Aspiration Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣤⡄⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⠀⣾⡟⠁⠘⠿⢿⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⣠⣶⠿⠛⠉⠉⠉⠉⠋⠀⢸⣧⣄⣀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣼⡟⠁⠀⠀⠀⣀⡀⠀⢀⣴⠟⠋⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣸⡟⠀⠀⠀⣴⡿⠛⢃⣴⠟⠁⠀⠀⢺⣆⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠐⠿⠋⣶⡆⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢹⣧⠀⠀⠀⠻⣧⣤⣤⣼⠟⠀⠀⠀⣼⡏⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢻⣧⡀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣼⡟⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠙⠿⣦⣤⣀⣀⣀⣀⣤⣴⠿⠋⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠷⠾⠿⠿⠛⠋⠁




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

⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣠⣾⡿⢾⣝⣆⡀⠀⠀⡾⡽⣚⢝⢧⠀⠀⢸⢸⣇⣤⣰⢟⡦⠀⠀⠀⣿⠃⠘⣷⠀⠀⠀⠀⣠⣴⠋⠷⣄
⠀⠻⣖⢿⢵⢗⡞⠁⠀⠈⢧⡫⣚⢜⡼⠀⠀⢸⢸⣫⣶⣵⣋⡁⠀⠀⠀⣞⣨⡀⢷⠀⠀⠀⠀⡇⠀⠀⠀⡿
⠀⠀⠈⠻⠾⠉⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠸⠮⠭⠭⠭⠭⠿⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠛⠉⠙⠛⠁
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⢠⣾⣿⣿⣽⣦⠀⠀⠀⣴⢫⣭⡝⣦⠀⠀⢀⡤⠶⠒⠲⠦⣄⠀⠀⣠⠞⡩⣋⠳⣄⠀⠀⢸⣱⠿⠿⣆⡇
⠀⢸⣿⣿⣿⡿⡿⠀⠀⠀⢻⠜⣛⣣⠏⠀⠀⠈⣿⡇⠀⠀⡾⠉⠀⠀⢿⡰⣮⢻⢇⡿⠀⠀⢸⠽⣛⣋⠷⣿
⠀⠀⠙⠿⠽⠞⠁⠀⠀⠀⠻⠼⠋⠀⠀⠀⠀⠀⠙⠉⠛⠋⠁⠀⠀⠀⠀⠙⠲⠵⠛⠁⠀⠀⠈⠛⠚⢷⡴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⢺⡉⠛⢩⠇⠀⠀⠀⣴⡾⠉⠹⣶⡄⠀⠀⣠⡖⣻⣟⠲⣆⠀⠀⠀⣀⡶⢳⢳⡄
⠀⣿⠭⣿⣹⣿⣿⡆⠀⠀⢠⠟⣀⢻⡄⠀⠀⠀⠻⣇⠀⢀⡿⠃⠀⠀⣿⠀⢿⣿⠂⣿⠀⠀⠀⡷⠆⠆⠰⣏
⠀⠛⠛⠛⠛⠛⠛⠁⠀⠀⠘⢦⣩⠼⠁⠀⠀⠀⠀⣾⣠⣸⡆⠀⠀⠀⠘⠧⠬⠥⠼⠃⠀⠀⠀⠹⠴⠷⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⢀⣠⡤⢴⡖⣆⠀⠀⢀⣤⣶⣶⣶⣄⡀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⣠⠶⠶⠴⠶⣄⠀⠀⠀⡤⢖⢒⡲⣄
⠀⣿⢸⡄⠀⡿⣻⠀⠀⢻⠨⠛⣛⠻⠭⡏⠀⢰⣏⣾⣦⣉⣉⣷⠀⠀⢿⡸⣷⣾⠇⡼⠀⠀⢸⢱⡿⠘⢿⢸⡆
⠀⠸⣆⣼⡤⠷⠛⠀⠀⠙⢦⡴⠒⢦⡴⠃⠀⠸⠯⠥⠿⠤⠤⠿⠀⠀⠀⠳⢮⡥⠞⠁⠀⠀⠘⢧⣐⣐⣢⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡀⠀⠒⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⣵⣋⠕⠀⢸⣉⢦⡀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠕⠀⢀⡇⠠⢗⡀⠌⠠⡖⠉⠁⠀⡸⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡂⠀⣿⠀⠈⠈⠂⠀⠈⠂⠀⣆⡀⣇⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⢰⡠⠐⠛⣽⠈⡆⠀⠉⠀⠱⠂⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣣⢥⠤⣀⠉⢰⢦⡀⠀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⠀⣯⢣⡑⣌⣑⠾⠗⡺⢾⢴⠊⡩⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⣿⠀⠉⠁⠀⠐⠩⢚⡝⡜⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⠤⢶⠉⠣⡀⠀⠀⠀⢠⣚⠿⢣⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠈⢣⡀⢉⢶⠒⠚⡍⢀⡠⠖⠓⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⠜⠁⣸⠀⠀⢸⢧⠀⠀⠀⠈⠣⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⡠⢤⠚⠁⠀⠀⡇⠀⠀⢸⠈⢧⠀⠀⠀⠀⠑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⢸⠀⠈⢦⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠴⠧⠤⠤⠼⠤⠤⠤⠬⠷⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠘⣧⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠹⣆⠀⠀⠀⠀⠀⢀⣾⠃⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣟⡀⠀⣈⣷⠀⠀⣠⠞⢠⡏⠀⣀⣀⠀⢹⡆⠳⣄⠀⠀⣾⣁⠀⢀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⠁⢀⡾⠃⠀⢸⡇⢸⣅⣩⡇⢸⡇⠀⠘⢷⡀⠈⣿⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣼⠁⠀⢠⣿⡇⠀⠉⠉⠀⢸⣿⡄⠀⠈⣧⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣿⠀⠀⣿⠈⣧⠀⠛⠛⠀⣼⠁⣿⠀⠀⣿⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢻⡄⠀⠹⣶⠻⣶⢶⡶⣶⠟⣶⠏⠀⢠⡟⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⡿⠀⠈⢿⡄⠀⠀⠀⠟⢸⡇⠻⠀⠀⠀⢠⡟⠀⠀⢿⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢀⣀⣈⣁⣀⡀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡏⢹⡏⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣬⣧⣼⣧⣤⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣏⣀⣀⣀⣀⣀⣀⣹⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉



⡟⠉⣿⣛⢻⢛⣻⡛⣟⣛⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣟⣻⣟⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢧⢻⡙⠿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠈⢳⣝⢦⡈⠳⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠘⢦⡀⠀⠉⠳⣭⣓⠿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠙⠦⣄⡀⠀⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢀⣨⠿⠿⣧⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠉⠳⢬⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣀⣤⣶⣒⠒⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢳⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣠⠞⠋⢉⣩⢽⡛⠳⢦⡀⠉⠳⡄⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡞⠁⠀⢠⡟⢤⣀⢳⣸⣇⡝⢦⡀⠹⡆⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠁⠀⠀⢸⠀⣀⣉⣶⣷⡏⡶⠚⢷⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⡀⠀⠀⠘⣆⠀⣰⠎⢹⠑⣏⠓⣸⡇⣸⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢧⡀⠀⠀⠘⠳⣄⣀⠘⢀⣈⡴⢻⣧⠏⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠳⣄⠀⠀⠀⠀⠉⠉⠉⠁⣠⡿⠋⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠛⠶⢤⣤⣀⣤⡤⠞⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠛⠋⠉

⠀⠀⠀⢀⡤⢼⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣲⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⣀⣏⢠⠖⡄⣙⣄⠀⠀⠀⠀⠀⡞⡴⣩⢳⣹⡄⠀⠀⠀⠀⣿⠀⢀⣤⣀⡼⠛⠀⠀⠀⠀⠀⠀⢫⣻⣫⠃⠀⠀⠀⠀⠀⠀⢠⣤⣼⣷⣶⠄
⠀⠀⠀⠳⣀⣩⣁⠜⠀⠀⠀⠀⠀⠀⠳⣝⣒⣊⠼⠁⠀⠀⠀⠀⣿⠐⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⣿⡇⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠂

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⣤
⠀⠀⢀⢔⠧⠨⠘⡲⡀⠀⠀⠀⠀⠀⢰⠏⠭⠙⣧⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⡴⡿⣡⠿⣷⡄⠀⠀⠀⠀⠀⡇⣈⣛⣣⢸
⠀⠀⢠⠀⡱⢀⠎⠀⡇⠀⠀⠀⠀⠀⠘⣦⣀⣤⠟⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣟⠛⡳⡀⠀⡟⠀⠀⠀⠀⠀⡇⣒⣒⢶⣛⡆
⠀⠀⠀⠑⠅⣰⡰⠋⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⡽⠚⠁⠀⠀⠀⠀⠀⠛⠒⠒⢺⡿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⣶⡆⠀⠀⠀⠀⠀⠀⣀⣠⣾⣦⣀⡀⠀⠀⠀⠀⠀⢀⣠⠄⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡄
⠀⠀⡠⡤⡎⢭⠉⣄⣀⠀⠀⠀⠀⠀⠀⢘⣿⡋⠀⠀⠀⠀⠀⠀⠀⢇⣿⣿⣿⣇⠇⠀⠀⠀⠀⠠⣾⡏⠀⠀⢿⡷⠀⠀⠀⠀⠀⠰⢶⡿⣾⡷⠆
⠀⠀⠧⠯⠧⠼⠤⠽⠽⠀⠀⠀⠀⠀⠀⣿⠉⣹⡆⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⢋⣃⣀⣰⣿⠟⠀⠀⠀⠀⠀⠘⣿⡿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠽⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉


⠀⠀⢀⡤⣤⣶⣎⣛⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⣠⢦⣠⣄⣀⡀⠀⠀⠀⠀⢀⡶⠛⢶⠾⠳⣦⠀⠀⠀⠀⠀⣰⠞⢹⡏⠳⣄
⠀⠀⢸⣖⢻⣿⡿⢴⡇⠀⠀⠀⠀⢸⣉⣿⠻⢿⣏⣿⠀⠀⠀⠀⢺⠥⠠⠝⢛⣛⡻⠂⠀⠀⠀⠀⢷⣄⠀⠀⣰⠟⠀⠀⠀⠀⠀⡇⢀⣼⣧⡀⣹
⠀⠀⠀⠿⠻⠘⠃⠉⠁⠀⠀⠀⠀⠈⠿⠉⠉⠉⠿⠏⠀⠀⠀⠀⠘⠚⠛⠒⠛⠛⠓⠀⠀⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠙⢯⣼⣯⡿⠋

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣴⣿⣿⣿⣿⣶⡄⠀⠀⠀⣠⣾⣿⣿⣿⣷⣦⡀⠀⠀⢀⡴⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⣶⣿⣿⣿⣿⣦⡀
⠀⠀⣿⣿⣫⣾⣶⣝⣿⣿⡄⠀⢰⣿⣿⡱⣢⣪⣻⣿⣷⠀⠀⣾⡇⣿⡿⢿⡿⣹⣿⡆⠀⢠⣿⣿⣿⡀⡀⣿⣿⣿
⠀⠀⣿⣿⣞⢷⢿⣳⣿⣿⠁⠀⠸⣿⣷⣳⠽⢝⣽⣿⡿⠀⠀⢿⡇⣿⣵⣷⣾⣿⣿⠇⠀⠘⣿⣿⣯⣸⠀⣿⣿⣿
⠀⠀⠈⠻⣿⣿⣿⣿⠿⠃⠀⠀⠀⠙⢿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠳⢶⣶⣶⣶⡶⠋⠀⠀⠀⠘⠿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⡀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣄
⠀⠀⣾⣿⣯⣿⣿⣽⣿⣷⡀⠀⢠⣿⡿⠿⠛⠻⠿⣿⣧⠀⠀⣼⣿⢏⣥⢠⣍⢻⣿⡄⠀⢀⣾⡟⣩⣝⣩⡍⣿⣷
⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⠇⠀⢸⣿⣿⡇⠀⢀⣿⣿⣿⠀⠀⣿⣿⡸⢋⢈⠻⣸⣿⡇⠀⠸⣿⣷⣜⠿⠟⣡⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣾⣿⠏⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⢿⣿⣶⣤⣶⣿⠟⠀⠀⠀⠹⣿⣿⣷⣾⣿⡿⠋
⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉
⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣾⣿⡍⠻⢉⣿⣿⣆⠀⠀⣰⣿⡿⠟⠉⢻⢿⣷⡀⠀⠀⣼⣿⠟⣻⡟⢿⣿⣦
⠀⠀⣿⣯⢭⣿⣹⣿⣿⣿⡇⠀⢸⣿⣿⡟⣀⠻⣿⣿⣿⠀⠀⣿⣿⣿⡂⠀⣸⣿⣿⡇⠀⢸⣿⣿⠰⣿⣿⠀⣿⣿
⠀⠀⢻⣷⣿⣾⣿⣾⣾⡟⠀⠀⠘⢿⣿⣧⣉⣵⣿⣿⠏⠀⠀⠹⣿⣿⣏⣄⣻⣿⡿⠁⠀⠀⢻⣿⣧⣬⣥⣼⣿⠟
⠀⠀⠀⠉⠛⠻⠟⠛⠉⠀⠀⠀⠀⠀⠙⠛⠻⠛⠋⠁⠀⠀⠀⠀⠈⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠉⠛⠻⠟⠛⠁
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⣠⣾⣻⣿⣿⣻⣷⣆⠀⠀⠀⣴⣿⣿⣿⣿⢿⣷⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄
⠀⠠⣿⣿⢹⣭⠽⡸⣿⣿⡆⠀⢸⣿⡯⣗⠀⠨⠟⣿⣷⠀⠀⣿⣯⢹⠛⡛⢻⣩⣿⡇⠀⢰⣿⡟⢷⢯⣈⣉⢻⣿
⠀⠀⢿⣿⣼⣶⡃⣁⣿⡿⠁⠀⠸⣿⣷⣈⣦⣼⣶⣿⡟⠀⠀⢻⣿⣄⣼⣿⣆⣼⣿⠃⠀⠈⣿⣯⣯⣿⣧⣤⣽⡿
⠀⠀⠈⠛⠿⢿⡿⠿⠛⠁⠀⠀⠀⠈⠻⠿⣿⡿⠿⠋⠀⠀⠀⠀⠙⠿⢿⣿⠿⠟⠁⠀⠀⠀⠈⠛⠿⣿⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡔⢉⡉⢢⠀⠀⠀⠀⡴⡯⢽⢦⠀⠀⠀⢸⠀⢀⠀⡠⠀⠀⠀⠀⠰⣿⣿⠀⠀⠀⠀⠀⢀⣠⣇⡀
⠀⠀⠡⣈⣁⠜⠀⠀⠀⠀⠳⣗⣺⠜⠀⠀⠀⢸⠐⠉⠉⠀⠀⠀⠀⠀⠐⠏⢿⡄⠀⠀⠀⠀⢿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠐⡀⢈⠠⠀⠀⠀⠀⢰⠋⠉⡇⠀⠀⠀⠀⢤⣶⣶⡤⠀⠀⠀⠀⣶⣫⠛⢦⠀⠀⠀⠀⡧⣭⢤⡇
⠀⠀⠢⠁⠀⠄⠀⠀⠀⠀⢸⡗⠚⠁⠀⠀⠀⠀⠞⠿⠿⠃⠀⠀⠀⠀⠣⣍⣦⠜⠀⠀⠀⠀⠧⠧⣽⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣀⢀⡀⡀⠀⠀⠀⠀⠈⢿⡟⠁⠀⠀⠀⠀⣖⣿⣿⣲⠀⠀⠀⠀⣾⠃⠘⣧⠀⠀⠀⠀⠠⣼⣼⠄
⠀⠐⠛⠆⠁⠛⠃⠀⠀⠀⠰⣏⣹⠂⠀⠀⠀⠀⠈⣻⣟⠁⠀⠀⠀⠀⢻⣆⣰⡟⠀⠀⠀⠀⠐⡟⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠠⡄⣶⣶⢝⠀⠀⠀⢠⣄⣀⣀⣠⡄⠀⠀⢀⠔⢢⣦⣤⡀⠀⠀⠠⡟⠛⠛⢳⠄⠀⠀⢀⡞⢹⡏⢳⡀
⠀⠀⢷⡽⠿⠛⠀⠀⠀⠘⣿⠓⠚⣿⠃⠀⠀⠨⠵⠅⠴⠶⠅⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠈⢷⣻⣟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⢀⠲⠿⣿⣿⠟⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣤⣤⣴⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣟⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣦⣨⣾⣿⣿⡿⠟⠛⠛⠉⠛⠛⢿⣿⣿⣿⡟⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠳⢦⣤⣤⣶⣿⣿⣿⣽⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡟⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠘⢷⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠘⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⣀⣼⢳⡀⠀⠀⣨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠣⠸⠀⢁⡀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⡷⠬⠤⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠀⠾⠐⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠁⠓⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣤⣤⣴⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⢟⣯⣽⣶⣶⣶⣶⣾⣷⣶⣶⣯⣻⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣫⣾⣿⣿⣿⠟⠛⠛⢿⡟⠉⠉⠻⣿⠿⠿⢿⣿⣿⡝⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣵⣿⠋⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⠿⠿⡝⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣁⠀⠀⠀⠀⠀⢀⣶⣤⣀⣠⣾⣦⣀⣀⣴⣦⣄⣀⣠⠀⠀⠀⡼⠷⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠛⠀⢀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠈⠀⠀⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠆⠐⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣟⡄⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⠀⠀⢿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⡿⢆⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠖⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⢸⣿⣿⣷⣄⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣤⣤⣼⡟⣿⣿⡄
⠀⠀⠀⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⠙⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇
⠀⠀⠀⣼⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇
⠀⠀⠀⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇
⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿
⠀⠀⠀⢸⣿⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣾⡏
⠀⠀⠀⠀⣿⣧⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⣿⣿⢷⣿⠁
⠀⠀⠀⠀⢿⣿⣾⠛⠛⠋⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⣿⡟⣾⡟
⠀⠀⠀⠀⢸⣿⣿⡄⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⣻⣿⠁
⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣽⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣏⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⣿⣿⢳⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢷⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣴⢯⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣮⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⢯⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡻⣿⣶⣄⣤⡁⠀⢀⡀⠀⠀⡀⠀⢀⣀⣀⣤⣤⣴⣿⣿⣿⢯⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣾⣟⡿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠦⣄⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣆⡴⠻⡆⠀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡤⠴⠚⣉⠈⠉⠀⢀⡉⠉⠹⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⡀⠀⠈⠭⠀⣆⠀⠨⠍⠀⠀⣸⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡄⢹⡄⠀⠀⠀⠸⠃⠀⠀⠀⣼⠁⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢂⠀⢳⡀⠀⠰⠯⠷⠀⠀⣰⠃⢀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠙⣶⠤⠤⠤⢴⡞⠁⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⢣⡀⠀⢀⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⣟⢮⡳⣌⠉⠉⠀⢻⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠻⣷⠍⠀⠀⠀⠀⠈⡶⠓⢦⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣄⣀⣸⠁⠀⠀⠱⣄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠚



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡣⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢰⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢨⠘⣿⣿⠗⠀⢀⣀⣀⣠⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⣠⣴⣿⠛⠋⠙⠉⠉⠉⠉⠛⠛⠛⠓⠶⣶⣄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡾⠋⠀⣿⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⡀⠀⢨⣿⠁⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠂⢀⡾⠋⠀⠀⠀⢿⣦⣀⣀⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⢸⡏⠻⣦⡀
⠀⠀⠀⠀⠀⢀⠤⢂⣴⠟⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠷⢦⣤⣀⠀⠙⢿⣿⡀⢸⡇⠀⢹⡃
⠀⠀⠀⠀⡀⠃⢠⡟⠁⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣾⣿⣧⡀⠻⣦⣼⣷
⠀⠀⠀⠀⠢⡀⢿⣇⣀⣀⣄⣀⣀⣙⣻⣶⣶⣶⠶⢶⣶⡶⠶⢶⣶⣤⣀⣠⣿⣿⣿⣿⣶⡄⠉⠃
⠀⠀⠀⠀⠀⠈⠐⢌⠉⣿⣵⡎⠉⠉⠉⠀⠉⠙⠛⠋⠛⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣜⡅⢻⡍⠁⢀⣠⣤⣶⣶⡶⣶⠶⠶⣶⣶⣶⣦⣤⣤⡀⠈⠀⠹⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⣇⣼⣿⣿⣋⣽⣿⣿⣷⣶⣶⣶⣶⣦⣤⣴⣽⣛⢷⣦⡀⡘⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⢿⣿⣿⣿⡛⡽⣿⣶⣶⣶⣤⣍⡛⢦⣍⠛⢿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⣬⢷⢹⣿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣷⡀⢻⣶⡌⠉⠙⢿⣿⠻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⣿⢹⡇⢻⡿⣷⣜⣿⣿⣿⣿⡿⡟⠇⣸⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠈⠀⠀⣮⣩⣿⣿⣿⣿⣣⣴⣂⣧⣤⣶⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡀⠀⠀⠙⢿⣻⣿⣿⣿⣿⣿⣿⣟⣭⡿⠃⠀⠀⠞⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⣧⡀⠀⠀⠀⠉⠁⡀⣀⣀⣀⣀⣉⢠⣤⣬⣦⣶⠋⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠳⠦⠶⠶⠾⠛⠛⠋⠉⠉⠉⠉⠫⡙⠊⠹⡏⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⢀⡀⠀⠀⠀⠀⠄⠠⠤⡀⠀⠘⠦⠀⠠⡄⢻⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢸⠇⠀⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⠀⠀⠀⠙⣿⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⢰⡇⠀⠀⠀⢰⡿⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣷⣤⣾⣷⣿⡇⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⡿⢿⣿⣇⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠛⠆⠀⠙⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠿⢿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣥⣤⣷⣤⣧⣤⣶⣥⣾⣯⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⣄⣀⣠⠤⠴⠖⠒⠋⠛⠒⠲⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⢆⠀⠀⠀⠀⠀⣯⠀⣀⣀⡤⠤⠖⢲⠒⠦⠤⣤⣀⣀⠈⠉⠉⠓⠒⠦⠤⣤⣀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡤⠴⠚⠀⠈⠓⠦⣤⠀⠀⡟⠉⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠉⠙⠒⠲⠤⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣦⠀⠀⠀⠀⡴⠁⠀⠀⡇⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣀⡤⢤⣀⡇⠀⠀⠀⡇⠀⠀⢀⠴⢦⡇⠀⠈⡗⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⡗⠀⠀⣼⠀⢀⣇⣀⣀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠶⠶⣄⡀⡶⠶⠶⠶⠚⠁⠀⠀⡇⠀⢼⠁⠀⠈⡧⠤⢸⡤⢤⡀⠀⠀⠀⠀⠀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⡇⠀⠀⠀⠀⠀⠀⢸⠁⢀⣸⠴⠶⠆⡇⠀⠀⡇⠀⢳⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠈⢹⠀⠀⠀⡟⠉⠉⣷⠂⢸⡀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣇⠀⠀⠀⣀⣀⠀⣸⠀⢀⣸⠀⠐⠚⠧⣄⠀⣿⠄⠀⡇⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢻⠀⠀⢠⠇⠈⢧⣿⡀⠈⠀⠀⢠⡀⠀⠀⠀⠻⠄⠀⣇⠀⠀⠀⢠⠇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⢧⠀⡞⠀⠀⢸⠀⠉⠲⢤⣀⠀⠙⠦⣄⡀⠀⠀⠀⢿⠀⠀⢀⡞⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠣⡇⠀⠊⣻⠀⠀⠀⠀⠙⣏⠒⠦⣀⠉⠓⠒⠶⢾⠀⣠⠞⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡇⠀⠈⠉⠳⠦⢤⡀⠀⠘⣆⠀⠈⠙⠂⠀⠀⢸⠞⠁⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠉⠢⠀⠘⣆⠀⠀⠀⠀⠀⢸⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠴⠖⠂⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⣰⣾⣿⣿⣿⣷⣆⠀⠀⢀⣴⣿⡿⢿⣿⣷⡄⠀⠀⢠⡾⣿⣿⣿⣿⣦⡀⠀⠀⣰⣾⡿⠿⣿⣷⣆
⠀⢰⣿⣟⣾⠿⣷⣻⣿⡆⠀⢼⣿⣯⢫⣯⡎⣿⣿⠀⠀⣿⡇⣿⢟⢿⣭⣿⡇⠀⢰⣿⣿⡇⡠⢼⣿⣿⡆
⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠸⣿⣷⣵⣾⣽⣿⡟⠀⠀⢻⡟⠷⠿⠿⠿⣿⠃⠀⠈⢿⣿⣷⣧⣼⣿⡿⠁
⠀⠀⠀⠙⠛⠿⠛⠋⠀⠀⠀⠀⠈⠛⠻⠟⠛⠉⠀⠀⠀⠀⠉⠛⠻⠟⠛⠁⠀⠀⠀⠀⠙⠛⠿⠛⠋
⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣦⠀⠀⢠⣾⣿⡿⢿⣿⣿⣆⠀⠀⣰⣿⢟⡛⣛⢿⣷⡄⠀⠀⣼⡿⠛⠿⡛⢿⣦
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣶⠀⠀⢰⣿⣿⠀⠀⣿⣏⠾⠃⠻⠇⣿⡇⠀⢸⣿⣇⠻⣿⠟⣼⣿⡇
⠀⠀⠻⣿⣾⣿⣷⣿⠟⠀⠀⠘⢿⣿⣷⣶⣿⣿⠏⠀⠀⠹⣿⣦⣥⣥⣾⡿⠃⠀⠀⢻⣿⣷⣶⣾⣿⠟
⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⣠⣤⣶⣤⣄⠀⠀⠀⠀⢀⣤⣴⣶⣤⣀⠀⠀⠀⠀⣀⣤⣶⣦⣤⡀⠀⠀⠀⠀⣠⣤⣶⣤⣄
⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⢰⣿⣿⡉⢋⣽⣿⣧⠀⠀⣼⣿⣛⠁⠙⣻⣿⡆⠀⢀⣾⡿⢛⣿⡛⢿⣷⡀
⠀⠸⣿⣗⣺⣿⣿⣿⣿⠇⠀⢻⣿⣿⢣⡌⢻⣿⣿⠀⠀⣿⣿⣯⡀⠠⣿⢿⡧⠀⢸⣿⣧⠸⣿⠇⣼⣿⡇
⠀⠀⠹⢿⣿⣿⣿⡿⠏⠀⠀⠈⠻⣿⣷⣶⣿⡿⠃⠀⠀⠘⢿⣿⣷⣾⣿⠟⠁⠀⠀⠻⢿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⢀⣴⠶⠿⢶⣦⡀⠀⠀⠀⣠⣶⣶⣷⣶⣤⠀⠀⠀⢀⣤⣶⣾⣶⣦⣄⠀⠀⠀⢀⣴⣶⣾⣶⣦⡀
⠀⢠⣿⡇⣿⣟⡇⣿⣿⡄⠀⢸⣿⢻⠏⠙⣮⣿⣷⠀⠀⣾⡟⠿⠿⠿⠟⣿⡆⠀⢠⣿⢟⣽⡛⠛⢿⣿⡄
⠀⠘⣿⣇⣿⡷⠛⢿⣿⠃⠀⢹⣿⡎⢣⣀⣧⣿⡿⠀⠀⢿⣧⢁⣴⣤⢁⣿⡇⠀⠸⣿⣷⣛⣿⣉⣱⣿⠃
⠀⠀⠘⠿⣿⣿⣿⠟⠃⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠀⠀⠈⠻⢿⣿⣿⠿⠋⠀⠀⠀⠙⠿⣿⣿⡿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⠀⠀⠈⣉⠁⡀⠀⠀⢉⣉⠀⠀⢸⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡀⠀⠀⠈⠁⡇⠀⠀⠈⠀⠀⠀⢸⠃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢣⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⢀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢴⠿⠿⠷⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⠀⠤⠐⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⡤⢶⣾⡄⠀⠀⠀⣤⣶⠦⡤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⢀⠸⡀⠘⠙⢇⣴⠆⢠⣟⡉⠀⢨⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠳⣾⠳⢌⠂⠄⣈⣇⠀⠀⠈⠣⡶⠻⡷⠊⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⣀⣀⣀⠀⠀⠀⠀⣀⠄⠂⠓⠦⠤⢀⡈⠈⠁⠐⠒⠂⠤⣈⡄
⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⣀⠔⠁⠀⠈⠢⢄⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠠⠤⠒⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠁⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠀⠐⠒⠒⠈⠉⠉⠀⠈⠁

⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣄⡀⢀⣠⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠉⠉⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠛⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⣛⠋⠉⠉⠛⠛⠉⠉⠙⣛⠁⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠈⠑⠦⠤⣤⡤⠤⠶⠊⠁⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠤⠖⠚⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⣧⡀⣀⠀⠀⢠⡿⢴⠄⠀⠀⢀⣴⠟⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢻⣫⣽⡀⠀⠘⠙⡿⠀⠀⠰⢯⣻⡦⠀⠀⠘⣆
⠀⠀⠀⠤⠤⠶⠖⠒⠋⠁⠀⠀⠀⠈⠁⠘⠇⠀⣀⣀⣁⣀⠀⢠⠟⠁⠀⠀⠀⠀⠈⠙⠒⠲⠶⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⣡⠤⠤⣌⡑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡞⣠⠚⠒⣄⢳⠈⡇
⠀⠀⠀⠐⠒⠒⠶⠶⠦⠤⠤⢤⣄⡀⠀⢸⡀⢧⠙⢤⠤⠋⡼⢀⡇⠀⢀⣠⡤⠤⠤⠴⠶⠶⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠱⢌⡙⠒⠒⢋⡡⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⣠⠖⠛⠉⠙⠳⢦⣠⠖⠛⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⣠⣴⣾⣿⣿⣿⣦⣄
⣼⠁⠀⠀⠀⠀⢀⡤⣅⣀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣇⠀⠀⠀⠀⡖⢺⡇⢸⠉⣷⢤⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠹⣄⠀⠀⠀⡇⢸⡇⢸⠀⣿⠀⡇⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠋⣿⢸⡇⢸⠛⣿⣿⣿⣿⠟
⠀⠈⠳⣄⠀⡇⢸⠇⢸⠀⣿⠀⣧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⣿⢸⡇⢸⠀⣿⣿⡿⠋
⠰⣏⠙⠮⡿⠇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠿⣿⣿⠀⠉⠈⠁⠘⠀⡿⠋
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠒⠀⠀⣠⣴⣾⠿⠿⠿⣶⡄⠀⠐⠀⠀⠀⣤⠀⠀⣠⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠈⣿⠠⠶⠶⠶⢶⡿⠾⠛⢫⣶⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⣿⡇⠀⠀⠀⢀⡀⢠⡏⢠⣾⠀⢀⣿⠃⠀⠀⣀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠻⣿⣄⠀⠀⠸⠷⠏⠀⣤⠁⠀⣼⡟⠀⠀⣼⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢟⣡⢀⣠⣤⣀⠈⠻⣷⣄⠀⠀⠀⣸⡏⠀⢰⣿⠃⠀⣼⣿⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⢠⡟⣵⡟⠉⠀⣹⠀⣀⡈⢻⣧⠀⢰⡿⠁⡰⢹⡟⠀⣰⣿⡇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠰⡟⠀⠀⣠⠏⣾⠋⠀⠀⣿⠀⢸⣇⡴⠁⠸⣧⠞⠁⢿⣇⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠙⠷⣤⡤⠞⠁⠀⠙⢧⣤⠾⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠆⠀⣀⣤⣤⣀⠀⠀⠀⢀⣤⡀⢀⠀⣦⣰⣦⣿⣠⡷⢀⡆⠀⠀⠉⢀⣾⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢶⡀⢠⣾⠟⠉⠉⠙⣷⡀⠀⢈⡛⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣠⡴⠋⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣇⠀⠀⠀⠀⢹⡇⢀⣾⡇⠀⠛⢻⣿⣿⣿⣿⠿⠏⠀⠙⠛⠁⠀⢠⣿⡇⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠻⣦⣀⠀⢀⣸⡗⣹⣿⠀⠀⢠⠀⣿⣿⣿⣿⠀⠀⣤⡬⠊⠻⠿⢿⣿⣷⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⡇⠀⠀⠉⠉⠁⣿⠀⣿⡇⠀⢠⠃⠀⣿⣿⣿⡟⠀⢰⣧⠀⠀⠀⠀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⠇⠀⢿⣇⡴⠁⠀⠀⣿⣿⣿⡇⠀⠈⢿⣄⣀⣀⣴⡿⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢿⡇⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⣀⠀⠉⠉⠉⠀⠀⢠⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢿⣦⡴⠋⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣤⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠀⢲⡄⢸⡄⠀⠀⡟⢸⡇⠀⢸⠃⡀⠀⠀⢳⠀⢸⠃⣿⠀⢀⡄⠀⣿⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⣷⠀⣾⠁⢠⡇⠘⣧⡀⠸⡇⢸⡇⠀⣼⠀⣷⠀⠀⣿⠀⢿⠀⣿⠀⠀⢧⠀⢹⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣿⠀⠰⠃⠀⠈⠀⠉⠀⠀⠹⡇⠀⠉⠀⠑⠀⠈⠁⠘⢦⠼⠁⠀⠈⠁⠈⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡇⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠑⠒⠠⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠴⠒⠒⠋⠉⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣧⡀⠀⠀⠀⠘⣿⣿⣿⡀⠀⢿⣧⣀⢦⠶⠚⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⣿⣿⣷⣄⠀⠀⠀⠘⣿⣿⠷⢴⠾⣴⠉⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠻⣿⣿⣿⣦⠀⠀⠀⣸⣧⣶⣇⢀⡟⢷⢻⠿⢻⣶⣶⠈⠉⠐⠢⡀
⠀⠈⠻⣿⣿⣷⡤⡾⠋⠈⡿⠋⣿⡇⢸⡇⠀⠘⣿⡿⠀⠀⠀⠀⠈⢢
⡀⠀⠀⠘⢿⠏⢠⣦⠀⢰⣆⠀⠸⣿⠈⣇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⣿⣷⣄⠠⡏⢠⣿⣿⣧⣿⣿⣆⠀⢿⢷⡟⣶⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡿⢱⣷⣼⣿⣿⣿⠙⣿⣿⣄⣶⠈⣧⢸⣿⡀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⠀⠀⢀⣤
⣿⣿⠇⣾⣿⣿⠻⣿⣿⣇⠘⣿⣿⢿⣇⢹⣬⡛⢹⡇⠀⣀⠀⠀⠀⣰⣿⠀⢠⣾⠇⠀⣠⣾⣿⠀⣠⡄
⠈⣿⠀⢻⣿⣿⣷⡌⢻⣿⣆⠈⢿⡈⢿⣶⡸⣇⡜⢳⠀⠀⣴⣶⣼⣿⡇⣴⣿⠋⣠⣾⣿⣿⣧⣾⣿⣧⡀
⠀⣿⠀⠀⠙⢿⣿⣿⣦⡙⢿⣧⡈⢳⠘⡟⣧⣈⠛⢎⣠⡄⠙⠏⣸⣿⣾⣿⣣⣾⣿⠟⣫⣾⣿⡿⠛⠉⣷
⢸⣿⣆⠀⠀⠀⠙⠻⢿⣿⣦⣌⠳⣄⠁⠀⠹⣿⢛⣾⣧⣻⢻⡇⡿⣿⣿⣿⠟⢋⣠⠾⠛⠋⠁⠀⢀⣀⡝
⡀⣿⣿⣿⣶⣤⣀⡀⠀⠉⠛⠿⣷⣬⡓⠀⢀⢱⣿⣿⣿⢾⣾⡃⡼⡽⠋⡁⠀⠉⣀⣠⣤⣴⣶⣿⣿⣿⡇
⡇⠈⠻⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣌⣙⣓⣼⣿⢿⣿⡟⢼⣿⣧⣠⢶⣯⠶⠾⠿⠿⠛⠛⠛⠋⠉⠉⠉⢹
⣷⣀⠀⠀⠉⠉⠉⠛⠛⣛⣋⣉⣩⣭⠵⣚⣟⡿⢿⣿⣶⣾⡿⢒⣚⣓⠲⠶⠶⢶⣶⣶⣶⣦⣤⣤⣤⣀
⢹⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢋⣡⣴⡿⠋⡉⣯⢿⣟⣿⡿⣿⣿⣗⠯⣝⡛⠶⣦⣤⣈⡉⠙⠛⠿⢿⣿⣧
⡆⠙⠛⠛⠉⠉⠀⢀⣠⣴⡾⢟⡵⢋⣔⣾⣷⡙⣯⣭⢿⣼⣽⣯⡳⡙⢮⡙⢶⣤⡉⠻⢿⣷⣦⣄⡀⠙⣿
⠿⣄⣀⣀⣤⣶⣿⡿⠟⣉⡴⠋⣰⣫⣿⣿⣿⣿⣬⣴⢏⡏⣯⢷⢳⡙⣦⠻⣦⡉⠻⣷⣄⡈⠙⢿⣿⡆⢸
⠀⠹⣿⣿⡿⠛⢉⣠⠞⠁⣠⣞⣵⣿⣿⣿⣿⣿⣿⠋⣾⢡⡟⢸⡎⢷⡘⣷⡈⢿⣦⡈⠻⣿⣦⡀⠹⡿⢼
⠋⠁⠈⠁⣀⡴⠋⠁⣠⡾⣫⣿⣿⠟⠁⠀⠀⠀⠀⣼⡏⣸⡇⢸⡇⢸⣧⠘⣿⡄⠹⣿⣄⠈⢿⣷⢀⡇
⣠⣶⣧⡉⠉⠀⣠⣾⢟⣽⣿⡟⠁⠀⠀⠀⠀⢀⣼⡿⢀⣿⠇⣾⡇⠈⣿⡆⠸⣿⡄⠘⣿⣆⠈⣿⢸⣷⣄
⣿⣿⡿⠛⣶⣾⣿⣿⣿⣻⠏⠀⠀⠀⠀⠀⣠⣿⣿⠁⣼⣿⠀⣿⡇⠀⣿⣧⠀⣿⣿⠀⢹⡿⢰⠇⣿⣿⣿
⡿⠋⠀⠀⣨⡛⠿⢟⠕⠁⠀⠀⠀⠀⣠⣾⣿⣿⠃⢰⣿⡏⢠⣿⡇⠀⣿⣿⠀⢸⣿⠀⣼⢇⡟⠀⠈⠻⣿
⠀⠀⣠⣾⣿⣿⡶⣄⡀⠀⠀⣀⣤⣾⣿⣿⡿⠃⢠⣿⡿⠀⣸⣿⡇⢀⣿⡿⠀⣿⡏⣰⢏⣾⣷⣄⠀⠀⠈
⢠⣾⣿⣿⣿⡟⠁⠈⣙⠿⢿⣿⣿⣿⡿⠛⠀⣠⣿⣿⠃⢠⣿⡿⠀⣸⣿⠃⣼⢟⡴⠃⠘⣿⣿⣿⣧⡀
⣿⣿⣿⣿⠏⠀⠀⣰⣿⣿⣶⠦⣤⣤⣤⣴⣾⡿⠟⢁⣴⣿⠟⢁⣴⠟⣡⠞⣡⣾⣧⠀⠀⠘⢿⣿⣿⣿⣦
⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⠃⠀⢠⣶⣦⡤⠴⠶⠾⣛⣋⡥⠶⣋⣵⣾⠁⠀⢻⣿⣿⣧⠀⠀⠈⢻⣿⣿⣿

⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⡠⢂⠀⠁⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⢀⢀⢂⠀⢀⢈⡄⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠸⡆⠘⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣀⡠⢄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠈⠂⢈⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⠉⠲⡄⠀⠀⠀⠀⠀⢀⠂⠁⠈⠂⠀⠈⡠⡀⠀⠀⠀⠀⠀⠀⠀⢂⠋⠋⠉⡑⣦
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠀⠦⠀⠶⠒⠛⡀⢣
⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠁⢀⡆⠂⢹⠐⠲⣇⡜
⠀⠀⠀⠀⠀⠡⣐⠠⠀⠀⣴⠾⢶⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠢⣂⠀⢸⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡀⠀⠈⠢⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⢀⠀⡄⠀⠀⠀⠀⠈⠙⠖⠋⠀⠀⠀⠀⠈⠙⠒⠋⠁
⠀⠀⠀⠀⠀⠀⡤⠷⠶⠊⣀⠀⠀⠀⠀⠀⠀⠘⠠⠈⠈⡁⠀⠈⢅⠀⠀⠀⠀⠰⣀⡰⠀⠀⢀⠀⠀⠀⠰⣆⡀⠆
⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠒⠒⠒⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣴⣶⡶⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠻⢿⣷⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣟⠇⣰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠆⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠿⠛⢿⣿⣶⣦⣄⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⡾⠟⠉⠁⠀⠀⠀⠀⠉⠙⠿⢿⡿⢿⣿⣿⣦⣤⣀⠀⣶⣦⣤⡠⠆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠛⠀⠀⠀⠀⢀⣠⣶⣷⣦⡀⠀⠀⢠⣾⣿⣯⠙⣻⣿⣿⡇⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠈⠹⣿⣿⣿⣣⡴⠟⠛⠻⣿⣾⣿⡟⢠⢻⣿⣧⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣁⣀⣀⡀⠀⠰⠿⢿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⡌⠣⠙⢿⣿⡇⣰⣧⠄⡀
⠀⠀⠀⠀⠀⠀⡀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠸⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⠃⠿⠇⠀⠁⢀⠀⠄
⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⣭⣽⣟⠻⢿⣿⣿⣿⣿⣷⣶⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄⣦⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣻⣿⣰⠦⠽⠭⠟⠛⡛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣆⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡿⠟⣋⣥⣴⢶⣶⣷⣶⣶⣶⣶⣤⣤⣁⠉⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⡟⢻⠋⢷⣄⢱
⠀⠀⠀⠀⠀⠀⠀⡀⣼⢀⣤⣶⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣿⣿⡾⠻⢿⢹⡇⡿⠀⢸⠙⠎⡅
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡊⡙⢹⠋⠻⣷⠺⢶⡷⠾⢷⣶⡾⣿⣿⣿⣿⣿⠿⣿⣄⠘⣿⣿⣇⠀⠀⣿⡇⠁⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡚⢷⣶⣿⣶⣴⣧⣤⣤⣿⣀⣌⣿⣄⣽⣿⠃⣸⠿⠀⢹⣿⣿⠀⠀⢸⡇⠀⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⠿⠟⠛⠛⠛⠛⠛⠿⠛⠿⢿⡟⠁⠀⠓⢒⣾⢃⢻⣿⠃⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠠⣾⡀⢲⣷⡆⠀⠀⣀⡀⠛⢷⣄⣰⣿⣯⣼⣧⠹⣇⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣷⣞⣿⣇⣿⣿⡿⢨⣼⣿⣡⡖⡀⠰⣿⣿⡐⣿⣿⣇⢻⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣷⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡀⢠⣽⣧⠹⣿⣿⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⡄⢧⢼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡀⠀⢻⣷⣿⣿⣧⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⢀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡈⣿⣿⣿⣿⣿⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠸⠻⠄⠘⢿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣍⡿⠛⣉⣶⣼⢋⠈⣿⣿⠀⠀⣿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣶⣾⣿⣿⣿⠿⠟⠛⠛⠻⠿⠯⠤⣤⡺⢍⠟⣱⣧⠀⣿⠻⠀⠀⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠻⠿⠿⠿⠿⠶⠿⠿⠿⣀⠒⣿⣵⠏⣸⣿⣯⢰⣿⡀⠀⠀⢹⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣹⠋⢰⠛⣿⣿⢸⣿⡃⠀⠀⢸⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⡾⢠⣇⣶⣿⣿⡞⢿⣷⡀⠀⠘⣇⠨⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣰⣏⠸⠿⣿⣿⡅⠀⣿⣇⠀⠀⢹⠁⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣫⣿⣿⣶⣶⠿⣿⣇⢰⢸⣿⠀⠀⠘⡆⠰⠀⠂⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡏⢹⣿⣷⠀⠀⢹⣏⠸⢼⣿⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⠀⠀⠸⣿⠈⢸⣿⠆⠀⠀⠈⠆⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⡄⢀⣴⣿⡄⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠈⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣤⣤⣤⣀⡲⠟⠀⣠⡶⣶⡄⠀⠀⣠⣶⡄⣾⣠⡾⠃
⠀⠀⠀⠀⣺⣼⠇⣶⣿⠟⠛⠉⣉⣀⣠⣬⣭⣉⣙⣛⡻⠿⣶⡿⠀⣿⠷⣶⣾⡟⣿⡇⠐⠫⠶⠿
⠀⠀⠀⠀⠉⠉⣴⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⢳⡆⢸⣟⣆⣛⣭⣾⣟⢷⣤⣴⡶⢿⣧
⠀⠀⠀⠀⠀⢸⣿⡇⠈⠿⠛⢿⣿⣿⠿⡻⡟⠰⣣⣿⡿⠓⢻⠁⣾⡏⢈⣿⠉⣿⣽⢘⡛⠋⣀⣢⣿⣤⣄
⠀⠀⣶⣄⢿⡘⣿⠇⢠⣦⡀⠘⢟⡅⠠⠿⣁⠀⢿⣿⡟⠀⣼⢰⡿⠀⣼⡟⠀⣿⢯⡿⠀⣰⣿⣿⠟⣩⣿⡇
⠀⠀⢬⣽⠓⠀⣿⠀⢸⣿⡷⠀⣿⠁⣾⣿⣿⣦⠀⢿⠃⢰⡏⢸⠃⢠⣟⣄⠀⢏⣾⡇⢠⣿⢟⣥⣾⡿⠋
⠀⠀⠀⠀⢀⣾⡏⠀⢸⣿⡷⢀⣿⠀⣿⢧⣿⢿⠆⣸⣀⣻⣾⣤⣷⣤⣾⣿⣷⡟⢻⣷⣶⣿⠿⠛⣡⡄
⠀⠀⠀⠀⣸⣿⢷⠀⣾⠻⢃⣼⣿⣦⣽⣿⢿⣷⡟⢻⠛⣿⠁⣿⣿⠿⢿⣿⣿⠀⣼⣿⣯⡀⠀⠸⠷⠶⠶
⠀⠀⠀⠀⣿⣿⣾⠀⣿⣿⣿⣿⣿⢿⣍⠃⠀⠛⠀⠞⣒⠁⢠⣶⣾⠿⣿⡿⠋⢰⣿⠋⡉⣿⣤⣤⡙⠷
⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⡿⠋⡀⢸⣿⠁⣾⠃⣼⠏⣹⠀⡏⢠⡟⢰⠏⢠⠂⣸⠇⣰⣾⡿⣡⣿⣿⠂
⠀⠀⠀⠀⣿⣿⠟⢸⣿⡿⠀⣼⢇⣿⡏⢰⡏⢰⠏⢠⡏⢸⠁⢸⠇⡟⠀⢊⡆⢫⣄⣻⣯⣾⣿⠿⠃
⠀⠀⠀⠀⣿⣿⡄⢸⣿⡇⠸⢏⢸⡿⣶⣘⣦⣈⡆⠸⣤⣨⣷⣶⣿⣾⡷⣿⣿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠸⣿⣷⣿⠋⡙⡲⢿⣿⠞⠉⠻⠛⠻⢿⡿⠛⠛⠋⠀⠉⠉⠁⠴⠟⣱⣷⡆
⠀⠀⠀⠀⠀⠀⠉⢡⡆⣿⡝⠇⠀⠀⠀⠀⠀⠀⠴⠟⣱⣷⡆⠀⠀⠀⠀⠀⠐⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄



⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⢢⣶⣤⣶⣶⣤⣤⢠⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣴⣤⣤⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣦⣤
⠀⠉⠻⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠉⣿⣿⡏⠉⠉⠉⠉⠉⠙⣿⣿⠀⠀⠀⠀⣴⣿⡿⠉⠀⠀⠀⠉⠻⣿⣿
⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⣿⣿⣶⣄⡀⠀⠀⠀⣠⣾⣿⠟
⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣉⣛⣻⣿⣿⣿⣿⣿⣟⣛⣁⣀
⣿⣿⣋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠒⠒⠤⡀⠀⠀⠀⢀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠈⢢⠀⡠⠁⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡐⠊⠉⠢⡀⠀⠀⠀⢈⡔⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢭⣶⡄⢃⠀⠀⢀⡜⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣶⣶⠤⠄⠘⡲⠀⢈⠝⣎⠤⠐⠍⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠎⢀⠠⠊⣀⣤⡽⡶⠇⢀⠎⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⠒⢲⡀⠀⢸⠒⠚⣤⡟⣆⢾⠟⡩⡷⡙⢀⠂⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠉⡆⣀⣈⢳⣖⠃⠑⡤⠤⣦⠞⣎⡴⣩⠟⡹⠕⠱⢠⠂⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠾⣻⣿⣶⡾⠿⠘⢄⡀⠈⠁⣀⣰⠥⠊⢸⢀⡣⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠈⠒⠤⣀⠋⠀⠰⠦⣀⠀⢀⠌⡼⠁⠀⠠⠁
⠀⠀⠀⠀⢀⣀⠀⡠⠤⠒⠊⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠉⠁⡜⠁⠀⡰⠁
⠀⠀⠀⠀⠰⠀⠒⢇⠀⠀⠀⣀⠤⠒⠁⠀⠉⠒⠠⢄⣀⠀⠀⠀⠉⠒⢤⡜⠀⠀⡐
⠀⠀⠀⢀⡀⣱⣤⡜⠦⢒⣉⣧⡀⣀⣀⣀⣀⣀⣀⣀⣩⢁⠢⣤⣤⢊⠍⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣁⣠⣤⣀⣉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠙⠻⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣷⡀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⢹⣿⠀⢼⣿⡟⠻⣿⣿⣿⡿⠃⣰⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⢀⣿⡆⠸⣿⣿⣄⠘⢿⡿⠁⣼⣿⣿⣿⠃⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⢀⣾⣿⣿⡄⠙⣿⣿⣷⡀⢀⣾⣿⣿⡿⠋⣠⣿⣿⡟⢁⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄⠙⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⡟⢀⣼⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠈⠋⠉⠉⠉⠉⠀⣸⣿⠟⢉⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣤⣤⣤⣤⣤⡄⠹⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠿⠿⠿⠀⠙⠿⠿⠟⠋⠀⠿⠟⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⠀⣠⣴⣶⣶⣦⣄⠀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣸⣿⣿⣉⡍⣿⣿⣧⢹⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣷⣿⣾⡇⢿⣿⣿⣯⣴⣿⣿⡿⢸⣷⣿⣾⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣼⡿⣿⣿⣿⡿⠟⠈⠻⢿⣿⣿⡿⠟⠁⠻⢿⣿⣿⣿⢿⣧⠀⣠⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢙⣻⣟⡋⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⣿⣿⣿⣿⣿⣿⠻⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⢠⣶⣿⡿⠋⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⣿⣿⣿⣿⣿⣿⠀⠈⠻⠿⠇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⠿⠋⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠙⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⡿⠋⣿⣿⣿⣿⣿⣿⠙⢿⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢹⣿⣿⠀⠀⠀⠙⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠙⠻⠋⠀⠀⠀⣿⣿⡏⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⡄⢀⠄⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠠⡿⠟⣣⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠟⠋⡀
⠀⠀⠀⣠⣾⣿⣦⣠⣤⠼⠤⢤⣄⡀⠀⠀⠀⢠⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⣶⠎⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠉⠙⠟⠋⠁⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⢤⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⢀⡄⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⣠⡄⠐⠂⢴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠈⠙⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠒⠀⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠘⢄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⢀⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠘⠰⠀⠀⠁⠀⠀⠀⠀⡅⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠲⠒⠖⠂⠰⠒⠒⠖⠂⠐⠒⠶⠳⠒⠰⠖⠖⠒⠂⠲⠲⠒⠇⠖⠒⠶⠲⠲⠒⠀⠶⠓⠲⠒⠀⠖⠖⠂⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⡴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⡀⠀⠀⢸⡀⠀⣧⠀⠀⠀⢀⡴⢦⡀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⡆⠀⠈⡇⠀⢸⠀⠀⠀⣾⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡤⠤⡇⠀⠘⡧⠤⢲⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⢠⠖⠒⠒⢒⠚⠛⠉⠹⡄⠀⢣⠀⡇⠀⠀⡇⠀⡸⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠰⡏⠙⢦⣀⣀⡇⠀⠈⢇⢸⠀⠀⠃⢀⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠉⠙⣄⠀⠱⡀⠿⡄⠀⠈⠈⠀⠀⠐⠀⠀⠀⣸⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠘⣆⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡴⠋⢉⡳⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠋⢉⡞⠁⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠙⠋⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⢀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣠⠴⢻⠁⡤⠊⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠦⢤⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡤⠖⠋⠀⠀⣠⠏⠀⠀⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠎⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⣄⡀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣠⢾⡁⢀⡞⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠀⠀⠀⠙⠲⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡴⠃⠀⢣⡞⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠸⣄⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠟⠉⠀⢾⣿⣶⣄⣀⣉⠀⠠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⣦⡀⠀⠀⠀⠉⠙⠺⣉⠉⠉⠈⠛⠋⠳⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠛⣿⣠⡄⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠊⠀⠑⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢹⣯⣁⠹⣿⣶⣶⣶⣿⣿⣶⣶⣤⣶⣶⣶⣦⠀⣠⠀⠀⠉⠄⠀⠀⠀⠊⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⣤⡀⠀⠀⠙⠻⣦⣽⣿⣿⣿⣭⣿⣿⣿⣟⡿⣿⣍⢻⠇⣹⣆⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠾⠋⠀⢃⠀⣤⣤⣀⡀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢃⡜⠋⠀⢀⣿⣿⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣿⣾⣿⣽⣋⣙⣿⣷⣂⡀⠀⢀⣀⣀⣤⣶⣿⣿⣷⢼⠆⣶⣦⠈⣿⣿⣇⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢮⣧⡘⣿⣷⠈⣿⣿⠀⡄⠀⠀⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣤⣤⣄⡀⠈⠉⠻⣿⡅⢸⣿⠀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡟⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣦⠀⠀⠙⣷⠸⣿⠀⠄⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣿⠿⣿⠏⣿⠇⠰⣶⠦⣴⣶⣠⣆⠈⣿⣿⣿⡂⢄⠀⠹⣧⢿⣷⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠹⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢿⣿⣿⡇⠈⣷⡀⢹⣿⣿⠀⠀⡀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⠀⠀⠄⣠⣆⠀⡄⢈⣤⢠⣴⣤⢀⠀⠀⠀⠈⠻⢇⣾⣿⣧⢈⣿⣿⡇⠀⠁⠀⠀⠀⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢧⡀⠺⣿⣿⣦⣹⠈⠙⠃⠈⢉⠘⠳⠮⠁⠀⠀⠈⣿⡟⡟⢹⡿⢩⠁⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠈⢻⣄⠹⣿⣿⣿⣷⣿⣿⢦⠄⣀⠀⠀⠈⠛⠀⠀⢹⣿⣷⠹⡇⣼⠀⠀⠀⠀⠀⠀⡏⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠿⢀⣿⣿⣿⣿⣿⠧⣾⡶⠆⠑⠀⠀⠀⣠⠀⢸⣿⣿⡄⣆⢹⠀⠀⠀⠲⠀⠀⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⣿⣿⣿⣿⡧⠚⢋⣰⣲⣼⠀⠀⠀⠀⢀⣾⡟⣿⡇⠃⣸⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠋⢀⣾⣿⣿⡛⠛⠤⠀⠃⠀⢸⡿⣷⢸⣷⡇⢻⡇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣛⡛⠛⠚⠠⠅⠐⢂⣀⣀⣶⣬⢠⡏⢸⣿⡇⢹⡇⠀⠀⠀⠀⠀⢈⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢟⠉⠍⠉⠛⠓⠶⣶⣶⣦⣭⣟⡟⣤⠇⠀⣿⣿⣇⢼⣿⠀⠀⠀⠀⠀⠈⣇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠲⢄⣸⡟⠉⠘⢸⣿⠀⠀⢿⣿⣇⠼⣿⡀⠀⠠⠷⠦⠀⢧⠀⠆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣄⠀⣿⡟⠀⠀⢀⡻⣿⣿⣿⣧⠀⠀⡀⠀⠀⢸⡆⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡏⠁⠀⠀⠈⡿⠙⢻⣿⣿⡄⠀⠀⠀⠀⠀⢻⡀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣿⣏⣀⣠⡤⢾⠗⠀⢸⣿⣿⡇⠀⠀⣤⣈⠀⠘⣧⠶⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⢛⣉⣥⣤⡶⠶⠁⠀⠹⣿⣿⠀⠀⠀⠁⠀⣠⢽⡀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣥⣤⣤⠴⠶⠁⠀⡄⢻⣿⡇⢀⠀⠀⠀⠈⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣿⣄⠰⣇⠀⠀⠁⠘⣿⣿⡀⠠⢠⠶⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⣿⠟⠁⠀⠀⠐⠀⢻⣿⣇⠀⠀⡹⠧⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠹⣦⣄⣀⣤⣤⣆⠘⣿⣿⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣠⢸⣿⠏⠈⢈⣹⣄⠻⣿⣧⠈⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣏⢿⣿⣇⠈⣉⣻⡆⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢹⡼⣿⣿⠏⠉⠙⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢹⡇⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡶⠶⠆⢸⡇⠀⢸⣇⣀⠀⠀⠀⠀⠈⠿⠶⢶⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢿⣟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡿⠛⢻⡶⢶⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣀⣤⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢾⡏⠁⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⣦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣼⠿⠷⠶⠶⠶⠶⠶⠶⠿⣧⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⡯⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⡀⢸⣏⠀⢸⡇⠀⠀⠀⠀⣾⡆⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⡶⠟⠃⢸⡗⠀⠀⠁⠀⣿⠀⠀⠙⠁⢸⡇⠠⣤⣀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⢸⣧⠀⢸⡇⠀⣿⠀⢠⡆⠀⢸⡇⠀⠀⠙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠾⠿⠶⠾⠇⠀⠿⠀⠘⠿⠶⠿⠷⠶⠶⠖



⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣻⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠠⡀⠘⠀⠀⡇⠀⡇⠀⡄⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡀⠀⠐⢆⠀⠈⢦⠀⢳⠀⡆⠀⡇⢸⠁⡸⠁⡠⠃⠀⣠⣦⡤⠤⠤⠴⠯⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣶⢶⡞⠒⠒⠒⠓⠒⠒⠓⠒⠓⠓⠒⠓⠚⠒⠓⠚⠓⠒⠚⠓⠒⠚⠛⢲⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣭⠀⠀⠀⠀⠀⢰⡀⡦⢰⡆⣴⠀⣤⢰⢢⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢣⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⣿⣶⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠛⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣉⣛⣿⣭⣛⠛⠛⠛⠻⠏⠛⠻⠋⠟⠻⠛⠻⠭⢍⣉⣉⣉⣉⣉⣉⢉⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣓⣲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣑⣲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡶⠦⠤⢿⢬⡄⠀⠀⣀⢀⣀⠀⡀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣽⠉⠁⠐⠒⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢸⣾⡍⠀⠀⠋⠘⠔⠀⠃⠀⠘⠀⠀⠋⠘⠘⠀⠉⠀⠀⠀⠀⠀⣿⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠘⠶⢶⡒⠲⠖⠒⢲⠖⢲⠒⡶⠲⡖⢲⠒⢶⠒⢖⠒⠲⡖⠒⠒⠺⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡽⠋⠀⡰⠃⢠⠃⢀⠃⡤⠁⠈⡇⠈⢆⠈⢣⠀⠈⠢⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⠇⠠⠂⠞⠈⠓⡆⢱⠀⠘⡆⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠎⠀⠐⠤⠂⠀⠐⠁⠈⡆⠀⠘⡄⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣸⠀⠀⠀⡇⠀⠀⢱⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡏⠀⠀⠀⠇⠀⠀⠘⡄⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡠⠓⠄⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣀⠄⠊⠀⢀⣞⠀⠀⠀⠀⠀⢈⠀⠈⠐⠂⠄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠂⠉
⠀⠀⠀⠈⠁⠒⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⣀⣤⠊⡙⠁⠑⠠⡀⢀⡠⠁⠈⠐⠂⠠⡤⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠠⠄⠀⡀⠀⠀⠈⠑⡋⠉⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠀⠀⡁⡀⢀⣀⠄⠠⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠀⠀⠀⠚⡀⠀⠀⡔⠞⠁⣏⡄⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠒⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠱⣀⣀⡇⢨⡆⢻⢠⠆⠤⠊⠀⡌⠀⠀⠀⠀⠀⠀⢈⣄⠀⠀⠀⡀⢀⡀⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠄⢀⠐⠂⠠⢀⠀⠀⠀⡐⢉⠈⣼⠈⡇⢸⠀⣤⠰⠇⡐⠀⠢⡀⡀⠔⠂⠈⠀⠈⠢⠄⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⠔⠊⠉⠂⠔⢀⣯⠀⢶⠀⠇⠀⠄⠻⠀⡎⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠈⠈⢄⠀⠡⠀⠀⠀⠀⠀⠀⠈⠐⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡨⠒⠢⣀⣀
⠀⠀⠀⣀⠠⠄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢡⣀⣀⣀⠁⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠰⢀⡀⠀⢀⠊⠀⢀⠔⠀⠀⠁⠢⢀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠈⠀⢀⠌⠀⠀⠀⠀⠀⣢⠀⠀⠀⠀⠀⡇⠀⠈⠑⠢⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠂⠀⡠⠐⢷⠠⠀⠀⡀⠔⠈⠀⣡⠠⠄⠀⠤⠇⡀⠀⠀⠀⠑⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠁⠀⠀⠀⠀⢀⠎⠀⠀⠀⠑⣔⠆⠀⠀⠀⠸⠀⣀⠀⠤⠤⠀⣠⠀⠀⠀⠀⠈⠐⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀
⠀⠀⡀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⢤⠀⠀⡠⢊⠇⠀⣀⢤⡄⠀⠂
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠀⠀⠂⠀⠀⠀⢀⡆⠀⢠⢃⠜⣀⣾⡴⢥⣖⠺⢟⣟⠒⠒⠋⠛
⠀⠀⠀⠀⣠⠞⠉⢹⡄⠀⠀⣴⢦⠀⠀⠒⢀⣎⠆⣠⣿⡚⢻⣅⠀⠉⠒⠚⠃⠀⠉⠀⠀⠀⠂
⠀⠀⠀⣰⠏⠀⠀⠈⣷⠀⢰⡟⠸⠀⡰⡄⢸⣿⣮⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⢠⡀
⠀⠀⠀⡟⠀⠀⠀⠀⣿⠀⣼⣇⡇⠀⣇⡴⠋⠀⠀⣸⣠⠗⢁⠀⠀⠀⣾⠛⢦⠀⣀⣀⣼⣟⣀⣤⡾
⠀⠀⠘⡇⠀⠀⡄⠀⣿⡄⣿⡟⠀⢀⠟⠓⠋⠀⠀⠻⠚⠷⠃⠀⠀⠀⣿⣆⢸⠸⠉⢹⣿⠏⠉⠁
⠀⠀⠀⠙⠦⠞⠁⠀⣿⡇⣿⡇⠀⠊⣀⡀⠀⠀⠀⠀⠀⠰⠀⢀⣠⣄⠘⣿⣟⠀⢀⣿⡿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⡇⢠⠟⠉⠉⢦⠀⣀⠀⠀⡀⢀⣾⢃⡟⠀⣹⣿⡀⢸⣿⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠄⠀⣿⡇⣿⣷⢿⢠⣶⠀⢸⢠⣿⢀⣾⡇⢸⣿⠞⠀⣰⢻⣿⡇⣾⣿⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⢀⡞⣿⡇⢻⣿⠘⣿⡇⢀⡿⢹⡟⡼⢸⠃⣸⣧⣀⡼⣡⠊⣿⡇⢻⣿⣀⣾⠏
⠀⠀⠀⠀⠀⢠⠟⠀⣿⡇⠸⣿⡆⢿⣯⠟⠀⢸⣿⠃⠘⠶⠃⠉⠉⡰⠁⠀⣿⠇⡈⠻⠿⠋⠀⠤
⠀⠀⠀⠀⢠⠏⠀⠀⣿⡇⠀⢻⣧⠀⠀⠀⠀⠘⠋⠀⠂⠀⠐⠀⠀⢣⣀⣼⠏⢀⣁⣀⣠⠆
⠀⠀⠀⢠⡏⠀⠀⠀⣿⠁⠀⠀⠛⢃⣀⡐⠀⢞⢢⡀⢰⠛⠢⡄⢠⡤⠬⢤⣀⠈⢓⡾⣟⡆
⠀⠀⠀⢸⡀⠀⠀⣰⡏⠀⠀⠀⠘⠛⠶⠾⠓⠮⣦⣧⣈⣓⣤⣘⣄⣉⣑⣶⡾⡟⠉⠀⠉
⠀⠀⠀⠈⠳⠤⠴⠋⠀⠀⠀⠀⠀⢉⠀⠀⢠⠞⡽⠁⠀⠀⣩⢻⠉⠁⡀⢸⣃⠇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⣀⠈⢸⡥⠎⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠛⠛⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣴⠾⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⣠⡾⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⣏⣠⡾⠟⠀⠀⣿⣆⣀⣀⣀⣠⣤⣤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁⠘⠟⠛⠉⠀⠀⠀⠀⠙⠛⠉⠉⠉⠉⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣠⡶⠛⠛⠋⠉⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠙⠻⣦⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠘⠋⠉⠙⠃⠀⢠⡀⠀⠀⠀⠛⠉⠉⠛⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠐⠟⠻⠆⠀⢹⣇⠀⠀⠀⠾⠛⠗⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⢀⣠⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢾⣧⣴⣴⣿⠆⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣻⡷⢶⣤⣤⣤⣤⣤⣴⠶⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣷⡀⠻⣦⡀⠀⠀⠀⠀⠀⢸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣾⣧⠈⢿⣄⠈⠻⢶⣄⣀⣀⣴⠟⠁⠙⣷⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⠙⢷⣄⠙⢷⣄⠀⠈⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣄
⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠙⢷⣄⠙⠻⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡻⢦⣄⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡾⠋⠻⣦⡀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠘⣧
⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢻⡆
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⣦⣄⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠘⣷
⠀⣼⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⢿⡄
⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⢰⣶⡄⣴⡶⢠⣶⠀⣦⣰⠄⠀⠠⣦⣤⣴⣴⡦⣶⡶⢴⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡋⢸⣿⡇⣿⣄⢸⣿⡄⣿⡟⠀⠀⠀⣿⣿⣿⢸⡇⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⣧⢸⡏⠀⣿⡁⢸⣿⡇⣿⣷⠀⠀⠀⣿⣿⡿⢸⡇⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠘⠃⠀⠛⠛⠛⠘⠛⠛⠙⠂⠀⠀⠙⠛⠃⠘⠃⠘⠃⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⢰⣶⠀⣠⣶⣦⣄⢠⣶⣄⠠⣶⡆⣶⣶⣶⣶⡆⣠⣶⣶⣤⠠⣶⣶⣶⣶⡆⢶⣆⢀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⢾⣿⣾⣿⠁⢸⣿⣿⣿⣿⣶⣿⡇⣿⡷⠶⠶⠀⠻⠿⣶⣦⡄⠀⢹⣿⠀⠀⠀⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠸⠿⠈⠻⠷⠿⠛⠸⠿⠄⠻⠿⠇⠿⠷⠶⠶⠆⠻⠷⠾⠿⠃⠀⠸⠿⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⢀⣀⣀⢀⡀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⣿⣿⡇⣿⢸⣿⣿⢸⣷⡏⠀⠀⢸⣿⣿⣿⢿⡇⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡇⣿⢸⣿⣿⢸⣿⡇⠀⠀⠈⣿⣿⡏⢸⡇⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢿⠏⡿⢸⠿⣿⢸⡟⣷⠀⠀⠀⣿⢿⡇⢼⠇⢿⠇⢿⢿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⣀⠀⢀⣀⠀⠀⣀⣀⠀⠀⣀⣀⣀⣀⠀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠸⣿⣏⣛⡓⢸⣿⣿⣿⣷⣸⣿⣧⣿⠛⠻⠷⠀⣿⣟⣛⣛⠁⣿⣏⣻⣿⠆⣿⡏⠛⣻⣿⠛⠃⠹⣷⣼⡟⠁
⠀⠀⠀⠀⠀⢠⣬⣍⣻⣿⢸⣿⣿⣿⠙⣿⣿⡟⣿⣤⣴⡶⠀⣿⣯⣭⣭⡄⣿⡟⢻⣿⡄⣿⡇⠀⣻⣿⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠈⠉⠀⠈⠉⠁⠀⠉⠉⠀⠀⠉⠉⠉⠉⠁⠉⠀⠀⠉⠁⠉⠁⠀⠈⠉⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣾⣷⠘⣿⠇⠀⠀⣿⣾⣾⡷⣷⢺⡿⢲⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⠙⠀⣿⠀⠀⠀⢻⣿⣿⢳⣿⢸⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣷⣿⣿⠀⣿⠀⠀⠀⢸⣿⣿⢸⣿⢸⣟⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠉⠀⠉⠀⠀⠀⠈⠁⠉⠈⠉⠈⠉⠈⠉⠉
⠀⠀⠀⠀⠀⢰⣶⣶⣶⣆⢰⣶⡶⠶⣶⣶⠶⢆⣶⡶⠶⠶⠆⣤⡶⢶⣦⠀⣶⡶⢶⣶⡄⣶⡶⠶⣶⣶⡶⠆⢶⣦⢠⣶⠂
⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣾⣿⠀⠀⣿⣿⠀⠘⣿⡷⠿⠷⠸⣿⡁⢰⣶⡆⣿⡷⢾⣿⠁⣿⡇⠀⢸⣿⠀⠀⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠘⠿⠛⠟⠀⠻⠿⠂⠀⠻⠗⠀⠐⠿⠿⠿⠿⠃⠙⠿⠟⠛⠃⠻⠃⠈⠿⠂⠻⠇⠀⠸⠟⠀⠀⠀⠘⠟





⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠻⠿⠯⣿⣿⡿⠿⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⣀⡀⠀⠀⠸⠀⠀⠀⠀⠹⣷⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠰⡆⠀⠀⠀⠀⠈⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⢴⣶⣿⣶⣶⠆⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢈⣻⣿⣿⣭⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠙⠄⠑⠉⡄⠀⡠⠒⢄⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡄⠃⠀⡂⠟⡀⠀⠀⢠⢀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣄⡀⠀⢀⡀⢠⠔⢄⣙⠃⠁⠀⠀⡀⠁⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠴⠀⠂⠀⠀⠐⢻⠀⠀⠹⠖⠃⠀⢠⣘⢤⠁
⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠈⠙⠄⠘⡀⢀⡈⢑⣤⢠⠄⡄⠀⠀⠠⣀⡉⠁⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠼⠆⢡⠀⠉⠴⠂⠈⠀⢄⠀⡙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣥⠤⢾⢀⠳⠾⣀⠰⠦⢶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠐⠘⠃⠂⠒⠐⠒⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠠⢀⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠀⠢⡠⠊⠉⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣍⠣⠡⣻⣦⠔⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠢⡑⠁⠀⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠀⠰⢂⠀⠀⠀⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠑⢄⠀⠀⠀⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐

⠀⢰⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⣶
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢰⡄⢠⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠘⣧⢸⡇⣾⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣀⡘⠆⣨⠄⠠⣅⠋⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⢸⡇⠀⠀⢸⠆⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⣈⠛⠦⠔⠋⢤⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠞⢁⡞⢰⡇⢳⡈⠳⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠁⠀⡾⠁⢸⡇⠈⢷⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⡴⠋⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⣸⠁⠀⣿⡀⠀⠀⢿⡇⠀⢀⠀⠀⠄⢀⡀⠀⢠⣾⠃⡼⠀⠀⣠⡤⠤⠤⢤⣿⠤⠴⠚⠁⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⡏⠀⠀⣿⡇⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠈⠁⣿⡟⠊⠀⠀⠈⠀⢀⡀⠀⣼⡟⠀⢀⡴⡄⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠁⠀⢀⣿⠀⠀⣰⠟⢀⣠⢄⣤⠀⠀⣠⡖⢺⣿⠁⢠⠀⠀⣴⢛⣿⠃⢰⣿⡇⠀⣾⠗⢃⡴⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⢀⡖⠒⢾⣿⣀⡴⠋⠀⣾⡇⣸⡇⠀⣰⣿⠀⣼⡟⢠⣿⠀⣸⣯⢾⡿⢠⠇⣿⠁⡼⠻⡤⠏⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠉⠒⢺⣿⢿⣄⠀⠀⠿⠖⢻⣇⡴⠹⣧⡼⠹⣧⠋⣿⣰⠋⠁⠸⣧⠞⠀⠻⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⡟⠀⠙⠳⣤⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⢀⣴⠞⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⢠⡟⠁⣶⠀⠀⠈⣿⠀⠀⠀⠀⠀⠠⠴⠶⢤⣿⣅⣀⡤⠀⠀⠀⠀⠠⠖⠒⣾⡷⠤⠶⠛⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⣿⠁⢠⣿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⣿⠀⠀⠀⠀⠀⣠⡄⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠿⠀⢸⣿⠀⠀⣼⠃⠀⠀⠀⡀⠀⢠⡆⠀⣾⡇⢀⠀⢠⣿⡄⣸⠁⡒⠀⣾⡟⠀⢠⡄⠀⣰⣿⠁⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣠⠞⣡⣤⡀⠀⣰⣿⣠⢿⡇⣸⣿⠀⣤⠀⡆⣿⣇⡏⣸⡇⣼⣿⠇⣠⣿⠃⣰⣿⡏⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⡿⠀⢰⣿⢦⣧⠔⠁⣿⡇⠸⣧⠏⣿⢰⣿⢸⠀⢹⣿⠁⣿⣰⠃⣿⣰⠏⣿⣼⢻⡿⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⢀⠇⢀⡼⢹⡇⠀⠉⠀⢿⠏⠛⠋⠀⠀⠁⠀⠈⠁⠀⠙⠉⠀⠀⠀⣾⠇⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠘⠇⠀⠀⠉⠁⠀⣼⢁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠓⢶⡄⠀⠀⣸⡟⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠖⠋⠉⠁⠉⠉⠙⢿⡧⢤⣄⣤⠾⠋⠀⣠⡿⠁⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣾⣿⡞⢶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠻⣿⣿⢀⡙⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢟⣉⣸⡄⢱⣿⣇⠀⠀⠀⠀⠀⢢⠀⠀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢘⣋⣤⣤⠈⠉⡉⢉⢉⠉⠉⡉⠲⣿⣿⡿⣶⡟⠁⠀⠀⣄⡀⠀⠈⣆⠠⣟⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠊⢧⣀⠀⠀⠺⣦⣼⡐⣿⣷⡘⠻⠇⠸⢧⠀⠀⠀⠹⣇⠀⠀⢸⣧⠛⢤⠀⢘⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠙⠻⠿⣷⣦⣟⢰⣿⣿⣿⣦⠀⠀⠈⢆⠀⠀⠘⣥⠀⠀⢸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠹⣇⣀⡀⠀⠀⠀⠀⠀⠀⣀⣛⣿⡀⠻⢿⠟⠋⠘⠷⠄⡈⣤⣀⠀⠻⠀⠀⢸⣟⣀⣤⠄⠀⡄
⠀⠀⠀⠀⠀⡀⢰⣿⣿⡿⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢦⡀⣀⠀⠀⠀⠔⠀⠀⠃⠐⠀⠀⠀⢸⣿⡏⠁⠀⠀⣷
⠀⠀⠀⢀⡞⢠⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣟⠁⠀⠈⣀⡈⣿⣦⠠⡄⠀⠀⢹⠀⠀⠀⠀⠸⣿⣿⣤⣀⣀⣸⣇⣀⣤⠆
⠀⠀⠀⢸⠀⢸⣿⣿⣷⡍⠆⠙⢿⣿⣶⣦⣤⣤⣤⣶⣿⣿⡿⠁⠈⢀⣿⣧⠈⢷⠀⣇⣤⠀⠀⢧⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀
⠀⠀⠀⠈⠀⠀⠹⠿⢿⣶⠀⠀⠀⠀⠙⠋⠙⠉⠉⠉⠉⠀⠀⠀⠀⣸⡇⠈⠇⢸⠀⢻⣿⠀⠀⢸⡀⠀⠀⢸⢣⣿⠟⠉⠀⠀⣀⡀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⣤⣶⣶⣷⣾⣾⣿⣿⣿⣷⡶⣬⣛⢾⣇⣨⠇⡏⠉⠀⠀⠘⡇⠀⠀⢸⢸⠋⠀⣀⡴⠞⠉⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣤⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣧⠙⣿⡄⣷⡆⠀⠀⠀⠇⠀⠀⡇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣼⣵⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣾⣇⠹⣧⣿⠀⠔⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡘⢿⣿⣿⣦⣶⣾⣿⣷⣶⣤⣄⠈⢻⣿⣿⣿⢹⣶⢇⠇⠀⠁⠀⣬⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠿⣼⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⠞⣿⡴⠀⠀⠀⠀⡇⠀⠀⠀⠄⠸⣷⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⢰⣿⠇⡇⠀⠀⠀⣷⠀⠀⠀⡇⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠰⠀⠈⠙⢻⣿⣿⣿⣿⣿⡏⠀⣿⣿⡏⣼⢣⣾⡇⠄⠀⢀⡿⠠⠤⠠⡧⠴⠿⠿⠤⢤⡄⠀⠤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣧⣴⠟⠟⠈⠁⣾⣿⠰⠀⠊⠸⣧⡄⠠⠄⢶⠠⣶⣶⣶⣎⣿⡀⠀⢹⡆⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠛⠿⠿⠿⠿⠿⠿⠻⠛⢻⣄⠀⠀⣴⠏⠻⡇⢞⡀⠀⠖⢷⠀⠲⠘⣦⠰⠶⠾⠿⠟⠃⠘⠈⠿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⣿⡟⢠⣮⣿⡈⡀⠘⠀⠛⣧⠀⢀⠸⣆⠐⣾⣿⣧⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⣷⠂⠉⠹⣇⢱⠀⠀⠀⠘⣆⠀⠀⠱⡀⠿⠿⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⠻⣿⣿⡇⠀⠀⣿⡌⢇⠀⠲⠄⠛⣆⠀⠀⠙⠂⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠹⣿⣧⡀⠀⢻⣷⡘⣄⡀⠀⠀⠈⢦⠀⠀⠙⠂⠀⢤⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢻⣿⣇⠀⢈⣿⣧⠈⠷⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⢻⣿⠀⠀⠨⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠘⠛⠁⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣄⣀⣠⠤⠴⠖⠚⠋⠉⠉⠉⠙⠓⠲⠦⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⢦⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣀⣀⣤⡤⠴⣶⠶⠤⣤⣀⣀⠀⠀⠀⠉⠉⠛⠓⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣠⡼⠁⠈⠳⣤⣀⡀⠀⠀⠀⡷⠚⠛⠉⠉⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠉⠛⠓⠲⠦⢤⣤⣀⡀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⣍⠀⠀⠀⠀⠀⠀⢈⡿⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡆⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣇⣠⡴⠦⣤⣈⡇⠀⠀⠀⠀⡇⠀⠀⠀⣠⠖⠲⣾⠀⠀⠈⡟⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇⠀⠀⠀⡏⠀⠀⣿⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣠⠴⠃⠀⠀⢸⠇⢀⣀⡏⠉⠉⠙⣇⣀⡀⢷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢹⡇⠀⠀⠀⡏⠉⠁⢸⡉⠉⢧⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢤⣼⡏⠉⠉⠁⣇⣀⣀⣘⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⡏⠉⠉⠉⡟⠃⠀⣧⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⢸⡇⠀⠲⠶⢧⣀⠀⠀⣧⡄⠀⢹⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀⣸⠋⠙⣆⢸⠃⠀⠚⠉⠀⠀⠀⠀⠀⠈⠀⠀⣧⡀⠀⢸⡆⠀⠀⠀⠀⢸⠇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢳⡀⠀⢠⡏⠀⠀⢹⡏⠳⢤⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⠀⢸⡇⠀⠀⠀⠀⡾⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢷⡀⢸⠀⠀⢀⣸⠇⠀⠀⠉⠓⢦⣄⣀⠀⠙⠲⣤⣀⡀⠀⠀⠀⡇⠀⠀⢀⡼⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠳⣾⠀⠀⠉⣹⡄⠀⠀⠀⠀⠀⠳⡍⠛⠲⢤⣀⠈⠉⠛⠒⠲⣧⠀⣠⠞⠁⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢸⠀⠀⠘⠁⠻⠤⣤⣀⠀⠀⠀⠹⡄⠀⠀⠉⠳⠆⠀⠀⠀⣿⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡄⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⡿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠤⣤⣤⠤⠶⠂⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣤⣶⣾⣿⣶⣦⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣰⣿⠿⠋⠉⠀⠀⠈⠙⠻⣿⣦⣠⡄⠀⠀⠀⠀⢀⣠⣠⣤⣤⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⣽⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⢠⣴⢞⣭⣷⣶⣶⣮⣝⡳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⣏⣉⡉⠻⣶⢠⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡄⢠⡿⣵⣿⣿⡿⠋⠙⢿⣿⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣟⠉⢹⠶⢻⡟⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠁⢼⣧⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣄⣸⠛⠋⣠⡾⠃⢀⣼⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡄⠀⢘⣏⢿⣿⣷⣄⠀⠀⣠⣾⣿⡟⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⡟⣩⡁⣀⡀⠁⠈⠻⣿⣦⣤⣄⣠⣤⣴⣾⡿⠋⠀⠁⠀⠀⢛⣮⡻⣿⣿⣷⣾⣿⡿⣟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣘⠋⠉⠛⢻⡟⠛⠉⣙⠃⠀⢀⣰⣆⡀⠀⠈⣙⠳⢯⢭⣭⠷⡞⣋⣠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡿⠛⠉⠁⠀⠀⠉⠙⠻⣿⣿⣇⡀⠀⠀⠁⠀⢀⣽⣷⣿⠿⠿⠿⠿⣿⣾⣯⡀⠀⠀⠀⣴⡿⠟⠋⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⣠⣤⣤⣤⣤⡀⠀⠈⢿⣿⣿⡀⠀⣶⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣶⣸⣿⠀⣰⣾⣶⡄⢸⣿⡆
⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⣰⣿⣿⠿⢿⣿⣷⡀⠀⠈⣿⣿⡏⠀⣸⣿⠟⢷⣦⣤⣶⠿⠿⣶⣤⣴⡾⠻⣿⣇⢸⣿⠀⠙⠿⠿⠁⢸⣿⠅
⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠘⢿⣿⣧⣀⣰⣿⣿⠇⠀⠀⣿⣿⡿⣤⣿⣿⠀⠀⢸⣿⠁⠀⠀⠈⣿⡇⠀⠀⣿⣿⣤⠹⣿⣶⣤⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⣰⣿⣿⠗⠀⢿⣿⡀⠀⠈⢿⣦⣀⣀⣴⡿⠃⠀⢀⣿⡿⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⣸⣿⣷⡀⠀⠀⠙⢻⡟⠋⠀⠀⢀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣶⣶⣤⣴⣶⣾⣿⣿⠿⠃⠀⠀⠀⠉⠈⠻⣿⣶⣤⣀⣸⣇⣀⣤⣶⣿⠟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠿⠟⢿⠟⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠿⢿⡿⠿⠛⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡊⡀⠈⡁⣀⣠⡤⠄⢀⠀⠠⠌⡡⠔⠊⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠄⢼⣇⣁⡤⠛⣉⣥⣤⣶⣶⣤⣀⠐⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠀⠐⠒⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠋⠄⢿⡏⠐⣿⣅⣂⣸⣭⣿⣿⣿⣧⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⣿⣀⣷⡀⠛⠉⠉⠉⠉⠛⠛⢿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⡇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⣼⣯⣼⠁⠀⠀⠀⠀⠀⠀⢀⣼⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣀⣀⣿⣏⡐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡠⠀⠀⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠞⠄⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠉⢹⣿⠙⣤⣄⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡇⡟⣿⡄⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⡊⠒⢦⡠
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡏⠐⢠⠀⡀⣷⡏⢿⡢⢰⣲⣾⡿⠟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡶⠟⠿⠉⠉⠍⠐⢶⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣹⠀⣧⡿⠀⠈⢻⣌⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⠀⠀⠀⠁⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣼⠀⣿⢇⠀⢈⣹⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⣤⣴⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢰⣿⠀⠀⠀⢸⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣀⠀⠀⢀⣟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠉⣇⠈⣿⠀⠀⢩⡟⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⠉⠉⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⣿⠀⢹⠀⠀⣸⣗⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⠀⠐⠒⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⠀⣿⡄⠀⠙⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢈⣁⢁⠈⣁⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠛⠀⠿⠗⠈⠀⠯⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠈⠐⠀⠀⠘⠀⠁⠁⠀⠃⠃⠑⠘⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠃⠈⠘⠈⠛⠉⠘⠀⠁⠀⠀⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠶⠾⠿⠷⠿⠳⠷⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁⠀⠀⠀⠀⢀⣴⣀⠀⠀⠀⠀⡉⠙⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠐⣷⠥⠀⠀⠀⠋⠃⠀⠀⠠⢾⠗⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⣰⣶⡀⠀⠀⣀⣠⣤⣶⡶⢶⢶⣴⣦⣤⣀⡀⠀⠀⣰⣶⡀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠉⢀⣴⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⠀⠁⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠐⣶⣧⠄⢀⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣄⠀⢠⣷⡆⠀⢻⣧
⠀⠀⣠⣤⣄⠀⣀⣾⣧⣤⣠⣅⣡⣤⢾⣯⣤⣄⣤⣤⣠⣤⣄⣀⣄⣀⣤⣤⣀⣤⣀⣤⣀⣌⣩⣆⣄⣥⣥⣤⣄⣿⣦⣀⣤⣄⣀⡀
⠀⠀⢿⡏⠉⢉⡉⠉⠉⣉⠁⠉⠉⣉⣀⠉⠉⢉⡉⠉⠉⣉⠉⢉⣉⢉⠉⠉⠉⠉⢉⡉⠉⠉⠉⡉⣉⡉⠉⠉⡉⠉⢉⡉⠉⠉⣿
⠀⠀⢻⡇⠀⣼⣿⠀⢸⣿⠄⢰⣿⠟⢻⣷⡀⢸⣿⣦⠀⣽⡇⢸⣿⠛⠛⠛⢰⣿⡟⠻⠷⠘⠿⣿⣿⠿⠂⠹⣿⣤⣾⠟⠀⠀⣿⠇
⠀⠀⢻⡇⠀⢼⣿⠿⢿⣿⡁⣾⣏⠀⠀⣿⡇⢸⣿⢿⣿⣿⡇⢸⣯⠿⠿⠆⠈⠻⠿⣿⣦⠀⠀⢿⡧⠀⠀⠀⢸⣽⠏⠀⠀⠀⣿⠆
⠀⠀⣬⡅⠀⢾⣯⠀⢸⣿⠅⠘⠿⣶⣾⠿⠁⢸⡏⠀⠛⣿⠇⠸⠿⠒⢶⡦⠘⢿⣶⣾⠷⠀⠀⣿⡧⠀⠀⠀⢸⡿⠂⠀⠀⠀⣿⡆
⠀⠀⣿⣧⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⢤⣤⡤⢄⣄⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⡤⣤⣤⣽⡃
⠀⠀⠀⠈⠉⠈⠈⢻⣇⠉⠉⣭⣄⠉⢻⣦⡀⠀⠁⠀⠁⠀⠈⠀⠀⠉⠀⠈⠁⠀⠁⠀⠉⢩⡿⠋⢀⣄⡈⠉⢈⣿⠇⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠛⠏⠁⠀⠙⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠁⠀⠉⠞⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠀⠀⣀⣀⡀⠘⠳⣶⣤⣄⣀⡀⢀⠀⠀⣀⣀⣶⡾⠋⠁⡀⣄⡀⠀⠀⢠⡎⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠘⠛⠀⠀⠀⣀⠈⠁⠛⠓⠛⠛⠋⠁⠉⠀⠀⠀⠀⠘⠛⠀⣀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⣤⢀⠀⠀⠐⠻⠏⠀⠀⢀⡶⣆⠀⠀⠀⠿⠆⠀⠀⢀⣠⢾⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢲⣤⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⡀⣴⡾⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠋⠋⠾⠛⠟⠿⠟⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠙⠛⠁⠀⠀⢳⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⣀⣰⣤⣴⣦⣄⣤⠄⠉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣶⣿⣿⣿⣿⣿⣿⣿⣏⣫⣜⣿⠶⣁⠀⣠⡶⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣏⣼⣿⠶⣿⣿⣿⣿⠟⢳⣟⣿⣶⣿⢾⡻⣿⡉⠚⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⣷⣿⣙⣿⣍⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣰⣿⣿⣿⣦⠀⠀⢀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠘⣧
⠀⠀⡠⠂⣥⣿⡿⢿⠿⢿⡍⢉⠻⣿⠿⢷⣽⣻⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⣸⡟⠁⢂
⠠⡎⠀⠰⣿⣿⣧⣾⠀⢸⣿⣷⣶⣌⢷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠛⢿⡿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡀⠀⠈⣇
⠀⠳⠀⠀⠛⠻⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⢀⣿⣦⡈⠁⠂⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⢀⠀⠰⠋
⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠉⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⠇⢰⣾⠟⠻⣿⡆⠀⠀⠀⠀⢈⣶⡄⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢀⡠⠂⠀⠀⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⡏⣱⣿⡟⣤⠀⢹⣧⡀⠀⠀⠀⢺⡆⠀⠀⠀⠀⠀⣰⣏⣀⣀⡤⡀
⠀⠀⠀⠀⠀⠀⢠⡖⠀⣀⣤⣴⣶⣿⡿⢿⣷⣶⣶⣤⣈⠉⠛⢿⣏⣿⣿⣿⣧⣿⠀⠀⡿⠃⠇⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⠋⠉⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢰⠏⣠⣾⢿⣿⣿⣽⣛⡷⠾⣿⣿⡟⠛⠛⠿⢶⡄⠈⡿⠿⢿⣿⠻⠠⠀⠇⠐⠻⠂⠀⢸⡇⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⣸⠃
⠀⠀⠀⢀⣤⡀⡀⠙⠧⠴⣏⢠⡟⠉⠻⠛⠻⢿⡦⠀⣤⠀⣈⠀⢦⣀⢠⡄⢱⡄⠀⠀⠀⣀⠀⠀⠀⢠⠁⠀⠀⠀⢠⡿⣿⣿⣿⣷⣤⣀⣿⣀⢀⣀
⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠘⠂⠙⠒⠤⠘⠄⠀⠀⠁⠈⠀⠘⠋⢀⡀⢸⠃⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⢠⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀
⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⣸⠃⢀⡄⠀⠀⠀⠀⠀⠛⠀⠀⠀⡾⣡⡿⠟⠉⠉⠀⠉⣉⡉⣉⣉⣯⣧⠞⠁
⠀⠀⠀⠀⠀⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣾⠇⠀⠀⠀⠐⠀⠀⠀⠀⡘⣴⡟⢁⣀⣠⣤⣴⠾⠟⢛⣭⡟⢉⠔
⠀⠀⠀⠀⢸⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢣⡙⠀⠀⠀⢀⡟⠀⠀⠀⢠⣽⠋⠀⠘⠋⠉⠀⠀⠀⠰⠋⡠⠊⠀⢀⡰⠄
⠀⠀⠀⢸⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢧⣼⡇⠀⠀⢠⣿⠁⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⢀⡴⠋
⠀⠀⠀⢈⢹⣇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢸⣿⠀⠀⠀⢸⠇⠀⠀⠀⣾⡇⢀⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡉⠰⠶⢿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢻⣿⡇⣿⡅⠀⠀⢀⡿⠀⠀⠀⣼⠉⢸⣿⣀⣰⡆⠀⠀⠀⡌
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣶⣤⣀⠀⠀⠀⠙⠋⣱⣿⣿⣇⣿⠆⠀⠀⢸⠃⠀⠀⢰⡿⠀⣀⡛⠉⠉⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣧⡄⠀⠀⢀⣴⣿⣿⣿⢩⡇⠀⠀⠀⣾⠀⠀⠀⣼⠃⣠⣿⡇⠀⠀⠀⠀⠀⡖⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣠⣶⠿⣿⣿⣿⣿⣿⡗⠀⠀⢰⡟⠀⠀⠀⣿⢠⣎⣙⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⠋⠁⠀⣴⢹⣿⡟⣿⠃⠀⠀⠈⡇⠀⠀⠀⣏⠰⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡿⠁⠀⠀⠋⢸⣿⣇⣿⠀⠀⠀⠀⣷⠀⠀⢠⣿⠀⠉⠛⠿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢿⣦⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠈⣿⠀⠀⠀⣟⠀⣶⣶⣶⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⣄⡀⠀⠀⣿⣿⣿⣿⡗⠀⠀⠀⢹⡄⠀⠀⣿⠀⣼⣿⣿⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢸⣿⠋⠀⠀⠀⣿⣿⠋⢿⣇⠀⠀⠀⠀⣥⠀⠀⢸⣆⠀⠙⠛⢿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣶⣿⣶⠶⠶⠀⣿⣿⣟⠀⣿⠆⠀⠀⠀⢿⡄⠀⠘⣿⠀⣀⣰⣤⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣾⣿⣿⣤⣤⣤⣼⢻⣿⡷⠀⣿⡃⠀⠀⠀⠠⣇⠀⠀⢻⡈⢿⣿⣿⣿⡀⠀⠀⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠈⠛⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠻⠀⠀⠅




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠉⠈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠉⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠉⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⣿⣿⡿⠛⠛⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠠⠐⠀⠁⠠⠤⡀
⠀⠀⠀⣀⡀⢀⠀⠀⠠⢤⡒⠂⠀⠠⠤⢄⠀⠀⠎⠁⠀⡰⠔⡼⠋⠉⠁⠠⠔⠂⣀⣐⠒⠀⠀⠀⠐⠉⠑⠄
⠀⠀⠋⠀⠐⠉⠈⠑⠀⠀⠱⠒⠀⠀⠀⠀⠁⠉⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠱⠉⠐⠉⠉⠉

⣶⣶⠶⠶⠶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠸⠞⠁⣠⡤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡤⠶⠚⠋⢉⣉⣉⠙⠀⠚⠁⣀⡤⠶⣤⠉⠳⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⡴⠞⡋⠉⢩⡇⠀⠀⢸⡃⠂⣤⠟⠀⠁⡀⢠⠈⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠞⠉⠀⣼⢁⣴⣏⠀⣴⠦⠈⠳⣤⣤⣤⡤⣴⢣⡏⣀⠀⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡼⠁⢠⠇⢰⡿⠋⢀⣸⡧⠿⣧⢀⡴⡆⣀⡀⢰⠇⣾⣴⢏⣼⣱⢃⡌⠙⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧⡴⠋⢀⣿⠀⡴⢋⡼⢁⡾⠁⣾⠋⣼⣽⡷⣿⡼⡟⠹⠞⣏⣡⡞⠁⢠⡇⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣌⠳⠶⠀⠀⠄⢸⠇⣀⡛⠋⠀⢸⣃⡞⠛⠋⠉⠀⠀⠉⠀⠂⠀⠀⡈⠁⠀⢴⡏⠐⣯⡅
⠀⠀⠀⠀⠀⠀⠴⠿⠃⠀⢰⡆⠀⣰⠟⠙⣧⠀⠄⠈⠉⠀⠀⢀⣤⠖⡀⠀⣤⢀⠀⣶⠗⡂⢀⡄⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠰⠂⠀⢠⣿⠀⣼⠃⠀⢠⣿⠀⠀⢰⡿⠀⣈⢀⡟⣠⢠⡼⣼⣨⢠⡟⣰⢃⣾⠱⠏⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⣾⡏⢰⠇⠀⠀⣸⣯⣤⣿⠖⣧⣴⡏⣾⣱⣧⣾⣠⢻⣧⢿⠞⠙⣿⠇⣠⡼⠃
⠀⠀⠀⠀⠀⠀⢰⠇⢰⣿⢃⡏⠀⣠⠞⣿⠇⣿⡞⣠⣿⠸⠏⠙⢉⠁⡿⢃⠈⠁⠀⢀⣼⣿⠿⢋⡀
⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⢸⠁⣼⠃⢸⡟⢀⣩⠰⣧⠏⡴⠤⠖⠙⠷⠶⠋⢀⣤⢾⣿⣿⣠⡴⠋
⠀⠀⠀⠀⠀⢰⡇⠀⢿⣿⡾⢰⡇⢠⡿⠁⠀⠙⠦⠴⠊⠀⠰⠀⠰⢀⡄⣠⠟⢡⣾⢟⡟⠀⠀⡄
⠀⠀⠀⠀⠀⠸⣇⠀⢸⣿⡇⠀⣙⣋⣠⠆⢰⡄⣦⢰⠄⠀⠀⠁⠀⣿⠠⣏⣴⡿⣫⠟⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠛⠁⢠⠏⠉⠁⢠⡿⠀⠋⠀⠀⠀⠀⠀⠀⠙⢧⣭⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣤⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡏⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⢸⡔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢰⠀⠀⠀⠀⠈⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢣⡄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠏⡇⠀⠘⢲⠒⠒⠒⠚⠀⠀⣀⡤⠺⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⠀⠀⠀⡆⢀⡀⠠⠀⠀⠀⠀⠀⠚⠃⠀⠀⠸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠾⢡⠇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠎⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⣀⣀⣀⡣⠀⠀⠘⠀⠀⠀⠀⠀⣐⣂⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢈⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢈⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⠀⠀⠀⠘⠒⠒⠒⠁⠀⠘⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿