⣿⣿⣿⣿⣿⡟⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠘⢿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⣿⣷⠰⣽⣶⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣥⣴⣶⣶⣦⣍⢿⣿
⣿⣿⣏⠉⢷⣌⢿⣷⡌⢿⡿⣗⡹⣿⣿⣿⢛⣭⣩⣽⢦⡚⣭⡹⣿⣿⣿⣿⡆⢿
⣿⣿⣿⣦⠨⣫⣮⣝⢿⣌⢿⣿⣿⡝⣿⣿⢸⡿⡝⢇⠿⡇⣿⣷⣭⣛⠻⠇⠇⣾
⣿⣿⣿⣿⣷⣝⢿⣿⣃⣻⢧⠹⣿⣿⡘⡇⡇⠂⣠⣶⣤⣦⡁⠻⣿⣿⡇⠄⢠⣿
⣿⣿⣿⣿⣿⣿⣧⡡⣿⣿⣷⡀⠘⠿⣿⠖⣠⣾⣿⣿⣿⣿⣿⢰⣤⣴⣧⢠⣿⣿
⡿⣛⣛⠿⣿⣿⣿⣿⣮⡻⣿⡟⠄⠈⢁⣼⣿⣿⣿⣿⣿⣿⠏⠄⡻⣿⣿⡆⣿⣿
⣇⣋⠙⢿⣶⣮⣝⡛⠿⢿⡀⠇⠄⣰⣿⣿⣿⣿⣿⣿⡿⠁⢠⣴⣾⣾⣿⡇⣼⣿
⣿⣿⣷⣬⣋⣙⠻⣵⣿⣿⡶⢀⣾⣿⣿⣿⣿⣿⣿⠏⠄⠠⣿⣿⣿⣿⡏⠃⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣮⣙⠙⣰⣿⣿⣿⣿⣿⣿⣿⠋⠂⠄⣼⣿⣿⣿⣿⠁⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⡿⠃⠄⢀⢲⣿⣿⣿⣿⡇⠄⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⣿⣿⣿⣿⡿⠁⠁⢠⣿⣮⣻⣿⣿⣿⣵⡜⢿⣿⣿
⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⡟⠐⠄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⢿
⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⡟⠐⣀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠒⠑⣴⣦⣾⣧⣤⢀⡤⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⢀⡘⠉⠁⣰⣾⣿⣿⣿⣿⣿⣿⣷⢀⡤⠊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢱⠊⡄⠒⠾⣿⣿⣿⣿⣿⣿⠿⠛⢹⣿⣯⣤⠤⠄⠀⠀
⠀⠀⠀⠒⢦⠂⠀⣇⠀⠸⠟⢈⣿⣿⡁⠺⠗⠀⣸⣿⣿⣃⠀⠀⠀⠀
⠀⠀⠀⠀⢘⢀⣼⠻⢷⣶⣶⣿⣿⣿⣿⣶⣶⣾⠟⣻⣿⡯⠁⠀⠀⠀
⠀⠀⠀⠉⠱⢾⣿⡀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠀⢀⣿⣿⠿⠛⠒⠀⠀
⠀⠀⠀⠀⠔⢛⣿⣷⡈⠒⠀⠀⠀⠔⠁⠊⠒⢈⣾⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠜⠛⠿⣿⣶⣤⣀⣀⣀⣀⣤⣶⣿⠿⣿⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡸⠛⢉⡿⠻⠟⣿⢿⡟⣏⠁⠀⠘⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠁⠀⠃⠘⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⡿⣿⡿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣻⡽⣷⢯⣟⣷⢿⣳⣟⣾⣽⣻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣟⡷⣯⡿⣽⣻⣯⢿⣾⣻⢯⣟⣾⢷⣻⣟⣾⡽⣿⣷⣦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢲⣿⣿⣻⢷⣯⢿⣯⣟⣿⣳⢿⣻⣞⡿⣯⡿⣽⣻⣟⣾⢯⣟⣷⣯⢿⣷⣌⡉⢒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠪⡐⣱⣿⣿⣳⢿⣻⣾⡿⣷⢿⡾⣿⣻⣟⣿⣻⣟⡿⣟⣷⡿⣯⣿⣻⣾⣽⣻⣟⣿⡴⣁⠎⠤⡑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠃⡌⢢⣽⣿⣿⣷⡿⣿⣟⡷⣿⢯⣟⣿⣳⡿⣽⣾⣻⢾⣟⣯⣷⢿⣯⢿⣽⢯⣿⣷⣿⣽⣿⡀⠉⠦⡑⠬⡘⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⡪⢸⣵⣿⢿⣽⢾⣻⡷⣯⢿⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣻⢾⣟⣾⢿⣽⣻⣾⣳⣟⣯⣿⣷⠀⠀⠈⠓⢘⢄⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠔⣈⠦⡸⠊⣰⣿⡿⣽⣻⡾⣟⣯⣿⠽⠛⠛⠛⠛⠛⠺⠿⢿⣾⣽⣟⣷⣿⣻⣾⢯⣿⣞⡿⣾⣽⢾⣻⣞⡿⣷⣄⠀⠀⠀⠑⠱⢌⠂⠦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⢊⠔⢢⠎⠀⠀⣿⣯⢿⣽⡷⣟⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠉⠉⠉⠙⠛⠻⠿⢷⣯⣿⢯⡿⣽⣟⣿⡄⠀⠀⠀⠀⠡⡚⠤⡑⢄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠌⡔⢡⠚⠁⠀⠀⢰⣿⣯⢿⣳⣿⡿⢿⠑⠒⠒⠦⠤⣄⣀⣀⠀⠠⠀⠀⠀⠈⢷⡀⠀⠀⢀⣤⠶⠚⠛⠉⠉⠛⠛⠻⢾⣿⣇⠀⠑⠀⠀⠀⠈⢢⠑⡌⡡⠀⠀⠀⠀
⠀⠀⢀⠊⡜⢠⠗⠁⠀⢀⠄⠀⢿⡿⠛⠉⠁⠀⠙⣆⠀⠀⠀⠀⠀⠸⣿⠏⠉⠉⠓⠒⠲⠬⡗⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠒⡀⠀⠀⢣⠢⡑⢱⠀⠀⠀
⠀⠀⡄⢣⠘⡆⠀⠀⢀⠂⠀⠀⢀⠇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀⣿⠉⠙⠒⠦⢤⣤⣐⣀⡀⠀⠀⠀⠀⠙⡇⠀⠀⠐⡀⠀⠀⢱⢈⠆⢣⠀⠀
⠀⡘⢄⠣⡜⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⠤⣀⣀⡀⡤⠴⠞⣋⡴⠞⠋⠉⠹⣄⠀⠀⠘⠟⠁⠈⠉⠉⠓⠒⠲⢴⡏⠀⠀⠀⠘⠀⠀⠀⢎⡘⠤⢃⠀
⠀⢌⠢⠱⠀⠀⠀⡈⠀⠀⣦⣤⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⢀⡄⠀⠀⢠⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠀⠀⠀⠀⢁⠀⠀⠀⡜⢠⠣⠀
⠸⣀⠣⡙⠀⠀⠰⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠼⠋⠀⠀⠀⣿⣰⠇⠈⠙⠒⠢⠐⠐⠒⠚⡝⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠆⠣⠌⡇
⡖⢄⠣⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⡄⠈⠙⠛⠿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠱⡈⢴
⠇⣊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠙⠷⣿⡲⠄⣀⠉⠉⠉⠙⠛⠛⠷⠶⢦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡑⢺
⠰⡉⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠙⠳⣦⣉⠒⠢⠤⣀⡀⠀⠀⠀⠈⠉⠙⠛⠷⢶⣤⣄⣀⣀⠄⠀⣡⠃⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⡄⢣⢘
⡥⢘⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠉⠙⠓⠲⠶⢦⣤⣤⣄⣀⣈⣉⣙⣛⣛⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢐⡈⢆⢺
⡇⢎⡐⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⣀⣀⣈⣙⣿⣿⣿⡿⢿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠰⡈⢾
⢸⠠⢌⢡⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡌⢢⠑⡆
⠈⡔⢊⠬⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡑⢢⢩⠀
⠀⢆⠣⢌⢃⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣜⡀⠀⠀⠀⠀⠀⠁⠂⠠⠀⢀⣠⣀⣄⣠⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⡐⡉⢆⡒⠀
⠀⠈⠖⡨⢌⡂⠀⠀⠑⠀⠀⠀⠀⠀⣠⡾⢃⠰⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡐⠱⡈⠦⠁⠀
⠀⠀⠈⡔⢢⠘⣄⠀⠀⠈⠄⠀⠀⣴⠟⢀⠂⠜⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠄⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⡠⣁⠣⣘⠁⠀⠀
⠀⠀⠀⠘⢄⢣⠐⣂⠀⠀⠈⢀⣼⠋⡐⡈⠄⣣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢊⠡⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡰⠐⡄⠣⠃⠀⠀⠀
⠀⠀⠀⠀⠈⢆⠱⡀⢇⡀⠀⣴⢋⠐⡐⢨⢰⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⢂⠉⡄⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠎⡰⢁⡺⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠣⡜⣠⢘⣾⠃⠄⠊⠤⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣦⡈⠄⡡⢈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣐⠡⢊⠴⠅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠦⡈⠜⡢⣍⡘⣴⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⠷⣴⢀⠢⠐⡈⠻⣦⡀⠀⠀⢀⠠⠐⠁⠀⠀⡀⢄⠱⣀⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠨⠔⢢⠙⡃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⠷⣆⠁⠆⢡⠈⠻⣦⡐⠁⠀⠀⢀⠠⡘⠰⣈⠲⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢜⠨⡌⡑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠤⠄⠀⠙⠻⣆⡂⡘⠠⠌⠻⢦⣄⠰⣁⠣⢌⡱⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢅⢣⠌⢢⡑⡂⠆⡤⣀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢈⡹⠦⡥⢚⠆⢣⡉⡱⡠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠦⠑⡥⢒⠰⡈⢍⡑⢢⠉⡝⢩⠙⣂⠒⡄⢊⡑⠢⢌⠱⣈⠆⠮⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠓⠈⠴⠁⠊⠴⠡⠎⠄⠃⠈⠥⠌⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⣟⡿⣻⢟⡿⣻⢟⡿⣛⢿⣛⢯⣟⣻⣛⣟⡻⣟⢿⡻⣟⢿⡻⣟⡻⣟⡿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣻⣵⣻⢮⢷⣯⢻⣞⢧⣟⢾⣹⢧⣟⣳⢾⣱⣏⠾⣝⡾⣳⣟⣮⢷⣛⡷⣟⡾⣝⣧⢿⣹⣿⣿⠖⠀⠠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣻⣶⣿⠷⣯⣟⣮⢷⣛⣮⢟⣮⣛⡾⣏⡾⣵⣻⣜⣞⣻⡝⣞⢷⣿⣜⢯⣷⣻⣽⣿⣽⣛⣮⣽⢿⣿⠃⢀⣤⣿⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢷⣿⣿⢿⣭⣿⣟⢻⣾⡿⣝⢮⣛⡶⣽⡳⣝⣾⠱⣧⣻⣾⣷⡻⣜⠯⢾⣿⣎⠿⣿⣿⡍⠉⡉⠛⠻⣿⣿⣿⣯⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⣿⣟⣾⡟⣯⣛⣬⣿⢯⡳⣭⢷⣫⣿⣷⡝⣺⣜⡓⢦⢻⣿⣿⣳⢭⡛⣬⢻⣿⣜⡳⣟⣿⣧⡌⠀⠘⠛⢿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠿⣿⡿⣷⣤⣠⣾⣿⣿⣾⢿⣿⣿⢃⡷⣟⣾⢯⡳⣽⢣⣟⣷⣿⣿⡸⣕⣾⡿⣜⢮⣽⣿⣿⣧⡙⣾⣭⣿⣷⢯⡽⣻⣿⣿⣶⣦⣀⠈⢿⣾⢽⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⣀⣠⣿⣿⣏⣿⣿⠟⣸⠏⣼⣿⣛⡮⣿⣿⣟⡧⢿⣽⣻⣾⣿⣿⣿⣿⣾⣿⡿⣽⣾⣿⠿⣿⣿⣿⢶⣹⣿⣿⣿⣳⢻⣿⢿⣷⡈⠋⠿⣿⣿⣮⣛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡿⣏⣷⣹⣿⣿⡿⣼⢻⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣽⣿⠇⠠⢿⣿⣿⣿⣷⣿⠹⣿⣿⣽⣿⣮⢿⣿⡄⡄⠸⢿⣧⢟⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⠋⢹⣿⣿⣿⣳⣮⣿⣿⣿⣿⣳⢿⣼⣿⡟⠀⣿⣿⡿⣿⣿⣿⣾⣿⠀⠀⠘⣿⡿⣿⣿⡿⠀⢹⣿⣿⣿⣷⣫⡞⣿⣵⡀⢸⣿⣏⡞⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢻⣿⣆⢸⣿⣿⣳⣿⣿⣿⡿⠉⣿⣿⣿⣿⡟⠁⠀⣿⣿⠁⣿⣿⣿⣿⠃⠀⠀⠀⢹⣿⢿⣿⡇⠀⠈⢹⣿⠿⣿⣷⣻⣜⣻⢿⡿⣿⣾⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⠿⠀⠀⠀⣿⠇⠀⣻⣿⣿⠏⠀⠀⠀⠀⠀⠈⠸⣿⡃⠀⠀⢘⣿⡇⢿⣿⣷⣏⣞⣿⣷⡹⣶⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⡿⠀⠀⠀⢸⡏⠀⠀⢽⣿⠏⠀⠀⠀⠀⢀⣀⣤⣤⣿⠷⠖⠚⠛⠛⠁⠈⣿⣿⣿⣾⣿⣿⣷⣻⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣧⠀⢀⣶⡆⠀⠀⠀⠠⡟⠀⠀⠴⠶⠟⠛⢋⠁⠀⢠⡀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣷⣿⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⠴⠶⠿⠟⠟⠛⠛⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⢡⣽⣿⣟⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠈⠋⠀⠀⠀⠀⠀⣠⣷⣠⣷⣦⣤⣿⣦⡀⣀⣠⢿⣿⠿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣿⣿⣿⣿⣿⣿⢿⣿⠒⠾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⢀⣤⠟⢷⣆⣿⣶⣙⣓⣾⣿⣿⣿⣿⣿⣷⣾⠿⠛⣁⣼⣿⣸⣿⢧⡀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠸⣿⡟⠛⢿⣿⡝⣿⣿⠛⢻⣿⣿⣿⣿⣼⣿⣿⣿⡿⠃⠀⠀⠙⠛⠿⠿⣿⣿⣶⣿⣿⣿⠟⠉⠀⠀⢠⣿⢿⣿⢿⣧⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣽⣿⡆⠙⠿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⣿⠸⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠷⣶⣾⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣿⠈⣿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢿⠀⠀⢹⡇⢹⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠷⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⢸⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⠃⠀⢸⡇⠀⠈⣇⠀⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⣤⣤⡴⠶⠶⠛⠛⠛⠃⠀⠀⠀⣼⡿⠀⠀⣼⠃⠀⢸⡟⣸⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠖⠃⠀⠀⠀⠀⢀⣴⠾⠋⠀⡀⣰⡟⠀⠀⣾⣵⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⣿⠁⠀⣼⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢿⡿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡷⣦⣀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠁⣿⣿⣿⠛⠛⠷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠛⣿⣧⠀⠙⠻⣶⣄⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⠉⠉⠛⠳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣇⠀⠀⠀⠻⢷⣤⡀⠀⠈⠉⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠀⠀⣾⠟⢿⣿⣿⡄⠀⠀⠀⠀⠉⠻⣦⣄⡀⢻⡅⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⡋⠀⠀⠀⣰⡟⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠒⠋⠉⠀⠀⠀⠀⢠⡾⠉⠀⠸⣿⡾⣷⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⠀⠀⠀⠘⠛⠻⠛⠋⠙⣿⣿⣇⠀⠀⢰⣿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠉⠙⢳⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡄⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣶⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢻⣷⡀⠀⠀⠀⠀⢀⣾⣿⣯⣗⣀⣤⣴⣶⣿⣿⡿⠿⠛⠛⠯⠭⢹⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠹⣷⣄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣹⣿⣧⣾⡿⠿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⣠⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣽⣿⠉⠀⠀⠘⣿⣯⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⠿⠿⠷⣄⠀⠀⠀⣰⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⠀⠀⠀⠀⠘⣿⡇⠀⠀⢀⣠⣴⣾⣿⡿⠿⠿⣏⡹⢧⠀⠀⠀⠘⢷⣀⣴⡿⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⣴⣿⣿⣿⠟⠉⠀⠀⠀⠈⠁⠈⠣⠀⠀⠀⠀⢿⣾⡟⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢹⣿⡿⠋⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢠⡾⠃⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡾⠁⠀⠀⠀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠠⠈⢻⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠠⠀⠄⠈⢿⣇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠘⢶⣄⠀⠀⠀⠀⠀⠙⢧⡀⠀⠉⠲⢦⡀⠀⠀⠀⢸⡇⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠒⠀⠄⠸⣿⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣄⠀⠀⠀⠀⠻⣦⠀⠀⠀⠙⠦⠀⠀⠈⣷⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⡁⠐⠈⢀⠀⠙⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⢿⣆⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠐⠀⢄⡁⠠⢀⠈⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣴⣌⠿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀
⠀⠀⠀⡠⠟⠀⣀⣤⠴⠒⠛⠛⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣦⣀⠉⢷⣄⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠠⢈⣀⠀⠄⡀⠄⠂⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠉⠻⣦⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣶⠿⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢿⣤⡀⠀⢀⣼⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠄⢀⠈⠠⠀⠄⠠⠀⠀⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠘⣷⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠘⠉⠀⠀⠀⠀⠀⣀⣄⣀⣠⣀⣀⣀⣀⣀⣀⠀⠈⠻⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⡈⠛⠿⠿⣯⣄⣤⣾⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢀⠂⣹⣷⡿⢷⣄⣠⣵⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⣸⣿⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⢀⣀⣤⠶⣞⣿⠋⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢳⡞⠀⠀⢀⣠⣶⢻⠯⣝⢮⣻⢯⡥⣄⡀⠀⠀⠀⠱⣄⣀⣴⣚⣉⣉⣉⣉⣹⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢳⣥⡟⠀⣠⢶⡟⡽⣎⢯⣛⠾⣯⡝⣮⢳⣭⢛⣦⡀⠀⠀⢹⡮⣕⢫⡵⣩⣮⣵⡋⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣭⣓⢾⣧⠾⣝⢧⡻⣵⢫⣞⡭⣟⢶⣹⣎⠷⣎⠿⡴⣻⡀⠀⠀⢻⣜⣣⢞⡱⢖⣣⢟⣆⠀⠀⠸⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣘⣷⢧⣛⢮⣝⡻⣜⢯⣳⢭⡗⣯⢞⡽⣎⣷⢺⣝⢾⣹⣓⢧⣧⠀⠀⠀⠉⠺⣥⢏⡳⢎⡞⣽⡀⠀⠀⢿⢣⡏⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣖⡻⢭⣛⡼⣭⢻⡝⣮⡝⡾⣼⡹⣞⢧⣛⣮⠽⣞⡽⣺⡝⣮⢷⣚⣧⡳⣝⠾⣜⡳⣤⡀⠀⠀⠘⢯⢳⡹⢎⡽⡇⠀⠀⢸⣏⢿⣿⡺⠽⣦⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠮⠷⠮⣽⣧⡿⣼⢧⡻⣜⢧⣻⣵⣳⡝⣮⢏⣷⣚⣯⢽⡺⣵⢫⣗⢯⡞⡶⡽⣭⢻⣜⡳⣵⢫⢶⡀⠀⠈⢷⣍⡏⡶⣧⠀⠀⢸⡞⣜⡲⣝⢦⡴⠋⠁⢀⠐⠀⠉⡕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⢀⡴⡾⣝⢮⡳⣝⢮⡳⢯⡞⠁⢠⣟⢾⣱⡻⢶⣹⢎⡷⣫⢗⣻⡼⢧⡻⣝⡧⣏⣷⢎⣷⡙⡞⣧⢻⡄⠀⠸⣎⢷⡉⢿⣄⠀⠸⣟⣬⢓⡮⢧⣛⣦⡀⠀⠦⣀⡠⠃⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣹⢳⡝⣮⢽⡺⣭⢻⡽⣇⣀⣾⡝⣮⡷⣯⣗⢯⡞⠉⢿⣭⡳⣝⢯⡳⣽⠇⣯⣿⣞⠶⣽⡔⢬⢷⣳⠀⠀⣿⢎⣿⡘⣮⢧⡀⠈⢷⣫⠜⣧⡳⢮⡽⣖⡨⢉⠲⣄⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠴⠊⠉⡝⠉⠙⡓⠦⡀⠀⠀⣠⡟⣮⢳⣭⢳⡝⣮⢳⣝⡞⣧⢻⣜⡳⢧⣻⢼⣟⡻⣜⢯⣇⣠⣼⢷⡹⣯⣷⢻⣼⢹⣳⡿⣿⡽⣶⣯⠘⣧⢻⡄⢀⣟⡞⡼⢧⣻⢮⠽⣆⠀⢻⣭⠘⣯⢗⣣⢟⣷⡈⢆⠘⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⠋⠀⠀⠀⡆⠀⠀⡼⠀⠙⢆⣰⢻⠼⣥⣛⠶⣫⢞⡵⣫⢞⣽⣺⢧⢯⡹⣷⢋⣾⡞⣵⣛⢮⣻⡽⣎⢷⣻⣽⣿⢣⡟⣼⣳⡇⠘⣷⢻⠹⣧⢹⢯⡳⣿⣿⡼⣹⢷⣸⠯⣽⡿⠀⢰⡟⡜⣎⣿⣜⡳⢞⣿⡄⢹⢣⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡇⠀⠀⠀⠀⣈⡵⠮⢤⡀⠀⠘⣯⣏⣾⢗⢮⣛⣵⣫⢞⡵⣫⢷⣏⡞⣧⡿⣱⢾⣳⡝⣮⡝⣾⢧⡟⣮⣟⢷⡟⣿⢫⣏⡷⣻⠀⠀⢿⣻⠀⠙⢯⣖⡳⢽⡞⣿⡵⣻⣽⣛⡼⣳⢦⣾⣳⠌⣿⡜⣮⣽⣫⡜⣿⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡏⠀⠀⢀⡞⠡⠐⡐⢂⠙⣦⢰⡿⢿⣞⢋⠉⠀⢰⡏⣿⢞⡝⣾⣣⢟⡏⣴⡟⣾⣱⢯⣷⡝⣿⣸⢟⡶⣯⡟⠀⣿⡝⣾⣱⡟⠀⠀⠘⣿⡃⠀⠙⣶⡍⢿⡇⠘⣷⡽⣿⣧⢻⣥⢻⡼⣯⢏⡷⣯⢵⣚⣿⣾⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⡀⠀⢸⡄⠡⠑⡈⠔⡨⣐⣾⠿⣶⠢⢽⠗⠀⢸⡇⣯⣾⢹⡷⣹⢾⢣⡿⣇⣿⡯⣟⣿⡞⣇⣿⣺⢽⡟⠀⠀⣿⡻⣔⣿⠃⠀⠰⠀⢹⡇⠀⠀⠈⣿⠼⡇⠀⠹⣞⣧⢻⡷⣎⢷⣹⣿⢮⡝⣿⣎⡷⣹⣿⠿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠦⣀⠻⣄⢃⣌⣢⠵⢋⣯⢳⣹⡄⠀⠀⠀⢸⣷⣿⣇⣻⢵⣻⡞⣽⢳⣏⣿⡿⣽⢻⡝⡦⡷⣏⣿⠁⠀⠀⣹⣗⢺⡟⠀⠀⠀⠀⠸⡷⠀⠀⠀⠈⣿⡇⠀⠀⢹⣿⠀⢿⡽⣎⢷⣿⢧⡻⣽⣯⢷⣣⣟⡇⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡼⣬⠳⣜⡇⢀⣄⠀⠸⣿⣿⣽⣞⢧⣿⣝⢮⣳⢿⢿⡽⡏⠈⡿⣴⢻⣽⠃⠀⠀⠀⢹⣎⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡀⠀⠀⣿⡄⢈⣿⣎⢿⢻⣿⣱⢻⣯⢿⣗⠾⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣜⢳⢭⣷⢸⣹⣆⣼⣿⣷⡞⣽⢺⣿⣮⢳⣽⡟⢸⣿⠁⠀⢿⡼⣫⠇⠀⠀⠀⠀⢸⢮⣇⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⢻⡏⠉⢹⣏⡟⢀⣷⣏⣻⣯⢟⣿⣯⢻⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡹⣞⠮⣽⡏⠁⠀⠀⢿⣷⢻⡜⣯⢿⣞⢧⣿⠃⢸⡏⠀⠀⠸⣗⡟⠀⣀⣀⣤⣶⢾⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⠃⠀⢿⢮⣳⣯⡟⣿⢻⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡳⣽⣯⢞⡵⣻⣄⣤⣤⣾⣿⣧⢟⣽⣻⣟⡾⡟⠀⢸⣁⡠⠤⠴⢿⠟⠛⠉⠉⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣾⣤⡖⢾⣿⡾⢷⢿⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⢿⣟⣮⢳⣻⢿⣽⣛⣾⣷⣿⡞⣷⣻⣿⣽⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⡞⣹⣾⡿⠛⢿⣿⡍⠙⠿⣿⢻⣿⡇⢸⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⣿⣿⣎⡷⣟⣿⣺⡽⣾⡽⣿⣽⣳⣿⡽⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⠿⢮⣄⠉⡉⠹⣍⢢⡀⠀⠀⠀⣠⠃⡞⠼⠋⢸⣧⣤⣼⡿⢿⠄⢸⠏⢸⣿⣿⣸⣟⡯⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⢸⣷⣻⡼⣟⣾⣳⡟⣷⣻⢿⡷⣭⣿⣽⣻⠀⢀⡠⣤⠖⣫⣿⣿⠟⣿⠁⣀⣿⣻⣷⡀⠙⠇⠠⢁⠘⢦⠉⠉⠉⣉⣀⠸⡅⠠⠀⠈⠻⣷⣻⣧⠞⠀⠂⠌⡘⣿⣷⣟⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣞⡷⣽⣻⢶⡯⣟⡷⢯⣻⣿⣳⣿⠖⠛⢏⠙⡀⢸⠘⢿⣟⠁⠀⢿⣟⢯⣻⡉⣹⠇⠀⠌⡐⠠⠈⡞⢀⠞⠉⠀⠈⠣⡙⢦⡉⠙⠒⠚⠋⣁⣀⢀⠘⢠⡴⣿⢿⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣟⡾⣳⢯⣷⢻⡽⣽⠟⠓⢻⣿⣇⢀⣠⡼⢄⣇⠘⡇⢀⠉⢃⡀⠈⠛⠿⢷⣿⠥⠶⠈⡐⠠⢁⣼⣁⠎⠀⠀⠀⠀⠀⠈⠉⠛⠒⠧⢬⣐⣀⣉⡤⠞⠁⠀⣯⡏⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⣳⡯⣟⣞⡯⢿⡇⠀⢀⣤⣻⣿⡿⣹⡆⠀⠈⠦⣳⠀⠌⡀⢧⣀⠀⣀⣀⡀⠐⠠⢁⣤⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⠂⠀⣿⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⣿⣽⡺⣽⣻⠀⢰⠟⢲⡿⢿⡿⣗⣧⠀⠀⠀⠈⠙⠒⠲⠤⢤⣉⣁⣀⣤⠵⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡠⠂⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⡷⣝⣧⢿⡄⠈⠆⢸⡇⠙⡯⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⡽⣎⣟⣧⠀⠘⡀⠁⢸⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠜⢻⣧⣿⣾⢷⣄⠈⠢⣄⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⣾⡹⢷⣤⣀⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠘⣿⣳⣎⢯⡟⣶⢖⡾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠳⣿⢮⣽⣎⠿⣼⣹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠀⣀⣀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣾⠻⡟⡶⢫⠟⡏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠻⣷⣣⣾⣿⡀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠙⢿⣿⢿⣇⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⢻⡆⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠧⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢀⣀⣀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠲⢄⣳⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠙⠒⠢⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⣠⠂⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠦⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⣗⡤⠊⠁⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⡇⠀⠀⠀⠀⠀⠸⡛⠒⠤⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⡀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⣇⠀⠀⣸⣿⣿⣶⣄⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡗⢦⠀⠀⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠳⠤⢄⣀⠀⠀⠀⡇⠀⠙⢦⣸⡇⢠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢿⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⢀⡏⢹⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠠⡇⠀⢀⠎⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡞⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣧⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠙⣆⠀⢧⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⢣⡾⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠐⠳⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⢿⡇
⣿⣟⣾⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⡀⠀⠀⠙⢿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣟⣯⢿⡇
⢸⡿⣞⣿⣻⣽⣿⣻⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣯⣷⣿⡿⣽⡿⣿⣦⡀⠀⠀⣿⣿⣟⣯⣷⣿⣿⣟⣿⡽⣞⣯⡇
⢸⡿⡽⢾⣽⣳⣟⣯⡿⣟⣯⣿⣟⣷⡿⣾⣟⣾⣯⢿⣿⣿⣯⣷⣿⣻⣿⣯⣷⡿⣷⣿⣳⣿⣻⣾⢿⣽⣾⢿⣽⣷⡿⣯⣿⣾⢿⣽⣾⢿⣽⡿⣿⣿⣿⣿⣟⣾⣿⣿⣽⣿⣿⣟⣷⡿⣟⡿⠽⠛⣾⡿⣯⣟⣷⣻⢿⡆⠀⣾⣿⡽⣯⡷⣟⣿⢾⣽⢻⡝⣮⡗
⠀⣿⡹⢧⣏⢷⡻⢾⣽⣻⡽⣾⡽⣾⣽⣳⢯⣷⣻⣟⣾⣻⣷⣟⡾⣽⣿⣻⢾⡽⣷⢯⣟⡾⣽⢯⡿⣽⢾⣻⣟⣾⣻⡽⣷⣻⢯⣟⡾⣟⣯⣟⣷⣻⣟⣿⣾⣯⣿⡷⣿⣿⣳⣟⡾⣽⣻⢇⣤⣾⣿⢻⣗⣻⢮⣏⢿⡇⠀⣿⢷⣛⡷⣻⡽⣟⣯⢞⡽⣚⠥⣏
⠀⢸⡝⣲⡙⣮⢝⡯⣖⢯⡽⣖⡻⡵⣞⡭⢿⡜⣧⢻⡜⣷⣻⡾⣝⡳⣿⡽⣫⡽⣫⢟⡾⣹⢏⣯⢽⣫⢟⣧⢻⡞⣵⣻⢳⢯⡻⣞⡽⣛⡾⣹⡞⣧⢟⡾⣹⢟⣿⣿⡟⣧⢟⡾⣹⢗⣯⢻⣭⢳⡭⢷⡺⣝⠾⣜⠯⠀⣸⣯⢳⡝⢾⡱⢏⡿⡜⣭⠲⣍⠚⡧
⠀⠈⣗⠤⡙⡔⢫⠲⡍⣞⠲⣍⠳⡝⡼⣩⢳⡹⣜⢣⡛⢶⡙⣿⡜⡳⢽⡗⢧⡛⡵⣋⠞⡵⣋⢮⢳⡙⢾⡘⢧⡛⢶⡩⢟⡎⢷⡙⢾⡱⣋⠷⣙⢮⡛⡼⢣⢟⡲⢣⠟⣜⣫⡜⢧⡛⣬⠳⣎⢧⡙⢧⡓⢮⡹⣌⢣⢞⡹⢆⡳⢎⢧⠹⡍⡷⢩⢒⡱⢨⠁⡷
⠀⠀⢹⡄⠱⡈⠥⢓⡘⠤⢋⡌⢣⡙⡔⢃⠧⡘⢆⢣⡙⠦⡙⠼⣧⢙⢺⡝⢢⡙⠴⣉⠞⣡⠙⣆⠣⡝⢢⠝⢦⡙⢦⡙⢎⡜⢣⡙⢦⠓⣍⢚⡱⢊⠵⣉⠳⣊⠕⣋⠞⡰⢃⠮⡡⢝⡰⢍⠲⡌⡙⠦⡙⠦⠱⢌⠲⢌⠲⢡⠚⡌⠦⡙⡰⡙⢢⠑⡄⠃⠌⡗
⠀⠀⠀⢧⠀⡁⠒⠠⢈⠢⢁⠘⠄⠒⡈⠆⠢⠑⠌⢂⠘⠤⠑⠌⢹⡆⢸⠁⠆⡘⠰⢀⠎⡀⠣⢄⠣⠌⡡⠊⠔⡈⢆⡘⠤⠘⠤⠑⠢⡉⢄⠣⠌⡡⢂⠅⠣⢄⠩⡐⠌⠱⡈⠆⡑⠢⠐⡌⠒⣈⠑⠢⠑⠌⡱⢈⠒⡈⠔⠡⠘⠠⠑⢠⠁⠇⠠⠡⠄⢁⠂⡭
⠀⠀⠀⠘⡇⠀⠀⠁⡀⠄⠂⠈⠀⠁⠠⠀⠁⠈⠐⠀⠈⡀⢈⠐⠀⢃⠨⠀⠂⠀⠁⠂⠐⠀⢁⠂⠐⠐⠠⠁⢂⠐⠠⠐⠠⠁⠂⡉⠐⠐⡀⠂⠄⡁⠂⢈⠐⠂⠐⠠⠘⠀⡐⠐⠠⠁⠂⠄⢁⠠⠈⠄⡁⠂⠐⠀⡐⠀⡈⠄⠁⡁⠈⠄⠀⠃⠀⠁⠀⠀⠀⡃
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡩⡝⣭⠯⣝⢯⢻⡭⢯⡝⣯⢯⣿⠿⠿⠿⠿⣿⣿⣻⣟⡿⣽⣻⢯⣟⡿⣽⣻⢯⣟⡿⢯⣟⡿⣽⣻⢯⣟⡿⣽⣻⢯⣟⡿⣽⣻⢟⣯⣟⣿⢻⣯⣟⡿⣻⣽⣻⡟⣿⢯⣟⣿⢻⣯⣟⡿⣻⢯⣟⣿⢻⣯⣟⣿⢻⣟⡿⣻⣟⣿⣻⢿⡿⣶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⠑⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⣜⠶⣣⢖⡞⡼⣭⢻⡝⣯⢟⡽⢯⣻⢽⣫⠿⣝⢯⠻⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠲⣩⠵⣙⢦⡛⡼⣊⣗⢺⢣⣿⠏⠉⡠⠒⠈⢢⡀⠀⠉⠳⣟⣾⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣻⢾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣞⢿⣞⣭⣟⡷⣯⢷⣻⣽⣻⠾⣽⣻⣞⣳⢿⣽⣻⢾⡽⣻⣞⡽⣞⡿⣾⣽⣳⣟⣮⣟⣯⣽⣻⣽⣦⡀⠀⠀⠀⠀⡠⠖⠊⠉⠁⠀⠀⠀⠉⠁⠒⠤⣈⠑⠀⠐⠀⠒⠀⠂⠤⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡑⢢⠹⢌⠫⠱⣋⠾⣱⢏⢷⣫⡝⡾⣹⢏⡷⣫⡝⣯⢽⡲⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠛⡜⢢⡝⢲⡱⢎⣭⡟⠀⠀⢸⠀⠀⠀⢀⠇⠀⠀⠀⠘⣯⡿⣽⢾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣻⢾⣽⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢾⣻⣞⡷⣯⣻⡽⣯⢷⣛⣾⣻⡗⣟⡾⣽⣻⢮⡷⣯⣟⡷⣯⢿⣽⢻⡶⣯⢷⣻⢾⡽⣞⣷⣻⢾⣽⣻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠉⠑⠲⢤⣀⠀⠀⠂⠈⠁⠀⠀⠀⠁⣌⠚⡵⢪⠳⣌⣳⠹⣥⠻⣜⢧⡻⣜⢧⡻⣝⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡝⣌⠣⢜⡡⢚⠤⣿⠀⠀⠀⣀⣷⢦⡖⣟⠶⣄⠀⠀⠀⠸⣿⣽⣞⣷⣯⣟⡾⣽⣳⢯⣿⢾⣽⣳⢯⣟⣾⣽⣻⢾⣽⣳⢯⣟⡾⣽⣳⣯⣟⡷⣻⣞⡷⣯⢷⡯⣿⢽⣞⣷⣻⣽⣛⡷⣯⢿⣽⣳⢯⡿⣽⢾⡽⣯⢿⡽⣏⠿⣯⢿⡽⣞⡿⣿⣾⣽⣻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠈⠙⠶⣄⡰⣀⢆⠲⣌⠳⡌⡝⢲⢩⠳⡜⢦⠛⡴⠋⠜⢊⠵⢉⠎⡱⢍⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠄⡀⢆⠩⠒⣌⠱⢊⣿⠀⠀⣰⢿⡸⢖⡹⣜⣫⡝⣧⠀⠀⠰⡏⠀⠀⠀⠀⣼⠏⠛⠛⣿⣯⣟⡾⣽⣻⢾⢯⡷⣯⣟⡾⣽⣻⢾⡽⣿⡿⣞⣷⣻⠷⣯⣟⡽⣾⡽⢯⣟⡾⣧⣟⡶⣯⢿⡽⣯⢾⣽⣯⡿⣽⣻⢾⡽⣯⢿⡽⣯⡝⣯⡿⣽⣛⣷⣻⣷⢯⣟⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠈⠳⣔⠪⡑⣌⠓⡬⢱⡉⢦⠓⡜⠢⢁⢀⠠⢄⡊⡔⢣⠎⡑⢊⡜
⠄⡀⠄⡀⢀⠀⡀⠄⢂⡁⢂⠰⠠⠑⣂⠱⢈⠆⡱⢈⠌⡱⢀⠣⢡⢺⡄⠀⢿⡲⢭⣋⢷⣩⠶⣍⣿⠀⠀⣼⣦⣄⠀⠀⣼⠏⠀⢀⣾⣟⣮⢷⣻⣗⣯⣟⡿⣽⣳⢯⣿⣳⣟⣯⡿⣷⣻⡽⣾⢽⣻⢷⣫⣟⣷⣻⣟⡾⣽⣳⡟⣾⡽⣯⣟⣽⣻⣞⣷⣻⡷⣯⢿⡽⣞⣻⣽⣳⢿⡵⣻⣷⣻⣞⣷⣻⣆⠙⢿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⣧⠑⠀⠁⠘⠀⠉⠂⡉⢄⠣⢌⠢⢑⠢⡱⣘⠁⠈⠁⠀⠀
⡘⠄⠒⡈⠄⠒⡈⠤⢁⠐⡈⠄⡡⠡⠐⠌⢂⡘⠄⢃⡘⠄⢣⠘⢄⠊⠽⣆⠈⢿⣧⡹⣒⢧⣛⡼⠏⢀⣾⣁⣸⢾⠀⢰⡟⠀⢀⣾⣿⣟⡾⣯⢷⣾⡳⣾⣻⠷⣯⣟⣾⣳⠿⣼⣿⣳⢯⣟⡷⣯⠿⣽⣳⣟⡾⣷⣯⣟⡷⣯⢟⣳⣟⣧⣟⣾⣳⢯⣞⣷⣻⡽⣯⢿⡽⣷⣚⣯⢿⡽⣧⢿⣳⣟⡾⣳⢿⣆⠀⠙⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠐⡌⢢⠉⢆⠢⡑⣊⠱⢄⠂⠀⠀⠀⠀
⡐⠌⠡⢀⠃⡐⢀⠂⠤⢈⠐⠠⠄⡁⢊⠐⢂⠐⡈⠄⡐⠌⠄⠊⠤⢉⠂⠭⣷⣦⣌⣙⡛⣋⣉⣤⣶⡿⠈⠯⠤⠏⠀⣾⠁⠀⠸⣻⡿⣽⣳⢯⣿⢷⣹⣯⣟⣿⢳⣽⢷⣯⣿⣻⢷⣯⣟⡾⣽⢯⣟⣷⡻⣾⢽⣳⢿⡾⣽⢯⣟⣳⣟⣮⣟⡶⣯⣟⣾⣳⢯⡿⣽⣏⣿⣳⢿⡜⣯⡿⣽⣞⣷⢯⡿⣽⢯⡿⡆⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠰⠐⣈⠒⡈⠤⢉⠢⢡⠑⠤⢋⠴⡉⢎⠱⢩⠄
⠐⡈⢁⠀⢂⠐⠀⡈⠠⢀⠈⠐⢀⠐⠠⠈⠄⠂⠐⡈⠐⡈⠄⡉⠐⡠⠉⣼⡿⣽⣯⣟⡿⣽⢯⣟⣳⡇⠀⢀⡀⠀⢠⣾⠀⠀⢠⣿⣽⣳⢯⣟⣾⢣⣿⢾⡽⣮⡿⣯⣟⣾⣳⣿⣻⢞⡾⣽⣻⢾⡽⡾⣽⣳⢯⣟⣯⣟⣯⣟⣾⢳⣻⢮⣽⣻⣵⣻⢾⣝⣯⣟⣷⣻⠾⣽⢯⣿⣖⢿⣳⣟⣾⣯⢿⣽⣫⣟⣿⡄⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠁⠀⠀⠀⠀⠀⠁⠀⠉⠀⢃⠐⡈⢄⠊⠔⠈
⠐⠀⠠⠈⠀⠄⠂⢀⠐⠀⠠⠈⢀⠀⠂⠐⢀⠈⠄⢀⠐⠀⡐⠀⡁⠠⢱⣿⣻⣿⣳⡟⣾⡽⣛⡾⣽⡇⠀⡏⢹⠀⢸⡧⠀⠀⣾⣳⢷⢯⣟⣾⢧⣻⡟⣯⣾⢷⣻⢷⣯⣟⡿⡾⣝⣯⣟⡷⣯⣻⣽⣿⣳⢯⣟⣾⣳⢿⡾⣽⣞⣯⣟⣯⣿⡷⣯⣽⣻⣾⣳⣟⣾⣽⣻⣽⣻⢮⣟⣯⣷⣻⣞⣿⣻⣞⣷⣻⣞⣷⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀
⠀⠌⠀⠄⠁⡀⠂⠀⠄⠈⢀⠐⠀⠠⠈⠀⠄⠠⠀⠂⠀⠂⠀⠄⠀⡐⣼⣷⡟⣿⣳⡟⣷⣻⣽⣛⡷⣷⠒⠃⠸⠦⢴⣿⠀⢀⣿⡽⣯⣟⡾⣽⠮⣽⣹⣾⡽⣯⣟⡾⣽⢾⣽⣻⣽⣞⣳⣟⣳⢯⡟⣿⣽⣻⢾⣷⣯⣟⣿⣳⡿⣼⣞⡷⣿⣿⡷⣯⢷⣿⣳⢿⣞⣷⣻⣞⣿⣟⣾⣳⢯⣷⣻⣞⣷⣻⣼⣳⣟⡾⣧⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠂⠀⠂⠀⠄⠁⠠⠈⠀⡀⠈⠀⠄⠁⠠⠀⠂⠀⢁⠀⠁⡀⠂⠀⣿⡾⢡⣿⣳⡟⣷⣻⡼⣏⣿⣻⡄⠀⠀⠀⠈⣿⡀⢸⣯⣟⣾⢳⡿⣭⣳⣟⡷⣯⢷⣻⣾⢿⡽⣯⣾⠋⣿⣞⡷⣯⣟⣿⠃⢹⣷⣯⢿⣿⣷⣻⢾⣽⣻⢷⣫⢿⡇⢻⣿⡽⣯⣿⣿⣻⣞⣷⡻⣞⣿⣿⡾⣽⣻⣿⣷⣻⣞⡷⣯⢷⢯⡿⣽⡄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠐⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠂⠁⠠⠀⠂⠀⠄⠁⠀⡀⠁⠀⠐⠀⠠⠀⠁⠀⡀⠂⠀⢀⢈⣿⠇⢸⣯⢷⣻⣗⣯⣽⣻⢞⣽⣧⡀⠀⠂⠀⠈⣇⣾⢷⣛⡾⣯⢟⣷⡿⣭⣟⡾⣯⣿⣿⢯⣟⣷⠇⠀⢸⣿⡽⣾⣽⣿⠀⠸⣿⣞⣿⡁⣿⣯⣟⡾⣭⢿⣽⣻⠀⠈⢿⣟⣷⣿⢻⣿⣞⣷⣻⡽⡟⢿⣟⣷⣻⣿⣾⣷⢯⡿⣽⢯⡿⣽⢯⣷⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠐⠀⠀⠐⠀⢀⠠⠀⠀⠀⠁⠀⠐⠀⠀⠈⠀⠀⠀⠄⠀⢠⣿⠀⢸⣯⣟⡷⣞⣳⡽⣞⡿⢾⣽⣻⢿⡿⣶⣶⣿⡿⣯⢿⡽⣽⣻⣿⣽⣳⢯⣟⣷⡿⣟⡿⣾⡏⠀⠀⠀⢿⣟⣧⣿⡿⠀⠀⢻⣿⣾⠀⢸⣷⣯⠿⣽⢯⣞⡿⠀⠀⠘⣿⣾⢿⡀⢿⣟⣾⣳⣟⡏⠘⣿⡾⣽⢿⣷⣻⣯⢿⡽⣯⢿⣽⢯⣿⡀⠀⠀⠀⠀⠘⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠋⠀⢸⣷⣻⢾⣽⣳⢿⣹⣽⣻⣞⣭⢿⣽⣳⠿⣼⣻⣽⣳⡟⣷⣿⣿⡾⣽⣻⣞⡿⢸⡿⣽⡟⠀⠀⠀⠀⠈⣿⣷⣻⡇⠀⠀⠀⢻⣿⠀⠀⢿⣯⡿⣽⣻⢾⡇⠀⠀⠀⠸⣿⣿⡇⠈⢿⣷⣻⢾⣏⠀⢹⣿⣿⠌⣿⣯⣿⣯⢿⡽⣯⡟⣿⣞⣇⠀⠀⠀⠀⠀⢷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠸⣷⣯⣟⡶⣯⣟⣳⣟⣶⣻⣞⣟⣮⡟⣿⣳⣟⣶⢯⣟⣯⣿⢿⣽⣳⣟⣾⠇⢸⣿⡿⠀⠀⠀⠀⠀⠀⠘⣷⣿⡇⠀⠀⠀⠈⢿⠀⠀⠘⣿⣟⡷⣯⣿⠀⠀⠀⠀⠀⠘⣿⡆⠀⠘⢿⣯⣿⣇⣀⣠⣿⣿⠒⣿⣷⢯⣿⣯⣟⡷⡇⠸⣯⣿⠀⠀⠀⠀⠀⠸⡌⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢾⣽⣳⢯⡷⣞⡷⢯⡾⣽⠾⣽⣳⢿⡼⣿⣻⣾⣟⣿⠘⣷⣻⢾⡟⠀⢈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠹⣿⣻⣽⡏⠀⠀⠀⠀⠀⢀⣸⣇⣤⠶⠾⣿⣻⡏⠀⠀⢹⡏⠀⣻⣿⣯⣟⡷⣯⣟⡧⠀⢹⣿⡆⠀⠀⠀⠀⠀⢳⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⡶⣯⣟⡽⣯⡽⣯⣟⣳⣟⣷⢯⡿⣽⣟⣷⣿⢾⡟⠀⣿⢯⣿⠁⠀⠨⠇⣀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣃⣀⣀⣀⣀⣀⣀⣀⣀⠀⢹⣿⣿⠁⠀⠀⠀⢠⠶⠛⠉⠁⠀⠀⠀⠸⣿⠁⢀⣀⣠⡧⢤⣾⣿⡷⠿⠿⢷⣯⣷⠀⠀⢻⣇⠀⠀⠀⠀⠀⠈⣇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢾⣽⣳⢾⣽⣳⣟⣧⡿⠷⣯⣾⣯⣟⡿⣽⣿⣯⢿⡇⠀⢸⣿⡇⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠉⠋⠉⠉⠉⠉⠁⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠞⠿⢋⣁⣤⣼⠁⢄⡿⢿⡇⠀⠃⢸⣯⣷⠀⠀⠈⠿⠄⠀⠀⠀⠀⠀⠸⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣷⢯⣟⣾⣳⡿⠃⠀⠀⠀⠻⣷⢯⡿⣽⡿⢾⣿⡇⠀⠀⠿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡤⡲⠟⢛⣉⣤⣴⣶⣾⣿⡟⢻⣿⣣⠌⣸⣟⣲⡇⢠⠁⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣽⣻⢮⣷⣻⡇⠠⠒⠦⡀⠀⢹⡿⣽⣿⠀⠀⠈⢳⠒⡖⠉⡗⢈⠡⠀⠄⣐⣋⣉⣩⣭⣤⣤⣤⣤⣭⣭⣟⡑⠒⠠⢄⡠⢄⡀⠀⠀⠀⠀⢀⣾⠁⢰⠁⢶⡿⠟⠋⠉⢰⣿⡿⣿⠁⡾⠙⠡⢀⣿⣿⣿⣇⣼⣾⡿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣞⣿⣻⢾⣽⠁⠀⠀⠀⣱⡄⠸⣟⣯⣿⣄⡀⠀⢸⠀⡇⠈⡇⢤⣶⣿⠿⠛⠛⠉⠉⠉⢁⣿⡿⣿⣻⣿⠙⠳⠌⡐⢀⢳⠠⡱⣄⣀⠠⠤⠊⠁⢠⠃⠰⠋⠀⠀⠀⠀⣿⣿⣽⡿⠆⡐⢈⠐⣸⣿⣿⡿⠛⣿⣿⡅⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠹⡄⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣾⡽⣯⣿⠀⠀⠀⣰⠃⠙⡄⢻⣯⣿⣿⢿⣷⠼⡀⢠⠀⢹⣄⠙⢷⡀⠀⠀⠀⠀⠀⣾⡿⣽⣳⢯⣿⠀⡐⠠⠐⠠⢘⡆⠀⠀⣀⣀⡀⢤⡀⠘⢦⠁⠌⠡⠐⡒⢒⠛⠉⡁⠠⠐⡀⠂⠄⣿⡿⠋⠀⠀⠹⣿⡆⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠘⣆⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⢿⣹⣿⠀⠀⢀⡇⠀⠀⢸⡸⣿⡿⣿⣏⣿⠀⠈⠹⡆⠈⡏⢷⡀⠹⢆⠀⠀⠀⠀⣿⡿⣷⣏⣿⣏⡀⢀⠁⡈⠰⣾⠇⠀⡏⠀⠀⠀⢸⠱⡀⠈⣇⠈⡀⢁⠰⢀⠈⠰⢀⠁⠆⠰⢉⣶⡏⠀⠀⠀⠀⠀⠸⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠀⠀⠈⢇⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⣽⣻⡇⠀⢨⡇⠀⠀⢀⣿⢿⠅⢸⣿⣽⠀⠀⠀⠈⠢⢼⣄⠈⠡⢀⠩⠐⡒⠒⠛⡉⢉⠉⠠⢀⠐⡀⠂⠄⣱⡏⠤⠎⠀⠀⠀⠀⠘⡄⠉⠈⠉⠲⠤⣆⣐⣠⣈⣐⣠⠬⠴⠋⠁⢠⠃⠀⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠈⠳⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡞⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣟⣷⡀⠈⠛⠀⠀⡏⠀⠈⠀⠀⢻⣿⠄⠀⠀⠀⡀⠀⠈⠑⠣⢄⣂⠡⢀⠁⠆⡐⠠⢈⠐⡀⣂⡤⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠸⡄⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠘⠢⣄⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⣜⡞⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢻⣾⣻⢿⣄⠀⠀⡄⠹⣄⠀⠀⠀⠈⣿⡆⠀⠀⣼⣇⣰⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠓⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠈⠓⢤⡑⢄⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠐⣾⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢣⠘⣿⣽⢯⣿⣧⠀⠘⢄⠈⡆⠀⠀⠀⠘⠃⠀⠀⢻⡷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢸⠃⠀⠀⢹⡀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣉⡲⣕⣄⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠛⠛⠀⠤⢀⡀⣀⣠⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⡆⠀⠀⠀⠀⠀⠈⠁⢹⣯⡿⣾⡽⣷⡀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣶⠘⠁⠀⡞⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢿⠡⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣯⣁⠀⠀⠀⠀⠀⣀⠀⠰⣿⣿⠻⢷⣆⠀⠀⠀⠀⠀⠀⠘⣿⣽⣷⣻⣟⣿⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡀⢹⠃⠀⢰⠃⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠘⣧⠱⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⠀⠀⠘⢿⣿⣿⠇⠘⣯⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣳⣟⣾⣿⣿⡗⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢸⠀⠘⣆⠱⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠄⠤⠄⠒⠉⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢿⣶⣿⣿⣿⡼⢿⣛⠿⣿⡀⠀⢀⣼⣦⣾⣿⣿⣻⣿⢾⣿⠘⣿⣷⠀⠀⠘⢆⠀⠀⠀⠀⠀⣠⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⡄⠀⠙⣆⠑⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢦⣿⣭⣿⣿⣿⣯⣽⡷⠟⠃⢀⣴⣿⣟⣧⢿⡿⣿⣿⣯⣿⠀⢹⣿⠀⠀⠀⠈⢆⠀⠀⠀⡰⠳⡏⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠡⠀⠀⠘⢦⠘⢆⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⢀⡤⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣟⡹⢉⣴⣿⣿⡞⢃⠄⢺⣶⣿⣿⢯⢾⣹⡽⣿⣿⣿⡇⠀⠀⢿⡀⢀⡀⠀⠈⢢⠀⠀⠀⠐⠀⢧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢳⡄⠑⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢎⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣭⣭⣷⣾⣮⣽⣳⣌⢻⣿⡟⣞⡯⢷⡽⣿⡇⠙⣇⠀⠀⢸⠇⠀⢹⡆⠀⠀⠑⣄⠀⠀⠀⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠒⠒⠒⠒⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⣷⣽⡿⠿⣿⢿⣿⣿⣿⣿⡷⣿⡿⣽⣫⣽⢻⣼⣻⡇⠀⠈⠢⡀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠓⢄⠀⠀⠀⠼⣇⠆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀
⠀⠀⠀⡀⠄⠤⢄⣀⣀⣀⠀⠀⠀⠑⠀⣀⠤⠊⠀⠀⠀⣽⣴⡆⠅⡹⣡⣿⣿⣛⡾⣽⣿⣻⣵⡻⣼⣛⡶⣏⣿⠀⠀⠀⠈⠢⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠑⢄⠀⠀⠀⠃⣼⡼⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠤⣀⣀⣀⡀⢀⡴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠑⢦⡈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣾⣿⣿⢻⣞⣽⣻⣿⢷⢯⣶⢻⣳⡽⣳⣛⡾⣇⠀⠀⠀⠀⠈⠢⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠟⠿⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡻⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠙⠢⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⡀⠀⠀⠀⠀⣽⣿⣿⣿⣻⢞⣿⣺⣷⣿⣿⢯⣟⡾⣏⣷⢻⡵⣯⢽⣻⡄⠀⠀⠀⠀⠀⠈⠢⢀⠀⠘⢄⢰⣷⣄⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⣴⣾⣿⡿⣯⢷⢯⣟⣾⣿⣿⣿⢯⣟⡾⣽⣻⡼⣯⢷⣫⢯⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠂⠩⠻⢷⠀⠀⠀⠀⠀⠈⠒⠤⣀⣀⠴⠊⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⢻⣳⣿⢯⣟⣳⢯⣟⣾⣿⣿⣿⣟⣿⣺⣽⣳⢯⢷⢯⣷⢫⣯⣽⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠⡆⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞⣿⡿⣽⣛⡾⣽⣻⢾⣿⣿⣿⣿⡽⣶⣻⢶⣯⡟⣯⢷⣞⣟⡶⣳⢯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣝⡷⢯⣻⢷⣯⣿⣿⣿⣿⣷⣻⠷⣯⣟⣶⣻⡽⢯⣞⡾⡽⣽⣳⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡴⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡟⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣛⣯⡟⣷⣿⣿⣿⣿⡿⣾⣽⡻⣗⣿⡺⣗⣿⢻⡾⣽⡽⡶⣏⣷⣻⣿⣆⠈⠠⠀⠀⠀⢀⡠⠔⠊⠉⠀⠉⠉⢩⠟⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢻⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡼⠁⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡽⡾⣽⣻⣿⣿⣿⣿⣟⣷⣳⢿⡽⣶⣻⡽⣞⣯⣟⣳⡽⢯⣷⡳⣽⣻⣿⣆⠀⢁⡤⠚⠁⠀⠀⢀⣠⠴⢒⡴⠃⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⢙⢳⡄⠈⠢⠀⠀⠀⠀⠀⢸⠀⠀⠀⢽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠃⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣽⣳⣿⣿⣿⣽⡿⣞⡷⣯⢿⣽⣳⢯⡿⣽⢾⣹⢷⣻⢟⣶⣻⣳⡽⣿⠿⠚⠉⠀⠀⠀⠀⠀⣯⣿⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⠣⢷⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢺⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢯⣿⣿⣯⣿⢿⣽⣻⣽⣻⢾⡽⣯⢿⣭⢿⡽⣯⢯⣿⠾⠗⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠏⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⠣⡛⢶⠀⠀⠀⠀⠀⠀⢧⠀⠀⢹⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡿⢃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⡠⢤⠤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠒⠀⠉⢉⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣽⣖⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠈⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⢿⡿⣿⡿⣟⣛⣛⡹⣉⢏⡙⣋⠟⡻⢿⡿⣿⣿⣿⣵⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣻⣽⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣞⣶⣧⢮⣑⡦⣉⢛⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⣀⠤⠒⣨⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⡶⣭⣻⢿⣿⣿⣿⣵⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢀⠠⠒⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣟⡿⣿⡻⠯⣝⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣯⣦⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⣴⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⠶⣦⣌⡙⠛⠟⠓⣯⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⡿⣿⣿⣿⡷⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⣀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠈⠓⠿⠽⠯⠟⠉⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡽⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠔⠈⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠘⢽⡿⣿⣿⢿⡻⢺⡿⣿⣿⣿⣿⡽⣿⣿⣿⣣⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠂⠀⣠⣤⣶⠶⠿⠷⠾⠿⠶⢶⣭⣿⣟⣿⢿⣟⣿⣿⣿⣟⡦⡀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢠⠁⠀⠀⠀⠀⠂⠀⠀⠀⢰⣿⣿⣿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣽⣿⣿⣿⣿⣿⣶⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⡐⠁⠀⠀⠀⡠⠂⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠇⠀⠀⠀⠀⠀⣿⠀⣼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣯⡄⠈⢂⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⠌⠀⠀⠀⢀⠈⠀⠀⠀⠀⠐⢠⣿⣿⣿⣿⣿⣿⠏⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠇⠀⠀⠡⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡐⠀⠀⠀⢀⠂⠀⠀⠀⠠⠁⠀⠀⠀⠀⠄⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣼⡇⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣳⠀⠀⠀⠐⡀⠀⠀⠀⢂⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⢀⠂⠀⠀⠀⡰⠁⠀⠀⢀⠈⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠛⠷⢶⣢⣤⣤⣤⣤⣤⡶⠟⠋⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⠄⠀⠀⠀⠐⡀⠀⠀⠀⠆⠀⠀⠀
⠀⠀⢀⠁⠀⠀⠀⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠈⠄⠀⠀⠀⠡⠀⠀⠀⠘⡀⠀⠀
⠀⠀⡌⠀⠀⠀⡘⠀⠀⠀⢠⠁⠀⠀⠀⠐⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⡀⠄⠂⠐⠀⠂⠀⠀⠀⠀⡀⠀⠈⠀⠀⠈⠻⢗⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⢾⠀⠘⡀⠀⠀⠀⠂⠀⠀⠀⢡⠀⠀
⠀⠰⠀⠀⠀⢀⠁⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠈⠀⠀⠀⠄⠐⢀⡂⠀⠁⠀⡀⠀⠀⡀⠈⠀⠄⠀⠀⠈⠙⠛⠷⠶⢶⣶⣶⠶⠶⠟⠛⠉⣼⣿⣿⣿⣿⣿⣿⡏⠀⠀⢡⠀⠀⠀⠘⡀⠀⠀⠀⡆⠀
⠀⡄⠀⠀⠀⡘⠀⠀⠀⠰⠀⠀⠀⠄⠀⠀⠄⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣧⠀⠀⡀⠀⢀⠐⣨⣴⠾⢟⣛⢛⡛⠿⣶⡁⠀⢀⡐⡀⠀⠄⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⡆⠀⠀⠀⠃⠀⠀⠀⢠⠀
⠀⠁⠀⠀⠀⠇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⠠⣠⡾⣿⣴⡉⠖⡌⢦⡙⡜⠬⣿⢶⠟⣛⠛⡿⢶⣦⣁⠀⡀⠀⠀⠄⠀⠀⠠⠀⠈⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢡⠀⠀⠀⢸⠀⠀⠀⠘⠀
⢰⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⡱⢢⡙⢻⠿⣼⣆⣱⢌⠳⡌⢧⡙⢤⢋⡔⢣⢌⡛⢷⣄⠠⠀⠀⠀⢀⠀⠀⠐⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄
⢨⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠄⠀⠐⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠻⣧⡣⢜⡡⠞⡤⢋⡝⢻⠳⢾⣦⣽⣆⣣⣜⡡⢎⡜⣡⠻⣷⡀⠀⠠⠀⠀⢀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇
⠰⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠈⠻⣶⣥⣋⠴⢣⠜⣡⢋⠖⡰⡌⡜⣩⢛⡹⠻⠽⠶⣷⣻⠇⠀⠀⠀⠠⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠀⠀⠀⡇
⢘⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⠛⠻⢶⣭⣦⣍⣎⣱⣘⢴⣡⣎⡴⣟⠾⠛⠋⠁⠀⠀⠠⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠸⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠄⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠄⡀⠀⠉⠉⠉⠓⠋⠋⠁⠉⠁⠀⠀⠀⠀⠀⠄⣈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⡀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⡀⠀⠀⠀⡆⠀⠀⠀⠇⠀⠀⠀⠀⠀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⡀⠀⠄⢐⣨⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⢰⠀
⠀⠃⠀⠀⠀⢁⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠂⠀⢀⠀⢠⣁⣠⣥⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠠⠀⠀⠁⡇⠀⠀⠀⡀⠀⠀⠀⠘⠀
⠀⠸⠀⠀⠀⠘⡀⠀⠀⠀⠆⠀⠀⠀⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠁⠀⠀⠀⠇⠀
⠀⠀⠆⠀⠀⠀⢁⠀⠀⠀⠘⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠀⠀⡌⠀⠀⠀⠘⠀⠀
⠀⠀⠘⡀⠀⠀⠈⠄⠀⠀⠀⠡⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠐⠀⠈⠀⠀⠐⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠈⠀⠀⠀⠎⠀⠀⠀⠰⠀⠀⠀⢀⠃⠀⠀
⠀⠀⠀⠡⠀⠀⠀⠘⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡥⣉⢿⣿⣿⣿⠟⠁⠀⠀⠀⠂⠀⠂⠀⠐⠀⠁⠀⠐⠀⠀⠈⢻⣿⣿⠑⢦⢩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀⠠⠀⠀⠀⢀⠌⠀⠀⠀⢠⠁⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⢡⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡚⠴⡡⣾⣿⠟⠁⢀⣀⣄⣤⡥⣤⡴⣤⣬⣤⣤⣦⣥⣤⣀⣂⣀⠀⠘⢿⣍⢆⠣⢎⡙⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠄⠀⠀⠀⢀⠎⠀⠀⠀⢠⠂⠀⠀⠀⡜⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢤⡙⢦⢱⣿⣥⠶⡟⣛⠫⣍⢣⡑⢦⡑⢆⡲⡐⢆⠲⡌⠭⣍⢋⠟⡻⠷⣶⣽⢮⣓⡌⢖⡩⢻⣿⣿⣿⣿⡿⡎⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⡠⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢦⣙⣶⠟⡍⢆⠳⣘⠤⡓⡌⢦⡙⠦⡙⢦⠱⣉⢎⡱⢜⡱⢌⠎⣜⢡⠓⡴⣈⢏⡛⣽⣦⡱⢣⡙⣿⣿⣿⢿⠁⠀⠀⠀⠐⠀⢈⠔⠀⠀⠀⠀⠔⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢤⣿⢃⠟⡸⡘⢧⡘⢤⢃⠻⣄⠻⣄⠻⡄⢧⡘⣄⠣⡜⣠⠛⡼⣀⠟⣸⢠⢃⡜⡠⡄⡜⣿⣇⠸⡘⢿⣿⡿⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⢀⠜⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⡏⢇⣿⡃⢎⡜⣡⠙⢦⡙⢦⡉⠶⣈⠧⣌⠳⡘⢦⠱⣌⠳⡘⡤⢋⡴⢡⢚⠤⣃⠮⡐⢧⡘⠴⡩⣾⢣⡙⣌⠻⣧⡀⠀⠀⡨⠊⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠘⢻⣿⣿⣿⣿⢋⠬⢿⣕⠪⡔⣡⢋⠦⡑⢦⡙⢦⡑⢎⡔⢣⡙⢆⠳⣌⢣⠱⡘⢥⢊⡕⣊⠖⣡⢎⡱⢆⡙⢦⡑⣿⡣⠜⡤⢓⠬⣳⣤⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠻⣿⡟⣌⠚⡬⢿⣶⡑⢦⡉⢖⡩⢆⡹⢤⡙⢦⡘⢥⠚⣌⠳⣄⢣⡙⡜⢢⠣⡜⢤⢋⡔⢪⠔⡣⢜⢢⣽⣻⣿⣵⢌⠣⢎⠥⣙⣦⡀⠀⠠⠊⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠈⠑⢬⡓⣜⣯⣷⣿⣦⣝⣢⠱⣊⡔⢣⠜⣢⠙⢦⡙⢤⠓⡌⢦⡑⢎⠥⡓⡜⢢⠣⡜⣡⢚⣱⣞⣿⣾⣿⣿⣿⣮⡓⡬⢚⢴⠸⠋⠁⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⠚⠿⣿⣿⣿⣿⣯⡿⢶⣾⣥⢾⣤⣋⣦⣙⠦⣙⡜⣢⣙⣌⣖⣱⡼⣥⣷⣞⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠋⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣗⢢⠒⡬⢩⠍⣍⠳⣙⡛⡛⢞⡓⣋⠞⡩⢍⠭⡑⠦⢼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠊⠱⠎⠆⡓⢦⠱⣉⠦⣑⠎⡜⡱⢊⠵⣉⢎⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
new o'grady abby wilde abby icon face soup2nuts noggin the n teennick show weirdness nickelodeon tom snyder animation tv sitcom squigglevision nicktoons melissa bardin galsky h. jon benjamin television network animation studio text art ascii art braille art braille pattern braille cartoon call telephone call telephone cell phone teenager symbol picture
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⣟⡿⣯⣟⣷⣻⣞⣷⣻⣾⣽⣻⣟⡿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣯⡷⣿⣻⣽⣟⣾⡽⣷⣻⡽⣷⣻⢾⣷⣻⣽⢯⣟⡿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣻⡽⣟⣾⣽⡷⣟⣷⢯⡿⣽⣻⡽⣿⡽⣯⣿⣞⣯⣟⣯⡿⣽⡷⣯⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣾⡽⣟⣯⡿⣾⣽⣟⣾⣟⡿⣽⣯⢿⣳⣿⣻⢾⣽⣳⡿⣽⣻⣽⣻⢷⣟⣯⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣳⣯⡷⣿⣻⣽⣿⣷⢿⣾⢿⣾⢿⡿⣾⢿⡿⣾⢿⡿⣯⣷⣿⣿⣽⣷⣻⣯⣟⣷⢯⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣾⣷⣿⢿⣟⡿⣽⡾⣽⣻⡾⣟⣾⢿⣽⣻⣯⢿⣽⣯⢿⣽⣳⡿⣞⣿⡽⣿⣻⢿⣾⣿⣽⣟⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⣻⣽⡾⣿⣽⣻⢯⣟⣿⣳⣿⣻⡽⣟⣾⢷⣻⣯⣷⣻⣯⣟⡷⣿⣻⢷⣻⣯⣟⣯⡿⣽⣻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢿⣽⣻⢯⣷⢿⣳⣯⣟⡿⣽⣾⣻⢾⣽⣻⢯⣟⡿⣽⣾⣳⣯⡷⣟⣿⣳⣿⣿⠽⠾⠿⠷⠿⢿⣽⣟⣾⣟⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣽⣻⣾⣻⢯⣟⣯⣟⣷⣻⢿⣽⣞⣿⣯⣿⣽⣻⣯⣿⣻⣾⣽⣳⣿⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣯⣟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⢿⣞⡿⣾⣽⣿⠯⠿⠾⠿⢿⣟⣛⡛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⣿⣞⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢾⣻⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣄⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⡆⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠀⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢼⣿⡟⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⣰⣆⡀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠃⠈⠝⠳⣝⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⣀⣀⣀⣀⣤⠴⠚⣿⠏⠀⠀⠀⠀⠀⠀⣈⠳⣌⠓⠦⣤⣀⣀⣀⣀⣀⣀⡤⠖⠋⠁⠀⠀⢀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣰⡏⢀⢦⡀⠀⠀⠀⠙⢷⣄⣹⠆⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣆⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣼⡇⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⣄⡀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣀⣀⣀⣠⣠⣤⣤⣤⣤⣄
⠈⠻⢿⣿⣿⣷⣶⣦⣤⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛
⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣦⣶⣶⣶⣶⣶⠶⠾⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⣹⡟⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣆⡄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⢀⣀⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⡶⠛⠋⢩⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡟⠙⠀⣐⣴⣾⣯⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⢞⢠⣤⣾⣯⣿⣧⠈⠉⠛⠛⠛⠻⠶⠶⠶⠶⢾⡇⠀⠀⠀⠀⠀⣠⡶⠳⢶⣤⡀⠀⠁⠻⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠸⠋⢁⢀⠠⠰⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢠⡟⠀⠠⠀⠈⢿⡄⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠁⠀⠀⠸⠛⠋⠉⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠆⡇⠀⠀⠀⢸⡇⠠⠐⠀⠁⠈⣿⡀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⢨⣻⡗⠀⠀⠀⠀⠀⠀⣿⢿⠀⢽⠀⠀⠀⠸⣇⠀⠄⠁⠂⠄⢸⣇⠀⠀⠀⠀⠿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⡀⠀⠀⠀⠀⠀⠀⣠⡾⣃⣼⠟⠁⠀⠀⠀⠀⠀⢰⣿⠃⠄⢸⡆⠀⠀⠀⣿⠀⠐⡀⠁⠄⠠⣿⠀⠀⠀⠀⠀⠙⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⢧⣤⣀⡀⠀⣀⣴⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣟⠐⠀⡀⣇⠀⠀⠀⢻⡄⠂⠐⠀⠂⠀⢽⡆⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⠉⠛⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠂⠐⠀⡀⢹⠀⠀⠀⢸⣇⠀⠁⠂⡁⠂⢸⡇⠀⠀⠀⠀⠀⠀⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠈⠀⠌⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠂⠀⢡⠀⣹⠀⠀⠀⠀⣿⡀⢈⠄⠀⠂⢨⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡅⠀⠂⠠⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠌⢀⠀⣀⣾⡅⠀⠀⠀⢹⡆⠀⡀⠂⠡⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠂⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠠⠀⠠⣼⣿⡇⠀⠀⠀⢸⣧⠐⠀⡁⢂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡄⠀⠁⡀⢺⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢈⠀⠂⣵⣿⠛⣧⠀⠀⠀⠀⣿⠀⠐⠀⢂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⠈⠀⢀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠂⠀⣼⣿⠏⠀⣟⠀⠀⠀⠀⣿⡀⠈⠄⠂⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠈⠀⢀⠘⣿⣧⠀⠀⠀⠀⠀⣰⣿⠃⠀⠂⠁⣰⣿⠏⠀⢠⣏⠀⠀⠀⠀⣿⡄⠐⠀⢁⠀⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢈⠀⢀⠸⣿⣆⠀⠀⢀⣼⣿⠃⠀⡀⠂⣡⣿⡟⠀⠀⢸⡧⠀⠀⠀⠀⣿⠆⢀⠁⢂⠀⣽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣃⠀⠄⠀⠄⠸⠿⣷⣤⡾⠯⠁⢀⠐⠀⣰⣿⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⣽⠆⠀⠄⢂⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠌⠀⡀⠀⠉⡉⠁⠀⠄⢀⠈⣰⣿⠏⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢿⡂⢈⠀⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠁⡀⠈⠄⠀⡀⠁⡀⢀⣾⣿⠋⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⣿⠄⢀⠂⡐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⡀⠄⠂⢀⠠⠀⣤⣿⡟⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠀⢀⠂⠄⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⣀⢃⣠⣤⣿⡿⠋⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠂⡈⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠿⠛⠉⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠠⠁⠄⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠄⠂⡈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⢂⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⢚⣛⣩⣤⣶⣄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⢉⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⣞⣛⣩⣥⣶⣾⣿⣿⣿⣿⣿⣿⡆⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⣿⣶⣤⡈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣛⣯⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⣷⣦⣌⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⡶⣻⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣯⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣗⢽⡄⠀⠀⠀⠀⣠⡶⢶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠻⣿⣿⣯⡟⠿⣿⣿⣿⣿⣿⣦⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⢸⠇⠀⣼⣿⡌⢳⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⠴⠛⠙⠻⢮⡛⢿⣿⣿⣿⣿⣦⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣼⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠌⣿⣿⣿⣿⡿⣷⠀⠀⢀⡿⠀⢀⣿⣿⣿⣎⣡⣬⣭⣭⣭⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣍⠿⣿⣿⣿⣿⣆⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣹⣤⠾⠛⣁⣠⣼⣿⣿⣿⣿⣿⣿⣿⠿⣥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢿⣿⣿⣿⣧⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠋⢉⣠⣴⣿⣿⣿⣿⡟⣹⣿⣿⣿⣻⣶⠋⠀⠀⠀⠀⠀⠀⣠⡶⠶⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠙⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⠻⣿⣿⣿⣧⡘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡆⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣄⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⣬⣭⡙⠛⣿⣿⣿⣿⣿⣿⣻⣿⣷⡌⢳⣄⠀⠀⠀⠀⣼⠏⠀⢀⣤⣄⣈⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣴⣿⣌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⢿⣿⣿⣧⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢧⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡻⣿⣿⠁⢀⣿⣿⣿⡿⢋⣉⣛⠻⠿⡿⡇⣹⣆⠀⠀⢰⡟⠀⢰⣿⣿⣿⣿⣿⣷⣦⣌⡙⠶⣄⠀⠀⠀⣸⠇⠀⣰⣿⣿⣿⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡈⢿⣿⣿⣷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢯⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣿⣿⠀⢸⣿⣿⠟⣰⡟⠉⠉⠛⢿⣿⣿⠟⠋⣻⠶⣾⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠻⣤⣠⡏⠀⢠⣿⣿⠙⣿⣷⡀⢻⣤⣤⣀⣠⣀⣄⣀⣀⣀⠀⠀⠀⠀⠙⣧⠈⢿⣿⣿⣧⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠛⠶⣤⡀⠀⠀
⠀⢸⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⢹⣿⣦⣼⣻⣉⡼⠋⠀⠀⠀⣠⡾⠋⠁⢀⣤⣾⣧⣿⣇⠀⢻⣿⣿⡉⣿⣛⠿⣿⣿⣿⣿⣿⣶⣼⠟⠀⢠⣿⣿⡇⠀⢹⣿⣷⣀⡀⢀⠀⡀⠀⠀⠈⠉⠉⠛⢷⣄⠀⠀⠘⣧⠈⢿⣿⣿⡆⢿⣷⣤⣤⣀⡀⠀⠀⠀⠀⢸⡇⠀⣰⣾⣏⠻⣆⠀
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⢶⠾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠘⣿⡀⠀⠉⠉⠀⠀⠀⣠⠞⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⡇⣼⣿⠿⠃⠉⢻⣿⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⡆⠀⠀⢹⡄⠘⣿⣿⣷⢸⣿⠁⠀⣉⡛⣦⡀⠀⠀⠘⣇⠀⣿⣿⣿⣷⠙⡇
⠀⢸⡇⣿⣿⣿⠄⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣴⣿⡇⠀⠀⠀⠀⢀⡾⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⢈⣿⣿⣿⠉⠁⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⡀⠀⠘⣧⠀⢹⣿⣿⣇⣿⠀⢸⣿⣿⠜⣧⠀⠀⠀⠹⣦⠘⢿⣿⣿⡇⣟
⠀⠀⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣤⢿⣿⡿⣽⡇⠀⠀⠀⣰⠟⠀⣠⣾⣿⣿⣿⣿⠟⢁⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡟⠛⣛⣛⣛⣛⣿⣿⣿⠿⠾⠛⠛⠛⠛⠿⠆⠈⣿⣿⣿⣿⠀⢸⣿⣿⡇⣿⠀⠀⠀⣀⣿⠀⢸⣿⣿⡇⣿
⠀⠀⢸⣇⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⢿⣿⣿⢾⡇⠀⠀⣼⠏⠀⣴⣿⣿⣿⣿⠟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣻⠁⠀⣿⣿⣿⠃⣼⠋⠉⢻⡆⠘⣿⣿⣷⡀⠻⣭⡽⠟⠉⠀⠀⣀⣤⣴⣶⣶⣿⣶⣶⣤⣿⣿⡿⣿⡀⢸⣿⣿⣇⠸⣇⢀⣠⡿⠁⠀⣼⣿⣿⠇⣟
⠀⠀⠀⣿⣸⣿⣿⡀⠀⠀⠀⠀⠀⠸⠷⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠨⣗⠀⢰⡏⠀⣼⣿⣿⣿⡿⠃⠀⢀⣾⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠐⠲⣿⠀⠨⣿⣿⡏⣼⠇⠀⠀⠀⢿⡀⠸⣿⣿⣷⠀⠉⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣦⡙⠋⠁⠀⣠⣾⣿⣿⡿⣼⡇
⠀⠀⠀⢸⡇⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢻⣠⡿⠀⢰⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⡿⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡃⢀⢿⣿⢳⡏⠀⠀⠀⠀⠘⣧⠀⢿⣿⣿⣷⣀⣴⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⢿⡿⣇⠘⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡿⣱⡟⠀
⠀⠀⠀⠈⣿⣹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡇⢸⣿⠇⠀⣿⣿⣿⠁⠀⣠⣾⣿⣿⣿⢟⡁⢿⣿⣿⠈⣿⡇⠉⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣔⠿⢿⡄⠀⠀⠀⠀⠀⠸⣧⠘⣿⣿⣿⣿⣿⣿⣿⡿⢛⣩⠴⠖⠛⠛⠛⣿⠃⠈⣿⣿⡟⣼⠗⠘⢧⡘⢿⣿⣿⣿⣿⣿⣿⣿⢟⣵⠟⠀⠀
⠀⠀⠀⠀⢻⡿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⢹⣿⠀⢰⣿⣿⣧⣴⣾⣿⣿⣿⡿⢋⣾⡇⢸⣿⣿⡄⣿⣿⡀⠸⣿⣿⣿⠰⣿⣛⣿⣿⣿⣿⣿⣿⣦⡙⠷⣤⡀⠀⠀⠀⢸⡇⠈⣿⣿⣿⣿⢟⣵⠞⠋⠁⠀⠀⠀⠀⢠⡏⠀⢠⣿⣿⡇⣿⠀⠀⠀⢻⣶⠙⢻⣿⣿⣿⣯⣴⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠦⢀⡀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡄⢸⣿⣿⣿⣿⣿⣿⡿⢋⣴⠟⢹⡇⢸⣿⣿⡇⢸⠟⢷⡀⢻⣿⣿⢁⡿⠉⠳⣮⡛⢿⣿⣿⣿⣿⣷⣌⠛⢦⣄⡀⠘⣧⠀⣿⣿⣿⣿⡈⠙⠲⢦⣤⣄⣀⡀⠀⣼⠁⠀⣼⣿⣿⢃⣿⠀⠀⠀⠀⣿⠀⢸⣿⣿⣇⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠁⠀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⢷⡌⢿⣿⣿⣿⠟⢋⡴⠛⠁⠀⢸⡇⠸⣿⣿⡇⣸⠂⠀⠙⢶⣝⣻⡾⠃⠀⠀⠈⠙⢦⣝⠻⣿⣿⣿⣿⣿⣦⣈⠻⢦⣿⣄⠹⣿⣿⣿⣿⣷⣦⣤⣀⣀⠉⠙⠳⠏⠀⢰⣿⣿⡿⣸⡇⠀⠀⠀⠀⣿⠀⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡇⠀⠙⢷⣭⣯⡵⠞⠋⠀⠀⠀⠀⢸⣇⠈⣿⣿⣿⢼⡅⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⠻⢿⣿⣿⣿⣿⣿⡆⣿⠙⢶⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢟⣛⣛⣯⣭⢤⣶⠟⠀⠀⢀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⣿⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⡙⢿⣿⣿⣿⡇⣿⠀⠀⠈⠛⢶⣭⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠃⠀⠀⠀⠀⢰⡟⠀⢸⣿⣿⡇⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢷⣝⣛⣻⣛⣭⣭⢭⡿⣯⣽⣿⣭⣽⠶⠷⠶⠖⠚⠛⠋⠉⠉⠉⠙⣉⢋⡉⠙⡙⠛⠛⠒⠓⠶⠶⢦⣤⣄⣀⡀⠀⠀⢿⠀⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣭⣿⣏⣼⠇⠀⠀⠀⠀⠀⠀⠉⠛⠲⠮⣭⣟⡻⠿⢿⣿⣿⡿⢼⠋⠀⠀⠀⠀⠀⠈⢿⡀⢹⣿⣿⣷⣹⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⢉⣩⣬⠷⠿⠛⠛⠉⠉⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣿⣾⣷⣶⣷⣶⣶⣶⣤⣤⣤⣬⣉⣛⠛⠷⠶⢤⣾⠀⢹⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣆⡸⣿⡿⢣⡞⠀⠀⠀⠀⠀⠀⠀⠘⢷⡘⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣀⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣵⠾⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⡿⣿⢿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡾⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⣭⣭⠵⠶⠞⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠲⠶⠿⠯⣭⣽⣟⡻⠿⣿⣿⣿⣿⣿⣿⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⠋⠀⣰⣿⣿⣿⣿⣿⠿⣻⣭⡥⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⡙⢿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡏⠀⣼⣿⣿⣿⡿⣫⡵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣿⠿⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢾⡀⢰⣿⣿⣿⢃⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣧⣸⣿⣿⡧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢷⣽⠿⣵⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
new o'grady logo title soup2nuts noggin the n teennick show weirdness nickelodeon tom snyder animation tv sitcom squigglevision nicktoons melissa bardin galsky h. jon benjamin television network animation studio viacomcbs viacom paramount global art ascii art braille art braille pattern braille cartoon call telephone call telephone cell phone teenager
🅾*ܦƦA̶∂ץ
new o'grady logo stylization soup2nuts noggin the n teennick show weirdness nickelodeon tom snyder animation tv sitcom squigglevision nicktoons melissa bardin galsky h. jon benjamin television network animation studio viacomcbs viacom paramount global art ascii art braille art braille pattern braille cartoon call telephone call telephone cell phone teenager
⠁⢂⠘⢀⠂⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡗⢠⠂⡔⣀⢂⡐⢀⠂⠔⢠⠂⠔⡰⢈⠴⢡⢫⡝⣿⣻⣿⣟⡿⣽⢿⣿⣿⣿⣿⣿⣿⣿
⠈⠄⡈⠀⠌⠀⠁⠠⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡏⢄⢃⡐⠄⠂⡔⠈⡈⠌⠠⢈⠂⡁⠊⡄⢣⢎⡽⣞⣿⡷⣯⣟⡾⣻⣿⣿⣿⣿⣻⣿⣿
⠐⠠⢀⠡⢈⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡏⢄⠂⠠⣜⣰⣤⡳⣔⡈⢒⡐⠂⡅⠓⠌⣣⢚⡼⣻⣾⣿⣳⢯⣟⡽⣿⣽⣳⡟⡿⣽⢻
⠌⡀⢂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣏⣄⡼⣯⣳⢯⣶⣻⣽⡁⢢⠀⢃⠤⢉⠢⡑⢮⡱⣟⣷⣿⣽⡳⣯⢽⣷⣻⢶⡻⣝⡾⣹
⢂⠐⠠⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡽⣛⡶⣯⣟⣶⣻⡞⠁⠤⠘⣀⠂⡄⢣⠙⢦⡹⢯⣿⣿⣞⣽⡳⢯⣿⣽⣳⢯⣝⣞⣳
⠂⡀⠡⠀⠌⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣽⣻⣽⣳⣿⠞⠋⡀⢊⢠⣁⡤⡦⠴⢆⢩⢒⡽⣯⢿⣷⣻⢶⣛⢯⣿⣞⡷⣯⢞⣮⢷
⠐⡀⢁⠐⠀⡁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠋⣩⠝⠛⡒⠒⠩⣕⠢⣄⠀⠀⠀⠀⠀⠀⣽⣿⡟⡑⠛⠙⡉⠁⢀⠢⣰⣬⣷⣿⣿⣿⣿⣿⣿⣾⣽⣯⣿⣿⣳⢯⡽⣞⣿⣿⣻⣭⣟⢮⣟
⠀⡐⢀⠂⠁⠀⡈⢀⣠⣴⣾⣿⣿⣿⠿⡿⠿⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⠴⠊⠁⠀⠀⠈⠓⢤⡀⠑⢌⠱⣄⠀⠀⠀⠀⢾⣿⡗⢐⠈⡀⢀⡐⣪⣿⣿⢿⣻⢷⣻⣞⡷⣟⣾⢯⣟⣿⣿⣿⣳⢯⣞⣳⢿⣷⣟⣾⣽⣻⣾
⠀⠐⡀⠄⠐⢀⣴⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣷⣶⣮⣽⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣶⣾⣿⣿⣦⡀⠀⢀⣤⣴⣤⣄⣠⣤⣤⣤⣄⡀⠀⠀⢰⣿⣿⢿⣿⣷⡄⢸⣿⣿⠀⠀⠀⡴⠁⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⢧⠀⠀⠀⣻⣿⣏⠀⠆⡀⣖⣿⣿⢿⣽⣻⢯⣿⢯⡿⣽⡿⣽⣻⣟⣾⣽⣻⣿⣳⢾⡽⣿⣿⣿⣿⣾⣿⣿
⠀⢀⠀⢠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣟⠉⣿⣿⣿⣇⣴⣿⡿⣯⢿⣿⣿⣻⣽⣻⣟⣿⣶⣤⣬⣭⣧⣾⣟⣿⠃⢸⣿⣿⠀⠀⡼⠁⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⣇⠀⠀⣽⣿⣧⡘⣰⣾⣿⣿⣿⠿⡾⣿⣯⣟⣯⡿⣯⢿⣽⢷⣯⡷⣿⣽⣻⣿⣯⣿⢿⡿⡿⣟⡿⣿⢿
⠀⡀⠀⣴⣿⣿⣿⣿⣯⣸⣿⠿⠯⠿⣿⣿⡏⠙⠿⠿⠟⠿⣿⢻⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⢿⣶⣮⣽⣾⣿⣿⣷⣿⣽⣿⠃⠙⢿⣾⠷⠿⣾⣽⣯⣟⣯⣿⣳⡿⠋⠀⢸⣿⣿⠀⢸⣁⣠⣤⣾⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣽⣄⡀⢹⡀⠀⣽⣿⣷⣽⣿⣿⠛⠁⠀⠀⠀⠀⠉⠻⣿⣽⣻⣯⡿⠛⠛⠛⠛⠷⣿⣻⣿⣿⢯⣳⣟⣼⣳⣏⡿
⠀⠀⣰⣿⣿⣿⣿⣿⡾⠉⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⢠⡴⠛⠉⠉⠉⠛⢿⣧⡾⠀⢸⣿⣿⠻⢿⣷⣯⣿⡿⠛⠉⠀⠀⠙⣧⠀⠀⣿⠀⠀⠀⠀⠈⠛⠿⣿⣻⣿⣄⠀⠀⢸⣿⣿⡴⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠳⡀⢀⣴⠯⠛⠋⠉⠉⠈⠉⠹⡚⠽⢷⡀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⣹⠃⠀⠀⠀⠀⠀⠀⠈⢿⣟⣿⣿⣷⣻⣞⣷⣯⣿
⠀⠀⣿⣿⣿⣿⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⡟⠀⠀⠀⠀⠀⠀⠀⠹⣧⣴⢿⣿⣿⣀⡼⣯⡿⠋⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠻⣷⣤⣼⣿⣿⣆⡀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣠⠗⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⢹⣿⣿⣿⣿⣿⡀⠸⠶⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⣠⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢨⣿⣿⣿⣿⣿⠀⢳⡀⠀⠀⠀⠀⠀⠰⣷⠀⣼⠀⢧⠀⠀⠀⠀⠀⠀⠾⠆⣿⠾⢻⣿⣿⣿⠟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⢺⣿⣿⣻⣿⣿⣀⣏⠉⠚⠓⠒⠒⠒⠒⠉⢁⣤⠀⠣⣠⡆⠀⠀⠀⠀⠀⠀⠀⠸⢀⣤⠟⣻⣿⣿⣿⣧⠳⣄⡀⠀⠀⠀⠀⢀⣴⠷⠲⣷⡀⠈⠁⠀⠀⠀⠀⠀⡸⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⣿⣿⣿⣿⣿⡀⠀⢭⡲⢤⣄⣀⣀⣀⣤⠞⠃⠀⢈⡳⣄⡀⠀⠀⠀⢀⣴⡟⠀⢸⣿⣿⣿⠰⢿⣿⢶⣤⣀⣠⣶⣀⣤⡾⠋⠀⠙⠷⢦⣾⣷⡤⠶⠿⣯⠉⠃⢸⣿⣍⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣰⠃⠀⠳⡄⠈⠉⠓⠒⠲⠐⠦⠒⠒⢺⠁⠜⠀⣿⣿⣿⣿⡿⠀⠀⠉⠙⠒⠒⠉⣟⡵⠀⠀⠈⣏⠲⠤⢤⠤⡤⠴⠊⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢂⣿⣿⣿⣿⣿⣇⠀⠀⠙⠒⠒⠊⠉⠑⠀⠀⠀⠀⠀⠙⠳⣍⣛⡛⠋⢉⣿⣧⡤⣼⣿⣿⣿⠀⠀⠉⠸⠃⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⢻⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠐⠷⠂⠀⠒⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣧⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿
⠀⠂⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣤⢶⠾⡶⢮⣴⠷⡶⣤⡀⠀⠀⢸⣯⡶⠷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⣦⣴⢟⡻⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⢻⣿⣿⠋⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⣾⣿⡿⣻⣿⣧⡤⠤⠤⠴⠶⠖⠚⠛⠛⠛⠛⠛⠒⠒⣲⣶⣶⣿⡿⢿⣿⣿⣿⣿⣿⣷⠄⢠⣤
⠀⡁⢿⣿⣿⣿⣿⣿⣿⣌⠀⠀⠀⠀⣾⣙⣎⣳⣭⢯⣧⢿⣼⣱⣻⣄⠀⣼⣛⠛⠲⣼⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣠⣞⣧⣽⡾⣷⣾⣵⣯⣷⡤⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⣿⣸⢛⣿⣿⡉⠉⠉⠉⠉⠛⠒⠲⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠘⡄⠀⠉⢻⣿⡿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⡶⠞⢋⣩⠞⠋⠁⢀⣾⣿⣿⢿⣿⣻⠏⠃⡠⠔
⠀⠄⣹⣿⣿⣿⣿⣿⣿⣿⣮⡂⠀⠀⠿⣯⣝⣱⢎⠳⣌⠳⣌⠳⣍⣻⣾⠏⠈⡹⡆⢸⣿⣿⣿⣽⣻⣦⡀⠀⠀⠀⠉⠻⣟⡟⣰⢏⡳⢎⣶⠋⠀⠀⠀⠀⢀⣴⣿⣿⣯⣷⣿⣿⣿⠇⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢻⠉⠳⢤⠀⣿⣿⣇⣿⣿⣿⣿⡏⠛⠻⢿⣍⣉⣉⣉⣁⣠⡤⠖⠋⠀⠀⠀⣠⣿⣿⣻⡽⣿⣾⣁⣆⠮⢤⡶
⠀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣑⠄⠀⠈⠉⠉⠛⠉⠛⠉⢋⣭⣿⣯⣀⢀⣁⣿⢻⣿⣿⣿⣾⣽⣿⡿⣷⣤⣀⠀⠀⢨⢣⠯⣮⠵⠛⠁⠀⠀⣀⣤⣾⡿⣿⣽⣻⣿⣿⢿⣿⣿⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⣿⣿⣿⣟⠡⢉⠋⢁⠉⢳⣄⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⣀⣴⣾⢿⣻⠷⣯⣟⡷⣭⣇⣤⡰⢥⡴
⢀⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⢠⣐⣤⣽⣾⣿⣿⣿⠋⠀⠀⠈⢿⣿⣿⢿⣿⣿⣽⣻⡽⣯⢿⣿⣷⣾⣸⡒⣒⣒⣶⣶⡾⢿⡻⠯⠷⠛⠛⠉⠉⠀⠳⣼⣿⣿⠀⢸⠛⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢣⠀⠀⢹⣿⣿⡇⠂⠄⠈⠠⠀⣰⠟⡗⠀⠀⠀⠀⠀⠀⠀⡶⣿⣟⣯⣟⣯⢯⣟⡷⡾⣽⣳⢽⣺⡵⣶⠖
⠀⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⠲⣧⡿⢦⠑⡜⢨⢁⣿⠀⠈⡏⠀⠀⠀⣿⡆⡘⢢⠑⠌⢂⠡⢀⠐⠠⠐⣠⣿⣿⣿⡇⠸⡄⠀⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡛⢦⡀⠀⠘⡄⠀⢸⣿⣿⡏⢀⠈⡀⠁⣰⠏⢀⡇⠀⠀⠀⠀⠀⠀⠀⢷⠈⣷⢯⡾⣽⣳⠾⣽⣽⡳⢯⣳⣏⡾⣝⡊
⡘⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢸⣿⣿⠐⢀⠒⠄⠊⠄⠁⢂⡼⠒⢋⣳⠤⠤⢤⠇⢷⡀⠀⠈⠀⠂⠐⠀⠈⠀⠁⣼⢻⣿⣿⣇⠀⢇⠘⣀⣀⡀⣰⠁⠀⠀⠀⠀⠀⣴⣖⠻⣍⢦⡙⣮⢹⢲⡄⠱⠀⢸⣿⣿⡏⠀⡀⠄⢰⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢺⣯⣟⡷⢯⣟⡷⡾⣽⢯⣳⡽⣝⡳⠀
⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⢫⢭⣹⣧⣄⣦⣴⣤⣦⣄⣄⡻⣏⠝⣿⣿⣧⠀⠀⠀⢸⣿⣿⠀⠀⠀⠂⠁⣠⠞⢿⣠⠞⠛⣻⠆⢸⣻⡄⠈⢧⡀⡞⠻⣆⠀⠀⠀⠀⢠⡟⢸⣿⣿⣹⠀⢸⣷⣿⣿⡟⠁⠀⠀⠀⠀⢐⣴⠳⣌⠳⣌⠦⡹⣆⢇⠳⣺⣆⠡⡀⣿⣿⣏⠀⠄⢠⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⡾⣽⣻⢾⣽⣻⣭⣟⣧⢿⡝⡇⠁
⢾⣿⣿⣿⣿⣿⣿⣿⡿⣙⣎⣳⡾⣋⠷⣘⠖⡦⣓⢦⡙⢮⡝⣻⢻⣼⣿⣿⣆⠀⠀⢺⣿⣿⠀⠀⠀⢀⡾⠃⢀⣾⡥⠖⢛⣻⠠⢁⣿⡷⣶⢶⣾⣇⠠⢹⡆⠀⠀⠀⣾⠁⣼⣿⣿⠻⡇⠀⢿⠃⠁⠀⠀⠀⢀⣠⡴⠻⣌⠳⣌⠳⡌⠶⣑⢯⢎⠵⣢⢻⣶⠠⣿⣿⡧⠀⢂⡾⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢿⣳⢯⣟⡾⣵⣻⢮⣯⢟⡼⢁⠀
⣿⣿⣿⣿⣿⣿⣿⠯⣕⣣⣾⢳⡱⣍⠞⣥⢛⡴⣩⠖⡹⢦⡙⢦⠳⣌⡛⣿⣿⣧⣄⣻⣿⣿⠀⠀⢠⠟⠀⢰⣾⠋⠳⣶⣏⣡⣢⣥⣿⣻⢞⡽⣞⣿⡄⠀⢿⠀⠀⣰⠇⢰⣿⣿⣿⠀⢷⠀⠘⣆⠀⠀⢀⣠⠼⣧⣍⠳⣌⠳⣌⢳⣘⢣⡍⡞⣏⠶⣡⢋⣿⡔⣿⣿⡗⢠⡿⠁⠀⣈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠛⣟⡾⣽⣳⢯⣟⡾⢍⠀⢐⡰
⣿⣿⣿⣿⣿⣿⣋⢾⣱⣿⣮⡱⢚⡬⣙⢦⢫⡔⣣⠏⡵⢣⡝⣪⠳⣌⢳⣼⣿⣿⣿⣿⣿⣿⠀⢰⠏⡀⣼⣿⠃⠠⣵⣿⣻⢻⡽⣏⡷⣏⡿⡽⣾⡁⢷⡈⠘⢧⣴⠋⢀⡟⢸⣿⣿⠀⠸⣆⠀⠈⠙⠋⠉⠀⢀⣸⣦⣳⡼⣳⡘⡖⢬⣃⠞⣸⢹⡲⢡⢳⡘⣿⣿⣿⣟⠚⠁⠀⣐⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⢀⠈⠙⠳⢏⡟⠎⠑⠀⢀⣲⢽
⣿⣿⣿⣿⣿⠳⣌⣷⣿⣿⣿⣿⡷⣮⣕⣮⡱⢎⡵⢪⡕⣣⢞⣥⣫⣼⢟⣻⣿⣿⣿⣹⣿⣿⢀⡟⠀⣸⡿⠃⢀⣽⣿⣣⣟⢯⡷⢯⡽⡾⣝⣷⣻⡇⠈⢷⡀⠠⢀⣤⠟⠁⢸⣿⣿⡀⢆⠨⢓⠲⠖⠖⠒⠚⠉⠀⠉⠁⢀⣿⠱⢎⡣⡜⢎⡥⣋⠷⣭⠶⠛⣟⣿⣿⡧⠀⢂⣰⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣐⠀⡁⠀⠀⠐⢀⠸⣴⢯⣟
⠛⠛⣿⣿⢣⣛⣾⣿⣿⣿⣿⣿⡟⡴⢪⡜⡽⢫⡝⣣⢛⡭⣋⢾⣿⣿⡜⡼⢿⣿⠳⣼⣿⣿⢸⠃⢰⡟⠁⠠⣼⢳⣯⠷⣞⣻⣞⢯⣟⡽⡽⡶⢯⣷⠀⠀⠙⠛⠋⠁⠀⠀⢸⣿⣿⡘⣌⠣⢎⠔⡈⢆⢉⡐⠠⢁⠐⠀⣸⡟⡍⠶⣑⢎⡣⢖⡡⢏⣽⠀⠀⣿⣿⣿⣧⢐⡾⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⢞⣻⢶⡱⣖⣞⡾⣻⣽⣻⢾
⠀⠸⣼⢏⢧⣿⡏⡜⡩⢏⡛⣿⡝⣜⢣⠞⣜⢣⠞⣡⢏⠶⣩⣿⡟⢿⢿⣜⢣⢎⠳⣼⣿⣿⢹⡄⠊⢀⢐⡼⢣⣾⢯⢿⣹⠷⣞⣻⣼⢻⡽⣽⣛⡾⣇⠀⠐⠓⠦⠀⢀⣀⣸⣿⣿⡱⢊⡕⢪⢌⡑⢂⠂⠤⡁⠂⠌⣠⣿⡛⡜⣱⢊⠶⡑⢮⡑⠮⢼⡆⠀⢸⣿⣿⣧⠉⠤⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣟⢧⣯⢳⣏⣾⡹⣗⣯⡽⢯
⠀⠸⣾⣎⢻⣿⣷⢨⡑⢣⢜⣿⡜⣬⢣⡛⡬⢎⡝⢦⣋⠞⣥⣿⣏⠲⡌⡞⠻⡞⢻⣿⣿⣿⠈⠻⠶⠞⠋⢀⣿⢯⣯⣻⣭⢿⣹⢧⡟⣯⡽⣞⣭⡟⣿⣆⠀⠀⠀⠀⠂⠀⢹⣿⣿⡱⣃⢮⡑⢎⡔⡃⠎⡔⣨⠑⣌⣾⢏⠲⣉⢦⢋⠶⡙⠦⢭⡙⢦⣇⠀⠘⣿⣿⡧⠈⢄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣟⡼⣳⢞⡶⣫⢗⣮⢽⣻
⠀⠀⠹⢷⣧⢚⣿⣧⡌⢡⢊⣿⡘⢦⢣⡝⡜⣣⠞⣱⢪⢝⡲⣿⡇⡓⠸⡌⠓⡬⠑⢾⣿⣿⡤⣤⣄⢦⣴⣿⢯⣟⡶⣻⡼⣏⣟⡾⣽⡳⢯⣻⣼⢻⣵⣻⣷⣤⣦⢴⡰⣆⣾⣿⣿⡳⣍⢖⡩⢖⡸⢌⠳⣘⠤⣓⣾⠏⣎⡱⢍⠦⣋⠼⣩⡙⢦⡙⢦⣹⠀⠀⣿⣿⣟⢈⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢼⡳⣏⢷⣫⢟⡼⣣⢟
⠀⠀⠀⣍⠻⣧⣚⡽⣿⣄⠢⣟⡜⣣⢳⢸⡱⣃⠻⣔⣋⠞⡴⢿⣽⡈⠱⣈⠣⢐⠩⣼⣿⣿⠉⠉⣹⣿⣿⣿⣷⣾⣽⣳⣽⣫⣾⡽⣶⣻⢯⣷⣭⣿⣶⣿⣿⣿⣿⡍⠉⠉⢹⣿⣿⡵⣊⢮⡱⢫⣔⢫⢞⣥⡷⠿⠿⠾⠶⠵⠮⣶⣍⣶⣡⣎⣥⣙⣦⣽⠤⠀⣿⣿⣯⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠙⢌⠃⡉⢊⠡⢉⠈
⠀⠀⠈⠀⠁⠁⠙⢶⣭⣻⡷⢿⣬⡑⢧⢣⡓⣭⠳⡜⣬⢛⠼⣹⣏⠛⠓⠀⠈⠉⠉⢹⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣷⣽⡶⣯⣷⣾⣿⣿⣿⣶⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣄⣢⣄⡥⢢⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣯⣽⠞⠻⣿⡌⢧⡹⣔⢫⡜⣆⢏⡞⡥⣛⣆⠀⠀⠀⠀⠀⠸⣿⣿⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⢸⣿⣿⣿⣟⣿⣏⣿⣿⣻⣞⣷⣻⢾⡽⣯⣟⡿⣿⣷⣾⣿⣿⣿⣶⣶⣶⣶⣿⢿⣿⣿⡇⠀⢀⣤⠶⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠦⣄⠀⠙⣿⣷⢿⣻⣿⢾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⣤⣿⣽⡏⢶⡱⢎⡣⢞⡜⣜⢲⡱⢣⡾⣷⣄⡀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢾⣷⣹⣿⣞⣷⣻⢾⡽⣯⣟⡷⣯⣟⣷⣿⣟⣯⢷⣻⣞⣷⣻⢾⡽⣯⣿⣿⣇⡴⠋⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠳⣆⢘⣯⣿⣟⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⢛⡝⢦⡓⣭⢚⡵⢚⡬⢣⡝⢣⠞⡴⣩⢝⡳⢦⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣷⣻⢾⡽⣯⣟⡷⣯⣟⣷⣻⣾⣟⡾⣽⢯⣷⣻⢾⡽⣯⣟⡷⣿⣿⡟⠁⠀⠂⠁⠀⠁⠀⠄⠀⠉⠳⠶⠶⠖⠋⠁⠀⠀⠀⠈⠀⠁⠂⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⡜⣣⠞⡴⢋⡴⢫⡜⣣⠞⣥⣛⣴⣣⣎⣵⣣⣽⣿⣿⣦⢖⡦⢶⡴⣲⣒⣖⣲⣒⢦⣒⢦⣒⢦⢲⡰⢆⡲⣔⢢⡲⣔⡲⣔⢦⡖⢶⣺⣿⣿⣿⢿⣳⣿⣳⢯⡿⣽⣳⢯⣟⣷⣻⣞⡷⣿⣯⢿⣽⣻⢶⣯⢿⣽⣳⢯⣟⣿⣿⡇⠀⠠⠐⠀⠀⠐⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⠥⣛⡜⣩⣼⢷⣾⣷⣿⣿⣍⠙⠛⠿⣿⣿⣿⣿⣿⠛⠞⠹⠓⠛⠳⠙⠚⠣⠛⠚⠙⠚⠙⠚⠓⠛⠋⠓⠋⠓⠛⠚⠓⠙⠚⠘⠃⢻⣿⣿⣟⡿⣯⣿⡽⣯⣟⡷⣯⣟⡾⣷⣿⠿⡛⣿⣯⣟⡾⣽⣻⣞⡿⣾⣽⣿⠟⣻⣿⡇⠀⠠⠀⠀⠠⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠖⠋⠁⠀⠀⠈⠙⠿⣿⣿⣧⠀⠀⠈⢿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢯⡿⣽⡿⣽⣟⡾⣽⣳⢯⣟⣿⠁⠑⠃⢻⣷⢯⣟⣷⣻⢾⣽⣳⣿⡋⢤⣿⣿⡇⠀⠂⠀⠄⠀⠄⠀⠀⠄⣸⡇⠀⠁⠠⢀⡐⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⢿⣽⣿⣳⢯⣟⡷⣯⣟⣾⣿⠀⡄⡀⢸⣿⣻⣞⡷⣯⣟⣾⣳⣿⡄⠁⣹⣿⡇⠀⠌⠀⠀⠀⠀⠀⠂⠀⣏⠀⠀⠀⢀⠀⢹⠆⠠⠀⠂⠄⠁⠀⠂⠁⢈⠀⢸⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣐⣀⣄⣂⣤⣡⣀⣌⣐⣿⣿⣿⣀⣐⣈⣿⣿⣿⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⠀⠀⣀⠀⢸⣿⣿⢯⣟⢾⣷⣯⣿⣾⣽⣳⣟⣾⣏⣖⣡⣒⣍⣿⣷⣯⣟⣷⣻⣞⣷⣻⣇⣀⣿⣿⣇⣀⣠⣀⣀⣁⣀⣀⣀⣀⣯⢀⣀⣁⣀⣀⣸⣇⣀⣀⣠⣀⣀⣀⣠⣀⣀⣀⣘⣯⣟⣼⣳
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