⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢩⠁⡈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠡⣌⢂⠳⡴⠘⣆⠀⢀⢄⠒⣈⣅⢃⡆⠠⣀⢀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡔⢏⠶⣩⠧⣽⣱⠤⡓⠣⢊⠼⡰⢌⢧⡘⡥⢌⠳⠄⡆⡌⡐⢄⠺⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠜⣠⢒⣍⡒⠭⣊⡝⣖⣻⡽⣯⢿⡴⣡⢖⡼⣑⠞⠦⠱⠁⣎⢰⡑⢦⠳⡜⢮⡳⣇⡄⡃⢦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢒⣴⡲⣎⣽⣫⢞⣰⢣⣾⢱⡻⣽⣳⣟⡿⣟⣾⡵⢋⠴⣉⠰⣈⠆⣅⢢⢇⣟⡎⡳⢌⣣⢙⠮⣱⢛⡶⣹⢰⣱⢒⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣙⢾⡹⢧⣾⠺⣌⢳⡛⢎⢣⡙⠶⡙⢮⡹⢛⠮⡟⣫⢶⢧⣳⣙⡞⣩⠎⡞⡜⣞⣱⣞⣶⣫⢞⣦⢳⡜⣥⠳⣭⠲⣍⡔⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡤⠀⡐⠢⢘⡦⣟⢮⢧⡙⠶⣌⠳⡌⢆⡹⢌⠢⣙⢲⡙⢦⣱⣉⠶⡱⣌⡛⣞⡳⣝⡺⣕⡾⣱⡞⣞⣧⡿⣾⣽⣻⢾⡭⣟⣞⡿⣖⣿⡸⢦⡙⡤⠱⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⡴⣻⣼⢳⣏⠾⣙⢎⡖⣩⡳⣭⢷⣜⡚⢶⣩⢖⣱⣩⡳⣭⢷⣜⡚⢶⣩⢖⣱⢖⣱⣩⡳⣭⢷⣜⡚⢶⣩⢖⣱⣩⢖⣱ █████ ⣿⡸⢦⡙⡤⠱⢀
⢈⡴⣻⣼⢳⣏⠾⣙⢎⡖⣩⡳⣭⢷⣜⡚⢶⣩⢖⣼⢳⣏⠾⣙⢎⡖⣩⡳⣭⢷⣜⡚⢶⣩⢖⣼⢳⣏⠾⣙⢎⡖ ░░███ ⣿⡸⢦⡙⡤⠱⢀
⢈⡴⣻⣼⢳⣏⠾⣙⢎⡖⣩⡳⣭⢷⣜⡚⢶⣩██████ ██████ ██████ ░███████ ⣿⡸⢦⡙⡤⠱⢀
⡆⠹⣑⢎⠳⢮⡝⣎⠲⣌⠳⣽⣻⣮⣷⣻⣷⣻ ███░░███ ░░░░░███ ███░░███ ░███░░███ ⣿⡸⢦⡙⡤⠱⢀
⡆⠹⣑⢎⠳⢮⡝⣎⠲⣌⠳⣽⣻⣮⣷⣻⣷⣻ ░███████ ███████ ░███ ░░░ ░███ ░███⣿⡸⢦⡙⡤⠱⢀
⢃⣒⢵⢀⡎⣄⠄⢌⡱⣌⢿⣳⡿⣟⣷⣿⣷⣿ ░███░░░ ███░░███ ░███ ███ ░███ ░███ ⣿⡸⢦⡙⡤⠱⢀
⠈⠇⠧⠖⠺⢨⠑⠛⠆⣹⠒⢪⣉⡺ ░░██████ ░░████████░░██████ ████ █████⣿⡸⢦⡙⡤⠱⢀
⡆⠹⣑⢎⠳⢮⡝⣎⠲⣌⠳⣽⣻⣻⠲⣌⣻⣻ ░░░░░░ ░░░░░░░░ ░░░░░░ ░░░░ ░░░░░⣿⡸⢦⡙⡤⠱⢀
⣌⠳⣽⣻⣮⣷⣻⣷⣻⣌⠳⣽⣻⣮⣷⣻⣷⣻⣷⣻⣾ ⢣⣝⡳⣖⣭⣞⡵⣧⣛⡴⣙⢮⡳⡝⡼⣣⢻⣹⢾⡿⡽⣞⣻⢯⡽⣻⣾⣽⣿⢾⣽⣷⠀⠀
⠀⠀⠀⡆⠹⣑⢎⠳⢮⡝⣎⠲⣌⠳⣽⣻⣮⣷⣻⣷⣻⣾⣭⣷⣾⣽⣾⣮⣝⣾⣳⣿⣼⣣⢳⣣⣛⢶⣣⢿⣼⣯⣿⣷⣽⣾⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣮⢢⠀⠀⠀⠀
⠀⠀⠀⢃⣒⢵⢀⡎⣄⠄⢌⡱⣌⢿⣳⡿⣟⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢦⣣⣭⡴⢄
⠀⠀⠀⠀⢰⡘⠂⠊⠙⠧⠛⢀⠂⣐⣈⠠⢁⠛⠜⠻⠁⣃⣌⣔⣉⢷⣫⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢽⡎⣼⠉
⠀⠀⠀⠀⠀⠈⠇⠧⠖⠺⢨⠑⠛⠆⣹⠒⢪⣉⡺⡔⣺⣴⠿⠃⡀⣡⣼⡄⡛⠹⠋⠟⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉⠉⢟⠻⠿⠿⠻⠟⠩⡁⡄⡁⡂⣀⣬⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠉⠉⠈⠉⠁⠀⠀⠙⣆⠠⢔⢖⠓⢡⣷⠛⠣⠬⡭⡉⠂⠋⠉⢄⡍⠛⠹⢏⢿⡛⡟⢿⡿⣿⡟⣛⠉⡄⣅⡀⢔⡐⡆⢖⠖⠁⠘⠋⠁⠈⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠿⢻⠁⡈⠁⠀⠀⠀⠈⠻⣓⠠⠀⢐⣉⠉⠜⢄⠈⢅⢠⠤⠅⠓⠈⡀⣢⠌⡣⢣⠾⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⢀⡀⡀⠀⠀⠀⡀⢀⣠⢁⡀⢀⠀⠀⠀⣀⠰⣤⠐⢛⣒⠾⠉⢀⠍⠁⠃⠔⠮⢰⠂⣉⠷⣮⣳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠖⠋⠙⠿⠐⢴⢀⠞⢿⠚⡶⠆⠶⣾⢿⡟⡝⠀⠉⠩⡓⠖⠚⠺⠨⠀⠀⠈⠀⠰⠥⠐⠐⠠⡊⢀⢃⡂⠁⠙⡸⡥⢛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⡿⣽⣻⣞⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⡀⢀⣴⣾⣿⣿⣿⢿⣿⡿⣿⣿⣾⣯⢷⣂
⢀⣰⣿⣿⣿⣿⣿⣿⢿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠻⡜⠀
⢻⢏⣿██████ ████████ ██████⣿⣷⣯⠻⡜⠀
⢀⣴⣾⣿███░░███░░███░░███ ███░░███⣿⣿⣷⣯⠻⡜⠀
⢀ ⣴⣾⣿░███ ░███ ░███ ░███ ░███████⣿⣿⣷⣯⠻⡜⠀
⢾⣽⡿⣟⣾░███ ░███ ░███ ░███ ░███░░░ ⢿⣿⣿⣾⡝⡶⣄⠀
⠌⠹⣾⡹░░██████ ████ █████░░██████⣿⣿⣯⣟⢯⢞⣯⢖⠠
⢆⠳⡌⣝ ░░░░░░ ░░░░ ░░░░░ ░░░░░░⣾⡹⢎⡗⣎⠒
⠀⠀⠀⠀⠀⠀⠈⢆⠳⡌⣝⢲⡝⣯⢳⡞⣵⢫⣗⡻⣝⢾⣛⢾⣛⠾⣭⢻⡭⣟⢾⡹⢧⠻⣝⢮⡝⡾⠼⣍⠳⢌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠘⢌⠣⠞⡰⢣⠚⡌⢧⡘⡱⢊⠞⢨⠓⡌⠳⣡⠓⡜⢌⠲⡉⢏⡱⢎⠲⡙⡜⠣⠎⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠈⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠄⢩⠁⡈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⠡⣌⢂⠳⡴⠘⣆⠀⢀⢄⠒⣈⣅⢃⡆⠠⣀⢀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢞⡔⢏⠶⣩⠧⣽⣱⠤⡓⠣⢊⠼⡰⢌⢧⡘⡥⢌⠳⠄⡆⡌⡐⢄⠺⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⣠⠜⣠⢒⣍⡒⠭⣊⡝⣖⣻⡽⣯⢿⡴⣡⢖⡼⣑⠞⠦⠱⠁⣎⢰⡑⢦⠳⡜⢮⡳⣇⡄⡃⢦⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⢔⢒⣴⡲⣎⣽⣫⢞⣰⢣⣾⢱⡻⣽⣳⣟⡿⣟⣾⡵⢋⠴⣉⠰⣈⠆⣅⢢⢇⣟⡎⡳⢌⣣⢙⠮⣱⢛⡶⣹⢰⣱⢒⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⢰⣙⢾⡹⢧⣾⠺⣌⢳⡛⢎⢣⣕⡾⣱⣾⣮⣝⣾⣳⣿⣼⣾⣮⣝⣾⣳⡞⣞⣧⡿⣾⣽⣻⢾⡭⣟⣞⡿⣖⣿⡸⢦⡙⡤⠱⢀
⡤⠀⡐⠢⢘⡦⣟⢮⢧⡙⠶⣌⠳⡌⢆⡹⢌⠢⣙⢲⡙⢦⣱⣉⠶⡱⣌⡛⣞⡳⣝⡺⣕⡾⣱⡞⣞⣧⡿⣾⣽⣻⢾⡭⣟⣞⡿⣖⣿⡸⢦⡙⡤⠱⢀⠀⠀
⡤⠀⡐⠢⢘⡦⣟⢮⢧⡙⠶⣌⠳⡌⠶ ██████ ⡵⣧⣛⡴⣙⢮⡳⡝⡼⣣⢻⣹⢾⡿⡽⣞⣻⢯⡽⣻⣾⣽⣿⢾⣽⣷⣹⣖⢧⠺⡀⠀
⡤⠀⡐⠢⢘⡦⣟⢮⢧⡙⠶⣌⠳⡌⡌ ░░░░░███⣛⡴⣙⢮⡳⡝⡼⣣⢻⣹⢾⡿⡽⣞⣻⢯⡽⣻⣾⣽⣿⢾⣽⣷⣹⣖⢧⠺⡀⠀
⡆⠹⣑⢎⠳⢮⡝⣎⠲⣌⠳⣽⣻⣮⣷███████⣼⣣⢳⣣⣛⢶⣣⢿⣼⣯⣿⣷⣽⣾⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣮⢢⠀
⠇⡯⡛⡁⢜⡲⢶⡽⣯⢟ ███░░███⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢦⣣⣭⡴⢄
⡘⠂⠊⠙⠧⠛⢀⠂⣐⣈ ░░████████⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢽⡎⣼⠉
⠒⠛⠉⠉⠈⠉⠁⠙⣆⠠⠀░░░░░░░░⡛⡟⢿⡿⣿⡟⣛⠉⡄⣅⡀⢔⡐⡆⢖⠖⠁⠘⠋⠁⠈⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀ ⠇⠧⠖⠺⢨⠑⠛⠆⣹⠒⢪⣉⡺⡔⣺⣴⠿⠃⡀⣡⣼⡄⡛⠹⠋⠟⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉⠉⢟⠻⠿⠿⠻⠟⠩⡁⡄⡁⡂⣀⣬⠀
⠀⠀⠀⠀⠀⠀⠀ ⠑⠒⠛⠉⠉⠈⠉⠁⠀⠀⠙⣆⠠⢔⢖⠓⢡⣷⠛⠣⠬⡭⡉⠂⠋⠉⢄⡍⠛⠹⢏⢿⡛⡟⢿⡿⣿⡟⣛⠉⡄⣅⡀⢔⡐⡆⢖⠖⠁⠘⠋⠁⠈⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢲⠿⢻⠁⡈⠁⠀⠀⠀⠈⠻⣓⠠⠀⢐⣉⠉⠜⢄⠈⢅⢠⠤⠅⠓⠈⡀⣢⠌⡣⢣⠾⠜⠉⠁⠀
⠀⠀⠀⠀
⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣶⡿⣽⣻⣞⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢀⣴⣾⣿⣿⣿⢿⣿⡿⣿⣿⣾⣯⢷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⣤⣴⣾⣿⣿⣟⣾⣿⡿⣟⣿⣿⣾⣿⣟⣿⣿⣿⣿⣽⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⢿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠻⡜⣺⣝⡾⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡶⣯⢻⢏⣿⣳⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣏⢷⣺⣝⡾⣤⡟⣏⢷⣺⣝⡾⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⣾⣷⣿⣿⣿⣿⣿⢿⡻⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⣿⣻⣿⣾⡝⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣹⣾⣯⣷⣿⣿⣞⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡵⣩⠞⣻⢿⣿⣿⣾⡝⡶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⢿⣽⣿ ██████ ████ ⣘⢮⣟⣿⣽⡿⣿⣿⣿⣿⣿⣿ ██████ ⢿⣿⢿ ██████⣏⢷⣺⣝⡾⣤⣄⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿ ███░░███░░███ ⣽⡿⣿⣿⣿⣿⣟⣿⣟ ███░░███ ███░░███⣻⢿⣿⣿⣾⡝⡶⣄⠀⠀
⠌⠹⣾⡹⣞⣿⣽⣻ ░███ ░░░ ░███ █████ ████ ░███ ░░░ ░███ ░░░ █████ ████
⠀⣘⢮⣟⣿⣽⡿⣿███████ ░███ ░░███ ░███ ███████ ███████ ░░███ ░███⣿⣿⣯⢿⣯⢿⣱⢻⡄⠀
⠌⠹⣾⡹⣞⣿░░░███░ ⣿⣽⣿ ░███ ░███ ░███ ░░░███░ ░░░███░ ⡹⢧⡹ ░███ ░███⡽⣟⣯⢟⣾⡹⢎⡗⣎⠒
⠌⠹⣾⡹ ░███ ⣛⢾⣛ ░███ ░███ ░███ ░███ ⡜⢌⠲ ░███ ⣡⠓⡜ ░███ ░███⣯⣟⢯⢞⣯⢖⠠⠀
⠌⠹ ⣌ █████ █████ ░░████████ █████ ⣹⢮⡟ █████ ░░███████⣯⢟⣾⡹⢎⡗⣎⠒
░░░░░ ░░░░░ ░░░░░░░░ ░░░░░ ░░░░░ ⣾⡹⣾⡹ ░░░░░███⣯⣟⢯⢞⣯⢖⠠
⠌⠹⣾⡹ ⣽⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣯⣿⣿⣿⣿⣯⢿⣯⢿⣱⢻ ███ ░███ ⡹⢎⡗⣎⠒⠀
⠌⠹⣾⡹⣞⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣟⣯⢟⣾⡹⢎⡗⣎⠒ ⢟⣾⡹⢎⢿⣱⢻░░██████ ⡾⢡⣋⠼⡐⠂ ⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠹⣾⡹⣞⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣟⣯⢟⣾⡹⢎⡗⣎⢮⡟⡾⢡⣋⠼⡐⠂⢮⡟⡾⠒⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣌⢳⡽⣹⡞⣧⡟⣷⢫⣷⣻⢭⣻⡽⢯⣿⢿⣯⢿⣿⣟⡿⣿⢯⣟⣿⢾⡽⢯⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⡌⣝⢲⡝⣯⢳⡞⣵⢫⣗⡻⣝⢾⣛⢾⣛⠾⣭⢻⡭⣟⢾⡹
⢧⠻⣝⢮⡝⡾⠼⣍⠳⢌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠘⢌⠣⠞⡰⢣⠚⡌⢧⡘⡱⢊⠞⢨⠓⡌⠳⣡⠓⡜⢌⠲⡉⢏⡱⢎⠲⡙⡜⠣⠎⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⠈⠁⠈⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠄⢩⠁⡈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠡⣌⢂⠳⡴⠘⣆⠀⢀⢄⠒⣈⣅⢃⡆⠠⣀⢀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡔⢏⠶⣩⠧⣽⣱⠤⡓⠣⢊⠼⡰⢌⢧⡘⡥⢌⠳⠄⡆⡌⡐⢄⠺⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠜⣠⢒⣍⡒⠭⣊⡝⣖⣻⡽⣯⢿⡴⣡⢖⡼⣑⠞⠦⠱⠁⣎⢰⡑⢦⠳⡜⢮⡳⣇⡄⡃⢦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢒⣴⡲⣎⣽⣫⢞⣰⢣⣾⢱⡻⣽⣳⣟⡿⣟⣾⡵⢋⠴⣉⠰⣈⠆⣅⢢⢇⣟⡎⡳⢌⣣⢙⠮⣱⢛⡶⣹⢰⣱⢒⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣙⢾⡹⢧⣾⠺⣌⢳⡛⢎⢣⡙⠶⡙⢮⡹⢛⠮⡟⣫⢶⢧⣳⣙⡞⣩⠎⡞⡜⣞⣱⣞⣶⣫⢞⣦⢳⡜⣥⠳⣭⠲⣍⡔⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡤⠀⡐⠢⢘⡦⣟⢮⢧⡙⠶⣌⠳⡌⢆⡹⢌⠢⣙⢲⡙⢦⣱⣉⠶⡱⣌⡛⣞⡳⣝⡺⣕⡾⣱⡞⣞⣧⡿⣾⣽⣻⢾⡭⣟⣞⡿⣖⣿⡸⢦⡙⡤⠱⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈ ⡴⣻⣼⢳⣏⠾⣙⢎⡖⣩⡳⣭⢷⣜⡚⢶⣩⢖⣱⢣⣝⡳⣖⣭⣞⡵⣧⣛⡴⣙⢮⡳⡝⡼⣣⢻⣹⢾⡿⡽⣞⣻⢯⡽⣻⣾⣽⣿⢾⣽⣷⣹⣖⢧⠺⡀⠀⠀⠀
⡴⣻⣼⢳⣏⠾⣙⢎⡖⣩⡳⣭⢷⣜⡚⢶⣩⢖⣱⢣⣝⡳⣖⣭⣞⡵⣧⣛⡴⣙⢮⡳⡝⡼⣣⢻⣹⢾⡿⡽⣞⣻⢯⡽⣻⣾⣽⣿⢾⣽⣷⣹⣖⢧⠺⡀⠀⠀⠀
⡐⠢⢘████████ ██████ ██████ █████ ██████ ████████⣿⣿⣿⣿⣿⣿⣿⣿⣳⣮⢢⠀⠀
░░███░░███ ███░░███ ░░░░░███ ███░░ ███░░███░░███░░███ ⣿⣿⣳⣮⢢
⢃⣒ ░███ ░░░ ░███████ ███████ ░░█████ ░███ ░███ ░███ ░███ ⣿⣿⣿⣾⢦⣣⣭⡴⢄
⠇⡯░███ ░███░░░ ███░░███ ░░░░███░███ ░███ ░███ ░███⣿⣿⣿⣿⣿⣿⣽⠳⠎
⠇⠧ █████ ░░██████ ░░████████ ██████ ░░██████ ████ █████⣿⣿⣿⣿⣿⣽⠳⠎
⠇⠧⠖░░░░░ ░░░░░░ ░░░░░░░░ ░░░░░░ ░░░░░░ ░░░░ ░░░░░⡄⡁⡂⣀⣬⠀
⠈⠇⠧⠖⠺⢨⠑⠛⠆⣹⠒⢪⣉⡺⡔⣺⣴⠿⠃⡀⣡⣼⡄⡛⠹⠋⠟⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉⠉⢟⠻⠿⠿⠻⠟⠩⡁⡄⡁⡂⣀⣬⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠉⠉⠈⠉⠁⠀⠀⠙⣆⠠⢔⢖⠓⢡⣷⠛⠣⠬⡭⡉⠂⠋⠉⢄⡍⠛⠹⢏⢿⡛⡟⢿⡿⣿⡟⣛⠉⡄⣅⡀⢔⡐⡆⢖⠖⠁⠘⠋⠁⠈⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣼⢳⣏⠾⣙⢎⡴⣻⣼⢳⣏⠾⣙⢎⠀⢲⠿⢻⠁⡈⣧⣛⡴⣙⢮⠈⠻⣓⠠⠀⢐⣉⠉⠜⢄⠈⢅⢠⠤⠅⠓⠈⡀⣢⠌⡣⢣⠾⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣻⣼⢳⣏⠾⣙⢎⡴⡀⣖⣭⣞⡵⣧⣛⡴⣙⢮⡳⡝⢀⠰⣤⠐⢛⣒⠾⠉⢀⠍⠁⠃⠔⠮⢰⠂⣉⠷⣮⣳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⣴⠖⠋⠙⠿⠐⢴⢀⠞⢿⠚⡶⠆⠶⣾⢿⡟⡝⠀⠉⠩⡓⠖⠚⠺⠨⠀⠀⠈⠀⠰⠥⠐⠐⠠⡊⢀⢃⡂⠁⠙⡸⡥⢛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⢀⣤⣶⡿⣽⣻⣞⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⡀⢀⣴⣾⣿⣿⣿⢿⣿⡿⣿⣿⣾⣯⢷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀ ⣤⣴⣾⣿⣿⣟⣾⣿⡿⣟⣿⣿⣾⣿⣟⣿⣿⣿⣿⣽⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⢀⣰⣿⣿⣿⣿⢿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠻⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⣀⡶█████ ⡻⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀⠀
⢀⣴⣾⣿░░███⣿⣿⣿⣿⢿⡻⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀
⢀⡾⣿⣿⣿⢿⣽███████ ██████⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣯⢿⣱⢻⡄
⢾⣽⡿⣟⣾⣿░░░███░⣿⣿ ███░░███⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣯⢿⣱⢻⡄
⠌⠹⣾⡹⣞ ░███ ░███ ░███⣿⣿⣿⣿⣿⣿⣿⣯⣟⢯⢞⣯⢖⠠
⠐⣌⢳⡽⣹ ░███ ███░███ ░███⢯⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂
⠑⠘⢌⠣░░█████ ░░██████⡽⢯⢿⣹⢮⡟⡾⢡⣋⡐⠂⠀
⡞⣧⡟ ░░░░░ ░░░░░░⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂⠀
⠐⣌⢳⡽⣹⡞⣧⡟⣷⢫⣷⣻⢭⡽⢯⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢩⠁⡈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠡⣌⢂⠳⡴⠘⣆⠀⢀⢄⠒⣈⣅⢃⡆⠠⣀⢀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡔⢏⠶⣩⠧⣽⣱⠤⡓⠣⢊⠼⡰⢌⢧⡘⡥⢌⠳⠄⡆⡌⡐⢄⠺⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠜⣠⢒⣍⡒⠭⣊⡝⣖⣻⡽⣯⢿⡴⣡⢖⡼⣑⠞⠦⠱⠁⣎⢰⡑⢦⠳⡜⢮⡳⣇⡄⡃⢦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢒⣴⡲⣎⣽⣫⢞⣰⢣⣾⢱⡻⣽⣳⣟⡿⣟⣾⡵⢋⠴⣉⠰⣈⠆⣅⢢⢇⣟⡎⡳⢌⣣⢙⠮⣱⢛⡶⣹⢰⣱⢒⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣙⢾⡹⢧⣾⠺⣌⢳⡛⢎⢣⡙⠶⡙⢮⡹⢛⠮⡟⣫⢶⢧⣳⣙⡞⣩⠎⡞⡜⣞⣱⣞⣶⣫⢞⣦⢳⡜⣥⠳⣭⠲⣍⡔⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡤⠀⡐⠢⢘⡦⣟⢮⢧⡙⠶⣌⠳⡌⢆⡹⢌⠢⣙⢲⡙⢦⣱⣉⠶⡱⣌⡛⣞⡳⣝⡺⣕⡾⣱ ███⡳⡝⡼⣣ █████⣖⣿⡸⢦⡙⡤⠱⢀⠀
⢮⢧⡙⠶⣌⠳⡌⢆⡹⢌⠢⣙⢲⡙⢦⣱⣉⠶⡱⣌⡛⣞⡳⣝⡺⣕⡾⣱⡞⣞⣧⡿⣾ ⣽░░░ ░░███⣿⣾⢦⣣⣭⡴⢄
⠇⡯⡛⡁⢜⡲ ██████ █████ █████ ██████ ████ ███████ ⣿⣾⢦⣣⡴⢄
⠈⠇⠧⠖ ░░░███ ░░███ ░░███ ███░░███░░███ ███░░███ ⣿⣿⣿⣿⣽⠳⠎
⢃⣒⢵⢀⡎ ███████ ░███ ░███ ░███ ░███ ░███ ░███ ░███⣿⣿⡿⣻⡎⣼⠉
⠈⠇⠧⠖⠺⢨⠑⠛ ███░░███ ░░███ ███ ░███ ░███ ░███ ░███ ░███⣻⢽⡎⣼⠉
⢃⣒⢵⢀⡎⣄ ░░████████ ░░█████ ░░██████ █████░░████████⢣⠾⠜⠉⠁⠀
⠑⠛⠆⣹⠒ ░░░░░░░░ ░░░░░ ░░░░░░ ░░░░░ ░░░░░░░░ ⡣⢣⠾⠜⠉⠁
⣫⢞⣰⢣⣾⢱⡻⣽⣳⣟⡿⣟⣾⡵⢋⠴⣉⠰⣈⠆⣅⢢⢇⣟⡎⡳⢌⣣⢙⠮⣱⢛⡶⣹⠿⠿⠻⠟⠩⡁⡄⡁⡂⣀⣬⠀
⠀⠀⠀⠀⠀⠑⠛⠆⣹⠒⢪⣉⡺⡔⣺⣴⠿⠃⡀⣡⣼⡄⡛⠹⠋⠟⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉⠉⢟⠻⠿⠿⠻⠟⠩⡁⡄⡁⡂⣀⣬⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠉⠉⠈⠉⠁⠀⠀⠙⣆⠠⢔⢖⠓⢡⣷⠛⠣⠬⡭⡉⠂⠋⠉⢄⡍⠛⠹⢏⢿⡛⡟⢿⡿⣿⡟⣛⠉⡄⣅⡀⢔⡐⡆⢖⠖⠁⠘⠋⠁⠈⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡐⠢⢘⡦⣟⢮⢧⡙⠶ ⢲⠿⢻⠁⡈⠁⢋⠴⣉⠰⣈⠀⠻⣓⠠⠀⢐⣉⠉⠜⢄⠈⢅⢠⠤⠅⠓⠈⡀⣢⠌⡣⢣⠾⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠋⠙⠿⠐⢴⢀⠞⢿⠚⡶⠆⠶⣾⢿⡟⡝⠀⠉⠩⡓⠖⠚⠺⠨⠀⠀⠈⠀⠰⠥⠐⠐⠠⡊⢀⢃⡂⠁⠙⡸⡥⢛⢆⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⢀⣤⣶⡿⣽⣻⣞⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⡀⢀⣴⣾⣿⣿⣿⢿⣿⡿⣿⣿⣾⣯⢷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀ ⣤⣴⣾⣿⣿⣟⣾⣿⡿⣟⣿⣿⣾⣿⣟⣿⣿⣿⣿⣽⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⢀⣰⣿⣿⣿⣿⣿⣿⢿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠻⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⣀⣴⣾⣿⣿⣿⣯⣾⣷⣿⣿⣿⣿⣿⢿⡻⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀
⡾⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣹⣾⣯⣷⣿⣿⣞⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡵⣩⠞⣀⠀
⢀⣴⣾⣿⣿⣿⣯⣾⣷⣿⣿⣿⣿⣿⢿⡻⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⣿⣿⣿⢿⣽⣿██████ █████ ████ ██████⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀
⢾⣽⡿⣟⣾⣿███░░███░░███ ░███ ███░░███⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀
⠌⠹⣾ ░███████ ░███ ░███ ░███████⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢯⢞⣯⢖⠠
⣘⢮⣟⣿⣽⡿░███░░░ ░███ ░███ ░███░░░⣿⣿⣿⣿⢿⡽⣟⣯⢟⣾⡹⢎⡗⣎⠒⠀
⣘⢮⣟⣿⣽⡿⣿ ░░██████ ░░███████ ░░██████⢯⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂
⣘⢮⣟⣿⣽⡿⣿⣿ ░░░░░░ ░░░░░███ ░░░░░░⣝⢮⡝⡾⠼⣍⠳⢌⠂⠁
⠐⣌⢳⡽⣹⡞⣧⡟⣷⢫⣷⣻⢭⣻⡽⢯███ ░███ ⣿⣟⡿⣿⢯⣟⣿⢾⡽⢯⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂⠀
⠐⣌⢳⡽⣹⡞⣧⡟⣷⢫⣷⣻⢭⣻⡽ ░░██████⣯⢿⣿⣟⡿⣿⢯⣟⣿⢾⡽⢯⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂⠀⠀⠀⠀
⢀⡾⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣹⣾⣯⣷ ░░░░░░ ⣯⢻⢏⣿⣳⣾⣿⣿⣟⣿⣿⣿⣺⣝⡾⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣯⣾⣷⣿⣿⣿⣿⣿⢿⡻⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠘⢌⠣⠞⡰⢣⠚⡌⢧⡘⡱⢊⠞⢨⠓⡌⠳⣡⠓⡜⢌⠲⡉⢏⡱⢎⠲⡙⡜⠣⠎⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠈⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠄⢩⠁⡈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⠡⣌⢂⠳⡴⠘⣆⠀⢀⢄⠒⣈⣅⢃⡆⠠⣀⢀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢞⡔⢏⠶⣩⠧⣽⣱⠤⡓⠣⢊⠼⡰⢌⢧⡘⡥⢌⠳⠄⡆⡌⡐⢄⠺⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠒⣈⣅⢃⡆⠠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⣠⠜⣠⢒⣍⡒⠭⣊⡝⣖⣻⡽⣯⢿⡴⣡⢖⡼⣑⠞⠦⠱⠁⣎⢰⡑⢦⠳⡜⢮⡳⣇⡄⡃⢦⠀⣫⢞⣦⢳⡜⣥⠳⣭⠲⣍⢳⡜⣥⠳⣭⠲⣍⡔⡈⢆⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⢔⢒⣴⡲⣎⣽⣫⢞⣰⢣⣾⢱⡻⣽⣳⣟⡿⣟⣾⡵⢋⠴⣉⠰⣈⠆⣅⢢⢇⣟⡎⡳⢌ █████ ⡽⣯⢿⡴⣡⢖⡼⣑⠞⠦⠱⠁⣎⢰⡑⢦⠳⡜⢮⡳█████⡜⣭⠲⡔⡈⢆⠀⠀⠀
⣠⢰⣙⢾⡹⢧⣾⠺⣌⢳⡛⢎⢣⡙⠶⡙⢮⡹⢛⠮⡟⣫⢶⢧⣳⣙⡞⣩⠎░░███ ⣶⣫⢞⣦⢳⡜⣥⠳⣭⠲⣍⡔⡈⣶⣫⢞⣦⢳⡜⣥░░███⡜⣥⠳⣭⠲⣍⡔⡈⢆⠀⠀⠀
██████ ██████ ████████ ███████ ██████ ██████ ███████⡿⣖⣿⡸⢦⡙⡤⠱⢀⠀
⢈⡴⣻⣼⢳⣏ ███░░███ ███░░███░░███░░███ ░░░███░ ░░░░░███ ███░░███░░░███░⣿⣿⣿⣿⣿⣿⣿⣳⣮⢢⠀
⢈⡴⣻⣼⢳⣏⠾⣙ ░███ ░░░ ░███ ░███ ░███ ░███ ░███ ███████ ░███ ░░░ ░███ ⣿⢾⣽⣷⣹⣖⢧⠺⡀
⢃⣒⢵⢀⡎⣄⠄⢌⡱⣌░███ ███░███ ░███ ░███ ░███ ░███ ███ ███░░███ ░███ ███ ░███ ███⣿⢾⣽⣷⣹⣖⢧⠺⡀
⠇⠧⠖⠺⢨⠑⠛░░██████ ░░██████ ████ █████ ░░█████ ░░████████░░██████ ░░█████ ⣿⣿⣿⣿⣾⢦⣣⣭⡴⢄
⢃⣒⢵⢀⡎⣄ ░░░░░░ ░░░░░░ ░░░░ ░░░░░ ░░░░░ ░░░░░░░░ ░░░░░░ ░░░░░⣿⣿⣿⡿⣻⢽⡎⣼⠉
⠇⡯⡛⡁⢜⡲⢶⡽⣯⢟⡭⢿⣽⡻⢯⣟⡷⣿⣻⢿⣟⡿⣿⢯⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠳⠎
⠀⠀⠀⠀⠀⠀ ⢰⡘⠂⠊⠙⠧⠛⢀⠂⣐⣈⠠⢁⠛⠜⠻⠁⣃⣌⣔⣉⢷⣫⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢽⡎⣼⠉
⠀⠀⠀⠀⠀ ⠇⠧⠖⠺⢨⠑⠛⠆⣹⠒⢪⣉⡺⡔⣺⣴⠿⠃⡀⣡⣼⡄⡛⠹⠋⠟⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡉⠉⢟⠻⠿⠿⠻⠟⠩⡁⡄⡁⡂⣀⣬⠀
⠀⠀⠀⠀⠀⠀⠀ ⠑⠒⠛⠉⠉⠈⠉⠁⠀⠀⠙⣆⠠⢔⢖⠓⢡⣷⠛⠣⠬⡭⡉⠂⠋⠉⢄⡍⠛⠹⢏⢿⡛⡟⢿⡿⣿⡟⣛⠉⡄⣅⡀⢔⡐⡆⢖⠖⠁⠘⠋⠁⠈⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢲⠿⢻⠁⡈⠁⠀⠀⠀⠈⠻⣓⠠⠀⢐⣉⠉⠜⢄⠈⢅⢠⠤⠅⠓⠈⡀⣢⠌⡣⢣⠾⠜⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⢀⣤⣶⡿⣽⣻⣞⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⡀⢀⣴⣾⣿⣿⣿⢿⣿⡿⣿⣿⣾⣯⢷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀ ⣤⣴⣾⣿⣿⣟⣾⣿⡿⣟⣿⣿⣾⣿⣟⣿⣿⣿⣿⣽⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⢀⣰⣿⣿⣿⣿⣿⣿⢿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠻⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ ⣀⡶⣯⢻⢏⣿⣳⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣏⢷⣺⣝⡾⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣾⣿⣿⣿⣯⣾⣷⣿⣿⣿⣿⣿⢿⡻⣟⡻⢿⢿⡛⣝⣶⣿⣾⣿⣻⢿⣿⣿⣾⡝⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⣿⣿⣿⢿⣽ enough>>⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡵⣩⠞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣽⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣯⢿⣱⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣘⢮⣟⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢯⢞⣯⢖⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⠹⣾⡹⣞⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣟⣯⢟⣾⡹⢎⡗⣎⠒⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣌⢳⡽⣹⡞⣧⡟⣷⢫⣷⣻⢭⣻⡽⢯⣿⢿⣯⢿⣿⣟⡿⣿⢯⣟⣿⢾⡽⢯⢿⣹⢮⡟⡾⢡⣋⠼⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢆⠳⡌⣝⢲⡝⣯⢳⡞⣵⢫⣗⡻⣝⢾⣛⢾⣛⠾⣭⢻⡭⣟⢾⡹⢧⠻⣝⢮⡝⡾⠼⣍⠳⢌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠘⢌⠣⠞⡰⢣⠚⡌⢧⡘⡱⢊⠞⢨⠓⡌⠳⣡⠓⡜⢌⠲⡉⢏⡱⢎⠲⡙⡜⠣⠎⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠈⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀