Salad Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢢⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⣀⡠⢐⡲⠿⣇⠀⠀⢱⡀⠘⡦⣤⠄⠒⠀⠐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⣠⢴⡏⠀⠀⢀⡎⣰⠉⠈⢁⣹⢦⡀⠀⠁⠀⠟⠀⡠⠴⠛⠂⠀⣀⣴⠷⢦⣤⣀⡔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢶⠏⢩⠀⠽⢿⡓⡠⠼⢧⣀⡇⢠⠊⠀⡤⢹⣶⢤⠀⠀⠀⠀⢀⣠⣴⠞⠁⠉⠳⡔⠂⠹⢁⢂⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⡈⠀⠈⠀⡈⠸⢯⠀⠀⠀⠙⢢⡁⣠⠋⡠⠊⣌⠜⡑⢛⢟⠟⢻⡶⠋⠀⠀⠐⡄⠇⠈⠃⡞⠘⠃⣻⡳⣄⡠⠀⠄
⠀⠀⠀⠀⠀⢸⠉⠀⠀⠈⠳⣄⠑⣄⠀⢀⣴⣧⡀⠑⣤⠶⠒⢛⡿⣯⣩⡤⠊⡖⠚⠛⠛⢆⡠⠊⠀⠀⠀⢰⠁⠳⠤⢤⡴⠃⠰⣋⠆⠁⡸⠁⢠⠆
⠀⠀⠀⠀⠀⠘⣆⠀⠀⣄⠠⣎⠀⢈⢞⠏⠁⠀⢹⣦⡇⣀⣄⡛⠀⠴⢀⠘⠐⠉⢢⣄⣤⠞⠵⣂⣀⠁⠄⢉⠃⡀⠀⠀⠱⠄⢲⠟⠀⢈⠅⠴⢇
⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠘⠚⢽⡏⡜⠠⢠⡀⠈⣷⡾⠀⠠⠂⠠⠃⣸⡲⡀⠼⡱⠋⠀⠀⠀⠈⢻⣠⠞⠁⠀⠀⣀⡀⠀⣧⢀⡠⠖⠂⢀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⡦⢤⣼⢱⡇⠀⢀⡀⡆⢻⡁⠀⡀⠀⢠⠀⠀⢰⣷⡠⣷⣟⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⣌⠀⠀⣿⠋⠁⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠻⢶⣼⡄⢷⠰⡀⣀⠀⢌⢿⠋⠇⣀⣀⣠⠞⠃⠭⣉⠉⠛⣾⡁⠀⡎⠁⡅⢀⡀⠰⠄⢀⠀⢀⡟⠛⣩⡿⡋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠉⠛⠾⣧⣱⣀⠠⠀⢻⢻⠉⠁⠑⣾⠀⠀⠀⠈⡗⠉⢩⣷⣦⣙⠦⢤⣤⣤⠤⠔⣉⣤⠿⠖⡋⠕⡊⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠙⠒⠳⠶⠧⣤⣤⣿⣄⣀⣀⣸⣃⣠⣏⣈⣧⡭⠿⠶⠶⣒⣚⡭⠥⢒⡪⠅⠒⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣒⣒⣛⡭⠭⠕⠒⠺⢍⡓⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣑⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡛⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⡓⠶⢬⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢒⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢌⣉⡙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⣉⣉⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡾⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⠈⠚⠉⠉⡷
⠀⠀⠀⠀⡼⠈⠓⢲⠤⠖⢚⣄⣥⣀⣱⣴⣶⠒⡷⠲⡔⠒⠈⢉⡀⠀⡷⠦⠒⠶⠚⢧⣶⡦⣤⠾⡄
⠀⠀⠀⠀⣣⠀⠀⠘⡿⢸⠥⠒⠤⠖⠓⡏⢈⠛⣄⢃⠷⠔⢊⣩⡿⢋⢧⡲⢤⣄⡮⢶⣎⡃⣠⠀⡇
⠀⢀⡠⠼⢇⠁⠌⠄⠉⡦⠒⠒⣒⡩⡖⢻⡌⠀⢘⠿⢲⠶⠟⢭⡜⠁⠄⠀⠠⢾⣃⠀⠀⡟⢀⡱⠓⣄
⠀⠸⣄⣈⠉⠓⠒⠒⠠⠿⠭⠥⠀⠹⠷⠾⠭⠤⠮⡴⠓⣈⡀⠠⠜⠈⠀⠉⠉⠉⣉⣉⣉⣤⠤⢀⡴⠃
⠀⠀⠀⠈⢣⡀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠲⠶⠂⢰⡡⠊⠁⠒⠒⠒⠒⠚⠋⠉⠉⠉⠀⢀⠀⢠⠏
⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠲⠦⠤⠤⠤⣤⣀⣀⣀⣀⣀⣠⡤⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⠴⣾⣲⠴⡲⣆
⠀⠀⠀⠀⠀⠀⢠⠚⠳⠵⠲⣆⠀⠈⣥⣼⢏⣿⡇⢉⠌⠉⢡⣿⠐⠦⠀⠀⠀⣠⣤⣴⡤⠿⠿⢆⢀⡀
⠀⠀⠀⢀⡴⠚⠛⣤⣄⣠⡇⠉⢻⣿⡧⢠⡈⢸⣿⣿⣠⠄⠈⢉⣿⣿⣷⣶⡟⠁⠈⠋⡀⢰⣠⡾⢛⠟⣳⠄
⠀⠀⠀⢘⣧⠀⠰⣾⣿⠟⠿⠲⣿⣇⣐⢦⡹⣼⣿⣿⣵⡶⠂⠈⢿⡟⠁⠄⢀⠀⣳⢴⣥⡘⠛⠛⢃⣀⣻
⠀⢀⣴⣿⡏⠀⣶⡏⠉⣀⣦⡆⢸⢿⣿⣤⣿⢟⡿⠙⣿⣿⢁⣰⣿⣁⣦⡼⢿⣾⣅⣾⣿⣿⣷⠦⣼⣿⣯⡄
⢠⡟⣿⣿⣷⡶⠿⢷⣏⣿⣼⡇⣀⣘⣿⠋⡴⠋⣤⢯⣿⣿⡿⢟⣿⣟⣩⠤⣤⡀⠜⠻⠿⢍⣻⣿⣿⣿⣿⡿⣦
⣾⣿⣿⣧⠀⠠⣀⡆⠈⣿⡿⢿⣿⣿⣡⠞⡁⡾⣫⣾⣿⣫⠖⣛⣉⠉⠻⡛⠿⠹⣿⢿⣿⣿⣇⣈⠁⢈⣿⡇⢹
⣿⢿⣿⣿⣤⣍⡛⠳⣴⡇⠀⡄⣿⣿⣧⣬⣼⣾⢿⣿⣿⣶⣾⣿⡿⢷⣦⣶⣾⣶⠈⠣⠈⠛⠿⠏⣠⣾⣿⣇⣼
⣿⠈⠻⢿⣿⣿⠡⠤⢼⣧⣼⠀⣸⡿⠙⠿⣿⣶⡾⣿⣄⣰⣋⣀⣤⣾⣯⣽⡿⣿⣿⣶⣾⡟⠻⢿⣿⣿⣿⢟⣹
⢸⡈⣷⣤⡉⠻⢷⣦⣄⣹⣿⣿⠿⠞⠲⣾⠛⠻⣖⣻⡿⢷⣦⣇⠀⢣⠉⢿⣧⡘⢿⣻⣿⣿⣦⡽⢟⣫⣴⣿⡿
⠀⢧⠹⣿⣿⣷⡦⠤⠉⠛⠛⠷⠶⣶⣦⣤⣦⣴⣈⣁⣴⣀⣉⣿⣷⣮⣧⣼⣿⠿⢾⣛⣛⣭⣵⣾⣿⣿⡿⣽⠃
⠀⠈⢧⠹⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⠃
⠀⠀⠈⢳⡘⢿⣿⣿⣽⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣟⡽⠃
⠀⠀⠀⠀⠙⢦⡙⢿⣿⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣛⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣝⠻⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣽⣶⣿⣿⣿⣿⠿⣫⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣌⣛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣿⣿⡿⠿⣛⣭⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣭⣭⣵⣶⣾⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠦⣄⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⣇⡀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⢴⠒⢣⡦⠔⢘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠖⠀⠀⠐⠠⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠙⠀⢀⠁⠠⡾⢸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⢻⠊⠀⣠⠀⡠⢰⠀⠈⠀⠈⢲⡀⠀⡠⠀⠀⢉⣽⣷⣶⣴⢂⡴⠒⠲⡄
⠀⠀⠀⠀⢄⠀⢄⠀⢀⡀⡀⡂⠀⠀⠀⠀⠲⠀⡐⠁⠀⠀⠁⠀⡀⡀⠄⠀⠀⠀⠀⠀⣠⣿⣮⡵⢭⣿⡌⢠⠄⣀⡟⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠶⠯⠅⠀⠾⠃⠈⣆⡀⠀⠀⠀⠀⠀⠈⠣⡤⠂⠸⡏⠉⠇⠀⠀⠀⠀⠀⠀⠉⠷⣟⣧⣾⡼⡗⠡⠂⠈⢳⣤⣤⢤⡄⠀⠀⠀⠸⢀⣴⣃⡀
⠀⠀⠀⠀⠀⡶⢀⡀⠶⠁⠀⠀⠁⠀⠀⠀⠂⠀⠀⢠⡽⠷⡆⠀⠁⠀⠀⠀⡰⠂⡤⠀⠀⢀⠀⡿⠤⠀⠑⠨⠀⢀⣋⠈⠂⢀⣾⣟⡭⢿⣯⣀
⠀⠀⠀⠀⡀⠀⠀⠀⢉⠵⠀⣠⣶⣾⣷⣤⡀⠀⠀⠀⠁⠐⠀⠀⣈⠂⠀⠀⡁⠄⠁⠄⠁⡄⡞⠀⠀⠀⠀⠀⠈⠁⢀⣤⠤⠾⢏⠣⣀⡔⣻⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣱⣿⡟⢘⢿⢽⡀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣠⣈⡀⢰⠃⢈⠸⠀⠀⠀⠄⠠⠊⠐⠐⠈⡓⢦⠘⣌⠮⠤⣴⣡⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣸⣿⢯⡉⣁⠞⡽⠉⠲⣄⠀⠀⠀⢀⣦⠈⠋⠉⠉⠑⠠⠍⠈⢠⡇⠐⠠⡺⠁⠔⠑⠶⠖⠾⢠⠀⠀⠉⠋⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠉⠓⠋⠀⠰⠞⠛⡟⠷⡒⣁⣀⣀⠰⠀⠀⠀⠊⠀⠀⡆⢁⠀⢀⡞⠒⠠⠌⠫⠄⠀⠘⠈
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁
⣀⣀⣀⣀⣘⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⡐⠉⠠⠀⠀⠀⠀⠀⠀⡠⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡈⠓⠔⡡⠀⠐⡘⠃⢐⡀⣨⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠜⠀⠀⠓⡄⠀⠀⠀⠎⠒⠓⠢⡤⠀⢤⢀⠗⠈⢱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠤⡀⠂⠀⠀⠀⣂⡈⠁⠀⠀⢠⠖⠈⠉⠍⠣⠀⠾⡗⢀⠖⠚⢼⠄⢄⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⡄⠄⠘⡀⠻⣤⠴⠆⡙⠛⠓⢄⠀⠀⡇⠀⠀⢀⡠⠄⣦⣈⣁⡉⠀⠀⣰⠀⠈⠁⠀⠥⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⡄⠐⡘⡀⠡⡴⠅⡘⠀⠀⠀⠀⣸⠤⠒⣇⢀⡰⠉⠁⠀⠀⠀⠈⢅⡱⠜⠾⣷⡀⠀⠔⢢⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣄⠔⡪⠉⣛⡛⠣⡀⠈⣦⡤⡕⡼⠁⡀⡴⠛⡐⠅⠀⠀⠀⠀⠀⠀⣃⠔⠁⣠⠏⠱⠎⠀⢸⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣠⣢⣎⡔⠉⠄⠌⢷⠑⡤⠉⠀⡙⢀⣬⡊⢈⡀⢰⣌⠙⡳⠂⣶⠴⢦⠋⢀⡾⢁⣀⠀⠁⠀⠌⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⡀⠀⠱⣀⠜⠙⡬⠆⠗⠠⣀⣡⠊⠀⠈⠁⠉⠁⠘⠷⠉⠀⠈⠑⢦⠔⣡⡤⠤⡈⠻⣀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⡀⠀⡂⠀⠙⠲⠀⠀⢸⠁⠀⠄⢤⠵⠤⠤⡔⠀⠀⠀⠀⠀⢠⠹⠋⠀⠑⠌⢤⠋⢰⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡮⡣⢄⡇⠀⠀⠀⠄⠀⠸⠰⠁⣰⠁⠀⠀⡰⠇⡄⠀⠀⠄⠀⠈⢀⠃⠘⠐⢢⡸⢔⢵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⠒⠤⢀⡺⠄⢠⣂⡇⠀⠙⡀⠈⠈⠁⢡⡀⢀⣀⣀⣴⢡⠮⠀⡒⠄⠒⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠉⠀⠒⠐⠈⠈⠩⠦⠤⠬⠥⠍⠁⠁⠂⠒⠀⠉⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠒⠷⠞⠉⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣾⠛⣆⣀⣀⠀⠀⣠⣤⡇⢳⡀⠀⢧⡀⠀⣀⣀⣠⣄⣀⠀⠀⣀⡀⠤⠔⠚⢩⠹⡇⠀⢀⣀⠀⣀⡾⠃⣀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⢴⠛⠀⠈⠀⣸⢋⡋⢀⡤⠧⡴⠷⠴⠶⢿⣿⢿⡉⡡⠛⡍⢻⡁⠆⠂⣀⣤⣄⣀⣸⠉⠙⠋⠈⠋⠉⣙⠻⣿⣏⠳⠶⠉⢷
⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠉⣿⠉⣻⠴⠚⢦⡴⠚⠉⢲⡇⢀⠉⠳⡌⢇⣹⠷⠒⠋⣉⣴⣾⠇⡹⢖⣚⡤⢤⢄⣮⣴⣶⣮⣹⠀⣤⠀⢸
⠀⠀⠀⢀⣀⣿⠉⠃⢈⣆⠀⠙⢶⣁⡤⠴⢤⠴⢚⣥⠾⣧⠐⢇⠀⢻⣿⣤⣤⣴⣮⣗⢋⡵⠋⠀⣈⠀⠀⣩⢽⠗⠀⠀⠈⣿⠊⠈⢧⡾⣤⡀
⠀⠀⡜⠉⠠⢤⣷⣄⣀⣈⠣⠀⢸⣧⠤⠴⠒⠒⢯⣠⡀⣹⢣⡀⢁⡼⢋⣤⣊⡩⠄⠈⠉⢧⣤⣬⣤⣤⠤⣭⠽⠶⠦⠤⠴⠧⠀⠒⠊⠀⢨⡇
⠀⠀⠳⠤⢤⣀⠀⠀⣉⡉⠉⠉⠛⠛⠒⠒⠒⠒⠒⠛⠛⠓⠒⠛⠚⠓⡿⠋⣁⡤⠤⠒⠒⠋⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⠤⠶⠖⠋⣠⠔⠋
⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠶⠶⠖⠂⣼⢠⠞⠁⠀⠐⠒⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠢⢀⠌⠀⠨⢤⠄⠄⠀⡄⠚⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡂⠀⠸⡄⠁⠁⢠⡾⠴⠥⣀⠀⢀⠀⡧⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⡀⠀⠀⠀⢤⠐⠛⠀⠀⢀⠆⠂⠀⠚⡀⠸⡞⠒⡤⠦⣥⠠⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠡⠈⠄⠳⡠⠴⢂⠚⠚⠆⠀⠀⡆⠀⠀⣀⠤⢼⣈⢃⡈⠀⠀⡄⠀⠁⠀⠡⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠰⠀⣄⣄⠀⡼⠅⡀⠈⠀⠀⣸⠄⠒⣇⢀⡎⠉⠀⠀⠀⠀⢥⠱⡚⠽⣆⠀⡀⠂⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠲⠔⡨⢂⡩⣍⡑⣄⢸⡶⢒⡘⠁⢔⢟⠉⠝⢄⣀⡀⠀⠀⠀⣡⠊⢀⡞⠉⠒⠀⢸⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠘⠚⢴⠀⢠⣀⢹⠈⡆⠀⠠⢁⠞⠆⡠⢆⠜⢘⣨⡉⠸⢟⡳⢁⠴⠓⠠⢤⡀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⠀⠒⠆⠈⢿⣀⠁⠑⡶⠀⠀⠀⢇⠀⠀⡀⠁⠀⠀⠀⠙⢧⡶⠉⢑⠄⢡⢖⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠧⡀⠀⠀⠀⠘⠀⠀⡃⡐⠁⠜⠉⠉⢉⠅⠀⠀⠀⠀⠀⠈⠆⢠⢀⠈⣃⢘⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠂⠅⡠⠀⣰⠀⣠⢀⠀⠘⡀⠐⠒⡉⡀⠀⠀⠀⢀⠌⣐⠀⡀⠄⠫⠑⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠈⠀⠒⠉⠉⠀⠠⠗⠤⠤⠲⠟⠦⠉⠉⠉⠈⠂⠈⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠤⠄⠀⠀⠀⠀⠠⠤⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⡀⡀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠂⡀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠳⢄⠀⡀⠀⠀⠑⠂⠉⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡆⢀⢜⠀⠑⣶⠒⣦⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠘⢇⢸⠁⡰⡀⠎⡇⠐⢂⠀⠀⠀⠀⠂⠱⢄⠀⠀⠁⠀⠸⠀⠰⢖⠢⢤⣀⣀
⠀⠀⠀⡠⣂⠵⡂⡉⢢⠄⠐⠒⠈⠉⠉⠉⡽⠄⡢⠰⢁⠄⠎⠢⣀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠖⡑⠠⡀⢱⣤⡀
⠀⢀⡾⡎⠁⠆⡈⡾⠁⠀⡠⠒⢐⢄⡠⢊⠜⠑⢦⠒⠂⢍⡀⢒⠨⠉⢡⠀⠀⠠⠤⠤⠤⡀⠀⢠⠀⠠⡀⠶⠀⠁⢸⠇⡅
⠀⠰⠀⠛⣈⣁⡜⠀⠀⢊⡀⢳⣼⣾⢗⡃⢅⠢⣡⡄⠧⠎⢥⣀⣠⢀⢠⠢⡀⠀⠀⠀⠀⠈⠢⡇⠀⠈⠠⡐⣤⢞⠍⡰
⠀⠀⢧⠀⠢⡀⠻⠀⠀⠢⣩⢛⡟⣁⠻⠂⠈⠁⢀⠄⣀⡀⠀⢡⠭⢡⠰⠑⢄⢹⢀⠁⢀⢱⢀⠐⢄⠀⢠⠀⡠⠊⡔⡃
⠀⠀⠰⠐⠠⡈⠉⠂⠠⠎⡸⠋⢌⣡⠶⣖⠒⠚⠍⠉⣉⣀⡠⠂⣭⡈⢰⡀⠱⡜⡇⡔⢀⡟⡎⣥⠂⡴⠇⠊⡠⠊⢀⠃
⠀⠀⠀⢀⠀⠈⠐⠢⠄⡀⠀⠁⠀⠐⠀⠈⠰⠖⠀⣀⠀⣅⠒⢛⣐⣲⣂⡱⠅⠤⠌⠙⠋⠐⠃⠉⢀⡠⠔⠊⠀⠀⡜
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠄⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠤⠄⠒⠉⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠄⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠑⠖⠋⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠑⢦⠀⠀⠀⠀⠀⠀⢀⣀⡸⠀⠀⠀⠀⠀⠀⠘⠦⣄
⠀⠀⠀⠀⠀⠀⡠⠤⠔⠂⠁⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠤⠂⠀⠀⠀⣀⣀⡇⠀⠀⠀⠀⠀⢠⠖⠉⢙⡤⣄⢀⡴⣺⣕⢦
⠀⠀⠀⠀⢀⠎⠀⢀⠤⣤⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢸⡄⠀⠔⠁⠀⢀⣤⣀⣘⠅⠀⠀⠀⠀⠀⠀⠀⠈⡳⢒⡽⠊⠹⣾⠏⠀⢸⢸
⠀⠀⠀⠀⢸⠀⠀⣿⠀⢀⡷⠀⢸⠁⠀⠀⠀⠀⠀⢀⡴⠋⢀⣠⣄⣀⣀⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠙⣄⠀⣸⢸
⠀⠀⠀⠀⠈⢢⡀⠈⠛⠛⠁⢀⠏⠀⠀⠀⠀⠀⠀⠸⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⣈⠢⣽⢸
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠐⡁⠀⠑⠌⣙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡞⠁⠀⠈⣇⠤⢤⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⢱⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄⡀⠀⡠⠖⠋⠉⠹⠶⣄⡤⠶⢼⡇⠘⡰⠊⡁⠀⡼⣀⣀⣀⠀⠀⠀⢸⠀⢄⠀⠀⢀⠠⢂⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠸⡟⠁⠀⠂⠀⠂⠀⢘⡏⣀⢉⡇⡞⠠⠊⡠⢾⠟⠁⠉⠈⠦⡄⠀⠘⢆⠀⠉⣉⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡿⠁⠀⠀⡇⠀⠀⠹⡏⢉⣿⡫⢍⡲⡏⢉⣈⡉⠳⢧⣔⡋⣴⠛⠀⠀⠀⠀⢠⠇⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢹⠣⢤⣀⡀⠀⠐⠀⣠⠟⠧⣴⠛⢖⠋⠍⢿⡴⣫⠟⠅⢈⡿⠀⠀⢀⣀⡠⠔⣻
⠀⠀⠀⠀⡼⠻⠷⠈⢳⡀⠀⠈⣇⠀⠀⠉⠉⠓⠒⠓⠲⠶⠷⠦⠤⠷⠤⠼⠶⠾⠾⠖⠚⠓⠚⠉⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠸⡄⢀⢂⠀⢻⡄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠹⡄⢂⠀⢀⠙⣆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣠⢴⡲⡄
⠀⠀⠀⠀⠀⠀⠹⡔⠀⠐⣆⠘⣦⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⠴⠚⠉⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡔⠔⢌⢦⡈⢷⡀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠁⠀⠠⡖⣏⠀⠀⠀⠀⠀⡰⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠢⡁⢵⣌⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠮⣑⠲⠤⠖⣊⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⣀⠀⠀⠄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡀⠐⠰⣦⡀⠀⣁⠈⢧⣀⣉⡈⣴⠋⠘⠀⠀⠉⢰⡢⡄⢸⣁⠒⠧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠷⠽⠾⣆⡙⠿⣷⡤⠉⢀⡉⢉⠓⠔⠐⠒⠂⠀⣌⣴⡷⢎⠺⠷⢶⢸⡏⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠈⠄⣠⣤⡤⢠⣽⣦⡤⣤⠶⠔⠀⠍⠠⠀⠀⡂⠀⢀⠈⠙⠿⣤⡀⣁⣠⠞⠁⠀⠉⠀⡙⠄⠤⡀
⠀⠀⠀⠀⠀⡰⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⢘⣿⣷⡄⠟⠒⠓⢮⣀⠰⠶⢿⣞⠉⠁⠈⠒⠶⢤⣝⡁⠀⠀⠐⠀⠐⡂⣠⠆⠴
⠀⠀⠀⠀⠀⢆⣠⡈⠐⠒⠚⠓⣤⣀⣀⣤⣾⣿⠟⠁⢀⠀⠀⠈⣿⡄⠀⠈⠻⣷⡄⠀⠀⠐⠀⠙⣿⡆⠀⠑⠒⢖⡧⠃⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠑⠙⠩⡛⠓⠋⠉⣿⠿⠿⢭⣴⣎⠀⢀⣽⡧⣿⠃⠀⠠⣸⣿⠀⡀⠄⠀⠀⠀⣸⢟⣄⣀⡗⢥⢶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠶⠄⠀⠀⡨⠛⡿⠿⠿⣿⣅⣀⣴⠟⣋⣏⣩⣲⡖⡒⠚⣉⡭⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠈⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠞⠀⢠⠀⠈⠀⠸⠓⠲⣄⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠹⣤⠴⢦⣀⡤⠗⠀⠀⣀⣀⣗⣁⠔⠊⠉⠒⢋⠅⠀⠀⢸⣃⡤⡄
⠀⠀⠀⠀⠀⣠⠶⠾⠁⠀⠀⠀⠀⠀⠉⠑⠀⢀⢶⠻⡈⡇⡟⡆⡶⣪⠕⣏⠉⠉⠻⡀⠀⠀⠛⠖⠒⢲⡀
⠀⠀⠀⠀⢀⣸⠦⠀⠢⠄⣄⡠⠔⢀⡤⢚⠒⣚⢧⠻⠅⣻⠮⠧⣅⡟⢡⠛⠀⢒⠤⡀⠀⠀⠀⠀⠈⢿⠛
⠀⠀⠀⢠⡏⠀⠀⢄⠀⡠⡺⡒⣄⠈⠫⠆⣏⣂⢳⡗⠞⣵⠁⡨⢮⣧⢋⠄⠶⢜⢤⡌⢯⢤⣍⢢⠤⣾⡤⠖⢦⡀
⠀⠀⠀⠀⢙⡇⢠⢶⢻⣌⡓⠞⣌⠖⠊⢁⡄⣀⣉⢳⣇⠱⣝⡍⠡⡛⢋⣮⡢⣘⠀⠀⡰⠒⠹⠶⠒⢋⠄⠀⠀⣷
⠀⠀⢀⣠⣾⡟⠃⠈⣮⡑⠷⠊⡎⠀⢙⡅⣤⣖⢒⣬⡣⣑⠀⡝⡏⠘⣿⢵⣌⣲⣝⡫⠔⠉⠑⢂⠈⣉⠥⡤⡶⠃
⠀⠀⢺⡀⠀⠈⠛⠚⠛⠻⡛⡏⢳⡄⢀⡀⣡⡴⣪⢎⣿⡟⢿⡕⡿⣦⢤⢋⢆⡸⢨⢷⣦⠕⠂⢛⠀⡨⡆⢇⡇
⠀⠀⢰⠃⡠⠒⠉⠀⢳⢤⠸⣒⡭⠋⢠⠖⠁⠠⢸⠚⡷⠾⠭⢊⠗⠒⡽⡀⠑⠵⠁⣪⢆⣀⠀⠉⡳⣘⢝⣾⠃
⠀⠀⢻⣀⣠⡄⠀⣤⣤⡄⡙⠢⡇⠸⠁⠀⠈⠞⣁⠤⠘⠒⠺⡿⣛⢭⠫⠙⡔⢒⡈⣝⣁⡈⠛⠭⢔⡵⠋⣸
⠀⠀⠀⠀⠀⣧⡅⠀⠙⠺⢾⣢⠿⣐⡗⣤⣈⠋⠰⢦⠻⡤⠄⣼⡉⢔⡇⠁⠸⠇⣄⠈⠀⠙⡖⠀⢠⠶⣦⡏
⠀⠀⠀⠀⠀⢹⣄⠀⠫⠂⠀⣈⡉⠓⠺⠯⠽⣴⣒⣛⣀⣰⣊⣚⣛⣁⣲⡭⠬⠿⠓⡤⠀⠰⠇⣴⣆⠗⣹⠁
⠀⠀⠀⠀⠀⠀⢧⠉⠂⠤⣀⡘⠁⠀⠪⠆⠀⢠⡆⠀⢀⢤⠀⠀⣤⡀⠀⢔⡄⠀⢻⡁⠀⠐⠀⡨⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠤⠀⠉⠀⠠⠬⠠⠤⠄⠒⠒⠉⠙⣄⣀⠜⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⠀⢿⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⡄⠀⢀⠘⣇⣠⣤⣀⠀⠀⠀⠀⣇⢼⠆⡇⠀⢸⣇⣀⡾⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠹⡄⢡⠀⠛⠁⠀⢹⡄⢠⡴⠶⠿⠊⠁⡇⠀⠘⢩⡟⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⣰⠖⠲⣄⠀⢀⣬⢷⡄⠹⠇⠹⡄⠀⠀⠀⠀⠸⠛⢻⣤⣄⡀⠀⠀⣴⠟⠳⣾⠁⠀⢀⡇⠀⠚⢻⡆⣀⣠⣀⠀⠀⠀⣀⣤⣤⡀
⠀⢠⡶⠲⢶⣿⢠⠄⢹⡾⠋⢳⣄⣀⠈⠉⠀⠉⣠⠾⠛⠉⠳⣴⠏⠀⠈⢷⡀⢸⡇⠀⠀⡀⣄⠀⡼⠀⠀⠀⣼⠟⠋⠀⠈⣧⠀⣾⠋⠀⠀⢹⣤⠶⠛⠳⡆
⠀⢸⡇⠀⠀⠉⠐⢂⠀⠀⠀⠘⢃⣹⡷⠶⠖⠲⣏⠀⢠⡀⠀⠙⠀⢠⣾⠋⠙⣛⠳⢦⣄⠉⠀⢰⠇⠀⡆⠀⠀⠀⠀⣠⠶⠿⠾⠇⠀⡆⠀⠘⠁⠀⠀⠀⣿
⣴⠶⠿⣦⠀⠀⠀⣁⣀⡀⢀⡴⠛⠁⢠⢒⡆⣠⠿⠆⣀⡙⠢⠈⠀⢸⡎⢣⡀⠣⡵⠀⠉⠳⣄⠈⠀⠈⠀⠀⠀⠀⢰⡇⠀⠀⢤⡐⢠⡇⣘⠀⠀⠀⠀⢠⡏
⣿⠀⠤⡤⠀⣰⠟⠩⡍⢻⡟⢁⣴⡦⠈⠉⣠⢿⣄⠀⠀⠋⠀⠀⢀⡀⠻⣆⠙⢦⡀⠀⢯⡷⠘⣧⣠⡴⠶⢒⡶⠛⠛⠛⢠⢠⡄⠁⢸⠀⢠⡠⠄⠀⠀⠙⠳
⠘⢷⣈⠓⠀⣿⠀⠀⢳⢸⣁⣀⣉⣀⠴⠚⠁⢀⡽⠗⠀⢀⡴⠚⠉⠉⠳⡌⠳⢦⣈⠓⠲⠤⠤⣿⠁⠀⠀⢸⡇⠀⠀⠲⣄⡈⠁⠀⠿⠀⠀⢁⣠⠖
⠀⠰⣟⣓⢀⣻⣄⣀⣘⣎⣿⣭⣭⣤⣤⣤⣾⣿⣤⣤⣤⣾⣤⣤⣤⡤⡤⠿⠤⠤⠭⠿⠷⠶⠶⠿⠤⠤⠴⣯⣿⣦⣤⣤⣤⣝⣂⣀⣀⣀⣐⣋⣀⣀⣀⣀⣠
⠀⠀⠘⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢉⡿⠃
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠻⣟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠙⣷⡶⠶⠶⠶⠶⠶⠖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⣐⣲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠐⠦⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢁⡞⠁⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⡀⠀⡀⠀⣀⠀⠀⢀⠲⢄⡀⡠⠄⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠠⡆⠁⠠⣄⠀⢘⠀⠼⠖⠀⠑⡆⢀⡀⠀⠉⠠⣶⣤⡝⠐⠃⠰⢃⣾⠑⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠠⠤⠀⣀⣀⣜⡀⠉⠀⠀⠘⠉⠀⠀⠀⠀⢲⣦⠀⡀⠀⡠⢜⡁⠀⠀⠀⠂⠚⠙⠁⠀⡀⣄⠀⠁⠀⢀⠀⠄⡀
⠀⠀⠀⠀⢀⠀⠀⠂⣠⡊⠀⠀⠁⣈⠀⠋⠉⠁⠀⠰⣆⣴⣤⣤⣀⠀⠠⠉⠀⠀⠉⠁⠀⠐⠂⠤⣀⢀⣶⣻⣿⣷⣦⡠⣈⠿⠒⢈⡀⠀⠒⢢⣾
⠀⠠⠃⠀⠀⠄⠀⠀⠀⠑⠄⠃⠄⠀⢀⠐⠄⠀⢀⣴⣿⣿⣿⣶⣿⣀⠀⠀⢈⡀⠀⠤⠀⠀⢀⠀⢄⠉⠙⣿⣿⣿⡿⣋⠀⠀⣈⡃⢈⠒⠊⡆⡀⢰⣆⣀
⠱⢆⢔⠈⢉⠀⠒⠀⠀⡁⠀⠚⠢⠂⠆⢰⣤⠔⠁⠄⠀⠐⡀⠒⠂⠀⠀⠲⡀⠈⠂⠀⡡⠀⠀⠂⠈⠀⠰⠈⡋⢧⠀⠃⢐⣤⠝⠐⡚⠃⠀⠀⠑⣢⡄⣤⠂
⠀⠈⠀⢁⠄⣅⠐⡠⢎⡀⢂⠀⠀⠀⢀⠹⡵⠂⠀⠀⠁⠄⠈⠁⠀⠀⠀⠲⣴⠀⠄⣀⣧⣤⣄⣈⠍⠈⠀⡆⡾⠓⠦⠀⠈⠃⠀⠆⠀⠀⠀⠀⠀⠀⡂⠁⣬
⠀⠀⠀⢨⡘⠞⠲⠀⠘⢀⡸⣄⠉⣀⠀⠄⡂⠀⠠⠀⠂⠀⠀⠀⠀⢖⠠⠰⠿⣦⠾⠿⣿⣷⣧⣼⠁⠌⢉⠛⠻⠀⠀⠉⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸
⠀⠀⠀⢧⠀⠂⠀⠀⢠⣼⠃⡿⡀⣠⣧⢶⡏⠀⢠⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠈⠁⠂⢾⡻⠟⢉⠠⡀⣦⣼⠆⠀⠀⠀⢀⠀⠹⡆⢀⣤⣴⣤⣄⠀⠀⣞⣱
⠀⠀⠀⢰⣄⠈⠠⡀⢀⡀⠉⠀⠀⠙⢧⠀⠀⠀⣸⢀⣤⣤⣾⣷⣤⡀⠐⠂⠀⠲⣂⠁⠀⢁⡤⡀⠩⠤⠄⠂⡐⢧⠂⠀⠁⠀⣢⢽⢿⣿⣿⣾⣧⡷⠚⢁⡏
⠀⠀⠀⠈⡿⢿⣦⣀⠀⡁⢰⡈⠁⠀⠈⠀⠀⠀⢉⣿⣿⣿⣷⣷⣾⣷⢠⡁⠀⠀⢀⣼⣀⠇⠂⠡⣶⡄⠲⠀⣶⢀⡅⠁⠀⡻⠋⠀⠘⡋⠝⠋⠁⣠⣴⣿⠇
⠀⠀⠀⠀⠸⡀⠙⠻⣿⣷⣧⣌⡀⠁⠈⠣⠔⠦⠮⠁⣀⣿⣿⡏⠁⡌⠉⠃⡀⠈⠀⠌⠀⢀⡀⠀⢨⠀⢀⠀⣉⠀⠠⠤⠐⠂⠈⠀⠀⣀⣤⣶⣿⠟⠉⡘
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠍⡛⠿⢿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠉⠀⠁⠈⠉⠀⠉⠉⠈⠁⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⠿⠛⢉⡄⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠙⢆⠈⠀⠰⠅⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠤⡉⠑⠒⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠒⠚⠉⠁⠀⠂⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠤⠤⠠⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠖⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⠉⠉⠩⠖⠒⣦⠊⢾⢤⣤⣤⣀⣀⣠⡶⠒⢒⣶⡀⠦⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⠀⢀⠀⠀⢰⠗⡤⢒⣉⠉⡉⠉⠉⣤⢴⡀⠐⠚⠒⠖⠂⠈⠦⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⢠⣷⠖⠂⠘⠁⢀⡀⣨⣾⠃⢸⠱⠎⠀⢊⠁⢀⣄⣀⠀⠁⣨⣷⣿⠻⣦⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⢤⣧⠟⠁⠀⠀⠀⠀⠀⠀⣅⣀⡴⣟⢀⡀⠀⢁⡀⠀⠀⢉⣬⡾⡁⠔⠋⠀⢻⡇⠀⠀⢼⠤⡀
⠀⠀⠀⠀⠀⠀⣀⠆⠝⢿⣿⣿⠏⡄⠀⠀⢰⠂⠈⠁⠀⣿⠙⣇⠈⠁⠼⣈⠀⡤⠂⠀⠉⠁⣠⡸⠢⠉⠠⠀⢹⣦⢲⡏⠀⢘⣀⡀⡀
⠀⠀⠀⠀⡐⠋⠀⠀⠉⢻⣿⣿⠈⠣⠤⠐⢙⣄⠀⠀⠁⠙⢧⡌⠀⠀⠀⠈⠓⠀⠐⠀⣠⡖⠈⢠⡆⢟⡛⠛⣛⣿⡿⠃⠀⢠⠟⡂⢅⡉⠱⣓⠂
⠀⠀⠀⢠⠀⠀⠀⠠⣀⣽⣿⢿⠃⠀⠹⡄⠀⣻⡀⠀⠀⠀⠀⠑⡄⢀⠀⣠⠤⠤⣄⣀⣿⣿⠂⠀⠰⠾⢋⣽⡿⠋⢀⣀⣴⣿⣾⣽⣿⢅⣸⠟⣵⡄
⠀⠀⠀⠈⡀⠀⠀⠀⢺⣿⠁⠈⣂⠀⠀⠳⡀⠀⠉⠋⠉⠀⠁⠙⠛⠁⠀⠀⠀⠀⠀⠙⢧⡀⠟⠚⠳⢶⣽⣷⣶⣶⣟⣿⣋⢿⡿⠿⢿⣋⣍⡆⣩⠇
⠀⠀⠀⡇⠃⠀⡀⠴⣾⣧⠀⠀⠸⣄⠀⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢰⣿⣿⣿⣿⡟⢿⣿⣿⠀⡛⣆⡀⠙⠧⣤⠋
⠀⠀⢠⠃⠀⠠⢈⣻⣿⡏⠀⠀⠀⠛⣻⣷⠀⠀⠀⠀⠠⠀⠀⡿⠀⠈⠀⠀⢀⡄⡀⠀⠀⡄⢷⣰⡾⢻⣿⣿⣟⣱⡿⠟⠁⠀⠡⣿⣿⣷⣤⠀⡱
⠀⠀⠘⡃⠀⠀⢀⠰⢿⣷⠀⠀⢀⠈⣼⡇⠀⠀⠀⠁⠀⠃⠐⣣⡾⠀⢠⣤⠞⢛⣅⢀⢼⡇⠾⣿⣿⣷⣿⠿⠋⠁⠀⠀⠀⣴⣾⣿⣼⢿⠗⠁⠀⠘
⠀⠀⠀⠑⡌⠀⠐⠬⣠⠿⠳⣄⠀⢄⣉⣧⣠⣀⣀⠀⠳⠀⢠⣬⡀⢰⣿⠇⣂⠛⣾⡟⣏⣛⣡⣿⡿⠿⣥⣀⣠⣶⣤⣤⣴⣿⢟⡯⠁⠀⠒⠀⠠⠄⣇
⠀⠀⠀⠀⠳⠄⣀⡵⠁⠀⠀⠻⣆⠀⠙⠙⠛⠛⠳⣷⡾⣤⢮⡾⣥⠹⢿⣞⣿⣿⣿⣯⡿⠋⠀⠀⠀⠀⠈⠉⠉⢿⡿⢿⣿⣷⢮⣁⠀⠀⠀⠀⠸⡔⣥
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠉⣳⣶⣤⣄⣘⣀⡉⠋⠉⠹⣹⠿⣫⡖⠻⠉⡀⠀⠀⣜⣤⠀⠀⠀⠀⠄⠀⠐⠆⣠⣿⣯⣽⢤⠷⠚⠦⠖⠂⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⡀⠈⠛⠺⠿⠿⣿⣿⣶⡦⣤⣷⡿⠋⠠⠀⠀⠀⠿⠀⠈⠻⠆⢦⢸⠃⢀⣠⣴⣾⣷⠻⠋⠁⠀⠀⢀⣀⣠⠄⢀⠰
⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠦⢿⣿⣿⡀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠘⠀⠀⠀⠈⣠⣾⡿⢟⡯⠋⠀⠀⠀⠀⠀⠀⢈⡉⠀⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠱⠄⠲⠄⠀⠀⠁⠀⠀⠀⠀⡰⠛⢿⣷⣶⣦⣴⠶⠲⠤⢤⣤⣀⡀⠤⠖⠒⢿⣿⠍⠊⠉⠀⠀⠀⠀⠀⠀⠄⠈⢁⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠠⡀⠀⠀⢀⣀⣤⣭⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠒⠒⠶⠶⠖⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⢀⡠⠠⢄
⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⣠⠶⣾⣁⣸⣤⠔⣯⢤⡛⢲⡙⣩⣵⣀⣴⣳⣲⡄
⠀⠀⠀⠀⠀⠀⢸⠘⠁⡠⢲⡠⡎⡉⠻⠧⡀⣅⣼⢛⡡⠞⣷⠎⠻⠅⠰⠏⡭⠛⣭⠠⠤⡄⣐⣦
⠀⠀⠀⠀⠀⠀⡼⠯⣙⡅⣨⣿⢟⣢⢀⣄⡹⢌⣹⣻⢷⠥⡖⠓⣻⣷⢖⡭⣵⣦⠤⠵⢾⣿⡟⣽
⠀⠀⠀⠀⠀⢸⣗⠦⢭⣜⣏⣿⣛⡉⠅⠈⠉⠲⣩⡿⣸⠛⠉⠉⠙⡳⣾⢔⣏⣀⢀⡤⠤⢚⣫⡿
⠀⠀⠀⠀⠀⠈⣿⠛⠒⠒⠦⠥⠬⠭⠭⠉⡉⣉⣉⣉⠉⠉⠉⠉⠭⠭⠭⠍⠀⠒⡒⠊⠉⢀⣀⣷⣀⣴⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⠒⠲⠀⠀⢶⡛⠆⣴⣳⢠⡀⣴⣳⡄⠰⡛⠙⣦⠰⠚⠁⣴⠊⠉⠉⠉⠉⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠘⠧⡼⠷⠞⠉⢰⣈⣅⣫⠉⠙⢦⠷⠞⠁⠀⡠⠼⠷⠤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠖⢶⡅⠠⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠐⠊⠀⠀⠰⠶⠎⠉⢣⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠙⠮⠮⠷⠄⠀⠈⠐⠂⠤⠀⠀⠀⠀⢀⣀⣀⠀⠀⠠⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢠⠃
⠀⠀⠀⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣀⠜
⡀⠤⠀⠀⠾⠶⠖⢚⣓⣀⣠⠤⠤⠶⠶⠆⠀⡀⠒⠠⠤⠀⠀⣠⡄⠀⠀⠀⠑⠤⢄⣀⢀⣠⡤⠞⠉⠉⠁
⠙⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⣄⡀⠈⠉⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣴⡋⢳
⣠⠐⠂⠀⣐⣀⣀⣀⣀⣀⣀⣀⢀⣐⣒⡚⠋⠉⠦⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠊⠳⢦⡤
⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠁⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⢒⡂⠭⠉⠙⢉⡉⠉⠉⠉⠉⣉⣉⣉⣉⠉⠉⠑⠒⠲⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣛⣭⠶⠚⠉⠀⡠⢒⣈⠝⢶⣚⠶⣿⣭⢿⣣⣭⣎⣶⠛⠷⣖⢶⠲⢶⣦⢬⣍⠙⢲⢤⡀
⠀⠀⠀⠀⠀⠀⣴⢟⡵⠾⢿⠀⣠⡠⢜⡣⣴⢛⡭⣴⡯⣞⡸⠷⣼⣟⣿⣋⣽⢾⣄⠀⠈⢈⠀⠘⢨⠸⢮⠷⣴⢍⠻⣷⣄
⠀⠀⠀⠀⠀⣼⣿⠁⠁⡤⢚⣏⠻⢌⠹⢿⡯⣽⣿⣭⣤⣌⣽⢿⣦⡿⢫⣗⡾⠓⣿⠛⢿⣿⣷⣮⡽⣾⡧⠔⣿⡌⡇⠛⢫⡇
⠀⠀⠀⠀⠀⣿⣷⡀⢮⣭⠿⣶⣗⣾⣖⣛⣳⣹⣯⣰⠗⡲⣿⠿⣭⡻⣿⠬⣽⠛⣩⡦⢜⣳⣏⡻⢵⣖⣿⣛⣅⣯⡗⣄⢾⡷
⠀⠀⠀⠀⠀⣿⠙⣯⣳⢽⣛⡿⢽⡦⣌⣙⣉⣫⡵⣟⣳⣯⣿⣿⣧⣽⡿⠷⣾⡿⠅⢀⣠⠜⣗⣼⣋⣩⡽⣿⡿⢿⣽⡿⢫⡇
⠀⠀⠀⠀⠀⢹⡆⠀⠉⡛⢲⢭⣍⡘⠲⣟⣳⢀⡞⢳⣶⣾⢷⠿⠟⣾⠿⣿⣶⣻⣾⢏⣻⠆⣽⣒⣾⣯⢿⣟⣿⢿⣻⠃⣼⠃
⠀⠀⠀⠀⠀⠀⢷⠀⢰⠀⢸⠐⠦⣭⣙⡒⠲⠯⠴⢾⣿⣷⣤⣷⣤⣈⣎⣁⣿⣷⣾⣿⣿⣿⠿⠿⠛⠛⠉⠹⠁⢸⡟⢰⡟
⠀⠀⠀⠀⠀⠀⠘⣇⠘⡄⠀⠀⠈⠐⠂⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠒⠒⠉⠉⠀⠀⠀⢀⢢⠏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠤⠤⠀⠀⣀⣤⠤⠤⠴⠖⠛⣉⡥⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠤⠤⠤⠶⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠳⢦⡀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢀⡴⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢰⡏⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣀⣀⡀⠀⢀⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠟⠀⠀⠀⠀⢰⡆⠀⠀⠀⠹⣦⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠻⣶⠋⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠷⣤
⠀⠀⠈⣧⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢠⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣄⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⡿⠀⠀⠀⠀⢻⡄⠀⠐⣦⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⠻⣦⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢠⡶⠛⠁⠀⠀⠀⠀⠀⢻⣄⠀⢹⡄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠉⢿⡀⠀⠀⣰⠇⠀⠀⠀⠀⣿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⡾⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣼⠃⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠞⠁⠀⠀⠀⠀⣸⠇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠸⣧
⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⡏⠀⠀⠀⣀⠀⠀⠀⠀⠘⣷
⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣀⢻⣄⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⢿⡀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡿⠶⠶⠶⠛⠉⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠸⣇⠀⠀⠰⠶⣤⣤⣤⣤⠶⠿⣦⡀⢹⡆⠙⠳⣦⣄⡀⠀⠀⠀⠈⠙⠛⢻⡇⠀⠀⠀⠀⡀⠀⣷⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣷⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⢸⡇⠀⠀⢀⣼⠃⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⣇⣤⡶⠟⠁⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢸⡇⠀⠀⠀⢸⡏⠀⠀⠀⠀⣰⡟⠀⠀⢀⣀⣴⠄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⢠⣤⣤⡴⠶⠛⠛⢷⣄⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣼⠋⠛⠛⠛⠋⠉⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⡀⠀⠀⢸⡇⠀⠀⣸⠇⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⣤⠴⠶⠶⠶⣤⡀⠀⠀⢹⡇⠀⠀⢸⠇⠀⢰⡟⠀⠀⠀⢀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀⢿⡀⠀⣿⠀⢠⡟⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣄⣿⣰⠟⣀⣤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠮⢤⡀⢈⠖⠉⠁⠈⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠁⠀⢠⡇⠸⣇⠀⠀⠀⠀⠀⠣⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠞⠋⠀⠀⠀⠀⠀⢇⠀⠙⢧⢰⣠⠞⠉⠉⢻⠉⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠰⠀⠀⠈⠣⣴⠛⠋⠓⠀⠀⠀⠘⢗⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢽⡄⠀⠀⠀⠀⠀⠈⠘⠓⢄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⡀⣡⠊⠀⠀⠀⠀⠀⢷⠀⠀⠀⢠⠀⠀⠀⠀⢸⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢇⠃⠀⠀⡀⠀⠀⢀⡞⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⣾⠘⢀⡴⠋⠀⠀⠀⣸⠀⠀⠀⠀⠀⣧⢠⠄⠐⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠳⡀⡇⣴⠊⠀⢀⠀⠀⠀⢱⡇⠀⠀⡄⠀⢳⠇⠀⠀⠘⡆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠱⡇⠃⢀⡔⠕⠈⠀⠀⢾⡀⠀⠀⠃⠠⠘⢀⠆⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠐⡄⡇⣇⠎⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠆⠖⠉⠀⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠘⡇⡿⢀⠔⠋⠀⠀⠀⢯⡀⢰⣄⠎⠌⠀⡀⠸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⡄⣧⢱⠎⠀⡀⠀⠀⡤⠚⠃⢠⢏⠌⡠⠎⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⠀⡰⠁⠀⠀⢳⠀⡠⢃⠞⢉⡶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠸⢸⡜⠁⠀⢠⣢⢞⠟⢡⠋⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣴⠘⡇⠀⠰⡿⣠⠊⡰⠛⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⡇⢶⢺⠟⠁⣼⠕⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏⠀⢇⣸⠏⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⣇⣠⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣀⣸⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠔⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⢤⡀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠆⠹⣆⠀⠀⣠⠟⠁⠀⠀⢰⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⠏⠀⠀⠐⢀⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢠⣴⢃⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠚⢳⡈⣧⢘⡇⡈⠉⠉⠉⠉⠓⠲⠖⢀⣴⣋⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠑⢭⣳⣷⠐⠂⠀⠀⠉⠀⠀⣴⠏⠈⠙⠫⡀
⠀⠀⠀⠀⠀⠘⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢿⢦⠡⠀⠀⢀⠰⢼⠃⠈⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠹⡶⢥⣀⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⢀⣠⠾⡾
⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠈⠉⠛⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠒⠒⠒⠛⠉⠉⠀⡸⠁
⠀⠀⠀⠀⠀⣞⠛⠁⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠓⢢
⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠭⣛⠛⠶⠤⢤⣄⣀⣀⣀⣀⣀⣠⣤⠴⠾⢟⡶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠠⠤⠤⠤⠤⠤⠤⠒⠒⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠉⠉⠑⠲⢤⣀⣀⣀⣀⠀⠀⢀⡴⠒⠒⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡖⠉⠀⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⢄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠐⠈⠀⣀⡀⣈⡦⣄⣀⣠⣄⡀⠀⠀⠐⡀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠓⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢀⠴⠒⠒⠚⠋⣁⡤⠤⣥⣀⣀⣉⠛⠋⠉⠙⠳⣄⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠢⢈⡼⠋⠀⠀⣠⠖⠋⠀⠀⠀⢰⠊⠉⠙⠦⣄⣀⠀⠀⠈⢧⠀⠀⠀⠀⢹⠙⢦⡀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡠⠖⠉⠀⢀⡴⠋⠁⠀⠀⠀⣠⠤⠊⠀⠀⠀⠀⠐⠉⢳⡄⠀⠸⡆⠀⠀⠀⠘⡄⠀⠻⡄⠀⠀⠸⣥⣀
⠀⠀⠀⣠⠞⠀⠀⠀⢠⠏⠀⠀⠒⣲⠋⠀⠀⠀⠀⠀⢰⠃⠀⠀⠑⠀⠀⠀⠀⠀⠀⢳⡀⠀⢳⡀⠀⠀⠀⠙⠢⢤⡘⣆⠀⠀⠀⠈⠳⡄
⠀⣠⠞⢁⡴⠤⣄⠀⡏⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⡀⠳⡄⠀⠙⠲⣄⡀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢠⠇
⠀⡇⠀⢸⠀⠀⠈⠳⣷⣠⠤⣴⡃⠀⠀⠀⠀⡤⠒⠉⠀⠄⠀⡀⠀⠀⠀⠈⠂⠀⠀⠰⠀⠙⣆⠀⠀⠀⠉⠳⣄⠀⠱⣸⠀⠀⠀⠀⣾
⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⡖⠀⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⢻
⠀⠈⣆⡼⠀⠀⠀⠀⡀⠔⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠘⡀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡴⠃⠀⢸⠀⠀⠀⠀⠈⢣⡀
⢠⡞⠉⠀⠀⢀⠂⢁⠀⠀⠀⢀⡟⠀⠀⢀⠴⠁⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠡⡐⠀⠀⠀⠀⡏⠀⠀⣴⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠹
⣸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⡟⠀⠀⢰⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢠⡐⠀⢰⠧⡀⠀⢧⠀⠀⠀⠀⠀⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠠⠍⢢⡟⠀⠈⠢⢘⡆⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠓⢀⡴⠚⠀⠀⠀⠀⡞⠔⡁⠊⠀⢠⠏
⢹⠀⠀⡇⠀⠀⠀⠠⡀⠀⠀⠀⠂⠈⠛⠲⢤⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠞⠀⠀⠀⠀⢀⣾⠁⠈⠀⠀⠀⢸
⠘⡇⠀⢠⠀⠄⠀⠀⠀⠀⠂⠠⠄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠒⠒⠒⠲⠦⠤⣄⣀⣇⣰⠃⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣸
⠀⢱⡀⠀⢂⠈⡀⠀⠀⡀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠤⠄⠀⡀⠀⠀⠀⠀⢀⠠⠂⠉⠙⣇⠀⠀⠀⠀⣠⠟⠂⠈⠀⠀⠀⠀⢀⡇
⠀⠀⠳⡄⠀⠡⡈⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠁⠒⠀⠐⠁⠀⠀⠀⠀⡟⠀⠀⢀⠴⡉⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠙⢦⡀⠈⠀⠀⠀⠀⡇⢀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⢀⡤⠞⠛⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠇⠀⠠⢀⡀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣀⠀⠀⣀⣠⠤⣶⠶⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠘⠀⠀⠀⠀⠁⠒⠒⢂⡴⠒⠲⢤⡀⠀⠀⠀⣠⢞⡴⠚⠉⠉⠉⠉⠉⢉⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣤⣤⣤⡤⠤⠖⠋⢠⠏⠉⠲⣝⠲⠴⠚⡵⠋⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⣏⠀⠀⠀⠈⠓⠶⠚⠁⠀⢀⣀⡤⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣲⣦⣤⣤⣴⣶⣒⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠶⠅⣈⣡⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡂⢀⣼⢟⢗⠄⢮⣼⡹⣤⠶⠄⠐⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⣴⢌⡭⢅⣈⠀⠃⠞⠐⠄⠢⠛⢽⡍⢀⠀⢀⣵⡔⢤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⣧⡹⢌⣄⢚⠜⠀⠰⢂⠀⠀⠈⣄⠼⠃⠀⣦⠈⠳⠭⠴⠋⡂⠉⠀⠂
⠀⠀⠀⠀⠀⢀⠀⡄⣚⣀⡉⠒⣒⠁⡛⢢⠀⠀⣀⠀⠲⠀⡦⠧⣙⠎⠀⠀⠀⣀⣖⣠⡄⢐⡀⡏
⠀⠀⠀⠀⠀⠈⠄⠀⠑⢄⣈⡉⢹⢳⠉⠢⡝⠉⠂⠀⣀⠀⠘⠠⠬⠞⠤⠄⠃⣀⣾⢞⣣⡶⠂⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⢥⣄⣐⣓⣤⠚⢇⠀⡊⢁⠀⠘⠀⠌⡀⢠⠉⠋⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠋⠠⠀⠛⠀⢀⣀⠀⡄⣀⢕⣀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠉⠀⠀⠀⠀⠀⠀⠠⠭⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⢀⢀⠀⠀⠀⡀⡔⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠀⠈⠉⠉⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⠲⠀⠀⢠⣶⣦⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⠀⠘⣶⣦⠀⣼⢹⠁⠠⡆⠀⡰⠷⠰⢀⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢻⠀⠀⠀⠘⠁⠀⡿⠞⠀⠀⠹⠞⠃⠀⢀⠄⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⡦⠀⠀⢹⡆⠀⠀⣶⠄⠀⠀⠀⠕⠀⠀⢰⢀⡋⠀⠻⣷⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠄⠁⠂⠀⠀⣿⠀⠠⢿⣦⠀⠀⠠⠀⣆⢰⡼⠊⣀⠔⠘⢧⠞⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠸⠀⢀⠘⠒⠀⠀⠈⠀⠘⠃⠀⠀⠂⡄⠙⡌⠀⠊⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡴⠂⠀⠀⡇⡼⠁⠀⢀⢴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠉⠀⢤⠀⠀⠸⠃⢀⡤⠟⠋
⠀⠀⠀⠀⠀⠤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠏⠀⠀⠀⡀⠀⢀⠄⢀⣬⡆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠠⠀⠠⠒⠀⡀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠄⠀⠀⡄⣠⠂⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⡧⠀⠀⠈⠀⣀⢤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡅⠄⠘⠀⠌⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠐⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠠⡄⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⣇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠈⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⠄⠀⠀⠂⠀⠀⠂⠀⠀⠀⠉⠈⠙⠉⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠄⠨⠀⠀⠀⠀⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⡚⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⢠⡶⢟⠛⠿⠖⠩⣶⣤⡂⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠉⠲⠾⠽⣽⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠐⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠒⠒⠒⠒⠒⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠋⣁⣠⣤⡶⠶⠶⠶⠒⠲⠶⠶⠶⢤⣄⣈⠙⠲⢤⣀⠀⠀⢀⠀⠀⠀⣀⣴⣾⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡈⡻⠆⠁⢀⣠⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡾⠛⠁⠀⠀⢀⡴⠒⡛⢛⡭⠟⠽⠿⠉⣻⣶⣤⣤⣀⠀⢀⠀⠉⢀⣠⡾⢿⡏⠁
⠀⠀⠀⠀⠀⢀⡴⠃⣠⡾⠋⠀⢀⣠⣶⣿⡿⡘⢱⣧⣍⡓⣉⣠⡯⠙⣟⣁⠠⡟⠷⠄⢀⣠⠶⠋⠁⠑⠄⠙⢦⡀
⠀⠀⠀⠀⢠⡞⠀⣴⠋⠀⢀⣴⡿⢫⠍⡽⡋⠀⣠⠀⠟⢳⠀⣩⠗⣚⠈⢩⣅⠉⣠⠴⠛⠋⢀⡀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢠⡟⢀⡾⠁⠀⢠⡾⢩⣤⡔⠛⢳⢿⣿⡟⢀⠰⡶⢊⢡⡎⠀⢘⡈⠩⠇⣿⣴⣄⣸⡞⡛⢆⡀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⡾⠀⣼⠁⠀⢠⡟⡤⣷⣶⡀⣸⠟⣁⣠⠏⣸⡔⠡⢤⡞⠁⢠⣤⣽⠟⣰⡧⠞⠉⣿⣿⡁⠀⣷⠀⠀⠀⠀⠈⣷⡀
⠀⠀⣸⠃⢰⠇⠀⠀⣾⠠⢁⠬⠁⣏⡉⠉⠉⠁⠀⢼⡁⠲⣶⠾⠿⠛⣋⣤⢞⡅⢀⡶⢌⠋⣈⢧⣶⣿⡀⠀⠀⠀⠀⢸⣧
⠀⠀⣿⠀⡾⠀⠀⢰⠓⢰⡞⢳⡄⠙⠃⣄⣀⣈⠛⡞⠳⠦⠬⠴⣶⡿⠋⢴⣿⣀⡘⠓⠀⠛⢯⢸⡏⢙⠌⠀⠀⠀⢠⠀⣿⡀
⠀⠀⡇⠀⡇⠀⠀⠀⠀⠘⣿⣷⣹⣷⣆⠈⠛⠻⣧⡈⢲⠟⠉⣉⣩⡇⡷⡘⢦⣠⣴⣂⡤⠂⣤⠷⢌⢻⣠⡄⠀⠀⠈⠀⣿⡇
⠀⠀⣇⠀⡇⠀⠀⣿⠴⣾⣿⣿⠁⠉⠀⢒⣀⡀⠈⣧⠌⢠⡊⢽⡟⢰⡧⡻⢈⠇⠠⣍⣤⠆⣤⣴⣯⡨⢾⡁⠀⠀⢠⠀⣿⡇
⠀⠀⣿⠀⠃⠀⠀⠈⠠⣿⠁⠙⡀⢲⠀⢀⡿⠿⣷⡇⣐⢚⣏⣆⠀⠀⡱⡡⠊⠁⢀⣶⡤⠞⢷⣇⣿⢳⣬⠁⠀⠀⢸⠀⣿⡇
⠀⠀⢻⡄⠀⠀⠀⠀⣄⣽⡷⢾⣤⣾⣿⣖⠃⣊⣛⣁⠁⡾⠁⢿⡀⢤⡜⢓⣶⣾⡿⠛⢛⣦⠀⡷⠃⣸⠏⠀⠀⠀⡆⢸⣿⠃
⠀⠀⠈⣷⠀⠀⠀⠀⠘⣷⠆⠈⣋⠉⢋⠀⠀⣼⠉⠻⣄⣀⣲⠛⠺⣦⠀⣾⠋⣩⢤⡈⠛⣯⠺⣦⣾⠅⠀⠀⠀⡰⢁⣿⡟
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⢧⡄⢉⡀⠉⠐⢀⢿⣷⢾⡿⠋⣸⣿⣷⠘⣷⣄⠃⢃⣾⠏⠀⣢⠆⣿⠏⠀⠀⠀⣰⢃⣾⣿⠁
⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠳⣾⣛⣛⣿⡷⢧⢮⣤⣤⠾⠛⢠⡟⠐⡃⠿⡿⠻⡇⠀⣨⣥⠾⠁⠀⠀⠀⡴⢁⣾⣿⠃
⠀⠀⠀⠀⠀⠘⢷⣄⠀⢄⠀⠀⠈⠻⣴⣟⠛⠠⢴⣎⣠⣤⡬⠡⣘⣎⣉⡷⠔⢂⣰⣆⡵⠃⠀⠀⠀⣠⠞⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠑⢄⡀⠀⠀⠉⠉⠓⠾⢿⣯⣽⣷⣭⣉⣀⣍⠀⠀⠈⠊⠁⠀⠀⠀⡠⠞⣡⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⡠⠔⣋⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣌⣉⠒⠢⠤⠤⢀⣀⣀⣀⣀⠠⠤⠔⢒⣋⣥⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⡖⢲⡶⢶⣶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢱⡏⢻⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑
⣀⠀⠘⠉⢲⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢢⠈⠁⠢⠀⠠⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⡂
⣽⡧⠀⠀⠚⠁⠀⠀⠀⠀⢀⠀⠀⡞⠀⢁⡴⢠⠿⢰⡇⢂⡆⡴⣰⣠⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⣁⣨⡀⠉⠱⡬⠁⠁⠉⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠋⠀⠸⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠣⠁⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⢈⡄
⠀⠀⡀⠈⠙⠛⠛⠒⠶⠶⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠞⠁⠀⠉⠁⠀⠈⠁⠀⠈
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⡩⠛⠭⡉⣣⠉⠉⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠐⢄⠘⡿⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⡄
⠀⠀⠈⠉⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠔⠁⠀⠐⢦⠀⣉⡤⣄⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡼⠀⢀⠀⣆⡀⠁⡀⡰⢂⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠠⠄⢀⠇⠀⠁⠀⠀⠀⠄⠘⠈⠜⢰⣧⠀⠀⢀⣌⠙⠋⠁⠁⠈⠶⠀⠤⠞⠀⠀⢀⠀⢀
⠀⠀⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⢸⠙⠛⡻⠛⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠄⠻⣷⣷⡄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢼⠀⡰⠁⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⣹⡲⠝⢲
⠀⠀⠀⣀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠐⠀⠀⠀⣰⡀⣷⡀⢐⢀⠀⠀⠀⠀⠈⠻⠗⢽⡁⠲
⠀⠀⠀⠛⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢢⠰⡜⡇⠀⠀⠁⠀⠀⢀⡤⠂⠀⠱⣏⣤⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⠀⠀⡀⠈⡆⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗
⢀⣴⠞⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢠⡀⠀⠘⣇⣀⣀⠀⠀⠘
⠁⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢷⣄⠀⠀⠀⠸⠃⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠶⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠶⠿⢛⣷⣀⠀⠀⢀⣀⣠⣤⣶⠶⠟⣛⣻⣭⣧⣤⡶⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⡯⡆⠛⢀⡚⠩⡬⢻⣷⣿⣛⣭⣭⡶⠶⠿⠛⣛⣉⣩⣥⣤⣶⠶⠾⠟⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣩⡥⠛⠯⢀⡙⠣⠴⠀⣿⣟⣭⣥⡶⠶⠾⣟⣛⣻⣭⣽⣷⠷⠶⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⡚⡍⣩⡤⠷⣶⣞⣫⣭⣭⣷⠶⠾⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠿⠾⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣤⡶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⣴⡿⠙⢛⡛⠉⠁⣀⠙⣛⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠟⠛⣋⡡⠆⡀⠉⠩⣤⡄⠙⠁⠉⣡⡝⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠶⠿⠉⣀⣤⠆⣉⠀⡈⠋⠀⠶⠶⠤⠋⢋⠀⠐⠷⣤⡌⠛⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢋⣤⡿⠉⠁⠛⢃⣈⣈⠺⢿⡟⠋⠘⣉⠉⢧⣤⡃⠀⠙⣂⡀⠻⢷⣶⡆
⠀⠀⠀⠀⠀⠀⢰⣿⠛⠡⠟⠉⢀⣐⣛⣁⣀⣈⣉⣀⣐⣒⣤⣀⣛⣋⣀⣀⣈⣁⣀⣀⣉⣁⡀⠳⠈⣻⣆
⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣧⠉⠋⠀⠛⠃⠀⠚⠂⠒⠒⠀⠒⠒⠀⠲⠶⠀⠲⠖⠀⠶⠶⠀⠰⠶⠀⠐⠒⠂⠀⠛⠃⠘⢻⣿
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠿⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⡶⠶⠿⠛⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠷⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⣄⣤⡤⠔⠒⠈⠉⠉⠉⠁⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢿⣠⣯⡠⠤⠀⠘⠃⠀⠾⣃⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⣤⣤⠶⠶⠶⠖⣲⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠫⠉⠩⣿⣦⠀⠰⢾⡏⠈⢡⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⢀⣀⣁⠀⠀⣠⣄⣀⡀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⢹⣿⡋⠀⠀⠀⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠢⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⣶⡄⠠⠀⠀⢀⡀⠖⠉⠶⠶⠶⠚⠛⠛⠐⢦⣸⠆⠀⠀⠀⠀⠀⠲⢤
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠠⠎⢀⣦⢀⠀⠀⠀⠀⢀⡄⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠄⠐⠛⠳⢦⡀
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠑⢳⡶⠒⢾⡍⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⢀⡾⠁⠀⠛⠿⠷⣦⡀⠀⠀⠀⠀⣄⡀⠊⠀⢈⡾⣀⠡⣄⠴⠀⠀⠀⠀⠀⠀⢠⣤⡴⠖⠀⠀⠀⠘⢧
⠀⠀⢀⡾⠁⠀⠀⣀⣤⣄⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢀⠞⠀⠀⠀⠀⠉⠉⠉⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⢃⡴⠁⠀⠀⠀⠀⠐⠆
⠀⣸⠶⠶⠒⠒⠀⠴⣴⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⣟⣴⣁⣤⠶⠒⠒⠓⠲⣤⡀
⢠⠃⠀⠉⠭⢭⣤⠒⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠆⠀⠀⠀⠀⠀⠀⡜⢹⣿⣿⡿⠛⠛⣚⡛⠲⢦⡀⠈⢻
⡟⠀⠀⠀⠀⠀⠉⠁⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⣟⡟⠁⠀⣀⠒⢬⡓⠀⢹⡆
⠇⠀⠀⠀⠀⠀⠀⠀⣀⢤⡘⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠎⠀⠈⡿⠁⠀⠀⠈⠓⠀⠀⠀⠀⡧⠰
⠈⢦⡀⠀⠀⠀⢀⠞⢁⠀⠙⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠈⠑⠂⠶⠈⡴⠋⠀⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢇⡤⠤⢤⡤⢤⡤⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠈⢃⠄⠊⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⠚⢁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠃⣰⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣄⠀⠄⢀⣼⠄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⢐⠥⠊⠀⠉⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠐⠢⠀⠀⠋⠘⠇⡠⢔⣩⠶⢥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠲⠶⠮⠥⠌⣈⣀⣀⣀⣀⣁⣀⣉⣐⣉⣁⣐⣷⠒⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣬⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⠘⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢤⣀⠜⠀⢰⠂⠁⢸⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⡏⠉⠁⠀⠀⠉⠈⠉⠀⢠⠒⠉⠋⠀⢠⡃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⡟⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠄⠀⢀⠃⠀⠀⠀⡉⠉⠓⠋⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢼⠀⠀⠒⠇⠀⠀⠀⠀⠀⠈⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠁⠀⡁⠉⠀⠀⠀⠂⠀⠀⠀⠀⠸⠀⠀⠎⠘⡀⠀⠀⠠⠀⠀⠀⡀⠂⠀⢀⠀⣹⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠲⠇⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠄⡀⠀⠠⣇⡀⠀⠀⠀⣠⠀⡄⠀⠀⢠⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠀⠠⠀⠀⠒⢤⠠⡀⢈⠀⡄⠐⠂⠘⢂⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠆⠘⠀⡀⠀⡀⢀⢀⠈⢀⠂⢀⠒⠀⠀⠀⠠⠀⠀⠀⠈⠊⡠⠀⢠⠀⠀⠀⢀⣈⣙⠆
⠀⠀⠀⠀⠀⠀⠈⢧⢀⡀⠀⠀⠀⠀⠀⢙⡋⠒⠁⠈⠁⡆⠀⠊⠀⠀⠹⡀⠀⡐⠀⠀⠀⠀⠀⠀⠁⡀⢸⣯⠵⠚⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠧⡄⠀⠀⠀⠀⣯⣄⠀⠀⠀⡠⠔⠀⠀⠀⠀⠴⡁⠰⠃⠀⠀⠐⠀⠀⠃⠁⠀⢨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠀⢰⠶⠞⢺⡉⠀⠀⢱⠄⢀⠄⠀⠀⡠⢠⡀⠀⠀⠀⢄⠀⠀⢀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣧⠀⠀⠘⡂⠠⡂⡤⢈⢀⠀⠣⡀⢀⡤⠊⠐⠀⠀⠐⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣤⡀⠉⠂⢘⠀⠀⠀⣀⡴⠁⠀⢀⠐⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣄⠀⠀⠉⠞⢀⠁⠑⡀⠀⠒⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠻⣄⢀⣠⡀⣑⠀⠁⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠄⢸⡛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠙⢀⡵⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⣴⣀⣴⢂⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣴⠎⢹⢧⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⡀⣀⡄⠀⣄⠀⢠⣷⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠐⠈⠉⠀⠀⠃⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠉⠑⠒⠤⠀⠀⠀⠀⠔⠋
⠀⠀⠀⠀⡐⠊⠀⠀⠀⠀⠀⠀⠄⠀⠐⠃⠐⡄⠂⡎⠀⡈⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⣘⠆⠱⠀⠇⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠄⠒⢀⠀⣼
⠀⠀⠀⠀⢹⠳⢦⣄⣀⠀⠈⠁⠀⠀⠀⠄⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹⢀⣀⡤⠶⠋⠆
⠀⠀⠀⠀⠀⢦⡞⡉⢉⠙⠓⠶⠶⠶⠤⣤⣤⣤⣬⣤⣤⣤⣤⠤⡤⠴⢶⠖⠛⠉⠡⠦⣀⠸
⠀⠀⠀⠀⠀⠈⢷⠒⠂⠀⣁⢆⠠⠎⡞⢀⠀⡄⡄⢊⢠⡄⣀⣀⡢⣌⡐⣑⣡⠺⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠣⡊⠠⠉⠛⢷⣔⠹⠖⡄⠲⢔⣿⣦⢼⠁⠀⡸⣀⣤⠏⠉⠈⠺⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢴⠒⣸⣇⢠⣿⣄⣀⡠⠠⣯⢀⡂⠒⠁⢸⣧⠃⡇⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡀⢨⠛⣻⣬⣦⣎⣆⣾⡥⠃⣿⡵⠛⠃⢈⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣤⣁⣢⣿⠊⣿⢋⣴⠾⢇⣨⣵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣛⠛⠚⠛⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄

⠀⠀⠀⡆
⠀⠀⠀⡇
⠀⢀⠂⠁
⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⠀⠘⠓⠠⠄⢀⠀⠀⠀⠤⠚⠁⠂⠀⠀⠀⢀⠤
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠊⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⣤⠤
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⢿⣿⡇
⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠟⠁⡴⠚⠋⠉⠁⠀⠀⠈⠉⠳⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠋⠀⠀⠀⠔⣡⣍⢢⠀⢀⣦⣤⡑⢠⢋⢡
⠀⠀⠀⠀⠀⠀⢛⢆⠀⠀⠀⠀⠰⣿⣿⠁⡌⣿⣯⠀⠀⠀⠀⠠⠈⣿⣿⢠⠀⢸⡿⣿⠧⠜⣎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠁⡀⠀⠀⠀⠙⢿⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⣠⢷⣦⣤⣶⣶⣤⣀⣠⣦⣠⡄⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠈⠻⢿⣿⣿⡿⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢠⡞⣀⠔⣆⠃⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠈⠡⠈⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⠣⠠⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠒⠦⣱⡆⡑⠀⠀⢀⠀⠠⠯⠀⠀⠒⠄⣀⠀⢀⡠⠈⠧⠄⢀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⣴⡛⠇⠳⡄⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠹⠉⠁⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠠⠢⠄⡀⠉⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠜⢱⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠀⠄⠀⠀⠐⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠈⠐⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠐⠿⠗⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠠⣴⡦


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢦⠐⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣠⣤⣤⣀⣐⣂⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡀⠀⠠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠈⡆
⠀⠀⢀⠀⠀⠓⠒⠢⡀⢑⣀⣇⠀⠀⠀⠀⠀⠀⠀⢠⢃⡿⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⣅⠀⠑⡄⠆
⠀⠀⢀⠵⣴⠦⣀⡂⠘⠮⠿⣈⡿⣄⠀⡄⠀⠀⠀⠈⢸⣇⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢽⠢⢀⡿⡆
⠀⠀⠁⢄⠀⠂⠙⢛⣾⡀⡀⠈⠻⢉⢄⡈⠀⠀⠀⣧⢈⣿⠟⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡄⠸⠛⠸⠑
⠀⠀⠀⠀⠻⢦⣀⠀⠠⡟⠛⠀⡾⢉⠀⢈⠠⡀⠀⡿⣅⢃⣼⡿⠀⠀⠀⠰⣆⠈⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⣀⠈⠈⠉⠋⠀⠀⠀⠈⠀⡙⣦⡀⠂⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠘⠷⠁⠀⠀⢀
⠀⠀⠀⠀⢀⠀⢀⢀⠀⣠⠀⣴⠀⠀⠀⠀⠀⠀⠀⠠⠤⠷⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠒⠒⠁
⠀⢀⠀⡀⠹⣄⡻⠰⡔⠃⠀⠞⡇⠀⠀⠀⠀⢀⡀⢀⡔⠀⠤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠈⠠⡇⠰⠈⢇⢸⡃⠀⡀⢪⡅⠀⠀⠀⠘⠀⠀⠐⡇⢀⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠟⢀⠄
⠀⠀⢀⣇⠀⢠⠈⡯⠱⠞⢁⡯⠁⠀⠀⠀⡀⢥⠀⠀⡙⠀⠤⢤⣤⣴⡴⠏⡜⠀⠀⠀⠀⠄⣷⠞⢉⠧
⠀⠀⠈⢻⢀⠘⡙⠓⠀⣼⣿⠃⠀⠀⠀⠀⠳⡨⢠⠞⠁⢠⠖⠋⠁⠀⠀⢰⡀⠀⠀⢀⣴⠞⠯⠀⣄⡀
⠀⠀⠀⠸⡏⣼⡡⠌⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣉⣤⣾⣀⣆⡀⠐⣴⠟⠀⠀⢠⠊⠁⠀⠀⠀⠈⠈⣿
⠀⠀⠀⠀⡏⡬⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠉⠛⠛⠚⠋⠁⠀⠀⠀⠂⠀⠀⠀⢠⠁⠹⣶⡃⡀
⠀⠀⠀⠀⠳⢣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⡋⡁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡐⠀⣌⠏⢰⠿⣭⡠⠆⠀⠀⠀⠈⢡⣀⣄⡐⠀⠤⡀⠀⠀⠀⠀⠀⡀⠰⢁⡆⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡻⣆⠠⣔⠰⢖⡼⢐⢒⡀⠀⠀⠀⢀⡈⠙⢻⢢⣤⡠⠀⠀⠀⠀⠨⠆⠀⢸⡦
⠀⠀⠀⢀⡃⠀⢤⣞⡈⣩⡏⣁⣖⠒⠒⠊⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣿⠛⠤⡀⠀⠀⠀⣷⢀⡔⢀⡇
⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⢂⣀⠀⠐⠒⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠛⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠛⠛⠛⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⣁⣤⣴⡶⠾⠿⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⣠⣶⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠛⠛⠛⠛⠿⢷⣶⠶⠾⠟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠳⣬⣄⣁⣀⣀⣤⣤⠴⠋⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⢷⣦⣤⣀⣀⣀⣠⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠚
⠀⠀⠀⣶⠾⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠷⠶⣶⡄
⠀⠀⠀⢿⡆⣤⠄⠠⠤⠄⠤⠤⠀⣤⠤⠀⠤⠤⠀⣤⡄⢠⣤⠄⢠⣤⠀⣤⣤⠄⣤⣤⠀⢤⣤⠀⣤⣄⣤⠀⣿⠁
⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⣀⠹⢿⣒⠖⣒⢦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⠒⢿⣿⠾⠋⠉⢳⣤⣿⣏⢁⣉⠋⠉⣉⣉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠉⣹⡇⠀⠀⠀⠀⠀⠐⡏⠁⠀⠈⠙⠉⠙⠛⠛⠉⠻⡛⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠽⠾⠁⠀⠀⡠⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡁⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡇⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣶⠫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢡⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⢀⣴⢋⠄⠀⢰⠒⠋⠁⠀⡽⠀⢠⠁⠀⠀⠀⠀⠀⣀⣴⡆⢸⡁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⡼⢁⡎⠀⠀⢸⡇⠀⠀⠀⠁⡠⠃⠀⠀⠀⣰⡾⠛⠉⠁⠀⠈⡛⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣄⡇⣼⠀⠀⠀⣸⡇⠀⠀⢀⡜⠁⢀⣀⣀⣠⡏⠀⠀⠀⠀⠀⢠⣿⠂⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⡇⡏⠀⢯⠈⠉⠀⠀⣠⠎⠀⠀⠁⠀⠀⢈⣀⡀⠀⠀⢀⣠⣿⠟⠋⣹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠷⣠⠎⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢠⠽⠛⠶⠟⠋⠀⠀⠀⣏⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⣸⠀⢀⣴⠟⠀⢀⣤⠴⢶⣤⣄⡀⠀⣸⠆⠀⠀⠀⠀⠀⡖⠛⣉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠠⠟⠀⠞⠏⠀⠀⠀⠀⢀⡾⠀⠀⠉⠛⠁⠀⡀⠀⠀⠀⠳⣽⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣤⣀⠀⠀⣀⡀⣠⣤⠖⠚⣛⣀⣀⣀⣠⣴⠞⠋⠀⠀⠀⢀⣸⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⣷⣈⣩⡽⠿⠛⠛⠓⠛⠿⠿⠿⠿⠻⠟⠛⠲⢦⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠚⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠶⠞⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠻⠶⠶⢶⣤⣤⣀⡀
⠀⠀⠀⢠⢖⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢗⢦
⠀⠀⠀⡇⢇⠀⢀⣠⡤⠴⠶⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠶⠦⣤⣀⡀⢀⠇⡇
⠀⠀⠀⠘⠤⣉⠛⠠⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠘⢋⡡⠞
⠀⠀⠀⠀⠀⠹⡉⠑⠒⠂⠤⠤⠭⠉⢉⣀⣒⣒⣒⣒⣀⣀⣀⣐⣒⣒⣒⣂⣈⠉⠩⠥⠤⠄⠒⠒⠉⡹⠁
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠂⠀⠤⠤⠄⠤⠄⠀⠀⠒⠒⠀⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣋⣙⣙⣋⣋⣉⣋⣙⣋⣛⣉⣛⣉⣙⣋⣛⣙⣙⣙⣙⣙⣋
⣿⣽⣿⣿⣭⣽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠛⠳⢦⣤⣀
⠀⠀⠀⠀⣀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣐⡛⡩⢢⠍⡐⢪⣔⠒⠠⡀⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠡⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀⠰⢚⠶⠆⠀⠉⡢⠊⠓⠝⠫⢀⣠⣐⠲⠄⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠄⠁⣈⡯⡄⣕⠊⠓⡶⠉⠁⠦⡁⠑⢦⡲⢭⣉⠄⠘⠟⠂⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠰⡀⠀⠀⠀⠀⣾⠁⠀⠀⢀⡾⢠⡻⠗⢮⡊⠙⠀⠠⠑⢬⣀⠈⠙⠄⢡⠋⠁⠹⠰⠧⠀⠀⡈⢑⢄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⠀⠀⠀⠀⡇⠀⠀⡔⠈⠡⣰⠃⢀⠀⠗⠁⠀⠀⠉⡘⠟⢂⡈⠀⠲⠂⠀⡋⠈⠀⡀⡠⢄⡄⠀⠓⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢠⠀⠀⠈⡇⠀⠐⠁⢠⠖⢳⡀⠈⠀⠣⡀⢀⠃⣀⠄⠒⠰⡇⢄⣿⢃⠀⠸⢗⡨⠊⣅⠥⣴⣠⣦⠤⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢣⠀⠀⢿⡞⠔⣀⡆⠀⠀⡵⢦⣤⣐⣀⣀⡘⠁⡠⡄⢰⡇⠀⠈⠓⠲⢄⠎⠀⢀⡃⠈⠊⡧⠄⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠘⣷⢳⠿⢣⡀⠺⠁⠈⣔⠉⢁⠀⢣⣐⠁⠐⢀⡇⠀⠀⠓⠓⣦⣞⡖⡈⠕⠀⢐⢩⠀⠂⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠈⢷⣀⢂⡞⠣⠸⠃⠠⠀⠈⠁⠾⠻⢌⠨⡀⠀⣢⠦⠤⠤⢖⡖⠰⡕⡹⠀⢌⠈⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⡆⠀⠈⢻⢿⣅⢁⠃⢄⣁⡾⠓⠺⠀⠀⠀⡑⠒⠋⠁⠀⡁⢀⡀⠀⠀⡔⠀⠸⢂⡴⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⠀⠀⠱⡝⠻⣦⣴⡁⢢⠖⠶⠃⠡⢂⢟⡙⠡⢗⡦⡉⢤⣉⡠⠈⣠⣤⠾⠋⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠘⢄⡀⠉⠛⠷⢦⣴⣭⣬⣴⣼⣁⣠⣭⣂⣥⣵⣶⠶⠟⡋⠁⠈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠐⡀⠀⠀⠀⠳⢤⠀⠐⠀⠀⠈⠉⠍⠉⠉⠉⠉⠉⠉⠁⠀⠀⠐⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣡⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢰⠀⠀⠀⠀⠀⠰⣦⣍⣓⠶⠦⣤⣤⣶⣦⡴⠶⠞⣋⣥⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣀⠣⡀⡄⠀⠀⠀⠙⢿⡿⢿⣶⣶⣶⣶⣶⣶⣿⠿⣟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢞⡄⢫⠹⡄⠀⠀⠀⠀⠉⠓⠲⠶⠤⠤⠴⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⡄⢇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈
⣿⠿⠿⠿⣿⢻⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⣿⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡞⢛⠏⠉⠉⠉⣈⠉⠉⠋⠭⡷⡲⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡟⢀⣀⡤⠄⠀⠈⠳⠤⠄⠀⠀⠈⢌⣒⣛⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣹⣿⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⢻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⣾⣿⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇⢼⣾⣧⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⣰⣷⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠁⢀⠀⠉⠀⠀⠀⠀⠀⠀⠚⠀⠀⢸⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡏⣱⡇⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣳⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣫⣿⣽⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡃⣾⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⡴⢚⣿⡿⠿⠛⢉⡉⣰⣟⣶⣼⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⠀⠀⣠⡼⠁⣹⠏⡝⠀⠀⣾⢁⣿⣿⠛⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣽⣿⣿⡿⠠⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⡿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡧⣯⣿⣿⣽⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣆⡻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣅⣀⡀⠀⠀⠀⠀⢠⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣼⢿⣿⣿⣷⣤⣼⣿⣷⣭⣿⠛⠗⠁⠀⠀⠀⢀⣨⣉⣺⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠝⠛⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣷⢆⣤⡄⠁⠻⠋⡶⢂⣤⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⢻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣦⣌⠀⣨⣉⠀⠸⠤⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣤⣤⣶⣄⢈⠛⠁⡈⢉⢻⣿⣿⣿⣿⡿⣿⣿⣾⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠿⠿⢿⠆⢤⠠⠚⣺⣿⣿⣿⣯⢽⣿⣿⢣⣽⠿⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠕⠈⠉⠛⠛⠛⠛⠛⠋⠀⢀⣤⣀⣒⡶⣦⣶⣿⣿⣿⡟⠻⠞⠿⠺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣿⣿⠿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⣶⠛⠛⢦⣄
⠀⠀⠀⢿⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡾⠋⠻⣦⡤⢤⣤⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠈⠳⣄⠀⠀⣀⣀⠀⣼⠋⠉⣷⠶⠶⢾⣇⠘⣰⡷⠦⣴⡏⠠⠈⣷⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠈⢷⣼⡉⠙⢧⣾⠶⢥⡇⠰⣀⣀⣏⣿⠋⣀⠄⠀⣹⠶⠚⠓⠪⢿⠉⠳⣤⡴⠶⠦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣛⣳⣤⣀⠀⠙⢿⡞⠉⢻⣆⠀⠙⣶⠁⠉⠉⣷⠶⠶⠶⣾⡵⠚⠉⠙⢦⣀⠷⠤⢏⠀⠀⠀⠈⣏⡉⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣼⠉⠁⢀⣉⣷⣄⣂⣹⠶⡋⠉⢳⣤⣈⣷⣀⡞⠁⠄⠄⢠⠏⠀⠚⠀⣠⡏⠁⡄⢀⠈⣧⡤⠶⠶⣅⠈⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠓⠦⣴⣋⡀⠀⠙⢻⡦⡤⠴⠲⡞⠁⡀⡀⠙⢧⣀⣠⠴⠛⠒⠲⣖⠋⢉⡉⠳⡄⠀⣠⠏⠐⢐⣀⡼⠗⠃⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡇⠀⠀⠀⠉⠉⠒⠚⠳⠦⠤⠼⣧⣄⣀⣁⣀⣀⣯⣁⣀⣠⣦⣤⡼⠧⠤⠤⠾⠷⠚⠛⠚⠋⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠚⠛⠉

⣿⠟⠉⠙⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢹⣏⣿⢉⢉
⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⣀⠀⠀⠀⠐⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠈
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠠⠀⠀⠀⠰⣀⠀⠀⠀⣀⡠⠔⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠐⠀⠀⠀⠀⠂⠉⠉⠉⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠
⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠠⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠰⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠀⠀⠀⠀⠀⢰⡖⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⢁⣥⢉⣍⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠺⠻⠿⠟⠻⠸⠿⠀⠀⠀⠀⠀⠳⠤⠄⠒⠁⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠛⠿⠽⠣⠞⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠐⠀⠀⠀⠢⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠓⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠁⠐⠀⠐⠂⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠆⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠦⠤⠤⡤⠴⠐⢂⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠
⠀⠀⡁⠀⠀⠀⠐⢄⣀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢧⡀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠠⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠒⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡏⠙⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡄⠀⠀⠈⢿⣿⣿⣆⠀⠀⢹⣿⣿⠀⠀⣰⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⠀⠀⠀⠻⣿⣿⣧⡀⠈⣿⣿⠀⢀⣿⣿⠏⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⣆⠀⠹⣿⣆⠀⣿⠇⣰⠗⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣀⠀⠀⠙⠿⣷⡄⠸⣿⠀⣸⣿⠃⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢀⣴⣦⣬⣙⡲⣤⣈⣙⡧⣜⣔⡡⢞⣋⣡⣤⡤⠀⠀⠀⠀⣄⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣶⣤⡈⣿⢀⡟⢠⡿⠃⣠⣾⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿
⠀⠀⠀⠈⠛⠿⣿⣿⡿⠛⣫⢽⢿⡬⢽⣋⣉⡉⠉⠛⠁⠀⠀⠀⠀⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠉⠉⢈⣉⢣⠏⡼⢡⠟⣡⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠈⠉⠀⡞⣡⡿⠀⣿⡆⠈⢻⣿⠂⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⣶⣶⣶⠶⠶⢟⣫⡵⢋⡼⣱⣫⣚⣥⡶⠾⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠃⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⠏⠀⣼⠃⣧⡙⠲⢶⣦⣤⡀⠀⠈⠙⠻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⢸⣿⣆⠀⠙⢿⣿⣷⡀⠀⠀⠘⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⢸⣿⣿⠀⠀⠈⣿⣿⣿⡀⠀⠀⠘⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠋⠉⠙⠓⠲⣄
⠀⠀⠀⢀⣤⡶⠤⠤⣀⠀⢠⡴⠶⠒⠒⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⣠⡤⠚⠉⠀⠀⠀⠀⠀⠑⠮⠆⠀⠀⠀⢀⢈⣃⣀⣤⣤⡤⠤⠤⡤⣤⣤⣤⣄⣀⣀⡀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠚⠁
⠀⠉⠙⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢽⠋⠁⣀⢩⡤⠤⣤⣧⣤⡀⠀⠀⠀⠀⠉⠉⠙⠋⠄⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⡉⠁⠀⠂⠀⠠⠤⠤⠴⠤⡀⠸⣿⠛⠉⠀⠀⠀⠀⠀⣀⠈⠉⠿⢿⣷⡦⠤⣤⣤⣄⡀⠀⠀⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣸⣷⠶⠂⠀⠀⠈⠀⠀⠀⠈⠆⠠⠀⠀⠀⠀⠀⠛⠛⠻⠶⢬⣈⢢⡀
⠀⠀⠦⣤⣤⣴⣶⣥⣤⡤⠾⠿⠛⠚⠛⠛⠛⠛⠋⠉⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠣⣷
⠀⠀⠀⡄⣿⣿⠻⠭⠁⠀⠀⠁⠈⠁⠉⠉⠁⠈⠁⠈⠉⠙⠻⠿⢍⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠒⠀⠀⢰⣿
⠀⠀⠀⣷⡈⠳⣦⡀⠀⠀⡀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠦⣤⠄⢀⣠⠖⣫⡟
⠀⠀⠀⢹⡹⣦⣈⠉⠛⠶⢤⣬⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠨⠂⠉⠀⢀⣀⣀⣤⠶⠚⢉⣤⠞⢩⡇
⠀⠀⠀⠈⣇⠀⠈⠙⠲⠤⢄⣀⡉⠉⠙⠋⠙⠛⠒⠒⠒⠒⠲⠶⠖⠒⠲⠖⠚⠛⢛⣉⣁⣤⡤⠶⠞⠉⠀⠀⣸
⠀⠀⠀⠀⠘⢦⠄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⣠⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⠋⠉⠉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣉⡉⠉⠉⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠋⢉⣀⣤⣤⠶⠶⠖⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⢦⣄⡀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⡴⠶⠛⠋⠉⠀⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠿⢿⣷⣄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢀⣠⡶⠛⠉⠀⠀⣀⣤⠴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠛⠁⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⣼⠃
⠀⠀⠀⢀⡾⠁⠀⢠⡟⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣠⡾⠃
⠀⠀⠀⢸⡇⠀⠀⠘⣧⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⢀⣠⡾⠋
⠀⠀⠀⠈⢷⡀⠀⠀⠈⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠛⠋⠁⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠈⠙⠛⠳⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠖⠛⠛⠋⠉⠁⠀⠀⠀⣀⣠⡴⠶⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣛⠛⠛⠓⠒⠲⠶⠖⠒⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠻⣇⡤⠞⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠁⠀⠀⣿⠁⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢠⡏⠀⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⢸⡀⠀⠀⠀⢀⣤⠶⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⣠⣾⠁⠀⢀⡶⠛⠁⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⢹⣶⠶⠚⠃⠀⢠⡾⠋⠻⢷⣶⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⡄⠀⠀⠀⢸⡇⠀⠀⢀⣮⡤⠴⠄⠀⢰⠟⠀⣠⠀⣼⠃⠀⠀⠀⠀⠀⣾⣿⣦⡀⠀⣠⡶⠛⠁⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⡏⢳⣀⣤⡀⠈⣧⠀⢀⣞⣁⣀⡀⠀⢠⡟⢰⢋⣿⢾⠃⠀⠀⠀⠀⠀⣤⣿⠿⠿⠟⠉⠁⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⢰⠀⠉⠈⠀⠀⠿⣦⣻⠀⢸⠋⠉⠁⠀⢀⣼⠁⣾⠟⠁⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠘⠷⠶⢶⡄⠀⠀⠀⠹⣦⢸⣷⠞⠁⣠⣾⣿⢠⡟⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠙⣦⡀⣶⡄⠿⠸⠃⠀⣰⣿⣿⣿⣼⡇⠀⠀⠀⠀⢀⡶⠛⠇⠀⠀⠀⠀⠀⢰⡾⠔⠀⠀⠈⣴⣿⣤⣄
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⢀⣠⡶⠟⢉⡴⠋⢉⡇⠙⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡿⠉⢹⡇
⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⢦⣄⡄⠸⣿⣶⠟⢁⣠⣾⣿⠃⣾⠋⠁⠀⠀⠀⢠⡟⠀⠀⠀⢀⠀⢀⣀⣿⣯⣤⠀⠄⠀⠀⣸⣡⣴⠿⣧⡴⠶⠶⠶⣦⣤
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠹⣷⠀⢻⣷⣴⡿⢿⣿⣿⣠⠿⠀⠀⣤⣤⣤⣾⠃⠀⠀⠀⢸⠀⣼⠟⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣾⡿⡄⠀⠀⠀⠈⢳⣜⡇⢸⣿⠋⠀⣼⢻⣉⡿⠂⠀⡼⠁⢠⠀⠈⠀⠀⢀⠀⣸⡿⠥⠤⠄⠀⠀⠀⠀⣰⠃⠀⢀⠀⠀⡐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠱⣦⣝⣿⠸⣿⠀⢰⢏⣿⣇⠀⢀⣰⡇⢀⣸⡇⠀⢀⠀⢸⡾⠇⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠂⢀⡴⠛⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠈⢦⡘⢿⣿⠀⣿⣠⡏⡜⢸⡟⠀⣾⠛⠃⣼⠏⠁⠀⢸⣦⠎⠀⠀⠀⠀⢀⣴⠿⢶⠟⠁⠀⠀⣸⡴⠋⠀⠀⠀⠀⣀⠀⢀⣿
⠀⠀⠀⢠⡾⠋⣿⡀⠀⠀⠲⣄⠈⢿⣌⣿⢰⣿⠋⡐⠀⡘⠁⢀⣿⠀⠀⡇⠀⠀⣶⣞⣉⠀⠐⠀⠀⢀⡾⠁⠀⠀⠀⢠⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⢻⣾⠋
⠀⠀⣰⠏⠀⡜⣿⠗⠀⠀⠀⠹⣧⠘⣿⡟⢸⡟⠀⠀⠠⠁⢀⣿⠁⠀⣤⡇⠀⠀⠈⠉⠉⠉⢀⣠⣴⠟⠀⢰⣀⣤⠶⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⢀⡟⠀⢸⠇⠹⣆⠀⠀⠀⢰⡹⣷⣽⠃⣼⠇⠀⠀⠀⠀⣸⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠋⣹⣡⡴⠖⠻⠯⠄⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣰⡎
⠀⢸⠁⢀⠏⠀⠀⠙⣧⡀⠀⠀⢿⣿⠏⢠⡿⠀⠀⠀⠀⢀⡏⠀⣲⠶⠀⠀⠀⠀⢰⣶⣫⠵⠚⠻⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢳⡆
⢀⡇⢀⡏⢀⡀⠀⣼⠋⢻⠀⠀⢸⠟⠀⣼⠇⣠⠂⠀⣠⠟⢁⠞⠁⠀⠀⣠⣶⣄⣸⡟⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣠⡴⠟⠁
⣼⠀⢸⠁⢸⣅⢠⡏⠀⢸⡇⠀⠈⠀⢠⣿⡴⠃⢀⣾⠋⠀⠀⠀⠀⢀⡾⠋⠀⠉⠉⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠛⠛⠉⠉⠁
⣿⠀⠸⠀⠀⠙⣿⠁⠀⣼⠂⡠⠀⢀⣾⣉⣠⡶⠟⠁⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⣤⣤⣴⡾⠟⠋
⣿⡄⠀⠀⢀⡼⠟⠀⠀⣿⡾⠁⢀⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⡿⠿⠶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣿⠟
⢸⣧⠀⠀⠸⣧⡄⠀⢸⣿⡷⠾⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⢉⣴⣿⣀⣶⡶⠿⠃⠀⠉⠉⠉⠉⠁
⠀⢿⣆⠀⢰⡟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣼⣇⣠⣴⠿⠋⠉⠉⠙⠁
⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⡴⠒⠒⠚⠋⠀⢀⣽⣿⠟⠁
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠙⠿⣷⣤⣤⣤⣴⣾⡷⣶⡶⠿⠿⠟⠛⠉
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⡀⢀⡀⢀⠀⢀⠀⣀⠠⢠⠀⡀⢀⡀⢀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠛⠘⠋⠘⠃⠙⠃⠛⠡⠋⠀⠀⠚⠯⡘⠃⠙⢁⠂⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢉⣄⣄⡀⢠⡦⠤⠀⡐⠀⠠⠀⠀⠀⠀⠠⠁⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠘⠛⠍⠿⠆⠃⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠁⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⣰⣦⣿⠅⠢⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⠸
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡠⠈⠈⢀⠁⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠈⡃⠀⠀⠁⠀⠀⠅⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢦⠰⠀⠀⠀⠀⠀⢀⠀⠴⠤⠦⠆⠀⠀⢀⢄⠀⠀⠠⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠚⣆⡀⠀⠀⠈⠂⠀⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠁⠀⠀⠀⠄⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠌⢠⠂⠀⠀⢐⣦⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠠⠀⠀⠀⠀⠐⠀⠂⠀⠀⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠘⠄⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⢿⢠⣾⣽⡿⠞⣿⠀⠰⡏⠥⠀⠀⢾⣿⣿⣹⠷⠀⡷⠺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣴⠚⠛⢳⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢏⠀⠈⠖⠀⠀⠠⡭⠉⠈⠙⠻⡟⠳⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠁⠀⠀⠔⠈⠀⠀⠀⠀⠀⡀⠀⠀⡤⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡛⠉⢀⠀⠀⠁⡀⠀⠆⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠴⠀⠀⡤⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⠀⠁⣿
⠀⠀⠀⠀⠀⠀⢀⣸⡇⣠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⡀⣿⣄⡀
⠀⠀⠀⠀⢀⡴⠋⣼⠁⠠⡄⠀⠀⠓⠀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⡄⠀⠀⠰⠀⠀⠀⠀⠀⠠⢠⣏⠈⣷⡄
⠀⠀⠀⠀⢸⣧⠀⢿⣝⠀⠀⠀⠘⠀⠀⠀⠘⠍⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢠⠟⡇
⠀⠀⠀⠀⢸⡈⠳⢦⣈⠓⢦⣄⡁⠀⠊⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠲⠀⠀⣀⣤⠞⢉⡴⠋⢰⡇
⠀⠀⠀⠀⠈⣇⠀⠀⠈⠓⠦⣌⣙⠶⠶⠶⢦⣤⣤⣌⣂⣀⣀⣀⣀⣀⣀⣀⡤⠴⠶⠞⣁⡤⠖⠋⠀⠀⡾
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⢤⣤⣄⣉⣉⣉⣉⣉⣡⡤⠤⠖⠚⠋⠁⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣈⠉⠓⠲⠶⠤⠤⣤⣤⣤⣄⣤⣤⣤⡤⠤⠖⠛⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⣤⣤⣤⣀⣤⣤⣤⣤⣤⠴⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠙⠒⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢄⣀⠀⣀⣀⡤⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡴⠋⠉⠉⠁⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠾⠿⣶⣶⠶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠒⠒⠀⠒⠒⠒⠒⠤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠈⢉⣁⣘⠛⢂⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣿⡇⠀⠛⠛⠉⠀⡟⠛⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠉⠙⠋⢀⠀⠈⠁⠀⢱⡌⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠄⠀⠀⠀⡖⠀⣀⠍⢄⣘⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠈⠉⠁⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠠⠶⠋⠀⠁⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⡄⠡⠀⠀⢈⠀⠀⣀⡀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠠⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠹⡄⠀⠀⠀⠘⢦⡈⠀⡷⠤⢤⣼⣎⡼⣦⡀⠈⠓⢄⠀⠀⠀⠐⡱⠡
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠙⣄⠀⠀⠀⠀⡉⠶⢧⣀⠀⠀⠈⢿⡈⠻⢦⣄⡈⠳⠄⣔⡜
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⡀⡠⢎⡀⠀⠀⠈⠉⠓⠂⠀⠀⠐⢄⠈⠉⠀⣜⣮⡷⢒⣿⣖⠀⠀⣀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⠦⢤⣤⡤⣄⡒⢤⣼⣿⡟⠚⠁⠿⣤⡙⣿⣻⢼⡑⣲⣄
⠀⠀⠀⠘⠛⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡝⣯⣟⠿⣿⣷⣜⣋⣛⡿⠒⣄⣰⠿⢃⣻⣻⣗⣤⡿⣋
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢄⠢⡲⢛⡓⠚⠴⠿⠯⠥⣿⠿⡫⠽⠛⢃⣭⣽⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠉⠓⠒⢶⠶⠤⠤⢼⠀⠀⠳⢖⠀⠠⢀⢄⠀⠀⠉⣉⣀⡴⠛⣤⣚⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢀⣿⣆⠀⠀⢸⡄⠀⠀⠀⠑⠦⣬⣵⣆⡠⣤⣄⣨⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢸⠀⢻⣆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⡈⠀⠀⠹⣧⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠇⠀⠀⠀⠘⠿⡌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⡤⡄⢀⢤⣤⡠⣄⣀⠠⢠⣤⠄⣤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠉⠁⠁⠁⠀⠁⠀⠁⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠁⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⡶⠀⠀⠠⠤⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠃⢠⠊⠢⣀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠧⣀⣀⢀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠣⣄⠘⠊⠱⣀⡼⠁
⠀⠀⠀⠀⠀⢀⠊⠀⠀⣄⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠉⢐⠒⠉⠘⣄
⠀⠀⠀⠀⠀⢘⡀⠀⠀⠇⠑⠤⢄⠠⠀⠀⠀⢱⠂⠀⠀⠀⠀⢸⡁⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠈⠈⠑⢦
⠀⠀⠀⠀⠀⠈⢏⢆⢀⠀⠀⠀⠀⠉⠉⠐⠖⠋⠀⠀⠀⠀⠀⠀⠏⢒⠈⠉⠁⠀⠀⠀⠣⠤⠲⠇⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠘⢥⣅⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢆⣠⡄⠀⢀⡠⠀⠀⢀⠔⠁⠘⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠒⣦⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠤⡀⠝⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠉⡦⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠇⠀⠀⠀⡜⢀⡤
⠀⠀⠀⠁⠀⢀⢤⡍⣄⠀⠂⠀⠁⠈⠀⠀⠠⠀⢸⡼⠣⣤⣤⠄⢉⣀⣀⡀⠀⠀⠬⠄⠀⠀⠀⠜⢇⣀
⠀⠄⠀⠀⠀⠙⢶⡃⠀⠀⠀⠀⠰⠀⢰⠮⣁⣀⠟⠀⠁⠀⠀⠀⠀⢨⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠆⠂⠀⠀⠀⠀⠀⠠⠤⠤⠖⠀⠀⠂⠐⢧⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠐⡰⠃⠀⠒⠄⠄⠠⠴⡒⠒⠛⠒⢂
⡆⠀⠀⠀⠀⠠⠎⠀⠀⠀⠁⠀⠀⠈⠉⠈⠁⠤⢀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠘⡇⠈⠉⠁⠰⠂
⠣⠤⢤⣤⣄⣀⠁⠀⠀⢀⣤⣀⣀⣀⣀⣀⡤⠒⠺⠭⠭⠭⠭⠭⠗⠊⠀⠀⠀⠀⠀⠤⠤⠤⠔⢃⠀⠀⠀⡀
⣆⣀⣀⣀⣀⣉⣛⣛⣚⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣛⣛⣋⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠂⠠⡄
⠀⠀⠀⠀⠀⡠⠒⢠⠖⠒⠒⠒⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⡀⠐⠀⠀⠀⠐⠈⠁⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠁⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠉⠂⡀
⠀⠀⠑⠄⠀⠀⠀⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⢀⡀⠰⠤
⠀⡀⠒⠀⠀⠀⠀⢠⠐⠀⠀⠀⠙⠄⠂⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠤⠀⠀⠉⠁⠈⢡⠀⠀⠀⡘⠀⢈
⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠒⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢠⣤⢁⠀⠄⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠂
⠀⠀⠁⠈⠈⡀⠀⠀⠀⠀⠀⠀⠰⢤⣤⠆⠀⠐⠂⠀⠒⢢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⡲
⠀⡀⠀⠀⠀⢀⢀⢤⢠⠀⠀⢀⣀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠉⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢶⢄⣀⠐⡒⢋⣂⠊
⠀⢀⡀⠀⣀⠜⠙⠣⡀⠀⠠⠜⢣⣈⠂⠀⠀⠀⠀⠀⠀⠒⢆⣨⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡃⠀⠉⠉⠈
⠀⠀⠀⠀⠙⠀⠀⠀⠈⠠⠀⠀⠀⡍⠈⠀⠀⠃⠀⠀⠀⠨⠉⠘⡁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢐⡀⠀⢀⠆⠀⠢⠐⠀⠴⠀⠂⠐⠞⡝⠡⠔⠲⢦⡤⢀⡠⠀⠤⠦⠈⠀⠀⠀⠄⡀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠈⠠⠤⠀⠀⠀⠈⠉⠁⠂⠀⠀⢜⠀⠀⢀⠄⠋⢇⠀⠀⠀⠉⢉⠹⠀⠉⠀⠀⠈⠀⠀⠁⠀⠈⠐⠀⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠂⠚⠥⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⡂
⠁

⡿⣿⢿⢿⡿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⣷⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⢀⣴⠟⠋⣉⡉⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣻⣧⣀⣠⡾⠋⠀⠈⢻⡄⠀⠀⢸⡇⠠⡏⠉⡟⠀⠀⠘⠛⠶⠶⠞⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⠀⠊⠀⠈⠉⠉⠃⠀⠀⠀⢸⡿⣦⣤⠾⢃⣀⡿⠸⣄⠀⢀⣀⡀⠀⣀⣄⡀⠀⠸⣇⣠⣀⣀⣠⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢸⡅⣰⠋⠉⠀⢠⡇⠀⢸⠏⣇⣠⡏⢠⡷⢁⡞⠋⠀⠉⠉⠁⠀⢹⡇⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣦⠀⠀⠀⠀⠀⠤⢦⠀⣰⠃⠀⠀⢸⣀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠈⠁⠀⠸⢦⡿⢀⠀⢰⠚⢶⠂⠀⡈⠷⠶⠛⠁⠀⠈⠛⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⡾⠁⠀⠘⠢⣝⡄⠁⠀⠘⠶⢤⡄⠀⠉⠙⢦⠀⠐⢄⡀⢀⢀⡄⢀⡴⠶⠶⠶⢃⡞⠛⠋⠀⠙⠲⡾⠃⢠⣀⠀⢰⡟⠛⢲⣏
⠀⠀⠀⠀⣀⣤⠾⠃⠀⠘⢦⡀⠀⠀⠀⠈⢻⡀⠀⠠⠀⣠⠏⠀⠀⠀⠈⠛⠲⢶⣍⠲⣮⠀⡞⠀⣠⠶⠶⠛⠀⠀⠀⠀⢠⠎⠀⣰⠋⠹⠤⠼⠃⠀⠀⠙⣷
⠀⠀⠀⣼⠋⠀⠀⠀⣤⣦⣴⠃⠀⠀⠀⠀⠸⡇⣠⢃⠀⠙⠶⣎⠀⣀⣤⣄⠀⠀⠙⡇⢁⣠⠇⠀⣏⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠋⠀⠀⠀⢀⣠⠾⠶⠶⠋
⠀⠀⠀⠻⣦⠀⠀⠀⠈⢧⢨⠀⠀⠀⢢⡳⣄⣧⢡⡎⠀⠀⢰⠇⠀⣿⠀⠈⣷⠀⢸⠁⡿⢁⠀⢀⣽⠀⠀⡀⠀⠀⢠⠀⠀⢀⠄⠀⠀⠀⠀⠈⣿⣀⣀⡀
⠀⠀⠀⢀⡼⠇⠀⠠⠴⡞⠈⣏⠀⠀⠀⠑⢌⠻⡆⢃⠀⠀⠘⠧⠴⠋⠀⠘⣧⠀⠈⠛⠧⡜⠉⠉⠁⠀⠀⢣⠀⠀⣸⠃⡴⠃⠀⠀⠀⠀⠀⠀⠈⢉⣩⡗
⠀⠀⠀⣿⠁⠀⣰⣄⠀⡟⠀⠙⢦⣤⡀⠀⠀⠑⢿⡌⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣀⡟⠀⠀⠀⠀⠀⢸⡇⡼⢃⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⡍
⠀⠀⠀⠻⣄⣰⡟⠉⠻⣇⣀⠀⠀⢀⡧⠀⠀⠀⠀⢳⡈⠀⠀⠀⠀⢀⠃⠀⠀⠀⡴⠋⡭⠀⠀⠀⠀⠀⠀⢸⡿⠁⡾⠀⠀⠀⠀⡀⠀⠀⠠⣀⡀⠀⣿
⠀⠀⠀⠀⠈⠉⠀⠀⠀⢩⡟⠀⠀⣿⡀⠀⠠⡀⠀⠀⢧⠀⠀⠀⣠⢎⠀⠀⠀⠠⡇⠀⠳⡄⠀⠠⠀⠀⠀⢘⠇⣸⠃⠀⢀⣴⠋⠀⠀⠀⢸⡟⠳⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⠘⠦⢦⡄⠈⢓⠦⣌⡄⢢⡜⣡⠃⠀⠀⠀⢠⡟⠀⣤⠃⠀⠀⡇⠀⠀⢸⠀⡏⠀⢠⡿⢹⣆⣀⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⡷⠀⠀⠑⢌⡃⠈⠰⠁⠀⠀⠀⠀⣿⠀⡞⠀⠀⠀⢰⡃⠀⠀⡌⢀⠇⠀⢸⣿⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠸⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⢆⠀⠀⠀⢿⡀⢠⠁⣸⡀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⢻⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⢀⡞⠁⠀⢀⡎⠀⠀⠀⠘⢰⡆⢠⡯⠂⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠈⢦⣄⡀⠠⣌⠀⠀⢀⣰⠃⠘⣧⠀⢸⡁⠀⠀⠀⠀⢠⡎⢠⠏⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠈⢳⠀⠈⡃⠀⠈⣇⠀⠀⢘⡇⢀⡷⠀⢰⠀⢀⠎⡰⠃⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣄⠀⢧⡀⠘⢆⠀⢻⠀⠀⠈⢧⡞⠁⠀⢸⡴⠃⡰⠁⣴⠷⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠙⢦⠈⢂⠈⡆⠀⠀⣠⠃⢀⡼⠋⣠⠞⠁⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡘⣇⠀⠣⠀⠀⠸⡇⠀⠞⠀⣸⣥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠖⠛⠓⠀⠀⠓⠶⢤⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣶⣶⠶⠶⣤⣤⣀⣀⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⣶⣶⣶⣶⣶⡾⢷⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣾⢷⣶⡿⠿⠿⠶⣶⠶⠾⠷⡶⢿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⢟⣜⣼⠷⢿⣳⣽⣞⣓⡯⢷⠴⠿⢝⣒⣃⣹⣶⣤⣙⣳⣝⣚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢟⡷⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣾⡣⣥⠭⠻⡳⠵⢻⣬⢶⠲⡝⣷⣯⣣⡝⣶⡌⠙⠳⡄⡖⣪⢿⣒
⠀⠀⠀⠀⠀⠀⢀⢤⣙⣷⣿⣿⣿⣿⣿⣯⢶⣤⢄⢠⡀⡀⠀⠀⠀⠀⠀⢏⣵⢹⢿⣝⣽⡼⣩⢲⡜⠿⣟⢮⢽⣿⢜⣡⠟⢡⡾⠳⢜⣾⢳⢯⢴
⠀⠀⠀⠀⢀⢴⣉⡿⢛⣛⢟⣽⠛⣟⢟⣭⡝⣺⢤⢿⢩⢾⠟⠀⠀⠀⠀⢞⢼⢛⣼⢧⣺⡽⣾⡇⡽⣺⣒⢞⢾⢸⢩⣶⣆⢸⢰⣫⢽⣫⢿⡫⢫
⠀⠀⠀⠀⠺⣶⣒⢽⣽⡡⡕⣫⣎⢻⢷⣭⣽⣽⣶⣾⡿⠁⠀⠀⠀⠀⠀⣽⣿⣷⣽⡮⣒⡭⣲⡷⡱⡀⢳⡷⠞⣸⠀⣋⡭⣞⣽⡟⣕⠞⣔⡞⡵
⠀⠀⠀⠀⠀⠀⠈⠋⠓⡭⠜⡆⣞⡥⡭⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢪⠏⣇⠳⠭⣟⠭⣞⠭⠾⢹⡖⣝⠛⠋⣼⡏⣾⢵⣻⡗⢞⡦⣥⠫⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠘⠳⣿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⡛⠋⢥⣾⣮⠙⢛⠛⠁⣿⣷⣦⣬⠝⠚⣋⠽⣹⢹⣿⢯⡱⣵
⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⡟⣋⣛⡢⣍⢴⣛⣛⢻⡆⡿⠋⠁⣴⡏⣵⣳⠹⡞⣛⢖⣽⣈⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⣵⢧⢯⣖⡺⢷⢟⣖⢞⠞⠨⣞⡛⢷⠘⠳⣜⡪⡿⡏⣝⠭⡣⢓⣏

⠀⠀⠀⠀⢀⣀⣤⣤⣤⠤⠤⠴⠶⠶⠶⠶⠆⠰⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⢤⣤⣤⣄⣀
⠀⠀⠀⠀⢿⠛⠲⠶⠶⠶⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⣤⠶⠶⠶⠚⢻⡇
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢷⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣰⠇⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⣧⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⡟⠀⠀⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠘⣧⠀⠀⠀⠀⢷⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⣰⠇⠀⠀⠀⢠⡟⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠈⢷⡀⠀⠀⠈⣧⠀⠀⠀⠀⣧⠀⠀⠀⠀⡿⠀⠀⠀⢠⡏⠀⠀⠀⢠⡟⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠻⣄⠀⠀⠘⣧⠀⠀⠀⢹⡄⠀⠀⢸⡇⠀⠀⢠⡟⠀⠀⠀⣰⠏⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠙⢦⡀⠀⠘⣧⠀⠀⠈⣧⠀⠀⣼⠀⠀⢠⡟⠀⠀⢀⡾⠁⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣦⣤⣿⣦⣤⣬⣷⣤⣤⣼⣦⣤⣿⣤⣴⣯⣤⣤⣴⣯⣤⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠶⠒⠒⠒⠲⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠐⠭⠲⢤⣀
⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡖⠉⠀⠀⠀⠀⠀⠀⠑⠪⣍⡲⢤⡀
⠀⠀⡜⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠈⠉⢻⣇
⠀⠀⡇⠀⠀⠂⠀⡀⠘⠥⠄⠠⠬⠟⠁⠀⠀⠀⠀⠀⢸⠀⢠⣔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠻⣄
⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⣸⠀⠘⡇⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠰⡋⠑⠋⡠⠐⢃⡏
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠐⡰⠃⠀⠀⢏⡀⢲⠚⠀⠎⠁⠈⢁⠠⠈⠴⠂⣀⣚⣥⡭⠭⠷⠒⠛⠉
⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠘⢗⣋⣀⣤⡼⠥⠽⠓⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢶⡉⠁⡿⣦⠠⠖⢰⡾⢉⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠚⠋⠉⠉⠉⠙⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⢀⡌⠉⣷⡇⠀⢼⣿⣤⠓⢧⠀⡀⠘⠀⠎
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢦⠀⠀⢀⠴⣧⡈⠲⠈⢣⠂⠀⡿⣿⠀⠀⢣⠀⠀⠰⡄
⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡀⠀⠘⠦⡙⠻⠀⠀⠀⠄⠀⠐⣹⠄⠀⠈⠀⠀⠀⢸⡀
⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢁⡟⠀⠀⠀⠈⠲⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⣿⠀⠈⢷⣒⠄⠠⠤⠤⠄⠠⠠⠀⠒⣂⣀⣥⠺⢁⣼⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠘⡦⠄⢀⠘⠧⠉⠙⠁⠀⠀⠉⠀⠀⠄⢁⠀⠄⡋⠉⢦⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢱
⠀⠀⠀⠸⡀⠔⠣⠄⣀⣀⣀⣈⡙⠦⠄⠀⠀⠔⠧⠐⠚⢀⢤⠊⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠹⡀⠀⡀⣀⠀⠠⠤⠤⢀⠀⢀⡠⠤⠤⠀⠐⣡⠞⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠁
⠀⠀⠀⠀⠀⠈⠒⠤⢤⣀⣀⡀⠀⠀⢈⣁⣀⣤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠔⠒⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠉⠁
⣿⣿⢛⠿⢛⡛⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡷⣿⣿⣿⣷⣶⣶⣦⣿⠏⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣞⡛⢿⡇⢻⡿⣿⣿⠿⡎⠉⢁⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⣦⣤⣬⣽⣿⣷⡠⡁⠐⠶⠿⠃⠀⣰⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣗⡒⠻⢿⣿⣿⣾⣦⣄⣀⣀⣼⣿⣿⣿⣿⣿⣟⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡆⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⢳⣦⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡿⡏⠙⢻⣿⣿⣶⣀⡀⡀⣉⠙⠛⠛⣻⣿⠘⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠁⢀⡀⣿⠿⣿⣿⣿⣿⣿⣧⣴⣿⣿⢿⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣹⡿⣿⣟⣿⣿⣿⢿⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⢩⣿⣿⣷⣿⣿⣿⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⢸⠛⠛⢛⣿⡟⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠰⣤⣴⡦⡰⠛⠁⠀⠀⠈⠐⠄⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⠀⠀⡀⠀⠀⠀⠀⠎⠀⣿⣿⡷⢲⣶⣿⣷⠁⣤⡀⡀⠀⠀⠀⠀⠈⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢷⣿⣿⣟⣦⣍⣩⣾⣿⣶⣾⣿⣷⣆⡀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⣿⡀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡈⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠞⠙⠈⣽⢃⠁⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠸⡟⠿⠿⣿⠟⠟⠙⠃⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⣶⣧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠼⣿⡃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠄⠀⠀⠐⠂⠠⠀⠀⠄⠀⠀⠀⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⢴⠾⠋⠶⣴⣦⣀⣠⠀⠀⠶⣦⣔⣋⣽⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⡼⣏⢀⣀⠀⢰⣮⣻⣿⣿⣿⣆⠸⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠿⠿⠶⠤⠀⠀⠠⣿⣦⣼⣿⣿⣿⣿⣿⣿⣆⠰⣦⠀⠀⠀⠀⠀⠀⢃⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⣀⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣌⡃⠀⠀⠀⠀⣴⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠂⠘⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⠮⠭⠭⠭⠍⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠭⠭⠭⠭⢶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣖⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣷⡦⣄
⠀⠀⠀⠀⡴⢫⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣴⠦⠤⠤⠤⠤⠤⠤⠶⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢪⠳⡄
⠀⠀⠀⠀⡇⠸⣄⠀⢀⣠⣤⠶⠶⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠶⠶⣤⣄⡀⢀⡼⠀⡇
⠀⠀⠀⠀⠘⢦⡀⠙⠛⠥⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠜⠛⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠘⣗⠢⠤⢄⣀⡉⠉⠑⠒⠒⠢⠤⠤⠤⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠤⠒⠒⠒⠉⢉⣁⣀⠤⠴⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠒⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠁

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

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⡇⠀⠸⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠰⠘⠀⠁⠀⠀⠈⠀⠀⠊⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠀⡀⢠⣤⢤⣤⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠎⢀⠄⠠⠀⠀⣀⣀⣀⠉⠛⣂⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠇⠀⠈⠀⠀⠑⠀⢠⣁⠈⢓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠞⣳⢦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢈⡡⠊⠀⠀⠚⠁⠀⠀⠀⢀⠤⡀⡌
⠀⠀⠀⣰⣚⢽⡗⢹⠁⠁⠀⠈⣇⠲⢠⠆⣈⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⢈⡁⠐⠀⠢⡀⠀⠀⠀⠀⡠⢋⠏
⠀⠀⠈⠙⠷⣻⠿⠚⣀⠀⣄⣠⢉⣰⡥⠊⢱⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠩⠥⠀⠀⠁⠀⠀⠀⠀⡵⠁
⠀⠀⠾⣏⣒⣙⣛⣦⢊⡙⠘⣃⣀⣀⡈⠉⠀⠐⠋⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⡇⢀⣀⡀⠀⠀⠀⠀⢀⠄⢠
⠀⠀⠀⠀⠉⠓⠢⠤⣤⡤⠤⠤⠤⣴⠖⠚⣷⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⠀⢤⠀⠀⠀⣀⡀⠀⠐⣁⠠⠊⠙⠄
⠀⠀⠀⠀⠐⠪⢅⠂⢀⠈⠀⠀⠉⠁⠞⠉⠀⠀⠀⡐⠀⠠⠀⠀⢀⠶⠤⠤⠄⠀⠀⠤⡀⠀⠀⠂⢉⡠⠔⠀⣀⢴
⠀⠀⠀⠀⠀⠀⠀⠉⠦⣀⠀⠀⠀⠀⢃⠀⢀⡤⠂⠀⠀⡘⠀⢀⠄⠠⠀⠀⢀⠀⣀⡠⢏⣈⣉⣉⣁⠠⠔⠊⠁⠀⠉⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⢈⠀⠀⠀⠰⠁⡠⠂⠀⠀⢀⡊⠀⡰⢹⠀⠀⠀⠀⠀⢀⡤⠒⠂⠉⠉⠉⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⠔⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠃⢈⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠈⠀⠀⠀⠀⠉⠈⠳⣄⡀⠀⠀⠰⠄⡠⠔⢁⡠⢄⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡀⠀⠀⠀⠱⠀⠀⢁⠀⠀⠀⠈⠉⠀⠀⠘⠂⠐⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡠⠀⡀⡌⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣨⠶⢃⡴⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⢀⡔⠁⡄⠈⢢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠈⢁⠔⠉⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠐⣉⡠⠄⠊⣀⠤⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠥⠐⠂⠉⠀⡀⠤⠊⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠀⢀⠀⠀⠂⠈⢀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⠦⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⠨⠃⠀⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⠤⢀⣀⠀⠈⠉⠐⠒⠒⠒⠶⠒⠀⠀⠀⠀⠐⠢⡉⠀⠀⠉⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠠⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⢡⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⠀⠰⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡾⠀⠈⠳⣄⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣠⠞⠁⠀⠈⣧⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢦⣾⡾⠁⢀⣤⠴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢤⣄⠘⣿⣷⣶⢤⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠛⠁⣀⣰⡋⠙⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⣼⣦⣬⣙⣲⣄
⠀⠀⠀⠀⢀⣾⡶⣚⣫⡽⠟⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠙⠲⢬⣭⣿⣆
⠀⠀⠀⠀⣼⠉⢯⡉⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣴⠋⢻
⠀⠀⠀⠀⣿⠀⠈⠳⣄⠀⣾⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠞⠁⠀⣸
⠀⠀⠀⠀⢸⡄⠀⠀⠈⣻⠃⠀⠀⠀⠀⠀⠀⡿⠈⠳⢦⣄⣀⣉⣳⣦⣄⡀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠹⣤⣄⠀⣿
⠀⠀⠀⠀⠈⣧⢀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣉⣭⠉⠀⠀⣩⣍⠛⠋⠉⠁⠈⠛⢦⣀⡀⠀⠀⠀⢀⣠⠟⢰⡇
⠀⠀⠀⠀⠀⢹⡌⠻⣦⣤⣤⣤⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠉⣠⠀⠀⠀⣠⡈⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⡏⢻⡀⣾
⠀⠀⠀⠀⠀⠈⣧⣾⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣀⣀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿
⠀⠀⠀⠀⠀⠀⣼⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢻⡀
⠀⠀⢰⣤⠤⠾⠃⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠳⠤⢤⡶
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣶⣤⣴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⣀⣙⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣞⣻⣿⣿⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⣀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠳⢦⣀⠀⠀⠀⢀⡿⣷⣶⣶⣚⣻⡇⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠶⢼⡇⠉⠉⠉⠉⠃⣧⣠⣤⡤⠶⢺⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢺⡿⠶⢤⣽⣦⡀⠀⣠⣞⣁⣀⣀⣤⡴⠾⣷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣸⠃⠀⠀⠀⠈⢻⢰⠋⠉⠉⠉⠁⠀⠀⠀⢻⡄⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡿⠀⠀⠀⢀⣀⣼⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠴⢾⣧⣤⠖⠛⠉⠉⣿⣘⣇⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⢉⣩⣧⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣉⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⡀⠀⠸⣇⠀⠀⣀⠀⠀⣸⠟⠛⠳⣆⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⠏⠛⣛⣋⣿⠋⠉⠻⡟⢻⣄⣀⣠⠟⠓⢲⣿⣿⣗⠶⣤⣹⣤⠞⢁⡿⢧
⠀⠀⠀⠀⠀⢀⡴⠦⠶⠤⢶⣾⣍⣹⡿⢿⣫⡽⠋⠹⣦⣤⣴⠇⠀⠈⠉⠁⠀⠀⣏⠀⠀⢹⡆⠈⠻⣿⣷⣾⢧⣾⣷⠶⠶⠶⠶⢦⡄
⠀⠀⠀⠀⢀⡾⠁⠀⣠⠶⠋⠁⣙⣿⣹⣿⡇⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠖⠋⠀⣠⣤⠏⢀⡟⣷⣀⡉⠳⢦⡀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠁⠀⣾⠃⠀⠀⢸⡿⣿⡷⣴⣿⣛⣋⣥⣼⣇⠀⣀⣴⠟⣿⣷⣄⣀⣠⠾⠟⠛⠶⠋⣠⡴⢻⣟⠉⣨⠏⠀⠀⢻⡄⠀⠈⢷
⠀⠀⠀⣸⠃⠀⠀⢻⣄⠀⠀⠈⢷⣄⠙⠳⠦⣭⣍⣉⣛⡛⠛⠛⠉⠉⠉⠉⣁⣉⣀⣠⣤⡴⠖⠛⢉⣴⣿⡙⡏⠁⠀⠀⢀⣼⠃⠀⠀⠘⣧
⠀⠀⣰⠇⠀⠀⠀⠀⠙⠳⣤⣀⠀⠈⠛⠶⢦⣤⣈⣉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⣉⣁⣠⣤⠶⠚⠉⠀⠀⠙⠃⢀⣠⡴⠛⠁⠀⠀⠀⠀⠘⣇
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⣄⣉⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⢀⣀⣀⣀⣤⣤⠴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠉⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣤⣿⡇⠀⠀⠀⠀⠀⠀⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣔⣿⣿⣦⢻⣿⣯⣿⣷⡀⠐⠀⠐⢀⣴⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⢻⣿⣅⣘⣿⡏⠙⣿⣿⣿⡇⠀⠒⠒⣿⣿⣿⣿⣿⠍
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⢹⣿⠿⣷⣾⠟⢿⡿⠟⢣⣀⠀⠈⠀⠃⠀⠀⢀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢸⡶⢾⣷⣤⣽⣿⣦⣼⣿⣆⣸⠏⠀⠀⣷⡀⠀⠀⣸⡏⢉⡉⢥⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠸⡇⠀⠀⠀⠀⠀⠈⠙⢿⡀⡈⠀⠀⠀⢹⣇⢀⣾⣿⠧⢹⣷⣾⣿⡿⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢷⡀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠁⠻⠿⢿⣆⡭⢀⢻⣿⡏⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠰⠄⠒⠀⢨⣿⡿⣿⡏⠙⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣧⡈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⢸⣿⣆⣴⡿⠟⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡼⠐⠀⠀⠀⠀⠀⠀⡀⠈⠛⠻⢧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠠⠰⣆⣃⣠⠶⡄⠂⠀⡀⠀⠀⠰⠀⠀⣇⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠻⣶⣄⡀⠸⡇⢿⡄⠘⡟⣀⣁⠰⢰⡆⠀⢠⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣏⣃⠉⣓⣞⣿⣿⣿⣄⣀⣻⣀⣛⣉⣹⣇⣘⡀⠤⢼⡀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠩⠍⣉⠁⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠈⠁⠀⠀⠀⢤⣦⢄⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠈⠋⠉⠈⠉⠀⠀⠉⠀⠀⢀⣼⠏⡀⡤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⡀⠙⠛⠛⠛⠀⠀⠀⣠⡿⠓⠀⣁⡀⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠛⠛⠛⠓⠀⠸⠋⠁⠈⠃⠉⠀⠈⠇

⣿⣿⣧⣀⠀⢉⣣⢳⣜⡓⠚⣧⠆⠍⣳⠽⢿⣽⣿⣯⣿⣿⣎⣻⣯⢭⡝⠁⠀⢹⠋⢰⠀⠹⡇⠈⠻⠈⠛⢿⣵⣆⡼⠃⠈⡾⠃⠀⣛
⣿⣿⣿⣿⣿⣿⣤⣄⣛⠃⠀⠘⠲⡄⠘⡷⣼⠟⠾⠷⣿⣿⢿⣻⣭⣟⣧⡖⠙⢐⡗⡀⠐⠠⡄⠀⠀⠀⠀⠀⣿⠃⠀⠰⠄⡑⣀⡤⠻
⣿⣿⣿⣿⣿⣍⣻⣷⡄⣿⣆⣤⡄⠀⠌⠀⣴⣼⡛⠻⢿⠟⠾⢳⢯⣎⠐⠁⣰⠼⣿⣿⣿⡇⠀⢠⡄⠀⠀⣄⠘⠀⠠⠂⠀⢻⣁⣠⣷
⣿⣿⣥⣄⣤⡟⢹⣿⣡⣯⡴⠁⣀⠄⠀⣀⡻⠄⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⣂⢀⡟⡜⠘⠁⠖⠐⠃⠄⠀⡁⠁⠀⠐⢺⡟⠉⠈
⣿⣿⣿⣿⣿⣷⣿⣟⣭⣥⣾⡿⣛⢢⡬⠽⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠃⠀⠀⠀⠀⠛⠂⣶⣀⢀⠁⣿⠂⠐⠀⠘⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢲⠛⠈⠀⠀⠀⠉⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡦⢽⣔⡏⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣾⣰⣶⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢺⢻⣥⡿⡽⡽⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣴⡆⠀⠀⠀⠀⢚⠉⠉⠀⠀⠀⢀⠀⠈⠃⢀⠤⠚⠋⢸⡅⠊⢱⠛⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢠⡀⠈⠃⠀⠀⡈⠥⠖⡿⠀⠀⠁⠀⠀⠀⠛⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠾⢛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⠙⢤⠀⠀⠀⡀⠀⠀⠀⠀⠘⢉⣱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡾⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠁⠛⠀⣀⠀⢤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣾⡅⠀⠀⠀⠀⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡆⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⡨⣾⣯⣀⣣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⢁⣹⠋⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣶⣄⠀⠀⠁⠀⠀⠀⢀⢘⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠳⠀⢱⡶⣂⣂⠀⠀⢺⠹⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⢡⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠺⠟⣒⢰⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢁⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡜⢁⡦⣤⠀⠘⠇⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢂⣈⣉⣁⣧⣿⢙⢾⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢥⣠⣭⢿⠛⣚⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡄⠀⠀⠀⠀⠀⠀⠠⢾⠈⠹⠧⣽⡟⠉⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠠⢞⡒⠂⠈⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠠⢠⠀⠀⠀⠀⠀⠈⣷⣦⣦⣤⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⢈⠃⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡐⠀⠀⠀⢸⡄⣠⠞⠠⠀⡴⠂⠀⡀⠀⡀⠀⣠⠄⣢
⠀⠀⠀⠀⠀⠠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠈⢞⠁⠀⠀⠀⡇⠀⠀⡇⠀⣹⠀⠻⠈⠁⠀⠀⠼⠈⠃⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⡦⠈⢆⠀⠀⠀⡇⠀⠀⠛⢠⠏⢀⠀⠀⢆⠀⢀⣤⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⡀⠀⠐⠃⠀⠐⠃⠠⠤⠵⠀⠤⠖⠉⠀⠀⢁⣠⠞⠀⠀⣿⣅⣠⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣄⠀⢰⡄⠀⡤⠴⠆⢢⠀⠀⡖⢠⡆⠀⡆⠀⠀⢿⣦⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⣴⠀⡇⠀⣡⠆⠀⢨⢦⠀⡇⢸⠀⠀⡇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⣸⡇⠀⢀⡇⣀⣃⡤⢀⡸⠀⣀⡇⠈⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡈⠀⠀⠀⠀⢰⠁⠀⠛⠟⠀⢀⢀⣄⠀⠀⠀⠀⠉⠑⠂⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡄⠁⠀⠾⠿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡄⠤⢠⠀⠀⣤⢠⠄⡠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠂⠈⠠⠀⠀⢀⠔⠈⠀⠀⠀⠀⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠢⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⢀⠀⠀⣀⡀⠉⠂⢄⠀⠱⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠀⠀⡁⠀⠀⠀⠀⠀⠀⠌⠀⢀⡨⠤⠤⠤⣀⡈⠑⠢⣀⠱⣀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⡠⠖⠉⠁⠉⠉⠙⠢⢀⠀⠀⣀⢢⢀⡀⠠⠀⢀⠞⠁⠀⠀⠀⠀⠀⠉⠢⡀⠈⠡⣽⠀⠀⠀⠰
⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠑⠀⡀⠀⠀⢳⡀⠀⣀⡤⠠⣤⣄⠀⠀⠀⠈⠄⠀⠘⠁⠀⠀⡐
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡞⢃⡀⠄⠀⠀⠀⠈⠙⢦⠀⠀⢠⠀⠀⡇⠀⢠⠅
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⠄⡀⠀⠀⠀⢃⠀⠀⠀⣜⣠⠴⠃
⠀⠀⠀⠀⠻⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠢⡀⠆⠀⠀⠈⡂⠏⣁⠘⠃⠇
⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠄⠀⠀⠀⠈⣀⢉⡃⡉⠀⠀⢀⣿⣿⣿⣴⣷⣧⣾⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⢸⡥⠤⠀⠀⠀⠀⠠⠤⠤⠄⡤⢤⠄⠞⠀⠠⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠁⠂⠤⢘⠇⠀⢀⠀⢀⠴⠃⠠⢊⠋⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠒⠏⢈⣥⠅⢈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠰⢣⠠⠃⢠⠖⠀⠀⠀⠀⠁⠀⠂⠉⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠄⠀⠀⠂⡳⡀⠀⠊⠀⠀⠠⠰⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢰⡀⠄⠠⠀⠀⠤⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠂⠰⣤⡀⢀⡁⠈⢧⣀⠉⠈⢠⡟⠀⠂⠀⠀⠁⡦⢤⡀⠉⣑⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠹⣆⣷⣼⡀⠻⣽⣦⡬⠋⠀⠋⠛⡓⠤⠀⠄⠄⠀⢂⡫⣼⢤⠃⢾⡵⣶⢲⡆⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡀⢃⡀⣤⣀⡄⣈⣷⣀⣀⣀⡴⠤⠌⡙⠀⡐⠂⡄⠀⠀⠈⠙⠻⣦⣑⠀⠂⣨⡾⠁⠀⠚⠁⠱⡀⢠⡀
⠀⠀⠀⠀⠀⢰⠈⠠⠟⠈⠀⠀⠘⠛⠀⠀⠈⢹⣿⣧⡀⠶⠠⠾⣤⡀⠠⠤⣾⣤⠖⠓⠀⠒⠤⢭⣨⡻⠉⠀⠀⠤⠀⠤⠔⢨⡄⢨
⠀⠀⠀⠀⠀⣄⠀⠄⠃⠤⠤⠶⢄⡀⠀⢀⣠⣾⣿⡿⠃⠀⠀⠀⠈⢻⡆⠀⠀⢻⣷⣄⠀⠀⠀⠀⠙⢿⣦⡄⠀⠢⠄⡤⣇⠎⠀⡬⠂
⠀⠀⠀⠀⠀⠈⠉⠣⠤⢖⡲⠦⠤⠟⠻⣿⣿⣿⠛⣠⠔⠀⠀⢲⣆⣿⡇⠀⢀⢀⣾⡏⠀⢀⡀⠀⠀⠀⣻⡗⡀⠐⣦⣂⣡⡤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠤⣜⣍⠀⠉⠉⢛⠷⣶⣾⣿⣯⡟⠁⢀⣤⡼⢿⠅⠾⢥⡀⢤⠴⠒⣻⠊⠙⠛⠁⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠐⠋⠈⠁⠙⠛⠛⠛⠡⠜⠉⠛⠙⠙⠒⠦⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⡟⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⡼⠁⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⢰⡇⡄⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⢸⠁⡇⠰⡄⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠁⡄⢸⠀⣇⠈⠀⠀⠸⣧
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣦⠀⢸⡄⣏⠀⢀⣀⠀⢿⡀
⠀⠘⣦⡠⣄⡴⠞⣛⡛⠳⠶⠶⣿⣿⣿⣾⡇⢹⡀⠛⢋⣀⡈⣧
⠀⠀⠈⢻⣶⡗⠠⢬⣉⠉⠙⠷⠦⣍⠉⠻⣿⣜⡃⠀⠉⣁⣀⢹⣇
⠀⠀⠀⢸⣿⣇⠲⢤⡈⠑⠲⠄⠀⠈⠓⠲⢬⡙⠛⠻⣦⣌⣉⠁⢻⡄
⠀⠀⠀⠀⢻⣿⣿⣦⡙⢶⣤⡀⠀⡀⢸⣆⠀⠀⠁⠀⠀⢉⠛⠛⢾⣷⡀
⠀⠀⠀⠀⠀⢿⣽⣿⣿⣌⡛⢿⣦⣤⣤⣌⠓⠤⠀⢠⡀⠀⠙⠓⠀⠉⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣝⢿⣶⣍⠻⣿⣿⣿⣆⠀⠀⠹⣿⣅⠀⠀⡀⠀⠀⠈⡉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⣿⣿⣷⣤⣝⠿⣿⣷⣥⣤⡌⠙⠳⠄⠈⠀⣀⡀⠈⠲⣤⣌⠙⠳⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣮⠻⣧⠈⠻⠿⣿⣿⣷⣤⡀⠀⢦⣬⣷⡀⠀⠈⠙⠳⣶⣤⣌⡙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠈⠛⢿⣶⣬⡛⢿⣿⣿⣥⣄⣉⠙⠿⣟⣦⣄⠀⠀⢈⠛⢿⣦⡈⠙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣿⣆⣝⢿⣟⠶⠌⠻⣿⣿⣿⣿⣷⣄⠈⠻⠃⠐⠛⠀⠀⠙⣿⣷⣶⣄⡈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⢻⣿⣝⢿⣷⣬⢻⣦⣌⣶⣭⣝⠻⣿⣿⣷⣶⣦⡀⠀⢀⣴⡄⠈⠙⠿⣿⣿⣶⡌⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⢻⣿⣷⣝⣻⣇⣉⣿⣿⣿⣿⣷⣭⣛⣻⢿⣿⣿⣦⣄⠉⠁⠀⣤⠀⠀⠙⠻⣷⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣝⢿⣿⡇⠀⢾⡿⠃⣽⣿⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠻⢿⣿⣷⡈⣿⠿⣿⣿⣿⣷⣮⣿⣿⣦⣍⣿⣶⣾⣿⣶⣤⣉⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⣦⡄⠈⢿⣿⡜⣆⢘⢿⠿⣿⣿⣿⣿⣿⣿⣷⣌⠙⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⠈⢷⣄⠀⣻⣷⣜⢦⠨⠳⡒⢿⡿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠞⠀⠀⠀⠀⠙⣷⣈⡈⠻⣷⣕⠄⠠⢄⢻⡀⠉⠉⠛⠾⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣬⣙⢷⣦⡀⠈⣧⠸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠔⠋⠀⠀⠐⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠈⡀⠀⠀⠀⢀⣹⡩⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠑⠚⠁⠒⠢⠀⠀⠀⡀⠘⣹⡅⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣛⣛⣿⣿⣿⣘⣿⣿⣿⣿⡿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠢⢴⡱⣶⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣿⣿⣿⣼⣿⣯⣟⣿⣿⣜⢿⣿⣷⡀
⠀⠀⠀⠀⠀⡖⠈⠀⢅⠀⠀⠀⢀⠀⠀⠀⠄⡀⠀⠀⠀⠉⢎⢻⡌⢧⡀⠀⠀⠀⠀⠀⣴⣺⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⡻⣿⣷⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠈⡆⠀⠀⠈⠛⢆⡀⠀⠈⢄⠀⠀⠙⠒⠷⡝⢦⢹⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⡄
⠀⠀⠀⠀⠀⠣⣄⡤⠴⠶⣄⡀⠀⠓⠀⢭⡢⣄⠀⠈⠙⣏⢳⣄⠛⣎⢻⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡇
⠀⠀⠀⠀⢀⠊⠁⠀⠀⢤⣀⣯⣍⣳⣦⡀⠈⠻⢷⣲⢄⡈⠲⣌⡙⠻⠌⣧⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⢿⣿⣿⣿⣿⣿⡇⢳
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠋⠙⠿⠟⠷⠿⠶⣮⣵⣦⣬⣉⡛⠒⠀⣹⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣉⡛⠛⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⠤⠒⠒⠢⠔⠒⠉⠓⠒⠶⠴⠴⠶⠛⠋⠑⠲⠚⠁⠀⠀⠀⠀⠉⠉⠙⠿⠿⠟⠛⠻⠷⠛⠋⠙⠛⠻⠿⠿⠿⠛⠋⠙⠒⠛⠃

⠀⠀⠀⠀⠀⣸⣟⠻⣦⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⠿⣿⣶⣾⣿⠖⠛⣹⣿⣧⣠⣶⣾⣿⣿⣶⣶⣶⣿⣷⣆
⠀⠀⠀⠀⣟⢹⣿⠀⣿⣿⣧⣤⣼⣿⣿⠖⠀⢿⡟⠿⠟⣩⣷⣾⣿⣿⣿⣛⣿⣦⡘⢿⣷⣶⣾⣿⣷⣶⡀
⠀⠀⠀⠀⢻⣌⣿⠀⣿⡎⠻⣿⡻⣿⣿⣿⣿⡿⢿⣶⣾⣿⠟⠑⢾⠋⠈⣿⡿⣿⣷⡀⠈⣩⣿⣿⠿⠿⣿⣿⠿⠿⣶⡄
⠀⠀⠀⢠⣾⣿⡟⠀⣿⡇⠀⣿⣧⢹⣏⡀⣀⢄⡀⠉⠈⠀⠀⠀⠀⠀⢸⣿⡾⠋⢹⡿⣶⡳⣿⡇⠀⣠⣶⣶⣄⠀⠘⣿⣿⡿⣶⡄
⠀⠀⠀⣼⣿⣿⡇⢸⣿⣿⡀⠸⣿⡎⣿⣿⣿⣟⣴⢃⠄⣠⠀⠀⠀⠀⠘⣿⣤⣶⡞⠿⠿⠿⠻⠿⠟⠻⠋⠀⢻⣿⣶⣄⠀⠀⢿⣿⣿⣷⡆
⠀⠀⣾⣿⣿⣿⠁⢸⣿⣿⡇⠀⠙⣿⣽⣿⣿⣿⣿⣿⣾⠋⠀⠀⠀⡸⡄⠀⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⢀⠄⣀⣴⣾⣿⣷⠀⣲⣿⣿⣿⠃
⠀⠀⣿⣿⣿⣿⠀⣾⣿⣿⣷⢀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢱⣻⡄⠀⠛⠫⠗⠀⡴⠁⢠⠆⣠⠏⢐⣿⣿⣿⠋⡿⢰⣿⠋⢠⣿⠀⢀⣴⣶⣦⡀
⠀⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣾⡇⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⢳⣿⣷⡹⣆⠀⠀⠀⡼⠃⢠⣿⡞⠁⠀⣻⣿⡟⠀⢸⡇⢠⡟⠀⢸⣿⣶⡿⠋⠀⠻⠟⣿
⠀⢻⣿⣿⣿⠃⢸⣿⡿⢹⣿⣿⠃⢀⣼⣿⣧⢻⣿⣿⢟⠀⠀⠀⠈⢿⣿⣿⣾⠇⠀⡼⠁⠀⣼⣏⡠⠀⢘⣿⣿⠃⠀⢸⡇⠈⢷⣶⡿⠛⠉⠀⠀⡰⠀⢰⣿
⠀⣸⣿⣿⣿⠀⣿⠟⣰⣿⣿⠏⠀⣾⣿⣿⣿⢸⣿⣷⣏⠀⠀⢦⣆⣸⣿⣿⡟⠀⣼⠃⠀⣰⠟⠋⠀⠀⢨⣿⣿⣄⠀⢸⡇⠀⠀⠀⠀⣰⠃⢀⣼⠃⠀⢸⣿
⣿⣿⣿⣿⡿⠀⠏⣼⣿⣿⠏⠀⠀⣸⣿⣿⡟⣼⣿⣿⠏⠀⠀⠘⣿⣿⣿⡿⠀⢰⡟⠀⢠⡏⠀⠀⠀⠀⠠⢿⣿⣿⣇⢸⡇⠀⣷⠀⣰⣏⣴⠟⠁⠀⣀⣀⣼
⠸⣿⣟⣿⡇⠀⢸⣿⣿⠋⢀⠀⠀⢿⣿⣿⢣⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⠃⠀⣿⠃⣠⡟⣀⣤⠖⠀⠀⢠⣿⣿⡟⠁⣼⠇⢀⣿⣰⡿⠋⠁⠀⠀⣴⣿⣿⠟
⣰⣿⣿⣿⡇⠀⣿⣿⢃⣴⡏⠀⠀⢈⣿⣿⢸⣿⣿⠃⢀⠀⢦⢠⡀⠘⠟⠀⣸⣿⣴⡿⠛⠉⠀⠀⠀⠀⠠⢿⣿⡇⢀⣿⠀⠸⣿⠟⠀⠀⡠⠀⠸⣿⡟⠁
⣿⣿⣿⣿⡇⠀⣿⣧⣾⣿⠁⠀⣾⣿⣿⣿⡇⣿⣷⠀⢸⡀⡘⢷⣷⡀⠀⢠⣿⡿⠋⠀⠀⠀⣠⠖⠀⠀⠀⠛⣿⡇⢸⡇⠀⣼⡏⠀⣠⡞⠁⠀⠀⢹⣧
⠸⣿⣿⣿⡇⢠⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⢸⣿⡷⠀⠀⢻⣿⣿⣿⡇⠀⣼⡿⢁⣤⣶⣶⣟⣥⠔⠀⠀⠀⠀⠸⣿⣾⠁⣼⣿⣴⠾⠋⠀⠀⠀⣴⡿⠋
⠀⢿⣿⣿⠇⢸⣿⣿⣿⣿⠀⠀⠈⢿⣿⡟⣿⣿⡇⠀⠐⣄⢻⣿⣿⠇⢀⣿⡿⠋⠁⠀⠀⠀⢀⣤⠎⠀⠀⠀⢀⣿⠏⢰⣿⠟⠁⣀⣤⠄⠀⢀⣿
⠀⠸⣿⣿⠀⣼⣿⡿⢡⣿⠀⠀⣾⣿⣿⡇⣿⡏⠀⠀⠀⢸⣾⣿⣿⠀⢸⡿⠀⠀⠀⣠⣤⠞⠋⢀⣠⡔⠀⢠⣾⠏⠀⣼⣿⣶⠟⠋⢀⣴⣾⡿⠏
⠀⠀⢿⣿⠀⣿⡿⠁⢸⡇⠀⠀⢹⣿⣿⡇⣽⡃⠀⠀⡆⠘⣿⣿⡟⠀⣸⡇⠀⢀⣾⣯⣤⣶⠾⠛⠁⠀⢀⣾⡟⠀⢠⣿⡏⠀⠀⠀⢸⣿
⠀⠀⢸⡿⠀⡿⠁⡀⢸⡇⠀⠀⣾⣿⣿⡇⢺⠁⠀⠀⢹⣄⣿⣿⡇⠀⣿⠀⢀⡾⠟⠉⠀⠀⡀⠀⠀⢀⣼⠟⢰⠀⣼⡿⠀⠀⣤⡾⠟⠃
⠀⠀⢸⡇⠀⠀⣰⡇⢸⡇⠀⣆⠘⢿⣿⣧⠈⢀⠀⡀⠈⢻⣿⣿⠃⠀⣿⣶⠋⠀⣀⣤⠶⠋⠀⣠⣶⡿⠋⣠⠟⢠⣿⠃⢠⡾⠋
⠀⠀⢸⡇⠀⣼⣿⡇⢸⡇⠀⣿⢠⠈⣿⣿⠀⢾⡆⠹⣆⠀⠙⡿⠀⢠⡿⠁⢠⡾⠉⠀⠀⠀⢰⣿⠋⠀⢰⡟⢠⣿⠃⢠⣿⠃
⠀⠀⢸⣿⠀⣿⣿⡇⢸⡇⠀⣿⢸⠀⣿⡇⠀⢸⣿⣴⣿⣧⠀⠀⠀⠸⠁⣰⠟⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⣡⣿⡁⢀⣾⠏
⠀⠀⠈⣿⠀⣿⣿⡇⢸⣷⠀⢸⢼⠀⣿⡇⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢠⣿⠃⠀⣸⣿⣿⠟⢡⡾⠃
⠀⠀⠀⣿⡄⢻⣿⠇⠘⣿⡀⢸⣸⡆⢻⣷⣳⡀⠈⣿⣿⣿⡟⠀⢠⠀⣀⣤⡴⠋⠀⢀⣴⡿⠃⠀⢀⣿⡿⢃⣴⡟⠁
⠀⠀⠀⢸⡇⢸⣿⣿⡀⣿⡇⠸⣿⣿⡈⢿⣿⣿⣦⠸⣿⣿⡇⠀⣾⡾⢋⣁⡤⠀⠀⣾⡏⠀⠀⠀⣸⣿⣷⡿⠋
⠀⠀⠀⠈⣷⠈⣿⣿⡇⢿⡇⠀⣿⣿⣧⠈⣿⣿⣿⣷⣿⣿⠀⢠⣿⠟⠋⠁⢀⠄⢸⡿⠀⢠⡇⢀⣿⡟⠁
⠀⠀⠀⠀⢻⡄⢿⣿⣧⢸⣇⠀⢹⣿⣿⠀⢻⣿⣿⣿⣿⠇⠀⣾⠃⠀⢀⡴⠋⢠⣿⠃⢀⡾⠀⣼⡟
⠀⠀⠀⠀⠘⣷⠘⣿⣿⡆⣿⡀⠸⣿⣿⠀⢸⣿⣿⣿⡟⠀⣸⡏⠀⣠⡟⠀⢀⣿⠏⠀⣼⡇⣰⡟
⠀⠀⠀⠀⠀⠹⣧⢻⣿⣷⢹⣧⠀⢿⣿⠀⣾⣿⣿⡟⠀⣰⣿⡇⣰⡟⠀⢠⣾⠋⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣧⣿⣿⣧⣿⣆⠸⣿⣇⣿⣿⠟⢀⣼⣿⣿⡿⠋⢀⣴⠟⢁⡞⢀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣆⣿⣿⡿⢋⣰⣿⣿⠿⠋⣀⡴⠟⠁⣠⡿⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣭⣭⣬⣁⡰⠿⠿⢋⡥⠴⠛⠉⢀⣴⣾⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠿⠷⣤⣀⣠⣤⣴⡾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣴⣶⣿⠿⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢂⢀⢤⠊⠀⠩⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⠀⢀⠀⠀⣠⠐⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠹⡨⠄⠉⠁⠀⠀⠀⠄⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠆⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠨⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡀
⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠃⠌⠠⠀⠀⣀⣀⣀⢠⡀⠀⠤⠆⢒⠀⠀⠀⠀⠔⡀⠌⠀⠀⠁⠘
⠀⠀⠀⢀⡌⡄⠀⠀⠀⠀⠂⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀
⠀⠀⡠⠁⠐⠤⠀⠀⠀⠂⠀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠄⠀⠊⠐⠠⡀
⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠘⠀⠀⢂⣠⡀⢠⣀⠂⠀⢸⠀⡐⠀⠀⠄⠀⠀⢀⠈⢂
⠀⢜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠐⢩⣆⠀⠀⣶⡙⠀⡈⠀⠡⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢃⠀⠀⡀⠀⠀⠀⠰⡦⠀⠀⠀⠀⢀⠀⠈⠉⠀⠀⠉⠁⢀⡃⠐⢤⠄⣀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠆⠈⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠑⢤⣀⣀⣀⣀⠴⢋⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠔⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡄⠀⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢃⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠠⠀⠄⠐⠒⠲⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠐⡄⠀⠦⠤⢄⠀⠠⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠞⡠⠁⠀⠤⠄⠀⠀⠈⡀⢀⠎
⠀⡤⠒⡤⠀⠀⠂⠀⠠⠁⠁⠀⡀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠠⠀⣄⠀⠀⠀⠀⡨⠶⠎
⠈⠂⠄⠜⠀⢀⠀⣀⡘⢀⣤⠜⢫⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡁⠁⠀⠀⠀⠀⠀⡥⠈
⠾⣄⣈⣉⣀⠀⡁⠈⣂⠀⠀⠉⠀⠒⠉⠀⠀⢀⡠⠄⠠⢄⡀⠈⠀⣀⡀⠀⠀⠀⠀⠄⢀⡀
⠀⢈⠉⠓⠲⠦⠴⠒⢒⡲⠞⡋⠵⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠐⡈⠄⠊⠉
⠀⠀⠉⠒⠄⡀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⠃⠀⠠⠋⠒⠀⠰⠠⠒⡄⠀⠀⠀⠄⠒⣁⠔⠃⢀
⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠠⠊⠀⠀⠠⠀⡠⠀⠈⠀⠀⠀⡱⡞⠑⠒⠀⠒⠂⢉⡀⠤⠤⠤⠈⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀⣠⠐⠀⠀⠐⠁⠄⠁⠀⠀⢘⠀⠰⠀⠇⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠐⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⢸⢀⣠⠔⣡⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠐⠀⡀⠀⢀⠀⠈⠉⠀⠀⠀⠠⠌⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⡀⠌⡀⠁⢪⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠕⢋⡴⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⡴⠀⠦⠀⠢⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠓⢋⡁⠚⢉⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠆⠀⠀⠀⠀⠙⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠄⠂⢁⠠⠂⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣀⠀⠀⠀⠀⠀⠀⠈⠂⠄⣀⠀⠀⠀⠁⠁⡀⠄⠈⠁⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⡀⡲⠀⢠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄⡀⠈⠁⠒⠒⠠⠤⠤⠤⠤⠀⠀⠀⠈⠦⣛⠈⠀⠂⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠇⠡⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢀⠀⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣯⣿⡶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣶⣺⣾⢉⣷⣾⣿⣿⣿⣟⣿⣿⡟⣆⢀⡤⣄⣀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣄⢸⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⡿⠛⢁⠆⣿⣿⡏⣽⣷⠏⢑⣶⣴⡆
⠀⠀⠀⣀⣀⣰⣿⣿⣃⢠⡍⡇⣸⣿⣟⠯⠁⡈⠋⠛⠻⣜⢻⠏⠀⠀⢸⢰⣿⣿⣇⣿⣿⣆⣼⣿⡿⠁
⠀⠀⣸⣿⣿⣿⣿⣿⡿⢠⣾⣹⣾⣿⡅⢠⡼⠁⠀⢢⡀⠻⣿⠀⠀⡀⠠⢼⣿⣿⣿⣿⠿⢋⠻⠟⡽
⠀⠀⠘⢿⣽⢡⣿⡿⠃⣠⣹⣽⠿⣃⠀⠀⠀⠀⠂⡭⢰⠀⡇⠀⠀⠈⢄⢸⣿⣟⣿⡇⣈⠄⢧⡼⠁
⠀⠀⠀⠀⢳⣿⣿⡇⢀⠐⣼⡿⡏⠀⠖⠁⠀⢠⡃⢡⠗⠸⡄⠀⠀⠀⡘⢸⣿⣿⢿⣇⣍⣸⡏
⠀⠀⠀⠀⢈⣿⣿⡇⢰⡞⣿⣿⣧⢐⠃⠀⡙⢢⠉⠘⣴⠻⣦⠀⠀⠀⠃⢸⣿⣧⣾⣿⡟⢁⣧
⠀⠀⠀⠀⢸⣿⣿⡇⠨⠇⣿⣿⡯⣿⠀⠀⠐⢌⠁⠀⠿⢀⣯⡀⠀⠈⡆⢻⣿⢹⣿⣿⠁⣼⠋
⠀⠀⠀⠀⢾⣿⣿⣇⠀⠐⢸⣿⣿⢉⠀⢆⠀⣀⠁⠈⣴⠻⣿⡟⠀⣀⠀⣿⡿⣰⡿⢃⡼⠋
⠀⠀⠀⠀⠸⣿⣿⣿⣷⣆⠀⢻⣿⡽⡀⠠⡑⠄⠇⢀⠀⢠⣿⣷⣄⣿⢠⣿⠿⣟⡴⠋⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠈⡎⣿⣿⡄⠀⠐⣰⠄⣸⠀⢸⣿⡟⢨⡏⣼⣿⡇⠠⣁⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠣⠀⠸⣿⣻⡄⢠⣺⠁⢊⠀⣾⣿⡿⠿⣰⣿⣿⡅⠀⠘⡅
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣁⠀⢀⠀⠙⣏⡃⢠⣿⠐⠧⢠⣿⡏⠀⣰⣿⣿⣿⠇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣥⠀⠈⣥⣿⡃⢸⣟⣾⠋⢀⣼⣿⣿⠟⡠⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣶⣦⣹⣿⣿⣏⣯⣿⣷⣏⠟⡛⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⣿⣿⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿

⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠦⢤⣀
⠀⠀⡞⢉⡀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⣷⣦⣌⠳⣦⡀⠀⠀⠠⠄⠀⠀⣄⠆
⠀⠀⠁⠀⠐⡆⠤⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⢹⡜⣷⣿⣿⣿⣷⡄⠹⣆⠀⢈⢀⠄⠐⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠁⠀⠀⠈⠀⡔⠐⠀⠀⠀⠀⠀⠀⠐⠠⡀⢻⡌⢿⣿⣿⣿⣿⣧⡹⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠂⠙⢦⣈⠻⠿⣿⣿⡇⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠐⡎⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢉⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠀⠤⠐⠊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⡇⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢟⠻⣦⣄⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢄⡑⠚⣱⡶⢻⠀⠀⠀⠀⠀⠈⠛⠀⢀⠀⠀⠈⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣆⡘⣈⢀⠳⡌⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢴⡀⠀⠀⠀⠀⠀⠊⠯⠾⠯⠽⠒⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⡀
⠀⠀⠀⡀⠀⠘⠀⡘⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣧⣅
⠀⠀⢠⠀⠀⠀⠘⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣷⡅⢢⢤
⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠊⠞⠻⣽⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢶⡟⡿⠁⠓⠞⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠰⢶⣤⡿⢄⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡎⠈⠇⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠉⠘⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠠⠀⢤⡤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⢀⡀
⠀⠀⢀⠠⡄⢰⠈⢢⠀⠘⠦⠜⠴⠒⠁⠀⣴⠂⠉⠈⠴⠀⠜⠀⢉⢲⡀⠰⡁⡇⢀⡏⠈⠙⠣⢌⣑⠒⠤⠤⡄
⠀⠀⠂⢈⣾⡾⠊⡡⠐⠒⠒⠤⣈⠀⠁⠀⣿⠄⣀⡀⠀⠀⠀⠀⣀⢠⡟⠀⠏⢀⡞⠀⠀⠀⠀⠀⠀⣹⠀⢠⠏
⠀⠀⠨⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠙⢢⡀⢯⡠⠄⠀⠀⠉⠉⠀⠀⠠⡇⠀⢠⠎⠀⠀⠀⠀⠀⡰⡫⠂⠀⡎⠂
⠀⠀⠀⠀⣞⠀⠀⠀⠀⡴⠒⠒⢤⡀⠀⡇⢀⣨⣅⠀⠒⠂⠀⢀⠐⠈⠀⠀⠸⣶⣤⣀⠁⠀⢰⢱⠁⠀⢠⢹
⠀⠀⣄⣀⠘⢦⡀⠀⠐⡇⠀⠀⠀⡇⢠⠇⡎⠀⣸⠇⢠⠔⠢⡀⠉⠉⢧⣀⣀⣀⣉⠙⠯⣶⡣⠻⠭⠭⠥⠂
⠀⢸⡁⠈⠳⣀⠙⢦⠀⠈⠒⠓⠋⢠⠎⠀⢙⣋⣁⡀⠈⠢⠤⡞⠀⠾⠽⣧⠤⠤⠔⢛⠀⠀⠀⠀⡰⠊⠓⡄
⠀⠘⣧⠀⠀⠈⠑⠦⣑⠢⠤⠴⠚⣡⠒⠉⠉⠁⠀⠉⢙⡆⡀⠀⠀⡇⠀⢸⣄⣀⣀⣸⠀⠀⠀⣰⠁⠀⠀⠘⡀
⠀⠀⢹⣆⠰⡋⠉⢢⠈⢣⠀⠀⡞⠀⢧⠀⠀⠀⠀⠀⡸⠀⠈⠱⡄⢸⠺⠶⢿⡖⠚⢻⠀⠀⠀⡟⠒⠒⠒⠒⡃
⠀⠀⢸⡘⣄⠑⠢⠞⠁⣸⠀⢰⠳⣇⢈⣆⡬⠥⠤⠤⠧⣄⣨⠊⢣⠘⡆⠀⠈⢧⠀⡏⢀⣤⠀⠈⠻⠶⠶⠚
⠀⠀⠀⠑⠮⣽⣶⡶⠞⠁⠀⠘⠶⠚⠉⠀⠀⣄⣀⢀⠀⠀⠈⠲⠚⢀⣙⠲⠶⠒⠚⠁⠹⠤⡇⠰⣖⣃⣘⡶⠄
⠀⠀⢠⠤⢤⡔⠒⣒⡈⠉⠙⢢⠊⢹⠀⠀⢀⡱⠽⣿⣀⡤⣄⡀⠀⣾⡻⢿⣖⣒⣒⣒⣒⠦⣌⠉⠒⠦⣄
⠀⠀⠀⣧⠘⠻⣶⣤⣀⠀⠀⠀⠡⡀⡇⢀⡏⠊⠀⠀⠀⠀⠀⡙⡄⠈⠻⠿⠶⠿⢿⣭⣭⣟⡾⣵⠄⠀⠈⡆
⠀⠀⠘⢏⠁⣂⠻⠮⣿⠳⣦⣄⡀⠐⣍⠀⣇⠀⠀⢠⠠⡀⠀⢀⠇⠀⣯⣕⣒⣒⣒⣂⠤⢍⠻⠃⠀⡠⠤⠧⡄
⠀⠀⠙⢦⠉⠺⢵⡤⣈⠒⠄⢉⠋⠵⠏⠀⠘⣆⢄⠀⠀⠀⢀⡜⠀⠘⠷⣿⣓⣲⣈⡩⠉⠲⡆⠀⢠⢧⠄⢴⡇
⠀⠀⢈⣿⣦⣖⡲⠈⠪⢕⠦⣥⠜⠀⣀⠤⣀⠈⠙⠛⠛⠛⠉⢀⣤⠖⠒⠒⠒⠦⣄⠉⠳⠬⠇⠀⠙⠺⠶⢯⠇
⠀⠰⠟⠋⠀⠀⠀⠀⠀⠀⠉⠀⣔⠋⠀⠀⢀⣉⠒⠤⢀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⡳⠀⣀⣤⡴⠶⠶⢤⡀
⠀⢰⢺⠳⡶⠶⠿⠿⠟⠚⡃⠀⣳⡄⠀⡀⠙⠛⠉⠙⠒⢳⠀⢯⡦⣄⠀⠀⠀⠀⢹⠁⡼⠡⡚⣀⠤⣄⠀⠙⡄
⠀⠈⠻⣇⠁⠀⠀⠀⠀⡸⠀⠀⣯⠀⠘⠛⠀⢠⢦⡄⠀⢳⠀⠀⠙⡾⡄⠀⠀⠀⠘⡄⣇⡔⠁⢧⣀⣿⢃⡀⡇
⠀⠀⠘⠯⣷⣤⣤⣤⡼⠕⠀⠀⠧⢤⣄⣀⣠⠬⣉⣀⣀⡼⠀⠀⠀⢧⣇⠀⠀⠀⢀⡇⠘⢮⣒⠲⠔⠲⣪⠟
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉

⣿⠋⠉⠛⠉⠙⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢏⣍⠛⠛⢿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⡇⡷⣸⠈⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠁⢙⠀⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠐⠐⠀⠃⠲⠑⠈⠻⠁⠜⠀⡰


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠀⠀⠐⠀⠂⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃
⠀⠀⠀⠀⠀⠠⠂⠠⠤⠒⠄⠄⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿