⠀⠊⣇⠋⠀⠀⠈⠑⠮⡙⠷⣮⣽⣿⣿⣫ ⣖⣶⣿⣭⣥⣤⣶⣶⣶⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠆⠣⠀⠀⢸⠀⢀⡵⢶⡆
⠀⢀⣿⡿⠋⠁⠀⠀⠀⠀⠈⠲⣌⠻⣿⣿⠃ ⣲⣶⣾⣿⡿⠿⠟⠛⠉⠛⠒⠚⠻⣿⢶⣶⣤⣀ ⠀⠀⠀⠀⠀⠀ ⠀⠸⣷⣧⢰⡁⡇⣿⢸⢈⣻⣯⡀
⣴⠟⡉⡇⠀⠀⢠⠀⠀⡀⠐⠁⢈⢦⡾ ⣶⣿⡿⠟⠋⣠⠤⡖⠂⡀⣀⢱⡈⠀⣴⣼⣤⣿⣻⢿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀ ⠀⣻⣻⣅⢻⡧⣿⠸⠸⣿⡽⠟
⠉⣤⡇⡇⡆⡆⢸⠀⡄⠗⠀⢀⣾⡞ ⣿⣿⡿⠋⢀⡴⠋⠀⢰⢧⠂⣇⣿⣿⣧⡆⣼⣾⣬⣿⣿⣾⠙⠻⣷⡒ ⠀⠀⠀⠀⠀⠀ ⠀⠈⢍⡟⣿⣇⢻⣴⣾⣿⣿
⢸⣿⡇⣇⣷⡇⢸⢸⡇⠀⢀⣾⡟ ⣷⣿⠟⢀⣾⡞⠁⣠⢰⣸⢨⡇⣿⣿⣯⣾⠁⠈⠻⡟⢿⣿⣿⣿⣆⠸⣿⣍ ⠀ ⠀⠀⠀⠀ ⢀⠎⣠⠏⠛⠿⡷⠶⠚
⢸⣿⣷⣿⡟⣇⣼⠿⠀⢠⣿⠏⠀⠀⣞⣿⠏⠀⣟⡟⠠⠀⣿⢸⢻⢸⣇⡿⣟⡿⠁⠀⠀⠀⢻⡌⠹⣎⣻⣿⢰⠸⣿⣖⠂⠀ ⠀⠀⠀ ⡎⢸⡇⣰⡇⣆⣇⠀⢰⣾
⢸⣿⣿⣿⢷⡿⡏⠠⠴⠛⠉⠀⠀⡰⣿⣿⢀⢸⣿⢸⢸⣇⣿⣿⣾⣿⠟⡼⠟⠀⠀⠈⠉⠁⠺⣿⠀⠈⣧⢻⣼⢠⣻⣿⠭⠗⠂⡀⠀⠀⣼⠃⣾⢸⣿⣷⣿⣿⣽⣾
⣾⣿⣿⡇⢂⢳⣹⠌⠀⠀⠀⠀⠀⢰⣿⣿⣼⣿⣏⣾⣼⣏⡿⠇⡿⠃⠰⠁⠀⠀⠀⣊⣭⣤⣄⣋⠀⠀⠹⣿⣿⠸⡷⣿⣧⡈⠭⣞⣀⣤⡏⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⢃⢸⠂⠻⡄⠀⠀⡠⠂⠀⣸⡿⣿⣿⣿⢻⣿⣿⣿⣾⣿⣷⡆⠀⢀⠄⠀⠈⠛⣿⣿⣿⣛⢿⣦⣠⣿⣾⣦⠃⢿⣿⣿⣦⡀⠀⣸⠇⣾⣿⣾⣿⣿⣿⣿⣿⣿
⡟⣿⣷⢸⢸⠈⠆⠙⣄⣘⣰⣾⣭⣿⢯⣿⣿⣿⣾⣿⣿⣿⠿⠟⠛⠀⠀⡾⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣤⢸⢿⣾⢯⠙⠓⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⢸⣼⣇⠘⠀⠘⢟⠛⢻⣾⡏⣼⣿⣿⣿⣿⣿⣿⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣼⣿⣿⡻⣿⢸⢸⣿⣻⡳⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⢹⣿⢸⣿⢿⢀⡆⠀⠹⣏⣼⡿⢸⣿⣿⣿⣿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢸⠃⣿⢸⢸⢸⡟⣹⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⣿⢸⣿⢸⣿⢸⡆⣈⠀⠀⢻⣾⣥⣿⣟⡇⣿⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⣰⣞⣛⣲⣆⠀⠀⠀⠀⠀⠀⢀⣟⢢⣾⣿⣿⢸⣸⡿⢛⣅⣿⣌⠿⢻⣿⣿⣿⣿⢿⣿⣧⣿
⣿⢸⣿⢸⣿⢸⡇⡿⢘⢢⠈⢿⣿⣿⣿⣿⡿⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⣘⣵⣛⣼⣿⣿⣾⠏⠀⢸⣇⠁⠻⣿⣷⣼⣟⣚⣿⣿⣿⣟
⡟⢸⠺⢸⣿⢸⢷⡇⢠⡸⠀⠀⢻⡝⠿⣿⣾⣿⣇⡽⢿⣗⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⢀⣴⠋⣿⣿⣿⣿⠟⠁⠀⢰⡟⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⣸⣿⣿
⢿⠄⠀⠬⢛⣸⠨⠗⠊⡡⠂⠀⠀⢿⠀⠈⠿⢿⣿⣇⣏⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡿⣧⣿⣿⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢹⣿⡾
⠸⣷⠢⠤⠤⠴⠖⠞⠋⠀⠀⠀⠀⠘⡆⠀⠀⠀⢹⣿⣿⣿⣞⣿⢹⠦⢄⡀⠀⠀⠀⠀⢀⣴⠿⠉⣸⣇⣿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢇⡸⠟⠀
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣏⠟⡄⠀⠉⠛⠒⠛⠋⡇⡎⢦⣿⣿⣿⢹⣿⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡜⡆⠀⠀
⡄⡎⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠳⡵⡀⠀⡄⢀⠀⢸⣼⠗⠀⢸⣽⣿⣾⣿⡄⠀⡐⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠞⠁⢹⣿⠀⢡⠀⠀
⢷⡟⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⡀⠀⠀⠀⠁⠸⠆⡼⠃⠀⠀⠀⣻⣿⠫⠽⠿⠶⠶⠒⠒⠛⠂⠀⠀⠀⠀⡠⠊⠀⠀⣼⡇⠀⠀⠀⠀
⡛⢠⠞⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⡷⠶⠟⠛⡋⠉⠉⠛⠛⠛⠭⠍⠛⠛⠛⢿⣝⡛⢂⣦⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⠢⣄⠀⣰⣿⣮⡦⠀⠀⠀
⡴⠁⢀⠀⠀⣿⠓⠄⢀⢴⣶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣤⣄⣄⣈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣯⢷⣔⡄⠀
⡇⠀⢸⠀⣇⡝⣷⣨⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⠀⠀⠈⢳⣉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⡂
⡟⢠⢸⣶⠇⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢀⠀⢹⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⡟⣿
⡇⣸⣿⡟⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⡇⣼⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⢀⡤⠦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢹
⣿⣿⣇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡍⠉⣠⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⠀⡀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⠈
⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢱⡐⣷⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⣇⠈⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿
⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠺ ⠀⠀⠀⡹⠿⠾⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢛⡿
⡅⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡜⠁⢸⢱
⢿⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⣄⣀⣤⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⠀⠀⢸⡿
⠶⢿⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣤⡤⠤⠴⠶⠾⠶⠖⠒⠒⠊⠙⠁⠀⠀⠀⠀⢸⡇
⡑⡘⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢩⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡇⡇⠀⠀⠀⠀⠙⠒⠶⠶⠶⠶⣶⠒⠚⠉⠀⡰⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇
⡇⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠘⣁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠇
⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠛⠷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⢶⣀⣶⣶⡐⠈⡏⢳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⢳
⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⣦⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣯⣴⢼⣿⣿⣷⣦⡤⠀⢀⣾⣿⡿⠛⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡴⠃⢈⣦⡾⠛⠿⠟⠛⠙⠋⠙⠋⠉⢙⣛⡿⣿⡟⢁⡴⠞⢉⡤⠾⠛⠂⠀⠀⠀⠻⣶⣄⠀⠈⠉⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠛⠷⣄⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀
⡤⠒⠒⠀⠀⠀⠀⠀⠀⢀⡔⠁⡠⣒⣡⣤⠤⠴⠴⠶⠒⠒⠒⠀⠀⠘⠛⠛⠛⠛⠓⠒⠒⣴⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⢛⡂⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀