⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⢀⠂⣀⣤⢲⡰⣍⠯⡜⣥⠫⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡤⣞⠻⡜⢧⡓⡞⢮⡱⢆⡻⠴⣩⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⢀⡿⢞⡻⣙⢏⣿⣹⢳⠻⣬⣣⠝⣆⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠐⠀⠀⠠⣝⡟⣬⠱⣍⠶⡸⣿⣡⢛⡴⣩⢛⣎⢳⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡆⠀⠀⠀⢀⡆⠀⡿⡔⣿⢰⣋⠶⣉⠗⣷⢣⡍⠶⣡⢏⡼⢧⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢣⠀⠀⠀⠀⣧⠀⡷⡹⢼⡣⡜⣎⠵⣋⣿⢣⡚⠵⣃⠞⡴⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠂⠀⠀⠀⠘⣆⠰⡙⣎⢷⡱⢎⡵⣹⢺⡣⣍⢳⡩⢞⡱⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠲⣭⠲⣍⢷⡍⣖⡯⣟⡱⢪⡕⢎⡣⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡘⢦⣝⡾⣜⢣⡕⣣⠞⣡⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡝⢦⡙⢶⡸⡹⣌⢳⣹⡶⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⢹⢢⡝⢦⡓⡵⢊⢧⡒⣿⡍⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⢧⢚⡥⣚⢥⣋⠶⡹⢼⡟⣔⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⡂⠀⡇⠀⢘⡀⠀⠀⠀⠀⠈⢯⡦⡐⣫⠴⣩⠖⣬⢓⡹⢺⣽⣌⢳⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠸⡇⠆⠀⠀⠀⢘⠇⠀⡇⠀⢸⢦⠀⠀⠀⢀⠀⠈⢳⣡⢥⣛⢤⡛⣤⢫⢜⣻⣼⢎⡵⢊⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡐⠀⠀⠀⠀⠀⡐⠐⡇⢁⠀⠀⠀⢯⢞⢰⡅⠀⠀⣎⡆⠀⠀⠈⣆⡀⠀⢣⢫⡜⢦⡹⠴⣩⠞⣼⡹⢎⠶⣩⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠁⠀⢀⠁⡀⢠⣦⣄⢡⠸⠀⠀⠀⡏⣎⠟⡎⢄⠀⢱⡗⣤⡀⠀⠐⡎⠦⡀⠳⣊⠗⣜⢣⡓⢮⡗⡿⣌⠳⣥⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠀⠀⡈⠰⡅⣼⡜⣿⠀⢂⢃⠀⠀⢳⡜⡭⡗⠊⠢⠀⢻⠈⠺⡤⢄⠩⡳⢥⣒⢝⣞⡬⣓⡜⣿⣸⠳⣌⠳⣌⢻⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⢀⠀⠀⡅⡛⣄⣻⡜⣹⡄⠘⡣⣆⠀⣹⢺⡵⡇⠀⠄⢂⣩⣧⣤⣽⣣⣻⠜⡦⢻⡶⣋⡟⡴⡯⠒⢏⡳⣌⠳⣌⡿⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡎⣸⠀⠀⣷⡱⢾⣹⣎⣵⡴⡀⠱⣭⢢⢣⢣⡟⢯⢺⡾⠛⣹⣿⣿⡛⠫⠙⠸⢻⠳⣞⢳⡜⣳⢠⠖⠈⢷⢌⡳⢼⠧⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⡎⠄⠀⢹⡱⢣⢾⠹⡱⡇⣘⣄⠡⡓⣎⠧⣺⠈⠋⠀⠀⣿⡹⣿⡷⠀⠆⠀⠸⣋⢖⡣⢞⣹⡞⠠⠀⡸⡎⣵⡟⣺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⡇⢣⠀⠨⣕⢫⡜⡄⢙⣷⣶⣶⡵⠛⠼⠗⠓⠃⠀⠀⠀⠻⡘⠆⠀⡠⠋⠀⡀⣎⠞⣬⢓⠾⠱⠃⡔⡸⣜⠾⣱⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠁⠀⢃⠈⣭⢖⠻⡗⠿⠋⣿⢿⡏⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠉⠀⠂⠄⡇⢉⠞⡴⣋⡇⠀⣩⢟⡱⣋⢷⡝⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣇⠀⠀⠉⠨⠪⢷⣽⣧⠀⢣⡜⠛⢰⠄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⢢⠀⢘⢮⣱⢺⣰⠾⠙⠊⠉⠉⠍⠉⡁⠀⠒⠂⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⡧⢎⡳⡄⠀⠁⠔⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠀⢸⡇⢮⡍⡁⠀⠀⠀⠀⠀⡠⠂⠀⠈⡰⠀⢀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢙⡬⢓⡵⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢸⣼⠳⡁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⢎⠳⡜⡇⢀⠔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠵⠇⠀⠀⢸⡻⠃⠈⠂⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⠘⡧⡹⢜⡦⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡴⢣⠎⠀⠀⢀⠟⠁⠀⠀⠀⡑⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢠⠐⠝⡎⣇⠈⠲⢀⠀⠀⠀⠀⠀⠀⢠⠎⡠⠃⠀⠀⡠⠃⠀⠀⠀⠀⠌⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢂⠈⢵⢺⠀⠀⠀⢨⠆⢄⡀⡀⠰⠃⠊⠀⠀⡠⠊⠀⠀⠀⠀⢀⠂⠀⢀⠈⠈⠄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠣⡀⠩⣧⠀⢰⠣⢀⠃⣠⠋⠐⡖⠒⠂⠁⠀⠀⠀⠀⠀⢀⠂⠀⢀⠂⠀⠀⠈⢀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠐⡚⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠑⠄⠘⢔⠁⠀⢊⠜⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠀⠀⠀⠂⠀⠀⢀⠠⠀⠀⠀⠈⠢⠀⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢑⠬⠢⣀⡟⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠄⠀⠀⠀⠀⠀⣀⠄⠃⠉⠁⠀⢀⠀⠀⠀⡀⢀⠗⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠁⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡐⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠐⠄⡠⠚⠀⢀⠀⠅⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠰⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⢀⠴⠁⠈⠢⡀⠀⠁⠈⠄⢂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⡘⠀⠀⠀⠈⡈⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⡇⢊⠄⠀⠀⠀⠀⠀⠀⢀⠠⠊⠔⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠐⡰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢲⠀⠀⠐⠃⠀⠀⠑⠂⠀⠀⡐⠐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢂⠀⢠⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡌⠀⠠⠁⠀⠀⠀⠀⠀⡠⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠌⠀⠀⠌⠀⠀⠀⠀⠡⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⠀⢀⠂⠐⢄⠀⠀⠀⠌⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠌⠀⠀⠌⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⠔⠀⠀⠀⠀⠠⠌⠀⢀⠃⠀⠀⠀⠀⠀⠀⣤⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠌⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠇⠸⠀⠀⠈⠢⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢰⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⢀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠃⠀⡌⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠔⡞⠀⠀⠀⡐⠀⠀⡈⠀⠀⢀⠀⠀⠁⠂⡼⡀⡐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⠀⠐⠄⠀⢠⠁⠀⠰⠀⠀⠀⠀⠈⠐⠠⢀⡆⢠⠑⠄⠀⠀⠀⠀⡀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠀⢁⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⠁⡎⢀⠀⠀⠢⡀⠄⠀⠀⠈⠀�