⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠋⠀⡼⢿⣿⡰⡚⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡫⠉⠁⠈⢻⣿⣜⡄⠱⡄⠀⠖⠄⡀⠀⠀⠀⢀⣀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠖⠀⢀⡀⡈⠻⠷⠾⣐⠛⡒⡄⠀⠈⡆⢀⣾⣿⡿⠟⠋⠁⠈⢽⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠔⠈⠁⡀⠀⠀⠀⠀⠠⢑⢠⣃⢘⡤⣹⣿⣿⣿⡁⠠⡄⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠁⢀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠋⠉⠐⠄⡛⠛⢿⠀⠀⠐⠓⠠⡄⢎⣙⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⠀⠀⠠⠂⠀⠀⠀⠀⢠⢞⡜⣠⣄⠀⠀⠀⠀⠌⠀⠀⠑⡀⠀⠀⢶⣡⣿⢿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡠⠀⠀⢠⠂⠀⠀⠀⠀⢠⠃⠄⡘⠋⢳⠀⠀⠀⠀⠀⡀⠈⡀⠈⡀⢠⡟⣿⠋⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠔⢁⠲⠁⠀⠀⡌⠀⠀⠀⠀⠰⡙⢀⠂⠄⡡⢸⠀⢰⠀⠀⠀⢡⠀⠰⠀⠈⡟⢻⡿⢧⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⢰⠀⠎⣇⠃⠀⠰⡇⠀⠀⠀⠀⡌⡇⠠⢁⠊⠄⡎⢀⠎⠀⠀⠀⢰⠀⠀⠂⠈⣵⠋⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠠⣬⠺⣁⣒⡲⠋⢠⣴⣯⣧⠀⡄⠀⡆⣧⠣⠔⢦⡨⢞⠐⡝⠀⠀⠀⡄⢣⠀⠀⠀⣀⣯⠀⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡇⠀⣜⣲⢻⣿⣷⣮⡠⠐⠞⣙⣿⡟⢻⣧⡇⠀⠧⣃⢻⢼⣦⣴⣭⣝⣧⠀⠀⠀⢣⠸⠀⠀⠀⢸⠛⢥⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢲⠁⡸⣉⠷⠂⣽⣿⣿⣏⡦⢫⠏⠭⣿⠦⡯⢏⠢⢜⣬⠻⣏⢿⢻⣿⣻⡿⡙⣆⠀⠀⠢⢣⣀⣴⢸⠀⠀⠙⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠡⠁⠄⠂⠄⢳⣿⣿⣿⡾⡎⣿⣿⣿⣿⣷⠡⢊⠔⣠⣂⡬⠽⢿⠿⠿⢛⢫⠙⠀⠒⠂⠲⡒⢁⢸⠀⢰⠀⡅⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⢁⢊⡐⠉⣠⠞⡏⢟⣎⣷⡜⡽⣿⣿⣿⣿⢧⣵⡾⠛⠧⠺⠊⢀⠠⢆⡐⠁⡀⠀⠀⡠⡷⠠⡘⡸⠀⡊⡄⠰⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡁⠆⠂⢤⠚⠁⠌⡇⣸⠏⡌⠀⡏⢻⣿⣟⡻⣿⣭⠀⣁⠊⠄⡉⠳⣂⣉⣰⠀⠀⢀⠔⢡⠀⡰⢡⠁⠆⢠⡁⠂⠣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠌⣁⠢⠌⠡⠸⡳⠃⡜⡆⠀⠁⠈⠅⢯⠽⣻⢿⠃⠄⠨⠐⠄⣆⣀⣀⡤⢠⡲⠁⠀⡇⠚⠊⠄⠀⠈⠠⡄⠱⠈⠣⠤⡀⠀⣀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡔⢀⠢⠌⢁⣰⠐⡅⢰⡃⠀⢃⠀⠱⡀⣣⡘⠋⠐⡈⢁⠊⣄⣤⡼⢑⣪⡱⠀⠀⢀⠀⠀⠀⠱⡀⠀⠀⠈⠣⠔⣀⠀⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⡀⢂⠰⠈⡴⠣⠄⢳⡀⠻⣂⡈⢆⠀⡀⢗⡓⡖⠓⡖⣣⢙⡴⢋⠴⠋⠀⢢⠀⠄⡐⡀⠀⡀⠄⠱⡄⢂⠠⠀⡐⠀⠑⠂⢄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢺⣷⡾⢷⣀⡾⣦⡀⠀⡔⠂⣅⠦⣈⢑⢎⡂⠐⡄⢻⡜⡤⠗⢤⢏⠔⠋⠠⠀⠂⠘⡄⠂⢄⢣⠐⠠⢈⠐⡈⠒⣄⡡⠐⣈⠣⡌⢀⠱⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⣀⣿⡗⢀⣾⠏⢸⢏⡑⡁⢴⡲⡗⢩⢐⡜⡑⣮⠓⣌⢢⢹⢾⢁⣛⠒⢠⣡⡗⡲⠓⡬⢙⣆⠘⢆⡓⢢⡡⢌⠰⡁⢆⡹⡱⢒⠢⣝⡄⡘⡗⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠷⠚⠋⠷⠛⢾⣴⣟⠎⠐⠒⠩⣫⣜⡩⣓⣬⡲⣃⠽⣎⢇⣻⣜⠢⠼⡩⢼⢠⠳⣅⡫⠔⣃⢫⡳⣆⡕⢦⡌⠳⢥⣙⢢⢒⡯⣌⢳⡰⣩⠖⡎
⠀⠀⠀⠀⡎⠈⢐⠏⠀⠄⠠⢀⠘⣠⣴⠁⠒⠒⠂⠀⠈⢉⡩⣍⠯⡱⢬⣚⣱⡟⢋⠔⣃⠒⡙⣜⡦⢑⢢⣉⠓⢦⢂⡕⢷⡸⣉⠞⣏⢖⡱⣍⡾⡱⢎⡥⢃⡯⣹⢘
⠀⠀⠀⠸⠀⠸⢽⣀⣐⣬⣶⠶⠛⢋⠁⠀⠀⠀⢀⡤⣞⢧⢳⣌⣳⣙⣦⠷⠋⠴⣈⡒⣤⠷⣫⢕⣣⣏⡶⡜⣍⡾⠡⢎⡰⢧⡙⡞⣜⡧⣚⢼⢣⡓⣭⣘⢏⢶⣡⠏⠀
⠀⠀⠀⠰⢐⠁⠂⣽⠁⠤⢀⠂⡁⡞⡠⠀⠒⠁⡞⢸⣟⣮⡻⣎⢸⣎⣀⡦⠈⢄⠉⡐⢯⣞⣫⠛⠚⣻⠾⠿⠮⢌⣱⣢⣵⣘⣧⣽⣞⣲⡭⢞⢣⠗⠚⠃⠉⠀⠀⠀⠀
⠀⠀⢀⣰⠃⢈⢸⡟⢀⠂⣁⠒⢠⢁⠠⠠⠐⡨⣯⣁⣬⠙⠋⡚⣟⠛⠉⠠⢁⢂⠰⠀⠌⠳⣧⠐⣸⡡⠤⠒⠊⠁⠁⠀⠀⠀⠈⢳⠬⡗⡜⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠆⡈⠄⢴⡷⢀⠒⠠⢈⢸⠀⠀⣤⠾⢁⣊⠉⠡⠒⢥⡲⠉⣽⠧⠢⠤⠦⠴⠬⠴⠶⠉⠉⠉⠷⣀⣀⡄⢀⠄⠒⢈⠉⠁⠒⡿⠯⢀⠈⠉⠶⠚⠀⠀⡀⠀⠀⠀
⠀⠀⡌⠐⡠⠐⡈⠄⢂⠌⡐⢠⡼⠔⠋⠉⡉⠀⠄⢂⠡⠈⠂⢗⠛⠡⡐⠀⠒⠀⠄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠡⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⠀⠒⠀⢀⡜⡃⠀⠀⠀
⠀⢨⠀⠌⠠⢁⠂⠌⣀⠶⠚⢉⢀⠂⡁⢂⠀⢈⠐⣀⠦⠋⠡⠀⡐⢀⠙⢎⠑⢄⠀⠀⠀⠀⠀⡎⠀⡰⠍⠐⡀⡅⠀⠀⠀⠈⡀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠈⠑⠠⠀⡀
⠀⡀⠌⠠⢁⠂⢌⡼⠉⠑⢄⠂⠄⠒⡀⠂⠌⡠⠞⠁⡄⠁⠂⠀⠄⢂⠂⡄⠑⡄⠑⠄⠀⠀⠀⠇⣬⠞⠁⢘⠀⡅⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠈
⠀⠃⠌⠐⡄⢨⠟⠀⠀⠀⠈⠳⡈⡐⠠⢡⠞⢁⠈⡐⠠⢁⠂⢉⠰⢈⠰⢀⠡⠈⠣⡈⠀⠀⠀⡶⠋⠀⠀⡌⠀⡇⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀
⢀⠈⠄⠱⢠⠏⠀⠀⠀⠀⠀⠀⢱⣀⡱⢃⣀⠆⠴⠒⠃⠈⠉⠈⠀⠐⠒⠢⠄⠅⣀⡙⢄⢀⠼⠁⠀⠀⢰⠁⠀⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀