Motion sickness Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⡿⠟⠋⢀⡌⠁⣼⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠁⣼⠛⡿⣿⣿⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠇⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠄⢸⣿⣿⣿⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⢹⣿⣿⠟⠀⠀⠀⠀⣠⣮⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣴⠿⣿⢿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⣼⣿⣿⣿⡿⠿⠆⠰⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣧⣤⣥⣬⣤⣄⠀⠀⠠⠔⠐⠀⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣬⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠄⠀⠠⠤⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠉⠀⠠⠛⢯⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣀⠤⠤⠤⠤⠤⠤⡤⠤⠄⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠋⠀⠶⣛⣉⣉⣉⣩⡭⠭⠉⠉⣶⠀⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡧⠉⠐⠒⠒⠒⠒⠒⠒⠒⠚⣛⣩⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⡀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡠⠈⡇⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⡿⣶⣿⡟⠁⠀⠀⠀⠀⢀⣈⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠤⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⠀⠀⠀⣠⣄⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⣾⣿⣿⣿⣿⠃⠀⠰⠈⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢃⢀⣀⠀⠀⢀⠄⡀⠙⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢼⠃⢢⡻⣨⠃⠀⠸⣘⡩⠂⠘⢿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⣆⡄⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠁⠀⠙⠲⠖⠋⠀⠙⠛⠉⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠉⠛⠒⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠸⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡃⠀⠀⠀⠀⠀⠀⡄⠲⣤⣄⣀⣤⣶⣿⣿⢧⣀⡀⠀⠀⠀⠀⠘⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠊⠀⠀⠀⠀⠀⠀⢀⣼⡦⢬⣛⣿⣿⣵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⣤⣤⣄⣤⣤⣿⣿⣿⣱⣁⣤⣤⣤⣤⣀⣴⠏⠀⠀⠀⢀⣀⡤⠖⠒⠚⠛⠻⢿⣦⣽⣏⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠩⢝⡛⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⡿⠋⡀⢐⣠⠴⣾⡟⠁⠀⠀⣀⠤⠖⠂⠈⠙⢻⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⡈⢉⡙⠿⢿⠿⡻⠋⣻⠟⡫⠖⣨⠔⢉⣤⣻⡿⠀⢀⡴⠟⠁⠀⠀⣰⠂⢰⣾⣿⡠⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠁⠠⠄⠁⣀⣴⠞⠃⢈⡀⢸⣼⣟⣿⣿⣿⡗⠶⠋⠀⠀⠀⢠⣸⡇⢀⢽⣿⣿⡅⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⣠⣤⣴⡾⠿⠶⠾⠛⢛⠛⠛⢇⣿⣿⣿⡏⠀⣴⡆⠀⢀⡇⢹⣿⡀⠀⣼⣿⣿⣟⡀⠀⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⣀⣤⣾⣿⡿⠃⠀⠀⠀⠒⠂⠀⠀⣠⣿⣿⣿⠟⠀⣸⣿⠀⠀⢸⣧⢸⣟⣣⣼⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⡿⣿⣶⣶⠶⠤⠤⢤⣤⣀⣀⡀
⠀⢸⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁⠀⢸⣿⠏⠀⠀⣾⣿⣿⡧⢸⣿⣿⣿⣿⡿⠿⠟⠟⣻⣯⣷⣆⣠⠤⠄⠀⢀⣀⣠⣽⣿⣿⣿⣿⡷⠚⠒⠤⠄
⠀⠀⠀⢀⣄⠀⣾⣿⣿⣶⣶⡦⣈⡽⣷⣤⡼⠁⠀⣾⣿⡟⠀⠀⣨⣿⣿⣿⣷⣻⣿⣿⣿⣿⣁⣴⣶⣾⣿⣛⠒⢒⣏⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣀
⠀⠀⣴⣾⣿⣿⣿⣿⣿⣟⣥⣤⣿⣿⣿⣿⣦⣤⣠⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠂
⠀⠀⣿⣿⣿⣿⣿⣿⡟⣨⠟⢻⢶⣿⣿⣿⣿⡇⠈⠙⠳⢶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⣃⣤⣤⣤⡀
⠀⠀⠈⠙⢛⣛⡛⣿⣇⣀⣐⣿⣿⠿⠿⠿⣿⡷⠀⢠⡀⠀⠀⠩⡿⠿⠿⢻⣿⣿⡍⠉⠛⠉⡉⢹⡟⣽⣿⠿⠿⠟⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠂
⠀⠀⠀⠈⠈⣡⠋⠉⠙⠿⣿⡟⠙⡿⢿⣒⡐⢶⠀⠈⢳⣄⠀⠀⠚⠷⢖⢻⣿⡘⣷⣷⣀⣱⣿⡄⣼⡏⠀⡀⢶⣄⣾⡏⡼⢫⣽⣿⣿⠿⣿⣿⠛⠛⠃⠉
⠀⢀⡀⠀⣬⣜⣀⡀⠀⠀⣼⠃⠀⢠⠀⣿⣿⡨⠀⠀⠀⣿⡄⠀⠈⠀⠈⠉⣿⣧⠨⣻⢿⣿⣿⣾⣿⣷⣜⢿⣶⣽⣿⣿⣷⣿⣽⣿⣿⣿⣿⣷⣶⣶⣄⣶⣶⣶⠆
⠀⢸⣿⠇⣿⠁⠀⠀⠀⣠⡟⠀⠀⡜⣰⢿⡿⡇⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⢽⣿⣿⣟⡼⣿⣿⣿⣿⣿⡀⠉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⣿⡏⠙⢿⣿⣿⣿⡦
⠀⢸⣿⠀⣿⠀⠀⠀⠀⣴⠇⠀⢀⣿⡡⡝⠂⢸⠀⠀⠀⢺⣿⡀⠀⠀⠄⠀⣿⣿⣿⣛⠛⣿⠿⣿⡟⢿⣿⣀⣽⣿⣿⣿⣿⣿⡆⠀⣩⠡⢠⠀⣷⣶⡿⣿⣿⣿⣶
⠀⠘⠇⠀⣿⠀⠀⡂⣨⣿⣤⣴⡟⠽⣵⣷⣶⡎⠀⠀⣠⢺⣿⠇⠀⠀⠀⠀⠿⣿⣿⣆⡀⣛⣤⣾⣿⣤⣿⣿⣿⣛⠩⠋⠉⠙⠻⠷⣿⣷⢻⣢⣿⣿⡿⣸⣿⣿⣿
⠀⠀⠀⢀⠐⠬⠵⠶⡿⣛⣵⣿⣷⡇⣿⣿⠿⠀⠀⠀⠃⢸⣿⣦⣧⠀⢀⡀⠰⠙⣿⣿⣾⡍⠉⠠⣾⣿⣿⣿⣿⣿⣶⣤⣤⣶⣦⣤⣤⣘⣶⣭⣵⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠈⠉⠁⠐⠚⠒⠶⠿⠿⠯⢿⡟⣿⠀⠀⠀⠀⢸⣿⣷⡿⠂⠀⡀⠀⠂⣿⣿⣆⣙⡛⠛⠛⠋⡉⠉⠉⠙⠛⠻⠿⣿⣿⠛⠛⠉⡙⠿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⢤⣤⣀⣀⣀⣻⣿⠀⠀⠀⠀⢺⣿⣿⣷⠀⠈⠀⣠⣾⣸⣿⣿⣿⣿⣿⣿⣾⢿⡷⢒⢂⡴⢤⣤⣽⢻⣦⣄⢉⠺⣦⡀⠙⢷⣭⡛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⢹⣿⡿⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣟⣻⣷⣿⣧⠿⣟⠿⠦⠈⠳⠀⠀⠈⠓
⠀⠀⠀⠀⠉⠉⠛⠛⠛⠚⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠛⠋⠛⠋⠉⠙⠟⠛⠛⠛⠛⠛⠛⠛⠛⠙⠋⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠉⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⣦⣄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⢰⡦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣼⢳⡴⣿⢠⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠁⠘⠃⡇⢾⠀⢘⡎⢳⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⣟⠙⢠⡄⠀⠀⠘⠦⠾⠁⣼⠀⣸⢠⡤⣄⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⣤⣸⠇⡾⣱⠞⠲⢄⡀⠀⠀⠃⠀⡏⢸⠀⢸⡆⣶⠀⣀⠀⣿⡇⠙⠻⢶⣿⡿⠟⢻⡇
⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠁⠘⠃⣿⠀⠀⣼⣥⠖⢠⡀⠀⠀⠘⠦⠾⢱⠏⣧⡏⠀⠘⠷⣦⣄⣸⡏⢀⣤⣾⡇
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠋⣷⢠⡟⡇⡼⢠⣤⡀⠀⠈⠀⢿⠃⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡇
⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢤⠀⠀⠁⠛⠀⣿⢁⡾⣤⢡⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⡇
⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢳⡞⢀⣴⡆⠀⠀⠀⠘⠶⢀⡀⢳⠀⣾⠛⠂⠀⠀⠀⠀⢀⣿⣿⣿⡆⠈
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡴⠻⣾⢃⡴⠛⠲⠀⠀⠀⠙⠋⢤⣨⡇⠀⠀⠀⠀⠀⣾⣿⣿⢿⣧
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣅⣰⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⡿⠼⠿⡈⢿⣆
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠓⠀⠁⠈⠻⣦⣀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡖⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⣿⡇⢨⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢹⣧
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠘⣧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣿⣿⣿⣿⣿⣿⠱⠂⠀⠀⠀⠀⠀⠀⠈⣿
⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠘⣷⣿⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣿⣁⣀⣁⣀⣋⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠹⣷⣄⡀⠀⣠⢀⡀⠀⡈⠉⠀⠀⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠈⠙⠻⣿⣷⣿⣿⣿⣷⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣷⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠛⠛⠶⣤⣀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠛⠉⠉⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠛⢦⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣠⡶⠛⠋⠉⠙⠻⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⢀⣤⡤⠦⡤⠀⠀⣠⡀⠀⢠⡤⠴⣤⣀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠁⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠁⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡧⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠰⠞⠛⠛⠶⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠶⣦⣤⣤⣤⣤⠶⢾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠴⠶⠦⠤⠦⠶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠦⠴⠤⠶⠶⠤⢤⣤⣀⡀
⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷
⣼⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣦⣦⣴⣶⣴⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣦⣴⣦⣤⣾
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡿⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠷⣤⡈⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣽⣿⡶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⣿⡆⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠛⢦⣄⡀
⢀⣠⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀
⣿⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀
⣿⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀
⣿⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣦⣄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠋⠉⢸⡏⠙⠶⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⠀⠀⢸⡟⠳⢦⣄⠉⠻⢦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠶⣤
⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⢻⣰⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⣤⠀⠁⠃⢇⢸⠐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⢐⡄⣦⡤⠄⠉⠀⠇⢘⣴⠢⡀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠉⠢⡀⣧⠖⣤⠀⠘⠤⠟⡷⣰⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⢀⠁⠡⠘⢸⢳⡦⢀⡀⠻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⣄⠈⠘⢧⠘⢅⢰⠄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⠻⡴⠃⠂⠀⠉⠠⠵⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠗⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢑⣿⣿⣿⣿⣏⡄⠀⠀⠀⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡾⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣻⡃⠉⣉⠙⠉⣉⣛⣠⠀⠀⠀⠀⢻⡇
⣿⠀⠀⠀⠀⠀⠀⣿⡏⠈⢹⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢳⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⣿⠃⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣿⡶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⠿⠓⠶⣦⣤⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⢰⡧⠀⠀⠀⠀⠸⣋⢿⣦⡀⠀⠀⠀⠀⡀⠀⢀⣉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠦⣘⢁⡇⠀⠀⣀⡀⠀⣀⢂⠈⢓⣶⣿⣿⣿⣿⣿⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⣿⣇⠀⠈⢻⣶⡁⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⢀⣰⡟⢿⡝⠙⢦⡀⠙⠟⢻⣿⣿⡃⠀⡀⠙⠳⣾⣿⡿⣿⢿⣿⣿⠉⠛⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠙⠛⠿⣿⣞⡁⠀⠸⡇⠀⠰⠟⠩⠯⢟⠀⢱⡄⠀⠀⠀⠀⠁⠘⠿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠈⣛⠛⠶⣶⣶⡶⠶⠗⠊⠀⢠⠀⠈⣿⡀⠀⠀⠀⠀⣶⣿⠖⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢺⡆⠁⠀⠀⠀⠀⠀⠆⠀⠀⠹⠃⠀⠀⠀⠀⠿⠁⢠⠻⣿⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣄⠸⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⢻⣿⣿⣦⠤⢤⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⣶⣿⣛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣭⣿⣿⡄⠀⠉⠀⠀⠀⠀⠀⠸⡀⠀⠀⣰⣆⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣰⣏⣹⣿⣷⢄⡀⠀⠀⠀⠀⠀⢻⡄⠀⣀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣬⡿⣿⣿⡾⠿⣦⠀⠀⠀⠀⠈⢻⣾⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠛⠤⠴⣤⡄⠀⠈⠙⠻⠶⣤⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠾⣿⣿⣍⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣡⣾⣿⣿⠟⡶⠀⢀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⣿⡃⠈⠀⠁⠈⠁⠀⠒⢛⣿⠁
⠀⠀⠀⠀⢀⠀⡀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⠋⠁⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠤⠀⠀⠀⠀⠈⠀⣀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣮⣿⣿⡀⠀⢀⣴⣤⣾⡄

⠀⠀⠀⠀⠀⠀⢀⣶⣶⡆⠀⠀⠀⠀⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⢴⡆⡖⢠⣴⣶⢴⢰⢰⠰⡂
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⡀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⣠⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠉⠉⠈⠘⠈⠑⠃
⠀⠀⠀⠀⢠⠊⡿⠿⠿⢿⠁⡆⠀⠀⡐⢹⣿⡿⣿⡿⢰⠀⠀⠀⡎⢺⠿⠿⡿⡇⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡀
⠀⠀⠀⠀⢸⡠⣖⡤⠤⣪⣆⡇⠀⠀⢳⢸⣶⣦⣶⣿⢸⠁⠀⠀⡇⣾⡢⠤⣴⡵⢴⠀⠀⠀⠀⠀⠀⢸⣥⠀⢸⢾⢸⡍⠀⡀⠀⠀⠀⠘⣥⠀⢰⢿⠀⣯⡀
⠀⠀⠀⠀⠀⠁⢿⣿⣿⡿⠈⠀⠀⠀⠀⠀⣿⣿⣿⠇⠉⠀⠀⠀⠈⢾⣿⣿⣿⠧⠁⠀⠀⠀⠀⠀⠀⠘⡿⡆⡼⣣⠾⠇⣴⠇⠀⠀⠀⠰⣷⡀⡛⢇⡴⡞⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⣀⣀⠀⠀⡗⣿⡏⣿⢺⣎⡏⠀⠀⣠⣀⠀⣷⢿⡟⣿⢻⣎⡟
⠀⠀⠀⠀⠀⢀⣀⢀⠀⣀⠀⠀⠀⠀⠀⡀⣀⡀⢀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⢮⡓⣶⣿⢻⠇⡏⡿⣸⠀⠀⠛⠻⡏⣷⣿⢸⡇⡟⣾⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠻⠼⠖⢳⢧⡟⠀⠀⠀⠀⠹⣎⠻⡤⠖⣷⢧⡟
⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡧⢷⣷⡟⠀⠀⠀⠀⠀⠀⠈⠹⡧⢷⣷⡿
⠀⠀⠀⠀⠀⣴⣼⣷⣦⠀⠀⢾⣿⣿⣄⠀⠀⠀⠀⠀⣀⣤⣤⡛⠟⠁⠀⠀⠀⢀⣠⣾⣷⠀⠁⠀⠀⠀⢀⡇⢸⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⣇
⠀⠀⠀⠀⢠⣿⣿⣿⡿⠆⠀⣼⣿⡟⠉⠳⣄⠀⠀⠀⣿⣼⣿⣇⡀⠀⠀⠀⠀⣿⣿⣯⡁⠀⠀⠀⠀⠀⢸⡇⣸⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⣿
⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣏⠉⠉⠁⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⠃⠻⠀⠟⠀⠀⠀⠀⠀⠀⠀⠸⠃⠺⠀⠿
⠀⠀⠀⠀⠀⢸⡏⢸⡇⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⡿⣷⠀⠀⠀⠀⢐⠋⠛⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠄
⠀⠀⠀⠀⠀⢼⡇⢸⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⡿⠋⠀⢻⡇⠀⠀⠀⡘⠀⠸⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠤⢀

⠀⠀⠀⠀⠀⠀⠐⢀⣠⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⢴⣿⡆
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠰⣿⡧⠀⠀⠀⢺⣿⣇⠀⠀⠀⠀⢀⣴⣮⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣴⣾⡏⠁⠀⣠⣦⣡⣶⠦⣤⣤⡀
⠀⠀⠀⠀⠀⠈⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡄⢠⣾⣷⣄⣤⣶⠶⠛⠉⣿⣧⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢸⣿⣿⡇⠀⣴⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⣿⣛⡉⠁⠐⣿⣿⣿⡿⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠘⠋⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠋⣿⡆⠀⠀⠀⠀⠀⠀⠀⠬⣿⠿⢻⣷⠀⠀⣿⣟⠋⠙⠀⠀⠀⠀⢹⣿⢻⣿⠀⠀⠀⠀⠀⢰⡾⠟⣦⡆⢹⠀⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣾⠇⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⡄⠶⢠⠸⡿⠀⠀⣿⠛⠒⠒⠇⠀⠀⠀⠸⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠈⠇⠀⠀⣿⢿⡇
⠀⠀⠀⣀⢀⣀⣀⢀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠘⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠴⠞⠋⢈⣷⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢽⠟⠁⠀⠀⢀⠴⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠤⠀⠀⠀⠋⣀⣤⠤⢤⣌⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠴⠶⠞⠛⡋⠉⡀⢄⡀⠀⠍⠳⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡭⠖⠊⠠⡐⠠⠤⠈⠉⠙⠳⠦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⡄⠀⠐⠀⠀⠀⠀⠂⠀⠤⢀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⡡⠀⠀⠀⠀⠀⠀⠀⠈⡀⠁⠐⡀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣧⠀⠀⠀⠀⠀⠀⠀⢸⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠓⠀⠂⠀⠙⣦
⠀⠀⠀⠀⣰⠇⠀⠀⠀⡀⠐⢀⡠⠚⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⡏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢈⠐⢆⠀⠀⠀⠨⣇
⠀⠀⠀⠀⡏⠀⠀⠂⢀⡴⠋⠁⠀⠀⠀⠀⣀⣉⣙⠳⠶⠏⠆⢠⣸⡇⠀⠀⠀⠀⠀⠀⣀⣿⡧⠀⠀⣶⣿⢿⢿⣏⣭⣤⣶⠿⠶⣄⠈⠲⡐⠀⠀⠀⢿
⠀⠀⠀⠀⣇⣀⢀⠀⣼⠃⠀⠀⠀⠀⠀⢸⡏⣛⣿⠿⠀⠀⢠⣤⣽⡇⠀⠀⠀⠀⢰⣿⣿⢿⣷⣤⣼⣿⣶⣶⣼⣿⠋⣿⠡⠁⠁⢹⣷⣶⣶⣦⣤⣀⣾
⠀⠀⠀⢰⡟⠉⠙⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⡏⠀⠀⠀⠀⠀⣾⡿⣿⣻⡿⠉⢻⣏⠙⠋⣻⣿⠀⣿⣥⠀⢀⣽⡇⠀⠉⠉⠉⠹⢿⣦
⠀⠀⠀⠘⣇⢀⠀⢐⠁⠀⠀⠀⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⢸⣷⣾⡿⠁⠀⠘⢿⣷⣾⡿⠋⠀⠹⣿⣿⣿⡟⠀⠀⢰⠀⡄⠀⢄⣿⠗
⠀⠀⢠⡞⠉⢣⡁⠒⠀⠀⡀⠀⣴⠞⡁⠀⠀⠀⠈⠄⠄⠠⠀⠀⠟⣧⠀⠀⠀⠀⠀⠙⣿⠇⠀⠤⠄⠠⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡤⢠⣾⣃
⠀⠀⠸⡇⠀⠀⢱⣾⡵⠀⢇⠀⠠⠊⠕⠀⠀⠀⠀⠀⠀⣠⠤⠴⢦⣏⠀⠀⠀⠀⠀⠀⠘⢆⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣃⣠⠟⠀⢹⡆
⠀⠀⠀⢻⡄⠀⠀⠈⣧⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠭⣭⠄⡟⠀⠀⢠⡤⠀⠀⠀⠘⢶⣐⠂⠀⣹⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠋⡀⠀⢸⠇
⠀⠀⠀⠀⠻⢶⣄⣠⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠒⠒⢀⡞⠁⢀⡴⣻⡆⠀⠀⠀⠀⢸⣋⣒⣛⡩⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢰⡇⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠈⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⠀⢠⠎⢠⣿⠈⢆⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⣾⣦⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⠤⠴⠞⠁⢀⣘⣦⣸⣿⣤⣬⡇⠀⠀⠀⢧⣀⡀⠀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⢀⠈⠉⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠉⠉⠁⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠉⠓⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣨⡽⠖⠀⠀⠀⠀⠀⠀⢀⣀⣠⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠶⠶⠶⠶⠖⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢟⣛⣛⡻⣿⣿⣿⣿⢟⣛⣛⡛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢱⣿⡿⣋⣿⡜⣿⣿⢇⣿⣿⢟⣽⡎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣜⢫⣼⣿⡿⣱⣿⣿⣇⠛⣵⢟⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣷⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣭⣶⣶⣍⢻⣿⡏⣶⡆⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⢟⣵⣿⡇⣿⡇⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣑⠿⠿⣋⣼⣿⣇⠿⠇⣿⢨⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣋⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣬⢻⣿⣿⣿⢟⣵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣛⣭⣭⡛⢿⣿⣿⣿⣿⣿⠸⠿⠿⠿⣿⣿⣇⢿⣿⡏⣾⣿⡿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢱⣿⡿⣫⣿⡎⣿⣿⣿⣿⣿⠸⠿⠿⠿⠸⠿⠿⠾⠿⠷⠿⠿⠇⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣎⠫⣾⣿⢟⣵⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡍⣭⣭⡍⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠃⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣘⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣦⣽⣿⡷⠶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣍⠛⠛⠉⠝⣠⣠⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣅⣢⠾⢁⡄⡡⢫⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠉⢀⡀⠋⡃⠄⣰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢾⣿⣿⣾⣽⣽⠾⡛⢛⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⡇⢐⣚⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠓⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠈⠤⠔⡊⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣶⣾⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⠿⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⢷⣦⣤⣤⣤⣶
⠀⠀⠀⢿⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠷
⠀⠀⠀⠀⠉⠉⠀⣼⡏⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢀⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⠿⣶⣄
⢀⣾⢷⣦⣴⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢤⣼⡏⠀⠀⠙
⠚⠋⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⣿⣿⣿⣷⣄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠛⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⡉⠛⠿⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⣴⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⣶⡄⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣿⣿⣷⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣿⣿⠇⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⡈⠻⣿⣿⣿⣿⣏⣉⣙⣿⣿⣿⣿⡿⠃⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣈⠙⢿⣿⣿⣿⣿⣿⡿⠟⢁⣠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⡈⠛⠛⠛⢋⣠⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠙⠙⠛⠙⠛⠋⠙⠉⠛⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠙⢿⣿⣿⣿⣿⠟⢁⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣄⠙⢿⣿⣷⣄⠙⠛⠛⢁⣴⣿⣿⠋⢠⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠙⣿⡿⠃⢀⠐⢿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣶⣿⣷⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢦⣄⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣷⣌⠛⠷⣦⣄⡀⠈⠻⣿⣦⣄⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠉⠉⠉⠀⠀⠀⠉⠛⠷⣤⡙⣆⠙⢷⡘⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣁⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠈⢷⡷⢻⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠛⣉⣭⣿⠿⠟⠛⠉⠉⠀⢀⣠⣤⣤⣤⣀⡀⡀⠀⠀⠈⠇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣤⡾⠟⠉⣀⣀⣤⣄⣀⡀⣰⣿⠟⠉⠉⠉⠛⢿⣿⣦⠀⠀⠀⠚⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣶⡿⠿⢻⣿⣿⡉⠉⡉⠛⠁⣠⠶⣶⣤⡀⠀⣬⣿⣷⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠋⠁⠀⠀⢸⡿⠙⠛⢾⣧⠰⣶⣿⠟⠋⢉⠀⠀⢾⣿⣿⣇⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢸⠧⣄⢀⡆⢨⡁⠙⢥⠀⢀⡞⠀⠀⢹⣽⣿⠂⡾⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⣿⠃⠈⡇⠀⠈⢧⡸⠁⢒⠉⠸⣿⡿⣼⠖⣫⡥⢤⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⡿⣧⣰⠃⠀⠀⣸⣷⡄⠀⠀⣸⣿⣿⠏⣼⣡⣄⡼⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢇⠛⣁⡼⣡⠴⡦⠀⡿⠈⢿⡄⠈⣿⡟⣿⢸⠏⢡⠟⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⣍⣉⣁⣘⣥⠞⠁⠈⠒⠒⠀⢀⠋⠻⣷⡿⣌⣀⣡⠔⣁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⠛⠻⠿⢟⣫⣵⡶⡖⠒⠶⣄⠈⠁⣁⠀⣿⠁⠈⠉⣛⣩⠟⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣬⣙⡛⠛⠛⢻⡽⠟⡏⠉⣀⣴⠞⢳⡄⠹⣇⢻⣷⢦⣤⣉⣭⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠛⠛⠉⢀⠀⠀⠹⣆⢹⡆⠙⠦⣄⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣦⠀⠀⠀⠟⠀⡖⣳⠀⠀⠙⠃⠀⠀⢻⡌⣧⣤⣀⠀⣀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠟⠀⠀⠀⢈⡀⠈⠀⠀⠀⣀⣤⠶⠖⠾⣇⢹⡀⠿⣤⠟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⡉⠁⠀⠀⠀⠀⠀⠀⢠⡟⢹⠦⠄⢠⣾⡏⡔⢺⢩⣛⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣞⡩⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠀⠀⣾⡏⣇⢻⣄⣸⢉⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⣀⣴⡿⠛⣻⡆⠀⣠⡶⣦⠀⠀⣾⠻⣇⢰⣿⡇⣿⢠⣉⠁⣼⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠻⠿⠟⠁⢀⣼⠟⠀⢰⡏⢀⣿⠀⠀⣿⡆⠙⠋⠈⣷⡸⣾⣸⡿⠋⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠒⢦⠀⠀⣴⡿⢋⢤⠀⣾⠀⢸⡿⠀⠀⣿⠁⠀⠁⠀⠘⢿⣶⣥⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⣼⡟⡠⢌⠁⠀⣿⠀⢸⣷⠀⢠⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠁⢰⠃⢸⡟⠀⠈⠻⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡑⣁⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡝⠿⣿⣿⣿⣿⣿⣿⠟⣫⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢟⣱⣿⣶⣭⣭⣍⡱⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⣫⣭⣭⣿⠿⠿⣿⣭⣭⣝⠸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢇⡶⣼⢧⡝⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⡿⣸⢧⡟⣼⢣⡝⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢇⣿⣼⣣⡟⣼⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⡏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡼⣿⣿⣿⣿⣿⣿⢸⢟⣵⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡷⣹⣿⣿⣿⡿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠇⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠈⠲⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠿⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠤⡀⢀⣀⣠⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠦⣄⠀⠀⢀⣀⡔⠉⠉⠹⠋⠀⣠⢾⡿⠋⠉⢳⠀⣀⠀⣀⣠⠴⠚⡿⠖⠋⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡧⣄⡁⠀⠀⣀⣠⣏⣄⣀⣀⣠⠴⠚⠙⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠀⠀⠙⣳⣤⡷⠶⠶⠦⠀⠉⠙⠳⣄⠀⠙⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠀⠀⠀⢠⣬⡷⣒⣛⣛⣻⡁⠀⠀⠀⠀⠈⠳⣄⠰⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡰⠋⠹⠯⢥⡤⠆⣀⣀⣀⠀⠀⠀⠀⠈⠳⣤⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⠀⢀⡀⣸⠀⠀⣠⡤⢬⡉⠉⠁⢀⣉⣉⠻⢦⡀⠀⠀⠀⠙⢯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠈⡷⣄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⢀⡽⠈⢧⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⡤⣧⠀⠀⠀⠀⣀⡤⠴⠶⠦⢤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠞⠁⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡟⠳⢤⠴⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣤⣤⣴⣶⣶⡄⠀⠀⠀⢹⠿⠁⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠿⡟⠂⢠⣶⣤⣤⣄
⠀⠀⠀⠀⠺⡿⠇⠀⣾⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⠛⠙⠛⠛⠻⠿⣶⣤⣀⠀⠀⠀⠀⠈⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⣴⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⣼⡟⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢻⣇⠀⠠⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⢛⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠀⠀⢸⣿⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠀⣿⡅⠀⠀⣴⡿⠛⠉⠙⠻⢿⣶⣤⣀⡀⣀⣤⣴⡾⠿⠛⣁⣀⡀⠀⠀⠀⢸⣿⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⡇⠀⢰⣿⠁⠀⠀⢀⣀⣠⣤⣿⡿⠿⢿⣿⣧⣶⣶⣿⠟⠛⣿⣄⠀⠀⢸⡿⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣶⣾⣿⡶⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⣿⣶⣶⣿⣷⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⡿⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⣿⣿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠂⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⣠⣾⠟⠛⠛⠛⠻⢿⣦⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡻⢁⡴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣷⠋⣼⣡⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣾⠁⡼⢫⠟
⠀⠀⠀⢀⠀⠀⠀⠀⣸⠃⠀⠁⢈⡴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣰⠋⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢋⡤⠖⠒⠦⣄⠀⠀⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⠘⠤⢄⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡾⠁⠀⠀⠀⠙⣶⠻⠅⠀⠈⢦
⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠐⠳⠤⣀⠀⠀⠀⠙⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣄⣀⣀⡠⠋
⠀⠀⠀⠀⠀⢸⡇⠀⣠⢾⠁⣴⠀⠀⣠⣤⣟⣦⡀⠀⠀⠉⠳⢾⡇⠀⠀⠀⠀⠀⢰⡏⠉
⠀⠀⠀⠀⠀⠈⢷⣼⠃⣾⠀⡟⣆⡼⠁⠀⠉⠻⣿⣦⠀⠀⠀⠀⠻⣄⠀⠀⠶⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠈⠀⠀⡴⠒⠛⠛⠿⢧⠀⠀⠀⠀⠈⠙⢛⡿⠋⠛⠶⢤⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠴⠖⢲⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⣄⠀⠉⠙⠓⠶⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⢤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠉⠓⠦⣌⣀⡉⠂⠀⢂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⣦⣄⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠄⠐⣯⠙⣧⠈⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡰⠀⠀⠀⠀⠀⠀⠈⣇⠈⠙⠾⣦⡀⠹⣮⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⠀⠀⣹⣦⣙⠀⠀⠀⠈⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠛⠦⣄⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢺⣁⣀⡽⠟⠢⠤⣄⣀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣲⠶⢤⣀⣈⡏⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠈⡷⣄⠀⠀⠀⠀⠳⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⠀⠀⠈⠉⠉⠒⠒⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⣷⢤⡿⠆⠀⢀⣀⣘⣦⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣄⡀⠈⠀⠂⠀⠀⠀⠀⠈⠉⢛⠶⣄⢠⠇⠀⠙⠚⠛⠉⠉⣿⣿⠱⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠁⠀⢉⡙⠢⣤⣀⠀⠀⠀⠀⣰⠏⠀⠘⠻⢦⡀⠀⠈⢦⡀⠀⣿⣿⣿⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡉⠀⠀⠀⢀⡴⠋⠁⠀⠀⠉⠛⠲⢦⣴⠏⠀⠀⠠⢴⣾⣷⠀⠀⠀⠙⢶⣿⡛⠛⠒⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣦⣿⡄⠀⢠⠞⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠷⠛⡄⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣳⠞⠉⢳⡄⠀⣠⣿⣿⢿⣠⠏⠰⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣸⠁⢀⡖⠈⡇⣰⢻⡟⠉⠻⠏⠀⣠⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠖⠒⡙⠶⠞⠀⠀⣿⠃⡾⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⢶⠚⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣰⠻⣄⣐⣦⠀⠀⠐⢇⡀⠀⠀⠀⠉⢻⠖⠲⠲⠶⠶⠶⠒⠒⠒⠛⠛⠉⠉⠁⠀⢸⠁⡼⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠈⠉⢈⡷⠒⠲⡬⠻⡄⠀⠀⢀⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡇⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣀⡴⠇⠀⠀⠀⢙⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣼⣀⣤⡤⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠃⠄⠀⠀⠀⠀⠀⠀⠐⠚⠛⣛⠾⢻⠿⠍⡁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣑⣀⢤⡐⠄⠀⠀⠀⠐⠂⠉⠀⠀⢀⡏⠀⠀⠀⠀⠀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⣻⣿⠿⠛⠛⠲⠤⠴⠦⠤⠶⠶⠒⠚⠛⠓⠒⠒⠶⠞⣽⣩⠏⠉⠙⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡘⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠇⠈⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⠀⢰⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣿⣧⠀⠀⠀⠀⠀⠘⠉⣿⡄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⡀⠀⣸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢨⣷⣿⣿⣿⣿⣿⠿⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠲⣿⣿⣿⡗⢲⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠛⢛⣛⣛⠛⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣼⣿⣏⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢫⣿⣿⣿⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣼⣿⣿⣿⣭⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣾⣿⣛⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣻⡿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠟⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠀⠀⠈⠻⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟





⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⣠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⢑⠆⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⢷⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⡶⣤⣤⣤⣀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⠀⠀⠀⠀⣀⣴⣶⣿⡟⢻⡹⠟⠛⠿⣟⣳⡬⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠆⠀⣤⣾⡿⢿⡏⣷⣮⡕⡕⣲⣧⡄⡾⢂⠂⣾⣿⢿⣿⣿⣿⣿⣶⣄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠀⠀⠀⠀⣠⣾⠿⡿⢧⣮⢾⣟⣴⣯⣷⣿⣿⣿⡿⣯⣟⣩⣽⣯⣽⡿⣯⣿⣿⣿⣷⠀⠀⢀⡤⡴⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⣼⡿⠋⢀⠀⣴⣿⠿⠛⠉⢁⣀⣠⣤⡠⠶⠤⠏⢴⣾⣵⣾⣿⠿⣧⠀⠙⢏⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⡇⠀⢾⣿⠟⠀⢀⠔⠛⠉⠁⣀⣀⣀⣠⣤⣤⣦⣜⣿⣮⣿⡄⠈⠢⡀⠀⠳⣄⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⣼⣶⡿⠃⠀⠻⠏⠀⠐⠁⢀⠴⠊⠉⢀⣀⣠⣤⣤⣤⣰⣿⣷⣿⣽⣿⡄⠀⠙⢢⡀⠈⢣⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⣴⢁⣽⠇⠀⠀⠀⠀⠀⠀⠀⠁⠠⠖⠉⠁⣀⣠⣤⢠⣝⣻⠈⠹⢉⡻⣿⡈⠢⣄⠀⠙⠆⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠻⢿⣿⣽⠿⠛⠉⢉⣤⣼⠏⢹⡍⣿⣦⡈⠒⠄⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣄⣀⠀⠀⠁⠠⣴⡃⠐⢘⠑⠋⠀⠁⠀⠛⡻⣷⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡀⠀⠈⠉⠲⡄⠀⠈⠛⠿⠟⣠⠚⠆⣹⢷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⣀⣠⠠⠖⠉⠀⠈⠻⢤⣀⠀⠀⠀⠀⠀⢀⡄⠀⠉⠓⠶⣾⣿⠏⢹⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠀⠀⣠⠋⡴⠓⠒⠒⠢⢄⠀⢀⡟⢡⡀⠀⠀⠀⠀⢠⠁
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⣄⡀⠀⠀⢈⣵⣿⠁⠀⢳⠀⠀⠀⠀⢸
⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⠛⠻⠷⠾⣿⣿⠀⠀⠘⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠋⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⢰⢻⣿⠀⠀⡞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠀⠀⠀⢀⡇⠀⠀⠀⠀⣠⢿⠿⢿⣿⡇⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠇⠀⠀⠈⢆⠀⠀⠀⠐⢶⣶⠤⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠻⣄⡁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠈⢆⠀⠀⠀⠀⠦⣙⠤⣌⡳⣀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⠣⣄⠀⠀⠀⠈⠁⠙⠙⠉⣁⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠑⠲⠦⠤⠶⠒⠉⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢡
⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⡄
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⠄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠐⠀⣴⠂⠀⠀⠀⠈⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠡⠄⠈⠀⠀⠀⠈⠀⠀⣌⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠂⢄⣀⣨⣂⠤⠉⠛⢋⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⢄⡀⠔⠁⠠⢂⠡⠐⠊⠈⢂⠁⠓⢄⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠘⠀⢤⡊⠐⠁⠀⠸⢤⠀⢠⠀⠀⠀⠆⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠐⢤⡈⠓⠒⠠⠀⠀⠰⢢⠀⠀⠀⠈⡀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⡈⠢⠀⣀⢁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠐⠄⠓⠛⠅⣐⠂⠠⠄⠤⠄⠤⠊⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠜⠒⠠⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⣉⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡰⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡐⡐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠸⠶⠖⠚⠋⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣰⣶⣶⣴⣾⣿⣿⣿⣿⣿⣽⣿⣶⣤⣤⡀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣷⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠀⠀⣾⣿⣿⣏⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡃⠘⠓⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⢀⣼⣿⣌⣿⣧⠛⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢿⡿⣿⣾⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⣽⣿⣷⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣭⣿⣿⣷⠻⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣠⣾⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣵⣿⣿⡟⠀⠙⠻⠿⠿⠟⠋⢿⣿⣿⣿⠿⣵⡿⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⣀⣠⣤⣤⣠⣾⣿⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⠿⠿⠛⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠈⠙⠻⠿⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠉⠉⠉⠉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠆⣀⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠁⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡄⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣈⠖⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡵⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡃⢠
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⡔⠒⠦⠀⠀⡀⠀⠠⠤⠐⠈⠙⠒⠒⠒⠂⠈⠛⠤⢀⡀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢱⠈
⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⡇⠀⠀⠀⠀⡄⠀⠀⠀⠞
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⡇⠀⠀⠀⢠⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⢀⣈⠳⠀⠀⠀⠄
⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠤⠄⣀⡀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢣⠀⡘
⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠀⢀⠎⠄⠁⠂
⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⠎⠀⢀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢣⠀⠀⠀⠀⠈⡕⠂⠲⠎⣌⠀⡠⠂
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢀⡌⠀⠠⠊⣀⠘⠶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂⠰⠂⠈⠑⠢⡀⠀⠀⢀⠟⠁⢸
⠀⠀⠀⠀⢠⣜⣁⣀⠠⠔⠈⡇⠰⠀⠜⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠀⠀⠀⠐⣤⠂⠹⠀⠀⠸
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠘⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⣏⠒⣂⠀⠤⠀⢀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠘⡀⠀⢢⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⠀⠀⠀⠀⠀⠰⠀⠑⠤⠉⠀⠒⠂⠐⢀⡽⠋⠑⣤⠀⠀⠀⠀⠀⠀⢃⠀⡰⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⡐⠂⠀⠤⢤⠌⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡎⠀⠀⢲⠀⣀⠀⠈⣴⠀⠠⠃
⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⡰⢩⠀⠀⠀⠈⠉⢐⠉⠀⠀⠘⠀⢣⠀⠀⠀⠀⠀⡆⠀⢀⡰⠧⠠⠀⠘⠀⠿⡀⢀⠷⡀
⠀⢀⡴⠀⠀⢹⡄⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠥⡸⠋⠀⠀⠀⢀⠁⠀⠘⢃⠈⠀⠈⠷
⠀⠸⡄⠀⢰⡋⠀⠀⢀⠊⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⡤⠀⢀⡀⢀⠃⠀⢀⡄⠀⢀⠀⠀⠀⢘
⠀⠀⢸⠀⠀⠀⠀⢀⠂⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⢻⠀⠀⡌⢠⠀⠘⢄⠀⣠⠌⢘⢣
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⣄⠀⠀⠀⠀⡈⠀⠀⡄⠈⡆⠀⠀⠀⠀⠀⡌⢀
⠀⠀⠀⠀⠀⠀⠘⠓⠲⢄⡀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠈⠢⢄⡀⠀⠁⠀⠐⠚⡄⠀⠀⠑⠘⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠒⠐⠂⠈⠁⠀⠛⢦⣄⠀⠀⠀⠀⠀⠑⠆⢀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⠀⠀⠀⠀⠀⠀⠈⠀⠚⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠰⠇⠀⠀⠀⠀⠀⠱⡄⠀⢀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢢⠴⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⢆⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠢⢀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡌⠀⠀⣨⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⡀⠀⠈⠐⠒⠂⠠⠤⠴⠛⠂⠤⠄⢀⣀⣀⠐⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠁⠀⢀⡀⠀⠀⢠⠶⢀⡀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠏⠁⠀⠀⠀⠁⠐⢢⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢄⠀⠀⠀⠀⠀⢠⡾⡀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠁⠐⠒⠈⠉⣀⠈⠒⠠⠤⠤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⢀⣀⠉⠐⠢⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣠⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢰⡿⠁⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⣀⠀⢙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣆⣀⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢹⣷⠀⠀⣻⡆⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⣾⡏⠀⠰⣿⠁⢸⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⠿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⢸⣿⠀⠀⣿⡇⢸⡇⠀⠀⠀⠈⠙⠿⣶⣤⡀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠛⠃⠀⠀⠛⠀⢸⡇⠀⠀⠀⠠⣶⠟⠋⠉⠀⠀⠀⠀⠉⠛⠿⣶⠀⠀⠀⠀⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣀⣀⣀⣀⣀⣀⣤⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠛⠛⠛⠛⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣷⣄⡀⠀⠀⠀⠀⢀⣠⣿⣷⣶⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠘⣿⡹⣧⠹⣿⡻⣿⣷⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣾⣷⠹⣧⠘⢷⡙⢷⡝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢹⡆⠈⣷⡈⢿⡄⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⡀⠸⣧⠈⢿⡄⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⠀⣿⠀⠸⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠈⠀⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠈⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁⣀⣤⠀⠀⠣⠀⠀⢀⠔⠀⠀⠀⠀⠄⣉⡀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠳⡥⣴⠠⢀⡰⠎⠀⠀⠀⠀⠀⠀⠠⠤⡀⢠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠁⠁⠘⢆⠀⠀⢀⣀⠀⠀⠀⠀⠘⠂⠀⠈⠀⢀⠀⢀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠓⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⢀⠀⠄⢂⠈⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⠷⡀⠀⠠⠀⠀⠀⠀⢀⡠⠲⢠⠀⠀⢀⠄⠀⠀⢠⡀⠈⠉⢡⢌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⡆⠀⠀⠀⠀⢾⠀⠠⠞⢁⠤⠊⠄⠀⠀⠀⠑⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡋⠒⠂⠤⠤⠤⡄⠒⣮⣤⢤⣄⢠⠀⠀⠈⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⠀⠀⠀⣤⡴⠁⠁⠀⢀⡘⠀⢻⡛⢄⠀⠈⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠄⢻⠁⠀⢦⠀⣀⡘⠁⠀⠈⣅⠀⠱⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⡠⠜⢄⠀⠀⠈⠀⠀⠀⠀⠀⢿⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠉⠁⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠈⠈⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠂⠀⠀⠀⠀⠀⠈⠓⡔⠂⠐⠀⠒⢀⡉⠄⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⠸⡀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡠⠁⠀⠀⠀⠈⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡰⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⠀⠀⠀⡸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣉⣉⣉⣉⡉⠤⠔⠀⠀⠀⠀⠀⢇⠀⠉⠀⠒⠀⠉⢀⡠⠃

⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠛⠲⢦⣄⡀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠳⣤⠞⠉⠙⠶⣤⣀⠀⠀⢀⡼⠋⠀⠀⢀⣠⣤⣀⠀⠀⠈⠛⠞⠋⠉⠉⠉⠻⣦⠀⠀⠀⣀⣤⠶⠛⠉⠳⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢀⡞⠀⠀⠀⠾⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠰⢦⣄⣸⡏⠛⠛⠛⠀⣠⡴⣿⣁⣴⠿⣆⠀⠀⠀⠀⠀⣀⠀⠀⣸⢷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠚⠛⠛⢹⣇⣠⠴⠚
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣴⠋⢠⡌⢿⣁⣴⠛⣳⠀⢀⣠⢾⡏⣠⡼⠋⢘⡇⠀⠀⢀⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡼⢧⡀⠈⢷⣄⣡⣽⣾⣯⠶⠋⠁⠟⠛⠁⠀⠀⠈⡛⠛⠋⠉⢹⡇⠀⣿⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠶⣞⠛⠉⢩⡞⠁⠈⠹⣄⠀⠉⠁⢀⣈⣷⠛⠉⠛⠀⠀⠀⠀⠐⠋⠉⠓⠀⠀⠈⠻⣴⠏⠀⠀⠀⠀⠀⠈⠉⠛⣳⡦
⠀⠀⠀⠀⠀⣀⡼⠟⣰⠏⠀⠀⠀⠀⢸⡟⢿⡋⠉⠉⠁⢠⣤⣤⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠚⢧⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⡾⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣤⠶⠖⠒⠶⠀⠀⠀⢠⡟
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠶⠦⣤⣤⡤⠴⢾⡏
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⣇
⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣟⣀⣠⣤⡤⠴⠶⢤⣤⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⣀⣀⣀⣀⣀⡀
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣩⠟⠉⠉⠉⠛⠶⣄
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠚⠋⢀⡀⠀⠀⠀⠀⠀⠈⢧⡀
⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣴⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤⣤⣤⣶⣿⣀⣀⣀
⣿⣿⠋⣛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⣿⡒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠛⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⣤⣴⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⡟⣠⠴⠚⠉⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠲⠤⣬⣍⣉⣉⣉⣩⣭⡭⠤⣿⠗⣸⣿⣷⣶⣶⡄⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢰⣶⣶⣶⡶⠒⠶⣶⣶⣶⣤⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⠟⠋⣁⠤⠀⠀⠈⠉⠉⠉⠻⢬⡉⠛⠻⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⢠⡴⠦⡀⠀⠀⠀⡤⢶⣤⠀⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣤⣅⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠛⠓⠒⠛⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣬⣙⣛⣛⣛⣩⣴⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠉⠁⠑⢦⡈⠹⡕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠈⣿⡆⠀⢸⡏⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠐⠲⢤⠠⠲⢤⠠⠞⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣤⠤⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡠⠤⠀⠒⠀⠀⠀⠁⠒⠒⠒⠒⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡏⠒⠶⠤⠤⠤⠤⠤⠄⠀⠀⠀⠒⡈⣇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠉⠑⠲⠶⠶⠶⠶⠂⠁⠀⡸⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⢳⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⠤⠒⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣨⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢁⣄⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠢⣤⣀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡿⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⡠⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⠄⠀⠀⠀⠀⢸⠈⠳⢄⡀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢫⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⢠⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠠⡇⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠷⠂⠀⠘⠀⠀⠀⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢀⠃⠀⠀⢀⢤⡄⢤⡒⠚⠀⠈⡆⠈
⠀⠀⠀⠀⠀⡎⠐⠐⠒⢀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⣸⠀⠀⠀⠀⠀⢧⡀⠀⡘⠀⠀⠀⢠⡀⠊⠄⣛⠡⠖⣂⢀⠀⠀⠢⡀
⠀⠀⠀⢠⠰⠀⠀⠀⠀⠀⠑⠦⢤⣀⡈⠀⠃⢠⡄⠘⢀⡀⠤⠤⣼⡔⠀⠀⠀⠀⠀⠀⠀⠙⡀⣧⠀⠐⠒⠢⠉⠒⠉⠀⠀⠠⡅⢂⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠈⠀⠀⠀⠀⣈⠁⠒⠂⠒⠒⢀⣤⣈⣀⣈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠚⠛⠋⠁⠀⢠⣴⣄⣍⣥⣤⠄⠦⠝⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⡶⠀⠀⠀⠀⠀⠀⠳⣶⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣦⣴⣧⡲⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠔⠺⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠟⠻⣿⣿⣬⣧⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠀⠀⠉⠁⠀⠀⠀⠀⠙⠒⠀⠀⠴⢿⣿⣿⣅⢨⡟⣿⣿⣷⣤⣤⣴⣾⡛⠲⠄⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠊⣉⣉⠉⣐⠾⠿⣿⣿⣿⣷⣿⣿⣿⡿⢟⢿⡗⠈⡤⠀⠠⠀⠀⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤⣔⠉⠀⠐⠋⠝⠋⠉⠛⠛⠷⣾⠛⡀⠐⢆⠀⢈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠠⠀⠀⠀⠀⢠⠀⠀⠸⠁⠀⢸⣄⠀⠀⠀⠀⢀⣠⣤⣤⠀⢟⠁⢿⠀⠀⠃⠀⠃⠈⡀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡀⠀⣰⠀⠄⠈⠙⣧⠘⠲⠿⠟⢍⡀⠉⠣⢸⣧⠀⠓⠀⠘⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⠈⠈⠉⠃⢸⠇⠀⠠⠔⠊⠁⠀⠀⠉⠁⠒⠓⠀⠀⢠⠿⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⠀⠀⠀⠀⠀⢣⣀⠓⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠀⡌⡇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢀⡀⠤⠄⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⡽⠀⠀⠀⠀⠉⠉⠀⠤⠤⡀⡀⠀⠀⠀⡎⢿⠷⣄⠀⠀⠀⡎
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢘⡈⠄⠊⠹⠀⠀⠀⠀⢀⠀⣁⢀⣀⣀⣱⠁⠀⠀⠀⠀⠉⠒⡼⠃⢄⠀⠘⠖⢀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠢⡀⠀⠀⠈⠉⠠⣀⡁⢈⡸⠀⠀⠀⢀⠟⠀⠋⠀⢀⡩⠖⠁⠀⠀⠗
⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠉⠃⠀⠀⢀⣀⠆⣀⠴⠋⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠒⠤⡀
⠄⠀⠀⠀⠀⠀⠂⠈⠁⠤⡔⠋⠐⠒⠚⠲⠖⠈⠉⠑⠢⣤⠤⠘⢳⠂⠤⠤⠀⠠⠖⢲⠍⠠⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡄⠀⠀⠀⠀⠐⡀
⠠⣀⠀⠀⠀⠀⠛⠉⠀⠀⠐⡀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡀⠘⠁⠀⠘⡆⢤⢀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠱⡄
⠀⠈⠁⠒⠒⠤⠄⣀⡀⣀⠀⠈⠀⠀⠀⠀⠀⠆⠈⢰⢦⡀⠀⡞⠁⠈⠀⠀⠀⠀⠓⠆⠀⠀⢀⠅⠀⠀⠈⠉⠒⠤⣀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢄⡀⠀⠠⠀⠠⠀⠀⠌⠃⠉⠀⡇⠀⠂⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣐⣤⣀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣸⡆⠀⠀⢀⠰⠋⠀⡇⠀⠀⠀⢀⠄⠁⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠈⢦⣀⠀⠀⠀⢀⠔⠁⢀⡀⠜⠀⠀⠀⠀⠀⠀⢠⠔⠈⠀⠀⠀⠀⠀⠐⠀⠀⠰⠇⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣁⣤⣐⣂⡀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠋⠁⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠃⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⠂⠁⠀⠀⠀⠠⠤⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢒⠒⢩⣝⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠘⢉⣔⡂⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠩⠴⠦⣭⡝⣣⠔⢺⢋⡠⠤⣀⠀⠀⠀⢀⡠⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⠒⢒⡖⢪⠞⠁⠀⡷⠁⠀⠀⠀⠈⠁⠉⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡀⢠⠊⠵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⡸⠀⢠⠔⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⢠⠃⠀⡆⠀⣰⠁⡸⠢⠤⠀⠀⠠⠤⠤⠔⠒⠂⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡎⠀⢀⡇⠀⢲⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠸⠁⠀⢸⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡴⠒⢾⠁
⠀⠀⠀⢀⠀⠀⠀⣾⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠌⠀⠀⠈⡂
⠀⠀⢀⠎⠀⠀⠀⡆⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠀⡰
⠀⠀⡜⠀⠀⠀⠀⠇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠤⠚⠁
⠀⣰⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢀⠇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇
⡘⠀⠀⠀⠀⠀⠓⠤⣀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡇
⢇⠀⠀⠀⠀⠀⠀⠀⠀⡩⠒⠒⠢⠤⠤⣈⣦⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⡇⠀⣀⡠⠤⠤⠤⢄⡀
⠈⠲⢤⡀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⡠⠛⠒⠒⠚⠙⡋⠀⠀⠀⠀⢠⠋⠉⠀⠀⠀⠀⠀⣸⠉⠳⡄
⠀⠀⠀⠈⠑⠦⣀⡏⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡆⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃⠘⣆⣀⡀⠀⠀⠀⢀
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢹⡀⠀⠀⠀⠀⠀⣞⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣌⡙⢤⠃⠀⠀⠀⠀⠀⠡⢋⡰⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣶⣶⣤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣘⣿⣿⣿⣿⣟⣠⣬⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠈⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡉⠛⠛⠛⠛⠛⠻⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠌⠛⠛⠋⠙⠛⠛⠳⢶⣦⡀⠀⠀⠀⠙⢿⣟⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⠙⣷⡄⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠈⣿⡄⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⠃⠀⠀⠀⠀⠰⣶⣶⡶⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠙⠷⠶⠶⠶⠖⠀⠀⠀⠀⠀⠈⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠰⠿⠿⠿⣷⣄⠀⠀⣠⡶⠿⣶⣤⡀⠀⣠⡾⣿⠋⠛⠀⠀⢀⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠈⠙⠿⠟⠉⠀⠀⠈⠙⠻⠟⠉⠀⠛⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠷⣶⣶⣶⣶⣦⣴⣶⣶⠞⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡷⣦⣀
⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠋⠀⠀⠀⠈⠛⠶⣆⠀⠀⠀⠄⠀⠤⠤⠄⢤⣤⠤⠤⠀⠄⣤⡀
⠀⠀⠀⢸⡏⠀⠀⠀⣀⣀⣀⠀⠀⠒⠶⠿⠷⠾⠷⠶⠶⠶⠿⠷⠶⣶⡶⢾⡣⠤⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠹⠆
⠀⠀⣠⣤⣥⠶⠶⢆⡈⠉⠉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⢾⠋⠉⠉⠉⠉⠐⠛⢶⡴⠿⣧⡀
⠀⠀⠉⠉⢻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠀⠀⢀⣄⣴⡾⠁⠀⢸⡇
⠀⢺⣀⠀⠘⣏⠉⠻⢿⣿⠷⠂⢀⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣀⣤⠄⠤⠐⠛⠛⠷⠀⠀⢈⡇⠀⠀⣸⠇
⠀⠈⠻⣦⣾⣿⣄⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠛⡄⠘⠇⢸⣿⣦⠞⠃
⠀⠀⠀⠀⢸⣿⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣿⠃⠀⣤⡄
⠀⠀⠀⠀⠀⢹⡆⠀⠙⠻⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠉⢀⣷⠈⠁⣼⡇
⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠉⠻⢶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣠⠶⠊⠁⠀⡀⢸⣿⠀⠀⢸⡇
⠀⠀⠀⠀⢰⣿⢹⡆⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣶⣾⣿⣿⣷⣾⣿⣿⣉⣿⠟⠉⠁⠀⠀⠀⠀⣧⢠⡿⠀⣸⡿
⠀⠀⠀⠀⢸⣧⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠀⠀⢸⡧
⠀⠀⠀⠀⢸⣿⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠃⠀⠠⡾⠃
⣿⠟⢷⣦⣤⣉⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢠⣷⠀⠀⠀⠀⢀⣀⣤⣤⠴
⠘⣷⠀⠀⠙⠛⣷⡦⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⣿⠀⠀⠸⣏⣀⣴⣶⠞⠛⠋⠀⠀⣀
⠀⢻⣆⠀⠀⠸⣇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣠⡶⢆⠙⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠸⣿⠀⠀⠸⠟⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣴⡁
⠀⠀⢻⣇⠀⢠⣶⠚⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠒⠲⣦⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠸⣿⣴⡿⠛⠶⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠶⠞⠛⢿⡆⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⢶⣤⠚⢢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⡸⠃⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠙⠻⢧⣤⣼⠟⠛⢂⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠊⠀⠀⠀⡄⢸⡇⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠯⠥⣤⠤⠤⠶⠶⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⢸⣿⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠟⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠈⣿⡄⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠈⠻⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⣈⣿⡀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣼⣃⣀⢠⣴⣶⣤⡶⠶⠶⠤⣶⣄
⣀⡴⠖⠛⠛⠉⠁⠈⠉⠙⣻⣿⡿⢶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠀⢿⣿⣉⣀⣀⣀⣀⣀⣀⣀⣤⡴⠋
⣹⣷⣶⣶⣶⣶⣶⣶⣦⣍⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠉⠁⠈⠉⠈⠉⡈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣰⣆⠀⢠⡀⠀⢀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⢠⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣸⣿⣿⣷⣼⣿⣸⣺⣾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢀⣼⣧⠀⣸⠀⠀⣾⣿⣿⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡺⣿⡇⠀⡏⠀⢰⣿⣿⣿⡟⣇⣇⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠼⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢆⣿⠅⢀⠀⠀⣸⣿⣷⣿⡇⣿⣿⠇
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣼⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⡀
⠀⠀⠀⠀⢠⡿⠲⡄⣀⣀⠀⢀⣤⣀⣀⡀⠀⣀⠤⠓⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⣽⣧⣤⡇⣧⣀⣾⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⡀⣀⠀⠁⠀⠠⠄⣀⠀⠀⢘⣿⣿⣿⡇⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇
⢀⣀⣤⡶⢿⣿⣿⣷⣿⣿⣿⡿⠛⠿⠿⣿⣧⣷⣤⡀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠉⠒⢸⣿⣿⣿⠇⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠈⢱⡤⢤⣥⣭⣭⣽⡿⠉⢻⣷⣟⣦⣴⣹⣿⣿⣮⣳⣶⣶⡀⢁⠈⠙⢿⡧⡀⠀⠀⠀⠈⢿⣿⣿⣿⣾⠛⠋⠉⠁⠈⠈⢀⠈⠛⠛⢿⣿⡇
⠀⣼⡇⠀⡖⠒⢺⣿⣧⣯⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⡋⠛⣛⣛⣙⣷⣾⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣟⠀⣠⣦⠼⠂⠙⢶⡷⢶⣒⣞⣉⣇
⢀⣿⡇⠀⣇⣀⣀⣉⣛⣉⣀⣀⣀⡀⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣾⠟⠁⠀⠀⢠⣿⣿⣿⡿⡿⠿⣿
⢘⣿⡇⠀⠆⠀⠀⠐⠆⠀⠰⠀⠀⠰⣷⠖⠲⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⡄⣾⣿⣿⣳⣿⣿⣿⣦
⠀⣿⡇⠀⠀⠀⠰⣆⠂⠀⠀⠀⠀⠀⣯⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⢿⠂⠀⡇⠀⣿⣿⣷⣿⣿⣿⣿⡿
⣠⣿⡇⠀⡀⣀⢀⣀⣀⠀⠀⠀⠀⣘⣟⡀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡄⠀⠀⢸⣿⣿⣿⣟⣸⡷⣾⡅⠃⣿⡟⣿⣿⣿⣿⣿⡇
⠟⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡇⠀⠀⢀⣿⣿⣿⣿⣹⡷⣏⣷⣴⣿⣽⣿⣿⣿⣿⣿⡇
⠈⣿⠃⠀⠃⠀⢀⡤⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⡇⡷⠀⠀⠘⣿⣿⢻⣿⣿⣃⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⡅
⠰⣿⡆⠀⡄⠀⠀⠉⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⣦⣭⣽⢛⣛⣉⣽⣿⣷⡇
⠘⣿⡇⠀⠓⠐⠒⠒⠒⠒⠒⠂⠐⢲⣿⠒⠒⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢉⣀⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡁
⢠⣿⡇⠀⣴⣶⣶⣦⣴⣤⣶⣶⣷⣿⣽⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣼⣿⣿⡄
⠈⢿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣇⣿⣾⣿⡿⣿⣿
⠀⠀⠈⠛⠉⠫⠿⢟⠻⠿⠿⡿⠿⠦⣤⣤⣾⣿⣿⣿⣿⣿⣟⣋⣱⣦⣴⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⢿⠿⢿⣶⣷⡀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣉⣈⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣉⣉⣛⣛⣇⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠶⣤⣄⣀⣀⣀⣠⣤⠴⠞⠉⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠈⠉⠉⠳⣤⣀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠉⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠋⠙⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣸⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸⠄⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣄⣼⠖⠋⠉⠉⢉⣀⢀⡤⣄⠀⠈⠉⠉⠉⠓⢾⣄⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⡟⠉⡿⠀⣼⠶⣄⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸⠃⢸⠇⢠⡏⠀⣟⡀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⣦⠀⢀⡟⠀⡿⠀⣼⠁⢸⠏⣹⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡆⣸⠁⢸⠇⢠⡇⠀⡞⠀⣿⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣧⡏⠀⠀⠀⠈⠁⠸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⠟⠉⠉⠛⠓⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⠀⠀⠀⠀⠀⣀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧



⣇⢸⠆⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠐⠒⠒⠒⠒⠒⠒⠐⠂⢾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⡇⠈⡆⡇⠈⠁⢠⢻⡀⡧⢼⢸⠀⠀⡇⠀⠀⠪⣄⠀⡇⠀⣅⡕⣸⠀⢱⢈⣖⠁⠬
⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣷⣶⣥⣧⣤⣤⣦⣤⣥⣷⣮⣼⣶⣤⣷⣦⣤⣴⣮⣤⣥⣤⣤⣼⣬⣶⣮⣤⣤⣥⣴⣦⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⣀⡴
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣄⣀⠙⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⠖⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣾⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠣⣶⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⢀⣼⡇⢀⡴⣿⠁⣠⠞⠁⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠰⠷⠚⠋⣹⠁⠀⣀⡀⠀⠀⠀⠀⠀⠘⠛⣶⡄⠠⣶⣟⡁⠀⠀⠀⠀⠀⠀⡴⠃⢻⣠⠞⠈⣷⠏⠀⢿⠞⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠋⣽⠃⣀⡀⠀⠀⠀⠀⠘⠿⣄⠀⠰⠚⠁⠀⠀⠀⠀⢀⡞⣡⣶⡘⠋⣠⣶⠀⣠⣤⠀⢀⣴⡇⠀⣠⠞⠁
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠰⡷⠊⡿⠀⠀⠀⠀⠀⠠⢖⡿⢛⡷⠚⠹⠷⠶⡄⠀⠈⠐⠃⠘⣧⠞⠁⢻⡶⠋⢿⣴⠋⠘⣷⠞⠁
⠀⠀⠀⠷⠶⢻⡇⠀⣀⠀⠀⠀⠸⡷⣻⠃⠀⠀⣶⢤⡏⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠉⠛⠳⢯⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⠷⠚⢻⣀⣤⡄⠀⠀⠋⠀⣠⠴⠾⠆⠀⠀⠀⠀⠀⠀⠀⣯⠴⣦⠀⠀⠀⠀⠀⠙⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠰⡧⠶⠂⠀⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⢾⠀⡴⠋⠙⢦⣀⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣲⠇⠀⠀⠀⠀⣤⣰⠛⣇⠰⣄⡀⣀⠈⠳⠇⠀⠀⠀⠹⡏⠓⢄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣴⠁⠀⠀⠀⢀⣠⠏⠁⠀⠈⠓⠛⠉⠉⠙⠒⠤⠦⡀⠀⣲⠟⠀⠈⢳⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠘⡆⠀⡶⠂⠈⠡⠤⠤⢤⣄⣀⣀⠤⠤⠴⠦⠀⠀⠓⠶⠛⢳⠀⠀⠀⢳⡀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢀⣤⣀⣰⡇⠀⡇⢠⡄⠀⢀⡠⠖⢊⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢳⡀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣠⠎⠀⠀⠀⣠⠞⠀⠈⠀⠙⠒⠻⣤⣷⠀⠈⠀⠠⣏⣠⠄⠀⠀⠀⠈⠁⠀⢠⣤⠜⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⣇
⠀⠀⠀⡴⠃⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⠴⣾⢻⠒⣦⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣠⠞⠇⠀⠀⠀⡿
⠀⠀⡼⠀⠀⠴⢯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠰⠃⠀⠘⠦⠔⠁⠀⣠⠞⠀⠀⠀⠀⣠⠴⠒⠉⠀⠀⠀⠀⠀⡼⠁
⠀⠀⣧⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⣀⡴⡞⠁⠀⢀⡤⠖⠉⠀⢻⢸⡀⠀⠀⠀⢠⠞
⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⡇⡏⠉⠉⠓⠲⠤⢄⣀⢸⡛⡛⠛⠛⠉⠀⢻⣴⠖⠉⠀⠀⠀⠀⠀⢧⢳⡀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠴⠧⠧⣤⠀⠀⠀⠀⠀⠈⠙⠃⢎⠢⠄⠀⢤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠣⣱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢶⣶⠒⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡋⣻⣿⣿⣿⣯⡥⣽⣿⣿⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠛⠛⠛⠛⢻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⣿⣿⣿⣧⡀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡽⢿⣿⣿⡿⣻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢺⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠆⠀⠀⠀⢀⡠⠄⠀⠀⠀⢀⡀⠠⠄⠀⠘⠁
⠀⠀⠂⠀⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠈⠢⡀⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠀⡀⠀⠁⠀⢀⠠⠂⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠘⢆⠀⢸⡆⠀⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠊⠁⠀⠀⡀⠐⠀⠉⠁
⠀⠀⣤⠂⠉⠳⠄⠀⣤⣾⡟⣃⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠈⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⣖⠁⠈⢳⡄⢠⡴⢛⠉⠀⣉⡁⢤⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢤⡀
⠈⢷⡄⠀⠙⢦⡀⢀⢳⡜⠈⠁⠎⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠓⠤⠤⣀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⢹
⠀⠀⠙⣦⠀⠈⠷⠋⠘⢷⣄⣀⣀⡴⠋⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠍⢻⠆⠀⠀⠀⠘⣷⡿⠿⠀⠀⡸
⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣤⣤⣀⠀⠲⢦⣄⠀⠀⡀⠁⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠈⠑⠶⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠈⠳⣦⣀⡈⢳⣰⣁⠀⠀⠀⡜⢀⠙⠻⣷⣶⣦⣄⣀⣀⠀⣸⡇⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠛⣀⣀⠤⠤⠖⠈⠉⠉⠉⠉⠛⠻⠿⣶⡶⠠⠂⠀⠀⠀⠙⠛⠛⠉⠀⢲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠋⢁⡤⠒⠀⠀⠀⠀⠀⠐⠢⡄⠀⠈⠙⢷⣄⠀⠀⠀⢀⡀⠤⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⣤⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢳⣦⡴⠋⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⡎⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⠀⠀⠀⠀⢤⡀⠻⠋⠀⠀⠀⡘⠿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡠⠤⡤⠤⠤⣤⢤⣄⣀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⢸⡇⠀⠀⠀⣠⣞⣛⣉⠑⠒⠃⠠⢶⣀⠀⢈⠙⢷⡀⠀⠀⠀⠀⣇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣰⠆⠀⠙⣾⡀⠀⡇⠀⠀⠀⠀⠘⡶⠚⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠁⢀⡴⠁⠀⠀⠀⢀⡼⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠛⠚⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⠤⢤⣀⣀⣿⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠖⠒⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡏⠉⠉⠉⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⣶⣶⣷⣿⣷⣾⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣷⣶⣾⣶⣷⣶⣶⣾⣷⣶⣶⣶
⣿⣿⣿⡇⠀⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠟⣋⣤⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢁⣶⣶⣦⣡⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⢃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡙⠻⢿⣿⣿⣿⣿⣿⣿⡿⢡⣶⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠈⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢋⣩⣤⣤⣤⣍⣁⠀⠀⠀⠀⠀⠀⠈⢿⣟⠻⣿⣿⣦⡈⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⢿⣧⣙⣿⡿⢿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⣿⣿⣿⡿⢋⣥⣤⣌⠻⣿⣿⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣾⣿⣿⣿⠆⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣼⣿⣿⣿⡟⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣸⣿⣿⣿⡟⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢰⣿⣿⣿⣿⠁⢿⣿⣿⣿⣿⠃⠀⠀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⣿⣿⣿⣿⣿⣿⣶⣤⣉⡛⢿⠀⠀⠘⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣌⡛⠻⢿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣴⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣉⡛⠿⠿⠋⡀⠀⢀⡉⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠙⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢀⣐⡂⡀⠠⡀⠀⠀⣀⣤⠀⠈⠂⠀⠠⠤⠄⠊
⠀⠀⠀⠀⠀⢉⠀⠪⢀⣘⠠⠃⠀⠀⠽⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠄
⠀⠀⠀⠀⠐⢶⡖⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣀⡀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠙⠋⠉⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠛⠻⠀⠀⠀⠀⠰⣶⠀⠀⠀⠉⡁⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠻⠀⠀⠀⢀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄⠀⠀⠀⠈⠀⠈⠀⠀⢶⣀⣀⣀⢀⣀⡀⢈⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠈⠉⠀⠘⠋⠩⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢄⣀⣄⣀⣀⣀⣀⣤⠶⠚⠶⡙⠋⠁⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⢶⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠑⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⣀⡤⢴⠊⠉⠓⠤⢤⠽⠶⡀⠀⠀⠀⠠⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠋⡟⠁⠀⠀⢻⡘⣇⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠘⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡤⠚⠀⠀⠀⠀⠈⢷⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠘⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⢀⠼⠃⠲⠶⠄⠴⠚⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠓⠦⠤⠤⠤⠒⠳⢄⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⣀⣀⣀⣀⡴⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢧⣀⡀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠉⠾⢛⡋⠉⠉⠉⠀⠀⠀⠀⠀⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠙⠓⠶⠶⠞⢛⡻⠁⠀⠀⠀⠀⠀⠀⠙⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠰⠀⠀⠀⠀⠁⠐⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣦⣤⣤⣤⣴⣶⣶⣤⣄⡀
⠐⢶⣶⣦⣤⣀⠀⠀⠀⠀⡏⠀⠀⢀⡤⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⢦⡄⠈⠹⣦
⠀⠀⠈⠉⠛⠛⠛⠀⠀⠀⢧⠀⡐⢁⡠⠤⢤⣈⠙⣿⣦⣄⣀⣀⣀⣀⡀⠀⠀⠈⣿⡆⠀⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠀⠀⠀⠀⠙⢷⣌⡙⠿⢿⣿⣿⣿⣿⣷⡄⢠⣿⣿⠀⣿⣷⣌⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠙⢿⣿⣿⠿⣿⣿⣿⣿⣿⡼
⠀⠤⠤⠶⠶⠄⠀⠀⠀⣾⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣵⠐⢻⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⡇⠀⡆⠈⡿⠛⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⡀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠙⢣⠀⠀⡇⠀⢸⠀⢠⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠛⠛⢢⠇⠀⠀⠈⠙⠛⠻⢶⣦⡀⠀⠸⡆⠀⠆⠀⡇⠀⢸⠀⠸⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⠞⠁⠀⠀⠀⠠⣄⠀⠀⠀⠀⠙⢦⠀⢧⠀⠘⣶⣗⡒⢺⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠛⠷⠶⡶⠆⠀⠀⠀⢸⡆⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⠀⢤⡀⠁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠈⡟⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢠⡇⠸⢛⡳⣤⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠻⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠦⢶⡶⠶⠖⠚⠛⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⢀⣨⣷⣄⠀⠀⠀⢀⣀⡤⠞⠋⠁⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⢸⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣲⣶⣶⣶⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⣀⣀⣀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⠿⠿⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⡄⣾⣿⣿⣿⣧⢠⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⢿⠁⠀⠀⠀⠘⡟⠛⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣾⣿⡿⠃⠻⣿⣿⣿⠟⠘⢿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⢀⣼⣄⠀⠀⠀⣰⣧⡀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣤⣤⣤⣬⣭⣥⣤⣤⣤⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠛⠛⠛⠛⠒⠛⠛⠛⠛⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀
⠀⠀⠀⠮⠏⠀⠀⢀⠀⠀⡋⠁⢀⠐⣔
⠀⠀⠀⠀⠀⡀⠐⠢⠳⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⢀⠁⠀⠀⠀⡰⠂⠉
⠀⠀⠀⠀⠒⠜⠀⠀⠀⠀⢀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠆⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠉⠃⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠴⠛⠓⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⡀⠀⠀⠀⡜⠔⠁⠀⠀⠀⠀⠱⣕⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠙⡄⠘⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢎⡞⠉⢐⢾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠥⠔⠦⣤⣤⣄⣀⡤⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠦⠤⠤⠼⠘⠇⣀⣁⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⡄⠀⡄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡅⠀⢠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣤⣤⣴⣶⣆⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠉⢿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣄⠉⠉⠀⠀⠛⠛⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⢀⠄⠀⠐⢸⣿⣿⣿⣿⡌⠀⠀⠀⠄⠀⠠⣀⠀⠀⢀⣀⣀⣤⣿⣿⣿⣿⣿⡆
⠄⠈⠙⡻⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣵⣿⠿⢛⠫⠁⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠋⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠈⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠟⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡖⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⢳⡈⠳⢤⣤⠴⠚⠡⢄⡀⠀⠀⠀⠀⡇⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⢧⠀⠈⢧⠀⠀⠀⠀⢳⡀⢦⠙⣄⠀⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⡆⠀⠘⣆⠀⠀⠀⠀⠃⠘⠂⠘⡆⠀⠀⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡠⠋⠹⡄⠀⠉⠉⠉⠉⠉⠉⠉⢳⡄⠛⠀⠀⡇⠀⠀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠐⢦⡰⠊⠀⠀⠀⠙⠶⠤⠤⢤⡤⠤⠤⠤⠾⠤⠤⠤⠤⠇⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠓⠲⠶⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣘⣆⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡖⠒⠒⠒⠒⠀⠀⠀⠒⠒⢺
⠀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠆⠈⠁⠧⠘⠀⠀⠈⠀⠐⠀⠉⠸⠀⠀⠀⠦⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣶⣄⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⢹⠟⣡⡆⢻⣿⣿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢿⠿⠟⣛⣭⣶⣧⣶⣾⣿⣷⣶⣶⣶⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⠀⠀⠀⢾⣿⣿⢫⣝⣿⡿⢿⣿⣋⡍⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⢻⣿⣦⣿⣿⣿⡌⢿⣿⣵⣾⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⣛⠻⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢦⠀⠀⠀⠈⢿⣿⢋⢸⢿⠘⡘⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡜⣎⢧⣅⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣰⡐⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣦⠻⣿⣌⡻⣿⡿⢟⣠⣴⣆⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⠟⣤⣶⣿⣿⣿⣿⣌⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡁⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇⣾⣇⣿⢸⠗⢯⣸⡯⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠈⠈⠉⠈⠉⠈⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⣤⣀⡀⢠⣶⣿⣿⣿⣿⣿⣷⣦⡀⢀⣠⣤⠤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⢀⣰⣶⣦⣭⣝⠻⠟⣫⣭⣴⣶⣷⣦⣤⣤⡄⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⢀⣾⣿⡿⠟⣛⣭⣶⣿⣿⣶⣬⣝⡻⢿⣿⣿⡟⠀⠖⠁⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠾⢛⣭⣶⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⠶⠀⠀⠘⣿⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡠⠆⢺⣿⣿⣿⣿⡿⣱⣶⣭⣛⣛⣛⢛⣭⣵⣾⣿⡷⠐⢦⡀⠛⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠈⣛⣛⢩⣵⢾⡿⣿⣿⣿⡿⠿⠷⣮⡍⣛⣛⡁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠀⢸⣿⣿⢸⣇⢯⣚⠎⣿⣿⠸⣩⢱⣸⡇⣿⣿⡇⠀⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣷⣶⣾⣿⣿⣷⣶⣿⣿⡷⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢸⣿⣿⠟⠿⣿⠟⠿⣿⣿⣿⡇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣷⣶⠀⠀⠻⣿⣿⣷⣶⣿⣷⣶⣿⠟⠀⠀⠀⢾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡀⠀⠀⠀⠈⠙⡻⠿⠿⢟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣷⣝⠿⣿⣿⣿⣿⡿⣫⣾⣿⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣝⣫⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠾⠛⠛⠛⠛⠻⠷⠶⣤⣄⡀
⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠉⠻⣦⡀
⠀⠀⢀⡾⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡇⠀⠀⠀⠀⠈⢿⡄
⠀⢰⡟⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠙⠊⠠⡒⡂⠀⠀⠀⠈⢿⡄
⢀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠺⣧
⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣇⣀⡠⠄⠀⢠⠊⠉⠐⡄⠀⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣿⠄
⣿⠉⠀⠀⠀⠀⠘⢄⣀⡠⠃⠀⠀⠠⡂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣀⣀⡀⠀⠀⠀⠀⠀⢠⠶⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⢀⣿⡀
⢹⡏⠉⠀⠀⠀⠀⠀⠀⠁⢀⡤⠒⠢⢄⠀⠀⠀⢀⠒⠦⠈⠁⠀⢸⡟⠙⠄
⢸⣇⠀⠀⠀⠀⠀⠀⠀⣰⢋⡀⠤⠀⠀⢧⠀⠀⠀⠲⠊⠀⠀⠀⣾⢇
⠀⣿⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⣸⡟⢺
⠀⢹⡇⠀⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠃⢀⣸⣙⡏⠀⢀⡿⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠖⠒⣄
⠀⠈⣿⠀⢹⡀⠀⠀⡀⢧⠀⠀⠀⠀⢶⡞⠀⠀⠁⠈⠁⠀⣼⣧⣄⠎⠀⠀⠀⠰⠰⠂⢰⠇⢹⡄⢀⣞⣡⡤⠖⠃
⠀⠀⢹⣇⣸⡧⠤⠀⠹⣌⠳⢤⣤⣴⠞⠀⠀⠀⠀⠀⠀⢀⣿⢼⠋⠀⠀⠀⠀⢀⣀⠴⠋⠀⣸⣁⡬⠥⠖⠒⠲⣄⠀⠰⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⣧⢤⡷⠒⠀⠀⠈⠛⠓⠛⣡⣴⠶⠿⠿⣿⠿⠿⠿⠿⠷⠶⠶⠶⠒⠚⠉⠀⠀⠀⠚⠋⠁⠀⠰⢀⣀⣤⣎⣠⣤⡤⠥⢤⡀⠀⠴⠁⠐⠁
⠀⠀⣸⡇⠰⠇⡎⢑⠀⠀⠀⠀⣼⣿⣿⣒⠒⠚⠴⠃⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠲⠔⠒⠋⠉⠉⠀⠀⣤⣤⣤⡖⠚⢁⣤⠴⢖⠲⢦
⠀⢀⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡯⠭⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠆⠈⠉⠓⠲⠧⠴
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠭⠥⠤⢤⠀⠀⠀⠀⢄⠀⠘⠂⠀⠀⠀⠤⠤⠄⢀⣀⠀⠀⠀⢀⠀⠉⠉⠙⠛⠛⠷⠤⣤⣀
⢀⡟⠀⠀⠀⠀⣀⠤⢄⠀⠀⠀⢿⣷⣖⣒⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠠⣠⡄⠀⠀⠀⠈⠉⠐⠒⠠⣤⠤⢠⣤⣤⣀⣀⣤⣬⠗⠀⢪⡵
⣼⡇⠀⠀⠀⠰⡁⠀⠀⡇⢀⠤⣸⣿⣄⣤⣶⡾⠿⠛⠛⠻⠿⢿⣿⣍⠉⠙⠛⠓⠦⢤⣀⠀⠐⠲⣦⠤⠤⠼⠂⠀⠀⠀⠀⠀⠀⠀⠐
⣿⠀⠀⠀⠀⠀⠙⠂⠊⠀⠰⠤⠃⠻⠿⠟⠁⠀⠀⠀⠀⠐⠲⠦⢬⣻⡆⠀⠀⠀⠀⠀⠈⠙⠲⣄⣸⠇⠀⠀⠀⠙⠯⣉⠉⢣
⣿⠀⠀⠀⠀⠀⠀⠀⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠀⠀⢸⣇⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⢻⡆⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⢀⠖⠁⢦⠀⠁⠀⠀⠀⣿⠀⠀⠀⠈⠁
⠘⣷⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡄⠀⠀⠀⠀⢰⡟
⠀⠙⣷⡤⠼⢷⡖⠒⠒⠂⠈⠀⠀⢢⡴⢮⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⠻⣦⣤⠛⠶⣆⡀⠀⠀⠀⠀⠟⠋⠑⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⠟⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⠟⠃⡀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡟⢉⡝⠀⠀⠀⢩⡟⠁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠉⠀⢰⠀⠀⠀⠀⠀⢠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣄⠀⢀⣽⣒⡠⢖⣢⣀⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⡏⠀⠈⠑⠋⢹⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠓⠦⣀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⢀⣼⣿⣶⣄⠀⠀⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⢻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠬⠭⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠉⠉⠉⠉⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣶⣶⣒⣒⣒⣒⣒⡲⠤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠛⠒⠒⠒⠒⠒⠒⠒⠲⠯⣵⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠂⢀⡤⠆⠀⠀⠰⢤⡀⠐⣇⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠇⠀⢈⣀⡀⠀⠀⢀⣀⡁⠀⢸⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣿⠀⢰⡋⠄⢹⡆⢠⡏⠠⠙⡆⠀⣿⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡟⠀⠀⠓⠶⠊⠀⠀⠑⠲⠚⠀⠀⢻⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇⠀⠀⠀⠀⢤⠀⠀⡤⠀⠀⠀⠀⢸⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢈⡷⢾⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠜⠁⠀⠳⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣀⣀⣠⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⣤⣄⣀⡀⠀⣀⣤⣤⣠⣾⣿⣿⣷⣶⣿⣿⣷⡄⢴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⠈⠉⢰⣿⣿⣿⣟⠋⣤⡙⣻⣿⣿⣿⣿⣟⠸⣿⣿⣿⣿⣦⠠⠴⠶⠶⠖⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡄⢠⣶⣶⣦⣿⣿⣿⣿⣇⣭⣨⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣶⣦⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣭⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⣴⣿⣿⣿⣿⠿⢟⡁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣶⣬⣙⡻⠿⠿⢟⣭⣙⣛⣫⣼⣿⣷⡝⠟⣛⣭⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⢛⣛⣫⣴⣷⣶⣬⣝⠛⠿⢛⣫⣭⣶⣾⠸⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢀⣽⣿⣿⣿⡿⢋⣼⠿⠿⣛⣛⣭⣥⣶⣾⣿⣶⣦⣭⣙⣛⠧⠹⢿⣿⣿⣿⣿⣷⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠷⠤⠀⣛⣛⣋⣭⣭⣥⡄⣶⣿⣿⣭⣭⣙⣿⣿⣿⣿⣿⣛⣭⣭⣽⣿⡇⣶⣶⣬⣭⣍⡁⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣟⡰⣿⣿⣿⣛⠛⣛⣿⣿⣿⣿⣿⣟⡛⢛⣻⣿⣿⢌⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡿⢃⣾⣿⣿⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠈⡛⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠈⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣬⣝⣛⣛⣩⣵⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢇⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠋⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⢿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠃⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣦⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡷⣿⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⠇⠛⠿⣷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⢤⣬⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠙⠙⠉⠉⠉⠉⠁