Rainbows Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠀⠉⠉⠉⠉⠁⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣀⠠⠐⠂⠀⠈⠀⣈⡉⠁⠀⠂⠀⢀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢁⠰⠊⠁⠀⠀⠀⠉⢀⠀⠀⣀⠈⠀⠐⠠⠀⠁⠀⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠁⠀⠂⠀⠀⠀⣁⠀⠠⠀⠀⠀⠀⣈⠀⠀⠀⠁⠀⠈⠢⡀⠱⡀
⠀⠀⠀⠀⠀⠀⡘⢀⠎⠀⠊⠀⠈⡠⠒⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠑⢄⠀⢄⠐⡀⠱
⠀⠀⠀⠀⢀⡠⠅⠌⡠⢀⣊⡠⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠀⠁⡀⢂⠘⡀⢀
⠀⠀⠀⠠⠁⠀⠀⠀⠑⠉⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠑⠐⠂⡵⠊⠀⠂⠁⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠄⣀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢⠤⡀⠀⠠⠒⠉⠉⠁

⠀⣤⣄⠀⠀⣠⣴⣶⣦⣄⡀⠀⠀⠀⠀⢀⡤⢖⣒⣒⠶⣄⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⣀⢤⣒⣒⢤⡀⠀⣤⡄
⠀⠉⠃⣠⣾⢟⣭⣭⡙⢿⣿⣄⠀⠀⣠⢫⣾⣿⣿⣿⣿⣮⡳⡄⠀⠴⣿⣯⢿⡻⣯⡳⠀⣔⣵⣿⢭⢍⢳⡝⡄⠙⠁
⠀⠀⢠⣿⢣⡟⣵⣾⡽⣆⢿⣿⡄⢀⡇⣿⣿⡟⠉⠉⠻⣿⣷⢻⡀⠀⠈⠀⠀⠉⠀⠀⢸⣼⣿⣿⠿⢷⣷⣿⣸
⠀⠀⣼⡿⣼⢻⡣⣪⣿⡹⣎⣿⡇⠘⠛⠛⠛⠀⡀⠀⠀⠉⠉⢁⣥⣶⣶⣤⡀⠀⢀⣤⣾⣿⣿⣏⠀⢈⣿⣿⣿⣤⡀
⠀⠀⠉⠉⠉⠀⠀⠁⠈⠁⠉⠉⡡⠂⠀⠀⠀⠘⠋⠀⠀⠀⣰⣟⣥⠶⠶⣮⣻⣆⠻⠿⡿⠿⠿⠟⠀⠘⠿⠿⠿⠿⠿
⠀⠀⣠⣶⣾⣷⣦⣄⠀⠀⢀⣔⡒⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣾⡵⢋⡙⣎⢿⢿⠀⠃⠄⢃⠘⠀⠀⠀⠀⠃⠐⢨
⠀⣼⣿⢋⣥⣤⡉⢿⣧⠀⢻⡿⠧⠀⠂⠀⠀⢈⢉⡁⠀⠀⣁⡁⠁⠀⠀⠈⠈⢈⠀⠀⠈⠀⢀⣀⣀⡀⠀⠈⠈
⠀⣿⠇⣾⣫⢬⣻⡆⢿⡇⠀⠀⠀⠀⢸⣡⢀⣿⢨⡇⡷⣸⣿⡨⡼⢁⣾⣤⠘⠯⡀⠀⢀⡴⢛⣭⢭⣝⠳⣤⠸⣾⠇
⠀⣿⡄⡿⠿⠟⠟⠛⠈⠋⠀⠀⣀⣀⡘⠣⠜⠸⠸⠇⠃⠙⠯⠇⠑⠊⠹⠚⠃⠠⠇⠀⣾⢡⢏⡴⠶⣌⠳⡌⢷⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⠟⣋⣉⣛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⣾⣼⣟⣭⠻⣷⡹⠜⠇
⠀⠰⠆⠆⡉⠘⠃⠀⢀⡾⣱⢟⣭⣭⣝⢷⡹⡆⠀⢠⣿⣮⡀⠀⣠⢞⡯⠿⠭⣗⢦⠀⠓⠛⠙⠁⠀⠀⢀⡀
⠀⠀⠛⠰⠀⠛⠀⢀⣼⣷⣯⡟⠀⠀⣸⣷⣿⣷⣤⠀⠈⠀⠀⣼⡵⣻⣞⣭⣟⢮⣿⣧⠀⠀⠀⠻⠃⠀⠚⠇⠀⣀⡀
⠀⠀⠀⣀⣀⣄⡀⢿⣿⣿⣿⡷⠆⠘⠿⠿⠿⠿⠟⠁⠀⠀⢠⣿⢿⣷⢁⢂⢈⣿⡿⣿⡆⢀⣤⡶⠾⠷⣶⣄⠀⠛⠃
⠀⢠⡾⢋⣡⣭⡙⣦⡀⠀⠀⠀⠀⠀⣄⣠⠀⢀⡶⢛⣯⣛⢦⡀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡾⢉⣴⡶⢶⣦⡙⣷⡀
⠀⣿⢣⡿⣩⣍⢻⡜⣧⠀⠀⣀⣶⡄⠛⠁⢠⣟⣾⠟⠉⠹⣧⣷⠀⠀⠶⠰⢎⡁⠄⢀⡿⢰⡿⣡⡶⣦⡙⣷⣸⣇
⠀⣿⢸⡷⣿⠽⠿⠿⠻⠀⠀⠙⠻⠃⠀⠀⣿⣾⢃⡾⢻⣇⣿⣾⠀⠦⣉⠰⠂⠁⢀⣼⣿⣿⣷⣯⠀⢸⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠙⠀⠛⠀⠀⠀⠀⠈⠻⠿⠻⠿⠋⠀⠀⠙⠋⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠛⠛⠉⠉⠛⠛⠓⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣁⣤⠴⠖⠛⠛⠉⠉⠉⠉⠛⠛⠲⠦⣤⣈⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⣠⠴⠛⢉⣠⠴⠖⠛⠛⠉⠉⠉⠉⠛⠛⠲⠦⣄⡉⠛⠦⣄⠙⠳⣄
⠀⠀⠀⠀⠀⢠⡞⠁⣴⠞⢁⣤⠞⠉⢀⣠⠴⠖⠚⠛⠛⠛⠛⠓⠲⠦⣄⡀⠙⠳⣤⡈⠳⣦⠈⢳⡄
⠀⠀⠀⠀⣰⠋⣠⠞⢁⡴⠋⢀⣤⠞⠉⢀⣠⡤⠶⠖⠒⠒⠲⠶⢤⣄⡀⠉⠳⣤⡀⠙⢦⡈⠳⣄⠙⣆
⠀⠀⠀⣼⠃⣰⠋⢠⠞⠁⣰⠏⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠻⣆⠈⠳⡄⠙⣆⠘⣧
⠀⠀⣸⠃⢰⠇⢠⠏⠀⡼⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⢧⠀⠹⡄⠸⡆⠘⣇
⠀⢀⡟⢀⡿⠚⠛⠛⠺⡅⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣧⣠⠿⠦⢿⡀⢻⡀
⣠⠞⠉⠉⠁⠀⠀⠀⠀⠙⠛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠶⠞⠁⠀⠀⠀⠛⠚⠳
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⢷⣀⡀⣀⡴⣤⣀⣀⡴⠛⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠛⠦⠤⠞⠶⣤⡤⠞

⠀⠀⠀⠀⢀⣴⠾⣿⣲⣄⠀⠀⠀⢀⣴⠶⠶⢶⣤⡀⠀⠀⢀⣤⠶⠶⢦⣄⠀⠀⢀⡴⠒⠙⠑⢦⡀⠀⠀⣠⢴⣲⣶⢦⡀
⠀⠀⠀⢀⣿⣷⡫⠻⣿⣿⡆⠀⢰⣟⣵⢿⣻⣷⡜⣷⠀⢠⣿⢺⠵⡶⣕⣽⡆⠀⡞⢀⡴⣛⢲⡀⢳⠀⢰⣷⢏⣥⣌⢳⣷⡀
⠀⠀⠀⠘⠁⠛⠛⠛⠙⠛⠻⠀⠿⠿⠿⠏⠈⠿⠿⠿⠇⠸⠋⠟⠏⠹⠿⠸⠿⠀⠇⠸⠗⠿⠿⠇⠸⠀⠿⠿⠞⠶⠞⠞⠿⠇

⠀⠀⠀⠀⣠⢴⣲⡤⣀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⡠⢆⣂⠆⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣸⣵⡽⠒⢿⣞⡆⠀⠀⠀⣸⣿⣟⣿⣿⡀⠀⠀⡰⣰⣵⣲⣷⡜⡀⠀⠀⠀⠾⠟⠭⣭⣻⣆⠀⠀⣠⢠⣶⢤⣶⣦
⠀⠀⢠⣿⣿⡆⠀⣼⣿⣿⠀⠀⠀⣿⣿⡏⣿⣿⡇⠀⠀⠅⣿⡟⠀⣿⠁⣂⠀⠀⣺⣛⣳⡛⣏⣻⣛⡀⠀⢃⣯⠃⣄⣯⣿⡄
⠀⠀⠀⠉⢉⠁⠀⠀⠉⠀⠀⠀⢀⡉⡉⠀⠉⣉⢁⠀⠀⠃⠛⠃⠀⠛⠈⠐⠀⠀⠛⠙⠛⠃⠛⠛⠛⠀⠀⠀⠀⠘⠛⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠀⠀⠐⠂⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⣁⣠⠤⠶⠖⠒⠒⠒⠒⠲⠦⠤⢄⣈⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⣀⠤⠒⠉⣀⡠⠤⠒⠒⠒⠀⠀⠒⠒⠒⠤⢄⣀⠉⠒⢤⡀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡠⠊⢁⡠⠖⠉⣀⡠⠔⠒⠂⠈⠉⠉⠉⠒⠒⠤⢄⣀⠉⠲⢄⡈⠓⢄⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡰⠋⢀⠔⠉⡠⠖⠉⣀⠤⠖⠚⠋⢉⣉⣉⡉⠙⠓⠲⠤⣀⠙⠢⣄⠉⠢⡀⠑⢄⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠞⢀⡔⠁⡠⠊⢀⠴⠊⣁⠤⠒⠋⠉⢀⣀⣀⠀⠉⠑⠒⠤⡀⠑⠦⡀⠑⢄⠈⢢⡀⠳⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠏⢠⠎⢀⠞⢀⡔⠁⡠⠚⢁⡠⠖⠊⠉⠀⠀⠀⠀⠉⠑⠢⢄⠈⠓⢄⠈⢦⠀⠣⡀⠱⡄⠱⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠎⢀⡏⣀⣏⣀⠎⢀⠞⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠳⡀⠳⡀⠱⡀⠱⡀⢱⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⡘⢠⠞⠉⠀⠀⠈⠲⡎⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢱⡀⢱⠀⢱⠀⢇⠀⠇⠀⠇
⠀⠀⠀⠀⠀⠀⢀⡴⠂⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠘⠚⠓⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⢧⠀⠇⠀⡇⠘⡇⠸⠀⢸⠀⢻⠈⠒⠢⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠀⠀⠀⢸⠀⢸⠀⢁⠀⡇⠀⡄⢸⠀⢘⠀⠀⠀⠘⡄
⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⠀⡸⠀⡌⠀⡇⢀⠃⢸⠀⢸⠀⠀⠀⢀⠇
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢇⣠⣇⣠⣇⣰⣇⣸⣀⡼⣀⠞⠀⠀⠀⠈⠢⡀
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠈⠢⣀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⣀⡠⠢⣀⠀⠀⠀⢀⡠⠒⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠙⠂⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠈⠑⠒⠀⠒⠊⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠊⠀⠀⠈⠀⠐⠀⠓⠀⠀⠀⠒⠐⠀⠀⠀⠐⠀⠁⠘⠁⠂⠃⠊⠑⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠚⣉⣉⣉⣉⣉⡉⠉⠒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⣉⠤⢒⣊⠭⠭⠥⠤⠤⠤⠤⢍⣉⡙⠒⠦⢄⡈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡡⣒⠭⢒⡩⠥⣖⣒⣒⣈⣉⣑⣒⡒⠲⠤⣈⡙⠒⢤⡈⠑⠦⡀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⣠⢎⡴⡫⢊⢵⡪⢕⣪⠭⣕⣒⣒⣒⣒⣒⠦⠭⣉⡒⠦⣌⠓⢤⡈⠓⢄⠈⠢⡀⠈⢢⡀
⠀⠀⠀⠀⠀⡰⠡⠫⠊⣾⣗⣵⣮⣓⠯⠟⠒⠒⠒⠒⠒⠢⠭⣑⠢⢍⡓⢤⡙⢦⡈⠢⡀⠑⣄⠈⢦⠀⠑⠄
⠀⠀⠀⠀⡼⣱⡵⣴⣷⣽⣿⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣍⠢⡘⢦⠙⢆⠘⢆⠈⢆⠀⢣⠀⠘⡄
⠀⠀⠀⢰⢳⣻⣽⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⡄⢳⡈⢧⠈⣆⠈⣆⣀⣧⡀⢹⡀
⠀⠀⣀⠼⢮⡷⠟⠋⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⡤⠷⠬⣆⡼⠊⠁⠀⠀⠈⠙⢧
⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑
⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠣⠀⢀⣄⠀⠀⡀⠀⢀⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠚
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣈⣲⣤⣴⣋⣳⣤⣴⣊⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠒⠒⠒⠐⠂⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠈⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⡀⠔⠂⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠑⠢⢄⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⠈⠀⡀⠄⠂⠉⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠉⠐⠢⢀⠀⠈⠢⢀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢀⠔⠁⢀⠄⠊⠀⢀⠤⠒⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⡀⠀⠉⠢⡀⠀⠑⡀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠊⠀⡠⠁⠀⡠⠊⠀⢀⠠⠐⠂⠉⠈⠀⠈⠀⠉⠐⠂⠄⡀⠀⠑⢄⠀⠈⢢⠀⠈⢂⠀⠐⡄
⠀⠀⠀⠀⠀⠀⡌⠀⠠⠁⠀⡔⠀⢀⠎⠀⢀⠔⠁⠀⡀⠄⠒⠀⠀⠀⠀⠒⠠⢄⠀⠈⠲⡄⠀⠑⠄⠀⠱⡀⠀⢣⠀⠘⡀
⠀⠀⠀⠀⠀⠰⠀⢀⠃⠀⡘⠀⢀⠃⠀⡰⠁⠀⡔⠉⠀⢀⠠⠀⠀⠒⠀⠠⢀⠀⠉⠢⡀⠈⢢⠀⠈⠄⠀⠰⡀⠀⢂⠀⠠
⠀⠀⠀⠀⠀⠁⠀⡀⠀⢠⠀⢀⡆⠀⠐⠀⢀⠎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠑⡀⠀⢡⡀⠨⣄⠀⢁⠀⠈⠀⠀⡂
⠀⠀⠀⠀⢠⣀⠠⠅⡠⠊⠀⠈⠁⢢⠁⠀⡌⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⡔⠁⠀⠀⠀⠑⠌⡀⠀⠇⠀⠁
⠀⠀⠀⠀⠎⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠁⠈⠁⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢲⠀⠀⠀⠀⠀⠀⢸⠆⠠⡄
⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠒⠂⠀⢄⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡄⡄
⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢀⠂⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠀⠡⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠃
⠀⠀⠈⠢⠀⠀⠀⠼⠄⠀⠀⠀⠀⢠⡂⠀⠀⢀⠌⠀⠒⠀⠉⠀⠀⠀⠀⠁⠂⠀⠐⠀⠒⠒⠁⠠⢀⡀⠀⠀⣀⠠⠔⠁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠊⠀⠉⠉⠉⠉⠉⠘⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⢀⡠⠠⠄⠐⠒⠐⠒⠒⠂⠠⠤⢄⡀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡠⠔⠈⠀⠀⠀⠤⠠⠤⠤⠤⠤⠄⠄⢀⠀⠀⠀⠢⢄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠤⠄⣀⠀⠈⠁⠢⢀⠀⠀⠠⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⠔⠁⠀⠐⠁⠀⠀⠀⠀⢀⣀⠀⠤⠀⠠⠀⠀⣀⠈⠁⠂⢄⠀⠀⠢⡀⠈⠢⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠂⢀⠔⠀⡠⠊⢀⡠⠒⠉⠁⠀⠀⠀⠤⠄⢀⡀⠀⠈⠁⠠⢀⠈⠢⡀⠈⠢⠀⠑⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⠁⠠⠂⡠⠂⢀⠔⠁⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠑⢄⠈⠢⡀⠱⡀⠘⡄⠈⠄
⠀⠀⠀⠀⠀⢀⠄⠚⠒⠃⣠⠃⣰⠥⠴⢁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠱⡀⠱⡀⠰⡀⢱⠀⢠⡀
⠀⠀⡀⠀⠠⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢰⠄⠛⠒⠓⢄⡗⠁⠀⠉⠁⠀⠈⠂⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡠⠊
⠀⠈⠢⣀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⢀⡀⠴⠊⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⣁⡠⠤⠤⠤⠤⠤⠄⢀⡉⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡠⠔⠊⣁⠠⠄⠒⠒⠒⠒⠂⠀⠤⢀⡉⠒⠤⡈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢁⠔⠉⡠⠒⢉⠠⠐⠒⣀⣉⠉⣉⣁⡐⠒⠤⢈⠑⠢⡀⠐⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡔⢁⡴⢋⡠⠊⡡⠔⣊⠥⠤⠐⠒⠒⠠⠤⢉⡒⠤⡉⠢⡈⠐⠀⠑⡄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⢠⠊⡠⠊⡴⢋⠔⣉⠄⠒⠉⠉⠁⠉⠉⠑⠂⢌⡐⢌⠐⠈⠢⡈⠢⠈⢀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⢰⠁⡜⢠⠊⡔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠌⢂⠐⡀⠁⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠼⠤⢇⣘⡠⠧⠮⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡌⠄⠤⢀⡀⠤⠨⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣞⣛⣿⣿⣟⣓⡶⣤⣀
⠀⠀⠀⠀⠀⣠⡾⣫⢶⣫⡽⢶⣒⣒⣶⠯⣝⡳⣭⡳⣄
⠀⠀⠀⢀⡼⣫⢟⡵⣫⡵⠛⠉⠉⠉⠉⠛⠶⣝⢦⡻⣮⢷⡀
⠀⠀⠀⣼⣱⢯⣟⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⡞⣯⢷⡀
⠀⠀⢸⡧⢯⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣻⡼⠾⣇
⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠐⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦
⠀⠈⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣉⢉⠉⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⡾⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⡄⠉⢳⡽⣞⢷⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠤⠠⠄⠤⠠⠄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⡿⠿⠃⠀⠀⢻⣹⡎⣷⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣻⣘⣷⢹⡇⠀⠀⠀⠀⠀⠀⢢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠃⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢢⠀⠘⠀⠀⠏⢀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢁⠠⠀⠒⠈⠁⠁⠒⠠⢄⠘⠀⡄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢒⠃⠀⠈⠁⠒⠂⠐⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠚⠑⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠤⠚
⠀⠀⠀⠀⠀⣀⣉⡁⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣀⡀⠈⠃⡝⠢⠔⠃⠉
⠀⠀⠀⠀⠀⠀⠉⡠⠀⢃⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⡤⠒⠊⠑⠉⠐⡧⡀⠀⡴⠋⠀⠀⢀⣀⠤⠤⠤⢄⣀⠀⠀⠀⠑⢄
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠴⣡⢨⠟⠁⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠈⢢⢀⡀⣀
⠀⠀⠀⠀⠑⠢⠀⠔⠐⠋⢠⠏⠀⢀⠎⠀⢀⡤⠒⠉⠉⠉⠓⠢⡀⠀⠸⡄⠀⠀⠇⠀⠀⠉⠐⠊⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠇⠀⡠⠋⣠⠖⠒⠋⠐⠢⡀⠈⢆⠀⢹⡀⠀⠸⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠘⠀⢠⠃⢠⠃⠀⠀⠀⠀⠀⠘⡀⠘⠀⠀⡇⠀⠀⡇⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠤⠼⠄⠜⠀⠀⠀⠀⠀⠀⠀⢇⣠⢇⣀⢇⣀⡰⠃⠐⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⢀⣀⡀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⡠⠔⠊⠉⠀⠀⠀⠉⠉⠒⢄⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡜⠀⠀⢀⡠⠔⠂⠉⠉⠉⠒⠢⡀⠀⠀⠈⢆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡜⠀⠀⡠⠋⠀⠀⣀⠀⢀⣀⠀⠀⠈⢢⠀⠀⠈⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢰⠀⠀⡰⠁⠀⡰⠋⠀⠀⠀⠀⠙⢢⡀⠀⢣⠀⠀⠰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⡄⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢰⠀⠀⢃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠤⠺⠤⣸⠀⣀⠼⠤⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡅⠀⣸⡀⠀⡇
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠋⠀⠀⠀⠈⠳⠤⠤⣀⠀⠀⠀⠀⠀⣠⠴⠃⠠⢧⠎⠁⠈⠳⠗⠊⢁⠉⠲⡀
⠀⠀⢀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⢀⡇
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⠜⠀⠀⠀⠀⡱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠄
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠈⠉⠉⠙⡄⠀⠀⠀⠀⣰⢆⡀⠀⠀⢀⠜⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣸⠗⠂⠐⠊
⠀⠀⠀⠀⠀⠀⠀⢸⠒⠤⠤⡞⠁⠀⠉⡏⠉⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠋⠈⠓⢤⠤⠚⠁⡇
⠀⠀⠀⠀⠀⠀⣠⠘⢤⠀⠀⡇⠀⡠⠴⠇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢢⠀⠀⢸⠀⢀⠔⠲⡄
⠀⠀⠀⠀⠀⠀⠣⣀⠴⠀⠀⡇⠀⠱⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠇⠀⢸⠀⠘⠤⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⣄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⢀⠖⠚⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠐⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠐⠠⢀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠔⢁⠠⠂⠁⠀⠀⠂⠉⠀⠀⠠⠄⠀⠀⠈⠁⠐⠠⠀⠀⠂⢄⠀⠢⡈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⠔⢀⠀⠀⡀⠀⠀⡀⠄⠀⠂⠀⠀⠀⠒⠀⠄⢀⠀⠀⢈⠐⢄⠀⠠⡈⠂⡀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠀⠔⠀⠀⢀⠀⠀⡁⠀⠀⠀⣀⣉⣈⣁⡀⠀⠀⠀⠈⠀⢄⠑⠀⠀⢄⠀⢄⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌⠀⠀⠠⠀⡠⠀⠔⢁⠔⠈⣠⠔⠊⠉⠀⠀⠀⠀⠀⠉⠒⠦⣀⠁⠀⠑⢄⠐⠀⠁⠀⠡⠀⢂⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠠⠁⠄⠠⠂⡐⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠑⠄⠁⠀⠂⠐⡀⠀⠀⢂⠘⡄
⠀⠀⠀⠀⠀⠀⢀⡃⢀⣠⣼⣴⢄⡐⠀⠁⡐⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠰⠀⠄⢰⣄⣦⣤⡀⢱
⠀⠀⠀⠀⠀⢀⣨⠟⠛⠋⠀⠀⠈⠣⡄⢠⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⡀⡀⠰⠊⠁⠀⠈⠛⠛⢷⣀
⠀⠀⣠⠶⠾⠋⠉⠓⠀⠀⠀⢀⡠⠠⣾⠛⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠼⠛⠻⠧⢀⣀⠀⠀⠀⠐⠋⠉⠻⠶⢦⡄
⠀⢐⠁⠀⠀⠀⠀⠄⠠⢐⡤⡾⠛⠓⢂⠡⡀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⡠⠁⠚⠉⠻⠶⣤⠠⠀⠄⠀⠀⠀⠀⠙
⠀⠀⢂⡔⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⣼⡇⠀⠀⠈⠀⠐⣄⠂
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⢈⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⡀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠈⣷⣄⣀⣀⣀⠀⣈⠟⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢍⡀⢀⣀⣀⣀⣴⡏
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉






⣿⢿⠿⡿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⠀⠀⡀⠖⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠡⠈⢁⠀⠀⡈⠀⡀⠀⠠⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠐⠀⠠⠦⠀⠀⠒⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠉⠀⠀⠐⠀⠀⠀⡠⠤⠀⠀⠀⠀⢣
⣶⡶⠶⠶⠶⢶⢶⣾⢷⣾⣶⣶⣶⣶⣿⣶⣾⣶⣿⣾⣿⣶⣶⣶⣿⣶⣾⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣀⣠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠘⣆⠀⠀⢀⣠⣤⣷⣤⣄⡀⠀⢹⣧
⠀⠀⠀⠀⠀⢰⣿⣠⡾⠟⠛⠛⠿⣶⣄⣤⣤⣼⣧⣤⣀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢸⣤⣾⠟⠉⠁⠀⠈⠙⠻⣦⡘⣿
⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠈⠛⠉⠁⠰⠶⢭⣙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣠⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣤⡀
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠙⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣭⣋⣠⣤⣶⣧⡀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠻⠷⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⠿⢿⣿⣿⣶⣤⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠉⢠⣤⠀⠀⠀⢰⣿⠄⠀⠀⢀⣤⡀⠈⠙⠻⣿⣿⣷⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣠⣾⣿⡿⠋⢁⡀⠀⠀⠈⠋⠀⠀⢀⣀⣀⣀⠀⠀⠈⠛⠁⠀⠀⣀⠈⠙⣿⣿⣧⡀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠻⠟⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠘⠿⠃⠀⠈⠻⣿⣿⣄⠀⠈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⢠⣿⣿⡟⢁⣤⡀⠀⠀⣠⠞⠉⠀⣀⣤⣶⣶⣿⣿⣶⣶⣦⣄⡀⠈⠳⣦⡀⠀⠀⣤⡄⠹⣿⣿⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⡏⠀⠀⠛⠁⢠⡞⠁⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⢿⣦⡀⠈⠳⣄⠀⠛⠁⠀⠸⣿⣿⡄⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⣤⡄⠀⣠⠏⠀⢠⣾⡟⠁⠀⣀⣤⠶⠞⠳⠶⢦⣄⠀⠀⠙⣿⣆⠀⠹⣆⠀⣠⣤⠀⢹⣿⣿⡀⠀⢀⡀
⠀⠀⠀⠻⠀⠀⢸⣿⣿⠁⠀⠙⠁⢠⡏⠀⢠⣿⠏⠀⢀⡼⠋⠀⠀⠀⢀⡀⠀⠙⢷⡄⠀⠘⣿⣇⠀⢹⡄⠘⠋⠀⠈⣿⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣀⠀⠀⣾⠀⠀⣿⡏⠀⠀⣾⠁⠀⠀⢺⣷⣿⡗⠀⠀⠀⢻⡄⠀⢸⣿⡀⠀⢷⠀⢀⣀⠀⢹⣿⣿
⠀⠀⠰⠖⠀⢀⣿⣿⡇⠘⠛⠃⢠⡇⠀⢸⣿⠁⠀⢸⡇⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⡄⠘⠟⠀⢸⣿⣿⡀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠁⠀⠘⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠃⠀⠈⠁⠀⠀⠀⠀⠛⠛






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠉⠐⢄⡀⠀⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⡘⠀⢀⣀⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⣀⣀⠘
⠀⠀⠀⠀⣀⡷⠛⠋⠉⠙⢠⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⡠⠊⠉⠙⠛⢷⣀
⠀⡰⠖⠛⠉⠉⠀⠀⢀⣄⡐⠋⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢂⣤⡀⠀⠀⠉⠉⠛⠲⢆
⠀⠁⠀⠀⠀⠀⢠⡞⠉⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠉⣳⠄⠀⠂⠀⠀⠈
⠀⠀⢳⡄⠀⠀⠀⢻⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⣠⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠷⣤⣤⣤⣤⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠋⠳⣤⣤⣤⣤⠾




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

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠉⠐⠢⢄⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠑⢄⠀⠀⢸
⠀⠀⣰⣿⣿⣿⡿⠟⠛⠛⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡔⠉⠀⠀⠀⠀⠑⢄⠀⠀⠈⠆⠀⢸
⠀⠰⠟⠛⢿⡏⠀⠀⠀⠀⠀⠀⠈⠿⠛⠛⠛⠂⢄⠀⠀⠀⡠⠥⠒⠢⣜⠀⠀⠀⠀⠀⠀⢀⠄⠖⠒⠖⠚⠢⣸
⢎⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡸⠀⠀⠰⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠸⠀⠀⢸⠀⢀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠂⢀⡠⠅⠰⠒⠀⠐⠆⠤⣈⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠓⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠈⠁⣀⡔⠊⠑⠢⠤⣀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢆⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡁⠀⠀⠏⠙⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⢱⠒⡛⠤⣀⠴⠒⠚
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠒⠒⠾⢄⡉
⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⡀⣈⢆⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⠀⠀⢫⠳⡀⢀⡜⠁⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⢊⡄⣨⠟⠁⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠈⢣⠀⡀⠄⣀
⠀⠀⠀⠀⠈⠒⠲⣀⢀⡤⠤⠊⠉⣰⡏⠀⠀⡰⠋⠀⠀⣀⠴⠒⠋⠉⠙⠒⠦⣄⠀⠀⠈⢆⠀⠀⠀⢏⠀⠀⠈⠓⠒⠖⠂⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡸⠁⠀⢀⠞⠁⣀⡠⢤⠤⠤⢄⠀⠈⠳⡀⠀⠹⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠁⠀⢠⠃⠀⡶⠋⠀⠀⠀⠀⠀⠑⡄⠀⠱⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠌⠀⠀⡌⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠠⠀⠀⡀⣀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠚⠢⠴⠣⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠧⣀⡰⢇⣀⡠⠛⠒⠊⠁





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

⠀⠀⠀⠀⡶⢀⣠⡀
⠀⠀⠀⠈⢷⣘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣤⠀⢀⡄
⠀⠀⢠⣤⣄⣿⣿⣯⣤⣀⢠⣠⣤⣀⡀⠀⢠⡏⣴⣦⠀⠀⠀⢀⣀⠀⡼⠀⠀⠀⣴⣦⠀⡿⠀⠈⣧⢰⣶⡆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⠡⣦⢹⡇⠀⠀⣷⣽⣭⣀⠀⠀⣿⣿⣾⡁⠀⣄⣀⣉⣭⣾⡁⠀⠀⠈⠳⣽⣶⣶⣆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⡷⠶⣾⡇⠀⠀⢿⣿⣇⡽⠂⠐⠟⢻⣿⣿⣄⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⢸⣿⡿⠃
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣇⣋⣼⡇⠀⢀⣼⠟⣿⡀⠀⠀⠀⠸⣿⣿⡿⠂⠀⠀⢿⡿⣿⠃⠀⠀⢠⡿⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣇⠀⠈⢿⣄⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⡇⠸⣧⠀⢠⡿⠁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣀⣀⣀⣹⣃⣀⣀⣘⣛⣃⣀⣀⣀⣘⣇⣀⣹⣀⣙⣁⣀⣀⣛⣀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⣴⣶⣆⣀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⡛⢛⣁
⠀⠀⠀⠀⣀⣙⣛⣩⡽⠇⠀⠀⣀⣛⣟⣁⠀⠀⡀⣸⢀⣼⣿⣧⣸⣿⡇
⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⡁⣿⠀⠈⢹⣿⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠘⠿⠿⠿⢻⣿⣿⣿⡻⠿⠿⠿⣿⣿⣿⣿⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠃⠀⠀⠀⠀⠀⣨⡿⠟⠦⠀⣀⣀
⠀⠀⠀⢠⣿⠿⡿⢿⣷⠀⠀⢰⣿⠿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⠀⣾⣿⣿⡇
⠀⠀⠀⢸⣿⠀⡇⢸⣿⠀⠀⢼⡏⠀⡇⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⣩⣿⣿⣮⡛⠛⠁
⠀⠀⠀⠀⠁⣀⣇⣀⠁⠀⠀⠈⢁⣀⣇⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣯⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠛⠛⣉⣉⣉⣉⣉⣉⡙⠛⠻⠿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡉⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⣡⣴⣿⣿⠿⠛⢉⣁⣤⣤⣤⣤⣤⣤⣄⣉⠙⠻⢿⣿⣷⣤⡉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⢠⣾⣿⡿⠋⣡⣴⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣤⡈⠻⣿⣿⣦⡈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⣴⣿⡿⠋⣠⣾⣿⣿⠟⢋⣁⣤⣴⣶⣶⣶⣤⣄⣉⠛⠿⣿⣿⣦⡈⠻⣿⣷⡄⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⣼⣿⡿⢁⣼⣿⣿⠋⣠⣶⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣷⣦⡈⠻⣿⣿⣆⠙⣿⣿⡄⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⢸⣿⡿⠁⣾⣿⡿⢁⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠙⣿⣿⡆⠸⣿⣿⡀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠁⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⢸⣿⣿⡀⢿⣿⡇⠸⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠐⠟⠛⢀⡉⠛⠃⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠛⢉⡁⠘⠻⠿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠃⣤⣾⣿⣿⣿⣿⣷⣄⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⣶⣿⣿⣿⣿⣷⣤⡀⠛⠛
⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣷⡄⠀⠀⠀⠀⠀⣠⣲⠯⠭⣖⣦⠀⠀⠀⠀⢀⣤⣶⣾⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣏⣀⠀⣈⣿⣿⣀⠀⠀⠀⠘⡟⠣⠀⠀⠀⠍⠁⠀⠀⠀⣿⣿⠟⠉⠙⢿⣿⡇
⠀⠀⠐⢄⣄⠀⠀⢀⣄⠜⠀⠀⠘⠛⠛⠛⠛⠀⠛⠛⠛⠛⠁⠀⠀⠀⠁⠀⠈


⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠁⠢⡀⠀⠀⠀⠀⢀⣴⣶⣿⣶⡶⣄⡀
⠀⠀⢀⣤⣾⠟⠛⠛⢿⣦⣄⠀⠀⠀⡂⡐⠁⠀⠈⠂⠀⠀⠀⠀⣰⣻⣫⠗⠛⠳⣿⣿⣿⡆
⠀⠺⠿⠿⠿⠂⠀⠀⠈⠉⠉⠁⠀⠀⢱⡔⠊⠀⠱⣦⠂⠀⠀⢰⣿⣿⣿⣶⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠐⠐⠁⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⡠⠐⡀⠀⡐⠠⡀⠀⠀⠀⠀⢀⡤⢖⣒⡶⢤⡀⠀⠀⠀⠀⢀⡠⠖⣒⡲⢤⡀⠀⠀⠀⠀⢀⡤⣖⣒⣒⠢⣄
⠀⠀⡌⠠⠁⠀⠒⠠⠱⠈⡄⠀⠀⢰⢫⡾⠛⠉⠛⣷⡽⡄⠀⠀⢠⢋⣾⠟⠛⠻⣷⡜⡆⠀⠀⢠⢏⣾⠟⠛⠛⣿⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁⠁⠀⠀⠈⠈⠁⠀⠀⠀⠈⠁⠈⠀⠀⠈⠈⠋⠀⠀⠀⠈⠋⠈


⠀⠀⠀⣴⣛⣛⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⣿⣶⣄
⠀⠀⠸⠟⠉⠻⣷⡜⣷⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢻⣦⢻⣿⣦⡀⠀⠀⠀⢰⡿⢫⣴⣶⣶⣬⠻⣧
⠀⠀⠀⠀⠀⠀⠸⠗⠈⠃⠀⠀⠀⣼⣿⡿⠉⠉⠙⣿⣿⡇⠀⠀⠀⠀⠀⣿⡆⢿⣿⣿⡀⠀⠀⢸⡇⣿⡿⠛⠻⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠁⠀⠀⠀⠳⠻⠇⠀⠀⠿⠱⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠐⠒⠒⠢⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⢀⡀⠤⠐⠒⠒⠒⠒⠒⠂⠒⠒⠂⠤⢄⣀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠊⠀⠀⠀⠀⢀⡠⠤⠒⠂⠈⠉⠉⠉⠉⠉⠀⠀⠐⠒⠠⠄⡀⠀⠀⠈⠓⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⠔⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠈⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠠⠃⠀⠀⢀⠎⠀⠀⠀⢀⠔⠊⠀⠀⠀⢀⡀⠤⠄⠀⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠑⠢⣀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠁⠀⠀⡐⠁⠀⠀⠀⠘⠁⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢄⡀⠀⠀⠀⠀⣱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⡔⠀⠀⠀⠐⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡤⠖⠁
⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠇⠀⠀⠀⠀⠀⣤⣀⣄⣀⡀⠀⠀⡔⠁
⠀⠀⡴⠋⠀⠀⠀⠀⠈⠙⠢⣀⠔⠂⠁⠀⠀⠀⠀⠀⠈⢓⣬⠀⠄⣀⡀
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡗⠀⠀⠀⠈⠳⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠡⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⠁
⠀⠀⠈⡾⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠢⢀⡀⠀⢀⣂⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⡠⠤⠚⠀⠙⠢⢤⣀⡀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣰⠾⢙⣹⣍⡋⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢰⡯⣵⡟⠉⠙⢿⣮⢽⡆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠉⠙⢿⣿⣷
⠀⠀⠀⠀⣼⠥⣿⠃⠀⠀⢘⣿⢽⡇⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣥⠀⠀⠀⠀⣿⣿⣿⣿⣦⣤⠀⠀⠀⢠⣾⣿⣿⣿⡆⠀⣶⣿⣿⣿⣿⡄
⠀⠀⠐⢿⣿⣿⣿⠿⠇⠸⢿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠁⠈⠁⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠂⢀⡀
⠀⠀⠀⢁⡈⠉⠁⠘⠀⠀⠐⠊⡉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣤⡀
⠀⠀⠀⢀⣴⣿⣿⡿⠿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠿⢿⣿⣿⣆
⠀⠀⣤⣾⣿⣿⡋⠀⠀⠀⠈⣯⣿⣿⣤⡀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣧⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣏⠀⠀⠀⢠⣽⣿⣿⣦⡄
⠀⠘⠻⠟⠟⠻⠃⠀⠀⠀⠀⠻⢿⢿⠿⠿⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⡿⠟⠀⠀⠀⠹⠿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠉⣂⣐⣀⣊⢉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣿⣿⣿⣟⢷⣦
⠀⠀⠀⠀⣰⣿⣿⠋⠉⠈⣉⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢠⠓⢢⣾⡿⠛⠛⣿⣷⠐⢱⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠝⠁⠀⠀⠙⣹⣿⣧
⠀⠀⣠⣦⣿⣿⣧⡄⠀⠀⠛⠿⣿⡿⠿⠗⠀⠀⠀⠀⠀⢸⣉⣺⣟⣀⡀⠀⢸⣿⣊⣹⣀⠀⠀⠀⠀⢀⢀⣸⣻⣉⠀⠀⠀⠀⠀⢠⣿⣿⠲⡂
⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⢀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠸⢿⣿⣿⠛⠿⠿⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⢴⣾⣿⣿⣿⡧⠀⠀⠀⢿⣿⣿⣿⣷⡦
⠀⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢊⣉⣉⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢈⠤⠀⠀⠌⠐⠄⠱
⠀⠀⠀⠀⢀⡤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠔⠀⠀⠢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣮⡉⠛⠉⠄⠂
⠀⠀⢀⡴⢋⡴⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡾⣬⠄
⠀⠀⡞⢠⠏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋
⠀⠀⠃⠛⠘⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢐⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⡀⠀⠀⠀⠀⢀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢸
⠀⣰⣿⣿⣷⣶⣦⠀⠀⠀⠘
⠚⠛⠛⠛⠛⠛⠛⠃⣠⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⠿⠿⠟



⠀⠀⠀⠀⡠⠄⠒⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣒⣒⣲⡦⣄
⠀⠀⡐⠁⠠⠔⠈⡉⠉⣑⡢⣝⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⢞⢽⣚⣷⣒⢭⡲⡵⣄
⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠙⢮⣾⡆⠀⠀⠀⠀⠀⠀⣀⡛⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⣳⣳⣫⠞⠛⠲⡵⡽⡽⣼
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠸⠿⡿⠷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠻⠛⠉⠃⠀⠀⠀⠛⠁⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠈⠈⠸⡇⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠸⡄⠀⠀⢼⡀⠀⠀⢿⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⢼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⢀⣠⣶⡿⠟⠋⢉⣉⣀⣀⡈⠉⠙⠛⠶⣄⠀⠀⠐⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⢀⣴⣿⠟⢁⣤⠶⠛⠋⠉⣉⠉⠉⠙⠒⢦⣀⠈⠙⢦⡀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢀⣾⠟⢁⣴⠟⢁⣴⣶⠿⠛⠛⠛⠛⠶⣤⡀⠈⠳⡄⠈⢳⡄⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢀⣾⠏⢠⡿⠁⣴⡿⠋⣠⣴⠶⠒⠒⠦⣄⠀⠙⢦⡀⠘⣆⠀⢻⡄⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣾⠁⣸⡟⠁⣾⠋⣠⣴⡶⢦⣄⠀⠱⡄⠈⣷⠀⢸⡄⠈⣷
⠀⠀⠀⢴⡄⠀⠀⠀⠀⣤⣤⣤⡀⢸⡇⠀⡏⠀⣿⠃⢸⡇⠀⣿⠃⠀⠀⢸⡆⠀⣷⠀⢹⡇⠀⡇⠀⣿⠀⢤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⠀⢻⡄⠈⣇⠀⠹⣤⣠⣤⣿⠇⢠⡟⢀⣿⠇⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠈⣷⠀⠸⡄⠈⢷⡀⠈⠢⣄⡀⠉⢉⣠⣴⠟⢀⣾⡟⢀⣾⠁⣸⡿⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⣄⠀⠙⢦⣀⡀⠉⠉⠉⢉⣠⣴⡿⠋⣠⡾⠃⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠟⠂⠈⢳⡀⠈⠳⢤⡀⠈⠙⠛⠻⠿⠛⠛⢉⣠⡆⠋⣀⣌⡝⠁⠉⠒⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠲⣄⡀⠉⠛⠒⠶⠶⠶⠶⠛⠋⣉⣤⣶⠿⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⣠⡈⠙⠛⠶⢶⣤⣤⣤⣶⡶⠿⠟⠋⢥⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢠⡀⠀⠀⢤⠀⠀⠀⣄⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⣯⣿⣿⣿⣿⣿⣷⢦⣀
⠀⠀⠀⠀⠀⠀⡴⣫⣾⣽⣻⠿⠟⠛⠿⢽⡺⣝⢯⣧⡀
⠀⠀⠀⠀⠀⣼⡽⣵⣻⠋⠀⠀⠀⠀⠀⠀⠙⢮⣷⣳⣳⡀
⠀⠀⠀⠀⢰⠿⠷⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠆⠈⢿⢿⢳⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡟⡏⣧⢷⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣟⣻⢸⡇⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠤⠒⠂⠀⠈⣉⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠐⠀⡠⠔⠀⠀⠁⠀⠐⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢁⠔⢉⡠⠔⠊⣉⡀⠀⠠⠀⠀⠀⠀⠀⢄⡈⠢⡀⠑⢄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡔⢁⠔⠉⡠⠂⢁⠠⠠⠀⠀⠀⠠⠀⡈⠐⢤⡈⠢⡀⠢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠎⢠⠋⡠⠊⡠⠊⢁⠄⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠼⠀⠇⠐⠁⡜⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⡀⠤⠤⡌⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⡠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠉
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣂⣀⣐⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣂⣀⣐⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣰⣿⣦
⠀⠀⠀⠀⠀⠀⣰⠆⣻⣾⠞⠀⠀⠀⠘⡛⠃⢰⡄⠀⠀⠀⠀⠀⣾⣿⣻⡇⠀⢸⡇⠀⠀⢸⣷⣿⡷
⠀⠀⠀⠀⢰⠟⢁⡠⠜⡃⠀⠀⠀⠀⣀⣤⠠⠌⣷⣄⣀⣴⠀⠀⠙⠷⣟⣷⣶⣿⠁⠀⠀⠀⠀⢐⣷⣾⣗⣦⣄
⠀⠀⠀⠀⠀⠀⣡⣶⡾⠁⠀⠀⠀⠀⠙⢿⣷⣃⣀⣀⣉⣭⠀⠀⠀⢠⣿⣿⣿⠇⢀⢀⠀⠀⠀⢰⣻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣼⣿⣿⡷⠦⡤⠄⠀⠀⠀⠀⠉⠙⠋⠉⠁⠉⠀⠀⠀⠾⠿⣿⠏⠀⠙⠛⠲⠶⠶⠿⠃⠘⣽⣯⣿
⠀⠀⠀⠀⢧⠙⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣿⡄
⠀⠀⠀⠀⠨⣷⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠉⣽⣿⡟
⠀⠀⠀⠀⠀⢹⡇⠘⣿⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⣿⣷⡀⠀⢿⣿⣷⣤⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⣧⠀⡿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠳⣄⠀⠀⠀⠀⠘⣿⣿⡄⠀⠉⠛⠛⠻⠿⠟⢻
⠀⠀⢀⣤⠤⢤⣤⣠⣇⣤⠤⠤⠤⠀⠬⣽⡷⠦⢀⣤⠤⢤⣤⡀⢀⣼⡥⢤⣝⡇⠀⠀⢠⣖⠛⠛⣤⠀⣤⡀⢤⣤⠤⣤⣉⠀⣤⡤⠤⠤
⢀⣰⠞⠳⣶⡞⠉⣰⡟⠓⠒⠒⠀⠀⣰⡟⠀⠀⣼⡟⠲⢶⣟⠁⢿⣇⡀⠀⣸⡿⠀⠀⠀⠙⢷⣤⣿⠀⠘⣷⡌⢻⣖⠒⠛⣦⣌⠻⣶⡒⠒

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣴⡿⣫⠽⣾⣽⣆⠀⠀⠀⣰⡾⢛⣉⣉⡛⢷⡄⠀⠀⢀⡴⣛⠭⠭⣙⢷⡄⠀⠀⣰⠋⠀⣀⡀⠈⢳⡀⠀⠀⣴⣫⡽⠿⢯⡳⣄
⠀⠀⠀⠀⣸⢹⡟⣕⣉⢪⣿⣿⡆⠀⣼⣟⣾⣟⡭⣝⣿⣎⣿⡄⠀⣾⡕⣵⣛⣛⣮⢣⣿⡀⢰⠇⢠⡞⣩⡙⣧⠀⣧⠀⣸⣳⡏⡬⠶⣄⢿⣽⡄
⠀⠀⠀⠀⠛⠂⠛⠋⠛⠙⠛⠛⠃⠀⠿⠻⠿⠟⠀⠘⠿⠿⠻⠇⠸⠟⠺⠳⠇⠸⠿⠇⠿⠇⠘⠇⠘⠇⠿⠇⠿⠀⠞⠀⠿⠿⠸⠱⠿⠸⠘⠟⠇

⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠠⠄⡄
⠀⠀⠀⠀⡼⡵⣚⣿⡓⣝⣦⠀⠀⠀⠀⢠⣾⣻⢿⣮⣆⠀⠀⠀⢀⡘⡰⣪⣭⣢⡱⠄⠀⠀⠀⠀⣠⡾⢛⡛⠷⣦
⠀⠀⠀⢸⣿⣷⡁⠀⢘⣿⣼⡄⠀⠀⠀⣾⣿⣱⢲⣿⣿⡆⠀⠀⠰⢸⣿⡗⠱⣿⢣⢃⠀⠀⠀⣼⣯⣞⣩⣍⢳⣹⣇
⠀⠀⠀⠻⣿⣿⠇⠀⠻⠿⠿⠇⠀⠀⠐⠿⠿⡟⠸⠿⢿⠇⠀⠀⡁⢺⣿⠁⠈⣿⠘⢰⠀⠀⠀⣿⢹⣾⡏⢹⡎⡟⣿⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠠⠄⠀⢠⣤⠰⠀⠀⠁⠈⠉⠀⠀⠉⠀⠈⠀⠀⠀⠉⠈⠉⠁⠈⠉⠁⠉⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣴⡿⣫⠽⣾⣽⣆⠀⠀⠀⣰⡾⢛⣉⣉⡛⢷⡄⠀⠀⢀⡴⣛⠭⠭⣙⢷⡄⠀⠀⣰⠋⠀⣀⡀⠈⢳⡀⠀⠀⣴⣫⡽⠿⢯⡳⣄
⠀⠀⠀⠀⣸⢹⡟⣕⣉⢪⣿⣿⡆⠀⣼⣟⣾⣟⡭⣝⣿⣎⣿⡄⠀⣾⡕⣵⣛⣛⣮⢣⣿⡀⢰⠇⢠⡞⣩⡙⣧⠀⣧⠀⣸⣳⡏⡬⠶⣄⢿⣽⡄
⠀⠀⠀⠀⠛⠂⠛⠋⠛⠙⠛⠛⠃⠀⠿⠻⠿⠟⠀⠘⠿⠿⠻⠇⠸⠟⠺⠳⠇⠸⠿⠇⠿⠇⠘⠇⠘⠇⠿⠇⠿⠀⠞⠀⠿⠿⠸⠱⠿⠸⠘⠟⠇

⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠠⠄⡄
⠀⠀⠀⠀⡼⡵⣚⣿⡓⣝⣦⠀⠀⠀⠀⢠⣾⣻⢿⣮⣆⠀⠀⠀⢀⡘⡰⣪⣭⣢⡱⠄⠀⠀⠀⠀⣠⡾⢛⡛⠷⣦
⠀⠀⠀⢸⣿⣷⡁⠀⢘⣿⣼⡄⠀⠀⠀⣾⣿⣱⢲⣿⣿⡆⠀⠀⠰⢸⣿⡗⠱⣿⢣⢃⠀⠀⠀⣼⣯⣞⣩⣍⢳⣹⣇
⠀⠀⠀⠻⣿⣿⠇⠀⠻⠿⠿⠇⠀⠀⠐⠿⠿⡟⠸⠿⢿⠇⠀⠀⡁⢺⣿⠁⠈⣿⠘⢰⠀⠀⠀⣿⢹⣾⡏⢹⡎⡟⣿⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠠⠄⠀⢠⣤⠰⠀⠀⠁⠈⠉⠀⠀⠉⠀⠈⠀⠀⠀⠉⠈⠉⠁⠈⠉⠁⠉⠀⠀⠀⠀⠀⠉⠁

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛




⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⣧⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣤⡄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠘⢷⣼⣦⣾⣷⣠⣿⠀⢐⣷⣶⠀⠀⣿⠀⠀⢀⡀⢰⣾⣆⣴⣦⠀⡀⢀⠀⠀⠀⢰⣿⣧⢀⣀⣤⠄
⠀⠀⢀⣤⢴⣿⣿⣴⢿⣿⣿⣿⣿⣯⣶⣾⣿⣯⣶⣾⣻⣷⣶⣏⣿⢟⣾⣿⣿⣏⠀⣿⣿⣷⣆⢀⣠⣿⣿⠋⠁
⠀⠀⠀⠙⣿⣿⣿⣿⡾⢿⣿⣿⣿⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣾⣿⣿⣿⡇
⠀⠀⠀⠘⣿⣿⡿⣳⡇⣿⣿⣿⣿⠈⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⡝⢸⣿⣿⡟⢿⣿⡿⣹⣿⣿⡗⣿⣿⣿⣇
⠀⢀⣠⣤⣿⣿⣿⣿⣷⣿⣿⣿⣿⡎⣻⣿⣿⣿⣷⣿⢽⣿⣿⣿⢀⣼⣿⣿⣿⣹⣿⣱⣿⣿⣯⣷⣿⣿⣿⣧
⠀⢿⡟⠛⠿⣿⣿⡇⢸⣿⡿⢿⣿⡇⣿⣿⣿⣿⣿⢻⢻⣿⣿⣿⡈⢻⣿⣿⣾⡿⣯⡽⣿⣿⣿⣿⣿⡏⠻⣿⣧
⠀⠈⣧⠀⠀⣸⣿⠀⣾⣿⠃⢸⣿⣿⡿⣧⡿⢻⣿⠚⣿⣿⣿⡟⣷⠺⣿⣿⣿⣿⣿⢿⣿⠋⢉⣿⣿⡆⠀⢙⣿⡇
⠀⠀⣼⠃⠀⡏⢿⢂⢹⣿⠇⢸⣿⢻⣿⣿⠁⠈⣿⡇⢙⣻⣿⠁⡧⡐⢻⣿⡿⣿⣿⢿⡇⠀⣸⣿⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⢸⠃⢸⡏⢠⣿⢳⠘⢈⠋⣿⡺⡆⠀⢿⡟⠈⣿⡿⠀⠰⠀⠈⣿⡿⢻⣿⣿⡃⠀⣿⠇⠸⣿⠄⢸⣿⡁
⠀⠀⠀⠀⠁⠀⢸⠁⠻⡇⠈⠀⠈⠀⣽⠅⠈⠀⢨⡟⠈⢹⡇⠀⠀⠀⠘⢻⡁⠀⠀⣁⠏⠀⣭⠀⠀⠀⠁⢸⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠸⠃⠀⠘⠇⠀⠀⠀⠀⠻⠁⠀⠀⠈⠀⠀⠙⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠉⠁⢀⣀⣀⣀⣀⣀⣀⡀⠉⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⢁⣠⣤⡶⠾⠛⠛⠋⠉⠉⠉⠉⠛⠛⠻⠷⣶⣤⣀⠈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⣠⡶⠟⠋⢁⣠⣴⡶⠾⠟⠛⠛⠛⠛⠿⠶⢶⣤⣄⡈⠙⠿⣦⣄⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢀⣴⠟⠋⣀⣴⠾⠛⢉⣀⣤⣴⡶⠶⠶⠶⢶⣦⣤⣄⡈⠉⠻⢷⣤⡀⠙⢷⣄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣰⡿⠃⣠⡾⠛⢁⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⡀⠉⠻⣦⡀⠙⢷⡄⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⣼⠏⢀⣼⠟⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⢿⣆⠈⢻⣆⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⠏⢠⣿⠃⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠹⣧⠀⢻⣇⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⣸⡏⢀⣾⠃⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢹⣧⢀⣿⣦⣽⣧⣤⣀
⠀⠀⠀⠀⠀⠀⢠⣿⡶⠿⠿⠿⣿⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⡿⠛⠉⠁⠀⠈⠉⠙⢷⣦
⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣷⡶⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀
⠀⠀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣦
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠙⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠉⢀⣀⡀⠤⠤⠤⠤⠤⢀⣀⡀⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⣤⠠⠤⠤⣄⣀⣀⠈⠉⠲⢤⡀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⠠⡤⠄⣀⣀⠈⠉⠒⠤⣀⠈⠓⢄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡠⠊⠀⡠⠊⠁⣠⠔⠊⠉⠀⣀⣀⣀⣀⣀⠀⠉⠑⠢⣀⠈⠑⢄⠀⠑⣄⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⠁⣠⠎⠀⡠⠊⠀⡠⠔⠊⠉⢀⣀⣀⣀⠀⠉⠑⠢⣄⠈⠑⢄⠀⠱⡄⠈⢦⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⣜⡀⣰⠃⢀⠞⠀⡠⠊⠀⡠⠖⠋⠁⢀⣀⡀⠈⠙⠲⣄⠀⠑⣄⠈⠣⡀⠘⣄⠀⣧⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠚⠉⠉⠉⠉⠓⢮⡀⡼⠁⢠⠎⠀⡠⠚⠉⠁⠀⠈⠉⠲⢄⠀⠳⡀⠈⢆⠀⡱⠖⠋⠉⠉⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⢀⠇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠱⡀⣈⡞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠈⠣⣄⣀⡤⠤⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡴⢤⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠓⠲⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⣉⣤⣶⣾⠿⠿⠿⠿⠿⢿⣶⣶⣤⣉⠛⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢁⣴⣿⠟⣋⣥⣶⡶⠿⠿⠿⠷⣶⣦⣭⡙⠿⣷⣤⡙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢃⣴⡿⢋⣴⡾⢛⣭⣶⣶⠿⠿⠿⢿⣶⣮⣝⡻⣷⣌⠻⣿⣆⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢁⣾⡟⣡⣿⢋⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⢿⣮⡻⣷⡌⢿⣧⠘⣿⣿⣄
⠀⠀⠀⠀⠀⣰⠋⠉⠉⠑⢾⠿⣰⡿⢱⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡘⣿⣌⢿⣧⠊⠉⠉⠑⣆
⠀⠀⠀⠀⣠⡇⠀⠀⢀⠇⠀⠀⠈⢧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠹⠁⠀⠘⣅⠀⠀⠀⠸⣄
⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢧
⠀⠀⠀⢧⠀⠀⠉⠑⠦⠄⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠤⠊⠉⠁⠀⠀⡼
⠀⠀⠀⠀⠑⠲⠶⠶⠶⠶⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠶⠶⠶⠶⠶⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠄⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠈⠀⠁⠀⡀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠌⡐⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⡈⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠁⠀⡌⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠈⡄⠀⠡
⠀⠀⠀⡠⠄⠠⠚⠉⠀⠈⠁⠣⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠃⠉⠀⠈⠙⠢⠀⠤⡀
⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠂
⠀⠀⠀⠉⠂⠤⠄⠢⠄⣀⣀⠠⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢀⣀⡀⠤⠂⠤⠄⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⣠⠤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣀⠀⠀⠈⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡠⠞⠋⠀⠀⠀⣀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠒⠶⢤⣄⡀⠀⠈⠙⠶⣄⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⠴⠋⠀⠀⢀⡤⠖⠋⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠈⠛⢦⡀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢁⡴⠃⠀⠀⣠⠞⠉⠀⢀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣀⠀⠀⠙⠷⣄⠀⠀⠙⢷⣄⠀⠀⠻⣆
⠀⠀⠀⠀⠀⢠⠞⢀⠀⣰⠋⠀⠀⣠⠞⠁⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠈⢷⣄⠀⠀⠙⣦⡀⠀⠙⣧
⠀⠀⠀⠀⢠⡏⠀⢀⡼⠁⠀⢀⡼⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠙⢦⡀⠀⠈⢻⡄⠀⠘⣧
⠀⠀⠀⠀⡞⠀⢀⡞⠁⠀⢠⠞⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠻⣆⠀⠘⣧
⠀⠀⠀⣸⠁⢀⡾⠀⠀⣰⠋⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠹⣆⠀⠀⢹⡆⠀⠹⡆
⠀⠀⢀⡏⠀⣼⠁⠀⡴⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⣦⠀⠀⢻⡄⠀⢿⡀
⠀⠀⢸⠃⣰⣇⣀⣼⠁⢠⠏⢀⣤⠖⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣷⡀⠘⣧⢀⡬⠷⠒⠺⢧⣄
⠀⠀⣸⠋⠉⠀⠀⠉⠓⢯⡴⠏⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠳⢤⡼⠋⠀⠀⠚⠉⠀⠙⣆
⢠⡴⠟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠙⠲⠶⠞⢻⡄⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢰
⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣰⢦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣀⣀⣀⣴⣤⣀⡀⣀⣀⡴⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣷⣶⣶
⣿⣿⣇⣤⣍⣤⣮⣬⣧⣥⣾⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣻⣿⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⢻⣿⣾⣿⡿⡇⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣽⣿⣿⣻⡟⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⡿⠻⣿⣶⣾⣿⣿⣿⡿⠁⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣛⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠘⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣷⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣽⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠿⠿⠿⠿⢿⣿⣷⣦⣀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⣠⡤⠔⢶⡷⠢⢤⣤⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⣀⣤⠚⣙⣥⣶⣶⣶⣤⣈⠉⠙⢦⣈⠻⣿⣧⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⢀⠟⢋⣾⣿⣿⣿⠿⣿⣿⣿⣷⣄⠘⢻⡀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢴⡯⢀⣾⣿⣿⠏⠀⠀⠀⠙⣿⣿⣿⣆⢀⣧⡀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⡜⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠹⡄⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢺⡷⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⢰⣷⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⣿⡟⠀⣸⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⢷⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⡿⠂⣿⣿⣿⠃⠀⠀⠀⠀⣀⠀⠀⠸⣿⣿⣿⠀⣾⠆⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣇⠀⣿⣿⣿⠀⠀⣾⣿⣿⣿⡷⠀⠀⣿⣿⣿⠀⣸⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⡟⠀⣿⣿⣿⠀⠀⠸⣿⣿⣿⠃⠀⠀⣿⣿⣿⠀⢻⠃⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢀⣇⠀⣿⣿⣿⠀⠀⠀⠙⠿⠃⠀⠀⠀⣿⣿⣿⠀⣸⡀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠈⠋⠀⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠙⠁⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⢤⡄⢠⠀⢠⠄⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⡇⠈⡇⢸⠀⢸⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠀⡇⠀⢧⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⢧⣠⠇⠀⢸⠇⠀⢸⣀⡀

⠀⠀⠀⢀
⠀⠀⠀⡄⢀⡘⣄⠀⢹⡀⢀⣀⠀⣠⠃⠀⠀⠀⠸⡟⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢣
⠀⠀⠀⢷⣿⣷⡾⠀⠀⠳⣾⣯⡾⠁⠀⢀⠀⢰⣿⣿⣷⠀⠀⠀⠹⣦⣶⣦⠀⠀⠀⠀⠘⢷⣿⡶⠃
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⡆⠀⠀⠀⠙⠛⣿⣿⡟⢧⠀⠀⠀⣿⣿⠟⠲⠶⠄⠄⠀⠸⣿⡇
⠀⠀⠀⢈⣿⣯⠁⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠃⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⢰⣿⣇
⠀⠀⠀⢸⣿⣿⣧⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠈⠉⣿⣿⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⡟⠁
⠀⠀⠀⠀⢰⢣⡃⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠘⠁⡇
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣉⡇⣿⠷⠆⠂⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠠⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⡆⠾⣿⢸
⢙⡇⣿⣶⠄⠀⡈⠢⡈⢀⠀⠄⠁⠬⢀⣀⠤⢒⠈⠅⠀⢀⡀⠀⠉⠁⠀⢐⡀⠀⠌⢑⠂⢄⡀⠀⠀⢰⠀⠀⠀⠀⠀⢈⠆⡇⢴⣾⢀
⠉⠁⠉⠀⠀⠀⡈⢀⠔⠁⠀⠀⢀⠔⡊⠔⢈⠡⠐⢀⠉⠀⠀⠀⠀⠀⠀⠀⠠⢉⠀⠂⠌⡐⠌⡑⢄⡀⠁⢐⠀⠐⠂⡂⠀⡇⠀⠉
⠶⣦⣶⣄⡀⠀⠀⠂⠀⠀⢀⠔⡡⠊⠠⢊⠠⠐⡁⠄⢐⡀⠁⠠⠀⠠⠀⠉⣐⠀⠄⣁⠂⢌⠐⢌⠢⡉⢢⡈⠈⠂⠆⠁⠀⡇⣀⣴⣤
⣶⡟⣿⣋⠁⠀⡀⠀⠀⡔⠡⠊⡐⢁⠔⠁⠔⡁⠐⣈⠥⠐⠂⠁⠀⠀⠁⠒⠢⠍⡀⠠⡁⠢⡑⠠⡑⢌⠢⡑⠄⠃⠀⠆⠀⡇⢙⣿⢻
⡴⠇⡿⠛⠃⠀⠄⢡⠜⡐⢁⠊⡐⢁⠄⡠⢊⠔⠉⡄⠠⠀⢀⡀⠀⢀⠀⠄⠀⣜⢂⠑⢤⡑⠌⠢⡑⢄⠠⠑⡈⢆⠀⠀⠀⡏⠛⢿⠸
⠀⠀⠀⠀⠀⠀⠊⡌⠐⢀⠂⠌⠠⢁⠎⡔⠁⠀⠈⡔⡀⠀⠀⠀⠍⠀⠀⢀⠨⠁⠀⢂⠀⠙⢄⠢⠐⡈⢂⠡⠐⡈⠆⠀⠀⡇
⢉⡇⣿⡶⠄⠀⢰⠠⠁⠀⡘⠀⢁⠂⡌⠀⠀⠀⡐⠀⡠⠀⢀⠊⠀⠀⡠⡑⡠⠤⢄⠡⢂⠀⠈⢆⠡⠐⡀⡄⢃⢀⠘⡀⠀⡇⠶⣾
⠀⠀⠀⠀⠀⠀⡆⣰⠈⠁⠒⠉⠘⢼⡀⠀⠠⠡⢻⢹⢁⢡⠂⠀⠀⡐⠌⠀⠣⠤⠞⠀⠡⢂⠀⢈⠤⠏⠉⠉⠈⠈⠑⠦⡀⡇⠀⠈
⠶⡆⣦⣄⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢈⠀⠢⢆⠈⢉⠀⣃⣀⡀⢺⢊⠠⢄⠀⢰⠤⠄⡄⠛⠀⢅⠀⠀⠀⠀⠀⠀⠀⢀⠄⣇⣠⣴⢠
⢾⡇⣿⣉⠀⠀⠡⡀⡠⡀⠀⠠⣀⡠⠁⠀⠀⢸⠀⢨⠀⡇⠀⠁⢸⠨⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠠⠠⠤⣀⠠⠤⠄⠂⠀⡇⢉⣻⢘
⠴⠇⠿⠛⠁⠀⠀⠀⣀⠀⠀⠀⠠⠤⠀⠀⠐⠘⠤⠼⠀⠧⠤⠄⢸⢀⠀⠈⠀⠸⠀⠀⠇⡆⠀⡀⠤⠤⣀⠀⠀⢀⡀⠀⠀⡇⠙⠻⠈
⣀⡀⣀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠠⣀⠄⠀⠀⠁⠀⠀⠒⠂⠀⠀⠸⠸⠀⠀⠓⠒⠀⠀⠀⠁⢈⣈⠀⠀⣀⠀⠀⠀⠀⠈⠉⡇⠀⢀
⣩⣿⣿⡷⠆⠄⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠼⠁⠀⠀⠀⠀⠀⠇⠾⣿⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠟⠋⠉⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⠁⠀⢀⣠⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠁⠀⣀⣤⣾⣿⣿⠿⠛⠋⠁⠀⠀⢀⣀⣀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⢀⣤⣾⣿⡿⠟⠉⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠉⠀⢀⣠⣴⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⢀⣴⣿⡿⠋⠁⠀⣠⣴⣿⣿⠿⠋⠁⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⣴⣿⣿⠏⠀⠀⣠⣾⣿⡿⠋⠁⠀⣀⣤⣾⣿⣿⠿⠟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⡟⠁⠀⣠⣾⣿⡿⠋⠀⢀⣤⣾⣿⡿⠟⠉⠀⠀⢀⣀⣤⣤⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⢠⣿⣿⠏⠀⠀⣴⣿⡿⠋⠀⢀⣴⣿⣿⠟⠉⠀⢀⣠⣴⣾⣿⣿⠿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⣠⣿⣿⠋⠀⢀⣾⣿⡟⠁⠀⣠⣾⣿⠟⠁⠀⢀⣴⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⢀⣤⣿⣿⣿⣶⣶⣾⣿⡟⠀⠀⣴⣿⡿⠃⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣾⣿⠿⠛⠉⠉⠉⠉⠛⠿⣿⣷⣼⣿⡿⠁⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠁⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠁⠀⠈⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⢰⣿⣿⠃
⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣧⣿⣿⡏
⠀⠀⠀⢀⣼⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡅
⠀⠀⣴⣿⡿⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃
⠀⠀⠀⠙⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠉⠀⠀⠀⣾⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠐⠉⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⢰⡟⢀⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣥⡶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⣀⠀⠀⢁⣀⣀⣀
⠀⠀⠀⠀⣠⣴⢿⣧⣿⣿⣿⣿⠀⢀⣴⡀⠀⠀⠀⠈⢻⣿⠛⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠄⠋⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⢈⠁⠂⣿⣿⣿⣿⣅⠀⠀⠉⠀⠀⢀⡴⠱⣿⣿⣧⡀⣰⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⣼⣧⡀⠹⠟
⠀⠀⠀⠀⠙⠛⠛⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⢾⠙⠗⣉⠻⣿⣿⣿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⡿
⠘⠃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠓⣀⠉⠀⠛⠉⠁⠀⠀⠀⠀⣀⣀⣀⠢⡤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠛
⠘⠛⠂⠀⠀⣴⣿⡿⠃⣿⣿⣿⠁⠀⠀⠈⡘⠆⡈⠉⣡⡄⠀⠀⣄⠀⠀⠀⠀⠣⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡀⠛⣓
⠀⠈⠁⠀⠰⠿⢿⣿⣷⣿⣿⣧⣦⠀⠀⠘⠉⡀⠓⣠⡅⢡⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⢿⣿⣿⡿⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠸⠀⠀⠀⠀⣛⣠⡤⢀⣬⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⢸⣿⡆⠀⠶⠀⠀⢸⣿⠏⠀⣾⣿⠃
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠈⣿⡇⠀⠶⠦⠀⠘⣿⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠓⠀⠀⠻⠄⠀⣿⠀⠀⠀⠀⠀⠀⠰⣹⣅⠀⠈⠉⠉⠁⠀⠀⠀⠿⠀⠰
⢀⡤⠤⠀⠀⠀⠀⠀⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡲⠄⠀⠈⠁⠀⢀
⢸⡧⠄⣰⠊⢳⡀⡖⢠⣎⣱⠔⡆⢰⢢⣎⣱⠄⡖⠁⠀⠙⡞⢡⡞⠑⡆⣶⠀⣶⢰⡆⢳⡄⡖⠑⣶⠀⠀⡧⠴⠃⣈⢳⠀⡖⠁⣿⠁⢦⢠⠆
⠘⠃⠀⠘⠲⠚⠀⠃⠈⠳⠶⠀⠘⠃⠈⠳⠶⠀⠃⠀⠀⠀⠃⠈⠳⠖⠃⠘⠖⠛⠘⠃⠘⠃⠓⢖⡇⠀⠀⠃⠀⠀⠳⠚⠀⠃⠀⠙⠆⢈⡟

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⡆⠀⢀
⠀⠀⠘⠿⣶⣿⣇⣴⡂⣰⠛⠀⠁⠈⠑⢶⣤⠀⠀⠀⣨⣽⠆⡛⡵⠚⠛⠃
⠠⡶⠶⣤⣻⣿⢿⡿⢺⣇⣀⣠⠁⣤⣤⡼⣞⣷⡀⠖⠋⢡⢎⡇⠙⢿⡆
⠀⠀⢠⣤⡍⣾⢀⠻⣿⣿⠛⠁⠀⠈⠉⠀⠹⣿⡇⠀⠀⠉⠘⡇⠀⠀⠁
⠀⠀⡿⠃⠀⣼⡌⠧⠸⠛⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⣰⠂⠀⠰⡦⠐⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⣿⠀⠁⠀⠈⣸⠿⠀⠀⠀⠀⠈⠉⠓⢤⠀⢀⠀⣷⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⢀⣀⢀⠈
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠋⠀⠀⠀⠆⠀⠀⠀⠀⢸⠀⠀⢡⣿⣯⣾⣷⠀⠀⣠⡄⠀⠀⡠⠾⡦⠀⠈⠁
⠀⠀⠀⠀⠀⣿⠁⠀⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠖⠋⠀⠀⠀⠊⢠⣨⡇
⠀⠀⠀⠀⠀⠇⠀⠀⡷⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⢤⡄⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⡀⣸⢷⣦⣤⣤⡆
⢀⠀⠀⢰⠊⠀⠀⠠⠁⠈⠢⣀⣀⣴⣀⡠⠖⠛⠁⠀⠀⡀⠀⠀⠙⣄⣠⠗⠁⠀⢀⠀⣤⠈⣶⢶⢦⣬⠅⠀⢀
⣿⣟⣤⠆⠀⠀⠀⣼⣧⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠁⠀⠀⠀⣠⣫⠄⢹⣷⣯⢾⣸⣿⣷⣦⣼
⣿⣿⣿⡄⠀⠀⢀⣿⣿⣦⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⢀⣿⣷⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣠⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠉⠉⢉⣀⣀⣀⣀⣀⡉⠉⠉⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⢁⣠⣤⠶⠖⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⠶⣤⣄⡀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⣀⡴⠞⠋⠁⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠓⠶⢦⣤⣀⡈⠙⠳⢦⣄⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⠞⠉⢀⣤⠶⠛⠉⣀⣠⣤⠴⠶⠶⠶⠛⠶⠶⠶⠶⣤⣄⣀⠉⠙⠳⣦⣀⠈⠻⢦⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣴⠟⠁⣠⡾⠋⢀⣠⡶⠛⠉⢁⣀⣤⣤⠴⠶⠶⠶⠦⣤⣤⣀⡈⠉⠛⠶⣤⡀⠙⠳⣄⡀⠙⢦⡀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⣠⡟⠁⣠⠟⠁⣠⡾⠃⢀⡴⠛⠁⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⠈⠙⢶⣄⠈⠻⣄⠀⠻⣆⠀⠹⣆
⠀⠀⠀⠀⠀⣰⠏⠀⣴⠏⠀⣴⠋⢀⣴⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⢷⡀⠘⢷⡀⠘⣧⡀⠹⣦
⠀⠀⠀⠀⢠⡟⠀⣸⠇⢀⡾⠁⢠⡾⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⢻⣄⠈⢷⡀⠘⣷⠀⠹⣆
⠀⠀⠀⠀⣿⠀⢰⡏⠀⣼⠃⢀⡿⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⡄⠈⣷⠀⠸⣇⠀⢻⡄
⠀⠀⠀⢸⡇⠀⣾⠀⢰⡏⠀⣼⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⠀⠸⣇⠀⢿⡀⠘⣇
⠀⠀⠀⣼⠁⢠⣯⣤⣼⣁⣀⣟⣀⣼⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣧⣤⣿⣤⣼⡇⠀⣿
⠀⣠⣤⠿⣶⠋⠁⠀⠀⠉⠛⠟⠉⠀⠀⠀⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡾⠛⠛⠛⠋⠁⠀⠀⠀⠈⠙⢷⣿
⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣄
⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠈⠙⠛⢷⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡷⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠞
⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⣤⠾⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣤⡶⠶⠋⠛⠲⠶⠶⠞⠛⠁

⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⣂⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠰⣾⢿⣿⣿⣿⣧⠀⠀⠀⠀⠠⢀⣀⢙⣫⣴⣾⣿⣀⣾⣿⡿⠂⠶⣆⠀⠀⣠⣾⣿⣿⣷⣦⠀⢰⡶⠀⢸⣿⣿⠿⠓
⠀⣴⣞⣺⣿⣿⣿⣿⣿⣡⣤⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠁⠀⠀⠙⢦⡀⢻⣿⣿⣿⣿⣿⣴⠏⠀⠀⢀⣿⣿⣿⣴⣶⣤⡀
⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⣿⠿⠛⣿⣿⣿⣿⣿⣦⢠⣤⠀⠀⠈⠛⣦⣍⣻⣟⣿⠟⠁⠀⢀⣴⣾⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠙⣹⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⡎⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠉⠉⣹⣿⣷⣦⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⢫⣄⠙⠛⠁⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⠀⠈⠛⣿⣿⣿⡀⠈⣷
⠀⠀⠀⠀⠠⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⢀⣹⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠘⢿⣀⠀⢠⣿⣿⣿⣷⡈⠏
⠀⠀⠀⠀⠀⣰⣿⡿⢹⣿⡿⠁⢀⣴⣾⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠹⠇⠀⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⡿⠋⠀⣼⡿⠁⠀⠻⣿⣿⣿⣍⠈⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢠⣾⠁⠀⠀⠹⣷⡀⠀⠀⠈⠛⠻⣿⣦⣿⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢡⣿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⢼⣿⣷
⠀⠀⢀⡿⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠃⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠉⠀⠀⠈⣿⡟
⠀⢀⡞⠀⠀⠀⠀⠀⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⢸⢿⣦⡄⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠘⠁⠀⠀⠀⠀⠀⠉⠀⣀⡠⣤⡄⠀⣠⡄⢙⡉⠩⠤⢀⣄⣀⠄⠀⠀⠀⢤⡤⠄⣙⠿⢄⡀⠀⠀⣤⡤⠀⣄⠀⣈⠉⣤⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠋⠓⠉⠙⠋⠘⠓⠐⠂⠐⠋⠉⠓⠀⠀⠀⠀⠚⠀⠘⠓⠀⠚⠁⠀⠀⠘⠃⠀⠙⠁⠉⠃⠙⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣀⣤⣶⣒⡽⠟⣃⣤⠶⢒⣹⡿⠂⠰⠞⣃⡀⠤⣤⣀⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⣀⣤⣀⠀⠀⣠⡤⠤⢤⣀⠠⠤⣤⡤⠄⠠⣄⣀⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠄⠀⠀⡀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠐⠁⠀⠄⡈⠤⠒⢀⠩⠀⠀⠀⠀⠉⠁⠒⠀⠈⠀⠀⠄⡀⠁⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡠⢊⠠⢂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠐⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠋⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⠁⠄⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠄⠑⢄⠀⠈⢪⢂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠆⠀⠁⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠌⢂⠀⠀⢡⠡⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢊⢣⠐⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⢃⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠌⠆⠀⢐⢠⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⣀⡀⠤⠄⠦⠤⠬⣠⠀⢁⢘⠀⡄⠀⠘⣐⡀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠓⠀⠄⠔⠘⠀⢀⢀⣀⣀⣀⠄⠀⠁⠈⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠤⠤⠀⡂⡄⠀⠀⠀⠓⠚⠁
⠀⠀⠀⠀⠀⠀⡀⠐⠀⣀⣐⣀⡀⠠⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⢈⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠀⠀⠁⠀⠀⠀⠈⠉⠉⠒⠢⠤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠈⠀⠀⠀⠠⠀⠄⠄⠄⠀⠠⠀⠠⠀⠠⢄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠤⠄⠀⡀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠁⠐⠤⠠⠂⠀⠀⡀⡀⠀⠀⠀⠉⠉⠐⠐⠂⠠⠀⠤⠄⠤⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠐⠂⠈⢉⡰⠒⠦⣆⠀⠀⠀⠀⢀⠤⠀⢃⠀⢜⠀⠼⡀⠠⢀⠀⠘⠧⠤⠠⠤⣀⣀⠀⠰⣨⠀⠦⠜⣁
⠀⠀⠀⠐⠁⠀⠀⠀⡴⠋⠀⠀⠀⠈⠻⣄⠂⠀⠘⡀⠀⠀⠀⠀⠀⠀⠸⠀⡌⠀⠀⠄⠀⠀⠀⠈⡧⠠⠀⠀⠑⠀⠈⠈
⠀⠀⡌⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠘⣄⠂⠀⡎⠀⠀⠘⠄⠠⠃⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤
⠀⢠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⠑⠀⢐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢊⠭
⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣎⠠⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠠⡀
⠀⠀⠐⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⠰⠁⠀⠀⠰⡅⠁⡴⠁⠀⠀⢐⡀
⠀⠀⠀⠀⠢⢀⠀⠀⠈⠦⣄⠀⢀⣤⠎⡁⠀⠀⠀⠀⠀⣄⣀⣤⣀⣠⠎⢀⠄⠐⠀⠂⠀⢐⠀⠀⠀⠀⠂⠀⠐⠙⠂
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠚⠉⠛⠀⡀⠀⠀⠀⠀⢀⡴⠉⠁⠀⠀⠉⠳⣎⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠒⠆⠀⢀
⠀⠀⠀⡀⠰⣀⡀⠀⠀⢈⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⣋⠁⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡠
⠀⠀⠀⢁⠀⢠⠀⠀⠐⠢⠄⠠⠵⠄⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⡼⠉⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⢉⠢⠤⣀⣀⠤⢞⠁⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⡠⠊⠀⠈
⠀⠀⠀⠠⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠁⠀⠀⠌⠀⠀⠀⠆⠀⠀⠑⠈⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠁⠲⠃⠑⠄⠀⠀⡘⠀⠂⡀⠀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠔⠁⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠄⠀⠁⠁⠀⠰⠀⠂⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠢⠀⠀⢀⠀⠂⠀⠀⠀⠈⠐⠢⡀
⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡩⢒⠫⢖⡤⢒⠤⠀⢀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠁⠢⠀⠄⠄⠀⠐⠐⠀⠉⠀⠀⠀⠀⠀⡡⢀⠅⡈⠕⠂⠉⠠⣄⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠚⢠⠀⢐⠂⢀⠁⠈⠐⠃⠐⠂⠤⠀⣀⠀⠀⠐⠳⠤⠤⠤⠄⠄⠄⠀⠀⠀⠐⣚
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠐⠁⠦⠈⠀⠘⠒⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⣂⠀⠀⠀⠈⠃⠀⠀⠀⠁⠀⠉⠉⠉⢩⠃
⠀⡊⠤⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠈⠀⠈⠁⠂⠀⠀⠁⠀⢠⠀⠀⠈⠐⠄⠀⠀⢀⠀⠠⠐⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿