⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣯⢉⠀⠤⢣⡌⠀⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⠒⢰⠉⣭⠀⠘⠀⠎⠀⠩⠋⢰⠒⠴⢐⢡⠠⡓⠆⢁⠀⡠⡃⡠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢲⡉⠘⢀⡏⣤⡄⠶⣾⠀⠄⢀⢃⢴⡖⢀⡬⣆⢀⠀⢨⡲⢄⡴⡅⡤⣈⢪⠕⠉⡔⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢹⣸⡷⢼⢃⣙⡴⢾⠖⡳⠒⠙⠋⢽⢿⣶⣶⣵⣉⠘⠱⣺⣃⠃⠑⣤⡪⠊⡵⠘⣳⠔⢥⣒⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡿⡳⣁⠔⠊⠉⡠⡪⠁⠀⠇⠀⠀⠀⠀⢒⢄⠈⠉⠛⠿⣾⣉⡘⡢⣆⢉⢆⠀⢑⠧⠒⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣋⠶⡪⠀⠀⢠⠊⡰⠁⠀⣰⠀⠀⠀⠀⢀⠈⡄⢢⠐⢄⠀⠈⠙⢶⡎⢒⡌⢀⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣶⡷⠡⠊⠀⠀⡴⡣⠀⠇⠀⠦⠻⠀⡆⠠⠄⠀⢁⠰⠀⠣⢠⠥⠀⠀⠀⠙⢷⣯⢞⢡⣃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⣛⡟⡐⠁⠀⠀⠝⠈⢀⢠⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⡄⠀⢆⠊⠱⠀⠀⠀⠈⢷⢯⠦⠹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠊⡬⡝⡐⠀⠀⠀⠌⠀⢀⠂⡀⠀⠀⠀⠀⠘⡘⡀⠀⠀⠀⠀⡇⠀⠈⡀⠀⢃⠀⠀⠀⢊⢳⠿⡝⠰⣢⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠝⠀⣰⠳⠰⠀⠀⠀⡘⠀⠀⡌⠀⡇⠀⠀⠀⠀⠀⠱⡡⠀⠀⠀⠀⡧⠀⠀⠁⠀⠈⡀⠀⠀⠈⡈⢿⣿⡑⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣄⡔⣷⠃⠇⠀⠀⢀⠁⠀⢠⠀⡘⡇⢠⠀⠀⠀⠀⠀⠀⢥⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡑⠁⣈⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⢿⡟⢰⠀⠀⠀⠘⠀⠀⡄⢠⠃⠇⢸⠀⠀⠀⠀⠀⠀⠀⠈⢸⣀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠿⡀⡸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⢉⠃⢀⠀⠀⠀⠀⠀⢰⡇⡄⠀⢠⢠⡆⠀⡄⠀⠀⠀⠀⢰⢸⠸⠀⢧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⢳⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⣿⠸⢸⠀⠀⠀⠀⢀⠸⢠⠐⠒⠚⢺⢲⠀⠳⠀⠀⢠⠀⢘⡠⡦⢤⣈⣄⠀⡇⠀⠀⠀⠀⠀⢀⠀⢸⠈⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠍⢸⢰⠸⠀⠀⠀⠀⠀⠇⣀⣀⡀⠀⢻⠀⠆⢠⢃⠀⢸⡀⢀⠃⠀⠀⠀⢡⡎⣷⠀⡄⠀⠀⠀⢸⡸⢸⡄⠘⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⠏⠀⣼⢸⠀⡄⠀⠀⢸⢸⠿⣿⣿⣿⣿⣾⡆⠈⢜⠀⠢⠈⢡⣼⣸⣤⣶⣶⣦⣿⡇⡄⠃⠀⠀⠀⠨⡅⢸⣿⣆⢃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣸⣿⢸⡆⠰⠀⢀⠈⡆⠀⣟⣀⣓⠫⠇⠁⠀⠀⠃⠀⠀⠃⠘⠫⡟⢕⡟⢻⡏⠻⣿⠀⠀⠀⠀⡷⠀⣸⡿⢿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠉⡈⠑⡀⡧⡀⢂⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠓⠈⡌⠀⠀⠀⢰⢁⢀⢻⡇⠘⢿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠣⡇⠀⠱⣸⢝⢌⢍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢰⠁⠀⠀⠀⣦⡾⡌⢸⠃⣀⡄⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡒⠘⢄⠀⠐⢶⡀⣿⠪⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⢿⣿⣄⠞⢺⠁⠐⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢇⠠⠆⡗⢋⡷⠀⠇⠀⠀⢀⡈⠋⠡⠀⠉⠡⠖⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢠⡇⢈⢹⣷⠤⢒⡁⢣⢡⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠘⣜⠢⡨⠁⡘⢄⢀⡴⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠹⠀⠀⠀⡎⡇⢸⢫⠃⢰⠘⡟⢿⣷⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⡌⡲⠁⣰⡠⠔⢉⡴⣃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⠁⠀⢠⠀⠀⢠⠁⠙⡀⣗⡉⠄⡄⢹⡨⢫⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡐⡨⢁⡠⢋⣠⠶⠋⠁⠀⠉⠂⠤⠀⠤⠔⠒⠉⢸⠀⠀⠀⠀⠘⠀⠘⢸⠀⠀⢡⠻⡟⢾⡅⠀⠑⠠⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠡⢪⣾⠟⣫⣴⣿⠁⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⢀⡠⢼⠀⠀⠀⠀⠀⢃⠑⢻⠀⠀⢸⣶⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠁⢠⠟⢁⡴⠋⠀⠀⠀⠈⠉⠉⣾⡰⠉⡟⠍⠙⠉⢄⣧⢾⠑⡄⠀⠀⠀⠈⠄⠈⡄⠀⡸⢸⠐⠼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠜⠁⡠⠋⢀⠔⠋⠻⠫⢉⠹⣿⣷⣈⡭⢥⡲⡯⢭⣁⣀⠨⠁⢸⠒⢄⠀⠀⠘⡄⠰⣰⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢰⡋⠀⠀⠀⠀⠀⢀⣦⣧⣂⠄⣹⣿⣿⠑⠢⣔⠒⡢⠐⠈⠀⠀⠀⠸⠀⠀⠉⠒⢠⣐⡀⠐⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠖⠀⠀⠙⢆⠀⠀⢀⣴⣿⡿⠛⢋⠇⢸⠘⠛⣠⠞⣼⣎⡡⣷⡀⠀⠀⠀⡆⠀⠀⠀⢀⡾⢀⠻⡀⠙⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⢣⠀⠀⠀⠀⢸⣀⣤⣾⣿⡿⠁⠑⢆⠐⠗⡤⠊⡟⡭⠃⡇⠩⡉⣉⠢⡠⢪⠀⠀⠀⢠⡞⢁⠆⠄⡇⠀⠡⠐⠌⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠩⠵⡤⡀⢄⣼⣿⠿⢋⣘⠎⠀⢀⠔⠀⠰⡇⢆⠂⠬⣢⣇⡊⠄⡢⠌⠁⠆⠀⠀⣠⠏⡠⣇⠌⠀⡇⠀⠀⠂⠐⠸⡀