Spool Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠚⠉⠉⠉⠁⠀⣀⣀⣀⣀⣀⠀⠉⠉⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⡀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⡇⠀⣠⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡯⠀⠀⢸⡇⣀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡽⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡯⢀⡤⠖⣿⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⡽⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣛⣵⣚⡥⠖⠋⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢟⣩⣿⣿⣿⣯⡥⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⠿⣿⣿⣿⣿⣯⣼⡯⢿⣵⣶⣿⣿⡯⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣯⠿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣿⣷⣿⡯⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣻⣭⣯⠏⢭⣿⣿⣿⣿⣿⡿⢯⣿⣿⣻⣿⡯⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠿⣛⣿⣾⠽⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡯⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠉⣴⣿⣟⣿⣿⡽⢿⣿⣿⣿⣿⡯⠿⣭⣿⣿⣾⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⣠⠞⣿⣿⣿⣿⣿⡽⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⣷⣤⣉⡛⠛⠿⠿⠭⠿⠯⣽⣿⡭⠿⠿⠭⠿⠟⠛⣋⣩⣴⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣭⣶⣦⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡈⠙⢦⡀
⠀⠀⠀⠀⢀⣠⣄⣀⢴⣾⣿⣿⣿⣿⣿⣷⡄⢹⡆⠀⠀⠀⠀⢀⣀⣀⢠⣴⣾⣿⣿⣿⣿⣿⣆⠈⢷
⠀⠀⠀⡞⠁⠀⠉⠙⢿⣮⡻⣿⣿⣿⣿⣿⣷⢈⡇⠀⠀⠀⠀⠀⠀⠉⠛⢮⡿⣿⣿⣿⣿⣿⣿⡄⢸⠂
⠀⠀⢸⠀⠀⠀⣀⠀⠀⠙⣿⡝⣿⣿⣿⡿⣃⠜⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⣮⢿⣿⣿⣿⠿⠀⠈
⠀⠀⠀⢇⠀⠘⣿⣷⠀⠀⠘⣿⢹⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⢹⡞⣿⠟⠁
⠀⠀⠀⠈⢣⡀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠢⢤⣀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠲⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣞⡿⣟⢶⣄⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄⠈⠳⡄
⠀⠀⠀⢀⡤⠶⢶⣦⣟⠻⢽⣳⣽⣾⣿⣿⣆⢸⡇⠀⠀⠀⠀⠠⠤⢤⣔⠻⢽⣳⣿⣿⣿⣿⣷⠀⢹
⠀⠀⢠⠇⠀⠀⠀⠈⠙⢿⣆⢿⣿⣿⣿⣿⡟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣻⣿⣿⣿⣿⣿⠇⢸⠁
⠀⠀⠸⡄⠀⢠⣤⣄⠀⠈⢻⣯⣯⣇⡿⠿⠵⠋⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠈⢷⣻⣿⢹⡽⠋
⠀⠀⠀⠳⡀⠈⠻⠿⠀⠀⠈⣿⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠘⡇⠟⠉
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠉⠒⠲⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣛⣿⠿⠿⢟⣛⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠁⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢀⣀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠚⠛⢻⡇⠀⠀⠀⠀⠀⠀⢽⣟⠛⠓⠲⠤⣄⠀⠀⠀⠀⠀⠀⢰⡏⠀⣠⡾⢛⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢱⡊⠁⠠⡀⠘⠷⢤⣤⣤⣤⣤⡤⠿⠋⠉⠀⠈⣱⠌⠹⡄⠀⠀⠀⠀⢸⣷⡾⣫⡴⠟⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢄⠙⠲⠦⢬⣉⣀⡀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠉⢁⡠⢾⡇⠀⠀⣀⣴⠟⣿⣿⠋⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠐⢒⣉⣥⠴⢻⡇⣠⣾⣿⣵⠞⠋⠹⣆⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠊⠉⠉⠀⣀⠴⡻⣻⣿⡿⠛⠁⠀⠀⠀⢹⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠳⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⢉⠥⣪⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣆⠀⠈⠲⢄⠀⠀⠀⠀⠀⣀⣀⣈⡉⠽⢶⠟⣡⣾⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡈⠳⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⢖⣡⠾⠛⠋⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠒⠦⠵⠤⠀⠀⠀⠀⠀⠀⡠⢊⣵⠟⠁⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣫⡶⠛⢂⣛⣉⡽⠿⠚⠩⠾⡇⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠠⡀⠀⠀⢔⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠳⡀⠀⠀⡨⢲⡤⠈⠁⠶⢶⠖⠂⠂⠀⠀⠀⠀⣀⡴⢻⡇⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠲⢌⡶⣪⡶⠋⠀⠀⠀⠀⠀⠉⠑⠒⠶⠖⠈⠉⠁⠀⣹⣧⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢔⣥⠞⠉⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢜⡵⣟⠅⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠐⣒⣦⡤⠴⠚⠉⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠾⢻⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠁⠀⠀⠀⢀⡴⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢸⡛⠮⡳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠁⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠸⣷⢄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⢄⣀⡤⠶⠋⣸⠇
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠮⣥⣀⣀⡀⠀⠀⠀⠀⠀⠐⠒⠊⢉⣁⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠛⠛⠛⠛⢛⣻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⣀⣀⣀⣀⣀⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠋⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⠀⠈⠉⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⡀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⣀⣤⡇⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⡇⠀⣰⠞⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⡯⠀⠀⢸⠇⣀⢤⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠯⣀⡤⠖⣿⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣻⣵⣊⡥⠖⠋⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣭⣿⣿⣟⣯⡥⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣭⣼⣭⣿⣷⣶⣿⣿⡏⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢯⣿⣽⣿⣿⣿⢽⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣻⣽⣿⣏⣽⣿⣯⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⠿⣋⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⣾⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⡠⠚⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⠲⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⠀⠀⠀⣷⣦⣍⣙⡛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣛⣉⣥⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠛⠉⠉⠛⠛⠳⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⠋⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⡰⣻⢟⡵⢚⡗⢀⡞⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢸⠛⠁⠘⠛⣋⡴⠋⣰⠏⠱⣄⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⣴⣶⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣄⣤⠶⠞⢉⣠⠞⢁⡴⠎⡈⠳⣄⠀⠀⣴⠏⠀⠀⠀⢠⣿⠋⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⣭⡵⢞⣫⡴⠛⣡⠀⠘⣣⠞⣁⡀⠀⠀⢀⡿⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⢋⣡⡴⠟⣡⡴⢋⡁⣴⠈⠉⡄⠀⣼⠃⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣅⠘⢋⣥⡾⢋⡼⠃⠀⣸⠇⠀⣿⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣮⡴⠞⠋⠀⢀⡴⠋⠀⠀⣿⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣤⣤⡴⠞⠋⠀⠀⠀⠀⣿⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠈⢷⣄⡀⠀⠀⣀⣴⣾⡿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⣶⣶⣶⡶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁




⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⠿⠻⡿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠖⠒⠒⠚⠛⠛⠛⠛⠛⠒⠒⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠄⢐⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣴⣧⡁⠀⠀⠉⠁⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠉⠉⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣽⠍⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠊⠓⠦⠀⠀⠀⠀⠀⢀⣠⠾⢋⠅⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠲⠦⣀⣀⠀⠁⠒⠢⠍⠀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣄⡀⢀⠀⠀⠀⠂⠤⢀⡀⢐⡤⠋⠉⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⡃⠉⠓⠀⠀⠤⠁⠐⠒⠈⣁⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡻⣟⢷⠀⠀⠀⠀⠀⠁⢀⠐⠂⠤⠬⣩⠏⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠪⡂⡀⢀⠂⠠⢀⡀⠀⠈⠉⣰⠞⠃⢒⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠠⢀⠈⠲⢄⠈⣉⠤⠺⠤⠤⠉⠉⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠓⠲⡄⠷⠀⡒⠁⡉⠉⠒⠒⠰⠖⠤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠂⠀⠈⠀⠀⣸⢗⡤⢶⣄⠀⠀⠀⠠⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡍⠀⠀⠀⠀⠱⠤⣈⠈⠛⠉⠽⠦⢀⠀⢹⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠸⣇⠀⠀⠀⠀⠈⠋⠩⠭⠷⣦⣤⣤⣤⣭⡶⠖⢿⡼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣀⣴⡖⠚⠉⠀⠀⠀⠠⠤⠴⠶⠾⠟⠛⠋⠉⠁⠀⠀⠀⣠⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢌⡿⡿⠏⠀⠠⠤⣀⣀⡀⠀⠀⠀⣀⣀⠀⠤⠀⠀⠀⠈⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠲⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿⠀⠀⢀⣤⡶⠿⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⠶⠾⣭⣭⣿⣛⣛⣛⣛⣛⣿⣛⣿⣛⣛⣛⣛⣛⣛⣿⣯⣭⠷⢶⣛⡃⠀⠀⠀⣿⡀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣝⣛⣳⠶⠶⠾⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠿⠷⠶⣞⣛⣫⣭⠄⠀⠀⠀⣙⣥⠖⢛⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡳⠾⣭⣭⣟⣛⣛⣻⡶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣞⣛⣛⣻⣯⣭⠷⠾⢃⣤⠶⠛⣉⢿⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣟⣳⠶⠾⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⠷⠶⣚⣥⠞⢋⣠⡴⠚⠉⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢯⣭⣟⣛⣻⡶⠶⠶⠶⠶⠶⠾⠿⠶⠶⠶⠶⠶⠶⣻⣵⣾⣿⡷⠟⠋⠁⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⣳⠶⠾⣭⣭⣽⣿⣛⣛⣛⣛⣛⣛⣛⡛⣛⣯⣶⣿⡿⠟⠫⠷⣞⣻⡅⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣭⣟⣛⣳⠶⠶⠶⠿⣯⣭⣭⣭⣭⣥⣬⣭⠷⠶⠶⠶⣞⣛⣻⣭⡷⠆⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⡶⠾⣭⣭⣟⣛⣛⣛⣛⣳⣶⣶⣶⣶⣖⣛⣛⣛⣛⣻⣭⣭⠷⢶⣛⡃⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣛⣳⠶⠶⢯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡽⠶⠶⣾⣛⣯⣽⠄⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣳⠶⢏⣭⣶⣿⠿⣓⡰⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣛⣛⣻⣭⣭⠷⣾⡃⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣵⣾⡿⠟⠭⢤⣭⣭⣽⣿⣿⣛⣛⣛⣛⣻⣿⣯⣭⣭⡽⠷⠶⣞⣛⣯⡅⠀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⡫⢥⣼⣟⣛⣛⡶⠶⠶⠶⠶⠾⠿⠿⠿⠶⠶⠶⠶⢶⣚⣛⣻⣭⡽⢶⠂⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠀⢈⣟⣻⠶⠾⣭⣭⣭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⠷⠶⣟⣻⡅
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠉⠀⠀⠀⢠⡴⠛⠿⣭⣟⣛⣳⠶⠶⠾⢯⣭⣭⣭⣭⣭⣭⣭⣭⡽⠷⠶⠶⣞⣛⣻⣭⡿⠟⠶⡄
⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣄⡈⠛⠶⠾⣭⣭⣿⣛⣛⣛⣳⣶⠶⠶⡶⠶⣶⣞⣛⣛⣛⣿⣭⣭⠷⠶⠛⠃⣠⣿
⠀⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣦⣤⣤⣈⣉⣉⣉⡉⠉⠛⠛⠛⠋⠉⢉⣉⣉⣉⣁⣤⣤⣤⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠈⠁⠉⠉⠉⠈⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡄⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⣰⢟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡾⢫⡾⢣⢎⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⡾⢋⣴⢟⣴⣫⢞⡴⣱⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣤⣴⠶⣛⣭⠾⣫⣴⣿⣿⣫⢟⡽⣡⢏⠎⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠛⠛⠻⠭⢵⣺⡽⣟⣽⣿⡿⣫⣾⣵⣋⣞⡼⣰⢀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣒⣻⠽⣞⣽⣿⡿⣿⣿⣫⢟⡽⣱⢃⠆⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡯⠽⣚⡽⣞⣿⣿⣷⣿⣞⣵⠏⣰⢏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⣵⣚⡽⣞⣿⢟⣵⠟⣡⡾⣣⡾⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢒⣫⠽⠞⣋⣤⠾⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣶⣟⣫⣵⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣙⣛⣟⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣍⣉⡉⠀⠀⠀⠀⠤⠤⢤⣤⣤⠄⠀⠈⠉⠉⢉⣉⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠻⠿⠶⠶⠶⣶⣶⣶⣶⠶⠶⠶⠿⠿⠟⠛⢹⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠸⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠘⣄⡠⡎⠷⡦⣄⠀⠀⠀⠀⣼⡿⣿⣿⡿⢷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢗⡺⠎⠙⠢⣄⠀⢿⣟⠶⢭⣉⣛⣒⡲⠦⠭⠭⠭⠭⠉⠩⢷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠙⠺⣗⠭⢑⣒⠒⠛⠛⢛⡛⠿⠿⠛⣛⣉⠭⣛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠙⠢⣄⡀⠀⠀⠀⠀⠒⠒⣚⣉⣩⡽⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⣤⣀⡙⢿⣭⣩⡭⠽⠟⢛⡩⣵⣾⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣉⣛⣋⠉⠉⠩⠅⢒⣂⣉⠭⠔⠛⣉⣠⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣤⣤⣄⣒⣂⣉⣤⣤⣤⠶⢶⣿⡯⠅⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢯⣭⣉⣋⡉⠉⠉⠁⠀⠈⠙⠢⣌⠛⢷⣄⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡓⠬⢍⣉⣙⣛⣛⡒⠒⠒⠒⠒⠊⢛⣢⣌⡛⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠹⣿⣿⣶⣶⣦⣤⡤⠤⠤⠴⠖⠚⠛⠉⠁⣠⣿⠷⣦⣝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⠤⣀⣉⠙⠛⠛⠿⠿⠿⣤⣤⣴⣶⠶⠾⠿⠛⣁⡴⢿⡏⠉⠒⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠁⠀⢸⡇⠀⠀⠀⠀⠉⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠶⠶⠒⠒⠒⠒⠒⠲⠶⢶⠶⠤⢤⣀⡀⠀⠀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢷⡄⠀⠀⠀⠀⢴⣶⣾⣿⣶⣶⠀⠀⠀⠀⠀⠀⠉⢳⡀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⢶⡶⠤⠤⠤⠤⠥⠬⠤⠤⠤⠤⠤⠤⠴⠶⢶⡿⣿⡇⠸⣆⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠟⣁⣴⢟⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣯⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡧⠚⣡⠴⠋⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⣿⣿⡿⣿⣿⣿⣿⣛⡿⢯⢟⢿⣿⣿⣿⣩⣴⠋⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣩⣽⣽⣷⣵⣫⣟⡿⢿⡻⣽⣿⣶⣿⣿⣿⡿⠀⠀⣠⣶⡿⠓⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣿⣿⣿⡿⣿⣿⣿⣿⣿⠽⣝⣓⣭⣚⡻⠿⢿⡇⠀⣴⠋⢸⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡷⡿⣾⣿⣻⠾⢋⣵⣾⠷⣿⣿⢯⣿⣿⣿⣇⣰⠇⠀⠀⠳⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣺⠿⣿⣿⣟⣥⣾⣷⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢟⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠞⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⣿⣽⣭⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⢀⣠⡿⣿⣿⣿⣿⣿⠾⡿⣿⢶⣿⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⣿⣿⣷⣤⣉⡙⠛⠛⠓⠿⠿⠟⠛⠛⠛⢛⣛⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣤⣬⠉⡉⢙⡛⠓⠒⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⣉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠥⠤⠤⠤⣤⣤⣤⠤⠤⠴⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠋⠉⠀⠀⢈⢢⡏⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠤⣄⡤⠖⠋⠁⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣋⣁⡀⠀⠀⠀⠀⠀⣱⡟⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⡴⠚⠉⣷⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⣡⠖⠋⠁⣠⠏⠀⠀⢀⣠⢾⠋⣿⡄⠀⠀⢀⡞⠁⠀⠀⠀⠀⢾⣀⣀⡴⠋⠀⠀⣀⣠⣤⣄⡿
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⣰⣿⠏⣀⡤⠞⠁⠀⣀⡴⠟⢁⣎⠞⠀⢻⡄⢠⠏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⠞⠁⠀⣀⠼⠙⡆
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠛⠛⠛⠉⠀⣀⣤⠞⠋⢀⡠⠛⠁⢀⡴⠋⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠋⠁⠀⢠⠇
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⣠⡴⢞⡫⢖⡣⡶⠛⠁⣀⠔⣫⢂⢎⣼⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⣿⣐⢄⣒⣀⣤⠶⠞⠋⣕⡪⠕⢊⡥⢊⡠⠔⣋⣤⢔⠕⡡⢊⠞⢀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠈⠉⠉⠉⠁⠙⣶⣈⣉⣠⡤⠾⠓⣉⠥⠐⣩⣾⡿⠕⠋⡠⢊⡴⢣⠂⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣠⣤⣬⡥⠴⠖⣚⣩⠅⠀⣠⡮⠔⢉⡔⡡⠃⣿⠞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡤⢀⣀⣀⣈⡉⠤⣤⠖⠋⠡⢚⠔⡫⠎⣠⢴⢃⡴⢻⣧⡴⠶⠦⣄⠀⠀⠀⠀⢿⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣐⡛⠤⠒⣉⠤⣂⠤⣊⠥⣊⠴⠊⣡⠗⡻⡲⢁⣼⠇⠈⢃⡿⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⠧⠝⣒⣉⡰⠞⢒⣉⠤⢒⡾⠵⣋⠾⣛⣵⠟⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠒⠀⠐⠒⢒⣉⣉⣠⠴⠟⢊⣽⠥⢊⡵⢋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠉⠉⣁⡠⠤⠊⣁⣤⠴⢋⣡⠞⣫⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣯⡥⠤⠖⣒⣩⣾⠷⢚⣩⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡀⠈⠉⠋⠉⣉⣡⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⡶⠶⠞⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠶⠶⠶⠶⠤⠤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠁⠀⠀⡀⠀⠀⠐⠛⠛⠓⠀⠀⠀⡀⠀⣠⠌⣷
⠀⠀⠀⠀⠀⢠⠚⠑⢦⠀⠀⠀⠀⠀⠀⠀⠳⡄⠐⠄⠈⠀⠀⠀⠀⠠⠀⠀⠠⠀⠂⠀⢐⡼⠋
⠀⠀⠀⠀⠀⠘⠀⢠⣶⣧⣀⠀⠀⠀⠀⠀⠀⢿⠠⢀⣒⢒⣒⡀⠲⠤⠀⠂⠒⢒⡂⢁⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⢮⣝⣶⣄⡀⠀⠀⣼⢹⣶⣾⠖⣴⣮⠑⠂⠤⠐⠂⠒⠨⣔⣽
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⠙⠢⣍⡓⠦⣼⡰⠿⡷⣯⣲⡶⣊⠷⢏⣐⡮⠽⣞⢉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠓⢦⣙⠳⢾⣷⣿⣿⣿⣿⣛⠩⠅⢲⠬⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⡿⣶⣬⣛⠾⣟⣿⣆⣀⡴⣄⢃⣤⢼
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣗⣟⣷⣭⣛⣪⢽⣋⢥⣄⡈⣨⠤⢾
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢻⣔⣿⣟⣻⡅⢻⠭⡳⣮⣟⣦⣍⢹
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⣑⡿⣿⠿⡭⢥⣂⠀⠈⠉⠬⠽⠿⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣟⣷⣞⢙⡙⣷⠷⢒⢿⢽⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠝⠭⠻⣟⠟⡭⢿⣷⠲⣾⢉⣅⡓⠿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⡀⠻⢥⣐⡠⠤⠄⢀⣂⠀⡀⣀⣀⡀⠄⠀⢄⣠⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠚⠭⠿⠓⡚⠒⠒⠒⠒⠒⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠒⠒⠒⠀⠀⠀⠀⠒⠒⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠂⠀⠀⠀⠀⡀⠀⢀⡀⠀⠄⠀⠈⠰⠀⠀⠀⠀⠀⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠐⠉⠋⠘⠈⠁⠀⠀⠀⢀⠀⠀⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠉⡀⠛⠀⠀⠀⠀⠀⣀⡀⣀⣀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣿⠳⣶⣶⣦⣼⣥⣈⠀⠀⠀⢀⣤⣾⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠄⡲⢭⢆⢨⣟⠁⠀⠀⠀⢼⡛⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣤⡀⠭⡨⢈⠀⡄⠀⠀⠀⠀⣛⣻⣿⣯⣵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⡼⠲⡔⠁⠇⢉⠀⠀⠀⠀⢀⠤⡽⢿⡞⢿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠥⢂⠬⣐⠠⠉⠀⠀⠀⠀⣸⠀⠩⣿⣟⠿⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠑⠒⠀⠉⠀⠀⠀⠀⠀⡴⠃⠀⠀⠈⠉⠻⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣦⡀⠀⠀⠀⠀⠔⢵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡠⣀⠀⠤⠐⠒⣄⡐⡀⢜⣿⡻⣒⣦⣤⣄⣀⣄⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢟⠾⣤⣈⡑⣒⠒⠢⠬⠌⠭⠬⠒⠞⢂⡚⢩⣷⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⣑⠅⠈⣁⠀⢀⠙⣉⡉⠙⣟⠙⣉⣹⡇⢈⣽⣏⣆⡍
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡆⢸⠃⠬⣓⠆⢤⡀⠠⠄⠠⣯⠀⣿⣿⣇⢨⣷⣿⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠮⡀⠴⠀⠺⢿⡤⢄⣒⡶⢦⣶⣿⣿⣷⢴⣞⡻⠗⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⡀⠀⠀⠉⠛⠗⠆⠯⢯⣿⣻⣿⣷⡾⠯⠖⠙⠂⣰⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⣄⡄⢀⢤⠄⡀⠀⠀⠀⣀⢈⡁⣀⢤⣴⣺⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠓⠐⠊⠓⠒⠓⠚⠛⠋⠉

⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠋⠉⠉⠛⠛
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣤⣤⣤⣤⣶⡿⠟⠉
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁
⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣾⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣀⡉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣤⣤⣄⣀⣀⣈⣉⣉⣉⣁⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣴⢏⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⣡⡆⠀⠀⠘⠋⣽⣭⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⣗⡲⠤⠤⠤⢤⠤⠤⠤⠤⠴⠖⠒⢋⣹⡇⠀⠀⢀⣼⣿⠋⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡓⠦⣍⣛⡓⠒⠶⠶⠶⠶⠶⠒⢚⣛⣩⢽⡇⠀⢀⣾⡿⠁⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡙⠲⢤⣌⣉⣉⣛⡛⠛⢛⣛⣉⣉⣡⡤⢾⡇⢠⣿⠟⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢿⡓⠶⢤⣬⣉⣉⣉⣉⣉⣉⣉⣡⣤⠶⠚⣰⣿⠋⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢦⡙⠳⣤⣄⣀⣈⣉⣉⣉⣁⣀⣀⣤⠄⣼⡟⠁⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣄⠙⢦⣌⠙⠷⣭⣉⠉⠉⠉⠁⠀⢀⣾⠏⡄⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣌⠳⣤⡈⠛⠦⣄⡉⠙⠲⠦⢤⣤⣾⣧⣼⡇⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠳⣄⠙⠲⢤⣀⠉⠛⠲⠦⣴⣿⣥⣤⣼⡇⠀⠀⠀⣠⠴⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⠙⠶⣤⣈⠙⠛⠲⣶⠿⠤⠤⠶⢾⣇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⣤⣤⣄⣀⣉⣙⢓⡾⢧⣤⣤⣴⣾⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⠞⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⣤⣈⠉⠛⠿⠿⢿⣿⣿⣿⣿⣏⣤⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⣀⣴
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠋⠉⠛⠓⠲⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣦⡀⠀⠀⠀⠀⠀⠈⢉⡓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠈⠻⣿⣶⣮⣝⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠀⠀⠀⠉⠛⢷⣤⣀⠀⠀⠀⠉⠛⠿⢿⣦⠉⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⣼⡳⣄⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣍⠳⣬⡙⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⣷⣶⣤⣤⣀⣀⣀⣴⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢧⣙⠳⣬⡙⠷⣬⡙⠿⣿⣶⣤⣀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡛⢦⣙⠳⣦⣙⠳⣬⣙⠳⢦⣍⡛⠿⣿⣷⣶⣤⣄⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⡛⢦⣍⠳⣦⣙⠳⢦⣍⠻⢦⣌⣛⠳⢦⣍⣙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⣌⡛⢦⣍⠳⢦⣍⠻⢦⣍⡛⠶⣬⣙⡛⠶⣤⣍⣛⠳⠶⢤⣭⣉⣻⠃
⠀⠀⠀⠀⠀⠀⠀⣰⡛⠷⣌⡛⢦⣍⠻⢦⣍⡛⠶⣬⣙⠳⢦⣍⣙⠳⠶⣬⣍⣛⠓⠶⠦⣬⠃
⠀⠀⠀⠀⠀⠀⣰⢧⡙⠷⣌⡛⢶⣌⡛⠶⣬⡙⠷⣤⣍⡛⠶⣬⣍⡛⠳⠶⣬⣍⣙⡛⢲⠃
⠀⠀⠀⠀⠀⣰⠻⢦⡙⠷⣬⡙⠶⣬⡙⠷⣬⣙⠳⢦⣭⣙⠳⠶⣬⣉⡛⠳⠶⢤⣭⣹⠇
⠀⢀⣤⠤⣴⣏⠻⢦⣙⠳⣬⡙⠷⣬⣙⠳⢦⣍⡛⠶⣤⣍⡛⠲⢦⣬⣉⣛⠓⠶⢶⠏
⢀⡿⣷⡀⠘⢭⡻⣦⣙⠳⣦⣙⠳⢦⣍⠻⠶⣬⣙⠳⠦⣬⣙⡛⠶⠦⣬⣍⣙⣻⠏
⡞⠀⠈⠻⣦⣀⠉⠲⢝⡳⣦⣍⠻⢦⣍⡛⠷⢦⣍⡛⠷⢦⣭⣙⡛⠶⠶⢬⣭⠏
⠹⣄⠀⠀⠈⠙⠻⣦⣄⡉⠒⠍⡛⠶⣬⣙⠳⠶⣬⣙⡛⠶⢦⣭⣉⣛⠳⢶⠎
⠀⠈⠳⣄⠀⠀⠀⠀⠉⠛⠷⣤⣄⡁⠂⠍⡛⠶⢦⣍⣙⠛⠶⠦⣭⣍⣙⠏
⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣉⡒⠪⠭⣙⡛⠶⠶⢤⣯⣀
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣶⣿⣿⣿⣶⣶⣬⣍⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠨⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠪⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠠⠀⠐⠈⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⠀⠀⠸⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣧⠼⠶⠦⢌⡀⠀⠀⣠⠾⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⡌⠈⠈⠈⠈⠙⢩⠁⠍⠉⡼⠹⠁⠋⢉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠱⠌⠒⠂⡶⠾⠛⠉⠙⠒⠚⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠘⠀⠀⠁⡇⠀⠀⠀⠁⠀⢀⢠⣾⠃⡆⠘⢠⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠠⠀⡀⠃⠀⠀⠀⡀⠀⢸⠸⡇⠀⡇⢠⠈⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠈⠉⠠⠄⠀⢂⠨⠜⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡤⠆⣤⣄⣇⣰⣸⣤⣀⣇⣰⣀⣄⣇⣄⣠⣘⣄⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠐⠂⠀⠈⠀⠀⠐⠸⠇⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠀⢀⣀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠉⠉⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠛⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠸⣖⠀⠐⡂⠈⠜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⠠⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠑⠲⠆⠉⠂⠘⠁⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⣀⣀⣀⠠⢑⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⣤⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⢀⡞⡇⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣼⡐⠦⣄⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⢣⣷⡎⠙⢰⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢣⣿⠟⠁⠀⡿⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣛⣛⣛⡛⠛⠛⠛⠛⣛⣛⡛⣼⠏⠊⠱⣄⡀⠀⡇⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠖⣒⣒⣚⣛⣭⡭⠭⠖⢰⡟⠤⠀⠀⠈⠙⠶⣥⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⠭⠭⠵⠶⢖⣒⣚⣫⢁⡿⣐⡋⠀⠀⠀⠀⠀⡆⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣒⣛⣛⣭⡭⠭⠥⠶⠒⣼⢡⠥⣒⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠖⣒⣒⣚⣛⣭⡭⢱⢃⣒⣫⠥⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡭⡭⠭⠭⠶⣖⣒⣚⣩⡭⠵⣖⣋⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣛⣻⣩⣭⡭⠽⠶⣒⣚⣭⠽⡖⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⣒⣒⣒⡛⡻⠩⠥⠶⣒⣫⠥⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠭⠭⠭⠭⠶⢰⢓⣚⣫⡭⠵⣖⣋⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣒⣛⣛⣩⡍⠠⠬⠶⣒⣚⣩⠭⡖⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠖⠒⠒⠛⢋⣭⠭⠶⠒⠋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠳⢤⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁
⠀⠀⠀⠀⢀⣀⣀⣤⠴⠚⠁⠉⠛⠓⠒⠶⠦⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠿⠿⢿⡿⠿⠿⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠓⠚⠛⠋⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⢾⣇⠀⠀⠀⠀⠀⠀⢓⣿⠶⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣴⠾⣿⡆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠔⠂⠀⠀⠸⣇⣀⡀⠀⠀⠀⣀⣰⡿⠒⠀⠀⠲⣌⠛⢦⠀⠀⠀⠀⠀⢸⣧⣴⢟⣡⡾⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠙⠦⣤⣈⡓⠂⠄⠉⠉⠉⠉⠉⠉⠀⡀⠠⠤⠴⠒⠋⣀⣼⠀⠀⠀⠀⣠⡾⣿⣵⠿⠋⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⠤⠤⠒⢋⡡⢾⠀⢀⣔⣼⣋⣷⠞⢿⡄⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠴⠒⠋⠉⣠⣿⣶⣿⣿⡾⠋⠀⠀⠈⢿⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⢊⢕⣵⣿⠟⠉⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⠻⡒⠒⠂⠀⠀⠀⠀⠀⠐⠢⠤⢤⣄⣤⡤⢚⣵⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢧⡀⠀⠈⠑⠄⡀⠀⠀⠀⠀⠒⠒⠒⠊⡩⢋⣴⣿⠷⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⣄⡙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣫⡴⠛⠉⠀⠠⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠛⠛⠂⠀⠀⠀⠀⣀⠖⣡⡾⢯⣄⣀⣀⣀⣠⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣵⠟⠉⠩⠥⠴⠒⠛⠉⠀⠚⢹⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡀⠀⠈⠐⢄⠀⠐⢪⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠱⣄⠀⢀⠔⣩⠶⠀⠀⠙⠻⣍⡉⠉⠁⠀⠀⣀⣠⠴⢛⣿⠀⠀⣀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⡮⢛⣵⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠉⠀⠀⢀⣠⣿⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⣪⡶⠋⠀⠈⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣙⣲⠶⠶⠚⠋⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡵⠟⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡠⠟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣿⠓⢬⡳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢾⡧⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠦⠤⠤⣀⣠⠤⠞⠁⣾
⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢭⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠉⣁⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡛⠛⠛⠛⠛⠛⠛⢛⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⢀⣱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣦⣴⣶⣶⣶⢤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⢀⣤⠶⠾⠛⠛⠛⢉⣍⠩⣄⢦⡐⠎⠧⠰⠄⠻⠂⠾⠉⠇⠚⠿⠘⣧⡿⣨⣏⠻⣯⢉⣹⠛⠛⠷⢶⣤⣤⣀
⠀⠀⣾⡁⠀⠀⢀⣀⣀⢀⠛⠃⠈⠀⠀⣠⣴⣶⣿⣿⣿⡟⠛⠓⠒⠒⠒⠳⠶⢭⡉⠉⠁⠺⢇⣐⣠⡄⠀⠀⠉⠛⠿⣦⡀
⠀⠀⣿⣿⣦⣄⣀⡀⠛⠉⢳⢀⡄⢠⣀⠙⠛⠛⠿⠿⠿⢿⣶⣦⣤⣤⣤⣤⠤⠴⠛⢀⠀⠀⣤⣍⠁⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⢿⣿⣿⡝⡙⢹⠛⠲⠶⠦⣤⣤⣈⣁⣘⡛⠂⠰⠀⠀⠀⢲⣆⠐⢻⡄⠶⠲⡾⠉⠳⠀⠉⣉⣀⣠⣤⡴⢶⢿⣿⣿⡇
⠀⠀⠀⠙⣿⡟⠻⠾⣦⣤⣀⣀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⢀⣀⣸⣾⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣷⣤⣀⣈⠉⠉⠙⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠖⠒⠚⠛⠛⠛⣹⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣓⠾⠭⢭⣟⣓⣶⣦⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⡏
⠀⠀⠀⠀⠀⢸⣿⣯⣭⣭⣲⣖⡲⠯⠭⠭⠿⣷⣶⣿⣿⣟⣿⣿⣯⢩⣭⣿⣯⣿⣿⡿⣿⣾⣿⣿⣯⣽⣿⣿⣗
⠀⠀⠀⠀⢰⣿⣿⠻⢯⣛⣛⡻⠿⠭⢭⣭⣗⣗⣒⣒⢒⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⢷⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠈⠻⣌⡉⠚⣷⣿⣭⣭⣝⣛⣒⣒⣶⣿⣿⡿⠽⠿⠿⢿⠭⠿⣭⠻⣽⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⡿⣷⣮⣭⣉⣉⡛⠿⢻⣿⣿⣻⣿⣿⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣚⣛⣿⣿⣿⣿⣿⣟⣿⡦
⠀⠀⠀⠀⠀⢠⣿⣿⣟⣓⠾⠭⣿⣿⣟⣻⣷⣶⣶⣯⣥⣥⣭⣭⣭⣽⣿⣯⣭⣭⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⣏⠁
⠀⠀⠀⠀⠀⣿⠿⣭⣽⣽⣿⡿⣿⣳⣷⣒⣶⠿⠿⠿⠿⠯⠭⣽⡭⠭⠽⠿⠿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣾⡿⢣⡟
⠀⠀⠀⠀⢀⣾⣷⣍⠓⣲⠬⠭⣙⣛⣶⣧⡬⠭⠭⠭⣭⣉⣉⣉⣉⣉⣻⣛⣋⣉⣉⢩⣭⣭⠿⠿⠟⣃⣠⣾⣏
⠀⠀⠀⠀⠘⣯⠻⣙⡳⢮⣽⣟⣒⣒⠲⠾⠿⠽⣿⣽⣷⣒⣒⣒⣒⠒⠒⠲⠒⢒⣚⣒⣯⣭⣶⣶⣯⣽⣿⣿⡟
⠀⠀⠀⠀⠀⢘⡿⣿⣭⣙⣛⠻⠿⠿⢿⣽⣿⣿⣷⣶⣶⣍⣡⣽⣿⣶⣶⡟⠛⠻⠛⢿⣷⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣴⡟⣷⢬⣙⣺⠿⠿⠿⠷⣶⣶⣶⣾⣿⣭⡭⢭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣟⣛⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢻⣭⣿⣓⣻⠿⣷⣶⣖⣒⠲⠶⠶⠯⠽⠭⠭⢭⣭⣭⣭⣭⣭⠭⠭⠽⠿⠿⠿⣿⣛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣛⡻⢿⡿⣿⣶⣦⣭⣭⣭⣽⣛⣛⣛⣛⣓⣛⣓⣒⣒⣒⣶⣿⣟⣛⣛⣿⣯⣽⣿⣿⣛⣿⡃
⠀⠀⠀⠀⠀⢸⣟⡛⣭⣍⣛⣒⡢⠭⢭⢭⣍⣉⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⠻⣦⡀
⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣾⡿⠯⣭⣟⣺⣓⣒⣒⣶⢒⣀⠀⠶⠶⠆⠒⠆⡐⣒⣶⣺⣷⣾⣿⢿⣿⣿⣿⣿⡄⠈⢻⣄
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣶⣶⡮⠭⣿⣿⣖⣷⣿⣿⡿⠿⠿⠻⡿⠿⣿⣿⡿⣿⣿⣿⣟⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⢸⣿⣝⣒⠒⠬⢭⣙⣒⣲⡶⠶⠶⠬⠿⠽⠿⠿⠿⠽⠿⠭⠥⠬⠴⢿⣟⣚⣖⣶⣭⠽⣿⣿⣿⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⢨⣿⢶⣬⣭⣍⣛⣓⣲⣾⣭⢭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⢿⢥⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣀⣴⠿⣟⡳⣦⣭⣝⣛⣿⡿⣭⣭⣭⣍⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣋⣉⣭⣭⣽⣷⣾⣿⣿⣿⣦⡀⠀⠀⣾⠁
⢀⣴⠾⠋⠀⠀⠀⠙⠻⢿⣷⣶⣬⣭⣭⣟⣛⣛⣓⣶⣾⠿⠟⠷⠿⠿⣿⢿⣿⣿⣛⣛⣛⣯⣽⣿⣿⠿⠿⠋⠉⠻⣶⣄⢸⡀
⢸⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣽⠛⣇⠀⠀⠀⠀⢀⡀
⠈⣿⣯⣿⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠃⠙⢷⣀⣴⠟⠛⠛⠳⢦⡀
⠀⠈⠻⣿⣧⣄⡀⠈⠙⠓⠶⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠴⠶⠚⣿⣏⣿⣿⡿⠛⠀⠀⣠⡿⣧⣄⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠉⠙⠻⠿⢶⣶⣤⣤⣀⣀⡈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⢀⣀⣠⣤⡿⠟⠛⠁⠀⣀⣴⠾⠋⠀⠀⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠶⣶⣶⣶⣶⣶⣦⣤⣤⠶⠶⠶⠾⠿⠛⠋⠉⠁⠀⠀⠰⠶⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢯⣫⡻⣷⢤⡀⡴⠋⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⡳⣕⣝⢮⡻⡻⣷⣄⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⣻⢽⡾⣯⡳⣝⢿⣮⡻⣝⢦⡀⠀⢈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣝⢿⢿⣾⣗⣯⣗⢿⣿⢷⣝⣮⡺⣷⣽⣷⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣟⢞⢮⡻⡳⣝⣟⣿⣺⢽⣺⣝⡺⢿⣟⡾⣷⣿⣯⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡻⣮⡻⡳⣝⢾⢮⡻⣿⣿⣿⡿⣷⣮⣗⡺⢭⣓⠿⢽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣍⢿⡯⣷⢽⡻⢮⡳⣕⢝⢮⡻⣷⣝⢷⣯⣟⡿⢿⣺⣭⣗⣲⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣝⢮⡳⡙⢾⣽⡿⣗⣯⣛⠷⣝⣿⡪⣷⢝⣮⣳⣯⣝⣺⠭⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣜⢮⣧⡑⣝⢦⡙⢯⣟⣿⣻⢽⣲⣭⣛⡺⢿⣿⣿⣷⣿⣮⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⢯⣳⣝⢿⣮⡳⢝⢮⡻⢿⣺⢽⣺⢿⣻⣯⣷⣶⣭⣝⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢯⣻⣿⣿⢿⣾⣝⡳⣽⣿⣦⡑⢽⡦⣙⢿⡺⢽⣒⠯⣟⣻⢯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣻⡳⣝⢟⢿⣿⡯⣗⣯⣷⣭⣛⠾⣶⣝⠮⣷⣍⡳⣾⣭⣓⣾⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⡳⣝⣝⢮⣫⡳⣝⢟⢷⣽⣻⢽⣿⢽⣶⣭⣝⡺⠿⣿⣦⣝⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣝⡾⣯⡳⣝⢮⣮⡳⣵⣟⢾⣽⣺⢽⣚⠯⣗⣿⣿⣖⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⢿⣲⣝⡺⢷⣝⢮⡪⣷⣝⣿⡻⣝⡺⠭⣓⡾⢽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣾⣿⡿⣷⡮⣝⡻⢮⣷⣽⣿⣿⣝⣿⣲⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⠀⠀⠙⠯⣗⡯⣗⣯⣷⣮⣭⣛⡻⠿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠈⠛⣷⡯⣟⡻⢽⣿⡿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠞⠁⠙⠳⣯⣽⣲⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠛⣳⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣠⠴⠚⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣋⡁⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡴⠊⠁⠀⡤⠚⢻⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢀⡤⢞⣭⠞⠉⣠⠏⠀⢀⣤⠾⢩⢧⠀⠀⡴⠃⠀⠀⠀⠸⣄⡤⠊⠀⣀⡤⠤⢤⡇
⠀⠀⠀⠀⢀⡴⠋⠠⣿⣯⠴⠊⠁⣠⠴⠋⣠⠗⠁⡨⢧⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡠⠔⠋⢹
⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣠⠴⡫⢅⣤⠞⠁⡠⠚⠡⢩⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⢸⣁⣀⣠⣤⠶⠚⣉⠴⠑⡨⣚⠥⢒⣥⣴⢗⠕⡜⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠈⠁⠀⠈⢯⣥⠤⠒⢋⠡⢐⣨⡷⠟⠋⡡⣊⢔⡕⢀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡓⠛⠛⠉⠁⠒⣈⡤⠞⠉⡠⡪⢊⡼⢋⢿⣄⣀⣀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣘⠫⠅⡊⠥⡠⢔⠅⡪⠔⣩⢗⠧⢊⣿⠀⢃⡷⠀⠀⠀⠙⠒⠚⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡔⠈⠊⠥⢚⣋⠥⢒⢞⣑⡵⡫⡽⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠅⠀⡰⠖⢉⡠⢞⡩⢞⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣖⡂⠨⠥⣐⣾⡭⢖⣫⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⠈⠛⠛⣉⣩⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣴⠏⠙⣧⡀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠀⣼⠟⠁⠀⠀⠈⠻⢦⣄⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⢿⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⡇⢸⢿⣄⠘⢷⣄⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣷⣇⠀⡇⠸⡄⢻⢷⣄⠙⠳⠶⣤⠾⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢹⡀⣿⣝⢷⣽⡀⢱⡈⢦⠹⣿⢦⣤⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠁⢧⠈⡇⣿⣌⠑⠯⣻⢶⣷⣄⣳⣌⣳⣌⣉⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣧⡘⡆⠸⡀⢱⡸⣧⡙⠢⢄⣉⠛⠛⠿⠿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⡆⢿⡛⢷⣄⢳⡀⠳⡙⢿⡓⠦⢌⣉⣙⣛⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠸⡄⢧⢸⣏⠲⢝⡻⢷⣄⣙⣦⡙⢶⣤⡤⣬⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⢧⠀⢧⠘⡆⢿⡓⠦⣉⠒⠮⢭⣍⣛⣛⣉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣏⢳⣜⡄⠈⢆⠘⢎⢿⣦⣄⠉⠓⠒⠦⢤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⢝⡿⣦⣈⣣⡈⠳⣝⢷⣭⣓⣒⣶⠟⠁
⠀⠀⠀⠀⠀⢀⣴⠏⠀⠻⣦⣌⡓⠯⢽⣛⣛⣛⣛⣛⣩⡿⠁
⠀⠀⠀⠀⠀⢸⡇⠳⠀⠀⠈⠻⢯⣕⣒⠤⠤⣬⣥⡾⠋
⠀⠀⠀⠀⠀⠈⢷⣄⠠⠀⠀⢄⢀⣼⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠀⠀⠀⠀⠀⢸⣩⠏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠉⠁⠈⣉⠑⢢⣿⡘⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⢌⣻⡇⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠣⠀⠠⢻⣿⢃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠇⢻⡄⠀⠀⠀⢀⢀⡜⠘⢯⢗⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠣⠀⠀⠀⠘⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡘
⠀⠀⠀⠀⠀⢀⡀⠀⠠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡔⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⣀⣠⠤⠄⠨⠈⠨⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⢠⠈⠀⠉⢻
⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣔⣾⡀⠀⠀⠀⠀⠀⢀⣧⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣤⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡏⠁⠀⠀⠀⠈⢱⣀⡀⠀⠀⠀⢸⠦⠤⠤⢤⣤⣤⣤⣤⣤⠤⠤⠤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠒⠓⠒⠒⠒⠒⠒⠛⢚⣻⠀⠀⠀⢸⠓⠒⠒⠶⠶⠤⠦⠤⠶⠖⠒⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣉⣉⣉⣉⣉⣉⣉⣉⣉⢼⠀⠀⠀⢸⣉⡙⠛⠓⠒⠒⠒⠒⠒⠛⠛⣋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⢾⠀⠀⠀⢸⣌⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠒⠒⠒⠒⠶⠒⠒⠒⠒⣻⠀⠀⠀⢸⠦⠤⠤⠤⣤⣤⣤⣤⣤⠤⠤⠤⢼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣙⠛⠛⠛⣋⣉⣉⣹⠀⠀⠀⢸⠒⠒⠶⠶⠤⠤⠤⠤⠤⠴⠖⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⢤⣭⣉⣉⣉⣉⣩⣥⡤⢼⠀⠀⠀⢸⣉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⢋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠲⠤⠤⠤⠤⠤⠤⠴⠖⢺⠀⠀⠀⢸⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡟⠓⠒⠒⠒⠚⢻⠋⠉⠀⠀⠀⢸⠦⠤⠤⣤⣄⣀⣀⣀⣤⡤⠤⠤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⢸⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠖⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢳⠒⠒⠒⠒⠒⠒⠒⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠶⠶⠶⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣭⡛⢯⣿⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣩⣛⢿⣿⣿⣿⡷⠜⣿⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠺⣯⣾⣷⣆⣬⠟⠁⠀⠀⠈⠛⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡺⢣⣮⣴⣄⣻⠟⠁⠠⣭⠝⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢻⣯⣝⣙⣻⡿⠋⠀⠀⠀⠀⠀⠶⢯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣷⣮⣦⣜⣩⡿⠃⠀⠀⢀⣀⡀⠠⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⢛⡟⠋⠀⠹⣄⠀⠘⠲⠝⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⣿⠀⠘⣇⠀⠀⠀⠙⡷⡤⠴⠾⠛⠯⡀
⠀⠀⠀⠀⠀⠀⡴⠋⢶⣄⠀⠀⠘⣆⠀⠈⠓⠶⠤⣤⠞⠀⢰⠂⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡼⠁⢈⢣⣻⣆⡀⠀⠈⠛⠶⠶⠶⠚⡟⠲⠚⠁⢄⡆⠀⡀⢹⡄
⠀⠀⠀⠀⢰⠃⠀⠸⣿⠇⠻⢷⢠⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⡇⣰⣿⠀⣧
⠀⠀⠀⠀⢸⣶⣶⣄⠘⢆⠀⣾⠟⠀⠀⠀⠀⠀⢠⡇⣇⠀⠀⠀⠉⣿⠇⠀⢸⡄
⠀⠀⠀⠀⠀⢹⡇⠈⠙⠲⢤⣸⡇⠀⠀⠀⠀⠀⠸⣤⡼⠀⠀⠀⠀⢿⡤⠖⢿⠁
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣤⡀⠐⠆⠀⣶⠀⠀⡼⠀⠀⢸⢿⣿⠀⠀⠀⠀⣠⢔⡎⢙⣲⡀
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⣷⣴⢄⣾⣉⣻⠙⣶⣾⠿⣛⣛⢿⡿⠶⠶⠾⠿⠿⠶⠶⠶⠮⠗⠋⢀⡾⣿⠃
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⣿⠂⢸⠉⢑⢈⢇⢻⠋⢠⠋⣨⣤⡉⢶⡀⠀⢀⠚⠛⠛⠛⠉⠉⠓⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⡗⢺⣤⡼⢢⠔⡸⠀⣼⠞⢣⠀⠈⠲⣛⡿⣿⣀⣀⣤⣤⣤⣤⡄⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠉⠓⠺⣟⠧⢼⣾⡱⣏⣽⣷⡦⣿⣿⣿⡿⣦⠀⠀⠀⠀⠈⠉⢻⣷⣍⡵⣿⡀⠄⣤⡤⣄⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣝⠿⣶⡬⣤⣍⣷⠶⠾⠿⢳⠦⣤⣤⣤⣤⣀⣹⣼⣻⠀⡓⣄⠀⠀⠀⠀⠈⠉⠁⠐⠒⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣤⣄⣀⣀⣀⡎⣿⠗⠸⡓⠓⣿⡇⠀⠀⠠⠔⡠⠈⠱⢆⠀⠀⣽⣿⡿⢀⠁⠋⢦
⠀⠀⠀⠀⠀⢀⣀⡠⠤⠴⠟⠛⠛⠉⠉⠉⠉⢹⢹⣏⠀⠀⢸⣾⣾⡟⠛⠛⠓⠲⠮⠶⠴⠾⣧⣀⣈⣿⠓⠿⠴⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠒⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠲⢀⠀⠃⠄⠻⣼⣿⠀⢠⡏⢉⣯⠗⠀⠀⠀⠀⠀⣀⣀⣤⡤⠾⠟⠛⠓⠶⠤⣄⡀⠀⠀⠀⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠈⠉⠛⣉⠩⠤⠀⠤⠒⠒⠉⠉⠀⠀⠀⣀⣀⡠⠤⢤⣒⣒⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⣀⣀⠠⠤⠤⣐⣒⣪⡭⠥⠖⠒⠚⠉⠉⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢄⣒⣢⡭⠥⠶⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⠈⣿⣿⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣶⣾⣷⣧⣤⣤⣬⣟⣻⣛⣷⣖⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣿⠀⠀⠀⠀⠀⠀⣩⣽⡿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢀⣀⣤⡶⠟⢋⣹⣾⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣵⡚⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⡇⠈⠉⠓⠿⢧⣂⠿⣻⣾⣿⣿⣿⣿⣺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣇⠀⠀⠀⠀⠀⢠⣿⣿⣶⣿⣿⣿⣯⢽⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠢⠶⠔⠄⢤⣄⣟⣾⣿⣿⣿⣿⣿⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⡇⠐⠢⠌⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⣤⣤⣶⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⡻⢷⣶⢛⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⠉⠟⠳⠦⣣⣹⣿⣿⡿⢿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⣿⠀⠦⠤⠤⠴⣽⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⣀⡀⠀⠀⠀⠺⣿⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⡁⣉⣹⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠉⠉⣋⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠓⠚⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠅⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⣀⡀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡀⢆⠀⠀⠀⢿⣿⣷⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡙⣿⣿⣎⢣⡀⠀⠈⠻⣿⡷⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣾⡻⡿⣌⠳⣌⠻⣿⣆⠙⢦⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢫⠟⢻⣿⣿⡿⢿⣌⠻⣿⣦⣈⢿⣷⣄⠙⠳⣤⣤⣠⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠫⡇⠀⠀⣿⣿⣿⣿⣶⣝⢷⣮⣻⣿⣷⣿⣿⠿⡶⢤⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢳⡀⠀⢷⡹⣿⣿⣿⣽⣦⣙⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠹⣦⡀⠙⠻⢿⣿⣷⣯⣽⣿⣇⣀⣤⠶⠚⠋⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⠻⣦⣄⡀⠈⠉⠉⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡙⠻⠿⠶⢶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠒⠒⠉⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⠄⠴⠄⠐⠂⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣠⠴⣋⡉⢉⡇⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣠⠞⣡⢾⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡴⠞⠁⣸⠿⢿⡃⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⣠⠶⠚⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⢯⣀⡴⠊⠁⠀⠀⠙⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⣡⠖⠋⠉⠙⠲⠦⣄⣤⠴⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡥⠖⠋⠀⠀⠀⠀⠀⢀⡾⠉⠙⣆⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡭⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⣠⠟⠀⠀⠀⠀⠳⣄⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⡽⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁
⠀⠀⢀⣠⠾⠛⠉
⠀⠐⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠐⠒⠲⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⠉⣢⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠑⠒⠶⠒⠚⠁⠀⠀⠀⠀⢀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢍⣓⠲⠤⠤⠄⣀⣀⣀⣀⣀⣀⠠⢤⣴⣚⡭⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡚⡛⡛⠓⠒⢒⣒⣒⣒⣈⣩⣭⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⣀⣉⣉⣛⣛⣒⣋⣩⣭⣵⣶⣞⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣴⡾⣿⠯⠭⠕⠒⠊⣉⣉⡤⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠤⠤⠴⠒⢒⣒⡉⠭⠥⠐⠒⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠻⣯⣭⣿⣗⣒⡲⠒⠛⠮⠭⠭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⠭⠤⠤⠤⠤⢴⣶⣶⣒⠶⠿⠝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⡉⢉⣉⣉⣉⣀⡤⠤⠔⣒⡭⢿⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣷⠤⠤⣤⡥⠤⠤⠤⠔⠒⠊⣉⡥⠔⣻⢤⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠻⢭⣅⣒⣒⣒⣒⣒⡒⠮⠭⢔⣲⠭⠟⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠊⠉⠁⠀⠀⠀⣀⣾⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠪⠽⣓⣒⡒⠤⠤⠤⠤⠤⠤⠤⢔⣒⡺⠽⠉⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣠⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣠⠤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠊⠁

⣠⡄⠒⠒⠒⠀⠘⠋⠉⠀⠉⠉⠉⠉⣭⣍⣙⣛⠛⢛⣋⣩⡭⠉⠉⠉⠉⠉⠉⠙⠁⠐⠒⠒⠒⢤⡄
⠑⠢⠭⠭⠍⠉⣻⣀⣀⣐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡂⣀⣨⡏⠉⠭⠭⠥⠔⠃
⠀⠀⡷⣦⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⣤⠶⠶⠶⢾⠤⠤⢀⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠑⢄⣀⠤⠠⣄
⠀⠀⣗⠒⠒⠀⠤⠤⠤⠤⠤⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠠⠤⠤⠤⠄⠐⠒⣒⣘⣹⠀⠀⠀⠀⢀⠜⣡⠒⡄⡸
⠀⠀⡇⠈⠉⠉⠉⠙⠃⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠘⠉⠉⠉⠁⠀⠀⢸⠀⠀⠀⢠⠎⠀⠙⠺⣤⣃⣀⠀⢀⣀⣀⡀⠤⠔
⠀⠀⣧⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⢼⠀⠀⢠⠃⠀⠀⠀⡠⠃
⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⠀⢠⠃⠀⠀⠀⡰⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠃⠀⠀⠀⡜⠁
⠀⠀⣏⣉⣀⣐⣒⠒⠒⠒⠒⠒⠂⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠐⠒⠒⠒⢒⣒⣀⣉⢉⣹⠃⠀⠀⢀⠎
⠀⠀⡧⠤⠤⠤⠤⠄⠉⣩⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⠉⠠⠤⠤⠤⢴⠃⠀⠀⢠⠋
⠀⠀⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠃⠀⠀⡰⠃
⠀⠀⡇⠤⠤⠤⠉⣩⣉⣉⣈⣉⣛⣁⣀⣀⣀⣀⣂⣀⣀⣀⣀⣙⣋⣉⣉⣉⡍⠡⠤⢤⠃⠀⠀⡴⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣼
⠀⠀⣇⡉⠉⠉⠉⠙⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠋⢡⠃⠀⢀⣎⣬
⠀⠀⣥⣀⣈⣉⣉⡉⠉⠛⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠘⠋⣉⠏⠀⢠⡏⠤⠴
⡴⣘⣓⡤⠤⠄⢀⣀⣈⣉⣉⣉⣉⣉⣉⡁⠉⠉⠉⠉⣁⣈⣉⣉⣉⣉⣉⣁⠏⠀⣰⠥⠤⢤⣒⣓⢦
⠑⠒⠠⠤⠬⠍⠉⢉⣌⣉⣉⣛⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⠛⢉⠏⠀⡴⠩⠭⠥⠤⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠚⣫⣿⣿⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡏⠞⠀⠀⠁⠂⠁⠀⠀⠺⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⡇⠀⠀⠀⠒⡀⠀⠈⡀⠀⠈⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠿⠿⠩⢽⣿⣿⣦⡁⠀⠀⠀⠔⣒⠾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣰⠀⠈⠀⠀⠙⠛⠱⣴⡤⠀⢒⣻⣟⡳⣼⠁⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⡠⣄⣀⣲⣺⠟⣉⡓⡥⢄⢨⠱⢜⣷⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⣿⢯⡛⠙⢟⣩⡄⢠⠉⢋⠢⢄⣠⣦⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡍⠀⠀⠀⠀⠀⠈⠿⣷⣴⡤⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣴⣶⡾⠃⢀⡔⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣷⣤⣶⡛⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⡄
⠀⠔⢀⢰⡖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣷⡿⢿⣿⣿⣷⣶⣶⣶⣶⡿⣿⣟⣷⣿⣿⢷⣤
⠀⢱⠈⣠⠌⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿⡿⣿⢿⣿⣷⣿⣿⡿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⢽⡆
⢀⡠⠛⠃⢴⠄⢄⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣞⣿⣽⣾⣯⣿⣟⣿⢛⣿⣾⣿⣿⣻⣿⣽⣾⣿⠄
⠀⠈⠀⠤⣀⠀⠀⠰⠈⠆⠀⠀⠀⠀⣴⣿⣞⣿⣟⣿⣿⣿⣿⣷⣿⢻⣿⣿⣿⣿⣿⣿⡿⣿⣻⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠲⡀⠀⠀⠢⡀⠀⢰⣿⣮⣿⣽⣹⣿⣿⣷⣯⣻⣿⢿⣟⣾⡷⣿⣿⡻⣿⣻⣿⣭⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠲⣿⣽⣿⡿⣿⣾⣿⣿⣾⣿⣿⡿⢿⠹⣿⣷⣿⣟⣷⡿⣿⣛⣿⢛⣭⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣼⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⣛⣻⣛⣿⣾⣟⡻⣯⣻⣷⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣤⡴⠿⠿⠯⠿⣿⣿⣿⣿⣎⣿⣿⢿⡿⣿⣿⣿⣿⣿⡿⣯⣽⣿⣻⠟⣯⣿
⠀⠀⢀⡀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠚⠿⣿⣾⣿⣿⣿⡿⣿⣿⣯⣿⣿⣿⣿⣽⣻⣾⣟⣿⡟⣻
⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢐⠢⠤⠲⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠁⠛⣿⣩⣿⣿⡿⠿⠟⠛⠉
⠧⡀⠈⠁⠀⠀⠀⠀⠀⠠⡀⠀⡀⢁⠀⠀⠀⠠⠀⠒⠠⠤⢀⣀⣀⡀⠀⠀⣀⠀⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⠴⠖⠒⠒⠲⣄⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠻⢄⣀⣀⣀⡠⠞⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢚⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡆⢭⣉⣁⣒⣒⣒⣒⠒⣒⣒⡒⠩⢍⣒⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⠭⠬⠭⠭⠭⠥⠤⣴⣒⡶⠾⠓⣋⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉⠉⠉⠉⣭⣭⣥⠴⠶⣶⣛⣻⠯⠕⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠟⠛⠓⠚⠋⢉⣉⣠⠤⠔⠚⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢒⣒⣒⣒⣒⣊⣉⢭⠥⠤⠒⠒⠈⣁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⠛⣛⣛⣛⣲⡖⠒⠿⠭⠭⠭⠭⠄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠭⠤⠤⠤⠤⠤⠴⢶⣶⣒⡺⣶⠶⠭⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡉⠉⠉⠉⢉⣉⣉⣀⣀⠤⠤⢒⣪⢽⡦⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⢬⣍⣉⣉⣉⡉⠩⠤⠤⠶⠒⠋⣉⡤⢺⣦⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⣥⣒⡂⠤⠤⠤⠤⠤⣤⢔⣒⡭⠤⣒⡽⠃⠈⡆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⠉⠙⠛⠛⠛⠦⠬⠭⠒⠒⠚⠉⠁⠀⠀⢠⡟⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣕⣢⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⡤⢴⣺⠽⠃⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠨⠭⠭⠭⠭⠭⠝⠒⠒⠋⠉⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠶⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣀⠔⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠁⠲⠀⡀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣠⡀⠀⠀⠀⢠⣮⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⣴⣶⣿⠿⠛⠁⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⠁⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⣷
⣰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⡆⠀⠀⠀⠀⠀⢀⣀⣀⡀
⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⣦⡶⢿⡩⣅⣘⣿
⣿⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠂⠐⠉⠁
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀⣤⣼⣿⣤⡀⠀⠀⣤
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣤⣄⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿
⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣷⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠉⠉⠻⣿⣿⠿⣾⣇⣿⣿⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣿⣧⣿⣇⢸⠤⠔⢢⣦⠄⠀⠀⠀⠀⠀⢀⣼⠟
⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣻⣿⣏⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠻⣯
⠋⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣻⡛⢉⢟⢿⠃⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⢠⣿
⣄⡀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣯⣿⣏⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠟⠁
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⠶⠶⠒⠒⠲⠶⣶⡶⠶⠶⠀⠲⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠛⠛⠒⠚⠂⠀⠀⠀⠀⢠⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣤⣤⠮⠛⠛⣩⠇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣰⢲⠛⠛⣛⣭⣿⠿⠄⠀⠛⠛⠛⠛⠛⠉⠀⠀⠀⣠⠀⠑⠢⢀
⠀⠰⠂⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⣟⠷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣛⠿⠿⠿⠿⢟⣋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⢻⡇⠀⠀⠀⠀⠀⠀⡪⣿⠛⠒⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣴⠟⣿⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢩⡖⠁⠀⡀⠈⠧⣄⣀⣀⣀⣀⣠⡾⠟⠁⠀⠀⠐⡌⠙⣆⠀⠀⠀⠀⠀⣿⣤⢟⣡⡾⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢄⠙⠶⢤⣌⣁⣂⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠒⠉⣀⡴⣿⠀⠀⠀⣠⣾⠻⣷⡞⠋⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠋⠀⠀⠀⠀⠒⠘⣉⡥⠞⡿⢀⣤⣾⣋⡴⠟⠙⣧⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠒⠒⠋⠉⢁⣠⢾⣟⣿⣿⠿⠋⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢉⢕⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⠈⠢⣉⠉⠀⠀⠀⠀⠀⠈⣑⣒⣲⠶⡶⠞⣡⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢦⡀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠈⠁⡠⢊⣴⠿⠛⠋⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠦⣭⣠⣄⣀⠀⠀⠀⠀⠀⢀⠔⣫⡴⠋⠁⠀⠀⠉⣰⣯⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣡⠾⠯⠵⢒⣒⣲⠶⠚⡽⣿⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢄⠀⠀⠀⡠⢚⣵⠟⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢣⡀⠀⠀⢁⠦⣀⠉⠛⢤⣤⠤⠤⠤⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢦⣙⢦⠔⣩⠞⠉⠀⠀⠀⠈⠑⠲⠤⣤⣄⠐⠒⠚⠉⢚⣿⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡠⢜⣵⠟⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣫⡶⡋⠀⠀⠀⠀⠈⠉⠐⠀⠀⠀⠒⠀⠤⢄⣀⣀⡤⠞⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣪⢾⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠒⠒⠚⠉⠉⠀⠀⢀⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡼⠛⠁⢸⡷⣝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⢸⣧⡀⠑⠈⠓⠂⠄⠀⠀⠀⠀⠀⠀⢄⣀⣈⣉⠀⠀⣀⡴⠋⡿
⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠙⢯⣑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠒⠊⠉⣀⣤⠞⠁
⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢲⡶⠶⠶⠶⠶⠶⠶⠶⣶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡤⠤⢤⠤⠤⠔⢦⠀⡇⢀⡟⢻⡆⠀⡇⣴⢻⢻⡟⣦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠣⠦⠾⠤⠶⠭⠼⠀⡇⣸⣁⣀⣇⠀⡇⠈⣛⣛⣛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⡧⠬⠭⠭⠭⠤⡇⢾⣹⣹⣏⡷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣶⠀⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⢀⢭⣭⣭⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣿⡆⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⠻⠼⠼⠧⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡇⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⣤⢲⢲⡖⣦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡟⡇⠀⠀⠀⡅⠈⠀⠁⠈⠀⡇⠙⠚⠚⠓⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠤⠜⣧⠷⠤⣀⠀⡀⠀⠀⢠⢴⠂⡇⢾⢹⢹⡏⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠎⢣⡏⣦⠉⡎⡆⠀⠀⣠⡞⠉⠀⡇⢀⣉⣉⣉⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⡓⢃⠿⣈⢒⡱⠁⠀⡮⣰⠁⠀⠀⡇⠻⣼⣼⣧⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠓⠒⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠀⢀⡉⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢤⡀⢿⡇⠀⠀⠀⣰⣿⢲⡗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣰⣀⠇⢨⡇⠀⠀⠀⢃⡼⠸⣎⣡⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⠀⠋⠀⠀⢉⡁⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣶⠀⣶⠀⣶⠀⠀⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠡⡜⢨⡷⢶⠀⠈⡇⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⢰⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⠀⡟⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠹⡄⢣⠹⡆⠀⢻⠀⠀⠀⠀⢈⠁⠀⠐⡇⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢯⠀⠿⠀⠿⠀⠠⠷
⠀⠀⠀⠀⠀⢳⡈⣆⢳⠀⠸⡄⠀⠀⠀⢸⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢷⠘⡜⡇⠀⡇⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⢧⠱⣹⡀⢸⠀⠀⠀⢸⠀⠀⢰⡇⠀⠀⠘⡇⠀⠀⠀⣾⠀⠀⠀⠀⠀⣶⠀⣶⠀⢲⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠈⢧⢣⢧⠈⡄⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸⠀⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡊⡆⠇⠀⠀⢸⠀⠀⢸⡃⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠈⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠰⠀⠀⠀⠸⠀⠀⢸⡇⠀⠀⠀⢹⡤⠤⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⣧⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠉⠁

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀
⢀⣨⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢰⣶
⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣽⣿⣥⡀⠀⠀⡀⣸⢿
⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣆⠸⡟⢹⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣤⣿⣿⣿⣿⣿⢾⡷⢾⣸⣤⣾⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⣸⣿⠀⢹⡇⢀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⣾⣧⠋⠉⠉⠛
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⣤⡤⠼⠿⠿⠿⠃
⠉⢻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⣿⣿⣻⣿⣿⣿⠋
⠀⢸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣼⣿⣇⣿⣿⣿⣿⡀
⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠁⢄⡠⠀⠠⠉⠙⠲⢤⣀
⠀⠀⠀⠀⢀⠄⠠⡄⠂⠀⠀⠈⢄⠙⠄⢀⡤⠔⢊⠁⠈⣑⢄⡀
⠀⠀⠀⠀⠈⠦⢀⡈⣦⠀⠀⠀⠀⣆⠸⣥⠔⠊⢀⠴⠊⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠈⡄⠛⢤⠎⣥⣀⣤⣀⡤⠀⠬⢆
⠀⠌⠐⠠⢀⠀⠄⡀⠀⠀⢧⠀⠀⠀⠁⢸⠈⢦⠤⠤⠤⠤⠤⠴⠒⠺⡄
⠀⠀⠠⣀⠢⢌⡑⠂⠭⣑⣚⣆⠀⠀⢀⠸⠀⠘⣏⣉⣁⣉⣀⡀⠠⠀⠃
⠸⠉⢀⠏⠏⠒⠤⣍⣒⠦⠤⣙⡄⠀⠸⠀⡇⠀⠸⠤⠤⠶⠀⠐⠀⠀⡀
⠸⡆⡌⠈⠀⠀⡜⢠⠋⢉⡟⠒⢳⠀⢀⠀⡇⠀⠀⣧⠀⠀⠀⡀⢀⠀⡇
⠀⢻⠁⠂⠄⢰⢁⠎⢠⠏⠀⠀⠀⡇⠈⡆⢣⠀⠀⢸⠐⠄⠀⠀⠀⡽
⠀⠈⢦⠀⠀⠇⡜⢀⠎⡠⠀⠀⠀⡇⠐⠘⣄⠳⠄⠸⠀⠠⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠳⡀⠀⠇⡸⡰⢠⠊⠀⠀⢰⠀⠀⠈⠁⠀⡎⠀⠈⡨⠓⢤⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⡱
⠀⠀⠀⠀⠈⠲⢄⣳⢡⠃⠀⠄⠀⠸⠀⠀⠀⠀⠀⣁⠼⠋⠀⠀⠀⠙⢆⠐⢤⡀⠀⠀⠀⠀⣀⠔⢊⡉⠥⠀⠀⠙⠂⠀⣀⠤⠒⢊⣉⠤⠒⠊⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⠄⢤⣧⡤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠑⠒⢒⡪⠕⠈⠀⠀⠀⢀⡠⠴⢊⣉⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢁⠀⠀⣀⣤⣐⣊⠥⠶⠮⠥⠤⠤⠄⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠊⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡩⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠖⠊⢹⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣶⣶⣤⡀⠀⠸⢀⠀⠇⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣶⣶⣮⣄⣲⣲⣷⣴⣶⣶⣾⣿⣿⣿⣗⣦⣸⣿⣿⣿⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡇⣿⣿⣿⣿⣿⣿⢷⣟⣿⣟⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⡇⣿⢿⣿⠛⠛⠛⠷⠿⠿⠿⠿⠛⠛⠻⣿⣿⡿⣿⣿⣿⣿⢻⢇⣿⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠏⡀⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⡿⣧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⡄⢤⣤⡤⢸⢣⣭⠀⠀⠉⠐⠒⠐⠐⠐⠚⠂⠀⣿⣽⣿⣛⣷⣿⣿⣿⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⣈⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣍⣉⣍⣉⣉⣉⣁⣀⣀⣠⣁⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠯⠽⠽⠿⣿⢿⣿⣿⣿⣿⣿⣻⢿⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠸⠛⠀⠀⠘⠿⠃⠀⠀⠀⠙⠁⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⢀⣔⣿⠣⠂⠀⠀⠈⠋⠭⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠈⠁⠠⣴⠁⢂⠉⠀⠀⠐⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣹⠟⠃⠀⠀⣠⠄⠄⠀⢀⡉⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⠒⢔⣅⠄⠀⠀⢀⣀⡤⠊⠽⠿⠛⡃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠋⠁⣠⡤⠖⠛⢿⢄⠈⠀⠀⠐⢒⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣺⡟⠧⡀⠀⠀⠀⡀⠂⣀⣐⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⢤⢜⠋⣲⣇⣦⣄⡀⠀⠀⠀⠀⠙⠿⢅⠈⠀⠆⠀⠀⠚⢁⡲⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣠⠖⠻⢿⣃⠄⡁⠄⠀⠉⢉⣦⠀⠀⠀⠀⠀⠀⠙⠛⠛⠷⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⡟⠠⢾⠷⠉⠁⢀⡀⠀⠀⡠⢴⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢸⠣⢴⢉⠀⠀⠀⢉⣀⠀⠶⠿⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠘⣿⠟⠁⣀⡤⠖⠿⡅⠈⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⢷⣵⣿⠻⣄⠀⠀⠀⠠⠂⣀⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⠻⢄⠁⡐⢶⢶⢞⣑⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠉

⠀⠀⠀⠀⡀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⠿⠿⡿⠻⠿⠿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢟⣭⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣜⠿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣻⣿⣛⣿⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣿⡇⣿⣿⡿⠿⣿⣿⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⢿⣜⣿⡇⣿⢏⣾⢧⣿⣿⣿⣿⣾⣷⣦⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣮⢿⣎⠇⢫⣾⢣⣿⣿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣦⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣣⡻⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣴⡿⠁⢹⣷⣝⡻⢿⣿⣿⣿⣿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢙⡿⠁⠀⠀⢻⡏⠙⠳⣎⢿⣿⢿⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⡾⠁⠀⠀⠀⠀⢻⣄⣀⡾⠈⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠉⠁⠀⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢷⠀⠛⢢⡴⢅⡀⠀⠀⠀⠀⣜⠉⠀⢣⠀⠀⠀⠀⣎⠀⠀⠂⠉⠉⣢⡎⠉⠒⠒⠀⢰⠋
⠀⠀⠀⠀⠴⠊⠉⡑⠂⠀⠀⠀⠀⠈⠄⠤⢈⡀⠀⠀⠀⢿⠀⠀⠀⣧⠀⠀⠀⡎⠉⠉⠁⠀⡝⠓⠃⠄⠐⠒⢠⡞
⠀⠀⠀⠔⠉⠣⡀⢀⠤⠀⢀⠀⠀⠀⠠⣀⡤⠉⠀⠀⠀⠻⠢⠘⠓⠁⠀⢀⠔⡇⠀⠀⠀⠀⢱⠦⠤⠤⠤⠤⣾⠃
⠀⠀⠈⠀⠀⢀⡔⠁⠀⠀⢸⠀⠀⠀⠀⠜⠱⡀⢈⠀⠀⠀⠀⠀⠀⠀⠒⠁⠠⢇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣯⠇
⠀⠀⠘⡀⠀⡜⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⠤⠄⢼⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠈⠂⢆⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⡀⠀⠐⡛⠂⠠⠤⠤⠐⣳⠈⠑⢆
⠀⠀⠀⠀⢀⡀⠙⠒⠀⠀⠐⠋⠓⠒⠊⣁⠀⠀⡠⠄⠠⢄⡀⠉⢶⠀⠀⡔⠉⣀⢀⡈⢢⠀⠈⠉⠁⠀⠀⠉⠁⠔⠒⠁
⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⡐⠡⠀⡎⠀⡆⢰⠄⢱⠀⠈⣦⠀⢄⠐⠇⠸⠁⡰⠀⠀⠄⠀⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠐⠁⠁⠀⠣⡀⠃⠈⢁⡜⠀⠀⠀⠣⠀⠐⠠⠤⠒⠁⠀⠀⠁⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠆⠈⢆⠀⠀⠀⡰⢀⠆⠀⠀⠀⠈⢀⣀⠁⢀⣀⣀⡔⢀⣀⣀⣤⣤⣤⣤⣄⣀⡃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠈⢆⠀⡀⠁⠎⠀⠀⠀⢀⠞⠁⠀⠀⠀⢸⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⢦⠁⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⢠⠤⢄⠀⠀⠀⠀⠀⡔⠉⠉⠑⡄⠀⠀⠀⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠼⢶⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠣⣀⠰⠀⠀⠀⠀⠀⢇⡀⠀⣠⠇⠀⠀⠀⢸⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠈⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢘⣇⠠⠄⠒⠋⠉⠒⠢⢄⠀⠉⢉⠕⠚⠒⡄⠀⢸⠀⢀⠃
⠀⠀⠀⠀⠀⢀⠤⠒⠃⣌⠁⠀⠰⠀⠀⠀⠀⠀⠀⠉⠉⠯⢭⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⢄⣀⣠⠇⠀⢸⣀⣸
⠀⠀⠀⠀⠐⡡⠊⠁⠠⢸⠀⠰⢀⠨⠑⢦⡀⠀⠀⢄⠀⠀⠸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠀⠀⠀⢸
⠀⠀⠀⡌⣰⠁⠀⢀⠀⡜⠀⠅⢪⠀⢀⠀⡇⠀⢀⣠⢴⢙⡞⡧⢤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⡅⢧⣀⠔⣡⠞⠀⠀⠈⠢⠬⠤⠚⠀⡰⠁⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠑⠤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠤⢄⣀⣀⣠⣤⣴⣤⣂⣀⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣒⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣽⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⣿⣣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡟⠹⠟⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡽⠑⠟⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡾⠁⢀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡸⠁⠀⣰⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡼⠁⢠⡞⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣰⠃⠀⡼⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡼⠁⣠⠏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⠃⢀⡞⠁⢀⡞
⠀⠀⠀⠀⠀⠔⠋⠀⠀⣼⠁⣰⠋⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⢰⠃⢠⠎⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡼⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣰⠋⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⣰⢃⡞⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡴⠃⠀⢰⠃
⠀⠀⠀⠀⠀⠀⣰⢧⠞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡼⠁⠀⠀⡏
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠞⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠈⠳⠤⢤⡤⠤⠤⠒⠒⠛⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠑⠤⢤⣤⠤⠤⠖⠒⠚⠉⠙⠓⠂
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⢠⡐⠓⢠⡦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⠒⡋⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠓⣋⡉⣙⣢⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⢀⠀⠅⠉⠠⠀⠉⠂⠀⠀⢀⡴⠋⡏⠉⠉⠉⠑⠒⡒⠒⠒⠒⠒⠛⣉⠠⠒⠁⠀⠀⠀⢸⠒⢂⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢨⡉⠑⠄⠈⡙⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇⠀⠘⠄
⠀⠀⠀⠀⠀⠀⣤⡀⠦⠀⠉⠃⠀⠀⠀⢸⠀⠀⠇⠀⢠⠊⠁⠀⠀⠈⠉⠑⢄⠀⠀⢰⠉⠀⠈⢡⠀⢸⠄⠞⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⢠⠀⣠⣀⠙⠀⠀⠀⠀⢸⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠢⠄⠤⠊⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁⠀⠀⠀⠀⠀⠈⠓⢤⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⢠⡄⣠⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣠⣄⣀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡴⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠳⡄
⠀⠀⠀⠀⠘⠛⠀⠴⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠠⠄⠤⠤⠤⠤⠤⠤⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡔⠀⣀⣀⠀⠀⢱
⠀⠀⠀⠀⠀⠔⠀⠘⢃⡴⠁⠁⠦⡠⡄⠀⠀⠁⠀⢠⠂⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠄⠀⠀⠀⠀⠀⡇⡇⠀⠻⠉⠁⠀⡸
⠀⠀⠀⠀⡀⣀⣠⠴⣋⠶⠃⠀⢀⡽⠁⠀⠀⡀⠀⠈⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠈⠉⠑⢾⣏⠄⢀⡴⠋⠀⠀⠀⠀⠐⢄⣀⠀⠀⣀⡠⠤⠒⠒⠒⠒⠂⢄⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠐⠭⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⠀⠀⡀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣦⣁⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠤⠀⠀⢸⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠨⢙⠻⣦⠑⡀⠀⠀⠀⠀⠀⢀⠀⠱⡀⠀⠀⠀⢸⠀⠃⢀⠂⠀⠀⡠
⠀⠀⠀⠀⢠⣎⣀⡤⠤⠼⡆⠀⠀⠀⠀⢠⠊⠀⠉⠐⠤⣀⠀⠀⠀⠡⡙⣧⠠⠀⠀⠀⠀⠀⠈⠠⠀⡠⠄⠊⠀⠹⠘⠃⠒⠀⢀⠔⠁
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡀⠀⠀⠠⠃⢀⡀⠀⠄⠀⢀⠇⠀⠀⠀⢀⠹⣆⠀⢄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⡀⠀⠰⢄⠀⠁⠀⠀⣀⠃⠀⠀⠀⠀⠀⠡⡙⠷⣦⣌⠖⠀⢰⠟⠥⠤⠄⣀⣀⣀⣀⣀⣀⣀⡠⠧⢴
⠀⠀⠀⠀⠰⠤⠤⠴⠖⠍⠐⠉⠀⠀⠀⠀⠉⠢⠄⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠋⠀⠀⠈⠒⠂⠀⠀⠀⠀⢀⣀⡀⣀⠀⠠⠤⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⡀⣀⣤⡴⠶⢚⡿⢁⡾⢋⣭⠛⠛⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠁⢀⣤⣤⣤⡀⠈⠉⠙⠻⣄⠀⢀⣾⠃⠚⢡⡾⠁⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⠈⠛⠛⠛⠁⢀⣀⣠⡴⠋⠀⣼⠃⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⣼⠃⠀⣰⠏⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣶⠶⠶⠶⣶⣚⣿⣿⠀⣼⠃⢀⣼⠋⣠⠶⠛⠉⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢯⣭⣭⣿⣭⣭⣭⢶⣿⣼⠇⢀⡾⢁⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⢸⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⡲⠶⠶⠶⢶⣚⣻⣿⠏⣠⡟⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⡇⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢯⣭⣭⣿⣯⣭⡭⣿⠏⣰⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⢀⡿⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣶⠶⠶⠶⢶⣾⠏⣼⡋⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣾⠷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠷⣯⣭⣽⣿⣯⣽⣟⡾⠛⠻⣦⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣄⣀⣀⣀⣀⣠⣿⣿⣡⣤⠾⠋⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⣀⣀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡆⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⡖⡗⠚⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠚⠒⠓⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡇⡇⠀⠀⠠⣏⣉⣹⣹⠆⠀⢀⡴⣲⣲⡄⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡇⠀⣠⠤⠤⠤⠤⠤⠤⡀⠸⡸⣄⡸⡹⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡇⡜⠓⠀⠀⠀⠀⠀⠀⣥⠀⠈⠙⠊⠀⠀⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡟⠁⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡾⠿⣦⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡶⣗⡊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠿⠾⠟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⠴⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡲⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡋⣢⡞⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡉⢫⠉⠙⠫⡍⢉⣭⡉⠉⠉⠉⣧⠟⢧⡜⢣⡬⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠚⠋⢀⣀⠀⠘⠦⣡⠗⠀⠀⠀⣏⡵⢏⡹⢮⣨⠾⣉⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⢆⠘⠚⡇⠰⣲⠀⢰⢋⡉⡆⣟⡲⡊⣱⣞⢙⢶⡉⡶⡊⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⢋⢸⠀⣠⡧⠖⠁⠀⠘⠮⣉⠀⡟⣦⡞⢣⡜⠛⣤⠛⣦⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠋⣸⠶⠕⠒⠉⡇⣠⠤⣤⡀⠙⡿⢅⡝⢧⡸⠫⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⢔⣡⣔⣒⣁⣼⣏⣀⣀⡉⠀⠀⡿⣉⡱⢎⣹⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣭⣒⣒⣮⣉⣉⣹⣆⣈⣃⣀⣀⡇⠈⢣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠛⠛⢛⣿⣿⢉⣹⣿⣭⣍⣥⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠙⠉⠉⠁⣀⣤⣤⣤⣤⣤⡤⠤⣴⡶⠾⠛⢛⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣤⣤⢤⡾⠟⠗⠒⠛⠛⠓⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣽⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣯⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡴⣶⠒⠒⢒⣲⣶⣤⣄⣀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⣹⣿⠛⣎⢷⠋⣉⣤⠤⠤⣴⣿⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⠖⠳⡄⠈⣧⠘⡎⢏⢁⡠⠜⠟⠻⠷⠒⠚⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⣠⠴⠚⢳⡀⠸⡆⢱⠘⣇⣀⡤⠤⠒⠒⠒⠒⠲⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠱⣞⢁⡠⠖⠚⣇⠀⢻⠈⡆⢻⢀⣠⡤⠴⣶⠒⠲⢶⡒⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⢦⡈⠻⣄⡰⠚⢻⠀⢸⠀⣇⢸⠉⠙⠦⣄⠀⠙⢦⡀⠙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠳⡄⠙⢦⡀⠙⢶⣹⠆⢸⠀⡟⢸⡗⢤⡀⠈⠳⣄⠀⠙⣆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢦⠘⢦⡀⠙⠢⣄⠈⠓⢿⣀⡇⢸⣧⠞⣹⣦⡀⠈⢳⡀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠳⣄⠙⠢⣄⠈⠙⠦⣄⣈⡽⠋⣠⠞⠁⢀⡷⣄⠀⢳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡏⠳⣄⠈⠑⣦⡴⠚⣁⡴⠊⠁⣀⡴⠋⢀⡼⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⣡⠟⢋⣡⠴⠚⠁⣀⡤⣾⡷⢦⣴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡼⠛⠻⠯⢤⣤⣖⣋⣁⣤⡶⢿⡜⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⣽⣆⡠⠤⠴⠲⣖⣒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣫⠽⠿⠟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢞⡯⢟⣗⠋⠉⠉⠉⠉⠉⠑⢮⡱⣄⠀⠀⠀⠀⠀⠀⢸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠕⢻⡱⣼⣼⡀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡄⠀⠀⠀⠀⠀⠘⡞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡳⠁⠀⠀⠙⢮⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⣧⢷⠀⠀⠀⠀⠀⠀⢳⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⡇⠀⠀⠀⠀⠀⢣⠘⡆⠀⠀⠀⠀⠀⠀⠀⠸⡸⡄⠀⠀⠀⠀⠀⣸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⠀⠀⠀⠈⢧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠳⡙⢄⡀⠀⢀⡠⢃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢳⠀⠀⠀⠀⠀⠀⠈⢆⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠭⣭⡭⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢣⠀⠀⠀⠀⠀⠀⠘⣆⢱⡀
⠀⠀⠀⠀⠀⣀⠤⣶⣶⣒⠼⣆⢧⠀⠀⠀⠀⠀⠀⠘⣆⢳⡀
⠀⠀⠀⢀⢞⡕⠋⠁⠀⠀⠉⢻⢸⣆⠀⠀⠀⠀⠀⠀⠘⡆⢧
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⣸⢸⢏⣆⠀⠀⠀⠀⠀⠀⠘⡌⣇
⠀⠀⠀⠘⡼⣄⠀⠀⠀⢀⡴⣣⠏⢸⣼⠀⠀⠀⠀⠀⠀⠀⠹⡜⡆
⠀⠀⠀⠀⠘⠪⢽⣿⣯⠥⠚⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠑⠀⠠⠀⣴⣦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⡀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⠀⠀⠁⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⣴⣶⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⡿⢿⣿⣦⠀⢻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠀⠀⣸⣿⡏⠀⠀⢹⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣠⡴⠋⠀⠀⣿⣿⣷⣤⣤⣾⣿⣿⡷⠀⠹⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⣀⠀⠀⠻⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠹⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⠋⠁⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠰⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢤⣀⠉⠙⠛⠛⠋
⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢶⠿⡀⠀⠀⠀⣿⣿⣿⣷⣶⠆⠀⠀⣰⣿⣶⣦⣤⣄
⠀⠀⠀⠪⣹⠷⠂⠀⠀⢀⣴⣿⣿⣿⠟⠉⠀⢀⣀⣤⣷⣾⣿⣇⠀⠀⠘⣿⣿⣦⡀⠀⣿⣿⣿⣿⡏⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠟⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠄⠀⠀⣿⠁⠈⠳⣄⠀⠉⠉⠉⣀⣀⡀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠀⠀⣀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠀⢸⡄⠀⠀⠈⢳⣄⣤⠞⠉⠈⠙⢦⡀⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⣤⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⣖⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣽⣿⣿⡆⠀⠀⠀⠁⠘⠁⣠⠴⠶⠾⣿⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣽⣿⣿⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠳⠦⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⡟⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠀⠉⠉⠉⠉⠉⠁⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡠⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⣠⡟⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣼⢏⣼⢏⡼⡴⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡶⢟⣵⢟⣵⢟⡾⣱⢣⢆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣴⠶⣛⣭⡶⣛⣵⣿⡷⣫⣞⣵⣫⢞⡜⡠⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠯⢵⣚⡽⣞⣿⣿⣿⣿⣿⣫⢞⡼⣱⢣⢆⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠩⣗⣺⡽⢟⣯⢾⣿⣿⣵⣿⣾⣵⣫⠞⡼⢠⡿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡯⠽⣞⣯⢿⣿⣿⣿⣿⡿⣫⠞⣡⡟⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣵⣚⡯⢟⣿⢿⣯⠞⢉⣴⢋⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⣺⠭⠖⢋⣡⡾⣋⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣶⣞⣻⣵⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣖⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠨⠉⢹⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣹⣿⡀⠀⠀⠀⠀⠀⢀⢀⣸⣇⠀⣀⣸⣀⠀⢀⣀⣠⠠⡄⡜⠀⣿⣿⣾⣿⣿⠿⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇⠄⣸⣷⠝⢇⢸⣿⣿⣷⣿⣿⢧⣾⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⡿⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣆⠀⠙⢿⣿⣿⣿⣋⣽⡟⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⡿⢿⣿⣿⣿⣿⣆⢠⣠⡑⣾⣿⢿⣿⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⢹⣿⣿⣿⣿⡜⣦⣭⣴⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢨⣿⣿⣿⢿⣷⣿⣿⣯⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡸⠃⠀⢻⣿⣵⣿⠟⣿⣿⣿⣿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣼⡿⣷⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⠍⠉⣹⣿⣉⡅⢸⣏⣉⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣠⣤⣴⣭⣍⡿⠛⠛⢋⣦⣷⡻⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣼⣿⣹⣿⣬⣿⣿⣿⠛⠻⠃
⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠃⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣾⣯⣯⣭⣽⣿⣿⣶⣿⣿⣿⣷
⠀⠀⠀⣸⣿⣿⢿⣻⢿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣷⣶⣶⣯⣤⣤⣼⣼⣽⣿⣿⣿⣿⣿⣿⣦⣄
⠀⣠⣶⣿⣿⣿⣿⣻⣿⣿⡵⠾⢿⣿⣳⣻⣿⣫⢽⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⠿⢃⡤⠟⣿⣯⣿⣿⣽⣷⣿⣿⣿⣟⣷⣶⣿⠿⠛⢾⣿⣽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⢿⠟⢀
⠀⠻⠿⠿⠞⠓⠒⠛⠓⠛⠛⠛⠋⠭⠭⠍⠿⣮⠿⠻⠛⢻⣻⡷⢶⣤⣿⣩⠀⢻⣷⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠯⢍⣿⡿⣿⣿⣿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠠⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢰⣭⣈⣇⣀⠀⠀⠠⠶⠖⣀⣀⣀⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠢⣘⡍⠉⠉⠉⠉⠉⠉⠉⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢸⠹⡉⠉⠉⠉⠉⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⢸⠀⠓⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢸⣗⡀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠀⢸⡈⠁⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⠀⠀⠸⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⠀⠀⠁⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠈⠉⠉⠉⠉⠁⠀⠀⢀⣨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠚⠛⠛⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠤⡀⠀⠀⠀⠀⣄⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠰⢳⠟⠵⠃⠀⡀⠀⠉⣄⠀⠀⠀⠉⣁⠀⠀⠀⠀⠂⠀⠀⠀⠉⣷⠂⠀⠙⠁⠀⢸⢩⣄⡶⠌⠀⠀⠀⣤⠁⠀⠙⠿⣷⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠟⢁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠆⠀⠀⡿⠋⠀⠈⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⢠⣬⣿⠛⠃
⠀⠀⠀⠀⢤⡀⠀⠀⠻⠀⠀⠀⢀⡾⣁⠀⠀⢠⣿⣁⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠐⢺⣿⣷⣶⣄⠀⠈⠀⠐⠀⠀⠀⠀⠙⠀⠀⠀⣾⠟
⠀⠀⠀⠀⠘⣿⣦⠀⢀⣠⠀⠀⠀⠀⠹⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠈⠉⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⣀⣘⢻⣷⣿⠇⠀⠀⣰⣀⡄⠀⠀⣰⠄⠀⢀⠀⠀⠀⠂⠀⠀⠀⣾⡟⠀⠀⠀⠾⠀⠀⡀⠤⠒⠄⠀⠀⠀⠀⠻⠆⠀⠀⠸⣂
⠀⠀⠀⠀⠙⠿⠛⠛⠋⠀⠀⠀⠨⣿⡆⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠠⠄⠀⠁⠀⠀⠑⠅⠀⠀⠀⠶⠀⠀⠀⠀⠙⠃