⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⡠⢀⠄⡠⢀⠄⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠰⢀⠆⡡⢂⡱⣈⢦⠱⣌⢦⡱⣌⢬⡑⢆⡒⠤⣁⢂⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡈⡔⢌⠢⡜⡤⣎⣵⣯⣶⣿⣾⣿⡾⣷⢿⡾⣧⣿⣮⣗⣧⡲⣌⡒⣄⠢⡈⠔⡀⢂⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠚⡰⢡⣎⣷⣽⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠑⢫⡞⡵⣋⠷⡙⢦⢳⡜⡤⡑⠢⢌⡐⠠⢁⠠⠀⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣀⢋⢤⣳⣽⣿⣿⣿⣿⠟⢡⡀⢆⡔⢡⠈⠄⠀⠀⠀⠀⠀⢸⣷⣛⢶⡱⢢⠍⡂⠆⡈⠱⠩⢳⠤⣌⠱⣀⠆⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⡰⢑⡤⣯⣾⣿⣿⢿⣻⡿⢁⣎⡶⣽⢋⠜⠂⠄⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⢁⠋⠌⡑⢂⠰⢁⠒⢢⠋⠘⠳⡜⠛⡀⠁⠀⡀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢠⡘⢴⣫⣾⣿⡿⡟⠞⢫⡟⢡⢎⡼⡝⢢⠁⢊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⡉⡜⣑⠚⠲⠡⠞⠁⠒⡔⠐⡈⠐⠀⠀⡐⢄⠂⠀⠈⠀
⠀⠀⠀⠀⠀⠠⠈⠠⡁⠜⢢⡼⣿⠿⠛⢉⠠⣐⡬⠉⠀⠀⠈⡐⠉⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣷⡥⣾⣣⡙⠤⡑⠢⠐⠀⢀⠢⠁⠂⠀⣮⠑⡌⠄⡁⠀⠀
⠀⠀⠀⠀⠀⠄⢂⠡⡘⢌⠷⠋⢁⣤⢶⣞⣿⣿⣿⠀⠀⢈⠻⡝⢒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⡷⣓⢦⡙⢣⡄⢡⠠⣉⠇⡀⠂⢀⠐⠨⢳⢌⠒⠠⠀⠀
⠀⠀⠀⠀⠀⡐⠠⢂⠑⣨⣴⡾⣟⢾⣋⠞⣹⣞⡿⡆⠀⠀⠤⠐⠋⠁⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣿⣹⠖⣭⢒⡜⢤⡛⢁⠈⠀⠀⠄⠠⠀⠱⢪⡑⠌⡐⠀
⠀⠀⠀⠀⠀⠄⡡⢆⣿⡟⣧⡛⣵⢺⡔⣮⢱⣊⣿⡅⡄⠀⠀⠀⠤⣤⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡟⣲⢯⡜⣦⢃⠀⠀⣄⠃⠌⠠⠐⠀⠳⣘⠰⢀⠀
⠀⠀⠀⠀⠌⢢⠑⣮⠷⢚⡔⡻⠈⢦⠙⣀⠣⡙⢮⠇⣿⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠻⡇⠀⢀⡞⡤⢊⡔⢁⠠⠀⠱⣌⠒⡄⠂
⠀⠀⠀⠌⠰⡁⢞⣼⢋⠔⠈⠁⠜⢂⠰⢀⠲⣉⠎⣧⢻⠀⠀⠀⠀⠀⠈⠑⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡝⠀⠀⠊⠝⡳⠃⠐⡂⠄⠐⠀⣎⠱⢠⠁
⠀⠀⠀⠌⣂⠱⢪⣽⠂⠀⠁⠈⠀⠀⠂⠈⢡⠘⡜⢦⢛⡄⠀⠀⠀⠀⠀⠄⠀⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢁⢂⠈⡀⠰⣌⠳⢠⠈
⠀⠀⠈⡔⢠⢉⢧⣻⠄⠀⠀⠀⠀⠀⠀⡁⠂⠌⡘⠤⢋⢦⠀⡂⠀⠀⢈⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢄⡞⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠲⡀⢂
⠀⠀⠐⡀⠆⡌⢲⡽⡂⠀⠀⠀⠀⠀⠁⠠⠈⠐⠠⡑⢌⣚⠀⡇⠀⠀⢬⡘⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢠⠞⠀⠀⠲⣙⡆⠀⠀⠀⠀⠀⠀⠡⠈⢐⢊⠒⡁⠄
⠀⠀⠐⠠⠘⡠⢃⡞⣇⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⡐⣈⢾⠀⠀⠀⠐⢂⠀⡀⠡⠀⢐⡀⠀⠀⠀⠀⠀⠀⢀⠐⢠⠋⠀⠀⠀⣁⠒⠀⠄⠀⠀⠀⠀⠀⠐⠀⠏⢎⡁⢂⠐
⠀⠀⠀⡁⠂⠱⠨⣜⡹⡄⠀⠀⠀⠀⠀⠀⠐⠀⠠⠠⡱⠞⠀⠀⠀⠘⠀⠐⡈⢄⡉⡀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠐⠀⠂⡌⠀⠀⠀⠀⠀⠠⢀⡹⢍⡒⠌⣀⠂
⠀⠀⠀⢀⠡⠈⡅⢢⠝⣱⡀⠀⠀⠀⠀⢈⠀⠂⢀⠁⢴⠋⠀⠀⠀⠀⠀⠀⠈⢀⠰⠜⢤⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢈⠒⡄⢀⠀⠀⠀⠀⠀⢄⠻⡜⢌⠐⡀⠀
⠀⠀⠀⠀⠠⠁⡄⠃⡜⣡⢷⡀⠀⠀⠀⠀⠐⠠⠀⣌⡎⠀⢀⢠⠐⡀⢂⡀⠀⠀⠠⠦⠀⠑⠄⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠠⢩⠔⠂⠀⠀⠀⠀⠀⡈⠷⣈⠆⢂⠀⠀
⠀⠀⠀⠈⠀⠡⣀⠣⢐⠡⡞⣹⢆⡀⠁⠠⢈⠐⡰⢦⣁⡎⢌⠒⡉⢀⠁⠀⠀⠀⠀⠀⠀⠄⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡜⠀⠀⠀⠀⠀⠀⢀⠳⡐⢈⠀⢀⠀
⠀⠀⠀⠀⠀⠁⠄⠂⡌⢢⠙⣬⢛⢦⣅⠢⢌⢼⡹⠏⡰⠈⠄⠃⠤⢈⠈⠁⠀⠀⠀⠀⠀⠀⠁⠂⡀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠐⡨⢄⠠⠀⠀⠀⠀⠀⠀⠣⢁⠂⠄⠀⠠
⠀⠀⠀⠀⠀⠐⢈⡐⠨⠄⡋⢤⢋⡖⢮⢷⡾⠎⠐⠀⠁⣀⠀⠁⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡙⠖⡆⡄⢀⠀⠀⡀⡑⡀⢀⠀⠀⠀⠀⠀⠀⠐⠠⢈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠂⠄⢡⠂⣉⠦⣩⠼⣭⡟⠡⠈⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡐⠈⢒⠉⠎⢎⠑⠲⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠡⢈⠄⡘⢄⡊⡔⠹⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠐⠈⢀⠁⠂⠈⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠈⠢⡑⢂⡐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⡀⠂
⠀⠀⠀⠈⠰⢀⠀⠁⡐⢈⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⠠⠀⠀