Ver Emojis & Symbols

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀
⣀⣤⡴⠖⣛⣫⣭⠵⠶⣒⣒⡶⠶⣯⣝⡳⢤⡀
⣩⡴⠖⢛⣩⡵⠖⣛⣩⡵⠖⣚⣩⠽⢖⣚⡭⠽⣄⢦⡲⣄⢀⡀⠀⠀⠀⣀⣠⠤⠶⣒⣛⣋⣉⣉⣙⣛⠛⠛⠻⠶⠶⠶⠶⠶⠶⠚⢋
⡤⠶⣛⣩⡤⠖⣛⣩⠴⢖⣋⡭⠶⣚⣩⠵⢖⣫⠽⣆⣙⣈⣣⠥⠖⣚⣫⠵⠖⣛⣉⣩⣭⣭⣉⣉⣉⠙⠛⠻⠷⣶⣶⣶⣶⡶⠾⠿⠛
⣒⣫⡭⢶⣚⡯⠭⣖⣚⡭⠵⣒⣫⡭⢖⣪⠽⣒⣫⣥⣿⣖⣒⣛⣩⡥⠶⢚⣋⣭⣭⣤⣤⣬⣍⣉⠛⠻⠷⣶⣤⣤⣀⣀⣠⣤⣤⣤⣶
⢦⣼⣛⣛⣻⣭⣭⠵⠶⣚⣫⡭⢖⣫⠽⣒⣫⣥⣤⣄⠉⢻⣿⢶⡶⢒⣛⣩⡥⠶⠶⠶⠦⣤⣍⡙⠻⢶⣤⣀⠉⠛⠛⠛⠛⠛⠛⠉⠉
⣤⣤⣤⣤⣤⡴⠶⠞⣋⣭⠴⣚⠭⣒⣭⣥⣤⣄⠉⢻⣷⢠⡟⣸⢹⡭⠥⠶⣒⣛⣛⣛⡲⠦⣌⡙⠷⣤⡉⠛⠿⣷⣶⣶⣶⣶⣶⣶⣶
⣈⣉⣉⣤⣤⠶⢞⣋⡥⣒⣭⣒⣭⣥⣤⣄⠈⢻⡇⢸⡏⣸⠃⣇⠳⣭⣛⡭⠽⠶⠶⠮⣍⡓⢦⡙⢶⣌⠻⣶⣄⣀⠈⠉⠉⠉⠉⠉⠉
⠛⣉⣉⣥⠴⢚⡫⣗⣯⡿⠭⠶⠶⣦⡈⣿⠇⣾⠃⣿⠁⢿⣄⣙⢓⣒⣚⣭⣭⣉⡛⠳⢦⣙⠳⣝⢦⡙⣦⡈⠙⠿⢿⣿⣶⣶⣶⣶⣤
⠛⣋⣭⢴⣪⣵⣮⣿⠷⠯⠩⠝⣦⢸⠇⣿⠀⣿⡀⠻⣧⣄⣉⡭⠭⠶⠶⠶⠦⢬⣝⡳⣦⣙⢷⡝⣦⣳⣌⠻⣷⣤⣄⡀⠉⠉⠛⠛⠻
⣛⢭⣺⣝⡿⠛⠉⠀⠀⠀⠀⠀⡟⣼⠀⣿⡀⠻⢷⣦⠤⢴⣒⣻⠭⠭⠭⠭⣝⣳⢌⣉⢤⡉⣦⣻⣌⢣⡙⣷⣌⠙⠿⣿⣿⣶⣶⣤⣤
⣳⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⣦⡈⠛⠶⢖⣒⠯⣝⡲⠯⣟⣛⣛⣯⠵⣿⣯⣮⣤⣽⣮⡷⣝⢮⡹⣮⡻⢿⣶⣄⣈⠉⠛⠿⠿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠷⣬⣉⣻⡭⢽⣒⡭⠷⠚⠉⠉⠀⠀⠉⠉⠑⠒⠾⠭⠭⠭⠭⠾⠷⠝⢮⡻⢦⣈⠙⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠭⢛⠶⣤⣈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣀⣀⣀⣤⠀⠀⠠⣤⣤⣴⠀⠀⠀⠀⠁⢀⣴⣶⣢⡴⠀⢠⣴⣿⣷⠾⠀⠀⠀⠁⠀⣅⢠⡄⣀⣠⣆⢀⣠⣰⣔⣦⣤⣼
⠠⢤⣤⣿⣿⠟⠁⠀⢐⣿⣿⡟⠀⠀⠀⠀⠀⠘⠛⣿⣿⠋⠁⠀⠀⢸⢿⠇⠀⠀⠀⠀⠺⣿⣶⣿⢿⡟⠋⠁⠈⠙⠻⣿⣿⡏
⠀⠸⣿⢻⣯⠀⠀⠀⠀⠟⢸⡇⠀⠀⠀⠀⠀⠀⠀⡟⣾⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠁⠀⠀⠀⠀⠀⠙⢻
⠀⠀⠉⢸⡏⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣯
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡯
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣤⡞⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⢤⣷⠀⠀⠀⠀⠀⠀⡇⣇⡀
⠀⠠⠚⣷⠿⡆⠀⠀⠀⣰⣟⣇⠀⠀⠀⠀⠀⠠⣯⡏⠓⢤⠀⠀⢀⣦⠿⣀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣗⠀⠀⠀⠀⠀⠽⣿⡤
⠀⠳⡶⠿⠽⠇⠀⠀⢠⣀⣿⣾⠇⠀⠀⠀⠸⠿⠛⠻⠶⠟⠁⠠⣼⠿⣦⣼⠇⠀⠀⠀⠀⢤⣴⠟⠻⠟⠃⠀⠀⢀⣀⡼⢿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⣸⠃⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢿
⠀⠀⠀⠀⢀⣿⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⡇
⠀⠀⠀⢠⡟⣏⣀⣤⣤⡄⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢀⣄⣤⣀⡰⡟⣇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣈⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣋⣠⣾⣿⣿⣿⣷⣿⣷⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡝⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣷⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣴⣶⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⠻⢿⣿⡿⠄⠈⠙⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠼⣿⣿⠿⢻⣿
⠀⠀⠀⣼⣿⣄⠀⠈⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠀⢀⣼⣿
⢀⡤⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢦⡀
⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠐⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⢠⣞⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣦
⠀⠈⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉
⠀⠀⢰⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣧
⠀⠀⠘⠳⠚⠙⠶⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡶⠟⠙⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣶⡀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣺⡟⢵⣿⣿⢻⣻⡇
⠀⠀⠀⠀⠀⢠⡄⢴⣭⣦⣄⠀⠀⠀⡀⣀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⢎⣩⣿⣶⣶⣿⣷⣾⣄⣬⣍⣋⡀
⠀⠀⢠⣀⢄⣀⣿⣼⣿⣇⣽⡶⣦⣄⢻⣷⣿⡇⢸⣿⣿⣷⣿⣿⣿⣿⣷⠀⢀⣾⣿⠞⠿⣿⢻⣿⣿⣿⣿⣯⡾⠿⣿⣿⣧⡀
⠀⠀⠘⠿⠿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠁⠘⣼⣿⣿⣦⣙⡛⢿⣿⠀⠈⢡⣤⣶⣾⡟⣿⣿⣯⣿⣿⣿⣿⣷⣼⣿⠟⠁
⠀⢈⣿⣶⠿⠟⡿⡵⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠉⠉⠋⠙⢛⡋⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣀⡀
⠀⠘⡟⠿⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠉⠆⠀⠀⠀⡴⢠⣴⣶⣶⣽⡳⠀⠀⢸⣿⡟⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠸⣭⣼⣿⣿⣿⣿⣷⣛⣿⣷⡜⠀⠀⢧⣠⡽⣻⣿⣿⣷⣷⢡⠀⠀⠈⣻⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⢟⢋⣻⡿⠁⠀⠰⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⡈⠻⠋⠀⠀⢨⠟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣛⠗⠀⠀⠐⠀⠀⠀⠀⠙⢯⣿⣿⣭⣿⣻⠋⠀⠀⠀⠀⠘⢧⡙⢧⣿⢿⠆⠀⠀⠨⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠈
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⢻⣿⣿⣿⣿⢶⣾⡿⠍⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠺⣭⣙⣧⠘⠟⢟⠿⣙⡇⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣣⣾⣿⣞⣶⣿⣿⣦⣤⡈⠙⠛⠀⢠⣾⣿⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠈⢹⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣻⠿⡿⠍⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⣿⣿⣿⣿⠾⣿⣿⣿⣄⠀⠈⠙⠻⠿⣿⣿⣿⡏⢿⣧⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠉⠀⠀⢹⣿⣿⣷⣶⣶⣶⡄⣠⣶⣾⡇⢾⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠋⠈⢡⣾⠟⣿⣿⡿⣿⣿⣿⣟⣾⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣷⡟⢛⣿⣿⣷⣿⣿⡿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⢸⠏⠛⢻⣿⡟⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⢤⣼⡤⡰⠛⠁⠀⠀⠁⠠⣀⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠰⠁⢸⣿⣿⢶⣶⣿⣷⠁⣄⣀⡀⠀⠀⠀⠀⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⣿⣿⣿⣲⣬⣭⣾⣿⣶⣿⣿⡷⣄⠀⠀⠀⠘⣏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣿⣧⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠅⠀⣼⣿⣿⣿⣿⣿⣿⡿⡽⠋⠁⠰⠏⡌⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠋⡙⢛⣿⠋⠉⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣿⣷⠎⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⣙⠃⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⡏⣀⣠⡤⢀⣈⣀⠀⠁⠀⢀⣀⡀⠬⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣋⡉⠉⠀⠈⠉⢙⡖⠋⠀⠀⣬⡿⣷⣿⣿⣆⠘⡄⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢤⣵⣦⡀⠀⠀⠀⠀⠀⢸⠿⠿⢿⣿⣿⣷⣶⣤⣀⠉⠉⢈⣧⣄⣿⣿⣿⣿⣿⣿⣆⢰⣄⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣀⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠙⠻⣧⣙⠂⠀⠀⠀⢀⣰⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠀⠚⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣆⠀⢀⣀⣀⣀⣀⣀⡀⢀⣼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣈⣿⣿⣿⣿⣿⣇⣨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡟⠁⠀⡄⠀⣀⠟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠸⣿⠠⢷⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠰⠶⢷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠀⠀⠀⠀⠀⢀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⢛⣽⣿⣿⠿⠛⠋⠉⢀⣀⣀⣼⣿⣷⣦⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠁⠁

⠂⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⢀⠄⠂⠀⠀⢀⠀⠀⠀⠂⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢀⡄
⠠⠎⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠘⠒⠀⠀⠀⢘⢀⠀⠀⠠⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠘⠒⠀⠀⠀⢰⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠰⢦⡀⠀⠀⡄⠤⠒⠀⠰⠀⠀⠀⠀⠈⠙⠉⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠰⢦⡀⢀⠀⡀⠤⠂⠀⠰⠂⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠐
⠀⠀⠐⠀⠀⠈⠈⠀⠀⠀⣀⡀⢀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠈⠈⠀⠀⠀⣀⡀⢀⠀⠀⢠⠀⢀⠀⠄⠀⠀⠀⠀⠀⢠
⠀⡀⠦⠀⡄⠀⠀⠀⠀⢰⠤⠜⠐⠀⠀⠄⠄⠀⠀⠀⠄⠀⠀⠀⡀⠀⣀⠀⠀⠆⠀⡄⠀⠀⠀⠀⢰⠤⠜⠈⠀⠀⠄⠄⠀⠂⠀⠤⠀⠀⠀⣀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠈⠀⠀⠈⠀⠀⠀⠀⠂⠀⢈⠢⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠐⠘⠀⠀⠈⠁⠀⠀⠀⠂⠀⠈⠲
⡀⠁⠀⠀⠀⠀⠸⢄⢀⠀⠀⢬⠀⢒⠀⡆⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠸⢄⠀⠂⠀⠌⠀⢒⠀⡆⠀⠀⠀⠀⠀⣀⠠
⠈⠀⢰⡄⠀⠀⠀⠀⠈⠀⠈⠈⠀⢈⠀⠃⠀⠀⠂⢛⠁⡇⠀⠀⠀⠀⠀⠈⠀⢰⡄⠀⠀⠀⠀⠈⠀⠈⠈⠀⠈⠀⠃⠀⠀⠀⢻⠁⡇
⠀⢲⡍⢴⣇⠀⠀⡄⡀⠀⠀⠀⠃⡀⠐⠀⠀⠀⠀⠰⠀⠸⠀⠀⠀⠀⠀⠀⢲⡍⢴⣇⠀⢀⡈⠀⠀⠀⠀⠃⡀⠐⠀⠀⠀⠀⠰⠀⠘
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡘⢀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣦⡄⢰⣃⠀⠀⠀⢸⠀⢀⠀⠀⡘⢀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣦⡄⢰⢁⠀⠀⠀⢠
⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠰⠐⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠚⠀⢀⠀⠀⠀⣿⣾⣿⠃⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠉⠠⣉⢈⡉⠀⣀⠀⠀⠈⠉⠉⠃⢀⣀⠘⢤⡈
⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠠⢶⠶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⢶⠶⠀⠀⠀⠀⠀⢀
⠀⠀⢈⠘⠂⠠⠠⠃⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢀⠙⠂⠠⠰⠃⠉⠀⠀⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠐⢢⠰⠀⠀⠘⠀⠰⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢢⠰⠀⠀⠘⠀⠐⡀⠁⠀⠀⠀⠀⠀⠘
⠀⢲⠈⠀⠁⠀⠀⠀⠀⠘⡉⠁⢠⠀⢠⠁⠁⠠⠀⠀⠈⠀⡀⠀⠢⢀⠂⠀⢦⠁⠀⠁⠀⠀⠀⠀⠘⡉⠁⢀⠀⢠⠁⠁⠠⠄⠀⠀⠀⡀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄⠁⠠⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠄⠀⢀⠀⠀⢠⠀⠀⠀⠁⠠⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⢀⠀⠀⠀⠈⠑⠠⠀⠠⠹⠀⠰⠀⡇⠀⠀⡀⣤⠀⡖⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠠⠀⠠⠘⠀⠰⠀⡇⠀⠀⡀⣤⠀⡖
⠀⣀⠼⢃⡄⠀⠀⠠⠀⠀⠀⠀⡄⠐⢀⠀⠀⠀⠀⢘⠀⢣⢀⠀⠀⠀⠀⠀⣀⠼⢃⡄⠀⠀⢠⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⢘⠀⢣⢀
⠀⠘⠂⠙⠓⠀⠀⠂⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠘⠂⠙⠓⠀⠐⠂⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠒⡄⠀⡔⠉⠉⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⡧⢤⠿⠻⠃⠤⣜⠐⠛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢠⢶⣄⠀⠀⣠⢶⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠆⠸⣿⡟⣀⠠⠿⠿⠧⠤⢽⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⠉⠉⠀⠉⠉⠁⠒⠤⡈⢦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠀⠐⠒⠂⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠰⡄⠇
⠀⠀⠀⢀⣠⠖⠚⠉⠉⠉⠉⠉⠒⠦⣀⠀⢩⠃⠀⠀⠀⢸⠢⠀⠀⠀⠀⠀⠁⠀⠀⠁⠒⠀⠠⠀⠒⠉⠀⢀⠄⠀⢠⠬⠄
⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠳⡈⠁⡇⠀⠀⠘⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⡀⠤⠐⠉⠀⢀⠇⠀⢠⠀⢄⠀⠀⡠⠂⠁⠀⡁
⢀⢞⠇⠀⠀⠀⠀⠐⢦⣀⠴⠊⠉⠳⡀⠀⠱⡀⢳⠀⠀⠀⢣⠀⠀⠀⢸⠀⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠘⢄⠀⢡⠈⠀⣠⠖⠁
⡾⢸⠀⠀⠀⠀⠀⡠⠊⠙⢆⠀⠀⢀⡱⡆⠀⣧⠀⠳⡀⠀⠀⠱⢄⣒⣙⡄⠤⠀⠠⠀⠀⠀⠤⠀⠐⠀⢀⡴⠋⠀⠀⠀⠀⢀⠀⠀⠁⠀⠁⡄⠀⢠
⡇⠘⡀⠀⠀⢱⢎⠀⠀⠀⠀⢳⡔⠋⠀⠹⡀⢹⢀⣀⡨⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⣋⣀⣀⣀⡠⠤⠒⠊⠀⠀⠀⠀⠀⣀⡀
⣧⠀⢣⠀⠀⠀⠀⠑⢄⢀⡔⠁⠘⣄⢀⣴⠗⠋⠉⠀⠀⠀⠀⠈⠉⠒⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠐⠈⠀⠀⠈
⠸⡄⠈⢧⠀⠀⠀⠀⠠⠻⣄⠀⠀⡸⠋⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⢀⠴⠋
⠀⠹⣄⠀⠣⡀⠀⠀⠀⠀⠈⢦⡼⡃⠀⠀⠀⠀⠀⢣⡴⠊⠙⠒⠂⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠴⠚⠒⠉⠁
⠀⠀⠘⢦⡀⠙⢄⠀⠀⠀⠀⠘⠳⠇⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠙⢦⡀⠑⢤⡀⠀⠀⠀⢵⠂⠀⠀⠀⠀⠀⠀⠙⠦⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠳⢤⣈⠒⢤⣀⠀⠑⢢⣄⡀⠀⠀⠐⠀⠀⡠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠮⢭⣐⣧⡀⠈⠋⠁⠀⢀⠔⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⢦⡁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠈⠣⣀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠈⠙⡖⠒⠒⢒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠋⠉⠉⠉⠒⠪⣆⠀⠀⡇⠀⢀⡯⠒⠊⠉⠉⠉⠓⠢⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢋⣭⠙⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⣭⡙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢡⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠰⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠄⠀⠀⠀⠁⠀⠀⠃⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢒⡂⠁⡀⠀⠀⠈⢹⡏⠁⠀⠀⣀⠨⢀⡒⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢀⠔⢊⡥⠒⠉⠀⢀⣀⣠⡞⢳⣄⣀⡀⠀⠉⠒⢬⡑⠢⢄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠹⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⢸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢏⣿⣷⢀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⡀⣼⣿⡙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⡸⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢻⣷⣼⡟⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⢃⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⠃⠁⠀⠈⠻⣿⣦⣦⡀⠀⢀⣀⣹⣾⣿⣿⣷⣏⣀⡀⠀⢀⣴⣡⣿⡟⠁⠀⠀⠈⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣬⣿⣿⡿⠃⠘⢿⣿⣿⣥⣶⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⣀⣀⣤
⠀⠀⠀⠀⠈⠉⠉⣙⠛⠛⠺⢿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⣸⣼⣿⠗⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠾⣿⣿⣦⠠⡀⠀⠀⠀⠀⠀⢘⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⡃⠀⠀⠀⠀⡀⢀⡄⣰⣿⣿⠷⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠛⠛⠉⠻⣿⣷⣿⣦⣽⣦⣼⣾⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣷⣴⣿⣴⣿⣾⣿⡟⠉⠛⠛⠒⠒⠒⠒⠲
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠑⡑⡀⠀⡀⠀⠁⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡑⠢⣀⠈⢢⡀⠤⢬⡄⠰⣴⡎⡄⡀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⣒⠢⠬⣵⣭⣵⣭⣤⣔⣖⣺⣿⣿⣿⣿⣷⡶⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠀⡀⠀⠀⠉⠐⡉⠉⠈⠁⠉⠉⠀⠱⣿⣿⣇⡏⠀⠀⣠⡦⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠉⠁⠂⠠⠤⣈⣔⣒⣤⣝⢿⡷⠻⠛⠿⣷⣴⣞⡥⠒⠁
⠀⠀⠀⠀⠀⠀⠨⠩⠄⠀⠀⠀⠀⠀⠀⢠⣅⣤⠥⠤⠽⠿⠿⣷⣾⠃⠀⠀⠀⢈⣿⣿⣒⠂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⡀⠀⡠⣤⢜⣸⣴⣥⣵⣒⠀⢢⣌⣽⣿⣦⡀⢀⣠⣼⣟⢿⡿⣃⣤⣮⡦
⠀⠀⠀⠀⠀⠀⠀⢀⡰⣁⣌⣮⡟⠋⠹⠏⠙⠛⠋⣬⠳⠾⠻⣿⣟⣿⣿⣿⣿⣷⣿⣟⡿⠿⡿⡿⠇
⠀⠀⠀⠀⠀⠀⠉⠹⣴⡿⣿⣷⣶⣷⣿⡾⣿⣿⣿⣿⣿⣿⣶⣭⡼⡿⠋⢿⣿⡿⣿⣿⣮⠪⡊⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠬⠐⠈⡁⠄⠎⢁⠐⠈⣁⣴⡿⣟⡿⠟⣁⠎⠐⠀⠀⠈⢿⠄⠃⠙⣏⢳⡤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⡢⡀⠄⡀⠒⣁⣤⣴⣿⡯⣊⢝⢅⢼⢧⠃⡀⠂⠀⣀⢠⠀⢀⠀⠈⣣⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⣿⣾⣿⣿⣟⣿⣿⠿⠿⡿⠿⡷⣷⣵⣽⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⠟⠛⠃⢀⠉⡀⠐⣭⣽⡻⢿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣖⡒⠳⢤⡄⠐⠢⠂⢄⡨⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠊⠁⠒⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠿⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠛⠈⠀⠃⢈⣿⠀⠀⠀⠀⠀⠀⣸⣿⠃⠂⠀⠐⠂⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠠⣴⠿⢿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⢤⣴⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢠⠀⣿⣿⣿⣷⣀⣀⡋⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠁⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⣼⠀⣿⣿⣿⣿⡿⣿⣦⣄⡀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠺⢿⣿⣿⣿⠁⠀⠈⠻⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢰⡿⣿⡿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⡟⠀⠁⠀⠀⠙⢏⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡟⠛⢻⡟⢿⣿⠀⠀⠀⠀⡼⢡⠯⡄⠀⠀⡤⢜⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠰⣧⣿⡀⠀⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⡿⣿⣷⠀⠉⢁⣴⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣽⣿⣼⣍⢹⠀⠀⠀⠀⡇⣿⣿⠀⠉⠛⠁⠿⢶⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣯⠈⠀⠀⠀⠀⢙⠀⠀⠀⠀⠇⡸⡿⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡟⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠝⢿⣆⢿⣿⣄⠀⠀⠀⠀⠀⠀⣰⣿⡟⣰⡟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⣿⠸⣿⣿⡆⠀⠀⠀⠀⣰⣿⣿⢃⡟⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠹⠀⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⠀⠇⠐⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣼⡇⣿⣿⣿⡇⠀⠀⣼⣿⣿⡏⢸⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣼⣿⣿⣿⣶⣶⣿⣿⣿⣇⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢿⣿⠛⠻⣿⣿⣿⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣼⡇⠀⠀⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣭⣿⣷⣰⣿⣿⣿⣿⣭⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠉⠻⠿⠋⢹⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣧⣄⣨⣍⣠⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣷⢿⣼⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣿⣷⣿⡘⣞⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⢸⣿⣿⣹⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⣿⣷⣻⡄⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣧⣹⣿⣿⣿⣧⣹⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡛⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠂⠀⠀⠀⠀⠱⡀⡀⠄⠐⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠢⠐⠀⠀⠀⠢⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠤⢄⡀⠠⠒⠒⠒⠠⠀⠀⢀
⠀⠀⠒⠓⠈⠐⢄⠊⠀⠀⠀⠈⠲⠁⠀⠀⠀⠀⣀⣴⡐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣦⡐⡄⠀⢄⢄⠀⠀⠀⠀⠀⣼⠉
⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⣿⣿⡇⠈⠈⠈⠈⠉⠉⠈⠃⠀⠹⠷⠤⠀⢀⣀⣤⣤⣀⠀⢀⠆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⣆⠀⠀⡄⠀⠀⠉⠀⠹⡄⠀⢱⣘
⠀⠀⠀⠀⠀⠀⢀⣀⠂⠒⢰⣮⣤⣄⡀⠀⠻⠿⠇⠀⠿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠓⠓⠂⣀⠀⠀⣻⢀⣘⡃⡂
⠀⠀⠀⠀⣀⡠⠼⠟⠛⠋⠉⠁⢀⣀⣀⣤⠤⠤⠤⠖⠒⠒⠂⣈⣀⣠⠤⠤⠤⠀⠂⣀⡀⢀⡴⠿⠿⢿⣿⣦⠀⠀⠉⠉⠐⠀⠀⣤⣤⠀⡀
⠀⠐⠚⠉⠀⣀⣠⠤⠔⠒⠛⠉⠉⢀⣀⣠⠤⠤⠒⠒⠛⠉⣉⣁⡤⠤⠖⠒⠋⠉⣉⣀⠠⠉⠈⣀⣀⠈⢫⣽⣇⣀⠀⣰⠾⠿⣶⣿⣿⠀⠈⠉
⠀⠠⠔⠒⠉⠁⠀⢀⣠⠤⠒⠚⠉⠉⠀⣀⣠⠤⠖⠒⠋⠉⢁⣀⣠⠤⠴⠒⠋⠉⠁⣀⢒⠀⠀⠻⠃⠀⢘⢶⠿⣿⣿⠡⣤⠀⢹⡿⠛⣠⠔⢡⠞
⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⡀⠄⠒⠉⠀⠀⠀⢀⠠⠐⠊⠉⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⠡⠀⡀⣀⣴⠻⢂⠖⠀⠙⠦⣀⣠⡾⠋⡴⠁⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⣡⠄⡖⠖⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣀⣤⣤⣤⣤⣤⣦⣴⣸⠤⠴⠂⠈⠤⠦⠄⠀⠉⠈⠁
⠀⠀⠀⠀⠠⢤⡤⣾⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡈⠉⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠉⠉⠀⠈⠈⠈⠙⠻⠿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣻⣿⣿⣿⣿⣿⣿⢋⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢫⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠈⠻⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠿⠹⣿⡿⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⠿⣯⠙⢷⣄⠙⢿⣿⣷⣆⣀⣠⣤⣤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⣶⣦⣾⣿⣷⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣿⡯⠀⠀⠙⠟⢦⣍⡛⠻⠿⠿⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠿⠞⠙⣻⣿⣯⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣿⣿⣿⣝⡛⠷⢤⣌⣛⣿⢿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⢛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢉⠁⠠⢀⣤⢆⠹⠖⣀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠚⠉⠉⠁⢈⠁⡈⢠⠀⠈⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠋⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⢽⠆⠀⠀⢠⣶⣶⣤⣸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠔⠀⠁⠀⠀⠀⠀⠀⠀⢠⣠⠀⠀⣠⣤⡘⠆⠀⠀⠙⠀⢸⣿⣿⣿⠹
⠀⠀⠀⠀⠀⠈⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣀⢿⣿⠟⠀⢀⡰⣨⣼⡆⠉⠉⠉⢈⠆
⠀⠀⠀⠠⡇⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⠈⠃⠀⢀⠂⠈⠀⠀⠈⠀⠀⡀⡈⠁
⠀⠀⠀⠀⠈⠂⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢶⡔⡤⠀⠀⢎⡙⠃⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡤⡤⠂⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢌⠀⠀⠀⠱⠂⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⠀⢤⠒⠐⢆⠁⣜⠀⢘⣀⣀⣼⠀⢀⣾⡖⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣀⣾⢦⠀⠀⣤⣬⡇⢸⡇⢠⣏⠙⠉⡄⠀⠀⠀⠀⠀⠎⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠋⠁⠻⣬⠀⠀⢉⠀⡄⠀⡏⠤⡜⠀⢐⡛⢀⠀⠀⢐⠞⠀⢂⣰⠴⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⠙⠁⠀⢞⠁⣄⠀⢀⠀⡜⠠⠟⢄⠀⠂⢀⠂⢀⠂⠘⠁⠀⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⢻⠉⢡⠀⢈⠀⡖⠐⢇⠀⠃⡽⠀⢀⠀⠀⠁⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠦⡈⠀⠀⠀⠀⠨⠀⢨⠠⠔⠪⠀⠀⠁⠀⠀⠁⠀⣠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠇⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⡀⣤⢄⣀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⠀⠀⠀⠀⠀⠀⠀⣘⡦⠔⠁⠀⠐⠈⠀⢰⠀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠐⣁⠀⠀⠈⠀⠀⠀⠀⠠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠧⠇⢇⣃⠾⢣⢻⡘⣎⢷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⣭⣝⣛⡒⠯⣕⡢⢗⠘⣎⢧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣍⡉⠛⢶⣍⠳⡕⡽⡎⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣷⡄⠹⣧⠹⡜⢆⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⠀⠹⣧⡙⣎⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⣿⣿⠇⠀⣹⢇⠎⣰⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⣿⣿⠀⣼⢱⡇⠸⣧⡳⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣰⣿⣿⣿⣆⠸⣎⢏⢦⡈⠻⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣴⣿⣿⣿⣿⡿⠀⢹⡌⡇⣻⡄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣿⠟⠁⠀⠀⠀⢀⣾⠇⣷⢻⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠟⠁⠀⠀⠀⠀⣰⣿⠏⣰⠇⢳⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⠃⢀⣀⠀⠀⢀⣰⣿⠃⣰⡏⣾⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢣⢇⣾⠿⢛⣛⣛⠛⢛⣁⣴⠏⣰⡇⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡎⡾⢸⡏⣰⢋⡶⣫⢔⡋⡅⡔⣺⣭⣴⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⣧⢸⡇⣿⢸⡇⢷⢨⢲⢡⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠛⠛⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⣠⣴⡾⠿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣁⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠶⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡄⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠋⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠐⠈⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠠⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⡵⠊⠁⠀⠀⠀⡠⠚⣱⡿⠁
⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⠶⠶⣶⣶⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⢠⠞⣡⣾⠋
⠀⠀⠀⠀⠀⠀⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⠟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⣿⣄⠁⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠶⠤⣬⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣀⠀⢀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⠞⠁⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣈⣉⣀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣿⠿⣿⣶⣦⣤⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣂⠀⠀⠹⠿⠿⠿⠛⠋⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣻⣿⣿⣷⣶⣤⣀⠀⠀⢠⡟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡽⢽⣷⠛⡟⢯⠙⢟⢷⡆⠁⠀⠠⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⡏⠁⣧⢼⣿⣗⠖⢜⣇⡈⡎⣿⡉⣿⣄⣘⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⣇⢸⢻⣾⣿⣿⡷⣼⣿⣛⣭⣯⣿⡟⠋⠙⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⣿⣿⣏⣿⣧⣾⣿⣿⢿⣿⡿⡟⣿⡈⡘⠘⢷⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢿⣧⣌⣻⣹⣿⣿⣾⣿⢿⠁⢹⢸⣇⣇⠂⠞⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡄⢹⠛⠟⡏⢛⣿⣇⣤⣼⣶⣾⣾⣻⣿⡛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣬⣶⡶⢿⡟⣿⣏⣿⣷⣾⡿⠋⢿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠾⠿⠛⢯⣥⣤⣾⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣽⣄⠀⠀⢀⣴⣿⣿⣿⣿⠷⠆⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠘⠛⠿⣿⡿⠃⠀⠀⢀⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣶⣶⣶⣶⣾⣿⣿⡏⠀⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢬⣓⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣊⠠⠋⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠐⠀⠀⠀⠀⠻⠀⢹⠖⠑⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⡗⠀⠀⠀⠉⢹⠛⣀⡖⣠⠅⠀⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⠀⠀⠀⣈⠀⠀⠀⣇⠀⠽⠖⣬⣓⡞⢉⠀⠰⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰⠀⠀⠀⠈⡀⢠⣌⣃⣄⣲⣿⣿⣷⣷⠉⠿⣷⢀⣠⣤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠰⡏⠢⢭⣿⣿⣿⣻⣿⣿⣿⡶⣾⠊⢉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠐⠄⠀⠈⠙⣤⠚⣷⡋⠀⢿⣿⡖⢻⣿⣿⣿⡯⢏⡥⠄⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠎⡜⠃⠘⣧⢷⣽⣥⡀⠐⠷⣿⡿⣿⣽⢿⣟⣿⡓⠂⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠴⠃⡄⢀⠀⠀⢀⣽⣧⢆⣛⣰⣆⣿⣿⡿⠣⠀⠀⠹⣟⣿⣿⣿⣿⣷⣮⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠃⢇⠀⢀⠀⠸⠀⣄⣧⠌⣷⣸⣾⣿⣿⣿⡏⠀⠀⢀⠔⡀⠈⢿⣿⣿⣿⣿⣏⡆⣤⠁⠰⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠘⠀⡠⣘⠀⣠⣦⢷⡈⠀⠛⠁⠉⠛⠿⠟⠋⠁⠀⠀⢀⠊⢀⠀⡚⠈⣿⣿⣿⣿⡿⣿⡛⠡⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣤⠀⢻⣶⡓⢾⣾⠗⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡀⠘⢠⣿⣿⣿⣿⣷⠯⡗⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣽⣿⣾⣥⡿⣷⣿⠃⠀⠀⢀⠀⢀⡀⠀⠀⠀⠠⡊⠆⠀⠀⢉⣧⠇⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣉⣟⢉⣶⣯⣯⣵⣻⣿⣿⠅⠀⡀⠀⠀⠒⠈⠨⠁⡀⠀⠀⡐⠂⠀⠀⠠⣿⣞⣾⣿⣿⣿⣿⡛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⢛⣿⢯⣿⠏⠀⠀⣤⠀⠆⠢⠀⠀⣂⠁⠠⠀⠀⠀⢑⡂⠐⣿⣥⣯⣭⣿⣅⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠇⠐⣿⣿⣿⣿⣿⣿⠛⠁⠀⣴⣾⣽⣻⠈⠱⢈⡐⠀⠂⠨⠅⠢⠈⠄⠧⣷⡜⢫⣿⣯⣅⣾⣿⢯⣻⢇
⠀⠀⠀⠀⠀⢀⣰⣿⡿⣿⣿⠻⡟⣉⣀⣀⣸⣿⣿⣿⣹⣧⣀⣀⠐⢢⠠⢀⠈⢀⠢⣵⣼⣿⣣⣽⣿⣿⣿⣿⣿⢿⡿⣦⢅
⠀⠀⠀⠀⠀⠂⠙⠀⠷⠞⠟⠻⣿⣿⣿⠻⣿⡟⣿⡿⣭⣿⣽⣿⣤⣄⣠⣤⣄⣭⣴⣿⣿⣷⣿⣿⣿⣿⣧⠙⣯⢼⠟⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠤⣽⠹⠏⢿⣶⣿⠟⣿⣿⣿⣿⠛⢿⡿⡿⠿⠋⠉⠃⠈⠓⢦⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠋⠉⢹⡛⠢⢹⣾⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣧⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⡄⠀⢀⣤⣤⣴⣖⣢⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢠⠆⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢗⣰⣾⣿⣿⣿⣿⡿⠛⢛⣻⣿⣿⣿⣿⣿⣿⣤⠉⠀⠒⠠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠋⣵⢿⣿⣿⣿⡿⠎⠙⠛⠛⠛⠛⠉⠀⠘⠉⠉⣀⣀⠀⠀⠀⠀⠐⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠀⠻⡟⠻⠿⣇⠀⢿⣿⣿⠿⠇⠀⠀⠐⠒⠂⠀⠶⠀⠀⠀⠀⣾⣿⣿⣷⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣾⣛⣻⢿⣦⠻⣦⣄⠙⢃⣀⡀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⢻⣿⣿⡿⠋⠀⣹⣿⠁⠠⣾⠟⣿⣿⣿⣿⣿⣹⣿⣿⣶⠀⠀⠀⡠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⣿⠁⠀⠀⠈⣉⣵⣾⠃⡖⠀⣿⣿⣿⣿⣿⢾⣿⣿⡇⠀⠀⠀⠀⠀⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢸⡇⢰⣶⢠⣾⣿⣯⠋⠂⠇⢀⣿⣿⣿⣿⣟⢻⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⡏⠈⢻⣿⣷⣶⡾⠿⠟⠻⠿⣶⠷⢶⣬⣽⣿⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠏⢀⠀⢳⣿⢋⠤⠒⠀⠈⠐⠈⠀⠀⢀⡙⠻⢿⣯⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⣇⠀⣏⣠⡾⠋⢠⠀⠉⠛⠂⠂⠀⠀⠀⠈⠴⠂⣦⣌⡋⠁⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣿⢀⡾⠛⡁⠀⠌⠁⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠉⣠⠃⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⣷⣶⠻⠃⡈⠀⠀⠀⢄⢀⠀⠀⠀⠀⣄⠀⠀⠀⠐⠶⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⠀⠀⣿⣶⣀⠀⠀⠈⠀⢤⣀⡀⠀⠀⠀⠁⠀⣀⡀⠀⠒⠘⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠰⣿⡆⠀⢿⣿⠋⠀⠄⠀⠈⠀⠙⠻⠶⢶⠶⠂⠻⣿⡟⣆⠀⠀⠈⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠆⠀⢸⣿⣇⢷⡀⣄⣐⣀⠀⠀⠀⠀⠂⢴⣶⣿⣧⠉⠂⢠⠆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄⣠⣾⣿⣥⣤⣼⣿⣟⠉⠱⣦⣤⣠⣴⣾⡍⣹⣿⣤⠀⠁⣼⠸⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠟⣟⣟⢻⣿⣿⣿⣿⣽⣟⣃⣘⣋⠁⡼⠿⣿⣿⣿⡿⢻⠀⢂⡸⠶⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡝⠻⠿⣿⠶⠿⠛⢽⡟⢿⣿⡟⠋⠍⠉⣻⣿⢾⣿⣿⡿⣾⡄⢉⠒⢐⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣤⣤⣤⣤⠀⣸⠉⠨⣍⢉⠁⠀⠈⠛⠛⠚⠻⠿⠇⢻⡇⢠⡀⠀⣂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠸⠷⠞⠃⣰⠿⠦⠓⠚⠀⠀⠲⠶⢦⡀⠀⠀⠀⠀⠀⠱⣶⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⣤⣤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⣥⡀⢀⣀⣀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷⣾⣿⣶⡤⠀⠀⠀⠠⢽⣦⣻⣿⢿⣿⣿⡛⠁⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⠀⠙⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢰⣿⣿⣆⡀⠀⣀⣤⣤⣼⣿⡇⠒⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣀⡄⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣷⣾⣿⣶⣶⣦⡀⠀⢀⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣹⣿⡇⠀⠘⠘⢻⣿⣿⣿⣿⣿⣿⣿⣇⠈⠙⡟⠋⠛⠿⠿⠿⣿⣤⣿⣿⣿⡿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⣄⠀⠀⠿⠋⠈⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⠷⢰⣶⡄⡿⢸⣿⡿⣿⠰⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣄⣸⠟⠋⠉⢉⣙⣷⣀⣤⣤⣤⡈⠻⠛⠛⠿⠿⢷⠈⣶⣶⠶⣌⣙⣡⣦⣬⣿⣁⣼⣷⣮⠆
⠀⠀⠀⠀⠀⠀⠐⣿⡿⠟⢛⠻⣿⡷⣾⡿⠀⠛⠛⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⣻⣿⡟⠿⣿⣿⣿⠋⣁⣀
⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⣶⣿⡿⡗⢠⣴⣟⣳⣶⠊⠉⠉⠉⠁⠀⣀⠀⠀⠀⠀⠀⢠⣀⡀⢀⣀⣙⠛⠥⠀⢠⣉⣿⣿⡿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⢟⢋⣿⣦⢂⣧⣬⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⢉⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣾⣿⡇⠀⠀⠈⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣑⡾⣱⣿⣿⠿⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠉⠻⣿⡏⠙⢁⣀⠀⢸⣿⡉⠘⠂⠀⠒
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣏⡁⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⡤⠀⣿⣷⣿⣿⣿⣿⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠹⠟⠋⠙⣿⣿⣿⠃⠀⠀⢀⣸⣿⣇⠀⠀⢠⣾⣿⣿⣦⠀⠀⠈⠁⠀⠀⠀⠉⡟⠀⠉⠉⠉⣿⣷⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠀⠻⡇⠀⣰⣿⣿⣿⠿⠛⢡⣀⣿⠏⠁⠀⠈⢻⣿⣤⣴⣶⣶⣶⣤⣇⢉⣀⡈⢃⡏⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠄⠀⠀⠁⣠⣿⣿⣿⡿⠠⠄⠲⠤⠭⠤⠀⠀⠤⠘⣿⡏⠛⠛⣿⣿⣿⣿⣿⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠹⣿⣿⡇⠀⠀⠴⠶⠶⣶⣾⣶⣤⣶⣿⡇⠀⠀⢻⣿⣿⠿⠁⠉⠉⠧⠀⠀⠀⠀⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠘⠛⠛⠛⠛⠻⠟⠛⣴⣿⣿⣦⣄⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣾⣟⠋⠉⠉⠰⣶⠂⠉⠉⣉⣿⣿⣤⣤⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⢠⣿⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡟⢹⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣖⣠⣿⣻⣿⣿⣿⣟⣖⠠⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣟⣛⣓⡒⠒⢒⠒⣶⠶⣶⣤⣬⣤⣤⣾⠿⠿⠾⠻⡅⠀⢀⡀⢠⣤⣤⡤⠤⠤⣤⣤⠤⣼⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣤⣾⣿⣿⣟⣋⣉⣿⣿⣏⣅⠀⠀⠀⠀⣬⡒⠛⠻⣿⡿⣿⣧⣤⣿⣶⣦⣶⢿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠁⢹⣿⣿⣿⣿⣿⣿⣍⣀⠶⠶⠛⠆⠀⠀⠘⡟⢻⢛⣫⣥⣾⣿⡿⣻⣿⣿⣿⣿⡀⢻
⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⢼⣿⣿⣿⣿⣻⡋⠉⠉⠙⠋⢿⣷⠄⠀⠀⣞⠻⢿⣿⠿⠛⣉⣴⣿⣿⣿⣿⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⣿⣿⣝⣿⣿⣿⣷⣶⣌⠁⠀⣉⡁⠀⠀⠀⠈⠰⣈⣤⣶⣿⣿⣿⠟⣸⣿⣿⠏⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⣯⣿⡋⠁⢀⣀⣀⣼⠇⠀⠀⠀⢺⢦⣬⡿⠿⠟⢉⣠⣾⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢿⣾⡿⣿⣿⣿⣿⠷⠀⠀⠀⣤⡀⠀⠀⢠⡖⠀⠂⢴⣶⣿⣿⣿⡿⠋⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣸⣿⣿⣿⣟⣋⠀⣀⠤⠂⠀⠛⠁⠀⠀⠀⢈⢑⡂⠀⠙⠛⢋⣁⣴⣿⣤⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣯⡉⠛⠿⣟⣛⠿⠀⠀⠀⠀⣶⠂⠀⠀⠀⠈⣀⠁⠀⠛⠿⢿⣿⣿⠀⢉⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⡿⠿⣯⣽⣉⠀⠀⣠⣴⡾⢀⡴⣠⣆⣀⠁⠐⣌⡻⠶⠤⠀⠀⢉⡠⢴⣧⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣤⣀⣀⣉⢿⡿⠇⠀⠀⡤⠈⣾⣿⣏⣙⡿⣧⠈⠀⠀⠐⠲⣾⣅⡀⠀⠈⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⡿⠿⣿⣿⡠⠀⠀⠂⠘⣡⣤⣿⣿⠿⢿⣇⣀⠀⠐⢌⠲⢤⠀⠙⢉⣠⣞⡁⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣦⣤⡴⠾⠓⠒⢂⣴⠾⢋⣹⣿⣿⣿⣺⡟⠛⢷⣄⠀⠑⠐⠒⢾⣧⣄⠙⢛⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣟⠛⠷⠶⡤⡔⠋⣁⣴⠚⠫⣿⣿⣅⣸⣧⣀⠀⠙⠷⣦⡀⢀⠠⣩⡤⢴⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣙⠛⠿⢐⠞⢡⡾⠋⠁⣠⣀⣿⣿⡿⢿⡇⠈⠻⣆⠀⠈⠻⣦⠀⠀⠀⢀⣉⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠈⠀⠀⠀⠈⢹⣿⣿⣷⢶⡟⠙⠀⠈⠧⠀⠀⠉⠈⠑⠄⠩⠥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⡟⠙⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡉⢈⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠛⠛⠀⠀⠐⠀⠱⠒⣄⣀⣹⠞⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠎⡀⠀⠐⠀⡄⠀⣠⠤⠀⠀⠀⠀⠀⡜⠶⣦⣅⢣⡖⠓⣴⠆⢤⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣷⠆⠀⠂⠀⡃⡾⣅⣴⣶⡀⠈⠁⠀⣿⣇⠈⢿⣿⣿⢦⡾⣀⡹⠶⠀⢟⢻⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢷⣼⣿⣇⠀⠠⡀⢿⣿⣿⣿⣿⡷⠀⠀⠀⠘⡍⢓⣚⠷⢾⡋⠛⣉⠁⠴⠋⢩⣯⠸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠿⢿⣿⣆⠀⢳⡞⢿⣜⢿⣿⣅⠀⠀⠁⢀⣿⣯⣛⣀⣀⠓⠰⡷⡦⠀⠀⢈⣍⢺⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢠⠌⠀⠛⠋⣸⣿⣧⣀⠉⠂⠈⠑⠛⠛⠀⣀⡴⠛⠛⠋⠙⢭⣛⢷⣶⠀⡄⢀⡀⢈⢳⠼⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢀⠞⢣⡾⠷⠉⠓⣦⣤⠤⠚⠂⠉⠁⠀⠀⠀⠀⠀⠀⠟⠿⠻⣄⠹⣄⢫⠤⢞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⣷⣤⡶⢊⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡏⠈⡰⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠈⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠆⢀⣀⠀⠀⠊⣀⠚⠀⠀⠀⠀⣀⣤⣄⡀⢸⡄⠀⠈⠛⠄⠀⠀⣩⠤⣤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠸⠃⠀⠀⠀⠘⢯⠙⠣⠴⠿⡎⠡⠀⠀⠀⠀⠀⠘⡷⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠲⣿⣿⠛⡿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⠀⠀⠘⠀⠀⠀⢠⡞⠛⡠⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠘⠁⠠⠇⢀⣳⣄⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣀⠾⣿⢞⡻⣴⡀⠘⠂⠈⠓⢄⣀⠀⠀⠀⠀⠀⠹⣿⡿⠖⠒⠒⠚⠻⠿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠝⡈⢉⣸⡟⢻⠤⢀⣨⡀⠀⠈⠛⢿⠀⢠⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣦⣿⡀⢻⣷⡆⢀⣨⠟⢀⠐⠂⠘⠀⠀⢻⠻⠻⢻⣿⣦⣀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠉⠀⢰⡏⠀⠨⠟⣩⣅⣚⠇⢀⡒⢃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠲⢶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠒⡄⠃⠀⠙⢠⡍⢀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠴⠂⡰⠍⢰⠂⠊⠓⠀⠙⠀⠀⠀⠃⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠃⡀⠰⠇⢸⡻⠟⠾⠛⣞⡂⠀⠶⢀⣀⠁⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣶⡖⢠⡗⠀⠶⠀⠈⢙⠄⣠⣠⠚⢠⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⣩⠃⢐⡦⠀⡖⠛⡤⠳⣥⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆

⣿⣿⣦⣀⣈⡳⠿⣜⡓⠺⡴⠈⢱⡟⢿⣼⢿⣿⢿⣯⣽⣯⣯⠙⠀⠘⠟⠠⠆⠹⡇⠙⠃⠙⠹⣷⣦⠼⠃⢑⠟⠀⣹
⣿⣿⣿⣿⣿⣶⡤⢭⣁⠀⠉⠳⠀⡟⠾⢋⣾⣻⣿⠟⡟⣷⣿⢶⠍⠁⣿⣠⣀⡰⠀⠀⠀⠀⠀⢹⠃⠀⠓⢠⡡⠴⢛
⣿⣿⠿⠿⢷⡼⣿⠎⠿⠲⠖⠀⠐⠀⣾⠾⡍⠙⠛⠙⠙⠛⠇⠈⠀⣗⠛⢷⢟⢇⠀⠰⢀⠀⠰⠄⡀⠈⢁⣠⣧⠴⠟
⣿⣿⣷⣶⣿⣰⣿⠾⠟⣣⣤⣆⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡴⠂⠛⠚⠀⣤⠁⡀⠈⠤⣤⠀⠀⠈⡿⠀⠀⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣕⠖⠋⠉⠁⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣓⢒⡆⡽
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⡇⣤⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢾⣟⣼⣿⣷⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣰⡆⠀⠀⠀⠐⠚⠙⠀⠀⠀⡀⠀⠃⠀⠨⠷⠊⣮⠹⢓⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠗⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢀⣄⠈⠃⠀⢀⡩⠔⢸⠁⠀⠁⠀⠀⠘⢿⡴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⣫⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠱⣆⡀⢀⠄⠀⠀⠀⠈⠉⣵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠉⠀⡄⠐⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⠀⠀⠀⢸⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠿⠻⡶⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠂⠀⠀⠀⠰⠖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠡⡶⣂⣂⠀⠐⡟⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣡⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢋⣀⣏⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣿⠃⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠦⣎⣴⣷⣗⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⣻⣼⡿⠗⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⢠⡕⠛⣯⣰⡿⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢡⡦⠦⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠛⠛⠋⠁⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⣼⣿⠟⠛⠛⠛⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡿⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢻⣿⡇⠸⣿⡇⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢨⣿⡇⠀⠻⣿⣦⣤⣤⣤⣾⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠉⠛⠛⠛⠛⢻⣿⡇⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠹⣿⣿⣶⣶⣶⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⡇⠀⠀⣼⣿⢿⣿⠃⢸⣿⣦⣤⣤⣤⣶⣿⣿⡿⠃⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣇⠀⠀⣿⡇⢸⣿⣄⣼⣿⢿⣿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⠇⠈⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⣠⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⡀⠹⣿⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠀⣠⣿⣦⠂⠈⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠈⠿⠿⠿⠿⠿⠟⠁⠀⣹⣿⣿⡞⠀⠙⠻⠿⠿⠿⠿⠟⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⡀⢠⣴⡶⠁⢸⣿⣿⣿⣷⡄⠘⣷⣤⣀⠀⠀⠀⠠⢴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢠⣀⠀⠀⠀⠀⠀⢹⣿⣶⣌⠁⠾⠛⠀⡄⠘⠛⠁⠙⠋⠛⠀⠘⢿⠉⠑⢀⣈⣵⡟⠀⠀⠀⠀⠀⢀⡤⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣸⣧⠀⠀⠀⠀⠈⣿⡿⣯⠰⣤⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⡶⠛⣿⣿⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠤⣤⣿⡇⠀⠀⠀⠀⠀⢹⡇⢹⣤⡿⡿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣸⡇⣰⡿⣿⠃⠀⠀⠀⠀⠀⢘⣿⣦⠤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⡃⠺⣿⣷⡄⠀⠀⠀⠀⢸⡁⠈⣿⡿⢿⣶⣶⢾⡶⢾⡶⢶⠶⣿⣾⣿⣿⡟⠁⢹⠀⠀⠀⠀⡀⠠⣾⣿⠛⢐⣿⡦⣄
⠀⠀⠀⠀⠀⠀⠀⡁⠀⣀⣀⣀⣀⢀⣤⣼⡀⠀⠀⠸⣇⠀⢿⣷⡸⠀⢱⠀⠀⢠⠀⢰⠀⡇⢸⣽⣿⠀⠀⠾⠀⠀⠀⠀⣧⣤⡀⣈⣀⣀⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠰⣤⣈⡙⠛⠛⠉⠙⠻⣷⣄⠀⠀⠹⢦⡈⠿⡇⠈⠉⠐⠋⠙⠁⠈⠘⠁⠀⠘⢃⣤⠞⠀⠀⠀⣠⣾⠟⠋⠙⢛⡛⢋⣁⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠲⠶⢦⣤⡈⠹⡷⢤⡀⠀⠙⢦⠈⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠟⠁⠀⣀⡠⠾⠟⢁⣤⣴⠾⠶⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣙⠁⠻⠦⣀⠑⠢⠬⠧⠀⠀⠐⠀⠈⠡⠖⠉⣀⠴⠞⢁⣉⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⣀⠈⠐⢤⣀⠀⠀⠀⠀⣀⡤⠒⠉⣀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢶⣴⣈⠉⠲⠶⣉⣁⣦⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⣿⣷⣦⣄⣀⠉⠛⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⣠⣴⣿⡿⠛⠉⠉⠛⢿⣷⣦⣄⠈⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠤⢤⣴⠾⠯⠅⠐⢢⣬⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢿⣤⣐⠂⠨⠹⠷⣦⡤⠤⠄⢀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠉⣠⣤⡓⠶⠄⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣀⠀⠀⠠⠶⢚⣢⣄⠙⠉⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢠⣤⣌⡡⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⣡⣤⡄⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⠃⠀⣀⣰⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠈⣻⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣀⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠛⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⣿⣿⡟⠉
⣿⣿⠃
⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢦⣦⣤⢻⣿⣿⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠙⠉⠉⠉⠉⠉⠉⣉⣡⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⣉⣹⣁⣭⣭⣽⣿⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⢺⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⢁⣠⣴⣾⣿⣿⣿⣶⣄⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⢿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡘⢣⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠑⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢏⢤⡡⠄⢀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠏⠈⡄⢃⠀⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣯⣙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⣤⣴⣶⣾⣿⣿⣿⣿⡿⠋⣿⣿⡄⠀⠀⠀⠈⠉⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣉⡻⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⢀⡟⠉⠙⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⣸⠇⠀⠀⠘⠿⢿⣿⣿⣿⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢂⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠒⠶⣦⡀
⠀⠀⠀⠀⢀⣠⠶⠾⠧⣄⡀⠀⠀⣸⠠⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⡡⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢰⡏⠀⠀⢄⣀⡀⢀⣀⠀⠀⠈⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠟⠛⠳⣆
⠀⠀⠸⣷⡀⠲⠶⠮⠉⠉⠡⠔⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠐⢤⡶⡤⠤⠄⠀⠀⢹
⠀⠀⠀⠈⠛⠿⠶⠶⠶⠾⠿⠿⠷⣶⣄⢀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⢀⣀⠀⠀⢀⡀⣄⣠⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣕⠢⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⢀⡴⠋⢁⡤⢶⣤⣼⣥⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠈⠳⣄⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⣴⠞⢋⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡢⡀⠀⠀⠈⠻⣏⠁⠀⠀⣀⣠⠤⠚⢉⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡕⢄⠀⠀⠈⠳⣄⠀⠿⠙⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣹⣿⣦⣁⡀⡀⠀⠈⠻⣶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⢰⡞⢿⣿⣿⣿⣌⠢⡀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⢈⣿⣼⣿⠟⠋⠙⢷⣇⡀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⢀⡤⠚⠉⠀⠀⠀⠀⣀⣤⡾⣻⡿⠋⠁⠀⠀⠀⠀⠙⠻⣦⡰⣄⠀⠀⠙⢦⡀
⠀⠀⣰⠞⠋⠉⠁⠀⠀⠉⠃⠀⠀⠀⢀⣀⣴⣿⢖⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣦⡦⡀⠀⠙⢦⣀
⠀⠀⣯⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⣫⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡌⢳⣄⠀⠈⠙⠛⠒⠒⠒⠒⠒⠒⡒⢦⣀
⠀⠀⠹⣦⣀⠀⠀⠀⢀⠀⠀⢀⡴⢪⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡄⢣⠀⠀⢦⣀⣀⠀⠀⢱⡐⠘⡀⠹⣦
⠀⠀⠀⠈⠛⠿⣶⣮⢁⠀⠀⠀⣤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠀⠀⢦⣭⣵⠖⠀⠀⠁⠀⣣⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡆⡉⠃⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠹⣷⣄⠀⠒⢒⣩⣃⣼⠟
⠀⠀⠀⠀⠀⠀⠈⢿⣜⡲⠶⠿⣫⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢤⣤⠈⣿⡿⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠠⠚⠼⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠈⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣉⣀⠀⠀⠀⠀⠈⠻⣷⠾⠿⠻⢿⠿⠯⠭⠭⠛⢻⠿⠷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣯⠃⠀⠡⡀⠀⡠⠤⠠⡆⠀⠤⠤⠜⠀⢠⠆⡌⢀⡌⠀⠀⢀⠋⠙⢻⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣸⡿⠤⠤⡀⠈⠢⠇⠀⢠⠀⠀⠀⠀⠀⠀⡸⠀⠥⠁⠃⠉⠉⠁⠀⠀⢇⣀⡯⠝⣿
⠀⠀⠀⠀⠀⢀⣿⠏⠁⠢⠜⠀⣀⠀⠀⡘⠀⠀⠀⠀⡠⠒⡱⢉⠆⠸⠀⡰⠁⠈⡆⠀⠀⠀⠑⢴⡇
⠀⠀⠀⠀⠀⢸⣿⢳⠀⠀⠀⢠⠁⠘⢄⡇⠀⠀⠀⠀⠈⠂⡌⠁⠀⡆⠠⠃⣀⣀⣡⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⣿⡧⡀⠡⢀⡠⠁⣌⠀⢰⢸⠀⠀⣀⣀⠀⠀⢸⠀⢀⠁⠈⠙⠖⠀⠀⠀⠑⠌⢲⡟
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⡀⠀⠀⠀⢸⢒⠕⠒⠁⠀⡅⠀⡘⠀⠘⠀⠀⡊⠁⡇⢀⠔⠒⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⡏⠉⠀⠀⠀⠈⣄⡜⠀⠀⡆⠀⠀⠑⠀⢈⠁⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣴⣶⠤⠭⠽⠿⠿⠿⠿⢧⣶⣴⣌⣀⠈⠒⡡⠠⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠛⠿⢿⣦⣤⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣀⡬⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣿⠟⠛⠀⠀⠀⠀⠀⣠⣴⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⡄⢀⣀⡀⠀⠆⠀⣀⠉⠉⠛⣿⠿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⣀⠀⢰⠛⣾⣖⠥⠄⠀⠀⠹⠗⡄⣀⣀⣄⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⠤⠖⠊⢉⣡⠶⣁⢿⣭⡟⣿⣭⣭⠁⠄⠀⡀⠈⠉⠁⢀⠂⠒⣄⠲⣔⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣾⡿⢿⣾⣾⣿⣿⡽⣡⡞⠀⢟⠀⢤⣁⢀⢠⠘⠀⠀⠙⢘⡴⢋⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⢠⣟⣷⣦⣤⠠⣌⣿⡾⢷⡯⡞⣿⡉⣿⠀⠈⢰⠣⣌⡙⢿⠦⠀⠓⣴⠮⠄⠔⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢏⣟⣻⣿⣰⣿⡾⡲⢾⠎⠿⡿⠗⢂⣼⣷⠘⢦⡄⠁⠀⠘⣀⠔⠁⠀⠐⠂⣰⡾⠛⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡻⣯⡿⣟⣿⣟⡇⢼⣻⢁⠊⢸⣷⣚⡁⠘⢌⠁⢀⠿⣉⡷⡽⣯⡀⠀⢀⠘⣷⣉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣾⢸⣿⣾⣷⣏⣼⠟⣉⠔⠛⠃⣠⣤⣀⣈⠳⣬⠃⢡⢐⠦⣿⣧⣗⠀⢧⣾⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⢽⣙⡾⣾⣿⣭⣿⣣⡞⣁⣴⠊⠉⠀⠀⠀⠈⠻⣯⡀⣰⢚⢷⡾⢋⡨⣑⣾⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣫⠷⣧⢿⣼⢻⣿⣼⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⢻⡿⢟⠧⣀⡿⢛⣴⣼⠷⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣻⣿⣯⣹⣮⣝⣽⣞⢽⣿⠿⠋⠀⠄⠀⠀⠀⠀⠀⣸⠁⣆⢦⣉⣧⢭⣤⣏⡱⠊⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣿⣿⣿⡝⣿⣻⣭⠏⠃⠀⠀⠀⠀⠀⠀⠠⣴⡿⣧⡈⠳⡏⠙⣯⡠⠤⢰⣦⠔⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠛⠲⣾⡏⢾⣿⡆⠀⠀⠀⠀⠀⠀⢴⣾⠟⢀⡜⢡⣼⠸⢷⣾⠀⠆⠈⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢠⠈⠉⡍⣿⡇⠀⠀⠀⠀⠀⠢⡀⠀⢀⣠⣾⣧⡹⣿⣳⢾⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠾⣝⠲⣧⣿⣇⠀⠀⠀⠀⢀⠈⠁⠀⠀⠉⣛⢿⣿⣷⡱⠁⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⡜⡉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⠟⡩⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣣⣸⣤⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⢠⣧⡾⠤⠶⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡝⡍⢳⣦⢤⣀⣀⡀⣠⣿⣦⣤⠎⢠⢳⠶⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣌⣮⣷⡤⡭⣿⣬⢟⢩⢭⣿⠒⠓⢺⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡏⢁⡴⠚⢻⠧⣤⣈⠈⢷⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡾⠀⣂⠷⡀⠀⠙⢆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠁⠀⠉⠈⠃⠉⠉

⡸⠇⠰⠃⣾⢂⡀⢊⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠙⠎⠃⠀⠀⡁⠀⠀⣤⠀⠀⣹⣷⡤⠐⠀⡀⠀⠿⠂⠀⠈⣉⢀⢝⡳⣄⠀⠀⠀⠈⠀⠾⠃⠘⢋⣿⢻⠟
⠀⠆⡀⠐⢃⡉⠅⠛⢹⡇⠀⠤⢤⡀⠀⣲⠀⢀⡀⠙⢤⡄⠀⠀⠀⠀⠀⠀⠀⠩⠅⠐⠀⠀⠁⠠⠄⠀⠸⠋⠀⠀⠈⢁⡷⣠⠀⢠⡀⠀⢀⣦⣄⠀⡄⠻
⠀⠀⠃⠀⠋⠀⠀⠀⢀⡁⠐⠶⡀⠅⡀⠘⢰⠦⢀⣀⠀⠀⡀⢠⠀⠀⠀⣠⠴⠖⠀⠀⠀⠀⠀⠀⠰⣄⣀⡀⠀⠀⡀⠈⢠⠡⢄⣾⠩⠉⠀⠈⠙⢷⣿⣶⡁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⡳⠄⠀⠀⠉⣄⠀⠐⠛⠛⢀⠈⣥⠄⠀⢀⣈⣥⣶⡿⢡⣆⢤⣦⢠⢀⣠⢿⣿⢀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢈⢩⣥⣶
⠇⠘⡓⠀⠀⠀⠀⠀⢈⡃⠣⢑⣈⠁⠀⠀⠀⢶⠶⠛⠋⠏⣩⠤⠞⠉⠉⡘⠋⠀⠀⣿⣷⣛⣴⢿⠃⢠⡅⠐⠻⣾⢶⠐⠆⠀⠀⠀⢻⡌⠀⣦⠀⢁⣺⡇
⠀⠀⠀⣀⡀⠘⠀⠀⠀⠀⠀⣠⣤⠆⠀⠀⠀⣷⣦⠴⠈⠈⠁⠀⠀⢰⣁⣨⡿⠀⠼⣿⡿⠉⠉⠀⢠⣿⠷⡀⣤⠀⠀⠀⠀⠞⠲⣥⠀⠹⢆⣿⣷⡀⠹⣷
⠀⠐⠡⠈⢡⠀⢀⠀⡀⠀⠀⣉⠋⠘⠀⠙⠀⢁⣠⣴⠣⠈⡀⠀⠀⠜⠨⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣶⡀⡈⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠿⣿⣷⣴⡟⠸
⠀⠈⠀⠇⠀⠃⠄⣀⠀⠄⢀⡈⠀⠀⠀⠀⠀⠻⠻⠧⠅⠈⢁⣀⣀⣩⣸⠂⢀⠴⠀⠀⠀⠀⠀⠀⡈⢳⡉⠛⠀⠻⣤⠀⣐⡰⣶⠂⠀⠀⠀⠰⠝⢿⣏⣀
⠄⠀⢀⣹⡆⠀⠈⢡⣴⠗⠀⢀⣤⣆⠀⠤⣀⣠⡤⢦⠄⠀⠙⠉⠋⢩⠃⠀⠨⣶⠂⣼⠃⠀⠀⣤⡙⣧⠉⠡⠍⠀⠒⠶⠀⢀⡀⠁⠃⡾⠐⠂⠀⢦⡙⠇
⠀⢠⣽⣿⠇⢀⣿⠀⢉⡀⠀⣠⡂⠀⠂⠐⢋⠁⢤⡴⣶⡶⠀⠀⢀⡁⠀⠠⣦⡦⢸⣏⣠⡄⢈⣿⠟⢨⡙⠿⠷⠈⠁⠀⠖⠀⠉⠀⠀⠀⠀⠀⠳⣄⠁⠀⠄
⣀⠘⠋⢠⠂⣸⠋⠀⢦⡙⢦⣛⢧⠄⠂⠀⠀⢀⠸⣧⢿⣥⡾⣠⠁⠁⡔⣦⣄⠀⠛⣍⠃⠀⡈⠁⣲⣄⠀⠀⠘⠇⡰⢂⠰⢀⠀⡴⠀⠀⢀⠻⣦⠙⠦⠄
⢉⡔⠚⢿⡇⠘⢁⠀⠀⠁⠈⠈⠓⠀⠀⠀⠀⠸⣆⠻⢤⠏⠐⠉⠻⢷⣶⣽⡟⠐⠂⢿⣋⡴⠀⠀⠋⣁⠀⠐⠠⠂⠀⠀⢀⣾⠀⠃⢠⠀⠀⠁⠘⢷⡘⣧
⣾⣷⠀⣾⠃⣴⠈⠣⠀⠀⢢⡀⠈⠃⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠈⢛⠫⢴⣄⠀⡄⠁⠀⠀⣀⠈⠝⠉⠒⠁⠀⠀⠀⣾⠏⣀⠀⠈⠀⠀⠀⠈⢦⠙⠌⠓
⠙⢿⠀⠠⠂⣿⡆⠀⠀⠀⠘⠳⣶⢦⡀⠀⠀⠀⠀⠀⣀⠠⠄⠠⡄⠂⠂⠀⠐⠂⢀⠀⠀⣠⠊⡽⠀⠀⠀⢀⠀⠄⠀⠀⡿⠀⢿⠀⠰⢀⣀⡐⢃⡹⢅⣰⣆
⠀⠀⠀⠀⢄⣿⣩⠄⠀⠀⠀⠀⢻⡌⠁⡀⠀⠀⠈⠓⣹⣿⣜⠇⢰⣦⡀⠀⠀⣀⠀⠀⢀⣤⣠⣮⠁⠀⡛⠡⠖⢊⣀⠀⢀⠹⠻⡀⠙⠉⣨⣤⠀⢥⣌⠭
⠠⠀⠀⠈⠴⠟⠁⠀⠀⠊⠐⢿⣆⣿⠀⡅⠀⠀⠀⠀⠀⠙⠛⠃⠈⠴⠦⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⡉⠙⢳⡶⠌⠋⠀⠉⠀⠘⠄⠀⠁⠀⠀⢀⣀⣈⡁⠊
⠀⠈⠀⡀⢰⣶⡀⠀⣠⡈⠂⠐⠋⠛⠄⠀⠀⠀⠀⠠⢠⣶⣶⠶⠊⠰⠶⠦⠾⠅⠀⠀⠀⠀⠀⢠⡆⠤⡀⠀⣴⠆⠀⠀⠀⣄⠀⠀⢀⠀⢀⠦⠚⣿⣟⠃
⠀⣠⠀⠿⠏⠀⠁⠀⠉⠛⠀⠀⠀⢰⠀⠀⠀⣇⣀⣴⡤⠏⠕⠀⠀⠀⠀⠀⢄⠀⡀⣀⣀⠀⠘⠘⠃⠴⠁⠘⠃⣘⠁⢀⣤⡏⠠⡀⠘⣦⠀⠐⠳⡮⠻⣷⣷
⠰⣿⣆⢠⢀⠀⠃⠸⢠⠷⡶⠄⠀⠀⠘⠁⡦⠋⢉⣩⡄⠀⠀⣤⡀⠀⡀⣹⠟⢀⣀⡉⠀⠷⣦⠀⠀⠀⢀⣤⣜⢿⡇⠸⣿⠃⠀⣾⣆⢿⡄⠀⠛⠁⠀⠘⣻
⠧⠈⠻⣶⠀⣀⠀⠀⠙⢦⣄⣈⠀⠄⠠⣦⠄⣉⢻⣿⠲⣿⠀⠘⠋⠘⠃⣤⠀⢠⣉⣉⠘⠁⠉⡐⠉⠀⠱⣿⠿⠆⠐⠐⠂⠀⡟⠉⠁⠈⢗⣀⡀⠀⠀⡀⢢
⢠⣤⡀⠀⠀⠻⢡⠄⠐⣩⠟⢋⡤⠻⠟⠀⠋⠉⠏⡻⠀⣂⠙⠁⢰⣿⢈⠥⠀⠈⠿⠋⠁⠀⠀⠁⠀⣠⠀⠄⠀⠀⠀⠀⠀⠘⢃⢀⡆⠄⠠⢛⠉⢦⣾⣿⣦
⢈⠋⠁⡀⡁⠀⢢⠴⠇⠴⠀⠀⠀⣈⣄⣀⡀⠀⠀⠀⢀⡉⢋⠘⠋⠉⠀⠀⠀⠀⢃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢁⠀⡸⠓⠀⠂⠘⠠⢘⣭⣄⣀
⠀⠀⠈⠀⠓⢈⡁⠀⠀⠀⠰⠆⡘⢿⠟⢉⡁⠀⠀⠀⠉⠐⠻⠄⢀⡤⢰⠂⣴⠠⠟⠀⠀⣸⡛⠁⠀⢀⠉⠓⢀⣀⣑⠀⢠⠌⠰⠆⠀⠀⠀⢠⠆⠀⠈⡭⣙
⡄⠺⢀⡀⠘⢉⡁⠀⠀⠀⠀⠰⠀⢀⠄⠘⢃⠼⣴⡿⠾⠃⠴⠲⡶⠴⠀⠀⣁⡀⣸⠇⢰⡿⢧⡀⣶⡌⠃⠰⣄⠙⠻⠁⣩⠆⠀⣰⡶⠀⠉⠀⠀⠀⠁⠑⠟
⠀⠲⠟⠀⠠⠟⠀⠓⠀⡤⠀⠀⣀⣴⡄⠐⢋⠀⠙⢷⣶⡄⠀⠈⣁⠀⡄⣰⠦⡖⠁⠀⡃⢀⣾⠄⢛⠛⠀⣀⣻⡧⠀⡀⠉⠘⣴⣿⠇⡿⣦⡠⡀⠙⣿⠶⠦
⠀⠶⢀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠿⡿⣱⡆⣿⣠⡄⠀⠜⠛⢧⡔⠉⠆⢰⣜⠁⠕⠀⠚⠇⠈⠋⠀⣀⣻⣄⠤⠴⡶⠀⠰⠇⢸⠋⠙⣻⠗⡈⠛⠻⠟⠓⡦⢀
⢀⣾⠿⠁⠀⠀⠀⠀⠀⠄⠀⠲⣄⠀⡿⠇⠉⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⠰⡗⠀⠀⠀⠉⠍⠁⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⠄⣈⠙⢾
⡉⢡⣺⢇⠠⠀⡀⢄⠡⠄⠾⢦⠈⠑⠆⠀⠀⠀⢠⣦⠃⠀⣃⠱⣄⡀⣤⡁⠀⣤⡍⢣⡹⠄⠀⣀⠀⠀⠀⠀⠀⠁⠀⠢⠀⣠⣤⡶⠆⡉⢉⡿⠃⠀⢈⡿
⣃⣾⣛⣿⣸⣆⣙⣦⣀⣀⣈⣀⣒⣂⣀⣀⣀⣀⣀⣤⣶⣀⣹⣷⣀⣁⣙⣷⣀⣁⣀⣠⣶⣘⣛⣻⣃⣀⣀⣀⣀⣀⣤⣒⣛⣉⣁⣀⣀⣀⣨⣥⣜⣆⣡⣿⣞
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠒⠒⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢹
⠀⡇⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡇⠀⠀⣀⣤⣶⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⣶⣤⣀⠀⠀⠸⡀⠀⠀⠀⢸
⢰⠁⠀⠀⠀⡼⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢳⠀⠀⠀⠘
⠸⠀⠀⠀⢠⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡇
⡇⠀⠀⠀⠘⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣶⣶⣦⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⠇
⡇⠀⠀⠀⢀⡇⠀⠈⠛⠿⢿⡿⠿⠟⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠈⠉⠛⠿⠿⠿⡿⠿⠛⠀⠀⠸⡀
⢡⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀
⠸⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠹⣗⠦⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⠤⢺⠏
⠀⠀⠘⡆⠘⡽⣿⣿⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⠟⠁⠀⠻⠟⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣟⠇⢰⠃
⠀⠀⠀⡏⠀⢱⠘⠿⠈⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⠋⡜⠀⢣
⠀⠀⠀⡇⠀⠈⡆⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⢠⠃⠀⢸
⠀⠀⠀⠙⢄⡀⡇⠀⠀⠈⣿⣿⣿⣇⣀⣀⣤⡤⣤⠲⡔⠒⡖⠒⣤⠲⡤⣤⣄⣀⣠⣿⣿⣿⠇⠀⠀⢸⠀⣠⠇
⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠸⣿⣿⣿⣿⣸⣸⣇⣽⣠⣧⣠⣧⣠⣿⣠⣇⣴⣸⣨⣿⣿⣿⡟⠀⠀⠀⣾⠋⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠻⠿⠿⠿⠧⠧⠧⠼⠼⣤⢇⠧⠼⠼⠦⠧⠷⠿⢿⠿⠟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⡀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⣀⡀⢸⣿⣿⣿⢀⣀⣀⣀⡀⣿⣿⣿⣇⣸⡿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡇⢸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣟⠉⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡇⢸⡿⢿⣿⢸⣿⣿⣿⡇⣿⡿⠋⠀⣀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡷⠋⠀⡀⠙⢿⣿⣿⣿⡿⠋⠀⣴⡞⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡿⠋⠀⣠⣾⣿⣦⡀⠙⠿⠋⢀⣴⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋⠀⣠⡞⢻⣿⣿⣿⢻⣦⣀⣤⡟⣿⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠾⠿⠇⠸⠿⠿⠿⠘⠿⠿⠿⠃⠿⠿⠿⠇⠸⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⣦⡿⣹⡟⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣦⠔⠛⠿⠿⠾⠋⠀⠀⠀⠀⠺⢧⣀⡀⢀⡾⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⣠⣾⡷⢷⣄⠀⠀⠀⠀⢀⣤⣠⡤⠞⠉⢀⠁⠱⠀⠒⠂⣴⡄⠀⠀⠀⠀⠀⢈⠿⠋⠀⠰⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢀⡼⠋⠁⠀⠀⠙⢻⣦⠀⠦⣉⢱⡏⣀⠄⠀⠋⠐⣠⡄⠀⢀⣿⣷⠀⠀⠀⢀⣴⣯⠖⠀⠀⠀⢀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⣀⡀⠂⢀⡀⠀⣻⣿⠀⣼⣿⣿⡀⡤⠚⠥⠋⠀⠘⢀⣼⠠⣻⣿⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠋⣠⠆⠠⠀⠀⠀⠀⠀⠀⢦⣼⣿⠞⠁⠀⠔⠉⠀⠠⣾⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⡠⠌⢉⣠⡾⠿⠋⠁
⠀⠀⠀⠀⠠⣿⣧⣤⣀⡐⢡⡔⡁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠃⠀⠀⠀⡀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⡀⢀⠴⠶⠟⢁⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣮⣼⣿⣦⣤⣀⠀⠀⠀⠀⣤⣿⡷⠀⠀⣀⠀⠂⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣷⢀⣴⣦⣀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣌⠙⠛⠁⠀⠀⠹⣷⣄⣤⣿⡿⠋⠀⠀⢰⣿⣆⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣿⣿⠿⠛⠋⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠢⣤⡀⠀⠀⠈⠉⠻⠿⠦⢶⣤⣶⣾⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠐⠠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣀⣠⣄⠖⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠈⠻⠟⠑⣷⣄⣀⠀⠀⠈⠓⢶⣤⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠐⠋⠟⠋⠀⠀⠀⠀⠀⣀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠛⢦⣦⢀⣄⠙⠷⣦⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠻⣿⡷⢿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠁⠙⠁⠀⠀⠀⢀⣴⣧⣠⡴⠂⠀⠀⣠⠞⠋⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢁⣾⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠔⠀⢀⠾⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣀
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠘⣦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡋
⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⣇⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠈⠳⢤⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣤⠴⠋

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠊⠀⢴⣾⣿⣿⠀⠘⠈⠙⠓⠀⠀⠒⠀⠀⠀⠐⠁⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⡿⠀⡀
⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⠀⠀⠀⠄⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠄⠀⠀⠀⠀⠀⠀⠀⠋⡟⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾
⢀⠔⠈⠁⠈⠁⣀⠀⠀⠀⠀⢠⣖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⢀⣾⣏
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤⠀⡴⠊⠉⠉⠐⢄⠀⠀⠀⠁⢄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣀⡀⢀⣤⣿⣿⣟⡡
⠁⠉⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⠦⣄⡠⠲⠒⠖⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⡀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠑⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡻⣿⣿⣷
⠙⠂⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠴⠊⠁⠀⠀⢀⣿⡟⠃⠀⠃⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠠⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀
⠀⠀⠀⠈⢱⣄⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠈⢆⠀⠉⠁⠀⢄⠵⠶⣦⠀⠀⠀⠀⠀⢀⠀⠀⢽⣿⣿⡇⠀⣾⠇⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢀⣀⢀⡀⠉⠉⢻⣿⣿⣧⢠⣿⣷⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠻⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠳⡀⠀⣰⠁⠀⠠⡄
⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⡀⠐⠃⠀⠁⠈
⠀⠐⢄⢿⡄⡀⠀⠀⠀⠀⠕⠀⠄⠀⠀⠀⠀⠀⠀⠒⢂⣩⡴⠋⡉⠀⠙⢷⡀⠈⠀⠀⠐⠒⠒⠄⠠⠄⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆
⠀⠀⠀⠀⠙⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠅⡔⠁⠀⠋⠀⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⣴⣶⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⡀
⡠⠖⠀⠀⠀⠀⠀⠀⠁⠰⣀⠀⢀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⠀⠀⠀⠈⠙⠙⠓⠚⠠⢄⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠉⠉⠒⠆⠒⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⣦⢠⠀⢀⣴⣿
⠀⠀⠀⠀⠇⠑⠂⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢺⣧⣠⣿⣿⣿⣿⠏
⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠸⠁⠀⠀⢀⣤⣞⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢀⣀⠀⠀⠀⠈⢻⣿⣷⣀⢠⠀⠀⣤⣿⣿⠋⢀⠀⠠⠠⠀⠠⠄⠀⡸⠉⠐⠙⠧⣐⠀⠤⠤
⠲⢀⠈⠁⠀⠁⠀⠀⠠⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠈⠻⣿⣿⠛⠃⢸⣿⣿⡡⠊⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⠒⠒
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣷⣶⣦⣉⡀⠃⢌⣿⣟⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎⠀⠀⠀⠐⠚⠉⠉⠉⠻⠛⠛⠛⢻⡿⢿⠁⣠⡆⢫⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠳⡄⠀⡀
⠀⠀⢠⡴⠤⣄⡾⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠻⠋⠉⠛⣆
⠀⠀⣾⠀⠀⠀⠑⠀⠀⠀⢾⠀⠀⠀⠀⢰⠋⠁⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠃⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠘⠦⣄⣤⣄⠀⠀⠀⠈⠻⢦⡀⠀⠸⣆⠀⠀⠀⠺⢤⣀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⢀⣠⡴⠞⠋
⢀⡖⠋⠉⠉⠓⣎⠳⣄⠀⠀⠀⠀⠙⢦⣾⠁⠀⠀⠐⠀⠀⠈⠙⣲⠞⠁⠀⠀⠀⠀⠀⣠⠔⠋⠁
⠸⡅⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠲⠤⠤⠽⢿⣶⣶⣲⣤⣄⡴⠊⠀⠀⠀⠀⠀⢀⣤⢾⣥⣀⡀⠀⠀⠀⢀
⢠⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠲⠤⣄⣀⡠⠊⠁⠀⠀⠈⠆⠉⠛⠶⠋⠉⠉⠳
⡏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠
⢷⡀⠀⠀⠀⣰⠋⠉⠉⠛⠛⠒⠲⣦⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠧⣄⡀⠀⠀⠻⡏⠁
⠀⠙⠲⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠞⠉⠉⠉⢛⠶⢶⡦⠤⣤⣄⠀⠀⠀⠀⠀⠈⡆⠀⠳⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠶⠊⠀⠀⠀⢀⡴⠁⠀⠀⠙⠢⡀⠻⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⡶
⠀⠀⣰⠲⡄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠰⡟⠳⣄⠁⠀⠀⠀⠙⠛⠻⡍⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⠦⠤⠴⡆⠀⠀⠀⢀⡗⠀⣾⠀⠀⠀⣤⣀⣀⣤⠇⠀⠀⠀⣾⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠖⠋⠀⠀⠙⢦⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⢀⠐⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠒⢄
⠀⣀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠿⠿⠟⡃⠀⢀⡀⣸⣤⣤⣀⣰⡇⠀⠀⠀⠀⣦⣠⣤⣠⡆⠀⣀⡀⡁⠀⠀⠀⠀⡀
⠘⢿⣿⣿⣿⣿⠟⠋⠀⠺⠿⠛⠇⠀⢠⠶⠁⠀⠢⣤⣤⣾⣿⣿⠝⠁⠀⠀⠤⣤⣴⣿⣿⠋⠁⠀⠄⠀⠀⠀⣠⡤⠒⠀⠀⠀⠀⢀⣠⠔
⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⢾⡀⣠⠀⠎⠀⠀⠀⠀⠱⢿⠟⣿⣇⠀⠀⠀⠀⠀⢿⡟⢻⡇⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠹⣿⣿⡏⠀⠀⠀⠀⠘⣧⣿⠀⠃⠀⠀⠀⠀⠘⡞⢠⣿⠇⠀⠀⠀⠀⠀⠐⠁⣿⡇⠀⠀⠀⠀⢱⡀⠀⢡⠁
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⢰⠀⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠸⠀⠀⠀⠀⠀⠀⢸⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠇⠀⢠
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⢸
⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⢸⢿⠀⡆⠀⠀⠀⠀⠀⠰⡄⣿⠀⠀⠀⠀⠀⠀⠀⢰⣼⡆⠀⠀⠀⠀⠀⠇⠀⢸
⠀⠀⢨⣿⣿⣿⡀⠀⠀⠀⠀⢸⠰⡆⠇⠀⠀⠀⠀⠀⣿⣿⣻⣆⠀⠀⠀⠀⠀⢈⣿⣸⣇⠀⠀⠀⠀⢈⠃⠀⠀⣄
⠀⢰⣿⣿⣿⣿⡗⠀⠀⠀⡰⣾⠆⢐⠂⠄⠀⠀⠀⣎⠀⣽⠧⣿⠀⠀⠀⠀⢠⡁⣸⡿⣼⡇⠀⠀⢀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠛⠋⠉⠛⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠙⠛⠉⠛⠋⠀⠀⠀⠀⠈⠛⠋⠉⠛⠀⠀⠀⠀⠃⠐⠙⠂⠈⠀⠀⠀⠀⠈⠉⠀⠁

⣶⠈⠀⢀⠀⠀⠈⠻⣿⣿⣿⠉⠒⠠⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⡇⠀⠀⠙⠃⢀⣤⣾⣿⣿⠿⠀⡀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠉⢹⡟⠋⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠛⢳⣶
⠁⠀⠀⠀⢀⣾⣿⣿⣿⣋⡀⢀⠀⠀⠀⠀⢸⣿⠟⢩⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠘⣤⣶⣶⡄⢀⣀⣀⠀⢹⣿⢻⣿⣿⣿⣿⡇⢴⠄⠀⠴⡆
⠀⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡆⠀⢄⠙⠿⠟⠁⠘⣿⣿⡗⢸⠃⣸⣿⣿⣧⣼⣷⣄⣤⢤⡄
⣶⣶⣦⢠⣿⠛⠉⠀⠀⠀⣀⣈⣻⣄⢀⣀⣴⣶⣶⣶⣤⠄⠛⠛⠛⠿⠛⠿⢿⠀⢸⣷⣶⠾⠿⣤⣈⣉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⣤
⠿⣿⣿⣿⣧⣴⣶⣆⠀⠿⣿⠿⠿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⠉⠙⠛⠿⢿⣿⢷⣿⣿⣿⡿
⣨⣦⡽⣿⡝⠛⠋⢁⣤⣤⡀⠀⣀⠾⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠻⠿⠋⣤⡄⠀⣠⡄⠀⢸⣿⠿⡑⡢
⣿⢿⠿⢻⠁⢤⣴⣾⣭⣭⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣵⣶⣶
⣯⣌⡈⢸⣀⣠⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠛⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠐⠀⣀⣀⠀⠀⠘⡿⡿⢋
⠛⢃⣵⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⢠⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠋⠉⠉⠙⠃⢀⣤⣾⣿⣿⣿⣶⣦⣼⢤⡂
⣃⣾⣿⣿⠿⠋⠉⠹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠈⠉⠀⠀⠀⢿⣿⣿⠀⣀⣀⣀⣀⣀⣿⡿⠛⠻⠿⠟⠻⣿⣿⣆⣭
⣿⣿⣉⠁⠀⠀⠀⠀⠙⠹⣿⣿⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠈⣇⠀⠀⠀⢀⣄⠀⢙⣿⣯⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣀⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣀⣀⠀⠶⠂⠀⠀⠁⠀⠘⡿⣽⠏⠉⠻⠿⠿⠟⢻⣿⠀⠀⠈⢹⣿⣿⡿⠿⢿
⢿⣿⣿⠃⠀⠀⠆⠀⠀⣠⣿⣯⣄⡈⠀⠀⠀⣿⡟⠉⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⣄⣿⢀⡀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠛⠁
⠘⢿⡇⠀⠀⣠⣶⣾⣿⣿⣿⣿⡿⢧⣤⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣀⣀⡀⠀⠀⠀⣡⣶⠀⢀⣀⡀⠉⠁⣜⠀⠀⠀⠀⠀⢠⡀⠀⠐⠞
⠀⠀⠃⠀⢰⣿⣿⣿⣿⣿⠋⠁⠀⠈⣉⣉⣉⣉⠘⠃⠁⠀⠙⠃⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣽⣦⣾⠃⠀⠀⠀⠀⠀⠀⣏
⠀⠀⣀⡒⢻⣿⣿⣿⣿⢿⠀⠤⠀⠛⣋⠉⠉⢉⣶⣶⡿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠄
⠀⢿⠟⠉⠁⠀⠉⠙⢿⣿⣦⠀⢰⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⢼⣿⣿⣿⠉⠙⠛⠻⣿⣿⣿⣿⡗⠀⠀⠠
⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⠟⠀⢸⣿⣉⡠⣀⣬⣹⣿⡟⣿⡟⠀⠀⠀⠀⠈⠁⠀⠀⠀⡿⢿⣿⣿⡏⠀⣈⣠⣤⣤⣤⣤⣤⣀
⠀⢀⠀⠀⠀⠈⠋⠀⠸⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣀⣀⣅
⣿⣆⢿⣿⣛⣷⣤⣤⣴⣿⣿⣿⣿⣿⣄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠘⠟⠃⠀⢸⣿⠛⠉⠉⠉⠉⠛⣿⠁⢀⣴⣿⣿⣿⣿
⠙⣿⡌⠛⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⠉⠉⠉⠉⠉⠙⡿⢀⣤⣶⣿⣶⣦⡀⠀⢀⣥⣀⠸⠁⣠⠀⠀⠀⣠⡄⠨⣤⣾⣿⡿⠋⠉⠛
⣀⠘⠇⠀⠀⠀⠀⠼⠿⢿⣿⣿⣿⣿⣿⣿⣿⠻⠃⠐⠦⠀⠀⣤⢀⣿⣿⣿⡿⠟⠛⠉⠻⣿⣿⣿⣿⣷⣦⠀⣀⣠⣀⣀⣠⣦⣼⣿⣿⡇
⠋⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⣹⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠰⠖⠸⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣧⣿⣿⠿⠃⠛⠂
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⢠⣿⠻⣿⣿⣿⣿⣿⣤⣠⣤⣶⣾⣿⣿⣿⣿⡄⠶⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠀⠀⠸⣿⣷⡀
⠀⢀⠄⠀⠘⢿⣿⣿⣿⣿⣌⣑⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⣴⣏⣭⣿⣿⣿⣿⣛⡉⠉⠁⢤⡤⣀⣤⣶⣶⣿⣿⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠟⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣯⣛⣿⣯⣭⣭⣭⣮⣴⠶⠬⢉⠉⣭⣥⣤⣈⣌⣁⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣍⠿⣾⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠿⠟⠉⠀⠀⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣶⣭⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡖⡐⢂⡬⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⡷⣫⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡡⢞⣵⡿⠀⠥⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣵⣴⣸⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢌⣠⣨⣡⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡫⠿⠿⠿⠟⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣵⣿⣿⣿⣿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠻⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠟⣫⠞⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣯⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠂⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣝⣻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣶⣻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣽⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣭⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠒⠒⠒⠚⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡤⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⣀⣀⡂⡠⠚⠈⠉⠑⠢⡀⠄⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⠠⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠉⠐⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡓⠤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠊⠹⡇⠀⠀⠀⠀⡤⣀⣀⠔⠑⠄⢴⢸⠏⠑⢂⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⡀⡔⢁⠂⢀⠔⠁⢰⠢⠄⠊⠀⠀⠀⠀⠀⠀⠀⠛⠢⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢇⡎⠀⣎⡖⠒⠁⢂⠀⠀⠸⠀⣀⠀⢸⡀⠀⡘⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠓⠇⠀⠀⠈⠒⠒⠁⠀⠀⠝⠀⠉⠉⠀⠀⢧⡆⠀⡥⠐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⢣⠘⡄⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⢠⠌⡜⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠱⡀⠀⠑⠫⠦⣄⡀⠀⠀⠀⠀⠀⣀⣠⠴⠅⠊⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠠⠀⠀⠃⠀⠁⠑⢄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡔⠊⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠄⠀⠐⠀⠀⠄⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠸⢱⢨⠏⠉⠀⠉⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡷⣳⡄⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠐⣫⣾⣶⣴⡍⣅⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢀⡧⣼⠁⢹⣟⡉⣿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣸⡏
⠀⠀⠀⠀⠀⠘⢘⠿⣦⣸⣅⣠⣿⡚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⡇⢴
⠀⠀⠀⠀⠀⡆⢺⢀⠇⣸⡠⡟⠈⣇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⢺⣟⡈
⠀⠀⠀⠀⢰⡇⣿⣾⣶⣾⣿⢿⡆⢯⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠏⠁
⠀⠀⠀⠀⠀⡯⣿⣿⡏⣯⠀⠀⢷⢼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⢿
⠀⠀⠀⠀⠈⢿⡏⢻⣇⣿⠀⠰⣾⡿⢿⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦
⠀⠀⠀⠀⢀⠈⠙⠿⠛⠿⢲⣏⠁⠀⠀⠀⠉⠺⢤⣆⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣎⡜⠀⠀⠀⠀⠀⣷⠶⠀⠀⠀⠀⠀⠀⠈⢻⣾⠒⢀⣠⣄⠀⠀⡆⠰⣵
⠀⠀⠀⠔⠻⠃⠀⠀⠀⠀⠀⠧⠐⠀⠀⠀⠀⠀⠀⠀⠨⠹⣟⠦⠉⠉⠀⠀⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠄

⠀⠀⠛⠂⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⠒⠒⠒⠒⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠙⢆
⠀⠀⠀⠀⠀⢀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⢀⡞⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⢀⠳⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠸
⠀⠀⠀⢸⠀⣿⢿⡆⠰⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠒⠀⠠⣟⣼⠀⡇
⠀⠀⠀⢸⠞⣿⡞⠀⢀⣤⣶⣶⣶⣶⣶⣔⠒⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⡀⠑⠀⠻⡗⠀⡇
⠀⠀⠀⢸⢲⡿⡤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣄⣽⡄⠇
⠀⠀⠀⠈⣿⢧⠑⣿⣿⣯⣯⠍⠩⠝⠛⣙⢻⡇⠀⠀⠀⠀⠀⠀⠶⢠⣿⢟⣋⡙⠋⠻⢝⣻⣿⣿⡏⠻⠈⣷
⠀⠀⠀⠀⢿⢸⢸⣿⡯⣽⣏⠀⠄⠠⢙⢿⣿⡇⠀⢀⣀⣀⣤⣀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠙⣾⣿⣧⠀⠀⣿
⠀⠀⠀⢀⡇⣸⡼⣿⣯⡿⠻⣦⣾⣂⣦⣼⠟⠀⢠⣿⣿⣿⣿⣿⣄⢄⠻⢿⣍⣠⣶⡴⣤⣴⣿⣼⠟⠀⠀⢹⡀
⠀⠀⠀⣼⣸⠃⠀⠨⠛⠛⠛⠋⠛⠉⠁⠠⠶⠀⣿⣿⣿⣿⣻⣿⣿⡇⡕⠠⠄⠉⠉⠻⢛⡛⠛⠉⣠⣆⠀⠀⡇
⠀⠀⠀⢻⢹⡄⠀⠀⠌⠀⠀⠀⠀⣤⠄⠀⠀⣰⣿⣿⣏⣿⣟⢻⣿⣧⠈⠀⠀⠘⣿⠙⠀⠉⠳⣄⠸⡇⠀⢠⡗
⠀⠀⠀⠀⠳⣙⢻⡦⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⣧⣽⣿⡿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣀⣀⣀⣈⣀⣹⣦⡾⠃
⠀⠀⠀⠀⠀⠈⠙⣷⣿⣶⣦⡈⠻⣷⣦⡴⡗⠀⠙⠛⠛⣧⠙⠛⠛⠉⠁⠆⢠⣶⠿⣿⣽⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⣿⣿⣆⣜⢿⣠⡃⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⣰⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠈⢿⣿⣿⣿⣿⣽⣡⡁⢸⠀⣤⠀⢤⠀⢆⡀⣠⣀⠀⠁⢿⠿⢿⡿⡟⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⢿⣧⠙⡛⢛⠉⢹⡏⢹⡟⠙⡟⠙⡿⠉⣿⠉⡟⢿⡏⢀⣾⢡⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⠃⠙⢷⣥⣌⣣⢸⠀⣰⢁⣸⣇⣀⣀⡀⢹⠀⣷⣿⡥⣾⠟⢸⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡇⠀⠀⠈⠈⠙⢻⡟⣿⢻⣟⢻⠿⠟⣿⠿⣿⢏⣿⠀⠀⢀⠒⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⡸⠇⠀⠀⠀⠈⠓⠞⣧⠼⠔⢯⡬⠤⠢⠿⢬⠿⠌⠀⠀⠀⠨⢀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣴⣶⣶⣶⣦⣀⣀⣀⣀⣠⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⣀⠀⣀⠀⢀⠀⢀⡀⠀⡀⠀⣀⠀⣀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣃⣀⣃⡀⠀⠀⠰⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⠸⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠿⡿⠿⡿⢇⣀⣠⠞⣆⢀⡀⠀⡇⠀⡇⠀⠘⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⢀⡴⠋⠀⠘⣧⡀⠀⡇⠀⡇⠀⠰⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠙⠲⢧⡀⠇⠀⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁
⠀⠀⠀⠀⢰⣶⡆⠀⠀⠈⠁⠉⠉⠈⠉⠈⠉⠁⠉⠁⠉⠉⠈⠉⠈⠉⠉⠉⠁⠉⠉⠀⠁⠀⠀⢰⣶⡆
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠢⠤⠤⣄⣠⡤⠼⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⣀⣀⣠⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠐⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢇⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠚⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠖⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣋⣿⣩⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢶⡀
⠀⠀⠀⠀⠀⢀⡤⢤⣀⣼⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠷⠚⠙⠳⣄
⠀⠀⠀⠀⠀⡟⠀⠀⠈⠛⠀⠀⠀⢸⡃⠀⠀⠀⠀⣴⠛⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠻⣄⡀⢀⣀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢿⠀⠀⠀⠀⢼⣀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⡤⠶⠚⠻⢯⡙⢦⡀⠀⠀⠀⠈⠛⢦⡀⡾⠋⠀⠀⠀⠀⠈⠙⠳⢤⣤⠞⠁⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠲⠿⠤⣤⣀⣀⣀⣀⡙⢿⣦⣀⣠⣄⡀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠓⠚⠿⠿⣏⣀⡀⠀⠀⠀⢀⠔⠊⠉⠙⢻⡓⠶⣤⣠⡴⠶⠶⢤⡀
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠁⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⢹
⠀⠀⢸⡇⠀⠀⠀⠀⠀⡴⠦⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠄⠀⠐⠀⠀⣤⡤⠴⠋
⠀⠀⠀⠳⣄⣀⣀⣠⠞⠁⠀⠀⠀⠀⠈⠉⠙⢯⡛⠒⣶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢯⠛⠲⣄⠀⠀⢈⡇
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠚⠁⠀⠀⢀⡴⠋⠛⢿⡛⠒⢶⠀⠀⠀⠀⠀⠀⢸⠇⠀⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠋⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠙⢦⣈⣣⣄⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣾⣹⡄
⠀⠀⠀⠀⠀⣾⣙⣆⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠸⡍⠙⢦⡀⠀⠀⠀⠀⠉⠉⢳⠉⠉⠁⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠓⠶⠶⢻⡀⠀⠀⠀⣰⠇⠀⣿⠀⠀⠀⣴⢤⣤⡤⠞⠀⠀⠀⠰⣯⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠚⠁⠀⠀⠘⠦⣤⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡴⠚⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠀⢀⣤⠴⠀⠀⠉⠀⠀⠀⠀⡋⠠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣐⠞⠉⠀⠀⣔⠒⣐⣂⠀⠀⠀⠍⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠞⠛⠉⠀⢀⠀⠀⠀⠀⢸⡒⣼⣿⣿⡀⠀⠀⣑⣘⣛⣻
⠀⠀⠀⠀⣠⡴⠖⠂⠉⠁⠀⠀⠀⣓⢱⣐⣶⣧⠀⠀⡬⠩⡿⢿⡇⠀⠀⣇⠰⣾⣿⡃
⠀⠀⠩⠞⠁⠀⠤⠒⠒⡐⣠⠀⠀⡖⠘⠧⢷⡆⠀⠀⢍⣉⣹⣭⡇⠀⠀⣯⣩⣿⣿
⠀⢀⡀⢀⡀⠀⢸⠒⣾⣟⣻⠀⠀⠫⠉⢿⣽⡟⠀⠀⡞⠒⢿⣿⡇⠀⠀⣗⢒⣶⣾⡄
⠨⠍⣲⣾⣾⣄⢰⠤⡬⡽⣿⣀⣀⡘⢒⣛⣻⡇⠀⢀⡯⢩⣯⣽⠇⠀⢀⡓⢠⣿⣷⡀⠀⠀⣀⠀⠤⣀⢄⠀⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡢⠀⠀⠀⠀⠀⢀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠙⠶⡟⠠⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⡄
⠀⠀⠀⠀⠸⣷⡀⢀⢲⢴⡷⣧⣵⣄⣷⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡐⡆⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣰⣿⣷⠈⠉⢙⣟⠁⢤⣠⠶⠚⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣙⡂⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⡀
⠀⠀⠀⠀⣿⣿⣿⣇⢷⢞⣩⠈⣻⡛⠒⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍
⠀⠀⠀⠀⣿⢿⢸⣷⢿⣽⣿⣄⠻⢷⡿⢿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠙⣧⠈⠛⠛⣻⣋⢻⢶⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣌⠁⠄⠀⠀⠀⠈⢰⠘⡦⣄⠀⣁⡭
⠀⠀⠀⠀⠀⣽⣧⣀⠀⠻⡙⠁⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣁⠀⠁⢀⠀⠀⣨⣴⠀⣻⡆⢀⠆⣼
⠀⠀⠀⣠⣾⣿⢾⣟⠳⡶⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⢠⣤⣾⣿⣿⡗⠹⢁⣾⠗⢋⡠
⠀⠀⢸⣿⣿⣿⣆⠈⢹⣶⣿⡄⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⡀⢀⣀⡀⠀⠙⠿⠟⠛⠐⠏⡁⠈⠉
⠀⠀⢸⣿⣿⣿⣿⣷⡘⢻⣿⡀⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠋⠉⣀⣤⣄⣤⣠⣴⠶⢚⡀⠀⡐
⠀⠀⢸⣿⣿⣿⣿⣿⣷⣼⣿⣷⣼⣿⣿⣿⣿⣿⣿⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠙⢳⣿⣿⣦⣄⢉⠛⠿⠃⠒⢈⢀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠃⠀⠂⠙⠛⠿⠟⠛⠓⠒⠂⠐⠂⠀⠛
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠹⣿⣿⣿⣷⣤⣀⣠⣴⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣤
⠀⠀⢹⡏⠀⠀⠀⠀⢰⡆⠀⠘⢻⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠰⣿⣿⣿⡇⠀⢸⣻⣟⡇⠀⠠⢙⣉⡄
⠀⠀⢸⡇⠀⠀⠀⠀⣼⡇⠀⢀⣾⠤⠀⠀⠀⠀⠀⠀⠶⣶⣷⣶⢶⠀⠀⠀⢸⣀⣀⣀⡀⡉⠉⠿⠇⠀⠀⠯⠽⠀⠀⠁⢸⡉⡇
⠀⠀⢸⡇⠀⠀⠀⣸⣿⠀⠀⠘⡙⡄⠀⠀⠀⠀⠀⢀⠀⣫⣿⣝⠀⡀⠀⠀⠀⠉⠁⠀⠀⠙⠀⠀⢠⡀⠀⠀⠀⢰⣆⠀⠀⠂⠁
⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡷⠻⡀⠀⠀⠀⠀⡜⠀⡁⣿⢈⠀⢃⠀⠀⠐⡆⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⢻⡏
⠀⠀⢸⡇⠀⠀⢸⣿⡇⠀⠀⠰⢷⡄⠱⡄⠀⠀⢰⠀⢈⣟⣛⣻⡁⠀⡆⠀⠀⡇⠀⠀⢸⡀⠀⠀⢸⠁⠀⠰⣤⣼⡷⣦⠂
⠀⠀⢸⣗⠀⠀⠈⣿⣇⠀⠀⠀⢸⠁⠀⠱⠀⠀⠸⠀⠸⠈⠈⢀⠃⠀⠃⠀⢠⡇⠀⠀⢸⡇⠀⠀⣸⡀⠀⠀⠋⢸⡇⠙⠂
⠀⠀⣻⣟⠀⠀⠀⣻⣿⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢇⠀⠀⣸⡧⠀⠀⢻⡇⠀⠀⠀⣼⣧
⠀⢐⣾⣿⡂⠀⠀⣼⣿⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⢿⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⠘⠋
⠀⣶⣿⣿⡆⠀⢀⡿⠟⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡛⠀⠀⢸⠀⠀⠀⢸⠀⠀⢤⣶⣶⣾⣯⣽⡍
⠀⠀⢻⡟⠁⠀⡾⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣳⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⢼⣄⠀⠀⣀⣤⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠐⠉⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠀⠀⠈⠀⠀⠛⠉⠉⠙⠓⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠉⠀⠀⠀⠈⠁⠐⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢸⣷⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⠄⠉⠁⣀⣀⡈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢟⢲⣶⣿⣿⣿⣿⣷⣾⠓⢳⢶⣿⣿⣿⣿⣷⣶⠺⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⢸⣿⣿⣿⣿⣿⠿⢿⡅⡝⠸⣿⣿⣿⣿⣿⣯⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⠳⠽⠝⠋⠉⠑⣢⣼⣿⣿⡜⠦⠍⠙⠉⠋⠕⠁⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠐⠀⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⢳⡀⠀⠀⠨⡋⠫⠁⠀⠀⣴⠛⣿⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⣜⠧⠤⣄⣄⣀⢠⣤⣤⡤⢟⣼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⠗⠲⠤⢤⣠⣀⠤⠔⢓⢥⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⢁⣐⣒⣀⠂⠁⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠉⠁⠀⠀⢀⡰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠤⠔⠋


⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢫⡝⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⢶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣜⣿⣿⣿
⠀⣀⣀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣨⣸⣿⣿
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣈⣁⣿⣿
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⠏⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⢞⡳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣴⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣨⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⢉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⡞⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣧
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠿
⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⢤
⣾⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣾⣿⣶⣶⣾⣷⣶⣶⣶⣶⣿⣿⣷⣶⣶⣷⣶⣶⣾⣶⣶⣾⣷⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠏⠍⠁⠀⠠⡄⠀⠈⠘⠟⢝⣲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⣿⣧⠴⠒⠁⠀⠀⠈⠉⠀⠀⠀⠓⠒⠾⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢏⣿⡧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢰⣿⣮⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⠜⠁⠀⠄⠀⠀⠀⠀⢠⠀⠀⡀⢸⣼⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⡏⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣼⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⣼⣧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⢟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡿⢿⡿⢛⣻⣿⣿⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⡞⣽⡿⡏⠉⣰⠦⣿⣿⣿⣿⣿⣿⣷⢼⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⢐⣿⣶⡟⠘⠀⠀⠙⢸⣿⣧⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣽⣿⠃⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣸⣿⣿⣿⣿⡟
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠘⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡝⣿⣿⣿⣟⢛⣯⣝⣿⣿⣶⠆⠀⠀⠀⠐⠿⣯⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⠻⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⢏⣁⠐⠲⠆⡤⢀⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠰⠊⢻⣿⣿⣿⣿⣽⣿⣿⣧⣤⠍⢀⣏⠈⠧⣌⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣶⣄⣉⡁⠌⠭⣿⣿⣿⣿⣻⣿⣾⡿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⢿⠿⠿⠿⠿⣿⣿⣿⣭⡽⠛⠛⠛⢃⣒⢀⣹⣿⣿⣿⣗⣿⣻⣽⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⣿⣿⣿⣿⣿⣧⠉⠈⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠛⠛⠉⠉⠉⠉⠛⠛⠿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣤⢀⣀⠜⠁⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢩⣤⣤⢻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⡇⠉⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠄⠀⠈⠀⠀⢰⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡠⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠒⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠃⡤⠀⠀⠦⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣄⠈⠀⠀⠐⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠌⠡⠄⠐⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠐⠶⡀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⡖⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣤⣤⣀⣀⣀⣀⣤⣤⣶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡁⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⣣⡌
⠀⠀⠀⠀⠀⢠⠀⠠⠐⢄⠀⠀⠀⠀⠀⠀⡐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠰⡇⢀⡈⠃⠀⠀⠐⣿⠆⠀⠀⠘⢇⡀⢺⡆⢈⠄
⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣄⠐⢀⡄⠃⣨⣀⣀⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠙⠆⣁⠘⣀⡓⠂⣀⣀⣉⣀⣀⢀⢚⡀⠃⣣⠸⠏⣀⠀⣀⡀
⠀⠀⠀⠀⠀⡀⠈⠙⢁⡈⠋⠀⢨⡅⠄⠛⢁⡈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠙⣅⣈⠋⢤⠞⣋⠉⢻⠯⣉⡹⠟⠉⣉⠳⣤⡝⢁⣈⠋⠀⠋⠁
⠀⠀⠀⠀⡀⠀⠄⠐⡀⠓⠀⠀⠈⠁⠀⠀⠸⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⠰⡇⠀⠀⣭⠐⠀⠀⠉⠀⠈⠀⢭⠀⠁⢄⠂⠙⠆
⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⢋⡅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠡⠁⠀⠈⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⢀⠀⠠⡄⢠⠖⠀⠀⠀⠀⠀⠀⠤⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣠⠄⠀⠀⣀⠀⠀⠀⢀⡀⠀⢀⢄⡒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⣤⠶⠀⠀⠀⠰⣤⡄⣤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠘⣃⡀⠋⢀⣄⣐⣀⣄⠈⠀⣀⠋⠀⠰⠖
⠀⠀⠀⢠⣧⢠⡄⠠⠄⠠⠉⢠⣸⣦⡞⣤⠘⠡⢠⣤⠀⣦⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠌⠩⠉⢩⡄⠀⠭⣭⡭⠄⠠⣼⠈⠁⠁⢤⠄
⠀⠀⠀⠈⠇⠀⠀⠀⣴⡖⡷⢀⠐⣀⡀⣀⠸⡗⣶⡄⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠲⠆⠠⠀⡀⣿⡦⠀⠄⠀⠶⡒⠒⢢⡄
⠀⠀⠀⠀⢀⡠⠀⠀⠉⢡⡄⠀⠀⠹⠁⠀⠀⣤⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢄⡜⠑⠀⠀⠚⠀⠈⠀⠙⠂⠀⠀⠛⣤⠄⠡⠄⠂
⠀⠀⠀⢀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐

⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠦⢄⠀⠀⠄⠀⢀⠠⠴⡄⢀
⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⢀⠀⣽⠀⢀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢢⡖⠷⠲⢶⡖⠀⢶⣾⢻⣶⠗⠐⣶⠶⠲⠟⣦⠓⠀⠲
⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠠⠿⠀⡝⡅⠺⠇⠨⠀⢀⡀⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⡖⢨⡡⣄⢠⡌⢁⠀⠋⣸⣿⡈⠃⢀⠉⣦⢀⣤⣉⠔⠆
⠀⠀⠐⠢⡐⠿⢒⣼⠂⠛⠓⡒⠚⠻⡛⠒⠂⠛⠂⢺⣕⠺⠇⠀⠒⠀⠀⠀⠀⠐⠛⡽⢛⢻⡿⣋⡟⠻⠞⠛⠻⡿⠏⠛⠨⠛⣯⡻⣿⢛⠻⠏⠛
⠀⠀⠀⠐⠂⠀⠀⠉⠀⠀⡄⠤⠂⣸⠀⠣⢀⠁⠀⠈⠈⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠁⢠⡍⢀⢉⣱⣆⣀⢳⣠⣷⣰⠇⣀⣶⢁⣁⡈⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠈⠉⠹⠨⣋⣉⠥⠘⠻⣽⠛⠠⢍⣉⡩⠈⠉⠉⠀⠘⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠆⢠⡄⠀⠀⠀⣤⠠⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀
⠀⠀⠀⠀⠀⣈⣉⣛⣳⡲⣊⡖⢳⢀⢁⣸⢓⣊⡞⣲⣛⣋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠚⢟⠓⣀⣚⣰⠄⡗⢤⣘⡆⡐⠛⠟⠂⣀⡀
⠀⠀⠀⣠⣶⣄⣹⣅⣀⣄⣤⠘⣩⡧⠨⣏⡁⢠⣄⣄⣀⣿⠁⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡦⢴⢶⣚⠱⠄⠄⠴⢈⣳⢶⠤⣶
⠀⠀⠀⠀⠁⠁⠼⢅⡀⡀⢀⠷⡼⠆⠇⠿⡴⣧⠀⠀⣀⠯⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⣤⣴⡀⣌⡳⠶⠿⠶⢋⡄⣰⣤⣤⡄⠈
⠀⠀⠀⠀⠀⠀⠒⠾⡿⠃⠸⢙⠇⠀⠀⠘⢟⠻⠈⢻⡿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠐⠁⠀⠀⠀⠉⠀⠁⠟⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣤⣦⣄⠀⣠⣶⣦⠀⣠⣤⣄⠀⠀⣠⣤⠄⠠⠀⠢⡀⠀⡀⠒⡆⠀⠀⠀⢄⠀⠀⠀⠀⡀⠀⠄⠀⢄⠀⠀⠔⠢
⠸⣿⣿⣿⣿⣿⣿⡿⠂⠿⠛⠯⠗⠘⠛⢋⡄⢈⣤⣜⣮⣿⣶⣶⡿⠀⢁⣦⣲⣨⣯⣶⡾⠇⠘⡀⠀⠀⠈⠁⣠⣄⠆⠀⠀⠀⠀⠀⢠⠤
⠀⠘⠛⣿⣿⣿⠁⠀⠀⠀⠃⠰⠄⠓⡜⠀⠀⠀⠙⠻⣿⣿⡿⠀⠀⠀⠀⠙⠻⣿⣿⡇⠀⠀⠀⠈⠒⠆⠐⣴⡏⠀⠀⠀⠁⠐⠀⢦⡍
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣷⡆⠃⠀⠀⠀⠀⠀⡏⣻⡇⠀⠀⠀⠀⠀⠀⠘⣻⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⣿⠁⡀⠀⠀⠀⠀⠀⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⠁⠃⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⢰⡄⠀⠀⠀⠀⠀⡇⢺⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⣿⢸⡆⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⢰⣹⠨⡇⠀⠀⠀⠀⢠⠷⣼⣖⠀⠀⠀⠀⠀⠀⢦⣷⠂⠀⠀⠀⠀⠀⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⠀⣽⡶⠂⠸⣷⠀⠀⠀⠜⢉⣿⣿⡉⠀⠀⠀⠀⠈⢹⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠿⠿⠉⠻⠋⠀⠀⠀⠘⢋⠅⠠⠠⠂⠀⠀⠰⠶⠟⠹⠿⠋⠀⠀⠀⠰⠶⠋⠹⠟⠁⠀⠀⠀⠄⠴⠟⠧⠄⠀⠀⠀⠀⠀⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⣠⣄⣀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⢠⣾⢰⣿⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢿⣿⣿⣯⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠻⠟⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⣀⣠⣄⠀⢀⡀⠀⢀⠀⠀⣄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠻⠟⣿⢈⠌⠁⡁⠉⠘⢶⣿⠻⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡄⠀⠿⠎⠂⠀⠉⠀⠈⢿⠏⠀⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⣀⣀⣀⢀⣀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢩⣍⠉⢉⡥⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢡⡌⠉⢉⡤⠵⠆
⠀⠀⠀⠀⣀⠠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⣠⠔⠛⠲⠣⣈⠀⠀⠀⠶⠜⠓⠦⣀⠀⠀⠀⠀⠀⠀⣀⠄⠄⠤⠤⠤⠄⣀⡀
⠀⢰⠂⠀⠝⠓⠲⠖⠲⢚⡂⠀⢙⡶⢤⣄⣠⠎⣡⠄⠛⠶⠖⢸⠉⠉⢻⠶⠶⠛⠢⣄⠰⣄⣀⣤⢶⡛⠁⢒⣓⠒⠒⠶⠞⠫⠄⠀⡄
⠀⠀⢢⣠⣤⡀⢀⡤⠖⢦⡈⠝⠋⡩⠖⣤⣍⠘⠓⠒⠒⠉⣻⣼⣛⣛⣺⣟⠙⠛⠒⠚⢋⣉⣥⡶⢍⠛⠋⢁⡴⠦⢤⣀⢀⣤⣄⡔
⢠⠚⠀⠀⠀⠙⣇⡀⠀⡠⠀⢀⣼⢁⠊⠀⣉⣱⣤⣀⠘⠋⠀⠀⠈⠉⠀⠈⠙⠂⣀⣠⣎⠉⠀⠑⡀⣧⡀⠀⢄⠀⠀⣸⠋⠀⠀⠀⠓
⠸⡀⠀⠀⠀⣠⡇⠀⠀⠁⡰⠉⢿⡌⢶⣉⡀⠀⠀⠉⠻⣤⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢈⣁⡶⢡⡿⠙⢦⠈⠁⠀⢈⣄
⠀⢱⠀⠀⣰⠋⢃⡀⠀⠸⣣⠟⣩⠻⢦⣙⠣⠬⢍⡥⢤⠄⢧⠀⢀⡀⠀⣼⠣⡤⢈⠭⡭⠔⣋⡴⠛⣍⡻⣌⣅⠀⠀⡨⠙⣆⠀⠀⡞
⠀⢸⠀⠀⠈⠀⠀⠙⡄⢿⡸⣏⡡⠒⣹⡥⠝⠒⠲⣥⠀⠀⣬⠉⠉⠉⠉⣯⠀⠀⣼⡄⠒⠫⢩⡇⠒⠌⣹⠏⡽⢀⠎⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠙⠷⣌⡳⢦⡤⠒⠀⠀⠀⠀⠀⠶⠟⠀⠀⠀⠀⠻⠶⠀⠀⠀⠀⠀⠢⢤⡴⠞⣡⠾⢋⣄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⢀⠛⡇⢃⡼⠛⣶⣄⡀⠒⠶⠭⠙⠉⣤⣛⠀⠀⠀⠀⣗⣤⡉⠛⠭⠷⠖⠀⣠⣴⠛⢣⡘⢸⠟⡇⠀⠀⡄
⠀⠀⠀⠀⠘⠀⠀⠘⡀⣻⣌⠳⣭⠔⠊⠉⣠⡤⠶⢛⡓⣨⢟⡀⠀⠀⢀⡻⣅⣚⡛⠦⢤⣔⠉⠑⠦⣩⠞⣡⣿⠄⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⡉⢓⣌⠙⠒⠠⣤⣀⡉⡄⢚⣡⡎⠁⠀⠀⠈⢳⣌⡛⠁⣀⣀⣤⡄⠲⠚⣡⡶⢉⠟⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠹⣄⠙⣉⠠⠛⣠⢄⣈⣉⠡⠐⣽⠏⢼⡇⠀⠀⠹⡧⠟⢬⠲⠌⣉⣁⣠⡄⠛⠅⠉⠊⢠⠏⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠈⡴⢋⠳⣌⠒⢎⣠⠘⠉⢀⡠⢞⡝⡳⠎⠀⢀⡀⠀⠱⢞⢪⡳⢄⡀⠉⠳⣄⡱⠖⣠⠖⠙⢦⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠰⣌⠃⣀⠟⠂⣀⣈⣀⡠⠐⣩⠜⣡⠚⡴⠉⠉⢦⠓⢌⠳⣍⠂⢄⣈⢁⣀⠴⠛⢁⡸⢣⠎⠀⠀⠀⡇
⠀⠀⠀⠀⣸⠀⠀⠀⢀⠘⡶⢉⠰⢎⣩⡌⢉⡠⢞⡡⢚⠏⡼⠓⠒⠒⠲⢦⠙⡓⢌⡳⢄⡉⢩⣍⡠⠄⣉⢴⠋⡀⠀⠀⠀⡗
⠀⠀⠀⠀⢸⠀⠀⠀⢸⣇⠱⡎⡱⢤⣇⣀⡡⠔⠋⡡⠋⣼⢣⣀⣠⣄⣀⡌⣧⠙⢌⠙⠢⢈⣁⣹⡤⢎⢁⠎⣸⡃⠀⠀⠀⠃
⠀⢠⠀⠀⡼⠀⠀⠀⢸⠏⢡⡌⢦⣈⡡⠉⠀⣠⠞⠁⣸⠏⣿⠁⠀⠀⠀⡿⠸⣇⠈⠳⣄⠀⠉⠌⢁⡤⢋⣜⠹⡇⠀⠀⠀⢣⠀⠀⡆
⠀⠘⠀⢠⡇⠀⠀⠀⣦⢷⡘⡜⢠⡌⠓⠛⣉⠀⠀⣰⠇⠀⣹⡤⠒⠒⠦⣇⢀⠈⣆⠀⠀⢉⠛⠚⢩⡄⢣⢎⡾⣡⠀⠀⠀⢸⡄⠀⠃
⠀⡆⠀⠸⡇⠀⠀⠀⠸⢾⡷⠘⣆⠈⡉⣋⡴⢃⡰⠃⠀⠈⠙⠂⠀⠀⠀⠿⠈⠀⠘⢆⠘⢦⡙⢈⠁⣰⠂⢾⡷⠉⠀⠀⠀⢸⠇⠀⢸
⢠⠀⠀⠀⠙⡀⠀⠀⠀⠻⣔⢏⠄⢙⣉⣡⡴⠚⠃⠀⠔⠀⡾⠀⠤⠶⠒⢛⠖⢂⠀⠘⠓⢦⣌⣉⡋⠡⡺⣆⡟⠀⠀⠀⢀⠊
⡎⠀⠀⠀⠀⡘⡄⠀⠀⠀⠜⢧⡛⠾⠣⠉⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⡀⠉⠈⠧⢞⣴⠋⠀⠀⠀⢠⢂
⢹⣆⣀⣄⠀⣻⠁⠀⠀⠀⠸⣌⠻⣹⡽⣢⠎⠀⠀⠀⠀⠀⠘⠚⠋⠭⠒⠋⠀⠀⠀⠀⠀⠑⣔⢮⣋⠿⣠⠇⠀⠀⠀⠀⣟⠀⣠⡀⣠
⣤⣬⣭⣬⣽⣭⣤⣤⣤⣤⣤⣽⣧⣴⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣵⣶⣼⣯⣤⣤⣤⣤⣤⣭⣯⣥⣭⣭
⣿⣿⣿⠋⠙⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⠀⠀⡴⠋⠉⠉⠦⠀⠀⣀⠀⣠⠴⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⣤⠞⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢱⣄⠰⠶⠶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠈⠑⠂⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠹⡖⠂⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠒⠂⣠⡀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⢀⡠⠲⢏⠀⠀⠀⠀⢰⡄⠐⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠂⢤⣄⠀⠈⠑⠦⣀⠀⠀⠀⠘⠉⠁⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⢠⡔⠒⠀⠹⣀⠀⢀⡇⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⡈⠱⡄⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⡰⠒⠈⠁⠀⢇⠀⠀⠀⠀⠈⠗⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠈⠑⢺⣆⠀⠀⠀⠀⠈⠃⠀⢲
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢨⢷⣄⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠂⠉⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⣀⠬⠗⠀⠀⢀⣷⠊⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⣠⣄⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⢓⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠔⠋⠀⠉⠤⠞⠁⠈⠐⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣀
⠀⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡹
⠀⠀⠀⢀⠱⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡠⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠐⠊⢹⠀⠀⠀⠀⠀⠀⠚⢅
⠀⢀⠔⠉⠀⠀⠀⢀⠠⠤⣀⠠⠜⠁⠀⠀⠰⠦⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⠚⠲⠀⠀⠀⠀⠀⠈⠲⠄⣀⣀⣀⠀⠀⠀⡷
⠀⠻⡀⠀⠀⠀⠰⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠙⣄⠰⡁
⠀⣀⠼⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣅⠀⡉
⡜⠁⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀⠤⢄⡀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⢀⡠⠤⣀⠀⠀⠀⠀⢸⢀⡴⠁⠀⠛⢤
⢇⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⣉⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢈⠀⠀⣉⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠾⢀
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠁⠀⠀⠀⠀⡆
⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⣀⠞
⠀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠘⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸
⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏
⠀⠀⢠⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡴⠶⢦⡀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠲⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡎⠁⠀⠀⡘⠑⢌⡁⠒⠀⠒⢉⣤⠃⠀⣦⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠂⢶⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠱⡀⠀⡄⠁⠀⠀⠀⠉⠉⠁⡰⠃⢀⠜⠘⠄⢀⠖⢉⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣠⡄⠒⢦⠀⠀⣠⠃⠓⡀⠃⣴⠁⠀⠀⠀⠀⠀⢀⡜⠁⢀⠎⠀⠀⢺⠃⢀⠞⣃⠀⠀⠀⠀⢠⣤⣀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⠁⠀⠀⢡⣀⠇⠀⠀⠀⠀⠀⣠⠊⠀⡰⠋⠀⠀⠀⠈⡖⠋⠀⠉⢣⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⠇⠀⢠⠈⢉⠟⠲⢢⣤⣤⣀⡔⠁⢀⡔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⡄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢣⡴⠃⠘⢤⠜⠀⠀⠾⠀⠀⠇⠀⡘⠀⠀⠀⠃⡸⠋⠀⣠⠚⡗⢢⡔⢢⡄⠀⠀⢸⠉⠉⣅⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⠀⣶⠀⠀⡇⠀⡆⢠⠟⠀⢀⠜⠋⢐⡇⠀⢱⡌⠀⠀⠀⠸⠀⠀⢘⠀⣤
⠀⠀⠀⠀⠀⠐⠊⠳⡀⢀⡔⠉⠁⠀⠀⠀⠑⢇⠀⠀⠀⢠⡷⠁⢀⣴⠏⠀⡄⠸⠁⢀⠘⡟⠒⠲⠀⠀⢿⠛⢻⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⠲⠇⠀⣴⣏⣀⡃⠘⠃⡄⢠⠋⠀⠇⢀⠜⠀⠀⢹⠀⠀⣰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠁⠚⠓⠻⠧⠤⠜⠃⠁⠀⠀⠀⠘⠒⠂⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠓⢦⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠃⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⢸⠆⠀⠀⠀⠈⠁⠈⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠆⠀⠀⠀⠀⠀⠀⣀⡰⢧⡠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⠀⡼⠢⠤⠄⠀⠛⠁⣀⣀⠴⠇⠀⡆⠀⠀⠀⢀⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⠤⠀⠘⠛⠁⠀⠀⣀⣸⡄⢰⠀⠰⠴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠦⢀⣀⣀⣀⣀⢀⣀⠀⠀⢻⠀⠀⠀⠀⠘⠛⢀⣀⡀⣶⣤⡦⣀⠀⠀⠠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢷⠄⠀⠛⠋⠁⢀⣠⠜⠁⡰⠛⣮⠦⠀⠀⠘⠚⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠉⠉⠙⠛⠉⠙⡋⠀⠀⠀⠀⢻⡉⠛⠉⢁⡴⠉⢀⡜⢁⡎⣠⠀⠀⠀⠰⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠙⠶⠟⠳⠐⠚⠋⠙⠋⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠈⠉⠉⠀⠀⠈⠉⠛⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡳⠖⠒⠒⢤⠀⢀⠤⠤⠤⡴⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢧⠀⠀⠀⠈⠀⡸⡀⠉⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⣠⠈⠳⠤⣀⠠⠒⠀⠈⠒⠶⠚⠁⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠑⠅⣀⠀⠀⠀⠀⠀⢠⣂⡰⠞⠁⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⡉⠉⠁⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠉⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠠⡀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢱⠀⠀⠈⠉⠛⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣀⡀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠠⠖⣶⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣶⠶⡶⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢤⣤⢄⠀⢀⣀⠠⣶⠀⣀⡀⠀⡠⣤⠄⠀⢀⡀
⠀⠀⣋⠣⠄⠀⠉⠁⠀⡤⡟⠀⠰⢤⣾⣄⠄⡀⢛⡤⡀⠈⠉⠁⠹⢶⣛⡂⠀⠀⠀⠀⠀⡠⠆⠸⠗⠂⠚⠋⢷⣤⡭⣆⠘⣿⢃⣼⢡⣤⡟⠘⠃⠘⠚⠅⠰⠄
⠀⡶⣶⠀⠀⠀⠀⣰⡌⠀⠀⠶⢳⣿⣟⣷⡾⢷⠂⠀⢉⣦⠀⠀⠀⠀⢳⢶⠀⠀⠀⠀⠀⠷⠂⠀⢠⣠⡄⠀⠀⠤⠗⠿⠗⣡⠺⠟⢹⠤⠀⠀⣠⣤⡀⠀⠐⠟
⠀⠰⣿⡀⠰⠶⠴⠿⡷⠬⠷⢶⡼⣙⣫⢛⣵⡤⠶⠇⢴⡿⠦⠶⠆⠀⣼⡄⠀⠀⠀⠀⢰⡇⠀⠀⠸⡄⠀⠀⠚⠃⠛⠛⠳⠀⠛⠛⠛⠘⠒⠀⠀⢠⠁⠀⠀⢸⡆
⠀⠀⠈⠛⠺⠔⠀⠀⠁⠀⠀⡸⡿⠟⢾⠺⢷⢷⠀⠀⠈⠀⠀⠐⠶⠚⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠙⠘⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣽⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⣖⣛⡛⢿⣿⣿⢿⣿⣿⠛⣛⣳⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⢀⣀⡀⠲⠆⣹⣇⠰⠆⣀⣀⡀⠀⠀⠀⠀⠀⠒⣄
⢀⣠⣤⡀⠀⡴⣯⣭⣿⣿⣿⣯⣿⣯⣿⣾⣯⣿⣭⣿⣿⣿⣯⣽⠧⠀⢀⣠⣤⣀⠀⠀⠰⠇⠀⠀⠀⢀⢀⣭⠐⡶⠲⣶⣤⡝⢩⣤⣶⠚⣶⠈⣧⡠⡀⠀⠀⠀⠸
⠀⠈⠁⠈⠑⠲⠖⢻⡿⣟⣿⣿⠇⢰⡦⠰⣆⠈⣿⣿⣟⡿⣿⠓⠖⠀⠉⠀⠋⠀⠀⠀⠘⠋⢄⡀⠴⣇⠋⠘⣹⣿⣾⢤⡮⣷⣯⢰⣬⣷⣿⣌⠊⢑⣹⠦⢂⡄⠻
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠹⣤⣈⣷⣿⢸⣿⣇⣤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠘⠃⠘⠋⠈⠉⠋⣶⡏⢻⣾⠉⠉⠀⠙⢡⡟⢃⣞⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣚⠀⠀⠀⠀⠀⠀⠐⠒⠰⢆⣿⣣⠦⠐⠒⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠀⣠⡄⡛⣠⡀⠀⠀⠀⡀⠠⣀
⠀⠀⠚⡍⢄⠀⢀⡀⣠⢂⠀⣀⡈⡲⢟⢷⡊⣀⡀⢐⢀⣀⡀⠀⣠⠎⡗⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⡠⢰⠶⢖⡉⡛⢑⠲⣶⡤⣀⠀⠀⠈⢷⣄
⠀⠀⠡⢙⢯⠍⢻⠽⣿⣿⠯⡉⢋⢱⣍⡾⠙⠉⠩⢿⣿⡯⣽⠋⠭⡏⠁⠁⠀⠀⠀⠀⠀⠀⢴⡼⡆⠤⠠⠼⢇⡼⢧⣽⡋⣉⡛⣧⡻⣅⠻⠦⠄⠄⣸⣼⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠣⣼⣟⡿⣟⣿⠴⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢘⠶⡒⣖⠏⠁⠐⣌⣀⣋⣀⡠⠀⠘⢇⡶⡒⢶⠡⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠑⠉⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠙⠉⠸⠛⠁

⠀⠀⠀⠀⣀⣀⡤⢀⠀⠛⣶⣤⡀⠀⣀⠀⠀⣠⣴⡞⠃⡀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⡀⠀⢠⣠⣦⣠⠄⠀⡀⣠⣀⡀
⠀⠀⢀⡎⠉⢏⡶⠣⠿⢆⣀⠇⢹⣤⣿⣡⣾⠰⣇⡐⠻⠇⢳⡌⣍⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡾⢧⠆⠉⣍⠱⡕⠶⠷⠞⡥⢊⣉⠑⢤⢽⠆⠀⢠
⠀⠀⠸⠇⠀⠏⠨⢮⠧⣬⠿⣀⠈⣋⣿⣙⠋⣀⡸⢧⠰⢶⠦⠸⢗⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⠐⠛⠞⣀⠂⠒⣶⠜⢾⢿⠞⢤⡾⠒⢒⣜⠎⠓⠀⢸⠇
⠀⠀⠀⠀⠀⠶⡄⠈⠓⢄⡀⠛⠀⠉⠻⠉⠀⠹⢁⣌⠔⠁⠀⡼⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣵⣆⢠⡄⡤⣾⠋⠒⠶⠽⠖⠊⢻⡦⡄⣤⣄⣆⣨⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣴⣴⣤⣤⣤⣴⣴⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣴⣷⣯⣥⣤⣤⣤⣤⣤⣤⣤⣬⣷⣷⣼⣯⣥⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⠁⣀⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⣀⠀⢠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣆⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠀⠀⣿⣤⣴⠂⡸⠀⠂⠀⠀⠉⠛⠀⢀⣉⣿⣭⡿⠖⠋
⠀⠀⠀⠀⠀⠲⣤⣴⣿⢁⣠⡴⠒⢲⠖⠀⢄⠁⠈⠀⠀⠀⠀⢠⣤⣥⣀⠁⡘⠓⠶⣤⡀⣤⠂⠩⠽⠛
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠏⠀⠀⠋⠀⠀⢀⡀⠤⣒⠉⠀⠀⢀⣀⣭⣁⠘⠻⠆⡄⢤⡌⠀⠀⢸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⣴⡎⢃⠌⢀⠀⠹⠂⠀⠀⠈⠉⠙⠛⠿⠋⣴⡄⢀⠹⡆⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠉⠀⢠⡆⢉⣆⣥⡆⢤⠐⠂⠀⠀⠐⠒⠶⠷⢶⣤⣀⠁⠈⠀⠀⠀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣡⠠⣏⢶⡻⠿⠞⢡⠌⣠⠀⠀⠀⣠⣈⠓⠲⠄⠈⠁⠸⢷⠆⣶⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠘⠣⣭⣤⣄⠀⠾⠁⠀⠀⠀⠈⠛⠻⢿⣿⣍⡛⠷⠆⣠⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣔⠲⢂⡉⠁⡖⢂⠀⠀⠀⢿⣶⣤⣀⠤⠉⠁⢤⣦⣌⠉⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠉⠓⠠⠅⠀⠉⠁⡀⠀⠐⣷⡄⠉⠙⠳⢶⣤⡀⠈⠋⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⣄⠀⠈⡁⠀⠀⠀⠀⠄⠀⠀⢴⣄⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⣁⠀⠀⠀⠂⠀⠉⠂⢠⡍⠀⠀⠈⠹⣦⡔⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⠒⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠌⠛⢀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡾⡆⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠟⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠙⢦⡀⠀⠂⣼⡗⠀⢷⠀⢀⣀⣤⣤⠠⠀⠤⠤⣴⣒⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠹⠀⠀⢃⠐⠦⣾⣏⢉⢄⣚⣟⠛⢉⣁⣉⣙⠻⢯⣭⣟⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢢⡀⠀⠀⠀⢀⣤⣄⣀⠀⣿⠟⠙⣤⠹⢿⡿⢟⣂⡾⣿⣿⢛⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣀⣀⠟⠉⠁⣋⠀⢾⠀⠀⠈⠙⢦⣙⢿⣍⣋⠑⠀⠀⠀⠘⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠘⠻⠀⠀⠀⠩⠦⢼⠃⣺⠀⠀⠀⠙⠳⣌⡛⠦⣚⣀⠿⠶⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠱⡀⠀⠀⠀⠀⢸⣭⠹⠁⠀⠀⠀⠀⠈⠛⠷⣄⣬⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⡦⣤⡀⠀⢀⡐⢣⣤⠀⢇⣤⡄⠀⠀⠀⠀⠙⢾⣽⣻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠈⠄⠀⢸⡏⠹⣶⠀⣌⠏⠓⠀⠀⠀⠀⢀⡈⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⣴⠟⠀⠀⠉⠀⡟⠀⠀⠘⢷⣴⣤⣬⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣾⣿⣻⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣟⣿⣷
⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⠛⣻⣭⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣯⣿⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⢿⣿⣿⣧⣀⣿⣿⣿⡛⣤⣽⣯⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣽⣯⣤⢛⣿⣿⣿⣀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣅⠀⠉⠙⢻⠁⠈⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠁⠈⡟⠋⠉⠀⣨⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠉⠉⠙⠳⢄⡀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⢀⡠⠞⠉⠉⠉⠉⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠤⠤⠤⠤⠄⠒⠛⠒⠤⣀⠀⠙⢷⡀⢰⡆⢀⡼⠋⠀⣀⠤⠖⠛⠒⠤⠤⠤⠤⠤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡙⣿⣿⢋⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣼⣿⣿⣧⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⣉⣉⣀⡹⠓⠚⠛⠉⣩⢿⣿⣿⡿⣍⠉⠙⠒⠚⢏⣀⣉⣉⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⢉⡠⣤⠞⠁⠀⢀⡴⠊⢠⢾⣿⣿⡗⡄⠑⢦⡀⠀⠈⠳⣤⢄⡉⠉⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠒⠋⢁⡰⣇⡠⠤⡶⠁⠀⡴⢃⠎⣿⣿⠱⡘⢦⠀⠉⢶⠤⢄⣸⣆⡈⠙⠒⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡤⠚⠁⣰⠃⠀⡜⠁⢀⠞⢀⡎⠈⣿⣿⠀⢱⡀⠱⡀⠈⢣⠀⠘⣆⠈⠓⢤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣤⡴⠁⠀⡸⠁⢠⠎⠀⡜⠀⠀⢿⡿⠀⠀⣣⠀⠹⡄⠈⢇⠀⠈⢦⣤⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⣶⣺⣇⣠⡃⠀⡼⠃⠀⠀⠸⠇⠀⠀⠘⢧⠀⢘⣄⣼⣗⣶⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠠⢶⣶⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⣄⣦⣥⣴⡗⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠙⡟⠁
⠀⠑⣿⣿⣿⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣯⡏⠀⠀⠀⠀⠂⠀⠀⢄⡏⠀⠀⠀⠀⠇
⠀⠀⠙⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣨⠳⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠿⢿⠀⠀⠀⠀⠀⠀⠠⠻⢷⠀⠀⠀⠀⢠⣧
⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠂⢲⠀⠀⠀⠀⠀⠀⠀⠇⣾⠀⠀⠀⠀⢬⣥⠄
⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡏
⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣄⣼⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⡨⣿⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⠻⢄⡀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠐⠒⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠰⣤⣾⣷⡏⠀⠀⠀⠀⡠⠀⠠⠀⠀⠶⡾⠻⣶⡾⠇⠀⠀⠠⠐⠀⠀⠐⠀⠀⠀⢠⣤⡼⠻⡿⠆⠀⠀⠀⠀⡠⠞⠒⠀⠀⠀⠀⢴⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣷⣦⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡼⢿⣯⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⣥⠙⠋⠻⢉⣶⢶⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠿⣿⣿⣿⣽⢃⣭⠠⣋⠈⣥⡾⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⣿⣿⣿⣏⡴⠖⠀⠰⠶⠴⠾⢛⡿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣟⣻⠏⠀⢐⠒⠲⠞⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠷⣖⠉⠅⣶⡘⠯⠀⠚⠂⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⣶⡶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡄⠀⢀⣻⡇⣰⠦⡄⠓⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠉⠛⠛⠒⠶⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⠇⠀⠰⠋⣹⣟⡉⠰⣼⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠙⠂⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣿⣯⡄⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣅⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣴⣾⣿⣤⣶⣾⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⣼⣿⣿⣿⣯⣥⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣇⣴⢨⡹⣿⠟⢋⣭⠻⠆⡀
⠀⠀⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡋⣿⣁⣿⠿⠏⠰⣿⠳⡆⠁
⠀⠀⠀⢰⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠃⠈⠛⠁⠀⠀⠀⠋⠀⠀⡀
⠀⠄⠁⠤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣼⠆⠀⠀⠀⠀⠀⢠⣯⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡄⢸⠆⠀⠀⠀⠀⠀⠘⣿⡋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣄⣠⢴⣥⣿⣤⡤⠤⠤⠤⣤⣤⣤⣤⣤⣿⣿⣿⣶⣄⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣶⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢄⡀⠐⠀⢀⣠⣶⣶⣮⣯⠍⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⢀⠀⠀⠀⢀⣤⣤⣾⣿⠟⠀⢼⣿⣿⣿⣿⠟⣀⠐⣶⣶⣶⣾⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⡋⠀⠀⠀⣼⣿⠿⠁⣴⣿⣿⣿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠛⣁⣀⣀⣾⠟⢡⣤⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠃⣠⣾⡿⠛⠛⣩⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⢀⣼⠟⠁⣠⣤⡾⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠟⠋⠀⢀⡼⠟⠁⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⠀⠀⠀⠀⣿⠇⠀⠀⣴⡏⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀⠀⠀⢸⣿⠀⠀⠀⢠⣿⡀⠀⠀⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⡆⠀⠀⢸⣿⠇⠀⠀⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣟⠁⠀⠀⢰⣿⡇⠀⠀⢸⣿⡇⠀⠀⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⢹⣿⣿⣶⡆⢸⣿⣇⡀⠀⢸⣿⣇⣤⠀⣿⡇⠾⡗⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢉⢸⣿⣿⣿⡗⢸⣿⣿⣿⣛⠸⠿⠇⠛⠀⠛⠁⠀⠀⠀⣿⣿⣿⣷⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⢸⣿⣿⡿⠷⠚⠛⠋⠉⡀⢀⡄⢠⡄⢰⡆⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢀⣤⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣴⢸⣿⡇⢠⡄⣶⠀⣿⠘⡏⠸⠇⠸⠃⠘⠁⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⢰⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⣤⡔⡄⣤⣼⣿⡇⠘⠀⠉⢀⣀⢠⣤⢠⣦⢰⡆⣾⡇⣾⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠼⠿⠂⠘⠛⣷⣤⣄⡀
⠀⠀⠀⠀⣷⣸⣿⣿⣿⣿⣯⣿⢋⡃⣩⢼⣿⡇⣼⡆⣿⠰⡿⠸⠟⠘⠃⠘⠃⠙⠁⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣶⣿⣿⣯⠀⣿⣿⣿⣿
⠀⠀⠀⡀⡁⢾⣿⣿⣿⣿⣾⣿⠙⠇⠛⣺⣿⡇⣠⠀⣤⠀⣶⢠⣶⢰⣷⢰⣿⢸⣟⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣤⣦⠀⣿⣿⣿⡿
⠀⠀⠀⡀⠿⢸⣿⣿⣿⣿⣿⣿⢸⡇⠿⢸⣿⡇⠛⠀⠛⠀⠋⠈⠉⠈⠉⠈⠉⠈⠁⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠗⠻⠟⢰⣿⣿⣿⢿
⠀⠒⠶⠶⠖⠚⠛⠿⠿⠿⠷⠿⠶⠶⠶⠾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠗⠒⠒⠒⠒⠚⠛⠛⠛⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠂⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⡄⠁⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠐⡑⠀⠀⠰⠀⠀⠀⠀⠈⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⣉⣀⣈⡁⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⣈⣀⣈⡀⠀⠀⠀⠸⣏⡿⠿⠿⡗⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠈⣁⣀⣈⠁
⠀⠀⠀⢩⠈⢈⠁⠀⠀⠀⠀⠈⠀⠐⠎⠈⠀⠀⠀⠀⢉⠈⢈⠁⠀⠀⠠⡰⠈⠀⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢀⣄⢀⣀⡀⢀⣄⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠔
⠀⢻⠤⠦⠟⠴⠦⢼⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⠀⠲⠀⠰⠀⠀⠀⠁⠀⠁⠁
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⠃⠀⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠲⠶⢚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠛⠃
⠀⠀⠀⣀⠀⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠈⠀⠡⠀⠂⠀⠀⠀⣾⠃⠘⠃⠀⠛⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠤⠀⠀⠀⠈⢀⠤⠠⢠⠄⠀⠀⠀⠀⡘⠆⠆⠾⡀
⠀⠀⡀⠰⣤⡤⠀⠀⠀⠙⢆⠢⠀⢀⠀⠀⠚⠁⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢠⡃⠠⠤⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣠⠄
⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠄⠀⠈⠁⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⢠⣴⠆⣶⣤⠀⠀⠀⠀⣴⡄⠀⣴⡄
⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⡁⡀⡁⠀⠀⠀⠈⠀⠀⣀⡀⠈⠐⠀⠀⠀⠀⣠⣤⡴⠂⠀⠀⠠⠀⢉⠤⢌⠁⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⠒⠢⠀⠀⠀⣴⡒⠉⠑⣒⠄⠀⠀⠤⣀⠀⠄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⢠⣦⣤⣤⣤⣬⣦⠀⠀⠈⠈⠀⠂⠈⠁⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⡉⠀⠈⡁⢀⠀⠀⠀⠸⠇⠀⠿⠀⡀⠀⠈⠙⠛⠁⡙⠛⢉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠒⢀⠀⠂⠀⠀⠀⠀⢈⠃⠀⢛⡀
⠀⠀⠂⠀⠉⡁⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡈⠁⠤⠀⠀⠀⠀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⡘⡁⠀⠀⠀⠀⠀⠈⢙⡛⠁⠐
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠘⠃⡅⠀⠀⠄⢠⡌⠀⠀⠀⠀⠀⠀⡀⡰⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀⠀⠀⠀⠀⠴⠿⣿⡿⠷⠄⠀⠐⡀⠌⠀⠀⠈⠄⡀
⠀⠀⣶⣄⡀⣀⣼⡆⠀⠀⠀⠀⠀⠀⣀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠗⠨⠀⠀⠀⠀⠀⡄⢈⠀⡦⠀⠀⠀⡀⠘⣀⠁⡊⢀
⠀⠀⠈⠦⠄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢶⣶⣿⣿⡶⠎⠀⠀⠐⢜⠃⠀⢛⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠤⢤⣤⣤⣀⡀⠶⡜⠁⢀⠀⣠⡴⠊⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣆⢀⣊⡾⠙⢁⣼⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⣿⢿⡏⠃⢀⡜⢋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠀⣧⣶⣿⡾⠥⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢓⢷⣄⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠒⢊⢻⠏⢹⣿⣿⣶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⣠⡖⠉⠁⠜⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣿⣿⣧⡀⠀⡀⣿⣿⣿⣷⣦⣦⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣙⣮⣿⣿⡇⣼⢠⣿⣿⡿⠛⠛⠫⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠋⠉⠉⠉⢻⣆⣿⠛⣿⣿⡅⢄⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⣿⡿⢡⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣀⣀⣀⣀⣀⣤⡴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡒⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⣹⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠠⢾⣿⢾⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡠⢜⣛⠀⠴⢴⣿⠿⠗⠦⣄⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⣤⣀⣠⣤⣤⣬⣉⣘⣋⠉⠘⣿⠄⠐⢊⣻⡴⠊⢁⣈⣛⣛⣦⣤⣤⣤⠤⠤⠶⢶⣶⣤⠀⡀
⠀⠀⠀⠀⠀⠨⢀⣈⡄⣠⣶⣶⣠⣴⣿⢿⡿⠿⢯⣉⡛⢶⣦⠠⡴⣿⠏⢷⡿⠛⠛⣿⣿⣿⣿⣿⣦⣠⣤⣤⡄⢼⣿⣗⡂
⠀⠀⠀⠀⠀⠀⢠⠀⢉⣿⣿⠉⡿⢸⣗⠸⣿⣿⣎⣉⠙⠋⠀⠀⣾⡆⠀⠀⠐⠊⣡⢿⣿⢃⣿⡜⣿⡇⢈⣿⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⢟⣧⣤⢸⣿⣆⠙⣿⡟⠙⠳⢦⠀⠀⢸⠇⠀⠠⠄⠛⠉⣹⢋⣾⣿⡿⣿⣿⣤⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⣿⡄⢿⣟⣧⡌⠓⠀⠀⢀⡁⠀⢸⠀⠀⠀⠤⠦⢒⣤⣾⣿⠟⣸⣿⢿⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠹⣟⣄⠙⢦⣆⠀⠀⣀⡈⠁⠀⢺⣇⠀⢀⣠⡠⠤⠤⠶⢃⣴⣿⢇⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⠙⢶⠃⠀⠁⣀⡀⣀⡄⠀⠀⢸⡿⠀⢀⡀⠀⠀⢀⠐⢋⡻⢋⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡍⢱⣀⠙⠶⠉⠁⠀⠈⡁⠀⠀⢺⣇⠀⠀⠀⠀⠈⠉⠒⠎⣡⣞⣽⡟⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠹⣾⠉⠀⠀⣀⣠⠤⠬⠂⡄⠀⣿⣟⠀⠒⢦⠤⣤⣄⣤⠚⠉⣿⠟⡸⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢶⠃⠈⠳⢄⠉⠁⠀⠀⡠⠋⢀⡀⣹⡃⠀⡀⠀⠀⠀⠈⠙⠳⠖⢁⠜⠳⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠌⠳⡞⠁⠀⣡⡤⠤⠖⠰⢂⠞⣥⢿⡇⠛⠀⠐⠂⠈⠀⢠⣠⠒⠛⠄⢠⢿⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢰⠂⡙⢲⡁⠀⠀⠀⠀⠀⡆⢰⣿⡺⣽⣆⠀⠀⢂⠀⠀⠀⠈⠻⠆⡰⠻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠻⡁⠀⢹⠂⠲⠶⠁⡸⠃⣾⢉⣻⣿⡿⠘⢦⠈⠶⣦⡤⢀⡠⠊⠛⣰⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡹⠃⠙⢦⠊⠀⠑⠒⠊⠁⡸⣹⡡⢸⣿⣇⡀⠈⠆⠤⠄⠒⠙⠷⠀⡰⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠱⡇⠈⠃⠀⠠⣤⠂⣰⡰⢉⡀⢼⣿⡏⠁⠀⠸⣦⣄⠀⣀⣠⠼⠇⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢇⠘⡄⢰⡦⢤⣄⢴⠟⠀⣸⠓⢛⣛⣿⠀⠐⢄⡈⠉⠁⣀⠉⠀⡼⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡂⢃⢁⡉⢤⠤⢴⡟⠀⠈⢹⣄⣈⣽⣿⠁⠀⠀⠈⠁⠀⠙⣲⠎⣠⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣜⠠⢤⡴⠋⠀⠀⢠⣌⠀⢈⣽⣿⡄⠀⠀⠀⠀⡀⠀⢙⡞⢣⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠻⠖⠋⠀⠀⠀⠀⠀⢸⠀⠸⢿⣷⠀⠀⠀⠀⠀⠀⠐⠠⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠀⠠⣶⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠀⠀⠀⠢⢩⣀⢀⢀⠀⣀⠀⣀⡍⠖⠠⠀⠠
⠈⠁⠈⠓⢀⠀⣀⠀⢮⡼⠸⢾⠕⠀⣀⢀⡀⠛⠀⠈
⠀⠀⠈⠁⡘⢃⠈⡂⠢⠀⠀⠀⠂⣈⢁⡘⣁⠈
⠀⠀⠁⠀⠈⠀⠰⠮⡄⠀⣀⠀⡬⠴⠂⠠⠁
⠀⠀⠀⠀⡀⠀⠁⢤⣄⠃⠀⠙⣤⡄⠁⠈⠀⠀⢀
⠀⠀⠁⠀⠐⠖⠀⠘⠇⡟⠒⢻⠸⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠚⠂⠆⠀⠀⣧⠀⠀⠠⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⠉⠀⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⣤⠃⠀⢀⠈⠀⡀⠈⠀⠀⢄⠀⠁⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡨⠀⠀⠀⠂⠀⠀⠀⠐⠀⣀⢈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠘⠁⠀⠀⠑⠀⠀⠀⠀⠀⠃⠀⠀⠘⢪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠂⠂⠚⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡁⠀⠀⠀⢈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠋⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠉⠉⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣀⣤⣤⣤⠀⠀⣠⣶⣦⣤⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣠⣀⢹⣿⣿⡟⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠉⠁⣿⣿⡈⠉⠁⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⣿⡆⠀⠉⠉⠁⢰⡾⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣭⣭⣭⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠠⠤⣀⠀⠰⣄⠀⠀⠀⠁⠀⠀⢀⠄⠀⠀⣀⡀⠀⠄
⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡈⠐⠠⠤⠤⠄⠂⠁⠠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⠂⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠀⣻⣿⠇⠀⠀⠀⠀⡘⣿⡖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠙⠿⠿⠋⣾⣿⠻⢃⠀⠀⠀⠀⡅⠿⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⢆⠀⠐⠲⣶⣦⣤⣤⠄⠀⠐⠿⠛⠤⠄⠀⠀⠀⠠⠂⠀⢀⣤⢭⣤⣤⡤⡤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠒⠚⢻⠀⠀⣿⣀⡠⠤⠰⠀⠆⠀⠀⠀⠀⠤⠤⣤⢤⡧⠀⠀⠈⠀⠀⢄⣀⡀⠠⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠁⠐⠛⠛⠛⠃⠀⠀⠀⠀⢹⠿⠛⠋⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢘⡀⡀⠤⠐⠈⠁

⠀⠀⢀⣀⣀
⠀⠀⠈⢰⡦⠬⣀⣀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠁⠒⠒⠠⠤⣀⡀
⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⢀⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⡇⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⡉⠉⠒⠲⠄⡢⡯
⠀⠀⠀⢸⡇⠂⠀⡠⡀⠀⡀⠢⡀⡂⢀⠀⠀⠢⡪⢆⠀⠀⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢨⡏
⠀⠀⠀⠨⡇⡀⠈⠐⢄⠈⠀⠀⠀⠘⠕⠁⠀⠀⠀⠈⡲⠋⠀⠱⠤⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢸⣗
⠀⠀⠀⠰⣗⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠸⣿
⠀⠀⠀⡠⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣿
⠀⠀⠀⠈⠒⠂⠬⢕⣒⡢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⢁⣒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠤⢀⣀⠀⠀⡄⠀⡀⠀⠈⡱⠀⠀⠀⠀⠒⠀⠸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠤⢅⣒⢢⣥⠀⢀⡀⢀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢱⠈⢘⠧⣄⣀⠰⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠉⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠂⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡅⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⣴⢠⠀⠀⠀⡄⠀⢀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⢀⡘⠀⠀⢀⠋⠀⠀⠀⣀⠀⠉⠿⠀⠀⠀⡇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⡃⠀⠀⡧⣀⠀⠀⠀⠈⠐⠀⠀⢠⢿⡀⠀⠰⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⢣⠁⠀⠀⡀⠘⠀⠀⠠⠀⠀⠀⢀⠳⠋⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⡄⠀⠀⠀⠁⠂⠀⠀⡄⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⡀⢹⡄
⠀⠀⡀⠄⠀⠀⢸⡀⠄⠀⠀⠐⣆⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⢠⠄⠁⣠⣣⣀⣀⡄⠀⠀⣸⠀⠀⠀⡠⠐⣗⠀⠀⠀⢀⡀
⠀⠀⠀⠸⡀⠀⢁⠀⢀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠉⠀⠁⢀⠀⠀⠀⠉⠀⠀⠀⠼⢈⢿⡇⠀⠀⢸⠛⠃
⠀⠀⠀⢀⢾⣿⠧⡤⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⣤⢾⣷⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢀⠳⣌⣺⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⢸⠀⠀⢠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡿⠀⠀⠠⡄⠀⠂⠀⡤⠄
⠀⠀⠀⠀⠀⠀⢴⡿⣿⠀⠀⠀⠀⠀⠀⢠⠐⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠐⢀
⠀⠀⠀⠀⠀⠀⢋⠶⠸⡀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠛⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⣆⠀⠂⠁⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⠍⠁⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢋⠑⡄⠀⠀⠀⠀⠀⠀⢐⣞⣲⣧⡀⠋⠀⣐⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⡿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠈⠉⣏⠉⡁⠠⠆⠁⣇⠋⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⠠⠀⠀⠘⠀⠠⢿⡆⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⢁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠋⠈⠀⠀⣐⠀⡄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠄⢠⡄⠉⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠸⣷⠑⡀⢀⢀⡁⢀⠁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠀⠀⢻⠆⢘⠨⠀⠀⠒⡧⡀⠰⡄⢧⠀⠀⠀⠀⠀⢴⣀⡀⢨⣎⠈⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠁⠀⢀⠀⠀⠈⠛⢦⣹⣄⣧⠀⠀⠀⠀⠀⠉⠀⠀⠈⢷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡅⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠀⢸⣷⣤⠀⠈⠙⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⠰⠐⠱⠂⠈⠿⠓⠆⠀⠐⠂⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁