⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡻⣟⣦⢘⠐⠆⣃⠎⡐⣀⣆⣌⣐⣂⠡⢒⠌⣔⠰⠢⠥⢂⠍⡛⣿⣿⣿⣿⡿⣷⣳⡐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠤⡱⢈⢛⣷⣬⣾⠾⣿⣽⣭⢏⡻⡽⣫⡟⣿⢲⣦⣵⣡⣃⢂⠜⣀⡆⡈⠿⢷⣿⣿⡟⡇⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢦⠚⡱⢂⣧⣞⣟⣎⡓⣁⠝⡲⡥⠨⠙⠣⢅⡰⢁⠠⢈⠁⠪⡙⢯⢷⣮⣁⡰⠸⠄⠂⢍⢻⠿⢯⠜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠎⢂⡰⣇⡿⣊⢶⡱⢮⡱⢋⡎⡕⡨⣕⡃⠶⣄⠩⣀⠑⡎⠂⢄⠈⢂⠑⠠⣻⢷⣔⡨⢡⣐⣉⠀⠀⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠘⢴⣚⡾⡽⣍⡳⢶⢣⠞⣱⡘⠴⡑⢒⣫⢖⢙⡳⣄⠑⠌⠆⠀⠑⠄⠡⠩⢚⢮⢟⣷⣌⢡⠴⡘⢃⠒⠄⡊⡄⠀⠀⠀
⠀⠀⠀⠀⠀⢘⡾⢣⣽⡽⣣⠟⣼⠠⣓⢺⢡⢎⡱⣉⠖⣌⡎⠥⡠⣂⠫⠌⣊⡑⠀⠀⢆⢅⠡⣂⠈⠹⢻⠧⡎⢩⠵⡸⣨⣿⣦⡐⠀⠀
⠀⠀⠀⠀⢀⡾⣑⢳⢆⡿⡜⣏⠰⡰⡍⢞⡌⢦⠓⡔⢪⢩⢸⡔⢱⣨⣜⡶⡤⠋⡔⣠⢠⢀⡀⠊⡞⡙⢚⢯⣷⡡⠩⣅⢍⣿⣿⣟⡆⠀
⠀⠀⠀⠀⣼⢣⢌⡟⣴⠚⡵⣇⡨⢅⠮⢹⠈⠧⡙⣌⢢⡀⡝⠹⡴⢮⢇⠢⠵⣌⢰⢀⠸⢩⡇⠀⠐⣪⠒⣶⢮⣷⠑⡲⢕⠚⡟⠁⠀⠀
⠀⠀⠀⢰⣋⡾⢌⠳⢌⠳⣌⡷⠟⡺⡜⡥⢟⠲⣍⠶⣙⡶⣏⠀⠘⣆⣭⠫⣓⢭⢊⡶⢻⢦⢁⠉⠄⠡⣿⣭⡷⣞⣏⠰⢎⠪⢹⠀⠀⠀
⠀⠀⠀⡯⣗⡏⣌⠳⣸⢿⡰⡇⠞⢧⢛⣜⡹⢆⡹⣜⣱⣎⢟⠊⠁⠈⠎⣝⢹⣱⢇⡚⣱⠮⡬⢠⡀⠂⠹⡿⣟⢯⣿⠐⢀⢃⢻⠅⠀⠀
⠀⠀⢸⡅⢺⢧⡏⢆⣻⣎⡗⡇⠈⠹⣎⡶⢬⡣⠳⢵⣚⢣⢸⣀⠀⠤⣀⣀⡧⡑⣯⡜⡵⣎⡵⢺⢋⢦⣀⠀⡻⢯⣛⢆⢈⠰⢺⠀⠀⠀
⠀⠀⣼⢀⣹⣻⣷⢺⢰⡿⢞⣷⠀⠈⠽⣜⡧⢞⡞⣋⠷⠘⠄⣰⡾⣿⣿⣿⠿⢿⢶⣭⣺⣱⡞⡽⡘⣮⣉⢯⣷⢻⣏⡖⠡⢈⢾⡄⠀⠀
⠀⠀⡏⢸⣞⡧⣟⡞⣏⣽⠹⡤⠄⠀⠀⠘⢝⠊⠘⠁⠁⠀⠀⠊⠀⡟⠻⣿⡿⣟⢀⠟⢾⡜⣾⡵⡜⠼⡽⡖⣞⣿⡇⡇⠘⢦⡧⠁⠀⠀
⠀⠀⡷⡋⢸⣽⡺⣽⡞⣭⡄⠙⣀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠉⠡⠫⠄⠀⠀⠩⠒⠟⣛⣦⣉⣛⣽⢼⡇⡣⢡⢿⢁⠀⠀⠀
⠀⠈⢧⠑⢌⢷⡻⣜⢿⣖⣻⢆⢄⣴⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⠨⠄⣪⡮⣿⣚⡾⣷⢧⣹⣺⠐⠀⠀⠀
⠀⠀⠘⡄⠀⠉⣿⡼⣧⢻⡽⡯⢯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣡⠼⢦⣶⣿⡿⣍⢳⡹⣟⣯⣿⡇⠔⠀⠀⠀
⠀⠀⠀⠘⢄⢰⠃⢙⣏⢷⣳⠷⣒⡂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⣠⠕⢫⢐⢎⢸⣿⣳⢏⣞⡵⢛⠻⣿⡇⢰⠀⠀⠀
⠀⠀⠀⠀⢠⠋⠛⣹⡛⣿⢯⠋⢃⡉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢀⢴⢃⢄⠨⠛⠉⢸⣳⣱⣚⡆⢣⣉⡄⠈⠣⠀⠀⠀⠀
⠀⠀⠀⢠⠃⠀⢠⣟⡇⢯⣯⠃⠠⢕⡼⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢁⢸⠦⠀⠢⠔⡀⢈⢻⣭⣇⢺⠅⡤⢐⡀⠀⠄⠀⠀⠀
⠀⠀⠠⠇⠀⢀⡿⣽⣆⢫⠂⢆⡉⢊⠀⠀⡀⠈⠀⠂⠄⢀⠀⠀⡀⢔⣌⢀⠀⠮⠙⠳⢂⠀⢁⠀⠔⠉⢙⣲⠖⢻⠜⠄⠐⡈⠀⠀⠀⠀
⠀⠠⠍⠀⢀⢮⠿⠇⢈⠃⠰⢀⢑⡭⠂⠘⡡⠂⠀⢡⠆⠐⣰⡽⠈⠋⠀⠀⡄⠀⠀⠀⠘⠀⠈⠁⡠⣘⠅⡒⠝⢗⠛⢊⣆⠐⡀⠀⠀⠀
⢠⡙⠀⢀⢎⣞⡏⢘⠁⡀⡆⣬⣏⡀⢀⠏⠀⠀⠀⡜⠀⡘⠉⠉⠈⠈⠀⠀⠄⠀⢀⣀⠀⠀⠀⡪⡪⠀⠈⠀⠀⠀⠐⠀⡚⡂⠂⠄⠀⠀
⠥⠀⢠⣃⣟⡒⠄⠅⠠⡐⢀⠂⢺⡕⠒⣸⠀⢀⡈⠩⢄⠀⠀⠁⠀⠀⠒⠂⠀⠀⠁⠀⢘⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠷⡁⡢⠀
⠂⣰⢅⣾⠂⠜⠌⢀⣩⠙⠄⠂⠀⠀⠉⡜⠈⠀⠀⠀⠴⣿⣷⣄⡀⠀⣀⣀⠀⡀⠄⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠥⠈⠌⢀
⠈⢰⡿⠁⢌⡊⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⡠⠊⠀⠐⠀⠈⢻⣿⡳⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠈⡄