Analog computer Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠛⠉⠉⠩⠍⠉⠉⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿
⣿⣿⡏⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⡇⠀⠀⠀⢀⣀⣼⣿⠋⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠙⣿⣧⣄⡀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⢸⣿⠛⠁⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠻⣿⡇⠀⠀⠀⢸⣿
⣿⣿⣗⣶⣶⣖⣺⣷⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣚⣷⢲⣶⣶⢺⣿
⣿⣿⣯⣿⡗⠂⠀⠀⢀⣺⡀⠀⠠⡂⢤⠄⢀⣰⣀⠄⠀⢀⡴⠀⠀⢰⡀⠀⠀⣀⢂⣠⢀⠀⢣⠀⠀⠀⠀⢺⣿⢸⣿
⣿⣿⡇⣿⡇⠀⠀⠀⣠⣽⠒⢀⢰⠡⠭⡯⠀⠼⠒⠀⠀⠉⠀⠀⠀⡇⡀⠁⠀⡄⠀⠄⠘⠀⣼⠸⠆⠀⠀⢸⣿⢸⣿
⣿⣿⡧⣿⣗⡀⣀⣀⡙⢻⠐⠃⠘⠀⠑⠃⠀⠀⠒⠁⠀⠀⠀⠀⠘⠀⠐⠒⠀⠀⠒⠀⠀⠈⡇⢀⣀⣀⢀⣸⣿⢸⣿
⣿⣿⡗⠛⠛⠓⢺⣗⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣻⡟⠚⠛⠛⢺⣿
⣿⣿⡇⠀⠀⠀⢸⣿⣶⣄⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣠⣶⣿⡇⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢹⠿⠦⢼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡧⠴⠿⡏⠁⠀⠀⠀⠀⢸⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣶⣦⣤⣤⣬⣥⣤⣤⣴⣾⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣤⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠛⠓⠒⠒⠛⠛⠶⢤⡀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⣀⡤⠟⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠙⠛⢦⡖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⣴⠛⠋⠉⠉⠉⠉⠀⣠⣬⡛⢦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠁⠴⠛⠳⠀⠀⠀⢀⣁⣀⡁⠘⢧⣴⣦⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡴⠚⣟⢻⣶⡶⢾⡍⠩⠍⢹⡒⠛⠉⠁⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠶⠷⠞⣿⣀⡈⠛⠛⠛⠋⠀⠬⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡌⣩⣤⣤⡰⣄⢀⠀⠀⢠⡞⠋⠁⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣄⡽⠿⠀⠀⠀⠀⠀⠀⠘⣧⣀⠸⠇⠻⠤⠾⠁⠸⠉⣁⡴⠏⠀⠀⠀⣤⠶⠋⠙⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⠀⠀⠀⢺⡋⠉⠀⠀⠀⠀⠀⠉⠙⢳⣴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⠋⠀⠀⠀⣸⡟⠛⠛⣦⣄⣀⠀⠀⠀⠈⠃
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣄⣠⣄⡀⠀⠀⠀⠀⢀⣾⡿⣇⠀⠈⠛⣶⣖⠛⠉⠀⠀⣰⢏⡾⠉⢷⡄
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⢹⡄⠀⠀⣠⡟⢸⠁⢻⡀⣠⠞⠁⠈⠳⣄⢀⣴⠋⣼⠁⠀⠈⢻⡄
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡴⠋⠀⣼⠀⠀⠉⠉⠳⣤⣤⠾⠋⠛⠁⠀⢿⡀⠀⠀⠀⠻⣆
⠀⠹⡆⠀⠀⠀⠀⠀⢠⡖⠛⣦⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠃⠀⠀⠀⠀⠹⡆
⠀⠀⢻⡄⠀⠀⠀⠀⠈⠳⠶⠛⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢠⣿⠀⠀⠀⢀⣠⣄⣄⡀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⣏⣽⣀⣀⣴⣟⣡⣤⣌⣭⣉⣷⡀⣀⣀⠀⠀⢀⣠⡴⠞⠁
⠀⠠⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣯⣭⣥⣬⣥⣬⣬⣤⣤⣥⣤⣤⣼⣿⣭⣽⣿⣿⣯⢥⣤⣤⣤⣤⣤⣤

⠀⠀⠀⢀⢤⡖⠀⠀⠈⠈⠉⢁⣈⠉⠉⢉⣀⠈⠁⠈⠉⢉⣉⠉⠉⣦
⠀⠀⠀⡏⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⡇⠀⢸
⠀⣴⢻⡗⡰⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⡿⠪⡏⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⡇⢘⡇⢨⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢸
⠀⡇⠠⡗⡕⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⡇⢁⣏⢪⡇⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠙⠣⣷⠁⡃⠀⠃⢳⡄⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡧⠀⢸
⠀⠀⠀⠘⠶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠠⠄⠂⡸
⢀⡀⠀⠀⠀⠀⠉⣛⠻⠛⠹⣭⣽⠽⠉⠍⠡⡭⠯⠫⠿⡛⠿⣀
⣿⠙⢦⣄⠀⠀⠀⠛⠿⢶⣤⣤⣄⣉⡀⣀⣀⣀⣤⡤⠒⠋⠀⠀⠉⠓⠦⢄⡀
⣟⠀⢀⢌⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣈⡛⢲
⣇⠐⠕⡀⠸⡇⠀⠄⠀⣀⣀⣀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⣿⡇⣾
⠈⠢⡀⠊⢸⡇⣀⣄⠀⠈⠉⠁⠠⣤⠀⢸⠂⠀⠀⠀⠀⠀⠐⠒⠒⠀⢿⠀⡿⠇⠿
⠀⠀⠈⢶⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠼⠀⢵⡆⢶
⠀⠀⠀⠀⠙⠃⠶⠀⠠⠤⠤⠄⠤⠄⠠⠠⠄⠤⠤⠄⠠⠠⠤⠤⠀⠤⠤⠄⠚⠆⠘
⠀⠀⡶⣄⢠⡤⣤⠤⢤⡤⠤⢤⡤⢤⢄⡠⠤⣀⠀⠀⣄⠠⠤⣶⠶⠤⣴⠤⠠⣤⠤⢤⣤⣤⣄
⠀⠀⠘⠲⡑⢮⡫⢅⠙⠏⠠⣴⠧⠀⣐⡇⢀⡺⠅⢀⡺⠍⢉⡺⠍⢀⡺⣉⣙⡺⠓⣒⡸⠆⠟⢷⣦⣄
⠀⠀⠀⠀⠈⠳⣮⣶⢝⠫⠁⢘⢯⣉⣘⣿⠀⠁⠻⢬⣅⣀⣌⣁⣀⣀⣉⣀⣘⣷⡈⠮⠉⡉⣿⣁⣻⣙⣿⣦⣄
⣀⣀⣀⣀⣀⣀⣀⣙⣾⣯⣤⣥⣦⣄⣬⣁⣬⣈⣀⣊⣚⣓⣓⣒⣐⣓⣚⣐⣐⣚⣐⣊⣘⣐⣐⣓⣒⣐⣐⣓⣚
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣛⡛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠲⠶⣬⣍⡙⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣿⣍⣉⣻⣶⣍⢻⡟⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣷⡟⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣤⡀⠀⠀⠀⠈⢻⡄⠀⢸⠏⠀⣀⣀⡀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢀⣤⠾⣋⣴⠟⢋⣠⣴⠟⠉⠹⣦⠀⠀⠀⠀⢻⡄⢿⣄⣸⠏⠉⢙⣷⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠶⢾⣟⣯⠶⠾⠋⠁⣀⣀⠀⠀⠹⣧⠀⠀⠀⠘⣧⠀⠉⠁⡾⠛⠛⣁⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⡆⠀⣿⣶⣿⠀⠀⢸⡇⢰⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣿⠀⠀⠶⠀⠀⢲⡀⠀⠀⠉⠀⠀⠀⣼⠇⢀⡿⢸⡇⠀⠀⠸⠧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠺⡟⠁⠀⠀⠀⠀⠀⢸⣿⠿⣿⡵⠟⠁⠀⠀⣾⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢠⡶⣶⡀⠀⢀⣠⡟⠁⠀⣿⠁⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⡀⠀⠀⠉⠉⢠⡞⠋⠁⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣦⠀⠘⢷⣄⣀⠀⠘⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⡾⠻⣏⣀⣀⣤⣼⣿⣧⣴⠿⠓⠿⣦
⢠⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⢀⡼⢋⡾⠁⣷⡤⠾⠋⠻⠧⣼⣿⠁⠀⠀⠀⠀⢹⡆
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡅⠀⢀⡾⠁⠻⣦⡀⢿⠀⠀⠀⠀⣸⠏⣹⣆⠀⠀⠀⠀⠀⣿
⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣼⠃⠀⣷⡼⠃⢸⡇⠀⠀⣼⠏⠀⢹⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠘⣷⡀⠀⠀⠀⠀⠀⢼⡟⠛⣷⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⢀⣟⣻⣦⣼⣿⣤⣾⣧⣤⣤⣾⡋⠃⠀⠀⠀⠀⠈⣿
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⡧⠾⢷⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣀⣈⠻⣦⣄⣀⣀⡼⠃
⢀⣄⣀⣀⣼⣷⣤⣤⣤⣤⣤⣤⣤⣀⣀⣤⣄⣤⣀⣠⣤⣤⣿⣧⣭⣉⣭⣬⣭⣭⣭⣬⣉⣩⣥⣽⣯⣿⣿⣿⣩⣀⣤⣤⣤⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⢀⣀⡀
⠀⠀⠀⡀⢒⠉⡠⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⢤⠈⠂
⠀⠀⠀⠃⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢐
⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣠⣤⡀⠀⡇⡅⠘
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠛⠛⠀⣴⣶⡄⠙⠛⠁⠀⡇⣇⣀⡀⣀⡀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠃⠀⠀⠔⠎⡥⠀⠒⠂⠀⠀⠀⠀⠀⠒⠂⠤⠉⡆
⠀⠀⠀⡀⢰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠁⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠃
⠀⠀⠀⢃⠈⡀⠑⠀⠠⠤⠄⠀⢀⠀⢀⠀⠀⠠⢼⢸⠀⠀⣠⠀⠸⡷⠀⢀⠀⠰⡯⠀⠀⠀⢸
⠀⠀⠀⠘⠠⠄⢉⣈⣁⠀⠐⠒⣒⠲⠶⠖⣒⡀⣸⢨⠀⢐⠀⡡⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠠⣿⠀⠀⠀⡥⠀⣠⠀⡄⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠃⡄
⠀⠀⠀⠀⠀⠀⡮⢁⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⣆⣑⡀⠈⢩⣅⣀⣄⣤⣠⣬⣌⣁⣀⡖⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠉⠭⠭⠭⠭⠭⠭⠉⠀⢰⠎⡙⢯⡿⣽⣯⣻⣟⣿⣻⣟⣿⣳⣟⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡢⡙⠙⠓⠛⠚⢓⣛⣘⣓⣛⣘⣓⣃⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⢚⣉⠉⡗⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠛⠚⠀⣧⠀⠀⠉⠛⠲⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠒⠚⠛⠋⠉⠉⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⣆⣀⣀⣠⣤⣤⠾⠀⣿⠀⠀⣀⣀⣤⣤⠤⠤⠤⠤⠤⠼⠿⠒⠒⠒⠚⢶⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣤⠤⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠓⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠶⢶⡄⠀⠀⠀⡇⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⣀⣠⣤⣤⠴⠶⠚⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠔⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠘⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⠓⠲⠶⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠦⢤⣄⣀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠶⠦⠤⠤⠤⠞⠁⠀⠀⢰⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠉⠉⠓⠲⣤⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡤⣾⣋⣁
⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉⠀⠈⠉⠛⠒⠶⠤⣤⣀⣣⣤⣄⣀⣀⣈⣉⡉⠛⠒⠶⠶⢤⣤⣤⡴⠿⠖⠋⠁⣠⡞⠀⠈⠉⠙⠲⣄
⠀⠀⡠⠒⠉⠁⠀⣠⠤⣞⣳⠶⣄⡀⠀⠀⣀⠤⡀⠈⠉⠉⠛⠓⠲⠭⢭⣭⣛⣒⠒⠒⠒⠒⠶⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⡆
⠀⣎⠀⠀⠀⠀⠈⠑⠒⣯⠴⠋⠁⣀⡰⢾⠽⣛⡷⠞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠙⠒⠲⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠉⠓⠒⠦⢤⣀⡀⠀⠀⠀⠀⠉⠈⡱⠖⠁⠀⠀⠀⣀⣠⢞⡫⣿⣷⣺⡤⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⣀⣤⣤⠤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⠤⣤⣀⣀⡀⠀⠀⠀⠁⠈⠙⠚⠷⠚⠁⠀⠀⠀⠀⢀⡴⠊⢁⣼⠀⠀⠀⠀⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠦⣤⣄⣀⠀⠀⢀⡤⢴⣚⠥⠖⠋⠉⠀⢀⡤⠶⣚⡉⠉⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠾⠖⠉⠀⠀⠀⠀⠀⠰⡏⢀⠤⠀⠙⣆⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⢤⣤⠤⢤⠤⢤⠤⠤⠤⠤⠤⠦⠤⠶⠦⠶⠤⠶⠦⠄⠀⠄⠠⣀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢸⣯⠽⠯⠽⠯⠭⠭⠤⠶⠤⠶⠦⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠶⠶⠤⠶⢿
⠀⠀⠀⠀⢸⡀⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠲⠖⠒⠶⠶⠶⠖⠲⠶⠦⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⢤⣤⣤⡀⢸
⠀⠀⠀⠀⢸⠀⣿⠀⣠⠤⠤⠴⠶⠶⠒⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡃
⠀⠀⠀⠀⢸⠁⡿⠈⡇⠀⢀⡤⠶⠶⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡁
⠀⠀⠀⠀⢸⠀⡇⠀⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⢸⠸⡇⠀⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠃
⠀⠀⠀⠀⢸⢸⡇⠀⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⠂
⠀⠀⠀⠀⢸⢺⡇⠀⣇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠸⡆
⠀⠀⠀⠀⢸⢾⡇⠀⣟⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠠⠆
⠀⠀⠀⠀⢸⣾⡇⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⡄
⠀⠀⠀⠀⠸⣿⡇⠀⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡇
⠀⠀⠀⠀⠘⡇⡗⠀⠹⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡇
⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡁
⠀⠀⠀⠀⠀⣇⡛⣛⣓⣚⣓⣒⣒⣒⣛⣛⣉⣙⣛⣓⣲⣒⣒⣛⣚⣛⣙⣉⣉⣉⣛⣛⡛⠓⠚⠒⠛⠒⠒⠒⠒⠒⠒⠓⠒⣓⠚⠛⠛⣛⠛⠛⠁⢸⡀
⠀⠀⠀⠀⠀⡟⠉⠉⣉⠉⠉⠉⡉⢉⣉⣉⣉⣁⣀⣀⣀⣀⢈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠋⠛⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⠉⠉⢻⡇
⠀⠀⠀⠀⢰⠁⠀⢘⡏⠉⣻⠋⢹⡏⢹⡏⠉⡿⠉⣿⠉⢹⡏⠉⣟⠙⡟⠛⣻⠛⣿⠉⢿⠉⢙⡏⠉⣿⠋⢻⠋⠉⡟⢹⡏⠙⡿⠉⣿⠈⠸⡇⠀⠈⣧
⠀⠀⠀⠀⡿⠀⠀⣸⠓⠒⠛⣿⠛⠓⢺⠗⠚⢻⠒⠛⣶⠚⠷⣶⠿⢶⡷⠶⢿⡶⠷⠶⣿⠶⠾⣧⠤⠿⣶⢴⣧⣤⣷⣼⡷⠲⡟⠓⢿⠒⠶⡟⠀⠀⢹⡄
⠀⠀⠀⢰⡇⠀⠀⡟⣀⣀⣀⣽⣄⣀⣸⣆⣀⣽⣄⣠⣿⣄⣠⣧⣀⣸⣇⣀⣨⣇⣀⣀⣧⡀⢀⣿⠀⢀⣿⢀⡇⠀⠀⠀⡇⢈⣇⠀⣸⣃⣀⣹⠀⠀⠀⣷
⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠈⡏⠉⠉⢹⠉⠉⢹⠋⠉⠹⡏⠉⢹⠋⢻⠀⠀⡟⢹⡏⠉⢹⡏⠉⠹⡆⠀⠀⢸⡀
⠀⠀⢀⡇⠀⠀⣼⠓⠒⠒⠟⢲⡶⠿⠶⢦⡿⠦⠾⢧⡶⠾⠓⠶⡿⠒⠒⠛⠒⠒⠚⠷⡶⠾⢦⡤⠶⠧⣤⢼⣦⣾⡤⢴⡷⢼⡧⠶⠤⡷⠤⠶⡇⠀⠀⠈⣇
⠀⠀⢸⠁⠀⠀⡏⠀⠀⠀⠀⣸⡇⠀⠀⢸⡇⠀⠀⢸⡀⠀⠀⢰⡇⠀⠀⠀⣀⣀⣀⣀⣇⠀⠀⣧⠀⠀⢹⠀⠀⣿⠀⢀⣇⣠⣇⣀⣀⣷⣀⣀⣧⠀⠀⠀⢿
⠀⠀⡟⠀⠀⠠⣿⡭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⡽⠿⠿⠿⠿⠯⢭⣭⣭⣭⣭⡭⠭⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠸⡇
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠛⠛⠛⠛⠛⠙⠉⠙⠋⠙⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣿⣭⣽⣭⣿⣿⣿⣿⡿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣷
⠀⢿⣴⠶⠶⠦⠤⢤⠤⣤⣤⢤⣤⢤⣤⡤⣤⡤⢤⡤⣤⣤⣤⣤⣤⣤⢤⣤⠤⠤⠤⠶⠶⠶⠒⠶⠒⠒⠒⠒⠚⠛⢛⡛⢋⡉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⠟⠁
⠀⠀⠈⠛⠓⠒⠲⠖⠶⠶⠶⠶⠲⠶⠒⠶⠒⠲⠒⠒⠖⠒⠖⠲⠶⠒⠶⠒⠒⠒⠛⠛⠛⠛⠛⠛⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠤⠤⠄⠐⠒⠒⠒⠒⠒⠒⠊⠉⠉⡕⠲⠖⠖⠒⠒⠒⠛⠉⠩⠉⡑⢄
⠀⠀⠀⠀⠀⢠⠚⠛⠉⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⡀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢸⠃⠀⢨⡵⠒⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣹⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⠀⠒⠂⡒⠀⣀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⢀⡇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⠼⠧⠤⠿⠤⠼⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢠⡤⠀⠄⠀⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠒⠚⠙⠒⣓⣒⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢸⠀⠄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣀⣤⣤⣄⣠⠟⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡇⠈⢉⣁⣀⠀⠀⠉⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢸⠀⠠⠘⣧⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡇⠀⠀⡇⠠⡏⠀⠈⣿⠆⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢸⡀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠓⠂⠉⠀⠀⠀⠇⠀⠓⠤⠷⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠑⠲⠤⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣉⡭⠵⡶⠒⠶⠲⠶⠶⠖⠤⠤⢤⡤⠤⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠶⠿⠿⠷⠶⠶⠶⠬⠤⠤⠤⢄⣀⣀⠀⠀⠀⡘⠑⣦⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡍⠉⠁⠀⠀⠈⠑⢒⠂⠂⠠⠤⠄⠀⢀⣀⠀⠀⠀⠀⢈⣈⣂⣤⠴⠊⠁⠀⡠⢒⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠦⠤⠤⣤⣄⣈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠚⠓⠒⠦⠤⠤⠄⣀⣀⣸⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠒⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢓⡄⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⢐⡆⠀⠀⢠⠏⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠀⠀⠀⠀⠀⢈⠂⠀⠈⠉⠉⠀⠀⢠⠏⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣶⣸⡢⠀⠀⠀⠚⡗⠄⠀⠀⠀⠠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢂⠒⠈⠁⠀⠀⠀⠸⣷⠾⠅⠀⠀⢀⣅⢯⠀⠀⠀⢀⣄⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡘⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡘⠻⠟⠀⠀⠀⢠⡌⣧⠀⠀⠀⠀⢴⣀⠅⠀⡀⠀⠀⡞⠀⡐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⢠⡜⠻⠋⠁⠀⠀⣰⣆⣷⡀⠉⠀⠀⡜⠀⡰⠀⠀⠀⡇⢀
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠠⡈⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡜⠀⡰⠁⠀⠀⢀⠁⠈⡆⢀
⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠐⠒⠚⠁⠀⠘⠀⢀⣀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⡜⠀⡰⠁⠀⠀⢀⠎⠀⢠⢁⠆
⠀⠀⢠⠊⠀⠀⠀⠠⢀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⢘⡀⠀⣠⠆⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⠁⠀⠀⠀⠈⠀⢀⠔
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⣀⠠⠆⠀⢀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠠⠃⠀⠀⠀⣀⠤⠒⠁⠀⡴
⠈⠣⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠴⠃⠀⠀⠠⠁⠠⢁⠀⠠⠀⠀⢀⣤⡴
⠀⠀⠀⠀⠈⠁⠒⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠁⠂⠀⠀⢀⠂⠁
⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠃⠀⡆⠀⠀⡶
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠛⠀⠘⠁
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⡠⠀⢀⠃⠀⠀⠀⠀⠠⠀⢀⠂
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠉⠀⢀⠎⠀⠀⠀⠀⠠⠁⢀⠆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠃⠀⠀⠀⠀⠠⠃⢀⠎
⠀⡇⠀⠘⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡎
⠀⢧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠃⠀⡜
⠀⠀⠉⠓⠒⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠂⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢀⡀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠲⠶⠖⠿⢉⠲⠶⠶⠆⠀⠀⠀⠐⠲⠶⠶⡁⠶⠶⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠸⣁⢀⡀⣀⠀⠀⠀⠀⠀⣀⢀⣀⠘⣀⢠⢁⡀⠀⠀⠀⠀⢀⡀⣀⡈⠀⣀⡈⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠛⠉⠉⠁⠀⠀⠀⠉⠁⡉⠋⠄⠉⠋⠈⠉⠀⠀⠀⠀⠛⠉⠛⠃⡀⠉⠩⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠊⠀⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠾⠿⠿⠿⢦⠼⠟⠛⠛⠃⠀⠀⠀⠐⠒⠚⠛⠿⠤⠼⠿⠘⠿⠄⠀⠀⠀⠨⠿⠚⠿⠤⡤⠿⠷⠺⠯
⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠠⠸⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣇⠀⠈⢨⡀
⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⡑⣃⣀⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⡀⣀⢠⠀⣄⡬⢤⡀⠤⠤⠤⠤⣤⡤⣄⣤⠘⠁⠀⠀⠨⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠷⠤⠾⠿⠃⠿⠿⠀⢀⣀⠀⠸⠿⠀⠿⢧⢀⠿⠿⡀⠿⠧⠀⡀⡀⠀⠸⠗⢘⠿⠇⠀⠿⠷⠐⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡆⠀⠈⢲⠊⠀⠀⠀⠀⠀⢀⠐⠖⠀⠆⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠁⠖⠁⠀⠀⠀⠀⠀⠲⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠉⢀⣀⠉⠀⠀⠈⠁⢀⠀⠀⠀⠢⠂⠀⠉⠀⠀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡤⠤⡤⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⣸⠀⠀⣳⠀⠀⠀⠀⣰⢋⣴⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⢨⡷⡇⡤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀⡾⠁
⠀⠀⠀⢹⠁⢐⡷⠀⠀⠀⠀⠘⢿⡟⣾⢂⣶⢐⣶⢰⣆⠀⠀⠀⠀⠈⠀⠈⡯⡇⠀⠁⠀⠀⠀⠀⠀⠨⠉⠉⠁⡾⣆
⠀⠀⠀⢩⡣⠊⠀⠀⠀⠀⠀⠀⠀⢬⡯⢨⣯⠨⣿⠬⣿⡄⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠙⠄
⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢙⣿⠉⠋⠉⠁⠀⠀⢀⣀⣀⣤⣋⣼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠐⠠
⢤⡀⢀⣴⣦⣾⣷⣤⣄⠀⠀⠀⠀⠀⢀⡀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢳⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠿⠉⠀⠹⠇⠀⠀⠀⠈⡿⠿⣿⢸⣿⣿⡏
⠀⠘⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣹⣏⣿⣻⣻⡇⠀⠀⠀⠀⣁⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⢰⡉⡎⣹⢸⣿⣿⣷
⠀⠀⠉⠾⠎⠛⠱⠿⠊⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠠⠿⠀⠾⠀⠧⠀⠠⠄⠀⠀⠀⠾⠿⠿⠿⠯⠿⠿⠿⠆
⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠳⢴⠀⠀⠀⠀⠀⠀⢰⣷⠖⣲⠒⡶⢲⢲⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⣇⠘⠇⣸⠒⠀⠀⠀⠀⠀⣼⠏⠀⠁⠈⠀⡿⣼⡇⠀⠀⠀⢀⣀⣰⣺⣲⣀⣀
⠀⠀⠀⢀⣻⣟⡅⠀⠀⠀⠀⠀⠀⢀⡀⣋⢙⡋⣙⣀⡀⠀⠀⠀⢀⣿⢀⡀⠠⠀⢸⣇⣿⡇⠀⠀⠀⢈⣿⣉⢹⠉⣹⣏
⠀⠀⠀⠚⠓⠓⠓⠂⠀⠀⠀⠀⠀⠐⠂⠒⠐⠂⠒⠐⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠙⠛⠃⠀⠀⠀⠐⠂⠒⠐⠒⠂⠒
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⡎⣭⣭⡝⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡀⡴⠋
⠀⠀⢰⣿⠀⠀⢰⡇⠀⠀⠀⠀⣀⣤⣄⢴⠟⠻⣇⠀⠀⠀⠀⠀⠀⠀⡇⠶⠶⢮⠀⣼⣿⡀⠀⠀⠀⢀⣴⣿⣿⣦⡀⢀⡴
⠀⠀⠘⣿⠀⢠⣿⡇⠀⠀⠀⠀⢿⣿⣿⣦⣄⢀⣭⣦⣄⠀⠀⠀⠀⠀⣏⣛⣛⣉⠀⠛⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠻⡄⣾⡿⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⢺⣿⣿⣿⡇⠀⠀⠀⠀⡧⠷⠿⢼⠀⠀⠁⠀⠀⠀⢀⣼⣿⠿⠻⠿⠟⠁

⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠈⠉⣤⣶⣦⡉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣷⣿⣷⡆
⠀⢰⣶⣶⣶⣷⣿⣿⣿⣿⡇⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⢻⣿⣿⣻⣿⣻⣿⡁⢤⠈⠁⠀⠀⠀⠀⠀⠀⠐⢤⠤⣿⡧⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠻⠿⠇

⠀⣀⣠⣴⣦⣤⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⡀⠠
⠀⠛⢛⣉⣉⣉⢩⣭⠡⣤⡄⣶⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠢⠄
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⣇⣿⣇⡀⠀⠀⠀⠀⢸⡇⠀⠀⡀⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢰⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠠⣾⣿⣿⡆⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠁⠀⠀⣿⣻⣿⣿⣛⣿⣻⡿⢿⣛⢿⣿⡟⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠶⠿⠿⠿⠷⠾⠿⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣄
⠀⠀⠀⢀⡒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠛⠓⠂
⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣤⣤⣀⣀⡀
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙
⠀⠀⢰⣿⢻⡖⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⢀⣀⣀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⢀⣸⣿⣼⣧⣿⣼⣇⣴⣿⣦⣤⣀⠀⠀⠀⣀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣙⣀⡀⠀⠀⠀⠒⣁⡐⠀⠀⠀⠀⠀⠀⠼⠾⠆
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠋⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠈⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿
⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⣠⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠰⠄⠀⠀⠀⠁⠀⣤⠀⠀⠀⠁
⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⡌⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⢰⠀⠃⡆⠀⢠⣤⣤⡀⠆⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠑⠂⠀⠴⣤⣄⠀⠀⢀⣴⣶⣶⣦⠀⠀⣤⡀⠒⠀⠀⠀⠀⠐⠓⠂⠀⠐⠀⠛⠛⠀⢰⡆⣿⡉⢸⣿⣿⣡⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠙⢯⣽⣽⣿⣛⣁⣀⣉⠋⠐⢲⣶⣶⡀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠉⣩⠄⣾⣿⣿⡦⠀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠊⠀⠀⠀⠒⠀⠀⠺⠿⠿⠿⠿⠿⠶⠶⠶⠛⠛⠙⠉⠉⠉⠁⠀⠀⠀⠀⠁⠒⠲⠬⢴⣿⣏⣹⣷⣠⣶⣿
⠀⠀⠀⢠⠀⢠⠀⠀⠇⠀⠉⣀⣌⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣏⣩⣉⢀⡒⠂⣰⠄⠐⠢⠀⠠⠤⠄⢀⢩⣙⡛⠿⣿⣿
⠀⠀⠀⠈⠠⣤⡰⣶⡎⠿⣷⢹⣿⡜⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢐⠒⠂⡮⠤⢴⣀⣠⡂⡀⣼⠃⠉⡸⠁⠑⡒⠚⠀⡤⠆⠀⣀⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠙⡇⠀⢱⠀⠸⣆⠈⢷⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠀⢀⠌⠀⢠⠃⠀⣰⠏⠈⠉⠋⠑⠓⡖⠐⠥⡤⢰⣀⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢿⠀⠘⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠤⢤⣆⣀⣠⠁⠀⣰⡟⠀⠀⡌⠀⠀⡌⠀⠀⢰⠁⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠁⠀⠀⠀⠀⠈⠻⠿⣶⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣶⠛⠠⠤⠼⣀⣀⠰⠁⠀⢀⡇⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡖⣾⠖⠤⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⣤⠤⣤⢤⠤⡤⠤⢤⠤⠤⡤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠉⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠒⠚⠚⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⢤⣬⠤⣤⠤⣤⣥⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠆⠀⡶⠀⠰⠀⠀⣦⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠠⢖⠀⠖⡀⢰⡀⠀⢞⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠃⠐⠒⠒⠀⠒⠒⠀⠂⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠐⠘⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡃⠐⠒⠒⠒⠒⠄⠠⠒⠒⠒⠒⠀⠀⠄⠒⠒⠒⠂⠀⠀⠴⠒⠒⠒⠒⠀⢠⠒⠒⠒⡒⠂⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡁⠢⠘⠩⠉⠤⠀⠐⠌⠭⠥⠈⠄⠀⠧⠈⠥⠼⠧⠀⠀⠡⠄⠡⠥⠤⠄⠀⠤⠥⠬⠥⠄⠀⢺
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⢀⣀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⣀⣀⢀⡀⠀⡀⠀⠀⡀⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⠀⠀⠄⠀⡇⢸⠀⠀⠀⠁⢸⠀⡏⠀⠀⠀⠀⣵⠀⣾⠀⣈⠀⠀⠁⢸⠁⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡃⠀⠀⠀⠀⡇⠘⠀⠈⠁⠀⢸⠀⡇⠀⠈⠀⠀⣿⠀⢻⠀⠀⠐⠀⠀⢸⠀⠠⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠙⠋⠑⠁⠈⠛⠋⠛⢉⠋⠀⠙⠋⠁⠈⠙⠁⠀⠘⠛⠛⠛⠃⠋⠈⡛⠛⠋⠉⠋⠀⢼
⠀⠀⠀⠀⠀⠀⠀⢸⠁⡏⠈⢀⠁⠉⡇⢺⠁⠀⠀⠉⢹⡀⡏⠀⠈⠁⠉⢑⠀⢺⠉⠀⠉⠈⠁⢸⠁⠈⠉⠉⠉⠀⢺
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠐⠸⠀⠀⡇⢸⠀⠀⠀⠀⢸⠀⡇⠀⠘⠀⠀⣾⠀⢾⠀⠈⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠚⠚⠓⠒⠃⠘⠓⠒⠒⠓⠊⠀⠛⠚⠒⠒⠐⠋⠀⠘⠚⠒⠓⠓⠋⠈⠓⠓⠒⠓⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠈⢈⠉⠁⡇⢸⠀⠈⠈⠁⢹⠀⡏⠀⠀⠁⠁⣣⠀⢾⠀⠀⠀⠀⠁⢰⠁⠀⠉⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠸⠀⠀⠇⢸⠀⠠⠀⠀⢸⠀⡇⠀⠀⠀⠀⣭⠀⢻⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠒⠒⠒⠒⠃⠘⠒⠒⠒⠒⠚⠀⠛⠒⠒⠒⠒⠃⠀⣼⠀⠠⡄⠀⢀⠘⠓⠒⠒⠒⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡎⠈⠀⠀⠀⡃⢸⠀⠈⠁⠀⢱⠀⡏⠀⠈⠁⠀⣷⠀⢸⠀⠀⠀⠀⠈⢰⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⠀⠄⠀⠇⢸⠀⠀⠀⠀⢸⠀⡇⠐⠀⠀⠀⣽⠀⠼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠛⠒⠛⠒⠒⠃⠘⠒⠒⠒⠒⠚⠀⠓⠒⠒⠒⠒⠃⠀⠘⠒⠒⠒⠒⠛⠘⠓⠒⠒⠒⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠠⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠶⠶⠤⠤⣤⣬⣭⣥⣤⣥⣄⣀⣀⣀⣀⣈⣭⣥⣬⣭⠴⠥⠶⠶⠖⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢁⣀⡁⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠙⠶⠦⣄
⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢀⣄⡉⠀⠠⠤⠀⠀⠀⢠⡚⠁⠀⠀⠀⠀⠀⠉⢹
⠀⠀⢻⡟⠀⠀⡤⠤⢤⠀⠀⠀⠀⠀⣠⣝⣁⠖⣐⠒⡞⢻⣧⣄⡀⠀⠀⠈⣅⢀⣨⣛⣥⣀⡾⠀⠀⠀⠀⠀⠉⢉⠏⠉⡍⠉⢉⠉⠁
⠀⠀⢹⣿⡶⠶⠦⢤⠌⠀⠀⠀⠀⢸⢹⣿⡟⠟⣧⣤⣧⠿⣿⣿⡇⠀⠀⠀⠘⠛⢻⣿⡏⠉⠁⠀⠀⠀⠀⠀⣸⣇⠀⢀⢗⡀⢀⡻⣂
⠀⠀⠈⢿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⣿⡟⠛⢀⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⣿⣿⣇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⣿⡇⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠉⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠈⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢀⡠⢄⣀
⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⢔⣁⢰⡆⣀⡱⠀⠀⠀⠀⣐⠖⠒⣒⠒⠒⣒⠒⡆⠀⠀⠀⣀⠈⢛⠁⠈⣻⠁⠈⡹
⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠋⠀⠀⠀⠀⠀⠠⣿⣿⡧⠠⠅⠈⣘⢟⡀⡇⠀⠀⣾⣿⣷⢰⠖⠒⠒⠒⠒⡆
⠀⠀⣰⣾⣧⣯⣾⣷⣄⠀⠀⠀⠀⠀⢀⣠⣩⡍⣤⡀⠀⠀⠀⠀⠀⠀⣠⣭⣭⣥⡀⣀⣐⣿⣿⣟⡇⠀⠀⣨⣭⣅⡸⣠⣴⠗⠀⠀⡇
⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠐⠛⠓⠂⠀⠀⠀⠀⣿⣿⣿⠿⠟⣹⣿⣟⠛⠃
⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⢀⡀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⡀
⠀⠀⢀⣴⣿⣦⠀⠀⠀⢀⣠⠀⠀⠀⣶⣦⠀⠄⢇⡼⠠⢀⣴⣶⠀⠀⠀⠀⠀⢠⣶⣴⣦⣐⡶⠧⠀⠀⠀⠀⠀⢀⣴⣶⠔⠲⡦⣡⠰
⠀⠀⠼⢹⣿⡙⢷⠄⢲⠉⢸⠀⠀⠀⣿⡏⠙⠂⢃⣱⠐⠋⢹⣿⠀⠀⠀⠀⠀⣼⣿⣿⡏⠛⠉⠀⠀⠀⠀⠀⠀⠈⢿⣡⣾⠁⠊
⠀⢀⢀⣾⡛⣧⢀⡤⠊⢠⣼⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣠⣋⣚⣁⣀⣘⣡⠤⠒⠁⠈⠀⠀⠀⡿⡿⠀⠀⠀⠀⠀⠀⢿⢿⠀⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡏⢸

⠀⠀⢠⣶⠄⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⢠⣶⡆
⠀⢠⣶⣤⣶⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣌⣍⣤⡀⠀⠀⠀⠀⣨⣧⡈⣿⢀⡀⣿⡇⣼⣥⠀⠀⠀⠀⣴⣭⣴⣄⣀⠤⠊⠉⠒
⠀⢸⣿⣿⡏⠙⢻⣸⣿⣿⣽⡇⠀⠀⠀⠀⠀⠛⠛⡟⠛⠃⠀⠀⠀⠀⢻⣿⡳⠋⣬⣧⡉⢳⣿⡟⠀⠀⠀⠀⠉⢹⠉⠁⠀⠁⠀⡖
⠀⠀⣸⣿⡇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠐⠒⠒⢢⠴⠓⠤⠐⠂⠀⠀⠀⠾⢿⣆⠐⢿⣿⠇⢀⡿⠷⠀⠀⠀⠀⠂⠈⠀⣆⣀⣀⣸⣿⡆
⠀⠀⠿⠸⡇⠀⢸⣿⣿⣿⣿⡇⠀⠀⠐⢶⣶⠞⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠈⢷⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠲⣶⡶⠃⠉⠁⢿⣭⡇

⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣦⡀⢸⡟⣁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⡀
⠀⠀⠀⠈⠙⠻⠌⠜⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢠⡀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠛⠙⢏⡇
⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⡆⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠞⢛⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣷⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠸⡆
⠀⠀⠀⠀⠀⣿⡥⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢾⡧⣿⠴⡧⢼⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠓⠒⢻⡀⠀⠀⠀⠤
⠀⠀⠀⠀⣸⡏⢉⡺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⡗⣿⠒⡗⢺⡗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⡖⠒⠒⢧⠀⠀⠀⠶
⠀⠀⠀⠠⣿⣿⣧⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇
⠀⣀⣀⣀⣀⣤⣤⣴⣶⡞⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⢹⠋⠉
⠀⠻⣿⣿⣿⣿⣿⣿⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⢠⣤⣄⣼⣿⡁⢹⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣽⣄⣀⢀⣀⡀
⠀⠀⠈⢻⣿⠿⠟⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⢨⣭⣯⣿⣭⡅⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⢡⣏⣺⣯⠽⠛⠉⠁
⠀⢰⡟⢳⡴⠖⠻⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣼⣿⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢳⣿
⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠓⢾⡇


⠀⠀⠀⢀⣀⣤⣄⣀
⠀⣠⡾⠋⣤⣶⣶⠍⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠺⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣭⣤⣦⡔⣠⡀
⢠⡟⠀⠀⠘⢿⠏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣆⣀⣀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣵⣿⣷⡀
⢸⡇⣶⣶⣶⠎⢶⣶⣶⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣽⢹⣿⣿⡗⡀
⠀⢻⣜⠿⠋⠀⠈⠻⢟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣉⣿⠻⠟⠃⢻⣧⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣇⣺⣿⣿⡇⡇
⠀⠀⠉⠳⠶⠴⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠷⠝⠿⣿⡯⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡐⠂⠶⢠⡄⠀⠀⠀⠉⠉⠉⠛⠓⠲⠶⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢰⡇⢀⠀⡀⠁⠀⠀⠂⠀⠠⠄⠀⠀⠀⠀⡀⠀⠀⠈⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠃⡈⠠⠀⢀⡐⠀⠀⠦⠀⠀⡐⠂⠠⠄⠁⡈⠉⡀⠒⡆⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠃⠡⠀⠠⠂⠀⠠⠀⠁⢀⠐⡀⠀⠁⠡⠘⠂⠰⠀⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠉⠛⠛⠶⠶⠦⢤⣤⣀⣀⣁⠀⠒⠀⠀⠉⠄⠂⠀⠀⢰⠁⠀⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠌⠉⠉⠒⠀⠠⠤⢀⣀⡀⠀⠀⠉⠉⠉⠛⠛⠳⠶⠶⣤⣤⣤⠀⣸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠀⠀⠐⠦⠤⣤⣄⣀⠀⠀⠠⠁⠀⠀⠒⠂⠠⠄⠀⠀⠀⢀⡀⠠⢸⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠢⠤⠖⣀⡄⠀⡍⠉⠏⠇⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠶⣤⡄⣸⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠎⢠⡄⢰⠄⣠⢈⡉⠉⠊⠀⠀⠀⠧⣀⡂⣠⡿⠉⠖⢢⠀⠈⢡⠟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣆⣀⣉⢀⡞⠐⠡⠚⠁⣸⠁⡰⠠⢦⠀⡄⠀⠉⠉⡉⠀⠁⠀⠀⡎⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡠⠀⠁⢀⠘⠁⠓⠂⠀⢠⠋⠀⠀⠒⠁⣸⠃⠌⡠⠂⠀⡟⠀⠀⣸⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡐⠁⢆⠆⣼⢀⢆⡐⠀⢠⠀⢀⠀⠀⠐⠘⠏⠐⠖⢠⠀⣼⠃⠀⢠⡇⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠗⠖⢒⣴⠃⣆⡠⠕⠀⡟⠀⢋⡶⡁⢠⠇⡠⠀⠐⠂⣄⠀⠀⢀⣞⢷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠖⢀⠀⢠⠀⠀⡁⠈⠉⠛⠀⠶⠄⣉⣠⡞⢠⣁⠈⠁⢠⠇⠀⠀⣼⠍⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡄⠀⠊⢀⡟⡰⢁⡰⠂⣼⠀⡄⠀⡤⢀⡀⠁⠈⠈⠛⠈⠟⠀⠀⣸⣛⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣀⠉⠉⠒⠚⠀⠂⠨⠥⣰⠃⡐⠠⠼⠇⣼⠁⠜⠀⠀⢀⡇⠀⠀⢰⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠜⢁⠘⠄⡟⠀⠐⠀⠀⣀⠉⠀⠉⠑⠂⠰⠇⠸⢠⣀⠄⡼⠁⠀⢀⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠘⠦⢬⣀⣼⢃⡀⠀⠂⢠⡏⠀⠃⣀⠁⣰⠄⣠⠀⠀⠀⡌⠁⠀⠀⡔⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣥⣀⣉⣀⡒⠀⠀⠉⠈⠃⠋⠡⠾⠀⠦⢄⢀⢠⡟⢀⠁⠒⠀⢸⠃⠀⠀⢠⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠹⣭⠉⠛⠒⠒⠦⠤⢤⣀⣀⡀⠀⠀⠈⠀⠘⠒⠂⠴⠏⠀⠀⠀⡆⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠶⢤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠦⠤⣤⣄⣀⣀⣸⣁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠲⠦⠤⠤⡤⢀⣠⣬⣜⣙⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠓⠲⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡏⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠒⠒⠲⠶⠤⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠉⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠢⠤⠤⠤⠤⠤⠤⢄⣠⠏⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⢩⡅⠀⣦⠀⢀⡀⠀⣤⠀⠀⠠⠤⣄⠀⠀⢀⣀⡀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⣀⣈⣀⣸⡟⠀⠺⠃⢰⡿⠀⠸⠇⢀⣿⠁⢀⣤⠀⣸⠃⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢉⠉⠛⣍⠈⠛⠿⠿⡛⠙⢶⡶⠶⠾⠛⣤⣤⣤⣤⡿⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡘⠀⠺⠃⢸⡟⠀⣚⠇⢀⡿⠁⠠⡄⠀⣿⠎⠀⡀⠉⢱⡄⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠈⠿⠿⢗⡛⢱⠶⠶⢤⠾⠣⣤⣤⣁⣰⣿⣀⡈⠉⠀⣾⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢲⠀⢸⡟⠀⢠⡄⢈⣷⠀⢉⡈⠉⣯⡀⠉⠩⠿⢛⡋⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠳⢶⣤⣤⡿⢧⣀⣉⣀⣼⡏⠀⠰⠃⢠⣿⠀⠐⠆⠀⣸⠇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡌⢠⢤⠀⢰⡆⢀⠘⠛⠫⣍⠬⠛⠛⠛⡛⢙⡶⠶⠤⣤⡿⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠠⣀⣘⡋⢀⣿⠃⠈⠱⠄⣸⡏⠀⠠⠀⠀⣿⠃⢀⣀⠉⢱⡆⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠉⠉⠉⠙⠁⠛⠓⠶⠶⠟⠧⣤⣤⣄⣼⢿⣀⡈⠉⠀⣾⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣷⣶⣶⣶⣤⣤⣤⣄⣀⣀⣀⠀⠁⠀⠉⠙⠛⠛⠋⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⢿⣿⣿⣶⣶⣶⣶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣿⡯⠍⠀⡭⣙⠙⠀⠀⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡽⠾⢿⣿⠛⠁⠀⠀⠴⠀⠈⠁⠲⣄⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⠅⢀⣴⣿⣃⣠⣄⣀⡀⠀⠔⠀⠀⠀⠈⠛⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⡤⢫⣿⣿⠏⠀⠀⣉⠙⠳⢦⡀⠀⠈⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠫⠐⡴⠃⢠⣿⡏⠀⠀⠘⠛⣆⠀⠈⠻⢶⡀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠠⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢟⠀⠀⣸⡟⠁⠀⣿⣿⣄⢘⠂⠀⢠⠃⠀⠀⠃⠌⡿⣶⡇⠂⠐⠲⠀⢷⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣆⠀⡼⢻⣿⣿⠁⠀⡴⢦⡞⢉⣾⠄⠀⠒⠈⠻⣶⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣗⠀⣿⠀⢸⣿⠀⣦⠀⣾⣥⣾⣿⢿⣶⣴⢀⣴⣻⠿⣾⣶⡆⠀⣻⣦⠀⢀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢏⡀⣿⠀⠸⣿⣿⣇⠀⣇⠈⢉⡡⠾⣿⣿⣧⣸⠁⠸⠟⣿⠃⠠⠃⡆⠀⡏⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠐⣿⣄⡀⠈⠛⢿⣷⣿⣧⣾⣷⣤⣿⣿⣿⣿⣤⣤⣴⣟⣤⣖⣨⠃⣘⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢻⣟⣫⣿⣦⡈⣠⣭⣿⣽⣿⣿⣉⢻⢿⣿⣿⣿⣿⣿⣿⡏⣈⢧⡀⠟⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠻⠋⠉⠉⠛⢻⣾⡿⣛⢻⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣧⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⠛⠿⠿⠟⠷⠷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⠅⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠄⠀⠀⢘⠟⠋⣿⣧⣿⣿⡿⢽⡿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠈⠀⠘⣭⡾⢶⣿⡻⠟⠋⣰⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣉⣁⣄⣠⣬⠋⠀⠀⣽⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣟⠋⠁⠀⠀⢀⣀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉




⣿⠿⠿⠿⠿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠄⠀⠀⠠⠤⠤⠤⠤⠤⠄⠀⠠⠤⠤⠤⠤⠤⠤⠄⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠠⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠐⠀⠀⠀⠀⠀⠂⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⢄⠀⠤⠀⠀⠄⢀⠤⠀⠀⠄⠠⠤⠤⠠⡀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢄⠀⠁⡸⠀⢀⣻⣀⡄⠰⣀⠙⢀⡀⢀⣘⣪⣀⠇⢂⠛⣁⡋
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⢀⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠐⠆⠸⠀⡁⠰⠀⠐⠐⠀⠦⠀⡁⢠⠀⠆⠀⠀⡇⠠⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡎⠠⡄⢸⠀⠁⢠⠀⠁⠰⠁⢤⠈⠂⠀⠀⠤⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠂⠀⠂⠀⠀⠂⠈⠂⠀⠀⠁⠀⠒⠀⠒⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠄⢰⠀⠂⠀⠀⠂⢀⢂⠀⠂⠂⠐⠀⡀⠐⠀⠐⣖⢒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠃⠤⠥⠌⠀⠠⠤⠤⠀⠀⠠⠤⠤⠂⠐⠤⠤⠤⠃⠐⠤⠤⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀⣀⠀⣠⠤⠶⠤⣄
⠀⠀⠀⠀⣠⠚⠉⠉⠉⠙⠢⠤⢤⡞⠑⠞⠁⠀⢸⠁⠀⠉⡡⠤⢤⡀⠈⢳⠲⠤⣄
⠀⠀⠀⢰⠁⢀⡤⠒⠦⣀⣄⡀⠀⠓⢤⡀⣠⠒⢉⣰⠉⠉⠀⠀⣀⣱⠀⠸⣄⠀⠈⠣⢤⡀
⠀⠀⠀⢸⡀⢺⠀⠀⠀⠉⠀⠃⠀⠀⠀⢱⣇⠀⠏⠀⠀⠀⠀⠘⠁⠀⣳⠀⠈⠳⠤⡀⠀⠙⠦⠲⢄
⠀⠀⠀⠀⢳⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⣌⡶⠒⠲⠤⠒⠢⢤⡀⠀⠁⠀⠀⠀⠀⢸⡤⠔⠒⠤⡼
⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⠙⠚⠉⢦⡀⠙⣄⡀⠀⠀⠀⡴⠲⠔⠉⠉⠳⡘⡆
⠀⠀⠀⠈⣇⠈⠉⠉⠱⣄⠀⠀⣀⢔⣒⣦⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠰⢣⡃
⠀⠀⠀⠀⠈⠑⠒⢤⣀⠴⣍⠉⢁⡜⢲⠚⡖⢻⠒⠒⠒⣿⠒⠒⢺⠓⡞⢲⣾⣦⣀⣤⣄⣀⣀⣀⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⡏⣏⢹⠉⠉⠉⣿⠉⠉⢹⠉⡏⣟⣏⣻⣛⣛⣻⣛⣛⣿⣹⣛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣲⣀⣀⣖⣆⣯⢿⢹⠉⠉⠉⣿⠉⠉⢹⢹⢋⣧⣯⢼⠤⠤⣼⠤⠤⣯⣼⡼
⠀⠀⠀⠀⠀⢀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣹⢸⢸⡇⠀⢠⡛⡄⠀⢸⢸⢸⢹⣷⢸⠀⠀⢸⠀⠀⡇⣸⡇
⠀⠀⠀⠀⠀⠘⢦⢤⣤⣤⣤⣤⣤⣤⣤⣼⣼⣸⣇⣠⡻⠋⢞⣆⣼⣸⣼⢸⣿⣸⠀⠀⣸⠀⠀⣇⣻⡇
⠀⣀⣀⣀⣀⣀⣸⢸⣽⢼⢽⣭⡯⡯⣯⡽⡿⢸⡵⣿⣧⠀⣼⣯⢿⠘⡿⣼⡏⢹⠉⠉⢹⠉⠉⡏⢹⣇⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣸⣺⢺⢺⣒⡗⡗⣗⡇⡇⣼⡝⠉⢉⣿⡉⠁⢻⣣⡇⡟⡇⢸⠀⠀⢸⠀⠀⣇⢸⢻
⠀⠀⠀⡏⢉⣉⠉⣉⠉⣉⠉⣉⠉⣉⣹⢡⠿⣼⠷⠶⠾⣿⠷⠶⢾⡧⢧⢹⠃⡎⠀⠀⢸⠀⠀⢸⠘⡜⡄
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⣿⡏⡸⠀⡇⠀⠀⠀⣿⠀⠀⠈⡇⠸⡈⣦⣇⣀⣀⣸⣀⣀⣸⣄⣧⣷
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⡿⢳⠗⢒⠗⠒⠒⠒⣿⠒⠒⠒⢷⠒⢷⠻⣄⣀⣀⣸⣀⣀⣀⣇⣘⣆⣧
⠀⠀⠀⢧⣸⣿⣤⣿⣤⣿⣤⣿⣴⠧⡼⠤⣼⠤⠤⠤⠤⣿⠤⠤⠤⠼⡤⠼⡦⢵⡤⠤⢼⠤⠤⠤⢼⡤⠽⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⡾⠒⢲⠗⠒⠒⠒⠒⣿⠒⠒⠒⠒⢷⠒⠺⡖⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⣦⣄⡀⠀⣠⣦⣄⠀⠌⠆⠀⠀⠀⠀⡴⠒⠚⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠳⢸⡇⣷⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠋⠉⠙⢦⣄
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⢰⠚⠁⡾⠛⠛⠛⠛⣷⠈⠳⡄⠀⠀⠀⠀⠀⢀⣬⠴⢥⣤⣄⠀⠀⠀⠀⠀⠀⠀⡤⠟⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠘⠲⠄⡇⠀⠀⠀⠀⣿⠠⠞⠁⠀⠀⠀⠀⣰⠛⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢀⣠⣤⡶⣰⡀⣠⠞
⠀⠀⡤⠴⠏⠀⠀⠙⠛⠓⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣐⡛⠿⣿⡿⠱⢿⣷⡀
⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⠀⠀⠀⠀⠀⠀⣇⣀⡀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣰⣶⣿⡷⠆⠁
⠑⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠛⠿⠷⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠛⠉

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⢶⡆⠀⠀⠀⠀⠀⡶⠒⠒⠒⠒⣒⠒⠒⠒⢲⡆⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲
⠀⠀⡏⠀⠀⣀⡤⠠⣀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⣀⠠⠠⡀⢸⡇⠀⠀⠀⠀⠀⡟⠀⣠⠖⠋⠈⠑⢦⠀⢸⡇⠀⠀⠀⠀⡇⠀⢀⡴⠒⠉⠙⠦⡀⠀⢸
⠀⠀⡇⠀⡞⠀⢰⣄⠈⢳⠀⢸⠀⠀⠀⠀⠀⠀⢸⠆⠁⠀⠀⠈⢺⡇⠀⠀⠀⠀⠀⡧⠀⠣⠤⠤⠤⠤⠴⠃⢸⡇⠀⠀⠀⠀⡇⠀⢯⣀⢲⠲⣴⢀⣨⠂⢸
⠀⠀⣧⣤⣬⣬⣤⣬⣥⣥⣤⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⠶⠶⠶⣶⣶⡶⠶⠶⠾⠃⠀⠀⠀⠀⣧⣤⣤⣤⣬⣤⣥⣤⣤⣤⣼
⠀⣴⣶⣶⣶⣿⣶⣶⣿⣶⣶⣷⣦⠀⠀⠀⠀⠀⢸⣷⣶⣦⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⢠⣴⠾⠟⠛⠷⢦⣄⠀⠀⠀⠀⠀⠀⠉⠉⢩⣭⣽⣿⣿⣭⣭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠉⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡴⠋⠛⢦⣀
⠀⠀⠀⢀⣀⣠⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢒⡒⠒⠃⠀⠀⠀⠀⠀⠀⠀⢰⡉⠀⠀⣤⡄⠀⠈⣳⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⣠⡏⠀⠁⢠⡇⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⣀⡺⠃⠿⠷⠘⢗⡀⠀⠀⠀⠀⠀⢠⣤⡉⠉⠁⣿⡧⠈⠉⠁⠀⠀⠀⠀⠀⠈⠧⠤⠤⠤⠤⠤⠤⠤⠤⠃
⠀⢾⠁⠀⠀⠀⠸⠇⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠿⠿⠸⠿⠿⠃⠿⠿⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠙⠛⠃⢀⡐⢂⡀⠘⠛⠋⠀⠀⠀⢰⠋⡆⢿⠿⠘⣟⡻⠃⠿⠿⡰⠙⡄⠀⠀⠀⠀⢘⣿⣭⣉⣋⣙⡉⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠠⠬⠥⠔⠀⠀⠀⠀⠀⠀⠺⣀⠘⢆⠛⠇⠻⠟⠼⠋⡴⠁⣀⠇⠀⠀⠀⠀⠘⠷⣤⠤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢺⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠈⠉⠉
⠀⠀⠀⠀⣠⠤⠖⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢦⡀
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⢲⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠘⢲⡀⠀⠀⠀⠀⠀⢀⠼⠁⠀⠀⠀⠈⠱⢤⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠓⠒⠂⠀⠀⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠀⠀⠒⠚⠀⠀⠀⠀⠀⠀⠘⠲⠶⠀⠀⠀⠰⠶⠞⠀⠀⠀⠀⠀⠀⠙⠶⠦⠀⠀⠀⠶⠶⠃
⠀⠀⠀⠀⠀⢐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⢠⣤⣤⡽⡿⡿⣇⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣦⣾⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣺⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡤⠤⢄⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⣿⣮⡳⣤⠀⠀⠀⠀⠀⠀⠀⢰⣷⣼⣿⣿⣰⡂⠀⠀⠀⠀⠀⠀⠀⣾⣷⣾⣷⣶⣦⣼⣶⣤⡀
⠀⠀⢸⡟⣿⣷⡟⢷⡟⡿⢺⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⢿⡏⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⠿⠿⠿⠿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⡉⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠒⠂⠀⠀⠙⠒⠀⠄⡀
⠀⠀⠀⢀⡠⠴⠛⠛⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⢀⡴⠊⠁⠀⠀⠀⠀⢀⣀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⡏⠀⠀⠀⣀⠔⢲⣿⠭⠥⠔⠓⠒⠀⠀⠀⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢳⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣰⠋⠀⠀⠀⣀⣠⡤⠶⠖⣒⣈⣉⣩⠭⠉⠒⠲⣄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢿⡀⠀⣀⡻⠮⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠏⠀⠁⠂⠆⠀⠀⠋⠈⠀⠇
⢈⠟⠋⠁⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠰⠶⠶⢋⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⣿⠀⠀⣀⠤⠶⣚⣛⣯⠥⠶⠒⠚⠃⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢱⠀⡄⠁
⠙⢦⣀⣀⡴⠋⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠴⠋⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢀⡞⢡⡞⠀⠀⢀⡤⠶⢶⣽⡋⣩⠟⠉⠋⠛⠢⡄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠸⡀⠀⢀⡿⢱⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁
⢸⠀⣀⣈⣩⣭⠤⠼⠤⠤⠤⠤⠧⠤⢤⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠠⠁
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠼⠀⠀⠀⠀⣸⣄⣀⣀⣀⣴⠁
⠀⠀⠘⢦⠤⠄⠲⠶⠒⠒⣶⣒⣒⣲⡒⠲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠤⢀⠃
⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⢀⣀⣀⣀⣀⣂⣉⣭⣽⡇⢈⠆
⠀⠀⠀⢼⠃⠀⢤⣤⣤⡤⠤⠤⠴⠶⡒⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⣀⣀⣈⣭⣤⣵⡶⢈⠆
⠀⠀⠀⣼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠝⡓⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣐⣢⣭⣭⣥⢈⠆
⠀⠀⠀⢼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠿⡖⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠉⠉⠉⢉⣩⣭⣥⣶⡎⣈⠂
⠀⠀⠀⠘⢧⣀⠀⠐⠒⠒⠒⠺⣋⣗⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠉⡭⢛⠜⠁
⠀⠀⠀⠀⠀⠉⢻⠛⠛⠛⠛⡿⢹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡛⣛⣷⠞
⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⠷⠾⠼⠶⠧⠿⠼⠼⠧⠧⠾⠼⠶⠧⠷⠾⠼⠶⠧⠷⠼⠼⠧⠷⠾⠼⠼⠧⠷⠾⠼⠶⠧⠷⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢻⡹⡏⠉⠉⠋⠙⢟⢻⠉⠉⠉⠉⠛⡟⡟⠉⠉⠉⠉⢻⠻⡏⠉⠉⠉⠉⠛⡟⡟⠉⠛⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣠⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢠⠞⣽⢸⠀⠀⠀⡠⢋⡇⡇⠀⠀⢀⡔⣹⡇⡇⠀⠀⢠⢞⡵⡇⣿⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣰⠣⠎⣸⢸⠀⠀⡼⠱⠃⡇⡇⠀⢠⠎⠜⣹⡇⡇⠀⣰⠣⢎⠐⡇⣿⠀⢠⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢰⠃⢂⠎⢾⢸⠀⡼⠐⣰⠃⡇⡇⢀⠏⠐⡼⢹⡇⡇⣰⠃⢃⠎⠞⡇⣿⢀⠎⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠇⢀⡄⠈⣼⢸⣼⠁⢠⠀⢁⡇⣧⡞⠀⡤⠀⣹⡇⣧⠇⢀⡄⠈⡜⡇⣿⡞⠀⡤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠏⠀⠀⠀⠘⢹⣸⠃⠀⠀⠀⠊⣇⡟⠀⠀⠀⠀⢻⣇⠏⠀⠀⠀⠘⠁⡇⡿⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣤⢞⡩⣍⠲⡤⣬⢏⡔⣒⢢⣀⡁⡸⠃⢂⣀⡄⠈⢀⡟⠐⠂⢀⠀⠉⢰⠏⠐⠀⡀⠀⠁⣀⡟⠐⠂⢀⠀⢹
⠀⣠⠞⠀⠀⢯⣏⢀⡀⠀⠀⠈⠛⠙⠀⠁⠉⠉⣧⡯⡾⠶⣄⣢⠎⡰⣣⠃⠋⢐⡷⢃⡜⡼⡐⡁⠘⣠⠟⡰⣣⠃⠋⠀⢻
⠀⢧⠀⠀⡔⠋⠁⢏⠙⠋⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢳⣴⣵⣳⣳⡷⠋⣠⢞⣜⣝⣝⣽⠟⢁⣞⣵⡵⣱⣳⢣⣾
⠀⠀⠭⠭⠭⠭⠉⠉⠉⣭⣭⡍⠉⢉⣉⠉⢉⡉⠉⣉⠩⠭⡉⠉⠹⠿⠏⠉⠉⠉⠩⠭⠭⠭⠉⠭⠉⠩⠭⠭⠭⠉⡩⠭⠉
⠀⠀⠠⠬⠭⠉⠉⠥⠤⠀⠰⠆⠀⠐⠒⠒⠒⠀⠀⠐⠲⠈⠉⠉⠀⠉⠉⠩⠍⠉⠉⠡⠄⠀⠀⠒⠒⠂⠘⠛⠦⠌⠵⠶
⠀⠀⠀⠀⠚⠛⠓⠀⠀⠀⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⣿⣧⣤⣄⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣤⣤⣤⣤⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⢀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠸⠇
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠟⠛⠋⢀⣶⣶⣶⠀⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣭⣭⣭⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⠛⠚⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠐⠆⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⢟⠋⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣚⣛⣋⣿⣿⣿⣿⣟⣛⣛⣃⣈⡉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁



⣏⣈⣏⣯⣟⣯⣿⣽⣽⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⠞⠋⠛⢦⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡟⣰⠋⠀⠀⠀⠈⢷⣘⣧⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡤⠶⠶⠶⣾⢠⣏⣙⣳⡶⠶⢛⣉⣭⣤⡶⠶⠶⠦⣍⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢰⡇⣼⠿⢋⣡⠶⢾⣉⠻⢿⣄⣧⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣆⠀⣠⣾⠇⣿⠞⠋⠀⠀⠀⠈⠛⢦⣌⠻⢦⡀⢀⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⢿⣡⣾⠀⡏⠀⢀⡴⠖⢦⡀⠀⠘⡏⢻⣦⣹⠟⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣦⡙⢿⠀⣇⠀⠘⢧⣀⣼⠃⠀⢠⣇⣼⠟⣡⣾⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠏⠀⠙⢿⡆⣿⢦⣀⠀⠀⠀⢀⣤⠾⢋⣥⠞⠁⠈⢷⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠸⡇⢻⣦⣍⡛⠶⣾⣋⣥⣾⠋⡟⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠳⠶⠶⠶⢿⠘⣟⣩⡽⠷⠦⣬⣙⡛⠺⠷⠶⠶⠶⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠛⠛⣇⢹⡅⠀⠀⠀⠀⡽⢩⡟⠛⠓⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⢦⣀⣠⠞⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣬⡤⠞⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⣿⣼⢒⡯⠁⣯⡷⢼⢫⡌⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠀⠉⠁⠁⠉⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣴⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢁⣶⣿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⠀⣾⣷⣤⣤⣾⣷⠀⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢿⣿⣿⣿⣿⣿⠟⢋⣠⣿⠋⣩⣍⠙⢿⣄⡙⠻⣿⣿⣿⣿⣿⡿⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠻⢿⣿⣿⣿⠀⢿⣿⣇⠸⣿⣿⠇⣸⣿⠿⠀⣿⣿⣿⡿⠟⢁⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣭⣭⣤⣤⠈⣿⣦⣤⣤⣴⣿⠁⣤⣤⣭⣭⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠛⠛⣉⣉⠛⠛⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠰⠰⠂⠇⠰⠀⠸⠓⠺⠐⠷⠸⠀⠇⠸⠅⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠛⠛⢻⡇⠀⣿⠛⠛⣿⠀⢸⡟⠛⢻⡇⠀⣿⠛⠛⢻⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣀⣀⣸⡇⠀⣿⣀⣀⣿⠀⢸⣇⣀⣸⡇⠀⣿⣀⣀⣸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠁⠉⠀⠀⢉⠉⠉⠁⠀⠀⢉⠉⣉⠁⠀⠈⠉⠉⡉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠉⠉⢹⡇⠀⣿⠉⠉⣿⠀⢸⡏⠉⢹⡇⠀⣿⠉⠉⢻⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣤⣤⣼⡇⠀⣿⣤⣤⣿⠀⢸⣧⣤⣼⡇⠀⣿⣤⣤⣼⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠉⠉⢹⡇⠀⣿⠉⠉⣿⠀⢸⡏⠉⢹⡇⠀⣿⠉⠉⢹⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣦⣤⣼⠇⠀⢿⣤⣤⡿⠀⠸⣧⣤⣼⠇⠀⣿⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣤⣤⣤⡀⠀⣤⣤⣤⣄⠀⢀⣤⣤⣤⡄⠀⣿⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠁⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠻⠶⠶⠾⠇⠀⠿⠶⠶⠿⠀⠸⠷⠶⠾⠇⠀⠿⠶⠶⠾⠃⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣰⣿⣿⠀⣾⣿⣷⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣰⣿⣿⡏⢸⣿⣿⣿⡆⢹⣿⣿⡀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠐⠿⠿⠿⠀⠿⠿⠿⠿⠷⠈⠿⠿⠷⠀⠀⠀⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣴⠟⣿⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠶⠟⠁⠀⣿⡇⠀⠙⢷⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⡀⠰⢶⣾⣿⣿⣷⣶⣶⣤⣀⡀⠀⠀⠀⠈⠇⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣠⣶⣿⣿⣿⣷⣦⣌⡙⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⣰⣿⡿⢋⣡⣌⠹⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣷⠄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣾⣿⣿⡄⠻⠿⢿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⠋⣰⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⣷⡄⢹⣿⣿⣤⡙⠛⠿⠿⠟⢃⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣌⡙⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠋⠉⠉⠉⠉⠉⠉⢻⡇⣸⡟⠉⠉⠉⠉⠉⠉⠙⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢀⣰⣆⠀⠀⢸⡇⢸⡇⠀⢠⣤⣤⣤⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠉⢻⠏⠁⠀⢸⡇⢸⡇⠀⠰⠶⠶⠶⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣇⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠿⠿⠿⠟⠿⠿⠿⠿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⣉⠤⠖⠒⠉⠉⠉⠉⠉⠐⠒⠦⢍⡙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣁⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⡙⢿⣿⣷⣄
⠀⠀⠀⠀⢀⡾⣿⠟⢁⢾⡿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⢆⠙⢿⡿⣦
⠀⠀⠀⠀⠛⠎⡁⡰⠁⠈⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠁⠀⠱⡈⡛⠎⠇
⠀⠀⠀⠈⠀⣼⡟⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣿⡿⠛⢿⡟⠛⣿⡟⠛⣿⠟⠻⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣷⣶⣿⣷⣶⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣧⣤⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣻⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣦⣤⡇
⠀⠀⢀⣴⣿⡟⣿⠻⠿⠿⠿⠿⠟⣿⣿⠿⣿⡿⠿⣿⡿⠿⣿⡿⢿⣿⡟⡿⠿⠿⠿⠿⢿⡏⣿⣷⣄
⠀⠀⠀⢿⣿⣿⡘⡆⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣶⣿⣷⣶⣿⡇⠸⣿⡇⠀⠀⠀⠀⠀⡞⣸⣿⣿⠇
⠀⠀⠀⠈⢿⣿⣷⡈⢄⠀⠀⠀⠀⣿⣧⣤⣼⣧⣤⣿⣧⣤⣿⣧⣤⣿⡇⠀⠀⠀⢀⠎⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠻⣿⣿⣄⠑⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⢁⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠉⠗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠷⠶⣶⣦⣤⣤⣶⣶⠶⠿⠿⠿⠟⠛⠉




⣿⣿⠛⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡩⠤⠟⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡸⠋⢮⢔⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠄⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⣢⢮⢀⡴⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢠⢎⢼⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠁⠀⢀⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠠⡆⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠠⠃⠀⠀⠀⠘⠁⠀⠀⡀⠀⠁⠀⠀⠠
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂
⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠂⠀⠀⠀⡀⠤⠐⠂⠁⡠⠌⡃⠛⠢⢀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠈⢢⠂⣔⣈⣀⡉⠀⠢
⠀⠀⠐⠄⡁⠐⢂⡄⠣⠊⠀⠀⠀⠒⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠢⢀⠐⠄⠀⠀⠀⠀⠠⠊⠛
⠀⠀⠀⠀⠀⠀⠀⠘⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠔⢀⠼⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠊⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠤⠆⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠙⡖⠀⠈⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠑⠒⡦⠀⠔⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠐⠀⠈⠉⠉⠉⠉⠉⠁⠀⢸⠀⠰⠄⢀⠀⠀⣀⠀⠠⠇⠀⠐⠂⠀⠐⠠⠄
⠀⠀⠀⠀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠁⠐⠂⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠦⠄⠀⠐⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠄⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡀⢀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠊⠀⠐⠒⠒⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠒⠁