Milkyway Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⢉⣠⣤⣶⣤⣄⡀⠀⠘⠃⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⣀⣴⡾⠟⠋⠁⠀⠀⠹⣷⡀⠀⠀⣼⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣸⠏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣿⠀⣰⠏⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⣴⠟⠁⣠⣾⠟⠱⡦⠀⠀⠀⠀⣤⡀⢛⡀⠀⢀⣾⠃⣰⠏⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣠⡾⠋⠀⠀⠀⠀⠀⣠⡶⣛⣭⣿⠙⠁⢀⣾⢃⣼⠋⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢠⠞⠋⠀⠀⠀⠀⢀⣴⢟⣵⡞⢋⣿⠇⠀⢠⡾⢣⡞⠁⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠁⠀⠀⠀⠀⠀⢀⡾⣡⠟⣿⣷⡿⠉⢀⣴⢏⡴⠋⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⣴⠋⠀⣿⢱⣯⣆⡿⠛⢁⡴⠋⠡⠊⠀⠀⠀⠀⢀⣾⠏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠛⠶⠞⣭⠀⠀⠀⠀⠀⢀⠔⠀⢠⡆⢠⡾⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣰⢳⠏⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣼⠃⡟⠀⠀⠀⣶⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⣧⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⣠⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠛⠶⠶⠾⠛⠋⠁⠀⠀⠘⢃⡴⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣫⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠠⠁⡾⣼⣶⣾⣃⣴⢦⣈⠄⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⣄⢼⣉⡿⠷⠛⠨⠙⠋⠁⠀⠀⠛⠺⡿⣧⣜⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡿⠋⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠙⠒⡢⢶⣄⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣴⣼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠔⠠⢀⢤⡖⠁⠶⠂⠰⠶⠄⣀⠀⠀⠈⠃⠛⢿⣯⡠⠄⠀⠀⠀⠀⠀⠐⠂⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⢎⠋⠈⠀⠀⠀⢀⠄⠀⠶⢀⣄⠸⣦⠼⡶⣶⠿⢾⢷⣤⣊⣮⡝⠰⠆⢀⠀⠀⠈⠚⢷⢀⡄⠇⡀⠀⠀⠀⣦⡅
⠀⠀⠀⠀⠀⠀⢠⣵⠞⠃⠀⠀⢠⣰⣬⣤⡶⠆⢹⣞⣿⡻⠋⠁⠀⠀⠀⣀⣀⡀⠀⠉⠉⠘⠳⣷⠈⠠⡄⠀⠀⠈⣶⡗⡐⠁⢀⠀⠀⠈⢡⢂⡀
⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⠠⢀⣸⡶⠗⠀⠘⣶⡿⠛⠈⢀⠀⡀⣐⢀⠉⡶⡾⢵⣬⣶⠂⠤⣀⠸⢯⡏⠠⢐⠀⠀⢉⣱⣇⠀⠇⠀⠀⢀⢋⣬⠀⠁
⠀⠀⠀⠀⢀⠯⠀⠀⢀⠀⢠⠾⠉⢀⠆⣴⠟⠉⢀⠀⣠⣦⡼⠿⠋⠀⠀⣀⣠⣄⣥⣈⠛⡐⢿⡰⠀⠹⡆⠿⡄⠀⠀⠫⣽⣄⠀⠂⠀⠀⢸⡇⠀⢁⢀
⠀⠀⠀⠀⠚⠁⠀⠀⢈⡴⠊⠀⠀⣠⡟⠁⠀⣠⣤⢶⡿⠇⠀⡠⢠⣭⣽⠾⠛⠚⠛⣛⠻⠾⣤⣇⣘⠀⢹⣦⢟⠀⠀⠀⣻⣛⠁⠀⠀⠀⡿⣶⠍⡀
⠀⠀⠀⠀⠀⠀⠀⢐⡭⠁⢀⠀⣫⠏⠀⡀⢀⣠⡖⠖⠀⢠⣄⣻⠟⢉⣤⠔⣠⣴⠿⠟⠿⢶⣬⢿⡩⠀⠘⣏⣬⡀⠀⢐⠳⢷⠰⠀⠀⠀⡾⣇⠚⠤
⠀⠀⠀⠀⠀⠄⢨⡟⠁⠀⠈⢰⠋⠀⠀⠀⣹⡿⠁⠠⠰⣾⠟⠃⠀⢀⡾⠋⣁⣠⣴⣾⣷⠀⢹⡿⢻⠀⢠⣦⣟⠂⠀⣬⣿⡇⠀⠤⠀⠀⣝⠯⠀⠚
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢰⣻⠀⠀⠒⠀⣿⠃⠀⢤⣾⡗⠀⡘⣵⡟⣁⣴⣿⠋⢡⣿⠿⠀⡼⠟⡅⠀⣿⡌⡉⠀⠀⣬⣟⡡⡐⠀⠀⠘⣿⡀⠠⡉
⠀⠀⠀⠀⠂⠀⣻⠃⠀⠀⣼⡟⠀⠀⡀⢸⡿⠀⠀⢷⡷⠀⢤⢳⡟⢠⣿⣿⣧⣶⣿⣿⣶⣾⡏⠆⠁⢴⡿⠗⠀⢠⣿⡛⠀⡄⠀⠀⠀⣼⢍⢉⡰⠁
⠀⠀⠀⢀⣁⣰⢿⠂⠀⠰⣮⣖⠀⠀⠁⢐⡧⠀⠐⢸⣿⠀⠘⣽⡀⠀⣿⣯⠻⢙⡿⣿⠟⠋⣀⣠⣞⣧⠀⠀⣤⣾⡷⠇⠀⠀⠀⣄⣼⣿⡄⣨
⠀⠀⠀⠈⡓⢉⡁⠀⠠⢂⣽⠻⠀⠀⠈⢯⣅⣀⠀⢺⣿⡄⠀⡿⣷⡀⠘⡟⢿⣦⡦⢴⡶⠻⠋⠱⠗⠀⣤⡾⡵⠙⠂⠀⠀⠀⣠⣸⣷⠒⠂
⠀⠀⠀⠀⠀⠞⡃⠀⠠⠈⢾⣏⡀⠀⠀⠄⢋⡗⠀⠨⡿⣷⣄⠀⠸⠿⣦⣄⣈⢉⡉⠑⠈⢁⣈⣴⣾⠟⠉⢖⠉⠂⠀⠀⣀⣰⣾⢛⡠⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⣿⡱⠀⠀⠀⣉⣮⡗⠀⠀⠐⠈⣧⡀⠀⢀⠻⢻⣄⠈⠳⡼⠏⠽⣯⣤⣝⡛⠟⡩⠉⢥⠀⠈⠀⠀⣀⣀⣤⡼⣉⠓⠈⠀⠀⠀⡤⢴⣇⠎
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⣿⣭⡀⠀⠀⠁⠩⣿⡄⠀⠀⢀⠛⠷⣄⡀⠛⢂⡻⣼⣟⣻⣿⣤⣤⣄⡠⣶⠴⠿⠛⡛⠁⠐⡈⠂⠀⠀⢀⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢉⠜⣇⡀⠀⠀⠀⠙⠓⣄⠀⠀⠉⠰⡝⠻⢶⣤⡀⠀⠁⠋⠁⢈⡡⠨⡅⣛⣀⡴⠟⠀⠐⠀⠀⠀⣠⣸⡟⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⣤⡄⠀⠀⠀⠛⠷⣄⠀⠀⠀⠙⠰⢟⣩⡷⣦⡄⢄⣀⠀⠀⠉⠉⠀⠀⢀⠀⢀⣠⡴⢗⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢡⣯⣷⣤⡀⠀⠀⠀⠈⠓⣶⣄⡀⠀⠀⠀⠒⠘⢋⡹⣟⠛⣿⠟⢿⠟⠟⣙⠋⠛⠉⠀⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⢯⣾⣁⡀⠀⠀⠀⠈⠙⠷⣷⢤⢠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠟⢠⢂⣄⠀⠀⠀⠀⠀⠀⠉⢹⡴⠖⢦⡶⣤⣤⣠⣤⢀⣤⡀⠠⢶⠖⡪⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢽⣁⡣⢀⡀⠀⡀⠀⠈⠀⠀⠀⢀⠗⠠⠀⠤⠈⢈⠉⠙⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠙⠶⠀⠗⣉⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂
⠘⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠉⠙⠻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠘⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣶⣶⣤⣀⡀⠀⠀⠉⠻⢿⣷⣦⣄⠀⠀⠀⠀⢀⣴⣄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⣄⡀⠀⠈⠙⠻⣿⣦⣀⠀⠀⠙⠁
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠿⣿⣿⣿⠿⠟⠀⠀⣠⣶⣶⣿⣷⣶⣄⡀⠀⠀⠀⠈⠙⠻⣿⣶⣄⡀⠀⠈⠙⢿⣷⣦⡀
⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⣾⡿⠉⠀⠀⢸⣿⣏⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⡀⠘⠛⠁⠀⠀⠀⠀⠀⠈⣿⡧⠀⠸⣿⣦⣄⠀⠀⠀⠘⢿⣷⠀⠀⠀⠀⠈⢻⣿⣄
⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠙⠻⢿⣷⣦⣤⣀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠈⠹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠹⣿⡆
⠀⡀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣶⣶⣶⣤⣤⣤⣤⣴⣾⣿⣧⣤⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠺⡿⠂⠀⠀⠀⠀⠀⠙⠿⣿⣦⣀⠀⠀⠉⠛⢿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣄⡀⠀⠈⠉⠛⠿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⡀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⣴⣾⡿⢿⣷⣆⠀⠀⠀⠀⠀⢠⣶⡄⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠈⢿⣷⣤⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣾⣿⣷⣤⣤⡀
⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠟⠛⠋⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠛⠛⠷⢶⣤⣄⡀⠀⠀⠀⠀⠉⠉⢻⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠀⠀⠀⠀⣴⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠛⠷⣦⣀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠁
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠶⠶⣶⣤⣤⣀⡀⠀⠈⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⢿⡄
⠀⢰⡟⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⢸⣧
⢀⣿⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣠⣶⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⢻⡄⠐⠾⢿⣿⣿⡿⠷⠂⠀⢰⡿
⢸⡇⠀⠀⠀⠀⣾⠃⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠗⠀⠀⠀⢹⡟⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⣼⣿⣇⣀⡀⠀⠹⣧⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⡾⠃⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⣿⡀⠘⠛⠿⢿⣿⡿⠟⠛⠁⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⢠⡄⠀⠀⠈⢷⣄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⣼⣧⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁
⣠⣤⣴⣿⣿⣦⣤⣄⠀⠀⠀⠈⠙⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠀⠀⣀⣄⡀
⠈⠉⠙⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠟⠛⠉⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆
⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠒⣄⠀⠀⠀⠀⠀⠲⣎⡱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⢠⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠐⠾⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡴⣆⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢀⠜⠁⠀⠸⠓⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⢦⣀⡇⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠐⠊⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣀⠀⠀⠈⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⣀⣀⣀⠤⣴⠞⠁⠀⠀⢮⣈⠇⠀⢸⣁⠤⠤⠒⠠⡀⠀⢀⡠⠔⠋
⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⣠⡀⠀⠀⠀⢀⠟⠒⠚⠛⢲⡀⠉⠉⠁⢀⣀⣀⣀⡠⠤⠄
⠀⠉⠁⠀⠀⠀⠈⠉⠒⠤⠤⠴⣚⠟⠁⠀⠀⠀⠘⠤⠇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠉⠒⠉⠉⠉
⠀⠀⠀⠀⣀⠤⠤⠤⠤⠴⠒⡻⠛⣄⠀⢀⡤⠒⢢⠀⠀⠀⢀⡞
⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⡴⠳⡀⠈⠲⡃⠀⢠⠏⠀⠀⢠⠎
⠀⠊⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠙⢦⡀⠈⠓⢯⣀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄⣠⣤⠤⠄⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣮⣀⣤⠀⠀⠀⠙⠢⣄⣀⢈⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣜⠀⠀⠀⣀⡯⠄⢊⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡯⣶⠀⠀⠀⠀⠀⢨⠏⠀⠀⠀⠀⠀⠀⠀⢀⠞⠵⠽⣒⣒⡭⢴⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡰⢃⣤⢀⣤⡴⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠗⠁⠾⠃⠈⠀⠀⠀⠀⠀⠀⣀⠶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣀⣠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣞⣢⡦⠏⠛⠟⠉⠉⠻⢱⣶⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡾⠋⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⡴⣆⣄⡠
⠀⠀⠀⠀⠀⠀⢀⣄⣶⠞⠁⠀⠀⠀⢀⠀⠀⣀⢀⣐⣃⣌⣁⠈⠑⠤⢀⠀⠀⠈⠛⣶⠂⢠⠀⠀⠀⢈
⠀⠀⠀⠀⠀⣠⡼⠋⠀⢀⣠⣀⣠⡄⢮⣵⣷⠟⠉⠉⠉⠈⠉⠙⠚⠓⢦⡄⠂⡀⠀⠘⢣⡇⠐⠀⠀⠈⠃⠄
⠀⠀⠀⠀⡴⠏⠀⠀⠀⣸⠾⠋⣑⣶⠟⠋⠁⢀⣀⠀⠡⠶⠵⣴⣄⠠⣄⠹⢕⠀⡀⠀⠈⣺⡀⠈⠀⠀⢚⡌
⠀⠀⠀⢠⠁⠀⠠⢀⠞⠁⢠⣴⠏⠀⢀⣠⡶⠟⠋⠠⣄⣤⣦⣦⣌⣉⠻⠄⠈⢏⣳⡀⠀⠰⣷⡄⠀⠀⢸⡇⡀
⠀⠀⠀⠀⠀⠀⣐⠋⠀⢰⡞⠁⠀⢘⣋⠋⢀⠰⣴⠟⣉⠁⣀⣴⢦⣍⣹⡶⠀⢸⡏⠂⠀⠠⣿⡀⠀⠀⣸⡟⢄
⠀⠀⠀⠀⠀⣶⠃⠀⢡⡏⠀⠀⢘⡟⠀⠀⡾⠟⠀⢈⡿⢋⣩⣴⣶⡌⢹⡿⠆⢠⣽⡃⠀⣼⣶⠀⠄⠀⣸⠧⠀⠂
⠀⠀⠀⠀⢰⡏⠀⠀⢼⠁⠀⠀⣼⠀⢀⣾⠃⢠⣱⠟⣤⣿⢋⣼⡟⣀⣞⠣⠀⣿⠎⠁⢀⡾⠩⠀⠀⠀⠻⠅⠠
⠀⠀⠀⠀⣨⡇⠀⢘⣛⠀⠐⠀⣏⠀⠈⣿⠀⠡⡏⠐⣿⣿⡿⣿⣿⠿⠃⢀⣼⠃⠁⣠⣟⡀⠈⠀⠀⣴⡓⠐
⠀⠀⠀⡛⢋⠀⠀⢘⡟⠀⠀⠲⣇⡀⠠⣿⡄⢸⢧⡀⠻⢷⣮⡅⣥⠶⠚⠽⠉⣠⣮⠝⠃⠀⠀⢀⣹⡯⠇⠁
⠀⠀⠀⠰⣈⠀⠀⠐⣿⡄⠀⠀⠩⡇⠀⠻⣷⡄⠈⡛⢦⣤⣉⠈⣁⣉⣤⣶⠟⠉⠎⠁⠀⠀⣤⣾⠫⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠧⠀⠀⠀⢾⡯⠀⠀⠀⢻⡄⠀⠉⠹⣤⡉⠊⠜⢿⢶⣷⣭⠀⠐⠀⣀⣠⡤⡶⠞⠃⠌⠀⠀⢀⡦⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣆⠀⠀⠈⠻⣄⠀⠐⠊⡝⢷⣄⡉⠉⠸⠋⠙⠋⣋⢛⣁⡵⠂⠀⠀⠀⣀⣰⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡄⠀⠀⠙⠷⣄⠀⠀⠁⠚⡹⠶⣦⢠⣀⢀⡈⡉⣀⢀⣀⣠⡴⣶⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢻⣶⡄⠀⠀⠀⠙⢦⣀⡀⠀⠀⠈⠀⠋⠹⠋⠙⠉⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⢆⠀⡀⠀⠀⠁⠉⠛⢦⡤⣤⣠⣀⣀⣀⢀⡀⠀⣤⠄⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⣉⡀⠄⢀⠀⠀⠈⠁⢀⠒⠈⠨⠈⠉⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠩⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⢸⠁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⣠⣶⣔⣂⣰⣶⠖⠀⠀⠀⠀⡀⣴⡟⣻⣿⣿⣦⠀⣾⣭⣧⠀⠀⠀⠈⠀⠁
⠀⠀⠀⢤⣴⣾⠟⡛⠩⠁⠀⠀⠀⠀⠀⠀⠀⠼⠻⣿⣿⣿⣿⡇⠀⡹⢻⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢠⠀⠀⠀⠀⡠⢬⣿⣿⢟⠗⡁⢀⡼⠋⠀⢠⣤⣶⣤⡀⠀⠀⠀⠀⡎⣾⠀⣀⢀⡆⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠋⢀⣀⣆⠀⡔⠋⢱⡀⠀⠸⣬⣷⠶⡋⠀⠀⠠⣿⣿⣿⣿⡷⠄⠀⠀⠀⡟⣿⣆⣀⣾⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠾⣵⣧⣴⡟⢳⣦⣴⣿⡿⠛⢿⣿⠀⠀⠙⢿⣿⠿⠃⠀⠀⠀⠀⡇⣿⣯⢨⣿⡇⡇
⠀⠀⠀⠀⢠⣀⣄⡀⠀⠀⠄⠰⠀⠀⠀⠀⠀⢸⣵⣸⣿⣿⡿⠖⠒⠚⢋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇⣿⣇⠀⣿⣇⡇
⠀⠀⣤⠀⠀⠉⠛⠷⣶⣄⡀⠀⠀⠀⠀⢰⠀⠀⠹⣯⣀⣿⡇⠀⢠⣴⣄⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡿⣇⢀⡿⡧⡇
⠀⠀⢀⡀⠀⣴⠂⠀⠀⠈⠙⠻⠦⣤⣤⣾⡀⣄⡀⠀⠁⠹⣿⡊⠉⣻⡟⢴⣔⣄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⡧⠀⡇⢳⡇
⠀⣠⢾⡽⠛⠿⣇⠀⠀⠑⢤⣤⣤⣶⠟⠉⠙⠛⠣⠄⠀⠀⠹⣷⣂⢩⡝⢾⣾⡟⠀⠀⠀⠀⠀⠀⢀⡴⣣⣶⢣⣤⠷⣶⡝⣦
⠀⠈⣻⣇⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠗⠈⡟⠇⠀⠀⠀⠀⠀⠀⠺⢛⡟⣧⣼⣺⣆⡟⣿⠻⠃
⠀⠴⠿⠛⠳⢤⡀⢀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢰⣸⠠⣀⠀⠀⠀⠀⠀⠈⣶⡟⠹⠿⠉⢷⡎
⠀⠀⠀⠀⠀⠀⠙⠛⠷⢤⣄⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠛⠶⣄⡶
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠳⠦⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠊⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠋⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠈⠙⠲⢬⣢⡀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⠀⠀⠀⣰⠋⠀⠀⠋⠈⠉⠰⠂⣀⠈⠀⢰⡄
⠀⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠠⠄⡄⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⢀⢌⠈⠀⠀⢠⠘⠁⠰⠆⠀⠀⠀⠂⣼⡟
⠀⠀⠀⠀⠀⠢⢀⣀⠀⢀⢀⣠⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣠⣴⣯⠞⢐⡂⠀⠈⢳⣄⡠⢠⢤⣏⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠷⠇⠀⠾⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠾⠛⠉⠀⣨⣴⣟⠁⠀⠀⠈⠻⠿⢿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⢀⠈⠀⠀⡀⠀⠀⠀⠀⠁⣀⣤⡴⠚⠉⠀⢀⣤⣶⠿⠛⠿⠿⠟⠺⠤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡰⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⢘⠄⠀⠀⢀⣜⠅⠄⢀⣠⣴⣿⣟⡭⠔⠒⠋⠉⠉⠉⠙⠉⠉⠀⣀⣀⣤⡤
⠀⠀⠀⠸⠀⢄⠀⡂⠀⠀⠀⡐⠀⠠⡘⠀⠀⣴⡟⢇⣠⣼⡿⠿⠛⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⣛⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠊⠀⡂⠀⠰⠈⠂⠊⠀⠀⠘⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣹⣿⣿⣿⠛⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣅⣨⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠘⠀⠀⠠⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣾⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠰⠆
⠀⠈⠿⠿⠀⠀⠀⠀⠀⢀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⣿⡿⠿⣿⣇⣽⣿⣿⣿⣿⣯⣹⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠂⠀⢉⠀⠤⠀⢠⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡟⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠙⠻⠿⣿⣿⣿⣷⢿⣽⣟⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣥⣤⡶⠞⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⢛⣃⠒⠒⠶⠶⢶⣶⣤⣝⡃⠀⠀⠀⣀⣤⡾⠁
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⣤⡍⠙⠳⢾⣿⣿⣿⠷⣶⣶
⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣀⡴⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⣀⣼⠏
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣴⠄⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣀⡀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⡟⣡⣄⡠⢤⡉⠙⠓⠶⢦⣤⣤⣤⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠷⣞⣙⡾⣅⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⢦⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠹⠽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣸⠷⣤⡇⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣷⣤⣿⣹⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⢧⡿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦⣴⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⣹⣦⡾⠛⢶⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢸⣥⣼⢷⡶⢿⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠈⠷⠾⠻⠞⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠐⣄⠀⠉⠛⠶⣦⣄⣀⠀⠀⠀⠀⣿⣦⠀⠀⣾⡆⠀⢀⣾⣇⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡀⢈⡷⣶⢶⡞⣏⠀⠉⠙⠓⠲⠦⠘⣿⠀⠀⣿⠿⠟⠋⠙⡏⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡇⠘⠁⠋⠘⢣⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣇⠀⠀⠀⠀⣧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢿⡀⢠⡿⠀⠀⠀⠀⢿⡇⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⠇⠀⠀⠀⠀⣸⡇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠛⠀⠀⠀⠀⠀⠀⠈⠋
⡿⠿⠿⠿⠿⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢔⣀⡀⠀⠀⠀⡀⠈⡀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠈⠀⠠⠂⠀⠀⠀⠐⡀⠄⠐⠪⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⡀⠀⠀⠀⠐⠀⠀⠀⠢⡀⠀⠀⡀⠀⢀⠀⠤⠀⢀⠀⡠⠂⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⢀⠀⠤⣀⢀⡀⠀⢀⡒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠈⠁⠐⠜⡋⠈⠀⠌⠐⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠔⠉⠀⠈⠰⡀⠀⠈⢲⠚⠒⠂⢄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⡀⠀⠀⠀⢀⠃⠀⠀⠀⠳⡀⠀⠀⠡⡈⠀⠐⠀⠂⠀⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠣⡀⠁⠢⠠⠔⠁⢐⠂⢄⠀⠀⠈⢂⠀⠀⢈⡶⡀⠀⠀⠐⠀⠀⠁⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄⡑⠢⡀⠀⣱⠐⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠈⠒⠂⠤⣀⠀⠀⠈⠂⢌⠚⢄⠀⡴⠚⠅⠦⠀⠀⢀⢠⠀⠚⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠘⠀⠀⠐⠒⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠉⠐⠤⠤⠋⠑⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠠⢀⠀⠀⠀⠀⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⡀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⠁⠀⠀⠠⠠⠄⠀⠀⠁



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

⣿⣿⣿⣿⡏⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⣿⣿⣿
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⠟⠛⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⠛⢻⣿⣿⣿⣿⣿⣷⠀⢻⣿⣿
⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⠏⠀⠀⠉⠛
⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⡀⠀⠀⠀⠘⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠃
⢠⣴⣤⣄⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⡿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⠿⣿⣿⣿⠛⠛⠁⠀⢀⣠⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢀⣿
⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⢿
⠻⠟⠁⠀⠀⠀⣀⣴⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⣰⣾⣿⣷⡀⠀⠉⠛⠛⠋⠉⠋
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠻⣿⣿⡿⠀⠀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿
⠀⢠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⣾⣿⣿⣿⣶⣶⣦⣄⡀⠘⠻⢿⣿⣿⣿⡿⠂⠀⠀⣾⣿⣿⣿⣿⣿⡿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠉⠛⠿⠛
⠀⠀⠀⠈⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⡄
⣶⣄⡀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣶⣤⣄⣤⣤⣤⣀⠀⠀⠘⠿⠿⠟⠋⠙⠛⠉⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣴⣶
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡗⠀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠘⢿⣿⣿⣿
⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻
⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣠⣶⣾⣿⣿⣦⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠉⠛⠛⠋⢀⣿⣿⣿⣿⣿⠏⠀⣠⣴⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣤⣀⠀⠀⠙⠻⠿⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠉⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣠⣶⣿⣿⣿⣷⣄⣠⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⣤⣄⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⢀
⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⣤⡀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⠋⠉⠀⣠⣾⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣠⣶⣾⣶⣿⣷⣦⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⢿⡿⢿⣿⠿⢿⣷⠶⡿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠒⠒⠒⠛⠈⢢⠞⠉⠑⠒⠢⠤⠤⠤⠒⠠⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠉⠓⠒⠦⢄⡀
⠀⠀⠀⢀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠀⢀⠴⠣⣄⡀⠀⠤⠤⠄⢠⣄⣀⡀⠀⠀⠀⠈⢦⠀⠀⠀⠀⡎⠀⢰⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⣀⠤⠔⢒⣋⠭⠛⠛⠉⠳
⠀⡇⠀⠀⠀⠈⠉⠐⠒⠢⠄⣀⠀⠉⠑⠢⢄⠀⠀⠣⠀⠀⢠⠁⠀⠈⡀⠀⠀⠀⡔⠁⠀⣀⠴⠒⠉⡠⠔⠊⠁
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠑⠀⠀⠁⠀⢾⠀⠀⠀⡇⠀⢀⠎⢀⡴⠋⠀⣀⠔⠉⠀⢀⣀⣀⣀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠬⠕⣦⠀⠀⠀⠆⠘⠉⠀⠚⠁⢠⠏⡠⠋⠀⣠⣾⠕⠒⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⢳
⢸⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⢀⠤⠊⠒⣢⣤⣼⣣⣾⣳⣿⣉⣴⠥⣖⡊⠁⠀⠙⠢⣄⠀⠀⠀⠀⢀⡀⡀⠀⣠⠏
⠀⢳⠒⠚⠉⢀⠤⢀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡠⠐⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠑⢄⠀⡀⠒⠀⠀⣰⠃
⠀⠘⢦⡀⠀⠀⠀⠀⠐⠁⡠⠂⠀⠐⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⠑⠢⣅⠈⢀⡠⠞⠁
⠀⠀⠀⠈⠣⣀⡀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠂⠀⠀⠄⢠⠀⡀⠀⠀⡇⠰⠐⡀⠡⡈⠂⠄⠁⠀⠉⢀⣠⠤⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠊⠉⠑⠲⠒⠢⠤⢄⣄⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⣀⣀⡤⠄⠒⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡁⠁⠉⠏⠉⠀⠈⠙⠁⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠰⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢦⢣⠀⠀⡜⠇⠀⡰⢫⡣⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡆⡘⠀⠘⡔⢁⠌⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⠀⠁⠀⣇⠎⠀⢐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢣⣀⠐⠁⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⢤⠙⢒⣤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠒⠒⠲⢦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣀⣠⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⠐⠈⠁⠀⠀⠀⢄⢀⠀⡐⠀⠀⠀⢀⣿⢀⣤⠶⠛⠉⠸⡏⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢠⠞⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠘⠓⠶⡾⢛⡿⠋⠉⠉⠉⠙⠓⠠⣄⡀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣠⠞⠳⡇
⠀⠀⠀⠀⠀⠀⢻⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⢷⡀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⡄⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠄⣣⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⣇⠀⠘⢧⡀
⠀⠠⠄⠱⡄⠀⠀⠀⠈⠢⡀⠀⠀⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠉⠀⠦⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢷⡀
⠀⢰⠖⠇⠀⠀⠀⠀⠀⠀⠀⠙⢳⡷⢦⡄⠐⠀⠈⣷⠒⠂⠐⠀⠲⠒⠒⢦⡀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠸⡇⠘⠁⠀⠀⠀⢻⣄⣀⣠⢀⡄⠀⠀⠰⠉⠂⡖⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣟⠀⢻⣾⡆⠀⠘⠀⣼⠻⡄⠀⠀⠉⠙⠲⠶⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢣⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠈⣷⠀⠃⢠⡏⠀⢹⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡀⠘⢷⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡀⢶⠀⠀⠀⠀⠀⢸⡇⠀⠈⣷⡀⠀⣿⠀⠀⠙⣆⠀⠀⠀⠀⢠⠄⠀⠀⣀⠀⠀⠀⢀⡾⠆⠉⠀⠖⠉⢿⣄⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢑⠠⡿⠂⠀⠀⠀⣸⠁⠀⠀⠘⡏⠰⡿⠀⠀⠀⠈⢷⡀⢀⠴⠐⠒⠢⠄⠀⠉⢂⢀⡞⠠⠐⠈⠀⠀⠀⠀⠻⢇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠾⠙⣧⠀⠀⠀⠀⣽⠄⠀⠀⠀⠹⣄⣧⠀⠀⠀⡠⠤⢋⠌⠁⠀⠀⠀⠀⢁⠀⣸⡋⠠⠄⠀⠀⠠⠤⢀⡀⠀⠃⠉⢰⡶⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⠇⠒⠈⠀⠀⠀⠀⠙⣆⠀⠀⠂⡴⠁⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢴⠖⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⣄⣠⠁⡂⠀⡀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⠜⣿⡀⠁⠀⠃⠘⠀⣴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⢀⡧⠤⠤⠀⡀⠀⠀⠀⠀⢀⡜⠃⠀⡠⣡⠊⠀⡿⣀⢀⡁⣀⣰⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢰⠆
⠀⠀⠀⢀⣠⠶⠛⠀⠐⠤⠀⡀⠢⡀⢀⡴⠋⠀⠀⢠⡜⠁⠀⢠⠃⠈⠉⠙⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⢈⠓
⠀⢰⣉⠉⢀⡀⠀⠀⠀⠀⠀⠈⣴⠟⠉⠀⠀⠀⢀⡿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡴⠊⠉⠁
⠀⠀⢉⡟⠁⠀⠀⠚⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢺
⠀⢀⡟⠀⡔⠁⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢿⡀⠀⠀⠀⠀⠀⠛⠁
⠀⢸⡅⠀⢀⠄⠀⠂⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀
⠀⠘⢧⣤⡥⢶⠱⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⡀⠀⠀⠀⠀⣶⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⡀⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠰⡄⠂⠀⠁⠀⡀⠀⠘⣷⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠿⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠁⠈⠀⠀⠈⢷⡄⠀⠀⠈⠳⣄⠀⠀⢀⡀⠄⣀⡔⠉⠀⠀⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⢀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠘⢯⣀⠀⠀⠚⠁⠀⠐⠉⠀⠴⠈⠲⡆⠀⠀⠀⠀⠀⠀⠠⠂⡀⠀⠀⠀⡿⣧
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⠀⠀⠀⠘⢷⡀⠀⠀⠀⠙⠢⣄⠀⠈⠀⠠⠀⠀⠀⡀⠀⠉⢲⡀⠁⠀⠄⠀⠁⠈⠃⠀⠀⡜⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠳⢆⠀⠀⡀⠄⠀⠀⣀⠄⢫⡝⡟⠁⠀⠀⠀⠀⠀⣤⠜⣡⡟
⠀⠀⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠙⠦⣤⣴⠶⠾⠉⠀⠈⢰⡟⠁⠀⠀⠐⢓⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠴⠊⣠⠞⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡂⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⣏⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠊⢤⡀⢰⡇⠀⠐⠊⣁⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣄⡁⠐⠀⢀⣠⠤⠂⠁⠀⠀⠜⠒⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡀⠄⠋⢉⡿⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣄⠀⣉⣠⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡗
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⡟⣷⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣷⠄⠀⠀⢸⣿⣿⣽⣿⣷⠀⣾⣿⣿⣽⣿
⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠘⢸⡿⢻⡇⠙⠀⠀⠀⢿⣿⡿⢿⣇⢹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⠁⣷⣿⣿⣷⣿⠈⠁
⠈⠛⠻⣿⡿⠟⠛⠀⠀⠀⠀⠀⢺⠃⠘⡟⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⣤⠀⠀⠀⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢑⣶⣾⣶⣄⠀⠀⠀⠀⠀⢾⣿⣷⠄⣀⣠⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠠⣿⣦⣤⣶⣶⠤
⠀⠀⠀⠻⣿⣋⣿⡿⠃⠀⠀⠀⠀⠀⠙⢡⣾⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣿⣿⣷⣊⣽⣷⠃
⠀⠀⠂⣸⣿⣿⣿⣿⡄⠂⠀⠀⠀⠀⠰⣝⠿⢋⣴⣿⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣻⣧⣞⣹⠿⣿⠖⠁
⠐⠃⠀⠀⠀⠛⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠈⠒⠛⠛⠐⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢐⠉⡆⠀⠀⠀⠀⠀⠀⢀⢶⣿⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣿⣿⠀⠀⠲⢦⡄⢀⣤⣶⣤⡀
⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⣾⡆⣻⣿⠿⣃⣠⢼⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿
⠀⣾⠿⣿⠿⣷⠀⠀⠀⠀⣾⣿⣿⡞⠛⠒⠛⢽⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠼⢦
⠀⡏⠀⣿⠀⢹⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⣤⣀
⢠⣿⣿⣿⣽⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡿⢷⣦⣀
⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣠⣴⣶⣯⣽⣹⣽⣷⣶⣤⡀⠀⠀⠀⠀⠀⢀⠋⠂
⢸⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⣸⣟⠛⠟⠛⠁⠀⠀⠀⠈⢹⠟⠛⠻⡟⠛⠛⢿⠉⠀⠀⠀⠀⠀⢀⠂⠘⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⡖⠚⠛⡟⠛⠛⡏⠉⢻⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣈⣇⣀⣤⣧⣤⠤⠷⠶⠾⠒⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⣍⠉⠉⠀⠀⠀⠀⢀⣴⠟⠛⠳⡄⠈⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡡⠞⠁⠙⢧⡀⠀⠀⠀⠀⠸⣟⣆⡀⣠⠇⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠗⠉⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠉⠛⠛⠁⢀⣀⣤⡴⠶⠚⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣯⣤⣤⣤⣤⣀⣀⣀⣀⣀⠈⢷⡄⠀⣀⣠⡴⠖⠛⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡠⠔⠒⠋⠉⠉⠉⠁⣿
⠀⠀⠀⠀⣿⣍⣉⡙⠛⣷⣆⡀⠀⠀⠀⠀⠀⢸⠓⠦⠤⠤⠔⠒⠒⠛⠛⠒⠒⠤⣄⣼⣄⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⡟⣧⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡸⣿⡿⠿⠿⠿⢿⣿⣻⣿⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⢸⠀⢀⣄⢀⣀⠠⠄⣶⠀⣿⣏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⣷⢿⣶⣶⣶⣶⣶⣖⣒⣶⣤⣶⣾⣯⣼⡇⠀⠀⠀⠀⢸⠀⢸⡉⠋⢹⡐⠇⠘⠂⠉⠈⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⢻⡘⣇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢸⢸⡇⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠘⣧⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠒⠒⠛⠚⠓⠤⠤⠤⠤⠤⠤⠴⠒⠢⡞⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡠⢤⡀⠀⡜⠀⠙⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠲⡄⠀⠀⡠⣿⢤⡀⠀⡼⠀⠀⠓⠊⠀⠀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡏⠀⠙⠦⠞⠀⡟⠀⠑⠚⠁⠀⠀⠀⠀⠐⣀⡤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⣧⣀⡀⠀⠀⠀⡇⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣳⠇⠀⠈⠙⠓⠶⢤⡷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢭⣭⣙⣒⣒⣒⣒⣫⡥⠾⠋

⠄⡠⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠉⢀⣄⡴⠀⠄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠠⠀⠌⠀⠀⠀⢠⡄⠀⠀⠓⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠂⠔⠀⢄⡂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠈⠓⠀⢀⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠉⠢⢄⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠐⠆⠀⠀⠀⠀⠑⢄⠀⠰⡄⠒⠀⠏⢂⢸⡤⢢⡀⠀⠀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠑⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠑⠦⠀⣴⢊⠔⢁⡼⡤⠊⢀⠤⢀⠈⠁⠒⢠⣤⡄⠀⠰⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣈⡁⢡⢁⡎⢠⢋⠜⠀⠀⡇⠀⢈⠀⠀⡰⢿⠞⠉⠐⠤⡇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠰⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠠⢧⠂⢀⢀⡀⠈⠀⠈⢀⡞⡷⠃⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠐⠂⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠠⢣⠎⡜⡱⠀⢠⠛⠟⠀⠀⢀⣀⣀⣀⣀⡀⠀⠉⠢⡀⠀⠃⠀⠀⠄⠘⠤⠀⠀⠁⢀⠤⠠⠠⠄
⠀⠀⠀⠇⠆⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠂⢀⢡⠇⡞⡐⠀⢠⠿⠏⠀⣠⣾⠟⠓⠋⠙⠚⠿⣳⣄⠀⠈⠢⡄⠀⠀⠈⠐⠀⠀⠀⠀⠀⠁⠁⠐⠄
⠀⠀⠀⠀⠀⡀⠤⠤⠴⠀⠤⡁⠴⢲⠤⣀⡘⠀⢈⡜⢸⢡⠁⢀⢿⡟⠀⣮⠟⠠⠂⠁⠀⠀⠀⠀⠈⢻⣥⠀⠀⠈⢆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠂
⠀⠀⢖⠈⠁⠀⠀⡄⠒⠒⠓⠈⠇⡏⢰⠃⠁⠀⠀⠀⠉⠂⠀⣼⣶⠀⢨⡟⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⣟⡆⠀⠀⠀⠱⡀
⠀⠀⠀⠁⠢⢄⣀⡀⠁⣐⣂⠴⠀⡇⢸⠰⠀⠀⢀⠀⠀⠀⢀⣧⡄⠀⠘⣣⠀⢄⠀⠰⠆⠀⠒⠀⠀⠀⠿⠇⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠠⠔⠇⠧⠘⠺⠀⠰⠁⠈⠂⠀⢸⣭⠁⠀⠀⠻⣦⡀⠀⠀⠀⠀⠐⠀⢈⢼⠟⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠂⠐⠁⠀⢸⣹⠀⠀⠀⠀⠙⠛⣶⣤⡤⣤⣤⡰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠢⠄⡀⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠦⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠐⠂⠁
⠠⠀⡌⠀⠀⢀⢀⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰⠄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠰⠀⠀⠀⡀⠉⠀⠀⠀⠈⠐⠂⠀⠠⠤⠄⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡸⠇⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣺⡿⣿⢻⣾⠾⣿⣿⣿⡆⢡⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢊⠓⢻⠑⠋⠉⠉⠩⠉⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⡀⠀⠀⠀⠀⠀⢀⢣⣀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢐⣡⣦⣬⣭⣬⣭⣭⣦⣬⡰⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣯⣭⣭⣽⣿⣿⣽⢇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣧⣤⠤⡤⣤⣾⡿⠲⢁⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣿⠤⠀⠈⢰⠘⢸⣇⢧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢙⢸⡯⠶⡒⡖⠼⠩⢂⢿⡸⡦⠀⠀⠀⠖⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⢠⣿⠿⠋⢀⣾⣿⣿⡇⠈⢷⢜⡃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⡟⠀⣀⣄⠻⠿⠛⠋⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⢸⡇⢰⣿⡿⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠘⢃⣤⣾⠇⢀⣼⣿⡌⢿⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⢸⠀⠰⣿⣿⠇⠀⣾⣿⣿⠁⠀⣹⡈
⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡁⣼⣀⠀⠀⠀⠀⣼⣿⣿⡟⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠁⣿⣿⣿⡿⠀⣾⣿⡿⠋⠀⠀⠻⢿⡇⠤⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⠿⠟⠁⠀⠈⠉⠀⢸⣿⣦⣤⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢿⡀⠀⣶⣶⣄⠀⠀⠀⠙⢿⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡇⠀⢹⣿⣿⡷⡶⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⢸⣷⣤⣀⠉⠁⠀⠀⣠⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡜⠻⠿⠷⠦⣤⣤⣤⢭⣽⠿⢷⡛⠄
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠉⠃⠉⠀⠀⠀⠁⠂⠀⠀⠈

⠀⠀⠀⢀⡀
⠀⠀⠀⣸⠷⠀⣠⡄⠀⠀⢠⣤⣤⣼⡏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⣾⣶⢀
⠀⠀⠸⣿⣆⣠⠟⠁⠀⠀⠀⠉⠙⢿⣿⡾⡇⠀⠀⠀⣠⣶⡤⠀⣐⠶⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠙⠛⠺
⠀⠀⠀⠉⠚⠙⠓⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣿⣿⡜⠋⠀⠀⠀⠀⠀⠀⠀⢸⡼⠟⡖⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⠄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⢴⣟⣻⡇⠀⠀⠄⠀⠀⡀⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⠦⠀⠀⠀⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠿⠿⠁⢨⠷⠿⠛⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠞⠀⠀⠀⠀⠀⢐⡄⢠⡅
⠀⠀⠀⢸⡄⠀⠁⠀⠀⠀⠀⠀⢀⣀⠄⣻⣿⠛⣁⠀⣀⡙⣉⡁⠀⠘⣃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⢀⠸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢻⣧⠀⠈⠀⢹⣧⠀⠀⠈⠀⠰⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠
⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡀⠀⠀⠈⠛⠀⠀⠀⠀⡀⠉⢁⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⡁
⠀⠀⠐⢦⢠⡀⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣈⠀⠀⠀⡀⢰⡇⠺⡖⡆⠀⠀⢀⡀
⠀⠀⠘⠋⠉⠃⠉⠀⠀⠀⠀⢠⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⢸⠁⠈⠡⠛⠀⠀⠈⡁
⠀⠀⢮⡄⠀⠀⠀⠀⠀⠀⠐⢨⠀⠀⠀⠈⠉⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁⠀⠀⠀⢠⣦
⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⣀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠘⢷⡂⠀⠀⠀⢸⣤⠀⠀⠀⠀⣴⠟⠀⠀⠀⡄⡠⢿⣿⡇⠀⠀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⣏⢠⡀⠀⢀⣴⠇⠀⠀⠀⠀⢼⠀⠠⠁⠀⠀⠀⠀⠀⠀⣠⡀⠘⣿⡀⡀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣴⡿⠸⢿⣦⡾⡅⠀⠀⠀⠀⠀⢸⡆⠐⠒⢲⢀⠀⠀⢠⣤⣼⣿⡟⠋⠰⢱⣤⣤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣁⠀⣠⣿⣿⠄⠀⠀⠀⠀⠀⢘⣇⣊⠀⢸⠹⠀⠀⠈⠉⠉⣹⣷⣻⣿⣏⠉⠉⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣙⠻⠿⠛⠋⠙⠀⠀⠀⠀⠀⠀⠈⠛⣀⡄⠁⠀⠀⠀⠀⠀⢾⠟⠁⢸⣿⠻⠃⠀⠀⠀⢰⡄⣿
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠈⠁⠉⠁
⣶⣶⠶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠲⡁⠁⠀⠀⠀⠁⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⣴⢅⠀⠀⢀
⠀⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠈⠆⠜⠏⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢕⠉⣈⠀⠀⠀⠰⣤⣾⠅⠀⠀⠀⠀⡀⡀
⡤⢠⡖⡁⠀⠀⠀⠀⢐⠀⣀⡄⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⣀⢢⠋⠠⠄
⢂⡀⠰⠔⠂⠀⠀⠀⠩⢁⠈⠳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠤⡈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡲⠂⢂⠀⠀⠠⠪⢦⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣠
⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⣆⠀⠀⠀⠐⠃⠸⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠨⢿⡦⠄
⠀⠀⠐⡿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢥⣰⠣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⡀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⢠⡼⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⡤⡅⠊⠲⠀⠀⠀⠀⠀⠀⠀⠢⢻⠕⠀⢀⡀⠀⠂⡀⡀⠀⠀⠀⠀⠑⠙⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠌⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣵⠒⠩⠄⠀⠀⢤⣄⠀⠀⠀⠄⠓⢪
⠀⠀⠀⠀⠀⡠⢰⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⣌⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣨⣯⠁⠀⠀⠈⠀⢱
⠀⠀⠀⠀⠈⢶⠟⠆⠀⠀⠀⠀⡀⠤⠀⠀⠀⠘⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠐⣲⠒⡀⠀⠀⠀⠀⠀⠐⠠⢢⢂⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡪⠄⠂⡭⠂⠀⠀⠀⠀⠚⢿⡬⠅
⠉⠛⠦⠀⠀⠀⠀⠀⠀⠀⠁⢌⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠨⣀⠀⠘⡠⠘
⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠢⠠⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠙⣾⠩⠅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⣋⠀⠄
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢦⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠔⠨⠙⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀⡠⠀⠀⠀⠀⠀⠀⠒⠞⠯⠀⠀⠐⠈⡃⠐⠙⠀⠀⠀⠀⠀⠀⠁
⠠⠀⠀⠀⠀⠀⢰⡌⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠃⠳⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⡁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⢀⠀⠀⠀⣀⠄⠀⠀⢄⡀⢠⠀⢈⠆⢀⡼⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⡄⠀⠀⠺⠠⠬⠁⢖⣂⠥⠚⠈⢀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠈⠀⠒⠒⠒⠀⣀⠁⠀⠄⠂⠉⠀⠀⠀⠀⠤⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⣀⣀⣀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣮⣭⣴⣤⣼⣾⣴⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣽⣯⠉⣹⣿⣟⡀⠀⠀⠀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⢋⣽⣿⣿⣧⡈⢣⣶⣤⣼⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣴⣾⣿⣿⣿⣿⣧⡾⠛⠿⢿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣷⣆⠀⠈⠻⣇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡃⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡇⢧⣾⢗⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⡿⡟⣻⠱⠀⠀⠀⠙⢚⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢾⣿⡿⠙⢿⣿⣿⣏⣉⢛⣀⣉⣍⣿⣙⣟⢲⣾⣶⣶⣤⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⠽⠶⠺⣿⣿⣯⣹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⢭⣯⣿⣿⣿⣿⣟⣿⣿⣿⣏⣽⣿⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣾⣯⣿⣿⣿⣿⣿⡿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⢿⣿⣿⢿⣷⣿⣿⣿⣿⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣻⣿⣿⣿⣿⢻⣯⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣻⣿⣿⣿⣿⠇⠀⠙⢿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣿⢿⣿⣿⣀⠀⠀⠀⠙⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣶⣿⣿⣿⣯⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣼⠿⣿⢟⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠗⠋⢿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣯⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠙⠻⢿⣿⣿⣿⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣿⣿⠀⢸⣧⡀⠀⠀⠈⣿⣿⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⢻⣿⣿⣷⣤⣾⣿⣿⣇⣄⣀⣿⣿⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⣰⣿⢿⣶⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⡺⢷⣤⡀⠀⠀⠀⠀⢀⣼⣿⣷⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠟⠛⠛⠛⠻⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣷⣯⣽⣯⣤⣴⣾⣿⣿⣷⣿⣧
⠀⠀⠀⠀⢀⣿⣷⠿⢟⡞⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⢟⠟⢛⡻⢿⣿⣿⠻⣿⣿⣽⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⢸⣵⣾⣻⢗⡤⢻⣷⣴⣿⣿⣟⣿⣿⣿⣾⡇
⠀⠀⠀⠀⢸⣿⣻⣿⣿⢆⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡘⣿⣾⡭⣟⡵⣞⢹⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣄⣀⣠⣴⣾⣿⣿⣤⣿⣿⣷⣔⠾⣯⣰⠟⣡⣾⣿⣿⡿⢋⣼⣿⣿⣿⣻⡏
⠀⠀⠀⠀⠀⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣶⣶⣿⣿⣿⣿⠏⢀⢾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⠁⠈⣿⣿⣿⣿⣿⣻⣿⣷⡿⠙⠱⠃⣠⣿⣿⣿⣟⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠈⣿⠋⠀⠀⢀⣿⣿⣻⣿⡿⣿⣿⡟⡡⠀⡀⢘⣿⣿⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⡆⠀⠀⡟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣠⣿⣿⣷⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠳⠀⠈⠁⠀⠰⠿⠏⠋⢹⣿⣿⣿⣿⣷⢄⣠⣾⣿⣿⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠑⡀⣉⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⠊⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰⡀⠀⠉⠁⠀⠀⠀⠈⠁⢀⡎⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣄⣀⠀⡼⠁⠈⢇⠀⢀⣠⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⣶⣶⠤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠃⠀⠊⠎⢁⡈⡀⠰⠀⠐⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡤⠄⠠⠀⠀⢤⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⣴⡇⠀⠀⠀⠀⢸⣤⠠⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠒⠒⠒⠂⢺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡟⠀⡇⠀⠀⠀⠀⢸⠀⢻⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡽⠀⠚⡏⠀⠈⠉⠀⢹⠛⠁⢯⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠴⡫⠃⠄⢀⡇⠀⠀⠀⠀⢸⡀⠀⠘⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠊⡠⠐⠀⠈⡏⠈⠉⠀⠁⢸⠁⠈⠂⢄⠑⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠊⡠⠊⠀⠀⠀⢀⣇⠀⡀⢀⠀⣸⡀⠀⠀⠀⠑⢄⠑⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⢠⢏⡔⣁⢀⣀⡀⣀⣀⣀⣀⡰⠃⠀⢰⡆⠀⠘⢆⣀⣀⣀⣀⣀⣀⣀⣈⢢⡹⡄
⠀⠀⠀⠀⠀⠀⠸⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⢸⡇⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠴⠀⢀⠀⢀⠀⡀⠀⠀⢸⡇⠀⠀⢈⠀⡀⠀⡀⠀⠦⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⠒⠂⠏⠹⣒⣒⣿⣟⣖⣒⡋⠸⠒⠒⠖⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠻⠿⠟⠛⠿⠿⠃⡀⠀⠀⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠚⠓⠒⠺⠂⠀⠀⠀⠀⠀⠀⠀⡗⠒⠚⠓⠒⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠁