Wing symbol Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⣀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣀
⠀⠀⠀⠀⠀⢹⡄⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢠⡏
⠀⠀⠀⠀⠀⠈⣿⣌⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣡⡿⠁
⠀⠀⠀⠀⠀⢧⡘⢿⣮⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣵⡿⢃⡼
⠀⠀⠀⠀⠀⠘⢿⣌⢻⣷⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⣾⡟⣡⡿⠃
⠀⠀⠀⠀⠰⣄⠈⢻⣷⣿⣿⣟⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣻⣿⣿⣾⡟⠁⣠⠆
⠀⠀⠀⠀⠀⠹⣷⣦⣙⢿⣿⣿⣷⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣋⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣿⣫⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠲⢦⣤⣬⣉⣿⣿⣿⣿⣿⣿⣯⣿⣿⣦⠀⠀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣉⣥⣤⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣷⣿⡇⢸⣿⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠾⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⠿⠟⠋⣹⣿⡿⠀⠀⢿⣿⣏⠙⠻⠿⠿⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠈⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⡤⣀⣴⡾⣃⠀⠀⠀⠀⠀⠀⠠⡆⠠⡆⠀⡴⠀⠀⠀⢴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠔⣴⣢⠭⢝⣛⣫⠵⠚⣋⠜⠃⠀⠀⢀⣄⣂⣥⣾⠤⣊⡥⠖⠉⣁⡴⠞⠁
⠀⠀⠀⠀⠀⢀⣤⣶⡽⠱⠃⣀⠬⠿⠭⠭⠥⠶⣒⣚⣋⡴⠛⠀⠠⣤⢠⢟⡿⢫⠞⠉⠠⠐⠒⠋⠱⠊
⠀⠀⠠⢀⣼⡟⡹⢋⣴⣶⣾⢛⣓⠿⠭⠭⣭⣭⣭⡭⠷⠛⠀⠀⠀⢋⢷⡞⣿⢥⠤⠀⠒⣢⠶
⠀⠀⠀⣾⣟⡴⣉⣿⣷⣭⡒⢭⣓⠶⣤⣖⣲⣶⣶⠚⠁⠀⠀⠀⠈⢄⠸⣧⡗⣤⢭⡟⠃
⠀⠀⣠⢇⡩⠆⠛⠛⠛⠛⠻⠷⠻⠿⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢊⠐⣿⣚⣛⡟
⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⠁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠚⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣽⣿⣿⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⣿⣭⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣻⣯⣽⣿⣿⣿⣾⣿⣿⣿⡶⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⢶⣿⣿⣿⣷⣿⣿⣿⣯⣽⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠟⣿⣿⣿⣍⡿⡿⡾⢻⣿⣿⣿⣿⡟⢷⢿⢻⣩⣿⣿⣿⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⢿⣿⣿⠟⣶⣿⣿⣿⣿⣿⣷⣾⠻⣿⣿⡟⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈⢀⣤⠀⠈⠢⣀⠀⠀⠀⠀⣀⠔⠁⠀⣤⡀⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠘⢌⡀⠈⠑⣊⡥⠔⠚⢡⡶⠉⣹⠒⡶⠼⠁⠈⠧⢶⠒⣏⠉⢢⣌⠓⠢⢄⣑⠊⠀⠈⡰⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠁⠋⠀⠂⡟⠡⢼⣋⠷⣸⡷⠃⠀⠀⠘⢾⣇⠾⣙⡇⠌⢻⠐⠀⠙⠈⠉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠠⡈⡒⠤⣀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⣀⠤⢒⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⡦⢀⡉⠲⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠖⢉⡀⢴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣤⣉⣳⡠⢈⡐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⡁⢄⣞⣉⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠬⠥⠼⡿⠿⢦⠙⠀⠀⠀⠀⠀⠀⠏⡴⠿⢿⠧⠬⠥⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣫⠥⢻⣭⡺⣦⡣⣀⠀⠀⣀⢜⣴⢃⣭⡟⠬⣝⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠵⣫⢾⣜⣫⣹⠀⠀⣏⣽⣣⡷⣝⠮⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠈⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠦⢀⢀⢀⣀⣀⣀⣙⣣⠬⢭⣭⣭⢩⠃⠀⠀⠀⠀⠘⡭⣭⣭⡤⠤⢝⣃⣀⣀⣀⡀⠀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣟⣉⠥⢛⣯⣘⠿⣿⡞⡀⠀⠀⠀⠀⢀⣳⣿⡿⣁⣼⡛⠬⣙⣻⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⡾⣥⢚⡽⣳⢾⣿⣾⡵⡆⢰⢮⣷⣿⡿⣟⢯⡓⣬⢷⡚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠤⣀⠀⠀⠉⠙⠊⠷⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠾⠑⠋⠉⠀⠀⣀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⣄⣉⢲⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡗⣉⣠⢴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣈⣹⣙⠲⠬⣑⠢⡄⠀⠀⠀⠀⠀⠀⢠⠔⣊⠥⠖⣋⣏⣁⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣤⣬⣯⣭⣑⣺⣇⠱⣀⠀⠀⠀⠀⣀⠎⣸⣓⣊⣭⣽⣥⣤⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣠⡬⢶⣖⣢⢝⠷⣤⡇⠀⠀⢸⣤⠾⡫⣕⣲⡶⢥⣄⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢤⡶⠛⣰⣫⣞⡼⠃⠀⠀⠘⢧⣳⡝⣖⠛⢶⡤⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢺⣃⠾⠽⠁⠀⠀⠀⠀⠈⠯⠷⣘⡗⠒⠛

⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄
⠀⠀⢀⣄⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢠⡀
⠀⠀⣼⣿⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣿⣷
⠀⣴⢹⣿⣧⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣼⣿⡏⣴
⠰⣿⣧⢻⣿⣷⡹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣾⣿⡿⣸⣿
⣀⢿⣿⣷⡹⣿⣿⣜⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣫⣿⣿⢟⣾⣿⡿
⣿⣮⠻⣿⣿⣮⣻⣿⣷⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣟⣵⣿⣿⡟⣱
⠸⣿⣷⣝⡻⣿⣿⣷⣽⣿⣷⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿
⢷⣝⢿⣿⣿⣮⣝⡿⣿⣿⣿⣿⣿⢟⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡛⣿⣿⣽⣿⣿⢿⣻⣵⣿⣿⡿⣫
⠘⢿⣷⣭⣻⢿⣿⣿⣷⣿⣿⣿⡇⣿⣿⣿⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⢟⣫⣾⣿
⠀⠈⡻⢿⣿⣿⣾⣿⣿⣿⣿⠟⣴⣜⡻⣿⣿⣿⣿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣟⣽⣿⣿⠟⣫⣦⠹⣿⣿⣿⣯⣷⣿⣿⣿⢟⠁
⠀⠀⠹⣶⣽⣛⣿⠿⣿⣿⣿⠆⡻⢿⣿⣾⣭⣛⢿⣷⣿⡻⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⢟⣯⣾⡿⣛⣯⣶⣿⣿⢟⠰⣿⣿⣿⡿⣿⣛⣭⣶⠟
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⡸⣿⣷⣮⣽⣿⣻⣿⣿⣿⣿⣦⡻⣿⡄⠀⠀⢠⣿⢟⣵⣿⣿⣿⣿⣟⣿⣯⣵⣾⣿⠇⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠘⢷⣶⣿⣿⡟⢡⣾⣭⣿⣽⣿⣿⣿⡟⣛⣭⣥⣤⣽⣷⠀⠀⣾⣯⣤⣤⣭⣙⢻⣿⣿⣿⣯⣽⣭⣷⡄⢹⣿⣿⣷⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣼⣇⣛⣻⣿⣿⣿⡿⢣⣾⠟⠛⠉⠉⠙⠻⠄⠀⠟⠋⠉⠉⠙⠻⣷⣜⢿⣿⣿⣿⣟⣛⢰⣧⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢇⡹⢿⣿⣿⣿⣏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡼⣿⣿⣿⢿⢟⡸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣾⡇⢿⣿⢿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⡿⢸⣷⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣷⢸⣿⣿⣿⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣿⣿⣿⡇⣾⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⣶⡝⠿⣿⢷⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣾⣿⡿⢫⣶⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣟⣦⢉⡿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣉⣵⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠻⣆⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⢴⠿⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠖⠀⠀⠀⠀⠀⠀⠲⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣶⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⠿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⢷⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠋⣰⢟⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣈⡿⡄⠙⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣷⣾⠁⡀⠀⠚⠻⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠛⠇⠀⣀⢘⣷⡯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⣾⡿⣟⢙⣵⣷⣢⣶⢰⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠆⣶⣴⣾⣮⠉⣿⣿⣟⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡟⣹⢻⡇⠾⢻⡟⢿⠋⣴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣄⠹⡟⣿⡟⠇⢹⡼⡎⣿⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⡕⢈⡆⣼⡾⣧⣆⡆⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢠⣰⡽⢳⡆⢮⠀⢍⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣾⡇⣾⡁⠻⠇⠘⢹⣧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⣜⠁⡸⠏⢸⣧⢸⡆⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠙⢹⡆⡇⣸⡏⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⣿⡆⣧⢰⡝⠛⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⢰⡸⢿⡇⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣿⣺⠸⢟⡆⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡇⠀⠇⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠝⡀⢸⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢸⡄⢻⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⢰⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡌⣿⣇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡼⡿⢰⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⣦⡹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣾⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⣓⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣚⠋
⠀⠀⠀⠀⠭⠽⠿⣿⣿⣿⣯⣿⣿⣶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⣶⣿⣿⣽⣿⣿⣿⡿⠭⠭⠄
⠀⠀⠀⠀⠀⠂⠀⠐⠚⢛⣷⡹⠷⣍⡿⣶⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣶⠟⣩⠾⢇⣾⡛⠓⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠘⢒⠂⣉⢽⣿⣕⠬⡿⣶⣿⣿⣿⣷⣶⣶⠇⠸⣶⣶⣾⣿⣿⣿⣶⢿⠥⣪⣿⡯⣉⠙⡒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢚⣿⢿⣶⣢⣫⣻⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣟⣝⣔⣶⣿⣿⡓⠦
⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠪⠿⢿⣿⣿⣿⣟⣷⣶⣶⢶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣶⣶⣾⣻⣿⣿⣿⣿⠿⠕
⠀⠀⠀⠈⢍⣉⡯⠽⢿⣮⢿⢿⣍⡛⢿⣿⣿⣦⣤⣀⣴⣶⡆⢰⣶⣤⣄⣤⣴⣿⣿⡿⣛⣩⡾⣯⣱⡿⠯⢽⣉⡩⠁
⠀⠀⠀⠀⠀⠂⠒⡒⠭⣿⣷⡢⠚⠟⣿⣿⣿⣿⣿⣿⣿⡏⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⠻⠓⢔⣾⣿⠍⢒⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠿⢿⣿⣿⣴⡔⡕⣯⣾⣿⣿⡟⠁⠀⠀⠈⢿⣿⣿⣷⣭⢪⠮⠠⠋⠛⠻⠿⠁

⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⣡⣤⣤⣤⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⣤⣤⣌⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠞⣡⣼⣿⣭⣭⣻⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣟⣭⣭⣿⣥⣈⢳⡄
⠀⠀⠀⠀⠀⣰⠏⣰⣩⣴⣊⣭⣋⠹⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⡿⠏⣙⣭⣙⣦⣍⣄⠹⡄
⠀⠀⠀⠀⢠⠏⣼⣿⡿⠿⡿⡿⡿⠾⣻⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⡟⠶⣿⠿⣛⢿⢿⣿⣧⠹⡄
⠀⠀⠀⢀⡞⢈⣡⣾⣤⣾⣧⣾⣷⣿⡹⣇⠙⠷⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠿⠃⣸⢏⣷⣾⣷⣼⣷⣼⣷⣌⡀⢳
⠀⠀⠀⢸⣷⣿⡿⡿⠓⠻⢣⠛⢻⠟⡟⢻⢧⡀⠉⠷⠤⠤⠟⠈⣻⡄⠀⠀⣰⣏⠁⠿⠤⠴⠞⠁⣀⡼⡟⢻⠻⡛⢹⡝⠗⠘⢿⣿⣿⣾⡇
⠀⠀⠀⣿⢿⢻⠀⢀⣷⣠⣿⣷⣿⣾⣻⡿⣧⣿⣳⣶⣤⣴⣿⣿⠛⠁⠀⠀⠈⠛⣿⣿⣦⣤⣶⣞⣿⣾⢿⣟⣷⣿⣾⣿⣄⣶⡀⢈⡙⡇⣧
⠀⠀⠀⣿⣆⣾⣦⣾⣿⣿⡿⠟⠻⠃⣿⣿⣧⣿⣭⣥⠄⢛⣹⡇⠀⠀⠀⠀⠀⠀⢻⣇⡃⢰⣬⣭⣧⣿⣿⣯⠘⠟⠿⢿⣿⣿⣷⡼⣧⣠⣿
⠀⠀⠀⡧⣿⣿⣿⡿⢻⠉⢠⣇⣾⣡⣴⣩⣦⣾⡴⡷⠿⠟⠻⠁⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⣾⢦⣧⣼⣍⣦⣼⣷⣸⡄⠉⡟⣿⢯⣿⣿⣿
⠀⠀⠀⢿⠸⠇⡇⠀⣾⣴⣿⣿⡿⢿⠟⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢻⡿⢿⣿⣿⣦⣧⠈⢸⠹⠇⡟
⠀⠀⠀⢸⡞⣀⣿⣾⣿⣿⢻⢃⣆⡾⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢧⣸⡙⡿⣿⣿⣶⣿⣠⢻⡇
⠀⠀⠀⠀⢧⢻⣿⣯⠿⠛⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠻⠏⣿⣿⡟⡾
⠀⠀⠀⠀⠘⣏⠻⢸⠀⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⡄⢠⡏⠟⣹⠃
⠀⠀⠀⠀⠀⠹⡄⢸⣧⣿⣿⣿⢿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡿⣿⣿⣿⣼⡇⣰⠃
⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣦⣄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⡼⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⣿⡞⣏⠙⢮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡵⠋⣹⢱⢫⢿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠻⡄⠘⣆⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣰⠃⢡⠇⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⡄⠘⣆⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣰⠃⣠⠋⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠹⡆⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⣰⠇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡿⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⢿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀

⣿⠿⠿⠿⠿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣛⣿⣿⣟⣻⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣶⡶⢖⣒⡶⢶⣶⣀⣤⡄⠀⠀⠀⠀⠀⠀⢠⣴⡶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣲⣿⠃⠌⠁⢁⠙⣿⣖⡒⠀⠀⠀⠰⣶⣶⡆⢺⣿⣿⣿⡷⢰⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⣶⣀⡀⣠⣶⠭⠍⠀⠀⠀⠀⠀⠛⣿⣷⡲⣝⣛⣫⣄⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠛⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣄⣀⡀⣀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⣽⣻⡞⠹⠯⠏⢶⣻⣯⡭⠁⠀⠀⠉⢿⣿⣷⡛⣿⣿⣿⢟⣾⣿⡿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣺⣄⠀⠀⠐⣸⣓⡛⠁⠀⠀⠀⠀⠈⢿⣿⣿⣬⣿⣇⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠩⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⢢⡴⠶⢦⡔⣶⣶⣶⡖⠀⠀⣠⣠⣠⣠⣶⢶⣒⡶⣶⢄⣄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣚⣒⢾⣿⣿⣿⡷⣒⣒⡒⠀⠀⠀⠈⢿⣿⣧⢏⠀⠀⠀⡹⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠙⠛⠋⠐⠒⠂⠀⠀⠀⠀⠀⠈⠽⠿⠯⠳⠶⠞⠽⠿⠏⠁

⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠁
⠀⢀⠈⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠋⢀
⠀⠈⠻⣶⣤⣙⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣟⣡⣴⡾⠋
⠀⠀⢤⣈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣠⠄
⠀⠀⠀⠙⠿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣭⣛⣛⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⣛⣛⣫⣽⣿⣿⣿⣿⣿⣿⣯⣴⡾⠟⠁
⠀⠀⠀⠀⠀⢬⣙⣛⣿⣿⣿⣿⣿⣿⠿⠭⠭⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠬⠭⠿⢿⣿⣿⣿⣿⣿⣟⣛⣩⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣛⣛⣋⣁⡀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⡠⠟⠁⠠⣄⣉⣛⣛⣻⣿⣿⣿⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣟⣋⣥⣤⠖⠂⣀⠈⠁⠀⠀⠀⠀⠉⢀⡀⠒⢦⣤⣭⣛⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣛⣿⣿⣿⣿⣶⡾⣋⣥⠖⠀⠀⠀⠀⠀⠐⢦⣍⡻⣶⣾⣿⣿⣿⣟⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠯⠉⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠀⡀⢀⣀⣀⢀⣀⠀⢀⡀⠀⣀⡀⡀⢀⣀⡀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⡀⢀⣀⠀⣀⡀⠀⣀⣀⡀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠘⣧⡸⣧⡸⠀⣿⠀⡟⢷⣌⠁⣾⠁⢈⣃⠸⣦⣅⠀⠀⠀⢸⡇⢸⣷⢸⣯⠤⠁⠿⣬⡁⢸⡇⣼⡇⢀⣁⠈⡻⣦⣸
⠀⠀⠀⠀⠀⠀⠙⠁⠹⠃⠐⠻⠀⠧⠀⠙⠀⠙⠦⠜⠃⠘⠤⠋⠀⠀⠀⠞⠧⠚⠃⠸⠳⠴⠃⠓⠼⠃⠞⠇⠘⠳⠼⠛⠸⠇⠈⠻

⠀⠀⠠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤
⠀⠀⠀⠘⢿⣿⣟⢷⡀⠀⠀⣰⢟⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⢄⠀⢀⢤⣴⣿⡟⠋
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠘⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠉⠛⠛⠋

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⢤⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣤⠄⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠙⠤⡀⢰⠁⠀⠀⢱⠀⡠⠘⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣀⠀⠀⠀⢀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡤⠀⠠⣴⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠈⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⣀⣒⣤⣄⠀⠀⠀⢀⣤⣔⣂⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⢲⣶⣤⣤⣄⠀⠀⠀⢀⣤⣤⣴⡶
⠀⠀⠀⠀⠀⠀⣻⣿⡅⠀⠀⣽⣿⡃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⠿⠷⠄⠰⠿⠿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⠀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠻⣿⣶⣶⣦⡀⠀⠀⣠⣶⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠐⠤⣄⣀⡀⠀⠀⣀⣀⡠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⠀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠷⠀⠰⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠻⠀⠰⠻⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⠇⢿⠿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄
⠀⠀⠁⠀⠈⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⢀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⢺⣷⣶⣦⣄⡀⠀⠻⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣤⡙⢿⣿⣿⣿⡇⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣌⠻⣿⡇⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⣷⣶⣶⣤⣈⠻⢿⣿⣿⣿⣿⣿⡇⣤⡁⠹⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠙⢿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⡇⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠃
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣦⡙⠻⠧⢹⣿⣿⣿⣦⣈⠻⢿⣿⣿⠟⢠⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣤⣤⣀⡈⠻⢿⣿⣿⣿⣿⣿⢠⣦⡀⠻⣿⣿⣿⣿⣷⣦⠉⠁⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠆
⠀⠀⣿⣿⣿⣿⣷⣶⣍⡻⢿⣿⣿⡇⢿⣿⣶⣌⠙⠿⣿⡿⠁⠀⠀⠀⠀⠀⣰⠀⡀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣌⠙⠻⠌⢿⣿⣿⣷⣦⡈⠁⠀⠀⠀⠀⠀⠀⠰⠂⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠄
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⢰⣦⣄⠙⢿⣿⣿⠇⠈⠀⠀⠀⠀⠲⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃
⠀⠀⣀⣀⠂⠈⠻⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣶⣝⠻⠆⠐⠀⠀⠐⠂⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠂⠀⠂⢀⡀
⠀⠀⠙⣿⣿⣿⣶⣦⣽⡻⢿⣿⣿⣧⠹⣿⣿⣿⣿⣿⠀⢀⠴⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠢⠄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣤⡉⢙⠃⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡘⣿⣶⣤⣈⠛⠿⠀⠀⠀⠠⠂⠄⠁⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣦⠀⠠⠀⠀⠀⠀⢀⠀⠐⠁⠀⣀⠠⠂⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢿⣿⣷⣶⣦⣭⡛⠛⠿⠷⠜⢿⣿⣿⣿⠀⠠⠀⠀⠀⠀⠑⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠠⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣄⢶⣤⣀⡙⠻⠿⠀⠀⠀⠐⠁⠀⠀⡀⢺⠄⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡜⣿⣿⣿⣷⣦⠀⠤⠀⠀⠀⠀⠺⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣉⡛⠿⣿⣿⣜⢿⣿⣿⡿⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣦⣌⠉⣁⡙⠻⠇⠀⠄⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⡙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠴⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⣻⣿⣿⣿⣷⡌⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠤⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣦⣅⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⡏⢀⡀⠀⠀⠄⠀⠀⠀⠄⢠⣠⠤⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡟⢂⠄⠀⠀⠀⠀⠀⠀⠀⠪⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⢨⠀⠉⠉⠀⢨⣂⣀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠰⠠⠐⠀⠀⡀⠙⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣽
⠀⠀⠀⠀⠀⠀⣆⠀⢳⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣰⠃⢀⡆
⠀⠀⠀⠀⠀⠀⢻⡳⣄⣧⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⣇⡴⣻⠃
⠀⠀⠀⠀⠀⠀⢀⠙⣌⠻⢧⡀⢈⢦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢎⠀⣠⠿⢋⡼⢁
⠀⠀⠀⠀⠀⠀⠸⣷⢼⣆⠀⠙⠦⣕⢭⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⢕⡥⠞⠁⢀⣾⢴⡿
⠀⠀⠀⠀⠀⠀⠀⡈⠢⣍⠳⢦⣕⠮⣙⢿⣧⡙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⣡⣿⢟⡩⢖⣥⠶⢋⡥⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣗⠮⣧⣀⠨⣙⠺⢿⣧⡙⠳⣮⣝⢦⡀⠀⠀⠀⠀⠀⠀⣠⢞⣭⡶⠛⣡⣿⠿⢚⡩⢀⣤⡯⢖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡉⠙⠒⠯⢷⣿⣙⠺⣿⣿⡄⢳⠀⠀⠀⠀⠀⢰⠃⣼⣷⡿⠚⣹⣷⠯⠗⠚⠉⣡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣗⠶⠬⠵⣾⣯⣑⠻⣿⣇⣿⠀⠀⠀⠀⠀⢸⣇⣿⡿⢓⣩⣿⡶⠯⠴⢖⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⡒⠲⠶⠿⢦⡬⠿⣿⣜⣆⠀⠀⠀⢀⣞⣼⡿⠯⣤⠾⠷⠖⠒⣺⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣓⣒⣛⣛⣿⣋⡽⢿⣷⡄⣴⣿⠿⣭⣻⣟⣛⣓⣒⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⢥⠤⠚⣫⠾⣵⠝⠀⠘⢵⡽⢮⡓⠢⢤⠭⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠐⠈⠀⠀⠀⠀⠀⠈⠐⠙⠂⠈⠁

⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢻⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣿⠃
⠀⠀⠈⢿⣷⡀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⣿⡟
⠀⠀⣄⠈⢿⣷⣄⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⣴⣿⠟⢀⡄
⠀⠀⠘⢷⣌⠻⣿⣮⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢋⣾⣿⢋⣴⡟
⠀⠘⢷⣮⣿⣷⣮⡻⣷⣝⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣵⣿⣿⣿⢿⣫⣴⠖
⠀⠀⠠⣽⣿⣿⣿⣿⣷⣝⡷⣝⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣿⣿⣻⣷⣿⣿⡥
⠀⠀⣤⣌⣻⣿⣿⣿⣿⣿⣿⣮⣝⣟⣻⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣋⡷⣿⢿⣫⣷⣿⣽⣿⣟⣋⣠⡄
⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣷⠭⣿⣿⣷⣦⡀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢰⣿⣿⣿⣿⠽⠾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢺⣿⣿⣿⣤⣄⢠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣯⣀⣤⣽⣿⣿⣿⢒⣿⣿⣿⡿⣿⣿⣿⣿⣶⡶⠖
⠀⠀⠠⢤⣴⡿⠟⢛⣩⣭⣤⣴⣶⡶⠾⢟⣽⡶⢷⡚⢛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⣳⣢⣴⣯⣟⠿⣶⣶⣶⣿⣭⣽⣟⣷⣿⣥⣤⣤
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⢟⣭⣖⣫⣤⡏⠴⣿⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡹⣛⢿⣿⡟⢯⣜⣲⣯⣟⢿⣿⣿⢿⣿⣭
⠀⠀⠀⠀⠀⠀⣴⡿⠿⣫⡴⢟⣿⣿⡿⠋⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣞⣿⡯⣍⢿⣳⣾⣿⡿⣖⠻⣿⣿⣿⣝⣷⣮⡻⠿⣮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣩⣶⠿⣛⣭⣴⣾⣽⣾⡴⡿⣻⢿⡿⣿⢽⣿⣷⠀⠀⠀⠀⠀⠠⣿⠿⢵⡪⣗⢿⡻⣷⣾⣿⣽⣿⡮⣟⡿⣿⣯⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠟⣡⣾⣿⣿⡿⣱⢞⡴⠿⢫⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⣴⣿⣥⣽⣿⣎⠳⢷⣽⣿⡿⣿⣮⣻⣮⡻⢷⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠉⠟⣼⢣⢏⢆⡔⡝⣻⣿⣿⣿⣞⡙⡦⠀⠀⡜⣻⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⡞⡯⠛⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠏⠋⠞⡾⣱⣿⣿⡽⢿⣷⣧⠀⢀⣷⣿⣿⣷⣾⣿⡿⣿⢿⠿⠏⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⠿⢿⢾⣆⢿⠀⢸⣿⣽⣾⡿⠿⠛⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣁⠀⠀⣠⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⠔⠋⠁⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡺⣟⣵⠿⠋⠀⠀⠀⠀⣠⠋⠀⠀⣀⣠⣤⣤⢤⣶⡤⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣹⣿⣾⣿⣇⣵⠊⠀⢀⡴⠚⣁⠴⠚⠋⠉⠀⣀⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠞⠁⠀⠀⢉⣿⣿⣿⡿⠋⠄⢺⣧⠔⠋⠀⠀⠀⠀⠀⠀⢫⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣰⢋⠀⠀⠀⡠⢋⣿⡿⢋⠄⣀⡴⠋⢀⡠⠂⠁⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣸⣷⣯⠂⠀⠊⠀⠋⣯⣾⣯⢞⣵⣢⣶⡿⠁⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⣿⡿⠁⠀⠀⠀⠀⢠⣿⣟⣵⣿⣿⠿⠋⠀⠀⣰⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿⠃⠀⣻⠆⡀⠀⠀⠀⠀⢸⢷⣿⣿⣿⠏⠀⠀⢠⣞⠃⠀⠀⣀⣀⣤⣤⣤⠤⢶⣦⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⣤⣡⡾⠁⠀⠀⠀⠀⣱⣿⣿⡿⠋⠀⠀⠈⠠⠞⠛⠋⣉⠉⠁⠀⠀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢼⣿⣿⠏⣴⣣⠄⠀⠠⠚⠉⣩⣿⡾⢃⣠⣤⣦⠶⠒⠋⠁⠀⠀⠀⠀⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣁⠘⠿⣡⣾⠟⢉⢀⡀⠀⠀⣴⣫⣵⣾⣿⠿⠛⠋⠀⠀⢀⣀⣠⠷⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠈⠝⢡⣾⣿⡏⠀⠀⠀⢠⠾⠛⠉⣀⡀⠠⠶⠤⣴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⣫⡀⠀⢉⣟⣩⣶⡆⠀⢀⣷⡶⠖⠒⠀⠀⠀⠠⠴⠯⠤⠤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⢿⣟⡃⢈⠸⢛⣉⠀⠀⢉⣼⣦⣤⣦⣤⠤⠤⠂⠀⠀⢠⣤⣬⠿⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢚⣯⡆⠀⣼⠟⢋⠠⠾⠟⠛⡛⠉⠁⠀⠀⠀⣀⣀⠤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠰⠿⠧⠤⢶⣾⡶⠆⢀⣠⣖⠀⠀⠀⠀⠴⢟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣚⣉⠀⠀⣠⣅⠀⠐⠚⠿⠿⠛⠁⣀⡀⠤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠿⠅⠒⢛⣉⠠⢤⣬⣄⣀⣀⠀⠀⠾⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⣀⣀⣀⡠⡤⠲⠗⠀⣾⢓⣈⣉⡍⢥⣤⣄⣚⡛⠛⢉⣁⣀⣠⠤⠄⠚⠋
⠀⠀⠀⠀⠀⣠⠚⠁⠼⠿⣤⠶⠇⠐⠶⠀⣀⣾⢟⣀⣬⡛⢉⣀⣬⣭⡉⠉⢀⡀⠝
⠀⠀⠀⠀⠰⠁⠀⠀⠐⠒⠰⣇⡀⠀⢤⠋⢃⠐⣤⣌⠉⣛⡀⠐⡍⣉⡙⠓⠀⠙⠦⡀
⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢉⢠⣤⣰⡄⣤⣧⡉⠉⣀⡈⢛⠛⠛⠦⠙⢟⠉⠛⠓⠚⠳
⠀⠀⠀⠀⠀⠙⢦⡀⢀⣲⠺⠁⠤⠴⠌⠁⠀⠑⢄⣤⣬⡛⠻⢯⡲⢦⠤⢄⡳
⠀⠀⠀⠀⠀⠀⠀⠙⠶⢮⡳⠦⠺⠦⢀⣠⣽⢛⡛⠋⠉⡉⠱⡦⢄⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⠃⠚⠉⠒⠤⠽⠏⠉⠉⠁⠛⠀⠈⠒⠧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢠⠖⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡤⠀⠂⠀⠹⠀⠀⠀⢸⠀⠈⠀⠰⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠱⢛⡀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠂⣈⠳
⠀⠀⠀⠀⠀⠀⠀⡠⣿⣷⢀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⢀⣰⣿⡷⠀⠀⠀⠀⠀⠀⣤⣶⡿⠃⣤⣶⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣦⣤⠛⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡟⠻⡄⠀⠀⠀⠀⠀⡿⠿⢷⣾⡟⢻⡿⠳⣄⣠⡀⠀⠀⠀⣀⣄⡴⠺⣿⠟⣿⣶⠿⠿⡇
⠀⠀⠀⠀⠀⣀⠜⠁⡀⠙⣿⠀⠀⢠⠀⠀⠀⠀⠀⠰⠀⠀⣻⠟⠀⣄⣈⢦⣀⡀⠀⠀⢸⣶⣦⣡⡁⢸⡛⠶⠸⠷⢉⠆⠀⢈⠱⠿⠀⠞⣻⡁⢩⣍⣶⣾⠃
⠀⠀⠀⠈⣽⣿⣾⣿⣧⣤⢻⣄⠀⢨⠶⠛⠀⠊⠙⠖⠀⢰⡿⣱⣶⡿⡿⣿⣿⡄⠀⠀⠈⠹⣿⣿⣷⣾⠿⣦⢒⣤⡌⠀⠀⠈⣤⣴⣢⣶⢿⣷⣿⣿⡿⠁
⠀⠀⠀⠰⢻⣿⠈⡅⣉⣽⣿⡵⠦⠀⢀⠰⠀⠙⠀⠀⠸⢻⣷⣯⣦⣄⣇⠻⣿⠹⠀⠀⠀⠀⠉⠿⡈⠉⣧⡀⣿⠋⠉⠀⠀⠈⠉⢻⡇⣠⡎⠉⣹⠏⠀⡀
⠀⠀⠀⠀⣼⢁⣿⣿⢿⣻⡾⢛⣀⠤⠒⠀⠀⠀⠈⠐⠠⣌⠛⢿⣏⡟⣿⣆⢹⡀⠀⠀⠀⠰⣄⡀⠙⢄⣿⡟⣿⢢⡜⠀⠀⠘⣤⢚⡟⣿⣧⠐⠉⣀⡰
⠀⠀⠀⢀⣿⣾⡏⢸⣿⠇⡕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⣷⡀⢿⣿⣇⠀⠀⠀⠀⠻⢿⣦⣼⣿⣷⡀⣰⠀⠀⠀⠀⢰⡌⣰⣿⡿⣧⣼⠿⠃
⠀⠀⠀⡼⠻⡏⢸⣿⠛⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⣷⣀⡟⠻⠆⠀⠀⠀⠀⠈⠹⣿⣏⠃⠹⡟⠀⠀⠀⠀⠘⡛⠁⢋⣷⡟⠉
⠀⠀⠀⠀⠀⣿⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠈⢿⡶⣀⣠⠀⠀⠀⠀⢠⣀⡠⣾⠏⠁
⠀⠀⠀⠀⠀⠛⡏⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠙⡈⠿⠀⠀⠀⠀⠸⠏⡠⠁⠿
⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢱⢸⠀⠀⠀⠀⢠⢠⠁⠆
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⠀⠀⠀⠀⢸⣸⡎
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⣠⠤⠀⠠⣠⣤⣬⣧⣐⣀⡀⠀⠀⣠⣐⣠⣮⣤⣬⡠⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⠰⠋⣾⢿⣿⠿⣏⣿⡻⠃⠀⠀⠛⢿⣝⣿⢿⣻⢿⡎⠳⡌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣠⠘⠀⣰⣿⣿⢿⡼⣯⠃⠀⠀⠀⠀⠀⠀⢫⡿⣯⢿⣿⣷⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠠⠂⠀⠐⠁
⠀⠀⠀⠀⠘⢠⡃⠿⠻⣸⣾⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣶⢿⣼⡸⢿⢧⢢⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠖⠶⠶⣶⣶⣶⣳⣾⠯
⠀⠀⠀⠀⠀⠈⠃⢠⡤⣿⡿⢦⡛⠀⠀⠀⠀⠀⠀⠀⠀⢣⠼⣿⡷⣠⠀⠟⠁⠀⠀⠀⠀⠀⠀⣿⡏⢻⣓⢲⣶⣯⣈⠿⢿⣿⣻⣵⣶⠄⠊⠁⣠⣂
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡸⡄⢈⣧⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⡘⣱⣿⡂⠀⠀⠀⠀⠀⠀⠀⢠⣿⢩⣾⣟⠏⠉⢉⣱⣾⣿⣿⣿⡿⠟⠂⠀⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢿⠀⣎⠹⣿⣟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢁⡅⢸⠗⠀⠀⠀⠀⠀⠀⢀⣾⣳⣿⠿⣱⣶⣶⣿⣿⣭⣭⣿⡿⠗⠢⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⡿⠦⠀⠀⠀⠀⠀⠀⠞⢿⣷⣿⣿⠃⠀⠀⠀⢀⠀⢀⣴⣟⣿⣿⠯⣤⡾⠿⠿⢿⣿⣛⣛⣛⣛⣉⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠃⠀⠀⠀⠠⣴⡾⣽⣿⠛⣫⣽⣶⣿⣿⣿⣿⣿⡟⠁⠠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠈⠱⣦⣿⣿⣿⣶⣾⣿⣛⠻⠟⠁⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⡿⠟⢿⠦⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠙⠹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣠⣾⣿⣿⣿⣿⣿⢿⣿⠏⠿⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⠹⣿⡿⣿⣿⣿⣿⣿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠤⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢐⠈⢵⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡤⠞⣛⡋⠉⢥⡀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡽⠃⢰⠋⢳⢼⣔⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⡶⠀⢠⢿⣛⠉⠁⠀⠀⠖⠈⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⡄⣠⣜⠫⠚⣤⢍⠲⢀⠂⠀⠲⠀⠀⡀⠀⠀⢠⡆⢠⣛⡋⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⣰⢿⠙⠃⠘
⠀⠀⠀⠚⠉⠀⠀⡀⠉⢛⣟⣽⠁⠀⠐⠃⢼⡽⠟⠃⠀⠀⠀⠀⠉⡶⠀⢠⠀⡬⠍⠁⠀⠀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⣿⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠽⠦⠙⠗⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣼⡀⠙⠃⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢨⣿⡍⠁⠀⠀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣟⠀⠀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⢿⡤
⠀⠀⠀⠀⠐⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡴⠶⠚⠁⢈⠉⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⠿⠟⣄⠀⢢
⠀⠀⠀⠀⢀⠠⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡲⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠉⠂⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠃⠋⢃⡄
⠀⠀⠀⠀⠘⡁⠐⠠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⣷⡀⠀⠀⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊
⠀⠀⠀⠉⠒⠈⢤⡀⠀⠀⢤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⠄⠈⠹⣧⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣼⣶⡀
⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢠⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠝⡿⢟⡴⢺⠄⠈⢃⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣿⡈⢁⠄
⠀⠀⠀⠀⢀⣀⠈⠀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠂⠀⠀⠋⢰⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣥⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠤⠄⠀⠠⠽⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣰⣳⠁⠀⢜⢴⡤⠊⠜⣧⢀⠀⠸⠀⢀⠀⠀⠀⠀⠀⠀⠠⢘⢿⠂⠀⠀⢀⣀⠘⢄
⠀⠀⠀⠀⢄⠐⠀⠀⠀⠾⣿⣇⠀⠃⡀⠀⠀⠀⠀⠀⢠⠟⢫⠸⠀⠀⠀⠀⠀⢠⡟⣧⣶⣴⡜⢾⠀⠀⠀⠀⢀⠀⠀⠐⠰⣿⣀⠀⠙⢿⣧⠈
⠀⠀⠀⠀⠀⠉⠊⡀⠀⠀⠽⣿⣷⡄⠀⠀⠀⢢⠀⠀⢸⠀⠈⠀⠀⠀⠠⠄⡠⠀⡼⢣⠛⠀⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠒⣀⢛⣧⣤⠀⠉⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠈⠻⢻⣦⠀⡔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠠⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠁⡿⢱⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠀⢢⠀⠀⠀⠀⠀⠀⠀⠁⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠤⠤⠄⡈⠙⠲⡀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢲⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠿⢄
⠀⠀⠀⠀⠀⠀⢀⡡⠤⠐⢶⣂⠀⠀⢀⠀⠀⠑⢄⠀⠀⠀⠀⠉⠠⢀⠀⠐⠒⢿⡦⠈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣿⡓⠄⠳⡀
⠀⠀⠠⠴⠲⠞⠡⠊⠀⠀⠀⠘⠦⠄⠈⠳⣄⠀⠈⠦⡀⠀⠀⠀⠀⠂⠉⠀⣲⣿⣟⣰⡇⢢⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⠳⠄⠀⠀⠳
⠀⠀⠀⠔⠈⣀⡠⠂⡠⠒⠀⠀⠀⠀⠋⠴⡌⣓⠀⠀⠈⠙⠷⠀⠈⠀⠀⠀⠉⣻⣻⡎⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢻⡂⠀⠀⢀
⠀⠀⠀⠐⠋⠥⢱⡇⠰⢂⠀⠠⠄⠀⠀⠀⠀⠁⠉⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣿⡤⢢⠀⠠⠀⠀⠀⠀⠀⠀⢄⡀⠈⣭⠅⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠊⠀⠠⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⣽⣄⣀⣀⣤⠀⠀⠀⠀⠀⠄⠈⠙⣰⣀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠙⠙⠛⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠋⠩⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈

⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄
⠀⠀⠀⣰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣆
⠀⠀⡴⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣸⢦
⠀⢸⠀⢹⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡏⠀⡇
⠀⡸⡇⠸⣇⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣸⠇⢸⢇
⢸⡁⢳⠀⠹⣆⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣰⠏⠀⡞⢈
⡼⡇⠀⢳⡀⢹⣿⣄⣠⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⣤⣠⡿⡏⢀⡞⠀⢸
⢇⠘⣆⠈⢻⣆⢹⣅⠉⠣⣀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⣀⠜⢁⣬⡏⣰⡟⠁⣰⠃
⠈⣇⠘⢷⣄⠹⡋⠛⢄⡀⠸⣷⣦⢤⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⡤⣴⣾⠇⢀⡨⠛⢛⠟⣠⡾⠃⣸
⠀⠸⠳⣀⠙⢷⣿⣆⡀⠈⣲⣼⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣧⣶⠉⢀⣠⣾⡾⠋⣀⠞⡃
⠀⠀⢢⠈⠳⣦⣿⣁⡉⠑⠲⢿⣆⡀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⣠⡿⠖⠊⢉⣩⣿⣴⠞⠁⡜
⠀⠀⠀⠑⠶⢈⡙⢿⡷⠖⠒⠻⣿⣀⡀⠈⠑⢦⠀⠀⠀⠀⠀⠀⡴⠊⠁⢀⣀⣿⠟⠒⠲⢾⡿⠋⣡⠶⠊
⠀⠀⠀⠀⠀⠀⠀⢿⣀⡠⠖⠊⢛⣿⣤⡆⠀⠘⢆⠀⠀⠀⠀⡰⠁⠀⢠⣤⣿⡛⠓⠲⢄⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠔⠁⡼⢻⡷⢦⠄⠈⠲⠀⠀⠞⠁⠠⡴⢾⡛⢧⠈⠢⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠴⢥⣼⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣧⡬⠦⠶⠁

⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿
⠛⠛⠻⢂⣤⣤⡞⠻⠛⢧⣤⣤⣜⠻⠛⠛⣠⣤⣤⡿⠿⠿⢧⣤⣤⡼⠿⠻⢿⣤⣤⣴⠟⠛⠻⣤⣤⣤⡸⠛⠛⢓⣤⣤⣤⠿⠛
⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣯⠀⠀⠀⣿⣿⣿⡁⠀⠀⢺⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷
⣶⣶⣾⠏⠉⠉⣹⣶⣶⡎⠉⠉⠁⣶⣶⣶⠈⠉⠉⣷⣾⣶⡏⠉⠉⢹⣾⣶⣾⠉⠉⠉⣾⣾⣶⠏⠉⠉⢹⣶⣶⡏⠛⠉⠙⣶⣶
⠿⠿⠿⣆⣀⣀⡼⠿⠿⢇⣀⣀⣸⠿⠿⠿⣄⣀⣀⡿⠿⠿⣇⣀⣀⣸⠿⠿⢿⣀⣀⣰⠿⠿⠿⣃⣀⣀⡸⠿⠿⢧⣀⣀⣐⡿⠿
⠀⠀⠀⣾⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠁⠀⠀⢸⣿⣿⡇⠀⠀⢨⣿⣿⣿⠀⠀⠀⣽⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣶⣶⣶⡙⠋⠛⢳⣤⣶⡜⠋⠛⢻⣶⣶⡶⠟⠛⠛⠦⣤⠤⣜⠛⠛⢡⣦⣶⣼⢛⠙⠛⣶⣶⣶⠟⠛⠛⢳⣦⣴⡎⠛⠛⢻⣶⣶
⣿⣿⣿⠄⠀⣀⢸⣿⣿⡇⠀⠀⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⡏⠉⠀⠈⠈⠁⠉⠉⠻⠥⠄⡀⢸⣿⣿⡇⠀⠀⠘⣿⣿
⠀⠀⠀⣾⣿⣿⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠄⠀⢰⣿⣿⣯⠁
⣤⣤⣤⠿⠟⠟⢧⣤⢄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣤⣼⠛⠛⠷⣤⣤
⣿⣿⣿⠆⠀⠀⠨⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⢀⣿⣿
⠉⠉⠉⣿⣶⣾⡉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢵⣲⣾⡯⢀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣶⣷⣾⠈⠉
⣀⣀⣀⡿⠿⠿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣀⣈⣁⣼⠿⡿⢧⣀⣀⣘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣄⣀
⣿⣿⣿⡂⠀⠀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢘⣿⣿
⠛⠛⠛⣷⣤⣦⡾⣻⠟⣽⣯⣿⣿⠁⡛⠓⣴⣤⣤⡟⠛⠛⢷⣦⣤⡞⠛⠛⢻⣦⣦⣦⠐⠐⠀⣀⠀⡀⠀⠀⠈⠢⣵⣤⣴⠛⠛
⠀⠀⠀⢿⣿⣿⡚⠫⠀⣹⣿⣿⣧⠀⠀⢀⣿⣿⣿⠃⠀⠀⣸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⡀⢀⣿⣷⣷⡄⠠⠀⢄⣹⢿⣿⠂
⣿⣿⣿⡆⠁⠀⣼⣿⣿⡇⠀⠀⢸⣿⣿⣿⠁⠀⠀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⠀⠀⠨⣿⣿⣿⡅⠀⠈⢸⣷⣷⡇⠀⠀⢘⣿⣿
⠿⠿⠟⣣⣄⣠⡞⠻⠿⢣⣄⣤⣸⠿⠿⠿⣆⣀⣠⠻⠟⠻⢃⣄⣀⡼⠿⠻⠿⣤⣠⣴⠿⠟⠻⣤⣤⣤⡼⠿⠿⢳⣀⣄⣌⠻⠿
⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣶⣶⣶⡍⠉⠉⢱⣶⣶⡎⠉⠉⠙⣶⣶⣶⠉⠉⠉⣷⣶⣶⡏⠉⠉⢱⣶⣶⣾⠉⠉⠉⣶⣶⣶⡉⠉⠉⢱⣶⣶⡎⠉⠉⠩⣶⣶
⠿⠿⠿⢅⣀⡀⠼⠿⠿⣇⣀⣀⡰⠿⠿⠿⢀⣀⣀⡿⠿⠿⣇⣀⣀⣸⠿⠿⢿⣀⣀⡀⠿⠿⢿⣀⣀⣀⡸⠿⠿⢧⣀⣀⣈⡿⠿
⠀⠀⠀⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠁⠀⠀⢸⡿⣿⡏⠀⠀⢸⣿⣿⣿⠂⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣯
⣶⣶⣦⠟⠙⠛⢳⣤⣴⡾⠛⠛⢫⣤⣴⣤⠟⠛⠛⣷⣤⣴⣫⣛⣛⣱⣦⣶⣤⠛⠛⠛⣶⣴⣦⡙⠛⠛⢣⣴⣦⡾⠋⠛⢱⣦⣤
⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⠉⠉⢹⣿⣿⣿⠀⠈⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿

⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⡎⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢳
⠀⡦⣀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣀⢶
⠀⢷⠈⢇⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡸⠁⡞
⢠⣜⡆⢌⢆⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⡰⡁⣰⣣
⠀⢣⠙⢆⠪⡳⣄⠀⠈⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠁⠀⣠⢞⠄⡴⢋⡜
⢠⣀⠳⡄⠑⢌⡠⡽⠦⣄⡀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣠⠴⢯⢄⡡⠊⢠⠞⣀
⠀⠳⡉⠛⠦⡐⠍⠙⠪⣒⠭⢓⣦⣄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣠⣴⡚⠭⣒⠕⢋⠩⢂⠴⠛⢉⠞
⠀⠀⠈⠢⣄⠈⠓⠿⣭⣉⡉⠛⡷⠊⠳⡀⠀⢹⠀⠀⠀⠀⠀⠀⡏⠀⢠⠞⠑⣾⠛⢍⣉⣭⠿⠚⠁⣠⠔⠁
⠀⠀⠀⠳⣞⠛⠒⠿⠯⢍⣈⣋⡺⣗⡂⠹⡄⠸⡆⠀⠀⠀⠀⢰⠃⢠⠏⢐⣺⢟⣙⣁⡭⠽⠷⠒⠛⣳⠞
⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⡴⢋⡦⢂⡿⣥⡜⢆⢱⡀⠀⠀⢀⠏⡴⢣⣬⢿⠐⢀⠙⢦⠤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠕⢹⢡⠾⢠⡎⡟⡹⠛⠳⠀⠠⠟⠛⡏⢻⢱⡌⠷⡌⡏⠪⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢧⠊⢧⢳⠃⠀⠀⠀⠀⠀⠀⠘⡞⡼⠑⡼⠈⠃




⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⡷⡀
⠀⠀⠀⠀⠀⣇⠙⣄
⠀⠀⠀⠀⡀⠸⡄⠈⢧⡀
⠀⠀⠀⠀⣷⡄⠹⡄⠀⠱⣄
⠀⠀⠀⠀⢱⡘⢦⡙⣆⠀⢌⠳⣄
⠀⠀⠀⠀⠀⢧⠀⠙⢮⣳⡀⠱⣮⡳⢄⡀
⠀⠀⠀⠀⠀⠈⢧⠀⢀⠙⢿⣦⡙⢿⣷⣽⡢⣄⢲⡦⣤⡀
⠀⠀⠀⠀⢹⣦⡈⢣⡈⠳⣦⣌⡻⣦⡻⣧⡉⢈⠻⣧⢀⣝⣦
⠀⠀⠀⠀⠀⢳⡙⢦⡱⣄⠈⢻⣿⣶⣽⣾⣿⣬⡿⡷⠿⠿⠿⢷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢳⡄⠙⠻⣷⣌⠙⢿⣿⣦⡀⣶⡟⢻⣄⢙⣷⣄⢑⣿⣯⣙⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣌⡙⠿⣦⣙⠿⡿⠾⣿⠷⠿⠾⣏⠛⢿⣟⣻⡿⢿⣶⡍⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡈⢳⣌⠛⣿⣿⣿⠷⠾⠷⡿⠷⣄⠐⣾⡿⠾⢻⣟⢻⣦⣤⣀⠀⠀⠉⣳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡓⠿⣷⣌⠻⢿⣷⣄⡐⠿⣷⣬⠿⢿⣦⣄⣈⣻⣿⣛⣷⡶⠖⠂⠀⠈⠻⣮⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠙⠢⣬⣙⡛⠷⢾⡷⠤⣌⣛⣯⣉⣀⣻⡿⣯⣿⣿⣟⣁⣀⠀⠈⣧⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⠻⣿⣿⠛⠋⠩⣵⣶⠞⠉⣾⣿⣟⣉⣀⣬⢿⣾⣏⡿⣷⡦⠀⢻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣝⡻⢶⣬⣍⣛⠟⠛⢻⡿⠃⠾⠿⠏⣠⣴⣏⣴⣫⢦⠀⣳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡒⠒⠚⢛⣓⣶⣦⣤⡤⣾⣿⣤⡤⠲⣶⠋⠸⠿⠳⡿⠿⢺⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣉⣙⣿⣉⣤⣽⣿⣿⢳⣾⣯⣤⡴⠚⡇⢁⣠⠊⣀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠹⣿⢁⣠⣽⡏⠿⣃⡌⠿⣻⣿⣶⢿⣄⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠒⠚⢋⡟⠙⣻⡴⠚⣻⡷⣾⢃⣴⠇⢼⡟⢇⢀⣳⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⢸⠧⠚⠁⣿⣰⢻⣤⠞⢦⡟⠼⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠝⢦⡘⣷
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠢⡙⢾⣷⣄
⠀⠘⢿⡓⠦⣄⡀⠀⠀⠀⠈⢧⡈⢢⡙⢿⣷⣄
⠀⠀⠀⠙⢦⡐⠭⣙⠲⠤⣄⣀⠙⢦⡈⠢⢌⠻⢟⡶⣤⣄⣀⡀
⠀⠀⠀⢰⡦⢬⣳⣦⣉⠒⠤⣉⠉⠒⠻⠶⢤⣉⠒⠬⢁⡚⠉⠍⠛⠛⠛⣻⠛⠛⢛⡛⠛⠛⠶⠶⢦⣤⣄⣀⠀⡀
⠀⠀⠀⠀⠙⠦⣄⠨⢉⠛⠲⠦⣍⣐⠒⠤⠄⣈⠙⠒⠦⠤⢉⣀⡀⠠⠤⠽⢦⣀⠀⠐⢯⡉⠉⠐⠒⠀⠉⠙⠻⠛⢤⡀
⠀⠀⠀⠀⠠⣤⠬⣽⣦⣬⣁⠒⠤⢈⣉⡓⠲⠦⠤⣍⣬⣀⡐⣇⠐⠀⠤⠄⠸⣉⠙⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤
⠀⠀⠀⠀⠀⠈⠳⢦⣐⠈⠍⣙⠓⠶⠦⢬⣍⣀⣒⣂⣀⠀⡀⠈⢙⡗⠂⣀⠀⣈⣱⠒⠛⠓⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠈⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣓⣶⣬⣍⣀⣐⡒⠂⠠⠭⠭⠭⠭⠉⠀⣉⣒⣤⢤⣤⡠⠽⠋⠁⠀⠀⠀⠀⢀⣧⣀⣀⠀⠈⠲⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⠀⠤⠉⢉⣉⣉⣙⣋⣉⣉⠉⠩⠅⠀⢀⣀⣳⠶⠀⠀⣀⠀⠀⠀⣀⣫⣀⡀⠉⠀⠀⠀⢣⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⢚⠋⠍⢰⣁⠂⠉⣁⠀⠀⠀⢎⡀⣀⣈⠉⠁⠀⠀⠀⢸⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢥⣄⣒⣒⣒⡒⣒⣒⣂⣉⣉⣤⠤⠖⠊⢉⡉⠈⣣⠴⠖⠁⠀⣏⢉⣉⠀⠀⢀⠄⠀⠈⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⠛⠛⠉⠉⠉⠤⠄⠀⠒⠐⣈⣠⠔⣋⠅⢒⣈⠤⠖⠺⡉⢁⡀⠀⢸⣀⡄⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⢒⡖⣛⣛⡩⢽⠟⠑⠈⣠⠖⢋⡠⢐⣠⠤⢺⢋⣥⠀⠀⣌⠀⡀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠶⢚⡟⡡⠊⣡⡔⢋⠔⢂⣼⠃⢀⠀⡀⠈⢻⢁⡄⠀⠀⠀⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣤⡴⢃⠔⢁⡴⢃⠌⣩⠓⢾⠁⠀⠈⢹⣀⡞⠀⢠⠄⠀⠀⠈⠙⠓⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡼⠑⣡⣴⢋⡴⢃⡴⢁⡜⣹⠆⢰⡀⠀⠉⢇⣠⠞⢆⠀⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠚⣱⠣⣊⡴⣻⡡⢋⣴⢃⢊⡼⡉⣹⠀⢨⢱⢸⠈⢻⠓⢤⡜⠢⣴⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⠀⠷⠶⠋⢸⡤⠞⡇⢠⡇⠀⣿⡘⣸⢱⢸⣇⣸⡇⢰⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⠻⡼⠁⠳⠛⠧⠞⠀⠁⠑⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⠺⠿⣌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⠿⠗⣤⡀
⠀⠀⠀⠀⠀⠀⡔⠑⢁⣴⣤⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢃⣤⣤⡉⠙⢦
⠀⠀⠀⠀⠀⣮⣤⣿⣸⣿⢿⣆⢌⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡥⣼⡿⣿⣇⣷⣤⣧
⠀⠀⠀⠀⠀⢠⡁⣸⣧⣠⣶⣟⢱⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣻⣶⣅⣼⣅⢸
⠀⠀⠀⠀⠀⠸⣿⣿⠛⢸⡿⢉⣌⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠛⣥⡙⢿⡇⠟⣿⣿
⠀⠀⠀⠀⠀⠀⡟⠛⢳⣾⣄⢨⣵⣷⡌⣿⣿⣷⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⣾⣿⣿⣡⣾⣮⣀⣸⣷⡟⠛⣿
⠀⠀⠀⠀⠀⠀⢻⣴⠟⣿⢿⡿⡟⠛⢉⣋⡻⣿⣃⠈⢣⠀⠀⠀⠀⠀⢀⠜⠀⣚⣿⢛⣙⡋⡛⡻⣿⡿⡿⠿⣤⡏
⠀⠀⠀⠀⠀⠀⠈⡿⣦⣿⣀⢀⣝⣷⣿⡟⢣⣿⣿⡄⡀⢣⠀⠀⠀⠀⡎⢀⢸⣿⣿⡘⢻⣿⣾⣯⠀⣀⣷⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠸⡈⢿⣿⣿⣿⡿⣿⣯⡙⠿⠷⠟⢻⣿⡇⠀⠀⢸⣿⠏⠻⠾⠿⢍⣽⣿⢿⣿⣿⣿⡿⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⣿⣿⣿⡿⡍⠉⠀⢲⣤⣀⠀⢿⠃⠀⠀⠸⡟⠀⣀⣤⡖⠀⠙⡁⢿⣿⣿⣿⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⡟⠈⢈⠁⠙⣦⣠⡴⣿⣿⣆⣚⡄⠀⠀⢰⣓⣸⣿⡿⣦⣄⡴⠋⠈⠑⠉⣫⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⣆⠀⠰⢠⣼⣷⣿⣯⠻⠉⡏⠁⠀⠀⠈⢹⠈⢟⣿⣿⣾⣡⡤⠎⠀⡰⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣦⢿⣶⣍⣿⢿⡟⢻⢶⠇⠀⠀⠀⠀⠸⡴⡟⢻⡿⣷⣩⣶⣷⣾⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⡻⣿⣿⣧⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⣿⣿⢟⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣷⣟⠻⠯⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠿⠛⣻⡞⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡿⣷⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣾⢿⣃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢻⣠⢹⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣵⡇⣄⠟⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡌⠛⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⠻⠰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢵⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄

⠓⠖⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠖
⠀⠒⠉⠀⠀⠀⡀⠀⠀⠄⠈⠂⠀⠦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠆⠀⠊⠀⠄⠀⠀⡀⠀⠀⠈⠓⠂
⠀⠈⢋⡥⢒⠁⢀⠀⠀⠀⠁⡀⠀⠐⠀⠄⠀⠀⠉⠃⠀⠀⠋⠁⠀⠀⠄⠐⠀⠀⡀⠁⠀⠀⢀⠀⢑⠢⣍⠃
⠀⠀⠀⠈⠉⠒⠓⣂⡀⠀⠀⠀⠐⠂⠀⠄⠠⠀⠀⠂⠀⠀⠂⠀⠠⠀⠄⠀⠒⠀⠀⠀⠀⣀⡒⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣶⣦⣴⣲⠄⠀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠂⠀⠀⠲⣄⠀⠀⠀⠀⠀⠐⡟⣕⢿⢻⣿⠇⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠐⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠠⠊⠀⢀⣤⣶⠛⣻⣿⠶⣦⣄⡀⠑⠄⠀⠀⠀⠀⢹⢣⢷⡼⣿⣷⠀⠀⠀⠀⡠⠊⢀⣠⣴⠶⡿⣿⠓⣶⣤⡀⠀⠑⠄
⠀⠀⠔⠁⢀⠶⢿⠁⣿⡰⢿⣌⣼⡏⢃⣟⣦⡀⠁⡀⠀⣴⣮⣯⣿⣍⡹⣷⡵⠀⢀⠌⢀⣴⣿⡉⢹⣧⣀⡿⢆⣿⠈⣿⠶⡀⠈⠢⡀
⠀⠀⠔⢠⣿⣧⣼⠶⢫⠃⡺⠉⣼⢳⠏⣇⣰⠻⣆⠐⡀⠧⡊⠐⠙⢁⠘⠟⠁⢀⠂⣰⠟⣆⣸⠹⡎⣧⠉⢷⠈⡜⡶⣧⣼⣿⡄⠢⠈
⠀⠀⠂⡸⣿⣯⠋⣆⡾⢷⢡⡿⢉⡦⢪⠙⢠⣆⣩⠀⠁⢰⣯⡢⡴⡿⣿⣽⣏⠏⠀⣏⢰⡀⠋⡕⢤⡉⢿⡊⡾⢷⣰⠉⣽⣟⠇⠐
⠀⠀⠀⠣⢻⡙⢶⡌⠱⡌⣸⡀⣬⠁⡜⣤⢃⠙⣹⠠⠂⢸⡝⢿⣦⡫⣵⢸⠀⠐⠄⣏⠋⡘⣠⢣⠈⣥⢀⣇⣡⠎⢡⡶⢋⡟⡜
⠀⠀⠀⠀⠈⣷⢑⢝⠶⣈⠋⠳⠛⣦⠁⣀⡿⣴⠏⠀⠀⢸⡨⡗⢿⢿⣮⡸⡀⠀⠀⠹⣦⠿⣀⠈⣴⠛⠞⠙⣁⠶⡫⡊⡾⠁⠠
⠀⠀⠀⠃⠀⠈⠈⣷⣅⠈⠻⣄⣸⠀⣰⠉⢀⠁⢠⠀⢠⢾⠷⢾⣿⡴⢝⠿⡀⠀⠀⡆⠈⡀⠉⣆⢀⣇⣠⠟⠁⣨⣾⠁⠁⠀⠘
⠀⠀⠀⠀⠀⠘⡄⠈⠉⡙⠦⣌⢳⡄⠁⣷⣾⠀⠀⠀⠈⠉⠉⣩⡯⠤⢄⠉⠀⠀⠀⠀⠀⣷⣾⠈⢠⡞⣁⠴⢋⠉⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠘⣦⣄⠈⢷⣄⡈⠻⣦⡿⡈⠀⠀⠀⠀⢠⣾⣞⣥⢾⠷⣏⠶⠀⠀⠀⠀⢁⢿⣤⠟⢁⣠⡾⠁⣠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢜⠟⢦⠈⠎⢙⢗⠾⣧⡀⠘⣦⣀⠀⣮⣿⠐⣿⡙⣮⣭⠆⠀⢀⣴⠃⢀⣼⠷⡲⡛⡱⠁⡴⠻⠣
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠈⠃⢷⡀⢣⡁⠘⣷⣄⢁⠀⠀⢰⣿⣏⢟⢁⠀⣿⡆⠀⠀⡘⣠⣾⠋⢈⡜⢀⡾⠘⠁⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢈⢣⢠⡀⢹⢦⣿⡦⡘⡆⠙⠆⠀⠀⠑⠽⠷⡬⠽⠟⠀⠀⠰⠋⢰⢃⢴⣿⡴⡏⢀⡄⡜⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⡉⠙⠈⠣⠀⠀⠀⠀⡠⣲⠎⣑⣢⣀⡀⠀⠀⠀⠌⠁⠋⢉⡜⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠟⢆⠈⢦⡁⠀⠀⣸⣿⠗⣾⠩⡿⣇⠊⠀⠀⢌⡴⠁⡠⠻⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠳⡄⠓⠆⠀⢛⣿⡨⣿⡫⢟⢟⠁⠀⠐⠎⢠⠞⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣆⠀⠀⠘⣿⢧⣹⣉⡴⣣⠇⠀⠀⣰⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢡⠘⠶⠀⢀⠈⢙⣋⢷⡚⠁⠀⠀⠾⠃⡄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠃⢀⠀⠯⢟⢻⢷⣶⠁⠀⠀⠀⠀⠘⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⡞⣿⢸⣿⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢯⣿⣸⢿⡀⢀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣃⡿⠛⣿⠶⣾⠞

⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠳⣌⠳⢤⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⡤⠞⣡⠞
⠀⠀⠀⠀⠀⠀⠈⠻⡿⢦⣔⢭⣛⣯⠓⢦⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⡴⠚⡽⣛⡭⣢⡴⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠲⣿⣦⡈⠑⡾⣿⡷⣦⣘⠿⣿⡓⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢞⣿⠿⣃⣤⢾⣿⠷⠊⢁⣴⣯⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠓⢮⣵⣿⣦⣌⡙⠲⢷⣄⠀⠈⠉⠙⠓⢦⣄⠀⠀⣠⡴⠚⠋⠉⠁⠀⣠⡾⠖⢋⣡⣴⣿⣾⡵⠚⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⠶⣤⣰⣿⣦⣍⡛⠒⠮⠷⣦⡀⠀⢰⠋⠙⠂⠰⠋⠙⡆⠀⢀⣴⠾⠵⠒⢛⣩⣴⣿⣆⡥⠶⣿⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠈⠹⢮⣍⡓⠶⠬⢬⣽⣦⡘⣆⠀⠀⠀⠀⣰⢃⣴⣯⡭⠭⠶⢚⣩⡵⠏⢁⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣟⡛⠒⠶⣿⣟⣛⠿⠿⠿⣿⣾⣆⠀⠀⣰⣷⣿⠿⠿⠿⢛⣻⣿⠶⠒⢛⣻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣛⠒⠶⠿⢿⣭⣭⠿⠿⣿⡿⠀⠀⣿⡿⠿⠯⣭⣭⡿⠿⠶⠒⣛⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣗⣒⣛⣛⣛⣿⣻⠟⠁⠀⠀⠈⠻⣟⣿⣛⣛⣛⣒⣻⣯⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⢀⠈⠫⡑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢊⠝⠁⡀
⠀⠀⠀⠀⠀⠀⠙⢷⡚⠷⢄⡀⢙⢖⠢⢤⡄⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⢠⡤⠔⣺⡋⢀⡠⠾⢓⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠓⢟⠶⣄⣀⠙⠻⣟⠢⣵⣤⡉⠘⠻⣕⠢⢼⢢⡀⠀⠀⠀⠀⠀⠀⢀⡔⡯⠔⣪⠟⠋⢉⣤⣮⠕⣻⠟⠋⣁⣠⠶⡳⠞
⠀⠀⠀⠀⠀⠀⠀⠲⣤⠵⣦⣈⠉⠛⣞⡓⢭⣲⣬⣙⠒⠺⣆⠈⢸⡇⠀⠀⠀⠀⠀⠀⢸⡅⠁⢰⠗⠒⣉⣡⣖⡭⢚⣳⠛⠉⣁⣴⠮⢤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠉⠒⢤⡭⠶⢽⣦⣌⣉⣂⢻⡄⢸⠃⠀⠀⠀⠀⠀⠀⠘⡇⢠⡏⣐⣉⣡⣴⡯⠶⢩⡴⠒⠉⢁⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣙⠓⠒⠤⢭⣶⡤⠭⢲⡶⠤⠌⣷⡜⢦⡀⠀⠀⠀⠀⢀⡴⢣⣾⠁⠠⢶⡖⠭⢤⣶⡭⠤⠒⠚⣋⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠶⠶⠤⠤⠽⠶⠦⣽⣿⣭⣭⣽⣦⡙⢦⠀⠀⡴⢋⣴⣯⣭⣭⣿⣯⠴⠶⠯⠥⠤⠶⢶⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣰⣖⣊⡭⢥⣴⣊⡽⣫⣖⡩⡿⢮⠇⢸⡵⢿⢍⣲⣝⢯⣑⣶⡬⢭⣙⣲⣆⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠡⠟⠩⠟⠿⠋⡧⠋⠀⠀⠑⢼⠑⠿⠻⠍⠻⠌⠁⠀⠀⠀⠀⠉

⠀⡀⠀⠀⠀⠀⠀⠤⠲⣆⠀⠀⠀⠀⠀⠀⣴⠒⡔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⢺⠀⠞⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠶⡤⠦⠤⠀⠐⠤⣠⠒⠄⠒⡇⢂⠌⠀⠀⠑⠝⢒⠠⠲⡄⠤⠂⠀⠤⠴⢤⠖⠂
⠀⠀⠀⠀⠁⠀⠠⠀⣀⡀⠈⠀⠀⠀⠉⠀⢀⣀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠶⠤⣁⠀⠀⢠⢀⣀⡤⠤⠈⠀⠀⠀⠁⠤⢤⣀⡀⡄⠀⠀⡈⠦⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠉⠉⠉⠀⠀⠤⠤⣄⢀⡤⠤⠄⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠖⠀⠤⠀⠤⠄⠢⠀⠤⠐⠀⢢⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⢀⡀⠀⠀⠀⠠⠠⠒⠂⠀⠀⠀⠒⠂⠠
⠀⠀⠀⠀⠀⠀⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡗⠀⠀⠰⡘⠐⠀⠀⠐⠐⠰⠀⠀⠉⠀⠐⠐⠚⠉⢉⠀⠀⠀⠀⢈⠁⠙⠒⠐⠈⠈⠁
⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡆⠀⠀⢀⣦⠠⠐⢀⣣⢀⠀⠀⢀⠤⠤⠤⠤⠴⠃⣸⡀⢠⣸⠈⠢⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠉⠁⠀⠠⢄⠁⠂⢶⡄⣀⡔⣰⢇⡟⢘⡆⢷⡁⣄⡀⣴⠔⠂⣁⠤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⡀⠆⠄⢀⠀⡀⠈⠉⣄⡈⠉⢁⠠⠀⠉⠛⠢⠆⢎⢼⠛⣉⠖⠁⠀⠓⣊⠙⢿⣘⠆⠄⠚⠋⠑⠤⢈⠉⠉⣠⠌⠁
⠀⠀⠂⡱⠊⠐⠁⠀⠀⠀⠐⠢⡄⠀⠆⠂⠀⠀⠀⠘⠆⠑⢌⠂⠀⠀⠉⠁⠢⣴⣂⣤⢠⠀⠤⠰⠲⠚⠃⠀⠀⠀⠀⠀⠛⠲⠒⠠⠄⢄⣤⣅⣲⡴⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢡⡈
⠀⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⡄⢤⡀⠀⣀⡄⢠⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠷⢎⣽⢹⣏⡣⠚⡁⠀⠀⢸⡉⢧⡀⠀⠀⢸⡟⣷⠀⠀⠀⠰⡟⢾⠀⠀⠀⢀⠞⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡮⣸⠨⡎⣇⡴⠁⠀⢸⠉⢧⠀⠱⡄⠀⠈⣷⣿⡖⠀⡀⣾⣧⡏⠀⠀⣰⠋⢀⡞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠏⠀⡟⡜⠀⠀⠀⡼⢦⠈⠣⡀⠘⠄⠀⢻⣿⣶⡗⢧⣾⢿⡇⠀⡐⠁⢠⠎⢀⡜⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠰⡿⠀⠀⠀⠀⢳⡀⠑⢄⢈⡺⣌⠰⢬⡀⠉⠀⠈⠉⣈⢴⠖⣠⢇⢁⠠⠋⣠⠏
⠀⠀⠀⠀⠀⠴⣿⣄⡀⠈⢄⠀⠀⡔⠁⢀⣴⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠕⣚⠦⠴⣏⠉⠂⠄⣟⠲⠤⢤⣵⣊⠙⢃⠙⢦⡀⢠⡞⢁⡜⢋⣑⣥⠤⠤⢚⡿
⠀⠀⠀⠀⠼⢶⡀⠙⢽⣦⡦⠂⠪⣦⣶⠟⡉⣰⠶⠆⠀⠀⠀⠀⠀⠀⣈⣀⡞⣹⡇⠀⡿⡝⠤⡦⠌⢛⠒⠒⢚⣩⣄⡘⠅⢀⡇⢿⠀⡸⣐⣠⣝⠒⠒⢒⡏
⠀⠀⠀⢀⠀⠂⢹⠶⣧⡜⠁⠀⠀⠘⢤⣿⠞⠉⠄⠄⡀⠀⠀⠀⠀⠀⣁⣩⣴⢳⠄⠀⢰⡙⠶⣤⡤⠈⠙⠻⣉⡤⠋⢒⠩⡜⠀⠸⢧⢙⠆⠁⢄⣉⠟⠋
⠀⠀⠀⡞⠙⠒⢦⣤⣰⡆⠀⠀⠀⠀⢰⣀⣤⠖⠒⠙⡇⠀⠀⠀⠀⡀⠉⠉⢐⡼⠀⠀⠈⢣⣄⠀⠀⠠⡤⠀⠀⠙⠚⠓⠶⠛⠀⠐⠳⠶⠛⠛⠋
⠀⠀⢠⡇⠇⠀⡄⠂⢸⡆⠀⠀⠀⠀⢠⣆⠀⡂⠀⠆⢳⠀⠀⠀⣸⣥⠤⠶⠋⠀⠀⠀⠀⣠⠬⢼⡃⠓⠛⠂⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⢈⠋⠤⠳⢣⠬⡼⠀⠀⠀⠀⠀⠸⡍⢤⠳⠖⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡠⠆⠌⠁⡜⡏⠀⡏⡇⠈⠤⠲⣀⠙⠦⡀
⠀⠀⠀⢆⠀⢨⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⡁⠀⠣⣤⠒⠄⠏⡈⡅⠀⡍⢈⠅⠔⠂⡤⠓⠀⠌⢢
⠀⠀⠀⠈⣰⠚⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢓⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠜⠈⢇⡼⠠⠢⡀⠉⠁⠀⠉⡇⣠⠣⠘⣄⡽⠀⣇⣈⡄
⠀⠀⠀⠰⣿⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⡼⠀⠀⠀⠀⠀⢀⡠⠔⢀⡠⠁⠈⠀⡈⠀⡘⢀⡉⠁⠀⠀⠀⠉⢡⠀⡄⠈⠄⠈⠀⠱⣄⠑⠤⣀
⠀⠀⠀⠀⠾⣆⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⣾⠇⠀⠀⡤⠖⠊⣁⣠⡶⠋⣠⠎⢀⡼⠀⡴⢧⡼⠀⠀⠀⠀⠀⠀⠘⢤⠼⣄⠘⣦⠀⢣⣌⠳⢦⣄⡉⠒⠦⣄
⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠙⠒⠉⢏⡥⠔⢿⡡⠔⠉⠣⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠊⠙⠦⣉⡗⠦⢍⡿⠉⠒⠁

⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⢠⡈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠
⠀⠀⠀⠀⠀⢳⣌⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣴⠃
⠀⠀⠀⠀⠀⠀⠙⣷⣝⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣵⡿⠁
⠀⠀⠀⠀⠀⠘⢦⣈⠻⣷⣝⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣵⡿⢋⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠙⢷⣬⣻⢿⣮⣿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⢟⣯⣾⠿⣫⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠛⢷⣿⣿⣿⣾⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⠟⠋⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣦⣭⣟⣻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣛⣯⣥⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢛⣛⣻⣯⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⣿⣛⣛⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣛⣭⣽⡿⣿⣿⣿⣿⡿⣿⠁⠀⠀⢹⡿⣿⣿⣿⣿⡿⣿⣭⣝⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⡀⠈⠀⠀⠀⠈⠀⣸⣿⣿⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣼⠋⣿⠉⠋⠀⠀⠀⠀⠀⠘⠋⢻⡏⢻⠄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠀⠀⠀⠀⠀⣠⣤⣤⡤⢤⣤⠤⠶⣦⣤⣤⣤⣤⠴⠖⠀⠀⠀⠀⢀⣠⢶⡚⡟⣻⣿⣿⣯⡷⠚
⠀⠀⠀⠀⠀⠀⠉⠻⣭⠭⠭⠭⠭⠭⠍⠉⠁⠀⠀⠀⠀⠀⣸⣁⣦⠶⣟⠻⡍⣿⣜⣛⣒⣒⡒⠛⠀⠀⠀⠀⠀⢺⡫⡝⢏⣯⣽⣛⣛⣓⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡭⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⢮⣗⠿⠍⠛⠳⠾⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠧⣟⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈

⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⠴⡶⠶⡶⠶⠖
⠀⠀⠀⠀⠀⣀⣴⢏⣾⣷⣿⠿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⢀⡼⣳⣾⣿⡿⠿⢭⡭⠝⠋⠉
⠀⠀⠀⠀⠀⣿⣴⡵⣝⢶⡭⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⠀⣭⣶⣟⠾⠭⠍⠛⠁
⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢋⣤⠆⠀⠀⠀⠀⠀⡘⠇⣾⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⣴⠾⢋⣡⠄⠀⠀⠀⠀⢸⣟⡸⢏⣾
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠓⢿⣥⠾⢛⣡⠀⠀⠀⠀⣼⡇⣻⠕⢟⣥⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠾⣛⣛⣛⣛⣛⣛⣿⡿⢿⠟⠋⠀⠀⠀⠀⠀⠀⣿⣚⣋⡁⠀⠀⠀⣠⡾⢓⡖⣨⡭⠔⠀⠀⠀⠀⢋⣽⣿⣿⣿⡿⢛⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⢘⣻⡷⢾⣭⠭⠍⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⢴⠿⠭⠁⠀⠀⠀⠀⢓⡚⣃⡶⠖⠀⠀⠀⠀⠀⠀⠘⢿⣻⠿⠏⣩⣾⠿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛

⠀⠀⠀⠀⠀⠀⣴⢟⡷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⢏⣾⢏⣲⣯⡟⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠞⣯⡿⢍⣽⡯⠭⠭⠭⠭⠭⠭⠭⠉⠀⠀⠀⣠⣾⢿⡿⢟⣛⣻⣛⣿⠿⠿⠿⡿⠛⠋
⠀⠀⠀⠀⠀⠉⠛⢬⠻⢏⣁⠴⣿⡳⠿⠭⠛⠓⠒⠂⠀⠀⠈⣯⣵⣿⠋⣤⣭⡭⠉⠉⠉⠀⠀⠀⠀⠀⠀⠳⠿⠯⠻⠯⠝⠷⠯⠍⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠻⢿⡾⣟⣴⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⣠⡟⣰⣿⠿⠏⣼⣟⣛⣛⣛⠿⠿⠛⠁⠀⠀⠈⠽⣿⣿⣿⣿⣯⢭⣭⣽⣿⣛⡛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠐⣾⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣩⢡⡝⠷⢍⡑⠿⠶⠮⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⣭⠟⠳⠖⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠐⠠⡀
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⢀⠇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⡀
⠀⡘⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢃
⢠⠇⠀⠀⠀⠀⠀⢀⠎⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠱⡀⠀⠀⠀⠀⠀⠸
⢸⠀⢠⠀⡄⢠⢀⠾⣠⠊⡐⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠑⣄⡷⡀⡄⢀⠀⡄
⡏⠀⡌⢠⠁⡦⠌⠀⠘⠺⣤⢣⢃⢂⠀⡀⢸⢀⢆⠆⠀⠀⠀⠀⠀⠀⠰⡰⡀⡇⢠⠀⠐⡐⡜⣤⠗⠃⠀⠡⢴⠀⡄⢡
⡇⠀⡇⢸⠔⠀⠀⠀⠀⠀⠈⠙⠛⠞⠷⠳⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠞⠾⠳⠛⠋⠁⠀⠀⠀⠀⠀⠢⡇⢸
⡇⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸
⡇⠀⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾
⣧⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠁⠀⢌⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⡡⠀⠈
⠀⠀⠀⠈⢦⡑⠈⠛⠔⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠢⠛⠁⢊⡴⠁
⠀⠀⢀⠀⠀⠙⠦⣼⣜⡮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⢵⣣⣧⠴⠋⠀⠀⡀
⠀⠀⠀⠢⡠⢄⠢⠈⢙⢻⣮⣮⠙⠦⡠⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⢄⠴⠋⣰⢵⡛⡋⠁⠔⡠⢄⠜
⠀⠀⠀⢀⠈⠀⢝⠦⣤⡠⣍⠊⠑⠦⣄⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣤⠴⠊⠑⣩⢄⣤⠴⡫⠀⠁⡀
⠀⠀⠀⠀⠁⠠⡢⢄⣀⠉⠀⢝⠲⢤⣀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣀⡤⠖⡫⡀⠉⣀⡠⢔⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⡛⠛⠲⠤⣄⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣠⠤⠖⠛⢛⣫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠦⢤⣤⡨⢤⡤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢦⡤⢅⣤⡤⠴⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠤⠑⡲⠶⠆⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠰⠶⠖⠊⠤⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⢶⣖⣒⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣒⣶⡶⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠛⣛⣓⡖⣭⣤⠀⠈⠢⡅⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⣤⡭⢲⣚⣛⠛⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠩⣉⣖⡤⠤⠀⠀⠀⠴⠃⠀⠀⠐⠦⠀⠀⠀⠤⢤⣺⣉⠉⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢭⣭⣗⣓⡀⠀⠒⡲⠀⠀⢖⠒⠀⢀⣚⣾⣭⡭⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠫⠥⠒⠈⠀⠀⠀⠀⠁⠒⠬⠻⠖⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠄⠀⠈⠁⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⣠⠔⠚⠹⣃⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⣹⠉⠑⠢⣀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⠞⢁⡠⠊⠐⢇⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⢤⡝⠈⠓⢄⠈⢳⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⡴⡏⢠⠎⢠⠊⢔⠼⠦⡄⠀⠀⠈⠓⠒⠢⣄⠀⢀⡤⠒⠉⠉⠀⠀⡀⢠⠞⠮⡢⠱⡀⢱⡀⢻⢆⡀⠀⠣⡀
⠀⠀⠀⠀⠀⢠⠃⠀⣴⠋⣨⡗⣏⣰⠇⢠⠃⠪⢢⡛⡳⠴⢆⡤⠖⠒⠈⠁⠈⠉⠑⠲⢤⡴⠶⠏⢳⡀⡁⢱⡀⢹⣀⡗⢫⡀⠹⡆⠀⠱
⠀⠀⠀⠀⢠⠃⢠⠔⠋⣴⠇⣠⠏⡹⢒⡿⣤⣇⢠⠁⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡆⢰⡀⡷⡼⢿⠛⡌⠳⡄⠹⣄⠙⢦⡀⠱⡀
⠀⠀⠀⢀⠃⢠⠞⢀⡼⠃⡰⠃⡴⢃⡾⠤⡏⢸⠋⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡏⠹⡀⡓⠬⢧⡘⣆⠙⣄⠙⣦⠀⠣⡀⠡
⠀⠀⠀⠂⣠⠋⢠⠞⢀⡜⣁⠜⠓⠉⠀⠀⠙⠻⢤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠴⠋⠁⠀⠀⠉⠚⠦⣈⣦⡈⢧⡀⠹⡀⠠
⠀⢀⣢⠜⠳⠖⠛⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠒⠛⠦⣑⠄

⠀⠀⠀⠀⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠙⣿⣦⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣀⣴⣾⡟
⠀⠀⠀⠐⣦⣽⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣤⠖
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣰⣿⣷⣄⠀⢠⣶⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠉⠀⠉⠙⠿⠿⠋⠀⠘⠻⠿⠟⠉⠀⠈⠛⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⡿⠇⠀⠀⠀⠀⠀⠀⠿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⡀
⠀⠀⠀⣠⣴⣿⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣿⣷⣤⡀
⣀⣐⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣓⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠰⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢀⡤
⠀⠀⠀⠀⠀⠹⢦⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣰⠇
⠀⠀⠀⢠⠀⠀⢡⡳⣄⠘⣝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⠇⢠⣴⡏⠀⣴
⠀⠀⠀⠈⢳⣄⠀⠹⡈⠣⡘⢎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣴⣿⠏⠀⢸⡏
⠀⠀⠀⠀⠀⠫⡳⣄⠈⠢⡈⠢⣧⠈⢷⡀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⣻⣿⣿⣿⣿⣷⢋⣴⣡⠟
⠀⠀⠀⠀⠀⠀⠙⢌⠳⢄⠘⡄⠀⠀⣤⢫⠂⣽⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⣼⣿⣽⣿⣻⡿⢵⡿⣻⠏
⠀⠀⠀⠀⢠⣄⠀⠈⠳⢄⠑⠻⣄⠠⣌⠃⠱⡄⠑⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣽⣿⣿⣷⣿⣿⣻⣻⣷⣿⡿⠁⢀⣤
⠀⠀⠀⠀⠀⠙⢅⠢⢄⡀⠱⡀⠈⠣⡹⣗⠀⣀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣩⣿⣵⣿⣻⠿⢋⣠⣶⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⠁⠚⢦⠀⠘⣬⡀⢀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣻⣯⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠉⠢⡀⠑⢦⡈⠢⣀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠟⠋⢡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⡁⠒⠬⠶⣄⠈⠻⢞⡓⠢⠀⠀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣋⣿⡿⢿⣿⣯⣶⣿⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠂⠤⢄⠀⠠⣤⡍⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⡿⠟⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⡐⠒⠶⠷⠦⢀⣉⠓⠦⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣷⣾⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡲⠤⠠⢄⠙⠳⠖⠖⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣵⣿⣿⣛⣿⠿⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⣤⠄⠊⣹⠋⠀⡄⠀⠀⠂⠈⢁⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣾⣟⣛⣿⡭⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠠⢤⡶⠋⠋⣙⣀⡴⠃⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣶⣝⣿⣿⣯⣥⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠐⣲⠋⣉⠁⠶⠴⣾⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣹⡿⣿⡟⢿⡧⠼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠾⠄⣰⢀⡜⢿⣞⡟⠋⠓⢿⠞⣷⢻⡟⢿⠯⣽⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠘⠉⠀⠀⠀⠀⠙⠛⠒⠿⠛⠃

⠀⠀⠀⠀⠀⣠⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⣄
⠀⠀⠀⢀⣼⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣧⡀
⠀⠀⢠⢾⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢈⡷⡄
⠀⠀⡇⠈⡇⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢺⠁⢸
⠀⢠⡗⠀⢿⡀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⡿⠀⢺⡄
⢠⡇⠹⡄⠈⢷⣆⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣠⡾⠁⢠⠏⢸⡄
⣸⡇⠀⠱⣤⠈⠻⣷⡀⢠⡙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢉⡄⢀⣾⠟⠁⣤⠎⠀⢸⣇
⣇⠘⣦⠈⠻⣶⡄⢻⡏⠙⠻⣄⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⣠⠟⢉⢹⡟⢡⣶⠗⠀⣴⠃⣸
⠘⡆⠈⣳⣄⠈⢿⡶⠷⣅⠀⠈⢕⣦⣄⣀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⣀⣠⣴⡪⠁⠀⣺⠾⢶⡿⠁⣠⣾⠅⢰⠁
⠀⠸⢦⡌⠙⢷⣬⣿⡄⠀⠙⠢⣄⣹⣟⠉⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠉⣻⣏⣠⠔⠋⠀⢀⣼⣥⡾⠋⢡⡴⠃
⠀⠀⢣⡉⠲⣆⡙⢿⠛⠓⠢⠤⣭⣿⠋⠁⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠈⠙⣿⣭⠤⠔⠚⠛⡿⣋⣰⠖⢉⡜
⠀⠀⠈⠳⢄⣈⠛⠻⣿⣧⣤⣤⣤⣽⣷⠃⠀⠀⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠀⠀⠐⣾⣯⣤⣤⣤⣼⣿⠟⠛⣁⡠⠞
⠀⠀⠀⠀⠀⠈⠁⠒⢸⠏⠁⢀⣀⠬⣿⣷⡏⢀⡀⠀⠸⡀⠀⠀⠀⠀⠀⢀⠇⠀⢀⡀⢹⣾⣿⠤⣀⡀⠀⠹⡇⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⠁⠀⣠⠖⢛⣿⣿⣀⡄⠀⠘⢄⠀⠀⠀⡠⠃⠀⢠⣀⣿⣿⡛⠢⣄⠀⠉⡗⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⣡⢀⡞⠀⡞⢩⠋⠁⠀⠀⠁⠀⠈⠀⠀⠉⠙⡍⢳⠀⢳⣀⣌⡗⠒⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⡍⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡖⠂
⣿⣿⣿⡷⠒⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣭⡉
⣿⣿⣿⣿⣶⣶⠆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⣉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠟⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⠄⠀⠀⠀⠀⠀⠈⠻⠿⠛⢿⣿⣿⣿⠀⠀⠀⢀⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⠻⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡿⠍⠓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢂⡀⠀⠀⢠⣀⣸⣿⣿⠀⠀⠸⢿⢿⣿⣿⡿⢿⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡿⢫⠍⢥⠈⢹⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠁⣤⠩⡭⢿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢛⡉⠀⣟⢀⡔⠒⣵⡌⢱⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣇⢡⣮⡑⢒⡀⣸⠁⢈⣛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠼⢿⣷⢻⠂⢈⡽⠛⡿⣧⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣼⢿⠛⢾⡁⠀⠟⢾⣿⠷⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣰⣀⡹⠿⣶⣆⡀⢷⡀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢀⡼⠁⣰⣶⠾⢏⣀⣇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣰⠟⣶⣶⣿⢛⣅⣀⣩⡟⠳⢀⡉⠛⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠾⠛⢉⡁⠞⢻⣍⣀⣈⡙⣿⣶⣶⡛⣧
⠀⠀⠀⠀⠀⣰⠏⣸⡟⠛⢣⣿⣿⣏⣿⣿⡶⣤⣁⠂⠀⠀⠤⢄⠉⢳⣦⡀⠀⠀⠀⠀⣠⡾⠋⡡⠤⠀⠄⠔⣈⣤⢴⣿⣿⢼⣿⣿⣎⠙⢻⣧⠙⣧
⠀⠀⠀⠀⢰⠃⢀⣿⠁⣠⠌⠋⠁⠃⠈⣠⣿⠹⣿⢻⣶⣖⠰⣦⣄⣛⠿⣷⡄⠀⢀⣾⠿⣑⣠⣤⡆⣰⣶⡟⣿⠏⣿⣄⠈⠀⠁⠙⠙⣄⠀⣿⡄⠘⣇
⠀⠀⠀⠀⣾⢀⢸⡟⣾⣿⡇⠀⣀⣿⣿⣿⢿⣧⣀⣾⣧⡜⠻⢟⠳⢈⣿⡋⠁⠀⠈⢙⣻⡃⠸⠻⠿⢣⣼⣿⣄⣴⣿⢿⣿⣾⣆⠀⢠⣿⣷⡿⣇⠂⢿
⠀⠀⢀⡴⠇⣸⡇⢸⢻⠛⠿⣾⠋⠹⠛⣅⠘⠋⣸⣟⠏⠹⣆⠀⠀⠘⣟⡉⠀⠀⠀⠈⣹⠇⠀⠀⣀⠞⠹⢻⣧⠈⠃⢨⡙⠏⠉⣷⡿⠛⡟⠟⢸⣿⠘⢦⡀
⠀⠀⡾⠛⠛⠻⡇⠈⠀⠀⢰⣿⠢⣀⣼⣿⣷⣴⣿⣿⣦⣴⡿⣻⣠⡏⠉⠁⠀⠀⠀⠈⠉⢙⣇⣿⣿⣦⣴⣿⣿⣦⣴⣿⣷⣀⠔⣿⡇⠀⠀⠘⢸⡏⠛⠛⢿⡄
⠀⠀⠀⠀⠀⢰⣇⣰⣀⣴⣼⣏⠀⣇⢹⣿⠋⢸⣯⡉⢹⣿⣟⡓⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣻⣿⣏⠙⣹⡇⠘⢿⡟⢸⠄⢸⣿⣦⣀⣎⣸⡇
⠀⠀⠀⠀⠀⢸⠛⣿⣿⡏⠻⠏⢰⣿⡄⠃⠐⣾⣿⣿⢻⣤⣶⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣷⣤⡿⢿⣿⣷⠆⠈⢀⣿⡆⠘⠟⢨⣿⣿⠋⡇
⠀⠀⠀⠀⠀⢸⡄⠟⣿⣷⠀⠀⢸⣿⡟⠂⣸⣷⡈⠁⢸⣯⡷⣦⣍⣧⡀⠀⠀⠀⠀⠀⠀⣴⣫⣴⣶⣽⡇⠈⠉⣼⣧⡰⢛⣿⡇⠀⠀⣼⣿⠛⠀⡇
⠀⠀⠀⠀⠀⠈⢧⣄⢸⣿⢷⢴⡏⣿⡿⠑⠆⣿⡿⢦⣮⡛⠻⠊⢳⡈⠁⠀⠀⠀⠀⠀⠈⢁⡾⠁⠻⢛⣹⣤⢿⣿⠳⠊⠿⣿⢳⡧⡾⢿⡏⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡌⣿⠀⠸⣷⡘⠀⠀⢠⡝⠁⢸⣿⣿⣷⢤⣀⣷⠀⠀⠀⠀⠀⠀⠀⢸⣀⡤⣾⣿⣿⣿⠈⠻⡄⠀⠀⠉⣾⡇⠀⢸⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢱⠀⠀⣿⣷⣄⡀⢠⠀⠀⢸⡝⢿⡟⢧⠉⠻⠄⠀⠀⠀⠀⠀⠠⠟⠋⣴⢋⣿⢋⣾⠀⠀⡄⠀⣠⣾⣿⡀⠀⡜⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠀⢸⡏⡟⠋⢷⣾⣆⠀⣼⣿⣯⡑⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠚⣽⣿⣷⡀⢠⣿⣾⠋⢹⠛⡇⠀⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡇⠀⠀⢾⣿⡟⣿⣿⠋⣿⢷⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⢻⠘⣿⣻⠹⣿⣷⠀⠀⢠⡇⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣄⣠⡞⠿⠀⢹⠉⠀⡟⠈⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠃⢸⡄⠈⡟⠀⣿⢻⣄⣠⣾⣿⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣟⣿⣇⠀⠀⢼⠀⣸⠃⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⢧⠀⣧⠀⠀⢸⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⡏⣿⣿⣄⢀⡌⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣳⡀⢠⣽⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⢀⣿⣿⡟⣾⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡟⣷⠹⣿⣿⣇⠙⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣴⢸⡿⠃⠠⡇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢘⠄⠈⢻⡇⣦⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢋⡿⠚⠁⣰⣿⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣾⣇⠈⠻⢹⡝⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡞⠁⢀⣶⠙⢛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⠋⣾⡄⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣩⣤⠴⠋⣿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⠙⠦⣤⣌⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⣿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣟⠷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⣯⣿⣿⣿⣿⣿⣶⣶⡦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣝⢷⣦
⠀⠀⠀⠀⢀⣴⢟⣿⣿⣿⣿⣿⢼⢿⣼⣽⣿⣿⡛⣿⣷⣤⡀⠀⠀⠀⢀⣴⣿⢿⢟⣯⡿⣿⣿⣼⢹⣼⣿⣿⣿⣿⣿⣻⣦⡀
⠀⠀⠀⠀⢨⢟⣿⣿⣿⣿⣿⠛⠟⣼⣏⢻⢱⣿⣷⡇⣏⢻⡇⠀⠀⠀⣼⡏⣽⢸⡾⣿⡟⣿⣹⣿⡞⡟⠹⣿⣿⣿⣿⣿⡛⡄
⠀⠀⠀⠀⣾⣾⣿⣿⡿⢿⢹⣰⣇⣟⢿⣿⣾⣿⣦⣽⣿⣾⡿⠀⠀⠀⢿⣷⣷⣿⣴⣽⣷⣿⡿⢻⣄⡷⣸⢙⠟⣿⣿⣿⣿⣗
⠀⠀⠀⣼⣿⣿⢿⣿⢳⣹⡜⣿⡿⣿⣼⣄⡏⣏⢹⣽⣟⠳⣆⠀⠀⠀⣔⠋⣿⣏⡇⣹⢹⣆⣟⣾⡿⣷⡯⣼⣰⢻⣿⡏⣿⣿⠷
⠀⠀⠀⢸⡿⣿⣿⢹⡈⠻⡟⡟⠷⢸⠙⢳⡟⣿⣬⢿⡀⠡⠈⠀⠀⠀⢠⠌⢀⡿⣧⣿⠟⣿⠉⣹⢰⠟⡟⣿⢻⢰⡏⣷⣟⣿⣇
⠀⠀⠀⣻⣿⣻⢹⡟⢷⠂⡇⣧⢹⠈⡇⠈⣇⣿⠙⡸⡇⠀⠃⠀⠀⠀⠘⠀⢼⢣⠋⣿⢰⠇⢠⠇⢸⢨⡇⠇⢸⡟⣿⢹⡏⣿⣞
⠀⠀⠀⢉⡿⣿⡿⣷⣸⡀⡆⢽⠘⣆⠘⡄⡏⠃⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠈⢩⠇⡏⣠⠏⣸⡃⣇⢸⣠⡿⣾⣿⢿⡉
⠀⠀⠀⠈⠀⣟⢻⣿⣿⣧⡇⣿⡘⠃⣿⣇⢻⡄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡏⢠⢿⠃⢙⣸⡇⣷⡼⣿⢷⣇⣇⢀⠁
⠀⠀⠀⠀⢠⠩⡋⢹⡇⡇⢱⢣⣿⠀⣻⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⣸⠀⢸⡇⠻⠃⠀⣾⡇⢹⠉⡄
⠀⠀⠀⠀⠈⠀⠃⢸⣷⡇⠰⣶⠿⢧⡽⠁⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢻⣴⠿⣧⣷⠀⢸⢹⠃⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠸⠈⠸⡀⠡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⡈⠈⠸⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡆⠀⡇⠀⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢰⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠃⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣧⡈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠇⢠⣇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⣵⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢺⡚⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⣄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠
⠀⠀⠀⠀⠀⠹⣦⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡿
⠀⠀⠀⢀⠀⠀⠡⡱⣄⠈⢞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠀⣢⣾⠁⢀⡄
⠀⠀⠀⠈⢷⡀⠀⠱⡌⠣⡈⢆⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢿⣿⢀⣾⣿⠃⠀⣻⠁
⠀⠀⠀⠀⠀⢻⠢⡀⠘⢆⡈⠢⣱⡈⠳⣄⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⢞⣵⣯⢟⣵⢿⡾⢁⡀⣴⠃
⠀⠀⠀⠀⠀⠀⠳⡌⠢⣄⠘⡄⠈⠃⢀⠹⡢⢈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣄⣰⣿⢻⣿⣿⣿⡟⣠⡿⣽⠃
⠀⠀⠀⠀⢀⠀⠀⠈⠢⡈⠳⢜⣄⠀⠈⠳⠑⡄⠙⠌⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⣿⣿⣻⣿⣿⣿⡿⣫⣾⣯⡞⠁⢀
⠀⠀⠀⠀⠈⠳⡄⢀⠀⠈⠢⡀⠙⠢⡘⣦⡀⠈⠂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⣿⢏⣼⡿⣿⡿⠋⢀⠀⡿
⠀⠀⠀⠀⠀⠀⠐⠄⡈⠒⠤⣱⣄⠀⠐⢚⠢⡈⠢⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣟⡾⢉⣤⣾⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⠤⢄⠈⠣⣀⠈⢗⠀⠢⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣯⣼⣿⣿⣿⠟⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠄⣀⠑⢄⠈⠓⢤⣝⡢⣀⠀⠀⠀⠂⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣷⢛⣩⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡈⠉⠛⠂⠀⠉⠣⢄⡉⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣋⣭⣿⣷⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣀⡁⠚⠦⡀⠙⠳⣀⡈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣫⣽⡿⣫⣿⠿⣛⠉⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢈⡉⠙⠙⠒⠠⣤⠈⠙⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣽⣿⠿⣿⣯⣼⣿⣶⣿⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⠟⠃⠐⠤⣈⣙⡩⠋⠀⠀⠀⠑⠤⣀⡀⠀⠀⢀⡀⣀⣶⣿⣿⣿⣿⣿⡷⢿⣿⣿⣭⡿⠛⣫⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣒⠶⠂⠁⣬⣁⣀⠆⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⢿⣿⣯⣩⣿⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠒⣲⠞⠉⢁⣬⣀⠔⠁⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣟⣿⣿⣍⣿⡿⠧⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢐⣼⢁⣠⠄⠶⠔⠿⣿⡿⣻⣿⡻⢿⠿⣿⢿⣿⣭⣿⣻⣷⣚⣿⠶⠾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠐⣸⣁⡜⢻⣞⡝⠋⠉⠺⡗⣻⡟⢻⠺⡿⠧⠽⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠀⠉⠀⠀⠀⠀⠈⠛⠛⠚⠟⠙

⠀⠀⠀⠀⠀⢠⡀⠀⡀
⠀⠀⠀⠀⠀⠘⡝⢦⠹⡀
⠀⣤⣀⠀⠀⠀⠙⣄⢙⢿⣄
⠀⠈⠪⣙⠒⠦⢄⡈⠢⡑⠈⠛⠦⣤⣀⡀
⠀⠀⠲⣚⠳⠦⣔⡀⠍⡉⠓⠤⢀⡀⠉⠉⠉⠉⢝⠉⠉⣉⠟⠛⠒⠦⣤⣤
⠀⠀⠀⣬⣕⣤⣀⡈⠙⠒⠢⠤⠀⣀⡁⣖⠁⠀⠈⣗⠒⠈⠂⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠈⠑⠦⢌⣉⠙⠒⠒⠤⠤⠤⠤⠀⠹⣁⠀⠈⠋⡉⠁⠀⠀⠀⡴⠂⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠐⠮⣉⡙⠛⠓⠒⠒⠒⠒⠒⠒⠊⠉⢹⡭⠀⠀⠀⢀⣰⣉⠓⠀⠀⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠲⣛⡛⠛⠒⠒⠒⠒⠒⠈⠉⣀⠧⠀⣤⢀⡀⢣⠤⠌⠁⠀⠀⢱⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡶⠶⠚⠒⠒⠈⠉⠀⣀⠄⠊⢉⡠⠌⡖⠂⠀⢄⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⠭⠝⣟⣁⣠⠖⠁⡠⠔⢚⡥⠀⠀⢤⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣤⠊⢀⡔⠉⡲⢴⠂⠀⢚⡠⠀⡀⠈⠙⠲⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⢴⠋⣀⡔⡑⡨⠂⡦⠈⠡⠔⡣⣠⡀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠒⠹⠬⠚⣧⢾⢀⡆⢰⣀⡇⢰⢸⡅⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⠋⠛⠑⠃⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢫⡁⠈⡲⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠰⡊⠀⣩⠁
⠀⠀⠀⠀⠀⠀⢀⢱⡖⢒⡀⠸⣉⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣏⡹⠀⣐⠒⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣤⣴⣇⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣷⣠⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢾⣟⠿⣺⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⠠⣑⢊⡲⠆⢠⠀⢠⠠⠶⣊⢐⡡⠘⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡌⠁⠭⣗⠠⠀⠠⢐⡧⠥⠉⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠐⠀⠀⠀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠐
⠀⠀⠄⠀⠀⠀⠂⠀⡄⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⠂⠀⠀⠀⡄
⠀⠀⠁⠀⡄⢔⠐⡇⢰⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢲⠀⡕⢀⠆⡄
⠀⠀⠀⣀⢀⠨⢧⡸⣎⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣏⡾⣠⠯⢀⢀⡄
⠀⠀⠀⢈⠒⢢⣌⢳⣽⡙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣹⣵⢃⣤⠗⢊
⠀⠀⠀⠢⠳⢠⠙⢷⣽⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣵⠞⢡⠴⠣⠒
⠀⠀⠀⠁⢀⡎⠐⢤⣇⠱⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣷⠔⠈⣆⠀⠁
⠀⠠⠀⠧⡀⣤⠓⢶⡿⣆⢏⠀⠀⡘⢦⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠞⠀⠐⢉⢇⡾⣷⠖⢣⡄⡠⠇⠠
⠀⠀⠀⠠⠬⣌⣙⠲⣿⡌⢃⠁⠆⡘⠢⣛⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡫⠚⡀⠖⢁⠋⣼⡷⢚⣉⣬⠤
⠀⠀⠀⠀⠀⡌⢉⣽⣟⣿⠦⠑⠀⣍⡓⢾⣿⡄⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⣸⣿⠖⣋⡅⠐⠡⢾⣟⣿⣍⢁
⠀⠀⠀⠀⠁⡠⠤⠤⠼⠿⣷⣌⠀⠄⢭⣻⣿⡦⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠠⣾⣿⣫⡅⠀⢪⣴⡿⠷⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢒⡛⢛⣛⣷⣦⡀⠡⠯⠽⢿⡦⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠠⣾⠿⠭⠯⠁⣠⣶⣟⣛⠛⣓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠙⠛⣻⣦⡄⠐⢛⢿⣦⡝⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⣥⣾⠟⠓⠂⣤⣾⡛⠛⠁⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠴⠿⡿⢧⣤⡜⠻⠦⣭⠢⢄⣀⠀⠀⠀⠀⠀⢀⣀⠤⢪⡵⠞⠛⣤⣤⠿⡿⠷⠭⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠙⠛⠛⠛⠿⠓⠛⠶⠒⠀⠐⠲⠖⠓⠻⠟⠛⠛⠛⠉⠁⠐

⢠⡀⠀⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠀⢀⡀
⠀⠙⠳⣦⣬⣙⡛⠷⣶⣤⣤⣄⣒⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠶⣒⣠⣤⣤⣶⠾⢛⣋⣥⣴⠞⠋
⠀⠒⠶⠤⣭⣭⣙⣛⣷⣾⣿⣓⣿⣿⣿⣟⢒⡤⡬⣈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣁⢤⢤⣂⣻⣿⣿⣿⣚⣿⣷⣾⣛⣋⣩⣭⠤⠶⠒
⠀⠈⠓⠲⠶⠶⠶⠿⢿⣛⣿⣿⣞⣛⣿⣶⣟⡽⣳⣧⣗⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⣺⣼⣞⢯⣻⣶⣿⣛⣳⣿⣿⣛⡻⠿⠶⠶⠶⠖⠚⠁
⠀⠀⠀⠀⠉⠛⢛⣛⣯⣽⣿⣿⣿⣷⣿⣿⣿⣷⣥⣾⢿⣷⣤⢁⠀⠀⠀⠀⠀⠀⠀⡈⣤⣾⡿⣷⣬⣿⣿⣿⣿⣾⣿⣿⣿⣯⣽⣛⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠠⠖⠛⣩⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠡⠄⠀⠀⠀⠠⠌⣹⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⢧⣍⠛⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢀⠀⠀⠀⡀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣷⣿⣷⠚⠀⠒⣾⣿⣾⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⢿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⡿⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠟⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠾⠟⣿⣿⣿⣷⠀⠀⢰⣿⡿⣿⣿⠿⢷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢾⣾⣿⣿⣿⡁⠀⠀⠀⢹⣿⣿⣾⣷⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡏⠁⢠⠂⠀⢢⠀⠙⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠈⠀⠀⠀⠀⠀⠆⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠒⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣦⣴⣖⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠈⠉⠑⠢⠤⡤⠤⠤⢄⠠⠀⠀⠀⠒⠤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠤⠤⠤⣄⠀⢤⠄⠈⠐⠤⣀⣀⡀⠀⠀⠀⠀⠉⠓⠲⢶⡒⠀⠉⠉⠁⠀⠐⠂⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠈⠢⡀⠁⠢⡈⠻⣌⠉⠉⠉⠙⠒⠦⣄⡀⠈⠀⠀⡀⠀⠀⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⠀⠀⢰⡀⠀⠀⠈⠒⢄⠀⠀⠠⡀⠈⠠⠈⠫⡍⠉⠀⠂⠄⡀⠉⠢⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⣆⠀⠀⠀⠈⢦⠀⠀⠀⠈⠢⠀⠈⠢⡤⠤⠀⠂⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢄⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠈⠆⠀⠘⣦⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡄⠘⢆⠘⠂⠀⠙⢆⠀⠀⠀⠀⠘⣄⠀⢩⠻⠦⢀⠀⠀⠈⠲⠤⣀⠀⠀⠀⠀⠀⠀⠙⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠐⢤⣤⠀⠀⠀⠀⠣⠀⠀⠀⠀⠃⠙⢬⠀⠀⠀⠈⢰⡦⠄⡀⠢⠉⠁⠒⠀⠠⠤⠤⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠀⠈⠇⠐⡀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠳⣦⣄⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢣⡀⠀⠠⡀⠀⠀⠡⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⢘⣴⠀⠀⡀⠀⠀⠀⢱⡀⠀⠘⠏⠀⠠⢌⣢⣀⠀⠐
⠀⠀⡀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠀⠈⠈⢀⡘⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢁⠀⠈⠉
⠀⡎⠀⠀⠀⠁⠀⠀⠀⠑⡈⢀⠔⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈⡓⠢⠄⠀⠀⠀⠀⠆
⠀⠣⢄⣠⠞⠀⠀⢸⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠧⡀⠀⠀⡇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⢄⠀⠀⠀⠧⠀⠀⠀⠀⠘⠢⡀⡷⠀⠀⠰
⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠈⠦⠀⠈⠀⠱⠀⠀⠆⠀⠀⠈⠀⠀⠑⠒
⠀⠑⠰⠀⠀⠁⢄⡀⠈⢀⠀⠀⠠⠀⠀⠀⠆⠈⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼
⠀⠀⢿⣆⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣼⡏
⠀⠠⣌⢿⣧⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢣⣾⠏⣠
⠀⢤⣝⣷⣝⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⣿⣣⠄
⠀⠀⢽⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡥
⠀⠐⢶⣿⣿⣿⣿⣿⣿⡿⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣽⣿⣿⣿⣿⣿⣿⣥⠶
⠀⠠⣤⣿⣿⣿⣿⣿⣿⡯⣿⣿⣏⣀⣹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡋⣘⣿⣿⡯⢽⣿⣿⣿⣿⣿⣯⣤⠄
⠀⠀⠴⠾⠛⣋⣭⣵⣶⡶⡾⢻⡿⣳⢚⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⣿⡿⣏⣶⣾⣿⠻⡶⣶⣿⣿⣿⣿⠿⠦⠤
⠀⠀⠀⠀⢚⣿⡿⢟⣵⣾⣷⡾⣸⣿⣿⣿⣿⣻⣿⡀⠀⠀⠀⠀⢸⣿⡿⣷⣾⣿⣿⣻⣶⣿⡿⣽⡿⣿⣟⠃
⠀⠀⠀⠀⠈⠉⢚⣫⠾⣛⣡⣾⣿⣽⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⣾⠿⣼⣾⣿⢿⣵⣿⣿⣿⣿⣿⣟⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢋⢿⡿⡿⣻⣯⠞⢫⣿⣿⣿⣷⡄⠀⠀⣰⣿⣤⣿⣮⣛⣾⣿⣿⣿⣿⢯⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠧⠵⢜⢮⢞⣿⣿⣷⣼⠀⢘⣵⣿⣏⣿⣿⣿⣿⡿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⢾⠹⠄⢸⣿⣿⠿⠟⠻⠁⠁

⠀⠀⠀⠀⠀⠀⠐⠆⠻⠀⠀⠀⠀⠀⠀⢢⠗⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⣛⠀⢐⡃⡐⠀⠐⠐
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠐⠲⡐⠖⠒⠀⠐⠦⠔⠀⠒⡫⠀⠈⠀⠠⡀⠸⠒⠂⠰⠄⠒⠀⠐⠒⠖⡰⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠆⡅⣀⢀⡄⡤⠤⠐⠂⠀⠀⠀⠀⠂⠢⠤⡔⣄⢀⡀⡰⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠈⠀⠀⠐⠒⢦⠄⡴⠒⠂⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⣜⠁⠀⠀⠂⠐⠉⠠⠂⠒⢀⢁⣆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠀⠠⡀⠀⠀⠁⣀⣈⡁⠈⠀⠄⢈⣑⡀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠘⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⠀⣀⠄⠀⢰⡁⠄⠀⠀⠀⠀⠁⠈⠁⢀⠄⡀⠀⢀⠠⡀
⠀⠀⠀⠀⠀⡄⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠄⡼⡃⠀⣜⠆⠄⠀⠀⠔⠂⠑⠒⠒⡋⣠⢷⠀⡾⡆⢙⠒⠒⠂⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣀⠀⢠⠀⠀⠄⠒⢤⣈⠉⢇⡤⣞⡴⢋⡼⠀⢧⡹⣦⡲⢤⠚⠁⣁⡤⠂⠠⠀⡀⡄⠀⣠⠄
⠀⠀⠀⠀⡀⢠⠀⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⢠⡀⢄⠀⠀⠀⠲⣤⡠⠐⠀⡠⠀⠈⠈⠈⡖⣋⣔⠊⠀⠀⠈⠑⣠⣙⢂⠃⠁⠁⠀⢄⠐⠂⢄⡤⠖
⠀⠀⠀⠊⠀⠁⠀⠀⠀⠀⠁⠹⠀⠜⠀⠀⠀⠀⠀⠁⠀⠃⠈⠀⠀⠀⠀⠙⠛⠖⠧⠺⠘⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠃⠖⠾⠲⠛⠋
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⡱⣦⢤⢾⣀⡽⠀⠀⠀⡶⢄⠀⠀⠀⠀⡽⣇⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡴⣿⢸⢱⡌⡤⠀⠀⡤⢷⠈⠳⡀⠀⠀⣏⣾⡁⠀⠀⢸⣏⡷⠀⠀⢠⠞⢀⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡣⡇⢸⡎⡛⠁⠀⠀⣧⠀⢣⡀⠙⡄⠀⢾⣿⣇⡥⣄⣹⣿⡇⠀⢠⠃⢀⠜⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢱⣧⢰⡼⠀⠀⠀⠸⡌⠳⡀⠑⢠⡌⢀⡈⠚⠻⠃⠹⠟⠚⣁⡠⢁⠄⠋⣠⠎⢸⠇
⠀⠀⠀⠀⠀⣠⣮⠉⠉⢆⠀⠀⠀⠘⠉⢉⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⢬⣁⡤⠆⠠⡀⢹⠦⣀⣁⣒⡝⡲⢆⠳⣄⠀⠀⣴⠛⣱⡖⢫⣒⣀⣀⠴⡏
⠀⠀⠀⠀⣤⣬⠙⠟⣦⣀⡀⠠⣀⣠⣖⠛⠁⣤⡄⠀⠀⠀⠀⠀⠀⠐⠁⡤⣻⡀⢸⡟⢆⡀⣈⠳⡦⠬⠭⢟⡓⠈⡆⠈⡧⣾⠁⢸⠁⢚⡻⠭⠤⢴⠞⠁
⠀⠀⠀⠀⠠⠙⠲⣵⣉⡝⠁⠀⠈⢯⣹⡬⠞⠁⠀⡀⠀⠀⠀⠀⠀⠘⡋⣠⢹⠀⠈⡌⣦⣈⣀⠀⠓⠶⡒⣈⠙⠡⢚⡘⠃⠘⢦⢲⠍⠋⣑⢒⠶⠚
⠀⠀⠀⡖⠣⠤⣠⣈⣹⠀⠀⠀⠀⢀⣯⣀⣡⠤⠚⠆⠀⠀⠀⠀⠀⠛⠋⢅⡾⠀⠀⠸⣄⠈⠉⠠⣄⠀⠀⠓⠴⠲⣤⠵⠀⠐⠯⣬⠖⠤⠊
⠀⠀⢠⠇⠀⠀⠈⠉⣩⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⢸⠀⠀⠀⣚⣃⣠⡤⠚⠀⠀⠀⠀⣨⣥⡖⠲⠾⠂⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⢘⠚⠴⠤⢦⣍⡟⠀⠀⠀⠀⠀⣟⢣⠴⡴⠜⠚⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⠞⠁⠤⢨⠁⢰⢲⠀⠲⢯⠀⢍⠢⡀⠙⢦⡀
⠀⠀⠸⡀⠀⠐⣸⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⠁⠔⢃⡀⠢⠸⡉⢊⠀⣘⠈⡩⠰⠲⣠⠓⠀⠙⣦
⠀⠀⠀⠁⣐⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⢓⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠂⠹⣀⠃⠐⢄⢈⠉⠀⠈⡋⢀⠶⠐⣇⡼⠐⢆⣀⡄
⠀⠀⠀⠰⣿⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣿⣷⠀⠀⠀⠀⠀⢀⡠⠐⢀⡔⠁⠉⠀⠀⢀⠀⡈⠉⠀⠀⠀⠈⢉⠀⠄⠈⠀⠈⠀⠡⣄⠐⠤⣀
⠀⠀⠀⠀⢿⣦⠸⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁⣼⠇⠀⠀⡤⠖⢊⣁⣤⠖⢋⡴⠃⣠⠆⢀⠾⠤⠇⠀⠀⠀⠀⠀⠈⢦⠼⢄⠈⣦⠈⠢⣈⠳⢦⣄⡉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠉⠉⠉⠯⠤⠒⠯⠤⠊⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠙⠢⠼⠗⠢⠭⠏⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣽⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣿⣿⣼⣿⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⡤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣚⣉⣝⣉⣉⣡⣶⣴⣿⣶⣀⣀⡤⠛⣷⣖⣀⣀⠀⢐⣀⣴⣟⣀⣀⠤⠀⠀⠀⠀⠲⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡭⣾⣟⣭⣯⣉⣻⣿⡝⢻⣿⣟⣛⣩⣽⣭⣿⣿⣿⣿⣿⣿⠿⠏⡁⠀⠀⠂⠀⠀⠀⣀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡔⣵⣾⣿⠟⠻⣷⣦⣍⠻⣿⣯⣥⣽⣿⣿⡟⠻⣿⣟⠢⠤⣀⠙⠿⣷⣶⣤⣶⣾⣷⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢠⢎⣾⣿⣿⣽⣿⡳⠌⣻⣶⣅⣪⡴⢿⣿⣿⢿⣌⣱⡈⠙⢿⣶⣶⣶⣶⣿⣿⡛⠛⠉⠠⠤⢤⡤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⢮⡙⢦⣜⣿⣭⣭⣟⠀⠻⣿⠣⡙⢿⡿⣟⢿⣿⣿⣮⣉⡒⠠⠀⠀⠀⠀⠀⠀⣀⣬⡿⠋
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠛⣷⣷⣤⣉⣿⣿⠿⠿⣿⣶⣿⣷⣌⠃⠙⢮⡓⢬⡛⢿⡻⠿⣿⣶⣶⣶⣿⡿⠿⠛⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⣽⣆⢻⣿⣿⡿⣷⣁⠈⢿⣿⣿⣿⣿⣶⣾⡿⠦⣍⠀⠈⠒⢄⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢳⣽⣯⣿⣿⣿⣷⡈⣿⣿⢿⣇⠙⢿⣿⣿⣿⣿⣷⣤⣉⠒⠤⣤⠉⠑⢤⣀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣿⣿⣿⣷⣾⠻⣦⣀⡑⢬⣻⣿⣮⡙⠙⠿⣟⠷⠶⣶⣤⡶⠿⠟⠀⠀⠀⠀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡿⣜⣿⡏⢇⠐⠹⣿⣿⣶⣄⠈⢻⡿⢶⣶⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄
⠀⠀⠀⣿⣿⣿⣿⣟⢻⣿⣍⣙⡏⠻⠏⢷⣙⣸⣿⣮⡓⠀⢼⣷⣷⣌⠢⡀⣽⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜⢸⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣷⡬⢿⡉⠁⠀⠀⠀⠙⠛⠉⠙⠿⣶⡾⠇⠈⠉⠛⠛⠛⠁⠀⠀⠀⠀⡐⢉⠇⠀⠀⠀⠀⡼⠀⣸⢇⡀
⠀⠀⠀⢹⣿⣿⢿⣿⣿⣿⣈⣛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⡿⠀⠀⠀⠀⣰⠁⢠⣟⡜⡇
⠀⠀⠀⠘⣿⣿⣿⡛⣿⣯⠛⠛⠋⠀⠀⠀⠀⣀⠠⡤⢢⠀⠀⠀⠀⠠⣀⣴⠆⠀⢀⡴⣣⣿⣻⡇⠀⠀⠀⣼⣿⣴⣿⠋⣸⠇
⠀⠀⠀⠀⢹⣿⣿⣿⣶⣾⡇⠀⠀⠀⣀⣄⣴⢾⣿⡿⠁⢀⣴⣿⣿⣛⣽⡟⠀⣠⢾⣿⣔⣿⢿⡁⠀⢀⣼⣿⣿⡿⠁⣰⣟⣆
⠀⠀⠀⠀⠀⣿⢿⡟⣧⡁⠀⠀⢀⣾⣿⣿⣿⣫⣽⠃⣰⣻⣿⣿⣿⢿⣿⠅⣸⣿⣿⣿⣿⣿⡋⠀⢀⣾⣿⠟⣽⣧⣾⠟⣡⡏
⠀⠀⠀⠀⠀⠈⠈⢷⡈⣧⠀⠀⣿⣟⢿⣿⡿⣖⡏⠀⣿⣟⣿⣿⣿⡿⠃⠀⣿⣿⣿⣿⣿⣾⡞⠀⣾⣿⣷⢊⢽⣿⣁⡴⣋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢹⡟⣸⣿⡻⣟⠁⠀⠹⣧⣿⣿⠶⣶⠀⠀⢻⣿⣿⣿⣿⣵⡋⠀⣿⣿⣿⠗⢉⣿⣋⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣿⣿⡦⠄⠀⠀⢠⣟⣿⣿⣗⠂⠀⠀⢀⣿⣿⣿⣟⣽⠄⠀⢹⣿⣿⣏⣠⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⣿⣯⣝⠀⠀⠀⢱⣿⣿⣕⠀⠀⠀⢰⣿⣿⡿⢿⣿⠶⠀⠠⢮⣿⣿⣦⡾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡳⠄⠀⠀⠀⠈⠙⠙⠊⠀⠀⠀⠀⠻⣧⠻⠆⠉⠀⠀⠀⠘⣿⣶⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢻⡛⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠃
⠀⠠⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠱
⠈⠀⣄⠀⠠⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⡔⠈
⠴⡀⠀⠀⠀⢀⠀⠀⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠁⠀⡀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⢑⠀⠑⢄⢈⢦⡐⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⣠⢎⢀⠔⠁⢀
⠉⠢⠀⠀⠀⠑⢄⠌⢿⡄⠙⣆⠈⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⡞⠁⣼⠏⢄⠔⠁⠀⠀⠠⠊
⠠⢄⠀⢀⠘⢄⠀⠳⡄⠙⠄⠈⡁⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡉⠀⠜⠁⡴⠃⢀⠜⢀⠀⢀⠤
⠀⠀⠑⢄⠙⠦⣝⣦⠙⢂⡀⣥⠛⢀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢀⠘⢣⡅⣀⠚⢡⣞⡥⠞⢁⠐⢁
⠀⠰⠲⠄⠙⠲⠬⢭⠛⠂⢁⡌⠑⠼⣜⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣼⠔⠉⣠⠁⠚⢫⠭⠴⠚⠁⠴⠢
⠀⠀⠀⠀⣈⠐⠲⠤⠤⠲⠀⠯⠉⠙⣳⡈⠙⡳⢄⠀⠀⠀⠀⠀⢀⠴⡛⠉⣰⡛⠉⠩⠇⠰⠢⠤⠤⠒⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢲⣂⣒⡣⠤⢀⡏⣐⠟⢢⣄⠀⢀⣤⠚⠖⡈⣇⠠⠤⣓⣂⣲⠚⠒⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡩⠥⠚⣠⠞⣡⢔⣊⠈⠋⠤⠀⠠⠜⠏⢈⣒⢤⡙⢦⠘⠢⠬⡉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠡⠠⡄⠁⠘⠀⠘⠀⠀⠀⠀⠀⠘⠀⢘⠀⢁⡤⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠻⠟⠿⠙⠀⠙