⠀
Ciallo～(∠・ω< )⌒☆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠫⠭⣳⣦⣄⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠴⠖⠒⠒⠛⠻⣶⡶⠚⠉⠀⠀⠀⣀⠤⠀⠀⠭⠷⠶⠤⣠⢎⠤⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⡥⠊⠀⠀⢀⣠⣞⢻⣧⣀⣀⣀⠔⠈⠀⢀⠀⠀⠀⠀⠀⣿⢛⣟⢿⣛⣣⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣡⠊⠀⢀⣤⡶⡿⡱⢃⣯⠇⢉⡔⠁⠀⢀⡔⠁⠀⠀⠀⠀⠀⠈⢻⡛⢳⣸⠍⢜⢷⡬⣍⡶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡴⠁⢀⣖⠟⢡⠎⡐⢠⡎⣽⢤⠏⠀⠀⢠⠎⠀⢐⠂⠀⠀⠀⡀⠀⢀⡳⣠⡈⢉⠵⣄⣼⡿⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡾⠋⢹⠁⣰⡟⠁⢀⡼⣺⢖⣽⣼⣏⡝⠀⠀⢠⠃⠀⡐⡙⢘⠓⠄⠀⣰⠀⠀⡆⣿⣺⣿⣧⠸⣏⠀⢣⠀⣀⡸⠃⠀⠀
⠀⠀⠀⢀⢼⠏⠀⠀⠈⢳⢫⡴⠾⢝⠞⠁⠄⢘⣧⡜⠈⣏⠍⣿⣦⣤⡁⡇⡼⠀⠀⠀⢻⠀⢴⡗⠿⠹⡿⢏⠑⢾⣦⣴⠞⠙⠉⠀⠀⠀
⠀⠀⢠⢿⠊⠀⠀⠀⢀⡼⣿⠀⢀⠆⠀⠰⢠⠚⢅⠇⠀⢹⡾⠛⠈⠛⣿⣷⡌⠀⠀⠀⣼⠀⢨⡝⠀⠀⠘⣿⣄⠀⡷⣧⠀⠀⠀⠀⠀⠀
⠀⠀⡎⣾⠀⠀⢀⡴⠋⠀⠹⡢⡇⠀⠀⡆⠀⠢⡸⠀⠀⠠⣇⠤⡼⠋⠃⠙⠇⠀⠀⢰⣟⣠⣬⡇⡤⠀⠀⡇⡏⠛⢳⣿⣾⣻⠿⣷⠀⠀
⠀⠀⣀⢻⠀⢠⠎⠀⠀⠀⢠⡞⠪⡲⢤⡇⠀⡆⠇⠀⢰⢘⡗⠶⠴⠂⠀⠀⠈⠒⢠⢿⣷⠟⢶⡏⠆⠀⢠⠁⡿⢀⡼⠋⣼⡤⠞⠀⠀⠀
⠀⠀⠑⠛⢣⠇⠀⠀⠀⢠⢫⢣⠀⠘⠢⢌⠁⠛⢀⢂⢸⢀⡏⠀⠀⠀⠀⠀⠀⠀⢏⡋⠁⣠⡿⡌⠀⢀⠎⣟⣿⣛⣿⣿⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡞⠀⠀⠀⢀⡇⢸⠈⡀⠀⠀⠈⡄⣽⢤⡂⠉⡘⠏⣷⣤⣀⠈⠢⠔⠀⠀⠀⢀⡏⠙⢧⣠⢜⡬⣿⣾⠟⡏⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠃⡆⠀⠀⡜⠀⠘⡌⣅⠀⠀⠀⠹⣇⠳⣍⡢⣅⠆⣈⡟⢻⢿⣶⢲⠶⢶⡞⣭⡤⣶⣺⣶⢿⡿⠺⢱⢐⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡄⠀⠀⢠⡃⠀⠀⢳⢩⢧⡀⠀⠀⠘⢴⠋⠛⡇⡉⢿⣓⣻⣾⣽⣷⣏⣁⣈⣁⣔⣿⡿⣜⣏⠀⣟⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢱⡄⠀⢸⡇⠀⠀⠈⢇⢧⠘⠦⣀⠀⣸⣤⠚⣃⠗⣽⢟⢙⣿⡿⢫⠃⠀⡝⠉⠀⢘⣧⡙⣅⡜⠉⢈⡽⠦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⠀⠘⡃⠀⠀⢀⡬⠒⠛⠒⠚⡟⢅⢽⣿⠁⠊⢙⢶⠿⠋⠀⣟⣿⣷⠁⠀⡷⢾⠹⣷⣺⡠⡖⠉⢲⣄⡙⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠳⡀⠡⡀⠀⠯⢤⣄⡉⢉⣙⢅⠄⠊⠁⠀⠀⡄⡌⢠⣀⣸⣿⣼⣋⣀⣴⣷⠀⠹⠺⢺⠄⠙⡄⠀⠁⠈⢺⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠵⠦⠄⠀⢠⠎⠑⠲⠮⡧⡀⠀⠀⢀⣷⡾⠿⠤⢾⣳⠏⠰⡞⠃⢸⠀⢠⠀⠸⠀⠀⢰⢘⠇⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡀⣀⣀⡠⣒⣾⣜⠷⣞⠛⠚⠛⠂⠛⠁⠉⠓⢾⡄⢸⡾⡌⣠⠃⠀⠀⣸⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡾⣽⣯⠼⢯⠉⠒⠒⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡵⠔⠁⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⠓⠒⠉⠀⠀⠀⠀⠳⣄⠀⢠⠿⠦⢄⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⠤⠄⠒⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠮⡓⠔⠛⠛⠚⠫⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣱⢫⢖⠰⠀⠀⡅⣆⢠⠱⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣸⣷⢃⡞⢵⠁⠀⢰⡿⣷⣣⠨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢰⣿⢃⣮⣿⡗⡄⡅⣾⡇⠘⣿⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡞⢸⣯⣾⢿⢿⣹⢰⣱⣿⠢⠤⠹⡇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣸⣥⣶⣶⣼⠛⠛⠛⣥⣶⣶⣼⡇⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⣿⣦⡷⠹⣏⣉⠜ ⠀⠀ ⠹⣏⣉⠜⡇⣬⣿⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⢿⣿⡄⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⢐⣿⣿⣿⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠇⢸⣿⣿⣟⠳⣄ ⠘⠲⡀⠤⠖ ⠀⣠⠿⣯⣿⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⣼⢿⠘⣿⠀⠈⢳⠠⢀⢀⡠⢴⠞⠉⢸⡿⣿⣿⠀⢸⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⢀⡏⣾⠀⣿⣆⡠⠞⠀⠀⠀⠀⠸⡤⣀⣾⡇⣸⠸⡆⢸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏⡼⠠⢿⣆⢱⠆⠐⢄⢀⠄⠀⡄⡠⠊⠂⣺⢀⡿⢧⣷⢸⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡽⢹⠐⡄⣟⣯⣇⣠⣤⣬⣦⣴⣬⣤⣤⢨⣧⢾⠁⢈⠘⢇⣧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⡃⢸⢰⢀⠹⣼⣿⡮⠭⣽⡟⡸⣿⢩⢩⣿⢯⠋⢔⢈⠀⣸⡿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⡋⡁⠠⠀⢆⣼⣿⢻⡇⠀⣿⡇⡀⣿⣼⢸⢻⣟⠀⠐⠄⡨⣱⢫⢎⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣿⡟⢘⢆⠀⡒⠸⣿⣅⢸⡇⢰⣿⡇⠁⣿⣿⠀⣾⣻⡷⠀⠳⢑⠀⡄⠞⣜⠽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⡟⣽⢢⣿⠘⡄⢰⡀⠈⢻⡿⡇⢸⡟⡄⠁⡟⣿⢰⣿⠛⠁⠀⡄⡂⠀⣇⠐⠉⣗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠁⣻⡟⣿⠀⠘⣄⢷⡀⠉⠈⠇⠸⡇⡇⠀⡇⣿⢸⠏⠀⢀⣼⡫⠀⠀⢿⢶⣖⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡘⣿⣦⣿⠀⠀⢘⢮⣿⠀⠀⠀⠑⠣⢇⢀⠥⠛⠁⠀⠀⢻⢧⢂⠀⠀⢸⣜⣽⢻⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⡘⢿⣿⠀⠀⠀⢫⡻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⢣⠆⠀⠀⣸⡿⢃⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⣈⠺⣟⣣⠀⠀⠀⠱⣧⡼⠵⠤⠤⠤⠤⠴⠶⠼⠭⣤⡷⠃⠀⢀⡾⢻⢕⠵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣻⢿⢀⣼⢂⠱⣄⣀⠀⠙⣷⣤⣤⣤⣤⣤⣤⣤⣤⣰⢟⣡⠤⠚⠁⠀⣾⠁⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠿⣿⣿⡜⡄⠀⠉⠙⣲⢼⣿⣿⣔⣵⣞⠝⣾⣿⢯⠁⠀⠀⠀⠀⠀⣿⣿⠻⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠷⣽⣿⠇⠻⣄⠀⠀⢹⡆⣿⢟⡿⣫⠎⣾⢋⢿⢸⡀⠀⠀⢀⣴⢸⢿⡷⠫⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘⢦⣽⠦⠴⠚⠙⣿⠟⣻⢿⣾⢋⢮⣼⠋⠓⠦⠤⣾⡥⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣦⢣⠀⠀⠸⡞⢠⣯⣺⢎⣼⠏⠀⠀⡼⣼⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣟⡝⣗⣂⠀⠀⠹⡟⡰⠓⡽⡟⠀⠀⢰⢣⣿⡹⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⢚⣴⢿⢄⠤⠂⠒⠛⣥⠴⠛⠉⠐⠢⣀⣽⣷⠉⢯⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣧⡞⣣⠊⣿⣆⠀⠀⢀⠜⠀⠀⠀⠀⣰⢿⣫⠋⣺⢀⡿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡟⡸⠔⢁⣶⠂⡿⣆⠠⡂⠀⠀⠠⣀⣴⡟⡏⡻⣄⠁⢰⡇⡞⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⡹⢊⡦⠄⢈⢶⠁⠽⢋⣄⣥⣦⣪⣻⡏⢀⠟⢢⡫⠶⡄⢘⢢⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠐⠀⣎⡼⠠⠂⠸⣞⢀⠯⢵⠏⣳⡪⠀⠈⢌⠘⠀⠐⣕⢕⣆⠐⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣔⠀⢈⡎⠱⣄⠏⡨⠂⠀⠐⠉⡕⡕⣤⠎⢀⠟⡀⠈⠀⡼⡊⣫⣀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡶⢡⠔⠁⠰⡕⠱⡆⠁⠀⢫⢀⠌⠈⢄⢎⢦⠎⠀⠃⢄⠀⠀⠀⢖⢹⣤⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣠⠊⢆⠂⠀⡠⢺⡵⡂⠀⡀⠣⡀⠐⠀⠠⡣⡳⡄⢧⡄⠐⠄⠀⢀⠇⡂⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⠀⠀⠈⣄⠜⠀⣿⠜⡕⡔⠁⠀⠑⠄⡰⠁⠐⣌⢜⣼⡄⠀⠈⠂⡌⠀⠱⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⡡⠗⠀⡰⠛⢄⢸⡏⢠⠞⡔⢄⠀⢀⡜⢆⠀⠈⠀⡜⢹⣧⠀⠀⡜⠐⢄⠁⠰⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⠎⣞⠞⠀⠀⠘⣏⣼⠁⠀⣎⢎⢦⠎⠀⠀⠺⣀⠎⠀⢸⡟⣌⢜⠀⠀⠉⢡⡇⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡌⠀⡸⠛⡔⡤⠀⢰⠝⢆⡀⠀⠀⡲⠣⡡⡢⠀⢀⠞⢆⠀⢸⢨⢯⠳⡑⡄⠀⡎⠘⣴⢸⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⢆⠜⠁⠐⡘⡜⢤⡞⠀⡏⢢⢀⠜⠁⠰⡑⣜⣤⠃⠀⠨⠣⣸⡏⠈⡔⢜⢎⡾⡀⠀⠉⢮⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⡀⠀⠀⠐⡼⢽⠧⠀⡇⢠⠻⡄⠀⠀⠀⣞⢧⠲⡀⠀⢠⢿⣇⠀⢇⢀⡽⠱⡍⣆⣠⠱⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠒⠸⠍⠞⠾⠳⡷⠁⠀⠨⢧⢀⠎⠀⢑⡵⣕⣴⠃⢸⡯⠒⠾⠮⠀⠚⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠒⠒⠠⠷⠀⢀⠢⠌⠚⠚⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠸⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠀⠀⠅⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠀⠀⢠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⢰⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⡀⠐⠀⠀⠆⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠘⠀⠰⣦⣠⣀⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠠⣠⣒⠆⢀⣃⣈⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣀⣀⣄⡼⠛⠛⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠉⢻⣅⣀⣀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⣠⣤⣬⣿⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⢀⡀⠈⣆⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣼⣧⣼⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀