Venomous Snake Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠉⠁⣀⣀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⣠⣴⢊⡞⠋⢹⠯⢟⠷⣦⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠞⠁⠀⠀⠀⠁⠀⠀⠸⢷⡘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠚⠀⡐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢴⡧⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣠⡷⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⡄⢀⡿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⣀⣹⠇⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⢄⣽⠏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣤⡾⢉⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠃⡀⢱⡶⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠐⣤⡼⣫⣴⠟⠁⠀⠀⠀⡠⠤⠶⠶⠟⠛⠻⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢀⠈⡶⣯⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⢄⣀⢏⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⢟⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠓⢦⡼⠃⠀⢀⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢖⡪⠽⣛⣭⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⢀⡾⠃⠀⢀⣿⣿⢧⣄⣀⣀⣠⡤⠤⠔⣒⡫⠭⢒⣊⣥⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⠛⠛⠛⠻⡿⠓⠀⣠⣏⣿⣥⣀⣀⣀⣀⣀⣠⣥⣤⣴⡶⠿⠿⠛⠛⠛⠛⠛⠛⠻⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⡄⠀⠀⢰⡷⠀⢤⡾⣿⣿⣿⣿⣿⡿⠿⠟⠉⠉⠀⠀⠐⠂⠉⠉⠉⠉⠉⠙⠲⡄⠀⠘⡟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣿⣷⠀⠰⣿⣿⠈⠻⣿⣤⣤⣤⣤⠤⠤⠶⠶⠖⠚⠛⠛⠛⠛⣛⣿⢾⠀⠀⣠⢣⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⡤⣿⣿⡄⠀⠨⢛⠳⠶⠶⢦⣤⣤⣤⣤⣶⣶⣶⡾⠻⠟⠡⠀⠀⢀⣵⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣀⠀⠈⠁⠐⠛⠛⠛⠋⠉⠉⠛⠁⣀⣀⣠⣤⣶⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣭⣿⣿⡿⠟⠋⠙⠛⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡽⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣤⣀⣀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣯⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⢟⣵⣯⢾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠛⣟⣼⣫⣿⣝⣿⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⢿⣧⣿⣞⡷⣻⣏⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣯⢾⡱⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣫⣿⣆
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣴⢻⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⣶⠶⢶⠆
⠀⠀⠀⠛⠛⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢞⣫⢟⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣛⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡶⢛⡽⣫⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡶⢋⣵⢿⣾⣿⣦⣀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣳⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣟⣵⢫⣟⣻⢿⣿⣿⣿⣿⣿⣿⣯⡛⣿⣲⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡟⣼⢏⣿⢿⣿⢿⣿⣿⣍⣶⡿⣾⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠇⠿⢸⡿⠿⠿⠻⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠛⠉⠉⠛⠛⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣤⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣶⣦⣶⣶⣶⣶⣶⣶⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⠷⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣠⠴⣄⡀⠀⣉⢀⣚⠂⠐⠀⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣯⣞⠐⣠⡁⢼⡿⣧⣳⣤⢀⠀⢀⣶⣶⡅⣐⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣿⣿⣿⣿⣭⣿⣦⣭⣿⣿⣿⣿⣿⣧⣠⣿⣯⢿⣿⠈⠄⠋⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠓⢛⣞⣾⣿⣿⣿⣿⣿⡻⣿⣿⣫⣿⣿⣛⣿⣿⣿⣿⣿⡤⠀⣤⣾⢦⣴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣛⣴⠟⣿⣿⣿⣟⡙⣻⣿⣿⣵⣾⣿⠀⠡⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⢸⠟⠹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠟⠉⠉⠉⠉⠘⠛⠛⠿⣿⣻⣿⣿⣿⣿⣿⣿⠏⠠⠀⠇⡃
⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣽⣿⣟⣿⣿⣧⣼⣶⣶⡓⣇
⠀⠀⠀⠰⣿⡛⣿⣭⣽⣻⣿⣿⡛⣛⣿⡿⣿⣬⠻⣿⢿⢻⢿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠙⣮⢳⣿⣿⣿⣿⣿⣾⡟⢨⢃
⠀⠀⠀⠀⠻⠽⣟⣧⣍⣭⡭⠛⠶⠝⠉⢤⣾⣤⣤⣥⣤⡙⠛⢙⡻⣿⣿⣿⣿⣧⠳⣫⠍⢏⣋⣹⣷⢦⣄⡀⠈⢿⠿⠿⢿⣿⠿⠟⠁⠂⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠂⠩⢸⣿⣿⣷⣆⠻⢇⣿⣿⣿⣿⣶⠁⣸⣿⣿⣯⢿⣖⢈⣻⣷⣌⠣⢂⣢⣤⣤⣤⣀⣄⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢀⠚⣿⣿⣽⣿⣇⢠⡻⣿⣿⣿⣿⣶⣿⣻⣿⣿⡿⠧⠀⣡⣼⣿⠰⣿⣿⣿⡿⠱⢀⣻⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠈⠉⠁⢿⡈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣻⣿⣿⣿⣿⠀⠙⠟⢿⡷⠚⠟⠁⢪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠽⠇⢰⢿⣿⣿⣿⣿⣿⡟⠯⠯⣰⣿⣿⢿⣿⡟⣰⣾⣶⣾⣇⡐⠀⠀⣸
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣟⣻⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠉⠠⣿⣿⣿⣿⣿⣷⣘⠀⠹⣿⣿⣿⡿⠁⢻⣧⣿⡟⠉⢙⡆⠀⡄
⠀⠀⠀⢀⣴⡿⠫⠻⢿⣿⣩⣿⢬⣻⢽⣿⣻⣿⣿⣿⣿⣿⠷⣦⡀⠀⠀⣤⣿⢿⠿⡟⣿⣽⣿⣶⠀⠈⣽⠟⣡⣤⣤⣸⡟⠻⠶⠞⠁⠠
⠀⠀⢀⡾⣿⣑⡻⡿⣋⣛⠿⣉⡳⢿⣻⡻⠿⢿⣿⢿⣿⣿⣿⣿⣷⣤⡀⠘⣁⢀⢠⣾⣿⣿⣿⣿⢳⣾⣷⣦⣿⣿⡿⠿⣤⡀
⠀⠀⣼⣛⣩⣿⡷⣴⠆⠉⠀⠺⠋⠀⠉⣭⡝⢚⣿⣿⡽⣿⣿⣿⣿⣿⣷⣄⠀⢦⣌⣻⣾⣿⠟⠙⣿⢿⢿⣿⠛⢿⣄⣐⣨⡏⢠⠀⠁
⠀⢀⡏⡍⠭⠑⢳⠛⡁⠐⠀⠀⠀⣄⣀⡈⢀⠀⠊⠚⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⡛⠦⢎⣄⠔⠘⢿⣬⣧⣿⠄⠀⠉⣋⣁⡴⡀⠀⢀
⠀⢘⣁⠠⠀⢈⠀⠀⠀⠀⠀⣰⠂⠀⠈⠙⢶⣄⠐⣤⡁⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⣾⣿⢶⣬⣍⣅⢤⡴⠦⠀⢡⣤⣻⠇
⠀⢨⣩⠓⠀⡤⠀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠀⠈⠻⣉⠃⠀⠸⡿⡝⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣷⣖⡔⣻⡇⠂⠀⠀⠈
⠀⠠⠠⠜⠀⠀⠀⠀⠀⠀⢀⠨⣀⠀⠀⠀⠀⠀⠀⠈⢻⣜⡀⠄⠀⠠⠽⠻⣿⣿⣟⣻⣿⣟⡿⣿⡟⡻⠻⢷⡒⣾⡗⠀⠁
⠀⠀⢃⢰⠃⡀⠁⠀⠀⠀⡀⠔⢉⠛⡶⣤⣄⣀⣀⡀⣀⣈⣻⣾⣿⣆⢀⠉⠉⠿⠾⠚⣻⢷⣿⡿⠡⠔⡡⢋⠛⠉⠀⠀⡀⠀⠆
⠀⠀⠀⢾⠆⠀⠄⠀⠀⣀⢀⣠⣠⣤⣤⠤⣬⡭⣭⣭⣉⣉⡉⠉⠙⠿⢷⣶⣤⣤⣌⠀⠀⢀⠁⠈⠁⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣠⣼⣿⣿⣿⣷⣤⣿⢠⣿⠀⡤⢀⡉⠙⠶⢤⣀⣉⢙⡛⡿⢿⣿⣶⡿⠿⠥⠶⠚⠯⣤⣀⠐⠀⠂⠀⠀⠀⠂
⠀⠀⠀⢀⠒⠀⣤⠾⠻⣙⣏⠧⠿⠿⠛⠛⠛⠿⠿⣾⣷⣴⣏⣠⡄⡀⠈⠉⠛⠯⣉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡾⠁
⠀⠀⠰⠀⣤⠛⣈⠦⠛⠉⠙⠂⠀⢤⠂⣀⢂⣀⣠⠄⠬⠽⠛⠿⣶⣏⣰⠀⣀⠀⠈⠙⠒⢤⣄⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠐⠈⡠⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣾⣀⡆⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡷⠂⠓⣒⣒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣾⠋⢀⠻⣅⣼⡟⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⡿⠻⠉⠁⢀⡷⣯⣼⣿⣿⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠋⠡⠆⢀⣂⣼⣿⣿⣿⣿⠋⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠛⢉⢤⣼⣿⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⣿⣇⣄⢠⢚⣻⣿⣟⢸⣿⠁⠀⠀⠀⢀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠃⢀⣉⣙⢯⣿⣿⣿⣏⡀⠀⠀⣴⡿⠊⠁⠀⠀⢿⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣹⣿⢴⢬⠤⠇⠈⠞⣿⣿⣟⠁⣠⡾⠋⠀⠀⠀⠀⠀⣿⣦⣤⡴⠾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡘⠴⣋⡖⡤⣡⢷⢿⢚⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣄⣈⣉⠁⡈⠈⢙⣛⠒⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣏⠙⣿⣿⣿⣿⣿⣦⣬⣉⣁⡐⠆⠀⣉⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⣟⢻⣿⣷⣦⡻⠇⢠⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣾⣿⣿⣶⣶⣶⣄⣀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣌⡐⢈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣨⣿⣿⣝⡂⢣
⠀⠀⢀⣤⠶⠶⣿⠿⢿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣹⣿⣿⣷⡈⡆
⠀⣴⡿⣧⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡶⢦⣄⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⡏⠃⠱
⣸⡿⢿⣽⣿⣿⣿⡿⢿⣛⣛⠻⡿⠛⠿⣿⢿⣿⣿⡿⠟⠒⠉⠉⠀⣀⠀⣀⠀⠀⠉⠉⠛⠿⣿⡿⣣⡄⡇
⣿⣷⣿⣿⣿⣿⡟⢳⡋⠀⠀⠈⠙⠊⣷⠵⠖⠋⠁⣠⡄⣠⣶⣿⣿⣶⡦⢽⡶⣾⣄⢀⡀⠀⠈⢳⣉⡼
⠹⣿⣿⣿⣿⣿⣿⡠⠗⠂⠔⣒⡊⠉⡤⢰⣢⣾⣷⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣏⣱⠄⠀⠀⠸⠄
⠀⠙⢿⣹⣟⣿⠿⣿⣿⣿⣶⣭⣵⣾⣿⣿⣿⠿⠛⠉⠉⠉⠀⠿⠸⠇⠰⡆⠰⠎⠻⣿⡿⣷⡆⠀⠐⠶
⠀⠀⡰⠯⠛⠿⢷⣿⣿⣿⣿⣭⡿⢛⡿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡿⢃⡀⠀⣦
⠀⢀⡿⠇⣑⠃⠀⠀⠀⠀⠀⠁⠚⠤⠀⠈⠿⢿⣿⣏⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢨⡀⠰⠈
⠀⢸⡖⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠹⣿⣽⣿⣟⣳⣤⣄⣀⡀⠀⣀⣠⣾⣿⣿⣀⠠⢘⠁
⠀⠈⣧⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡐⠿⠙⣟⢿⣿⣼⣿⣿⣿⡿⢿⣿⠉⡠⡶
⠀⠀⠘⣷⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⣁⠙⠋⠿⠛⠋⠁⣀⣤⠚⠋
⠀⠀⠀⠈⠻⣷⣦⣍⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⢾⣦⣭⣍⡑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣮⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢦⣤⣾⠿⠁
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣛⠫⠼⠿⠿⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⠖⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣤⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣋⣛⣉⣡⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠭⠍⠉⠉⠉⠉⠉⠉⠩⣭⣽⣿⣿⣿⠿⠭⠥⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣅⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⡿⡁⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⣦⠤⠄⠀⠠⠔⠒⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⣀⣤⣴⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠏⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠉⣻⡟⠀⠀⠘⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣄⣠⣾⣿⡃⠀⠀⠀⠀⠉⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⡶⠤⣿⣿⡁⠀⠀⠀⠀⠀⠀⠤⠐⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣿⣿⣿⣿⣹⣿⣻⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡟⢻⠉⡏⡽⢻⢻⣿⣟⠟⣿⠿⣊⣷⡄
⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⠻⣀⠣⠈⢦⣡⣷⣸⣸⢰⠉⣷⡿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⡑⠢⠄⢉⡵⠟⠋⠉⠉⠛⣧⢿⣿⣯⣟⢶⣽⡇
⠀⠀⠀⠀⠀⢸⣿⣿⢿⡦⣉⠘⢒⡻⠁⠀⠀⠀⠀⠀⠘⢿⣷⣿⣟⣧⢻⣿⣦⣤⣄⣠⡄⣤⡤⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣗⠂⠬⠩⠇⠀⠀⠀⠀⠀⠀⠀⢺⣿⠿⣿⢼⡐⣿⣿⣿⢿⣿⣯⣦⣀⣀⣀⠀⢀⡀⠢
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣍⣀⣀⣱⡀⠀⠀⠀⠀⠀⠀⠰⣿⢷⣿⣯⣿⣾⣿⣟⣷⡿⠛⠞⣶⣯⣉⢿⡧⣿⡂⢀⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠤⠐⢓⡄⠀⠀⠀⠀⠀⠀⠈⠛⣦⣨⣬⣌⡇⢹⢿⣆⡇⣒⣦⣏⣋⣛⢤⣬⣥⠬⠖
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡍⠩⠥⢚⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠼⣄⡞⢿⣻⢸⡿⣿⠏⠁⠀⠨⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣆⣂⣉⡤⠋⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢬⡳⢬⣷⣼⣷⣤⠤⠠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿⣿⢳⡴⠖⠊⣠⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣽⣷⣬⣧⠀⠀⠀⠈⠹⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣎⠿⣿⣉⢁⡤⠋⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡢⡙⢧⡄⠔⠋⢀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣟⢶⣳⡖⠒⣁⡴⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣗⢿⣏⢉⣀⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢺⣿⣉⡁⣠⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⣿⣍⣉⣀⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⡿⣯⣿⠤⠤⠖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢾⣿⡟⠳⢿⡾⣯⡿⣾⡯⣴⢏⡿⠒⠒⠘⣯⣿⣧⣶⣄⣄⠀⠀⠀⠀⣼⢿⡇
⠀⠀⠀⠀⣠⡶⣿⢿⡿⣿⠟⣛⣡⣿⣯⢼⢮⣯⣿⠿⣣⣟⡷⠂⠒⢺⢷⣿⡿⠼⠾⣿⡿⣆⠀⠀⠘⢷⣿⣶⣦⣄⣀
⠀⠀⢀⣾⣿⣳⣿⣿⡾⣡⣾⢻⣿⠋⣵⣿⣵⣾⡶⣿⢋⣿⡋⠀⢙⣿⣿⣉⣿⣠⣶⡿⠳⢿⣇⠀⠀⠀⠈⠉⠛⠿⣿⣿⣦⡄
⠀⢀⠞⣼⡇⣿⣼⣏⣿⢯⣜⣧⣽⠿⠾⢻⣿⡓⣿⣳⣿⣯⠁⢀⡽⠻⣿⡿⠂⠃⣛⣱⢣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠹⣯⣹⡆
⠀⣸⠓⣿⡇⠸⣧⣽⣯⢸⡟⠁⠀⣀⡴⢋⣿⢱⡿⣋⡾⠦⢠⣔⣠⣴⡿⣿⣿⠛⣭⢇⢺⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢿⡇
⠀⣿⣷⡙⠿⠶⣠⠈⠁⠸⡿⣶⡟⣛⣴⠟⢡⣾⠟⣻⣉⡶⠟⠋⣱⠿⠿⠟⠿⠛⢉⣤⡿⢃⣤⡞⢛⣋⣹⣿⣿⣿⡼⣿⣿⣾⠃
⠀⢻⣌⣹⡖⢀⣼⡇⣰⢦⣀⣙⣛⣍⠑⠾⣻⣴⣾⡻⠉⣩⣟⣴⣾⣿⣟⢛⣿⡶⠞⠉⡰⠟⣿⣿⡿⢿⣷⠾⠿⠿⠶⠿⠛⠁
⠀⠘⡿⣿⣧⣾⣁⣰⠟⣲⢤⡞⠣⣭⢻⡿⡽⣰⣿⢿⠟⣹⣿⣾⣷⠿⠓⠋⠁⠀⠀⠀⢿⣼⣿⣯⠛⢶⡼⣷⣄
⠀⠀⠘⢮⣙⢿⣦⡸⣷⣉⣳⠶⣟⠳⣟⠄⣿⠛⢟⡲⣮⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⣷⣾⠛⣛⣽⣦
⠀⠀⠀⠀⠈⠑⠚⠷⠮⠯⠿⠶⠾⢷⣿⠈⠓⠀⣹⣴⡟⠽⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠿⣬⣁⠁⣢⡌⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣇⠺⣷⠶⠖⣶⣷⡞⢻⣟⠻⠏⡻⣿⣛⣿⡿⢿⣻⣟⡛⢿⣦⣿⣣⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡟⣤⢻⣶⢶⣬⣭⣷⠤⠾⣿⣼⡇⢻⠿⣥⣼⣋⣉⣿⠿⢶⡿⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡘⠃⠆⣤⣶⡶⠾⣷⣶⣦⣤⣀⣀⠘⣉⠋⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠺⠿⠷⠶⢿⣯⣭⡿⠿⠽⠿⠟⠛⠉⠁
⠀⠀⢀⡀
⣿⡿⣛⣛⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣧⣼⣷⣶⣶⣾⣶⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣤⡶⠶⠶⠶⠒⣫⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⣠⣤⣄
⠀⠀⠀⠉⠉⣛⣛⣛⣛⣛⣉⡉⢙⣛⣻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢺⣀⣴⠏⢀⣿⠆
⠀⠀⢀⣶⡿⠟⠛⠛⠛⠛⠉⡣⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠻⠿⣷⣶⣶⠿⠋
⠀⠀⠸⣿⣦⣤⣤⣴⡶⢤⠼⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣴⣶⠿⢿⣷
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢠⣴⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣤⣀⣀⣤⣾⠟⠁⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣴⣿⣿⣾⣿⡿⠿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠃⠀⠀⢿⣿⣿⣿⣿⣿⣶⣿⠿⠁⠀⠀⠈⠉⠉⠉⠛⢷
⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣥⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣩⣿⣿⣭⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀⠀⠀⠀⢻⣿
⠀⠀⠀⢈⣡⣶⣍⡙⢛⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⡼⢿⣿⡿⣿⣷⣶⣶⣦⣼⡟
⠀⠀⠀⠸⣿⣭⣭⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡫⢽⣿⣝⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢶⠛⢿⣿⡌⢝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡻⣛⠿⡿⢶⣾⣯⣿⢺⠀⢸⣷⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⢹⣏⠻⠿⣟⢻⣧⣰⠏⠀⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠾⠬⠿⠓⠋⠉⠙⠉⠁⠀⠀⣾⣿⣯⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⢀⣼⢿⣾⣿⡧⠁
⠀⣷⡄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠛⣹⣫⡿⢿⣿⣿⣶⡾⣝⢷⣯⡽⠃
⠀⠻⠷⠶⠿⢛⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡺⠋⠉⠛⢻⣦⣾⢫⣾⣟⣿⡟⠃
⠀⠀⢀⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢈⣽⣷⡾⣷⢿⣿⣤⣶⣤⣶⣤⣤⣤⣄⣀⢾⣛⠿⣿⣶⣶⣾⢿⣯⣾⢿⣯⠿⣯⡅
⠀⠀⣾⣿⠁⠀⠀⢀⡤⣶⣖⣒⣶⣄⠀⠀⠀⠀⠀⠀⠀⠴⣋⣵⢻⣷⣿⡿⠿⢿⣷⣿⠿⣿⣻⣿⣻⠷⣾⣏⣻⣿⡟⢷⣿⣾⣿⣷⣽⡿⢿⢳⣿⡏⣿
⠀⠀⢿⣿⣷⣤⣖⣿⢿⡿⠯⠿⣽⣳⣴⠦⠀⣀⣀⣤⠾⢊⢿⣽⣷⠟⠁⠀⢠⣮⣿⣽⣿⣟⣿⣿⢿⡿⣷⣾⣛⢦⡙⢿⣧⣬⣁⣈⣡⣤⣿⣿⣟⣖⣿
⠀⠀⠈⠛⠿⠿⠟⠛⠁⠀⠀⠀⠈⠻⣼⢧⣵⣯⣭⣴⣾⣻⣿⠟⠃⠀⠀⠀⣼⡜⣯⡻⡇⢸⣿⢇⣼⡇⠀⠉⠻⣿⣗⣷⣉⣿⠿⢿⣿⣭⣿⣤⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠿⠿⠻⠛⠉⠀⠀⠀⠀⠀⠀⠸⣜⠻⡿⠿⢟⡯⢟⡽⠁⠀⠀⠀⠈⠙⠓⠺⠟⠿⢶⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢰⡤⠶⠒⡦⠴⠖⣦⠤⡶⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢶⣶⣦⣴⢶⣦⣀⣠⣤⣤⣀⠀⣀⣠⣖⡏⠽⠩⡴⢨⠓⢒⠭⢗⣒⠏⡵⠠⣞⡲⣀⣋⣙⢗⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣣⣄⣙⡅⠻⣷⢶⣛⣿⡟⣯⣿⣻⣿⣉⣏⡹⣩⣿⣾⣴⣇⣾⢩⡒⣋⣬⠶⣍⡙⢤⡱⢤⠷⢬⢦⡙⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⢾⣿⣏⣿⣷⣤⣭⣉⣹⣛⣿⣉⣿⣭⣾⣿⠮⠟⠛⠛⠛⠉⠀⠉⠙⠛⠛⠒⠷⠶⣕⣆⣑⣊⡒⠣⡌⠚⢄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢿⠛⠛⠿⢿⣿⣿⣿⣾⠛⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣾⠼⣍⢢⡑⢆⠉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣣⣾⢋⡾⠋⣀⣠⠤⣤⠶⠖⠂⣠⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢬⠳⡜⡎⢃⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣼⣿⡿⣣⢞⡵⢫⠟⣹⣛⡵⠒⣊⣉⠳⠦⠙⢦⠛⣦⢴⣄⣤⣄⣀⣀⣠⣴⣟⡴⢛⡵⢙⠉⡛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣼⣿⣯⠗⢡⡿⢉⠖⣋⢵⣂⡶⣉⡑⢲⣛⠮⡉⠯⡉⠦⡓⢞⡒⣺⣺⠽⣺⡟⣖⣲⠆⠜⣣⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠉⠉⠀⠀⡏⣑⠻⠴⡡⣾⢏⣿⠿⣉⡳⡌⠶⡘⢲⣉⢲⣉⠦⣉⠧⢌⣛⠵⢏⡤⠥⠔⢛⣁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢷⠛⡼⢤⢳⡙⢎⣾⡿⠋⠁⠉⠛⠛⠧⣬⣦⡌⠲⠌⠁⠣⠤⠗⠉⢴⣊⡩⠗⠁
⠀⠀⠀⠀⠠⠤⠄⢂⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡓⢼⠲⣍⠧⢗⢿⣄⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠋⠓⠂⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡨⡒⢮⣱⠚⣭⢝⠻⣶⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢭⡓⠤⢇⡁⡌⢧⠥⠌⠦⣛⣏⣙⢶⡶⢤⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡝⢯⣦⠛⢬⠫⣙⣯⡹⢬⠖⣌⠲⣌⢲⣙⢫⣍⢻⣴⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠍⠛⡥⠬⣓⡲⢍⡵⠶⡶⢞⣒⣘⡲⣉⠯⡹⠬⡗⢬⠢⣜⠳⡄⢦⢈⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣡⠚⣱⣩⡕⢚⣥⡕⠲⣙⢢⠘⢦⠻⡙⣿⢾⡳⠞⠻⣌⣧⡜⢌⣛⣹⡘⠦⣙⠸⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⢂⢼⣩⠔⡶⣞⣭⣒⣮⣭⣬⠧⡼⠬⢭⣙⡞⠭⣿⢢⡀⠀⠀⠉⠻⣷⡖⣍⠧⣘⢦⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⡾⡸⡀⢎⣱⡾⠋⠉⠁⠉⠛⢶⣵⡘⡦⢣⣹⡛⡌⢧⢹⡳⣤⣀⣀⣽⡟⡬⢢⠟⡼⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⠧⠧⡓⢦⣻⡇⠀⠀⠀⠀⠀⠀⠈⠛⢩⣏⢣⠳⣬⢆⢲⡛⣚⡻⢟⣻⣟⣗⡩⠖⡡⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣄⠦⡝⡮⢙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣷⡛⢤⠻⢼⠧⣝⣻⠤⡎⠠⠇⣘⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡗⢧⣹⡖⢢⠫⡝⢶⠦⣤⣀⣀⣀⠀⠀⠀⠀⠙⠂⠩⣮⣍⠓⢚⡭⣩⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢞⣥⡘⢎⣳⣙⣎⣓⢤⡹⢬⠋⢝⣛⡓⣲⠶⡤⠄⣀⡉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢶⣞⠲⡖⠲⡌⠪⣍⠳⢄⠳⣎⠛⣥⡹⢍⡹⣑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠨⠷⢶⣓⣧⣘⠦⡝⠠⡙⢆⠣⡬⢥⡙⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠉⠙⠛⢷⣜⣆⡻⣵⡖⣄⢣⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣹⣒⡩⣗⢒⡭⡉⠯⠴⠶⠤⢄⡀⠀⠀⠀⢘⣿⣷⣲⣙⣆⣡⡸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢰⠋⣯⡐⢫⠶⢋⣈⠶⣜⠓⣍⢣⡉⢶⡙⢧⡶⢦⡟⢻⣿⡗⡧⢾⣰⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡸⢚⠴⣃⡯⣷⣿⠤⣛⢭⡙⠤⠶⠌⠂⢜⡒⠯⣵⢚⡥⠯⡽⠴⠊⡠⠯⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⡸⢻⢞⡥⣿⣿⠿⠟⠙⠛⠛⠖⠳⣎⣱⠦⣽⠒⢮⠉⢖⣉⡟⣉⣈⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⢹⡉⢾⣵⢾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠟⠂⠚⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⢻⢘⠯⣿⡻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠺⣈⡲⢍⣻⣿⣿⣷⣤⡀⣀⡀⠀⠀⣀⠀⣀⣀⣀⣤⣤⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢯⣙⡎⠣⠿⢼⠇⡾⢟⡯⢽⣛⡿⢿⣙⡯⡯⢿⣾⠾⠿⠺⠷⠿⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⣃⣉⣮⣱⠎⣹⢬⣕⣒⣭⣽⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠛⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣠⣴⣊⣙⡿⣷⣴⡢⣉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡠⠴⢶⣟⣁⣀⡀⠠⢤⣦⡔⠚⢉⠤⠈⢷⠀⣄
⠀⠀⠀⠀⠀⠀⣠⣶⣉⣉⣉⡉⠛⠶⣮⣙⠻⢶⣭⠶⣀⠈⠙⢦⣄⠀⠉⠉⠒⠉⠷⣤⣀⣀
⠀⠀⠀⠀⣠⠞⢉⣽⣧⡀⠉⠙⠻⢦⣄⡉⠛⠒⠶⠤⢼⠦⢱⣤⡌⠓⣊⣑⣓⡀⠖⠰⡉⠉⠉⠐⠠
⠀⠀⠀⣸⠋⢠⣾⢧⣜⡻⠶⠶⣶⢀⣼⡿⠷⣦⣤⣀⣀⣀⣀⣤⢤⣤⣍⣉⣡⣞⠛⣴⣏⣦⣤⣄⡀⢠⡀⠀⣄
⠀⠀⠀⣿⠀⣾⢏⣿⣙⡿⣾⣶⣿⠻⣅⠸⢆⡘⠄⠛⢙⣍⡅⢁⢸⠀⢹⢤⣤⣤⣤⡉⢸⣇⣤⡞⡻⣧⠿⣄⠀⠠
⠀⠀⠠⡧⢰⡟⢾⣛⣿⣹⣟⣿⡏⠳⠌⣙⡊⠱⢶⣿⣿⡿⠟⠛⠾⢤⣈⢠⡻⣦⣴⡽⣷⣍⣉⢉⣁⣋⣻⠂⠒⣀
⠀⠀⠀⣷⠈⣿⡄⠙⣷⢣⡟⣿⡉⠲⠦⠀⠀⣾⢻⣿⠋⠀⠀⠀⠀⠀⠙⣾⡅⣫⡞⢰⡿⣿⣿⠟⠉⠉⠛⠛⢛⠃
⠀⠀⠀⢹⡆⠙⢿⣴⠏⣿⡇⢹⣍⡐⠒⠀⢲⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠳⣸⣧⣼⣧⠀⠀⠀⠘⠀⠉
⠀⠀⠀⠈⢿⡀⠀⠹⠆⣿⣇⠈⡦⢌⣁⡓⣸⡇⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡘⢻⡉⠻⠂⠀⠠⠤⣄⡀
⠀⠀⠀⠀⠈⢿⡄⠀⠈⢻⣿⣄⢲⡆⠀⣤⣤⠿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢿⣶⡇⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠛⢦⣿⡆⠀⠀⠒⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⠀⠀⠀⠉⠹⣁⣀⣀⡀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠸⢦⡀⠀⠖⢁⡸⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠈⠳⣖⢂⣉⡠⠎⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡙⢧⣉⣀⡤⠟⠀⣹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣝⣤⣤⡤⠞⠁⢀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣽⢦⠐⠒⠉⢀⠿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣳⡆⠚⠋⢀⡼⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣽⡞⠉⠁⢀⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⣳⠒⠒⠋⢀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⢸⡷⠶⠶⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣷⠤⠴⠖⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠀⣤⣴⣟⠀⠆⢸⠶⠤⠒⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣏⠉⣿⣿⣶⠘⣿⣿⣿⣷⣿⠶⠶⠖⢙⣿⡿⠻⠶⢶⣀⡀⠀⠀⠀⠀⢠⣧⣼⡁
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣿⣯⡙⠿⠻⣿⣿⣿⣶⣿⡇⠀⢨⡿⣿⣿⣿⣿⣤⣤⡤⣾⣿⡗⢸⡷⢆⣘⢛⣳⣄⠀⠀⠈⢿⣭⣵⢦⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠞⣡⣤⣤⣯⣩⠀⣰⣶⣍⢹⣿⣿⣿⡇⢠⡿⣷⡮⠉⣹⡷⠤⠤⢴⣿⣧⠌⢤⣶⣾⣿⣿⣿⣿⣆⠀⠀⠀⠉⠙⠲⢿⣿⣿⠷⣦⣀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠈⢁⣴⠌⣹⣿⣧⣴⣾⣷⣄⠁⠀⣼⠗⠀⠰⣾⣿⣍⠿⣿⡟⠻⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣼⣿⣷⡀
⠀⠀⠀⢰⣿⣿⣿⡿⠏⠙⠿⣿⣷⣤⣾⠟⠛⠉⠉⣰⣿⣿⣿⣿⣿⣾⡟⠒⠐⠾⠉⢉⣿⣯⠅⢀⣤⣶⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢏⣇
⠀⠀⠀⣿⣿⠏⡠⠀⢀⣠⣤⠛⢿⣿⠁⠀⣀⣴⠛⣭⡉⠻⣋⡛⣤⣟⠛⢀⣿⣡⠶⣿⣉⣿⣷⣦⣝⠁⣀⢹⣿⠃⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣇⡸⡿
⠀⠀⠀⣿⣿⣄⠀⣶⣿⠏⠉⠀⠀⣹⣿⣿⣿⣿⡀⠛⠁⠚⠿⢣⣾⣥⠾⣿⡿⣿⡞⠻⠟⠿⢿⣿⡅⣸⣿⠞⣡⣴⢚⡛⠿⣯⡹⣿⢉⣽⣿⣯⣥⣾⡿⠁
⠀⠸⠀⣿⣿⣧⢰⣿⡇⠀⣴⣤⣤⠉⢻⣿⣿⣿⣷⣆⣀⣤⣶⣛⠻⠿⠾⠿⣂⠺⢿⠛⢿⣶⣨⣿⠷⠋⠁⣴⣯⡿⠟⠻⢷⣿⣷⠿⣽⣿⣿⣵⠾⠛⠁
⠀⠐⠀⠸⣿⡇⠈⣿⡁⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⢋⣅⡼⠿⠁⠾⠷⠾⣿⠁⣾⣧⠿⠛⠉⠀⠀⠀⠀⣿⡏⡀⢸⣿⠛⣿⣻⣦⡀
⠀⠘⠀⠀⠹⣟⠈⢿⣿⡀⠀⠀⠄⠈⠙⣿⣿⣿⡿⠧⢈⣿⡇⠸⣿⠂⣾⣆⡿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣸⣿⡿⠿⢿⣿⣿⣆
⠀⠐⠀⠀⠀⠈⠳⢮⣛⣻⣷⣤⡀⠐⢺⣿⣿⣿⠓⣀⣿⣿⠿⠂⠻⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣏⣀⣀⣾⣶⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠻⣿⣿⠿⠁⠠⢾⣷⣆⠙⣿⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣴⠖⠛⡛⠻⠿⣿⣿⡅⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠠⣼⣷⣤⣿⣿⣿⠿⠏⣀⣼⣿⣿⣿⡿⢿⣿⠏⣡⣴⣦⠀⠄⠁⠀⢿⣿⣿⣨⡾⠃
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⠠⣿⣿⣿⣿⠉⠠⠘⠻⠟⢻⣿⣿⡄⠈⣤⣴⣿⡟⠋⠀⠈⠀⢠⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣟⣿⣿⣿⣇⡀⠀⠀⠰⣾⣿⣿⡃⠈⠻⠻⠿⠿⣿⣷⡄⢀⣌⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⣤⣤⣤⣤⣿⣿⣿⣀⣴⣶⣶⣶⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣞⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢃⡁⠠⢹⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣾⢿⡇⠀⢻⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣴⣿⡶⠈⠹⣿⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣇⡅⠀⣙⢻⣷⣄⠀⠀⠀⠀⠈⡏⠀⠀⠀⠉⠀⣄⡈⡁⢿⠁⡄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠡⠋⡿⠄⠈⡃⠀⠀⣉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠕⠐⠉⣐⣄⣀⣀⠄⠀⠀⠀⣠⡀⠀⠀⠈⠻⣿⣿⣿⣿⣧⡀⠀⢀⣀⡀⢂⢀⣇⠈⢡⢳⡂⠀⢉⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠟⣨⡎⠀⢐⢂⠋⠘⠀⠀⣠⠆⠈⢿⣿⣿⣿⣿⡄⠁⠘⠁⢨⣍⣀⢂⣀⡇⠁⢲⠁⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠡⣬⠤⣴⠀⠀⣄⠀⢑⣰⡀⠀⠻⣿⠙⢿⣿⣆⠠⢦⡂⡴⠿⣯⡉⡣⠤⣼⣦⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠴⠀⠀⠆⠁⠀⢈⣀⣀⣀⣀⣁⡀⠁⠀⠀⠹⣿⡀⢿⣿⡄⠼⠾⢗⡋⠀⠙⢷⣆⡾⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢾⢟⠻⣟⢟⣋⣉⣛⣉⡛⣿⣶⣄⢻⣧⡉⣿⣷⠈⢀⠘⣤⣰⡛⡀⢻⣷⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣾⣿⣿⣿⡟⣿⡶⠀⠘⠁⠋⠛⠛⢻⣿⡿⣿⣯⣿⡏⣽⣿⡤⣤⣤⣀⡐⠓⠀⠋⠸⠏⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠾⣿⣿⠛⠁⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣇⢘⣿⡇⢤⣤⠍⠹⠳⣦⡀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣷⣾⢛⢿⣿⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡟⢸⣿⡟⠛⠛⢿⣷⣦⣿⣿⣤⣰⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠿⠿⠻⠻⠶⣶⣟⠀⣸⣿⣀⣀⣀⣤⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠿⠚⠚⢻⣿⣿⣿⣿⣿⣿⣿⣶⣷⣕⣼⡿⠁⢈⣿⣏⡈⢉⡁⠀⣿⣿⣿⣿⣼⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢻⣿⣻⣿⣟⠃⠒⠢⠤⠤⠀⠻⣿⣿⣿⣦⣀⣉⣽⣿⡿⠛⢀⣰⣾⣿⣿⣿⣶⣶⣿⣽⣿⡿⠿⠟⠛⠚⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⡀⠈⠋⠻⢿⣿⣶⣶⣶⣶⣤⣤⣼⣿⣿⣿⠿⠟⠋⠉⡅⣠⣾⣿⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠫⣶⣶⡄⣀⢀⠂⠺⠋⡘⠋⠉⡡⣌⢈⣀⣠⣴⣶⣾⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⢤⠶⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠳⢯⣿⣯⣏⣟⣟⣾⣾⡽⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣫⣐⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢛⠻⠭⢛⠻⠿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣦⣡⣾⠋⠉⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⣁⣽⣟⠙⢏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⡭⠁⠙⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⠃⠀⠀⣸⡟
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣼⡟⠏⢠⣴⣶⠟⠀⢀⣠⣴⠶⠾⠿⠿⣿⣷⣶⣦⡀
⠀⠀⢀⣴⣾⣿⡯⢉⣀⣰⣤⣬⣉⣙⣛⢶⢦⣤⣴⣾⠟⢷⣰⣿⡿⢋⣠⡴⢛⣩⣥⣤⣵⣦⣤⣄⡈⠻⣿⣿⣆
⠀⠀⣾⣿⣿⠀⣴⣿⣿⣯⣭⣍⣉⣙⣙⠛⣛⣽⣽⣄⣀⣬⡿⠿⢛⣻⣽⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿
⠀⢸⣿⣿⣟⢀⣻⠛⠛⣿⣿⣿⣿⣍⣉⣉⣤⣿⡿⣿⡿⠋⣠⣴⣿⠿⠋⣩⡴⠟⠉⠀⠉⠙⣿⣿⣿⢇⣾⣿⡿
⠀⠸⣿⣿⣿⣆⠩⢦⡀⠀⠀⠉⠉⠉⠉⠀⠀⢀⡴⣃⣤⡾⠟⠉⣠⡶⠛⠉⠀⢀⣀⣤⣴⣾⣿⣏⣵⢿⣿⠟⠁
⠀⢸⣿⣿⣿⣿⣶⣄⣙⣲⢤⣤⣄⣀⣤⡴⠚⣫⣴⣿⠏⢁⣴⠟⠉⢀⣠⣶⠿⠟⢛⣋⣽⣾⣿⣿⠷⠛⠁
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣦⣴⣶⣼⢿⢟⣡⡾⠋⠀⢀⣴⣿⠛⣩⣶⢟⣩⠽⠛⠋⠉
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⠿⢿⣿⣿⣭⣉⣴⠿⠋⠀⠀⢠⣿⣿⡟⢸⣿⡷⠋⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠈⠻⢿⣿⣿⢿⢿⠟⠿⠺⠚⠃⠛⠉⠁⠀⠀⠀⣴⣿⣿⣿⣿⡈⠻⢷⣶⢶⠶⠟⠛⢛⣉⣛⣟⡻⢷⣦
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢸⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣶⣿⠿⠿⠿⠿⠿⣿⣮⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠛⠋⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠛⠛⠷⣶⣤⣤⣤⣤⣶⣶⣶⣿⣿⣟⣻⠶⢤⢤⢤⣾⣳⡿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣿⣿⣷⣶⣿⣭⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⢿⣷⣿⣾⣷⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢤⡟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡿⠋⠉⠉⠉⠛⢿⣿⡿⣦⠀⠀⠀⠀⠀⠀⢀⣾⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣮⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⢐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⣹⢦⣀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠈⠛⢿⣿⣍⡳⣦⣀⠀⠀⠀⠻⣿⡿⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⣴⣻⠟⠛⠛⠿⣿⣷⣄⠀⠀⠀⠈⠛⠷⣧⣿⡓⣦⡀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⢨⢿⡏⠀⠀⠀⠀⠘⢿⢻⣆⠀⠀⠀⠀⠀⠈⠙⢷⣿⣟⣦
⠀⠀⠀⠀⠀⢾⣳⣀⠀⠀⠀⠀⠘⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⢻⡿⢽⣇
⠀⠀⠀⠀⠀⠈⠙⢽⣶⣤⡀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣷⡞⠛
⠀⠀⠀⠀⢤⣄⠀⠀⠉⠻⢿⣶⡄⠀⠹⡿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣯⠅
⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠹⣿⡄⠀⠹⣟⣛⢶⢶⣶⢾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⢀⣿⠁⠀⠀⠀⠙⠚⠮⠼⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡮⢝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣯⣥⣿⣿⣿⠛⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢶⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠛⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⢿⣿⣮⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⢻⣾⡿⠋⠉⠛⠛⠛⠻⢿⣿⣿⡟⣿⣇⠀⠀⠀⠀⣀⠴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⣶⣾⡅⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣮⣿⣦⣀⣤⣮⣁⣀⡀⠀⠹⣦⡀⢀⣠⠚⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣽⣿⢷⣄⣀⣀⠀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣦⡌⡛⠿⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣿⣩⣽⣷⣯⣟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠾⠟⠛⠛⠛⠛⠛⠛⠻⠿⣷⣯⣿⢻⣿⣿⡼⣞⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢤⣄⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣿⣻⣿⣟⣭⠏⡇
⠀⠀⠀⠀⢀⠄⢢⢚⣅⣋⣰⣸⢥⣜⣲⣿⣯⣭⣛⣿⠟⣲⡦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣮⣿⣿⣶⣶⠓
⠀⠀⠀⠾⡋⢦⡜⣗⣷⢽⣿⣿⣹⣷⣽⣷⣿⣿⣿⣟⣥⡯⢐⡟⣼⢩⡿⣖⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣾⢿⣏⣽⠃
⠀⡰⠃⠢⣹⣮⣷⣿⣟⠋⢹⣿⠀⢸⡟⠀⣸⡟⠙⣷⣿⣦⣿⣽⢷⡾⣼⣃⣿⡿⣿⢿⣿⣷⣿⣿⣿⢿⡏⢳⡵⠁
⠰⢏⡕⡐⢮⣿⣷⡟⢻⣦⡈⡻⠦⠘⠓⠠⠿⢀⣰⣿⠁⢨⡿⠳⣿⣷⣯⢾⡽⣿⣿⣿⢿⡾⣷⣽⣽⣷⠾⠋
⡇⠣⠮⣬⣿⣿⣿⣤⣀⣨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠃⠀⠿⠉⣹⡟⢒⣗⣺⣼⣮⠽⠞⠛⠉
⣧⠐⠒⢒⡼⣽⣿⣿⡍⣉⣄⡀
⠸⠓⣍⣉⣵⠿⢇⣻⡟⣿⣿⣴⣷⣲⣦⣤⣤⣤⢶⡶⢖⣒⢶⣿⣟⣿⢿⣻⣿⣽⣛⢿⣖⣲⣦⢤⣄⡀
⠀⠱⣟⢫⣥⢟⠯⢞⣽⡽⢩⣿⣹⣿⣛⣿⡿⣟⣯⣃⠉⡋⢥⣘⠩⠌⢥⣃⢸⣒⠌⡊⢕⣨⠁⢅⢩⠫⠶⠄
⠀⠀⠈⠻⣠⣿⢣⣾⢶⣗⣿⣮⢹⣛⡭⣗⣫⣭⠽⣆⣗⢲⡱⣞⣗⢻⠽⣖⣞⣗⣯⣿⣟⣶⣲⣨⠡⠍⠭⣐⢳⡄
⠀⠀⠀⠀⠀⠁⠚⠷⠿⠽⣏⣻⣻⡧⣟⣻⣬⣺⡯⣗⣻⡹⣯⡷⡾⠴⠎⠳⠛⠛⠓⠛⠂⢿⠻⣿⣥⡍⣐⠤⡚⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠀⢉⣁⣈⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡛⠉⢻⣷⡮⣕⠽⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢺⣧⠀⠘⣿⣇⠀⢸⣿⠁⢈⣿⠋⠀⣶⠂⣲⣇⠈⠙⢻⣿⣿⣿⣾⠹⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠿⣷⣤⣨⣿⣷⢶⣽⣿⢦⣴⣿⣇⣠⣿⣇⠀⣿⣇⠘⢻⣷⣤⣾⣿⣿⣿⠿⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠷⣶⡦⡟⣋⡉⠭⣥⣬⣿⠾⠿⠿⠛⠚⠛⠻⠿⠿⠿⣿⣿⣟⣻⣽⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣬⡕⡀⡆⣖⣿⣿⡁⢀⣀⣀⣀⣠⣤⣤⢶⡶⡶⡲⠶⣻⠷⠿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢧⢻⣷⣽⣜⢌⡟⣿⣿⣿⣯⡿⡟⣝⣿⣿⣿⣷⣼⣾⣶⣯⡿⡹⢘⠯⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡟⢫⣻⡿⢿⣿⣷⣯⣿⣿⣿⣿⣿⣿⡽⠿⠟⠛⠛⠻⢿⣿⣟⣆⡚⣽⣶⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠿⠿⠿⠷⠾⠟⠛⠋⠉⠁⠀⠀⣀⢀⣀⣀⣀⣴⣿⣿⢿⣽⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⢿⣿⢯⣿⢿⣻⣿⣿⣿⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣷⣽⣽⣿⣾⣿⣿⣻⣼⣻⣼⡲⣷⢺⣟⣾⡷⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠿⠟⠛⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣶⣶⣶⣾⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢄⠤⢲⠶⣚⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡦⠼⡀⢼⠝⢣⣾⠧⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⠝⢲⣏⣠⠒⢉⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣎⡼⣺⠓⣍⣠⣿⣿⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣖⣠⣫⢿⣡⣤⠬⣉⣛⠳⡾⢷⣶⣾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠴⣎⣸⣩⠟⠲⠤⠅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢠⣠⣍⣝⣝⢉⣐⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡀
⠀⠀⠀⠀⠀⠀⢈⣉⣽⣉⣏⣩⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⣑
⠀⠀⠀⠀⠀⠀⠸⠿⢶⣾⣷⠖⢒⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡄⠠⣀
⠀⠀⠀⠀⠀⠀⢈⡞⣶⡿⣾⣉⣩⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⢾⠉⢳⡀⠀⡆⠀⡿⠀⠷⠢
⠀⠀⠀⠀⠀⠀⠈⢧⡷⠶⢾⢻⡤⠒⢩⠗⡤⢀⡀⣀⠄⡖⠉⠷⡀⠀⣦⣨⡗⠲⣟⡘⢷⣤⣇⡠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠘⣴⢼⠾⡗⢿⠶⣁⡰⠁⣸⠀⢸⠀⢸⠀⠘⣵⠾⢻⡴⢟⣻⣯⣉⣯⢳⣼⡧⡜⢁⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡷⢼⣋⠳⡿⢷⣤⡇⠀⢉⡀⠘⢻⡗⢛⣶⣉⡹⢿⡄⣽⢳⣈⡟⣏⣷⡿⢋⠤
⠀⠀⠀⢀⣠⡴⢢⣭⢟⣻⣟⣢⣿⡯⣙⡶⢞⣘⣻⣤⠛⢲⡛⣱⡿⠖⠉⠉⠙⢦⣸⣾⠋⣷⣿⢰⣁⣷⣠
⠀⢀⡔⣯⠜⢛⡷⠆⠾⣯⣩⡿⢮⣻⣞⡓⢤⠟⠁⣤⣏⣭⣛⠉⠀⠀⠀⠀⣠⣞⣽⣸⠶⡇⣸⠋⣹⡿⠶
⢠⢊⢏⣼⠖⠙⡷⠒⢿⡤⣀⡹⣶⠒⠛⢯⠿⡟⠺⢯⡿⢶⡟⠙⢗⡒⢶⣋⣡⣞⣨⣯⡴⠋⡿⣾⣱⠗⡆
⡮⣹⠻⣉⢶⠚⡷⢚⡯⣤⣽⣶⣮⠓⢶⠚⢦⣈⣷⡖⠻⢦⡽⠶⢞⠛⠚⢧⣤⠏⢤⠞⢑⣿⡴⣩⡟⠗
⢇⣨⣾⢃⢠⣴⡗⢿⣰⣯⡀⠀⠉⠓⠦⣷⣄⣸⣦⣈⣶⠤⣽⡶⠤⣽⡛⠚⢷⡖⠋⠙⡯⠚⣻⡿⠁
⠸⡤⠚⢧⣹⡦⢷⠜⢶⠷⣿⣶⣲⣶⠶⡿⢾⡷⣦⣌⣲⣤⣐⣳⠦⠴⣿⣋⡉⣺⣏⣤⡴⠞⠋
⠀⠱⣖⢋⡼⠉⣶⠛⢿⠯⡿⢼⠛⢿⠙⢷⡀⢻⠄⠙⣍⣱⠶⢝⣿⠖⠾⣧⠾⠓⣿⠁
⠀⠀⠈⠙⠠⢞⠁⢀⠆⢠⠀⢸⠀⢨⡀⣸⠧⠴⠒⠉⠁⠀⠀⠀⠈⠁⣎⣁⠴⠊⢹⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠀⠚⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠤⠤⠴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠤⣶⡦⡤⣤⣀⡀⠀⠀⠀⣀⣤⠾⡑⠦⣔⣶⠏
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠙⢿⠛⠋⠉⠉⠉⠛⠛⠿⣾⣯⣿⣽⣹⣬⣦⣵⡶⠛⠁
⠀⠀⠀⢀⣀⠐⠚⣤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⣤⣤⣬⣯⣴⣶⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣤⠀⢀⢀⠀⠀⠀⢠⠀⠀⠀⡀⡀⠀⢰⠀⠀⢰⠀⢀⠄⡄⠀⠀⣀⣆⣀⠀⠠⠤⠄⠀⢸⢀⢻⡆
⠄⣯⠐⠐⠈⠀⠀⠻⠿⠿⠀⠀⢀⠀⠃⢸⢸⡖⢸⠀⠁⢀⡀⠀⠀⠻⠛⠛⠀⠀⢨⡈⠁⢸⠸⢿⡇
⠀⠗⠀⡰⠏⠀⢀⠀⠀⡀⣀⠀⠀⠳⢄⢸⠀⠐⢸⠀⡠⠞⠀⢀⣄⠀⣀⠀⣆⡀⠀⠛⠄⣸⠀⣻⡇
⠀⠋⡀⣄⠀⠐⠹⠁⣿⡆⠹⠋⠀⢠⠄⢈⠁⠁⢉⡀⢠⠄⠀⠙⠋⢸⢹⠀⠓⠁⠀⠤⠂⢌⠉⢹⡇
⠠⠩⠀⠀⣀⣴⡆⢠⣏⢧⠸⣶⣄⡀⠀⠀⠑⠀⡢⠀⠀⣀⣴⡾⠁⠾⠼⡆⠹⣷⣄⣀⠀⠀⠕⢸⡇
⠀⠀⡴⠿⢿⡟⠠⡇⠠⠸⡇⠸⡿⠿⠷⠄⠀⠀⠀⠰⠿⠿⣿⠁⢸⠀⠀⢻⠀⢹⡟⠛⠳⠄⠀⢸⡇
⠠⢄⠀⠀⠀⠁⢸⡇⣦⠠⡇⠀⠁⠀⠐⡔⠲⠀⠔⡔⠀⠀⠉⠀⢸⢰⡖⢸⠀⠀⠀⠀⢀⣄⠒⢸⡇
⢀⠊⠁⠀⠴⠀⠸⡇⠀⠀⡇⠀⠰⠆⠀⠀⠁⠀⠈⠈⠀⠰⠆⠀⢸⠀⠀⢸⠀⠀⠲⠆⠀⠀⠁⣸⡇
⣷⢘⣦⠀⡀⠀⣌⡓⠒⠘⣃⡀⠀⠀⣠⡖⢰⢻⠀⣷⡄⠀⠀⢠⣍⠀⠂⢉⣠⠀⠀⠀⣠⡇⢰⣿⡇
⢿⡀⠉⢀⠠⢤⠈⣿⡿⣾⡏⢰⠄⣀⠙⠁⣼⡼⡄⠉⠁⡀⠤⠄⠹⣿⢿⣿⠋⠴⠄⡀⠙⠁⡼⣿⡇
⠀⣷⠀⢀⢀⠀⠀⠈⢡⠉⠀⠀⡀⡁⠀⢸⠄⠀⢾⠀⠀⡀⡀⠀⠀⠉⡄⠁⠀⢀⠀⡁⠀⢸⠄⣿⡇
⠄⣿⠐⠁⠈⠀⠀⠻⠿⢿⠀⠀⠀⠀⠂⢸⢰⡤⢸⠀⠂⠂⠁⠀⠘⢿⠿⠿⠀⠀⠀⠐⠂⢸⢰⣼⡇
⠀⠗⠀⡰⠏⠀⢀⠀⠀⡀⣀⠀⠈⠳⡀⢸⠀⠀⢸⠀⢀⡼⠁⠀⡀⠀⠀⠀⡀⢀⠈⢦⡀⢸⠀⢽⡇
⠀⠋⡀⣄⠀⠐⠻⠁⣾⡆⠹⠛⠀⢀⠤⠘⠒⠒⠚⠀⢅⡀⠀⠺⠟⢰⢺⠀⠿⠒⠀⢀⠀⠚⠒⢺⡇
⠠⡉⠀⠀⣀⣴⡆⢠⣭⣧⠰⣦⣀⠀⠐⠈⠢⠀⠎⠁⠀⠀⣠⣴⠂⣸⣸⡄⢲⣤⡀⠈⠀⠉⠢⢸⡇
⠀⠀⡴⠿⢿⡟⢀⡇⠀⢸⡆⠹⡿⠿⢦⡀⠀⠀⠀⣠⡶⢿⣿⠃⢰⠀⠀⢷⠀⢻⣿⣷⣦⡀⠀⢸⡇
⠠⢄⠀⠀⠀⠁⢰⡇⣦⢀⡇⠀⠁⠀⠀⡠⠤⠀⡤⡠⠀⠀⠉⠀⢸⢠⣤⢸⠀⠘⠁⠀⠀⠠⡤⢸⡇
⢀⠊⠁⠀⡴⠀⠘⡇⠁⠀⡇⠀⠰⡄⠀⠉⠂⠀⠐⠙⠀⢠⡄⠀⢸⠈⠁⢸⠀⠀⢤⡀⠘⠑⠀⢸⡇
⣷⢘⣦⠀⠀⠀⣘⡃⠒⠘⣃⡀⠀⡀⢀⡆⢠⢾⠀⣦⡀⠀⠀⢀⡺⠂⠆⠺⠀⠀⠀⠀⢀⡄⢠⣾⡇
⢻⡀⠉⢀⠠⢤⠘⣿⣶⣾⡟⢠⡄⠀⠛⠃⣸⣸⡀⠙⠃⠀⣠⡈⢻⣶⣦⣼⠟⢀⡀⠀⠿⠃⣸⣿⡇
⠀⠃⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠁⠀⠐⠀⠀⠳⠀⠀⠁⠀⠀⠀⠛⠈⠋⠀⠁⠀⠃⠀⠠⠉⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡄⠀⣴⣯⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣂⡀⠁⠀⠀⠉⠛⠛⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠻⣿⡿⠓⣸⡇⣴⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣒⣲⠿⠭⠭⠭⣟⣛⣽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣭⣭⡍⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣭⣶⣿⣟⣛⣿⣛⣿⣷⣄⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣫⣾⣿⣝⣃⣿⣿⣿⣿⣿⣿⣿⡿⢷⣌⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣼⣿⣯⣽⣿⣿⣿⣿⡟⠷⢸⣿⣿⣧⡀⠹⣷⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⢱⣿⣿⣟⣂⣿⣿⣿⣿⣷⣿⠿⠿⠿⢿⣷⣼⣧⠁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣼⡜⢿⣿⣿⣿⣿⠿⠋⣡⣴⣶⣶⣶⣽⡪⣽⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣬⣭⣥⣖⣷⣾⡟⠉⠀⢨⢙⢿⣿⣾⣿⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠁⢸⣿⣿⠇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣭⣶⣶⢏⣉⡉⢦⡀⠀⢀⣠⣾⡿⠋⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣯⣴⣿⣿⣿⣿⣿⣿⠿⠟⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣛⠉⠉⠉⠀⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡄⡤⣘⣁⡀⠀⢄⡤⡞⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⡈⢀⠋⠐⠋⢣⡭⣤⡾⠁⢀⣀⠨⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠲⠀⢶⡰⣤⠅⠃⣦⡗⢀⢂⡤⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠹⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⢉⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠙⠄⠃⠸⣧⠘⠢⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⢻⡶⠓⠆⠀⠋⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢀⠺⠃⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⡄⠀⡀⠀⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠈⠂⠀⠀⠀⠀⣼⣅⠂⠀⠼⣄⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠁⠰⠀⠀⠀⠀⣀⠄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠴⠚⡤⠀⠄⠀⠀⡀⣠⠄⢸⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡇⢀⠳⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠠⠞⠠⢶⣦⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⣈⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠒⠀⢠⠀⠀⠀⡀⠊⠀⠀⠐⠂⠈⠀⠀⠀⠀⠑⠀⠆

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

⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣻⣽⣾⣽⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⡇
⣿⣺⣿⣿⣿⣟⣷⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁
⣿⣜⣿⣿⣿⣿⢟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠛⠛⠛⠛
⣿⣿⣷⣯⣯⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡰⠊
⠀⠀⢠⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⣶⣶⣦⣤⣶⣦⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣀⣀⠀⠀⡀
⠀⠀⠀⢠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐
⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠉⠉⡭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸
⠀⠀⡶⢴⣤⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠋⠨⠕⠀⠘⠔⠬⠓⠳⠀⠀⢸
⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣸⣇⣠⣶⣿⣶⡄⣤⠀⠀⠀⢸
⠀⠀⣴⡶⣶⠠⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣤⢏⣹⠿⠿⠇
⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣾⠟⠛⠛⢿⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⣀⣀⣀⣘⣋⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⢂⠀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠠⠄⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⠀⠁⠀⠀⠘⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠂⣄⠀⠀⠀⠀⢠⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠆⠀⠀⠀⢀⠀⠈⢄⠐⠂⠐⠂
⠀⠀⠀⠀⠀⠀⢄⠻⡇⠀⠀⠀⡸⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠔⠀⠀⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠈⠐⠂⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⡀⠀⠀⡀⠀⠐⠀⠀⠄⡀⠐⠄⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⡀⠐⠉⠀⠀⠀⠀⠰⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠅⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣈⠒⡑⣂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⡿⠇⠿⠿⠅⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⣰⠀⠠⡄⡄⢀⠗⢃⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡉⠋⠐⢠⡀⠀⠀⠀⠀⠀⢀⡀⠛⠊⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠖⠖⠀⠀⢇⣁⠀⠀⠀⠀⠀⡐⡱⠀⠀⠀⠀⠀⠐⠴⠀⠀⠀⠀⠀⠊⡁⠀⢀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠁⠀⠁⠀⠀⢒⡄⠀⢸⠀⠀⠀⠀⠀⠁⠀⢀⠊⠁⠙⡀⠀⢀⡇⠀⠀⠀⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠸⠁⠀⠀⠀⠀⠀⠨⢴⠀⢈⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠁⠀⠂⣠⠀⠀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠀⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡇⠀⠡⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⡊⡂⠀⠀⠒⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠉⠁⠒⠪⠀⠀⣰⠃⠀⠀⠀⠀⢆⡀⠀⠉⠒⠊⠉⠀⢠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡡⢄⡀⠀⠀⡠⢎⡘⠀⠀⠀⠀⠀⠐⣈⢄⠀⠀⠀⠀⡠⢆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠅⠨⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⡇⢈⠀⡡⠌⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠿⠻⠿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣶⣦⣀⣙⡛⠽⠿⢖⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⠋⠟⠋⠿⣟⣷⣦⣤⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢾⡔⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⣶⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠉⠉⠉⠁⠈⠉⠉⣹⣷⣍⡓⠠⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⠁⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣉⣀⣀⣀⡀⢀⡀⢀⢀⣀⣀⣤⣶⡾⣽⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣗⣾⣧⢟⣾⣿⠛⣟⢹⣿⣿⣧⣿⣿⣿⡿⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠀⠉⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⣀⠠⣤⢶⡟⢿⣝⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢀⡀⢸⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠃⠀⠀⠈⠀⠀⠀⣈⠥⡓⠏⢟⣿⣿⣿⣿⣧⠀⢀⣤⣶⣶⣶⣦⣤⡄⠀⢳⣤⣾⠁⠀⠀⠳⣄
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠻⢃⠀⠀⡠⠂⣰⡚⢧⡐⣬⣶⣿⣿⣿⣿⢿⠃⣴⣿⣿⣿⣿⣿⣿⣿⡷⠒⢻⣧⡈⣷⣿⣿⣦⢹⣷⡄
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⣿⠅⠀⠀⠈⣙⣷⣿⣷⣟⣿⣿⣿⡏⠀⠘⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⢿⣿⣿⣿⡿⣸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⢀⡀⢀⢴⣿⣻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠘⢿⣿⣿⣿⣯⢿⡯⠜⠀⠀⠀⢠⣿⣿⣿⠻⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣄⠰⣿⣷⣵⣿⣿⡿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⠤⠌⠉⠙⠛⠋⠀⠀⠀⠀⣠⣿⣿⢿⠦⠇⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⠜⢿⡟⣡⣤⣤⣤⠶⣠⡶⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣛⡘⠂⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣼⣶⣿⣾⣯⣿⣣⣿⣿⣿⣿⢫⣶⣦⡤⢤⣤⣄⠤⠀⠀⠀⢸⣿⣯⣿⠇⠁⠀⣀⡼⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣹⣿⣽⣿⣿⣳⣶⣦⣤⣤⣤⣼⣷⣾⣭⢿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⡌⠙⠛⠛⠋⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⢻⣿⣿⣍⡉⣿⢻⡿⢿⠿⡿⣿⢿⡖⠖⠉⠰⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⠻⡏⠹⠻⢷⣶⣧⣬⣀⣅⣘⣀⣁⣀⣤⣾⣿⣿⣿⣷⣄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢻⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠛⡻⠟⠿⠿⠿⠙⠛⢦⠙⣿⣿⣿⣿⡆
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠧⢦⠀⡤⠄⠀⠀⢀⣴⡿⣿⣿⣢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢶⣄⠀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣿⣶⣿⣿⡿⣿⣗⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣶⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠙⠿⣍⣉⠀⠉⠉⠉⠉⠁⠀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠈⠙⠛⠛⠶⠶⠶⠒⠚⠉
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠚⠻⠛
⠀⠘

⠀⠀⠀⣀⡤⠶⠖⠒⠲⣄
⠀⡤⠞⠉⣀⣀⡀⠀⠀⠉⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠘⢷⣦⣌⢉⠈⠀⠀⠀⢀⠜⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠋⣉⢉⠉⣉⣉⣉⣉⡤⠋
⠀⠀⠈⠉⠛⠓⠒⠒⠺⣧⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢦⠽⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠻⢄⣀
⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⣏⠀⠀⢸⡉⠉⠛⠛⠒⠒⠶⠤⣄⣘⠻⣦⢄⡈⠉⠛⠒⠲⠦⢤⣀⡀
⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢧⡅⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡙⠛⠿⢶⣤⣄⣀⠀⠀⠉⠲⣄
⠀⢠⡞⠁⠀⠀⠀⠀⠀⣀⣸⡦⠀⠀⠈⢷⣒⣖⣲⠤⢤⡀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠉⠛⢷⣦⠀⠀⠈⠳⡄
⠀⡿⠀⠀⠀⠀⠀⢠⣮⠟⠋⢻⡆⠀⠀⠀⠉⠳⢬⣉⣛⣮⡆⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢹⡄
⢰⣧⠀⠀⠀⠀⠀⡧⡇⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇
⠈⣟⣆⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⣸⠃
⠀⠹⣟⣆⠀⠀⠀⠀⠀⠉⠙⠳⠶⢤⣤⣀⣈⣉⠉⠛⠛⠛⠛⠉⠉⢀⣀⣀⣠⡤⠶⠛⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠈⠯⣓⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠈⠳⢭⣓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢒⣮⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⢭⣽⣓⣲⣒⣶⠤⡤⠤⡤⢤⠤⠤⡴⣒⣖⣒⣯⡭⠷⠞⠛⠉⠀⠀⠀⠀⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠉⠉⠉⠉⠒⠦⣄
⠀⠀⠀⠀⣀⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⡞⠁⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢶⠉⠉⢩⠉⠓⣄⠀⠀⢣
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⠞⢣⠀⠠⡇⠀⢸⠀⠀⢸⡄⠀⢸
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⡇⠀⠀⠀⢀⡾⣁⠀⠈⡇⠀⡇⠀⡌⠀⢠⢾⠁⠀⡌
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡇⠀⠀⢀⠎⠀⠈⠳⣄⢸⠀⡇⡸⢁⡴⠃⡎⢀⡼
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣧⢰⠀⠀⠀⡞⠀⠀⠀⠀⠈⠦⣳⡷⣷⣋⣠⡞⣠⠋
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡹⠀⠀⣠⡇⣶⠸⠀⠀⠀⡗⠒⠒⠒⠒⠒⢒⡺⡷⢬⠳⣮⠞⠁⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⢰⠃⠀⠀⠀⠀⠀⣠⠶⡅⠀⡔⢁⡠⠞⡱⢡⠇⠀⢇⠀⠀⢇⠀⠀⠀⢀⠔⠉⢠⡧⣾⢷⡼⣆⠀⠀⠀⠀⢀⡴⡏⠀⠀⢣
⢀⡏⠀⠀⠀⠀⢀⣜⠁⠀⢣⣸⣖⣉⣠⡜⣡⠏⠀⠀⠘⢦⡀⠈⠓⠦⠤⠯⠖⣚⠭⠊⠀⠀⣇⢸⠀⠀⠀⠀⣾⢰⠁⠀⠀⠀⠑⢄⡀
⡸⠀⠀⠀⠀⣠⠋⠀⢉⣩⢕⣿⠓⢴⣫⠔⠁⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠉⠀⢀⣠⠤⠤⡟⢰⠓⠲⡤⢼⣴⣾⠀⡴⠂⠒⢦⠀⠙⠦⡀
⡇⠀⠀⠀⢰⠗⠚⠉⢉⡴⣊⢾⠷⣴⠋⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⢀⡤⢴⠇⣸⠒⠠⢧⣀⣈⡟⠀⢇⠀⠀⡸⠀⠀⠀⠈⠲⡄
⢧⠀⠀⠀⠘⢤⣤⠴⠟⢊⠕⠋⠀⠈⢦⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠞⠁⢀⠎⢠⠃⠀⢠⣟⡭⡻⠁⠀⠀⠉⠉⠀⢰⠊⠉⠑⡄⠈⢦
⠈⢦⣀⢀⣀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠈⣇⠀⢱⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⡼⠁⠀⢠⠎⣠⠏⠀⠀⡞⢉⠔⠁⠀⢀⠤⠢⡄⠀⠘⠦⣀⠴⠃⠀⠘⡆
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢳⠀⠀⠀⠀⠀⠀⣼⠀⢸⠁⢀⡴⢃⡴⠁⠀⠀⠀⣏⠁⠀⠀⠀⠘⠤⠴⠃⠀⠀⢀⠖⠓⡄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢇⠀⠀⠀⠀⠀⡇⠀⢈⡴⠋⣠⠎⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠢⢤⣀⠀⠀⠀⠈⠢⠜⣁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⢆⠀⠀⠀⠀⢧⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⢆⠀⠀⡠⠋⢀⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⢳⡜⠁⡴⠻⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⡎⠀⣾⡀⠀⠱⡄⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠶⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⡸⠀⠙⢦⠀⠙⣄⠀⠱⡄⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⣀⣀⣀⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⠷⡄⠀⠀⠳⡀⠈⢆⠀⠱⡀⠀⡴⠋⠀⢀⡠⠖⠋⠁⠀⠀⠀⠈⠳⣄⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠘⢆⠀⠀⠹⡄⠘⡆⠀⢧⡞⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⠉⣧⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠳⡀⠀⠙⡄⢳⠀⢸⠀⢀⡞⠀⠀⠀⠀⡠⠴⠲⠾⣉⣉⣉⣈⡇⠀⣿⠉⣉⠒⠭⡙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠹⡄⠀⠹⡞⠀⢸⢀⡎⠀⠀⠀⠀⢸⣖⠒⠲⢤⣤⠖⠒⢩⠋⠉⣇⣠⠤⠟⠒⠛⠢⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢱⠀⠀⠀⠀⠘⡆⢀⡇⠀⡇⡼⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠑⠒⠚⠒⠉⠁⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⣇⠀⠀⠀⠀⢘⡞⠀⡼⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⡄⠀⠀⣠⠎⠀⣼⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠹⣀⠜⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣡⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⣠⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⢍⣁⠽⠁⠀⠉⠹⡛⠛⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠙⠻⣦⣀
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢈⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠈⠉⠲⢤⡀⠀⠀⠈⢄⣨⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⣿⠀⠀⢄⣀⡠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡇
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠒⠲⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣧
⠀⠀⠀⠀⠀⠹⣧⡖⠒⢆⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠤⢀⠤⣀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⢿⡄⠀⠳⠄⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣥⣀⣈⠆⠀⠀⢆⡈⡹⢷⡄⠀⠀⠘⣷⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡍⠑⡙⢧⡀
⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⢦⣤⡀⠀⠈⠙⠳⣤⡀⠀⠀⠉⠀⠈⢿⣆⠀⠀⢻⡇⠉⠳⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⠁⠈⠻⣦
⠀⠀⠀⢀⣴⠟⠁⠀⢀⣀⠔⠀⠀⠙⠷⣤⡀⠀⠀⢻⣆⠀⠀⠀⠀⠸⣿⡄⠀⠈⣿⡀⠀⡠⠤⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⡜⢷⡀
⠀⠀⢀⣾⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠐⠈⠻⢶⣤⣾⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⣧⠀⠣⣀⡔⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢻⡄
⠀⠀⢸⠇⠉⠉⠀⠀⢠⡴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣿⠁⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠖⠦⡀⢿
⠀⠀⢹⡄⠀⠀⠀⠀⣿⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⡇⢸⡇
⠀⠀⠘⣇⢐⠀⠂⠀⢹⣄⡀⠀⠀⠀⠈⠙⢷⣦⣄⣀⣀⣠⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆⢀⣀⣀⡀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠈⠀⣿⠇
⠀⠀⠀⣿⠀⠈⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⡀⠈⢡⡀⢀⡉⠁⣤⣤⣤⣤⣴⠾⠋⠀⡴⠲⣼⡟
⠀⠀⠀⣿⠀⠈⠆⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠁⠀⠙⠚⠁⠀⢀⠀⠀⠀⠀⠀⢱⡾⠋
⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠐⠉⠉⢂⣀⣤⡾⠋
⠀⠀⠀⠀⠹⣦⣲⡆⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⢂⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⣭⣭⣭⣭⣁⡉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡎⣿⣿⠿⡉⣵⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢺⣿⡞⠓⣿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⠟⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡄⠀⠉⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣵⣤⠀⠀⠀⠛⠃⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⣿⣿⡷⠒⠀⠀⠀⠀⠀⠤⠄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣶⣶⣶⣶⣴⣦⣤⣶⠤⢶⠶⠶⠞⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢶⠄⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡤⣿⣿⣿⣿⢿⣿⡗⢾⢷⡸⠿⠛⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣧⣿⣿⡟⣁⠸⢿⣷⣶⠈⠛⣠⣶⣿⠇⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⣿⣿⣿⣷⣦⣉⠻⣿⣿⠿⣋⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣿⣿⣿⣿⣿⣿⣿⠷⢈⣅⠚⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⣿⣿⣿⣿⣤⠀⢠⣾⣿⣿⣿⣦⡍⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣱⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠛⣿
⠀⠀⠀⠀⠀⠀⢀⠀⡀⣠⣄⣤⣠⣤⣤⣤⣼⣧⢸⣽⣿⠿⣿⣿⣿⣿⣶⡶⠦⠤⠐⢿⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠱⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣷⣶⣶⣶⣶⣆⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣭⣉⣉⣉⣉⣉⣁⣀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠛⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠭⣒⠒⣿⣽⣾⣷⠿⢿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⢌⣉⣉⠉⠀⠴⠚⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠃
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⢿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡶⠶⠶⠟⣛⣛⣻⣻⣻⣿⡷⣦⣄
⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⡿⢿⠿⢛⠛⣛⣻⣭⣥⡤⣶⣷⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⢿⠿⠿⠿⠟⠛⣚⣊⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠛⠛⢛⠛⠛⠛⠻⠿⢶⣶⣶⣶⣶⣶⠶⠟⢋⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⣀⣤⣔⣴⣿⣾⣿⣶⣟⣦⣶⣦⣴⣤⣠⢤⠄⢠⣤⡴⣯⠿⠁
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⣠⣴⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠘⠛⠚⠃⠉⠁
⠀⠀⠀⠀⠀⠀⣼⣿⢡⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣟⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡛⣋⣵⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣷⡎⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⣛⢩⣦⠿⢛⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠻⣿⣿⣗⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⣦⠉⠛⠿⣿⣶⣦⣤⣤⣤⣤⣶⣶⣿⠿⠛⢋⢁⡲⣼⣞⣻⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢱⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣂⡄⢀⡀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⣹⣿⣯⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢣⣔⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠤⣤⣅⣔⣄⣤⣦⣴⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢡⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⣁⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣮⡿⣭⣭⣤⣶⣷⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⡛⠿⢛⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢿⣟⡭⣷⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠼⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣭⣭⠀⣡⣤⣭⠽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⠂⠀⠀⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠘⠃⠀⠀⢸⠆⡀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠾⣓⡲⠤⠤⠤⠤⠤⣶⣋⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠓⠶⠦⠤⠤⠤⠤⠤⠶⢶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⠂⡅⠀⠀⠀⠀⠁⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⢑⠀⡒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠆⠠⠀⠀⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣶⡏⢛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⢀⠀⠀⢀⣀⡠⠤⠤⢈⣉⠉⠉⠉⠙⠋⢹⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠸⣿⡇⠀⠀⡴⢉⣀⠀⠀⠀⠀⠈⢳⡀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⡇⠀⠰⡇⣿⣿⣷⠀⢰⣾⣶⡄⢳⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠀⠳⣍⠛⠁⠀⠘⠿⠿⢃⡜⠀⠀⠀⢸⣿⣻⣿⣿⣿⣽⡇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠠⡀⠈⡇⢰⡶⣴⡆⢰⠋⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣿⡇⢰⠁⡈⠒⠙⠋⠙⣋⡙⠚⠀⠊⢸⡀⠀⢸⣿⣷⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣇⠀⢄⡀⢀⡉⠅⠒⠊⠭⢛⡀⠀⠙⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⢿⣷⣦⣵⣉⡀⠀⠀⠀⠀⢀⡈⠣⣈⠁⠀⢸⣿⣿⣿⣿⣿⠟⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡉⠻⠿⣿⣿⣿⣿⣶⣶⣾⣾⣶⣶⣶⣶⣿⣿⣿⠿⠛⢁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣌⣉⣉⠉⠛⠛⠛⠛⠛⠛⢉⣉⣁⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⠿⠿⣿⣿⠿⠿⠿⢿⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡂⠈⠀⠀⠀⠀⠀⠉⠁⠀⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠂⠀⠀⠀⡶⢶⡆⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠘⠏⢸⠃⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⣿⡀⠀⢰⠆⠀⠀⣬⣄⣾⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠻⠿⠿⢷⣶⣶⣶⣿⣶⣿⡿⠿⠿⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡶⣶⣶⣶⣤⣤⣤⣶⣾⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠤⠛⠛⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢈⣉⣉⡡⠀⠲⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠘⠋⠉⠀⠀⠀⠀⠙⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣮⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣿⡿⢋⣼⣿⠁⠤⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠙⣿⣷⡔⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣟⠁⢮⡍⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣿⣿⣮⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣿⣿⣶⣦⣥⣄⣐⣒⣒⠒⠂⢀⣀⣒⣒⣀⣀⣀⣁⣤⣼⣿⣿⠛⢻⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇⢸⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⠿⠛⡡⢮⡙⠻⠿⢿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⡡⠒⠂⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠒⠒⠒⠬⠭⣍⡻⣿⣿⠸⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⡟⢰⠃⠀⣀⡀⠀⢀⣤⣤⡀⣷⢠⠞⠳⢀⡴⣤⣠⡀⢀⣹⡾⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⡇⣿⠰⣿⠉⠻⡆⣼⢁⡈⡇⣿⠈⠳⡄⣸⣇⢸⣿⡇⢸⣩⡆⣿⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢿⠀⢠⡏⢻⡌⢩⡇⣿⢠⣀⡽⢿⡇⣸⢻⣇⢸⠀⢰⣿⡆⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢸⡷⠋⠀⠈⠛⠛⠁⠉⠀⠉⣀⠈⠛⠋⠾⢸⣇⠀⣼⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⡇⣿⠀⢸⣇⠀⠀⠀⠀⡠⠂⠈⠉⠈⠉⠻⣄⠀⠀⠘⠋⠸⠛⣿⡇⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⡜⢱⠃⠀⠘⠉⠀⠀⠀⣰⡅⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠙⣾⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⡌⣧⠀⠀⠀⡤⣄⠀⠛⡇⣴⣷⠀⠰⣿⠇⡿⠀⠀⢀⠀⠀⣼⢡⡎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢸⣧⢸⡀⠀⢰⠁⢻⣄⠀⣆⡀⠁⢴⡦⠀⠀⠀⡀⠀⣸⠀⠀⢻⣿⣧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢸⣿⢸⡇⠀⠀⠙⠣⢌⣑⠮⣉⠣⢤⡤⢆⣠⣈⠀⠈⠁⠀⢼⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣼⣿⠀⣧⠀⠀⠀⠀⠀⠀⢉⠲⠯⣐⠺⠷⠍⢀⣀⠀⠀⠀⡸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣇⠹⣄⠀⠀⠰⣌⣀⢀⡰⠞⠉⠉⠓⢦⣄⣠⡿⠀⣠⢃⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⡯⣿⣿⣷⣌⡙⠢⢄⣀⡉⠋⠁⠀⠀⠀⠠⣤⣌⠭⠤⢘⣡⣾⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣇⢻⣿⣿⣿⣿⣷⣶⣶⣬⣍⡓⢦⡴⠊⣩⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣍⣉⡛⠛⠿⠿⠿⠷⠶⠶⠶⠶⢾⣟⣛⣋⣩⣽⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠶⠶⠶⠶⠒⠚⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡶⢿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⣿⣍⣤⣿⠰⣎⣿⣿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⡟⡛⠟⠛⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⢁⡡⢼⣻⡴⠏⢑⣦⠙⣾⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢉⡐⠂⠁⠀⠈⠤⠀⢹⣿⣦⡀⠀⠀⠀⣀⣼⡿⣡⣤⠒⢇⠑⡴⠛⢠⡤⠛⠈⣠⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠐⠄⠀⣠⠆⣁⣤⠃⢈⠰⢘⠻⠿⡷⣾⢿⠿⠋⢶⠑⣆⢳⣤⣿⡟⢰⡟⠁⠀⢀⣥⣼⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠡⠄⡀⠉⠑⢷⣄⠙⠢⡘⠈⠄⠡⠚⡠⢊⠷⡜⡺⢋⡟⠛⣾⣿⣳⣼⣧⣴⢾⠋⣡⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⣊⠸⢒⠡⠛⠲⣬⢷⣾⡶⣶⣐⣚⣂⣨⡷⠿⡤⣞⡡⠽⣿⠛⠻⣷⣿⢴⠏⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣄⣀⠰⢸⢿⠉⢳⡿⠿⠿⠽⠖⠛⠘⠓⠛⠷⣶⣉⠶⣶⣾⡿⣟⠄⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡆⣀⠶⣏⣁⠼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⠾⠟⠋⠀⠀⡏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠀⣾⠇⠀⠒⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠐⠒⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣴⣿⠇⣼⠋⣠⣤⡉⣭
⠀⠀⣀⣴⣾⠿⡟⢻⠻⠟⠻⡛⢛⠿⡛⠛⠿⠿⡿⢿⣛⡽⠛⠉⠉⠡⠀⠀⠸⡈⠗⠠⡀
⠀⣴⡿⠏⢙⠲⢀⠂⠑⣈⠠⠥⣬⣤⣡⣈⣄⢡⣠⠞⠁⠀⢦⠀⠀⠀⠇⠀⠀⡃⢸⠀⡍⠲⡀
⣸⡿⠃⠃⠈⠀⠀⠀⡀⠾⠛⢓⠀⡏⢙⠏⣤⠞⠉⢂⠀⠀⠈⢇⠀⠀⢸⠀⠀⠁⠘⢀⠇⢀⠻⡄
⣿⣏⠀⢀⠀⡀⠀⢸⣀⢀⡖⠉⠉⢉⡽⠋⠁⡀⠀⠀⡄⠀⠀⠸⠀⢀⣸⡤⠤⣇⣸⡘⠀⡜⠀⣠
⣿⣯⠐⡀⠀⢣⡀⢡⡀⠈⢧⠤⡆⠉⡄⠀⠀⡇⠀⠀⡇⢀⣀⡴⣛⣁⣃⠐⡀⠀⠈⠁⢞⡠⠖⢉⠂
⢻⣿⡌⠀⠀⠀⠙⠦⡹⣄⣀⡔⠁⢀⠇⠀⢀⣇⣀⣤⣿⣿⣿⠿⠟⠛⠻⣿⣆⠄⠐⠀⠺⣥⠀⠺
⠘⣿⣷⡀⠨⠠⠐⡠⠀⡀⠀⠑⠲⠚⠖⠒⣏⣵⣾⠿⠛⠉⠀⠀⠀⠀⠀⢹⣿⠀⠁⠋⠠⢷⠤⢾
⠀⠈⠻⣿⣶⣬⣉⣄⣃⣔⣠⣦⣦⣼⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠐⡉⢠⡼⠲⠆
⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⣛⣩⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠿⠛⣉⠂⠄⡅⢁⣦⡷⠎
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⢙⠩⡉⠏⠉⡹⢉⠏⡹⢁⠆⡰⢀⠢⠑⠦⠉⠀⠀⢬⡷⠋
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠉⠄⡁⠂⣁⣀⢀⣀⣁⣈⣀⠁⠀⠀⠁⠀⠀⠀⠀⠀⣈⠴⠋
⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⡠⠶⠬⡛⢛⣋⣩⣭⡽⠶⣾⣷⣿⡲⢶⣶⡐⠋⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣂⣐⠀⡧⠤⠐⣉⠉⡉⢹⠀⡇⠀⠆⠀⢠⠉⠳⣏⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣂⠓⢤⣔⢁⣀⣄⣼⣴⠷⣶⣤⠔⠃⢀⡀⣽⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉⣁⣠⣴⡗⠓⢀⣉⣁⣠⣣⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⡋⠹⣄⠑⣤⢤⣾⣟⣋⣉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠑⠲⢠⡟⠁⠿⠿⢟⣛⣛⡻⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠈⠓⠒⡀⠓⡤⠶⡞⣻⡉⠟⢿⣦⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣭⣤⡊⠥⠚⠉⠁⠀⠀⢀⡜⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣛⣯⣯⣿⣉⣛⣛⣁⣀⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣼⠟⠉⠉⠉⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢿⣄⣀⣀⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠿⠿⠋⠁⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⣍⡻⢭⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⢶⡾⡿⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣾⢯⣿⡟⣦⣤⣤⣤⣴⣶⣾⣟⢿⠛⠋⠛⠋⠈⠈⠁⠁⠛⠏⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠊⢹⣿⠿⣫⣤⠉⠉⠙⠛⠙⠉⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠍⠁⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⣤⣾⠁⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠩⣽⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠽⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⢚⡟⣟⣟⣻⢿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡿⢿⡷⢶⣶⣶⡶⣶⡿⠛⣋⠉⠀⠀⠀⠐⠉⠉⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣄⠀⠀⠂⠠⢏⡎⡈⠀⠁⠀⠁⠀⠀⠀⢀⣀⣠⠤⠴⠖⠒⠛⠹⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⠻⣦⣤⣄⣀⣁⣁⣀⣠⣤⣤⣶⣶⣿⣿⣥⡀⠀⠀⠀⣀⣴⣶⣶⣬⡻⣿
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣿⣿⣿⡀⣀⠀⠻⢿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣿⡿⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⡏⣴⣷⣿⣿⣿⡟⢟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣧⠀⠀⠹⢿⣿⣿⣿⠿⠟⠁⠀⠈⣰⣿⣿⡼⢿⣿⡿⠈⢢
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢰⣿⣶⣴⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣻⣇⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⣾⣄⠀⣾⣷⣿⣿⡿⠋⠀⣀⣠⣄⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠛⠋⠈⠁⣶⠦⣤⣤⡏
⠀⠀⠀⠀⠀⢠⡟⣿⣿⣷⣾⣿⣿⣿⣶⣶⣾⣿⣿⣿⡟⣷⣶⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⢸⡇⢻⣿⣿⡇⠀⠉⠉⠉⢹⢫⣿⣿⣿⠟⠯⠛⠛⠛⢻⣿⣿⣿⡶⢲⠀⠋⠘⠀⠉⠙
⠀⠀⠀⠀⠀⠀⢿⡀⠛⣿⣿⣶⣤⣄⣀⣠⣷⣾⠟⠋⠀⣠⣶⣿⣿⣶⣦⣝⠹⠛⣾⡐⠂⠘⠊⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠛⠙⠛⠛⠋⠃⠁⢀⣠⡴⠟⠑⠇⠱⠄⠠⠘⣈⣳⣦⡀⢻⣶⡞⠚⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠶⠚⠛⣏⠁⠀⠀⠀⠀⠓⠀⠈⠀⠒⠀⠞⠻⣆⠘⣿⣄⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⠹⣷⣄⡸⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣠⣤⠤⠴⠶⠖⠒⠒⠒⠲⠦⠤⠤⠷⠮⠛⠿⠶⣶⣶⣶⡶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣲⠶⢮⡅⠂⢀⣡⣤⣋⡉⠉⠀⠰⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⣿⣷⣶⣿⣭⡒⢢⡅⠲⣿⣻⣦⣷⣤⢄⡰⢀⣷⣿⣎⢀⡲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣭⣿⣿⣿⣿⣽⣿⣷⣮⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⡆⠫⠘⡙⡓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⠿⠶⢢⠾⡿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠐⠈⢃⣴⣷⣤⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢺⣫⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⡿⢿⡿⢯⣹⠿⣿⣿⣿⣿⠛⣿⣷⣿⣫⣽⣾⣷⠸⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠟⠛⠛⠛⠓⠛⠶⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣽⡇⢈⢸⡕⢦
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣷⣴⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢭⣿⢿⣿⢿⣿⣏⣄⣮⣤⣤⠷⣤
⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡟⡾⣹⣿⣿⣿⣿⣿⡿⣿⢉⠆
⠀⠀⠀⠀⢻⣷⣮⣟⠛⠻⠿⢿⣿⣶⣶⡿⠋⣙⣛⣋⡳⠟⠑⣯⣿⢿⣿⣿⣿⣿⣿⣿⢛⣿⢿⢶⣲⡦⢤⣄⡀⠀⠀⠘⢯⣿⣿⣿⣿⣿⣿⣿⡏⡈⢺⡀
⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠛⠉⠉⠈⠀⠀⠘⠻⢟⠟⢿⣿⣿⣦⣄⠈⣭⣿⣿⣿⣿⣿⣧⠘⡟⣡⣽⣶⡶⣾⣋⢻⣶⣄⠈⢯⢉⢋⡹⠻⠉⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠅⣀⢾⣿⣿⣿⣷⡌⠛⣿⣿⣿⣿⣿⣇⢳⣿⣿⣿⣿⣽⡯⠀⠮⠿⣿⣌⣡⣴⣿⣷⣟⢟⠶⣶⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠬⠹⠟⢷⣾⠿⣷⢸⡮⣻⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣓⣣⣴⣾⣿⣧⠹⣿⣿⣿⡯⣈⣤⡴⢋⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠀⠂⠂⢻⡆⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⣸⣿⣿⣿⣿⣏⠀⠘⠙⣛⠟⡉⠛⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣻⣿⡿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠈⠹⠷⣰⡿⢟⣿⣿⣿⣿⣿⡿⣯⠭⢼⣿⣟⣿⣿⣿⢣⣾⣷⣾⣿⣤⣅⡀⠀⡱⠆
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢄⠀⠀⠀⠀⢀⠁⣾⣿⣿⣿⣿⣿⣷⡌⢈⠘⣿⣿⣿⣿⠋⡀⠿⣦⣾⡏⠀⠙⡧⠀⠠
⠀⠀⠀⠀⣰⣯⠿⠽⠿⣿⣟⣹⣿⢮⣗⣎⣻⣝⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢤⣟⢿⡿⢿⢻⣿⣿⣿⣶⡐⠀⣽⠿⢃⣤⣤⣤⣼⠟⠻⠷⠞⠃⠠⠆
⠀⠀⠀⣼⢷⣿⣚⣛⡓⣋⠛⢟⣹⡳⣾⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣦⡀⠘⢯⣱⡄⣴⣿⣿⣿⣿⣿⢷⣶⣷⣦⡹⣿⣿⡿⣷⣄⠀⠀⠀⡐⠈
⠀⠀⣸⠛⠋⣹⣿⡬⣬⡥⠕⠂⢾⠗⠠⠙⣙⣜⢫⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣄⡈⢲⣄⠹⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⠻⣯⠐⠘⣸⡇⢀⣠⠛
⠀⠀⡟⢻⢛⡫⠵⠶⠷⠂⠀⠀⠀⠀⡠⡀⠉⠋⠀⠁⠻⠷⡽⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢯⣔⣯⠠⠀⡘⣿⣝⣷⣿⡇⠀⠈⠻⠟⢉⡀⠃⠀⢸
⠀⢰⠓⢉⠄⠰⠂⠉⠀⠀⠁⠀⢠⠔⠘⠙⠻⢦⡒⡀⠄⢈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣛⡿⣯⣶⣬⣉⡛⠛⢁⣀⣴⡂⠝⢋⣁⢷⡆⡜
⠀⢸⠛⣧⠀⡀⡉⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠙⠷⣼⠿⠆⠀⢐⣷⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡍⡙⣿⣩⣉⣹⣦⠀⠄⠉⠋⠛
⠀⠘⠛⡆⠀⠋⠁⠀⠀⠀⠀⠉⠘⡀⠀⠀⠀⠀⠀⠀⠘⢦⡔⠤⠈⠉⠁⢨⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣧⣋⢊⣿⡄⠨
⠀⠀⠇⢃⣰⠀⢀⠀⠀⠀⠀⠐⣈⠾⣦⣀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣾⣤⡈⠉⡩⠽⢿⣷⣟⣻⣿⣾⣯⣿⡯⠒⡥⣹⢷⡾⠟⠀⠀⠀⠀⡀
⠀⠀⠘⠜⣇⠕⠀⡀⠀⠀⠐⠈⠁⠐⠁⠛⠻⠳⠶⠶⠶⠴⠴⠴⣿⢿⣿⣿⣔⡀⠂⠈⠛⠍⠳⠛⡻⠟⠋⠔⠉⠔⠁⠊⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠘⠏⢀⠙⠂⢀⠀⡷⢤⢶⣶⣿⣾⠛⢻⡟⢻⡿⠶⠶⠤⣤⣀⡀⠉⠛⠿⣿⣷⣷⣦⣄⣄⠠⣀⣀⠀⠀⠀⣀⡴⠖⠂⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣤⣴⢾⡿⣿⣿⣿⣿⣿⣧⣾⡇⢸⡗⢠⡄⠈⠉⠓⠦⣤⣄⣭⣙⡛⢻⠻⠿⠟⠛⠓⠛⠉⠛⠲⢤⡄⣀⢈⡡⠀⠀⠀⠉
⠀⠀⠀⠀⡈⢁⣨⡞⠯⠹⣬⡦⠗⠛⠛⠉⠉⠉⠛⠛⠻⠿⣷⣿⣧⣴⠖⣀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠟
⠀⠀⠐⢂⡰⠌⢁⡼⠚⠋⠁⠘⠁⠁⠰⠎⣤⠊⡠⠢⡴⠤⠶⠉⠛⠛⠷⣯⣀⡆⢀⡀⠀⠈⠉⠓⠶⣤⣀⡀⠀⠀⠀⢀⣀⡼⠁⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠂⠊⣡⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣅⡐⠀⠀⠀⠀⠀⠉⠉⠉⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣥⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣿⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠿⢻⣯⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⡛⠿⠿⠟⠛⠛⠊⠉⠉⠉⠻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⠀⢀⣿⡁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⠿⠿⢿⣿⣿⠀⢾⣿⡿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⢿⡟⠁⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⣶⣞⣿⣿⣿⣿⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠷⠟⠛⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠋⠉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢠⣤⣤⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠛⠛⢛⣻⣛⡱⠶⠈⡉⣭⢥⡀⠹⣿⣿⠂⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢿⠟⣛⡙⠃⠀⢰⣿⣭⣛⡻⣀⡸⣟⣻⠞⢿⡌⢁⣴⣰⣞⣯⡁⣶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢛⣭⡀⣀⡷⣽⣟⢣⡾⢎⣡⡯⠻⠷⠬⠵⣿⠇⣾⣧⣛⣾⣧⢿⣛⡟⠀⠛⠚⢋⠁⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣋⣭⣁⣼⢿⣾⡹⠿⠓⠀⠁⠀⠀⠀⠀⠀⣀⣄⡀⠈⠉⠉⠋⠸⣿⣿⡟⣂⣴⣟⣁⣿⠁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢸⠟⣉⣾⣟⣠⡼⠋⠁⠀⠀⢀⣠⣶⣶⠾⠻⣿⣟⠉⢿⣿⣯⣽⡦⢠⡀⠉⢡⡝⠻⣯⣯⡷⢠⡍⣥⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⣼⣆⠙⢿⣿⠏⠀⠀⠀⣠⣴⣿⢫⠾⣁⡐⣳⣏⣙⠛⡾⢿⣽⢿⡷⠶⠏⠀⠀⠘⠂⠈⢻⣤⣄⡴⣀⣴
⠀⠀⠀⠀⠀⠀⠀⢿⡴⠿⢶⡟⠋⣸⡇⠀⠀⢠⣾⢏⡼⢛⣷⢶⡿⢻⣿⣿⡿⣻⠛⣫⣉⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠹⠞⣷⠏⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢿⣦⡄⢸⡏⣈⢿⡇⠀⠀⢻⣿⣻⣧⣌⣉⣉⠑⠾⣿⣿⣿⣷⣞⠋⣿⡀⠀⠀⠀⠀⢠⠇⠀⣉⡀⠀⣻⡷⢾⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠋⢿⣆⣿⣇⠘⣿⣧⣀⣀⣿⡿⠟⠉⢀⠉⠀⣁⣶⡄⢻⣦⡉⠘⢧⡀⠙⠛⢷⣦⡼⠋⠀⠰⠆⠀⠀⢸⣧⣤⡹⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣮⠈⠙⣿⣦⣀⣼⣿⢏⡼⣷⠀⠀⣀⣛⡛⠁⠈⠙⠢⣌⣻⣧⣤⣿⢷⡄⠀⠀⠀⠀⠀⡂⠀⠀⠀⣰⣿⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣘⡛⣌⣉⣁⣴⣾⣇⠀⠀⠤⣌⣏⠁⠀⠀⠀⠀⠀⠉⠈⠛⠟⠛⠁⠀⠀⠀⢀⠄⠀⠀⠀⢠⢿⡟⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠘⠛⠛⠑⠎⠀⠀⠀⣤⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⣠⡿⠾⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢤⠀⢠⡀⠀⣴⣦⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⣴⠛⠛⢷⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡐⠂⡀⠀⠀⠀⠀⢀⣠⣿⡧⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠊⣬⣛⡳⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⣰⡶⠛⢿⣿⣼⣣⠿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣤⣠⣤⣴⣶⣾⠛⢻⡿⣿⠆⣴⣾⣾⣿⣿⣶⣶⣶⣶⣶⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⡀⢀⠄⣴⣦⣾⣿⡿⣷⣟⡛⢉⡹⣿⢟⣷⣿⣴⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣷⣏⠉⣷⡶⡆
⠀⠀⠀⢠⠀⠀⠀⠀⣠⣀⣷⠛⡿⢛⣶⣟⠛⢡⣤⣛⡉⠿⢧⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢤⣼⣿⣟⣷⡟⠙⠛⠛⣃⠠⣼⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣼⣛⠭⢿⠟⠻⣽⣿⡧⠛⠛⠉⠈⠉⢀⣴⠟⣿⡟⣿⣿⣿⡿⠻⠉⠉⠁⠀⠀⠀⠤⠠⠄⠤⠤⠀⠄⠉⠙⠿⣤⣾⣿⣿⣿⣭⣛⣉⣉⣤⡀
⠀⠀⢲⣤⣿⣯⣭⡙⣶⣾⣿⡟⠋⠁⠀⠀⠀⠀⠀⢰⣟⢳⣴⡛⠿⣿⠏⠁⠀⢠⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⡘⠻⣿⡏⠸⡿⠛⢩⣻⣷
⠀⠀⣦⣀⣹⣧⠸⡷⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣯⣾⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠂⠹⣧⣤⠶⣶⣤⣻⣿⣧
⠀⢸⣏⣙⣁⢛⠉⣰⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠸⢷⢿⠛⢿⣤⠀⠀⣀⣤⣤⣶⣾⣿⡿⢀⣩⣷⡾⢫⣾⣟⠻⡀⢦⣄⠀⠀⠀⣟⠻⣿⠟⢧⣹⣦⢰⡄
⠀⢸⡟⠛⣿⠛⣿⡛⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⡷⠰⢶⡆⣾⣹⡿⠟⢋⡨⠟⠛⢛⣿⡄⢋⣭⡴⢶⣌⠀⣿⣆⠀⣾⣿⣠⡄⠀⣼⣶⣧⣄⠀⠿⣿⠙⡆
⠀⠘⡷⠿⢿⣾⣿⠇⡰⣤⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⣶⠶⢤⣿⡷⣾⠃⣤⠴⣦⣌⣉⠀⢀⣾⣯⠿⣿⣩⣿⣽⠁⠘⠀⢉⣘⣁⣿⣟⡛⣿⢉⣇⣘⠈⣠⠁
⠀⠀⢻⣿⣶⠟⢃⣼⣷⡙⢊⡡⡐⢦⣀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡀⠿⠂⣸⠟⣾⣿⣽⠿⠛⠋⠁⠀⠀⠀⠀⠉⠙⢷⣤⡘⢻⡿⣿⣿⡏⢻⠿⠿⣿⠛⢀⠏
⠀⠀⠈⠻⣿⣿⣎⢹⣯⢰⣟⡷⠁⢾⠿⠖⠢⣄⣀⡀⠀⠀⠀⠉⠉⠛⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣮⡑⠏⠙⢳⡿⢿⣴⣿⣿⠏⢠⠜
⠀⠀⠀⠀⠙⢿⡟⢉⣯⣌⡛⣤⡠⣬⣶⠶⠺⣦⠙⠙⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣷⡾⢧⣉⡷⠖⠁⢩⣇⠸⣿⠉⠁⢠⠏
⠀⠀⠀⠀⠀⠈⠛⠻⣯⣽⣇⣈⣡⣮⣹⠿⡑⠿⠃⠘⠷⢀⣰⣿⢻⣿⡋⣖⣰⡷⣰⣟⣉⣻⡿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣉⣽⠆⢠⢾⣿⣦⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠁⡌⠛⠻⠿⣿⣅⣼⣿⣿⡄⠻⠃⣼⠟⣡⣾⠿⣷⠈⡁⣨⣿⠿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣯⣿⠿⡀⠻⣮⣳⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢀⡈⢉⠙⠛⠻⠶⢾⣷⣿⡉⣥⣶⣶⣄⣸⣿⣿⣶⣿⣿⣧⢴⡟⣿⣿⡿⠿⠟⠋⠁⢁⡼⠋⠀⢽⡋⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠛⠛⠛⠋⠛⠘⠁⠉⠀⠀⢀⡀⠦⠈⢹⡷⢀⣰⢿⡀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠄⠤⠤⠄⠘⠛⠉⠀⠀⠀⢠⡟⠁⢿⡧⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠀⠀⡐⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⡉⢁⣸⡷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⣉⠀⠀⣠⠦⣤⣔⣤⣴⢶⣤⣄⠠⡄⠀⠀⠀⠀⢀⣠⡴⢅⣸⣏⣽⢿⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆⣴⠛⣷⣄⣿⠷⠿⠿⠋⠱⣶⣿⣾⣷⣤⠀⠀⣠⡴⢋⣵⣶⣾⣿⣭⣵⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣿⣿⣾⣏⠀⠀⠀⠀⣀⣀⣈⣧⣰⣿⣸⣷⠘⣦⣱⣿⣙⣇⣾⣁⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠸⣿⣤⣍⠙⠿⢟⣉⡙⢿⣿⣿⣿⡀⣹⣿⡄⣿⠟⠙⠛⣟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⠰⣿⣷⡾⢿⣷⡼⢯⣽⠷⣿⣻⣿⢸⣇⣸⣿⣩⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⠤⢠⣶⣤⣟⣋⣉⣀⠾⢿⡟⢸⡟⠛⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣩⠏⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢻⣾⠋⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡿⠛⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠆⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣥⠄⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠟⢸⡟⢗⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢘⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂


⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⢀⠀⠴⠤
⠀⠀⠀⠀⠀⠀⢀⣬⡁⣨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡤⠀⠀⠀⠀⠀⠈⠃⠈⠀⠆⢀
⠀⠀⠀⠀⠀⠀⢨⣅⣉⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⢀⡝⡪⠇⠱⣦⣰⡇⠀⠀⠀⠀⠀⠀⠀⡗⢿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢀
⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘
⠀⠀⠀⠀⠀⠀⢠⣀⡘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⢦⠀⠀⠀⠀⠀⠀⠀⠠⠉⠻⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⠖⣀⣩⣽⣯⡝⡳⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⢟⣫⠽⣿⡂⠈⠛⠣⠄⠀⠠⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⡄⠶⠿⠿⠿⣯⣽⣿⣿⠛⣿⣷⣤⡀⠀⠀⠀⠀⠻⣿⣿⣷⣵⡄
⠀⠀⠀⠀⢰⣿⣿⠆⡴⣿⢫⡌⣿⣶⣾⣶⣿⣯⣻⣿⣦⡀⠀⠀⠀⠹⣿⣧⣶⣿
⠀⠀⠀⠀⣿⣿⣿⣾⣿⠏⠁⠀⠀⠀⠁⠛⢿⡈⢻⠿⣿⣿⠷⣦⣤⣾⣿⣿⣟⣿
⠀⠀⠀⠀⣿⣧⣿⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡛⣿⣾⣿⢿⣿⠟⠻⠟⠃
⠀⠀⠀⠀⣿⡝⣿⢵⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠊⠉
⠀⠀⠀⠀⢸⣿⣷⣮⣿⣿⡀
⠀⠀⠀⠀⠈⢿⣿⡿⣷⣮⡛⠧⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣤⣲⡤⢶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⣿⣿⣯⣬⣽⣷⠶⣿⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣽⣿⣷⣬⡅⣿⣿⣟⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⠿⠿⢿⣽⣧⣹⡿⣿⣷⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣿⣿⣯⠟⣟⠛⠫⠷⠟⠛⠛⠒⠋⠀⠉⠁⠙⠻⣎⣿⣿⣿⣿⡉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡾⣿⣷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠲⣶⣂⢶⣷⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⡛⣿⣿⣇
⠀⠀⠀⠀⠠⣠⡼⠷⢋⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⣾⣲⣶⡤⣤⣤⡀⢠⣤⣶⣫⣿⣿⠁⠙⢿⣼
⠀⠀⢀⢀⣟⣹⡷⠶⣬⣥⢻⣿⣿⣷⣿⣿⣭⣹⣛⣿⣿⣿⢿⣶⣾⣷⣶⣾⣿⡶⣿⣿⢗⣾⣿⣽⣶⡄⠀⠈⠉
⠀⠀⣾⣏⢿⣯⡴⠛⠋⣵⠾⠚⠉⠋⠉⠛⠙⠛⠛⢿⣿⣯⣼⣿⡛⠿⣿⣿⣿⡷⡿⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠸⢻⣿⣇⠁⢰⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠛⠛⢛⠿⠿⣇⡀⢸⣿⣴⡶⠿⠛⠉
⠀⢸⣿⣿⣟⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁
⠀⢸⣽⣿⣿⣿⡏⢇
⠀⠰⣯⡻⣿⣍⣴⢸⣷⣦⣄⡀
⠀⠀⠈⣿⣿⣿⣶⣿⡻⢦⣯⣽⣿⣏⣛⣿⣿⢿⢷⠉⣮⣉⢨⣿⣿⣗⢓⢀⣶⣤⣠⢀
⠀⠀⠀⠈⠻⣟⣿⣿⣿⡷⣻⢻⣾⣭⣭⣽⣷⣼⣿⣿⣿⣿⣿⡟⠛⣩⡿⣿⢿⣿⣄⣾⣿⡆⢄
⠀⠀⠀⠀⠀⠈⠙⠹⠿⠷⣷⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⣿⣷⣾⣿⣿⣯⣿⣿⣿⣥⣿⣿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣿⣿⣷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡞⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀⠛⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣯⣃⡾⠁
⠀⠀⢀⣠⣶⣖⡉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠃⢘⣧⠟
⠀⠐⠉⠙⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⠭⢟⣒⣒⣒⣒⣒⢛⣛⣩⣥⠤⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⡠⠄⠁⠉⠀⢀⣠⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠢⠁⡂⠀⠀⢈⡄⢴⢦⣂⡀⠀⠈⠈⠁⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠄⢉⠐⣤⣤⣀⡀⣺⢧⠴⠤⠃⠀⠀⣀⣀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠡⡈⢃⣐⠜⠉⠀⠀⠈⠁⠁⡤⠀⠤⠄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠇⡈⠒⡘⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢈⠠⠬⠁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠐⠒⢘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠈⠁⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠒⠈⢁⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠈⠠⠖⢈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠠⠒⠁⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⠈⣀⠐⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠂⠠⠂⠉⡅
⠀⠀⠀⠀⠀⢀⡠⡴⠶⢏⠙⣍⢷⡶⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠩⠐⠂⠠⢴
⠀⠀⠀⠀⣐⡛⠣⠖⣉⠔⠊⠉⠉⠉⠉⠘⠾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠐⠊⣉⡀⢼
⠀⠀⠀⡴⠁⠈⠌⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡑⠤⠐⠺
⠀⠀⢰⡗⠂⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡍⢵⠀⠀⠀⠀⠀⠀⠀⠀⡿⠠⠔⠲⠈⢻
⠀⠀⢸⡋⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡍⠀⠀⠀⠀⠀⠀⠀⢠⣁⠑⣈⠓⣈⠇
⠀⠀⠘⣏⠠⠤⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠄⠢⠀⢤⡜
⠀⠀⠀⢩⡠⠒⠠⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⡃⠥⡉⠂⢑⠞
⠀⠀⠀⠀⢢⡀⢁⡈⠤⢳⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠚⡁⠄⢀⠈⠂⢠⣨⠋
⠀⠀⠀⠀⠀⠐⢆⠀⠂⡃⠘⢡⠉⠛⡂⡘⠒⠓⡛⢉⠩⡁⠢⢘⠐⢄⠐⠐⠁⡸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠤⡄⠘⢀⠆⢠⠁⡆⢤⠠⠁⢢⠐⠀⠃⢀⠃⡄⢈⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠶⣠⣆⣰⠀⣆⢀⡆⣼⣤⡡⠼⠒⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠜⠁⣀⣈⡀⠀⠠⠤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠇⠟⠉⠐⢲⣾⡟⢻⣿⡞⠳⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢀⠀⠀⣀⡤⠤⠐⠒⠒⠒⠒⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡟⠕⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠘⠦⣄⣀
⠀⠀⠀⠀⢰⡄⠀⠀⠀⣀⡀⠀⣄⠀⡄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠿⠟⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠶⢟⣁⢤⠖⢀⣿⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⢀⡠⠖⠛⠀⠀⠋⠁⣤⣤⡾⡅⠀⠀⠀⠀⠀⠐⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⣠⣖⠋⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⡡⢤⡀⢈⡄⠸⡄⠃⣾⠃⠀⣀⣠⣤⣄⣀⣳⣆⠀⢠⣤⣴⣀⣀⡈⠳⡔⢾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠊⠀⢠⡆⠀⣠⣿⣿⣷⣿⢄⣶⣿⣤⡿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣾⠍⠻⣿⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⡟⠁⠈⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⡿⠏⠙⣠⣾⣟⠻⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣽⡿⠋⠀⠀⠀⠈⢿⣿⠟⠀⠀⠻⢿⡟⠻⠝⠋⠈⠀⠀⣱⣿⣿⡟⠛⠋⠘⣆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣿⣉⣀⡀⢀⠀⠀⠀⠀⠑⣿⠆⠀⠀⢀⣀⡀⠀⠀⠀⠀⠸⣿⡿⢿⠇⣀⡀⠀⣸⠀⠐⠃⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠻⢿⣿⡇⢼⠿⢶⣾⣶⣛⣤⠀⠀⠀⣀⣤⣤⣀⠘⠓⠀⠀⠀⠀⠀⢯⣥⣠⡦⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⡽⠇⠀⠀⣸⣿⣿⣿⣿⢿⣷⣾⣿⣿⠀⠫⠃⠒⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⡀⠀⣻⣿⣿⣟⡛⣼⣿⣇⠘⣿⣿⡜⣿⣿⣏⠙⠀⠀⢠⣶⠀⣈⢈⢀⣄⡈⣿⣯⠳⣿⢶⠀⢠⣄⣀⣀⣀⡀⡤⠖⠒⠉⠉⠂
⠀⠀⠀⠀⠀⢿⡟⠛⠛⠛⠲⠼⠛⠛⠻⣿⣧⠹⣿⣿⣄⠙⣟⣿⡜⢿⡏⠈⡀⠄⠜⠋⣀⠉⠀⢀⠀⠈⣿⠁⡴⢀⠀⠀⠀⠀⠉⠉⡉
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⣻⣿⣿⡄⣹⢻⣃⡀⢑⠤⠄⠀⠀⠀⠀⠀⠘⠐⠒⢲⡇⢰⣿⣏⠀⡀⠀⠀⠀⠘⠛⠚⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣾⠟⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠸⣿⣿⣼⣗⣶⡿⢁⣤⣶⣿⣿⢕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢾⣿⣏⠹⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⡿⡝⠙⠙⠋⠀⠻⠟⠛⠻⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣾⣿⣷⣦⣌⣉⠀⠙⠘⠻⣻⡟⣶⣤⡄⣀⣤⣀⣤⣾⣿⣶⡶⢾⣿⠋⠟⠋⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢌⡙⠛⠛⠋⠋⠀⠀⠀⠀⠉⠁⠘⠿⠅⠉⠟⠻⠿⠁⠋⠉⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣡⡤⠤⠼⣿⠶⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣿⢿⣗⢲⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⢀⠁⡟⠁⠀⠀⠀⠈⠓⠾⠀⠠⠀⠀⠀⠀⠀⣸⡏⣿⠛⠛⢿⣷⣹⠲⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⣤⣷⣤⣤⠴⠒⣒⣉⣉⠀⣲⡄⠀⠀⠀⠀⠸⣇⣽⡀⠀⠀⢀⣴⠚⢛⣷⡆⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠻⢶⣤⣤⡀
⠀⠀⠀⠀⠀⢀⠤⠤⣭⣿⣏⠉⠀⠀⠀⠀⡇⢹⠀⠀⢀⡴⣶⣾⣋⡀⠀⡔⠋⣴⡟⢻⢛⣿⠂⠀⠀⠀⠀⣴⣿⠟⠻⢟⣄⠀⠀⠙⢿⢢⡀
⠀⠀⠀⢀⠀⡇⠀⠀⠈⠻⣿⡳⣄⣀⣀⡴⢁⠎⠀⠀⠸⣿⠿⠿⠿⠿⢛⣥⣾⡏⢀⢯⣴⣿⣤⡀⠀⠀⠀⢿⡷⣀⡀⡨⡾⣦⡀⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠻⢤⣀⣀⣀⡀⣙⠲⠤⠤⠔⠋⠀⠀⠀⠀⠈⠓⠲⢶⠿⠛⠉⠀⠈⠿⡜⠋⡩⢻⡷⠀⠀⠀⠀⠙⠛⠷⠗⠛⢻⣿⣷⡈⠟
⠀⠀⠀⠀⠀⠁⠂⠀⠉⠩⠿⠿⠭⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠠⣀⠟⠁⠀⠀⠀⠀⠀⠢⠀⠀⠀⡀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡖⠒⢋⠌⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣃⣵⣶⣶⣶⣛⣻⠋⠁⠀⠀⠀⠀⠀⠀⠠⢴⣀⠀⠀⠈⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣭⠿⢛⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠚⣑⠢⠤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠖⠒⠒⠲⣶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡶⠶⣶⣾⣿⣿⣿⣖⠒⢲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⣿⣿⠋⡿⠋⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢰⣿⣿⣿⡈⣧⡀⠀⣰⠃⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣾⣿⣿⣿⣷⣾⣿⣯⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠦⠄⠉⠉⢉⣉⠉⠉⠛⠋⠉⠉⣉⡉⠉⠉⠁⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣞⣘⢧⡤⠶⠶⢤⣴⢇⣻⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢹⠏⣀⠀⠀⣀⠘⡏⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣸⡜⠿⢣⡘⠿⢣⣇⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠐⣯⢹⡟⢧⣤⣤⡾⠻⡎⣩⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⣀⡀⠈⠉⠀⠀⠀⠀⠀⣀⡉⠥⠄⣀⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠹⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⡇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠻⣿⣿⣿⣿⣿⡿⠉⠀⠀⠉⢋⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠾⠿⢿⣿⣿⠿⠶⠶⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣙⣿⣖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠁⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠉⠀⠀⢀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⢀⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣷⢀⣠⣤⣴⣤⣤⣄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣷⡄
⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣹⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⡉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢁⣀⣠⣤⣴⡶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠉⠉⠁⠈⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⡀⢀⣀⣀⣀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣿⠋⠙⢛⠛⣛⣛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⣩⠀⠀⠁⠀⠨⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⡿⠀⠀⡇⠀⠐⠞⣿⣿⣿⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⠀⢀⡀⠀⠀⣤⣻⣿⣿⣿⠋⠈⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠈⠳⣦⡀⠀⠀⠰⠦⣀⠀⠀⠛⠻⠷⠷⠶⠶⠾⠿⠿⠟⠛⠉⠀⣀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠈⠙⠓⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣦⡄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠀⠀⠀⠀⣛⢨⣿⡇⠐⠆⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⣿⣿⣿⣿⢛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠟⠛⣿⣤⠛⠃⢤⡶⠶⠶⠶⠛⠛⠛⠓⠒⠶⠶⠶⢿⡿⠟⢁⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⣿⣿⡿⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⣿⠀⢻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢿⡜⢿⣦⣀⡉⠉⠛⠒⠲⠆⠰⠰⠶⠒⠚⠉⠉⠈⠁⠀⠀⠀⣹⠀⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠸⣇⠀⠀⠉⠛⠛⠒⠲⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠠⢀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠙⣤⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠑⢄⡀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠙⠦⠁⢄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣓⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠻⣦
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢀⣤⡄⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢂⠘⣧⡀
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢃⠈⢷⡀
⠀⠀⠀⡼⠀⢀⣴⡏⠀⠀⣰⣿⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⣷
⠀⡀⢰⠃⣴⣿⣿⠁⠀⢠⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢂⠸⣇
⢠⠁⡎⣼⣿⣿⡟⠀⠀⣼⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢾⣿⣿⣿⣿⡿⠿⢿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡀⢿
⠈⣦⢹⣿⣿⣟⠇⠀⠀⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⠋⠉⣿⣧⣄⣼⡷⣾⣧⣄⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁⢸
⣇⢻⣼⣿⣿⣿⡇⠀⠰⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣼⣶⣾⣧⣼⣿⢛⡿⠋⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠈
⣯⢸⣿⣿⣿⣿⡇⠀⢰⣮⣽⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⠿⠾⠧⣉⣿⣿⣾⢧⣤⣶⣾⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠸
⡟⢸⣿⡿⠿⢿⣧⠀⢸⣿⣿⡇⠀⣾⣭⣽⣛⡻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⣴⠟⠛⠛⠁⠀⠀⠈⠛⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠃⢸⢠
⠇⣿⣿⣿⣿⣿⣿⠀⠀⠿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣬⣭⣭⣷⡄⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⢀⡿⠘⢰
⢸⡇⡿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢸⣿⣿⣿⣾⣿⣿⠟⣿⠇⣸⠇⡆⣸
⠈⣿⢱⢿⣿⣿⣿⣿⡀⢸⣿⣿⡿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⢠⡿⠀⢀⡿
⠀⠹⡏⡌⢿⣿⣼⣿⣧⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣵⣿⡇⣿⣤⠄⠀⠀⣼⣿⣿⣿⣷⣤⡀⠀⠀⠀⣿⣿⢻⣿⢿⣿⡟⢠⡿⠁⠀⣼⠃
⠀⠀⠻⡼⡌⢻⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠙⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣿⣿⣷⣾⣿⠟⢠⡿⠁⠀⣼⠏
⠀⠀⠀⢻⣌⢂⠻⣿⣿⣿⣇⠘⢻⣿⣿⣿⣿⣿⣿⣭⣦⣬⣷⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⠋⣠⠟⠁⠀⣴⠏
⠀⠀⠀⠀⠹⣦⠀⠘⢿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣹⣿⣿⣿⡿⢿⣿⡟⣻⣿⣿⣿⣿⠟⢡⡾⠋⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⡾⠋⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡶⠟⠉⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠛⠉⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⢉⣀⣤⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣄⡐⠒⠦⢤⣤⣀⣈⣉⣉⣉⣉⣉⣉⣉⣀⣀⣤⣤⡴⠶⠛⣋⣩⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⣤⣬⣍⣉⣉⣉⣉⣉⣉⣉⣉⣭⣤⣤⠶⠾⠛⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⣝⠿⠛⠚⠁⠐⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠿⠇⠛⢉⠀⠀⠀⠀⠀⠈⠉⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⢟⠯⣽⠶⣖⠲⡟⢿⡦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠸⣷⡤⢈⡿⠞⠓⠀⠀⠀⠀⠀⠀⢀⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⣯⣞⣉⡑⠐⠾⣿⣮⣳⣽⣾⣧⣟⢰⢁⣿⣶⣦⢤⢦⡌⢂⠀⠀⠀⠑⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⢤⠤⣤⣬⣙⣷⣮⣽⣿⣿⣿⢱⣿⣿⣿⣾⣯⡿⠷⡇⢤⣀⣢⠀⠀⠀⠐⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠓⠒⢿⣿⣿⣭⣻⡿⠟⠛⠻⣿⣿⣿⣿⣶⣟⣛⣛⢿⣿⠀⠀⠀⠀⠀⠙⢯⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠛⣉⣽⢿⣿⠟⠁⠀⠀⠀⣽⣿⣿⣤⣀⣝⡛⠿⣿⣿⡀⠀⠀⠀⠀⢀⣾⠛⢇⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠰⡍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⡴⠟⣿⠀⠀⠀⠀⣼⣿⣿⣿⡟⡙⠿⡟⣷⡿⣿⠂⠀⠀⢞⣅⠈⠑⠀⠈⣹⠾⣧⢀⠶⣤⡀⠀⠈⢀⡄⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⣠⣿⣟⠀⠀⠀⠀⢿⣿⢹⣿⣧⠙⣦⠘⣆⣧⠇⠀⠀⢀⡞⠁⠀⠀⣢⠀⣇⠀⠀⠉⠙⠦⢥⡼⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣛⡥⢀⡀⠀⡀⠉⠛⠺⢿⣿⠆⢸⢧⡼⠋⠀⠀⠀⡾⠂⠀⠉⢰⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠈⠙⠳⣆⠀⠭⠄⠂⠈⠀⠀⠀⠀⣎⠁⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣀⠀⠀⠀⠈⠋⠲⣄⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣄⠀⠀⠈⠙⢦⣄⠀⢸⠁⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣁⠀⠀⠀⠘⢷⡍⠀⠀⠀⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⠂⠀⠈⢻⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⢘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢀⠀⠘⣧⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⠀⠀⣼⠁⠀⠠⠞⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⡀⠀⠀⣠⠋⢀⣀⣄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡠⠁⠀⢠⡟⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢀⣬⠁⠀⢀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣀⠴⠋⠀⠙⠃⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢦⡾⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⢠⣶⣌⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣟⣿⣿⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠱⣿⣿⣿⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⣳⣷⣌⣿⣯⢿⣿⣿⣦⣀⠀⠀⠀⣻⣼⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⠾⣯⣽⣶⣿⣧⣽⣾⢻⡇⣻⢿⣷⣶⣴⣿⣽⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣯⣶⠿⣶⣿⣿⡏⠉⠉⠙⠻⢯⣿⣿⣧⢿⣿⣭⣿⠟⣿⢹⠏⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣧⣽⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠫⠿⣾⣻⣴⣏⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⡟⠿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢹⣻⠾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⢿⣿⡿⠟⣿⠷⣥⡟⠛⢷⡛⠉⣳⡞⠛⢿⣻⣿⣭⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣇⣹⠟⠛⣾⣅⣀⣼⣳⣾⣏⠿⠿⢯⢷⡶⣿⣄⣹⣏⣝⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣯⣭⣷⠟⢻⣝⡿⠻⢮⡿⠋⣳⢯⣀⣾⠟⠳⣾⣿⠬⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⢻⣽⣇⠈⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣿⣿⣷⣵⣿⣭⣿⣿⣖⡛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣽⡏⢳⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣛⢻⣿⡛⣿⣟⢻⣿⠛⣻⡻⢿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⢯⣯⠟⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣍⣽⢛⣿⣉⣽⣏⣹⣏⣉⣷⠟⢷⣼⣿⣉⣝⠻⠟⡿⣿⣿⣿⣿⣿⡿⡿⠿⣟⢻⣷⠿⣦⢾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⣧⣾⣽⡷⠋⠀⠀⠀⠈⠉⠙⠛⠻⠷⢾⣏⣹⡶⢿⣷⢿⣬⣷⣦⣾⣦⣿⠷⣿⠛⣳⠴⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⣿⣒⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣬⣥⣿⣿⣷⣴⣿⣥⡿⢧⣼⢷⢶⡿⠝⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣖⣝⠻⣿⣶⣶⣶⣶⣶⣾⡿⠿⠿⠻⣻⢯⣙⢛⣛⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⣿⣷⣶⣠⣦⣤⣕⣿⣶⢿⣴⣿⣾⣻⣾⣿⢿⣽⣾⣿⣾⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠷⠿⠾⠟⠿⠛⠛⠉⠉⠁⠉⠁⠁⠉⠙⢿⣿⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⢦⣤⣤⣀⡀⠀⠀⢀⣠⡴⣿⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⣷⣿⣶⣶⣶⣌⣿⣟⣛⣟⡿⣷⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⡏⠀⠀⠀⠀⠉⠙⠛⠛⠛⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⠖⠄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀⢀⣿⣀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⣠⡤⠾⠃⢈⣷⡀⠀⠬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢸⠇⢠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⠀⠀⠀⠀⠀⣀⣠⣞⣀⡁⠀⢀⠀⣀⡾⠹⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⣿⠙⠏⠉⠀⠀⣩⢙⣭⢟⣋⢉⠛⠿⡟⣏⠁
⠀⠀⠀⠀⠀⢰⠟⠛⠖⠶⢦⡤⢤⣤⣤⣤⣤⡤⠤⠶⠚⠃⠁⠁⠔⠀⣀⣤⠴⠒⠉⠹⢦⣌⠙⠻⠦⠾⠆
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠄⠀⠀⠀⠀⠤⢀⡀⡄⠀⡀⠈⣿⡲⠂⠀⠛⡉⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠴⠀⠀⢉⠂⠀⠀⠉⠀⢀⣁⠀⠬⠀⠀⠶⠊⢁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⢸⡆⠀⠐⠆⠀⠈⠂⠋⠀⠂⠈⢁⡀⠤⠖⠂⠀⠠⠂⠉⠀⡀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠈⠿⠄⠐⠒⠒⠒⠒⠛⢻⡟⣩⠡⠐⠒⠂⢰⠁⣠⠖⠋⠉⠁⠉⠉⠑⢢⡀⠘⡆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠣⠄⣀⡀⢀⡏⢸⠁⣀⣀⠀⠀⢀⣀⣀⠀⢁⠀⢸⡀⣀⡠⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠀⠀⠀⠈⣇⢛⠀⠛⠿⢃⡀⠿⣿⠿⠃⢸⡀⢸⠋⠁⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠁⠀⠀⠀⠙⢮⡓⠳⡄⢈⠉⡀⣠⠖⠒⠊⣠⠋⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠙⠳⠼⣭⣥⣭⣥⡤⠖⠋⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠦⢤⣤⣄⣠⣤⣤⡤⠤⠴⠶⠛⠁



⠀⠀⣀⠀⠀⢀⠀⢀⠀⠀⢀
⣿⣯⢩⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⢀⡴⠿⠛⠛⡟⡹⢀⡀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⣴⣦⠿⠞⠛⠉⠳⣬⣢⡀⠀⣼⠟⢡⣾⣧⣴⣾⡟⠛⠛⠛⠙⡧
⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣶⢡⠛⢠⡝⢦⡀
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⣷⣄⠀⢻⣄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⣾⠿⠻⠉⢉⡻⢿⣽⣿⣿⡍⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡷⢄
⠀⠀⠀⠀⠀⠀⣰⡿⠛⠋⠀⠀⠀⠀⠀⠀⢀⣤⣾⠏⢧⣉⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠹⣇⢧⠉⠛⠻⣿⣿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⢿⣾⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⡀⢸⡿⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠾⣤⣬⣥⢌⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠖⢦⣙⣛⣓⣿⣟⣦⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢹⣄⣀⣉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣷⢻⡏⢻⣿⡷⠹⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⡞⢆⠈⢿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣞⢦⡀⠹⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡻⣆⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣎⢣⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⢧⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⠇⢺⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠍⢸⣠⣶⡿⡶⣔⡂
⠀⠀⠀⠀⠘⣃⠰⢜⠏⣲⢿⢏⣶⢦⢤⣀⣤⣤⣴⡷⠏⣠⣿⣶⣿⣯⣛⡋⡛⢶⠀⠀⠀⠀⠀⣠⡤⠤⠄
⠀⠀⠈⠠⠈⣀⢭⣀⢙⠦⡓⣔⣞⢚⢲⡂⣹⡉⡝⠉⠻⢟⣭⢗⡾⣿⣽⡯⣕⣾⣀⣀⣀⣰⠜⠁
⠀⠀⠀⠀⠀⠑⢉⣻⣿⢿⣿⣶⣶⣿⣷⣷⣍⣦⣗⡕⣪⠥⣒⠭⣿⣿⡉⠔⠛⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠈⠁⠒⠁⠬⠿⠿⠛⠛⠛⠉⠁⠀⠉⠉⠉⠛⠓⠃⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣰⡖⡶⠐⠒⠂⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢺⡽⠟⢭⠁⣦⠠⡌⣈⠁⡘⠀⢰⡋⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢾⣓⣯⢝⣁⢛⠀⠄⠀⠐⠀⠠⠬⠉⡘⠃⢈⡱⣉⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣖⡸⠈⢈⡶⡱⣋⣿⣏⡼⠛⠉⢉⡳⢦⠀⠀⠀⠀⠀⠀⠉⢪⢁⢿⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⡬⠛⠉⣀⣰⢤⡏⡞⠻⣿⡡⠟⠁⠀⠀⣷⡴⢦⡱⣄⡀⠀⠀⠀⠀⢀⢉⡠⠟⣻⡇
⠀⠀⠀⠀⠀⠀⡰⣟⢣⠞⠁⣠⡴⠞⠉⢀⡞⣵⣿⣿⠽⢷⣯⢑⡆⠀⢩⢿⣿⣩⣷⡯⢽⣒⡒⠿⣤⠩⣶⡞⣷⠁
⠀⠀⠀⠀⠀⢼⣏⣹⠃⢰⡞⠋⠀⠀⢀⡞⣿⣷⣴⣿⡟⠲⠚⠉⠀⠀⠀⠳⣭⠿⠛⠷⣾⡿⠷⣾⡿⣻⣭⡴⠁
⠀⠀⠀⠀⢰⣯⢿⡏⢀⣏⠀⠀⠀⣀⢾⣵⣏⣹⢟⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⠶⠿⠶⠖⠛⠁
⠀⠀⠀⠀⢸⡿⢶⡿⢦⣍⣐⣂⣸⣭⠛⢿⣿⡿⡾⠁
⠀⠀⠀⠀⠈⢧⣉⠷⣞⣿⣧⣨⣿⣿⠟⣩⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠿⢦⣀⣽⣷⣶⣶⠶⠛⠁