⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡞⠀⢀⡠⠤⠔⢒⣒⣒⣓⡶⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡒⢦⡍⣳⠱⡜⣢⠳⡜⣢⠳⢬⢍⡫⢝⡲⠶⢤⣇⠀⢀⣠⠗⣈⠄⠀⣀⣈⣡⣈⣉⢓⡂⠄⣀⠀⠀⠀⠀
⠤⣀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⡔⣢⠳⡜⢣⠞⣡⠞⣡⢳⠱⣃⢧⢓⡥⢛⡬⢎⡱⣋⠴⣋⠶⣌⣛⠻⣾⣘⠦⢎⡝⣆⠳⣤⠓⡜⢦⡙⢮⣔⣍⡲⠀⠀
⠀⠀⠉⠢⢄⠀⠀⠀⠈⢆⠀⠀⠀⣠⢚⡜⡲⢥⠳⣩⢇⡛⡴⢋⣶⢩⠧⡍⣖⠯⣔⢫⡔⣫⣖⡍⢞⡡⡞⣔⠣⡝⡴⡉⠻⣜⠲⣌⠳⢆⡻⢸⣅⠻⣭⡁⠀⠀⠀⠀
⡒⣒⢒⡒⢂⠽⠦⣄⣀⠀⠳⣠⢛⠀⠉⠒⢹⣆⠻⢴⢎⠵⣊⢷⣿⡘⠶⣉⡾⠁⠈⠳⡜⡥⢚⣮⠃⠳⠙⣎⠑⠉⠐⠁⠠⣈⠳⣬⠿⠬⠷⠧⠮⠷⢦⢽⣳⣄⠀⠀
⡱⢎⡖⣙⢎⠶⡱⣊⠷⣭⠟⣥⢋⡆⠀⠀⡼⠀⠀⡞⠀⠀⢨⠇⣏⠀⠁⢠⠇⠀⠀⠀⠙⢤⣀⢸⡓⣄⣀⡘⣆⣀⣀⢤⣀⣈⢦⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡱⢎⡼⢡⢎⠧⣓⢥⣫⠟⡜⣆⢻⡔⠀⢰⠃⢠⢶⣧⣰⣶⣏⣀⣧⡤⢤⠏⠀⠀⠀⠀⠀⠀⣻⠶⣳⠈⢫⡝⣹⡳⣮⢎⣳⡜⣬⢳⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡱⢎⡲⡍⡞⢼⡘⢦⡟⡼⣑⢎⡟⣔⢫⢿⣊⠗⡏⣗⢲⡎⠀⠀⣧⡙⡟⠀⠀⠀⠀⠀⠀⠀⠁⠙⡜⡆⠀⠙⣦⢳⠈⢮⡱⢻⡔⣣⢻⡜⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣱⣃⡷⠼⠽⠖⠙⣺⢱⡚⢬⢺⡱⣊⡽⢺⢥⢻⠁⡧⡟⠀⠀⠀⣧⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠈⢻⡆⠀⠻⣥⠻⣔⢣⢿⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⣇⠳⡜⣣⢻⡔⢣⠇⢸⢎⡏⠀⡿⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⢧⢻⡜⣚⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣯⠱⣣⠕⣫⢜⡏⠀⠈⣾⠀⠀⣀⣤⠴⠶⠶⠶⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠛⠛⠛⠳⠶⣄⠀⠈⢫⡜⢇⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠧⠿⠤⣫⡽⢺⠀⠀⠀⠁⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠁⠈⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡞⠀⣀⢤⡀⠈⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⢠⠃⠀⡤⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠀⠈⠀⠀⡇⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢇⠀⠀⠀⢳⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡄⢣⠘⠄⢣⠘⠄⢣⠘⢄⠣⠘⡄⠣⡘⣀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠓⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⡨⠐⡌⡘⢄⠊⠜⡀⢎⠰⢈⠅⢢⠑⡐⢄⠂⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⣀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣇⠱⣀⠣⠐⡌⠤⢉⠂⡅⢢⠘⢄⠊⡔⢨⠐⠌⡒⢸⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡼⡄⠀⠀⠀⠀⠀⠀⣇⠢⡐⠌⡡⠒⡈⠆⡑⢨⠐⡌⢂⠅⢢⠁⢎⠰⢁⠺⠀⠀⠀⠀⠀⢀⡞⡑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣪⠕⣎⠽⣄⠀⠀⠀⠀⠀⠸⣄⠡⢊⠤⠑⡨⢐⠡⢂⠅⢢⠁⠎⡄⠩⢄⠊⡴⠃⠀⠀⠀⠀⣠⠞⣄⠙⢦⣈⠙⢦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡤⢊⡕⢮⢱⡚⣬⢚⡜⣣⡄⠀⠀⠀⠀⠙⢦⡁⢢⠑⡄⢃⡘⠄⡊⠤⢉⠔⡈⢅⢢⠝⠁⠀⠀⢀⣠⠞⣥⠛⡬⢆⠀⠈⣷⣠⡙⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠔⡩⣔⠫⡜⢎⡱⣚⠴⣩⢖⡵⠉⠑⢄⡀⠀⠀⠀⠙⠢⢖⡈⠔⡠⠃⠜⣀⠣⣈⡴⠞⠁⠀⢀⡠⠖⠉⠙⣾⢰⠫⡜⡭⣒⠀⢳⠈⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣫⡼⢵⡪⠵⣙⠎⡵⣊⠵⣲⠋⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠈⠉⠓⠛⠒⠋⠉⢁⣀⡤⠔⠚⠁⠀⠀⠀⠀⠈⢳⡝⡜⡶⢭⣖⣸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⢇⡛⣬⡙⣖⡩⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠙⠚⠓⠋⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⠚⠋⠁⢻⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠐⢈⠑⠢⢄⣀⠀⠀⠀⠀⣀⠤⠃⠄⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠉⡉⢉⠡⠐⠂⠁⠀⠀⠀⠀⠀⠈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀