⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⣯⠳⢷⠾⢻⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⡀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢄⣀⠀⠀⠙⣶⣿⠆⠀⠀⠘⠿⣦⠀⠀⠀⠀⠀
⠀⠀⣠⠴⠒⢲⡦⣄⣰⠀⢰⡄⢸⢃⡄⡿⣸⢀⣠⠤⠦⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠈⢦⠀⠀⢾⣴⣶⡆⢀⣶⠶⠚⠃⠀⠀⠀⠀
⠀⢰⣧⣤⢦⠀⠀⠆⢉⣦⡘⢟⠣⢿⠃⡇⡿⢁⡈⣀⣀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠘⣿⣦⢠⣴⣦⠜⡆⠀⠀⢹⡈⢻⣾⠃⠀⠀⠀⠀⠀⠀⠀
⢠⠯⠀⠈⠉⠀⠎⠑⢶⣾⣷⡞⢆⣟⡼⣠⠩⡯⠛⠅⠀⣀⡤⠴⠦⠇⠀⠀⠀⠀⠀⠙⠋⠀⠛⠧⠀⡇⠀⣀⣈⣇⣸⠡⣴⣴⠀⠀⠀⠀⠀⠀
⠸⠿⠹⠿⠒⣢⣄⣠⠄⣈⡿⣷⣽⡿⣷⣟⣞⠔⠳⡒⠾⠣⢄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⡯⠭⠖⢲⡧⣏⠑⢮⡀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠞⠉⠈⠁⢼⡭⠽⣟⣽⣿⣷⣛⠻⠏⡤⡦⢤⣠⠀⠀⡙⢿⠸⢷⡀⠀⠀⠀⠀⠀⣴⡿⠋⢹⠁⠀⠀⢸⣸⠉⠙⡄⠘⢦⢀⡀⠀⠀⠀
⠀⢰⢁⡔⠢⠖⠛⠆⠸⠌⠉⣽⣿⣿⡯⠤⡨⠬⠥⣀⣀⠀⠀⢨⠃⠀⢸⡟⣆⠀⠀⢠⡾⠁⠀⢀⠇⠀⣄⡄⣼⠇⠰⡤⣼⣤⣼⠏⣧⠀⠀⠀
⠀⣄⣎⡞⢀⡤⠟⣀⣬⡤⡞⢗⠁⢻⣰⣪⢄⡀⠀⠉⠀⠙⠢⡏⠀⠀⠀⠀⢸⠀⢠⡟⠀⠀⠀⡜⠀⠈⠟⣹⠏⠀⠀⣽⡄⠉⠁⠀⠿⣧⣀⠀
⠀⠹⡟⣰⣿⠒⠉⠁⠀⠀⡏⠈⢀⢸⡅⠀⠉⠾⡀⠀⠀⠀⠀⢱⠀⣰⠀⣀⠗⠒⠉⠉⠉⠉⠻⡁⠀⠀⣰⠋⠀⠀⢘⡿⠃⠀⠀⠀⣤⠔⠛⠃
⠀⠀⠱⠿⠃⠀⠀⠀⠀⠀⢧⠀⠘⠸⠙⣄⠀⠀⠀⣤⡠⠀⠀⡾⣲⠛⡸⢛⡀⢀⡀⣀⡠⠔⠒⢱⡄⡴⠃⠀⠀⠀⠚⠒⣻⠿⣦⣰⠇⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡄⠀⠀⠈⢦⣀⡀⠈⣻⢣⢲⣱⢁⠴⣡⢔⣮⠟⠊⠁⠀⠀⠀⣸⠟⠁⠀⠀⠀⢀⣠⡾⠁⠀⠈⠹⢰⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡈⢪⡀⢄⣧⠶⢛⡢⠆⣶⣯⣾⣷⣷⣿⡾⢇⣤⠆⠀⠀⢀⣤⠞⠃⠀⣴⣒⣺⠿⠟⠋⠀⠀⠀⠀⠀⡞⣰⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⢺⣷⡋⡽⠋⢁⣠⡼⢷⣾⣿⣿⣿⡿⣽⡝⡉⣑⡢⠽⠔⠚⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠄⡼⠀⠚⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠶⠗⠈⣑⡶⠋⢀⡀⠈⠀⠀⠄⢢⡋⠁⠹⡧⠀⠉⢻⡙⠓⠢⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⡜⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⢾⣟⣧⣷⣋⣁⣀⣀⠤⠔⠚⡟⠐⠀⢀⡇⠈⠀⠰⣇⡀⠀⠀⠀⢄⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⣋⢀⣰⡴⠈⢆⠀⠀⠀⡇⠀⠀⢠⠇⠀⠇⢠⠗⠋⠒⠦⣄⠈⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠿⠁⠛⡩⠚⠉⡟⠲⡄⡇⠀⠀⠀⠀⣾⢠⠎⣀⡤⠴⠾⠭⠶⢍⣉⡉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣇⣀⠀⢸⡠⠼⣇⠀⡴⠓⢦⣿⣯⢮⠥⠄⠠⠤⣄⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⡇⣱⣧⡴⠙⡧⣾⠟⠻⣶⣶⣯⣿⣵⣫⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣉⡡⡟⠢⣧⡜⡦⠜⣿⡯⣬⣽⣱⠟⡠⡄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠻⣯⡍⠁⢉⣳⠟⢿⠇⠉⢳⡀⢿⡇⠀⠀⠀⠀⢠⠃⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣥⣶⣜⡟⡔⠙⠑⠢⡀⣑⠤⠹⢦⠤⠤⢒⣵⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠿⣎⢿⠀⠀⠀⢠⣏⠀⠀⠀⠀⢱⡐⠺⠿⠿⠟⠁⠀⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢧⣀⡈⠻⡦⣀⡠⣷⡿⠇⠀⡀⠀⢈⠼⣑⣒⡤⠤⠄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣢⣠⡎⡴⠎⠋⠽⢿⣿⣿⣽⣿⣵⢆⡼⢤⣄⠀⠀⠀⠀⢠⠞⣭⡝⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠃⢣⡀⠀⠀⠀⢺⣿⣿⣿⣾⠉⠈⠁⠀⢳⠀⠀⠀⠻⠀⢈⡵⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⡂⢤⣠⠚⠙⠉⢻⠀⠀⠀⠀⣽⡟⢵⣈⣀⣤⡶⠶⠊⠀⠠⢼⣆⡴⣋⡴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠫⡇⠀⠀⠀⠈⠓⠤⢠⡔⢫⡘⠄⠀⠀⢱⢀⣀⠀⢀⣴⢠⣾⠿⠧⢤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡶⠉⠩⠵⢶⣿⣰⡀⠀⠀⣀⠀⢨⣿⡦⡉⠒⠒⣒⣯⢘⣏⠛⠋⣸⣋⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡉⠀⠀⢀⡤⣶⣻⣿⣷⣶⣿⣶⣶⣅⣿⣿⣌⢦⣼⣠⣤⣸⣋⣀⠀⡤⠭⠓⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣶⣳⠀⠀⠀⠀⠀⠙⠪⠬⣵⠅⠀⠤⡞⣛⣿⣿⠏⢱⡉⠙⢝⣖⠿⣿⡝⢮⣭⡤⣴⠟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⡿⣻⣛⢳⡀⠀⢀⣀⣤⣤⣄⡇⠀⠀⢀⡀⠁⠹⡼⠀⠀⢸⢀⢀⣼⠀⠀⢙⣀⣤⢚⣯⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢾⣿⣿⣿⣿⠿⠦⢄⣘⣟⣿⣿⡷⣄⠴⠋⠀⢀⡴⣇⠀⠀⢸⠉⠁⢈⢷⠭⣉⠘⠟⣺⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠽⠛⠁⣠⢶⡶⠋⠀⠉⠉⢀⠙⠢⢶⣒⡽⠹⣮⣵⡒⠋⠀⠀⠸⣿⢏⢗⢷⠀⢸⡠⣶⠂⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣦⠟⢀⣾⣿⣿⠇⣇⠻⣝⣻⣆⡀⠀⠀⠹⣼⡧⣄⡁⠀⠛⠦⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡏⠀⢘⢟⡫⠥⣴⡿⡿⣢⠤⣄⠉⠀⠀⠀⠀⠉⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⢺⠯⡾⠳⣀⠔⡞⣾⡿⢿⣝⢼⠋⢀⣧⠤⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⠀⣀⡄⢰⠇⠀⠀⠀⣟⣚⣷⣀⡰⣷⣠⠟⣃⢀⡞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣏⠛⢹⡇⢸⢠⢀⠀⢀⣟⣁⣀⡩⣾⣾⣿⡿⢯⣥⠭⢭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠾⣥⡄⣰⠾⢻⡿⠟⣔⢿⣿⠋⠈⢊⡿⢻⡿⣿⡀⠙⡽⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠏⠀⠘⣇⢰⣿⠿⠿⠠⠶⢻⠂⢸⡧⠈⢷⠢⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣎⣡⡄⠀⠀⠀⠸⣆⡜⠳⣧⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⢹⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣿⡳⣦⣀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣶⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⣠⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣸⡏⠻⢷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣉⣳⠄⣀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀�

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠳⡄⠀⠀⠀⠀⢠⠴⠒⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡶⢶⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢹⡄⠀⠀⣰⠋⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡼⠀⠀⠛⠒⠒⡦⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣷⠀⢰⡏⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣹⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⡶⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢽⠀⢸⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢷⡤⠞⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢀⠄⡀⣸⠃⡀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠜⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠳⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣰⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠁⠈⣧⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⡇⠀⠘⠁⠀⠘⠲⢤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⣠⠤⠤⠄⠙⡇⠀⠀⢨⠷⢶⡋⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢷⣀⡴⠂⢠⣇⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣤⡴⠋⠀⠹⣽⣛⣛⣿⠋⠉⠉⢁⡴⢋⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠉⠁⠀⠀⠀⣠⡞⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠓⠦⢤⠤⠴⠶⣺⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡰⢲⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠲⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠁⠈⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⡀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠁⠀