Dampish Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣩⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢀⠤⢄⠐⠿⠂⠀⢠⣯⡿⠁⠀⡸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠒⢦⠀⠀⠀⠉⠀⠀⠣⣠⠶⠁⢀⠤⠚⠁⠀⣀⣈⠒⡿⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⣤⡴⠀⠀⢀⡴⠒⢄⠀⣀⠤⢚⠕⠲⣽⠇⡼⢠⣼⠆⠙⢃⠖⠙⣄⠀⢠⠒⣢⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠬⠽⠀⠀⡔⠊⣑⣦⠿⡋⠁⠀⠢⣀⣰⠏⣠⡝⠋⠀⢀⣠⠜⢀⣀⡈⢦⣈⢛⡁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⡞⠙⣧⣾⠃⣀⠤⢀⣈⡁⠀⠈⣁⠀⣰⠋⢀⡠⠯⣠⡼⠀⢣⡀⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⢄⡀⢀⡠⠖⠋⠀⢯⡝⠛⡇⠀⢀⡇⠤⣯⠛⠁⠀⠘⠾⠀⡆⠀⡊⠀⢀⠈⠁⠀⠀⠹⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⢿⠁⠀⠀⡄⢰⠀⡘⢠⠁⠀⠃⠀⢀⡾⠀⣞⣱⠀⠀⠀⠸⡄⠑⠄⠪⠊⠀⠀⠀⢀⠘⣅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠢⠼⢄⣼⠇⠰⢰⢡⢃⢣⣅⡇⠀⠀⠑⠚⠟⠁⣠⣚⡅⠀⠀⠠⢤⠘⠀⠀⠀⠀⢀⠤⡀⠙⡇⡸⡞⠀⠀⣴⠉⠈⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⠀⠀⠀⢠⠢⢠⢃⠇⠆⡌⡾⣴⡟⠀⠀⠀⠀⠀⠘⠶⠏⠀⠀⠀⣈⣉⡴⠀⣏⡆⠀⠘⠶⢁⠀⡆⡁⡇⢠⠋⠉⡑⡬⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠄⠀⠀⢀⠀⠀⠆⡆⡌⡼⠰⢠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢮⡀⠠⡇⠀⠀⠀⠀⠀⠰⠀⠀⠃⢀⢃⠀⠓⠏⢚⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢢⠐⠡⢂⠐⡘⢠⢃⠃⡆⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠜⠞⣵⡆⠀⠀⠠⣲⡼⠘⢀⡀⠈⡮⠀⠀⠀⠈⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣐⡀⠀⠸⣄⠀⠡⣂⠁⡆⡜⢸⠀⢣⠃⠀⠀⠀⠀⡠⠒⢢⡀⡘⠱⠤⠥⠆⠀⠈⠁⠀⠂⠆⠉⠀⠀⠸⡇⢘⢦⠖⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣸⠀⠈⠳⡀⠥⢂⠀⠃⠇⡘⠜⠀⠀⡠⢤⠀⠙⠦⠟⢀⠇⠀⠀⠀⠀⣰⠸⠀⠀⢀⠤⢄⠀⢰⠀⠈⠁⠘⠦⠮⠃
⠀⠀⠀⠀⠀⠀⠀⡎⠈⢵⠀⠹⣥⠀⠀⢱⠀⠁⠂⠘⢠⢁⠃⠀⡎⢴⠈⠒⠉⢧⠠⠊⠀⠀⢠⠸⠀⣠⠔⠊⡆⠸⠀⠈⠳⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⢹⠀⠀⠀⠱⡄⠀⠀⠀⠘⠸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠔⠋⠀⠀⢰⠃⠄⠇
⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠶⠀⠈⣜⣤⠣⠀⠘⠤⠔⠉⠱⡀⢀⡔⠀⠀⠀⡀⠀⢀⠀⢀⡌⠀⠀⠀⠀⠀⢸⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠤⠤⡀⠈⠀⢣⡑⡀⠀⠀⠀⠀⠈⠉⠀⡀⠆⢃⡤⠒⠁⢷⣘⠇⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣔⠄⠀⠀⠀⠙⢄⡁⠀⠀⠀⠀⠤⢂⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⡴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠔⡀
⠀⠀⢀⠤⠤⣤⢦⡄⠀⣀⢀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠉⠉⠀⠀⡀⠀⠀⠀⠀⢀⡖⢉⣵⡄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⡀
⠀⠀⠛⠀⠬⠸⣋⣉⣈⡓⠆⠀⠉⠉⠉⠠⢾⠆⠑⢦⡖⣊⣉⠁⠄⠉⣱⡶⠤⠤⠥⠤⠤⠐⠒⠒⠉⢀⣎⡵⠐⠂⠤⠤⠄⢠⡄⢈⣒⣛⣉⠀⠀⢠⠔⠒⡏⢙⣆
⠀⠀⠀⠀⠮⣁⣀⡠⠤⠤⠒⢳⠘⠚⠛⠶⠶⠦⠴⠤⠄⢀⣐⣂⣀⣤⠞⠓⢭⡭⡭⠭⢭⣭⠭⠉⠀⣉⠀⠉⠬⠭⠭⠾⡽⢷⣀⣁⡐⣲⢴⣈⣱⢌⡥⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠴⠐⣒⡀⣶⡲⢤⣀⣸⠛⠣⢤⡤⣤⠏⠭⢡⡜⢉⣣⡜⠛⠉⠙⠣⣄⠋⠰⡁⠉⠓⢼⣒⣢⠃⠀⠀⠀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⢬⣶⠯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠓⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣭⣔⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠛⠿⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡷⠀⠀⠀⠈⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠬⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⣰⣶⣤⣄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⣧⡉⠛⠻⢿⡇⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠭⠤⠀⠀⢀⠀⠊⠛⡄⣄⡜⠁⡈⢀⣀⠂⢀⡀⠀⠀⢀⣀⡀
⠀⠀⣀⠤⠄⡒⠖⠛⠉⠉⠁⣀⡤⠴⠖⢒⣋⣩⠭⠭⢉⡉⠉⢡⠇⠈⡧⠬⣩⣉⣉⡚⠒⠒⠦⣄⡈⠉⠉⠑⠋⠤⢀⡒⠠⠄⣀
⠐⠉⠀⡴⠉⠀⠀⠀⠐⡈⣼⠁⠀⣰⡾⠋⠁⠀⢰⠁⠀⠀⠒⠁⠀⣀⡐⢤⢀⡀⠨⡉⢻⣮⡅⠈⠻⢶⣔⠀⠀⠀⠀⠘⢲⣄⠀⠉⠒⠤⡀
⠀⠀⠀⣇⠄⡀⠀⠀⠀⡂⣿⠀⠀⠐⠷⣄⢀⠀⠀⠉⠒⠤⣤⡄⣀⡈⠉⣓⠱⠡⠐⠁⣼⠋⣳⠀⠀⢨⠙⡅⠀⠀⠀⡂⢕⢽⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠢⣄⡄⢄⢄⠀⠈⠺⣄⠦⠀⠀⠉⠚⠒⠬⠶⣶⣶⣦⣦⢿⣿⣶⣶⣶⢪⠬⠄⠊⢁⢔⠖⣑⠔⠀⠀⡐⡑⣌⠦⠋
⠀⠀⠠⢄⠀⠀⠈⠀⠈⠪⠦⣆⣄⣉⢁⠉⠈⠀⠪⠧⢶⣒⣲⣷⣬⣤⣆⣠⣀⢠⣀⣒⠞⠭⠅⠐⠋⡁⣄⣌⡴⠔⠋⠁⠀⣀
⠀⠀⠀⠀⠉⠐⠢⠤⠤⢀⣀⡀⠀⠈⠉⠉⠓⠒⠒⠐⠤⠤⠦⠾⠿⠶⠖⣍⣾⠤⠥⠤⠴⠖⠐⠒⠋⠉⢁⠀⠤⠄⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠒⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⠈⠤⠄⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠤⠄⠀⠀⠀⢀⡀⢀⣀⣉⣉⠉⡉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣼⣶⣾⣭⡁⠒
⠀⠀⠀⠀⢀⡴⠿⣶⡷⣶⢏⣵⣿⠵⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⡟⢻⡓⠆⠄⠀⢀⣠⠤⠄⢀⣀
⠀⠀⠀⠀⠘⠀⣶⡿⢻⣯⢿⡾⠃⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⡇⠹⡟⠀⠀⠀⠟⢻⣦⠳⠿⢻⠍
⠀⠀⠀⠀⠀⢀⠏⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⢄⡀⠀⠀⠙⠤⡀
⠀⠀⠀⠀⢀⠎⠀⢀⡴⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢄⡀⠈⠒⢄⡀
⠀⠀⢀⡴⠃⢀⣤⠊⠀⠀⠒⠂⡖⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣄⠈⠢⣄⡄
⠀⠐⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⠈⠃
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠣⠴⣦⡄⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠾⣄⣀⡀⠘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣄⣀⡈⠙⢢⠄⠀⢀⣀⣴⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠒⢲⠓⠐⣾⠿⢇⣴⡾⠛⠉⣩⡿⡋⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠩⠐⠂⠀⠀⠀⠀⠀⡈⠁⠈⠑⠲⣶⣿⠗⠘⢧⠐⠂⠤⢀⡀
⠀⠀⠀⠀⢠⠔⡃⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨⠻⣷⡀⠀⢸⠀⣤⣄⣀⠈⠒⠂⠀⠀⢀
⠀⠀⢀⡼⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⢀⠀⠈⠙⢶⣨⡴⣂⡍⠙⠛⠒⠲⢤⣄⣀⠈⠁⠀⠂
⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠀⠉⠸⣿⣷⣄⡠⢐⠦⢄⣂⠍⠉⡛⠒⠒⠤
⢠⡏⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠉⠉⠻⢶⣦⡘⠁⠉⠶⠲⣶⣶⣿
⣾⠐⢁⡚⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣤⢶⡤⠏⠁
⡇⠀⠀⣠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉
⡇⠀⠀⠣⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⡄
⢡⠂⠸⡤⣛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠘⡄⠆⢡⠗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠾⡇
⠀⠱⠒⣘⡮⣀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢠⣓⣡⢽⡁
⠀⠀⠱⣍⡄⠡⠔⣃⣀⠄⠐⠐⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⢶⠐⣿⢏⠁
⠀⠀⠀⠘⢶⠐⠲⣝⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣸⣷⡦⡘⣱⠇
⠀⠀⠀⠀⠈⠳⣆⠓⠒⣎⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠁⢀⡀⠈⣽⣫⢿⣿⠌⠂
⠀⠀⠀⠀⠀⠀⠈⠣⡄⠀⢼⣇⣦⢤⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣀⠰⠋⢰⠽⢃⣬⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⡿⢿⡷⢦⣀⠋⣀⡠⡄⠀⠀⠈⡠⠦⢐⣏⡀⣉⠛⣉⡷⠋⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠢⠈⠷⢿⣩⠤⢏⣲⠮⣩⢸⠄⢼⣚⢨⠙⠰⣺⡾⠧⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⢝⣛⣅⣩⠲⢏⡙⡆⠋⠤⡚⣿⠇⠀⣡⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠏⣹⣔⣛⣉⡀⠙⠓⠈⠉
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⢏⡿⠋⠈⠻⢦⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠖⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣡⠶⠊⡙⠛⠛⠋⠁⠀⠀⠀⠀⠻⠦⣤⣀⡾⠃⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠋⠀⠀⠀⣠⣾⠟⠛⢷⣄⡀⠀⠀⢠⡶⣴⠖⠋⠀⡠⠀⠙⠀⠉⢠⣷⠀⠀⠀⠀⠀⢀⡜⠋⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠙⢿⡄⠑⠠⠘⠧⠴⠂⠀⠀⠀⣴⡄⠀⣼⣿⡇⠀⠀⣀⢴⡿⠊⡁⠀⡀⢀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⡤⠂⢀⡤⠀⠀⣿⣷⣀⣿⣿⣷⠔⠊⠐⠉⠀⠈⡀⠾⢁⣽⣿⡆
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠠⠊⣠⠎⠀⠀⠀⠀⠀⠀⠀⠘⣶⡿⠋⠀⠀⠊⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠊⣠⣴⠟⠛⠁
⠀⠀⠀⠀⠘⠻⢿⣶⣶⡁⠞⣥⡀⠀⠀⠀⠀⠀⠀⠀⢰⢟⠁⠀⠀⠠⡂⠀⢠⣮⣿⣿⣿⣿⣿⣿⣿⠀⣠⡀⠚⡙⠉⢠⣦⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠉⢿⣿⡿⠛⠛⠶⣄⠀⠀⢠⣾⣿⠟⠀⢀⣴⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⢾⣿⣶⣾⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣌⠀⠀⠀⠈⠹⢷⢾⣿⡟⢁⠀⢀⣸⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠋⠁⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠙⠓⣤⡄⠀⠀⠀⠉⠉⠉⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⢀⠀⠀⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣾⡿⢡⡄⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⡠⢶⣾⠟⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠒⠦⣄⣀⠀⠈⠛⣦⣀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⢷⣿⣦⣴⣽⣿⣿⣿⣿⣿⣿⠿⡿⠛⠿⠛⠋⠁⠀⠀⣠⡀⢀⣠⠀⠀⠀⣠⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠈⠛⣩⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⡠⠀⢀⣴⣾⣿⠟⠋⠁⠀⠀⠈⠁⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢴⡟⢦
⠀⠀⠀⠀⢀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣤⣾⣏⣈⣰⣒⡆⢠⡦⠤⠞⣷⡀
⠀⠀⠀⠀⠈⠛⠁⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣦⣅⡈
⠀⠀⠀⠀⠀⠀⠀⠜⢃⡑⠀⠱⡟⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠐⢏⠱⠠⠘⣠⣾⣶⣄⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣙⣿⣿⡿⠻⣿⣿⠁⠀⠀⠀⠀⣀⠀⠀⠀⣤⡄⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢻⣿⣿⣿⣦⡀⠤⠄⠀⢀⠄⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠋⠀⠀⠀⠀⣸⣿⣖⡂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠆⡙⠀⢸⠀⡄⠀⠙⢿⣿⣿⡟⣷⡿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⣦⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⠃⠐⠀⢁⣤⡀⠁⢒⣒⡀⠙⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣏⣽⡴⣯
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢩⣶⡀⢣⠀⢷⣿⣿⣿⣯⣤⡉⠁⣀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⣼⣿⡉⢹⣹
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣷⣄⣱⣶⡭⢨⣭⡿⠽⣧⠈⢹⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠟⢻⡿⡉⠹⠉⠁⠀⢀⠱⠀⠀⠀⠀⢀⠈⡌⢹⠀⢰⠀⠀⠀⣀⣟⠻⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢉⣤⣄⣠⢼⣱⢳⣼⠯⣥⣀⠄⣀⡆⢀⣤⣠⣌⢹⣅⡘⠀⡎⠀⡄⢰⠟⣯⡤⣰⠖⢻⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⣠⣿⣿⠛⣠⡏⣶⠿⠉⢓⠳⣼⣻⣿⡇⠈⢉⠀⠈⠌⠺⠛⢧⡇⠀⢁⠊⣰⠟⣲⣶⣶⡧⡇⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠘⢯⡟⡟⢹⡅⣂⡙⣱⣏⢿⣛⣪⣿⡧⢤⣿⣥⣴⢀⠅⡄⡉⢀⢀⣾⣾⣫⣾⣹⣾⣯⡽⠇⣠⣿⣿⠁
⠀⡔⠂⠉⠉⠉⢬⣿⣿⣿⣷⣤⣍⡛⠻⢶⣭⣙⢖⡥⣔⣯⠮⣶⣯⣿⣿⣿⣗⢊⣌⣖⣵⣾⣿⡟⣿⣩⠿⠖⢂⣡⣴⣾⣿⣿⡟
⣀⣳⣆⢩⣋⣉⡉⢹⣿⣿⣿⣿⡀⠉⠓⠲⠤⢬⣍⣐⣛⣛⠛⠛⠛⠛⠻⠿⠛⠛⢛⣛⣛⣁⣩⣥⠤⠶⠒⠛⠉⠀⠿⠿⠿⠿⠁
⠀⢸⠃⠀⡖⠀⠀⠀⠀⡠⠖⠒⠓⠒⠀⢤⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠸⠁⠀⢻⡘⠀⡀⠀⢧⣀⣐⠘⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⡇⠀⢸⠆⢠⡇⠀⢸⡗⠁⠈⠢⠀⠇⢀⡤⠔⠒⠂⣔⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⣷⡀⢺⠀⢤⠀⠀⠸⡿⠀⠀⠀⡠⠞⠁⠀⠀⣀⠜⢉⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠒⠉
⠀⠀⠙⠛⢾⡷⠐⠒⠂⢸⡃⠀⠀⢰⡁⣀⡠⠴⠚⠁⠀⣸⠁⠒⠂⠀⠀⠀⠀⠀⢀⠀⢀⡡⠤⢤⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠙⠛⠒⠒⠉⣦⠠⠤⢸⡌⠉⠒⠒⠒⠒⠒⣿⠄⠶⠶⠶⠒⢒⠛⠒⣂⡈⠡⠔⠂⠄⠐⠲⣴⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠥⠤⠴⠚⢄⠀⠀⠀⢠⠴⠏⢠⣤⣴⠶⠚⢿⣤⣠⣭⣭⣭⣲⣮⣤⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠤⢀⠔⠉⠐⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⡠⠁⠈⠔⡠⢂⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠂⠄⠀⡠⠠⠂⠀⠀⠠⠊⠀⠀⠀⢀⠔⡡⡀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⣀⠀⠀⠀⠀⢀⢀⠁⠈⠈⠈⠉⡠⠁
⠀⠀⠀⠀⠀⠀⠃⢠⠀⡠⠀⠴⠀⠀⠖⠀⠰⠂⢀⠄⠀⠀⡐⠁⢀⠟⠉⠐⠁⠀⠤⠂⠀⠀⠀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠠⠂⠠⠀⠰⠀⠀⠃⡔⢀⠊⠀⠀⠠⠮⠄⠀⢲⣂⠀⡰⠂⠀⢈⡀⠀⠚
⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⢀⠀⢠⠀⠀⡰⠂⠀⠰⠇⠒⠒⠒⠒⠀⠀⠀⠄⠀⠊⠠⠆⠀⠈⡠⠀⠐
⠀⠀⠀⠀⠀⠀⡌⠀⠀⡄⠀⠉⠀⠃⡤⠀⢀⠀⠀⠀⠰⠂⠠⠊⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠀⠰⠁⡄⠀⠀⠊⠀⠸⠁⢀⠔⠁⠀⢀⠔⠁⡰⠀⡀⠀⠊⠀⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠘⠀⠈⠀⠠⠂⠀⠔⠁⠀⠀⠀⠀⢀⠀⠀⠈⠀⣀⠀⠋⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢠⠇⠀⠀⠄⡠⠂⠀⡀⠈⠀⠀⠀⠋⢀⠀⠀⠈⠁⠀⠜
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢠⣊⣀⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡨⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠁⠀⡔⠀⠀⠀⠀⡠⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣰⠹⡆⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢀⣿⠀⢰⠀⣰⠉⣇
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠋⠀⣸⣿⣶⠈⠻⠃⠀⠻⡆
⠀⠀⠀⠀⠀⢀⣴⠋⠱⡄⠀⠀⣿⣿⠃⠀⠀⢀⡇⠀⣧⠀⠀⣀
⠀⠀⢀⣠⠶⠛⠁⠀⠀⠛⢷⣤⣿⣿⡀⠀⢀⡾⠀⠀⠻⠟⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠈⢳⡄⠀⠀⠐⢄⠀⠀⠙⣿⣿⣧⣶⣿⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⣾⣿⣿⡿⠃
⠀⠀⠀⣠⡟⠀⠀⠀⠀⠳⣄⠀⢻⣿⣿⣿⣷⠀⡄⢀⣏⣠⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⡴⠖⢿⠀⣴⠋⢻⣿⣿⣿⡿⠁
⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠘⢷⣼⣿⣿⣿⡟⢀⣷⡾⠋⠀⠀⠈⠛⠀⠀⠀⠀⢀⣠⠊⠀⠀⣿⡞⢡⣴⣿⣿⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⣸⣧⡈⢿⣿⣿⣿⣉⣼⢋⠄⠀⠀⠀⠀⣧⠀⠀⢶⣠⡟⠁⠀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣼⣷⣼⣧⣠⣿⣿⣧⠈⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⡸⢀⠆⠀⢉⠀⠀⢠⡇⣠⣾⣿⣿⣿⣿⣿⡟⢻⡞⠋
⠀⠀⠀⢸⣿⣿⣛⣽⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣇⡀⠃⠀⠀⠛⠋⠀⠀⢸⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣷⣿⡟
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣾⣿⣿⣿⣷⣿⣿⣿⡯⠚⢷⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⣿⣿⣿⣿⣿⣾⠀⠀⢀⠀⠀⠀⠀⠀⢸⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⣤⠖⠛⠉
⠀⠀⣾⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣏⠁⠀⠁⠘⡆⠀⠀⠀⠀⣼⣿⡿⢿⣿⣿⣿⡟⠀⠀⢸⡇
⠀⢠⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣯⡂⡀⠀⣄⠘⣆⠀⢀⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⢷⡄
⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡞⠉⣧⠈⣿⣾⣿⣿⡿⣿⣿⣿⠟⠀⣀⡴⠾⠛⠉⠁
⠀⣾⡿⠃⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⠏⡇⠀⠘⣷⢿⣿⣯⣾⣿⠿⠿⠋⢠⠞⠉
⢰⣿⣿⣿⡟⣩⠇⠀⠀⠀⠸⡄⠀⠀⠈⣿⣿⣿⣿⠟⢠⠇⠀⢀⣿⣿⣿⣿⣿⣷⣨⣶⣾⠃
⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠹⣄⠀⠀⢿⣿⣿⡟⠀⢸⠀⠀⢠⣿⣿⣿⣿⡿⣿⠟⠋⠻⣦⡀
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠑⢄⠀⢿⠀⠀⢸⣿⣿⣿⠀⣼⢠⣴⣿⣿⣿⣿⣯⡄⢀⠀⠀⠀⠈⠉⠙⣻⠏
⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠻⣾⡀⠀⠘⣿⣿⣿⠀⢹⣾⣻⣿⣿⣿⣿⠏⣴⡃⠀⣀⣀⠀⢀⣸⠏
⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣿⣿⣿⢀⣾⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠁⠀⠀⣼⠇
⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣿⣿⣷⣿⣿⠛⠉⠙⠳⠶⠤⠤⠄⢺⡇
⠀⠀⣿⡿⠛⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠿⣿⣯⣤⣤⣤⡴⠶⠶⢶⡶⠶⠛⠁
⠀⠀⣹⠇⠀⠀⠀⢀⢀⣀⡴⠿⠓⠒⠒⠲⣿⣿⡿⠛⠁⠀⠈⠉
⠰⣿⣥⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⣿⣿
⠀⠀⠀⠉⣽⠀⠀⢠⠤⠴⠖⠛⠁⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠄⠀⠀⠀⠀⠀⠴⠒⢢⠀⠂⠀⠉⡀⠸⣁⡂⠀⠒⠀⠀⢀⢀⠉⡉⠐⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠐⠀⢤⣄⡾⠴⠦⠾⢤⢇⣰⠿⠋⠉⠉⠉⠉⠉⠉⠉⠈⠉⠊⢆⠈⢂
⠀⠀⠀⠀⠐⠀⠀⠀⡀⠈⠀⠀⠀⢄⠁⠀⠓⠋⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⣡⠀⠀⠀⠰⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⣀⡀⢀⣀⣂⠆⠰
⠀⠀⠀⠐⠀⠈⠈⣁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣤⣴⣶⠴⢀⡀⠀⢢⡬⠉⢀⣾⡢
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣈⠁⡇⠠⢊⡟⠱⠈⢁⡐⡿⠈⣑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡈⠈⠉⠁⡉⣀⣠⣴⢿⡟⠁⣠⣣⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣩⠟⠋⢛⣟⠙⡓⠋⣠⣿⡭⢀⡤⠋⠛⠆⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠢⠥⠤⠼⠿⠷⠚⢉⣁⣴⡟⠀⠠⢀⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⠓⠲⠤⠴⠴⠖⠒⠉⠀⠀⢈⠉⠒⢀⠠⠯⠤⠤⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠂⠀⠀⠀⠂⢀⣀⠠⠤⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠄⠉⡩⢂⠘⠈⠉⡁⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠡⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⣡⠀⠀⠀⢸⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⢤⣶⣶⣦⡀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠔⠃⡀⠘⠆⢸⢿⣿⣿⢿⠋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡠⠒⠂⡟⠂⢄⣟⡘⣙⠘⢻⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣇⣀⣀⣇⢀⠀⠀⡄⠀⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⡀⠀⠀⠀⠈⢋⣭⡉⠉⠉⠁⠀⠇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡙⠢⣤⡤⠴⠋⡍⠒⠀⠀⠀⠀⠆⢪⣥⣌⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠷⠊⠁⣄⢀⠀⠁⠀⠸⠀⠀⠀⠀⣀⣸⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠖⠋⠙⠃⠀⠠⡏⢹⠀⠀⠀⢠⠀⠀⠸⠀⣶⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⡅⠀⠀⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⡀⠀⣥⠀⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⡄⠀⢸⠃⢀⠀⡼⠀⠀⠠⠀⢀⠃⠀⠀⠀⡟⠀⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠇⠀⠰⠆⢁⡼⠁⠀⠀⡀⠀⠸⠄⠀⠀⠀⡇⣄⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠒⠺⠷⡶⠶⠒⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢸⠇⢸⣀⠴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⣇⣀⣀⡘⡇⠀⠀⠀⠀⠀⠀⠀⢨⣅⡾⠀⠋⢀⢠⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠀⠀⠀⡏⢸⠀⠑⠛⠲⣶⡄⣀⠠⠀⠀⠀⣼⠁⠀⠀⡼⠀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡿⠺⣇⠀⠀⠀⠚⠑⠫⡄⠀⠀⡜⠳⡧⠀⠀⠷⠀⢠⡿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠀⢻⣆⠀⠀⠛⠀⠀⠀⣠⢾⠇⣾⠆⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⢰⠋⠀⡾⠋⡷⣄⣀⣀⣠⠞⢁⡎⣠⠁⠣⡉⢀⠙⡀⣨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠈⢯⣸⠃⠁⡗⠛⡁⡸⠣⣤⡞⡰⠋⢠⠀⣧⣰⣦⢧⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢇⣸⠀⠀⡧⢀⡟⣁⢠⣿⠃⠀⠀⢸⠀⡟⠁⠙⠚⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⢧⣄⡘⡇⣰⢂⡇⠀⣼⠀⠀⣀⠋⠀⣋⣠⠴⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠀⠈⣧⠉⡱⠃⠸⢱⡀⠘⠳⠲⠟⠊⠉⠁⣤⢼⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠒⠒⣶⠒⣿⣤⣌⣳⡀⢚⣠⡗⠀⠀⠀⠃⠀⠀⠀⢹⣹⠦⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠴⠤⢤⣌⠭⠭⠥⠝⢙⠿⠭⠿⠶⠶⠶⠶⠂⠠⠴⠶⠤⢷⠤⠤⠤⠤⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⠤⠭⢤⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠠⠀⠀⠀⠂⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓
⣦⠤⠦⠤⠤⠤⢤⡤⢤⡀⠖⠒⠶⠤⠦⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠛⠒
⠀⠶⠶⠶⠦⠠⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠦⠤⠤⠄⠀⠀⡀⠠⠄⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⢀⠀⣤⣤⣄⣀⣀⣀⣀⣀⡀
⣦⣿⡿⠛⠿⠯⠿⠿⣿⣿⣿⡟⠛⠒⠒⠛⠙⠛⠉⠉⠉⠉⠉⠛⠛⠉⠁⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠍⠩⠛⠛⠓⠀⠛⠉⠛⠛⠛⠛⠛
⣿⣿⣿⡿⠶⠶⠶⢶⡶⣖⣀⣠⣀⣀⠀⠀⠀⠀⠤⠄⠀⣠⣤⣀⣀⡀⢀⡀⠀⠄⠀⠠⡄⠀⠠⠄⠀⠤⠤⠄⠀⢀⡀⠤⠠⠤⠤⣤⠄⢀⣀⡀⣀⣀⣀⣀⣀
⢠⣤⣤⣄⣀⣀⣴⠔⠀⠀⠀⠤⠤⣤⣤⣤⣠⣤⣤⣄⣠⣄⣠⣄⣀⣀⡀⣀⣀⠀⣀⣀⡚⠛⡛⠚⠛⠒⠒⠂⠲⠤⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠬⠷
⠀⠀⠀⣀⣈⣱⣶⠶⠶⠶⠶⠶⠆⠀⠐⠶⠄⠀⠠⠩⣭⣴⣶⡦⢤⣭⣯⣍⣭⣉⣉⣉⣙⣛⣛⣛⠛⠓⠒⠀⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠘
⠀⠀⠶⠿⠿⠟⠉⠉⢉⡙⠙⠋⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⢀⠀⠀⠈⠀⠈⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⣿⡟⠒⠶⠦⢤⡄⠀⠈⣄⡁⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⠀⠀⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⠐⠂⠈
⠐⠒⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⠄⠄⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠠⠤⠒⠀⠠⠤⠤⠤⠤⢤⠀⠒⠒⠒⠀⠠⠤⠄⢠⣄⠀⠀⠲⠴⠀⠠
⠤⠄⠀⠀⠀⠈⠛⠛⠛⠋⠁⠁⠀⠀⠀⢀⣀⠀⣀⣀⣀⣐⣒⣶⣶⣦⣤⣄⣹⡟⠛⠙⠀⣐⣒⣲⣶⣶⣶⣶⣦⡴⠀⣀⣠⣄⣘⣓⠀⠠⠬⢤⣭⠙
⠀⣀⣀⣀⣀⣀⣀⣲⣤⣤⣤⣤⣤⣤⣤⡶⢷⣾⣿⣻⡿⢛⠛⠛⠶⠶⠶⠶⢤⣤⣄⣀⡛⠛⠛⠛⠿⠃⠠⢤⣤⣤⣤⣍⣉⣛⣉⠉⠙⠚⠛⠻⠗⠒⠒⠂
⣭⣭⣭⣍⣉⣙⣛⡛⠿⠿⠶⠶⣶⠿⣿⣿⣶⣾⣯⣭⣭⣭⠽⠽⠿⠐⠒⠶⠶⠶⠾⢯⣭⠉⠉⠙⠿⠶⠶⠶⠶⠶⠾⠍⠉⠉⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⢀
⠆⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⣄⣤⣤⠤⠶⠶⠷⠿⣿⣿⣟⣛⣛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣂⠉⣉⠑⢂
⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⡠⢣⠊⣠⣤⣤⡱⡀⠇
⠀⠀⠀⣿⣧⡴⠀⠀⠠⠄⠀⠀⠖⠀⡎⢸⣿⣿⡁⣹⠇⡀
⢀⡠⠔⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⣷⡿⠋⠀⡇
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⢦⠀⠇
⠈⠛⠭⣐⣒⠂⠀⠤⠤⠤⠤⠤⠤⠀⠠⠒⠂⠁⠀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⢠⠄⢍⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⠲⡄
⠀⠀⠀⠀⠀⠐⠄⠔⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠒⢄
⠀⠀⠀⠐⠀⠂⢀⠀⠀⠠⠠⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠈⠒⠆⢨⢠⠀⠠⣀⠇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢦⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⢀⠘⠘⡆⠀⠀⡀⠔⢉⡷⣄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠱⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣠⠖⠉⠀⠈⠳⣄⡀⠀⠀⠀⢀⠆⠀⠀⡷⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⢣⣀⣀⣠⠔⢋⠀⠀⡐⠠⠁⠰⡢⠈⣉⠗⠂⠁⢀⣠⠾⣁⠀⠐⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢄⡸⠀⠄⠀⣀⠔⠋⠀⣀⠴⠚⠉⠀⡀⠐⡐⡠⠄⡠⠤⢄⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⣉⡀⠀⠀⡖⠉⢰⠉⠀⡔⠀⠀⡐⡜⠀⠀⡇⠀⠀⠈⠑⠢⢄⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠀⢀⠔⠁⠈⢀⢇⠀⠀⠑⠐⠃⡖⠊⢸⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢠⠂⠀⠀⠀⢢⠢⢤⠀⠀⠀⠑⠢⠴⠃⠀⡔⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠠⠜⠀⠀⠀⠀⠸⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⠀⠀⠇⠀⠘⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠠⠄⠀⠀⠀⣄⠀⠃
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠀⣤⢀⣤⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⡠⠪⠀⡀⠀⠋⠄⠂⠀⡠⠔⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣷⣿⣯⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⡠
⠀⠀⠀⠀⠀⠸⣶⣁⡬⠀⠀⠀⠀⢠⣤⣴⡿⠟⠁⠀⣻⡶⠂⠁⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠫⣿⡥⢀⣶⣶⣴⣿⡿⢡⣾⣿⡾⠋⠈⠀⠀⠀⠀⠀⠀⠀⠠⠬⠷⡄⠀⠀⠀⠀⠄⠈⠀⠀⢂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⣿⢉⡙⣡⣿⡟⠁⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠠⢶⣖⡀⠰⣿⣾⣿⡉⠙⣯⡉⢿⣿⣿⢴⣿⣿⣇⢀⡤⣰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠉⠉⠓⣒⣦⠌⠙⠒⠻⠇⠸⠧⠟⠛⢛⠋⠹⠟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠒⠒⠉⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⡔⠤⣦⠀⡄⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠒⠀⠒⠾⢿⣦⡹⠆⣻⢤⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡄⠺⣿⣿⣦⣄⡎⢠⣞⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣸⣽⣶⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣸⡅⠀⠘⣿⣿⣿⢃⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠙⡐⣤⡀⠀⠀⠀⠀⣠⣥⣼⢸⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣷⡀⠀⢿⣿⡿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣹⣿⣿⡄⣶⣤⣰⡿⡻⠋⣾⣏⣠⠤
⠀⠀⠀⢴⠖⣠⣤⣤⣾⣿⣿⣹⣿⣿⣧⣽⣿⣧⣈⣿⣿⣷⣶⣬⠶⣦⡀⠀⠰⣶⠶⢈⣿⣿⣷⣤⣻⣟⣋⣘⣿⣨⣿⣿⣥⡤⠦⢀⡴⠆
⠀⠀⠀⠈⠛⠒⠒⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⠉⠉⠉⠈⠉⡭⠀⠀⠁⠀⠀⠀⠀⠉⠉⠀⠀⠉⣉⣉⡉⠉⠉⠉⣉⡑⠖⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢀⠔⠈⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠁⠂⠀⠈⠁⠀⡀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⡀⠀⠀⠀⢀⡆⠀⢀⣀⣀⣀⠟⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⡀⠀⠀⠈⠑⠀⢀⠰⣂⡁⡄⠀⠀⡤⢃⢾⠌⠏⠹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢍⠂⢈⡉⠠⠀⠀⠀⠠⡦⣀⣤⠄⢀⠀⠈⣀⣁⡈⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⡀⠐⠄⠀⠲⠒⠒⠊⠛⠁⠀⠋⡑⢉⠁⠊⠠⢼⢶⠧⠤⠇⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠔⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠠⠦⠴⠶⡴⠒⠒⠉⠁⠀⠘⠀⠁⠁⠙⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠒
⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢀⡆⠂⢆⣰⢶⡂⢠⣶⣤⣔⣛⣉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⣺⠠⠾⢛⠋⠉⠁⠀⠈⠉⠉⠉⠁⠨⠓⠶⠒⣒⠁⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⡋⠁⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠚⠉⠁⠀⢉⠻⡖⣼⢿⡀
⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⠋⠙⠷⢄
⠀⠀⠀⢀⡀⠸⠁⢄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⡀⣔⡽⣮⣷⡀⠀⠀⢘⠉⡇
⠀⠀⠜⠉⠙⣮⡐⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⡓⢒⠒⣿⡿⠿⣯⡇⠞⠉⠲⣮⠃
⠀⠀⢠⠀⠀⠈⢻⢀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢁⠈⠁⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⢄⠰⠈⠘⣇⠇⠥⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣤⠤⠤⠴⠶⠶⠞⠛⠛⠉⠁
⠀⠀⠀⠘⣄⠀⠀⡿⠀⠀⣬⣟⠒⠦⢠⠊⠀⠠⠘⣠⣽⠷⠟⠿⢂⣀⡶⠔
⠀⠀⠀⠀⠘⢷⣀⠀⠀⢀⣿⠛⠓⠒⠂⠒⠁⠐⠈⠅⠠⠄⠠⠈⠯⠤⠄
⠀⠀⠀⠀⠀⠈⠈⢣⣴⣿⡿⠷⢶⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠈⢀⣏⢛⣝⣦⡀⠈⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⠀⠙⢯⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⣀⠀⠀⠀⠈⠀⡎⠀⠀⠀⠀⠀⠳⠀⠐⠀⠀⠐⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⡀⢀⡠⠁⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⢧⢀⠀⠀⣀⠜⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠅⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⡀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⢊⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠁⣤⠔⠂⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠂⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠊⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠈⠑⢦⠀⠀⠀⡀⠀⠠⠀⠀⠈⡖⠀⠀⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠡
⠀⢀⠀⢄⠀⠀⢀⠠⠼⡀⠀⠀⠀⠀⡨⠂⠂⠄⠀⠀⠂⠀⠀⠀⢆⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠠⠤⡠⢄⠀⠀⠀⠀⠀⠀⠀⠍
⠀⠀⠀⠀⠂⠀⠄⠀⠀⠐⣄⢀⡀⢠⠁⠀⠀⡠⠀⠀⢠⡠⠀⠀⠀⠁⠀⣠⠤⠠⠤⡔⠁⠀⠢⠀⠀⢐⠒⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠤⠃⠀⠀⠀⠑⠀⠐⠁⠀⢠⠁⠀⠀⢀⠀⠀⡜⠁⠀⠀⠀⠡⡀⠀⡠⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠑⠔
⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⠀⡀⠀⠈⠂⠀⠀⠂⠀⠀⢆⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⡨⠀⠀⠐⠀⠀⠀⠀⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠒⡁⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡠⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠂⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⠀⡠⠤⣠⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠤⠒⡆⠀⢀⢀
⠀⠀⠀⠐⠁⠀⠀⠦⠤⠄⢢⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠲⡄⠀⠀⠈⠎⠀⠁⠀⠐⢅⡱
⠆⠀⠀⠣⠄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢄⣀⡀⡀⠈⠉⠀⠀⢀⠀⠀⢄⠀⠀⠘
⡀⠀⠀⠀⠀⠔⠉⠉⠢⣀⣀⠀⠠⠒⠒⠀⠀⠀⠀⠈⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠈⠀⠀⡀⠀⠀⣂⠀⠀⠀⠅⠀⢀
⣈⣋⣀⣀⣀⣄⣀⣀⣈⣀⣀⣈⣁⣀⣀⣀⣁⣀⣀⣐⣂⣀⣀⣀⣰⣊⣉⣉⣑⣠⣂⣀⣢⣀⣀⣀⣀⣈⣀⣀⣈⣂⣀⣐⣁⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠼⠇⠀⠀⠀⠀⠀⢀⠀⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⡠⠔⠤⡐⠛⠀⠀⣰⠭⠏⡀⢀⢞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠉⠓⡄⠀⠀⠉⠀⠀⠱⠴⠖⠀⡠⠖⣋⠀⢀⠤⣈⢹⣗⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⣠⡗⠁⠀⢀⡔⠒⣢⣀⡠⠔⢫⠒⠛⡾⠃⣞⡶⡿⠀⠉⠰⠉⠱⡄⠀⣎⣱⠄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⠁⠀⡔⠁⣨⡷⠛⡇⠀⠀⠱⢤⡾⠃⣴⡌⠁⠀⣠⠔⠃⡤⠤⡘⣆⠌⢥⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢃⢌⣀⡳⠾⠃⡤⠒⣤⣤⡀⠀⢠⢄⠀⡞⠀⡠⠚⠣⣴⠃⠈⢦⣐⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢒⢦⣠⠴⠊⠁⠀⠳⠞⠉⡕⠀⡠⠗⠒⣿⠉⢀⡀⠈⠛⠀⡇⢨⡀⠀⡔⡐⠀⠀⠀⠻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡔⠚⢇⠀⡀⡰⠘⡘⠸⣰⠀⠀⣅⢀⣴⡟⠀⢧⠯⠀⠀⠀⠘⡄⠉⠀⠉⠀⠀⠀⢠⣄⠱⣤⡄⠀⠀⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠙⠛⠒⠋⢰⢡⢁⢣⢁⠗⢣⠀⠀⠈⠁⠉⢠⠶⣽⠂⠀⠀⢆⡆⢨⢀⡄⠀⠀⣔⣢⠀⢡⠠⡟⠀⣠⠼⣄⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢃⢁⢃⠆⡌⡐⡜⠛⠋⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡠⠖⠶⡁⠘⠶⠀⠀⠉⠁⠂⢡⠐⢡⠀⢇⣠⢀⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⠀⠀⢢⠀⠈⡘⡜⡸⢠⢱⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠓⢄⣼⢂⠀⠀⠀⢀⠀⡂⡄⠈⠀⣸⠀⠀⠉⠠⣎⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⡇⠀⠡⢂⠱⢁⢃⠇⡌⡜⡠⠀⠀⠀⠀⠀⣀⡀⠀⢠⣇⠀⢔⠌⠁⠿⠀⢀⢀⠰⠟⠁⠀⣶⠀⡼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡄⡄⠙⢢⡀⠱⣂⠘⡘⢠⢡⢠⠃⠀⠀⠀⠀⠮⣀⡼⠀⡆⠈⠉⠉⠀⢀⠀⠀⠐⠈⠀⠀⠀⣀⠘⠤⠃⡉⣈⡇
⠀⠀⠀⠀⠀⠀⠀⡤⠠⡄⠘⣷⡀⠀⠱⡈⠡⡀⠁⡎⡈⡌⠀⡠⢊⡹⣄⠴⡌⢀⡴⠁⠀⠀⢀⠰⠘⣀⢤⡀⡎⠉⢧⡀⡧⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠘⠤⡨⠇⠀⠙⡇⠀⠀⠳⡀⠀⠀⠀⠁⠁⠇⡇⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⣨⠔⠋⠀⢰⠁⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⢇⠆⠠⡀⠘⣄⢀⠴⢦⡈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⡇⠀⣦⠂
⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⣁⡀⠘⠊⠣⡑⡀⠈⠁⠀⠀⠓⠔⠋⠀⢀⠄⢂⡠⠖⡆⠰⡇⠀⠀⠀⠀⠀⠻⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢌⠂⠀⠀⠙⢌⠠⠀⠀⠀⠀⢀⠄⢂⡤⠚⠉⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠑⠢⡄⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢸
⠀⠀⢀⡠⢄⣠⢄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⡴⠒⣢⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄
⠀⠀⠎⠤⠌⠽⣃⣃⣘⢤⠀⢉⣒⣒⣀⣩⣯⡑⣤⣤⠔⢒⣈⠉⢑⣲⣤⠤⠌⠉⣭⠥⠤⠤⠔⠋⠀⢙⠦⠤⠤⢤⢄⠀⣄⠈⠂⢒⣚⠂⠀⠀⡤⠠⡖⠒⣄
⠀⠀⠀⠀⣆⡀⣀⣀⡠⠤⠴⡖⠒⠒⠒⢲⣒⣒⣒⡒⠀⢘⣋⣀⣠⡼⠧⣄⣀⣀⣀⣀⣀⣈⠉⠀⠉⠉⠀⢀⠀⠵⣎⣷⢮⡭⡥⢤⣬⡌⣓⡌⣁⡚⠉⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠄⠒⠒⣲⡶⢤⣀⢱⠞⠣⢀⣀⣬⠿⢍⣁⡚⠛⣮⠔⠛⠛⠛⢮⡘⠃⢘⠉⠙⠮⡛⠓⡎⠀⠀⠉⠀⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⢤⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣅⠉⠳⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⣒⠚⣉⣉⣙⠨⡁⠀⠌⢧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠉⠁⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⢀⣈⡅⠀⠒⣻⢣⣾⣷⣶⣶⣷⡀⠀⠀⠀⠤⠂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠛⠛⠻⣀⡤⠖⠀⣠⠶⠶⠞⠛⠉⠁⠀⢀⡀⠴⢿⡼⣿⣿⣿⣿⡟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⢛⣥⣿⣴⠀⢀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠐⢂⡉⡠⠶⠶⣿⠻⠮⠽⡭⠵⠊⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣴⣧⣿⣿⣟⣟⣏⣽⣥⣴⣶⠾⠛⠋⣁⡁⣠⣴⣾⣿⣾⡅⠀⣀⣼⠀⠀⠀⠀⠀⠀⢀⣀⠤⢔⠪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣿⣿⣽⣿⡟⢻⠋⠉⠁⣈⢁⣠⣤⣀⡾⡿⢛⣿⣿⣿⡿⣿⢇⣩⣜⣋⣀⣠⣤⣴⠶⢚⣭⣶⠊⠁
⠀⠀⠀⠀⣀⠄⠀⠀⠤⢾⣿⣻⣿⡻⢿⣟⣿⣦⣤⣷⣤⣾⢻⢿⣿⣿⣿⠞⣀⣿⣿⣷⡿⢣⢷⣀⢤⣭⠿⢛⣩⣤⣶⣾⢿⠿⠃
⠀⠀⢠⡎⠁⠠⣴⠐⠲⠀⠀⠢⠽⠻⠿⣿⣿⣛⣛⠿⣿⣿⡊⠌⠉⠉⠁⢸⣿⣿⣫⣿⣧⣀⣀⣤⣦⣴⣿⡟⣻⡿⢃⣀⠝⠁
⠀⠀⣿⣷⣀⣵⣽⣷⣶⣤⣬⡁⠀⠀⠰⢬⡿⣿⣿⠓⣊⠙⣿⣶⣴⣷⣾⣿⣿⢿⠿⠏⠉⠙⠛⡻⠫⠙⢿⣿⣿⠗⠋
⠀⠀⢿⣾⣿⢿⣯⡻⣿⣿⣿⣯⣤⣀⢢⡉⠁⠙⢿⣿⡤⠆⠘⣿⢉⠀⠰⠞⠋⠀⠀⠀⠂⣠⠀⠀⠀⣀⣾⡿⠃
⠀⠀⠈⢷⡜⢿⠻⣿⣿⣽⡿⣿⣿⣿⣿⣿⣆⣀⣸⣿⣧⡠⡀⢿⣿⣇⠀⡄⡀⠙⢶⣶⣾⣿⣶⣶⣾⣿⡋
⠀⠀⠀⠀⠑⢮⠐⠀⡿⢿⣿⣯⡻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣸⣿⣿⡄⠈⣧⡄⠀⠹⣿⣿⣿⣿⣿⠿⣿⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠙⢄⣈⠂⠈⠛⢿⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣏⣧⡀⢸⣿⠴⠆⢸⣟⣉⡡⣙⠦⠈⠓⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⣀⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⣿⣶⣶⣾⡿⢻⠿⢷⣚⣓⣚⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣄⡙⠻⢶⣭⣟⡛⠻⢥⣈⣛⡛⠻⠿⠿⠷⠶⠖⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣭⣽⣿⡻⢤⣌⣩⣖⣒⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠉⠁

⣯⠀⠀⠀⢸⢸⠀⢀⣿⠎⠀⠀⢐⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠲⠤⡀⠀⠀⠀⢀⣤⣤⡀
⢻⠀⠐⠀⡇⢦⠂⣼⠋⠀⢀⢔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⢤⣤⣤⢤⣤⣤⣤⣤⣾⢇⣄⢰⣤⡜⠦⣄⣴⠏⠀⠀⠙⡆
⢸⠀⠀⠀⢀⡎⢰⡧⢂⠔⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⡾⢋⣉⡭⠁⣀⠀⠐⠁⠀⠀⠒⠫⠿⢛⢺⣿⡿⠏⠀⠀⢀⠀⠀⠀⠀⠶⢧⣄⣀
⢸⠀⠀⡄⢸⠃⡾⣡⠂⢠⠃⠀⠀⠀⠀⠀⠀⢀⣤⠶⢋⠁⣀⢠⡷⠎⠉⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣙⣢
⠜⠀⠀⡇⡘⠀⡷⠁⠠⢃⠀⠀⠀⣀⣀⣤⠞⢉⣤⠰⠈⠺⠋⡌⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠒⠋⠉⠉⠀⠀⠀⠀⠀⣹⠃
⠀⡀⠀⢃⠃⢸⠃⢠⢣⠯⢧⣤⣿⡿⠋⣷⢦⣿⡿⠀⠀⠀⣶⡾⠆⠀⠖⠀⢀⠀⠀⠀⠀⠀⠰⠀⢴⣶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⣂⡡⠚⠁
⡆⡇⠀⣾⢠⡏⢀⢢⠋⠙⣩⠞⠉⣚⠁⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠎⡀⠀⠉⠀⠀⠒⠁⠀⠒⠁⠐⣁⠠⠐⠒⢀⣩⡴⠋⠀⢀⣀⢴
⣷⠁⠀⢹⢸⠃⣞⠆⣠⠾⠁⣴⣾⠋⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⡉⠉⠁⠀⠐⠚⠀⣠⠌⠁⠂⠁⠀⠄⢲⠀⠀⣹⣿⣿⣿⢿⣯⣭⣥
⣿⠀⠀⢸⣿⣰⣼⠛⠁⠀⣶⡝⠃⡀⠀⣺⡀⠀⠀⠀⠀⠀⡀⠆⠀⠐⠀⠀⢰⣾⣿⣿⣯⢠⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡄⠈⠉⠁⠃⠉⠉⣽
⢿⠀⠠⢸⢸⣯⠀⠀⠀⠀⠀⠰⠄⣁⡀⠙⢷⡄⠀⠀⠀⠃⠀⠀⠀⢀⡴⣺⣧⣮⠙⠷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠠⣏⢱
⢸⠀⡆⣾⢸⠸⢧⡀⠀⠀⠀⢠⣿⣿⣿⣦⣦⡽⣄⣀⠀⠀⠀⠀⣠⠟⠈⢩⡤⠄⠀⠀⠀⠈⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠈⡇
⡘⠀⣿⣿⠿⡄⠈⢧⣀⠀⠀⠀⠿⢿⣿⡧⣩⣅⡈⢷⣃⠀⢀⢴⡏⠀⠀⠀⠀⠀⠀⠀⡄⣀⠺⠒⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣇⣀⣠⣀⡀
⣷⣶⣿⢿⣿⡿⠿⠿⠷⠶⠤⣄⠀⠀⠀⠠⣿⣿⣇⡌⢿⣴⡟⢸⡇⠀⠀⠀⠀⠀⠀⢠⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸⠋⠁⠉⠉⠙⠉⠉
⣯⣍⣿⠋⢁⠀⠘⠷⠀⢴⠇⣀⠈⠓⢤⣀⠀⠉⠀⢁⡘⣿⡃⠙⣿⡬⠃⠀⠀⠀⠀⠸⡧⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡎⠀⢠⡇
⣲⠾⣿⠀⣟⠀⠀⠀⠀⠠⣾⡇⢰⣿⣶⣌⠓⠄⠀⣘⠃⢹⡇⠀⠹⣧⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢼
⡛⠿⣿⣿⠻⣅⠀⠀⠀⠀⠉⠁⠈⢿⣿⣿⣥⡈⢢⠙⠃⠀⣇⠀⠀⠹⣤⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡀⠀⠀⠀⢀⣀⣴⡇⠀⠀⠀⠘⠦⣀
⠒⠩⢍⣻⣷⡘⢧⣄⠀⠀⠀⠀⠉⠀⠈⠉⠛⠃⠀⠀⠘⠃⣿⡆⠀⠤⢼⣆⠀⠀⠀⠀⠀⠙⠧⣄⣬⣠⣀⣴⠴⢿⣿⢟⡴⠗⣶⣤⣌⠳⣦⢭⣷⡄
⠀⠀⠀⠈⠛⣿⣦⡈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣯⣽⠷⣄⠀⠀⠀⡀⠀⢠⡴⠾⠚⠁⠀⠀⠈⠉⠀⠀⠀⠀⠉⠑⠮⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠿⣦⡀⠈⠙⠷⣦⣤⣀⣀⣀⣀⣀⡠⠚⠉⢉⠛⣿⠿⠿⠟⠛⢷⣄⢀⣹⣶⣤⣀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣄⡀⠀⠨⡉⠉⠉⠁⠀⠀⠀⠀⠠⣤⣄⣉⣀⣒⣺⠿⣆⢁⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢬⣳⡤⠀⠀⠀⠠⣑⠲⢦⠀⠀⠈⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢄⠀⣀⡊⠉⠛⠦⣅⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⡳⣄⠀⠀⠈⠙⠗⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣷⠄
⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣄⠀⠀⢤⠀⠀⡀⠀⢀⠀⠷⠀⠀⠀⡄⠀⡦⠀⢀⠀⢰⡄⠀⢀⡀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⡀
⠚⢰⡀⠈⠀⠀⠇⠀⠸⠆⠀⠀⡆⠀⠁⠀⠀⠀⠘⠀⠈⠀⣄⠘⠇⠀⠀⠀⠋⠀⣤⠈⠃⠀⠐⠖
⠀⠈⠁⠀⢸⠀⠀⢠⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣹⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⣆
⢲⠀⠀⡄⠀⠀⠀⠐⠃⠀⠀⣆⠀⢲⠀⠈⠀⠀⡄⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠴⠀⠗⠀⠸⠀⠀⢈
⠈⠀⠀⠋⠀⢰⡄⠀⢰⠀⠀⠁⠀⠀⡀⢀⡀⠠⣧⣀⡀⠀⠀⠛⠀⠀⠀⢲⠀⠀⠘⠀⠀⠀⡀⠀⡀⠘
⠀⢀⡆⠠⡆⠀⠀⣀⠤⢐⣠⠻⢛⠥⠢⠐⠀⠀⢈⡄⠂⠌⠉⠙⠒⠶⣤⡬⠀⣀⠀⠀⠀⠸⡥⠀⣥
⢀⠀⠋⠀⣠⣔⠚⠉⡴⡫⠡⢊⠩⡂⠈⠀⠀⠀⠀⠐⠈⠂⠉⠀⠀⠀⠈⠙⠲⡠⠈⠁⠢⢄⡀⠀⢠⡄
⠸⠀⡠⠊⠀⠁⠀⡜⢘⠨⡂⢑⢅⠂⠁⠀⠀⠀⠀⠀⠁⠁⡀⠀⠈⡀⠀⠀⠀⠘⢦⠀⠀⡀⠈⠢⡈⠁
⢀⢎⣢⠴⠀⠀⢰⢐⠕⠨⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⡀⢀⢀⠀⠀⠀⠈⣧⢐⠀⠀⡄⢝⡄
⠟⠉⠀⠈⠉⠀⣬⡵⠖⠓⠉⠈⠉⠉⠈⠙⠓⢦⣤⡀⢠⢠⣤⠴⠿⠓⠂⠡⠠⠤⠾⢜⡵⠚⠉⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣗⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣉⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠁⠀⠂⠀⠀⠂⠔⠄⠠⠢⠠⠈⢄⠁⠌⠀⠨⠢⢀⠕⢔⢄⢀⢀⠀⡠⡂⡠⢀⢄⠔⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠞⠓⠒⠋⠙⠒⢲⡂⠀⠐⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠠⢇⡄⢠⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡖⠈⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢁⣼⡆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠫⠜⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⡨⡼⣿⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠃⠀⢨⠆⡳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⡒⠒⡫⠊
⠀⠀⠀⠀⠀⠀⠀⣰⠃⡆⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⡲⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠒⠤⣀⢀⠔⠉⡔⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣶⠀⠀⠀⢠⠏⠀⢀⠀⡘⠕⢠⡎⠀⠀⣀⠅⠋⠀⠚⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢷⡆⠀⢀⡏⠀⠀⢄⠀⠈⠀⠱⠜⠒⢉⡡⠄⢄⠐⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⡇⠀⡼⠀⠀⠀⠀⠀⠀⠐⠠⢶⠊⠁⣀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⣆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⣿⢸⠀⠀⠀⠀⠀⠀⠀⣠⠠⠄⢚⠃⢀⣩⠎⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣉⠛⢆⡀⠀⢀⣠⡴⣋⣁⠀⣴⢉⣹⡀⢸⡀⣏⠉⠉⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⠶⡶⠶⠖⠲⠶⠶⡞⠀⢻⠀⠀⠉⠉⠁⠉⠉⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡾⢰⠓⠒⠒⠒⠒⡇⢃⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠞⣇⠎⠀⠀⠀⠀⠀⢡⡸⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠄⢀⡀⠀⡀⠀⠠⠤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠐⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠂⠐⣀⡀⠀⠀⠠⠀⠀⠠⠀⠀⠈⠉⠄⡄⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⢄⡀⡀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠰⠠⠀⢈⠀⠁⠐⠄⢔⠀⠉⠛⠲⠒⠺⠁⠀⠀⠑⢔⠀⠁⢅⠔⣐⡀⠁⠈⠁⠀⠈⠮⠤⡀⠀⠀⠉⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠞⠉⠱⠒⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣄⡴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡉⠣⠀⠅⠈⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠁
⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣄⡤⠀⠠⣊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡈⠀⡄
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠀⠀⠋⠀⠀⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⢀⠄⠀⠀⢀⠄⠀⠐⠀⠈⠉⠀⠀⢀⠀⢀⠄⠀⢀
⠀⠀⠀⠀⠤⠀⠠⠄⠀⠐⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠁⠀⠀⡀⢀⢀
⠀⠀⠀⠸⠔⠀⠀⠆⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⢈⡀⠀⣀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⠀⢥⠀⠀⠀⠀⣀⠀⠀⡄⠀⠚⠀⠀⠁⠈⡁⠀⠀⠈⠀⠀⠁⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠃⠀⠉⠀⠀⠌⠀⠀⠘⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠫⠶⠖⢝⢢⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠚⠋⢁⠀⠰⡐⣾⣻⡇⠻⡏⢹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣶⡶⠾⠟⠋⠉⠀⣀⠀⠛⣷⡀⠉⠉⠋⡁⠘⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠛⠉⣀⣠⣤⣴⣶⣿⣾⡗⢠⠉⠀⠀⠘⠁⣀⣰⠞⢃⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⣛⣤⡾⠛⠉⠉⠀⠉⠉⣽⣿⡇⠹⢾⡷⠀⠀⠛⢋⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠛⠁⠈⠉⠀⠒⠿⢶⣶⣤⡤⠀⠘⡿⠁⠀⠀⠀⣀⣀⠀⢽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣡⣴⣶⣶⣷⣶⣤⣤⣤⣀⣈⠉⠁⢀⢀⠀⠀⠀⢠⣾⣿⣿⢷⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢛⣋⠉⠉⠙⠉⠉⠉⠛⠛⠿⢷⠀⣼⠸⣧⡀⠀⠀⠻⠏⢉⣀⣹⣉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣤⣬⡉⠓⠲⠦⣤⣤⣤⣤⣤⣶⣾⠇⠀⣿⡿⢷⣤⣀⣀⣀⣉⣱⣿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣶⣦⣤⣤⣭⣍⣉⣴⣶⣶⣿⣦⣴⣽⣯⣭⣭⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣶⡶⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⡿⣿⠿⡟⣿⡟⠃⠗⠀⠟⢻⡿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠁⠏⠀⠀⠋⠁⠀⠀⠀⠀⠀⠃⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡧⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⢚⡃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠃⠹⡄⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⠔⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠐⠠⠀⣀⣀⣀⣀⡤⠚⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⢴⠴⢿⣿⣟⠉⢧⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⣿⣽⣤⣤⣤⣤⣤⠤⢴⣿⣿⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣰⠙⡾⢻⣿⣿⠠⢤⣴⣖⣒⣒⣒⣿⣿⡟⠁⣦⡂⠀⠐⠃⠉
⠠⠤⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣦⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠋⣱⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠
⠀⠀⠀⠀⠀⠀⠠⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⡞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣆⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣈⣩⠛⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢋⣼⡆⠀⠀⠀⠀⠈⠀⠉⠑⠢⢄
⠀⢀⠔⠒⠉⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⠩⣥⠄⠀⠀⠀⠀⠀⠀⢀⡀⠔⠊
⢰⠁⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢒⣤⣿⣋⣉⣉⣉⣉⣩⣭⣭⡭⠭⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡀
⠀⠀⠈⠀⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⠓⠚⠉⠭⢤⣦⡤⠤⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠎⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⣷⠀⠀⠀⠀⠐⠂⠨⢍⠀⣤⠴⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣛⡍⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠘⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⠠⠤⠄⢀⣀⣀⣀⡀⠀⠀⠀⠀⠠⠀⠐⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⣰⠛⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠦⠤⠶⠃⠀⠀⠀⠀⠻⣦⣀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⡶⠛⠉⠛⢷⣄⠀⠀⠀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢳
⠀⠀⣀⣠⣄⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠈⠛⠛⠞⠃⠀⠘⠷⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⢸
⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⣠⠶⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⣼⠁
⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⣿⠀⠀⠀⠀⠀⢿
⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡏⠀⠙⠷⠾⠋⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠹⢦⣄⣤⠶⠛⠙⢷⡄⠀⢸⡇⠀⣠⡶⠶⠶⣄⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠛⠁⠀⡏⠀⠀⠀⠈⠳⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⠶⠋⠉⠉⠙⣆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠛⠁⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⠞⠿⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠿⢻⠟⣡⣤⣄⠾⡿⠿⠿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡿⠿⢻⢿⡧⢹⣦⣄⣠⣤⣴⡾⠟⣛⣡⡼⢻⡻⠟⣿⣾⣻⣿⣿⠓⠂⠄⠐⠆⠈
⠀⠀⠀⠀⠀⣀⣴⣶⡚⣿⣶⣿⣿⣆⣀⣀⠀⣿⢆⣙⡛⢛⣭⡭⠶⢿⠿⢦⣐⣛⢡⣾⣿⣿⡷⠚⠃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠑⢀⣋⣀⣈⣿⣿⣿⡿⢛⣭⣭⣭⣭⣭⣬⣽⣷⢶⣶⣿⣾⣿⣿⣿⣿⢣⣿⣿⣿⠟⠁⢀⠀⠀⠀⠐⣀⠔
⠀⢀⣤⣄⠘⢿⣿⣿⡿⢛⣡⣾⣿⣿⣿⣿⣿⣯⠍⢿⠟⡘⣿⣿⣻⣿⣿⣯⡏⢸⣿⡿⠋⠀⠀⠀⣠⠴⠞⠋
⢠⠘⣿⣧⠖⠻⠿⣿⣿⣿⣿⣿⣿⣿⠋⢶⡎⠉⠀⠀⠀⠀⢀⡽⣿⣿⣿⠏⢁⣿⠋⠀⠀⠀⠐⠁⠀⣠⡆
⢠⡞⢿⡇⠀⢀⣀⣴⣿⣿⣿⣿⡜⠁⠛⢀⡀⠀⠸⣿⠇⢀⣠⣤⣿⠟⠉⠀⠈⠋⡴⠂⢀⡀⢤⣖⠟⠋⢹⡀
⠀⣥⣼⣯⣶⡾⠋⠀⠀⠙⣿⣿⣿⣿⡷⠈⠁⠶⠆⣠⣴⣿⡟⠻⠇⠀⢰⠄⢠⡿⢀⡴⡉⠀⠸⣟⢷⣾⠄⣷
⠀⠈⣠⣽⣿⣿⣦⣴⠞⠛⠛⠻⣿⡟⢿⣿⣷⣧⣾⣿⡿⠋⠙⠋⠀⢀⣼⡿⢟⡼⡋⠀⠀⠀⠀⢹⣞⣧⡦⢹⡇
⠀⠈⢿⣋⣽⣿⣿⣿⣾⡶⠿⠿⢿⣧⣼⣿⣿⣿⣿⣯⣍⠀⠀⣤⠽⠟⢋⡴⠟⠋⠀⠀⣀⡀⠀⠀⠈⠻⠆⠘⡇
⠀⠀⠐⣿⠁⢈⣻⣿⣿⣧⣄⠀⠀⠙⣟⠋⣿⣿⣿⣯⣠⡄⠖⠹⣖⢊⠟⠁⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠠⠐
⠀⠀⠀⠠⡷⢿⠋⠿⣿⣿⣿⣤⡾⠶⢼⠈⢩⣿⣿⣿⣯⠀⣠⣾⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠹⡄⢲⣄⠈⠻⣿⡿⣄⠀⠀⠀⢠⣿⣿⡿⣿⣷⣅⡤⠸
⠀⠀⠀⠀⠀⢿⠈⣿⣦⠀⢊⠱⣦⣵⡖⠀⠀⠀⠀⠀⠈⠛⠿⣷⡄⢤⡤
⠀⠀⠀⠀⠀⠈⣆⢸⣿⣷⡈⢷⣞⢿⡗
⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⣿⣌⢻⣞⣣
⠀⠀⠀⠀⠀⠀⠀⣷⠠⠙⣿⣿⣇⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣀⣛⢿⣶⠹⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⢀⡖⣃⢀⣀⣠
⠘⠲⠤⡤⠀⣠⣠⡇⠀⠀⠀⠀⠀⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⢰⠉⠇⠀⢀⣀⠀⠀⢸⣈⣄⠀⢀⣄⢳⢺⠰⠾⡗⠛⠛⠋
⠀⠀⠀⠀⠈⠁⠂⠠⠌⠉⠀⠀⠀⠀⠴⠃⠿⢲⡤⠤⠤⣶⠀⠙⣃⡿⠀⠐⢸⡇⠀⠨⣃⣤⣉⠉⢻⡄⠀⡀⢠⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⡆⠚⠉⠀⠀⠀⠢⠐⠀⠀⠀⡉⠺⠀⢸⠧⠀⢠⠎⢣⠀⡆⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠗⠁⠀⠀⠠⢄⢠⢴⣇⠄⠀⠀⠀⠀⠀⠀⢀⠀⢠⡾⠀⠱⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠘⡇⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⠈⢁⣀⠆
⠀⠀⠀⠀⠀⠀⠈⡔⢁⠭⡉⢦⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠆⡠⠒⠊⠀⠓⠺⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⡀
⠈⠠⢉⣉⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⢔⠀⠀⡃⠀⠀⠀⣀⣀⣀⠀⠀⠤⠀⠀⠠⠴⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⠐⠀⠀⠁⠉⠁⡈⠁⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠂⠀⠀⠂⠒⠒⡀⠀⠀⢀⠂⠉⠉⠉

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⡮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⣀⣀⣀⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⣀⠀⠀⠀⠐
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠐⠂⠒⠒⠛⠛⠽⠶⠒⠶⠆⠻⠤⠤⠤⣤⣤⣭⣤⡛⠚⠛⠛⠒
⣒⣂⣈⡉⠹⠄⣀⣠⣤⣶⣶⣿⣿⣾⠿⠷⠦⠴⠄⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠛⣓⠒⠒
⣿⣿⣿⡿⠿⠟⢻⣿⣿⣿⣿⡿⢷⣶⣾⣷⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠀⠀⠁⢐⣢⣤⣤⣤⣀⣀⣀⣀
⣍⣉⣛⣿⣿⡯⠭⠭⠽⠿⠟⠉⠉⠉⠉⠉⠉⠉⢉⣉⣩⣭⣭⣭⣭⣭⣭⣽⣿⣿⡶⣶⣲⣶⣶⣖⣂⣀⣒⣒⣒⣾⡿⠿⠿⠿⠛⠛⠛
⣿⣿⣟⡛⠋⠉⠛⠛⠛⠛⠓⠒⠢⠌⠉⠉⠉⠉⢉⣉⣉⣁⣤⣄⠀⠀⠀⠀⠀⠀⣈⣛⣩⣭⣭⣭⣥⣬⣭⣭⣽⣿⣷⣶⣶⣤⣭⣭⣉
⠀⠀⠀⠈⠹⠶⠶⠶⠾⠿⢿⣷⣤⣤⣤⣶⣶⣾⠿⠯⠷⠶⠶⠶⠶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿
⣶⣿⣿⣿⣿⡦⠤⠀⠀⠀⠒⠛⠿⠿⣯⣭⣥⣤⣤⡤⣤⠤⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⢛⡛⢋⣀⣤⠘⠋⠉
⠉⠋⠀⠒⠒⠒⠠⠶⠶⠄⠀⠛⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣒⣒⣂⣀⣒⣲⣷⠾⠒⠒⠛⠛⠛
⣛⣻⡿⣿⣿⣿⣿⣻⣛⣛⣛⣛⡛⠛⠛⠛⠻⠿⢿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡤⠀⠀⠀⠤⢤⣄⣀⣀⣀⣈⣛⠛⠛⠺⢿⡿⢿⣿
⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣷⡶⠶⠶⠶⠶⢿⣿⣟⣛⡛⠻⠿⣿⣿⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣉⣡⣤⣤⣴⣶⣖⣶⣶⣶⠶⠶
⣤⣤⣤⠤⣤⢤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠦⠄⠀⠀⠒⠶⠶⠶⠶⠶⢚⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣭⣭⣭⣥⣤⣤⣴⣶⣶
⠛⠁⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣶⣶⣶⣶⣶⣤⣦⡾⠿⠿⠳⠿⠿⠿⠶⠆⠀⠀⠒⠚⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣂⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣶⡶⠶⠶⠒⠒⠒⣒⣲⣾⣿⣧⣤⣤⣤⡶⠶⠶⠿⠷⠞⠛⠛⠛⠛⠛⠛⣉⡀⠛⠋⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣤⣴⡶⠾⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠠⠤⠀⠀⠒⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⡶⣦⣤⣤⣤⣤⣤⡤⠤⠤⠦⠀⠠⠠⠀⠤⠤⢤⣤
⣶⣶⠾⠛⠉⠉⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠛⠛⠛⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣚⡛⠻⠿⠾⠿⠿⣿⣿⡿⠿⠶⠶
⣤⣴⣶⣾⣿⣿⡿⠿⠿⠿⣿⠿⠛⠛⠛⠻⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣲⣶⣶⣖⠒⠚⠛⠉⠉⠉⠁⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠬⢭⣭⣭⣭⣉⣙⣛⣛⣛⣿⣿⣟⣛⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣈⣭⣿⣿⣿⣿⣷⣶⣤⣤⣤⣌⣉⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⡛⠛⠛⠛⠛⠉
⣀⣠⣤⣴⣆⣠⣭⣭⣭⣭⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠿⠯⠽⠿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣄⣀⣀⣀⠀⡉⣉⣉⣉⣉⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿

⠌⠀⠌⠀⠠⠀⠀⠄⠀⠁⠀⠀⢀⠂⢀⠀⢀⠀⠤⠈⠀⠂⣐⠀⠄⠀⣰⠈⢀⠆⠀⠄⡀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠁⠆⢁⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⠀⣠⠉⠀⠆⢘⠁⠁⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠰
⠀⠀⢀⠀⠠⠀⠀⠂⠀⠀⠈⠀⠀⢐⠀⠄⠄⠄⠄⡈⠀⠄⠀⠄⠀⠂⡀⠀⠀⠀⢈⠀⡈⠀⠀⠐⠂⠌⠀⠠⠈⡀⠁
⠀⠚⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡄⠠⠀⠁⠀⠀⠁⡀⠈⡋⠀⡘⢀⠂⠐⠃⠄⠀⠄⠀⡥⠈⠁⠈⠁⠡⢨⠁⠀⠒
⡠⠀⠀⡀⠀⠀⠀⡀⠄⠂⠈⠠⠄⠘⠀⡁⢀⠀⠃⠀⠀⠂⠀⡂⠠⠀⠀⡀⠀⠃⢈⠀⡕⠰⠆⡁⠀⠀⠄⠐⢀⠩⠰
⠁⢀⠐⠀⠀⠀⠀⠀⠆⠁⡀⠰⠀⠐⠁⠄⠀⣀⠀⠂⠀⠀⠠⠁⢠⠄⢀⡀⠀⢀⢁⠀⡀⠁⠀⠀⢉⠀⠀⢐⠂⢀⡁
⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⢁⠀⠀⠈⠀⢠⠂⠈⠌⠈⠁⠤⠡⠔⠀⠀⠀⠠⠄⠀⠄⠀⠐⠀⢈⡀⣀⠰⠀⢐⠁⠀⠄
⠀⠡⠄⠀⠆⡀⠀⠀⠀⠀⠁⠖⠀⠀⠀⠀⠂⠉⠀⠀⠘⡀⠀⠈⠆⢁⠀⠘⡀⠒⠐⠠⡀⠐⠂⠀⠩⠈⢠⠌⠀⠐⣁
⡉⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠐⠀⠉⠀⡐⠀⠴⢠⠁⠄⠀⢀⠐⢃⡂⣠⢈⡀⠀⢀⠂⠄⠀⠒⠘⢀⠀⠤⠀⡄
⢀⢀⠀⠀⠁⠀⠄⠁⠀⠄⠀⠀⠉⠀⠀⠄⠀⠀⠄⠰⢀⠀⠁⡒⠈⠀⡄⢀⠀⠀⠀⠘⠀⠆⢐⠀⠘⠃⡘
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠑⠀⠘⠀⢀⠠⠈⠀⢀⠀⠤⢘⠈⠁⠄⠂⠄⠀⠀⠁⢀⠀⢈⠁⠀⠁⠐⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠀⢀⠰⠀⠒⠀⠀⢀⠨⠀⠆⠀⡀⠀⠀⠰⠆⠀⠂⠤⠈⣀⠘⢈⠁⠤⢠⠈⠀⠤⠐⠀⠒⠀⠤⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠒⠠⠑⠀⠀⠀⠂⠀⠃⡤⢀⠃⠂⠀⠀⠀⠄⠀⢀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠐⠠⠄⠀⠂⠀⠀⠈⠀⡀⠀⠀⠠⠈⠄⡐⠀⢠⠡⠄⠐⠀⠆⠠⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⢀⠀⠁⠀⠀⠃⠀⢀⠀⠚⡈⢀⢀⠀⠀⠂⠰⢀⠀⠁⠀⡁⣀⠀⠄⠀⠅⠀⠀⠀⡀⢀⠁⢀⠠⠀⠀⠈
⠀⠂⡀⠀⢠⡀⠀⠀⠀⠠⠀⠂⠀⠀⠂⠀⠂⠂⠀⠠⠀⠁⠀⠀⠀⠄⠀⠀⠐⠂⠤⠘⠀⠀⠀⠀⠈⠀⠆⠈⠀⠂
⠐⡀⠀⠉⠄⠀⠀⠀⢀⠀⠄⠉⡄⢁⠀⠂⠀⠀⠀⠁⠀⠀⠈⢀⡀⠄⠀⡀⢀⠁⠀⠀⠈⢀⡁⠂⠐⢀⠀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠸⠃⠰⠀⠀⠂⠀⠀⠀⠀⠀⠄⠐⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡁
⠘⡒⠀⠀⠰⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⢀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠂⠄⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠁⠀⠀⡀⡈⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠰
⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⡀⠀⠀⠄⠠⠀⠀⢀⠛⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠐⠠⠀⠁⠀⠀⢀⠀⠀⠄⠀⠀⠀⡀⠀⠈⢀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡐⠐⠂⡀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣷⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣟⣵⣮⣈⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣉⣥⣍⢈⣿⣿⠟⠻⢯⠹⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠔⢿⣿⣿⣟⣒⡢⢤⣄⣀⢀⡀⢨⣯⡷⠆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠜⠁⠀⠀⠙⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠇⠀⠀⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣽⣿⣿⣏⣤⠞⠀⠓⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣿⣶⣿⣿⣿⣈⠈⣿⣤⡄⠀⢀⡴⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣧⣾⣿⣿⣿⣿⣯⣤⡝⣿⣿⣤⠎⠰⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⣷⣶⡀⢀⣠⡞⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣉⣿⣿⣦⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠾⢛⢻⣛⣿⣭⣭⣬⣽⣿⣿⢿⣿⣿⣟⠻⠛⡗⣠⠏⠈⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠞⠛⠋⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣲
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣶⡄⢉⣾⣷⣄⠀⠰⣿⡀⢠⣄⠀⢀⣠⣤⣤⣄⠀⠀⢀⣀⣤⣤⣄⠀⠀⠠⣶⣦⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣿⣿⣷⠀⣼⣿⡁⠸⣿⣇⠘⢿⣿⣿⣿⣿⡄⠈⢿⣿⣿⣿⣿⣄⠰⣿⣿⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢝⣿⣿⢯⣿⣿⠀⢿⣿⠃⢀⣿⣧⠐⣿⣿⠀⠙⢻⣧⠀⣾⣿⠀⠉⢻⣿⠀⢿⣷⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠻⠿⠢⣿⡏⠀⢿⣿⠀⢈⣿⡗⢀⣿⣿⠆⠀⣿⡿⠀⣿⣿⠆⠀⣽⣿⠀⠀⣹⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠁⠀⠸⣿⣇⠀⣿⣿⣦⣼⣿⠃⠰⣿⣿⣾⣶⣿⠟⠀⣽⣿⣿⣵⣿⡟⠀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠻⡧⠀⠘⢿⣿⡿⠟⢠⡄⢼⠿⣿⠋⣭⠄⢀⣸⡿⢿⡏⠉⠀⡘⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠐⠀⠈⠀⠀⠀⠀⠈⠁⢀⣻⣶⣠⡿⠉⣄⢀⠀⠀⡀⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣔⠂⡈⢁⡀⠈⣇⠈⠹⣿⣿⣿⠅⠀⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⠀⠀⠀⡀⠈⣷⣀⠀⢹⣜⣷⣿⣷⣦⣽⣿⣿⢚⠂⠶⢀⠀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠺⠋⣶⢿⣿⣴⣶⣾⣿⣿⣿⡛⠛⣻⢻⣾⣷⣀⢳⣴⠏⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⡐⠀⣶⢆⡐⣂⡁⠛⣸⣿⣿⣿⣵⣿⠤⣨⣅⠙⢚⣿⣿⣶⠾⡟⠇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣃⠀⢀⡈⠴⡄⣛⣾⡟⣯⣿⣿⠟⣱⣾⡿⠑⢿⣿⣛⢻⣷⣦⣜⢣⣄⢂⣤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⠼⣿⣧⣹⣿⣷⣿⠟⣽⣣⡾⠋⠀⠀⠀⢹⣿⣿⣿⣿⣭⣡⣟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⢀⡄⠽⣿⣿⣿⠟⣃⣼⢿⣿⣛⠀⠐⣋⣁⢸⣿⣿⣿⣿⣿⡉⣻⡿⢧⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠂⠈⣈⢧⣚⣿⣿⣏⣰⡿⣡⣟⠉⢁⡀⣀⠈⠁⣸⣯⣿⣟⣿⣿⠿⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣤⠉⠤⣾⣽⣾⣻⢿⣿⣧⣿⣿⣿⣯⡥⠯⢽⠜⠛⠛⢛⡿⢿⠿⢷⣟⣂⣷⠿⣀⡀⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⡽⠋⢳⠿⠿⢿⢻⢿⣦⠂⠰⠐⣶⣶⣶⣿⡿⢾⣷⡍⢙⠛⠠⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⢶⣤⠶⠞⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣶⣦⣄⣀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⠞⣤⣿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣧⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⢾⣿⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠲⠻⣿⣿⣿⣟⠛⣹⣿⣛⣻⣻⣟⠻⢿⣾⢿⣿⣿⢿⣿⣿⣿⣿⣿⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣿⣟⠿⢙⡄⢻⠁⠰⣿⣿⣿⣇⠺⣿⢨⣹⣿⠀⣚⣍⣿⣿⣿⢾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⣆⣿⣿⣻⠀⠀⠌⠂⠈⣽⣿⡃⢈⡐⣿⠁⠀⠿⠀⢹⢯⣼⣿⣿⡆⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠽⣿⡻⠉⢻⠂⠀⠀⢤⡼⣷⡆⠈⠐⠧⠀⠀⠚⠀⠀⢚⢩⣽⣿⡅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡏⢛⡇⠸⠆⠀⠀⠞⢯⣿⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠺⣽⣄⣂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣬⣭⣤⣭⣯⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣾⣿⣿⣿⣷⣶⣿⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠆⠀⠠⡄⢊⢹⣿⣷⣶⢖⣓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠓⠛⠓⢚⣿⠻



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠄
⣶⣦⣴⣿⣶⣶⣦⣤⣤⣤⣤⣤⣶⣦⣦⣤⣤⣶⣤⣤⣼⣿⣧⣬⣽⣿⣦⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣛⣻⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠛⠉⠉⠉⣉⣉⡉⠉⠉⠉⣉⣉⣉⡉
⢿⣿⣿⡿⠿⠿⠿⠿⣻⣛⣟⣿⣿⡿⠿⡿⣿⣿⠿⠟⠛⣿⣿⠿⣻⣿⡋⠀⠀⠁⠀⠀⠀⠠⠶⠶⠾⠿⠿⠶⠀⢻⣟⣻⣿⡿⣿⣿⢻⡿⣿⡿⢟
⣾⣤⣿⡾⢶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠿⠿⠁⢾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠉⢠⣶⣴⣶⣷⣴⣶⣶⣿
⣾⣿⣿⣷⣼⣿⣭⣯⡙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣦⣀⣀⡀⠀⢙⣿⣿⣿⣿⣽⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠐⠂⠀⠀⢰⣆⢈⣿⣿⣿⠿⠿⢿⣷⣶⣤⣝⠙⣿⡏⠉⣻⡿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣟⢿⣿⣋⡁⠀⠤⠖⠒⠲⢦⣤⣤⣄⣀⣀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⣦⣶⡀⢭⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡩⠭⡒⠤⠤⠀⠂⠠⠤⢔⡩⠭⡑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢎⠶⠶⢸⠀⠀⡀⢀⠀⠀⡎⠶⠶⢈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⠒⠒⠉⣀⠠⠤⡠⠤⢄⡈⠒⠒⠋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠐⠒⠒⠉⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡰⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠲⡀
⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⢇⠀⢆⠀⠀⠘⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡏⠀⠀⢀⠇⢠⠃
⠀⠀⠀⠀⢀⡠⠬⠧⢀⠁⠀⠀⠱⡀⠀⠀⠈⣆⠀⠀⠀⠀⠀⡜⠀⠀⠀⡐⠀⠀⠀⢂⠴⠧⠤⣀
⠀⠀⠀⠀⠓⠒⡴⠀⠀⠁⠀⢀⠀⢑⠄⠀⠀⠈⡁⣢⠠⣖⣈⠀⠀⠀⢜⠀⢀⠀⠀⠁⠀⠐⡦⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠠⠤⠊⠲⠤⠽⠀⠀⠸⠥⠔⠊⠑⠀⠂⠀⠈⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠉⠁⠀⠀⠸⡄⠠⣬⣁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⢳⣀⣘⡬⠽⠶⠀⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠦⠤⠒⠋⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠲⡄⢠⡀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠺⢤⣠⡾⢡⠋⠇⣀⡤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠆⠀⠈⢡⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣉⣺⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣎⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⡶⢤⡀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣤⣄⣀⣀⣀⣤⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠙⠻⠿⢿⠟⢻⣿⢿⡟⢻⣏⢉⡔⢲⣦⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠘⠦⠬⠋⠘⠧⠤⠏⠈⠣⠤⠟⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠟⠿⠷⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⢻⡇⠀⠀⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⡾⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⡼⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⣠⠞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣰⠏⠀⠀⠀⢉⡷⠦⣄⣀⣀⣀⣀⣀⣀⡤⠶⢯⡁⠀⠀⠀⠳⣄⠀⢀⣀
⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⣟⠁⠀⠀⠀⣰⠋⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⣿⠉⠉⠉⠙⠲⢤⡀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢰⠃⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⠀⠀⣠⠤⠤⢤⡀⠀⠀⠀⠀⢳
⡞⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠘
⣧⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢠
⠹⡄⠀⠀⠀⠀⠛⠶⠶⠞⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠛⠶⠶⠞⠁⠀⠀⠀⠀⡼
⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠈⠙⠦⣄⣀⣀⣀⣀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣀⣀⡤⠞⠉
⣶⣶⠶⠶⠶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⣀⣀⡤⢤⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠙⢋⡀⡙⠃⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣩⣻⡆⠀⠀⣀⣀⣠⠤⠷⣄⡘⢧⣐⣛⣦⣼⡵⠧⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⢇⡬⠖⠚⠉⠉⠀⠀⠀⠈⢻⣙⡞⠃⢹⠞⠉⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣦⠽⡶⠒⠒⠚⢛⡽⣿⠀⠀⠉⠀⠉⠉⣇⠀⠀⠰⡏⢭⡉⠉⠉⠉⢹⡛⠾⠟⠓⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠊⢻⣦⠘⡇⠀⡔⠲⠋⢠⠇⠀⠀⠀⠀⡠⣄⢻⠀⠀⠀⢻⡀⠹⣄⠀⢀⣼⠇⠀⣦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⢸⣿⠀⣧⢸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠓⠊⢸⠀⠀⠀⠀⢷⠀⠘⡆⣏⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡿⡏⠀⡏⢸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⣷⢹⠀⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢀⣿⠇⠰⣇⡼⠀⠀⣼⠀⠀⠀⠀⠀⠀⢯⡽⠀⡇⠀⠀⠀⠀⠸⡄⠘⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢠⡿⣄⣀⣀⣀⣀⣤⣤⠴⠶⠶⡶⠶⠶⠶⡶⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⡄⠀⠀⠘⡇⡴⢡⠜⠛⠛⠛⢻⠀⠀⢰⠋⠉⠉⠙⢳⠀⠀⠀⠀⠀⠀⠀⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⠀⠀⢰⣧⡄⠀⢸⠃⡇⠈⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠘⠿⠁⠀⠸⣴⠃⠀⡟⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢧⡼⠒⠒⠛⠛⠃⠘⠛⠛⠛⡟⠀⠀⠀⣠⠋⠉⠉⠹⣄⣀⠀⠀⠈⢯⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣭⣝⣛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠲⣄⣀⣀⣠⠖⠒⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠙⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡗⠀⠠⢤⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⣀⡀⠀⠀⣷⡇⠀⠀⠘⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⢦⠀⠙⠿⣿⣥⡤⠀⠊
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢰⠀⠀⠀⠀⢸⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢤⡀
⠀⠀⠀⠀⠙⠦⠘⠀⠀⠀⠈⠳⠤⠤⠄⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡠⠂⠉⢹⢶⡄⠀⢸⣆⣀⡀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠈⠛⠛⠛⣧⡀⠀⠀⠀⠀⠀⢀⣄⣀⣀⡀⠰⣇⠀⠀⠀⠀⡌⠀⠀⠉
⠀⠀⢠⠈⠉⢻⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⠤⠤⠒⠉⠀⢤⠀⠈⠳⡝⠳⠦⠴⠊⠀⣄⠈⠃⠰⠂
⠀⠀⠈⠳⠐⠁⠀⣸⠁⠀⡀⢀⠤⢤⣤⡀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠦⠄⠈⠀⠀⠀⠹⡄⠀⠀⠄⠠⠬⡀⠀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢾⣴⣇⡀⢀⠜⠁⠀⢈⡠⣤⡀⠀⣸⠻⣦⠠⣿⠺⣶⣦⠀⠀⣏⠀⠀⠀⠀⠀⢸⠀⠑⠀⠰
⠀⢤⡀⠀⠀⠀⠈⢷⠀⠀⠉⠉⢉⡉⠙⠻⣦⣹⠋⠉⠛⣷⠛⠈⢛⡓⣿⣶⣞⡿⠃⡀⣿⣤⡄⡃⠺⠟⡻⡆⠠⣶⠆
⠳⢤⣥⣆⠀⠀⠀⠘⡄⠀⠀⣴⡉⠟⠀⠀⣹⣿⡀⠀⣠⣿⡎⠙⠛⠇⠛⠉⠁⠀⢞⡼⢟⠛⢿⡦⡀⠀⠚⠫⠳⡄
⠀⠈⣡⠈⠉⠉⠀⠀⢷⠀⠀⠘⠷⠦⠤⠔⠁⠈⠋⠉⠁⠚⠛⠃⠚⠛⠛⠛⠐⡞⠛⣇⠃⠀⠃⠈⠀⠀⠀⠀⢀⣇
⠀⠀⠛⠆⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠚⠺⠍⠀⠀⠀⠀⠀⠀⠀⠉⠞⠒
⢠⡁⠀⠀⠀⠀⢀⠀⠀⠀⠙⠛⠲⠦⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⣒⣒⣻⡏⠳⣤⠀⠠⡄⠀⡀⠀⠀⠀⠀⠆
⠀⢧⠀⢀⠀⠀⠈⢧⡠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⡛⠛⠛⠋⠉⠉⠀⠀⠳⠤⠤⠀⠹⢇⣸⡆⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠙⡆⠀⠀⠀⠀⠀⡴⠋⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⢮⠀⢻⠀⠀⠀⠀⡼⠁⢰⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⢾⠁⠀⣀⡔⠁⠈⡆⢸⠀⠀⠀⠸⠁⡀⠉⠡⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠂⠀⠀⠀⠂⣉⠁⠀⠀⠀⢹⡘⡃⠀⠠⠁⠔⠀⠀⠀⠁⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠁⠀⢀⡓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⣴⠂⠠⠈⠀⠀⠀⠈⡔⠒⠒⠒⠒⠒⠲⠤⣤⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⠄⠀⠀⠀⠀⠈⠀⠉⠉⠉⠙⠛⠲⣶⠦⢤⣄⣻⣕⢤⣀⠀⠀⠀⠙⠂⡁⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⢀⠀⠀⠀⢻⠀⠀⠠⠎⠥
⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠉⠙⠚⠫⠒⠒⠒⠂⠑⣀⠀⠄⠒⠚⠒⠂⠀⠀⢠⢾⡋⠂⠀⣸
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⣸⠁⠀⠀⣿
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢱⠏⠀⠀⢀⡇
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠈⠳⣤⠎⠀⠀⠀⢸⠁
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠄⠀⡠⠋⠀⠀⠀⠀⡞
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣀⢤⠒⠁⠀⠀⠀⠠⠜⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣀⠠⠴⠊⠁⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠼⢀⡤⠶⠚⠉⠇⠀⠀⠀⠀⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢲⣠⡄⠀⢀⣉⡉⠉⠉⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠵⠸⡉⠀⠩⣉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⣏⣧⡴⠃⠀⠀⠉⠉⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠓⠒⠲⠶⠖⠒⠒⢦⡇⢸⢿⡉⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠺⠟⠒⠲⣄⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢘⡷⠆⠀⠤⡍⠙⡖⠒⢺⡁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠲⠀⠀⠚⠋⠀⠉⠁⠀⣶⠞⠘⠤⠋⠰⠁⣰⠋⠉⠁⠀⠽⢆⢀⣀⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣚⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠂⠀⡠⠊⢹⡉⡆⠐⢙⡆⢨⠁⠀⢻⠀⠀⠀⠀⠀⡿⠉⠀⠒⠒⠤⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠶⠊⠀⠀⠀⣯⡤⢬⠉⠀⠀⡠⠦⢼⡖⠒⠂⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠤⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢈⣇⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⢿⣒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠤⢤⣤⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠆⠐⠀⠆

⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠋⢈⣿⢳⣶⡼⣇⠐⢀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠸⣿⣾⣏⠲⣿⣻⠾⣵⡆
⠀⠀⠀⠀⢰⣀⠀⠀⠠⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠀⣧⡉⠈⠠⣓⡌⡠⢄
⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢶⣶⣾⠀⣢⣀⣻⡿⣦⣶⣄⢠⡀⢂
⠀⠀⠀⠀⢸⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⡦⠀⡀⠐⣽⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣷⡈
⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡦⢠⡤⣿⣶⣶⣿⣿⣷⣄⣿⣶⡿⢯⣝⣷⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⢠⡀⠀⠀⢼⡟⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠼⢿⣿⢻⣟⢻⠳⠀⠿⣿⣿⢄
⠀⠀⠀⠀⢄⢸⣿⠀⠀⠀⢸⠉⠂⠀⢸⣷⣮⣟⠻⣿⣿⣻⣿⣿⣿⣿⣿⣷⡛⢋⣙⣻⠏⠁⡁⠀⠀⠑⡀⠉⠈
⠀⠀⠀⠠⣸⣿⠁⠀⠀⠀⢻⠄⠀⠀⠠⠛⠀⠹⡆⠉⠘⠺⠻⣿⣿⣿⣿⣿⡇⢡⠈⢾⣽⣽⣷⢿⣶⠼⣿⣿⡿
⠀⠀⠀⠰⣹⡟⠇⠀⠀⠀⢸⣄⠀⠀⠀⣄⠀⠈⢡⣤⣤⣤⣄⣸⣿⣿⡿⠿⣉⡛⢾⢻⣿⣿⣷⣿⣿⣶⣬⣁⢄
⠀⠀⠀⠸⢿⣿⡆⠀⠠⠀⠾⣏⠂⠀⠈⠫⠀⠀⠀⠀⠚⠙⠛⠋⠿⣯⣽⣁⣉⣁⣀⣬⣽⣿⣷⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢤⣼⣥⠲⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣤⣄⣉⣛⠛⠛⠛⣻⣟⢻⣿⣾⣿⣿⣿⣿⣿⡤
⠄⠀⠀⡀⣦⣽⣿⡁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⢉⢠⡤⡎⠛⢻⣽⢻⣻⣻⠗
⠀⠀⠈⠙⠳⠿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣴⣤⣶⣦⣄⣐⠛⠲⠂
⠀⠀⠀⠀⠀⠀⠘⠛⢛⣻⣶⣶⣶⣦⣼⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠄⠀⠀⠀⠀⢂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣤⣿⣏⣿⣿⣿⣍
⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻
⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢿⡿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠙⠻⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣤⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠛⠁
⠀⢀⣤⣀⢒⣾⣷⣤⣤⣤⣭⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠤
⠀⠀⠐⠀⠉⡹⢟⡛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠻⠧⠅⠈
⠀⠀⠀⠀⠀⠁⠑⠋⠀⠀⠐⠾⣿⣿⣿⣿⣻⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠧⡿⢅⡀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣤⣴⣶⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣦⣴⣦⣤⣦⣴
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠉⠕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⡢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⠈⡄⡀⢀⢀⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠜⠒⠈⠁⠒⢄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠑⠒⠒⠢⡤⠒⠚⠀⢀⠂⠄⠔⡠⡠⢃⢊⠎⠀⠀⠀⠀⠀⠀⡄⢣
⠀⠀⠀⡠⠄⠠⢼⠀⠀⠀⢀⢀⠄⡠⢀⢀⢀⠄⢄⣄⣐⣆⣐⣀⣀⡀⣠⣠⡥⠚⠘⠺⡴⠋⠁⠳⡎⠀⠀⠀⠀⠀⠀⠀⠄⠸
⠀⠀⡜⠀⢀⢤⢀⢄⠔⡀⠡⢂⠜⡴⠥⠆⠚⠈⣩⠜⢋⢩⠉⠉⠙⠩⢍⣉⠒⠲⢤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠑⠤⠤⠤⠤⠀⠂⣒⠶⠂⠁⠀⠀⢀⡤⠊⠀⠀⠀⠂⢣⠀⠀⠈⠐⠀⢙⠢⣕⠀⡨⢉⠐⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠈⡆⢁⠄⠀⠀⠂⠠⠈⠓⢄⠑⡡⢂⠄⢉⠑⠤⡀⠀⠀⠀⠀⠀⠀⠋⠐⠄
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡐⢍⡀⠀⠀⠈⠒⠤⠀⠑⢄⠕⡨⠐⡨⢐⣌⣲⣄⠀⠀⠀⠀⠀⠀⠓⠢⡀
⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⢀⠜⠀⠁⠀⠀⢀⣀⣀⣀⣀⣀⠠⠀⠇⠀⡂⠤⠄⠒⠒⠒⠀⠠⢈⣢⣀⠕⠊⢁⠀⠄⠈⢀⠂⠄⡀⠠⠀⠀⠀⡅
⠀⠀⠀⠉⠉⠉⠁⠒⠠⢁⡬⠔⠒⠈⢉⠄⠍⠀⠀⠀⠀⢿⠁⠁⠚⠁⠀⠀⠀⢠⠀⠀⡠⢀⠀⠌⡙⡰⠡⠂⠌⡰⢠⠂⠎⡐⠡⢂⢂⠂⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⣀⣀⣻⣏⣐⣁⣊⡐⠀⠁⠂⠈⠀⠀⣁⣊⣈⣀⣀⣁⣈⣀⣁⣁⣈⣐⣀⣁⣀⣈⣀⣀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⡤⠀⣠⠀⠀⠴⠀⠀⠀⡤⠀⠀⢠⠀⠀⠀⠄⠀⢀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣜⠇⢀⡀⢸⡃⠀⠀⠸⠁⢰⡌⠀⠰⠊⠀⠀⣢⠆⠀⢰⡁⠀⠀⠗⠀⠀⠗⢠⠃⠰⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢀⡀⠁⢰⡥⠀⠸⢀⠀⢠⠚⠀⠀⠀⠰⠂⡜⠁⠀⢀⠀⠀⢀⠴⠀⣀⡒⠀⢀⡶⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢀⡀⠀⠀⢈⡸⠀⠘⠃⠀⠀⠸⠊⠀⠀⠀⢀⡭⠀⠀⠘⠃⠀⠉⡀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⢸⢻⡀⢀⡀⢀⠴⠀⠀⣀⠀⢀⠄⢀⣈⠁⢀⠀⠀⠼⠃⢀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⡀⠂⠈⠁⠀⢰⠄⠀⠛⠀⠈⠁⢀⡪⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⡀⠀⠠⢀⠀⡀⠀⢀⠀⡀⠀⠀⢀⠀⠀⢀⠀⡠⠀⠀⡀⢀⠀⡠⠀⡀⠀⠀⡀⠀⠀⡀⢀
⠀⠀⠀⠉⠂⠁⠊⠔⠨⠊⠔⠄⠈⠔⠡⠊⠔⡡⢂⠅⢊⠔⠡⢊⠄⡥⢊⠔⠨⠔⡡⡪⢂⠁⢊⠔⡡⢊⢔⠡⢊⠔⡥⢊⠂⠕⠊⠠⢊⠄⠔⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠌⠘⡄⠐⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⡄⢀⠀⣀⡃⠀⠑⠠⠛⣦⣤⢡⡴⣿⢀⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠙⠋⠀⠀⠀⢁⡄⠱⡀⠙⠋⠁⠀⠀⣤⢀⣘⠜⠏⠀⣏⡄⠀⡜⠀⠀⠠⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠳⠀⠨⣴⣶⣄⠀⢰⣿⠛⠌⠃⣰⣀⣻⠧⢼⡁⠀⠠⢤⡎⠀⢠⠀⠀⠀⠊⠙⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢳⠀⣴⣇⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣵⡌⠠⢀⣿⠀⢠⠀⢨⠟⣭⡷⠀⠈⠀⠀⠀⠑⡆⠁⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⢿⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣟⣦⡹⣇⠀⠘⠀⣠⣼⠇⢀⣠⠀⠀⠀⠀⢠⠐⣀⠂⠀⠀⣴⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢀⣀⣈⢣⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠻⢿⣶⣴⣷⣿⣋⣉⣉⣉⠄⠀⠀⠀⠘⠀⠃⠀⠀⠈⠀⠀⡼
⠀⠀⠀⠀⠀⡴⠋⢰⠋⠁⢳⡌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡈⠉⠟⠉⠉⠀⠀⠀⠐⢀⠀⠰⡄⢠⡇⠀⡠⠀⠈⠰⠧⠖⠃
⠀⠀⠀⠀⢸⠁⠀⠈⠦⣀⠀⠹⣦⠣⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣹⡎⣿⣿⣵⢋⣀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⢍⡛⠃⣉⠢⡀⠀⠀⠈⠐⠠⢄⠀⠀⠀⠀⠈⠀⠐⠒⠂⠀⠐⠶⠤⢄⣀⢙⠿⢿⣿⣻⣾⣵⡋⠈⠛⠀⠀⠀⠀⠀⠀⠀⢁⡐⠄
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⢷⡈⠓⢦⡀⢷⡀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠈⠃
⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠳⣄⠀⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠸⠃⠀⢱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⡵⠶⠄⠀⠀⠀⢘⣆⠀⠘⠳⢄⡉⠲⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠨⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⡠⠟⠀⠀⠀⠀⢌⠙⠲⢤⣐⡀⣀⣀⣐⣶⣄⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⡠⢿⡦⠀⠙⢆⠀⠀⠀⠈⠉⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠉⢍⠲⠤⠤⠽⠇⠰⠊⠀⠀⠀⠐⠀⠁⠀⢉⡲⠖⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⢩⠇⠀⠀⠀⢀⠔⠀⠀⣽⢤⣤⢿⣇⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⠀⡾⠁⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠉⡉⠟⢁⡠⢂⡠⠶⢥⣄⣀⣠⠇⠾⣧⣶⣿⢠⠆⠜⠀⠈
⠀⠀⠀⠈⠉⠉⠉⠒⠉⠲⣦⣄⣡⣀⣠⢀⠰⠏⣐⣲⢤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠠⣀⠈⠹⠛⠛⠶⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢭⣄⣐⠛⠉⠀⠀⠉⠓⠶⠤⢤⣤⠤⠄⠀⢀⣀⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠃⠀⡟⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣀⡀⠀⠀⠀⠠⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣠⡤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡀⠀⠊⠀⠀⣴⢏⠄⠉⢠⠟⠉⠉⠉⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣤⠖⠀⠘⠀⠀⠀⠀⣸⠁⠇⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢰⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠈⡧⠥⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⠎⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣻⣛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢞⣫⣷⣿⣿⣿⣿⣾⣝⡳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣛⣽⣾⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣷⣭⣓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⡿⢿⣣⣈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣼⣿⡇⣾⣿⡆⡟⣫⣵⠾⣿⣿⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣛⣃⣛⣛⣃⡇⣿⡇⠿⣸⡿⢿⣿⡿⣫⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢫⣾⡮⢫⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢶⣶⣶⢰⣶⣶⣶⣶⣶⣾⡇⣿⣿⡧⡿⣫⣾⣷⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡆⣿⣶⡷⣿⡿⣿⣿⡿⣧⡻⡿⣣⣜⣻⣟⣣⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⣛⣛⣛⣛⣛⣛⣛⣃⣛⣛⣋⣛⣓⣈⣻⢿⣿⣿⠿⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠉⠉⠑⠀⠤⡀
⠀⠀⠀⠀⢀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⡐⡡⠆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⠰⠀⠀⠰⠑⢄⡀⢤⢀⠀⠠⡄⣀⡀⠠⣀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⣄⠃⠘⠀⠈⠒⠆⠈⠁⠃⠀⠉⠉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠎⠀⠀⠀⢀⣠⠔⠀⠐⠁
⠀⠀⠀⠀⢰⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠈⠆
⠀⠀⠀⠐⠉⠃⠀⠀⠠⠟⠀⠀⠀⠂⠀⠀⠐⠞⠃⠀⠀⠅⠋⠁⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢪⡾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠁
⠀⠀⠀⠈⠒⠢⡘⠀⠀⠀⠀⠠⠂⠀⠰⠄⠀⠀⠀⠃⠂⡐⠒⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠸⡾⠃⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡠⢽⣮⣀⠡⠀⠀⠐⠤⠀⠀⠀⠈⢆⡨⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠆⠐⠄⠋⠀⠀⡰⠀⠀⡀
⠀⠀⠀⠀⡸⠁⡀⠄⠌⠉⠒⢀⣤⠤⠤⢤⣐⠊⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠁⠀⠀⠀⠈⠀⠊⠀⠄⠀⠀⠀⠂⠛
⠀⠀⠀⡼⠂⠪⠄⠰⠋⠈⠁⠀⠙⠦⣤⠼⠁⠀⠉⠐⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠠⠤⠤⠁⠀⢒⠀⠐⠂⠉⠠⠄⡤
⠀⠀⠀⠉⠠⠄⠄⢼⠀⣀⠀⡀⠀⠀⠀⠀⠀⢰⠤⣀⡸⠠⠀⣈⡖⠒⢦⡀⠀⠀⢴⡇⢠⡀⠀⠀⠀⡄⠀⠀⠈⠠⠐⢼⡀⠀⠃
⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠈⠘⡀⠀⠁⠀⠀⠈⠁⠀⠉⠠⠈⠱⠬⠹⠆⠓⠃⠀⠀⠀⠀⠀⠈⠀⠳⣄⠅⠀⠦
⠀⠀⠀⠀⠀⠉⠁⠤⠀⠀⠀⠃⠀⠀⠆⠀⠀⡴⢳⡀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠙⢶⡞⡀⠶⠑⠒⢡⣄⣷⡀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⢐⠀⢀⡖⠀⠀⠀⠠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠄⡀⠹⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠩⠙⠉⠉⠉⠀⢌⠑⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠷⠈⠻⠏⠛⠆⠀⠃⠉⠀⣿⣩⣿⠀⠹⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠄⣂⡮⣤⡄⠀⢁⣌⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠶⠶⠾⠿⣿⣷⣧⠀⠀⠀⠉⠰⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠤⠤⠶⠼⡥⠧⠐⢸⣧⡌⡉⣰⠧⠈⠠⠦⠀⠀⠀⠀⠀⢀⡐⢀⠀⡆⠀⠠⡄⠠⢹⣄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⢀⠀⠀⠀⠠⣋⣧⡋⠀⠀⢾⣅⡀⠀⠄⠀⠀⠀⠀⠀⠀⠘⢡⢒⠄⠀⠀⠀⠀⢦⣞⠸⠃⣈⠙⠂⠈⠉⠡⡆
⠀⠀⠀⡠⠒⠈⠉⠠⣀⠀⠀⠠⣀⣀⠀⠀⠀⠘⠠⠐⠂⠉⠈⠉⢀⡉⠀⠀⠀⡀⠐⠐⠪⡧⠀⠀⠂⠀⢠⡀⢫⣋⣉⡁⠀⢈⡀⣀⠒⠀⠀⠈⠁⠐⣂⡤
⠀⠀⠀⠈⠀⠐⠂⠠⠄⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠤⠤⠢⠀⠁⠀⠀⠈⠉⠫⠭⣍⡁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠒⠐⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠀⠀⠀⠠⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤⠬⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢂⠤⡀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠨⡐⠀⠂⠀⠀⠀⠀⠀⢐⡪⡀⠀⡀
⠀⠀⠀⠀⠀⡔⠉⠈⠁⠀⠀⠈⠂⠒⠢⠀⡀⢠⠢⠀⠀⠨⡀⠀⣠⠀⠠⠀⠀⠀⠀⠐⡁⠁⢃⢠⡄
⠀⠀⠀⡠⠁⠁⢂⣠⠂⠉⠐⠀⠄⡀⠠⢀⠐⠢⠀⠀⠀⠀⠁⠀⠀⠀⢠⢁⠀⠀⠀⠀⡇⠐⠈⡡⡀
⠀⢀⠴⠀⠐⠁⠃⠐⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠑⢆⠀⠀⠀⡀⠀⠀⢸⠑⠁⠀⠀⠀⡤⠂⠀⡖⠉⢢⠰⠄⠽
⠀⠈⠒⠂⠒⠀⠀⠢⠤⠐⠂⠀⠊⠑⠀⠐⠒⠒⠁⠀⠀⠀⠀⡉⠀⡂⠀⡁⠀⠀⠀⢠⠂⠀⠀⠀⠂⠈⠒⢂⠢⠀⠄⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⢱⡆⠀⠀⠀⠀⠀⠁⠀⠉⠀⠈⠒⠃⠐⠂⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠁

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡄⠀⠀⢸⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⠒⡼⠰⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⣤⡈⠃⡾⠸⠈⣁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡔⠁⠀⣸⠀⠁⠁⠀⠀⠀⠐⢀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡓⠒⠒⠓⠒⠔⠢⠄⠀⠠⠀⡶⠀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠱⢄⣀⣀⡀⠐⠃⠀⠀⠀⠀⣢⠴⣒⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡸⠴⠊⢁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠓⠀⠀⠜⢉⠀⠀⠀⠀⠀⠀⡄⠸⢡⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢋⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡀⠀⠀⡆⠀⠟⠀⠀⡰⠀⠀⠀⠀⠸⠀⠀⠀⠘⠀⠠⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⠀⠈⠀⠀⠂⢀⠔⠀⠀⠀⡄⠀⠃⠀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡄⢰⣤⣀⣀⠀⠀⡄⠀⠀⠓⡾⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢸⣄⣧⠀⠀⠈⠹⢯⡶⡃⠀⠀⡼⣧⠀⠀⣈⠀⠘⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⠇⢸⣆⠀⠀⠦⠀⠈⠁⢠⣾⣷⡏⠀⠀⠁⠀⢸⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠠⠟⣦⡀⠀⠀⣀⠔⢡⠏⡘⢓⣒⣒⣒⠂⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣆⡆⠀⣷⠘⠋⡙⢃⣀⡏⡜⠁⠀⣷⢸⡌⢇⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡘⢁⠃⠀⣧⠀⠘⠁⢀⡷⠀⠀⠀⠇⢸⠁⠑⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠘⡦⣀⡣⢠⢃⡄⠠⢿⠀⢀⠈⢀⣉⡤⢴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⡸⠂⡵⠃⢸⠱⡀⠘⠒⢚⡏⠉⠀⢶⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠂⠉⠉⠉⠯⠹⠷⠴⢼⣦⣬⡴⣇⣀⡀⠈⠀⠀⠀⢸⠼⡓⠒⠲⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⡗⠲⠀⠠⠭⠤⠉⠀⠉⠉⠉⠉⠉⠉⠁⠉⠀⠻⣌⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠰⠂⠐⠀⠀⠐⠐⠀⠀⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣍⢷⡄⠙⢦⣄⣀⡀⠀⠀⢀⡠⠞⡩⣢⢞⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣬⣿⡎⣧⠈⠀⠀⠉⠉⠉⠉⠉⠀⠈⠙⣳⣿⣉⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠋⣠⠇⠀⠀⣠⠀⠀⠀⠀⠀⣄⠀⠀⢳⣉⠛⠟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠍⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠰⠤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠚⣁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡗⢰⣶⣶⣶⣶⣶⣶⣶⣶⡾⠓⠲⠶⣦⠄⠒⠚⠴⠛⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣾⣿⣿⡟⠟⠰⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⡟⢿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠈⣿⣷⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠿⠈⠉⠀⣭⣀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡮⠀⠘⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠚⠀⠀⠀⠀⠉⠛⠛⠋⠀⠉⠉⠉⠉⠉⠡⠀⠀⠀⣤⢀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⡇⢠⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠅⡈⡙⡟⢳⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⡞⠉⠈⠁⣿⠀⠲⢿⣇⡄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠃⠁⢘⣿⣿⡍⣷
⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⢿⡆⠀⠈⢻⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⡄⠀⠀⣿⣿⡁⣼⠁
⠀⠀⠀⠀⠀⠈⣷⡀⠀⠈⠘⣷⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⣠⡏⢰⠀⠀⠀⣿⣿⣱⠇
⠀⠀⠀⠀⠀⠀⠈⠻⣟⣶⡾⢿⡇⢠⠀⠸⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠐⣿⡇⠇⠀⠰⣸⣿⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⢿⡄⠁⠀⢹⣿⣧⡀⠁⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⣨⣽⡇⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡆⠘⣧⣧⠀⡀⠙⠻⠿⣷⣤⣤⣀⣀⣐⣤⣶⣴⠾⠿⠛⠋⠁⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⡄⠻⣿⣿⣁⡀⢀⣀⠀⢬⣉⣛⣉⡉⣉⣥⡤⢤⠴⠂⠀⢀⡄⢻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣿⠦⠟⠀⠉⠻⢦⡙⠳⣦⡉⠫⢅⠉⠉⠀⠀⣀⡤⠒⠋⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⢦⣈⠙⠦⠔⠱⣤⠤⠞⠉⠀⠀⣸⢫⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢇⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠙⠛⠛⣩⣿⠿⠿⠯⠙⠷
⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⣼⠥⣴⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⢠⣄⣤⣀⠀⠀⠀⠀⢀⡀⣤⣀⢀⣠⣠⣄
⠀⠀⠀⠀⠀⠠⣙⠷⠖⠲⠷⠶⡮⠅⣭⣿⣷⣖⣻⣾⣿⣶⣿⣿⣿⣷⣶⣶⣶⣞⣿⣿⠿⣿⣿⣿⣏⣽
⠀⠀⠀⢀⣀⣀⣈⣓⣲⣿⣖⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣭⣤
⠀⠀⠀⢰⣷⣶⣶⣶⣤⣤⣭⣭⣍⣉⣉⣙⣛⠛⠛⠛⠛⠛⠿⠻⠿⠛⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⢤⣝⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣴⣶⣤⣄⣉⣀⣉⣀⢀⣉
⠀⠀⠀⠘⣿⣿⣶⣬⣉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦⣄⡉⠛⠿⢿⣿⣿⣿⣿⣿⣿⢡⣶⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠉⠙⢿⠟⢏⣸⡈⢑⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠈⠙⠃⢺⡿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠀⠀⠈⠉⠋⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⣤⠤⣤⠤⠴⠖⠒⠛⠓⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠛⠉⠛⢲⡉⠋⠀⠻⣔⣀⡤⠤⣴⣒⣓⣲⡚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⣆⣀⣈⣡⠴⠚⠉⠁⠀⠈⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣀⡤⠖⠚⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳
⠀⠀⠀⢰⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠮⣭⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡇⢀⣀⣀
⠀⠀⠀⢰⣒⡦⠀⣀⣤⣤⣄⡉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⣀⣴⣶⠿⠚⠀⠻⠶⠟
⠀⠀⠀⠀⠉⢀⣀⣓⣶⡤⠾⠃⠀⠀⢳⣤⣀⠀⠀⢀⠀⠀⢀⡴⠋⠉⣀⣤⡘⠮⠶⠭⡖⠃⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⢰⠋⠉⠁⠈⠙⠲⠤⠤⢤⣀⣈⠛⠛⠛⠛⠛⢫⠟⠒⠒⠚⠁⢰⠃⠀⢾⡭⠽⣀⣠⣤⡀⠘⠓⠒⠋
⠀⠀⠀⠀⠈⠳⣕⠤⣀⣀⡀⠀⣀⣤⣤⣭⡿⠀⠀⠀⠀⠘⠷⠶⢦⣄⣠⢿⡖⠛⠛⠒⠛⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠋⠁⢶⣛⣒⣶⠿⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⠗⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣘⠇⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢰⣴⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⡇⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢂⣼⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣴⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣿⣷⣦⡀⠀⠀⠀⠀⠀⣿⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⣤⠀⠀⣾⣿⣏⣿⣿⣿⣿⢿⡟⠿⢳⡆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⠞⠋⠀⢀⠀⠀⢻⡆⢀⣿⢻⣿⢿⡟⣿⢯⢸⡇⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣰⡆⠀⠀⠀⠀⢀⣤⡴⠶⢾⣦⣀⠀⠁⢠⣿⠸⣿⢹⡇⣿⣼⠈⣷⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡾⠋⠀⠀⠀⢸⡇⠀⠙⢦⣼⢋⣀⠠⢼⣁⠉⠹⠁⣿⡞⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⣠⠇⠀⠀⠀⣹⡎⠁⠀⠀⠈⠑⢆⠀⠀⢰⠙⡂⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠛⠤⢤⣤⣤⣿⣥⣤⣤⣤⣤⣄⣼⡇⠀⢸⣄⠁⠀⣟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⣹⡌⠋⠀⠀⠀⢀⡟⠀⠀⢸⡏⠀⠀⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢿⣁⠤⠤⠚⠋⠀⠀⠀⢸⠃⢀⣠⡶⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⠀⠀⠀⠀⡏⠙⠳⢤⣤⡤⡤⠞⠋⠁⣶⠈⠉⠀⠒⠒⠀⠀⠀⠀⢸⠿⠋⣩⣤⣶⣦⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⠃⠀⠀⢰⣇⣠⡴⠞⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠐⠉⠀⣽⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣤⡞⡛⠁⠀⠀⠀⣿⡀⣠⡀⢸⡇⠂⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢰⣦⣤⣿⡾⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣴⠾⠋⠙⢷⠇⠀⠀⠀⢀⢸⡟⢙⣿⢸⣦⠀⠀⠀⡆⢹⠀⠀⠀⠀⣤⠀⠀⣇⠀⢸⠂⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠠⡇⣸⡏⠀⠁⠀⠀⠀⠻⠋⠀⠀⠀⠐⢏⠀⠀⣿⠘⠛⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣤⡾⠛⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣰⡿⠋⠀⠀⠻⠇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠙⠋⠀⠀⣿⠀⠀⠀⢰⡏⣿
⠀⠀⢰⣟⠀⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡟⠀⠀⠀⣄⠁⣸⡏⠀⠀⠀⢠⣧⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢨⣤⢻⡆
⠀⠀⠸⣿⣀⣿⠀⠀⠀⠀⣸⠇⠀⠀⢸⣁⡄⢰⡎⠃⣴⠟⠀⠀⠀⠀⣼⠃⠀⠀⢸⡇⡆⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠈⠿⢿⡁
⠀⠀⠀⠹⡿⣇⠀⠀⠀⢠⠉⡆⠀⠀⠘⠻⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⣸⡆⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⣸⡇⢸⣇⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢠⣾⠳⢶⣤⣬⣿⣧⣤⣤⣤⣤⣴⠾⠋⡀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣿⠁⡸⢻⠀⠀⣠⣴⣾⠃
⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⣽⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠀⢸⡏⠀⣇⣸⠶⠛⠋⠀⠙⣧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⣿⠃⠀⠙⠃⠀⡀⢀⣠⣾⠃
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠙⣿⡿⢻⡿⠒⢶⣏⣠⣤⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠓⣼⡟⠀⠀⠀⠀⢠⣷⠈⠉⠙⢷⣄⢰
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⡿⠁⢸⣇⠀⠀⠙⠁⠈⠙⠿⣿⣷⣦⣤⡀⢸⣧⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣴⠃⠀⠀⣤⡾⠃⣿⠆
⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⢀⣽⣦⡈⣿⡄⠀⠀⠀⠀⠀⠀⣸⠻⢦⣼⠛⠃⣿⠀⠀⠀⠀⣼⣿⣙⣷⠀⠀⠀⠀⣟⠀⠀⠀⠀⢙⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠉⠹⣿⠀⠀⠀⠀⠀⢸⡄⡄⠀⠉⠻⣶⠏⠀⠀⢀⣼⡟⢠⣻⡿⠁⠀⠀⠀⠛⠃⠀⠀⠰⣟⠳⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣨⡿⠃⠀⢻⣧⡀⠀⠀⠀⠘⠷⠃⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣸⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⣸⡇⠈⢿⣄⠀⢐⢸⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣼⢻⣏⣼⣿⣥⣤⣤⣤⣤⣤⣦⣤⣤⣴⡿⠃
⠀⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⢰⡏⠀⠀⠸⣶⡟⠉⣿⣦⡀⠀⠀⠀⠀⠀⣀⣴⠟⠀⣰⠟⠀⣹⡅⢰⣯⣀⣀⣀⣀⣨⣿⣀⣀⣀⣿
⠀⠀⠀⠀⠈⣿⠀⠀⠰⣷⠀⠸⣧⣀⣀⣸⠁⠸⣀⡗⠀⣹⣿⠖⠛⢶⣾⠋⠀⠀⢰⡿⠀⣸⡟⠁⡀⠀⢹⡇⢸⡟⡿⢸⡟⠙⠻⣧⡀
⠀⠀⠀⠸⣆⡟⠀⠀⠀⠀⠀⠀⠻⣥⣭⣿⠀⠀⠉⣿⠟⠉⢹⡆⢀⡾⠛⢷⣄⣤⣿⠃⣼⠏⠀⢰⡆⠀⢸⣷⢀⣿⣷⡌⢻⣦⡀⢈⣿
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣾⠃⢠⡏⠀⠀⠀⣿⠀⠀⠈⣷⡾⠁⠀⠈⢿⣽⡇⠘⠁⠀⠀⠸⣷⠀⢰⡿⠾⠁⠻⣥⣼⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⡄⠻⢆⣼⠇⠀⠀⢀⣿⠶⠶⢾⡇⢳⡶⠶⠶⡾⣿⠀⠀⠀⠀⠀⡇⢸⠀⠀⣻⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠈⣿⡀⠀⠀⣸⠹⠀⠀⣸⠇⢸⡀⠀⢰⠀⣿⠀⠀⠀⢠⠀⠻⠆⠀⠘⠟⠀⠀⣀⣠⣶⠘⡟⠁
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠰⢀⡇⠀⠀⠈⣿⠓⣤⣾⡀⠀⣼⠇⢰⣾⠇⠀⠈⠛⣿⠀⠀⠀⢸⡆⠀⣀⣀⣤⣴⠾⠛⠋⢱⡿⣤⠇
⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠛⠁⠀⠀⠀⠙⣷⡀⠈⢁⣼⠋⠀⢸⡇⢸⡆⠀⠀⠻⠶⠶⢶⡎⣿⠛⠉⠉⠁⠀⣠⣤⣤⣾⣇⠉
⠀⠀⠀⠀⠀⠀⠈⠉⢀⡀⣀⣀⣀⣀⣠⡶⠋⠁⠰⣿⠁⠀⠠⣀⡧⠈⣷⡀⠀⠀⠀⠀⠠⣇⡿⠀⠀⠀⠀⠀⢹⣧⢤⣼⠟⠁
⢀⣠⡶⠶⠛⠛⠛⠛⠋⠉⢩⡴⠟⠛⢿⡷⠦⢤⣀⣈⣷⣄⠀⠛⣁⣠⣾⠗⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣤⢻⣀⡼⠷⠶⣶⣦⣤⣄⣀⣀⡀
⠻⣧⣄⣀⣀⣀⣀⣀⣀⣀⠈⠑⠚⠒⠛⠛⠛⠛⠛⢙⣿⠙⣿⣿⠿⠛⢿⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⣧⣘⠉⢛⣦⠀⠀⠀⠀⡉⠉⠉⠙⢛⣷
⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⣿⠷⣤⠚⠁⠈⠉⠉⠉⠉⢀⡏⠙⠒⠒⠛⠛⠒⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠋⠈⠉⢹⡟⠉⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣤⣈⡉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣱⡆

⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣆⢠⣄⡆⠀⠀⣠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡶⠈⡀
⠀⠀⠀⠀⠀⠤⠀⣴⣿⣾⣿⣿⣿⣿⣾⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠦⣄⠀⠀⣠⣿⣾⣿⣾⣶⣾⠃⢀
⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⡀
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠠⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠒⠶⠤⠀⠀⠀⠀⡉⠉⠋⢻⣿⣿⣿⣿⣿⣿⡿⠿⣁
⠀⠀⠀⠀⠀⠀⠐⠀⠟⢿⣿⣿⣿⣿⢿⣿⠛⠦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠾⠛⡿⠛⢿⠟⡏⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠘⠉⠁⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠾⠇⠀⠀⠀⠋⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⣶⠶⠶⠶⠶⠾⣿⣠⣿⡶⠶⠶⠶⠶⠶⠶⢶⡶⠾⣿⣨⣿⢀⣿⠶⣶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠙⠛⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠿⠶⠶⠶⣶⡶⠶⠶⠾⠷⠶⠶⢶⡶⠶⠶⠾⠷⠶⠶⢶⣶⠶⠶⠶⠿⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣦⣿⣦⣶⣶⣶⣶⣶⣶⣾⣷⣴⣶⣶⣶⣶⣶⣴⣿⣦⣶⣶⣶⣶⣶⣾⡇

⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠆⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⢀⡀⠀⠰⠦⠀⠀⠀⠰⠆⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡄⠀⠀⠀⠀⠶⠆⠀⠀⢠⡄⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠓⠀⠀⠀⠀⠀⣤⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⣿⣷⡄
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠈⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⢾⣿⣿⣿⣿⣿⣿⠆⢾⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠈⠛⠛⠛⠛⠛⠁⠀⠀⣼⣿⣿⣦⣄⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⢀⣤⣶⣶⣶⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠙⠻⣿⣿⣾⣿⡿⠛⠉⠙⠻⣿⣿⣾⣿⡿⠟⠉⠉⠻⣿⣿⣿⣇
⠀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⢿⣿⡆
⢿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⣴⣶⣶⡄⠀⠀⠘⣿⣿⠀⠀⢉⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠙⠛⠛⠁⠀⠀⠀⢻⣿⣧⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁
⢀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠻⣿⣷⣄⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠻⠿⠿⠿⠟⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⠿⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣭⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠉⠉⠉⠉⠉⠉⠙⠲⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠉⠉⠛⠻⠶⡤⡎⢠⠀⠀⡠⠁⠒⣁⠤⠠⠅⠠⠤⠄⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠉⠛⠓⠢⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠂⠀⠈⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡀⠀⠀⢀⣠⡟⣣⠴⠂⢉⣥⠞⠉⣠⡶⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠛⠶⠛⢦⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠄⡒⠡⠒⣰⠋⠘⢉⣤⣶⠆⠈⠁⠀⣼⠋⠀⠸⣶⣦⠀⠀⠢⣌⣷⣁⠀⠀⠀⢦⣈⠢⠙⢦⠀⣿
⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣽⠃⠀⠀⠀⢡⠘⢷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⢹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢶⣄⡀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⡉⠲⢇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣈⣦⢠⡄⠉⠙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠻⠛⢀⠔⠂⠀⠀⠀⢼⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠐⠀⢹⠉⠀⠀⠈⠀⠢⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠂⠀⠀⠀⠐⠇⠤⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡄⠀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣠⠗⠂⠉⠑⢂
⠀⠀⠀⠀⠀⠙⠤⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠁⠀⠠⢀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡰⠃⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠒⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⢂⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠻⠦⣀⣀⣀⣀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣦⣤⣤⣤⣤⣤⣤⣤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣶⠢⢄⣀⣀⡀⠐⠘⣇⠀⠀⣤⣬⠽⠆⢢⡀⠄⣲⣶⡄⠀⢀⣀
⠀⠀⠀⡜⠁⠀⠀⠀⠈⠉⠈⠆⣠⡀⠈⠁⠐⠛⠀⠐⠂⠘⠛⡂⠀⠸⠀⢠⠇⠈⠉⠀⠀⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣎⠀⠀⠀⡠⠈⠁⠀⠉⠙⠣⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⢀⣄⡠⠀⠐⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠈⡀⠲⢀⡈⢀⠐⠀⢀⠀⣾⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⢠⠈⠀⣀⣄⡠⠃⠀⢀⠃⠀⠀⠈⠂⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡼⠂⠊⠉⠀⠀⠀⠱⠈⠀⠀⠀⠀⠑⠀⠀⠀⠀⢸⠀⢠⡀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢁
⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⢈⠀⠀⠀⠀⠀⠀⠘⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⢤⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢰⡆⠙⠊⠁⠀⡀⠈⢁⠰⠄⠀⡤⠀⣀⠐⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠀⠀⠀⠀⢠⡀
⡇⠨⠃⠀⠀⠀⠀⠄⢀⠀⠀⠀⡀⠀⠀⠉⠉⠁⠐⠀⠒⠒⠐⠒⠒⠚⠒⠾⠃⠈⠀⠐⠀⠀⠀⠀⢹
⠘⠛⠧⠤⠴⠤⠤⠤⠤⠴⠶⠶⠤⠤⠴⠄⠀⣈⣻⠄⠀⠀⠀⣀⠀⠀⢰⡄⢀⡀⠀⠀⠀⠀⢀⣤⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠢⢶⣤⢀⢄⡀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠑⣇⣚⢡⡞⡥⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠬⢢⠃⠙⠙⢇⡇⢸⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⣸⠀⠀⠠⢀⡷⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠉⠉⠁⠓⠀⠁⠸⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠰⠁⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⡱⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠇⢠⠁⠀⠀⠀⣨⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⣄⡁⠀⣀⡤⠄⠗⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠗⠉⠀⠂⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣨⠀⠀⠀⠈⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠁⠐⠠⠰⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠂⠂⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣧⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⡘⢀⠢⠃⠀⠀⢀⠄⠃⠀⢀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠉⠉⠛⠀⠀⢀⡇⠀⠀⠀⠀⡠⠈⠀⢼⣄⣀⢀⠔⠁⠰⠀⡸⡊⢰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡞⠁⠀⠀⠀⠀⢃⠀⢀⠊⠀⠙⠊⠀⢀⡶⢂⢫⡑⢄
⠀⠀⠀⠀⠀⠈⠒⠀⠀⡀⡀⠀⢀⣦⡴⠋⠠⢔⣶⣶⠒⣲⠗⠀⠀⠀⠀⣀⣀⠴⢏⣠⣈⣄⠝⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⡁⢤⣤⡤⢎⣉⣀⠿⠉⠓⠲⡦⢀⠀⠀⠀⠀⠀⠻⣭⣹⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠼⠿⠇⠼⢿⣏⣉⣶⡆⠐⡏⠀⠙⠛⠛⠛⠙⠻⠿⠀⠿⠧⠼⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠄⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢦⣄⠀⠀⠀⠀⠀⣠⠞⠋⠉⠀⠨⣍⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠙⡇⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠙⢦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠴⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠉⠛⠓⠦⣄⡀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠘⠳⢦⡀⠙⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢬⣙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⢳⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠦⣤⣀⣀⣀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⢝⡲⣄⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠙⣎⢧⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠰⣆⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣀⣀⡠⠔⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣰⠾⠛⠛⠳⣤
⠀⠀⢀⣀⣤⣤⡼⠃⠀⠀⢀⣀⣘⢧⣤⣀⣀
⣠⡾⠋⠉⠀⠀⠀⠀⠰⣋⣭⣥⣭⡙⢦⡀⠉⠛⠶⢦⣤⣀⡀
⢿⡀⠀⠀⠀⠀⠀⠀⢰⣏⠁⠀⠙⣿⡎⣿⡀⠀⠀⠀⠈⠉⠙⠛⠛⠳⠶⢶⣤⣤⣀⡀
⠈⠻⣶⠤⣄⡀⠀⠀⠸⣿⣷⣶⣾⠿⣡⣿⣿⣷⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣤⡀
⠀⠀⠘⠷⣬⣙⠲⠶⢤⣈⡓⠿⠶⢾⡟⠡⣯⢽⠻⠿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⢀
⠀⠀⠀⠀⠀⠙⢿⡶⠤⣌⡙⠲⠤⡀⢳⣄⣀⡼⠃⠀⠀⠈⠛⢿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⣛⣶⣄
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠉⠓⠦⢄⣀⣈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠙⢿⣗⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣤⡀⠀⠀⠀⠀⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣧⡀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡧⡙⢿⣦⣄⡀⠀⠀⢀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟⠒⠒⠀⢀⣼⡧⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠼⣍⠀⠀⠀⠨⢽⣿⣄⡀⠈⢣⡀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⢹
⠀⣴⠶⢶⠴⣞⣛⣭⣥⡦⣀⣴⠈⣤⡄⠜⠷⣮⣽⣿⣶⣝⣦⠀⠀⠀⠀⠙⣆⠀⠀⢠⠏⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠻⠮⠞⠁⣨⡴⣞⣡⡼⠋⢻⣄⢻⣍⠓⠶⠶⣎⣱⢇⡿⠁⠀⠀⠀⠀⢀⡟⠀⣀⡾⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿
⠀⠀⠀⣾⠋⣡⡞⠋⠁⠀⠀⠀⢸⡆⣉⡷⣀⣀⠈⠁⣼⠃⠀⠀⠀⠀⠀⣸⠛⠛⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⣾⠃
⠀⠀⠀⠉⠛⠉⠀⠀⠀⣠⡶⢦⣈⣙⣋⣙⣏⡈⠳⣤⠏⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠤⢬⣍⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⢀⡈⢳⣦⠤⠤⠶⠚⠉⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠳⠖⠛⢉⣉⣀⣤⣀⣀⣀⣠⣤⡾⠟⠁⠀⠀⣾⣏⣙⣽⣲⢶⠀⢀⡠⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣀⣨⠽⢛⠭⢊⣡⡔⠉⢀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣭⡭⠕⢂⣥⣾⠵⢋⣰⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢋⣤⡴⠾⠋⠸⣧⣤⡿⠁

⢀⣴⣶⣄⣀⠠⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⣿⣦⠀⠐⠚⠃
⠘⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⣦⢠⣾⣦
⠀⠀⣈⡻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣟⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠉⡟⣻⣿⣷
⠀⢾⣿⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉



⠾⠿⠀⠀⢀⣀⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠸⡿
⠀⠀⠰⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣬⣿⣿⠆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠿⠇
⡠⣤⣿⣿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢫⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣴⣾⣷⣦
⢿⣿⣿⠃⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠘⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠋⠻⣿⣿⠟



⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠰⣿⠇⠀⢀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⡆⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣤⡀⣶⣿⣿
⠀⠀⠀⣼⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⢃⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣣⢜⣿⣯
⣰⣹⣿⣿⡛⢁⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠹⢿⣿⠿⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠉⠹⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠁⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⡇⠀⠀⠀⠀⠀⡞⠉⠉⡟⠉⠉⡇⠀⠀⠀⠀⠀⢈⡋⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠤⠤⣧⠤⠤⡇⠀⢀⡠⠔⠊⠁⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣗⠀⠀⡇⠀⠀⡇⡞⠁⢠⠒⡄⠀⠀⠀⠀⠀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⡇⠀⠘⠶⠋⡴⢦⡀⣠⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠞⠀⣠⠿⡅⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⡏⠉⠉⢻⠉⠉⠉⠉⠉⠉⠁⡇⠀⠀⢸⡠⠞⠁⠀⡗⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⢰⠒⠛⠒⡆⠀⠀⣀⣀⣀⠘⢆⡠⠞⠑⠶⠶⠊⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⠒⠒⠃⠀⣸⠉⠉⢉⣇⠀⠙⠢⢄⣀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢠⠀⠠⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣿⣿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣤⠖⠀⢖⠂⢰⠀⡀⠐⢐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣤⣤⣠⣄⣬⣄⣠⣸⡀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣯⣤⣤⣬⣤⣶⣴⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣶⣶⣿⣿⣿⣯⡿⠛⠛⠛⠉⠉⠻⠯⠯⠿⠯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠛⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣶⡞⠛⢿⡛⠛⠙⠉⣿⡏⢰⡖⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇⣰⠼⠁⠀⠀⠀⣿⡇⢙⡋⠃⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢲⠿⠗⠻⢳⣶⣶⣶⡶⠿⠷⣿⣷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠹⢿⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⢀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣶⣶⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣾⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⣿⣿⠁⢀⣾⣿⡟⠉⠁⠐⠲⠿⢿⣛⡺⠟⠿⠿⠟⠛⠟⠛⠿⠍⠛⠉⠉⠀⠀⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⢸⣿⡟⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⠀⣴⣿⣿⢃⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⡇⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠿⠿⠄⢴⣿⡿⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢠⡀
⢀⡴⢂⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠘⢇
⢿⡆⠘⠀⠀⣴⢿⣷⣾⡟⠀⠀⠀⠀⠀⠀⢣
⢀⣷⠀⣠⣾⠏⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠸⣛⣛⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠋⠉⠉⠁⠀⠀⠉⣉⣩⠻⡆⠀⣼⢫⣍⡉⠉⠉⠉⠉⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣈⣉⡉⠉⠉⠉⣉⣉⣁⣠⣼⠇⠀⢻⡦⣄⣉⡉⠙⠛⠓⠒⠒⠋⢁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠇⢀⣤⣼⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠾⠷⠀⠈⣿⣿⡇⠀⠀⠀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⢸⣿⣦⣠⣾⣶⣿⠆⠀⢀⣀⡈⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⣾⣶⣶⣦⠀⠨⣿⣿⡇⠀⠀⢸⣿⢿⣿⣿⣿⣷⣤⣄⠀⠙⠁⠛⠀⠉⠛⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⠀⠀⣴⣿⣿⡿⢟⣡⣶⣶⣿⢃⣿⣿⡈⣿⣿⣶⣶⣿⣭⣟⡛⠀⣾⣿⣷⣶⣦⣤⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⢿⣿⣷⣶⣤⣬⣿⣶⣾⡿⠛⢛⣉⣥⣾⣿⣿⣿⣶⣬⣍⣙⣋⣉⡛⠿⣷⣶⣾⣿⣿⣿⣷⣾⡿⠃
⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣦⣭⣉⣙⣛⣋⣉⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⣭⣭⣭⣭⣤⣴⣶⣿⣿
⠀⠀⠀⠀⠀⠸⢼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣛⣋⣁⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉⠉⠘⠛⠋⠀⠀⠀⠀⠀⠀⢾⣻⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢨⣶⠦⠤⣤⠤⠶⠛⢉⣉⣭⡶⠶⠤⣤⠤⠶⠚⢋⣉⣭⣭⠶⠤⠤⣤⠤⠶⠚⢉⣩⣭⡵⠶⠦⠤⠤⠴⠚⠃
⠀⠀⠀⢠⡤⠶⠖⠒⣒⠒⠛⠋⣉⣀⣤⡶⠖⠒⣒⡒⠚⠛⣉⣀⣤⡴⠶⠒⣒⣒⡒⠛⠋⣉⣀⣤⡶⠖⠒⣒⣚⠛⠃
⠀⠀⠀⠠⠴⠒⢫⣭⣭⣉⠙⠲⠭⠭⠤⠴⠾⣭⣭⣉⡙⠒⠯⠭⠤⠴⠚⠯⣭⣍⣉⠛⠲⠭⠭⠤⠴⠺⠭⣭⣍⣉⠃
⠀⠀⠀⠐⠒⠶⣦⣄⣈⣉⠛⣓⣒⡒⠒⠶⢦⣤⣀⣉⠙⢛⣒⣒⡛⠓⠶⣦⣄⣈⣉⠛⣓⣒⣒⠛⠲⠶⣤⣄⣈⡉⠃
⠀⠀⠀⢈⡛⠲⠤⠤⠵⠚⠭⢭⣭⣉⡙⠒⠦⠤⠴⠚⠫⠥⢤⣬⣉⠓⠲⠤⠤⠽⠚⠯⠥⣤⣍⣉⠓⠲⠶⠴⠒⠫⠅
⠀⠀⠀⠈⣛⣛⣛⡛⠛⠷⢶⣤⣄⣉⣙⣛⣛⣛⡛⠛⠶⣦⣤⣈⡉⣛⣛⣛⣛⠛⠛⠶⣦⣤⣈⣉⣙⣋⣉⡛⠛⠳⠆
⠀⠀⠀⢈⣭⡤⠬⠭⠙⠒⠶⠤⠒⣋⣩⡤⠶⠮⠍⠓⠲⠤⠤⠒⣉⣥⡤⠶⠭⠙⠓⠲⠶⠒⣊⣩⣤⠶⠦⠍⠛⠲⠆
⠀⠀⠀⢈⣀⣤⡴⠾⠛⢋⣉⣉⣉⣉⣁⣤⣴⠶⠛⠋⣉⣉⣉⣉⣉⣁⣤⡴⠾⠛⠋⣉⣉⣉⣉⣁⣤⣤⠶⠟⠛⣉⡁
⠀⠀⠀⠨⠅⠒⠲⠶⠚⣋⣥⡴⠶⠦⠍⠒⠒⠶⠒⣋⣩⡤⠶⠖⠊⠁⡒⠶⠶⠚⣋⣭⡴⠶⠖⠈⠑⡒⠒⠒⣛⣩⡄
⠀⠀⠀⠘⠛⣉⣉⣉⣉⣉⣠⣤⡶⠞⠛⢉⣉⣩⣭⣉⣡⣤⣴⠾⠛⠋⣉⣩⣭⣭⣉⣠⣤⡶⠾⠛⢉⣉⣭⣭⡭⣁⡄
⠀⠀⠀⠘⣛⡉⠥⠖⠶⠶⣤⣐⡒⠒⢚⣋⠡⠖⠲⠶⢤⣄⣒⠒⢚⣋⣉⠐⠒⠲⠦⣤⣐⡒⠒⢚⣋⡉⠐⠒⠶⠦⡄
⠀⠀⠀⢨⣍⣉⠙⠛⠶⢦⣤⣬⢭⣭⣍⣉⠙⠛⠷⠶⣤⣤⠭⠭⣭⣍⡉⠙⠻⠶⢦⣤⣭⠭⢭⣭⣉⡉⠛⠻⠶⠦⡄
⠀⠀⠀⠰⣬⣉⣛⣒⣒⣠⡐⠒⠒⠶⢬⣍⣛⣓⣒⣠⣄⣒⠒⠲⠦⣬⣙⣛⣒⣒⣠⣐⡒⠒⠲⠦⣭⣉⣛⣓⣂⣄⡂
⠀⠀⠀⠠⡤⠬⠭⣭⣅⣉⠉⠛⠳⠶⠤⠤⠭⠭⣤⣌⣉⠙⠛⠶⢦⣤⡬⠭⢭⣤⣈⣉⠙⠛⠶⠦⠤⠤⠭⣤⣄⣉⡁
⠀⠀⠀⠰⠖⠒⣒⣲⣤⣍⣛⣛⣢⡤⠖⠚⢓⣒⣦⣬⣙⣛⣒⣢⡴⠀⠀⣀⣀⣀⣬⣉⣉⣁⡥⠶⠛⣛⣓⣶⣬⣍⡋
⠀⠀⠀⠰⠾⠛⠋⣉⣠⣤⠤⠤⠤⠴⠶⠛⠋⢉⣠⣤⠤⠬⠥⠤⠴⠶⠊⠉⢁⣠⣤⠶⠶⠶⠶⠶⠛⠛⢉⣡⣤⡴⠇
⠀⠀⠀⢐⡲⣟⣛⣉⣡⠴⠖⠛⣛⣒⡢⢭⣛⣉⣩⡤⠖⠚⣋⣙⣒⠦⣝⣛⣉⣡⡤⠖⠛⣋⣛⣒⠬⣍⣉⣩⡤⠶⠂
⠀⠀⠀⢀⣤⡤⠤⠦⠤⠶⠞⠛⠉⣁⣤⡤⠴⠦⠤⠶⠶⠛⠋⣁⣠⣤⠶⠶⠦⠤⠶⠾⠛⠉⣁⣠⣤⠶⠶⠲⠶⠖⠃
⠀⠀⠀⢈⡤⠴⣒⣛⣋⡛⠒⠯⣍⣉⣡⠤⣖⣛⣉⣛⠒⠯⢭⣉⣩⡤⢖⣚⣉⣉⡛⠺⠭⣍⣉⣡⡤⢖⣛⣉⣉⠓⠂
⠀⠀⠀⠰⠶⢦⣤⣄⡉⠙⠛⠶⠶⠶⠶⠶⣤⣄⣈⠙⠛⠲⠖⠖⠒⠶⢶⣤⣀⡉⠙⠛⠶⠖⠒⠲⠶⢦⣤⣀⣉⠙⠃
⠀⠀⠀⠘⠲⠦⣤⣭⡭⠝⠛⠉⠉⠙⠓⠦⢤⣬⡭⠽⠚⠉⠉⠉⠛⠲⠤⣤⣭⡭⠝⠚⠉⠉⠉⠛⠲⠤⣤⡭⠭⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⡠⠒⢛⡉⠛⠒⢦⣀⠀⠀⠀⠀⠨⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠔⡡⣫⡟⢀⡤⠛⢦⡀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⣾⠫⠞⣵⣹⡏⢰⣿⣆⡇⠀⢰⠀⢷⣄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢀⡞⠁⠀⠣⣭⠽⠳⢤⣭⠞⠁⠀⢸⠀⢸⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⣰⠏⣠⠴⠒⠚⠋⠉⠉⠛⢲⡄⠀⠀⢸⠀⠈⣇⢸⣤⠖⠒⠒⠲⢤⣀⠀⠀⠈
⡏⠀⢧⣀⠀⠀⠀⢀⣀⣤⠾⠁⠀⠀⢸⠀⠀⢻⠘⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠐
⠻⡄⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠙⢦⣄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣏⠛⢦⣄⠀⠈⠢⠄⣤⠘⣆⣸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⡟⠀⠀⢸⡟⠶⣤⣀⣠⣴⠏⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠸⡄
⠀⠀⢠⡇⠀⠀⡼⠁⠀⠀⠈⠁⣯⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⣀⡀⠀⠒⢮⡁⢚⠄⢣
⠀⠀⠀⠳⠶⠚⠁⠀⠀⠀⠀⠀⠘⣾⢦⣤⠴⠞⠁⢀⡠⠖⠋⠉⠉⣧⡤⠤⢷⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠻⡄⡖⠒⠚⠉⠀⠀⢀⣀⣼⠁⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢤⠇⡇⠀⠀⠀⠀⡞⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣠⠃⡇⠀⠀⠀⠀⠙⢤⡀⠀⠈⠳⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡗⢀⡇⠀⢀⣀⣀⠀⠀⠉⠓⢤⡀⠈⢦⡀⠀⡐⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠘⠣⡀⣇⠀⢌⠟⠉⠉⢁⣒⣛⡂⠒⠛⠢⠈⠓⢦⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣇⣀⡇⠀⠀⡇⠈⠑⢾⣀⡄⣞⠀⣫⠈⠉⠉⠙⠓⠒⠦⠾⠀⠳⣌⡑⠒⠠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⡇⠰⡇⣹⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⣇⢸⠀⠀⠀⠀⡇⠀⠷⢣⣏⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⢦⡑⠿⢸⠀⠀⠀⠀⣇⡴⠲⢤⠞⠲⣄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡤⠾⡄⣀⣀⡔⠻⡇⠀⠸⡄⠀⠘⢦⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⢀⡔⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⠀⠀⡴⠛⢾⠁⠀⣿⠁⢸⡀⠀⢳⠀⠀⠹⡄⠀⠈⠳⢶⡛⠋⠉⠙⠻⢄⠀⠀⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠷⣸⠃⠀⡏⠀⠀⡇⠀⢸⢧⠀⠀⢧⠀⠀⠈⢦⡀⠀⠀⠈⠳⡀⠀⠀⠀⠳⡄⠘⢯⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⡽⠋⣹⠀⠀⡇⠀⠀⢻⠀⠘⡎⢧⡀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠹⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⣿⡀⠀⢻⡀⠀⠈⢇⠀⠘⢆⠙⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⠀⢸⡍⠲⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⢏⢧⠀⠀⠱⣄⠀⠈⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⢧⢀⡘⢿⡛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡳⢟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡇⠀⠀⢸⣸⡏⢳⡉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠤⠚⢧⠜⠁⢹⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⢀⡉⠀⠀⠀⠀⣧⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡼⠀⠀⠀⠉⠙⠒⢲⠒⠒⠋⠁⠀⠀⠀⠘⡟⡟⠉⠉⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠉⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠠⠾⠀⠐⠂⠀⠰⠉⠀⢀⠀⠀⠀⠀⢨⠂⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠴⠁
⠀⠒⠛⠄⠀⠀⠀⠠⠣⡦⠀⠠⠌⠀⠀⠀⠐⠄⠀⠀⠠⠅⢴⠒⠀⠤⠁⠀⠚⠙⠇⠦⠀⠀⠐⠢⡖⠂⠠⠬⠀⠀⠀⠈⠃⢀⠀⠠⠅⢴⠒⠀⠤
⣤⡔⡲⠚⠓⡄⠀⠀⠹⠅⠀⡇⠘⢦⣤⣒⠔⠛⢢⠀⠀⠈⠏⠀⢸⠀⠓⣤⡔⡦⠒⠓⡌⠀⠀⠹⠅⠀⡇⠘⢢⣤⣲⠔⠛⢢⠀⠀⠈⠯⠀⢸
⠐⣊⠀⠀⣬⠤⠆⠐⢂⠀⣠⠄⠀⠀⢚⡁⠀⢠⡥⠴⠀⠓⡀⢀⡤⠀⠀⠐⣈⠀⠀⣬⠤⠖⠘⢂⠀⢤⠄⠀⠈⢘⡁⠀⢠⡥⠶⠀⠒⡀⠠⡤
⠀⠀⣆⣠⣶⠀⠠⠀⣸⠄⠀⢠⣀⡀⠀⢰⣂⣴⡆⠀⠄⢀⡧⠀⠀⣄⣀⠀⠀⣖⣠⣶⠀⠠⠀⣸⠄⠀⢠⣀⡀⠁⢰⣀⣴⡆⠀⠄⢀⡧⠀⠀⣄
⠀⠀⠩⠀⠀⠴⠄⢤⣥⡄⠀⢌⣃⠀⠀⠘⠍⠀⠠⠦⠠⣬⣤⠄⠠⣙⡄⠀⠀⠩⠁⠀⠴⠄⢤⣥⡄⠀⢌⣃⠀⠀⠈⠍⠀⠠⠦⠠⣬⣤⠄⠠⣙
⠀⣄⠙⠀⠀⠀⠈⣠⡘⠀⡤⠀⣭⠁⢠⠈⠂⠀⠀⠈⢀⣄⠋⢠⠄⢨⡅⠀⣄⠙⠀⠀⠀⠉⣠⡘⠁⡤⠀⣭⠁⢠⠈⠁⠀⠀⠀⢁⣄⠋⢠⠄⢨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠒⠒⠒⠒⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠀⠉⠉⠉⠉⠉⠁⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣠⠖⠢⡤⣄⠤⠖⠒⣦⠤⠴⡎⠉⠳⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠧⢤⠤⠤⠤⠤⠤⡤⠤⢤⠤⠤⠤⠤⠤⠯⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⢻⠀⠀⠀⠀⠀⡇⠀⢸⠓⠒⠒⠒⠒⢒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⡟⠒⠋⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠦⠤⠤⠤⠴⠁⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡇⠀⠀⠀⠀⠀⠀⢀⡤⠤⡞⠉⠉⣣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⢸⠀⠀⠀⢠⠔⠒⠚⠀⠀⠀⠀⠈⠀⠈⠳⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⣘⣆⣀⣀⣸⡀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠚⠓⠊⠉⠒⠚⠒⠒⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠂⠀⠀⠡⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠘⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠄⠀⠀⠀⠤⠀⢠⠀⠀⠀⠈⢄⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⣠⠤⠊⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠤⠰⠄⠂⠀⡄⠀⠀⣠⣀⣀⡀⠉⠙⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠐⠒⠂⢼⢛⠉⠉⠈⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠃⠀⠛⠁⢼⠀⠀⠀⠀⠀⠀⠐⠄⠐
⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⡘⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⡠⠳⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⡈⠢⠁⠀⠤⠀⠀⠤⠄⡄⠀⠐⠀⠀⠎⠰⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠠⠘⠛⠿⠤⢰⡖⢲⠇⠀⠚⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠒⠀⠀⠠⡄⠀⠀⡀⡀⠀⠐⢀⠀⠁⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠁⠀⠡⢒⡄⣁⣛⠄⠁⠀⠃⠂⠈⢄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⡀⠀⠀⠀⠩⠁⠀⡫⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⠉⠉⠃⠈⣋⠁⠈⠉⠉⠘⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠀⠀⠉⠁⡀⠤⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⢐⡒⠂⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠄⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠰⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠀⢦⣄⠀⠀⠈⠣⣜⠢⡀⢀⡀⠸⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⢻⣧⡀⠀⠀⠈⠳⣌⠉⠀⠀⠀⠘
⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⣠⣤⣤⣀⠀⠙⢿⣻⡄⠀⠀⢘⡧⠀⠀⡀⠺⡆
⠀⠀⠀⠘⠏⢹⡄⠘⡄⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣽⣷⠀⣎⠻⣿⢀⡀⠈⠂⢩⡚⠇⢀⢰
⠀⠀⠀⠀⠀⣄⢡⠀⠇⠀⠀⠀⣀⠀⠀⠀⠀⠘⣻⣿⠀⠸⣿⣿⣿⣿⡏⠀⠙⢿⣿⠈⠁⠀⠀⠈⠁⣀⠈⢸
⠀⠀⠀⠀⠀⢈⡄⠳⠀⠰⠂⠩⠛⠀⠀⠀⠀⠀⢿⣇⠀⠀⢻⣷⣶⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠉⢠⣾
⠀⠀⢾⠽⠭⠌⢁⠀⠄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢸⣿⣿⣿⣿⣆⠀⠘⢿⣄⣀⣠⡄⠀⢶⣥⢀⢹
⠀⠀⠀⠀⠀⠀⠈⣧⢀⡀⠉⣢⡀⠀⠀⠀⠀⠀⢠⣿⡟⢠⣿⣿⣿⣿⣿⣿⡆⠀⠈⣿⡙⢛⣷⣶⣄⠠⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢎⠁⠀⠻⢷⡀⠀⢀⣠⡾⠹⠛⠀⣾⣿⣿⣿⢹⣿⣿⡇⠀⢠⣿⠟⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣾⣷⡀⠛⣻⡉⣉⣘⣹⣶⡆⢻⣿⣿⣿⢸⣿⣿⡇⠀⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⢡⡈⠩⠒⠋⢉⣿⣿⠁⠈⣿⣿⣿⣸⣿⣿⡇⠀⠘⣷⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡾⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⢀⣿⡆⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣷⣿⣄⠀⠹⢿⣿⣿⣿⡟⠁⠀⣼⣿⣿⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⡆⢠⣾⣿⣿⣿⣿⣶⠀⠘⣿⣿⣿⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⠃⠀⣿⢿⡟⣷⡶⣴⣶⣶⠆⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡿⣿⣿⣇⠀⠈⠛⠛⠛⠉⠀⢀⣼⣧⣾⣷⡿⠃⠙⠛⠉⠐⠇⠀⠀⠘⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣷⡹⣿⣿⣦⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢣⣾⣿⢇⡔⠀⠀⣰⣶⣾⠁⡠⣄⢰⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠿⣿⣿⣿⣿⣿⣷⣆⠀⣾⣿⣿⣿⠟⣁⣨⠻⢷⡟⣼⣷⠀⠻⡿⠁⠀⠘⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⡿⠀⣠⣿⣝⠛⡿⠿⠿⠆⠻⠿⠛⠛⠋⠉⠀⠀⠊⠀⠉⣡⣄⡞⠁⠀⣀⠸⢀⣂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣶⣶⡄⠀⣿⡿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⣠⠋⠀⠀⢀⡇⠀⠊⡭⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠛⠻⠿⠋⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⠉⢡⣦⣄⣀⡘⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠉⠐⠂⣈⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣃⠀⢉⡀⠈⠐⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠄⠘⢆⢸⣷⡄⠻⠟⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠥⢤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢱⠈⡗⣌⠳⣝⠁⡦⠀⢀⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⢠⡀⡆⢡⢸⡀⠈⠂⠀⠀⠈⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⠆⠈⠰⡄⠀⠀⢰⡗⠀⣠⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠓⠀⠀⠀⢿⣆⡴⠃⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠐⢿⠶⠀⠛⠶⣤⣁⢠⡌⠀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⢲⠆⠀⠀⠀⠀⠀⢹⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠁⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⣀⣠⣴⣄⡀⠀⠀⠀⠀⢸⡃⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡤⠀⠀⢀⡀⠀⣴⣿⣿⣿⣿⣿⣯⣿⡶⣤⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠰⠚⠁⢠⠀⠈⢷⠀⣿⢻⣿⣿⣿⠏⢸⠃⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠀⠀⠀⢀⡤⠶⠒⢻⡧⠤⡀⠀⣿⠸⠇⡇⢸⢶⠸⣇⣿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡇⠀⠈⠻⠷⠖⠐⠓⠦⡈⠐⠛⡽⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡤⣄⣄⠽⣀⣀⣀⣸⣇⣀⣀⣀⣀⣹⠀⠀⣇⠂⠀⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠟⢹⡝⠋⠉⠉⢉⡝⠀⠀⡛⠀⠀⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⣦⣀⠀⠀⠀⠀⢀⣠⠞⠿⣅⠲⠂⠉⠀⠀⠀⣇⣀⡤⠶⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⠀⠀⠀⡎⠉⢑⡶⠖⠒⠉⠁⢸⠀⠀⠀⣉⠀⠀⠀⠀⠟⠁⡴⠶⡿⠆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣸⡷⠞⠋⠀⢠⠀⠀⠀⡾⠅⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣰⣧⣴⣇
⠀⠀⠀⠀⠀⠀⠀⣦⢀⣠⡴⠛⢧⡄⠀⠀⠀⢸⡷⢻⡇⣧⠀⠀⢠⠹⠄⠀⠀⢠⡄⠀⣟⠉⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠀⣠⡟⡟⠁⠀⠀⠀⠀⠀⠀⠘⡃⡇⣾⠁⠉⠀⠀⠈⠟⠀⠀⠀⠸⡇⠀⣏⠘⠃⠀⢸⡇
⠀⠀⠀⢀⡴⠟⢹⡀⠃⠀⠀⠀⢠⠀⠀⠀⠀⠙⢠⡟⠀⠀⠀⠀⠀⠀⡀⠀⠸⣦⡇⠀⡇⠀⠀⠀⣸⡇
⠀⠀⣰⠟⠀⠀⠈⠉⠀⡀⠀⠀⢸⠆⠀⠀⠠⢀⡾⠀⠀⠀⣆⠀⠀⢀⡇⠀⠀⠈⠀⠀⡇⠀⠀⠀⠃⣧
⠀⠀⣿⡀⣦⠀⠀⠀⢠⡇⠀⠀⡇⠀⢠⠸⢂⡾⠁⠀⠀⢀⡟⠀⠀⡆⢁⠀⠀⠀⠀⢰⡇⠀⠀⠘⢻⣿⠃
⠀⠀⠘⣿⣏⠀⠀⠀⡘⠀⠀⠀⠿⠗⠉⣠⡞⠁⠀⠀⠀⢈⡃⠀⠀⠳⠎⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠈⢣
⠀⠀⠀⢠⡿⠳⠶⣤⣿⣧⣤⣤⣤⠴⠞⢩⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢠⡆⠀⣾⠀⡌⡇⢀⣠⣴⡏
⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⢠⡟⠀⣧⠟⠋⠁⠀⣹⠆
⠀⠀⠀⠀⢰⠇⠀⠀⠀⢼⣧⣤⣤⣄⣀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠄⣾⠃⠀⠀⠀⣠⠰⠾⢯⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡿⠁⣿⠀⠘⠿⠛⠻⢶⣶⣤⣀⠀⢸⡄⠀⠀⠀⠀⣼⡇⠀⠀⠀⢀⡿⠀⠀⣠⠟⢺⠄
⠀⠀⠀⠀⠻⠃⠀⠀⠀⢀⣿⣄⢻⡄⠀⠀⠀⠀⠀⣽⠯⣬⠟⠊⡇⠀⠀⠀⣼⣿⣷⠀⠀⠀⢘⠃⠀⠀⠙⣳⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⠈⣿⡀⠀⠀⠀⢰⣀⡀⠀⠙⠶⠃⠀⢀⣾⡏⣬⡿⠃⠀⠀⠘⠋⠀⠀⢸⡏⠾⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡞⠉⠀⢸⣷⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣰⢿⣿⣷⣿⡷⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⢰⡄⠀⠀⣸⠃⢠⡟⠁⠰⣼⡷⢻⣆⠀⠀⠀⠀⠀⠀⣠⠞⠁⣾⠙⣿⠛⣻⠛⠛⠛⠛⣿⠛⠛⢻⡇
⠀⠀⠀⡘⣧⠀⠀⣿⡄⢸⣄⣀⣠⡏⢳⢸⡏⢻⣶⠴⠦⣴⠞⠁⠀⣼⠃⢸⡟⠁⠉⢹⡏⢻⢿⢻⡿⠲⢿⡁
⠀⠀⠀⣧⡝⠀⠀⠀⠀⠀⢻⡭⣽⠁⠀⢻⡿⠋⢹⠀⣠⠟⢷⣤⣴⡏⣰⠋⠀⣼⠀⢸⣇⢸⣿⡌⢻⣄⡀⣹⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣟⠀⡞⠀⠀⢸⡅⠀⢈⡿⠇⠀⠀⢿⣿⠀⠁⠀⠀⢸⡆⢠⡟⠋⠈⠷⠶⣿⣏⠉
⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠉⢶⠇⠀⠀⡸⡏⠉⢻⠁⡟⠉⢹⠛⡏⠀⠀⠀⠈⣤⠃⢠⡷⠀⠀⠀⢀⢻⡿
⠀⠀⠀⠀⠀⢰⡇⠀⠈⡇⠀⠘⢷⡤⣀⡇⡀⢀⡎⢀⡷⠀⠘⢶⡇⠀⠀⢰⡀⠀⠀⢀⣀⣤⠶⢚⣿⣸⠆
⠀⠀⠀⠀⠀⢸⡄⠀⠻⠃⠀⠀⠘⣦⡈⠛⣠⠟⠀⢻⠇⡆⠀⠀⠷⠤⢤⡾⡷⠚⠛⠉⠁⣠⣤⣼⡇⠉
⠀⠀⠀⠀⣀⣈⣁⣀⣀⣤⣤⣤⡴⠋⠁⠸⣏⠀⠠⣸⠆⢻⡄⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⣹⡦⢶⡛⠁
⣤⠖⠛⠋⠉⠉⠉⠀⢠⣞⣋⣙⣿⣒⣦⣤⣼⣧⣀⣩⣤⣾⡋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⣧⣼⡛⠛⠓⠲⠶⠤⠤⣄⣀
⠙⠛⠶⠶⠶⠶⠶⠶⢤⣤⡄⢠⡤⠤⠤⠤⠾⠃⡿⠿⣉⣼⣿⣻⣿⣿⠶⠶⠶⠶⠶⠤⠴⠷⠆⠤⢿⣤⠤⠤⠤⣤⣤⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣏⣈⠓⠂⠐⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤

⣀⠀⠀⠠⡄⠀⠀⠀⠀⠀⡀⠰⡆⠀⠀⠀⣤⠀⢰⠄⠀⢀⠀⢰⡄⠀⠀⢀⠀⠀⠀⠀⠦⠀⠀⠀⢀⠀⠀⠀⣀
⠼⢀⡄⠈⠃⠀⠘⡇⠀⠀⣧⠀⠀⠀⡄⠀⠛⠀⠀⠀⠀⠿⠀⠈⠁⢀⠀⢽⠀⠀⠀⠀⠚⠀⢀⡀⠸⠆⠀⠀⣽
⠀⠘⠗⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⢶⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⢠⡄
⢀⠀⠀⠀⠀⠛⠀⠀⠀⡧⠀⠀⢀⠀⠀⣠⠀⠈⠆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡀⠀⣆⠀⢘⡄⠀⠘⠖
⢸⠀⠀⢼⡄⠀⢀⠀⠀⢀⠀⠀⢨⡆⠀⠸⠀⠀⠀⠀⢸⡇⠀⠋⠀⠀⢸⡅⠀⠀⠀⢀⠀⠀⠸⣥⠀⠁⠀⠈⠁⠀⠀⣆
⠀⠀⠀⠈⠀⠀⢻⠆⠀⠘⠇⠀⠀⣀⣀⡀⠤⢀⠲⠒⠺⢧⠤⠄⣀⣀⣀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⢀⡄⠀⢠⠀⠉
⠀⠀⣷⠀⢾⠀⠀⠀⣀⠔⢂⡩⡾⢝⢉⡒⢕⣊⠅⠀⠀⢨⡆⢅⠂⢀⠈⠉⠛⠳⢖⡒⠠⠤⣀⡀⠀⠀⠸⣾⠀⢪⠄
⢀⠀⠙⠀⠀⣠⡐⠙⠀⡠⢺⠭⡢⢋⠥⡂⠅⠂⠀⠀⠀⠀⠘⡀⢇⠂⠈⢀⠀⠀⠀⠈⠳⣕⠆⠈⢉⠢⢄⡀⠀⠀⣤
⠸⠆⢀⡔⡫⠔⠁⠀⡰⠁⢑⠥⡪⢔⠨⢒⠁⠀⠀⠀⠀⠀⠀⠃⢑⠄⠀⠀⠢⠀⠀⠀⠀⠈⢧⡢⢀⠠⠀⠈⠢⡀⠙⠁
⠀⡠⢧⣀⡄⠀⠀⢰⣁⢔⢕⣪⡲⠑⠍⡀⠄⠀⠀⠀⠀⠀⠀⢸⠴⠊⡀⠠⠀⠁⠀⠀⠀⠀⠂⢳⣕⡠⢁⡀⠀⢜⢆
⣼⠖⠓⠓⠒⠧⢀⡨⢔⢅⣕⠵⠮⠖⠒⠖⠤⠦⣤⣠⣀⠀⠀⢐⠨⡐⠠⣘⣪⣥⣀⣂⠤⠀⣀⠄⢳⣊⣔⠤⠙⠒⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠓⠦⣘⡵⠟⠋⠁⠀⠀⠀⠀⠀⠉⠈⠉⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⡇⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣇⠀⢀⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣉⣉⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠐⠒⠄⠢⠀⠄⡪⠐⡡⢂⠅⡪⢀⠔⡠⡂⢔⠔⡠⢂⢔⠔⡠⡢⢀⠀⡢⢀⢄⠀⡀⡀⡀⢀⠄⡀⡀⢀⢀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠈⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢱⡇⠀⠒⢶⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢇⣾⠀⠀⠀⠈⠃⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠻⣆⠀⠈⢮⣳⣦⣀⣀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢙⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠤⠤⣀⠀⠀⠀⢠⡏⠁⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠛⣚⣂⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⡎⠀⠀⠐⠒⠛⡆⠀⠘⢿⣶⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠀⠀⠉⠙⢷⣀⠀⠀⠀⠀⠀⠀⣠⠦⠤⠤⠤⣀⠘⣇⡀⠀⠀⠀⢠⠇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡄⠁⠀⢻⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠒⠊⠁⠀⠲⡄⠀⠀⠱⡌⠛⠶⠶⠚⠁⠠⣀⠀⠙⠀⠒
⠀⠀⠀⠀⠀⠀⠙⠦⠔⠁⠀⢰⠇⠀⢀⡀⢀⣠⣤⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠁⠀⠀⠀⠹⡄⠀⠀⠤⠤⠤⢄⡀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⣏⣰⡇⠀⠀⠸⠇⠀⠀⠀⣀⣠⠀⠀⠀⡾⢿⡄⢀⣶⣶⣶⣦⡄⠀⠀⣷⠁⠀⠀⠀⠀⠀⠹⠄⠑⠆⠁⣠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⣿⠀⠀⠛⠿⠿⠶⠶⠶⢶⣤⡀⣾⠷⠛⢶⣦⣰⡇⠘⣿⠀⣿⣀⣤⢹⣿⠀⠀⢹⠀⠀⠀⠀⣤⠰⢦⡄⠀⢀⣄
⠀⠀⠀⣎⠉⠷⢀⠂⠀⠀⠀⢸⡆⠀⠀⠀⣠⠶⣶⠀⠀⠹⣿⡏⠀⠀⠀⣹⣿⠶⠶⢿⡇⢻⡿⠿⠚⢁⡔⠲⡾⠤⣤⡀⠀⠀⠀⢠⡿⢄⡙⠊
⠀⠀⠀⠉⠹⣿⠚⡦⠤⠄⠀⠀⣷⠀⠀⠀⣿⣄⠉⠀⠀⢠⠿⢿⣤⣤⡴⠃⣿⣀⠀⢸⣇⣸⣇⠀⠀⠘⢧⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⣆⠀⠀⠈⠛⠻⠖⠚⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠈⠀⠀⢠⡇⢈⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡄
⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⣄⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠘⠓⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠛⣦
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⣚⣛⣻⠙⢷⣀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡌
⠀⠀⠀⠀⢧⠀⢀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠶⠶⠶⠞⠛⠛⠉⠉⠀⠘⢤⣀⢀⡀⠻⣞⠀⣎
⠀⠀⠀⠀⠈⠳⢤⡀⠀⢀⠀⠀⠛⠦⢄⣀⡀⠀⠀⢀⣀⠀⢴⡂⠀⢠⣶⣀⡀⠀⣀⡀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠙⠶⢍⣉⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠁⠂⡴⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢱⠀⠰⡢⢌⡑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⢵⡔⠘⠓⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣜⠊⠘⠒⠚⠉⠀⠀⡉⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡰⢡⠃⠀⠀⠀⠀⠀⠀⣜⠎⠀⠀⠀⠀⠀⠀⠀⠠⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠊⢠⠃⠀⠀⠀⠀⠀⠀⣌⠎⢀⠖⠢⢄⡀⢀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢴⣯⡀⠀⠀⣠⠊⠀⢠⠃⠀⠀⠀⠀⠀⠀⣜⠎⠀⡎⠀⠀⡰⢁⡞⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣢⠜⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⣜⠏⠀⠀⠈⠂⠐⠁⠎⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⠀⠀⠀⡌⠰⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡀⠀⠀⠀⠀⠀⣜⠎⠀⠀⠀⠀⠀⠀⡜⠀⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⣜⡏⠀⠀⠀⠀⠀⠀⡰⠀⢀⠁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⡀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢀⣀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⡛⠻⠿⡿⢿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⡿⠟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⢶⣶⣾⡀⣻⠿⠿⣅⣀⣷⣶⣶⣶⣶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣦⣤⣥⣭⣷⣶⣶⣾⣭⣤⣭⣭⡅⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠨⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠱⠂⠐⠒⠒⣄⠠⢄⢀⡀⠧⠀⢀⢀⢀⠀⠀⠄⠀⠔⠉⠀⠀⠀⠀⠑⡀
⠀⠀⠀⣀⠀⣐⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢤⢀⢀⠀⠁⢀⢀⡠⠆⠦⣠⠆⠂⢦⠎⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠌⠀⡀⠀⠀⡀⡀⡠⠀⢊⡄⠴⠐⠚⣊⠝⠛⡛⠛⠛⠡⣙⡛⠠⠤⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠂⠤⠤⠤⠀⠀⡲⠖⠈⠁⠀⠀⡠⠊⠀⠀⠨⠐⡄⠀⠀⠐⠈⡓⢤⡀⠈⢑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠠
⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠠⡀⠉⠢⡑⠁⡠⠂⠉⡒⢄⠀⠀⠀⠀⠀⠈⠁⢢
⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠐⠀⠈⢢⠂⠐⠨⡂⠴⠵⢦⠀⡀⠀⠀⠀⠈⠐⠄
⠀⠀⢠⠀⠀⠀⣀⠀⠄⡐⢁⡀⠀⠠⠤⠄⠀⠀⢠⡬⢀⣰⡠⠐⠂⠉⠉⠈⠉⠐⠂⠵⡔⠉⢀⠀⠄⠀⡐⡐⠀⠀⢂⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠁⠀⢠⠂⠁⠀⠄⠀⢨⣧⠀⡀⠀⠀⠀⠂⠂⠀⠄⠀⠀⠠⠡⠡⠀⠈⠌⠔⠠⠠⠁⠂⠂⠢⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠘⣿⠂⠐⠐⣀⠀⣀⠀⢀⡄⠀⠀⡂⠒⠀⠒⠐⠒⡐⠒⠒⡒⠒⢒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⠂⢀⠀⣿⠀⠀⢰⠃⣠⡁⠀⡤⠀⠀⣀⠅⠀⡐⠃⠀⡬⠃⠀⡬⣰⠂⠍⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡀⠉⢠⡉⠀⠏⠀⠀⠴⠀⠉⠀⠄⢠⠂⠀⢁⠀⠀⠩⠄⢀⡐⠀⢀⡆⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⢀⡀⠀⠀⣨⠀⠘⠃⠀⠀⠰⠁⠀⠀⠀⡎⢀⠀⠛⠀⠈⣁⠀⠈⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡏⡇⢠⠄⢠⡂⠀⢀⠄⢀⠄⢀⡌⠀⡀⠀⠰⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣡⡜⡀⠀⠀⠀⠗⠀⠈⠀⠈⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢔⠄⡂⢐⠀⠠⡀⠀⢐⠀⡂⢀⠄⡀⠀⠔⠠⠀⠀⢔⠀⠀⠔⠠⠀⠀⠄⠀⠀⢀⠄⡠⠀⢀⢀⠀⡠⢀⠤⣀⢄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠈⠀⠀⠈⠐⠁⠀⠊⠐⠁⠁⠈⠈⠀⠀⠀⠁⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣰⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⣉⣡⣬⣭⣭⣛⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⡿⠟⣻⠏⣀⡤⢬⡙⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⡿⠿⠛⠉⠉⠀⣠⣾⣿⢸⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⡿⠿⠿⠛⠛⠉⣁⣤⣶⢻⣿⣿⣿⣿⣿⣿⣧⣙⣿⣿⣿⣿⣿⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⣾⣿⠿⠛⣋⣭⣤⣴⣶⣶⣶⣶⣾⣿⣟⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣪⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣡⣾⣿⡿⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⣻⡵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡄⣠⢞⣵⣾⣿⣿⠋⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣩⡶⠛⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣫⠞⣱⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⢛⣩⠶⣻⠟⠋
⢀⣀⣤⣀⣀⠀⠘⠿⣿⣷⣣⣾⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⡿⢫⠞⣫⠶⠋⠁
⣰⣿⣿⣿⣿⣿⣷⣶⣤⣉⡛⠿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⡟⣱⣿⣿⣷⡀
⢿⣯⣿⣷⣌⠛⢿⣿⣿⣿⣿⣷⣶⣬⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣷⣿⣿⣫⠞⠙⣿⣿⣿⣿⣦⡀
⠸⡽⣿⣿⣷⣝⢦⣌⠛⠿⣿⣟⣿⣿⣿⣿⣷⣬⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡁⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⡄
⠀⠹⡜⣿⣿⣿⣧⡙⠿⣶⣌⡙⠻⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣷⣾⠿⠟⠙⣎⢿⣿⣿⣷⡄⠀⠀⠀⢹⣿⠿⣿⡟⠿⠿⢷⣄⣀⡀⠀⠉⠁
⠀⠀⢻⡌⢿⣿⣿⣷⡀⠈⠛⢿⣷⣦⣍⡛⢿⣿⣿⣿⡾⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠘⣆⠻⣾⣿⣿⣆⠀⠀⠺⠟⠀⣹⣷⡀⠀⠀⠈⠛⠟
⠀⠀⠀⠻⣮⡻⣿⣿⣷⣦⣤⣤⣬⣿⣿⣿⣿⣿⣿⠟⣁⡴⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⢿⣿⣿⣦⠀⣠⣴⠟⠉⠻⠇
⠀⠀⠀⠀⠈⠻⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣯⣤⣤⣤⣤⣤⣶⡦⠀⠀⠀⠀⠀⠀⠉⠢⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣟⣛⠿⠶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣯⣉⠉⠉⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣶⣦⠀⠉⠉⠙⠛⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⠁⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⢱⡌⠓⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠞⣴⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⣤⡘⠲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⠖⠋⠉⠁⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡏⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⡀⠀⠀⢀⣤⣿⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⠛⠉⠙⣦⣤⡟⠀⠀⡷⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣠⠏⠀⠙⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠓⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣿⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣄⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⡫⠟⠻⣷⡄⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣫⠕⠋⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⠛⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⣠⣶⡿⣟⠵⠊
⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⣀⣴⡿⢟⡽⠚⠁
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡯⠞⠁
⢀⣾⠃⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⢸⠇⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠉⠛⣿⣷⡀⠀⠀⠀⠀⠀⠘⣧
⣾⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⣿
⢻⡄⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⢀⡿
⠈⣷⡱⣄⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠈⢷⣝⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠙⢷⣝⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠈⠛⠶⢮⣤⣄⣀⣀⣀⣤⣤⣶⡿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢻⣿⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠷⠒⠒⠒⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢰⣶⠀⠀⢠⣶⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⣿⣄⣀⣸⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡏⠉⠉⢹⡏⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⡀⠀⠈⠁⠀⠀⠘⠃⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣶⣤⣤⣤⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡁⡐⡙⢦⡛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠇⡌⠀⠀⠈⠢⢄⡈⡻⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⠀⠀⠈⠙⠻⣿⣿⡿⠿⠛⠛⢛⡛⠿
⣿⣿⣿⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⠡⡄⠤⠐⠈⠉⠑⡄
⣿⣿⣿⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠔⠑⢄⠘⡦⡀⠀⠀⠀⡇
⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠐⠄⠀⢠⢠
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠂⣸
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠀⠂⠒⠁⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠂⠢⠀⠀⠀⠀⣀⢀⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠰⠄⠔⠀⠀⠀⠀⡁⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⠤⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢂⢀⠀⡀⠀⠀⠢⡀⠀⠒⠠⠀⠀⠀⠀⠈⠑⠀⠐⠀⠀⠈⡁
⠀⠀⠀⠀⠂⠈⠀⠤⠀⢀⠀⠀⠀⠠⣀⣂⠀⠁⢀⡆⠀⠀⡇⠀⠀⠀⠄⠀⠀⢠⠠⡠⠤⢄⡀⠀⠄⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠁⡀⡄⠀⠉⠙⠉⠛⠁⠀⠀⠐⡆⠀⠀⠀⢡⠅⠀⠀⠀⠀⠀⠓⠒⢄⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⢀⣘⠁⠀⠉⠑⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⣀⢀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠐⠒⠀⠐⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠒⠐⠂⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠒⠀⠀⡄⠀⠀⡀⠀⠀⠄⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠂⠀⠣
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠈⠦⠀⠐⠂⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠁⠀⠆⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⢈⡀⠀⠀⠀⠀⡀⠀⠀⢈⠀⠀⡀⠀⠦⠅⠀⠈⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⣀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠘
⠀⠀⠀⢀⡁⠀⢀⠀⠀⠒⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠐⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⢐⡀⠀⠀⠀⣀⠀⠀⡀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠋⠀⠘⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡅⠀⠀⠐⠀⠀⠊⠀⠀⠂⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⡠⠐⠃⠀⡀⠀⠐⣅⡦⠈⠀⠰⠇⠀⠀⣄⠀⠀⣀⢀⣄⢀⠀⢀⠤⠚⠁⠀⡀⠀⠘⣱⠆⠉⠀⠰⡁⠀⢀⡌⠀⢀⡀⣠⡆⡀
⠻⣀⡀⠀⡴⠷⠤⣤⣁⣀⣖⡂⠐⣦⠔⠚⠀⠈⠁⣀⠀⢀⡜⠙⠫⣀⡀⢠⠾⠷⢤⣴⣀⣠⣖⡂⠲⣦⠐⠋⠀⠉⢁⣀⠀⣀⠜
⢰⠉⠈⢀⣀⡀⣀⠏⠀⢀⠀⠈⠋⠙⠂⢤⠄⠀⠉⠉⠁⠈⠁⠀⠠⠉⠈⣀⣀⡀⡠⠃⠀⡀⠀⠈⠋⠙⠠⡤⠀⠀⠉⠉⠁⠈
⠒⠛⣨⣅⠀⣈⡁⠀⠘⠁⠈⠈⠉⡵⠂⠀⣀⡠⠒⠉⠓⠀⢀⠔⠚⢃⣹⡁⠀⣉⠀⠀⠫⡁⠀⠈⠉⡵⠀⢀⣀⠤⠒⠉⠒⠀⣀
⢶⠀⠀⠈⠉⠀⣣⠄⠀⡁⠀⠀⠀⠀⡘⠀⣀⡀⣀⡄⠒⠒⠛⠲⢖⠁⠀⠈⠉⠈⣧⠀⢂⠁⠀⠀⠀⠀⠏⢀⣀⠀⣀⡄⠒⠚⠓
⠤⠗⠠⢤⠄⣢⡝⠛⣉⣀⣠⠔⠚⢻⠖⠛⠉⡙⠁⠙⢀⣀⠤⠤⠼⠂⠤⣠⢀⣬⡟⠛⣉⣀⡠⠐⠛⢻⠒⠋⠉⡉⠀⠋⢀⣠⠤
⠀⠀⢀⡬⠊⠀⠈⣯⠅⠀⠀⠀⢀⠜⠀⠀⠐⠁⣀⠔⢴⣇⠀⡀⠀⠀⢠⡴⠉⠀⠙⡯⠀⠀⠀⠀⢀⠇⠀⡀⠊⢐⡠⠆⢼⡁
⠴⢲⠋⠀⢀⠠⠞⢁⠄⠀⠉⠒⠫⠤⠒⠋⡈⢈⣄⣤⠀⠀⠈⠀⠔⢒⠁⠀⣀⠰⠋⣀⠀⠈⡙⠚⠧⠤⠚⠁⡁⢸⣀⣄⠀⠀⠉
⡴⠪⠀⠀⠻⠈⠀⠉⣦⢠⠃⣠⠆⢀⣀⠠⢰⠊⠉⠀⢈⠆⠒⣡⢔⠮⠀⠈⡗⠉⠀⠙⡆⡰⠁⡠⠀⢀⡀⠤⡴⠋⠁⡀⠡⠖⠒
⠀⠀⢀⠖⠱⣤⠤⠶⠑⣋⠼⠅⠊⢉⡰⣾⠁⠀⠀⠒⠉⣲⠎⠀⠀⠀⠠⠊⠳⡤⠴⠞⠓⣣⠽⠄⠈⢁⡴⡾⠀⠀⠀⠊⠁⣲⠊
⢀⡔⠀⠰⠃⡄⠀⢀⣎⠀⣀⢖⣡⣄⣚⠁⠀⠀⡠⠐⢺⡃⠀⡀⢀⠔⠀⠲⢁⡇⠀⢠⣋⢀⡠⢊⣥⣔⣊⠀⠀⠀⠀⠐⣻⠁⢀
⡌⠀⠎⣤⠞⠙⠒⢻⣅⠴⠞⣩⣏⣙⠆⠀⠈⡡⠀⢒⠁⡈⡴⢃⡅⠀⢆⡤⠊⠑⠒⢻⡥⠴⢚⣡⣉⣳⠂⠀⠉⡇⠀⡚⢁⣁⡜
⣿⣻⣿⣻⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⣶⡶⠶⠶⢶⣶⠶⠶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠿⢶⡶⠟⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣀⠀⠀⢸⣧⣤⣤⣤⣄⣴⡿⠛⢿⣾⡇⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡘⠛⣠⣤⡿⠛⠉⠉⠉⠙⠛⠀⠀⠀⠿⠟⠿⣶⣄⢳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣏⣼⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⣿⣛⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦⣄⣤⣾⠟⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠠⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⢀⡂⢼⡉⠁⠓⠁⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡜⠀⡀⢀⣁⠀⠀⠀⠀⢠⡀⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⣀⠀⠀⠀⠰⠀⠣⠄⠀⠀⠂⠀⠀⠈⠀⠀⠆⠈⢴⡒⠁⠀⠀⠀⠠⠀⡐⠕⠀⠀⠠⠂⠀⢀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢢⠣⡀⠀⠀⠀⢪⠠⡀⠀⢀⠷⣚⠆⡀⠀⠀⠀⢆⢠⠀⡑⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣀⠂⠀⠀⠀⠈⠘⠋⡀⠀⠀⠂⠐⠀⠀⠁⡘⡰⢉⠆⠐⠊⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠂⠈⠠⢈⠀⡠⢠⢯⠏⢀⠀⡀⣂⣔⠀⢀⡂⠀⢙⡁⠁⠀⠀⡂⢼⠇⡬⠀⢀⢀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⣁⣤⣖⠊⠈⠷⠤⠔⠧⠤⡀⠀⢬⣡⡍⠔⠚⠒⠒⠊⠋⠋⡛⠹⣗⢲⠟⣦⣒⠆⠰⢒⠚⠈
⠀⠀⠀⢀⢄⠀⠈⠀⠀⠕⠮⣄⠀⠀⢀⡜⠑⢤⡶⠴⠃⠀⠀⣠⠢⣔⠀⣀⠬⣆⡠⢯⡀⠤⠺⠎⠸⡟⠉⠚⠂⠊⠀⠐
⠀⠀⠀⢀⡁⡀⡄⠀⡀⠠⠀⠨⠙⠤⠾⠒⢈⣠⡝⠁⠠⠆⢉⡁⠤⠠⢉⡉⠠⠌⠠⠐⠁⠀⠀⠀⠀⠀⡢⠀⠲⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠈⠄⠄⠀⠀⠀⠀⠀⢰⠀⠀⠻⠓⠢⠖⠀⠓⣯⣥⣈⣴⠂⢀⠤⠒⠉⡀⠄⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⢡⡦⢄⠀⠐⠀⢀⠔⠠⠀⠀⠀⡄⠠⢆⢭⠉⠁⠈⢀⠄⢔⠀⠀⡀⡀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⢐⢠⣦⣤⠇⠀⠢⠤⠔⡛⠂⠀⠀⢠⠔⢣⠞⠚⠋⠐⠃⠈⠀⠠⠀⠆⠔⠈⠀⠠
⠀⠀⠀⠀⠀⠢⠹⡄⠀⠀⠠⣢⡄⠀⡀⠠⠔⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠔⠁⠀⠀⢠⠀⠀⠀⠐
⠀⠀⠡⠀⠀⠀⡤⠚⠖⠐⠀⠀⠡⠀⠀⢀⢄⠄⠠⡀⠂
⠀⠀⠀⠀⠤⡎⠀⠤⠀⠤⠈⠠⠀⠄⠀⠁⠀⠠⠠
⠀⠀⠀⠈⠠⠈⠀⠀⠉⠠⠀⠀⠀⠄⠀⢀⣪⠉