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