Utensil Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⣴⡷⠀⡔⠉⠀⢻⠀⠀⠀⠀⠀⠠⠉⢀⠀⠀⠀⠀⠀⣔⢉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⣼⣿⡇⠀⠀⠀⠀⠀⣰⡿⠃⢰⠂⠀⢀⠄⢀⣾⡇⠀⣾⣿⣶⡄⣴⣿⠀⠀⡸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⣼⣿⡟⣠⣶⣶⣄⠀⢰⡿⠁⠀⡸⠀⣠⠊⢀⣾⡟⠀⠀⣿⣿⠟⣸⣿⠃⠀⡰⠀⡸⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣸⣿⡟⣰⣿⣿⣿⠏⢠⡿⠁⠀⠀⣷⡞⠁⠀⣼⡟⠀⠀⣰⠏⠀⣰⣿⠃⠀⡰⠁⢠⠁⢀⣾⣨⠇
⠀⠀⠀⠀⠀⠀⣼⠏⠀⣼⣿⡿⠁⣿⣿⣿⠏⢀⡾⠁⠀⠀⣼⡏⠀⠀⣸⡟⠀⠀⣰⠏⠀⢠⡿⠃⠀⠠⠁⢀⠂⠀⣼⣿⡟
⠀⠀⠀⠀⠀⣼⠃⠀⣼⣿⡿⠁⢠⡿⠋⢀⣠⣾⡇⠀⠀⣼⡿⠀⠀⣰⡟⠀⠀⣰⡏⠀⢠⡿⠁⠀⢠⠃⠀⡜⠀⣰⣿⡿
⠀⠀⣴⣶⣿⣇⠀⠘⣿⠿⠁⢠⡿⢁⣴⣿⣿⣿⡆⠀⣸⣿⠁⠀⢠⡟⠀⠀⣼⡟⠀⢀⡾⠁⠀⢠⠃⠀⠰⠀⣠⣿⣿⠃
⠀⣼⣿⣿⣿⡿⠀⣼⠁⠀⣠⡿⢁⣾⢯⣟⣞⣿⠇⣰⣿⠃⣀⣴⡿⠀⢀⣾⡿⢡⣴⣿⡇⠀⢀⠂⠀⢀⠃⠀⣸⣿⠛
⠰⣿⣿⣿⠟⠀⠈⠁⠀⣰⣿⠃⠸⣿⣿⣾⣾⡏⠀⠿⢋⣾⣿⣿⡇⠀⣼⡿⠡⣿⣿⣿⠇⢀⠂⠀⠀⠌⠀⢰⢣⠇
⠀⠀⠉⠁⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠈⠙⠋⠀⠀⠀⠘⣿⣿⡿⠃⠀⠈⠀⠸⠄⠨⠉⠀⠈⠀⠀⠘⠀⠀⣯⡞
⠀⠀⠀⠀⠀⠀⠀⠰⠟⢡⣾⠆⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠁⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⠀⢀⡀⠀⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡄⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⣴⡿⠀⣸⡿⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⢡⣶⠀⣿⣿⣿⣿⡏⢰⡿⠀⣼⣿⠃⢠⣿⠃⢀⣾⣿⣿⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣾⠂⠀⣼⠋⠁⠀⢠⣿⠏⠀⣿⣿⠿⠋⢠⡿⠁⣸⣿⠇⠀⣼⡟⠀⣼⣿⣿⣿⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢀⣾⠋⠀⣼⠃⠀⠀⢀⣿⠏⠀⢀⡟⠁⠀⢀⣿⠃⢰⣿⡟⠀⢰⣿⠁⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⣾⠏⠀⣼⠃⠀⠀⠀⣾⠃⠀⢀⡞⠀⠀⠀⣾⠃⠀⢠⡿⠀⠀⣿⡏⣸⣿⣿⣿⣿⣿⠀⢠⢡
⠀⠀⠀⢀⣴⡟⠀⠀⠀⢀⣾⠏⠀⣼⠃⠀⠀⢀⣾⠃⠀⢀⡾⠁⠀⠀⣼⠃⠀⢀⣾⠁⠀⣸⣿⠀⠙⠿⣿⣿⣿⡿⢀⠆⡆
⠀⢠⣾⠿⢿⣧⠀⠀⠀⡜⠉⠀⣰⠏⠀⠀⣰⣿⣿⠀⢀⣾⠃⠀⠀⣸⠃⠀⠀⣼⠇⠀⢀⣿⠇⠀⠀⠀⡿⠁⠀⠀⡜⡸
⠀⣿⣇⣤⣾⡟⢀⠔⠊⠀⠀⣰⠏⠀⠀⣰⣿⣿⠃⢠⣿⠇⠀⣠⣴⡏⠀⠀⣸⡟⠀⢰⣾⣿⡀⠀⠀⢰⡇⠀⠀⡼⢠⠇
⠀⠙⠛⠋⠉⢰⣃⡀⠀⠀⢰⠏⠀⠀⣰⣿⣿⠃⢠⣿⡟⠀⢰⣿⣿⡟⠀⢰⡿⠁⣠⡟⡟⣿⠄⠀⠀⣾⠁⠀⣰⠃⡜
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⠀⠀⠀⣰⣿⣿⠃⠀⠺⠟⠀⢀⠳⣙⡟⠀⢠⣿⠁⠀⢺⣷⣷⡟⠀⠀⣸⣿⠀⢠⠇⢰⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠃⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⢠⣿⡇⠀⠎⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠈

⠀⠀⠠⠋⠛⠂⠸⡟⢿⣏⡇⢰⣿⣿⡆⢀⣾⣿⣿⣦⠀⣿⣿⣿⣷⠀⣿⣿⣿⡆⢀⣾⢿⣆⠀⣴⣿⣿⣦⠀⣴⣿⣿⡄⠀⣰⠀⠀⣾⡇
⠀⠀⠘⡄⣄⡄⠀⣇⠘⢻⡇⠘⣿⣿⠇⠘⢿⣿⣿⡿⠀⢹⣿⣿⡇⠀⢿⣿⣿⠇⠈⢷⣼⠏⠀⠛⢿⡿⠛⠀⠹⣿⣿⠃⠀⣿⠀⢰⣿⡇
⠀⠀⠀⢻⡿⠀⠀⠙⣿⠛⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⢹⡏⠀⠀⠀⣿⠃⠀⠀⠈⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⠁⠀⢸⣿⠀⢸⣿⡇
⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠈⣿⠀⠈⢻⡇
⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠈⡋⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠸⡇⠀⠀⠀⢿⠀⠀⠀⢸⡇⠀⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⠀⠀⢿⠀⠀⠀⢨⣯⠀⠀⠀⢸⡅⠀⠀⠀⢿⡇⠀⠀⣿⡇⠀⢸⡇

⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠠⡏⡇⠀⠀⠀⠀⠀⡏⣇⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠙⠓⢦⡀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠀⡇⣯⠀⠀⠀⠀⠀⢸⢸⡄⠀⠀⢠⡶⠶⠶⠞⠀⠘⠛⠛⠛⠃⠀⠹⠶⠶⠶
⠀⠀⠀⢸⠁⠀⠀⠀⡠⢤⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⠀⢳⠏⠀⠀⠀⠀⠀⠘⡞⠀⠀⠀⢸⡇
⠀⣀⠀⢸⡄⠀⣀⠤⠇⠰⠧⣄⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⣞⠉⠳⢦⡷⠚⠷⠶⠶⠦⠀⠐⠛⢶⡃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠈⠓⢦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⣿⢻⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⢸⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣷⠀⠀⠀⢸⠀⠀⠀⠀⠠⠱⠘⠘⠐⠀⠀⠀⣠⠞⠙⢦⡀⠀⢸⡇
⠀⠸⣄⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⣠⡟⠀⡤⠄⠚⠲⠤⡄⠀⠂⡄⠀⠃⠃⠀⠀⣴⠁⠀⠀⠀⢱⡀⢸⡇
⣀⡀⠈⠙⠓⠶⠤⠤⠤⠤⠤⠤⠴⠖⠛⠁⠀⢰⢳⣶⣶⣶⣶⣇⠀⠀⠁⡄⠀⢰⢠⠀⡇⠀⠀⠀⠀⠘⡇⢸⡇
⠙⠯⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⢼⢻⢿⢻⣸⠈⠀⠀⠇⡇⠸⠸⢀⡇⢀⣀⣀⣀⠀⣇⢸⡇
⠀⠀⠀⠉⠛⢷⣦⡤⠤⠤⣤⣤⣤⠀⠀⠀⠀⠸⣍⣘⣘⣙⣘⡽⠀⠁⢥⣤⣣⠄⠀⠘⠿⣽⣽⣿⣿⡿⠟⢸⡇
⠀⠀⠀⠀⠀⠈⢻⡒⠒⠒⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠘⠓⠒⠒⠒⠚⠒⠛⣓⣚⡒⠓⠛⠚⠒⠚
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⢸⠹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠙⢦⠳⣤⡀⠀⠀⠀⠀⠀⢀⠴⠊⠉⢁⣀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣾⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⢿⣄⠀⠀⠀⡴⠁⢠⡶⠛⠉⠉⠙⠳⢦⡀⠙⣆
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠸⢧⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢣⡀⠀⣼⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⢻⡀⠘
⠀⠀⠀⠀⠈⠳⣤⣄⣀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠘⢤⣷⣶⣶⣶⣶⡶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠴⠃⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠹⣆⠀⠀⠀⠀⠀⠀⢀⡼⠁⢰
⠀⠀⠀⣠⠤⠖⠒⠛⡟⠛⠛⢻⠗⠲⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠛⠒⠚⠒⠶⠤⠤⣀⡀⠀⠀⠀⠳⡀⠈⠳⣤⣄⣀⣤⡴⠟⠁⡠⠋
⠀⠀⡞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⣠⣖⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣳⣤⣤⠀⠈⠳⢤⣀⣀⣀⣀⣠⠴⠊⠁
⣠⡤⣿⠲⠭⣭⣖⣒⣒⣒⣒⣒⣒⣮⡭⠴⢺⡧⣤⡀⠀⠙⠛⣿⠻⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠿⢻⠟⠛⠀⠀⠀⢠⣤⢤⣤⣀⠀⣠⡤⢤⡄
⠉⠙⣻⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⡟⠉⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢸⠂⠈⠙⠋⢿⠀⢀⡿
⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢳⡏
⠀⠀⠀⠙⠶⣤⣀⣀⣀⣀⣀⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⣶⣤⣴⣶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠖⠒⠒⠒⠒⠒⠶⠤⣤⣀⢀⣀⣀⣤⣴⣚⡭⠟⠀⠀⠀⢰⣍⣉⣉⣀⣀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣱⡆
⠀⠀⠀⠀⠀⠀⡾⠉⠀⢀⣀⠤⠤⠤⠤⠤⢤⣀⡀⠀⠈⢻⣭⠟⠋⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢿⣦⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⢉⣢⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣉⡉⠛⠓⠒⠒⠚⠛⠋⣉⡥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡤⠖⠒⠒⠒⠲⣄⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠒⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠅⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡁⠒
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠀⡆
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⣤⠀⠂⠰
⠀⠀⠈⠀⠀⠀⠈⠬⠑⠂⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠤⠐⠒⠒⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⣴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢷⠃⡆⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠘⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⡀⠈⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⣸⣿⡿
⠀⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⣿⢀⡀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠰⣶⡆⠀⠀⠀⢹⡟⠁
⠀⢹⡄⠀⠀⢥⣀⠀⠀⢰⠆⠐⠰⣿⡇⠀⣿⣿⠸⡧⠀⠀⠘⠛⢿⠀⠀⠙⠛⡟⠾⠆⣺⠂⠀⠛⠇⠀⠀⢀⣿
⠀⠈⣇⠀⠀⠘⣇⠀⠀⠘⡄⠀⠀⢸⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣆⠀⠀⣼⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢶⠰⡇
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀⠁⠈⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣠⠞⠁
⠀⠀⣀⣀⣀⠀⠀⢀⣤⣴⣦⣿⠀⠀⡅⢀⣾⣿⣧⠀⠀⠀⢾⣿⣿⡆⠀⢴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠛⠛⡏⠁⠀⠀⢿⣿⣿⣿⠟⠀⠀⡃⣼⣿⣿⡇⠀⠀⣴⣮⡉⠉⠀⠀⠈⠿⠿⠟⢋⣀⡀⠀⢀⣤⣶⣿⣿⣿⣿⡷
⠀⠀⠀⠁⠀⠀⢠⣶⣾⣭⣄⣀⠀⠀⠘⠻⠿⢿⠇⠀⠀⠈⠙⠛⢦⡀⠀⠀⠀⠠⣾⣿⣿⣿⣦⠀⠹⠿⣿⡿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⠉⠙⠲⠆⠀⣴⣶⣿⣷⣦⣄⡀⠀⠈⠳⣄⠀⢀⣙⠛⠟⠛⠃⠀⣀⣀⣩⣤⣀⡀
⠀⢠⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠰⣶⣶⠀⢲⣿⣿⣿⡆⢀⣶⣿⣿⣿⣿⣿⣿⠏
⠀⠈⠹⠿⠿⠗⠀⠀⠀⠀⠈⠙⠲⠶⠤⡄⠀⠉⠻⠿⣿⣿⠿⠁⠀⠙⠛⠀⠘⠿⣿⠏⠀⠀⠉⠛⠻⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⣄
⠀⠀⠀⣀⣀⠀⠀⢈⠀⠈⠹⠷⢶⠖⢒⡾⠀⠀⢀⣿⣿⣇⠀⠀⠀⢀⣯⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⠅
⠀⠀⠀⣿⣿⠇⠀⠈⠀⠠⣤⣽⣿⡯⠭⠭⠀⠀⢸⣿⣿⣿⠁⠀⠀⢸⣿⢸⣧⠶⠾⠿⠿⠶⠶⠀⠲⠶⠿⠿⠷⠶⠂⠰⠶⠿⠿⠷⠶⠆
⠀⠀⣿⣿⣿⣿⠀⠀⢠⣤⡄⣤⣤⢠⣶⡄⢰⣦⣬⣭⡉⠁⣤⣤⡄⢸⣿⢸⣿⠀⣠⣶⣿⣿⣷⣦⣤⣄⢀⡒⠒⢺⣿⣿⠀⣿⠰⡷⢸⡇
⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⢸⣿⡇⠈⣁⡀⣀⡀⠀⢈⣉⡀⢸⣿⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⠉⠀⣷⠀⡇⢀⡇
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠘⣿⠇⢿⡟⠀⣿⣿⣿⢸⣿⢸⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠛⠀⠃⠈⠃
⠀⢸⣿⣷⢸⣿⡇⢾⣿⡇⢀⣾⣿⣿⣷⡄⠀⣿⠀⢸⡇⠀⠈⣿⠀⢸⣿⢸⡏⠀⠀⣠⡍⠉⠀⠉⠉⢀⣈⣁⣀⢀⣤⡾⠃⢿⠀⡷⠐⡇
⠀⠀⠙⠁⠈⠛⢁⡈⠋⢀⣚⠻⠿⠿⠟⠓⠀⣿⠀⢸⡇⠀⠀⣿⠀⠀⣿⠀⢳⣤⣶⣿⣿⣶⡤⡄⢰⣿⣿⣿⣿⣿⠁⠀⠀⢸⠀⣿⠀⡇
⠀⠀⣿⠇⣿⡇⢿⡿⢰⠘⣿⠀⣹⣿⠂⠉⣠⣽⣄⡈⠁⠀⠀⠉⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⡜⢸⣿⣿⣿⣿⣿⠀⠀⠀⡘⠀⠉⠀⠃
⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⡇⢠⣿⣿⡆⠀⢿⣿⣿⠏⣭⣭⠁⢀⠀⢀⣀⣀⣀⠻⠿⠿⠿⠿⠟⠀⢀⣙⠛⠛⠛⠁⢰⣾⣿⣿⣿⣶⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⣤⡀⠀⠈⠛⠉⢰⣿⣿⡆⢸⠀⣿⣿⣿⣿⠀⣤⣾⣦⠀⢶⣴⣿⣿⣷⡶⣄⠠⣾⣿⣿⣿⣿⣿⡧
⠀⠀⢈⣤⣤⣴⣠⣤⣤⣤⣥⣄⢿⣿⣿⠆⣀⠀⠀⠘⠿⠿⠃⢸⠀⣿⣿⣿⣿⠀⢿⣷⡶⠀⠀⠸⣿⣿⡿⠗⠃⠀⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠻⣿⣿⡏⠘⢿⣿⣿⡿⠃⠀⢰⣾⣿⣿⣿⣷⡄⠀⠀⠰⣾⡶⠿⠿⢿⡿⠀⢀⣉⣀⠀⣤⣤⣬⢉⣤⣤⣄⢰⣶⡍⣽⣿⠉⢹⣶⡀
⠀⠀⠀⠻⠟⠁⠀⠀⠀⢒⠲⣄⠰⢿⣿⣿⣿⣿⣿⡿⠇⢠⣤⡬⢠⣤⡤⢠⣤⡄⢸⣿⣿⠀⢿⣿⡿⠘⣿⣿⠟⢸⣿⠇⢿⣿⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣾⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⢿⠃⠀⢻⠃⠈⡿⠁⢸⣿⣿⠀⠀⡏⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁⠀⠀⠛⠀⠀⠛⠀⠀⠛⠀⠀⠉⠁⠀⠐⠛⠀⠀⠘⠛⠀⠘⠛⠂⠚⠛⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⣀⣀⣀⠀⠀⢀⣀⠀⠀⢿⣿⣛⣋⣁⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⣿⣿⣿⣿⣿⠿⠛⠉⠀⠘⢻⣿⣿⣿⣿⡿⠃⠀⣿⣿⣿⣿⣿⣿⣿⠀⢤⣿⣿⣿⣿⣿⣧⠄⣼⣿⣿⣿⣿⣷⠀⣠⣾⣿⣿⣿⣧
⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠻⠿⠿⠿⠿⠃⠀⠘⣿⣿⣿⣿⠇⠀⠘⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠉⠉⠁


⣿⣿⢿⠿⡿⠻⠿⡿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡶⠀⢠⠂⡀⠄⢠⡦⢠⠀⠀⣤⡀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢸⢿⡀⠘⢾⣷⡄⠸⢇⢸⠦⠀⣧⡇⠀⠀⠈⢧⠀⠀⠀⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠛⢣⠀⠋⠙⠓⠀⠂⠈⠃⠀⠙⢿⠀⠀⠈⠉⡀⠀⢰⠀⢰⣿⡙⣂⢀⣐⢒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠉⠘⠉⠅⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠆⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣞
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠰⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⠁⠀⠀⠐⡆⠀⠒⠤⠤⣀⡀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡖⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠉⠙⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠙⣇⡀⠀⣼⡇⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰⠻⡇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠜⠀⠃⠀⡀⠀⠀⠉⠓⢦⢸⡄⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡁⢀⣃⠀⠀⠀⠀⣸⡾⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠄⠠⠀⠏⢇⣄⠀⣧⣿⡿⠀⠀⠀⣠⣿⠇⠀⠀⠀⠄⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡿⠋⠑⠲⠴⠯⠽⠏⠀⠀⠣⣀⠀⡨⠛⢶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠋

⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣶⡄⠀⠀⣴⣿⣿⣦⡀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠠⡾⠛⡦
⠀⠀⠀⠀⠀⣿⢻⢹⢹⢹⢹⡇⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢃⠁⡄⠠
⠀⢀⣠⣀⠀⢸⣾⣼⣼⣸⣸⠃⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣠⣼⣧⡀⠀⠀⠀⠀⣸⠀⠀⣄⠀⠀⣠⣄⡀
⣾⡯⢆⡺⡄⠈⣿⣿⣿⣿⡿⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⡿⠀⢠⢗⡰⢽
⢿⡇⣸⡞⠀⠀⠀⠉⣿⡏⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⠘⣰⠁⠀⠀⢳⣇⢸
⠀⢻⣷⣆⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣸⣿⣿⣿⣿⣀⣀⣀⣀⣻⣷⣟⣀⣀⣀⣰⣾⡟
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠰⣶⡶⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⠶⢶⣶⡶⠶⠶⠶⢶⣶⣶⣶⣶⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⢶⣶⠆
⢠⡞⠁⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⢸⠈⢳
⢸⡀⣀⠳⣀⣠⠅⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⢰⣿⡇⠀⢨⣄⣀⠞⣀⢀
⠈⠿⣞⡀⠀⠀⠀⠀⢻⣹⠇⠀⠀⠀⠀⢸⣉⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢀⢻⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣀⣀⣀⣀⣀⣈⣿⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⢀⣀⠀⢀⠀⣀⣀⡀⡀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠒⠒⠒⡄⢹⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⠘⠒⠐⠒⠒⠒⠒⠂⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠀⠀⠀⢸⢠⣀⣀⣀⣀⣀⣀⣀⣀⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⢸⣀⣀⣀⣀⣀⣀⣀⢀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡸⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠠⠠⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣀⣀⣒⣒⣒⡒⣂⣀⣀⢀⠀⠀⠀⠀⠀⠒⠒⢒⡲⢁⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢨⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⠸⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠦⣤⣤⣤⣤⣤⣤⣤⣴⠴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠉⠉⠀⠀⠀⠈⠀⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⡉⠉⡉⠉⠉⠉⠁
⠀⠀⠀⡔⢀⠀⠠⢀⠀⢀⡀⠀⣀⠀⢀⡀⠀⡀⠂⢀⠀⣀⡀⠀⣀⣀⢀⡀⡀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠀⡀⠠⠀⠀⣠⠈⢠⡤⣄⠀⠑⣄
⠀⠀⡼⠀⠦⠤⠤⠬⠤⠦⠡⠴⠌⠠⠄⠥⠴⠭⠥⠤⠥⠤⠬⠤⠬⠥⠬⠭⠴⠤⠤⠤⠅⠰⠨⠄⠀⠠⠀⠸⠄⠣⠀⠈⠓⠓⠲⠬⠦⠤⠊
⠀⠀⠳⠖⠲⠒⠒⠒⠶⠲⠖⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠒⠒⠖⠲⠒⠒⠒⠲⠒⠒⠶⠒⠒⠒⠖⠶⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡟⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡙⢻⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣾⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢦
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⡏⢓⣓⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⣀⢔⣼⡾⠿⢛⠛⠟⠲⢦⣤⡄
⠀⠀⠀⠀⣴⠋⠁⠀⠈⠉⢧⠠⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢄⡀⠐⠋⠀⠀⠀⠀⠀⣱⣿⢾⣿⣝⣻⣿⡬⣤⡾⡿⣱⠁
⠀⠀⢀⠀⢻⣶⣤⣤⣴⣲⣿⡥⣾⣿⣷⣦⣄⡀⠀⠀⠀⢀⣠⣤⠶⣺⡋⠉⠻⣦⡙⢦⡀⠀⠀⠀⠀⠀⣏⠙⠺⠽⠿⢠⡿⠷⠟⠷⠓⡛
⠀⠀⣮⠀⣟⠏⠉⠻⠿⢗⠻⠿⠟⠋⢉⡿⢈⡇⠀⠀⢰⠙⣛⣫⣰⡷⠃⠘⣁⣨⣽⣾⣛⠆⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠈⠑⠤⣭⣶⣄⣣⣤⣬⣄⢀⠈⠁⠐⠁⠀⠀⠀⠀⠠⡇⠀⠉⠉⠛⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠶⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⢀⣲
⠀⠀⠀⠀⢀⣠⡴⡖⠞⠉⡳⢶⣤⣤⣀⡐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣀⣀⡘⠛⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠒⠒⢒⢉⣤⣿⣶⡤⣅
⠀⠀⡐⢂⣼⣭⣳⡶⣬⣅⡲⠠⣺⣿⣷⡌⢢⡀⠀⠀⠀⢀⠀⠀⣐⣋⣡⣬⣗⣳⡿⡝⠳⡀⠀⠀⠀⢠⢾⣿⣡⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⡆⢹
⠀⠰⠀⢞⠿⠿⠷⠿⠝⣿⠯⠡⠷⠿⢛⠟⣸⠇⠀⠀⡐⡣⣶⠿⠛⠛⠉⢁⠔⢉⣀⠵⠐⠁⠀⠀⠀⠘⢌⠢⠛⢃⠙⠶⠿⠛⠛⢛⣋⡤⠔⣁⠜
⠀⠀⠓⠤⣀⠑⠀⠀⠀⠀⠀⢀⣀⣈⣡⠞⠁⠀⠀⠀⠘⠷⣧⡀⠄⠐⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠂⠚⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⢀⣠⠀⠄⠄⢐⡒⢒⠖⠐⠒⣖⢦
⠀⠀⢀⠤⠄⣶⡶⢦⣶⢶⢿⢶⣿⣿⡏⢷⡀⠀⠀⠀⠀⢀⠤⠒⡒⠲⣶⢺⡞⢩⠻⡀⠈⢱⠀⠀⠀⠀⠀⡰⢻⣿⣷⠛⠻⠭⠝⣠⡼⠦⣤⣘⣎⣦⡀
⠀⠰⢣⣯⣽⣭⣙⣩⠏⠹⣬⡗⠺⣿⣷⣾⡿⣆⠀⠀⢀⠁⠦⣰⡄⢳⠈⣃⣸⣁⣿⣿⡿⣿⣷⠀⠀⠀⠀⠇⢸⣿⣿⣿⣖⠶⠛⠬⣛⣓⡖⠁⢸⢸⡇
⠀⠰⣌⠻⢤⣙⢯⣉⡙⠿⠶⠾⠿⠁⠀⡰⢣⡟⠀⠀⢸⣧⠆⣀⢉⡧⠀⢾⠛⠙⢋⡧⠊⠀⣼⠀⠀⠀⠀⠘⢄⠋⠀⠒⠸⡀⠀⠀⠨⠇⣀⡴⢋⡜
⠀⠀⠈⠑⠦⢍⡙⠋⠉⠀⠀⠂⢀⣀⣡⠴⠋⠀⠀⠀⠀⠙⠢⢝⡻⠖⠀⠀⠈⠉⠀⢀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⠤⠀⠤⠤⠭⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡆⣜
⠀⠀⠀⡔⠒⠻⣍⢻⡍⣹⠦⣠⣤⣄⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣠⣤⣄⣀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⢿⣽⣿⣿⣷⡤⣄
⠀⣴⣾⡷⣤⡤⠛⠉⠛⡝⠳⢮⣛⡿⢻⣦⡀⠀⠀⠀⢀⣤⣴⡎⢉⣉⠙⣿⣿⣦⣾⠛⢱⠿⣝⢢⡀⠀⠀⠀⢠⡞⢫⠶⣶⡿⠀⠀⠀⠀⣸⣜⣾⡱⡄
⠘⣇⠣⡀⠀⣷⡙⠀⢠⠳⠐⢍⡹⠳⡄⣱⣹⠆⠀⠀⣾⢿⠁⠑⣏⠂⠑⠀⣀⣿⣷⠚⣁⣳⣨⢋⡇⠀⠀⠀⡌⠀⡟⡦⠖⠊⠓⣤⣤⣤⣿⠉⢈⠇⡏
⠀⠈⠳⢤⣄⡘⠻⠶⠶⠶⣶⡐⠒⠒⣛⡽⠋⠀⠀⠀⠘⢎⠀⠠⠌⠉⠁⠈⠀⠉⠥⠤⠒⢚⡵⠟⠁⠀⠀⠀⠘⢄⠐⢌⠂⠄⠾⠁⠧⠒⠉⡠⢊⡼⠁
⠀⠀⠀⠀⠀⠙⠛⠛⠓⠒⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠲⠒⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠬⠀⣠⣤⠀⠤⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠿⢿⣶⣶⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⠤⠤⣤⣀⣀⡉⠉⠙⠛⠿⠿⣷⣶⣶⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠀⡟⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⣤⣀⣉⠉⠛⠚⠿⠿⢷⣶⣦⣤⣄⣀
⠀⠀⠀⣀⣠⠤⠖⠛⠉⠀⢠⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠤⣤⣀⣈⡉⠉⠛⢿⢷
⣴⣾⣋⣉⠀⠀⢀⣠⠴⠒⢻⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡇⠀⡟⣸
⡇⠀⣀⡉⠉⢻⠉⠀⠀⠀⡿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⢃⡇
⣇⠀⡏⢹⠀⢸⠀⠀⠀⢠⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡾⢸⠁
⣿⠀⣿⢸⠀⢸⠀⠀⠀⢸⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⡟
⢿⠀⣿⢸⠀⢸⡆⠀⠀⣾⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⢸⠇
⢸⠀⢸⢸⡄⢸⡇⠀⢀⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡇⡾
⢸⡄⠘⠾⠇⠸⡇⠀⢸⠃⠈⠙⠓⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣼⣸⠇
⠘⡇⠰⣿⡇⠀⡇⠀⠈⠙⣒⡶⢤⣀⡀⠀⠈⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⣏⡿
⠀⠙⠲⠦⢤⣤⣧⠴⠞⠋⠁⠀⠀⠀⢉⣽⠶⠦⣤⣀⡀⠀⠈⠉⠛⠲⠦⣤⣀⣀⠀⠀⢀⡏⠀⣼⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠯⣭⣙⡓⣶⣤⣄⣀⡀⠀⠉⠉⠛⠚⠁⢠⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⢹⡟⠓⠶⠤⣤⣀⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣍⠳⠦⣄⣀⡀⠀⠀⠀⠀⢀⣠⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠬⣭⣭⣛⣛⣛⣭⠴⠋

⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣴
⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠘⠛⠂⣠⣾⣷⡦⠀⠀⠀⠀⣛⠅⠀⠀⠀⠘⣛⠃
⡏⣾⣿⡇⠀⢠⢤⣤⣤⠀⢀⣀⣀⣀⣀⠀⠀⠀⠘⢿⣷⡄⠀⢸⣿⣿⡟⠀⠀⠀⢠⢖⣿⣷⡄⠀⢠⢞⣿⣷⡄
⡇⣿⣿⡇⠀⢸⢸⣿⣿⠀⠸⡅⣿⣿⣿⠀⠀⠀⠀⠈⠛⢿⣆⠾⠋⠉⠀⠀⠀⠀⢸⢸⣿⣿⡇⠀⢸⢸⣿⣿⡇⠈⢆
⡇⣿⣿⡇⠀⠈⢳⡟⠁⠀⠀⠙⢾⡟⠋⠀⠀⠀⠀⠀⠀⣠⡹⣷⡀⠀⠀⠀⠀⠀⢸⢸⣿⣿⡇⠀⢸⢸⣿⣿⡇⠀⢸⣿⡶⠦
⣇⣿⣿⡇⠀⠀⣨⣇⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⣾⠟⠀⠘⢿⡆⠀⠀⠀⠀⢸⣼⣿⣿⡇⠀⠸⣼⣿⣿⡇⠀⢸⠹⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⣖⣒⣒⣒⣒⣒⠀⠀⠀⣶⣒⣒⣒⣒⣒⠀⠀⠀⠀⠘⢶⠀⠀⠀⠰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣘⣃⡀
⣿⣿⠿⠿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⠶⠶⠶⢾⡅⠀⠀⠀⠀⠀⠀⠀⢰⠀⣆⠀⠀⠀⢰⣿⣿⡄⢸⢸⣿⡇
⣿⣿⡇⠀⣸⣿⠀⠀⠀⣿⣟⢀⡏⢸⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠼⠀⠟⠀⠀⠀⠘⢿⡟⠁⢸⢸⣿⡇
⣿⣿⣮⢰⣿⣿⠀⠀⠀⣿⣿⢸⣿⢸⣿⠀⠀⢀⣠⠤⠜⢮⣉⣩⠞⠡⢤⣄⠀⢸⡛⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⢸⢸⣿⡇
⣿⣿⣯⣬⣿⣿⠀⠀⠀⣿⣿⣼⣿⣼⣿⠀⠀⡞⠀⠀⠀⠀⣴⠀⠀⠀⠀⠈⡇⠀⠳⡘⢿⣿⣿⣿⣿⡿⠃⠀⢸⡇⠀⠈⢩⡍⠁
⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⠀⠓⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠃⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠘⠃⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡤⠦⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⣻⠈⡇⠀⠀⠀⢀⣤⣞⠉⠳⣯⡀
⢠⣟⣭⣤⣭⣛⣷⣶⣤⡀⠀⠐⢿⣾⢛⣂⣉⣂⣀⣋⣀⣚⢻⣾⠃⠀⠀⠀⣠⢴⣾⣿⣷⣤⡁⠈⠀⠀⠀⠀⣋⣀⣀⣀⣀⣀⣘
⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡆⠀⠈⠁⠈⢧⣻⣿⣿⣿⡿⠃⠈⠁⠀⠀⢀⡞⢱⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠻⣜⣿⣿⣿⣿⠟
⣏⠙⠛⠛⢋⣡⠴⠶⠦⠤⠇⠀⠀⠀⠀⠀⠈⠙⡏⠁⠀⠀⠀⠀⠀⠀⠸⠁⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠉⣿⠉
⠈⠙⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠒⠛⠒
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡄
⡤⢤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⣴⣦⡆⣼⣿⡇⢀⡴⠋⢉⣀⣀⠉⠳⣆⠀⢠⣿⠀⣼⡆⢀⡄⠀⠀⢀⡀⠀⠀⠀⠀⡿⢈⡇
⣷⣶⠒⢺⠃⠀⠀⠀⠀⢠⣿⡇⢿⣿⡇⠙⣿⠃⡞⠀⣴⠋⠁⠉⠳⡄⠈⣇⠸⣿⠀⣿⠇⣾⡇⠀⠀⣾⣿⠄⠀⡶⣶⣶⣶⣶⣆
⢺⣀⠴⢾⠀⠀⠀⠀⠀⠀⣿⠀⠈⣯⠀⠀⣿⠀⣇⠀⢷⠀⠀⠀⢀⡇⠀⡿⠀⣿⠀⢻⡄⢻⡇⠀⠀⢸⡏⠀⠀⢧⢻⣿⣿⣿⣃
⢸⡟⠐⣾⠐⣶⣄⣀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠙⣆⡈⠙⠒⠒⠋⢀⡼⠁⠀⣿⠀⢸⡇⢸⡇⠀⠀⢸⡇⠀⠀⠘⠞⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠒⠒⠒⠒⠀⢄
⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⢡
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠑⠢⠀⢀⣀⡀⠀⠠⠂⠄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠏⠉⠉⠉⠩⠽⠿⠿⠿⠿⣷⠀⠀⠂⠀⡠⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠦⠂⠀⠀⢀⢂⠄⢎⣡⠀⠀⠀⠀⠀⢰⡠⠤⠔⠀⠀⠀⣿⠀⠤⠄⠊
⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠑⠢⡀⠀⠄⠀⠀⠰⠾⡀⢸⠣⠃⠀⠀⠀⠀⠨⡁⠀⠀⠀⠀⠀⣿⠀⠀⡠⠀⠂⠈⠀⠀⠈⠐⠢⡀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠉⠀⠀⠀⠈⠄⠀⠀⠀⠀⠢⣙⡓⠂⠄⠀⠀⠀⠀⠠⡳⣴⠣⠄⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠂⠀⠀⡁⠀⠀⠉⠉⡡⠀⢄⠀⠀⠁⠈⠉⠉⠁⠉⠉⠍⡉⠉⠁⢸⠀⠂
⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⢀⡀⢎⠀⠀⠀⠀⢐⠒⠐⠄⠀⠀⠀⠀⠀⠀⢈⠊⠀⠓⣤⠀⠀⢸⠀⠈⠂⠀⠀⢀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠆⠈⠀⠀⠀⣠⣄⣤⡀⠀⠀⢰⠀⠀⠈⡳⢄⠴⡓⠀⠀⢸⠀⣠⠊⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⣀⣀⣀⣒⣠⣬⣦⣤⣴⣤⣤⣤⣬⣦⣶⣤⣥⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠤⠠⠄⠀⠄⢠⠈⡗⡺⣾⣽⣧⣗⣛⣗⠒⠚⠛⠛⢭⡷⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⡤⠬⠤⡅⢭⠸⡅⢯⠿⣿⢹⡿⣤⠀⡤⠕⣀⠱⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠤⠤⠤⠤⠤⠍⠉⠁⠨⢭⣁⣉⣉⣩⠭⠽⠬⢤⢬⠭⣬⣥⣭⣿⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣁⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣁⣠⣠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⢠⠀⠀⠀⠀⠀⠀⡀⢀⠄⠠⢀⠀⠀⠀⡠⠀⠀⠀⡀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠀⠀⣀⡢⠀⢂⠀⢀⠀⢂⠀⠀⠀⠊⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠐⠄⢠⣂⡉⠦⠂
⠀⠀⢠⡀⠀⠀⠀⠑⠀⠀⠢⢀⠀⠀⠁⠀⢐⣓⡅⠀⠀⡐⡀⠀⠂⠀⠀⠀⠀⡀⠁⠀⠉⠂
⠀⢆⠀⢀⠀⠀⡠⠐⢂⠂⠂⠠⡀⠀⢰⠍⠘⣵⠂⠀⢠⠊⠀⠐⠀⠰⠐⡠⠊⠀⠈⠁⠒⠂⠀⠀⠈⠡
⠀⢀⢄⠈⠀⢈⠀⢀⠤⢀⡦⠦⠏⢀⠤⢄⡀⠻⠀⠀⠈⠂⠠⠛⠑⠀⠀⠀⠀⢀⡀⠁⠁⠀⠂⠁⠂
⠀⢸⠀⠣⠀⠉⠀⠡⠬⠅⠒⠊⠀⡘⠀⠀⡌⠀⢀⠀⠀⠦⠄⠀⣠⣤⢶⣞⣤⠀⢀⠀⠀⠀⠀⡄⠒⠆
⠀⠸⡐⢀⡇⠀⠀⠖⠂⠀⠀⢠⠆⠑⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⡈⠹⠉⠉⠉⡁⠀⢀⠘⠀⠈⠁⠈
⠀⠀⠈⠁⠐⠢⠀⠄⠀⠀⠀⡀⢀⡠⣶⠴⠀⠀⡀⠀⠀⠰⠳⠀⠀⠀⠀⠉⠀⠀⠠⠀⠄⢀⠄⠙⣈⣠
⠀⠓⠀⠀⠀⠀⠀⠀⡄⠀⠄⠐⠂⠉⠠⢊⠐⠃⢃⡲⠖⠀⠀⠀⠀⠤⠀⢀⡀⢈⡀⢀⠀⡀⠀⡀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠴⠔⠒⠂⢉⠴⠀⠀⠀⡀⠀⠀⠂⠅⠀⠀⠐⠈⠠⠈⠀⠃
⠀⢂⠀⠀⠐⡀⠀⠀⢴⡄⠀⠀⣠⠤⠤⠸⢇⣀⠐⠋⡀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨
⠀⡠⢐⠂⠚⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠉⠁⡀⠁⠀⠀⠀⠂⠠⠈⠁⠀⠀⠀⠂⠐⠉⢀⠀⠀⠀⠈
⠀⠀⠠⢀⠀⠀⡔⡄⠀⢀⠀⠄⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢄⠀⠲⠆⠈⠁
⠀⠀⢀⣀⠀⠀⢡⠁⡀⠠⠁⡆⠀⠂⠀⠀⢀⠀⢰⠂⡀⠀⠀⠀⠀⢀⠰⠂⠀⠐⢣⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠖⠀⠀⠀⡀⠐⠀⠾⠀⠀⠀⠈⠀⠠⠀⠀⠠⠀⠀⠂⠁⠀⠀⠀⠀⢀⠜⡄⠀⠈⠿⠂⠁
⠀⠀⠂⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁⠀⠀⠄⠀⠀⠄⠒⠒⠪⠐⠂⠁⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⡐⡀⠈⠁⠠⠒⡀⠃⠀⡙⠀⠀⠀⠀⠀⢀⠀⠀⠠⡰⠠⢀⠆⠄⠂⠀⣀⠀⠀⢀
⠀⠐⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠃⠀⠂⠠⠀⠀⠉⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⡉⠀⠀⠀⢩⠃
⠀⢰⢙⠡⠃⠀⠚⠀⠂⠀⠀⡐⠀⠀⡡⠐⠘⠂⠀⢀⡀⠍⠀⠀⠀⠀⠀⡙⠙⠁⠀⠀⠀⠐⠀⠀⠐⢀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠋

⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡎⠀⠐⠁⠀⡠⢀
⠀⠀⠄⠀⠀⠐⠀⠀⠀⠈⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⠠⠄⢀⡀⠀⢀⡇⢸
⠀⠀⠀⠐⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠂⠀⢂⠠⠄⣁⢀⣈⣉⣀⠉
⠀⠘⠀⠠⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠉⠉⠐⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠞⠀⡉⠒⠢⠻⠤⠤⠀⠔⠉
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠌⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠐⢄⢴⡆⠀⠀⠀⠀⠠⠀⣀⠈⠙⡀
⡀⠀⠀⠈⠂⠄⣀⡈⠂⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⡉⠻⠀⢀⡤⠂⠀⣎⠂
⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠴⠰⠈⠤⣀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠠⠘⡦⠴⡤⠤⠖⠁⡀⠔
⠀⠀⠈⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠈⠢⡀⠀⠁⠀⠀⠈⠲⠄⠀⠀⠈
⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⣀⠀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⢄⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⢀⡠⠲⠀⣶⠤⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⡈⠀⠀⠀⠐
⠀⠀⠎⣠⠊⠙⡟⢲⢳⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠖⠲⠤⢀
⠀⠀⣥⠨⡓⡿⣞⠄⡽⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠎⠀⠠⣄⢡⠀⠈⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠈⠳⠍⡵⠙⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢣⡀⠀⠀⢨⠀⠀⠀⣹⠷⠈⠉⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⠘⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠓⢦⠀⠀⠀⠀⠀⠀⠑⠂⠤⠄⠒⠁⠀⠙⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⡔⠒⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⡴⠃⠀⠀⠀⠀⠀⠤⠒⠀⠉⠉⠀⠀⠀⠀⢀⠀⠈⠀⠐⠀⢠⠘⠂⠀⣀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⢈⠉⠁⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠂⢰⡀⠲⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠐⡀⠀⠀⠀⠀⠘⠈⠀⠈⢰⠃⠈⠁⣈⣀⠀⠀⡀⠒
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠠⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⣶⣿⣿⠆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠀⠠⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢈⠁⠒⠔⠃⠀⠈⠿⠛⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠐⠒⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠘⠑⠂⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠒⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠚⠛⠛⠛⠛⠓⠶⠶⣤⣄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣞⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣫⡿⠖⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠶⠶⠦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⣾⠋⢰⡾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⠾⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠉⠉⠉⠉⠉⠛⠓⠒⡆⠀⣿⠀⢸⠀⠀⢀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠉⣙⣛⣛⡓⠒⠒⠒⠒⠒⠃⢀⡏⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⠀⠀⠀⣿⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⢸⡇⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⠃⠀⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⢀⡏
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡟⠀⠀⣾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠓⠒⠒⠚⠛⠛⠀⠀⢀⡟⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⢀⡟⠀⣾
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢿⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠁⠀⢸⣇⡴⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⣸⠃⠀⢀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠩⠉⠉⢩⠉⠉⠉⠛⠛⠛⠛⠛⠀⠀⡿⠀⣠⡿⠉
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⣀⡴⠋⠈⠉⠉⠉⠛⡟⢛⡿⠛⠓⣷⡒⠶⠶⠶⠶⢶⣦⢤⣤⣤⣤⣤⣴⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⣠⠖⠚⠁⢾⣇⡀⠀⠈⠙⠛⠓⠒⠒⠛⠁⠀⣠⡿⠀⠈⠣⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣧⣀⣀⣀⠈⠻⠯⣿⣶⣶⣶⣶⣶⣒⣒⣾⡽⠟⠁⠀⠀⠀⠀⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡤⠤⡤⢤⡤⠤⣤⢤⣤⣄⣈⣉⣉⣉⡉⠙⠛⠛⠛⠷⠾⠯⢭⣭⣥⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠋⡿⠓⡾⠓⣲⠓⡶⠧⢤⠧⢤⡯⣤⣽⣉⡟⢀⡖⢲⠖⢦⠤⢤⡀⠀⢩⠟⣇⠀⠀⠀⠀⣠⡴⢶⢞⡿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢸⣉⡽⠉⣹⠛⢲⠟⢲⠓⢲⠿⢤⡾⠤⣼⢥⣼⠁⡜⢉⡟⢒⠟⠒⡾⠁⡰⠋⣴⠏⠀⠀⣠⣞⣁⣠⣧⠋⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠤⠤⠬⣉⣉⣉⣙⣛⣒⠛⠒⠛⠲⠾⠤⠴⠧⠴⠃⢸⣉⣽⣉⡟⠓⡾⢀⡜⣡⠞⠁⠀⠀⣰⠋⠀⠀⠀⠈⠉⠲⢄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠓⠒⠶⠶⠶⠯⠭⣭⣭⣉⣓⣒⣒⣒⠒⠒⠦⠤⠤⢭⣭⣉⣠⢋⡼⠃⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠓⠲⠶⠶⠶⠿⠟⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣴⣲⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⠀⠀⢸⢰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠀⠉⠉⡏⠀⠀⢸⠀⠀⢸⢸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⢀⣤⣠⣦⣾⡀⠀⢸⢸⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⢸⠉⠉⠉⠀⠑⠁⠙⣋⠙⠿⠿⣳⣜⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣭⣐⣂⠩⢝⣛⣿⣿⠿⠀⡀⠀⢀⣇⣀⣸⣀⣀⣀⠀⡛⠆⢼⣿⢬⣥⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⡟⢫⣽⡾⡎⠉⠉⠉⡏⠉⢸⠀⠀⢸⠀⣻⠆⢀⡄⣪⣿⣿⣿⢹⢀⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⢸⣿⡇⢸⡇⣼⢹⢱⠁⡆⠀⠀⡇⠀⠸⠆⠐⢾⠂⠈⡷⠈⣸⢧⣿⠟⢉⡼⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠿⢇⡘⠗⡏⢸⢘⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠙⠞⠛⡢⢋⠔⠁⣨⠦⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠘⠈⠀⡇⠀⠀⣧⠤⠤⠤⠤⢼⠀⠀⠀⠈⠻⡿⢂⡤⠚⠁⠀⠘⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⡆⠀⠀⠃⠀⡀⢚⢦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢩⣿⡍⣙⣤⣿⣄⠀⠀⠀⢰⢁⡉⠀⠼⢧⣠⡤⠤⠤⠤⠤⠤⠤⠄⢰⠳⠃⡠⠌⢢⠀⢠⣆⠀⠀⢹⣿⡇⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠮⢙⡰⣿⣿⢿⠇⢸⠀⢸⣿⠐⠂⢰⠍⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢾⡄⣸⠴⢤⡀⠡⢸⡿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⣦⠀⠀⡗⠘⢿⣤⡐⠳⠛⣼⠟⠤⠤⠤⠤⠤⠤⠤⠤⠘⣷⡗⠤⠔⡃⡀⣬⠁⠀⠀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⡀⠰⡄⠀⡇⠀⠀⡀⢹⣤⣴⣇⡀⠄⢠⡄⠀⠠⠄⠀⣤⡀⠈⠃⠀⡰⠁⠀⣾⡇⠀⢀⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣶⣶⣴⣟⠊⢸⡇⣤⣶⡾⣿⣋⡀⣰⠄⡶⠀⠀⠀⠀⠀⠘⣧⣀⣀⡜⠁⠀⠀⢿⡇⣾⣼⡇⢸⠇
⠀⠀⠀⠀⣀⠤⣤⣶⣿⣿⣿⣷⣬⣍⠙⠳⠤⠵⣿⣋⡐⣿⡇⠀⠨⣤⣇⣀⣀⣀⡀⣠⡀⠹⠻⡻⣧⣤⣀⠀⢸⣿⣿⡟⠀⠸
⠀⢠⣶⠉⠀⠀⠻⣿⣿⡿⠿⠿⠛⠋⠀⠄⠀⠀⠀⢹⣷⠈⡃⠀⠀⢀⣠⡅⠀⣉⠄⢸⡏⠳⢤⣻⣮⣶⡆⠃⢸⡟⠁⣀⣤⣶⡇
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⣼⣿⠀⠥⠛⠟⢫⣾⣷⠀⢸⣷⣶⣶⣴⣯⡍⠉⢹⣿⣿⡿⣳⣾⣿⡿⣿⣧
⠠⡟⠁⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡄⢰⢦⣩⣿⣆⢠⡄⠲⠀⢯⣍⣣⣼⠯⠉⠉⠉⠉⠡⠚⢸⠟⢁⣴⣿⣿⡿⣿⣿⣿⡀
⠀⠀⣀⣈⣉⡟⠙⠋⡿⠛⠛⢻⠛⠉⡿⠑⣦⡄⠀⢹⣿⣷⡠⢷⠂⠓⠂⡀⠀⠀⠐⠀⠁⠀⠀⠀⠀⢠⢔⣿⣿⣿⣿⣽⣿⣿⣟⡧
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣷⠘⡆⠻⣿⣧⠈⠇⢈⠁⠀⡀⠀⠀⡤⠀⠀⠀⠀⠠⢸⣿⢟⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣿⣇⠠⣑⠌⠁⡡⡀⠈⡄⠐⢽⣄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⠉⠻⠛⠻⣿⣿⣿⣿⠀⠀⢿⣿⠆⠻⠿⠾⢰⣧⠀⢰⠀⠈⠻⣦⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠀⠀⢸⣿⣦⣤⣄⣰⣿⠃⠀⠈⡄⠀⠀⠑⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢏⡾⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠉⠙⠃⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⠿⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣅
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⣰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡏⢸⡂⢻⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⢀⡞⣵⣛⠶⠀⠀⠀⠀⠀⠀⣀
⠀⠐⠚⠓⠀⢇⡗⡆⠀⠠⣭⡭⣥⠆⠀⠀⠀⢷⠘⠃⠀⡽⠀⠀⣀⡤⠀⡀⠀⠀⠴⣣⠯⣾⠟⠁⠀⠀⠀⠀⢠⡯⣹⠇
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠚⠁⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣄⣠⣀⠀⠀⠀⡀⠄⡀⠉⠀⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠄⢠⡲⠄⠀⠀⠠⣄⠻⠈⣠⠇⠀⠀⠈⠙⠛⠁⠀⠀⠀⣡⡆⠈⠐⢦⠀⠀⠘⠛⢿⡟⠉
⠀⠀⠀⠀⠶⠀⠀⠀⠠⡌⠂⣋⡀⠀⠀⠀⢀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⢀⠶⠀⠸⠋⣀⣉⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⠒⠆⡀⠀⠀⠈⠛⠠⣤⠀⠀⠀⠀⠰⠦⠆⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠍⠙⠳⣦
⠀⠀⠀⠀⣠⣀⡀⠀⢠⡎⠀⠀⠀⠀⣴⠀⠈⠣⠀⠠⠈⠁⠀⢀⠀⠀⠀⢀⠀⠀⠀⣒⠆⠀⠀⠀⠀⠀⠀⠈⠀⣠⠔⠚⠁
⠀⠀⠀⠀⠼⣝⠇⠀⠀⠁⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠴⠆⠀⠶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠠⠀⠘⢡⠀⠀⢀⠀⠆⢐⡤⠂⠀⠄⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠖⢤
⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⢤⠀⠀⠀⠀⠤⠀⠠⠦⠜⠀⠐⠒⠐⠊⠀⠀⠀⠐⠂⠂⠀⠤⠄⠀⠀⠈⠂⠄⠀⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⠆⠀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⢠⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢻⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠛⣼⣧⡹
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡐⠀⠀⠀⠀⠀⠀⠀⣴⡶⣲⢶⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠴⠆⠀⠠⠶⠀⠀⠀⡆⢈⢛⠀⡀⠀⠀⢠⣤⣤⡄⠰⠆
⠀⠑⢶⣦⣶⣶⠎⠀⠀⠙⠳⠿⠷⠛⠀⠀⣄⡈⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠠⢺⠏⢻⡍⣱⠀⠛⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠉
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢰⡆
⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢴⠆⠀⠀⠀⠘⢻⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⠆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣡⣴⡀⠀⠀⠀⠀⠀⣄⣀⣀⣸⠟⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠄⠈⠀⠐⠄⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⣌⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤
⠀⠀⠐⠃⡠⠾⡁⠀⠐⠒⠒⠀⠙⠀⠀⠀⣦⣽⡷⣦⡁⠀⠀⠀⢀⡆⢈⡷⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠖⠒⠒⠛
⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⣤⡄⠀⠀⠀⠒⠊⠐⠃⠘⠃⠀⠀⠠⠁⠁⠭⠀⠀⠀⠈⠉⢴⠆⠻⠂⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠛⠓⠁
⠀⠀⠦⠀⢀⠀⠀⠀⠀⠀⠉⢡⡀⠀⠀⠀⣀⣤⡶⠖⠀⡀⠀⡀⠂⣀⠰⠆⠀⠀⠀⠒⠲⠂⠀⡄⠀⠀⠘⠋⠀⠠⡖⢳⡄
⠀⠀⠰⠿⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠐⢺⡗⠀⠀⠠⣤⣄⣀⣧⡔⠀⠀⠀⠀⡠⠀⠀⠁⠈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣟⠏⠛⣿⠉⡟⠛⣟⠟⣛⡿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⠰⣖⣤⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⣾⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡵⢎⢾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠷⣿⡿⣯⣙⠗⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠙⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡿⢻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠖⠚⠛⠛⠛⠙⠋⠋⠙⠛⠛⠓⠒⠒⠒⠒⠲⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠸⠆⠀⠐⠒⠲⠒⠖⠒⠒⠐⠒⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠄⡤⠠⢀⠄⠀⣤⣠⣤⣤⠄⠤⠀⠤⡤⠤⠤⠤⣤⣤⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣤⣀⣀⠀⠠⢢⠀⠀⠀⡄⠀⠒⠒⠀⡠⠒⠀⠄⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠰⡄⠀⢈⠂⠰⡨⠤⠒⡄⡄⠀⠀⠀⡆⢀⡀⠀⡠⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠟⠀⠉⠉⠁⠀⠀⠈⠁⠉⠀⠈⠉⠁⠀⠀⠀⠈⠁⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠳⠤⠤⠶⠒⠖⠠⠲⠒⢶⠒⡲⠶⠶⠶⠲⠶⠦⠦⠤⠠⠇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⢤⡄⠀⢠⠞⠉⠉⠉⠙⢳⠀⠀⠀⣠⡄⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣀⠈⠉⠀⠀⠈⠳⠒⠶⠒⠚⠋⠀⠀⠀⠀⠀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠚⠒⠓⠚⠛⠛⠛⠛⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢷⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠲⡄⠀⢸⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠾⠃⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣒⣀⣒⣀⣀⣀⣠⣏⣀⣤⣤⡤⠴⠶⠖⢺
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⣒⣖⣒⣶⣒⣒⣖⡒⣲⠖⠒⡶⠖⢤⠤⠭⢭⠭⢭⣍⠉⠉⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡾⢁⠾⢤⠾⢤⡾⠥⣤⠯⢬⡽⠭⢭⠿⠭⣽⢯⣉⣽⣋⡲⣾⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢠⠟⡠⠛⢲⠛⢲⠞⠒⡴⠃⢢⠞⠤⡴⠧⢤⠾⠥⣤⠮⣤⢞⡗⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢠⠟⠐⠿⠿⠿⠿⠿⠿⠿⠷⠾⠟⠖⠾⢷⣶⣿⣶⣺⣗⣲⡽⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⡿⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⣤⠴⠞⠋⠉
⠀⠀⠀⠀⠙⠛⠛⠛⠒⠒⠲⠶⠶⠶⠶⠶⠦⠤⢤⣤⣤⣤⣄⣀⣀⣀⣀⣿⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣦⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣧⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣷⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⣠⠞⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⢀⣤⠞⢉⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⢀⣠⠴⠞⣋⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣠⡴⢞⣫⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⢀⣤⣶⣿⡷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣤⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢀⣠⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣞⣫⡥⠶⠶⣦⡀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⣭⠶⠛⠉⠀⠀⠀⠀⢸⡇⠀⢠⡾⠁
⠀⠀⠀⠀⠀⣀⡴⣛⡵⠞⠉⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣰⡟⠁
⠀⠀⠀⣠⢞⣭⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⢾⡟⠁
⠀⣠⢞⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣴⠞⣡⠟
⣼⢫⡟⠁⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⣁⡴⠋⣡⡾⠃
⣿⠈⠷⣤⣤⣤⣤⠶⠾⠛⠉⣀⡴⠞⠉⣠⡾⠋
⠘⢷⣤⣄⣀⣠⣤⣤⠶⠞⠛⢉⣀⣴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡏⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣹⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⣏⡀
⠀⠀⠀⠀⠀⢀⡼⢋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡙⢦⡀
⠀⠀⠀⢀⡴⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢦⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠉⠉⠁⠀⠀⠀⠐⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣀⣀⣀⡠⠶⠾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⣤⣤⣤⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠁⠍⠻⡇⠀⠀⠀⠀⠀⢀⠤⢤⣀⡀⠀⠉⠹⢦⡀⠀⠀⠈⠂⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡇⠀⡀⠐⠉⠛⠛⠳⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡸⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⠶⠛⠁⠀⠀⠹⢦⣀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⣤⠄⠀⠠⠴⣤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠸⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠋⢀⡀⠀⠀⠀⢩⡿
⠀⠀⢠⣀⠀⠀⠀⠀⠉⠛⠲⢿⣆⣻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠤⠀⠀⠈⠁⠀⣀⠼⠀⠀⠀⡞⠀⠀⢀⣿⠀⠀⠀⠀⣸⡅
⠀⠀⠼⢿⣗⡦⣄⣀⣀⡀⠀⣤⣀⣠⣭⣥⡿⠋⠁⠀⠀⠀⠀⠀⠤⢄⡀⠀⠉⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⢠⠾⠇⢣⣤⢀⠔⠀⠀⠀⠀⢀⡿
⠀⠰⣤⣄⣀⠀⠉⠈⠛⠃⢀⣿⠀⠀⠘⠁⠀⠀⠀⠀⠐⠒⠲⠤⠀⠀⠀⠀⣀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠁⠿⠀⠀⠀⢀⣠⡏
⠀⠀⠈⠙⠛⠛⠤⠶⣶⡄⠸⠃⠀⠀⠀⢀⣀⡀⠉⠉⠀⠀⠀⢀⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣷⢀⢀⡴⠚⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢞⡘⠇⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⢤⣀⡀⠀⠀⠀⠀⠀⠈⢂⣾⡿⠉⠁⠀⠀⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠈⠹⢿⣤⣤⡶⠶⠋
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣆⠀⠀⠀⠙⠻⢿⣾⣽⣛⠳⢦⣄⣀⠠⠔⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠦⣄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠉⠛⠻⡷⢶⣏⠉⢠⣄⠴⠒⠛⠁⠀⠀⠀⡠⠂⠂⢬⣀⠀⠀⠀⠀⢈⡶⣄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠴⠛⠋⣿⠿⣶⡉⠀⠘⣇
⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡄⠀⠀⠀⠙⣾⠟⠀⠀⢠⡏
⠀⠀⠀⠀⠉⠻⠿⣶⣶⣀⣐⠲⣶⣶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠠⢄⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠘⢤⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠷⠶⠿⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏⢯⣭⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⠿⠛⢉⣇⣴⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⢀⣀⣾⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⣉⣠⣤⣤⠶⠾⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⣥⣶⠾⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣡⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠉⠉⠻⣿⠉⢠⡟⠁
⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⠃
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⡿⠋
⠹⢴⣤⣤⣤⣤⣶⣶⣞⣻⠭⠭⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⡰⠋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠡⡐⢌⠳⡀⣷⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢶⣿⡵⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠞⠉⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠂⢌⣿⣠⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠴⠖⠋⠑⢦⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⢿⠘⠛⢻⢇⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⣸⣿⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⣀⣟⡟⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⡬⢧⣿⠾⠓⠁⠀⡠⠤⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⣲⠆⠘⠁⠈⣭⣭⡇
⠀⠀⠀⠀⠀⠀⠀⢾⡰⢧⠐⢛⣦⠀⠀⠀⡇⢰⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⢹⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣻⠀⠀⠀⣷⢸⡄⠀⠀⠀⠀⠀⠰⠰⠀⠀⠚⠸⠂⠀⠀⠀⠀⠀⠀⠀⡟⠐⡏⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⣧⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢠⠀⡀⠀⢀⡀⡄⠀⠀⠀⠀⠈⠀⢰⠇⢸⠇⠀⠀⠀⣠⢞⡵⠒⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⣴⡇⠀⠀⠘⡇⢷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⡟⠀⣽⠀⠀⡴⢛⡵⠋⠀⠀⠀⠱⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢧⢸⡀⠀⠀⠀⠀⠒⠒⠀⠚⠀⠰⠀⠀⠀⠀⠀⠀⢸⡇⢨⡇⠀⠈⠓⣯⠰⡋⢶⠟⣱⠀⣸⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢄⠀⠀⠀⠀⢸⠈⣇⢀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠀⣼⠀⠀⠀⠀⠸⡄⠈⠠⠞⠁⢀⡏
⠀⠀⠀⠀⢀⡤⡶⠋⠀⠀⠀⢀⣤⣓⠂⠄⡀⠘⢦⢈⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⢀⣤⣤⣤⣤⣤⡤⠶⠃⠀⠀⠀⠀⠀⠙⠚⠉⠉⠉⠉⠁
⠀⠀⠀⠠⡏⠈⠂⠤⢤⣴⡶⢍⠫⠤⠴⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢻⡴⡿⠐⣲⡄
⠀⠀⠀⠀⠙⠶⣤⠤⠤⠴⠶⠾⣐⣶⡾⠟⠁⢀⣀⣀⣀⣀⣀⣀⣈⣷⣶⣖⣒⣒⣒⣿⣁⣀⣀⡠⢤⣤⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢠⠇⣦⠗⣆⠖⢠⢄⡴⡄⣠⠀⠀⠀⠀⠀⠀⠀⠊⠇⠫⠊⢆⠀⢀⡄⡐⡋⠀⠀⠉⠐⠠⣠⣄⡀
⠀⠀⠀⠀⠀⢠⡀⠠⠂⠀⠀⠀⠀⠀⠀⢠⡏⡜⠒⢋⢛⢖⢼⢸⣷⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠘⠂⠫⠘⣉⣡⣿⣣⣤⣴⣴⡿⠀⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢀⣃⣀⣁⣴⣋⠁⠀⠀⢀⡞⠴⡳⠰⣋⠇⠈⢢⠀⠀⠘⢖⣾⣊⣀⡀⠀⠀⠩⠆⠠⠟⢋⣉⣃⠀⠉⠉⠉⠉⠉⠀⠀⠘⢣⡀⠐⠃
⠀⠀⠀⠀⢺⡭⣤⣤⣤⡤⠤⣿⠀⠀⠈⠓⠒⠲⠶⠶⠒⠒⢺⡄⠀⣴⡟⠤⠔⠒⠒⠒⠒⠒⠚⠻⠛⠋⠉⠃⠀⣀⣤⡤⠞⠏⠃⠀⠀⠀⠈⠻⣉
⠀⠀⠀⠀⠀⣣⡀⠀⠀⠐⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⢭⠓⠈⡤⠀⣀⡜⣀⠀⠀⠀⠀⠀⠙⠫⡉
⠀⠀⠀⢰⠏⠁⠭⠖⣛⠻⠭⠆⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢃⣚⣨⢴⣺⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢠⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣤⣿





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡃⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣯⡁⠛⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣀⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠒⠚⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣶⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣟⣻⣿⣿⣯⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣝⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠁⣴⠋⠹⠇⠈⠛⢮⠽

⠀⠀⠀⠀⠀⠀⠀⠀⡞⢉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣤⣶⣤⣶⣧⣴⣦⣴⣦⣤⣶⣤⣶⣤⣵⣦⣴⣦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⢻⣿⣾⣿⣾⣿⣶⣿⣷⡟⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠐⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠂



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⣀⣤⡄⠀⠀⠀⠀⠀⢰⢰⢰⢰
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⣿⣿⣿⣧⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣾⣸⣸
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⢼⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⢀⣾⣿⣿⡿⠟⠋⠉⠉⠉⠛⠻⣿⣿⣿⣦⡀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠃⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠙⣿⣿⣿⣦⣄⡀⠀⠀⠀⣀⣠⣶⣿⣿⡿⠃⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠛⠛⠀⡄⡏⠉⠉⢹⢠⠀⠛⠛⠛⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⣤⣤⠀⠃⣇⣀⣀⣸⠘⠀⣤⣤⣤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠉⠉⠀⠀⠀⠐⠒⠀⠀⠀⠉⠉⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠾⠃

⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠆⣀⠄⡆⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢦
⠀⠀⠀⢘⡀⡘⠠⡴⡀⡀⡛⠀⡄⠀⠀⠀⠀⡀⣀⣀⣠⢿⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠
⠀⠀⠀⣀⠤⠆⠀⡀⠹⢠⠓⢰⠇⠀⠀⡀⠀⠀⠙⠋⠁⠈⠙⠋⢛⣾⣅⡀⠀⠀⠒⠄⣀⣀⡀⣀⢀⣀⡀⠔⠛⠀⠀⠈⠤⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠅⠐⡳⠀⠉⢡⠖⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⢶⣀⠆⢠⠤⢤⠤⣤⠤⣤⠀⣤⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠠⠄⡘⢷⠸⠝⠖⡁⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠙⠷⢾⣤⣴⣄⣤⣄⡼⠶⠛
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠀⠁⠁⠀⠀⠀⠳⠀⠀⣤⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣹⣦⡀⣠⣠⣿⣿⣿⡟⠀⠀⠀⡀⠙⣀⢤⣈⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠄⠐⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⣿⣿⠿⠿⠁⠀⠀⠀⠃⠀⠀⠁⢠⡎⠀⠀⡼⠀⠀⡄⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⡰⠊⠉⠿⣦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠦⠔⠁⠀⣰⠁⠀⠀⣇⠀⠀⠀⠀⠀⢀⣀⣹
⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⣤⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠰⢾⡇⠀⠀⠀⠈⠲⣶⣤⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⡇⠀⠀⢐⣿⠀⠀⠀⠀⠀⠈⠴⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⠾⣠⡿⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⠀⠀⠇⠀⣼⡿⠁⠀⢀⠀⠀⠀⠉⠁⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠘⡆⠀⢸⡃⠀⠀⢀⠀⠀⠀⠀⠀⢀⢨⡆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠧⠀⣸⠀⠀⠈⢤⣆⠀⢸⠀⢀⣼⣼⠃⢀⠄⠰⣼⣻⣸⣧⣴⣦⣄⠀⠀⠄⢠⡟⠀⠀⠈⠻⣦⡀⠀⠀⠄⠀⣤⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⡔⠒⠉⠒⢣⠋⠁⠀⠹⢻⣇⠀⠀⠈⢷⠀⠀⠀⠀⠈⠛⠻⠾⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡀⣀⣿⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐⡿⠀⠀⠀⠉⠲⠦⣤⣴⡾⠿⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣤⡄⣠⡾⢇⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣶⣶⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣷⣦⠀⠀⢀⡏⠀⠀⠀⠀⠀⣨⡛⠓⠉⠇⢸⠅⡀⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣢⣾⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠁⠀⠀⠁⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢁⢠⠂⠀⠰⡁⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⡀⡐⡐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠃⠀⠃⠈⠈⠀⠀⠈⠘⠀⠁⠋⠀⠀⠁
⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣶⡄⠀⠀⠠⣶⠀⠀⠀⢠⣶⠀⠀⠀⢠⣦⠀⠀⠀⣴⡆⠀⠀⠀⣶⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃⠀⠀⠀⣿⠀⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢻⡇⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⢠⣾⣿⣦⠀⢠⣾⣿⡆⠀⢰⡿⠷⡄⠀⣾⣿⣦⠀⢰⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣸⣧⡇⢰⣄⣀⣠⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⣿⣿⡇⠀⣿⣿⣾⡇⠀⢻⣷⡏⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠃⠈⠛⠿⠟⠁⠀⠀⠒⠀⠀⠀⠙⠛⠋⠀⠀⠛⠛⠁⠀⠛⠛⠛⠛⠀⠈⠛⠁⠀⠘⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠛⠋⠿⠶⣤⡀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠐⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡅⢠⢈⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⡇⠘⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡇⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠘⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠂⠀⠀⡇⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⡄⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠄⢈⠑⠢⠤⡄⢀⡀⠤⠤⠖⠻⠂⠀⠀⠀⠀⠀⠃⠀⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀
⠀⠀⢀⢤⡯⠴⠚⠛⢿⠄⠀⠀⠀⣀⠋⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠀⠀⡠⢤⡀⠀⣤⣀⢀⠀⠀⠠⣤⣤⡄
⠀⠀⢸⡅⠉⠈⣀⣀⠈⣧⠀⠠⠊⠀⠀⠀⠀⠀⠀⢢⢣⠀⠀⢀⠔⠲⡢⡀⠀⠀⠀⢸⡆⠸⠀⠘⡇⠀⡻⢯⡟⠀⠀⠀⡇⠀⡆
⠀⠀⠀⢷⠈⠥⠀⠒⢂⠺⡄⠀⢄⠀⠀⠀⠀⠀⠀⢘⡼⠀⢠⠊⡀⡀⠘⢴⡄⠀⢐⠀⡇⠀⢑⠊⠀⠀⠑⡔⠁⠀⠀⢀⠇⠀⡇
⠀⠀⠀⢫⠔⣈⠉⠩⢤⡸⠇⠀⠀⠙⠀⡆⠒⢐⠘⠉⠀⠰⠁⠀⠈⠉⠀⠈⢳⠀⠘⢲⠚⠀⠀⢘⠀⠀⠃⡄⠀⠀⢠⠊⠀⠀⠸⢢
⠀⠀⠀⠈⠍⠀⠬⠅⠒⠂⠁⠀⠀⠀⡖⠒⠲⠖⢲⡆⠀⠁⠛⠛⠛⠛⠛⠋⠊⠁⠀⠀⠒⠀⠐⠊⠀⠀⠑⠁⠀⠀⡘⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠭⡭⡭⠭⠭⠭⠭⢭⠭⠭⠭⠕⠀⠀⡇⠀⠟⠑
⠀⠀⠀⢀⠔⡉⠤⠒⠨⢕⠢⡀⠀⠀⠀⠀⢀⡠⠐⠚⠓⠂⢄⠀⠀⠀⠀⢰⠸⠷⠃⣠⡤⣄⡹⠿⢤⠆⠀⠀⠀⠀⠋⠈⠉⠈⠁⢩
⠀⠀⢠⢡⢊⠤⡀⠀⠀⠀⠱⠰⡀⠀⠀⠰⡑⠁⡎⠀⠀⠀⠀⠑⠄⠀⠀⢸⠈⠀⡾⣥⡄⡀⣿⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⢈⢰⡃⠀⢟⠸⢸⣳⡇⠇⠅⠀⣀⣃⣀⣈⣁⣠⣤⣤⣤⣤⣸⣀⠀⢰⠀⠀⠙⣿⣁⣻⠟⠀⢸⡇⠀⡎⣤⣠⣤⢠⡄⣤⠠⢼⡆
⠀⠀⠈⢌⠓⡔⠁⠘⣍⣩⠞⡸⠀⠘⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠃⠸⠴⠤⠄⠉⠀⠈⠀⠤⠎⠇⠠⠁⠉⠀⡁⠉⠈⠈⠈⠵⠒
⠀⠀⠀⢀⠁⠯⠐⡂⠇⡀⠊⣠⣖⡒⢦⠀⠀⠀⣀⣀⣀⡀⠤⢀⠢⡄⠀⠀⣠⠀⠐⠒⢂⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠜⠀⠀⠀⢅⠅⠀⠟⢶⠲⠽⠀⠀⡎⢠⢢⢀⠠⡀⠑⢁⠿⠀⠀⣇⣤⠬⢤⣤⣴⠀⠀⡠⣴⣡⣤⣤⣤⣤⣤⣤⣌⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠀⠀⡄⠀⠀⣧⢄⣈⣘⣀⣡⢰⡩⠋⠀⠀⢸⠇⣀⡾⠿⡾⠀⠀⢠⠊⣠⠲⣠⣦⢴⠂⣦⣤⠙⢺
⠀⠀⠀⡤⠀⠒⠀⢠⡀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠚⠚⠂⠉⠁⠀⠀⠀⠀⠘⣎⠛⣃⣠⡇⠀⠀⡌⠣⠙⠚⠙⠁⠘⠂⠃⠋⠴⢺
⠀⠀⠠⢉⡀⠠⢀⣈⡅⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⣀⡀⢀⠀⠀⠀⠀⠀⡠⡀⠈⠉⠈⠉⣀⠀⣀⡈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁
⠀⠀⢰⠜⠉⠉⠁⠨⡄⠀⠀⡇⡧⣒⣒⣒⣒⣓⣒⣚⣓⣚⣒⣒⣒⣒⡂⡇⡇⠀⠀⣊⡉⡤⠁⠀⠨⠍⡂⠳⢢⣀⠀⠀⠤⠤⢄
⠀⠀⠀⠪⣂⠄⣐⠕⠁⠀⠀⡇⠧⠤⠤⢄⠀⠀⠀⠀⠁⠀⠀⢠⠤⠠⠤⠇⡇⠀⢰⠉⠂⡇⢸⠈⢨⠀⡌⢑⡞⠉⠀⢸⣁⣀⡌⡇
⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⡇⡏⠉⢹⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⡇⡇⠀⠰⢗⠤⣇⣈⣈⣈⠤⣐⠇⠘⠦⠀⢘⠀⠇⠃⡇
⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠧⠇⠀⠸⠼⠀⠀⠀⠄⠆⠀⢀⡸⠼⠀⠀⠣⠇⠀⠀⠀⠉⠑⠂⠐⠊⠈⠀⠀⠀⠀⠀⠘⠦⠤⠦⠃
⠀⠀⡀⡀⡀⠀⣀⠀⣀⣤⣤⠦⠖⠀⠀⠀⣀⠠⠤⠤⣤⠄⢮⠘⠀⠀⠀⠀⠀⠀⢀⣠⣤⢄⠤⢒⡸⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⣘⣀⣘⣙⣀⣀⣋⣀⠀⠀⠀⠀⡠⢊⠔⠆⠀⡜⠀⠀⡰⢢⠀⠀⠀⠀⠀⠀⠀⣻⣷⠜⠀⠀⠀⠀⠀⠀⠀⢠⠒⠯⠽⠒⢤⡀
⠀⠘⡀⡄⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡁⢸⠈⠦⡄⠈⠒⢋⠔⡸⠀⠀⠀⠀⡠⣶⣲⣾⣷⣖⣶⣄⠀⠀⠀⠀⠀⣮⠤⠒⢊⡍⠴⡆
⠀⠀⣸⠮⡂⣀⠀⡠⠴⡅⠀⠀⠰⡀⣓⣀⣓⣒⡃⣐⣈⣐⣚⣀⠄⠠⡄⠴⠿⠿⠻⠿⠿⠞⠿⠿⠦⠤⡤⠀⢸⡒⣒⣉⡩⠄⠒⠁
⠀⠀⠀⠁⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠠⠠⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠆⠰⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣀⠀⢀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠐⠉⠀⠈⠋⡀
⠀⠀⠐⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠀⠀⠀⠁⠁⠒⠦⠴⢤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠐⢿⣾⣿⣿⣿⣿⣿⣿⣾⣿⡶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⣤⢬⣉⡅⡉⠽⠉⠿⠯⠶⠷⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⠽⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠄⠀⠀⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢄⠀⠁⡀⢠
⠀⠀⠀⠐⢪⣷⣻⠯⡑⠀⠳⠟⣓⡃⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⠹⠧⠃⡁⠤⠚⡤
⠀⠀⠀⠀⢸⡋⠚⠧⢵⠒⢲⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡜⣒⠙⠉⣀⢐⠸⡆⣀⡚⡀
⠀⠀⠀⠀⠀⣷⠋⠠⢈⣵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡟⠻⡶⢄⠻⣯⠑⣾⡟⢘⡟⣾
⠀⠀⠀⠀⠀⠘⣆⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢛⢯⠟⣾⣠⣿⣯⣽⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠁⠚⠾⠉⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⡀
⠀⠀⠀⢤⠂⠀⢨⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠇⠀⠀⠀⠀⣀⠴⠖⠒⠲⢤⡀
⠀⠀⠀⢹⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠸⠀⠀⠀⠀⢰⠃⠀⠀⠰⠂⠀⠙⡄
⠀⠀⠀⡆⠇⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠓⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡇⠀⠉⢀⡀⠒⢀⢷
⠀⠀⠀⠡⣀⡀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢀⡌⠀⠀⠀⢀⡤⣀⢹⠀⡀⠀⠑⣄⠁⠈
⠀⠀⠀⠀⠀⠹⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡀⠈⠛⠀⠀⠰⠁⢀⠆⡆
⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⢧⠀⠠⠀⠁⣀⠜⠣⠀⡇
⠀⠀⠀⠀⠀⠀⢡⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡎⠁⠈⢧⠀⠀⠀⠀⠀⢠⠃⢨⠁⠀⠀⠀⠀⠀⠀⠈⢇⠀⠐⠊⠀⠒⠁⢀⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣤⠄⠒⠒⠊⢉⣇⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⢱⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⠀⠀⠀⠀⣸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢷⡻⡄
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠈⡇⠀⠀⠀⡇⠐⠞⢠⠀⠀⠀⠀⠀⢹⢀⠀⠀⢸⠀⠀⠀⢠⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠞⠁⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⢸⠈⠀⠀⢸⠀⠀⠀⡜⠀⡌⡌⠀⠀⠀⠀⠀⡠⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡇⠀⠀⠀⠇⠀⢱⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠘⣄⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠡⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⢘⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢄⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢀⡞⡇⢹⣗⠄⠀⠀⠀⠀⠀⢀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣾⠁⣇⢰⠹⠈⠀⠀⠀⠀⠠⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠸⣿⡀⢘⣦⣀⡴⠀⠀⠀⡐⠁⠀⢀⠀⠆⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠯⠴⠋⠀⠀⠀⡐⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢀⠈
⠀⠀⣠⠔⠉⠁⡰⠉⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠄⠤⠐⠁
⠀⠀⡇⠮⠵⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠⠀⠀⠀⠀⠀⡠⠊⢠⠃
⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡠⠊⡠⢊⠐⢀⠀⠈⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⢊⠔⠈⠔⢁⠔⡡⠂⡀⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠴⠐⠁⠀⡡⠀⠀⠊⡠⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠉⠢⡀⠑⠀⡀⠀⠀⡠⠊⠀⡠⠈⠉⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠢⡈⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢄⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠐⢄⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠄⠁⠀⠀⠁⢄⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠁⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣴⣿⣿⢟⣫⣭⣭⣭⣛⢿⣿⣷⡀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⣼⣿⡿⣱⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣧⢻⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⠁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⢿⣿⣷⣝⣻⠿⠿⢟⣫⣵⣿⡿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⣴⣷⣦⠀⠀⣶⣶⣶⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⢀⣼⣿⣶⠄
⠀⠀⠀⠀⠈⠻⣿⠟⠀⠀⠻⣿⠏⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣠⠟⠋⠁
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠈⢿⣆
⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠸⣿⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠈⠿⠇

⠀⠀⠀⠀⠀⢀⠀⠀⢶
⠀⠀⠀⢠⠀⠁⡀⠀⠚⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠤⠦⠴⠴⣦⠖
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⡞⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣤⡶⣦⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠂⣤⡤⠤⠀⢀⣶⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠁⠀⠀⢄⢸⠳⣾⣗⠇
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠐⠒⠒⠖⠒⠖⠒⢛⢛⢓⠒⢺⣟⠀⠀⠀⠀⠁⠒⠚⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡨⠼⠚⠀⠀⠀⠀⠈⡉⡈⡘⡀⡘⠀⢂⡁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷
⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⡄⠐⠐⠈⠈⡀⣐⣀⣀⣀⣠⣿⠀⠀⠀⢠⢷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠑⣄⠢⡈⢻⠀⠀⠀⠠⣸⠀⠀⠀⠠⣤⣀⣨⡿
⠀⠀⠈⠀⠀⠀⠀⢻⣇⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠳⣈⣺⠀⠀⠀⠀⢸⣷⠀⠈⠛⠳⠧⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣀⠤⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠚⡻
⠀⠀⠀⠀⠀⢄⡠⠤⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠞⠁⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀
⠀⠀⡠⢀⠀⠃⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⢴⠾⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠘⢈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⣀⠄⠐⠀⠀⠉⢁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠀⠠⠴⠒⠈⢘⡉⠀⠀⠀⠐⠂⠈⠉⠉⠀⠀⢀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠄⠀⠀⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⡠⠄⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡠⠀⠀⡄⡀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠰⡀⢢⡀⠀⣀⢀⠤⠐⠂⢘⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⠤⠀⡂⠀⠀⠀⡆⠀⠠⠤⠐⠴⠂⠆⠐
⠀⠀⠀⠐⠄⠀⢀⠘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⡡⠀⠀⡇⠆⠀⠀⠃⠀⢀⣴⠄⠀⠀⠀⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠋⠡⠀⠀⠠⠀⠀⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠂⠀⠀⠀⠚⠉⠁⠀⠀⠤⠄⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⢘⢈⢸⡬
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠉⠀⠀⠁⠈⠉
⠀⠀⠀⠂⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠜⠐⠂⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠈⡀⠆⠀⠀⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⢐⠀⠀⠀⠀⡂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⡀⠁⡄⢀⢈⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡞⡉⢳⡄⠀⠀⠒⠀⠀⠀⠀⠀⠠⠤⡄⠴⠦⠀⠄
⠀⠈⠑⠤⠁⠀⠠⠔⠀⠀⠇⠀⠀⢀⠈⠒⠀⠂⠶⠒⠒⠚⠛⡆⠀⠀⠀⠀⠐⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠈⢁⢀⠁⠒⠤⡀
⠀⠀⠀⠀⣀⡂⠂⠀⠀⠀⠀⠀⠀⠘⣄⠋⠄⠴⠌⡃⠉⠀⢠⡇⠀⠀⠀⠀⠐⠁⢇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠌⠀⡤⠤⠀⢠⠀⠄⠄⢸
⠀⢠⠀⠀⣘⠑⠀⠀⠀⠔⡃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠒⠒⠀⠀⡠⠊
⠀⠀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠄⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠑⠂⠂⠀⠀⠀⠀⠀⠀⠀⢤⡀⠉⠑⠒⠚⠊⠉⢀⡠
⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⠁

⠀⠀⠀⠀⠀⣠⠶⠈⠛⠛⠛⠋⠱⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⣤⡄⠀⣴⡆
⠀⠀⠀⣰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⣇⠀⣿⣷⠀⣿⣿⡀
⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⢹⣿⠀⣻⣿⡄⡏⢹⡇
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⣿⡆⢿⢿⡇⠀⠸⣿
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡆⢸⢸⡇⠀⠈⣧⠀⠀⣿⡆
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡇⣼⢸⣧⠀⡸⣿⢀⡄⢹⡇
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣇⣿⢸⣿⠀⡇⣿⢸⡇⠘⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⡏⠘⣿⠀⡇⣿⣾⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⡇⡀⣿⡖⡇⢹⣿⠃⠀⢿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⡇⡇⢻⡇⡇⢸⣿⢰⠀⢸
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⡇⢸⣿⡇⠘⣿⢸⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⣷⡇⠸⣿⡆⠀⠿⢻⠀⢸
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣰⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣰⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢰⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⣀⣠⠞⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠉⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⡶⣒⣒⣒⣒⣒⣲⣶⣒⣒⣒⣒⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣒⣒⠒⠒⠒⢶⣦
⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣿⣹
⠀⠀⠀⠀⠀⡏⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⢲⡆⣿⢸⡆
⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇
⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇
⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢸⠃
⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢸
⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣼
⠀⠀⠀⠀⢘⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⣿
⠀⠀⠀⠀⠀⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿
⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⣿
⠀⠀⠀⠀⠀⢹⠀⠻⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠃⠀⣧⡏
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢠⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠶⠶⠶⠶⠶⠶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠤⠤⠤⠤⠄⡆⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣚⣛⣛⣛⣉⣉⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣤⣀
⠀⠄⠀⠀⠀⠀⠀⠀⣰⢏⡭⣭⢭⡭⢭⡭⢭⠭⢭⠭⢭⡭⢭⡭⢭⡉⢩⠭⣽⠿⡿⢿⠻⣆⠀⠀⠀⣾⣡⠜⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⡾⢭⠯⢽⠭⢽⠭⢽⠭⢽⡭⢽⡯⠭⡯⠭⡇⠘⣟⣻⣛⣻⣚⣧⠹⣆⠀⠀⠹⣅⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣰⣏⣈⣓⣛⣒⣛⣒⣚⣒⣚⣒⣒⣓⣚⣓⣒⣓⣒⣛⣀⣱⣤⣷⣤⣷⣤⣇⣹⣆⠀⠀⠘⢧⡀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠻⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠛⠶⠴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⡴⠒⠛⠋⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣤⣤⣤⣤⣤⣤⣤⠀⢹⡆
⠀⠀⠀⣼⣧⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⡇
⠀⠀⠀⢻⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⢸⢸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⢸⡏⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠘⡇⣇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⡇⢿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⢿⢸⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡧⠀⡇
⠀⠀⠀⠀⢸⡘⡇⠈⣧⣤⠤⠤⠤⠤⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠉⢉⣉⣉⣉⣉⣉⣀⣀⣇
⠀⠀⠀⠀⠈⣇⣧⣤⠤⠤⠤⠶⠶⠖⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⢉⣉⣁⣂⣀⣀⡀⠘⣆
⠀⠀⠀⠀⠀⢿⠹⡄⠀⢀⡤⠤⡤⠄⢤⠒⡖⠒⡖⠘⣏⢹⣉⣙⣍⣉⣅⠨⣦⠽⡤⢧⠼⡄⠘⣆
⠀⠀⠀⠀⠀⠘⣆⢳⡀⠈⢧⠄⠺⡖⠚⡖⠙⡉⢹⣉⣹⣄⣵⡤⠴⡤⠼⡆⠲⡒⢳⠚⡗⠙⡄⠘⣇
⠀⠀⠀⠀⠀⠀⠘⣆⢻⡀⠈⢷⠒⠳⠀⠙⡉⠹⡀⢣⠀⢱⣀⣣⡀⢵⡤⠼⡤⢷⠐⢳⠚⡂⠹⡀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄⠘⣷⠒⢳⠒⠹⡉⢻⣉⣇⣀⣣⣀⣧⣠⣥⠤⠵⠴⠷⠚⠓⠛⠋⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⡀⠘⠒⠚⠛⠋⠉⠉⠉⠉⣭⡤⠤⠤⠴⠶⠒⠒⢲⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⣀⡀⢀⣀⣀⡀⠠⢷⡀⠀⠀⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠒⠒⢚⣒⣂⣈⣉⣤⡤⢤⣴⣶⣶⣾⠯⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡷⠤⣤⣤⣶⣖⣒⣚⣻⣿⣭⠭⠭⠽⠿⠓⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⣶⢸⢰⡆⡆⠀⠀⠀⠀⣴⣷⠀⠀⠀⠀⣠⣴⣶⣶⣄⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⡏⢸⢸⡇⡇⣠⡤⠤⣸⣿⣿⠠⠤⠄⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⡇⡇⠀⠀⠀⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⡇⢸⢸⡇⣿⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣇⣸⢸⡇⣿⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢦⡀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢀⡟⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢻⡄
⠀⣾⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠁⠀⠀⣾⣿⣿⣿⠀⠀⠀⠈⠙⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⣷
⢰⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢠
⠸⣇⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸
⠀⢻⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⡟
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣇⣀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⣀⣸⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠉⠙⠓⣿⣿⣿⠐⠛⠋⠉⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠿⠿⠇⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⠲⢶⣶⣤⣤⣤⣤⣤⣤⣶⣶⠒⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠿⠛⠉⣿⡏⠙⠻⢷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣠⡀⠀⠀⣿⡇⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⣿⡇⠀⣴⡆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠀⡀⠀⣿⡇⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡗⠀⣿⡇⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⢸⣿⠀⠀⠘⠃⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⣿⡏⠛⠻⢿⣿⠀⣶⡆⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⣴⡿⠛⠿⠷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠁⠀⣀⣿⡇⠀⠀⢸⣿⠀⠻⠃⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠟⠀⢀⡀⠀⢀⣀⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣴⣶⠿⠛⣿⡃⠀⠀⢸⣿⠀⠀⢠⡄⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⢸⡇⠀⠸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⢀⣀⣿⡇⠀⠀⢸⣿⠀⠀⢸⡗⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⡶⠿⠛⠛⣿⡇⠀⠀⢸⣿⠀⣀⡀⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⢸⡇⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣠⣿⡇⠀⠀⠈⠁⠀⣿⡇⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⠈⠁⠀⠈⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠛⠛⠉⣿⣷⠿⠻⢷⣦⠀⠉⠀⠀⠀⣿⡇⠀⠈⠁⠀⢸⣿⠀⠀⢰⡆⠀⢰⣶⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣠⣴⣿⠃⠀⠀⠀⢻⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⠿⠀⠀⠘⠃⠀⠘⠛⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠋⠉⢻⡇⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⠀⢠⡄⠀⢀⣾⠟⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣿⣦⣀⣀⣠⣾⠏⠉⢉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⣿⠀⠸⠇⠀⠸⣿⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡏⢻⣿⠋⠁⠀⠀⢸⡟⠛⠛⠛⢻⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠙⠻⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣿⠇⢸⣿⠀⣤⣤⣤⣼⣷⣤⣤⣤⣼⣿⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢰⡇⣾⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿
⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇⣿⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠶⢦⣄⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠙⠈⠁⣿⠀⠀⣴⠟⠁⠀⢀⣠⣤⣤⣤⣄⡀⠀⠉⠳⣄⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣄⢀⣴⠏⠀⣾⠃⠀⣠⡾⠋⠁⠀⠀⠀⠈⠙⢷⡄⠀⠙⣧⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣼⠃⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡇⠘⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣷⠀⣷⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⢿⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢰⡏⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠘⣧⡀⠀⠻⣦⡀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢀⡾⠁⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⠀⠀⠈⢷⣄⠀⠈⠙⠳⠶⠶⠶⠞⠋⠁⠀⣠⠟⠁⠀⠀⢸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⣀⣀⣀⣤⡴⠟⠁⠀⠀⠀⠀⣿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⣋⣁⣤⣀⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣾⡭⠿⠿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⣽⠟⢹⠃
⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⢠⡟
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⠼⠖⠋⠀⠀⠀⣠⠟
⠀⠀⣇⠠⢠⣤⠤⠤⠴⠒⠛⠉⠁⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠙⠷⣦⣄⣀⣀⣀⡀⠀⠀⢀⣀⣀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠠⠤⠤⠀⠐⠐⠒⠒⠒⠒⠒⠒⠠⢤⡀
⠀⠀⠀⠀⠠⠔⠀⠀⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠿⠿⠟⠛⠋⠀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⡄
⠀⠀⢹⠀⠀⣀⣀⣤⣤⣤⣤⣴⣦⣤⣤⣴⣶⣶⣶⣾⣿⡿⠿⢿⡿⠛⠟⢛⡝⠉⠉⢹⢋⣿⡇
⠀⠀⣸⡆⠀⣿⣿⣿⣿⣿⠟⠻⠛⠛⠙⠉⢻⣅⣸⡿⢋⣰⢀⡠⡀⠀⡠⡎⠀⠀⠐⠀⠀⢿⣳
⠀⢠⣿⡇⠀⢿⣿⣿⡿⡃⠀⠀⠀⠀⢀⡴⠃⠛⠋⡴⢿⣧⣟⣼⠟⣠⣿⠀⢀⠀⠀⠀⠀⢸⣿
⠀⠸⣿⡇⠀⢸⡿⢋⠜⠁⠀⢀⠀⣠⣪⠀⠀⠀⠀⠀⠀⢸⠟⠁⢀⡽⢫⢦⠀⡀⠀⠀⢠⣨⣿⡆
⠀⠀⣿⣿⠀⢠⠔⢡⢀⡄⠀⠀⠘⠋⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢞⡄⠁⠀⡀⠓⣿⡇
⠀⠀⢙⣿⠀⢸⠖⣱⣯⠀⠀⠂⠀⠘⣯⠪⠆⣠⢃⠔⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⣖⡴⠁⣤⣿⣿
⠀⠀⢸⣿⡇⢸⡾⡈⠃⠀⠀⠀⠀⠀⠈⠐⢻⣷⡋⠀⣠⣂⠀⠀⠀⠀⠀⠀⠀⠉⣾⠇⠀⠀⢸⣿
⠀⠀⠈⣿⡇⢸⠷⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠙⢁⡴⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠰⣺⢸⡆
⠀⠀⠀⣿⡇⢸⠠⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢿⢿⡇
⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢀⡄⠀⠀⠀⠀⠀⠟⠀⠀⢸⣿⡇
⠀⠀⠀⠘⣿⢸⠀⣣⡎⢘⡶⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠁⠀⠀⠀⠀⢠⠞⠂⠀⠘⣷⣧
⠀⠀⠀⠀⣿⢰⡿⡹⢡⠆⡀⡀⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡀⠀⠀⠀⠞⠀⠀⠀⠀⡿⣸
⠀⠀⠀⠀⢹⣮⡇⠑⠁⠈⠘⠀⠀⠈⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢞⡴⠄⡀⠀⠀⠀⠀⠀⠀⠀⣴⢿
⠀⠀⠀⠀⢸⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡵⢀⠈⠀⠀⠀⠀⠀⣻⣿⠄
⠀⠀⠀⠀⠀⣿⡥⠂⠀⠀⠀⠀⠀⠀⠀⠠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠂⢀⠀⠀⠀⠀⢼⣿⡄
⠀⠀⠀⠀⠀⣿⡷⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠰⡡⣠⠀⠀⠀⠠⠀⣸⣿⡇
⠀⠀⠀⠀⠀⣿⢷⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⢹⢸⢊⡴⠃⠀⠀⠀⠀⠀⠀⠀⡠⠈⠁⡼⡁⢀⠀⠀⠀⢀⣾⠃⢀⡔⡄⠀⣠⡾⣿⣿⣧
⠀⠀⠀⠀⠀⢸⠀⣿⡠⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠰⢛⣴⠀⠀⠈⡡⢢⢾⡿⠀⣼⣟⣽⣿⣿⣿⠄
⠀⠀⠀⠀⠀⢸⡄⢻⡅⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡠⡾⣁⠂⢀⣜⣰⣏⣜⡵⣺⣿⡿⠿⠿⠋⢹⡇
⠀⠀⠀⠀⠀⠘⡇⠘⣿⣶⣀⣊⣀⣠⣿⣠⣦⣴⣶⣿⡿⢷⠟⣻⣟⠛⠛⠛⠋⠉⠁⠉⠁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠈⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡴⠉⠈⠁⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠈⠉⠁⠁
⣿⣿⡿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣿⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣤⣀⠈⠙⠿⠟⠀⢼⠘⣄⢸⣧
⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣤⣀⣀⣼⣿⣴⣿⡆⢀⡀⡇⠀⠀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠀⠂
⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠊⠁⠀⣀⡉⠛⢿⣷⠘⢿⣿⠈⠀⠊⠀⠀⡃⠀⢀⡀⣀⠀⠀⠀⠀⠀⠐
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢋⣴⠋⠀⠀⣼⣿⡯⢡⠀⠀⢹⣦⣸⣿⡄⠀⠀⠀⠰⠛⠛⣿⣿⣿⣁⠀⡀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖⡒⢀⣴⠞⠁⢰⠘⠀⡀⠻⠿⠛⠁⠀⠀⠘⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣷⡀⠄⠀⠀⠀⢀⣸⢆⡀
⠐⠠⠿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠟⠉⠀⠀⠀⢸⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣾⣿⣠⣀⣀⠀⠀⠀⠗⠙⣿⣿⣿⣿⣿⣏⣀⣤⣾⣿⣿⣿⣦⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡯⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡇⠈⠉⠁⠹⣆⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⠣⣂⡀⢸⠳⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣸⡇⠀⠀⠀⠀⠘⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣷⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠿⠷⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⣦⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⢮⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣼⠋⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣀⡀⠙
⠀⠀⠀⠀⠀⠒⠶⣶⣤⠤⢤⣤⣤⣶⣿⠆⣀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⣰⡇⣸⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣭⣭⣭⣤⣨⣛⣳⢦⣄⣤⣴⡍⢀⠤⠞⠋⠰⠁⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢍⣩⠟⢠⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠙⠛⠛⣋⡈⣩⣌⣁⢀⣀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣀⠀⠀⠀⠀⢱⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣵⡆⠘⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣌⣛⠛⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⣸⣦⡀⠀⠀⢸⣿⣿⣿⡿⠿⠛⢛⣉⣀⣨⣭⣭⣴⣶⣶⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⠈⠂⠀⠀⠀⠀⠀⠀⠠⠐⠁⣭⠟⠀⢀⠀⠀⠀⠀⠐⢻⣷⠀⣾⡿⣿⣿⣿⣤⣤⣤⣾⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠈⣷⠾⠄⠀⠀⠀⠀⠇⢀⡀⠐⠀⠀⠀⠀⠰⠂⠉⠀⠚⠓⠸⢫⣤⡛⡉⠁⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⠁⠋⠀⠀⢀⠁⠀⠀⢀⡒⠮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢡⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⢾⣿⣿⡟⢭⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠂⢀⠀⠀⠀⠟⠲⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠞⠃⠿⢿⢦⠹⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢦⣴⣿⣷⣤⣬⠋⠐⢦⣶⠶⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢽⣷⡄⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⣀⡀⠼⠅⠀⠉⣦⠟⠓⠤⣺⣟⣻⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠐⡀⠸⣿⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠃⠈⠀⠀⠀⠀⠈⠉⣽⠿⠭⢤⣀⠀⠀⠀⠀⠤⣄⡰⠁⠀⠈⠀⣐⣤⣤⣴⣶⠷⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠵⣈⣁⣀⣈⠽⠋⠀⠁⠀⠠⠀⡀

⠀⠀⠀⠀⡧⡷⢗⢛⠡⡠⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠐⠂⠈⠁
⠀⠀⠀⠀⢱⠏⣛⣁⠬⠔⠒⠸⠀⢂⠠⠄⠀⠒⠈⠈
⠀⠀⠀⠀⢘⠉⠁⠤⠐⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣻⡿⣿⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠠⣤⠠⠠⠀⠀⣿⣛⣷⡿⠫⣿⣿⣼⠀⠀⠀⠀⠐⠒⠓⠀⠐⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⣰⡂⠀⠀⠀⣯⣭⣭⣤⣬⡍⢙⡙⠀⠀⠀⠀⢰⡂⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡤⡄⠀⡷⢶⡟⢻⣿⠖⣾⡿⠀⠀⠉⠁⠉⠉⠉⠉⠉⠁⠀⠀⢰⠆⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠉⠁⠀⠀⠀⠐⡆⠀⡀⠀⣿⣿⡟⠉⢹⣸⣿⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣃⠀⠁⠀⣿⣿⡇⠀⠸⣿⣿⣷⠚⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⢅⡀⠀⠀⠋⠙⠛⠀⠀⠻⠿⠿⠲⠶⡤⠁⠍⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⡀⠀⠀⠀⠀⠀⠀⠏⠀⠙⠀⣐⣶⣸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠐⠒⠒⠈⠉⠉⠁⠒⠒⠒⠀⠀⠒⠒⠢⠤⣀
⠀⠀⠀⢀⡂⠐⠰⠀⠀⣠⠠⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠄⠈⠉⠀⠂⢄⣀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣖⠒⢰⠤⡄⡀⠀⠀⠈⢀
⠀⠈⠦⣌⠋⠀⠶⠴⠶⠂⠘⠟⠀⠀⡁⢀⠈⡄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠃⠲⠶⢀⢠⡄⠀⢀⡄
⠀⠀⠑⢝⠢⡀⠠⡀⠀⠠⢁⠂⠒⢠⢂⣊⣩⠁⠀⠀⢀⣠⡄⠀⢐⠀⠐⢰⠲⣍⣈⣀⣀⠀⠀⠈⠀⠀⢠⠇⠀⠊⡇⠀⢙
⠀⠀⠈⠛⢷⣤⣀⣁⡈⢁⢛⣶⠴⡯⠝⠒⠉⠀⠀⠀⡙⠀⢠⢒⠋⠄⢆⣀⢈⣑⡇⠁⠀⣀⠀⠀⠀⢀⠊⣠⠎⢀⡇⠀⢨
⠀⠀⠀⠠⠀⠀⠁⠉⠀⠠⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⡁⢸⡡⢼⠀⠀⠀⠀⡈⠁⠂⠀⢀⡀⠀⣠⡔⢁⡌⠀⣠⠞⠀⠀⠔
⠀⠀⠀⠀⠀⡤⢠⣔⠒⣀⢶⣆⣀⠠⠀⠀⠀⠀⠀⠀⠈⢺⠱⣏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⠞⠉⠔⣟⣤⠖⠁⠀⣀⠂
⠀⠀⠀⠀⢤⡀⠀⠀⠉⠛⢷⠞⠐⣊⣄⡀⠀⠁⠀⠘⣀⠸⡔⠋⢁⠐⠒⠒⢒⡈⢩⠏⠋⠥⢈⠄⡤⠁⠴⠖⠋⣨
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠠⡄⠹⡤⢠⣶⠅⠀⠀⠀⠀⠙⠉⣧⡀⠑⠤⠤⠖⠉⠀⣀⡴⣊⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⡀⡀⢀
⠀⠀⠀⠈⠃⠀⢀⡀⠀⠀⠀⠀⣧⠈⣶⠈⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠶⠶⡖⢺⡁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⣄⠈⢆⢅⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢨
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡈⠳⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠣⠤⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⢶⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠁⠀⠂⠀⠐⠒⠒⠒⠀⠠⠬⠭⠭⠭⠉⠉⠛⢉⣙⣛⠛⠛⠒⠺⠶⢶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⢀⠀⠀⠀⠀⡇⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠉⣐⣒⡒⠠⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⡉⠰⢠⠀⠖⢀⠄⠉⡁⠁⣒⠒⠠⠭⠅⢁⣒⠒⠠⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠤⠐⡠⠄⡀⠐⢂⠀⠙⠁⡄⠈⣠⠒⢁⡠⢄⠒⠤⠀⢉⡉⠁⣒⠂⠤⠭⠭⢁⣒⠂⠴⠃⡇⡀
⠀⠀⠀⠀⢀⡠⠒⠉⡀⠀⢁⠀⠈⠠⠄⠀⠡⠀⠈⠀⠒⠈⠔⠂⠄⠈⢡⠐⠈⠀⠠⠆⠀⠤⠈⢀⠀⠀⠆⠀⠤⠀⣀⢥⣟⣉⠇
⠀⠀⠀⠀⢨⣉⠉⠒⠒⠂⠥⠴⢅⣀⡐⠀⠄⠁⠀⠀⠀⠈⠁⠀⠀⠆⢀⡄⠀⣁⠀⠊⠀⠔⠂⡡⠀⠈⣁⠤⠒⣉⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠠⠤⠤⣀⣉⠉⠑⠒⠂⠤⠤⢄⣀⡠⠂⠐⠆⢀⠀⠈⡀⠀⠃⣀⠤⠒⣉⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠦⠤⠤⣀⣉⡉⠐⠒⠒⠤⡤⠒⢉⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠓⠆⠈⠰⠀⠀⠀⠨⠄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⢐⠀⠆⠀⠀⠀⠒⢌⢩⠉⠀⡇⡃⣀⣈⣈⣈⠀⠄⠀⠀⠀⢤⠀⠁⠀⠀⣀⠀⣱⢆⠀⠀⠀⠠⠀⠠
⠀⠀⠁⠐⡀⢨⢄⡅⠀⠈⠎⠉⠬⠵⠉⡇⡂⡀⢐⠨⡆⠀⠀⠀⠀⠘⠀⠀⠀⠘⠈⡈⠃⠨⠀⣀⣀⡰⠀⠀⠀⠀⠈⠁
⠐⠀⠐⠄⠌⠍⠠⠴⠶⠶⠖⠁⠀⠀⠀⡇⣀⣀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠗⢋⠈⠂⢸⠉⠀⠀⡀⠈⠂
⠃⠀⠀⠐⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢒⢠⠉⠉⠘⣀⠀⠀⠁⠀⠀⠀⠐⣦
⠀⠀⠀⠀⠠⡄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠏⠸⠀⠀⠀⠘⡄⣀⠀⠀⡒⠛⢳⠒
⠀⠀⠀⡇⠐⠒⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠰⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠴⠆⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣃⣤⡄⠀⠀⠀⢈⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡿⡟⢻⣷⠿⠛⠋⠙⠛⠛⠻⠿⠻⣿⢽⣏⣱⡟⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠡⢿⠇⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠰⠤⣼⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠉⠛⠛⠓⠂⠂⠠⠤⠤⠤⠤⢤⣤⢀⡀⢸⣿⣿⣿⣷⠶⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣤⣻⣾⣿⣿⣍⣉⣓⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣷⡅⡄⠀⠀⠀⠀⣀⣼⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠻⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣟⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⡯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠔⠒⠒⠐⢛⣀⣉⣉⡈⠉⠉⠉⠉⠉⠁⠀⠴⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠖⠞⠚⠒⠒⠒⠒⠚⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠒⠀⠉⠉⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡰⠠⢁⠠⠡⡡⡁⡐⢀⢣⣧⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⢁⢁⠂⡄⡑⠡⠀⢀⢂⡴⡷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠃⠂⠂⠌⠘⠡⠡⢁⠂⣼⠂⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠀⠌⠈⢌⠄⠀⠁⠁⠆⣼⠃⠅⢿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠆⠜⡌⢀⠂⠆⢀⠀⠌⣰⢃⡮⠠⢻⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡐⡀⠘⢠⠋⠄⡄⠀⠌⣰⠇⡾⢁⠐⢻⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⡰⡐⠠⡇⠀⡐⠌⡘⢠⠏⡸⢁⢂⠂⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⠐⡐⠁⡝⡐⠐⠀⡐⢠⠏⡰⢃⢂⠂⠲⢻⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠀⡐⢀⠛⠀⠁⠐⠔⢠⡎⣰⢃⢊⢎⢮⠡⢹⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠡⠁⠠⠣⠡⠠⠁⠀⢠⡟⣰⢣⢂⠂⢢⢁⠃⢩⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢡⠣⠁⠡⢠⠁⠠⡰⠁⡙⡠⠃⠃⢌⢢⢁⢂⢒⠉⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠃⠃⠴⠡⢃⠶⠠⠁⠰⠴⠕⠌⢎⠊⠆⠀⠂⠞⠄⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⡂⣰⣆⣀⢀⣉⣉⣉⣉⣀⢀⣀⣀⣀⣒⣒⣒⣒⣒⣒⣒⣞⣒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣾⣾⣟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⠀⢈⠉⠪⣟⠝⢹⣬⡝⣭⣫⣝⣭⣋⢫⣝⣭⣪⡝⣭⢫⣭⣝⣫⣠⡉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠂⠀⠀⠀⢀⣀⣀⣀⣀⣜⣀⣠⣁⣀⣈⣀⣀⣉⣀⣒⣃⣰⣄⣱⡐⣒⣘⣆⣐⣒⣐⣄⣀⣀⣀⠐⢒⡢⠵⣆⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⡰⠁⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⠃⠀⣠⡀⣀⣀⣀⣀⣀⣇⠀⠀⣢⢐⠒⡀⢣⡐⣤⠚⢢⡀⠀⠀⠀⠀⠈⢆⠲⠈⢧⡙⡄
⠀⠀⠀⠀⠀⠀⢀⠎⡔⠀⠀⠀⠀⠀⠈⣹⠋⣉⣉⣃⡈⣨⡁⠈⠀⣉⠀⠀⢈⡀⠀⠈⡁⠀⠀⠈⣊⠢⡙⠀⡙⣬⣥⠛⣍⠀⠜⢏⠨⡠⡂⠀⢳⣜⡄
⠀⠀⠀⠀⠀⢀⠎⣈⠀⠀⠀⠀⠀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⣬⡍⠋⠁⠿⡹⢀⡀⢉⣈⡛⣁⣁⣹⡻⡀
⠀⠀⠀⠀⢀⠎⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠥⠍⢭⠁⠉⠈⠀⠀⠙⠬⡑⠭⣋⠉⡋⠧⣉⡋⠙⠛⠦⣳⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠈⠑⠢⣉⠢⢕⠨⣙⠣⡢⢅⠂⢳
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢍⡢⢅⠂⢅⠨⡀⢃
⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠀⠚⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⣀⣌⡂⢸
⠀⠀⠘⠯⣀⣒⣖⣶⢖⣖⡰⣤⢤⢤⠤⠤⠤⢤⠤⠤⠤⠤⠤⢤⠤⠤⢤⢤⠤⡤⡤⡤⠤⠤⢤⠤⠤⠤⠤⡤⠤⠤⢤⠤⡤⠤⠤⢤⠤⢤⢤⠤⡤⣤⣤⣤⡼⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠘⠁⠙⠋⠊⠘⠉⠛⠋⠋⠚⠋⠛⠋⠚⠙⠛⠛⠉⠛⠛⠛⠛⠛⠘⠑⠃⠛⠉⠚⠑⠛⠛⠋⠋⠉⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣀⢀⠠⢀⠄⠠⠀⠒⠀⢐⠀⠀⠀⠠⠄⠀⠀⠀⡰⠄⡐⠀⠀⠐⢂⡒⠀⡐⠠⢀⠂⠠⣐⠀⠀⠂⠀⠐⠀⠀⠂⠀⠂⠠⢂⠁⢐⡀⠀⡢⠔⡀⢀
⠀⠀⠀⠀⠀⠁⠀⠁⠐⠈⠀⠀⠉⠐⠀⠀⠊⠀⠂⠀⠒⠁⠒⠁⠐⠊⠀⠊⠁⠂⠁⠐⠈⠀⠂⠁⠐⠈⠀⠂⠀⠔⠊⠀⠊⠁⠐⠀⠔⠊⠁⠂⠁⠐⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⢀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⣀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠔⣒⣚⣉⣛⠒⠒⠒⠋⠁⢀⣠⠖⠋⠁
⠀⠀⠀⢀⠄⣊⡵⠚⠉⠀⠀⠀⠀⠙⢆⠀⢀⡴⠋
⠀⢀⠔⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟
⢀⠊⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡜
⡇⣸⣿⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⣡⠎
⢧⠘⢿⣿⣶⣤⣤⣴⡶⠟⣋⠵⠋
⣀⣑⣦⣭⣭⣭⣭⣶⣞⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡿⢟⣻⣛⢳⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠻⠿⣿⣿⣿⢿⠿⠟⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠠⢤⣄⡀⠀⠀⣀⣀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡿⠀⠶⠀⢷⠀⢨⣍⡉⢃⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣷⠀⠀⢠⡆⢀⡀⠀⠀⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠊⠤⢄⣀⠐⢄⡴⢣⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣆⠀⠀⠓⠀⢀⠎⠔⡱⢈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⢻⠀⠟⢷⣤⣤⡤⣼⣾⢸⣧⣿⠇⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣶⣿⣿⡿⠿⠟⢛⡝⢻⡟⢸⠀⠈⢢⡀⠀⣠⣿⠈⠁⡌⠁⢀⣾⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢩⡀⠀⠈⠀⠀⠀⡼⠀⠸⠁⠸⡄⠀⣠⣿⣦⠀⢿⣷⠈⠃⠀⠘⣉⠉⠛⠛⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠈⡇⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⣇⠰⢉⣿⣏⠃⢰⣿⣧⡀⠀⣀⢘⢦⠀⠀⠀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣛⠃⠀⢱⠀⠀⠠⠤⠥⠶⣤⡄⠀⠀⢻⢠⣿⣿⣿⡞⣼⣿⣿⡥⠈⢠⠏⠀⠳⡀⠀⠜⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠃⠈⠙⢦⣸⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⣷⠂⠐⠻⣀⠀⠀⠙⢌⣠⡾⣿
⠀⠀⠀⠀⠀⠀⣾⡅⠉⠐⢦⡄⣠⣤⠿⣷⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⢻⣿⣿⣆⠀⠀⢱⠁⠀⠀⠀⢻⡴⠛⠆
⠀⠀⠀⠀⠀⢰⣿⠐⢄⡀⠈⠙⠳⡜⣻⡿⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠹⣿⣿⣆⠀⠀⠁⠈⠀⠀⠀⢷⡀⢨⡀
⠀⠀⠀⠀⣠⠿⣋⣠⣤⣭⣝⡛⣧⣴⣿⡇⠀⠀⣿⠙⡆⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠹⣿⣿⣶⣄⠀⠀⠀⠀⠀⢨⡙⢦⢱⡀
⠀⠀⢀⣌⣵⣪⠽⢿⡧⣄⡈⠉⣸⣿⢿⡇⠀⢸⡇⠀⠹⡄⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠹⣿⡿⣟⢧⡀⠀⠀⠀⠀⢇⠀⢠⡇⡀
⠀⠀⢸⣿⢟⠝⠀⠀⠀⠉⠻⣼⣿⣿⣷⡡⣀⣾⠁⠀⠀⠹⡄⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣿⣇⡿⣦⡁⠀⠀⠀⠀⠈⡆⣼⢠⠇
⣀⣀⣰⡀⠎⠀⣠⠔⠋⠀⢀⡠⣹⡿⠃⠈⢞⢛⣲⣀⣀⣀⣙⣀⣀⣀⣀⣸⣏⣀⣀⣀⣀⣠⣿⣿⣯⣄⡹⣷⣦⣀⠀⠀⠀⠀⣱⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠉⠉⠙⢷⣤⣴⠃⠀⢠⠊⢡⢾⣿⢀⡙⢣⠈⠙⠧⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠻⠿⣟⠉⠙⠛⠿⢮⣽⣿⣄⣤⠾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠈⠙⠛⠿⢿⣶⣷⡸⣨⣧⢠⣙⠇⠄⣁⠒⠸⣿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠤⠟⠛⠀⠉⠳⠭⠤⠀⠐⠉⠁⠉⠂⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⡀⢤⣄⣒⣦⡠⠤⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⡠⠼⠷⠞⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⣀⣀⡠⠤⠖⠚⠛⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⡟⡦⢠⡿⣆⢰⡟⣷⠀⠀⠀⠀⣴⢞⠋⠉⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡆⢰⣿⡆⢰⡟⣆⠀⠀⠀⢀⡴⠛⠉⠉⠙⠳⣄
⠀⠀⣾⠀⡇⢸⡇⣿⢸⡇⢹⡆⠀⢀⡾⣵⠋⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⡿⢸⡇⢸⠃⣇⢸⡇⢻⡀⠀⢠⡞⡴⠋⠀⠀⠀⠀⠈⢷
⠀⢠⡏⢰⡇⢸⠇⣿⠸⡇⠸⣇⠀⣾⣹⠇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⡇⢸⡇⣼⠀⣿⢸⡇⠸⡇⠀⡾⡼⠁⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢸⡇⢸⡇⣾⠀⢹⡀⡇⠀⣿⢰⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⠀⢸⡇⣿⠀⢿⢸⡇⠀⣷⢸⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⢸⡇⠘⠷⠟⠀⠘⠷⠇⠀⣿⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⣼⢸⡇⠀⠀⠀⠀⣿⠀⠘⠷⠏⠀⠸⠾⠃⠀⣿⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⠹⣆⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡆⠻⡄⠀⠀⠀⠀⠀⣰⠇⣸⠃
⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣠⡏⠀⢻⡄⠈⠛⠶⠶⠶⠛⠁⢠⡟⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢷⡀⠈⠓⠦⠤⠶⠚⠁⣠⠏
⠀⠀⠘⠳⢦⣤⠀⠀⣤⠾⠋⠀⠀⠀⠙⢦⣤⡀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡄⠀⠀⣤⠶⠋⠀⠀⠈⠻⢦⣄⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿
⠀⠀⠀⠀⢸⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⣼⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹
⠀⠀⠀⠀⣿⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⣿⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠈⠻⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠙⠷⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠦⠶⠛⠁⠀⠀⠀⠀⠀⠀⠙⠶⠶⠾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠉⠉⠑⠒⠂⠀⠤⠤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠒⠶⠤⠤⢤⣄⣀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤⢈⠑⠂⢅⠂⠄⡉⠲⡍⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⠘⠀⠈⠐⢨⠐⡢⠄⣉⠖⢩⠙⠲⢎⡑⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⡀⠀⠀⠀⠀⠎
⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠐⠢⠄⣉⠤⢈⡑⠂⡤⠂⠢⢤⣁⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼
⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣁⠘⠠⠐⠋⠤⢈⡰⠆⠀⠀⠀⠠⠗⢀⠄⡀⠀⠀⠀⠀⠀⠀⠤⣀⠠⠇
⠀⠀⠀⠀⠈⠳⢄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢀⡠⠚⢠⡄⠈⠂⣄⡑⠄⠊⣉⡁⠤⣀⡨⠒⠎⠁⠀⠀⠀⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠠⠠⠂⠈⠀⠄⠒⠀⠄⠐⠒⠤⠀⠒⢠⠄⠂⠁⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⡀⠀⢤⠈⠉⠠⠀⠈⡁⠤⠒⠁⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠁⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⢀⣠⠴⠚⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿