Zoo Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⡏⢸
⠀⠀⠀⠀⡀⣳⢸⡆⣠⡤⠀⣀⣀⠀⠀⠀⠀⢸⠙⣠⠃⠖⠃⠻⠀⠀⠀⢠⡀
⠀⠺⣀⡀⠠⢠⡀⠉⠁⠧⠴⠃⣏⢀⠀⠀⣀⠊⣀⠀⢀⠪⢁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀
⠀⠀⠀⠀⣠⠊⣡⠔⢰⢄⠄⠠⡜⠁⠀⠀⠈⢿⣩⣤⣶⣬⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢳⡀
⠀⠀⠀⠰⠅⠊⠁⠀⣠⣫⣶⡿⢁⣤⠀⢰⡆⠘⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢰⠏⠀⠀⠘⣇⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠉⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⣴⢃⣞⢃⡼⢀⡒⡶⢾⣿⢁⣀⠀⢀⣾⡇⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣀⠀⠀⠀⠀⠀⠀⢠⡄⠙⡆⠀⠀⠀⠀⣀⠀⡏⢱⢹⣟⠘⠻⠏⢀⣫⠭⠖⠋⠁⠲⠦⣦⠘⠱⣋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠹⢄⡀⠀⠀⠀⣠⠟⠀⣰⠇⠀⠀⢀⠄⠘⠿⢷⠈⠀⣉⡤⠖⠈⠀⠀⠀⠀⢀⣠⣄⡀⠀⠉⠙⠓⠒⠒⠚⣩⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠳⢤⣈⣉⡈⢉⠀⠠⠞⢣⡀⠀⠀⠋⣈⠉⠰⠀⡠⠞⠥⠤⠞⠠⢀⢀⣿⠀⠈⠉⠁⠀⠀⠀⠀⠀⣠⡀⠀⠉⣠⣟⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠠⣀⣗⣉⠀⣠⠊⠀⠀⠀⠀⠀⠙⡄⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⣄⠉⢀⣠⠞⡩⢫⡞
⠀⠀⠀⠀⢀⠄⢄⢀⡏⠀⡰⠋⣹⠀⠀⠀⠀⠀⢀⠇⠀⠀⢰⠯⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡌⢀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠉⠉⠛⠐⢋⣀⡴⠃
⠀⠀⠀⠀⢣⠠⠀⠻⡀⡰⠁⢠⡷⠂⣰⠀⣀⠀⠸⡄⠀⠀⢻⠀⠹⡾⢁⠄⠀⠀⠀⠠⣀⢀⠘⠀⠄⠀⢀⠿⡄⠀⠀⠈⠙⠲⠦⠤⠤⠞⠉
⠀⠀⠀⠀⠈⢆⠀⠀⠱⠇⠀⠚⠀⠀⠉⠀⠛⠐⣄⠱⡀⠁⢀⠕⢠⠋⠀⠀⠀⠀⠀⠀⠀⠳⡌⠂⣀⠔⠋⣼⠀⠀⠀⠀⣠⠚⠓⢶⣤
⣀⠠⣇⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⢋⣤⢹⡤⠏⣀⠈⠂⢀⣤⠃⠀⣀⡀⠀⠀⠀⡀⠀⠀⢻⣌⠁⠠⣀⡟⠀⠀⠀⢸⡇⣾⣷⠆⢻⠇⢤⡀⡀⠀⢀⣀⣀⣀⡀
⢅⡀⠀⣨⠀⢤⡀⢀⠄⠐⠈⠀⠀⠉⠘⠛⣼⠁⢠⠋⣠⣾⣿⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣾⣷⠦⠀⠀⠘⣧⠈⠁⠀⠀⠀⠀⠀⠉⠛⠛⢁⣤⡈⢳
⠊⠀⢸⠡⣶⣦⠉⠀⠀⠀⠀⠀⢀⡠⡄⠀⠘⢧⡶⠾⠿⠿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡍⠉⢹⡅⠀⢀⣴⡾⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠛⢁⣼
⠘⠀⠀⠳⢌⡋⠀⠔⠂⢸⠀⠙⢆⠀⠀⠀⠀⠈⢷⡀⠀⠀⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⣄⠈⡇⠀⣾⠄⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⢻⡃
⠁⡰⠒⠀⠀⡽⠀⠀⠀⢸⣤⣶⣾⡇⠀⠀⠀⠀⢨⡇⠀⠲⣝⠁⠀⠦⣄⣀⣀⠀⠀⢀⣀⡴⠆⠙⡄⠈⢣⣻⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣻⡇
⡼⢱⠀⠀⠀⣧⠀⠀⠀⠀⡉⠙⣿⠀⢸⠇⠀⢀⠞⠁⠀⢀⡟⠀⡀⠀⠀⠉⠉⠉⠉⠉⠁⣀⡀⠜⠁⠀⠀⢻⡧⣿⣀⣀⠀⠈⠉⢹⣿⢶⣄⠀⠀⠀⠀⠀⠀⣿⠁
⠘⠚⢢⠞⠀⢻⡄⠀⠀⠀⠓⠔⠃⠀⣀⠤⠖⠁⢀⠠⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠧⢹⣿⡋⠀⢦⣠⠏⠀⡀⠹⡆⠀⠀⠀⢠⣼⡟
⠀⠀⢿⢀⣀⠀⠉⠓⠂⠀⠀⠒⠈⠁⢀⠀⠀⠈⠀⢀⣠⡀⠀⠀⠀⣠⣶⣶⣦⣤⣄⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠈⠀⠐⢠⡉⠀⠉⠀⠀⡇⠀⢀⢐⣽⠟⠲⣄
⠀⣠⢎⡞⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣴⣾⣿⣿⣿⡟⠀⠀⢠⣿⣿⠋⢻⣿⣿⣧⠀⣰⣿⣿⠟⠛⣿⣿⣦⠀⠀⠀⠀⣾⣷⠶⠦⣤⡼⠿⠷⠛⠉
⢰⠃⣾⢸⠀⠀⣼⡇⠀⠀⠀⠨⣇⠀⠈⢿⠿⠟⣿⣿⡟⠀⠀⠀⠘⣿⣿⣦⣾⣿⣿⠟⠀⠸⣿⣿⣀⣠⣿⣿⣿⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠
⡏⠀⢻⡘⣠⠞⠀⣷⠀⣠⡇⠀⢹⡀⠀⠀⠀⣰⣿⣿⣥⣤⣶⣾⣆⠈⠛⠻⠟⠛⠁⠀⠀⠀⠙⠻⠿⣿⠿⠟⠁⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠳⣀⠴⢳⡀⠀⢰⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢠⢱⡄⢀⣩⣤⠀⠀⠀⠸⣿⣇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⢾⡎
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢸⡄⠉⠁⠀⣿⣆⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣷⠂⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠈⣮⣿⣷⠀⠀⠀⠈⡇⠀⠀⠀⠻⣿⡄⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠅
⣶⣶⣶⣶⣶⣷⢷⣾⣿⡿⣷⣿⣿⣶⣿⣶⣿⣾⣾⣿⣿⣶⣾⣷⣿⣿⣷⣿⣶⣷⣶⣶⣶⣾⣷⣾⣿⣾⣿⣿⣶⣶⣶⣾⣶⠿⡶⠶⠾⠷⠿⣿⡷⠷⠶⡾⠶⠾⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⢁⠄⠿⠈⠀⠂⢀⠆⡁
⠀⠀⠀⠀⠘⠠⡀⠀⡴⢓⣶⡀⠀⠀⠀⠄⠀⠀⠀⠠⢌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸
⠀⠀⠀⠀⠀⠀⢠⠉⢀⣈⠋⠀⠀⠀⠤⢤⣥⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠐⢿⠿⣷⢠⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄⠀⠀⠀⠀⠊⠁⠸⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡁⠡⢀⡀⠀⠀⠀⠀⠀⢀⠄⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠖⠠⠤⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠈⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠠⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠘⠈⠀⢦⠀⠀⠠⠤⠤⠠⠀⠀⠀⠀⢈⠀⠀⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠠⠀⢀⠃⠀⠀⡁⠀⠠⠀⠢⡀⠀⠀⠀⢆⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠄⠀⠀⠀⠀⠀⠂⠀⠱⢄⠀⠀⠃⡀⠀⠒⠐⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⢨⠀⡄⠀⠠⠀⠐⢃⠈⠉⠀⠀⡠
⠀⠀⠀⠀⠀⠀⡄⡀⢀⡀⢀⠄⠈⠀⠀⣀⡠⠀⢃⠀⢠⡄⠀⠸⠀⡅⢀⡀⡆⢀⠀⠠⢀⡀⡀⢠
⠀⠀⠀⠀⠁⡀⡀⠀⠀⠀⢠⠈⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠃⠈⠈⠀⠀⠀⠀⠚
⠀⠀⠀⠀⡚⠻⠬⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⡠⠀⠀⠀⠀⠰⠼⡢⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠢⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠉⠒⠁⠈

⠁
⠀⠀⠀⠀⠰⠂⠄⠀⢀⠀⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⣶⡎
⠀⠀⣀⣤⣾⢻⢮⢹⠁⠘⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⣴⣾⢇⣴⣿⣭⠸
⡶⠺⠙⡎⣷⡆⢶⡼⡆⣼⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠸⢣⠾⠖⠘⠋⠉
⡇⡆⣇⣿⡏⡇⠠⣵⣷⣷⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡧⣇⣿⡏⣇⢷⣈⣶⣾⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣛⠲⣍⣳
⡇⣿⡏⣇⠻⡄⠉⢿⣿⣿⠏⠀⠀⠀⠲⠶⣶⠆⢠⠖⠒⢦⡀⢠⡶⠒⢦⡀⠀⠀⠀⠀⢸⣇⠲⠈⠀⠀⡀⢀⣼
⡇⡏⣇⠻⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡼⠃⠀⣿⠀⠀⢸⡇⣿⠀⠀⢈⡇⠀⠀⠀⠀⢧⣙⠁⢀⡤⣞⣼⣿⣇
⠑⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠆⠘⠶⠴⠞⠁⠘⠳⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠂⠁⠀⠀⢀⢀⡆⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿
⠀⠀⢠⣘⣾⣾⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠈⠻⣿⣿
⠀⠀⠈⠛⠛⠻⣿⡇⠀⠀⣠⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉
⡄⠀⠀⠀⠀⣡⣮⠀⠀⣼⠏⠀⠀⠀⠀⠉⠳⠀⠀⠐⠀⠀⠀⠀⠂⠐⠞⠋⠀⠈⠀⠈⠻⣄
⠂⠀⠀⠀⠀⠈⠁⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣼⡟⠁
⠀⠀⠠⠊⠀⠀⣄⢀⣄⠀⠀⠙⠢⠄⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⡀⢀⠀⢄⣀⣠⠔⠁⠀⠀⠀⠙⠀⠀⠀⠈
⠃⠀⠀⠀⠀⠠⣤⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⢡⣩⣶⢄⣀⣀⠀⠀⠀⢹⡆⢻⡏⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⢤⣄⣤⣀⢤⠿⠏⠈⠀⠂⠀⠀⠀⠀⠀⠀⣠⣿⣷⣶⣿⣿⣿⣷⣶⣶⣿⣿⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⢋⠈⠉⢠⣤⠀⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣟⠡⠀⠠⢶⢶⠀⢠⠄⢁⣉⠻⢷⠃⠀⠀⠀⠀⠀⠀⣿⣿⣭⣬⣿⣿⣿⣿⣿⣿⣏⣹⡿⢿⡿
⠀⠀⠀⠀⠀⢀⢠⡏⠈⢨⡜⠀⡿⠀⠀⠀⢚⣿⠀⠻⠀⠂⠀⠀⠀⠀⢀⣿⣿⣿⣯⣿⣿⣿⣿⣧⣼⣿⣿⣗⣿⣷⡆
⠀⠀⠀⠀⠀⣾⠀⠴⠀⠀⠠⢴⠁⠀⠀⠀⠀⣴⢀⢠⠤⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⢽⢈⡀⡆⢀⢰⣶⣤⣤⡄⠀⠀⠩⠴⠷⠁⠀⠀⠀⢀⠀⢽⣿⣏⣿⣿⣿⣟⣯⣽⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠙⠀⠞⠀⠀⠀⠀⠀⠑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⠜⡥⠉⠩⢉⠉⠿⡾⠈⠀⠀⠐⠠⠄⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠉⠀⠛⠃⠒⠚⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠡⢬⣿⠧⢤⠬⡝⣧⠒⠜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢨⡫⠤⡠⢌⠻⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢹⢂⡞⣷⢖⣮⠴⣸⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠛⡰⢢⡧⢆⠅⢃⠀⢸
⠀⠀⠀⠀⣠⣤⣤⣞⣿⢀⡼⠛⠛⢻⣇⠀⣧⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⣠⢀⠃⢀⠔⠃⠘⢄⠀⢘⡀⢘⡀
⠀⢰⣶⣾⣿⣿⣏⣽⣽⡿⠀⠀⠀⢠⣿⣴⣁⣩⣴⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡖⢂⢀⠠⠤⣩⢋⠧⠆⠀⠀⠀⢸⡀⢎⡈⠅⠖⠢⠤⣄
⠀⠈⣿⣟⣁⣦⣤⢿⣿⣧⠠⢀⣴⣿⣻⣿⣿⣿⡿⠿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⢎⢉⡀⢀⡄⠃⠀⡀⠀⢠⡴⠋⠀⡸⠁⢄⠐⠄⠤⢀⠈⡄
⠀⠀⣿⣴⣿⣤⣿⣿⣿⠙⣦⠺⣿⡏⢹⣿⣿⡟⣱⣤⡄⢹⣿⡿⠀⠀⠀⠀⠀⠀⠈⢠⢔⡤⠐⣅⢦⡌⢡⡀⠲⠲⠉⠂⠟⢀⠈⡦⢤⠀⠁⢀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⣹⣿⣿⢁⣸⣿⣿⣏⢙⡿⠛⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⡞⡈⠁⠀⠁⠀⢁⠀⣧⢭⡇⢀⡬⣆⢈⠀⠓⠊⠰⢄⡘
⠀⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣓⣦⠀⠀⠀⠀⠀⢠⠔⣦⣀⠀⠀⢀⡠⠋⣛⡁⠀⣉⣉⠀⣈⣦⡈⠉⢐⠠⣞⣲⡄
⠀⢯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣨⡟⠀⠀⠀⠀⠀⠸⡉⠀⢹⠉⠉⠁⢘⡹⠟⠃⢸⠋⠙⡷⡏⠈⣻⠉⠀⡸⠀⢩⠃
⠀⠘⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠘⢿⣛⣛⣈⣳⣞⣁⣙⣛⣋⣀⢀⠇⢠⠃
⠀⠀⠹⣬⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⡸⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠎
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⣴⣾⣿⣷⡀⣿⣿⣿⠀⣿⣿⣿⠠⣿⣿⣿⢰⣿⣿⣷⠀⣾⣿⣿⡆⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣔⢿⣿⣿⣿⡌⢿⣿⣿⣷⢹⣿⣿⡇⣿⣿⣿⡄⣿⣿⣿⡄⣿⣿⣿⠀⣿⣿⣿⠁⣿⣿⣿⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡻⣿⣿⣿⡎⢿⣿⣿⠎⣿⣿⠇⢿⣿⣿⠇⢿⣿⣿⡇⣿⣿⣿⢨⣿⣿⡿⢠⣿⣿⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣶⡿⠿⢷⣬⡙⣿⣿⣷⣜⢿⠿⠋⠀⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⠛⢱⣿⣿⠁⠴⠆⠹⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠰⠀⣙⠻⣿⣿⠿⠋⠀⠀⠀⠀⢠⣤⡀⢿⣿⡌⣿⣿⠃⣸⣿⠟⠀⢀⣀⠀⠀⠀⠀⠀⠀⠙⠟⠐⣃⠐⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠺⠀⣉⠀⠀⠀⠀⣠⣴⣶⣶⣦⡀⠻⣷⠀⠻⣧⢻⡿⢠⡿⠃⠀⣠⡿⠛⣀⣤⣤⣀⠀⠀⠀⠀⣶⣤⣠⣴⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠸⣿⣷⣘⣀⣉⡀⠀⠀⠾⢿⣿⣿⣿⠉⢻⡄⠸⣧⠀⠹⠎⠇⠾⠁⢠⡾⠋⢠⣾⣿⡇⠀⣙⣷⡤⠀⠀⢙⣛⣛⣛⣋⣉
⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⠀⢹⠆⠀⠀⠀⠀⠀⣿⠀⠠⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣝⣛⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⣭⣭⣴⣶⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣭⣛⡻⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣈⣛⣉⣩⣥⣴⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣶⣤⣭
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣀⠀⠀⠀⢸⣿⣷⣬⣙⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⢛⣋⣥⣶⣦⠀⠀⠀⠀⠀⢰⣏⣀⣤⣤⣴⣶⣶⣦⣤⣸⣇⠀⠀⠛⠁⠀⠀⠘⡻⢿⣿⣿⣿⣶⣬⣭⣭⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⡿⠟⢰⡆⣀⠀⠦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠟⠁⠿⠁⠀⣼⣿⣷⣮⣍⣛⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⣋⣥⣶⣿⠀⣠⠉⡀⠶⠈⠛⠿⠋⠀⣿⣿⠁⠀⠙⠟⠋⣀⠰⠶⢀⡋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣄
⠀⠀⠀⠀⠀⠀⠛⠛⣋⣩⣴⣾⣿⣿⣿⣿⣿⡄⠉⣀⡉⢀⡘⠋⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠛⢰⡆⠈⠁⠀⢹⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣇⠀⠉⠁⠉⠁⠀⠀⠀⣠⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣦⣭⣛⠻⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠛⢋⣥⣾⣿⣿⡿⣿⣦⣀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠉⠻⣦⣄⡀⠀⠀⣀⣠⣾⣿⣿⣯⡛⢿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⢋⣼⣿⡿⣿⣷⣶⣶⣿⡉⠀⠀⠀⠀⠀⠀⣀⣩⣿⣿⣿⢿⣿⣿⡙⢿⣿⣿⣦⣙⠻⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⣵⣿⣿⠟⣴⣿⢃⣿⡟⣿⢻⣿⢶⣾⡿⣿⣿⡛⣿⣧⢿⣿⡘⣿⣿⣿⣦⠻⣿⣿⣿⣷⣄⠙⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⣡⣾⣿⣿⢋⣾⣿⠇⣾⡿⢰⡟⢸⣿⡘⣿⣷⢹⣿⣧⢹⣿⡎⢿⣷⡜⢿⣿⣿⣷⣌⠻⣿⣿⣿⣷⣦⡀⠉
⠀⠀⠀⠀⠀⠀⠀⢿⡿⢋⣴⣿⣿⣿⡿⢡⣿⣿⡟⣸⣿⠇⣾⡇⢸⣿⡇⣿⣿⠸⣿⣿⡆⢿⣿⡌⢿⣿⣌⢿⣿⣿⣿⣷⡈⠻⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡟⣰⣿⣿⡟⢠⣿⡟⢸⣿⡇⢸⣿⡇⢸⣿⡇⣿⣿⣷⠸⣿⣿⡌⢿⣿⣦⠹⣿⣿⣿⣿⣦⡈⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⣴⣿⣿⣿⢡⣿⣿⠃⣿⣿⡇⢸⣿⣿⢸⣿⣧⢸⣿⣿⡆⢻⣿⣷⡘⣿⣿⣷⡘⢿⣿⣿⣿⣿⣦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠁⣼⣿⣿⣿⠃⣾⣿⡏⢸⣿⣿⡇⢸⣿⣿⠸⣿⣿⠘⣿⣿⣿⠘⣿⣿⣷⡘⣿⣿⣿⣄⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⣼⣿⣿⠇⣸⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⣿⣇⢹⣿⣿⣧⠹⣿⣿⣿⣦⡙⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⢰⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡀⣿⣿⣷⢸⣿⣿⣿⡈⣿⣿⣿⣆⢻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢁⣿⣿⣿⡏⢰⣿⣿⣿⡇⢸⣿⣿⡇⣿⣿⣿⡀⣿⣿⣿⣇⢹⣿⣿⣿⡄⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⣿⣿⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⡇⢿⣿⣿⣿⡄⣿⣿⣿⣷⡈⢿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⢸⣿⣿⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⣧⠸⣿⣿⣿⣧⠸⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⡀⢿⣿⣿⣿⡄⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠿⠿⠇⠸⣿⣿⣿⡇⠘⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠙⢿⣿⣿⣿⣿
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⣿⣿⣿⣷⣦⡀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⢟⣽⠁⠀⠀⠀⡈⠀⠈⠐⠀⢰⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻
⡿⣱⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⣴⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿
⣿⡇⠀⣿⣿⣿⠀⠘⣹⣿⣿⠈⠉⠀⠈⣿⣿⣿⣿⣿⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⣿⡇⠀⠛⠛⠛⠀⠀⠘⠛⠛⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠘⠓⠐⠀⠀⠈⠀⠀⠀⠀⠛⠛⠃⠀⠀⠘⠃⠀⠀⠘⠛⠃⠀⠀⠀⠀⠘⠃⠀⣿
⣿⣇⣀⠀⠀⠰⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠀⠀⠀⠐⠀⠒⠂⠀⠂⠀⠀⠂⢀⣹

⠀⠀⠀⠀⠀⣀⢀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠢⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⡀⠀⠈⠁⠒⠄
⠀⠀⠀⢀⡀⣀⠀⣸⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠨⠰⠈⠀⢠⠀⠀⠴⠄⠀⠈⠀⠀⠁
⠀⠈⠘⠘⠁⠏⠋⠃⠦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠛⠹⠐⠀⠤⢸⠅⠀⠀⠀⠀⠶⠃
⠀⠀⠀⡣⢰⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⢤⡵⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠘⢀⣠⣬⣬⡀
⠀⠀⠀⠉⠀⢂⠠⠤⢁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠀⠈⢿⣽
⠀⠀⠀⠠⠀⡈⠄⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡷⣆⠀⠀⠀⠀⠀⠀⢀⡀⣴⡿
⠀⣀⢀⢀⠀⠀⠄⠂⠀⣀⠚⠛⠶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠀⠀⠀⠐⡾⠛⠛⠁⠈
⠲⠃⠘⠎⠀⢿⠀⠀⠸⢭⢀⡀⠘⢟⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠐⡀⠀⠀⠀⠀⠡⠒⡡
⠒⠀⠷⢄⠒⢡⡀⢀⠀⠊⠀⠈⠖⠊⠀⠀⠀⠄⠄⠰⠄⠀⠀⠀⢄⡀⠁⠀⠀⠀⠀⠀⠀⠈
⠈⠆⠂⠈⠀⠈⠀⠀⠠⡀⠀⠀⠠⠀⠀⢈⠀⠀⠀⠘⠀⠂⠀⠀⠤⠔⠀⠀⠀⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠀⠄⠂⢐⠀⠰⠁⢀⢤⡉⡽⠀⠉⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠠⠐⠀⠈⠃⠀⢀⡄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢄⠽⠿⢿⣯⠁⠀⠀⠀⠀⠀⠀⠐
⠉⠀⠀⠀⠀⠀⠀⠂⠁⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠁⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠈⠂⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢿⡿⠉⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣇⣀⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣔⣀⣀⣀⣀⣈⣙⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣦⣀⣀⣐
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⠀⠃⠀⠘⠃⠀⠘⠀⠀⠛⠀⠀⠛⠀⠈⠃⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⢲⡄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⠉⠐⠇⠀⠸⠇⠀⠺⠀⠀⠶⠀⠐⠆⢠⡴⠆⡌⠂⠀⠀⠀⢸⡅⠠⠀⠀⠠⠠⠔
⠀⡀⠀⢰⠀⠀⠀⠑⠒⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣺⢺⠀⠀⡇⠀⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢠⠀⠀⡀
⠀⠃⠀⢸⠀⠀⠄⠰⠄⠄⡀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣾⠰⠀⠂⠰⡇⠀⡇⠀⠰⡄⠀⢸⠆⣤⠀⡀⠀⠁⠘⠀⠀⠃
⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠒⠀⠀⠀⠀⠀⠀⢠⠃⡂⠀⠀⢴⡇⢀⣇⠀⢐⡇⠀⢸⡇⠖⠀⠀⠀⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠁⠀⠀⢀⡇⣀⡧⢀⢈⣇⠀⣸⠇⣏
⠀⢰⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⢇⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⡠⠊⠀⠊⠀⠀⠀⠰⡇⠀⡇⠀⡗⡁⠂⣼⣿⢯⢳⢀⠀⠀⡆⠀⢰
⠀⠈⠀⠀⠂⠀⠀⠄⡄⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡸⠁⠄⠘⠁⠀⠀⠀⢀⣇⣢⣷⣼⢢⡀⣰⢸⡙⠀⠀⢰⣶⡄⠇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀⠀⠀⠀⢸⣅⠛⡏⠉⠀⢡⡇⢼⡆⠀⠀⡇⠡⣈⠃
⠀⠀⡄⠀⠬⠀⠀⢀⠴⢦⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠓⠤⠐⢤⣘⣸⣇⠤⠤⣀⣀⣹⠆⠀⡄
⠀⠀⠁⠀⢘⠰⠐⢦⡤⡆⠈⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠉⠉⠁⠈⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠈⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⢂
⠀⠀⣀⠀⢰⡠⠤⡄⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢹⠀⢀⡀
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡄⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠔⢄⣨⣨⣝⡑⣆⣲⢊⡁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⢢⡤⡆⠋⠁⠉⠉⠈⠉⠁⠰⠆⠰⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢧⡼⠀⠀⠀⠀⠔⠣⢄⡀⠀⣀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⣀⠲⠀⠔⠀⠈⠁⠀⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠐⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⣀⣀⡠⢄⠄⡀⣤⡀⠀⠀⡀⠀⠓⠌⠀⣐⡦⠤⠐⠒⢒⠒⢤⠔⠚⣤⠁⠀⠹⣧⡌⠤⠒⠀⠀⢈⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⠚⠀⠀⠀⠀⠧⠃⠘⠞⣯⡏⠽⡏⠙⣇⠋⠑⡓⣤⠀⠀⠀⢀⠅⡌⠀⠐⠭⠆⠀⣀⠘⠵⡆⠀⠀⠀⠀⢉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⡍⢹⠀⢩⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠢⠀⠀⡤⢰⡦⣤⢠⠤⠞⠢⠀⢠⡋⠉⠉⢆⢸⠀⠀⠀⠀⠈⢆⠐⠃⣠⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡣⠤⠀⠈⡩⡦⡇⢠⠀⠇⢠⢂⣼⢱⡀⠦⣏⠀⡀⠀⠀⠀⠀⢠⢄⠀⠈⠀⠀⠀⠀⠀⡆⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⡀⢀⠔⠐⣤⠾⠥⡇⣀⡰⡇⢘⣰⠤⠊⢀⠋⣤⡾⢎⢇⠀⢸⡀⢣⡀⡀⠀⠤⠁⠀⠁⡃⠀⠀⠀⠀⠀⣄⡀⣀⡔⠣⠀⠀⢀
⠀⠀⠀⠀⢨⠀⠀⢝⡦⠤⠇⠀⠤⠤⠌⠉⠉⠀⠤⠀⠰⠓⠀⠐⠓⠀⠛⠛⠃⠀⠐⠃⠀⠀⠂⠐⠒⠐⠛⠂⠀⠀⠀⠚⠛⡒⢛⠓⠓⡆⠡⡀
⠀⠀⠀⠀⠠⠉⠈⣨⡇⠀⣶⣶⡮⠉⢁⠉⠉⠁⠈⠁⠀⠀⢠⠉⠉⠉⠉⠉⢀⣀⠤⠀⣀⠀⠀⠀⠀⢈⡉⠉⣈⡀⠀⠀⠹⠭⢿⠀⠀⣏⠱⠄⠦⡀
⠀⠀⠀⠠⢟⡐⠚⠉⡇⠀⣷⠎⠀⠀⠈⠀⡀⠄⢲⢚⠝⠡⠃⠀⠀⠀⠀⡔⡱⢻⣳⡀⠀⢡⠀⠀⠆⢹⣟⣦⠀⠈⠆⠀⠠⠐⣼⠀⠀⡃⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠨⠡⠋⡇⠀⠁⠀⠀⠀⠈⠁⠀⢐⠞⠁⣰⣦⠀⣀⠠⠤⠀⠇⢇⠀⠀⠐⡄⡜⠀⠰⠀⡇⠻⠋⢣⠀⡄⠀⠀⠀⠀⡀⠀⡇⠉⠃⢡
⠀⠀⠀⠀⠀⡘⠒⠉⢚⠀⢃⡄⠀⠀⠀⠀⠰⠁⠀⠰⠑⠈⠁⠀⠀⠆⠐⣄⣀⣩⣶⡾⠋⠁⢼⠧⣄⣈⣁⣲⡞⠈⠀⠀⠀⡀⡀⠁⠀⣧⠨⠙⡅⡀
⠀⠀⠀⠀⠐⡁⢀⣀⣸⢀⠛⣄⢀⡀⠀⠀⠛⠻⡥⠙⠛⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⠋⠉⠈⠀⠀⠀⢀⣾⢿⡷⣯⣖⠀⠈⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠤⠒⢘⢜⠘⠛⠛⠛⠂⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠉⠉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣋⠀⠀⠀⠣⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘

⠀⠀⠀⠃⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢸⣣⣼⣦⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⡿⢿⠟⠿⠆
⠀⠀⠀⠀⠀⢠⣶⣿⠞⢹⢻⣿⡦⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠
⡀⠀⠀⠀⢀⣟⠛⠀⠀⢰⠀⠋⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢂
⢿⠀⠀⠀⠾⣿⡆⠂⣄⣸⠀⠈⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓
⣿⡆⠀⠀⢸⣿⣃⠀⠙⠛⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣡⣴⠀⠀⠀⠀⠀⣼⣾⣷⣆⢠
⢿⠃⠀⠀⠀⠼⢿⣶⣶⣖⣦⣼⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⠟
⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⣶⣶⢰⣶⣶⠎
⠀⠀⣀⡀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⢻⡟⠀⠀⠀⠀⠀⠀⠠⣄⠠⣶⠖⣀⠂
⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠈⢣⣶⣦
⠀⠀⠀⠀⠠⠶⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠠⣽⢹⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣿⡮⣭
⠀⠀⠀⠀⢀⠀⡀⠀⠄⠇⠀⠀⠀⠀⣀⣀⠔⠒⣒⠒⠠⣄⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢏⢀⠀⢐⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢰⣿⡷⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣿⣷⣾⡧
⠀⠀⠀⠶⢤⣤⡤⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⠛⠛⣿⣷⣿⠆
⠀⠀⠀⠀⠸⢿⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⡏⠀⠀⠀⣿⣿⣧⠄
⠀⠀⠀⡖⢢⣤⣴⠐⡇⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉⠖⠚⠀⠀⠀⠀⠀⢨⣿⣿⡇⠀⣶⠄⢿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢲⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⢄⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⡻⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡄⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠤⠤⣾⣿⣟⣶⣃⠀⠊⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠠
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠆⠑⣤⡟⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⢿⣿⠁⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣤⡏⠀⣼⠇⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠁⢸⣦⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⣀⡄⠘
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⠋⠀⣴⣿⠃⠀⠀⠀⠁⠀⠀⠀⠘⡿⢽⡢⢄⡀⠀⣀⡆⠸⣿⣷⣷⣼⠋⠀⠀⠀⠀⡄⠀⠀⢣⠀⠸⠇⠤⣿
⠀⠀⠀⠀⠀⠀⠀⡻⣦⡀⠘⣶⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠘
⠀⠀⠀⠀⠀⣎⢰⡇⢸⣿⡆⢹⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⢸⣯⠀⡘⠉⣷⡀⢹⡄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡀⠄
⠀⠀⠀⠀⠀⠈⠁⠘⠁⠈⠙⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣰⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣷⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠶⠶⠶⠶⠾⠑⠛⠁⠀⠀⠀⠠⠒⠛⠹⠉⠃⠁⠙⠁⠀⠀⢢⠄⠋⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⣄⠀⠼⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠀⠀⠀⠀⡀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⢸⡦⣤⠀⢠⣤⠿⠛⢿⠀⢹⠀⡁⠀⠀⠀⢀⡌⣠⣦⠀⠂⢸⠤⠀⡀⣴⠆⢀⡴⠀⠀⠀⠀⢠⣿⠀⣰⠟⠦⠀⠀⠔⠃
⠀⠀⠀⢠⠊⢀⡾⠀⠈⠀⠀⠀⠀⠀⠈⣆⢘⣴⠃⠀⠀⢀⣼⣴⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠘⠁⣼⠁⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⣼⣠⡏⣇⠀⡂⠀⠀⠀⠀⠀⠀⢻⣸⡟⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠸⣁
⠀⠀⠀⢽⣿⡄⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢡⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠄⠀⠀⠀⢀⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡀⡠⣴⠃⠀⠐⡋⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢰⡃⠀⠀⠀⠀⠁⡀⠒⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡆⢇⠠⠚⠒⡀⠀⠁⠀⠀⠉⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠀⠙⠺⠄⠀⠀⠀⠀⠀⠈⠉⠀⠉⠖⡂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠍⠀⠀⠀⠠⠄⠀⠬⠈⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⢫⡑⠢⡀
⠀⠀⠀⠀⠀⠀⣀⠤⣺⢀⡀⠀⠀⠀⠀⢨⡑⠒⠂⠢⠬⠤⠤⠤⠤⠤⠤⠔⠠⠒⠚⠋⡅⠀⠀⠀⠀⢠⢊⠄⠒⠀⠈⠁⠀⠉
⠀⠀⠀⠀⣠⡎⡄⠊⠀⠀⢀⢀⣓⠀⠄⠈⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠁⠀⠀⠀⠀⠈⠨
⠀⠀⠀⡼⠀⠑⣀⡀⠀⠀⠀⠄⠀⠀⠀⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡠⠄⠐⠂⠰⢄⡀
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡄⠀⡆⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⡰⠁⠀⠀⠀⠀⠀⠠⠉⢆
⠀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢸⠀⠀⡇⠀⣠⠖⡋⠉⠉⠙⡳⢤⠀⢰⠁⠀⡇⠀⠀⠁⠀⠀⠀⠘⠀⠀⡆
⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⢸⡷⠀⠀⢸⣷⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⡆⠀⠀⣀⠀⠀⠀⠀⠈⡿⠀⠀⡇⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠑⡶⠢⠤⠤⡤⠤⢤⠤⠤⡤⠂
⠀⠀⠀⠘⡄⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⠳⢤⣀⣀⣀⣀⣠⠔⢋⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢁⠀⠀⠀⠈⠉⠀⠀⠀⢸⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢆⣀⣀⣀⣀⡀⠤⠔⠚⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸⠤⣄⣀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣙⣶⡄⢴⣧⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⢙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣠⣶⣦⠀⣠⣴⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠐⠿⠿⠋⣼⣿⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠰⣿⠀⠀⠀⠀⠀⠙⠋⢠⣄⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣀⣄⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠚⠛⠉⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⣠⣀⠀⠰⣿⡿⠀⠀⠀⠀⣀⣤⢨⡇⠀⠀⠀⠀⢀⠰⡐⠖
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠀⠀⠀⠘⠋⢱
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠈⠄⠀⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠞⣶⣢⠀⠀⠀⠀⠀⢰⣢⠔⠒⠒⠒⠒⠒⠲⢖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⠀⠠⠌⠳⣄⠀⠀⠀⠀⢸⠀⠛⢠⣌⡆⠘⠀⠣⣤⠤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠈⢧⡀⠀⠀⣨⣦⡀⠀⠀⠈⢆⠀⠠⠛⠄⠀⠀⣀⠀⣤⠀⠉⠀⠾⠇⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣶⣿⣿⡉⠳⣄⠹⣦⣴⣿⣾⠇⠀⠀⠀⠀⠙⣶⡖⢒⣌⠀⠉⢀⡀⠀⠛⠃⢠⣄⠛⠃⢸⣦⡀
⠀⠀⠀⠀⢀⣤⠚⠹⡇⠀⢿⠀⠹⡆⠈⠳⡄⠈⠳⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⢩⡀⣈⠉⢠⡄⠈⢃⡀⠿⠂⣀⡀⢰⡶⠀⡦⣍⣒⠒⣶⣶⡦
⠀⠀⠀⣰⡏⠸⣆⠀⢻⡀⠘⣧⠀⠹⣆⠀⠙⢦⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠉⡷⢠⠊⠉⠉⠉⠉⠑⢻⡁⡎⢑⠸⠃⠀⠀⠈⠉
⠀⠀⢰⠃⡿⣄⡙⢦⡀⢷⡀⠈⣧⣀⠈⠷⣤⢄⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⢰⣼⠀⠀⠀⠀⠀⠀⠀⣷⡇⠸⣶
⠀⠀⠀⢰⣆⢹⢹⡈⡟⠉⠁⠀⠀⠈⢷⡀⡇⠸⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⣀⣄⣀⣀⡤⣈⣤⡀⢉⡴⠶⢄⡀
⠀⠀⠀⠀⡟⡿⢨⣹⠇⠀⠀⠀⠀⠀⢨⣙⠇⢸⣤⡇⠀⠀⠀⢀⣀⣤⣤⣲⣶⠶⠭⠿⠽⠷⠚⠓⠛⠚⠓⠛⠀⠉⠀⠉⠉⠀⠀⠀⠉⠉⠑⠒⠒⠒⣤
⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⣉⣀⣀⠉⠀⠀⡤⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣋⣹⣉⢭⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠁⠉⠉⠓⢦⡉⠙⠒⠒⠒⠒⠒⠢⠤⣄⡀⠀⣀⠀⢀⠤⠤⠤⠤⠤⠤⠤⣄⠀⣤⡀⢠⠴⠖⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⢀⣀⣀⠀⣀⣀⡀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠉⢦⠏⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠣⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢳⠁⢤⢀⠒⠀⣤⠈⡟⠁⢻⠀⠀⠀⢀⡄⢀⡄⠀⠀⠀⠀⠀⠀⠠⡋⠑⠒⠒⠒⠲⢤⡤⢤
⠀⠀⠀⣠⠔⠚⠋⠉⠉⢹⡄⠀⠸⡀⠀⠘⣿⠃⠀⢠⠃⠀⣸⠀⠀⣀⠴⢛⠛⣆⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀⠨⣴⣁⣀⣀
⠀⣰⢿⠁⠀⠀⠀⠀⠀⠀⠳⣀⠀⠑⠦⢄⣀⡡⠴⠋⠀⡰⠃⠀⣞⣉⡀⠀⠀⢸⡿⡄⠀⢠⢊⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠑⠢⣄⢀⡀
⣰⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠙⣦⠶⠀⣿⣧⠀⢲⠈⠁⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠏
⠀⠀⢸⢀⡶⡄⢠⡤⠤⠤⠤⠤⠤⣄⠀⠴⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢰⣿⠾⡆⠈⠳⢄⣀⡀⣀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⢸⠀⡇⡿⠀⠀⠀⠀⠀⠀⢹⢸⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣟⣿⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠞⠀⠳⠃⠀⠀⠀⠀⠀⠀⠘⠞⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⠽⡄⠀⠀⠀⢸⠀⠀⣠⡀⠀⢠⠖⠒⠒⠲⡄⠀⢠⡀⠀⢸
⠀⠀⠀⢀⡤⠤⢤⣀⣠⣤⣄⣀⡀⣠⠴⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣴⡼⡗⢶⠀⠀⠀⠸⡀⣀⡇⡇⠀⣸⠀⠀⠀⠀⣇⣀⡾⡇⠀⡸
⠀⠀⣰⠃⠀⢀⠞⠁⠀⠀⠀⠀⠹⡅⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢯⣹⣄⣀⣀⣀⡀⣀⣀⣉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⡇⠀⠀⣜⡀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠿⠿⠁⢉⣴⣤⠀⠀⠉⠉⠉⢿⠿⠋⠲⢤
⠀⠀⠹⣄⡀⢫⠁⠀⠀⠈⠉⠁⠀⠘⠤⣀⣀⡠⠎⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⢸⡿⠃⠀⢠⣤⡀⠈⠛⠋⠀⢰⣿⠆⠀⠀⢰⣿⡆⠈⣇
⠀⠀⢀⣀⠉⠙⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠈⣇⠀⠀⠙⠛⠃⠀⢸⣿⠆⠀⠀⠀⢾⡷⠀⠉⠀⡴⢻
⠀⠀⠘⢌⠙⠒⠃⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣿⢸⢳⠰⡿⠳⠶⠖⠒⠒⠒⠒⠛⠉⢳⢠⢿⢠⠇⢸⡀
⠀⠀⠀⠀⠉⠓⠒⠒⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⡇⢸⠘⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⢸⢸⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡄⠀⠀⡤⠤⠤⠤⠤⢤⡀⠀⢀⠀⠀⣿⠀⠀⠀⠀⡇⣾⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢻⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⣿⠀⠀⠀⠀⣇⡿⠀⢸⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡸⢸⡀⢀⠇⠀⠀⠀⠀⠀⢇⠀⡼⡇⠀⡟⠀⠀⠀⠀⢿⡇⠀⠘⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⢇⡾⢸⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠄⠀⠠⠄⠀⢴⠄⠀⠄⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠈⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠇⠀⢠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⢺⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⣠⣷⣤⣤⣿⣿⠋⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢿⣿⠟⠁⠀⠀⠀⠈⢉⠉⣩⣿⣧⠀⠀⠁⠀⠀⠠⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁


⠀⠀⠀⠀⠰⠶⠀⠀⠰⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⠀⠀⢠⣤⢀⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⣠⣾⡟⠛⣿⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⣿⣷⣶⣶⣿⣿⣿⣿⠟⠙⠻⣿⣦⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢀⣿⢿⣿⠛⢿⣿⣿⣿⡄⠀⣠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠘⢿⣿⣿⠇⠘⣿⣿⣿⡇⢰⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣏⠀⢀⣀⡿⠟⠋⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⢀⣀⣸⣿⣿⣿⣿⠟⠛⢁⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⢀⣴⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠶⠶⠿⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣾⠿⠿⠿⠿⠿⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠒⠀⠀⠀⠐⠂⠀⠐⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⠆⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢿
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠿⣿⣿⡆⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⢰⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣠⡀⠀⣸⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⠏
⢀⣴⣿⣿⣿⣿⠋⠁⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠋⠁⠀⢻⣿⠋⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢻⣿⣄
⣿⣿⣿⣿⡿⠗⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠙⢿⠦⠾⠆⠀⢹⣷⣦⣀⡀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢺⣿⣇⣀⣀⡀
⣿⣿⣿⣿⡀⠀⠄⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣄⠀⢠⣤⠀⢠⣿⣿⣿⣿⣿⣶⣦⠻⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠸⣿⣿⣿⠃
⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⡇⠀⢀⣀⣠⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⣾⣿⠀⢾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣿⣿⣻⣿⣿⣿⣿⣶⣄⠀⠈⠻⠿
⣿⣿⣿⣿⡀⠀⠀⢹⣿⣿⣿⣷⣶⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⣿⡀⠘⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⣠
⣿⣿⣿⣿⡿⢿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡦⠀⣴⣦⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣼⣿⣭⣤⣀⣤⣭⣥⣤⣀⣀⣤⣤⣤⣤⣤⣤⣬⣍⣀⣀⣀⣀⣬⣭⣭⣭⣩⣥⣤⣤⣤⣤⣤⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠛⣿⡟⠛⠋⠙⠛⠻⡛⠛⠛⠛⠛⣉⡉⠉⠛⠛⣛⣛⠋⠉⠉⠻⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⠷⢿⣿⣿⣿⣦⣾⠿⠿⣷⣤⣾⠿⣿⡿⢷⣶⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣉⣉⣀⡀⠀⠘⠟⠀⠀⠀⠀⠀⠙⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠿⠟⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⣀⣠⣀⣀⣠⣀⣀⣤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠋⠀⠀⠁⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⠛⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡀⠀⣠⣤⠈⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠸⣿⣿⣿⡟⠻⣿⣿⣷⠀⠘⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣷⣴⣿⣿⡿⠁⠀⢻⣿⣿⡆⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⡛⢄
⠓⠐⠴⠶⢤⠂⠂⠀⠀⠀⠀⠀⠚⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣫⠸⠑⠄⠀⠀⠀⠀⠀⠢⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢠
⠀⠂⠀⠉⠀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠔⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣢⡒⠀⠀⠀⠀⠈⡄⠀⢠⠄
⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⣤⣈⡈⣵⣆⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢠⣤⡄⠙⠁⠀⠀⣤⣀⣠⣄
⠀⠀⠀⠉⠉⡁⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠃⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀
⠀⠀⣨⠰⠦⠙⢂⠀⠀⠀⠀⠀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠄⣂⡒⣀⡐⢤⠀⠀⠀⠀⠀⠀⠀⠀⡴⢾⢰⠆⠂
⠀⠀⠡⣄⢀⠄⠀⠀⠀⠀⢀⠠⠃⠚⠂⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⣥⣴⡄⠁⡀⡅⠀⠀⠀⠀⣰⡒⠀⠃⢸⠈⢀⣠⡴⠃
⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠉⣦⠀⠀⠀⠀⠀⣇⠈⠛⠁⡀⠁⢃⠀⠀⠀⠀⠁⠀⠀⣀⠀⡄⠸⠿⣄
⠀⠀⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡆⠲⢆⡁⣀⠀⠀⠀⠈⠑⠒⠂⢀⠀⠀⢡⡀⠀⠀⠀⠀⢤⣿⡀⡇⢠⠀⠀⠁
⠀⠀⠀⢰⣶⣦⣧⣄⠀⠀⠀⠀⠀⠐⠆⠀⠀⠢⠀⠀⠀⠀⠀⠀⠁⠡⠜⠥⠉⠁⠀⠀⠀⠀⠸⠇⠸⠸⠇⠈⠉⠀⠀⠀⠀⠀⠙⠀⠁⠉⠁
⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠴⢒⠶⣀⠀⠀⠀⠀⠀⢠⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡛⠆⠀⠀⠀⠀⠀⢀⡇⠦⠡⢜⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⢘⠻⠟⠐⠇⠀⠀⠀⠀⠁⠀⠠⡄⢺⣆⣀⠀⠀⠀⠠⠓⠁⠀⠄⠠⠀⣤
⠀⠀⠀⠉⠠⣄⡌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡘⡰⠆⢀⠀⠀⠀⠀⠀⠩⠉⠃⠀⢸⡀⠀⠁⠀⠀⢰⠤⠴⠂⠘⡀
⠀⠀⠀⠀⢀⡁⢀⡀⠀⠀⠀⠀⢀⠀⠀⢂⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡌⢴⠁⡞⠼⠒⠀⠀⠀⠀⢠⣄⡉⣥⡌⠁⠀⠀⠀⠀⠭⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠡⠠⢤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡖⢄⠄⠀⠀⠀⠀⠀⠀⠀⢒⣦⠳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠨⠰⡿⠂⠀⠀⠀⠀⠀⠀⠄⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⡀⠀⠀⢄⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠔⢠⠄⠳⡀⠀⠀⠀⠀⠀⠜⡥⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⢄⡀⠃⠀⠀⠀⠀⠀⠄⡔⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡔⠁⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⡀⠀⣀⡀⠐⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣴⣶⠦⠀⠰⣿⣦⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⠀⠀⠂⢠⡄⠐⠀⠀⠃⠀⠀⠀⢿⣿⣿⣿⡗
⠀⠀⠀⠛⢁⣶⣶⡀⠈⠁⣡⠀⠀⠸⡿⠀⠀⠀⠀⠘⡀⣆⠀⠊⠑⠂⢰⣀⠇⠀⠀⠀⠈⠿⣿⡿⠃⠄⠀⠀⠀⠤⠀⠠⠂
⠀⠀⠰⣦⣤⣭⣤⣤⣶⡿⢻⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠋⣤⡄⠀⢠⣤⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠢⡭⣭⣭⠭⠶⢚⠋⢀⡄⠈⠢⠀⣰⠀⠀⠉⣠⣤⣶⣿⣿⣶⣤⣄⠀⠀⠘⠄⠌⠀⠀⠈⠁⠀⠂⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠤⠴⠶⠋⠀⠀⠀⢠⣤⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠄⠀⠈⠉⠀⠘⢿⡟⠁⠀⠨⠉⠉⠅⠀⠈⠻⡿⠇⠀⠄⠀⠀⠀⠀⠀⣀⣀⠀⢘⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠁⠀⣤⠀⢀⠐⠀⠈⠠⠀⠀⠀⠀⣠⡀⠀⠀⢸⡴⠂⠀⠈⠉⠘⢦⠈⠩⢓⠲⠤⣼
⠀⠀⠈⠀⠀⠀⠉⠁⠈⠉⠀⠀⢀⡈⢈⠀⠀⠘⣿⣆⠐⠂⠀⠀⠐⠀⠐⠒⣰⣿⠃⠀⢠⠀⠀⠀⠀⠀⠀⢀⠠⠀⢘⡀⠀⠀⠁
⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⡀⠀⢸⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⡧⠀⠈⠀⠐⠒⠀⠀⠁⣀⣄⣈⠛⠃
⠀⠀⠙⢿⠇⠈⠓⠒⠚⠀⢠⡄⠀⠀⠼⠷⣄⡈⢻⣿⠿⠛⠁⠈⠁⠈⠙⠿⣿⡟⠁⠀⠁⠀⠀⠀⢠⣴⣬⡍⠛⠉⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡘⠇⠀⠁⠀⠀⢁⠘⠃⠘⠀⠀⠈⡀⠀⣿⠀⠀⠀⠀⣶⠖⣡⣶⠞⢠⠿⠏⠰⠃
⠀⠀⠛⠶⣦⡐⠒⠛⠛⠈⢻⣷⣄⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠉⠀⠩⠄⠆
⠀⠀⣠⣆⠻⣶⠤⠀⠠⠰⠞⠻⠛⠆⠀⡄⠃⠀⠘⠀⢠⠄⠀⠀⠀⠀⠀⡄⠀⠄⠸⢛⠃⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠹⣿⣧⠈⠀⠀⠀⠀⠀⠀⠄⠂⠀⡇⠀⠠⠄⠃⢰⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⢸⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠆⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⠈⠀⠀⠰⢷⠀⠀⠀⠀⠂⠀⠀⠀⠠⠖
⠀⠀⠀⠂⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣃⣩⣚⣝⣽⣼⣍⣡⣸⡇⢸⣤⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⡀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢠⡀⠀⢀⣿⣿⣿⠟⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠄⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠊⠀⠀⠀⢀⣀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣿⣿⣿⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠈⠻⠋⡀⠀⠈⢘⠃⠀⡀⠂⠀⠀⠈⠉⠍⢉⠛⠛⣛⠀⡀
⠀⠀⠀⠀⠀⢄⣀⣀⣀⡠⠔⠁⠠⠂⠀⠀⠀⠀⠀⠀⠑⠄⡁⠀⠀⠀⢀⡀⠴⠂⠁⠀⢆⠀⢀⣀⠀⠂⢀⠠⠀⠀⠀⠉⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠑⠂⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢐⡒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠞⠁⠈⠱⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⠀⠀⢀⠠⡀⠀⠀⢀⠅⠇⠀⠀⢠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⣸⢤⣂⠾⠍⠉⠉⠉⠉⠉⠵⠶⣦⣆⡀⠀⠈⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⡪⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣦⡀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣶⡶⢆⠀⢀⣶⡶⡄⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠢⠤⠜⠀⠘⠤⠠⠎⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡠⢤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠘⠤⠜⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡠⠔⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⢄
⠀⠀⠀⠀⢸⠀⢀⠃⠀⢀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠓⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡜⠀⠸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢃
⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡇⠀⠈⡆
⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢰⠀⠀⢠⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⠀⠀⡆
⠀⠀⠀⠘⡄⠀⠘⡀⠀⠀⠈⠒⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠒⠁⠀⠀⠀⠀⡌⠀⢠⠃
⠀⠀⠀⠀⠐⢄⡀⢘⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠤⡀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣀⠀⠈⠄⢁
⠀⠀⠀⠀⠀⠠⠃⠔⠠⡀⠀⡈⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠆⡑⠄⢀⡀⡄
⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢂⠠
⠀⠀⠐⠀⠀⠠⠐⠁⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠐⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⢂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢰⠀⠀⠀⠀⠀⠀⠠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠣⣀⣀⡀⠄⠀⠀⠠⠑
⠐⠒⠂⢰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠂⠀⠀⠀⠀⡀⢠⡤⠌⠀⠀⠀⠃⠂
⠉⠀⠀⠀⠀⠃⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⠀⠒⡀⠁⠀⠀⠁⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⣤⠢⠄⠠⠀⢄⡀⠀⠀⠈⠀⢀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠐⠂⠀⢀⣿⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⠀⠐⠒⠒⠂⠀⠉⠈⠁⠀⠀⠈⠉⠁⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠀⠛⠒⠒⠀⠀⠤⠤⠀⢀⣀⡀
⠄⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠤⣦⠙⠶⢄⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣺⡇⠀⠑⣤
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠈⡘⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⡀⡠⠔⠂⠂⠀⠋⠀⠀⠀⠀⢠⣷⡄⠀⠈⠇⠀⠙⠁
⠀⠀⠀⠠⠰⠂⠀⠐⠿⠃⠀⠀⠐⠟⠐⠃⠀⠀⠀⠀⠀⡤⠤⠒⠀⠁⠀⠀⢀⠄⣿⠀⠀⠀⠀⠀⠘⣄⢷⠆⠀⢀
⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠒⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠻
⠀⠀⠀⢴⡁⠘⠺⠋⢉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡓⢖⠘⠣⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠐⠀⠅⠀⠀⠘
⠀⠀⠀⠀⠁⢀⠀⠀⠤⠀⠶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡛⠀⠀⠀⠑⠤⠤⠼⠀⠀⠀⠀⠀⠀⢁⡤⠓⠦⠡⣁⢈⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠐⠀⠂⡁⠀⣌⠋⠃⠀⠀⠀⠀⠀⠀⠐⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⣀⡈⠀⠀⠀⠑⠤⠉⡄⠀⠀⠔
⠀⠀⠀⠀⠀⢰⠌⠀⠀⠁⠀⠒⠁⠀⠀⠀⠂⠀⠀⢀⡼⠁⠀⠉⠉⠉⠙⠋⠙⠋⠛⠛⠘⠰⠛⠓⠀⠇⠀⠀⠁⠀⠉⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠠⠀⠀⠀⠀⢡⡾⠁⠀⠐⠀⠀⢀⡔⠀⠀⠠⠠⠀⠀⠄⠀⠀⡘⠀⠀⠀⠀⠀⢀⠀⡄⢠⣀⡄
⠀⠀⠀⠀⠀⠰⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠰⠀⠀⠀⠀⠀⠀⣀⡀⠰⠄⠀⠤
⠀⠀⠀⠀⠀⠄⠰⠦⠀⠈⠀⠚⢂⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠒⠰⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀
⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣴⢠⢦⢠⣠⢰⢰⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠰⠄⠀⢸⡟⢻⢸⣸⢸⡇⢸⢸⡃⠙⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠐⡀⢀⠀⠀⠀⠀⠀⠀⠁⠆
⠀⠠⣶⡶⠶⠂⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠒⠀⠂⠁
⠈⠀⢠⣤⣦⠀⣀⠀⠄⠀⠀⢀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⢀⠀⠠⠀⡀⠀⢀⠀⠀⠀⠀⠂⠄
⠀⠁⠀⠙⠁⠄⠀⠀⣠⣤⣤⣥⣤⣄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⡇⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣟⣿⣿⡇⠀⠀⠀⠀⠀⠘⠃⠱⠀⠀⠀⠀⠀⢐⠀⠃⠀⠚⠀⡂⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠁⠀⠈⣿⣟⣻⣯⣛⣿⡇⠀⠀⠀⠀⡔⠀⠀⠐⠒⠂⠐⠀⠀⠈⠀⠀⠀⠁⠀⢡⠀⠀⠀⠀⠀⠾⣧⡀
⠘⣦⢠⠀⡄⠁⠀⢀⡉⠛⠛⠛⠛⠋⠀⣀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣷⣄⠘
⠀⣟⠈⢈⡇⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠒⠘⠁⠀⠰⠀⠀⠆⠀⠀⠀⠀⠀⠀⡘⣀⠀⠈⠀⠀⠐⠀⠉⠁
⠀⠿⣸⣸⠇⠀⠀⠀⠀⠀⠀⡚⠥⠀⠀⠠⡀⠀⡐⢀⠐⡀⠐⠀⠰⠀⠊⠠⠠⠀⠰⠀⡀⠀⠁⠁
⠀⠀⠀⣀⣤⣤⣄⡀⠘⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⡖⢶⢲⣶⠒⢲
⠀⢀⡾⣫⠽⣿⣝⢷⡀⠒⠂⠀⠀⠀⠀⠀⠀⢀⣀⢄⠀⠀⠀⠀⠀⡀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠛⠛⠃⠀⠙⠛⠛
⠀⠘⠛⠁⠀⠈⠉⠛⠇⠀⣶⡶⣶⢶⡶⢶⡆⠀⠡⠊⠀⡴⠄⠀⠊⣰⡄⠀⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠠⣤⡀⠀⠀⢠⡤⠀⠀⣷⠀⠈⠸⠀⣀⣷⠰⠞⠓⠀⣤⡄⠀⢀⠈⡡⠂⠉⠀⠀⠂
⠀⠀⣿⢷⡆⠰⡿⠧⠀⠀⣿⣠⣄⣆⣄⣡⣿⠀⠀⠀⠛⠶⠂⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⡀⠈⡉⠀⠀⡀⠀⠄⠀⠠⠤
⠀⠀⡐⠂⠀⠀⠈⢂⠀⠀⣿⢭⡏⡏⢛⠹⣿⠀⠠⠤⣤⣤⢤⡀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠰⠿⠃⠀⣶⣶⡿⠆⠈⢿⣿⣧⣴⣷⢼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠆⠠⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠄⠀⠀⢇⠀⡀⠀⠀⠈⠀⢸⠀⠀⠀⢁⣀⣀⠀⠀⠀⠈
⠀⠠⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠐⠁⠈⠀⠀⠻⣿⡿⠃⢀
⠈⠀⠀⠀⠀⠀⠄⠀⠈⠀⠠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⡆
⠀⠀⠀⢠⡄⠀⠢⠀⠀⠀⠀⠉⠁⠀⠀⠀⠆⠀⠀⠀⡀⣊⠄⠁⠀⠀⠀⢀⣴⣄⠂⠀⠀⠀⠐⠀⢀⠀⡄⠀⠀⠀⠀⠤
⠀⠀⠀⠈⠁⠀⠨⠀⠀⠀⠈⠶⠨⠾⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠻⣵⠞⠁⠀⠀⠀⠀⡀⠀⠀⢀⡅
⠀⠒⠒⠒⠒⠒⠂⠀⠀⠆⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⡉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣍⡙⠛⠿⠿⢿⣦⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠉⠀⠀⠀⠀⠈⠙⠳⠶⠞⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢹⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⡘⠋⡉⠉⣙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡦⣤⡀⠀⠀⣤⠶⠞⠛⠒⠤⠀⠈⠉⠥⣿⣾⣦⠙⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⢿⠷⠀⠀⠠⠞⠻⣿⠶⠀⢆⡴⠋⠘⣡⡦⣤⣤⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢤⡇⢠⠾⢻⣿⣿⣿⣏⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣿⣿⣿⣿⣿⡘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⢾⠿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣷⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣤⣶⣾⣿⡿⠋⠀⣰⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠀⠀⠀⠀⠀⣴⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣰⡿⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣇
⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⣀⣤⡾⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣾⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠛⢉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⣠⣶⣿⠟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢀⣴⣾⣟⣭⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⣀⣤⣴⣿⠿⠋⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿
⠀⠀⠀⣴⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⣉⣤⣤⣤⣶⣶⠿⠿⠟⠋⠉⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⠇
⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣛⣋⣉⣉⣉⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣿⠟
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣠⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠲⢤⣄⣀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣶⣶⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣶⣤⣤⣬⣭⣭⣭⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⢤⣤⠄⠀⠀⠀⢤⡦⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢀
⠀⠀⠀⠠⢀⠀⠀⠄⠀⠀⠀⠀⠀⠨⠑⠮⠅⠀⠀⣾⠃⠸⡷⠀⠀⢰⣿⡏⠿⠁⠀⠀⠐⠶⠤⢶⡄⠀⠰⠿⠟⠻
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⣄⡀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡌⢥⠂⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠐⠠⡄⠀⢸⣿⣿⣿⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠠⣧⣸⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠁⠐⠦⠍⠉⠛⠀⠀⠨⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⣀⡀⠀⠀⣄⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⣂⣴⡀⠀⢰⣦⡄⠴⠂
⠀⠀⠉⠞⠀⠻⠆⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⠄⠀⠀⠙⠛⠘⠛⠃⠀⠘⠿⠣⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢿⣿⡿⠂⠀⣾⣿⣿⣷⡄⠒⣀⢀⡀⠂⠀⢒⣀⠤⠀⣀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠘⠛⠛⠋
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⠉⠀⠀⠁⠀⠁⠀⠐⠂⠹⠞⠀⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⢀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣧
⠀⠀⠀⠀⠀⣼⡅⢨⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄⣴⠦⠐⢶⡄⠐⠶⡀⠠⣶⢤⣠⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢿⡇⣸⠠⠈⢁⠠⢶⡶⠀⢠⣄⢰⠀⢿⡄⢀⣸⡟⠀⠀⠱⡀⢻⣿⠋⠈⢈⠇⢰⣶⣦⢠⡀⠀⢀⠀⣀⣿⣷
⠀⠀⠀⠀⠀⢸⡷⠃⠀⠀⠈⢳⠈⣿⡄⣀⣿⡎⠻⠾⠿⠿⠋⠀⠀⠀⠀⠹⠟⠁⠀⢠⣞⣠⣿⣾⣏⣟⠁⠀⠀⠙⢷⣿⡿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣷⡾⠟⠋⢉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢉⠙⠻⢷⣾⠏⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⢀⠀⢀⠀⠀⢸⠏⠉⢻⣦⠀⠋⣿⡄⠀⣾⠟⣭⣭⣯⣿⡆⡴⠙⣷⠀⠀⠀⠀⣻⣤⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠀⠀⠀⠀⢈⣰⡄⣼⣿⣶⠀⣿⡇⠀⡇⡄⣿⣏⡉⠉⠀⢷⢰⣿⠀⠀⢰⠤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠸⢹⣷⠟⢹⡟⠛⣿⡇⠀⡟⢡⣷⣶⣿⠆⠀⠈⣾⡇⠀⠀⢸⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⣷⠀⣾⡇⠀⣿⡇⠀⡷⠃⠿⢇⡀⣀⡀⢠⢿⡄⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠐⠾⠃⠷⠟⠸⠶⠿⠁⠀⠳⠶⠶⠿⠶⠿⠃⠙⠿⠟⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡠⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠈⠀⠀⠀⡤⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠐⠀⠈⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢦
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⢠⠀⠀⠐⠢⣄⠀⠉⠉⠓⠶⣤⡀⠀⠀⠀⢀⡴⠋⠀⠀⠞⠀⠁⣉⠤⠞⠁⠀⠀⣀⡴⠖⠋⠉⠁⢀⡤⠒⠀⠀⢀
⠀⢸⡀⠀⠊⠉⠉⢣⡀⠀⠀⠀⠀⠙⢦⡤⠔⠋⠀⠀⠀⠀⠀⣀⣈⡁⠉⠒⢤⣴⠞⠁⠀⠀⠀⠀⣠⠋⠉⠉⠂⠀⣸
⠀⠈⣧⠀⠀⢀⠔⠒⢷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠉⢫⡉⠙⠓⠶⠏⠀⠀⠀⠀⠀⣰⠗⠲⢄⠀⠀⢠⡏
⠀⠀⠘⢦⠀⠈⠀⠀⠀⠱⡀⠀⠀⠀⠠⠴⠦⠀⠀⠀⠀⠀⠀⠙⢦⡡⠀⠠⠶⠤⠀⠀⠀⠀⡰⠁⠀⠀⠈⠀⢠⠞
⠀⠀⠀⠈⠳⣄⠀⠀⠀⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⠇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠓⣤⠀⠀⠀⠀⠀⣴⡞⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⣶⡄⠀⠀⠀⠀⢠⠔⠋
⠀⠀⠀⠀⠀⠀⠸⠥⠆⡀⡀⠀⣼⣿⣇⠀⠀⢀⣿⣆⠀⠀⠀⠀⢀⣾⣇⠀⠀⢀⣿⣿⡄⠀⡄⡀⠦⠽⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠊⠑⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢀⡗⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡹⡏⠀⠉⢻⣿⡟⠀⠀⠀⠀⠘⣿⣿⠋⠁⠈⡿⣹⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠙⠮⣖⣶⡾⠟⠀⠀⠀⡀⠀⠀⠘⠿⣶⣖⡮⠞⠁⠀⠈⡇
⠀⠀⠀⠀⢀⣠⠤⠤⠶⠚⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠊⡉⠖⠂⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞⠒⠦⠤⢤⣀
⠀⠀⠴⠚⠛⠓⠒⠒⠤⣄⠀⠀⠀⠉⠉⠒⠒⠒⠶⠆⠀⠤⠤⠤⠐⠶⠖⠒⠒⠊⠉⠁⠀⠀⢀⡤⠔⠒⠒⠛⠛⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⣆⣀⠴⠋⠁⠀⠀⠀⠉⠳⢄⣀⣂⣨⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⣠⣶⣄⠀⠀⠀⢀⣴⣾⣷⡶⣦⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⣰⣿⣿⠏⠀⠀⣠⣿⣿⣿⡟⠀⢸⡇⠀⢸⣿⣿⠁⠀⠀⢠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⢠⣿⣿⠇⠀⠀⣴⣿⡟⠉⢿⡇⠀⣾⣧⣴⣿⣿⡇⠀⢀⣶⣿⣿⣿⠁⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⢀⣴⢿⣿⡟⣀⣠⣴⣿⡿⠀⠀⠀⠙⣿⣿⠿⢻⣿⣿⠀⠀⣾⡿⣿⣿⡇⠀⠀⣠⣮⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣁⣴⣶⠟⢁⣿⣿⣿⠿⠛⢻⣿⡇⠀⠀⣠⣾⣿⠃⠀⠘⢿⣿⣴⡿⠋⠀⢿⣿⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⢁⣠⣾⣿⡟⠀⠀⠀⠈⠻⣧⣴⣾⣿⠟⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠁⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⢻⡇⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠘⣿⡄⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠙⣷⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⢀⣀⣤⡾⠛⠁⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⠀⣰⢿⣿⣿⠀⠀⠀⣤⣶⣤⠀⠀⠀⠀⢀⣤⣾⡿⢟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⣴⠃⣼⣿⡏⠀⢠⡾⢻⣿⡿⠀⠀⢀⣴⣿⠟⣡⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⣼⠃⣸⣿⡟⢀⣴⠏⢀⣿⣿⠇⠀⢰⣿⡿⢿⡿⠿⠛⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⣼⠃⢠⣿⣿⣥⣾⠃⠀⣼⣿⡏⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⣠⣴⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⣾⠃⠀⠸⣿⣿⠟⠁⠀⠀⠻⣿⣤⣾⠟⠉⠻⣦⣤⣤⣴⣶⣿⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠈⠁⠀⠀⠀⠒⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠌⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠈⠀⠀⡀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢹⠛⠑⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣄⠀⠀⠑⠂⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢈⣢⡄⠀⠀⠀⠀⠀⠀⠙⠁⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠖⠠⠃⠡⠘⡄⠘⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢠⡇⠀⡀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢆⠀⠀⠱⠘⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⢂⠀⠀⠱⡈⢎⠐⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠂⠋⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢂⠀⠀⠱⡈⢆⠠⠄⠀⠄⠀⠀⠘⠘⢦⠐⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢢⠀⠀⠑⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢣⠀⠀⠐⡀⢢⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⡄⢣⡄⠀⠀⢠⡠⠄⠀⢀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢣⠀⠀⠘⡄⠣⠀⠀⠀⠀⠀⠀⠈⠢⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠣⠀⣀⠜⠊⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠉⠀⠀⠀⢀⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠔⠈⠉⣄⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⡡⠔⠊⠀⢀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠤⠠⠤⠊⠉⠉⠁
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣷⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⠃⣿⠇⠀⠀⠀⠀⣠⣤⣤⣤⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠈⠹⠆⠁⠀⢰⢢⠀⣀⡹⠿⠿⠿⣿⣿⣿⣿⡟⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⠁⠀⠀⠀⢠⠔⠊⠉⡩⠃⡸⢎⠁⢰⡖⣤⣀⠀⠙⣿⣿⣦⣄⠀⠤⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣉⣘⣋⠀⢀⠀⠤⠈⠀⠈⡆⠈⠓⠻⢯⣿⠦⡾⠛⠿⠟⠀⢀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣹⠇⢀⡀⣏⠀⠀⡈⣀⣠⠔⠊⠀⢡⠈⠲⠳⡀⠀⠀⡹⠀⠀⢀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡶⠫⠊⠁⣤⣤⠱⡄⠀⠀⢹⠒⣤⠤⢚⠤⠗⠴⣧⣄⠠⠱⠀⠀⢘⣁⣶⣛⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⣤⠡⣾⡗⣙⣿⣤⣿⠂⠀⢨⠊⠀⠀⠀⠀⠀⡀⠀⠋⠳⡅⠀⠀⠉⠉⢻⣿⡇⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠀⠀⢸⠀⢀⣉⡟⣿⠿⢛⡓⠒⠚⠤⣄⠐⡶⠀⠈⢁⡂⠀⠀⠙⠦⠤⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡸⠦⢛⠾⡄⠀⠀⡜⠁⠀⠻⣾⣣⣤⠒⠈⣱⠄⡰⢾⣿⢃⡔⠉⠲⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠁⢪⡷⣄⠘⣀⡀⣠⠞⠋⡳⠉⠀⢀⣣⠠⣞⡉⢡⢈⡉⠢⡜⠈⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢂⢀⢘⡐⢜⣄⠀⠉⠃⠀⠁⠀⠰⠣⣀⠔⠁⠀⠀⠀⠈⠻⣋⠔⢲⠜⡄⣽⢊⠅⣀⠪⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢃⠀⣀⠝⡖⣼⡱⠀⠶⠀⠀⠛⠀⠀⢫⠀⠘⠇⠼⠿⠛⠀⢹⢀⠎⠐⢰⡧⠤⣌⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠐⢐⣨⠔⠛⡃⠀⢠⣤⣴⣦⠀⠀⠘⠀⡄⢠⠀⣴⡄⠀⠘⠃⠀⢰⠘⡃⠀⠢⡑⣂⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣐⣈⣏⣂⣀⣑⣊⣁⣀⣀⣀⣇⣓⢘⣀⣛⣁⣀⣸⣀⣀⣈⢀⣇⠀⠁⠄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⢘⣂⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠉⠋⠉⠀⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣷⣶⣄⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠀⣄⢀⣀⣀⣀⣴⣿⣿⣷⠤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠷⣀⠀⠀⢀⠉⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⡜⣻⠀⠀⣹⡆⠀⠐⣀⠘⠃⣐⠃⠀⠀⢠⡆⠀⢱⠒⢛⢳⠦⠐
⠀⠀⠀⠀⠊⠀⠐⢬⣒⢥⡬⣟⠁⠀⠉⠁⠀⠀⠈⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠨⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠐⠠⠀⠀⠀⠀⠀⠀⢸⣀⠆
⠀⠀⠀⠀⠀⠀⠖⠰⠆⠀⠒⠘⠃⠀⠀⠀⠀⠀⠀⡼⣆⠀⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢈⠀⠀⠀⠀⢄⠂⠓⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡴⡒⢃⠈⡐⠀⠀⠀⠠⡄⡄⠀⠁⠀⠀⠀⠀⠀⠄⠎⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣀⠥⢀⡐⡀⠐⣀⠈⡀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⢔⠁⡔⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠒⢀⠃⢐⡈⠀⢩⡀⢡⡄⠀⠀⠀⡆⠀⣤⡆⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣀⠀⡘⢃⡄⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠈⡋⠈⠃⠀⡀⠀⠀⠀⠂⠀⠰⠄
⠀⠀⠀⠀⡠⠋⠈⠒⠋⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠐⠙⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠒⠚⠉⠛⠋⠋⠋⠀⠠⠦⠤⠆⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣄⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⢀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠁⠋⠀⠈⢍⡱⠐⠈⢹⠂⠈⠃⠈⠒⢔⡰⠁⠀⠐⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢀⡈⡈⠑⠄⠀⢣⢀⣀⡄⠠⠀⠺⠐⠄⠈⢣⡠⠊⠅⢰⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠠⠂⠀⡇⠁⠀⠀⠀⠊⠉⠀⠀⠀⠢⡴⠂⠈⠄⠈⡁⢀⠶⢠⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡐⠀⠀⠀⢡⠈⢄⠀⠘⠀⠀⠀⠈⢄⠀⠈⠄⠀⢸⠔⠃⢬⡀⢠⠇⠘⠖⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠑⡌⠑⠊⠑⢄⠀⠀⠈⡄⠀⠀⠀⢸⣀⣀⣀⣟⠥⠀⣀⣜⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⡈⠢⡀⠀⠀⡄⢀⠂⢨⠎⠀⢸⡀⠀⢀⠆⠣⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣀⡎⢘⠣⡀⠅⣸⣔⠴⠃⡠⠁⠑⠐⠈⠉⠙⡁⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠀⠀⠀⣿⣶⣿⣿⣿⣿⣦⡑⠒⠒⠛⢁⡠⠊⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠡⠠⡀⠨⢹⣄⣨⣿⣿⣿⡏⠉⠀⠉⠁⠀⠀⠀⠀⠀⣀⣾⣷⠀⠘⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠡⡑⡐⡄⠻⠿⡧⠼⠋⠀⠀⠀⠀⠀⠨⢛⡶⡖⣞⢏⠳⠅⠀⠀⠀⠀⡘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠂⢀⠣⠀⠐⡐⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⢀⠂⠀⠀⢸⠀⠠⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠊⠁⠟⣴⠑⢄⠁⠐⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⡰⠁⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢊⣇⣉⡉⠀⠀⣥⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢎⡜⠀⢀⠞⠀⠂⠠⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡐⠁⠠⠞⠁⠐⠊⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠎⠎⢀⣴⡁⠀⠀⣀⠤⢄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡄⠀⠈⠢⣀⠀⣀⠌⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠸⣀⠟⡄⠙⡄⢰⡁⡀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠈⣦⡘⠘⠀⠀⠀⠀⠣⠃⠴⠁⠀⣘⠀⠀⢉⡈⠀⢠⠓⠤⢉⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀⣀⣀⡠⠔⠚⠣⢉⠴⢶⠒⢦⠀⠒⠁⠀⠀⠀⡇⠑⢾⡥⡈⠙⢃⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⢱⡂⠀⢀⠀⠀⢃⢠⠀⠀⠀⠀⠐⢄⠀⡠⠂⠀⠀⠂⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠳⢴⠋⠀⠀⡆⢢⡀⠸⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠉⡎⠁⠈⢫⠀⠀⠈⠲⠇⠑⢄⠀⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠠⠙⠢⠠⠊⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠄⠀⠒⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡒⠉⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠜⠀⢀⡻⠁⠀⠠⠤⠈⠁⠀⠀⠀⠀⠀⠦⠀⠀⠀⠈⢷⡀⠄⠀⠈⠣⡄
⠀⠀⠀⠀⡐⠀⠀⠀⢹⡇⠀⠠⣾⣿⡆⠐⠀⠀⠀⠀⠂⣠⣾⣽⣦⠀⢸⣿⡆⠀⣀⠀⠱⡀
⠀⠀⠀⢀⡇⣀⠀⠀⣿⡇⠀⢀⠈⠉⠄⠀⠀⠀⠀⠀⠈⠃⠈⠉⠀⠠⠄⢻⣧⠀⡏⠀⠀⠀⢀
⠀⠀⠀⣸⡞⠋⠀⠀⢹⡇⠠⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⢸⣿⡆⠀⠀⠀⠀⠠⠦⡀
⠀⠀⠀⣿⣿⣦⣀⢀⠘⣇⡖⡀⡀⠀⠀⣰⣶⣶⣶⣿⣦⡀⢀⠀⠀⣀⡉⣾⣻⣷⢿⣶⠀⣰⡦⣴⠆
⠀⠀⠀⢻⣿⣿⢫⣯⡇⣟⢇⠘⣧⠠⠀⠻⢿⣿⣿⣿⠿⠁⠀⠀⣴⠟⣡⣿⣿⣿⢸⣿⣟⠋⣴⠋
⠀⠀⠀⠈⠳⣿⣿⣟⢁⣿⠀⠁⠘⡀⠀⠀⠀⣈⠋⠁⠀⠀⠀⣸⠁⠀⢉⠃⣈⣿⡸⣿⣏⡸⡜
⠀⠀⠀⠀⠀⠛⣿⣏⣼⣥⠗⠀⡀⢿⣦⣴⣶⠿⢿⣶⣶⣤⢖⡹⠋⠀⠁⠁⠸⡻⣇⠿⣿⡶⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠉⠀⠙⢿⡄⠀⠀⠀⣼⣿⠋⠀⠀⠀⠐⠀⢀⣨⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡀⠀⠀⠈⠿⢶⣶⠾⠟⠁⠀⠀⢀⡀⠰⡄⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠻⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠿⠿⠟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢷⣀⠀⢀⠀⠀⠀⠀⠀⠄⢨⣅⠰⠄⠀⠀⢄⡀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⠿⠦⣷⢲⣤⡶⠾⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠐⡇⡾⣫⠾⣧⢤⡄⠀⢠⢞⠿⣷⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⠋⠉⠓⢡⣠⠁
⠀⠀⠀⠀⠈⣷⡀⠀⢳⡀⠀⣀⢿⡟⠡⡎⠀⡄⡇⠀⢸⡘⠆⠈⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠉⢀⣤⠞⠿⠃
⠀⣀⠄⠂⢀⣿⣿⡆⠉⢷⣶⡏⢉⢧⠀⢻⠓⢣⠇⠀⣾⣿⠆⠀⠀⠀⠀⠀⢰⣀⠀⠀⢀⢁⡀⢹⣄⠠⡟
⠸⡿⠀⠀⡏⠉⠈⢷⠀⠀⠈⠻⡌⣧⢳⣀⡴⠃⠀⣰⡿⢿⠂⠀⢠⣶⣶⣶⠇⠈⠂⠀⣸⠉⠉⢐⠨⢧⣀
⠀⠀⠀⠀⠀⠠⠀⠈⠇⠀⢀⣴⡷⠸⠋⠁⠀⢀⡼⣯⣟⡞⠀⠀⠀⠀⢸⡟⠁⠀⠀⢸⣇⠀⢰⡏⠀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠁⠀⠀⠀⣔⣭⣿⣮⣛⠁⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠉⠳⠚⠷⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢎⠟⡟⡝⣿⡇⠀⠀⢢⠴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡍⢲⢊⠂⡓⡬⢷⡩⣇⠀⡠⠿⠅⢾⣙⣿⣇⢀⣀⣀⣀⣤⣤⠴⣆⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢇⡍⡦⢚⣣⠋⠠⢽⡇⠘⠿⠋⠁⠿⡿⢻⢳⣋⢟⣿⢴⢫⢗⡭⡛⢒⠏⠑⠢⠴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⢂⡁⣀⡕⠀⠀⡹⠢⠾⡛⣀⠀⠀⠀⠀⠻⠅⢋⡫⣿⢻⣸⠛⠘⣋⣵⡆⠁
⠀⠀⠀⠀⠀⢀⣶⡦⠀⢀⢋⠁⢑⠀⠀⠀⠀⠇⠃⠀⠀⠑⡁⠀⠀⠀⠀⠀⠁⡰⠟⠀⠛⠂⠀⠈⠁⠍⠂
⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠸⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⢀⠠⠀⠀⠀⠀⡀⢀⣧⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠤⠶⠚⢀⡜⢡⣠⣼⣡⣴⡄⣐⣼⣿⣿⣿⠇⠀⠀⢰
⠀⠀⠀⣦⣴⠎⠁⠐⠖⠀⠀⠀⠀⠀⠀⠠⡀⠀⠹⣆⡽⢭⠉⠹⠿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⡀⢠⣤⡷⣄
⢰⠀⠀⢸⡿⠀⢀⠀⠀⠐⣧⣆⠀⠀⠐⢰⣷⠀⣦⠹⢄⠨⠀⠀⢠⣿⠿⣿⣿⣿⣦⣤⣴⣿⣿⣧⣿⣿⠇⠘⡇
⠘⣆⠲⣼⠁⠀⢸⣿⣶⣶⣿⣿⣶⣶⣾⣿⣟⣾⢯⡀⠀⠀⠀⢀⠎⣀⡴⠛⢿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣆⠀⠙⠶⠄
⠀⠈⣿⡇⠀⠐⠛⢿⣿⣿⡿⠿⠿⠛⢹⣿⣻⣿⠀⠀⠀⠀⢰⣴⡞⠋⠀⠀⠘⠿⣿⠀⠀⠀⣿⣿⡏⢻⡋
⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣸⣿⣹⣿⠀⠀⠀⠀⠘⠻⠟⠀⠀⠀⠀⠠⠙⠆⠀⣰⣿⡏⠀⣸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠈⠙⠛⠁⠀⠈⠉⠁

⠀⠀⠀⠤⠀⠀⠠⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⡠⡤⢠⡄⠀⠀⠀⢀⡀⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⡤⡄⢀⠁⠀⢠⡄⠀⠀⡂⡀⠀⠀⠀⠀⠀⢀⢡⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠀⢠⠢⠀⢄⠕⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠀⢀⠀⠀⠀⡈⣠⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⠄⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠸⠰⢳⣦⠁⠀⠉⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡂⠀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠇⢀⡀
⠀⠐⠐⠀⠉⠛⠒⠆⠀⠀⢠⠀⠀⠀⠀⠈⠀⠘⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠀⠀⠠⠄⠐⠛⠀⠀⠐⠒⢀⡄⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠
⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠎⠄⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢔⠄⠑⠀⠁⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠉⠁⠀⠀⠀⠀⠀⠒⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠠⠄⠂⠀⠐⠠⠀⠀⠠⠤
⠀⠀⠀⠐⠀⢀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠐⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⡂⠀⢠⠅⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠖⠐⠾⠣
⠀⠀⠀⠐⠂⠀⠑⠀⠄⠀⠀⠁⠀⠋⠃⠀⠀⠘⠉⠀⠀⠀⠐⠀⠀⠋⠀⠀⠀⠀⠐⠀⠀⠀⠠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⠄
⠀⠀⣤⡄⠡⠄⠀⠀⠀⠀⠀⠀⠂⠀⠐⡐⠂⠀⠀⠀⠈⠀⠐⠀⠀⠀⠒⠲⠒⠐⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠤⣤⠄
⠀⠀⠀⠀⡄⣅⡀⠀⠀⠠⠦⠄⠀⠀⠀⠰⠀⠀⠀⠈⠥⠖⠀⠀⣔⠠⠀⠀⠐⠡⢐⠄⠀⠀⠀⠀⠂⠠⠀⠁⠀⠀⠂⠀⠀⠒
⠀⠀⣀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠒⠀⠀⠐⠂
⠀⠀⠁⠀⠂⠂⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠈⠀⠐⡃⠀⠀⠸⠂⠀⠐⠆⢀⡀⢆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠧⠀⠀⠠⠄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡈⠀⠉⠈⠀⠱⠎⢠⠃⠈⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠰⣄⡀⠀⠀⠀⢈⠀⠀⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘
⠀⠀⠀⠀⠐⠀⠂⠀⠀⠒⠀⠀⠄⠀⠀⠀⠂⠀⠔⠀⠀⠈⠉⠀⠀⠀⠂⠄⠰⠀⠀⠀⠀⠀⠀⢈⠈⠀⠉⡀⠸⠀⠀⠀⠀⠨⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠘⠐⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠈⠘⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣄⡀⠀⠀⠀⠀⠀⣠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣴⡏⠀⡠⡄⠙⡆⠀⠀⣠⣾⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠉⢧⡜⠈⡇⠀⠳⠤⠴⠷⢶⡾⠁⠈⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡀⠀⠀⢀⣧⠀⠹⡄⠀⠀⠀⣰⠛⣆⠀⠀⣸⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⠃⠀⠀⠈⡟⣆⠀⠙⢦⠀⢼⡁⠀⠈⠙⢲⡇⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠹⡌⢧⡀⠈⠙⢦⣉⠓⠦⣤⠞⠀⠀⣀⣤⠾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠐⠀⠘⢦⣉⠳⢤⣀⡈⠉⠙⠓⠛⢛⣉⣡⠤⠖⢻⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢬⣉⣉⣛⣛⡭⠭⠷⠖⠲⠖⠉⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢰⠞⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡤⠴⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣴⢦⠀⠀⠀⠈⠁⠀⠈⠻⣆⠀⠀⠀⠀⢀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⠁⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⣀⠔⠒⠋⠙⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣠⣼⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣠⡴⠞⠁⢸⠀⢰⠇⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣇⡇⠀⠀⢸⠀⢸⡉⡭⣍⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⢷⠀⠀⢸⡄⠈⠳⠶⠛⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠙⠳⢦⣴⣇⡀⠀⠈⢧⡀⠀⢳⡀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠳⣄⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠒⠒⠛⣩⠥⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠓⠦⠤⠤⠀⠀⠀⠀⠀⣼⣀⣀⣀⣀⡃⢋⡷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠉⠉⠉⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⣀⡀⠀⠀⠀⣀⣠⣞⠳⢤⣤⣀⣀⣀⣠⡤⠴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠒⠒⠒⠛⠉⢸⡏⠉⠛⣛⠉⠁⠀⠀⠈⠉⡿⡄⠈⠳⢤⣀⡀⠉⠀⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢀⡼⠁⠀⠀⢸⡀⠀⠀⠀⠀⢠⠇⠙⢦⣀⠀⠈⠉⠉⠉⠉⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠛⠁⠀⠀⠀⠈⠳⣄⣀⣀⡴⠟⠀⠀⠀⠉⠓⠲⠶⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠘⢻⡂⠀⠀⠚⢷⠆⢀⣀⣷⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠷⢶⠀⠀⠀⠠⣤⣤⣬⣿⣷⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠈⠙⣯⠉⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠿⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠙⢻⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⡟⣩⣿⣿⡯⠆⠀⢱⢹⣿⣿⣿⡒⠢⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠻⣟⡃⠀⠈⠙⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠴⠞⠿⣾⡿⡓⢀⡀⡈⣧⣿⣿⣿⣯⣤⡨⣿⡟⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⢉⣙⣿⣷⠃⣾⠙⣹⢺⣽⣿⣿⣿⣿⡗⠩⠘⠳⠆
⠀⠀⠀⠀⠀⠀⠶⣦⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢈⡁⠠⢼⣿⡟⡀⢸⣽⠃⢹⣾⣿⣿⢋⣉⣉⠓⠤⠀⠒
⠀⠀⠀⠀⠀⠐⠶⠿⠿⢶⡶⠶⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⡍⠁⢶⡃⢼⣿⢂⣾⣿⣿⣿⣿⣮⣈⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⠎⡿⢶⣧⣇⢺⣿⢷⣿⣽⣽⡿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠰⣾⢿⣦⡲⠃⢸⣦⡃⢿⣾⢸⣿⣿⡿⠟⢋⠀⢹⣿⣻⣿⣿⣿⣷
⠀⠀⠀⠀⠸⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠿⡖⣽⠈⠁⠈⠿⠁⡀⠀⠙⠣⣘⡉⢸⣿⠃⠀⢀⣼⠀⠘⣿⣿⡿⠋⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣠⠘⣇⠀⠀⠀⠀⣀⣠⡀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠸⢿⠀⠀⢸⣟⣁⠾⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣍⣿⣿⡦⡀⠀⠀⡔⠁⠀⠀⠘⠁⣀⣉⣤⣠⣤⣴⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣤⣤⣤⣄⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠐⣿⣟⣼⣦⣄⠀⠀⢀⣴⣿⣿⢿⡟⣽⠛⣿⡏⢨⣿⠻⡏⠀⣾⣽⡟⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠛⣛⣴⡿⣧⣟⣿⣿⠈⠓⠞⠿⠿⢧⣿⣾⡏⢰⡧⣰⠿⠁⢠⠾⣦⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⣨⣿⣿⣿⣻⡏⣀⠀⠀⠀⠀⠀⠉⣻⢀⡿⠁⠃⣶⣾⢑⡄⢻⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠘⠻⢿⢟⣽⣿⣾⠇⣄⠀⢠⣴⣀⡘⡹⣈⠑⠖⠀⠋⠁⠚⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠒⢀⡌⠈⢩⠿⢻⡿⠡⠷⢾⢟⣿⢿⣜⣋⠀⠀⠀⣴⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡃⠀⠈⠉⠸⠛⡰⠛⠚⠛⢛⠛⡻⠟⠁⣰⡋⠠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⢠⠈⠢⢤⡀⡀⠘⢼⣿⢷⣾⢿⣾⣧⣴⠟⣻⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⡀⣆⠀⠀⢿⠶⠀⣠⡆⢙⠿⣤⣾⣠⣴⣤⣾⣿⠟⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣏⣩⢰⣦⠘⢀⡎⠙⢀⠎⣰⠏⠀⢨⣿⣿⠏⡠⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⠙⠂⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⣾⣻⡿⢛⣤⠊⢠⠂⡞⢠⠏⠀⣀⡾⠛⣄⠀⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠘⣹⡜⣣⣶⡏⡀⠀⡾⠀⠁⠀⢀⡄⠉⢁⠈⡃⣰⣾⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠋⠀⡄⠀⠀⠀⠀⠀⠀⢻⡼⡼⡟⠰⢁⡾⣁⠈⠀⣠⠎⢀⡔⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿

⠀⣀⣤⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣀⣤⠄
⠀⠁⠭⠉⢦⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠠⠓⠋⠀⠩
⠘⠄⢀⢠⠜⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡈⢁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⠛⠂⠀⠀⠀⠀⠈⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠰⢣⡀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡐⠒⡀⠀⣾⠇⠀⠀⠀⣈⠱⠄
⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠔⠉⠀⠀⡸⢠⠉⠀⠀⠀⠀⠉⡰⠀⠦⠄⠀⠀⠀⣩⣀⣀⠀⠁⢠⣤⣄⣀
⠀⠀⠀⠛⠛⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⠉⠁⠓⠀⠀⠀⠀⠀⠀⠉⢉⠀⠀⠀⠈⠉⠉
⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣉⡉⢠⡉⠐⣄⠀⠀⠀⠀⠠⢘⣝⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠴⠄⠁
⡀⠀⠂⢈⠁⠐⠀⠀⠀⢀⠄⠀⠀⢸⠀⣤⣾⣦⠀⠄⢸⠀⠀⠀⠠⠊⠉⠀⠈⢩⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⡙⠁⠀⠀⢌⠀⠀⠀⠀⠀⠀⠈⡄⠼⣵⠠⠤⡄⠀⠀⠀⠀⠀⠒⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠒⠂⢠⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠰⠐⣡⣀⠀⢧⠀⠀⠀⠀⠀⡀
⠀⠀⡠⠀⠘⡀⢠⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⡊⠘⡅⣖⠀⡙⠛⠀⠀⠀⠀⢠⣤⡄⣼⣤⠈⠀⠀⠀⠀⢀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢐⠐⠝⠉⠃⠧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠲⢀⠀⠀⠀⠀⠀⠀⠸⢁⣆⠸⠁
⠀⢀⠽⡰⠧⠉⠀⠀⠈⠣⡀⠀⠀⠀⠨⠁⠤⠀⠀⠀⠀⠉⠑⡄⠀⠀⠀⠀⠁⠉⠀⢀⠄⠀⠀⠀⠀⠀⢉⡀⠀⡀⠈
⠀⠘⢦⠠⠆⠂⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠹⠋
⠀⠀⠀⢁⠖⠀⠀⠀⡀⡀⠀⡜⠆⠀⠀⢂⡇⠀⡏⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠲⣆⠎⠀⠱⣤⡤⠀⠀⠀⠀⠘⣿⣄⣐⢼⣄⢠⡀⣐⣤⠄⠀⠀⠀⠀⢀⣄⡅⢠⣤⡀⠀⠀⠀⢠⣬⣥⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣌⢳⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⢸⣧⣠⣦⣀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢟⢿⣿⣿⣭⡍⠉⠐⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠹⠟⠉⠉⠁⠀⠀⠀⣿⣿⣶⣤⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣦⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣴⡇⠀⠀⠀⠀⠀⢸⣿⣿⠻⠛⠻⢿⣿⣿⣿⣷⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠛⠳⠋⠁⠀⠀⢤⣍⠉⠁⠀⠀⠀⠈⠉⠻⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⠁⠀⠀⠐⢧⡴⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⣀⣀⢀⣰⣆⠀⣀⠀⢰⣷⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣥⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠋⠿⠏⠹⠟⠉⠛⠻⠋⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⣄⠀⡀⡖⠸⠂⠀⠀⠀⢀⣀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⢀⡀⠀⠀⠈⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⣧⡰⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⢻⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⣼⣧⣤⣄⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⠏⠀⠀⠀⠸⣤⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠈⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⢿⣄⣄⡀⠠⠚⠛⠛⠛⠛⠒⠓⠀⠉

⠀⠀⠐⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡔⣚⣮⢮⣠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢢⣀⢀⣜⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠦⠁⢸⣇⠠⠄⣤⠀⠀⠀⠀⡘⢫⢥⡈⡴⠆⡤⣸⠊⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢗⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣄⢄⡈⠒⢦⣸⡿⡛⠍⠂⠀⠀⠀⠀⠀⠓⠦⣴⣧⡄⡇⣏⡡
⠀⠀⠀⠀⠐⠀⠀⠠⠆⠘⠀⠈⠑⢤⡀⠀⠀⠀⠂⠀⠀⠀⠌⠓⢺⣵⡀⣍⣔⣢⣄⣀⢄⣀⠀⠀⠀⠙⠒⠋⠁⠟⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⣦⠤⠀⡀⣙⣉⠓⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⣲⣂⢈⠟⠙⢙⠳⢕⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⢉⠻⡦⡈⠑⠀⠂⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⡇⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠑⠟⠷⠆⠀⠀⠀⠀⠀⣀⠀⠄⠠⠂⠄⣠⢳⠞⢀⡄⠉
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⡀⠀⠀⢉⡔⠊⣠⠃⡀⡑⡖
⠀⠀⠀⠀⢀⠐⠀⢀⠈⠣⡀⠄⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠓⠪⣽⣳⣶⠋⠀⠀⠀⠀⠈⠀⠀⢈⡻⠮⣱⣣⢰⣡⡊⠙⠂⠅
⠀⠀⠀⠀⠌⠀⡀⣀⡑⠤⠄⢲⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⢧⣈⣉⣩⣽⣇⠿⡃⠀⠀⠀⠀⠀⣀⠐⠒⣀⣀⣽⣿⣾⡁⠀⠁
⠀⠀⠀⠀⣩⠞⠉⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠺⠍⣀⣹⣆⠿⠋⡧⠚⣿⡏⠑⠀⠀⠀⠀⠈⠉⡵⢨⢟⠞⣹⢏⠃⠈
⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢒⡠⠔⢋⡏⡈⣢⣃⠄⠓⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⢛⠃⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠜⠠⠂⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣝⣫⣽⣩⣟⣹⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠓⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠿⠻⣦⡀⠀⠀⡀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠂⠀⣀
⠀⠀⠀⠈⠙⠛⢻⣿⣦⣄⠀⠀⠀⠀⢸⡴⠚⠛⠀⠠⠷⠦⠤⠄⡀⢰⠀⠀⢸⣿⡌⢀⢁⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠶⠀⠘⣿⣿⠀⠈⢢⣤⡄⠘⢤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣾⣿⠃⠀⠀⠀⠀⢀⣄⠀⠀⣠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣴⠟⠀⠀⠀⠀⠀⠀⠑⠀⠀⢤⣴⠀⠀⠀⠀⠀⠀⠈⡿⠛⠻⠁⠀⠀⠀⠀⠀⠸⠃⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⠀⡨⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢲⡇
⠀⠀⠀⠐⠀⠐⠃⠀⠀⠀⠀⢀⠀⠲⢠⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣦⡦⠀⠀⡰⡿⠀⠀⢿⢦
⠀⢀⠀⠠⠀⠀⡀⠀⢰⡀⠀⢀⡀⠀⢾⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠛⠻⣿⣿⣧⠀⠈⠀⡇⠀⠀⢸⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⢰⠈⠁⠀⠘⠻⣆⠀⠈⣧⣤⣤⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢴⠀⠀⠐⠄⠀⠀⠀⢩⣮⢧⣀⠀⠀⢸⣴⠆⠀⠀⢸⠁⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⣀⣀⣾⠿⠋⠀⠀⠀⠀⠐⠂⠐⠒
⠀⠀⠒⠀⠀⠀⡄⠀⠺⠁⠃⠀⠀⠀⠰⣼⣭⡯⣷⡆⠀⠀⠀⠀⠀⠘⠃⠀⠰⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⠤⣄⣀⠀⠀⢤⡀
⠀⠀⢸⣶⡄⠀⣿⣦⣤⣴⡆⠀⠀⠀⠘⠎⠐⢾⡟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠚⠉
⠀⠀⠘⣿⣿⠿⠻⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⢻⣿⡿⢶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⡀⠀⣄⡀⢀⡀⠸⠦⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠃⠀⠆⠈⠀⠂⠀⠀⠰⠚⢁⡀⠀⠸⠿⣿⣿⡿⠟⢿⣿⠛⠛⠛⠳⠄⠀⠘⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⢰⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠸⠟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⢸⡓⠃⠀⠀⠸⠀⠛⢃⢀⡀⢀⠀⠀⠀⠀⢠⠶⢦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣾⡧⣦⠀⠀⠀⠁⢀⠸⠹⠂⡀⢈⠇⢳⠆⢀⣤⣿⣶⡟⠂⠀⢀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⡿⠊
⠀⠀⠀⠀⣠⣿⣿⣇⢲⡄⠀⠀⢀⣦⠇⠀⠀⠷⢐⠀⠀⠀⢸⡟⠠⣉⣿⣷⠀⠈⠀⠀⠀⢾⣄⡀⠀⣀⣀⣄⠀⢀⡇⠀⠀⠀⠙⢟⢿⠃
⠀⠀⠀⣠⣿⣿⣿⣷⡋⠀⠀⠰⠁⠈⠀⢀⠞⠀⠆⠀⠀⠀⠘⡇⠀⠸⣇⢿⡀⠀⠀⠀⠀⠀⣿⠁⠀⠉⣿⠏⠀⢸⠀⠀⠀⠀⠀⡀
⠀⠘⠋⠉⠀⠛⠛⠛⠉⠀⠀⠀⠀⠂⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠋⠒⠊⠀⠉⠀⠁⠉⠀⠀⠀⠀⠀⠑
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣽⣭⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣾⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⡶⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣄⣠⣤⣀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⣦⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣴⣧⠛⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠠⣾⣏⢉⣭⡉⠉⢹⣿⣿⣿⣤⣭⣿⣶
⠀⠀⠀⠀⢸⣿⣷⣄⡟⠀⠀⠀⠰⣲⡆⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠆⠀⠀⠀⢻⣿⡋⠿⣿⣶⣼⣿⣯⣿⠟⠻⠛⠻⠆
⠀⠀⠀⠀⣸⣿⣿⢿⣁⣤⠀⠀⠐⠁⠐⠀⠀⠀⠀⠀⠘⣿⣿⣧⣿⠛⠛⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢸⡿⠁
⠀⢀⠤⡴⠛⠷⠿⠋⠙⠁⠀⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⠀⠀⢸⣿⠋⢿⣿⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢨⣑⠀⠀⠀⠀⠀⠀⠀⠶⠟⠁⠚⠋⠀⠀⠚⠋⠀⠐⠞⠃⠀⠀⠀⠀⢯⣇⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢮⡅⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢿⢗⡅⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⢀⡇⠒⠙⠛⠳⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢾⡱⠎⠀⠀⠀⠀⠀⠀⢸⡄⠀⠙⠄⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⢀⣀⣠⣤⣶⣶⣷⣿⡿⠷⠒
⠀⠀⠀⢀⣠⣤⣶⣿⣻⣿⡷⢠⡃⠀⠀⠀⠀⠀⠀⢹⡇⠐⠂⠄⠿⠄⠀⢸⣿⣿⠞⠁⠀⠀⠀⠀⢀⡞⠁⠘⣲⣿⡿⣿⣿⣿⠿⢿⡉⠁
⠀⠀⠀⢺⣿⡿⠏⣷⡛⡝⣿⡎⠷⠀⠀⠀⣴⣶⣤⣼⠁⠀⠀⠆⠀⠀⠀⢸⣯⣬⠶⠖⠃⠀⠀⠀⠀⠛⠿⠿⠛⣩⠟⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⣷⠀⠀⠿⠈⠄⢹⠃⠀⠀⠀⢀⣥⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦
⠀⠀⠀⣤⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⢛⠟⣋⠽⠷⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⣤⣾⡗⠀⠁⠀⠀⠀⢀⡀⠀⣴⣿⣿⣿⠋
⠀⠀⠐⡿⢸⠁⠀⠀⠀⠀⠀⡄⠀⠀⠘⠁⢰⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠃⠀⠈⢉⣿⣿⣿⣿⣿⡖⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠙⠛⠂⠀⠀⠀⠀⠀⠀⡘⠻⡟⠋⠁⠀⠀⠈⠛⣇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢣⡀⠀⠀⠀⠀⠆⠀⢄⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢷⣜⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠉⠁⠀⠀⠻⡿⠻⣿⣦⣄⣀⣀⣀⣠⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣼⣿⣿⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠀⠈⢃⠙⠋⠙⣿⠲⣄⠉⠉⠙⠋⠉
⠀⠀⢹⣿⣿⣿⡿⠈⠻⣿⣿⣿⣼⣿⣿⣿⢿⣏⠋⡟⠋⢿⡆⠀⠀⠀⠐⣿⠿⢿⣤⣤⣤⠾⢧⢦⣰⡿⠀⣿⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⣨⣿⣿⡿⠛⠁⠚⠛⠛⠙⡿⣹⡏⠀⠀⠀⠁⠙⠒⠛⠁⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠋⠀⠀⠀⡶⢿⣿⣽⣿⣷⣿⣿⡄
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠥⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠀⠀⠀⠀⠀⠀⠺⡟⠛⠛⠛⠛⢿⠁
⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣈⡄⣀⠄⠀⠀⠠⠂⠁⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢩⠀⠀⡠⠀⠀⠀⠀⢀⠈⠁⠀⠀⠉⠀⠦⠘⡄⣀⠐⢀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠉⢀⠆⠀⠐⠀⠀⠈⡀⠔⠛⡄⠋⠀⠀⠀⠈⠢⣀⠢⠀⠀⠀⠂⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠁⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⢠⠀⠈⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⣀⣤⠀⠀⠀⡰⣞⣻⣷⡿⠂⢠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢢⠀⠁⢸⠁⡄⠀⠀⠀⡐⢁⠈⠀⠀⠀⠀⠀⢁⣽⠿⠋⠀⠀⢠⠀⠀⠀⠠⠂⢐
⠀⠀⠀⡀⠂⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢢⠘⡀
⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠁⠒⠀⠀⠀⠀⡀⠀⣠⠀⢤⠑⠠⢠⠀⡀⠀⠀⠀⠀⡀⢤⠂⠁⠀⠀⠀⠀⠀⢰⠊⠈⠂⠀⠀⠡⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⡀⠠⠀⠒⠀⠀⠀⠀⢀⠀⢈⠠⠀⠁⠠⠈⠀⠀⠀⠀⠀⠊⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠐⠀⢀⡃⠀⠀⠀⠀⠁⠀⠸⠀⠐⢢⠄⠀⠀⠂⠀⠀⠀⢸⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠌
⠀⠀⠀⠀⠀⢀⠀⠀⠌⡀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⢀⢀⠼⢣⣚⣁⣤⠀⠂⠀⢀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⢒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠠⠤⢖⣈⠉⣀⠔⠀⠁⠀⠀⠈⠠⣀⡬⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠋⠀⠀⠀⠀⠠⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠁⠀⠊⡠⠂⠁⠀⡀⠄⡐⠂⢀⡾⠁⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠂⠠⠊⠀⢀⠔⢁⠔⠉⠀⠀⢸⠁⠀⠀⢄⠀⢀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡱⠂⠰⠁⠀⠠⠃⢀⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⣛⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠈⠀⠈⠀⠀⡃⠀⠀⠀⠀⡆⠀⠀⠀⡄⠀⠈⡄⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠰⠃⠀⠀⠀⠀⣤⠐⢨⠀⠀⢀⠀⠘⡇⠀⠀⠀⡇⠀⡀⠔⠀⠀⢀⠄⠀⡀⠘⠀⠀⠀⡠⠂⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢅⣰⠂⢠⠴⠆⠀⢀⠀⠀⢠⠦⠀⠞⠀⠀⠀⠀⠁⠊⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠄⠀⠑⠀⣄
⠀⠀⠀⠀⠀⠀⠁⠱⠁⠘⠤⠐⠁⡠⠐⠁⠈⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠺⡀⠀⠀⣠⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⢂⠀⠀⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁⠀⠀⠀⠈
⠀⠀⠐⠄⠀⠀⠀⡷⠠⠀⠴⠂⠤⠀⠚⠀⠀⢀⣀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⢀⠤⠀⠳
⠀⠀⠀⠀⠁⠀⢂⠀⠂⠠⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠁⠀⠒⠂⠒⠒⡇⠀⠀⠀⡀⠀⠈⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢀⠀⠀⠀⠀⠁⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠐⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢢⡠⠂⠉⠈⠐⡄⠐⠀⠀⢀⠠⠤⢤⠂⠁⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠌⠠⣀⠀⠀⠀⠀⠤⠠⢠⠊⠁⠈⡁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡔⠁⠀⠀⠀⢡⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠄⠀⠲⠉⠉⠀⠀⠄⠀⠈⠀⡀⠤⠤⠆⠀⠀⠀⠈⠂⠤⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠈⠁⠢⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠈⠐⠸
⣶⣾⣿⣷⣿⡿⢶⣿⣿⡿⣿⣶⣶⣶⣾⣷⣷⣿⣷⣶⣶⣾⣿⣿⣿⣿⣾⣿⣶⣷⣿⣾⣿⣷⣷⣷⣶⣶⣿⣷⣷⣿⢾⡾⠾⠿⠶⣾⣶⡾⠶⠶⠶⢶⡶⠶⠶⠾⢿

⠀⠀⠀⠀⠀⡠⡂⠒⠒⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⢾⠿⡀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⡤⠴⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠄⠻⠟⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⡀⠀⠀⠂⣠⣤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⡀
⠀⠀⢀⡤⠤⠼⠴⠶⠬⠷⠈⠤⢤⠀⠀⠀⠀⠀⠀⠀⠾⠗⠙⠋⠀⠐⠡⠄⠀⠀⠐⠤⠄⠠⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠄⠀⠠⠁⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠠⡼⠆⠀⠀⠄⠀⡀⢠⠔⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠠⠀⠁⡀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠨⠀⠀⠄⠀⡀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠈⠻⠂
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⣴⣦
⠀⠀⠀⠀⠀⢄⠀⠈⠛⠋⠈⠁⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠠⠉⠑⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣉⠉⢁⡀⡀
⠀⠀⠀⠀⣶⠑⡆⠀⢄⡰⠀⡲⠪⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢤⠀⠈⠈⠄⢠⠊⣄
⠀⠀⠀⠀⠈⠀⠈⠐⠊⠓⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠒⠓⠂⠊⠀⠁

⠀⠀⢀⡀
⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣀⣠⠤
⠀⠀⠀⠀⢾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡟⠉
⠀⠀⠀⠀⠸⠻⣏⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣿⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠈⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠰⠀⠈⢻⣇⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⣸⠀⠀⢸⠃⠀⢀⡿⠀⣀⣠⡤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣶⡖⠉⣤⢤⡤⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧⠀⠀⢿⠀⠠⠘⠿⢧⣍⣁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣄⡀⠀⠠⡄⠀⠀⠀⢀⠀⠀⠀⣿⣷⣴⣷⣬⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻⠀⡠⠚⠧⣤⡀⠀⠂⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠀⠀⠘⠢⠐⠊⠀⠟⠁⠀⠙⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⠸⣧⣀⣀⣀⣀⣉⣉⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠉⠳⢤⡀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣰⢙⡆⠀⡴⠀⡄⠐⡾⠒⢰⠀⣠⠀⡦⡠⡆⡠⣆⠀⡄⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠉⠹⡄⠧⠞⠧⠐⠧⠄⠺⠔⠻⠀⠟⠁⠻⠁⠸⠄⠟⠀⠳⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠀⠀⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⠀⠀⠀⢠⠇⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠁⠘⣇⠀⠀⠠⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣴⠃⠀⠀⠀⠀⠀⠈⠓⡄⠀⣸⠀⠀⣠⠔⠉⠀⠀⠠⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢠⡟⠀⠀⠤⠀⠀⠀⠋⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⠁⠀⠀⠀⠀⠀⠠⣄⡘⣦⣯⡴⠋⠁⠀⠀⢀⠀⠀⠈⠑⠢⣄⡀⠀⠀⢻⡄⠀⠀⢰⡟⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠛⣿⣏⡉⠉⠉⠉⠉⠁⠀⢀⡐⠀⠀⠙⢷⣄⠘⣿⠀⣠⡟⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢸⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢿⣿⣦⡟⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⠿⠿⠿⢯⡤⣤⣀⣀⣀⠚
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠒⠤⣀
⠀⠀⠀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣿⣿⢤⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣁⣀⢀⣤⣶⣿⣿⣿⠇⢸⠳⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⠟⣛⣥⣶⠟⣿⡟⢩⡿⣫⢀⠘⣇⠀⠀⠀⠑⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢢⡤⠖⣪⡅⣰⡿⠟⠫⢀⣠⢾⡿⠐⠛⢱⣿⠘⠄⠻⠣⡄⠀⠀⢀⣙⢮⠁⠐⠦⣄⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠘⠋⢠⠖⠀⢀⣠⢴⣿⠏⡄⠀⣀⣴⣿⣿⡆⠰⣀⡀⠀⣷⢄⡀⠹⠄⢀⡀⠀⢈⣙⠓⣿⣼
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡵⣆⣥⡶⠞⢁⣴⣿⠟⣾⠁⡼⠿⠋⢀⡝⠻⣄⠀⠁⣠⣀⠓⠈⡀⢀⡆⠙⢰⣴⡠⣃⣏⣻⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣻⠋⠸⢋⣥⡶⠾⣿⡿⠋⠰⢃⠾⠁⢷⠀⢿⠁⠑⡹⠀⠀⠀⠹⠀⠸⡇⠸⡇⡀⣿⣿⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠁⢀⣨⠉⢁⣤⡆⠉⠀⠀⣴⡟⠀⢰⡈⠀⣼⢠⠄⠃⡈⠣⠀⡇⢀⣆⣧⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠶⠾⠛⠛⠛⠓⠻⠛⠛⢿⣄⢠⡀⠁⠘⢠⣾⡷⢐⣿⣸⣠⡀⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢳⢸⡇⣰⢀⣨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⠀⣶⠀⣤⣼⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢿⣇⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠻⣿⣿⣿⣿⣾⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠹⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠁⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠁⠀⠀⣠⣶⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠠⢀⡄⣠⢔⣒⠰⢱⣦⣄⢄⠀⠀⠀⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡄⣴⣾⣿⣿⣦⣼⣿⣷⣿⣿⣿⣦⡀⠀⠀⠈⡈⠉⠂⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣦⣾⠇⠀⠂⠀⠈⠐⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨
⠀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠙⢿⣿⣏⡀⡀⠀⠁⠀⠀⣇⠀⠀⠀⡰⠀⠀⣀⠀⣠⢀⢀⡀⠀⠀⠀⠀⢀
⠀⠈⠢⣠⠸⣿⣿⠋⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⠿⣿⠀⠀⢄⠀⠸⡄⡀⢠⠃⠀⣠⡔⢊⣤⠲⣪⣍⢊⣿⣿⣿⣿⡑
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⣤⣾⣿⡂⢀⣀⣀⠀⠘⣆⢇⡤⠞⠁⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⡠⢁⠿⠇⠀⣀⠔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⣄⣧⡼⢸⡤⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠈⠢⢄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠘⠂⢙⠛⢦⣒⣒⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⢹⠇⠀⠂⠀⠠⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⠛⠁
⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠂⠀⢰⠀⠀⠀⠈⢳⡄⠀⠀⠀⢀⣠⣿⡿⣿⣿⡿⠻⠿⠿⠷
⠀⠀⠀⠀⠈⠁⠀⠁⠀⠊⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢹⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣶⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣾⣶⣤⣤⣤
⣠⡤⠊⠋⠙⠘⠁⢢⣤⠀⠀⠀⠀⠀⠀⠀⢀⠽⠁⠉⠟⠙⠹⣇⠀⠀⠀⠀⠀⠀⠀⠸⠋⣠⡀⠀⣠⡈⠛⠀⠀⠀⠀⠀⠀⠐⡿⠾⠋⠁⠀⠀⠉⠻⢿⣤
⢸⣛⠂⠀⣀⡀⠐⣛⡏⠀⠀⠀⠀⠀⠀⠀⢸⢍⣀⣂⣀⣂⣈⣿⠀⠀⠀⠀⠀⠀⠀⡆⣾⡿⠃⠀⠻⣿⡆⠀⠀⠀⠀⠀⠀⢾⣿⠁⠀⠐⣀⡀⠀⠀⢻⡟
⠈⢥⠄⠈⠙⠉⠠⡬⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣿⣿⣯⣿⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠘⠿⠂⢀⠔⠀⠀⠀⠀⠀⠀⣼⣿⣆⠀⠀⠙⠉⠀⢀⣾⣷
⠻⠀⢱⠂⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢷⣶⣤⣴⣾⠿⠇
⠸⣄⡿⢀⡀⣀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣩⣝⣩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣤⢀⡄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⢀⠆
⠐⢾⡅⢸⡇⣿⠀⡽⠆⠀⠀⠀⠀⠀⠀⠀⢀⡗⠺⡸⠺⡰⢺⣆⠀⠀⠀⠀⠀⠀⠀⠺⢿⣷⣿⣶⣷⣾⠿⠂⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠈⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠼⠿⠀⠾⠧⣴⣶⡄
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⠖⢿⣧⣤⣶⣤⣄
⡀⠔⠈⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠸⣴⣶⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⢀⣯⣤⡿⠛⠉⠋⠛⠻⣧⣤⣄
⠘⠀⠀⣠⣤⣤⡀⠀⡇⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⡀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠻⣧⣿⡁⠀⠁⠀⠁⠀⢸⣤⡿
⠈⢄⠀⠙⠻⠛⠁⡠⠁⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠸⡲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣑⣢⣄⣀⣤⡐⠀⣰⣒
⠀⠀⡑⠂⠀⠐⢪⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠷⣦⠀⠀⢠⠾⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⢪⡁⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀⠀⢸⣿⣦⢻⠳
⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⡀⠰⠰⠖⡀⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⣸⣿⣼⡏
⢰⣩⠀⣀⠀⣀⡀⣈⡰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣨⡅⠶⠰⢈⡝⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⢺⣿⠿⢿⣿
⠀⠀⠙⠒⠛⠳⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠲⡔⠌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠐⠈⠢⡨⡠⢆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠐⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠰⠿⠁⠈⠄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⡈⢞⠁⠰⠔⠋⢤⡐⠀⠀⠋⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠐⠢⡴⠒⠒⠰⠾⡁⠀⠀⠀⠉⣈⠀⠀⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠀⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠆⠀⠀⠀⠈⠉⠂⠀⠖⠛⠂⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠠⢄⠀⢐⣀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⣹⡄⠀⠀⣀⠔⣠⣞⠒⠁⠀⢆⣿⠱⡀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⢀⡄⠀⠙⡰⢻⠇⣀⠀⡻⣿⡷⢼⡆⠀⠀⠈⠁⠀⠑⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡀⠀⠀⠄⢹⡄⠀⠉⠱⠤⠉⡉⠀⠀⠂⠘⢀⠴⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠉⢢⡀⠀⠀⠀⠀⠈⣒⡶⢦⡀⠱⣀⠀⠀⠀⠀⠈⢢⠀⢶⠪⡁⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠉⢳⠀⠀⢆⡔⠁⠀⠀⠀⢦⡈⠑⠂⡀⠀⠀⠀⠆⠀⠏⠙⢏⣹⢋⢀⠔⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⢰⡣⡖⠀⠨⠀⠀⠀⡼⢰⠃⠀⣤⣶⡀⠀⣀⠜⠀⠈⠠⠀⢀⠇⠠⣁⠄⠠⡀⠼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠦⡀⠜⣡⡉⠂⠀⠀⣠⡾⠁⢁⡠⡀⠀⠀⢈⣉⠤⣎⠀⠀⣠⠓⠋⠀⠀⠡⠤⠀⡀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡀⠉⠐⠂⠉⢐⠁⠀⠈⡷⠁⠀⠐⠁⠠⠀⠘⠠⠜⢇⠀⠒⠒⠄⠰⠢⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣃⠜⠀⠀⠀⠀⠀⡨⠀⠀⠀⡇⠀⠀⣰⠀⣠⠆⣀⠰⠁⠈⠳⠒⡄⠀⠀⢰⠦⣀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡅⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⡱⢤⠔⠉⠉⠁⠀⣀⡀⠀⠀⡄⠀⠈⠒⡲⠓⠔⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⢄⡀⣄⠀⠀⡼⠁⢀⠀⠀⢠⠀⠨⠄⠈⡗⠈⠀⠀⣠⡆⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⣄⠀⠁⠁⣧⠀⠀⠐⠀⢀⠑⠤⠀⠔⠁⠀⢒⠈⠀⠳⡀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠂⠤⠒⠀⠓⠤⠤⠴⠚⢄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⢸⣽⣶⣿⣿⣿⣶⣯⡆⠀⠀⠀⠀⠀⣠⣤⣶⣦⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠨⠄⡸⠀⣀⡀
⠀⠀⣾⣿⣿⡟⣩⠹⣿⣿⡷⠀⠀⠀⠀⣼⣿⣶⡀⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠙⠋⠶⠈⣡⠈⠛⠁
⠀⠀⠞⣿⣿⡄⠀⠀⣿⣿⡛⠀⠀⠀⢠⡟⠛⠋⠐⠉⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠈⠁⢿⠇⠀⠀⠿⠙⠃⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀⣄⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠛⠻⠿⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⣩⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠓⠒⠒⠛⠛⠁⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠘⠂⠀⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⢩⡥⠀⠀⠀⢔⢀⡆⢀⣶⠠⡆⡆⣴⠀⣤⢰⢤⡄⣰⡄⣆⠀⡆⢀⣦⢰⣄⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠣⠆
⠀⠀⠀⠀⠀⣲⣾⡮⠄⠀⠈⠛⠒⠀⠀⠀⠀⠘⠊⠃⠈⠹⠀⠃⠃⠛⠀⠛⠘⠘⠀⠙⠃⠛⠀⠃⠈⠛⠘⠛⠃⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠊⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠦⠤⠴⠦⠴⠸⠠⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠸⢆⡄⠀⠀⣠⠾
⠀⠀⠀⢰⣄⢀⣀⡀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⢿⣿⡄
⠀⠀⠀⠀⠁⠈⠉⠁⠈⠁⠀⠀⢰⣦⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠐⢿⡶⠛⠚⠛⢷⡿⠆⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣿⡇⠻⠃⣿⡇
⠀⠀⠀⠀⣤⡤⠀⣀⣠⡄⠀⠀⠘⣿⡆⠀⠀⠀⢸⣿⠃⠀⠀⢸⢿⣶⠁⠀⠒⠀⠈⢷⣾⠇⠀⠀⠀⠀⠀⠿⢿⢤⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⣂⣀⣀⡩⢭⠅⠀⠀⠀⠘⠇⠀⠀⠀⠸⠃⠀⠀⠀⢰⣶⣿⠀⠀⠀⠀⢀⣼⣶⡆⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⣿⠃
⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⣴⣿⢲⣶⣾⢻⣷⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⠁
⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⢉⠟⠈⠁⠀⠀⠀⢠⣤⣤⠆⠀⢙⣻⣃⠀⠐⣶⣶⡆⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⣿⣿⣿⡆⠀⠀⠉⠀⠀⠀⢸⣿⣿

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠄
⠀⠀⠀⠀⢀⠀⣴⠦⠀⢀⠂⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠳
⠀⠀⠀⠉⠊⠐⢋⠃⠂⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡐⠀⠈⡀⠀⠀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠠⠐⠀⠀⠂⢰⠀⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⠀⣡⠘
⡳⠉⠔⠆⠀⠢⠐⠁⠀⠁⠉⠙⠀⠀⠄⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠁⠀⠊⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠠⠒⠉⠂⠀⠐⢤⠀⠀⠄⠀⠀⠈
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠂⠠⠀⢀⣠⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⠈⣀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠰
⠄⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀⢈⠁
⠐⠀⠀⠈⠁⠀⠀⠀⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀⠄⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⢁⠀⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢸⠂⠀⠒⠐⠄
⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⣠
⠀⠃⣄⠘⠂⡀⠀⠄⢨⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠉⠀⠀⣰
⠀⠀⠈⠀⠀⠑⠐⠄⢌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⡀⢠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣆⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⢀⠇⠘⢀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠱⠄⠀⠁⠀⠀⠀⡀
⠀⠀⢴⣒⢆⢱⢝⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡈⠀⠀⠈⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠙⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣛⣋⠉⠓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠓⠶⣤⣤⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠞⣿⣟⠁⠀⠀⠀⠀⣄⡽⠀⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣾⠀⠐⠈⠁⠀⠀⠀⣀⡀⠉⢤⣄⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠉⠉⠁⠸⠄⠀⠀⠀⠀⠀⠲⠆⢉⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡚⠉⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠀⠈⣧⠀⠀⠘⣆⠀⠀⠰⡀⠀⠀⠀⡠⣄⡴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⡄⠀⠀⠘⡆⣠⡔⠛⢦⣄⡠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠘⡇⠀⠀⣠⢿⣇⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣰⠋⠈⣸⣾⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠷⠛⠓⠚⠁⠋⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡰⠁⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⠀⠀⠀⡜⡻⠁⠀⠉⠃⠀⢸⡇⠀⠀⠈⠀⠻⣶⣄⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣹⣦⢤⣾⣾⡤⠤⠤⠤⠶⠒⠟⠓⣶⠒⠊⠉⠉⠛⠿⠿⣦⡀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⢸⡄⠀⠀⠀⠀⠀⣐⠦⣝⢶⡀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⣀⣼⢧⣤⣀⣀⣀⢢⣭⠟⠉⠉⢻⠄⠄⢀⡠
⠀⠀⠀⠀⠀⠘⢦⣀⣤⣄⣀⣠⣤⣤⡤⠤⠶⠒⠛⠉⠛⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣈⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠈⡟⠛⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡋⢣⠀⠀⠀⢹⠠⡇⠀⢠⣿⠟⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠣⠤⠒⠚⠀⠙⠢⢾⡏⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣦⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠈⢙⡏⠀⠀⣀⠀⠀⠀⠀⠀⢀⡆⢙⣮⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠦⠀⠶⠛⡇⣸⣀⣽⣧⠀⠀⠀⠀⠘⣿⣿⣿⠇⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⣿⣿⠏⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⣤⠤⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⢴⡊⠁⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠁⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⠤⣀⡀⠀⠀⠀⣀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⣀⠉⠉⢹⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠘⠛⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠠⣾⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠈⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡀⠀⠀⣾⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠿⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⢹⣶⣦⠀⠀⠀⢀⡀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠙⢿⠇⠀⠀⠀⠉⠁⠀⠀⠀⠻⠟⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠙⠿⠃⠀⣠⣄⠀⠀⢾⣿⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡰⢡⠿⠿⠀⣀⡀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⢠⣧⣄⠀⠾⣿⡟⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡌⡏⠛⠋⠀⠀⣀⡀⠐⠿⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⣠⡳⠀⡾⠆⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇
⠀⠀⣴⣶⣾⡗⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⢸⡇
⢀⣸⣿⣿⣿⠃⠀⠀⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡾⠀⡇⠀⠀⠀⠀⡆⢰⡄⠀⠀⠀⢰
⠀⠉⠉⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠇⠘⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡌⠀⠀⠀⠀⠸⠀⠀⢣⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠃⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡜⠀⠀⣷⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⢸⠀⠀⢰⠁⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⡅⠀⣼⣤⣤⣼⠀⠀⠀⠜⠀⠀⢠⠁⠀⠀⣿⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⣿⣿⣿⣿⡄⠀⠀⣿⣶⣶⣾⠀⠀⠀⣿⣶⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⢰⠄⠐⠰⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠉⠛⢢⡀⠀⠀⢀⠀⠀⠀⠠⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢢⣤⠊⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡴⠛⠥⠀⠀⢩⣿⡄⠀⠀⠆⡀⠘⠃⢀⢚⠃⠀⠀⠀⣤⡆⠀⠘⣰⠋⢹⠛⣶⣦⠠⠂
⠀⠀⠀⠀⠀⠠⠂⠀⢁⣐⠦⣍⡂⣙⠪⠗⠆⠀⠚⠛⠀⠀⠀⠈⠱⠴⠃⠘⠀⠀⠀⠀⠀⠍⠀⠀⠀⠉⠀⢈⠁⡋⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣛⠦⣝⠊⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡂⠰⠀⣀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠶⠀⠀⠛⠃⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡼⣇⡆⠀⠠⠆⠸⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠔⠃⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠈⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢤⡄⠒⠀⠀⠀⠙⠄⠀⠂⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢐⡒⢊⠙⢡⠀⡀⠃⠀⠀⠀⠀⢰⡀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠘⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⡤⠀⠐⠊⡀⠐⠀⠀⠁⠀⠀⠀⠀⠘⢡⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠀⡴⠂⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⣠⣊⣰⠄⢈⠁⠋⠀⠶⠉⠰⢘⠀⠀⠀⠀⢸⡈⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠃⢀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠰⠖⠀⠀⠚⠂⠀⠛⠀⠀⠀⠀⢸⡇⠀⠙⠿⣣⡄⢠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡄⢀⡉⠡⡦⠀⠀⠀⠀⢠⢠⣤⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠈⡋⠀⠙⠁⢀⣱⠀⠀⠀⠀⠐⠋⠁⠐⠆⠛
⠀⠀⠀⠀⠀⠀⡠⠂⡒⠤⡴⠋⠈⠑⠶⠚⠁⠀⠀⠁⠀⠀⠀⠀⠀⠤⠱⠆⠀⠐⠃⠉⠁⠀⠀⢘⠐⠀⠀⠀⠁⠹⣤⣀⡀⠐⠢
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠠⠂⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠟⠛⠛⠛⠉⠑⠋⠈⠃⠙⠀⠀⠰⠶⢶⠶⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡠⠀⠀⠡⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠉⠈⠛

⢋⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠧⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⡈⠉⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠘⠀⢀⠀⠀⡀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⣐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠂
⠀⠠⠀⠀⠀⠴⠂⠈⠉⠻⢃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢀⠀⠀⠀⠀⢈⠀⠘⠀⠀⠀⡁⠀⠀⠲⣶
⠀⠀⠀⠀⠀⠐⠊⠀⠰⠀⠘⠀⠀⠀⠀⠀⠀⡀⠉⠑⠒⢄⡀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡄⡀⠸
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠀⠀⠀⠀⠐⠈⢉⡀⢌⠠⠱⠃⠤⠂⡀
⠀⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⢠⠠⢀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠶⠬⢾⣷⣿⣴⠤⠴⠄
⠀⠀⠀⠦⢬⡄⠀⠀⠀⠀⠐⣠⡴⡋⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⣍⠤⠖⢂⠖⠟⢟⢣⡀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠞⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠀⠀⠠⠂⠷⠐
⠒⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⢀⠤⠠⠀⣀⡀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠄⠀⠀⣀⠄
⠀⠀⠀⠀⠈⠀⠈⡈⠰⡏⠀⠠⠂⠀⠀⣀⡡⠎⠀⠀⠀⠀⠀⠼⠛⠆
⠄⡄⠀⠄⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠁⠀⡀⠀⠀⠀⠀⠁⢒⠂⠐⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠈⠀⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣠⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠐⠀⠒⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⢀⠀⠐⠀⠀⠀⠒⢤⡀⠀⠶⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⡙⠳⣤⣄⡀⠢⠄
⣒⣖⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣈⣛⣂⣀⣁⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣸⣷⣿⣶⣶⣄⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡀⠕⠀⠀⠀⢀⠠⣐⣧⣼⣂⠤⡀⢸⠁⠃⠀⢰⠉⠉⢉⣉⣉⠉⠈⡃⠀⠡⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣸⡟⡉⢍⡩⢝⣿⡇⠀⣾⠛⠛⡟⢻⠏⠙⢿⠀⠈⠁⠀⠣⡀⠀⢸⠙⠛⠷⠶⠛⠃⡛⠈⢀⡸⠀⢸⠀⣸⠿⢿⠿⣧⠀⠟⠐⠄⠀⠀⣖⣈⣁⣀⡂⢵
⠀⢀⠾⣯⠾⢿⡿⢷⣽⠧⡀⣿⠀⠀⠀⠸⠄⣁⣼⡀⠀⠀⢠⡤⢶⠀⠀⠢⢀⣀⠀⣀⠔⠁⠀⠀⡇⠀⢸⠀⢻⣶⠟⢷⡿⠀⠀⢸⠀⠀⢠⠃⠤⠀⡤⠄⠚⢂
⠀⠀⢒⣿⣦⡾⢷⣾⣿⠒⠁⣻⡀⣰⢀⡀⡀⠁⣼⡇⠀⠐⡁⠀⢐⠆⠀⠀⠀⢄⣤⠀⠀⡀⠀⠀⣁⠀⢸⠀⣀⣙⣿⣛⣁⠀⠀⡀⠀⠀⢈⠀⡔⢉⡢⠀⠀⢸
⠀⠀⢡⠘⢿⣶⣶⡿⠃⠁⠀⣼⡍⢹⠉⠛⠛⠋⣻⡇⠀⣀⡃⢀⠀⣄⡀⠀⢠⣆⠀⠀⠘⠃⠾⠃⠈⠀⢸⠀⠿⠿⠿⠿⠯⠇⣠⠃⠀⠀⢸⠀⠑⠂⡤⠂
⠀⠀⠀⠀⡠⠁⠈⢢⡀⠀⠀⢿⣇⢸⠀⢀⡄⡀⣾⡇⢪⠰⠱⢆⠰⠘⢀⠇⠀⠀⠠⠀⡔⢀⠀⠺⠃⠀⠘⢲⠂⠀⠀⠒⠒⠒⢻⠀⠀⠀⠘⠀⠠⠂⠐⠆⠀⠁
⠀⠀⢠⠊⣄⣀⣀⠀⡌⢂⠀⠈⠛⠛⠋⠉⠉⠉⠉⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠁⠄⠀⠶⠀⠀⠀⠀⠈⠉⠁⠀⠒⠚⠀⠀⠀⠀⡀⠅⢁⠐⠀⠀⣀
⠀⠀⠀⠈⠀⣀⡀⠀⠁⠈⠀⠀⢀⠂⠉⢢⠀⠀⠎⠉⠑⡀⢠⡆⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠂⠀⠀⠀⠀⠀⠀⠉⠀⠐⢲⠀⠈⠀⠁⠀⠀⠈
⠀⠀⡀⠀⠀⠻⠁⣀⠀⠠⠄⢠⠸⠀⠺⣭⠍⠩⡀⠀⠛⡇⠈⢄⠀⢀⡜⠀⠀⠀⠐⠀⠀⢀⡀⠠⠤⠘⠂⠀⠀⠤⡠⠀⠀⠀⠀⠀⠖⢠⠀⢀⢀⡀⡀⠀⡀
⠀⠈⠀⠣⠀⢎⠩⠤⠀⠒⠈⠁⠀⠆⠤⠔⠀⠀⡑⠤⠔⠀⠀⡠⠃⠘⢄⠀⠀⠀⢠⠄⠊⠁⠀⠀⣤⣴⡆⠀⠀⠀⠱⠀⠀⠀⠀⠀⡄⢸⢠⠁⠀⠀⣼⠋⠀⠉⢢
⠀⠐⢄⣀⠀⠀⠀⡨⣱⢠⡆⠀⠀⠠⡴⠄⠀⢸⣿⣧⣄⡀⠨⡀⠀⠀⢀⠀⠀⠀⠈⡆⠂⠀⠀⠀⠈⠛⣁⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⠈⠆⡀⠀⢣⠁⠀⠂⢈
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠃⠊⡀⠀⠈⠢⠀⢰⡿⢛⡛⣛⢿⣆⠙⠒⠀⠋⡸⢝⢩⠀⢱⠀⠁⠀⠠⣀⣳⠱⠘⠀⠀⠀⣴⠀⠀⠐⠂⠉⠉⠀⠀⠀⠉⠉⠑⠲⠐⠁
⠀⠀⠰⠋⡉⣉⠓⡄⣠⠚⣁⠈⢣⠀⠀⠀⢻⡏⠁⠀⠀⠹⣟⠀⡄⡦⡀⠙⠫⠓⠁⠀⠇⠀⠀⠀⠀⠀⠀⣀⠠⠔⠈⠁⢀⠺⠀⡤⠀⡄⠀⣤⠀⣤⠀⡄⢒⡀
⠀⠀⠸⡄⠀⠄⣠⠆⢅⠈⠀⢄⠜⠀⠀⠀⠭⡇⠀⠀⠀⢠⠇⠀⢹⠰⠉⣆⠀⠀⠀⠀⠁⠈⠀⠀⠈⠈⠁⠀⠀⣤⡤⠀⠈⠀⢸⡧⠈⡇⢠⡿⡅⣿⣦⠇
⠀⠀⠀⢀⠉⡉⢁⠀⠀⢉⣃⠁⠀⠀⠀⠀⠀⠈⢢⠀⡤⠂⠀⠀⠀⠒⠁⢀⣁⣴⡢⡀⠀⠀⢿⢰⡏⣼⡇⠀⠀⠡⡔⠀⠀⠀⠀⢉⢀⠉⠈⠁⣀⡉⢀⠀⢴⢭⣕
⠀⠰⠆⣿⢼⡇⣾⢸⡇⢸⡇⣷⠀⠶⠀⢀⣴⣶⠊⠀⠈⣶⣦⣄⠀⢠⣴⣿⣿⣿⣿⡀⠀⠀⠸⠿⠇⠿⠑⠀⠀⠀⠀⡔⠈⠅⠐⠐⠉⠉⠁⠈⠉⡉⠑⠒⠢⢝⢻
⠀⠀⠀⢙⣈⣁⡁⠈⠁⠈⠁⠉⠀⠀⢀⠊⡻⣿⣷⣶⣶⣿⣿⠋⢆⠨⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⢀⡸
⠀⠀⠰⠱⠶⠷⣶⠟⡆⠤⠀⠀⢀⡔⢁⠌⠀⢻⣿⣄⣿⡿⠁⠑⢄⠣⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣀⣠⠀⢀⠀⠀⠈⠄⠉⠁⠀⠒⠒⠒⠒⠒⠂⠀⠈⠉⢀⠁
⠀⠀⢀⠀⠀⠠⢂⠀⡇⠸⠇⡰⢁⠔⠁⠀⢀⠜⠻⠿⠿⠻⡀⠀⠀⠑⢌⠢⡀⠀⠀⡠⠔⠉⡇⠀⢈⡄⢎⠀⠘⡓⠢⢄⠈⠢⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⢄⠘⠢⢄⣀⡠⠼⠅⡁⠠⠔⠘⠒⠈⢉⣁⠌⠠⡀⠀⣁⡈⠉⣁⡀⠘⠐⢤⠀⢸⠁⠂⠜⠀⠀⡌⠀⠈⡆⠀⠙⢄⠊⠇⠀⠖⠁⠀⠀⠀⠀⠀⠀⠈⠡⠆
⠀⠀⠉⢐⡒⠠⠤⠀⠒⠁⠠⡀⢀⠈⠘⠀⢠⠀⢀⣀⣙⠁⠒⠛⡈⠁⡀⢀⡠⠀⠸⡀⠘⠲⢤⣤⠇⠪⠆⠠⠴⠖⠛⢀⠇
⠀⢀⠔⠁⣀⣤⣄⡀⠑⢄⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢀⠐⠦⡀⠀⠀⠀⠈⠀⠀⠀⢀⡠⠊⠀⣀⠠⢠⠀⠀⠀⠀⡖⠖⠖⠒⠒⢒
⠀⣀⠀⢚⣛⣛⣛⣛⡂⢄⡃⠀⠀⢠⣤⠤⠄⢀⡀⠀⢐⠲⠱⠄⠀⠀⠀⠀⠀⠸⠀⢡⡄⠈⠁⠐⠂⠐⠐⠀⠀⡁⠄⠖⠉⠀⠀⠀⢃⠀⠀⠀⠇⠀⠀⠀⠀⠈
⠀⢻⣽⠟⠋⠉⠉⠻⣏⡙⠃⠀⠀⠂⠀⠈⠉⠁⠙⠀⠈⠵⣑⠒⠁⡰⢂⡄⠀⢸⡉⠥⠞⠢⡀⠀⠀⠀⣀⣴⠉⠀⠀⣀⠠⠦⠐⠊⠁⠀⠀⠀⠁⠀⠉⠠⠀⢠
⠀⠀⣼⡀⠀⠀⠀⢀⡯⠃⠀⠀⢰⠃⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⣈⠙⠒⡇⠀⠸⠀⠀⣀⣀⢁⠀⠀⠀⠉⠉⠑⠀⠁⠀⢀⡀⡰⠒⣄⡤⠀⠀⢀⢀⣤⢤⡀⠸
⠀⡔⠁⠑⢄⠀⡠⠊⠉⢢⠀⠀⢸⢠⣤⣿⣶⡆⡈⠀⠀⢀⢄⠒⠁⠀⢉⠀⠀⠀⢃⢸⣏⣻⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠗⠀⠙⠃⠄⠀⠀⠸⢿⣤⠇⡄
⠀⠁⠀⡠⠊⠀⠐⣄⠀⠘⠀⠀⢸⠈⠛⠋⠀⢠⠁⠀⠀⡆⠀⠀⠀⠀⠀⢂⠀⠀⠀⠆⢉⠁⠀⠘⡄⠀⠀⠰⡤⢺⠀⠀⠀⠆⠀⠀⠀⠀⠸⠀⠘⡄⠀⠀⢠⠁
⠀⢠⣾⣿⣷⣶⣶⣿⣷⡄⡆⠀⠈⠦⡀⠀⢠⠇⠀⠀⠀⠘⢦⣀⣀⣀⣠⠆⠀⠀⠀⠰⡀⠀⠀⢀⠕⠀⠀⠘⠑⠎⠁⠀⠀⠘⢄⠀⠀⢀⠃⠀⠀⠃⠤⠤⠜
⠀⠙⠛⠛⠛⠛⠛⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢈⠁⠀⠠⠀⠀⠀⠀⠀⠚⢹⡣⠀⢀⣼⠉⣥⡀⠀⢠⣶⢻⡟⠀⠀⠠⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠘⠛⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⣄⣄⡄⠀⠀⠀⠀⠀⣠⣼⣄⣠⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢤⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠀⠈⠋⠀⠀⠛⠉⠁⠀⠀⠀⠀⠘⢀⠠⠀⠙⣿⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡙⠟⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⢰⡆⣶⠀⠀⣿⣿⡷⠀⠀⠀⢴⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢥⠈⠂⠀⠀⠠⠀⢸⠙⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠐⠗⠚⠀⠀⠀⠀⠉⠀⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠂⢂⠘⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠘⠶⠀⠮⠁⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⡶⠴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣰⣦⣶⣦⣖⣰⣰⡀
⠀⠀⢶⣶⡶⠀⢴⣶⣶⣦⠀⠠⣀⢀⡠⠀⠀⢄⠠⡀⢀⠀⢠⣶⣦⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠉⠀⠀⠀⠉⠛⠉⠀⠀⠉⠈⠁⠀⠐⠈⠷⠂⠋⠀⠀⠙⠋⠀⠀⠘⠛

⣿⣿⣿⣿⡜⣿⡌⠻⣦⣿⣧⡹⣦⡙⠻⢷⣶⣤⣬⣿⣿⣿⣿⣿⣿⠏⣴⣿⣿⡿⢟⣫⣾⣯⣶⣿⡿⢃⣴⣟⣴⠟⠀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⠘⣿⣆⠈⠻⣿⣿⣾⣿⣶⣤⣀⠉⠙⢿⣯⠙⣿⣿⣿⣼⣿⣿⣯⡾⢛⣩⣽⣿⣿⣿⣿⣿⣿⠟⢁⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⠘⣿⣧⠀⢹⣿⢉⡉⠛⠻⢿⣷⣄⢸⣿⣀⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⡿⠟⠋⢉⡉⣿⣏⣼⣿⡿⠋⣼⡿⣸⡿⣿⣿
⣿⣿⣿⣿⢿⣿⣄⠘⣿⣇⣿⡇⣿⣙⡓⢦⡀⠉⠻⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⠟⠁⣠⡴⡛⢍⣷⢹⣿⡿⠋⣠⣾⠟⢀⣿⢣⣿⣿
⣿⣿⣿⣿⣧⡻⣿⣦⠸⣿⣿⢸⡇⡟⣖⢶⡙⣦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡼⠕⣶⡿⣦⢹⢸⣿⣣⣾⠟⠁⢀⣾⣣⣿⣿⣿
⣿⣿⡜⣷⡙⢷⣝⣿⣷⣿⣿⢸⡇⣧⣜⣛⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣕⡻⣾⣶⢸⢸⣿⡿⠋⣀⣴⣿⣿⡿⣻⣿⣿
⣿⡿⣿⡸⣿⡌⠻⣿⣿⣿⣿⣯⣧⢫⣮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⡅⣾⣾⣿⣷⣿⣿⡿⢛⣥⣾⡿⣿⣿
⣿⢿⣾⣿⣿⣿⣦⣌⣻⣿⡛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣛⣿⣿⣿⣾⣿⡿⣫⣾⣿⣿
⣿⠷⠄⠉⠛⢿⣿⣭⡉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣽⣿⣿⣿⡿⠿⠛⢻
⣿⣛⣛⣭⣽⣿⠿⠿⠿⢦⣄⠀⠀⠀⠀⠀⡞⠁⠀⣿⠻⣆⠀⠀⠀⠀⠀⡴⢛⣯⠀⠙⣇⠀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⢿⣿⡿⠟⣛⣛⠃⠈⠀⠀⠀⠀⠀⢳⡀⠰⣿⠀⢸⡆⠀⠀⠀⢸⠁⢸⣿⠀⢠⠇⠀⠀⠀⠀⠀⠀⢙⣛⣛⠿⣿⣟⡻⠿⣿⣿
⣿⢋⣴⡿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣿⣠⠞⠀⠀⠀⠀⠈⠧⣄⣿⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣗⠦⣿
⣿⣟⣩⣾⣿⠏⣀⣤⠴⣲⣶⣶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡯⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⢶⣶⣶⢦⣤⡈⢻⣿⣿⣿⣷⣾
⣿⣛⣿⣿⣏⡾⠋⣠⡾⠋⠁⠀⣴⣿⠏⠛⠶⣤⣀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⣀⣴⠾⠛⢹⣿⣆⠀⠈⠙⢷⡄⠙⣦⣿⣿⣹⣿⣿
⣿⣿⣿⢿⣿⡇⣰⠏⠀⠀⠠⠞⠋⣼⡄⠀⠀⠀⠉⠛⠓⠒⢦⣹⡿⣅⠶⠒⠚⠋⠉⠀⠀⠀⢨⣇⠙⠣⡀⠀⠀⠙⠄⢸⣿⣿⣻⡟⣸
⣿⣏⣇⠈⣿⡇⠋⠀⠀⠀⠀⠀⠘⣹⣥⠀⠀⠀⠀⠀⠀⠀⣰⠃⣇⢻⡄⠀⠀⠀⠀⠀⠀⢠⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣷⣿
⣿⣿⣿⡄⠸⣷⠀⣄⠀⠀⣀⣠⡾⢻⣿⠀⠀⠀⠀⠀⠀⣠⠏⣰⣿⡄⢻⡄⠀⠀⠀⠀⠀⢸⣿⡻⢦⣄⡀⠀⠀⡄⢀⡿⢹⠃⣿⣿⣿
⣿⣿⣿⣿⣄⠘⠇⢹⡷⣤⣁⣠⣴⡿⢿⣴⠀⠀⠀⠀⢰⠏⣴⠃⡇⠹⣆⢻⡄⠀⠀⠀⢸⣾⡿⣿⣦⣀⣀⣤⢾⡇⠼⠁⠀⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣤⣽⣦⣶⣟⣉⡀⠘⣿⣰⠂⠀⢠⢏⡼⠁⠀⡇⠀⠘⢦⢳⡀⠀⠰⣸⣿⠁⢀⣙⣷⣦⣶⣯⣤⣤⣴⣾⣿⣿⣿⣿
⣿⣝⢿⣿⡌⠉⢙⣿⣿⣿⣿⣭⣉⠻⣦⠸⣿⠀⠀⢸⣿⠀⠀⠀⣧⠈⠀⢨⣿⡇⠀⠀⣿⠁⣴⠛⣩⣽⣿⣿⣿⣟⠋⠉⣰⣿⠟⣩⣿
⣿⣿⣧⠙⣿⣤⣿⣿⠻⣿⡙⣿⣿⣧⣹⡆⣿⢦⡀⠸⣿⡇⠐⠂⡀⠐⠀⢸⣿⠁⣠⠾⣿⢸⣇⣾⣿⣿⢫⣿⢛⣿⣷⣰⡿⠃⣾⣿⣿
⣿⣿⣿⡆⠘⣿⡿⣿⣆⣿⣷⣿⡏⢿⣿⣷⡿⠀⠙⣆⣿⣧⠀⠀⠛⠀⠀⣿⡏⡴⠃⠀⣿⣿⣿⣟⢻⣿⣾⣿⣼⡿⣿⣿⠁⢸⣿⣿⣿
⣿⣿⣿⣇⠀⢿⣧⡊⣿⣿⠛⣿⣧⣾⣿⣿⠁⠀⠀⠸⣿⣿⠀⠇⠀⠈⢰⣿⣿⠃⠀⠀⠻⣿⣿⣷⣾⣿⠙⣿⣿⢑⣿⡏⠀⣾⣿⡿⢸
⣿⠸⣿⣿⣄⠘⣿⣿⣿⣩⣈⣢⣬⣿⣿⣟⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⣿⣥⣅⣲⣙⣿⣿⡿⠁⣰⣿⡿⢃⣼
⣿⣿⣾⣿⣿⣷⣤⣭⣛⣛⠿⢿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣼⣿⠇⠀⠀⠀⢰⣿⣿⣿⣿⠿⢟⣛⣩⣥⣴⣾⣿⣿⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢠⠔⢁
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢰⡟⠀⡖⠂⠀⠀⠀⠹⠄⠀⠀⣀⡀⠀⠀⠾⠷
⠀⠀⠀⠀⠔⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⢠⣂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠾⠚⠦⢀⠈⠩⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣦⠘⠒⠈⠆⠀⠀⢀⠀⠀⠀⡀⢻⠈⢰
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⣠⣦⣄⣀⠀⠀⠙⠦⠤⢀⠀⠀⠀⠀⢀⣀⡴⠂⠀⠀⠀⠀⠙⠃⠀⠀⠦⠀⠀⠈⠉⠀⠐⠇⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣷⣸⣯⣛⣿⣯⣫⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢡⠀⠀⠀⣀⢀⡀⠤⠤⡀⠀⠀⢀⠐⠈⠉⠆⠀⠀⠀⠀⢀⠋⡍⠁⠀⠂⢄⡀⠀⠀⠤⡤⠂⠃⠀⠀⠄⠂⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠂⠉⠀⠀⢨⡇⠀⠐⠋⠀⠀⡌⠀⢠⠀⠀⢀⠀⠀⠀⢸⠀⠈⠢⡀⠀⠀⠙⡄⠀⠀⠀⡘⠀⠀⠀⡄⢀⠔⠁⠄
⠀⠀⠀⠀⠀⣤⠀⠀⠉⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠀⢠⠊⠀⠀⢘⠀⡀⠈⠑⠀⠀⠀⠆⠀⠀⠐⢄⠀⠀⢰⠀⠀⠠⠜⠀⠀⠀⠘⠇⠄⠊
⠀⠀⠀⡰⠈⠿⠀⠀⠀⠐⠀⠅⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⢮⡔⠁⠀⠀⠉⠄⠀⠈⠢⠀⠀⠀⠑⢀⡘⠀⠀⠀⠀⠀⢀⠔⡀
⠀⠀⠰⠀⡘⠀⠐⣀⣀⠀⠀⠀⠀⠀⠐⠭⠁⠀⠀⡀⠀⠀⢄⠀⢸⠀⠀⡠⠂⠀⠤⠀⠀⠀⠈⠁⠀⠂⠈⠡⠀⠀⠀⠀⠐⠀⢀⠐
⠀⠀⠠⠊⠀⠀⡌⠀⠀⠀⠁⠆⡀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠂⣸⡀⠊⠀⠀⡐⠀⠀⠰⣅⠈⠰⡄⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⣡⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠈⠐⠂⠠⡭⠤⠀⠒⠈⠀⠀⠀⠇⠀⠉⠂⡼⠀⠀⠀⠀⠀⠀⣇⣀⡈⠠⠭⠛⠐⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⡢⠄⠁⠀⡠⠶⢄⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠃⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠏⠁⠁⠀⠀⡌⠁⢰⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢠⠈⢁⠛⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⡄⠀⠀⠀⣀⠀⠘⠤⡇⠀⠀⡄⠂⠀⠀⠀⡀⠂⡰⠀⠀⠀⠀⠀⠈⠖⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢆⠀⠀⡆⠀⢀⠃⠀⠀⠘⠄⠒⠀⠠⠈⣄⠀⠈⠃⠀⠀⠈⠛⠈⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⡇⠑
⠀⠀⠀⠀⡠⠐⠀⡀⠀⠀⢀⡠⠛⠄⠀⠀⠑⢄⣁⡀⠂⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⡐⠤⣘⡀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠱
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠃⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠉⠂⣄⠀⠀⠀⠀⠀⢈⠉⠁⠀⠀⠡⠀⠀⠰
⠀⠀⢸⡀⠤⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠁⠢⢄⡀⠀⠀⠑⠀⠄⣀⡀⢉⡄⠂
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠰⢠⠀⠀⠇⠀⠀⠸⠀⠀⣄⠀⠲⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⡠⠂⠀⠀⠀⠀⡄⠀⠈⠛⠀⠀⠀⠀⠋⠁⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣉⡉⠱⡦⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠠⠀⠀⠀⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⢀⠀⠒⠀⠀⢠⠂⢂⡠⠂⠉⠂
⠀⠀⠀⠀⠰⡁⠀⢌⡐⠢⢄⠀⠀⠀⠀⣄⠒⠈⠉⠀⠀⠀⣠⡄⠀⠀⠈⠉⠁⠒⢠⠀⠀⠀⠀⢠⠉⢂⡀⠀⠀⠀⢠⠊⢰⠄⠀⠀⠀⠀⣀⠂
⠀⠀⠀⢀⣀⡈⠢⠀⠀⠂⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⢐⠉⠀⠀⠀⣠⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠃⡀⠀⠀⡀⠀⠀⠀⠵⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠷⠀⠀⠠⠈⠃⠀⠀⠀⠁⠄⠀⡀⠀⠀⡠⠊⠀⠀⣤⡐⠁
⠀⠀⠀⢀⠠⠀⠀⢀⠀⢛⠀⠀⠁⡀⢁⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠠⠊⢠⠀⢰⠀⠀⠈⠂⡀⠆⠀⠜⠀⠀⢃⡠⠊⠀⠀⠀⠀⡠⠄
⠀⠀⠐⠁⠀⡠⠒⠁⠀⢸⠀⢤⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⢀⡠⠊⠁⠐⠂⠀⠈⠁
⠀⠀⠇⠀⠀⠀⡠⠂⢂⠀⠀⠀⠀⡀⡠⠀⠀⠀⣤⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⡷⠁⢠⠀⠀⠀⠀⠀⠀⠰⠔⠈⠀⠀⠀⠀⠀⠀⢀⣀⡔⠢
⠀⠀⠈⠁⠀⠉⠀⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠈⠢⠈⠐⡄⠀⠀⠀⡀⠀⢦⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠀⠁⠀⡆
⠀⠀⠀⠀⢀⡀⠤⠠⣀⠤⠤⢀⡀⠀⠀⠀⠀⠀⡄⠀⠡⣠⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⢰⠀⠢⡌⠈⠆⠀⠱⠀⠀⠀⠈⠢⢄⡀⠀⠇
⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⢡⠀⠈⠻⡄⠀⢠⠀⠀⠰⡶⠃⠀⠀⠀⠠⠄⠲⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠣⡀⠐⢀⠀⠇⠀⠘⠀⡐⠀⢀⠜⠀⠀⠀⠀⠂⠀⠐⠰⣦⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠁⠀⠆⠀⠐⢢⡠⡀⠀⠀⠀⢁
⠀⠀⠀⠈⠢⠀⠢⣀⠀⠀⠌⢀⠔⠁⠀⠀⠶⡄⢠⡀⠈⠒⢀⠀⢢⡀⠀⠀⠀⡠⠀⠀⠀⣄⠀⠀⠁⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠋⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠽⣶⠧⠐⠁⠀⠀⠀⠀⣀⠐⢄⠁⡀⠀⠀⠈⠈⠑⡀⠀⠀⠃⠀⡠⠊⡸⠀⠀⢀⢀⠀⠈⢃⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠣⠈⠶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⡀⠖⠁⠀⠘⢦⡀⠀⠂⣤⣤⠀⠀⠀⠆⠁
⠀⠀⠀⢠⠲⠀⠀⠀⠀⠀⠀⠘⠁⠀⢉⠐⠢⢄⠀⠀⢀⠐⠈⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠣⣀⠁⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣰⡆⠔⡠⠞⠀⠀⡌⠡⢀⢀⡴⠚⠀⠀⠀⠠⠐⠃⠐⠺⠀⠀⠀⢀⡀⢴⠀⠀⠀⠁⠀⣀⠀⠌⣰⡄⠀⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⡙⠉⠁⠀⠀⠀⠘⣧⠀⠙⠁⠀⣠⠀⠀⠀⠓⢄⠀⠀⠀⢈⠀⢠⠉⢠⠁⡆⠀⠀⠀⠀⠈⢁⠈⠛⠀⠈
⠀⠀⢀⠂⠀⠉⠀⠐⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣄⠄⢀⠇⠀⠀⠀⠀⠀⠁⢂⠤⠁⠀⠘⣠⣄⠔⠁⠀⠀⡟⠀⠐⣼⠦⠐⠒⡰⠆
⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⢠⠪⠀⠘⠢⠀⠀⠄⡁⢀⠌⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠃⠀⡀⠋⠉⠉
⠀⠀⠀⠱⢀⠀⢀⠂⠀⢠⠆⠀⠀⠀⠘⢆⠘⠃⣄⠓⡀⠈⡷⠁⠀⠠⠐⠃⡰⠆⠀⠀⣀⠄⠻⢄⠀⠀⢰⢂⠐⠀⠠⠀⠾⠇⣀⠀⠀⠶
⠀⠀⠀⠀⠀⠁⠪⠀⠒⠁⠈⠀⡀⠀⠄⠀⠉⠓⠈⠰⠆⠀⠇⠀⠠⢇⡰⠟⠰⠆⠀⢰⡀⠀⠀⠀⡆⠀⢰⠈⡀⠰⣤⠎⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠐⡣⠀⠀⠀⠀⠀⠀⠑⡇⢀⣦⠋⠴⠚⠁⠀⠀⠀⡄⠀⢀⡘⠁⠀⠀⣄⣀⠘⠉⠒⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠆⢀⣀⠙⠀⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠀⠘⠛⠒⠀⣀⡀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣄⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠲⠄⢀⢀⠀⢀⣤⣶⣶⣶⣤⣤
⠀⠀⠀⢠⠄⠂⠆⣼⣿⣻⣿⣿⣿⠿⣿⡇⢠⡩⠤⠖⠃⠂⡀⠀⠀⠈⠀⡠⠀⠈⠁⢀⠀⠄⠀⠈⠒⠂⢸⡷⣿⡸⢿⣿⣿
⠀⠀⠊⠀⠐⣃⠰⣿⡏⡿⣉⣙⣳⣼⣿⡿⠀⠀⠀⠀⠋⢀⠀⠀⠠⢀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⠀⢸⣿⡟⠟⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠄⠸⢿⣾⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠼⠒⠀⢆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣿⣧⣶⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡈⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠉⠉⢻⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⡒⠄⠀⡠⠀⠀⠠⠀⠀⠀⠀⠈⠠⠤⡀⠀⠂⠀⠀⠀⠈⠁⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠉⢩⢈⠀⡄⠀⠑⠠⠀⠀⠀⠄⠀⢰⢀⡆⡄⢀⡀⠀⠀⠈⣃⡀⡄⠀⠀⠐⠀⠀⠀⠀⠐⠂⠠⠀⢈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣚⡆⠀⠀⠀⠀⠀⠀⠀⠠⠑⠈⠀⠀⠉⠐⠁⠀⠀⡌⠦⢆⠂⠘⠄⠀⠀⢀⣀⣀⣀⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠠⠁⠀⠄⠀⠀⠀⠀⠈⠀⠀⣴⢋⢻⣻⢿⡹⣿⠙⣿⠛⣧
⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡘⣱⣼⣊⣥⣵⣶⣾⠷⠋
⠀⢸⣿⢸⠐⡇⡇⣿⢈⡇⢺⡜⡇⣻⢸⢸⣿⡿⠀⠀⣠⣶⡶⣶⢶⡶⣶⢶⣶⣤⡀⠀⠀⠀⠈⠛⢻⠉⠉⠅⠀⠀⠀⠠⠆
⠀⠘⠿⠾⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠟⠁⠀⣼⣿⣿⡇⡘⣈⣀⣀⢸⣿⣿⣿⡆⠀⠀⡄⢤⠀⠀⠀⢀⠀⠀⠀⠈⢥
⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⣀⢀⡔⡦⠀⠀⠀⠀⣿⠩⡏⣏⢿⢹⢹⡏⢹⢹⡹⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠁⠄⠰
⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⠀⠸⠸⠰⢁⠀⠀⠀⠀⠹⢶⣧⣿⣾⣾⣦⣷⣾⣼⣷⡿⠀⠀⠂⣠⠀⠀⡀⢀⠐⠀⠨⠔
⠀⠀⠦⠘⡀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⢀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠁⠩⠁⠁⠁⠀⠀⠀⡄⠂⡀
⠀⠸⠂⠀⠀⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢁⠅⠀⠐⣒⠀⠀⠀⠀⠀⢀⠴⠒⡀⠀⢁⠊⡠⢖⠀⠀⠊⠀⠀⠘⠘
⠀⠀⠁⠄⠀⠀⠀⠀⢠⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢀⠄⠀⢀⣜⠠⠊⡐⠀⠀⠂⠀⠀⠉⠃⠀⠀⠀⠀⠐⠂
⠀⢀⣀⣀⣀⣀⣀⣀⣀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠠⠀⠈⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠂⠀⠒
⠀⣾⢹⡏⣿⢹⡟⣿⢹⣇⠀⠀⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠲⠜⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢐
⠀⣿⣼⣧⣯⣴⣧⣿⣼⡟⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠠⢐⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⣀⣀⣬⣀⣀⣀⠀⠊
⠀⠈⠛⠛⠛⠛⣿⡏⠉⠀⡀⣇⡡⠄⠠⠄⠀⡀⠀⠁⠀⠉⣈⠉⠁⠽⠀⠀⢀⠉⠁⠀⠀⠀⠀⢀⣿⢫⡽⢛⠟⣻⠉⢻⡆
⠀⠀⡘⠠⣀⠀⠀⢁⠀⠀⠁⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⡂⣴⣶⣶⣶⣦⢰⡀⠀⠀⠀⠀⠀⠈⣿⡘⣴⣤⣧⣹⣀⣾⠇
⠀⠀⠀⠃⠛⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠂⠠⠤⠀⠁⠙⠛⠛⠛⠋⠈⠂⠀⠀⠐⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠶⣄⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⡏⠀⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⣀⠜⠀⠈⣼⡀⡀⡄⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⢨⣄⠀⠀⠀⢰⢃⡏⠀⠀⠑⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠙⠳⢤⣸⣯⣀⡠⣦⢦⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠞⡐⠐⠀⣀⠄⣹⡪⠑⠒⠨⠴⡿⣆
⠀⠀⠀⡀⠀⠀⠀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢹⠂⠅⠥⠈⠀⠀⢾⢠⡌⢫⣦⡔⡱⢫⠂⠀⠀⠀⠀⣤⡀⠀⠀⡷⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠉⠩⡉⣋⠋⢰⠀⠈⠉⢁⡔⢦⡀⠀⠀⠀⠀⠀⠀⡏⠈⠀⣠⠖⠂⢾⢸⡁⡗⠈⡴⢣⠃⠀⠀⠀⠀⣰⠻⡝⠒⠫⠄⠀⣉⡭⠙⢉⠋
⠀⠀⠀⠀⠀⠐⣌⣗⢶⠤⡀⠀⠀⠱⡀⠉⠉⢳⠤⢶⡑⢤⡇⠡⣸⠁⠀⠀⣮⡸⠉⡰⠥⣴⣉⡀⣀⠜⡃⠋⠰⠀⡃⢀⠞⠀⠈⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢃⠃⠈⠀⠉⠓⠤⠌⡁⢄⠀⡐⠛⢰⡯⠁⣀⢘⢊⣲⣀⣴⣿⢀⠞⡠⠺⠰⠦⣝⡄⢸⡇⠀⠇⣲⣄⠡⠠⠤⡤⠀⢀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⣠⠚⣆⣄⠀⠺⠀⢨⡧⢃⠟⢹⠃⣷⠀⡴⠃⡀⠀⠀⠈⡷⣽⢖⠗⠊⡠⠬⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⢠⡟⠚⠃⠘⠂⠚⠘⢁⠁⠀⢀⢁⡷⠾⣧⣀⠁⢸⠉⣧⠀⣿⠊⠁⠘⠀⠀⢀⣴⠛⠀⠀⢗⠟⠀⠀⠄⣦⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⢀⡀⠔⡁⢠⠈⠀⡩⢶⢻⠎⠙⠳⡄⠳⣜⢦⣹⠃⠀⠀⣀⣰⣈⠕⣮⡁⢤⠀⣉⣀⡴⢹⠟⣋⡶⠒⠂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⣈⠂⡌⠀⠀⠏⣏⠉⡭⠘⠷⣤⣈⠭⠅⣀⣰⡏⠉⠁⠀⡘⢷⠸⠇⠝⠽⡶⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈⢧⠜⣂⣠⢄⠭⣺⠧⡤⢶⠔⢶⣯⣤⣧⣎⠹⠀⣀⣄⢀⠠⡘⢽⣄⢀⢀⣘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡤⢿⡿⢹⠁⡘⠁⠀⠑⠐⠑⣃⠘⣁⡽⠃⠀⠈⠦⣄⠀⠀⡠⢛⠻⠀⠘⡻⢗⠲⢦⣵⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣴⣊⡁⠀⠎⠀⠹⢄⠀⣄⠀⡠⢴⠈⣧⡶⠟⠀⠀⠀⠀⠀⠈⠻⡛⡩⠴⢒⠞⠐⠣⠠⠝⠛⠃⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠒⠚⠛⠲⣤⣍⡥⠥⣌⣯⠔⠉⠀⠀⠀⢰⠇⠀⠀⠀⠀⠱⡰⠞⠋⠁⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⣜⣿⣶⣔⠆⠀⠁⠉⠀⠀⣠⣤⣶⣦⣄⠀⠀⠀⠀⢀⡀
⠀⠈⠃⣻⠏⡀⠀⠀⠀⣀⠀⢽⣟⣻⠟⠈⠑⠶⢶⡦⠈⠀⠀⠈⠉⠩⣥⡬⢿⣿⣭⡧⣦⠀⠀⠀⠀⠠⠀⠤⠀⠀⣰⣠⣌⣄⣀⠠⢤⣦⣽⣥⣔⠄
⠀⠀⠀⠈⡷⠀⠀⠀⠀⠉⠑⠀⣿⡏⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠉⠑⠈⠀⠀⠀⠉⠙⠿⣷⣶
⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢻⣷⡆
⠀⠀⢸⣦⣶⡖⠀⢀⣠⣾⣿⡿⢻⣿⣿⣿⣿⣿⣴⡶⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣄⠱⣲⣄⠀⡠⡇⠀⢻⡇
⠀⠀⠈⠛⠛⠛⠛⠻⣿⣿⣿⢷⠋⠸⣿⣿⣿⣿⣿⠀⠀⢀⠄⠉⣷⣄⢠⣄⠀⠀⢀⠄⠐⣀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣿⣿⡿⡣⡚⠑⣿⣿⢽⡧⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣂⣠⠙⣿⣿⣿⡗⣂⣷⣾⡆⠀⠈⠻⣿⣿⣶⣄⣸⣿⣧⣿⣼⣴⣿⣇⣼⣡⠄⣴⣿⣿⣿⣿⣔⡡⣀⠀⡁⠀⠀⢈⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠁⠙⠻⢿⡟⣿⣿⣿⣿⣷⣿⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣤⢂⣤⠈⣄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢀⡘⣿⣿⣿⣿⣏⠉⠿⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠉⠿⢿⣿⣿⣿⣿⣽⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⡀⠈⣿⣿⡏⢿⣿⣷⣿⠃⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠛⡟⠿⡶⠶⣿⠿⡟⢲⣭⣿⣿⣿⣿⣿⡕⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣽⠾⢎⣻⣿⣾⣿⡯⢿⠶⠚⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣃⠧⠀⠚⠉⠀⠀⢻⣿⣷⣶⡟⠌⢻⡆⠀⢼⣿⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣽⣿⣿⣿⣿⣿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⡄⠀⠹⣿⣿⣿⢱⣾⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣢⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠆⠀⠀⠘⣿⣿⣀⢸⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣻⣿⡏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⠄⠀⠀⠀⠀⠘⣿⣟⠳⣇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⢹⠛⠄⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣏⡷⣿⡅⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢶⣮⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡶⢤⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⢀⠀⢰⣦⡄⠀⠀⠀⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠆⠀⠢
⠀⠀⠀⠘⠆⠀⠜⢃⠠⠈⠁⠀⠁⠀⠈⠀⠀⡄⠀⠀⠀⠀⠠⠠⠀⠀⠄⠀⣠⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠰
⠀⢀⠀⠐⠂⠀⢀⠘⠄⠈⠠⠀⡃⠀⠐⠀⠀⠆⠀⠀⠂⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠆⠐⠀⠀⣁⡼
⢢⠓⡖⣄⠀⢦⡀⠊⠀⠑⠐⠓⠃⠀⢈⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⠂⠀⠀⡈⠀⠀⠀⠀⠀⠀⠋
⠁⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠈⠀⠀⠠⠆⢠⠀⠈⢢⣀⠀⢀⡀⠀⠀⠘
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠀⠀⠀⠀⠀⠐⠆⠐⠂⠀⠀⡈⠀⠀⡀⠉⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠄⠀⠀⠂⠈⠃⠤⠀⠂
⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠉⠀⢀⡜⠀⠈⠂⠀⠘⠀⠀⠀⠀⠀⠈⢨⡀⠀⠀⠀⠀⠠⠂⠈⠁⠀⠐
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⠀⠀⠠⠴⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⢰⠀⠀⠀⠈⠁⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠜⠀⠀⠀⠀⠀⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠴⠄⠀⠈⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠐⠄
⠈⠈⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⠀⠀⠁⠀⠀⠁⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠖⠂⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠙⢀
⠀⡀⢀⢀⠀⠀⠀⠀⠀⡆⠀⠀⠄⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠈⢀⠀⠀⠡⠆
⠀⠀⢧⠈⠐⢤⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠁⠒⠐⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠡⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣮⢶⠄⠠⠂⢀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢄⡀⠠⠄⡀
⠀⠀⠀⠀⠈⣄⣸⠿⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠁⠃⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠄⠄⠀⠀⠀⠤⠄
⠀⠀⠶⣍⢷⣘⢝⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠐⠆⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢀⠀⣀⠙⠀⠉⠀⠀⠀⠀⠀⢀⠀⡀⠈⢀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡾⠟⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣀⣤⣤⣤⣤⣤⣶⡶⠶⠿⠿⣿⠉⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⣴⠂⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠛⠛⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠘⠒⠂⠀⠀⠀⠀⠀⠀⢀⣾⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡤⠀⠀⠸⠿⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⠀⠀⠘⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⠎
⠀⠀⠀⠀⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⡀
⠀⠀⠀⣰⡇⠀⣾⣿⣿⣴⡿⠂⠘⣷⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⠏⢀⣠⣄⠀⠀⠀⠀⠀⠀⠘⣿⡍⠐⠂⠐⠺⠗
⠀⠀⠀⢻⣷⣀⠘⣿⣿⣿⣧⣶⣆⣼⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡌⠐⠃⠀⢲⠆
⠀⠀⠀⢸⣿⣿⣶⡼⣿⣿⣿⣿⡟⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⠁⠛⡃
⠀⠀⠀⠸⣿⣿⣿⠃⢿⣿⣿⣿⠁⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⠽⠒⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆⠋⢰⢀⠃
⠀⠀⠀⠀⠿⠿⠷⠀⢸⣿⣿⣿⢠⣿⣿⡇⠀⠀⠀⠀⠀⠴⠡⡁⣠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠠⡄⡄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠁⠀⠀⠀⠀⡾⣧⢸⣶⡿⢛⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⡆⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡸⣾⣶⣤⣀⠀⣠⣤⢻⡏⣜⣤⠰⢁⢋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠈⢰⡞⠄⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⣨⣿⡟⣕⣿⣿⣧⣽⣷⣿⣿⡆⠀⠹⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡄⠀⠀⢨⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⢌⢷⠸⣇⡿⢸⢸⣹⣽⣿⢿⣹⠿⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣄⠉⢀⡄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣲⡈⢇⣿⣷⢸⡾⣞⡛⢞⠳⣭⣉⡡⠇⠀⠀⠀⠀⠀⠀⣰⣶⢶⣾⣇⠀⠀⠀⠀⠠⡄⠀⠻⠟⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠹⣯⠘⢾⠏⢧⣑⣷⣂⠀⠑⠦⠈⠀⠀⠀⠀⠀⠀⠀⠰⠋⣀⣤⣷⣮⠷⣦⡀⠀⠀⠀⢄⡀⠀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣜⠃⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠁⠀⠀⠀⠀⡺⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠁⠀⢀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢄⠀⠀⠀⠃⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢀⣴⣿⡀⠀⢹⡆⣦⢴⡖⣶⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡄⠘⠓⠀⠐⠀⠀⠀⠀⠰⣀⡀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠛⢻⡏⠡⠴⠚⠓⠿⠸⠇⠿⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠉⠁