Yarn Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠉⣸⠃⢀⡏⠀⡿⠀⢸⠋⢹⡗⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣾⠃⢠⡏⠀⣼⠃⢰⡇⠀⣾⠀⣼⠀⠀⡟⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣧⠀⢷⣠⡟⠀⢰⠇⢀⡾⠀⢰⡇⢀⡟⠀⢸⠇⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠹⡆⠈⣿⠀⣰⠏⠀⡼⠁⢀⡟⠀⣼⠁⠀⡿⢀⡟⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡀⢻⡄⠈⢷⡏⢀⡼⠁⢀⡾⠁⣰⠇⠀⣸⡃⣼⠁⢰⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡀⢳⡀⠹⣄⠀⢻⡾⠁⢀⡾⠁⢰⠏⠀⣰⠏⠙⠳⠦⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⢷⡀⠻⣄⠈⣷⠟⠀⢠⡞⠀⣰⠏⠀⣰⠏⠛⠦⣤⣀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⢳⣄⣹⠟⠁⢀⣴⠋⢀⡴⠃⠀⣴⠋⠳⢦⣄⡀⠉⠙⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠟⠁⠀⣠⠞⠁⣠⠞⠁⢀⡾⠛⠦⣄⡀⠈⠙⠓⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⠞⠁⣠⠞⠁⢀⣴⠛⠦⣄⡀⠈⠙⠳⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣾⣁⣀⣠⡞⠛⠦⣤⣀⠉⣛⣶⡴⠛⠁
⠀⠀⣠⠶⠛⠛⠛⠓⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠈⠉⠛⠛⠛⢒⣾⠟⠋⠉
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣤⣤⣤⣤⡽⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠉⠛⠲⠶⠤⠤⠤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠂⠀⠐⠻⠿⣟⣛⣦⣝⠓⢯⣙⣛⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣐⡚⣻⣍⠻⣿⣷⣦⣤⡤⠾⠛⢉⣉⣻⣄⠻⣤⡼⢷⡈⠹⣽⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⢸⣿⠋⢹⣿⣆⠈⢷⣤⠼⠿⠡⠴⠒⠞⠉⠙⠛⠛⢷⡈⢳⣶⠷⣄⠘⣥⠴⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣾⡇⠸⡟⠀⠿⠛⠛⣧⡀⣧⣤⣤⣶⠶⠖⠲⢶⣶⣾⠊⢛⣿⣄⠱⣦⢾⡄⠘⠋⠲⢽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⠿⠿⡇⠀⠇⠀⣿⣿⠟⠉⣇⠈⢿⣿⣿⣷⣦⣠⣤⣟⣁⣴⣿⣿⠟⣤⠈⣏⣉⡄⠘⠷⣦⣌⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⣀⣠⣴⣿⡀⡇⠀⡿⠷⠖⠛⠻⣆⠈⣿⡏⣉⣉⣉⣉⢉⣉⣉⣉⣛⣚⣻⣄⠘⣟⣻⡄⠐⡶⠧⣝⣾⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⣷⣿⣯⠴⠛⠛⢿⡇⠠⣧⡶⠲⣾⠛⢻⡄⠈⣏⢙⡟⠉⢁⣾⣿⠟⠉⣽⣿⡍⢿⡄⠙⣿⣧⠀⢹⡆⣦⢬⣽⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢹⠋⣀⣤⢶⣾⠛⣇⠀⣟⡛⢶⡋⢰⠻⢿⡄⠘⣿⠁⢀⣿⣿⣋⢠⡾⠿⠿⠿⠲⢿⡄⢹⡿⡄⠈⣟⠛⠓⠛⣷⠀⢷⡀
⠀⠀⠀⠀⠀⠀⡀⢈⣽⠀⠘⣿⣿⣆⠜⢁⣼⣧⠐⡎⣗⠀⠙⢿⣷⣤⠷⠀⠹⣏⠈⡁⣈⣁⣀⣤⣤⣤⠄⡶⣾⣇⠘⡿⢷⠀⢹⡈⠀⠁⠉⡇⢸⡷⡄
⠀⠀⠀⠀⠀⠈⡁⢸⠿⢧⠀⠸⣿⣯⣠⣾⣿⣿⠄⡆⢹⣧⠴⠛⠁⣀⣴⣧⠀⠸⣏⠙⣉⣉⣤⣤⠆⠰⠋⠉⠀⢨⡁⢐⣸⡆⠘⢷⣶⠒⣿⣷⠘⡿⣧
⠀⠀⠀⠀⠀⢰⡆⠈⡷⢾⡆⠀⢷⢤⣤⣀⣀⣹⡆⢸⠀⣇⡠⠔⠛⠉⢉⣀⣅⠀⢻⡹⠋⠉⠀⣀⣀⣤⢦⠴⠶⢟⣧⠈⣿⣷⠀⢇⣻⣤⠿⡇⢠⣷⢿
⠀⠀⠀⠀⠀⢸⣷⠀⠹⣧⡻⡀⠈⢿⣧⠀⡸⠟⢣⢈⡇⠈⣦⣴⣓⠙⠫⠦⢼⡆⠀⣷⡶⠻⠿⠿⣿⣷⡓⣶⣤⣼⣿⡀⢴⣾⠀⢘⠋⣀⣴⣡⠾⢋⡼⡇
⠀⠀⠀⠀⠀⠀⠻⣆⠀⢿⠙⠳⣀⠀⢿⡋⢁⣤⣾⡀⢇⠀⢻⣴⠟⠻⢶⣄⡀⠱⡀⠈⢷⣦⣀⣀⠀⢈⣉⣭⠿⠟⢛⡇⠈⣶⠇⢸⡿⠗⠋⣡⣶⡏⢘⡇
⠀⠀⠀⠀⠈⢦⡀⠙⣇⠈⢿⣄⣸⣇⠈⢳⣟⠛⠛⣷⠘⣇⠘⣯⠤⣴⡿⢿⣛⡷⣿⠀⠘⡦⠀⠙⠛⢿⣁⣤⣤⣶⠾⠷⠈⢻⡆⠀⣦⡴⠋⡝⢹⠇⣼⠁
⠀⠀⠀⠀⠀⠘⣷⣄⠘⢧⠈⢿⣋⡼⠷⡀⠩⢷⣄⣹⣦⠸⡆⠘⣆⡀⠐⠈⠉⠉⢙⡇⠀⠹⣶⣄⠀⠀⠉⠻⢥⣀⣠⣼⠀⢺⡇⠀⣿⠃⣰⣷⡌⢠⠇
⠀⠀⠀⠀⠀⡀⠹⣟⢳⣤⡑⣆⠙⢷⣄⣽⣆⠀⠻⣿⣿⡄⠱⡀⠹⣿⣷⣶⣶⣤⡤⣷⡄⠀⠻⠉⠑⣤⣄⡀⠀⠉⠙⠿⣄⢸⣇⠀⠃⠐⠛⣹⢁⠞
⠀⠀⠀⠀⠀⠑⢦⣘⢏⣴⠿⠾⣿⣄⠈⠯⣍⣹⣄⡈⠣⠌⡄⠻⡀⠙⣧⢀⣀⣀⣀⣠⣧⡀⠀⢳⣯⣤⣬⣍⣻⡦⢤⠀⢿⠀⣿⠀⣶⣀⣤⡷⠋⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠶⢴⣿⣿⣷⣦⡈⠫⢟⠳⣄⠀⠹⣆⠙⡄⠈⢏⡈⠈⠋⠁⡈⢳⠀⠀⢻⡟⠋⠉⠁⠀⠀⣨⣿⠀⣟⣀⣿⠟⠋⢀⣠⣾
⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠉⠉⠉⠋⠛⠓⠘⠟⠻⠓⠢⠬⠳⡷⠤⢄⣿⣿⡿⠟⢛⣋⢣⣀⣀⣧⣤⣤⣶⠾⡿⠣⠼⠛⠛⠁⠀⣠⢴⡟⣯⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣝⠛⣍⠓⠲⣦⠶⢤⢤⣤⣁⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡀⣀⣀⣀⣠⠴⣶⠉⠏⣰⣯⣀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⢾⣷⣄⠈⠻⣷⣶⣶⣷⠟⠿⢻⣧⣄⡘⠻⣿⣏⠉⠛⣿⣟⠙⠛⠛⣿⡏⠉⢻⡋⣹⣽⣿⡿⠟⠀⣿⢀⡿⠟⠿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣷⣤⡀⠙⢿⣿⠶⠖⠛⠛⠋⠉⢛⣷⡌⢳⣤⣀⠈⠻⢶⣿⡶⠛⣄⠀⠳⣷⠛⠉⢀⡍⠀⡂⣸⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠤⣤⡝⣢⣀⡈⠳⠶⣴⣶⣶⣟⠉⠙⣷⡀⠻⣮⣝⠶⣤⣀⡉⠙⠛⠧⠤⣽⣶⣾⣿⣇⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢦⣄⡀⠉⠉⠛⠳⠶⠮⢿⡄⠙⡏⠉⠳⠦⠉⣉⡒⠦⠤⠤⠤⠤⠴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣯⣤⣬⣾⣷⣤⡤⠤⠤⠤⣽⣆⠈⠳⣤⡶⣶⣍⡉⠛⢿⠷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠭⡤⠶⠖⠛⠛⠛⢳⣤⠈⢻⢿⣿⠿⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⢀⣴⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⣰⠏⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣿⡿⠯⣤⣤⡤⠭⠭⠽⣿⣾⢏⡀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢟⡵⣫⠾⠭⢭⣙⡒⠮⢍⡛⢿⣍⣾⠋⠼⣿⣷⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢣⢎⡼⠋⠉⠓⠲⠤⣍⡑⠢⢌⡓⢮⡙⢮⣵⡿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣡⢃⣾⣉⠽⠶⣶⣤⣄⡀⠉⠓⢤⡙⠢⣌⠲⣝⢯⣝⣚⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⢣⠇⣾⡭⠖⣚⣩⠥⠴⠒⣛⣲⣤⡀⠉⠢⣌⠳⣌⢣⡹⣮⢕⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⡞⣸⡧⠖⢋⣩⠴⠒⣋⣭⠭⢶⣾⣿⣢⡄⠈⢢⡈⢦⡙⣜⣷⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⠇⡿⠤⣞⣉⠤⠒⢉⣡⠴⣲⡿⢫⠤⠖⠚⢢⡀⠙⣄⢳⡘⣾⣷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⢰⣏⠒⠦⣍⣙⡚⠻⣦⣾⡿⠡⠤⠶⠒⠚⣉⡹⣄⠘⢆⢱⡘⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⢸⣟⢷⡦⢤⣀⣩⡿⢻⡿⠁⠒⠛⠛⠉⠉⣁⣴⠋⣆⠘⡆⢧⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡳⣝⣶⣾⢏⣩⡿⠁⠓⠒⠒⠚⣉⣉⣴⢃⡜⢸⡆⢹⠸⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣬⣾⡟⢭⣳⡟⣠⣉⣉⣉⣉⣉⣥⡔⣡⠎⡰⢃⣿⢈⣿⠏⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡑⢮⣳⡟⣐⠮⢝⣓⠶⢤⡴⣫⠞⡡⢎⣴⣿⣿⠟⣁⡀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⣷⡟⣐⡮⢭⣓⣺⢟⡫⣞⣵⣮⣶⣿⡿⠛⠁⠚⠙⠛⠛⠛⠷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠛⠛⠿⠷⠿⠿⠿⠛⠛⠉⠁



⠀⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠨⣅⣔⡀⠈⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠙⡀⠉⠀⠼⠃⠉⠘⡛⠳⠀⠀⠀⡂⠓⢀
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠘⢠⢇⠀⣧⠸⡬⠭⠄⠊⡠⡘⠄⣀⣠⠤⠖⠒⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣆⠻⠀⢩⣴⣟⣶⣽⠆⢊⠁⠀⣀⠀⠀⠲⠤⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠹⢂⠡⣄⠻⣿⠟⡠⠂⠤⢀⣠⠤⠐⠂⠂⢐⣠⠠⠄
⠀⠀⠀⠀⠀⠀⠁⠀⢀⠈⠀⠂⠀⠃⠡⡈⠶⢁⠎⢀⡀⢀⠈⠀⣠⢤⠼⠚⢉⠠⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡈⠂⠑⣨⠃⠎⡀⣦⡷⠁⠀⠈⠐⠁⠐⠂⠀⠀⠀⠂⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⠁⠀⠀⠀⠎⢠⠈⣿⡻⠇⣁⠔⡡⢢⣒⢦⠆⢆⠶⠆⣠⣁⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣝⣷⣄⣲⠃⡆⢊⠌⠁⡸⠋⡜⠵⢉⠔⢁⠈⠀⡄⣴⡁⡋⢠⠠⡈⢆⠀⠒⠶⣤⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⠠⠀⡇⠎⠀⠠⢁⡞⡰⠚⢁⡴⠁⠆⢠⢟⠟⠀⠁⡀⠀⠀⠄⠃⠬⠀⠀⡙⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠇⠀⠠⠁⡘⠰⠂⠀⣰⠃⡀⠁⣼⠉⠀⠀⠀⠠⠈⠀⠀⠈⣦⠓⠈⠌⠄⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡆⠀⠀⠠⠀⠀⠀⢮⣀⣴⡙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢐⠠⡐⣧⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⢀⡶⠁⠀⠀⢹⣧⣈⠻⠿⠹⢸⡀⠆⠀⠀⠀⠰⠀⠀⠆⡗⣍⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣤⠖⠠⠚⠐⠟⠛⠷⢦⣀⠂⠀⠁⠂⢠⠀⠀⠀⠀⠀⢸⣙⣽⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠐⠀⠐⠨⢓⠈⠀⠁⠀⠐⠂⠌⣉⠲⢀⠀⠐⣻⣶⠀⠀⠀⠠⠄⠀⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠲⠋⠄⠐⠀⠢⠀⡁⠀⠠⠅⠀⠌⡀⠒⠿⢠⠀⡀⢘⡛⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢄⠰⠄⠀⢀⠒⠀⠀⢑⡷⠂⠄⡨⠀⠠⠩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠁⠀⠐⠦⣀⣀⡽⢫⠆⠀⣰⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢭⡑⠟⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢆⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⢎⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢔⣠⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡞⠡⢩⠏⣉⠢⢄⡀⠏⠱⠲⠄⣀⡴⡱⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢩⠁⡜⠠⢁⠣⢀⠂⠍⡢⠈⢳⠀⠂⣠⢋⠾⣄⠀⠀⠀⠀⢀⡠⠔⡪⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠆⠐⢀⢃⠏⠒⠄⠑⠢⡈⠢⣙⠀⡖⡵⠉⡆⠤⡑⣄⢔⡢⠵⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡄⠀⠸⠀⡅⡄⡸⢈⠢⢕⠈⡢⡈⠢⣈⣯⡞⢰⠀⣅⠁⠢⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⠀⡀⢀⠀⢠⠑⡈⢅⠢⡑⢌⠪⠢⣸⠁⠀⠘⠀⠉⢍⠢⣄⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡆⡇⠸⠀⠸⡄⠘⡄⠢⠈⠢⡑⡀⡎⠀⠆⡄⢀⢇⠈⢓⢄⠑⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⠀⠃⠇⠀⠀⢠⠈⢄⠈⢢⠑⢄⠐⣼⠁⡸⠀⠀⡘⢀⢂⠈⣃⠑⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⢣⡀⢠⠘⠀⢠⠑⢄⠑⣄⠑⢄⣰⠂⠠⠁⡄⢠⠣⠈⡀⠄⢙⠢⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠄⢳⡈⡀⠀⢸⡑⢄⠐⢄⠓⣤⠃⠠⠁⡜⢠⠟⡀⠂⢠⢰⢀⢷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢜⡷⡈⠦⠑⣼⡐⡀⠅⢠⡉⢢⡕⠀⡔⢁⠌⡠⠋⠰⢁⢀⡠⠚⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡊⠕⠂⠁⠈⢊⠢⣱⢄⠛⢥⠘⢠⡨⠋⡠⠊⡠⠃⠜⠁⡠⠤⠚⡉⢐⣠⠇
⠀⠀⠀⠀⠀⠀⢀⡠⠔⣊⠥⠒⠉⠀⠀⠀⠀⠀⢀⠝⣡⠊⡑⠢⡙⠣⣤⠎⠠⠞⠐⡓⠈⠁⠀⠂⢁⡂⠔⠁
⠀⠀⠀⣀⠴⣊⠥⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡔⣣⠎⠀⠈⠂⠕⣤⣑⠢⢍⠛⠥⠄⣒⣀⢠⣴⡶⢋
⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠛⠂⠉⠉⠀⠀⠈⠀⠀⠀⠀⠤⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠀⠀⠀⠐⠒⠀⠀⠀⣀⠀⡀⠈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠠⢀⡀⠀⠀⠀⠀⠀⢀⠨⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡈⠄⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠅⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢁⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡔⢲⢶⠂⠤⢀⡀⡠⢊⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠥⠀⠐⠀⡎⡌⠀⡄⢠⠈⠓⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣒⠀⠈⡝⢰⢰⠁⣸⠁⡞⠀⠀⢿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠐⡀⢐⡲⢠⢃⠂⡴⡏⡼⠁⠀⡀⡸⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠣⡰⢈⡔⡡⢃⠊⡼⢁⡅⡀⠀⠰⢀⡋⠀⢸⠀⠀⠀⢀⠴⠚⠉⠉⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠁⡵⢊⠔⡡⠃⡜⠀⡜⢡⠁⠁⠁⠘⠀⠀⠸⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣎⠔⢁⠜⢁⠊⢀⠞⠀⠂⠈⡄⡬⠭⠉⣩⢃⡴⠋⠀⠀⠀⣠⠄⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⢶⠁⠔⢁⠔⠁⠆⠀⠀⡔⡘⠩⢄⡰⠋⠉⠀⠀⠀⠀⠀⠙⢦⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠃⠀⠙⠶⣅⣀⡜⢀⠄⠜⠂⡠⠄⠋
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡠⠊



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣸⣽⡵⠮⠶⠷⠷⠶⠦⣄⠀⠀⠀⠀⢀⡴⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣝⢮⡻⣷⣒⣒⡩⠭⠭⠭⠭⠭⣒⣛⠦⣠⠖⠉⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⡙⢮⡓⢝⠢⣝⠶⣖⣒⣒⣒⣒⣒⢒⣤⠾⢵⡀⠀⢀⣠⠴⠿⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠽⣛⣦⣙⠦⣙⠢⣝⣦⡿⣻⣻⣏⣷⢏⢫⣙⣯⣷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢴⡻⣯⡌⡸⡳⢌⣱⠞⣩⢞⡵⢃⢽⡜⡜⡆⠇⢷⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢣⠱⡜⢧⣇⡷⢞⡡⢊⡵⢋⠔⢁⣴⣳⢱⢹⢸⣸⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣳⡼⢞⣩⠖⣩⠖⣡⠖⣡⣴⣿⡾⣿⡏⡞⡖⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠵⢚⣉⣴⣿⠵⣋⡥⠾⠯⠿⣒⣫⢭⣿⡇⠇⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣹⢝⢛⣩⠵⠿⠭⡭⢭⠭⠭⢖⣚⢭⣿⠱⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠊⠁⠀⠉⠋⢛⣟⡛⠿⠛⠿⡛⠿⡵⠋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⢀⣠⠤⠖⠒⠒⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⢤⣠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢲⠒⡽⠫⢍⡉⠉⠉⠁⢲⠂⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⣰⠃⣠⠃⣼⣙⠲⢄⡈⠑⠦⣄⠀⡆⠈⡆⢛⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⡎⠀⢰⠃⣰⠃⡾⢄⡈⠙⠢⣍⠓⢤⡀⠙⠓⠀⢻⠈⡇⠀⢫⣝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡹⠀⡸⠀⢠⠇⢰⠇⡼⢤⡀⠉⠓⢄⡀⠙⠢⡉⠢⣌⠀⢸⡄⢓⠀⢸⣀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡯⢀⠇⢀⠇⠀⡜⢀⡏⣰⣙⠢⣌⠓⢤⡀⠉⠢⣄⠈⠳⣬⠀⠈⡇⢸⠀⠀⣧⡙⠲⢄⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢰⠇⢸⠀⠸⠀⢠⠃⣼⢁⣧⡈⠑⢦⡑⠦⡉⠢⣀⠈⠳⣄⠈⠀⠀⡇⢸⠀⠀⣇⠈⠑⠦⣈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣸⠀⡇⠀⡇⠀⡘⢀⡇⣸⢇⠙⡷⢄⠈⠳⣌⠲⣌⠣⡀⠈⢲⠀⠀⡇⢸⠀⠀⡿⣗⠦⣀⠈⠑⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⡇⠀⡇⠀⡇⢸⠀⡏⠘⣆⠘⢆⠙⢦⡈⠳⣌⠳⡈⢦⡸⠀⢸⡇⢸⠀⠀⡇⠈⢆⠈⠓⢄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡇⠀⠃⠀⠀⢠⠁⡸⢰⣆⠀⠈⢆⠈⢦⠀⠙⢦⡈⠣⡘⢦⡇⠀⢸⠀⡘⠀⢠⠳⡀⠈⢷⢤⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠃⠀⡃⠀⡀⢸⠀⡇⢸⠉⢦⠀⠈⢣⡀⠱⡄⠀⠙⣄⠙⣾⠀⠀⡏⠀⡇⠀⡸⡄⢱⡀⠈⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠸⣇⠀⡇⠀⡇⢸⠀⡇⢸⣆⠀⠳⡀⠀⠙⢄⠈⠢⡀⠈⢳⠇⠀⠸⠀⣸⠁⢠⠃⠘⡄⢣⠀⠸⣌⠢⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡀⠹⡄⢇⠀⡇⠸⠀⡇⢰⠈⢣⡀⠘⢦⡀⠈⠳⣄⠈⢢⡎⠀⢠⠃⢠⠏⠀⡜⡆⠀⢱⠈⡆⠀⢟⠢⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⡀⠱⣸⠀⢸⠀⡆⢁⢸⠷⣄⠙⢦⡀⠙⢦⡀⠈⢳⠎⠀⢠⠏⠀⡞⠀⡸⡆⠸⡀⠀⡇⢸⠀⠸⢦⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠳⡄⠙⣇⠈⡆⢃⢸⠀⣇⠈⠳⣄⠙⢦⡀⠙⢢⠏⠀⢠⠃⢀⡜⠀⡼⢧⢱⠀⠇⠀⢸⠈⡆⣠⠟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑⣄⠙⢄⠈⢣⣰⠸⡈⡆⢋⠱⣄⠈⠑⢤⣈⡶⠃⠀⡰⠃⢀⠎⠀⣴⢹⡘⡌⡆⢸⠀⢈⡤⠛⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠈⠳⡄⠙⢧⣃⢳⠘⣆⠈⠑⢤⣠⠏⠀⢀⠞⠁⡠⠋⢠⠎⠘⡎⡇⢇⣡⡼⠖⠉⣠⠖⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢄⠈⠢⡀⠙⢾⡆⢫⠑⣤⠞⠁⢀⡴⠃⢠⠞⢁⡔⠁⠀⣀⡷⠟⠊⢁⡠⠔⣋⢴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡑⢤⡈⠳⣄⠈⠺⢟⣀⣀⡔⠉⣠⣴⣁⠴⠯⠐⠒⢉⣀⡤⠔⣊⡡⠔⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣙⠢⣄⠙⠢⣄⡉⠻⢭⣥⡠⠤⠤⠶⠒⢚⣊⡭⠴⠒⢋⣡⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠽⣦⣄⡉⠒⠦⢄⡉⠒⠶⢍⣉⣥⠤⣒⡮⠿⡏⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠚⠛⠒⠒⠒⠉⠉⠀⠀⠀⠈⠓⠠⠤⠭⢉⣁⡒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡩⠶⠂⠲⠶⠦⠬⠭⣭⣍⣛⣒⣒⣒⣒⣒⣒⣫⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣠⠔⣫⠜
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⣋⡩⠭⠥⠶⠶⠶⠦⠬⠭⠭⠭⠭⠭⠭⠭⠥⠒⠋⠁
⠀⠀⢀⡠⠔⠊⣁⠤⠖⠊⠉
⣠⠔⢉⡠⠔⠋⠁
⣷⣶⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠱⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⣄⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠔⠶⠂⣰⠆⠰⢿⠀⣧⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠎⢙⠂⢦⣤⠆⠂⢉⠠⠔⠃⢀⠗⠂⡉⠝⠒⢤⣀⠀⡠⠋⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢉⡐⠂⠤⣈⠔⠃⢀⠠⠒⢁⡠⢸⠇⢸⠒⠀⡁⠤⠒⠀⣩⠟⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠠⢀⡀⡑⠊⠁⠀⠊⠀⡀⠞⢁⠠⡞⠀⡼⠆⠁⢀⡠⢀⡿⠁⣠⢻⠁⣄
⠀⠀⠀⠀⠀⠀⣴⠇⠈⠁⠂⡄⠉⠀⠐⠁⢀⠔⠈⡠⠂⠁⢠⡇⠐⣇⡀⠦⣁⡰⠊⢀⠾⠃⠈⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡼⢀⡀⠀⡐⠂⢀⠄⠀⢀⠐⠁⠀⠊⠀⠠⠂⢀⠀⢈⡉⠐⣠⠜⢁⣴⠛⡄⠀⡆⠀⠀⡆⢱⡄
⠀⠀⠀⠀⣼⠁⠈⠀⠚⠀⡠⠃⢀⠔⠁⠀⠀⢀⠤⠈⠀⡠⠞⠀⡿⢁⡶⠁⡠⠎⠈⢣⠀⠀⠀⡄⠀⠃⠈⢳
⠀⠀⠀⢰⡇⡀⠀⠈⢀⠎⠀⡰⠁⡠⠊⠀⠀⠀⠀⣠⠊⠁⢤⡀⠙⢎⣀⠶⢁⠀⠰⡌⠀⠘⢀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⣸⢀⠠⠁⢀⠂⠀⠜⢁⠌⠀⠠⠀⠀⡠⠞⠀⠁⠀⠀⠙⢦⡀⠙⠄⠀⠂⣄⠀⠀⠀⠸⠀⠈⠀⠀⠈⢱
⠀⠀⠀⣇⣾⠁⡀⠀⢠⠂⢀⠊⢀⠐⠀⠀⠼⠇⠀⠈⢢⡀⠈⢄⡀⠙⠄⠀⢂⠀⠁⠀⠆⠀⠆⠀⠂⠘⠀⠀⣼
⠀⠀⠀⢿⠃⠠⠁⠀⠃⡐⠀⢠⠈⠀⡠⠀⠐⠀⢘⣦⠊⢑⣆⠀⠐⠄⠀⠀⠀⠏⠀⠐⠀⠰⠀⠆⠀⠇⠀⠀⢿
⠀⠀⠀⢸⡄⠂⠀⠀⡰⠀⠠⠃⠀⠘⡃⠀⠀⢀⠞⠁⣴⠏⢰⢦⠀⠈⠄⠀⡟⠀⠀⠃⠐⠂⢰⠀⠐⠀⠁⠸⡏
⠀⠀⠀⠈⣿⢀⠁⢠⠁⡀⠀⢀⠆⠀⠅⢠⡶⠃⣠⠞⢸⠂⣸⠀⠓⡀⠀⡶⠀⠀⠀⠀⠂⠀⠆⠐⠃⡘⠀⢢⠃
⠀⠀⠀⠀⠸⣏⠀⠀⠰⠀⠀⢚⠀⢀⡠⠋⢀⢾⠁⢠⡇⠀⡍⢂⠀⢠⡜⠁⢀⠀⠀⡌⠀⠘⢠⠁⢀⢳⢠⡏
⠀⠀⠀⠀⠀⠘⣇⡀⠃⢠⡄⢸⣀⠞⠁⣴⠃⠰⠀⢸⡇⠸⡇⠜⢡⡐⠀⢀⠂⠀⠐⠀⡌⠀⠆⠀⠆⢠⠟
⠀⠀⠀⠀⠀⠀⠈⢷⣀⠸⠀⡼⠃⣠⠊⠁⠀⠀⠀⢸⠀⣰⠏⠀⠈⠁⡀⠀⠀⠄⠀⡘⢀⠈⢠⠁⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠏⢀⠖⠋⠀⠀⠀⠀⠀⠸⠀⡿⢀⠎⠀⡠⠁⠀⠈⠀⠀⢀⠂⢀⣣⠛⠃⠚⠓⠛⠛⠓⠀⠠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡰⠻⣤⣀⠀⠀⠀⠀⠀⡆⢠⡄⠂⢀⠀⠀⡀⠀⢀⠀⣀⢂⠴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠒⠲⠤⣄⡈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⡴⠋⣠⠎⠀⠀⠀⠉⠐⠲⠤⢤⣀⠇⢸⣃⡀⠁⣀⣈⡀⠴⠆⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠙⡀
⠀⠀⠀⠀⣠⠎⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⡜⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠇
⠀⠀⢀⠞⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠰⠖⠋⢀⡴⠋
⠀⡴⠋⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠤⠐⠒⠒⠈⢉⠁⣠⡄⠒⠊⠁
⣸⡧⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⣁⡀⠤⠤⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣈⠁⠘⠛⠓⠒⠒⠀⠀⠐⠒⠒⠒⠒⠂⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠉⠉⠉⠉⠀⠀⠒⠒⠲⠶⠆⢠⣀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠔⠐⠒⠒⠈⢉⡀⣤⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠤⣽⡏⡽⣶⡒⢂⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠐⣀⣑⣺⣿⣿⢹⢯⣇⠈⢙⣿⣿⣷⣄
⠀⢰⣄⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⢹⡎⠀⠔⠊⠁⠉⠉⠰⣿⡪⢺⣿⠀⠀⠀⠛⣛⣿⡆
⠈⠿⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡾⠀⢀⣴⡶⢿⠿⠿⢻⣿⣵⣿⢾⣟⠟⠛⠛⠛⢛⡗
⠀⠀⠀⠀⠀⢠⣟⣿⣽⣿⣻⣻⡿⣿⣿⣿⣿⠿⢞⠋⠁⠄⠀⠠⡠⠶⣿⢻⠻⢾⣷⣄⣤⣤⣤⣾⣷⣤⢤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢐⣯⢟⣷⣿⣿⣿⣿⣻⡾⣿⣿⡷⠒⡤⠐⠲⢶⣶⣶⣿⣿⢸⣭⣻⣿⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⡴⣤⣀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣽⢾⣿⣿⣿⡷⣿⡿⣯⢿⣿⣧⠘⣶⠈⠐⣠⠫⣿⣿⡟⣼⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⢿⣿⣿⣿⡿⢿⡿
⠀⠀⠀⠀⠀⠀⢾⣩⣿⣿⣿⣿⣽⣽⣯⣿⣵⣿⣦⣬⣄⣾⡿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄
⠀⠀⠀⠀⠀⠀⣹⡷⣿⣿⣽⣯⣾⣗⡴⣿⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⢟⢿⣿⡿⣿⢽⣿⡆
⠀⠀⠀⠀⠀⠀⠨⣷⣳⣿⣿⣵⣯⣪⣟⣳⢿⡞⣷⣟⢽⡞⣱⢯⢾⣜⡵⣿⡼⣯⢾⡵⣏⠶⡳⢕⡹⣝⣷⣯⢟⣽⣯⢿⡷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢿⡵⠳⣿⠾⡵⢿⡾⣷⢯⢿⣽⣵⣯⣎⣿⣱⢏⢿⡴⣽⢾⡩⣹⢾⣫⡟⢜⢻⣱⣟⢿⡱⡫⡦⣽⡻⠮⣿⣿⡯⠁
⠀⠀⠀⠀⠀⠀⠀⡺⡛⣿⢿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣾⢾⣿⣿⡾⢷⡷⣿⢿⡳⣿⢾⣷⣞⢿⣷⡿⣿⣿⣾⣴⣯⣾⣽⣽⣾⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠙⠋⠋⠋⠙⠉⠻⠋⠿⠽⠯⢿⡽⠿⠽⠿⠿⠼⣯⠿⠿⠿⠧⠿⠼⠽⠯⠿⠿⣿⡯⠿⠇

⠀⠀⠀⠀⣀⠠⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡀⡀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠒⠲⠄⠒⠀⠐⠒⠦⠀⡀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡆
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠐
⠀⠑⡄
⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠒⠙⠂⠒⠒⠒⠢⠤⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠤⠀⠀⠀⠂⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡆⢀⠀⠀⠀⠁⡇⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢢⠞⠉⠠⠶⣴⢄⠀⡅⢀⠐⢠⡇⢠⡄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠚⠁⠈⢉⡰⠚⠀⠠⠅⠂⠀⠉⠐⠢⠆⢳⡟⠁⠂⠈⠘⠋⠠⢀⠔⠀⠀⠀⠀⠈⠰⠄
⠀⠀⠀⢀⣀⠀⣠⠤⠚⠓⠲⢤⣀⠀⠀⢨⠀⠢⠄⡀⠀⡇⠀⠀⠀⠄⢀⢠⡏⣀⡀⠀⠀⠀⠳⠉⠈⢂
⠀⠀⠀⠈⢭⡞⢁⠀⠀⠀⠀⡀⡘⢣⡀⡀⠀⠀⠀⠋⠺⡇⠐⢀⠀⠀⠀⠀⠀⠓⣧⡀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠈⠀⠴⠂⠀⠀⠉⢱⢇⢀⣧⠈⠒⠆⠀⡸⢳⣟⠀⠀⠀⠀⠀⠀⠃⠀⠸⣗⢦⡴⠆⠀⢂⠎
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⣿⣿⠏⣹⠠⣼⣀⡴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣁⣉⠷⠔⠁
⠀⠀⠀⠀⠈⠠⡀⢀⠀⢺⠟⠋⢁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⠴
⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⢬⡙⢞⠉⠙⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⡈⢆⠳⣠⠔⠁⠀⠀⠀⠀⠀⠀⠠⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⢠⠟⠉⢢⠱⡀⢰⣄⠀⠀⠀⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⠴⡻⡀⠀⠀⠣⡑⢄⢢⠙⠦⡔⠁⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠠⣄⡤⠊⠁⠀⢇⢣⠀⠀⠀⠙⢮⣓⡵⠼⠤⠔⢛⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⡈⡄⠀⠀⠀⠀⡨⢶⡀⣰⡊⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢰⠀⣀⠠⠐⠒⠒⡇⣇⠀⠀⠀⣠⠋⠳⡝⡻⣼⢆⠀⠑⢄⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡞⠋⠀⠀⠀⠀⠀⡇⡏⠙⠢⡾⠢⣱⣼⡶⡷⠃⠀⠑⢄⠀⠑⣀⠀⠁⠑⠤⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠢
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⣀⠀⠀⣤⠧⠄⡲⠥⢤⣏⣴⡖⠁⠀⠀⠀⠀⠱⣄⠈⠢⡀⠀⠀⢀⡽⠖⠢⠤⣸⡀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⡡⠋⠉⠀⠠⡊⠀⠀⢠⣃⠾⡀⠀⠀⠀⠀⠀⠀⡼⠒⠲⣮⢦⡞⠁⠀⠀⠀⠀⠀⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠱⡴⢩⠏⠀⣱⡀⠀⠀⠀⠀⠀⣇⠀⠀⠈⣣⠈⠒⠤⣀⠀⢀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢀⠜⡾⠧⡀⠀⠸⡱⡀⠀⠀⠀⠀⠘⣄⣠⠊⠀⠀⠀⠀⠀⠻⠉⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣰⣧⠞⠀⠀⠈⠢⣄⣹⡧⠀⠀⠀⠀⠀⡎⢳⠀⠀⠀⠀⠀⠀⠀⠹⡓⠒⠪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⣈⠜⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣧⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠋⠳⡈⢣⡀⠀⠀⣀⣠⣤⡶⠾⣟⢯⢳⠲⡶⣦⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠙⢶⡫⢛⡩⣄⡲⠭⣛⣆⡏⡇⠃⢸⢈⡄⡇⢻⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⢳⡄⠻⣵⣋⠥⠒⣉⠥⢼⢹⣴⢰⢸⠀⠁⡇⠸⢸⠯⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢿⣞⠔⡡⢚⢦⡈⢣⣔⡩⠔⣚⣽⡇⡏⢸⢸⢠⢀⠃⡇⢼⠳⡱⡝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⢳⡙⢾⠕⣡⢞⡳⣄⠙⢶⡩⣒⢿⠀⣿⢸⢸⡟⢸⢠⠁⡮⡱⡝⣷⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⢎⠢⡙⢌⠻⣵⢋⡴⡻⣦⡀⠙⣴⡞⢸⠰⢸⡘⡇⡌⡌⢰⣗⡝⣿⣷⡷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢆⠳⣝⠢⡑⢮⡳⣮⡔⡱⣻⣦⡸⢡⢳⢃⢏⡃⣯⢳⢁⣛⣾⠞⢋⡥⢚⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠣⡑⢬⡑⢬⡳⢍⡒⢽⣾⣵⠟⣵⡧⢣⠏⢌⢘⢿⠏⡼⠥⢒⡨⢕⡪⠕⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡳⣝⠢⣙⠢⣍⠒⢯⡷⢚⡵⡫⢊⣔⣱⡲⡫⢊⠜⣼⣃⠩⠐⣊⠡⢐⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠛⠎⠷⠞⠓⢚⡫⢕⡾⢛⠽⢒⢵⡾⢋⠜⣡⢊⠾⣇⡠⠬⠐⢒⡨⢥⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣉⣉⣉⣉⡭⠤⣚⠥⣊⠥⢊⠕⣩⠔⣡⠞⣱⢯⣦⡈⠳⣮⠍⢐⣢⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⡤⠔⠒⣉⠵⢊⡡⠚⡡⠚⣡⠞⡡⢮⣥⠭⠭⢝⣦⡈⠻⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣖⣉⡤⠖⣉⠴⢋⡠⠊⣡⡚⣇⡩⢔⣒⡭⠵⣊⡽⢦⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠻⠤⢶⣋⠴⢿⣧⠩⠭⠤⠐⠒⠈⠉⠀⠀⠀⠑⢄⣑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁






⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣀⠂
⠀⠀⠀⢰⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢴⠴⠀⠀⠐⠁⠀⠂⠀⠂
⠀⠀⠀⢀⠀⠀⠈⠐⠠⠀⠀⢄⠄⠀⠈⠀⠀⠀⠀⠈⠀⠁⢄⠁⠀⠀⠈
⠀⠀⠀⠈⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠂
⠀⠀⠀⠀⠐⠈⠢⣠⠎⠀⠀⣠⡴⠆⠀⠀⠀⠀⠶⠦⣄⠀⠀⠀⠀⢉⠄
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠁⢾⣶⠀⠀⠀⠀⠀⣡⡄⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⡀⠆⠐⠿⡧⠄⠤⠴⠀⠚⠛⠀⠠⢀⠀⠀⠈⢤⡤⠀⠀⠀⠀⠄⡀⠌
⠀⠀⠀⠀⠴⢟⡄⢀⠔⠀⠀⠀⠀⠀⠁⠀⢀⠐⠁⠀⠀⠀⠀⠀⣯⠀⠬⠙⠁⠰
⠀⠀⠀⠀⠀⠉⠁⠘⠂⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⢀⡀⠐⠃⢀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⢄⠈⠋⠋⠉⠀⡘⠒⠁⠈⠐⠐⠃⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⢉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⡔⠀⢸⣄⠁⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠡⡤⠊⠐⡩⢊⢓⠆⠀⠈⠉⠛⠋⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀⠀⠀⠀⠀⡀⠀⡜⠀⠀⢍⠀⣀⠀⣠⡠⠺⠀⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠉⠳⡀⠀⠀⠀⠁⢸⠀⠠⢨⠀⢀⠜⠡⠀⠀⠈⠀⠀⠏⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⢀⡠⠚⡅⠀⠀⠀⢠⣄⢢⠀⡘⣢⠦⠀⠤⣈⠆⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠤⢤⠟⠀⢿⣷⡀⠉⡀⠄⢀⡄⠀⠁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⠀⠀⡶⠁⠈⢻⠒⠨⠤⠮⠤⠄⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣒⣈⣠⡤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⠀⠐⡄
⠈⢄⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠒⡄
⠀⠈⢆⠀⠈⢆⢀⠠⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡜⡀⠤⢀⡀
⠀⠀⠀⠣⡀⠀⢃⠀⠠⡤⠄⡀⠀⠀⠉⠁⠐⠒⢲⠁⠀⡜⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠑⡄⠀⠑⡦⠼⠀⠀⠉⠒⠠⠄⣀⡀⡆⠀⡜⠀⠀⡠⠊⠉⠉⠓⠒⠀⠠⠤⢀⣀⣀
⠀⠀⠀⠀⠀⠈⢆⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠀⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠑⢄⠀⠀⠀⠀⠠⠚⠲⣿⠀⠀⢀⡜⠀⠀⡝⠉⠁⠒⠂⠀⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠣⣀⡠⠒⠛⡦⡜⠘⣆⠀⡜⠀⢀⡜⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠠⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠⠊⠀⢀⣴⠥⡇⠀⠈⠛⠢⢤⡊⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢠⣴⠭⠄⠠⠼⢦⡀⠀⠀⠀⠙⢆⠀⠀⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠰⡡⠊⠉⢁⠂⠉⠁⠉⠒⠢⣄⣀⠈⢆⠀⠃⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠔⢻⡁⢀⡰⠃⠀⠀⠀⠀⠀⠀⡇⠈⠑⢺⡄⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠇⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢳⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢆⠀⡼⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟⢦⠒⠚⠒⠠⢄⠀⣀⠠⡤⠋⠀⠀⢈⡞⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡇⠀⢣⡄⣀⣀⠔⠉⠀⡰⠁⢀⣀⠤⠾⠒⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡇⠀⠀⠳⡀⠈⠉⠒⠢⢗⡈⠁⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠘⢢⡀⠀⠀⠀⠈⠉⣁⠖⠈⠉

⠀⠀⢀⡶⠚⠋⠙⠛⠃⠂⠀⠀⠉⠉⠀⠉⠁⠈⠀⠘⠛⠛⠛⠉⠛⠛⠃⠀⠀⠈⠉⠀⠀⠉⠀⠀⠐⠊⠛⠛⠋⠙⠛⠙⠂⠀⠀⠈⠉⠁⠉⠉⠁⠀⠀⠒⢦⡄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠐⠠⠀⠀⡀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠁⠂⠶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠈⠁⢀⠀⠘⠀⠠⢄⡀⠈⠉⠓⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠁⢀⣀⠄⠊⠁⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⡀⠀⠉⠓⠢⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣠⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠚⠖⢠⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠰⡀⠠⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⢀⠀⢀⢀⠀⠀⠈⠄⣠⡀⢌⣠⣀⣌⣠⣡⠄⢄⡠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠁⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡎⠀⠀⠀⣴⡀⠀⠀⠀⢀⡴⠀⠀⣠⠎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠋⠀⠀⠀⠀⠋⠀⠠⠀⠂⠀⠀⠀⠁⠀⠀⠄⠊⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠘
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⢸
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠙⢦⡄⢀⣀⡀⠀⠀⠀⠀⡀⣀⠀⣀⣁⣈⣀⣀⣀⣀⣀⡀⣀⠀⢀⠀⠀⠀⢀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⢀⢀⣀⣀⢀⣀⣀⣀⢀⡴⠋
⠀⠀⢀⠀⠀⡀⠀⡀⠈⠉⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⠉⠁⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠉⠁⠀⢀⠀⠈⠉⠉⢉
⣿⡟⣉⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⡪⠀⠀⠐⠀⠀⠀⠀⠀⢐⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠚⡳⡀⠀⢀⠊⠀⠀⠀⠀⢈⣯⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠄⠀⠀⠋⠰⠃⠈⠉⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣤⠀⠀⠀⠀⣤⣀⣀⠠⠔⠈⠁⢠⣤⡾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠀⠋⠹⠧⣤⡀⡀⠀⠀⠀⣠⡤⠿⠋⠈⠀⠈⠉⠛⢤⣦⣀⣀⠀⣀⣠⠶⠖⠉⠁
⠀⠀⠀⠀⡴⠾⠉⣀⣤⠔⠊⠐⢦⡀⠀⠉⠹⠿⣦⡾⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡖⠁⣀⡞⠁⠀⠄⡀⠀⠀⠀⠀⠀⠀⠰⢿⡇⠀⢀⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⢿⠃
⠀⠀⠰⣅⠀⡍⠀⡐⢓⡟⠉⠑⡄⠀⠀⠐⠀⠀⢾⡦⠀⠂⠀⠈⠓⠀⠀⠈⢀⠀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢐
⠀⠀⠰⡅⠀⡗⠀⠈⢛⣣⣄⡐⢆⠀⠀⢸⠀⠐⣾⠇⠀⠀⠀⠈⠵⢀⠀⠀⡤⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⠁⢠⠀⠀⠂⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢆⡀⠙⠤⠀⠀⠀⠈⠁⠀⠀⡠⠓⠀⠐⣿⡆⠀⠠⠀⠀⠀⠹⠀⠗⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠳⡔⠀⠈⠲⠤⠦⠴⠚⠁⢀⣀⣼⣿⡿⢧⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣰⣾⠛⠻⠷⣤⡄⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠈⠀⠲⠄⢤⠀⢠⣠⣷⣾⡿⠏⠉⠁⢀⠉⠉⠿⣦⣄⠀⡀⢀⣀⣴⡖⠉⠁⠀⠀⠀⠀⠈⠉⠿⣤⡄⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠏⠉⠁⣀⣜⠒⠛⠂⢄⡀⠘⠉⡿⢷⣾⠿⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⣠⠏⠉⠀⠀⠀⠀⠀⠑⠲⠄⠀⠸⣿⠀⢰⡎⠀⣀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⠀⠘⠀⢀⡙⠲⠀⢸⡀⠄⠀⢘⠀⠀⢿⠂⢈⠆⠀⢤⡄⠀⠀⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠓⠀⠀⢋⡱⢤⡨⡀⡀⠀⠨⠀⠀⢾⠃⠰⠂⠀⠉⢰⠄⡄⠤⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠈⠄⠀⠙⠋⠟⠀⠇⠀⣠⠴⠀⠀⣾⠁⠈⠲⣆⣄⡀⠀⠃⠀⢀⢠⠞⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠀⠘⠂⠠⠄⢠⣠⠴⠞⢫⣀⡼⠉⠁⠉⠡⠤⠄⡈⠙⠳⠶⠜⠋⠀⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠣⠤⡀⢀⠀⢀⡠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠤⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⣠⡸⠋⠁⠀⠀⠀⠉⠀⣉⢐⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⠁⠀⠠⡆⠀⠀⠀⠀⡈⢁⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢘⡁⣲
⠀⠀⠀⡐⢀⠀⠀⠈⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣭
⠀⠀⠀⠹⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠚⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣖⣤⡄⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢈⡁⠐
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣼⡟⠉⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠒
⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠂⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⣁⠀⠠⠀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⡁⡤
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⣿⣿⣿⡿⠨⣼⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⠀⠀⠀⢀⡁⢠⡄⠄⢀
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣛⣛⡿⠇⢀⠏⢹⢿⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠘⣿⣃⡠⠂⢸⡏⠩⠁⠖
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠙⢫⡂⡦⢰⣟⡂⠀⠀⠀⠀⠊⠀⢀⠀⠀⠀⠀⢿⣯⡖⢲⢻⡍⢸⡍⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠙⣾⠛⢷⠒⣟⢂⠐⡀⠀⢘⢂⡀⠰⠟⠾⠛⠛⠚⠈⠃⠘⠀⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣶⠀⠈⢄⠉⠀⠚⢻⢻⡁⣀⣀⣀⠀⠀⠀⠀⠀⠐⢛⠄⢐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⢸⡏⠙⢶⣘⠀⠀⠀⠀⠀⠀⠉⣩⡯⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⢅⣾⡥⠆⠀⠙⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡼⣁⣾⠚⡞⠛⠀⠀⠰⣶⣄⡀
⠀⠀⠀⠀⠀⣰⠷⠹⢹⡆⠀⠀⠀⠀⠀⣈⢳⣳⢂
⠀⠀⠀⠀⠀⢸⢊⣏⣼⠃⠀⠀⠀⠀⠀⠈⣮⡉⣼⢣
⠀⠀⠀⠀⠀⠀⡘⠙⠑⠀⠀⠀⠀⠀⠀⠀⠻⠌⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠉⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⠈⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣼⣯⣀⡀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠻⣯⡁⢰⡟⠻⣦⡀⢨⡿⠛⠷⣤⣠⡶⠟⠉⠙⠻⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣹⣇⣤⣬⣿⣾⡷⠶⠾⠿⠾⠷⠶⠶⢾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣴⠶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⣀⣀⣤⣤⣤⡶⠶⠶⣶⠶⠶⣶⡶⠶⠶⢶⣶⢶⣤⣤⣤⣸⡇
⠀⠀⠀⠀⠀⢀⣠⡶⠟⠙⣿⠉⠉⠀⢿⡀⠀⠀⠀⣿⠀⠀⠘⣷⡀⠀⠀⢻⡆⠀⠀⢈⣿⠁
⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠘⣧⡀⠀⢸⡇⠀⠀⠀⢿⡄⠀⠀⠘⣷⡀⠀⠀⢿⡄⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⣄⡘⣷⠀⠀⠀⢸⡇⠀⠀⠀⠘⣧⠀⠀⢈⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠈⠻⢿⣄⣀⠀⠈⣿⠀⠀⠀⠀⣹⣧⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠷⠶⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⡇⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠆⠋⡌⣿⡧⠈⢯⢩⣾⠗⡤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠹⡀⠀⠀⢘⣿⡏⠀⢨⣿⡏⠀⠰⡇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡄⠀⢳⠀⠡⠀⢻⡇⠀⣼⡟⢣⠀⣾⠁⠀⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠙⡄⠀⢧⠀⠀⢈⢡⢰⣿⢁⣈⢱⠃⠈⢐⠀⢠⠖⢱⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠎⣸⠀⠀⠀⠂⡆⠀⢄⠀⠈⢢⣿⠗⠉⢀⡇⠀⠇⣸⠾⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠁⠨⣢⠄⠂⢦⠀⠂⡀⣷⡄⠀⢻⣦⠀⡘⠀⠀⢀⠇⠀⠀⣀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠁⠀⠀⠀⠘⡄⠀⠙⣿⣿⡄⠀⠹⣷⠃⠀⠀⡼⢀⡤⢺⠁
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⢀⡀⠀⣛⣠⢡⣿⠿⠽⠆⠄⡿⠀⡀⢀⣞⡅⣦⣼⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡭⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠃⢠⠁⡼⠀⠀⠀⠀⠀⣀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠛⢉⣉⣉⡉⠀⡌⢠⣇⣀⠠⠤⠤⡀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⢏⠉⢹⣿⢿⣿⣧⡉⣵⠂⠠⠃⠠⠤⠤⠤⠤⠮⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣲⣿⣿⣸⣿⠅⠑⡟⠀⠀⠀⠇⠄⠄⠠⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⢸⣿⡂⠀⢁⠀⠀⣐⠁⡠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢹⣿⠋⠐⠞⠓⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠠⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠑⠄⠀⠀⣀⠨⠓⠤⡀
⠀⠀⠀⠐⢄⠈⠢⡀⠀⠀⠰⡈⣖⡉⠔⢂⡠⠒⠉⠢⡀
⠀⠀⠀⠀⠀⠈⠉⠑⡀⠀⠀⢡⠘⢢⣔⣁⣀⣀⣠⠀⠱⡀
⠀⠀⠀⠀⢀⠀⢀⠀⠱⠀⠀⠀⠀⡀⢢⠠⠤⠤⠀⠒⠂⢳
⢐⡀⢢⢄⡂⠌⣐⠊⠩⢧⠀⠀⡄⡇⠈⢧⠤⠤⠄⠀⠀⠈
⢨⠀⠌⠄⠈⡱⢲⠬⣥⣒⣆⠀⠀⠹⠀⠘⡍⠉⠁⠀⠀⢠
⠈⡶⠀⠀⢀⢃⠎⡰⠃⠀⠸⠀⢆⢸⠀⠀⡏⠀⠀⠀⢐⡞
⠀⠐⡄⠀⠀⡜⢠⠁⠀⡀⠀⡆⠈⢆⠣⠀⡇⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠘⢄⠀⠀⢆⢂⠌⠀⠀⡄⠀⠈⠁⠀⡂⠀⡠⠓⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⢀⡇
⠀⠀⠀⠀⠑⠢⢏⣈⠀⠀⠀⡆⠀⠀⠀⡠⠔⠋⠀⠀⠀⠙⢄⠑⠄⡀⠀⢀⡠⠊⠁⠀⠀⠀⠈⢀⠠⠔⢂⡡⠄⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠤⠒⠁⠀⠀⡀⠤⣒⡉⠄⠒⠉⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠀⠀⠒⠒⠒⠒⠂⠚⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠭⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠒⣾⠟⢻⣿⠟⠛⢻⡿⠶⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⡟⠉⡿⠃⠀⣼⠁⠀⢸⡇⣀⣠⣾⡶⠶⠶⠾⠿⠿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⣴⠏⠀⢰⡇⢀⣰⣧⡴⠶⠛⠋⠉⠁⢀⣀⣀⣠⣤⣤⣤⣤⣬⣝⣛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣽⠃⠀⣼⠃⠀⣀⡼⠷⠛⠉⠀⢀⣀⡤⠴⠶⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⡟⠀⢠⣿⡴⠞⠉⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⠶⠶⠶⠶⢦⣤⣤⣙⣷⡄
⠀⠀⠀⠀⠀⢀⡴⢻⡟⠀⠀⡇⠀⢸⡏⠀⠀⢀⡴⠞⠉⠀⠀⠀⢀⣀⠤⠖⠚⠛⠋⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠙⠛⠿⣦
⠀⠀⠀⠀⢠⣾⠃⢸⡇⠀⠀⡇⠀⢸⡇⣠⠾⠋⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠙⠛⠶⢤⣄⡀⠙⣧
⠀⠀⠀⢠⢿⡿⠀⢸⡇⠀⠀⡇⠀⠸⣿⠁⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣧
⠀⠀⠀⡿⢸⡇⠀⢸⡇⠀⠀⣷⠀⠀⣿⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣀⠀⢹⡆
⠀⠀⢸⡇⢸⡇⠀⠀⣿⠀⠀⢻⡄⠀⠸⣧⡴⠋⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⢀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿
⠀⠀⣼⡇⢸⣇⠀⠀⢹⡆⠀⠘⣷⠀⠀⠹⣇⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⠤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠈⢻
⠀⠀⣿⡇⠀⣿⠀⠀⠈⣷⠀⠀⠸⣇⠀⠀⢻⡄⢠⡞⠁⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⣬
⠀⠀⣿⣧⠀⢹⣇⠀⠀⠸⣆⠀⠀⠹⣆⠀⠀⢻⡟⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⢤⣤⣤⣀⣀⠀⠘
⠀⠀⣿⢸⡆⠀⢻⡄⠀⠀⠹⣆⠀⠀⢻⡄⠀⠀⢻⡄⢀⡞⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⣀⣤⣴⠞⠛⠋⠻⣯⠀⠀⠙⢦⣄⡈⠉⠙⠛⢾
⠀⠀⣿⠈⣧⠀⠈⢿⡀⠀⠀⠘⣧⠀⠈⢿⡄⠀⠀⢻⡏⠀⠀⠀⣠⡶⠋⠀⠀⠀⢀⣴⡞⠉⠈⠹⣆⠀⠀⠀⠈⢷⣄⠀⠀⠈⠙⠓⠶⠶⣾
⠀⠀⢹⡆⢹⡆⠀⠈⢳⡄⠀⠀⠈⢷⡀⠈⢷⡀⠀⠀⠹⣄⢀⣴⠋⠀⠀⠀⢀⡴⠋⠀⢻⡀⠀⠀⠙⢧⡀⠀⠀⠀⠈⠳⠶⢤⣤⣤⣤⣤⣼
⠀⠀⠈⣷⠀⢿⡄⠀⠀⠹⣆⠀⠀⠘⣷⡀⠈⢷⡄⠀⠀⠘⢿⠁⠀⠀⢀⣴⣏⠀⠀⠀⠀⢳⡄⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⢹⡆⠈⢿⡄⠀⠀⠘⢧⡀⠀⠘⣷⡀⠀⠻⣦⡀⠀⠈⢳⣄⣠⡞⠉⠹⣆⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠉⠛⠶⠶⢦⣤⣤⣴⣶⣾⠃
⠀⠀⠀⠀⢿⡀⠀⢻⡄⠀⠀⠈⢳⡄⠀⠘⣷⡀⠀⠈⠻⣄⠀⠀⠙⢿⡀⠀⠀⠘⠷⣄⡀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠈⢷⡄⠀⠙⣦⠀⠀⠀⠹⣄⠀⠈⢷⡄⠀⠀⠈⠳⣄⠀⠀⠙⢦⣄⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠈⠳⣦⡀⠀⠉⠛⢦⣄⣀⠀⠀⠉⠙⠛⠓⠶⠶⣶⣤⣶⣤⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⢷⣄⠀⠈⠳⣄⠀⠀⠙⢶⣄⡀⠀⠈⠛⢶⣄⠀⠀⠀⠉⠛⠶⢤⣄⣀⣀⣀⣀⣀⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⠙⢷⣄⠀⠈⠳⣄⠀⠀⠈⠙⠶⣤⡀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣿⣷⣄⡀⠈⠳⢦⣄⠀⠀⠈⠙⠷⣄⡀⠈⠙⠳⠶⠶⠶⣶⣶⣶⠞⠛⠁
⠀⠀⠀⠀⣀⣤⠞⠛⠿⠶⣦⣄⡀⠀⠀⠈⠉⠛⠛⠻⠶⣦⣌⣷⣦⣀⣀⠀⠈⠙⢶⣦⣤⣤⣴⡶⠛⠉
⠀⢀⣴⠞⠉⢀⣤⠶⠶⠶⣤⡈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⣿⠻⣿⠋⠁⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠛⠛⠓⠶⣤⡀
⢠⠟⠁⣠⡾⠋⠀⠀⠀⠀⠀⠙⠶⣄⡈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣼⠀⠀⠀⣀⡤⠖⠋⠉⣀⣠⣤⣴⣶⣦⣤⣄⠀⠹⣆
⣼⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠈⠙⠲⣤⣀⠀⠀⠀⢀⣠⡴⢟⣡⡾⠋⣠⡴⠛⠁⢀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹
⣿⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣉⣛⣛⣋⣉⣥⠶⠛⣡⡴⠛⠉⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢉⣀⣴⠞⠉⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣰
⢻⣄⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠁⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣴⠏
⠀⠙⠷⣄⡈⠙⠳⠦⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠖⠛⠋⢉⣀⣤⠶⠛⠁⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠞⢋⣡⡴⠞⠁
⠀⠀⠀⠈⠛⠷⠶⠶⢤⣬⣅⣀⣀⣀⣀⣀⣤⣤⡤⠶⠞⠋⠉⠁⠀⢀⣠⠶⠚⠋⠉⠉⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⡴⠋⣁⣤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⣭⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⠀⠙⡿⠗⠲⢲⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢹⣿⠷⢾⣶⣶⣾⣿⣿⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡘⣷⡀⠀⠀⠀⠀⠀⠰⢄⡲⣭⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢷⡀⠀⠀⢀⣴⠟⠲⣽⣿⣿⣿⡄⣿⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⣦⣀⣾⣿⣦⣀⡀⠑⠫⣛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣶⣤⣙⡻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⣏⡿⠸⡷⢈⠛⠛⢻⣟⠿⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡿⣿⠁⠄⠀⠘⠀⢀⠏⠉⢳⣌⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⡾⣰⠃⢀⣤⣴⣶⣶⣴⣄⠀⠀⠙⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠞⠁⠏⢠⣾⢻⣿⣿⠟⢿⣿⣷⣤⡀⢿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠚⠀⡼⠀⣿⣿⠀⢿⣿⠀⢰⣿⣿⣿⡽⠜⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣴⠋⠀⠀⢠⠀⢠⣿⣿⡇⠘⣿⡄⢸⡿⣿⣿⣧⡚⢿⣿⣿⡿⣿⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠘⠇⠀⠀⢠⡄⠀⣸⣿⣿⣿⡄⢸⡇⣾⣿⡏⢿⣿⡇⠀⠹⣿⣧⡹⣧⠀⠙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡇⠀⢠⠟⠀⣰⣿⣿⣿⣿⠷⢼⣷⣿⣿⡀⢸⡟⣧⡀⠀⢻⣿⢿⢿⣷⡀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠂⠀⣾⢱⣿⣿⣿⡟⠀⢸⣷⣿⢻⡇⠘⣧⣿⣦⡀⢸⣏⠈⢂⡙⣿⣆⢹⣿⡄
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⢜⣧⠀⣿⣿⡙⢷⡌⣿⡄⠀⠱⡸⢿⣿⡿⣧⡀
⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⣾⣿⠇⠘⣿⠀⣿⢿⡇⠀⢻⠛⢷⣤⠀⠘⣼⣿⡅⠹⣷
⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢰⣿⣱⣿⣿⣿⣿⣿⣷⠀⣿⣿⠀⠀⣧⢀⣿⠘⣧⠐⠘⡀⠀⠙⣷⡄⠘⣿⣇⠀⣿⡆
⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⠀⣠⡾⢋⣿⣿⣿⣿⣿⣿⣿⡆⢸⡇⠀⢰⠇⢸⡟⠀⢹⡆⠀⢁⠀⠀⠈⣿⡄⢸⣿⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠛⠶⢦⣾⣏⣴⣿⣿⡿⢹⣿⣿⣿⣿⢷⣸⡏⠀⢿⠀⠀⡇⢠⠀⣷⠀⠈⣄⣀⣀⣘⡇⢀⣷⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣷⣿⣿⣹⣿⡏⣼⠉⣷⠀⠀⠀⠀⣷⣶⣾⣿⣧⡀⢻⡟⠛⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⠿⠟⢻⣄⡿⠂⢹⡷⠶⠾⠾⠟⠉⠉⠛⠛⠛⠛⠁⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢴⠾⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣋⣉⣋⣉⣉⣩⣏⣉⣽⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠴⠒⠒⠛⠉⠉⠙⠲⡖⠚⠛⡟⠲⢤⣀
⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡧⠤⢤⡿⣦⣤⣈⣙⣲⣄
⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠉⢇⣀⡠⠤⢼⣅⣀⣀⣀⠀⠉⠉⡇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠉⢁⣘⡠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠓⢦⣀
⠀⠀⢀⡜⠢⣄⠀⠀⡰⠋⠁⣀⠽⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠴⠖⠻⡄
⠀⠀⢸⡁⠀⠀⠙⠲⣇⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠶⠒⠒⠛⠉⠉⠁⣀⣀⣀⣤⠤⠤⢼⠁
⠀⠀⠀⣳⢄⡀⠀⠸⠀⢹⠲⣄⡀⠀⠀⠀⣠⠴⠒⠋⠉⢁⣀⣀⣤⠤⠴⠒⠒⠛⠉⠉⠉⣀⣀⣤⠤⠖⢺⡄
⠀⠀⢠⡇⠀⠙⠲⣴⠀⠀⠀⠀⠙⠦⣄⢰⠃⠀⠖⠚⠉⠉⢁⣀⣀⣀⡤⠤⠖⠒⠛⣉⣉⣉⡤⠤⠴⠖⢺⡀
⠀⠀⠀⠳⣀⠀⠀⡜⠙⣶⣄⡀⠀⠀⠀⢙⡷⠲⠒⠚⠛⠉⢉⣉⣠⠤⠴⠖⠒⠛⠉⠉⣀⣀⣤⠤⠴⠶⣏
⠀⠀⠀⠀⠈⠓⢦⡇⠀⡇⠀⠉⠲⢤⡀⢸⠀⠀⠀⠒⠛⠉⠉⢁⣀⣠⡤⠴⠖⠚⠋⠉⢁⣀⣠⡤⠤⠖⢯
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣇⠀⠀⠀⠀⠈⢛⡷⠤⠶⠖⠒⠛⠉⠉⣁⣀⣤⠤⠶⠒⠚⠋⠉⠀⢀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⢸⠀⠀⣤⠤⠶⠒⠛⠉⠁⣀⣀⣀⡤⠤⠶⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣦⣀⣤⠤⠶⠒⠚⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⢩⠗⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⣨⠃⢈⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⠇⠀⠀⠀⡴⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠶⠤⣄⠀⠀⡇⢸⠀⠀⢀⡜⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠖⠓⠒⢤⡱⡄⡇⡟⠀⢀⠞⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⡏⠀⢀⡠⠴⢿⡚⢳⡓⢦⣯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡞⣠⢾⣙⠒⠦⠤⠷⡄⠙⣄⠱⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡠⢊⡡⠤⠤⢄⡙⣄⠀⠀⠀⠀⠀⢀⡴⠃⣀⠜⡽⠧⣄⣈⠉⠓⠒⠲⠞⢦⡈⠳⢌⡑⠮⣧
⠀⠀⠀⠀⠀⠀⢸⠁⡞⠀⠀⠀⠀⢱⢸⠀⠀⠀⣠⠔⢋⡠⠞⠁⢸⠳⢤⣀⡈⠉⠉⠉⠉⠉⠉⢙⣦⡀⠉⠲⢬⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡙⢤⣀⣀⣀⣼⡼⠴⠒⣋⡤⠖⠉⠀⠀⠀⣿⠚⠁⣠⠟⠉⣻⠒⢲⠟⢉⣿⣠⡬⠗⣦⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⣤⣴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⢹⠖⠋⢀⡠⠞⢁⠴⠁⣠⡚⠒⠒⢊⣉⣁⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠒⢉⡠⠞⠁⣠⣞⠓⠭⢭⣉⣉⣁⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⡠⢶⠛⢦⠈⠓⠤⣀⣀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⢠⠞⢁⠞⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢦⡀⠀⠀⠀⠀⠀⠀⠙⠲⠧⠤⣕⣦⡤⠴⠚⠉
⠀⠀⠀⠀⠀⢠⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠤⢤⢳
⠀⠀⠀⠀⠀⠈⣇⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠳⣄⠀⠀⠀⠀⠀⠘⡆⢳⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⣑⠒⠦⠴⠖⢒⣛⠦⣙⠳⠤⣄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠚⢉⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠑⠲⠤⢤⣀⣈⣉⣁⣀⣀⣠⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠃⠀⡎⠉⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣠⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⢴⣶⣶⢶⢶⢶⢤⣄⣰⠃⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡎⢏⣧⢃⢷⡟⣱⣟⣕⣵⣩⣾⣿⣦⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⢿⣿⢸⣿⡾⠟⣋⣭⡥⠷⣒⣶⣾⣫⣿⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⢿⢯⡻⡼⠞⣡⠦⣕⣾⠷⣛⢟⠿⣫⣵⣾⡱⠾⢋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣶⠏⣌⣾⢏⣴⠞⡡⡪⡪⢗⢝⠕⣡⣾⣿⣿⡷⢾⣛⣲⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢿⡄⡧⢡⡾⢡⢊⢎⢎⡴⡡⣢⣾⣿⡿⢛⣵⢾⡻⡇⠅⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⢧⢡⢻⢡⢃⢆⢏⡞⣴⣿⡟⣱⢟⣵⣿⣵⢸⡄⣿⠀⡄⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣼⡏⡆⡎⡘⣬⢎⣾⡿⣱⣿⢣⠯⢙⡻⠿⠟⢶⢷⡞⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣾⡇⡇⡇⣿⡏⣾⢧⢣⣿⡇⡾⠭⠅⣐⡛⠉⠀⠠⣭⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⣷⢸⢻⢹⠸⡡⣧⣷⡫⠄⠠⠄⠒⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠺⣼⡜⡕⠟⡿⣿⣯⡫⣛⠝⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⣷⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠤⢤⡔⢲⢦⠀⠈⢧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠲⠒⠿⣿⣠⣀⡴⣾⠁⠘⢸⣧⡀⠘⡟⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠐⣩⣌⣃⠀⠀⠀⠀⠀⠈⠻⢿⡿⠀⠀⠈⢹⣷⡀⢹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠰⣾⠫⠋⠝⡿⣷⣦⣄⡀⠀⠀⢀⡇⠀⠀⠀⠸⢹⠛⣾⢡⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡃⢻⡂⠀⠜⠐⠉⠈⣽⡿⢷⣝⣺⡇⠀⠀⠀⡇⡿⢠⢣⢏⡟⠨⠃⣿⠁
⠀⠀⠀⠀⠀⢨⠁⠸⣷⡴⠁⠀⠀⣼⣇⢃⠈⢿⢿⡇⠀⡀⢀⣇⡷⡱⢫⠎⠀⠀⣼⣟⡇
⠀⠀⠀⠀⠀⣯⠀⠀⠹⣅⡔⠈⣸⣷⡘⡀⠀⠈⠈⡇⠀⢟⢸⠟⠈⠀⠁⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠘⣧⣆⣿⠻⠑⡀⠀⢠⡄⣇⣶⠞⠁⠀⠀⠀⠀⣴⣿⡯⢷⠘⢿⡄
⠀⠀⠀⠀⠀⠀⣣⠀⠄⢀⠈⢻⣿⠢⠀⠰⣄⢰⠟⠋⠀⠀⠀⠀⠀⣠⢾⣿⣓⢝⠈⣧⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠰⡘⠷⢬⣦⣷⣴⡿⠷⠖⠚⠉⠀⠀⠀⠀⠀⢀⣴⢟⠻⡇⢻⣟⢣⣉⣿⠃⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠉⠒⠶⣤⣤⡤⠔⠀⠀⠀⠀⠀⠀⢀⣤⣶⡟⠻⡈⠀⢻⣄⣿⣼⣇⠟⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣉⠤⠤⠀⠀⢀⣠⣴⣾⠻⣽⡎⠁⠀⠘⢄⢱⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠻⢉⡀⢋⠻⣇⠠⣹⣄⣀⡦⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠵⠾⠷⠟⠉⠁

⣿⣿⠻⠿⢻⠿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢀⠴⠒⠊⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡆⠀⠀⢀⠔⠁⠀⣠⠔⠁⠀⠀⠀⢀⣠⣤⠶⡖⡖⡲⠲⢖⢴⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⡇⠀⣰⢃⡠⠔⠊⠀⠀⢀⣠⡴⢾⢋⠁⠀⠀⡇⣧⣗⠬⢖⡮⢃⠭⢛⠭⢛⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⡰⠋⠁⠀⠀⠀⢀⡴⡏⢸⠇⣾⡄⡀⣇⡶⡫⢋⡵⢊⡥⠊⡡⠂⣡⢖⠥⡊⠝⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⡾⠁⢀⠔⡆⠀⣰⠛⡀⠇⢸⢸⡏⢇⢧⢟⠞⡱⠋⡐⠋⡠⠊⡠⢊⠵⣛⠩⠔⣪⠔⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠱⣾⢁⡴⠁⡰⠁⡰⡏⠆⠱⡸⡈⡎⡿⣼⢧⢃⠎⣠⠊⢀⠞⣠⢊⣴⣛⡭⠅⢒⡩⠔⢊⡤⢚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡀⠀⣏⡞⠀⡴⠁⣰⠇⢿⡜⢆⢱⠳⡸⣽⠏⡏⠸⢠⠃⢠⠋⡰⢡⠾⣅⣐⠲⠬⠅⠒⣊⣥⣐⣋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢃⠀⣿⡠⠞⠀⠀⡏⡄⡿⠹⣌⢢⡳⡙⣼⢰⠀⠇⡌⢠⠃⡼⢡⢿⣥⢤⡶⣄⠲⢎⡋⠹⢖⣒⣒⣚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⡇⠀⠀⠀⠘⣇⢡⢷⢇⢯⡷⡝⢮⣷⢸⢸⠀⡇⡎⡰⢡⡟⢆⢫⡑⢭⣛⠓⠶⣈⣑⣶⣶⣤⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡇⡇⠀⠀⠀⠀⡏⢂⢮⢎⢾⠃⡜⡷⢼⣾⡘⡀⡅⡇⠇⡿⡜⢆⠣⡙⢄⠙⢍⡒⢦⠠⣭⠭⣽⠿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⣼⠀⠀⠀⠀⢹⣌⢪⣮⢮⡟⡸⢡⠎⡽⣯⡻⢟⠷⢦⣟⢮⣢⡳⣜⠦⡑⠦⣙⢢⣵⣾⣛⣉⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⠀⠀⠀⠀⢏⠣⡹⣷⣷⡇⡎⡜⢰⠁⡜⣳⢽⣢⢍⣻⠭⣙⡛⠿⠿⠷⣞⣛⣹⣤⣤⡴⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⣆⠘⢮⡫⣿⢀⠃⠇⡘⢰⠁⡾⣿⣓⠾⢭⣒⡭⢕⣒⣒⣒⣒⠢⠶⠶⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠘⢕⠦⡙⠪⢿⡐⠀⡇⠸⢸⣍⣥⡐⠪⠥⠖⡋⠵⣒⠶⣲⠶⣲⡿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢌⣳⣌⡓⠢⠽⣇⡇⢸⢸⡓⠒⠒⠢⠍⠡⣒⠩⢔⡪⢔⣩⡯⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠂⠻⠶⠾⠷⢒⡂⠀⣬⡥⠴⠨⠥⠖⠋⠁

⠈⠀⠐⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠠⠾⠤⠖⠄⠀⠀⢠⣥⣷⡦⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠤⠒⠄⠀⠀⢀⣯⣴⡆⠀⠀⠀⠀⠤⠂
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡽⣿⠂⠀⠀⠠⠀⠠⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣽⣿⠀⠀⠀⡰
⠉⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠘⠛⠛⠉⠀⠀⠄⠀⠀⠀⠠⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠀⠀⡀⠀⠀⠒⠒⠒
⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠸⠂⠸⠀⠀⣷⢾⠀⠀⠐⠒⡖⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠇⠂⠈⠀⠀⣷⢶⠀⠀⢰⠂⡖
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⡇⠀⠴⠚⡤⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⡇⠀⠴⠛⡤⠀⠀⣴
⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠶⠂⠀⠀⠉⠉⠀⠀⢲⠀⡇⠀⠶⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠶⠂⠀⠀⠉⠉⠀⠀⢲⠀⡧⠀⠶⠿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠉⢹⡀⠀⡀⢀⠀⠀⠸⠄⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⢹⡀⠀⣀⢀⠀⠀⠹⠄⡇
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠂⠃⠀⠉⠉⠀⠀⠀⢀⡶⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠂⠒⠒⠃⠃⠀⠉⠉⠀⠀⠀⢀⡴⡄
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡘⠾⣷⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡘⠾⣷⠀⠀⠀⢀⣀
⢶⠖⠀⠀⠰⠖⠶⠂⠀⠀⠀⠂⠀⠀⠘⢿⣦⠀⠀⠀⠀⣾⣿⣆⠀⠀⢶⠖⡀⠀⠰⠖⠶⠂⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⢀⣾⣿⣦
⠈⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠰⠾⠀⠲⠆⠀⠀⢠⣏⣳⡆⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠀⠔⠆⠀⠀⢀⣧⣾⡆⠀⠀⠀⠀⠠
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⡽⣻⠂⠀⠀⠰⠀⠠⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣽⢿⠀⠀⠀⡐⠀⠤
⠁⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠈⠙⠛⠉⠀⠀⠄⠀⠀⠀⠠⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠈⠛⠋⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣄⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣄⠀⠀⡀⠀⠀⠒⠒⠒
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠃⠩⠀⠀⡷⢶⠀⠀⠰⠀⡖⠀⠀⠀⠉⠉⠈⠈⠁⠀⠀⠀⠀⠀⠈⠇⠁⠈⠀⠀⡷⢶⠀⠀⠰⠀⡖
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⡇⠀⠴⠛⡴⠀⠀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⡇⠀⠔⠋⡤⠀⠀⣤
⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠲⠶⠆⠀⠀⠉⠉⠀⠀⢲⠀⡇⠀⠶⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠰⠶⠆⠀⠀⠉⠉⠀⠀⢲⠀⡧⠀⠶⠿
⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠉⢹⡀⠀⣀⢀⠀⠀⠸⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⢹⡀⠀⣀⢀⠀⠀⠹⠄⠇
⢠⠀⠀⠀⠀⡀⠀⠀⠀⠂⠒⠒⠃⠃⠀⠉⠉⠀⠀⠀⢀⡶⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠂⠃⠀⠉⠉⠀⠀⠀⢀⡶⡄
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠾⣷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡘⠾⣷⠀⠀⠀⢀⣀
⢶⠖⡀⠀⠰⠖⠶⠂⠀⠀⠀⠂⠀⠀⠘⢿⣆⠀⠀⠀⠀⣾⣿⣦⠀⠀⢶⠖⡀⠀⠰⠖⠶⠂⠀⠀⠀⠂⠀⠀⠘⢿⣦⠀⠀⠀⠀⣾⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠔⡪⢀⠖⣪⡵⢟⡿⢠⡿⣔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠆⡮⢊⢐⠕⢕⡴⢏⢁⠋⠀⡈⢭⡂⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⡔⠡⠣⠂⠚⢂⢀⠇⠑⠁⡈⠌⢿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⠐⠣⣡⡁⠈⠄⠎⠀⠁⠀⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⢀⠀⠈⠄⠐⡰⠁⠀⠀⠡⡄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⢀⣖⣀⢀⡅⢀⡤⡂⣠⢰⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣀⠁⠉⠀⠉⠀⠉⠉⠈⠉⠀⠈⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡮⠉⠉⡹⠏⠩⢯⠉⠉⢋⠉⠉⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡱⠀⣜⠀⢂⢒⡘⡡⡀⠀⠢⠄⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢁⡐⠀⡀⠈⢂⢳⢐⠀⢆⠀⠘⢴⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡅⠔⠐⡐⡠⢂⢃⠥⠀⢢⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢌⠢⢸⣆⠈⢧⡢⡊⢳⣡⠕⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠔⠛⠓⠑⠙⠚⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣤⣤⣄⢀⣀⣀⠀⠀⢠⣾⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣴⡿⠛⣿⡇⠈⢿⣇⠈⢿⣿⠋⠻⣧⣴⣿⣿
⠀⠀⠀⠀⢀⣠⣼⣿⠀⠹⣿⡄⠈⢿⡄⠀⢻⣆⠈⢿⡆⠀⣽⣿⡿⢻⣇
⠀⠀⠀⠀⣿⡋⠙⣿⣇⠀⢻⣷⡀⠘⣿⡄⠀⢿⡆⠘⣿⣾⣿⣿⡃⠈⣿
⠀⠀⣴⡿⢿⣧⠀⠸⣿⡄⠀⢻⣷⡀⠸⣷⠀⠸⣿⢠⣿⣿⣿⢿⡇⢀⣿⡿⠻⣷
⠀⠀⣿⡄⠈⢿⣧⠀⠙⣿⣄⠀⠹⣷⣄⣿⡆⠀⣿⣿⣿⣿⠏⢸⣷⡿⠋⠀⣠⣿⣅
⢀⣴⣾⣿⡄⠀⢻⣧⡀⠈⢿⣦⡀⠈⢿⣿⣇⢠⣿⣿⣿⣿⣶⠿⠋⠀⣠⣾⠟⠉⣿⡆
⠸⣯⣀⡙⣿⣄⠀⠹⣷⣄⠀⠹⣿⣆⡀⠙⠿⣿⣿⣿⠟⠋⠁⢀⣤⡾⠛⠁⢀⣴⣿⡀
⣾⠟⠛⠿⠿⠿⣦⡀⠈⢻⣦⡀⠈⠻⣿⣦⡀⠈⠛⠿⣦⣴⣾⠟⠉⠀⣠⣴⡿⠋⢨⣿
⢻⣷⣦⣤⣤⣤⣘⣿⣆⠀⠙⢿⣦⡀⠀⠙⠿⣷⣦⣀⠀⠉⠛⠿⢶⣿⣿⣅⣀⣴⣿⠃
⢾⣇⡀⠉⠉⠉⠉⠉⠛⢷⣄⠀⠙⠻⣷⣤⡀⠈⠙⠻⢿⣷⣦⣤⣀⡀⠈⠉⠉⠙⠛⣿⡄
⠀⠙⢻⣿⣿⣷⣶⣶⠶⠶⠿⠿⣦⡀⠀⠙⠻⣷⣦⣤⣀⠈⠉⠛⠻⠿⢿⣿⣶⣶⠶⠟⠁
⠀⠀⢿⣇⣀⣀⣀⣀⣀⣠⣤⣤⣬⣿⣷⣦⣀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⣀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠉⠛⢻⡟⠛⠛⠋⠉⢩⣿⠃⢀⣿⠛⢿⣶⣤⣀⡀⠈⠉⠉⢙⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠛⠋⠉⣉⣉⡉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠘⠿⢶⢶⣶⣶⡿⠃⢀⣼⠇⠀⣼⠏⠉⢻⣿⡻⠿⠟⠻⠿⢷⣶⣶⣤⣤⣤⣴⣶⡿⠛⠉⣠⣴⣾⠿⠟⠛⠛⠻⠿⣶⣦⡈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣴⣿⣿⣀⣴⣿⣄⣤⡿⠛⠻⠿⣶⣦⣤⣤⣀⣀⣉⣉⣉⣉⣠⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠉⠛⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⢀⣾⣿⣿⠏
⠀⠀⠐⢿⣿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⠁⠂⢈⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⣄⠬⠒⡁⠁⠠⠀⣉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡅⠄⠘⠀⠄⠁⠖⡽⠰⢄⣚⠓⢉⢩⣀⠀⡁⠀⠂⠀⠈⠀⠂⢸
⠀⠀⢀⠴⡘⡈⠁⠆⠦⠀⠁⠉⠐⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡌⠀⠆⡁⢀⠢⣀⡑⠀⠀⠢⠀⠰⠧⠀⠂⢈⠁⡄
⠀⠀⢏⠣⣻⢖⢄⡤⠒⣰⠀⠀⠀⠀⠡⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠠⠀⠀⠈⠄⠑⡀⠱⡀⠀⠀⡄⠄
⠀⢸⠜⣲⠡⢡⠆⣍⠠⠒⠇⠀⠀⠀⠀⠐⠄⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⡀⠀⠀⠐⠀⠰⠀⠡⠀⠂⠠⠄⡘
⠀⠀⠣⣃⢠⣁⠬⡀⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠌⣀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢂⠃
⠀⠀⠀⠈⠙⠐⠚⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠌⠀⠄⠀⠐⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠌⠀⠒⠀⠀⠉⠀⢐⠀⢂⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠤⠤⢤⠀⡈⠀⠀⢀⠁⠀⠄⠀⢀⡡⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢅⡀⡀⠈⠀⠀⠀⠄⠀⠀⠂⠀⠐⠀⠀⠠⠀⠑⠒⠂⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠑⠂⠒⡄⠀⠀⠈⡁⠀⠁⠀⠀⠁⠀⠀⡐⠐⠐⠀⢂⢡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⢀⠟⠒⠲⠂⠪⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

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

⠀⠀⠀⠀⢶⣶⡀⠀⠀⠐⢿⣿⣿⡿⠀⠀⠀⠸⠛⢿⡇⠀⢰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣷⣿⣿⠅⠀⠀⠘⣿⠧⢴
⠀⠀⣶⣶⣾⣿⠇⠀⠀⠀⠀⠈⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠆⠀⠠⠓⣤⠂⠀⠈⠉⠉⠃⠀⠀⠘⠟⠉⠃⠀⠀⠀⠀⠿⠀⠘
⠀⠀⠈⠈⠋⠁⣤⠀⠀⠀⠀⠀⠀⣹⣷⣦⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⢀⢀⡀
⠀⠀⠀⠀⢐⣾⣿⣿⣧⡀⠀⢸⠀⣿⣿⣿⡀⢀⣀⣀⣄⡀⠀⠀⢀⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⢀⡇⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠃⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣧⢸⣿⣿⣿⡇⠀⠀⣸⣿⣇⠀⠀⡿⡛⠢⠀⠀⠀⠀⠀⣀⠀⢠⣿⣿⣿⠁⢀⠀⠀⢙⡟
⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⡿⢸⣿⣿⣿⣅⠀⠈⢿⡟⡛⠀⠈⠁⠇⠀⠀⠀⠀⠀⠃⠉⠠⣼⣿⣿⡟⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠠⠌⢋⣿⡇⠀⠀⠀⠀⠐⠋⣿⡇⠀⢻⣿⣿⡿⠀⠀⢈⡁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣧⢰⡆⠀⠀⠀⠀⣼⣧⠀⠀⢯⣿⠡⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⠇⠀⠀⠀⠀⠈⣿⡀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠻⡆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⠁⠀⠀⠀⠠⠀⣀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠃⠀⠀⠀⠀⠀⠀⠿⢧⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⡛⣋⣛⣛⢁⣛⢛⣛⡛⡃
⣶⣶⣶⣶⣷⣿⣿⣿⣶⣾⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠴⢴⢤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⠹⡌⡘⡘⡾⡪⣪⢮⢏⢏⢶⣄⡀⠀⣠⣾⡏⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡇⢸⠀⠇⡇⡇⣯⡪⣖⢕⠟⣡⢞⣌⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣮⣿⣿⢸⢸⢰⢠⢠⢿⡪⢚⣵⢞⣮⣾⣿⣟⢏⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢭⣓⢿⢹⡌⡆⠆⢆⢆⢎⢿⢹⣸⣾⣿⡟⡍⡿⡜⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠵⣒⣽⡎⣷⡘⡌⢜⢎⢎⢎⢿⡟⢹⢸⣹⢳⢸⢱⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠍⣒⣚⣷⢹⢳⡜⢎⢪⡢⡳⢕⢝⡮⣾⡇⡞⡼⡜⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣭⣒⣒⣚⣆⢣⢻⠢⣑⠿⣪⣷⣭⣚⡷⢾⣯⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣾⣾⡌⢣⢣⠹⡕⣮⣑⡫⢕⣃⠀⠐⣖⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⣆⠣⡱⡜⢌⢦⡻⡕⢾⡭⣭⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠋⠀⠀⠉⠙⠓⠛⠛⠚⠓⠟⠺⠓⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢤⡠⢤⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⣾⣟⠷⣶⣤⡤⠽⠛⣛⣳⡝⢯⡽⢆⠘⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡏⣿⠃⣾⣷⡌⢷⠒⠋⣒⣛⣋⣈⣉⣙⣦⠱⣟⢣⠈⣶⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⣿⡇⢹⠀⣧⣶⠟⡌⢿⣿⣿⣍⣈⣹⠟⣠⣾⡷⡘⠿⠧⠀⣬⣝⠿⣆
⠀⠀⠀⠀⠀⠀⡀⡼⢋⣠⣴⣷⠠⠀⡿⠗⠚⢻⡈⢿⣋⣉⣉⢉⣉⣉⣛⣒⣳⡘⣟⣧⠐⡿⠽⣾⡄
⠀⠀⠀⠀⠀⢸⡇⢸⡿⠒⢉⣩⣷⠐⣷⣏⡿⢩⣧⠘⢯⡟⢀⣾⡿⢃⣼⣿⣌⣧⠘⣿⡄⢹⣷⣖⣿⡀⣆
⠀⠀⠀⠀⠀⢘⣃⠀⣶⣯⡩⢋⣼⠠⣟⡌⠳⣿⣍⣧⠘⣧⠚⠛⣂⣉⣁⣨⢡⣬⡇⢳⢧⠀⡇⠀⠚⣇⢸⣆
⠀⠀⠀⠀⠁⢸⡿⡀⢸⡿⠤⢾⣿⡆⠎⣷⠖⢋⣠⣼⠆⠸⣏⣉⣭⠤⠖⠐⠉⠀⣩⠀⣮⡆⠻⣶⠲⣿⠸⢿⡄
⠀⠀⠀⠀⣷⠀⣯⢷⠀⢫⣶⠀⣾⣇⢰⠰⣆⡩⠤⣴⠒⡄⠹⣁⣠⣤⣶⣞⣟⡛⢻⡆⢙⣇⠸⡼⠛⡋⣸⠟⣇
⠀⠀⠀⠀⠹⣆⢸⡟⠦⡈⢿⠞⣀⣼⠸⡀⢻⡽⠶⢤⣈⠹⠀⢻⣤⣀⡉⠙⣚⡿⠿⢷⠈⣭⠀⡷⠞⢋⣵⠎⡷
⠀⠀⠀⠐⣄⠙⣆⠹⣦⡿⡈⠻⣍⠙⣧⢳⡈⣷⠲⠟⢿⣟⣧⠈⣶⡈⠙⠻⣤⡶⠶⠛⡀⣹⠀⣶⡞⣹⠹⢡⠇
⠀⠀⠀⠀⠹⡷⣌⢣⡙⢾⡉⣦⠘⢷⣾⡆⢃⠸⣦⣤⣀⣀⣘⡄⠈⠿⠦⣀⠀⠙⠒⢾⡇⢹⡄⠟⢰⢿⠇⡜
⠀⠀⠀⠘⢦⣙⣏⡷⢿⣦⡙⢏⣓⣆⠙⠍⡄⢆⠙⣍⣉⣉⣁⣽⡄⠐⣶⣭⣝⣲⡤⠀⣹⢸⡇⣰⣠⣼⠊⢀
⠀⠀⠀⠀⠀⠉⠉⠓⠺⠿⣿⣦⣍⢻⣳⣄⠘⢆⣃⠈⢧⣥⣁⣠⣹⡀⠘⡟⠁⢀⣀⣤⢿⣠⡧⠿⠛⣡⡴⠇
⠀⠀⠀⠀⠈⢛⠶⣆⠤⣄⣠⣀⣀⠀⠁⠉⠉⠉⠉⠁⠚⠙⠋⠓⠒⠛⠒⠛⠋⠋⠉⠁⢉⣠⡄⠶⣫⡏⢙
⠀⠀⠀⠀⠀⠀⢩⡿⣶⣌⠳⢶⣾⣿⠿⢻⣯⣄⣛⡷⡂⠓⠶⣗⠛⢻⣷⠘⢿⢙⣿⡿⢟⠈⡇⡾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣙⢛⠳⢤⠙⠻⣟⣉⣉⣁⡬⢿⡌⢷⡦⣌⠛⠿⢋⣦⡈⢻⣉⣤⡾⢠⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠛⠶⣌⡉⠛⠻⠦⢬⣿⡌⢻⠓⠿⠓⢂⠠⢌⢉⣹⣟⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢯⣬⣿⣶⠦⠠⢠⣽⣆⠙⢦⣶⣮⣉⡻⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠉⠉⠛⠂⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢀⡤⣖⠒⠒⠒⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀
⠀⠀⠀⠀⢀⡔⠫⢍⣢⣙⠦⣹⢦⠀⠑⣝⢦⡀⠀⠀⣀⡠⠤⠐⢤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⠟⡙⣿⢉⣭⣟⡻⠲⢤⡀
⠀⠀⠀⢀⠜⠒⠈⣙⢿⣛⢶⣞⢯⣳⣳⣽⣿⡷⠀⠛⡂⠈⠓⢦⢢⣳⣢⢯⢳⣄⠀⠀⠀⠀⠀⣀⡔⠛⢹⢻⢸⢣⢧⢹⢸⣿⠋⠻⣦⣙⣦⡀
⠀⠀⠀⠘⠕⢒⣃⣲⣤⣬⣲⣼⣿⣿⠿⣿⣥⣌⣐⣊⠺⢴⣕⣆⢫⢷⣹⢸⠀⢼⢷⡄⠀⠀⣰⢟⡀⢄⣿⡇⡎⢟⠎⡮⣿⣖⡭⣔⡦⣝⣿⣷⡀
⠀⠀⠀⠂⢈⠴⢻⠿⢻⠋⢩⣹⣯⠀⠰⣤⠪⢙⡿⣯⣽⣦⣹⣾⣮⣸⣿⣿⢜⡾⣭⢿⠀⠀⣿⣯⣿⣿⣿⡟⢣⡞⢠⠃⣿⡲⠬⣕⡫⢺⢽⣿⡇
⠀⠀⠐⣦⢋⡄⣼⡆⣏⢮⡸⡈⢮⡫⣦⣖⣭⣲⣽⣿⣿⣷⣿⣿⣿⡿⠿⠿⠥⠖⠽⢻⡆⠀⣿⢿⡟⣹⢽⡇⢿⠞⢸⣷⢻⣄⣶⡿⣿⢶⣽⣿⣿
⠀⠀⠀⠹⣩⢽⣻⡧⣌⠗⢽⣝⡲⢍⡢⣿⢾⣾⣿⣿⣿⢿⢋⠙⢍⡛⠓⠲⣶⢻⣴⣿⠀⠀⢻⣧⢟⡿⣿⣿⣾⡇⠘⢻⢸⣿⢋⠔⢡⢮⣿⣿⠇
⠀⠀⠀⠀⠙⠿⣅⢷⡉⢷⡾⣦⣭⣷⣿⠶⠻⣿⢿⢋⢿⢸⡯⣿⣿⠲⢌⢳⣗⣿⣾⠃⠀⠀⠈⢿⣿⣹⣵⣿⡘⣧⠄⣿⡾⣿⣿⡖⣩⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠘⠾⣾⣻⢸⣿⣾⣭⡛⣿⣿⣿⣿⠋⠀⠀⠀⠀⡈⠳⣿⣶⣿⣷⣟⢼⣷⣧⢛⠉⢞⡛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣸⠿⠿⠿⢿⣿⠽⠋⠀⠀⠀⠠⠂⠉⠀⠀⠀⠙⠻⠿⣿⣼⣿⣷⡾⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠳⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠐⠒⠂⠀⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⠯⢋⣡⡾⢟⠍⡨⢍⣷⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⣒⢖⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⢊⢽⡿⠃⣠⢞⣥⠞⠑⣩⣞⣡⣽⡀⡌⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣵⣲⠿⢿⣿⣿⠏⣨⣾⠟⣦⡀
⠀⠀⠀⠀⠀⢠⠎⠁⣸⠏⢠⠞⣕⠴⠃⣠⢟⣳⠦⣍⡻⢧⡹⠘⡌⢧⡀⠀⠀⠀⠀⠀⢠⣾⣿⡭⠴⣂⣤⣭⠷⠾⠷⡿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⢠⣥⣤⣶⠃⣠⢋⢞⡕⠀⡼⠭⣴⣦⣉⠓⠯⣲⢝⢦⣁⢸⣧⠀⠀⠀⠀⠀⣞⣯⡹⣞⡯⣗⣚⣿⣭⣭⠷⡿⣭⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣼⣙⣿⢃⣰⠃⡂⡜⢀⣾⡷⣶⣤⣄⢯⠷⡶⣾⣕⢥⡝⢦⣿⡆⠀⠀⠀⢰⣿⣷⣝⡶⣝⡿⣿⣽⣱⣶⣷⡾⠾⣿⣷⣽⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣧⡏⣼⡏⡜⣸⠁⣼⡿⠞⢋⠔⣩⡞⢯⣉⢻⢭⡳⢧⣌⣿⡇⠀⠀⠀⢸⣿⢿⣿⣿⣾⣽⡲⠯⠟⠳⠿⣯⢭⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡇⣿⢸⢣⡇⢠⣟⠭⢂⡏⣾⢋⡞⣡⣿⢳⣝⢽⡻⣝⢿⡇⠀⠀⠀⠘⣟⢷⣌⡉⣛⡛⢣⣤⡦⠤⠨⠽⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⡇⡏⣯⢿⢳⢸⣧⣞⣽⢸⣵⣿⡼⢿⢇⢸⣿⢳⣽⣾⡟⠀⠀⠀⠀⠀⠙⣿⣷⣧⣥⣍⣛⣛⣛⣋⣉⣛⣫⣽⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠹⡇⡇⠀⢸⢸⣸⣷⡿⣻⡞⢟⡝⣄⡿⡸⢸⡎⣼⣻⡟⠁⠀⠀⠀⠀⠀⠀⠙⢯⣿⣷⣿⣿⣿⣟⣶⣿⣾⣿⣿⣿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠘⢧⣿⣼⣸⡿⣿⣾⣯⣳⡹⣿⡿⢡⢳⠏⣴⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣿⣿⣿⣿⠎⣻⣌⠳⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡩⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⢉⠴⠆⠖⠂⡀⠈⣁⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⣀⣈⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣽⣧⣧⣧⣧⣧⣿⣼⣾⣼⣒⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡶⠓⠀⠀⠀⠒⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠃⠀⢸⣿⠄⠀⠀⠀⠀⠉⠉⣪⣿⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣄⣀⠀⠀⡤⠀⣠⡄⠀⠀⣸⠁⠀⢀⣤⢴⣖⡿⠋⢹⣿⣽⣻⣿⣆⠀⠀⠀⠀⠀⣾⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⣷⣜⡿⣿⡿⠂⠀⢾⣽⠃⠀⠀⣿⠶⡿⢟⠀⣁⠲⣅⠀⣰⣿⣿⣿⠟⣋⣴⠀⣀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⡔⠀⠈⢲⢿⣝⣿⠃⠀⠀⠊⣿⠁⠀⠀⢹⠀⠀⡀⠃⠬⡱⣿⣿⣿⠿⣋⣴⠞⣉⡴⢾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢱⠄⠙⠒⣶⡆⣰⡷⣠⢾⣿⡟⠀⠀⠀⠾⢿⡀⣆⠀⡘⡀⠘⠁⢀⣶⣷⠞⣋⣵⠿⣋⣵⣾⣿⣷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡈⠀⠀⠀⣻⣴⣟⣺⣷⣌⣻⣧⠀⢀⠂⠀⠄⡀⢿⡀⠰⢹⣼⣷⡟⣫⣴⠿⣫⣴⣾⣿⣿⣿⣿⣿⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢋⣀⣘⣉⣥⣶⣿⣿⠿⠛⠛⢿⣄⣾⣌⠂⠂⣧⣷⣥⠀⢷⣻⣷⣿⣯⣷⡿⣿⣷⣿⣿⣿⣿⣿⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡙⣿⣿⣿⣿⣿⠛⠀⢀⠀⠀⠠⠂⠙⢿⣿⣷⣾⣿⣿⣇⠘⢿⣿⣿⣿⣯⣷⣫⣿⣿⣿⣿⣿⣿⡇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣯⣿⣷⣿⠁⠣⠀⢡⣀⣠⣶⣄⣀⡠⠟⣫⡴⢛⣽⣿⣿⣾⠿⠛⢻⡿⠛⣛⠛⢻⣿⣿⣛⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠠⣄⡲⠄⢉⣛⣠⠿⣋⡴⢚⣩⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⡏⣘⣿⣿⣯⡹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⢷⡤⢋⣥⠞⣩⣶⠛⢿⣿⣿⣿⢑⠰⠀⢂⣤⡄⢀⡀⡼⢿⣿⣟⣟⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠾⢋⠴⡯⠞⠃⠀⠀⠈⠙⠛⠋⠁⠐⠁⢇⠀⠈⠘⢡⢏⣟⣻⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣶⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠾⠄⣼⣿⣿⢏⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⢿⣛⣿⡶⢟⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠾⠛⠛⠋⠉⠁⠙⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⡀⢤⠒⠉⢀⡁⠂⠐⠃⢂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠄⡠⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⠄
⢉⠢⡌⡀⠰⠀⠄⠈⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠠⠄⠁⠄⠀⠀⢀⠠⠖⠘⠀⠂⠠⢀⠀⠀⠀⡆⠠⠀⠂⠀⠀⢸⠀⢁⠄
⡀⠠⠀⡄⠚⢀⠆⢠⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⢁⢁⡉⡀⠐⢀⠈⢄⠀⠀⠀⠀⠃⠀⠀⠠⠋⢸⠀⡀⠈⠀⠀⠬⢁⠀⠀⠙⠦⠔⠁⠀⠀⢹⠀⠀⢠
⡇⠀⠠⠐⠈⠀⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⢀⠘⡊⠀⠀⠀⠀⠄⠣⠈⢢⠀⠀⠀⠀⠀⠀⡆⠴⠘⠃⡀⠔⢁⠼⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⡇⢰⠐⡂⠀⠀⠀⣡⠞⠴⠂⠀⡀⠀⠀⠀⠡⠀⠄⠀⠌⠀⡠⡄⡰⢉⠀⠂⠀⡁⠈⢃⠀⠀⠀⠀⠀⠐⠀⠂⣀⠠⠆⠁⠨⢅⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⣀
⠒⠤⠦⠥⠔⠂⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠘⢄⠸⡀⠂⡀⠈⠠⠄⠈⡀⠄⣠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠠⢁⡐⢀⣀⡴⠊⠀⢰⠀⠀⠀⠀⠀⠘⠄⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⡰⠄⠒⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⡀⠁⠒⠀⠂⢠⠈⢁⡐⠉⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋
⠀⠆⠄⠀⠀⠀⢄⠡⠤⠄⠐⠒⠂⢄⡀⠀⠀⠀⠀⠓⣄⠀⠈⠉⠁⠉⠤⠂⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⡀
⠁⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠲⠤⡀⠀⢀⡠⠔⠖⡲⢒⡡⡊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠐
⠈⡰⠴⢤⡀⠀⠈⠄⣀⠄⠀⠀⠀⠀⠀⠀⡞⡀⠐⠐⠀⠘⡆⠀⠀⠀⣨⠀⣠⠊⠁⠀⠀⠈⠛⡱⠁⡸⣎⠰⠈⠀⠐⠀⠀⠀⠀⠀⢠⠄⠀⠀⢰⢆⠀⢃⣀⠀⠶
⡜⠋⠳⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠠⠀⠈⢠⠇⠀⠀⠀⠏⡰⢁⠄⠁⠄⠀⢂⡐⢁⠜⢃⠘⡀⢡⠈⡀⠀⠀⠀⠀⠀⡆⠣⠤⠔⠁⠀⡇⠀⠀⠘⠡
⠐⢐⠂⠑⠃⠢⡀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠑⠢⠀⠐⠁⠀⠀⠀⠀⠸⠀⠂⢠⠛⡀⠃⠈⣠⠎⠁⠲⡄⡄⠈⠀⠇⠀⠀⠀⠀⡀⠃⠓⠘⠓⠐⠂⡇
⠀⢺⠀⢀⠀⢸⠃⠀⠀⠀⡀⠀⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠛⡀⢡⠀⠀⠁⠄⠁⠠⠀⠙⢄⠖⠀⠀⠀⠀⠀⡇⠀⠰⠀⠰⠀⠀⠇⠀⠠⠀⠂
⠉⠉⠉⠉⠁⡟⠀⠀⠀⢀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⡃⠈⠀⠀⠰⠄⠈⠢⠀⡠⢌⠀⠀⠀⠀⠀⠀⢱⠀⠈⡇⠀⠃⠐⠒⠒⠺
⠀⡏⢈⡉⠘⠁⠀⠀⠐⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠙⢤⡀⠀⠘⠄⠈⠠⠈⠉⠐⠠⡀⠀⠀⠀⠀⠈⢦⠀⠙⠀⠐⠒⠒⠒⠚
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠈⠓⠒⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠀⠉⠁⠈
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠋⠀⢉⠼⡋⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⢇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡔⠁⡄⠁⠀⡰⠋⢀⠘⡀⠀⠛⢆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡌⠁
⣠⠴⠶⠒⣒⡤⠀⠀⠀⠀⡄⠃⠀⢠⠀⡜⠡⠀⠀⠀⠇⠀⢀⡨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣂⠴⠆⢀⡄
⢉⢑⠶⠋⢀⠤⠐⠀⠀⠀⢃⠀⠀⠀⠶⠤⠠⠤⠤⠤⠔⠚⢉⠔⡇⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠊⢤⠒⢉⡠⠔⡏⠀⠀⠀⠀⠀⠈⠙
⠤⣁⡠⠊⡡⠐⠀⠉⠀⠀⢂⠀⠁⠀⢀⠲⠀⠀⠀⠂⠒⠈⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠃⠤⣑⠢⣙⠣⡔⠚⡃⠀⠀⠀⠤⠂
⡐⠨⢉⠛⠂⠦⠄⢠⠀⠀⠈⠢⡡⡀⠀⠑⠈⡓⠠⢤⡄⢀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⢸⣉⣐⣬⣑⣤⠵⠚⢋⡇⠀⠀⠃⠁
⠄⠑⠀⠈⠑⠂⠠⡔⠀⠀⠀⠀⠈⠚⠶⣄⡀⢠⣁⡒⠶⠚⠁⠈⠈⠠⠩⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢄⡠⠤⠤⠐⠊⣁⢷
⠄⢈⠠⣄⣈⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠄⠠⡀⢀⠤⢀⠀⠀⠈⠲⠤⠶⠒⢒⣩⠴⠊⠁⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⡠⢄⡀⢄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠤⣒⡨⠵⠃⠀⠀⠀⠀⠀⠈⠁⠂⠐⠀⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⢄
⠀⠀⠀⠀⠀⠀⠱⡀⢀⠄⠀⠀⠀⠀⠀⠀⠢⠜⠀⠀⠀⠀⠐⡩⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⣬⠃⢲⠀⠀⣠⡄⢀⡀⠀⠀⠄⠠⢀⡀⠀⠀⠀⠢
⢒⠨⠅⠒⠒⠒⣤⡀⠀⠀⢀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⢀
⣀⣄⣒⣈⣁⣠⣤⡌⣁⡔⣁⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣄⣲⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣖⡕
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⡿⢋⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠂⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⠀⠠⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠘⢿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⠉⠻⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠿⣿⣿⣷⣎⣙⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠛⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣾⣿⣿⡛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣤⣾⡿⢋⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣠⣿⢿⣿⡟⠀⣫⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣾⣿⣿⣿⣫⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⡿⠛⠈⣁⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⡿⢹⡏
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣴⣶⣾⣿⢩⣿⣾⣿⣿⢿⣿⣯⢸⣿⢹⣿⣍⣁⣠⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣷⣍⣿⣟⠻⣿⣯⣿⡀⣿⣿⣿⠿⠛⠁⠀⠐⠋⢀⣀⣿⣿⣿⣷⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠰⣏⡀⠁⠈⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⡏⠀⠙⠿⠾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⣿⡆⠄⣠⡾⠏⠀⠘⠁⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⢒⠒⠛⢉⣍⠉⣩⡉⠙⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠈⠀⠀⠉⠀⠀⢸⠈⠀⢧⠀⠀⡇⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⡀⠀⠀⠘⠃⠀⠘⠀⠀⣠⡿⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠙⠒⠬⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠋⠁⣤⡶⠀⠉⠉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⡤⠴⠞⠋⠁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢣⣼⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣀⡀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣟⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣥⣤⡤⠤⠤⠴⠦⠐⣒⣒⣒⣢⣬⠩⠉⠛⠉⢿⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⠦⠀⡿⠤⠤⣤⠶⠶⠾⠿⠭⢽⠟⠒⠒⠒⠒⡾⠋⠉⠉⠉⠉⠉⠙⢦⡀⠀⠒⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣟⡰⠊⢀⡴⠞⠛⠳⣄⠈⢷⡀⠈⠀⡸⠁⣠⠖⠃⣀⠢⣄⠀⠀⠱⣄⠀⢂⡴⢻⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⢀⡴⠋⠒⠀⢀⡀⠘⡀⠀⠙⠒⠚⠁⠀⠁⠠⠄⠀⠀⠈⢢⠀⠀⠈⠉⠉⢀⠼⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡇⡼⠁⠀⠀⠀⠈⠀⠀⠡⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣀⢳⡀⠀⠀⡰⢁⠀⡇⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣡⣇⣀⣀⠁⠀⠀⠀⠀⠀⠙⢦⣤⣎⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠼⠶⣆⠀⠐⠒⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⢸⡤⣬⣉⣉⣩⡭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠶⠶⠒⠒⠒⠚⠛⠋⠉⠉⢩⡍⠉⠉⢹⡀⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢰⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠠⢴⣿⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣤⣄⣀⣀⡇⠀⠀⠀⠀⠀⠀⠈⠶⠦⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡄⡇⡉⡝⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⣠⢾⢶⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠞⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣋⡟⠚⠎⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠤⣤⣀⣀⣀⣀⣀⡀⠀⠀⢀⢀⣀⣀⣠⡤⠶⠛⠉⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠈⠉⠉⡙⡳⡆⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠴⠀⣀⠈⡆⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⠀⠀⠀⠰⠀⠀⡏⠀⠨⡻⣆⡲⣤⠶⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢅⣃⠀⠀⠀⠀⠀⠆⠀⢅⠀⠀⣀⡬⠛⠁⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⡆⠀⠀⠀⠀⠈⣄⢸⠋⠉⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠙⡄⠀⠀⠀⠀⠈⠻⡄⠄⠤⠀⣀⣄⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⠒⠛⢆⠀⠀⠀⠀⠀⠙⢿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⢨⠡⣄⠀⠀⠀⠀⠀⠉⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠲⠤⣁⣀⣤⠴⠞⠁⠀⢀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣉⡵⠓⠄⠀⢠⠔⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠃⡠⣀⣀⣀⡀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠛⠇⠀⠀⠛⠃⠀⠀⠀⠉⠁⠀⠀⠰⣶⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⢾⡿⠱⢁⠀⢀⡘⠹⠟⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⣠⣶⡐⠎⠀⠁⠂⠀⠁⢈⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢆⠼⠋⠀⠀⠄⠒⢀⣈⣬⣤⣛⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣻⠆⠂⠀⣀⣰⡖⠂⠜⠙⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⣠⣴⡏⠉⠈⠉⠀⢀⠀⠀⣐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⣠⣄⡀⠀⠀⠀⠀⠈⢻⣾⠇⠉⢆⠀⠀⠀⡤⡐⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡀⠀⠀⠀⠀⠀⣠⣶⣿⣶⠶⣟⡿⢿⡷⣤⠀⠀⠀⠀⠈⠙⠶⠦⣤⣤⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⣾⠝⣯⣿⠿⠁⠭⠟⠘⠧⣉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⣧⣢⠞⠁⠀⠀⠒⢈⠥⣴⣾⡍⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⣷⠽⠋⢀⣠⡴⣿⡁⠊⠈⠠⠤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢹⣄⣶⡿⡅⠀⠀⠁⠠⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠙⠻⢄⣈⡐⢶⢶⢋⡲⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣿⣿⠟⣽⣿⠋⡩⢹⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣇⣾⣿⡇⢠⣿⡇⢀⣴⣳⡟⣛⠉⠙⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡿⠋⢿⣿⢻⣿⢂⣾⡟⡞⣼⣿⣿⣋⣭⣭⣥⣜⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⢷⣰⣤⣇⣷⡏⣼⣿⣹⣱⣿⣿⣿⣿⣿⣭⣼⢖⣶⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⣿⣿⣬⣶⡿⡻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⠭⠷⢾⣿⣶⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⡏⣿⣿⣿⣽⡇⣧⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣖⠬⣐⢶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣿⣶⢬⣉⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡝⣷⣬⣯⡻⣿⢿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣶⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡷⢶⣍⠛⢧⣹⣿⣿⡗⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣾⣝⠻⢿⣿⣿⣷⣤⣉⣹⣿⣿⣿⢿⣿⣿⣿⣿⣷⣦⣌⡒⠭⢿⣿⣿⣼⣼
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠙⢮⣛⠿⣆⣬⠉⠉⠉⢉⡁⣀⣤⣶⣿⡿⣺⣿⣿⣿⣿⠛⠳⣤⣶⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⡙⢿⣶⣮⣽⣯⣽⣿⣮⢿⣿⣾⣟⣽⣿⣿⣿⣿⣿⣷⣼⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡻⢿⣷⣾⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⣿⣿⡿⣿⣿⣿⢿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣷⣷⣶⡶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣿⢿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣯⡹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣯⣽⣯⣿⣿⣻⣿⢿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠻⢷⡖⠢⢤⣄⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠻⠶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣷⣻⣿⣿⣝⣷⣿⢿⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠙⠦⣀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣖⣿⢿⣿⣮⣿⣿⣿⠟⠁⠀⠈⠉⠛⠿⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠈⠓⠤⣀⡰⠋⠈⠉⠱⠿⠿⣿⣿⣿⢸⡿⠿⠏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷
⠀⡠⠔⠉⠁
⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣻⢿⣿⣿⣿⣿⢿⣯⣾⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣾⣹⢟⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣽⠿⣿⣿⣿⣿⣿⣾⣿⣿⣦⠀⠀⠀⣀⣤⣤⢖⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣥⡶⠶⢴⠿⠾⣵⣿⣿⣿⣿⣿⣧⣶⡿⠟⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣶⣷⣾⣶⣷⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣿⢿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣵⣿⣿⡿⣟⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣠⣴⠾⠛⠻⣿⣿⣿⣿⣿⣿⣿⣟⣷⢸⣾⣞⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣴⠾⠛⠛⢦⣀⠀⢀⡼⠛⠿⢛⣽⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⢀⣀⣀⣀⣀⡠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠙⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠁
⠀⠀⠀⠀⠀⠀⣤⠀⢀⠃⠀⠀⡀⠐⠐⠀⡀⠆⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠆⠄⠆⠂⢐⡶⠨⠆⡉⢧⠐⠇⠩
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠚⠁⠠⠓⠆⡀⠁⠀⠀⡀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠢⠄⢁⠠⠠⠁⠆⠠⡜⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠐⠀⠀⠀⠂⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⢢⠀⠀⠀⠀⠀⠀⠀⠘⠧⠯⠿⠿⠇⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⡀⠀⠀⠀⠀⠦⢀⡘⠀⠀⠀⠀⠀⠀⠀⠠⡇⡐⣼⣯⠂⠀⠀⠀⠀⠀⠀⠔⠠⠠⠀⠐⠂⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣤⣿⣾⣿⣿⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⣿⣝⣿⢹⣿⣿⢿⡯⡿⡻⣭⠟⢶⣶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⡌⠐⠘⢷⣰⣀⢞⠹⣷⡗⢸⠡⢴⣃⣴⠂⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠈⣿⣿⣿⡷⢒⣗⡳⢫⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣁⣽⣵⢿⣾⢱⣯⣟⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣮⣿⣵⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⡇⣹⡻⣭⣾⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠻⢿⣟⠳⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠇⢙⡟⠉⠐⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⣙⣃⣺⣿⣘⣓⠐⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠯⡟⠛⠶⢶⡿⠼⢰⠣⡍⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡽⠨⡿⣿⣽⣛⣻⡡⢼⠠⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣉⣯⣰⣉⣿⣿⢫⣘⣂⣀⣀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣴⢃⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⣿⣿⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⠃⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡀⠀⣳⣿⣴⣿⡌⠴⣶⣦⣄
⠀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠤⠒⠒⠚⢻⡟⣿⣧⠀⠉⠿⢿⣆
⠐⠿⠛⠛⠿⠿⢿⣿⣿⣷⣶⣶⣤⣽⠇⣀⣴⠶⠶⠶⢾⡇⣾⣿⡶⠶⠟⠛⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠉⠐⠀⠀⣔⣻⣯⡟⣿⣧⣴⣶⣶⣿⣶⣶⣦⣤⢄
⠀⠀⠀⠀⠸⣟⣿⣿⣿⣿⣿⣿⣿⣿⠉⣒⠈⡙⢿⣿⣿⣜⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣰⣦
⠀⠀⠀⠀⠈⣿⣻⣿⣿⣿⣿⣿⣾⣿⣧⣛⣠⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢉⠉⠉⠙⠁⠉⠁
⠀⠀⠀⠀⠀⣻⢿⣿⣿⣿⣷⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣇
⠀⠀⠀⠀⠀⢺⡽⣻⣿⣿⣿⣯⣿⣿⣽⣿⡿⡽⡻⣳⡿⣺⣾⡿⡿⣫⣛⢕⡽⣿⣿⢿⠽⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⣯⣭⣿⣽⣽⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣟⣯⣾⣧⣥⣷⣷⣟⣍⣿⣿⣮⢽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠻⠻⠛⠿⢻⣻⣿⣿⣿⡾⢾⣗⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⢤⣤⢤⣄⣀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣿⣹⡇⣇⣿⣄⡟⣆⢳⣿⡙⣦⡀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠹⡿⡇⢻⢳⣸⡹⣿⢹⠸⣞⣿⣧⢸⡛⡄⠀⠀⣇⡇
⠀⠀⠀⠀⠀⠰⢹⠁⣿⣦⣧⣿⢾⡆⢻⣸⢻⢳⣇⣧⢹⣼⣾⡇⢸⡀⠀⣿
⠀⠀⠀⠀⠀⣧⡞⣇⣷⢹⡌⣿⠼⣿⣌⡇⠘⡆⢿⢹⣻⢿⣿⣲⣸⡇⠀⣿
⠀⠀⠀⠀⠀⡏⣇⢻⣿⣸⢳⡟⡇⣇⣿⢿⡄⣿⣸⢧⣿⢸⡇⣿⡇⡇⠀⣿
⠀⠀⠀⠀⠀⢹⣏⣆⢿⣻⡇⣧⣿⡜⡿⣼⢧⣹⣿⠘⣿⢸⣇⢸⡀⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠻⡼⣾⣧⣹⡌⢿⢹⣷⣿⡸⠻⣿⣆⣿⣼⢻⡏⡷⠉⠙⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠺⣇⢹⣧⠊⣿⠹⣿⡇⣇⣿⡟⣿⣿⡸⠛⠁⠀⠀⡇⡇⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠽⠦⠽⠧⠼⠿⠛⠋⠁⠀⠀⠀⠀⠀⢧⠇⠀⠀⠀⢱
⠀⠀⠀⡤⠒⠊⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⠤⠤⣀⣀⣀⣀⠜
⠀⠀⠀⠳⢤⣄⠤⠤⠤⠒⠒⠒⠒⠒⡄⠀⠀⠀⠀⣀⠤⠴⠖⠠⠤⢄⠀⠀⠀⠀⠀⠀⢀⠔⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣉⠉⠉⢁⣀⡤⠔⠋⠁⠀⠀⠀⠐⠟⠋⠁⠒⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠈⠁⠂⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⣀⠀⠀⠀⢸⣯⣿⣿⠿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣷⣶⣤⣤⣈⣉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠙⠿⣿⣿⣿⣿⣿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠺⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⣤⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⣘⣩⣽⣿⣿⣶⣤⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣟⣷⡄⠀⠀⢻⣿⣿⣿⣯⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⢠⣀⣸⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣻⣿⣷⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠒⠒⠒⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣀
⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣷⣤
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣬⣧⣾⣿⣿⣿⣽⣿⣿⡿⠿⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⢀⡀⠀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢬⣿⣾⣧⠀⣠⣅⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⡟⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⠃⠉⢰⣿⣿⣿⢿⡿⠻⢡⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣟⢁⣀⣐⣀⣿⡟⢁⣿⣁⠀⣀⣸⣿⣿⣿⣿⣿⣿⣟⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⡿⣋⣛⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣼⣷⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠆⠀⠀⠀⠀⢀⡴⠋⠙⢦⡀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠄⣰⣿⣮⣻⣶⣶⡟⣁⠀⠶⣤⣤⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣵⣿⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣬⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⢤⣤⣀⡀⠀⣈⢉⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣿⣿⠾⣿⣟⣥⡀⢉⡤⠞⠉⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣮⣿⣿⡟⢳⣿⣷⣮⣱⣦⠐⠛⡰⢁⠃⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢻⣷⣾⣿⣿⡟⢻⣿⣶⣯⡿⣷⠰⢁⠎⢈⡠⠞⣁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣼⡱⣿⠣⣿⣿⣿⢌⣿⣿⣿⣯⡿⠟⣛⠀⣜⡠⠊⡠⠞⣡⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠟⣾⡿⣼⣷⣿⣿⡙⣦⣼⣿⣿⢋⣴⣿⠽⠀⢉⡤⠚⣡⠞⠩⠡⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡡⣧⢋⣦⣙⣶⣾⣿⣿⣿⢿⣿⣽⠟⣡⣿⠟⣡⣾⢿⣀⣀⣚⣁⣤⣶⣶⣤⣌⡁⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡼⣱⢏⣾⢳⣿⣽⣿⢿⡿⠿⠞⣛⣡⣾⠟⣡⣾⣿⣿⣿⣿⣟⣿⣽⣿⣿⣽⣿⣿⣿⣿⣷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡾⣱⢏⣾⠿⣛⣩⣥⣴⢴⣶⣶⣎⠿⠟⢁⣼⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣻⣿⠿⣟⣻⣭⣶⣿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣧⡿⢱⡿⠞⣡⣾⡿⠿⠟⠛⠛⠙⣉⣁⣴⢂⣾⣿⣿⣿⣿⣿⣷⡿⣿⣿⢟⣩⡴⢶⣿⢛⣿⣧⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣷⣾⢇⣟⠃⣾⡹⢋⣠⣶⣾⣿⣹⣿⣿⢟⠋⣾⣿⣿⣿⣿⣿⣿⣿⣟⠟⣵⠿⣿⣵⣿⡟⢻⣭⣅⣙⣿⣿⡿⢁
⠀⠀⠀⠀⠀⢰⡟⣿⣿⢸⣻⢰⢃⣤⠿⡿⢿⣻⡍⣭⣽⣶⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⢔⣥⣉⣽⣷⣴⠿⠿⠟⢛⠁⢰⡈⠄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⢸⣻⢠⣾⣻⣵⣿⣿⣿⡟⠿⢟⣋⢁⣿⣿⣿⣿⣿⣿⣿⣽⣏⣾⣇⢨⣉⣽⣿⡟⢫⡄⡴⠉⠑⠦⣝⠢⣄⣸
⠀⠀⠀⠀⠀⢿⣟⢿⣿⠸⣿⠸⣡⣿⣿⠋⣽⣶⣴⣿⣿⢇⣾⣿⣿⢿⣾⣿⣿⣷⡝⣾⡿⡟⢋⣹⣿⠏⢤⠸⡆⣿⠘⡏⠐⢌⠑⠠⠄
⠀⠀⠀⠀⠀⠸⣿⣏⢿⣧⡻⣷⣻⡟⣽⣯⠻⡝⠋⣙⣀⡜⠿⢿⡽⣿⣾⡿⣿⡏⡼⢿⣆⢻⣿⣿⡏⣤⡈⣦⠐⠘⣇⠰⡀⠆⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡟⣷⣌⠳⣌⠻⢯⣵⠎⠋⠀⠀⠀⠀⠀⠀⠈⠈⠛⢣⣾⣷⡿⠋⢿⣿⠟⠀⠦⣄⡛⠀⢀⡘⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡗⡯⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠚⠛⢡⠋⠉⠓⠦⣍⡑⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠧⠸⡗⠢⣄⡉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀