⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠄⠤⠠⠄⠤⢠⠐⡠⠐⡄⢲⢠⠆⡰⠠⢄⠂⠤⡐⠠⢄⡀⢆⠠⠐⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⡈⠄⢃⠌⣂⠱⡈⢆⢡⠊⡔⣡⠘⡄⡒⢌⠰⡁⢎⡘⠤⣁⠃⢆⡘⢄⢢⡴⢠⡐⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⢌⠠⡉⠔⡨⢄⠣⡘⠤⢂⡃⠖⡠⢃⡆⢱⡈⠦⡑⢢⠘⡔⢢⠉⡖⢈⡔⠢⢌⠡⢚⡩⢄⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠔⡈⢄⠢⢥⡙⠆⡌⢆⡱⢌⡡⠜⣨⠑⠮⠔⣡⢏⠰⢡⢃⡱⠘⣄⢋⡄⠳⢌⠱⡈⢜⡳⣈⡞⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⢉⠐⡈⠤⠘⠤⡘⢄⠣⢒⡰⢂⡜⡘⢤⡙⣘⠲⢄⠎⡜⡡⠆⣅⢋⠔⡢⢌⡱⢈⢆⡉⢆⠸⡥⠧⣸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠔⡀⢊⡐⠤⡉⢢⡑⢌⡡⢣⡐⢣⠔⡩⢆⡜⠤⡓⡌⢎⠴⡑⢪⡐⢎⡸⢐⠷⣰⡉⢆⠜⡠⢃⠜⡱⢌⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⢂⠌⡐⠄⢚⡡⢘⡅⢢⡑⢆⡩⢆⡹⡐⢎⡔⣳⠱⣎⠜⡤⣙⠢⡑⠦⣑⢊⡜⠰⡩⢌⢒⠡⠎⡌⠱⠊⠕⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡔⢈⡐⢈⠜⡈⠤⡉⠔⢣⡘⢢⡑⠦⣡⠙⢦⡘⡱⢧⠛⡜⡰⢂⢇⡹⠰⢌⡒⠬⣑⠢⢅⠪⡘⢔⢨⢁⠃⡈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⢂⠄⢃⠰⡈⢆⢡⠙⢢⢡⠣⠜⡑⠦⣙⢢⠱⣑⢪⠱⣌⠱⣉⠲⢌⡓⢬⠐⣳⠠⣍⠢⢃⡱⢨⠘⠤⢣⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢁⠢⠌⢂⠡⠒⡌⢢⠙⢢⠅⣎⠱⣉⠖⡡⢎⡱⠌⣆⠳⣈⠳⢌⡓⣌⠲⡡⢍⡱⠘⢆⡑⢣⢐⠡⢊⠔⡁⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂⠔⡈⢂⠁⡓⣘⢣⣉⢆⣜⣠⢃⣆⢊⡑⠢⢷⠊⡴⢧⡘⢆⠣⡜⠤⢣⡑⢎⡰⢉⠆⡜⢠⠊⢆⠡⢊⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⢆⠔⡣⠝⡼⢣⠿⣼⣻⢾⣽⣻⣞⣿⣻⢿⣳⣷⣾⣶⣬⣦⣓⡬⡑⢣⠘⢦⣑⡊⠔⣈⠆⡉⢆⢣⠂⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢉⠂⠀⠀⠀⠀⠉⠉⠒⠩⣛⡞⣧⢻⠶⣏⡟⢣⠙⠈⠄⢁⠠⣁⠌⣉⠣⢏⢦⡉⠷⡘⢄⢊⠱⡈⢆⠘⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢆⡈⠆⡉⠌⠑⡀⢆⡀⠆⠰⡙⢮⣻⡽⣞⡜⢦⡘⠔⢊⠢⠙⠍⡞⡱⢲⢌⢦⣙⢦⡑⢌⠢⡑⠬⣀⠃⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢢⠐⡁⠀⡜⣥⠀⡄⣼⡘⠤⠘⢲⡽⣻⢧⡛⡔⡌⡜⣦⡄⠂⠤⣄⠁⣃⢎⠲⡍⣖⠩⢆⡡⠘⠴⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠱⣈⠒⡐⢢⡙⡜⡱⡙⢆⠡⢎⡽⣯⣏⠷⣸⠰⠱⢌⠼⡩⢗⢎⡳⣜⢪⡕⣚⡌⠳⡌⢒⢀⡐⠈⡌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢖⡡⢎⡱⣂⢖⣡⢓⡍⢆⠱⣎⢿⡵⣞⢯⣳⣭⡳⣎⢶⡱⣎⢾⡱⣎⢷⡸⡱⡜⡱⢈⠆⡸⡥⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⠢⡝⢮⡱⢭⡺⣔⢫⠔⣊⠲⣭⣟⢾⡹⣎⢷⣚⣷⣻⢮⢷⣹⣎⣷⢻⣎⠷⣣⢇⡱⢊⡔⢱⢣⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡑⡜⢣⡝⣣⠗⣎⢇⡚⢄⡳⣳⣞⣯⢳⡝⣮⡝⣾⣭⢿⣹⢶⣻⣞⡿⣜⡻⣔⠪⡔⣡⠒⠬⣏⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠤⡙⢢⠝⢦⡛⡌⢦⡙⠦⣝⣷⣻⣞⣧⢟⠶⣹⢶⡹⣎⡗⣫⠳⣝⡞⣧⠳⣌⠳⡘⣄⠊⡔⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣁⠣⡚⠥⢎⡱⢂⠌⠘⡙⢾⡹⢞⡜⡦⢎⡱⣮⢟⡵⣫⢗⡹⢆⡙⢦⠛⣤⢣⠱⢄⠒⡘⠴⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⢡⠙⣌⢣⠳⣉⠎⡔⡰⢂⡵⢪⡝⡞⣭⢳⢭⡞⣱⢏⠮⡱⢋⡜⢆⠯⡔⢣⠃⡌⢠⢙⢢⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⢂⠱⢈⢆⡛⣬⢚⡵⣩⠳⣞⣣⠽⡹⢎⠟⠮⡙⢃⡊⢖⡡⢏⡜⣊⠖⡙⢆⠱⠐⡠⢋⠤⢉⡐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠌⢂⠘⠀⡉⠰⣁⠣⢄⡡⢊⡱⣌⡜⢦⢱⢣⡝⢎⡜⢢⠜⠤⢋⠜⡠⢂⠡⢒⡉⠒⡄⢂⠡⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠄⢣⠘⡐⠣⠜⣣⢛⡼⣋⠷⡑⢎⢆⡏⢶⡉⠖⡬⢁⠎⡘⢄⢊⡐⢄⡣⢣⠌⡡⠐⢂⠔⢂⠌⡐⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠣⢌⠱⡈⠄⠃⠒⠡⢊⡕⣎⠞⣜⠡⢎⡱⠘⡄⢊⠔⠨⢠⠜⣎⡱⡁⢆⠡⡑⢌⠢⣁⠎⡰⢁⠣⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⢈⠆⡱⢊⡐⢠⣅⠳⡼⣌⠯⡰⣉⠲⡀⢇⡘⠄⡊⢅⢣⠞⢦⡑⢌⠦⡑⢌⠢⣑⠢⡱⠡⡍⡒⢡⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠢⠘⡄⠣⠌⡱⢌⡳⡑⢎⡱⠱⡄⢣⠘⠠⠐⡌⢰⡉⢆⡛⠔⡸⣌⠲⣁⠎⠴⣁⢚⡐⢣⠒⣉⢆⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠄⡁⠂⠐⡌⠰⡉⢆⠱⠡⠘⠠⡈⠔⡡⡘⠰⡘⢢⠑⣪⠱⣌⢳⡐⢊⠱⢠⢃⠬⣑⠪⢔⡊⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠃⠌⠐⡈⠄⢃⠡⡐⢡⠂⡅⢣⡜⠢⡍⠴⡹⣌⠧⡘⢌⠢⢡⢊⠲⣄⢋⠦⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠐⠈⢀⠠⠀⠀⠠⠐⠈⠐⠠⠘⠠⠡⢘⢀⠃⣼⠋⢌⠱⢨⡑⢳⣌⠳⡈⠔⡈⠆⣌⠣⡔⣩⠒⡍⢎