Athletic shoe Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⣠⢋⡠⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠙⢄⣰⢃⠞⠀⠈⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣩⠭⠿⣶⣯⠥⢞⡽⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠯⠭⠽⣗⣲⢾⠖⠋⠉⠙⠉⠉⠁⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣒⣒⣒⣒⠤⠼⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣤⡤⠤⣍⣙⣦⡇⠀⠀⢀⠖⠉⢧⠀⢀⡰⠋⡴⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣭⣍⣉⡛⢲⢸⠀⠀⣰⠋⢀⡔⢋⡴⠋⣠⠞⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣊⣉⡉⠓⠒⠯⡍⡏⠀⣰⠃⢠⠏⡴⠋⡠⠊⢁⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠒⠿⠭⢗⡞⣹⠁⢠⠇⢠⠏⡼⢁⡞⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⠭⠭⢽⣒⣞⡵⠃⢠⠏⢀⡏⣸⢁⣞⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡼⠁⠀⠀⠹⣄⡞⢰⢃⡞⡞⢀⣠⠖⢋⡤⠖⢉⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠈⢠⠏⡜⢸⠁⣉⡤⠚⣉⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡥⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⢀⡴⢃⡞⢡⠇⢋⣡⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠏⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⣠⠴⢋⡴⠋⣠⠏⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠮⢤⣀⣀⣀⣸⣀⣀⣤⠤⠒⣋⡥⠞⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣒⠦⠤⠤⠤⠤⠴⠖⠚⣉⣡⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣠⡴⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⢲⣄
⠀⠀⠀⠀⢠⣶⣸⡝⡿⢷⣤⣄⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⢻⣧⠈⠮⣗⣦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠹⣌⡾⢀⣀⣀⡀
⠀⠀⠀⠀⠈⠳⣝⢷⣵⣄⣀⣀⣥⠱⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢝⢧⡀⠀⠉⠉⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⢤⡘⢆⠀⠙⢎⣧
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⣛⣛⣃⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢵⡊⢢⣀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣍⢛⠳⡖⠺⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠛⠯⣁⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⢄⠳⣼⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠱⣜⢯⡉⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣻⣶⠤⠤⢤⣬⣤⡷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⢦⣑⠢⠭⣉⣥⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣑⣌⡳⠵⠶⠶⢶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣇
⠀⠀⠀⠀⠀⣠⣾⣿⡙⢄⠣⣤⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⡏⢿⠠⣤⣤⠤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⡉⠀⠹⣷⣮⣤⣴⠁
⠀⠀⠀⠀⠀⠳⣝⢿⡗⠀⠉⠉⠉⢧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡈⠳⢌⢦⡀⠙⢦⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠳⣤⡈⠳⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠑⢿⢦⡤⡤⠤⠼⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡑⢝⣦⡈⢳⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢌⠻⡄⠇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣝⢶⡲⣏⡉⠻⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⢿⣆⠙⠒⢢⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⢾⠤⠤⡱⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣷⣝⠦⠽⣷⣶⣶⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⡣⡙⠢⠤⠤⠤⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⡢⡓⠶⠄⠤⠭⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢀⡴⠃⠀⠘⢄
⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⡠⠋⠀⠀⠀⠀⠀⠊⠗⠲⣄
⠀⠀⠀⠀⠋⠀⢀⣀⣀⣀⣀⡤⠤⠔⠒⢒⠒⠚⠛⢀⠿⡆
⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠠⢤⡠⠤⠤⠴⠒⠊⠁⠸⣇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠐⠒⠒⠒⠋⠅⠐⢦⠠⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⢸⠀⠀⡼⢀⠀⠠⢤⣙⠆⢤⡀
⠀⠀⠀⡇⠘⡆⠀⠤⠤⠒⠋⠀⠀⢀⣀⠀⡇⠀⠀⠁⠙⠢⠄⠀⣠⡴⠘⠀⣽⠄⡠⡀
⠀⠀⠀⡇⢰⠃⠤⠤⠤⠤⠔⠒⠊⠁⠀⠀⠈⠓⠒⠒⠒⠒⠒⠤⢍⣀⠚⠂⢠⡠⢘⢁⢤⣤⡀
⠀⠀⠀⡇⠀⠑⠦⣄⡀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⡠⢀⡄⠀⠈⠉⠓⠢⠤⣙⠁⠘⠉⠪⠑⠒⠒⠦⠤⠤⠤⠤⢤⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠛⠲⢶⣤⣄⣀⣀⠀⠀⠀⠴⢋⡴⠋⣠⠊⣠⠂⢀⡞⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠉⠀⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠩⠷⣂⣤⣄⣀⠀⠁⠚⠁⣠⡿⠁⠀⠀⠀⠀⠑⠤⣤⡤⠤⠤⠒⠉⠁⠀⠀⢀⠤⠂⢸
⠀⠀⡔⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⢀⡀
⠀⠀⢣⡀⠀⠀⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣠⠤⠔⠂⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠙⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⠤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠒⠒⠒⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢋⡉⠙⠛⠛⠉⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⣴⣋⠔⠂⠀⣀⣠⡤⠤⠤⠿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡧⠖⣋⣩⣤⠶⠶⠖⠒⠚⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢋⣴⠞⠋⠁⠀⢻⣿⣿⣿⣿⣷⣌⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢋⣴⠟⢁⡤⢒⡀⠀⠀⠙⣿⣿⣿⣿⣿⣦⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢁⡾⢁⣴⣿⣷⣩⠖⣣⠀⠀⠘⢿⣿⣿⣿⣿⣧⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢁⣾⢁⣾⣿⣿⣿⣿⣯⠵⣊⡄⠀⠈⢿⣿⠿⠿⠿⠷⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⣼⠃⣾⣿⣿⣿⣿⣿⣿⣾⡡⠖⣂⣤⣴⡶⠶⠿⠿⠿⠟⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣤⣿⣿⣿⡇⢰⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⠷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⣴⣶⣾⣿⣿⣿⡿⠀⣾⠇⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣬⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣷⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⢛⣩⣭⣭⣭⣭⣭⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠐⠿⠿⠿⣿⣿⡿⢫⣿⠀⣾⣿⣼⣿⣿⡿⠃⠀⠀⠀⠀⢀⣠⡶⢟⣫⣵⣾⡇⣿⣿⣿⣿⣿⣿⣿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⣿⣿⣿⣷⣶⣾⠿⠛⢁⣾⡇⢰⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣴⡿⣫⣴⣿⣿⣿⣿⣇⣿⣿⣿⡿⢟⣩⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡟⢀⡴⠛⣧⣼⣷⣤⣤⣤⣤⣶⣿⣿⠀⣼⣿⣿⣿⡟⠁⠀⠀⢀⣴⣿⣣⣾⣿⣿⣿⣿⡿⠟⠛⣻⡟⣩⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⢀⡾⢡⡞⢠⣿⣿⣿⣿⡇⠘⣿⣿⡏⢀⣿⣿⣿⡟⠀⠀⠀⢠⡾⣋⣍⡛⠿⣿⣿⡿⠋⠀⠀⣴⣯⣼⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢠⡇⢸⡇⢸⠁⣧⣸⣿⣿⣿⠇⠀⠘⣿⠇⢸⣿⣿⠏⠀⠀⠀⣰⡟⣱⣿⣿⣿⣿⡿⠋⠀⠀⣠⡾⣫⣭⣭⣭⣤⣴⡟
⠀⠀⠀⠀⠀⠘⠇⢸⡇⢸⢀⡼⣿⣿⣿⣿⠀⢀⡀⠀⠀⣾⣿⠏⡾⠀⠀⣼⠏⣼⣿⣿⣿⣿⡟⠀⠀⢀⣾⣯⣼⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⠙⣦⡿⣿⣿⣿⠀⣸⣷⡀⢠⣿⠏⢸⡇⢀⣾⠟⣛⣛⣛⣻⣿⡟⠀⢀⣴⢟⣵⣦⣭⣍⣻⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢿⢙⣿⣿⡏⠀⣿⣿⣿⣾⠃⠀⣾⣀⣾⢣⣾⣿⣿⣿⣿⠟⠀⢠⣟⣱⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⢸⣿⣿⡇⢸⣿⣿⣿⠃⠀⠀⣿⡿⢡⣿⣿⣿⡿⠟⢁⣴⠆⠘⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢀⣠⣤⠶⣶⡟⣻⠇⣼⣿⣿⠀⣿⣿⡿⠁⠀⠀⠀⢻⢷⡿⠿⠛⠉⣠⣾⣿⢃⡶⣲⣾⣿⠟⠁
⠀⠀⢀⣴⡿⢉⣴⠞⠻⠿⠋⣴⣿⣿⣿⢸⣿⡿⠁⠀⠀⣰⡷⠠⠄⢀⡤⢠⣴⢿⡿⣱⢟⣼⢫⡾⠃
⠀⢠⣿⣿⠀⣾⣿⡿⠓⢒⣾⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⡿⠁⢄⣤⡦⢠⣾⣠⡶⢠⣶⢰⡆⣴⡄
⠀⣼⣿⣿⣄⢻⣿⡞⣡⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣾⠏⠀⢀⣾⠋⢠⡿⢡⡿⠁⢐⣧⣈⣷⣾
⠀⣿⣿⣿⣿⣷⡿⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⠋⠀⣠⣿⠇⣰⠟⣛⣛⣛⣻⢸⡟⣩⣭⣭⣧
⣰⣿⣿⣿⣿⣿⣷⣠⣶⣶⣶⣿⣿⠏⠀⠀⣠⠟⣛⣛⣛⣋⡿⣴⢣⣾⣿⣿⣿⡿⣜⣸⣿⣿⠿⠇
⢻⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⡾⢫⣾⣿⣿⣿⣿⣿⣧⠿⠿⠿⠿⣿⡱⢋⣵⣶⣶⣾⡟
⠈⣿⣷⡌⠛⢿⣿⣿⣿⡿⠋⠀⢀⣴⠿⠴⠿⠛⢛⣻⣿⢟⣵⣾⣿⣿⣿⣿⡿⢓⣛⣋⣭⣭⣴⠗
⠀⠘⢿⣿⣆⠀⠀⠀⠀⢀⡠⠖⣫⣴⣿⣿⡿⢿⣿⠟⣛⣋⣭⣭⣥⡶⠾⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠻⣿⣿⣶⣶⠞⣛⣋⣫⣭⣭⣴⣶⠶⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠈⠛⠿⠿⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠇⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⠂⢀⠔⠂⠠⠄⣈⡀⠀⣀⡴⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⢀⣀⠠⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⢁⠀⠤⠤⢠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠀⠼⠄⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⣠⢠⠆⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⢁⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢑⠂⢈⣀⣀⣀⣏⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡠⠂⠁⣀⠠⠕⠒⠐⠒⠨⠁⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⠐⠒⠀⠄⡀⠀⠀⠀⠀⠀⠀⣠⠎⡠⠊⠀⠁⠀⠓⠀⠀⠀⠀⠵⠒⣊⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠢⠔⠈⠉⠉⣉⠑⠁⠀⠀⠀⠀⢀⡴⢁⢀⡴⠀⠀⠀⠀⠘⠃⡀⠀⠤⠀⠠⢌⠒⠛⢂
⠀⠀⠀⠀⠀⠀⠀⢠⠘⠃⠤⠴⠖⠂⠀⠞⠀⠀⠀⠀⠀⢠⠎⠀⣠⠋⠀⠀⠀⠀⠀⠀⠘⠖⠂⠀⡂⠂⢀⡈⠯⠣
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢠⠀⢀⠵⠀⠀⠀⠀⢀⠔⠁⢠⠞⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣐⠻⠴
⠀⠀⠀⠀⠤⠐⠒⠒⠂⠤⣀⡈⡄⠀⠀⠀⠀⣠⠔⠉⠀⣰⠏⠀⢠⠈⠑⠤⡀⠀⠀⠀⠀⠠⠶⠤⢤⠤⣤⣤⣓⣒⣒⣒⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⡠⠔⠋⠀⠀⠀⣰⠋⠀⠀⠈⠓⡢⠤⣈⠢⡀⠀⠀⠀⠐⡆⠐⠛⠉⣁⣈⣉⣉⣈⣳⣽⣦⣀
⠀⠰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠁⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠁⠠⢁⢸⡦⣀⠀⠀⢁⡼⠋⠉⠉⠉⠉⠉⠉⠉⢉⣉⡹⠋⠢⡀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⠉⠒⠛⠀⠄⠀⠀⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠒⠤⠤⠤⠤⠄⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⢂⢈⡀⣀⠹⡀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣈⠁⠴⢀⣉⡁⠀⠙⠻⢶⠤⣀⣀⣀⠴⡺⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠰⠈⢹⠄⣈⠧⠖⠊⠉⠀⠐⢤⡐⢤⣀⠙⠒⠶⠖⢊⣠⠤⠖⠊⢇
⠀⠀⠀⠀⣀⡠⠤⠤⠖⠒⠋⠉⠁⠀⠢⠬⠷⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠉⠒⣠⠊⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠋⠀⠐⠤⠄⠀⠤⣀⣀⣀⣀⡠⠤⠤⢄⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠜⠁⠀⠀⠀⠀⠀⢀
⠀⠀⢰⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⢀⣀⡀⠤⠤⠤⠴⠐⠒⠒⠒⠂⠈⠉⠉⠉⠉⠉⠀⢠
⠀⠀⠀⠳⣄⡉⠉⠒⠒⠦⠀⠀⠠⠤⠤⠤⠒⠒⠉⠉⠉⠀⠀⠀⣀⠠⠄⠀⠒⠒⠒⠒⠢⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠓⠖⠦⣄⣠⣄⣀⣀⣠⣀⠀⠀⢀⣀⠀⠐⠈⢉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠈⠀⠀⠈⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠠⣉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠴⠀⠀⠹⣦⡀⠠⠤⠞⠁⠀⠀⠀⠈⠂⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠉⣀⠔⠁⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠻⠆⠁⠀⣠⠤⠤⣀⡀⠀⠘⠱⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠚⢛⠿⠿⠦⠀⠀⠀⠈⠉⠒⠦⠤⣄⣠⣤⠴⠚⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣆⣘⢛⠷⠷⠦⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢺⣄⢀⣙⠛⠛⠑⠀⢀⣠⠔⠒⠀⠉⠉⠁⠤⠤⠤⠤⠤⠤⠤⣴⠞⠁⣠⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢻⡄⢀⣩⠌⠙⠁⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣁⡤⠚⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠻⣦⡁⠉⠊⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡡⠴⠊⠁⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⢦⠀⢀⠈⠪⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠵⠚⠉⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠱⡀⠀⠀⠀⠁⢸⠀⠀⠀⢠⠏⠀⠐⠦⣄⠀⠀⠀⠀⢀⡤⣾⠗⠋⠀⠀⠀⣠⠴⠚⠉
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠉⠀⠀⠀⡾⠀⠀⠀⠀⠈⠙⠢⢄⣚⠭⠊⠁⠀⢀⡤⠖⠉
⠀⠀⠀⠀⡀⠐⠦⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⠴⠚⠁
⠀⠀⠀⢀⠱⣄⡀⠀⠈⠉⠉⠓⠚⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠀⢀⡤⠖⠁
⠀⠀⠀⠘⢦⡀⠉⠓⠶⠤⠤⣄⣀⣀⣀⡀⠀⣀⣠⡤⠤⠖⠒⠉⠁⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡛⢶⣄⠀⠀⠀⠀⠀⠙⠀⠀⠀⡽⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⠄⠙⢷⣄⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠿⠿⠿⣮⣿⡷⠀⣀⣀⣀⣀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠸⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢻⣒⢶⠶⣴⣿⣷⣾⣿⣿⣿⣿⡭⠍⠉⢛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠿⠿⠶⣷⣵⣿⢿⣿⣭⣉⣉⣭⣤⣤⡤⢴⣶⠻⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⢶⣶⢤⣤⣄⠟⣼⠟⠉⠉⡉⢉⠉⠁⠀⢈⣿⡇⢹⡇⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡞⠻⠿⣌⣳⣴⡿⢋⡾⠃⢠⠆⣼⢃⠈⢀⣞⣵⠟⠉⠀⠈⡇⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⣿⣏⠙⣷⣶⣦⡽⢋⣴⠟⠁⣠⠃⣼⣧⢋⣴⡾⠋⠀⠀⠀⠀⣠⣿⣦⣴⣶⡿⠟⠛⠉⠉⠉⠉⠉⣉⡙⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⣤⣴⡶⢿⣿⡟⢳⣤⣙⣶⣼⠿⢋⣴⣿⣣⣢⣶⣷⣾⣿⣿⣿⣿⣤⣶⣶⣾⣿⢿⣿⣿⡿⠋⣁⣤⣴⣶⣶⣿⣿⡿⣿⣿⡇⠀⢸⣿
⠀⠀⢀⣴⡾⠿⠛⠛⠻⣏⡉⠉⣹⣿⣿⡿⠟⣛⣩⣭⣩⣥⣶⣿⣿⡿⣛⠛⠍⠉⣉⣉⣉⣁⣠⣤⣤⣀⣤⣶⠾⣿⣧⣤⣾⣿⣿⣿⣿⣿⢟⣽⢞⣭⣿⡇⠀⢸⡿
⢠⣴⣏⡁⠀⠀⠀⠠⠲⣯⢿⣟⣻⣷⠶⠶⠛⠛⠉⣩⡿⠛⠉⣭⣿⣿⢟⣛⠿⣷⢭⣭⡥⢶⡶⣬⠭⣭⡿⡋⢾⣿⣿⣿⣿⣿⣿⡿⣫⠾⣋⠵⡩⣺⣿⣄⢠⣼⣇
⢸⣿⠉⠉⠉⠻⣷⣦⣔⣣⣼⣿⡩⢀⣠⠄⢂⣴⡟⣩⠔⠛⠀⠀⢸⣿⣿⣿⢀⣷⠀⢿⢁⣼⡇⠸⠈⣼⢸⡀⢿⣿⣿⣿⣿⣟⡍⣈⡀⠂⠀⠂⢠⣿⠟⠛⣿⠏⣿
⣿⣿⣁⣀⡀⠀⠈⠉⠉⠉⠛⠛⠿⣯⣥⣥⣿⡟⢰⠃⠀⠀⠀⠀⠀⢩⣴⡀⢸⣿⣧⠈⢿⣿⣿⡄⠸⣿⡀⢷⡈⢿⣿⣿⣶⣀⣂⣀⡠⣠⣶⣶⠋⠁⢀⣴⣿⠀⣿
⠙⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⡀⢸⠄⠀⠀⠀⠀⠀⢘⣟⠃⣾⠋⣾⣧⣈⣿⣯⣿⣦⣹⣷⣬⣙⣄⣹⣯⣉⣉⣙⠛⠻⠟⠋⣁⣤⣾⣿⡿⠿⠀⣿
⠀⠐⠂⠀⢉⣉⡉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠻⣇⢸⣄⠀⠀⡄⠀⠀⢀⣿⣦⡿⣿⣿⡿⠿⠿⠿⠿⠿⠟⡛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⣀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠹⣿⣏⡀⡀⠀⣄⠆⢸⠟⣯⣽⠷⣶⣶⣶⣾⣿⣶⣦⣭⣭⣬⣴⣴⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠋⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣥⣾⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⠃⠋⢙⣦⣤⡀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⣿⣿⠋⠁⠀⡘⢸⣿⣿⡇⠙⢶⣦⣤⣌⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢒⣈⣡⣴⣿⡿⠃⠀⠀⢀⠅⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⡸⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠛⣉⡭⡿⠛⠛⠉⠀⠀⠀⢀⠎⣼⣿⣿⡿⠁⠀⢀⣿⡏⠁⠀⠀⠀⠀⢨⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡄⣾⢁⢾⠁⠀⠀⠀⠀⠀⠀⢌⣾⣿⣿⠟⠁⠀⠀⣼⠟⣇⢠⣤⣤⡤⢤⠆⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢿⡝⢗⢳⠋⠀⠀⠀⠀⠀⠀⢸⣾⣿⡿⠋⠀⠀⣠⣾⠯⣪⣉⡼⣢⢂⠟⢿⣆⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠁⣺⠃⠸⡽⠂⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⢀⣠⡾⢻⢏⠀⠘⠏⣰⠇⠰⠒⣉⣿⡄⢀⡐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⣀⠏⣠⢋⡛⠂⠀⠀⠀⠀⠀⠀⣼⠃⠀⣴⣿⠻⣄⠸⣼⣤⠤⢾⣿⢀⣋⣉⢩⣽⣿⣌⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⡡⡚⠫⢩⣥⠃⠀⠀⠀⠀⠀⣸⠇⢠⣾⠉⠘⢷⡚⠓⠌⢁⡠⠜⣡⣾⣩⡤⠀⠶⢿⡿⣦⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡜⡅⢛⠐⣿⡌⠀⠀⠀⠀⠀⢠⡟⢀⡿⠃⠀⠀⠀⠙⠷⢊⣡⡔⠊⠘⣿⣧⡶⠖⠂⠺⣿⡈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢡⡜⡈⢻⠲⠿⡿⠀⠀⠀⠀⠀⢀⡾⢁⣾⠏⠀⠀⠀⠀⢰⠊⢿⡘⣇⠀⠀⠐⢟⠂⣹⢥⣼⡏⠀⢾⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣠⡞⣷⡾⣲⣯⠟⠀⠀⠀⠀⢠⢆⡼⢁⡞⠁⠀⠀⠀⠀⠀⠁⣄⣿⡇⢹⠀⠀⠀⠈⠑⠒⠛⠉⠁⠀⠈⢹⣿⡆
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠁⠀⠉⡠⠒⣨⣾⣿⣼⣷⠞⣵⠋⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡇⢸⣿⣷⣦⡢⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⣼⣟⠀⠀⠀⢀⡴⣫⣶⣿⣿⣿⣿⠟⣡⣾⣫⡄⠊⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⡘⣿⣿⣿⣿⢮⡢⡀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠰⣿⣝⡂⠀⣒⣩⣾⣿⣿⣿⠿⣋⡵⠞⢋⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡙⣿⣿⣿⣿⣿⣾⣧⣆⣀⣥⣼⣿⣿⡇
⠀⠀⠀⠀⠻⣿⣿⣿⡿⢿⣿⣟⡯⣷⣿⣷⣿⣿⡁⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣍⣛⣿⣭⣿⣿⣷⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⢭⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠤⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠴⠀⠀⠘⢷⣄⠀⣀⠤⠞⠁⠀⠀⠀⠀⠘⠆⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⣠⠞⠁⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢷⣄⠚⠁⠀⠀⣀⡀⠀⠀⠀⠈⠏⢧⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡊⠀⣤⣾⣦⣤⣔⠉⠉⠉⠉⠒⠢⢤⣀⡈⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⣷⣄⣀⣀⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⢈⠉⠛⠓⠒⠛⠋⠁⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⣩⣦⣤⣭⣍⠙⠛⠁⠀⠀⠀⢀⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠘⣧⠤⣄⣉⠉⠉⠉⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠒⠲⠶⠦⠤⠤⠤⠴⣲⡾⠋⠀⣠⠞⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢿⡄⢄⣈⠔⠈⠓⠁⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⣀⡴⠋⠁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⢿⣦⡣⠈⠫⠑⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣁⡤⠖⠋⠁⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠁⠀⢢⡀⠀⠀⠻⣕⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⣩⠴⠋⠁⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⣄⠀⠀⠀⠀⠣⠀⣦⠀⠀⠀⠀⣰⠃⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡯⠞⠉⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠠⠞⠀⠀⠀⢠⡇⠀⠀⠀⠈⠳⢤⣀⠀⠀⣠⠖⣫⠞⠉⠀⠀⠀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠴⠋⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⢀⠀⠈⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠈⣁⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⣠⠖⠉
⠀⠀⠀⠀⡄⠳⣄⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠻⣄⠀⠉⠓⠶⠤⢤⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠚⠉⠁⠀⣀⡤⠒⠉
⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⢀⡀⠈⠉⠉⠉⠀⠈⠉⠀⠀⣀⣀⣠⡤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠋⠉⠙⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⠄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢄⠀⠀⢸⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⡇⢱⠀⠀⠀⠀⠈⢷⣿⣤⣤⣶⣤⣤⣄⠀⣀⡤⠖⠛⠉⠉⠉⠙⠳⣆⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⣧⣞⣀⣀⣀⡀⠠⠚⠉⠉⠁⠀⠈⠉⢻⠟⠁⠀⠀⠀⠻⣍⠑⠢⢄⠘⣿⣆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠚⢋⠋⠉⠛⠛⠿⣷⣄⣙⣶⡤⠴⠶⠶⠾⣦⣄⠀⠀⠀⣀⠀⠉⠒⠦⢅⢸⣿⡆⠀⠀⠠⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⢨⡏⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡴⠛⠉⠳⣄⠀⠀⣠⣾⡿⠿⠟⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠂⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠈⠂⣰⢋⠴⠚⣉⣩⣤⣤⡀⠉⠓⠶⠤⠤⠤⠤⠄
⠀⠀⡔⠀⠀⢢⡀⠀⠀⣼⠃⠀⠀⠀⠀⢀⡤⠶⠻⢦⡀⠀⠀⠀⠀⣿⡧⠀⠀⠀⢦⠉⠁⠀⠈⠁⣠⢴⡾⠟⠻⣧⣀
⠀⢸⠃⠀⠀⠀⠙⠳⣤⢿⣇⣀⣀⡤⠞⠉⢀⣠⣤⡴⠷⠦⠤⠀⠀⣻⣥⡤⣤⣀⡀⣄⡀⠀⠀⠈⠐⠉⣠⠖⠛⠋⢙⣿⣶⣤⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⡶⠟⠉⠀⠀⠀⢠⡴⢚⡫⠽⠛⢿⠛⠉⠻⢾⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣽⡶⠆⠀⠀⠠⠤⣄⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣠⠤⠐⠀⠀⢀⡄⠐⠁⠀⢀⣠⣼⣷⣶⣤⡀⠙⢷⡀⠐⠦⠀⠀⠀⠀⠀⠀⢈⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⠀⢁⡀⠐⠈⠉⢀⣠⣬⣿⣦⣤⣬⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇
⢰⡀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠈⠋⠀⠀⠈⠑⠉⢉⡤⠟⣿⣧⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠈⢷⣄⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠙⠂⠀⢀⠐⠉⠀⠀⠀⢈⡿⣿⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟
⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠂⠀⠀⠈⠁⠊⡡⠞⠛⠛⠉⠀⠂⣄⣀⣀⣤⠤⠖⠊⣡⡾⠋⣀⠔⠁
⠀⠀⠀⠀⠈⠛⠿⣶⣤⣤⣤⣀⡀⠀⠉⠻⣦⣀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⢀⣀⣴⣾⡿⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠳⢦⡀⠀⠙⠷⣤⡀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠙⠳⢦⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⠈⠙⠿⠲⠦⢤⣤⣤⣤⣤⠤⠴⢖⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⣟⣋⡠⠴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⢣⠀⠀⠀⠀⠀⡠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠣⡓⠤⣀⡠⠤⡶⠆⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠑⣄⠀⠀⠀⠀⣀⠇⠛⠋⣥⣀⡀
⠀⠀⠀⠀⠀⢀⠠⡀⠐⠢⢄⣀⠼⠂⠀⠈⠩⠔⠂⣀⠈⠛⠋⣱⣦⣄
⠀⠀⠀⠀⠀⢄⠀⠈⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠩⠤⠒⢀⡀⠙⠋⢁⣦⣠⡀
⠀⠀⠀⠀⠀⠀⠙⠢⢀⡀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠠⠔⠂⣀⠈⠛⠁⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠈⠑⠢⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠢⣄⡀⠀⠀⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⡀⠀⠀⠉⠑⠒⠂⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠂⠀⠤⠤⠤⠔⠒⠊




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⠀⠀⠀⠀⠐⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢘⠀⠀⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢀⠈⠀⣠⢄⣤⣶⣟⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠂⠀⠁⠀⠤⣴⣿⣿⣿⠟⠛⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⣀⣴⣾⡆⠈⠛⠛⣀⠄⠒⠉⠑⡄⠲⣄
⠀⠀⠀⠀⠑⣤⣤⣤⣶⣶⣿⣿⣿⣿⣇⡀⠀⣾⣀⠈⠉⡙⠛⠫⠀⢁⠀⠀⣲⠆⢠⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠫⠏⠙⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠄⣠⣶⠿⡟⠦⠠⣤⠤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠒⠒⠈⠉⠀⠀⠀⠀⢀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⢆⠘⢆⠀⠀⠀⠀⠀⠀⢠⡟⠰⡄⠰⡄
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⡄⠈⠑⠒⠒⠒⠒⠂⠎⠀⢤⠬⡤⣬⠦⢀
⠀⠀⠀⠀⠀⢀⠇⣀⠀⠀⠙⠲⢤⣀⣀⣀⠤⠖⢊⠁⠀⠙⠀⠀⢡⡖⢂
⠀⠀⠀⠀⠀⠘⠀⠈⠻⢶⡤⣀⣀⠀⠀⠀⣀⣀⡤⠝⠒⠒⠲⢤⡀⠠⠒⢉⡆⡀
⠀⠀⠀⠀⡰⠠⣀⠀⠀⠀⠉⠒⠬⣉⠉⠉⠁⠀⠀⠀⢀⡤⠂⠀⠈⠲⣄⠋⢀⡜⣷
⠀⠀⠀⠰⡇⠐⠄⡙⠢⢤⣀⠀⠀⠀⠉⠒⠤⣀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠋⠀⠤⢤⣀⣀
⠀⠀⠀⠀⠑⢄⡀⠀⠁⠂⠀⠍⣀⡀⠠⠤⣀⡀⠉⠒⠦⢍⡒⠤⠀⣠⠞⠀⠈⢆⠀⠁⠀⠀⠀⠈⠉⡳⢄
⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⡀⠀⠀⠀⠉⠀⠀⠈⠉⢒⡢⠤⣀⡁⠚⠁⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⠤⠄⡀⠀⠀⠈⠁⠒⠬⢍⡑⠒⠤⠤⠀⠀⢀⣀⣀⠠⠤⠤⣒⠉⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣀⡀⠀⠈⠉⠐⠒⠒⠒⠒⠒⠒⠊⢉⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠒⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠴⠒⠒⠒⠦⣄⠀⠀⣠⠴⠒⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡠⠛⠁⠀⠀⠀⠀⠀⠈⠳⠈⠀⠀⠀⠀⠀⢀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣗⢤⡒⠤⠤⠤⣀⡐⠛⣉⣙⣓⠲⣄⡀⠀⠀⢸⠆⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⢒⡓⠦⢬⣙⠒⠮⣽⠆⠀⠉⠙⠲⢍⡛⠛⠥⢊⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠳⣌⢦⡉⠩⢿⣒⣦⠨⣙⠲⠾⠆⢀⣠⡤⣤⣀⠀⠀⠀⠉⠑⡴⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣣⡑⢤⠠⣤⣦⠥⣄⠀⠈⣩⠴⠊⠓⠒⠚⠉⠀⠀⣀⡬⠓⠢⠀⣠⠎⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠑⠒⠮⢭⣚⣦⡀⠉⠉⣉⡴⠚⠁⠀⠀⠀⠀⠀⣠⠔⠋⢁⡴⠚⠁⡼⠁⠀⠀⢀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠀⠀⠉⠓⠲⠤⢄⣀⣈⣉⡥⠶⠚⠁⠐⠤⣄⡀⠀⣀⠴⠊⣁⣠⡶⠟⠒⠀⡼⠁⠀⣠⠶⠋⠀⢸
⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠉⠉⠙⠋⠉⠉⠁⠀⠀⢀⣼⠷⠚⠋⠁⠀⠀⠀⠸
⠀⠀⠀⠀⠞⠀⠀⠉⠒⠒⠒⠒⠚⠉⠉⠉⠁⠉⠉⠙⠒⠦⢤⣀⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢰⠚⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋
⠀⠀⠀⠈⠳⣄⠀⠠⣤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠛⠉⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠈⠉⠓⠈⠓⠦⣄⣈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣤⠴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠤⠤⠤⠤⠤⠤⠴⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢐⢦⡐⠉⠉⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡆⠹⠆⠁⠘⠒⣂⡤⠔⠀⠈⠓⠀⡀⠀⠀⠀⢀⣴⠟⣉⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠆⠰⣊⡥⠀⣀⠤⠖⠉⠁⠀⠀⢤⣀⠀⠀⠈⠑⠲⠶⠿⠛⠉⢁⡔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⠁⠃⠀⣈⠥⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⢀⠴⠋⠀⠈
⠀⠀⠀⠀⠀⠠⠤⠤⠒⠂⠀⡠⠂⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡠⠚⠁⢀⠴⠚⠉⡇
⠀⠀⠀⠀⣈⣉⣓⣒⣒⠂⠀⠐⢦⡀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠤⠚⠁⠀⠀⠐⣁⣀⠤⢒⠀⡄
⠀⠀⡇⠀⢀⣉⠉⠉⠛⠉⠂⠀⠀⠙⢂⣙⠲⠄⠀⠀⢀⣀⠤⠤⠤⠀⠒⢒⡲⠒⠒⠒⠒⣒⠤⠦⠒⠊⠅⠐⠂⠉⠁⠀⠸⡄
⠀⠀⢧⡀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠋⠉⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠒⠒⠈⠉⠈⠃
⠀⠀⠀⠈⠑⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠉⠑⢦⡀
⠀⠀⢀⣀⣠⣤⢤⣤⣾⣷⣤⣀⠀⠀⠀⠀⠑⢤⡀
⢀⡜⠁⠀⠀⠀⢸⠀⡤⢦⠈⠹⣷⣀⠤⠖⠒⠦⢷⣀
⢸⠀⠀⠀⠀⠀⡟⠀⠀⡇⣧⠴⠋⠁⣀⡤⠴⠶⢶⣬⡇
⣸⠀⠀⠀⠀⠀⡇⠀⢴⡇⡧⣤⡶⠋⠁⠀⠀⠀⠀⣳⡀
⡇⠀⠀⠀⢀⡼⠁⠀⢀⠇⢷⣿⡁⠀⢀⣠⠴⠚⠋⠉⠉⢓⣦⡀
⡇⠀⢀⡴⠋⠀⠀⠀⣸⢸⡤⠽⣿⠟⠋⢀⣠⠴⠖⢋⣉⡭⠭⠷⢄⡀
⢹⣶⣏⣠⡤⠴⠒⠋⡇⢸⡀⢸⣷⣶⠊⡿⣷⡤⠖⢉⣁⡤⢤⣤⣤⣷⡀
⢸⠻⣿⣷⡀⠀⠀⠀⡇⣯⠟⠀⣉⡴⠊⢰⣣⣴⣾⣩⠔⠊⣉⡤⠤⣶⣿⣷⣄⡀
⢸⠀⠈⢿⣿⡀⠀⠀⢹⡰⡖⠋⠁⢦⠴⣄⠀⠈⣏⣀⣴⣏⡴⠚⣉⡭⠴⠶⠶⢭⣆
⢸⠀⠀⠈⢿⣷⠴⠚⠉⠱⣜⢦⡀⠀⠀⠘⠖⢄⠈⠁⢸⣃⠴⢿⣷⣤⡴⠒⠋⠉⣉⣉⡳⡄
⢸⠀⠀⠀⠸⣿⡇⠀⠀⠀⠹⡆⢳⡀⠀⠀⠀⠀⠑⠀⠀⣠⣾⡿⢿⣁⣠⡴⠚⠉⢉⣉⣭⣿⣦⡀
⢸⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⢀⡤⣺⠟⠁⠀⢀⣽⣿⣷⣾⣿⣿⡿⠿⠛⠛⠙⠲⢄⡀
⣾⣤⣀⡀⠀⢹⣿⠀⠀⠀⠀⣿⠀⡇⠀⠀⢀⢔⡽⠊⠁⠀⠀⢠⡿⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄
⡟⠲⠬⣍⣛⠺⠿⢧⣤⣄⣀⣿⢠⡇⢀⣴⡷⠋⠀⠀⠀⠀⠀⢻⡣⣀⣀⣀⣠⣤⣴⢐⡀⣄⣠⣀⣆⡰⣴⡳⠽⠊⠱⡄
⠹⣄⡀⠀⠈⠉⠙⠒⠒⠒⠒⢧⠘⣷⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠉⠉⠁⠀⠉⠑⠒⠒⠚⠋⠉⢁⣀⣠⠴⢚⣽⠦
⠀⠈⠛⠷⢶⣦⣤⣤⣤⣤⣤⣌⣧⣈⡓⠮⣍⡓⠒⠦⠤⠤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠒⠒⣛⣋⣩⡥⠶⠛⣉⣠⣴
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⣿⣽⣲⠭⣟⣯⣛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢛⣋⣉⣉⣥⣤⣶⣶⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣾⣭⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡔⠈⠑⢆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢱⣄⡀⣘⠀⠀⠀⡇⡠⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠄⠤⠀⢊⠉⢻⠉⠀⠀⢰⠉⢩⠋⠛⡏⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⡎⢀⢀⠀⢈⡆⠊⠉⠒⠀⠒⠁⠙⠢⠐⠃⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⡋⠊⠴⣾⠿⣀⣀⣀⠀⠀⠀⠀⡠⠔⠊⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢞⠆⠒⠉⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣢⠤⠤⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⢀⡠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠤⠔⠊⠁⢀⡰⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⣀⠠⠐⠊⠁⣀⠴⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⠠⠤⢲⠋⢀⣀⡤⠖⣛⠢⠬⣁⠒⢤⣀⠤⠊⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⠢⢔⠛⠥⡜⣀⠀⠉⠈⠉⠁⠀⡀⡡⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠒⠪⢕⠢⠬⠭⢿⡤⡁⠒⠀⢐⠬⠡⠔⠁⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠈⠉⠀⠀⠁⡠⠭⠙⠁⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠀⢎⠀⠀⣀⡀⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡶⣦⡔⠂⠒⠲⠶⠶⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡉⠉⠉⠓⢤⣤⣤⣀⣀⠀⠀⠉⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⣀⠤⣶⠞⡋⠉⠉⠉⠍⣙⠻⢟⠿⠟⣶⠆⠀⠀⠈⠉⢙⡷⠦⠤⢤⣀⡙⠲⣄
⠀⠀⠀⠀⠀⣠⠾⠟⠀⠈⠁⢀⣤⠶⠋⠀⠀⣠⠀⠃⠀⠀⠀⠀⠀⠉⢠⡔⠊⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠙⠛⠶⠷⣦⣤⣀
⠀⠀⠀⠀⣞⣁⣤⣖⣚⣋⣉⣉⣉⣀⣀⣀⣀⡘⠀⢠⡀⠠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣄⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢡⠟⠁⢀⡼⠋⠀⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡱⠶⠾⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢠⠊⠀⠀⢸⡇⠀⡇⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣤⣤⣄⡠⣀⣠⣤⣄⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢤⠃⠀⠀⠀⡘⠀⠀⡇⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠃⡀⠀⠀⠀⢀⣠⡴⠿⡉⠁⢈⡀⠊⠀⠈⠀⠈⢁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡹⠆⠀⠀⠀⠀⡇⠀⠀⡇⠀⡼⠁⠀⠀⡄⠀⠀⣸⠟⠃⣀⣤⡶⠞⠿⠉⠀⢀⣀⠀⠈⣿⠀⠠⢈⠀⢀⠰⠞⡋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⣄⠃⠀⠀⠀⠀⢀⠃⠀⠀⢧⡾⠁⠀⠀⠀⠇⠀⠀⢃⠀⠫⠀⠈⠉⣀⣂⣀⠀⠀⠹⡇⠀⢿⠤⠑⢂⣠⠄⠀⢾⣁⠀⣧
⠀⠀⠀⠀⠀⠀⣀⣧⡴⣿⡀⠀⠀⡄⠀⢸⠀⠀⣰⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠒⠂⠤⠤⠬⠭⠭⠤⠀⠙⠃⠀⣭⠤⠚⠋⠀⠀⠀⠀⠻⣦⠼⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡅⠀⢸⠀⠀⠸⡀⢰⠟⠀⠀⠀⠀⠀⠀⠈⣧⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⡆
⠀⠀⠀⣠⠤⠼⠷⡏⠉⠉⣿⠀⠸⡆⠀⠀⡧⠀⣆⢠⠂⠲⠀⠐⢢⢀⡟⠀⠻⣦⣾⠟⠀⢀⣤⣶⣤⡔⠒⠖⠈⢲⣤⡀⠀⠐⠂⢤⡀⠀⠀⠀⣈⣻⡦⠤⣄
⠀⠀⡘⠀⠀⠀⢀⡇⠀⠀⢸⣧⣸⠇⠀⠀⢱⡄⠈⠙⠂⠀⠀⢠⣴⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣏⣻⠎⠀⠀⣌⣀⠀⡳⠋⠀⣠⠌⠛⠠⠤⡌⠀⠇
⠀⠲⡇⠀⠀⠀⠀⡇⠀⠀⢸⡿⠋⠀⣠⠞⠉⣧⠀⠀⢀⡄⠀⢸⣿⣿⣿⣿⡶⠀⠐⢶⣿⣿⣿⣿⠟⠃⢀⠀⣼⣯⡉⠛⠁⢀⠀⠙⢷⡖⠒⠀⢶⠉⠀⠀⠀⢸⠆
⡇⠐⡇⠀⠀⠀⠀⡇⠀⠀⢸⡁⠀⢸⣧⠀⣶⣿⡇⠀⠘⢿⠀⠈⣿⣿⣿⣿⠇⠀⠀⠸⣿⠟⠉⠀⠀⣀⡶⠼⠛⠉⠀⢀⠔⣿⡇⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⢸
⡇⠀⡇⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⢸⣿⣱⣿⣿⣿⠀⠀⠈⡄⠀⠈⣿⡿⠃⠀⠀⠀⠀⠙⢷⣤⡰⠛⠁⠀⠀⠀⢀⣴⣿⣞⣿⡇⠀⢸⠇⠀⠀⡼⠀⠀⠀⠀⢸
⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⢣⣠⡼⠁⠀⠀⢀⣄⣤⡀⠀⠀⠈⢧⣄⡀⢌⡦⢠⣿⣿⣿⣿⡿⠀⠀⡄⠀⠀⢀⡅⠀⠀⠀⠀⠈
⢡⡀⢰⠀⠀⠀⠀⠘⡇⠀⠀⠘⡀⠀⠈⠻⢿⣿⣿⣿⠖⠚⠋⢉⣀⠀⢀⠆⣾⣿⣿⣷⠀⠀⠀⣀⡉⠛⠛⠳⣿⣿⣿⡿⠛⠁⠀⢀⠃⠀⠀⣸⠁⠀⠀⠀⠀⠇⢀
⠘⣷⣦⡜⣶⣀⠀⣀⣿⠀⠀⠀⠳⠄⠀⠀⠀⠈⠛⠉⠀⠀⠀⠿⡟⠀⡀⣸⣿⣿⣿⣿⡆⢀⠀⢻⠿⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⡾⠀⠀⢀⣿⡀⠀⣀⣶⢡⣼⣾
⠀⠉⠚⢷⡹⣿⣿⣿⣿⣇⢦⣴⣿⡶⠤⠄⠀⠀⠀⣀⣀⣀⠀⠀⠀⠸⢡⣿⣿⡃⢙⣿⣿⡌⠇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠠⠤⢾⣷⣦⡴⣸⣿⣿⣿⣿⢇⡾⠓⠃
⠀⠀⠀⠀⠻⢮⣙⣛⣛⡻⠶⢻⠷⠿⣶⣄⡀⣘⣻⣿⣿⣿⡷⣄⠀⠀⣾⣿⡿⠃⠘⢿⣿⣧⠀⠀⣠⣾⣿⣿⣿⣟⣂⢀⣠⡞⠟⠿⠏⠶⢟⣛⣛⣋⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⡇⠉⠉⠻⣌⠁⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠁⠘⠈⢰⡏⠙⡇⢸⠋⠉⢰⠛⡷⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣯⡟⠀⢀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢰⡇⢠⠀⠀⢾⠀⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⢸⡁⣿⠀⠆⠘⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⠋⡗⣾⠻⡆⠀⠀⡀⣾⠙⠀⣤⠀⢸⠁⠀⠀⣿⢀⡼⠛⠀⡌⠉⠀⠀⠀⠉⠁⢠⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣿⠀⡇⢀⣴⡇⣿⡄⠉⠀⠀⡄⠀⢹⠀⡇⠈⠀⠀⠀⢰⠀⢸⡇⢰⡛⠤⢿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡏⠀⡇⢸⡃⡇⠾⠹⡆⠘⢣⠆⢀⣼⠀⣷⠐⡄⠀⡀⢸⢠⣸⡇⢸⡇⠀⢸⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠇⠘⠃⡇⠸⡄⡇⢰⣶⠀⡏⢹⠀⣽⠀⡇⢠⣌⠁⠘⢸⡇⢸⡇⠀⢸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⣄⣰⠀⢧⣰⠇⡇⢸⡇⠶⠇⣼⠀⢿⠀⠳⠖⢀⡆⢰⡈⠻⠛⠀⠀⢸⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠁⠀⡇⢸⡇⠀⠀⣿⠀⢸⡆⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⠀⠀⠀⠀⠀⠀⢰⠁⠀⡇⠀⠀⢿⠀⢨⡇⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢸⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠈⠳⠋⠀⠀⠀⢠⡇⢸⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠋⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣤⣜⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠈⢇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢄⡀⠀⠂⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡤⢀⡀⠔⠆⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⢠⠀⠈⠁⠀⠐⢃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠄⣀⠀⠈⠁
⠀⠀⠤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⣀⠀⠀⠀⠠⠀⠀⣀⣀⣀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⢠⠂⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣤⣀⣀⣀⣀⣀⣀⡠⠤⠴⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢈⣉⣁⣀⣤⠤⠤⠒⠒⠒⠈⠉⠉
⠀⠈⠓⠲⠶⠤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠶⠤⠤

⣶⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣿⣶⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠛⠢⡀
⠀⠀⠀⠀⠀⢰⠃⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢒⡒⢦⡀⠀⢸⡄
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠛⠿⣶⣶⣮⠿⠋⠁⠀⠘⠛⣪⢭⡤⣡⡾⣀
⠀⠀⠀⠀⠀⢠⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠚⠃⣪⠃⠤⠄⢤⡀
⠀⠀⠀⠀⡰⠇⠀⢀⡀⠉⠑⠒⠲⠤⠤⠒⠒⠋⢁⡀⡀⠀⢠⡄⣀⠁⠠⠿⢨⡿⣿⣲⣤⣀
⠀⠀⠀⡘⠀⠀⠀⠀⠈⠁⠒⠠⢀⠀⠀⢀⠔⡙⡀⢃⠑⡈⠂⠐⠠⢘⠰⢤⡈⠉⠽⣶⠶⠿⠱⠂⠀⣀⠀⡤⠄⠤⢠⡄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⡬⢐⡈⠄⠀⠂⠁⠨⡒⠠⡈⢀⠐⠱⠂⠀⢆⠉⠘⡁⢎⠡⣂⠔⠄⠆⠊⠁⠘⢆
⠀⠀⣠⠒⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣈⠉⠙⠓⠒⠒⠀⠃⠀⠀⠀⠀⠀⠤⢈⣀⡁⠀⠈⠀⠀⢀⣀⠠⡴⠖⡏⠸
⠀⠀⡇⢀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠉⠉⠹⣟⣛⠒⠛⠮⠭⠭⠄⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⣀⡀⠤⠤⠄⠒⠂⠁⢀⣀⠔
⠀⠀⠈⠢⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠉⠒⠄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⠒⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⣀⠁⠂⢄⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠀⡐⠁⣴⣤⣀⣈⣻⠀⣖⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢰⣅⠈⢀⡤⠂⠈⠙⢷⡄⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢇⠀⠀⠀⠀⠀⣉⠄⠙⡞⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠄⠁⠀⠀⣳⠂⠰⢄⠐⠁⠀⠴⠁⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡵⠀⠀⢐⠁⠀⠃⠀⠀⠈⢣⣀⢀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⠀⢹⠇⠀⠀⠀⠈⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠠⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠐⢀⠎⠀⠀⠀⠀⢰⠀⠀⠀⡈⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠸⠀⡁⠀⢠⠃⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠠⡆⡀⠁⠀⠀⠀⠀⠀⠀⢠⡑⠄⠀⠂⠀⠀⣌⠎⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠱⠁⠄⠀⠀⠈⠀⠀⢀⡨⠉⠉⠓⠰⣶⡀⢟⢀⠔⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠃⠒⠒⠀⠈⢀⡀⠀⠁⢀⡠⠜⠓⠒⢚⣿⢾⡈⠀⠁⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠤⠄⠀⠀⠤⠀⠀⠤⠤⠀⠁⠀⠀⠒⠁⠀⢠⠾⣽⣧⡀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠁⠀⡏⠀⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⢢⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣒⠵⢒⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡯⢚⣡⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⡡⠖⣋⠵⠚⠉⡕⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠴⣫⢶⠏⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢟⣋⠥⠔⡺⠁⠀⠀⠸⠁⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠔⡡⠞⠁⡞⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠀⠀⢰⠃⡏⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⠁⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠃⠀⢀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡠⡾⠀⢀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡾⠀⠀⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣰⠋⢀⠇⢠⣳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⠃⠀⢰⡇⣿⡇⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢰⠃⠀⡞⢀⢿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⣠⠃⠀⠀⢸⢠⡏⠁⠀⠀⠀⢀⠀⢴⣉⡀⠀⠀⠀⠁⣀⠜⠀⡼⡞⣼
⠀⠀⠀⢀⣠⠤⠒⠉⠉⠈⠉⠉⠁⠀⠀⠀⣼⢸⠸⠀⠀⢀⠖⠁⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢠⢳⠁⠟
⠀⠰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣫⠃⠐⠃
⠀⠀⠈⠙⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠶⠋⠀⠙⠂⠀⠀⠀⠐⡂⠤⠤⠤⠤⣤⣤⣶⠾⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣦⣤⣿⡀⠀⡴⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⣴⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⡖⠃⡮⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣸⣿⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢒⣧⠀⠀⠠⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⢿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠧⠦⠔⠂⠉⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⢸⣿⣿⡿⠿⠟⠛⠛⠉⠉⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⢀⠀⠀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢀⣀⣠⣤⣴⣶⣿⣿⣿⡿⢃⣷⢠⡠⠀⣿⠀⠃⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⣰⠀⠀⡀⢰⡇⠀⠘⠂⢠⡀⠀⣐⣒⣔⠒⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⡛⠀⣸⣿⡐⠠⢰⣿⡄⣈⡩⠉⡉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣆⣿⡤⠎⠉⢻⠥⡤⢀⠀⢞⠑⠚⢉⢡⠘⠛⣓⠿⠛⠫⠁⠡⠈⡀⠪⠩⣖⢄⢀⠈⠉⡃⠶⠸⠿⡧⠘⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠰⠋⢉⠀⣠⢶⡁⢀⠈⠁⠀⠈⠐⠀⠾⠖⠒⠉⠀⢀⡠⠄⠳⠀⢰⣇⠀⢄⠀⠉⠑⠙⢸⡧⣄⠀⠐⠈⡶⠚⠁
⠀⠀⠀⠀⠀⢀⠀⠘⠫⣀⠔⠂⠀⠀⠠⠀⡀⣿⢠⡆⠈⠒⠂⠀⠀⠀⢠⠀⠂⠁⢀⠀⢠⡇⣸⣿⠀⠀⠁⠀⠀⠒⠠⠒⠉⡆⠀⠀⡇
⠀⠀⢄⠀⡠⠀⠀⢀⠀⠀⠀⠀⠁⠈⣀⣀⣀⡻⠊⠁⢀⣄⠄⠀⠀⠀⣼⡆⠤⣎⣀⡠⠼⠷⠿⠛⠓⠉⢋⠄⠂⠁⠀⠀⠁⡇⠀⠀⠃
⠀⠀⠋⠠⠦⠁⡂⠠⠀⠈⠁⠂⠀⠻⠿⠿⠽⠿⠂⠀⠀⠀⠀⠈⠙⠀⠿⠷⠈⣀⡀⠪⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠶⠄⠘⠀⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠃⠀⠠⠦⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠋⠭⢜⡀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢁⡴⢢⠞⡴⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡴⢋⡴⣣⠞⠁⠀⣀⣀⠀⠀⠀⣠⠞⣉⢀⡼⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⢡⠞⡴⢋⣠⠴⠛⠁⣹⡄⢀⡾⣡⠞⣡⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⢠⢏⡼⠗⠋⠁⣠⡴⢚⣥⣇⡞⡴⠃⡴⣫⠞⠀⣠⠴⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣷⡟⡼⠁⢀⡴⠞⣡⠞⠋⣼⡟⣰⢁⡾⣱⣧⠖⠋⠁⣀⡴⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣼⢰⣇⡴⢋⣠⣏⠀⠀⢰⡿⢡⣧⡾⣱⠋⠀⣀⡴⢛⣡⠞⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣴⠇⠘⢋⡴⠋⠁⣿⠀⢀⡿⠁⠀⣿⢁⡇⣠⠞⢉⠔⠋⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⣠⠎⡟⠀⢠⠎⠀⠀⠀⣇⣠⠏⠀⠀⢠⠇⢸⠟⣁⡴⠛⡇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⢀⡴⠃⣼⠁⢠⠏⠀⠀⢀⡤⠛⠁⠀⢀⡔⡿⠀⢀⡴⠋⠀⠀⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣇⣠⣤⠴⠶⠛⠉⢀⡼⠃⢀⡟⠀⢀⠔⠉⠀⠀⠀⣠⠞⣰⠃⢀⡞⠀⠀⠀⢠⡇⢀⡟
⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠻⣄⣀⣀⣀⣠⠴⠋⠀⠀⣞⣠⡎⠀⢀⣀⣠⡤⠞⠁⣠⠏⠀⡾⠀⠀⠀⠀⢸⡇⣸⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⡠⠞⠉⠘⣷⠛⠉⠉⠀⠀⣀⡴⠋⠀⡼⠁⠀⠀⠀⠀⢸⢀⡏
⠀⠀⠀⠢⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠁⠀⠀⠀⠀⠈⠙⠒⠒⠚⠋⠁⠀⠀⡸⠁⠀⠀⠀⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠚⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⣤⣤⣤⡤⠤⠴⠒⠋⠁



⣤⣤⣤⣴⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣬⣴⣬⣽⣴⣾⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣒⣲⠻⣟⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⢾⠉⠁⠀⠀⠀⢠⡞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠒⠦⣤⡤⠴⢾⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠖⠒⡏⠐⢣⣀⡠⡍⠀⣷⠀⠀⠈⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⢔⣲⣤⢷⡀⠌⡓⠚⠁⢤⡿⢦⣤⣖⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⣇⠀⡇⣾⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⢿⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣚⡱⣉⡉⠩⠭⢇⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣈⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠎⡔⢁⢂⡄⡆⢪⠳⠃⠀⣀⠀⠀⠀⢰⣿⡥⢹⢏⣭⡙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⠇⡀⠀⡈⠘⠃⠈⠀⢀⠀⠀⠑⠁⢀⠀⢸⣏⣛⣨⣦⣩⢼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠿⠀⣀⠀⠰⠃⣠⠗⠒⢲⣈⣧⣈⢳⠖⣲⠀⠥⠃⣼⣏⡺⡇⣺⡕⠾⣿⠟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣩⢇⡴⠛⢻⠖⢦⡏⢻⣠⠾⣏⣙⠁⠀⠀⠀⠘⢧⣵⣷⡾⠟⠋⢱⣿⡖⠛
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣲⣼⡇⣾⠙⣧⠈⢳⡀⠹⡄⠙⣍⠹⡄⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⣀⢿⡄
⠀⠀⠀⠀⠀⠀⢀⡞⡞⠉⢹⣽⠛⣆⠘⣆⠀⢳⡀⠙⠀⠘⣦⡗⠀⣿⡇⢰⣆⢸⡇⣠⣤⡀⣾⣏⠘⣷⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠀⠙⢒⡿⠛⣠⢼⣆⠘⠆⠀⠁⠀⠀⠀⠈⢧⠀⢸⣇⣾⢿⣾⣿⣏⣿⣧⣠⣽⠇⠻⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⢀⡏⠀⠀⢻⡀⠙⠆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠻⠟⣤⠉⣤⢙⣫⣌⣡⡄⣶⣿⣴⣶⡄
⠀⠀⠀⠀⠀⠀⢸⡆⠈⢧⡀⠀⠀⣹⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠹⣶⣿⣿⣏⣿⠻⣦⡿⢹⣏⣈⢠⣶⠷⠄
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠉⠛⢻⠛⢾⠙⠲⢤⣀⠀⠀⠀⠀⠀⢳⡀⢠⣄⠠⣤⡿⢡⣍⠁⣶⣄⣿⣸⡏⢹⡇⠙⢷⣆
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣠⠟⠓⠋⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢳⡈⣿⠀⣹⡇⣿⣻⣧⢻⡟⣿⡇⣿⣼⢷⣄⣠⡿
⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡜⠁⢹⡟⠛⣷⣿⠋⠙⠿⠷⠈⠃⠘⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠲⠦⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠊⠁⠀⠀⠘⠗⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣃⣤⣶⡆⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣸⢹⣿⣿⣯⣅⠀⠻⣿⣿⣿⣷⠀⢸⣷⣤⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢰⡽⠸⠿⣿⣿⣿⡆⠘⢿⣿⣿⣿⠄⣼⣭⡈⠋⠀⠀⡇⣔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢺⣄⣄⠀⠘⠛⠿⠃⠀⠀⠀⠉⠁⠀⠙⠻⣯⠀⡀⠀⣇⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢦⡆⣆⢹⣃⡄⠀⠀⠀⠀⠀⢠⢶⣶⣦⣤⡤⠷⣾⠀⢁⠀⢛⣨⢾
⠀⠀⠀⠀⠀⠀⠰⡰⡄⣿⣴⠘⣷⣶⣶⣧⣤⣄⡢⠄⢸⡟⢋⣈⣙⠶⠉⣭⠘⢷⠋⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠰⠞⠿⢻⠉⠁⠉⠛⠃⠹⠿⣿⣿⣷⣀⠛⠃⣌⣬⣶⢁⢸⢟⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠣⣵⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣥⡛⢢⠌⡍⣱⡷⠟⠠⠻⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠚⠶⠶⠤⠤⠤⣀⣀⡨⡥⣤⡤⠸⣦⠐⢊⡉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⠀⢒⡩⠲⡤⠄⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠘⡎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⢳⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡀⠐⡆⠀⠀⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠙⢦⣿⠴⠚⠛⠛⢲⣋⣁⣤⣄⣀⣀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⢉⡿⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣲⠶⡟⠀⠀⠀⠀⢀⣠⢾⣟⡲⠶⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠳⠤⠤⢤⡖⠋⠘⣇⠈⠉⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡴⠋⡇⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⡇⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣄⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣠⠆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠘⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣴⠃⠀⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣼⡄⠀⠀⠀⠀⠀⠀⡀⠂⡨⠙⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣷⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡀⢸⣗⠀⠀⠐⠚⡏⠉⠀⢸⣿⡆⠀⠀⠀⢸⢠⣏⠀⠀⠘⠃⢹⣿⡿⠇⠀⠀⠰⣿⣿⠀⠉⢙⡓⠂⠀⠀⢸⡇⠀⡀
⠀⠀⠀⠀⠀⢌⡀⢉⡿⢂⣶⣶⡾⠹⠄⠀⠛⠻⣅⠀⠀⠀⠘⢿⣿⣿⡏⣾⣿⢟⡝⠁⠀⠀⠀⢀⠟⠛⠁⠀⠞⢳⣶⣶⡀⢻⡋⢀⡱
⠀⠀⠀⠀⠀⢸⣿⣟⡄⣼⣿⠟⢀⣤⣶⣼⠓⣴⠿⢆⣀⣂⡠⢤⡀⢹⡇⢸⣿⠁⣀⣠⣤⣄⣐⡻⢧⣌⢷⣶⣤⡀⠙⢿⣷⣀⣻⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⣴⡿⣿⢟⣿⣊⡴⠞⠉⠉⠉⠉⠻⣾⣿⡇⣼⣿⣾⡿⠋⠁⠀⠀⠉⢳⣾⠻⣟⢿⣿⣦⡀⢹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣧⠉⢿⣿⠇⣼⡟⠁⣡⡿⢡⡟⠣⢄⠀⠀⠀⠀⣀⠈⢻⣟⣵⣮⣝⣂⠤⠀⠀⠀⠀⠀⠘⣷⠹⣧⡁⢹⣷⡈⣿⣿⠃⣠⡇
⠀⠀⠀⠀⠀⣿⣷⣌⢿⣸⡿⠀⠰⣿⠁⣿⠇⠀⠀⠀⢀⠞⣡⣚⣉⡝⢫⣻⣅⣤⢹⡼⣰⠀⠀⠀⠀⠈⣿⡇⢹⣇⡀⢿⣇⣻⢃⣾⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣷⢶⣧⡟⠒⣿⡗⠀⠀⠀⢸⣆⠸⣍⣹⠷⢿⣿⣯⣭⡻⣾⠃⠀⠀⠀⠀⢉⣿⡗⢸⣿⡇⣼⣿⢟⣿⣿⠃
⠀⠀⠀⠀⠠⣄⡈⠳⣌⠈⠻⣾⡏⣿⢀⣿⣿⠀⠀⠀⠀⠻⣦⡀⠻⢿⣷⣿⣳⣿⣿⣯⡑⢆⠀⠀⠀⣸⣿⠁⣸⡝⣿⠟⠁⣠⠞⢁⣠⠄
⠀⠀⠀⠀⠀⠙⢿⣿⣾⣷⣄⠈⠻⠜⣧⠘⣿⣧⡀⠀⠀⠀⠈⣻⣶⣄⡙⠻⣽⡋⣿⣦⣿⠈⡇⠀⢰⣿⠏⢡⠯⠟⠋⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣙⠺⢭⣿⣷⣄⠀⠘⢷⡈⢿⣷⡶⠶⠶⠶⠿⠞⠉⠛⢶⣤⣉⣐⡿⢃⡼⠁⣴⣿⠋⣢⠏⠀⢀⣴⣿⡭⠗⢋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠛⢇⣘⣮⣷⣼⣟⢿⣦⣤⡒⠤⠄⠠⠤⠄⠈⠛⢋⡴⠟⢤⣾⠟⣗⣼⣧⢖⣠⠟⠛⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⢾⣿⣿⣿⣿⣞⠏⢻⢮⡉⢻⣧⣤⡀⠂⡀⢀⣨⣴⣾⠋⢀⣳⡾⠋⢠⣾⠡⢏⣾⣿⣿⣿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠈⠉⢉⣵⡿⠻⣿⡈⠳⣄⠙⢿⣯⣬⠻⣯⠅⣀⠀⢷⣼⠟⢀⡴⠃⣸⠿⠿⣷⣍⠉⠁⠀⠠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⢸⣿⣷⠄⣸⣻⣗⠈⠢⣄⠻⢿⣷⠌⠐⣽⣾⠟⠁⡰⠊⢐⣿⣿⡀⢴⣿⣿⠀⢀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠟⠀⠈⠳⠵⠾⠋⠁⠙⣟⢷⣾⡷⣠⠻⣿⣿⡿⢋⣠⣾⡿⣺⠟⠀⠉⠻⠦⠷⠋⠀⠺⠁⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠢⢄⡀⢨⣻⣿⣿⠍⢳⣌⣋⡴⠛⣿⣿⣟⡥⠀⣠⠤⠀⠀⠀⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⣿⡋⠉⠁⠙⠟⠁⡉⢉⣹⠟⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠓⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠙⢿⣶⣄⣀⣀⠀⣠⣾⡿⠋⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠁⠀⠀⠀⢀⣼⣿⣆
⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠹⣿⡄
⠀⠀⠀⠀⢀⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡀
⠀⠀⠀⠀⣾⡟⠈⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠹⣿⣄
⠀⠀⠀⠀⠹⣷⣄⠀⠀⠈⠉⠛⠻⠿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⢿⣧⡀
⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣶⣦⣤⣀⡀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣶⣤⣀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⡉⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣬⣙⠻⢿⣶⣤⣤⣀⣀⠀⠀⠀⢀⣀⣤⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣶⣭⣽⣻⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢐⣿⣷⣦⣠⣄⡀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣠⣴⣦⡀
⠀⠀⠀⠀⠀⠀⡔⢠⣿⣟⣽⣿⣿⡵⣶⣾⡗⢻⣆⠀⠀⠀⠀⠀⠀⣰⡿⣷⡆⣼⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠰⣿⣤⣿⣿⣿⠟⠁⠀⡀⠈⠋⠁⢸⠿⠳⡀⠀⠀⣠⢾⣿⣿⠦⠰⢿⣿⡛⠋⠻⣿⡆
⠀⠀⠀⠀⣾⢩⣿⣿⣿⣿⡄⡉⢻⣿⠂⠀⢀⡄⠀⠀⢸⣠⡞⣵⣿⠿⠧⣤⣦⡑⡘⣿⣷⡄⢸⣿⡀
⠀⠀⢠⠀⣭⡟⠿⠇⠹⡟⢳⣀⠀⠀⠁⢠⡾⠁⠀⢀⣾⣿⡧⣿⡇⢇⠀⠘⠛⠀⢠⣿⣿⡛⢾⣿⣧
⠀⠀⠈⠷⣟⣻⡶⣰⠿⠀⠘⢿⣿⣿⣿⡿⠁⠀⢠⡾⠻⣿⣧⠈⠻⣄⠁⠀⠤⠞⠓⣹⡿⣻⡆⢻⣿
⠀⠀⠀⠀⠈⣽⣿⣤⠀⣰⠓⢴⠞⢻⠟⡸⠃⣠⠟⠀⠀⢻⣿⡆⠀⣇⠀⠀⢀⣴⡊⣹⢿⣻⣧⠾⠋
⠀⠀⠀⠀⣰⣿⣿⡿⣧⠈⢷⣄⢄⢬⣼⠇⣰⡟⠀⠀⠀⠘⣿⡇⠀⠃⢳⡄⢧⡾⣣⣭⣼⣯⠁
⠀⠀⠀⢀⡿⢹⣿⣷⣌⣛⡟⣿⣿⣦⣌⡑⠻⣀⠀⠀⠀⠀⣿⡇⠀⣦⣼⠻⠾⠟⣿⣿⣼⢿⡄
⠀⠀⠀⣼⠇⢿⣿⡐⠛⠛⢛⣿⡍⢿⡏⢹⠇⠈⣤⠀⠀⠀⢿⡇⠀⢹⣿⣋⣁⣿⡶⢻⣿⡛⣧
⠀⠀⢠⡿⠶⢿⠿⣿⠻⣿⣿⡿⣿⣿⣦⣎⡀⠀⠛⠀⠀⠀⣿⡄⠀⣾⡿⡿⢛⣁⣴⣿⣿⡄⣿
⠀⢀⣼⡇⠀⠅⣶⠛⢻⣿⠃⢴⣯⣿⠙⣏⠙⠷⣄⠀⠀⣰⣿⣇⡴⠟⠋⣠⣿⠟⢩⣹⣿⡟⣾
⠀⣸⣿⠀⣴⣦⠬⠭⣿⣿⠟⠚⡋⡟⢀⣿⡀⠀⠈⠱⣴⣿⣿⠥⣶⣾⡿⠶⠿⠗⢻⣻⡟⢡⡟
⠀⣿⣿⣄⠈⠁⣠⣾⣿⣶⣦⠴⡿⡇⣸⠛⠙⠶⠤⢀⡼⢋⣠⠶⠿⢛⡓⠚⠛⠒⠛⠳⠇⢼⠃
⠀⣿⢹⣯⠷⠾⠿⠿⢿⣿⣿⣷⣄⢶⡟⠀⠀⠀⢰⡾⣷⡟⣛⣉⣩⣤⣿⣿⣿⣿⣟⣶⣶⡤⣤⢄⣀
⠀⣿⡎⣿⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠀⢀⡀⢰⢿⣿⣯⠄⣤⣝⠛⠋⠉⠉⠑⠚⠛⢿⡿⠀⠃⠑⢿⡆
⠀⢿⣷⡘⣧⡀⠀⠀⠀⠀⠀⢠⠞⠁⢠⣾⣿⣷⣾⣿⡏⣴⣾⣿⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠁
⠀⠘⣿⣷⡌⠳⢦⣄⣀⣠⡶⠋⡴⠀⠻⣯⠥⠋⠠⠙⣿⣿⣿⡏⠠⣤⣀⣀⣀⣴⣟⡄
⠀⠀⠸⢿⣿⣶⣦⣤⣥⣤⣴⠞⠁⠀⠀⠀⠀⣠⣤⠀⠙⢿⣿⣷⣤⣾⣿⣿⣿⡿⠛

⠀⠀⠀⠈⠉⠙⠛⠉⠛⠉⠁⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠈⢻⣟⠛⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠛⢶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠐⠂⠤⠄⠤⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠐⠂⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡈⠠⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠄⠀⠐⠃⠀⠀⠀⠀⠀⠀⣠⠞⢁⠴⠁⠀⠀⠈⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⡀⡄⠀⠠⠃⠀⠀⠀⠀⠀⢀⠜⡁⠀⠁⡄⠀⠁⠀⢁⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⢁⡀⠠⠠⠠⠥⠀⠀⠀⠀⠀⡴⠁⢀⠀⠀⠀⠠⠀⠀⢀⠈⢀⠢⠤⡀
⠀⠀⠀⠀⠀⠀⡀⠆⢈⣠⠀⠀⡸⠀⠀⠀⠀⢠⠎⢀⠔⠁⠀⠀⠀⠀⠰⠄⠀⠄⠈⣀⠲⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⡰⠀⠀⠀⢀⡴⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠲⠆
⠀⠀⠀⠐⠚⠀⠀⠒⠠⢐⡀⠀⠀⡠⠔⠉⠀⡼⠁⠀⣄⠁⠢⡀⠀⠀⠀⠚⠃⠐⣢⡶⠟⠷⡿⣟⢦⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠵⠒⠉⠀⠀⢀⠜⠁⠀⠀⠈⠉⠐⠈⢢⣀⠀⠀⠑⢡⡥⠤⠶⠶⠶⠶⠿⠷⢦⢤⡀
⠀⠈⠒⠄⠀⠄⠒⠊⠉⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠒⠠⠴⠁⠀⠀⠠⠤⠤⠄⠒⠈⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠂⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⠁

⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⡠⣤⣠⣾⣷⣶⣿⣿⡀⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄
⡿⢡⡇⠀⠀⠠⣤⣶⣴⣾⡛⢿⣿⡟⠁⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠁⢸⣿⠀⠀⠀⠀⠀⠉⣉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⠿⠟⠉⠉⣿⣶⣤⣤⡤
⠀⣾⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⠁⠀⠀⠈⢻⣿⣿⣾⣿⣷⣿⣿⣿⣿⡉
⣿⣿⣄⠀⠀⠀⠀⠀⢸⠿⣿⡿⢻⣿⠿⢿⣿⣿⣇⠀⣠⣦⡀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠
⡏⠈⠉⠀⠀⠀⠀⠀⢸⠿⣿⣧⣄⣹⣆⣤⢿⡟⣻⣿⣤⣿⡽⢏⣿⣿⣿⣯⡀⣬⣝⡮⣿⠃⠀⠀⠀⠰⣷⡀
⣈⠀⣪⠀⠀⠀⠀⠀⠈⣠⣤⣽⣿⣿⠽⠟⠻⢾⣿⣦⣈⣽⣿⣿⡿⠛⣩⣽⡿⠛⣿⠷⢿⠀⠀⠀⠀⠀⠙⣿⣄
⠇⢀⣹⠀⠀⠀⠀⠀⠀⢹⣿⡻⠚⡯⠙⢶⣦⣬⣿⣿⣿⣿⣻⣿⣶⣿⣟⣃⣷⣞⣿⣫⣹⣄⠀⠀⠀⠀⠀⠘⣿
⠀⣾⣿⠀⠀⠀⠀⠀⣤⣨⣧⣴⡶⣿⡿⢛⣋⡍⢹⣿⣿⣷⣶⠋⠉⠛⠿⢿⣿⣶⣿⣶⣸⣏⡀⠀⠀⠀⠀⠀⠙
⢸⣿⡏⣴⣿⠀⠀⠀⠸⢿⣧⣤⣼⣿⣀⣈⠟⣤⣤⣴⣿⣿⣿⣿⣷⠐⠦⡼⠿⠟⣟⣿⣿⠿⠁
⣾⣿⣷⣿⡟⠀⠀⠀⠀⠀⠈⠓⢿⣿⣝⣿⣴⣿⣿⣿⣿⠟⠉⠉⣀⣀⣉⣰⣶⣶⠻⣋⡀⠀⠀⠀⠀⠀⠀⢰⡀
⣿⣿⣿⣿⠃⠀⠀⠀⠰⡿⢀⠀⠀⣿⢿⣹⣿⣿⣿⠿⣷⣶⣶⣾⢋⢻⡏⣷⣿⠋⢀⡙⠋⠀⠀⠀⠀⠀⠀⣼⣧
⣿⣿⣿⡏⠀⠀⠀⠀⠀⣄⠈⠁⠀⣿⠀⢹⣯⣼⣯⣰⢹⠛⢸⣷⣿⣷⣼⠿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡠⠁⠻⣼⣿⣿⣿⣿⣿⣾⠀⣾⣿⣿⣿⠅⠨⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠈⠀⢼⣿⠄⢸⣿⣿⡟⢿⣿⡀⣿⡿⠋⠉⠀⢠⣿⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠨⣿
⣿⣿⣿⣠⣾⣿⡆⠀⠀⠀⠀⠀⠈⢁⡄⠀⣿⣿⡇⢸⣿⣿⢿⣤⣤⠔⠀⢸⠏⢠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸⡁⠀⢿⣿⡇⠸⡇⠁⠘⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠑⡀
⠀⣠⠟⠁⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⣰⠃⢀⣤⣶⣿⣿⡇
⢠⡿⡄⢀⠀⠀⠀⠀⠀⠀⠉⣀⠴⠚⠁⠀⠚⢛⣉⠍⢡⡗⢄
⣼⢧⡙⠦⣄⣠⣤⡤⠴⠒⠋⠑⠀⠀⠀⠀⠀⠉⠡⠾⠛⠃⠺⠗⢦⡀
⣿⠀⠙⠲⠶⠶⠒⠚⠉⠀⠀⢀⣐⠒⢄⠀⠀⠀⠀⠻⠏⣼⣿⣿⠃⣨⣗⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⠀⠀⠀⠀⠀⠠⢐⡪⠄⠈⠀⠀⠙⢮⠳⣄⠀⠀⠀⠈⢉⡭⠁⣴⣭⠍⣡⣼⡀⢀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠑⡀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠉⠳⣄
⢻⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⣌⢦⡀⠀⠀⠀⠀⢘⡉⢩⣤⠄⢀⣡⣤⠅⠰⢄⡀⣸⠿⠿⠿⢿⣦⠀⠙⢦⡄⠀⠂⠈⠀⠀⠀⠀⠀⠀⢀⢿⡆
⣾⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢄⠀⠀⠀⠀⠀⠉⠴⠚⠋⠉⠀⠀⠀⢀⣼⢹⣧⣄⠲⠶⠀⠀⠀⠀⠀⠁⠒⠤⢤⣀⣀⣀⣀⡤⠋⡼⢿
⣿⠀⠈⠉⠉⠛⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠱⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠴⣉⣉⣄⢩⣭⠅⠀⠀⠀⠀⣀⠤⠤⢀⠀⠀⠂⠠⠤⠤⠴⠚⠁⢿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⣄⡀⠀⠀⠀⠀⠀⠱⠸⠀⠀⢀⠀⠀⠀⢀⠠⣪⣶⠄⠹⡿⠿⣦⠉⠀⠀⠀⢀⠞⡥⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸
⠹⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠇⠀⠀⠀⠁⢠⠄⣤⣶⡄⠲⣾⣦⡀⠖⠀⠀⠀⠀⡰⢋⠞⠁⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⢸
⠀⠀⠉⠉⠙⠛⠛⠓⠶⠶⠤⣄⣀⠀⠀⠀⠀⠉⠒⠤⢀⡡⢀⣠⠴⠂⠱⢦⣤⣀⡒⠶⡄⠠⠀⠀⠀⠀⢀⠜⡡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⢀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠈⠉⠙⠗⠀⡁⠀⠀⠀⡠⢋⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡐⢡⠋⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠃⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠊⠀⠀⠀⠀⢀⣀⣤⡤⠶⠖⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠙⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠉⠁⠒⠂⠀⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠄⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⢠⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡷⢿⣿⣿⣷⣶⣶⣦⡿⠏⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⢾⣫⢻⡇⠸⡿⡿⠿⠻⡆⠈⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣡⣶⣶⠶⣬⣿⣿⣄⣄⠘⠛⠟⠁⢀⣼⣿⣿⣷⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡭⠙⢻⣿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣍⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠀⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣽⣿⣿⣷⡀⠀⠘⠻⣿⣿⣿⣿⣿⡟⣿⣮⣹⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⢃⠘⠙⣿⣿⣿⣤⣤⣤⣤⡈⢉⣩⣽⣿⢸⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠿⠗⠀⠠⠄⠛⢋⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⣯⡽⣯⣿⣿⣛⣵⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠃⢰⣿⣿⣿⣿⣿⡯⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⢸⠁⢀⣴⠟⠃⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢠⠚⢿⣿⣄⣈⣙⣿⣏⠎⠀⠀⠀⠀⠀⠈⠐⠻⢷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⡀⠀⠀⠂⠀⠐⠀⠀⠀⠀⡎⢠⣿⣿⣿⡘⠿⠿⣻⣤⣓⣶⣦⣄⡀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⣷⡆⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⠷⣿⠟⡄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣅⡄⣹⠿⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣯⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣶⡌⠁⠀⠀⠧⢀⠀⠀⡀⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣁⣤⣴⠖⢢⣤⣤⠀⣀⠀⠀⢤⣅⡰⢟⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣅⣀⠀⠀⠀⠀⣩⡏⢁⡀⠀⢠⡟⣿⣿⣿⣷⡀⠅⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⣄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⢷⣦⠄⠀⠈⢈⣷⣄⣽⣿⣿⣿⣿⣿⣷⡀⢦⡀⠀⠀⠀⠀⠀⢸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄⣀⡀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣎⣛⠀⠀⠀⠀⢠⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠐⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣾⣿⣿⡌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣿⣿⡽⣿⣆⠘⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⠟⠀⢰⢀⣿⣿⣶⢄⡀⠀⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢃⣿⣿⡏⠀⠀⠀⠸⢸⣿⣿⣿⠀⠙⢾⣾⣷⣤⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣉⣡⣠⣶⣿⣿⠟⠀⠀⠀⢠⢃⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⡿⠼⠦⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠃⠚⠋⣩⡭⠿⠛⠛⠋⠁⠀⠀⠀⢠⠃⣼⣿⣿⣿⠃⠀⠀⢸⣿⠋⠁⠀⠀⠀⠀⠀⡱⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⢤⢠⡞⢁⣾⠁⠀⠀⠀⠀⠀⠀⢀⢃⣾⣿⣿⡿⠃⠀⠀⢠⣿⢻⣇⢀⣄⣀⣠⣤⡴⢁⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⡟⠺⠷⣯⠟⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⠏⠀⠀⢀⣴⣿⡫⣜⠛⣨⢜⡭⡼⢶⣖⠀⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⢨⢿⠀⣗⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⢀⣴⡾⢻⠊⠀⢹⠓⢡⡏⢀⡠⠼⢿⣇⠀⠀⡠⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣸⠇⢐⠦⢇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⣴⠟⡉⠀⡇⡆⠀⢀⣴⢯⠁⡴⠄⠚⢿⣟⣆⠚⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⠖⢁⣴⡧⣾⢒⠆⠀⠀⠀⠀⠀⠀⣸⠇⠀⣰⡿⢻⣆⠹⣦⡙⠿⠓⠁⣹⠟⣰⠷⠖⠈⣛⣻⣿⣧⡒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⣴⢫⣌⣣⡼⠾⠀⠀⠀⠀⠀⠀⢰⡟⠀⣼⡟⠀⠀⠙⢦⣅⢈⡢⠔⠊⡡⢾⣿⡶⠞⠓⠈⣛⣻⣏⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢮⣀⠈⢄⣹⣿⠂⠀⠀⠀⠀⠀⢀⡿⠀⣼⡏⠀⠀⠀⠀⠀⡙⣋⡤⡶⠉⠀⠀⠿⣿⡟⢋⡁⠈⣭⣿⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢀⠸⢋⣛⢳⠋⠀⠀⠀⠀⢀⠀⣾⠃⣰⡟⠀⠀⠀⠀⠀⢠⠏⢘⣷⠸⡆⠀⠀⠈⢪⡫⢸⠗⠶⣿⠍⠀⢳⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣷⡾⣋⣿⠽⠉⠀⣀⠀⠀⢀⠎⣼⠃⣴⠋⠀⠀⠀⠀⠀⠀⠈⢰⣼⣿⠀⣧⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠈⢼⣿⣧
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠈⣀⠔⠊⣹⣿⣧⣬⣷⡾⣡⡞⠁⠀⠀⡀⠀⠀⠀⠈⠁⣿⣿⣿⡀⣿⣿⣷⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⡆
⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⣠⢞⣡⣾⣿⣿⣿⣿⡿⣋⣾⢟⣡⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⢸⣿⣿⣿⣿⣦⡢⡀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⣾⣏⠣⣀⣀⠤⢊⣵⣿⣿⣿⣿⣿⢟⣡⡾⠛⢋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⢻⣿⣿⣿⣷⣿⣮⣵⣢⡤⠄⣂⣰⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣷⣶⣶⣿⣿⣿⣿⡿⣟⣽⣾⣉⣭⣶⠊⠉⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏
⠀⠀⠀⠀⠀⠉⠛⢿⣿⣯⣿⣿⣿⣯⣿⣷⣾⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣍⡛⠿⠿⠿⠿⢿⣿⣿⣟⣿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠾⠿⠿⠿⠛⠛⠋⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡐⡀
⠀⠀⡠⠄⠒⠒⠒⠠⢀⠀⠀⢀⣀⡀⠀⠀⣹⣄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⢎⠁⠀⠳⣖⠉⠀⢙⣦⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⡀⠀⠙⢦⠐⠁⠈⠑⠅⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⡇⠀⠀⠀⠈⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠊⠀⠀⢀⠀⠘⠢⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠊⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠖⠒⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠀⠀⠀⠀⠨⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡤⠖⠒⠒⠶⠶⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⣤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠄⠒⠀⠀⠀⠒⠐⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⣡⣬⠥⠤⠤⠤⠖⠒⠒⠒⠦⢄⡀⠀⠀⠀⠐⠀⠀⣀⣀⣀⣤⠤⠤⠔⠒⠒⠋⠉⠉
⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⢠⠔⠚⠓⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠉⠉⠉⠁
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣨⡍⠉⢉⣉⠽⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣠⠤⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⢀⣠⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⠴⠊⠁⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠔⠒⠒⠒⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠃⢀⡠⠔⠋⠉⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⡽⠉⠀⠀⣀⠤⠚⠉⠁⠀⣀⡠⠤⠒⠛⠉⠉⠈⠀⠀⠀⣀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠳⠤⢶⠋⠁⠀⣀⡤⠖⠋⠁⠀⠀⢀⣀⣀⠤⠖⠚⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠹⣅⣀⣠⠴⠒⠋⠁⠀⠀⠀⠠⠀⠊
⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠤⠤⠤⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠤⠤⠴

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡇⢀⡠⠀⠦⢬⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠈⠈⠈⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠐⠄
⠀⠠⠂⢠⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠐⠄⠀⠀⠀⠂⠀⠈⠀⠀⠀⠠⠉⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠓⠈⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠁⠐

⠀⠀⠀⠒⠲⠄⠀⠀⠀⢠⡄⡄⢠⡄⠀⢀⣦⠀⣠⠠⢠⡄⡄⠀⠀⠀⣰⡄⢠⡀⠀⢠⠤⡀⠀⠀⣄⠀⢀⢠⡄⣠⠀⡄⢰⡆⢰
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡏⢱⢸⡇⠀⠞⢻⠀⣿⠀⢸⡿⡄⠀⠀⡰⠛⡇⠘⢿⡇⢸⠇⡇⠀⠀⢿⣴⡆⢸⡇⣿⢸⡇⢸⡇⢸⠁⠀⠀⠀⠈⣀⠄⠄⠃
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠁⠈⠀⠈⠁⠉⠀⠈⠁⠀⠀⠀⠁⠀⠉⠀⠈⠁⠈⠉⠀⠀⠀⠈⠈⠁⠈⠁⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⢿⡀⣏⡐⠈⡏⢀⡿⠁⢰⡏⠀⣷⣀⠂⣯⠀⠀⠀⠀⣴
⠀⠁⠀⠀⠀⠀⠈⢛⡃⠙⠀⠀⠀⠀⠀⠀⠸⠇⠀⠏⠸⠇⡟⠂⠘⠇⠸⣧⠄⢸⡇⠀⡏⠿⠀⢘⠇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠄⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⡀⣀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠠⡀⠀⠀⠁⠀⠍⠁⠀⡂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⡀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠧⣧⡆⢠⠀⠀⠀⠀⠀⠀⠠⣠⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⡈⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠁⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⢀⡦⠀⠀⠀⠀⠀⠀⠀⣀⠔⢁⠄⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠠⠀⠀⠀⠀⠀⠀⢠⠞⠡⠖⠁⠀⠀⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠘⠀⢠⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠘⠃⠀⠀⠀⠄⢐⠈⡃
⠀⠀⠀⠀⠀⠀⢀⠈⠒⠈⠁⠠⡍⠀⠀⠀⠀⡠⠋⣠⠆⠀⠀⠀⠈⡀⠀⠂⠀⠂⢉⢑
⠀⠀⠀⠀⠀⠐⠀⠀⠉⡁⠀⡈⠀⠀⠀⢀⠜⢁⠔⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⢩⣀
⠀⠀⠀⠠⠤⠀⠤⢀⡀⠀⠉⠁⠀⣀⠔⠁⢠⠏⠀⡁⠢⣀⠀⠀⠀⠀⢀⠀⠈⢉⠁⠂⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡤⠔⠊⠀⠀⢰⠃⠀⠀⠑⠀⠠⠑⢄⠀⠀⠰⠄⢀⣉⠀⠤⠤⠈⠀⢥⣄⡀
⠀⠘⠤⠄⠠⠤⠤⠒⠊⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠸⠑⠤⢀⡔⢉⠀⠀⢀⣀⠠⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣦⠀⣀⣴⣿⣿⣿⣿⣿⡿⠋⠁⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⠁⠀⣠⣴⣤⡀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣤⣾⠿⠋⠻⢿⣦⣄⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠙⠿⣷⣤⡀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠁⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠉⠀⣠⣴⡿⠟⠁⠀⠀⠀⢀⣤⣦⣄⣤⣤⣄⠀⠀⠀⠀⠙⠿⣷⣤⡀⠈⠙⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠁⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢸⣿⣿⣿⣿⠟⠉⠀⣀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⡿⠋⠁⢀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠉⠻⣿⣿
⠀⠀⠀⠘⠉⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣶⣶⣶⣶⡄⢠⣶⣶⣶⣶⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠂⠠⠄⣁⠀⣀⠜⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠐⠒⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢈⠁⠀⣨⠂⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⠔⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠃⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠔⢁⠀⠤⠀⠤⠀⡘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠘⠀⠠⠀⠀⠀⠀⠀⠀⢀⠔⠁⠂⠀⠀⠻⠀⠀⠀⠠⠆⣐⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠈⠁⠁⡍⠁⠀⠀⠀⠀⡰⠃⢀⠔⠀⠀⠀⠀⢃⠀⠀⠀⠀⠆⢃⣑
⠀⠀⠀⠀⠀⠀⠠⠉⠐⠒⠃⠀⠐⠃⠀⠀⠀⢀⠜⢀⡴⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠠⠄⢋⣃
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠁⠒⠋⠀⠀⢀⠔⠃⢠⠏⠀⠢⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣄⣉⣁⣀
⠀⠀⠀⠈⠀⠀⠀⠈⠉⠐⢧⠀⢀⡤⠒⠁⠀⢤⠏⠀⠈⢦⢀⠙⠢⡀⠀⠀⠀⢀⠀⠡⠞⠀⠀⠐⠐⠂⠡⡀
⠀⢰⠀⠀⠀⠀⠀⠀⣀⠠⠔⠋⠁⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠑⠘⡦⡀⠀⠈⢀⠖⠒⠀⠉⠉⠁⠀⠈⣙⡳⠀⡀
⠀⠀⠉⠁⠀⠊⠉⠁⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠒⠃⠀⠀⠀⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠁⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠤⠄⠀⠀⠠⠤⠄⠀⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣄⣤⣠⣄⣀⠀⣀⡀⠀⣀⣀⣄⢀⣠⡀⣤⣠⣤⢠⣤⣤⢤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠛⣿⡇⣿⢛⡟⢿⣴⡿⢱⣿⣿⡸⣿⠸⣿⡃⣿⣉⠿⢸⡏⢿⡄⢻⣿⡙⢷⠟⣿⡧⣾⣿⡏⢸⡟⠛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⡇⢸⣧⡙⢸⣿⠃⢸⣿⠉⠁⢿⣷⣿⡅⣿⣿⠄⠘⣷⠈⣷⠀⣿⠃⢠⢤⡿⠁⠀⣿⠃⣿⠁⠀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡠⠀⠹⡇⠀⣿⠀⢸⣿⠀⡤⢸⣿⢻⡇⣿⡧⢠⠁⡿⢀⠏⠀⠋⣠⠃⣼⠋⣠⠆⡏⢸⣟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠲⠦⠀⠀⡀⠉⠐⠘⠏⣨⠇⢸⡏⠈⡇⠸⡏⠆⠀⠁⣉⢬⣰⢄⠀⣸⠀⢠⠟⠸⠁⡾⠁⠀⣸⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⡀⠀⢠⠀⠀⠀⠠⢧⣇⠈⣀⡷⠀⠔⠃⠀⠑⡲⠽⢎⠕⠁⠀⠑⡣⠙⠀⡉⠐⠀⠀⡇⣦⣼⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠱⠀⠧⠘⣡⡥⢬⢆⣨⣉⠀⣤⣶⣶⡿⢚⠶⠖⠚⠁⠀⠀⠀⠀⣰⠻⡆⠈⠲⡄⢐⡇⠸⠁⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⡇⡰⣾⠋⠀⠀⠣⣉⣥⠞⠁⣀⡿⠚⣁⣀⡤⡴⠂⠒⠤⡀⠀⠙⢷⣌⠛⢀⠘⠠⡄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡜⠡⡕⠁⣠⠔⣤⣄⣙⢆⠀⠀⠀⠑⢜⡙⠌⠑⠈⡰⠁⢀⠹⣦⡀⠀⠎⠳⣌⠻⡆⠹⣄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣖⠟⣠⠞⠃⠀⠡⠈⠘⢷⠀⣀⣀⠀⢀⣉⣦⣰⣾⠃⢀⡾⠁⠐⢛⣢⣰⡔⠈⠳⡙⣆⠹⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠢⢅⣀⠊⠀⣦⣴⣾⣵⡞⠟⠁⣿⡿⣿⡿⠛⠁⠀⢸⣧⡤⠤⢬⣽⣭⠃⠀⠀⠹⡌⣄⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡆⣤⠁⠀⠙⠿⣿⣟⣥⣶⣄⣈⢷⡖⡲⠀⡠⣰⣿⣿⡆⠀⢸⣇⠀⡀⠀⠀⠀⢻⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⣿⣿⢀⡀⢠⣿⢻⣿⣿⣆⠛⠘⢯⣴⣿⣎⣻⣿⣿⡿⢀⣿⣿⣿⣥⠀⠀⢀⠈⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⢉⡿⠼⠿⠿⠋⣿⡿⣿⣿⣧⠆⢰⡈⢀⡀⠈⠉⠁⠀⠈⣿⢿⣿⣿⠀⣰⡋⠀⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠁⢨⡇⠐⠂⠔⠘⠿⢇⡸⡿⠳⠇⠌⠙⠈⢉⡀⠀⢀⡤⠊⠀⠀⠘⣿⠾⠟⠁⠀⡟⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡠⣷⣰⠶⢶⡀⢶⠘⠳⠀⡆⠰⡀⡈⢋⣿⣿⠷⠊⠀⠀⠀⠀⠀⢷⠀⠀⠀⣸⠃⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠋⣠⠐⣬⣳⣆⣤⢤⡴⠆⢠⡠⣆⠀⡀⠘⠋⠙⣴⣠⣀⡔⠈⠳⡀⠈⡧⠀⡴⠋⣜⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⣟⠉⣣⠈⢨⣭⢀⠄⡄⠤⡄⢄⡡⢈⠉⣶⡄⠉⠛⠛⠉⣠⣾⡀⢙⣠⢃⡞⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⡇⡇⣼⡟⠂⢀⠀⠀⡠⡄⠐⠁⠀⠀⠰⡿⢧⡤⠒⠋⠀⠀⡟⠛⠒⠊⢸⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣟⢿⣰⠀⠀⠱⠀⠠⠀⠀⢀⠀⠀⣼⠶⠋⠀⠀⢀⠠⢠⠷⣇⢇⢠⠼⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢤⡍⠀⠀⠈⡴⠟⡀⠂⠀⠀⢠⠆⠀⠀⡤⠾⢛⡡⠎⢸⡏⢸⠀⠀⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠲⠠⠑⠆⠿⣸⣓⣳⡍⣇⠼⠓⡷⢒⢒⠒⠊⠉⢁⣶⠀⢸⠁⠈⠘⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⡄⠠⣾⢸⠗⢉⢸⡏⣁⠾⣄⢀⡌⢷⠋⢙⠀⡆⠀⠀⠁⠸⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢺⠀⠈⠛⢧⢪⠎⠙⠘⠀⠀⠀⠀⠘⠀⡀⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢸⠂⠘⡰⠀⠐⠔⠁⠈⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠻⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⡀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠉⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠘⢷⡄⠀⠈⢿⣶⣶⣿⣿⣿⣿⣿⣷⡶⠟⠉⠀⠀⠀⠀⠀⢀⣀⣈⣿
⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⡀⠀⣿⠀⠀⠈⠻⣦⡀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣤⣶⡛⠋⠉⠉⢻⣷⣄
⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠉⠉⠛⠻⠿⣦⣄⡀⠀⠈⠻⣦⡀⠀⣹⡿⣿⡟⢁⣀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣤⡀⠀⢹⣿⢷⣄
⠀⢀⣾⠋⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡈⠛⣿⠏⢠⡿⣰⣿⣿⠂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⡟⠀⢙⣷⣄
⠀⣾⣧⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⡿⠿⠷⠿⣧⡻⠿⢃⣾⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣠⡾⠃⠙⠻⣦⡀
⢸⡏⠹⣧⡀⠀⠙⣷⣀⣀⣤⣤⣤⣤⣤⣤⣀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠈⣿⡶⢿⣥⣀⡀⠀⠀⠉⠉⠉⠉⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠈⠛⢷⣤⡀
⣾⠇⠀⠘⢷⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⣤⣴⠶⠶⣿⣄⠀⠈⠉⠛⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⠀⠀⠀⠀⠻⣷⣄⠀⠈⠻⣿⣿⣿⡟⠁⠀⠀⠀⢀⣴⣿⣿⣷⣄⡀⠀⠈⢻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⠀⠀⠀⠀⠀⠀⠙⢷⣄⣼⠏⣻⠏⣴⣶⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣿⠉⠻⣿⡷⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢰⡟⢸⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⡿⠻⣦⣈⠉⠛⠻⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠋⠀⠀⠘⣷
⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⣧⣀⣉⣴⡟⠁⠉⠙⠛⠛⠿⠿⠿⠛⠛⠉⠀⣠⣼⠟⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣦⡀⠀⠀⠀⠀⢸⡏⠀⠀⣿⣏⡉⠉⠉⠛⠷⢶⣤⣤⣀⣀⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡏⠛⢷⣤⣀⠀⣿⠁⠀⣸⡏⠉⠛⢶⣤⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾
⠘⠷⣦⡀⠈⠙⠿⣿⣀⠀⣿⠁⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣷⡶⣦⣤⣤⣤⣤⣤⡶⠶⠟⠛⠋⠉⢠⡿
⠀⠀⠈⠻⢶⣄⡀⠈⠙⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠶⠶⠶⠶⠶⠶⠟⠛⠋⠁⠀⠀⠀⠀⢹⡷⠶⠶⠶⠶⠶⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠈⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠉⠙⠛⠷⢶⣤⣤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣤⣤⡶⠾⠛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⢦⠀⣠⢫⠖⢆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⣳⣧⣤⣜⣠⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠶⢶⣦⢾⠓⠛⠛⠛⠋⠁⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⠿⢖⡚⡏⠀⠀⢀⣄⠀⠀⢀⡜⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠷⢶⣻⠁⠀⡴⠁⡨⢃⡴⢋⠜⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⡛⠛⠿⣞⡿⠀⡜⢀⠎⡴⢉⠔⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣛⣛⡛⢷⣻⠃⡸⢁⠎⡜⡰⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠒⢫⠟⠁⢰⠁⡜⡸⣰⡟⠀⣀⠄⢀⡤⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣠⠃⠀⠀⠀⠙⡰⣱⢳⠑⣊⠵⢊⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠕⠀⠀⢀⡔⠁⠀⠀⠀⢀⠔⡱⢃⠇⣫⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⢀⠎⠀⠀⣀⡤⢒⡥⠊⡠⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡭⣑⣒⣚⣒⡈⠭⠔⢊⡡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡅⠀⠀⠀⢀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧⠀⠀⠀⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢁⠀⠀⠀⡼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⣄⠀⠠⡥⢀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⢼⠀⠀⣠⢫⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣡⠉⢢⡀⢣⠀⢸⠳⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣠⢚⡅⠀⡎⢀⠔⠙⡜⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡇⠀⠀⠑⣌⡇⠰⠀⠈⢢⣲⢤⡛⢄⡌⢣⡤⢛⡤⣧⠔⠁⠀⡇⣼⣠⠋⠀⠀⢻⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠒⡺⠟⠉⠻⣇⠀⠀⠀⠹⡌⡃⠸⠁⠈⡆⣸⢠⠋⠀⠀⠀⣼⠏⠉⠳⣆⠲⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠱⡄⢷⡄⠀⠀⠏⠑⠢⢄⡀⠑⣶⠃⠀⠀⠸⣿⠂⢀⡠⠔⠊⡍⠀⠀⢠⡞⢠⠎⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⠒⠼⣾⠈⢆⠀⢸⠀⠀⠀⢹⠒⢿⠢⣄⡠⠔⡿⠚⠇⠀⠀⠀⡇⠀⡴⢁⣷⠇⠊⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣔⣉⡇⠈⢣⡘⡀⠀⠀⠀⡆⠸⡀⢨⠀⢠⠃⢸⠀⠀⠀⢠⢀⠞⠀⢘⣉⣦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⠢⣀⠱⡇⠀⠀⠀⢇⠀⢣⠸⠀⡌⠀⡐⠀⠀⠀⣼⠊⣠⠔⣏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⢱⣜⣄⢀⡠⠚⢦⡈⢶⡴⢀⡴⠓⢄⡀⣰⡥⠎⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡒⠤⣆⠉⢻⢄⠀⠀⢉⣺⣗⡁⠀⢀⡠⡟⠁⣸⠤⢒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡚⠻⠿⣶⣻⡎⠁⢸⠀⠈⢱⣛⣶⠿⠟⢓⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡙⢦⡀⠀⢨⠀⠀⢸⠀⠀⠈⡇⠀⢀⡴⢫⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢣⠀⠙⢤⡋⢀⡠⠊⠓⢄⠀⢣⡴⠋⠀⡎⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⣨⡦⠒⢘⡷⠋⠀⠀⠀⠀⠑⢾⡃⠢⣴⣀⣀⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⡰⠋⠸⡀⣎⠱⣆⠀⠀⠀⢀⣴⠎⣷⢠⠃⠑⢄⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⡼⠁⠀⠀⠱⣘⠦⣍⠑⣄⣴⠋⣥⠼⣁⠆⠀⠀⠈⢦⡃⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⡇⠀⠀⠀⠀⡏⠀⣘⠁⢸⠁⠉⠇⠀⢛⠀⠀⠀⠀⢸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⢿⣑⠟⣂⡴⢦⡐⠻⣈⡟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠜⠛⠒⠠⠀⠒⠛⠣⣇



⢀⣀⣀⠀⡀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣶⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣈⠻⣦⣄⣀⣀⣀⣠⠴⣫⣾⣿⡿⣫⣿⣿⣇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡿⢛⣿⢋⣽⣿⣿⣿⣿⡉⠛⠷⣮⣷⣯⣭⣭⣴⣾⣿⡿⢋⡼⢵⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⢋⣴⣿⣷⣯⡟⣿⡿⣿⣿⡇⣷⣦⣄⣉⠛⠛⠛⠛⢛⣉⡴⠋⠐⠙⢛⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠟⢻⡿⢀⡴⣿⣇⠿⣿⡷⠁⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠈⢽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢮⠇⣠⡾⠋⠀⢿⣏⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠙⠛⢁⡴⠊⠙⢳⣦⡀⠀⠙⠉⠈⠻⣦⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⢸⣿⣿⣿
⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠝⣿⣆⣀⣀⣀⣀⣹⣿⣦⠀⠀⠀⣰⢏⣽⣿⣿⡿⢻⣿⣟⣿⣿⣿
⢀⢀⣴⣾⣿⣼⣀⣀⣀⣤⣤⣤⠤⠤⠶⠒⠒⣛⣭⣭⣭⣁⣤⣤⣞⠳⣬⣙⣷⡤⢞⣵⣿⣿⣿⣿⠇⡿⣿⣿⣿⠋
⠘⣾⣿⣟⣟⣭⠭⠽⠀⠀⠀⠀⠀⠀⠀⣠⣺⠟⠛⢉⣿⣛⡿⣿⣿⠷⣌⡻⣷⣾⣿⣿⣿⣿⣿⡿⣸⢃⣼⣿⠉
⢰⣿⣿⣷⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⢰⣷⣏⣀⣴⣯⣿⠟⣷⣏⢿⡷⡄⠉⠻⣿⣿⣿⣿⡿⠟⣱⠇⢸⣿⣿⡇
⠈⠛⠿⢿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⢸⣿⣟⣛⣯⢻⠻⠋⠀⠀⢻⣿⢸⠿⠶⠮⣭⡤⠴⠞⠁⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠛⠛⠻⣽⣾⣯⢽⣿⣿⡟⣀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⣿⣾⣿⠇⠉⠛⠶⣤⣀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⣉⡉⢻⡅⣴⡇⠀⠀⠀⠀⠈⠙⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠻⠿⣿⣿⠛⢱⡿⣄⡀⠀⠀⠀⠀⠀⣿⣿⢿⣦⡀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠓⠶⣤⣈⣉⣀⡾⠁⠈⠻⣦⡀⠀⠀⠀⣸⣿⣧⢽⣿⣦⣮⣴⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢸⣿⡦⠶⠛⠉⢻⣿⢦⢈⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⣠⣾⢫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⢹⣯⡻⣿⢟⠝⠁
⠀⢀⣾⣿⣿⣌⣂⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣟⢿⣷⣄
⠀⣸⣿⡿⣿⣿⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠋⠀⠀⠁⠙⣯⣧
⠰⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠈⠛⠿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣷⣦⣀⡀
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣴⡿⠋⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣴⠟⠁⠀⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⣠⡾⢯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⣠⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣦⡀
⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣿⣿⣿⣿⣿⣿⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⣾⣿⣦⠈⠢⣀⣠⡴⣶⡟⠲⣄
⠀⠀⠀⠀⣸⣿⣿⣿⣦⡀⠈⠻⢿⣻⣿⣅⠈⠢⡀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣳⡀⠀⠀⠙⢿⣿⣆⠀⠘⢦⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠙⢿⡆⠀⠀⠙⣄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢔⠠⡀⠈⠳⣄
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢻⡆⡀⠀⠀⠀⠈⠳⡙⢦⡀⠈⢢⡀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣾⣿⡌⢢⡀⠀⠀⠀⠈⠢⡑⠄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⣿⣄⠹⣄⠀⠀⠀⠀⠈⠢⣄⣀⣀⣉⣲⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠻⣿⣿⣿⣿⣿⣦⡘⢦⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⣵⣀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠷⠶⠿⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⡴⢁⣴⢂⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠠⠔⠂⣸⢡⠏⣈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢿⣿⠀⢁⡉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⣿⡄⠀⠁⣎⣷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠘⢿⣤⡀⠀⠳⠞⢉⡿⣶⣰⣿⠖⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡀⠀⠀⠀⠀⠀⠈⠛⠷⠦⣤⣤⣤⡼⠟⠁⣠⠞⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⠀⠀⠘⣆⢳⡀⠀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢉⡤⢲⠋⠀⠀⠀⠀⠀⠀⠙⠄⡠⢄⣠⢤⣀⡴⠖⠦⢄⡀⢀⡠⣄⢀⠥⣀⠔⠤⠋⠉
⠀⠀⠀⠀⠀⡖⢁⡠⠤⠐⡞⡴⠃⡃⣿
⠀⠀⠀⠀⠀⠙⢇⠀⠀⠸⣷⡇⠈⠁⢻⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢿⣇⠀⠉⣩⢳⣄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⢻⣦⡀⠈⠸⡥⠟⢒⣦⡄⣴⡦⠤⠀⣀
⠀⠀⠀⠀⠀⡿⢄⠀⠀⠀⠀⠀⠉⠹⠶⣤⣤⣄⣩⣬⣿⠟⠁⣠⠊⠉⠱⡄
⠀⠀⠀⠀⠀⢷⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⡞⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠈⢇⢉⣄⡀⣀⡀⢀⡤⠤⣄⡀⠀⢀⣀⠀⢘⡂⢀⢆⡰⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠉⠉⠀⠀⠀⠉⠀⠉⠈⠁⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠱⠀⠐⠠⡀⢣⡜⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⡀⠂⣸⣇⠠⢀⣤⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣿⣿⣿⣹⣿⣿⡿⢿⣿⣿⣏⣿⣿⣿⣿⣿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⡉⠻⠟⠛⣋⣻⣿⣿⠇⠸⣿⣿⣟⣙⠛⠻⠟⠉⣤⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣉⠐⠶⠗⠛⡛⣿⣿⡟⠀⠀⢻⣿⣟⣛⠛⠲⠶⠂⣉⣬⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣉⠃⠶⠶⠜⠛⠻⣿⣿⡇⠀⠀⢸⣿⣿⠟⠛⠣⠶⠶⠘⣉⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣙⠛⠁⢴⣦⠼⠿⢿⣿⣿⡇⠀⠀⢸⣿⣿⡿⠿⠧⣴⡦⠈⠛⣋⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡛⠛⢡⣤⣄⢶⣾⣾⣿⣿⡇⠀⠀⢸⣿⣿⣷⣷⡖⣠⣤⡌⠛⢛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠓⠀⠈⠀⢤⣦⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣴⡤⠀⠁⠀⠚⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡾⣶⣶⣶⣶⣶⣶⣌⣽⣿⣿⠁⠀⠀⠈⣿⣿⣯⣡⣶⣶⣶⣶⣶⣶⢶⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠾⠟⠛⠻⠿⠿⣿⣿⣧⣿⠃⠀⠀⠀⠀⠘⣿⣼⣿⣿⠿⠿⠟⠛⠻⠷⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠏⠀⠀⠀⠀⠀⠀⠹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢀⠙⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢱⡀⠁⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⡾⣡⣾⡁⠀⠀⣰⣿⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠟⣡⣾⡿⠋⠀⢠⣾⣿⣿⣿⡄⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠁⠀⢰⣿⣿⡿⠟⠉⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⣆⡄⠀⣿⠿⠋⠀⠀⣀⣤⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⢿⣿⣿⣿⣿⡞⠁⠀⢀⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠣⡴⠀⠀⢻⣿⡿⣫⣿⣦⣴⣿⣋⡈⠉⣩⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠰⣃⡀⠋⠁⠚⠀⢐⠾⣮⣜⣛⣛⣛⣛⣭⣵⠾⣋⡥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⣠⣶⡿⢋⡠⣯⠈⠉⠀⢠⣴⣿⣿⣶⣭⣽⣛⣋⣩⣥⢴⣾⣿⠇⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣻⡿⠟⠋⠉⠀⢘⣇⠉⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢠⣾⣿⡿⣸⣿⣿
⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣴⣾⣿⣿⣾⣥⣽⣿⣿⣿⣿⣿⣿⣿⡿⡃⣀⣤⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣇⣀⡀⠀⠀⣀⣠⣤⣤⣤⣄⠰⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣤⣶⣾⣎⠩⣿⡇
⠀⠀⠀⠀⠀⠙⠻⢿⣯⣿⣛⡿⠿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⢹⣿⣿⣿⣿⣿⡧⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣮⣭⣽⣿⣿⣿⣿⣿⣭⣭⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠘⢒⣀⣈⠀⠀⠀⠉⠉⠉⠙⠛⠛⢻⡿⠏⠉



⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤⣠⣤⣄⡀⠀⢸⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠙⣿⣿⣿⣷⣼⡄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⢀⣀⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣄⣹⠀⠀⠀⠀⠀⠀⠘⡄⠉⠩⣶⣳⡶⠿⠛⠋⣁⠤⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⣿⠟⢇⠀⠀⠀⢀⣠⣴⡾⣆⠀⠀⣨⢷⣒⡮⠿⠒⢉⣠⣼⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⡌⠙⠛⠛⠁⢠⣼⣖⡲⠿⠓⢋⣁⣤⣚⢷⣀⠈⠉⣹⢤⣒⠯⠓⠋⢁⣀⣬⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠙⣄⠀⠀⠀⠀⠀⣼⣶⠾⠿⠛⢋⣩⢤⣾⠿⡙⢦⠉⠉⢹⡶⣾⡗⠛⠛⠉⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠧⣄⣀⠀⠈⠓⠤⣄⡀⠀⠀⢸⣶⡶⠿⠛⠋⣁⣠⣤⣿⣆⠳⡀⠀⠀⠀⠈⠁⠒⠒⠒⠋⠀⠙⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⠙⢦⡀⠀⠀⠉⠑⢤⠀⠀⢱⡶⣽⠟⠛⠉⠉⠀⠀⢱⡙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣳⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠦⣄⠀⠀⠳⡀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠉⠓⠲⠂⠔⠒⠁⠙⢦⡈⠉⡷⠊⠉⠉⠉⠙⠓⠒⠒⠚⠉⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠒⠦⣌⣦⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠈⠛⢷⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠉⠒⢲⠔⠊⠁⠀⠀⠉⠑⠒⠐⠒⠉⠀⠀⢳⠤⠤⠤⠤⠐⠒⠒⠊⠀⣠⣾⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣄⣀⣀⣀⣀⣀⣤⡀⠀⠀⠑⢄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡆⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠷⡄⠀⠀⠀⠉⠒⠒⠒⠒⠛⠲⢤⣤⣀⣀⣤⣤⣤⠤⠴⠋⠀⣠⢷⣶⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠴⣶⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⡿⣿⣿⢿⣕⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡢⡀⠀⣀⣀⣠⣯⡟⠁⢀⣸⣇⡀⠈⢻⣽⣄⣀⣀⠀⢀⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣉⠁⠀⠉⠙⣗⠕⠩⠝⠪⣺⠋⠉⠀⠈⣉⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⠿⣧⢀⣠⣜⣯⠴⠞⠳⠦⣽⣓⣄⡀⣼⠿⠃⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⡄⠀⠁⣰⢯⣳⣾⢡⢾⠽⠯⣗⡌⣷⣞⣽⣆⠀⠀⢠⣷⢤⡀
⠀⠀⠀⠀⠀⠀⣰⣻⠟⠉⢷⢤⡾⣼⠾⣛⡛⠈⡚⠎⠱⠃⠉⢛⣛⠳⣧⢶⡤⡾⠉⠻⣞⣆
⠀⠀⠀⣀⣀⣰⣿⣯⣄⣰⡕⡁⣰⠇⣞⠖⡺⠬⢾⣷⣾⡿⠤⢗⢲⣳⠸⣆⢈⣪⣆⡠⣽⣿⣆⣀⣀
⠀⠀⠀⠉⠉⠹⣿⣟⠉⠹⡳⡁⠹⣆⢯⠧⢵⠂⣾⡿⢿⣷⠒⡾⡼⡽⢰⠏⢈⢜⠏⠑⣻⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠹⡿⣦⣀⡾⠚⠷⢿⢦⣭⣥⢀⢤⣇⣸⡬⣀⣼⣭⡶⡟⠾⠓⢷⣀⣴⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⠃⠀⠀⠹⣞⣽⢿⡘⢼⣲⣖⡯⢣⡿⢯⣷⠏⠀⠀⠘⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢠⣶⡟⠈⠙⢫⣟⠲⢦⡴⠖⣻⡍⠋⠁⢻⣶⡄⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣉⡀⠀⣀⣠⡯⡣⣔⣆⢔⢽⣄⣀⠀⢀⣉⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠕⠁⠀⠉⠉⠙⣟⣧⡀⠈⠹⢏⠁⢀⣼⣻⠋⠉⠉⠀⠈⠪⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢽⣷⣿⣿⣾⡿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢠⡄⠀⠠
⠀⠀⠀⠀⠀⢀⠀⣴⣛⣶⣄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡀⠀⣀⠀⠀⠁⢄⣤⠒⠀⠁
⠀⠀⠀⠀⠀⢸⡆⢽⣟⣻⡝⢣⠈⠀⠀⠌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠃⠀⠉⠀⠀⠲⣌⠡⠆
⠀⠀⠀⠀⠀⠈⠁⠈⠻⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠲⢾⣷⠀⠰⡖⠀⠠
⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢀⠀⡀⢰⢒⠄⠀⢴⠄⠈⠰⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠦⣤⡈⠀⠀⠈⡀⠁⠀⠉⡔⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡧⠀⠐⢁⠁⣁⠀⢀⣡⡦⠠⠐⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣅⠉⠙⠀⣷⢄⠀⡘⠛⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠐⠈⠄⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⣤⠀⢀⡀⣀⠠⣄⠀⠀⠼⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠑
⠀⠀⠀⠀⠀⢠⡝⠀⠈⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠐⠀⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠠⠀⠐⠀⠀⠀⠀⡞⠠⡀⠁⠂⠀⠀⠀⠀⠀⢁⠤⠠⠐⠄⠠⢄⣀⡐⠶
⠀⠀⠀⠀⠀⠀⠀⠿⠗⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠀⠀⠀⣀⡏⣡⣴⠴⣠⣴⢶⡴⡀⠁⡴
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⡀⠀⢴⠄⢱⡈⡘⠷⠇⢾⣃⣙⡗⠲
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠇⠀⠘⣄⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⢸⠠⠘⠈⢣⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⣎⠀⠀⢀⡠⠎⠀⠀⠀⢸⡇⢰
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠏⠀⠀⠰⠀⠀⠀⠀⠀⢸⠃⢸
⠀⠀⠀⠀⣸⡀⠉⠉⠽⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⣠⢞⣹⠛⣠⡶⠖⢀⠀⠀⠀⠀⠀⠀⢀⡎⣰⣿⣦⡀
⠀⢸⣃⠀⠘⢷⡄⠰⠂⠀⠀⠀⠀⠀⠀⠀⣞⣴⣋⣀⣀⡀⢀⣀⣨⠢⣀⣀
⢀⠈⠉⠀⠀⣾⠻⣶⣄⠀⠘⠀⠀⠀⠀⣸⡟⠉⠫⣀⠴⠄⢀⣤⢞⣯⣽⣏⠓⢄
⠇⠀⠀⠀⢠⠔⢂⣽⡈⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⡜⢀⡜⡹⠉⠓⡛⠲⡎⡄⠀⠃
⠀⠀⠀⠀⣠⡽⢈⡁⠙⢷⠀⠀⠀⠀⢀⣟⢧⡀⠄⠀⢀⠼⢆⠀⠂⠈⢳⠀⠶⠒
⠀⠀⠀⢀⣉⠀⣌⢁⠀⠘⠆⠀⠀⠀⠈⡿⢍⡻⢴⡚⠋⠀⠀⢣⠀⠉⠀⢨⠩⢿⣝⣦⣀
⠀⠀⢈⡿⠍⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠙⢦⡀⠀⠀⠑⡄⠉⠀⢋⡉⣙⠿⢿⣵⣦⣄
⠀⠀⣎⠀⠀⠀⠀⢃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠸⡄⠘⠁⠉⠀⠀⠀⠀⠀⠈⠑
⠀⠀⡇⠀⠀⠀⠀⠀⠳⣄⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⡗⠀⠀⢀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢇⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⣀⣀⣀⣠⡤⠔⡪⠝
⠀⠀⠈⠛⣒⣒⠒⢉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠋⢁⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠛⠛⠉⠉⠀⢀⣠⡤⠖⠋⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⡤⠤⠶⠖⠚⠋⠉⠁⣀⣤⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢳⡀⠀⠠⠴⠶⠚⠋⢉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢳⡀⠀⣤⠤⠶⢚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⣀⣤⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣄⣀⣀⣠⡼⠁⠘⠀⣀⣤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠛⣿⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁⠀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁⠀⣀⣀⣤⣤⠶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠀⢀⣀⣀⣤⡤⠶⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠶⠶⠶⠶⢾⣿⠿⠿⠤⠾⠿⠿⢿⣾⣯⣿⣿⣿⡿⠿⠟⢯⡙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⣲⣰⣯⠷⣿⣿⣿⡄⠀⠀⢀⡤⣄⣤⣤⣠⡀⠀⠁⠈⡛⠓⠀⠀⠈⠉⠤⣾⣶⣛⡂⠳⠤⠠⣀⣀
⠀⠀⠀⢀⣀⣤⣪⣵⣿⣾⣿⣾⣿⣿⣿⣿⣷⣿⣷⣶⠶⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠉⠁⠒⠋⠑⠲⣢
⠀⠠⣶⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⢿⣿⠉⢉⡉⣿⣿⣿⡿⣿⣿⣿⣿⣧⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡀⠀⠀⠁⡷⠄
⠀⠀⣻⣿⣿⣻⣿⡿⣿⠟⠛⢿⣉⣽⡿⣶⣿⣟⣡⣤⣿⣿⣿⣷⠾⢿⣿⣿⣿⣆⣀⣘⣒⣒⣒⣒⣒⣒⣀⣐⣂⣀⣀⣾⣿⣿⣿⣇⣀⠠⠴⠟
⠀⠀⠙⠿⣾⣿⡿⣶⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣷⡾⢳⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉
⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⡿⠯⠿⠛⠛⠛⢿⣿⣷⡻⣟⣡⡿⣺⡿⢹⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⢿⣿⣙⣿⡾⠟⠁⠸⣿⡿⣿⣿⡟⠉⠛⠿⠿⠛⠛⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠒⠠⢄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣠⡴⠂⠦⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠂⠄⡓⢀⠀⠀⢀⠀⠀⡄⠀⠀⡀⠀⢀⣠⣀⡀⠁⠀⠁
⠀⠀⠀⠀⠀⠙⠔⠠⢀⠀⠐⠀⠈⠁⠀⠀⠘⠀⠁⡅⠀⠰⠃⢀⠊⠁⢀⠁⠀⢐⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠑⢼⠃⠂⠈⡀⠀⠀⢀⡀⢠⠠⠅⡔⠀⢠⠄⠐⢀⣉⡀⠀⢩⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⡰⠛⢂⡐⠢⡀⢠⠀⡆⢠⠄⠸⠜⢋⡏⠡⢀⠀⣞⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠠⠉⠆⠤⣌⠠⠄⠷⡰⡖⡀⠁⠤⢨⡤⡀⠒⠉⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠤⠐⠃⣙⢘⢠⠀⣠⠀⠆⢱⡀⠦⡚⠓⡁⠚⠀⠄⢀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠰⢅⠀⠀⢠⠍⠀⠠⠔⠃⠀⠀⠘⠓⢤⡌⠀⠑⡄⠀⠀⠜⠢⡂
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠡⠤⠁⠀⠀⠀⢠⡤⠈⠓⠠⣡⠂⠀⠀⠀⠈⣦⠤⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠁⠀⠀⠀⠀⠀⠈⠃⠀⡀⠐⠃⠀⠀⠀⠀⠈⠈⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠄⠖⠡⠀⠀⠀⠀⠀⢄⠀⠀⠄⠁⠂⠠⢀⠀⠀⠀⠐⠀⠀⠀⡰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠑⠀⠀⠀⠀⠀⠷⠀⠨⡇⠀⠺⠃⠀⠀⢀⠀⠀⠀⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠐⢠⡀⠀⢂⡀⠀⠀⣠⠊⠀⠀⡠⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠦⠀⠈⡓⠁⠀⠄⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠈⢉⡉⠉⠀⠈⠁⠀⠀⠀⡉⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⣈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⠔⠁⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠒⠤⢄⡀⠑⢤⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠋⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠉⠒⠤⢀⡀⠀⠈⠐⢄⠑⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠃⠀⠐⠁⢀⠄⢀⠎⠀⡠⠊⠑⢄⡀⠉⠂⠄⣀⠈⠉⠀⠒⠂⠀⠄⠸
⠀⠀⠀⡀⢊⠢⡏⢂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⣡⠔⠁⡠⠊⠀⠀⠀⠀⠈⠐⠠⢄⡀⠉⠁⠒⠠⠤⠄⠀⠀⠆
⠀⠀⠈⠪⡙⠆⠉⠀⠚⠐⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠁⠤⠒⢋⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠂⠤⠤⡜⡀
⠀⠀⠀⠣⡉⠀⠀⠀⠀⡠⠓⢄⠀⠀⠀⠀⠀⠘⠦⠀⠖⠂⠉⠁⠀⠀⠘⠟⠀⠀⠀⡀⡀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠇⡣⠁⡇
⠀⠀⠀⠀⠈⠑⢠⠐⠉⠀⠀⠀⠑⣄⠀⠀⠀⠀⠈⠪⣰⡀⠀⠀⢀⢀⠀⠀⠀⠀⡀⠈⢀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠰⠉⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠑⢄⠀⣐⠒⢀⠀⠱⡀⠀⠣⠠⠇⠀⠀⠀⠈⠓⠉⠀⠀⠀⠘⠤⠜⠀⠀⣠⡃⠐⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠙⠢⣀⢀⠎⠊⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠈⢃⡠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⢀⠏⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⠠⠔⢺⣄⠀⠀⠀⠀⢱⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠁⠈⠁⠉⠁⠀⠀⠀⠜⠈⠳⡀⠀⠀⠈⢆⠀⢂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠐⠒⠖⠂⠄⠠⠀⠒⠉⠀⠀⠀⠈⢢⠀⠀⠀⢯⣤⡶⢗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡜⢨⠹⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠎⡇⠹⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⢀⣀⣀⡀⠆⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡕⠀⢀⡠⠔⠈⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠽⠤⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⢒⢶⠖⡃⠠⣠⣶⡅⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⠶⠖⠃⠀⠀⠀⠜⠊⠁⠀⠀⠘⠃⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠺⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⢳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠠⣴⣶⣦⠁⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⣠⡀⠀⢠⡀⠀⠤⠀⣀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠘⠆⢸⣶⣿⠋⠉⢀⡀⡀⠐⣄⣤⠆⣄⣤⣄⢦⡉⣿⠲⣄⠻⡦⠀⠀⠈⠙⠃⠠⣀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣼⡏⣠⠖⠁⠀⠉⠛⠈⠉⠃⠀⠀⠛⠈⠙⠳⢗⣸⢷⡃⠰⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣼⠁⠀⣀⣀⣐⡢⠰⣴⣤⣼⣶⣇⢀⣴⣦⣤⣤⡀⠀⢠⣶⣦⣤⡀⠀⠀⢸⣿⡎⢻⣷⣇⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀
⠀⠀⠀⠀⠀⢽⠁⣼⡟⠛⠛⠛⠛⠛⠻⣿⣿⣿⠶⣿⡿⣯⣽⡷⠀⢨⣿⣯⣭⢹⣷⣴⣈⣩⣿⣖⣿⣿⣦⡤⠀⠀⠀⣀⣀⠀⠌⠷⡀
⠀⠀⠀⠀⠀⠘⣾⢿⠀⠀⠀⠠⠀⠀⠀⣿⣿⠋⠀⣾⣆⠹⠿⠃⠀⠀⢿⡿⠳⠻⠟⠉⠉⠀⠈⣼⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⢀⡔⠀⢀⡼⠃⠀⠂⠁⠀⣠⠀⢀⡀⢤⡀⠁⠀⠀⠀⣠⣀⣤⣾⣿⠿⣿⣿⠟⠋⠀⠈⣿⠀⢹⡟⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⡠⢠⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠀⠀⠀⠀⠀⠈⠱⠜⠿⠋⠀⣿⣿⠀⠀⠀⠀⠙⡷⠋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⠀⠀⠈⡇⢘⡧⣀⣠⣴⣶⣾⣿⣿⣶⣤⣀⡀⠀⢠⡄⠀⠀⠀⢹⠇⢀⣿⡏⠀⠀⠀⠀⠘⢶⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡇⠹⠛⠿⠿⢷⣤⣼⡀⣀⡠⢩⣿⡇⢸⣷⣤⡴⠏⢀⣼⣿⣇⠀⠀⠀⠀⠀⠀⣿⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠚⠋⢩⣤⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡈⢳⣿⣿⣿⣯⠓⠂⠀⠶⠶⠿⠛⢫⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣧⠘⡏⢹⣿⣿⣿⣶⣄⣀⣀⡀⣼⣿⡾⠟⠛⠋⠹⠿⢿⡿⡟⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠁⠈⢿⣿⠫⢿⠻⢦⠀⠂⠛⠉⠁⠀⠀⠀⠀⠀⠸⠁⠁⠀⠈⢻⣧⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠒⠠⠖⠋⠳⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠚⣀⣠⣤⡉⠉⠑⠢⣄⡈⠀⠈⡏⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠉⠑⠷⡜⠪⠀⠉⣉⠽⠚⠁⠀⠉⠲⢄⡵⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠢⢠⠈⠫⠇⠉⠃⣀⠤⢒⡭⠒⠁⠀⠀⠀⠀⠀⠀⠀⡰⢳
⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠂⠂⠤⠬⢴⠒⠈⠀⣠⠔⣊⠵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⢾⡀
⠀⠀⠀⠀⡀⠀⠤⣀⣀⡀⠀⠀⠀⠀⡰⠢⠔⠋⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⠜⠀⣇
⠀⠀⠀⡸⠀⠉⠒⠲⠤⠤⢍⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠉⠀⠀⠀⢻
⠀⠀⠀⠱⣄⠈⠉⠓⠒⠒⠤⠤⢄⣉⣒⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠶⠒⠒⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⢄⣀⣀⣀⣀⣀⡀⠀⠠⠤⠒⠁