Breasts Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡿⠿⡿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠸⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠄⢀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠈⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠞⠀⡀⠐⠁⠲⢆⠀⡐⣐⡈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⠛⣾⣷⣿⣿⡧⠙⢿⣷⣮⣠⣄⡀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢀⠈⢳
⠀⠀⠀⠀⠄⠂⢠⣴⣀⡆⠀⣨⣤⣾⣿⠈⢥⣽⠿⡢⠠⣽⢣⣌⡙⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢙⣷⡀
⠀⠀⠀⠀⠀⠀⠝⠋⠁⢠⣼⣿⣿⢿⣿⣷⡶⠶⡶⢶⡶⡭⢿⣍⣛⣦⠿⠿⠿⣦⣶⡄⠀⠀⠀⠀⠀⠈⠳⣜⠋⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢈⠻⠿⡹⣷⣤⣈⣀⠛⣀⠈⠹⠿⠿⠶⡀⢦⣅⣀⡀⠀⠀⠀⠀⠀⠀⢸⠠⣼⣿⡆
⠀⠀⠀⠀⠠⠀⢀⠀⣌⣙⡁⠍⣙⣷⠶⠸⢛⣿⡛⠻⢿⣖⠙⣷⠀⢿⣆⠘⢷⣶⣍⠋⠠⡖⠀⢄⠀⠀⠀⠘⠇⣻⣿⣷
⠀⠀⠀⠀⠀⢰⠟⠆⠸⣿⣷⣾⣿⣯⣿⠞⠸⣿⣯⡀⠻⡏⠀⢯⡷⠻⡜⣃⠂⣽⣻⣿⡦⠈⠁⡛⢿⣷⣦⡀⠈⠻⣿⣯
⠀⠀⠀⠀⠀⢘⠀⠀⣠⡬⣶⢈⠿⢛⢛⣧⣿⠿⣯⠟⣒⠆⢀⣤⡙⠷⣤⠁⠀⢿⢓⣮⣻⡦⢬⡝⠀⠈⠙⣻⠦⢀⡉⠻⣇⡀
⠀⠀⠀⠀⣤⣘⡆⠀⣼⢷⣶⠻⢷⡷⣿⣶⢲⡿⣭⡟⠟⠃⣀⠉⣵⠺⢿⣷⣴⢆⡉⠉⢨⣉⣬⣭⣤⣒⠘⣓⠈⣉⣘⣣⣘⣛⣧
⠀⠀⠀⠀⠈⢻⠇⠻⠉⠈⠿⣿⣿⣘⡅⣸⣿⣧⣻⡟⣿⣾⣿⣿⣏⣶⣟⣿⣿⡿⣋⣀⣩⣿⣟⠛⠉⢙⣞⠋⡉⠉⠉⢠⡍⢛⣻⠂
⠀⠀⠀⠀⠀⠂⠀⠠⣶⣴⣶⢿⣿⣍⣿⣽⢿⣿⣿⣖⣓⢿⡧⣀⣭⣽⣯⣤⠒⢚⢫⢶⠿⢆⣘⣛⣂⣤⣠⢕⠰⢒⣫⣽⡷⠿⠟
⠀⠀⠀⠀⠀⢠⠀⠀⠙⣿⠷⠞⠹⠿⡙⠷⣤⣶⣿⡟⣿⣏⣛⡛⣷⣟⣻⡞⣓⠿⣟⡥⠶⣻⣿⣻⢿⣋⣼⠋⣠⣼⣿⠇
⠀⠀⠀⠰⠆⠘⣷⣤⠠⡀⠐⠀⠀⢎⣩⣀⣶⠶⣿⡗⠉⠛⠉⢽⠛⠶⠻⠿⣫⣾⣿⣿⣦⣟⣭⣿⡿⠟⠿⢰⣿⣿⡟
⠀⠀⠀⠀⠘⠤⠾⠄⠀⠘⠷⠃⠉⠉⡙⣯⠁⡄⠰⠋⢰⣷⣾⡶⣹⢻⠟⣸⣿⠟⢫⣾⣿⡟⠛⢫⠆⢀⣰⠿⣼⡿⠁
⠀⠀⠀⠀⠀⠀⢺⣶⣠⣠⡷⣠⣶⣄⠠⣞⢻⣰⣦⣦⠈⣻⣿⡶⢻⣣⣴⠿⣋⣴⣤⠟⠉⢀⠶⠁⣠⣼⡿⣤⣬⠁
⠀⠀⠀⠀⠠⢀⢈⣿⡿⢷⣴⣯⡄⢹⠿⣻⣇⡹⠷⣦⣄⣯⣾⣷⣿⣯⣡⣾⡿⠋⢁⠀⠒⡡⢦⣴⣿⣿⣿⡖
⠀⠀⠀⠘⢶⣁⣿⣵⣠⠶⣤⠛⠳⠾⢠⣾⣿⣥⣤⣿⣿⡿⢾⣵⠟⠋⢻⣥⠤⠀⠀⠀⣩⣶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠈⣿⡁⣤⣄⠀⠀⠀⠄⠀⠀⠈⠉⠳⠟⠓⠀⠘⠗⠊⠀⠈⠓⠀⠁⠀⣁⣼⣿⡛⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣶⣶⣿⣿⣿⣇⣀⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠩⠻⠿⣿⣿⣦⠀⠀⠀⣀⣀⠀⣤⣾⣿⣿⣿⣿⣿⢿⣽⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣾⣿⣿⣧⣀⣙⣿⣿⣿⣿⣿⣿⣟⠹⣿⡿⠮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠠⣼⣿⠿⣿⣿⣿⡿⠿⠿⢿⣭⣿⣿⣿⣿⣿⠿⠿⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⢶⣶⣶⣖⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣮⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢿⡿⣻⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡿⢿⣛⣿⣣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣏⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⡿⣯⢿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣻⣿⣬⣿⣵⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⢿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣮⣿⣶⣭⣵⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⢿⢟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣸⣿⣿⣿⣾⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣝⣟⣷⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣼⣫⣿⣿⡯⣿⡿⠿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠤⢄⠀⠀⣠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢀⠀⣀⢹⠀⠀⠀⠀⠀⠀⡇⠠⠄⢀⣄⡀⠤⢸⠇⠀⠀⠀⠀⠈⠓⠋⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⡠⠆⠀⠈⠓⠶⠚⠀⠀⠀⠀⠀⠀⠉⠓⠒⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⠀⢀⡰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⠤⠒⠀⠘⠶⠭⠔⠁⠀⠀⠀⠀⣼⠀⠀⢀⠀⠀⡀⢀⡘⣇⠀⠀⠀⠀⠈⠳⣬⣠⠜⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⡤⠜⠀⠀⠓⠬⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⢀⠀⣠⠀⠀⣀⠀⡇⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⣀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠹⣬⣁⡤⠏⠀⠘⠷⣄⣈⠴⠁⠀⠀⠀⠀⠀⠘⢧⠤⠎⠳⠥⠇⠀⠀⠀⠀⠀⠀⠘⠳⠶⠋⠀⠈⠙⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠹⣤⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣀⢀⢸⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣏⠠⠀⢀⡆⠀⢦⡀⠰⢨⠇⠀⠀⠀⠀⠸⣄⣃⣀⠜⠀⠙⠒⠊⠀⠀⠀⠀⠀⠀⡇⡀⢰⠄⢰⡀⢜⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⡄⢠⡀⢀⡄⡗⠀⠀⠀⠘⢧⣛⠀⣀⠔⠀⠘⣄⠀⠐⠆⡸⠀⠀⠀⠘⣇⣤⢀⡄⠀⠠⣄⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠒⠈⠁⠀⠀⠀⠀⠈⠉⠉

⣤⣤⡴⢶⣛⣵⡾⠃⠀⠀⠀⠀⣻⢾⣽⣳⠟⢟⣷⣷⡛⠀⠀⠀⠀⡄⣤⠠⡦⢰⠆⣠⠀⣠⠠⠀⠀⠀⢸⣆⢢⣤⢠⣦⡙⡇⠀⠀⠘
⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⠿⠚⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠡⢤⠶⠂⠄⠰⠄⣤⠋⠚⠀⠀⠀⠘⢿⡄⠿⠦⠹⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⢀
⠀⠀⢀⣴⡆⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡀⠈
⣶⣿⣿⣿⠃⠀⠀⠀⠸⣷⣤⣤⣀⣀⣄⣀⣤⣶⡾⢛⠀⠀⠀⠠⠛⢦⣤⣄⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⢿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠲⢦⣬⣯⠉⠩⣭⣡⣤⡴⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣶⣶⣾⣿⣷⠀⠀⠀⠀⠈⠉⠉⠻
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠠⠀⠰⠃⠶⠀⠀⠀⠀⠀⡾⢃⣤⢄⣤⠄⣼⠀⠀⠀⠀⢬⣄⣀⣀⣀⣀⣤⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣱⣄
⠘⠃⠚⠀⠗⢴⠀⠀⠀⠀⠐⢿⠃⠾⠏⣼⡟⠀⠀⠀⠀⠐⣬⣭⣭⣭⡽⠶⠛⠁⠀⠀⢸⣤⡀⠀⠀⠀⠁⣀⣴⣿⣿⡆⠀⠀⡑⣄⠰
⠃⠂⠘⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠡⡰⠆
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠏⠈⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢢⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢀
⠚⠋⠸⠀⠀⠀⠀⢰⣿⣦⣤⣄⣀⣤⣴⠀⠀⠀⠘⢿⣦⣤⣄⣀⣀⣐⣠⣤⣴⣿⠀⠀⠀⠀⠀⠀⣄⣤⡤⣤⣾⣫⣿⣵⡆⠀⠘⠳⠖
⠀⡄⠀⠀⠀⠀⠀⠘⠿⠿⠟⣿⣿⣿⡟⠀⠀⠀⠘⠷⣤⣤⣹⡭⠉⢹⣯⣤⡴⠂⠀⠀⠀⠀⠀⠸⣿⣷⢿⠍⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠑⠛⠉
⠀⡀⠁
⠐⠁⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⢀⠀⣴⠟⡁⠀⠀⠀⠀⢠⣄⠀⠀⢀⣠⣤⣷⡄⠀⠀⠀⠀⢀⣄⢱⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠋⢿⣿⣿⣿⣿⣿⣿⣿⢻⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣽⣼⣿⣆⢀⠀⠀⠀⠀⢀⣚⡾⢿⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⢀⣾⣿⣿⠿⢿⣧⢍⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣷⣤⣀⡛⢺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣴⣿⣿⣿⠿⢿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣞⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠇⠀⠈⢹⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡿⠁⠀⠀⠀⠀⠀⠘⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⠛⠉⠉⠉⣉⡵⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠦⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠒⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠂⠀⠀⠀⣀⠠⠤⠤⠤⠦⠤⠤⠤⢤⣀⣀⠀⠀⠀⢀⣀⣀⣤⠬⠭⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠔⢩⠃⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⢄⠀⠀⣷⠀⠀⠀⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⡆⢀⡇⠀⠀⣀⣀⣀⣈⣙⡛⠀⠀⠒⠋⠁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠤⠬⣍⠓⠾⠀⠀⠀⢸⠁⠀⠛⠀⢸⠍⣹⠈⠉⠉⠉⢣⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⠚⠲⢤⡀⣠⠞⠦⣅⣀⠀⢀⣠⠎⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠙⡇⠈⣹⢧⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⣀⠤⠤⣄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠁⢱⢤⡀⠀⠀⠀⠀⠀⠁⠀⢤⣀⣀⣀⡼⠀⣸⠁
⠀⠀⠀⠀⠀⢀⡠⠖⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡴⠁⢀⠏⠓⡦⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⢏⢀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧⣠⣋⣀⣘⣁⣰⡭⠭⠟⠒⠂⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠀⠀⠀⠀⠉⠉⠁⠀⣀⣀⡤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠈⢦⣀⡤⡔⠒⠒⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣹⢃⣀⢿⡄⠀⠀⠀⠉⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡴⡊⠁⢀⡔⠐⠒⠒⠙⢷⠋⠀⠀⠀⢸⣤⠟
⠀⠀⠀⠀⠀⠀⠙⠲⠥⠞⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠸⡉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⣤⢤⡤⠴⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣸⣸⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡲⣾⣤⣤⣽⡤⢤⣷⡖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠧⠭⠟⠚⠉⠑⠺⠿⠾⠟⠃

⣿⣄⣤⡾⣿⣿⣿⡿⠷⢤⡀⠀⠀⢈⣷⠀⠀⡞⢀⣦⡀⡏⡀⡇⠀⣿⣼⠀⢾⣷⡇⠀⠀⣿⣿⠇⠀⠀⠀⣼⠃⠀⠀⠀⢸⣷⡆⣇⡀⠠⢸
⣿⣯⠟⠀⡔⠰⠀⠀⠀⠠⠙⣦⠀⢠⣿⣸⣴⣴⣿⣿⣣⣿⠿⠻⢾⣿⣿⣉⣾⠿⠛⠒⠚⠿⢧⣖⢀⣀⡸⣿⠀⠀⠀⠀⢸⣿⣿⣟⣛⣶⣿
⣿⣿⣾⡀⣶⣶⣠⣴⣆⣄⢱⣾⣷⡿⠋⠉⠉⠉⢻⣿⣯⠴⢤⣀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣯⣹⣿⣿⣤⠴⢦⣤⣼⣿⠛⣿⣿⠋⢸
⣿⣿⠛⠛⣿⠋⠉⠉⠉⠛⢿⣿⣿⢠⠀⠀⠀⠀⣷⣿⣧⣠⠖⠋⠉⠉⠲⣆⡀⠀⠀⣀⣤⣤⣤⣀⢾⣿⡿⠋⠀⠀⠀⠈⣿⡇⠀⢸⣿⣀⣸
⣿⡇⠀⢺⢹⡄⠀⠀⠀⠀⠀⠹⣷⣾⠀⠀⠀⠀⡏⣿⢸⡟⠀⠀⠀⠀⠀⢸⡷⠶⢴⣿⠃⠀⢸⣿⣿⠏⠀⠀⣠⣤⣶⣤⣿⣧⠶⠛⠉⠙⣿
⣿⡇⠀⠸⣆⣿⡄⠀⠀⠀⠀⠀⢘⣿⣴⣰⠀⣤⣇⣿⣿⣷⣤⣠⣠⣤⣶⣾⣿⣷⣄⣿⠀⠀⢰⣿⡏⠀⢠⡾⠋⠁⠀⠈⢻⣧⣀⡀⠠⣰⣿
⣿⡇⢶⡛⠛⠛⠛⠓⠶⠶⢤⣶⡿⡿⠿⢿⣿⣿⣿⡟⠉⠉⠉⡙⠿⣿⢘⣿⢻⢹⣿⢹⣿⣦⣼⣿⣇⣠⣾⠃⠀⠀⠀⠀⡀⣿⡉⠙⠛⠿⣿
⣿⣷⣠⣽⣦⡀⠀⠀⠀⡄⣾⠃⠀⠀⠀⠀⢻⣻⡿⠡⠄⢠⢠⢠⢀⡇⢸⢸⢸⢸⣿⡇⣷⣿⣿⡿⠋⠀⣿⠀⠀⠀⠀⠀⠀⢻⣧⣀⣄⣠⣿
⣿⠟⠀⠀⠈⠳⣄⣧⢲⣿⠇⠀⠀⠀⠀⠂⢀⢿⣧⠀⠀⢸⠸⡜⣾⡇⣿⢸⢸⢸⣿⡇⣿⣿⣿⣧⢀⣀⣿⠀⠀⠀⠀⠁⠀⢸⡇⠀⠉⣽⣿
⣿⣆⣀⣀⣤⠴⠿⠛⠻⣿⠀⢰⢸⠀⠀⠀⠄⣾⣿⡌⢸⠘⡆⣇⣿⣷⣿⢸⢸⢸⣿⣇⠏⠈⣿⣿⣿⣿⡿⣶⣄⠀⠀⡄⠀⢸⡇⢀⣼⠟⢸
⣿⡟⠋⠁⠀⠀⠀⠀⠠⣿⠀⠘⠸⠀⠀⠀⠀⣿⣿⣷⠸⡆⣿⢻⠋⠻⣼⢸⢸⢸⣿⣿⠀⠂⣿⡟⠁⠀⠀⠀⠙⣷⡆⡇⠀⢸⣷⠟⢁⣤⣿
⣿⣿⣤⡖⠂⣀⣄⣠⣼⣯⠀⡄⠀⠀⠀⠀⡇⣿⣿⣿⣧⣿⣇⣸⡀⠀⢻⣸⢸⢸⣿⢻⣇⢸⣿⡇⠀⠀⠀⠀⠀⠈⣿⣇⡆⣿⣥⠶⠛⣉⣿
⣿⡿⠞⣿⠉⠘⣧⠀⣾⣷⠆⡇⡄⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣏⣇⠀⢸⣿⣿⣿⣿⢸⣮⣿⣿⣿⣶⣦⣤⣤⣀⡀⠘⣿⣿⣿⣥⣶⣿⣛⣿
⣿⡿⢦⣜⣷⣄⣽⡾⢿⣿⠀⡇⡇⠀⠀⡇⡇⣿⣿⣿⣿⡏⣉⢻⡾⣿⢾⣿⡇⡇⣿⢸⣿⠟⠉⠀⠀⠀⠀⢙⣿⣿⣿⣿⡿⠛⠙⠛⠻⣿⣿
⣿⣿⡷⢮⣍⣻⡇⠡⠀⣿⡆⡇⡇⠀⠀⡇⡇⣿⣿⣿⠟⠓⡹⠛⢦⣸⡏⣿⡇⡇⣿⣼⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠹⣧⠀⠀⠀⠀⠈⣿
⣿⡷⠟⠒⠀⠙⣿⠄⠀⢸⡇⡇⣇⠀⢀⡇⡇⣿⣿⣿⠦⢴⡇⠀⢸⣿⣧⣿⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⢸
⣿⣇⣠⣴⣷⣼⣽⣿⣦⣿⣇⠁⢋⠀⠸⡇⡇⣿⣿⣇⠀⠀⢝⣦⣼⠁⢀⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠠⢸
⣿⣿⠿⠋⠀⠛⠁⠀⠙⢿⣿⣸⢸⢸⠀⡇⡇⣿⣿⣿⣿⣿⠋⠁⠈⢹⣿⣟⣫⡿⠟⠛⠛⠛⠻⢷⣤⡀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣾
⣿⡁⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣾⣾⣧⣿⡿⠿⠿⠿⢿⣇⡀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⡇⠀⠀⠀⢰⡟⠀⠀⠀⢀⣾⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⢿⣷⠿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⢀⣾⠃⠀⠀⢀⡾⠋⣻
⣿⠟⢦⡀⠀⠀⠀⠀⣴⡞⠛⢻⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣛⢻⠀⡀⣄⣤⢀⡇⠀⠀⠀⠀⠀⣽⡈⣿⡀⣼⠃⣀⢠⣴⢿⡿⢿⣿
⣿⠀⠈⣿⡇⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣿⣆⣦⡏⠟⡾⣴⣠⠄⠀⠠⢀⣻⣟⢾⣿⣹⣶⣻⣏⢹⣿⣦⡈⣹
⣿⠀⠀⣿⡇⠠⠀⣸⣿⣷⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢻⣽⣽⣮⠷⠾⣿⣙⠉⡰⢲⡟⠺⡿⣿⣿⣿⣿⣿⡿⢸⣨⣿⡿⢷⢻
⣿⠀⠀⣿⡧⢀⡼⠋⠉⠀⠉⠍⢻⣧⡆⠀⠀⠀⠀⠀⠀⢀⢠⢸⣿⡟⠁⠀⠈⢷⡀⠈⠻⣖⣿⠺⢷⡈⢧⠙⠿⡜⢿⡼⠥⣾⣛⣋⣴⠟⣻
⣿⣤⡴⠛⠛⠛⠛⢦⣀⠀⣠⠴⠾⣿⣧⠄⠀⠀⠀⠀⢀⢠⢸⣸⡇⠁⠀⠀⠀⠈⣧⢀⠄⣿⡟⢷⣤⣬⢾⠟⠋⠀⡟⠀⠀⠈⣧⠈⠙⠿⣽
⣿⡏⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠈⠻⣷⣴⣴⢀⣦⣸⣼⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⡗⣿⣿⣻⠏⢰⡏⠀⠀⢸⡧⠀⠀⠀⢸⡆⠀⡠⢹

⠀⠐⠂⠀⡄⢳⢄⠀⠀⠀⠀⠀⢼⠂⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⡴⠣⠁⣴⡇⠀⠀⠐⠀⠀⠠⣈⠞⠈⣆⠀⢸⢂⣼⣿⣿⣬⣀⣀
⠀⢀⠀⢰⡅⠘⡇⠈⠀⠀⠀⠀⣸⠀⢠⣾⡿⣿⡇⠀⠀⠀⠀⠀⡼⠃⠀⡰⢁⠃⠀⠀⠀⠀⠀⣠⠋⠀⠀⠈⠀⣸⠜⣽⠟⣿⠻⣿⣿
⠀⢸⣧⡘⠀⢀⠙⡀⠀⠀⠀⠀⡏⣰⣿⠟⠁⣿⣇⣤⣶⣾⣿⣿⡷⣤⡐⠀⣸⢒⠠⠀⠀⠀⡔⡇⠀⠀⢀⡄⠀⣿⣼⡿⢀⡏⠀⠑⠘
⠀⠸⣿⣧⠀⡀⠀⠸⡀⠀⠀⠀⣳⣿⠏⠀⣠⣟⣻⣿⣿⢫⣬⣄⢩⣷⡟⣆⡧⠈⠀⠀⢀⠎⠀⠀⠀⠀⢸⣷⣴⣿⣿⠃⢸⡏
⠀⠀⠸⣿⡄⠀⠀⠉⢿⡄⠠⠀⣿⡟⠀⠘⣿⠐⣿⣿⣿⡈⣙⡋⠠⣭⠠⣿⡱⠀⠀⢠⠏⠀⠀⠀⠀⠰⠇⢀⡻⣿⠁⠀⣾⠁⠀⢡
⠀⠀⠁⣿⣧⠀⠀⠀⣸⣷⠀⠀⣿⡇⠀⠀⠙⣦⣽⣿⣿⣿⣿⣦⣠⠄⠂⢺⠄⠀⢠⠏⠀⠀⠀⠀⠀⣽⣾⣥⠔⠋⠀⢰⣿⠙⢶⢾⡇
⠀⠀⠀⢹⡏⣷⡀⠀⢸⣿⡅⢠⣿⡇⠀⣐⣶⣿⠿⠿⢿⣿⡟⠻⣿⣿⣿⡿⠀⣠⠋⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⢀⣿⣿⡆⠀⢠
⠀⠀⠀⢸⡇⣿⡇⠀⢰⣿⠃⠸⣿⠀⣸⣿⣿⣿⣶⣶⣿⣿⣿⣦⣤⣤⣿⣀⣰⠡⠴⣶⣾⣾⣿⣿⣿⣿⠏⠰⠀⢠⣾⡿⣷⠈⠀⠀⣻
⠀⠀⠀⣸⣷⣿⠂⠀⢸⣿⠀⢀⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣉⣩⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⢏⠅⠀⠀⢀⣾⡿⠁⠈⠀⢀⣼⣿
⠀⠀⢀⡟⣿⣿⠀⢀⣾⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣼⣿⠿⢡⠟⠁⠀⠀⣾⣿⠃⠀⠀⢠⣿⡿⢹
⠀⠀⢸⠁⣿⡏⣠⣾⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠒⠶⣶⣾⡿⠛⢀⡏⠀⠀⠀⣼⣿⠏⠀⠀⢠⣿⡟⡰⠿
⠀⢀⡏⠀⣿⣷⣿⢧⠤⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⢿⠁⢀⠀⡇⠀⠀⣴⣿⠏⠀⠀⣴⣿⠏⠀⠎
⠀⠸⠧⠄⣿⣿⡇⠘⣦⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⣿⣿⣿⡆⢀⠂⣴⣶⣦⠀⠀⠀⠈⣃⠀⢠⡇⠀⣰⣿⠏⠀⣠⣾⡿⠃⠀⠁
⠀⠈⠀⠀⣿⣿⣿⠀⠹⡄⠀⠀⠀⣿⣿⣿⣿⡏⠀⢸⣿⣿⣧⢤⣾⣿⣿⣿⣿⣄⠀⠀⠑⢄⢸⠀⣴⣿⠏⢀⣾⣿⠟⠁
⠀⠰⠤⢀⣿⣿⣿⡄⠀⢳⠀⠀⠀⢿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⢾⣿⢋⣴⣿⠟⠁⠀⠀⠀⠀⠀⡠⠚
⠀⢀⠀⢸⣿⣿⡿⠸⢄⠀⢇⠀⠀⠘⣿⣿⣿⣧⣠⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠻⢷⣆⡀⠀⢱⣿⡿⠃⠀⠀⠀⠀⠀⢀⢞⠱⡀
⠀⠀⢀⣿⣿⣿⡇⠀⠀⢵⢼⡀⡈⠀⠙⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣦⣤⣤⠻⠿⢶⣶⣿⠛⠻⢶⣖⡂⠀⢀⡿⡘⡄⢳
⠀⠀⣿⣿⣿⣿⢇⠀⠀⠀⢧⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⣷⡀⠀⠀⠙⢧⡀⠀⠈⠉⠋⣿⠀⣡⠘⢉
⠀⢸⣿⣿⣿⡇⠘⣆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣟⠿⠿⣿⣿⢿⣷⣦⠀⠈⢻⣿⣿⣶⣄⣀⡀⠙⣷⣄⠀⣸⡿⣍⠀⠀⠈
⠀⣿⣿⣿⣿⠁⠀⠈⢧⡀⠀⠀⠀⢀⠀⠀⠀⡠⠞⠤⣈⡁⠀⠀⣰⣿⡇⠀⠀⣿⣷⡆⠈⣧⠙⢿⣿⣿⣿⣶⣌⣿⣿⣿⠃⠈⠳⢤
⠀⣿⣿⣿⡿⠀⠀⠀⠈⢐⢄⠀⠀⠀⠘⢦⡞⠁⠀⠂⠈⠃⢠⣾⠟⣼⠈⠃⠀⣿⣿⣷⡀⣷⠀⠀⢙⡿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢠⡝
⠀⢻⣿⣿⠀⠢⠀⠀⠀⠈⢢⠣⡀⢀⡴⠋⠀⠢⠀⠀⠄⣴⣿⡋⢸⠏⠒⠄⠀⠿⣿⣿⣧⢹⠀⠘⠁⠀⡈⣻⣿⣿⣿⣿⣿⣿⣷⣄⣱
⠀⣿⣿⣯⠀⢀⠀⡀⠀⠀⠀⢣⡸⠎⠀⠀⠀⠀⠀⢈⣼⠟⠁⣇⣾⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠂⣀⠞⠠⠃⠎⠳⣌⢉⠉⢻⠿⠿⢟
⠀⣾⣿⣿⠀⠈⠀⠛⠐⢂⠄⡟⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠠⢸⠇⠀⠀⠄⢀⡠⣾⣻⣿⣿⡁⠌⠡⠀⠀⠘⠀⠀⠟⣦⠹⣤⣀⢃⡘
⠀⢻⣿⣿⠀⠀⠀⢠⠜⠇⡄⠀⠀⠀⠀⠐⠀⢰⣿⠃⠀⠀⢀⡏⠀⢀⠤⠚⣡⠞⠁⣸⣿⣿⡗⠈⠀⠀⠀⠀⠀⠀⠀⠁⡷⡀⠈⠁⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣼⣿⣷⣾⣷⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠉⠉⠁⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⡷⠾⠶⠾⢆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⡗⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢸⡟⠀⢀⣴⢦⣤⣀⡀⠀⠀⠀⠀⠰⠀⢸⣯⠀⠀⢐⣤⣽⡯⢼⣿⢿⣰⣦⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠸⡇⠀⠈⠉⠈⠁⠙⠣⠑⠀⠀⠈⠘⠀⢸⡏⠀⠀⠀⠀⠹⠉⠀⠁⡀⠘⠿⢣⠏⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⡄⣿⣦⡄⠆⢀⣹⣷⠀⠀⠀⠀⠀⠄⣆⠀⣿⣄⠀⠀⠀⠀⠀⠀⣥⣦⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⣿⣿⣿⣿⠻⣬⠀⠀⠀⠀⠀⠈⡕⣻⡄⢻⣿⣿⣿⡅⡟⢀⣀⣤⣶⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣝⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣳⡀⢿⣿⣿⣿⣿⣿⣷⡿⢿⣍⡉⠁⠶
⠀⠀⠀⠀⠀⠀⠒⠲⣤⣀⠈⢻⣎⢿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠉⢷⡈⢿⣿⣿⣿⣿⣿⣧⣄⣹⣿⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠙⠯⢿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡝⢿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⡆⠀⠀⠀⠀⢰⣦⡀⠀⠈⣿⣷⡌⢿⣿⡟⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⣆⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠻⢷⠀⠀⠨⠿⢿⡌⣿⡇⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠙⠲⠤⠤⠖⠒⠒⠛⠛⠛⠛⠋⠒⠒⠲⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣌⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠋⢸⣧⠴⠖⠛⠲⣄⠀⣄⣻⠉⠓⠲⠿⡍⠓⠲⠦⠿⠏⠛⠲⢦⣄⣀⠀⢦⣤⣀⠀⠑⠦⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠢⢾⡀⡮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢀⡞⠠⠌⠉⠓⠛⠀⠉⠓⠦⣌⣷
⠀⠀⠀⠈⠛⣟⣛⣒⣒⠒⠒⠠⠤⠤⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠠⠶⢦⠀⠉⠁⠀⠀⠀⣀⣀⠀⢀⠴⠒⠓⣄⢠⠞⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢀⡠⠔⣊⣁⣀⣀⡤⠤⣤⠤⣤⣤⡬⠍⠛⠛⢛⣿⡿⠶⠶⠶⠦⠈⠧⣄⣀⣀⣠⡄⠀⢠⡴⢋⡽⢩⠅⢰⠋⠀⠀⠀⡜⠈⣦⠄⠀⠀⣸
⠚⠋⠉⠉⠉⢻⡅⢠⠖⢾⠉⠹⡇⠀⣵⣔⣚⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢻⡉⣵⢻⠀⢾⠀⠀⠀⡰⠃⠀⠈⢟⠛⣛⡡⠤⣄
⠀⠀⠀⠀⠀⠀⠳⠜⠢⡀⢣⠀⡇⠐⢋⣁⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢣⣸⣿⠀⠀⠑⠒⠊⠁⢀⠀⠀⠨⠟⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠉⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠳⣼⡄⠀⠀⠀⠐⢦⠉⠄⠀⢀⣀⣀⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣇⢠⣤⣤⣀⣀⡀⣀⡰⢛⣶⡤⢾⣿⡆⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣙⡆⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠒⠛⠋⠉⠉⠹⣄⣈⣉⢙⡄⠀⠀⠉⠀⠁⠸⡅⢀⣼⠉⠹⣆⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⡟⠉⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣏⡃⠀⠀⠀⠀⠀⠀⠘⠲⢋⡆⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢇⠀⠀⠀⠀⠀⠀⣎⠁⠀⠘⠛⠊⠁⠀⠀⠀⠀⠀⡀⠈⢧⣀⠀⠀⠙⠳⢤⣤⣤⣤⣤⣤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⡾⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⢀⣨⣽⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⢶⢲⠊⡿⠀⠀⠀⠈⠓⠦⣄⣀⣀⡀⠀⣰⠁⣧⠔⣹⢿⣿⣤⡀⠀⣴⢮⣉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣦⠁⠀⠀⠀⠀⠀⢰⠃⡏⠉⢩⠏⠁⠀⠉⠀⠀⠀⠙⠦⣙⢺⢁⣤⡨⢏⡁⣹⡤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⣯⣄⡀⠀⠀⠀⠀⢿⠾⠗⠂⢺⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢰⡶⣄⣹⠁⠀⠀⠀⠀⠉⠉⠒⠒⠒⠀⠤⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⡜⠻⠏⡟⡿⡲⠶⡾⢶⣊⠻⠟⠻⠇⠉⢳⠀⣀⡠⠤⠒⠊⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⢀⣃⡤⢖⡽⠿⣧⡀⠈⢑⣲⣭⣛⣓⠶⢲⡏⣟⡓⠒⠶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣉⣴⣾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⠥⣶⣛⡃⢂⣴⡧⠯⢬⢤⠖⠒⢺⠻⡉⠁⠀⠈⠉⡿⠿⣷⣶⣶⣤⣤⣍⣉⣉⠒⠒⠲⠦⠤⢴⠋⣠⣾⠟⣋⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡸⠀⢸⠉⡏⠻⣳⠀⢸⠾⡆⠀⠀⡇⢧⠀⠀⠀⠀⢹⣤⣤⣤⣌⣉⣉⡛⠛⠻⠿⠿⢿⣶⣶⣶⠾⣋⡥⠊⢹⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⠇⠀⢸⠰⡇⠀⠉⠀⠈⠉⠁⠀⠀⢳⠼⡄⠀⠀⠀⢸⢸⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢤⣄⣼⡧⠚⠁⠀⠀⢸⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠇⠀⠀⠀⣎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⣀⡸⠓⣧⣎⠀⡀⢀⠁⡠⠈⠀⣨⠻⢈⣠⣀⡐⠫⠓⡦⢲⡖⣔⡀⠀⠀⡧⡤⢀⠪⢇⡠⠽⣿⢸⡸⠈
⠀⠀⢣⠠⢀⡇⠛⠠⢯⣧⣟⣉⣶⣴⡐⠚⡩⢤⠈⣙⡏⠙⢏⠁⠠⣬⠛⣫⢬⠅⠆⢹⣡⠀⢠⢂⡈⠧⢀⠉
⠀⠀⠠⠂⢸⠓⣌⠘⠳⡞⣽⡟⢒⠯⡇⠀⢠⡀⠈⠋⢹⠼⠘⡠⠔⠃⠀⠘⠰⣎⠀⠘⠂⠂⢉⣁⣀⡠⠴⠦⢴
⠀⠀⣠⡀⠆⠈⢀⠄⠀⠁⠉⠙⠚⠦⡼⠀⠲⡷⡤⢤⠬⢶⠛⠀⠀⠀⠀⠀⠀⠈⠡⣿⣿⡿⣿⡛⣥⣀⡂⠐⠨
⠀⡆⢩⠘⢠⢚⠀⢂⣐⡂⣐⠤⣄⠀⡘⡄⣟⣍⢍⣿⣿⡏⠀⡀⠴⠀⠁⠈⠀⠐⠀⢻⣈⣹⡇⣷⢏⠁⠸⡈
⠀⠓⠐⠋⣶⠀⣤⣭⣶⠀⠀⠀⣤⡑⡆⢹⢤⣿⠀⣿⣿⠱⠀⠿⠿⠇⠀⠀⠿⠉⠆⢸⡿⡿⣿⣝⠀⡁⠈⠀⠢
⠀⠀⠰⣦⢸⠟⠙⠘⠋⠃⠀⠺⠯⠿⠇⢫⠒⠛⠃⡿⠿⠀⣇⠠⠄⠀⠀⠀⠀⠠⢀⣬⣼⣥⣬⣧⣼⠁⢸⢅
⠀⢐⢾⣷⠀⠀⠓⢄⠀⠀⠀⠀⡠⠒⠀⠀⢀⠐⠀⢠⠄⠉⢘⠀⠀⠐⠀⠀⡞⠀⢽⢯⣤⣤⣀⡀⢉⣠⣨⡀
⠀⠘⢰⢸⡉⠀⠀⢀⠍⣲⢦⡀⠀⠀⠀⢸⠊⢀⣂⡉⢸⠀⣇⠤⢀⣠⣀⡀⠘⠄⡍⠐⠈⡗⠮⢤⢠⠀⢠⠀⢀
⠀⠀⠰⢸⠀⢠⡪⠑⠦⣤⣜⠟⠳⠀⢠⠆⢰⠀⢽⠏⢠⠊⠁⣦⠉⠀⠈⣰⠆⠀⠘⡆⣇⣁⣿⠀⢸⠀⠰⠤⠉
⠀⠀⢥⠿⡄⢠⠀⠸⡶⢣⢝⣲⢾⢰⡇⠘⠘⠂⠙⠀⢨⢠⠀⠁⠀⡀⠀⠘⠀⢠⠄⢿⡍⣉⣉⣉⣙⡂⡤
⢀⡀⢠⡄⠀⢺⠀⠱⢨⢋⠦⢱⡾⡟⠀⡀⠀⠀⠀⠀⠙⢿⢘⠀⠀⠀⠀⢀⠀⠈⠄⠗⠒⢰⣐⠀⠈⠃⠰
⠙⠋⠶⡄⢻⠸⠀⡖⠢⠍⠖⠸⠀⠓⡄⢠⢀⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⢀⠀⣀⣀⣈⣂⠂
⠀⠀⢬⣀⡌⠁⡰⠀⠀⠈⡁⠀⠉⣁⢱⢸⡂⠀⠀⠀⠀⡸⠀⣀⠀⠀⠀⠈⠀⠀⠀⢀⠁⠲⠤⠽⣽⠀⠈
⠀⠀⠛⢉⡖⠐⠀⠀⠠⠀⠀⠸⠀⠘⡂⠃⠃⠀⠀⢀⣖⡃⠐⠁⠁⢀⡀⡀⠀⠤⠄⠈⣉⠛⢛⢛⢃⠀⠈⠉
⠀⠆⠽⢸⠀⡤⠀⠀⠀⠂⠀⠀⠀⠀⠇⠸⠷⠶⠦⠉⢯⡄⢀⠒⠄⠉⠀⠓⠀⢀⡄⠀⠂⠀⠀⠻⠾⠓⢾⢾⡀
⠀⠆⡽⢸⢧⡀⠀⠀⠀⠀⠀⣄⠀⠢⠄⢖⡁⠀⠀⠀⠀⡃⠉⠀⠀⠃⠀⠰⠠⡄⠀⣴⠠⠀⡀⠀⠘⠂⢨⠀⠈
⠀⡄⢠⡼⡾⠡⠄⣀⠀⠀⡔⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠈⡀⠙⠙⠁⠀⠆⠀⠀⢀
⠀⠉⢠⣐⠢⠲⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠿⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠄⠒⠀⠃⢀
⠀⠀⠘⢉⠈⠐⠲⣦⠀⠀⣠⠐⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠾⠀⢐⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠉⡀⠈⢹⠘⡆⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠉⢆⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⡦⠐⠀⣰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠈⢿⣿⣿⣿⣿⣿⠋⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠈⢻⣿⢿⡿⠁⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⠀⠀⠀⡀⠐⡈⣋⠂⠀⠀⠀⠀⣈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢻⣿⣿⣶⣄⠀⠀⠀⠀⢨⣴⣿⣿⡿⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠭⠿⡿⠟⠀⠀⠀⠀⠸⢿⡿⠯⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⣀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣴⣶⠆⠀⠀⠀⠀⠀⠘⢧⣁⣙⣛⣉⣵⠋⠀⠀⠀⠀⠀⠐⣶⣦⣌⢲⣀
⠀⠀⠀⠀⢦⡴⣶⣶⡄⠈⠸⠛⠛⠁⠀⠀⡀⠀⠀⠀⠀⠈⢿⣻⢟⡿⠁⠀⠀⠀⠀⢢⠀⠀⠈⠛⠛⠃⠉⢠⣴⣶⢦⣴
⠀⠀⠀⠀⠈⠾⠿⡿⢷⠀⠀⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠐⢋⠀⠀⠀⠀⠀⠀⠀⡾⢿⠿⠷⠃
⠀⠀⠀⠀⠀⠈⡖⢄⢸⣧⣴⡶⠂⢀⠀⠀⠸⢷⣦⡀⠀⢀⣀⢀⡀⢀⡀⠀⢀⣴⡾⠏⡀⠀⡀⠐⢶⣦⣼⡇⣀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⡬⣷⣟⡀⠀⠘⡦⡄⠉⠁⠀⢸⣿⣿⣿⣿⡇⠀⠘⡏⢀⢴⡃⠀⠀⣙⣶⠥⣼⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠙⢿⣤⣌⣿⣁⡴⠊⠀⢻⠀⠀⢈⠌⠉⠻⡿⠋⠁⡀⠀⠀⡟⠀⠙⢦⣈⣿⣁⣤⡿⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠈⠀⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠏⠀⠀⠀⠻⢿⣿⣿⡆⢰⣿⣿⣿⠟⠀⠀⠀⠘⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣿⣿⣾⠟⠉⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⢿⡿⠛⠁⢠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠡⠙⠿⣦⣶⣤⡀⣠⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣤⠀⠀⢀⣹⣿⣿⣿⡿⣿⡿⠆⠀⠤⣄⠀⠤⡀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠼⠟⠋⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⢤⣀⣤⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⡃⢠⣤⣤⣤⡄⠀⠀⠶⣲⣷⠒⠒⠾⣿⡏⠀⢠⣿⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡀⢿⣿⡿⠑⡄⠀⠀⠀⠿⠿⠀⠀⠀⠉⠃⢠⣿⡟⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠋⠏⠀⠀⡴⠁
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠾⣷⣦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣴⣮⡄⠈⠁⠀⡸⠁
⠉⠁⠀⣀⠿⡇⠀⠐⣧⡀⠀⠀⠀⠀⠙⠿⠧⢀⠸⣿⣿⣦⣀⠀⠀⠶⠖⠀⠀⡠⣺⣿⣿⡇
⠀⠀⠀⠡⠤⠀⠀⠀⢈⣽⡗⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡆⠙⣶⠦⠄⠀⠀⢰⡈⠳⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠋⠀⠀⣰⣆⣀⠀⠈⡡⠊⠉⠉⠉⠛⠛⠅⠀⠀⠀⠈⣿⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣶⣤⣄⡄⠀⢀⡀⣤⣴⣶⣤⣶⣄⣐⣥⡘⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠷⢶⡶⠾⠿⠿⠛⠋⠻⢿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣸⣿⣿⣿⣿⣿⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠀⠉⠉⠁⠒⠢⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠀⠙⢆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢄⡀⡰⠁⡴⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠾⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡏⢀⡵⣕⠀⠀⠀⠀⠈⢢⣀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡏
⠀⠁⠢⠀⠀⠒⠄⡀⢀⠔⠀⠈⠊⠐⣈⡻⠃⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢰⠁
⠀⠈⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠌⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡇⠀⠀⠀⠀⢸
⠀⢰⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⡠⢂⡔⠛⠃⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⡇⠀⠀⠀⠀⢸
⠀⠘⠦⣀⡀⢀⡠⠃⠀⠀⠀⢀⠤⣚⡐⢛⣤⠤⣀⡀⠀⠈⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⠀⠀⢧⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠞⠁⠄⠀⠣⠄⢠⠤⠊⠉⠓⠢⢤⠴⠃⠀⠀⠀⠀⢀⣀⡤⡞⠁⠀⣸⠀⠀⠈⠳⢤⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠒⢉⣉⡀⠔⠀⡠⠔⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠁⠀⠀⠀⠀⡸⠀⠀⡱⠦⠴⡄⠀⠀⢰⡆⠠⣥⠀⢀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⣇⣀⣀⣧⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⢸
⠀⠀⠀⠐⠲⢄⣄⣠⢶⠊⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣄⠀⣰⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⢀⠄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠔⠀⢀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠁⠣⢀⠀⠀⢀⡀⠀⠀⠀⣸⣤⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⡀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⣶⣿⣶⣼⣿⣷⣧⣾⣼⣿⣷⢂⣤⡀⠀⠀⠀⠀⡠⠔⠋⠀⢠⠖⠋
⠀⠀⠀⠀⡄⢄⠀⠀⠀⠀⠀⠀⢤⡈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋⡤⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣤⣞⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠂⡈⠁
⠀⠀⠀⠠⠤⠤⠴⠒⠀⠀⢠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠚⠙⠓⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣱⣿⣿⣿⠻⠿⠋⠉⠿⢻⣿⠃⣼⣿⣿⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢈⣩⣽⡒⠀⠘⠋⠀⢘⣩⣤⣼⢿⣿⣿⠛⠁⠀⠀⠀⣀⠀⢈⡀⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠈⠁⠛⠋⠀⠀⠀⠀⠉⠀⠛⠉⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠁⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⣤⡤⠄⠀⠀⠠
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⡀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣦⣄⡑⠀⠠⠀⡀⠀⠀⠀⠀⠀⠈⠠⠀⣈⣤⣾⣷⣶⣤⣄⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣴⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣍⢺⣷⣶⣖⢲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⣼⠆⢼⡃⠀⠇⢙⣷⠈⢱⣤⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣿⠻⣾⣷⣆⣷⠟⠈⠓⢶⡒⢧⠀⠀⠀⠀⠐⣦⡜⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢿⡶⢻⣻⠉⠉⠀⠰⢣⣾⢏⡏⢡⠀⠀⠀⠀⢾⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠺⡿⣶⣯⠓⣒⣄⠀⠉⠁⢸⡏⡈⠀⠀⠀⠀⢀⣹⣿⣷⣜⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠛⠻⢮⢿⣿⣟⠁⠁⢀⣠⠀⣧⠏⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣝⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠻⣿⢿⠷⢦⣬⣤⠂⠈⠄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣝⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢰⡆⢚⣏⠐⣾⣟⠛⣷⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣷⠀⣿⡧⠤⠿⢧⣌⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠯⣀⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⢷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢒⡾⠟⢋⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⢁⢤⣾⡯⠖⢛⣩⠝⠛⠉⠉⠉⠉⠉⠉⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠟⠁⠀⠀⠁⠾⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣀⡾⢋⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⠶⠾⠝⠻⠷⠶⠦⠽⣶⡀
⠀⠀⠀⠀⠀⠀⣴⣿⠋⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⢰⡏⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣷⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⢀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠘⣧⠀⠀⡆⢿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⣨⠄⠒⠒⠒⠒⠢⢬⣁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠡⠈⢧⡸⡀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠈⠉⠉⠉⠲⣄⣂⠤⢀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⢀⡼⣣⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠁⠈⠳⣷⡀⠀⠀⠀⠀⢸⡇⠀⣠⠖⠒⠲⢤⡀⢸⡇⠙⢦⡀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠶⠟⠛⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣤⡀⡞⠳⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢱⢠⠇⠀⠀⠙⢦⡀⠀⠀⠀⠀⣀⠀⠀⠀⡀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡎⣹⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡀⠀⠀⠀⠈⣝⠳⣄⠀⣀⣈⠁⠈⠉⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠈⢀⠀⠀⡀⠀⠀⠸⡆⢠⠞⢉⡉⢳⣀⣠⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⠒⠒⠶⢦⣤⠀⠀⠰⠞⠋⠀⢄⣴⣾⣿⠛⣟⣿⠋⠀⠀⠁⠈⢀⠊⡀⢸⣏⢢⡘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣶⣯⣴⣀⠀⠀⠀⠀⠀⠀⣸⣏⢹⣿⣿⠇⡾⠃⠀⠀⠀⠀⣠⠀⡠⠁⡼⢻⡄⠱⡀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣏⠈⡉⣿⣷⣄⠀⠀⠀⠀⠛⢈⣲⣬⡵⠎⠀⠀⠀⠀⠀⠀⢿⠀⢀⡼⠁⠀⠹⣆⠁⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣵⣬⠿⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠙⠀⠀⠀⠘⢦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⢣⡀⠀⠀⠀⠀⠳⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⡀⠱⣄⠀⠀⠀⠀⢡⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠀⠀⠀⡀⠠⡶⠃⠀⠀⠀⠀⢀⣤⠞⠁⠟⢻⡏⠙⠷⣤⣅⣀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣍⠑⠆⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠈⣿⠀⠀⠈⠻⡙⢿⠶⣤⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠀⢳⡀⠹⡇⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⢇⠀⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⣤⠤⠀⠀⠀⠀⢰⡇⠘⣷⡀⠀⠀⠀⠀⢸⠀⢹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠁⢰⢸⠛⢦⣄⠀⠀⢸⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⠈⠀⠀⠙⣧⠀⠀⠀⣟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣧⠸⠀⠀⠀⠀⢸⣆⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⡠⢒⡽⢷⡀⠀⠀⠀⢸⣏⡴⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢠⣿⢙⣁⣏⣹⠂⣐⠠⣀⣠⣴⡟⠀⠀⠐⠉⠀⠈⢷⠀⠀⠀⡼⠋⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⣿⠁⣀⠀⠀⢉⣼⠾⠛⠉⢁⣿⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⡜⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠋⠐⠐⠐⢺⡏⠀⠦⣠⡶⠋⠁⠀⠔⠃⣸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣷⣮⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⢀⣾⣤⠶⢻⡿⠁⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀⡀⠀⢀⣠⠾⠛⠁⠀⠀⣾⠁⠀⠀⠀⠀⣠⡟⠁⠀⢀⣀⣤⡴⠞⢋⡼⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠁⢠⣴⠟⠁⠀⠀⠀⠀⣼⠇⠀⠀⠀⣠⠾⢋⣠⣶⣞⣫⣭⡴⠶⣿⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣤⡞⢁⣀⣀⣀⣠⣤⣞⣁⣀⡠⠶⠛⢛⣋⡽⠟⠉⠉⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠀⠀⠀⠆⠀⠀⠀⠀⠋⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⠄
⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠀⣠⣾⠂
⣿⣿⣿⣿⣿⢿⡷⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⢄⣀⠀⠀⠆⠀⣀⠀⠄⠀⠀⠀⠄⣠⣾⣿⣿⡀⠀⠠⠄
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠀⠀⠉⢻⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⡅⢠⣾⣿⣿⡀⠀⠀⠆⣠⣶⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⣶⣄⠀⢻⣀⣴⣦⡀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠆⢰⣿⣿⣿⣿⣴⣿⣿⣿⣿⡃⠠⣠⣾⣿⣿⣿⣿⣿⠟⠂⠀⠰
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⡿⢿⣷⣄⢿⣿⣿⣷⣤⣿⣿⣿⣿⣿⠀⠀⠠⠀⠀⣿⣋⣛⣿⣿⣿⣋⣻⣿⣿⣡⣴⣿⣿⣿⣿⣿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠆⠀⠀⠠⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣴⠞⣥⣌⢳⣄⠀⠀⠀⢸⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⠟⡛⣩⣌⠙⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠂⠀⠀⠀⠂
⣿⣿⣿⣿⣿⠻⣿⠛⣿⣿⣿⣿⣷⣄⠀⠀⠀⢿⣆⡛⣋⡼⠋⠀⠀⣦⠈⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣶⣥⣙⣋⣠⣰⣿⣿⣿⠿⠋⠀⠀⠀⢀⣤⠀⣠⡄
⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⣻⣿⣷⣄⠀⠈⠛⠛⠉⠀⠀⠀⠀⣿⣼⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣴⣶⣶⣿⣶⣾⣿⣶⣿⡄
⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣾⡟⣼⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣶⣌⠛⠿⠿⠟⠋⢠⣿⣿⣿⣯⡓⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢻⣿⣿⣿⣷⡀⠀⠀⣴⣿⣿⡿⣷⠾⣍⠋⣀⡀⠀⠹⣿⣿⣿⠋⠀⠀⢠⡀⠀⠀⠂⠀⠀⠀⠄⠀⣴⠛⢦⡀
⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣠⣾⣿⣿⣿⣿⣛⣻⠶⡶⠆⠀⠀⠀⠈⢿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣄⠙⠶⠎⣡⡄
⣿⣿⣿⣧⠀⠙⡿⢿⠀⢸⣿⣿⣿⣿⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣭⣓⣀⡛⣃⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⣿⣶⣤⣶⣿⠇⠐
⣿⣿⣿⣿⣷⡔⡿⢻⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⠿⣶⡿⣭⠉⣥⡌⠁⠀⠀⣸⣷⡀⠴⠂⠀⠀⠂⠀⠀⠀⠆⢀⣾⣿⣿⡿⠟⠛
⣿⣿⣿⣿⣿⡏⡟⣻⠄⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢿⣿⣿⣿⣿⣛⣿⠰⠶⠆⠀⠀⠀⢠⣿⣿⣷⣄⣠⠀⠀⠀⠀⢂⣀⣤⣿⣿⣿⡿⠳
⣿⣿⣿⣿⣿⡟⣛⢻⣧⡀⠀⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⣴⡿⣿⣿⣿⣭⠿⣭⣛⣀⡛⠃⠀⠀⣨⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⡿⠏⠀⠀⠀⠐⠂
⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⢷⣤⣀⡀⠀⠀⠀⢀⣀⣤⣶⣿⠏⠀⢻⣿⣿⣿⣶⡿⣭⠉⣥⡀⠀⢰⣿⣿⡄⠙⠻⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠂⠀⠀⠐
⣿⣿⣿⣿⣿⣏⣟⣻⣿⠇⠀⢻⣿⣿⣷⣄⣾⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣍⣿⠲⠶⠂⠀⠀⣾⣿⣿⡇⠀⠐⣿⠀⠙⠿⠉⠰⣿⠀⠀⠆⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⡿⢶⢛⣈⡛⠀⣸⣿⣿⣿⡇⠀⠘⣿⡆⠀⠀⠀⣺⣿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣛⡬⠉⠄⢀⣿⣿⣿⣿⡇⠀⠂⠉⠻⢷⣶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣯⣽⠒⠶⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⣿⣿⣭⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢿⣿⢶⢏⣁⢀⣿⣿⣿⣿⣿⣷⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠐⠂
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⣿⣛⡦⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣿⢁⡀⠀⠀⢻⣿⡒⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣀⣀⣉⣉⣉⣉⣉⣉⣩⣤⣿⡇⠀⠀⠘⣷⢉⣿⣿⣿⣿⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠙⠂⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠙⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠂⠀⠀⠀⣴⣾⡿⠋⠂⠀⠀⠐⠂⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡖⣟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⣿⠿⢿⢿⣷⠄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣧⠐⠀⠀⠀⠒⠀⠀⠀⣶⣿⣿⣋⣀⣀⣤⣀⣀⣀⣀⣐⣂⡀⠀⠐⠂
⣿⣿⣿⣿⣿⠋⠀⠀⠀⢰⣶⣶⣤⣤⣄⣀⣠⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣇⠀⠂⠀⠀⠀⠰⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢻⣿⣿⣿⣷⡀⠀⠘
⣿⣿⣿⣿⣿⣤⢠⡤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡄⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⢻⣟⣻⣛⠃
⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠶⣛⣿⣿⣷⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠐⠂⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠺⢚⣯⣽⣿⡟⠒⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘
⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣩⣩⣶⣿⣿⠇⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⣀⢀⡐⠂
⣿⣿⣿⣿⣿⠈⠃⠈⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠴⣿⣿⡟⠀⠛⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠘⠃
⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠂⠀⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡀⡀⠀⠐⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠆⠂⠀⠐⠄⣀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠠⠀⠀⢀⠀⠘⠖⠀⠀⠀⠰⠐⡂⠐
⠀⠀⠀⠀⠀⠀⠤⡌⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⡄⠀⠐⠈⠒⠉
⠀⠀⠀⠢⠂⠀⠀⡄⣀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠤⠩⠀⠀⠀⢄⠀⠀⠀⠀⡠⠀⡀⠀⠁⠀⠀⠀⠀⠠⠈⢁
⠀⠠⡀⠀⠀⠀⢀⠀⢈⠁⠀⠀⠀⠈⠀⣤⠄⠀⠘⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠂⠈⠀⣀⣁⠈⠀⠀⠘⠁
⠹⠆⠀⠀⠐⠀⣁⣠⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢨⣤⠠⣄⡖⠢⠀⣀⠀⡀⠀⠈⠹⢆⡀⠀⠀⡀⡐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡦⢀⠄⠀⠀⠀⠀⠙⠁⠐⠀⠀⠆⠈⠀⠁⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠁⠀⢀⣄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠳⡂⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠛⢄⡀⣀⠀⠛
⠀⢘⢀⠀⠀⡼⡏⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⡀⠐⠂⠀⡓⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠦⠄
⠀⠦⠀⠡⠔⠀⠸⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠀⠈⠁⠗⠀⢦⡀
⠀⠠⣄⠓⠀⣆⠸⢧⢀⣀⣀⣀⠸⠏⠁⠀⠀⠀⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠢⠄⠐⠿⠀⠀⢠⠀⠀⠀⠀⠰⡦⠃
⠀⠀⠈⠁⠈⠁⠀⠤⠴⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠴⠆⠀⠰⠦⠆⠈⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣰⢁⡁⠀⣰⣆⠀⢰⡖⢀⡀⣀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⡛⢦⣀⣀⣀⣀⣠⣞⡉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠀⠉⠉⠉⠉⠉⠘⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠐⠿⠽⠆⢠⡄⠘⠉⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠠⣤⠼⠧⡤⠄⠀⠀⠀⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⣴⠀⠀⠀⠀⣧⠖⠋⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⠀⡴⠚⠛⠛⠋⠉⣿⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠁⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡿⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢀⡼⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢀⣼⠈⢳⡀⠀⠀⠀⠀⠀⠀⣷⢰⠇⠀⠀⢰⠇⠀⠀⠀⠀⠀⠐⣿⣀⡀⠈⠳⡄
⠀⠀⠀⠀⠐⠟⢃⣠⣴⣿⣴⣶⣿⠟⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠓⢿⣤⣶⡴⠿⠖⠲⠶⠶⠶⠖⠋⠁⠈⡿⠀⠀⡷
⠀⠀⠀⠀⠀⢰⣿⡿⣟⠛⠛⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠚⠛⠛⠛⠛⠛⠛⠛⠋⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣾⢹⣦⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⣀⣀⣤⠤⠤⠴⠶⠶⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣌⡓⠿⢶⣤⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉


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

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⡄⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⠂⠀⠀⠣⠖⠚⠋⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠀⠘⣄⠀⠀⡀⢊⢻⡅⣀⣠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠆⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⡄⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⢀⡐⠖⠒⠀⠀⠈⠀⠀⠀⠀⠈⠙⢧⠀⡄⠀⡠⠐⠉⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠉⠑⠖⠒⠆⠙⠁⠀⠀⠐⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠲⠂⠁⠀⠀⠀⠀⠀⠒⠐⠒⠒⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⡀⠀⠀⠀⣅⠀⠈⠀⠀⠀⠠⣶⡀⠀⠀⠀⠉⠡⠘⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⡘⠂⠀⢀⡀⠀⠀⠙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⣌⣻⣶⣶⡄⠀⠀⠀⠀⣀⠚⠤⣀⠇⠀⠀⠈⠀⣀⣀⠀⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣔⣋⣀⣀⡄⠋⡀⢲⡶⠛⠈⠉⠉⠀⢂⠄⡠⠞⠀⠀⠀⢈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⠠⠒⠀⠤⠐⠂⠀⠀⠀⡀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⠛⠉⠀⠀⠀⢀⡀⠀⢠⡄⠀⠀⠐⢆⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⢀⠀⠀⠀⠀⠀⡠⠄⠂⠠⠀⢲⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠈⠂⠉⠁⠀⠀⣴⠀⠀⠀⠈⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⡾⠀⠀⢀⠂⠀⠀⠳⡀⠀⠀⠘⠷⠄⣀⡐⠠⠀⠀⠴⠀⠇⠀⠀⠀⠀⠀⠈⠲⡀⣼⠇⠀⠀⠀⠀⡇⠀⠀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠐⠄⠤⢶⠀⠀⠠⡏⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢉⡅⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⣀⠠⠀⠀⢰⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣄⠀⠀⠈⡄⠀⠓⠀⠐⠀⠀⢀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⡠⠂⣽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠄⠒⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠦⠀⠀⢁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠉⡔⠀⠀⡠⠊⠐⢀⡆⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠤⠶⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⠄⢀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡅⠀⠄⣸⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⢀⡠⠉⠀⠓
⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠁⠀⡶⢋⠀⠀⠀⠀⠀⠀⠒⠀⠀⠤⣦⠤⣤⢤⣤⣤⣤⠀⠐⠛⠒⠈⠉⠉⠉⠉⠉⠉⠳⢾⡃⡟⠀⠉⠁⠀⠀⠀⢀⠦⠠
⠀⠀⠀⠀⠀⠀⠀⠐⡀⢈⣠⠀⡃⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⡀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣙⠷⣏⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠸⠄⠈⠂⠈⠠⣤⢵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠈⠂⠤⠀⠀⠀⡄⠀⠈⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠹⣦⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣦⠀⠑⠄⠀⢰⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠀⠀⢀⠀⠀⠀⣄⡀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠒⠀⠘⢦⡀⢀⠞⠉⠉⢰⠶⠆⠠⣤⢄⣰⡒⠀⢹⣄⠈⢢⠈⠓⠤⠤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡕⢤⡀⠀⠆⠀⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⢀⡆⢄⠁⣀⠴⠀⠄⠀⠹⡄⢀⡀⢀⡀⠛⠀⠀⠀⢦⠁⠁⠤⠉⠙⣦⠀⠱⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠬⢒⠠⠦⠄⠀⠀⠀⢠
⠀⠀⠀⠀⡐⠒⠣⠠⠔⠂⠀⠀⠀⠀⠀⠀⠈⠲⡙⠂⠑⠂⠀⢀⢀⠀⠱⣄⠀⠤⠀⠀⢳⣄⠀⠢⡀⠙⠦⠠⠐⣄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠐⠆⠤⠀⢀⡼
⠀⡀⠀⠀⠁⠉⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢢⡀⠀⣀⠺⠄⠀⠀⠈⢢⡀⠀⣀⣸⡜⢣⡀⠀⠄⡀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢰⠀⠀⠀⢀⠈⠙
⢈⡁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠙⢶⡁⠀⠀⠁⠔⠒⠀⠙⠦⠀⠬⠥⠽⠽⠶⠠⠘⠖⠐⠚⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠙⢤
⢸⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡁⠂⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠄⠀⠀⡀⠀⠀⢀⡀⠀⠀⠃⢠⡀⠀⠀⠀⢰
⠰⠃⠶⡤⠀⠀⠈⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡕⢶⡀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠒⠀⠁⠐⠁⠀⢀⣂⡈⠓⠺⠛⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣳⠄⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⣆⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣴⠶⠚⠛⠉⡉⢹⡇⡀⠀⢐⢀⡴⢀⠴⠛⢆⠀⠀⠀⠘
⠠⠀⠀⠀⢂⡑⣾⠃⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⢘⣆⢠⡙⣢⣤⣴⣴⠖⠒⠉⢉⢛⣄⡀⢠⣀⡈⠀⢰⡂⣈⠙⣻⣰⡀⠁⠀⠀⠀⠈⢂⡀
⠀⠈⠀⠁⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⢻⣿⠟⠿⢿⣿⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣷⠏⠀⣿⠋⠀⠀⠀⠀⠀⠀⠙⠲⣽⡄⠀⢰⣶⡀⠹⣿⡄⣿⠋⠙⢿⣻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣻⡛⣿⡟⢹⡇⡴⠁⢀⡼⠁⠀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣭⣷⣤⣾⣿⣿⣿⣿⠃⠀⠀⠀⠙⢦⣻⡿⢿
⠟⠛⠙⠲⣍⣻⣿⣇⣹⡟⠀⠀⢿⠑⢠⠞⢀⣀⣤⠤⠄⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠙⣇⠞
⠄⠀⠒⠀⠀⠉⢿⣿⠟⠻⢦⣄⣸⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿
⠈⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢉⣿⡤⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⣿⣿⣿⡀⠀⠀⠸⣧
⠀⠀⣀⣠⣤⣤⠤⢼⣿⠒⠒⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⡏⠉⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠘⣿⡀⠀⠀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣇⣿⣦⡀
⠀⠀⠀⠐⣶⣤⣄⣀⠀⢹⣿⡄⠀⠀⠀⠀⣿⣇⠀⠀⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠆⢠⣤⡈⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢻⣿⣿⡁⠀⠀⢿⣧⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣤⣾⣿⣿⣿⡻⣿⣿⣿
⠀⢀⠀⠀⠸⡟⠙⠿⣄⠀⢸⣿⣀⣀⣀⡀⠀⢿⡇⠀⠀⢶⡖⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣷⣿⣿⣿
⣤⣼⣧⣤⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠳⠀⠀⠈⠀⠠⠟⣿⣿⠛⠛⠉⠉⠈⣽⠷⠏⠀⠀⠀⣤⡙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣤⣤⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⢀⣀⠀⠀⠀⣀⣰⣾⢿⣷⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢸⡟⢻⣷⣴⣄⣻⣿⣆⠀⢠⣿⠛⣿⡄⣿⣿⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣿⣿⢿⣿⣿⣿⣿⡿⣿⣦⣾⡏⠀⣿⣇⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⡇⠈⣿⡇⢻⣷⠀⠘⣿⠇⠀⠀⢹⣿⡿⠿⠇⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠿⢷⣤⣴⣶⣬⡟⢃⣶⡿⠃⠀⢸⣿⠀⠀⢸⣿⣤⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⣀⣾⡟⠉⠉⢻⣿⣾⡟⠀⠀⠀⠀⣤⣄⣀⣾⡿⢿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠋⠋⢿⣧⣀⣀⣼⣿⠻⣿⣄⣀⣀⣤⣨⣿⣿⣿⣥⡄⣈⣉⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠀⢠⣤⣽⣿⣟⣿⣥⣶⣾⠛⠛⣿⣯⣿⠟⢿⣿⠛⣋⣿⡛⠛⡏
⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⢸⣿⣇⣹⣿⢿⣿⣀⣀⠀⢀⣿⡋⣿⡇⢸⣿⣾⣟⠋⡀⠀⠁
⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⢀⢹⣿⣿⣿⣁⠸⣿⡟⠉⠀⢸⣿⠿⣿⣧⢸⣿⠘⣿⣿⠛⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⡇⠙⢿⡷⣿⣷⣿⠿⣿⡯⠀⢚⣿⣼⣿⠀⠘⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢾⣷⣾⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢷⣾⡇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠋⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠙⠛⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢀⣀⠘⣿⡆⠀⠀⠀⠘⠿⣷⣄⠀⠀⠀⢀⣤⣾⠿⠂⠀⠀⠀⠀⣿⡇⣀⡀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣾⣿⣤⣿⣷⣤⣄⣀⠀⠀⠈⠻⣷⡄⢠⣾⠟⠁⠀⠀⣀⣠⣤⣴⣿⣧⣿⣷⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⡟⠋⠉⠉⠉⠉⠛⠿⣷⣦⡀⠀⠹⣿⣿⠏⠀⢀⣴⣾⠟⠛⠉⠉⠉⠉⠙⢻⣷⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣿⣿⣀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⡅⠢⠄⠀⠔⠁⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠂⠀⠀⠀⡀⢤⡝⣦⠉⠁⠀⠀⢀⡘⢧⡛⠂⠀⠀⠀⠀⠀⠈⠑⠒⠂
⠀⠀⠀⣸⡱⡀⣀⠎⠀⠀⠀⠀⠀⠀⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠃⠺⣂⢠⡄⢨⣥⠤
⠀⠀⡀⠹⣱⠡⠃⠀⠀⠀⠀⢀⠀⠀⠀⠨⣄⣷⠄⠒⠀⢲⢏⣄⠀⠀⠀⠀⠀⠀⣽⣍⠦⠀⠮⣶⠻⠀⠀⠀⣀⠀⣄⠀⠀⠀⠠
⠀⠀⡇⠀⠉⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠉⠁⠀⠀⠀⢠⠊⢃⠿⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠀⠈⠀⠀⢀⡻⠋⢛⡶⠂⠀⡆⠀⢈
⠀⠀⠁⡀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⣾⠛⡆⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣶⠺⠧⠀⡘⠀⠀⣈
⠀⠀⠀⠩⡀⠀⠀⠠⠂⠀⠀⢠⢃⠤⠔⠒⠒⠁⠀⠀⠘⠿⠞⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣼
⠀⠀⠀⡇⠉⠁⠀⠀⠀⠀⣠⠋⣁⣴⣾⡟⠋⠲⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠠⠛
⠀⠀⠀⠙⣄⠀⠀⣀⣠⠞⠉⢀⠉⠁⠚⠒⠊⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠈⠑⠺⠇⠀⠠⢀⡈⣁⠀⠀⠀⠀⠀⠀⠀⠤⠔⠪⠁⠓⣒⠒⠢⡄⠀⠤⡀⠀⠀⠀⠀⢀⣀⠤⠐⠊⢁⣀⠀⣠⠀⡴⢩⠁⠀⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠈⢄⡀⠆⠀⠀⠀⠉⠲⣤⣀⣀⡀⠀⣀⣀⡤⠂⠀⠀⠀⠀⠘⠀⠀⠘⢄⠔⠒⠽⠷⠃⠀⠀⠀⢠⠎⢂⣁⠴⠛⠁⠀⠀⡴⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠑⠤⣀⣀⠠⢤⠀⠐⠀⠀⠸⡛⢻⡋⠀⠐⠒⢊⣠⠅⠓⠘⠤⠤⠀⠀⠊⠴⢔⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⡀⠀⠀⡀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⢤⠤⠘⠀⠀⢃⣈⠭⠛⠁⠀⠀⠀⠄⠀⠀⠀⢀⢀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄⣀⣘⠦⠄⠀⡇⠀⠀⠀⢀⠄⠂⠀⠀⠠⠀⠀⢸⠀⢧⠤⠤⡬⡥⠢⡀⠀⠀⠀⠀⡄⠀⠀⡨⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠱⡄⢲⡆⠀⢸⠀⠀⠀⡰⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⡴⠊⠉⠀⠀⠀⠀⠀⠹⣻⣇⠀⡜⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣠⣔⠰⢠⠏⠀⠀⠀⠙⡄⠀⠀⠀⠀⢻⠈⢦⢀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠪⡄⠉⣰⡟⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⡹⠁⠀⢠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡚⠂⠀⡰⢡⣅⠀⠀⠑⠲⠤⣀⠀⠀⠀⠀⢸⣧⠎⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠢⣀⠁⡠⣉⠀⢢⠀⢄⠀⠀⠉⠒⠠⠀⡸⠁⠀⠀⠐⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠙⠲⡥⣀⠀⠑⠀⠑⠀⡁⠤⠄⠀⢁⡀⠀⠠⢚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠛⠛⠋⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡠⠐⠂⠀⠀⠀⢤⡀⠀⠀⢿⣤⣶⣶⣶⣶⣦⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠈⠙⠿⠿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠉⠻⠿⠿⢀⣠⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⡄⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣀⣤⣤⣶⣿⣿⣿⣿⣿⡀⠀⢀⣀⣠⠴⠒⠒⠊⠉⠉⣄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠛⢿⠿⠻⢿⣿⣷⡿⠿⠛⡳⠀⠉⠃⠀⣴⣂⡀⠀⠀⡆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠈⣀⢠⡀⡀⢋⠀⠀⠀⠀⠁⠀⢡⠀⠀⠀⠀⠈⠋⠀⢠⠎⠀⢸⠁
⠀⠀⠀⢀⡤⠄⠀⠀⠋⠙⡄⢻⣿⡾⣇⠄⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⣀⣃⠄⡀⣰⠀⠀⠀⠀⠀⠀⠀⠾⠁⢀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠀⢠⡔⠀⢱⡚⢠⡔⣷⡀⡀⠀⠀⡠⡔⢀⣄⡤
⠀⠀⠀⠀⣴⠔⢠⣿⠗⣠⡟⠀⠀⠀⠀⠀⠱⠀⠶⠤⠏⢋⡼⠯⠵⠃⠂⠝⠃
⠀⠀⢀⣾⠃⠀⣿⡏⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⣼⣯⡄⣸⣿⡃⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆
⡀⢀⣿⣿⣷⢿⣿⡇⠸⣿⡀⠀⠀⠀⠀⢧⠀⠶⢄⡀⠀⠀⠀⠀⠈⠁
⢻⣎⢿⣿⣧⣼⣿⣯⠀⢹⡇⠀⠀⠀⠀⠈⢳⣴⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠉⠙⠿⣿⣶⣤⣄⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣰⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠙⠻⢿⣷⣶⣶⣶⣶⣾⡿⠿⣿⣇
⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⣼⣿⠟⠉⠁⠀⠀⠀⢻⣿
⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⣠⡆⠸⣿⡇
⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣷⡙⠻⣶⣤⣀⠀⠀⣀⣀⣠⣤⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⣾⣿⡇⠀⢿⣿
⠀⢸⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⣷⡀⠈⡙⠿⣿⣿⣿⡿⢿⣿⡄⠀⠀⠊⠁⠀⠀⠀⣀⣴⡿⠟⠁⠈⣿⡀⠘⣿⣇
⠀⠀⣿⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠻⣷⡀⠈⠳⣄⠉⠛⠿⣦⠹⣧⠀⠀⠀⠀⣀⣴⡾⢿⣉⡀⠀⢠⠀⠸⣧⠀⢹⣿⡄
⠀⠀⠸⣿⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⢷⡀⠀⣿⡇⠈⠀⢠⣴⣾⠟⠋⢤⣬⢿⣿⣷⡏⠀⣀⣹⣧⠀⢻⣿
⠀⠀⠀⣿⣷⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⡇⠀⠀⠀⣸⣿⡆⣿⣇⠀⠀⣾⣿⠀⠀⠀⠀⠉⠂⠋⠉⠓⠀⠈⢿⣧⣀⣾⡟
⠀⠀⠀⢸⣿⡆⠀⠀⠈⣿⣿⠀⠀⠀⠀⢸⣷⡀⠀⠀⣙⣛⠁⢸⣿⠀⢀⣿⡏⠐⢦⡀⠀⢀⣰⣶⠦⠄⠀⠀⠀⠻⣿⡟
⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠹⣿⣄⠐⣿⠙⣧⢠⣿⠀⣸⣿⠇⠀⠈⢻⣶⡿⠻⣇⢠⣶⣄⠀⠀⠀⢻⣿⡀
⠀⣤⣶⠿⠟⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⠻⣷⣿⠀⣿⣿⠏⢰⣿⡟⠀⠀⠀⠸⠟⠁⠀⠈⣃⣈⡉⣷⣄⠀⢸⣿⡇
⢸⡿⢀⣤⣤⣤⣤⣤⣴⣿⣿⣧⣄⡀⠀⠀⠀⣿⡄⠘⠛⠀⣿⠇⣠⣿⡟⠀⠀⠀⠀⢀⣠⣴⣞⣛⣉⣍⣉⣻⣿⣷⣼⡿
⢸⢇⣾⠟⠛⠛⠉⠉⠉⢙⣻⣿⣿⣿⣷⣦⣄⠈⠿⣶⣶⡾⠋⡴⠟⣿⣷⠀⠀⠀⠀⠉⠉⠙⠓⠿⢬⣍⣋⣙⣹⢿⣧
⣼⡿⠃⠀⢀⣠⣴⣾⡿⠿⠿⠛⠛⠻⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠐⠶⢤⣤⣤⣈⣉⣁⣼⣿
⠁⢀⣴⣾⣿⣿⣭⣄⣀⣀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠻⣧⡀
⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠉⠛⢿⣧⡀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣶⣤⣀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣦⣄⡀⠀⠘⣦⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠙⢿⣿⣷⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣈⣻⣷⡀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣆
⣿⣷⠿⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠙⢲⡀⠀⣰⠞⠛⠛⠋⠙⠛⠛⠓⠲⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣔⣩⠤⣤⠀⠀⠀⠹⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠛⢉⡴⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⢀⢈⡗⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠛⠁⠀⠀⠉⠓⠦⣄⣀⠐⢶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣄⡉⠳⣄
⠀⠀⠀⠀⢀⡀⠀⠀⢹⡄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣓⠮⣷⣄
⠀⣠⠶⠛⢉⢉⠙⠲⣼⠃⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠠⡀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠙⠂
⢰⡇⠀⠀⠉⠘⢳⠀⠹⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠻⣦⢹⡀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⢰⣤⣀⠀⠙⢷⡀
⠈⠛⠲⠤⠤⠤⢤⡄⠀⠀⠀⣀⣤⣴⠲⡖⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢧⠁⠀⠀⠀⠀⠀⣀⣀⠘⣆⠙⠳⢦⣽⣏⠓⢦⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⣾⣿⣿⣇⠀⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣇⠀⠀⢀⣀⣉⣉⣉⠀⠸⡆⠀⠀⠀⠉⠀⠀⠈⠛⢾
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⠀⠻⣇⣹⣾⠀⢹⣆⠀⠀⠀⢷⠀⠀⠀⠀⠀⣿⡴⠚⠉⠉⠀⠈⠉⢻⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⢧⣈⡷⡁⢸⢦⡀⠀⠘⣆⡀⠀⢠⢀⣿⠘⠀⠀⠀⠀⢀⣠⠞⠀⠀⢧⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡄⠀⠀⠙⢦⣼⠧⣄⣹⢦⡀⠀⠉⠓⢶⡛⠙⠲⠴⠶⠖⠛⠉⠀⠀⢀⣠⠼⠛⠉⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠻⣦⡀⠀⠀⠻⣦⣼⠳⣦⣽⡷⣤⣜⡂⢃⠀⠤⠆⣀⠀⢠⠢⠀⢀⢤⣀⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠀⠐⣿⠻⢦⡐⠈⠀⠙⠓⢾⣟⠛⢮⣿⠛⠶⣦⣌⣀⣁⠀⠈⠈⠀⢈⠉⠉⠙⡏⠁
⠀⠀⠀⠀⣠⠞⠀⠀⢰⠃⠀⠀⠸⣆⠀⠙⠦⣀⠀⠀⠀⠈⠙⠺⢤⣉⣳⠟⠤⢤⣼⣉⣉⡟⠉⠈⠀⠀⠀⣿
⠀⠀⠀⡴⠃⠀⠠⠽⡟⠀⠀⠀⠀⠙⢆⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠉⠙⠒⠾⠧⢤⣯⡀⠀⠀⠀⠀⣰⠇
⠀⠀⡼⠁⠀⠀⠀⣸⠃⢀⣠⣤⣶⣚⡿⠃⠀⠀⠀⠀⡼⠻⡝⠛⠲⠦⢤⣤⣀⣀⣀⣀⣈⣀⣀⣠⡤⠞⠋
⠀⡼⠁⠀⠀⠀⠀⣯⠶⢋⣿⡿⠟⠛⢦⣀⣠⠖⣲⠴⠗⠒⠛⠒⠶⡞⣽⣶⠀⠀⠈⠈⠉⠉⠁
⡼⠁⠀⠀⠀⠀⠀⠛⠋⠉⠀⠙⠦⣄⡀⠉⠉⠈⡉⠓⠶⣄⠀⠀⠀⡗⢙⠿⠶⣦
⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣧⠀⠠⡈⠓⢦⡼⠀⠀⠀⠈⠋⠙⢺⠃
⠀⠈⢳⡈⠙⠓⠶⠦⣤⣄⣀⣀⣀⠀⣼⢈⠳⣄⣸⠦⡼⠃⠀⠀⠀⠀⡴⠒⠻⡆
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢉⣉⠉⣿⢸⡀⠀⠁⠀⠀⠀⠀⠀⢰⡋⠙⢶⡞⠁
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠐⠀⠀⠀⠿⢿⡈⢧⠀⠀⠀⠀⠀⠀⠐⣺⡛⠛⠻⣄
⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠳⢄⠀⠀⠀⠀⠀⠹⡟⠲⠶⠋
⠀⠀⠀⠀⣼⢷⣶⢤⣤⣀⣀⣀⢀⣀⣠⣏⣀⣙⣦⣤⣀⣀⢀⣀⡴⢃
⠀⠀⠀⠀⠙⠶⢍⣛⠳⠤⣬⣭⣏⣁⣀⣀⣭⢿⣩⣃⣈⣉⡿⠁⢀⡾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣻⡿⣿⣿⡦⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣷⠶⠶⠄⠀⢀⣀⣤⣶⣿⢿⣿⣯⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢞⣻⡿⠿⠽⠿⠛⢛⣷⢈⣿⡟⡿⣿⠋⡯⢳⡌⠉⠙⠶⡶⣶⣾⣿⣿⣿⠯⣽⣶⡿⠿⠿⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣤⣤⣴⠾⣿⣾⢋⠓⡑⢂⠴⢣⣿⣾⣿⣷⣶⣦⣤⡛⠬⠵⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡃⠀⠀⠀⠑⠻⣾⣾⣫⣥⣽⣥⣬⣷⣷⣾⣶⣾⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠐⠀⠛⠿⡿⣛⡸⠿⠿⢻⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰
⠀⠀⠀⠀⠀⠠⣄⢀⠀⠀⠀⠈⢁⠀⠀⠉⢦⣄⣀⠀⡀⢀⠀⠀⣀⣠⡴⠊⠀⠀⢀⠀⠀⠙⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠈⢿⣯⣷⣈⢉⠤⠛⠉⠁⠀⠀⠠⠀⠀⠉⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣼⣿⡢⡀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠙⠳⣇⢈⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣽⠇⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣶⠖⠒⠛⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡞⠋⠉⠉⠓⠦⣄⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣁⣠⠞⠀⠀⠀⠀⠀⠀⠈⠙⠲⣾⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⢀⡴⠶⠶⢤⣀⠀⢀⣀⣀⣀⣀⡟⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡾⠀⠀⠀⢰⡏⠀⠀⣴⣚⠉⠉⠻⢧⡀⠀⠈⠉⠳⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⣼⠁⠀⠀⠀⠈⢷⡀⢸⡇⠈⠙⢦⠀⠈⢷⠀⠀⠀⠀⠘⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠈⢷⠀⠓⠦⣤⠞⠀⠀⣸⠀⠀⠀⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠲⢤⣀⡀⠀⠈⣧⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡞⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣘⡇⠀⠀⠈⠉⠛⢲⡇⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⣸⠋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⢀⣠⠶⠚⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢈⣩⠷⠒⠒⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠈⠙⣳⠖⠛⠻⣍⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢻⠀⠀⢠⡟⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⡟⢸⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⣾⠃⣀⡤⠶⠒⠛⢛⣋⣩⡽⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣷⣸⣾⢗⣋⡤⠴⠖⠚⠋⠉⢁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡿⢟⣉⣠⣤⡤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠾⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣿⣿

⠀⢘⣛⡛⠯⣪⢿⣿⣿⡿⡦⠹⠇⠺⣿⣐⣦⣼⡊⠞⡉⠊⡠⠐⠈⠈⡸⠃⠀⣶⠋⠀⠂⠀⠀⢈⠀⠲⠌⢀⢭⣴⣂⣿⠂⠻⢏⡼⣿⢿⣯⡯⣴⠟⣛⣛⡛
⠀⢸⡏⢩⡆⠰⣿⠿⠛⢻⡽⠎⠲⠶⣰⠈⡻⠒⡀⠁⠄⣠⠤⠴⠀⣊⣤⠴⡾⢬⣙⣒⣒⠀⠔⠤⣍⣑⠒⠶⣈⠓⠂⡒⢂⣒⣽⢿⡟⠛⠿⣿⢁⢮⣌⠈⡟
⠀⠘⠣⢙⠑⣡⡇⣬⡿⠋⢐⡿⡙⡢⢃⠔⠠⠂⣠⠖⢋⡤⣶⠛⣿⡩⡓⣏⠘⡾⡅⠿⣹⠏⣻⡶⢦⣬⣙⠲⣄⠑⢄⠑⠴⣥⡲⢦⢱⡿⣗⡨⣄⠀⠙⠐⠷
⠀⢸⠏⢸⣿⡿⠷⠭⣍⡛⡮⠍⠊⠔⣁⡴⢞⣷⢋⡾⠋⠻⣠⠂⣸⠆⡇⣘⣼⠶⠛⠲⠿⢾⣭⣧⡸⠰⠛⣳⣌⠁⠀⠀⠤⣤⣭⣭⢩⢉⠭⠶⠯⣽⣧⠙⡿
⠀⢸⢇⢘⠏⡶⣿⠗⠈⠃⡥⢋⠔⡁⢊⡴⢻⢛⡼⡈⡆⢆⢹⠰⡄⣱⠞⢋⠠⣤⠊⠉⡀⠀⣠⠌⠹⣼⢶⠋⡈⡷⣄⠀⠀⠈⠻⣿⣇⠘⠼⣛⠷⡌⡏⣰⣧
⠀⢸⡟⣽⠄⣒⠒⣪⢂⠞⠁⠀⠔⣠⣿⡘⣸⢻⡳⢁⠋⠜⠄⢎⣾⣇⠴⠃⣰⠃⡠⠊⡠⠃⠑⣔⢀⡟⡌⡎⣱⢁⠽⣶⡄⠀⠀⠈⢿⡌⢦⢛⢛⣀⣏⣿⣟
⠀⢸⣭⡟⠀⢤⠒⡴⠏⠠⠀⠌⣰⣿⣰⢶⣛⣿⣖⠵⠓⠋⣿⣛⣉⣁⣀⣠⡇⣊⣥⡬⠀⠰⠆⣌⣾⣃⡹⡸⠁⣁⣂⣯⡼⣄⠠⠀⠄⢻⡄⠲⡚⠉⠛⣽⡿
⠀⢸⢋⢔⣦⠆⠟⡐⠀⠁⢀⣴⡇⡿⣅⢀⣨⢣⣿⠀⢀⣔⡘⣋⣿⡍⠡⠈⢼⣿⠇⠀⠀⡐⣾⣹⣗⣿⡃⣷⣉⠀⣩⡎⣵⠜⣦⠀⡈⠀⢻⡄⠡⢷⢢⡜⢿
⠀⢠⠱⣷⣖⡡⠀⠀⠀⢀⣿⠃⡇⣹⡟⢫⣉⡎⢹⡀⢪⠳⠉⡜⢻⡘⠢⣄⠀⠉⠈⠀⠀⠁⠀⣰⢧⢡⢋⣩⠿⡜⢋⡜⣛⠁⠻⣧⠀⠀⠀⠛⢌⢲⡧⡸⣦
⠀⢐⠒⠆⡊⠀⠀⠐⠀⣎⠌⢢⡜⡇⣇⣼⠙⢘⣆⡌⡆⣆⡇⢳⠌⣷⣼⡈⠳⣤⢀⠐⢒⡠⣔⢧⣸⢞⡈⢋⢀⣿⠎⢞⢩⡄⢢⣽⢆⠀⠀⠀⠈⠔⢷⢬⡟
⠀⢸⣟⡄⠃⠀⢀⠁⣸⣯⠂⠈⣁⣿⢻⣇⣨⣣⣏⢌⣴⣭⣹⡌⢾⠟⢼⣛⣦⡈⢢⡼⠘⣧⡙⠘⠇⢜⣹⠀⢟⢀⣡⣽⡿⡠⠟⠍⣻⡄⠂⠀⠐⠘⣿⢸⣿
⠀⢰⠍⡔⣠⠁⠀⠀⡸⢻⣶⡷⠿⠿⠈⠻⣇⠝⢹⠯⠀⠀⣰⡿⢸⡞⢓⡏⠡⠀⣾⠇⠂⢀⠙⠲⣄⠠⢩⡼⠣⣡⣿⢿⡷⠿⣷⣻⠋⡇⠀⠀⠀⠃⢸⡷⣿
⠀⢸⠧⡔⠹⠀⠀⠀⠀⡾⣬⣝⣃⠀⠀⠀⢯⡞⠟⠛⣁⠛⢟⣀⣿⠁⣟⠀⠂⢸⡏⠀⢊⠁⡠⠂⠈⢷⣾⢂⢖⣿⠀⠀⠀⢛⣫⣥⣧⠀⠀⠄⠀⠀⠈⢣⠙
⠀⠀⠉⠁⠀⠄⠀⢀⢰⠟⡯⠥⢧⢤⡤⣤⣌⠳⣇⠨⠧⢊⠆⣿⠇⢸⠁⠈⢀⣿⡍⠀⠀⠀⢳⡄⠀⠀⠻⣆⣾⣁⣀⣠⣤⠬⠥⢊⢺⡄⣄⠂⡀⠀⠀⡈
⠀⢐⠒⠒⠒⠒⠒⠚⢸⡇⠉⠒⣸⢉⡅⠂⠙⢷⡌⠙⠲⢦⣔⡾⠀⠘⣇⠀⠈⣿⠇⠀⠀⠀⣼⢛⢦⡀⠀⠈⠻⡟⠉⣿⣫⠐⢧⣛⣿⡇⢙⢀⠈⠁⠉⠄⠤
⠀⢘⡀⢀⣀⣀⡀⢸⢸⣏⡁⢠⡟⢸⢾⠶⠲⠋⡽⢦⡀⠀⠈⠳⠀⠀⡼⣇⠀⢸⠀⠀⠀⢰⣏⡟⣸⠝⣦⡀⢸⠀⠀⣸⢟⠂⠀⡺⢏⡄⠀⢰⠀⠀⠀⠀⠥
⠀⢨⢶⠂⢕⡄⣩⢀⢸⡟⣡⠟⡘⡃⣎⠐⣡⠈⡷⣻⣼⠗⣦⣄⣡⡾⣡⢿⡄⠀⠀⠀⠀⣾⡟⣴⡅⣾⢹⣷⣬⣀⣴⢫⣎⢣⠱⠘⡈⡇⠀⢈⢩⡝⠉⣌⠛
⠀⢰⠂⢠⣸⢁⠛⢸⢸⡦⠳⠀⢇⠜⢈⡞⡠⡏⠁⡇⡝⠠⠷⣀⣭⢺⣼⠾⡇⢀⠀⠀⡀⢿⣇⢡⠋⡌⣧⣸⣮⢋⡸⢫⠟⡘⢸⢇⢣⡇⢠⢸⣆⢳⢀⠊⣶
⠀⠈⠀⣸⢃⠆⠀⢸⢸⡶⠖⠛⣌⣋⠒⠤⠤⣵⡳⠊⢲⠤⢲⣹⠾⣻⡇⢨⠀⠄⡠⠊⡠⠚⢿⠻⣤⡠⢷⡷⡥⠬⢴⡧⠾⠶⠓⠚⢢⡇⢰⢸⠈⠄⢿⠀⢹
⠀⢠⠀⣽⠘⡀⠀⠘⢸⡧⢀⣴⠏⣼⣅⡀⣀⣾⢡⢞⣦⣠⠞⠁⢰⠃⢡⢠⠰⢊⠔⠃⠀⠀⠘⡆⠈⠳⣼⢏⡀⢈⣍⣴⣯⡂⢀⠐⢋⡅⢸⠈⠀⡘⣸⠀⣨
⠀⠀⢠⠁⠱⠈⠳⠀⢸⢡⠡⢡⠶⠌⣸⢇⠹⣠⢏⣦⡾⠋⠀⢠⠏⠀⠈⡤⠞⠁⠀⠀⠀⠀⠀⢹⠀⠀⠈⢳⡟⡙⢇⡾⢫⠅⡰⠃⢣⡆⢸⠸⠃⠐⠁⢁⠈
⠀⠀⠃⡀⡱⡡⠀⢠⢸⡄⠇⠎⡤⣄⡣⢸⠗⣵⣿⠋⠀⠀⠀⠞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠙⣷⡎⣷⣿⠀⡇⢃⠈⡃⢸⠀⠸⡕⠁⢈⠿
⠀⠀⠠⠋⠈⠁⠀⠈⠀⡵⢈⠂⠑⡄⠠⡟⣴⡟⠁⠀⠀⠀⠌⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢷⣷⠱⢠⢃⠼⡄⡆⠰⠀⠀⠁⠈⢣
⠀⠀⡆⢀⢂⠅⡆⠀⠀⣷⠘⢪⠖⢫⢋⣴⠏⠀⠀⠀⠀⠈⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⢻⡄⠱⡄⠒⣼⡆⢸⠀⡀⠀⣆⠀⡄
⠀⢰⢇⠸⣤⠀⠀⠀⠀⣿⡯⠴⢲⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢻⣇⠈⢩⡽⡇⢸⠀⠀⢀⡿⠰⢰
⠀⢠⡸⢆⠹⣆⡶⠀⠀⣿⢀⣎⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⡰⡇⢸⢠⡄⡾⢠⢧⠈
⠀⢠⡁⠘⣇⠹⣀⠀⠀⣿⣷⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠌⢷⣱⡇⢸⢈⡿⠰⠇⠀⡆
⠀⢨⠱⠾⠄⠲⢻⠀⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⢸⡥⠁⠀⠎⣠
⠀⣠⣀⣀⣀⣀⡘⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⢀⡀⣀⣀⣁⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣷⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠉⠀⠙⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠞⣶⡞⠛⠛⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠠⣄⣀⣉⠒⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠈⠓⠉⣙⣍⡉⠧⠄
⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⣠⠇⠀⠀⠈⠑⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⣶⢠⡄⢰⡌⠳⢟⡀⠀⠀⠀⠐⠒⠙⠀⠐⠖⠀⠈⠲⢄⡀
⠀⠀⢠⠀⠀⠀⢘⣁⡤⢄⡐⠚⢁⠀⠀⠠⠀⠀⠀⠘⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠩⡥⠾⠳⣦⠙⢛⡋⢁⣠⣀⠀⠀⣠⡤⠤⠤⠄⠀⠡⣀⠀⠙⣦
⠀⠀⠿⠀⠀⣀⠀⡡⠐⠀⠀⠀⠀⠈⠢⡀⠀⢆⠀⠀⡇⠀⠘⡀⠀⠀⠀⠀⠀⣀⠴⣤⠶⠶⠀⠀⠀⠙⠃⣼⡙⣯⡁⠂⠀⠀⠀⠀⠀⠰⠄⣀⣀⠀⠋
⠀⣤⡆⠈⠁⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⡠⠁⠀⠰⠃⠀⠀⠀⠀⠄⣹⡿⣹⢇⣠⠀⠀⠀⠰⠿⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘
⢠⣿⡒⣤⣤⠂⠀⠀⠂⠈⠉⠀⠀⠈⠐⠄⠀⣼⡂⠁⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⣨⣯⣤⠰⠷⣰⠶⣟⠂
⠃⢻⣝⠄⠀⠀⠁⠀⢀⠄⣀⠤⠀⠀⠉⢺⣦⣿⠗⠂⠀⠘⢻⢧⡴⠀⠀⠀⠀⠀⠀⠀⢴⢶⣼⠇⠀⠹⠿⡏⢋⠀⠀⠀⣄⡀⣠⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⣠⠊⢃⣹⠀⠀⠀⠀⠀⠀⠀⠰⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠟⠙⢷⣶⠄⠀⡀⠀⠀⣙
⡄⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠀⠠⢀⣴⠿⡇⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣧⡤⢾⡆⠀⢠⠁⠀⠀⠙
⠘⣶⠒⠈⠁⠀⣠⠖⠀⠀⠀⠀⠀⢀⣀⣠⠴⠎⠀⠀⠀⡾⣿⡶⠋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⡌⠀⠀⠀⣿
⠀⠉⠤⠠⠄⠂⠁⠀⠀⠀⣼⠶⠋⢉⣠⣦⡤⣄⠀⠀⠈⡁⠋⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⡟
⢸⡆⠀⠀⠀⠀⠀⡐⢀⡾⠁⢤⣾⠟⣿⣟⣀⠈⠃⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠹⣦⣀⣀⣠⣈⡴⠛⡠⢣⠀⠀⠘⠉⠋⠀⠀⠀⠀⠀⠠⠀⢈⡁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠘⠀⠀⠀⢀⣰⠄
⠀⠀⠀⠉⠺⠷⠀⠀⢀⣀⠀⢉⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢦⡻⠀⡰⢦⣌⠑⠶⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠉⠁⢀⣀⠀⣠⠆⢠⠋⡉⠀⠀⢀
⠀⠀⠀⠀⠀⣄⠐⢠⠄⠀⠋⠁⠘⠂⢤⡀⠀⠀⠀⠀⠀⠀⣀⢀⠔⠁⠀⠀⠀⠀⠈⡀⠀⠀⠳⣄⡤⠲⠲⣿⠷⠁⠀⠀⠀⠄⣨⡍⣶⠋⣠⠿⠊⠁⠀⠐⣼
⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⡄⠀⠀⡀⠀⠉⣈⠉⠁⠀⠀⠉⠉⠣⣄⠀⠀⠀⠀⣀⡀⠠⢄⠀⠀⢹⡦⣶⡷⠂⠀⠤⠤⠴⠄⠚⠩⡆⠻⡉⢀⣀⠀⠠⠄⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⣧⠀⠀⠀⠇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠀⠉⢄⡀⠀⠀⠀⣸⠇⠈⢧⠀⠤⢤⣴⠶⠛⠁⠀⢸⠀⠀⠁⠀⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⡆⠀⠀⠠⡄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠘⣟⠙⡀⠀⠀⠈⣶⢖⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣐⣦⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣤⡘⠒⠒⠂⠳⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⡟⠐⢷⡒⠟⠶⠾⡌⠐⢄⠀⠀⠀⠀⢀⠖⠀⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡠⠤⠃⠀⠀⠙⣧⢸⣷⠁⠀⢸⡀⠀⠀⠀⠌⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠊⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⡜⠀⠀⢀⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣰⡔⣺⠋⠀⠃⢠⡘⠇⠀⠀⠀⠀⠀⢹⡇⠻⡄⠁⠀⠠⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣴⠛⠿⠉⣴⡇⠀⠀⠀⠁⠀⠻⠀⠀⠀⠀⠀⠈⣷⠀⠻⢞⠄⠁⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⢊⡄⠙⢃⠀⡐⢻⠍⠑⠢⣄⡀⠀⠀⠂⠀⠀⠀⠀⠀⣿⠀⡠⠊⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠀⠀⡔⠀⢷⡀⢀⠀⠀⠉⠐⠢⠆⣀⠀⠀⠀⠀⣿⠞⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠢⢼⠀⠰⣾⠀⠈⢢⡀⢤⡀⠀⠀⠈⠑⠂⠤⢰⠏⠀⠀⠀⠈⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠘⠳⣼⣄⠀⠀⠱⠀⠘⠂⠀⣁⡠⠤⠀⠃⠀⡀⠀⠠⢲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈⠳⡉⠑⠲⠦⣠⣄⣁⡀⠠⠴⠖⠛⠁⠀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⣼⠉⠁⠒⠒⠠⠤⣤⣥⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠲⣿⠀⠀⠀⠀⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡌⠀⢰⡇⠀⢀⠀⠀⢸⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠙⠿⣀⣠⣿⡇⠀⣸⠀⠀⣻⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢈⠉⠉⠉⠉⠈⠓⠂⢿⣇⡀
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧

⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣿⣿⣿⣷⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣟⡛⢉⣁⣀⠀⢠⣤⣤⢬⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣯⣬⣿⣿⢛⣿⣴⣿⣿⣉⣾⣿⣧⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⡋⣝⣿⣾⣿⣏⣄⠿⢿⣿⡟⣷⣄⣹⠛⠿⢿⡇⠀⠀⠀⠀⠀⠀⡞⠛⠋⠻⣿⡟⠛⠂
⣿⣿⣟⢛⣿⣄⣸⣿⡿⢿⣿⣿⣿⣿⡛⠛⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣄
⣿⣿⣿⣷⡟⠍⢛⣿⣷⣬⣥⣿⣁⡉⣿⠿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣀⣀⣄⣀⣀⣀⡏⠀⠀⠀⠀⣶
⣿⣯⡉⢟⣿⣿⣿⣇⣰⣾⣄⣹⡿⢿⢛⢶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣉⣷⣆⢉⣭⠉
⣿⣿⢿⣿⣯⣬⣼⣏⢹⣻⣿⣿⡷⢾⣿⣟⠻⣿⣿⣇⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤
⣿⣷⣦⣭⣽⡇⢸⣿⠛⣙⣿⣯⣥⣾⣷⣦⢼⣿⣿⣷⠀⠠⠠⣿⡏⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀
⣿⣿⣷⣜⣿⣿⣿⠛⣿⣿⠟⢣⣥⣿⣴⣯⣶⣿⣿⣿⠀⠀⢠⣿⡇⣸⣷⢸⣿⣿⣿⣿⣿⣷⣶⣾⡇⠐⡒
⣿⡿⠛⠉⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠉⠈⠻⢿⣿⣿⠄⠀⠈⠉⠱⠉⠉⠖⢿⠏⠉⠉⠁⠉⠉⠉⠉⠀⠈
⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠶⠿⠿⠿⠿⠿⠿⠶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠰⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⣀⣠⣄⣸⣿⣧⠀⠀⠀⠀⣀⣈⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡁
⠀⠀⠀⠀⢀⣾⠟⢉⡉⠙⢻⣿⠀⣤⣞⣋⠠⠤⠤⣤⣹⣿⣧⡀⠀⠀⠀⠀⣴⣿⠟⣉⣁⣉⣛⢶⣄⠀⠀⠀⢠⣾⠛⢉⣉⡛⣦
⠀⠀⠀⠀⣼⠃⠀⢀⣹⡆⠸⠟⢸⡏⠀⠀⠀⠀⠀⠀⠈⠙⢻⡇⠀⠀⠀⣾⡿⠟⠛⠉⠉⠀⠀⠀⢛⡇⠀⠀⠀⠁⠀⣾⡟⠀⣼
⠀⠀⠀⠀⣿⡀⠀⢾⣯⣀⣠⡀⠈⢛⠲⠴⠤⠤⠤⠤⣼⣿⣿⠇⠀⠀⠀⣿⣦⣤⠀⢀⣀⣀⡠⠴⡟⠁⠀⢀⣀⣀⣀⣿⣷⢀⡿
⠀⠀⠀⠀⠸⠇⢀⣼⡿⠟⠋⢁⠀⠀⠘⠒⠂⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⣹⡿⠟⠛⠀⠩⠥⠄⠚⠀⠀⠀⠀⠉⠛⠿⣿⣧⡼⠃
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⣀⣀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣰⣦⣄⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⣾⠋⠀⠐⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠺⠶⠿⣦⣤⣠⣾⡿⠉⠛⠋⠀⠀⠀⠀⠀⣠⡶⠛⠉⠈⠉⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣤⣴⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠉⠉⠉⢹⡇⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⣀⣼⣷⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠛⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠼⠛⠉⠙⠛⠻⠷⢶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠛⠋⠉⠀⢠⡿⠁⠀⠈⠙⠻⣦⠀⠀⢻
⠀⠀⠀⣠⣴⠞⠋⠉⠉⠉⣀⣤⡶⠾⠶⣦⡀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣶⣶⣶⣶⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢸⡅⠀⢀⣀⣤⣄⣼⡇⠀⠘⣷⣤⣄⡀
⠀⢀⡾⠋⠀⠀⠀⠀⠀⢾⣏⣁⡀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠞⠋⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠻⣦
⢰⣿⠗⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣷⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡄⢹
⣿⠃⢀⣴⠇⠀⣠⣤⣄⠀⠀⢀⣠⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣠⣤⠖⢻⡇⠀⠀⠰⣆⠀⠈⣿⡿
⣿⠀⢸⡏⠀⠀⡏⠀⠙⠷⠾⠛⠋⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠀⠀⠸⠀⠀⠀⠀⣿⠀⣰⡟
⠸⣧⣼⡇⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣾⣿⡆⠀⢺⡆⠀⠀⣠⡿⠞⠋
⠀⠀⠈⠙⠶⣤⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣤⣿⡧⠀⠈⠻⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠉⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⠄⠐⠒⠒⠶⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⠉⠉⢹⡿⠉⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⡀⠉⠙⠙⠛⠛⠛⠋⠉⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣀⣀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠉⠙⠛⠿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣤⣤⣤⣶⣶⡶⠟⠋
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⢋⠟⠁
⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡘⣦⢹⡟⡄⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣮⠙⣎⢧⠱⡘⣹⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣷⣎⡻⣗⣕⡜⢷⣹⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣤⣙⠻⣝⡮⣻⣿⣾⡏⣧⣸⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣌⣛⠲⢭⣚⢻⣿⣿⡟⣿⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡉⠓⠾⢽⣿⠃⢀⣠⣽⠃⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⣉⣙⣳⣇⠠⢿⠉⣽⡾⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠋⢉⡽⠋⠀⠀⠀⠸⣷⠒
⠐⢶⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠒⠛⠛⠂⠀⠀⠈⠳⠄⠠⣤⣴⣶⣤⣤⣀
⠀⠉⣷⡶⠶⢛⡛⣛⠓⠒⠲⠶⠦⠤⢤⣤⣀⡠⣄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢸⣿⡿⠿⢿⣿⣿⣄
⠀⠀⠈⠛⣟⣟⣉⣩⣭⠭⠍⠉⠉⠽⣿⣿⣿⣴⣦⣾⣦⣦⠐⠀⢠⣤⣴⣶⣿⣷⣶⣤⣀⣠⣀⣀⣠⣼⡏⠀⠀⠀⠈⢩⠽⠷
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢏⣩⣴⣿⡿⠟⠛⠿⣿⣿⣿⣤⣍⢛⠛⠒⢸⣿⣦⣤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⣿⣿⠛⠓⠒⠒⠾⠿⣯⡀⠀⠀⠁⠀⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠂⠒⠒⠒⠒⠒⠒⠀⠐⠆⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠒⠒⠒⠒⠈⠉⣉⣈⠱⢆⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⡶⠖⠚⠉⠁⣠⠄⠚⡱⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠋⠀⢠⠞⠁⡾⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢴⡏⠀⣸⠀⡷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣇⠘⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠿⠿⠿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣤⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠛⠿⣷⣄⠀⣀⣴⣾⠟⠁⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣏⣽⣷⣤⣹⡍⣼⠋⢉⣉⠷⣆⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠒⣀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠿⠟⠀⣸⠃⣿⣺⣿⡆⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣾⠟⠛⣿⡟⠁⠀⠀⣀⠀⠀⠀⠀⠈⠷⠶⠶⠾⢷⣦⣿⣏⣉⣀⡤⠟⠀⠀⢸⣿⣤⡀
⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⡇⠀⠀⠀⠘⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣶⣤⣀⢘⣿⠀⢻⡆
⠀⠀⠀⠀⠀⣾⠇⠀⠀⣿⠁⠀⠀⠀⣠⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣤⣸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⢰⡿⢸⡇⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⢀⣿⡇⡠⢿⡄⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡏⠀⠀⢸⡇⣼⠁⠈⢻⣦⡀⠀⠈⠛⠿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣼⡇⠀⠀⢸⡏⠈⢦⡔⠁⠈⠻⣦⣀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⢿⣿⡿⠿⢿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⢠⡄⠈⢿⣤⠊⠑⢦⣄⡀⠈⢙⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⣿⣧⡀⢷⡀⠈⠛⠷⠶⠶⠶⠿⠛⠋⠁⠀⢈⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⣿⡏⠻⣤⡙⠶⣤⣀⡀⠀⠀⠀⠀⢀⡴⠛⠋⠛⢦⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠠⣿⣧⣤⣌⣛⠶⣤⣀⠀⠀⠀⢀⣴⠋⠀⠀⡀⠀⡈⣧⣤⣤⣤⣶⠶⠿⠛⠃⢠⠇
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠈⠉⠙⠛⠿⣯⣝⠓⣶⠞⠁⠀⢀⠀⢻⡀⡂⢹⡀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠘⠿⠶⣶⣶⠶⠶⠶⢶⣤⣀⠙⣿⠋⠀⠀⢀⣼⡇⠸⡇⢷⣼⠛⠛⠛⠛⠛⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠳⣤⣀⣤⡶⠋⡘⢣⠀⣷⡞⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣘⢉⡽⠀⢠⠃⠈⡷⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣠⡏⠀⣼⣁⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠞⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⢿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⣾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⣿⠈⠉⠉⠉⣹⠋⢹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⣧⠀⠀⢰⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣼⣷⡤⠹⣧⢀⡿⠀⠠⣾⣧⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⣀⣠⡤⠶
⣤⣤⣀⠀⠀⠀⠀⣀⣤⡶⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢙⣿⠶⠟⠋⠁⢀⣼
⢳⡀⠉⠛⠶⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣠⡿⠃
⠀⠻⢦⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⠾⠛⠻⠿⠶⣶⡶⠶⠶⠶⠶⠶⢶⣦⣤⣤⣤⣤⣴⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠆⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠃⠀⠀⠀⠊⢀⢀⠄⠰⡆⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠢⠂⠀⡀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⣀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⢀⡴⠇
⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠃⠐⠧⠒⠒⠈⠀⠈⠒⠂⠚⠀⠄⠄⠐⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠁⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠤⠀⠤⠄⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠉⠓⢄⡀⡀⠀⠀⠀⠀⠴⢠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣗⣪⠄⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⣤⠀⠀⢀⣠⣥⣀⡝⣎⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⢣⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢀⣿⣷⠐⠚⢿⡗⢉⣉⣭⠵⠒⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠣⠅⠀⠀⠈⠀⠀⠀⢢⣀⡀⢀
⠀⠀⠀⢸⣿⣿⡇⢦⢞⡃⢐⣿⠶⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⢸⡿⠿⣷⢿⣿⣯⡜⠿⡿⢿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⡀⠀⠀⠀⠀⢀⡀⢰⠀⠀⠀⠐⣂
⠀⠀⠀⠈⢻⡀⠛⢛⣿⣈⠻⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣌⠐⠄⠀⠀⠀⠰⠸⠦⡄⠀⠴⢀
⠀⠀⠀⢀⣼⡷⣦⣀⣙⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⢤⣀⠀⠀⢀⣴⣾⣠⣿⢀⡌⣸
⠀⠀⢠⣾⣿⡝⠳⢽⣋⣏⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠐⠒⢿⣿⣿⣏⢁⠼⠋⠥⠂
⠀⠀⢸⣿⣿⣿⣦⠸⢿⣿⢸⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠶⠒⢀⠀⠉⢀⣀⣬⠔
⠀⠀⢸⣿⣿⣿⣿⣦⣸⣿⣄⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣾⣍⡙⠛⢿⡿⠢⠄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠦⠦⠠⠙⠻⠿⠿⠛⠒⠂⠀⠀⠀⠹
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀⣀⣀⡀⣸⡆⠀⡊⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣠⣶⣻⣿⣿⣿⣿⣿⣧⡼⢥⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠺⠄⠀⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠛⠛⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⡙⠋⠁⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⢩⡀⣀⣀⣠⣤⣶⣾⣿⢣⡆⡀⢀⣇⠄⣽⣿
⠀⠀⠀⠀⠀⠀⣼⠀⠀⣴⠀⣀⣸⡄⠀⠂⣤⠀⣀⠢⣔⠺⣿⣿⣿⠿⡿⣿⡿⠟⠁⣼⣇⠀⢸⣷⢈⡉⠉⠁
⠀⠀⠀⠀⠀⠀⣿⡀⣶⠿⠊⢀⠝⠓⠴⠀⠍⠉⣠⣐⡩⠌⠋⠉⣀⠀⢠⠀⠒⠒⠤⠄⣠⠉⠛⠛⢄⡀
⠀⠀⠀⠀⠀⠀⠟⢁⠄⠀⠀⠉⠀⡆⡀⠀⠤⠀⠉⠀⡀⠀⠂⠁⢀⡄⣿⡀⠀⠂⠀⠄⠋⠑⡄⠀⠈
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⡛⠉⠠⡄⠀⣀⢠⣧⢤⡦⠀⠼⠗⠛⠓⠈⠁⠀⠁⠀⠀⠇
⠀⠈⠀⠁⠠⢀⠀⠀⢀⡀⠙⠛⠛⠋⠀⠀⠀⠀⠈⠈⠛⠀⠐⠡⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠙⠻⠷⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡜⡰⠃⡠⠊⠁⠀⠀⠀⣈⠩⠝⠉⢆⠀⠙⢎⠳⣥⠀⠀⢀⣠⢏⢦⠀⢠⡔⣞⣠⡤⡄⡠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡜⡰⢁⡜⣠⠔⠊⠉⠉⠁⠀⠀⠀⠀⠈⢆⠀⠀⢣⠸⡆⠀⠀⠀⠈⠈⠀⠀⠀⠉⠈⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⢠⠃⠎⡴⠷⠦⣤⡀⠀⠀⠀⠀⣠⠤⠶⠬⣄⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠇⡇⣰⢮⣴⣶⣶⣤⡉⠀⠀⠀⠀⣡⣴⢶⣦⣬⢆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢸⢠⡑⡄⠈⣄⣻⣿⠛⠀⠀⠀⢀⠻⣿⢂⡽⠁⠠⢣⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡌⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡆⡸⠹⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠈⢧⠀⠀⠠⣄⡀⠑⠀⠘⠀⣠⠄⠀⠀⡸⢠⠃⢸⠃
⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡂⠀⡗⢄⠀⠈⠣⣁⠀⢂⠜⠁⠀⢀⠜⠗⠁⢀⠎
⠶⠈⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠇⠀⣑⢤⡀⠀⠉⠀⢀⡠⢺⠁⠀⢀⠴⠃
⣲⠒⠃⠀⠸⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠚⠣⣴⠊⠀⣰⠊⠉⠀⠈⠉⡅⠸⠒⠂⠁
⠹⠞⢲⠊⠁⠀⠈⠷⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⣇⠀⠀⡥⠔⣯⣃⠀⠀⠀⠀⠀⠈⡧⠤⠄⣀⣀
⠀⠀⠀⡇⠀⠀⠀⠈⡄⢑⡤⠔⠖⠈⠉⠀⠀⠀⡰⠉⢦⠎⠀⢀⠎⠀⠑⠂⠤⠄⠒⠉⠀⠀⠀⠀⠀⠈⠉⠒⠠⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⡧⠔⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢆⠂⠂⢧⡀⠀⠀⠠⠛⠢⡘⠀⢀⠔⠁⡀⠀⠠⠜⣡⠆⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡹
⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⡟⠢⣀⠃⠀⠀⠙⣴⠃⠀⠠⠙⣦⠀⠘⡏⠀⠠⠍⠄⠀⠀⠀⠀⠀⢀⠞⠁⠀⠙⢦⡀
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠣⠤⠌⣹⠦⠀⢰⢃⠀⣀⡢⣄⠀⠓⡤⠦⡞⠀⢀⣀⡄⠀⠀⠀⢀⠏⠳⡄⠀⠀⠀⠙⢦⡀
⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢃⢨⠀⠈⠝⠋⠉⠩⠇⠐⢟⠉⠉⠂⠉⠉⠉⠁⡟⠀⠀⠈⢦⡀⠀⠀⠀⠙⢄
⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢦⡀⠈⠾⡀⠀⠠⠶⠾⠁⢀⣅⠀⢻⡶⡆⠀⠀⠀⢰⠁⠀⠀⠀⠀⠈⠢⣀⢀⣀⠀⢧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢈⠚⠀⡱⠀⠀⠀⠀⠀⠇⡹⠄⠀⠉⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⡸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠠⣀⡔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠔⠁
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣻⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠀⣀⣴⠃⠀⠀⢀⡠⠒⠁
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⠁⣤⠏⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠩⡁⣀⠞⠁⢀⡱⠔⠊⠁
⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⡄⠘⡏⠹⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡔⠃⠀⢀⠂
⠀⠀⠀⠀⠈⠑⠒⠂⠀⠐⠒⠉⠁⠀⠀⠀⠙⠶⠓⠁⠀⣠⠮⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠫⢄⣂⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⠈⠑⠦⡀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠈⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⣠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⢷⢣⠀⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢳⢸⢸⣸⢹⡴⡻⢁⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠈⡇⡿⣸⢃⡜⢁⠔⠁⣪⢖⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡇⠳⡡⢋⠔⣁⠴⠋⣀⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠜⠁⢔⣫⠵⢚⣉⠥⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠐⠭⠥⠖⠊⢁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⣶⡆⠀⠀⠀⠒⠒⠒⠒⠂⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠨⠁⠀⠀⠀⢈⠉⠓⠒⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⠿⠟⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢤⣉⠓⠂⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣦⣀⣠⣤⣾⡿⠃⠀⠀⠢⣄⣄⠈⠲⣄⠈⠁⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⢷⡄⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⣿⣿⣿⣿⣤⣄⡀⠀⠀⢀⠙⠄⠀⢀⣀⡀⠠⠤⠤⠔⠒⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠛⢿⣷⣿⣦⡁⠀⠀⠀⠀⠀⠀⠠⠤⠔⠒⠒⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠑⠄⠀⠀⠀⠀⠈⠹⢻⡿⠃⠀⠀⠀⠈⠠⠀⠀⠀⠐⠲⠶⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠐⠒⠒⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⣠⠴⠢⠈⠀⢀⡈⠑⠲⠤⠀⠃⠘⣆⠀⠐⠌⠃⠀⠀⠀⠠⣀⠀⢉⡑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠶⠚⡴⠎⠋⠀⠀⠀⠐⢦⡈⠓⠤⣀⠀⠀⠀⠘⡆⢆⠀⠀⠀⢄⠐⢄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣩⢵⡆⠀⠀⠀⠀⢠⠀⣄⠳⡄⠈⠲⣄⠀⠀⠀⠀⠀⢹⠈⢆⠀⢀⠈⠳⡈⠳⢄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠢⠭⠭⣐⠴⣫⢢⢀⠀⠀⠐⡆⡆⠘⣆⠈⢢⡀⢀⠀⠀⠀⠀⠀⠀⡇⠘⡆⠀⢣⡀⠘⠦
⠀⠀⠀⠀⠀⠀⢀⣰⣲⡯⢷⠞⢡⠇⡎⢸⠀⡇⢣⠸⡄⠘⡆⢀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠠⠙⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠵⡾⢃⡼⠁⡾⠀⡇⢸⠀⠳⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣾⠕⣹⢃⠀⡇⡠⢃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠟⠁⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⢿⡿⢿⣿⣷⣦⣤⣤⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⠈⠀⠀⢿⣿⣿⣿⣿⠿⠟⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡶⣦⣤⣤⣉⡀⠀⠀⠀⠀⠀⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣾⢶⣷⣺⣻⣿⣿⣽⡷⣦⡀⢀⡠⠛⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡷⡾⠺⣿⣯⠉⠎⢳⡀⠙⣎⢿⣇⣀⣀⠀⠚⢀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣽⠆⢘⣧⠼⣿⣿⡗⠇⢌⣷⢐⡼⡌⣿⡏⢹⣷⢀⣈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⣿⠂⢺⢿⣼⣿⣿⣿⣧⣬⣿⡿⠟⣋⣏⣷⣿⠛⡍⡽⡷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣆⣿⣧⣾⠾⣿⣟⣉⣿⣧⣿⣾⣿⣿⣿⣿⣿⡇⠆⢃⠠⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⣿⣷⡛⢻⣿⠿⣿⣿⣿⣹⣽⣿⣿⡏⢧⢹⣷⠸⡘⡈⡸⡆⠑⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⡌⠿⣷⣦⣼⣷⣿⣿⣿⡿⠿⠛⢧⠀⠸⡌⣿⣶⣧⣁⣁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢧⠀⢻⠙⠛⢻⠈⣻⣿⣧⣤⣶⣾⣶⣷⣿⣟⣿⣿⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣾⣄⣸⣦⣶⡿⣿⠟⣿⣏⣹⣿⣤⣾⡿⠋⢹⡿⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣾⣽⣷⡶⢿⡛⣉⢉⣩⡇⠀⠀⠀⠀⠀⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣆⠀⠉⠁⠀⠀⣻⣿⣿⣿⣶⣤⣤⡀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⢦⠀⠀⢀⣾⣿⣿⣿⡿⢿⠟⠛⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠉⠉⠛⠾⠿⠋⠀⠀⠀⢀⣾⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣴⣦⣤⣶⣾⣿⣿⣿⠃⠸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠆⠀⢻⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠘⠀⠀⠒⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣠⡀⠀⠀⠀⠀⡀⠑⠲⠴⠒⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠁⠈⠐⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⢀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⡀⠀⠀⠄⠁⢠⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⡄⠀⠀⠀⠀⠡⣬⠀⠸⡉⠀⡜⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡜
⠳⠄⠀⠜⠁⠐⠀⡅⠉⠉⠈⠀⠀⠀⠀⠀⡠⠊⡜⠓⠂⠤⢤⠊⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⡄⠠⠤⠔⠈⣠⣾⣤⣀⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠤⠤⠐⠋⠁⠙⠁⡐⠀⢹⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⠀⠑⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠘⢦⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⠵⠀⠀⢀⡤⠊⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠤⠤⠤⠄⣀⡨⠀⢨⠁⠒⠚⡄⠱⡤⠤⠄⠒⠊⡡⠐⠂⠉⠀⠀⢀⠔⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠄⢀⠀⢠⠤⠤⠀⣠⠖⠒⠚⠒⠒⠢⢼⡄⠱⡤⣄⣄⣀⡟⠉⠉⠒⠒⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢾⣀⣼⣀⡸⠀⠀⠀⡇⠀⡄⠀⠀⡀⠀⣄⠈⠂⠘⢄⠀⠸⣀⡆⠀⡄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣆⣀⣀⡧⠤⠇⠈⠒⠢⠚⠀⠀⠀⠈⠉⠙⠒⠚⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠀⢲⡀⠀⠠⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠶⠶⢺⠋⠀⠀⣤⡤⠄⠀⣀⠄⠆⣐⣠⢂⠠⢄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡘⠀⠀⠀⢳⣦⠤⠄⢀⡠⠔⢫⠸⠒⠁⠀⠀⠈⣗⢈⡆
⠀⠀⠀⠀⠀⠀⠈⠉⢁⣤⠾⠤⢤⢀⠞⠉⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⣇⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠈⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠶⠿⠶⠷⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡤⠴⠖⠒⠒⠒⠒⠒⠶⠦⢼⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⡀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠔⠚⠛⡿⠻⠿⠿⢿⣿⣿⣶⣦⣤⣤⣀⣰⠀⢀⣠⣤⣶⣿⠿⠟⠛⠉⠁⣧⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠡⠿⠟⠉⠉⠉⠉⣿⠀⠈⠟⠿⠿⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠈⠢⢀⡀⠀⠀⢀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠠⡤⠀⠀⠀⠉⠒⠤⠤⠀⠠⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠹⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢱⡀⢨⡗⠒⠶⠤⣤⣤⣤⠤⡤⣤⠤⠐⠒⠚⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠙⢾⠁⠀⠀⠀⣼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠱⢦⡀⠀⣏⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣧⠔⣆⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⣄⣀⡀⠀⠀⣷⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠃⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠀⠀⠀⠀⠈⠓⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠠⢤⣀⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠴⠊⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⠒⠄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠉⠁⠀⠲⢄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⡈⢀⠴⠀⠀⠡⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠈⣀⣀⡀⠼⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠔⢪⡁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⢄⠁⠀⠀⠀⠀⠀⠀⠘⠁⠂⢢⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠈⣤⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⡀
⠀⡐⠂⠀⠂⢴⠂⠉⠀⠀⠀⠘⠿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⡇
⠀⡇⠰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠙⠒⢳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⣰⡿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⠓⠲⠤⠤⠶⠒⠻⣁⡠⠊⠉⠳⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠂⠀⡐⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣧⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⡜⣸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⡜⢀⠇⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⠴⢋⠔⠊⠀⠀⠀⡘⡠⠎⠀⠀⠀⡴⠁
⠀⠀⠀⢀⢀⣀⣀⣀⠠⠄⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⢄⡀⠀⠀⠀⠀⠘⡅⠀⠀⠙⠢⠴⣅⠴⡴⠋⠀⠀⠀⠀⢸⠁
⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠚⠉⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠸⢆⡠⠀⠀⡀⣠⠏
⠀⠀⠸⢅⣀⣤⠤⣤⠤⠤⠠⠤⠔⠒⠒⠚⠛⠉⢉⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⡀⠀⢀⡀⣀⡤⠒⠚⠉⠁

⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢸⣿
⠀⠀⠀⠀⠘⣿⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣸⡟
⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⣿⡟⠀⠀⢰⡿⢿⡟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿⠿⣷⠀⠀⠘⣿⡇
⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⢀⣿⠃⠺⣷⣤⠀⠀⠈⠁⠀⠀⣀⣄⠀⣸⡿⠀⠀⠀⠸⣿⡀⢀⣄⣀⠀⠀⠉⠀⠀⢠⣴⡿⠂⢻⣇
⠀⠀⠀⢸⣿⠀⠀⠀⠉⠐⠿⠿⠷⠀⠻⠛⠉⢀⣿⠃⠀⠀⠀⠀⢿⣇⠈⠙⠻⠇⠰⠿⠿⠗⠈⠁⠀⠀⢸⣿
⠀⠀⠀⠘⣿⡄⠀⠀⣶⣿⣶⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢰⣾⣷⡆⠀⠀⣼⡟
⠀⠀⠀⠀⢻⣷⡀⠀⠻⠿⠟⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠘⠿⠿⠃⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠙⠿⣶⣦⣤⣤⣤⣴⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣤⣤⣤⣤⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗

⠀⠀⠝⠋⠀⠀⠀⠈⠙⠊⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣭⡴⠃⠘⢄⣀⡴⠋⢀⠃⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢠⠄⠀⢀⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⡄⡄⠀⠀⡆⠀⠀⠀⠀⠀⠐⠊⠹⢀⡡⠞
⠀⠀⠀⠀⢸⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠊⠀⠀⠈⠔⠀⠀⠠⠃⠀⠀⡇⢇⠠⡄⣱⠀⠀⢀⠀⠀⠀⠀⠐⡄
⠀⠀⣤⡠⠊⠢⢀⣤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠚⠁⠈⠙⠋⠁⠀⠀⢤⣀⡤⠀⠢⣴⡽
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⣀⠸⠀⠀⠠⠡⠀⠀⠀⢠⡀⠘⠀⣠⠠⠁⠀⠀⠀⠀⠊⠀⠀⠐⠒⠚⠁⠀⠠⡀⠀⠀⠀⠀⠀⡆⠀⠀⣀
⠀⠀⠀⢘⠄⠀⠀⢀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠢⡀⠀⠀⡈⡄⠀⠨⣱⠠⠁⠀⠈⣐⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣤⠀⢰⡆⠀⠖⢺⡄⠀⠈⠢⠌⠠⠃⠑⠒⠂⠁⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⡄⢰⠃⠀⠀⡀⠀⠀⠀⠐⡆⠘⢈⠊⢀⡜⠃⣀⡨⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠊⠀⣿⢀⢄⠀⡇⣽⠀⠀⠀⡷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠈⠲⠥⠞⠁⠘⠦⠤⠞⠃⢀⠜⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⣶⣳⡠⠀⠀⢰⣋⡷⡐⠀⠰⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣐⣀⠴⡞⠠⠀⡴⠀⠀⠀⠐⠚⠋⠁⠀⠀⠀⠈⠉⠀⠀⠳⠴⠋⠀⠲⠶⠟
⠀⠀⠀⠀⡀⠀⢠⢀⡄⠀⠐⡆⠀⠀⠀⠀⠀⠀⠈⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠇⠀⠀⢰
⠤⠀⠀⢰⠁⠀⠈⡿⡇⢀⡀⣧⠀⠀⠀⡐⠀⢀⠀⡀⣈⣧⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⠀⡸⠀⠀⠀⠁⡠⠀⠀⡀
⠀⢀⠜⠈⠢⠧⠴⠃⠙⠾⠖⠃⠀⠀⠀⠙⠚⠁⠀⠈⠙⠋⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠀⠀⣀⣀⠜⠀⢀⡀⠀⠀⠀⢒⠄⢨⠀⠀⠔⡐⠀⠀⠀⠀⠐⡦⡀⠀⠀⠂⢳⠀⠀⠀⠀⢰⠀⠀⠀⡈
⠀⠀⠀⠀⢦⠀⠀⢀⢱⡀⠀⠀⠐⠓⠁⠀⠀⠐⠚⠊⠀⠀⠀⠀⠊⠀⠀⠐⠒⠉⠀⠀⠐⠃⠁⠀⠘⠃
⠀⠙⠦⣉⡸⠋⠓⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⢠⠀⠀⠀⠀⢀⢳⠀⡄⠀⠀⠀⡀⠀⢀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠠⠔⠃⠀⠘⠶⠚⠀⠈⠛⠛⠀⠰⣫⠆⢀⡇⠀⠋⢼
⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠰⢰⠀⠀⢸⠀⠀⠀⠀⠀⢠⠆⠀⠀⡀⠀⠀⠀⠀⡆⠀⠀⠠⠔⠊⠀⠒⠒⠉
⡆⢠⠶⣦⠸⠀⠀⣜⢻⡆⠇⠘⠄⢆⠴⠈⠢⠧⠜⠁⠀⠀⠀⠀⣾⢀⠀⠀⡟⢸⠀⠀⠀⣿⠀⢀⠄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣾⣷⣶⣶⣦⣤⣴⡆⢷⣿⣿⣶⣠⣄⣠⠀⠄⣀⣀⣠⣴⣾⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠻⢿⣿⣿⣿⣿⣦⡽⣿⠟⠛⢱⡼⠃⣠⣶⣿⡿⠟⠋⠉⠁⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣤⣶⣾⣾⣿⣾⣿⣿⣿⣿⣧⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡻⣿⣿⣷⡀⠀⠀⠀⣾⣿⣿⣿⣿⣟⢻⣿⣿⣷⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢘⡿⠌⢳⣿⡏⠀⠀⠀⡿⢇⡙⠿⠿⢃⣼⣿⣿⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⡟⣿⢿⣿⣾⣿⣭⣤⣴⣿⠟⢰⣿⣿⣿⡄⠀⠀⢳⣿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣜⡷⠊⠈⠉⠛⠛⠛⠛⠉⠀⠠⣛⣿⣿⣿⣿⡀⠀⠈⣿⣇⠀⠀⠀⢹⣿⣿⡆
⡿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣰⣿⣿⣍⡅⠀⠀⢸⡿⠆⠀⠀⠀⢹⣿⡇
⣷⣌⡻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⣿⣦⠀⠀⠈⣦⠁⠀⠀⠀⣼⣿⡇
⣿⡛⠁⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⣈⣿⢧⠀⢀⣏⡀⠀⢀⢰⣿⣿
⠻⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⢿⣿⣿⡿⣿⠃⠀⠈⢹⣿⠇
⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠀⢻⡇⠀⠀⣼⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣃⣀⣤⡑⠀⠀⣿⠇
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣄⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⣿⣿⣿⣿⣿⣶⣴⠿⠤⣶⡂⠀⠀⢰⣤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠹⣧⣬⡏⢀⡒⠺⠾⢿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣟⢋⣉⡴⠀⠀⣿⣿⠂⢀⣾⡟⠀⢠⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⢠⣿⣿⣿⣿⣿⣽⣿⣿⣿⠛⣿⣿⡇⠀⢰⣿⣿⠀⠀⣿⠀⢰⣟⡔
⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣀⣼⣿⠃⠀⢸⣿⡏⠀⢀⣿⢀⣾⣿⠁
⣿⣿⣿⣶⡟⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⡀⠀⠀⢠⣿⣿⡿⣿⡍⠀⠀⣸⣿⣅⠀⣿⡏⣿⣿⠃
⡟⣿⣿⣿⣷⡟⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⠟⠛⠉⣉⣡⠞⢩⠀⠉⠁⢀⠀⠀⠀⠐⢿⣿⣿⣤⣿⢳⣿⠃
⠁⠙⢿⣿⣿⣿⣿⣠⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⣜⣿⣶⣿⣿⣿⣿⣿⣄⣀⣀⣤⣔⣿⣿⣿⣿⣿⡏
⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⡀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⢠⡀⠀⣿⡄⠀⣼⡇⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠈⣷⡄⠸⣷⠀⣿⡇⠀⣿⠀⠀⢀
⠀⠀⠀⠈⢷⣄⠘⢿⣦⡹⣧⡸⣿⡀⣿⠀⢀⣿
⠀⠀⠀⢠⣄⡻⣿⣮⣟⢿⣯⡳⣝⢷⣿⡆⢸⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢾⣽⣳⢵⡿⣿⣾⡁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡷⢯⣽⣻⡴⠌⢧⣴
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠯⣽⣿⣷⣾⠯⠑⠈⠻⣶⡀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁⠀⠈⠻⢦⡀⠀⣀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣻⣽⡿⢟⣭⢿⡂⠀⠀⠀⠀⢙⣾⠟⠙⠛⠛⠛⢛⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⣭⣾⣟⣵⣟⣵⣠⣀⠀⠀⠙⣿⣦⣤⣤⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⡿⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⠃⢀⢠⡀⣠⣴⣶⠾⠟⠋⠉⠀⢀⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠄⠐⣙⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⡎⠁⠀⠹⣄
⠀⢠⣶⣤⣄⣀⣀⣤⣴⣶⣾⣿⣿⡟⠀⠀⠺⣿⣿⣿⣟⢓⣆⠀⣀⣤⣾⡛⠁⠀⠀⠀⠙⢷⣤
⠀⢀⣩⣭⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣶⣿⣿⡏⠙⠛⣉⠭⣵⣾⣿⣿⢿⣫⣵⣦⡦⣄⣀⡀⠙⠛⢏⣀⣀⣀⣀⣠⣤⠄
⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⠃⢰⣿⣿⣯⣿⣿⣿⣵⢟⣼⢻⢿⣇⣷⣦⣘⣿⣯⣉⡉⠉⠀⠀⢀⣀⣀
⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣾⡿⣫⣿⢣⡿⣼⣿⣿⣿⣿⣿⣿⡿⣿⣛⠛⠛⠛⠛⠁
⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⢿⣿⣟⢾⣝⠻⠷⠶⠶⠶⠖
⡀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣽⣟⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣶⣦⣄⣀
⣿⢦⡀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢷⣦⣈⠉⠉⠁
⣧⡀⠙⠆⠀⠀⠀⠀⠘⠛⣿⡟⣿⣿⢿⣿⣿⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠻⣿⢿⣿⣿⣿⣿⣿⡟⠻⣷⣄⠈⠉⠓⠂
⣿⣿⣴⡀⢀⣤⡀⠀⠀⠀⠀⠀⠘⠋⠈⠛⠋⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠙⠛⠙⠻⠄⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠂⠀⢸⣿⣧
⠀⠀⠀⠀⡀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣷⣄⠀⠀⠉⠛⢿⣿⣿⣿⣿⠃⠀⠀⠀⠉⢋⡄
⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠉⢿⡻⠏⠆⠀⠀⣠⣶⣿⠁⠀⠐⣦⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⡀⠑⠀⠁⠀⢺⣿⣿⣿⣿⣶⠤⠍⠀⠀⠻⣿⣶⣦⡙⣶⠀⢀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⢀⠰⢴⣶⣶⣶⣾⡄⠀⠁⠀⠀⠙⠋⠀⠀⠉⠀⠠⢀⠀⠀⠀⠉⠉⠙⠀⠀⣿⣿⣿⣝⡋
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣽⣿⡿⠿⡇⠀⠀⣠⣀⠠⢰⠃⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⢋⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠰⠻⠇⠀⠀⠤⣄⡂⣛⣯⣴⣿⠀⠂⠀⠀⠀⣾⠀⠀⠀⠀⠓⢶⣶⣾⣧⣰⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠈⠙⢿⣿⡻⠇⠀⠐⠀⣆⠘⢉⣼⠀⠀⠉⠻⣾⣧⣤⣿⡿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢰⠀⠘⠀⡿⠙⢤⣀⠘⢿⣏⣀⣼⡟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣀⣀⠀⡀⣀⣠⣴⣾⡴⠀⠀⠀⠇⠀⠀⠉⠙⢋⣩⣿⠋⢀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⡷⠀⠘⠀⠀⠀⠀⠀⢀⡀⠋⠁⠶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡿⠀⠀⠀⠈⠻⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠓⢤⡀⠀⠀⠹⡆
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠙⣄⠀⠀⢿
⠀⠀⠀⢰⡟⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⣀⣀⣤⡴⠶⠛⠻⠋⠀⠀⢀⠐⠀⠀⠀⢿⠀⠀⢸⡄
⠀⠀⠀⣿⠁⠀⠊⠀⠀⠀⠀⠐⢀⡤⠖⢋⡙⠉⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⢀⣀⣀⣸⠀⠀⢸⡇
⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⣠⠥⡞⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⡁⠉⠛⠋⡄⠀⣼⠃
⠀⠀⠀⢻⣦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⠞⠋⠁⢀⡄⠱⡄⠀⠀⠀⠀⠀⡀⠀⠰⠾⠇⠀⠰⠀⡇⠀⣿
⠀⠀⠀⠀⡿⠀⠂⠀⠀⠀⠀⢸⡄⠀⠀⠀⢤⣀⠈⠛⢃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⡇
⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⡀⠈⠃⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠈⣿⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠑⢄⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢤⠂⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠘⢷⡀⢀⠆⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠉⠙⠓⠶⠤⣄⣀⣀⣀⣴⡟⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠐⠠⠀⠠⠀⠀⢤⠤⠀⣀⡀⠀⠉⠁⠀⡗⠠⢀⡘⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢶⡶⠁⠀⠀⠉⠀⠀⠀⡦⠀⠀⠈⠑⠢⡀⠀⢷⠀⠀⠅⠀⠀⢻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢠⠜⠀⠀⠀⠀⠀⠀⠈⠃⣜⠰⠀⠐⡀⠀⢈⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠂⠄⠀⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠃⠠⠀⠈⠆⡈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⢀⠀⠀⠈⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠀⠙⢣⠀⠘⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠐⠀⠄⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠣⡀⠀⠑⠧⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠳⠠⢤⠄⠀⢸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⢣⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠙⢀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠤⠀⠃⠈⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⡦⢀⠀⠠⣽⡄
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⡀⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠇⠀⠉⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠈⠄⠀⠀⠀⠀⠀⢀⠈⡑⠊⠀⠀⠀⠀⠀⠀⠀⢈⠢⣖⠀⠈⡒⢄⡀⢀⣼⡂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠸⠉⠀⣷
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⠀⠀⠀⠀⠀⠢⠠⠆⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢤⠀⠀⠸⡀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⡸⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠔⠁⠀⠀⠀⢰⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣷⡄⢠⡟
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡇⢹⡞⠁
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣥⣤⡶⠀⠂⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣨⡷⠆⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠻⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⠶⣤⡀⠀⠀⢹⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⢂⡆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡤⠖⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣱⣀⣹⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⣵⢧⠋⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣛⠛⠛⠂⢀⣀⣀⣤⣾⣿⣛⣴⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⣀⠛⠛⠉⠀⠀⠿⣿⣿⠉⢅⡊⠩⢹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢝⠧⠻⣷⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⠰⡹⡱⣕⢮⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⢳⠔⠔⡡⢠⢻⢰⢻⠉⢠⣤⢀⣦⠈⠂⠓⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⢪⢦⢃⣆⣌⣌⢤⠖⠈⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣀⠀⢤⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠱⠋⠊⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⢰⡇⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣾⣿⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡜⣡⣾⣿⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣴⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣄⢠⢣⣿⣿⣿⣿⠟⠋
⠀⣸⣦⡄⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⡤⢊⣡⣴⣶⣿⣿⣿⣿⣶⣝⣿⣿⣿⠟⠁
⠀⢿⣿⣿⣿⣿⣷⣦⣭⣑⣒⣲⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣤⣥⣵⣿⣿⣿⣿⣿⣿⣿⡇⠀⡰⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠉⠛⠙⠛⠉⠉⠀⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣿⣿⠏⠀⣿⣿⣿⣝⣿⣿⡟⣿⣿⣬⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣇⠀⠐⣿⣿⡿⢿⣿⣿⣿⣝⠏⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡞⣿⣿⣿⣿⣿⣷⢠⡀
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣯⠝⠋⡀⠀⠹⣎⣛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⢸⠁⣽⣿⣿⣿⠹⡟⢰⡇
⠀⠀⠀⠀⠀⠀⠸⠛⣿⡿⠇⠀⠐⠀⠀⠀⠹⠿⠟⠻⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠃⡟⠀⢱⣿⠻⣿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄⠀⠀⡌⢠⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡸⠁⠀⠀⢳⡀⠙⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠻⠿⠿⠃⢀⠜⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⠁⠀⠀⠀⠀⠙⢦⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠲⡟⠲⡞⢇⢀⣼⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡄⠀⡘⣦⡙⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⡿⣉⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⡼⣿⣿⣿⣿⣿⣧⢻⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢤⣴⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣎⠭⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠐⠀⠘⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠺⣻⣿⠿⢿⣛⣻⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠾⣄⣀⡰⠤⠜
⠀⠀⢪⡀⠀⠀⠀⣀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠛⠉⢩⢤⡍⠘⠩⠞⠁
⠀⠀⠀⠈⠉⠓⠚⠁⠰⡀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠼⠤⠂
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢦⣤⡀⣠⢎⡢⡀⢀⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣀⣰⠋⠀⣄⠀⣝⠕⠁⠈⢪⣏⠀⣠⠀⠹⣆⡠⠤⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣷⠉⠑⠋⠵⣾⢿⣿⠏⢠⠀⠀⡄⠱⣻⡿⣗⠮⠓⠈⠙⢼⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⠍⠁⠀⢨⠹⠀⠑⡄⡇⢠⠙⡯⣶⣤⠋⠙⣤⣶⡟⠋⡄⢰⢠⠋⠀⣿⠁⠁⠈⢨⡆
⠀⠀⠀⠀⠀⢸⡂⠀⣿⣿⣀⢈⣑⡏⠉⠚⢴⢡⠳⣣⡾⠷⣜⠞⡌⡦⠛⠉⢹⣊⡁⡅⣿⣿⣀⢠⣇
⠀⠀⠀⡖⡍⠛⠛⢛⡂⢒⠛⡛⣝⣧⣸⣷⣎⢏⣴⢫⠇⢠⢹⢣⡸⣡⣾⣇⣸⣡⠄⣿⡇⢀⠐⠒⠛⢫⢹
⠀⠀⢀⣱⣣⠀⠓⠤⡵⠼⠦⢽⣟⢍⢏⢫⢋⣺⣏⣤⠟⠻⣇⣣⣷⡻⢩⡫⡫⢻⣯⠾⠧⢮⠤⠊⠀⣎⣇⡀
⢠⡾⠋⠁⣹⣣⠈⣉⣣⠀⢶⣾⡗⠵⣷⣷⡏⠀⠈⢯⠀⠀⡿⠁⠀⢹⣿⡯⣊⢽⣷⡶⠀⣜⣉⠉⣼⣎⠈⠙⢷
⠘⣧⠀⠙⣿⢷⠷⢽⠻⡟⠭⢛⣻⣵⠊⠉⠛⢄⡀⠘⡂⡐⠃⠀⡠⠛⠉⠙⣆⣝⡫⢵⣚⠢⣄⣮⣾⣿⠋⠀⣼
⠀⢈⢗⠮⠊⣁⠐⣤⠵⣼⠶⠭⣒⣭⡦⣄⣀⠀⢔⣵⡷⢯⣮⡢⠁⣀⣠⠴⣯⠑⣛⠦⣔⠯⣿⠃⣠⠑⠫⡺⣅
⢴⡱⡁⠀⠀⠀⣏⠀⢾⣇⣀⡩⣿⡁⠀⠀⢀⢐⡻⣏⠀⠀⣹⣏⡅⠁⠀⠀⢈⡿⣊⠉⢹⡷⠀⣹⠀⠀⠀⢈⢎
⠀⢙⡮⣢⢄⡋⢠⣿⣲⠝⠲⣭⢄⣻⠖⠋⠉⢀⠪⡻⣷⢞⢟⠕⠀⠉⠙⠻⣛⠭⣒⠶⡟⢖⠛⠄⢉⡠⡺⢵⡁
⢀⡿⠀⣠⣿⣿⡿⠋⠢⡭⢗⣪⣝⠹⣄⣀⣤⠊⠀⢠⠉⠨⡄⠈⠑⣤⣀⡠⢟⣯⣥⣒⣼⣦⣗⢶⢷⣿⣄⠀⢻
⠘⢷⣄⠀⡹⡝⣀⣉⡝⠀⠾⢿⣗⡨⣺⣿⢇⠀⢀⣞⠀⠀⢳⡀⠀⣸⢿⢿⢖⢼⡿⠷⠀⢻⣉⡀⢫⢏⢀⣠⡾
⠀⠀⠈⢹⡻⠀⡠⠒⡳⢲⡶⣻⣧⣪⣪⣃⣮⢿⢣⢻⣦⣴⠛⡹⡯⣡⣣⣱⣑⣽⣷⠲⡖⢞⠒⢤⠀⢫⢏⠁
⠀⠀⠀⣇⣣⣤⡤⠄⠁⢸⣿⠐⢛⡏⢹⡿⡟⡎⢣⡇⠃⢰⢣⠟⣱⡹⢿⡏⢻⣝⣬⣤⠥⠤⢤⣤⣠⣚⠼
⠀⠀⠀⠀⠀⢹⠁⠉⣿⣿⢸⠈⡩⣇⣀⣤⣿⠖⡩⡟⢶⡾⢫⢦⢃⠗⣤⣀⣸⢍⡉⠉⣿⣿⠀⢨⡇
⠀⠀⠀⠀⠀⠸⡆⡀⢀⢀⣾⠀⣠⠃⠇⠘⣫⣏⠠⠛⣄⣠⠛⠿⣯⢄⠃⢸⠘⢄⠀⣦⡃⠀⣀⢐⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡗⣄⣀⢤⡲⢽⣾⣯⢆⠘⠀⠀⠃⡠⣿⣷⡿⢖⣠⢄⣀⣿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠊⠹⣆⠀⠋⠀⣹⡳⡀⢀⢔⣝⠀⠙⠀⣰⠏⠉⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠛⠁⠈⠪⡹⠋⠈⠛⠲⠮⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⡿⢿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣝⣫⣵⣮⣙⣛⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢻⣿⢟⣉⠿⣿⡿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣯⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⠻⣿⣿⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣬⣯⣴⣿⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡸⣿⡏⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣧⣝⣼⣮⣛⣡⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⡻⢿⠶⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣶⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢾⣿⣿⡟⢿⣯⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣎⣛⣛⣡⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⢿⡿⣿⣿⣿⣿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡸⣷⣿⢇⡸⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⡿⣿⣿⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣧⡻⢿⣭⠿⣣⣶⣭⣭⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣧⡻⣿⡿⢣⣬⣛⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⢛⣛⣛⣵⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⡻⠟⣸⣿⣿⣿⢫⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣎⣛⣛⣤⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠺⣟⡛⠛⢲⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠙⢾⡓⠿⠉⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣤⢤⣤⢬⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡿⠦⠉⠃⠉⠀⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢈⣛⣶⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⡏⠉⠛⠿⣍⡉⠉⠛⠛⢩⣭⡭⠿⣿⣿⠳⢶⡶⠶⠶⠒⣶⣤⠴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⡀⠀⠀⢸⡇⠀⠀⣤⣈⡙⢄⠀⠀⠀⠬⣽⣿⡗⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠜⠉⠀⠀⠀⠀⢷⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈⣿⡋⠉⠀⠀⠀⠘⠁⢀⣠⡤⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡟
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⣻⣿⡹⠀⠀⠀⠀⠀⢸⣿⣿⣳⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⣿⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠉⠁⠀⡀⠀⢀⠀⠠⠉⠉⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠘⠀⣀⣉⣶⣏⣀⠐⠀⠂⢀⣠⠴⣿⠋
⠀⠀⠀⢀⣾⠇⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠉⠓⢦⣄⣀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠘⢧⡀
⠀⢀⡤⠞⠁⢀⡀⠀⢰⡟⠀⠈⠻⣦⡀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⣴⢋⡤⠖⢠⡏⠀⢀⡿⠀⠀⠀⠀⢸⣿⡋⣀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠈⠙⠷⠤⠴⠛⠛⠛⠁⠀⠀⣀⡴⠋⠁⠘⢛⣷⡄⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⢀⣰⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⠀⣢⡀⠀⣨⣿⠿⠒⠛⠋⠛⠓⠶⠶⠶⠶⠚⠛⠋⠉⠛⠻⣦⡀⠀⢀⡐⢿⣿⠑⠀⠈⠛⢦⣄⡀
⠀⢀⡤⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀⣾⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⡟⠃⠀⠀⠀⣶⣄⣈⠙⠳⠶⣤⣀⡀
⠀⠿⠧⣤⠖⠀⠀⣠⡆⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣼⡋⠀⠁⢀⠀⢠⣄⡀⠉⠙⢶
⠀⠀⠀⠻⠤⠴⠚⠁⠹⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⡅⠈⣳⣄⢈⡿⠶⠖⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣯⣥⣬⣽⣧⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣯⣾⣿⣿⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⡿⠋⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣾⢿⣿⣭⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠈⢳⡄⢀⣠⠴⠛⠛⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣠⣾⣿⣿⡿⠟⠋⠉⠉⠉⠙⠻⢿⣿⣿⣷⡄⢀⣠⢿⡏⠁⠀⠀⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣴⠂⠹⣿⣿⣿⡏⠀⠀⢿⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⣿⣿⣿⡏⠀⠀⠀⣴⣿⣿⡿⢎⣴⣶⠛⠹⣿⣿⣿⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠰⣿⣿⣿⣿⣭⡶⠒⠛⠁⣿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢻⣿⣿⣧⠀⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⢠⣿⣿⣿⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣷⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⠀⠉⠁⠀⠀⠀⣠⣾⣿⣿⡟⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢻⣥⠀⠀⠈⢿⣿⣿⣿⣦⣄⡀⠀⠀⣀⣤⣾⣿⣿⣿⡟⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢧⡀⠀⠹⣧⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠳⡄⠀⠈⠻⣦⡀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠶⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠺⢿⣿⣿⣿⣧⣼⣤⣾⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣷⣤⣧⣼⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡍⢻⣿⣿⣿⡟⢻⣿⣿⣿⣿⢁⣽⣧⡈⣿⣿⣿⣿⡟⢻⣿⣿⣿⡟⢩⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⣉⣿⡗⠐⣿⣏⣠⣿⣿⣿⣿⣿⣿⣄⣹⣿⠒⢺⣿⣉⣹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁

⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⢛
⣻⣿⡭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠏⢤⣴
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠰⠂⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡇⠀⠀⠙
⣿⣿⣟⣋⡀⠀⠀⠀⠀⠀⢠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⡿⠤⠄⡀
⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠶⣶⣶
⣿⣿⣿⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠁⠀⠀⠀⢐⣛⣿⣿
⣿⣿⣿⣟⣋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢩⣽⣿⣿
⣿⣿⣿⠯⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣿
⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠛
⣿⣿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢾
⣭⣇⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡛⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣀⣀⡤⠤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠛⠉⠁⠀⠀⠴⠾⠗⠒⠒⠒⢒⣲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⠶⠀⢀⣠⡤⢖⠲⡄⠀⠀⠀⠚⠉⠉⠉⢉⣭⣶⠶⠄
⠀⠀⠀⠀⠀⢀⣠⠶⠺⣍⠀⢀⣠⠟⠛⠉⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡭⠵⠦
⠀⠀⢀⡤⣞⠭⠖⠒⠒⠦⣤⣋⠤⠤⠶⠲⣶⢺⠃⠀⠀⠀⠀⠀⣠⠖⠒⠲⡶⠿⠖
⢠⠖⠉⠀⢯⡉⠉⠉⣋⡽⣇⠀⠀⠀⠀⣀⡴⠋⠀⣴⢀⡤⠀⠘⠡⠾⢋⡾⠁⠀⠀⠀⠀⡀
⣏⠀⠀⢀⠤⠽⠯⣍⠁⠀⠈⠱⠒⠉⠉⠉⠉⡤⢾⡵⢋⣡⣾⣭⣽⠿⣥⣀⣀⠀⠀⣖⢼⢹⣞⡆
⠘⠦⣀⠘⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉⠀⢀⣀⡀⠀⡿⡶⠒⠦⠬⠭⣈⠉⢸⠁
⠀⠀⣆⣿⠿⣶⡶⣶⠒⠲⣖⠒⠛⠋⠉⢡⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠓⠲⠤⣄⡀⠈⠙⠃
⠀⠀⠈⠑⠚⠄⡆⢘⠒⣚⠭⣦⠀⣠⠔⠁⠱⡄⠀⠀⠀⣠⠴⠦⢄⡀⢀⣀⣠⡔⠊⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠋⠥⠟⠀⠀⠀⠙⠛⠁⠀⢀⣀⡹⣄⡀⡼⠁⠀⠀⠀⠈⠙⠷⠀⣷⡾⠛⠛⠛⠭⣭⣕⣦⡀⠀⠀⠀⠀⠀⢀⡔⡄⠀⢠⢌⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠯⣗⡢⢽⣷⣄⡀⢀⡾⣓⠦⠤⠖⠉⠉⠛⢿⢿⣼⠁⠀⢹⡧⠐⠆⠐⢀⢠⠾⠀⠖⠶⢬⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢥⣌⣓⣬⡣⣙⣼⡇⠀⠉⠒⠦⣄⣀⣠⠞⠮⠟⠤⠴⠚⠀⠀⠁⠀⠈⠈⠲⡆⢸⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣭⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠀⣀⡀⠀⠀⡀⢠⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠉⠉⠁⠀⠈⠉⠋⠉⠙⠛⠋⠉⠉⠉⠉⠓

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠿⠀⠀⠇⠻⠼⠃⠇⠀⠇⠿⠸⠀⠿⣸⢯⡄⠀⠿⠀⠘⠧⠟⢸⢯⡍⠷⠼⠃
⢀⢀⣠⠫⢂⠢⠍⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⢁⠀⡼⠠⠐⠒⠻⠄⡀
⡴⠂⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠂⠀⠀⢀⠀⠀⠀⠰⠶⡄⠀⠀⢬⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠁
⠀⠀⣀⣤⡄⠀⠀⢰⣿⣾⠁⠀⠈⠀⠀⠀⠀⢀⠀⡔⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠁⠀⠀⠴⠂⠀⠀⠀⠖⢖
⠀⠀⠘⠿⠃⠀⠀⠀⠉⠁⠀⠀⡀⠀⠀⠀⠀⠤⠎⠑⠙⣫⠀⠀⠠⡀⠠⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⢤⣀⣤⡎⠀⠐⠋⠁⠀⠀⠀⠀⡨⠆⠀⠀⠄⠃⠆⠣⠐⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠺⠃
⢀⡄⠀⠀⠀⢀⠀⠀⠄⠀⣄⠀⢡⠀⠀⢀⠜⠀⣠⠊⠀⠀⠈⠈⠀⣀⢀⡁⠀⠀⠀⠀⢁⠀⠀⠀⡀
⠀⠁⠀⠠⠒⠂⠀⠀⢀⠁⠅⠀⠆⠒⠀⠈⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠂⠀⠀⠈⠂⠤⠌⠉⠀⠐
⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠂⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠄⠠⠀⠇⠀⠁⠀⠀⠀⠀⠂⠠⡀⠀⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄
⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠒⠈⠈⠀⢄⠰⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀
⠀⠀⠂⡀⠢⣀⠀⠀⠀⢀⠤⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⣆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣸⣀⠀⠀⠀⠀⠀⡰⣻⡳⣀⠳⣦⣄⠀⢀⣠⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠊⠁⠈⠉⠓⠒⠒⠚⠣⢿⢫⣴⣵⠘⠀⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⡗⠪⠒⠛⠋⠀⢀⠀⠀⢠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢄⣀⣀⡀⢤⣾⠇⠀⠀⠀⠀⠀⠈⡗⠒⠁⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠒⠒⣒⠮⢡⠎⠀⠀⢀⡰⠃⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠀⠛⡄⠀⠀⠀⠀⠀⢠⠃⠀⠀⡐⠑⣂⡥⠚⠒⢚⡿⠀⠀⠀⠀⣿
⠀⠀⠀⡄⠰⢆⠀⢸⣀⡀⠀⢠⠃⡤⠤⢀⡀⠀⠈⠒⠒⢊⠠⠒⠉⠉⡧⠖⣋⠀⠀⠀⠀⠀⡿
⠀⠀⡜⠻⠁⠘⠋⠉⠈⠉⠑⡇⢘⠄⠀⠀⢳⠀⢀⠔⠊⠁⣠⠔⢊⠼⠚⠉⡀⢱⠀⠀⠀⠀⡇
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠑⣭⢞⣀⡠⠁⣸⠐⣕⡀⢰⡟⡡⠚⠁⠀⣠⠜⣱⠃⠀⠀⠀⢰⠃
⣤⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡤⠞⠁⠀⠀⠉⢹⣞⢁⠄⢠⠚⠁⠔⠁⠀⠀⠀⠀⡞
⡍⠇⠀⠀⠀⠀⠀⡴⢋⠀⢀⣴⠋⢳⣀⡀⠀⠀⢀⡤⠋⠈⠘⢲⠋⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠇⠀⠀⠀⠀⠀⠀⠈⠛⡤⠄⠈⠆⢸⠀⠙⣶⠊⠁⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠸⡀⠀⠀⠀⢀⠀⡸⠳⠇⠀⠀⢸⠂⠀⠀⡽⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠱⣄⠀⠀⠘⡗⠁⠀⠀⠀⠀⠀⠀⢀⡴⠃⣀⡠⠔⠊⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣋⣽⣿⣧⠴⣶⣤⣀
⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⣰⣿⣆⣀⣠⣤⣁⣤⣠⣶⣄⣀⣄⣉⣈⠁⢀⣀⠐⠂⠈⠛⣦⣄
⠀⠀⠀⠀⣰⣏⡴⡛⠛⠉⠀⠈⠪⣻⠁⠙⡭⡹⢹⣹⢹⡙⡏⣉⢋⢋⠟⡯⢴⣦⣀⡉⡤⠈⢣⡀
⠀⠀⠀⠀⡟⠁⠀⠀⠄⢀⠂⠄⡐⠈⢶⣄⠌⣱⡾⣏⣧⣕⣼⣏⣡⣪⢊⡴⠓⠉⡹⠶⣗⣄⠀⢱⡀
⠀⠀⠀⠀⢷⡀⡀⠀⠀⠠⠬⣒⣬⣑⣦⣜⡷⠿⠷⢿⣿⣿⣿⣿⣥⣿⣥⢤⣴⣮⣴⣵⣮⠿⣌⣋⠡
⠀⠀⠀⠀⠀⠻⣤⠒⣒⠺⠷⢶⣬⣽⣻⣿⡇⠀⠀⢰⡟⢿⣿⣶⣦⣤⣄⣀⡤⠍⠉⢉⡬⠟⢻⣥⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠒⢬⣥⠶⢒⣛⣻⣿⠀⠀⠀⢸⠀⢸⣧⣙⠡⡉⠙⡻⠽⢍⠛⡻⠶⠄⣼⡛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢾⣿⠀⠀⠀⠀⡆⢻⣿⣿⡀⠀⠀⠈⠂⡀⣑⣌⣢⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⡇⣼⠻⢽⣧⠴⠖⠚⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠠⣶⣾⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⣠⠂⣤⡀⡻⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣰⣵⣿⣾⣿⣿⣷⣮⣬⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣀⡀⣤⣀⣼⠟⠋⠁⠸⠸⡟⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠇⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⣗⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⡏⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⣀⣻⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡶⢀⢀⣤⣤⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢣⢠⡉⡈⡄⡀⡖⣶⠦⣴⢿⡶⢠⢷⣿⠁⠀⠀⠀⠀⠀⠀⡀⣾⢿⢸⡏⡟⢻⢸⣿⡿⣿⢷⣦⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⡀⠈⠋⠁⠁⡀⠐⠀⡀⢠⠠⣠⡘⡀⠀⡟⠀⠀⠀⠀⠀⠀⡄⠳⠼⠸⡃⠁⠣⢸⣟⣻⣿⣿⣆⣏⣿⡄⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⠃⣜⢠⢌⠠⠀⠀⡀⠁⢁⢨⣥⣁⡁⣼⠁⠀⠀⠀⠀⠀⢰⢳⡶⡆⣯⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡇⠁⢡⢿⢸⠇⠇⠳⠹⢸⢿⠾⣾⠛⣟⣿⠀⠀⠀⠀⠀⠀⣼⣲⡄⢇⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⠁⠆⢈⠀⠈⠀⠀⠀⡀⠠⠠⣀⢠⠽⢽⡿⠀⠀⠠⠄⡀⠀⠍⠭⠭⠭⣙⠺⣛⡛⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣧⢠⢱⡇⡞⡀⣦⡼⢠⡁⡌⡀⠳⡈⠃⠀⢀⠨⠀⠀⠀⠀⠀⠀⠀⢛⣰⣏⠻⠏⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠇⠀⠀⠑⢇⢣⠋⠁⠀⠤⠀⠰⠄⠀⠀⠀⠀⠀⠐⠀⠘⠛⠂⠀⠈⠉⢉⠉⠐⢠⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠘⡄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠙⠶⣶⣦⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⢀⣤⣀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⢀⡀⠀⢀⣀⡀⢀⣀⠀⢼⣄⢳⣷⣄⠀⠀⠈⠻⣶⠶⠽⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣦⠀⣼⠁⢻⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠐⠖⠈⣧⡀⠈⠙⣋⣭⠹⢄⣀⣥⣾⠿⡟⡆⠀⠀⠀⠀⠀⠀⠀⢠⣴⡉⠙⠻⣦⣄⠀⣴⣫⣿⡿⠛⠀⠷⠶⠎⠰⠆
⠀⠀⠀⣦⣤⣦⡀⠀⡘⣃⡀⠀⠀⠰⠂⣞⣀⣴⣯⡶⠺⠷⠄⢳⡍⠷⠀⠒⠂⠞⠃⠀⠀⠀⠀⠀⠈⠻⠿⠦⣄⣀⣈⠖⠋⠙⠻⣧⠒⡰⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠸⣿⣿⣿⣷⠟⠉⠛⠢⠤⠀⢸⣿⢿⣟⣦⡀⠀⠀⠀⠀⠉⠻⠶⠄⠰⠶⠶⠶⠤⠤⠀⠀⠀⣀⠢⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢿⣿⣿⠏⣦⠀⠀⠀⠀⠀⣾⣿⡿⣧⠿⣿⡦⣤⣤⡀⠀⣤⣤⡤⠤⠤⠀⠀⣠⠀⠀⠀⢠⡈⢄⠀⠙⠛⠀⠀⠀⠀⠀⢠⠀⣤⠀⠀⠐⠂⠰⡖⢲⡆
⠀⠀⠀⢠⠜⠈⠁⠀⠈⠓⣄⠀⠘⢼⣿⣿⡇⢻⡠⣿⠱⣿⣿⠓⢷⡟⠀⠀⡆⠐⠀⠀⠀⠀⠀⠓⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠁⠈⠐⠀⠀⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⢾⣄⠒⠘⠿⠿⠃⠀⠀⢸⡦⣿⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠘⠻⠋⠁⠀⠈⠓⠢⠄⠀⡀⠀⠀⠈⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠀⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠆⠀⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡈⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⠀⠁⠉⠓⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠈⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⠛⠗⠲⣤⣤⣄⣠⣴⡞⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⢄⡑⠒⠖⣃⠶⠴⣂⠊⠀⠀⠀⠀⠀⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⢀⣦⡍⠻⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⣺⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⣉⣠⣴⡤⠚⠓⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣶⡶⠶⠴⠶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⠀⣀⣠⡀⠀⣀⣀⠠⠄
⠀⠀⢆⡀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡖⣫⢵⠿⠻⠟⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠚⠋⠉⠁⠰⠋⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠉⠉⠁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣁⡤⠤⠤⠤⢤⣀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠞⣆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸
⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠘⠀⡜⠀⢻⡀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠀⠀⠒⠲⢤⡞⠀⣠⠏
⠀⡀⢀⡠⠴⠒⠚⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⡀⠀⢀⠃⠀⠈⢧⡀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠁
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⢊⣀⠀⢀⠤⡈⠀⠈⢀⠀⠀⠀⠛⢦⣤⡴⠃⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡰⠁⠀⡇⡇⠀⠘⣆⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⢧⠁⡷⡷⠀⢸⠀⠀⠘⢄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠦⠤⠋⠀⠹⣄⣀⡜⠀⠀⠑⡌⠢⣄⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠊⠉⠉⠉⠈⠉⠉⠙⢢⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣇⠀⠲⠀⠀⢀⡾⠆⠀⡼⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠘⠦⣜⣀⣆⣨⠧⡤⠞⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇⠹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⡤⠤⡞⠉⠳⣶⢶⡖⠛⡉⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢸⠁⠀⠹⣄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠛⠛⠉⠀⢹⠀⠈⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣸⠃⠀⠀⡼⠂⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣠⡴⠯⠚⢀⡴⠁⠀⠀⣰⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⡄⠀⠀⠀⠠⡜⠲⠖⠁⠀⠀⡀⠀⣀⡴⢚⠁⢀⠄⠀⣼⠁⠀⠀⢰⠃⠀⢠⠏
⠀⢀⡠⢤⣀⣀⡀⠀⠀⣀⣀⣠⠴⠞⠁⠀⠀⡟⠙⠓⠒⠒⠘⠲⣄⠀⠀⠀⠹⣎⠀⠈⠛⠖⠾⠴⠖⡵⠋⠉⠉⠉⠀⢠⠏
⣰⠋⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣤⠼⠗⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⠧⡜⠀⠀⡆⠀⢹
⣇⣠⡇⢠⠀⠀⢀⠀⢀⣀⣀⣤⠴⠞⢋⡥⠖⠒⠊⠉⠉⠉⠀⠀⠀⢀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠚
⠀⠉⠛⠾⢦⣤⡼⠏⠉⠉⠀⠀⠀⠀⡟⢠⠂⠀⡖⠀⠀⣴⠶⠚⠋⠉⠉
⡀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠓⣻⣤⣴⣧⣤⡾⡁⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀⣀⢀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠐⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⠏⠁⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⣧⡠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣽⣧⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢀⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⣿⣧⢸⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡛⣏⣿⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⣻⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⣿⣬⣿⣦⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣿⣻⣿⣄⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣈⡿⣿⣿⣿⣿⢦⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢿⣧⠙⢹⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣾⡿⠛⠚⠛⠛⠛⠛⠓⠛⠓⠲⠴⠦⠴⠶⣶⣶⣶⣶⣶⣶⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⣀⢀⣀⠀⠀⡀⠀⠀⢀⡤⣼⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣯⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠤⢼⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⡿⠟⠋⠀⠀⠀⠀⠰⠀⣀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞