White dwarf Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠫⢾⣧⠀⠀⢀⡀⠀⠀⠀⣼⣿⣿⡿⠻⠿⠿⣼⣿⡿⣿⣿⣷⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠊⢻⣧⣠⣿⣿⣄⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠉⣿⣮⣻⣿⡇⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠨⣿⣿⣿⣿⣿⣷⣤⣿⣸⣿⡿⢷⡔⡄⣀⣾⡿⣿⣷⣿⣿⣿⣿⣿⡆⠀⠀⣀⣤⣤⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣦⣤⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣯⣾⡹⣯⠉⠉⡁⠁⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣧⡘⢿⣿⢟⢥⣦⡤⢨⣶⣾⣇⣼⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣤⣴⢿⣿⣿⣦⣁⣬⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣶⣦⣶⣾⣿⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⢟⠻⠟⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣰⣿⣿⣿⣿⣏⣙⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡱
⠀⠀⠀⠀⠀⠀⢀⡀⢶⡀⣸⢂⣄⠀⠀⠀⠈⠁⡀⠀⡆⠀⠀⠀⠀⢀⠰⢲⠔⠒⠆⣀
⠀⠀⠀⠀⠀⠀⡞⠓⠶⡏⠉⢫⣤⠀⠀⠀⠀⠀⠀⠀⠉⡂⠀⠀⠀⣮⣞⠉⠙⣷⣯⣈⣆
⠀⠀⠀⠀⠀⠀⣿⣭⣭⣥⡄⠴⠖⠀⠀⠀⠀⢂⠁⠀⠀⠀⣆⠀⠀⠀⠉⡦⣠⣯⡛⢡⣾
⠀⠀⠀⠀⠀⢰⣷⣶⠖⢶⣿⡆⠫⡤⠀⠀⢐⠀⠀⠀⠀⠀⢼⡀⠀⢂⡀⠐⠛⠱⣉⡙⠛⠂⠀⠀⠄
⠀⢀⣀⠀⠀⠘⠛⢛⢶⡞⠉⠃⠀⢸⠄⠀⣮⠔⠣⣄⡠⠷⣶⡇⠀⠀⢡⣤⠤⠔⠛⢧⣄⣀⣄⠚
⠀⢈⠁⠀⢴⡠⢤⣁⠀⠑⠀⢀⠀⠜⠀⣾⠋⠀⠀⠀⠀⠀⠸⣿⠇⠀⣽⣇⠀⠀⠀⢀⣀⣴⣯⡐⠺⣛⡀⠔
⠀⠈⠀⠀⠀⢹⣄⣈⡉⣆⣴⣼⠇⠀⠀⢹⡆⣣⡄⠀⠀⡀⠥⣿⠊⠠⢅⣿⣿⡆⣠⣿⣻⣹⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠸⠉⣹⠿⠿⠋⠉⠀⠁⠀⠀⢀⠀⠙⠔⠀⠀⢀⠀⠀⠀⠀⢹⠛⠛⢿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠆⠒⠒⠚⠰⠞⠀⠀⠀⠀⠀⠁⠁⠀⠉⠉
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣀⠘⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡙⡟⢩⠖⠒⠉⠁⢀⡠⠇⡰⠁⠀⠀⠀⠀⣀⣀⡠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠉⠓⠧⣧⣀⣦⠤⣒⠉⠉⠦⣀⡅⣠⠤⠶⠯⠍⢉⡉⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠔⢲⡭⠌⣀⡰⠒⠋⠀⡠⠒⢲⣾⡷⠛⠒⠒⢤⡀⠈⠑⢦⡀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⡕⠀⣀⠴⠁⠐⠋⠁⠐⢦⡀⠀⠘⣿⣷⣄⠀⠙⡄⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⣄⣀⢠⢁⠞⢁⣀⠀⢠⣤⣄⠀⠀⠀⠰⣦⠀⠙⢿⣆⠀⠸⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣏⡎⣼⠿⣿⡗⠉⠉⠉⠀⣠⡄⠀⠈⠀⠀⠀⣿⠀⠀⠇⢀⠂⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿⡃⠇⠀⡛⠷⣄⣀⣴⣟⠻⣿⡀⠀⠀⣠⣾⣿⠀⢸⢠⡎⢸⢄⡀
⠀⠀⠀⠀⠀⠸⠢⡀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⣿⡇⠀⠀⢡⣀⣈⡛⢻⣿⠆⠀⠀⠀⠸⠋⠉⠉⢢⠶⢾⠉⠋⠀⡵
⠀⠀⠀⠀⠠⠘⠀⠈⠖⠅⠀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⢺⣿⣷⠀⠀⠀⠉⠀⠀⠞⠃⠀⠀⠀⠀⡀⢠⠄⠒⠋⠀⠀⠑⠒⠊⠁
⠀⠀⠀⠀⠀⢡⣀⣀⣄⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⣽⢿⣿⣶⣦⣤⣤⣶⣶⣶⣶⣶⣦⠴⠖⠉⠁
⠀⠀⠐⠈⠉⠉⠀⠀⠠⠄⠜⠢⡀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣀⡜⣀⡀⠀⠉⠛⠛⠒⠉⠀⠈⠱⣤⡀
⠀⠀⠀⠀⠒⠒⠁⠀⡠⠤⢀⡀⠈⠂⣄⣀⢀⡀⠀⢠⠂⠀⠁⠁⠀⠉⡹⢀⠤⠤⣀⡊⠉⠉⠉⠉⠉⢆
⠀⠀⠀⠀⡀⠄⠔⠚⠀⠀⠀⠈⠁⠀⠀⠀⠀⡨⠧⣧⡀⢠⡄⠀⠀⠀⠳⠁⠀⠀⢈⡴⠊⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢨⢃⢐⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⠤⠔⣡⡄⠀⢠⠟⣶⢄⣀⣠⠎⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠇⠀⠀⠀⣄⠀⡞⢇⠣⠤⠞⢸⠛⠉⢸⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠊⠀⠡⣟⡂⠀⠀⠀⠸⡀⠀⠈⢦⣀⠤⠊⠉⠱⡄
⠀⠀⠀⠀⠂⠀⠀⠀⢀⣲⠞⠀⡠⠴⠪⡅⠐⠀⠏⠦⠤⠤⠲⠚⢏⠉⣉⡽⠓⠊⠉⢻⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠈⠣⣀⠠⣀⠀⠸⡨⠰⣄⣹⡉⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⣀⠀⠀⠈⠲⣀⣸⠃⠈⠁⠢⢈⠉⠻⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠊⠙⠁⠈⠓⠲⠀⠀⠘⢄⣠⣇⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣧⣴⣾⣷⣬⣙⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⠇⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⣄⣤⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢱⣾⠋⣿⠏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣧⣿⣼⣿⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡶⣶⠶⢿⣟⣛⣿⣽⣿⣟⣛⣿⣿⣿⣯⣉⣛⣻⣶⣶⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣿⣿⡿⢶⣿⣿⣶⡷⠾⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡌⣿⠁⠀⢉⣭⢞⡀⢀⣳⣮⡉⠀⠈⣿⢡⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⢷⡾⠉⠈⣩⢿⡟⠉⠁⠉⢳⣼⢷⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⣀⣠⣾⣿⣯⣽⣾⣶⣄⠀⠈⣶⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣾⣿⣿⣿⣿⠁⠀⠉⠻⣿⣿⣯⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⠏⣿⠀⢠⠀⠀⣿⣿⣸⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣷⡹⣇⣾⢀⢀⣿⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⣷⣿⣿⡷⠿⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡿⠻⡟⠓⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⣴⡦⠤⡀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⣤⠀⠾⣿⣗⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀⣀⣆⡞⠁⠀⠀⠀⠙⢧⣰⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠙⠀⡀⠀⠀⡠⢴⠎⠉⡁⠀⠠⢄⠀⠀⢀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣾⠇⠀⠀⠀⠁⡀⡀⢰⣿⣭⡤⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣏⠀⣤⣤⡏⢈⣤⣤⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠖⠛⢿⣿⣿⣿⢳⣅⣘⡇⢀⣁⣸⠤⠟⡿⢿⣷⣄⠐⢤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⠁⠀⠀⠀⠀⠀⠹⡇⢻⣦⣼⣁⠤⢄⢹⣅⣠⡾⠁⠀⠙⠉⠳⣄⠀⠠⡏⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡀⣻⡿⠁⠀⢰⠻⣿⣿⠁⠐⠀⠀⠀⠀⢼⣧⣄⠀⠣⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣥⡀⠀⣀⣤⠈⣠⡟⠁⠀⠀⠈⠐⠀⢻⣆⢀⡖⢶⠄⢀⣸⣿⣮⣿⣦⡠⠞⢙⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡋⠁⣩⣾⣿⣧⣙⣠⣤⠿⡆⠀⠀⠀⠀⠀⠰⣾⣿⡷⣷⣷⣾⣿⣿⣿⣿⡿⠿⢠⡶⠋⣠⡽⠿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⢾⣿⣯⣿⣿⡿⠋⠁⠀⠘⢦⣄⠀⢠⠔⠁⠈⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣶⣷⢾⣁⡠⠂⠉⣿⠂
⠀⠀⠀⠀⠸⣷⣿⡽⢂⠀⡄⠀⡸⣿⣯⡾⣷⡆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠰⡴⠿⣮⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⢠⣾⣅⠑⢦⡀⢀
⠀⠀⠀⠀⠀⣿⣿⡇⡠⠀⠀⠠⡇⠺⡟⠃⠈⠉⠁⠀⠔⠀⠠⢀⡀⠀⠀⠀⢀⠔⠀⠀⢹⡿⠀⠀⠀⠈⠀⠀⠈⠈⠉⠉⠉⠀⠙⢷⣎⣶⣿
⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠤⠤⢤⣵⣟⣦⣀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠋
⠀⠀⢀⠀⣾⡍⠉⠉⣧⣄⣼⡏⠀⠐⢤⣤⣄⠀⠀⠀⠀⢐⡏⢀⠵⠊⡈⢹⡏⠈⢸⣧⠏
⢤⣤⣾⣿⡟⠀⠀⡴⠁⣿⣿⡟⠀⠀⠘⠛⠛⡇⠀⠀⠠⠉⣿⣷⣶⣶⣶⣾⡛⠟⠻⣎⠢⡀
⠀⠀⠉⠉⢻⣦⣜⣀⡀⢿⡿⠳⠖⣦⣦⣶⣤⡇⠀⠀⠐⠷⣿⡿⣷⣾⣿⣇⠀⠀⠀⡴⠂⢷⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⡷⠒⠚⠋⠀⠀⠀⠀⠀⠘⣶⣏⣙⣿⣏⡀⢠⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⡉⡁⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣶⣤⣤⣤⣤⠄⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡗⠾⢭⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢇⠀⠀⢻⣯⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠋⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡟⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣁⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⢀⢀⣀⠭⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠉⠁⢠⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠺⣏⣙⣿⣿⡃⣠⡔⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⣴⡟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡈⠙⣿⣿⣟⣿⢀⡀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣄⠀⣀⣠⣼⣷⣾⣤⣤⣤⣤⣠⣴⠶⢲⣶⣦⣿⣿⣷⣿⣿⣿⣿⣿⣃⣀⣠⣄
⠀⠀⠀⠀⠀⠶⠬⡭⠀⠩⠍⠁⠉⠉⠍⠉⠀⠀⠯⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠻⠍⠹⠶⠛⠲⠒⠀⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⡟⣷⠀⡀⠉⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⣤⠾⠋⢡⡾⣿⣷⣤⣄⣴⣿⡟⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡴⠿⡁⠈⠹⢤⣚⣣⡴⠋⢙⣥⠸⠿⢿⣷⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⢀⠀⠈⢿⣴⠾⣹⠝⠀⠀⠀⠀⠁⢿⡟⠑⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠚⡁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢿⣯⠁⠀⠀⠀⠀⠀⢀⣾⣁⣠⠚⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⢳⣄⣸⣇⠚⠓⣠⣿⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣖⢶⡤⡶⡠⢤⣾⠟⠀⢬⠗
⠀⠀⠀⠀⠀⠀⠀⢠⡌⣿⣯⣾⣳⣽⣟⢡⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⣿⣷⣶⣿⡏⠁⠀⠁
⠀⠀⠀⠀⢀⢐⠀⣎⠐⠛⠒⣿⡾⠶⠢⠤⡅⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣼⣿⣿⣿⣿⣧⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⡟⠁⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⡿⣿⢿⣿⢿⡿⠛⠛⠃
⠀⠀⠀⠀⠀⣈⡿⠿⠳⠿⠿⠷⠺⠗⠿⠿⠿⣿⡅⠈⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠜⠙⠛⠃⠡
⠀⠐⠀⢠⣶⣶⣿⣿⣿⣿⣿⠷⠴⣿⣿⣶⣶⣿⡗⣿⠛⡆⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⢀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠐
⠀⠀⠀⠛⢹⣿⣿⣿⣷⣷⣽⣋⣈⣿⣿⣿⣿⣿⣧⣍⣠⠁⣀⣀⡀⠀⠀⠀⠀⡿⠉⢻⡇⠀⠀⠀⠀⠀⠀⠈⢃⠉⠉⠁
⠀⠀⠀⠀⢸⠟⠛⡃⠿⠿⠟⠀⠀⠿⣿⡿⢿⡿⠿⠋⠉⢿⠙⠉⠀⠀⠀⠀⠀⠆⢀⣨⠁⠀⠀⠀⠀⠀⠀⠀⢹⣀
⠀⠀⠀⠀⠈⠂⠀⠛⠛⠒⠂⠠⠀⠄⠶⠾⠷⠄⠐⠂⠀⠘⠀⠀⠀⠀⠀⠐⠇⠐⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠽⠺⠇⠰⠶

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⠾⠛⠛⠛⠛⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠹⣇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⢹⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⠇⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡈⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⣰⡟⠀⠙⣣⠀⠀⠀⠀⠰⡦⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠋⠉⠀⠈⠛⠛⠳⠶⠞⠋⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠛⠉⠙⣷⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣤⣀⣤⡿⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⡀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠈⠛⢦⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣶⣤⣀⡀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠹⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠈⡳⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠉⠁⠲⠶⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠷⣤⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⠻⣧⡉⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⠻⣶⣄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠈⣷
⠀⠀⠀⠀⣀⣤⣼⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⣠⠞⠉⣴⡟⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⡇
⠀⣰⠏⠀⢰⡟⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣸⣧
⢰⡇⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣿⠻⣧
⣾⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣼⡏⠀⢹
⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣼⠏⠀⠀⠘
⣿⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⣀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⢀⣾⠋
⢻⣇⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⢀⠖⠉⠀⠀⠈⠙⠶⣄⣴⠟⠁⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⢸
⣸⣿⡀⠀⠘⣷⡀⠀⠀⠀⠀⣼⣏⣠⣤⣤⣶⡾⠟⠋⠁⠀⠀⢰⠎⢠⡶⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⢀⣾⠋⠀⠀⠀⠀⠀⢀⣾
⣿⠙⣷⡀⠀⠈⣿⠟⠁⠀⠈⠛⠛⠛⠋⣀⡀⠀⠀⠀⠀⠀⠀⡄⢠⠟⢀⡴⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⠀⠀⠀⠀⢀⣾⠋
⣿⠀⠈⠻⣆⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢳⡎⢠⡾⠁⣠⠾⠷⣄⣀⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⣠⣾⠃
⣿⠀⠀⠀⠈⠻⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡈⠳⡄⠀⠀⠘⢷⣿⣤⡾⠋⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⣾⠟⠁
⢻⣇⠀⠀⠀⠀⠀⠈⠛⠶⠦⣤⣤⣄⡈⠻⢦⡀⠙⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠁
⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣙⣶⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠛⠉
⠀⠀⠙⠿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣾⠿⠟⣿⡏⠁
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⣿⠟⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⣿⡇⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠶⠶⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠻⠟⠛⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢿⣆
⣤⣤⣤⣤⣤⣶⠶⠟⠉⠀⠀⠁⢀⣀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠙⢿⣥⣀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⡀⠀⠀⠀⠈⠻⣦⣀⡀
⠀⠀⠉⠛⠿⠿⣷⣶⣶⣶⠿⠛⠛⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣴⡿⢿⣦⣄⠀⠀⠀⠀⠉⠻⢷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⢀⣈⣿⡿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣿⣿⣟⣛⣉⣀⣀
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠰⠤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠑⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠓⠛⠂⠀⢺⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠤⠀⠄⠀⠄⠴⠄⠀⠀⠀⠀⠂⠀⣀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⠀⠒
⠀⠀⠀⠐⠀⠀⢄⡀⡀⠀⠈⠀⠀⠀⠀⠁⠂⠀⠑⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠐
⠀⠀⢰⠀⠀⠀⠀⠛⠘⠀⠀⡀⠀⠀⠀⡶⠀⢀⡀⠀⠀⠀⠀⠈⡀⠀⠀⠄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠒⢾⣠⣀⠄
⠀⠀⠈⠘⠁⠀⠀⠘⠁⠀⠀⠉⠈⠐⠀⠈⠑⠀⠙⣧⠀⠈⠑⡀⠀⠀⠠⢀⠀⠀⢻⡄⠉⠀⠤⠁⠀⠀⠀⠀⠘⠀⢃⠀⠀⠈⠃⠎⠁
⠀⠀⠀⢀⡀⠀⣠⠀⡀⢀⡀⠀⠀⠄⠀⠠⢄⡀⠀⡟⣀⢀⣀⠀⠁⠀⠐⠉⡄⢀⢸⡇⡀⢀⠀⠀⠀⠠⠀⢀⡀⠀⠀⡀⠀⡠⠄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠁⠈⠒⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠠⠤⠾⠃⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⠀⢀⣀⠠⡄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢝⠀⠀⠣⠀⠀⠀⠀⠀⠁⠀⠀⠴⢤⡀⠓⣄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⡴⠀⠀⢀⣠⠂⠀⡖⠁⠒⣈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠠⠤⠀⠤⢀⠢⠀⠀⠟
⠀⠀⠀⠀⠀⠘⠢⠄⡤⢠⠠⠄⠂⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠃⠈⠃⠈⠀⡁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢨⣀⢀⡞⠁
⠀⠀⠀⠈⠀⡀⠀⠀⠐⠀⠀⠀⠀⠠⢠⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠍⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣉⠇
⠀⠀⢀⠘⠦⢀⠀⠀⠠⡀⢀⢂⠔⠓⡆⡠⠊⠀⠀⠈⠀⢀⠀⠀⠈⠀⠀⠀⠀⢀⣀⠀⠈⢂⠀⠀⢀⡀⠐⡀⠀⠀⠀⢀⡀⠳⣴⣆⠀⠀⣀⠀⠸
⠀⠀⠈⠰⠠⠂⢠⠀⠢⡀⠀⢰⡄⠀⡿⠒⡄⠀⠀⣀⠄⠀⠇⠈⢀⠀⠀⠀⡀⠀⢰⠁⠀⠴⠀⠀⡈⠁⠀⠁⠀⠁⠊⠉⠀⠀⠙⠗⠀⠀⠙⠆⢀
⠀⠀⠀⠈⡒⠈⠧⢤⠄⢴⠀⡼⠄⠐⢈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⠀⠈⠁⠀⠄⠀⡔⢀⠀⢠⠆⠀⠀⠀⠀⢠⠀⢀⣀⠀⠃⠀⣀⠀⢤⠘
⠀⠀⠀⠈⠂⠐⠂⠁⠀⠁⠀⠈⠒⠀⠀⠀⠀⠀⠀⠈⠀⠙⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠃⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠈⠑⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠘⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⢀⣀⠉
⠀⠀⠀⠀⠠⣒⣄⠀⠀⠀⠀⠀⠑⠀⢀⠀⠠⡲⡰⣀⠀⠀⠀⣶⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⢀
⠀⠀⠀⣤⡻⣧⡘⠃⠀⠠⠃⠀⠙⠞⠀⠀⠩⢠⣼⣲⠀⠀⠀⣀⠄⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⡀
⠀⠀⡀⢉⠤⠈⣀⠀⠀⣀⠀⠀⠀⢀⠀⠰⠁⠿⣯⠿⠇⠀⢀⠁⠀⠀⢀⡀⠀⣠⠐⠀⠒⠤⠀⢰⡀⠀⠀⠀⣷⠀⣠⠀⠚
⠀⠀⢷⣄⠀⢀⡼⠀⠀⠙⠆⠀⠀⢼⠀⠀⢠⡀⠀⠀⣠⠀⠻⣄⠀⣀⣰⠗⠀⡆⠀⠀⠀⠰⠄⠈⠳⡀⠀⡄⠏⠀⠻⠠⢄⡀⡀
⠀⠀⠈⠉⠟⠙⠁⠀⠀⠠⠶⠄⠤⠦⠀⠀⠈⠙⠻⠋⠁⠀⠸⠟⠻⠟⠻⠇⠀⠀⠤⠄⠤⠄⠀⠀⠑⠿⠾⠓⠀⠀⠘⠆⠐⠌⠏

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠋⠉⠉⠙⠉⠛⠛⠙⠋⠉⠛⠛⠛⠛⠛⠛⠉⠙⠋⠉⠛⠙⠋⠉⠋⠈⠉⠉
⡀⠀⠀⢀⡀⠀⣀⣀⡀⠀⢈⠀⢀⡀⣀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⢀⢶⣶⣶⣶⠄⢶⣶⣾⣿⠀⣿⣾⣿⣿⡄⣼⣿⣿⣿⡄⣽⣿⣿⣿⡇⣸⣿⣿⣿⠇⢸⣿⣿⣿⠇⢸⣿⣿⣿⠇
⣤⣀⣿⣍⣿⣤⡌⢿⣿⣿⣤⣼⣿⣿⣿⣧⣿⣿⣿⣿⣦⣿⣿⣿⣿⣧⣾⡟⣴⡟⣤⣼⣿⣿⠃⣴⣼⠯⣿⣇⣤
⠿⣷⡞⡠⠠⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡏⠀⠉⠀⠀⠀⠢⣬
⠢⣀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟
⠀⡀⠀⠀⠀⠀⠀⠠⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠱⠌⠁⠀⠀⠀⠀⢨⠄⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⢀⠀⠀⠀⠀⠀⠠⣌
⡇⠈⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠹⣮⣼⣿⡿⠁⠀⡀⠨
⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢨⠛⠙⢿⣿⣿⣿⣿⣿⣿⣏⣿⡿⢐⣼⠟⠋⠉⠋⠀⡀⡠⡀
⡇⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠸⠀⠀⠈⣽⠿⣿⣿⣿⣿⣿⣿⡁⠙⠀⠀⠀⠀⠃⠀⠃⠁
⠃⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⣰⠀⠀⠈⠉⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⠀⠀⠂
⡅⠀⠀⠀⠀⠀⠀⢊⣙⠂⠀⠸⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠊
⣣⠤⠠⠀⠀⠀⠀⡀⠈⣉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠐⠴
⡄⠂⠀⠀⠀⠀⠀⣃⢈⣀⡄⢠⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠀⠀⠁⠄⠀⠀⠀⠀⠉⠀⠁
⢶⡅⠀⠀⠀⠀⠀⡿⢧⠎⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠄⢰⠀⠀⠀⠐
⠉⠁⠀⠀⠀⠀⠀⣧⣶⣦⡤⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⣤⠠⠛⡀⠀⠀⠀⠈⢀
⠘⡧⠀⠀⠀⠀⠀⠨⠀⠀⠀⣯⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⢠⠀⠈⠀⠀⠀⠀⠀⣀⣤⣀
⣾⡀⢀⣆⢠⠁⠠⠖⡄⢢⠀⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠇⠀⠀⣻⠅⠩⠀⡀⠶⠀⠀⡀⣫⣿⣿
⣿⡿⣿⣶⢿⣄⡠⡄⢉⡦⡄⣿⠀⠀⠀⣿⣿⣿⣿⠋⠀⠈⢻⣿⣿⣿⡄⠀⠀⣿⠂⢄⠀⢠⠠⢤⣴⢇⣹⣝⣭
⣿⣿⡛⣰⠴⢆⡀⣾⡉⠄⣠⡾⠇⢀⣠⣿⠙⣻⣿⣶⣤⣾⣿⣿⠿⣿⡗⠀⠀⣿⡇⠘⠀⢋⠀⢺⠿⢦⣴⣾⣿
⣿⣿⠿⢻⡅⠈⠉⠡⠇⠀⡤⣶⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣦⠖⢿⣿⠁⢀⠋⠛⢻⡐⠿⢿⣿⡿
⣿⣿⣦⣈⡀⣀⡀⠴⠓⣩⣌⣀⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡟⠈⣽⣷⣄⠁⠀⣈⣀⡀⠀⠁⠠⣄⣼⣶
⣻⡟⣿⣿⣷⣤⣤⠶⠟⢋⠁⡽⠉⣹⢏⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣷⡉⠛⠀⠀⠈⠉⠑⠒⠶⠆⠈⠁
⣿⣿⣿⣿⣾⠛⠛⣦⠨⠥⢀⣧⣤⣻⣿⣇⠀⢘⣿⣿⣿⣿⣿⣿⣿⣹⠏⢀⣿⠈⠑⢢⣶⠀⠀⠀⠀⠀⠈⢂⣤
⣿⣿⡿⢿⢿⣷⠂⠸⡗⢰⣾⡿⣿⣿⣿⡟⠳⡞⢻⣿⣿⣿⣿⣿⣽⣿⣿⣾⡿⠀⠀⠀⠀⠈⠀⠏⠀⠀⠐⠉⠉
⣏⡁⠀⠀⠉⠁⢰⣶⣭⠾⢭⣿⣿⣿⣿⣷⣼⣹⣿⣿⣯⣿⣿⣿⣿⡿⠤⡜
⣿⠅⠤⡤⠀⠀⠈⢛⣯⣤⣾⣷⡀⢸⣿⣿⡏⠀⢩⡙⠻⠟⠛⢻⠷⣆⣀⢈⢀⠀⠀⠀⢀⠴⠞⠁⡄⠀⣀⡰⠞
⣿⣷⠂⠳⢧⡄⠀⠀⢿⣿⣿⣿⡇⠨⠛⠻⠛⠒⠋⠁⠀⠀⠀⠀⠀⠘⠜⠈⠋⠀⡂⠀⠰⠖⢿⣿⣟⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣽⠉⠉⠛⣿⡟⠿⠶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠷⠂⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣹⡿⢷⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣎⢿⣆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣀⠴⠒⠈⢉⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢤⣄⣠⡟⠈⢿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠠⠊⠁⠀⠀⠐⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣧⠶⠛⠛⠛⠷⢦⣤⣿⠉⠀⠀⠸⣿⠀⠀⢸⡇
⠀⠀⠀⡀⠁⠀⠀⢀⠤⠄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣄⣀⣤⣤⡶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢿⡇⠀⢸⡇
⠀⠀⢰⡀⠀⠀⣠⠃⡴⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⢹⣇⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⡎⠁⠀⢀⡀⡘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠾⠋⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠉⠀⢂⡈⢁⠗⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠄⠀⠀⠀⠀⠀⣿⡆⠀⠀⢸⡇⠀⣾⠁
⠀⢸⠀⠀⢀⡃⠸⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣤⡀⢸⡇⠀⣿
⡀⢸⠀⠀⢸⠀⡦⠒⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠙⠾⣇⢀⡿
⠅⠶⠀⠀⢸⠀⠇⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⡄⠀⠀⠈⠻⣇
⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡟⢷⣄⠀⠀⠈⢳⡄
⠀⢳⠀⠀⢸⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠘⣧⠀⠙⢷⡄⠀⠀⢻
⠀⠀⢣⠀⢸⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⣠⡟⢹⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣿⠀⠀⠀⢻⠀⠀⢸
⠀⠀⠀⠲⢄⣴⡏⠒⢀⣀⣀⣀⣠⡤⠖⠋⠀⣠⡾⠋⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢻⡄⢀⣰⠏⠀⠀⣸
⠀⠀⡖⠒⠚⠟⠁⣄⠘⣿⠉⠉⠀⠀⣀⣤⠞⠋⠀⠀⠀⢸⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⢸⣇⠼⢷⣄⢀⡾⠋
⠀⠀⢷⡀⠧⢠⡴⠋⠀⢿⣤⣴⠶⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣿⠥⣄
⠀⠀⢆⠙⠶⣤⠗⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡶⠁
⠀⠀⢋⠓⠦⡇⢼⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣦⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠛⢁⣴
⠀⠀⠀⠱⣖⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⡄⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠓⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠈⠫⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⠿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣤⣤⣴⣶⣶⣶⠿⠿⠛⠛⠉⠉⣿⡁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⡗⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣀⣨⣿⣦⡀⠀⠀⠀⢸⠋⡿⠶⠞⠛⠃⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠉⠁⠀⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⡗⠀⠀⠀⠘⢷⣶⡶⠿⠛⠉⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠶⠛⠛⠋⠉⢿⡀⠀⠀⠀⢀⣿⠀⠀⠀⠠⣦⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢀⣶⠀⠀⢸⡇⠀⠀⠀⢸⡏⠀⠀⠀⣠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⣀⣴⠟⠿⠶⠚⠛⠀⠀⠀⢀⣾⠃⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠶⠶⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣀⣤⡿⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡟⠉⠙⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠂⠉⠉⠉⠋⠑⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠶⣤⠀⠀⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⣦⣤⣤⡤⠶⠞⠋⠹⣧
⠀⠀⢀⡀⠀⢞⠑⣄⠀⠀⢀⣠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⠀⠀⠀⠀⠀⢿⡄
⠀⠰⣇⠈⠳⣄⠆⠈⡆⠀⡞⠀⢀⡤⠟⠀⠀⠀⠀⠀⠀⢠⠞⣉⡉⠳⣦⣀⠀⠀⣴⠾⠗⠀⠀⠈⠛⠆⠀⠀⠀⢀⣼⣇⡀
⣀⣤⣌⠳⡄⣩⡾⠀⢰⡄⢠⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⠀⢰⠀⠙⠛⢿⢧⣤⣄⣀⣀⣀⣀⣀⣤⣤⠶⢟⡋⠠⠙⡆
⠓⢤⣀⠉⢰⡟⠀⠀⣠⡼⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠒⠚⡅⠒⠀⠸⣇⡰⠆⠉⠉⣙⠋⣹⠉⠀⠀⠀⠇⢨⡐⢂⡷
⡄⠀⠉⠛⠟⠀⠀⢰⠃⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⡨⠂⢠⠋⠀⠐⠻⠂⠉⢉⡴⠶⠶⣦⡉⠡⣤⡀⠀⠀⠆⠀⠙⠋⠁
⠀⠀⠐⠂⣄⠀⠀⠙⠀⠀⠀⢀⡌⠀⣻⣦⣀⠀⠀⠀⢰⠁⠀⠘⠀⠀⠀⢸⣄⠀⠈⠷⡄⠀⠸⠃⠀⡸⠃⠀⠈⠀⠀⠳⠄
⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⢀⡾⠀⡘⠃⠀⠉⠓⠦⣤⣠⣆⡀⠀⠰⠦⠄⢺⠛⠷⣤⣄⣀⡀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠓⡿⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠐⢯⠒⠤⠼⠟⠋⠀⠀⣀⠤⢀⠤⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠓⠒⠂⠀⠐⠐⠚⠁⠀⠀⠀⠀⠀⠀⣠⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣸⠁⠀⠀⠀⠀⠀⠀⢄⡠⠀⠈⠳⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⠉⢩⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠻⢦⣄⣀⣀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠘⢷⣀⠀⠠⣀⣀⣀⠀⠀⣠⠴⠛⠉⠉⠋⠁⠀⠀⠙⣄⠀⠀⠀⠐⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣀⠀⠀⠀⠘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠶⣤⣄⣀⣀⠀⠀⢰⠂⠉⠉⠉⠀⠀⠐⠒⠒⠢⡀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠋⠙⠄⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⠉⠉⠉⠁⢹⠀⢸⠉⠉⠉⠉⠉⠉⠀⠀⣧⠴⠶⠶⠞⠛⠉⠉⠀⠀⠀⢸⠦⡀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⣤⣀⡀⠀⠀⠀⢼⠀⡿⠀⠀⠘⠀⠀⠀⡀⢰⡇⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡁⠀⢀⡄⠉⠙⠛⠒⠒⢿⣀⠙⠒⠀⠀⠀⠀⠐⠃⢸⡷⠒⠒⠒⠛⠋⠉⠉⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠫⣧⣀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠒⠒⠒⠛⠛⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠛⠶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠴⢶⠖⠛⠛⠛⠉⠉⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠉⢿⠉⠉⠉⠉⠁⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢻⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠺⢿⣶⣄⣀⡀⠀⠀⣀⣴⠟⢢⡄⠀⠀⠀⠀⠀⢠⡟⠛⢛⣧⣀⣀⣠⣤⡶⠞⠋⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⢀⡅⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⣀⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠙⠛⠶⠶⢦⣤⣤⠶⠶⠶⠖⠛⣟⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⣤⣤⣤⣴⡶⠾⠛⠋⠀⠉⠛⠶⠶⢦⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣰⣧⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠞⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣷⣶⣶⣶⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣭⣿⣿⣿⣿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⣴⣿⡏⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⣢⠎⠀⠀⠈⠓⣤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣉⠀⠀⢀⡄⠞⠀⠀⠀⠒⣀⠀⠄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣿⠁⣀⣠⠀⠀⠀⢻⣖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⣿⣲⣿⢦⣋⣛⠀⠛⣃⡸⣿⣷⣄⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠊⠁⠀⠀⠀⠈⢋⠹⣶⣯⠥⢠⣹⣅⣴⠃⠈⠋⠑⣤⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠈⠄⣿⠋⠀⠸⡙⢻⡇⠈⢀⠀⢀⢸⣷⢤⡀⠠⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠿⠛⣟⣦⡔⠎⠃⣾⡃⠀⠀⠀⠀⢠⣿⣆⣩⣋⣴⣾⣿⣿⣿⢊⣡⠞⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣥⣾⣿⣿⣿⡿⠋⠁⠱⣄⡀⢀⠐⠈⠉⠀⢹⣿⣿⣟⣿⣿⣶⣼⣦⣜⢁⠄⢛⡧
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠄⠄⢀⢿⣿⡟⣷⠀⠀⠀⠀⠙⠀⠀⠀⠀⠐⠜⢷⣿⠛⠛⢿⣿⡿⣿⣿⣿⣰⢾⣌⠢⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠴⠁⠀⠸⠈⠋⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⡎⠀⣀⡟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢠⠿⠻⢲⡀⣠⠗⠀⢀⣀⠀⠀⠀⠀⢠⠏⣉⠍⠛⣿⠛⢲⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢤⣬⣷⡿⠁⢀⠄⢻⣿⠂⠀⠘⠛⢛⠀⠀⢰⢻⣮⣤⣤⣶⡗⠖⠺⠥⡄
⠀⠀⠀⠀⠀⠈⠉⠹⢦⣭⣤⡿⠟⠒⠲⠶⣶⡾⠀⠀⠘⠺⡿⣷⣿⣿⠀⠀⢠⠆⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠉⠀⠀⠀⠀⠀⠙⠷⣾⣿⣦⣴⣤⠤⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣀⣀⣀⠀⠂⠺⢿⣿⣿⣿⣿⣶⠨⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠉⢹⡏⠀⠀⠀⠀⠘⣿⣿⡿⠁⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢸⡃⠀⠀⠀⠀⠀⣽⣿⡁⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠦⠄⡐⠟⠀⠀⠀⠀⠀⠀⢸⡿⢷⣤⡶⠁⣣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠁⠀⣤⢿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠚⢿⣷⣾⡧⢀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣀⣠⣠⠿⣶⣥⣤⣤⣄⣴⠖⢶⣦⣿⣿⣾⣿⣿⣿⣟⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠖⠂⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠛⠚⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⣖⠮⠥⡲⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣾⣿⣿⣄⣠⢯⣿⣷⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣿⣟⣩⣿⣿⣿⣿⣿⣯⣾⣿⣌⣛⣿⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⣛⣉⠀⠉⠉⠈⣉⣛⣻⣿⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣭⡙⠻⠿⠛⠛⠻⢟⣋⣭⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⡿⠼⣿⣶⣷⠷⠾⣾⣿⣿⠧⢾⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣄⢀⣀⡵⠓⠂⠐⠚⢮⣀⡀⣠⣿⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⣿⣿⣿⣥⡿⠶⠿⢿⣷⣾⡿⠿⠖⢿⣬⣿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣯⠞⠙⡁⠀⣀⣀⣤⠛⢛⣦⣀⣀⠀⠈⠋⠳⣽⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⢏⣄⣼⣷⣾⣿⣿⡿⢿⠿⠿⣿⣿⣷⣶⣤⣠⠹⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣾⣿⣿⠋⢿⡏⠙⠀⠀⠀⠀⠉⢹⠿⠙⣿⣿⣷⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣦⢸⠳⣀⢸⣄⣤⡇⣤⠞⡇⣴⡿⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣹⣧⣿⣿⣼⣏⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠻⣿⣿⠟⠋⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⡠⠴⠒⠌⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢭⣰⢹⠐⡁⢀⡠⠤⣖⠁⡎⠀⣀⣠⠤⠤⠴⠖⠀⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣆⡠⡤⡛⠃⢉⠭⠆⠀⡨⢝⣣⣮⡤⠤⣈⠁⠒⠤⣀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠉⡇⠀⢀⡜⠀⠞⠛⠩⣄⠀⠀⢿⣦⡀⠈⠣⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⢠⢃⠞⢁⠀⠀⣠⣄⠀⠈⠀⢤⡄⠙⢿⣆⠀⢳⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⣹⡎⣾⢿⣿⠊⠉⠉⠀⣤⡀⠀⠁⠀⠀⣿⠀⢸⠀⡀⡸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣿⡅⠃⠈⠛⠢⣤⣴⣏⠻⠯⠀⠀⣠⣾⣿⠀⡐⣼⣁⠧⣄
⠀⠀⠀⠀⠀⡉⢂⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣸⣿⡇⠀⠀⠧⠤⠌⢹⡿⠀⠀⠀⠀⠁⠀⢀⡷⠋⢧⣈⣀⡼
⠀⠀⠀⠀⢁⠀⠀⠋⠀⣜⠀⠀⠀⠀⠀⠀⢸⠀⠀⢬⢼⣿⣷⣀⠀⠀⢀⣀⣋⣀⣀⠀⣀⡰⠤⠋⠁⠀⠀⠀⠈
⠀⠀⠀⠤⠼⠒⠚⣓⡒⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢻⠙⠛⠛⠿⢿⣟⠿⠛⠛⣟⠉⠉
⠀⠀⠀⠀⠤⠄⠀⢀⣀⠀⠘⠦⣀⠀⠀⠀⠀⣸⠀⠘⠓⠈⠗⡲⢀⣀⡀⡤⠒⠒⠒⠛⢢
⠀⠀⠀⠀⡀⠤⠰⠁⠀⠈⠐⠀⠉⠉⠀⡱⢤⡇⠀⣀⠀⠀⠀⠷⠁⠀⠈⡡⠆⠀⠀⠀⣰
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡝⡙⡄⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠆⢊⢤⠀⢀⠟⣷⣠⢤⡔⠃⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⠀⠀⢀⠦⡀⡍⠌⠒⠊⢸⠉⠀⢀⠀⠀⢀⡴⡁
⠀⠀⠀⢀⠀⠀⠀⠀⣀⣠⠃⠀⠀⡄⢀⠸⣧⠀⠀⢀⣘⣤⡀⠬⢧⣖⡩⢤⣘⣦
⠀⠀⠀⠈⠀⠀⠀⠐⠛⠀⡀⠉⠉⠳⣄⠀⠃⠏⢉⠉⠀⡑⢠⠞⠃⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠳⣄⠃⡶⠘⠠⢙⠚⠒⢤⢤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠔⠺⠋⠑⠠⠀⠀⠡⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⢤⡀⢸⡄⣴⡄⢸⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡠⢄⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣙⣿⣧⣶⣜⣿⢋⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠘⠆⠁⢐⠀⣟⣀⣤⣠⣿
⠀⠀⠀⠀⠀⢂⢸⣓⡛⢹⣿⡿⠯⠬⡇⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠙⠃⠼⣽⣠⣿⡿⣿⡠⠄
⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⠷⣿⣿⣿⣿⣋⠈⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢰⡤⢄⡮⢙⡈⠉⠉⠁⠒⠁
⠀⢠⠀⢄⣠⣼⣟⣛⣛⣛⡋⣻⣛⣛⣛⣿⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡽⢄⣴⠷⠊⠇
⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⠭⢿⣿⣿⣿⣿⣹⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢣⡽⠳⠂
⠀⠀⠀⠀⢸⠿⠿⢿⣿⡟⠉⢻⣿⣿⣿⣿⡿⠛⢷⠿⠛⠁⠀⠀⠀⠀⠀⣄⠛⣀⣤⣠⡀⡀⠀⠀⠀⠀⢀⢀⣄
⠀⠀⠀⠀⠘⠀⠘⠲⠆⠠⠤⠤⠬⠿⠯⠅⠆⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⠙⠒⠃⠶⠀⠼⠷⠒⠂⠐⠲⠟⠷⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣟⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣦⠀⢨⡧⠀⠐⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢢⠀⠀⠀⣠⠿⣦⣾⣿⠃
⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣬⣽⣿⠁⠐⣿⡿⠃⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠑⠢⠄⣀⣀⣀⣀⣀⡀⢰⡀⠀⠀⢀⡖⣣⡴⢶⣍⡐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⣥⣤⣀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠳⢶⠀⠑⢤⣼⣿⣷⠀⠈⠓⢀⠀⢳⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⢿⡇⠘⠟⠉⠙⢻⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠅⠀⠀⠈⣹⢻⣦⠤⣾⡼⣇⠸⡷⣤⣧⣄⡀⠀⠀⠀⠄⣷⣄⡾⢃⠎⠀⢸⡇⢠⡀⠀⠀⢸⡇⠀⡰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢠⣿⣿⣿⣿⠉⢠⡷⠶⢦⣿⡐⣿⣾⡀⠿⣴⡆⠀⠀⠀⠀⠹⣷⠀⠀⠀⠈⠋⢹⠀⠀⠀⢸⣯⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣾⣿⣄⣠⠘⠙⢿⣧⣀⠀⢅⢤⣠⣌⣱⣿⣿⡧⢰⡏⣿⠀⢃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟
⠀⠀⠀⠀⠀⠀⢀⢀⠐⣿⡈⠈⢻⣧⢛⠛⠳⣦⣄⣹⣿⣷⣚⢸⣷⡿⠿⣶⡝⢧⣾⣷⣄⢆⢁⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠜⠋
⠀⠀⠀⠀⠀⠀⣼⣿⠁⠘⣧⠻⡀⠻⣦⣀⣤⣽⣿⡿⠋⠉⣉⣿⡁⠀⠀⢨⣿⡘⢿⣿⣶⣿⣿⠻⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡼⠛⠀⠳⣨⣦⣝⡶⢞⣻⣿⣿⡿⠀⢿⣄⠹⣷⣦⣤⣦⣼⡿⠻⣏⢹⣿⣿⣇⡴⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠘⠹⢿⣦⣻⠛⢿⡿⡀⢰⡙⣷⣿⣿⢯⣱⣧⠀⠀⠀⠀⠀⢸⣄⡂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠟⢿⣿⢻⣿⣿⠇⠉⠀⠈⠈⢿⣿⠀⠀⠹⠗⠀⠁⢩⣿⣿⣿⣽⡏⠀⠀⠆⠀⣴⡄⠙⣛⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢒⣶⣦⣀⣩⣿⣿⣿⣇⢀⡀⠀⠀⠘⠙⣆⠀⠀⣷⠀⢠⡈⣿⡏⠀⣾⡇⠀⣰⠆⢰⣿⣿⣋⣉⡙
⠀⠀⠀⠀⠀⠀⢉⣉⡈⠛⠉⣭⣀⣨⣿⣿⣿⣿⣿⡈⣿⠀⠀⡄⠻⣿⠀⠀⢸⡀⠈⣆⠘⢿⡿⢿⣷⠶⠿⠓⠄⢿⣇⣀⠾⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠙⠛⠛⣿⣿⣿⣏⣾⣿⣿⣃⠀⡀⠀⠘⠇⠀⠐⣧⣀⣻⣦⡌⠁⠄⣀⣦⠀⠀⠀⢸⡏⠿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⣟⣿⡿⣏⢻⣿⣿⣿⣧⣹⡀⠀⠀⢀⣸⡇⠈⠉⠉⠁⢲⣶⠟⠛⣴⡖⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠀⠀⠀⠀⠈⢻⡆⠈⠃⢻⣿⣿⣿⣏⡃⢠⡀⠀⢹⣿⠐⠶⣤⡘⠛⣦⠻⣿⠉⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠈⠿⢦⣠⣾⣿⣿⣿⣿⣿⣾⣿⣦⣤⣿⣷⣤⡀⠙⣦⠙⢾⣸⠁⠀⠀⣿⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠲⣾⣿⣿⠸⣿⣧⡙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠀⠋⠁⠀⠀⢀⡷⢼⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠄⣤⡟⣿⡀⣿⡛⢡⣎⡙⣩⣆⣘⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣶⣾⣶⣿⣿⣏⣿⡇⢿⣿⠾⠿⠿⠿⠿⠛⠛⠛⣉⣉⡭⠛⠀⠀⠀⠀⠀⢸⡃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠻⣿⣿⣿⣏⠛⠳⣤⠤⠄⠒⠒⣶⣶⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢸⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠋⠀⠉⠁⠈⠋⠙⠀⠀⠀⠀⠀⠀⣾⠛⠛⡛⠉⠙⠉⢉⠉⠉⠱⠀⠀⠀⠀⢸⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢄⣀⣾⣷⣦⣠⣠⣴⠇⠀⠀⠀⠀⠀⢹⣿⣶⣿⣦⣀⣤⣿⣶⣦⡞⠀⠀⠀⠀⠸⠁⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠹⣟⣛⣿⣟⣿⣿⠿⠛⣤⣀⡀⠀⠀⠰⣏⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡿⠏⠉⠛⢿⡧⠀⠀⠀⠀⠀⠀⠀⠸⠿⣼⣿⠛⠃⣀⡀⣀⣹⡋⣬⠀⠙⠀⢹⣇⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣤⣾⡿⣇⠈⢹⣷⠶⣮⣥⣽⣧⣑⠀⠀⣿⣧⠰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⢀⣠⢿⠀⠀⠀⠀⠀⠉⠙⠓⠾⠿⠿⡿⠶⣶⣮⣍⣀⣴⣦⣿⡿⠟⠒⠸⢧⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⡙⢋⡛⡫⡿⠁

⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡄⠀⣀⣀⠀⠀⠀⣀⠰⣆⡀⣀⣄⣀⣀⠀⠀⢀⡀⠀⠀⠖⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠈⣥⣯⠶⣶⣐⣬⣿⣵⣆⡼⣹⣥⣴⣶⢾⣟⣾⣿⣿⣿⣵⣦⣴⣶⣿⣷⣴⣶⣿⣯⣤⣷⡚⣼⠷⠟
⠀⠀⠀⠀⠘⠰⣯⣿⣷⣾⣿⣿⣷⣿⣾⠋⣏⣼⣿⠌⡻⠧⠽⣿⣷⣯⣿⣿⣿⣿⣿⣳⣶⣿⡧⡄⠈
⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣯⣿⣿⣿⢢⣼⣿⠎⣡⣘⢿⣶⡮⣮⣿⣿⣿⣿⢍⠽⣿⣿⡿⣿⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠓⠚⠛⡜⡏⠱⣷⣿⡏⢐⠻⠿⢿⡼⢯⣵⣿⣿⣿⣹⣅⠑⠍⠙⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠁⠀⢰⡽⣿⣮⣻⡖⢠⣾⣷⣸⡌⣿⣿⣿⣿⡀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠒⣿⣬⡿⠀⠀⠀⠙⣛⢻⣾⣬⣿⣟⢩⣿⣇⢹⣯⣽⠃⠀⠀⡹⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠐⠀⣹⢯⠟⣟⣿⣿⣿⣿⣿⣸⠟⠿⠠⠄⠀⠘⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠌⠀⠏⡩⢻⠻⠉⠉⠘⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠸⣠⠄⢠⣠⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⡀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠻⣧⠀⣀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣾⠷⢴⣦⣤⡼⢗⣀⠀⠀⢸⡆⡤⠀⡸⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣻⡖⠙⠂⢸⡄⠀⠀⠀⠀⠀⣸⡏⠉⠀⠀⠀⠻⣿⣶⣿⣿⣧⡀⠀⢳⡇⠐⠃⢠⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⠀⢹⡇⠀⢠⠀⡿⠀⠀⠀⠀⠀⣹⣶⠗⢶⡾⠃⣀⣽⣯⣿⣯⠻⣿⡷⣌⣷⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢴⣤⢘⣻⠇⢰⣾⡀⠀⠀⠀⠀⠀⣼⣿⣀⡠⣀⣿⣿⠋⣿⣛⣯⡓⠊⠓⢛⣧⣾⣟⠉⠧
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣤⣿⣶⣿⣿⣇⠀⠀⠀⢀⣼⡿⣾⣯⢦⣼⣿⢇⣼⣿⣿⣖⡈⠉⠉⢿⡶⢉⣥⡀⠲
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⣤⣼⣿⣿⡿⣿⠉⠻⠀⢀⣴⣿⣿⣿⢋⠝⣚⢿⣧⣿⣷⣿⣬⣿⣷⠶⠶⣮⣅⡸⣏⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⣿⠏⠙⢿⡇⢹⠀⠀⠀⠘⣿⣿⣿⢃⡤⠗⢉⠶⣿⣿⣾⡿⣿⠧⣬⣧⣤⣀⡹⡗⢹⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠁⠀⠀⠈⣿⡄⡄⠀⠀⢀⣿⣿⣿⡴⣿⡖⣣⣾⣿⣿⣿⣿⣿⣿⣿⣭⣀⣩⣿⡆⠏⡟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠸⣿⣣⡄⢀⣸⣿⣷⣿⣽⡟⣴⣿⣿⡿⡏⣻⣿⣿⣿⣛⣙⡛⢿⣿⣿⡆⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠙⠛⡷⣬⡉⣿⣿⣟⢛⣷⡿⣿⣿⣟⣟⢿⣿⠛⠛⠛⠛⠻⣷⣿⣿⠀⢩⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⣴⠖⢳⣽⣷⣿⣿⣿⠋⣬⣾⢿⣇⣿⣿⢋⣿⠀⠀⠀⢠⣤⣿⣿⠏⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡌⢡⡿⣿⣿⡏⢀⣾⣿⣿⣽⣿⣏⣉⣹⣧⣭⣤⣤⣻⣿⣿⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣁⣽⣟⣿⡷⣿⣿⢻⣟⠿⣏⠴⢞⣻⣽⣤⡶⢬⣡⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⢘⡷⣿⣶⣿⣿⣿⡏⠀⢘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠛⢿⣿⣿⣿⣿⣽⣿⠟⣿⣿⣿⣧⣄⡘⣿⣿⡿⣧⠀⣾⣿⣿⣿⣇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣾⢿⣷⠨⣿⡏⠙⣿⣿⡀⠁⠐⢫⣿⡛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣜⠛⢸⣿⣧⣸⣧⣴⡟⠋⠻⣶⠞⠋⢹⣷⡬⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣀⡿⢺⣿⡄⢻⡟⢷⣤⡀⠀⢀⣤⣞⣿⣷⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠻⠁⠘⣿⣿⡌⢷⣾⣿⣿⣴⣿⠟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣏⢀⣰⠀⠈⣿⣿⣬⣿⣿⡙⢏⣰⣴⣿⣿⣿⣿⣇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣏⣻⡿⠀⠀⢿⣿⣿⣲⣿⡷⠞⠛⠉⢉⢻⣿⣿⣿⠀⠀⠀⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⠃⠆⢀⡸⣿⣿⣿⣷⡗⣦⣹⣿⣻⣼⣿⣿⣿⡆⠀⣆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠀⠦⠀⢈⠳⣿⣿⡿⣿⣿⣯⣽⢀⣰⣾⡿⣿⣿⡇⠀⠻⡄⠃⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣤⣤⣽⣿⣷⣿⣿⣯⣾⣟⠿⣿⣿⣿⣿⣟⠀⠀⠹⣦⢠⡀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣯⣿⣿⣿⡆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⣬⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣠⠀⡀
⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣯⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣴⣦⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠛⠿⠻⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠿⠿⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣫⣿⢿⣿⣿⣿⣿⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣷⡾⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣒⣉⠉⠉⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠹⣄⣤
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠉⠙⠛⠒⠲⠒⠒⠋⠁⢸⡆
⠀⢠⠒⢄⠰⡈⢆⠀⡴⠊⠙⣦⠀⠀⠀⠀⠀⢀⡤⠿⣄⡀⠀⠀⣀⣤⠀⠙⠻⣦⠀⠀⠀⠈⣧
⣀⣈⡢⣄⢱⡵⠘⡄⠃⠰⠋⠀⠀⠀⠀⠀⠀⣏⠸⠁⡸⠙⠒⢶⣏⣀⡀⠀⠀⢀⣀⣠⣤⠾⠋⠳⡄
⠃⢄⣉⣰⠏⠀⢀⠼⠃⠐⣆⠀⠀⠀⠀⠀⠀⠙⠒⢒⠧⠃⠀⣇⡰⠈⠉⢏⢏⡍⠉⠀⠀⠀⣤⣂⡿
⢎⣉⠉⠛⠀⠠⡏⠀⠀⠀⡻⣄⠀⠀⠀⠀⢀⠔⠀⠃⠀⠈⠁⠀⢰⡞⠛⠲⡄⠐⣦⠀⢀⠂⣈⠉
⠀⠀⠈⠓⢄⡀⠀⠀⠀⡜⠀⡞⠓⢦⣀⡀⢰⡀⠀⢀⡀⠀⣷⣄⡀⠙⠀⠈⠁⠴⠁⠀⠀⠀⠀⢥
⠀⠀⠀⠀⠀⠙⠲⠤⡾⠁⡼⠀⠀⠀⠀⠉⠉⡟⠀⠀⠀⢡⡂⠈⢹⠿⠃⠀⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣰⠁⢰⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠙⠂⠂⠀⠲⠞⠁⠀⠀⠀⠀⣠⣄⡰⠂
⠀⠀⠀⠀⠀⠀⢠⣇⣀⡏⠀⠀⠀⠀⢀⣤⠄⠀⠉⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⠏⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⠶⠶⡾⠃⠀⠀⠀⠀⠈⠓⠦⠤⠖⠲⠦⠤⠒⠁⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⣀⡀⠀⠀⠀⢠⠤⠀⠀⠠⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣇⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠉⠙⠓⠒⡏⢀⡀⠀⠁⠀⠀⢠⢸⡤⠴⠶⠖⠛⠋⠁⠀⠀⡷⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠦⣤⣀⣀⡀⡇⢸⠃⠀⠘⠀⠀⠸⢸⡇⡀⣀⣀⣠⣤⠴⠖⠛⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣠⡆⠀⠀⠉⠉⠳⠤⣭⣥⣀⣀⣈⣁⡼⠋⠉⠉⠁⠀⠀⠀⢀⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⢦⣄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠶⠶⠚⠛⢩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠉⠉⠙⡟⠉⠉⠉⠉⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣿⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣄⣿⡀⠀⠀⠀⠀⣀⡿⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠻⠶⣤⣤⣤⡴⠟⠉⠆⠀⠀⠀⠀⢸⡅⠨⠿⢦⠶⠶⠛⠉⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠷⣤⣄⣀⣀⣀⣀⣤⠤⢴⠂⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣠⣤⠶⠛⠳⢦⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣸⠀⠀⠀⠀⠀⠀⠉⠉⣿⠉⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⠀⠀⠀⣀⣠⡶⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣠⣿⣄⣀⣀⣀⣀⣀⣠⠤⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⣷⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⢆⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⠀⠈⡧⠀⠨⢆⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⡀⠀⠀⢀⣿⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣁⣠⣶⡏⠈⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⢸⡄
⠀⠀⠈⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢀⡀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠃⠀⡋⣁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠉⠁⠲⠶⠆⠴⢤⣤⡀⠠⡀⢻⣿⣯⠛⠳⡌⠳⣄⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⡿⠛⠿⣦⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠘⠻⢿⣷⠆⢀⣀⡦⢸⣧⣀⡀⠀⠀⠀⠀⣀⣆⠀⣾⠋⠟⠈⡇⠀⠀⠀⠀⣿⠀⢀⡞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠖⢠⣦⣤⣴⡍⢻⣝⣋⣹⡄⣯⡿⠋⣟⣤⠀⠀⠉⠛⣷⡃⠀⠀⠀⠷⠺⠂⠀⠀⣿⡇⣾⠇⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠘⢿⣿⣿⠁⠘⠏⠉⠛⢓⣻⣷⡂⣹⢿⡀⡄⠀⠀⠈⠋⡄⠀⠀⠀⠀⠀⠀⠀⢺⣿⠏⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⣦⠔⢿⡏⣷⣿⣀⠈⢻⣶⣌⣶⣟⣿⣿⣭⢿⣇⣽⡛⣁⠷⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣦⠈⢿⢰⡈⣷⡈⠀⠹⣿⣿⡿⠛⠷⡞⠋⠉⢹⡇⣹⣿⣿⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣷⠃⣈⣃⠳⣌⣻⣶⣿⣿⡏⣠⡠⠾⣟⣀⣀⣸⣿⣧⡿⣿⣿⣿⢁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠛⠀⠀⢷⣿⣿⣿⣵⣾⣿⣿⠁⢸⣷⣎⣻⣿⣿⣿⠃⣘⠷⣹⣯⡷⢏⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠠⠀⠈⣻⣿⡇⠈⢫⡆⠙⠂⣿⣿⣷⣿⣿⠀⢀⡀⢀⡈⢻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⣄⠙⢟⣿⣿⣇⠀⠀⠀⠈⠿⣆⠀⠈⣄⠀⠀⣿⣿⠋⣻⡇⠀⢰⠀⣼⣿⡤⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡻⠒⠠⠶⠻⠛⠓⣾⣿⣿⣿⠀⣧⠀⠀⠰⣾⡆⠀⠛⠀⢰⠈⣿⣤⣿⣧⣀⣿⡀⢻⣿⠃⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣾⣦⣴⡾⡿⢿⣿⣿⣿⢿⣶⣿⡄⠈⠀⠙⡇⠀⢸⡄⠸⣦⡘⠋⠉⠛⡉⠀⠀⠈⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⢾⣿⣿⣧⠘⡄⠀⠘⠀⢸⡟⠶⠿⠟⣀⣐⣾⡏⣀⡄⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠈⠹⣯⠙⠎⢻⣿⣿⣿⡿⠄⠀⠈⢻⣦⣀⣀⡀⢼⣛⣥⣼⠛⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⢻⣦⠀⣸⣿⣿⣿⣷⣼⣧⣄⠘⣷⡈⠙⠻⣄⠿⣬⠛⠀⠀⢀⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣄⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣷⣤⣽⠇⡽⠋⠀⠀⢸⣂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠉⣿⣿⡈⣿⠿⣀⠻⠿⡋⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣠⣤⣤⣾⡿⣾⡇⣿⣦⣿⣿⣼⣿⣾⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⣧⢛⣉⣁⠠⢤⣤⣤⣤⣴⣶⣿⡁⠀⠀⠀⠀⠀⡧⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠁⠈⠛⠻⠿⠆⠈⠉⠁⠀⢠⣾⠿⣿⠿⠿⠿⠻⠿⢆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠀⣴⣦⡀⠀⢀⡄⠀⠀⠀⠀⢸⣧⣤⣦⡀⠀⢴⣦⣄⣨⠀⠀⠀⠀⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣾⣿⣿⡃⠀⠀⠀⠀⣠⠄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠻⢿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠀⢻⡶⢀⠀⡄⢹⡶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠉⠀⠀⠀⢻⠀⠀⠀⠀⠀⣠⣼⡯⠺⢿⣄⣀⠓⢴⡞⠇⠃⢀⣤⠀⣷⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⢀⣸⡇⠀⠀⠀⠘⠿⢯⣷⣤⣾⣯⣽⡛⠛⠛⢃⡀⣼⣿⡇⢹⡿⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠒⠲⡿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠀⠀⠙⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠉⠀⠀⠐⠒⠒⠂⠀⠐⠒⠒⠒⠶⠶⠶⠀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢶⠶⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠄⠉⠀⠐⠎⠀⠈⠉⢛⣷⣤⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡞⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠐⠈⠁⠐⠉⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⣤⣀⣤⣤⣄⡀⢳⡞⠃⠘⣇⠀⢸⡇
⠀⠀⠀⠀⡐⠁⠀⢀⠄⠀⠀⡆⠀⠀⠀⠀⠀⠘⣦⣄⣀⣀⣤⣶⡿⠋⠁⠀⠀⠀⠙⢿⡀⠀⠀⢻⠀⢸⡇
⠀⠀⠀⠰⠄⠀⢠⠂⠎⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠀⢀⡀⢀⣀⡜⠂⠀⠘⣧⠀⠀⢸⡆⢸⡇
⠀⠀⠀⠳⠀⠀⠄⡌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠉⢉⣉⠀⠀⠀⠀⣿⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⣸⠠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⡦⣀⢸⡇⢸
⠀⠀⣄⡀⠀⡁⡔⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣇⠈⠛⢧⣾
⠀⠀⠀⠁⠀⡇⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿⢦⡀⠀⠙⣦
⠀⠀⠀⠄⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡄⠙⢦⡀⠈⣧
⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⣀⡤⠊⢀⡞⢩⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠘⡇⠀⢨⠇⠀⣸
⠀⠀⠀⣠⠀⢾⠏⠈⢶⠖⠒⠋⠁⣠⠖⠋⠀⢸⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⣧⣰⣏⠀⣠⠏
⠀⠀⠀⠻⣔⠤⡴⠃⢸⣧⠴⠖⠋⠁⠀⠀⠀⢸⡇⠈⣧⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣿⠀⠈⢻⠥⣄
⠀⠀⠀⠱⣌⢳⢺⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣧⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣿⠀⠀⢸⡏⢰
⠀⠀⠀⠈⢢⣽⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣿⠦⢤⡤⠴⠃
⠀⠀⠀⠀⠀⠙⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣶⠶⠶⣶⠛⠛⠋⠉⢹⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⣧⠀⢸⡧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡤⠿⢶⠀⠀⠀⡏⠹⠒⠋⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡄⠀⠀⢿⣀⣤⡴⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠶⠖⠚⠛⡇⠀⠀⠀⣿⠁⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣼⣇⣀⡟⠀⠀⢀⡟⠀⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣤⠶⠋⠀⠉⠁⠀⠀⢀⡾⠁⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉

⠀⢀⠀⢀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠣⡀⠀⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢈⣀⠀⠀⢀⠝⠐⢫⡀⠐⠀⠀⠀⠈⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⠤
⠀⢸⣸⣿⣿⣇⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈
⠀⠘⠛⠛⢻⠴⣷⣲⣀⠀⢀⣴⠀⣠⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠐⠒⠊⢁
⠀⢀⠀⠀⠠⡄⠀⠙⢿⣿⣏⣽⣿⣿⣤⣖⠀⠈⠛⠂⠀⠄⡀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⢀⠀⡀
⠀⢰⠀⠀⠐⠀⠀⠀⢈⡛⠙⠛⣿⠟⠉⠻⢷⣳⡀⠀⣀⠀⣡⠀⠀⢄⠀⠀⠀⠀⣀⠈⠉⠉⠉⠑⠒⠤
⠀⠸⠁⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⣼⢬⡝⠛⠻⡿⠇⠀⠀⠛⣢⠑⠀⡶⠊⠀⠀⠀⠀⠀⢀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡝⠀⠀⠀⣀⣤⣾⠿⢿⠀⡀⠀⠀⠀⡀⢀⡀⣦⠀⢀⣠⡴
⠀⠀⠀⠀⠀⡰⠂⢀⠀⠀⠀⠀⠀⡄⠊⠀⡀⠀⣀⠀⣰⡟⣿⠋⠀⣼⡟⠀⠀⠀⠉⣠⠊⣽⣦⡼⠋⠀⠀⡄⠀⣀⡀
⠀⠀⠀⠀⡀⠀⠀⠘⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠹⠘⢿⡟⠋⠒⣄⣾⣧⢄⣢⠤⠛⠁⠈⢸⡎⢳⡄⢀⠀⠈⠁⠈⠃
⠀⢰⡞⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣉⣈⡋⣀⢈⡟⠈⠉⠻⢦⡀⢀⡄⠀⢳⠈⡄⠉⡃
⠀⠘⢠⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⠀⠀⠤⢲⣦⡞⠓⠛⠤⣿⢿⣍⣶⡀⠀⠀⠻⣄⢢⠀⡃⠳⣡⠐⠊⠑⠄⠄
⠀⠀⡠⠢⠶⣤⢄⠀⣰⣄⡾⠤⠀⠰⢆⣠⠾⣟⣀⡹⢍⣹⣿⠃⣜⣫⠀⠀⢢⡄⠀⢹⡘⠆⣿⣿⣿⣾⠟⠀⠀⠀⠄
⠀⠘⡁⠄⢄⠀⢈⣽⣉⠤⠔⠈⠐⢺⡏⠁⣀⣾⠿⢳⣶⣿⣥⠐⡏⠛⠀⠀⠀⠛⢦⣀⡟⠀⢂⡀⢋⣿⡦⠴⡆
⠀⢈⠀⠀⠀⠁⡁⢀⠀⠀⠳⠄⠀⢈⡠⢞⠙⣿⢳⠞⠋⠻⠛⢊⣧⣽⣤⡀⠀⠀⠀⢹⡇⠸⢤⠀⡈⢙⠷⣿⣷⣶⡆
⠀⢸⣤⣠⡄⠀⠀⠀⢀⡕⠢⠁⣠⡄⠂⢠⣿⣿⠟⣧⣥⡄⣠⢊⡀⢬⠿⣟⣷⡞⠋⠀⠉⢦⠀⠦⠀⠀⠀⠀⠈⠻⡇
⠀⢸⡿⣿⣦⠠⣦⣤⣿⣤⣶⣾⣿⣿⢿⣿⣿⣝⡁⠘⣷⠟⣹⣬⠅⠀⠀⠀⢙⣁⠀⢀⡠⠜⠀⣀⠀⠄⠀⡤⠄⠂⠅
⠀⢸⠿⠹⣿⢇⡟⠻⣿⣏⠙⠉⠀⠁⠀⠈⠺⠻⠟⠰⠯⣶⣤⣽⢷⣄⣠⡤⠾⡿⠚⠩⠀⠈⠉⠀⢈⡠⢨⣀⠀⠀⠂
⠀⢘⠀⠀⠄⠄⠀⠀⠈⣋⣀⠀⣠⠀⠀⠀⠀⢱⠊⠁⢠⠄⠈⣭⠀⢩⡙⡖⠋⠀⠀⠀⠀⠑⠂⠀⠊⣀⡁⠉⠋⠶⡆
⠀⠸⠂⠥⠄⠂⠐⠺⣇⡀⠀⠉⠉⠙⢾⠷⢶⣶⣄⠒⠀⠀⠀⢀⡀⠀⣤⣿⠀⡐⠲⠔⠂⠈⠁⠀⠀⠀⠀⣀⠀⠀⠂
⠀⠀⢀⣤⣠⣠⢠⣄⣭⡟⠑⠒⠦⡶⠋⠀⠀⠠⠌⠀⠀⠀⢀⡈⢁⣠⣤⣾⠁⠀⠀⠀⠘⣉⣀⣀⡀⠀⠀⣈⠁⠟⡁
⠀⠈⠀⠀⠀⠀⠀⠀⢀⣓⣤⣤⣾⠀⠠⠃⠂⠒⢀⣠⡄⠀⠘⣆⠀⠀⠠⣿⠀⠀⠀⣠⡉⢽⡄⠀⠀⠐⠊⠉⡳⠶⡆
⠀⠀⠀⠀⠀⢰⡂⣿⡉⣩⣀⣅⣨⣇⣀⠀⠀⠀⠈⠉⠀⠀⠀⠘⣦⠀⠀⢻⡄⠀⠀⠉⠁⠀⠀⠈
⠀⠰⠀⠀⠀⣬⠟⠋⣉⠈⣅⡈⢯⡀⠈⢠⠀⠀⠀⠀⠀⠀⠀⣠⠛⠐⠒⠛⠛⢢⠀⠀⠀⠀⠀⠀⢀⠀⣀⠠⣤⠤⠄
⠀⠀⠀⠀⠘⠁⠄⠀⠈⠀⣰⠁⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠘⠦⣴⠄⠰⣶⠈⠀⠀⠁⠀⠀⢀⠂⠀⠀⠀⠩⡇
⠀⠀⠀⠀⠈⠆⠠⠀⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠤⣾⡇⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠂⠐⢤⠀⡤⢄⣸⠻⣺⠟⣿⠟⠂⠀⠀⠀⠀⠰⣤⣾⣥⠀⢀⣿⣇⢀⠀⡰⠋⠀⠀⠀⠀⠀⠘⣷⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣅⣄⠀⠀⠀⠀⠑⣦⡿⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⠞⠀⠙⠳⡄⠀⠀⠀⢀⠈⣷⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠈⣦⢀⡀⠀⣼⠏⠀⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠂⠀⠂⠚⠀⠐⠒⠚⠒⠛⠚⠓
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⢀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⣰⣿⣏⠉⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠞⠁⠈⠉⠳⣄⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠃⠀⠀⠀⡠⠴⠊⠉⠁⠠⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣾⡟⠀⢀⡀⢀⠀⠸⣯⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣤⣿⣠⠶⣾⡀⡶⢶⠀⣿⣷⣅
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠻⡟⢿⣙⣲⠞⡀⢶⠞⠈⣽⠙⠻⠷⣌⠓⠂⢀⡄
⠀⠀⠀⠀⠀⠀⠘⢿⣥⡀⠀⠀⠀⠀⠀⠱⠈⣿⣿⠎⠉⡿⣿⣿⠃⡄⠀⠀⠈⣻⣄⠉⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣶⣄⠀⠀⣀⡀⢃⡟⠒⠀⠀⠃⠉⢿⡄⢠⢦⣤⠀⣹⣿⣽⣦⣈⡖⢻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣻⣟⠉⣩⣿⣿⣯⣓⣤⠿⡆⠀⠀⠀⠀⡰⣾⠿⢾⣿⣶⣿⣿⣿⣿⡿⠥⡶⢋⣬⠛⣷⣦
⠀⠀⠀⠀⣀⣀⣰⠿⠶⠾⠿⣷⣿⣿⠋⠀⠀⠘⠳⣄⣀⠖⠁⠀⠀⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣾⣤⡒⢀⡽⡂
⠀⠀⠀⠀⢿⣿⡏⠔⠐⠀⡼⣿⣿⠛⠿⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⡰⠋⢿⣿⠉⠉⠻⠿⠿⠿⠿⣿⣇⠿⢷⣌⡳⣀
⠀⠀⠀⠀⣿⣿⡷⠃⠀⠀⠇⠘⠃⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⣀⣼⡀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⢠⣿⠛⠒⣆⢠⡼⠃⠀⢀⣀⠀⠀⠀⠀⢠⡏⣉⠽⠙⣻⡟⠛⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢤⣤⣿⣾⠇⠀⡴⢹⣿⡿⠂⠀⠛⠛⢻⠀⠀⠠⢻⣿⣥⣤⣴⣾⡳⠖⢯⠣⡀
⠀⠈⠉⠹⣶⣬⣤⣸⡿⠓⠒⡶⠶⣶⡿⠀⠀⠐⠾⣿⢿⣾⣿⡇⠀⠀⣠⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉⠀⠀⠀⠀⠀⠻⢿⣭⣿⣧⣄⣄⣠⣤⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣀⣀⡀⠀⠀⠀⠀⠠⠰⣾⣿⣿⣿⣿⣧⣄⣸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⢿⡟⠁⠀⠀⠈⠙⢿⣿⣿⣿⠃⡈⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠸⣿⡿⠁⠰⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⢠⣼⠇⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⣀⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠉⢁⣦⡅⠀⠀⠀⠀⠀⠀⠀⢻⣍⣿⣿⣇⣤⡚⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠐⣟⢙⠇⠀⠀⠀⠀⠀⠀⠀⢸⣧⣈⣿⣿⣿⣇⣤⠀⠙
⠀⠀⠀⠀⣀⣠⢄⠲⠾⠿⠷⠤⠴⠖⠛⢿⠿⡷⠿⠿⠿⠉⠙⠛⠛⠿⠿⠿⠿⠻⠿⡷⢶⣞⣶⣀⣀
⣠⣄⣤⣠⣭⣽⣭⣥⣭⣤⣤⣤⣠⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣄⣤⣭⣄⣭⣤⣤⣤⣭⣥⣤⣤⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣶⣶⣶⠤⠤⠀⠀⠤⠄⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢶⣶⣶⣶⣾⣾⣷⣶⣾⣷⣶⣶⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⠛⠿⢿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣧⡴⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣟⢬⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⣄⣤⣴⣶⠾⠿⢛⣫⣯⣿⣯⡊⢤⣙⢶⣭⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣴⠟⠉⣉⣬⠿⠷⠶⣤⣍⣁⣘⣋⣙⣻⢶⣿⣧⣼⣿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⣴⠟⠀⠀⠀⢀⡰⠟⠉⡉⠙⠛⣉⣟⣻⣿⣿⣾⣶⠶⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡼⠁⠀⠀⠀⣠⡞⠁⢀⣼⣤⠄⢆⡛⢷⣼⣳⣈⢿⣷⢤⠤⠔⠁⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⢀⡾⣧⠀⠃⠀⠀⣠⠜⠃⣠⣶⡿⡟⠀⠦⠍⠛⢶⣌⡋⣹⣿⣿⣦⡑⣤⠆⢸⣿⠘⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣴⣆⣼⠀⢿⡘⠀⣠⣊⣤⠴⠿⢻⡿⢷⣶⣤⣄⣀⣉⣢⣼⣿⣿⢫⣽⣿⣿⣽⣰⣿⣇⢸⡶⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢻⣿⣤⡈⠛⠛⠋⡿⠁⠀⠀⣸⠃⣴⣟⠿⣭⣉⡉⠋⢡⡞⣷⣏⣴⣿⠿⣿⣻⣿⣿⣼⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⠟⠉⠙⠿⣿⣿⢿⣸⣇⣸⠏⠸⣿⠀⢠⠸⠃⠀⠀⢰⣟⣘⣿⡝⠳⢦⣍⡙⠁⣾⠀⠜⣿⣼⣿⠀⢺⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣄⠀⠀⠀⠉⠼⣿⣿⡇⠀⠀⠹⣧⠀⡆⠀⡀⣠⣿⠛⢷⣍⠛⠶⣠⡌⠁⠘⡇⠀⠀⠀⢻⡯⠄⣿⣟⣰⡿⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⢄⠀⠘⣿⡏⣟⠀⠀⠀⠼⣷⣏⠀⢰⡿⠃⠀⣸⢌⡛⢷⣬⡁⠀⠀⡇⠀⠀⠀⣾⡇⠀⣿⡿⣿⣷⣻⣽⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⢹⣧⢹⣤⠁⠀⠀⠘⢿⣦⣿⠁⠀⣠⣿⣯⣠⠂⡹⠻⣄⠰⣏⠀⠀⠈⣿⡇⣰⣿⣿⢾⢿⡳⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡈⣶⣦⠀⠀⠀⠀⢹⣿⠀⢀⣿⡿⣈⠙⠿⢶⣅⢟⣷⣿⡀⢳⡾⣿⣿⣿⣿⣿⣤⢻⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣷⣾⢸⣷⡄⠀⠀⠘⡟⢀⣾⣿⣻⢋⠁⠀⡀⢉⢻⡜⣿⡇⢬⣸⠇⣿⣿⣿⣿⣿⣿⣿⣻⡿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⢧⣠⣾⣇⣸⣿⢿⣯⠏⣠⣴⣴⠿⡗⣿⣿⡏⠂⡟⣠⡿⡋⠟⣹⣿⠨⣿⢿⢻⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⠿⡿⣿⡼⣿⣿⢁⣿⣿⣼⣿⡾⠟⠃⠀⠘⣿⣿⢿⣇⣠⣵⡿⢱⢷⠀⢸⣿⠀⠹⠿⠉⠯⠭⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠘⠃⣿⣿⣸⣿⣿⣿⣿⣶⠀⢀⠀⠄⣿⡇⢸⡿⠛⠋⠆⣸⣾⡇⢸⣿⠀⠀⠰⠾⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢹⣧⣄⣠⠄⣸⡿⠻⣿⣿⠁⣿⣿⡟⠀⢨⠀⠄⣿⣇⣼⡇⠀⠀⠀⢸⣼⠏⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⢸⣿⠻⠟⠛⠉⠀⠀⣼⣿⡄⠋⢻⣧⠀⠀⢀⢠⣿⣿⣿⠀⠀⠀⡄⠘⡿⣡⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣤⡀⣆⠀⠀⢞⣿⣿⡇⣁⡜⢿⡆⠶⠛⢻⣿⡿⣿⡀⢀⣌⡴⠀⣿⢿⣧⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣾⣧⣴⣿⣿⣿⣧⢡⣴⠺⠺⣦⢀⣿⡿⣰⣿⣷⣬⣿⣴⣿⢃⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣴⡿⢻⣿⣁⡀⠀⣯⣼⡟⢱⣿⣿⣿⣍⣩⡬⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⢺⣿⡌⢏⣸⣿⠻⣧⣼⣏⡹⢩⣿⣅⠐⢸⣿⡟⣀⡾⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⣿⣿⡟⣴⣿⠘⣿⣆⣿⠛⣧⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣹⣿⣿⣵⣟⣿⣿⡌⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⡿⠋⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠋⠋⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⢀⡄⠀⣠⠔⠒⠈⠰⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⡀⢄⣀⣿⡿⣶⣿⣤⣔⣤⣶⡤⡀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⢛⡧⣿⣹⣿⣿⣿⣿⣿⣷⡤⣌⣉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡧⣙⣿⣿⣿⡏⠀⣿⠀⠙⠋⠀⡯⢩⣟⣿⡿⣿⣿⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⣼⣯⣷⣮⠉⠙⢃⡀⠀⠙⠆⢀⡀⠁⠀⡔⠋⠁⠘⢾⣿⣷⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢂⡤⠴⣼⠛⠻⠉⠉⠗⠀⠀⢨⢹⠀⢀⡆⠘⠇⠀⠀⠠⠒⠓⠀⠈⠛⠿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢻⣀⡬⠁⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⢿⣿⢓⠀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⣿⣿⣾⣿⡟⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢁⣿⣽⣷⣶⣿⣀⠀⠄⠐⡂
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡢⣔⣼⣿⡏⠻⠿⢿⣿⣶⠆⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣹⣦⣐⣰⣿⣿⣯⣿⣤⠈⠀⠀⢤⠖⣨⣇⣤
⠀⠀⠀⠀⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⢸⡾⣿⣇⡟⢘⡟⣿⣯⡴⠄⢰⣿⣿⣿⣷⣗⣤
⠀⠀⠀⠀⡼⡁⠀⢠⣀⠀⠀⠀⠺⣿⣻⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡿⠃⠈⣵⣿⣶⡇⢸⠟⣿⡷⢀⣰⣿⣿⣿⣿⣿⣏⡨
⠀⠀⠀⠀⠀⠀⠈⠻⣥⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣻⣿⣿⡇⠀⡳⣾⠾⡇⢘⢀⢻⣷⣿⣿⣿⣿⣟⣿⣟⣧⣠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⠄⠀⠀⠀⠀⠀⣶⢄⣀⠀⣤⣠⠔⣿⠻⣯⣿⢿⣶⡿⠻⠿⡇⠀⠀⢨⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⣿⣧⣤⣀⠀⠀⣿⣓⣂⣀⢀⡈⣽⣠⣻⣿⣧⣬⣿⠑⣿⠀⠀⡇⠀⠀⠈⠀⣻⣿⣿⣯⣝⣉⣉⣉⣟⣁
⠀⠀⠀⠀⡐⠃⡀⠀⠈⠉⠁⠀⠀⠉⠓⣀⠼⠿⠿⠷⠶⡿⢮⣥⡿⣿⣿⣿⣿⡆⢸⣄⠀⡇⠀⠁⣾⣶⣿⣿⣿⣿⡟⠁⠀⠉⠿⠁
⠀⠀⠀⢴⡇⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢯⣽⠿⣿⣿⣿⡾⣷⣿⣷⣿⡇⣾⣼⡄⣧⠀⣤⣽⣿⣿⣿⣿⣿⣧⣶⣶⠑
⠀⠀⠀⢴⣯⣌⣹⠿⠃⠀⠀⠀⠂⠀⠀⠘⠛⠛⠚⠳⠚⠻⣿⡿⢛⣿⣷⠿⠟⢻⡟⠛⠛⠛⠛⠛⢿⠛⢻⡉⣽⣿⡟⣽⡅⠓
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢍⣾⣽⡶⢟⣡⣏⢙⣦⡄⣠⡀⠀⠾⠦⢼⡉⣿⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠒⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠛⠏⠐⣾⣵⢾⣆⠉⢈⡵⠀⢀⠀⠶⠶⢿⡀⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠂⠀⢀⠀⠠⠀⠈⠛⢻⣅⣀⣀⣨⠟⠉⠁⠀⠀⠀⠀⠀⠀⠌⠋⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠃⠀⠀⠁⠀⠀⠀⠀⠀⠐⠠⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢒⠈⠉⠉⠉⠑⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⢦⡄⠀⠀⠀⠉⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⠻⠶⣤⣄⣀⣀⡀⢀⣀⣀⡷⠚⣧
⠀⠀⠀⠀⠀⡶⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⡉⠉⠉⠀⠀⠀⢻⡀
⠀⢠⡊⠲⣄⢣⠈⢣⠀⣰⠋⠁⢉⡧⠀⠀⠀⠀⠀⠀⣠⠖⠛⢷⣄⠀⠀⠀⣠⣴⡆⠀⠉⠻⢧⠀⠀⠀⠀⢸⣇
⢀⣈⡛⢤⡈⢣⡦⠘⡄⠙⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⡏⠸⠁⠀⠏⠙⠲⣾⣏⣀⣀⠀⠀⠀⠀⣀⣀⣤⣶⢿⠉⢳⡄
⠫⣈⡉⠛⣼⠋⠀⠀⣹⠟⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⢻⠦⠄⢛⠴⠀⠀⡀⠨⠍⠉⠻⢻⠛⡛⠉⠉⠀⠀⢘⡠⠀⣰
⡀⠈⠙⠻⠏⠀⢀⡞⠁⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⡴⠀⡔⠁⠀⠶⠆⠉⢋⣴⠶⢦⣍⠉⢡⡀⠀⠀⡀⠀⠙⠟⠃
⠀⠀⠐⠀⣀⠀⠘⠃⠀⠀⠀⡜⠀⡳⣦⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢠⣄⠀⠈⢧⡀⠀⠼⠃⢀⠛⠀⠀⠁⠀⠒
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⡸⠀⢠⠃⠀⠙⠳⠤⠤⢱⣄⠀⠀⠦⠄⠸⠛⠷⣤⣄⣀⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⠃⢠⡏⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠴⡑⠠⠼⠛⠁⠀⢀⡠⠄⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠉⠀⠁⠀⠉⠐⠋⠀⠀⠀⠀⠀⢀⣴⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣰⠁⠀⠀⠀⠀⠀⣠⣠⠀⠀⠈⠳⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡽⠃⠱⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣤⣤⣤⡿⠁⠀⠀⠀⠀⠀⠙⠦⣀⣀⡤⠤⣄⣀⣠⠔⠋⠁⠀⠉⠀⠀⠀⠘⢆⠀⠀⠀⠉⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⠄⠀⠀⠀⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⡄⠠⠤⠄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢟⠀⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠓⠲⠖⠒⠲⠀⢰⠒⠂⠐⠒⠒⠀⡄⢹⣀⣠⣤⣤⡴⠶⠚⠉⠁⠀⢠⡄⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣄⡀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠲⠀⠀⠀⡇⢸⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⠚⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢈⠙⠛⠲⠦⠤⢾⡀⠸⠀⠀⠀⠀⠀⠠⠁⣾⡤⠤⠴⠶⠒⠛⠛⠉⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠖⢿⡀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠶⠶⠶⠶⠛⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⠶⠒⠚⠋⠉⠉⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠉⠉⢹⠉⠉⠉⠉⠉⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⢾⡇⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀⡀⢿⡀⠀⠀⠀⠀⠀⠀⣸⡇⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠺⢿⣦⣄⣀⣀⣀⣀⣴⠟⠳⡄⠀⠀⠀⠀⠀⣼⠉⢉⣷⣄⣀⣤⣤⡶⠟⠉⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⡀⠀⠀⠉⠉⠉⠉⠉⠁⢀⣀⡧⠀⠀⠀⠀⠀⢻⡀⠀⠉⠉⠉⠉⠀⠀⠀⣀⣠⣶⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠙⠛⠳⠶⠶⠖⠒⠛⠛⠉⢫⠀⠀⠀⠀⠀⠀⠘⠷⠶⣶⣦⣶⠶⠶⠞⠛⠋⠁⠀⠉⠙⠛⠶⠶⠶⠶⠴⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⣄⣀⣀⡀⣀⣠⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢤⣤⡿⣦⣄⣀⣀⣀⣠⣤⡤⠶⠞⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⠁⢀⠐⢉⣷⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣠⣧⠀⡘⣡⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠀⠀⠀⠀⢀⠃⠀⠀⢨⣥⣿⣄⢙⠉⢋⢁⡿⣷⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠖⠦⠘⡉⢴⠃⣉⠴⠇⢈⠁⣌⡀⠁⠈⡀⠀⠠⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⣌⠉⢢⠀⠀⠐⠀⠈⡄⠏⠉⠉⢸⣧⣹⡌⠑⣵⠞⠠⠄⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⣔⣶⠩⡑⡌⠑⠤⣀⠃⣋⢀⡇⠀⠀⣸⠚⠽⡸⢞⠁⠀⠂⡈⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⡄⠚⣉⣿⡗⣴⣷⡀⠀⠀⠀⣷⣼⠀⠀⠀⡸⠐⠉⠀⡐⡾⢐⠒⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⠾⡀⢱⡟⠏⠈⣿⣿⡟⠁⢠⠞⠋⠏⠈⠄⠃⠀⡇⠀⠀⠂⡍⠤⠄⠖⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⢀⠵⣼⣶⠶⢾⣿⣿⡟⣦⢦⠀⠘⢦⣤⡦⡆⠈⠐⡀⠀⠘⡁⡀⠰⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠖⠁⠀⠀⠀⣽⠏⢰⡏⠈⠱⠠⠽⢿⡇⠸⠀⠊⠱⠀⠀⠉⠄⠔⢩⣀⠀⠃⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡸⠛⠆⣸⠁⠀⠀⠀⠀⠀⠈⠠⣬⠴⠺⢧⠀⢄⠊⠘⢠⠁⠝⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢾⡀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣧⠀⠄⢈⠖⠠⠈⠀⠀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠙⠳⣄⡇⡀⠀⠀⠀⠀⠄⠀⠀⣸⠂⣄⣼⢿⡇⡀⠀⠀⠡⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡄⣧⡀⠄⢊⠝⢇⣃⣀⣀⠄⠀⠀⠀⠀⢸⠋⠉⠀⢠⡷⠙⢤⠀⠀⠀⠘
⠀⠀⠀⠀⠂⡀⠀⢤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠠⣤⠠⠰⠉⠟⠀⠀⡏⠉⠙⠛⠛⠋⠉⠁⠀⠀⢵⣒⣺⠓⠀⠘⣀
⠀⠀⠀⠀⠀⠁⢹⡁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢉⠤⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣹⡧⠤⠴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢻⠃⠀⠀⠀⠠⡴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠤⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣿⡏⠙⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⢟⡄⠑⣽⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣡⣄⣴⠏⢒⣾⡇⠓⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⣴⣿⣿⠂⠄⠀⢹⣶⠂⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣦⣤⣤⣿⣞⡓⡀⠀⠀⠀⠘⠀⢽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣼⣿⣿⣿⣍⠉⣁⡀⠀⠀⠀⣠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠻⠟⠻⠟⡛⠉⢿⣿⣿⣿⣷⠂⠀⠩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⠠⠴⠚⠛⠢⢜⣿⡟⠒⢲⠞⠁⠀⠈⠙⣿⣿⠃⠀⠀⣀⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣺⣿⡏⠀⠀⠀⠀⠀⠀⠉⠛⠇⣀⠀⣀⠐⡤⠠⡟⠉⠀⠀⢀⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣤⠶⠊⠉⠁⠀⠇⠀⢹⣶⣶⣿⣿⢻⢿⣿⣿⢻⠆
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⠉⡛⠆⠀⠀⠀⠀⢀⢀⢈⣿⣿⣿⣾⢀⣿⣿⣿⣷⡀
⠀⠀⠀⠘⢿⠟⠋⠙⠛⠋⠁⡀⠀⠀⠘⢻⡇⠁⠀⠀⠀⠀⠀⠀⠈⢀⣉⠩⢈⣉⣨⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠁⠀⢀⢀⢀⠀⠀⠱⠀⠀⠀⠸⠓⢇⠀⠀⠀⠀⠀⠀⠀⢴⡶⠂⣶⣶⢾⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠘⢫⣿⢣⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⢴⡿⠃⠀⠺⡇⢸⡏⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠳⠐⠒⠹⣦⣀⣀⣴⣿⠿⡛⠚⠛⠀⢠⡇⠀⠀⡀⠀⣬⡁
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠄⠀⠀⠀⠈⠉⠁⣁⣀⠁⡀⠀⠀⡾⣷⠄⠀⠋⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢴⡶⣶⣾⣿⣿⣾⠋⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠉⣉⣉⣁⠐⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢠⠔⠊⠁⠀⠀⠀⠉⠑⠠⢀⠀⠉⠁⠂⠠⠄⠀⠀⠠⠤⠄⠒⠂⠀⠀⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠥⠴⠖⠒⠛⠛⠛⠛⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⢀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠠⣅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣠⡴⠚⠋⠉⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠀⠀⠈⠳⡄⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠹⡆⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⠞⠁⢠⡶⠟⠛⠂⠀⠀⠀⠒⠛⠛⠻⣦⠀⠀⠀⠈⢷⡀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⠏⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⣧⠀⠀⠈⡇⠀⠀⠀⠀⡠⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢙⡟⠀⠀⠀⠀⡠⠒⡒⢦⡀⠀⠀⣠⠞⡉⠉⢢⡀⠀⠀⠀⠀⣿⠀⠀⣸⠃⠀⢏⠙⢦⠀⡴⢁⡜
⡀⠈⡑⢤⠔⡡⠂⠀⠀⠀⠀⠀⠀⠀⢧⣈⡇⠀⠀⠀⢻⡄⠀⠁⢀⡇⠀⠀⢿⡀⠉⠀⣸⡧⠀⠀⠀⠀⣿⡧⢳⠃⠀⠀⠀⡟⠈⠀⠱⢏⣤⠈
⡀⠦⠨⠂⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠙⠒⠒⠋⡠⠆⠀⠈⠉⠉⠙⠉⠀⠀⠀⠀⢰⣟⣀⠜⠀⠀⠀⡠⢃⡤⠠⠤⠂⠀⠉
⠈⠥⠐⠒⠄⠂⢐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⡿⠁⠠⢄⡀⠀⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠪⣰⡴⠋⢉⡇⠀⠀⣠⠿⣆⠀⠀⠀⠀⠀⠒⠄⣠⠴⡇⠀⠀⠀⠀⠀⢡⣴⣿⣄⢀⣦⠀⠈⢷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡴⠉⠳⢤⠞⠹⠀⠈⠳⢦⣀⠀⠀⠈⠲⠤⠞⠁⠀⠀⣀⣤⠾⠋⡼⠀⢹⠏⠀⢳⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠷⣄⡀⠈⠀⢰⠀⠀⢀⣀⠬⠟⡷⠶⠶⠶⠶⣶⠛⠛⠉⠀⢀⡼⠁⠀⠀⢀⣤⣾⠣⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠘⡴⠚⠉⠀⢀⠞⠀⠀⠀⠀⠀⠀⠱⡄⠀⣠⠞⠀⠀⠀⠀⠉⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠀⠀⠻⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⢢⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⣄⡀⠀⠀⠀⠀⣅⠰⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠙⠳⢶⣤⣀⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⢠⠶⣦⠀⠀⠀⠀⠀⠀⢀⣤⣷⣄⠀⠀⠀⠉⠙⠿⠲⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⡶⠾⣻⡟⠁
⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠠⣿⠀⠀⠙⢧⣄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣼⠟
⠀⠀⠀⣿⠀⢻⡄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢍⡳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢧⡀⠀⠀⠀⠀⢰⡟⢦
⠀⠀⠀⢸⡄⠀⠻⣄⠀⠀⠀⢀⠜⢉⣷⣀⣀⣀⣸⠏⠉⠛⠲⠦⣤⣄⣀⣀⣀⣀⣀⣤⣴⠶⣿⠫⠀⠀⢸⡇⠀⠀⠀⠀⣸⠀⣸
⠀⠀⠀⠀⢷⡀⠀⠙⢦⣠⠖⠃⣠⠎⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠸⣇⣀⣆⣴⠟⠀⠀⠀⣠⠞⠙⢀⡟
⠀⠀⠀⠀⠈⠳⡄⠀⠀⠉⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⠙⢦⡀⢠⡾⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡙⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⠀⠁⢠⣘⠀⣚⠀⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠂⠀⠀⠀⠋⠰⣆⣤⡦⠀⠈⠀⣤⠸⠇⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠃⠀⠀⠀⠀⢠⣄⣀⡽⠛⡑⠀⠠⠄⣼⡆⣆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡤⠶⠒⠋⠉⠈⠛⢳⣤⡀⠀⠀⢠⡽⠙⠾⠉⠓⠶⢤⣤⠴
⠀⠀⠀⠀⠀⠀⠰⢀⣤⣀⢀⣀⣶⠎⠀⠀⣠⠀⠀⠈⢹⣷⣀⠛⠁⠀⢀⠀⠄⣀⡀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣩⠅⠀⠀⠀⠘⣿⠖⠲⡤⢀⠘⠏⠀⣠⠔⢫⡔⠀⠀⠠⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡥⠂⠀⠀⠀⠀⣀⡰⠆⠀⠀⠈⠀⠛⠁⠀⣾⡇⠀⠀⠠⢌⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠐⠆⠀⡠⠊⠛⠅⢀⠀⠀⠀⠀⠀⠀⣠⡽⠛⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠤⠀⠀⠀⠰⡀⠀⠈⢻⠀⠀⠀⠀⠀⠐⡍⠈⢋⡄⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢒⣾⡋⠀⠀⠀⠀⠀⢀⣧⡶⠋⠁⢼⣿⡍⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⣋⡈⣄⠀⠄⠛⡏⠒⠀⠀⢸⠴⡟⣡⠀⠴⣄⣀⣻⡌
⠀⠀⠀⠀⠀⠀⠐⠀⠈⢀⣠⠀⠉⣧⣼⡆⠀⠀⠀⠠⠄⠀⢉⠔⠁⠀⠀⠀⠠⣨⣧
⠀⠀⠀⠀⠀⡀⠤⣄⠴⠋⢈⡴⠁⠏⠈⠁⠀⠰⡀⠀⠀⠀⢉⡤⠀⣀⡀⠀⠂⣿⠿⠱⡜⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⢀⠄⠀⠈⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⣄⣀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢈⣵⠟⠀⠀⠈⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣤⣤⣤⡀⡀⠠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⡃⠀⠀⠀⠀⠀⠀⠠⠀⠒⠚⢉⠀⠡⠀⠒⠀⣠⣀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡌⠉⠁⠀⠀⠀⠀⠀⠀⠁⢀⣤⣟⢀⡀⠀⢀⡀⠀⠀⠈⠀⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠯⠠⢄⣀⡀⠈⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⣿⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢲⣇⠀⣸⡏⢀⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡠⠲⣿⡝⠛⠛⠆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢶⣤⣽⠛⠙⠳⠏⠁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠦⡀⠀⠀⠀⠀⡼⢃⡶⠛⠳⢶⣮⣟⠃⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⠼⠆⠀⠀⠻⠛⠁⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠐⢃⠀⠀⠀⠀⠻⢿⣇⡀⠀⢘⢿⣿⡷⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⡶⠶⠾⣷⠐⠟⢋⡀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠈⡷⣰⣿⡷⣍⣀⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⡶⠶⣾⣿⣷⠘⢿⣡⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢆⠀⠀⠄⠛⠛⢺⠉⠉⠛⠓⠳⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢈⣿⢿⡿⣄⣠⡿⠿⢿⠀⠀⢹⡶⠀⠀⢘⠇⣀⣴⠀⠀⠀⣦⣄⣉⡇⠀⠀⠀⠓⠀⠀⠀⠀⣈⣽⡏⠀⠀⠀⠀⠀⢤⢂⠀⠀⠀⠄
⠀⠀⢴⠦⠤⠀⢀⠈⠀⠈⡄⠸⢯⡁⠀⠀⠀⠀⠀⡟⠀⢀⢼⡟⠁⠈⠑⠳⠒⠉⠉⢿⣿⣄⠀⠀⢠⣿⡿⠚⠛⠁⠀⠙⠟⠓⠆⢼⣆⠀⠘⡄⢀⡀⠀⢀
⠀⠀⣘⠀⠀⠠⣼⡐⠢⣤⣀⠀⠀⠙⠀⠀⡈⠄⢰⠃⢀⡽⡞⠁⠀⠀⠀⠀⠀⠀⠀⠸⣸⡾⠁⠀⢸⣿⣇⡀⠀⠀⠀⠀⢀⣀⣤⣿⣇⡠⠋⢿⢉⡀⠤⠊
⠀⠈⠉⠀⠀⠀⠈⢱⣆⠈⠈⢉⠐⠠⡁⣄⣿⡆⠀⠀⠀⣻⣧⠐⢇⣀⠀⠀⠀⠀⠠⠂⣿⣶⠏⠀⡈⠩⣯⣷⣧⠀⠈⣩⣿⢻⠛⡟⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡿⠷⢷⣼⣼⣷⣷⢿⡯⠀⠤⠀⠀⠈⠏⠑⠚⢢⡀⢀⠀⠒⠈⠉⠸⠋⠀⠉⠉⠹⢻⣼⣿⡇⣾⣿⣿⣾⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⡰⠿⠿⠏⢀⣀⠰⠀⠀⠀⠀⠀⠀⡤⠀⠀⠱⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢸⣉⣀⡈⠻⣏⣉⣀⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠧⠼⠒⠒⠺⠴⠲⠼⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠉⠛⢄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡐⠂⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⡏⢀⣀⠂⣀⡀⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠚⠻⡿⣟⠪⡼⠀⢭⠅⢚⠻⣷⢄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣄⠀⠀⠀⠀⠰⠘⣿⠃⠁⠾⣶⠏⠀⠀⠈⢳⡄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠷⣦⣀⠠⠄⣰⠁⠀⠀⠀⢘⣦⠐⠂⣀⣼⣿⣷⡦⢊⡻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣂⣾⣿⣿⡶⠚⠉⢤⡀⠀⡠⠙⠋⠙⣿⣿⣿⣿⣯⣥⣯⣔⢃⠙⣷
⠀⠀⠀⠀⠀⠀⠰⣾⡏⠀⠄⢠⢿⡿⠷⠀⠀⠀⠈⠀⠀⠀⠀⠰⠻⣿⡛⠛⠿⠿⠿⣿⣷⠴⢯⡐⢄⣀
⠀⠀⠀⠀⠀⠀⢰⣿⡕⠀⠀⡀⠈⠁⠀⠀⠀⠀⢀⣄⣀⣀⣴⡀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋
⠀⠀⠀⠀⠀⣀⣾⠉⠉⢤⣾⡁⠀⣤⣄⠀⠀⠀⣎⠐⠂⢩⣏⣉⡿⠁
⠀⠀⠀⠀⠛⠛⣇⣀⠂⢸⣿⣄⣀⣀⣰⠀⠀⢠⣿⣟⣿⣟⠋⠉⢡⢡
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠖⠘⠉⠀⠀⠀⠸⢾⣽⣿⣀⣀⣁⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⡀⠀⠰⢿⣿⣿⣿⣦⠘⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠈⢹⡇⠀⠀⠀⠙⣿⣿⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣼⠀⠀⠀⠀⠀⢿⣧⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠉⠁⣠⡁⠀⠀⠀⠀⠀⢸⣍⣷⣏⣠⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠀⠀⣺⣩⣀⢀⡀⢀⡀⣀⣈⣧⣬⣿⣿⣧⠆⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠉⠉⠉⠋⠁⠉⠋⠉⠉⠈⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠓⠐⠀⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⡩⣟⣋⢍⡓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣴⣯⢟⠁⠈⣫⣽⣦⡘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡿⢿⣿⡾⣮⣷⣾⣵⢷⣿⡟⢿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⣿⣿⣶⣿⣿⡿⠿⢿⡿⠿⣿⣿⣿⣶⣾⣿⡏⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣽⣿⣿⣭⣤⣤⣭⣤⣤⣤⣤⣤⣭⣿⣿⣯⣗⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣦⡌⢙⠋⠉⠉⠘⣋⣥⣶⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⡿⠲⠾⣿⣿⡿⠓⠛⢿⣿⣿⠷⠒⢿⣿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣧⡀⣀⣠⡞⠛⠀⠀⠛⢳⣄⣀⢀⣼⣿⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣯⣼⡷⠾⠿⣿⣷⣾⡿⠿⡷⠮⣧⣽⣿⣿⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣞⡽⠋⢛⠁⠀⢀⢀⡨⠿⠿⢄⡀⡀⠀⠈⠛⠛⢯⣳⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⡟⣁⢀⣿⣤⣾⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⣄⡀⢈⢻⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣰⣿⣿⣿⢿⣿⡏⠟⠈⠘⠁⠀⠛⢹⣿⡿⢿⣿⣿⣦⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣇⠀⣽⡇⠀⢠⠀⠀⡄⠀⢸⣧⢁⣸⣿⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⢿⣧⣧⠘⣶⡼⣷⣿⢇⣾⠃⣾⣼⡿⠋⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡷⣾⣿⣿⣿⣿⣷⢾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢿⡿⠋⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡗⠶⢾⡉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣹⢶⠞⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣗⣻⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣻⣓⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠓⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠴⢄⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠁⢀⣤⣴⣀⡀⢠⡤⢤⣾⡀⠀⠀⣸⣦⠤⣤⠆⣀⣤⡤⣄⡀⠙⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣻⡄⠀⠀⣽⢛⡈⠋⣙⣿⣿⣷⣾⣽⠿⠂⠺⣯⣽⣶⣿⣿⣟⠋⠉⣘⢻⡅⠀⠀⣼⣃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡎⢻⣇⠀⠀⣼⣿⣽⠃⠍⠉⣛⣭⣻⣿⠂⠀⠀⠸⣿⣫⣛⡋⠩⠉⢻⣽⣿⡄⠐⢀⣿⢃⡾⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⣴⡏⣀⠀⣹⡛⠀⠀⠀⠀⠛⡿⠃⣦⡀⠀⠀⣠⡄⠻⠟⠁⠀⠀⠀⠈⣻⡁⢀⡘⣿⣼⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⠹⢟⠛⠈⠋⠁⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠉⠋⠘⢻⠿⣩⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⢟⣻⣷⣿⡿⣧⠁⠀⠀⠀⠀⠀⣠⠞⢱⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⠀⠀⠀⠀⢡⡿⣻⣷⣿⣟⢿⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣧⢸⣿⡟⣿⣤⣀⣴⠚⢛⣇⠀⠀⠁⠀⠀⠀⠀⠁⠀⢀⣟⠛⢶⣤⣠⣴⡟⣿⣿⢠⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⣿⡋⠻⣿⣌⠓⣡⣿⠇⣈⣿⣿⢛⣿⣷⣦⣄⠀⠀⠀⢀⣤⣶⣿⣿⢻⣿⣍⡐⢿⣯⡁⢯⣼⡿⢃⣿⡟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⣿⢿⣷⣿⣿⣿⣡⠗⣰⣿⣄⡁⠈⡹⢿⣿⣿⣿⣶⣾⣿⢿⣟⠻⡅⠀⣁⣼⣿⡐⢶⣽⣿⣿⣷⣿⢿⣷⣼⡆
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣾⢿⣿⣿⣻⣶⣿⣟⠻⣿⣿⡶⠛⠁⣛⣩⣿⣭⣉⡃⠙⠳⣾⣿⡿⢟⣿⣧⣾⣹⣿⣿⢿⣼⣾⣿⣿⣿⣦⢀
⠀⠀⠀⠀⣤⡄⣼⣿⣿⣿⣵⢌⡹⠌⣿⣿⡇⢸⣿⡿⢿⣿⣿⣿⣿⣿⣋⣉⣉⣉⣉⣻⣿⣿⣿⣿⣿⠟⣿⣿⠀⣿⣿⡋⠼⣋⢠⣽⣿⣿⣿⡆⣤⡄
⠀⠀⠀⠈⠉⠁⢻⣿⣿⣧⣿⣧⣾⣿⢋⣿⣷⣾⣿⣿⡿⠟⠛⡛⢹⢟⡿⣻⠋⢻⡛⣟⢯⠙⡛⠻⠿⣿⣿⣿⣶⣿⣏⢻⣿⣧⣾⣧⣿⣿⣿⠃⠈⠑
⠀⠀⠀⣿⣿⡆⢾⣷⣿⣿⣿⠩⣿⣿⣦⣾⢿⣯⣿⠻⡄⠀⢸⣷⣤⡞⠀⠿⠀⠸⠇⠘⣦⣼⣿⠀⠀⡼⢿⣯⣿⢿⣦⣾⣿⡏⢻⣿⣿⣷⣿⢂⣿⣿⡇
⠀⠀⠀⣿⡿⢿⢿⣷⣿⣽⠿⢶⡟⢿⢿⣷⣶⣿⡁⣐⡄⣰⠇⡏⢹⡇⠀⣸⡿⢿⡀⠀⣿⠉⡇⢳⡀⢔⡀⣹⣷⣴⣿⢿⠟⣷⠜⢿⣿⣿⣽⣿⢿⣿⡇
⠀⠀⠀⠹⣿⣟⣾⣿⣿⣿⣶⣿⣷⣾⣤⣄⣸⣿⣿⣿⣷⣏⣼⣿⣄⣷⣶⠇⠀⠀⢷⣶⣏⣾⣿⣌⣷⣿⣿⣿⣿⣀⣥⣴⣶⣿⣷⣾⣿⣿⣿⣎⣿⡿⠁
⠀⠀⠀⠀⣹⣿⡜⣿⣶⣤⣭⣿⣿⣿⣺⣿⣷⣮⣍⡉⡿⠟⣹⣿⡿⠉⠁⠀⠀⠀⠀⠉⠹⣿⣿⡙⠻⡏⣩⣫⣶⣿⣿⣺⣟⣿⣿⣥⣴⣾⡿⣼⣿⡁
⠀⠀⠀⠀⢟⠹⣿⣿⣸⣿⣯⣿⣿⣿⣾⡿⠟⣛⢿⣿⣤⡿⢿⣿⣀⣰⣄⣿⣶⣾⣆⣠⣀⣸⣿⠿⣧⣼⣿⠿⠛⠿⣿⣾⣿⣿⣯⣽⣿⣸⣿⡿⢹⠃
⠀⠀⠀⠀⢸⣇⢻⣿⡟⣡⣾⣿⣿⣿⣿⡟⢛⠻⢷⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣶⠿⣻⠛⣿⣿⣿⣿⣿⣦⣙⣿⣿⢣⣿⠂
⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣟⣺⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣏⣴⣅⠀⠀⣽⣿⣿⣿⣷⣿⠛⢻⣯⣤⣶⣶⣶⣦⣬⣿⠟⢻⣿⣿⣿⣿⣯⡅⠀⢀⣱⣌⣿⣿⡿⠿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠋⠰⣿⢁⣴⣿⣡⣼⣭⢙⡿⢛⣉⣹⣿⣿⣿⣿⣾⣿⡿⣯⢛⡏⠟⣫⡿⣿⣿⣾⣿⢿⣿⣿⣉⣹⠻⢟⢩⣿⣭⣹⣷⣄⠹⡇⠈⠃
⠀⠀⠀⠀⠀⠀⢾⣿⠟⣹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡄⠙⡿⣿⣷⣶⣦⣤⣤⣶⣶⣿⡿⡟⠁⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡙⢿⣿⠂
⠀⠀⠀⠀⠀⠀⢸⣿⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣦⢿⠿⣟⠉⠀⠈⢛⡿⠿⢷⣾⣿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣾⣿
⠀⠀⠀⠀⠀⠀⣞⣫⣤⣿⣿⠋⠀⠉⠉⠛⠛⠙⣿⡀⣠⣿⣿⡇⢰⣿⣿⣤⣀⣠⣼⣷⣶⠀⣿⣿⣧⠀⣸⡟⠉⠛⠋⠉⠁⠈⢻⣿⣧⣬⣛⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣿⣿⣉⣙⠛⢟⣉⣹⣿⣧⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⢻⣿⣽⣿⣿⣷⣿⣿⣿⣽⣿⠏⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉