Sugared Emojis & Symbols

⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⢄⡀⡚⠑⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠠⣀⡀
⠀⣂⠳⣠⡴⢯⡁⠀⣈⠆⠀⢙⡤⠞⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠃⠴⠙⡌⠄⢉⠁⠉⢳⠆⠀⡆
⡠⠊⠀⠀⢀⠝⠻⠀⠀⠠⣀⠇⣷⢴⠈⡡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⢀⡈⣣⠀⢸⠀⢸⡄⣈⡿⢗⡔⠊
⠣⠀⠖⠣⡈⢑⣔⡌⡈⢂⢐⡶⠙⠢⠤⠃⠀⠀⣠⠄⠰⠒⣒⡲⠂⠤⢄⠀⠉⣟⡴⠈⠁⠁⠋⠁⠉⠉⠉
⠀⠀⠀⠀⠈⠁⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠂⠬⠄⣋⣉⣉⣑⡍⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠘⠀⣐⠀⠀⣀⠀⢀⣇⠜⠁⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢠⠒⡋⢂
⠀⠀⠀⢀⡀⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠔⠀⠀⠆⠈⠀⢎⡀
⠀⠀⠀⠀⡓⢄⡈⠢⠄⣀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠀⠤⠜⡀⠁
⠀⠀⠀⠀⠘⢄⡈⠀⠂⠠⠀⡴⠊⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡀⠀⠠⠖⠉⠀⠀⠉⠰⠆⠀⠀⠙⠠⠠⣠⠶⠊⣑⡢
⠀⠀⠀⠀⠀⡸⠈⠗⠒⠒⠉⠀⠀⠀⠀⠀⣀⣈⠓⢆⠀⠀⠀⠀⠁⠀⠲⠄⠀⠂⠀⠀⡸⠀⠀⠀⠀⠐⠂⠑⠂⠐⡄
⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡀⠛⠶⠄⣀⣀⠤⣄⠀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢠⠃⡘⠀⠀⠀⠀⠀⠀⠣⢄⡂⣄⣀⣀⠬⠄⣀⡀⣀⠐⠉⠂⢈⡄⠈⠁⠀⠀⢀⡠⠴⠲⠶⢤⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠴⠁⠀⠀⠀⠀⠀⠀⠑⠤⣈⡀⢀⡅⠀⠀⣇⡀⢀⡁⢀⠜⠚⠀⠀⠀⢀⠞⠁⠀⢀⣀⡀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⡟⢀⣀⠔⢁⣄⢹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⠀⠢⡀⠀⠀⠀⠀⠀⢧⡀⢸⡀⡨⠶⠚⠠⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠂⠛⢍⢂⠀⢱⡄⠀⡃⠀⠀⠀⠀⠀⠀⠑⠯⣙⣦⡤⠴⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⠈⠁⠀⠀⠑⡀⠀⢀⣦⠴⠋⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠱⡀
⠀⠀⠀⠀⠑⡒⠠⠤⠀⠑⠄⠑⠠⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⡏⠀⣈⣒⡖⠊⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠉⠉⠙⠛⠒⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢖⡿⠗⠒⠒⠲⠦⣄⣀⠀⠀⣀⣀⡤⠤⠦⣤⡈⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡞⠀⠀⠀⣀⠀⠀⠀⠈⠙⠉⠉⠀⣀⣦⠀⠀⠳⡄⠀⠀⠙⢦⣀⡠⠤⢤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣼⠁⠀⠀⠲⡾⠇⠀⠀⢄⡰⠀⠀⠀⠙⠋⠀⠀⠀⠙⢦⣀⡔⢾⠀⠶⠦⠘⠁⢀⣤⠍⢓⣄
⠀⠀⠀⠀⠀⣼⠟⠛⠉⠉⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡔⠛⡋⠠⢶⡀⢜⠛⠀⠛⢓⣀⡛⣁⠑⡄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⣠⠴⢒⣲⡿⠿⠿⢭⣝⡲⢄⠀⠘⠃⡸⠀⠈⠙⠁⠺⠇⠈⠙⠐⠛⠁⠉⠀⠛⠀⠘⡀
⠀⠀⠀⢰⢿⠀⠀⠀⠀⠐⠶⠶⠀⢀⡾⢁⡴⠋⠁⠀⠀⠀⠀⠀⠉⠺⣧⠀⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⡿⢸⡆⠀⠀⠀⠀⠀⠀⠀⡞⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠜⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⢷⠀⠀⠀⠀⢲⡄⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⢸⠀⠀⢀⣀⡀⠉⠘⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⢷⠀⣼⠀⠀⠉⠉⠀⣀⣀⠘⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣲⢿⠙⡀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠔⠊
⠀⠀⠀⠸⡄⣿⠀⠀⠀⠀⠀⠈⠉⠁⠈⠻⢷⣄⡀⠀⠀⠀⠀⢀⣠⠞⠁⠸⡄⠉⠉⠀⠈⠒⠂⢦⠀⠀⢀⡜⠉⠳⠄⠀⠜⠁⡘
⠀⠀⠀⠀⢳⡸⡄⠀⠀⠀⠀⠘⢦⡀⠀⢀⠀⠈⠉⠛⠓⠛⠋⠉⠀⢠⣤⣦⡇⠀⢀⠀⢠⣶⡦⠈⠓⢐⠊⠀⣶⣶⠀⠀⠁⢀⠃
⠀⠀⠀⠀⠀⢳⡹⣄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣠⡄⠀⠀⠘⢷⡀⠀⢰⠏⢿⠀⠘⡀⠀⠉⠁⠀⠈⠉⠀⠀⠉⠁⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠙⣎⠙⠲⠤⣤⣀⠀⠀⠀⠀⠘⠉⠀⠐⢦⡀⢀⠀⢀⡞⠀⠘⡇⠀⡃⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢨⠟⠉⠙⠾⠤⡔⠒⠟⠉⠉⢣⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠙⢦⣀⠀⠀⠀⣀⣼⡀⠀⠀⠀⠀⣽⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠯⢭⣍⣉⣁⣀⣹⣦⣤⡤⠔⠛⠲⠤⠤⠞⠉⠉⠁⠀⠒⠒⠀⠈⠉⠉




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⣤⣀⠀⠀⠀⢀⣴⠞⠛⣆
⠀⠀⢀⣀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠙⢷⡀⠀⢾⠁⠀⠀⣻
⣠⠾⠋⠙⡇⠀⣼⠃⠀⠀⠀⠀⡠⢒⡆⢘⡇⠀⠈⠳⠚⠋⠉
⢧⠀⣀⣀⡿⠀⢻⡄⠀⠀⠀⠀⠢⣀⣀⣼⠃⣠⠶⠶⠶⣤⡀
⠈⠛⠉⠉⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⠉⠛⠛⢻⠀⣀⢀⠈⠹⣦⡀
⠀⢀⣴⠞⠛⠛⠷⣦⡈⠛⠶⢤⣤⡴⠶⠒⠲⢦⣦⡁⢈⡃⠀⠘⣷⡀⠀⠀⠀⠀⠀⣀
⢀⡾⠁⠀⠀⠀⣀⣈⢻⡄⢠⡞⠁⠀⠀⢀⣀⠀⠸⡮⣉⠀⠀⠀⠘⣷⠀⠀⢀⡴⠟⠉⣷
⢸⡇⠀⠀⠀⢈⠰⠞⣸⠇⣾⠀⠀⠀⠀⣇⠚⠀⢠⣇⠈⢢⠀⠀⠀⢹⡇⠀⢸⡇⠀⣀⣹⠄
⠘⣧⠀⠀⠀⠈⠓⠾⣯⣄⣹⣇⠀⠀⠀⠈⠑⠰⠿⠼⢦⣬⣆⣀⡀⢸⡇⠀⠀⠙⠋⠉⠉
⠀⠈⢷⣄⠀⠀⠀⠀⠀⠈⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠈⠐⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣶⡶⠒⠒⠢⡌⠀⠀⠀⢰⢋⠉⠡⣀⠀⠀⠁⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⢤⡜⣄⠀⠀⠀⠉⠀⠠⠉⠑⢄⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠳⠀⠁⠈⡳⠦⠀⠀⠘⠢⡀⠀⠀⢳⡀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⣧⠀⣸⡟⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⠶⠶⠶⠶⠶⣤⡀⢣⡀⢸⠀⣿⠛⠉⠉⠉⠙⠛⠶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠿⠇⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠙⢷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠈⠙⠲⠦⠤⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠋⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠚⠛⠛⠓⠒⠒⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢠⠞⠁⣠⠴⠃⠀⢸⠁⢻⠀⢠⡞⠆⠀⣠⠞⠉⣀⣽⠀⠀⠀⠀⡞⠉⠹⡄⠀⠰⠏⠀⠀⠀⠀⠈⣧⠀⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⢸⣁⡀⠀⠀⢸⠀⢸⠀⢸⠇⣿⢰⠇⢠⡞⠁⠀⠀⠀⠀⠀⡇⣀⠀⢧⠀⠀⡇⠀⣿⢑⡆⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠢⠤⣭⣉⠉⠑⣼⡂⢸⠀⢰⠀⣿⣾⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⣿⡄⠸⡄⠀⣇⠀⠈⠉⠀⣠⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢸⡇⠘⣆⡼⠀⣿⣿⠀⢿⠀⢾⡉⠉⠑⢆⡸⠀⠓⡃⠀⢷⠀⣿⠀⢀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⣤⠞⠀⣸⡇⠀⠀⠀⢠⠇⢸⡄⠈⠳⠚⡁⠀⡞⠉⡇⠀⢠⠛⡄⠘⡄⢸⠀⢿⢳⡀⠘⣆⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣏⣁⣀⣠⡤⠞⠁⠸⣄⣀⡴⠋⠀⠀⠙⠶⠤⠾⢧⣤⠇⢠⡃⢠⠇⠀⠹⡀⢳⠘⡆⢸⠈⢧⠀⣸⡆⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠱⠞⠀⠛⠋⠀⠈⠛⠉⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣁⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣄⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡿⢋⡁⡄⢀⡈⡝⢿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⣸⠋⠄⢀⠤⠈⡃⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠘⠉⠉⠉⠉⠉⠋⠉⠙⠋⠛⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⢾⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣰⣶⣆⠀⠀⠀⣠⡴⠶⠶⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣟⠿⣽⠟⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣇⣀
⠀⠀⠀⣼⣿⣿⣿⣧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⡉⠈⠙⠻⠆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣁⣁⣈⣉⣤⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣴⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠷⠂⠀⢀⡀⣀
⠀⠀⠀⣀⣀⣀⣰⣁⣄⣸⣀⣀⣀⡀⠀⠀⠀⠀⠘⠟⠱⣷⠄⢰⡐⣦⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⢀⣼⣿⠟⠀⢠⠼⠿⠟⠉
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⢷⡜⠟⠀⠀⠀⠀⠀⠀⢻⠛⠛⠦⣀⠴⠛⠋⡟⠀⠀⠀⠀⠀⠙⠃⠀⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⠛⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠂⠀⠀⠀⠀⣼⠛⣷⣼⣿⣶⡄⠹⣆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⣤⣤⣤⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡧⠀⣿⠀⠀⠀⠀⠀⠀⠛⠿⠿⢛⣡⣴⡶⢶⠂⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡉⠻⠿⠛⢷⣼⠃⠀⠀⠀⠀⠀⠀⠿⠛⣋⣉⣱⣤⠽⠖⠂⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢈⣿⣀⣀⣀⠀⠀⢠⡤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠭⡝⡁⣠⡾⠃⠀⠈⠉⠉⠉⠉⠛⠀⠀⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠥⠚⠁⠂⠠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢲⣡⡀⠀⠀⠀⠀⠠⡀⠀⣉⠖⠒⠲⠶⡖⠒⠒⣦⠀⠀⠀⠀⠐⠒⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⢬⠯⢄⠜⠀⡠⠒⠒⠢⣤⠊⣡⠖⠋⠉⢳⠈⠀⠀⣭⡀⠀⠀⠀⠀⠘⢦⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢙⠚⠒⢌⠢⢐⡁⠀⠀⠰⢎⠟⠲⠀⠀⢀⠏⠀⠀⢤⣌⠰⣀⡠⠖⠋⠙⣆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢄⠀⢀⡀⠀⠀⠀⠀⢧⡜⠀⠀⡨⢦⠭⡉⠐⠒⠂⢻⡀⠠⠤⠒⠧⠀⢀⡴⢃⠜⠃⠨⠚⠛⢉⠞⠁
⠀⠐⡆⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠣⣀⠈⠀⠀⠀⠀⠁⠀⠀⢀⡠⠖⢣⠔⠁⡰⠂⠀⠐⠊⡡⠢⡤⢄
⠀⠀⠘⠀⠉⠁⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠤⠤⠒⠊⣁⠤⠒⣁⠴⢋⠿⠳⠀⠀⠼⢱⡜⠒⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⡄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡝⠒⠂⠤⠄⢀⣀⡀⠤⠤⠒⠉⠁⢠⢋⠟⠀⠀⠈⠧⠾⠥⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣻⠰⢾⢺⣆⡶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣶⣄⠀⠀⠀⠀⠀⠀⢀⡜⠁⠐⠚⠁
⠀⠀⠀⡀⠀⠀⠀⢠⠘⣣⠖⢌⢻⡜⣶⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⡻⢿⣷⣄⠀⠀⠀⡠⠊
⠀⠀⠀⠇⠀⠀⠀⠀⣾⡙⠙⠛⢩⡭⠄⠀⡇⠀⠀⠀⠀⠀⠀⢠⠊⢀⣠⠊⠊⠀⠀⠙⡿⢧⣠⠞
⠀⠀⠀⢁⠀⠀⠀⠀⠉⠈⠄⠙⢢⠀⠀⠀⡗⠢⢄⡀⠀⠀⠀⠰⣀⡘⠙⠃⠀⢀⠴⡟⠳⢄⠁⠀⠀⠀⢀⢀⡀⢀⠎⠸⠧⠀⠀⠀⡀⠀⡴⢊⢝
⠀⠀⠀⠈⠂⠄⢠⡐⠒⠙⠀⠉⠡⠋⠠⠴⠃⠀⠀⠈⠓⠤⣀⠀⠈⠣⣀⡀⣀⣀⡜⠉⣷⠘⡦⠀⠀⢀⢴⡢⡘⠫⡌⠀⠀⠀⠀⠀⡠⠂⢔⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠐⠂⢤⠀⡄⣤⣄⡀⡀⠀⠀⠉⠒⠤⣀⡀⠤⠘⣗⠉⢒⣶⠁⡰⢐⡥⠊⠀⠈⠀⠌⠲⡐⠒⡲⡊⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠁⠒⠂⠦⠤⠤⠤⠜⠿⢒⠇⠀⠀⠀⠀⠈⠉⠲⢥⡈⠉⣩⠙⡡⡞⠀⠀⠀⠀⠀⠀⠀⠑⠌⠻⣮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⢍⡀⠈⢆⡀⠤⣄⢀⣀⣀⡠⢒⡳⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⢲⡊⠐⠈⠀⣀⠔⡩⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⢀⡠⠌⠀⠀⢴⣊⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠁⣀⠠⠐⠂⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠀⡀⠤⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠊⠉⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠙⢦
⢀⡤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣄⡼⠀⠀⠀⠀⣀⣀⣀
⡆⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡔⠉⠁⠈⠀⢱
⠹⣄⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⡀⠀⠀⡞
⠀⠈⠳⣄⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢠⠖⠉⠙⡆⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠱⡄⠀⠀⠀⠀⠸⠤⠶⠴⠃
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠖⠛⠒⠘⠲⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡤⠖⠚⠙⠲⠊⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠓⢦⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠑⢦
⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢱⢄⣙⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠹⣄
⠀⢀⣠⡤⢼⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠦
⠀⢏⡀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⢠
⠰⣏⠀⠀⠀⠉⠒⠒⠦⠤⠤⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠤⠒⠒⠋⠀⠀⠀⢀
⠀⢈⡏⠑⠂⠄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢸
⠀⢸⠀⠀⠀⠀⠀⢀⠤⢀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠐⢐⠀⠀⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⢫⡀⠧⢀⠀⠃⠁⢰⢡⢀⠔⢉⠄⠠⠇⠀⢀⠂⠀⢂⠀⠀⠊⢠⠤⠀⠱⠀⡆⡈⠀⠀⠀⠀⢠⠇
⠀⠀⢳⡀⠀⠀⠀⠀⠈⠑⠀⡁⡄⢀⡜⠸⡄⠀⠃⣀⠀⢀⠀⠈⠠⠟⠈⡄⠀⠀⠈⠂⢵⠂⠀⠓⠃⠀⠀⠀⣠⠋
⠀⠀⠀⢳⡀⠀⠀⠰⠢⠭⠔⠁⠣⣀⡠⠃⠰⣄⠑⣋⠀⡤⢘⠆⠰⠢⠀⠀⠀⡀⠈⢠⣀⠵⠐⠇⠀⠀⢀⠜⠁
⠀⠀⠀⢠⠗⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠁⠀⠑⠈⠀⠈⠁⠀⠁⠀⠀⠀⠠⢾⠁
⠀⠀⠀⠀⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠖⠚⠉
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠎⢁⣿⠄⣀⣀⣀⣠⡄⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠢⢤⡞⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠄⠌⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣒⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢍⣖⠋⠀⠀⠀⠀⠀⡀⠀⣠⠄⠒⣤⠀⠀⠘⠀⠀⠀⠀⠐⢎⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠓⠀⠀⢀⠀⠀⠰⢿⠎⠆⠀⢀⠏⠀⠠⣌⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⢠⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠐⠀⢹⡀⠐⠒⠓⢀⡠⢊⠔⠁⠀⠀⠉
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢉⠗⢁⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⢀⡀⠀⠀⠀⠀⢐⣈⠤⠚⢡⢮⠉⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠶⢩⡯⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣄⠀⠉⠀⠈⠉⠀⡠⠂⠠⠗⠁
⠀⠀⠀⡄⠀⠀⠀⠁⠀⠂⠓⣸⣷⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⣷⣄⠀⠀⢀⠔
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠙⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢜⠀⠁⠀⠄⣉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠉
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡈⠒⠒⠒⣾⠤⠟⡆⠀⣀⢄⡠⠀⠠⠀⢤⠀⣀⣀⠄⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠤⠈⢀⣉⣉⠷⠤⡄⠀⠀⠀⠑⠢⢄⡈⠲⢖⠛⣠⠇⠈⠀⠀⠀⠀⠀⠑⢤⣂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠐⠙⢉⠀⠀⢀⠠⡀⠀⢀⣀⢄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠅⠂⠀⠈⠀⠠⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠈⠁⠀⠀⠀⠀⠸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠊⠁⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠁⢀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡞⠁⠽⠿⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⣀⣠⠴⠛⠛⠳⡄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣵⣋⣉⡝⠁⠀⠀⠀⣸⣥⣤⡧⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢀⣠⣾⠿⠛⢉⣤⣤⡤⡔⠛⠓⠒⠓⠶⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⣀⠴⠛⠁⢀⣠⠞⣿⣚⣯⡀⠧⡀⠀⠀⠀⢀⡧⣤⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⢀⡤⠖⠋⠁⢀⣠⠖⡏⠀⠀⡇⡇⠀⠀⠀⢸⣄⣀⣀⣸⣇⠘⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⢀⣠⡴⠚⠉⠀⢀⡤⡞⠉⠉⠉⢱⣤⣴⣇⡟⠉⠉⠙⠛⣆⠀⠀⠀⢸⣉⡩⠭⠛⠛⡶⢤⡀
⠀⠀⠀⠀⠀⡠⠞⠉⣀⡤⠖⠋⠁⠀⣀⡴⢚⡇⣠⠦⣄⣠⠤⠾⣭⣤⣸⠀⠀⠀⠀⡏⠉⠉⠉⠉⢹⡿⠤⠤⣄⠀⡇⠀⠙⣦
⠀⠀⠀⠀⣮⣤⠴⠚⠉⠀⠀⣀⠴⠊⢷⡀⠈⢷⠃⠀⠀⠈⠉⢲⠀⠈⠉⠉⠙⠛⡻⣇⣀⣀⣀⣀⣸⠛⠛⠓⠚⢳⠟⠀⢀⡟
⠀⠀⠀⠀⠘⣆⠀⠀⣠⠴⠋⠁⠀⠀⠀⠙⠶⣇⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠋⠀⠉⠉⠉⠉⡏⠀⠀⠀⢀⣸⡤⠞⠋
⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣶⣧⣤⣤⣤⣄⣀⣸⣇⣤⣤⣤⣤⣤⣿⣶⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠚⠚⠛⠛⠛⠚⠛⠚⠉⠉⠁

⡠⠊⠉⠓⢄
⢇⠀⠀⠀⠀⠳⣄
⠈⢦⡀⠀⠀⠀⠈⢢⡀
⠀⠀⠙⢦⡀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⢳⡀⠀⠀⣀⣀⣀⣀⣀⡴⠾⠁⠈⠁⠀⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠹⡞⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠚⠉⠳⡄⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀
⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠘⠒⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⢀⠴⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⡤⠒⠒⡺⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⡷⠄⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠀⠀⠻
⠈⢧⣄⣀⠀⠀⠀⠉⠉⠙⠒⠒⠂⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠤⠤⠄⠐⠒⠒⠀⠉⠉⠀⠀⠀⠀⠠⢴
⠀⢰⠃⠀⠈⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠸⣅⠈⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠈⠓⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣛⣓⣲⣲⣶⣶⣶⣶⣤⣤⣤⣤⣴⣦⣶⣶⣖⣒⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣧⠀⠀⠀⠀⠀⠹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣧⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⢧⡀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣵⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢷⡀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡄⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣆⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣦⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣧⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣷⡀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢟⣦⠀⢠⠔⠋⠀⠈⠀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡟⠃⢀⡤⠄⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠏⢀⡀⠀⠀⠠⣤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠟⣤⡿⢇⢠⠎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⡀⣸⠃⠸⣿⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠹⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⡇⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠁⠀⠀⠀⠀⠈⠉⠛⠋⠉⠶⠶⢤⣄⣼⡇⠀⠺⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣠⠶⠆⠙⠉⠋⠉⠉⠁⠰⠶⠶⠦⣀⣀⡀⠀⡿⠉⠀⠤⠀⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡿⠃⠀⠆⠀⢠⠀⠀⢻⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀⠈⠍⠓⢤⣀⠀⠒⠂⠠⠄⠐⠒⠒⠒⠂⠉⠀⢀⡾⠀⠀⠈⠀⢀⠈⢡⡈⠙⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠙⢦⡄⢡⡀⠈⠑⢢⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠀⠀⠀⡷⠀⢸⡀⠘⠷⣤⡀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠈⠁⠾⣦⡀⠀⠈⠛⣉⠰⠆⢀⣀⠈⠉⠀⠀⠀⠀⠐⠁⠀⢸⠀⠀⠀⠀⠈⠑⢦⡀⠈⣷
⠀⠀⠀⠀⠀⠀⢀⠉⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠶⢄⣈⠳⠄⡀⠀⠈⠙⠿⢂⡤⠶⠤⠀⢰⣏⣀⣈⣀⠀⠀⠀⠀⢙⡶⢿
⠀⠀⠀⠀⠀⠀⠸⠀⢰⣉⣙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠶⣄⣀⡀⠀⠀⠒⠤⠄⣀⠀⠀⠀⠀⠙⠋⠠⠤⢄⣠
⠀⠀⠀⠀⠀⠠⡇⠀⡄⠻⡌⠀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠀⠠⠤⠴⠶⢦⣤⡄⠀⠠⣤⠤⡏
⠀⠀⠀⠀⠀⡄⠀⣀⢣⣄⡿⠸⠀⡆⢠⢤⡉⠑⠒⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠃⠀⠙⢦⡀⠀⢧⡞⢠⡏⠀⢠⠿⠀⢠⣄⠀⠉⠉⠐⠶⠦⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠦⣀⠀⢠⣤⢲⡼⣶⠀⣼⡜⠃⠀⢀⠘⠦⣀⣤⠀⡰⠆⠀⣈⡉⠉⣉⠉⠘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠈⠛⠦⢄⣀⠀⠛⠐⠏⡀⠀⠀⢸⡦⠖⣹⣧⠀⠙⣦⠀⣭⠀⣸⠤⠀⣠⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠤⠤⢀⣀⡀⠈⠀⠸⠇⠙⠠⡤⠏⠀⠟⠀⢽⡀⢀⡟⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠒⠂⠀⠠⢤⣤⡤⠀⠀⠀⠚⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠉⠉⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠈⢣⡀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠐⢀⡠⡟⠛⠋⠉⠉⠱⡄⠀⣀⣀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉
⠀⠀⠀⢴⡆⠀⠀⠀⣏⠦⡤⠚⢁⣀⣇⡀⢀⣀⡤⠤⠷⡞⠁⢈⡷⠋⠀⠀⠀⠀⣀⣤⠴⠚⠉⠁
⠀⠀⠀⢠⡴⠶⠒⠒⢻⠒⡏⠉⠉⠁⠀⢹⢻⡄⠀⠀⠀⢙⡴⠋⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠘⡄⢣⠀⠀⠀⠀⢸⠘⡘⣆⠀⡴⠋⠀⣀⠔⠊⡏
⠀⠀⢀⣨⣧⢤⡄⣀⡠⠧⠼⠤⠶⢶⢤⡸⡴⠧⠬⣞⣀⡴⠊⠀⠀⠀⣇⣀⡀⠰⡶
⠀⣞⠉⠁⠀⠀⢇⠀⢣⠀⠀⠀⠀⠸⡄⢻⠁⠀⠀⠀⢠⠟⠋⠉⠉⡏⠀⠀⢷
⣀⣹⣄⣤⣤⣤⣼⣤⠬⠦⠤⠤⠤⠤⠧⠼⢤⣤⣤⣤⣼⣀⣀⣀⣀⣷⣀⣠⣼⣤⡤⢤⡀
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠤⠔⠀⠀⠀⠀⠀⠐⠒⠶⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠹⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠓⣲⡆⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢀⣠⠴⠒⠛⢹⠳⢦⡀
⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠃⠀⠀⠀⠀⠀⣠⠞⢁⡤⠴⠒⠛⣗⠾⢇⡀⠀⠀⢸⠀⠀⣇
⠀⠀⠀⠀⠈⠳⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠊⠁⠀⠸⡇⠀⠀⠀⢸⠀⠀⢹⠀⠀⢸⡆⠀⡟
⠀⠀⠀⠀⠀⠈⢧⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣩⡴⠃⠀⠀⠀⠀⣇⣀⣁⣀⣸⣄⣀⡾⣶⠶⠞⠷⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠿⠂⠀⣿⣷⠀⠀⠈⠓⠋⠀⠀⠀⠺⠽
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣶⣿⣿⠻⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡐⠃⠀⠀⢀⣠⣴⣾⣿⢿⡦⣹⣿⣿⣿⣿⡶⠄⠦⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢟⠀⠀⣹⠟⢻⡇⠙⡛⠋⠋⠁⠀⠓⢲⣗⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠯⠀⠈⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⣹⣷⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡟⠀⠀⠘⠉⠀⠀⠀⠀⣀⠀⠀⢃⡀⠐⣾⣿⣄⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡱⠈⠁⠀⠒⠁⠀⠀⠀⢀⡄⠹⠶⠀⠘⠟⠀⠉⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⣀⣠⣴⣶⣄⠀⢸⡷⠀⣤⣶⣤⡀⠀⠀⠀⠀⠀⡇⠀⠐⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠁⠈⣿⣧⣽⢟⠝⣃⡄⠀⢰⡇⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠳⠀⠹⣿⣿⣿⣿⣿⣿⠃⢀⡀⠈⣿⠶⣷⣿⣿⣿⡟⢄⣼⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠛⠻⣿⣿⠋⢀⣾⣷⡀⠘⣿⠧⠿⠛⠋⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡁⠈⠀⠰⠄⠀⠀⠈⢠⢨⣿⣿⡟⡀⠉⠀⠀⠐⠀⡄⠹⣿⣿⣭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢻⣔⡠⠄⢤⠄⠰⠁⠘⣎⠿⢿⣵⠇⠐⣦⠠⡄⠠⢐⣢⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢸⠹⡿⠾⢿⠛⣶⣦⡄⠀⠀⠀⠐⠀⠀⠀⠀⢠⣶⣶⢿⣿⣿⣿⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡥⣶⣶⣿⡾⣻⡇⠹⡿⠷⠤⡤⠤⠠⠦⠤⢠⢶⣿⣿⠏⠸⣿⡿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⢫⣿⡦⠃⠝⡇⠀⠐⠀⠀⠀⢤⢤⡤⣤⡤⠶⣔⡟⠆⢠⣈⣉⣉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠁⠙⠁⣀⠘⠃⠀⢀⠙⠒⠶⢴⢶⣶⣶⠷⠟⢛⡁⠀⣾⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠁⣀⡁⠀⠁⠀⠀⠀⠀⠣⢀⣴⣦⡲⠿⠆⠀⠀⣼⣿⣿⣿⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣥⠒⠠⠴⠦⣄⡀⠀⢸⣿⡿⠇⠀⢀⣠⣾⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢌⠙⣿⣶⢿⣷⡖⣿⣿⣿⣻⣦⠈⠛⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⢀⣦⣾⠶⠀⠩⢿⡟⠛⠙⠛⠛⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠛⠈⠉⠀⠀⡀⢠⡇⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠙⠇⢀⠘⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠛⠲⢦⣄⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠳⣤⣤⡀⠀⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠲⢦⡀
⠀⠀⠀⠀⢀⣤⡞⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀
⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⢦⡀
⢠⠞⠻⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣦
⠈⢷⣤⠀⠈⠉⠙⠒⠂⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠚⠉⠁⢀⣼
⠀⣼⠃⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠀⠀⠀⠀⣠⠖⠋⢙⡧⠀⢰⠒⡆⠀⢠⢤⠀⠀⣠⠖⠒⢲⠀⠀⠀⢀⡴⠶⡄⠀⠀⡴⠊⠉⠉⠉⠳⡀⢀⠀⡀⠀⠀⢸
⣿⠀⠀⠀⢠⡇⠀⡞⠁⠀⠀⢸⠀⣿⠀⢸⠘⡄⡼⠁⡴⠚⠉⠀⠀⠀⢸⠁⠀⢹⠀⠀⡇⠀⡶⢦⡀⠀⣇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠣⣄⣙⣛⠒⠢⣼⡀⢿⠀⢸⠀⣷⡇⢸⠃⠀⠀⠀⠀⠀⣼⢸⣇⠈⡇⠀⣇⠀⠙⠚⠀⣠⠏⠀⠀⠀⠀⠀⢸
⢻⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⢸⡇⢸⣀⡏⢰⣿⡀⢸⠀⢴⡒⠒⠲⡄⡇⠘⠿⠀⢹⠀⢹⠀⢀⠀⠸⡁⠀⠀⠀⠀⠀⠀⣾
⢸⡄⠀⠀⠀⠀⢀⣀⣠⠼⠀⣸⡇⠀⠉⠀⡸⠈⣇⠈⠓⠖⡁⠠⡖⢻⠇⠀⡜⢧⠈⣇⢸⠀⢺⢧⠀⠱⡄⠀⠀⠀⠀⢰⠇
⠀⢳⡄⠀⠀⢸⣉⣀⣠⡤⠞⠁⠱⣄⣠⠴⠁⠀⠘⠳⠤⠖⠧⠤⠇⢸⠀⣼⠀⠈⣆⢸⡄⡇⢸⠈⢇⠀⣹⠀⠀⠀⣠⠏
⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠚⠁⠉⠉⠀⠈⠉⠀⠀⢀⡴⠋
⠀⠀⠀⢺⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠋
⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠒⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢠⡄⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢏⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠉⠂⠀⠀⠄⠓⠀⠂⠐⠒⠂⠖⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠈⠉⠣⠀⠈⡹⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀
⠰⡆⠀⣀⠂⠰⡀⠀⣀⣤⢦⠠⠔⢲⣄⣀⢀⠀⠀⢀⠠⠄⠸⠀⠀⠂⠀⠀⠀⡇⠀⠧⠀⠔⣩⢬⠑⡀⠀⠀⠈
⠀⠘⠛⠂⠀⠀⠀⠰⠁⠛⠛⠛⠒⠛⠛⠷⠁⠀⠀⠈⠀⠀⠀⠀⠀⠈⠢⠀⠰⠁⠀⠀⠀⢀⡁⢀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢲⠆⠒⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠂⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠒⣮⡀⠢
⠀⠀⡤⢀⣀⡀⢰⢰⣤⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢠⠄⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⠀⡀⡆⠀⠘⢸⠈
⠀⠀⠀⠀⠀⠀⠙⠚⠋⠉⠉⠙⠛⠋⠂⠀⠀⠀⠀⠀⠀⠀⣀⠄⡴⠂⢍⠁⢀⠀⠧⠤⠂⢀⠇⢲⠀⠙⢦⠀⠇⠁⠀⡀⡄
⠀⠀⠀⠀⠀⠀⣀⡀⠲⣜⠚⠴⠟⣻⡀⠀⠀⠀⠀⠀⠀⡴⡄⢃⡡⠠⠮⣹⠾⢿⣗⠰⢍⠁⠀⠀⠀⠀⠈⠱⠀⠀⠀⠁⠁⢀
⠀⠀⡀⠀⠀⠀⡏⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠁⠀⠂⠉⠁⠡⠄⠰⢈⢠⠄⠀⠀⣁⣀⣀⠈⡀⠀⠈⠀⡀⠘
⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠘⠇⢴⠢⠠⣭⠆⢨⣐⣢⡀⠀⠈⠈⠂⠈⡽⢋⣻⠛⠀⠀⠆⠀⠀⠁⡂
⠀⠀⠣⠤⢄⣀⣀⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣀⡡⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠠⢀




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠐⠄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢑⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣈⡙⠁⠀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⢳⡚⠁⠀⠀⠀⠀⠀⠀⢀⡤⠊⣡⠴⠒⢢⡘⠂⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠟⠀⠀⠀⠀⠀⠀⠀⢠⡝⡤⢫⠀⠀⠀⣸⠁⠀⢀⡈⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⢀⣀⡨⢵⠃⠀⠀⣀⣴⠃⠀⠀⡼⢋⡦⠈⢚⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠊⠀⠀⠀⠘⠒⠀⠖⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠈⠀⠀⠀⢀⣴⠊⡠⠊⣀⠀⠁⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠤⠤⠤⠀⠀⠀⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠊⣁⠼⠋⣠⢾⣥⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠐⣊⣡⠴⠋⢡⢎⡉⠁⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠜⢶⡐⣇⢂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠘⠉⠉⣀⠀⢀⣣⠞⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠵⠜⢺⣩⢳⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠼⢾⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠃⠈⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠞⡡⣪⠗
⠀⠀⠀⠀⠀⠈⠐⠢⠼⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠈⠣⣄⣀⣀⣤⡪⢑⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡪⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠲⠀⠂⢲⡀⡢⢠⢤⣤⢀⠀⠀⠀⠉⠒⠤⣀⡠⠐⢘⣏⠉⢐⣧⠂⢰⢂⡴⠂⠀⠀⠀⠢⡙⢢⡑⢀⢖⠕⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉⠑⠒⠒⠶⠶⠀⠐⠛⠓⡿⠀⠀⠀⠀⠀⠀⠙⠒⢄⡀⠉⡩⣈⡡⠞⠁⠀⠀⠀⠀⠀⠀⠈⠐⠍⠳⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢅⡀⠈⠀⢀⠠⣆⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠊⠁⢀⠜⠀⠀⢠⡔⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠈⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠀⠀⢀⡠⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠀⠀⣀⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠋⠉⠉⠁⠀⠀⠀⠈⠙⠒⠚⠛⠙⠛⠛⠶⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⢀⠀⠀⠰⠆⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠃⠀⠉⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢹⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠐⠤⡈⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠳⣄⠁⢀⠀⠄⠒⠺⡗⠓⠓⠲⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣧⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠠⠊⠀⡈⢷⣠⠴⠒⠊⠉⠉⠙⠓⢦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⢺⢸
⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠁⠀⢀⡾⠁⡰⠊⠁⠀⠀⠀⠀⠀⠀⢀⣼⣥⠤⠀⠀⠰⠀⠀⠀⠀⠉⠒⢦⣞⠑⠘⠪⣿
⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠀⠀⠀⠃⠀⠁⢀⡀⠀⠀⠀⢸⣻⣾⣁⣀⠀⠀⠀⣀⣤⠴⠚⠉⠁⠀⠀⠀⣤⠀⠀⠠⠀⠀⠀⠀⣰⠏⢷⡈⣰⠇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠆⠀⢠⠀⠀⠀⠈⣠⠤⠖⠛⠉⠉⠉⠉⠉⠉⡷⠋⠁⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⣷⠏
⠀⠀⠀⠀⠀⠠⡇⡇⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⢀⡀⠀⠀⠀⠤⠂⠀⡸⠁⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠁⠀⠴⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠀⠀⠀⠠⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢹⡄⡄⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠅⠀⢀⠄⠦⠈⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡜⠾⠈⠛⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠒⠊⠉⡅⡠⢰⢢⠀⢠⢣⠈⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⠀⠀⡌⢉⠉⣙⡛⠛⡛⡁⠃⢁⢄⢉⠀⠀⡿⢠⣵⠲⠀⢼⣱⠳⠯⡞⠌⠈⢀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠲⠣⡡⠬⢬⢠⡡⣩⣾⡶⡁⡄⠈⠞⠿⠇⠊⠏⠇⠀⣠⣥⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣀⣀⣀⠂⠁⠁⠈⣁⣀⣽⢄⣠⣤⡤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠦⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣦⡤⠀⢀⠀⢀⠀⠶⠀⠁⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠦⢄⣙⣢⣶⣠⡀⡇⠰⠀⠀⣀⣴⠆⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣧⠄⡠⠚⢙⡏⠀⠀⠠⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠻⣿⠀⡗⠖⠈⠉⡄⠀⠐⡆⠀⠀⠀⣰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⣉⡉⠉⣛⣳⣦⣀⠀⠹⢸⣿⣄⠀⠀⢰⣶⣶⡿⠂⠉⠛⠉⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⢦⣼⠁⡠⢴⣈⣿⠟⠁⠀⢢⣀⣨⡁⢀⣀⠀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⠞⠉⢻⡛⢲⣦⣼⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠩⠑⣤⣀⣿⢋⠩⢠⡏⠟⠁⢀⣠⠤⠴⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠸⡖⢀⣠⣿⣿⣿⡇⡀⠙⢣⡴⠚⠋⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠠⠀⢀⣀⡀⠁⢙⣿⡿⢻⣧⣗⣛⣉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⢠⠈⢹⡟⠉⠋⢹⡁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠤⣾⠲⡾⢇⠀⠀⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⢸⡀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢺⡟⠟⢸⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⢸⡃⠸⠘⠏⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢏⠘⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⠀⢇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⣿⣶⣿⣧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡇⣿⠈⣽⠇⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠃⢿⠀⣼
⠀⠀⠀⣠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢸⠀⣿⠀⡀
⠀⠀⠀⠻⡄⢁⡄⣄⢠⢠⡄⡄⣄⠠⣄⠀⢸⡇⠀⣠⢠⢀⡀⣄⢠⢄⠀⠀⢸⡅⠀⣸⣶⣿⣄⡇
⠀⠀⠀⢴⢹⠾⡇⣇⢼⢸⡿⡇⣇⠀⢻⠀⠸⡇⡠⣏⢸⢸⡇⡇⢾⠀⠀⠀⠸⡷⠾⢻⠋⢿⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣸⡇⣇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠛⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣶⣛⡀⠘⠛⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠿⠒⠈⠉⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢩⡀⠀⣦⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣌⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠙⠒⠒⠒⢶⠛⠉⠙⠐⠒⠒⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⢢⡴⠋⠙⢆⠀⠈⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⢈
⣤⠀⠐⠀⡤⢢⡤⠤⠤⠤⡤⣄⠀⡀⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠂⠤⠴⠁⠀⠀⠈⡄⠀⢎⠀⢀⠔⢉⡑⢢⠀⠀⠀⠈⢏
⠈⣦⠽⣏⣅⣀⣛⣉⣹⣻⣿⣿⣾⣆⣴⣿⣿⣫⠆⠀⠀⠘⠣⢀⣀⡈⠑⠒⠒⢇⠀⠀⣠⠁⠀⠀⠀⠀⠘⠋⠉⢀⠀⠀⠀⠀⢸⡄
⠀⢀⠀⠀⠀⠀⠀⠀⢁⣠⣀⣀⣀⣀⣀⣀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠉⠉⠁⣤⡄⠀⠀⠀⡶⠤⠔⠋⠀⠀⠀⣀⠜
⠀⢸⠀⠀⠀⠀⠀⠐⣽⣿⣻⣿⣽⣿⣶⣛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡆⠆⠀⠀⠀⡗⠀⠒⠒⠂⡩⢛⣣⣴⣒⣀⡠⠀⣀
⠀⢸⠀⠀⠀⠀⠀⡆⡬⢼⣿⣤⣭⣭⠬⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡸⠀⢸⠀⠀⢠⠁⠀⠀⠀⠀⣧⠋⠀⠋⡇⠀⢈⢷⡦⡈
⠀⠸⠦⠄⣀⣀⣀⡃⡧⣜⢣⣷⣤⣿⢴⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⢀⡴⠁⠀⡸⠀⠀⢈⡑⠚⢕⢄⣀⢛⠀⢸⠀⠃⠀⠘⢸⠁⠁
⠀⠀⠀⠀⠀⠀⢨⠛⠛⠉⠛⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⡴⠒⢤⡁⠀⢀⠀⠧⠤⠖⠁⡼⠁⣺⠀⠈⢾⠀⠘⢸⠀⠀⡆⡈
⠀⠀⠀⠀⠀⠀⢨⣀⣴⢦⠖⣿⣬⡿⢟⣶⠀⠀⠀⠀⠀⠀⠀⣀⣢⠀⠄⢣⠀⣶⡋⢿⣿⣿⡶⣰⣍⠋⠀⠀⠀⠀⠀⠈⡕⡆⡈⠀⠀⠃⠇⠀⠇
⠀⠀⠀⠀⠀⠀⢨⢻⠊⠉⠉⠁⢀⠀⡽⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠚⠧⡀⠠⠼⠷⣖⣋⣩⢤⠒⠇⣀⡄⠀⠐⠂⠀⠘⡼⠇⠀⠘⢸⠀⢰
⠀⠀⠀⠀⠀⠀⡈⠀⠙⠈⠁⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣔⣂⣩⣥⣔⡶⣒⠦⠤⣄⡀⠀⠈⠑⠥⢣⠔⡶⢠⠵⢶⢾⠉⠈⢆⡇⡆⠀⡄⢰
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠠⠤⠄⠒⠃⠀⠀⠀⠀⠀⠀⠀⠘⢍⠛⠂⠋⠹⠉⠻⠽⠰⣼⠂⠀⠀⠀⠀⠙⠲⠧⠔⠚⠂⠧⠀⡈⣣⡅⠀⡆⡌
⠀⠀⠉⠑⠒⠴⠧⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠀⠤⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⡿⠿⠿⠿⠿⠛⠋⠉⠙⠻⢿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢿⣿⣿⣦⣤⣴⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣉⠛⠻⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⠀⠈⠻⣿⣿⣷⡄
⠀⠀⢀⣾⣿⡟⠁⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿
⠀⠀⠈⢿⣿⣆⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠟⠁⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠙⢿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣾⣿⣿⣿⡿⠋⠀⠀⠀⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⢀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣀⣤⣴⣶⣶⡄⠀⣶⣦⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠇⣰⣿⡿⠛⠉⠉⠁⠀⠀⣿⡏⠀⠀⠀⠀⣿⡇⠀⢀⣴⣶⣿⣿⣷⠀⠀⠀⠀⢀⡄⠀⠀⠀⣶⣶⣶⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⠀⣿⣏⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⡇⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⣿⣿⠙⢿⣷⡀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⠀⠹⢿⣷⣤⣀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢸⣿⡇⣸⣿⠇⠀⣀⣀⣀⠀⠀⠀⣼⣿⣿⡇⠀⠀⣿⡏⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠉⠛⢿⣿⣦⠀⠀⣿⣷⠀⠀⠀⣸⣿⠃⣿⣿⠀⠀⠛⠛⢿⣷⠀⣰⣿⣏⣿⣿⡀⢸⣿⣇⢀⣼⣿⠇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⢹⣿⣆⠀⣠⣿⡟⠀⢿⣿⡄⠀⠀⢀⣾⡿⢠⣿⡿⠿⠿⣿⣧⢸⣿⣿⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⠇⠀⢿⣿⣿⣶⣿⡿⠟⠀⠀⠀⠙⠿⣿⡿⠟⠀⠀⠈⠿⣿⣷⣾⣿⠟⠁⠻⠟⠁⠀⠀⠹⣿⢾⣿⡏⠻⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠻⠿⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠉⠉⠛⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⣼⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠹⣿⣿⣷⣦⣤⣤⣤⣴⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣦⡀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣿⡿⠿⠿⣿⠉⠛⠋⠀⠰⠞⠛⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⠛⠀⠀⠀⠀⠀⠤⠤⢆⣀⠀⠀⠀⠈⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡇⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠣⠄⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡐⠄⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣴⣿⣶⣦⣦⣄⡀⠀⠀⠈⠻⣿⣿⣦⡀⠠⢼⣇⠀⢀⠀⠀⡄⠀⠀⢀⣀⣤⠖⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠋⠀⠀⠈⠛⠀⠈⠻⠛⠛⠻⢷⣄⡀⠈⠻⢿⣿⣾⣷⡌⠉⠛⠁⠛⣭⡀⠛⠉⡿⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣧⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⡀⠀⠈⠙⢦⠀⠀⠈⠉⠀⠙⠛⠀⠤⠶⠿⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣇⣹⠾⠻⠛⠀⠀⠐⠆⠉⠈⠙⠖⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⢀⣤⡴⣺⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⣀⠀⠐⠒⠒⠞⠲⢌⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠿⠁⣾⣿⣿⣿⣿⣿⣿⣧⣻⣦⣀⡀⠚⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢦⣼⡄
⠀⠀⠀⠀⢴⠆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣻⣷
⠀⠀⠀⠀⢸⣧⡈⠻⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣦⣄⣀⠀⠉⠁⠐⠀⠒⠚⣥⣶⣿⡿
⠀⠀⠀⠀⠘⣿⣟⠳⣄⣙⠻⢿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣽⡟⠿⠿⣿⠿⠿⠟⠋⠁⠈⠉
⠀⠀⠀⠀⠀⠈⢿⣿⣶⣬⡃⢤⣈⡙⠿⠿⠿⠿⠿⠛⠛⠋⢉⡋⠰⢲⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣾⣿⣿⣏⣃⣀⠳⠴⠦⠶⠖⢀⣠⣶⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠉⠛⠲⠶⠿⠿⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢖⣛⣛⣓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⣿⣿⣿⣿⣿⣿⣷⣭⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⣿⡟⠛⢻⣿⣿⠟⠛⢿⣿⣷⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣿⣿⣷⣤⣼⣿⣿⣧⣤⣾⣿⣿⣧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⣿⣟⠻⣿⣿⣿⣿⣿⣿⡟⢻⣿⡟⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣧⢻⣿⣦⣌⠛⠿⠿⠛⢋⣴⣿⣿⢣⡟⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⣭⣭⣭⡛⠳⠦⣤⣀⡀⠈⢷⣝⢿⣿⣿⣷⣶⣿⣿⣿⢟⣵⠟⢀⣀⣤⠴⠞⢛⣭⣭⣭⣝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⡿⣛⣼⣿⣶⣯⣽⣛⠶⠿⠇⠛⠻⣿⣿⠟⠛⠱⣿⠶⢞⣫⣭⣶⣿⣧⣘⢻⣿⣿⣿⣧⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⣿⣿⣿⠗⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠉⠉⠄⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⡰⢿⣿⣿⡟⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣝⡻⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣾⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣛⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢮⣭⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣭⡵⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣮⢻⣿⣿⣿⣿⣏⠀⠀⢈⣿⣿⣿⣿⣏⡴⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⡏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣾⣿⣿⣿⣿⣧⣀⣀⣠⣿⣿⣿⣿⣿⡜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⢭⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⣷⣬⣍⢻⣿⣿⣿⣿⡿⢋⡼⠋⠀⠀⠈⠻⣮⠻⣿⣿⣿⣿⣿⢫⣭⣴⣿⣮⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⣿⣿⣿⣷⣌⣛⢻⡿⢋⡴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣌⢿⡿⢛⣋⣼⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⢿⣿⣿⣿⣿⡿⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⣿⣿⣿⣿⣿⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣭⣭⣥⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣭⣭⣭⠶⠋



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⡶⠶⠶⠶⣶⣶⠶⠶⡶⢶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠋⠉⠀⠀⠀⠉⠙⠒⠢⠤⣄⡀⠀⠹⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠓⠒⠶⣤⡀
⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣄⣀
⠀⠀⠀⣠⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀
⠀⠀⠀⢧⡀⠉⠒⠀⠀⠤⠀⢀⣀⠀⠀⠀⠀⠀⠈⢀⣁⣀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠴⠒⠉⣹⠆
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢠⡇⠀⠀⠀⣀⡤⣄⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡠⠤⠤⡀⠀⠀⠀⠀⠘⡇
⠀⠀⢸⠃⠀⠀⡜⠁⡔⠊⠀⢸⢸⠀⢸⢡⢠⠊⡠⠔⠁⠀⠀⡏⠈⡇⠀⡇⢀⣄⡀⠘⡀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠱⢤⣓⡒⠢⣼⠸⠀⠀⢸⡏⢸⠁⠀⠀⠀⢸⢱⡇⢹⠀⢇⠀⠓⢁⡰⠁⠀⠀⠀⢠⡇
⠀⠀⢸⡆⠀⠀⠀⠀⠀⢘⡆⢹⠀⠧⠃⡼⡇⠸⡀⡯⠉⣑⣼⠈⢣⠀⠇⢸⠀⣄⠘⡄⠀⠀⠀⠀⣸⠁
⠀⠀⠀⢷⡀⠀⢠⡖⠒⣉⡠⠛⣄⢀⡠⠃⠙⢄⣈⣴⣀⡇⡆⢠⠀⢣⠸⡘⠀⡏⡆⠘⡆⠀⠀⣰⠃
⠀⠀⠀⠀⠳⡄⠀⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠈⠒⠃⠓⠁⠈⠋⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣴⠏



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⡀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡀⠀⠄⢀⣀⣀⢀⡈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⢀⡠⠄⠠⡀⠀⠀⠀⠈⠃⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⠉⠀⠀⠀⠈⢢⠀⠀⢠⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣁⠈⠂⠊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⠣⡀⠀⠀⡠⠂⠐⠒⠀⠐⠁⠀⠀⠀⠃⠀⠀⠤⡀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡄⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⣀⠤⠤⣀⠀⣀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠣⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⠀⠀⠑⡀⠀⠈⢆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣎⢄⡀⠀⠀⠣⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣀⣰⠀⢀⡠⠜⠒⠒⠈⠁
⠀⠀⠀⠀⢀⠔⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠁⠀⠀⠀⡃⠈⡆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢰⠂⠐⠒⠚⠢⠔⠊⠁⢱⠀⠀⡎⠀⠈⢆⠀⠀⠀⡠⠠⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢃⠀⠀⠀⠑⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠁
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠘⣄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠒⠀⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠒⠒⠒⠒⠒⠂⠒⠒⠒⠀⠒⠒⠀⠒⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠤⠄⠠⠄⠀⠒⠒⠒⠀⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠉⠛⠿⢿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⡷⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣶⣶⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣤⣶⣶⣷⣿⣿⣶⣄
⠀⠀⠀⠈⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠛⠛⠋⠀⠀⣀⠀⠀⠀⠘⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⠛⠛⠉⠀⠀⣀⠀⠀⠀⠘⠉⠛
⠀⡀⡄⣠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣹⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⣄⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣹⠀⠀⠀⠀⣶
⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠃⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠃⠩⣆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠗⠣⠶⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠟⠣⠶⠂⠀⠀⠀⠀⠤
⣤⠀⡀⠀⠀⠀⠙⠾⠤⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠋⡘⠒⠒⠀⠀⠁⠀⠀⣤⠀⡀⠀⠀⠀⠙⠺⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⡐⠒⠖
⠀⠀⠁⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠁⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠
⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢠⠖⠒⠒⠦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡅⣀⡄⠀⢠⠖⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆⠠⠄⡀⠀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠠⢌⡀⠀⡃
⠆⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠠⣖⡶⠂⠀⠀⠀⠘⠂⠠⠠⠔⠁⣀⡀⠀⡂⠈⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠁⣀⡀
⠃⠀⠀⢸⠰⠋⠘⠃⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡍⠙⢠⠆⠀⠀⢸⠐⠋⠘⠃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡍⠉
⠀⠀⠀⠈⠳⠤⡤⠞⠁⠀⢀⣀⠀⠀⠀⣾⣷⠀⠀⠀⠈⡁⠈⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⠤⡤⠞⠁⠀⢀⡀⠀⠀⠀⣸⣷⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿
⠀⠀⠀⠤⠀⠀⢀⠀⠀⢶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠄⠀⢲⣶⣶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⠛⠛⠉⠀⠀⡀⠀⠀⠀⠘⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⠛⠛⠉⢀⠀⡀⠀⠀⠀⠘⠉⠛
⠀⡀⡄⢠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣻⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⣠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣛⠀⠀⠀⠀⢶
⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠃⠉⣦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠃⠩⣦⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠕⠃⠶⠂⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠙⠁⠀⠀⠈⠟⠣⠶⠂⠀⢀⠀⠀⠤
⣤⠀⡀⠀⠀⠀⠙⠺⠤⠄⠀⠀⠀⠀⢀⠀⠀⠰⠀⠋⡐⠖⠐⠀⠀⠁⠀⠀⣤⠀⡀⠀⠀⠀⠙⠲⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢋⡐⠖⠚
⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⢠
⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢠⠖⠒⠒⠦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢠⠖⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣆⠠⠌⠁⠀⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡆⠠⠌⡉⠀⡃
⡆⠈⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠃⣀⡀⠀⠂⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠁⣀⡀
⠃⠀⠀⢸⠐⠋⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠝⢰⠆⠀⠀⢘⠐⠋⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⡝⠙
⠀⠀⠀⠈⠷⠤⠤⠞⠁⠀⢀⣀⠀⠀⠀⣾⣷⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⢸⠀⠀⠀⠘⠳⢦⡴⠞⠁⠀⢀⣀⠀⠀⠀⣸⣷⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿
⠀⠀⠀⠤⠀⠀⢀⡀⠀⢲⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⢲⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⢘⢿⣿⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣫⡶⢋⣞⢼⡟⢮⡝⠦⡈⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡡⡆⠀⢩⡴⠺⠋⠀⣷⢸⣇⠀⣽⡄⢻⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣷⡶⠿⠥⣶⠶⢚⣁⣼⣏⣠⣟⠁⣸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⢉⣡⠤⢶⠶⠚⠛⠿⠍⠁⣀⡀⠠⠚⡿⢃⣼⣷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠴⠊⠉⠀⢀⣀⣤⣴⣶⣶⣿⣧⡤⠤⣤⡴⢶⡿⢻⣿⡿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣠⣶⠾⠟⠛⠻⢏⣁⣀⡠⠴⢶⠞⣋⣴⣟⠧⢸⣿⣿⡜⣿⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣀⣶⠞⠉⢀⣤⠴⠒⠈⠁⣁⡤⠴⠒⠊⠉⠉⠰⠋⢠⡿⣿⣿⠇⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢰⡟⠀⢠⡴⠋⠀⣀⣤⠖⠋⠁⢀⣀⡤⠤⠐⠚⠛⢋⣡⡾⠛⣃⣼⣿⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠘⣿⣇⢰⡏⠀⠀⣰⠋⠀⢀⣠⠖⠉⠁⢀⣠⡤⠶⠒⢋⣩⠐⠋⠉⠈⢠⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠀⠈⠻⢌⣧⡀⠠⡇⠀⢠⡞⠀⣀⣴⠾⠋⠀⠀⣠⣶⣿⣥⣤⣤⣴⣾⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣛⠳⠤⢄⢠⡉⠙⠲⠷⠤⣿⣥⣴⣿⣯⣤⣴⠶⣾⠛⣛⣗⣴⣾⣽⣿⢿⣟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠄⠀⠈⠀⠁⠉⠙⠒⢶⠶⠶⠶⣦⣽⡶⣿⡿⢿⡟⢻⡛⠏⣿⢸⡇⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠀⠷⠀⡏⢰⡇⢸⡇⣼⣿⢀⡇⣼⢳⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢰⠀⣇⢸⠁⢸⢀⡇⣾⣼⣧⡏⡸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⢸⡄⣟⢠⠀⣿⢸⡁⠦⡿⢸⢃⣷⣿⣿⣿⣵⣄⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢰⡄⣇⢝⢾⠠⡀⢠⠘⠀⡇⣟⢼⢰⡇⣼⣿⢲⡏⣿⣾⣿⣿⣿⣟⣿⣿⣿⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⣯⠿⡜⣾⣇⠱⠈⡅⡇⣿⣻⣿⢸⣯⣯⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣮⠛⢓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⣿⣤⣧⣃⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠙⠫⠷⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⡿⣿⣿⡿⣿⣿⣿⡿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣼⠏⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⣠⣴⠾⠋⠀⠀⠀⢀⣿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⢀⣴⡿⠉⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⢀⣴⠟⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⡀⠀⣰⡿⠁⠀⠀⢀⣀⣀⡀⠀⣴⠟⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⣀⣤⣾⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠈⢻⣶⣿⣤⣴⠶⠟⠛⢻⡏⠻⢿⣯⣀⣀⣤⣴⠾⠛⢻⣿⠛⠷⢶⣶⡟⠋⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡟⠉⠁⠀⠀⠀⢸⡏⠀⠀⠀⣿⠁⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡿⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢿⡄⠀⠀⠀⠘⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠘⣷⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢹⣧⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⣼⡇⠀⢸⡏⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⢿⡆⠀⠀⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣦⣾⣧⣤⣤⣿⣄⣀⣀⣀⣴⣿⣤⣴⣿⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣶⡶⢶⠶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⣶⣶⣶⢶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣾⡄⣶⣖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⢀⣶⣶⠘⠿⠋⣀⠉⢀⠈⠛⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢐⡒⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠥⠤⠖⠀⠠
⠀⠀⠈⠀⠐⢌⠻⢿⡿⠂⢸⣿⣿⠿⠃⠀⠀⠀⠀⠁⠀⠀⢁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⢈⠐⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡁⡂⠐⡀⢐⠀⣂⢡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠅⠤⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⢌⢂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰⡶⠄
⠀⠀⠀⠀⠀⢂⢐⠐⠂⠐⠀⡃⣈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠙⠋⠈⣡⣴
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⡀⠁⠠⠤⠄⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣀⠠⠆⠀⠤⡀⠣⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡅⢠⣳⡶⠀⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠤⡅⠛⣀⠈⢀⠁⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠢⠀⠀⠀⠀⠆⠀⠀⠲⠒⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣴⣶⠦⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⣄⣸⣶⡟⣹⡏⢿⡇⠀⠠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠂⠀⢸⡶⢋⣿⠛⣿⡍⢛⠂⠛⠃⠊⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠿⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢠⡏⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⠃⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣸⣿⠀⢹⠀⢀⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠉⠻⠀⠈⠀⡾⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠴⠛⠉⠀⣠⡤⠶⠚⠛⣻⡆⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣀⠤⠴⠚⠉⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣤⣤⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠘⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⡿
⠀⠀⠀⢀⣠⣴⡶⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⢀⣴⠟⠋⠀⢀⣤⠴⠖⠒⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⣤⣤⣤⣤⣴⠟
⢠⡟⠁⠀⠀⠜⠉⠀⠀⠀⠀⠶⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⠟⠁
⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠰⣶⣤⣤⣤⣤⣴⡶⠾⠛⠉
⠀⠈⠻⢷⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣸⠁⢀⡆⠀⠀⢿⡇
⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⣦⡀⠀⠀⠋⠀⣼⠁⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢀⡏⠀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠘⣇⣰⠏⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠈⠁⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⣾⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⡶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⢉⡿⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀⢀⡴⠋⣠⠎⠙⠳⣤⣈⣉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢫⡟⠁⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠈⠉⠛⣶⣤⡉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⣴⠏⠀⠀⢠⠞⢠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡤⠞⢁⡜⠛⢦⣀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣰⠋⠁⠀⠀⣰⠋⣰⠋⠀⠀⠀⠀⠀⢀⡴⠚⣁⡴⠚⠉⠀⢠⠞⢉⠟⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢰⡇⠀⠀⢀⡼⢁⡼⠁⠀⠀⠀⠀⠀⡴⠋⡴⠚⠁⠀⠀⠀⢠⠏⢰⠏⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡴⠋⠀⢀⡴⠋⣠⠞⠀⡤⠖⣲⡶⠶⠾⠷⠾⢧⣤⡀⠀⠀⢀⡟⢀⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⢠⠏⣠⠞⠁⠀⣾⢀⡾⠋⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⠞⢀⡞⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⣰⠃⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⣷⠋⠀⠀⠀⠀⠀⠀⢀⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣠⠏⣠⠏⠀⢀⣠⠞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣁⠴⣁⠴⠒⢋⣠⠴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⠟⠀⠀⠀⠀⢀⡴⠋⣹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢳⠚⣡⠴⠛⠉⠀⠀⠀⣿⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣠⠴⠋⡴⠛⠁⢹⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⣌⣙⠲⠶⠶⠶⢛⡇⠀⠀⢀⡴⠚⢉⣠⠶⠋⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣿⠦⠤⠶⠟⠁⠀⣠⠏⣠⠞⠉⠀⠀⠀⢀⣠⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡼⠁⠀⠀⠀⠀⢀⡴⠃⡴⠃⠀⠀⠀⠀⣰⠏⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⡤⣤⠀⠀⡠⠞⢉⡴⠋⠀⠀⠀⣀⡤⠖⢋⣠⠞⠁⠀⠀⠀⠀⠀⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡇⡾⠁⡴⠋⠀⠀⢀⡴⠚⣁⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⣸⠁⣀⣤⠴⠟⠛⠛⠛⠶⠶⢤⣀⡀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠙⠛⠲⠶⠶⠤⠤⠤⠴⠶⠞⠛⠛⠒⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢀⠔⠂⠀⠀⠀⠀⠺⣇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢸⠠⡀⠀⠀⠀⠠⣺⠆⠿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠸⠀⠉⠛⠷⠿⠛⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠐⠻⣦⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢶⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣐⠲⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⣰⠋⠃⠒⠂⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠁⢰⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠛⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣐⣤⢀⣽⠃⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⠁⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣌⣡⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⠿⣿⣿⠿⣛⣛⠿⣿⣿⠿⣛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣝⡛⢿⡿⣛⣫⣝⣛⢿⡿⢛⣫⣝⣛⢿⡿⢛⣋⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣝⠻⢟⣭⣭⣭⣍⡻⢟⣩⣭⣭⣍⡻⠟⣫⣭⣭⣭⡻⠟⣫⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⣁⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢶⣄⠀⠀⢀⠀⢹⢿⣿⢇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠀⠉⠙⠳⠶⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⣀⣬⡷⠾⡋⠁⠟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣠⠀⠀⠀⢤⠀⠀⠀⠉⠛⠒⠶⠚⠲⠶⢶⢲⣾⣺⢗⡪⣽⡿⠚⡂⠀⢀⣴⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠉⠛⠛⠻⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠹⠻⠻⠁⠐⡿⠙⠙⠁⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣀⡠⣄⡀⠈⠛⠻⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⣂⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢟⠛⠉⠛⠷⣷⡤⣤⣄⡀⠀⠀⠀⣀⣴⣖⣳⠤⠀⠀⠀⠀⠐⠷⣶⣢⣤⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠛⢿⠛⠛⣛⠷⠶⠿⠿⠟⠛⠛⠿⣟⣻⡿⠛⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡛⠁⠀⠀⠀⠀⢋⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠣⡈⠿⠛⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡖⠄⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠸⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡐⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠙⠓⣦⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡭⣽⣯⡍⠁⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⡶⠞⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠩⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡍⠑⠿⡷⡀
⠀⠀⠀⠀⠀⠀⠸⣵⣀⣀⣤⣦⡄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣌⣻⣷⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠧⡀⢠⣄⣀⣀⣀⣀⣀⣀⣠⠈⠉⠬⣅⣀⣠⣤⣠⣤⣤⣠⣼⡿⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄
⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠄⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⠃⠀⠂⠐⠈⠠⠀⠈⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⢠⠀⠂⠀⠐⠀⠂⠀⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊⢥⡿⠳
⠀⠀⠀⠀⢣⠀⠁⠀⠀⠈⠀⡰⠐⢆⠀⢩⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠩⠀⢘⣄⢀⠀⡰⢅
⠀⠀⠀⠀⠈⡄⠁⢸⠉⠑⠒⠁⠀⠈⠂⠔⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⡀⠀⠀⠉⠈⠁⠠⠱⡀
⠀⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⣤⡦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⢤⡞⡻⠁⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡡⠊⡜⠀⠀⢇⠁⠚⠤⡔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢰⠁⢐⠁⠀⠀⠀⠳⡄⠀⠀⠻⡝⢧⡇⣐⢲⣄⣀⡤⡀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⡀⡤⠒⢺⡅⠀⢠⠀⠐⡆⠀⠀⠀⠀⢸⠀⠀⠀⣟⠻⠀⢏⠁⠈⢢⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⡀⡜⠑⠤⠌⢦⡀⠘⣦⣀⢀⡀⠜⠀⠔⠊⠇⠓⢖⠈⠙⢍⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠕⠒⢘⡛⠊⠍⣢⡠⠊⠢⡠⠚⠳⣠⠞⠒⠤⠒⢆⡤⠲⢖⡚⡳⣆⣞⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡹⠁⢙⠒⠶⠀⢵⠀⠀⢆⠀⠀⡆⠀⠀⠇⠀⣘⡠⠚⡉⠁⠄⠀⠀⠀⠠⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠘⡀⠘⡀⠀⡆⠀⢸⠀⠀⡇⠀⢸⠀⡠⠋⠀⢂⠀⠀⡤⠤⠊⠢⢄⡀⠁⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢱⣀⡵⠤⣰⠀⠘⡂⠀⠀⠀⡌⢠⠁⡀⠀⠀⢪⠝⠉⠈⠉⠈⢰⠇⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠈⠹⠆⠀⠺⡁⠈⠛⠀⠀⠈⡇⠀⠇⠀⠀⠀⠇⢰⣀⡀⢀⡁⠀⡑⠲⠄⠒⠒⠅⠀⠀⡘⠑⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠑⡌⠁⠘⣄⡠⠤⡀⠀⡤⠤⠰⠋⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠠⠊⠑⠠⠄⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀⠀⠀⠈⠉⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠤⡤⢤⠤⡤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⠀⠃⠘⠀⠃⠘⠀⠃⠘⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠉⠉⠋⠙⠉⠉⠉⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠤⠒⣤⣤⣒⣒⣦⣤⡒⣲⡇⠀⢀⣀⣀⡀⠤⠤⠐⢒⣒⣒⡒⠒⢊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢆⠀⠒⠊⠉⠉⠀⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⡴⣂⠉⠉⠒⣤⠔⠒⠒⣲⢆⠀⠀⠀⠀⠣⡀⠀⠀⣀⡀⣀⢀⡄⢸⣾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢰⠀⠀⠙⠎⣿⣁⣀⣠⠞⣁⠈⢇⠀⡀⠀⠙⠁⠓⢃⠛⡏⠛⠉⠀⢸⣿⠀⠀⢸⠀⠀⠧⣀⠀⡀⣤⣀⣶⢰⠀⢸
⠀⠀⠀⠀⠓⡤⠜⠋⠉⠒⡢⡄⢣⠀⢁⠜⠀⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣘⡏⠀⠀⢰⠀⠀⠊⠁⠓⠃⣉⡇⠉⠀⠀⢸
⠀⠀⠀⠀⢸⠁⠒⠲⡔⢉⠀⢸⠤⠷⠋⠀⠀⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⣄⠀⠀⢃⠀⢁⡜⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⡇⠀⣀⣀⣀⣀⣀⣀⠀⠠⠄⠀⡇
⠀⠀⠀⠀⠀⠈⠉⠒⠸⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡇⡠⠤⠤⠤⠄⠒⠒⠒⠈⠉⠓⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡚⢦⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡰⠚⠙⠒⠐⢦⡀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⢀⠀⠑⡄⢣
⠀⠀⠀⠀⠀⠀⣰⣋⣀⣀⣀⣀⣀⣀⣹⣄⠀⠀⣠⠔⡋⠀⠀⢰⡜⠋⠀⣀⠜⠚
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡝⡅⠀⠀⠇⠁⢀⡪⠔⠊⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠈⠀⠀⠀⠀⡇⠀⠳⡘⢆⡠⠴⠒⠁⠀⠀⡀⠴⠔⠒⠢⣀⠀⠀⠀⠀⢀⣀⣀⠀⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⠀⢀⡀⢀⡰⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⡙⠒⠒⠒⠒⠚⠃⢐⣀⠭⠤⠤⠀⠒⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠤⠔⠒⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠁⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠹⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡤⠴⠒⠋⠁⠀⠀⣀⡤⢾⡇
⠀⠀⠀⠀⠀⢸⠒⠚⠉⠉⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠈⢦⣠⣤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠴⢶⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢝⢢⣀⡠⠴⢲⠶⠦⣄⡀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⡅⠉⠀⣰⠋⠀⣰⠃⠙⣎⣇⠹⣄⣀⣠⣄⣀⡀⠀⠀⣠⠴⠶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣰⠒⠀⠀⢀⡏⠀⢰⠇⠀⠀⠘⢻⡶⢫⠇⠀⣾⠀⠉⢲⠞⠔⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢼⣘⣿⣠⠴⢦⠀⢸⠀⠀⣾⡋⠉⠭⣛⠿⠀⢸⡀⠀⢹⠀⠀⠀⠐⣃⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡄⠀⡏⢳⡄⠀⠒⠀⠀⠀⣇⠀⠸⡆⠀⠀⢀⠀⠩⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡟⠀⡪⠀⣄⠀⠸⣄⠀⠹⡄⣠⠏⠙⠲⠯⠥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⣢⠞⠉⠙⠲⠾⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣧⡤⢤⡤⣤⡷⠀⠀⠀⠀⠀⠀⠀⢠⠟⠲⠤⠬⡇⠀⠀⠀⠀⠀⠀⣠⠼⠁⠀⠀⠈⠦⣄⠀⠀⠀⠀⠀⠀⡟⠲⠊⠙⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢦⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⣇⢀⣀⠀⢀⣀⠀⣸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⢛⡏⠀⠀⠀⠀⠀⠀⠈⢻⡀⡍⢩⠄⡏⠁⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣇⡖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣄⣠⢧⡀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠉⠱⡖⠁⠀⠀⠀⠀⠀⠀⢀⡤⠧⠾⢤
⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⡞⠛⠒⠛⠛⠛⠋⣻⠀⠀⠀⠀⠀⠰⣧⣠⢄⣤⣤⡷⠀⠀⠀⠀⠀⠀⠀⣸⠖⠦⠔⠺⡇
⠀⠀⠀⠀⠀⠘⠲⣍⣙⣚⣉⣙⣒⣋⡹⠚⠁⠀⠀⠀⡿⠿⠿⠿⠿⠝⠛⢿⠀⠀⠀⠀⠀⠀⠘⢦⣶⣤⡞⠀⠀⠀⠀⠀⠀⠐⢾⣛⣒⠒⠒⣓⣛⡶
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠙⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⡎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡗⢯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⡔⣩⠥⠬⣝⢦⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣯⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠎⣡⠤⣍⠓⣄⠀⢳⠀⠀⠀⠀⠀⢸⢸⠁⡏⠵⣸⢀⡇⠀⠀⠀⠀⠀⢸⡁⢀⡀⢀⡀⢀⣧⠀⠀⠀⠀⠀⠀⣿⣿⣼⣧⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⡁⣄⠈⡇⢸⡆⣸⠀⠀⠀⠀⠀⠈⢮⡳⢬⣯⡵⠾⠃⠀⠀⠀⠀⠀⣿⠙⣯⢹⡏⢹⡇⣹⠂⠀⠀⠀⠀⠀⣿⣿⣯⣍⣉⣽⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡳⣌⣙⣁⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢿⢸⡇⣼⢠⡏⠀⠀⠀⠀⠀⠐⡏⠉⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠓⠛⠛⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠠⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⢮⡹⣆⠀⠀⠀⠀⠀⠀⠀⢧⢠⡤⣸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠸⠁⠀⢀⠁⠀⢳⠀⠀⠀⠀⠀⠀⣰⢻⡄⢳⠀⡟⠋⠀⠀⠀⠀⠀⢰⡋⠚⠁⠀⠙⢋⣷⠀⠀⠀⠀⢰⢏⠀⢧⠀⠀⡼⠁⡹⡆
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠃⢀⡏⠀⠀⠀⠀⠰⣎⠳⣀⢣⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠰⡏⠀⠀⠀⠀⠀⠸⣄⢹⡚⠓⠚⢑⡟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⡖⠛⠋⠀⠀⠀⠀⠀⠀⠘⠲⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⠲⣄⠙⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⢀⠔⠁⢀⡸⠉⠒⢄⠀⠐⠗
⠀⠀⠀⢎⠄⠚⠉⢀⡀⠤⠚⠆⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⠚⠛⢢
⠀⠀⠀⣧⠔⠒⠋⠁⠀⠀⣀⡔⢾⡏⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⢈⠟⠚⠑⠒⣉⠦⡀
⠀⠀⠀⠈⠦⣤⠄⣒⠊⠩⢀⢱⣀⣹⣆⡀⠀⠀⡄⠀⠀⠄⠀⡠⠚⠀⠉⠉⠉⠀⠀⢹⡀⠘⠃
⠀⠀⠀⠀⡐⢩⣆⠀⢰⠶⠋⡥⠤⠤⠒⢌⣉⡒⢄⠀⠈⠀⠠⠋⠉⠉⠉⠐⠒⠒⠒⠋⢹⣌⣉⠲⣄
⠀⠀⠀⠀⡇⣿⡇⣷⢋⠔⢊⠀⠲⠀⠐⠂⠀⠡⣀⢱⠀⠀⢰⠒⠊⠙⠋⠑⠊⠑⠛⠖⣞⡛⢿⣷⠈⡆
⠀⠀⠀⠀⢃⠹⣷⡇⡜⠀⠀⠀⢈⣒⡊⠀⠀⠀⢨⡀⡇⠀⢸⠀⠀⠀⠃⠀⠐⠃⡤⠞⣣⠼⠼⢿⣃⠇
⠀⠀⠀⠀⣀⠑⢬⡇⡱⠀⠀⠀⢪⣀⡱⣀⣀⣀⠰⠥⠷⠤⠾⢄⣄⣀⡒⠤⠔⠀⠺⣴⠁⠘⠃⢀⠙⡄
⠀⠀⠀⠈⠛⠃⠀⢣⠘⡆⠀⠂⠀⡜⢩⣄⣦⣴⣿⣿⣿⣿⣿⣶⣶⣦⡌⠙⡤⢒⣐⡣⡧⣌⠒⠈⢀⠏⢹
⠀⠀⠀⠀⢰⢒⠉⣻⠉⠛⣧⠤⣀⡏⠒⠊⠭⠿⠻⠿⠿⠿⠿⠛⠯⠍⠒⠉⡟⣁⡎⢘⢸⠀⣉⡊⠉⠢⠋
⠀⠀⠀⠀⡧⠠⠊⠀⠰⠀⠘⡖⠂⠻⡀⠀⠀⢠⣦⠀⠀⠀⠀⣤⠀⠀⠀⢠⠁⠁⣀⠎⡜⠀⠙⠋
⠀⠀⠀⠀⢣⡀⠀⠂⠀⡠⠀⢸⠀⠀⠳⡀⠀⠀⠠⣄⠀⢀⡠⠀⠀⠀⢠⠏⠭⠭⠔⠊
⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠴⠃⠀⠀⠀⠈⠲⢤⣀⡀⠀⠀⢀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢧⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠻⣧⠉⣹⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠉⠛⠛⠷⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠟⠛⠋⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠋⠉⠉⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⡆⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣶⠤⣤⣤⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⣁⣀⡀⠀⢻⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣀⣄⡀⣀⠀⣀⢀⣤⣤⡀⢀⣶⡄⠸⣯⣼⡇⠀⠘⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⢀⡻⢦⡅⣿⠀⣿⢸⡅⠰⣦⢸⡷⠻⡆⠿⠀⠙⠂⠀⣿⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠈⠓⠚⠃⠙⠶⠛⠀⠙⠛⠉⠈⠀⣀⣀⣠⡤⠶⠒⠛⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠀⠀⠀⠈⠉⠛⠒⠒⠶⠶⠶⠶⠖⠒⠒⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠷⠶⠶⢦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡶⠶⠶⠞⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣰⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠹⢦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⣿⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠖⠋⣁⡤⠴⠒⡦⠀⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠒⢋⣡⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡄⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠃⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠴⠚⠉⢉⡤⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣶⡶⠋
⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢠⣤⣀⣀⣠⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⡀⠀⠀⢠⠇⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⠀⠀⠀⡏⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠐⣇⡼⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠞⠁


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

⡠⠊⠉⠓⢄
⣇⠀⠀⠀⠀⠳⣄
⠘⢦⡀⠀⠀⠀⠈⢢⡀
⠀⠀⠉⠢⡀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠳⡀⠀⠀⣀⣀⣀⣀⣠⡴⠾⠁⠀⠀⠀⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠹⡞⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⢄⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠚⠉⠳⡄⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄
⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠘⠒⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄
⠀⠀⠀⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⡴⠒⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⡷⠄⠀⠐⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀⠛
⠈⠧⡤⣀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠠⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠄⠒⠒⠂⠉⠉⠉⠀⠀⠀⠀⠄⢾
⠀⢰⠃⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠸⣄⠈⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⣾⣟⣼⠄⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⣠⡐⡦⣀⠀⠀⠀⠀⠀⠀⠂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠘⣷⢣⢠⡍⠀⠀⠀⠀⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⡰⣟⡲⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⣀⢸⡶⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⡗⠀⠀⠀⠀⠀⠿⠮⠙⠁⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠰⣬⡳⠁⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠃⠀⠀⠠⣿⠊⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠉⢙⡇⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⢠⣴⣿⠃⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠻⢿⡿⠏⠀⠀⠀⠀⣸⣷⡿⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠾⣟⡀⠀⠀⠀⠀⣴⢿⣿⣷⡄⠀⠀⠀⠀⣀⣾⣿⣦⠀⠀⠀⠀⢾⣿⣿⠇⠀⠀⠀⠀⣶⣤⣴⣦⣶
⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⠀⠀⠘⠁⣾⣿⣿⡿⠀⠀⠀⠀⠉⠛⣛⣽⠃⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⢀⠄⢼⠷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠆
⠀⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⢀⠮⠁⠀⠀⠀⠀⠀⠐⡃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⢀⣯⡀
⠀⠀⠀⠀⠠⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠂⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣤⠖⢿⠉⡟⢑⠦⣄⠀⠀⠀⠀⠀⠀⠀⡖⠒⢏⠉⠓⢦⡀⠀⠀⡞⢳⠞⢳⠞⢛⠖⢛⡖⢛⡆
⠀⠀⠀⠀⢀⠾⣀⠳⣸⣼⣡⣋⠴⠚⢧⠀⠀⠀⠀⠀⢠⠟⢦⡀⠑⢄⠀⢳⠀⠀⣇⡏⢀⡎⠀⡞⠀⡞⠀⡼⡇
⠀⠀⠀⠀⢸⠦⠬⢵⣿⣿⣿⣷⣚⣉⣙⡆⠀⠀⠀⠀⠈⣇⠀⠙⢦⡀⠑⡏⠀⠀⣟⣀⣜⣀⣼⣀⣼⣁⣸⣁⡇
⠀⠀⠀⠀⠸⡖⠒⣩⢿⢿⢿⢯⠲⢤⣹⠁⠀⠀⠀⣠⢞⡽⠓⠲⠶⠛⠒⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡽⣏⣠⠏⡼⠸⡆⢳⡴⠃⠀⠀⣠⢞⡵⠋⢀⣀⠤⣀⣀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠦⣄⠀⠀⠀⢠⠒⡿⠛⠛⠓⣦
⠀⠀⢀⡴⡫⠊⠀⠉⠓⠓⠒⠋⠁⠀⠀⠀⣞⡵⠋⠀⠀⡇⠀⠀⠈⢉⠇⠀⠀⣼⠁⢠⠖⠓⠂⠀⠘⡆⠀⠀⡞⠉⠛⠓⠒⠋⢹
⢀⡴⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡜⠀⠀⠀⠹⣄⠀⠁⠀⠀⠀⡰⠃⠀⠀⣇⠀⠀⠀⠀⠀⣀
⠻⠚⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣼⡅⠀⠀⠀⠀⠈⠙⠒⠒⠒⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢶⠲⢤⠋⠉⠉⠉⠈⠈⠙⡤⠖⡆⠀⠀⠀⡼⠉⠉⠉⢧⠀⠀⠀⠀⢠⠤⣄⣀⠔⠚⠉⠓⢦⣀⣠⠤⣤
⠀⠀⠀⠀⠀⢯⢀⣸⣄⠀⠀⠀⠀⠀⢠⣇⠀⡝⠀⠀⢰⠁⠀⠀⠀⠈⣇⠀⠀⠀⢞⠀⠀⡏⠀⠀⠀⠀⠀⡯⠀⠀⣣
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠺⠤⠤⠤⠤⠤⠿⠀⠀⠀⠾⠴⠒⠛⢦⣀⣀⣀⠴⠋⠒⠮⠇
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⡅⡇⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⢸⢨⠆⠀⠀⠀⠀⡏⠀⢠⠃⠀⡼⠁⠀⡼⠁⠀⡼⠀⢈⡷⡄
⠀⠀⠀⠀⠀⠀⢘⡅⡇⠀⠀⡎⠁⠀⠀⠀⢹⠄⠀⢸⠠⡃⠀⠀⠀⠀⠈⠓⠛⠒⠚⠓⠒⠚⠓⠒⠚⠓⢲⠋⠀⢹
⠀⠀⠀⠀⠀⠀⢨⠆⡇⠀⠀⠈⠒⠶⠴⠒⠋⠀⠀⢸⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠚⠒⠋⡽
⠀⠀⠀⠀⠀⠀⠰⠷⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⣓⡦⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠈⠛⠳⠛⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣿⣄⡀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣿⣁⡽⢀⣀⠈⠛⣦⡴⠞⠋⠁⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣀⠀⠀⠠⡏⣹⠇⢀⡼⣧⣠⣤⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⠀⣏⣈⡷⠀⠀⠉⠁⠀⠈⠓⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⢋⠀⠀⠉⡴⢤⡀⠠⡞⢳⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⣏⣹⠀⠀⠙⠦⠇⠀⠉⠉⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠈⠁⠀⠀⠀⣀⡤⣄⠀⢰⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡤⠇⠀⣞⣹⠆⠐⢧⡤⠏⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⣸⣷⡀⠀⠀⢁⣤⣄⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⣠⡾⠋⠀⠙⠷⢦⣼⡧⣾⠟⠋⠁
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠸⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡴⠛⠉⠻⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣿⣛⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


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

⠀⠀⠀⠀⠀⢀⣤⠖⠂⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣀⡀
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠇⠀⠠⠲⠏⠣⠀⣠⠤⠄⠀⠈⠀⠀⠀⠀⠁⠐⠠⣴⣇⠀⠀⣀⡠⠆
⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⣇⠀⠈⠀⢀⣀⡀⠀⠀⣀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⣀⠀⢴⡇⢀⣶⠘⠦⡌⣀⣾⡧⠃⠀⣾⡧⠃⢀⣿⠁
⠀⠀⠀⠀⠀⢀⠤⠒⠈⠹⣿⡄⠀⢸⣇⠜⣿⠀⢠⠁⠀⢿⡀⢀⠜⠻⣀⡠⠊⣿⠀⠀⠠
⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⣿⠁⠀⠀⠉⠀⢻⣠⠂⠀⣶⠀⠉⠁⡀⠀⠀⠀⠀⣿⠀⢠⠃
⠀⠀⠀⠀⠀⠣⣀⣀⡤⠟⠁⣰⡇⠀⠀⣼⠆⠀⠀⢀⡏⢀⣤⠀⣠⡄⢀⠀⣤⠘⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡟⠀⠀⠀⠸⡇⢸⡏⠠⣟⠀⢾⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠃⠀⠀⠀⠀⠓⠀⠀⠀⠈⠁⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣀⡀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⢠⣾⡿⠁⠀⣼⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢠⣿⠟⠁⣠⣾⠟⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠈⠁⢀⣴⡿⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⣴⡿⠋⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠛⠛⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⣠⡄⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠸⠗⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⠁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠸⠗⠀⠀⠀⠙⠻⢿⣦⣄⡀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠀⠰⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⡀⠀⡀⠀⠈⠙⠿⣶⣤⣿⠃⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋⠀⠀⠀⠾⠎⠛⢿⣦⡀⠀⠀⣠⣿⠏
⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢠⣤⠀⠀⠠⣦⠀⠀⠀⢀⡀⠀⠀⣤⡄⠙⢿⣦⣼⡟⠁
⣰⣾⣿⣻⡿⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠋⠀⢀⣤⠀⣤⡄⠹⣿⣿⣶
⣿⡏⠙⠻⠿⣶⣦⣄⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⢠⣦⠀⠈⠋⠀⠀⠀⠀⠉⣀⣬⣶⡿⠟⠉⣿⡆
⣿⡇⠀⠀⠀⠀⠈⠙⠛⠻⠿⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⡶⠿⠛⠋⠁⠀⠀⠀⢻⣇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠋⠁⢸⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢰⣶⣶⡾⠿⠟⠛⠉⠁⠀⠀⠀⠀⣾⡇
⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠃
⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⠿⢛⣿⡿⠁
⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠻⠿⠿⠛⠛⠛⠋⠉⢁⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠩⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⡀⠀⢀⣀⡀⢀⡀⠀⢀⠀⠀⢀⣀⡀⠀⢀⣄⠀⠀⣀⠀⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⠁⠰⣿⡉⠋⢸⣿⠀⣿⡇⢰⡿⠙⠃⠀⣼⣿⡄⠀⣿⣷⡄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠙⣷⡄⢸⣷⠀⣿⠃⢸⡇⢺⣶⠀⣿⣾⣧⠀⣿⣿⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠈⠀⠻⠶⠿⠁⠀⠻⡾⠏⠀⠸⣷⡿⠁⢸⡿⠀⢿⠆⣿⡿⣧⡀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡦⠓⠀⠠⢤⣤⣤⣤⠀⠀⠀⠀⠀⣤⡤⠤⠶⠒⠋⠁⠀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⣀⣀⣬⣬⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣁⣁⣀⡈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠀⣂⠶⠒⣀⠴⠖⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⡠⠄⠂⢉⠠⠔⠊⠀⠀⢀⠀⠤⠐⠉⡻⢖⠠⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠋⠁⣀⠠⠊⣀⠔⠉⠀⠀⣀⠠⠒⢉⡠⠤⠐⠊⠁⡠⠊⣉⠬⠛⠀⠐⢄
⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠉⡠⠔⠊⠀⢠⠔⢈⠤⠠⡔⠊⠁⣀⣀⡠⠔⠉⠄⠈⠀⢀⡠⠄⠒⠂⢑⣀
⠀⠀⠀⢰⠁⠀⢀⠔⢁⠔⠉⢀⠠⠔⡞⠁⠀⠥⠖⠒⠻⣄⠔⠧⠬⡁⠂⠁⡠⠄⠂⣁⠤⠐⢉⡡⠒⠉⣆
⠀⠀⠀⣾⢀⠎⢡⠔⠁⢀⠔⢁⠤⢺⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⡠⠒⠉⢀⠠⠐⢁⡠⠊⠁⠘⡄
⠀⠀⢀⡿⠃⠰⣁⠄⠊⣁⠔⠁⠀⠈⢺⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡠⠊⡡⠔⠊⠁⠀⠀⢀⠠⡇
⠀⠀⠸⡨⠀⠉⢀⠔⠉⠀⠀⠀⡀⠐⢀⠠⠘⠉⠈⡉⠔⢀⠤⠊⠁⠀⢀⠀⠊⡠⠊⠀⢀⣀⠤⠀⠊⣀⠄⡇
⠀⠀⠀⢳⠧⡈⠁⠀⠀⠀⢠⠊⡠⠀⠁⡀⠄⠒⢁⠠⠒⠁⠀⢀⠠⠂⣁⠤⠊⠀⡠⠒⣁⠤⠔⠂⢁⡀⢀⠃
⠀⠀⠀⠀⢣⡈⠑⠢⡀⠀⠃⢰⡠⠊⡁⠄⠒⠉⠀⠀⠀⡠⠊⢁⠔⢊⣀⠤⠒⢉⠤⠊⠀⠀⣀⠔⠁⡸⠃
⠀⠀⠀⠀⠀⠑⢄⠀⠑⡄⠄⠈⡠⠊⠀⠀⠀⠀⠀⠀⠐⠀⣔⠅⠊⣁⠤⠐⠊⠁⠀⠀⠀⠊⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣸⠀⠀⢠⠐⠒⠒⠦⡀⠀⠀⠘⠤⠠⠐⢈⡠⠖⠉⠀⠀⠀⠀⣸⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠮⣄⡀⠀⠀⢡⠀⠀⠀⡴⠁⠉⠁⠀⠀⢀⣀⣄⢀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠦⡀⠔⠓⠒⠒⠂⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡉⣆⡀
⠀⠀⠀⠀⠀⠀⠀⡠⣤⠤⣴⣷⣏⣴⢗⡄⠀⠀⠀⣀⠤⠤⠤⠇⠀⠀⠐⢢⠀⠀⠀⢀⣠⠤⢤⢼⠑⠀⠨⢳⡄
⠀⠀⠀⠀⠀⣴⠋⡔⢁⠞⢀⠼⡛⠓⠉⠀⠀⢠⠊⠀⠀⠀⠀⠀⡗⠒⠂⠁⠀⢀⡔⠫⢐⠠⢀⠀⢸⠒⠛⠈
⠀⠀⠀⠀⣸⠃⡜⡰⠃⡠⢋⡼⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⣜⠀⠈⠐⠨⢐⠀⡾
⠀⠠⢔⣶⢿⣜⣰⠁⣔⣡⠟⠁⠀⢀⠄⠒⠚⠂⡀⠀⠀⣀⡴⠋⠀⠀⣠⠰⢖⠳⡨⢀⢐⢨⡰⠟
⠀⠙⢵⠁⡜⡿⠉⠉⠉⠀⠀⠀⠀⠈⠢⠀⠀⢀⠏⠉⠉⠀⠀⠀⠀⠀⠓⣌⠐⡐⡎⠉⠉⠁
⠀⠀⠈⠙⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠋⠉⠙⠛⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠛⠋⠉⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢷⣄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣴⣿⡿⠛⠛⠛⠿⠿⢿⣶⣦⣄⣀⠀⢀⣴⣿⠏⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠋⠁⢀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⡏⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣹⣿⡿⠶⢶⣶⣶⣶⣶⣶⠾⠿⠛⠁
⠀⠀⠀⠘⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⡿⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⣰⣿⠋
⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣀⣠⣴⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣋⣁⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛
⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟⠛⠋⠉⠁⠀⠀⢀⣀⣠⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠿⢿⣿⣿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉




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

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⣀⠌⠉⠠⣃⠀⠀⠀⠀⠀⠸⠉⢶⠃⡇⠀⠀⠀⠀⠀⠐⡧⠶⠤⠴⠯⠭⠍⠠⠤⠬⠟
⠀⠀⠀⠀⠀⢏⠀⠉⠂⣾⢡⠀⠀⠀⠐⠂⠄⠀⣹⠀⠚⠀⣨⠃⠀⠀⠀⠀⠀⠑⢠⠞⠀⠀⢀⠀⡄⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⠀⡰⠁⢀⠀⣿⠀⡀⠀⡁⠀⡀⢀⡄⢸⣄⡈⠀⠝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡌⠀⠀⣀⡀⠀⠀⠠⠤⡀⠀⡇⠉
⠀⠀⠀⠀⠀⢈⡆⡀⢀⡽⢆⡀⠀⠀⣀⣀⣠⡤⠞⠀⠉⠓⠲⠚⠀⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢰⠃⠀⡀⠣⢟⡀⠴⢐⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠸⣨⠔⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⢣⠈⡇⠀⠀⠀⠀⡜⠀⠀⠚⠀⠥⠝⠰⣉⠇⣴⠂⣷
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠒⠃⠙⠲⡄⠀⢠⡇⠀⢎⣨⠂⢜⠂⡶⠀⠘⠔⠁⢻
⠀⠀⠀⠀⠁⠀⠀⠀⣠⠀⠀⠀⠐⢮⡁⠀⢯⠀⠀⠀⠀⠀⠀⠀⢰⠒⠠⡀⢠⠀⠀⠀⠀⣰⠃⠀⠈⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠒⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⢔⠒⠁⠀⣰⠃⠀⠓⠶⠖⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠖⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⡨⠆⠀⠀⠀⠀⠀⠸⠧
⠀⠀⢐⡆⠀⠀⠉⢀⠴⠂⠉⠀⡤⠉⠙⠦⡀⠀⠀⢀⢒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠓⠁⠀⢀⣀⠀⣀⡀⠀⠁⠔⠒⢢
⠀⠀⠈⢠⢢⠄⡔⠁⠘⣀⡤⠤⣄⡀⠀⠄⠙⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⡠⠔⠢⡄⠀⢀⠔⠊⠁⠀⠀⠀⠈⠓⣎⠀⠀⡞⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠆⠀⡞⠀⠀⡼⠁⠀⠀⣄⠙⢦⠀⡤⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⢦⠏⡀⡜⠀⡐⡐⠀⡀⢀⢘⡇⠀⠈⠓⡆⠀⠀⣹⡗
⠀⠀⢰⠀⢸⡃⠀⠐⡇⠀⠄⠀⢸⠂⠘⡇⠀⠀⢸⡄⠀⠀⢴⡞⠀⠀⠀⣏⠅⠀⠐⢿⡔⡜⠀⡔⡰⠀⡰⢡⢃⣼⣁⠀⠰⡞⠁⠀⠈⠓⠃
⠀⠀⢸⠀⠈⣇⠀⠄⠈⠲⠤⠴⠋⠀⢰⠇⠘⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢈⡆⢈⠈⡴⠻⢤⣜⣜⣀⣔⣴⠷⠋⠀⠙⠣⣀⡟
⠀⠀⠀⢧⠠⡌⠦⣀⠀⠀⠀⠐⢀⡰⠋⠠⠀⢀⡟⠀⠀⠀⠀⣠⠀⠀⠀⢯⡐⣡⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠳⣄⠀⠈⠙⠒⠒⠛⠉⢀⡀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠖⠀⠀⠀⠀⠕⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣤⣤⡭⠴⠛⠁⠀⠀⠀⠀⣀⣠⠎⠉⠐⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣍⡉⠙⢳⡄
⠀⠀⠀⡰⠤⠆⠀⠀⢴⡄⢰⢸⠀⠀⠀⠀⠀⠈⠃⠀⠈⢆⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⡞⠡⣠⡞⠉⠉⡇⠈⣿
⠀⠀⠘⠢⡤⠷⠀⠀⠀⠀⢸⢸⡆⢀⠀⠀⠀⠀⢀⣀⠀⠀⠖⠲⠶⠞⢣⡀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⣰⠋⣄⣰⠋⠀⢠⡞⠁⣸⡟
⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢸⠸⡇⠘⠇⠀⠀⠀⠬⠄⠀⡐⠀⢀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣧⡜⠁⠀⠀⠈⠙⠛⠋⠀⠀⡀
⠀⠀⠀⠀⢠⢄⠀⠀⠈⠃⢸⡆⡇⠀⠀⠀⠀⠀⠀⢠⠞⠃⠐⣒⢋⣀⠀⢀⡆⢳⡀⠀⠀⠀⠀⢠⢾⠘⣦⠋⠀⠀⠀⠀⣠⡂⠀⠀⠀⠘⠃
⠀⠀⠠⠒⠇⢸⠀⠀⢀⠀⠈⡇⣧⠀⠀⠀⠀⠀⢠⠃⣈⠣⠐⠊⢀⠂⢂⢠⠀⣸⠃⠀⠀⠀⡰⢧⢀⡿⠃⠀⠀⠀⠀⢀⡽⣓⢦⡀
⠀⠀⠀⠁⠀⠞⠀⠏⢏⠇⠀⡇⢿⠀⠀⠀⠀⠀⠘⠦⣌⣃⡈⠀⠚⢀⣑⣨⡴⠋⠀⠀⠀⠀⠳⠼⠟⠁⠀⠀⠀⠀⠀⢾⡘⠀⡇⢱⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠀⢧⠜⠀⠀⠀⠰⡷⠂⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠫⠭⠴⠃⣠⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⣧⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠄⢳⣴⣎⠑⢀⠉⢠⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣈⡛⣺⣿⣄⠷⡀⠈⠄⠀⠆⢩⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣉⣽⣿⣿⡥⣶⣷⣦⡴⢾⣿⣥⢍⢼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣹⡇⣊⣶⣦⢿⡿⢻⣟⣉⢁⣄⠀⠛⣿⡎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⣻⡟⢸⣿⣍⡰⣶⠾⡻⠇⣻⣅⢿⡷⣠⠄⢻⣧⠈⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣾⣿⠻⣽⣇⠈⢯⣿⣿⣶⣾⣿⣋⡈⣧⡼⢾⠃⣀⣻⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠛⡟⣿⣆⠈⠛⠳⠄⣉⠛⣿⡿⢿⠿⠿⣻⣿⣿⠟⠛⠉⣁⡴⠀⠀⠀⠀⢘⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠁⠶⣿⣿⣄⠀⠀⠀⠀⠉⠛⠲⢤⡄⠒⠛⢋⡥⠖⠛⠉⠉⠀⢀⠜⠁⠀⣼⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡄⠀⠈⠻⣿⠳⠦⠤⣤⣀⣀⣀⣽⡷⠒⠉⠀⠀⠀⢀⣤⣎⣠⣤⣤⢾⠁⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠠⣿⣿⣿⠀⡀⢰⣼⣦⣤⣤⣤⡾⠟⢋⡁⣀⣀⣀⣤⣤⠖⣻⠛⠉⡼⠋⠀⠸⠀⠈⣧⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠁⠙⢿⢷⣦⣤⣮⣿⣿⠿⠶⠛⠉⠉⠉⠉⠉⠁⠀⢀⡼⠁⠀⠠⠀⠀⠀⡆⠀⠀⡼⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⠀⠤⣚⣿⣫⣽⡎⠁⠀⠀⠀⠀⠀⢀⣀⡠⠾⠋⠀⢀⡴⠀⠀⠀⠀⠀⢀⣼⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠀⣀⣼⣷⣋⣀⡤⠔⠊⠁⠀⠀⣀⣴⡦⠖⠋⠀⢀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣐⠛⠿⠿⠿⠶⢶⣦⡶⢾⢛⡋⠉⠉⠛⠛⠻⠿⠶⠶⠖⠛⠉⠁⠀⠀⣀⣴⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢶⠟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠁⠀⡍⠙⠏⠁⠀⠲⢦⣶⠶⡖⠒⡲⠞⢻⠛⠉⠹⠏⠀⠂⢳⢠⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢨⡇⠘⡀⢰⠄⢠⠀⢠⠀⠀⠧⠀⠀⠀⠘⠃⢸⠃⠇⢸⠁⡄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣧⣄⣇⢸⡄⠀⠀⠈⡄⠀⢰⠀⠀⠀⢸⠀⢾⠀⠀⡘⢠⡧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢿⣧⣿⣏⡿⢸⣧⠐⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⡕⠀⠀⣇⣘⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣦⣿⣿⣿⣅⣀⡻⠆⠈⠀⢷⣀⠘⠀⣀⢀⡾⠀⠃⣐⣀⣩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢿⡿⢽⣿⡿⣿⣿⣶⣶⣶⣷⣶⣶⣶⣿⣶⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡚⢿⣿⢿⣿⣽⣟⣛⣻⣿⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠛⠍⠛⠷⠛⠛⠉⠉



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⢸⢻⣿⢿⣳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠛⢵⡞⢣⣾⠸⡏⢷⡏⠳⣌⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡱⢮⢀⢠⡖⠙⠁⢀⡿⢸⣧⠐⣿⠀⣿⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠛⠒⣻⣛⣩⡤⠿⠧⠺⠏⢠⣟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⡠⠴⠒⠛⠛⠉⠁⢛⣃⡀⠤⠐⠊⠉⣋⣴⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⢀⣠⣶⣶⣿⠿⠿⠛⠛⣛⣻⡿⢛⣽⠏⣿⣿⡝⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣀⡴⠟⠋⠉⣉⢹⠭⠤⠒⢊⣉⣻⣅⠴⢛⡯⢃⣿⣿⣿⢸⣇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡞⠋⠀⣠⠖⠋⠁⢀⣤⠖⠂⠉⠁⠀⢀⣀⣨⡤⠞⣹⣿⠏⣸⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣧⣿⠀⣰⠋⠀⠀⣰⠞⠉⠀⣀⠤⠖⠊⠉⠀⣀⣀⡴⠞⣋⠤⠞⠟⢳⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠘⢿⡄⣧⠀⠀⣴⠁⠀⣰⠞⠁⢀⣠⡴⠚⠋⠉⣠⡴⠋⠀⠀⣀⣤⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⢤⡀⠀⠉⠚⠧⣄⣿⡀⣼⡏⢀⣴⣿⠁⢀⣀⣤⢾⣿⡏⢛⡿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢆⠉⠉⠊⠓⠰⠤⣍⣉⣙⣛⣻⣛⣻⣟⣿⣵⣾⣴⣾⢿⠿⡟⢻⠏⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⡍⢩⠉⣏⠉⡯⢹⠇⢹⡇⣾⣼⢸⡇⣿⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡗⢸⠀⣸⢁⡏⡇⣸⢧⡏⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⢸⡆⡿⢘⠀⡾⢸⢃⣉⡏⣿⢸⣿⣿⣿⣆⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⡄⢡⠰⢠⠀⡆⢀⠰⠈⡇⡻⣸⢰⡇⣼⣴⢼⢳⣿⣾⣿⣿⣿⣿⣿⣶⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡺⡎⣦⣇⠡⠀⡇⡆⣷⢾⣾⢸⣷⡟⣿⣿⣸⣿⣿⣿⣿⣿⣿⣯⡿⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⢿⣿⣄⣧⣓⣱⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⡿⡏⠻⢿⠷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠶⠶⠶⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠳⢤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡶⠶⠟⠋⠉⠀⢀⡿⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠻⣦⡀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⢤⣀⠻⣤⣈⡙⠳⢦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠖⠋⣁⡰⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠉⢳⡘⢷⢮⣯⡹⣦⣤⣀⣀⣩⡭⠿⠿⠿⠭⣤⣤⣤⡴⠶⠞⣉⡴⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡆⠹⣟⠳⢦⣍⣉⣁⣀⣀⢀⣀⣀⣀⣀⣤⠤⠖⠛⠉⢀⡴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢰⡄⠈⡇⢹⡀⢸⡆⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢀⣀⣠⡤⠄⠀⠉⢠⡿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠃⠀⣧⠀⠀⠐⠒⠒⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⣠⡴⠋⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⣼⠀⠀⡿⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠴⠒⠋⠁⣠⠞⣽⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣸⠇⡿⠀⢰⡗⠦⣄⣀⣀⣀⣩⡥⠶⠛⠒⠚⠛⠓⠶⠶⢛⣩⣾⡃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡿⢰⡇⠀⣾⠷⢦⣬⣉⣉⣉⣀⣀⠀⢀⣀⣀⣀⣤⣴⠾⠛⠉⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⠃⣼⠀⢸⠏⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⢀⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⠏⣰⠇⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠚⠉⣠⡿⣧
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢠⡞⢁⡼⠃⣰⠋⢠⡞⢣⡉⠓⠶⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠾⣫⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣞⣩⡴⢋⣠⠞⣁⡴⠋⠹⣦⡳⠶⣄⠀⢀⣈⣭⣙⣛⣛⣛⠛⠛⠛⠛⠋⣉⣤⠞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠠⠖⠛⠚⠋⠉⠀⠀⠀⠈⠛⠶⣬⣍⣉⡀⠀⠀⠀⠈⠙⠛⠛⠋⠉⢉⣉⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠹⣿⣿⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠉⠉⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⡘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣴⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠋⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠉⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣤⣶⣿⡿⠟⠁
⠀⣴⣾⣿⡿⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣦⣤⣄⣀⣀⣀⣤⣤⣶⣿⣿⡿⠟⠉
⠀⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠘⣿⣿⣄⣀⣀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣷⡄⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⢠⠠⡄⠤⠠⡄⢤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣃⣘⣀⣃⣈⣀⣃⣙⣀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣒⡚⡰⣶⣮⣭⣷⣶⢞⡑⣇⠀⢠⠤⠤⠤⠒⣒⣂⣉⣭⣭⣉⠉⢹⠃
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠈⠣⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⢠⠛⠤⣀⣀⣙⠖⠊⠉⢩⠟⢆⠀⠀⠀⢘⣢⡄⢠⢠⣄⡤⡤⡆⠈⣿⠀⠀⢸⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡀⠀⢸⣡⣇⠒⠐⢶⠁⢠⠈⡆⠠⠀⠈⠀⠈⠉⢌⠗⠉⠁⠀⠀⣿⠀⠀⢸⠀⠀⣓⠤⣀⡤⣶⠰⡷⠫⠀⡇
⠀⠀⠀⠀⢹⣚⡉⠀⢀⡭⠛⡄⢧⢀⡜⠁⢸⠤⠤⠤⠄⠀⠀⡀⠤⠤⠤⠬⠿⠀⠀⠘⠀⠀⠁⠀⠉⠰⠴⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢸⠀⠈⠙⡇⠦⡄⣿⠘⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠦⣄⡀⣇⣀⠔⠁⠀⠀⠀⠀⠀⠢⠤⢤⡄⠀⣀⣀⡀⢠⡤⠔⠁⠀⠀⠀⡇⠀⠤⠤⠄⠀⠒⢒⣂⡈⣅⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠧⠞⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⢣⠙⣆
⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⡠⠔⠋⠀⢀⣴⠄⠀⢣⣸
⠀⠀⠀⠀⠀⠀⡏⠈⠂⠘⠀⠀⠐⠀⠛⡆⢠⠔⠉⠘⢠⠤⠞⡳⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠀⠀⠀⠀⢰⠀⢺⡘⢄⠀⢀⡠⠴⠊⠁⠀⢀⣀⡠⣀
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠀⠀⠀⠀⡸⠀⠀⠑⠜⠋⠉⠀⠀⠀⢠⠮⠥⢀⣀⣈⣑⣄⣀⠤⠒⢒⣂⣈⣉⣉⠩⠭⠝
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠐⠒⠒⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⣀⡤⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⣒⠺⣄⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⣽⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡥⡦⡙⡦⡍⢆
⠀⠀⠀⠀⠀⢀⣐⡙⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡈⠈⠀⢇⢣⠀⠀⠀⠀⠀⠀⠀⠈⡄⣦⢧⡑⢧⡆⡌
⠀⠀⠀⠀⠀⠹⣀⣹⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠧⠤⠤⠼⠤⣆⠀⠀⠀⠀⠀⠀⠀⢎⡴⢋⣋⠷⣜⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⢲⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡀⠉⠢⡀
⠀⠀⠀⠀⠀⣼⡓⢓⣲⣒⠛⣲⡄⠀⠀⠀⠀⠀⠀⠀⢏⠉⠀⠀⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⣏⢈⡧⠤⡇
⠀⠀⠀⠀⠀⣿⢿⣻⠇⠿⣻⢿⡇⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢠⢖⠫⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⢎⠢⡑⢌⡞⠀⠀⠀⠀⠀⠀⠀⠀⣸⡒⣊⣑⢒⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡭⡣
⠀⠀⠀⠀⠀⡠⠚⡵⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠚⠒⠒⠒⠲⡇⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣨⠟
⠀⠀⠀⠀⠈⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠒⠒⠒⠓⠀⠀⠀⠀⠀⠀⠈⠃⠍⠍⠩⠍⠋

⠀⠀⢀⣠⣶⣶⣤⡀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⣠⣶⣿⣿⡆
⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⠟⠁
⠀⠀⠉⠛⠿⠟⠉⠀⠀⠀⠀⠿⣿⣿⡿⠇⠀⠀⢠⡾⠋⠉⠁

⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⣶⣿⣿⣷⡆⠀⠀⠀⢀⣤⣶⣶⣤⡀
⠀⠀⢿⣿⣿⣿⣶⣦⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠿⣿⠿⠛⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠈⠻⠿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠠⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⣾⣿⣿⣿⣷⣦⠀⠀⢰⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠻⠟⠹⠿⠋⠁⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠘⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⣠⣴⡄⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⢀⣤⣾⣿⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣾⡿⠟⠋⠀⠀⠀⢾⣿⣿⡿⠟⠁⠀⠀⠘⠿⢿⣿⡿⠿⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⣠⣾⣿⣿⠇⠀⠀⣠⣾⣿⣿⣿⣷⡀⠀⠀⢀⣼⣿⣿⣶
⠀⠀⢼⣿⣿⡿⠋⠀⠀⠀⠻⣿⣿⣿⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿