Tempura Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⡏⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠⠧⡄⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡄⣿⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⡴⡹⠄⠲⢇⠀⠄⠒⡆
⠀⠀⠀⠀⢀⠀⠤⠤⠤⣄⡠⠤⠤⠤⠤⢤⡤⣤⢤⡤⠥⠤⡷⠇⠀⠀⠈⠆⠀⠀⢸⡤⠤⠤⠤⠀⡀
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢈⡭⠖⠙⠥⡐⣄⠟⠀⠀⠀⡏⠀⠀⡆⠀⢣⠀⠀⠀⢣⠀⠀⠀⠀⠸⡀
⠀⠀⠀⢸⠀⠀⢀⡀⠐⢂⣈⣉⠐⡩⠛⢰⢱⠁⡀⠀⠀⠀⡅⠀⠀⠀⠀⡇⠰⣀⠀⠈⡆⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠊⠡⠔⠒⢉⡥⠒⠐⣩⡦⠝⣸⠋⠀⠈⠂⠀⢐⠇⠀⠀⠀⠀⡇⢅⠢⡱⡀⠚⠀⠠⠀⣀⣣
⢠⠐⠂⠉⡄⠹⠤⢔⡪⠴⣲⢆⣵⢟⡹⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡇⠈⠧⢥⡸⡄⠀⠀⠀⠀⠀⢡
⠀⢇⠀⠀⢨⠰⡉⢉⡤⡪⢚⠕⢡⠃⠀⠀⠀⡖⠀⢀⡼⠀⠀⠀⠁⠀⢰⠷⡄⡠⠶⣅⠘⡄⠀⠀⠀⠀⡞
⠀⠈⡄⠀⠈⠳⢍⠉⠪⠔⠊⣠⠊⠀⠀⠀⠀⠀⢔⢩⠀⠀⠀⠠⠀⠀⣯⠄⠓⠣⠠⢜⢦⡱⣄⠀⠀⣸⠁
⠀⠀⢸⡀⠀⠀⠀⡝⢒⠗⠊⠀⠀⠀⠀⢠⠀⠠⡎⡎⠀⠀⠀⠀⡠⠈⡡⠔⢱⢴⣦⠤⡱⣇⣨⡑⣤⠋⡄
⠀⠀⡆⢣⠀⠀⢀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠄⠀⠀⡇⡎⠀⠀⢸⠸⠤⢜⡄⢸⣕⣾⡸⠀⡇
⠀⢠⠇⠈⠆⠀⡸⠀⠘⢆⡀⠈⠉⠉⠀⢀⡞⣇⠀⠀⠁⠀⠀⠀⡇⣏⢰⠍⡵⡴⡍⠹⡇⢸⣀⠜⢤⡀⢸
⠀⢸⠀⠀⠐⠀⡇⠀⠀⠀⠈⠒⠒⠒⠊⠁⠀⢑⣦⢤⣀⣀⡀⡠⠽⠌⠙⢮⣠⡳⠣⠋⣠⠿⠁⠀⠀⢣⢸
⠀⢸⠀⠀⠀⢲⣇⡀⠤⠤⠄⠒⠒⠒⠈⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠈⠓⠂⠀⠤⠴⠊⠀⠐⢄⣀⡠⠞⢸
⠀⠈⠠⠥⣀⣀⣀⣒⣒⣀⡡⠠⠠⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠅⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣦⣤⣶⠿⣷⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⢉⡅⠀⠘⠿⠿⠟⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⣾⡟⠀⠀⣠⣾⠇⠘⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣛⣃⠀⠸⠟⢁⣀⣀⣈⣙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⣿⠟⠻⣷⣴⣾⠿⠛⠛⠛⠛⠉⣴⣶⣶⣄⣀⣴⣾⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⣰⣆⢀⡀⠉⢻⣷⠀⢀⣤⣤⣤⣼⡿⠁⠉⠛⠛⠋⣤⡀⠹⣿⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡿⠀⢠⣿⠇⢹⣷⢠⣾⣟⠀⣿⣏⠉⠛⠉⢠⣄⠀⠀⠀⢸⣿⠁⠀⠀⣉⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣿⣯⠀⠀⠀⠛⠋⠀⠸⡿⠀⢘⣿⠆⠘⢿⣧⡀⠀⠘⣿⡆⠀⠀⠿⠇⢀⣴⣾⠟⠋⠁
⠀⠀⠀⢀⣴⣶⣶⣾⠿⢿⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠻⠛⠉⠀⠀⣠⡀⢰⣿⠀⠸⣿⡿⠋⠀⠀⠀⠙⢿⣦⡀⠘⢋⣠⣄⡀⣠⣿⠏⠁
⠀⠀⠀⣸⣿⠀⠈⠁⣀⠀⠁⠈⠛⠉⠙⣿⣶⣶⡿⠿⢿⡿⠛⠁⠀⠀⠀⠸⠿⠿⠟⢡⣾⣿⣤⣴⣿⠃⠀⠀⠀⠀⠀⠀⣹⣿⣶⡿⠋⠙⠿⠿⣿⣦
⠀⠀⢰⣿⠋⠀⢰⣿⠿⠃⠀⠀⢀⣄⠀⠈⠀⠉⠁⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠈⣿⡏⠁⠀⠀⠀⠀⠀⠀⣸⣿⠋⠉⢁⠀⢀⡀⠀⢈⣿⡇
⠀⠀⣼⡿⠀⠀⠘⠛⠀⠀⠀⠀⣼⡟⢀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡶⢀⣠⣿⠇⠀⠀⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⢿⣧⠙⢿⣦⠘⠛⢿⣧
⠀⢠⣿⠟⠀⣠⡀⠀⠀⠀⠀⠀⠘⠋⠻⣷⣤⣤⣤⡄⠀⠀⠀⠀⠀⠛⠛⠁⠀⣴⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠀⠀⣸⣿⠀⠈⢿⠇⢀⣠⣿⠃
⠀⢻⣿⣄⡀⠙⢿⣶⡿⠃⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⣀⠀⠀⠀⠀⢠⣤⣤⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠀⠀⠛⠃⠀⣠⡀⠀⠻⣿⣇
⠀⠀⠉⢻⣷⡀⠀⠀⢠⣤⣤⣴⣾⠗⠀⠀⠀⠀⠀⢀⣼⡿⠁⢀⣤⣀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⢀⠀⢹⣷⠀⢀⣼⡿
⠀⠀⠀⠀⣿⡟⠀⠀⠈⠉⠉⠉⠀⢀⣀⣠⣦⠀⠐⠿⠛⢡⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⡟⠁⠀⣀⣴⣿⠃⢸⣿⠺⢿⣿⡁
⠀⠀⠀⠀⠙⢿⣶⣶⡀⠀⣠⣀⢀⡙⠛⠋⣥⣤⣾⣶⣴⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⠀⠘⠟⠛⠁⠀⠈⠁⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠻⠟⠿⣷⣾⠟⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣤⣤⣴⡿⠿⢿⣶⣾⢿⠇⠀⠀⠀⠀⣶⣤⣤⣶⠀⣴⡿⠃⠀⠰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡟⠛⠛⠋⠉⠛⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠛⠀⠀⣀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⢀⣾⠟⠃⠀⠀⠀⠸⣿⣄⢰⣦⣄⣠⣤⣾⠗⠀⠀⢠⣄⠀⠀⣀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠈⢿⡇⠀⠀⠀⠀⠀⠘⠋⠀⠉⠙⠛⠉⠀⠀⠀⠀⢸⣿⠀⠀⣹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢠⣦⣀⣠⣾⠇⠀⠀⠀⣰⣿⠀⠀⠀⢀⣄⠀⠈⣁⣀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠉⠛⠋⠁⠀⣠⣴⣾⠟⠁⠀⢀⣤⣿⠏⣀⣴⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣿⣆⣀⡀⠀⠀⠉⠉⠀⠀⠀⠀⠙⡋⠁⢀⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣇⠀⠀⣀⠀⠀⢀⣴⣤⣾⡿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠿⢷⣶⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⡟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡰⠉⠧⠬⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡖⠒⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢰⠀⢸⠀⠀⠀⠙⠫⡉⢓⠲⣄⡇⡌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢼⠀⠘⢦⡀⠀⠀⠀⠘⢦⠉⠘⡴⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡄⠀⣆⠙⣆⠀⠀⠀⠀⡷⠤⢄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠳⡀⠘⠄⠳⢄⠀⠀⢼⢀⡤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢠⠄⠀⠀⠀⠀⢀⠘⡄⣠⠋⠘⢀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡤⠋⢀⠀⠰⡆⠀⠈⢠⡗⢡⠀⠰⠋⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠀⢠⠋⠀⠈⢡⠖⠋⠉⠀⠉⢀⡀⠀⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡸⠀⠀⠐⡁⢀⡔⠚⠁⣀⠤⠒⠀⠀⠜⢀⠞⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣘⡁⢀⡴⠉⠉⠉⠀⠚⠉⠀⠀⣰⠁⠀⠀⠈⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡠⠎⠀⢈⡥⠤⠂⠀⠀⣀⠤⠚⠀⠀⠁⠀⠐⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠟⣀⠀⠐⠉⠉⠀⢀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⡤⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣜⠁⠀⠠⠖⠒⠚⠁⠀⠀⠀⠀⠀⢈⠀⠀⠔⢁⡔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡰⠃⢠⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡈⠉⠓⠒⠒⠋⢀⣀⡀⠉⠉⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠒⠒⠒⠚⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⠞⠛⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠰⠀⠀⠀⠀⡘⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠁⠀⠀⠀⠇⠀⠀⠀⡠⠁⠀⠸⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⠀⠀⠀⢧⠀⠠⠆⠀⢀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⣠⣼⠟⠉⢉⠁⠉⠙⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⢈⡁⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⣴⠟⠋⡍⠀⠀⠁⠀⢠⠆⠛⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⢠⡟⠁⠒⠒⠂⠠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠿⠶⠟⠁⢀⣠⣄⡘⠻⠶⣶⡄⠀⠀⠈⠂⠀⠀⡠⠔⠂⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆⠠⢠⡟⠉⠀⠀⣠⠶⠿⠿⠟⠋⢉⠉⠻⣆⡀⠘⢿⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠋⠀⠀⣴⠟⢃⠀⠀⠀⠁⡀⢸⠀⠀⢈⡹⣷⠈⠻⣦⠀⠀⠀⠠⠊⠉⠁⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠁⠢⡀⠀⢀⠀⠄⠀⠆⠁⢸⡆⠀⢹⣧⠀⠀⠠⠄⢀⣀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣷⠀⢸⣏⠀⣀⣀⣀⣀⣼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⡷⠟⠉⠻⣦⠀⣼⡃⠈⠀⠀⡠⠒⠈⠉⠀⠀⠉⠐⠄⢀⡾⠀⠀⠙⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠀⠀⠉⠀⠀⠀⠀⠙⣷⡘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠄⡤⠄⠀⢄⡄⠀⠀⠀⠀⠈⢿⡌⢿⡄⠂⢀⣤⣤⣴⠶⠶⠶⠟⠋⠉⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠠⣈⣿⡈⢷⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢾⡟⠻⡛⠛⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⢀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠗⡀⠈⢦⠈⠉⠉⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠁⠀⢀⠔⠀⠠⡑⠀⠀⠀⣠⣴⡿⠀⠀⠀⠀⠀⠀⣠⡾⣫⣾⠟⠀⠁⠀⠈⡆⢀⠤⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠉⢁⡴⠋⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⠋⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠾⢷⣦⡶⠟⠁⠀⠀⠀⠀⠀⣠⠾⣫⣾⠏⠀⠀⠀⠀⠀⠀⡠⢊⡰⠖⠒⠒⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣾⠟⣿⣄⡀⠀⠀⠀⠠⠊⠀⠀⠁⠀⠀⣤⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣴⠟⠁⠀⠀⢹⣿⠁⠈⠉⠒⠀⠀⠀⠀⢈⣿⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢃⣴⠟⠁⠀⠀⠀⠀⠀⢻⣦⡀⠈⢂⠀⠀⠐⢲⣿⣣⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠶⣾⡿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⢃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⡿⠁
⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣡⡿⠁
⠀⠀⠀⣠⣾⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣡⡟
⠀⣠⣾⠟⣡⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣱⠟
⣾⠟⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡃⣰⠏
⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⢁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣃⣠⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⢿⣿⡿⢿⡿⣿⢿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣦⣬⣦⣾⣤⣼⣧⣴⣿⣥⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡀⡀⢀⠀⠀⠀⠀⣀⣀⡀⠀⣀⢀⢀⣀⢀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠃⠃⠛⠀⠘⠛⠙⠙⠈⠁⠀⠁⠛⠈⠉⠻⠛⠚⠋⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠞⠳⠽⠀⠸⠶⠗⡲⠀⠘⠷⠿⠦⠶⠅⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⣈⣷⡀⠀⠀⠀⣀⢀⡀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⡀⣀⠠⠠⠒⠾⡾⠷⠀⠀⢢⣀⡞⠫⠆
⠀⠀⠠⣴⣸⢟⣻⢉⠀⠀⠀⠐⢂⠀⢉⠒⠠⠄⠀⠀⠠⠠⠈⡀⠀⠀⠠⠀⠡⢘⠀⡁⠀⠒⡀⢹⠇⢀⠄⡀
⠀⠀⢸⡿⣿⢀⠉⠤⠁⠁⠄⠰⠀⠂⠠⠀⡁⠰⠀⠀⡡⠀⠈⣄⣐⢀⠉⠤⠀⢙⠉⠀⠑⠀⠰⠁⣰⡿⣢⡖
⠀⠀⠀⠀⡘⣦⡄⠀⠀⠢⠀⠀⠠⠀⠀⠀⡰⡁⠨⡀⢀⠤⠚⠡⠀⠠⠀⠀⣠⠀⠤⠤⠠⠐⠋⠈⠙⡶⡛⠷⢖⡄
⠀⠀⠀⠀⠃⠁⠊⠙⡒⠶⢄⠤⣤⠩⠤⠢⠁⠠⠀⡈⡅⢀⣠⠒⠉⠉⠈⠥⠀⠀⠀⠂⢀⢀⡠⠔⠊⠙⡿⠖⠛
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠂⠐⠂⠀⠐⠀⠀⢀⠀⠀⠅⠁⠜⡀⠀⠃⢀⠀⡐⠀⠌⠑⠊⠔⢀⠀⠐⢉⡴⠃⠐⡀
⠀⠀⠀⡃⠄⠀⠀⠀⣄⠁⠉⢠⣤⠴⠂⠔⡲⠂⠀⠀⠀⠠⢰⠋⢁⠀⠀⠔⠀⠀⠒⠂⠀⠀⢂⡠⢞⠄⠀⠄⡐⡀
⠀⠀⠀⠿⣕⠠⢀⠈⠈⢄⡀⠀⠀⠠⠤⠀⡰⠑⠀⠀⠰⢑⢇⠀⢠⠀⠠⠤⠀⠀⠀⢀⣡⠴⠋⠐⠁⠀⠀⠀⣨⠎
⠀⠀⠀⠀⠀⠙⠲⠬⣄⣀⠙⠓⠦⠤⠐⠈⠁⠀⠀⠀⠀⠀⢄⠑⠦⠤⠤⢄⠤⠔⠛⠉⢀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⣤⣀⣀⣀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⣀⣀⣤⠴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⣀⠂⢀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢣⢱⢙⣸⢸⢀⡔⠂⠀⢠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣼⠸⣼⣹⣸⢸⣠⡍⢡⣫⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⣸⣼⣯⢿⣁⣠⢸⣷⣿⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠘⠁⠴⠁⠉⠈⣹⠀⡈⠙⠃⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⡐⢂⡞⠀⠀⢼⡇⠀⠁⢈⠈⠧⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠉⠀⡠⠁⡄⠀⢄⠀⠙⡆⠔⠁⠀⡀⢠⠀⡇
⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⡄⡐⠂⡈⠀⠀⠀⠀⠘⠁⠀⡄⠀⢁⠈⢁⠙⢄⠀⠀⠀⣀⠀⠠⢤
⠀⠀⠀⠀⣀⠀⠁⣀⠸⢉⠤⠂⠀⡀⠀⣰⠉⠉⠀⠀⠀⡠⠀⠁⠀⠀⠁⠀⠀⡁⠀⢄⠐⢇⠉⠡⠀⡂⠐⠆⠆
⠀⠀⠀⡆⠰⠀⢀⠅⡀⠀⠀⠀⠘⡠⠘⠀⠀⢀⡀⠀⠀⠀⢀⡘⠘⠀⠀⢆⠀⣸⠀⠐⠀⠉⢲⠈⠁⠂⠀⠀⢀
⠀⠀⠀⠃⢀⠀⡄⠈⠠⠀⠠⠀⠊⠀⡀⠀⠀⠈⠀⠀⠀⡠⠀⡁⣠⠀⠀⠈⠀⢀⡀⠠⠔⠁⢀⡘⢀⠀⠀⠐⠈⡄
⠀⠀⠀⠀⢀⠘⡄⠀⠁⠀⠈⠼⠁⠰⠀⠀⠀⠀⠀⠀⠀⠁⢀⡁⠀⠀⠀⠃⠐⠀⡸⢀⠀⢰⠀⠁⠈⢧⠀⠀⠇⢰
⠀⠀⢠⠀⠸⠀⢧⣄⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⢀⠀⢸⡀⠀⠐⠀⢠⠀⡱⠸⠄⠀⠁⡀⡄⣹⠀⠀⢰⠀⡆
⠀⠀⠘⠀⠀⠀⠀⠘⠛⢳⠀⠀⡇⠀⠀⡀⠀⠀⠀⠐⠁⠈⢀⡿⠡⠀⠀⡠⠀⠀⢩⠂⠀⠀⠚⠁⠃⣸⠀⠀⢃⡄⢸
⠀⠀⠆⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠂⠀⣾⡋⠀⣀⡀⠋⠀⢀⡰⢾⣀⠑⣂⠀⣴⠾⡛⠄⠀⠸⢧⠀⠆
⠀⢰⠀⠰⠀⠠⠀⠀⠀⠀⠀⡈⠳⠶⣶⠀⣄⡶⠧⠜⠋⠁⠻⠤⢄⡴⠦⠶⠚⠀⠀⠉⠙⠉⠉⠁⠑⠌⠂⠀⠀⠋⡆⠸⡀
⠀⠈⠓⢤⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠤⠤⠒⠚⠁⣀⡧
⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⣤⣀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⣀⣀⡤⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠴⠶⠶⠖⠒⠒⠚⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠯⠄⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⣀⣀⡀⢀⡤⠋⠉⠉⠀⠉⠀⠈⠛⠒⠒⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠤⣀⠋⠀⢀⠠⠀⠀⠉⡦⡀⠀⢀⠴⡷⠶⠂⢀⠀⠀⠘⠁⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠑⡜⠀⠚⠁⢀⣀⣀⣊⠑⠲⠦⠤⢯⡽⠆⠲⠚⠛⠛⠧⠈⠂
⠀⠀⠀⠀⠀⠁⠀⢀⠒⠀⠀⠀⠀⠂⠀⢂⣀⠒⢀⠀⠡⠍⢡⠂⠉⠀⠀⠀⠈⠀⢄⠸⠋⠀⠀⠐⠬⢒⡀⠀⡀⠀⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠐⠈⠐⠀⠀⠀⠁⠀⠀⠀⢀⠔⢀⠄⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢄
⠀⠀⠀⠀⡀⠀⠠⠄⠀⣀⢀⠀⠀⠤⠔⢊⡠⠔⠁⠀⠀⠀⠀⠀⢠⣀⠀⠀⣀⡠⠀⠀⠀⠁⠢⢄⣀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠳⡀
⠀⠀⠀⠀⠉⠒⠀⠤⠤⠤⠤⠤⠤⠒⠊⠁⠀⠀⡠⠂⠀⠀⠀⠀⠐⠤⠤⠬⠥⠐⠁⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⣠⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⣀⣀⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⠀⠀⣀⣀⠀⣀⠀⠀⠠⠤⠤⠤⠄⣀⣀⠒⣒⣚⣉⣉⡉⠭⠬⠥⠁⠒⠂
⠀⠀⠀⠀⠠⠌⠉⠉⠉⠉⠉⠉⠩⠭⠥⠤⠤⠀⠀⠐⠒⠒⠒⠒⠀⠀⠉⠉⠉⠉⠁⠀⠉⠁







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢠⠄⡤⡤⠀⠖⠠⣀⡄⡠⠀⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⡀⣀⠄⠀⠀⡀⣀⡀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⠅⢀⠀⠂⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠐⢁⠀⠡⠊⣰⠧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⠖⢦⡤⠟⢦⡔⢁⠔⢁⡼⠅⢂⠠⠌⢉⠗
⠀⠀⠀⠀⢀⣠⠤⠎⠁⠀⠀⠀⠀⠀⠈⠀⠀⠉⠖⠒⠲⢄⠀⠀⠀⠀⠀⠀⣀⡀⢀⠔⠒⠦⠖⠒⠒⠏⠀⠀⠀⠀⠀⠀⠀⢀⣗⡥⡚⠥⢐⡉⠤⣊⠞⠁
⠀⠀⣀⣠⢼⠀⠀⠀⠀⠀⠀⠒⠄⠀⡀⢀⣀⠀⠀⠀⠀⠀⠉⠉⠓⠊⠒⠊⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣹⣆⣈⡥⠤⠚⠁
⢀⡞⠁⠀⠀⠀⢀⠄⠈⠑⠄⠀⠀⠀⠁⠀⠁⠉⠂⠀⠀⠀⢀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⢒⡀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⣶⠁
⠘⡇⠀⠀⢀⠀⠈⠀⠀⠀⠉⡂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠰⢆⠀⠀⠀⢠⠄⠀⠀⠀⡰⠁
⡞⠉⠀⠀⠑⠀⠀⠀⠀⠀⠀⠜⠀⠀⠃⠁⠀⣰⠀⠀⠀⠀⠀⠄⢄⠀⠀⠂⠀⠀⢚⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⡰⠚⠋⠀⠀⠀⠀⡠⠤⠤⡀
⢑⡄⠀⠀⣜⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣀⡀⠀⠀⠀⠀⠐⢣⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄⠀⠀⠀⢀⡶⠖⠚⠁⣠⣤⡔⠉⠙⠏⠀⠀⠀⠙⠋⠉⠑⢦⡀
⢺⠀⠀⠀⠀⠹⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⣰⠁⠀⠀⠀⠠⠅⠀⠀⠀⠉⠀⢁⠖⠚⠉⠀⢀⡠⠼⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣷⣀
⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⣀⠽⠉⠁⠀⠀⠀⣠⡇⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⣁⠀⠀⠠⠀⠀⠀⢸
⠀⠀⠀⠇⠀⠀⠀⠀⠐⠲⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠈⠀⣤⣤⠤⠊⠀⠀⠀⠀⠀⢰⠉⠁⠁⠐⠁⠑⢠⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠈⠑⠒⢶⡀⠀⠀⠀⠐⠀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠀⠀⠀⢀⠖⠚⠁⠀⠀⠀⠀⠀⠀⡰⠉⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⣄⠀⠀⠀⠀⣀⣀⣠⣀⣀⣀⠟⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⣀⣴⠋⠉⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠁⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠒⠲⠇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢐⠆⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡴⠶⠏⠀⠈⠁⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⢀⡀⠀⠈⠐⠀⠀⣀⠄⠀⠀⠠⠃⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠲⢤⡀⠀⡔⠋⠙⡞⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠸⣂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⡖⠊⠁
⠀⠀⠀⠀⠰⡋⠉⢀⠀⠈⠀⠤⠄⠉⢠⠟⠛⠁⠀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⡰⠀⠀⠀⠐⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠈⠑⣦⣄⡒⠀⠀⠀⠐⢈⡧⠀⠀⠣⣤⠀⠀⠡⢤⠄⠀⠀⠀⠀⣆⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⣸⠋⠁
⠀⠀⠀⠀⠀⢠⠞⠁⠀⣉⣉⣛⡛⠨⠁⢻⡇⠀⠀⠈⢊⠀⢀⠀⠩⠀⠠⢠⠀⠀⠀⠁⢀⠉⠑⠂⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⠀⠀⢀⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠈⠒⠢⠤⣀⣒⠒⠀⠒⣈⡴⠛⠉⠳⠤⠴⢦⣀⢀⡠⢦⣀⣠⣦⣀⣁⡾⢦⣄⣀⣀⣠⠗⠦⠤⠞⠛⠒⠛⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠄⡤⠤⠀⠔⠠⢀⡄⡤⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⡀⢀⠀⢀⠀⡀⣀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⠡⢀⠀⠂⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠐⠁⠀⠡⠊⣴⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⢤⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣤⠖⢦⡤⠟⢮⡄⢁⠔⢀⡼⠁⢒⠠⠈⣉⠇
⠀⠀⠀⠀⢀⡠⠤⠎⠁⠀⠀⠀⠀⠀⠈⠀⠀⠙⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⡀⢀⠔⠒⠤⠖⠛⠒⠯⠀⠀⠀⠀⠀⠀⠀⠀⣇⡥⠚⠁⠒⡈⠄⣢⠞⠁
⠀⠀⣀⡀⣾⠀⠀⠀⠀⠀⠀⠒⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠉⠉⠓⠊⠐⠊⠀⠈⠙⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠠⠄⠀⠀⠀⠀⢹⣆⣠⡤⠴⠚⠁
⠀⡞⠁⠀⠀⠀⢀⠔⠈⠑⠆⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡔⠢⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣶⠁
⠘⡇⠀⠀⢀⠀⠈⠀⠀⠀⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⢆⠀⠀⠀⢀⡀⠀⠀⠀⡰⠁
⡞⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠔⠀⠀⠂⠁⠀⣰⠁⠀⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠉⠀⠀⠀⢀⣠⠤⠤⡀
⠑⡄⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠁⠀⠀⢀⡤⠀⠀⠀⢀⡴⠶⠊⠁⣠⣤⡔⠉⠙⠏⠀⠀⠀⠙⠋⠉⠑⢦⡀
⢺⠀⠀⠀⠈⠹⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⡰⠁⠀⠀⠀⠠⠁⠀⠀⠀⠈⠀⢃⠖⠚⠉⠀⢀⠠⠼⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣷⣀
⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⣀⠜⠉⠁⠀⠀⠀⣠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣇⠀⠀⠀⠀⠐⠲⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠈⠀⣤⣠⠤⠊⠀⠀⠀⠀⠀⢐⠉⠀⠁⠐⠀⠑⢀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠑⠒⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢆⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠁⠀⠀⠀⠀⠀⠀⡰⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⣄⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠞⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⣀⣴⠋⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠒⠲⠅⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢐⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡴⠶⠏⠀⠈⠁⠀⠀⡀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⣀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠲⢤⡀⠀⠔⠉⠙⡞⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠰⣃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡖⠊
⠀⠀⠀⠀⠰⡊⠁⠀⠀⠬⠤⠄⠠⠭⢠⠟⠛⠁⠀⠀⠀⠀⢀⡀⠀⠘⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡰⠀⠀⠠⠤⠀⠀⠀⢀⣀⠜⠁
⠀⠀⠀⠀⠀⠈⠑⣦⣄⡀⠒⠀⠐⠀⢈⡧⠀⠀⠡⣠⠀⠀⠡⢠⠄⠀⠀⠀⠈⢆⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⠋⠁
⠀⠀⠀⠀⠀⢠⠞⠁⠂⠉⠙⣋⠈⠩⠁⢹⡆⠀⠀⠈⢋⠀⠀⠀⠁⠀⠠⠀⠀⠈⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡿⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠒⠢⠤⣀⡐⠒⠀⠐⣀⠴⠋⠉⠳⠤⠴⢦⣀⢀⣠⢦⣀⣠⣦⣀⣁⡼⢦⣄⣀⣀⡰⠗⠦⠤⠞⠛⠒⠛⠁⠈⠈⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡔⢹⣀⡠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡰⡅⢸⢸⡏⣰⣿⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢱⢹⠈⡟⢠⢋⠞⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡏⢀⡃⣸⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣗⡧⣼⠷⣿⡞⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡝⢁⠀⣒⢸⣜⠀⡉⢯⠄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⠜⡀⠖⠄⠀⢸⠀⠤⠄⠸⡀⢈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠙⢹⢉⡀⠀⠄⠀⢸⠀⠄⠀⠂⣅⠈⠠⢜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡥⠤⢠⢃⠄⠀⠠⠄⠀⡾⠤⠀⠈⠀⣧⠀⢀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠀⢰⣄⠀⡼⠉⢀⡀⠀⠂⠀⡟⠂⠀⠀⠱⡀⠘⠉⠀⠦⡌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢔⣊⠐⠂⢤⠀⠀⡱⣁⠤⠀⠉⠁⠀⠀⡇⠘⠙⢁⡀⢱⠀⠀⢀⣠⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠌⠀⠀⠀⢤⠀⠸⠀⣠⣀⡀⠀⠀⠀⣺⠐⠀⠀⠀⠹⠘⡐⠂⠈⠀⢀⡀⣍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣜⠠⡄⠘⠀⢀⡀⢀⠜⡂⢀⠀⠀⠀⠁⢀⡇⠈⠀⠉⠛⠁⣨⣄⠀⠊⠀⣈⠁⠀⠲⡝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠍⠢⣴⠒⠖⣢⣤⢏⡌⠉⠉⣁⠈⠁⠀⢾⠀⠀⠃⠀⠢⠤⡅⠏⢢⠈⠀⠀⠀⣁⠀⠦⢠⣇
⠀⠀⠀⠀⠀⠀⠀⢻⡂⠀⠀⠁⠉⢸⠀⣉⠀⠐⠀⠈⠀⠀⡎⠀⡃⠀⠀⠋⢀⠀⠰⡜⡌⠳⣌⣥⣀⣀⠐⠂⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠫⡢⡀⠀⠀⠀⢁⠀⣀⠉⡀⣈⣁⡞⠁⠀⢳⢀⡂⠀⠴⠀⠤⠀⡸⠀⠈⠑⠖⠜⢣⣞⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠵⣢⠤⣈⡢⢄⠮⠩⠕⠋⠀⠀⠀⠈⢻⣙⠲⡀⠲⢀⠎⠀⢀⣀⠤⣔⠮⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠠⠄⣐⢒⠀⢤⡤⠤⠤⠤⢌⡍⠒⣒⡃⠢⠌⠓⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣥⣬⣭⣍⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣉⣉⣭⣭⣹⣿⡅
⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢳⠀⡀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⢳⠆⠀⠀⢼⡄⠀⠀⠄⠀⢧
⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⢼⡇⠀⠀⠀⠀⠘⠦⣀
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠆⢀
⠀⠀⠀⠀⠀⠀⠈⢷⢀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠂⠀⠀⠀⠀⢈⠝⠳⢦⡀⠀⠐⣀⣤⡾⢿⡀⠀⡀⠀⠀⠀⠀⠀⠠⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠙⠶⣄⡒⠀⠶⢀⣤⡴⢆⠟⠝⠋⠉⠀⠀⠀⣳⣀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠙⠲⣬⣯⢮⠶⠫⠂⠀⠀⠀⠀⠀⠊⠁⠈⠓⠠⠤⠤⠤⡔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡅⠄⠀⠀⢀⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⡏⠁⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠄⠐⠈⡻⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡐⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠢⠀⠀⠂⠀⠀⠀⠀⠤⠠⣟⣵⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⢬⣀⣀⣀⡀⠀⠀⠈⢒⠉⣀⠔⠀⠐⣒⠁⠁⠀⠀⢀⠤⠺⣦⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠠⡀⠀⠲⠈⠑⢀⡁⠀⠀⠀⡌⠀⠀⠀⠁⠀⠈⠠⢀⡠⠚⠁⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠢⠤⠀⠀⠈⠀⠀⠀⠀⠐⠄⣀⣈⣁⡠⠤⠒⠉⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣶⢲⣶⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⡏⣿⠆⡴⣎⣾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠛⠛⡋⠓⠳⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠀⠀⠀⣿⢀⠀⠄⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠂⠈⠀⠞⠀⠀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠐⠀⠀⡀⠈⠀⠀⠠⠀⢁⠀⠀⠀⠄⢀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠁⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢠⠀⠄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀⠀⠐⠄⠀⠔⠀⣨⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣁⠴⢏⠀⢀⣁⡠⠚⠦⡨⠤⠞⠉⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⠀⠀⠀⠀⠀⠀⠑⠋⠁⠁⠀⠀⠈⠉⠁⠀⠀⢀⣀⣀⡀⠀⠀⠀⠘⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠤⠤⣄⣀⣀⣀⠀⠀⠀⣀⣉⣉⣀⣀⠤⠤⠴⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠒⠃⠀⢀⠀⠁⠙⢳⣄⡀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀⠠⠤⠂⠀⠐⠁⠀⠠⢤⡆⠀⠉⠒⠉⠐⠂⠈⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠉⠙⠒⠚⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡠⠄⠀⠀⡄⠀⠀⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠊⠀⣀⡰⠁⡠⠀⠒⠒⠉⠉⠉⠋⠉⠑⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡐⠁⡠⠊⠀⠀⡀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠠⠞⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠀⠀⢠⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠖⠁⠀⠐⠄⠀⠀⣀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠢⣀⣀⣀⡀⠀⠀⠀⠠⠂⠀⠤⠒⠂⠐⠢⠀⣀⢀⠆⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠁⡀⠀⠉⠓⢐⠒⢤⣀⢀⣀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠂⢄⡀⠑⠄⠈⠓⠀⠀⠈⠶⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⣤
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⡀⠀⠀⢦⡁⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⡄
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠤⠔⠂⠀⠀⠀⠠⠒⠊⠈⠉⠀⠀⠀⠀⠀⠘⠆⠠⠈⠑⢦⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⠤⠔⣀⣠⠤⠢⡤⠤⠤⠶⠠⠶⣂⣚⡦⣀⣀⡀⢧⡀⠀⠀⣵⡀⠀⠀⠀⠉⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠉⠒⠎⠉⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⡞⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣻⣧⠈⣿⣿⣹⣟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⠋⣋⢙⣾⣿⡞⠀⠀⣾⣿⠦⢼⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠋⣴⠞⠉⠈⡉⣻⣿⠀⢈⣈⣸⡆⠀⢰⣀⢻⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠛⠉⠃⢰⣷⣉⡤⣤⣅⡭⢻⠇⠀⠺⣉⣩⣧⢀⠀⣟⠀⢹⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⢴⠟⢹⣦⢠⡀⠰⢷⡿⠐⠀⡾⠸⣿⡿⣿⠀⠈⣷⠈⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⣠⠏⣄⠉⢀⠝⢹⢿⣿⠗⠠⢾⠦⣶⣼⡇⡏⠀⠈⢻⣦⣠⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⢒⡶⠛⠖⠛⠃⠈⠸⣇⣼⡿⡤⠒⢦⠀⢘⣾⣧⣼⡀⠀⠋⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠀⠀⠀⠠⣖⠟⠀⠀⠀⠀⢠⢀⡼⣿⣿⡴⠁⠀⠈⠀⢸⣿⣿⣼⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣴⣤⣼⠋⠀⠀⠀⣠⣇⠀⢠⣿⣿⣎⠀⠞⠛⠠⠤⢾⣿⣿⣻⡗⠀⣰⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠐⠊⢈⠄⢈⣻⣿⢿⡿⢷⡴⢃⢊⡀⣀⣼⠟⣿⣧⣄⡐⠉⢁⡠⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣏⣀⠀⠄⢴⠈⣶⡞⣹⣓⣿⡟⠹⠁⢸⡾⢻⣿⠏⠉⣹⣿⣘⡁⠰⢻⡁⣠⣼⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣤⣴⡘⡛⢩⣿⣿⣿⣏⡀⠀⢛⡅⢰⡈⣽⣿⣿⣿⣾⣿⣇⣀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡴⣉⠀⠤⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠶⠶⢶⣶⠶⠶⠶⣶⠶⠶⠶⢶⡶⠶⠶⠶⣶⠶⠶⠶⢶⡶⠶⠶⠶⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣸⣧⣀⣀⣀⣿⣄⣀⣀⣸⣧⣀⣀⣀⣿⣀⣀⣀⣸⣇⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⢹⡟⠉⠉⠉⣿⠉⠉⠉⢹⡏⠉⠉⠉⣿⠉⠉⠉⢹⡏⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠿⠷⠶⠶⠾⠿⠶⠶⠶⠿⠶⠶⠶⠾⠿⠶⠶⠶⠿⠶⠶⠶⠾⠷⠶⠶⠶⠿⠶⠶⠶⠶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⡉⠉⠉⠉⢹⡏⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⢸⣿⠀⠀⢰⣟⣻⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢙⣛⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣟⣻⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⡾⠛⠛⢷⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⣿⠀⠀⠀⠀⣻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠻⣦⣀⣀⣴⡟⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⣉⣉⣁⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⠿⠻⠿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⢿⣦⡈⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡤⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢯⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⡇⠀⣀⣤⡖⢻⠉⢙⡗⣶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⣿⡞⢻⣠⡷⢾⡋⠹⡗⢿⣤⣏⢹⠗⣶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢾⢻⣿⣿⡿⢻⣅⣿⢼⡗⠺⡧⣿⣀⡏⢹⠓⣿⣤⣏⣽⠓⡶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢻⣁⣧⢾⣿⡟⣿⣿⠾⡏⣻⣼⡷⠾⡧⣿⣈⡟⢻⠦⣿⣸⡏⡿⢻⡧⣾⣨⡟⢳⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣿⣋⢙⣠⣴⠟⣟⣿⠶⣟⢹⣤⡷⠶⣧⣾⣙⡟⢾⢤⣿⣸⠛⡷⢾⣧⣟⠘⢛⣻⡶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣟⢻⣶⣴⣞⠛⣸⡦⢿⣹⣧⣿⣾⣷⣾⣙⡗⢾⣤⣏⣹⢻⡧⣜⣀⣨⡟⣿⣾⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢻⣷⣷⣾⡟⣻⣶⣟⡻⢿⣽⡿⣯⣷⣿⣽⡿⣤⣏⠻⢺⣥⣞⣻⣻⡷⣿⣹⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠻⣧⣿⣾⡟⢻⣤⣏⣹⠛⣦⣿⣃⠞⢋⡷⠟⣛⡭⣿⢻⣤⣿⢻⢻⣧⣿⣻⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⡟⣧⣼⣙⡷⢾⣄⣏⢹⠳⣷⣼⡏⢻⠚⠒⢾⢉⣧⣿⢻⣅⣿⢿⢿⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⡷⣿⣼⡉⡷⢾⣅⣟⢻⠶⣿⣸⡏⢻⠶⠶⢾⠛⣇⣿⢾⡏⣧⣼⢺⣏⣯⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢿⣼⡟⣷⢼⣇⣿⢻⡦⣿⣈⡟⢻⠦⢤⣾⠾⣏⣿⢼⡟⣇⣼⢾⣻⣧⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣼⡏⣿⢺⣧⣿⠙⡷⢾⣤⣀⣼⠾⡏⣹⣼⡟⣏⣽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢼⣇⣿⠛⣧⣼⣀⣀⣸⣴⡟⢻⣨⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣇⣸⠉⠉⢹⣠⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⡀⠙⢦⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣠⠞⠀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡴⠁⠀⠀⠓⠦⣌⡙⢲⠄⠀⠀⠀⠀⢠⠖⣺⡏⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡼⢸⠁⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠤⣤⣤⠤⠤⠤⠤⣤⣤⠤⠤⠤⢤⣤⡤⠴⠧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢦⣠⠞⠁⠈⠳⣄⣠⠞⠁⠈⠳⣄⡴⠋⠀⠈⠢⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠙⢦⡀⠀⣠⠞⠳⣄⠀⢀⡴⠋⠳⣄⠀⢀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠾⠶⠶⠶⠿⠾⠷⠶⠶⠶⠷⠿⠶⠶⠶⠾⠷⠿⠾⠷⠶⠶⠶⠶⠶⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣵⡾⣙⢿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣾⡿⣸⢯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣭⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡋⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⢙⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠰⠦⠤⢤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⢲⡴⠤⢄⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣚⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣤⣤⣤⣤⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢷⣶⣦⣤⣤⣾⣿⣿⣿⢿⣿⣿⡿⣷⣶⣿⣶⣦⣽⣿⣿⣻⣿⣶⣴⣦⣤⣴⠉⣴⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠉⠉⠛⠻⠋⠙⠛⠛⣿⣶⣿⣿⣽⣽⣿⣿⣿⣋⣛⣛⡿⠛⣛⣋⣵⠞⠑⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠃⡰⠋⠀⠀⠀⣭⡉⢉⡉⣉⡙⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠋⣰⠃⠀⠀⠀⠀⣙⠁⣹⡁⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠛⠀⠛⠁⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠛⠙⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠉⠉⢉⣏⠉⠉⠉⣹⡉⠉⠉⠉⣟⠉⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠉⠉⠙⡏⠉⠉⠉⢹⠋⠉⠉⠉⣟⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⡟⠛⠛⠛⢻⠛⠛⠛⠛⡟⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠺⡷⠒⠒⠒⢾⠗⠒⠒⠒⣿⠒⠒⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠶⠷⠶⠶⠶⠾⠶⠶⠶⠶⠿⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡆⠻⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣯⣽⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣭⣿⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣠⣾⠟⠛⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠻⢷⣆
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⡿⢿⣿⣿⠿⢿⣷⠀⠀⢠⣿⠿⢿⣷⢠⣤⣤⣤⡄⠀⢰⣿⣿⠿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠘⣿⣿⢀⣾⣧⣼⡿⠿⣿⡇⣼⣯⣼⣯⠉⣿⣧⣤⣿⣿⣿⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢿⣇⠀⣿⡇⢸⣿⠉⣿⡇⠀⣿⠃⣿⠋⢹⣿⠀⣿⡏⢹⣿⢹⣿⡿⢿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡀⠀⢸⣿⢀⣿⡇⣸⣿⢀⣿⡃⢸⣿⢀⣿⡀⢸⣿⠀⣿⡇⣸⣟⣸⣿⡇⣸⣗⢀⣿⡇
⠀⠀⠀⢠⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⡄
⠀⠀⠀⠘⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠃
⠀⠀⠀⠀⠀⢻⣇⢠⣾⠆⠀⣼⡗⠀⢠⣾⠇⠀⣰⡿⠀⠀⣴⡷⠀⢠⣾⠇⠀⣠⣿⠂⠀⣴⡿⣸⡿
⠀⠀⠀⠀⠀⠘⣿⡌⠁⢾⣧⠉⠀⢿⣎⠁⠸⣷⡌⠁⢺⣧⠉⠀⢿⣦⠁⠰⣷⡌⠁⠸⣷⡉⢀⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣧⣶⠆⠉⣴⡦⠈⢁⣴⡆⠈⢡⣶⠀⠉⣰⡶⠀⢁⣴⡆⠈⢡⣶⠄⠉⣰⣾⡟
⠀⠀⠀⠀⠀⠀⠘⣿⡏⢶⣆⠛⠀⣶⡌⠋⢰⣦⡙⠁⢴⣦⠙⠁⣶⣌⠋⠰⣶⡙⠃⢰⣦⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡌⠛⣠⣤⠈⠋⣤⡄⠙⢁⣤⠀⠛⣠⣤⠈⠋⣠⡄⠙⢃⣤⡄⠙⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠛⠁⠀⠘⠛⠀⠀⠛⠋⠀⠀⠛⠃⠀⠘⠛⠁⠀⠘⠋⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⡟⠉⣿⣛⢻⣛⣻⣛⣟⣛⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠷⣄⡀⠀⠀⠹⣦⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⡾⠃⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⣴⠏⠀⠀⢀⡾⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣄⣠⠞⠁⠀⠀⠀⠘⠷⣤⣀⡀⠈⠙⠳⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⡞⠻⣧⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢰⡏
⠀⠀⠀⠀⠀⠀⠀⢾⣿⠛⠛⠛⠛⠛⠛⢛⡿⢿⣟⠛⠛⠛⠛⠛⠛⣻⡿⢿⡟⠛⠛⠛⠛⠛⠛⣿⠿⣿⡛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠳⣄⠀⠀⢀⡴⠋⠀⠀⠙⢷⣄⠀⠀⣠⡾⠋⠀⠀⠙⢦⡀⠀⠀⣠⠞⠁⠀⠈⠻⣦⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢻⣶⠋⠀⠀⠀⠀⠀⠀⠙⢳⣾⠋⠀⠀⠀⠀⠀⠀⠙⣶⡞⠁⠀⠀⠀⠀⠀⠈⢻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡴⠋⠉⠻⣄⠀⠀⠀⠀⣠⡾⠋⠙⢷⣄⠀⠀⠀⠀⣠⠞⠁⠙⢦⡀⠀⠀⠀⢀⣴⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣆⣠⡾⠋⠀⠀⠀⠀⠙⢷⣄⣠⡞⠁⠀⠀⠀⠀⠙⢦⣀⣴⠟⠁⣾⠁
⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠈⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠙⢻⣦⡀⢠⡴⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠋⠈⣷⠀⣀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢠⡟⢀⡈⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤⠶⠋⠀⠈⠙⠂⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣟⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⢛⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⡾⠁



⡟⠙⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡟⠙
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⢀⠖⠢⡄⣤⠐⡶⠂⢠⡄⠀⡴⠢⡀⡄⠀⠠⠖⠂⠀⢠⠐⠀⠒⡖⠂⡔⢢⡀⡤⠒⢄⢠⠄⡤⢠⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⠀⢀⡇⣿⠀⣯⢀⡶⠸⡀⡟⠘⡄⡇⠀⢸⠃⠀⠀⠈⠑⡆⠀⡇⠀⡗⢺⡸⡇⠀⣸⢰⠟⣄⢸⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣾⣿⣷⣶⣿⣶⣷⣾⣶⣶⣶⣿⣿⣶⣿⣿⣶⣿⣷⣶⣾⣿⣶⣶⣷⣶⣷⣶⣷⣾⣿⣷⣾⣶⣾⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡟⠛⠛⢿⡟⠛⠛⢿⠟⠛⠛⣿⠟⠛⠛⣿⠟⠛⠛⣿⠛⠛⠛⣿⠛⠛⠻⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣼⣧⣤⣤⣼⣧⣤⣤⣼⣤⣤⣤⣿⣤⣤⣤⣿⣤⣤⣤⣿⣤⣤⣤⣿⣤⣤⣤⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⡀⣀⣀⣀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⡴⠶⢦⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢾⡁⠀⢀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠈⠛⠓⠛⠁⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠙⠳⠶⣤⠴⠾⠋⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⡴⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⢩⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉⢻⡋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣶⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣶⣿⣅⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢦⣰⠟⠛⠳⣶⠚⢳⡶⠷⣄
⠀⠀⠀⠀⠀⢠⣤⣴⣿⣥⣤⣤⣿⣦⣤⣤⣼⣿⣯⣤⣤⣼⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⡀⠀⢀⡀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠙⠋⠀⠘⡛⠀⠀⢛⠃⠀⠙⠋⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠻⠃⠀⠘⠟⠀⠀⠻⠃⠀⠘⠟⠀⠀⡿
⠀⠀⠀⢠⣤⢤⡼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⢀⡄⠀⠀⠀⢸⡇⠀⣿⢹⡇⠀⠀⠀⣿⠀⠀⠀⢸⠇⠀⠈⠻⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠋
⠀⠀⠀⠀⢹⡄⠀⠈⣧⠀⠀⠀⠈⠛⠛⠃⢸⡇⠀⠀⠀⣿⠀⠀⠀⣾
⠀⠀⠀⠀⠸⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⢀⡏
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⠄⢠⡾⠃⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⡀⠀⠀⡀⢀⡀⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠈⠁⠉⠀⠁⠈





⠀⢸⡟⠙⢳⡄⢸⣏⣉⠀⢽⡋⡉⠀⣿⠙⣷⠀⠀⢰⣟⠉⠁⢸⡏⢻⡆⠘⣧⣰⠏⠀⡇⠀⣿⣧⡀⣿⠀⣴⠟⠉⠃
⠀⢸⣇⣀⣼⠇⢸⣏⣉⠀⢾⣉⡉⠀⣿⠛⠉⠀⠀⢸⡟⠉⠀⢸⡟⢿⡀⠀⢸⡏⠀⠀⡇⠀⣿⠈⢷⣿⠀⢿⣄⢙⣿
⠀⠀⠉⠉⠁⠀⠈⠉⠉⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠉⠀⠈⠁⠀⠀⠁⠀⠉⠀⠈⠉⠀⠀⠉⠉⠉
⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⣼⠋⠉⠁⣰⠏⠉⢻⡆⢰⡟⠉⠹⣦⠀⣿⣰⠟⠀⣿⠀⢸⠿⣄⢸⡇⢠⡟⠉⢉⠀⠀⠀⣿⡉⣹⡆⢀⡟⢻⡀⠀⡿⣧⡀
⢿⣄⣀⡀⠻⣆⣀⣸⠇⠸⣧⣀⣠⡟⠀⣿⠙⣧⠀⣿⠀⢸⠀⠹⣾⡇⠘⣧⣈⣹⡇⠀⠀⣿⠋⠉⠀⣼⠷⠺⣧⠀⡇⠈⢷
⣶⣿⣿⣷⣶⣿⣿⣷⣶⣶⣾⣿⣿⣶⣶⣿⣶⣾⣷⣿⣶⣾⣷⣶⣿⣷⣶⣾⣿⣿⣶⣶⣶⣿⣶⣶⣶⣿⣶⣶⣿⣶⣿⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣶⣖⡲⢄⡀
⠀⠀⠀⠀⠀⢀⣠⢴⣎⡉⢶⠄⠺⣻⣿⣿⠀⣹⡆
⠀⠀⠀⠀⢰⠋⢺⣟⢿⣿⡆⠙⣃⣈⡭⠖⠂⣸⡧⢤⡀
⠀⠀⠀⠀⠘⡗⣤⠤⠽⠛⠋⢹⣧⣼⣿⣾⠿⢋⣩⣵⣮⣶⣄⡀
⠀⠀⠀⠀⠀⡇⢸⢀⡴⠒⡫⠟⢛⡿⡴⠛⢻⠋⡴⢁⡇⢨⡙⠿⣦⣀
⠀⠀⠀⠀⠀⢹⢸⡈⡷⣜⢇⠀⣏⢰⠃⠰⠂⠼⢡⠏⣟⢆⢳⢣⣻⡛⢷⣦⣀
⠀⠀⠀⠀⠀⢸⡘⡇⣇⡈⠳⣕⢾⢻⣴⠃⡜⢠⠏⠘⢻⡈⢆⢢⢡⡓⡱⡉⣯⡓⣮⡑⢦⡀⡀
⠀⠀⠀⠀⠀⠀⡆⣁⢹⢸⠀⠈⠳⢝⢯⣻⣤⡆⡼⠁⠾⠣⡘⠆⠃⠓⡱⡀⡟⢏⣗⡛⡿⣍⡉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠙⢿⣸⣿⠀⡴⠓⢦⡑⢿⡧⣹⢷⡛⢻⡿⢷⣜⡆⢣⡱⢝⡟⢎⡇⣳⣼⡲⢝⡲⣄⡀⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⡁⠀⠀⠈⠳⣝⠮⡳⣽⡳⣖⠈⢛⠻⢦⣄⢹⣧⡼⣿⣭⢜⣠⠴⢹⠲⣝⠂⣀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠑⢤⡀⠀⢀⡘⢳⠈⠪⣑⢯⡹⡖⢒⡾⣻⣩⢷⣟⠭⣺⠏⠀⡄⡞⠀⠈⠑⢮⣣⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡁⠀⠀⠙⠦⣜⣀⣸⠀⠀⠈⠳⣝⡓⢚⣚⠭⠒⠉⠓⠊⠁⠀⢀⡇⡇⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣙⣦⡀⠀⠀⠀⠙⠛⠁⠀⠀⠀⡀⢹⠉⣄⠀⠀⠀⠀⠀⠀⠀⢸⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢷⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣦⡀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢦⡀⠀⠀⠀⠘⢸⠀⣇⠀⠀⠀⠀⠀⠀⢀⣠⠜⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢦⡀⠀⢸⠘⠀⢠⠀⠀⠀⣀⠤⠒⣉⡭⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢦⣈⢸⣀⣀⡤⠖⣋⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠛⠏⠙⢃⡖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⡤⣴⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣠⡀
⢰⣆⣀⣀⡀⢀⡀⢀⣀⣸⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⠀⠠⠈⠀⣀⡤⠤⠶⠛⠳⠦⠤⣄
⢸⡇⢀⠉⠁⠀⠉⠀⠀⢸⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⡀⠲⠿⠶⠶⠶⠶⠶⠶⢶⡾⠷
⢸⡇⢸⠐⠚⠚⠘⢸⢺⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡷⠒⠂⠒⠒⠒⠂⠒⠒⢾⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠒⠒⠖⠒⠒⠒⠒⠒⢺⡇
⢸⡇⢼⣀⣘⣘⣈⣸⣘⣸⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠐⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠈⠷⢦⠤⠤⠤⠤⠤⠤⠤⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠦⠤⠦⠤⠤⠦⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠤⠤⠤⠤⠤⠤⠤⠾⠁

⠰⡋⡣⠰⣏⡳⠀⣏⣱⠀⢎⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢠⠏
⣠⠾⠶⠶⠾⠶⠶⠶⠶⠶⠶⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢛⠛⠛⡛⠛⠛⠻⢛⠛⢳⡄⠂⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⢠⠏⠀⠀⡄
⣿⠀⠀⠀⡴⠀⣤⠀⡰⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠉⠓⠲⢶⠿⠶⠖⠊⣥⣀⡀
⣿⠀⣀⠀⠁⠀⠃⠀⠃⠀⡀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⠀⠄⠀⠤⠀⡀⠀⢸⡇⢭⠨⡅⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣤⣠⣤⣾⣿⣤⣄⣀⣤⣿⠉⠁
⣿⠀⣹⣤⣤⣤⣤⣤⣤⣴⣃⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣳⣄⣀⣀⣀⣴⣋⡀⢸⡇⣻⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠿⠋⠀⠀⠀⠀⣿
⠙⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⠿⠿⠿⠿⠿⠿⠿⠷⠞⠁⠺⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⣀⠀⠐⠈
⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⣼⠟⠉⢷⡀⠀⠀⠀⠣
⢀⡙⣬⣴⣃⡀⠀⢠⠏⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⢳⣴⠟⡡⢀⠕⠀⠙⢦⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡇⠀⡀
⠈⠴⢋⡛⠆⠁⣾⠈⢦⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣠⠟⠡⡊⠒⠀⠀⣠⡴⠚⠋⡝⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣾⠁⢠⠏
⠀⠀⠈⠁⠀⠐⠿⠇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣀⡴⠛⠁⣦⠀⠀⠧⠸⠀⢠⡄⠀⠀⠀⠀⠀⢤⡀⠘⠁⠀⠃⠀⠘⠀⢀⣤⣠⣤⣤⣤⣶⣶⣶⣦
⡷⠤⠶⠦⠴⠶⠤⠶⠦⠴⠶⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢻⡓⠒⢒⠒⠒⣻⠁⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠾⠉⠁
⠻⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⣤⣈⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠀⣿⠀⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⢠⡄
⠀⠀⠀⢸⡿⠇⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢿⡀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢻⠆⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⣉⠉⣉⠉⢉⠉⢉⡉⠉
⠀⠀⡀⠀⠋⠀⠀⠀⠉⠓⠒⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠾⠾⠆⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⣿⠀⠰⠇⠀⠯⠀⠾⠀⠼⠄
⠀⠀⣷⠤⠶⢤⠴⠦⠤⠶⠤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠴⠶⡤⠶⠤⠴⠦⠴⣿⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠖⠚⠛⠛⠛⠛⠛
⠀⠀⣯⣀⣂⣀⣓⣀⣀⣈⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣊⣂⣀⣂⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠀⢿⣈⣓⣒⣒⣒⣒⣒⣒⣒⣚⡁