⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⠠⢀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠜⠐⡁⠋⣰⠊⢁⡲⠉⢀⡠⠞⠉⡉⠤⠄⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡐⠈⣒⢂⣰⠁⣐⡒⠀⠬⠗⠀⢄⡪⠀⢀⠔⠌⠂⠀⠀⠀⠄⠁⠂⠀⠀⠀⠄⡐⢈⠐⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠁⠀⢨⣤⡤⣤⢤⡄⠀⣉⡃⠀⠬⠃⠀⡢⠑⠁⢄⠕⠉⠁⠀⠐⠈⡀⠐⡀⡁⢆⠰⡁⢂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢄⠠⠷⡾⢞⣵⣟⣯⢗⢮⡵⣟⡹⢄⣄⠀⡄⠀⠐⠁⠀⡠⠊⠁⠈⡐⠠⢡⠐⣌⠢⢃⠜⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠠⢤⠻⣇⣿⣼⣿⣼⠿⣧⡘⢣⠛⢸⢠⣀⡀⠀⠀⠀⠀⠀⢀⠜⠃⢇⡄⢻⡀⢇⠘⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠴⠾⠞⣯⠷⡿⢯⣛⢧⡿⢱⣩⠦⡉⠦⢆⠄⠉⠂⠨⠁⠀⠀⠀⠐⠨⢦⡹⢡⠎⠠⢈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠚⠓⠙⠫⠭⠗⢼⡩⠏⡝⡛⠶⢻⣄⡀⡐⡤⠀⠀⠀⠀⠀⠀⢧⠓⡅⢊⠁⠄⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠘⠈⠀⠉⠀⠉⠁⢐⠃⠠⠴⠀⣉⠀⠑⠀⠂⠈⠉⠓⠆⠀⠀⠀⠀⠀⢰⢫⠱⢌⠂⠌⡀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⢓⠂⠌⠄⠐⠂⡄⣺⡃⠀⠀⠀⠀⠀⠀⠬⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⣍⠢⠌⡐⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠄⡅⣘⠑⠊⠵⠃⠖⠃⢥⠄⢀⡐⢃⡀⠄⡀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⢠⠛⡤⢁⢂⠐⠈⡀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢏⠆⠀⠀⠀⠀⠀⠀⠘⠒⠰⠄⡘⢁⡊⢐⠋⠐⠖⠀⠴⠆⠠⠆⠀⠖⠀⡚⢀⡊⢁⠉⠈⠁⠄⡀⠀⣌⠳⣀⠣⠀⠌⡐⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⡁⣈⠐⠂⠬⢀⣉⠁⢘⡃⢀⣈⠀⣈⠁⢈⡅⠈⠅⠠⠄⠔⠐⠂⠨⠠⠀⡀⢎⠱⡀⢂⠁⢂⠐⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡍⠠⠁⠀⠀⠀⠀⠀⠀⠀⠆⠅⣈⠁⡖⠀⠥⠀⣤⠄⠠⠆⠠⠆⠀⠴⠀⠰⠂⢐⠀⡊⠨⠀⢂⠠⠀⡐⠎⡄⢁⠂⠈⢀⠐⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⣄⡠⣾⢭⣀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂⠅⣨⠁⢘⠃⠐⡒⠀⠲⠂⠐⡃⠀⡃⢀⡈⢀⠅⠠⠀⠂⠈⠄⠀⣰⠁⠊⠄⠂⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⢶⣛⢧⢿⣱⢯⡷⣎⠟⢾⣣⠄⠀⠀⠀⠀⠀⠀⠄⢉⠐⠂⠤⠠⡬⠀⣨⡅⢀⣉⠁⣉⠁⢨⠄⠠⠀⠐⠀⡊⠨⠠⠂⠀⣀⠷⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠿⡘⠋⠈⠘⠙⠚⠁⢹⡐⠘⣯⠐⠀⠀⠀⠀⠀⣔⠆⢘⠐⠀⠆⢠⠅⠀⣭⠁⢈⡋⢀⣩⠀⠨⠀⠴⠀⠂⡀⠁⠄⠄⠀⠐⡩⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢨⣻⠑⠀⡀⡀⠀⠀⠀⢯⣱⣆⠸⣳⢆⢠⠀⠀⡈⠋⢀⠀⢘⢀⡃⠰⠆⠠⠆⠀⠴⠄⠠⠂⠐⠒⢀⡁⡨⠀⡤⠠⠀⠀⢠⠑⣨⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⢗⡯⠓⠈⠄⡁⠀⠀⠈⠒⠉⠀⠋⠉⢈⠡⢤⠠⠀⠀⠤⠂⢈⡁⣘⠀⠲⠓⠀⠖⠀⢚⠃⢈⠁⡨⠀⠔⠀⢂⠠⣄⡭⢖⣉⣥⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣟⣫⡘⠁⡈⠠⢐⠀⡀⠠⢄⣈⣀⠠⡀⠠⠀⠠⠁⡀⠀⠠⠀⡄⠄⣉⠁⣘⡁⠈⡋⢀⡉⠀⠄⠠⠖⢐⣠⠼⢚⣩⡔⣶⢯⣞⡷⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡾⣵⢫⡑⠠⢁⢆⠓⢠⣓⡾⣽⢧⠹⣽⠢⠄⠐⠄⡀⠀⣀⣂⠈⡀⠐⠀⠨⠀⠨⠄⠠⠀⠰⠆⣔⣪⣭⢶⣞⣯⢷⡻⣞⡽⣮⢝⠏⠀⠈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡹⣎⢷⡡⠂⡌⢢⢡⡿⣭⢿⡭⣏⣟⡪⣝⠀⠄⠈⡠⡈⠘⠿⣷⣴⣀⡁⠈⠀⠈⠀⢲⣢⣾⢿⣿⢽⡞⣟⣮⣟⡾⡽⣏⠿⣌⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡹⣎⢷⡡⢃⡘⢤⣻⢽⣛⢮⡳⢣⠎⠐⠀⠐⠌⠁⠄⠈⢘⡁⣁⠜⡩⢙⣙⣳⣶⣾⡿⣟⡯⣟⡮⣏⢿⣹⢮⡽⣽⣻⢮⣻⠌⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡱⢭⡲⡱⢣⠜⡂⡟⢮⡙⣎⠑⡃⠈⣠⣞⣹⡲⢤⣀⣀⣀⣨⣤⣴⡾⣟⣯⢟⣳⢯⡳⣏⢷⣹⡞⣽⢮⡷⣯⠿⠝⢉⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠄⠀⠅⣸⢘⡣⢕⢣⢃⠞⢀⠉⠆⠑⠠⠈⠀⠀⠀⠚⠲⢛⢯⡻⣽⣻⡽⢯⢷⡻⣝⢮⣏⡳⣭⢳⡝⣞⣧⠿⠝⢋⠱⠤⢖⠫⣝⠃⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠩
⢤⠐⠀⠰⣇⠣⡜⡈⠦⠉⡀⠂⡌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠡⢛⠹⢎⡵⢋⡞⡴⡻⡜⢏⠚⠡⢀⠄⣠⢋⡞⡱⣍⠗⠁⢤⢰⡒⡶⣹⠭⣯⡝⣏⠿⣼⠀⡀
⠂⠀⠀⠀⢨⠓⠘⣴⠁⠒⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠈⠘⠊⠃⠉⠁⠐⠚⠈⢹⢳⢲⠙⣦⢫⠘⠁⠀⠀⠀⠒⠃⠉⠉⠁⠐⠀⠐⢠⢠⡄⠀⠂⠀⠀
⠁⠀⠀⠀⠀⠉⠒⠀⠈⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠂⢁⠀⠀⢈⠄⠰⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⠒⣀⣂⣀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠂⠀⠀⠂⠀⠁⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠀⢀⠒⠀⢀⡉⠠⠄⡀⡄⡏⢘⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠆⠤⠁⠀⠃⠈⠄⠈⡁⠀⢀⠀⠀⠨⠀⠀⠀⠀
⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀