⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠹⣦⠸⣏⢼⠛⢻⡆⣴⣛⣳⡄⠀⠀⣿⠋⢷⡄⣾⠛⣷⢠⡟⠛⡷⠛⣧⢺⡟⠛⣆⠀⠀⠘⠇⠀⠲⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠾⠁⠘⠇⣺⠳⠞⠁⠘⠶⠖⠀⠀⠀⠿⠲⠟⠀⠛⠶⠋⠐⠏⠐⠏⠀⠷⠸⠗⠾⠃⠀⠀⠚⠇⠘⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠈⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡴⠞⠉⠀⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠑⢦⣀⣀⣀⡤⠤⣄⣀⡀⣻⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡰⠞⠁⠀⠀⠀⠀⠨⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⢿⣍⠉⠀⠀⠀⠀⠀⠙⢷⠀⠀⠱⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀
⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣰⠋⠀⣠⣷⣄⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⣀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣰⠃⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠹⡆⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠈⠃⠀⠀⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⣹⠀⠀⠀⣀⡬⠤⠤⢤⡀⠀
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⡤⣄⡀⠀⡘⡘⢦⡀⠀⠀⠀⠘⣏⠈⠉⠹⠃⠈⡇⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠱⢆⡀⠰⢊⠶⣩⢝⡷⣆⢹⣂⢧⣀⠀⢀⡀⠈⠳⣄⡀⠀⢀⠀⠛⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠁⣀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠳⣄⠎⣰⠫⢷⣺⣯⡽⣚⣿⣭⢠⡙⣇⠀⣰⠃⠈⠉⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠖⠘⠁⠀⠀⠀⠙⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⣟⡼⣫⢷⠀⠂⢀⠈⠝⢿⡻⢯⠷⣿⢦⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠖⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢞⡷⣿⠧⠀⢨⡟⣞⣈⠀⣀⠉⠎⢿⣿⡘⡞⣶⠋⠹⠦⣄⡀⠀⠀⠀⠀⠒⠋⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢰⣁⢞⡹⢟⣮⣁⠰⢈⠂⡄⢀⠏⡜⢲⢋⡳⡒⢶⣩⣙⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣿⣦⣝⡸⢫⢟⣿⣦⣌⡠⠏⠦⣑⡮⡀⠥⠙⡡⢖⡥⢲⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢂⠠⢁⣎⠳⣽⣳⢏⣟⡳⣏⡞⣝⡲⣱⢄⡢⠘⠥⢊⡝⢳⠲⣄⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢂⠒⢦⣎⠷⡱⢎⠡⠈⡝⣳⡽⣎⡷⣭⢞⡵⣛⢦⣃⣌⢢⡙⠰⡭⢺⢥⡛⡶⣄⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⠆⣹⢳⠞⣍⠣⠌⣂⠡⣜⡱⣞⡱⣏⠷⡏⠘⢩⢞⡖⣎⡳⡜⡥⣜⡡⠞⡸⠱⡌⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠘⠤⢁⠒⣄⢳⣎⢷⡩⢷⡙⢎⡐⠡⣌⠺⢽⠺⡱⢉⡐⢀⠹⣜⣡⢓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⢠⣉⠶⣋⡜⡮⡕⢣⠉⠤⣈⡕⣎⠱⢂⠱⢐⢢⣜⣯⢳⡭⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠖⠈⠀⠐⠸⣑⠈⠤⡘⢤⠳⡘⡤⢓⠌⠞⠀⠈⠉⠘⠳⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀