⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⣁⣧⣖⡖⠠⢠⠀⠀⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣶⡭⣛⠫⡞⠡⠀⡤⢦⠆⠨⠀⠀⢸⠋⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⢈⠀⢭⣉⠂⡄⢠⠖⣸⠑⣆⡦⠊⢀⠀⡂⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠚⣁⣀⡀⣤⣰⢶⢷⢼⣿⠏⡡⢠⢗⡙⣶⣞⠛⣍⣪⣼⡠⠠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄⣎⡠⢠⠉⠋⠓⠉⠋⢨⠘⠚⢉⡄⠁⢾⡌⣗⢿⠛⠲⠛⠋⡝⠑⠀⠌⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠥⠄⡚⣜⢣⣴⡨⢁⡀⣈⡅⠀⣀⠀⠈⣄⣀⢿⣯⡔⢊⢺⣷⠆⣷⠶⠂⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢁⣨⡅⠨⣤⣭⣵⣿⢿⢏⠿⠯⡁⠹⣿⡯⡜⠫⢯⢿⡾⣻⡅⣠⣆⣄⣰⡐⠲⠼⢶⠒⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⢈⠙⡋⣟⡛⣷⠴⢼⠓⠋⣺⣴⣷⣷⢾⣿⡿⣡⣠⣸⠗⠻⠹⠿⣟⢥⠯⣿⠻⢅⢴⢎⠄⠀⡄⢠⣀⠀⡀⠀⢄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢘⠳⠋⣤⣶⡿⢜⣳⢦⢶⣌⣩⠶⢠⣤⣯⠷⠈⠬⡉⠎⠎⣀⡌⠟⣝⣿⠇⡚⠒⠔⢀⣴⣍⣾⢲⠋⠟⠈⠙⠑⠉⢀⠄⠀
⠀⠀⠀⡀⣽⠿⠻⡈⠱⢻⣽⡟⣶⣚⡻⢏⢹⡋⠁⣀⣂⣤⣴⠄⢤⣐⣴⡾⣶⠯⣄⣉⢓⡭⢍⡆⡀⣈⣿⣷⡷⠶⠒⢂⣠⣠⢶⣾⣳⣯⣵⡄
⠀⠀⠀⠰⠴⠀⢘⢉⣧⣥⣏⠳⢈⣫⠞⣿⣷⢤⣤⣿⣿⣾⣧⣾⣿⣿⣿⣗⣿⣿⣿⠋⣚⡃⠿⡭⠹⣷⣿⠾⡿⢤⣤⣜⢿⣯⡿⣷⠯⣽⣿⡾
⠀⠀⠀⠀⠀⠐⠞⠻⣿⢟⣿⢿⠷⠥⣼⣷⢷⣯⠟⠻⠙⢉⡿⣿⢻⣹⣿⣿⢉⢳⣿⣿⣯⡶⡄⡶⢦⣷⣶⣿⡬⢥⠨⣭⣹⠏⠁⡘⢫⠉⠈⠀
⠀⠀⠔⣼⢂⠬⢌⠧⢋⡛⢡⣮⡡⠈⠓⣃⢀⣒⣊⣽⠻⣛⠟⢿⢸⣯⣿⣓⣿⡟⣷⣟⣿⣿⣿⣿⣻⣷⣟⣒⡺⠏⢰⡿⠿⣶⣶⡻⠒⡿⠦⡀
⠀⢆⣀⣆⣸⣿⠋⡴⢲⡁⡋⠀⢴⣮⣷⠟⠫⠿⣿⢶⢅⢴⣇⣸⣷⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣟⣲⢦⠦⢋⡀⢿⣾⣷⣶⣤⠋⠆
⠈⠘⠛⠼⠿⡝⣻⠛⠻⠀⠀⠐⠛⢹⣱⣟⣽⣯⣿⡟⡊⣿⣷⣖⢽⣿⣿⣿⢿⣿⠀⠀⠘⠋⠃⠁⠀⠀⠨⠟⠿⡷⣥⣉⠁⠘⠉⠊⠚⠚⠓⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠋⠹⣎⢻⣿⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⡕⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀