Degree Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⣀⣴⣾⠽⠻⣦⣀⠀⠀⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⠀⠀⢀⣠⡴⢿⡯⠉⣀⡴⠈⣉⡿⣷⣤⣀⠀⠀⠈⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⡊⠅⠐⢉⣡⣴⡾⡯⣅⣿⣞⣵⣽⣷⣶⣿⣿⢋⣹⣽⡿⣿⣶⣤⣄⡀⠀⠀⠁⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠒⣈⣀⣤⣶⣞⣿⡿⣷⣷⢾⣻⠽⣟⣻⣟⢿⣿⠾⣻⣻⣿⣿⣷⣿⣿⣯⣽⣿⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢸⡻⢿⣿⣿⣿⣿⢻⣿⣿⣫⣟⣽⣿⣿⣳⣮⣿⣷⣶⣿⣿⣿⡵⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣌⡙⠻⠿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢤⣍⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣽⠟⠋⢁⣧
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣬⣉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⣼⠿⠋⠁⠀⠀⢸⣿⡄
⠀⠀⢠⠔⠀⠀⣠⠴⢶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣦⣈⠻⢿⣿⣿⣿⡿⠛⣡⣾⡟⠁⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢀⡼⢷⡀⠈⢷⡀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⢋⠠⣿⣿⣿⣶⣤⣉⣏⣠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠿⠛⠇
⠀⠀⠀⠠⣏⡑⠈⢳⡄⠈⢳⡀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣙⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠲⣅⢻⣦⠀⣹⡾⣦⠀⠀⠙⢿⣿⣟⣿⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣓⡎⢛⣦⣤⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⡠⠊⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣏⠁⠉⡒⢤⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢁⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡘⠛⠦⣤⣁⠈⠈⣓⣦⣤⡀⠀⠐⠒⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠨⢙⠻⣚⣯⣞⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠔⢻⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠘⢿⣷⣶⣦⣭⣭⣙⣒⠲⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣭⣍⣛⣒⠲⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣛⣛⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢏⣼⣿⣿⣿⣿⣿⣶⣭⣛⠿⣿⣿⣿⣿⣿⣷⡜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⢿⣿⣿⣿⣿⣆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣧⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣿⣷⣌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣦⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣷⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠟⠀⠀⠀⠀⢹⠉⠛⠛⠿⠿⢿⣦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠈⠙⠛⠷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣶⣤⣀⡀
⠀⠀⠀⢀⣀⣤⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣀⡀
⣤⣶⣟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⠛⢻⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⣶
⠀⠉⠛⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠋⠉⠙⠛⠛⠻⠿⠶⠶⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⣀⣠⣴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣹⣿⡿⠟⠿⠿⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠛⠿⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠋⠉⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣶⣤⣀⡀⣀⣤⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠶⣶⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⠶⠿⠛⠛⠀⠀⠀⠀⢸⣿⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠈⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣈⣩⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⡛⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣭⣟⣻⠿⠿⣛⣯⣵⣶⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⣼⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠪⠅⣀⣀⡈⠛⠻⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠀⣿⡦⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠒⠒⠂⠤⠤⠄⣀⢀⡠⠖⢫⣿⣇⣀⠷
⠀⠀⠀⠀⠀⠀⠀⣀⣈⡽⠿⢀⣒⠒⠠⠤⠤⠤⢀⣀⣀⣀⠀⠀⠀⠀⢸⠀⣀⢼⣿⣿⠉⡇
⠀⠀⠀⠀⠀⢰⠋⠒⠢⣇⡀⠀⠀⠀⠉⠒⠒⠠⢤⡤⠄⠒⠉⠉⠉⠒⠚⠋⠁⢈⣭⣥⣶⡯⣟⣶
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠒⠒⠤⠄⣀⡀⠀⡇⠀⣀⣀⣤⣄⣒⡬⠭⠙⠩⠍⢁⠨⠭⠀⢿
⠀⠀⠀⠀⠀⢨⠿⣒⡒⠠⠤⠤⢀⣀⣀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⣀⣤⣔⡂⠭⠶⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠒⠂⠤⠄⣀⠈⠉⠀⠒⠒⠀⣤⣤⠀⣘⣀⠤⠄⠒⠈⠉⠁⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠉⠒⠢⠤⢀⡀⠀⠀⠀⠀⠉⠱⡎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⢀⣀⣇⣀⠀⠤⠤⠀⠒⠂⠉⠉⠁

⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣿⢩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡍⣿
⠀⠀⠀⠀⣿⢸⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣷⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣴⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣄⣼⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⢿⣿⣿⣿⡛⠙⣻⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⡴⠿⠚⣛⡛⠻⠶⣦⣙⠻⣿⣾⣿⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⢟⣰⠟⣡⣶⣿⣿⣿⣯⣙⡷⣮⡙⢷⣝⢻⣿⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢏⣼⢃⣾⣿⣿⣿⡿⢋⡴⢻⡿⣎⣻⡌⢿⡌⢻⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⠟⣭⣭⣭⣭⣭⣭⣭⣭⣭⡙⣿⣿⣿⣿⣿⣿⡿⢸⡇⣾⣿⣿⡿⢋⡴⢋⡿⣫⡾⣫⣇⣿⠘⣷⠘⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⡘⢿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣷⢸⡇⣿⢻⣋⡴⢋⣴⣫⡾⣫⣾⣿⣿⣿⢀⣿⢸⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡌⣷⡸⣶⠻⣶⣫⡾⣫⣾⣿⣿⣿⣿⡟⣸⡇⣾⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣷⡌⢷⣌⠷⣌⣛⢶⣿⣿⣿⣿⡿⢋⣼⠏⣴⣿⣿⡇⣿
⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢆⡙⠷⢦⣍⣛⣛⣛⣩⣥⡶⠛⣡⣾⣿⣿⣿⡇⣿
⠀⠀⠀⠀⢿⣌⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠏⣼⣿⣿⣦⣭⡍⠉⣍⣡⣴⣶⣷⠸⣟⣛⣛⣛⣡⡿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣸⣿⣿⣿⣿⡿⠀⠁⢻⣿⣿⣿⣿⣧⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢿⣿⡿⠁⠀⠀⠀⢿⣿⡿⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠘⣿⠃⠀⠀⠀⠀⠈⣿⠇⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠈⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⢀⣤⡾⢷⣤⣀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⣀⣴⡾⠛⠁⠀⠀⠈⠛⢷⣦⠀⠀⠈⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠠⣾⠟⠉⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀⠀⠉⠻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⢛⡛⢻⡿⠛⠛⢻⣟⠛⡛⣻⡿⠛⠛⢿⣟⠛⠛⣻⡟⠛⠛⢿⣟⠛⡛⣿⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⢻⣿⠋⠀⠀⠘⢻⡟⢻⣿⠃⠀⠀⠘⣿⡟⢻⡟⠃⠀⠀⠙⣿⡟⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⠀⠀⠀⠀⣾⡇⢸⣿⠀⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⠀⣿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⣿⡇⠈⣿⠀⠀⠀⠀⣿⠁⢸⣿⠀⠀⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⣿⣶⣄⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⢹⡏⠙⠻⢶⣤⣿⣤⣤⣿⣤⣤⣤⣤⣿⣤⣤⣿⣤⣤⣤⣤⣿⣤⣤⣿⣤⣤⣤⣴⣿⣤⣤⣿⣤⡶⠟⠋⢹⡏
⢲⣤⡀⠀⠸⣿⠀⠀⠀⠀⠉⠉⠛⠻⠿⣯⣭⣉⠉⠉⠉⠁⣀⣀⣀⣀⠈⠉⠉⠉⣉⣭⣽⠿⠟⠛⠉⠉⠀⠀⠀⠀⣿⠇⠀⢀⣤
⠀⢿⡟⠿⢶⣿⣦⣤⣤⣤⣤⣄⣀⣀⡀⠀⠉⠛⠷⣦⣄⠈⠛⠛⠛⠛⠁⣠⣴⠾⠛⠉⠀⢀⣀⣀⣠⣤⣤⣤⣤⣴⣿⡶⠿⢻⡿
⠀⠘⣿⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠻⢷⣦⣄⡈⠙⢷⣄⠀⠀⣠⡾⠋⢁⣠⣴⡾⠟⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠸⣷⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣌⢻⣆⣴⡟⣡⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⢹⣧⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⢿⡆⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠈⣿⡄⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢠⣿⠁
⠀⠀⠀⠀⠀⠘⣷⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠹⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⣼⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⢶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⡶⠶⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢶⣤⣀⠀⢸⡇⠀⣀⣤⡶⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⣷⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠴⠶⠶⠖⠒⠒⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢻⡄
⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢻⡄
⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠲
⢿⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠴⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠙⠛⢿⢻⡏⠉⠹⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢧⣀
⠀⠀⠀⠈⢧⢹⡄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠈⢧⢻⡄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⢧⢻⡄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⣤⣴⠶⠞⠶⢶⣤⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⢧⠻⡄⠀⠙⣷⠶⠶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⢣⡴⠚⠛⠛⠲⣌⠳⣆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⢻⡄⠀⣿⠀⠀⠀⡇⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿⢡⡏⠀⠀⠀⠀⠀⠘⣧⢹⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠙⢷⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠸⡇⠀⠀⠀⠀⠀⢀⡟⢸⡋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⠻⣿⠀⠀⠀⡇⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠩⣇⡙⢦⣀⣀⣀⣤⠞⣡⡏⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣼⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⢶⣬⣭⣥⣴⠚⢿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⡇⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⢰⠇⠀⠀⢰⠏⣧⠀⠀⠈⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢦⡟⠀⠸⣦⠟⠛⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⢳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣴
⣿⣿⡟⠻⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠟⠋⠉⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠉⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠶⠶⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⢀⣠⡾⠟⠉⠁
⠀⠀⠀⠀⢀⣴⠾⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠟⠷⣦⡀
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠹⣿⠛⠷⢶⣦⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⡶⠾⠛⣿⠏⠀⠀⠀⠘⣷⡀
⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢹⡇⠀⢀⣄⡀⠉⠉⠉⠙⠛⠛⠛⠛⣿⡟⠛⠛⠻⣿⠛⠛⠛⠛⠋⠉⠉⠉⢀⣠⡄⠀⢰⡟⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠉⠛⠷⠶⢶⣶⠆⠀⠀⠀⣿⣇⣀⣀⣀⣿⠀⠀⠀⠰⣶⡶⠶⠾⠛⠉⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣀⣤⣤⡄⠀⣠⣶⠟⠋⠉⠉⠙⠻⢶⣄⠀⢠⣤⣤⣄⣀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⡏⠀⠠⡾⠟⠋⠉⠉⠉⠁⢰⡟⠁⠀⢀⣾⣷⡀⠀⠀⢻⣆⠈⠉⠉⠉⠙⠻⢷⠄⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠸⣧⠀⠀⠀⠀⢀⣾⢃⣀⣠⣤⣤⡶⠶⠶⠿⠟⣿⠁⠸⣿⡛⠁⠈⢛⣿⠇⠈⣿⠛⠿⠶⠶⢶⣦⣤⣄⣀⡈⣿⡀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠹⣧⣄⣀⣠⡾⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣻⣇⠀⢸⣿⣤⣤⣽⡇⠀⣰⣟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢷⣄⣀⣀⣼⠏
⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣦⣈⠋⠁⠈⠙⣁⣴⠟⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠈⣽⠟⠻⠟⠻⣯⠁⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣠⡀⠀⣼⠏⠀⠀⠀⠀⠹⣧⡀⢀⣤⣘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⣷⣾⠋⠀⠀⠀⠀⠀⠀⠘⣷⣾⠏⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠋⠈⠛⠛⣷⣴⠾⠟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠈⢻⡧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⣷⣦⡀⣀⣀⢀⣴⣶⡿⠶⠶⠶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠋⠙⠛⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠶⠟⠛⠶⣦⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠛⠉⣀⡈⠙⠻⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠛⠁⣠⣴⣿⣿⣿⣷⣤⡀⠙⠻⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠋⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠟⠋⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠉⠛⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⡿⠟⠋⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠈⠛⠿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⢸⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡈⠙⠻⠿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠟⠋⠉⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡏
⣀⣀⠀⠀⠀⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠙⠿⣿⣿⣤⣤⣤⣤⣤⣼⣿⡿⠛⠉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢀
⠘⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣈⠉⠙⠛⠿⣿⣿⣶⣄⠈⠻⣿⣿⣿⣿⣿⡿⠋⢀⣴⣾⣿⡿⠟⠛⠉⢉⣀⣀⣠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠉⠛⢿⣷⣄⠈⢻⣿⣿⠋⢀⣴⣿⠟⠋⢁⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢻⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠻⣧⡀⠛⠃⢠⡿⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⢿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠁⠀⠀⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠘⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠸⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠈⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠀⢸⠿⠋⠁
⣾⣾⣷⡾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣷⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣷⣶⣿⣿⣶⣶⣷
⣿⣿⣿⣀⣀⣤⣤⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⢹⡏⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢷⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠈⢧⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠹⣆⠀⠀⣀⣸⣧⡽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠙⠲⠦⢤⢼⣾⢋⣭⠴⠖⢻⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠶⣶⡶⢾⢿⡀⠀⠀⠸⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⣴⠋⠈⣇⠀⠀⠀⢻⡄⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣇⡴⠞⠁⠀⠀⢻⠀⠀⢀⣠⠗⣀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⣧⡖⢿⢷⡋⣿⠁⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣈⣉⣥⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢯⣄⡀⠀⠀⠀⠀⠀⠻⣤⣤⣤⠟⠛⠛⠛⠛⠛⣛⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡟⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠶⣤⣀⢀⣠⡴⠞⠋⠀⠀⡇⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⣸⠋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠞





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠟⠛⠛⠛⠿⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢋⣠⡤⠶⠚⠛⠓⠀⠀⠀⠈⠙⠻⣿⣦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢁⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠿⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⠏⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠛⠛⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⠀⠀⣀⣠⣴⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠉⠛⠛⠒⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉⠀⠉⠛⠻⠿⢿⣿⣿⠿⠿⠟⠛⠙⠻⠿⣿⣶⣶⣶⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⣠⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠹⣿⣆⠀⠀⠀⣰⣿⠛⣿⣦⠀⠀⠀⠀⠀⣤⠀⢶⣿⡶⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠘⣿⣆⠀⢰⣿⠇⠀⠘⣿⡇⠀⠀⠠⠿⢿⡀⠀⣿⠀⢀⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠘⣿⣆⠈⢿⣷⣤⣴⡿⠃⠀⠠⣦⡀⠀⡙⣦⣿⣴⡟⡁⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠉⠉⠉⠀⠀⠀⠨⡿⠋⠉⢉⣿⣿⢿⡉⠉⠙⢿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠟⠁⣿⠀⠙⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠀⣠⣿⣦⠀⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠸⣾⡿⠀⠀⠀⢀⠔⠈⠚⢿⠇⠀⠀⣀⣾⣶⣿⡷⠀⠀⠀⠤⠤⠬⢥⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠛⠻⠻⠿⠟⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠰⣷⠀⠰⣷⠀⠀⠀⠚⠀⠈⠐⢄⠀⠀⢠⣾⣿⣷⣦⡀⠀⠀⢀⠔⠠⣀⠀⠀⠀⠀⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠁⠄⠄⠠⠁⠀⠀⠈⠩⠩⠉⠍⠁⠀⠀⢇⡀⣀⠀⠱⠀⠀⠸⣿⣿⣿⣷⠆

⠀⠀⠀⠀⢠⠰⢠⠀⠀⠀⠀⣠⠂⠢⢄⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⢀⠄⠢⢄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢂⢀⢀⡓⠀⠀⠀⠄⠀⠀⠀⠅⠀⠀⠸⠿⠿⠿⠿⠂⠀⠀⠅⠀⠀⠀⠱⠀⠀⣠⣾⣿⣿⣽⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠀⠀⠀⠉⠈⠀⠁⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠈⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣾⣀⠀⠀⠀⠀⢀⡀⣠⣄⡀⠀⠀⢰⣿⣿⣿⣦⡀⠀⠀⠀⡀⡠⢤⡀⠀⠀⠀⢀⣀⠤⣄
⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠠⠊⠀⠀⠙⠛⠀⠀⠈⠉⡍⢭⠉⠀⠀⠀⠊⠀⠈⠑⢪⠀⠀⢰⣿⣿⣿⣦⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣴⡇⡀⡀⠀⠀⠀⡠⠤⣀⣿⡀⠀⠀⣴⣿⣷⣾⣷⠂⠀⠀⠠⢔⣒⡤⡀⠀⠀⠀⡠⢄⡤⡄
⠀⠀⠀⠀⠻⣷⡥⠀⠀⠀⠨⢁⠀⣀⣈⠍⠀⠀⠉⡍⠉⢩⠉⠀⠀⠠⠊⠠⠀⠈⠑⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⣬⡆⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⣀⣀⡀⠀⠀⠀⠄⣀⣀⡀
⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⣣⣆⠀⠀⠀⠀⠀⢘⡧⠤⠀⠀⠀⠀⢰⡏⠀⣉
⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠙⠚⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠛⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠉⠀⠀⣠⠴⠚⠛⠳⡤⠶⠒⠲⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢿⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⠯⠖⠚⠳⡄⠀⠀⠀⠀⢩⡟⠁⢀⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⢀⣠⡿⠒⠒⢶⡀⠈⠻⠶⠟⠉⠉⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠓⠀⠀⠀⠀⠀⠘⠷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢶⣶⣤⣀⠀⠀⠀⢀⣀⡀⠀⠀⢻⣷
⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⠟⠀⠀⠀⠀⠘⠿⠿⠿⠿⣶⣄⠘⣧⣀⡀⠀⣀⣿⠈⠙⢷⣄⣰⡟⠙⣇⠀⠀⠘⣿⣇
⢰⣿⠇⠀⠀⠀⣠⣤⣤⡀⢺⡟⠃⠀⠀⠀⠀⠀⠀⠈⠁⣠⠴⠒⠒⠲⢤⡀⠀⢀⠤⠒⠒⠒⢦⣀⠉⠁⠈⠙⠛⠛⠛⠁⠀⠀⠀⠉⠉⠀⠀⠻⢶⣶⠾⢿⣿
⢸⣿⠀⠀⠀⠿⠯⢤⡈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠙⡴⠁⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣾⣿⣤⣀⣀⣀⣀⠀⣿⢀⣀⠀⠀⢀⣴⡿⠛⠛⠻⣾⡇⠀⣀⣀⢀⣀⣀⣀⣇⡀⣀⣀⣀⣀⡀⠀⢹⠀⣴⠞⠉⠉⠉⠓⠦⣤⣤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣿
⣿⡿⠈⠉⠉⠉⢻⡇⠉⠉⠉⠉⠙⣾⣿⠀⠀⠀⠀⢘⣿⠁⢹⡿⠀⠀⠀⠈⡇⠀⠀⢼⡿⠀⠀⠁⡿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠹⣿⣀⠀⠀⠠⣂⢽⣦⡀⠀⠀⠀⢀⣴⢻⣄⠀⠀⠀⠀⢀⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⡄⠀⣿
⣿⣿⠀⠀⠀⠀⣿⠠⣶⡧⠀⠀⠀⠀⠉⠛⠿⢿⣶⡕⠊⠈⢿⣶⠤⠶⣻⠋⠀⢻⣳⠶⠴⠶⣻⠏⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⣧⠀⣿
⢸⣿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣦⣀⠀⠙⣷⡋⠁⠀⠀⠀⠉⠛⠒⠋⠁⠀⠀⠈⠻⣦⣤⣤⣤⡀⠀⠀⠀⠀⠚⠋⠀⠀⠀⣸⠇⢠⣿
⠈⣿⣇⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈⠛⢷⣄⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢻⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡽⠷⠶⠿⠷⠴⠶⠶⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣾⠋⠀⠀⢠⣿⡏
⠀⠀⢻⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⡟
⠀⠀⠀⢻⣷⡄⠀⠀⠀⢻⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢰⡟⠀⢠⣿⡟
⠀⠀⠀⠀⠻⣿⣆⠀⠀⠘⣷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣴⡿⠁⣰⣿⠟
⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠈⠻⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠚⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠓⣦⢀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣾⡋⠀⠀⠙⠲⠤⠤⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⡿⠟⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠠⣂⠢⠀⠀⠀⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠁⠀⠀⢀⡀⠒⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⠀⠀⠀⠀⠀⠀⠈⠀⠑⡀⠀⠀⠀⠀⠈⠁⠒⠀⠀⡠⢁⠀⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⣀⣀⣀⣀⣀⣀⡀⠃
⠀⠀⠀⠀⠀⢠⢱⣯⣵⠁⠀⠂⣾⣭⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠂⡄⢣
⠀⠀⠀⠀⠀⠀⠊⠙⠉⠂⠀⠑⠉⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠃⢁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠒⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⢈⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⡀⠘⡀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⡀⠀⠤⡀⠀⠈⠃⠀⠀⠀⠀⣄⣀⡠⠀⠀⠀⠀⡰⠋⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠁
⠀⠀⠀⠀⠱⡀⢀⠖⠁⠢⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠈⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠤⠱⠋⠉⠒⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠑⠄⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡊⠀⠀⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠐⠀⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃
⠀⠀⠀⠀⠀⠄⠤⠌⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠔⠢⠤⠀⠀⢀⡴⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢈⠄⡀⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣖⡒⣒⠦⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⡴⡙⣰
⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⢃⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣒⠚⣒⡫⠖⣒⡚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⡀
⠀⠀⠀⠀⠀⠠⠀⠒⠃⠀⠀⠀⢈⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠆⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠃⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠐⠢⠄⠀⠀⢀⠔⠒⠃⠀⠀⢑⠀⠀⠀⠀⠀⠀⢀⠐⠠⠄⠀⠀⠀⠀⠀⠐⠛⠠⠀⠀⠀⠀⠀⢀⠐⠂⠤⠀⠀⠀⠀⠀⠐⠚⠢
⠀⠀⠀⠃⠀⠀⠀⠀⢰⠈⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠏⠁⡈⠁⠹⠁⠀⠀⠀⠀⠀⠀⠀⠠⠈⠼⠉⠱⠉⠸⡉⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠁⠈⠱

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⢀⢻⣶⣷⣾⢁⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⠀⢀⣳⣾⣾⣁⠀⠀⠀⠀⢰⣿
⠀⠉⣹⣿⣿⢟⡉⠀⠀⠈⣿⣿⣄⠀⠀⠀⠀⢠⠂⠀⠀⠉⠠⢄⠀⠀⠀⠀⠘⠙⠻⠄⠀⠀⠀⠀⠈⠙⠦⣤
⠀⠀⠁⠐⠃⠈⠁⠀⠀⠀⠈⠛⠿⠗⠂⠀⠀⠈⠂⠀⠀⠀⠀⠊
⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⠀⡀
⠀⠀⡰⢸⣿⣿⠶⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⡠⠒⠢⡀⡀⠀⠀⠀⠀⣰⣦⡀⢿⡗⠀⠀⠀⠀⣾⣿⣇⠈
⠀⠈⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⢸⠀⠀⠀⠀⠈⢠⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠈⠘⠋⠉⠛⠈⠁
⠀⠀⢄⠠⡀⠄⠀⠀⠀⠀⠄⡠⢀⠤⠀⠀⠀⠀⢡⢀⢠⢀⢠⠀⠀⠀⠘⠺⠿⠋⠀⠀⠀⠀⠀⠀⠤⠆
⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢠⢽⣿⣿⠥⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠄⠄⡀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⢀⠄⠠⣁⠈⠂⠢⢀
⠀⠐⠀⠈⠉⠝⠂⠀⠀⠀⠀⠀⠉⠑⠦⠀⠀⢰⠁⠀⠀⠀⠑⢠⠀⠀⠀⠘⢻⠟⠀⠀⢠⠁⠀⠀⠀⠐⠂⡀⠠
⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠐⠆⠶⠀⠀⠀⠀⠀⠀⢶⠀⢶⠀⠈⠀⠀⠀⠀⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣹⣾⣾⣁⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⣠⣄⢸⡏⣠⣄⠀⠀⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠈⠛⠛⠆⠀⠀⠀⠀⠀⠛⠳⡤⠀⠀⢠⠂⠀⠀⠉⠱⢀⠀⠀⢈⣩⡵⢮⣝⡁⠀⠀⣫⠭⢝⣛⡭⠭⣇
⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠘⠀⠀⠙⠋⢸⣧⠙⠋⠀⠀⠒⠋⠓⠒⠊⠑⠒
⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠘⠃⠈⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⠄⢀⡄⠀⠀⠀⣀⠀⣤⣦⡀⠀⠀⠀⠀⠀⢤⣧⡤
⢠⣤⣤⣤⣤⡄⠁⠀⠀⠾⠷⠴⠿⠶⠿⠗⠀⠀⠀⣿⠀⠙⠛⠀⠀⠀⠀⠀⠀⠉⠏⠁⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠄⠀⠀⠀⠀⣰⣯⣠⣾⣀⣼⣇⠀⠀⢰⣿⡦⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⢱⣿⣿⣿⣧⡀⠉⠉⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣿⡿⠀⠈⣿⡿⢀⣀⣀⡀⣿⣿⣿⣰⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠰⣿⠇⢸⣿⣿⣇⠛⠋⠁⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⣾⣿⣷⡸⠛⠉⢸⠁⢀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠿⠋⢹⡇⠀⣀⡘⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⠟⠉⣿⠀⢀⣘⢳⣾⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢹⡇⠀⢀⠛⣶⣿⣧⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢳⣾⣿⠀⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠃⠘⠟⠿⠀⠻⠿⠗⠘⠿⠛⠃⠻⠿⠟





⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠢⠴⠣⠂⠀⠂⠉⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⢆⢀⡔⠊⠀⠀⠀⡠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠌⢁⠀⠀⠀⢀⠃⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠠⣂⣠⣀⡁⡠⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡀⡀⠠⣀⡀⠀⢀⡀⢠⢤⠶⢠⠊⡇⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠡⠄⠠⠥⠥⠴⠥⠤⠍⠈⠀⠄⠐⠂⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⢀⣠⣤⠶⠶⢶⣤⣄⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠙⠛⠷⢶⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠘⠶⠶⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠙⠉⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣠⡞⠀⠀⠉⣛⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠋⠉⠙⠻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠁⠀⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠈⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⣀⣤⣤⣶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠋⠉⢀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠄⢠⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣀⠀⠠⢄⣀
⠀⠀⠀⢠⣄⣤⡾⣆⣾⣟⣉⠳⡖⠉⢁⡄⠀⢾⣠⣄⠀⠰⠤⣄⣉⢳⠉⢱⣮⡙⣮⣷⠀⠀⠀⢀⣀⣀⡴⠖⠲⢦
⠀⠀⠀⠀⠉⠛⠿⠛⠛⠻⣷⣶⣶⠎⣿⣧⣼⣶⡉⢉⠉⠀⠀⢺⣿⣼⡷⠘⢻⢳⣿⢧⠀⠀⣴⠋⠀⠋⢷⠀⡁⢸⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣋⡁⠙⢻⣿⣷⠍⣐⡎⡝⢀⠉⣾⢏⠙⢿⣌⡀⢸⠃⠀⠀⢄⣸⠀⠀⣺⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢶⣿⠋⠽⠿⠿⢉⡙⢯⣿⡿⠿⠏⢙⣻⡇⣹⡇⢂⣾⡀⣇⣿⠀⠀⠀⠀⣿⠀⠀⣿⢀⡟
⠀⠀⠀⠀⠀⢀⣠⠤⣿⡗⠀⡞⠃⢀⣤⣷⣿⣿⣿⣶⣴⣦⠴⣶⠟⠿⠞⠛⠿⡋⠀⣗⣾⣿⠀⠀⠀⠀⣿⠀⢠⡇⢸⠇
⠀⠀⠀⠀⠀⣿⣯⣍⣈⣀⣽⣿⣾⣿⡟⣻⣿⣿⣿⣿⣷⣦⣶⣿⣶⣤⡤⠚⠻⠿⣶⠿⠃⣿⠀⠀⠀⠈⣿⠀⢸⡇⣿
⠀⠀⠀⠀⢀⣙⣋⡀⠀⣀⣯⣽⡁⢈⣻⣉⣋⠀⠙⠿⠦⠽⣿⡟⢓⣨⣶⣞⠕⢀⡴⠖⠶⣿⠀⠀⠀⠀⣿⠀⢸⡇⢿
⠀⠀⠀⠀⢸⡯⢥⡏⠀⢿⠶⢾⠁⠘⣷⠶⡏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡿⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⢸⡇⢸
⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⡆⢸⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢸⡇⠀⠀⠠⢠⡇⠀⠀⠀⢸⡆⠈⠃⢸⡀
⠀⠀⠀⠀⢸⡇⠀⣇⠀⢸⡅⢸⡆⠀⡇⠀⡇⠀⠀⠀⠀⣀⣠⣴⣾⡿⠛⡏⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠘⡇⠀⡗⠀⣷⢠⣤⣶⣿⠿⠛⠋⠁⠀⠀⡇⢰⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣼⠀⠀⢸⡀⣸⠀⠀⣷⢠⡇⠀⢹⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣠⡴⠶⠶⠶⠒⠛
⠀⠀⠀⢀⣿⣀⣀⣈⣇⣿⣀⣀⣸⣸⣇⣀⣸⣇⣸⡇⠀⣀⣀⠀⣀⣀⠀⡇⢸⡇⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠈⠜⣻⡇⠀⢿
⠀⠀⣸⣟⣋⣉⣉⣭⣭⣽⣭⣭⣽⣭⣽⣯⣭⣭⣽⣧⠀⢿⣿⠀⣿⡏⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡇
⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡏⠀⣤⣤⠀⠀⢠⣤⣄⠀⠀⣠⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡇⠀⣿⣹⠀⠀⢸⣧⣿⠀⠀⣿⣼⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⢸⠀⠀⠀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⠇⠀⣸⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣯⢽⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠲⣞⣀⣠⡟
⠀⠀⠀⣿⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣠⣧⣾⣄⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠯⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣠⣴⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⢸⣇⣀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠙⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⣠⡾⠛⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠛⢶⣄⣠⡴⠶⠶⢶⣤⡀⠀⠀⠀⠀⠉⢻⣆
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣀⠀⠹⣇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠻⣶⣿
⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄
⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠙⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⣀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⣠⡾⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁
⢰⣿⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⢀⣤⡶⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⣿⣇
⠀⠛⠷⠶⠾⠋⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢿⡇⠀⠀⢠⡾⠟⠉⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠈⢿⣄⣀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⢸⡇⠀⠀⣿⠁⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢀⣴⠾⠛⢹⡇⠀⠀⠉⠉⠁⠀⠀⠀⢀⣠⡾⣿⠀⠘⣿⡀⠀⢀⣿⠃⠀⠀⠙⠷⣶⠾⠋
⠀⠀⠀⠀⢠⡿⠁⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⣿⠃⠀⠈⠛⠛⠛⠁
⠀⠀⠀⠀⠈⢿⣤⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⠓⠓⢦⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⠓⠒⢦⡀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠘⠚⠒⢦⡀
⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠃⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠃⠀⠀⠀⠘⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠀⠀⢈⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠬⣷⡧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠘⠆⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠅⠷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣂⡤⠶⢤⡉⠀⣀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠇⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠈⠙⢆⠀⠀⢹⠈⠁⠀⠀⠀⠀⠀⣤⡀⣰⠊⠉⠙⢦⠠⠴⠂
⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⡌⠛⠂⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⢸⠇⣀⡀
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠁⢈⠓⠶⠒⠋⣄
⠀⠀⠀⠀⠀⠳⢤⣠⣄⣀⣀⣀⣀⣀⣀⣄⡤⠔⠃⠀⠀⠀⠈⠳⣤⣄⣄⣀⣀⣀⣀⣀⣠⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠸⠇⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡋⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣤⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⠖⠒⢦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠸⡄⠀⠀⢠⠀⠀⠐⠒⠀⣇⠀⠀⢀⡇⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⢸⣁⡇⢠⣄⠀⠀⠀⠇⠀⠀⠀⠁⠀⠀⠈⠇⠀⠀⠀⡠⠈⠓⠒⠋⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠰⠏⠀⠀⠀⣀⣠⡤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⠉⠁⣀⣀⣠⣄⣀⣀⠈⠉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡄⠀⠀⠐⠋⢀⡠⠖⢋⣩⢇⣠⠤⠞⠈⠉⠲⢄⡀⠛⠇⠀⠀⢠⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢸⢡⡞⡆⡇⠀⠀⠀⣠⢋⡖⠉⠉⠀⠸⠀⠀⠀⠀⢀⣀⣀⠙⣄⠀⠀⠀⢸⢸⢹⡎⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⡇⠀⠀⣰⠗⠋⠀⠀⢰⣊⣁⣀⣀⣀⠀⠳⢤⣬⠷⠈⣆⠀⠀⢸⢸⢸⡇⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⢠⢤⣸⠀⠀⢸⢸⢸⡧⡇
⠀⠀⠀⠀⠀⠀⢸⢼⡇⡇⣇⠀⠸⡇⠀⠀⢠⠞⠉⠉⠉⠙⠒⠚⠉⠀⠀⠀⢸⠆⢹⠇⠀⣸⢸⢸⡇⡆
⠀⠀⠀⠀⠀⠀⡞⢸⠃⢳⢸⡄⠀⢧⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡼⠀⢠⡇⡞⠘⡇⢳
⠀⠀⠀⠀⠀⠀⠱⣌⣓⡋⠘⠀⠀⠈⢧⠀⠀⠑⠦⡄⠀⠀⠀⠀⠀⠀⠀⢀⡏⡴⠁⠀⠀⠣⣍⣛⡁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠈⢳⠀⠀⠀⠀⢀⡸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⡀⠉⠓⠦⠤⠬⠧⠤⠴⠚⠉⢀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⣀⣀⣤⡤⠴⠚⠉



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢹⣆⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡾⠀⠀⠀⠛⠛⠛⠋⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⢷⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⡞⠁⠀⠀⠙⢦⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠙⠋⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⡻⣆⢻⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⢷⣌⣷⡘⢿⣷⠘⣧⡾⢻
⠀⠀⠀⠀⠀⢰⣦⡀⣿⣇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣦⠉⠛⠁⠈⠉⠀⠛⢃⡟
⠀⠀⠀⢠⣦⣌⣿⡻⣿⢿⡿⣿⣴⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠹⢮⡛⠃⠀⠀⠀⠙⢣⡞⠀⢀⣀⠀⣤⡀⢠⣄⠀⠈⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⡏⠀⠀⢸⡝⣿⡇⣿⣿⢹⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣤⡀⣼⢧⢀⡶⣦⢸⡇⠀⣶⠾⣷⠈⠃⠘⠋⢾⡾⢻⠆⣿⠀⠀⢠⣦⡀⣿⡆⢀⣤⡄
⠀⠀⡶⣼⡏⣷⣿⢸⣿⠃⡿⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⣰⠏⠀⣿⢀⠀⢸⡌⣷⡟⣿⣸⢃⣇⣴⡦
⠀⠀⢷⡘⣿⠘⠟⠈⠛⢸⣧⡿⣦⠀⠀⠀⠹⡆⠀⠀⠀⣴⠃⠀⠀⣿⣏⠻⣾⡇⠻⠃⣿⡟⢸⡟⣹⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢁⣴⡃⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⣿⠙⢷⡀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢀⡇⠀⠀⠀⢠⡴⠋⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢿⡀⠈⠷⣄⣀⠀⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠈⣷
⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠘⣧⠀⠀⠀⢸⣇
⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⢻
⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⣽⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⢀⣋⣀⣀⣀⠈⠉⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡴⠛⠉⠉⠉⠉⢉⣭⣙⣿⣿⣿⣿⣿⠁⡛⠳⣦⡀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⣰⠋⡀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⡗⠀⢐⠈⢳⡄⠀⢳⡀
⠀⠀⠀⠀⠀⢰⠃⠀⣸⠃⢂⠐⠊⢐⢀⠀⠀⢀⣾⣿⣿⣿⣿⡟⣛⣸⣿⡀⢀⣆⠹⡆⠀⢳
⠀⠀⠀⠀⠀⡾⠀⢰⣿⠀⠀⣠⣶⣶⣶⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦⣿⠀⠘⡇
⠀⠀⠀⠀⠀⠇⠀⢸⣿⡇⠀⠻⢿⣿⡿⣿⣿⣾⣿⣿⣿⠟⠩⠀⠀⠀⠈⠈⡉⢿⣿⣿⡇⢀⢷⡤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡀⠠⠀⠀⠀⠀⢀⠀⣾⣿⣿⡇⠈⠻⠃
⠀⠀⠀⠠⢾⡷⠀⠸⣿⣿⣿⡿⢛⠛⡉⠉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⠁⠀⡞
⠀⠀⠀⠀⠀⣇⠀⠀⢻⣿⣿⣿⣴⡙⠁⠣⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⠏⠀⣸⠁
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠻⣿⣿⣿⡿⠞⠔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠙⢿⣿⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠛⠿⣿⣿⠻⡟⠻⠛⣟⢻⣛⡽⠿⠋⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠈⠉⠉⠉⠉⢉⠉⠁⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠂⠰⢿⡒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⡾⠟⠀⠀⢸⣟⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣀⠀⠀⠀⢸⣧⠀⠀⠀⣾⣿⣯⡀⠀⠀⠀⠀⢰⡿⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠿⣶⠄⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀⠀⠀⠛⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠻⣶⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⢀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠠⠃⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂⠄⠁⢡⠈⠀⡀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⡆⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⠃
⠀⠀⠀⠶⣦⣄⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠀⠠⠃⠀⢤⡂⡀⢱⠈⢡⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⡶⠟
⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠘⣄⠈⠢⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⣤⠀⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠐⢂⠈⠁⠀⠀⠀⠀⠀⠀⢠⡶⠷⢶⣄
⠀⠐⣿⣀⣠⡿⠀⠀⢀⠀⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣾⢠⡿
⠀⠀⠈⠛⠋⠁⠀⠀⠀⠉⢅⠸⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠤⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⡆
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠛⠻⠇
⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⡡⡀
⠀⠀⣿⠸⣿⠙⡷⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠻⢶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁
⠀⠀⠀⠀⢀⣴⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠸⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⡶⣦
⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣤⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡿⠻⣶⡀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣴⡾⠃⠀⠀⠙⠛⣿⠛⠃⠀⠀⠀⣿⡀⠀⠀⠀⠹⣧⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢺⡐⠭⣧⠇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣸⣥⣤⠖⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⡂
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⢶⣄⠀⠀⡀⠀⢖⡲⠀⡊⠁⡆⠈⠉⠁⠀⣼⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡝⠛⣏⣹⠄⠀⣠⡄⠉⠈⠁⠀⠀⠀⠀⠀⡟⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⢡⡀⠀⢽⠆⠀⢀⢠⠀⠀⠀⡀⡔⠃⠀⠁
⠀⠀⠀⠀⠀⡀⠖⣀⣀⠀⢠⠖⠒⢄⠀⢿⡀⠀⠀⠀⠀⠄⠂⠀⠠⢇⣹⠃⠀⠄⠒⢌⠂⠀⢀⣼⠃
⠀⠀⠀⠀⣼⣿⠉⠉⠁⠀⠹⣀⣀⠜⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠸⡀⠀⡠⢀⢠⣾⡿
⠀⠀⢀⣴⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⢨⡿⣿⡀
⠀⠰⠟⠁⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡰⣠⠔⠠⠉⣀⣸⣷⣶⣶⣶⣶⠀⠀⢨⡄⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡉⢟⠉⠐⡀⢠⣾⡿⠟⠋⠙⠛⠿⠋⠀⠀⢿⣿⣟⠂⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠠⢊⡈⠀⣒⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠄⡰⢀⠠⠿⣿⣧⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠰⠣⠉⠉⠀⠁⠂⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠋⠀⠀⠀⠀⠀⠈⠧⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⢴⡡⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢀⣸⣿⣿⣿⣿⣿⡤⢹⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠈⠉⠉⠀⠀⠀⡅
⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⢸⡀⠀⠀⢰⣿⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⡧⡀⠀⠸⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢣⢹⣦⣄⣠⣄⡘⠒⠛⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣈⣉⡸⠁
⠀⠀⠀⠈⡎⢿⣿⠿⠟⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣰⣿⣿⣿⣿⣿⣿⡇⢠⠃
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣄⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⠃
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠆⣠⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⡐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣉⣉⡙⣁⠀⢈⠨⠀⡁⠀⠑⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠀⠐⠂⠈⠀⠀⠈⠒⠴⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡗⣭⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣰⡏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⢰⣟⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣷⣾⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠛⠀⠀⠀⢀⣀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣶⣶⠞⠀⠀⠀⢤⣤⡴⠀⠀⣤⡄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⣆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡟⠀⢀⣤⡀⠘⣿⠁⢠⡄⢸⡇⣠⣼⠇⣄⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣷⣾⣿⠀⣿⣿⣿⡇⠙⢻⡇⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⠀⣿⡿⢿⡇⣶⣾⠻⡆⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⠸⣿⡏⠈⣿⠀⠙⠃⣸⡇⠉⠸⠆⠐⠃
⠀⠀⣠⣴⣶⣶⣿⡇⠀⠀⠀⣤⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠸⣿⡿⠃⠀⠠⣿⣿⡀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠁
⠀⠾⠿⠛⠛⠉⠉⣿⣷⣶⣾⣿⡇⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛



⠀⡁⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢘⠉⢵⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡐⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠔⠁⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⢀⢠⠆⠸⠀⠀⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠀⡀
⠀⠀⡀⠀⠀⠂⠁⠀⡀⠰⠀⠀⠀⠀⠁⠈⠀⠀⠃⠀⠂⢀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⢀⠀⠁⠀⠀⡀⠁⢀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠐
⠀⠀⡀⠀⠀⠀⡄⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠤
⠀⠀⠀⢀⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠆⠀⠀⠘⠀⠁⠀⡀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⡙
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⣀⠍⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠃⠀⠀⠈⠠⠆⠈⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⢰⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠄
⠀⠀⢀⠀⡀⠤⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠋⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁
⠄⠐⢩⡉⡑⠤⠤⠤⠤⠑⡀⠀⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠂⢀⠀⠂
⠀⠀⢇⡀⢐⠀⠙⠃⠘⠚⢡⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⠀⠘⠀⠀⠀⠀⢠⣋⠱⢢⣄⠁⠀⠀⠔⠃
⠀⠀⠀⠨⣥⣉⠥⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⠀⠀⡞⠠⠤⠉⣀⠀⡃
⠀⠀⠀⠀⠃⡤⢀⠉⡁⠀⠀⠀⠀⠀⢀⠀⡬⠀⠀⠼⠀⠀⢐⠃⠀⠀⠀⠀⢠⠖⠁⠀⠉⠀⡠⠂
⠀⠀⠀⠀⠀⠀⣇⡩⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠈⠉⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⠀⠀⠀⠀⠀⡀⠀⡶⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⡤⠴⠋⠉⠑⡄⠀⢧⡀⠀⠀⣀⠈⣴⣶⣦⠁⣀⠀⠀⠀⠠⠿⣽⡽⢷⠀⠀⢀⣤⣿⣿⣿⣼⣿⣷⣄
⠀⠀⠀⠀⣰⠊⠀⠀⠀⠀⠀⠙⢢⢀⡟⠀⠀⠉⢀⠻⠿⠟⡀⠉⠀⠀⠀⠀⠻⣽⡽⠛⠀⠀⠘⢿⡿⣿⣯⣿⢿⣿⠟
⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠁⠀⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⡏⡱⠄⠀⠀⠀⠀⢀⡔⠚⠁⠀⠈⢧⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⡇⢪⡁⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢈⡍⢩⡄⢠⡉⠀⠀⠀⠀⠀⠀⠸⣄⣀⠇⠀⠀⠀⠀⠉⠉⢉⠉⣉⠉⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠈⢡⡌⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣶⣄⠀⠀⠀⠀⠀⢰⢠⢠⢀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠠⠤⣼⣿⣿⣿⣏⣀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⠈⠀⠀⠀⣀⣶⣶⣶⣾⣁⣋⣹⠆
⠀⠀⠀⠀⠐⢲⣿⣿⣿⣿⡟⠃⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠋⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⡀⠀⡇⠀⣠⠀⠀⠀⠀⠀⠀⠘⣛⣓⣒⣒⣛⡛⠁⠀⠀⠀⣠⠤⠊⠉⠙⢦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣀⠈⣴⣶⡦⠵⠊⠉⠓⡄⠀⠀⠈⠷⠶⠶⢶⠶⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠈⢲⠀⠀⠀⣠⣶⣿⣆
⠀⠀⠀⠀⠀⣀⠹⠚⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⠉⡭⠭⠭⠁⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⣿⣾⡟⠋
⠀⠀⠀⠀⠈⠁⠘⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠰⡿⠀⢾⠇⠰⠿⠆⠀⠀⠀⠈⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠘⣄⡰⠙⣄⣤⢀⡿⠀⣠⠴⡇
⠀⠀⠀⡀⠀⠀⢠⡄⣽⠑⠾⠀⠈⠃⠀⠙⠈⠃⠰⠞⠁⠐⠇⢀⣠
⠀⠀⠀⠙⢟⠃⠶⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⢩⠃
⠀⠀⠠⣤⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⣠⠶
⠀⣀⣀⠨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⣀⣀
⠈⠙⠒⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠒⠊⠉
⠀⣠⣔⣋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠦⠄
⠀⠀⠀⠀⣼⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣆
⠀⠀⠀⠈⠁⠀⣯⠴⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⡄⠁⠀⠀⠀⠀⠀⡴⠈⠀⣠⠛⢩⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣇⠞⠻⢀⡜⢧⡞⣆⡞⠳⣄⣯⠙⠶⣄⡘⢆⠀⠀⠀⢀⣼⡗⠀⠀⢿⠀⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠟⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠙⠺⣦⠀⠀⣼⠏⠀⠈⠁⠀⠀⠠⡀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⢸⡇⢀⡖⠂⠀⠀⠐⣒⣚⡇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠚⠁⠀⠀⠀⣾⢡⡀⠀⠀⠀⠀⠀⠀⠈⣡⠀⢡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣾⣇⠀⣠⠀⠀⣀⠀⠀⣿⡀⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠹⣤⣤⠋⠀⣴⢟⣧⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠖⠟⠛⠛⣡⣠⠆⣀⣀⣴⡿⠋⠘⣿⣷⣄⠀⠙⣿⡳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⣾⠛⠄⠀⠀⠈⠃⠉⠀⠉⠛⣯⠠⠶⣄⠈⠉⠻⠷⣦⡈⠹⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⢦⡀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⣤⣹⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡶⡄⢀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠃⠀⡈⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣀⡀⠀⠀⣦⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣠⡤⠀⢀⣴⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⢿⠇⠀⠀⠀⠉⣿⠨⠲⠕⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠘⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡗⠀⠀⠀⢧⠀⠀⠀⠀⣿⡄⠀⡢⠀⡀⢅⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠈⢣⠀⠀⠀⠸⡇⠂⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⡏⠀⢦⡄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠫⠄⠀⠀⠀⠇⢠⠈⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠆⡀⢀⠀⠀⠀⢠⡄⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠣⣈⣀⣴⠆⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠉⠑⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⢀⣿⣿⡄⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⡦⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢸⠀⠴⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠙⣿⠀⢸⠀⠀⡼⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠆⠀⣿⡀⢸⠀⢠⠃⣸⣾⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣞⠁⠀⠀⠀⠀⠀⠙⠻⣿⡿⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⠠⣿⣦⠾⢃⣤⠜⠃⠀⠀⠀⠀⠀⠀⠠⠈⠁⣿⣧⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠴⠂⠀⠂⢸⡄⢻⠻⠗⠒⠻⠻⣗⣶⣤⢆⡀⠀⠀⠀⠈⠀⠁⠠⣄⠀⠀⠀⠀⠀⡈
⠀⠰⡓⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣤⣒⣆⣸⣧⠉⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠞
⠀⠀⠈⠢⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠘⢁⡟⣷⡿⢦⠀⠀⢀⡠⠤⢄⡀⢠⣀⡔⠀⠀⠈⡇
⠀⠀⠀⠀⠈⠎⠀⠀⠀⠀⣶⠀⠀⡀⠀⠀⢀⠀⢥⣉⡤⠭⡀⢸⣧⠅⠠⠔⠀⢱⡉⠀⠈⢆⣹⡆⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠈⠠⡀⠇⠀⣼⠒⠁⠠⣄⡜⢀⣀⠀⢹⠁⠀⠈⠘⣀⠤⠀⠀⠀⠀⢂⠀⠀⠀⠙⢿⡤⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡴⠞⠁⠀⠀⢈⠜⠁⠀⢀⠝⠉⠑⠀⢄⡨⢌⠀⠀⢁⠀⠀⠀⢦⡀⠀⠀⠀⠉⢨
⠀⠀⠀⠀⠀⠀⠀⠰⣄⢀⡀⢀⣠⠏⠀⠀⣠⠏⠀⠀⢠⢤⢄⣀⡈⣦⠀⠀⢣⡀⠀⠀⠙⢶⣤⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⢟⠃⢀⣀⢴⡟⠀⢀⠠⠃⠠⠊⠓⠀⠚⠳⢄⣀⣙⠦⠤⠠⠜⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣙⣛⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣰⣤⣦⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣀⣀⡀
⠀⠰⣾⢟⣽⣿⣟⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣻⣺⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡨⣟⣻⣿⣿⣷⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⣻⣿⣻⣿⣿⣿⣼⡷⠂⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣞⠈⠁⠀⠀⠀⠈⠁⠀⠑⠀⠀⠀⠀⠀⠉⠉⠉⠻⠿⠛⠛⠛⠋⠉
⠀⠀⠿⣷⣿⣽⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠻⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡀⣀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠿⠂⠸⠗⠀⠿⠂
⠀⠀⠀⠁⠘⠁⠃
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣄
⡖⠀⠈⠁⠉⠀⠉⠂⠀⠐⠀⠀⠀⠀⢀⣀⣾⣴⣤⣶⣶⣄⣤⣄⡀⢈⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣤⣶⣦⡀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠈⠱⠄⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⢿⡿⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠰⠷⠀⠾⠆

⠀⠀⠀⣴⠳⡖⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⢽⠤⢵⣶⠥⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⣿⡷⠂
⠀⠀⠉⢾⣡⣆⡓⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⢀⣀⣀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢸⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢸
⠀⠀⠈⢸⡗⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣋⡁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⡇⢸
⠀⠀⠀⠈⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣧⣼
⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡧
⣤⣤⣤⣤⣬⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣥⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠁⠀⠀⣄⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠐⢷⣄⠀⠀⠙⢧⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠙⠓⠛⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⠋⠉⠙⠳⣦⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠞⠃⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣤⡼⠃⠀⣠⡤⢦⡀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⣠⡞⠛⠉⠀⠀⢻⣄⣤⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠖⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⠶⠖⠒⠲⠶⣤⣄⣀⣀⣀⡤⠀⠹⡆
⠀⠀⠀⠀⢀⡿⠀⠀⢀⡾⠛⠳⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⠀⢸⡇⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠇⠀⠀⢺⣅⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠁⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣿⠀⠶⣤⣄⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠈⢷⡀⠘⢧⣄⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠦⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠷⣤⣀⠉⠉⠉⠉⠉⠉⠙⠛⢦⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⢦⣤⣤⠶⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸⡟⠉⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠉⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡄⠙⢦⣄⡀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢿⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠈⠻⢦⣀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⣟⣻⡛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⣃⣽⣶⣈⣿⡟⢀⣤⣶⣟⣿⣿⣿⠟⢋⠉⠹⠛⠛⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠻⠁⢀⣘⣿⣿⣿⣿⣿⣿⣿⡟⠟⠒⠛⠁⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⢃⣤⣴⣤⣀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠙⠛⠛⠛⡃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢉⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣆⠀⢀⡀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣰⣿⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣹⠿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡏⠹⠇⠀⠀⠀⠀⣿⣿⢹⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⢧⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⠻⣶⣶⠟⠛⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣻⣿⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠸⠀⠀⠀⠰
⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⣀⡀⣀⠀⠀⠁⠀⠀⣀⠄⠀⠀⠀⠀⠀⡈⠐⠄⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠉⠂⠀⡠⠊⠁⠀⠀⠀⠀⠉⠢⡀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⣀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⠀⢀⡀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⢠⠔⠀⠱⠀⠀⠀⠀⠀⠀⠀⡰⠁⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⡀⠂⠒⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣄⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⡀
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢀⠀⠀⠀⠀⠀⢀⠢⠄⠀⠀⡀⠀⡀⠀⠠⠄⠐
⠀⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠰⡀⣀⠀⠂
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿