿⢀⡀
⠀⢠⣿⣿⣿⣿⠚⢷⣿⡛⠀⠀⠀⠀⠐⢛⣿⡾⠓⣿⣿⣿⣿⡄⠀⠀⠀⣈⡻⣾⠟⠛⣵⣿⣿⣧⠀⠀⠀⣼⣿⣿⣮⠋⠻⣷⢟⣁
⠀⠸⣿⣿⣿⢏⢀⣞⣯⡛⠃⠀⠀⠀⠘⢛⣽⣷⣀⡹⣿⣿⣿⠇⠀⠀⠀⣉⣻⣿⣆⣸⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣇⣴⣿⣟⣉
⠀⠀⠉⢩⣷⢯⡿⢿⡎⠛⠀⠀⠀⠀⠀⠛⢱⡿⢿⡽⣾⡍⠉⠀⠀⠀⠀⠈⢉⡶⣟⣾⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⣿⣷⣻⢾⡉⠁
⠀⠀⠀⠈⠀⠘⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁

⠀⠀⠀⠠⣔⡿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣴⣾⣿⣿⢿⣦⠄⠀⠀⠀⠀⠀⠀⢠⣤⣸⣆⣰⡆⠀⠀⠀⠀⠀⠀⠀⢰⣆⣰⣇⣤⡆
⠀⠀⠰⢶⣯⡿⢽⣿⣿⣿⣇⠀⠀⠀⣸⣿⣿⣿⡯⢿⣭⡶⠆⠀⠀⠀⢀⣶⣶⣯⡳⠿⣿⣵⠟⠀⠀⠀⠀⠀⠻⣮⣿⠿⢞⣽⣶⣶⡀
⠀⠀⠶⢟⣿⡁⠘⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠃⢨⣿⡻⠶⠀⠀⠀⢸⣿⣿⣿⣷⢀⣽⣷⠟⠃⠀⠀⠀⠘⠻⣾⣷⡀⣾⣿⣿⣿⡇
⠀⠀⠰⠟⣽⣿⣞⣮⣟⠛⠃⠀⠀⠀⠘⠛⣻⣵⣻⣿⣯⠻⠆⠀⠀⠀⠀⢿⣿⣿⣿⡽⣮⡟⠛⠁⠀⠀⠀⠀⠛⣻⣽⢯⣿⣿⣿⡿
⠀⠀⠀⠀⠛⠀⠻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠟⠀⠛⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠗⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠛⠁

⠀⠀⢀⣤⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣤⠀⣴⢀⣠⠀⠀⠀⠀⠀⠀⠀⣄⡀⣦⠀⣤
⠀⠀⣾⣿⣿⣿⣳⣟⣯⣤⠀⠀⠀⠀⢀⣤⣼⣻⣞⣿⣿⣿⣷⠀⠀⠀⠀⠰⣦⣻⣿⣯⢟⣯⣤⡄⠀⠀⠀⢠⣤⣽⡻⣽⣿⣟⣴⠆
⠀⢸⣿⣿⣿⡿⠈⢻⡿⣦⡄⠀⠀⠀⢠⣴⣿⣟⠁⢿⣿⣿⣿⡇⠀⠀⠀⠶⣮⣿⡃⢠⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡄⠘⣿⣵⠶
⠀⠈⠿⠿⣟⡵⣾⣿⡻⣦⠀⠀⠀⠀⠀⣴⢟⣿⣶⢮⣻⠿⠿⠁⠀⠀⠀⠰⠾⣛⣿⣺⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣟⣾⣻⠷⠆
⠀⠀⠀⠘⠛⢹⠏⠹⠇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠹⡏⠙⠇⠀⠀⠀⠀⠀⠀⠐⠻⣷⣿⣿⡿⠟⠀⠀⠀⠀⠀⠻⢿⣿⣿⣾⠟⠃

⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄⠀⡀
⠀⠀⢀⣈⡷⣯⢿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⡿⣽⢾⣁⡀⠀⠀⠀⠀⣀⣘⡿⣞⣷⣾⢇⣤⠀⠀⠀⠀⠀⣤⡸⣷⣾⣳⢿⣃⣀
⠀⠀⣉⣽⣿⠏⢻⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⡏⠹⣿⣯⣁⠀⠀⠀⢰⣿⣿⣿⣎⠉⢻⣟⣥⡄⠀⠀⠀⢠⣬⣻⡿⠃⣱⣿⣿⣿⡆
⠀⠀⢉⣵⢿⣦⣠⡻⣿⣿⡟⠀⠀⠀⢻⣿⣿⢟⣤⣴⡿⣮⡉⠀⠀⠀⠘⣿⣿⣿⣿⢤⡾⢿⣥⠀⠀⠀⠀⠀⣬⡿⢷⡤⣿⣿⣿⣿⠇
⠀⠀⠈⠁⣿⠛⣷⠻⢷⠀⠀⠀⠀⠀⠀⠀⡾⠟⣾⠛⣿⠈⠁⠀⠀⠀⠀⠹⣿⣿⣿⣯⣿⠧⠀⠀⠀⠀⠀⠀⠀⠾⣻⣽⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⢠⣿⡇⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⠀⠀⠒⢤⡀⢀⡀⠀⠈⠑⢶⣄⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠳⣝⡛⢶⣤⡀⠈⠁⠀⠀⠁⠀⠀⠀⣰⠆⠀⢛⣿⣟⠀⠀⢀⣤⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠍⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⡿⠀⠀⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⣀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠀⠀⠀⠀⠘⠙⣷⡄⠀⠀⠀⠀⠀⣧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠐⠄⠀⡟⠀⠀⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⢿⠿⠿⠋⠁⠀⠀⣠⡔⠀⠁⠀⠀⠀⠀⡀⠀⠀⢹⣿⣎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠙⢿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⡀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠙⠒⠠⢄⣈⡀⠀⠀⠤⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠀⠀⠀⠈⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⢀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

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

⠀⠀⢠⣆⠀⠰⢆⠀⠀⠀⢀⡏⠐⠒⠐⠒⠮⠁⠀⣔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠐⠢⠅⢻⡄⢄⠈⠳⢤⣀⣸⠁⠀⠀⠀⢠⠁⣰⡟⠁⠀⠀⠀⠀⠀⠀⣶⠀⠄⢀⠀⠀⠀⠀⠈⠗⠶⠊⠉⠉⠉⠁⢀⠀⢀⣦⡀⠀⠀⠀⢠⠇
⠀⠜⠀⠀⢙⠄⠁⠀⠀⢹⡇⠀⠀⠀⢀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⡀⠘⡇⠀⠀⠘⠂⡀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠳⣄⡀⠀⡝
⠀⡅⠀⠀⠀⣧⠀⠀⣀⣾⠁⣀⡀⠴⠂⠨⡂⠀⠀⠀⠀⠀⠘⢳⡗⠀⠀⠙⣄⠀⠀⠀⠀⠑⠄⠀⠙⢆⠀⠀⣀⣀⡀⢱⠀⠀⠀⠀⠙⣾⠁
⠼⠁⠀⠀⠀⢹⡆⠀⢩⠉⢤⣄⠒⠒⠢⡷⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠁⠂⠈⠻⡉⠉⠀⠀⠸⡇⠀⡀⠀⢠⡿⠁
⠀⠁⠀⠀⠀⠘⣇⠀⠈⠆⠁⠘⢳⣄⡰⠃⠀⠀⠐⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢀⠀⡈⠒⠄⠀⠀⡅⠀⡈⢻⡙⢟⠈⠉⠁
⠐⠀⠀⠀⠀⠀⠿⠀⠀⢠⢰⠀⠀⠹⣅⣄⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⢂⠀⠈⢫⠆⠀⠀⠀⣠⠎⠀⠈⠂⠀⠀⠀⢻⡀⣀⠘⠇
⠀⠀⡀⠀⠀⠀⢥⡂⠀⠀⡀⠄⠀⠀⠈⠓⣆⠀⠀⠀⠀⠀⣇⠁⠀⠀⠀⠀⠈⢄⠀⠀⠐⢱⡀⣼⠁⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⢸⡀
⢰⠀⠉⠙⠉⠓⠾⣇⠀⠀⢂⠀⠂⠀⠀⠀⠘⢷⡀⠀⠀⢠⠇⠀⠀⠠⢀⠀⠀⠀⠁⡀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⣼⠐⠒⠚⠡
⠈⠀⠀⠀⠀⠀⠀⢽⠀⠀⠈⡀⠀⠠⡀⠀⠀⠈⠿⣆⢀⡟⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⢄⠀⠀⠙⢧⡀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡏
⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠻⣯⠀⠀⠀⠀⠀⠀⠈⡀⡀⠠⣀⠈⢆⠀⠀⠈⠳⣄⠀⠀⡰⠃⠀⠀⠀⢰⠄
⠀⠐⢄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠦⠒⢒⣶⠆⠙⢷⡀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠲⡂⡀⠀⠀⠙⢷⣞⣅⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠃
⠀⠀⠁⢱⠤⠤⠄⠸⣇⠀⠀⠀⢀⡄⠀⠀⠠⠊⠁⠂⠀⠈⢻⡄⠀⠀⠀⠀⠀⣣⠄⢤⠄⠀⠙⢌⠂⠀⠀⠀⡿⠀⠈⠳⠄⢰⠃
⠀⠀⣠⠋⣤⡀⠀⠀⣷⢀⠔⠁⠈⠓⢄⡰⠋⠈⠑⠇⠀⠀⣈⢽⣆⠀⠀⠀⠀⠁⠏⠁⠀⠀⠀⠈⠱⣄⠀⠐⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠰⠰
⠂⣼⠁⠀⠀⠠⠈⠓⡻⠁⠀⠀⠀⠀⡼⠃⠀⠀⠀⠌⢇⠋⠀⠀⠹⣆⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⣜⠁⠀⠀⠀⣀⡌
⣾⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣽⠶⠛⠁⠀⠈⠂⡀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣴⠏⠙⠛⠛⠉⠙
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠂⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠂⠘⣆⠀⠀⠀⠀⠀⠀⢹⡅⣼⡏⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡆⠀⠀⢠⡴⠋⠀⠉⠉⠉⠀⠀⠛⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢻⠆⠈⠁⠀⠈⠁⠀⠀⠀⠀⡼

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠠⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⣅⡀⢤⣀⠠⠦⠤⠘⠙⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⢶⠀⠀⠘⠁⠐⠀⠄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠃
⠀⠀⠀⠆⡠⠈⡄⢀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠖⠋
⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠚⠋⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣢⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠇
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠔⠀⠉
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠱⢀⡀⠀⠀⠀⠀⠀⠀⠄⠸⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠘
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠀⡀⠈⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡍⠄⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⠀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⠼⡥⠥⠀⠀⠀⠀⠔⠈⠀⡀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠄⢠⠂⠀⠆⣀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠁
⠀⠀⠀⠀⠀⢀⠆⣤⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠁⡀⠀⢠⡀⠰⠦⠐⠛⠪⡉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠊⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠆⠈⠑⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣄⠰⠛⠠⢀⠁⠀⠠⠀⠁⠀⠀⠀⠀⢀⠀⢀⠀⠄⣤⡀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠐⠆
⠀⠠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⣠⠷⠟⠁⡁⠘⠁⠲⠀⠈⠁⡄⠀⠀⠀⠀⡀⠀⠈⢲⠈⣄⣛⠓⠂⢠⠆⠀⠀⢰⢂⠀⡇⠀⠀⠀⠅⠠⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠁⠈⠁⠀⠀⠀⠉⢌⠀⠀⠀⠈⣢⠁⠀⠀⠀⠀⢀⠀⠀⢀⠒⠂⠈⠉⠀⠈⠌⠹⡀⠀⠇⠀⠀⠘⠀⠀⠠⠀⢘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⡀⠓⠀⠀⢀⠂⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⢀⠐⠀⠁⠀⠀⠐⠆⠁⡀⠀⠀⠀⡀⠠⠀⠆⠀⠀⠀⠐⠈⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢄⠐⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⠃⠀⠀⠀⠁
⠀⠀⠠⡄⠀⠀⠀⠠⠤⠠⠤⢈⠔⠉⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠈⠀⠐⠀⠀⠀⠀⡀⠒⠂⠀⠀⠐⢀⠢⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢦⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⠀⠂⠀⠃⠈⠂⠀⠁⠀⠀⡀⡀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠐⠀⠐⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠉⠉⠉⠙⠉⠉⠁⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠂⠀⢁⠀⠀⠀⠀⠀⠀⠀⣀⠗
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆⠀⠰⠅⠐⠃⠀⠀⠀⢀⠠⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠈⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠆⠀⠀⡀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠊⠀⠀⠀⡀⠈⠁⠀⡈⠀⠀⠀⠀⢠⡌⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠄⠀⠐⠀⠀⠀⠀⡠⠁⠀⠀⠀⣀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠉⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⢁⡏⠳⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⠃⠀⠀⢸⠃⡴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣰⠏⢈⡁⠀⢀⢀⡟⠀⠀⠙⠛⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡾⠻⣦⡼⠁⠈⠁⠀⠘⠃⠀⠸⣼⡥⠆⠀⠀⣼⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⣰⠟⠙⢧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣼⠋⠀⠀⠀⠀⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⠶⠋⠀⠀⠀⠀⠸⠇⠀⠀⠀⣷⠀⠀⠀⠹⣶⣃⡤⠞⠁⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢹⡄⠀⢀⡼⠋⠁⠀⠀⢀⣠⠀⠀⠙⠛⣻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠃⠀⠀⠀⣧⠀⠀⠀⠈⣇⠀⠀⠀⠀⢻⣤⡾⠁⣀⣀⣤⠶⠋⠁⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢸⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⠟⠛⠋⠉⠁⠀⠰⠖⠂⠀⢾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠛⠃⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⡄⢀⡼⠋⠀⠀⠀⠀⣀⡤⠖⠀⠀⢀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⣻⡿⠧⠤⠴⠶⠚⠋⠁⠀⠀⠀⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡳⠾⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⣷⡀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠈⣿⣶⣟⣁⣀⣀⣀⣀⣤⡤⠶⠞⠂⠀⠀⠰⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⠆⠀⡀⠀⠀⠹⣦⡀⣠⣼⠟⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣍⣛⣓⣀⣸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⡿⢿⡁⠈⠛⠳⠶⢤⣤⡤⠀⠠⠶⠶⠆⠀⠀⠀⠈⠳⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⠈⢳⣄⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀⠙⠷⣌⡉⠀⠀⠀⢻⡛⠛⠒⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣿⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⢠⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⠀⠀⢀⡿⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⠇⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣿⠏⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣦⠀⠀⠀⠈⠀⣄⠀⠀⠀⢠⠀⠀⠀⢠⣤⣼⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⢿⣖⠄⠀⠀⠃⠰⡄⠀⢸⡄⠀⣠⣿⣿⡿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠐⠀⠀⢹⣧⡀⠀⠀⠀⠷⠀⢨⠀⣴⣿⣿⣿⠒⠀⠀⠠⠂⠀⠀⠀⡀⢠⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡇⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠙⣷⣄⠀⠀⠀⡤⠀⢶⣿⣿⢛⣠⣠⡶⠩⠄⠐⠀⠉⣈⣥⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⡆⠈⠃⣄⠀⠀⠀⡁⠀⠀⠾⣿⣿⡄⠀⠀⠇⢀⡾⢉⡅⠸⠋⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⣷⡄⠀⠀⠑⠤⣀⠁⣄⠀⠀⢼⣿⣷⡇⠠⢀⣾⡇⠈⠀⡀⣠⣤⣾⣿⡿⠟⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢿⣧⡀⠀⠀⠀⠀⠰⠀⠤⠀⠈⠻⣿⣿⢁⣾⣟⣴⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⢹⣿⣾⣿⣿⡟⠛⠋⠁⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠸⣿⣶⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⠏⠉⠉⠘⠓⠒⣈⠳⠆⠿⠈⠛⠰⠓⠰⠂⠐⢂⣼⠛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠠⠆⠀⠀⣰⡟⠀⠀⠀⡴⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢩⣿⣷⣤⡄⠀⠀⡀⠀⢠⡿⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⡀⠀⠀⠀⠉⠤⠀⠀⠈⢿⣿⣿⡄⠀⠛⠀⢸⠃⠀⠈⠀⠀⠀⠀⠀⠀⡀⣴⣾⣿⣿⠏⠁⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡉⠢⠀⠀⠀⠀⠈⠐⠦⠀⠉⢿⣷⣄⡀⢀⡁⠀⠀⠀⠀⠀⣰⣶⣤⡾⠿⠛⠉⠁⣀⢀⣤⣤⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⣧⡀⠈⠓⠀⠤⢀⠀⠀⠀⠀⠈⠙⠛⢷⣿⣵⣶⣶⣶⠶⠟⠛⠋⣁⡀⠤⠄⠛⠘⠋⣤⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠻⣿⣧⡀⠀⠀⠀⠘⠁⣄⠀⠀⠀⠀⢸⡏⠉⠉⠉⠀⠀⡐⠖⠀⠉⠀⠀⠀⠀⣠⣾⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⡀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠀⠀⠐⢛⣿⣿⣶⣄⠀⡀⠀⠀⡀⠀⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⣦⣾⣜⡋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠀⠀⠈⠙⠛⢿⣿⣿⣧⣀⠀⠰⠀⣿⠀⠀⠄⠀⠀⠀⣀⢠⣴⣿⣿⡯⠄⠀⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⠙⠿⢿⣦⡀⠀⢿⠀⡘⠀⠀⠀⣶⣿⣿⣿⠟⠁⠀⠀⠀⡀⠚
⠀⠀⠀⠀⠀⠀⠀⢰⣶⢀⡀⣀⠀⡀⠙⠃⠀⠀⡀⠀⠀⠙⢿⣷⣾⣸⣆⠀⣸⣷⣾⠟⡋⠁⠀⠀⠀⠀⣀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢽⠳⣤⣄⠀⠀⠙⠀⠂⣄⠀⠀⠈⠁⠂⠙⠛⣿⠿⠿⢿⠟⠉⠁⢠⠄⠶⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠻⣿⣦⣄⡀⠀⠀⠑⠄⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠒⠀⠒⠐⠂⠐⠂⣰⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠉⠋⠟⣿⣿⣶⣤⡀⢃⠀⠀⢀⣾⠃⠀⠐⠀⠀⠀⠀⢀⣀⣀⣤⣶⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠉⠻⠿⡿⣦⣄⠀⣼⣿⣆⣀⣠⣦⣴⣶⣾⣿⡿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠶⠂⠀⠛⠻⣿⣿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠉⠀⠐⠐⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢀⣴
⠀⠀⣸⠀⢠⡾⠀⠀⠰⣶⡀⣀⣤⡄⠀⡸⡼⡱⠀⠀⠀⠛⣿⡶⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠻⡄⡾⠃
⠀⢠⠘⠔⢉⡄⠀⣤⣄⠙⠛⠛⠋⠀⢰⡝⢮⠔⣣⠆⢠⣴⣍⣀⠀⢀⢸⣿⣿⣳⣆⡀⠀⠀⠀⣜⣰⡿
⠀⠈⠷⣄⠋⢠⡆⠈⠿⠆⢰⡾⠟⠀⢳⡙⡄⢊⣡⠆⠀⠉⠛⠋⠀⣿⣷⣿⣿⣿⣿⡿⠀⠀⣶⣼⠏
⠀⠀⢧⡀⠰⠋⠀⠀⢻⣶⣂⣴⡆⠀⢦⠱⢞⣩⡴⠀⢠⣴⣴⡆⢸⣷⣾⣿⣿⣿⣿⣿⡷⠀⠘⣿⠖⣀
⠀⠀⠈⠳⢄⡀⠀⠀⣶⣍⢋⣭⡄⠀⢻⠕⣩⠁⠀⠀⠈⡁⠉⠁⠰⣷⢻⡿⢿⣟⣳⣿⡁⢻⡆⢸⠾⠛
⠀⠀⠀⠀⠘⠁⠀⠀⠈⠻⠟⠋⠀⠀⠀⠉⠁⠀⠀⠀⠘⢿⠿⠷⠀⠉⠋⠁⠈⠻⠿⠟⠁⠀⠀⢣⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠀⢸⣷⡄⢀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠸⣿⠀⣴⣶⠀⠀⠀⡀⠀⢿⣠⡄⠀⢸⡆⠀⡄
⠀⠀⠈⢿⡇⢀⣤⡄⠀⠀⠸⣿⣿⠀⢀⡀⠀⠀⠀⣤⣍⡁⠀⠀⠀⠻⠆⠀⠟⠀⠀⣀⡁⠸⠇⠀⣠
⠀⠀⠀⠀⠸⡿⠛⠁⠀⠀⠀⠈⠇⣴⣿⠟⠸⠷⠀⠻⢙⣋⡀⠰⡷⠟⠙⢂⠐⠶⠶⠙⠛⠓⠀⢸⠟
⠀⠐⣾⣿⣦⡆⣴⣶⣶⠀⢿⣦⠀⡟⠁⣀⡀⢺⣿⡀⠸⠿⠃⠀⢰⣷⠀⠈⣠⣶⠆⠀⠀⠈⠑⠄⠖
⠀⠀⠈⠉⠀⢰⠛⠛⠁⠀⠘⠻⡇⣥⣾⣿⠇⠀⠀⣌⠁⡔⠁⠀⠀⠙⢂⡵⠋⠁⠀⠀⠘⠿⠦
⠀⠀⠀⢴⣿⡿⢀⣤⡄⢾⣶⣦⢸⠟⠛⠉⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⢈⣀⠄⠀⠀⠀⢠⠰⠃
⠀⠀⠀⠀⠉⠀⠞⠛⠁⠈⠛⠛⠺⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⡼⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢄
⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠴⠒⠉
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠘⠢⡀⠀⠀⢀⠀⠀⡌⠀⢠
⠀⠀⠀⠀⠀⠘⣷⠄⠈⠁⠀⠀⠀⠀⢠⣤⣤⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⢿⣄⡛⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠄⠀⠀⠀⠀⢈⢿⣶⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡀⠀⠣⢤⣀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡈⠓⠲⠦⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠹⡀⡔⣠⠀⡟⢂⢂⡄⢰⠴⣠⢲⢰⡔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠈⠀⠉⠀⠁⠁⠈⠀⠁⠈⠈⡄⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⣸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠀⠀⠀⠀⢄⠀⠀⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠓⠀⠀⠀⠀⢀⠱⣴⣣⠔⠉⠀⠀⠀⠑⠤⣀⠀⠀⢳⡀⠀⣠⠏⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠈⠻⡿⠉⠉⠁⠉⠀⠠⠄⠀⠙⢦⣘⣇⢠⠏⠀⢀⡤⠞⠁⠀⠐⢀
⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣴⣚⡉
⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠉⠉⡉⠁⠒⠦
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢯⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢃⠈⣆⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣗⡲⠶⠶⠤⢦⣾⣄⢹⣿⠀⠀⠀⢀⣠⠤⠖⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠤⠶⠶⠶⠷⠾⠻⣷⣿⠀⠀⡜⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣰⠀⡈⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣾⣉⠹⣛⣳⣶⣼⣿⣷⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠉⠙⡇⠀⠀⠀⠀⣀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡀⠀⢴⠿⣋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⣄⠀⠀⢧⣸⣿⣾⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣮⠳⣦⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠙⠛⢿⠀⠀⣀⣤⣤⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⡿⢋⢱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢏⣴⠴⠃⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⢉⣡⡴⢚⢏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠊⡀⠀⡾⢋⠆⣩⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡳⣦⠀⠀⠀⣴⢁⣼⣯⣷⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⡇⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⣿⠙⣎⣷⠀⢠⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠙⢆⠀⠀⠀⡀⡿⡆⠀⠀⠀⣿⡿⣦⡀⠀⠀⠀⡿⠀⣹⡏⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡄⠀⠀⣆⠀⠀⡇⠧⢻⠀⠀⢰⡏⠁⢀⠙⣦⠀⠀⢳⣿⣿⣏⠤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠡⠀⠀⠀⣸⠀⠀⢣⠀⡀⢧⠀⠈⠿⣄⡀⢀⣿⠁⢀⣸⠿⠿⠿⣏⡉⠁⠀⠀⢈⣹⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⠘⣼⡇⠀⠀⠀⠡⠐⣆⠀⠀⠀⠀⠹⣿⡷⠖⠋⠀⠀⠀⠀⠀⠉⠒⠙⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠘⣿⠀⢀⡠⠔⠚⠓⢶⣶⣶⣶⣶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠚⣿⡖⠒⠒⠒⠒⠒⠒⣿⠋⠁⠀⠀⠀⠀⠀⠈⠙⠿⠭⢿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢿⣄⠀⠀⠀⠀⣼⢫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢈⢿⡆⠀⢀⣴⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣺⣘⠇⠀⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠤⠤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⠠⠤⠤⢄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠠⢄⠀⠀⠀⠈⠒⢄⡀⠀⠀⢌⡉⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠠⠀⠀⠤⢄⡀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠑⢤⡀⠀⠀⠉⠢⣀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⣄⠀⠀⠀⠑⣄⠀⠀⠱⡄⠀⠀⠢⡈⠓⢄
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠁⠀⠒⢄⡀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠈⠓⢄⠀⠀⠀⠙⢦⡀⠀⠀⠈⠢⡀⠀⠀⠈⢢⡀⠀⠘⣆⠀⠀⠙⢄⠀⠑⢄
⠀⠀⠀⠀⣠⠋⠀⠀⠠⣀⠀⠀⢀⣀⣉⣢⣀⣀⣀⣀⣀⣈⣦⣤⣤⣤⣤⠵⠦⠤⡤⠤⠽⠶⠶⣶⠶⠾⠶⠤⠤⡤⠽⠦⠤⣬⡷⣤⣤⣌⣧⣈⣄⣳⡀
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠉⠉⡉⠄⠋⠁⠀⠀⢀⠴⠋⠁⠀⠀⡠⠊⠀⠀⢀⡤⠊⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⠞⠀⠀⠀⡴⠃⠀⢀⠔⠁⢀⠜⡩⠟⠛⠛⠖
⠀⠀⠀⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⣀⠴⠋⠀⠀⣀⠔⠋⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⡰⠃⠀⠀⢀⠞⠁⠀⣠⠋⠀⠀⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠤⠊⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣠⠊⠀⠀⠀⡰⠃⠀⢀⠔⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⡠⠞⠁⠀⠀⣠⠎⠀⠀⢀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠈⢀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢀⣀⣀⣀⠠⠤⠄⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣆⡀⠀⠀⠱⣦⣴⣿⣿⣿⣤⣤⠆⠀⠀⣀⣤⣾⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣄⣼⡀⢹⣿⣿⣿⣿⣿⠃⣰⣀⣼⣿⣿⣟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣷⣼⣿⣿⣿⣿⣯⣰⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣡⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣷⣴⣿⣿⣿⣯⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⢿⡿⠛⠉⠈⠙⠻⡿⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣼⣿⣿⣿⣿⣧⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣝⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⡇⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⠣⢟⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠁

⢲⣤⣤⣤⣤⠠⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢠⣀⣄⡀⠀⠀⠐⡶⣶⣶⡶⠶⣶⣶⣤
⠀⢹⣧⡉⠙⠷⣷⣷⡘⡦⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⠩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⡟⠛⡄⠀⠀⢘⣶⢮⡱⣞⢀⠓⠀⠁⢂
⠀⠀⠍⠿⢗⣀⠀⠈⠉⠃⠁⣿⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠴⢒⠓⠲⠸⠄⠀⠀⢿⣿⢿⣦⣈⢣⠀⠀⣼
⠀⠀⠘⢿⣭⡽⠞⣣⡄⡀⠀⠙⠃⠀⠀⢀⣔⠀⢸⡁⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⢀⠀⠀⠂⡄⠀⠀⠨⠿⣷⣎⡈⠁
⠀⠀⠀⠀⠑⠂⠁⠀⠈⠺⠷⠦⣀⠠⠀⠀⠙⠛⠎⠓⠚⠓⠲⠇⠀⠀⠀⠀⠀⠉⠀⣤⣀⢻⣄⣄⣬⡿⣿⣷⠿⠆⠀⠀⠀⠻⠯⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣅⢹⣶⣽⣟⣿⠿⠛⠀⢀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠰⠀⠀⠀⡄⡏⠉⠠⠀⠢⡀
⠀⡀⠀⠖⠀⠀⠀⠀⠀⠨⢻⣤⠀⠀⠀⠀⠀⡐⢿⠇⢰⢃⠀⠀⢀⢠⢤⡄⢀⢀⠀⣤⡤⢀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢩⠀⠸⠀⠀⠰⠆
⢸⣷⠋⢰⠆⠀⠰⡄⠀⠀⠂⢽⡇⠀⠀⠀⠀⡝⣿⠀⢨⡟⠀⣰⢻⠿⣼⢣⡤⠾⠋⣁⢴⠖⠀⠀⠀⠀⠀⠀⠈⣑⠦⠀⠠⡀⠀⠀⠀⠀⠀⠀⣆
⣸⣿⡿⠁⠀⠀⣤⠘⣆⠈⣻⣲⡇⠀⠈⡐⢀⣤⡌⠀⣼⡧⣠⣿⠂⠴⠋⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⣀⠐⠀⠀⠀⠀⠀⠀⠀⣸
⢹⣛⡄⠂⠄⠀⠀⢀⠀⢠⣜⡟⠀⠀⠀⠁⠀⠙⠁⠀⠻⠁⠛⠁⠀⠠⠤⣼⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡤⡄
⠀⢿⠡⢎⡄⠀⠀⣄⢁⡰⡎⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡐⠷⠶⢶⣔⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⣬⣌⡀
⠀⠘⢷⣎⠄⠀⢦⢰⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠿⠳⠦⢤⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⢻⡆⢼⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⢛⠑⠀⠀⠀⢀⡀⡐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⣧⣄⣀
⠀⠀⠀⠀⠁⠀⠀⠀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢳⠘⡅⠘⢧⢉⠀⠙⠟⠟⠈⠉⠀⠀⠀⠀⠀⢫⣄⢀⠀⠘⠀⠀⠸⣯⠿⡿⣷⣶⡆⢠⣄
⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣀⣤⣤⡶⣾⣾⣷⣦⣄⠀⠀⠙⢿⡄⡀⠀⢠⣶⣿⣄⠸⠇⢸⡟⢿⡿⣠
⠀⠀⠀⠀⠈⠳⣯⣟⣷⢮⡙⠆⠀⢀⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⠋⠻⣮⠻⣿⠝⣻⠆⠀⠀⠀⠙⠁⠀⢘⡻⢿⡖⠂⠀⠘⠀⠞⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠟⠂⢤⣄⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣽⡷⠖⣚⣶⣦⡆⠁⠉⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣯⣙⡀⠀⠈⠐⠋
⠀⠀⣴⣶⡶⠶⢷⠖⠂⠀⠀⠘⠳⣶⣿⣛⠲⡄⠀⠀⠀⢀⠴⢿⣿⢯⣭⠄⠀⠈⠙⠉⠄⠀⢀⠀⠀⠀⠀⠁⠀⠈⠻⢿⣿⣽⣥⡄⠀⠰⡀
⠀⠀⢈⣙⣛⣛⣛⡛⠃⠀⢤⡙⢷⣤⡀⠉⠙⠉⠀⠀⣠⣾⡛⣛⣫⣤⠴⢀⣀⣴⣤⡾⠂⣀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⣾⣿⣿⣯⣿⣯⡅⢀⡐⢦⡙⠳⣽⣻⣆⠀⠀⠀⠀⠉⠛⠟⠿⣿⣿⣿⠟⣻⣿⡏⡅⣴⣟⣰⣿⠇⠀⠀⠀⠀⠀⠀⢦⣶⡆⠀⠀⣠⡄
⠀⣈⣭⣭⣽⡶⠄⠠⣌⣳⣦⡛⢷⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⢳⣿⣿⠿⠏⠀⠀⠀⠀⠀⢰⠤⢹⣙⣤⡞⣽⢟⡏
⢼⣯⣿⣿⡿⠟⠀⠸⣿⡿⣿⣟⠿⠿⠀⠀⠀⢀⣠⣤⠤⢦⠀⠠⣤⣤⣀⠀⠈⠉⠁⠁⠁⠀⠀⠀⠀⢠⣶⠀⢀⡶⣢⣾⡿⠋⣻⣿⣆⣋⡜⢳⡀
⠀⣤⡶⠟⢛⡯⢠⣷⣬⡻⢿⣿⡆⠀⢀⣤⡾⠿⡛⠣⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢸⣤⡌⠀⠛⠙⠳⢚⢉⣭⡸⣟⣿⡯
⠘⠻⠟⠛⣩⣧⡌⢻⣿⢿⡄⠀⠀⢠⡾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠁⠀⠀⠀⠀⣀⠄⠤⠚⠀⠉⢀⡈⢠⣥⣈⡘⠻⣷⣾⣥⣿⣧
⠀⠀⠀⢸⣿⣿⡇⠀⠙⠻⠃⠀⣠⣏⠀⠀⠀⠀⠀⠀⢠⢂⢂⣾⣶⡾⠁⠀⠀⠀⠀⠀⠊⠁⣀⣠⠴⢤⣯⠉⠙⠿⣿⣿⡛⢦⣬⣽⣣⡌⠉
⠀⠀⠀⠘⢿⠟⠁⠀⠀⠀⠀⠈⠉⠉⠙⠓⠀⢠⣤⣤⣷⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠲⣄⣤⡀⠘⢀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⣊⡁⠀⢠⡆
⠀⠀⠀⠀⠀⠀⢄⠀⠉⠉⠉⠟⠛⠙⣦⡈⠃⠀⠀⢸⡇⠀⢣⠀⠈⢉⠛⡳⢄⠀⠹
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⢸⡇⠀⠌⠀⠐⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡀⢂⠀⢸⡇⠢⣤⠀⢀⠀⠀⠀⠀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠐⠂⡄⠀⠀⠀⠀⠼⠀⢸⡇⢠⡆⠀⠀⠱⣄⠀⢀⠀⠀⠀⠀⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⡄⢸⡄⣾⠀⠀⠀⠀⠀⠲⠀⢀⠰⠀⠁⠠⠂⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠃⠀⠀⡠⠄⠠⢄⡀⡃⠀⡠⠄⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⠀⠂⠀⠀⠀⠀⣀⡙⢧⡾⠄⣀⡀⠀⠀⣀⡀⠀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⣄⠀⠀⠀⠀⢤⠀⠄⢀⠇⠂⡀⠀⠀⠀⠀⠉⢁⠈⠱⡀⠀⠀⠀⠀⠉⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠉⠀⠀⠀⠀⢰⡄⠀⠀⠀⣦⠀⠀⠀⠀⠈⠀⠀⠙⡆⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⢀⠤⠖⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠸⠃⠀⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢸⡇
⠀⠀⠀⡀⠚⠁⠀⠤⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⡄⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⠇
⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢰⠃⢠⠇⠀⠀⡄⠀⠀⠤⠒⠒⠢⡤⢀⡀
⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⢀⡄⠀⠀⡴⠒⠀⡈⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠐⠖⠲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠔⠁⠀⠀⠀⢰⠀⠈⠃⠀⠀⠶⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠋⠉⠉⠙⠉⠑⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡆⠀⣀⠀⠚⠀⠐⠓⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡍⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠒⢠⠄⠀⠀⠘⣦⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠄⠐⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄
⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠒⠂⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠀⠀⠀⠁⠀⠀⠁⠀⠸⠃⠰⠀⠀⠀⠀⠀⡀⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠷⣴⠃⠀⠈⠣⠤⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠶⡀
⠀⠀⠀⠀⢀⡀⠐⠂⠶⢄⠀⠀⠀⡀⠈⠀⠀⠀⠈⠉⠉⠀⢆⡀⠀⠰⠂⠀⠀⡀⠀⠀⠃
⠀⢠⠄⠈⠀⠀⠀⣀⣀⣀⠰⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠆⣀⠠⠀⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⠃⠠⠄⠀⠀⠀⠀⠀⢦
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠁
⠘⠃⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡀⠀⠀⠀⢺⡄⠀⢰⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⡀⢀⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠄⠀⠘⠱⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠀⠀⠀⠓⠛⢁
⠀⠀⠀⠀⠁⠓⡀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⡚⢠
⠀⠠⠀⠈⠀⢠⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⡉⡸⠀⡀
⠀⠀⠀⠀⠀⡤⠀⢤⠀⡻⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠐⠲⠤⡀⢀⠜
⠀⠂⠀⠀⠈⠀⠠⣀⠆⡴⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠐⠆⠄⢀⠀⠠⠒⠁
⠀⠀⠀⠀⠨⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠈⢥⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⡀⠀⠀⢨⠟⢃⠀⠂⠤⠄⠀⠊⠐⡀⠀⠀⡤⢄⠀⠀⠀⠀⠀⡄
⠀⠀⠸⡁⠀⠀⠀⠀⣴⠂⠀⠀⠀⣉⣁⠤⠀⠀⠀⠀⠘⢅⢁⠂⢀⠄⢄⠀⣤⠘⠂⠀⠀⠀⠀⠀⢀⠢⠤
⠀⠀⢘⡇⠀⠀⠀⡶⢗⠀⠀⠀⣀⣀⠀⠀⠄⠀⠀⠀⠖⠂⠠⢤⠞⠀⢀⠈⠁⠀⣀⠄⠀⠀⠀⢤⠀⠑
⠀⠀⢸⠁⠀⠀⠢⣭⠵⠀⡀⠀⠀⠀⠁⠀⢀⠄⠀⠀⠀⠐⢃⣬⣄⠛⢆⠲⠷⠢⠀⠀⠀⠀⠠⠀⠀⢈⣤⡀
⠀⠀⡎⠀⠀⠙⠦⠶⠍⡉⠀⠀⠲⠄⢀⠠⠡⠀⠀⠀⠀⠀⠘⠀⠀⠫⠀⠆⠠⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠉⠲⢶⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁
⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠠⠞⣏⡥⠟⠲⠆⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠸⣟⣶⣾⣿⣷⣄⢠⡿⠀⡾⠋⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⣠⣤⡴⠞⠛⠋⠉⠉⠛⠶⢦⣤⡀⠉⠻⢾⣽⣿⣿⣸⡇⣼⠁⠀⠀⢀⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠘⠻⣿⡿⢶⣦⣤⣤⣄⡀⠀⠀⠀⠙⢦⣀⡀⠉⠙⠻⣇⠙⢛⣦⣠⣴⠿⠋⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣤⣼⣍⠉⠛⢛⠿⣻⣿⣻⠿⣛⣻⡿⢿⣿⠟⠋⣿⣥⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠟⠛⢋⣩⠽⣯⡿⢻⣠⣾⣿⡀⢰⣿⣌⣿⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⣱⣾⠋⣴⣿⣟⣿⢾⣧⣈⣷⣧⢹⣿⣧⡼⣿⣷⣶⣶⠾⠿⢷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⣼⢻⡇⣠⣿⣿⢽⣿⣳⡹⣿⣿⡻⢦⣹⡏⠀⣿⠻⣿⣿⣝⣳⡶⣬⡉⡻⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⡟⢁⣸⡿⣿⣿⣷⣺⣧⠹⣵⣿⡿⠟⠻⢿⣿⣄⣿⡇⠈⠙⠛⠿⢿⡶⠞⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⣶⠟⠉⠀⠉⠙⣿⣩⣯⢳⡈⣿⢤⣤⣄⣀⣤⠞⣿⢿⣶⡶⢶⣛⡛⢿⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠋⠀⠀⠀⢀⡴⣶⣿⣭⣿⡧⣷⣟⣤⠽⠚⣹⠇⢰⣿⡈⠻⣟⢿⠿⣿⢶⣦⣭⣄⣉⠿⢶⣤⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢀⣴⣿⣝⡖⠛⣧⡻⣑⣿⡥⠴⠒⢋⣡⣴⣿⠙⢿⣟⠛⠛⠿⠦⢽⣭⣯⣽⡿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠈⢻⣿⡧⠶⠛⠛⣩⣿⡟⣿⠀⣧⠈⢛⠶⢤⣖⣈⣉⡭⠝⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃⠽⠂⣀⣴⣾⢿⣿⣿⣿⡀⢹⣾⡘⣤⡀⢭⢙⠱⢦⣄⠐⠙⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠤⣈⠂⣵⡿⢋⣡⣾⢛⣿⡿⣿⣿⣿⣷⣿⣻⡸⡆⢧⢰⡘⣷⣍⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⡑⢦⣨⣿⠏⡇⣸⡿⠃⣾⣿⡍⣿⣻⠿⢿⣿⣿⣿⣷⣼⣤⣧⣽⣿⣗⡸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢄⡑⢄⣸⣾⡏⡙⣸⣴⠟⠉⣩⣿⢻⣿⡜⣷⣽⣓⠿⣿⣿⣿⡍⠉⠉⠉⠛⠛⠛⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⠀⢵⣢⣴⠟⡏⢸⣰⣿⡋⠔⠊⢁⣿⣿⡄⣿⣧⠋⣿⣿⣷⢾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣤⡴⢾⢛⡏⡼⣸⣴⠟⠁⣼⠀⠐⢂⣻⣿⣿⣇⢸⡟⣆⣿⣷⢬⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠏⢡⠀⡞⡨⢣⣷⠟⠁⠀⢰⡇⠀⠀⢩⣿⣿⢻⠸⡌⣧⣿⡇⢸⣦⣝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠀⠀⠈⣀⣴⠟⠁⠀⠀⠀⣾⡇⠀⢀⣿⣿⢸⡘⡆⣧⣿⡿⠃⠀⣷⡌⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣣⡴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⣼⠁⢀⣿⣿⡿⠀⡇⣧⣿⠟⠀⠀⠀⣿⡙⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⡿⢹⣷⡆⣁⡿⠃⠀⠀⠀⠀⢿⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⣿⡟⡿⠈⣧⣶⠟⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣻⣧⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠶⠛⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⡀⠀⠄⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠁⠀⣰⠏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢠⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣴⡿⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠄⠀⠀⠃⠀⠀⠀⣼⣿⠟⠋⠁⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⣠⣶⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⠷⡿⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⣥⠀⠀⠀⣰⣿⠆⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⢳⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣾⡿⠋⠁⠀⠀⠠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡯⠤⠤⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠔⠊⠉⠉⠉⠀⠀⠀⠀⠉⠉⠁⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠁⢀⠄⢀⠀⠀⢀⠔⢁⡠⠊⢀⠔⠁⡠⠂⢀⠔⠈⣠⠔⠈⠀⠄⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⢠⠖⠁⡠⠋⢀⠜⢁⡴⠋⢀⠔⠁⡠⠊⢀⡔⣁⣴⡊⠤⠴⠮⢤⠖⠓⠖⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⡰⢁⠔⠁⡠⠊⢀⡔⠁⡠⣋⣠⠴⢧⠒⠚⠗⡋⠙⠛⠥⠌⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡜⢀⠔⢀⠞⣠⠋⢀⠜⣁⣴⣯⠖⠚⠙⠳⢄⡀⠀⠉⠒⠤⣀⠉⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⡜⢀⠎⣠⢋⣰⠥⣴⡛⠉⠑⠢⠄⠉⠑⠒⠤⢄⡈⠉⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉
⠀⠀⠀⠀⠀⢠⣥⠾⠾⠏⠉⠒⠤⠄⠈⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠔⠒⠉⠉⠁
⠀⠀⠀⢠⡖⠋⠁⠒⠒⠂⠤⠤⠤⠒⠒⠒⠂⠀⠀⠒⠒⠉⠉⠉⠉⠉⠉⠁
⠀⠀⡴⠋

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣼⣷⡀⠄⠀⠀⠀⣀⠀⣠⣾⣦⠀⠀⠀⢀⢤⠀⣿⡦⠀⠀⠀⠀⠀⢠⣄⠀⣠⣦⠀⠀⠀⠀⢸
⠀⠀⢀⡷⠊⣻⣿⡟⢣⡀⠀⣿⣷⡟⣿⣿⠀⠀⠀⠀⠀⠘⡏⡛⣠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⢀⡴
⠀⠀⢠⡤⢾⣿⣿⡛⢿⡆⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⣿⣷⠡⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠈⢿⠂
⠀⠀⠸⢡⣾⢻⣿⢉⡶⠇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡿⠃⠈⠁⠀⠀⢸⣿⣿⣗⣿⣿⣿⠀⠀⠀⣽⠄
⠀⠀⢸⠴⢋⣼⣟⠓⣥⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠀⠐⢹⡋⠐⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⡆
⠀⠀⠈⢠⠴⣿⡑⢤⡄⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁⠀⠀⠀⠈⡇
⠀⠀⠀⢁⣴⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⣢⣤⣤⣾⠛⠂⠀⠀⠀⢸⡟⣿⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣿⣬⣿⠇⠀⠀⠐⠀⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⡀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⣶⣶⣠⣄⠀⠀⠀⠘⣿⣿⠖⣿⠂⠀⡀⠅⠀⠀⢸⣿⣿⠁⠀⠀⣿⣿⣿⠇⠀⠀⢀⣬⡏⢀⡾
⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠘⠳⠸⣆⠱⠱⠈⠀⠀⠀⠈⠻⠃⠀⠀⠀⠘⠿⠋⠀⠀⠀⠨⠙⢷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡰⠇⠠⠐⠂⠀⠀⡢⡗⢄⠀⠀⠑⢄⠀⡇⡆⠀⡄⠡⠀⢸⠆⠌⠂⠀⠰⠈⠂⠈⣄⠀⠀⠀⢀⠂⠀⠼⠐⠄⠀⠀⠀⠈⢃⠀⠀⠁
⡗⠀⢀⠈⠀⠀⡐⠄⡦⠀⠱⠄⠀⠀⠑⠏⠀⠰⡀⢂⠁⠱⠀⠔⣁⠀⠀⠀⠀⠀⠹⡆⠀⠀⠨⠀⢀⠏⢐⠃⠀⠀⢀⡀⠀⠠⡀
⠀⠀⠈⠀⠀⢸⠀⠀⡳⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⡖⠀⢀⠄⢀⣤⠀⡀⠀⠀⠘⠄⠀⢨⠀⡜⣀⠊⠀⠀⠀⣞⢇⠀⠀⠐⠀⢀
⡠⠄⠤⢀⠀⠀⠀⠀⣹⠀⠁⠀⠀⢀⠤⠶⡏⠀⠀⠀⢸⠧⠀⠈⠀⢸⠸⡀⠈⠳⡀⠀⠀⠀⠀⠋⠉⠁⠀⠀⡠⠁⣸⢈⢄⠀⠀⠠⠊
⠙⢤⡀⠀⠳⡄⠀⠀⡸⠀⢀⠤⠊⢡⠋⢨⠁⠀⠀⠀⡆⠀⠀⠀⠀⠨⡀⠺⡄⠀⢖⠀⠀⠀⠀⠀⣠⠀⠀⡌⠀⠀⣽⠀⠈⢦
⠡⣄⠙⢤⡀⠈⡄⠀⠃⠀⠈⠀⡰⠂⠀⣙⠀⠸⠆⡈⠀⠀⠀⠀⠀⠀⠙⠤⡙⢦⣸⠀⠀⠀⠀⡜⠋⠄⠀⠠⡀⠀⣲
⢀⠈⠑⠀⠊⠟⠓⠀⠀⠀⠀⡴⠁⠀⠠⠃⠀⠀⡙⢦⠐⠢⠤⡀⠀⠀⠀⠀⡉⠈⠉⠀⠀⠀⡜⢨⠅⠱⡄⠀⠀⠀⠹⠁⠀⠀⠀⢱⢦
⢤⠈⠒⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢀⠂⠈⢣⠀⡀⠈⠀⠀⠀⡐⣿⠠⢀⠀⠀⢘⠀⠰⠂⠀⠰⠀⠀⠀⠀⠇⠀⠀⠀⠀⢇
⠀⠓⡄⠈⠀⠀⠀⠀⠊⠀⡠⠊⠹⠟⠂⠀⠀⠀⠄⠀⠀⠹⣤⠄⠀⠀⠰⠀⠸⡄⠀⠉⢠⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠺
⠀⠀⠘⢆⠀⠀⠀⠀⠀⡘⠁⢀⡜⠀⡃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠂⠀⡀⠶⠀⠀⠀⠆⠀⠈⠁⠀⢀⢧⠀⠀⠀⠎⢣⡀⠙⠢⡀
⠀⠀⠀⠀⠑⠠⠀⠀⠀⠊⠀⡰⢁⡐⠀⠀⣀⣀⡀⢤⣰⠂⠀⠀⠀⠀⠈⡀⠈⠰⡄⠀⠀⠀⠀⠀⠀⠀⠌⢏⠀⡀⠀⠸⡈⠳⡄⠀⢱
⠀⠀⠀⠀⢀⡀⠈⠀⠀⡱⠮⠔⠊⢀⠀⠁⠉⢁⠰⢨⠁⠀⠀⡰⣶⠂⢄⠉⠀⠀⢷⠁⠀⠀⠀⠀⠀⠎⠀⢻⠀⠈⢆⠀⠑⠂⡈⠢⢄
⠀⠀⠀⢐⠹⠏⠱⡀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⡠⠃⠀⠀⠀⠂⠹⡀⠀⠱⠀⠀⠀⢢⠀⠀⠀⠀⠘⠀⠀⠈⡄⠈⠈⠀⠀⠀⠀⠁⠉
⢀⠀⠀⠅⠨⡅⠀⠠⠀⠀⠀⠀⡠⠘⠉⠀⠠⠖⠁⠀⢠⠇⠀⠰⡀⠑⡄⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠹⣇⠂
⠀⠱⡄⢱⡀⣧⠀⠸⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠹⠎⢄⠀⠈⠢⢌⣢⣜⠀⠀⠀⠀⡠⠒⢃⡵⣓⠀⠀⠈⢦⠀⠀⠀⡄⠙⠧
⠀⠀⠀⠀⠑⢄⣧⡎⠀⠀⠀⠀⢀⠄⣿⣂⠀⠀⠰⠁⠘⡆⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⠔⠁⠀⡜⠀⠠⣄⠀⠀⠀⠀⠂⠠⠀⠳
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢠⡆⠀⠆⠈⠢⡀⠈⣇⠀⡀⠃⠀⠀⠀⡄⠀⠀⢐⢰⠋⠀⡠⠊⠀⠀⠀⡇⣯⠒⢄⣀⠀⠂⡀
⠉⠱⣄⠀⠀⢀⠀⠀⠀⠰⠀⠀⠀⠰⠈⠀⠊⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⠞⢷⠀⠀⠈⠇⠂⠉⢠⡀⠀⠀⠀⡆⠐⢆⠀⠀⠰⠀⠈
⠀⠀⠈⠁⠀⡜⡡⡀⠀⠀⠀⠄⠀⡖⠀⢀⠅⠀⡦⡀⠀⠘⡄⠀⢀⠶⠁⣘⠩⠀⠀⠀⠀⢀⠐⣿⠡⡀⠀⠀⡇⠀⠈⣇⠀⢀
⡩⠻⠀⠀⠠⠁⣇⠉⢆⠀⠀⠀⣾⠅⠀⠉⠀⠸⢰⠑⢄⠀⠀⠀⠉⠀⠠⠄⠀⠅⠀⠀⠄⠀⠀⠏⠀⠡⠄⠀⠁⠀⠀⠸⡆⠁⠀⢀⠠
⠀⢀⠁⡰⠁⠀⢧⠀⠀⢰⠀⢠⠃⠀⠀⠀⢠⠁⢰⠆⠈⠐⡀⠀⠀⢀⡏⠄⠰⠁⠀⠀⠂⠁⠰⠂⠀⠀⢘⠀⠀⠀⠀⠀⢃⠀⢀⠊⢀
⡠⠊⠀⠀⠂⠀⣶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠇⠈⢀⡃⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⡳⠀⠀⠀⠋⠀⣷⣄⠀⠀⠀⠀⢠⢀⠇
⠀⠀⢀⡀⠀⠀⡙⠀⠀⠀⠀⢀⢶⠤⢀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠐⠿⠠⠀⠀⠀⠀⢃⠰⠁⢢⡀⠀⠈⢾⠴
⠤⠂⡿⡇⠀⠠⠃⠀⠀⠀⠀⠨⠀⠣⡀⠡⠀⠀⠀⡇⠀⠀⣀⠀⠀⠂⠀⠠⠹⡜⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⡞⠀⢉⡄⠈⡆
⠀⠸⠂⠠⡀⠀⠀⢠⠀⠀⠀⠰⡀⠀⢳⠀⡃⠀⠈⠀⡀⠎⡟⠄⠀⠀⢀⡓⠀⢷⠀⠈⢢⠀⠉⢀⠠⢶⢦⠀⠑⠀⠀⢂⠀⠀⠀⡐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣄⡀⠀⠀⠀⢺⣿⣿⣿⡄⠀⠀⢠⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣤⡀⠘⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣄⠘⣿⣿⣿⡇⢠⣿⣿⣿⣿⠀⠀⢀⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣶⣶⣦⣤⣄⡙⠻⢿⣿⣿⣧⠘⣿⣿⡇⢸⣿⣿⣿⠇⢀⣴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠻⣿⡆⠸⣿⡇⢸⣿⣿⠏⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⣦⠈⢿⠀⣿⠁⣼⡿⠋⣰⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⠶⠦⠌⠁⠈⠀⠁⡴⠋⣀⣼⣿⡿⠟⢋⣠⣴⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⢉⣠⣤⡤⠖⠀⠀⠀⠀⠀⠐⠚⠛⠉⣁⣤⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠋⢁⣴⣾⣿⡿⠋⣠⡴⠃⡄⢀⠀⣄⠙⠻⠿⠿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⢁⣾⣿⠁⣸⡇⠸⣧⠈⠻⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⢠⣿⣿⡿⢀⣿⣷⠀⢻⣷⣦⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠃⢀⣿⣿⣿⡇⢸⣿⣿⣧⠈⢿⣿⣿⣷⣦⣈⠉⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⢸⣿⣿⣿⡇⠘⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⢻⣿⣿⣿⣇⠀⠈⠛⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢿⡟



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

⠀⠀⠃⢀⣠⠀⠀⣀⠀⠀⠀⠈⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠊⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠆⢀⠊⠀⠀⠂⠀⠰⡀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢤⡀⠈⠀⠰⠆⠀⡀⠀⠲⠀⡁⠠⠀⠠⠀⢠⠃
⠁⠀⠄⢨⠜⠀⠀⠀⠀⠂⡠⢌⠀⠀⠀⡀⠀⠀⠠⠈⠀⠀⢰⠀⡀⠀⠙⠀⠀⠁⡀⠓⠀⠀⠀⠠⠄⠀⠀⠉⠠⠀⠀⢀
⠁⠀⢀⠀⡄⠀⠀⠀⢀⠈⠁⠀⠉⠑⠂⠀⠀⠀⠤⠀⠀⠀⣨⠀⠀⠀⠤⠄⠀⢉⠃⠀⠀⠀⠆⠀⠀⠀⠀⡀⠀⢐⡀⠐
⠀⠀⢿⠀⠀⠀⣀⠜⠀⠀⠀⢤⣀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠉⠙⠻⠀⠀⠀⠘⠂⠀⢡⠀⠈⣁
⠀⠀⠘⠃⡠⠈⠀⠀⠒⠒⠲⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠃
⠀⠀⠠⠂⠀⠀⠄⠐⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠉⠀⠀⠀⠀⠀⢈⣙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⡄⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⢷⡀
⡐⠦⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣹⡄⠀⠀⠀⣀
⠙⣦⡀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠬⠗
⡩⠀⠀⠚⠉⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣯⡧⠀⠀⠀⠀⠀⠂⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡄
⡀⠀⠢⠀⠀⢀⠀⠀⠲⠦⠤⡄⠀⠀⠐⠀⠀⡐⠀⡦⠐⢦⡀⠀⠂⠀⡐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⢀⣀⠖⠉⠀⠀⠠
⠳⠀⠀⠀⡀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠁⠀⠨⠁⠀⠀⠠⠀⠀⢀⠀⠀⡤⠄⠀⡀⠀⠔⠁⠀⠘⠀⠠⠆⠀⠀⠂⠀⢠
⡀⠠⢂⠀⡀⠀⠀⡤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠐⠀⠀⠇⠀⠀⠀⠀⡄⠀⠠⡄
⠁⢀⣬⠾⠕⠂⠄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⢠⠞⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰
⠂⠀⠀⢀⡀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠤⠤⠀⠐⠀⠶⠀⠀⠀⠤⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡰⠀⣄
⠘⠀⠀⠀⢀⡈⠁⠘⠀⡄⢰⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢠⠘⠒⠀⠂⠀⢀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠈⠀⠀⣌⠁⢰⠿
⠖⠐⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⢀⠐⠀⠄⠈⠀⠈⠁⢀⠀⢀⠀⠁⠀⠀⠀⣶⠦⠆⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠋⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⡀⠀⠠⠀⠀⠲⠀⠈⠤⠉⠀⠀⠀⡄⠁⠀⠀⡀⠈
⠀⠀⠀⢀⠀⠀⠁⠀⠀⢀⠁⡌⠨⠂⠄⠀⠀⠂⠠⠄⠀⠐⠁⢀⠀⠀⠈⠃⡀⠀⠁⠤⠀⠆⠀⡄⡸⠂⠀⠀⠀⠠⠈⠀⠀⠀⠂
⠀⠠⠐⠀⠀⠀⠀⠁⠀⠀⠀⣤⡀⠅⠊⠁⠀⠀⠀⠢⠀⠀⠀⠀⠀⣤⠀⠀⠀⠐⢠⠀⠐⢊⢀⡰⠁⠆⢚⠈⠀⠀⠀⠐⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠒⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⣍⠀⠀⠠⣀⠀⢀⠠⠘⠝⠋⠂⢐⠠⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⢸⢀⠔⡁⠈⠀⠀⠠⠀⠀⠀⢀⢉⡀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠂⠀⠀⠘⠂⠠⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠓⠀⠀⠸⠉⠀⠀⠀⠐⠀⠀⢓⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠆⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⢄
⠀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠀⢹⠀⡀⣀⠀⠀⠀⠀⠆⣊⠑⣢⢉⢛⠐⢺
⠀⠀⠀⠀⠀⠀⠈⢳⣿⡒⠂⠀⠁⠀⠀⠀⠀⠀⣄⣀⡈⠢⢄⣿⣷⠲⠋⠀⠀⠀⠈⠸⠬⣱⣇⠸⢸⣂⠉
⠀⠀⠀⠀⠀⠀⠠⠊⠃⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠙⠒⢷⣀⣡⡦⠤⣀⣄⡄⠀⠀⠘⠒⠋⠘⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠖⠀⣄⣬⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠘⡳⠤⣤⡀⠪⠑⠂⠦⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠢⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⣨⠆⠁⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡀⠈⠑⣃⠴⢁⠂⠐⣢
⠀⠀⠀⠀⣐⠀⠀⠑⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡛⣫⣕⣶⡆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣞⣀⣣⡊⠑
⠀⠀⠀⢐⣀⡀⠠⠑⠖⢨⠁⠀⠀⠀⠀⠀⢀⣀⢉⡚⢬⣭⡼⢿⣜⣇⠀⠀⠀⠀⡠⡀⠓⣤⢵⣿⡿⢇
⠀⠀⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⢴⣿⠟⡁⡏⢩⡟⠈⠀⠀⠀⠀⠀⠜⠐⢋⣱⠗⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠩⠀⠖⡀⠚⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠤⠴⠖⢒⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⢿⠛⠻⡒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠲⡄⣀⠔⠋⣀⠀⣄⠑⠄⠐⢄⠐⢍⠳⣄⠀⠀⠀⠀⡿⠀⡀⢸⡀⠀⠉⠳⣄⠀⠀⠀⠀⣠⠞⠹⠉⡙⠒⣄
⠀⠉⠓⢬⠀⠁⠄⠊⢉⠐⠷⠦⢧⣀⠱⠈⢧⠀⠀⢰⡃⠠⢄⠀⣇⠈⢀⠀⢈⢣⠀⠀⢰⠃⡀⣧⠜⠀⠄⠘⢆
⠀⠀⠀⠀⠳⣄⠀⠉⡀⠤⠤⠐⠂⠉⢉⡳⠼⣇⠀⠀⢇⠐⠤⢀⠸⣟⠁⡠⠀⠸⡆⠀⡏⠀⠑⢴⢀⠈⠀⠄⠘⡆
⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠖⠒⢒⣉⣡⠖⠋⠉⠛⠦⣌⠳⢔⠠⠴⣿⣯⡀⣀⢣⠃⠀⠣⡈⠐⠨⣧⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⣀⣀⣀⠀⠀⠀⠈⠙⠲⣭⣒⠦⠤⣝⣆⡞⠀⠀⠀⠙⢖⠠⠀⢹⣄⡰⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠤⢉⡒⠒⣒⢶⡟⠉⠉⠳⢦⣤⣝⣷⡀⠀⠀⠀⠀⠙⠒⠒⠛⢷⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠊⠑⣲⠴⢖⠞⢩⠃⢸⠇⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⣤⣀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠐⢉⣽⢉⠇⠀⡜⠀⠘⢀⡞⠀⠀⠀⠀⠀⢀⣠⠴⠶⠤⢄⣀⣠⡼⠛⠛⠲⠶⠶⠯⠶⠟⠛⠛⠛⠛⠷⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠐⡙⢱⠘⠀⠀⠁⢀⡴⠋⠀⠀⠀⠀⡤⠒⠋⠀⠀⠒⠤⣤⠖⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠰⠃⠀⣠⣤⠤⠞⠁⠀⠀⠀⠀⢀⠎⠀⠈⠉⠉⠙⢲⠔⡇⠆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠉⠉⣁⡶⢖⠋⢠⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠥⢌⣁⣉⣋⣀⣂⣀⠥⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⡨⠡⠆⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⣍⢘⡅⠀⠀⢄⠀⠀⠀⠀⠠⠙⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠆⠠⠆⠀⠀⠂⠀⠂⠀⠀⠌⠈⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠁⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠓⠠⠤⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⢲⠘⣰
⠀⠀⠀⠱⡈⡠⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢲⠀⠘⠃⠀⠀⠡⠀⠀⠠⣄⠀⢠⡆
⠀⠀⠐⢄⠉⣠⠖⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢦⠀⠰⠇⠀⠀⠀⠀⠀⠰⣌⠀⢈⡶
⠀⠀⠀⠒⠤⠤⠂⠀⠀⠀⠂⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠦⠀⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢀⢀⡄⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⢸⠞⢣⣟⠀⠀⢠⡁⠆⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠀⢀⡁⠀⢈⡀
⠀⠀⠀⢷⠀⠰⣋⠄⠀⠰⠅⡫⠀⠀⠀⠀⠀⠀⠀⡐⠄⣨⠀⠠⠄⠀⠠⠄
⠀⠀⠸⣦⠀⢰⡋⠀⠀⢨⠀⣚⠀⠀⠀⠀⠀⠀⠀⢍⠀⠐⠀⢀⠂⠀⠀⡃
⠀⠀⠀⠺⠀⠉⠁⠀⠀⠰⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠉⠲⠔⠒⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢄⠀⠐⠀⠀⠀⠰⠀⠀⡌⠁⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢁⠐⠀⡈⢢⠁⢀⠀⢐⠀⠀⠴⠀⠐⠀⠀⠉⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠁⠠⣀⠈⠆⡈⠀⠘⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠈⠰⠦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢄⠀⠈⠢⡀⠀⠑⠚⡅⠀⠃⠀⠀⡄⠀⠸⠀⠀⢸⠀⠀⢘⠐⠀⠀⠈⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠣⣄⠀⠀⠐⠤⣀⠘⡄⠀⠀⢀⠀⠀⡀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠤⣀⠀⠈⠑⢄⡀⠀⠄⠀⠁⡀⠀⠄⠀⢠⠀⠀⠀⡆⠀⠀⠀⡠⠀⠀⠀⡁⠄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡀⠀⠙⠦⣀⠀⠈⠂⢄⡀⠀⢃⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠀⢀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠈⠑⠢⡀⠀⠈⠑⠰⢇⠀⠑⠂⠈⠀⠠⠀⠀⠀⠇⠀⠀⠀⠢⠀⠀⠀⠂⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠑⠦⠀⠀⠀⢆⠀⠀⠀⠠⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣞⠀⠀⢄⠀⠀⠀⡄⠉⠢⣄⠀⠀⠀⠀⠑⠂⠠⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠱⠦⢀⠀⠀⠀⠀⠙⠂⡀⠀⠀⠀⠀⠙⡄⠠⠀⡀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢘⠀⠄⠀⠀⠀⠀⠉⠒⠀⠀⠀⠈⠀⠀⠂⠄⠀⠀⢠⡆⠀⠠⠀⠇⠀⠀⠀⢀⠄⠂⠀⠀⢀⠐⠀⠀⠀⡐⠠⡂
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠠⠢⢀⠀⠀⠀⠀⠈⠑⠤⢆⠀⠀⠀⠀⠁⠂⠦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⢀⠌⠄⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠐⠂⠉⠐⢆⣀⠀⠀⠀⠀⠈⠘⠀⣀⠀⠀⠀⢡⢀⠁⠀⠀⠀⢀⡀⠐⠁⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠒⠀⠈⠑⠠⢀⠂⢀⠀⠀⠀⠀⠐⠂⠀⢭⡀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠤⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠠⠖⠀⠀⠀⠒⠀⠀⠀⠈⠀⠤⠤⢀⠀⠀⠀⠀⢳⠀⠀⡀⠀⠀⣤⠀⠂⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⡀⠀⠀⠀⠀⠀⠒⠈⠉⠁⠀⠀⡀⠀⠁⠐⠐⠄⡇⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⡀⠀⠀⡀⠄⡠⠀⠂⠁⠀⠀⠀⡠⠀⠁⠀⠄⠀⢀⠀⠠⠄⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡌⠀⠄⠀⠘⠀⠀⠤⠒⢁⠔⠀⠀⠀⢇⠀⠀⠈⠒⠒⠂⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢀⠀⠈⠀⠀⣀⠴⠁⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀
⠀⠠⠷⢨⣉⡦⡄⠀⠀⠀⠀⠀⠀⡠⠴⠒⠢⢄⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣝⣧⡄⠀⠀⠀⠀⠀⠀⣠⡴⠶⠦⢄⣠⠂
⠀⠀⠙⠸⠾⠿⠧⠄⠀⠀⠀⠀⠺⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠧⠄⠀⠀⠀⠀⣾⠏⢠⣤⠄⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠒⢒⡲⠊⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣓⣒⡶⠛⣹⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢉⠏⢁⢀⣠⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣻⡟⢩⣂⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠿⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⣄⢈⡉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣉⠛⢶⣄⡀
⠀⠀⠀⠀⠂⠈⠢⠀⠉⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠘⣿⣍⠉⠙⠋⣻⣦
⠀⠀⠀⠈⢆⠀⡆⠀⠰⢄⡀⠁⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣠⣿⠈⠳⣬⣉⢙⣽⣷⣄
⠀⠀⠀⠀⠀⠙⠿⠢⣤⡄⢹⣶⣲⣶⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣿⣦⣽⣿⣿⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⢀⠔⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⡰⠃⠀⢀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡆⠀⢀⠞⡠⠊⠁⢀⢈⣁⠠⠄⠐⠊⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠑⠐⠂⢥⢠⡇⣠⠏⠀⢑⡤⠖⠉⢁⣀⡀⠀⢀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⢀⣀⠁⠲⢤⣤⣌⣿⣿⣿⣯⠖⠉⠀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠈⣀⣀⣤⣵⠤⠾⠿⣿⢿⣫⣀⠀⠀⣀⢀⠀⣨⣥⣄⠀⠉⠁⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡀⠀⠀⠀⢀⡼⠋⠈⣿⡉⠈⠉⠴⠀⠀⠀⠀⡀⠀⠀⡀⠈⠈⠑⠰
⠀⠀⠀⠀⠀⠀⠇⠀⢀⠄⢀⠌⠀⢀⡠⣫⢤⠀⡠⠃⠳⣄⡐⠤⠀⠐⠁⠐⠄⡀⠀⠈⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠘⢠⠋⡠⠃⠀⠐⠁⠈⠀⢰⡷⢱⠁⡀⡿⣄⠈⠁⠐⣀⢀⠄⠀⠈⠐⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠢⠰⠁⠀⠈⢠⠁⠀⠠⢣⠁⠈⠚⢠⠃⢘⣆⠀⠀⠑⠤⡈⠑⠄⠐⠠⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⢀⠇⠀⡐⠁⡆⠊⠱⠀⡏⡔⢢⡹⢦⣀⠀⠀⠀⠉⠂⢀⠄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠀⢰⠃⠀⡇⠀⠀⢰⡆⠀⢨⡇⠀⢣⡉⠒⠤⡀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢆⠀⢁⠀⢀⠈⠀⡂⠈⢃⠀⠀⠱⣌⠁⢀⠁⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣁⠘⡀⠀⠑⠄⠀⠀⠀⠀⠙⣗⢂⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠐⠒⠒⠒⠠⠮

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣰⢂⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢶⡼⢃⡞⠀⠀⠀⢧⠀⠋⣩⠅⠀⠀⠀⠀⢀⠄⠀⠀⠀⣿⠁⠶⠟⠋⠀⠀⠀⢀⠀⠀⠀⢠⡄⠘⢁
⠀⠀⠈⠃⠞⣱⠀⠀⠀⠈⠃⢊⡅⠀⠀⠀⠀⠠⠈⠀⠀⠸⣄⠘⠴⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡴⠟
⠀⠀⠸⣆⠘⠉⣠⣤⠰⢖⡲⢩⢆⣴⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⡿⠀⠀⠀⠀⠘⠀⠀⠀⣶⣄⠌⣠⡄
⠀⠀⢠⡈⠓⠈⣨⡅⢀⡈⢷⡘⠋⣡⠀⠀⠀⢠⠀⠀⠀⠀⡈⢷⡈⠀⣠⠀⠀⠐⠀⠀⠀⠀⢈⣉⡾⢋⠁
⠀⠀⠀⠙⠂⠊⠁⠀⠀⠛⠖⠴⠛⠁⠀⠀⠀⠐⠒⠀⠀⠀⠙⠒⠵⠞⠋⠀⠀⠀⠄⠀⠀⠀⠈⠋⠙⠋

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡄⣤⡄
⠀⠀⢀⡜⢠⡶⠃⠀⠀⠀⠀⠀⠀⠀⢰⣦⡙⢋⠼⣻⡷⠀⠀⠀⠀⠀⡠⢰⡄⠱⢠⠏⠀⠀⠀⢰⣦⠈⢉⡀
⠀⠀⠀⠃⣰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⢠⠴⢞⠀⠀⠀⣯⠑⢙⠟
⠀⠀⢰⡎⢰⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡨⠴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣠⠞⠀⡀⣶⣬⠤⠼⣤⠄
⠀⠀⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣏⣤⠄⠀⠀⠀⠀⠀⡀⠀⠀⠒⠋⠘⢮⣢⠞⠁⠀⣧⡀⣴⡆
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠲⢤⣿⠴⠂⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈