Tangier Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠆
⠀⠀⢀⣤⡰⠀⠀⠀⠉⠁⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⣀⠀⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠸⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣂⣸⢯⣠⣮⣴⣥⠼⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢿⡿⠀⣀⠀⠀⠀⠀⠀⣀⢻⣿⡿⣏⣿⣥⡤⠤
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⣥⣈⡉⢳⣴⡌⠀⢨⠄⣹⣿⣿⣿⣯⣄⣑⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠈⠁⠀⠉⠁⢹⠟⣿⡿⡿⣿⣿⡟⠟⠉⠇⢠⣴⣤⡀⠀⠀⣠⣶⣆
⠀⠀⠀⢰⡄⠀⢉⠐⠄⠀⠀⠀⣽⠀⣲⠀⡄⠀⠀⡀⠸⠄⠿⠇⠂⣻⠆⠘⠃⠀⢀⣿⣻⣽⣿⠀⢸⣽⣛⣏
⠀⠀⣠⣿⣧⣰⣿⣇⡅⠐⡶⠲⣤⠀⠉⠈⠃⠀⠄⠃⢠⡤⠤⠄⠀⠻⣷⣀⡀⠀⠈⣿⣿⣿⣿⡟⣿⡯⡿⡇
⠀⠀⡋⢹⣿⠇⣿⣿⠀⠀⠀⢼⠿⠗⢿⢴⡆⡀⠀⠀⠈⣠⣲⡆⠀⠀⢸⣿⡇⠀⠀⣟⣿⣷⣿⣇⣿⣿⣿⣷
⠀⠀⠁⢸⣿⠆⣿⡿⣿⠃⠀⢩⠀⠆⠴⠀⠅⠀⠀⠀⠀⢻⢻⡆⠀⠀⡀⠀⠀⠀⠈⠛⠙⠛⠉⠹⡏⠛⠙⠛
⠀⠀⡄⢸⣿⡇⣿⡇⠇⠀⠀⢸⠀⠀⠀⠀⠀⢈⣉⣲⣆⡿⡿⠃⠀⠂⠐⠀⢢⠀⠀⠀⠀⠀⠐⠐⢱⡀
⠀⠀⠁⠈⠛⠁⠙⠃⣀⠀⠀⢘⠀⠀⢀⠠⠴⠾⣿⣿⣟⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⢧
⠀⠀⠘⠈⠀⠉⠁⠀⠫⠇⢀⣸⣤⣞⣻⣿⣿⣿⠿⠿⠿⠿⢿⣒⡒⢠⣄⣦⣄⣤⣄⣀⣀⠀⠐⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠉⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠉⠁⠉⠉⠉⠛⠓⠛⠋⠁

⠋⠙⠁⠁
⡖⠶⠶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣶⣍⢁⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⣠⣄⠄⣠⣤
⣿⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢾⣷⣿⣷⡞⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠛⠉⢁⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⢠⡄⠀⠀⣿⣿⣿⣿⣶⣷⣷⣶⣾⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣦⣀⣿⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠿⠿⣿⣷⣦⡀⠀⣿⣿⣿⣿⣷⠿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⣶⣶⣾⣿⣿⣧⠀⣿⣿⣿⣿⣿⣷⣻⣿⣇⣀⣠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠋⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷⣸⡏⠁⢸⣿⣅⠀⠀⢨⣿⣿⣽⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣼⣿⣿⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣻⣿⣿⡿⢿⣿⣿⣿⣟⣿⣿⢿
⠿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣍⢿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣷⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣟⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣿⣿⣿⣿⣷⡾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⣿⣾⣵⣼⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⢀⡆⣰⢣⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡆⠐⠀⠀⢠⣼⣷⣬⢣⠄⠉⠀⠀⠀⣀⣂⡂⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠆⡁⠀⠂⢠⣿⣟⠋⠀⠁⠈⠀⣔⣴⣇⢹⣑⣐⡐⣪⢀⣷⣆⠆⠀⠀⣀⠆
⠀⠀⠀⠀⠀⣠⡃⠀⠀⣨⡠⠇⠀⠀⢀⣿⣿⣤⡆⠀⡀⣾⢿⡿⣾⣯⣥⣽⣯⡮⠽⣿⢿⡿⠾⡀⡉⠈
⠀⠐⠀⢒⠀⠜⠀⠀⠀⣿⣿⡆⠀⣴⣿⠿⢿⣿⡇⠀⣿⣷⢿⣿⣿⣿⣿⡄⠀⠧⠀⣿⠀⠰⠃
⠀⠀⠀⢸⡗⠀⠀⢀⣼⣿⣿⣿⢰⣿⠇⠀⠀⠙⣧⠀⠸⢿⣿⣿⣿⣿⡿⠃⠀⠐⢐⣿⠂⠀⠀⠀⢀⡀
⠀⠀⢂⡈⠀⠀⠠⠊⣿⣿⣿⣿⣿⣿⣶⣶⣀⣀⣨⣤⣦⠈⠻⠭⠈⠉⢀⣀⠀⠀⢸⣿⢰⢧⡀⠀⠁⠋
⠀⠀⣘⡃⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⡋⠁⠀⠀⣠⣄⣀⣤⡹⣿⣓⣚⣟⣿⣆⣅⣤⣀⡀
⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⢟⣿⣍⠉⠉⠉⠀⠀⠀⠀⠘⢡⡀⠅⢠⣤⣬⣭⣍⣿⣿⣿⣀⣸⣿⠏
⠀⠀⣰⣿⣿⣿⣿⣾⢿⡿⢿⣿⣿⣿⣿⣅⣀⣠⠤⣤⣤⣤⢤⡤⢽⣿⣾⣿⣾⣿⣿⣿⣿⣿⡿⠁⠁
⠀⠀⣿⣿⣿⠿⣿⣵⣿⡿⣷⣾⣿⣿⣿⣏⠁⠀⣤⣾⣿⣃⣄⣿⣥⠼⣶⣻⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⣿⣻⣟⣿⣟⠻⣿⣷⣿⣿⡤⢿⣧⣼⣿⣶⣟⣯⣻⣿⣿⣿⣟⡿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠀⠛⠛⠁⠉⠉⠻⠛⠛⠁⠈⠋⠉⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣄⣰⡾⠠⠉⣩⣦
⢀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠂⠀⠀⠀⠀⠚⠁⠀⢀⣼⣿⠋⠒⠀⠀⠀⡀⠀⣀⣀
⢨⣷⣿⣾⣿⣷⣶⣤⣄⡀⠀⠀⠒⠒⠒⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⣀⣄⣀⣠⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠄
⠈⠿⢿⣿⣿⣿⡿⣿⠟⢫⠁⠀⠀⢀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠈⠉⠉⢻⣿⡿⠋⠁⠀⠀⠀⣄⠀⡄⡆⠀⣀⢀
⠀⠀⠀⠀⠈⠉⠓⠃⠀⠘⠃⠀⠀⠻⠄⠀⠴⡶⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⢀⡤⠀⠀⠀⠠⠤⠄⠀⠠⠄
⠀⠀⣶⣶⠦⠤⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠘⣿⣿⣵⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠁⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠉⠉⠀⠀⠀⠰⠟⠋⠁⡿⠭⡄⠉⠀⠀⠀⠀⠀⠀⠸⠛⣏⠉⠘⠿⠄⠀⣀⡀⠀⢀⠀⠀⡿⠀⠀⠀⠀⠀⠆⠀⠀⠀⣴⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢰⣆⠀⠀⠀⣴⡄⢘⣿⡄⠀⠀⢚⡏⠃⠀⠀⢀⣀⡀⠀⠂⠀⡀⠀⠀⠀⠀⠀⢁⡀⠋⠀⡀
⠀⠀⢀⡴⠃⠁⡀⣸⣻⡭⠀⠀⠀⠀⠈⠀⠈⠀⠀⢀⠸⣿⡇⠈⠛⢯⠒⠻⠻⠀⠀⣀⣤⣼⢟⡶⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⢀⣿⣷⡑⠆⢸⡏⠙⢩⡆⠀⠀⢰⠸⡿⠃⠛⠻⠀⡄⣿⣿⠀⠀⠈⣇⠀⠳⣠⡾⢏⣴⣟⣾⢡⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⣾⣿⣿⣧⣴⣿⣿⣂⣤⣟⠀⠰⠄⠁⣾⡀⠀⠀⡀⡇⣿⡿⠀⠀⠀⠉⠀⢰⣿⣿⣿⡏⣿⣿⠾⡷⣦⡀⢀⠐⠀⠀⢸⡇⢀
⢸⣿⣿⣿⣿⣤⣿⣾⡟⢿⡿⠋⠀⠀⣀⢻⣉⢲⢀⣖⠇⣟⠃⠀⠀⠐⠜⠀⢸⣿⡿⣿⠀⣿⣿⡆⠁⠉⠻⣷⡄⠀⠀⡻⡿⠁
⠀⣿⣿⣿⡟⡁⣿⡏⣧⠀⣸⡄⠈⠉⠀⠘⠛⠲⠎⠉⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⣱⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⣤⣠⣤⣤⡄
⠀⣿⣿⣿⡇⠇⢸⡇⢹⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠾⢷⣿⢲⣶⠠⣿⣿⣿⠀⣿⣿⠀⠀⠀⢸⠂⣠⡴⠚⠓⢈⣿⡿⠿⠿⠇
⢀⣿⡏⣿⡇⠀⢸⡇⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠯⢿⡞⠋⠉⠌⠛⠁⢙⢿⣿⣦⣼⡿⡧⠀⠀⣘⣷⣿⣆⠀⠀⣷⠂
⠀⣻⣿⣿⣇⢀⡼⣧⣘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠐⢀⢂⣀⡀⠀⢻⣿⢻⠟⠀⢠⣀⢸⢿⡿⣿⣷⣾⡿⡗
⠀⠙⠛⠿⡿⠟⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠿⣿⣿⣶⣦⣿⣸⠀⠀⠲⣿⣦⢜⡇⢿⡛⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⡏⠁⠀⠀⠀⠁⠀⠁⠀⠉⠇

⠀⠀⠀⠀⣀⣀⡀⣀⠈⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠠⡀⣶⣢⣀⣄⣠⣤
⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣤⣀⡀⠤⡄⠀⠠⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣶⣶⣷⡔⠛⠻⠿⢿⣧⣴⣾⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣴⣶⣿⣉⣉⣉⡀⠉⢹⣏
⠀⠀⠀⠀⣥⡍⠉⣂⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠛⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⢀⣛⡛⣛⣛⣻⣻⣝⣯⣽⣿⣾⣿⣯⣽⣯⣴⣭⣽⣯⣭⣭⣭⣭⣽⣿⣯⣴⣭⣀⡘⢋⣕⣂⣙⣷⣶⣿⣿⣖⣻⡿⠿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣉⣉⠉⠉⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠛⣻⠿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠄⠀⠈⠓⠀⠀⠈⠉⠉⠛⠙⠻⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡀⢊⡁⠘⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠰⣦⡀⠀⠀⠛⠶⣀⠀⠀⠀⠠⠀⣀⡀⠀⠉⠉⠉⠉⠙⠛⠛⠊⠙⢟⠳⢶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠄⣀⢀⣀⡀⠀⠙⠹⠦⠀⠀⠈⠃⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠞⠈⠁

⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠨⠿⠿⢿⣟⡿⠿⢿⣿⣿⣿⢷⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠄⠉⠛⠛⠳⠶⣦⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢍⠙⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣳⣖⣢⡤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠒⠆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠾⠒⠒⠀⠀⠃⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠂

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⡀⣀⣀
⠀⠀⠒⠒⠖⠋⢉⣉⣉⣁⣀⣀⡀⣠⣄⠀⠐⠁⠛⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠿⠿⠦⠉⠉⣛⣻⣿⣿⣿⡇⣹⣿⣷⣶⣧⣠⢈⣶⣝⢿⣷⣀⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣾⣿⣶⣶⣤⡈⠉⠄⠒⠓⣴⡟⠛⣻⣿⣿⣿⣿⣿⣿⡈⠛⠛⠿⠛⠋⠁⠀⠲⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠿⠶⠗⣰⣴⡄
⠀⠀⠿⣿⣿⣿⣿⣿⣦⣀⣀⣀⡀⠠⢋⠉⠩⢤⣿⣿⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣦
⠀⠀⠛⠿⠿⢿⡿⣿⣭⣿⣹⣿⣿⣀⡘⠙⠂⠀⠽⣿⣿⣯⣁⡀⠀⢀⣠⣄⣀⣒⣒⠀⠀⠤⠶⠷⠶⢀⣠⣄⣠⣤⣤⣴⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣒⣒⣲
⠀⠀⠀⠀⠀⠀⣐⣶⣦⣈⣭⡋⣭⡻⠟⣿⣿⣷⣄⠛⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣶⣶⣶⣦⣤⣬⣭⣽⣿⣿⠯⠿⠟⢛⣛⣛⣛⡻⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠚⣢⣭⣽⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢿⣿⣭⣻⣛⣺⢿
⠀⠀⠀⠀⠸⠿⠿⠛⠉⠉⡍⠋⢉⣉⣭⢿⣿⣿⣿⠿⣿⡿⠿⠟⠛⠉⠁⠀⠄⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠀⠀⠀⠈⠁⠀⠀⠐⠒⠂⠀⠀⢀⣀⣀⣀⣀⣀⣀⡈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠓⠚⠋⠉⠙⠛⠛⠙⠛⠛⠛⠻⠛⠒⠒⠂⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠋⠙⠛⠛

⠀⠀⠀⠈⠷⠐⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠟⠋⠉⠉⠙⠛⠓⢸⣟⣿⠷⢴⡟⠻⠿⠆⠀⠒⠈⠁⠉⠉⠩⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⣤⣄
⢁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⡀
⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⢴⣤⡄⠀⠀⢀⡀⡠⣾⣿⣿⣧⣟⣧⣼⣡⣤⣤⣤⣤⡤⠤⠶⢚⡂⣂⣀⣀⣀⣀⣙
⠰⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⠁⣙⣩⣬⣤⣄⣈⠠⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿
⠿⠉⠉⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠍⠉⠁⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣛⣛⡁⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠀⠄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿
⠀⣀⣀⣤⡄⣠⣤⣄⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⣿⣿⣿⣿⣦⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⢀⣠⣶⣶⣤⣽⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⢻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⣷⣾⣿⣿⣿⣻⣿⢽⢱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢁⣼⣿⣿⣿⣿⣿⣾⠛⣷⢜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣀⣈⣿⣿⣿⣿⣿⣿⣿⣈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠟⠛⣯⣽⣿⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣃⣿⣿⣿⣿⣿⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⢠⣄⣀⣀⣀⡀⡀⠀⠀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢸⣿⣿⡿⠛⠛⢛⣿⣛⠛⠛⠛⣛⢛⡿⠿⠿⠛⠛⣛⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣏⠛⣤⣙⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⢿⣿⣿⣿⣿⣷⠛⠚⣛⠋⢛⣉⢛⣉⡼⠿⢿⣿⣿⣿⡿⠛⡻⣿⣿⣿⣟⣿⡇
⠀⠀⢸⠿⠿⠿⠿⠟⠟⠛⢻⡿⠓⢐⠲⠮⣩⠖⠾⣿⠞⢣⣴⣿⣟⣿⣿⣿⣿⣟⣻⣯⣀⣠⣤⣴⣰⣤⣭⣭⣽⠿⣿⡇
⠀⠀⠀⠒⠒⢀⡤⡷⠶⠄⠘⠓⣒⣿⣿⣶⣶⠛⣷⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣾⡇
⠀⠀⢰⣿⣧⣴⣤⣶⣷⣿⣿⣿⣿⣟⣴⣿⣿⢙⣾⣻⡿⢷⣾⣿⣭⣴⠿⠿⠟⠛⠛⠛⣿⣿⡿⠿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⢸⠛⠋⠉⠉⠿⠛⠛⠇⠀⠛⠛⠉⠡⠄⠛⣽⣯⠀⠈⠙⠛⠛⠀⡀⢀⣤⣀⣤⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣷⣾⣿⣶⣶⣶⣦⣤⣤⣀⣾⣿⣿⣿⣉⡀⠀⠀⠀⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉
⠀⠀⠀⢀⣤⣶⣶⣶⣤⣦⣤⣴⣤⣤⣄⣀⡀⠀⠀⠀⠀⣰⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣠⣾⣿⣿⡆
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠈⠛⠋⠁⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣄⣤⣠⣄⣀⣀⣀⣠⣀⠀⡄⢀⠀⡀⣀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⡇⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣀⣀⢀⣀⠈⠉⣍⣽⣿⣿⣛⣩⣭⣉⠁⣴⠀⡇⠀⠀⣀⣸⣧⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡋⠼⣿⡛⠛⠛⠿⣿⣷⠀⠀⣧⠀⢘⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈⠀⠀⣀⠀⢿⣀⠀⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⣿⣿⣿⣿⣿⡛⠛⠳⣶⣦⣴⡄⢀⢤⣼⣿⣷⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⡆⠃⠀⢈⠁⢸⣿⣿⣿⣿⣿⡿⣿⠋⠀⠀⠈⡹⢿⣿⣼⣷⣿⣿⡉⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⡅⠀⢀⡅⢸⣿⣿⣿⣿⣿⣠⣾⣇⠀⠀⠐⠶⢟⣿⣿⣿⡿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡇⠀⠰⡇⢺⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣷⣾⣿⣿⡿⣋⣿⣀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⡇⠀⢸⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡆⠀⡄⠀⠸⡗⣠⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⡆⠀⠀⡆⢘⣿⣿⣿⡿⠋⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠃⠀⢸⣷⣸⣿⣿⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠃⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡃⠀⢸⡿⢿⡟⠀⠀⠀⣰⡟⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⡇⠀⢸⣷⡟⠀⠀⠀⢰⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡇⠀⢸⡟⠀⠀⠀⡀⣿⣿⡁⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⡁⠀⡎⠀⠀⠀⢸⣧⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿
⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⢠⢺⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠅⠈⠀⠀⢀⢀⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⡓⠲⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢀⡀⠀⢠⣄⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⠀⠀⠈⠀⠐⠒⠒⠂⠂⢰⣿⢿⡶⠀⠀⠐⠀⠚⠙⠉⠓⠛⠕⠷
⠀⣀⣀⡀⠀⠀⠀⠀⠁⣄⣀⣀⣀⣠⣤⠤⣤⣯⣤⣦⠄⢰⡼⢿⣿⣧⢀⡀⠀⠠
⠀⣾⣾⣀⠀⣤⠸⠃⠀⠋⠋⡉⣵⣿⣿⣤⣌⣘⣹⡿⠶⢌⡀⠒⠚⡟⠘⣁⡴⡶⢤⣿⣿⣦⣤
⠀⣿⣿⣿⣶⣿⣧⣤⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⣷⡆⠟⠓⢉⣿⣶⣯⣴⣻⣿⣶⣟⣧
⠀⠙⣛⣻⣿⣯⢹⡯⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠇⠠⣤⠒⠒⠛⢽⣿⣭⢽⡟⠉⢹⣿⣉⠉⣿⠉⢉⡄
⠀⣼⠿⣯⢻⡿⢺⣿⣿⠟⢋⣭⣷⣦⣄⠉⡄⠀⠠⢶⣿⡿⠿⠿⠿⠋⠿⢫⠡⣶⣤⡴⠻⠀⠀⠐
⠀⢹⠀⢾⣟⢛⠿⠿⠇⠀⢸⣿⣿⣿⣿⣦⣿⠀⠀⠀⠁⠉⠀⠁⠀⠀⢀⢾⠀⢸⣿⣿⣿⣟⠁⠀⠈
⠀⠈⠀⠘⠛⠁⠀⠀⠀⠶⠾⠿⠿⠿⠿⠷⣿⣠⠤⠄⠀⠀⠤⠤⠤⢤⠿⣏⣆⣈⠉⠙⠛⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡤⠂⠀⣠⠶⠂⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣇⠀⣼⣁⣴⣶⡖⠫⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠄⠀⠀⠀⠀⠛⠙⠀⢀⡿⢛⣯⠀⣀⣴⠿⠀⢶⣦⡀⣰⣦⣄⣀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠥⠜⠹⠿⠇⠀⠩⣿⠿⢻⣿⣿⣧⡩⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡖⣲⣿⣿⣿⡀⠝⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠛⢉⣤⣿⣿⣿⣿⣷⣮⣴⣆
⠀⠀⠀⠀⠀⢤⣤⣾⣤⣤⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢢⣤⠤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⡀⣰⣿⣷⣌⣭⣭⣸⢠⠐⠀⠘⣛⢛⠓⠲⣷⢶⣿⢿⣿⣿⡻⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣭⣠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣄⣆⣀⡀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢃⣠⣤⣶⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣻⣟⢿⣿⣿⣿⣟⣻⣿⣷⣆⣸⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣶⣾⣿⣿⣿⣿⠿⠛⠙⣻⠟⠉⢹⣿⣿⣯⣉⣀⡠
⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣟⠁⣠⠔⡚⣠⣥⣤⢀⢤⣭⣿⣿⠛⠛⠋
⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣼⣿⣿⣋⠀⣿⣷⣿⡟⠁⠀⠿⠿⠚⠛⠻⠟⠂
⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡿⢟⣛⣽⣿⣿⣿⣿⣯⠀⠀⢸⣶⣶⣶⣤⡍⠀⠂
⠀⠤⣬⡽⣿⣿⣾⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠶⣿⠖⠿⣿⣿⣿⣿⣄⠙
⠀⠀⠉⠁⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠳⠽⡿⠛⠛⠛⠛⢻⠿⡇⠹⣼⣤⣤⣶⣶⣤⡹⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠙⠻⣻⣿⣿⣿⣿⣦⣶⠞⠃⠀⠀⠀⠌⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⢒⣿⡀⠤⠤⡇⠀⠀⠀⢀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣳⣤⣤⣷⣴⣶⣾⣿⣿⣿⠁
⠀⠀⠈⠀⢀⣀⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣋⣯⣟⣿⣆⠀⠀⠀⠀⠐⠦⠄⠐
⠀⠀⠠⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣏⣽⣿⠟⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠉⢉⡉⠁
⠐⠚⠛⠿⠷⠶⠾⣟⠛⠛⠹⠛⠿⣷⣿⠟⢻⣿⣿⡿⠿⠽⠛⠛⢛⣖⣿⢿⣿⡟⠉⠉
⠀⠀⠉⠛⠛⠀⠰⠦⢭⣍⣉⣁⠀⠈⠛⠋⠬⠽⣿⠅⠀⠒⠒⠒⠒⣂⣉⡭⠉⠉⠀⠒⠒⠒⠢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠁⠀⠈⠉⠑⠒⠀⠀⠀⠉⠉⠓⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡀⣷⠀⣼⢀⡴⠎⠀⠀⠀⠀⢐⢺⡏⠄⠀⢀⠉⢲⠀⠀⠀⠀⠀⠙⠛⢶⣄⠀⢰⠟⠀⠘⣆⢣⣈⣴⢀⡔⠀⠀⠐⣿⣄⠀⠀⠀⢀⣹⣧⣤⣤⣤⣾⠟
⠀⠀⠀⠈⢷⣼⣼⣷⢟⣀⣀⠀⠠⢤⠔⠀⣹⣇⠄⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠻⣦⠓⠀⠐⡖⣲⠀⢟⢃⣿⡵⠂⠀⠀⢸⣿⣤⣶⣿⠿⠟⢛⠉⠉⠉⠁
⠀⠀⠀⣀⠀⠙⠿⠟⠛⠉⠁⠀⠈⢻⣏⡀⠨⣧⠄⠀⢆⢀⡀⠀⠊⠵⠀⠀⠀⠲⠀⠀⣟⠀⠀⠀⠐⠈⡖⣆⢨⠄⠁⠀⠀⢀⣼⣿⡿⠋⠀⣀⣤⣬⣷⣷⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⡠⠐⣷⠄⠘⣾⣫⠄⠀⠉⠐⣀⠀⠀⠀⡆⠀⠀⠈⠡⠀⠀⠘⠿⠿⢃⠀⠀⠀⢴⣿⣿⠏⠀⠀⣀⣿⣿⣿⣿⡿⠓
⠀⠀⠀⠀⢁⠄⠀⢀⠀⠀⠁⠀⠀⠀⠠⠿⣬⣿⠊⢱⡿⠄⢀⠀⠀⠀⠉⠀⠤⠀⠈⣀⠠⠲⠀⠀⠀⠰⠖⠚⠟⠀⠀⠀⠀⠉⠁⠀⠀⠀⣸⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣹⠛⠂⢠⡉⠦⡒⠤⠄⠀⠐⡸⠐⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⣀⢀⡀⡀⠀⠀⢱⡄⠀⠇⠀⠀⠈⠿⠉⠁⠀⠰⢐⠣⠼⠀⠆⠠⠈⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠛⣿⡇⠀⣴
⠀⢀⣀⡀⠀⢀⡀⠁⠀⠀⢨⣵⢀⣟⠀⣰⠀⠀⣀⣤⣄⡀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣀⠀⠀⠀⠐⠂⠀⢰⠀⠀⠀⠀⠀⣿⡇⠀⡿⠀⠀⠀⠀⠈
⠀⣿⣿⣿⡀⠸⣿⣾⣷⠀⢨⣶⢾⣭⢴⡍⠀⢀⣛⣓⣉⣵⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠠⡄⠀⠐⠁⠀⠀⠀⠀⠀⣿⣧⡾⠃⠀⠀⠀⠠⠀⠄
⠀⢹⣿⣿⠇⢠⣿⡿⠃⠀⠀⢰⣿⡿⡦⠀⠀⠘⣿⠿⠷⠾⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⠿⢀⡤⠁⠀⠀⠀⠀⠀⣭⣻⡰⡞⠁⠀⢰⠶⢖⣻⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣿⡇⠀⠀⠀⠀⠀⠎
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠏⠋⠀⠀⠀⠘⢿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠃⠀⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⣶⣾⣷⣀⠀⢀⡀⠴⢃⡄⢀⣠⡄⠀⠦⠀⠀⠀⠐⣄⠀⠄⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠑
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣴⡇⠀⡆⠀⠀⣿⣿⣿⣿⡀⢲⡙⡘⣆⣃⠀⡁⡦⢀⡃⠈⠀⠀⠠⡀⢂⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢶⠘⡁⠈⠁⠀⠘⡛⡴⠁⣠⣶⣤⠀⠈⠆⣡⠀⠠⢀
⠀⢠⣭⣏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⡏⠀⣀⠈⠁⠀⠈⠀⠀⠁⠀⢸⣿⣿⣿⡇⠀⠀⠈⠛⠟⠋
⠀⠈⠖⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠀⠀⠀⠀⢹⣿⣿⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠄
⠀⠀⠍⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠠⠄⠀⢸⣿⣿⣿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣠⣼⣦⠀⠀⠀⠐⠀⠛⡛⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣤⢀⡀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⢠⠰⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢀⡄⣸⣿⡼⠇⠀⠀⢸⣇⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⡆⠉⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣀⡏⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦
⠀⠀⠸⣿⣿⡯⠀⠀⢀⠀⢨⣷⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠖⠀⠀⠀⠸⣄⣧⢰⡄⣿⠃⡏⣤⠀⠀⠀⡄⢀⡠⠂⠀⠀⢀⣤⢄⡀
⠀⠀⠀⠙⣿⡇⠀⠀⠼⢷⣘⣏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡄⣇⣿⢠⡇⣿⠀⠀⠀⢃⠀⢀⠀⠀⢀⠿⠇⡋⢿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣶⢿⠃⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢚⣇⠰⠄⠀⠀⠀⢣⢹⣿⣸⣇⠇⠀⠀⠀⡎⡀⣻⠀⠀⠈⡆⠃⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣌⡁⠀⢫⡔⡮⠁⠀⠀⠀⢻⣿⣿⠞⠀⠀⠀⠀⠰⣃⣿⠀⠀⠀⠑⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠠⠀⢀⡿⡿⢗⢐⡱⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣻⣿⠀⠀⠀⠀⠱⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠒⠒⠒⣿⡂⠤⠤⣯⠀⠀⠀⠀⣀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣦⣤⣼⣴⣶⣾⣿⣿⣿⠏
⠀⠀⠈⠁⢀⣀⣀⡀⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣋⣯⣽⣻⣇⠀⠀⠀⠀⠀⠲⠄⠐⠒
⠀⠈⠡⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣟⣽⣿⠟⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠈⠍⣉⠁
⠒⠚⠛⠿⠷⠶⠾⣟⡛⠛⠫⠛⠻⣷⣾⠿⢛⣿⣿⣿⠿⠯⠟⠛⢛⣷⣛⡿⣿⣿⠉⠉⠁
⠀⠀⠉⠛⠛⠀⠐⠦⠭⣍⣉⣁⠀⠈⠛⠋⠥⠽⣿⡧⠀⠐⠒⠒⠒⣒⣀⡭⠉⠉⠀⠐⠒⠒⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠃⠀⠀⠉⠑⠒⠒⠀⠀⠈⠉⠙⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣇⡶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠻⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠒⣦⣵⣸⡟⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢆⡁⢂⠘⠈⡌⠘⢀⠠⠆⠀⠀⠀⠀⠔⢁⠄⠊⡁⠄⠂⢘⠻⣜⣻⠶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢤⡀⠙⢦⡸⣿⡤⠋⠀⠴⡳⣖⠠⣄⡎⠠⢂⡤⠊⠀⡠⠊⠁⢠⢹⣮⣳⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⣢⣌⡙⣿⣿⣿⣾⠧⠒⢖⠾⠎⢣⠀⠱⣧⠊⠀⢀⠜⠀⠀⢀⠃⠈⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢦⡤⠀⣡⢚⡟⢇⡉⣗⠢⡎⡄⠀⢡⠀⠘⣤⠐⠁⠀⢀⠀⠁⡰⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠃⡼⡵⠛⠁⡎⢁⠈⠁⣾⠀⠀⠰⠀⠀⢣⠀⠰⠄⠄⠀⠁⡠⠞⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠭⠭⢉⡚⠀⠀⢡⠀⠲⠀⠈⠟⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⣶⣤⣢⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠤⠤⠀⠀⠀⡅⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠂⢤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢫⡁⠒⠠⠤⠄⢚⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣁⡂⠐⢒⡩⡆⠇⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠐⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠈⠀⠀⢸⠀⠀⠸⠀⠀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⠰⡀⠠⠀⠀⠀⠇⠀⢸⠀⠀⡄⠀⢠⠁⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣄⣥⣀⣆⠀⡀⢰⡀⢨⠀⢀⣇⣀⣼⣤⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠷⣧⣭⣩⣍⣿⣍⣏⣉⣋⣍⣩⣥⣤⠴⠟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠔⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣣⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡾⢋⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀⣀⡴⣫⡾⣫⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢃⠀⠀⠀⠀⣠⠞⣫⢾⣫⡾⣻⠿⣋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠀⣠⡴⢛⡵⢚⡵⢟⡥⢞⡡⢞⡥⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⣟⣡⠖⣫⠞⣩⢖⡫⢖⡩⢖⣡⠞⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢻⡴⢚⢵⡪⢒⣩⠖⣋⡴⢛⡵⣫⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⠀⠀⢺⡕⣫⠖⢋⣴⠞⡩⢖⣭⢞⣩⢞
⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣻⣵⡟⠀⠀⠀⠀⠀⠀⠀⠀⢊⣠⠾⣋⠔⣫⠖⣫⠶⣫⣴⣿
⡶⠮⣍⡛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠟⣃⡭⠾⣋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⢞⡵⣊⡵⣻⡵⠞⣉⣤⣴
⣉⡛⢦⣍⡳⢬⡙⠷⣦⣀⠤⠤⠤⠤⠶⣶⡿⠿⠛⣉⡡⠔⢚⣉⣥⣶⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣾⡿⣺⣵⠾⠛⢋⣩⣴
⡯⣝⡓⠮⣝⡶⣌⡳⢬⡙⢷⣦⡤⠭⠵⠖⣚⣋⣭⣴⣶⡿⠿⣛⣩⠵⣒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣈⣠⣤⠶⠟⣛⣽⣿
⣭⡓⠭⡓⢮⣙⠦⣝⠶⣝⠦⣈⠻⣿⡛⠉⠝⣓⡫⠭⠔⣒⣩⠥⠒⠋⣉⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣡⣴⡶⢟⣿⣟⡵
⢌⡙⠷⣦⡑⠈⢑⠈⠳⢾⣿⡮⣓⠌⠳⣌⠡⠶⠒⠓⢉⣁⣤⠴⠞⣛⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⣠⣴⡿⣫⠞⣡
⠶⢦⣅⡈⠙⠷⣦⣈⠢⣄⠙⢿⣮⣷⢤⡈⢣⡐⢒⠈⠡⣁⣢⡼⢟⣋⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢛⡿⢋⡼⢡⡞⢁
⣿⣷⣮⣝⡳⢦⣄⠉⠻⣮⣓⢷⡿⣛⣷⣹⣤⡴⠶⢾⣛⣉⠙⠲⠦⣬⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⠔⢉⡴⣫⡶⠋
⠭⢍⣛⣻⣿⣷⣬⣽⡤⠶⠿⠛⠛⠯⠭⣉⡓⠲⠶⣤⣍⡙⠛⠶⣤⣀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⣥⠞⣫⡾⢋⣤⠾
⢷⣶⣤⣐⠲⢤⣤⣀⣀⡀⠐⠛⠛⠛⠒⠶⠦⣭⣝⣒⠾⠿⣷⣦⣤⣉⡛⣿⣀⣀⠠⠤⠄⠀⠀⢴⣢⡼⠛⣁⡴⣛⣡⠆⠙⠴⣋⡵⢛
⢦⣌⠓⠮⣽⣒⠶⠬⣭⣝⣛⣛⡛⠛⠛⠒⠲⠶⠾⠽⠿⠷⣶⣾⣿⣿⣿⣿⡋⡏⠉⠉⠉⠀⠀⠒⠒⠒⣈⠡⠬⠭⠭⠥⠵⡯⠵⠚⢋
⡳⢭⣓⠦⣬⣉⡛⠶⢤⣮⣭⣭⡭⠿⢿⣿⣶⣖⣒⣒⣲⣶⣶⣶⣯⣽⠟⠉⣇⢱⠀⠀⠀⠀⠀⠀⠭⠀⠀⣒⣠⣤⣶⡶⠶⠷⠖⣛⣋
⣍⣓⠮⣭⣛⣿⡿⣿⣦⣶⣤⣍⣩⣭⣭⣧⣤⠤⠶⢿⣿⡿⣟⣫⣭⠿⢷⣾⣿⡘⣤⣶⣤⣀⣠⣴⣶⡾⠟⠛⢉⣁⣤⣴⡶⠿⢛⣛⣉
⣚⢿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣶⣶⣶⡶⠿⢛⡩⠥⠴⠶⣖⣒⣛⣉⣽⠿⣱⣭⣿⡿⠟⠋⢉⣠⣤⣶⣿⣿⡿⠿⠿⠛⠛⢉⣉⣉
⠿⣿⣶⣾⠭⢭⣭⣭⣽⣿⠿⠿⣛⣋⣩⣴⣶⣬⣥⣬⠄⠩⠭⠭⠭⢖⣪⣶⠿⠛⢉⣁⣤⣶⡿⠿⠛⣋⣉⣡⠤⠴⠒⠚⠛⠛⠉⠉⠉
⣽⣶⣶⣿⣿⣿⣯⣭⠶⢂⣉⣡⠤⠤⠒⣒⣒⣒⣒⣒⣒⢒⣿⡿⠿⠋⣁⣤⡴⠾⢛⣉⣥⠴⠖⠚⠉⣉⣀⣀⣤⣤⣤⡶⠶⠶⠶⠟⠛
⣭⡭⠭⣷⢒⣪⡭⠖⣛⣩⠥⢖⣛⣋⣉⣭⣭⣭⣉⡭⠟⢋⣡⡴⠾⠛⣉⡥⢖⣚⣩⣥⡶⠶⠟⠛⣛⣉⣭⣭⣴⠶⠶⠶⠶⢞⣛⣛⣛
⢖⡶⠟⣋⡭⢄⣒⣭⣶⡶⠿⠿⠿⢯⣤⡤⢞⣫⣭⠶⣛⣩⣥⣶⣾⡿⠶⢛⣋⣩⣥⣴⠶⠾⢛⣛⣉⣭⠤⠴⠖⢒⣛⣉⣉⣉⣉⣉⣉
⠛⠚⠛⠑⠚⠛⠻⠟⠛⠻⠿⠷⣶⣿⣿⣛⣫⠵⣖⡿⠿⢛⣋⣭⡴⠶⠛⣛⣭⡭⠶⠖⢚⣛⣭⡭⠶⠶⠚⣛⣛⣉⣭⣭⣭⣥⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠂⢐⢧⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⢸⡌⢀⣤⡞⠐⠃⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⡂⢀⠔⣸⣿⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⡉⣰⡿⣿⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣤⠾⢂⣾⣿⠀⡟⣧⠀⠀⠀⠈⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⢈⠘⠁⠀⣾⣏⡏⠀⡇⢿⡀⠀⠀⠐⠒⠀⠀⠀⠸⠆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡤⠁⠀⠀⣾⣿⣿⡇⠀⡇⢸⡇⠀⠀⠀⠀⠑⡀⠀⢠⠅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⢎⡀⠀⢀⡿⣿⣿⣿⠄⠠⡇⠀⣿⡂⠀⠀⠀⠀⠈⠆⢀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣤⣉⣀⠀⡀⠀⡇⠀⢻⣏⠀⠀⠀⠀⠀⠀⠸⡷⡶⢦⣤⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣤⣼⣶⣤⣤⣤⣃⣀⣀⣀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⢠⣴⠶⠾⠿⡭⣤⣒⡚⠛⣛⠛⠛⠻⠿⠟⠛⠻⠿⠿⠿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⠁⠤⠤
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠃⠀⠤⠖⠊⠉⠩⠵⠖⠛⢳⡖⢀⣤⡴⠶⠶⢟⣩⠴⠤⣤⣴⣶⡆⠨⢤⡤⠉⠀⢀⢀⡤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠴⠤⠈⠭⢉⣉⡥⠴⠶⠒⠒⠒⠲⠄⠈⠉⠉⠀⠀⠀⠉⠛⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⡉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⣀⣀⣈⣁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⣀⣈⣠⣤⠤⠀⠌⠥⠴⣺⠁⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⠐⠂⠀⠣⠁⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠤⣀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠤⠊⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠖⠉⣀⡤⠒⠈⢁⡠⢀⠔⠀⠀⠉⠉⡁⠀⠀⠁⢉⠁⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠃⠀⡠⠊⠁⠀⢀⠔⠉⣠⠃⠀⠀⠀⠄⢠⠀⠸⠀⠀⠸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡑⠀⣠⠊⢀⠂⠀⡰⠃⠀⡴⠁⠀⡜⠀⠀⠀⡎⢠⠃⡇⠀⢠⡙⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡔⠁⠀⠀⢀⠜⠁⡠⠊⠀⢰⢰⠁⠀⠀⡜⠀⡜⠀⣻⠀⢸⢡⠸⡄⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⢀⡠⠚⠁⠀⠀⡠⠨⠀⠸⢸⠀⠀⡜⠀⡜⠀⢈⠉⡆⢸⢸⠀⢣⠀⠸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠁⡰⠁⢀⡰⠋⡰⠁⠀⡇⡆⠀⢈⠀⡜⠀⠀⢸⠀⡇⠸⢸⠀⠸⡀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⣁⠔⠉⢀⠜⠁⢀⠜⢰⠁⠄⣡⠞⠀⡀⢀⣾⠀⡇⡇⢸⠀⠀⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠔⢃⠠⠔⠁⣠⠃⡠⠊⠁⠀⡜⠀⡜⢸⢠⢡⠁⡌⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡇⢰⠁⠀⠀⠌⠀⡼⠀⢸⠀⠆⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠐⠀⠘⠀⠀⡆⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠰⠁⢀⠊



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠣⡀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠑⣄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠂⠒⠀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⣀⠀⠰⡧⠽⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢢⡄⠀⠈⠀⢀⡇⠀⣀⠠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢍⣭⡝⢛⣒⢦⣈⣀⡀⠀⠀⠀⠀⠀⣿⠐⠀⠀⠛⠀⠄⢠⡄⢈⣑⣠⣴⠎
⠀⠀⠀⠀⠀⠠⠤⠶⣤⣤⣤⡀⣀⣀⣤⣀⠘⣿⣿⣾⣿⣶⣬⣭⣽⣏⣉⣾⣀⣐⣃⣀⣶⣤⣤⣽⡶⠶⠛⢻⡟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⢐⣶⣶⣶⣮⣿⣟⣻⣿⣿⣿⣿⠿⣿⣿⠫⣿⣿⣧⠖⢦⣭⣭⣭⠨⢭⣥⣶⣢⣤⣿⣟⠛⢻⣶⣶⠏⢀⣒⠂⠀⠀⠁
⠀⠀⠉⠀⠀⠚⠤⠀⠙⠛⢛⡛⠡⠐⠺⠿⠶⠦⣀⣬⠛⠛⠿⠿⣒⡾⠛⠉⠠⣾⣿⣥⢂⠀⢩⡍⠀⣉⠉⠒⠂⠉⠉⠀⠀⠘⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠛⠀⠲⠂⠘⠛⠛⠻⠤⠀⠀⠐⠒⠀⢲⡀⠉⠉⠩⠤⠄⠀⠀⠉⠥⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣭⣭⣽⣤⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣾⣷⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡠⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠱⠄⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⢦⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠂⢾⡷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⠙⠆⢆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠸⢻⡏⠀⡇⠸⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠁⡌⡇⠀⢧⠀⢩⣄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⢸⠇⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢘⡀⠀⡈⢿⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⣇⠀⠦⠈⠟
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⢀⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⡑⢀
⠀⠀⠀⠀⣸⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠷⢀⠀⠀⠀⠀⢀⡹⢦⣶⡀
⠀⠀⠀⢀⣿⣿⣦⠂⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠲⠶⣽⣾⣿⣿⣦⡀
⠀⠀⠀⠈⠛⠛⠷⠾⠷⣤⣤⣤⣀⣀⣸⣻⣰⣀⣀⣠⠀⡀⠀⠀⠈⢂⠀⠀⠀⠀⠈⠉⠙⠛⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣄⣼⣭⣭⣿⣿⣡⣶⠰⣧⣧⣤⠧⣀⣸⣦⣤⣴⠶⠒⠒⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣴⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠙⠹⠟⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⡟⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⢰⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⣧⢸⣿⣇⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⣶⡄⢀⢰⡇⢠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡄⢰⢀⡇⡇⠀⠀⠀⢿⣿⣙⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⡇⣼⠈⣷⣼⠀⣶⣦
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣧⢸⣸⣿⠃⡇⠀⠀⠈⠛⣿⣿⡿⠿⣿⡿⠋⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣾⣿⡏
⠀⠀⢸⠀⠀⢰⣿⠁⠀⠀⢸⣿⣿⣿⠏⠸⠇⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣶⣾⣾⣦⣼⣿⡇⠀⠰⣸⣿⣿⣿⠀⢤⣼⠀⠀⠀⣸⣿⡿⡇⢸⣿⣇⢀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡓⣿⣿⡖⣿⣿⣿⣿⣿⣿⣾⣿⣷⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⢿⣿⢟⣷⣿⣿⣿⣿⡿⢯⣬⢄⡹⣿⣿⣿⣿⣿⣿⡿⢹⣿⡿⣭⠞⡁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡬⣯⣡⣽⠂⡽⠏⠟⣟⣷⣾⣇⡀⠀⢹⣿⠛⠻⣿⡿⢋⣹⣿⡁⠁⠐⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⢻⠅⣈⣥⠹⡇⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⢾⣻⣿⣿⣿⣷⣾⡶⢶⡿⠿⠿⢿⠿⡿⠿⠿⠿⣿⣿
⢸⣿⠷⠀⠈⠉⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿
⠰⠆⠒⠤⠤⠠⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠋
⣀⣤⢤⣶⣾⡿⠿⢻⡿⢋⣭⠉⠁⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣤⣴⣿⣿⡽⠃
⠻⣿⠀⠫⢥⣀⠒⠛⠳⣿⣿⡀⠀⠀⠀⠌⠉⠁⠃⠀⠁⠀⠁⠁⠉⠉⠁⠀⠄⠀⠠⠀⠤⠰⠨⠭⠭⠭⣼⣿⣏
⠀⠈⠓⠦⣠⠒⠒⠾⡶⠠⠒⠂⠀⠠⡄⠀⡀⠀⢂⠉⢀⣀⣀⡄⠀⣀⣀⠀⠀⠈⠀⢀⣀⡤⣶⠟⠛⠓⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣴⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⠤⠤⠤⠤⠤⠤⣶⣖⣚⣩⣵⠞⠁⠀⠀⠀⠀⠙⢮⣋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢌⣆⠤⢆⡄⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠰⠀⠀⠀⠌⠢⠈⠢⡈⠂⠂⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⡇⠀⠄⣀⠂⢄⠢⠀⢈⠀⣀⠠⠄⠤⢱⣄⣣⡀
⠚⠁⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⢄⡀
⠀⠀⠀⠀⠓⠤⢄⡀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠘⣠⠴⠊⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣁⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠿⠘⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⡠⠖⠀⡠⠒⠀⠀⣏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢹⠀⠀⠀⠀⠀⠨⠭⠄⡠⠾⢑⠟
⠀⠀⠀⠀⠀⠀⢸⠤⠒⡉⡀⢀⠌⠀⠀⠀⠀⢣⠄⠀⡀⠀⠄⠈⠙⢁⡘⠤⠐⠈⠁⠀⠀⠑⢌⠠⠀⠐⠄⡴⠊⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣁⡠⢊⠊⢠⠊⠀⠀⠀⠀⠀⢹⡒⠁⢀⣀⣀⠴⠈⣡⢀⠄⠠⠠⠴⠄⢀⣀⢀⡉⠀⡄⠐⠒⠉
⠀⠀⠀⠀⠀⠀⡝⡰⢁⡴⠁⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣠⣟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡈⠀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠂⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠀⠀⠀⠀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣠⡤⠼⠗⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠉⠁⠀⠀⠀⠀⠀⢠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⡤⠤⠶⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠖⠛⠋⠉⠁⢸⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣻⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⡏⣄⣀⡠⠤⢲⠚⠀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣤⡤⠶⠒⢺⠏⠁⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡆⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠈⠀⠈⠆⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⢀⣴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⢀⡠⣆⣴⡟⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣠⠴⡶⠛⠭⠠⢠⣏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⡾⡔⠚⠋⡀⠟⢀⣠⣴⣶⣖⣾⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠉⠀⢀⡧⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣗⣊⣥⣴⣾⣿⣿⣿⠿⠛⡿⣿⣿⣿⣋⢀⡀⣀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠈⣛⠛⡛⠋⣋⣯⣍⢓⣻⣷⡎⢿⣻⣯⠙⣿⣿⣿⡟⠛⠶⣶⣿⣷⣞⣉⣀
⠀⠀⠀⠀⠙⠉⠀⠀⡠⠙⣉⣠⣿⣭⣽⣿⣿⡞⢛⣯⣥⣶⣿⣟⡛⠟⢛⣩⣶⡈⠀⣍⣛⣛⠛⠻⣿⣿⡿⢶⣿⣯⣟⡛⠁⡤
⠀⠀⠀⠀⠀⠒⠒⠂⠉⠉⢭⣥⠄⢘⣿⣛⡉⠉⠥⠼⠛⠋⠉⠩⠔⠂⣸⡿⣟⠁⠀⢶⣭⣹⡧⣠⠤⢴⣶⣶⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣦⠄⠀⠉⠁⠀⠀⠀⠉⠙⠉⠀⠀⠒⠬⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠿⢷⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⠀⠀⢸⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⣿⠀⠀⠸⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⠋⢿⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡇⣿⠀⣷⠀⣿⠀⣴⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠈⠃⢸⡷⠘⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⡂⡼⠀⠛⠀⣻⡄⠀⠀⣠⣾⣮⣴⣆⠀⠀⢰⠀⣿⡀⢰⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⡇⢹⣾⠆⣼⠛⡇⠀⢀⣛⣹⣿⣿⣿⣤⠀⠈⢠⠏⠃⠈⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡇⢹⣇⣼⣡⣤⣀⣶⡄⠀⢹⣿⣿⣿⣿⣠⣿⢠⡀⢸⠀⠆⢸⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⢻⣿⡿⢿⠞⣷⠀⣆⣿⢹⣿⢻⡉⣿⠿⠁⠸⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⣼⡏⣧⣸⠁⠈⠀⠆⢾⣿⣿⢸⣿⢹⣷⣿⡀⠀⡾⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⣿⠃⠟⢹⠀⠀⠀⢰⠸⣧⡏⣸⣿⣸⣧⠿⠧⢘⡇⢠⢠⡿⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⠀⡀⢙⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣶⣿⡿⣦⣸⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⠀⠁⢸⠀⡄⢰⡆⠀⢸⣇⣿⣿⡧⡻⢇⣿⡛⡧⠙⣿⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⠀⠀⢸⡀⠀⠈⠇⠇⢸⣿⣿⡟⠁⡇⢈⢸⠁⡇⠸⢻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠃⠸⡇⢠⠀⡆⠀⢸⢻⣿⡇⢀⠃⠘⢌⠀⠁⠘⢸⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠁⠀⡇⠀⠀⢿⠀⢸⣿⣿⡇⠸⠀⠀⠈⠀⠀⡆⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠐⡄⢿⠀⠀⣼⠀⠸⢿⣿⡟⠀⠂⠀⡜⠀⠀⢸⣿⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢱⠸⡇⠀⢸⠀⢸⣿⣿⡇⠈⠀⢸⡇⠀⣀⢰⣿⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⡆⢰⠀⢸⠀⠸⣿⣿⣧⠈⡀⠐⡆⠀⢉⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠁⠘⠀⢮⠀⣸⣿⣿⣿⠀⡇⢰⣇⠀⡄⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⡄⢀⠟⣸⠀⢿⣿⣿⣿⡆⡗⣸⡏⣰⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⣿⣿⣿⣿⠈⣐⢻⣥⣾⣿⣿⣿⣿⣴⣿⣷⣿⣿⣿⣿⣿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⡾⠟⠟⠯⠬⠭⠍⠿⢭⠭⠍⠉⠉⠙⠛⠛⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡙⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⠦
⣤⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣽⣿⡿⠿⠧⣽⣿⣿⣿⣿⣿⢿⣿⣷⣶⣶⣦⣤⣤⣄⣽⣿⣷
⠛⢻⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠶⠶⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣦
⠀⠀⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠘⣿⣿⣿⣿⣆⣀⣀⣀⣰⣶⣶⣶⣶⣾⡿⠿⢿⡟⠛⣿⠛⢛⠉⠻⠏⠁⠉⠙⠟⠛⠛⠿⠻⢿⢿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠭⠿⠀⠠⠾⠀⠀⠒⠒⠒⠂⠀⠙⠀⠀⠀⠉⠀⠀⠴⠀⠐⠇⠚⠛⠛⠿⠻⠿⠿⠩⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣿⣿⣿⣷⡤⠄⠀⠀⠀⢀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠠⠄⠀⠤⣤⠀⣈⠉⠹⠯⠄
⠀⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠿⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁

⠀⠀⠀⠀⠀⠀⠐⠒⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⢖⣦⣾⣿⡿⣿⣿⡟⢸⢞⢲⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣭⣽⣿⡿⢋⣵⣾⣿⣿⣿⢳⣿⡿⡇⠹⣙⡢⠋⠁⡬⠛⠁
⠀⠀⠀⠀⠀⠤⠶⣾⡿⢋⣴⣿⣿⣿⣿⣿⠃⠙⡛⠀⠀⠠⡀⠀⠀⠈⠉⢙⠇
⠀⠀⠀⠀⠄⠲⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡀⠀⠀⠨⡀⠀⢁⠤⠃
⠀⠀⠀⠠⠶⢾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠂⠈⠳⠤⠝⠁
⠀⠀⠀⢀⣴⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋
⠀⠀⠀⢠⣼⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⢀⡠⠄
⠀⠀⠀⢀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣴⣤⣶⡿⠋
⠀⠀⠀⠁⣽⠨⣿⣿⣿⣿⣿⣿⣝⡛⣿⢕⣣⢴⠟⠛⠉
⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⡀⠅⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠐⠀⠱⠹⣿⣿⣿⣿⣯⢢⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠸⣄⢣⢽⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣧⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠹⡆⣬⡻⣿⣿⣿⣷⣷⣄⢀⣠⠾⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⣿⠑⣮⠿⣿⣿⣿⣿⣀⠉⠋⠉⠙⠶⠆⠀⠀⠀⠀⠀⠀⠐⣘⣧⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜⡓⢮⡛⢿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⢤⣄⣉⡛⠿⠿⣿⣶⣶⣶⣶⣾⣷⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠋⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⢠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠆⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢃⢠⠜⢀⡀⠠⡄⠀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢠⠀⣸⣼⡟⢛⣻⣿⣿⣾⣿⡿⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠛⠉⣰⣿⣿⣿⠛⣦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣠⣦⡀⠀⢸⣿⠟⢯⢃⡴⠞⢋⣴⣿⣏⣴⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⣻⣿⣥⠶⠋⣷⣶⠖⣩⣴⣶⣿⠿⢿⣿⣿⡿
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣯⣹⣿⢽⣿⣿⣾⣯⣥⣤⠟⠋⠩⣥⡾⣿⣿⣿⣧⣄⠐⠂
⠀⠀⠀⠛⠾⠷⣶⣶⣿⣿⣦⣭⣿⣿⣾⣧⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠈⣻⣷⠶⠄
⠀⠀⠀⠀⠀⠀⠩⠷⠋⠉⠉⠉⠀⠉⠉⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠢⠤


⣿⡏⠉⢻⠟⡿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀
⠀⠀⠀⠈⠚⠉⠳⠀⠀⠀⠀⢀⢪⠉⠋⠄⠀⠀⠀⢠⣵⠌⠦⢡⠸⠀⠀⠀⠀⠊⢠⠀⠀⠀⢠⡾⣿⢆
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠗⠁⠀⠀⠀⣸⡑⡆⢰⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⢠⠁⡍⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡴⠀⠂⡄⢚⣧⣥⣬⡴⡏⠀⠠⠀⠁⠀⠀⠀⠀⠀⠂⡅⡇⣷
⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⢰⠀⡠⡀⠀⡃⠀⢠⠃⠀⠀⠉⠉⠀⠀⠀⠠⠀⡀⠀⠀⡀⠀⡀⠐⣡⣇⡇
⠀⠀⠀⠀⢱⠀⠇⠀⢠⠃⠀⠀⠑⠤⠒⠒⡌⠀⠀⠀⢀⣠⣶⣀⠀⠀⠀⠐⠄⠀⠀⠏⠀⠀⠀⠹⠿⠁
⠀⠀⠀⡀⠙⠀⡤⠠⠃⠀⠀⠀⠀⢂⠀⠀⠄⠀⠀⡜⢡⠊⠉⠑⠙⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⢀⠞⠁⠉⠢⠀⠀⠑⠌⣄⣀⡠⠖⠁⠀⠀⢠⠀⠀⣠
⠀⠀⠀⠀⠈⣦⠃⠀⢀⡠⢅⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠙⠀⠀⠐⡤⠊⠉⠈⠑⡄⠤⠚⠀⠀⠀⢠⠂⠢⠀⠀⠀⠀⠉⢀⠀⢀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠒⠆⠀⠬⠇⠀⠀⠀⠀⢆⠀⠀⣰
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⢄⡀⠀⡰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⣩⣴⡀⠀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠟⡀⠀⠀⠀⣀⠴⣈⡷⠖⡢⡄⠀⠀⠲⠃⠀⠈⡋⠀⠀⠀⠀⠐⠂⠀⢠⡀⠜⠄⡀
⠀⠀⠀⢠⡌⣷⡄⠃⠀⠀⡜⠁⠂⠀⠁⠀⠈⠸⠀⠀⠀⡠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠠⡀⠺⡇⡼⣂⠂
⠀⠀⠀⠘⠹⠇⡅⠀⠀⠀⡇⠀⠀⠀⠈⠀⢀⢀⠃⢀⡠⣷⢣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠁⠛⠋⠉⠁
⠀⠀⠀⠀⢰⠀⠇⡀⠀⠀⠰⡀⠂⠀⠀⠀⡌⡜⠀⠃⠀⠈⢣⢠⠀⠀⠀⣀⠀⣀⠀⣀⠴⡶⡄⢀⢠⠒
⠀⠀⠀⠰⣎⠀⢸⡷⠀⠀⠀⠑⢄⢆⢐⣰⠜⠀⠀⢃⠀⠀⢸⠸⠀⠀⠸⣇⢀⠾⡖⣇⡄⡇⢇⣸⢨⣱⠄
⠀⠀⠀⠀⠚⣧⣸⠃⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠠⡀⢙⡆⠀⠀⠀⢀⠀⣄⣦⣀⠀⠄⢀⠀⡠⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣄⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠋⡝⠁⢹⠉⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡘⢠⠀⡎⠀⡈⡻⣧⡀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠻⠛⢷⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠇⠀⣇⠈⢰⡇⠀⠁⠱⢈⣷⠀⠀⠀⠀⠀⣤⡿⡼⠀⠀⡆⢸⠛⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡇⠃⢸⡇⠀⢠⠰⡏⠸⡷⠁⠀⠀⠀⣾⠁⡇⢰⠀⢁⠀⡇⢹⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⣄⡇⠀⢸⡇⠀⠎⢠⡆⠀⣿⠀⠀⠀⠙⣿⠐⣧⠀⠀⢸⠰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⢸⡀⠉⡇⠀⢸⡇⠀⡆⢐⠇⠀⣿⠂⠀⠀⠀⣿⠀⢸⠀⠈⠸⠀⠘⠀⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⢶⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠃⠀⡇⠃⠀⠃⠀⠀⢀⡇⠀⢹⠀⠀⠀⠀⣿⠀⠻⡀⠀⣀⠇⠘⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠃⢸⡆⠹⢳⡔⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⡇⠀⠀⣴⠇⠀⢸⠇⡔⣸⡇⠀⠀⠀⢹⡄⠀⡅⠠⢫⠀⣼⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢾⡁⢰⡄⣿⣄⡤⠀⠀⠠⣼⡇⠈⠀⢰⡇⠰⠀⡇⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⣸⡗⠀⡆⠀⢸⠀⣯⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⡘⠁⢸⠇⡏⣿⠀⠀⠀⠀⢸⡇⡀⠀⠀⡇⠀⠀⡇⢀⠆⠀⠀⠀⣾⠀⠀⠀⠀⢸⣇⠀⡝⠀⢸⢀⡗⢠⡗
⠀⠀⠀⠀⠀⠀⢠⣯⠀⢹⠀⠇⡠⢟⠀⡇⣿⡀⠀⠀⠀⢸⡇⡇⠲⠀⡇⢀⠀⡀⠀⠀⠐⠀⢀⣿⠃⠀⠀⠦⣸⠏⢶⠀⠀⡜⢻⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⡃⠀⠸⠀⡷⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠈⠀⡅⠀⠀⢰⡀⠀⣿⠀⠀⠀⣨⡟⠀⡜⢀⣴⠃⡬⢠⡿
⠀⠀⠀⠀⠀⠀⠰⣧⠀⢸⢢⠙⡆⢀⣄⡆⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠓⠀⠃⠀⠀⣸⠇⠐⣿⣀⣤⠾⠋⣠⡎⠀⣠⠃⡰⢁⣾⠁
⠀⠀⠀⠀⠀⠀⠰⣿⠀⢰⠀⢰⡀⠘⡇⠆⣿⠀⠀⠀⠈⢺⡇⡿⢆⠀⡇⠀⢠⡄⠇⠀⣧⠀⢠⡿⠭⠼⠒⢉⡳⠤⠚⣃⠟⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣆⠘⣱⠀⠇⢰⢿⡄⠀⠀⠀⢸⡇⡇⠀⠀⡇⠂⢸⡇⠀⠀⣿⠀⢸⡟⠒⢻⠋⣉⡹⠶⢺⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⠀⢻⠀⢸⠘⡜⢷⡇⢠⣠⣸⡇⡇⠀⢠⣇⠀⢸⡇⡄⠀⣻⡄⢸⣏⣹⣯⣥⣴⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣇⠘⢦⠈⢧⡈⠫⠿⠿⠿⢹⡇⡇⠀⠀⠏⠀⢘⠃⠈⠀⣿⠁⢸⡭⠍⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⡗⠈⠳⢄⣉⠚⠳⣆⡉⠨⣷⡇⠐⣄⠀⠀⠀⠀⠀⠀⣿⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠘⠷⣤⡤⢉⣉⣉⡩⠴⣲⣿⡇⠀⢹⠀⠀⠈⣦⠂⠀⡹⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣄⣀⣀⣀⣴⠶⠛⠁⢸⣿⠀⢸⠀⡄⠸⠏⠀⠀⢷⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢿⢸⠀⢀⠀⠁⠰⠀⢠⠀⠼⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⠀⠸⢦⠀⡀⠙⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠐⠈⠀⣷⠀⢰⠸⡆⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⢸⠀⠀⠿⠀⠀⢸⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢘⠀⠀⢰⡄⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣀⠀⢸⠁⠀⢸⠀⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠰⠈⠆⠘⠀⠘⢸⠀⣿
⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⡀⠀⠿⠀⠀⣈⠀⣿⠆
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⢾⣿⠀⢸⠃⠀⣟⠀⡔⡏⠀⡿⢶⣤⢤⣤⣀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠚⠋⣩⡀⠀⠁⢸⣿⠀⠈⠀⡄⣿⠀⠀⡇⢸⡇⠀⠰⠄⠠⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠄⠀⠒⠂⠻⢿⡷⠂⡆⠀⡿⢀⣀⣷⠟⠀⠠⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠙⢻⡷⠶⠿⠟⠋⠀⡀⠀⠙⠀⠰
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⢀⡀⠀⠈⠥⠤⠀⠀⠀⠤⠄
⠀⢀

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣄⡀⢈⣛⡛⠿⣿⡿⠛⠛⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣽⣿⢿⣿⣿⣏⢻⣷⣶⣿⠐⠂⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⡗⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⠘⠿⠲⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣠⣿⢷⣿⣿⣿⣿⡏
⢸⣿⣿⣿⣧⢀⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡟⠿⠃⣸⡿⠿⠟⠹⠗
⢸⣿⣿⣿⣿⣾⡿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣬⣿⣿⣟⠿⡿⠛⢻⣿⣿⠀⠀⠁
⢸⣿⣿⣿⣯⣽⣀⡈⠏⠉⠀⣤⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⡦⠤⢴⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠤⢤⣿⠇⢀⠀⠀⠀⠄⣀⣀⣀⣴⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⢻⡿⠽⡿⠿⠛⠛⠉⠉⠉⠉⢸⡿⠀⡈⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣾⣇⣶⡇⠠⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⢀⣉⣀⣀⣸⣃⣼⣿⣿⣿⣹⣽⣯⣽⣿⣿⣿⣿⣯⣽⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡉⠉⠉⠉⢩⣉⣉⣭⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⡀⡀⢠⣐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣧⡀⠀⠀⠲⣟⣻⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣂⣿⣿⣽⣟⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠿⡻⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⠉⣨⣴⣿⣿⣿⣿⣿⡟⢿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣶⣼⣾⣷⡟⢩⣿⣿⣿⣛⢛⣭⣿⠎⣉⡠⢧⡃⠉⢻⡆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⣟⣟⣭⣭⣽⢻⣬⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣭⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠞⠁⢁⣬⣶⣿⣿⣿⣿⣿⢿⣯⢿⣿⢿⣿⣿⣦⡥⢿⣿⢿⣿⣿⣿⡿⠒⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡟⣼⣿⣿⢿⣹⣿⣟⣻⣿⢹⢿⣿⣿⣿⣿⢸⢻⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠷⣼⣿⣿⣿⣆⣻⣿⣿⣖⢿⡜⠘⠏⢹⣿⣿⣌⡀⠀⠹⠛
⠀⠀⠀⠀⠀⣼⠿⠟⠏⠈⢠⣿⣿⡝⠯⡧⢹⣿⣯⡓⠸⣷⠀⠀⠏⢿⢿⡓⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡿⡝⠆⠀⢸⣿⣦⡉⠀⣿⢀⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠑⠈⠀⠀⠀⠻⠇⣩⣶⣿⡝⢿⣿⡿⣶⣤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡿⣫⠵⢿⣹⡇⠀⠀⠹⡄⢹⠷⠄⠀⣀⣙⠿⣔⣲⣤⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠛⠛⣿⣷⣾⣖⣲⣤⣄⣿⡗⠛⠛⠓⠂⢲⣶⡼⠶⢦⣸⣷⣶⡿⠿⠿⠿⠛⠛⠛⠻
⠀⠀⠀⠀⠛⠉⠛⠒⠒⠒⠚⣁⣤⣤⠤⠤⠌⠈⠉⠒⠒⣿⡇⠉⢁⣷⡆⢠⠈⣡⠈⣋⣉⣣⠤⠴⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡾⢸⢻⢃⣮⢞⢥⠀⠠⠤⠭⣭⣿⣿⣯⣈⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣬⡏⢀⡟⣯⣈⣬⡃⢻⣾⣯⣀⠀⠐⣾⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠒⠊⠉⢛⡽⠋⠋⠀⠸⠘⠹⠉⠳⠈⠙⠛⠿⠿⢽⣿⠿⠿⠓⠒⠓⠂

⠀⠀⠀⠀⠀⠀⡀⠐⠢⢄⡀
⠀⠀⠀⠀⡀⠀⠁⠁⠢⠄⡈⠑⠢⠄⡀
⠀⠀⠀⠀⠀⠈⠠⢄⡀⠀⠀⠈⠐⠠⢄⠉⠐⠠⡀
⠀⠀⠀⠀⢆⠀⢀⠀⠈⠑⠢⢄⡀⠀⠀⠈⠒⠠⣀⠙⠂
⠀⠀⠀⠀⠨⡀⠸⠧⡌⠃⠒⠂⠀⠓⠀⠀⢘⠀⠀⣘⡖⠠⡀⠐⠠
⠀⠀⠀⠀⠀⢿⠀⢁⠀⠂⠀⠢⡈⠉⠢⣀⠀⠁⠠⢀⠀⠀⠀⠁⠢⢀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⡝⠂⠄⢂⡀⠀⠈⠢⡀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⢀⠙⠠⢀⠁⠢⣀⠉
⠀⠀⠀⠀⠀⠀⠈⢌⠓⣀⡥⢀⡰⠄⠘⠂⠀⠀⠉⠁⠀⠀⠀⠋⠀⠀⠀⣀⡄⠑⠢⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠙⠻⣥⣠⠀⠄⠐⠂⠀⠀⠀⠂⢁⠀⡀⠀⠀⠉⠢⣀⠀⠀⡉⠢⠄⠀⠰⡤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠉⠛⠲⢦⣀⡀⠠⡀⠒⠀⠑⠄⠑⠀⡀⠀⠘⠁⠀⡇⠀⠀⠀⢠⠁⠰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠈⠙⠓⠾⢦⣀⣀⠀⠀⠀⠀⠀⠐⠀⢀⠁⠀⠀⠀⡀⢀⡇⢀⣤⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠀⠈⠉⠛⠳⠦⣄⣀⠀⠀⠀⠀⣂⣴⠶⠿⠟⠛⠛⠓⠛⠋⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⢀⠀⠑⢄⡀⠀⠀⠀⠀⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢈⡑⢄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠳⠊



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⡠⠐⣲⣷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⠭⠁
⠀⠀⠀⠀⡴⠛⣻⣟⣿⣡⢾⠏⠚⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⠏⣯⡉⠀⠀⣠⣶⡒⣂⣤⣤⡀
⠀⠀⠀⠀⠀⢸⠟⠹⠓⡹⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⡙⢀⠀⠀⠋⠘⢷⠈⠋⠗
⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⡀⠀⠑⠠⡀
⠀⠀⠀⡠⠃⠀⡠⠋⠀⠤⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠑⠀⡀
⠀⠰⠞⢁⣴⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠗
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⢿⠿⡿⡿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣾⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⡄⣻⣶⣤⣀⣀⡀⠀⠀⠀⣀⣤⠞⢉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣦⣤⡎⢀⣀⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠇
⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣻⣿⣿⣟⣻⣯⣿⣿⣟⣾⣻⡿⣻⡟⣻⡿⣻⡿⣿⡿⣿⢿⣿⣿⣿⣿⣷⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠏
⢀⣠⡴⠾⠟⠛⣿⣶⡛⠀⠙⠻⣮⣉⣠⣤⣤⣥⣿⡬⢥⣬⣧⣭⣠⣟⣘⠛⠁⠋⠘⠋⠾⠇⠸⠟⠹⡿⢻⣿⣿⣿⡿⣶⣦⣤⣤⣾⣷⣶⡟
⠀⠙⢣⡀⣀⠻⠿⠟⠀⠀⢀⠀⣻⡟⡟⠓⠉⠉⠈⠉⠉⣁⣀⣨⠭⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠾⠿⢿⣿⣿⣻⡅
⠙⠻⢦⣥⣞⡃⠀⠀⠀⠀⣴⡀⣿⣓⣳⣤⣤⠖⠈⠉⠉⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠉⠁⠉⠀⠀⠀⠀⠻⣝⠛⢻⡀
⠀⠀⠀⠀⠉⠛⠻⠶⣶⣮⣿⣿⡟⣛⣛⣿⣿⣿⣭⣭⣭⣵⣶⣶⠶⠶⢷⣴⣤⣶⣴⣶⣶⣾⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣿⣿⣯⣭⣭⣭⡭⠽⠿⠿⠿⠟⠛⠛⠛⠻⣿⡻⠏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣷⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣘⣷⣤⣧⣾⡻⠋⠉⠙⠛⠲⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣣⠅⠼⠘⠞⠒⠝⠸⠞⢀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣬⣭⣻⣿⣿⠵⠾⠿⠿⠒⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⢾⡿⢛⡿⣯⣛⠟⠻⣶⣤⡈⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠞⣵⣿⡆⣇⠙⣦⡀⠈⠙⠆⠙⠅⠀⠀⠀⠀⣠⣼⣷⡛⣚⠷⠦⠀⢀⣳⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⡄⣤⢻⣿⡄⠹⢶⣽⣿⣄⠀⠀⠀⠐⡀⠀⠐⣣⢞⢿⣷⣬⠈⢳⢤⣴⠞⣻⣿⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢡⠻⠘⣿⡇⠘⠀⢹⡷⠙⠐⠆⠀⠀⠀⠀⣸⠧⠈⠈⣿⣟⢷⡀⢸⡏⢺⡏⢌⠓⣆⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⢠⡀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠸⣿⡁⠀⠀⠀⠁⠂⠰⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⣄⡀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠠⡀⠀⠈⠙⢦⣀⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠤⠬⠯⠿⠿⠤⠴⠖⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣆⣤⡀⠀⠀⠹⣿⡄⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢈⣉⡀⣠⣤⠴⠚⠋⠀⠀⢠⢴⠖⠈⠀⠀⠤⠐⠂⠙⢿⣯⢦⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⡤⠶⠶⠶⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠈⠐⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣯⣷⡀⠀⠈⠳
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠤⢤⠤⣤⡤⠂⢀⡤⠖⠲⠿⠟⠛⠋⢀⡾⠀⠀⠀⠀⠀⢀⣤⠖⠒⠈⠁⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⢞⣋⣩⣥⣤⡤⣶⢶⡶⠶⢶⣦⣤⣄⣀⣀⣀⣠⣤⡤⡶⠚⠋⠀⠀⣀⣀⠤⠚⢉⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠠⠤⠤⠤⠤⠴⠶⠖⠒⠒⠂⠉⠉⠉⠉⠀⣀⣀⡤⠨⠀⠀⠴⠒⠊⠁⢀⡀⠄⠚⠁⠈⠀⠀⢀⣜⠛⣋⣲⣆⣤⡤⠟⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢉⣉⠥⠀⠀⠀⠀⣀⠠⠄⠀⠲⠉⠀⠀⠀⠀⠀⣠⡖⣥⣦⡾⢸⡞⠈⢙⡓⠢⠄⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠚⠉⠀⣠⠴⠒⠋⠉⠀⠐⠂⠀⠠⠂⠀⢀⠤⠐⠛⠱⠋⠽⠇⠀⠙⠋⠙⠛⠑⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣠⣤⣤⠤⠤⠤⣤⠤⣤⣀⡀⣀⣤⣰⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⣍⠻⣗⡒⠰⣟⡳⢉⣽⣟⢿⣿⡿⣶⣭⣟⠯⣫⡿⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢸⠐⣽⡧⠹⡿⠑⠺⡻⡿⠻⠍⡣⢛⢿⣿⡿⣿⣿⣮⣔⢩⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢘⣏⣶⣘⣿⡀⠇⢠⢀⡇⠀⠀⠐⠀⢸⣆⡠⢃⣿⣿⣿⣿⣷⣻⣽⣿⡀
⠀⠀⠀⠀⠀⠀⣴⢛⣭⣍⣉⡉⠘⠒⠋⢙⣷⠦⠤⠤⢔⣘⣠⠔⣨⠀⢛⣹⣿⣿⣿⣞⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠦⣦⡐⠀⠀⠉⠉⣛⣯⣤⣤⣄⣤⣾⣉⣁⠚⣠⣿⣿⣾⣽⣿⡿⣿⡾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣴⡖⠮⢿⣿⡿⢿⡛⠷⠊⠁⠀⠙⢿⣿⣿⡿⢛⣭⣬⣿⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣴⣤⣄⣀⡀⠀⠈⠁⠀⠙⢛⣫⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⡀⠀⠙⣿⣯⡹⣿⠀⠀⠀⠀⠐⣿⢿⢿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡿⠓⠦⢼⣾⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⡄⣤⣄⡀⢰⣾⢷⡏⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣀⣀⣀⣀⣀⡼⠃⣽⡿⣷⣝⣯⣿⡾⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠿⣿⣿⠀⠀⢹⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡯⢿⣿⣤⡐⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣽⢿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣡⢿⡿⠁⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠛⠛⠻⠿⣿⣆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣤⣤⣤⣏⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣣⣿⣧⣤⣤⣤⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠐⢂⡄⠉⠉⠉⠁⠐⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣥⣄⣀⠀⠀⠺⣿⢶⣿⣿⠄⣠⣶⣶⠀⠀⠉⠑⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣼⣿⣿⣿⣿⣧⠀⢀⣠⣀⡠⢋⣾⣿⣿⡿⣣⣼⣿⠟⢠⣄⣤⣬⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠀⣼⠟⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠉⠉⠋⣾⣿⣿⣿⠙⠿⠿⠜⠛⠛⢂⠤⣜⡂⠤
⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⢃⣼⡟⡌⠁⠋⢻⣿⣿⣿⠏⢰⠰⣴⡀⠀⠰⠀⠁⢀⠴⠒⠒⠒⠒⠀⠀⠀⢴⣿⣿⣶⡶⠖⠒⢷
⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⣷⣾⠛⢡⠀⠀⠀⠸⣻⣿⠃⢀⡟⣧⣿⣧⡀⠀⠀⠠⠃⠀⠀⡀⠊⠐⠀⣠⣶⣿⣿⣿⣿⠿⣆
⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⡏⠀⢠⠀⠀⡀⡀⠈⠃⢰⣼⡇⠸⣿⣿⣷⢀⠀⠀⠀⡠⠊⠉⠀⢢⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰
⠀⢀⡴⢋⠝⣫⣿⣿⣿⣿⣿⠇⠀⢸⡀⠀⠱⡐⣄⠀⢸⣿⣿⣄⠈⠛⠿⣿⣦⠀⢸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⡏
⣰⠋⠀⠀⠊⣡⣿⣿⣿⣿⡵⠂⢀⣾⡇⠐⢄⠘⠮⡳⢎⢿⣿⣿⣷⣦⣄⣀⠈⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⡃⡜⠀⡞
⢻⣀⠀⠀⠀⠺⣛⣭⠞⢁⣠⣶⡿⠃⠘⡄⠈⠓⢤⣘⣆⠳⢍⡻⠿⠿⠿⢿⣿⡦⠀⠀⠀⡈⠉⠒⠄⡈⠙⠻⠿⣿⠞⠀⡸
⠀⠈⠙⣶⡾⠟⠋⠀⠀⣿⡟⠉⠀⠀⠀⠈⠦⡐⢤⣈⠉⢅⣀⠈⠉⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⣉⡒⠇
⠀⠀⢸⡇⠀⢀⣴⣾⣷⠋⣽⣗⡀⡀⢀⣠⣤⣌⡒⠤⣉⠉⠩⠕⠲⣄⡀⠀⠀⠀⠉⠒⠦⠤⠤⣤⣀⣀⣀⣀⠀⠀⠀⠉⣢⠁
⠀⠀⠘⣇⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠭⠀⠀⠐⠊⠁
⠀⡴⠋⠁⠩⠾⠟⣻⣿⣎⣝⣛⣷⣆⣀⣈⣉⠉⠛⣿⣿⣿⣿⣿⠀⣶⣤⣄⣀⣤⡤⠤⠄⠒⠈⠁
⠾⠒⠒⢶⡠⡄⣍⠹⣿⠟⢿⣿⣿⣿⣫⡞⠁⠀⢸⣿⣿⣿⣿⡏⢸⣿⡟⢿⡿⠙⠀⢀⠁
⠀⠀⠀⠀⠳⡱⣌⢷⡅⠀⠸⢟⢭⣻⡿⣷⣄⠀⠀⠈⠙⠿⠟⢀⣿⣿⣿⢸⣷⡦⢔⡀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⣠⣤⠄
⠀⠀⠀⠀⠀⠙⢾⡶⠇⡠⠶⣶⣦⣬⣉⡛⠻⢷⡀⣤⣀⠀⠠⣿⣿⣿⡟⣼⣿⣷⢰⣍⣾⣿⣿⣿⣿⣿⣿⠧⣀⡴⣨⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣛⣶⣮⠉⠛⠛⠛⠚⢻⣦⣝⢷⣤⡀⠈⠉⠰⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⡇⢰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣿⣶⣄⣀⠈⠁⠀⠹⠟⠙⠿⢿⣿⣿⣿⢧⣓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠙⠋⠁⣠⠞⠉⠻⢿⣿⣿⣿⣷⣦⣄⡀⠀⣠⣴⣿⣿⣿⠛⡗⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠹⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣻⣿⣷⣿⡏⠒⠄⢹⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣝⢷⡝⢟⢮⡋⠓⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠠⣀⠙⠦⡀⢨⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢔⡀⠑⢄⣸⠿⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠅⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠆
⠀⠀⠀⠲⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆⡼⢠⠆
⠀⢀⠀⠢⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠⠇⠀⠉⠁
⠀⠀⠀⢆⠆⠀⠀⣸⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⢠⠀⠰⡄⠀⢀⢀⡎
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡆⠀⡇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢘⢣⡄⢠⡀⠀⠘⠆
⠀⠀⠀⢤⣠⡄⠧⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣰⠀⠀⠀⠀⡿⠛⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠈⠻⡄⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⢀⠀⠀⠀⠀⢦⠀⠀⠈⠁⠀⠀⢀⣠⠁⠀⢸⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡇⢠⡆⠀⣰⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⣆⠀⠀⠀⡈⣤⣀⣰⠇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠱⣌⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠙⠓⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠰⠀⠀⠀⠀⠀⠀⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠋⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡺⠋⠋⠛⢂⠀⠀⠀⠀⠀⢠⢡⢋⠉⠇⢡⠣
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠐⢸⠀⡇⠁⡄⠀⠀⠀⠀⠀⠀⠐⢀⠁⡆⠀⢰⠘⠀⠀⠀⠀⠀⠆⡆⠘⢰⠸⠈⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠈⢠⢸⠀⡇⢀⢠⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⠀⠈⠀⡆⠀⠀⠀⠘⢠⠀⠀⠘⠀⡀⠇⠆
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠈⢸⠀⡇⠸⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⢸⠀⠀⢀⠀⡇⢠⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⢸⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠄⡄⢀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⡇⠘⠀⡇⢸⢸⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠘⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⡀⡇⢸⠀⠃⠸⠀⠇⠀⠀⠀⠀⢸⠀⠇⡁⢠⠀⢸⢸⠀⠀⠀⠀⠰⠹⠀⢁⢩⠣
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⡇⢸⢠⠀⠀⠀⠀⠀⠀⠀⠂⠘⢠⠀⠃⠸⠀⡄⠘⠀⠀⠀⠀⡇⠀⢨⢸⠈⠀⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⢰⢸⠀⡇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⠀⡄⠀⠀⠀⡄⡆⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⢸⠀⠀⠇⠀⠀⠀⠀⠀⡀⢁⠈⡀⠆⠸⠀⢡⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠃⡄⠈⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⡇⠈⠀⠀⢠⠀⠀⠀⠀⠀⠆⠸⠀⢁⢸⠀⠇⠠⠀⠀⢸⢰⠀⡇⠀⠀⢸⠀⢠⠀⡄⠀⠀⢠⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠃⠀⠀⠃⢸⠀⠀⠀⠀⠀⠰⡀⢣⠸⡀⠆⠸⡀⠣⡀⠀⠀⠀⠃⠀⡇⠀⡄⠈⠀⡇⠀⠀⠸⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⢠⠀⢰⠀⡄⢸⠀⠀⠀⠀⠀⠀⠱⡀⢆⠱⡈⢆⠑⢄⡈⢣⠀⠀⢠⠀⠁⠀⡇⢠⠀⡆⠀⠀⡄⢀⠀⠸⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠂⢀⠀⡇⢸⠀⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠱⡈⢆⠱⣄⠑⠠⠌⣹⠀⠀⢸⠀⠀⠀⡇⢸⠀⡇⠀⠀⠇⢸⠀⡆⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⢌⡑⠢⠄⣸⠀⡆⠀⠀⡇⠀⡇⢈⠀⠀⠀⢠⠀⡆⢠⠀⡆⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠘⠀⢸⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢈⡐⠂⠰⠀⡇⠀⠀⡇⠀⠀⢸⢀⠀⢠⠃⡘⠀⡆⠀⠁⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⢸⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡆⡇⢠⠀⠃⠀⠂⢸⢀⡦⠁⡰⠃⡘⠀⡐⠀⠇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⠀⠀⡸⠊⢀⠎⢀⠜⠀⡰⠁⡜⢠⠃
⠀⠀⠀⠀⠀⠀⡀⢠⠀⢠⠀⡇⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢸⠀⠀⢀⠖⢁⠔⠁⡠⠋⠀⡔⠁⡸⠀⠎
⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢁⠊⡔⠁⡠⠊⠀⢠⠊⠀⡰⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠾⡘⢀⠎⠀⢀⠔⠁⡠⠊⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⡀⣧⢂⡠⠒⢁⠠⠊⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⡝⠻⡄⣉⠠⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⡇⢰⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢸⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡄⢸⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠃⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⢛⡛⠓⠲⠶⢤⣀
⠀⠀⠀⠀⠈⢻⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠋⠁⠒⢤⣀⣭⣽⠿⠶⠶⠶⠾⣿⣦⣄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⣉⠉⠉⠉⠉⠉⢉⡁⠀⠀⢒⣲⣶⢶⠟⠉⣡⠏⠀⠀⢀⣠⡴⠶⠾⢿⣷⣦⡀⣴⠿⠈⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣍⠓⠲⠶⠶⠶⠾⢒⠿⠋⠉⡰⠋⠀⠰⠃⢀⣤⡾⠋⠁⠀⠀⠀⠀⠈⠙⣿⠏⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⠀⠁⠀⠀⠈⠀⢀⣀⣤⠾⠛⢁⣀⣀⣀⣀⣀⣀⣀⡀⣰⡟⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟⣛⣻⣿⣶⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠁⢀⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣼⣇⣠⡿⠻⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠛⠛⠦⠀⠈⠙⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⢀⡼⢃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢀⠀⠀⣠⣾⠿⠋⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢠⡟⣀⡾⠋⠁⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⡟⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡜⡿⠁⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡼⠁⠈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⡼⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⡼⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋⣠⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠉⠉⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⢀⣴⢟⣁⣤⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠸⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠂⠀⢀⣴⣿⣿⣿⣭⣤⠴⠶⠖⢻⣿⣯⣤⣤⣤⣀⣀⣀⣀⣤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁
⠀⠀⠲⠿⠻⠭⠉⣡⣀⣀⣀⣀⣴⣁⣀⣀⣠⠤⠤⢤⠤⠤⡌⣿⡓⠒⠂⠀⠤⠠⠤⠀⢀⣠⣤⣤⣤⣤⣤⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣛⡛⠻⠿⣯⣭⣄⣀⡈⠃⠸⠧⣬⣍⣀⣀⣀⣀⣀⣀⣀⣀⣐⠆⠀⢉⡿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⡿⠛⠛⠛⠻⢿⣿⣟⠶⠶⠶⠶⣬⣭⣭⣭⣤⣤⣤⡶⠶⠚⠋⣁⣠⡾⠀⠠⠔⢒⣋⣥⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣾⠁⠀⠀⠀⠙⢿⣷⣤⡀⠀⠚⠁⠀⠉⢻⣿⣿⣿⣿⠿⠛⠛⠉⣀⣤⡶⠾⠛⠉⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠀⠀⠀⠀⠉⠻⢿⣟⣓⠛⠀⢀⣠⡟⠈⠙⠛⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠷⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⢀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡟⠀⡀⠀⠠⠴⠀⠀⠀⢀⡀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⢀⣀⣠⡄⠀⠠⢄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⣀⣤⢾⡟⣿⠛⢛⡀⠀⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣩⠿⠼⠓⠋⠻⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠁⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢀⡀⢴⡶⠚⡿⠇⠀⠀⠸⣗⠒⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡨⠀⢀⣤⣾⡯⣶⠚⣿⡾⣤⣼⡦⠴⠶⠾⣶⡿⠦⠴⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⣷⠾⢛⣉⡥⠷⠞⠒⠛⢟⠉⠉⠀⠀⠀⠀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠠⣄⠸⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣶⣿⣿⣿⣿⣛⠿⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣤⠶⢺⡿⢸⣶⣞⢫⣾⢿⣿⣿⣿⣙⡻⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠛⡉⠀⢸⣷⢞⣵⣞⣷⣾⣿⣿⣿⣿⣿⣿⡦⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣟⣷⡿⠺⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⠇⠀⠁⠀⠀⠈⠹⡿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠴⠦⣤⡶⠶⠖⠒⠲⢶⣶⣤⡽⠿⠿⠉⣤⣦⡀⢀⣀⣰⣶⣇⠀⢠⡀⠃⠐⠶⠖⠀⠀⠀⠀⠒⠶⠖⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⡗⣰⡿⣶⣶⣶⣤⠀⠐⠒⣯⣷⡷⠈⣽⣾⣿⡏⣀⡘⠻⣿⣿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠡⣶⣾⣍⠙⣃⣠⡔⢛⡿⠃⠀⠚⠿⣻⣥⠙⢿⣷⣄⠀⠀⠀⠀⠈⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠙⠛⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣆⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣶⠲⠂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⣸⡏⠀⠈⠻⣧⠄⠂⠀⠀⠀⠀⠰⠀⠺⡶⣶⣿⡿⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣦⣠⣦⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣉⡓⣦⠀⠀⠀⣿⡃⠀⢤⡀⠹⣦⡚⣾⡆⠀⠀⠀⠂⣁⣶⣿⡿⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⣣⠟⠀⠀⠀⢌⠛⢣⣜⡻⣄⠘⠶⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣽⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣁⣨⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣶⡎⠈⢹⣿⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠄⠀⠀⠀⠀⠀⠀⠻⡶⢹⠷⠚⢿⣶⣿⠃
⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⢺⣿⣧⠀⠀⢀⣼⣏⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠞⠛⠘⠀⣤⡠⡅⣠⠀⠀⠀⠙⠾⠶⠶⠼⠟⠉
⠀⠀⠀⣿⣿⣿⣷⣦⣤⣤⣤⣤⣽⣿⣿⠀⠀⢸⣿⣿⣦⣤⣀⣤⣶⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⢰⡒⢝⠶⣰⣿
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢙⣭⣉⣇⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⡻⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠶⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⢇⡄⠀⣰⠆⠀⠀⣺⠁⠀⡀⠉⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠹⠿⠦⢤⣴⡞⠀⠙⠉⠁⠀⠀⢸⠃⡆⠘⣷⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⢸⣇⣧⠐⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⢢⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠹⣿⣿⣶⣧⡟
⠐⠀⠀⠀⠀⠀⠀⣿⣁⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠛⠛⠋⠀⠀⠀⠘⠗
⣸⠇⠠⠄⠀⠁⢀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡦
⠁⠀⣧⠀⠋⠀⡀⢠⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣀⠀⠦⠄⠀⠀⠀⠁⠀⠀⠀⢀⠀⡀⠀⠀⠈⠉
⠀⠀⢸⡖⠂⠈⠀⡼⠀⠀⠀⠀⠀⠀⠰⢼⣦⠀⢸⡇⠀⠀⢀⠇⠀⠀⠀⢨⠁⢢⢠⠀⠀⠀⢸⣀⠀⠀⠸⠶⠃
⠀⠀⠀⠀⠰⢪⡿⠃⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⢾⣧⣼⠷⠃⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⡤⠚⠋⠀⠀⡆⢠
⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠘⣧⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⢛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡅⠀⠀⢸⠀⠀⠀⠈⠋⢀⠠⠀⠀⠰⣄⡴⠀⠓⠂⢀⣀⣀⠰⠁
⠸⡤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡀⠀⣆⣸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢰⠀⡀⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢠⡄
⡀⠀⣀⡀⠀⠀⠀⢠⠂⠀⠀⠀⣠⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠈⢢
⠧⢀⠈⣇⠀⠘⠠⡇⠀⠀⠀⠀⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⡔⠀⠄⠀⠀⠀⠀⢦
⢷⣸⠀⠹⠃⠀⠀⠁⠀⠀⢠⢏⡆⢰⡞⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⢀⠠⡁⠀⠀⠀⠀⠀⡀⠀⢸⠇
⢀⠹⠀⢠⡄⠀⠀⠀⠀⠀⣹⣼⡆⣾⢰⠇⠀⠀⠀⠀⠀⠀⠀⠘⣇⣧⢡⠀⣇⡿⠀⠀⠀⠀⠀⠀⣘⠟⠀⢀⠠⠀⠀⠙⣿
⠾⠃⠀⡾⠛⠀⠀⠀⠀⠀⠻⣿⣷⣷⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠳⠷⠋⠁⠀⠀⠀⠀⠀⢀⡀⠈⠀⣀⠀⠂⠀⠀⢻
⡅⠀⢸⠃⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⠀⠀⢠⡜⠀⠀⠈
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⣥⠞
⠐⠀⠚⠛⠁⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠶⢢⣴⠄⠀⠀⠀⠀⠀⠀⠘⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⢸⡀⠀⢀⡀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢿⠢⣀⢸⡇⠀⢸⣿⡆⢄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠈⠆⠈⣻⡇⠀⢰⠟⠀⠀⠱⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⢸⠐⠀⠀⠀⠾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⡈⠀⠀⠀⠀⠀⡿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠥⢧⠁⠀⠀⠀⠀⠀⢿⢏
⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⠀⠀⣸⣯⡝⠀⠀⠀⠀⠀⠀⣸⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢅⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣧⢰⠀⠀⠀⠀⢀⡄⠋⠁⠀⠁⠁
⠀⠀⠀⠀⠀⢠⡶⠃⠀⠀⠀⠐⠶⣿⠿⡚⣥⡤⠄⠀⠀⠀⢸⣿⡈⠀⠠⠄⢀⣤⡿⠁
⠀⠀⠀⠀⢠⡿⢧⠖⠡⠤⠤⠤⠦⣿⣿⣿⣿⠀⠐⠃⠀⠐⢚⡻⢛⣤⣴⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⢻⠛⢻⣦⠀⢀⣠⣼⣿⣿⣿⠿⠛⠛⠿⠁⡸
⣤⣤⣄⡀⢀⠀⠀⢀⠀⠀⢀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡵⠾⣂⣰⡆⣸⣿⠀⣤
⣿⣿⣿⠛⠁⠈⢑⡀⠿⠦⣬⣛⣿⣿⣿⣿⣿⣟⣻⣿⣿⣧⣀⣤⣾⣿⣿⣿⡅⣿⠋⢹⣿⣷⣦⣤⣤⣖⠅
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⣄⡙⠻⠿⠿⢿⣟⣿⠿⠛⠉⠉⠙⠻⠍⠙⠛⠋⠁⠈⠀⠘⣿⣿⡇⠉⣿⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠄⠈⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⢻⣧⠈⠉⠻⢷⣦⡀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣴⣦⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡟⠁⣀⣤⣾⠟⠋⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⢸⣿⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣴⡾⠟⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣠⣴⡿⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⠑⢀⠔⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠘⠇⠀⠈⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠑⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠠⠀⠘⠆⠀⠀⠈⠇⠀⠀⠿⢸⡇⠀⠀⣄⠀⣷⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠞⠀⡇⠀⠀⡁⢠⡏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⡄⠑⣤⠀⢀⠀⢰⠀⠀⠀⠀⡇⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠛⠀⠈⠀⢠⠀⠀⠀⠀⠁⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⠀⠀⠀⠤
⠀⠀⠀⠀⠂⠀⣿⠀⠀⢸⠇⢠⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⢤⡀⠀⠀⠀⠀⡄⠀⡇⠀⠠⠀⡇⠈⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⣈⠀⠇⠀⠀⠀⠀⠀⠀⢀⠀⣠⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠸⣇⠀⠀⢿⠀⠄⠀⠀⠀⠀⣆⠀⠀⣠⡟⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠳⣄⡈⠃⠤⣈⡲⢀⡀⠀⠀⠀⠁⠀⠾⢋⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⣌⣀⣀⣀⡀
⠀⠀⠀⠐⠃⠘⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣾⠿⠿⠿⠿⠟⠿⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⡿⠾⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣄⣲⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠋⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⡀⠊⠀⠈⠙⢦⡀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠰⠀⠀⠀⠀⣾⣿⡏⣴⡆⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⡧⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡶
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⡿⢀⠀⠀⠀⠀⣿⡟⢡⣿⡇⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⢸⠀⠀⠀⠀⣿⠀⢹⣿⠀⠀⢿⣿⠟⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⢀⠀⣿⡄⠀⢹⣿⡇⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⣿⠀⡄⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠠
⠆⠀⠀⣿⣧⣿⣇⠀⠈⣿⡇⠀⠘⠀⠀⠀⣿⡀⠸⣿⠀⠈⣿⠇⢰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⠀⠀⠀⠀⠀⡃
⡄⠀⠀⢻⣿⢿⣿⠀⢁⢻⣧⠀⢸⠀⠀⢰⡟⠃⢸⡟⠀⢰⡟⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⡀⠰⠀⠀⠀⠀⢰⡇
⠰⡆⠁⣸⣿⣆⠙⣧⠘⠀⣿⡀⢸⠄⠀⢸⡇⠀⣿⠃⠀⢾⠁⣴⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠸⣄⠛⢿⣿⣧⡈⢣⠀⠸⢧⠈⠀⠆⢸⡇⢰⡟⠀⠀⠀⣴⡿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠈⠂⡀⠙⢿⣦⠠⠖⠀⠈⠀⠠⠀⠀⠁⡞⠃⢀⣠⡾⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡀⠀⠈⢦⣀⠙⢷⣄⡀⠈⢤⠀⠀⠰⠂⠀⠀⠛⠉⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠁⠐⠒⠈⠉⠱⠦⣬⠻⠷⡄⠡⠀⠰⠀⢀⣤⠶⠚⠁⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣶⣿⣶⣤⣤⣤⣼⣿⣿⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣾⣿⣀⢀⣀⣨⣿⣿⣷⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠻⠿⠿⠿⠿⠿⠿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⠓⠘⠛⠈⠉⠃⠐⠀⠈⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢾⣄⣱⠖⢀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⣄⡠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡖⢠⠚⠑⠶⠚⣯⣹⡖⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⢢⠜⠉⠀⠈⠀⠀⠠⠀⠀⠈⠁⠐⠠
⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⡐⠈⠀⠁⠠⠎⣿⠙⣏⡉⠳⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠡⡀
⠀⠀⠀⠀⠰⠃⠀⠈⠀⠰⠁⠈⠁⠀⣉⠰⡏⠘⠃⠈⠱⠞⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠆
⠀⠀⠀⠰⠂⢰⡁⠀⠸⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⢠⡆⠀⡉⠛⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠀⢧⡤⠐⠇⠐⠁⠀⠀⠀⡄⠀⢀⠀⠀⠀⠠⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⢠⡄⠀⠀⠀⠀⢠⠀⠆⠀⢢⠀⠁⠀⠈⡀⠐⠂⠀⠁⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⢁⠀⠰⠏⠀⠈⢃⠀⠀⠀⢀⠀⠀⠀⠱⠀⠀⠀⠀⠉⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠦
⠀⠀⠀⠘⠃⠀⠰⡶⠀⠈⠡⣄⠀⠀⠃⠀⠀⠰⠀⠶⠘⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡄⠈⠂⠀⠀⠘⢄⡀⠀⡄⠀⠰⢀⡀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠰⡷⠀⠀⠀⠀⠀⠀⡇⠀⡀⠈⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠻⠀⠈⠻⠀⠀⢀⣁⣈⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣾⣿⣷⣶⣷⣶⣿⣿⠿⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠈⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠐⡋⠐⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⠖⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⣈⣀⡰⢁⡎⠀⣀⠀⠀⠀⠘⠂⣀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡞⠛⠙⠽⡯⠙⠙⣿⣿⠿⢷⣤⣀⡠⠀⠀⠀⠠⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣙⣾⢄⠀⠀⠠⠁⠚⡉⠨⢢⡙⣐⠒⢹⠕⠶⣤⠴⠀⠀⠀⣠⢏⡔⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠐⠒⠀⢀⣴⡿⣙⣍⣵⠋⢠⡔⠄⢢⠀⠀⠀⠀⠝⠀⠀⠀⠱⠌⠊⠀⢤⣀⣴⣷⡿⢀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⣤⡤⠀⢀⣴⣯⣿⣟⠛⠿⠷⠤⠟⠛⠦⠀⠀⣄⢀⠤⠀⢧⢪⠔⠁⠀⠀⠀⠸⢏⢻⣿⣿⡀⠀⠀⠀⠀⡠⠖
⢀⠏⠀⢔⡕⣊⠒⣍⠿⠀⢀⡶⠀⠀⠈⠀⠠⠄⠋⠅⠰⠈⠊⠼⠇⡠⠀⠀⠠⠠⣀⣾⣿⡋⠁⠀⠀⠀⢸
⡋⢣⠀⠸⡘⠿⢀⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠨⠡⠁⠡⢠⢁⣠⣀⡶⠖⠒⣶⣾⣿⣯⡁⠀⠀⠀⠀⠈⢣
⠑⠈⠓⠀⢈⢙⡉⠄⠀⠀⠀⠀⢀⠘⡠⡀⠂⢀⡤⠰⣢⣌⣋⣰⣽⠏⠱⠈⠀⠸⣿⣿⠎⠓⠄⠀⠀⠀⠀⠐⢆
⠀⠀⠲⢄⠀⢠⠀⡀⠀⠠⠠⠐⢁⣼⡇⡀⠠⠀⡰⠀⣶⣿⣿⣿⡟⠀⠀⠀⠒⠒⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠉⠒⠄⣀⣀⣤⣖⣄⢺⣿⣧⣈⢀⣀⣠⡾⣿⣿⣿⠏⠀⠀⠀⠀⠀⣸⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠳⡿⣿⣿⣿⣷⣻⣿⣿⡿⠟⠀⠀⠀⡐⠀⢠⠇⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠙⢿⣛⠛⠛⠛⠿⠛⠦⡀⠠⠀⠈⠀⠀⢸⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠡⠀⠀⠀⠁⠙⠲⠤⡀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⠀⠀⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣇⠠⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠀⠀⠀⠀⠀⡀⢀⣀⣧⠜⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠦⠶⠒⠚⡟⠉⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢬⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⡢⠐⠀⠀⠈⠉⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠚⠋⠉⠁⢸⠇⠀⠀⠀⠀⠰⡆⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢻⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡃⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡇⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠷⣾⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⢤⠖⠻⠟⠁⠂⡂⡾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣀⠦⡜⡾⠉⠉⡠⠘⢁⣤⣴⣾⣿⣯⣷⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⡀⠿⠐⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣬⣥⣶⣿⣿⣿⣿⣿⣋⠻⢿⣿⣿⣿⣁⣀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⢀⡖⢮⣙⣛⡛⠉⢩⣽⣭⣙⣋⣿⣶⠳⣿⢿⣯⢙⣿⣿⣿⠝⣛⠷⣴⣶⣶⣾⣍⣀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠠⠌⠋⣁⣬⣿⣭⣿⣿⣿⡞⢛⣯⣥⣶⣿⣿⣛⠛⠛⣉⣵⣆⠁⢨⣉⣛⣛⠙⠻⣿⣿⠿⠶⣿⣯⣟⡛⠁⠠⠄
⠀⠀⠀⠀⠀⠐⠒⠂⠉⠉⠉⣭⣥⠀⢼⡿⠛⠋⠁⠤⠼⠛⠋⠉⠩⠕⠂⢀⣿⠿⡋⠀⠰⣮⣍⣻⠥⠤⠤⢴⣶⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠁⠀⠀⠀⠘⠻⢿⣷⣶⡄⠀⠒⠉⠀⠀⠀⠈⠙⠛⠉⠁⠀⠢⠭⣭⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠋⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠈⠈⠙⣧⠴⠶⡄⠀⠀⠸⠷⠞⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠀⠱⠀⠀⢠⣤⣤⣤⣿⣭⣭⣿⣭⣭⣭⣯⣭⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣭⣭⣭⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢉⣿⣿⣿⡉⣻⣿⣿⡏⢙⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⠿⣶⣶⣶⣾⣿⣭⣿⣛⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⣿⣿⣶⣾⣯⣭⣭⣭⣿⣿⣿⡭⠽⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢
⠀⠀⠀⠀⢘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠪⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⣄⠀⠀⠀⢀⡀
⠀⠘⠷⣄⠂⠈⢽⣇⡕⠏⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠲⠄
⠀⢠⣄⠙⢻⡀⠱⢃⣴⣤⣧⣦⣶⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⣀⡀
⠀⠀⠨⢧⠈⢥⣠⢀⣌⡀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠑⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠈⣣⠜⣉⡁⠙⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡜⢲⠟⠛⠷⢧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⡆⠃⢀⢠⠇⡄⢠⠃⡄⢀⠄⠀⠀⠀⠀⠂⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡰⣌⢆⠣⢱⣠⣘⣘⡰⠡⢃⠎⡰⢋⠀⠀⣀⠀⠀⠀⢀⠀⡀⠀⢀
⠀⠀⠀⠠⠔⠀⢀⠀⠈⣇⠀⠀⠀⠐⠦⣄⡐⠦⣀⠦⡑⢌⠾⠋⠉⠀⠀⠀⠉⠓⢮⢊⠴⣋⠴⠊⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⢈⠳⠀⡿⠒⠒⠒⠠⠤⣀⣉⠓⠬⡑⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠵⢚⣁
⠀⠀⠀⠀⠁⠀⠈⠂⢧⢈⡉⠓⠶⠆⠀⠠⠬⢭⡑⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠭⠤⠒⠒⠉⠁
⠀⠀⠀⠛⠀⠀⠀⠨⠶⢦⡉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈
⠀⠀⠐⠂⠀⠈

⠀⠀⡀⡀
⣤⣤⣉⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠘⢯⡛⠃⠉⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢻⡆⠀⠀⠀⢸⠿⠀⠋⠰⣀⡀⠀⠀⠀⠀⠙⠳⢤⡀⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠃⣼⠇⠀⠀⠀⠀⢣⡠⠃⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠠⠀⠀⠀⢀
⠀⠀⠶⣿⣿⣿⣿⣷⣦⡀⠀⠀⢠⣿⡭⠀⠀⣿⠀⠀⠀⠀⠀⠀⡖⠊⠠⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠱
⠀⠀⠀⣝⡻⢿⣿⣿⣿⣿⡄⠀⠘⣿⣇⠀⢐⠏⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣿⣄⠀⠀⡀⠀⢁
⠀⠀⠀⠀⢁⣤⣯⣿⣿⣿⣷⠀⠀⠘⣿⡶⠃⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢤⠍⠀⠀⠀⠀⠀⠀⢀⠐⠁⢰⣿⣿⠃⠠⠀⠀⠠⠘⠄
⠀⠀⢀⠶⠋⢉⠉⠛⡻⠟⠋⢤⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠊⠀⠀⠀⠀⠀⣠⣶⣆⣀⣶⣿⣿⣿⡧⣥⠀⠀⠀⢠
⠀⠀⠙⠒⠯⠽⠛⠉⠀⠒⠀⠀⠀⠀⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡿⣿⣿⡍⠀⠁⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠋⠝⠑⠈⠳⠁⠀⠀⡀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠒⠀⠂⠀⠀⠀⢀⣀⠄⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣀⡀⢀⠍⠤⠤⢀⣠⠤⠒⠉
⠀⠀⣠⣄⠐⠚⠛⠛⠻⠷⢦⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠙⠻⣶⣄⠀⢉⣙⠻⢿⡳⢿⣦⣎⣛⡛⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⠿⠛⠻⠿⣷⣶⣦⣄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠁⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⣀⣰⣤⣔⠄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢸⡇⠀⠁⠠⣴⣶⡿⠟⠛⢿⣿⣇⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠸⡅⠀⠀⠀⢈⣿⣧⣄⣀⣽⣿⡿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣷⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠫⣿⠟⠻⠟⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⣦⣶⣤⣠⣾⣷⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣈⠀⠀⠀⠀⠀⣀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⠝⢋⡹⠿⣦⡀⠀⠀⠀⠀⠀⣠⡶⡿⢛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡁⡰⢁⠔⣁⠔⢊⡭⠟⢶⣦⠀⢠⡾⢫⠊⢀⠼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠾⠿⠿⠷⠷⢧⣾⣡⣞⡡⠖⣻⡟⠁⢠⡟⣰⠃⢠⠏⢈⠝⣻⣷⠆
⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠐⠲⢤⡀⠀⠉⠙⠒⠭⣛⢷⣯⣽⠃⢀⡿⣰⠇⣠⠏⢠⠏⢈⡾⠃
⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠈⠑⢌⠳⣄⣸⡷⢋⡴⢋⣴⠏⢠⡟⠁
⠀⠀⢀⣴⡏⠀⠀⠀⢰⣿⣳⠀⢠⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠀⠈⠻⠿⠿⢞⣋⠵⢢⡟
⠀⠀⠸⣏⠳⠆⠀⠀⠈⠛⠋⠀⢸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣒⠂⢸⠃
⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⡼⠀⠀⣸⣧⣀⠀⠀⠀⠀⠀⣠⠶⢶⣦⣍⠲⢤⡀⠸⣇
⠀⠀⠀⠀⠀⠈⠛⢶⣤⣤⠄⠈⠀⣀⡼⢿⣗⢭⡳⣆⢀⣠⡾⣟⢦⣄⠹⣿⣝⢦⣍⠢⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠿⢯⣤⣤⣽⣿⠾⣿⣿⡧⡙⢮⣱⣿⠇⠹⣟⢧⡈⢷⡀⠈⡻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣟⢦⡑⢌⠪⣳⡾⠋⠉⠀⠀⠀⢻⡆⠻⡄⠹⣄⠪⣑⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣝⣧⡙⢦⡑⢽⣧⠀⠀⠀⠀⠀⠀⢻⣄⠹⡄⠘⢦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣺⣿⣦⣝⢎⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⢦⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⢯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠍⠀⢈⡻⠟⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀⠀⠀⣸⣿⠖⠋⠉⢛⣛⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢠⡏⠉⠙⠛⠛⠉⠙⠛⠛⠋⠉⢉⢍⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡿⡇⢀⣼⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢨⡎⠀⠀⠀⠀⢀⣀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠉⠙⠚⠚⠛⠉⠉⠁⠀⢀⢢⠃⠀⠀⠀⠀⠀⠀⣈⡟⠉⠉⠉⠉⠉⠉⢉⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠃⠀⠀⠀⠀⠀⠀⠀⣸⠀⣀⡀⢤⠄⠀⢀⢣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⠤⠤⠤⠴⢶⣦⠀⠒⠂⣊⠜⢀⡐⠒⠒⠒⠂⠉⠉⠁⠀⠉⢸⠋⠀⠀⣌⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢀⠀⠠⢄⠀⠈⡀⠀⡸⠀⠀⣀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠐⠌⢫⠉⠉⠙⠛⠋⠀⠀⠀⠐⠒⠈⠂⠀⡨⢻⠊⠀⠉⠀⢠⣷⣿⣿⣟⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠃⠀⠀⠀⠀⡸⠀⣀⡠⠔⠋⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⣀⣀⠤⠒⠋⠉⠀⢀⡠⢺⠇
⠀⠀⠀⠀⠀⠀⢶⡒⠛⠒⠦⡉⠓⢤⣀⡴⠃⠀⠀⠀⢀⣀⣀⡀⠀⠤⠤⠄⠒⠒⠉⠉⠁⠀⠀⣀⠠⠔⠊⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠘⢏⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠒⠒⠈⠵⢦⠀⠀⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠈⢷⠀⠀⠊⠀⠀⠀⠀⢀⣄⠈⠁⠉⠀⢠⣞⡆⠀⠀⠀⣀⠑⠉⠂⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠣⣀⠀⠀⠀⠀⠀⠑⠘⢀⣀⡀⠤⠤⠀⠐⠒⠈⠉⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡒⠀⠀⠀⠒⠒⠒⠒⠂⠈⠉⠉⠉⣁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠤⠤⠤⠤⠤⠤⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢳⠀⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡜⣧⠀⢻⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣽⡄⠈⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡀⢨⣿⡄⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠠⠐⠒⠁⠈⠉⠀⠀⠀⢸⣧⣼⠟⢻⡄⠀⠰⡀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⣿⣄⠀⠀⢀⡄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⢿⢸⡆⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⢀⣠⣀⣶⡾⠿⠯⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠉⠛⠃⠒⠶⠶⠦⢤⣤⣴⡇⠀⣠⣾⣦⣴⣯⣀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠉⠙⠻⠿⢯⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⠸⢿⢰⣶⡤⣬⣤⣤⣀⣄⡄⠀⠀⢀⣀⣀⣤⠤⡶⠃
⠀⠀⠀⠀⠀⠰⣬⣵⣾⣿⣿⡏⠉⠉⠀⠀⠀⣀⡀⣀⣒⣒⣴⠺⣥⡿⣿⠶⠞⠛⠫⠉⠑⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⠿⣿⣦⣦⣤⣤⡤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠬⠽⠷⠶⣿⣿⠠⠔⠒⠤⠄⣀⣀⣤⠤⠀⠀⠤⣤⣤⣤⡼⠛⠛⠁⢠⣤⡤⠤⠄
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⣉⡉⠀⢀⣀⣀⣀⣉⣉⣉⣀⠀⠄⠀⠀⠀⣉⡥⣤⣄⣓⡙⠉
⠀⠀⠀⠀⠀⠀⠠⠔⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠇
⠀⣀⣀⣠⣤⣤⣤⡀⢀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀⠀⠸⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣽⣿⣶⣶⣶⣶⣦⣴
⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣠⣤⣶⣿⣿⡇⠀⠀⠘⡇⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿
⠀⣄⡀⠀⡀⠀⠀⠀⣤⣤⣀⣀⣀⠀⠀⠀⠈⠤⠖⠲⠾⡇⠛⠋⠉⠉⠙⠋⠉⠉⠀⠀⠀⠉⣭⣿⣿⡿⠿⣿⣿⣿⡇⠀⠀⠈⠉⡉⢭⡉⣿
⠀⣿⣶⣾⣿⣿⣿⣶⣾⡇⡼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣿⣿⣷⣶⣶⣶⣶⠆⢤⠆⠰⣿
⠀⣿⠛⣿⣿⣿⣿⣿⣿⠟⢀⣀⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⠀⠀⠤⢶⣿
⠀⣿⣶⣿⣿⣿⣿⣿⣿⣇⣹⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⠿⢿⡿⠿⢿⠿⠿⠿⠿⣿⠿⠿⣿⠿⣿⣿⣿⡿⠆⠀⠀⠀⢾
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠉⠙⠁⠀⠠⠭⠄⠈⣽⡋⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠀⠀⠀⠀⡄⠀⠠⠄⠀⢀⡀⢸
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠂⣆⣠⣤⣼⣅⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠈⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣷⣶⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⢂⣾⣧⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠂⠀⠰⡶⠾⣿⣦⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠓⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣭⣁⡄⠀⢶⣿⣶⣼⣧⣤⣤⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣿⣿⣿⣿⣿⡟⠛⠿⠿⠿⢿⣶⢦⣤⣤⣤⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣟⠻⢿⠷⣶⣦⣤⣤⣤⣤⣄⠁⠈⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠭⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠦⠤⠤⠾⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⢦⠁⢈⣀⠀⠄⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠂⢨⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠐⠀⠐⠀⠠⣢⢠⢁⠀⠀⠢⢠⡾⠀⠉⠠⠿⠇⠄⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⢮⡁⠁⠈⠉⠹⣘⠉⣀⡄⠀⠀⠆⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠁⠐⠋⠓⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⡇⢀⠶⣾⣤⣤⡿⡦⠀⡀⣾⣷⣴
⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠉⠀⠀⠁⠘⠚⠀⠀⠀⠀⠙⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠂
⠀⠀⠀⠂
⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣄⣀⡀
⠀⠀⣀⡀⠄⠒⠻⠿⠿⠽⠿⠻⠿⠿⢿⣿⣷⣶⣄
⠀⠘⠛⠿⣿⣯⣽⠓⠐⠶⠦⠤⠤⣤⣤⣠⣉⣙⡻⢷⣶⢢⣀⡂⠀⢀⡲⣲⣶⣶⣦⡄⢀⡀
⠀⠀⠀⠀⠈⠛⢿⣿⣶⣷⡀⠀⢐⠀⡀⢍⡙⡻⠛⣛⠮⢷⣽⠻⣷⣄⡷⠀⢉⣉⣙⣁⠄⠈⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣾⣛⣿⣵⣶⣾⣽⣿⣶⣤⢿⡞⣿⣿⣞⣋⣉⡁⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠉⠉⠉⠉⠻⠻⢿⣿⠿⢫⠴⠒⠹⠛⢼⡛⢻⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⣿⣿⣿⡟⠋⠑⠀⠀⠀⠐⢜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠄⠀⠀⠀⠀⠀⠀⠈⡯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⣴⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢠⡳⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣽⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⢰⡽⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⣻⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⢆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣩⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⣿⢷⣔⠘⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣵⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⢸⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣇⠀⣠⡀⠀⡀⠀⠀⠀⠀⢀⣤⢄⡀⠀⡘⣹⣶⣥⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣶⣿⣷⣷⡆⣵⣼⣿⣾⣿⣿⣿⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠓⠲⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡒⠒⠒⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇⠘⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡇⠀⢳⠘⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡇⠀⠸⡇⠹⡹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡇⠀⠀⡇⠀⢣⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡇⠀⠀⣿⠀⠘⡇⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⡇⠀⠀⣿⠀⠀⣧⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⢸⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⢸⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢸⡇⠀⢸⠇⠀⠀⢸⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⠀⠀⠈⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣿⡇⣸⠁⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⣷⣇⣀⣀⣀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣖⣾⢯⣽⣶⣶⡿⠽⡿⠷⠖⠒⠛⠛⠛⢲⣾⣿⣿⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠵⠒⠚⠉⣉⣀⣀⣀⣤⣤⣤⣴⣶⣶⣿⣿⠿⠟⠛⠉⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣿⣿⡾⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⢉⣉⣀⣀⣤⡤⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣤⡤⠤⠤⠤⠤⠴⠶⠶⠖⠒⠚⠛⠋⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣆⣴⡾⠷⠢⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣬⣝⣿⣿⡷⡶⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⢏⡽⡛⣝⠙⠷⣦⠠⡀⠀⠀⠀⠀⢠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠀⣿⡇⢱⣘⣷⡀⠀⠁⠀⠀⠀⠠⣸⣿⣏⠀⢍⠁⣠⢾⣶⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⢹⡗⠀⠈⣿⠙⠠⠀⠀⠀⠀⡾⠉⠘⣿⣧⡈⢸⠳⡟⢹⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠉⢿⡅⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢄⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠓⡂⣂⣀⣲⢄⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⡀⠀⠀⠈⠑⢦⡀⠀⠀⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢻⠛⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠳⣄⡀⠀⠘⢦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⡀⡀⠀⠙⣶⠄⢴⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠲⣀⠹⣷⣄⢀⡈⠈⣲⣄⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠆⠀⠀⠀⠀⢀⣠⡴⠞⠊⠉⢉⡽⠥⣑⣌⠿⣹⡽⣟⣠⣶⠉⣿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⣴⠾⠉⠀⡄⠀⣴⠖⡀⡄⢠⣆⠹⣿⣇⣤⡀⠘⢙⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⣭⢏⣴⣾⢐⡋⢡⢰⣷⡷⡿⠿⢿⠿⠿⠿⠿⢷⣄⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠿⠿⠷⠿⠷⠿⠋⠃⠀⠀⠀⠀⠀⠑⠀⠐⠀⠈⠁

⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠘⢿⣿⣤⣀⡀⠀⠀⣿⡇⠀⠙⣿⣯⣄⠀⠀⢸⡀⢠⡄⢠⣶⡄⣿⡇⢀⣤⣿⣿⢠⣿⣿⡆⣴⡆⢰⣷
⠀⠀⢾⣿⣿⣿⠋⢰⣧⣿⡇⠸⣦⣹⣿⣇⣰⡦⠘⣇⢸⠅⠀⢿⣷⣿⠀⢸⣿⣿⡏⠀⠀⠈⢷⣿⡇⢸⣿⣶⣦
⠀⠀⠈⠛⢛⠃⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⠀⠿⠼⠀⠀⠸⣿⠟⠀⠸⣿⡿⠁⣠⣄⡀⣸⣿⡇⠸⣿⣿⡇
⠀⠀⠀⠀⣾⡇⠀⠘⠛⠉⠁⠀⠸⣿⣿⣿⡇⠀⠀⣜⡞⣇⡞⣠⠀⢀⣀⣀⣀⠀⢺⣿⣿⠁⣿⣿⡇⠀⠉⡉
⠀⠀⠀⠀⢻⡇⠀⢰⣧⢰⣿⡄⣠⠈⠙⡉⡀⢀⡄⠀⣿⣿⣿⡄⠀⣾⣿⣿⣿⡇⢸⣿⣿⡄⠈⢋⣀⠀⢸⡇
⠀⠀⣸⡄⣼⡇⠀⣀⠙⢿⣿⣿⡿⠀⢱⣿⣿⣾⣠⠀⢻⣿⣿⠁⠀⠙⠿⠿⠿⠁⠈⣿⣿⣿⡀⢸⣿⡄⢸⡇
⠀⠀⢿⡇⣿⣇⠀⣿⡇⠸⣿⠀⠀⠀⠲⣿⣿⣿⠃⢀⠀⠙⠁⡴⣿⣳⠄⢠⣤⣤⣀⠸⣿⣿⠇⠘⣿⡇⣿⡇
⠀⣀⢸⡇⣿⣿⠀⣿⡇⠀⢀⣤⣤⡄⠀⠈⢉⠁⠀⣿⣷⣶⠆⠈⠁⠋⠀⢿⣿⣿⡗⠀⠉⢁⠀⢳⣿⣧⣿⠃
⠀⢻⡏⢿⣿⣿⠀⣿⠇⠀⠘⣿⣿⡛⣀⡀⢿⠇⢀⣾⣷⠁⢰⣿⣿⡆⠀⠘⣿⣿⠇⠀⠀⣾⡇⣎⢻⣿⡿
⠀⠘⣿⣼⣿⣿⡾⠟⢠⣾⡆⠁⠀⠀⠿⠷⢾⣦⢸⣿⡟⠀⠀⠛⠉⠡⡄⠀⠘⠃⠀⣿⢠⣿⣿⣿⠀⠀⣤⣤⡄
⠀⠀⠀⢸⣿⣿⠀⠀⣼⣿⣿⡆⠀⣴⣷⡄⠀⣿⣿⣿⡄⢠⣴⣧⠞⡀⣴⣾⣷⣦⡀⢸⣿⣿⢿⣿⠀⠀⣿⣿⡁
⠀⠀⠀⠘⣿⣿⠀⠀⠸⣿⣿⠇⠸⣿⣿⡿⠀⢿⣿⣿⠃⠰⣿⣿⠏⠐⣿⣿⣿⣿⡅⠘⣿⣿⣼⠏⠀⢠⣿⣿⡇
⣀⣀⣀⣀⣉⣁⣀⣀⣀⣈⣁⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣉⣁⣀⣀⣈⣉⣁⣀⣀⣀⣉⣉⣀
⣿⣟⣟⣛⣝⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢻⣟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢷⣽⣷⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣦⣤⣄⡀⠀⠀⠆⠀⠀⠀⠈⢻⠀⠀⠸⢧⠀⠀⠀⢀⣴⣾⢿⠿⠟⠉⠉⠋⠛⠛⢻⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠒⠶⣤⣀⣈⠀⠀⠀⣈⡀⠀⠔⠙⠉⢀⣤⣄⣦⣴⣶⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢻⣿⣿⣿⣄⠀⠀⠀⣻⡿⣿⣦⣾⣿⣿⣷⢰⣶⣿⠾⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠙⠀⣸⣼⣿⣿⣿⣿⣿⣁⣀⠄
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⢿⠂⠀⠀⣰⣈⢠⣿⠿⠟⠛⠋⠁⠈⠁
⠀⣠⣴⣿⣿⣿⣿⣶⣦⠌⠿⢿⡆⠀⠀⠀⠀⣄⡴⠖⠓⠲⠋⠀⠀⠀⢄⣀⠀⠀⠢
⠠⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠉⠑⢢⣄⠀⠀⢳⠠⣠⣤⣤⣤⣶⣶⣦⣤⣄⣤⣤⣤⡤
⠀⠀⠀⠀⠀⣀⣀⣄⣠⣤⣴⣂⡀⠀⣰⠏⠋⠡⣀⣠⣽⣷⣶⣾⠟⠋⠉⠉⠛⠿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠖⠛⠋⠉⠁⠀⠀⠀⠀⠨⣡⠞⠁⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⡹⣏⠉⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣁⡀⠤⠚⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⠀⡀⠀⠀⠀⠀⠀⣳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣤⣀⣠⣬⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⢠⣀⡄⢷⣾⠾⡅⠀⠀⠀⠀⠀⠀⠀⢚⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⡇⠀⠀⠀⠄⠀⠀⢀⠎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢠⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢴⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠤
⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣦⣤⣇⣀⠄⠀⠀⢀⣼⣿⡿⠀⠀⢀⣀⠄⠄⠐⢻⣿⣿⢑⣾⠄⠀⠒
⠀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠭⣖⣊⡭⠽⢟⣿⣹⣿⣿⣷⣶⣾⣿⣛⣁⠀⡁⠤⠠⢖⠒⢀⣈⣻⠃⠘⡁⠀⠀⠒⠀⠤⠄⠁
⠀⠀⠀⠀⡀⠬⠢⠴⠒⠤⠤⢽⣿⣿⣿⣷⣲⣶⣦⡤⠤⡤⠤⢤⣄⣀⣀⣈⣨⣑⣮⣧⣿⣶⡿⠤⠀⢱⠀⠌⠉⠡⠤⠤
⠀⠉⠁⠭⠿⠶⠶⠶⣤⣤⣬⡍⠉⠙⠛⠻⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠑⠢⠄⢸⣄⣀⣀⠀⠤⠀⣀
⠀⠀⠀⠐⠚⠉⠓⠀⠀⠘⠛⠩⠟⠓⠂⠐⠓⠐⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠛⠢⠴⠐⠒⠒⠉⠳⠀⢠⣀⣀⣤⡄⠤⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⠿⠿⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣾⣷⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡾⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡿⠁⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣿⠃⠀⠀⢠⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⡿⠀⠀⠀⡄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣺⡇⠀⠀⠀⠁⠀⡜⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⣿⡇⠀⠀⢨⠀⠀⠀⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣹⣷⠀⠀⡄⠀⠀⠄⢼⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⢹⣿⡆⢀⠁⠀⡀⠠⢼⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⢿⣿⡌⠀⠰⠀⠀⣾⡇⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠘⣿⣷⡀⡀⠀⠀⠈⡇⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⢿⣷⡇⠀⠀⢠⣿⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢄⣦⠈⢿⣧⠀⢐⣾⣿⡄⠀⠀⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠉⠺⠾⣿⣧⠀⠁⣿⣶⡀⠀⢉⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢐⣾⣿⣿⣧⠀⢻⣿⣯⣶⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣠⣴⣾⡿⠟⠋⠁⠀⢙⠁⠉⠉⣩⣭⣍⠉⢉⣴⡿⠁⠐⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⢿⣶⣶⣾⣷⡾⠿⣦⣄⣬⡉⣿⢿⠿⠿⠿⡿⢶⣾⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣴⣮⣤⣤⣬⣤⣴⣦⣌⣙⣏⣉⡛⠻⣛⣛⡹⢟⣋⣟⣉⠉⣉⠛⣿⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⣿⠿⠿⠿⠛⠛⠛⠛⠋⠉


⡶⠶⠶⠷⠖⠲⠶⠶⠶⣶⣷⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣶⣶⣷⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⡄⠀⠀⠀⠲⡦⠀⢠
⠀⠀⢀⠀⠀⠀⢀⡆⣰⠃⡀⠀⠀⠀⠀⠀⢠⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀⢼⣣⢀⡓⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠈⠳⠥⠅⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⢠⣉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠁⠀⠀⠀⢙⣋⠠⠤⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠂⠀⠀⢀⠠⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⢢⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠌⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣔⠀⠀⠀⡀⠀⠀⠀⠀⠠⡄⡴⠀⠀⢰⣿⠃⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⢀⠠⠋⠀⡈⠈⠀⠀⢁⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⡀⠀⡇⠀⠀⢀⣸⣀⠀⠀⣱⢶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠎⠀⠀⠀⠀⡀⢠⠸⡇⢀⡇⠀⠀⠀⠉⠉⠀⠀⢹⢸⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢇⢐⣠⡗⠚⠁⠰⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢀⠆⡄⠀⢄⠀⠀⠜⢀⠄⠈⢺⢸⠁⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠽⠿⠟⠀⠀⠀⠁⠁⢀⠁⠀⠀⠸⢼⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⣙⡁⠀⠸⠶

⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣤⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⡿⣿⠿⠷⢬⡀⠤⣽⡿⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⢸⢃⠀⠈⠃⢰⠋⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠁⠀⠀⠀⢇⠀⠀⠈⠀⢸⠀⠴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⢿⡋⠒⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⢡⡀⠀⠀⠀⠀⠀⢳⠀⠀⣀⣿⣄⣦⣤⣀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⣙⣶⣆⣶⣶⣶⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⡛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠀⠀⠀⢀⣀⡄⢀⡉⠉⠑⠒⢒⣒⣂⠠⠄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢒⣒⠒⠀⠠⣤⣄⠀⣀⣀⣀⢉⣉⣉⣉⣀⣀⣤⣤⡶⠞⠋⣉⠁⠀⠀⢐⢒⡟⠉
⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣐⣠⣬⡥⠶⠶⠶⣾⣻⠻⠿⠟⠛⠛⠋⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠈⠁⢲⣶⡤⣄⠀⠁⢠
⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣶⣶⣶⠿⠟⠛⠉⠀⡾⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠛⢛⣉⣉⣉⣥⣤⣤⣤⣤⣤⣤⡀⡀⠀⠈⠀⠀⠀⢀⣀⣠⣤⠶⢻⡅⠀⠀⠀⢀⡠⠔⢋
⠀⠀⣶⠀⠐⠒⢀⣉⣉⣙⣋⣉⣭⠭⠤⠶⠞⠛⠛⠋⠉⠁⠛⠙⣋⣁⣀⣉⣉⡽⠟⢛⠛⠛⢛⡭⠍⠑⠊⠉⠒⠺⠿⠖⣒⠉⠀⠀⣀⣈⡦
⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠖⠒⠋⠩⠍⠐⠊⠉⠀⠂⣉⡠⠖⠋⠀⠀⠀⠀⠀⠀⡀⢀⡀⠐⢺⣷⡞⣶⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠀⠀⣀⣠⡤⠖⠒⠉⠔⠈⢂⠀⡀⠀⠀⠀⢀⡤⢺⣼⣮⡿⠯⣵⣿⠁⣤⣴⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠋⠉⠉⠁⠀⠠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠈⠉⢀⡛⠴⠞⠃⠀⠀⠉⠀⠉⡁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⠂⢠⡀⣦⠀⠀⠀⣤⠣⣆⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⡠⠀⠀⣀⠀⠀⢀⡘⠡⡵⠘⣶⣿⣧⣴⣷⣟⠛⠁⡠⠔⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠈⠀⡠⣮⣿⣷⣾⣶⡉⠢⠛⠅⣽⣿⠟⣱⠏⠉⠠⡚⢀⣾⣷⣷⣆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣘⣛⡛⢳⣿⡿⠛⠛⠓⠀⠈⠀⠀⠀⣁⡀⠒⣋⣿⣯⠛⣭⣽⢿⡗⢺⠟
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣾⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠐⠚⠯⠩⠭⢉⣀⣉⣄⣨⡏⢀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⣛⣉⣭⣴⠂⣤⣠⡄⠴⣄⣂⣰⣒⣠⠂⠒⣦⢄⣀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢸⠀⠀⠿⠟⢋⠉⠉⢽⣶⣾⣿⣻⣷⢇⡼⢻⡿⠙⠀⠀⡉⢜⡿⢿⣿⣿⣿⣂⡼⠏⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⡀⠀⢰⡖⢰⣴⢻⣿⣿⣿⡿⣿⢿⣯⣷⢸⣻⡦⠀⡀⠐⡀⠚⢿⡿⢟⣱⠟⠁⠀⢀⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢳⠀⠈⠅⢋⣉⡼⠻⠛⣿⣵⣣⣿⡻⣿⣟⣻⢹⣶⡟⢋⣖⠼⠂⠀⠋⠁⠀⠀⠀⢁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠧⡀⠈⠳⠟⣾⠳⠉⣿⢳⣇⣿⣄⣿⣟⡆⠈⠭⠶⠷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠚⠿⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⠶⣶⣶⣦⣶⣦⣦⣶⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⠓⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠿⠌⠁⠀⠀⣠⣤⣶⣽⣿⠷⣆⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠛⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡻⠇⣀⣀⣤⣼⣿⣟⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⢻⠋⣠⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠭⣠⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣿⣿⣿⡿⠛⠻⡿⣇⠛⠸⣽⢿⡟⢁⣡⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡼⠛⠉⠹⠁⠀⠀⠀⠈⠓⠓⠛⢉⠞⢠⣿⣿⣿⣿⣿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠴⢟⣋⣉⠉⠉⠉⠉⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⢃⡴⠊⢉⣤⠄⠉⣰⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⡟⢧⠀⠀⠀⢀⡀⠈⠒⠀⠀⠀⠐⠈⠀⠀⠉⣀⣤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣎⠓⢦⣰⣆⡙⠳⠦⠔⠀⠀⠀⢀⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⣤⣶⣿⠿⣛⠓⠂⢉⣿⣿⠟⠛⠶⢦⣭⣉⣉⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⣾⣿⣿⣮⣶⣭⣾⠏⠀⠀⠀⢀⣠⣴⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⢀⣠⣤⠶⢾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⢿⣽⠀⠀⢉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⡀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣀⣀⣊⢻⣧⣦⣸⣾⡇
⠀⠀⠀⡠⠂⠀⠀⢰⣿⠏⠉⡉⠑⠒⣨⣿⣿⣷⣄⠀⠀⠀⠀⠀⡿⠁⢐⣢⣾⣿⣿⣿⣿⣿⣿⠃⠈⠻⣿⡿⠏⠙⣛⡡⡄⠁⢄⠀⠀⡀
⠀⠀⢸⡇⠀⡆⢧⣷⡉⠻⣟⣀⠀⠠⢄⣄⡈⠻⣿⣷⣄⡀⠀⠀⠛⣿⣿⣿⣿⡯⠥⢴⣶⣿⣧⣤⡤⠾⢷⠿⠛⠉⠀⣠⢡⠆⡜⣀⡼⠛
⠀⠀⠀⠻⡠⣟⠿⣿⡻⢷⣾⣿⣟⠲⡶⢭⣉⣉⠉⣙⣿⣿⣿⣦⣾⣿⣿⣿⣿⢷⣿⣿⡟⢛⣿⣶⡶⠿⠛⠭⡠⠴⢚⣥⢟⡼⠣⠋
⠀⠀⠀⠀⠘⠪⢻⣾⣿⣿⣿⣿⣿⣷⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⢛⣫⡥⣶⣦⣤⣤⣶⣾⡻⣵⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠀⠹⠿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⡿⠟⢯⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠿⠿⣶⣾⣿⣿⣷⡶⠟⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⡆
⠈⠠⠡⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠂⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠐⠀⠀⠀⠀⠀⢠⠠⡅⠇
⠀⠀⠀⠂⠀⠀⠀⠀⠀⢘⢰⡆⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠲⣾⠗⡛
⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠈⠉⡽⠙⠆
⠀⠀⠀⢀⡄
⠀⠀⠂⠠⠇⠀⠀⡔⠀⠀⢀
⠀⠀⠈⠀⢈⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢂⠀⠈
⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠤⠀⠀⠐⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡔⠀⢡⠀⣀⣀⣀⡀⠀⠀⣀⠤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⡠⠟⠁⠀⢘⠉⡡⠀⠀⠀⠀⡄⠀⣀⡠⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠰⠞⡠⠄⠂⡠⣃⡴⠖⠒⠛⠛⠛⠛⠋⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠋⠀⢠⡼⠊⠉⠉⠉⠑⠲⠤⢀⣀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠀⢠⡽⠁⢂⠀⠀⠤⠤⠤⠤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢏⠙⢾⠛⠛⠛⠓⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠈⠆⠢⠐⠈⢤⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⠀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢶⠆⢦⣤⣦⠐⠿⠿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⡸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡠⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢉⣹⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣄⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣭⣶⣤⣤⣆⣀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠂⢹⣏⣽⣶⠀⠀⠀⠠⠄⠀⠀⠠⠤⢆⣀⣴⣿⠱⢟⠋
⠀⠀⠀⠀⣀⣀⡀⠀⠠⠄⠀⠐⢟⣻⢿⣿⣿⣿⣿⣶⣶⣞⣀⡀⠂⡀⠀⠀⢠⣼⣿⣿⡟⠀⠀⣀⣀⡠⠦⠐⠒⠉⢹⣿⣿⡇⢸⡿⠂⠀⠐⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠶⠆⠀⢚⣒⡀⣈⢯⣟⠶⠭⢍⣟⣟⣿⣯⣿⣿⣿⣷⣶⣴⣿⣿⣟⠛⢉⣁⣁⢠⡤⠴⡖⠲⠋⡀⠈⢿⡟⠀⠸⡁⠀⠀⠀⠲⠀⢠⣤⠉
⠀⠀⠀⠀⠀⠀⣀⣂⣀⣂⣤⣀⣀⣈⡻⣿⣿⣶⡶⢶⣤⣥⣉⣉⣙⣉⣉⡉⠉⠉⣍⣉⣉⣠⠠⠦⠞⠃⣬⣑⣒⣫⣩⣿⡅⠂⠀⢇⠀⠁⠶⠶⠆
⠀⠦⠤⠀⠤⠦⠤⠴⠆⠁⠀⠀⠉⠩⠽⠿⠿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣼⣧⣿⣿⣶⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣧⡘⠅⠀⣼⣀⣉⡀⠀⠈⠉⠉⠁
⠀⠀⠀⠐⠚⠛⣛⣛⠋⠙⠛⠛⣿⣶⣆⣀⣀⠀⠉⠉⠙⠛⠻⠻⠟⠛⠿⢿⣿⠿⢿⣿⣿⣿⣟⣻⣿⠿⠛⠉⠁⠠⠄⣀⠍⠒⠀⠻⠒⠶⠤⠄⠀⠉⠒⠠⠤
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠩⠭⠉⠉⠁⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠈⠓⠲⠶⠅⠚⠋⠙⠃⠙⠂⠀⢀⡀⣀⣲⠦⠄⠰⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠁