Mountain Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⢳⣦⡀⠀⠀⢀⣀⣴⠞⠃⠀⡾⣿⣿⣿⣦⣀⣀⡀⠀⣠⠶⠶⢛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⣡⠴⣻⣿⡛⣳⣖⡭⠋⠉⠀⣀⠀⠙⠿⣿⡇⠘⠉⣩⣿⣾⢧⡄⠀⢾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠺⢽⠿⠛⠉⠀⡠⠶⠖⠋⣽⣷⡦⠀⠉⠁⠠⣾⣿⣿⢿⣷⡦⠀⠈⠋⠀⢹⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⠛⠷⠍⠀⠀⠀⠀⠀⠈⠉⠑⣿⣀⢤⡐⠄⠀⢺⣿⣿⣿⣿⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡄⠀⠀⠉⠛⠻⢿⡪⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⣶⡶⠶⠶⠶⠿⣿⣤⣴⣧⣧⣧⣶⣶⣿⣀⣠⣴⣾⠶⠷⠤⣴⣿⣷⣤⣤⠤⠤⠤⠴⣾⣿⣶⣀⣠⣤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⡒⠒⠾⠭⠽⣛⣷⣤⣀⠀⠀⠀⠀⠀⠤⠤⠤⠬⣉⣉⣉⣉⠐⠒⠒⠢⠭⠍⢙⠒⠲⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠭⠍⠉⣙⣒⡲⠭⢍⣓⠂⠤⠀⠀⠠⣤⣤⣄⣀⣶⣦⣬⣭⣭⠓⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠠⠤

⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣼⣿⣧⡀⠀⢀⠀⠀⠀⠀⢀⣼⡏⢻⡗⢄⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢠⣿⣿⣿⣄⢀⣿⣧⠀⠀⣰⠿⠉⢆⠀⢻⡀⠈⠢⢄⣤⣶⣿⡏⢢⡀⠀⠀⢀⣤⣀⣠⡾⠃⠑⣤⣆⢰⣿⡀
⠀⣿⣿⣿⣿⣷⣼⣿⣿⣄⣼⣿⣦⣄⠀⠑⠈⢧⡀⠀⢘⣿⡿⠋⡇⠀⠉⢶⠲⢅⠘⣿⢝⠁⠀⠀⣼⣿⣿⣿⣇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠉⠓⠀⠀⠀⢁⣴⠿⠋⠀⠀⢻⠀⠀⠀⠑⠀⠑⠘⠀⠀⠀⢀⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠸⠿⣟⣿⣿⣿⣿⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⡀⠀⠀⢠⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣴⣿⢦⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⠟⣷⣿⣿⣿⣿⣿⣿⣦⠂⣴⣿⣿⣿⣯⣴⣿⣿⣀⢀⠠⡀
⠀⠀⠀⠀⠀⢀⣶⠿⠮⣿⣿⡘⣿⣿⡄⣌⠀⣠⣦⣦⢀⠸⠃⠀⠀⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⢢⣍⠛⠘⠻⢾⣿⣿⡏⣌⣧⣥⢤⠄
⠀⠀⠀⠀⢀⣾⡜⢂⣀⣽⣿⣿⣽⣿⡑⣿⣿⣆⡻⣿⣥⣤⡚⢿⣎⡀⠐⢳⢯⡿⢿⣋⣙⣛⣬⡉⢿⣿⡏⢰⣷⡞⢴⣾⢏⡙⢿⣿⣿⣿⣌⣃
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣄⡻⣿⣿⣿⣏⣀⠀⣝⠳⡀⣽⡀⢀⣿⠿⢻⣿⡆⢵⣾⣿⣧⠐⢿⠠⣤⡙⠈⠁⣈⠿⣿⠛⣻⣿⣇
⠀⠀⠀⡼⡿⣿⡿⠛⡩⢚⣿⡏⢹⣧⣾⣯⡿⢿⣾⣿⣿⣿⣧⣼⣮⣿⣿⣌⣓⣨⡿⠘⢿⣿⣿⣦⢿⣿⣿⣿⣿⣧⣹⡿⠇⣀⢼⣦⣡⡚⢻⣿⣿⡄
⠀⠀⢠⣇⠀⠃⣀⣸⣿⣿⣿⣶⣿⣿⣿⣷⣦⣦⣼⣿⣿⣿⣿⣿⣿⣿⡿⢛⣽⣿⣿⣶⣦⣬⣟⣻⣷⣿⢿⣿⣿⣿⣿⣷⣄⣼⣎⣿⣿⣿⣼⣷⣆⣄⡀
⠀⠀⠀⠉⠉⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠯⠭⠍⠉⠉⠉⠹⠟⠉⠉⠈⠛⠛⠟⠿⠿⠉⠉⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠙⠛⠛





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⡛⣉⣙⣛⡟⣫⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⢧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠋⡰⢃⣞⠣⣀⠀⠁⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠠⠔⣿⡿⠃⠀⢠⣾⡿⠀⠈⠀⠀⠀⠙⢳⣦⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡇⠀⠀⢀⡀⢀⡤⢞⣉⣤⡖⠘⢟⡉⠀⠀⠀⢦⡀⠀⠀⠀⠻⢦⠀⠐⡶⣶⣿⣿⠉⣆⠀⠀⠢⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢐⣲⣾⡿⠿⠿⠛⠉⠁⠝⠒⢂⣠⣴⣶⣶⣿⣿⣿⣤⡀⠀⠙⠃⠀⠀⠈⠻⣄⡀⠀⠀⠈⠓⠠⠀⠈⠛⠁⠀⠛⠓⠦⢄⡈⠑⠤⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠾⠿⠿⣿⣿⣿⡿⠟⠋⠁⠈⠻⢶⡆⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠄⠀⠀⠀⣤⣤⣤⣼⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⢀
⠀⠀⠀⠀⠀⢀⡄⢦⣄⠀⠃⠎⠙⠂⠀⢶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠀⣤⢀⠀⠀⠈⡏⠀⢻⡦⠀⢦⡀
⠀⠀⠀⠀⠀⠀⣁⠀⢉⠰⣄⠀⠀⠀⠐⠦⢙⡀⣜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠸⠃⠀⠁⠈⠃⠀⠀⠁⠀⠈⠀⠀⠈⠃⠀⣀
⠀⠀⣠⠀⠃⠀⠏⠀⠈⠀⠙⢶⡇⠘⠀⠤⣀⠑⠈⡀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⣤⠔⠀⠀⠀⠀⠀⠐⠀⠇⠀⠆⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸⢻⠷⣤⠀⢀⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠟⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠙⠏⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀⢠



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠆⠈⢡⡙⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢫⠀⢀⡁⠀⠐⣤⣄
⠀⠀⠀⠀⣠⠂⢠⠀⡜⠑⣀⠀⢀⠀⠀⠀⠙⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣶⣧⡈⠀⠀⠀⠈⠁⠠⣄⠀⠹⢦⡀
⠀⠀⠀⠀⠁⠂⢘⠀⠀⢀⠉⠀⠜⠀⠀⠀⢼⠁⠘⢿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠛⢿⣿⣦⡀⠐⠁⠀⠀⠀⠑⣄⣀⠉⢲⣤
⠀⠀⡀⠓⢠⠀⠸⣆⠀⠀⡠⠀⠀⠀⠘⢦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠻⣿⣷⣄⠀⠀⠀⠀⠈⢿⣷⣜⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⢾⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠉⣰⣎⡴⢃⣰⠃⠀⠈⠢⡀⣠⢴⣏⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡒⠁⠁⠁⠊⠈⠀⣠⠏⡸⠀⠀⠀⠀⠘⢏⠋⢸⡆⠈⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⢰⡇⠀⠀⠀⠀⠀⠊⠁⠂⠁⠀⠀⠑⠄⠀⠀⠁⠀⠀⠀⢠⠀⣸⡆⢠
⠀⠀⠀⠀⠀⣸⣄⣾⣷⣿⣸⣇⣧⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⡄⠀⣰⠀⣼⣇⣿⠧⠟⠂
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣿⡀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣧⣠⡿⠖⠋⠁
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⡲⢤⠄⠠⠷⠘⠛⠒⠛⠉⠁
⠀⠀⠀⠀⣰⣿⡆⠀⢰⡀⠀⠀⠀⢀⡀⢄⡴⠏⠚⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠺⠇⠰⢉⣰⣡⡊⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣷⠀⠀⡀⠀⠀⣺⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠏⠙⢄⠢⢄⠀⠄⠰⣿⡇⠀⢸⣿⡄⢠⡇⠀⣠⠿⠿⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⢀⡜⠀⠀⢣⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⡘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢠⣾⣥⠜⠀⠁⠀⣀
⠀⢀⣀⣴⣄⠀⠰⣦⠔⠃⣀⠀⢴⣄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢠⣿⣷⡶⡈⠀⠀⠘⢿⡀
⠀⠉⠉⣥⠴⣾⠧⠾⠦⠀⠉⠙⠳⠨⠓⠀⠀⠀⠀⠀⡀⢠⡴⣰⠾⢃⣶⣿⣿⡿⠈⡥⠐⠀⠀⠀⠐⠀⣀⣴⡞
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢁⡼⡿⠋⠉⠈⠐⠺⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣞⢀⣾⣧⠆⠈⠁⠀⣀⡤
⠀⠀⠀⠀⠀⠀⣰⠻⢏⣾⣿⡶⢦⠀⠀⠀⠙⢧⠀⠐⡆⠀⢸⣆⣠⣄
⠀⣠⠄⣴⠂⠞⣻⣶⣿⣿⡿⠂⡀⠀⠀⢠⡄⠀⠲⢤⣀⣆⣾⠿⣋⣁⠀⠀⠀⠀⠀⢀⠠⢆
⠀⣀⠀⡄⠀⢸⡿⠋⠀⠚⠀⢀⣿⡀⣶⣼⣧⣾⣾⣤⡾⠿⠷⣶⡿⠋⠀⠀⠀⠀⠠⠁⠀⠀⡀
⢀⣿⣼⣷⡀⢠⣤⣾⣶⣴⣿⣾⡿⠟⠻⠿⠛⠉⠁⠀⠴⠟⠛⠉⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⡆
⠈⠉⠉⠙⠓⠫⢤⣀⣀⠂⣨⠉⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠉⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠒⠼⠿⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣴⣤⠂⠀⠀⢀⣿⣿⣷⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠀⠊⠁⠀⠀⠀⠚⠁⣿⣿⣿⣿⣆⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣦⡀⠙⠳⠌⠺⢦⣄
⠀⠀⠀⡀⣀⣀⣀⣄⣀⣀⢀⣀⣀⠀⣀⢀⡀⢀⣀⡀⠀⡀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠉⠁
⠀⠀⣩⣍⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠰⠿⠿⠿⣦⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⣾⣆⣿⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣁
⠿⠿⠿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠆
⠀⠀⠀⠀⢹⣿⡀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂
⡄⠀⢠⠄⠈⠁⢠⠀⠙⠧⠀⢀⡀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠽⠞⠂⠀⠀⠀⠀⠀⢀⠀⠘⠓⢆⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⣄⣦
⣷⡀⠈⣰⠂⣠⣾⠇⠀⠀⠀⣾⡇⢠⡧⠀⣠⣠⠀⢠⡄⣀⠀⠀⠀⠀⢀⡄⠀⠐⠛⠓⠆⠀⡀⠀⠀⢀⠀⠴⠋⠀⠀⠀⠈⠷⠀⣄⠀⠀⠿⣿⣿
⠿⠧⠀⠃⢠⣿⡿⠯⠀⠠⠀⠛⠙⣿⣷⠀⢻⡆⢰⣏⠁⠉⠀⠠⡆⠀⠈⠁⠃⠀⠀⢀⣀⠀⠱⠦⠠⡞⠒⠼⢁⠑⡈⠀⣦⢠⠀⠁⠀⠀⠀⠉⠋
⠀⠠⠂⠀⣼⣿⡧⠀⠀⠀⠀⠈⠀⠉⢉⡁⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠐⠶⠿⠇⠶⠾⠀⠁⣸⣿⠀⠈⢰⣇⢠⡀⢰⡄
⡸⠃⢠⡆⠛⠛⠓⠀⢤⣄⣀⡀⠙⠂⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣧⠈⢗
⠁⢀⣿⣓⠀⠻⡄⠀⠀⠉⠁⢀⠁⠀⠀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠥⠀⠀⠈⠉⠉
⠀⣰⣧⡈⠁⠀⠀⠀⠈⠀⠀⠈⢿⡀⠀⠀⠀⣈⠁⠀⢰⣆⡀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠛⠑⠖⠀⢒⣢⡀⡙⣠⣤⣤⣼⠇⠀⠀⣀⣀
⠀⠽⠻⠋⠁⠀⠀⢀⣀⣄⢀⣀⣬⣿⡤⠥⠤⠾⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠼⠷⢦⣄⣀⡙⠃⠤
⠀⠀⡀⠀⠀⠈⢀⣀⣤⡾⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠶
⣀⣠⣤⡴⠶⠾⠛⠛⠛⠋
⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⠄⣶⡿⠂⠀⠀⠀⠀⢀⢿⣿⣿⣷⣄⠀⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠘⠁⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣷⣄⢻⣷⣄⠀⠀⣀
⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢰⠇⠀⡆⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⣿⣦⡀⠉⠿⣦⣈⢳⣤⡀
⠀⠀⠀⠀⢸⣗⠀⠀⡄⠀⠁⠀⢸⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠻⢧⡙⣿⣶⣄⡀⠀⢀⣀⣤⣤⣄
⠀⠀⡄⠀⣹⣿⡀⢠⣷⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⢻⣿⡿⠿⠿⠟⠛⠛⠛⠛⠻⠶⠀⠉⠀⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⣸⣷⠀⣿⣿⠅⢾⣿⡆⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⡖⣿⣿⢖⣿⣿⣗⠀⢠⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣦⣤⡀⠀⢀⣤⣴⡿⠂⠉⢻
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣤⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⣿⣿⡟⢊⠥⠤⠎⢘⣿⣇
⣿⣿⣯⣝⣻⡿⢻⣿⣿⣿⣶⣾⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠁⠀⣀⣤⣤⣿⣿⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠰⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠒⠒⠲⢄⡀
⠀⠀⠀⠀⠄⠊⠀⠀⠀⣀⡽⠓⢝⣧⣭⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡆⢤⡘⡧⣤⠀⠙⡄
⠀⠀⠀⠁⠀⠀⢰⡴⠚⡁⠀⠺⠓⣇⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢦⣍⢦⡑⡜⡰⠚⠀⠓⣄
⠀⠀⠀⠀⣠⠤⠚⢠⠊⠱⣤⣴⢀⡋⠠⠍⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠀⠲⠮⠲⣄⣟⡴⢏⡰⢢⡏
⠀⠀⠀⣰⠁⣀⡠⣣⠋⠳⠤⠬⠦⣏⡠⠳⣶⠲⠂⠀⠀⠀⠀⠀⠀⠀⠈⠦⡘⢆⣢⣔⢆⡿⠂⢜⡼⢃⠃
⠀⠀⢠⡧⢞⡡⢞⡕⠋⠂⠀⢀⣀⣏⡴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡵⠲⠭⣣⡷⢊⠟⠶⠛
⠀⠀⠀⠺⠛⢉⣉⣀⣀⢀⡤⠊⠀⡟⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣄⠀⠈⡟⠁
⠀⠀⠀⠀⠻⢿⣿⣿⢿⠋⣀⣤⣾⠱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣟⡳⢤⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠛⠋⠩⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠓⠀⠈⠉⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠤⠟⣻⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢔⡾⠟⣷⠽⢥⣌⡽⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⢀⡤⡷⠁⣈⢃⡾⣮⣭⣿⣍⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠠⠥⠀⠘
⠀⠀⠀⠀⢠⡟⡸⡡⠀⣏⣾⡃⢠⣤⠬⢍⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠁⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⢠⣮⠞⠕⢀⣔⠝⣿⢋⣅⠢⡀⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠑⢬
⠀⠀⠀⠿⠃⠀⠴⠋⠀⠔⢿⣏⠔⠙⠲⠷⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⣜⢁⠜⠹⠘⠦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣀⡵⠥⠀⠀⠒⠠⢤⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠿⠿⠾⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣰⢷⡔⢮⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠃⡼⠃⠀⠉⠈⠻⣿⣿⣿⣦⣀⠀⢀⣤⠾⠫⠞⠉⠁⣙⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠞⠀⠈⠀⠀⠀⠀⠀⠀⠙⠏⢿⡙⢿⡿⣟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⡿⣶⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠉⠙⠳⠦⣀
⠀⠀⠀⠀⠐⠁⠀⢠⣇⣸⣧⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣤⣀⣀⠀⠀⣾⠀⣀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⢀⡠⠴⣚⣫⡭⠥⠶⠶⢒⣲⣶⡶⠶⠶⠶⠦⠤⣤⣀⡀⠈⠉⠙⠛⠻⠿⢷⣿⣄⣀⣼⣿⣼⡇⠀⠀⣸⡄⣾⡆⢀⣀⠤⠂
⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠀⠠⢄⣀⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣿⣿⢠⠀⠿⣿⡟⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢰⣿⣇⡸⣿⣟⠀⠀⠀⠉⠃⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣾⣿⡁⠀⣼⣿⣿⣷⣿⣿⣷⠀⠀⠊⠀⠢⠀⠀⠀⢶⣾⣧⠀⠀⡤⢠⡶⣿⠉⠀⠃
⠀⠀⠀⠀⣀⣠⣾⠁⠆⢀⣠⣾⡇⠀⠻⢾⣿⣿⣿⢀⣾⣿⣿⢻⣿⡷⣿⣿⣷⣦⣀⡀⠠⠀⠀⠠⢾⣷⠁⠀⣨⠀⠀⣿⠁
⠀⠀⠀⠀⣯⣿⣿⡀⡀⣿⢿⣿⡁⡠⠀⡀⠿⡜⢿⡇⠹⠟⠋⡌⠀⠈⠙⠉⠹⠿⣿⢷⣄⡀⠐⠄⡸⢁⠰⢳⡏⠀⣄⠀⣀⠸⣧
⠀⠀⠀⠀⢋⢉⣨⢠⣯⣺⣼⣸⣡⣧⣆⣿⣀⣷⡌⣥⣿⡄⠱⣿⡄⣂⠀⠀⠀⠀⠀⠙⢋⡻⣿⠠⠀⣾⡇⢺⣷⠀⣿⣇⣿⣽⣿⣶⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣤⣷⡀⠀⠤⣤⣶⣶⣾⣷⣿⣾⣿⣿⢷⣿⢿⣿⣿⣿⣿⣿⡟⣿⠃
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡌⠉⠙⠛⢿⣿⣿⣼⡟⡟⡯⣿⣯⣷⣿⣿⣿
⠀⠀⠀⠀⠘⢿⣏⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⢁⡀⠀⡀⢰⢠⢟⠯⣯⣁⣷⢹⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣇⣿⢿⡿⣿⣻⣽⣿⣿⡿⠿⠛⠋⠉⠁⢠⡀⠀⠀⠀⠀⣰⡀⣼⣷⣤⣾⣿⣿⣿⡤⠊⠉⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⢹⣺⡟⠉⣿⣿⣿⣿⡄⠀⣾⡆⠀⠀⢽⡅⠀⠀⠤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢼⠁⠷⣾⣿⣿⣿⡤⠆⣿⣫⡄⠸⣿⣿⡅⠀⠀⠀⠀⠈⢈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣾⣿⣿⣿⣶⣨⣿⣟⣡⡔⣿⣷⠞⣀⠀⠀⠀⢀⣸⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⡷⢂⠀⢀⣈⣿⡷⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣀⣈⣻⣿⣿⣿⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⡅⢠⣽⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⣿⣿⣟⢦⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⣾⡆⢀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣠⣾⣷⣿⡿⠛⠻⣿⣗⣤⡀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⢀⣠⣾⣿⣿⣿⣿⣿⣿⣦⣠⣿⣇⣸
⠀⠀⠀⠀⣴⣸⣷⢠⣤⣞⡟⡿⡟⣿⣿⣦⣄⢀⢩⣈⣿⣶⣤⣿⣷⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣾⣽⣿⣛⠛⠻⠿⢿⣿⠟⡏⣿⣿⣿⣧⣇
⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⠿⠟⠛⠋⠉⠉⠙⠛⠿⡿⣿⣿⡟⣿⣿⣿⣧⣀⠀⠀⠀⠀⠠⠶⠾⣿⣿⣿⣿⣿⣿⣥⣀⣉⠉⠉⡁⢀⣀⣤⣴⣶⣿⣿⣿⣿⣯⡀
⠀⠉⠁⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⡴⢦⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣦⣤⣾⣿⣿⣷⣝⣿⣿⣿⣦⣀⡀⣀
⠀⠀⢀⣴⣦⣀⣴⣿⣿⣷⣶⣶⣿⣿⣾⣿⣿⣿⣿⣷⣤⣄⣀⣀⣾⣄⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣴⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠈⠉⢹⡿⠯⠧⠉⠉⠉⠉⠉⠉⠁⠛⠛⠉⠉⠉⠁⠉⣈⡿⠿⢿⠿⠷⠶⠀⠀⠀⢠⠾⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⢷⣄
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂
⠀⠀⠀⠀⢀⡠⢚⡘⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡼⠉⢦⡴⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁
⠀⠀⣠⣾⣷⣾⣿⣿⣿⣿⣻⡛⣦⡀⠀⠀⠀⡠⠞⢉⠟⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠉⠋⠀⠀⠈⢧⣄⠀⠀⠀⠀⠀⠀⠐⠋⠀⠂⠀⠀⠀⡄
⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠄

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⠄⠀⢀⡾⠀⠀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠉⠁⠈⠶⠀⠀⠀⢰⠦⡴⢶⢿⠷⣦⠾⠿⢶⢶⡶⠿⠷⣦⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⣦⠀⣼⡿⠉⢠⣛⡿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣋⣤⣾⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠠⠄⠸⣯⣿⡁⢀⡿⡻⠀⢈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣾⡿⠿⣿⣿⣿⡆⣤⣴⣆⣴⣶⡴⠖⠂⠀⠀⠀⠀⢀⣠⣄⣤⡴⢖⠂⠀⢀⣀⣬⣤⡈⠁⡠⣀⠈⠉⢁⡀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣤⠶⠾⢿⣿⣿⣿⣟⣿⣊⣁⠀⠀⠀⠀⠀⢀⠴⠯⠟⠻⢋⡅⠀⠀⡲⢋⡟⠁⢘⣷⠘⠣⡈⠁⠈⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⣡⣰⡿⣿⣿⣿⣿⣿⡿⣷⣄⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⡀⠀⢰⠃⠀⢸⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣟⣴⠟⢹⣿⠛⡟⠛⣿⡆⠉⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⡀⠀⠺⠀⠘⡆⠀⠀⢀⡀⠀⠀⢼⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⠁⠀⣸⣯⣸⠇⠀⠙⡥⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠺⡆⠀⠀⠁⢸⡃⠀⠀⠸⠄⠀⠈⠠⠂⠀⡿⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠿⠿⠃⠀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⣷⠀⠠⠁⡆⢸⠇⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢸⠄⠀⡞⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢀⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢸
⠀⠀⠀⠀⢧⢀⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣲⣄⠀⠀⢀⣹⣇⠀⣿⠀⠀⠈
⠀⠀⠀⣀⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⣎⡨⢡⣏⡜⢛⡩⠯⢳⣿⠀⣿
⠀⠠⢽⡿⣿⡟⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣬⢎⠥⡄⠤⢉⣵⠔⡫⠐⢖⣾⣿⣧⣿⣶
⠠⠤⢼⣿⣿⣿⣿⣶⣗⠢⣄⣂⣤⣦⣄⡀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠸⣉⣀⡬⠽⠥⠐⣈⣉⣴⣬⣱⣾⣽⣿⣿⣿⣿⣓⣞⡂
⠀⢰⣿⣿⣿⠿⠾⠿⣭⠭⢿⣿⣿⣿⣿⣿⡶⠂⢸⠃⠃⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣷⣾⣷⣶⣶⣶⣾⣿⣿⣿⡿⢿⣿⣿⠿⣟⠋⠉
⠀⠸⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⠟⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠿⢯⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣬⣭⣿⣇⠙⠻
⠀⡤⢿⠋⠐⠞⠻⠿⣿⡿⢛⠆⠐⠛⠏⠀⢀⠀⠘⠀⠂⡈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠋⢤⣾⣿⡿⣿⠿⠻⠿⣏⣱⣿⠿⠟⠺⠛⠛⠛⠈⢻⣆⠀⠙
⣤⡼⠁⠀⠀⠀⠀⠉⠉⠀⠾⠅⢃⡀⠐⠇⠀⠀⢼⢸⡇⡗⠀⠀⣀⣀⣠⣤⠤⣤⣴⣲⠟⣉⣉⣭⣽⡛⣿⡿⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂
⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠒⠉⠒⠛⠒⠒⠀⢻⢻⠃⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠛⠛⠒⠋⠁⠊⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣏⣭⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡦⠌⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠨⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠉⢤⠀⠀⠀⠀⠀⠀⠈⠁⢠⠄⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠊
⠀⣄⢰⢾⣇⡄⣶⣰⣠⣦⡄⣴⣼⣆⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⠐⠂⠀⠀⠀⠀⣀⠈⢻⣋⡀
⠘⠛⠛⠻⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣉⣹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠂⣠⡓⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠘⠒⣫⣽⣷⡬
⠀⢠⣷⣄⣤⣏⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢾⣃⡘⠻⣭⣹⣯⠖
⠈⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠐⢜⣻⡭⠄⠀⢤⣸⡧⠞
⠀⣿⣿⣿⣿⣿⡿⠿⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⣷⣁⠈⣒⣿⣯⣉⢀⣰⣿⣿⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⢀⠤⠤⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠄⠀⠀⠀⠀⠀⠀⠀⢰⠓⣦⠀⣀⠀⠀⠀⠑⠚⠒⠒⠒⠓⢒⠒⠂⠀⢂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠴⠄⠀⠁⠀⠀⠀⠁⠀⣿⡄⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡷⠀⠠⣦⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠚⢁⡿⠀⡰⠁⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠿⠢⠄⣀⠀⢀⠈⠀⠀⠀⠀⠀⠈⠀⣀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠁⠀⠀⠐⢧⠀⠄⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⡀⢈⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⢂⣀⠀⠐⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣷⠘⠂⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⡀⠈⠀⠀⢠⠞⠚⠁⠉⠁⠀⠀⠀⠀⠈⠷⣶⡁⠀⠀⠀⠻⢷⠠⠴⠠⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⣤⣀⡰⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠹⢆⡀⠀⠀⠀⠀⠀⠀⠸⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠁⣀⣀⣀⠰⠋⠀⡀⠀⠀⠀⠀⠀⣼⠦⠀⠀⠀⠀⣀⣌⣯⠤⠤⠴⠿⣶⣷⡥⣀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡬⠥⠄⠒⣩⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡂⣡⣴⡖⠋⠉⠀⠀⠀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠉⠁⠀⠀⠤⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⢀⠀⠀⣀⣀⣀⣀⢀⣾⣿⣯⣴⣶⣾⣷⣶⣦⣤⣀⡀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⣿⠇⠈⠉⠉⠉⢉⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣯⡙⠳⢭⣗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠇⢰⡿⠀⢀⡀⢊⡴⠃⣀⠀⠀⡀⠀⠀⠁⠀⠈⠙⠻⢿⡻⣦⡍⠻⣷⣌⡓⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡞⢀⡜⣡⡴⠋⢠⠿⠁⠰⢿⡷⢠⠀⠁⠀⠀⠀⠈⠁⠀⠀⠙⠺⡟⢦⡄⠙⢷⣦⣄⠈⠉⠁⠻⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⡾⠔⣩⠤⢀⣵⠾⠚⢁⠔⡀⠁⠈⠳⡄⠀⠀⠀⠀⠀⡀⠀⠀⠈⠂⠙⢧⣄⠀⠉⠛⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣬⣷⠊⡡⠺⢋⡔⣫⣦⣵⣊⣀⡠⠒⠀⣤⣴⣄⠀⠢⠈⠀⠀⠀⠀⠀⠰⡈⠙⢿⣦⡀⠀⠈⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠈⠙⠉⠀⠂⠂⠉⠙⠚⠉⠉⠀⠎⠐⠒⠒⠂⠀⠀⠀⠀⠘⠂⠀⠙⠛⢶⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠄⠄⠂⠀⠀⠠⡀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠈⠀⣠⠔⢦⡀
⠀⠀⠀⠀⠀⢀⡔⠋⠀⠈⢲⣄⠀⠀⠀⢀⡴⢦⣠⠞⡠⢄⠳⡄⠀⠀⠘⠓⠒⠒⠚⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠀⠻⣄⠁⠈⠁⠙⣄⢠⢦⡀⠀⠈⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠓⠒⠀⠀⠀⣰⠋⠐⠁⢀⡀⠈⢦⡑⢂⡜⠙⣧⠢⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⠁⡴⠢⠔⠁⠈⠢⠄⢱⠎⠰⠀⠘⢆⠠⠙⣆
⠀⠀⠀⠀⠀⢀⣿⣄⢀⠔⠉⠻⡀⠈⠀⢀⡴⠒⣄⠀⣠⠋⡠⠠⠊⠢⠈⣧⠔⠉⠢⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢨⣿⣿⡁⠐⠒⠀⠙⢆⡴⠋⡀⡀⠀⠑⢦⡀⠀⢀⣠⠴⠊⠁⠔⠀⢠⣮⠳⣴⣿⣿⣄
⠀⠀⠀⣼⣦⢚⣿⣿⣁⣀⣠⣶⠞⠁⠀⠈⠀⠀⠀⠈⠢⠉⠚⠁⠀⠀⠀⠁⠀⠐⣿⣿⣷⣼⣿⣿⣧⡀
⠀⠀⣰⣿⣷⣿⣿⣿⣿⣦⣿⣿⡷⣠⠴⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣺⣿⣿⡿⠿⠿⢿⣿⡄
⣰⣋⣉⣙⣁⣀⣈⣻⣛⣿⣋⣙⣛⣁⣀⣀⣀⣀⣘⣦⣒⣓⣢⣚⣙⣊⣁⣀⣀⣈⣿⣋⣀⣀⣀⣀⣙⣎⣋⣉⣳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣠⡏⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⢀⡶⣾⣿⡇⠀⢿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡤⠚⢑⣽⣿⡋⠟⠀⠸⢿⣧⠀⠀⠀⠀⣤⡄
⣄⠁⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢴⣿⠿⠗⠀⠀⡜⣹⣿⠁⠀⠀⠀⠀⢿⣦⠀⠀⠰⣿⣿⣷⡀⠀⠀⡀
⣿⣷⣆⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⢀⠀⠀⣀⣀⣸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄⠙⠁⠀⠀⠐
⣿⣿⣿⣿⣆⡀⣴⣿⣿⣿⡟⣻⣿⣿⣶⣄⣈⠉⠸⢿⣿⣿⣿⢠⡀⠀⠀⠀⠘⠀⠀⠀⢹⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣽⡙⣿⡿⠿⢿⣃⣀⡈⠿⣿⣿⣿⣄⣀⠀⡀⠈⠳⠄⡘⠛⢿⣿⣯⢡⡀⢤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠉⢉⣴⣦⣾⣿⣾⣿⣿⣿⣿⣟⠿⢿⣿⣻⣿⣦⡘⠷⠄⠀⠈⠃⠀⢿⣿⣧⣡⠈⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⠃⠉⠛⠉⢀⣰⣶⢄⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿
⠻⣿⣿⣿⣟⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⡻⣿⡆⠐⠀⠠⠘⠋⠑⠆⢥⣀⠀⠀⠀⢀⣠⣾⣿⣷⣶⡶⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣤⣈⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⠁⣙⢛⠒⣐⣤⣶⣶⣤⣄⡀⢀⣠⣾⣿⣿⣿⣿⣿⡟⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣯⣽⣿⣿⣿⣛⣋⣉⣉⡈⠉⢉⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⢀⢸⡀
⠀⠀⠀⠀⠀⠰⣤⣤⣄⣼⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠐⣿⣼⣷⠂
⠀⠀⠀⠀⣀⠀⣀⠉⠛⢿⣷⣾⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠴⢶⣿⣿⣿⣿⣼⣦⡀
⠀⠀⠀⠹⢿⣷⣛⣿⣟⣻⣁⣉⠙⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣤⣴⣏⠈⠀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⣿⣻⣿⣼⣧⠄
⠀⠀⠀⠀⠀⠉⠛⠋⠉⣿⢿⣿⣿⣿⣇⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠛⠲⣧⣀⠀⠀⠀⢤⣧⢆⣠⣿⣏⡛⣿⣿⣿⡷⠦⠤
⠀⠀⠀⢸⣿⣄⣔⣦⣰⡟⣶⣿⣿⡿⠃⢀⡠⠎⠁⠀⠀⢀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠤⣴⣷⡿⠆⣾⣿⣼⣿⣷⣿⣆
⠀⠀⠀⣠⡉⠉⠛⠛⣣⣾⣿⣯⣽⣦⡶⠄⢀⡰⠀⠤⠚⠈⢀⠀⠀⠀⠠⡄⠀⠀⣀⠀⢀⣀⣒⣾⣿⣄⣺⣻⣿⣛⣳⣯⣿⣙⡛⠂
⠀⠰⣿⣿⣍⣤⡀⢁⣸⡇⡭⣯⣵⣾⣷⣿⣧⠄⠀⠠⠁⠀⠀⠀⠒⠒⠖⠛⠚⠛⠻⠿⠿⢯⣯⣽⣿⣌⡵⢻⣽⣝⣛⣿⣿⣿⣅⡀
⠀⠀⠀⣄⣸⢾⡿⢆⣹⡇⠿⠿⠿⣿⡯⠾⢯⣤⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣴⣶⠟⠛⠙⠙⠛⠉⣿⠹⠿⠟⡟⠛⠛⡇⠶⠠⠈⠈⠁
⠀⠀⠀⠀⢀⣀⣘⠛⠛⡟⢢⣄⡀⠐⠀⣀⡀⠀⠉⠙⠋⠋⠙⠊⢈⣉⡉⠈⠉⠁⠀⠀⡀⡄⣤⡐⠿⠶⠦⠤⠠⠔⠶⠷⢿⣶⠦⠂
⠀⠀⠀⣀⠙⣛⣝⠛⠚⣇⠨⡀⠙⣻⣏⣹⡛⠂⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠒⠈⠁
⠀⠀⠛⠻⢿⣾⠟⠀⠈⣿⠀⠆⠀⠿⢿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢀⣤⣀⣀⣤⠤⠶⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⢛⣃⣀⣀⡀⡀⢠⣠⣴⣶⣶⣶⠀⠈⣧⣴⣤⣱⣤⣤⡀
⠀⠀⠀⠀⢀⣀⣴⣾⣾⡿⠀⣄⡀⢀⣀⣰⡄⢰⣄⢀⢀⢠⠀⢀⠀⠀⠀⠘⢿⡿⠿⠟⠋⢉⣉⣁⣠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠿⣾⣿⣿⢸⠿⠆⠿⠶⢶⣧⠄⠀⠀⠈⠉⠉⠁⠀⣀⣀⣀⣀⣀⣤⢤⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⠤⣈⡀⠲⢦⣄⠀⠀⠈⠉⠘⠓⠦⠀⢤⠤⠤⠤⠄⠈⠉⠉⠋⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⢳⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⣡⣿⠈⠢⠀⠀⢱⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⠏⠀⠀⠀⠀⢀⡴⠟⢁⡀⣴⠿⠋⠀⠀⡀⠀⠀⠈⢿⡀⠀⢀⣠⣤⣶⢿⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⢤⣴⣾⣿⠿⠟⠋⡳⠀⠀⣁⣴⣭⣶⣿⣯⡀⠈⠓⠦⠀⠀⠻⣆⠀⠀⠀⠙⠤⠈⠉⠻⠟⠀⠷⢤⣀⠙⠢⢀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣠⠶⠾⢿⣿⣿⡿⠟⠛⠉⠙⢶⡄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠳⠤⠀⠀⠀⣠⣤⣤⡿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠒⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠁⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠉⠈⠀⠀⠸⡀⠀⠀⠀⠘⠤⢄⠀⠀⠀⡀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢀⠄⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⡠⠒⠠⡀
⠀⠀⠀⠀⢀⢠⢀⠀⠀⠀⡀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣀⡀⡐⡄
⠀⠀⠀⠀⠾⢸⢸⡆⡇⡄⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣀⣠⠤⣴⠒⠋⡉⠉⢀⣈
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠇⢼⢸⣿⣧⣤⣶⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⢒⢊⢻⡅⠞⢁⢐⠀⠱⢶⣯⠶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠙⡿⢿⣿⣿⣾⣇⡇⢩⣀⡄⠀⠀⠁⠉⠉⠉⠉⠉⠀⠈⠁⠀⠁⠀⠀⠘⠂⠨⠧⠤⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉⠘⠛⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠤⠄⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠠⠀⡀⠀⠀⠀⠀⠰⠄⡀⣄⢀⠀⢒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠉⠁⠉⠀⠀⠀⠀⠘⠙⠍⠀⠁⠀⠀⠀⠀⠈⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠈⡱⢲
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣹⠃⡴⡇⡀⢇⣀⣀⠀⠀⠀⠀⠀⠀⣀⣤⠠⢀⣀⣀⣠
⣀⡤⢤⣤⣾⡿⡀⠑⠺⠟⡛⡄⠐⣢⣾⣿⢿⣿⡁⠘⢡⢿⠹⣸⠟⠉⢶⠶⡾⢉⣩⣿⡿⠄⡐⠦⢀⠈⣉
⣿⣶⣿⠿⣿⣇⠉⠢⠑⣤⡀⢠⣿⣿⡿⢫⣼⣹⡿⢦⡈⠀⣠⣿⢳⢧⢈⠓⠴⣟⠹⠁⣯⣾⡉⢁⠀⢨⣿
⣿⣿⣧⢺⡇⠈⠓⠀⠐⣡⣴⣿⢟⣽⠳⣿⠿⢻⠁⣀⣽⣟⠙⢆⠌⡉⠳⡝⢆⣀⣠⣾⣿⢯⠱⠘⢠⠏⣽
⡿⣿⠃⠀⡿⠦⢀⣤⣾⣿⢿⣯⡾⢿⠄⣹⣤⣴⣾⣿⡟⣉⢳⡄⢀⡀⠑⠶⠿⣿⡿⢻⣿⠓⣤⣀⠉⠐⢁
⠊⠁⢀⣨⡴⢾⣫⣿⣻⢷⣞⣹⣥⡶⢿⣿⣿⠿⣿⢟⣽⢿⣦⡈⠀⡻⠳⢄⡐⠪⠉⠐⠛⠢⣈⠈⠀⢐⠟
⠒⠉⠝⠫⠔⣫⠿⠋⠐⠋⠉⠈⠡⠒⠉⠀⠡⠞⢻⠋⠀⠀⠃⠙⠳⠀⠀⠈⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣦⢷⢾⣉⡇⢇⣸⢸⢦⡏⡏⣰⢷⣘⣯⡷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⢀⣸⡇⠀⠀⢸⣆⠀⣴⣰⣿⠇
⠦⠖⠋⠁⠀⢠⡀⢸⣿⣀⡏⣿⡿⣄⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⣧⣸⣿⠟⣼⣿⠃⠠⠑⠠⠀⠀⠀⡀⡆⣀⠄⡤⢂⠆⠀⢤
⠅⠀⠀⠀⡀⠀⠈⢻⣿⣦⣿⡏⢀⣤⢠⣨⡧⠚⠻⢿⡻⢧⡀⡆⠊⢀⢃⠞⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣶⣿⣿⠟⠛⠳⠞⠛⢾⡛⠢⡾⣿⣋⣉⠟⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⢿⠋⠠⡀⠀⠀⠀⠀⠙⢾⣁⠙⣲⠉⠓⠤⡀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠁⢠⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⡼⠀⠀⠀⠀⠈⠂
⠿⠆⠀⠆⢰⢲⣿⣿⡿⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⡀⠀⡀⠀⡀⣾⣿⣿⡇⠀⢀⠈⠀⠀⠐⠘⠂
⠹⣶⠛⣄⡧⡼⠋⠉⢃⣥⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠⣶⣶⣶⡶⣶⣾⣷⣶⡶⣀⠀⠰⠲⣐⢂⠀⣀⣠⡎⠕⠆
⡟⢹⣿⢙⣿⢷⢂⡎⡘⣠⠗⠁⠀⢤⡦⣄⠀⠀⠀⠀⠀⠠⠄⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢀⠌⠀⠀⠈⠀⠙⠏⠉
⠶⢻⡿⣾⣿⣿⡅⣷⣿⠥⢀⠄⠀⢁⡷⠈⠓⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠒⠒⠲⠶⠖⠆⠀⠶⢶⡶⢶⣤⣶⣶⣤⡴
⠀⣼⡇⡇⣻⠝⣿⠟⣏⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠐⠒⠄⠀⠁
⠀⢸⠀⢷⠛⠐⣧⠸⠡⠺
⢲⣦⣷⣸⣀⣾⣿⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡠⠔
⠛⠛⠙⡿⠿⣿⣿⡟⢦⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⢄
⠀⠀⢠⠔⠈⣹⣮⣷⣠⣴⣟⡚⡻⣿⣷⡄⠀⣠⣀⡔⠁⠀⠀⠀⠀⠀⠀⡐⡰⠋⠀⣯⡁⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣄⡀
⡁⠄⠀⠀⠈⣙⣉⣉⣿⣯⣉⣵⣷⣾⣿⣷⣾⣿⣿⣿⡄⠀⢀⡀⣄⣀⣠⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⢃⠈
⣄⣅⣰⣮⣥⡈⣙⣿⣯⣽⣯⣠⣾⣾⠋⢻⠿⠟⣻⣿⣿⡿⣿⣿⣿⡏⣽⡟⠁⢀⣀⢀⠀⠀⠀⢠⣀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⢙⣿⣿⣿⣻⡿⣲⠞⠯⠷⠿⣿⣿⣿⢿⣂⠊⠿⣶⠎⠁⠉⠙⠀⠀⠀⠶⢦⠀⠀⠀⠀⠀⠠⣀
⣿⣿⣿⣻⠟⠁⠒⣤⣤⡶⠾⢿⣷⣾⣥⣴⣏⣼⣿⣯⣿⣯⣿⡟⠀⠀⠀⠀⠙⣀⣀⣿⣿⣥⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣴⣦
⢿⣿⡿⣯⣤⣆⡐⠘⠛⢶⣶⣶⣿⣿⣿⣿⣿⣧⣄⡠⠈⠿⢿⣿⣿⣿⣿⣶⣾⣿⣿⠿⠋⠁⣀⣀⠀⣀⣠⡤⠖⠛⠀⣀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⠇⠹⠛⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⡀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⣾⣷⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⢹⣿⣇⢀⣤⣄⢀⣀⠀⠄⠀⠛⠁
⠀⣦⣤⣀⢀⣠⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣾⣿⣷⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠰⠆
⠀⠛⠻⢿⣿⣿⣿⣯⣶⣠⣴⣶⡀⢀⣠⣶⣄⠀⢠⣶⣄⣀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⣀⡤
⠀⢀⡀⢠⣬⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠿⠀⠀⠀⠀⠀⢠⣤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀
⢠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⡿⠿⠛⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⡄⠀⠀⠀⠀⠙⠃
⠀⠻⠟⠛⠿⠟⠿⠟⠿⠻⠯⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⣿⠟⠃
⠀⢐⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠀⠀⠀⠀⢤⣾⣿⡂⢸⣿⣄⠀⠀⠀⠀⠀⣠⣤⠄
⠀⠼⣿⣿⡷⡄⠀⠀⢀⣀⣤⡶⠾⢿⣏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠁⠘⡁⠀⠀⣠⠾⡋⠉
⢖⣻⣿⣿⣿⡛⠋⠉⠉⣻⣍⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣻⣿⣿⣿⣿⣟⠓⠀⠁⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⣄
⣽⣿⣿⣿⣿⣿⣟⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣼⣿
⣿⣥⣽⣯⣿⣟⠛⠛⠛⠋⠀⠈⠁⠒⠒⠒⠂⠐⠐⠂⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠠⠰⠿⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣷⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢆⠰⠀⠆⡆⡠⠂⡠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠒⢢⠠⣑⢌⠢⢇⣑⡴⡡⢊⠤⠒⠉⣠⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠳⡌⢭⠎⠁⠈⠑⠬⣵⢶⡱⢏⠈⠀⠒⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⣆⡠⢄⠀⠀⢉⡾⠇⣀⣀⡴⣰⡀⠈⠀⠀⢀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠀⠀⠀⣠⠔⣲⠞⡽⠉⢢⡈⠀⠊⠀⢁⡀⠀⠰⠋⠂⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⢀⡠⠂⡟⠀⠀⠀⣰⠁⠀⠀⠙⢢⡤⠶⠉⡏⠑⢄⣀⠀⠀⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣖⠿⠀⠎⠀⠀⣠⠊⠘⡄⠀⢀⡴⠋⡠⠀⡰⠉⠂⠀⠈⠛⢶⡤⢀⡀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡈⠁⠀⢀⠀⠀⠀⢀⠐⠁⠀⠀⢀⣴⠁⠀⡞⠁⣠⠛⠦⣀⠀⠀⠀⣀⠈⠲⡈⠒⢄⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢗⣶⢁⡄⡴⠁⠀⠀⡠⠋⠀⠀⢀⠔⠁⢈⠀⠀⠀⡰⠁⠀⠀⠀⠑⠄⣈⣿⣅⠀⠀⠀⢠⡘⣶⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠠⡄⡹⢗⡈⠀⠀⠀⡴⠁⠀⣠⠄⠁⠀⠀⡎⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣻⠢⠐⢄⠀⢈⡪⣏⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡑⢻⣮⠃⣀⠀⠀⠀⣠⣄⠁⠀⠀⠀⠀⠀⢼⡧⠀⠀⠀⢺⡗⠀⠀⠀⢊⣽⣑⠂⠀⠙⠀⣵⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠽⣧⠣⠈⠻⡀⠀⣺⣗⠀⢀⡀⠒⠿⡈⢽⡯⠀⠀⠈⢽⡯⠁⠉⡢⠶⣼⠀⠀⠱⠄⠘⣼⡦⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣼⣃⠆⢀⠀⠀⢺⣗⠀⠀⢀⣤⡀⠈⠻⠅⠀⣀⠐⣸⣇⠂⠀⠀⠀⠸⡁⠀⠀⣤⢘⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⡉⠓⠴⢇⠀⠀⠴⡷⠄⠠⣄⠀⠀⠀⠑⠴⢄⠀⠀⠤⡀⠀⠁⢀⠀⢳⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠿⢬⣱⠀⡄⠀⡑⠀⢚⣏⠂⠀⠈⣄⣀⣀⣠⠀⠈⠓⠀⠀⠘⣀⠀⣏⡧⠿⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣒⡷⢼⡌⠀⣤⠈⠡⡷⠍⠤⡰⡿⡔⠂⠚⢃⠀⠀⢈⡅⠀⣹⣠⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣙⠦⢦⡃⠤⠇⢤⣰⡵⠽⠼⣤⠤⠤⠯⠉⣨⡧⣴⣫⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠟⠂⠒⠠⠥⠤⠴⠿⠃⠒⠲⢟⣣⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⣶⠀⠀⠀⡀⢀⣼⡁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⢰⣿⣏⡀⠀⠀⢀⠀⠈⠃⠈⠈⢡⣿⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣄⡀⠀⠘⠻⠆⠀⠛⣡⠀⠀⠻⠿⣷⣤⣤⣄⠀⠡⠀⠀⣠⣿⣧⣄⣀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠸⣿⡿⠛⠋⠁⠀⠀⠀⠘⠛⣿⠄⠀⠀⣤⠈⠉⠉⡈⠀⠀⢠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣌⠀⠀⢀⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠧⠄⠀⠈⠙⣿⣿⣿⣷⠤⠀⠀⠀⠄⠀⢸
⠀⠠⢶⠶⣾⣿⣿⢿⣿⣿⣿⠀⠈⠀⠁⠉⠃⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⡀⠀⠀⠀⢈⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠓⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣾⡷⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⣴⣿⡜⢱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠛⠿⠂⠀⠀⠂⠀⠷⢀⡀
⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣿⣿⠋⠀⠀⠀⠝⠡⡄⢄⠀⣲⣿⣿⣼⣷⣶⣎⣦⣀
⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢷⣿⣿⡇⠀⠀⠀⢀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⢐⣿⣧⠀⠀⢠⡀⠀⠀⠀⠀⣰⡈⣤⣂⢀⣤⣁⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣺⣿⣯⡀⠀⢾⣧⣤⡜⣁⣾⣿⡇⠨⠃⢈⣵⣟⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡹⣿
⠲⠿⣿⡿⣂⣰⣿⣿⣷⢸⣿⣟⣿⣿⠄⢠⡎⢩⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣾⣻⣿
⣙⣿⣿⣿⣏⡵⣿⣿⣗⣼⣿⣿⣽⣿⣿⣼⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⢿⣿⣿⣿⠿⢿⣿⣿⠿⠿⣿⣿⣿⠻⣿⣿⣿⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠸⠏⠀⠐⢻⣿⠃⠀⠈⢹⡿⠃⠀⠈⠻⠃⠀⠈⠉⠛⠛⠛⠋⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢹⠓⢄⠀⠀⠀⠀⠀⠀⢀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢹⠉⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠸⡀⠄⠁⠢⠀⠀⡠⠒⠡⠁⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⡠⠔⠁⠘⣆⡈⠁⠀⠀⠀⠀⠉⠙⠠⡀⠀⠀⠀⠱⡘⢔⣌⠴⠋⠀⡠⠃⢠⠀⢠⠀⠀⠈⠑⠢⢤⠤⣤
⠀⢀⣠⠔⠉⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠚⠉⠀⠀⠀⢀⠀⠀⢸⠀⠈⢢⡀⠀⠀⠀⠀⠀⠈
⠚⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠃⠀⠀⠉⠰⠂⠄
⠀⠀⠀⠀⣆⠰⠀⠀⣠⡀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙
⠀⠀⠀⡐⣸⠇⠱⠀⠯⢯⠁⠀⠀⠀⠀⡌⠲⠀⡀⠂⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⠀⠉⠀⠠⠀⠁⠤
⠉⠉⠶⣣⡿⡄⠁⣛⡁⡇⠈⣂⠀⠐⠺⠀⠠⠆⠰⣼⣁⡀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈
⠶⠶⠖⠛⠒⠛⠚⠛⠃⠒⠒⠒⠒⠚⠛⠛⠛⠛⠓⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠓⠚⠛⠚⠒⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣀⣤⢀⣾⣇⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⣶⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣼⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣄⣤⡀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⣠⣶
⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⢠⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⣴⣿⣷⣄⣠⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⢠⣾⣿⣿⣿⣷⣼⣧⠀⠀⠀⣼⣿⣾⣿⣿⣿⣄⠀⠀⠀⠀⣴⣿⣿⣷⣤⡀
⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠐⠛⠛⠛⠛⠛⠛⠛⠃⠀⠐⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⣀⣐⠚⠛⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣶⣄⠀⠀⠀⠀⣾⣿⣿⣷⣄⡀⠀⠀⠀⣠⡄⣴⣶⣿⣿⣧
⠀⠀⢴⡾⡿⣿⣿⡿⠷⢦⠄⠀⠀⢤⠿⣿⠿⠿⢿⠿⠦⠀⠀⠀⠤⠾⠿⣿⡿⣿⠿⣿⣷⠄⠀⠀⣿⣿⡿⡿⠿⢿⠄⠀⠠⡿⠿⠿⢿⣿⡿⢿⠅
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣼⣷⣤⣾⣿⣆⠀⠀⠀⠀⣼⣷⣄⢀⣤⡀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣠⣤⠀⠀⠀⠀⠀⠀⣰⣿⣦
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡄⠀⠀⣠⣾⣿⣿⣿⣷⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠠⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣷⣦⣿⣿⡀⠀⠀⢠⣦⣾⣿⣇⠀⢀⣿⡀
⠀⠐⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠐⠟⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠞⠛⠛⠛⠛⠛⠛⠀⠀⠀⠸⠛⠛⠛⠛⠛⠛⠓⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⢠⣾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠂⢠⣿⣿⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣠⣿⣿⣿⡃⠀⠀⠻⡿⢿⣿⣿⣿⣿⣇⠀⠀⠀⣄⡀⢀⢰⣆⢐⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⣰⣿⣿⣿⣿⡷⠀⠀⠀⠙⢮⡻⣏⣻⣿⣿⣷⣶⣴⣿⣿⣿⣾⣿⣿⣿⣇⠀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⢂⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⢯⡻⣾⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣦⣿⠀⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⡘⣧⣽⣟⣿⣿⣿⣿⢿⣿⡷⣦⣬⣿⣿⣿⣿⣿⣦⣾⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠛⢷⣌⡛⠂⡀⣠⣤⣍⣲⣾⣿⣿⣿⣿⣿⣯⣥⣶⣧⡶⣿⣿⣿⣿⣿⣽⣿⣿⠀⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡆⣸⣿⣿⣿⣿⣿⡿⠛⠷⣤⡟⢿⣷⣮⡙⠋⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡌⡿⠒⢿⣿⡗⢦⣿⣿⣿⡿⠋⣵⣾⣿⣿⡟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢁⣿⢷⣤⣽⣿⣿⣮⣿⣿⣿⣾⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣶⣿⣧⣤⣿⣿⡟⠛⠁⠈⣹⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠛⢻⣿⣿⣿⡟⡟⢿⣿⣿⣿⣿⣿⣯⣴⣶⣿⠟⣿⢉⣹⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣅⣹⣿⣿⡛⢿⣷⡍⠛⠿⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣛⠻⢿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿⢟⠛⣹⣯⣽⣿⣿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠿⠟⠛⢃⣤⣶⣿⣿⣿⣵⣄⣤⣴⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠰⣠⣶⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡉⠧⠀⣶⣿⣿⣿⡋⠉⠉⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠃⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣃⠢⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣤⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⢿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⠛⠛⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠋⠸⡟⠛⠀⠀⠀⠀⠈
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏
⣿⣿⣿⣷⣦⡄
⣿⣿⣿⣿⡟⠁
⣿⣿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⣄
⠀⠐⠐⠋⠉⠉⠱⠤⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⠉⠀⠀⣀⣀⣀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⣤⡀⢀⠀⣴⣿⣦⣤⣶⣂⣀⣀⣨⣍⠁⠀⠁⠙⠒
⠀⠀⠀⠀⢀⣤⠠⠷⠞⠁⠀⠀⠀⢀⣠⡴⠿⠛⠛⠋⠁⠀⠀⠀⠘⠋⠉⠉⠁⢀⡤⣶⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡤⢴⣶⢾⠤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣰⣮⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠉⠙⠩⢘⡑⢆
⠀⠀⠀⠀⠀⠀⢀⠀⠒⣉⣠⣬⣇⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣦⣤⠀⣴⢻⠷⣿⣿⡷⠇
⠀⠀⠀⠀⠀⣀⣸⣇⣀⡿⣿⣿⢭⡗⠚⠁⠀⠀⣠⣦⣤⣴⡿⠿⢿⣿⣿⡿⠛⠛⣳⣦⣤⣥⣸⣷⡶⠆
⠀⠠⠙⠛⠛⠛⠋⣭⣍⡉⠉⢻⠎⡡⠿⡿⠶⠓⠛⠉⠉⠀⢀⠀⠈⠉⠛⡀⠀⠘⠋⣙⢹⡁⠀⠈⠉
⠀⠉⠁⠀⠀⠀⠀⠙⠋⠉⠉⠒⠉⠈⠛⣈⣀⣠⣤⣤⠀⠀⢉⠀⠁⠀⠀⠀⠀⠐⠚⠛⠛⠓⠒
⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⣤⣶⣟⣯⡿⠛⠛⠛⠉⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⣀⣀⣴⣦⣶⣿⡯⠿⠛⠋⠉⠁⠀⢠⡀⠠⠀⠀⢀⣤⠄⢀⣠⣤⣤⡤⠖⠂⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠰⠿⠇⠎⠉⠙⠄⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠋⠁⠓⠚⠛⠋⠁⠀⠀⠀⠀⣀⠀⠁⠄⡀⢐⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢾⣿⣿⣿⣾⡗⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣴⣴⣿⠿⠀⠀⢀⣿⣿⣿⣿⡿⠶⠞⠃⠀⠛⢿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⡄⠀⠈⠙⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⠏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡆⠀⠀⠀⠀⢀⣽⡟⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢩⣿⡇⠀⠀⠀⢴⡟⣸⢃⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⣼⣿⠁⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡃⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠂⣿⡦⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡉⢀⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⣜⠀⠀⠀⠀⢀⣼⣿⣿⣿⠛⣿⣿⣽⢿⠀⠈⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⠀⠀⢀⣠⣶⣿⣿⣿⠏⠁⠘⢻⣿⡇⠘⣦⣰⡌⣿⠟⣠⣾⡇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣆⠀⠀⠘⣿⣟⠛⠛⠉⠀⠀⣿⣆⠙⠛⣠⣿⣬⣙⣧⣼⣿⣿⣧⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣄⣀⣴⣿⣿⣿⡅⢤⢿⣿⣧⠀⠈⢿⣦⣄⠀⠀⠀⠈⠋⢀⣴⣿⣿⠋⠉⠙⢿⣿⣿⣿⠁⠀⠓⢤⣸⣴⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣃⣹⣿⣷⣤⣤⣼⣿⣵⣦⣠⣶⣾⣿⣿⣿⣿⣷⣄⠀⠈⠻⢿⣿⣷⣤⡀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣰⣯⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣤⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠂⢀⣈⠻⣿⣿⣦⡄⠘⠛⠈⣥⣀
⠀⠀⠀⠀⣠⣜⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣬⣱⣍⡁⠀⠀⠀⠀⠈⠁
⠀⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣄⡀
⠐⠋⠈⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠛⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠻⠋⠁⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠙⠙⠛⠁⠀⠀⠀⠹⠟⠛⢿⣿⣿⡿⠙⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢿⣿⣿⣿⣿⠃⠈⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⣈⣿⡡⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠺⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠮⣂⣶⢨⡧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠆⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠉⠸⠿⣿⣿⠿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⢆⡉⠀⠁⠀⠀⣀⣀⣀⠀⡐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠈⡉⠉⠉⠭⣈⣁⠀⣀⡀⠀⠀⠀⢀⠀⠀⠠⢶⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⢀⣀⠀⠘⠀⠀⣀⠀⠈⠉⠉⠙⠛⠉⠉⠁⠀⠀⠀⠒⢌⠁⢀
⠀⠀⠴⣿⠿⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠈⠉⠙⠓⠶⠿⠶⢶⣦⣤⣴⡦⠄
⠀⠀⠀⢀⡀⣀⡀⠀⠰⠀⡐⠒⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠓⠓⠒⠒⠶⠆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠘⣿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣼⡀⢀⣼⡿⠃⠀⣼⠃⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣿⣿⣦⣾⢿⣎⡄⠚⠁⡸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⡀⠆⠰⡋⠙⣿⣿⣷⣀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⠟⠁⠀⠀⢁⣼⣿⣿⡧⣸⣿⣿⣿⣿⣇⢸⠃⠒⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢀⠈⠀⠀⢸⣧⠎⠀⠀⠐⠀⣿⣿⣿⣇⣿⣿⣿⡿⠛⣿⠆⠀⠀⠨⣿⣿⣟⣻⣿⣿⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⢃⣶⡟⠉⠀⠀⠀⠀⠀⠀⢺⣿⣿⡏⠀⠛⢿⣷⣾⠶⣁⠀⠀⠀⢘⣿⣿⣿⢿⣿⣿⣯⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢉⡸⠿⠃⠋⠉⠀⠀⠀⠀⠀⢰⣆⠀⢸⣿⡻⣦⣵⣤⣸⣤⡛⢿⡾⣀⢀⡀⢀⠙⢿⢹⡇⣩⠙⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠈⢰⠀⠀⡄⢀⣷⢀⣦⢸⡆⢸⣿⠀⣆⠙⠟⠀⠙⠠⠀⡈⠛⠀⠈⠁⢸⡇⠿⠷⠈⢼⠇⠿⠼⠱⠏⣰⡧⣀⣧⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡆⣿⣦⡄⣿⣼⣿⠿⠟⠛⠋⠉⠙⠳⢿⣠⡄⠀⣄⡄⢰⣧⠸⠇⠸⢰⣸⠷⠂⠀⣤⢰⢀⡄⣠⠀⠀⠟⠐⠀⠉⠉⠃
⠀⠀⠀⠀⠀⠀⢀⡄⣾⣧⣿⣷⠿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠿⢿⣾⣿⣼⡄⢉⠙⢩⡀⠀⢀⡿⠚⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢾⠇⠀⠀⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣬⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⢀⣴⠞⠁⠀⠀⠛⣿⣧⡻⣄⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠞⢱⣝⢦⣠⠴⠋⣭⡋⠁⠀⠀⠀⠀⣰⡙⣦⠁⠈⢶⣞⠋⠀⠘⣏⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⢱⣄⣈⠽⠋⠁⠠⠞⠛⠻⢶⣄⢀⣠⢣⣿⣷⢸⣇⠀⠐⢮⣉⡙⢦⡈⠳⣝⠛⣲⣄⡀
⠀⠀⠀⢀⡠⠔⠊⠁⠀⢀⣠⣾⡞⠋⠁⠀⠀⠀⠀⢀⣠⠴⠶⢟⣩⡴⠏⠉⠻⡌⣿⢦⣀⠈⢿⠉⠳⢭⣂⠈⠢⠘⠷⢍⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠭⠝⠛⠁⢀⣤⣦⢠⢠⠀⠀⠀⠀⠀⠘⠉⠀⡀⢠⣤⡀⠀⠈⠆⠈⠓⠦⠁⠀⠀⡀⠑⠀⠲⢶⣆⣈⡀⠀⠁
⠀⠀⠀⠀⣀⣀⡤⠤⠤⠴⠾⠟⠛⠛⠛⠛⠛⠛⠓⠶⠴⠦⠤⠴⣶⣿⠿⣿⣿⣷⡦⠶⣦⣤⣤⣤⣶⣿⣿⣶⣶⡤⠤⠭⠂⡀
⠀⠀⠈⠁⠀⠀⢀⣀⡤⠴⢶⣛⣛⣛⣿⡭⠭⠭⠭⠭⠭⠭⠭⠶⢶⣂⣬⣉⡉⠙⠃⠠⠄⠉⠙⠉⠙⠃⠀⠈⠉⠉⠉⠐⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⠿⢿⡿⠿⠿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠈⢽⣅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠰⢿⢦⣀⣯⣽⢯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⠀⢀⣆
⠀⠀⠀⠀⠀⠤⢿⣾⣏⣻⡽⣾⣹⣷⣦⡠⠆⠀⢀⣀⣰⡿⠦⠌⠀⡀⠀⠓⠦⠤⠖⠀⠀⠰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⣭⣄⣼⣗⡀⣤
⠀⠀⠀⠀⠰⣶⢖⣿⣿⣿⡿⢽⣿⣦⣬⣦⠐⠒⠠⠀⠠⠴⠒⠲⣖⡈⠁⠀⠀⠚⠉⠀⠀⠈⠉⠉⠂⠀⠀⡑⠂⠀⠀⠰⣾⠏⣿⣾⣿⣿⣿⣿⣧⡴
⠀⠀⠀⣠⣶⣶⡩⢾⢻⣿⣿⣺⣿⣿⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⢀⣀⣀⣤⣤⠨⠄⠀⠀⠘⠛⣛⡻⡟⢿⣟⣿⣿⣯⣷⠱⡆
⠀⠀⠀⠁⠋⠶⣛⡿⢻⣿⡏⢹⡬⣿⣟⣀⠀⠀⠀⠁⠒⠢⠤⠄⣤⣦⣤⠖⠀⠈⠁⢠⡴⠞⠋⠉⠁⠀⠀⢀⠀⠀⠉⠛⠻⠶⣿⣿⣧⣽⣇⠈⠈⣸⡇
⠀⠀⠀⠀⠀⠀⣮⣿⣤⣍⡉⢾⠀⣈⡻⠓⢴⣿⣷⣶⣤⠾⠖⠒⠋⠉⠉⠀⠀⣄⣠⣠⣀⣀⣠⣀⠀⣀⠀⢀⣀⠀⣉⡀⠢⠄⡧⢤⣧⣬⣿⡏⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠶⢾⠚⠊⠂⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠉⠁⠈⠉⠉⠉⠙⠛⣗⣲⣿⣿⣽⣿⣷⣶⡇
⠀⠀⠀⠀⠀⠴⠾⣿⠼⠧⢤⣹⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⢀⠀⢀⣀⠀⠠⠀⣀⢀
⠀⠀⠀⢚⣶⡓⠀⠀⢀⡀⠒⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠀⠤⠄⠄⠀⠄
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢠⣌⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⡀⢀⠠⠤⠄⠒⠂⠀⠀⢰⣿
⠀⢀⣾⣷⠀⠀⠐⠰⠀⠀⠈⠛⠛⠿⠃⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡐⡱⠐⢶⣶⣶⡀
⠀⠈⠹⠋⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠐⠃⠀⠀⢀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠿⡿⠟⠙⠁⠀⠀⠠⡄⢀
⠀⢀⠀⢀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠠⢄⡀⠈⠉⠛⢦⡀⠀⠀⠀⠀⠀⣀⣤⣀⣴⣶⣶⠿⠿⢶⣦⣤⣽⡷⠖⣿⣭⣥⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠛⠀⠀⠀⠀⠉⠃⠀⠀⠐⠚⠛⠛⠉⠁⠀⠀⠀⠘⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⠀⢀⠠⠀⠀⠐
⠀⠀⠀⠠⡿⠄⠀⠀⠄⠂⣿⡇⢀⣤⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠿⣿⣿⠇
⠀⢀⣼⣆⠀⠚⠛⠿⠷⠎⡏⡗⢿⣿⣿⡗⠢⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠦⠌⡤⠥⣼⣰⣾⣦⠀⠀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠈⣙⣋⣀⣀⣀⣀⣀⣠⣤⣥⣀⣸⠀⠼⠧⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠲⡚⠳⣶⣿⣿⣿⣿⣾⣿⣉⣉⣉⣠⡼⠶⠶⠶⢶⠶⠦⠄
⠀⠀⣿⣿⣿⣿⣿⡿⡿⣿⢿⠿⡻⡻⣟⢟⠷⡲⡶⣶⢦⣤⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⡿⣻⢏⠝⡽⣫⢫⢞⡝⡹⣫⢏⠟⡽⣻⢶⢿⣔⡃
⠀⠀⠋⠙⠉⠁⠁⠉⠈⠈⠁⠁⠉⠈⠈⠁⠁⠉⠈⠈⠁⠁⠉⠉⠛⠀⠀⠀⠈⠉⠉⠉⠈⠈⠁⠁⠉⠈⠀⠁⠁⠈⠈⠁⠁⠉⠈⠀⠁⠁⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀
⠀⣰⣦⡀⣀⢀⠀⠀⢤⠄⠁⠈⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣉⠀⠀⠀⠒⠢⣀
⢠⣿⣿⠧⠀⠀⠐⡒⠒⠀⠀⠠⣿⣿⣧⠒⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢉⣶⣿⣿⣿⣦⣀⣀⣈⣫⣦⣤⣤
⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠈⠈⠀⠀⠠⠀⠨⠁⠉⡏⢹⣿⣿⣯⣿⣿⣿⣿⣽
⠀⠿⠿⠿⠿⠿⢿⣿⣯⠉⠉⠉⠉⠁⣿⣿⠖⠠⠤⣤⣤⡤⡤⡶⡶⡶⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠂⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠉⠚⠌⠌⠌⠂⠀⠀⠐⠋⠋⠉⠙⠁⠈⠈⠂⠀⠑⠈⠈⠊⠀⠑⠉⠉⠋⠋⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠂⠐⠀⢸⣿⡆⠀⠀⡀⠀⠀⠀⢠⡄⣿
⠀⢀⣸⣿⣿⣿⣷⣶⣾⣿⣿⣤⣿⣧⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⣿⣾⣷⣾⣮⡄⠈⠑⣿
⠀⠸⣿⣿⣿⣿⡟⣿⢻⣿⠛⣿⡛⢻⡄⢀⣠⣄⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⣤⡶⠶⠶⠶⠶⠶⠤⢦⣤⣴⣤⣄⣈⣋⣡⣿⣿⣿⣿⣿⣿⠉⢹⣏
⢀⣀⣀⣈⣿⣀⣿⣿⣿⣿⣿⣿⣿⢿⣰⣿⣿⣿⣷⠈⠉⢻⠙⠁⠀⠀⠀⠀⣤⠀⠑⣒⣒⣒⣒⣀⣥⣤⣁⣤⣾⣿⣿⣛⣟⣛⡿⣿⣿⣿⣿⣿⣿
⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⣡⣼⣿⣿⣿⣿⣷⣶⣿⣶⣶⣖⡀⠀⠀⢚⣳⡶⣖⢯⠻⡙⣍⢮⠳⡙⣌⢮⡳⡝⣎⢫⡻⡝⢟⢶⡿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠁⠁⠈⠀⠁⠉⠈⠀⠁⠈⠈⠀⠁⠈⠈⠀⠁⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣤⣶⡿⠎⢁⠀⠁⠀⠀⣤⣤⡐⢒⣿⣟⣿⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢠⠔⠰⢛⣐⠾⢿⣄⠀⢾⣋⡽⢟⣏⡿⣤⣀⠀⠀⠀⠀⠀⠉⡛⠿⣿⣿⣧⡈⠉⠀⠀⠀⠀⠀⠀⠀⣀⢙⣿⣿⡀
⠀⠀⠀⠈⠀⠈⠉⠁⠈⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠉⠑
⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⣠⣴⣎⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠃
⠀⢠⡶⣭⣧⣉⡁⠀⠀⠀⠀⠀⠀⠐⠶⣷⣄⠀⡀⣀⣠⣄⠀⠀⠀⠀⢀⣀⣤⣶⣦⠀⠻⢮⡀⠀⠀⠀⠀⠀⣄⠠⣤⣶⣾⡏
⠀⢾⣅⠀⠛⢻⣧⡙⠂⠀⠀⠠⠄⢀⠀⡬⢋⡽⢿⣿⠿⣿⠤⠀⠀⠉⠉⠙⠃⠸⠿⠀⠀⠀⣈⡕⠀⠀⠀⠀⠘⠛⢺⣿⣿⡟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡦⢤⠀⢀⡴⡖⡗⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⣤⣾⣾⡀⣾⠀⠀⠐⠊⢻⡦⠀⠈⠀⠀⠀⢀⠄⠀⢀
⠀⠀⠀⠀⠀⣠⣠⠶⢸⡁⣀⡤⢼⣿⡟⢾⢟⣿⣾⣷⠀⠀⠀⠀⠀⠠⢤⣦⣶⡿⣇⠀⢯⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⡄⡾⡽⠟⣳⣄⠚⢶⣴⣿⠌⠹⠾⣟⣻⢉⣯⠿⠆⠀⠀⠀⠀⠀⠀⣰⡟⢦⣙⠃⠀⠱⠿⢧⡀⠀⠀⠉⠛⢟⣿⠻⣿⠂
⠀⠀⠛⠀⠀⠋⠀⠉⠐⠚⠃⠈⠃⠀⠘⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠑⠀⠀⠀⠂⠉⠐⠀⠐⠂⠈⠙

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

⠀⠀⠀⠀⠀⠀⢀⢰⡦⢀⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣶⣄
⠀⠀⠀⠀⣠⣄⣱⣺⣿⣼⡿⣿⢥⡿⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣥⣾⣿⣿⡿⠂⣽⣦⣀
⠀⠀⠰⠫⣽⣹⣿⣿⣿⢿⣿⡷⣿⣿⢿⣿⣿⡟⣦⠄⠀⠀⠀⠀⠀⢀⣠⣀⣔⣿⣿⣿⣿⡿⠿⣡⣰⣶⡿⢿⣿⣷⣄⠀⡀
⠀⠀⠀⠀⠀⠘⠴⠚⠽⠼⠟⠓⠯⠼⠙⠭⠛⠉⠉⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠓⣤⣿⠏⣤⠙⢦⣴⡕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⢀⡀
⠀⠀⠀⠀⡠⣪⡾⢅⣼⣿⣇⡼⠃⠀⠀⠛⢄⠀⠑⠤⠀⠀⠀⠀⣀⣴⡶⠒⣦⣠⣀⡀⣀⢤⡶⣿⣇⡴⠟⠑⡷⢦⡀
⠀⠀⠠⣾⠟⢛⡴⣿⠿⠹⠿⠇⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠴⠾⠿⠏⠁⠀⠳⡍⠙⠃⠀⠈⢈⠼⠋⠀⠀⠀⠀⠂⠉⠈⠁⠠⠄
⠀⠀⠀⠀⠀⠁⠐⠋⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢴⣤⠴⠊⣼⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢉⣑⣄⡠⢄
⠀⠀⢀⣠⣤⣶⣷⣶⣯⣿⢿⣿⣿⡿⠽⢿⣿⣿⢶⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⠆⣛⠧⠀⣤⠎⣴⠃⠈⣷⣤⢤⡀
⠀⠐⠀⠩⠍⣛⡚⠽⠟⢛⡩⠄⠒⠐⠒⠒⠒⠬⠭⣙⣛⠒⣐⠀⠀⠲⠟⠆⠀⠛⠦⠀⠨⠓⠚⠉⠐⠉⠚⠣⠖⠉⠓⠂⠄
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣽⠏⣸⣿⣧⡀
⠀⠀⠀⠀⠀⢀⡔⠂⢊⣤⡴⣡⢄⡄⠀⣈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢚⠙⡻⠃⢸⣿⣿⡿⠿⣺⣷⣄⣀
⠀⠀⠀⢀⣀⣪⣴⡶⠿⠿⠟⠛⠛⠛⠛⠛⠒⠒⠶⠶⠦⠀⠀⠀⢀⣤⣶⣏⣽⣿⣏⣨⣿⣧⣽⣿⣟⣋⣾⣿⣿⣯⣽⣷⣦⣀
⠀⠀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢠⠤⣀⣾⣴⣬⣦⣴⡓⢦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿⣎⢤⣄⣼⡃
⠀⠀⠀⢠⣴⣿⣶⣿⣿⡿⠿⡿⣿⢷⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣰⣿⢿⣿⡿⣦⣭⣿⣿⣾⣦⣤⣤⡀
⠀⠀⡴⢛⣧⣮⣈⡀⣡⣾⣶⣄⣡⣴⣦⣉⣽⣮⡛⠂⠀⠀⠀⢀⣼⣽⣿⣷⣿⠿⣻⣿⡤⠟⠀⠻⢽⣷⣿⣆⠹⡽⣧⡐⡄
⠀⢠⡴⠿⠟⠛⠻⠟⠛⠛⠙⠛⠉⠉⠉⠉⠋⠉⠛⠂⠀⢀⣴⣍⣴⣿⣤⣶⣛⣳⣽⣿⣛⣓⣴⣶⣖⣋⣉⣍⣹⣼⣮⣯⣽⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠑⠤⣄
⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⣾⡵⠈⠀⠈⢀⣀⠄
⠀⢀⣠⡶⢦⢀⡸⢶⠞⠃⣠⡀⠲⣦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣠⣿⣷⢟⡀⠀⠀⠈⢿⡄
⠀⠀⠉⠴⠖⣿⠗⠞⠓⠈⠀⠈⠛⠈⠉⠁⠀⠀⠀⢀⣀⠠⣖⡴⠟⣣⣾⣿⣿⡿⢀⡔⠈⠀⠀⠀⠈⠀⢤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠜⡿⠋⡀⠈⠐⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⠏⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣰⣏⢠⣾⡷⠋⡄⠀⠀⣤⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣼⠻⢫⣿⣿⠿⢶⡀⠀⠀⠈⠳⠀⠘⠇⠀⢸⣧⣼⡤⠄
⠀⠴⠀⠾⠁⢋⣫⣿⠿⢿⡟⠁⣄⠀⡄⢠⡆⢀⢓⠦⢤⣦⡿⠛⣏⣤⠀⠀⠀⠀⠀⣀⠔⢢
⠀⣠⢀⡆⠀⠴⠟⢁⠀⠉⣀⢠⣿⣄⣷⣼⣷⣿⡿⠶⠿⢛⡛⣿⠟⠉⠀⠀⠀⠀⡐⠀⠀⠀⢀
⢠⣿⣾⣷⡄⢠⡤⠿⠶⠾⣿⣿⠿⠋⠛⠛⠉⠀⠀⠀⠞⠛⠉⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⣇
⠀⠀⠀⠈⠉⠑⠶⢤⣠⡁⣴⠀⢀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢂⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠚⠛⠛⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⡠⠀⠀⠀⠀⠈⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠀⠀⠑⠄⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⣠⠀⠀⣿⠗⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⣀⠀⠀⠀⣼⡀⠈⠁⠈⠂⠀⠀⢀⣼⠋⠀⠀⢰⣄⠀⠀⠀⠈⠈⠀⠀⠴⣿⠀⠀⠡⠧⠀⠀⠀⠤⡗⠈⠳
⠀⠀⢀⣴⣿⠀⠀⠀⠙⠃⠀⢀⡄⠀⠀⠀⠈⠉⠛⠂⠀⠀⠀⠴⠷⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⢴⣶⠀⠀⢤⣤⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣷⣄⠀⠀⠐⠀⠀⣠⣦⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣆⠙⠣⠀⠀⠀⢸⡿⠃⠀⠁⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⢀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠛⢻⣇⠶⢤⣀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⣼⣯⡄⠀⠀⠀⠀⢀⣄
⠀⠀⣠⣿⣤⠀⠀⠉⠙⣿⣆⠀⣀⣀⠈⠙⠦⠀⠀⢀⣴⠆⠀⠀⠀⣠⣾⠆⠀⠈⠉⠛⠂⠀⠀⣰⣿⠟⠁⠀⠀⠀⠠⣿
⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠛⠷⠆⠈⠁⣠⡆⠀⠀⠿⠿⠦⠄⠀⠘⠿⢷⡤⠀⣀⣤⠀⠀⠀⢰⣿⣆⠈⠳⣄⠀⠀⠀⠉⠓
⠀⠀⠈⠟⠿⠦⠀⠳⠤⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠯⠀⠀⠀⠀⠉⠛⠓⠂⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣩⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠞⠋⡴⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⣃⠂⠀⠛⡦⡀⠀⠀⠀⠈⡗⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣡⡄⠀⠐⠛⠀⢀⣞⡜⣀⠀⠹⣇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢇⡤⠀⠀⠀⡞⢰⣯⣿⣆⣀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⣲⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⣿⣿⣿⡿⡶
⠀⠀⠀⠀⣴⠀⠀⠀⣹⣦⡀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⢿⣻⠾⠃
⠀⠀⠀⢸⢃⣤⠄⠀⠀⠉⠿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⢨⣾⣇⠀⠀⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⣠⢿⣫⠄⣠⡄⠀⠀⠀⠀⠽⣿⡶
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⢀⡴⣻⠷⠀⢀⠀⠀⠀⠀⠀⠥⣾⡻⣅⠀⠀⠀⠀⠀⠉⠘⠃⠀⢣⣄
⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⡼⣱⠟⠀⠀⠀⠀⠀⠀⠀⢙⣯⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⣬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠂⠀⢀⣠⠄⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠁⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⡿⠃⠀⠀⠘⠅⡀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠂⠀⠀⠘⢫⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠵⢀⠔⠀⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡇⠀⠀⠀⠰⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣰⠃⠀⠁⠀⠀⠉⠁⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡆⠀⠈⠱⠢⠀⠀⠂⠀⠀⠀⠞⠴⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠠⠖
⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡠⠖⠁⠀⠰⠋
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⠀⢱⡀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠙⢦⡑⠀⠀⢠⣮⡏⠓⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠙⢧⣤⣼⣿⠁⠀⠆⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡂⠀⢀⣠⠀⠸⠿⣆⠀⢀⡀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⢊⡄⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠁⠀⠙⣿⡆⠀⠀⠈⠓⠀⡡⠀⠀⠀⠛⠙⠂
⠀⠀⠀⠀⠀⢸⣿⡟⣡⠞⠁⠀⠀⠟⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⣸⣿⠏
⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢦⣤⣤⣀⡀
⠀⠀⣠⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⣄⡉⠉⠛⠲⠶⣤⣄⣤⣄⣀⣀
⠀⣰⣿⣿⣟⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠈
⣴⣿⣿⣿⡏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣷⣦⣀⡀
⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣤⣤⣀
⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠠
⠀⠀⣠⣔⣄⣨⣴⣿⡧⠈⠩⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⣯⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⢀⣾⡆⢻⠀⠩⣿⣯⡖⠃⠂⠈⢿⡀⠀⠀⠀⠀⠀⠤⣗⢤⣀⣌⣳⣼⣛⣒⣋⢦⡀
⠚⠛⠓⠾⠿⣷⣿⣿⢷⣤⣜⡀⠢⣤⣤⣤⣤⠲⣿⣚⣛⣳⣿⣏⠉⣹⣍⣓⣦⣸⣿⣶⡀⢀⣤⣄⣀⡀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⠀⡀
⠀⠐⠀⠀⣸⡯⣿⡃⠀⢰⠀⠀⠀⠉⠉⠂⠀⠼⢿⣿⣿⣾⢿⢷⣶⣾⣿⣯⣷⣿⣿⣿⣿⡙⣯⢽⡿⣏⡆⠰⡿⢩⡍⠳⠛⢦⣤⠭⠽⠧⠀⠒⠂
⢨⡅⠤⡀⠻⠺⡋⢧⠀⡚⠡⠀⠀⠀⠠⠀⠀⠀⠀⡔⠀⠀⠀⠀⠈⠀⠉⠉⠉⠙⠛⠛⠿⠿⠿⢯⣴⣶⣏⣘⡉⠈⠁⠀⠤⠒⠉⠀⠀⠀⡀
⣸⣿⠶⢦⡄⢻⡿⣦⠈⠀⠀⠀⠀⢁⠀⠐⠀⠀⡅⢻⢂⠓⠀⠀⡀⠙⣇⣰⣁⣶⣤⡤⡦⠶⠶⠶⠶⠛⠛⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉
⢾⣿⠛⠹⠿⠿⠤⡷⠆⢀⡄⠀⠀⠂⠀⣀⢀⣰⠟⣹⣊⣠⠌⠷⠼⠶⡿⠭⣭⡤⣀⠀⡀
⢠⢿⡿⠀⠀⠈⢀⣷⠆⠀⠀⠀⠈⠀⠀⠠⢭⣥⣤⠤⠀⠂⠰⠦⠶⠂⠇⢸⣶⣤⣄⣘⣋⢹⠓⠲⠦⡄⣀⡀⡄
⠀⠈⠛⠛⠛⠁⠋⠋⠐⠀⠀⣀⠀⠀⠀⠉⠁⠂⠀⠀⠠⣄⡀⠀⠀⠒⠓⠀⣈⠉⠩⠙⣛⣿⡶⡶⣤⣄⡀⢀⡟⠳⠦⢄⣲⠦⠤⢴⡆⣀⣀⡀
⠀⠀⠀⠀⠘⠒⠒⠀⠒⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⢢⣅⡀⠀⠀⠀⠀⠀⠉⠁⠐⠐⠀⣭⣟⣩⣭⣇⣉⣄⣒⣰⣦⣤⣰⢤⡀⠈⠉⠉
⠀⢔⡟⠻⠉⢉⡀⠀⠀⠀⠐⠀⠤⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠛⠈⡖⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⢿⣿⣿⣿⣿⣿⣤⡒⣤
⠀⣞⠛⢀⡀⠀⠀⠀⠀⠠⣤⠀⠄⢈⠐⠆⢂⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠡⢂⣀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠋⢹⠿⠿⢿
⠈⠏⠀⠀⠁⠀⠀⢤⣉⠠⠈⠁⢣⡀⢀⠀⠉⠀⠀⠀⠈⠛⠢⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠐⠉⣁⣤⠐⠛⠙⠃⠤⠄
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠠⢉⠀⠑⠀⠀⠀⢀⠘⡁⠀⠀⣀⡈⠓⠶⣤⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣇⠀⠀⠀⠀⠀⢀⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⡼⠓⣸⣿⣆⢢⠀⠀⡠⠊⢸⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷⠾⣿⢦⣤⠀⠀⠀⢊⠖⠁⢸⣿⣿⢿⣷⠟⠀⠀⢰⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⢀⡴⢛⡷⣮⢳⣦⠊⢀⠀⠀⠀⢻⣿⣿⣿⣠⠤⠤⠓⠀⠾⣿⣿⣿⣃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⣸⠉⢿⣾⢟⡏⠀⠹⢦⣀⠤⣌⣽⣿⣿⣿⣆⠐⠀⠄⠈⡻⣿⣿⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠍⢁⠾⢠⡄⠠⠀⠈⠑⠄⠈⠈⠉⣿⣿⣷⣤⡀⠀⠀⠈⠁⢻⣿⢿⣷⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄⣄⣄⣤⣀⣀⣰⠶⠿⠿⠟⢛⣇⢀⣀⣀⢀⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠃⠙⠂⠀⠀⠛⠁⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠛⠻⠿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠐

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣸⣿⣿⣷⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠛⣿⣿⣯⢇⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠰⠟⠙⣿⣿⣿⣷⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⡌⠁⠃⠀⠀⠀⠈⠾⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡤⡴⠀⠀⠀⣠⢀⠦⣠⢽⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢀⠇⠀⠀⠁⢐⣥⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡥⠃⣀⢄⠤⣢⠔⠋⢿⣯⣵⣠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢊⣴⡷⠋⢀⠤⠊⣁⣠⡾⣿⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣷⣾⣿⣿⡥⠚⢁⣠⠾⡋⠕⣪⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠀⣠⣤⠏⢸⣻⣿⣿⣿⣧⡶⠻⠕⡩⠔⣉⠀⢂⡀⢡⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣇⣤⠐⣿⡯⣃⢝⣽⣮⠖⣫⣐⣉⠔⡊⠑⠊⠉⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⣴⣯⡾⠟⠉⣈⠴⢊⣽⣿⢶⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢾⡟⠉⣠⠔⣊⠴⠒⣩⠼⢛⡿⠷⠛⣃⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⣏⠔⣋⠔⠊⣠⠔⣋⠴⠚⣁⠴⠚⣉⡄⠤⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢛⡵⠊⣡⠔⣫⠴⢋⡡⠐⢉⡠⠖⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣌⠛⡫⠋⠀⠁⠐⠋⠴⢋⡡⠒⣉⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣹⣯⡴⠁⠀⠀⠀⠀⠀⠐⠉⠠⠚⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⢰⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⣴⣿⣷⣦⣀⣄⠀⠀⢀⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣶⣤⣤⡀⢀⣴⣦⣀
⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣠⣦⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦⣀⣤⣄⠀⠀⠀⠀⠀⢀⣴⣾⣶⣤⣀⣄⠀⠀⠀⠀⢀⣤⣤⣤⡀⢀
⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣾⣿⣿⣿⣿⣿⣷⣦⣤⡀

⠀⠀⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⣀⣠⡄⠀⠀⠀⣀⣀⣴⣿⣷⣦⣀⣀⣀
⠀⠀⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣤⣶⣷⣤⣴⣶⣿⣿⣿⡇⠀⢠⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣾⣷⣦⣤⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣿⣦⣀⠀⠀⠀⠄
⠀⠀⢀⣠⣴⣿⣿⣿⣦⣄⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣦⣤⡀⠀⠀⢀⣀⣀⣤⣶⣿⣿⣿⣿⣷⣤⣤⡂⠐
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢠⣶⣄⡀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀
⠀⠀⢀⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣦⣴⣶⣤⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣄⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠲⢤⣄⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⢀⡀⢊⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠠⢇⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠁⢔⠀⠀⠰⡇⠁⠈⢣⣌⡇⠀⠲⣿⠀⠀⠀⡀⡞⠑⢄⠂⠀⢠⠀⠣⡔⠈⠾⡖⢄
⠀⠀⠀⠀⠀⠀⠀⡀⢉⠳⣄⠁⠀⠀⠀⠘⠢⠀⠀⠘⠓⠀⠛⠠⠃⠀⠀⢧⠀⠀⠀⠀⠸⠄⠆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡀⠀⠀⠀⠀⠀⣠⣚⠱⠮⡼⠀⠌⠰⠆⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠨⡂⣓⠃⡖⠰⣄⠢⢎⡃⠀⠉⠐⠧⠀⢠⠁⠛⠂⣦⠀⠀⠀⠀⢈⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡗⣧⠃⠰⡄⠀⠈⣆⠁⡄⠀⠀⢀⠈⡐⠉⠀⢀⡠⢧⡀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠺⠈⠉⠂⣤⡄⠑⢀⠃⠁⠀⠀⠀⠀⠰⠀⠀⠊⠐⠀⠀⠀⠌⠀⠀⠁⠀⠘⢠⠄⡾⡀
⠀⠀⠀⠄⠂⠂⠀⠀⢍⠀⠀⠁⢀⠸⡄⠀⠀⠀⠀⠀⠀⢠⠀⢀⡄⢀⢜⡅⠀⠀⠀⢀⡴⡆⠀⠀⠁⠈⠀⠰⠀⠰
⠀⠀⠀⣀⢡⠞⠀⣄⣄⡁⠀⠃⠀⠀⠀⠈⠀⡀⡀⠀⡀⠀⠄⢀⠀⠀⡜⠁⠀⠀⢀⠠⢸⠆⣄⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠈⠀⠀⠀⠘⣀⠬⣋⣀⠆⠙⠤⠘⠀⠠⠽⣖⣶⡠⢆⠚⠚⠒⢀⠀⠠⢖⡃⠀⣸⠇⡌⠂⠀⣄
⠀⠀⠌⠀⠀⠀⠀⠐⠘⡎⠈⢹⠞⡄⠀⠖⠀⠐⠀⠀⢿⢧⢂⠉⡶⢄⢈⠞⠉⡋⠉⡀⠄⠀⢀⣀⠣⠈⠆⠂⢀⠈⠃
⠀⠀⠀⠰⠀⠀⡄⠀⠀⠙⠊⢫⡌⠁⠀⠙⠀⠀⠀⢚⣟⠁⢚⢰⠦⢄⠑⢖⠃⠤⠤⣤⣠⣦⣼⡏⠰⠀⠔⠐⢂⠠
⠀⠀⠀⠀⠡⣄⠀⠐⠀⠀⠙⠛⣦⡗⢢⡁⠀⠔⣰⢾⣷⠒⡼⠆⣠⣤⣶⠼⢤⡀⠀⠀⠀⢙⣃⠀⠙⠁⢀⣴⢛⡁
⠀⠀⠀⠀⠀⠀⠀⠐⠦⠐⠀⠘⡀⠛⣂⣴⠖⣿⢿⣟⡛⢻⣿⢟⡈⠡⣄⣂⣉⣉⣳⣶⣯⢏⡀⡘⢉⣀⡔⠈⠃⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣶⣾⢟⣠⣈⣛⡠⠋⠔⠁⠃⠀⠙⠗⠶⠉⠉⠁⠀⠘⠁⠈⠀⠀⠀⠁⠀⠈⠁

⣿⣟⣻⠿⠿⠿⠿⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣴⡛⢆⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⣦⡀⢤⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⡇⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⣰⡋⠔⡉⣸⣧⡚⠃⠀⢿⡦⢀⠀⠀⠀⠀⠀⠀⢚⠀⠣⠙⣇⠈⠉⠷⢯⠀⢿⢀⠀⠀⠀⠀⠀⠀⣠⠎⢈⠷⠄⠈⠀⣰⠏⠇⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣆⠐⠾⣿⠈⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣏⣷⣔⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⠀⢶⣿⡁⠢⣠⣶
⠀⠀⠀⠀⠀⠰⠦⡽⠿⠿⠼⠿⠶⠾⠿⠶⠯⠤⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠐⠛⠚⠛⠛⠛⠛⠛⠒⠛⠛⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣖⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡂⡀
⠀⠀⠀⠀⠀⠀⣀⢼⣇⡈⢿⣿⠑⢾⣇⡑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡞⢿⣿⣶⣥⣾⣓⠤⡀⠀⠀⠀⠀⠀⠀⣠⢠⣾⠃⢿⣿⣧⠈⣤⡄
⠀⠀⠀⠀⠀⠘⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠷⠿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠶⣀⠤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⡀
⠀⠀⠀⠀⠀⠀⡄⢤⣾⡇⠹⣗⣀⣓⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠏⠛⠃⠐⠻⡦⠌⢀⠿⢤⡀⠀⠀⠀⠀⠀⠀⣀⢤⣴⡇⣻⣿⠀⣼⣻⡄⢀⡀
⠀⠀⠀⠀⠀⠘⠙⠛⠋⠛⠛⠛⠙⠋⠛⠙⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠋⠛⠛⠛⠉⠉⠛⠛⠙⠙⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣯⠑⣄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡎⣅⢤⡤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢤⡆⠹⠿⢭⠀⠐⢋⣈⠦⢤⡀⠀⠀⠀⠀⠀⢀⣤⣾⣦⠻⢿⣿⣦⠚⢿⠧⡳⠄⠀⠀⠀⠀⠀⠀⢤⠚⠀⠙⠡⠞⠈⠡⠿⠛⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢏⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣿⡿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⣨⣿⢿⡌⠛⢷⡄⠀⠀⠀⠀⢀⣴⡿⡇⠁⢹⣷⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⣾⣟⠣⣜⣷⠢⣌⢿⡄⠀⠀⣰⣿⠋⢸⡅⡀⢀⣿⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⢀⣿⣯⣕⠆⠙⢷⠄⠙⢻⣶⣿⣿⣿⡆⠀⣷⠰⣰⡿⢦⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⡡⠀⣰⠏⠀⢉⣿⣇⠀⠈⠳⢤⣀⠙⢿⣿⣼⡈⠀⠘⣷⣟⠙⠲⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣐⣵⠋⠀⠀⢴⣾⠯⡓⠤⠀⠀⠀⠈⠑⠢⣸⣿⣷⣄⠀⠙⣿⠛⢲⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠐⢱⣧⡆⠀⠀⢈⣿⣗⠦⡀⠀⠀⠢⣄⠀⠐⠬⡻⣿⣿⣆⠀⣿⠰⠶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢈⡟⠀⠀⠀⢸⡿⣿⣷⣦⡀⠀⠀⠀⠉⠒⠤⣬⣾⣿⣿⣷⣿⣟⠲⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠊⠀⠀⠀⠀⣽⣷⠦⣍⠉⠻⢦⣀⠀⠈⠂⠀⠹⣿⣿⣿⣿⣿⣿⡶⠿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⣠⠞⠀⠀⣸⠏⢿⡗⠮⠝⠢⠀⠉⠓⢦⣤⣀⠷⣬⠻⣿⣿⣿⣿⣇⠓⠦⣍⣊⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡶⠛⠁⠀⠀⠀⠀⡠⠊⠁⠀⢠⡞⠁⠀⠈⢿⣶⠄⠀⠀⠀⠀⠀⠉⠣⡉⢻⣟⡿⣿⣿⣿⣿⡅⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣛⢿⣿⣿⣷⣄⠲⡄⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⠿⣿⣿⣦⣝⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠊⠀⠀⠀⠀⠉⠲⠄⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⣀⢠⠀⠲⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡾⠛⡹⠆⠘
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢀⡄⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⣰⣿⡟⣟⠡⠀⠀⠀⢠⣶⡄
⠀⢀⣤⣶⡿⠳⢂⣠⠻⢟⠋⠁⣠⣦⣈⡻⢶⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⣡⣿⣿⡿⢛⣄⠀⠀⠀⠈⠻⡅⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠡⣴⠶⣻⠿⠲⠟⠓⠊⠀⠀⠉⠻⠰⠋⠁⠀⠀⠀⠀⠀⢀⡀⢤⡾⣡⡾⠟⣡⣾⣿⣿⣿⡗⢀⡴⠀⠁⠀⠀⠀⠈⠂⠤⣤⣴⡟⠋
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠁⢀⣿⣿⠟⠙⠡⠋⠴⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠋⠞⠁⠐⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣾⢋⣀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⢀⣾⡿⡛⠁⡆⠀⠀⠑⣴⡟⠂⠀⢀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣟⠹⢣⣾⣿⣿⠿⣶⡉⠀⠀⠀⠙⢿⠀⠀⠻⠁⠀⢈⣿⣠⣷⣤
⠀⣀⣄⢀⣴⣃⠖⠽⣣⣶⣿⣿⣿⠟⠀⡀⠀⠀⠀⢠⠀⠀⠰⣤⣄⢠⡄⣾⡿⢟⡋⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡄
⠀⠉⠀⢠⠀⠀⢀⣿⡿⠋⠁⠼⠃⠀⢰⣷⠀⣸⣀⣿⣄⣾⣶⣆⣠⣿⣿⣯⣤⣼⣷⠟⠀⠀⠀⠀⠀⢀⠎⠁⠀⠘
⠀⢸⣆⣸⡆⠀⠈⡉⠀⣧⢀⠀⣰⣤⣾⣿⣷⣿⣿⣿⣿⠿⠟⠋⠉⣩⣤⣥⠾⠛⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢣⡀
⢠⣾⣿⣿⣿⣆⣠⠷⠚⠛⠟⠛⢻⡿⡿⠛⡁⠈⠉⠁⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⠊⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠈⠑⢺⣦⣦⣠⡉⢰⡆⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠾⠿⠾⣧⣀⡀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠔⠢⡀⠀⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠦⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠂⠤⢀⡠⠊⠁⠀⠀⠈⠀⠀⠀⠈⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠠⠀⠂⠉

⠀⠀⢰⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣆⢹⣀⡇⠀⣄⢺⡥⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⣿⢼⣷⣟⠀⣧⣽⣯⠀⣗⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠙⠿⢿⣿⡀⣿⣾⣯⢠⣿⣿⡄⢿⠀⣸⠄⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⣗⣯⣼⠠⢀⡀
⠀⠀⠀⠀⠰⠏⠙⠚⠿⢼⢿⣿⢖⣿⣀⣽⣅⣿⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⠓⢿⣞⡗⢰
⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠤⠄⠰⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠮⠂⠀⠀⠘⡄⠀⢠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠑⠁⠁⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠷⡀⠀⢄⣵⠀⠘⠀⣀
⠀⡀⣤⠀⢀⡔⠐⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢣⣤⢆⠀⠸⠈⠆⣙⣒⣌⠂
⠀⣀⠍⣠⣵⢢⠑⠁⢁⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢸⠂⡄⠶⠄⠈⢲⣹⡹⠘⢟⡉⢥⠘
⢀⠟⠘⣷⣦⣤⣦⣿⢣⣦⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⢀⠀⠨⡎⣄⣟⣁⣶⣄⡷⡏⢿⣷⣍⠀⡆

⠀⠀⠀⢰⡆
⠀⠀⠀⣼⡁
⠀⠀⢠⡿⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀
⠀⠀⣎⠁⣀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠁
⠀⠐⠻⠤⢀⣿⡅⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢟⡉⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣯⣾⣿⣷⣦⣤⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⣶⡀
⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⢛⣷⡿⢹⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢁⡠⠖⣿⠟⠋⠀⠀⠀⠀⠀⠚⠄
⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢻⣿⣉⡀⠀⠀⠀⠀⠈⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⢄⠀⠀⠀⠀⠉⠂
⠴⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣠⠄
⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠛⠛⠿⣿⢿⣿⣿⣋⠉⠉⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⡀
⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠈⠙⠛⠶⠄
⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠺⠅⠀⢀⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒
⠀⠀⠀⠠⣤⠐⠆⠀⢀⠀⠀⠠⣄⠀⠀⠀⠀⠐⠒⠐⠂⠀⠀⠀⠀⠀⠛⠁⠀⠀⠁⠀⠀⠉⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉

⣲⠂⢠
⠰⠄
⣺⡆⠀⠀⠀⠀⠀⠀⠠
⠯⠀⡀⠀⢀⣄⣤
⠰⣿⣿⣾⣿⡿⡟
⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⡇⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠰⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠘⠃⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡵⠀⡄⠀⠰⠶⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢴⣿⠛⢿⣟⠐⠀⠁⠀⠀⠀⠀⠀⠠⣀⢀⠀⠀⢀⣴⠞⣷⡀⠀⠀⠀⠀⠀⣀
⠀⠐⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⣿⠐⠀⡇⠀⠀⠀⢀⣀⡀⣴⣶⣿⣿⠋⠁⢼⣏⣿⣆⡀⢀⣠⣿
⣷⣤⡀⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢼⣿⢁⣿⣿⣿⠏⠀⠀⠀⢻⣿⡟⠁⣼⡿⣿⣶
⣿⣿⣿⡀⠀⠀⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⣿⡿⠟⣉⡜⠉⠀⠀⠀⠀⠀⠀⠉⠙⢒⡬⢹⣿⣿
⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢿⡿
⣀⠙⠿⠄⠰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢖⣀⣤⣤⡶⣦⡄⣀⠀⠀⠀⠀⠀⣀⠀⠈
⣿⣷⣄⠀⠀⠛⠿⣷⣆⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⣠⣾⣿⣿⣦⣥⣀⣰⣶⣿⣷⣶
⣟⣻⣿⣷⣄⢀⣴⣬⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣼⣿⣿⣧⣠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⢻⣿⣿⡛⢿⡿⢻
⣉⠛⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣼⣿⣿⣷⣤⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢏⠙⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢿⡆⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⢻⠘⢿⣦⣽⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠄⠀⠀⠈⠻⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢸⠀⠀⣽⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠙⠻
⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⠀⠀⠀⣹⣿⣿⣿⣿⣦⣤⠄⢀⣤⡀⠀⠀⠀⠀⠀⠸⣇
⣤⣀⡀⠨⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠇⠙⣟⢠⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⢶⣄
⠛⠿⠛⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢿⣧⡀
⣀⠠⢂⣵⣶⣤⣴⣡⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣶⣄⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⣃⡀⠀⠀⠀⢀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠈⠀⠀⡀⢀⠀⠀⠀⠀⠈⠛⠻⠿⠇⠀⠀⣠⣿⣿⡿⠟⠀⠀⠀⡖⠀⠀⢀⠀⠀⠀⠀⠈⡇⡂
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠁⢠⡀⠀⠀⠀⠂
⠾⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠙⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡁⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣄⣀⠀⠀⠀⠀⢠⠆⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣽⣿⣽⣷⣄⠀⣀⣤⣀
⠀⠀⠂⠀⠀⠀⠁⠈⢀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⢠⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠖⠾⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠛⠷⣴⣤⣿⣿⣿⣿⣷⣶⣒⠛⠠⠈⠉⠹⣛⣩⣽⣽⣿⣿⣧⣯⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠠⠀⠙⠚⠀⡠⢸⣿⣿⣿⣟⡶⠾⣿⣟⡁⠈⠰⠀⠀⠈⠁⠈⠛⢷⣿⣿⣕⣄⡀⠀⣀⣿⣿⣷⣤⣶⣦⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡠⠀⠀⡀⠀⠈⠀⠀⠙⠛⣻⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦
⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠿⢿⣿⣿⣿⣿
⠀⠀⠰⠀⠒⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⣿⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡄⣠⣶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣦⣴⣶⣿⣿⣶⣶⣤⣀⡀
⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⢿⣿⣭⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣠⣄⣤⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡄
⠀⠀⠀⠀⠴⠾⠿⠿⠿⠿⢿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣦⣄⣀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣦⣀⣀⡴⢦⡄⠀⣤⢔⣾⣷⣏⣽⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⠀⠀⠀⠀⣠⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠚⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠉⠀⠉⠀⠉⠉⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣃
⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣶⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣽⣿⣶⣒⡢
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡘⠶⣽⣿⣿⣿⣾⠤
⠀⠀⠀⠀⠀⢀⠲⣿⣿⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣟⣃⣀
⠀⠀⠀⠀⠀⠨⣽⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⢠⡛⢶⣿⣿⣿⣿⣿⠟⣁⡀
⠀⠀⠀⠀⠠⣬⣿⣿⣿⡯⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⡫⡙⢷⣿⣿⣿⣿⣿⣟⣫⣥
⠀⠀⠀⠀⠘⣶⣿⣿⣿⣿⣷⣖⣫⣀⣀⣀⡀⣀⣀⣀⠤⠀⠀⠀⣐⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⡿⡟
⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣛⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠐⠶⢾⣿⣿⣿⣿⣿⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠂
⠀⠀⠀⠠⠴⠾⢿⣿⣿⣿⣿⣦⣤⠔⠀⢠⡄⣀⠀⠀⠀⡀⣦⣘⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠯⢥⠀⣀⢸⣃⣿⢀⣟⢸⣇⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣾⣠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣛⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣾⣿⣧⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠲⢿⣿⣟⣋⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢹⣿⣿⣿⣯⣥⡴⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣾⣿⣷⣖⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⣿⣿⣿⣿⣷⣞⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣙⣿⣿⣿⣋⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⡐⠀⠀⠀⠀⠀⠀⠈⢻⣶⣾⣿⣿⣿⣿⣿⣯⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣬⣿⣿⣿⣭⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠦⠀⠀⠀⠀⠀⠀⣄⡰⠿⣿⣿⣿⣿⣿⣿⣴⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠰⢦⣿⣿⣿⣿⣿⣥⠖⠁⡀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⣴⡙⠛⣿⣿⣿⣿⣿⣿⣿⡟⠋⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣒⣿⣿⣿⣿⣍⣥⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣿⡞⣩⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⣩
⠀⠀⠀⠀⠀⠀⣤⣙⣻⣿⣿⣿⣿⣧⣤⣠⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣵⣦⣬⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢨⣻⣿⣿⣿⣿⣿⣿⣿⣯⣭⣴⠶⠴⠶⠤⠤⠠⠤⠤⠤⠶⠚⠁⠀⠀⠀⣠⣬⣿⣯⡴⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⡇
⠀⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⣿⣿⣿⡛⠛⢉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠰⠀⠚⠲⠷⣾⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⣤⣀⣹⣿⣿⣿⣿⣿⣿⣿⠞⠛⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣥⠄
⠀⠀⠀⠀⠀⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠐⠲⠼⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠚⠃⠀⠀⣧⠀⣤⠀⠀⡄⠀⣆⠀⣿⡠⣍⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣧⣭⣀⠀⠀⠀⢰⡟⠀⣿⠀⢰⡇⠀⣿⠠⣿⣶⠾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣅⣸⡆⢰⡷⣾⣿⣏⣿⣶⣿⣧⣠⣿⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠬⣟⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡁⠒⠀⠀⠉⡀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠘⠉⠰⠃⠀⠀⠀⠁⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣦⠆⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠀⠀⠀⠀⠐⠇⠀⠳⠆⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⢲⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡀⠀⠀⠀⣠⠀⠰⢠⠀⡠⠂⠀⠘⠠⠀⠀⠀⠀⠀⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠔⣤⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠤⠀⠀⠀⢤⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡄⢸⡦⠀⠄⠀⠀⠀⠀⠀⠠⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠠⠶⠀⠀⠀⠈⠙⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠀⡆⡆⠀⢸⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⢠⢰⣻⣿⠀⠀⠀⠀⠀⢠⡄⢸⠀⡀⠀⠀⣠⣇⣿⣴⣷⣧⣴⢺⡇⣴⣼⣿⡖⣤⣄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣤⣿⠸⡀⣾⣿⣿⣿⡇⠀⠀⢰⣦⣼⣧⣿⣶⡇⠀⠒⠾⢿⡟⠉⠻⣿⣟⣨⢻⣽⣿⣼⢣⠙⣿⡀
⠀⠀⠀⠀⠀⠀⣀⣧⣾⣿⣿⣿⣤⠇⢹⣿⣿⠙⠀⠀⠀⠘⠟⣿⣿⣿⡿⠆⣀⣀⣀⡜⠀⠀⠀⢹⡶⢺⣿⠦⣿⠇⣽⣦⢙⡇
⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⠗⡿⠀⠀⢿⠏⡀⢲⣣⣠⡜⠀⡘⣿⡏⠀⠀⠀⠆⢘⣧⠀⠒⠢⠀⣹⡏⢸⣧⣿⢾⣭⠻⣍⠁
⠀⠀⢠⣿⣿⣿⣾⣿⠿⠯⠻⠾⠃⠀⠀⢺⠀⠀⠸⣯⡿⠁⣀⠀⠻⡿⠧⢴⣶⣴⠃⠀⢀⣀⣄⣀⣸⠿⣾⣽⡟⢂⣿⠦⡇
⠀⠀⠿⠟⠋⣉⠁⠀⢀⣠⡄⠀⠀⠀⠀⠁⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠋⠉⠛⠚⠋⠛⡈⢁⣸⠄⠈
⠀⠀⠀⠀⠀⠋⠀⠀⠤⠤⠧⠀⠴⢶⣄⡄⠀⠤⢤⡤⢤⡄⢠⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⣄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠛⠁⠶⠺⠷⠶⠶⠾⠯⠀⢀⣀⣀⣀⡙⢓⣚⣦⠐⠛⣦⣀⣘⡧
⠀⠄⠀⠖⡀⣠⣤⡤⠄⡀⢠⣄⠀⠀⢀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣾⣿⣴⣄⠻⣧⣰⡴⡿⣦⡆⣬⣿⡀⣆⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢷⣿⣿⣿⣿⡿⠟⠻⣿⣷⣿⡇⠀⡀⣆⣄⢀⢸⣿⣷⠐⣼⣧⠀⠀⢀⢧⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠝⢻⣿⠛⠛⠛⢿⡆⠀⠅⡽⢻⣿⣾⣿⣿⡄⣥⣿⠀⠀⢰⢼⣷⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠭⠄⠉⠀⠀⢸⣭⣭⢍⣻⣿⣭⣤⣤⡖⠃⠺⠿⢿⣉⣉⣱⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠀⠐⠘⠻⠗⠚⠟⠻⠟⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡹⠼⣖⣦⣤⣀⠀⢀⣀⢠⣤⣶⣷⣦⡀⠀⠀⠶⠶⠶⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠭⠈⡀⢶⣿⣿⣿⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⢻⣛⡛⣉⠱⣄⢙⡛⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⠙⠛⠢⡬⠴⣀⣺⣿⡧⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠠⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡿⠉⠀⠈⠉⠱⠀⠀⠀⠀⣖⣡⣀⡥⠖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⢧⣠⣤⡔⠙⢲⠀⠀⠀⠀⠹⣿⣿⡠⣄⠄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡴⠊⠁⣤⡐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢘⡁⠐⠂⣀⡏⠀⠀⠀⡠⠔⠙⢦⠀⠀⠁⡸⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⢀⣅⡔⠢⠤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⡁⠀⢬⡽⠃⢠⡴⠈⠁⠀⣄⠺⢆⢨⠉⠓⣄⣀⠀⣠⡔⠶⠊⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⠴⠗⠀⠀⠓⢠⠈⡶⠂⠂⢱⠊⢣⠀⡉⠶⢠⣟⣌⠉⠰⠆⣤⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣇⡇⢴⢢⢞⡈⠆⠻⠀⠀⢾⡄⢎⢲⠰⡀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡸⠈⠄⢇⡈⠻⣙⠈⠏⢀⣤⠸⠀⢙⠑⡌⡄⢍⣧⣥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⣼⠀⠀⠀⠀⠂⣠⠞⡷⢣⡀⠊⣀⣆⠛⣋⡇⢳⠷⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠠⡇⠀⠐⠂⠀⡷⡸⡁⠀⢟⠲⡏⠀⠄⠀⠃⣷⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⠇⡜⠁⠉⠉⠉⠙⡄⠃⠹⢄⠀⢣⡧⣀⡠⢀⡀⡸⡧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⣸⢹⠋⠁⠀⠀⠀⡛⡇⢰⠈⠳⣄⠻⡔⠀⠃⢀⢿⠵⠋⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢒⠆⣿⢸⠀⠀⠀⠀⡀⠛⠁⠀⠑⢴⡄⡑⢀⡇⠀⠀⠀⠀⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠽⠀⢎⠀⣿⢸⠀⠀⢠⡖⠀⠀⡇⠀⠀⠸⡇⠱⠚⠀⠀⠀⠀⡀⠁⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢠⢇⡀⠈⠢⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢨⡂⢸⣸⠀⠀⣈⠐⠀⣀⣷⠀⠀⢸⡟⠀⠀⢠⠄⢰⠚⡄⠀⠀⠀⢀⡔⠘⢆⠀⠀⠀⠀⡆⠎⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⢀⢀⠎⠟⢶⠇⠁⢸⠈⠑⢲⠉⡌⠉⠀⢸⠀⠀⢸⢨⠘⠒⠃⠀⢼⠀⠘⢦⠀⠠⣫⡿⠀⣰⠃⠀⠀⢠⡃⣀⠀⠀⢀⣈⣹
⠀⠀⠀⠀⠀⠀⡇⡸⢰⠀⢸⠀⡇⠈⠀⠀⡞⠀⠐⡀⠀⢸⠀⠀⢸⠀⠲⠤⠚⠀⡆⠀⠀⠈⠓⠋⢾⣀⡰⠃⠀⣀⡤⡚⠉⣨⠅⢘⣁⣠⢴
⠀⠀⠀⠀⠀⠀⠴⠃⡦⡀⣾⠀⣣⠃⠀⢠⠃⠀⠀⠁⠀⢀⠀⠀⠘⢤⣀⡀⠀⢀⡇⠀⠀⠀⠀⠠⣶⣤⣄⡤⠞⠉⡠⠔⠋⠉⠉⠁⠀⠀⢈
⠀⠀⠀⠀⢀⡞⢀⡀⠁⠀⠎⠀⡟⠀⠀⠏⠀⠀⠀⢰⠀⠈⡄⠀⠀⢠⠈⠉⠉⠈⠀⠀⠀⠀⠀⣼⢈⣱⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠸⠂⠁⢺⡀⠀⢆⠀⡇⠀⢠⠀⠀⠀⠀⠸⡀⠀⡇⠀⠀⢸⠂⣾⠀⠀⠀⢠⠔⠂⢛⠡⠈⠻⠗⠤⠤⡄⠀⠀⠀⣀⠠⠔⠊
⠀⠀⠀⠀⠸⣧⡶⢮⠄⡄⠀⠈⡇⠀⡎⠀⠀⠀⠀⠀⢧⠀⢠⠀⠰⡽⢁⠛⡢⠀⠔⠁⢀⠤⠒⠒⠴⠢⠤⣒⣀⠗⢒⣢⣄
⠀⠀⠀⠀⠀⠀⠣⣠⠜⠁⡤⠀⠰⢸⠀⠀⠀⠀⠀⠀⠈⢇⠸⡀⠀⢰⠀⢶⢷⡀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠠⠐⡏⠚⠀⠀⠀⠀⠀⠀⠀⢠⡆⢡⡀⣴⠰⢌⣁⡈⠓⠚⣂⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⣰⠃⠶⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠹⠢⣁⠒⠑⠢⠬⠝⠋⠈⠉⠉⠉⠑⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠠⠑⡄⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠥⠃
⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⣦⠀⠀⢽⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⡰⡿⣄⣹⣽⣯⠭⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠀⢰⡄
⠀⠀⠀⠀⠐⢻⣿⣾⣷⣿⣽⠿⡦⠂⠀⠠⠄⠚⠓⠂⠀⢀⠈⠑⢒⡋⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⢾⣦⣿⣥⣴
⠀⠀⠀⢈⣙⠿⣿⣿⣿⣹⣿⣿⣛⠃⠀⠀⠀⠈⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣼⣿⣿⣿⣿⣿⢞⡀
⠀⠀⠐⠻⣻⡮⣷⣿⣿⢻⡻⣷⠄⠀⠀⠀⠠⢄⣀⡀⢀⣀⣀⠄⠑⠂⢀⣠⠶⠒⠛⠋⠀⠀⠐⠠⠴⣺⣽⣿⣟⣿⠛⠛⢨⡇
⠀⠀⠀⠀⠀⣝⣷⣙⡛⢾⠁⠹⡟⢥⣶⣦⣤⡤⠦⠴⠛⠛⠃⠀⡀⣀⣉⣀⢀⡀⠀⠀⠈⣁⠀⢒⠠⠄⣹⣈⣏⣹⣷⢲⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣿⠿⢾⠚⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠉⠉⠉⠛⢻⣲⣿⣿⢿⣾⣷⡄
⠀⠀⠀⠀⠒⠻⠗⠛⠠⣼⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⠐⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣦⡀⠀⠀⠀⣀⣀⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⢀⣼⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡟⣿⣿⣿⣿⣦⣄⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣴⡿⣱⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠛⠋⠘⠋⠘⠛⠛⠛⠋⠛⠛⠛⠉⠛⠛⠛⠉⠉⠛⠛⠉⠙⠛⠛⠋⠋⠘⠛⠛⠛⠛⠃




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢮⣈⡿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡷⢖⣋⣐⣚⠋⠓⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡫⠚⢏⠀⣟⣩⠭⠿⠿⠭⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⣀⡤⢄⣿⡀
⠀⠀⠀⠀⠀⣴⠞⡼⠁⢠⣄⢱⢟⠶⠶⠾⣶⠶⣾⠁⠀⠀⠀⠀⠀⠀⠀⣄⣰⣿⡥⠶⢆⣀⣘⣻⣦⣤⣀
⠀⠀⠀⠀⣰⢏⡼⡡⠁⢸⣀⡿⢅⣲⠶⡒⠢⠬⠟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡷⠖⠠⡧⢀⡉⢛⣿⣯⣿⣧
⠀⠀⠀⣰⣷⢋⡔⠁⡴⡻⢺⣟⢉⣤⡑⢌⡉⠂⢄⠀⠀⠀⠀⠀⣰⣿⠿⣿⣿⠶⠚⢁⣯⣀⡙⠻⣿⣷⣽⡻⣷⡄
⠀⠀⢞⠟⠁⠊⡠⠞⠈⠀⠘⣏⡯⠘⠝⠲⠿⣦⣀⠑⠄⠀⠀⠈⠁⠁⠚⠽⠛⠛⠟⠛⡿⠉⠉⢛⡛⠂⠁⠈⠀⠉
⠀⠀⠀⠀⠀⠒⠒⠒⢒⣠⣤⣿⣼⡐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠧⣴⣶⣿⣿⡆⣀
⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣮⡿⢟⣽⣾⠿⣻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠔⡓⡰⣬⠂⠀⣙⣺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⢞⠟⢯⡤
⠀⠀⠀⠀⠀⠀⢀⠼⠃⠐⡒⢿⢊⣔⣐⣒⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⡀⣿⣊⢸⢇⡘⢯⠖
⠀⠀⠀⠀⠀⣔⣋⡐⢐⣛⣏⣿⣁⣠⠤⠬⠍⢿⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠈⢉⠒⢸⡆⠈⣓⣌⡀⠀⡀
⠀⠀⠀⠀⠰⠗⠒⢒⣮⡀⠈⣻⡵⠛⠻⠭⣛⢐⣛⣳⡄⠀⠀⡆⠀⠀⠀⠊⡀⠀⢲⣦⣭⡔⢨⡇⢘⡒⢤⡀⠉⠀⡀
⠀⠀⡆⠀⠀⢀⠔⡩⣿⣌⠢⣿⢄⣠⣤⡀⠀⠉⠀⡸⠁⠀⠀⠐⡀⠀⠀⠁⠀⠠⠂⠀⠀⠀⠈⡇⠀⠬⠲⠋⠀⠠⠁
⠀⠀⠘⣤⠞⠁⠀⠔⠈⠊⠀⣿⠋⠘⠛⠛⠦⡀⡰⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣷⣶⣄⣀⣀⠔⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⣿⣀⣀⡴⠒⣲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣤⣶⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠈⠑⠢⠴⣶⣿⣿⡿⠿⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⠀⢠⣧⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠴⠒⠒⠂⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠉⠑⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠹⣷⣾⣿⣤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠀⠀⣀
⠈⠲⠿⠤⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠲⠶⣷⠖⠒⠒⠃⣾⣶⣿⣁⣲⠓⠒⠒⠒⠒⠒⠒⠂⠂⠶⠴⠶⠤⢤⢄⣠⣀⡠⠄⠠⡄⠀⠀⠀⠃
⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠘⠃⠒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠒⠀⠀⠀⠀⠀⠀⠀⠐⠠⠶⢶⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣄⣴⠿⠿⠿⠻⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⡟⠛⠛⠉⠉⠛⠀⠁
⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⣷⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣦⡶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠠⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣀⣀⣤⣴⣿⣛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠂⠳⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃⠈⠀⠀⠀⠀⠀⠀⠲⠶⠒⠆⠤⠖⠲⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢻⣧⣀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣾⣇⠘⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⠈⠻⣿⡀⠹⣧⣰⣶⣄⠠⠀⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⡿⢷⡀⠆⠉⠻⡄⠈⠿⠛⣻⠶⠀⢠⡄⠹⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢯⣇⡀⣿⣦⣀⠀⣂⣈⣁⠁⠈⠉⠁⠀⠀⠉⠀⠀⠀⠀⢴⣄⣤⢀⡀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⣠⢀⣥⣿⣶⣦⡘⠙⠛⠛⠋⢉⠉⠉⣁⠈⠓⢰⠦⡀⠀⠀⠀⣠⠤⠚⠁⠙⢷⡄⠀⠁
⠀⠀⠀⠀⠀⠈⠝⢦⣵⢟⣻⢦⠄⢀⠀⣷⠀⣾⡆⠐⠻⠂⢤⠈⠣⢘⢂⡶⠾⢻⡇⠀⣦⡀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠶⢺⣿⣟⣒⣒⠀⢀⣿⠅⢸⡇⠀⠀⠀⢺⡀⣄⢸⡈⣷⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠶⠛⠞⢱⠈⠉⠉⠀⠀⠛⠁⠀⠀⢸⡇⠀⠘⠁⠿⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁






⣿⣿⣿⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣻⣿⣿⣛⣻⣟⣻⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣾⡏⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣧⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡈⠻⣧⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠻⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠘⠻⢿⣿⣿⣿⡓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢲⣾⣿⣿⣿⣿⡇⢰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢿⣷⣤⣄⠈⠛⣿⣷⣄⢨⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⡮⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠟⢿⣧⡀⠈⠋⠻⣿⣦⡘⠿⣿⣦⣹⣿⣆
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣬⣿⣿⣦⣤⣀⣈⣃⣉⣲⣽⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠁⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠉⠉⠉⠁⠈⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣨⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⣀⣤⠞⢡⣾⣵⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣽⣿⣆⢀⡼⣿⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣼⣿⣿⣿⢏⡼⠋⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠋⣼⣹⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣯⡁⢀⣾⣿⡿⠛⠁⠈⠀⠀⢰⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢁⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⡔⠀⢠⡿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⣿⣿⣿⣿⣿⣿⣦⣤⣴⣤⡀
⠀⠀⠀⠀⢀⣴⣞⣋⣹⣷⣿⣿⣿⣿⣽⣋⣴⣺⣿⣿⣋⣀⣤⣿⣁⣤⣬⣭⣝⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣽⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣟⣟⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣯⣿⣿⣿⣟⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡽⢿⢟⣽⣿⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢉⣡⡤⠄⠘⠿⢯⡏⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣀⣾⣯⣴⣿⣟⣁⣽⣶⣾⣤⣾⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⣀⣴⣿⣿⣿⣿⣿⡿⣷⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢠⣤⠀⣠⠀⢀⡄⣀
⣆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢰⣶⡀⢀⣼⢿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣼
⣿⣾⣦⣾⣿⣧⡀⣶⡆⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿