Floral Heart Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢤⡀⠀⠀⣿⠸⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢱⠀⠀⢿⠀⠹⡄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⡢⢤⠄⠘⣧⡀⢹⣠⠃
⠀⠀⠀⠀⠀⠀⡴⠁⣰⠀⠸⢰⠃⣸⠀⠀⢩⣼⡅
⠀⠀⠀⠐⠢⠬⣔⠚⣁⣀⡠⣃⠴⠃⠀⠀⠘⠛⠋⠀⠀⠄
⠀⠀⠀⢠⣶⡞⣿⢻⡿⢷⣭
⠀⠀⢰⣾⣏⢧⣫⣯⣞⣯⣽⣦⡀
⠀⠀⢰⣷⡮⠭⣿⣿⣯⡳⣮⣷
⠀⠀⠀⢹⣿⣋⣵⢣⣇⣿⣾⠉
⠀⠀⠀⠀⢀⣹⣛⠻⠟⠁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⡠⠄
⠀⠀⠀⠠⣟⣿⣿⡇⠀⠀⢀⠙⣴⣷⣇⡤⡚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⢤⡀⠀⠀⠘⠛⢀⠀⢸⠸
⠀⠀⠀⠀⠙⠻⢛⡁⠤⠨⡸⠀⠃⠉⣼⠁⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⡞⡑⢀⣀⣄⣀⠔⢰⠣⠀⠈
⠀⠀⠀⠘⠦⣒⣁⠤⠊⠀⢀⡩⠢⠀⣇⠀⢻⠈⡖⡭⠉⢣⠀⠀⠀⠀⡏⢀⡼⢀⢱⡾⣫⣯⡻⢷⠈⢆⢁⠠⠂⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⢊⡠⣎⣠⣽⣄⠯⠚⡇⠃⠄⠊⠀⠀⠀⢀⣴⣮⣴⣎⢸⣯⣿⢻⣵⣽⠁⠤⢤⣀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣰⡯⣿⣿⣿⣧⠀⠘⠄⠀⠀⠀⠀⣿⣿⢹⢡⢟⣽⢿⣟⠻⢟⠛⠈⡐⠢⠤⢬⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣯⣫⡾⠇⠀⠀⠌⠢⠀⠀⢿⡿⢬⣪⣿⣷⢶⣛⣿⠳⣄⠙⠦⣈⣠⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⣓⡯⢻⢻⢳⣝⡿⠃⠀⠉⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣯⣾⡾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠠⡀⠠⠒⠀⠀⠀⠀⢀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⣄⡄⠤⠤⢬⣽⣤⣂⠀⢗⣁⡀⠀⠀⠀⠀⠀⢘⠑⠀⡒⢢⠄⠀⣀⡸⢭⢾⢚⡄⢠⣦⣌⡇
⠀⠀⠀⠀⠀⢀⡴⠋⡤⠀⣄⠀⠨⠐⠁⠈⡠⠛⣦⠈⠆⠀⠀⣀⣀⡈⢲⡎⡹⢻⢚⣯⣾⣟⣤⣾⡄⢿⡿⠀⠈⠆⢠⣄
⠀⠀⠀⠀⡀⡋⠀⠄⠈⠀⠁⠀⠀⠀⠈⠝⠟⠅⡄⠠⠀⠀⠙⠤⢴⠏⣅⠀⠀⠈⠀⡎⠁⠈⡈⠛⠁⠶⠀⣔⣯⣇⢙⣋
⠀⢤⡄⠙⠛⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⡀⠔⠉⠀⣿⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⢋⣤⡘⠛
⠀⠉⠉⢠⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠂⠺⠀⠈⠢⣼⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡁
⠀⠀⠀⡠⠇⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢾⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠗⢶⣾
⠀⠀⠺⢾⡇⠳⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⢳⣤⡝
⠀⠀⠀⠁⠑⣦⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⢘⣱⠙⢯⡟
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢲⣁⠌
⠀⠀⠔⡱⡙⠄⢠⣢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⣿⣀
⠀⠀⠋⠀⢯⠦⠑⠻⠓⢁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⣶⢿⠉⠈
⠀⠀⠀⠀⠀⠑⠀⠀⢠⣞⢠⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣠⣿⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠸⣻⡂⠀⣜⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣦⣌⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⡗⣄⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣠⡈⠁⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣬⢗⡷⢲⣴⡠⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⣀⢭⡛⠑⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢡⣇⣀⠀⠀⢀⠀⢀⣀⣀⠒⠋⠂⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠃⠉⡛⢢⡂⣤⣾⡇⠇⢱⠀⠊⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⠚⠀⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢀⣠⠭⠭⠀⠀⠠⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠠⠤⠄⠭⠭⣅⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⢀⡠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡆⢠⠀⠀⠒⠢⡤⠊⠉⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠀⣀⠀⠀⠀⠀⠸⣆⣀⣇⠌⠀⠀⢀⠀⡇⠀⠀⠀⠑⡏⠑⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠹⣿⠶⠼⢄⠀⡁⠀⠉⡀⠀⢰⠁⠉⠃⠀⠀⠀⡠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡸⢰
⠀⠀⠀⠐⢿⣀⠀⠀⢠⠃⠀⠀⠈⠢⡘⡄⠀⣤⡤⣤⡊⠀⢀⠔⠊⠀⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⢃⠎
⠀⠀⠀⠀⢠⣤⣭⠦⠘⢦⣀⢀⣀⣀⣈⣙⣿⣼⢾⣧⢟⣶⠕⠈⠁⠢⡀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⠞
⠀⠀⠀⢀⡀⠈⡛⠓⡲⢃⠤⠀⢀⣐⣒⣻⡾⣻⣬⣽⠿⣛⡀⣀⡠⠊⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣣⠊
⠀⠀⡀⠀⠹⣿⠋⠲⣥⠁⠀⠘⢓⠂⡄⠀⢈⠗⡧⣣⣮⠛⠒⠒⠠⢄⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠕⠁
⢠⣴⣋⣉⡉⣡⠄⠀⢈⡄⠀⠀⠀⠑⣔⡀⡀⠈⡀⠀⠀⠁⠂⢄⠀⠘⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁
⠛⠁⠉⠈⢸⣇⣠⠊⠁⠈⠒⠠⡔⠈⢩⠉⠀⠀⠑⢄⡀⠀⠀⠠⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡫⠞⠁
⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠈⠆⠀⠑⣄⢀⣀⡸⠁⠉⠉⡱⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣚⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⠈⡗⠤⣀⣤⣞⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡯⠻⣿⣍⠀⠈⠓⠦⣀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⡇⠑⢄⠙⠃⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢷⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟

⠀⠀⠀⠀⠀⠀⡀⠀⡠⠐⣂⣉⣭⠭⠭⢄⣢⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣂⣬⠭⠭⣭⣐⣢⣄
⠀⠀⠀⠀⢀⠜⠷⣊⠔⢩⠔⠁⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠶⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠑⠪⡳⡄⡀
⠀⠀⠀⠀⡌⢸⠀⡅⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢔⠘⡄
⣦⠀⠀⠰⠀⡀⠀⣷⡁⠐⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘
⠹⢌⠢⡄⢣⣇⣰⠋⠀⡘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠸⡀⠑⠌⡆⡏⢸⢀⡔⢁⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠢⠬⡷⠓⢴⡋⠉⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠰⡀⠇⠀⠀⠈⢲⠔⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠞⣧⡀⠀⠀⠁⠆⠀⠀⡗⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⢰⠊⠁⠀⡈⠴⢾⣄⣀⠐⠴⢖⠒⠒⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰
⠀⢀⠱⢄⠀⠀⡠⠞⡿⣍⠐⠀⠀⠉⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⠃
⠀⣊⠤⠒⠉⢹⠀⠰⠀⢂⢀⠤⠠⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠂
⠀⠉⠀⠒⠒⣊⡄⠀⠀⣠⠁⠀⠀⢷⡎⡠⠒⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠊
⠀⠀⠀⣠⡊⠤⠌⠲⠌⣸⠀⠀⠀⢸⠏⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠠⠃
⠀⠀⠀⠋⠒⢠⠤⠒⠒⠚⡀⠀⠀⡎⡰⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡔⠁
⠀⠀⠀⠀⠀⡃⠀⠀⠀⢀⣈⠺⣤⣿⡠⣒⡀⠤⠶⢥⡘⡠⠐⠚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⠊
⠀⠀⠀⠀⠀⠈⠉⠢⣀⠀⢀⡤⡛⣿⠏⠭⡁⠀⠀⠀⠘⡇⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠂⢈⠋⠘⠀⠙⠈⣆⠈⠀⠀⠀⠀⡸⡰⠃⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠸⠑⣂⣤⠔⠉⠲⡁⠀⡀⠀⢸⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⣀⣀⡠⠊⢸⡁⠀⠀⠀⠠⣘⢀⡧⠂⡉⠓⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠔⠂⠈⠉⡢⠶⠐⡢⠼⣿⣶⡁⠄⠀⠀⡸⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢒⠞⠁⠀⠀⠀⠜⠋⢋⠊⠲⡄⠚⠠⠤⠤⠍⡦⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⡀⠠⢠⡎⠀⠀⠀⠀⣽⡓⢦⠀⠒⡈⠀⣀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠢⠠⠤⠠⠉⡿⠐⠨⡙⠲⡇⠤⢀⣀⡑⠂⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠱⡀⠐⡔⠉⠒⠄⠀⠄⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⣦⣴⡀
⣿⣿⡿⠻⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⢳⡴⠀⠐⠸⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⠁⠈⠀⠀⠘⠓⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣻⣾⡇⠀⠀⠀⠓⡄⣀⠀⢻⡧⢶⡇⠀⠠⠖⠀⢰⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢻⣿⣿⣤⣀⠀⢰⡦⢈⠀⠀⠀⠈⣀⢙⣘⠀⠀⢨⣿⣽⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣓⣔⣿⣷⡾⢭⣺⠰⣄⣰⠙⢉⣥⣇⠀⣠⠾⣿⣧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡥⠨⡉⣤⠖⢀⡭⣦⢃⣣⡖⠊⠀⠉⠸⠟⠐⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡯⣹⣷⠚⢁⣀⣄⢦⡀⠀⣰⡀⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⣿⣿⠾⣏⠁⣴⣿⠛⠉⢉⣉⣉⣼⣝⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠂⠠⠽⣸⣿⣿⣿⣿⣿⣦⢿⡋⠀⡔⠉⠈⠿⠺⡏⢸⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡄⠀⢸⣿⣿⣿⢏⠀⠙⢏⠀⣿⣶⠋⢑⣷⣄⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀⢀⡈⣿⣿⣯⢰⠇⠀⠀⢸⡏⣨⣧⣾⠟⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠄⠹⣿⣿⡾⣀⠀⠠⣿⡀⢼⠛⢋⣹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠙⠀⠀⠘⣿⣷⣔⠀⡠⠋⠀⢸⣴⣿⠯⠛⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⠁⣀⣴⣿⡟⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠃⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡶⢾⡷⣆⠀⠀⠀⣰⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⢠⣉⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠛⡆⠡⠒⢛⡄⠄⣼⠁⡈⠐⣿⣷⣶⠒⠐⡄⠀⠀⢠⠀⢠⡄⠘⠿⠇⠀⠈⠉⡿⠀⠸⠟⠂
⠀⠀⠀⠀⢀⠼⠋⠓⠾⠁⠘⠻⢤⠽⣦⠋⠀⠀⠂⠀⠈⠇⠀⠀⠐⢄⠀⠁⠀⠈⢠⣤⣦⡀⠀⠀⢂⡷⠲⠀⠀⠀⠀⠀⠒⠈⣳
⠀⠀⠀⠀⠀⢄⣠⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡐⢀⡆⠀⠀⠀⠀⠀⣊⣀⣤⡤⣉⠉⠿⠁⠀⠀⢀⣤⡤⠄⠀⢀⠀⠀⣈⣠⢿⠁
⠀⠀⢀⠀⠘⣾⣿⣿⣿⢀⣤⡦⠤⢶⠟⠲⠄⠈⠙⢷⡇⠀⣴⣴⣆⠀⠀⠙⢿⣄⠟⠀⣠⣴⠶⠺⠋⠙⠀⡔⣇⣴⣀⠀⠈⠰⠃
⠀⠀⢸⢧⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⠴⡿⢋⡁⠁⠀⠈⠸⠄⡈⡙⠀⠀⠀⠀⠀⢀⠀⠀⢈⠙⣯⢨⡇⠀⣹⠷⠖
⠀⠀⢸⠀⠀⠀⠁⠀⠀⣀⣠⡢⢸⡦⣀⡀⠀⠘⣡⣾⡇⠸⡿⡋⠀⠀⡀⣈⠀⠀⠀⢆⣲⣾⣄⠉⠀⠀⠀⠁⡯⠁⠀⠀⠀⠀⣰⠛⠃
⠀⠐⣿⠊⣀⠀⠀⡀⠀⠀⡀⢹⣿⡒⠡⠂⢀⣌⠁⠁⠉⢀⡄⠁⠈⣭⣤⣏⢠⠀⠀⠸⣍⡥⡿⣷⠂⠀⢀⣦⣁⠀⠀⢤⣀⠀⠈⠑⠾
⠀⠀⠙⢴⡟⠻⡟⠀⠀⠀⠖⠁⡄⣄⢉⠀⢰⡿⠆⠀⣴⣉⠁⠀⢸⠉⠛⢿⣤⣴⡄⠀⠉⠹⣖⠄⠀⢰⠋⠀⠱⠾⠁⠈⠋⠉⠓⢰⣄
⠀⠀⠀⠘⠲⠖⠀⣑⣦⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣛⠉⠀⠀⠘⠿⠶⠚⠳⡇⢀⣀⣀⣀⠀⠀⠈⠽⢖⠒⣀⠄⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣈⣉⣛⣆⣠⣾⣾⣗⠀⠀⠀⢰⡄⠀⠀⠀⢀⣰⣦⠔⠁⠀⣴⣿⣿⣿⣿⡎⠁⠀⢀⠀⠀⠀⠠⣤⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠊⠙⠉⢸⣯⠙⢿⠽⠄⠀⢀⠘⢁⡀⠊⠐⣾⣿⣿⠒⠀⠀⢻⣿⢿⣿⣿⠟⠀⠀⠘⢦⣴⣿⡄⠆⠀⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⠟⡾⡆⠀⠁⠀⠀⠊⠀⢸⡟⡆⠀⠀⠸⠃⠈⠂⡀⠀⠛⠛⢻⠉⠛⠀⢠⠴⠠⢾⡿⡁⢐⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠁⠀⣇⠀⢠⣀⠉⠂⢸⣇⠃⠀⠀⢀⣡⣤⣀⡤⠆⡀⠀⠀⠀⠆⢆⢀⡄⠀⠉⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⠀⢛⣿⣷⣀⠈⡏⠀⠀⢈⡁⠭⠯⣿⠃⠄⠀⠀⠀⠤⢴⠟⠅⡶⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⣿⢁⠀⠀⠀⠰⣃⡇⢀⣀⠺⠃⢈⣠⣠⡄⠒⠈⣁⠹⠷⣿⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠰⠻⣦⣭⣤⠄⡵⠀⠀⣶⣿⡿⢻⣦⠜⢃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠈⠃⠀⠀⣠⡜⠻⣄⡀⠀⠓⠸⢧⣽⠶⣍⣍⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠈⠉⠀⠈⠉⢉⡿⠖⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⡀⠰⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⡀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⡄⠀⠂⠀⠈⠻⣆⠀⠉⠳⣤⡀⠀⠀⠀⢀⣀⣤⠞⠀⠀⠀⠀⠻⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡀⠸⠂⠀⠀⠀⠀⠘⠆⠀⠀⠀⠑⠆⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⣀⣤⣤⡤⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠲⡎⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⡈⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠠⡸⠬⠡⠀⠂⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠷⣄⠀⠀⠘⠛⠫⠟⠓⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠖⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣶⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠈⠁⠀⢀⠀⠀⠀⣀⡐⠈⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀⢔⣢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠀⠀⠀⠀⠀⠀⠠⠀⠀⣱⢤⣤⠛⠁⡄
⠀⠀⠀⠀⠀⠙⠀⠁⠀⠀⠀⢀⠐⠊⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣀⡀⢀⠀⠔⠈⠀⠀⠀⠀⠀⣀⠀⢀⠶⠐⢦⣯⡾⠠⡤⠁
⠀⠀⠀⠀⠰⡄⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⡀⠀⢢⢠⠖⣜⢁⠀⠀⠀⠰⠁⠀⠄⠁⠀⠀⠀⢀⢸⡆⠀⠀⠄
⠀⠀⠀⠋⠃⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⡀⠀⠁⠀⠀⠈⠀⠂⠠⢼⠒⣏⠉⠀⠀⠈⠓⠀⠘⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠰⡤⡶⠀⠾⠃⠴⢀⡀⠂⠀⠀⠀⠀⣤⠀⠀⠀⠁⢀⣄⠀⠀⠀⢀⠀⣀⠀⠀⠁⠀⣀⠀⠀⠐⠒⠆⠀⠀⠊⠀⠰⣲⠀⠀⠀⠤⠀⠀⠀⡠⠂
⠀⠀⠉⠋⣤⡄⠀⠠⣤⠀⠈⠁⠀⠀⠀⠗⢶⣧⠶⠎⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣙⠀⣤⠀⣤⠀⢠⡄⡦⠀⠀⠈⠀⠀⠰⠆⠀⢀⠔⠰⡀
⠀⠀⢀⡀⢰⡄⠀⢀⠄⠀⣠⠀⠀⠀⠀⠀⠋⠸⠗⠀⠀⠀⠀⡠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⢀⠀⠀⡄⠀⡀⠀⠀⠀⠉⠀⠀⢡
⠀⠲⠾⠁⣀⠂⠀⠈⠀⢀⠁⠐⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⣆⠑⣅⠀⡄⡐⠊⠀⠀⠀⠘⠂⠀⠀⠀⠈⠀⠀⠴⠶⡷⣞⡋⠀⠀⠐⠆⠀⠀⠀⢂
⠀⠀⠀⠘⠋⣤⠀⠀⠀⠈⠁⢀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠄⠀⠉⠀⠀⠀⠊⠘⠋⠀⠀⠈⠀⠀⠀⠀⠘⠃⠘⠁⠀⡀⢐⣠⠡⠰⠆
⠀⠀⠀⠙⣃⠌⠀⠀⠨⠀⠀⠏⠴⠁⠀⠁⠀⠀⢀⡀⠄⠀⠀⠀⠄⠠⠀⡄⠀⢠⠄⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠗⠃⠂
⠀⠀⠀⠈⠁⢠⡓⠀⠀⠀⠶⠂⠀⠀⠀⠀⠐⠀⠀⠆⠀⠘⠀⠀⠀⣀⠬⠙⠘⠹⣤⠠⠀⠀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠦⣀⡸⠃⠀⠀⠀⠀⠀⠀⠁⣨⠁⠂⠀⠀⣯⡁⠀⠀⠐⠗⠀⠀⠶⠖⠀⠙⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠑⡖⠃⠁⢘⡲⠶⠗⠀⠀⠉⠀⠀⠀⠀⠖⠲⣬⠁⠈⠀⠀⠀⠤⠆⠠⣄⠀⠴⠃⠀⠠⠠⠄⠀⠀⠀⠈⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠀⠠⠴⠂⡀⠀⠨⠷⠄⠀⠀⢄⡀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠀⠀⡄⠀⠤⡄⠘⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⠇⠀⠀⠀⠀⠮⠄⠓⠁⠀⠦⠀⠀⠐⠀⠀⠲⠆⠀⣀⠀⠖⠃⠀⠀⣈⡁⠨⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠰⠂⠀⣤⣄⡴⠀⠀⠀⠐⠀⠀⠀⠘⠓⡀⠙⠀⠀⠀⣴⠁⡉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠛⠂⠈⠋⢀⡀⠘⠷⠀⠈⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠹⠕⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢀⡀⠀⠂⠀⣀⠀⠀⠀⠟⠸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠶⢤⣧⣤⡄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠲⢄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⠉⡁⢀⠀⠤
⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⢠⠽⡀⠘⠆⠀⠢⠡⠀⠄⠀⢐⡀⢈⠠⡂⠠⠆⠀⠂⢈⠃⡠⠄⠉⠀⠴⣂⡪⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠊⠉⠣⠐⠠⣀⡐⢀⠓⠄⠠⠯⢽⠓⠚⢿⡷⠹⠈⠂⠀⢀⡠⠀⠃⢀⡾⢤⡃⢸⣰⢀⡀
⠀⠀⠀⢀⢠⣻⣀⠛⡶⠴⠀⠀⠀⡀⡌⢉⡿⢋⡀⠸⢛⡄⠎⢨⠀⠀⡁⠀⢀⡄⠀⢻⣀⠘⣷⣍⠡⠀⠀⢀⢎⠐⡀
⠀⠀⠀⢠⣄⠐⠊⠁⣥⠀⢨⣴⡾⠋⠐⣷⣄⡄⡁⠈⠁⠷⡀⠈⣧⢸⠀⣠⠌⠀⠠⠼⠠⠁⠐⡀⢀⠀⠀⠈⠀⠐⠆
⠀⠀⠀⠀⠀⢤⣶⣶⡦⠀⠘⢉⣁⣄⠛⠀⠈⠀⠀⠀⠀⣀⣀⣰⠏⡾⡼⢋⡀⢀⡤⠀⠈⠄⠀⠁⠀⣾⠛⣷
⠀⠀⠀⠀⠈⠐⣯⡿⠀⠀⠀⣈⠏⠯⠀⠀⠄⠀⡐⣀⡅⠈⠀⣠⠞⣉⠡⣾⠉⠐⠢⠀⠄⣨⡂⠀⠈⠽⢷⠿⠈⡀
⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⣾⣿⣆⠀⣿⣧⣄⡀⡀⢽⣻⠉⢱⠋⠀⢻⡁⠙⡙⠒⠆⢘⠉⠉⢼⠁⠄⠐
⠀⠀⠀⠀⠀⠐⠺⠦⠀⠀⠈⢉⡟⣠⠉⢋⣩⠀⠀⠈⠁⠨⠉⠀⠔⠁⢁⡄⢫⠀⢠⣾⣿⣇⢀⣀⡀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣤⠲⣁⣜⢙⠆⠀⠂⣀⣠⡘⠐⠆⠀⠀⡀⢫⡗⠩⠑⣞⠚⢻⣾⢀⣀⢈⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⣝⣇⠰⣍⠼⠀⠀⢬⢀⣹⣿⣧⠈⠀⠉⣀⡦⣀⠔⠉⠗⠛⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⡌⢐⡘⠀⠀⠹⠘⡋⠠⠅⢀⡀⣼⣿⠦⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢇⠂⠀⠐⢄⠀⠀⠀⠈⠠⠉⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⡤⣀⠲⠄⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢣⣤⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⢎⠻⣦
⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣒⠃⠀⠱⡻⢄⣀
⠀⠀⠀⠀⠀⠀⠻⠌⢷⠒⢠⣾⠟⠁⠀⠀⠀⠈⠑⢆⡠⠊⠁⠀⠀⠀⠈⠻⣿⣄⠠⢘⠥⠋⠁
⠀⠀⠀⠀⠀⢀⠠⢌⣿⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠠⣬⠚⢳⣦⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢂⢿⡷⣄⠹⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⣮⡳⣯⣷⡳⡼⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁
⠀⠀⠀⠀⠀⣿⠈⠛⢷⣭⣙⣶⣬⣽⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⢿⣗⢉⢸⣿⠏⢁⣐⡮⣉⡽⠿⣷⢦⡀⢀⡴⠾⠟⢒⣲⡶⠂
⠀⠀⠀⠀⠀⠀⠛⢧⡎⣿⡀⠉⢹⣿⠘⠓⣿⠯⠄⠱⠎⠶⢝⣮⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠟⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠴⠀⢠⠔⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠂⠀⠖⠀⣀⡀⠀⠀⠀⠀⠰⠂⠰⠎⠁⠀⡀⡀⠀⣴⠇⠀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⣿⡁⢸⡁⣨⡇⠀⠀⣀⠀⣨⣞⠀⢸⣋⣿⣖⠀⠘⢩⢠⡗⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣿⡁⠀⠀⠰⣿⣿⣷⣄⢈⠀⡀⢰⣏⣿⢋⣹⣿⠀⠈⠁⠉⡀⣤⡠⢦⡄⠃⠀⠤⠀⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠰⠙⠟⠛⢻⠁⠀⠀⠸⡿⢏⢣⣴⣷⣷⣿⢟⣳⠏⢁⡯⣿⣉⠐⠒⠤⠧⠐⢸⠇⢀⣀⢠⡶⡀
⠀⠀⠀⠀⡠⠸⣔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠨⠶⠠⡽⣿⣿⣿⣿⠓⢛⢳⣾⠍⠉⣇⡀⠀⠀⠀⠂⠈⠀⠘⠄⠲⡄⠖
⠀⠀⠀⠀⠷⡤⠌⠀⠡⠀⠀⢠⣌⠁⠋⠯⠂⠀⠀⠳⣻⣿⣿⣟⣦⠀⣀⠈⠀⠀⠁⠀⠸⠀⠠⠄⠀⠠⠀⠐⠞⠃
⠀⠀⠀⠀⠀⠐⡂⣨⢌⣧⣼⠭⡁⢀⡈⠁⠶⡆⠀⠈⠉⠒⠛⡟⠛⢦⡀⠓⡀⠀⠂⠀⠀⠢⠰⣤⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⢠⣺⢷⣜⣹⢿⣀⡏⠡⢸⡇⠀⡁⠊⠉⣆⠬⡀⠀⠀⠀⢘⠁⠉⠀⠀⢐⣄⣆⠀⢄⠄⡌⠀⠄⠰⡝
⠀⠀⠀⠀⠀⠈⠁⠛⠹⠩⠀⠁⠀⠒⠞⠉⠂⠀⠀⢐⣿⡳⠃⠀⠙⠃⠀⠈⣀⠀⢈⠈⠀⠠⣈⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠳⡆⠀⠁⠒⠀⠓⠀⢁⠂⠀⠉⠀⠖⠁⠠⠀⢴⣤⣷⣶⡄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⠇⠈⠁⠀⠀⢦⠀⠀⠀⠐⠉⠃⠂⠀⠀⠀⠀⣭⠻⠟⠛⢶⠀⠀⠀⢰⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡁⠀⠈⠢⠊⠂⠈⢠⠀⠈⠀⠀⠀⢐⣠⠤⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⢁⠀⠀⠐⡲⠿⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣧⡄⣤⣀⠀⠰⠚⡄⢀⠀⠀⠐⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⠐⠀⠀⠁⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣼⣶⣮⣽⣵⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⡶⠶⢤⡀⠆⠀⠀⠀⠀⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⠐⠄⠀⠈⡆⠀⣉⠀⠀⢻⡀⠀⠜⠑⡐⠈⢃⠂⠀⣀⠀⠢⠨⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠘⠀⡀⡎⡀⠊⡱⢺⠀⠀⢠⠈⣊⠋⠉⠁⢹⣎⣀⣰⢀⡀⠀⠀⡄⣸⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠀⡀⠠⣴⡥⠰⠀⣈⢰⡄⡀⠴⡀⠀⠀⢢⠐⡌⢪⡙⠀⡧⠂⢳⠀⠇⠀⠀⠄
⠀⠀⠀⠀⡀⠠⠈⠀⡀⠊⠀⠐⡤⠘⠉⠉⠙⠒⢥⠀⠞⠱⠆⡱⠖⠁⠈⠁⠓⠠⡱⢪⢀⣠⠉⢟⠀⠀⠜⡠⡀
⠀⠀⠀⠀⠠⠀⠀⠐⠁⢄⢤⠍⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢳⠿⣁⡀⠀⠀⡀
⠀⠀⠀⠠⠀⡙⠳⣤⣤⠎⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⡕⠉⠙⡋⠀⠀⠐⠁
⠀⠀⠂⠲⠀⠇⠡⠀⠈⢣⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠾⢅⠀⡠⠓⠜⠄
⠀⢠⠐⠀⣤⠰⠦⠽⣰⡁⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠀⠁⡀⠏⡇⢠⡤⡦
⠀⠘⡐⠀⠀⡐⠄⡤⠁⡈⢲⠋⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠄⢸⠟⢅⡀⠰⡄⣱⡄
⠀⠀⠈⠒⠒⡚⠂⢹⣄⣀⠞⠳⢶⡋⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⢀⠖⢠⠖⠋⠀⠸⠋⠀⡤⠀⠀⠠
⠀⠀⠀⠠⠀⠤⠰⠛⣧⡧⡀⠀⢀⡷⡄⠚⠏⠦⣀⠀⠀⠀⠀⢀⠔⠁⠘⡈⢀⠠⠀⠖⠠⠃⠀⣀
⠀⠀⠀⠀⣀⡄⡁⢀⠩⢏⢸⠉⠈⡗⠣⢄⠸⣄⣈⣓⣄⠀⡰⠋⠈⠡⣄⠁⠀⡔⢋⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠐⠀⢠⠄⠈⢍⣠⡎⣆⠰⡮⡵⠴⠮⢙⠈⡒⢱⠓⢢⢈⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⡐⢜⣘⠡⠈⠆⠆⠤⠐⠯⠠⢓⠉⠢⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠈⠁⠛⠀⢠⠒⠄⡁⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⣀⠂⠈⣿⠀⠀⠀⣩⣇⠐⣤⠄⢠⣄⣤⡀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢠⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⠀⠀⣿⢰⠀⠀⢀⡥⠂⣶⠆⠐⣹⢿⢹⢣⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢧⠀⢀⡄⢹⡰⢀⠀⣸⣇⠀⠀⠀⠀⢀⣴⡟⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠒⠀⣀⠀⠈⠀⣀⠰⣀⣸⠇⣿⡇⣽⡦⢿⡦⢳⣤⡞⠀⠸⣏⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⠃⠀⠀⢀⠴⢾⠁⠀⠀⡼⠉⠘⣧⠀⢀⠘⠃⣞⡀⠈⠃⠀⡟⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠄⠐⠀⠀⠀⠱⡄⡈⢂⠀⠀⠉⠀⠈⠀⡻⢿⠿⡷⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⢀⡀⠀⣿⡅⢈⣇⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡴⠀⠠⢤⡀⠉⠉⠛⠃⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠇⠈⠁⠲⠎⠐⠀⠀⠘⠀⠘⠁
⠀⠀⠀⠀⠀⠀⢀⡀⡀⠐⢁⠀⠀⡘⠀⠠⠀⠀⡀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠷⢝⠀⠀⠀⠀⠇⠀⠛⠛⠋⣧⠰⠆⠁
⠀⠀⠀⠂⣜⠂⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⢠⣶
⠀⠀⠀⠀⠀⠁⠠⢠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣄⡀⣀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⢀⠄⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⢀⡄⠀⠶⠞⢿⡏⠋⠀⠉⠁⣹⣤⡄⠀⣇⠰⡄⠀⢘⡆
⠀⠀⠀⠀⠀⠀⢨⡶⠙⠆⠀⠀⠀⠐⢀⠀⠉⠋⠀⠘⡠⢾⣅⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠉⢻⡟⢠⣿⡀⠈⢠⠈⠧
⠀⠀⠀⠀⠀⡁⠀⠀⠀⡀⠀⠀⠀⠄⠀⡀⠀⠣⠀⢸⢆⡏⠉⠁⠠⢾⡆⢰⠁⠄⠠⠤⢿⣄⣸⠃⠀⠤⠈⠲⣇
⠀⠀⠀⠀⡀⠀⣰⠀⠀⠟⠀⢴⠇⠀⣾⠉⠠⣼⣶⠀⠀⠑⢄⣦⠀⠈⠁⠀⢸⢷⡀⠀⠀⠻⢿⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠈⠟⠓⠀⠐⠀⠂⡆⢰⠋⠃⠀⠸⠾⠁⠀⠀⠀⣱⠄⠠⠒⠄⠸⠋⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⢀⢇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⠁⠀⠀⠐⠒⠀⠀⠀⢀⠀⠁⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁⠠⠖⠁⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠆⠀⠀⢠⠀⠀⡀⠟⠁⠀⠀⠀⠰⠄⠶⡀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⢀⡄⣠⠂⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⢀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠠⠤⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡤⠀⡀⠐⠀⠀⠂⢠⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡀⠀⠃⠠⠀⣢⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠎⠁⠀⠃


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣩⣿⣭⣭⣯⣥⣭⣽⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣭⣿⣿⣯⣭⣭⣯⣭⣭⣭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⣀⣤⣶⢦⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⣁⣤⠤⠀⠀⢤⡀
⠀⠀⠀⠀⠀⢰⣂⣤⡞⠻⣿⣶⠀⣀⣾⣿⣷⡿⣳⢻⣯⡄⠀⣱⣶⣤⡀⠀⠀⡀⠀⢈⠒⣶⢯⡄⠀⢸⠟⡦⣷⢯⣽⡾⣝⣿⣀
⠀⠀⠀⠀⠀⣼⡿⠋⠉⠒⢻⣿⠆⠉⢺⢹⣿⣿⣽⣧⠛⠁⠀⢸⡹⣧⠙⢦⠀⠀⣴⣉⡛⢯⡀⣿⠀⠙⣼⠡⣌⣦⣿⠟⢺⡿⠉⡁
⠀⠀⢀⡀⠈⠻⡦⣤⣠⡔⠈⠉⠀⠀⠹⠮⡽⢿⡉⠉⠀⠀⠀⠈⠳⣯⣷⣸⡇⠺⢉⢸⠻⢡⣇⠀⠀⠀⠘⢳⣆⠳⡤⢄⡇⠸⠞⠁
⠀⠀⠈⢀⣴⠀⠀⠈⣁⣠⢔⣂⣴⡄⢄⠀⠀⠘⠁⡀⢔⣂⡷⠢⣤⠄⠙⠻⡇⠀⠈⠉⠃⠈⢛⡤⠤⠦⣄⠀⠹⠏⠉⠟⠁⢀⣶⣷⣞⣆⢰
⠀⢀⣾⣟⢺⠂⠀⢀⣧⡽⣋⣽⣍⡻⣆⡁⠀⠀⢨⠂⣽⢻⠹⣦⡙⡄⠀⠀⠀⢰⡟⢹⠿⣷⣆⠙⢦⣤⠟⠁⠀⠀⠀⠀⢠⣯⠊⠤⣉⠛⣇⡴
⠀⣾⣹⠇⢸⢱⠀⣿⢻⡼⣿⢧⣽⢻⣽⡇⠀⠀⣻⣘⣿⢝⡷⢣⠟⡟⠀⠀⢀⣼⣥⣿⣆⣹⣛⠀⠀⠀⡔⠀⠀⠀⠣⠀⣸⡿⣥⣳⠝⣩⢾⣷
⠀⢷⣿⣫⠟⠀⢦⣿⣼⣟⣺⡩⣿⣯⡝⢻⠀⠀⠀⢿⡬⠋⢁⠿⠊⠠⢒⢀⣀⠈⠙⠶⠶⠞⣁⣀⣘⣊⣿⡇⢒⣦⠄⠀⡷⣵⡻⠟⢊⣁⡼⡟
⠀⠈⠛⠉⣀⡀⠈⠛⢻⣝⣛⣒⣋⣡⠄⠊⠀⣀⠀⠀⠉⠓⠛⠀⠐⢻⣯⠉⣿⡎⣆⠀⠐⠋⢨⣿⣟⣽⣯⣴⣿⡏⣻⠀⠀⢨⡟⢲⠟⠛
⠀⠀⠀⢾⠿⣸⠆⠈⢳⠀⠽⠉⠩⠁⠀⠀⠀⡿⡟⠛⣷⣦⡀⠀⣿⢿⣿⣿⣕⢳⠏⠀⠀⠤⣸⠋⢌⣬⣻⠿⣿⣿⡁⢀⠂⠀⢀⣤⠤⡄
⠀⠀⠀⠘⢤⡵⠂⠀⠀⣠⠞⣛⠲⣦⣀⠀⢀⣼⣧⢾⣿⣁⣕⠀⠘⢟⣿⣛⢹⡷⠀⣴⣧⠀⠻⣾⡐⣿⣿⣿⣽⠇⠀⠈⠀⣴⣴⡿⠶⣾
⠀⠀⠀⠀⠀⠃⠀⠀⣰⣿⡿⠛⠉⣫⡟⠰⠞⠲⢷⣤⣅⣼⠉⠀⠀⠀⠈⠁⠀⠀⠸⣿⡷⠀⠀⠉⠉⠉⠁⠀⢀⠀⠀⣀⣀⠈⢿⣀⣠⠞
⠀⠀⠀⠀⠀⠐⣆⢰⣿⡍⣏⠛⠛⣉⢀⣴⣶⣀⣀⠀⠈⠘⠀⠀⣠⣤⢲⣼⠃⣰⠀⡾⠃⠀⠀⣠⣶⣿⣦⣴⣮⠀⠀⣿⠁⣹⠄⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠈⠻⣷⠏⣀⣟⡀⡾⢶⣿⠾⣏⡇⣦⠀⢐⣿⣟⣠⡄⡿⡆⣹⡠⠖⠈⠀⠀⣙⣯⡉⡵⣬⡘⢧⠀⠈⠣⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⡄⣿⢻⣿⣿⢗⡿⣧⢿⡀⠸⣿⠛⠉⣣⣅⣱⣿⡿⠀⠀⠀⠐⢿⠿⣿⣶⠞⡷⣸⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣾⣟⣿⢟⠛⣡⡾⠀⢠⣦⣐⣻⣿⢋⣏⡜⠁⠓⠀⠀⠀⠀⠘⢶⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠨⠭⣽⠯⠟⠊⡀⠀⠀⠒⢬⡍⠁⡾⠋⠁⠀⣠⣞⣋⢉⠛⢦⠈⠃⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣀⣤⡄⠀⠀⠀⠀⠀⡀⠘⢿⣟⣉⠹⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠓⠉⠉⠉⠀⢀⣴⡆⠚⠷⣜⡀⠈⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⣾⡧⢼⠷⢦⠚⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⢷⢽⣶⣠⣤⣷⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠛⠿⢿⠅
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠉⠉⠉⠉⠐⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠉⠉⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⢀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⡄⠀⠀⣤⣦⠆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢦⣦⡤
⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠸⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠸
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡀⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃
⠀⠀⠡⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⢠⠁
⠀⠀⠀⠀⠀⠈⠄⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⣿⣇⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣾⠊
⠀⠀⠀⠀⢠⠊⠉⠛⢿⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣀⠟⠊⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡵⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢠⢸⠁⠀⠑⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡄⠚⠢⠄⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡠⠁⡤
⠀⠀⠀⠀⠀⢀⠄⡀⡆⠀⠀⣀⣠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡈⠀⠀⠀⡦⠀⡠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⢰⠀⠈⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠁⠀⠀⡆⠞⠀⢄⠀⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠛⠓⠨⠇⠀⠀⠀⠀⠀⠰⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡠⠂⠒⠀⠀⢻⡄⠈⠍⡀
⠀⠀⠀⠀⠀⠈⠐⠄⢀⡀⠀⠀⢀⡄⠄⠤⠀⠀⠀⢀⡰⠛⠀⠢⣀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⣠⡀⠀⣷⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠱⠀⠶⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠐⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡈⠀⠀⠆⠘⠣⠘⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠄⠀⠈⠁⠐⠸⠆⠒⠃⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⣹⠁⠙⠂⠀⠘⠀⠰⠃⠀⡴⢀⣼⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠍⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠉⠁⠀⠀⢀⣤⣄⡀⠀⠈⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠁⠀⠀⠈⡠⠀⠀⠀⠀⠀⣀⣤⡬⢦⢀⠄⠀⠀⠀⠀⠀⠈⠑⢂⠠⣼⠋⠁⠉⢻⡆⠈⠀⢀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢑⡡⠊⠀⠀⠂⠀⠀⠀⠀⢰⠧⣼⣋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠹⢧⣤⣤⢼⠓⠀⡀⠈⠹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠚⠉⠀⠐⠀⡀⠀⠀⠐⣀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠋⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⣍⠀⡰⠁⠀⠆⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠃⠀⠀⠀⠠⡈⠀⠀⠀⠀⠴⠠⠄⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠐⢄⠀⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣿⣤⣏⣹⣏⣼⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⢸⡦⠞⠛⢛⣓⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⣛⣿⣷⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀⠀⠀⠀⡄⢡⡮⠂⢉⣽⠿⠿⠿⣿⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣡⣶⡿⠟⠉⠉⠉⠉⠻⣿⡹⡄
⠀⠀⠀⠀⠀⠀⠀⣈⣆⠈⢕⣦⠖⢚⣛⢛⣿⣋⠀⠀⠀⠀⠀⠉⠳⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠘⠻⠤⣈⣷⢞⠿⣒⣁⠀⢹⢄⠈⢦⠀⠀⠀⠀⠀⠀⠈⠻⣿⢷⡀⠀⠀⠀⠀⠀⢠⡟⣡⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡜⡎⡰⠯⡹⢎⠈⢣⡼⢄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⡾⣱⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢇⠑⡗⠒⢣⠾⠔⣊⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⣸⣧⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⣈⣁⠽⠒⠋⠉⠙⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⢠⠤⠤⢄⡈⢓⡿⠧⡴⠻⠥⠰⢄⡜⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠢⢬⢏⢆⡤⢧⡀⠀⠀⡜⠉⢹⢢⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⣠⠐⠪⠕⣾⠁⢸⠀⠀⠨⢿⣾⡄⠀⠰⣼⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢢⢾⡀⢀⣠⠋⠀⠈⠙⡖⠁⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠸⣄⣀⡤⠤⢧⣤⠫⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣒⠤⠤⡎⠀⠀⣠⠞⠈⢃⠀⢠⠟⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⡡⠻⡈⡟⠉⠉⠓⢤⣞⣿⣷⡄⠔⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠃⠑⠃⠈⠒⡶⠖⠛⢮⣻⡻⠣⢄⡀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⢰⠉⠈⢧⡀⠀⣣⡴⠊⢁⠝⠁⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢤⣠⢮⠻⠙⢿⢻⣾⣗⠀⠒⢄⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡷⣄⢰⢄⡉⠛⢿⣿⣄⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠜⠀⠀⠉⠀⠀⠀⠀⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢈⣳⣴⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠂⠀⢀⡀⡌⠀⠀⠉⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠁⠀⠀⠁⠈⠀⡀⠒⡛⠀⡀⠠⣶⣼⡅⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣺⣑⣤⠠⣐⡞⠁⠈⠁⢘⡂⢦⣀⠩⢻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⣿⣿⣏⡶⢛⠀⢀⣴⡖⠀⠂⠤⣿⠷⣴⣤⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⡨⠀⠛⠡⠟⣠⡀⠺⢿⡿⣅⡂⠀⢀⣴⣿⣿⣿⠟⠁⢀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣿⡇⢀⠀⠀⠀⢹⡇⠀⠈⠀⠛⠁⠖⠲⡿⠛⠋⠁⠀⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⣤⠘⢧⣌⢦⣀⠀⣭⡷⣀⣀⣤⣴⡾⣇⡀⠐⠤⢀⡔⠊⢩⡄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⢄⣀⢠⡜⠒⢲⡘⢦⠘⣧⢉⡞⢹⣾⡏⠡⣤⣼⣇⣝⢲⣦⡤⠘⠃⠀⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⣠⠄⣧⡜⢀⢿⣼⡇⠹⡟⠀⠀⠘⠳⣈⠻⠀⠿⠀⣠⡆⣀⡄⠀⠈⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣍⡵⠚⠃⢀⣸⡄⣿⡿⣄⠳⣄⣀⣠⠀⡘⣠⢃⡧⠐⠛⠣⣠⣄⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⣱⠒⣾⠊⡡⠆⢹⡔⡉⠀⡈⠛⠛⠛⣿⢋⠮⠷⡀⠀⠄⠀⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠍⡀⢠⠀⠀⡻⠛⠻⢤⣀⠀⡰⣦⣤⣅⠤⠲⠀⢠⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⡄⢢⠈⠅⠶⠛⢢⡀⠙⠿⠇⠋⠁⠀⠀⠀⠀⠀⠀⡴⣾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠈⣠⣌⣓⢶⣄⡈⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⠱⣤⡿⢍⣹⢞⣫⡭⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣰⡻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⢣⢣⣴⡒⣿⣆⢸⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣱⣮⡊⠠⣿⡿⢛⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⡷⠉⣝⡉⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⠛⠙⠓⢶⣶⡲⠗⣠⡏⣰⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣾⣷⣯⣶⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠿⠋



⣿⣿⡿⠛⠟⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇
⠀⢠⣄⠀⠳⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡰⠃⢀⣤
⠀⣈⠿⠇⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⡇⠿⢏⡀
⠀⠹⣿⠀⠹⠿⠃⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠻⠿⠁⢸⡿
⠀⡔⠁⣉⠙⠢⡁⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇⡡⠚⢉⡅⠑⡄
⠀⠑⠶⠋⠀⠠⢘⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣞⠠⠀⠈⠳⠖⠁
⠀⠀⠀⠀⠀⠀⢙⡈⣆⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢂⡞⣘⠁
⠀⠀⠀⢤⣤⡄⠀⢿⠟⣎⣥⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⣍⡞⢿⠏⠀⣤⣤⡄
⠀⠀⣠⣤⠉⣡⡁⢀⣀⠘⢿⠟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢿⠟⢀⣀⠀⣠⡉⢡⣤⡀
⠀⠐⠛⠁⠀⢿⠃⢸⡟⢠⣾⠗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢿⣦⠘⣿⠀⢻⠇⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠈⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣶⣀⡀⠀⠀⠚⣣⣶⣛⣻⣝⣧⣤⠆⠈⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡤⠂⠀⢀⣴⡞⢻⣂⣤⣌⠳⣄⣂
⠀⠀⠀⠀⠀⠀⣟⣴⣿⣏⡙⣿⣻⡃⢰⡞⣿⣾⣿⣟⣿⡹⢿⡦⠀⠀⣿⣿⠷⣤⠀⠀⠔⠈⢀⣔⣩⣿⠳⣇⠀⢸⡟⡽⠻⣟⢲⣯⣛⢦⣿⣶⣄
⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠉⠛⣿⡟⠀⠈⣇⣹⣟⣻⣾⣷⠋⠀⠀⠀⢧⡟⣷⠘⢳⡀⠀⢰⣧⣤⣙⢦⡀⣿⢀⠈⢴⡇⠲⢼⠾⢿⠛⣹⢿⠀⡌
⠀⠀⠀⡠⠊⠉⢻⠶⣆⣤⡔⠁⠀⠀⠀⠀⠿⠶⠿⢿⡅⠈⠀⠀⠀⠀⠈⠻⣧⣷⣸⡇⠘⢣⣀⣜⢋⣰⣇⠀⠀⠀⠀⠙⣷⣄⢻⠦⣸⡇⠘⠛
⠀⠀⠈⢁⣠⣶⠀⠀⠈⣉⣀⠴⣃⣠⣦⠠⡄⠐⠀⠚⠁⣀⠰⣖⣺⠗⢤⣤⠈⠙⠿⡇⠀⠀⠉⠉⠀⠈⢛⡤⠴⠶⣤⡀⠈⠿⠋⠏⠟⠁⢀⣶⣿⣞⣷⡀⡦
⠀⠀⣰⣾⠏⣿⠀⠀⢀⣏⡻⢟⣫⣯⠛⢷⡈⠂⠀⠀⠀⠕⢸⡿⡍⣳⣼⠿⠐⠀⠀⠀⢠⡾⠋⡽⢿⣷⡌⠻⣖⣂⡼⠇⠢⢀⠀⠀⠀⢐⣫⠝⣩⡉⠙⢿⢁⡇
⠀⣼⠻⣿⠁⡿⣤⠠⣟⢿⢙⣿⡯⣹⡿⣯⣿⠃⠆⠀⢺⠰⣿⣟⢗⣬⣉⣷⡗⠀⠀⠀⢸⡟⣰⣧⠘⣹⠻⠀⠀⠈⢠⠆⠀⠀⠑⢄⠀⣸⣿⢃⡶⣻⠗⣨⣿⡇
⠀⢯⣳⠷⢲⠇⢹⡀⣿⢸⣿⣽⠞⣿⣵⢛⡼⡤⠂⠀⠉⣻⣙⡷⠚⠐⣯⠸⢃⡠⠐⠒⠙⠻⣯⣍⣉⡿⠃⠀⢠⡄⢷⣔⣀⡤⠀⠈⠀⣯⡫⣽⡾⠥⠚⠁⣸⡇
⠀⠘⢿⠷⠋⠀⠀⢹⣿⣿⢷⣶⣛⣽⠿⠛⢁⡷⠀⠀⠀⠈⠻⠤⢴⡏⠀⣠⡼⡶⠶⣿⡒⡄⠀⠈⢡⠔⠚⣶⡾⢶⡿⢋⣰⣞⠫⣦⠀⠋⠙⣦⣍⣳⣾⡟⠘⠃
⠀⠀⠀⢀⣴⡆⣤⠀⢀⡽⠓⢶⡶⠶⠶⠟⠈⠀⠀⣄⣄⣀⣄⡀⠀⠀⢀⣡⡼⢹⣆⠘⣇⡸⠆⠀⠀⠀⢸⡿⠃⠛⣾⣿⣿⣿⡔⠏⠀⠀⠘⠋⠸⠋
⠀⠀⠀⢘⡛⢳⡟⡄⠀⠙⠄⢛⣀⡀⠀⠀⠀⠀⠀⠏⡧⠀⣼⣟⢳⠀⠨⢯⣡⣬⣗⣭⣑⠃⠀⣀⠀⠁⡎⢀⠀⣶⣄⣻⡽⣿⠳⠀⢰⠁⠀⠰⣾⡛⠻⡀
⠀⠀⠀⠀⠙⢷⠟⠀⠀⠀⣰⡟⣍⣙⣛⣦⣄⠀⣰⠲⣷⠺⣿⢧⣴⣄⠀⠘⠇⢿⡭⠀⠟⠁⡘⣿⡇⠀⡙⣟⣍⣻⡿⠿⡷⠟⠀⠀⠀⠀⢺⣾⡿⠛⠺⡇
⠀⠀⠀⠀⠀⠈⠀⠁⠀⣼⣿⡛⠉⢉⣉⡼⠃⠚⠋⠛⠿⠦⣤⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠃⠀⠀⠀⠀⡉⠁⠀⠀⡄⠀⠀⣠⣄⣈⢻⣤⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠱⡄⢸⣻⡏⣿⠙⠛⢉⡀⣠⣴⣶⣀⣀⡀⠀⠉⠃⠀⠀⣤⣤⢳⣾⠃⢠⡆⢸⠟⠀⠀⠀⣠⢶⣿⢶⣠⣶⡄⠀⠀⣟⠀⣙⡆⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣇⡾⢀⣸⠃⢰⡿⣶⣿⠾⣏⣇⢲⡀⠀⢸⣿⣟⣠⡈⣿⡧⢸⣇⡴⠀⠉⠀⠀⡻⣫⢩⣵⣌⣃⢻⡄⠀⠙⠦⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣽⣇⢸⡗⢳⣷⣿⡴⣿⣏⡿⡁⠀⣭⡿⠿⠉⣇⡃⢱⣿⣿⡆⠀⠀⠀⠰⣷⣽⣿⣦⡬⢿⡄⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣾⣧⣹⠿⣷⡿⡗⢋⣥⠃⠀⣩⡁⢴⣶⣿⡿⡻⢣⠟⢰⠄⠀⠀⠀⠁⠠⣬⣭⣴⡞⠎⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠻⠟⢷⡮⣴⡯⠏⠀⠀⠩⣙⠲⠛⠋⣰⡷⠋⠀⠁⣠⣴⠶⠶⣤⡀⠀⠏⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠈⠁⣠⡆⠀⠀⠀⠀⠛⠂⢀⠋⠀⠀⠀⣴⣿⣶⡶⣴⣬⣝⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣃⡰⠶⢷⠆⠀⠀⠈⠀⣀⣖⠠⡌⠻⣶⣤⠈⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡍⠀⠀⠀⠀⠀⢠⡿⢯⡈⠙⠲⣤⡄⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⣿⣷⠺⠛⠓⡎⢙⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⢷⢿⣶⣢⣤⣾⢾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠁⠛⠿⠿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⡀⠀⠀⣄⠆⠀⡁⡶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣴⣄⢀⣴⠂⠀⢰⢠⡛⢳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡯⠞⠁⣠⣿⢀⠐⠛⣶⣦⣤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡷⠀⠈⠀⣷⠀⠋⠗⠠⢼⡿⠟⠉⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣄⣙⢮⠦⣠⣟⡤⠴⣶⢳⣄⠀⣤⠈⣥⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢪⢀⠘⡨⠂⣷⠃⣿⠃⠙⢏⠛⠘⠋⣀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⢈⣀⢶⢸⣿⡜⢦⣤⣀⣤⣳⠀⠉⠀⠤⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⠀⠃⢈⠾⢧⣄⠀⣤⣜⡁⠍⠠⠈⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⢈⣐⠋⢆⠙⠏⠁⠀⠀⠀⠀⠐⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣐⠞⣣⡾⣗⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡎⢶⣿⢦⡓⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢾⠙⡗⣋⡀⠀⠀⠀⠀⢀⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠉⠁⣲⣿⣫⣾⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠈⠉⠉⠉⠀⠀⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠈⠀⠀⠀⠉⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊
⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠗⠒⠒⠠⢄⠀⢠⠒⠉⠀⠀⠉⠢⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⡠⠄⠠⢄⡀⡆⠀⠀⠀⠀⠀⠃⢐⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⡜⠁⠀⠀⠀⠈⢁⣀⣀⣀⡤⠒⠛⠐⠂⡠⠂⠉⠉⠉⠒⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢇⠀⠀⠀⢀⠎⠁⠀⠀⢸⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠈⡆⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠁⢢⡄⠄⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠢⡀⠀⠀⠀⢀⡰⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⢠⠊⠁⠀⠘⣄⠀⠀⠀⠀⢀⠗⠐⢒⠆⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠰⠀⠀⠀⠀⠈⠑⠀⠀⠒⠁⠀⢲⡎⠀⠀⠀⠀⠀⢠⡗⢄⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠑⢄⢀⠄⠒⠀⠐⠠⡀⠀⡠⠤⠿⣦⣄⣀⣀⡠⠎⢡⠈⡌⢉⠜⠉⣈⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⠎⠀⠀⠀⠈⢊⠒⢍⠂⢄⠀⠢⡈⢶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠐⣄⠀⢀⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⢀⣉⣢⣌⠂⢽⠙⡑⢄⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⡠⠊⠁⠈⠐⠁⠀⠀⠀⠈⠣⠀⢀⣤⠮⠛⠓⠒⠒⠒⠭⣺⡀⢋⣢⣕⠤⡀⢀⠔⠊
⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡃⠀⠀⠉⠣⡙⣡⢻⠉⠑⠂⠭⢘⡲⠌⡓⢬⡑⢄⡀
⠀⠰⣀⠀⢀⣀⠱⢄⠀⠀⢀⠴⠁⠀⠀⠀⠀⢰⠅⠘⡀⠀⠀⢀⡠⠊⠑⠢⢅⡛⠶⣌⡢⢄
⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠀⡐⠠⡀⠀⠀⢀⠆⠈⢄⡳⠤⠂⠁⠀⠀⠀⠀⠀⠀⠁⠂⢍⡒⢭⡢⢄
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠇⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⣿⣏⠷⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠇⠀⠾⠁⠀⠀⠀⠀⠘⠉⠁⠐⣄⡀⠶⢀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢦⠈⠘⣦⠟⢻⠀⠉⢠⠄⠪⢀⣤⢀⢆⡵⠏⣴⠖⣛⣻⣷⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣅⡤⠾⠧⠖⠉⠐⣶⠎⠀⢠⣶⣟⠛⢸⠃⢠⡿⠀⠈⢹⣍⠛⠧⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡤⢂⡀⠀⣸⣾⠃⠀⢀⣿⡿⠉⠻⣾⣇⠘⣇⠀⠀⢃⠈⠁⢠⢇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣁⠀⠀⠦⠼⣿⣠⢀⣾⣿⣷⠎⠀⢹⣟⠣⡌⠒⠶⣿⡴⢷⡟⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠊⢘⠿⣷⣄⠀⢸⣿⣮⣿⣿⡿⠀⠀⢈⣿⣄⠱⢮⡠⢄⣤⣎⡤⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠏⢀⠆⠀⠀⢻⡆⡯⢬⣿⢿⣿⣿⠂⠀⢼⣿⣿⢭⡒⣐⠺⡩⢿⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠈⠀⠀⠀⢸⣁⣿⣼⠋⠀⠻⢿⠿⠳⡋⠑⠹⡖⠂⢠⠀⢄⣸⡇⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠦⢄⣤⣴⡛⣑⣬⠟⠀⠀⠀⠐⠂⠀⠀⠀⠀⢷⡀⡆⢀⠘⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⢳⣤⣶⣇⣰⣿⡿⠁⠀⠀⠀⠀⠀⠋⠁⠂⢀⠈⢏⠀⠹⠖⠒⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⠃⠑⢂⠑⠲⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠐⠁⠐⠀⠀⠀⠀⠈⠀⠉⢰⣿⠷⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣀⣀⣤⡀⢀⠆⢐⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣉⣠⣿⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣀⡀⢀⠀⠁⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠻⠉⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⣳⣤⣠⡸⠖⠒⠀⠀⢀⣶⣄⠀⠀⣤⡀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠈⠙⠿⣿⠋⢹⡀⠰⠆⠀⠘⠙⠿⠳⣶⣶⣬⣄⡔⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⣰⣦⢤⡘⣟⠛⠀⠈⢻⡎⠁⠺⡤⠒⠀⣶⠿⠟⠛⠻⢂⣸⣧⣈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡠⠚⡁⠐⠲⠶⣦⡥⠴⢆⣤⠛⠦⡄⠃⠤⣤⣡⠖⠉⠉⢁⠘⡿⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠴⣾⡅⣸⠆⢈⡸⣧⠀⣐⡿⢤⣀⠰⠦⣄⡀⣿⠀⠀⠀⠄⠘⠄⡀⠀⠀⣸⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡞⢿⣶⠓⠰⠀⠙⣿⠀⡠⠠⢸⢱⠀⢀⣿⣾⡦⡑⢦⣤⣼⠶⢀⠀⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⢿⣌⢃⠀⠀⠀⣠⠏⣤⠠⡀⣞⣽⣿⣼⡃⠽⣷⣹⣄⣀⡤⢠⣾⠔⠗⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⡛⢿⣿⡿⠛⠁⣴⣏⣭⡾⠻⠫⠀⠈⠀⠀⠀⢝⠛⠛⢀⣤⠿⢃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠤⠶⠶⣾⡿⠋⠁⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢡⡅⠀⡰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣾⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢠⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠔⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢫⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣶⡾⠗⣢⣗⢠⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣶⣷⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣟⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣽⣯⣽⣿⣿⣿⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠜⡄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠐⠶⡆⠀⠀⠀⠀⡀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣆⣔⣠⡤⣠⠄⠒⠀⠉⣡⣄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⢻⡿⢿⡗⠁⢀⣴⣧⠻⣿⡿⠷⡤⣦⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡢⠀⠀⣿⡟⢠⣲⣾⣿⠛⡽⠋⡀⡈⣄⣲⠟⠿⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣆⣀⠟⠃⢾⣿⡟⠉⠸⢃⢀⡵⣫⡽⢷⣞⣾⡅⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠂⣄⠀⣡⠿⠍⢨⢙⣛⣉⡍⠤⡖⠯⣾⢹⣿⠈⠻⢝⡓⡐⡆⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⡟⠉⣀⣎⡀⠀⣾⢟⣿⡵⣬⢳⠹⠓⣿⣌⢣⣀⣡⣀⣠⣷⡗⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣰⣎⡘⢲⢨⠸⡱⢻⣯⣵⢇⢜⡄⣿⠸⡝⠁⠈⢉⡉⢁⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⡟⣨⢸⣧⣣⣍⣁⣻⣭⡮⠞⡼⠀⠈⠻⠒⠾⠯⢋⡁⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠿⣵⣴⡷⣫⡟⠈⠈⢬⣤⡾⠒⠋⠁⠀⠀⠀⠂⠀⢀⣬⣀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠟⣯⡖⠀⠀⠀⠠⠂⡅⠀⠀⡀⠀⠀⠀⠀⠛⣿⠟⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⢸⣷⢄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⣀⣀⣀⠠⡄⡠⣲⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣻⣏⣡⣿⣥⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⡷⠤⠤⠄⡀⠀⢀⠔⠂⠀⠐⢢⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⣿⣿⠿⠿⣿⣿⠁⠀⠀⠀⠈⠂⠆⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿
⡟⠁⠀⠀⠈⠉⣀⣀⡀⡠⠀⠒⠸⢂⠄⠂⠁⠁⠒⢄⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣇⠀⠀⠀⡐⠁⠀⠀⠨⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠇⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⣿⣿⡦⠄⡀⠀⠀⠀⠀⢂⠀⠀⠀⠈⠢⡀⠀⠀⢀⠐⠁⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⣿⠉⠀⠀⠑⣀⠀⠀⠀⡠⠋⠀⠰⠂⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠹⡇⠀⠀⠀⠀⠀⡏⠢⠄⣀⢠⡌⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⠔⠉⠀⠀⠁⢄⢀⠔⠉⠙⢷⢄⠠⢔⠊⠈⡄⢂⣰⡁⠄⠐⠊⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠡⠉⠢⢑⠢⣈⢢⢭⢀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠛⠆⡀⠊⠀⠉⠒⢄⠀⠀⢀⣴⡴⠀⠀⣙⠦⣽⠈⡦⡑⢄⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈⠛⠠⣶⡖⢲⡆⠬⠙⡂⠼⣌⠳⣅⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⠀⠀⠀⠱⡀⠀⠀⠀⠠⠂⠀⠀⠀⠈⣿⠀⡃⠀⠀⠀⣉⣶⣭⣐⠹⢦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⠁⠀⠁⠀⠈⢠⣄⠀⠀⠀⢠⣿⣆⢰⣀⣴⣾⣿⣿⣿⣿⣿⣶⣮⣑⠪⢙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠒⣓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡂⠔⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⢈⡅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠀⠒⠍
⠀⠀⠀⡤⠋⠇⠀⠀⠀⠀⠀⠀⠰⢋⠁⢢⠀⠀⠀⠀⠀⠈⢠⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⡄⠤⠀⠀⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠠⠄⠀⡀
⠀⠀⣀⠆⠈⢁⠀⠀⠀⠀⠀⣁⣵⠰⢀⡁⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠉⠀⠀⠠⠄⠀⠀⠀⠀⠈⠂⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠸⠷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠤⣐⣤⡔⠈⠁⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠡⠟⠘⢀⢻⠇⢦⣠⢀⠗⠜⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠉⡉⢈⠁⠀⠲⠄
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠐⠂⠀⠁⠈⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣶⠗⣾⠶⠦⠿⠖⠳⠶⠄⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⡗⠈⠉⠀⠉⠇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢦
⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⠀⠀⠀⠀⠀⢐⡂⣆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣄⠀⠀⢀⡀⠀⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⠀⣬⣿⡧⠄⠀⠐⠿⠃
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠁⢰⠄⠀⠀⢠⠂⢠⠠⡰⢆⠀⡦⠀⢰⢠⠄⠦⢀⠀⠀⢀⡘⠂⠀⠁⠀⠀⠀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡌⠀⠀⠉⠀⠁⠁⠀⠁⠈⠀⠉⠁⠀⠀⠁⠉⣉⠐⡦⠚⠁⠀⠀⠀⠀⠀⢀⣶⣤⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡭⠛⠛⢛⠤⠐⠊⠉⠀⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⠾⠋⠀⠀⠀⠀⠘⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠐
⠀⠀⠀⠀⠀⢄⡿⠋⠀⠀⣿⡏⡃⠀⣠⠎⠀⣀⡀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣠⠊⢟⣧⣤⢀⣰⣀⣤⠉⠀⠀⠀⠀⠄⡽⠛⠺⣼⠀⠀⠀⠀⠀⠀⢈⡙⣻⢟⡄
⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⢀⡴⠃⠀⠀⠀⢤⠶⣱⠀⠀⠀⠀⠀⢀⡴⠘⡿⣿⠷⠺⡟⣻⡿⣟⠏⣯⢻⣀⠋⠀⠉⠈⠁⡈⡁⠈⠀⣀⢀⠀⠀⠀⠬⠽⢿⢯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢉⡤⠈⣤⣜⢆⣦⣹⣿⢳⣶⣏⢻⣿⡕⠀⠀⠀⠀⠈⠁⠀⠀⠘⢃⠃⠀⠀⠀⠒⠈⢇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡠⢺⢿⣏⣛⣿⠿⣼⣟⡛⣺⢷⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡿⣬⣱⣿⣿⣷⣿⠻⠼⢁⡿⣹⡟⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠈⠉⠉⢨⠀⡄⠉⢠⡄⠘⠘⠆⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡰⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠀⠠⠃⠀⠩⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢠⠜⠈⠙⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣓⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⢀⣀⣰⠨⠹⢹⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠄⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢲⡆⣀⡤⠀⠈⡆⠀⡾⣠⣾⣾⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢹⠷⠀⡼⠋⠀⠀⢀⣀⡀⠱⠿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⢀⠞⣯⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠁⠻
⠀⠀⠀⠀⠀⠀⣠⡀⣏⠻⣿⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⡀⠀⢴⣶⡆⠀⡀⡤⠀⠀⠀⠀⢀⣀⠀⠀⠀⣤⣠⡀
⠀⠀⠀⠀⠨⣶⣦⢰⣤⡳⣯⠀⠀⠀⠀⠀⠀⠀⠙⡆⢠⡄⠠⠀⠈⢼⡟⢚⠹⠯⠀⡀⠀⠠⠟⠋⠀⠀⢸⣏⣿⡓⡀
⠀⠀⠀⠐⢷⡹⢿⣿⣿⣿⣋⣿⣀⠀⠀⠀⠀⠘⣄⣆⠀⠘⠁⠀⠀⠀⠀⠀⠐⠂⠀⠻⠅⠐⠆⠀⠀⠀⠈⣏⡍⣙⢩⣥⢀
⠀⠀⠀⠀⠈⠛⠀⠔⠶⣾⣿⡿⠿⢓⣶⣄⠀⠀⣸⣿⠀⢠⡄⠀⠀⠀⠀⢀⡑⢒⠄⠄⢸⡶⠄⠀⠀⠀⢠⡿⣾⣿⠾⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣝⢃⡀⢜⣯⣹⣤⣦⣤⣌⠁⢺⡅⢠⣄⠀⢠⠃⠘⠉⠀⣀⠰⡀⠀⠀⢀⡠⡾⢿⣿⡆⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡦⣙⡮⠘⠓⠲⢶⡙⠛⠻⠀⠀⢙⠷⡄⠀⣌⠳⡄⠀⢀⠐⠂⠉⠸⣳⡆⢠⣟⣧⠄⠘⢫⡟⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠆⢠⡀⢐⣆⠒⠋⠀⢈⡴⢫⡦⠈⢠⠁⣴⠁⠜⠁⠀⠀⠈⠀⠘⠟⠁⠒⠁⠈⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠓⢀⡿⣅⣰⠿⠒⠉⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡐⢀⣿⠖⠈⣸⡿⠟⠀⠀⢀⡠⠤⣢⡄⠘⠢⣀⣀⣀⣬⣷⣌⡀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⣠⣶⠯⣤⠐⣾⠋⠀⠀⠀⣰⣾⡟⠛⠛⠒⠋⠀⠈⠉⠉⢀⣿⡙⠷⠈⠛
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡄⠀⣤⣶⡿⣉⠿⣛⣁⢸⣷⡆⠀⢸⣿⣿⠇⠀⠀⢀⣤⠶⠶⣾⣿⠿⢿⡷⠄⠵
⠀⠀⠀⠀⢺⡀⠀⠃⠀⣤⣤⣯⣄⢻⣿⣷⢿⡀⢃⠗⣸⣿⣤⣤⡼⠟⠀⠀⠀⠠⠃⠀⠀⠀⠊⡷⠃⣷⣏⠀⡌⣏⣄⢒⡀
⠀⠀⠀⠀⠀⠠⠒⢤⠀⠀⠀⠀⠈⣿⣿⣿⣼⣧⣯⡾⠋⠉⠻⣯⣤⠟⠀⢠⣤⣇⣠⣴⠖⢆⡠⡇⠀⠀⠁⠀⠻⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⢸⣿⣿⣿⣯⣼⠇⡘⠀⠀⠈⠿⣀⠀⣸⣿⣿⣏⡀⠀⠀⣷⡿⣷⠄⠀⠀⠠⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡶⠀⠂⢀⡀⠀⠘⣿⣿⣷⢿⡇⢀⣴⡄⠀⠀⠀⠀⠀⣿⣏⠁⢸⣇⠀⣜⣿⣶⢟⠤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠆⠀⣿⣻⣶⣯⣇⠘⢻⠁⠀⠀⠀⠀⣴⡟⠧⠰⣿⣿⣿⣾⣇⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠂⠉⠁⢤⣤⡄⣀⠀⠘⣿⣦⣟⣷⣔⡍⠂⠁⠀⣠⠶⣿⡆⠀⢠⡾⠃⠿⠏⠀⢸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⣤⠀⠀⠀⠘⢿⣽⣿⡍⠠⢻⡀⠀⠚⠀⣽⠋⠀⢈⡞⠀⠀⣶⣿⡿⢿⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⢾⣳⡀⠀⠀⣠⠞⢩⠀⠀⠘⢿⣾⡿⣛⣷⠒⠈⠁⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣁⣥⣴⠃⠀⠀⠀⣀⢠⣾⣿⠒⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣏⡀⠀⡀⢐⢿⣾⣟⣇⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣥⣼⣷⣴⣿⡿⢛⣿⠏⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠟⠋⠖⠁⠀⠀⠀⠀⠁