Jittery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠒⠳⢶⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⣠⠬⠤⡀⠠⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣛⡛⠓⠛⠒⠂⠖⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠉⠉⠁⣀
⠀⠀⠀⢠⠎⠀⠀⠄⠈⠓⠒⠚⢷⠀⠀⠀⠀⠀⠀⢀⣀⡰⠻⠭⣯⠽⠿⢿⣾⣗⡂⠀⠀⠀⠀⣼⡇⠐⠉⠁⢀⠀⡀⠁⠀⠀⠻⠄
⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠈⢣⠀⠀⠀⠀⣠⡿⢁⠀⠠⠀⠀⠀⠀⠠⠀⠈⣷⡦⠀⠀⠀⢉⠀⢀⠀⠀⡈⠀⠁⣀⡀⡀⢠
⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⢨⠀⠀⠠⠤⠀⠀⠀⠛⠒⠀⠀⠐⠀⠀⠀⠀⠈⠅⠀⠙⠉⠁⠂⠀⠈⠉
⠀⠀⠐⠢⠈⠠⣀⣠⠄⠀⠙⠒⠁⠀⣡⠀⠀⠀⠀⠀⡀⠀⠶⠓⠒⢲⣾⠉⠃⢀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⣀⠀⢀⣠⡜
⠀⠀⠘⢶⡄⠀⠀⠀⠀⣀⠀⠀⢀⡀⠋⡄⠀⠀⠀⠀⢣⡀⠀⠙⣛⣛⡛⠁⢠⠌⠠⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⡾⠿⠋
⠀⠀⠐⠀⠱⡀⠈⠢⠄⣴⡂⠐⠁⢀⠂⠀⠀⠀⠀⠀⠈⠙⠷⣶⣾⣿⣶⣾⡟⠀⠄⠀⠀⠀⠀⠀⠀⢀⠂⡀⠐⠒⠀⢀⣤⠀⠠⡀
⠀⠀⠀⠀⠀⠈⢄⠀⠐⠻⠒⠀⣠⠊⠀⠀⠀⠀⠈⠰⠄⡀⠀⠈⠉⣹⡆⣣⠀⠀⠀⢤⠀⠀⠀⠀⡀⢀⢰⡙⠓⠐⠀⠙⠁⡇⢀
⠀⠀⠀⠀⠀⠀⢶⣿⣦⠤⠖⣾⣿⡶⠂⠀⠀⠰⠀⣠⣾⠇⠀⠀⠀⢸⡇⢸⠇⠀⠀⠀⠀⢀⠀⠠⢀⠄⠿⣆⠀⣾⣿⡆⠀⠊⢸⡆
⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠉⢘⣻⣷⣶⣀⠘⢿⡀⠀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⠶⠖⠒⠒⠂⠀⠀⠀⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⢸⡟⢻⠁⠀⠀⠀⠁⡐⠈⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠠⣄⡀⠊⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢶⣀⣚⣩⠀⠀⢸⡇⠸⡇⠀⠀⠀⠀⠰⣄⣠⣀⣠⡀
⠀⠀⠀⠀⠀⠀⣾⠇⠀⢣⠀⠠⠴⢂⡀⠀⠀⠀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣭⡾⣿⢆⡇⠈⣷⠀⢳⡄⢤⣴⣾⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⡟⠠⠀⠸⣆⣀⣠⣽⣿⠀⠀⠐⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠾⡿⠁⠀⠀⣿⠀⠘⠀⢸⠟⠛⡄⠀⠀⠀⡇
⠀⠀⡀⠀⠃⠀⡇⡀⠀⠀⠀⠉⠛⢻⣿⠗⠂⠀⡴⡖⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠤⣿⠀⢠⣶⣮⣦⣤⡾⡇⠀⠀⠁
⠀⠀⠀⠀⣤⡀⣡⣤⠔⠀⠀⠀⠀⠈⡏⠀⠉⠐⠀⣿⢏⣀⣀⣀⣀⣀⣠⣀⣤⣤⣤⡤⠶⠋⠀⢈⣀⠈⠒⠀⠀⠀⡆⠀⠀⣃
⠀⠀⠀⠀⠉⠛⢻⡇⠀⠀⠀⠀⠐⠾⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢽⣿⢸⣿⠋⠈⠀⠀⠛⡃⠨⠏⢧⡴⠊⠀⠐⣷⣶⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠂⠚⢻⣸⡧⠄⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠛⠛⠛⠛⠷⠶⣤⣤⣤⣤⣶⣆⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠋⠘⠷⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⢴⡶⣿⠀⠀⠀⠀⠀⠀⠀⢈⣿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠈⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⢸⣇⠀⢠⢤⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠙⢦⣄⡼⠁⢀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⢶⡄⠀⠀⠀⠙⠶⢤⣴⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣴⠟⠀⢠⡏⣠⡄⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠶⢀⡇⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣾⠃⣀⡀⠸⣇⣀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠞⠁⢀⡲⠀⠀⠀⠀⢷⣄⣀⣠⠴⠒⠿⢶
⠀⠀⠀⠀⢠⡟⠀⠘⠓⠀⠨⠽⣋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣍⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⢒⡓⢀⣼
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣉⣿⡍
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣛⣛⣛⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠭⠿⠶⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⣀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⣀⣤⣤⠶⠟⠋⠁
⢰⣟⡷⣀⣀⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣠⣾⣿⡄⠀⠀⠀⠀⣀⡴⣿⠸⣧⣄⣀
⠀⠉⣼⠏⣍⣉⣉⣉⠙⢋⣭⠿⣿⠛⠛⣿⠋⠁⢿⣄⣻⣄⠀⣀⡼⢋⣠⠟⠀⠀⠉⠙⣷⣦⡀
⠀⠀⣿⠀⠈⠉⠉⠁⠀⣿⣇⣀⣼⣀⣀⣸⣄⣀⣀⠀⠙⠻⠿⠿⠛⠋⠁⠀⠀⢠⣤⣤⣟⠉⢻⣆
⠀⣀⣹⡆⠀⠀⠀⠀⠀⣤⣩⣽⡏⢉⣩⣭⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣹⣷⠀⢻⡆
⠘⢿⡿⠛⠶⠶⢶⡶⠶⠟⠉⠀⠀⠘⠻⠛⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢻⣶⡄⢈⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠿⢿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠉⢉⣉⣛⣛⣛⠛⠋⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣹⡟⠋⠉⠉⠙⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⡿⠀⠀⠀⠀⠀⠹⣷⣾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣖⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⢻⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⠁⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢘⣄⠀⠀⢀⡬⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠽⠀⠈⠉⠀⠹⡐⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣀⠀⠀⡸⠙⣗⣀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠐⠆⠠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠘⢽⡄⠀⠇⠀⢱⠃⠀⠐⠐⣮⠚⢹⡀
⠀⠀⠀⠀⢀⠋⠀⠚⣥⡀⣡⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠜⠀⠀⡌⡇⠀⠀⠀⠻⠛⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢂⠌⢰⠛⡶⢉⢱⠀⠀⠀⢐⢨⠆⠀⠀⠀⠀⡐⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⠢⠐⣘⠒⢳⠎⠸⠀⣼⡗⡍⠟⠘⢢⡤⣤⣞⡄⠺⡇⠀⢰⠒⢤⠀⣄⠀⣀⠤⡐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢉⠔⢫⠣⠔⠂⠤⠴⣃⣰⠆⠘⣻⢶⡟⠈⠅⠠⡀⠀⠀⠉⠑⠀⡀⢄⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠠⠭⠤⠄⣸⣿⣁⣄⢀⣀⣐⡄⠀⠀⢰⠈⡀⢄⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⢿⣿⣧⠀⠀⠀⡘⠀⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⣶⣶⡞⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣐⣫⣑⡀⠀⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⠶⣀⡀⠀⠀⠀⠀⣀⢖⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠡⠀⠹⠦⠤⠄⠀⠈⠓⠲⠶⠾⠉⠄⠠⠖⠉⠀⠤⠍⠕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠾⠛⠛⠛⠷⠶⢶⣤⣄⣀⣀⣤⣶⡆⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⠛⠋⢹⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠉⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⣀⣀⣾⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢻⡏⠛⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⣧⡀⠘⢻⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡉⠉⠛⠛⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣶⡞⠀⢠⠶⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⠙⢷⠀⠀⠀⠀⠉⠛⢛⡿⠃⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⡟⠰⠶⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠘⠃⣼⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⣾⠁⢠⡄⠈⢧⣀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⠞⠃⠀⣄⡓⠀⠀⠀⠀⠻⣄⣀⣤⠞⠛⠛⠻⣦
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠛⠀⠠⠼⢋⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⢘⣋⣀⣰⡟
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣩⣽⣏
⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣛⣛⣛⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠯⣭⠭⢥⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠾⠛⠁
⠀⣩⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣿⣯⠉⠉⠉⠁⠀⠀⣠⣾⡏⣿⣁
⠀⠙⠛⣵⠟⠛⠛⠛⠛⠛⡟⢛⣻⣶⣴⣤⣶⡶⠞⢫⣟⠘⢧⡀⠀⠀⣠⡾⠋⣸⠇⠈⠛⠻⢶⣄⡀
⠀⠀⠀⣿⠈⠛⠶⠶⠋⠀⢰⣿⠁⢹⡆⠀⠀⣧⠀⠀⠉⠛⠾⣷⣦⣾⣭⠶⠛⠉⠀⠀⣀⡀⢠⡟⢿⣦
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠛⠒⣿⠷⠶⠶⠿⠶⠶⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⠛⠻⣧⡄⠹⣷⡀
⠀⢰⣶⣽⣦⣀⡀⠀⢀⣀⣾⠾⠿⠋⠀⣶⣟⡷⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⣾⣛⠀⢹⣇
⠀⠈⠛⠋⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⠉⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣹⣿⣤⣤⣽⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡶⠦⢤⣤⣄⣀⣀⣀⣀⣀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣤⣬⣭⣭⣍⠁⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣹⡏⠉⠉⠀⠀⢿⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⡿⠀⠀⠀⠀⠀⠈⠿⣶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡔⠛⢿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣩⣤⣀⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⡀⡀⣒⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⡿⠛⠻⣿⣿⡩⣍⡿⠋⢁⠵⡤⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⠀⠀⠀⠀⠀⠀⠀⠈⣒⠲⣤⣉⠁⠈⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠉⠉⠈⠉⣸⣿⡿⠓⠚⢿⣿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠒⠒⠒⢲⠲⣿⡿⠁⠀⡠⣾⡿⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠃⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⣶⣶⠲⠾⠾⠿⠿⠿⠿⠿⠿⡿⠁⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⣶⣶⣶⠷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⡐⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⣿⣶⣶⣶⣿⣿⣿⣿⠃⢀⣾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⢿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣷⣿⣾⣿⣿⣿⣿⣿⡏⠻⣷⣴⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡿⠿⠿⠿⠿⢿⠿⠿⠦⠿⠿⠿⠿⣿⣿⡆⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣅⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢊⡄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⠟⢿⣛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢂⠙⠉⠽⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠐⠈⠉⠁
⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⠀⡀⣀⢀⡀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠁⠀⠀⠚⠈⠃⠀⠀⠉⠉⠀⠁⠀⠀⠀⠈⠁⠃⠀⠈⠉⠀⠁⠁⠉⠈⠁⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠼⠰⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⠀⠀⠒⠔⠆⠀⠀⠐⠀⠰⠀⠀⠐⠖⠄⠀⠐⠂⠀⠀⠀⠀⠰⠰⠂⠄⠰⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣰⢊⠉⠉⠉⠑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⣀⣠⣷⠋⠳⣄⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⣌⢧⡀⠀⠀⠐⠃⠀⠀⣠⠖⠋⠀⠀⠀⠘⡇⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⠏⢳⣽⠶⠒⠒⠲⢦⡼⠱⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⡴⠋⠀⡞⠀⠀⢀⣀⣠⣦⣧⣤⣄⡀⠀⣀⡤⠞⠳⢄⡀⠀⠀⡠⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⢚⣩⣥⣶⣶⣶⣶⠞⠛⠋⣁⣀⠀⠀⠀⠙⠶⣞⠁⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⠀⢰⠋⠉⠉⠉⠙⢛⣛⣻⢿⣉⣠⠴⠚⢯⠉⡿⠙⠳⣤⡀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠳⣄⠀⢸⠀⢀⠔⢺⡉⣻⡈⢇⠀⠀⠀⠀⠀⠈⠛⠁⢀⣶⣿⡏⠓⠶⠦⡖⠋
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠉⠋⢀⠎⠀⠀⠈⠁⢧⠸⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣀⣀⡤⠊⠀⠀⠀⠀⠀⢸⠀⣧⡠⠶⠒⠛⠛⠓⠚⠿⣿⣿⣿⣧⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠋⠀⠀⠀⠀⣠⠴⠶⢤⣀⠉⠻⣿⡆⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⠀⠀⠀⣠⠎⠀⠀⠀⠀⠈⠳⣄⠈⠇⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡀⡞⠈⡟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣⣸⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠷⠚⠛⠓⠚⠷⠶⢤⣄⣀⡀⠀⠀⢠⠚⣦⠀⠀⡿⠀⠀⠀⠀⠀⢘⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠳⠤⠿⠤⠚⠁⠀⠀⣀⡤⠖⣋⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⢋⡉⠀⠘⢒⡡⠋⠤⠤⠤⢄⣠⡞⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⠓⡶⠤⠤⣤⣤⣤⣤⣤⠤⠴⠖⠚⠉⣩⢤⠀⠀⠓⢟⡠⠖⠋⠀⠠⢤⡤⣄⠀⠈⠁⠀⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣽⣾⣀⡀⢶⡱⠄⠀⠀⠰⣭⡆⢀⣀⣙⣾⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⡇⢠⠃⣠⢄⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢤⡴⠊⢁⣠⠴⣆⠀⠉⠉⠉⠒⠒⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠉⠁⠈⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠽⠆⠀⠀⣴⣉⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡖⠀⢠⢤⣀⡅⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠇⠀⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⢺⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⣶⢮⠉⠙⠛⠛⠉⠉⠉⠀⢀⡤⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⡬⠇⠀⠈⠙⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⠀⢠⣀⣠⠟⠀⠀⠀⠀⠀⠘⠦⣀⣰⡀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⣀⣤⣀⠀⢀⣠⣄⡀
⠀⢸⣿⢯⣿⡇⣿⣿⣿⣿⠀⠀⣠⢴⣦⡴⣤⣤⣤⣤⠀⢻⢯⣤⣤⣦⣤⣠⣤⠀⣠⣤⣤⡴⢸⣟⣥⣤⣤⡴⣤⣤⣤⡄
⠀⠈⠛⠻⠛⠁⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⡀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⢀⣹⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⣾⢀⣀⣀⠾⡻⢦⣤⡀⠀⠀⠀⠀⣠⣾⢎⡉⡀
⠀⠀⣀⡼⢻⣿⡟⠷⠦⠀⠀⠀⠀⢀⣿⠗⢲⠖⠀⠀⠂⠀⠀⠀⠀⠈⠉⣿⣦⢠⣾⣿⣿⣦⠀⠀⠀⢿⡟⠋⣉⣛⣠⣠⣀
⠀⠀⠉⢀⡾⠉⢿⡄⠀⠀⠀⠀⠀⣾⣿⠟⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡟⣿⣿⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⢹
⠀⠀⠀⣼⠇⠀⠘⣧⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢬⣙⢞⣩⡔⠋⠁⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⠋⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠐⣶⡄⠀⣰⣦⠀⠀⠀⢴⣦⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⣤⣄
⠀⠀⠀⢀⣤⣾⠉⢀⠀⠀⠀⣪⣼⠋⠀⠀⠀⠀⠀⢰⣾⣶⠀⣷⣷⢆⡀⢠⣶⣿⡆⠀⠀⠀⠀⠀⣹⣿⡟⠦⠴⣿⣿⣧
⠀⠀⠀⠀⢹⣿⠛⠉⠀⠀⠀⢻⣿⠓⠉⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡄⠉⣻⣾⣿⢿⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢉⣿⣿⡆
⠀⠀⢠⣤⣼⡿⣷⡀⠀⠀⣤⣨⡿⣆⠀⠀⠀⠀⠀⠚⣿⡟⠒⣿⣿⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢉⣿⣏⠀⠀⢸⡿⣏⠁
⠀⠀⠀⠀⠈⠁⢸⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⡿⡇⠀⠾⢿⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠞⠁⠿⠀⠀⠸⠇⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠈⢧⣠⣶⡄⠄⠀⠀⠀⠀⠀⣴⡶⠄⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⠙⣯⡄⠀⠀⠀⠀⠀⣽⣾⡖⠒⠒⠓⢠⣿⡿⣤⣀⡀⠀⠀⠀⠰⣿⣿⡀⠀⢨⣿⣦⡀
⠀⠀⠀⠀⢀⣴⡿⠟⠛⠉⠉⢠⣿⢷⡀⠀⠀⠀⠀⠻⣿⣿⣀⣴⠷⣿⡿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⡛⠲⠾⢟⣿⣷
⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⣀⣼⣿⡄⠁⠀⠀⠀⠀⠈⢻⡜⣿⡁⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠇⠀⢸⡟⣿⠃
⠀⠀⠀⣠⣾⠟⠉⠁⠀⢴⠟⠉⠉⠀⠀⠀⠀⠀⠀⢰⡶⠁⠘⠇⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠸⠃⠙⣧
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢦⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⣉⠉⠉⠉⠒⠒⠃⢸⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠭⢤⡄⢀⣀⣤⠐⠦⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠠⢀⡀⠀⠀⠀⠠⡈⠉⢹⠀⡿⠀⡳⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⣱⠋⠀⢀⠀⠈⣣⠖⠚⠒⣌⠀⣼⢀⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⠂⢰⠃⢠⡄⠀⠸⣆⡏⢸⡼⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣠⠼⡄⠀⠀⠀⢠⠟⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡔⠊⠛⠒⠦⠤⣀⣀⣀⣈⣁⣀⣀⠝⠢⣤⡴⠋⠀⠠⢟⠩⡭⢹⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠖⠀⠐⣸⠋⠁⢠⡍⣈⠤⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠤⠀⠄⠀⢀⡠⠴⠊⠁⠀⠀⡴⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⢾⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣠⠾⡝⢺⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⢿⠀⠐⠒⠒⠒⠊⠉⠀⠀⡇⡞⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠓⢮⣠⠃⠀⠀⠀⢰⣏⡭⣉⠝⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠊⣁⠬⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⣷⠀⣠⠤⠤⠐⠒⠊⠉⠉⠀⣀⠤⠐⠉⡧⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢀⠔⣹⡿⢮⣡⠊⢳⠀⢀⣠⠤⠒⠉⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡋⢰⠡⣀⡔⠃⠀⠀⠉⠁⠀⠠⡄⠀⠀⠀⠀⣀⡇⠀⠀⠀⠈⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⠇⡜⠉⡇⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣒⠒⠒⠂⢠⣤⡴⢶⠴⣏⢀⢎⡞⠀⠀⢸⠀⠀⠀⠀⠀⢀⡜⠛⠿⠿⢿⠏⢹⡇⠀⠀⠰⣱⠃
⠀⠀⠀⠀⠀⢠⢴⣒⠒⠒⠛⢠⣤⡀⠀⠀⠀⢰⡏⠉⠀⠀⠉⣉⣽⠷⠞⠹⠋⢶⣄⠀⠠⢮⢤⡒⠒⠒⠃⠠⣼⣇⠀⠀⡴⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣸⣄⣀⠀⠤⠀⣇⡈⠉⢀⣀⣀⡉⠸⠄⢄⣸⠀⠀⠀⠉⠉⠁⠀⡟⠒⠚⠃⠠
⠀⠀⠀⠀⠀⢨⠀⠀⣠⢀⡠⣤⠜⠃⠠⠤⢤⣯⠁⠒⠒⠒⠂⠛⢹⠀⢸⠉⠒⠒⠒⣒⡈⠁⣯⣍⣳⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢸⡀⢸⢰⠒⡇⠀⠈⠉⠉⠉⠉⢸⠀⠀⠀⠀⠀⠀⡼⠀⢸⢠⠎⡩⣿⠙⠃⠀⠀⠀⠛⠛⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠉⠹⡼⣟⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡟⠒⢺⠘⡷⡄⢸⠀⠀⠀⠀⠀⠀⢠⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣧⡀⠀⠀⠀⠀⠀⡾⠲⠶⠶⠶⠶⠚⠁⠀⠘⠳⠷⠍⢿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠦⠤⠤⣤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⢒⠭⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡰⠥⠄⢂⣀⣁⣤⠤⠤⠤⢤⣤⡀⠀⠀⠀⠀⢄⠒⠢⠥⣐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣩⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠶⠭⣅⣒⠤⢤
⠀⠀⠀⢀⠀⡠⠀⡀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦
⠀⠀⠀⠊⢰⢁⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣉⡉⠁
⠀⠀⠀⠀⠃⠸⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡽⠯⠩⣍⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⡀⡀⠀⠀⠀⠡⠖⠒
⠀⠀⠀⠀⠀⠀⠘⠀⠁⠈⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣠⠆⠀⡔⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠒⠒⢢⡀⢇⠀⣠⣤⠄⠀⢘⡥⠤⣼⠀⠀⠀⠀⠀⠀⡇⠀⢳⡀⣄⣠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠤⠄⠧⢼⠀⢀⣟⠀⠀⡏⠀⠀⢀⣀⢰⠀⠀⠀⢀⠇⡀⠀⢷⠸⣘⡆⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠏⣴⣒⣲⠆⠀⠀⢸⢭⡄⠀⢧⠀⠀⠈⡄⠉⠀⠀⢀⢎⡞⠉⡇⢸⡇⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣄⠁⢈⣀⡤⠒⡄⠘⡤⠳⡄⠀⠉⠒⠋⠉⠂⠀⠀⠅⠘⣀⡠⠃⣸⢃⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀⡀⢱⠀⢧⡔⠉⣲⢄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⣹⠰⠈⡆⠈⢦⡐⠁⠀⠀⠉⠉⠐⠀⠉⠁⠀⡠⠚⠁⠀⠀⠀⠀⠠⠥⠴⠲⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠁⠈⠀⠑⠁⠀⠀⠀⠒⠀⠀⠂⠀⠈⠉⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⢀⡀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⠀⠀⠄⠀⠀⠀⡈⠀⠀⠀⣠⠴⡞⣽⠄⢀⣠⠆⢰⠀⡆⠀⠀⠀⠀⠀⠀⠁⠒⡀⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⡅⠀⠀⢀⠁⠘⠢⠼⠉⡾⠀⠀⠂⠛⠯⠒⠈⠋⠳⠀⠀⠀⢀⠈⠀⠀⢀⣨⠖⠀⠡⡖⠲⡄⢀⠵⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡇⠀⠀⡌⠀⠀⠀⠀⠤⣇⡀⣀⢠⡀⢠⢠⡄⠤⢄⣄⠈⡀⠁⠀⣠⠶⠏⠀⠀⠀⠀⠈⠉⠁⠛⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡟⠉⢹⠇⠀⢀⠀⠀⠀⠀⢹⣁⠘⠃⠈⠮⠄⠀⠁⠀⠐⡁⠀⡘⢭⡍⠎⠴⢡⠆⢠⠄⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢸⠀⠀⠀⠉⢢⢀⣀⠗⠀⠉⣂⠀⠤⠄⠀⠀⠌⠏⡁⡠⠋⠀⠁⠀⠀⠁⠀⠈⠃⠀⠋⠰⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢸⠀⢸⠀⠀⠀⠀⠃⣀⡉⠀⠀⠀⠀⠀⠉⠓⠠⠭⡜⠁⠓⠀⡀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠛⠛⠉⠉⠉⠉⠈⠉⣉⣉⣉⣉⣑⣲⣤⣀⣀⣀⢀⡀⠰⢤⠤⠌⠉⠠⠋⠜⡡⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠰⠦⠤⠤⠤⠤⠤⠤⠬⠉⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢅⣂⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⢁⡀⠀⠠⢝⡢⠤⠤⠤⠤⠤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠟⠛⠛⠛⠻⠶⠶⣦⣤⣀⣀⣠⣴⣶⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠛⠛⠋⢻⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⣶⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⣤⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⢦⣤⣤⣤⣤⣤⣤⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠘⢷⣄⠈⣹⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠘⣧⣀⣀⣀⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠀⣰⠟⢉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣄⠘⡇⠀⠀⠀⠀⠀⠉⢹⡟⠁⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢰⡟⠐⠟⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠉⣰⡇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⣈⣟⡀
⠀⠀⠀⠀⠀⢠⡟⠀⠴⡆⠈⠳⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣟⠋⠀⠠⣌⠁⠀⠀⠀⠀⠹⢦⣤⡴⠞⣉⡉⠉⢻
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠀⠠⠖⢋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣁⣠⣾
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⢩⣽⣿⡁
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠛⣛⣛⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣭⣭⣭⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋
⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋
⠛⣋⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⣷⡗⠒⠒⠒⠂⠀⠀⠀⣰⣶⢿⡟⠉⠁
⠸⣿⠾⣡⣴⡶⠶⠶⠶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣤⣴⢿⡟⢻⡄⠀⠀⠀⠀⣠⡾⠋⡇⠘⠷⢶⣤⣀
⠀⠀⢸⡏⢠⣤⣄⣤⡤⠀⣁⣴⠞⠻⡏⠙⠉⢻⠁⠀⠘⠷⣤⣻⣦⡀⣠⡞⣁⣤⠾⠃⠀⠀⠀⠈⢻⣷⣄
⠀⠀⢸⡇⠀⠀⠉⠁⠀⠀⢸⣿⣀⣠⣿⣀⣀⣸⣇⣀⣀⠀⠀⠉⠛⠿⠟⠛⠉⠀⠀⠀⠀⢰⣶⣤⣾⠁⠙⢷⡄
⠀⣀⠸⣧⠀⠀⠀⠀⠀⠀⣠⣉⣉⣿⠉⠉⣩⣍⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢙⣿⡆⠈⣿⡄
⠀⣿⣿⡟⢷⣤⣤⣤⣤⣴⡿⠋⠉⠁⠀⠸⢿⠿⠃⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠸⣯⣤⠀⠸⣧⡀
⠀⠈⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣿⣶⣾⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠶⠶⠦⣤⣤⣤⣤⣤⣤⡴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣠⣤⣤⣤⣤⣤⣤⡀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠃⠀⠀⠀⠀⢸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⡟⠀⠀⠀⠀⠀⠀⠻⣶⡾⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢹⡃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠲⠬⢔⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠳⡀⠀⠀⡈⠀⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠃⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡆⢰⢠⠊
⠰⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣦⠀⠀⠀⠀⠀⠀⠆⠀⠈⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⠁⠀⠀⠙⠓⠛⠳⣄⠀⡠⠁⠀⠀⠈⣦⣄
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠈⠁⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠂⠀⠠⠄⠀⠐⠂⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡆
⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠃⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁
⠀⠀⠀⠀⠀⠀⣠⡗⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠃⢀⠀⠘⠤⠀⡚⠂⢦⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⢘⠨⠹⡀⠀⠀⠀⠈⠟⠛⠛⠋⠉⠉⠀⠉⠥⠠⠦⢬⡑⠒⡇⠀⠀⠀⠱⠄⠈⠉⠉⠚⣸⡗⢚⣯⣽⠆⡾⠀⠀⠀⠸⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠴⠀⠀⠰⠒⠐⠒⢦⣤⡤⠖⠒⢒⡳⣶⡄⡀⠀⠀⠀⠀⠀⠀⠉⣪⣿⣿⡟⠈⠀⡀⠁⠀⢀⣀⡁
⠀⠀⠀⠀⠀⢠⠸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠇⠀⠀⠀⠀⣘⠑⢨⡀⠈⠉⠁⢀⡀⠀⣁⠀⠀⠀⢀⠉⣭⢦⡀⠀⠉
⠀⠀⠀⠀⠀⢀⡱⠊⡇⠀⠀⠀⠐⠃⠀⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡉⠀⠿⠆⠀⢤⣽⣣⡀⠀⣘⠒⠀⠀⠏⠒⣻⢻⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠠⠥⠀⠀⠈⠁⠀⠠⠄⠀⠠⠤⠬⠅⠀⠉⠇⠀⠀⠈⠙⠀⠀⢀
⠀⠀⠀⠀⠆⠀⠄⠀⠄⠠⠀⠠⠀⠠⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⣀⢀⣀⢀⣀⣀⣀⣀⢀⢀⡓⠀⠉⣉⠈⠲⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠒⠂⠉⢠⠁⢄⠻⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⣁⡰⢠⣁⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⠖⠋⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡠⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠈⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⡘⠲⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣡⠀⠀⠈⢢⠀⠀⠀⠀⢸⡀⣀⣀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⡀⠀⠀⠸⣆⠀⠀⡴⠊⠉⠀⠀⠀⡅⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣴⠃⡠⠒⢾⢦⠀⠣⣀⣀⣈⣵⠞⠢⠤⠎⢀⣀⣀⣀⣀⣀⣠⡤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⢀⡬⠿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠶⠒⢀⡀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠠⠔⠉⡇⠀⠀⠀⠀⠀⡇⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⠦⢄⡀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⠀⣜⣋⡳⣄⠀⡇
⡤⠘⠃⠛⣭⠓⣄⣄⠀⡔⡖⣠⣠⠄⠀⠀⠀⠁⢤⡌⠉⠁⠲⠇⠀⣯⢉⡹⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠰⣪⠕⣿⠢⠌⣀⡙⠀⢉⣧⠀⠀⠀⠀⠀⠀⢸⡉⠉⠒⢤⡇⠀⣷⠜⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢩⣀⠀⠀⠀⠀⠀⠰⠆
⠈⠁⠀⠀⡇⠀⠀⠀⠀⡠⠖⠺⣇⡠⠤⡀⠀⠀⠀⠉⠢⣀⠀⠈⠓⢭⣀⠀⠀⠀⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡝⠛⠾⠱⣀⠞⠧⢴⡂⣀⣰⠄
⠀⠀⠀⢰⠀⠀⠀⠀⢀⡱⠤⣤⠋⢀⠀⡜⠀⠀⠀⡔⠛⠉⠳⣄⠀⠀⣤⣱⡤⠤⡝⠓⢷⠄⠀⠀⠀⠀⠀⢠⠋⠑⢄⡠⠼⢿⡀⠑⠒⠂⠤⠄⠒⠺⢵⡄
⠀⠀⠀⠘⢦⣀⠀⠀⠘⢤⣀⣈⠖⠊⢸⠁⠀⢠⡞⠀⠀⠀⠀⠀⠳⠎⠀⠙⣖⣰⠃⠘⡄⠳⣀⠀⠄⠂⠀⢰⠀⡀⣨⣇⣀⠴⡃⠀⠀⠀⠀⠀⡀⠀⠀⠀⢩
⠀⠂⠀⠀⠀⠈⠉⠃⡷⠦⠂⠶⠤⠐⣄⠱⢄⡠⠙⡦⣄⢀⠀⠀⠀⠀⠀⠀⡏⠉⡄⠀⠸⡞⢃⠀⣀⠤⠔⣚⣀⠉⢉⡀⢀⣠⠃⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠨⣄⠠⠊⠀⠀⡐⢌⠣⡈⣠⢊⡴⠃⠁⠀⠀⠀⠀⠠⠶⠇⠀⠘⠅⠀⠈⠓⢭⡤⠒⠉⠁⠸⣀⡀⢤⡈⠤⠒⠂⠤⠤⠤⠒⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢹⣁⣀⡀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠛⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠑⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠉⠀⠀⠉⠉⠉⠉⢩⡃⠀⠀⠀⠀⠈⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⢤⣀⡠⠊⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠼⣇⠀⡻⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠚⠓⠳⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⣈⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠒⠋⠉⢿⡒⠲⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡆⢹⡄⢎⢻⢦⡀
⠀⠀⠀⠀⠀⡴⢋⣤⡶⠟⠛⢉⣉⣁⣀⣀⡀⠀⠀⠀⠀⠈⣿⡿⠀⡇⢸⡈⡇⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠸⠁⣿⡏⢀⡴⢋⠁⡞⢿⣍⣉⡙⠛⣦⣄⣀⣼⢟⠇⢰⠇⢸⢧⡇⠸⡟⠷⣦⡶⠶⠚⠓⠶⣦⡙⢦
⠀⠀⠀⠀⠀⠀⣿⠻⢿⣤⣘⣧⣈⠲⢬⣍⣙⣛⣛⣛⣉⣁⣈⣴⣿⠀⠻⣤⠛⡆⢿⡀⠈⣿⣶⠶⢦⡀⠈⢻⠈
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠻⠿⢿⣶⣶⣬⣭⣍⣉⣉⣩⣥⣤⣶⣒⣋⣁⣼⣣⣤⡷⠾⣿⠇⠀⠀⣿⠀⣸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣠⣬⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⣿⠀⠀⢀⡟⢀⡿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡄⡇⣶⣿⢸⠀⠀⠉⣍⣓⣒⠲⢤⠀⣀⣴⣤⣀⠀⠀⢰⣿⠀⢀⡾⠁⣼⠃
⠀⠀⠀⠀⠀⣇⢸⣇⠀⠀⠀⢸⣧⣬⣭⣤⠼⠄⠀⠀⡇⣿⣿⢀⡏⢸⠏⠀⠈⢻⠀⠀⢸⡿⠖⠋⢀⡼⠃
⠀⠀⠀⠀⠀⠙⠄⠻⣦⠀⢶⠦⢤⣀⣀⠀⠀⠀⠀⠀⠛⠒⠲⠾⠁⣼⠀⢠⠀⣸⡆⢠⣿⢧⠴⠞⢋
⠀⠀⠀⢀⡀⠀⣀⡀⠘⢷⣤⡀⠀⠈⠻⢿⡓⢺⡟⢻⡏⢹⡏⠛⣿⣇⣤⡿⠞⢋⣴⠟⠁⠀⠒⠚⠁
⠀⠀⢰⡏⢠⡞⠁⠀⠀⢠⢩⡿⢷⣦⣄⡀⠉⠛⠛⠛⠛⠛⠛⠛⠛⢋⣁⣤⡶⠛⠁
⠀⠀⠸⡇⢺⡀⠀⠀⠀⠘⠦⠙⠶⢤⣍⣛⠛⠓⠶⠶⠶⠶⠶⠞⢛⣋⣽⠍⠛⢦⣀
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠑⢄⡀⠀⠀⠉⠉⠛⠛⠛⠓⠚⠛⠛⠋⠉⠀⡆⠀⠀⠙⢧⠈⢷
⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠈⠑⠢⢤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⠴⠃⠀⠀⠀⢸⡇⠸
⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣤⣿⡀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠛⠛⠛⠛⠛⠳⠶⢦⣤⣤⣤⣶⣆⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠸⠷⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢾⠿⠟⠀⠀⠀⠀⠀⠀⢀⣼⠟⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⣠⠶⠋⠁⠀⠀⠀⠉⠛⠶⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠹⣆⠀⠒⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⠛⠛⠛⠛⠙⣇⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠈⢳⡶⠃⢀⡴⠚⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣉⠹⡆⠀⠀⠀⠈⠛⢻⡟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣰⠟⠁⠀⣾⠀⠿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⣠⡇⠀⢀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣸⣇
⠀⠀⠀⠀⢠⡟⠀⢶⡀⠙⠦⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢿⠉⠀⠠⠍⠀⠀⠀⠀⠻⠦⠴⠚⣉⡉⠙
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠋⠡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣶
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣴⠾⠟
⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣖⣒⡚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⣴⣶⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁
⢉⡭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⣿⡋⠋⠛⠁⠀⠀⣠⣾⢻⣏⠁
⠘⠛⣱⠞⠛⠛⠛⠛⢻⠛⣻⣷⣦⣴⣶⡶⠛⢹⡋⠻⡄⠀⠀⣠⠞⢁⣼⠀⠙⠛⠷⣦⡀
⠀⠀⣿⠈⠛⠛⠛⠁⠀⣿⠁⢈⡇⠀⠈⡇⠀⠀⠉⠛⢿⣶⣾⡵⠞⠋⠁⠀⢀⣀⣀⡟⠻⣦⡀
⠀⠀⢿⡀⠀⠀⠀⠀⠀⡉⣛⣻⠛⠛⣛⡛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⢳⣆⠘⣷⡀
⠰⣿⣾⠷⣤⣤⣤⣤⣼⠟⠉⠉⠀⠺⠿⠇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢿⣭⠀⠘⣧⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠿⣶⡾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠛⠛⠓⠒⠛⠛⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡟⠛⠛⠋⠙⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣼⠃⠀⠀⠀⠀⠹⢦⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⠓⠲⠶⠞⠧⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⣠⠔⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢲⠚⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⢓⣒⠒⠒⠺⣇⠀⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⣰⢫⢙⡄⠀⠀⠀⠀⠀⠀⢠⡇⠄⡇⠀⠀⠈⢹⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠆⠙⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⢑⠞⠁⠬⠀⠀⠈⠢⠔⢪⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠸⣿⣿⣛⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢩⣷⣀⣀⣀⣀⣀⣀⠀⠉⢉⣹⣿⠛⠀⠀⣠⢶⢻⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠤⠤⠈⣽⠛⡏⠉⡏⠘⠳⢷⣤⣾⠥⠊⠀⣈⢹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⣇⠀⠀⠀⣭⣽⠛⣻⡛⢻⡆⠀⠀⠀⠀⠀⠀⡏⢙⡦⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠛⠋⠁⠀⠀⠉⠁⣸⠁⠀⠀⠀⠀⠀⠀⣿⠈⣿⣤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠤⣄⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡶⠖⠒⣦⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⠁⠀⠀⠘⠲⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣂⣀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡤⠀⢒⣈⣭⠤⠤⠴⠶⠶⣶⣄⣀⣀⡀⠀⢄⠑⠒⠯⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠵⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠺⠭⣕⣒⠄
⠀⠀⠀⠀⠠⢀⡄⣀⠄⣠⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠬⠿⠦
⠀⠀⠀⠀⠀⡌⢰⠁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⣤⠤⠤⠤⠽⠒⢀⢀⡠
⠀⠀⠀⠀⠀⠀⠈⢈⡳⣤⡀⠀⠀⠀⢠⠄⠀⠠⠴⠶⠒⠒⠒⠂⠉⠀⢑⣢⡳⠄⠀⠉⠭⢥⢒⣒⡀
⠀⠀⠀⠀⠀⠀⠀⢯⠤⢐⡆⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣠⠀⢀⠞⠁⠀⠈⢪⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⡤⠤⢤⠀⢧⠀⢀⣀⠀⠀⢔⣋⣀⠏⠀⠀⠀⠀⠈⡇⠹⣄⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢧⣸⠀⢩⡇⠀⢠⠋⠀⠈⣣⢰⡄⠀⠀⢀⠇⠀⠸⡎⣏⢧⢳
⠀⠀⠀⠀⠀⠀⡴⢰⢠⡇⡴⢁⣔⣒⡤⠀⠀⢸⣡⠀⠘⡄⠀⠈⣹⠛⠃⠀⢀⢎⡞⠹⡄⣿⢸⢱⠘
⠀⠀⠀⠀⠀⠀⠠⠘⠀⠇⢧⡈⢈⣁⡤⠔⡆⢸⡤⠣⡀⠈⠑⠾⠋⠳⠶⠒⠅⠈⣀⠴⠁⡟⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀⢀⢠⢱⠀⢧⠆⠉⠦⢄⣀⣀⠀⠀⣀⣀⠀⠀⢀⠞⠀⠀⠀⠀⣀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⠊⡀⡄⠈⢢⡎⢠⠎⢈⠏⢹⣉⠉⠀⢀⠔⠋⠀⠀⠀⠀⠀⠢⠐⠛⠬⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⠀⠀⡄⠀⢰⠀⠀⠈⠉⠃⠉⠉⠁⣀⡤⣾⣁⡀⠀⠀⠀⣀⣠⠬⠭⢷⢬⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠠⠀⠈⡆⠀⠀⠀⣨⠀⠀⠀⠀⢀⣠⠔⠚⠁⡀⠀⠀⠈⠉⠙⠓⠢⠤⣄⣀⣻⡤⣌⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡆⠀⡏⠉⠉⠉⠇⢆⠀⣴⢎⡙⠘⢋⣰⣼⣁⠸⡴⡇⠀⠀⠀⢀⠔⠁⠈⠣⣄⢂⢄⣀⡀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⣧⠀⠀⡘⠀⠀⠉⡁⢸⠃⠀⠀⠀⠉⠀⠀⠀⠈⠀⠔⠠⠊⠀⣀⡴⠛⠁⠀⠘⠢⠼⠂⣎⡉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡆⢰⠤⢴⡇⢀⠀⠀⠀⠉⠓⣞⠁⣇⠸⣞⡁⠹⠚⡅⡐⠁⢀⡜⡣⣽⢂⢀⡄⢀⡤⢄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⢸⠀⢸⠁⠀⠀⠢⣄⠀⢠⢏⣓⠢⠤⣤⣀⠀⠀⢴⠖⡆⡸⠒⠛⠁⠀⠞⠀⠘⠤⠤⠃⣼⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⡄⢸⠀⠀⠀⠠⢇⡙⠃⠀⠀⠈⠉⠒⠺⠥⣜⡚⠘⠾⣀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠚⠒⠓⠛⠁⠙⠀⣉⣈⣉⣑⣢⣤⣀⣀⡀⠀⡄⠰⣥⢠⠋⠉⠜⠠⢫⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠐⠒⠢⠤⠤⠤⠤⠤⠙⢉⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢅⣀⠀⢀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⣀⣀⡢⣬⣒⠤⠤⠤⠤⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⣰⠉⢳⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠁⠤⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠺⠰⠉⠆⠀⠀⠀⠀⠀⣶⣏⣳⡖⠀⠀⠀⠀⠀⢀⣘⣁⠀⠀⠀⠀⠀⠀⠹⠺⠈⠁⠀⠀⠀⠀⠀⢨⡀⠗⣈⠂
⠀⠀⠀⠐⠿⠗⠃⠀⠀⠀⠀⠀⠁⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠺⠏⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢘⣏⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡉⣯⠩⠀⠀⠀⠀⠀⠀⡑⣇⣿⡋⠀⠀⠀⠀⠀⣾⠃⢷⡄⠀⠀⠀⠀⠀⢸⠦⠿⠀⠀⠀⠀⠀⠀⠠⠛⡈⠓⠆
⠀⠀⠀⢓⣿⡀⠂⠀⠀⠀⠀⠨⠃⣇⡿⢡⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀⠀⠀⠀⡅⠀⠀⣏⠀⠀⠀⠀⠀⢐⠀⠁⠘⡂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⢸⣁⡿⠀⠀⠀⠀⠀⠀⠹⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠴⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠰⣤⣤⡔⠢⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡀⠀⠀⠀⠀⠐⢀⡊⣒⠀⠀⠀⠀⠀⠀⠀⡤⢢⠄
⠀⠀⠀⢐⢠⢰⠂⠀⠀⠀⠀⠀⡜⠀⠂⠀⠀⠀⠀⢀⢀⡻⠻⡟⡀⠀⠀⠀⠀⠀⠈⠀⠃⠔⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⠈⢹⡸⢀⠁⠀⠀⠀⠀⠐⠢⢝⢡⠃⠀⠀⠀⠀⠀⢿⡘⣿⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠘⢖⣲⠗
⠀⠀⠀⢻⣒⣚⡗⠂⠀⠀⠀⠀⢶⣌⣰⠦⠀⠀⠀⢀⠁⠪⡄⠼⠉⠀⠀⠀⠀⠀⠀⢇⡼⢀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢨⣡
⠀⠀⠐⡘⠁⠋⠪⠀⠀⠀⠀⠀⢈⠇⣺⠀⠀⠀⠀⠀⠀⠒⠐⠀⠠⠀⠀⠀⠀⠀⠼⠃⠷⠀⠀⠀⠀⠀⠀⠀⠚⠳
⠀⠘⠒⠄⠀⠀⠔⠀⠀⠀⠀⠀⣰⠐⡰⠀⠀⠀⠀⠀⠬⠀⠀⠈⠤⠀⠀⠀⠀⠈⢦⣛⣠⠆⠀⠀⠀⠀⠀⠀⠂⠘⠂
⠀⠈⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢤⠔⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⠘⠆⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣶⣤⡴⡇⠀⠀⠀⠀⠀⠘⢡⠛⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡆⣖⠀⠀⠀⠀⠀⠠⠌⠀⠀⠠⠄
⠀⠀⠠⠄⣿⠅⠃⠀⠀⠀⠀⠀⢂⠸⠀⡂⠀⠀⠀⠄⠀⡌⠈⣄⠀⠀⠀⠀⠀⠀⣠⡞⠤⠀⠀⠀⠀⠀⠀⢴⡄⠀⣼
⠀⠀⠀⠶⠊⠛⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠑⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⡿⡇
⠀⠀⠀⢰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣴⣇
⠀⠀⠀⠀⠙⣿⣿⣿⣽⣿⣶⣤⣀⢀⠰⠃⠘⠆⠀⢀⣤⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣙⣻⣿⣿⣿⣿⣿⣷⡇⠡⠄⠸⣾⣿⣿⣿⣿⣿⣟⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠉⣵⣿⣿⣿⡽⣛⢵⡂⠙⠋⢐⡪⣝⢯⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠷⠀⠀⡀⢀⣰⡄⠀⣸⢿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢰⢹⣿⣾⣿⣿⡏⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠂⠁⣠⣴⣿⠿⠋⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⠭⠭⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣵⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠸⢿⠿⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢢⢂
⠀⠀⠀⠈⠖⡼⢀⣃⡤⢠⡄⣀⠀⢄⡘⠃⠘⠃⣀⠀⢀⠠⡄⢰⣔⣇⢧⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⡧⠀⡄
⠀⠀⠀⠀⠘⡍⣑⡒⠽⡶⠳⢺⢧⣦⡍⠁⠈⢉⣴⡤⣟⠺⢳⡮⠔⡚⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠮⢷⠢⠌
⠀⠀⠀⠀⠀⠀⠨⠦⠎⠑⠘⠋⢋⣹⡄⠀⠀⢠⣏⠙⠋⠋⠚⠹⠴⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣮⡯⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣴⣤⣤⣤⣶⣦⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⡀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣛⡻⠿⠿⠿⢛⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠀⢠⣀⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢩⣙⣛⣛⣋⡭⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢻⣛⣩⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣿⣿⡷⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢾⣿⣿⣿⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⣿⣿⡀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣉⡀⠀⠀⣿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⣀⣠⣾⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣦⣀⠀⠀⠀⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣀⣰⣿⣿⡿⣋⠹⡏⣼⢹⣿⡄⠀⠀⠀⠀⣰⡿⣿⣮⡿⠩⣿⣿⣿⣧⣀⣀⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⣿⣿⣟⠁⡁⢙⡀⠄⠠⠎⠞⠛⢦⣾⣆⣼⢋⣇⡱⠀⠀⢰⡋⢈⠙⣿⣿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⣿⣿⠄⠓⠸⠧⠀⠀⠂⣆⡄⠈⣿⣿⣰⣄⡏⡃⡀⠀⠞⠁⠄⠰⠿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⠲⣶⣾⣶⡷⡖⠒⢦⣿⣟⡻⢿⣶⣶⣶⣻⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣟⠻⢿⣷⣿⢿⡇⢑⠍⣉⠀⣿⡏⠐⣻⣿⠉⣹⠿⣷⣾⣿⢿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡉⢶⣊⠁⠉⠒⠀⡍⠀⠀⠀⢽⡇⠀⠀⢷⣧⠐⠊⠉⠙⣻⣾⣸⣳⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢷⣟⠲⠍⣀⠖⠀⣤⢀⠀⠀⠀⠸⠃⠀⠀⢀⡆⣤⠑⢟⣈⡹⢟⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢿⣿⣶⢾⣥⢴⣆⠤⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⢿⣬⣶⣶⣯⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠏⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⣄⠴⣶⢲⡆⢤⣴⣤⠄⣰⢲⡶⢂⣤⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠻⣧⣄⠀⠹⠀⣽⡇⠰⠉⠀⣠⣾⠋⠀⠀⠀⠀⢠⣾⠏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢻⣿⡄⠁⠏⢀⠁⣰⡿⠉⠀⠀⠀⠀⠀⠀⢊⣽⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⡿⠞⠀⠈⠻⣏⠀⠀⠀⠀⠀⣴⣶⣶⡽⢻⡿⡿⢻⣹⣾⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⣤⣄⡘⢿⣿⠇⠀⢇⠃⠀⣿⣿⠋⣀⣴⡄⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡠⠀⠀⢠⠤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢧⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡶⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢶⣦⠆⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡾⣏⡙⣃⢈⡄⠀⠀⠤⠄⢀⠀⠀⡀⢠⣶⡄⢀⡀⠀⠀⡠⠤⠀⠀⠀⢈⣠⣼⣧⣄⡃
⠀⠀⠀⠀⠀⠀⣨⣭⣿⣿⣟⣯⡭⡄⠀⠀⠀⠀⠀⠈⣓⢉⣿⣿⣿⡉⢉⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⣿⣋⣀⡀
⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⡇⢇⠰⠀⠀⠈⠙⠱⠋⠁⠞⠈⣿⠉⠣⠀⠙⠟⠛⠁⠀⠀⠎⠀⣿⣿⣿⣿⠁⠰⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⣿⣿⡷⠦
⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⡟⢸⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⠇⠹⣷⣿⣍⣠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠉⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠢⡤⠤⡤⠤⣠⣀⣀⡀⣸⣴⣿⢹⣷⣼⠄⣀⡀⣠⡠⠤⡠⢦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠘⣦⣽⣿⣿⣻⣭⡍⡏⠈⡏⢩⢙⡹⠻⠙⣣⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⢀⣠⠄⠀⠰⠁
⠀⢂⡛⣯⠛⠘⠫⠝⣿⡛⠅⠣⠀⠓⠘⣛⣚⠠⠛⠈⠋⡏⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢠⠀⢀⠀⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠉⠈⠂⠀⠈⠁⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⣀⠠⣤⠀⠀⠀⣤⢄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⠁⠀⠀⠀⠉⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠴⠀⠂⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠢⠀⠀⠠⠊⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂⠀⠉⠀⠁⠂⠺⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡤⠀⢄⡀⠸
⠀⠀⠂⢬⠓⠉⠀⠄⠐⢒⡏⠈⠈⠀⢟⠒⠀⠀⠀⠑⢫⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠻⠈⠀⠠⠟⢃⡀
⠀⠀⠀⠀⢣⡖⠢⡍⠙⡻⢃⠀⠀⠀⠚⢛⠁⡥⠒⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠠⠃⣀⠘⠄⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⣰⡇⠀⠀⠀⢳⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡀⠀⠀⠀⣸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢣⡀⠀⢀⠃⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠠⠀⠀⠀⠀⠀⢄⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠁⠇⠀⠀⠀⠀⠀⠰⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢠⢠⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠤⠀⠀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠆⠉⡞⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠓⠀⢃⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠣⡀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢈⠀⠀⠀⠉⠀⠉⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⠎⠁⢱⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠀⠐⢤⠊⠁⠀⠉⠓⠴⡀⠀⠒⣁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⢴⡃⠀⠀⠀⢘⡆⠌⢀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠆⠀⠀⠀⠀⠀⢆⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢈⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠜⠁⢂⠘⡀⠀⠀⠀⠘⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⢲⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡤⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⢀⠠⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⢀⠀⡀⠀⣠⣿⣄⠀⢀⠀⠀⠀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣄⠈⢲⣷⣶⠿⠿⠿⣿⣿⡶⠁⣠⠶⠁⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠂⠉⠉⠁⠉⢉⣛⣿⣿⣶⣤⣄⣀⡈⢓⣿⣿⣿⣧⣰⣤⣿⣿⣿⣛⣁⣤⡴⠶⠟⠻⠿⠍⣉⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⣀⣤⣎⣁⣈⣹⣿⠟⠙⢻⣿⣿⡿⣿⣿⡿⠋⠻⠍⠲⣤⣤⣤⠷⠦⢄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠉⠀⠀⡤⢻⠛⠀⠀⠀⠀⢸⣿⣟⣛⣿⣿⣷⡀⠀⠀⠀⠈⢦⠉⠲⣄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣟⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠢⣀⠀⠀⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠖⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠈⠛⠶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠻⣿⣿⣿⡿⠛⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⡰⠃
⠀⠀⠹⣿⣿⣦⣀⠀⠀⡰⢆⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⠻⣁⡐⠙⠆⠓⠈⣇⣀⣀⣼⣇⣀⣈⠧⠀⠠⠐⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⢀⠀⠤⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⢠⣴⠖⠋⠉⠙⠄⠈⠀⡄⠀⠁⠒⠂⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠉⠁⠀⠀⠀⡀⣠⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⠀⣀⢤⡆⠀⠅⠂⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠽⠍⠙⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠂⠀⠀⠐⠂⢄⡀
⠀⠀⠀⣠⣴⣶⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠉⢓⡐⠒⠂⠀⠀⠈⠉⠻⣦
⠀⡴⣾⠿⠿⡶⡤⣄⠈⠀⣖⢲⡖⢲⣴⣤⣄⠀⠀⠀⢀⠀⠴⢶⠋⢻⡀⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⢀⣻⠄
⠀⠀⣙⠻⡱⣓⡗⠀⠘⢼⠃⣜⠣⡞⠥⠗⢽⣳⠄⠀⠀⠀⠀⠘⢷⠮⢶⣦⣤⣸⣷⣤⣶⣷⣶⣶⡶⠿⠛
⠀⠀⠈⠋⠀⠈⠈⠱⠤⢥⠔⢤⠞⣥⠖⠀⠲⠟⠁⠀⠀⠀⠀⠀⠘⠀⣀⡿⠙⢇⠈⠉⠉⠉⠉⠙⠶⠶⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣴⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠡⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢀⠀⣰⡓⣐⣄⣶⣷⣰⣄⠀⠙⠻⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⠳⣄⡀⠀⠀⠀⠀⠈
⠀⢀⡏⣴⣆⡀⣿⣿⣍⣽⣿⠏⡷⢧⣀⡄⢋⠁⠦⠀⠀⠀⠀⠀⣀⣤⣠⣴⣤⠴⠊⢉⣿⢟⡶⣺⢿⣷⣾⠉⠈
⠀⠘⢦⡟⠁⠀⠉⡿⠛⠁⠉⠙⠃⠀⠺⢣⣄⠱⠀⡁⠀⠀⣠⣾⣿⣿⡇⣼⡿⢿⢸⢧⡿⣻⠟⢯⡞⠙⡾
⠀⠀⠀⠑⢰⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢠⠄⠀⠈⠙⠛⠉⠉⠁⠁⠀⠀⠉⠉⠉⠑⡄⠀⠀⠠⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⣥⣾⣧⣬⣤⡄⠠⣤⠀⡀⠀⢰⠀⠀⠀⡡⠤⠁⠀⠀⠐
⠀⠀⠳⡀⠀⠀⠀⢀⣴⠋⢳⣆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊⢱⡄⠀⠀⠀⠀⠀⠀⣀⠘⢺⠿⢣⡜⠿⡖⠃⣀⠀⠀⠀⠀⠀⠢⡠⣆⠀⠀⢀⣠
⠀⠀⠀⠀⡘⠂⠂⣈⢻⡄⣼⢋⡀⠀⠐⡂⠀⠀⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠛⡿⠋⠉⡄⡀
⠀⠀⠀⠀⠀⠈⠁⠉⢁⠸⢀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠑⣄⡳⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡈⠀⠀⠀⠀⢀⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⢄⣀⠴⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⠆⡀⠑⢦⢠⠖⠁⠰⠄⠀⠀⠀⠀⠀⡀⢡⠌⠉⠁⡎⠀⠀⠀⠀⠂⠉⠉⠀⠀⠀⠙⣗⢸⡏⠁⠀⠀⠀⠉⠐⠂⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⢀⡡⢬⡇⠀⣿⠤⣅⠀⠀⠀⠀⠀⠀⠈⠴⠈⠹⠁⠶⠒⠁⠀⠀⠈⠂⠀⠀⠀⡀⠀⣯⢸⡃⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⢇⠈⠳⢤⠛⠈⢃⠴⠋⣀⠆⠀⠀⠀⠀⢠⠀⠛⠂⠛⠀⢤⠀⠀⠀⠀⠀⠀⢹⣏⢇⣀⡘⣏⣀⣠⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠙⠂⠂⠀⡉⠀⠒⠒⠁⠀⠀⠀⠀⠀⠄⠈⠓⠐⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⢹⡛⢟⠻⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⠒⠲⠤⠐⣄⣧⣥⡔⠡⠤⠒⠂⠀⠀⠀⠀⠀⡆⠀⠀⡥⠀⢀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠀⠀⣶⡐⠙⡆
⠀⠀⠀⠀⠀⠀⠐⢻⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⠔⠛⠢⣈⠆⠀⠀⠀⠀⢀⠘⣇⠀⠀⢰⡤⣴⠀⠀⢀⡟⢀⠀⠀⠀⠀⠀⣹⣇⢀⡇
⠀⠀⠀⠀⠀⠀⡠⡖⠋⠙⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠦⠤⠏⠀⠀⠀⠀⠀⠀⠀⢼⡄⢀⣻⣿⣿⢒⡀⣼⠁⠀⠀⠀⠀⠀⠀⣿⣷⣾
⠀⠀⠀⠀⠀⠌⠐⢇⠀⢀⠟⠀⠣⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠸⠐⣄⠀⠀⠀⠀⡌⠸⣇⠀⠙⢿⠿⠋⢀⣿⠞⡄⠀⠀⠀⠀⠀⢸⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢀⢴⡄⠈⠀⠀⠀⠀⠐⢀⠘⡦⠀⠈⠀⠠⡞⢀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠑⠂⡀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠰⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡽⠤⡧⠬⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠗⢏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠤⠐⠂⢆⡇⠀⠀⠀⠀⢤⡀⠀⠒⠒⠀⢀⡤
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠹⣦⡾⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠴⠖⠢⠔⢣⠤⠀⠀⠀⢰⠒⠇⢹⠋⠉⠉⠸⠐⡆
⠀⠀⠀⢀⠄⠁⠀⠀⠁⠀⠀⠊⢃⠀⠀⠀⠀⠀⠀⡆⡠⠊⠤⠆⠤⠄⠢⡀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⣄⠀⢠⡕⠀⣠
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢰⠂⠀⠀⠀⢠⠀⡀⠀⠹⠁⠨⠖⠀⠐⠲⠀⠹⠅⠀⣀⢠⠀⠀⠀⠀⠃⡀⠀⢈⠀⠀⠀⠀⠀⠢⡀⢦⠂⠐⡄⢀⠔
⠀⠀⠀⠀⠀⠀⢙⠒⠶⠚⡘⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⣿⣼⣾⣇⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠆⢠⣷⢠⣾⡇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡠⢿⠟⠉⣿⣿⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⢸⣻⣾⣿⡏⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣶⣦⣴⣶⡶⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣁⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⡞⠙⣿⣶⡄⣿⡀⢰⢸⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⣿⡿⢄
⠀⠀⠀⠀⢀⠴⠛⢀⣴⣿⣿⣿⣿⣧⣼⣦⣷⡄⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⣿⣿⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠹⣿⣿⣿⣿⣿⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠰⢷⣤⣿⣿⡿⡆⠁
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⠛⠋⠉⠁⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡈⠻⠿⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡆⢰⠀⡄⠀⣿⠀⠀⠀⢣⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⣦⣷⣶⣿⣶⣷⣴⠇⣸⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣤⣄⣀⣀⠀⠈⠦⠠⣄⡀⠙⢦⡟⣋⣙⣿⣿⣿⣿⠶⠃⣀⡴⠰⠀⠉⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⡠⠐⠋⠁⠁⠀⠈⠉⠛⠛⠲⠤⠌⣹⣶⢤⣀⣀⣉⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣖⣋⡩⠭⠛⠛⠒⠀⠐⠀⠂⠈⠑⠢⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠀⠐⠲⠖⠚⠛⢲⠟⠽⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠿⠶⠤⣤⠄⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣠⢴⠏⠀⠄⠀⣼⡇⢠⣿⣿⣿⡌⢿⠁⣙⢿⡉⢹⣦⣀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⡼⢀⡄⠀⠘⠁⣭⣿⣿⣿⣿⣿⣦⡀⠘⠆⢁⢹⡇⠈⠑⠦⡀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⠀⠀⠀⣀⣿⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢜⣶⣇⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⣿⡾⢻⡏⢿⣿⣷⣿⣿⣿⣿⣿⠟⢹⣦⣿⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠙⢿⣿⣿⣿⠟⠋⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠀⠀⠀⠈⠉⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⣻⠿⢿⡁⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠿⢛⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⠶⣿⣡⣚⡷⠊⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠿⠗⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⣤⡶⣾⣿⣿⠶⣦⣄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠎⠹⠃⣤⡄⠀⢀⣤⡀⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⣘⠀⡀⠀⢼⠆⠀⡀⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡿⣴⢿⣦⢸⢠⣾⠷⡜⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡊⠺⣦⠀⠀⠀⢾⡷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⣆⠘⡟⢰⢈⡿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠀⠐⠀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⠀⠹⠾⠞⠁⢸⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢂⢐⠞⠂⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⡀⢈⡄⡀⠀⢀⠀⠀⠀⠀⠀⣊⣀⢀⠀⠠
⠀⠘⠓⠀⠀⠈⢐⣁⠀⠀⠀⠀⠀⠀⣲⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣦⡾⡉⡹⡓⠒⠁⠀⠀⢠⠆⠈⣹⠟⠷⡄⠊
⠀⠰⢹⡄⠀⠀⠀⠉⡧⠀⠀⠀⠐⠀⢣⢺⠃⡏⠀⠀⠀⠀⠀⠀⠚⠁⢠⣾⢋⡔⠘⠐⠊⠀⢠⡀⡘⠁⣠⡀⣠⠡
⠀⠀⠹⢄⠀⣀⠀⠄⠁⠀⠀⠀⠀⠠⠊⢹⠡⠁⠀⠀⠀⠀⠀⠊⠁⠀⠚⠕⠂⣸⠀⠀⠀⠠⠚⠀⠁⢀⡈⠀⡤
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠠⠀⡤⡼⠀⠈⠈⠄⠀⠒⠁⠀⠀⠀⠐⠀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⢈⣉⠑⢨⡚⠠⠄⢐⠀⠀⠀⠀⢸⠀⠠⡀⠀⠀⣡⢜⠞⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡀⢀⣈
⠀⠀⡔⠉⠇⠀⡡⠝⡠⡍⠁⠑⠀⠀⠀⢸⠀⠀⠁⠀⠀⢦⠈⠆⠑⠌⠀⠀⠀⠀⠠⠀⠀⠀⠤⡚⠈⢀⣤⡀⢀⢠⠄
⠀⠘⠀⠀⠀⠤⠔⣾⠸⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠠⠶⡦⠤⠀⠀⡀⠀⠉⠰⢸⠀⣈⣭⣀⢀
⠀⠀⠀⠀⠀⠠⠔⠁⢀⠀⠀⠀⣰⠀⢰⡴⢻⡆⠪⡁⢠⣞⡹⢠⡎⠀⢸⠇⠰⣉⠂⠀⠁⠄⢰⣾⣛⣭⠾⠯⡲⡀
⠀⠀⠀⠀⠀⠂⠀⠰⠁⠀⠀⡄⢿⡠⢺⠀⢸⡠⢄⣸⠾⢧⡤⠚⢧⡤⠾⠤⢄⣨⡇⠀⠀⠀⠁⡇⠡⢶⣺⠁⠇
⠀⠀⠀⠀⠀⠀⢀⠰⣀⠀⠰⠀⠀⠀⢀⠀⡇⡀⢀⢀⢀⠀⡀⡇⢸⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡉⠁
⠀⠀⠈⠂⢀⡲⠊⠌⢶⠈⠀⠈⠀⠀⠸⠄⠇⠃⠘⠹⠰⠛⠆⠧⠸⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⢶⣀⠊
⠀⠁⠀⠉⠀⠁⠂⠀⠼⡁⠂⠒⠀⠈⢠⢤⠤⡤⢀⠀⢀⠀⠀⠀⢀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠐⠀⢽⣿⡅
⠀⡀⠄⠂⠁⠀⠀⢠⠀⠈⠄⠀⠀⠀⠀⠀⠒⢩⣥⣄⣩⠇⠀⠁⠞⢦⠼⠧⣄⣤⠤⢄⡀⠀⠀⠀⢀⢚⣘⡶⡀
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡀⠠⣎⣠⠀⠑⡌⠉⠆⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠁⡠⠃⢰⣶⡺⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⢁⣆⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⣴⣆⣠⠂⠀⠀⠀⠀⢠⢼⡖⣄⣈⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠠⡤⠀⡏⠊⠀⠀⠀⣠⡄⠀⠀⠀⠈⣋⠉⠉⡇⢀⡀⠀⠄⣀⣀⣧⠙⢦⣌⣀⡐⣁⠀⠠
⠀⠸⠁⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠁⠀⠘⢢⣀⡯⠂⠀⠀⠈⠰⢼⠀⠠⡎⠁⠀⠀⠀⠀⠀⠸⠇⠴⠉⠁⠙⠈⠂
⠀⠀⠐⠦⠄⡀⠀⡀⠑⢢⡀⠀⠀⠀⠀⡐⡻⣿⡅⠐⠀⠀⠀⠂⢂⠀⠀⠙⡤⠀⡀⠀⠀⠀⠠⠤⠤⢠⣧
⠀⠀⠀⠀⠀⠈⠁⠈⠉⠢⣉⠄⠀⠤⠀⠸⡴⠋⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⡀⠸⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈

⡻⢶⠀⡃⠀⠀⣤⡤⠀⣀⠀⠀⡀⠠⢰⣶⡆⠄⢀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠠⣀⡤⣤⣀⡤⠀⠀⠀⠀⠀⠀⠀⢸⠀⡾
⡿⣿⣉⣁⠀⠀⠀⠊⠌⣉⠙⠯⠙⢛⣿⣿⣿⡒⠫⠖⠒⠀⠀⠀⠀⠀⠀⣀⣀⠴⣿⡀⢁⣿⡦⣀⡀⡀⠀⠀⠀⠀⣈⣉⣿
⣿⣿⢡⠸⡀⠀⠀⠶⣶⣤⡴⠖⢂⡾⠻⣿⡟⢷⡐⠒⢦⡤⣶⡦⠀⠀⠀⠈⠁⣼⢩⢿⡟⡉⢷⡈⠁⠀⠀⠀⠀⢠⠃⣾⣿
⣿⣿⢸⡄⠁⠀⠀⠀⠀⠉⠀⠀⠘⠁⠀⣿⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⣸⠟⠄⣸⣃⠠⠺⣧⠀⠀⠀⠀⠔⠀⢀⣿⣿
⣿⣿⢸⡏⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠃⠈⢫⡄⢂⠑⢿⡇⠀⠀⠀⠀⢼⠛⣿⣿
⡟⠃⡼⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⠁⣀⣼⣆⡀⠀⢈⢿⠀⠀⠀⠀⠘⡄⢿⣯
⠿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⡴⠊⠁⠈⠁⠈⠂⢠⣀⡄⠀⠀⠀⠊⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠁⠀⠁⠐⠀⢀⢀⣤⣶⣄⣠⠄⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⡷⢶⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⠦⠀⠀⢀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡾⣟⡻⣦⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟
⣿⣄⣀⣄⣀⣀⠠⠴⠖⠂⠀⠀⣘⣛⣷⣿⡷⣯⣙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠰⠒⠂⢀⡤⣄⣠⣄⣃
⣿⣿⠉⠈⡁⠀⠀⠀⠀⠀⠀⢰⠁⣿⣿⣿⣿⣏⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠙⢒⡈⣽
⡟⠘⢇⠀⠙⣻⡽⠟⠓⠀⠔⠀⢰⣿⣿⣿⣿⡿⢸⡀⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤⣠⣄⣤⠀⡠⠀⠘⠻⠿⡶⠋⡉⣼⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢻⣿⣿⣿⣿⣷⢸⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣿⣿⠁⢴⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⣽⣿⡟⠃⡸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣷⡼
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣧⣤⣤
⡇⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⠄⠀⢀⡎⠀⢸⣿⣿⣿⣿⡇⠀⢱⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣤⠖⠈⠀⠀⠀⠀⠀⠀⠁⢀⣤⣿⣿⣿⣿⣿⣿⣦⡀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣻⡟⠂⠀⠠⠄⠀⠀⠀⠀⠀⠈⡄⢿⣿⣿⣿⣿⡿⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠌⠻⠿⡿⠟⠡⡆
⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠠⣄
⢾⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠹⣧⠀⣽⠶⣄⠀⠀⢀⡴⢾⡅⢠⡿⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣇⣸⠀⡀
⠀⠀⠀⠀⠀⠈⢱⣿⣷⡊⠀⠀⠀⠀⠘⣇⠨⠳⣬⣦⣤⣮⡔⠫⢀⡟⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⣤⣸⣇⣤
⠀⠀⠀⠀⠀⠐⢹⣿⣿⡙⠄⠀⠀⠀⠀⠈⠙⠋⠉⢹⣿⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡿⣿⠃⠀⠀⠀⠀⠀⠀⠱⠀⢀⠘⡟⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⡦
⠀⠀⠀⠀⠀⠀⢸⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣰⣶⡆⠀⠀⠀⠻⠿⣿⣿⣿⣶⣶⡎⣳⣶⣶⣿⣿⣿⠿⠋
⠀⠀⠘⣾⢿⣟⣶⣤⣠⣞⣿⣿⡾⠃⠀⠀⠀⠀⣻⠿⣟⠀⠀⠀⠀⠀⢀⣨⣽⣿⡿⢿⠿⣿⣿⣭⣅⡀
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠘⠛⠛⠉⠉⠀⢸⠀⠀⠉⠙⠛⠛⠀⠀⢠⣾⣧⡄
⠀⠀⠀⠀⠈⠛⠛⠁⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣛⡻⣿⣦⡀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠻⠽⢿⣿⣶⣞⣳⣶⣿⡿⠮⠞⠁
⠀⠀⠀⠀⠀⠀⠐⢬⠕⠀⠀⠀⠀⠀⠀⠾⠛⠋⠀⣀⡀⠈⠛⠿⠆⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠀⠺⠿⠿⢻⡟⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣦⣄⠀⠀⠀⢀⣴⣶⢿⡷
⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢿⣿⣏⠈⠣⠀⠰⠃⢨⣿⣿⠃⠀⠀⠀⠠⢀⠰⢆⠀⠄
⠀⠀⠀⠀⠀⢀⣶⣿⣿⣆⠀⠀⠀⠀⠈⣻⣷⡶⠒⣿⡗⠲⣾⣷⠋⠀⠀⠀⠀⠄⣾⡆⣸⡇⠠⠀⠀⠀⠀⠀⣠⣽⣯⣄
⠀⠀⠀⠀⠀⣼⣿⡛⣛⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠙⢀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⡧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣿⠏⣭⡭⢹⣿⠀⠀⠀⠀⢸⣿⡷⠃⠀⠀⠶⣿⣟⠀⠀⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠘⠋⠁⠈⠉⠈⠙⠃
⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠟⠧⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠸⠷⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⡿⣭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢾⠻⠳⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣄⣸⣇⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⣸⣇⣠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣯⣽⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣿⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣽⠯
⠀⠀⢀⡤⠄⠐⢲⡶⠀⠀⢑⠃⠀⠀⢦⣒⢒⠒⠤⣀⠀⠀⠀⠀⠄⠊⣀⠛⢁⡉⠂⠀⠀⠀⠀⢀⡠⠄⠂⢲⡶⠀⠀⢑⠀⠀⠐⠶⣒
⠀⠊⠁⠀⠀⠉⠘⠀⢠⡎⠀⢈⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣭⠀⣭⡵⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⢠⣎⠀⢀⣦⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠊⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⡠⠴⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠷⠦⣀⠀⠄⠠⠀⢀⡠⠴⣾⣿⣿⡿
⠴⢞⣫⣿⠟⠁⠀⠀⠀⠀⢄⠰⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠙⣿⣞⡿⠶⢬⣑⡴⢧⣊⡥⠴⢞⣫⣿⠟⠁⠀⠀⠀⠀⢄⠰⠀⠆
⣶⣴⡿⠃⠀⠀⠀⠀⠀⠀⢰⣄⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⠾⠋⢁⠔⡮⡉⠻⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⢰⣄⠀⣤⡄
⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⢾⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢤⡴⠁⢧⠿⡘⣦⣶⣿⠆⠀⠀⠀⠀⠀⠀⠀⢻⠙⠀⣿⡇
⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⠨⡘⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡷⠟⠀⠀⢷⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠀⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢛⠣⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢸⣿⣏⡀⠤⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⢀⢟⠧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠸⠷⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡽⣽⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢾⠻⠳⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠆⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠑⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠴⣦⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⢘⡏⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⢸⠇⠀⠞⠋
⠀⢠⠤⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣄⣰⢋⠘⢦⣠⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠠⠤⠤⡄
⠀⠈⠀⠀⠀⠀⠀⠀⠉⠈⠈⠉⠉⠉⠉⠉⠛⢷⣶⣄⣿⣁⠼⠳⢬⣿⣤⣶⠞⠛⠉⠉⠉⠉⠉⠀⠀⠉
⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⢤⠤⠤⠈⠙⣿⠁⠀⠀⢈⣿⠉⠁⠤⠤⡤⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠄⣀⣀⡀⠀⠤⢀⣴⣾⡿⢿⠄⠀⠀⠠⣿⢿⣲⣦⡄⠤⠀⣀⣀⣀⡠⠤⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠔⠒⠈⠁⠀⠀⢀⠏⡄⠀⡀⠀⡿⡄⠀⠀⠈⠀⠒⠠⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢹⠀⡃⢺⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⡀⣷⠘⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠈⠀⠀⠀⠀⠀⣷⣿⡇⠀⠀⠀⠈⠁⠂⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀
⠀⠀⠀⣾⣿⡆⠀⢀⣴⣾⣿⣷⡄⠀⣠⣤⣴⣶⣶⣶⣿⣶⣶⣶⣶⣤⣄⡀⢀⣠⣤⣶⣶⣶⣶⣿⣶⣶⣶⣶⣤⣄⠀⠀⢀⣾⣷⡄
⠀⠀⠀⢿⡿⠃⠀⠈⠉⠛⠙⠛⠃⠀⠙⠛⠿⣿⣿⣯⣿⣿⣿⣿⡿⠟⠛⠁⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠟⠀⠙⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠀⠻⠿⠋⠀⠀⠀⠀⠀⠙⠿⠿⠋
⠀⠀⣱⣿⣷⡀⠀⢀⣴⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⢾⣿⣿⡇⠀⠛⠛⠟⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣇⣀⣀⣀⣀⣀⠀⠀⠀⢀⣾⣿⣿⣆
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠁⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⢠⣀⣀⠂⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⢹⡏⠙⠛⠛⠛⠁⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⢰⣿⣷⠂⠀⠀⠀⠠⣳⣿⣎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠈⢋⣤⠀⠀⠀⠋⣿⠿⣿⡆
⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⣀⡀⠀⡀⠀⢀⣤⣴⣿⠇
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠈⢿⣿⠟⠁⠀⠀⢠⣤⣶⣶⣶⣿⠟⠛⠉⠀⠀⣤⣶⣶⣶⣾⣿⠿⠟⠋⠀⠀⠙⠛⠂⠀⠀⠈⠛⠛⠋
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢸⠉⠒⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠶⢆⣀⢀⠀⣀⠦⢎⣾⠃⠘⣿⣿⣷⣦⣀⣀⣴⣾⣿⣿
⠀⠀⠒⠢⠖⠀⠀⠈⠈⠙⠛⠛⠋⠁⠀⠀⠘⢹⡖⢦⣄⣀⣀⣀⣀⠀⠀⠹⢧⡀⠛⢿⣟⠋⢀⠾⠃⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣴⣾⠇⠐⠛⠛⠿⠿⠿⠷⠂⠀⠸⣧⣘⠘⠈⣡⣾⠀⠀⠀⠀⠀⠸⣿⣿⠌⠁⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉
⠀⠀⢀⣄⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣼⣆⣀⡀
⠀⠀⠰⣿⠄⠀⠀⠀⢀⢾⣿⠄⠀⠀⠀⠀⠀⠀⢠⣠⣤⣀⣀⣀⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠿⠿⠿⠟⠛⠛⠛⠛
⠀⠀⢰⣿⡆⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠘⠙⠿⠿⠿⠿⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠆
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣀⣀⣀⣀⣰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠖⠖⠃⠀⠀⠀⠀⠈⠙⠿⠿⠿⠟⠛⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣽⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿