Effervescence Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⡀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢠⡤⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⣰⡗⣀⡄⢠⡎⣲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠉⠉⢩⢧⣮⡷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠐⢲⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣠⣾⡏⠀⢠⠀⠁⠀⢚⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣄⣬⣿⣿⡅⢀⣾⣢⡴⠀⣉⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣨⡳⠄⠀⠀⠁⠀⡀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣿⣃⠈⢉⣷⣿⠿⠿⠄⠀⣀⣤⠀⠀⠀⠀⠀⠤⡟⣎⢥⠖⣁⢠⣞⣤⡌⡉⠂⠃⠀⢀⡀
⠀⠀⠀⠀⠀⣸⣾⣿⡟⢻⡿⢯⡿⠛⠻⠿⠙⢇⠀⢀⠀⣍⠙⠀⠀⠀⠀⣤⡴⠵⠮⣓⠄⠋⠉⠃⠊⠐⢁⠀⠀⠄⢀⡌⠁
⠀⠀⠀⠀⣰⣽⠛⠧⠀⠈⠙⠀⠀⠀⠀⠀⣸⢿⠐⠳⡿⠻⡤⠀⠀⢀⢸⡿⠑⠃⠀⠀⠁⠀⠀⠀⠀⠀⣤⠆⠀⠘⠂⠂
⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣙⣿⣇⢀⡗⢲⡷⠀⠀⢰⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣧⠐⠀⠈
⠀⠀⠀⠀⢺⠄⠀⠀⠀⠀⠠⠀⠄⠁⣤⣰⣬⠙⣿⣯⡧⠾⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⡄⠙⠯⠰⠄
⠀⠀⠀⢠⣹⣷⠠⡄⠀⠀⣀⠐⢀⡌⣻⡿⢛⣾⣿⡋⠀⠀⠀⠀⠀⠴⢍⡀⡢⠀⠀⠀⠀⠀⠀⠨⠗⠂⠓⠸⠉
⠀⠀⠀⠈⠙⢾⢿⣶⣰⣷⣯⢄⣾⣷⣿⣣⣾⣿⠻⠅⠀⠀⠀⠀⠀⠀⢈⢱⣍⡤⠐⠲⠄⠀⡲⣆⢃⡰⠀⠓⠑
⠀⠀⠀⠀⠀⠈⠛⣿⣿⢿⣿⣼⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠗⠫⠾⠆⠖⠸⠛⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠙⠛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⣚⣛⣭⠭⠽⠗⠂⠀⠀⠀⠀⠐⠛⠿⠿⠯⠭⢽⣿⡶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠛⢛⠒⠲⠶⠶⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⠤⠴⠶⠖⣛⡋⠉⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣠⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠴⠚⠉⠁⠀⠀⠀⢀⠤⠤⡄⠀⠀⠀⠀⡀⡀⠀⠀⠀⠉⠙⠓⠶⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⣤⣀⠀⠀⠀⠀⠀⠃⠀⠒⠃⠀⡠⠀⢤⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠓⠶⠦⣤⣤⣄⣀⣀⣀⣙⣛⣉⣀⣀⣀⣠⣤⠴⠞⠋⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢮⡹⠂⠀⠀⠉⢉⠛⠛⡍⠉⠉⠉⠉⠤⠤⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠐⢦⠀⠀⠈⠑⠊⠑⠀⠀⠀⠀⠢⠖⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠪⠽⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣉⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣄⠀⠈⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⠛⠛⠛⠛⡲⠦⣄⡀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡈⠻⢦⣄⣀⡤⠖⡋⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⡤⠶⠚⠋⠉⠙⢦⣄⡈⠉⠓⠶⠦⢤⣤⣤⣿⠉⠙⠛⠲⠦⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡁⠀⠠⠐⠂⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣤⡴⠃⠠⠤⠀⠀⠀⠀⣩⣿
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠁⣿
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠈⠉⠛⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠒⠚⠛⠉⠁⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣴⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⡀
⠀⠂

⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠶⠶⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠷⠶⠶⣶⣦⣤⣤⣀⣀
⠀⢀⣤⣶⠾⠛⠛⣉⣩⣤⡴⠶⠶⠚⠛⠛⠓⠂⠉⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠳⠶⠶⠶⢦⣬⣍⣛⠛⠷⣶⣤⣀
⣼⡟⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⢻⣷
⣿⠿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡶⠿⢻
⣿⠀⠀⠀⠭⢭⣙⣛⡛⠻⠿⠶⠶⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠾⠟⢛⣋⣩⡤⠀⠀⢸
⣿⠅⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⠶⠶⠟⠋⠉
⣿⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣶⡶⠶⠶⠶⠶⠶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⢻⡇⠀⠀⣀⣠⣴⠶⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠳⠶⢦⣤⣀⣀
⢸⣧⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠲⡄⠀⠀⠀⠀⠀⠀⢀⡀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣶⣤
⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠠⢤⠴⠟⠀⠀⢀⡀⢠⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿
⢸⡇⠉⠛⠻⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣀⣀⣬⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉
⢸⡇⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⢶⣦⣤⣤⣤⣀⣀⣀⣀⣀⡈⠉⠉⠀⠀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠛⠋⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠖⠲⡆⠀⠀⠈⠉⠉⠙⠛⡻⠿⠿⣟⠛⠛⠛⠛⠛⠋⠉⠉⣁⣀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⡞⠁⠈⢳
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠒⢶⡄⠀⠀⠀⠀⠈⠉⠉⠁⠐⠀⠀⠀⠀⠀⠀⠓⠶⠶⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣤⠼⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⢤⡀⠀⠀⠕
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠉⣷⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⣅⣀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠀⠀⠀⠀⠀⠠⠤⢤⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢦⣀⡼⠇⠀⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡲⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠣⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⣀⣀⣄⣨⡀⢀⣀⠀⠀⠈⠿⠀⠀⢼⣏⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⠉⠉⠉⠉⠉⠉⢛⠻⠟⣐⣀⣀⠀⢉⠉⠀⠀⠀⢈⢤⡉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠙⢷⣤⡀⠉⠀⠙⠚⢁⣠⡴⠟⠛⠿⣦⣄⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣧⡀⠠⠈⠛⠷⣦⣴⡞⠛⠁⠀⠀⠀⠀⠈⠙⠿⣦⣤⣄⣀⣀⡀
⠀⣿⠀⠀⣀⣤⡶⠾⠛⠋⠉⠀⠈⠛⢷⣤⣀⠀⠀⠉⠛⠛⠷⠶⣦⣤⣤⣤⣥⣤⣿⡇⠉⠉⠛⠛⠻⠶⣦⣤⡀
⠀⣿⡶⠛⠉⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠉⠛⠛⠶⣦⣄⣀⡀⠀⠤⠀⠉⠉⠉⣩⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤
⠀⣿⡷⣄⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠷⠶⠶⠾⠋⠀⠉⠛⠓⠶⠤⠀⠀⠀⠀⣀⣴⢿
⠀⢻⡇⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⠀⢸
⠀⠸⣧⡀⠀⠀⠉⠛⠻⠶⣦⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠶⠾⠛⠋⠉⠀⠀⠀⢀⣼
⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠙⠻⢶⣄⣐⠠⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣭⣭⣍⣀⣀⣀⣀⣀⡀⠀⠀⠤⠤⣄⣀⣀⣀⣤⣴⠶⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⡶⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⣯⣿⣿⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡁⠀⠀⠈⠻⣯⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣹⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠿⠿⠟⢛⣛⣒⠚⠿⠿⠿⢿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣷⣦⣤⣤⣭⣭⣭⣭⣭⣥⣤⣤⣶⣿⣿⣿⣿⣿⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠒⠲⠶⠶⠾⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠲⠶⠶⠶⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢢⡀⠈⠍⠉⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠃⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣀⣤⣤⣤⣤⣤⣤⡤⢤⡤⣤⢤⠤⠤⡤⠤⡤⠤⠤⠤⣤⣀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠙⠙⠙⠛⠉⠙⠉⠉⠉⠉⠉⠉⠉⠁⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠁⠂⢀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⡀⠀⢰⠘⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠀⢁⠀⢈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⡿⢀⠘⠸⡀⠁⠀⠀⢀⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠃⠀⠰⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⡄⠘⡇⠀⠀⡀⠀⡀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⢨⠘⠀⠀⠁⠠⡄⠀⠀⣡⡄⠀⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸
⠀⠀⠀⠀⠀⠀⠀⢹⠀⡀⢠⠀⠀⠀⠀⡀⠀⠛⠛⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠱⡄⠀⠀⡰⠄⡰⢶⡤⣉⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢠⡀⠀⢾⢧⡠⠱⢎⠛⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠐⡀⠁⠀⠘⢎⠻⣆⡈⠻⣌⠈⢢⣀⠀⠀⠀⠀⠀⠀⠔⢁⠌⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⢦⡢⣈⡀⠑⢬⡙⣲⣌⣳⣌⡇⠀⠀⠀⠀⠀⠀⡠⠊⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠉⠪⣀⠀⠁⠘⢻⣿⡵⠋⠀⠀⠀⠀⢀⠠⠊⣠⣾⣷⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⣄⣖⠀⠀⠀⠉⠀⠀⠀⢀⡀⢐⣆⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠶⠶⠶⠶⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠚⠛⠋⠙⠉⠉⠙⠛⠛⠒⠲⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀
⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⡀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢠⡀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⣰⠏⠀⠀⠀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢄⡀⠀⠀⠙⢧⡀
⣸⠃⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⢳
⡟⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠈
⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⣇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀
⣿⡄⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⡼
⡗⠈⢦⡀⠀⠀⠈⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠉⠀⠀⠀⢀⠞
⣷⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠶⠖⠒⠒⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⢀⡠⠊⠁
⣿⠀⠀⠀⠀⠀⠁⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠂⠉
⣿
⣿
⣿
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠰⠒⠦⠤⠤⠴⠤⠶⠒⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛
⣿⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢹
⣿⠀⠀⠀⠈⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⢸
⢿⡀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⢸
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⡖⢲⠴⠤⡀⠀⠀⡠⠾⢄⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⣷⠀⠀⠀⠀⠀⠀⠙⠻⣄⣀⡟⠀⠘⣇⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠖⠁⣠⠖⠲⡤⠤⡄⠀⣰⠋⠉⢳⣀⣄⡀⠉⠀⠀⠀⡴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⢻⣤⣤⣏⣀⡟⠀⠙⢤⡤⠼⣅⣀⡇⠀⠀⠀⠀⢧⣀⣼⣉⡇
⠀⠀⠀⠀⠀⢰⠚⢲⡀⠙⠶⠋⠀⢺⡀⣀⣸⠁⠀⠀⣀⣀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠘⠲⠞⠁⢀⡤⢤⡀⠀⣿⠁⠈⡷⠀⢸⠁⠈⡇⢀⡖⠛⢾⠉⢹⡖⠚⠲⣾⠉⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⣀⡟⠀⠈⠙⠋⠁⠀⣼⠓⠚⣧⠈⠧⣤⠜⠛⠙⢇⣀⣠⠏⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡖⢓⡖⠛⢢⠀⠘⠲⠖⠃⠀⣀⣤⡀⢀⣤⣞⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢹⡄⠀⠓⠞⠧⣤⠜⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇⠀⠈⡷⠚⠁⡰⠚⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠚⠀⡴⠒⢦⡀⠀⢠⠴⠦⡄⠀⢠⡏⠉⢻⡍⠑⢲⠞⠓⡆⠀⠳⠤⠴⠃
⠀⠀⠀⠀⠀⣰⠛⢲⡀⠀⠀⠈⠣⢤⠼⠁⠀⢻⣀⣀⡇⠀⠀⠑⠶⠊⠀⠀⠈⠓⠖⠃⣀⣤⡀
⠀⠀⠀⠀⠀⠘⠲⠚⠁⠀⢀⡤⢤⡀⠀⢠⠶⢾⠈⠀⡷⠀⠀⣀⠀⠀⢠⠞⠛⢲⡀⠸⣅⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⣀⡟⠛⠻⣤⠼⠋⠋⢀⣠⣼⠉⢹⠄⠈⠳⠤⠚⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢧⣀⣠⠏⠀⠀⠀⢾⠀⠈⡿⠉⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠰⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠒⠢⣤⣄⣀⠀⠀⠀⠀⠀⢀⣴⣿⣞⡛⠻⡆⠀⢀⣀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣤⣴⣶⣤⣍⣻⠀⠀⠙⠛⠻⠃⢢⠈⠙⠂⠰⡄⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠛⠋⠀⠀⠀⡄⠀⠀⠀⣦⢄⣀⠤⠓⠙⠦⠀⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣷⠀⠀⠀⠀⠄⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⢠⠗⠒⠠⢠⡏⢸⠃⠀⠀⠀⠀⡀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣤⠞⣁⣀⣀⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⢸⠇⠈⠃⠀⠀⠂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⣀⣀⡤⢞⠁⢈⠉⠻⠛⣃⠀⡀⠀⠀⣼⠁⠀⣀⣤⠟⠀⠀⠉⡱⠆⠀⡅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠠⢀⠀⠱⠦⠾⢻⠃⠀⠀⠀⠀⠀⡠⠈⠀⠀⣸⠀⠀⠀⠀⠀⢠⡾⠃⠶
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⡶⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⣀⡑⣎⡀⠀⣠⣔⢻⡀⠀⠀⠀⠀⠈⠀⢀⠌
⠀⠀⠀⠐⠂⠀⠀⠀⢀⡮⠀⠀⠀⠀⠀⢰⣁⡀⠚⠃⢿⠓⢦⣤⣤⡄⣹⣆⠀⢀⠀⠀⠀⠀⢸⠟⠋⠫⡉⠀⢰⡾⠳⢤⠰⣠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⢸⠛⢁⠀⠀⠈⢷⣀⣼⠋⠀⠀⠙⢦⠈⣿⣷⣄⡀⣴⣀⢀⣀⣀⣦⣞⢧⠁⠒
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣠⣤⡿⠛⠟⠀⠀⠀⠀⡈⢿⠟⠛⠉⣙⡿⠿⠿⢿⣁⠀⠀⣆⠑⠢⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠘⠷⣶⠶⠶⠿⣿⣿⣿⡏⡀⠤⠘⢤⡞⠁⠀⠀⢆
⠀⠐⠂⠀⠀⠀⣘⡃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠈⠂⠠⣤⠊⠀⠀⠀⢠⣿⡤⢿⣦⣄⡐⠈⠉⠙⠷⡄⠀⠀⠀⠈⠀⠀⠀⢼
⠀⠀⠀⠀⠒⠒⠃⠀⠀⠀⠀⠠⠒⠈⠡⣶⠄⢀⣀⠀⠀⠀⠀⠘⠦⣀⣀⣹⢋⡽⠵⠿⠶⣿⠳⠠⣀⠀⢀⡼⢀⣀⠐⢦⡀⠀⠠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠘⠇⠀⠀⠈⠑⠒⠒⢋⠀⠀⠉⠀⠈⠁⠀⡆⠀⣹⠞⠾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⡀⠀⣬⠀⠁⣰⡇⠀⠀⠀⠃⡀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⢄⢀⠴⠎⠀⠀⠈⠁
⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⢢⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢃⠀⠸⠃⠃⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⣀⠤⠄⠀⠁⠀⠀⢠⠜⠋⠐⡀⠀⡠⠒
⠀⣀⣀⠤⠊⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢀⠤⠂⠀⠀⠀⠀⢀⣾⠟⣁⡄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠙⠦⣤⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠠⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠘⠁⠀⠀⢰⣄⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⣧⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⢩⣥⣶⡾⠟⣇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠚⠋⠉⠀⠀⠀⣿⠈⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠉⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠟⠋⠙⠛⠒⠶⣤⡀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡼⠃
⠀⢀⣴⠖⠻⠟⠛⠓⠶⢦⣄⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⢠⡿⠁⠑⣄⠀⠁⢄⠀⠀⠈⠙⠶⣄⣿⠛⠛⠛⠓⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⢧⠀⠀⠀⠑⢄⠀⠑⣄⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⣿⠘⢆⠀⠀⠀⠀⠑⢤⡈⠳⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠸⣆⠈⢣⡀⠀⢠⠀⠀⠙⢦⡈⠳⣄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠄⠂⠀⠀⣴⠏
⠀⠹⣦⠀⠙⢦⡀⠈⠁⠀⠀⠙⢦⡈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠈⠳⣄⡀⠙⠲⢤⣀⠀⠀⠀⠉⣢⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣤⠞⠋
⠀⠀⠀⠀⠈⠙⠶⣤⣀⡈⠉⠉⠋⣉⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠙⠉⠉⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⢀⣤⠞⠋⢀⣹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⠟⠉⠀⠀⠈⠁⢀⡤⠞⠉⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣤⣤⡤⠖⠛⠁⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢀⡠⠐⠁⠀⣠⠶⠋⡀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢀⣤⣴⠖⠚⠛⠛⠛⠛⠒⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠶⠋⠀⢀⡴⠊⠁⠀⠀⠁⢀⣠⠞⢡
⠀⠀⠀⠀⢠⣶⣏⡉⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠾⣥⣀⣀⣴⣋⣀⣀⣠⣤⠴⠞⠋⢁⣠⠟
⠀⠀⠀⢰⡟⠀⠀⠉⠓⠦⣄⡀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡉⠉⣉⣉⣁⣀⣀⣤⣤⠶⠛⠁
⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠉⠛⠶⣤⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠉⠉⠁
⠀⠀⠀⠸⣧⠙⠲⢤⣀⠀⠀⠂⠀⠀⠀⠙⠳⢦⣄⡀⠈⠙⠶⣤⣴⢿⣇
⠀⠀⠀⠀⠹⣧⡀⠀⠉⠙⠒⠦⢤⣄⣀⣀⣀⣀⣈⣹⡷⠶⠖⠋⠀⢀⣿
⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠁
⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣬⣍⣙⣿⣶⣶⣶⣶⣶⣿⣛⣩⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⣤⡤⠤⠤⠤⢤⢤⢤⣤⣤⡤⣤⠤⢤⣤⠤⢤⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠤⠦⠚⠗⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠤⣠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⢤⡤⢤⣤⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⡠⠂⠀⠠⢂⠀⡠⠐⠠⠀⠠⢀⠐⠀⠐⠀⠐⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠾⠶⠶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⠶⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠘⢄⡀⠀⢀⡠⠃⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣈⠀⠁⠀⢤⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠉⠀⠀⡀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠉⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠀⢠⠀⠁⠶⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠟⡤⠠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣐⠀⣀⡥⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠒⠋⠉⠁⠉
⠀⠀⠀⠀⠴⠉⠈⠀⣀⡔⠒⠂⢠⠤⠒⠒⠒⠒⢳⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠃
⠀⠠⠊⠀⠀⠀⠀⠀⠁⠀⠀⡀⠸⠀⠀⠀⠀⠀⠸⡀⠀⠁⠀⠀⠀⠄⠀⠀⠀⢠
⠆⠀⠀⠀⡠⠤⣄⠀⠀⠀⠒⡝⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀
⠀⠀⠀⠀⠫⣤⠟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⡠⠛⠋⠉⢹⠀⡠⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⢀⠔⠆⠀⠀⢑⡶⠀⠀⠐⠂⠁⠀⠀⠀⠀⠘⠉⡠⠔⠊
⠀⠀⠀⠀⠑⠀⠀⡠⠀⠁⠀⠀⠀⢀⡠⠒⠁⡀⠛⢦⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⣀⠴⠋⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣴⣾⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠉⠉⠀⠀⠀⠠⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣋⣿⣿⣿⣿⡿⠟⠙⠛⠉⠉⣻⣥⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠛⣹⡿⠿⠋⠉⠁⠀⠀⠀⣀⣴⡟⢋⡙⣹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⣶⠟⠛⢻⠵⠾⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⢫⣀⣀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠶⠞⠛⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⣟⡛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⡞⣮⣽⣓⣰⣶⣈⣹⣭⣿⣛⣿⢿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⣼⣿⣿⣿⣿⣾⣿⣷⣿⣿⣟⠷⣻⣿⣿⣿⣟⣭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⣼⣼⣯⣿⣿⣿⣿⣿⣿⣿⢼⣟⣾⠟⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⢾⣿⣿⣿⣿⣿⣿⢿⣿⡿⠯⣯⣾⢃⣼⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣰⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⡿⢿⣫⣾⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⣰⣿⣿⡟⡄⣿⣿⣿⣿⣯⣛⣥⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢠⣿⣿⡿⣞⣛⡿⢟⣫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢠⣿⣿⡿⣴⣞⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⢠⣿⣿⣟⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⢀⠀⠀⠀⠀⠀⠊⠀⠠⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡠⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠄⠀⠂⠀⠀⠐⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠠⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡴⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⠀⠈⠉⠉⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣤⣤⣤⣤⣤⣤⣤⢤⣤⢤⠤⡤⠤⣤⠤⢤⠤⠤⢤⣤⣤⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠩⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠐⠉⠀⢀⡀⠀⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⠘⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸⢰⠀⠁⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠂⠀⠰⠆⠀⠁⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡄⠀⡇⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠐⠀⠀⠁⠀⡄⠀⠀⣩⡄⠀⣤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⢠⠀⠀⠀⠀⡀⠀⠙⠓⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠐⡆⠀⠀⣐⠄⣠⢦⡤⣈⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠠⡠⠀⢸⢷⡠⠑⠆⠛⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠐⡄⠁⠀⠈⢮⠻⣆⡀⠳⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠠⠂⡠⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⢢⡠⡐⡀⠑⢄⡙⢦⣌⣳⣄⡿⠀⠀⠀⠀⠈⠀⢀⠜⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⠪⡉⠀⡀⠘⠛⣿⣩⠛⠀⠀⠀⠀⠀⣀⠔⢁⣴⣿⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣈⡔⠂⠈⠀⠉⠁⠀⠀⠀⠀⠐⣦⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠷⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡠⢲⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⡤⠄⢖⣒⣚⡯⠽⣍⠉⢢⠀⠀⡠⠊⢀⢐⠷⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⠐⠒⠂⢉⣉⡀⠴⠖⠒⠋⠉⠉⠁⠀⠀⠉⠘⡄⢠⠷⠊⠀⡠⡫⣑⡽⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⠈⣉⣁⡀⠤⠤⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠉⠀⠠⡰⢕⡬⠊
⠀⠀⠀⡠⢔⡾⣍⡡⠤⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠠⡐⢕⣬⠚⠁
⠀⠀⣸⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⢌⡪⣺⡟⢝⡄
⠀⠀⠉⡄⠀⠀⢃⠀⠀⠀⠀⠐⠒⠒⠒⠀⠐⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠪⡢⣵⠎⠙⡌⡈⣷
⠀⠀⢠⢃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢄⢔⢌⡺⠊⠀⠀⠀⢱⡐⡌⣆
⠀⠀⠀⡎⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⡠⡪⣪⡵⠋⠀⠀⠀⠀⠀⠈⣧⠐⢜⡄
⠀⠀⠀⠰⠸⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⣮⡿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⡀⢹⡀
⠀⠀⠀⠀⢃⢃⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠠⠄⠐⠀⠈⠻⠣⡐⡡⡠⡢⡠⠢⢀⢀⠀⠀⠀⠀⣧⢀⠈⡇
⠀⠀⠀⠀⠘⡌⡆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⠐⠕⡕⡡⣡⣠⣂⣀⣸⣎⣘⡇
⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⢿⣿⣽⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢣⢣⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠟⢒⣲⣶⡶⣖⣶⠶⠖⠒⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢎⡆⠀⠀⠈⡄⢀⡀⠀⠀⣀⡀⠤⠤⢒⠲⡉⣉⣡⣴⡼⣞⡿⠯⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⡜⢄⠀⠀⠘⠔⠒⠈⠉⢀⣀⣠⣴⣶⡷⠿⠟⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⣦⣤⣦⣶⡦⠯⠟⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⡈⡉⢁⠀⠠⡠⢀⢄⠠⡀⢄⠄⡀⢄⠠⡠⡀⢄⠤⡠⢀⣀⢄⢀⡠⡀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠈⠐⠑⠑⠊⠊⠐⠁⠊⠈⠀⠁⠉⠀⠁⠁⠀⠑⠁⠁⠈⠁⠁⠈⠉⠀⠁⠁⠈⠈⠑⠁⠉⠈⠉⠁⠁⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⣠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⡤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠈⠁⠀⢰⡾⢂⡤⠀⣰⢂⣲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠛⠛⠉⣹⣠⣽⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣠⣽⠏⠀⢀⠀⠂⠀⢰⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡙⢾⡿⠗⠀⠀⣼⠄⣀⠀⠐⠾⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢕⢈⠀⠀⠰⠀⡀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣾⡿⠀⠲⢿⡐⣧⣠⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠐⠆⡀⠄⠀⢀⠢⢀⠰⢆⡀⠂
⠀⠀⠀⠀⠀⠀⢀⢺⣿⣯⣽⣿⢿⡥⣂⣄⣰⣯⣟⡛⠉⠁⠀⠠⢶⣏⠀⠀⠀⠀⠀⠀⠠⡈⠄⡉⠑⣶⡬⢿⢙⡳⡐⠆⠀⠀⠀⠀⠂⠤
⠀⠀⠀⠀⠀⢠⢾⣿⡿⠋⢙⣾⡙⠚⠋⠁⠛⠋⢈⣣⠄⢀⠄⣴⡦⠀⠀⠀⠀⠀⣢⡶⡛⠉⠃⠤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡂⠠⠄
⠀⠀⠀⠀⢀⣶⡟⠙⠷⠂⠀⠀⠁⠀⠀⠀⠀⠀⣸⢻⡂⠉⢻⠋⢙⠆⠀⠀⠀⢸⡿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁⡀⠈⠁⠈
⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣈⣩⣷⢀⣼⠃⣞⡟⠀⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⣧⠈
⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠠⠈⢀⣀⣠⣬⡙⣿⣿⣽⣥⠏⠀⠀⠀⢠⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⡀⠘⠫⠠⠆
⠀⠀⠀⢀⡜⣿⡆⢠⡀⠀⠀⠀⠀⠄⢀⠘⣾⣿⠿⣥⣿⡷⠃⠀⠀⠀⠀⠀⢠⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠈⠢⠴⠉
⠀⠀⠀⠈⠛⢯⣼⣦⡤⢠⣦⡾⠀⢀⣛⣣⣿⠂⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠐⠏⣓⢓⡀⠀⢠⠀⠀⢠⡤⠑⠀⣄⠠⠆⠄
⠀⠀⠀⠀⠀⠀⠻⢾⣿⣷⣿⣿⡄⣯⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣐⠠⢆⣤⡀⣁⠀⡤⠏⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡽⠟⠻⣿⡿⠋⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠠⠈⠁⠀⠈




⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⡿⠻⡿⠛⠿⢿⠿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠿⠿⣷⣶⣤⡀
⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄
⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣦⣄⣀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠁⠀⠀⠀⠀⠀⠉⠙⠻⣷⣄
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⠀⠀⠀⣀⣰⣿⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣤⣶⠿⠟⠛⠋⠙⠛⠛⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⣄⡀⠀⣼
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠈⠙⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠛⠿⣷⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⣸⣿⠀⠀⢀⣴⡿⠃
⣿⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⣿⣇⣤⣶⡿⠋
⢹⣷⡀⠀⠈⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠿⠛⠋⠁
⠀⢻⣷⡄⠀⠀⠙⠻⠿⠷⠀⠀⠀⠀⠀⠀⣠⣾⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠈⠛⠿⣷⣶⣤⣤⣤⣤⣴⣶⡿⠟⠋
⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣶⣶⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠠⠄⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠢⠄⠄⢢⣀⣰⣀⠐⢰⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⡷⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢈⠑⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡄⠸⠀⠀⠀⠀⠁⠀⠊⠀⠀⠒⠒⠒⢦⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⠀⠀⠄⠀⠄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠠⢀⡀⠄⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠉⠀⠀⠔⠉⠉⠉⠉⠑⠀⠀⣀⠜⠁⢠⠆⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠤⡀⢀⠀⠀⡀⠃⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡁⡠⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠠⠃⠀⠀⠀⠁⠐⠂⠁⠰⡀⠀⠀⠀⠁⠉⠁⠀⠃⠀⠀⠀⠀⠰⠈⠉⢳⠀⠀⠀⠀⡞⠀⠈⠀⠈⠀⠊
⠀⠀⠀⢀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠆⠈⢀⠜⠀⠀⠔⠐⠀⠐⠀⠀⠀⠐⠂⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂⠀⠻⠀⢀⣀⣀⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠄⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠠⠅⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠠⠤⠤⢴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣉⣛⠒⠒⢚⣛⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠖⠐⠒⠚⢏
⠀⠀⠀⣶⠠⠤⠤⠤⢴⠀⠀⢿⣱⢒⠒⠒⠒⣺⡇⠀⠀⢸⠀⠀⠀⠉⠈⠈⠁⠀⢷⡒⠒⠐⠐⣲⣹⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⢡⠀⠰⢂⣈⡉⡉⢩⠁
⠀⠀⠀⢿⠄⠀⠀⠠⡜⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⢄⠀⠀⠤⠤
⠀⠀⠀⠈⠀⠀⠀⠀⠱⡄⠀⠀⢰⠀⠒⠂⠀⠻⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⠀⠀⢸⠀⠀⠂
⠀⠀⠠⠈⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⡁⢩⣉⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠇⣀⣀⠀⢸⠀⠀⠠⠤⠤
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠇⠀⡇⠸⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠒⠀⠀⠐⠂
⠀⠀⠘⠢⢤⣀⣀⣀⡤⠄⠀⠱⠄⣀⣀⣀⡀⠇⠀⠀⠀⠀⠙⠠⠤⠤⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠋⠉⠀⠀⠁⠀⠈

⣿⡿⠛⠛⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡖⠀⢀⣶⠀⠀⠀⣀⣤⡶⠶⠶⢦⣄⡀⠀⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⣀⡀⠀⠰⣿⡀⣰⣿⠃⢀⣴⡎⠉⠁⠀⠀⠀⠀⠉⠻⣷⡄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠴⠂⠀⠈⠃⠰⠆⠉⠻⠛⣿⣶⣿⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⢹⣇⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⢸⣿⣦⣠⠀⠀⠀⠈⠻⠿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠘⢿⣿⣿⣷⣾⣦⡀⠀⠀⠛⠓⣶⡶⢦⣄⠀⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠄⠘⠿⣿⣿⣿⣿⣿⣷⣄⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠄⠀⠀⠀⠀⠈⠉⠻⠿⠿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣧⣽⣆⡀⠉⣿⣷⡀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⣿
⣿⡇⣰⣿⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠟⠋⠉⢹⣿⣿⣿⠟⢷⢠⣿⣿⣿⣿⡟⣡⣤⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣶⣾⣷⠶⢄⡘⠁⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠠⣄⡀⠘⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠁⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣯⣴⠈⠀⠀⠀⠀⠀⠀⢀⣀⠾⠁⠀⠀⠀⠘⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⢶⡆⠀⣿
⣿⡿⣿⣿⣿⣿⣬⡇⠀⠀⠀⠀⠀⠀⠀⡈⠛⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⠿⠏⠉⠀⠀⠀⣤⠀⠀⠀⠀⠀⠁⠀⣿
⣿⡇⠀⠈⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠟⠛⠁⠀⢠⡀⠀⠀⣠⣀⣤⡤⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⣠⡀⠀⢺⣷⣶⠾⢿⡎⠁⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⡎⢽⣄⠐⣿⣧⠀⠘⠻⠧⠀⠀⣀⣀⠀⠀⠀⠀⠀⢰⣤⣿
⣿⡇⠀⠀⢀⠀⠀⠀⠀⠘⢿⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⠾⡟⠛⠃⠀⣼⣿⣿
⣿⡇⠀⠀⠈⠀⠄⠀⠀⠀⠀⣹⣄⣸⣿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⢀⣿⣿⣿
⣿⡇⠀⠂⠀⠀⠀⠀⠀⢰⡿⠿⣿⣿⣿⠿⠇⣀⠄⠀⠀⠘⢿⣶⣄⣀⣀⣿⣀⣀⣠⣶⠟⠓⠄⠀⠀⠀⠀⠙⢀⣾⣿⣿⣿
⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡿⠀⠀⠀⠸⣷⡀⠀⠀⠙⠿⣿⣿⣦⣽⣿⠋⠁⠀⠀⠀⠀⢀⣀⡰⠶⠊⠉⠉⠉⣿
⣿⣿⣿⣿⣿⣿⣶⣆⡀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠈⢿⣿⣿⣿⣷⣄⣤⣴⢀⣠⡌⠉⣀⡀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⣶⠀⠀⠀⠀⠙⢣⡀⠀⠀⢀⣼⣿⡿⠿⣿⣿⣿⣤⠀⠈⠱⠿⣯⣽⠆⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠉⠀⡄⠀⠀⠀⠾⣇⣀⠰⠟⢁⣿⠀⠀⣠⠿⣿⠋⣶⣦⣄⠀⠟⠁⠀⠀⠀⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⢿⣀⣼⠋⠀⠀⠀⠀⠉⠙⢷⣄⠀⠰⡄⠀⠀⢸
⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⣶⠀⠀⢸
⣿⡇⠀⠈⠙⠿⣿⣿⣿⣿⣿⠿⠏⠀⠰⣶⣶⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⣿⣶⡞⠁⣼⡏⠙⡟⣡⡔⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢹⣿⡄⠘⢿⡅⠀⠀⠙⣃⣿⣃⠀⠀⣰⡆⠀⠀⠲⣄⠀⠀⠀⣿⣦⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠾⠿⢋⣿⣸⣿⣄⢀⣄⠙⠋⢻⣿⣿⣿⡿⠛⢲⣿⠃⠀⠀⣰⣿⡆⢀⣼⣿⣿⣶⡆⠀⢸
⣿⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣶⣶⣿⠿⠛⠁⣤⣿⡇⠀⠀⠸⣿⣿⣿⣇⢀⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣾
⣿⡇⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢠⣿⣿⡇⠀⠀⠰⣦⣼⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠿⠏⢀⣀⣠⡀⣿
⣿⣿⠶⠿⠿⠿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢠⣿⣿⣿⠇⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠈⠃⡀⠀⠙⣿⡏⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⢸⣿⣿⣿⡦⠀⠀⠉⠛⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⢀⣀⣸⣿⣷⡿⠁⣱⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠘⣿⣿⣿⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⣠⣤⣠⣿⣶⣾⣿⠿⠛⢋⡀⠈⣁⣀⣼
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠘⠀⠟⢻⣿⡆⠀⢀⡼⠿⣶⡶⢿⣿⠿⡿⠟⠛⠋⠙⢿⣷⣤⣄⠻⠿⠛⠀⠈⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢴⣿⣓⠀⣿⠀⢠⠶⠋⠀⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣷⠶⣶⣄⠀⠀⣤⠄⠚⠛⣿⠛⢧⢀⣶⠀⢸⣟⠀⠀⠀⢸⣿⣿⠀⠈⠃⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣾⣿⣿⣿⣷⣤⣄⠀⠀⢻⡀⠀⢸⣿⡀⠀⢻⡇⠀⠀⢸⣿⣿⡇⠀⠀⢠⣀⠄⠁⠀⠀⠀⠀⠀⠰⠀⠐⠂⠠⣼
⣿⣿⣿⣿⣿⣿⣿⠏⠉⡀⣸⣶⠀⠀⣿⡀⠘⣿⠀⠀⠸⡇⠀⠀⢸⡇⣿⡀⠀⣰⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢀⣾
⣿⣿⣿⣿⣿⠋⢀⣴⣿⣿⣿⣿⡄⠀⠈⢇⠀⠿⠀⠀⠀⠙⠀⠀⢸⡗⣿⡇⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣰⣾
⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⡿⠋⠀⠀⠀⢸⡇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠘⠃⠈⠀⣴⡾⠿⢦⣤⢀⡀⠀⠀⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠙⢿⣿⢆⡀⠀⢠⡞⠀⠈⢿
⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣄⡾⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣾⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣇⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⡀⠀⢀⡄⠁⢀⡀⠀⠀⣽⡿⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢛⣿⢿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣾⡿⢿⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸
⣿⡇⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡀⠐⠂⠀⢹⡇⠀⠀⠀⢸
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⣾⠃⠀⠀⠀⣼
⣿⣿⣿⣿⣾⡗⢺⠃⠀⠘⠁⠀⠀⠀⣀⠛⠀⠀⣌⠉⢻⡟⠛⠿⠋⠁⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⢸⡏⠀⠀⢠⣾⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⣸⠃⠀⣴⡟⢿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⢀⡄⠀⠀⠀⠙⠦⣀⠀⢀⣀⣤⣀⣀⣀⣀⠀⢸⡟⠀⣸⣿⣿⣦⣾
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⢀⣼⣿⣦⠀⠠⠄⠀⠛⣷⣿⣿⣿⣿⠿⠿⠻⣦⣿⡇⠀⣿⣿⣿⣿⣿
⣿⡟⠉⠁⠉⠙⢿⣆⠀⢀⣀⠀⣀⠘⠀⣀⣀⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠋⠉⠉⢿⣆⠸⠆⢠⣿⢁⣀⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠙⣷⡎⣡⡞⠁⠀⣰⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣿⣿⣿⣿⣷⣿⡿⠉⠁⢠⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⢀⠐⢋⡙⠛⠁⠀⢀⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⠀⢀⠘⢿⠛⠻⣿⣯⣿⣿⣿⣾⣿⠁⠀⠀⢸⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠘⠃⡀⠀⠀⠈⠉⣿⣿⠃⠀⠀⠀⢶⣄⢹⣧⠈⠀⠀⠀⠀⣶⣿⠛⣿⢻⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⣀⣰⠿⠇⠀⠀⠀⣼⣿⣇⡄⠀⡀⠀⣾⣻⣁⣀⣤⣠⣾⣦⣼⠟⠁⠀⠀⣼⡇⠀⠀⠀⠀⠀⣠⣿⡿⠻
⣿⡇⠀⠀⠀⠀⠾⠟⢫⣴⠾⣦⣤⣶⡿⢁⣼⡷⣈⣷⣴⣿⣿⣿⡏⢻⣿⣿⣿⣿⠀⠀⠧⢸⣿⠁⠀⠀⠀⣰⡞⠉⠁⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⡘⢿⣴⣿⣿⣿⣷⣿⣿⣶⣿⣿⣁⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⢠⣿⡟⠀⠀⣠⡾⠃⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡿⢻⣿⣿⡟⢹⣿⣿⡏⠉⢻⣿⡇⠈⣿⣿⣿⡄⠀⣀⣸⣿⠁⠀⣰⡟⠁⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣏⣵⣾⣿⣿⣇⠘⣿⣿⡟⠀⣾⣿⠁⠀⢻⡿⣿⣷⣤⣽⣿⠏⢀⣾⠟⠀⠀⠀⠀⠀⠀⣴⣿
⣿⣧⠀⠀⠀⠀⣀⣿⣿⣿⣃⣼⡟⠛⠁⠈⣿⣾⣛⣹⣿⡀⣿⣏⠀⠀⠘⢃⣿⣿⣿⣙⢻⣧⣜⠋⠀⠀⠀⠀⠀⠀⣸⡉⢸

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠛⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡟⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⡴⠞⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢷⡀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢳⡄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢻⣄⣤⣼⠿⠛⠟⠛⢶⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣦⣄⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢧
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠻⢦⣤⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣁⣬⠟⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠶⣶⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣶⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡇⢸⡏⢹⡏⢹⡏⢹⡏⢹⡏⠉⡏⠉⡇⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣄⣸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⡇⢀⣇⣠⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠙⠛⠛⠻⠿⠷⠾⠷⠾⠷⠾⠿⠿⠛⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣉⣉⣉⣛⣛⡋⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠛⢻⡇⠀⠀⠀⠀⢀⣴⣟⡱⠋⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠛⠻⡿⠷⠶⣦⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢰⡿⠃⠈⠹⣦⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⣠⡇⠉⠛⢸⡇⠀⠀⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡇⠀⠸⣧⣀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣷⣾⠟⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣛⡛⣟⠛⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⣀⣿⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠁

⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⠀⢀⣀⣤⣶⡾⠿⠛⠛⢋⣉⣡⣤⣤⣴⠶⠶⠶⠶⠔⠒⠂⠀⠀⠀⠀⠐⠒⠒⠶⠶⠶⠶⢶⣦⣤⣤⣭⣍⣉⣛⠻⠿⢷⣶⣤⣀⡀
⣠⣾⠿⠋⠉⠀⠰⠶⠞⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⠀⠉⠻⢿⣷⣄
⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿
⣿⡋⠻⠿⠷⣶⣶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⡿⠿⠛⠉⢸
⣿⡇⠀⠀⠐⠒⠤⣬⣍⣉⣛⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠾⠿⠿⠛⠛⢋⣉⣁⣤⠔⠂⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⠶⠶⠿⠛⠉⠉⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠶⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⢀⣠⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⢶⣤⣄⡀⠀⢸
⢸⣷⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣾
⢸⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠴⠞⠃⠀⠀⢀⣀⡠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿
⢸⣿⠈⠙⠻⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠁⠀⣀⣼⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠋⠁⢈
⢸⣿⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣶⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠿⠟⠉⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡉⠉⠛⠛⠛⠻⠿⠿⠿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠾⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠋⠛⢷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠓⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠤⡄⠀⠀⠨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⡔⠉⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠳⠦⠶⠋⠀⠐⠆⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠆⣀⣀⣀⣀⣀⠀⠀⡄⠀⠀⠦⠽⠀⠀⠀⢘⠉⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠛⠛⠛⠛⠛⠛⠛⠶⢶⣦⣤⣀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡿⠻⣷⣄⠀⠀⠠⠀⠀⢌⡱⠀⠀⢉⣻⡿⣶⣤⣈⠀⢀⠀⠀⠀⠠⠬⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠈⠛⢿⣦⣄⡀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠿⣦⣄⠚⠀⠈⠙⠻⠿⣿⣍⣀⡀⠐⠁⠀⠀⠈⠀⠀⠉⢻⣿⡶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⡇⠀⣀⣤⣶⠾⠛⠋⠉⠁⠀⠀⠀⠈⠛⢷⣦⣄⡀⠀⠀⠀⠉⠙⠛⠿⠷⢶⣶⣤⣤⣤⣤⣾⣿⠂⠀⠀⠈⠉⠙⠛⠿⢶⣦⣄⡀⠀⢸
⠀⢸⣷⠞⠋⠁⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣤⣄⣀⠀⠀⠤⠤⠀⠀⠠⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣼
⠀⢸⣿⣦⡀⠀⠀⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⢶⣶⣶⣶⡶⠿⠋⠉⠙⠛⠲⠤⣄⡀⠀⠀⠀⠀⠀⢀⣴⢿
⠀⢸⣿⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁⣾
⠀⢸⣿⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡾⠟⠋⠁⠀⠀⠀⣿
⠀⠀⢿⣷⣄⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣐⠠⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢶⣶⣬⣭⣭⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⢤⣤⣤⣀⠀⢀⣀⣠⣤⣴⣶⠾⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠛⠛⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢀⣤⡶⠶⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣰⠟⢹⡆⠀⠀⠈⠙⢷⣄⠹⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣾⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢻⡄⠀⢻⡄⠀⠀⠀⠀⠙⢷⡀⠉⠛⠛⠛⠛⠛⠉⠀⢀⣴⠟⠁⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠈⢷⡀⠀⠻⣦⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢈⣻⣦⡀⠈⠻⢦⣀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠁
⢀⡴⠾⠛⠋⠉⠉⠻⣦⣀⠀⠉⠛⢳⣶⠏⠀⠀⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⣀⣤⡴⠶⠶⠚⠲⠶⠶⣤⣄⡀
⣿⢶⣤⣀⣀⡀⠀⠀⠀⢉⣻⣶⣶⢿⡇⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⣶⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿
⢿⣀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠁⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣠⣴⠞⠋⠀⠀⠀⠀⠀⣿⠉⠛⠓⠶⠶⠶⠶⠶⠶⠚⠛⠉⢸
⠈⠙⠛⠶⠶⠶⢤⣤⣤⠴⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣄⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟

⡱⠊⠀⠀⠀⠀⠰⠀⠐⠁⠀⢈⠖⠁⠈⠀⠀⠀⠆⠀⠊⠀⠀⡱⠊⢠⠀⠀⠀⠰⠈⠐⠀⠀⢈⠖⠁⠀⠀⠀⠀⠆⠀⠈
⠠⠤⠄⠀⠀⠀⠤⠄⢌⠀⠐⠁⠤⠤⢈⠀⠀⡡⠠⠠⡑⠀⠊⠀⠤⠄⠀⠀⠈⠤⠤⢌⠀⠐⠁⠤⠄⠀⠀⠀⠠⠤⠠⡑
⢀⠀⠀⠐⠂⡈⠄⠀⢀⠕⢀⠀⡀⠀⠀⠓⠄⠢⠀⠀⡨⠢⡀⠀⠀⠀⠐⠂⠀⢄⠀⢀⠀⢀⠀⠀⠀⠀⠒⠀⠠⡀⠀⡀⠢
⠄⠑⠂⠀⠀⢐⠀⠑⢅⠀⠀⠁⠀⠒⡀⠀⠀⡂⠀⠊⡀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠑⢅⠀⠀⠁⠀⠒⠀⠀⠀⠀⠈⠢⡀
⠔⠒⠂⠁⠀⡠⠀⠒⠀⠁⠀⠁⠒⠒⠄⠀⢀⠀⠐⠂⡈⠀⢈⠔⠒⠢⠀⠀⡀⠐⠒⠀⠁⠀⡡⠒⠒⠄⠀⢀⠀⠒⠂⠈
⡀⢀⠀⠠⠚⠀⠀⠀⠀⡀⠚⢄⠀⡠⢂⠔⠃⠀⠀⠀⢁⠔⠣⡀⢀⠔⠀⠘⠀⠀⠀⠀⡠⠚⢄⠀⡠⠀⠄⠃⠄⠀⠀⢀⠔
⠜⠁⠀⠀⠀⠀⠘⠀⢈⠀⠀⡠⠋⠀⠂⠀⠀⠀⠃⠀⡁⠀⠀⠜⠁⠰⠀⠀⠀⠘⠀⢈⠀⠀⡠⠋⠀⠀⠀⠀⠀⠃⠀⠁
⠔⠀⠂⠄⠈⢠⠂⠀⠢⡁⠈⠀⠂⠐⠢⡁⠀⠔⠀⠐⠌⠀⠁⠐⠀⠒⠌⠈⠀⠂⠑⠢⡁⠈⠀⠂⠐⠠⠁⠁⡐⠈⠐⢌
⠁⠀⠀⠈⠑⠄⠢⠀⠠⠊⠢⡀⠀⠀⠄⠉⠢⡐⢄⢀⠔⠁⢀⠀⠀⠀⠈⠑⠄⠢⡀⠠⠊⠢⠈⠀⠀⠔⠉⠢⠐⢄⠀⠔⠑
⠃⠀⠁⠀⠀⠠⠀⠀⠠⡀⠀⡐⠀⠉⠀⠀⠀⠄⠀⠑⢄⠀⢀⠀⠈⠁⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠑⢄
⠈⠉⠁⠀⢁⠔⠉⠉⠀⠀⢁⠀⠉⠉⠀⠀⡡⠂⠉⠁⡄⠈⡠⠊⠉⠑⠀⢉⠔⠈⠉⠀⠀⢁⠐⠉⠉⠂⠀⡠⠂⠉⠁
⢄⡀⠊⠔⠉⠐⢄⠀⢀⠄⠉⠢⣀⠔⠡⠊⠁⠂⡀⠀⡠⠀⠀⢀⡀⠊⠔⠈⠀⢀⠀⢁⠔⠉⠢⣀⠄⠡⠊⠁⠀⡀⠀⠀⠈
⠊⣀⠀⢄⢀⠀⠀⣀⠠⡀⢀⠔⢁⡀⠠⡀⡀⠀⣀⡀⠀⠀⡠⠊⣀⠘⢄⢀⠀⢀⣀⠀⡀⣀⠔⢁⡀⠠⡀⡀⠀⣀⡀⠄
⡈⠀⠈⢢⡀⠠⠁⠀⠑⢀⠀⠀⠀⠀⠑⣀⠀⠈⠀⠈⠀⡀⠀⠉⠀⠉⢢⡀⠀⠁⠀⠑⢀⠀⢀⠁⠀⠑⣄⠀⠈⠀⠈⠂⡀
⡀⢢⡐⠁⠈⠢⠑⢄⠔⠁⠁⠄⠀⢀⠊⠀⠁⡈⠢⡀⠀⠀⠠⠀⠀⡔⠁⠈⠂⠑⢀⠐⠀⠀⠀⠁⢀⠂⠀⠑⠌⠢⡠⠊
⠁⠀⠀⠠⠀⠔⣀⢀⠑⠄⠀⠄⠀⣀⠀⠄⠠⢂⡀⣈⠢⠀⠠⢀⠀⡀⠀⠀⠔⣀⢀⡑⠀⠀⠀⠀⢀⠐⠄⠠⢀⡀⣈⠢
⠀⠀⢀⠀⠠⡈⠀⠀⠀⠀⡠⠊⠀⠀⡁⢀⢔⠁⠀⢀⠆⢀⠄⠀⠀⢈⠀⡠⠊⠀⠀⡠⠀⢠⠀⠀⠀⠁⢀⠔⠁
⢢⠔⠁⠊⠀⠈⠢⠀⠠⠀⠀⠐⡤⠊⡐⠁⠀⠑⠔⠁⠔⠀⠈⠢⠔⢁⠊⠀⠈⠢⠈⠠⠀⠀⠑⡤⠊⠐⠁⠀⠑⠄⠀⠄
⡁⠤⢀⠢⠤⠀⡠⠤⡀⠠⠄⠊⠤⠄⡐⠤⠔⢀⠤⢄⠃⠤⠐⡁⠤⠈⠢⠤⠀⡠⠤⡐⠠⠄⢊⠤⠄⡐⠤⠄⠀⠤⢄⠀⠤
⢄⠀⠀⡱⢄⠘⡀⠀⠀⠠⠀⠠⡀⠀⢈⠦⡀⢀⠀⠀⠑⠄⠀⠀⠀⠀⡰⢄⠀⡀⠀⠀⡠⠀⠠⡀⠀⢈⠦⡀⢀⠀⠀⠀⠄
⡄⠁⢌⠀⠀⠑⠈⠢⡀⠀⠀⠂⠈⠲⡁⠀⠈⠄⠑⢄⠁⠀⠁⠀⠑⠎⠀⠀⠁⠈⠲⡈⠀⠀⠀⠀⠲⡁⠀⠈⠂⠑⢆
⠠⠀⠄⠑⠀⢊⠄⠀⠌⠀⠀⠂⠄⠠⡈⠂⠐⡡⠀⠠⠑⠀⠀⠠⠀⢄⠐⠀⢊⠄⠀⠌⠂⠐⠀⠄⠠⠀⠂⠐⡡⠀⠠⠑⠂
⠀⠀⣀⢀⡐⣀⠀⢀⡀⣀⠐⣀⠀⣀⠀⣀⢊⡀⠀⣀⢃⡀⢂⡀⠀⣀⢀⡐⣁⠀⢀⡈⣀⠐⣀⠀⢀⠀⣀⢊⡀⠀⣀⢀⡀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡇⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠄
⣀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⣠⣤⣤
⠋⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠘⠟⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⣶⡆⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⢰
⣿⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸
⠉⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠄⠁⠁⠢⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠊⠀⠐⠄
⠀⠀⠀⠀⠄⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⣨⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⣴⣄
⡷⠀⠀⠀⠀⠀⢴⣿⣿⣿⣦⡀⠀⠀⣿⠇⠀⠀⠀⠈⠢⣾⣿⣿⣿⣆⠀⠀⠸⣿⠀⠀⠀⠀⠀⠲⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠇

⣤⡄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢠
⣿⡇⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⢸
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⣦⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⢰⣶⠀⠀⠀⠀⠀⣶⣶⣶
⠁⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠈⠉⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢶⣤⣀
⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣀
⠀⠀⢀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠒⠂⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠖⠠⣄⡀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⣠⡞⠁⠀⠀⠀⢀⣠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠙⢷⡄
⢠⡟⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⢻
⣿⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈
⣿⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⣿⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⣿⡄⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⢀
⣿⠙⣄⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠉⠀⠀⠀⢠⠏
⣿⠀⠈⠢⣄⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⠔⠁
⣿⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⣿⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠚⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⠤⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⠐⠒⠊⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⣿
⣿
⣿
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⠀⠀⠀⠀⠀⠀⠠⠀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠈⠉⠀⠒⠒⠒⠐⠒⠒⠙⢢⣀⠁⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠓⠂⠀⣀⠤⠋
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⡌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢇
⣿⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⣿⠀⠀⠀⠀⠀⠙⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠶⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠞⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠠⣤⣀⡀⠀⢀⠀⢀⣼⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢰⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⣸⢳⡖⠀⠀⠉⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣀⡤⠚⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⠉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⡀⠓⠋⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠒⣼⠶⠴⠚⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⡿⠇⠀⠀⠱⣈⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⣀⣠⣴⣧⠀⠀⠈⠁
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠐⠤⣄⢶⡾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢹⣛⣛⣯⡅⠀⢢⠁⣠⠄
⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⢻⣋⠙⠻⠿⢿⡄⠂⠈⠚⠁⠀⠀⡀
⠀⠀⠀⠤⠤⠂⠀⠀⠀⡀⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠞⣿⢽⣯⣷⡄⠀⠀⢉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⠁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⣇⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⢀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣠⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿