Messy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⣩⠦⠔⢒⣒⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡡⠞⠉⠀⠀⠀⣭⣽⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢮⣡⠋⠀⣀⣠⠴⣶⠺⡉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠚⠛⠛⠋⠟⠁⠀⠀⡷⠶⣫⡬⣿⠒⢋⡳⠃⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠀⠀⠀⠸⠀⣀⣠⣤⠓⠂⠁⠀⡿⠒⠉⡀⣠⠊⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡶⠒⠚⠁⠀⠉⠙⣒⠾⠋⠁⠀⠀⣱⠀⠀⠀⣳⠄⠒⠈⣳⡀⠀⠀⡇
⠀⢀⡤⠖⠒⠋⠉⠉⠁⠀⠀⠀⢀⡠⢤⣚⣉⡄⠀⠀⠀⠀⠀⢾⠄⠀⣜⠁⠀⠀⣠⠾⠤⠤⠾⡁
⠀⠈⠓⠶⠤⠤⠤⠐⠒⠒⠈⠉⠁⠀⠀⠟⠛⠒⠈⠉⢉⡗⣺⠛⠀⠀⠈⠓⠛⠋⠀⠀⠀⠀⠐⠚⠋⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣉⣉⠛⠧⠞⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠈⠃⠀⠀⠀⠀⠀⠠⠔⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⢀⠤⠎⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡄⠀⠀⠘⠲⠤⠖⠒⠉⠓⢤⣀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠄⠀⠀⠀⣀⠔⠁⠀⢸⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣤⣤⣄⣀⣀⠀⠀⣀⣠⠴⠊⠁⠀⠀⠀⡆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡏⠉⢷⠤⣄⠈⠉⠉⠉⠀⠀⠀⠀⠀⡤⢌⣳⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡀⢸⠄⠀⠀⠀⣠⠤⠤⠤⠞⠀⠉⠒⠉⠀⠉⠉⠉⠉⠉⢳⣀⣠⣤⣤⠇⡀⢙⡅⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢍⡿⠛⠘⣆⣠⠴⢻⡆⠀⠀⠀⠀⣀⠀⡀⢀⠤⡀⢄⠀⠀⠈⡇⠒⠒⢲⡄⣹⢯⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡧⠴⡅⢠⡔⠊⢯⡇⠀⡀⠀⠀⡛⠢⢠⡸⣀⣄⠈⢦⠤⣀⡇⠀⠀⠀⠉⠹⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠚⢹⡖⠃⠀⠘⠷⡏⠀⢀⢄⠸⣐⠄⣎⡂⠸⠚⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢊⠉⠁⠀⠀⠀⠰⠀⠀⠘⠤⠃⠾⠀⠀⠀⠀⢀⣀⣘⡆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢰⡆⠀⢠⣇⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⡗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣸⠛⠛⠋⠉⠉⡽⢩⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣠⣤⣤⣧⣼⣤⠤⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣗⢲⠤⠤⠤⣤⣤⣇⣀⣠⢤⠴⢓⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢻⣉⠤⠒⣫⠕⠋⠪⢶⣤⣘⣉⡇⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠭⠤⠖⠚⠉⠀⠀⠀⠀⠀⠈⠙⠛⠭⠭⠝

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⢐⠥⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣠⡄⣀⡀⠀⠀⠈⠁⠐⡆⠃⠀⠀⠀⠉⠐⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢤⢁⣩⠀⠀⠀⠛⠒⡋⠀⠇⢇⣀⢄⢀⢀⠀⠀⣠⠊
⠀⠀⡠⡂⠤⢀⣀⠀⠀⠀⢀⠂⠠⠖⢢⠄⠀⠀⣈⢁⡀⠀⠠⠀⠀⠈⠉⠓⠥⣅⣠⡧⠟⠒⠄⡀
⠀⠀⠀⠙⠮⣄⣀⠌⠄⢘⠓⠰⢞⠋⠀⠀⠤⢬⡍⠅⠀⡠⠁⠐⠀⠀⠀⠀⠀⡠⠛⠷⢬⢭⠵⠮⠷⣄
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⠤⠥⣌⣑⣤⣘⣛⡀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠐⠐⠀⢌⣸⢂
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢒⡒⣶⢤⡤⠀⣀⣀⣀⡀⠠⠊⣠⣍⠐⠂⠤⢀⠀⠀⠀⠀⠀⠁⠂⢤⠔⠁⠠
⠀⠀⠀⠀⢀⠰⠍⣀⠀⠀⠐⠈⠀⢀⣀⡒⠷⠒⠀⠀⠚⠛⠋⢀⣀⣼⡶⠤⠄⠉⡆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣈⠁⠈⢀⠔⠊⠉⠁⢈⣉⣈⠉⠒⠂⠤⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⡀⠀⠈⠒⠁⠀⠀⢀⠔⢁⠶⠤⠈⢁⣐⠒⠶⢅⠴⠍⠁⠀⣂⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣈⠉⠂⠠⢤⣐⣊⡡⠎⠙⠈⠠⠔⡩⠁⠈⢀⣾⠦⠄⠀⠈⢀⠴⠒⠉⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⢥⣀⡙⠲⣖⡡⠴⠊⠍⠀⢀⣠⠶⡹⠊⡠⠷⠂⢀⠊⢛⠶⠡⠤⣴⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠠⢌⠉⠘⠚⠹⠵⠲⠾⠟⣛⡒⠀⠠⠒⠂⠅⡠⠃⠀⠆⢐⠴⠋⠀⠐⣂⠍⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢄⡢⢕⠨⠒⢈⡐⠤⢄⠀⠀⠀⠀⠀⠈⠉⡒⠢⠤⢊⡀⠀⢀⠀⢒⠢⠀⣀⡊⠁⢀⠯⣮⣷⠡⠱
⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⠐⠠⠄⠀⢀⠠⢉⠲⠖⣒⣭⠴⠦⣄⡀⠀⠀⢇⠁⠒⠒⠠⠤⠎⣘⡚⠂⢀⣤⢐⠂⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠈⠀⠈⢠⠖⠁⠈⠙⠣⣤⣘⠙⡆⠀⠈⠳⣕⡀⡀⡠⡠⠀⢸⢀⢒⠤⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠔⠁⠀⠀⠀⠀⠀⠀⠉⠓⠃⢂⠀⠀⠀⠉⠙⠒⠲⠵⣭⣿⣅⣀⡤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠑⠡⠂⠋⠐⠕⠅⠠⠂⠄⠀⠨⠂⠀⠢⠊⠔⠀⠊⠔⠐⠁⠪⠂⠐⠅⠀⠠⠠⠠⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣄⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⡀⠀⠀⠀⠀⢠⣠⡿⢻⡿⣿⣿⡿⣻⣟⣭⠿⣛⡛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡴⠋⠒⠤⢀⣴⣿⣟⡃⢿⣽⢡⠟⣷⣿⡟⠑⠉⣀⣀⠀⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⡙⠲⢤⣀⠻⣟⠻⣵⣸⣿⣿⢀⣿⣿⣇⣰⣿⣭⢿⡋⢻⢹⡏⢿⡉⢶⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⠻⣷⣦⣍⠳⣌⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣅⠸⣇⠀⠀⣧⠘⣷⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠳⠦⡉⠛⣧⠙⢆⠈⠻⣿⣿⣿⣿⣿⡿⣇⠛⢻⣷⣌⡛⠶⣌⠓⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⣄⠈⠣⡈⠷⣤⡞⠻⣯⡉⣿⣧⣼⣿⣦⠰⣍⡻⢦⡙⣦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢆⣽⡿⢦⢀⣶⣾⣷⣦⡈⣿⣇⣨⡁⢙⣿⣷⠮⢉⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢉⡴⠞⠉⣹⢳⡟⣳⣿⣿⣼⣿⣿⣿⣏⣹⡟⣹⠎⡉⢹⣟⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡄⠻⠒⣨⣽⢿⢋⡝⠙⣿⢋⣿⢹⣿⢻⡿⣿⡿⡿⣿⣽⠛⣾⡿⢃⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠟⢁⣴⣿⣿⢳⣾⣿⠁⡾⢨⢸⡇⣸⣿⡜⡷⢹⢻⡇⠹⣿⣿⢿⣡⠞⠁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⢻⣿⣿⡏⣸⣿⣿⣤⣷⢨⣿⣇⣿⣿⣧⢧⢸⠈⣿⠀⣿⢿⣧⠙⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣸⣿⣿⡗⢸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣞⣴⣿⣇⣿⣾⣿⡄⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣷⡸⣿⡿⢿⣿⠿⠿⢿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠉⠉⠛⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣻⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⡀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡏⢹⣷⡄⠀⣀⣭⣿⣧⣈⣉⣼⡟⠻⣿⣦⡝⢊⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢁⡴⠟⢁⠎⡾⣡⣽⣟⣿⠋⠙⣿⢡⡾⢩⠅⡀⣩⠞⢰⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⢀⣰⠟⠰⠐⡁⡟⣿⠏⠀⠀⠹⡟⢡⠏⠎⡴⢃⣴⠟⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠁⣴⠃⡼⢀⡼⠋⠀⠀⠀⠀⠙⢏⣠⡾⠑⣼⠃⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠻⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⢀⠀⠀⢀⠀⠀⣀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠶⠀⣻⡀⡇⡌⠀⠀⢿⠀⡇⡜⠀⠀⢘⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡇⠀⡇⠛⡇⢧⠀⠀⠈⠻⠀⡇⠀⠀⢸⠀⡗⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠉⠁


⣤⣤⣤⣄⣤⣀⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣤⣀⣤⣀⣤⣄⣠⣄⣀⣀⣀⣀
⣿⣛⣟⢻⣛⣿⣋⣙⡛⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣛⣙⣟⣛⣻⣿⣟⣻⣿⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠈⢷⡯⡄⠂⣴⠂⡂⢰⣾⠐⣫⡯⠬⡷⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣇⡼⣤⠈⠃⡷⠟⣻⣬⡏⣤⡟⠀⡀⡶⢰⣁⣠⣄⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠍⣆⠁⠰⣰⣿⢺⢚⣠⠋⢀⡿⣉⠽⠻⡟⡟⢷⣾⠍⢩⣔⠃
⠀⠀⠀⠀⠀⠀⢰⠃⣰⡋⠒⢻⣽⢹⣼⠟⣟⣼⣇⠱⡽⣟⢦⣤⣹⡴⣟⣳⠟⣿⠁⡁
⠀⠀⠀⠀⠀⠀⣘⣶⠏⣿⣿⣞⡹⢾⣽⡿⠟⣱⡟⣺⣿⢘⢮⣟⣿⣄⡅⣀⡶⠄⠀⡗
⠀⠀⠀⠀⡜⢊⡭⠿⠺⡟⢳⡞⠿⢸⣼⣿⣟⣭⡿⣿⣿⡀⢞⣤⡿⣿⢳⣿⡻⣆⡿⢁⠆
⠀⠀⠀⡀⠀⠘⠒⠉⣎⣤⣾⣿⠘⢻⣟⢿⣯⣿⡟⣹⠸⠙⢻⣏⡰⡿⡀⣹⣏⣹⠉⠋
⠀⠀⠀⠀⢸⣧⣾⣀⠞⢻⣯⣭⠙⣗⢰⣞⣿⣷⡿⣷⢠⠳⣷⣟⣷⣿⠷⣿⣿⣃⡏⢠
⠀⠀⠀⠀⠈⡀⢫⡟⢏⣰⣞⠧⣕⣏⡹⢻⣷⣼⠀⠎⠈⠧⠹⣹⣿⣉⠦⣿⣿⣿⡿⡸
⠀⠀⠀⠀⠘⠉⠈⢹⣻⡄⣽⣶⡿⣮⢻⣯⣿⣁⣷⣠⣾⠚⣾⣏⠟⠑⢮⣼⣸⣿⣰⢧⠐
⠀⠀⠀⠀⠀⢹⣅⣡⣷⣿⢹⡿⣇⣧⣟⠃⡟⣁⡟⢉⣿⣭⣿⢿⡆⠒⣬⣿⢹⣇⣀⣟⠠⠈
⠀⠀⠀⠀⠀⠀⢾⠈⠙⢈⣿⣿⣿⠳⣿⣷⣶⠏⢹⡏⣽⡿⢙⢯⡠⣶⣻⣏⠀⣿⡊⠻⡖⠒
⠀⠀⠀⠀⠀⠀⠈⠒⢱⡜⠉⣾⣷⠖⣿⣿⣇⣸⢌⡑⢫⢹⡋⡑⠀⡽⠀⢿⣽⡿⡇⢀⡁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⣿⣭⣉⣿⣞⣡⣽⡰⢷⠈⢾⠹⠅⠒⢣⣠⣿⣅⣳⣴⡍⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡧⠁⠀⠀⠈⠈⠱⠎⠑⠀⢧⠀⢀⠀⠉⠟⣯⠙⢿⣷⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠒⣿⣋⡧⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣟⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⡄

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠴⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠐⠲⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡅⠀⠝⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠄⠀⠤⠀⠀⠀⠀⠀⠠⠾⠥⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣈⠲
⠀⠀⠀⠀⠀⠀⠀⢄⠬⢞⣿⠀⠀⠀⠀⠀⠀⠐⠐⠀⠛⠒⠲⠤⠀⠀⠀⠀⠄⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⠛
⠀⠀⠀⢀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢒⢀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡄⣤⡀⢠⠆⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠘⠈⠁⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⡀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⡀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡠⠀⠁⠒⠄
⠀⠀⠀⠀⠰⠀⠀⠁⣁⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠁⠀⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠁⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⠠⠀⠠⠀⠀⠀⠀⠀⡀⠘⠒⠒⠀⢤⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡀⠀⠀⠀⠀⢀⣐⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠸⢳⣆⠀⠘⠈⠙⠁⠂⣶
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡉⠀⠀⠀⠀⠈⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠘⠛⢦⣌⠁⠀⣁⠲⠖⠛⠚⠛
⠀⠀⠀⠀⠈⢁⠠⠉⠈⠉⠋⠭⠀⠀⠀⠀⠁⢠⠀⠁⠅⠀⠀⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠴⠍⠋⠁⠀⡀
⠀⠀⠠⠤⠴⠀⠠⢀⠔⠒⠉⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠂⠀⠀⠂⠀⠀⡀⠑⢤⣤⡑⣀⡍
⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣤⠀⠐⣶⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠁
⠀⣰⠖⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⠛⠃⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠨
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡄⠀⠀⠠⠒⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣠⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⢀⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠦⠀⠀⡚⠙⡁⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⠋⠁⠀⠠⠐⠠⠈⠋
⠀⠀⠀⠀⠀⠄⢆⠉⠀⠁⢈⣀⡀⠀⠀⠀⠐⠦⠚⠀⢀⡀⠦⣄⠐⠂⠀⠀⠀⠀⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠀⡀⠀⠁⣴⡆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠊⠈⠁⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢀⠀⠀⠀⠀⠀⢀⢀⡰⡔
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⣐⢂⠌⠠⡑⠮⠕⢉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢜⠓⠛⠐⠠⠝⠑⠦⠓⠆⠠⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠞⠃⠞⠀⠀⠸⡀⠀⠀⠀⢀⠄⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⡌⠓⣄⠀⠀⢣⢀⠀⡰⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠧⠒⢬⠦⠀⠈⠶⠉⠱⡾⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠸⡀⣺⠧⠄⠰⠎⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠠⢉⠇⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢲⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⡀⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠽⠍⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠀⢾⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⡉⠀⠉⣇⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠑⠛⠤⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣧⢽⠀⠀⠈⡓⢨⠦⢄⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠐⠂⠤⣀⡉⠑⠒⠂⠤⠤⠄⠀⢀⠀⢣⠰⢿⡓⢊⣠⠁⠀⣠⠋⠀⠀⢨⡉⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠐⠢⠄⣀⠀⣠⠂⠑⢆⠀⠀⠉⠀⠉⡠⠊⠁⠀⠀⠀⠸⣁⠁⠢⢀⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠁⠀⠀⣈⡄⢂⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⡏⢰⢦⡀⠹⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠐⠆⠀⣀⢀⡀⠧⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠈⢻⠒⠐⡒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠧⣀⣀⣀⣀⣀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢀⡠⠀⣋⠉⠉⠩⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠻⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢓⣄⠰⠀⡏⠀⠀⠀⣶⠢⠄⠀⠀⠀⠰⢆⠆⠘⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⢸⠀⠃⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⣮⠴⠀⠐⠒⠚⠲⠡⡚⣤⡤⣤⣤⠦⠞⣰⠞⠁⠀⠀⠀⠀⠀⠀⡀⠤⠠⢄⡁⢸⢸⠀⢤⣇⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢦⡀⠀⠀⠀⠀⠀⠉⢣⣦⣟⣧⣬⣬⡁⠀⠀⠀⠀⣀⢠⠔⠁⠐⠢⠀⠀⠑⠞⣼
⠀⠀⠀⠀⠀⢀⢠⡠⢆⠀⠀⠀⠀⠈⠂⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠈⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⡄⣠⢄⣀⠕⡿
⠀⠀⣠⠔⠊⠙⠯⠈⣉⠐⣋⠸⠥⠃⠀⠀⠀⠀⢀⡀⠐⢦⠀⠐⢐⠄⡀⠀⠀⣀⠀⠀⠀⠀⠀⢤⣤⣀⣀⢀⠀⠀⠀⠈⠁⠉⠀⠀⠧⠄⠽⠊
⠐⠎⣀⣀⠤⠄⠒⠈⠉⠁⠀⠀⠀⣠⠴⣇⢠⠀⡞⠉⠐⠚⠀⠀⠀⢀⣀⠀⢀⠼⠂⠀⠀⠀⠐⠃⠀⠀⠘⢯⠷⠤⠠⠄⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠁⠀⠀⠀⠀⠀⠠⠄⠥⠊⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⣀⣠⣀⣀⣀⡆⠀⠀⠀⢀⠀⠀⠠⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣟⣙⣿⣿⣿⣷⣤⣰⣿⣷⣼⣷⣶⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⡿⣻⣄⣻⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⣟⣿⠟⡻⣶⣯⣿⣿⡟⢿⣿⣿⣿⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⢡⣏⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠄⠀⠊⠈⠛⣿⡿⢻⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣠⣼⣷⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣦⡠⢄⢋⣹⢿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⣾⢿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⣮⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠖⠊⠁⠁⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠐⢄
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠱⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⢖⡆
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡤⠒⠀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⡀⠔⠓⠛⢮⣟⠹⣤⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠁⠀⠀⠀⠀⠀⢙⡆⢀⡀⠄⠂⠁⠀⠀⠀⢀⣀⡹⣦⠴⠃
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⡤⠤⠊⠀⡏⠉⠉⠉⠉⠉⡻⢻⠉⠀⣾⠳⡀
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⣦⢧⡄⠤⣄⣀⣠⠃⢸⣤⣼⠏⠀⡇
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠉⠉⠉⠀⡇⠀⠈⠋⠁⠀⠀⡇
⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⢤⣀⡀⡸⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠉⠙⠒⠒⠼⢧⣀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⢲⡀⣠⠎⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⠃⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⢄⣀⡀⠀⠀⣇⣀⡀⠀⠀⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣶⠶⣦⣄⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣥⣀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⡀⢻⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢟⡿⠉⢿⡀⢹⡇⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⢋⡞⠀⠀⢸⣧⠀⠇⠸⣿⣿⣿⣿⣿⣿⣿⣶⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣹⡏⢰⡞⠀⣰⡇⠈⠿⠀⠂⢀⣿⡿⣿⡏⢾⣿⣦⣦⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡬⠙⢻⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⠃⢸⠀⢰⣿⠁⠀⠀⠀⢀⠞⣿⣿⣟⡹⣿⡄⢀⡙⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠳⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⠿⠀⠈⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⠟⠉⠛⠟⠙⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢉⢐⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠓⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣼⣿⣦⡊⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⡧⠀⠀⠀⠀⢻⣿⣿⣷⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⠙⠛⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠘⢿⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣹⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣓⣦⣼⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠛⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡧⠤⠤⠄⠠⠤⢄⡀⣼⠉⠉⣦⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣩⣴⡞⠉⢱⠖⠊⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠚⠙⡟⠙⡅⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢾⡀⠀⠈⢲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⠁⢀⡇⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠙⣦⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡋⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠤⠤⠴⢢⣀⡤⠦⢤⣄⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠓⣦⠀⠀⡇⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⠀⠀⠀⡇⠀⠀⢰⡅⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠻⣄⡀⡇⠀⠀⠀⢰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣠⣄⢳⣴⠋⠉⠀⠀⠘⠁⠈⠁⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⢹⡇⢀⣠⠤⠊⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠙⠲⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠀⠀⠀⠀⠀⣀⡼⠛⠁⠀⠀⠀⢠⢿⣰⣏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢦⠀⠀⠀⣀⣀⣠⡤⣈⣧⠀⠀⠀⠀⠰⡄⠀⠀⠀⣖⡦⠀⠀⠀⢰⣡⠴⠤⠤⣤⠄⠀⡎⠸⠃⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⢀⡼⢦⡀⠀⠀⠀⠈⠓⠶⠖⠋⠀⠀⠀⣠⠎⢹⡄⠀⠀⡟⠀⠀⣇⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡄⢾⠁⠀⠀⠘⣄⠀⠀⡎⠀⠀⠉⠒⠦⢄⡀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢸⠿⢦⡰⠃⠀⠀⢈⠇⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⡧⢤⠀⠀⠈⠳⣴⠷⢄⡀⠀⠀⠀⠀⠈⠁⠒⠒⠋⠁⠀⠀⠀⣠⠏⠀⠈⡇⠀⢀⠤⠾⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣁⡤⠞⣆⠀⠀⠀⢸⠀⠀⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣸⠀⢠⡞⠳⠶⢤⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠶⠚⢩⠇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⠛⠒⠶⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠒⣩⡇⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢼⡓⠶⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⠘⡆⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⣸⢹⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠙⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢽⠷⠣⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠃⠀⠁
⡦⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠶⠅⠁⠀⠀⠀⠈
⠀⠀⠀⠐⣠⠂⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠀⠠⠀⠘⠆⠀⠀⠀⢀⡀
⠀⠀⠑⠈⠐⠀⢡⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐
⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠁⠀⠀⠀⠀⠤
⠀⠀⠀⠀⡀⠀⠀⣢⠗⡈⠀⣀⠈⠀⠌⠈⠀⠉⠈⠳⠤⠤⡀⠀⠀⠀⠀⢰⢄⢠⡅⢀⠀⠀⠀⠀⠀⠠⠄
⠆⡉⡅⠁⠸⡆⠀⠁⠀⠈⠀⠈⠀⡸⠂⠀⠀⠀⠀⠉⠋⢀⢁⢀⠠⠄⠀⠀⠀⠀⠀⠒⢺⣸⠇⣼⠤⠀⠈⠀⣄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⢀⣴⣾⣿⢭⣓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣭⣽⣿⣿⣷⣶⣶⣿⣯⣭⣍⣙⠺⣷⣝⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⠛⠉⠉⠀⢠⣾⠋⠀⠀⠀⠙⢿⡄⠉⠉⠛⢷⣮⡻⢟⡺⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⠿⢸⡇⠀⠀⠀⠀⠙⢿⣆⠈⢮⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠈⢻⣆⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣭⣛⠛⠛⠋⠀⢀⣦⡀⠀⠀⠀⠀⠈⣿⡘⡏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⢀⡞⠀⢿⠀⠀⠀⠀⠀⢻⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⠿⠀⠀⠀⠀⢀⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⣶⣶⣶⡶⠶⠶⠾⢿⣿⠛⠛⠉⠉⠁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡤⠶⠛⣋⡉⠉⠛⠳⣦⡀⠀⠀⠀⠸⣷⣶⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠞⠉⠙⢦⠀⠀⢸⣷⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢹⡄⠈⠉⣽⢻⠙⠛⢛⡿⡟⠛⠛⢻⡟⠉⠉⠉⠉⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠈⢷⣀⡼⠉⣆⣧⣠⣼⡴⢳⡀⢠⡞⠁⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠈⠛⠁⠘⢧⡀⣠⠴⠃⠈⢷⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⢇⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⢆⡽⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⡀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡟⠛⠛⡛⠛⠛⢻⣿⠷⢦⡤⠾⠿⠾⠾⠿⠿⠿⢿⣿⠿⣿⡿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⣠⣤⠶⠒⠚⠛⠒⠒⠒⠶⢤⣄⡀⠀⠀⠀⠸⣧⣀⣰⣿⡿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿⡇⠀⢴⣷⣶
⠀⠀⠀⠀⠘⠿⢧⣀⣀⠀⠀⠀⢀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠈⣉⣉⣉⣀⣀⣸⣿⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣬⣿⡀⠈⠛⠛⠛⠛⠁
⠀⠀⣀⣤⠤⠤⠤⠤⠄⣉⡩⠉⠁⠈⠉⠁⠐⠒⣲⡿⠂⣴⡋⠉⠁⠀⠉⠉⣩⡙⢶⡀⠀⢠⡞⠉⠉⠀⠀⢀⣀⡈⢳⡄
⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁⠀⠀⠈⠻⠶⠶⠶⠞⠛⠙⠷⠾⠃⠀⠈⠛⠶⠶⠷⠛⠋⠉⠷⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠂⠉⠉⠉⠉⠉⠉⠐⠒⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠎⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠉⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⡘⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣰⣶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⣇
⡇⠀⠀⠀⠀⡰⠃⠀⢀⠊⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠱⠈⠙⠢⣀⠀⠀⠀⠀⠉
⡇⠀⠀⠔⠊⠀⠀⠀⠈⠄⠈⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠀⡰⠀⠀⠀⠈⠑⢢⠀⠀⢳⠄⠄⠤⠤⠤
⢓⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁⠀⡿⠀⠀⠀⠈
⠘⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⠐⠀⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⡇
⠀⢇⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⡼
⠀⠘⡄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠎⠀⠀⠀⢠⠃
⠀⠀⠱⡄⠀⠀⠀⠙⢄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⡰⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣄⠀⠡⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠌⠀⡠⠞⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠙⡉⠐⠒⣲⠀⢠⡖⠒⠂⢉⠉⠀⢀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⣹⠻⠯⡍⠉⠀⢀⠤⠚⠀⠈⠗⢤⡀⠈⠉⡩⠭⠛⣍⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⡘⢢⡓⠂⠴⠃⣄⠀⢊⠃⠀⣆⠙⠤⠐⢳⡐⢣⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠑⠒⠊⠀⠇⠀⠀⢸⠀⠑⠒⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠒⠒⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⢀⡞⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⠤⠤⠤⠤⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣴⣇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⡀⠀⡤⠀⡀⠰⠆⠀⠰⠀⠈⠂⢸⡄⣯⠃⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⢂
⠁⠀⠀⠀⠀⠀⠃⠳⠀⠀⠐⠀⠅⠀⡀⢻⠁⣽⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠃⡏⠀⠁⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡆⡤⢀⡀⠀⠀⠐⠀⠊⠀⠀⠀⠎⣀⡷⠉⠃⠨⠆⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈
⡅⢻⢊⣁⢀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡦⡄⠀⠀⠀⠠⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⣡⡤⠀⢀⣄⣄⣠⡦⠀⡀⠀⠁⠀⠈
⠄⠛⠉⠓⠘⠙⠀⠀⠀⠀⠀⠀⠿⠿⠀⠟⡀⠀⠐⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠆⢠⣃⣧⣄⣌⣄⣁⠀⠀⠠⢉
⡀⠀⠀⠀⢀⢀⡁⠀⠀⠀⠀⠠⠄⠄⢀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⠠⠀⡄⠺⣿⡿⠋⠐⠸⢏⡝⠀⢂⠀⠨
⠁⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠐⠀⡀⠭⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⠈⡛⠃⠀⢀⠁⡜⢉⠘⠇⠄
⠄⠆⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠶⠒⠀⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⡸⠈⠀⡥⠀⠀⢠⠧⣤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⢼⠠⠁⠀⠀⠈⠡⠙⠀⠀⠛
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⢀⠠⡀⠀⠀⠄⠀⠀⠈⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣤⠄⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠈⠘⡈⠀⠀⠀⠀⠀⢈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠈⠉⠉⠉⠉⠀⠒⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠠⠄⠐⠀⠐⠀⠒⠀⠀⠠⢄⡀⡠⠀⠒⠒⠀⠤⣀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⣀⣀⠀⠤⠤⠤⠀⢀⣀⡈⢆⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣒⣛⣉⡉⠀⠒⠒⠒⠀⠤⣀⡀⠀⠉⠐⠒⠤⢄⡀⠀⠀⠇⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⢄⡀⠀⠈⠑⠢⢄⡀⠀⠀⠈⠐⠤⣘⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢺⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⠀⠈⠑⠦⡀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠸⠸⡎⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⠈⠑⠢⣀⠀⠀⠀⠉⠢⢀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⡄⠀⠙⣆⠀⠀⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣑⠢⠄⡀⠀⠀⠑⠦⡈⠆
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠁⠀⠀⠈⠳⣄⠀⠀⠀⠉⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠊⠱⢦⣤⣤⢘⡘⡄
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⡰⠉⠛⢦⣄⡀⠀⠀⠀⠈⠐⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠉⡙⠘⡄
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⠜⠀⠀⠀⠀⠉⠊⠕⡒⠠⢄⣀⠀⠀⠀⠈⠁⠒⠀⠀⠠⠤⠤⠤⢠⣤⡤⠤⠐⠒⣛⣱⡚⠤⠚⢁⠇⠘⢄
⠀⠀⠀⡠⠊⠀⠀⠀⣀⠔⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠬⢉⣀⠒⠒⠒⠒⠐⠒⠒⠂⢈⣁⡠⠤⠴⠖⢉⣉⡀⠠⠤⠐⠃⢤⠀⠀⠉⠀⠈⠁
⢀⡴⠊⠀⠀⣀⠄⠊⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠒⠀⠤⠤⠀⠀⣠⠤⡄⠒⠁
⠈⠉⠐⢶⡭⢤⠤⠔⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⣄⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⡸⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢆⠉⠐⠒⠈⠁
⠀⠀⠰⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢂
⠀⠀⢡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜
⠀⠀⠀⠑⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠠⠤⠀⣀⣁⣒⣀⣀⣒⣉⠀⠠⠤⠐⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡠⠖⠉⣤⡺⠭⢝⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣁⣀⠤⠒⠉⠀⠀⠀⢸⣽⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡟⠴⠞⠂⠀⠚⠒⢃⠞⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠇⠠⠆⠀⠀⠠⠀⠹⢋⠁
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⢄⠀⠉⠀⡨⠁⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠤⠀⡄⢄⢀⠀⠀⠐⠀⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢱⡄⢀⠷⠀⠀⠀⠀⠀⢀⡜⡀⡸⢀⠀⠉⢀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢘⡾⠄⠀⡀⠀⠀⢸⠀⠠⠀⣠⣴⣶⣦⠀⠐⠀⢫⠉⠂⠂⠚⠓⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⠬⡤⣞⣒⣒⡺⢮⣠⣿⣇⢈⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠄⠄⠈⠁⠄
⠀⠀⠀⠴⢳⠀⠀⠀⠐⡁⢘⣶⡄⣶⣶⣶⡄⠉⠉⠉⠀⠀⠈⠀⠄⠀⠀⡀⠀⡀⣉⠀⠀⠄⠁⠀⠘⢦⡀
⠀⠀⠂⠒⠺⠷⠀⠤⠀⠰⠏⠻⣿⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠧⠉⠉⠀⠀⠀⠰⠃⠞
⠀⠀⠀⠀⠀⠀⠰⢴⢒⣲⡂⠀⠉⠛⠛⢁⣀⣀⣀⡤⡤⣤⣀⣀⣀⠠⠤
⠀⠀⠀⠀⠀⢰⣶⣿⠫⠈⢱⡆⠐⢸⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡷⠁⠄⡀
⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠙⢦⡄⡘⠉⠉⠉⠋⠋⠋⠋⠉⠉⢉⣁⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠃⠢⠬⠤⠥⠜⠉⠉⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⡞⢛⣳⣶⣶⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⠿⣻⣵⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠋⣵⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢤⡀⠀⠀⠀⠀⡤⠶⠢⠀⠀⠀⠻⠛⠿⠿⠟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣄⠀⠀⠀⠀⠠⣴⣤⠀⠀⠀⠀⠀⠀⠤⣚⢹⠀⠀⠀⡠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠛⠃⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠘⡷⠘⠀⡠⠖⠁⣸⠀⢀⣀⣀⣀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡴⢫⢀⠠⠚⠉⠉⡉⣩⠄⢀⡴⠁
⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠉⢀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡄⠹⡁⣷⣥⣵⡶⠶⣒⣀⡸⠥⠖⠋
⠀⢠⠂⠀⠓⣺⣧⣀⡀⠀⠀⠀⠀⠀⠀⠳⡄⠘⢯⣥⠬⠽⡿⠁⠀⠀⠀⠀⡰⠀⠀⣹⣥⡏⠉⠉⠉⠁
⠀⡜⠂⠀⠛⣀⠠⠙⣿⡓⠦⠀⢀⣤⣾⣿⣿⣦⠘⠃⠀⠘⠁⠀⠀⠀⢀⣴⠁⢴⣾⣿⡇⣿⣿⣶⣶⣤⣄⣀⡀
⠀⢣⠐⠈⠀⠜⠂⢠⡊⠀⠀⣹⣶⣿⣿⣿⡆⢹⣇⠙⠛⠉⠀⠀⣠⣶⣋⠥⢒⡩⢞⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠈⠢⡀⠀⠐⠃⣠⠃⢀⣾⣿⣿⣿⣿⣿⣷⣾⣿⣷⢤⡤⠶⠛⠉⡁⠄⠚⠍⠂⢁⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡄
⠀⠀⢀⠋⠒⠀⠀⠁⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠭⠵⣶⠒⣒⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡄
⠀⢀⠂⠀⠀⠀⠐⠁⠀⠀⠈⠙⢿⣿⣿⡟⣿⣿⣿⣿⣷⣿⣌⣢⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣦
⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⣴⡿⠟⠉⢸⡿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⣦⣌⠛⢿⣿⣿⣿⣿⣿⡿⠿⣿⣮⢿⣿⣿⣿⡿⠟⠋⠉⢧⡀
⡇⠀⠀⠀⠀⠀⢨⠀⢀⡠⠞⠁⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠄⠐⠂⠀⠀⢀⣼⣿⣿⣦⣴⣦⡭⡉⠁⠠⠀⠀⠙⠓⠻⠿⠥⢀⡀⠀⠀⣀⣙⠢⣄
⢧⠀⠀⠀⠀⠀⣂⠴⠋⠀⠀⠀⢰⣉⣉⣒⡦⢤⢤⣲⣖⣦⣔⣛⣭⣭⣽⣿⣾⠿⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠢⡀
⠸⠦⠤⠖⠒⠊⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢿⠿⠟⡿⠿⣿⣛⣛⣻⣽⣋⡄⠀⠀⠀⠘⠦⣅⡀⠀⠀⠤⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣯⣭⣭⣟⣿⣿⣿⣭⠽⣿⣷⡿⣶⣿⠽⣧⡦⠀⠀⠀⠀⡆⠉⠲⠀⠠⠄⠒⠒⠊⠁⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢂⢱⢼⣻⣿⣿⡿⣿⣶⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⢋⠹⠓⠂⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠤⠤⠖⠚
⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠘⠛⠠⠟⢿⣿⠿⡿⣽⣿⣭⡭⣿⡿⠟⢿⠛⠋⣋⣀⡤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠶⠦⠤⠬⠤⠤⠤⠼⠵⠒⢒⣚⡋⠍⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢉⣴⣶⡦⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⣶⣿⣿⠟⣴⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⢿⡿⠟⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣀⣀⠀⠀⠀⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠈⠁⠄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⠀⠀⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠲⣤⡴⠂⠀⠀⣠⢿⠞⠀⠐⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠉⠀⢿⣇⠀⠀⢀⣰⣞⠅⠀⠀⣰⠃⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠙⢻⠁⣉⣶⡁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⢳⠤⣄
⠀⠀⠀⠀⠀⠀⠠⢤⣄⣀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⡟⢱⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢠⢀⣵⠖⠗⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠰⡄⢚⣧⡈⡆⠀⠨⠳⣄⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠃⠈⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣴⣛⣁⣠⡽⡇⠈⠳⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠁⠀⠀⢧⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣦⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢀⠂⢸⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⣀⣀⣀⣀⣀⣀⠀⣸⣿⣿⣶⣦⣴⣿⣿⣷⣬⣵⡼⢠⠀⢿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣠⣇⣀⣀
⠀⠀⠀⠀⠀⠀⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢉⣴⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⣾⣿⣿⠟⣵⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⢿⡿⠟⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⣀⣀⡀⠀⠈⠿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠜⠂⠉⠁⠄⠂⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⠳⣤⡴⠂⠀⠀⣠⢿⠞⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠉⠘⢿⣇⠀⠀⢀⣰⣞⡅⠀⠀⣰⠃⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠙⢻⠁⣙⣿⡁⠀⢀⡰⠃⠀⠀⠀⠀⠀⠈⢳⠤⣄
⠀⠀⠀⠀⠀⠀⠠⢤⣄⣠⡤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⡟⢱⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠠⣈⣵⠖⢷⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠰⡄⢚⣧⡜⣆⠀⢨⠳⣄⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠇⠈⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣴⣛⣁⣤⡽⡇⠈⠳⠄⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠩⠉⠁⠀⠀⢧⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣦⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢑⠂⣸⡦⠀⠀⠀⢀⣀⢀⢀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⣀⣀⣀⣀⣀⣀⡄⣸⣿⣿⣷⣦⣴⣿⣿⣷⣮⣷⡼⢤⠀⢿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣠⣇⣀⣀
⠀⠀⠀⠀⠀⠀⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⡒⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⣿⣿⡿⠯⠻⠃⣀⣠⣀⡀⠀⠀⠀⠈⠀⡀⠀⠈⠉⠉⡛⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡴⠋
⡀⣀⣰⣦⣴⣿⣿⣿⣯⣤⣤⠤⠀⠀⠀⠀⠈⠒⠲⠺⠟⣟⠉⠙⣉⡉⠀⠀⠀⡀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⡎
⠉⢿⢿⡿⠛⠛⢋⣍⠉⠁⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢨⣥⣄⣀⣀⠀⠀⠀⢤⣄⣀⣤⣀⣉⡶⣶⣦⠀⠀⠀⠻
⠀⣰⡶⠒⠀⠈⠁⠁⠀⠀⠋⠑⠒⠄⠀⠸⠇⠈⠉⠈⠥⠀⠀⠀⡀⠀⠄⠀⠈⠙⠊⠉⠉⠉⣉⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠈⠙⠋⠹⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⠀⠀⠀⠀⠀⠤⠀⠠⠜⣡⣶⡾⠆⡀⡄⠈⠁⠀⢀
⠀⡤⠤⢰⢆⣠⢀⠘⠒⠀⠀⢁⣀⠀⢀⠀⠀⠀⢤⣈⠀⠀⠀⠀⠀⠈⣉⣹⣓⣒⠚⠁⠀⠀⠐⠂⠀⣁⠈⠉⢠⢤⠀⠀⠀⣀⡤⠀⠀⢨⣿⣽⡿⡿⠛⠁⠀⠀⠈
⠀⠀⠀⢈⣉⣙⡛⠢⣀⠌⠉⠩⣍⠉⠀⠉⠈⠛⠛⠉⠠⠀⠶⢲⣤⣧⣤⣴⣾⣿⣿⣶⣶⣤⣤⣤⡀⢀⣤⣤⡄⣠⡶⣦⣤⣬⣤⣤⣴⣿⢿⣿⣿⣿⣤⣤⣴⣶⠶
⣤⡄⣤⣛⣿⣿⡤⣬⣿⣷⡦⠂⠘⣶⣶⣤⡄⢀⣴⣶⣆⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣮⣉⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠟⠿⣿⣿⡏⣤
⣤⣴⣿⣿⣋⣛⣿⠿⠿⢿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣷⣾⣯⡿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠒
⣿⣿⣽⣿⣿⣯⣿⣷⣾⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠿⠉⠁⠉⠺⠿⠤⠿⠿⠯⠍⠁⢬⣁⡀⠀⠀⡀⠀⠀⠀⠰
⣿⠿⣿⠿⠿⠿⠻⢿⣿⣏⣽⣿⣿⣿⣿⣿⢻⣏⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣷⣦⣿⠀⠀⠀⠀⠄⣀⢀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣶⣶⣶⣶⣿⢺⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣆⢈⡀⠀⡈⣛⣿⣿⣿⣿⣿⣿⣧⡤⣮⣽⡾⠇⠀⠙⠋⠙⠛⠛⠛⠋⠒⠂⠀⢀⣴⣧⡤⣤⣄⠀⠀⠈⠈⠉⣀
⠁⣿⣿⣿⣿⡳⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣷⡤⠤⠀⣄⣀⢙⡿⠛⠛⢛⣛⠛⠉⢀⡈⠠⠀⢠⢴⣶⣿⣤⠄⠀⠀⠀⠀⠰⠹⣿⣿⣿⢛⠿⠟⠉⠀⠀⢈⡉⠯
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠠⠀⣠⠀⠀⠀⠴⢻⣟⣈⣃⠉⠀⠄⠀⠁⠀⠒⢐⢷⣦⣌⡉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⣄⣀⣾⠀⠀⡀⠽⣻⣋⣀⡀⡀⠀⠘⠀⠀⠒⠸⠆⠄⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⢀⡰⠦⠒⠦⠾⣿⢿⣿⡿⠿⠿⠿⠟⠀⠀⣀⠀⠀⠀⢀⣠⣤⡀⣀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠄⡀⠀⠀⠁⠀⠀⠀⠀⠒⠺⠒⠀⠤⠤⠤⠒⠒⠒⣯⠝⠋⡏⠉⠄⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⡠⠆⠁⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⢨
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⡬⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠇⠀⠀⠀⠀⠀⠀⠒⠛⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠃⠠⡄⠦⠀⠀⠀⠠⠄⡰⠃⠐⠃⠀⠀⡆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢀⠇⠹⠅⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢠⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⣐⠛⠳⣤⣄⣀
⠀⠀⠀⠀⠀⠀⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢂⡤⢀⠀⠀⠀⠐⠚⠁⠀⠐⠁⠈⠉⠓⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠄⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠘⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀
⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠙⣄⡙⠀⠀⣠⡄⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠋⠀⠀⠁⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⠔⠀⠖⠒⠉⠉⠒⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡠⠠⠈⢀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠠⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⢦⡀⠀⠀⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠄⡀⡀⠠⡄⠘⠒⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⡀⠀⡀
⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡌⠠⠁
⠀⠀⠌⠏⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⢎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠄⠀⠀⠀⠀⠀⠀⡘⠋
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠙⡶⠃⠀⠀⠀⠀⠈⠘⢝⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⢤⠀⡠⠃
⠀⠂⠀⠀⠀⡢⢮⠁⠃⡀⢀⣶⠐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⡴⠉⠱⠶⠠⠂⠐⠢⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⠳⠢⠄⠀⠄⠀⠀⠀⠠⠖⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠑⠄⠀⠈⢀⠀⢀⠀⠀⢀⠀⡈⢀⡴⡢⢄⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠂⠀⡀⠈⠁⠀⠒⠦⢀⠀⠁⢰⠀⠀⠀⢀⢖⠅⠈⠠⠐⠒⠂⡛⠱⠌⠁⠼⠀⠀⠂⠀⠐⢀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠆⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠁


⡂
⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣟⣿⣿⣻⣋⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣻⣿⣟⣻⣛⣻

⠀⠀⠠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠏⢂⠄⠀⠈⠀⠈⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠁⢘⠉⣜⢻⣿⣿⣿⣿⣯⢉⣻⣽⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢂⡤⠀⠀⠀⠁⡀⡈⠀⠀⠀⠂⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢄⢢⢀⠻⠷⡝⢃⡞⠹⣿⣯⣿⣿⣿⣯⣭⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠽⠈⠀⢠⣧⠉⣫⣿⠿⣿⢿⣿⢿⠿⠙⠿⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡦⠆⣥⢼⠖⡴⢻⣙⣿⣸⣤⣼⣶⠟⢲⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠮⠙⣿⡛⣲⣟⣹⣟⡿⣿⣴⣿⣿⣯⣽⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢉⠹⠻⠏⠩⠍⢉⡸⣯⠉⠉⣿⠛⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠆⠀⠀⠀⢻⠻⢲⢦⡄⣠⣬⠁⡀⠀⠸⣅⣸⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠉⠂⠸⠃⠨⡿⠈⠉⠀⠀⢸⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠠⣔⠀⡀⠀⣦⣸⠟
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠁⢀⣀⠘⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣿⣿⣼⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⠀⠠⠀⢠⣾⣿⣿⠿⣿⣿⡟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡆⠂⠀⠀⠀⠀⠀⠈⠃⠖⠋⣴⣿⣿⠿⣶⣯⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠠⢆⢾⣿⡶⣿⣯⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡿⣭⣿⣿⣟⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣷⣿⠛⠳⡀⣫⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠧⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠉⠻⣿⣷⣄⡀⢀⣀⣠⣤⢿⣿⣿⡦⣤⣄⣀⡀⢀⣠⣾⣿⠟⠋⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢠⣀⣈⣙⠻⢿⣿⣇⠀⠀⢸⣿⣿⠁⠀⠀⣼⣿⡿⠟⣋⣁⣀⡤⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣈⣉⡉⠀⠀⠈⠿⠀⠀⠀⣿⡟⠀⠀⠀⠟⠁⠀⠀⢉⣉⣁⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠛⠉⠀⠀⠀⣀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⠀⠀⠀⠙⠛⠛⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣀⡀⠀⠀⣀⣤⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣤⣀⠀⠀⢀⣀⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠃⠀⠉⢹⣃⣀⣵⡄⠀⠀⠀⠀⠀⠀⢰⣯⣀⣹⡍⠁⠀⠘⠛⠛⠛⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣠⠇⠀⢀⣀⣀⡀⠀⠹⣶⣆⡼⠁⠀⠀⠀⠀⠀⠀⠀⢈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠿⣿⣿⣷⡶⠶⠖⠀⠀⠀⠀⠉⣡⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⠀⠀⠐⠲⠶⢶⣿⣿⡿⠿⠟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣀⡤⠖⠒⠛⠒⠦⢤⡀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣀⡤⠖⠒⠛⠒⠲⢤⣀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡄⢠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠉⠻⣶⣤⣄⣀⣀⣀⣀⣤⣴⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⣤⣤⣾⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠛⠀⢠⠀⠀⠀⠀⠀⠀⠀⣷⠀⠉⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⠉⠛⢻⡟⠛⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⢳⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣙⢦⡀⠀⠀⠀⠈⠓⢤⡤⣤⡤⠤⠞⠁⠈⠳⠤⢤⣤⢤⡴⠚⠁⠀⠀⠀⢀⡴⣋⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠦⣄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣀⣀⡤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣄⠈⠉⠉⠀⣠⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠛⠁⠀⠀⠀⠀⠉⠛⠿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠶⠶⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠉⠉⠓⣆
⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠉⠲⠤⢒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡈⠀⣠⠊⢁⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢑⠶⠤⣄⣀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⡇⢠⠇⠀⢸⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠉⢙⠓⠦⢤⡖⣿⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣇⡼⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠠⠁⠀⠀⣀⠴⠚⠉⠑⠢⣄⠀⠸⣝⠒⠺⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⢳⡀⠀⣀⠀⠀⠀⠑⣄⠀⡸⠓
⠀⠀⠀⠀⠇⠀⠔⠋⠁⠀⠀⠀⠀⠀⠈⢣⠞⠈⠳⣄⠀⠀⠀⠀⠀⠉⣽⡃⠀⠀⠀⠀⠀⢹⡀⠀⠑⠦⠏⠣⣀⠀⠀⠀⠉⠀⣠
⠀⠀⠀⠘⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠺⣿⠀⠀⢀⣬⣳⠄⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠈⠁⠐⠂⠂⠈
⠀⠀⠀⡇⠀⠆⠈⠀⠙⠓⠦⠤⣤⣤⠤⢿⠀⠀⠈⠛⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡄⠄⠊⠀⠀⠀⠀⠀⠷⠐⠒⠒⠒⢞⠉
⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠀⡜
⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⣟⠲⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡿⠒⠒⠲⠶⠶⠒⠒⠚⠋⠉⢁⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⢶⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠦⠤⣤⠀⣤⣤⣤⣤⠤⠤⠴⠒⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⢄⣀⠀⢠⠀⠀⠀⠀⠀⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠤⠽⠿⠭⠝⠛⠓⠦⠭⢉⣛⣿⣃⡠⠕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣄⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⢀⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⣈⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣏⣀⣨⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠹⢷⠙⢿⣿⡝⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⢁⡀⠀⠀⠀⠀⠀⣀⡉⠀⠀⣿⡿⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢁⠟⣧⠀⠘⠁⠈⠀⠀⠀⠀⠈⠀⠙⠀⢀⣟⢣⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⠾⠟⣿⣿⡿⠘⢤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡼⠀⢸⣿⣿⡛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⠀⠀⣿⠳⣄⠀⠀⠸⣋⠙⣙⠟⠀⠀⡰⢻⡿⠀⠀⢸⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢿⣓⣦⠿⣄⡈⠓⠤⣀⣈⠉⣁⣀⠤⠊⠀⢸⠇⠀⠀⠸⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠒⠶⢶⣿⣦⣖⡛⠒⠟⠒⠛⠢⣀⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠨⠭⣽⡿⠉⠛⠻⢷⣦⡤⠖⡋⠭⠉⠉⠙⢿⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠤⠤⣼⡋⢰⠃⠀⠀⠀⠀⢸⢠⠊⠀⠀⠀⠀⠀⠀⠻⢭⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⠁⡞⠀⠀⠀⠀⠀⠈⠳⣤⣄⣀⣀⣀⣀⣤⡴⣋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⠞⠊⠓⠒⠒⠒⠒⠒⠒⠒⠚⠓⠬⠭⣥⣴⣞⣚⡥⠊

⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣷⣷⡄⢠⣤⣮⣻⣿⣿⣿⣿⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠁
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠃⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⢏⠉⠇⠀⠀⠀⠀⠈⠀⠀⢻⢿⣄⣍⠉⣤⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣮⣠⡤⣿⣿⣿⣿⣿⡿⠟⣿⣦⣤⣼⣾⣷⡔⠉⠀⠀⠀⠀⠀⠘⠊⢿⣰⣶⡿⠃⠘⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡶⢶⣿⣿⣿⣿⣽⣿⣧⠞⠁⠀⣤⡀⠀⠀⠀⠀⠘⠉⠁
⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣽⣾⠆⣀⣴⣶⣿⢿⣷⡄⠀⣄⠀⠀⠒⠂
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⠸⢟⣻⣿⣿⣿⣿⣯⣿⣿⡿⠿⣥⣀⠘⣿⣿⠃⠀⠈⢻⣿⡄⠹⡶⠶⠄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣩⠉⢻⣇⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⢟⡛⠻⣿⠇⣺⣿⣶⠂⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣈⣿⣿⡇⠸⠛⠉⠀⠐⠉⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠏⠙⢿⣿⡿⠟⢀⣤⠀⠀⠀⠿⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⠙⠻⣿⣷⣤⠄⣿⣿⣷⢰⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢉⠉⠈⠉⠀⠀⠈⠋⠉⠀⢻⣿⣿⡃⢷⣇
⣿⣿⣿⣿⣿⣟⣿⣿⡅⠀⠿⠀⠀⢀⣀⣀⢠⡄⠀⠐⣞⣉⣽⠿⠶⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠉⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⠿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⣿⣿⡀
⠀⠀⠀⠀⢀⠀⠀⠀⣠⠔⢂⣀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⣐⠀⠀⠀⠈⠺⠠⠖⣀⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣄
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠸⡀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⢤⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⠀⠠⠀⡀
⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸
⠀⠀⠘⠹⠷⠾⠉⠆⠀⠀⢀⣠⡀⠀⠀⠀⣀⠸⣀⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⠇⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⢄⠀⢀⠴⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠉⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⠊⠁⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠊⠂⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠦⣀⠉⠂⠤⣀⣈⣉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⠒⠃⠑⠂⠠⠈⡑⡲⠤⠤⢤⠄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠔⠈⠙⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢰⢅⠀⠐⡤⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠹⡻⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⡖⠄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⡠⠁⠈⠑⢀⠣⢲⠢⡀⠀⡤⣦⡂⠁⠀⠀⠀⠀⠀⡠⠒⠒⠀⠀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠑⠒⠚⠊⠀⠁⠠⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠓⠒⠐⠐⠂⠄⡀⠀⠀⠀⠀⣠⠀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠄⠈⠀⠀⢀⠔⠃⠀⠂⡀
⠀⠀⠀⠀⢠⡇⢰⠡⠣⠀⠀⠈⠑⠈⠁⢈⡀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⣀⣀⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠁⠘⠃⠘⠀⠀⠀⠀⠀⠀⣆⠀⠀⠈⠢⢀⠀⠀⠀⠀⠄⠂⠠⠀⠀⠀⠀⠀⠀⠁⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠑⠀⠤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠀⠐⡁⠀⠁⠀⠀⠘⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠌⠣⣀⡀⠀⠀⠀⠀⢀⠠⠀⠁⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⠞⠀⠀⠉⠁⠀⠀⠀⠀⢀⡀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⡂⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣛⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣛⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢀⠂⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡀⠀⠀⠀⠘⠙⠠⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠈⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠂⡄⢀⠀⠁⠂⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡅⠀⢀⠀⠀⠀⠀⠓⠀⠈⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⠀⠀⠀⠀⡀⠀⠀⠠⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⣠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⣠⠀⢐⠟⠃⠀⠀⠀⠰⢴⣆⠈⠂⠐⢋⣧⠂⠀⠀⠂⠀⠀⡘⠀⢀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠂⠁⠝⠁⠀⠀⠀⠶⠀⠲⠃⠸⣆⣈⡖⠿⠁⠋⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠔⠘⠄⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⢡⠀⠄⡀⠠⠈⠀⡀⠶⢠⣿⣴⠖⣲⣥⡆⠀⠀⠀⠀⠀⠀⠾⠈⠁⠀⠰
⡔⠄⠠⠀⠀⠀⠀⠀⣤⠄⠈⠀⠀⢀⠀⡬⡉⠤⠰⠂⠬⠆⠀⠡⠄⠀⠀⠀⠀⠀⡀⡉⠋⠉⡀⠘⣧⠀⠀⠚⠑⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢠⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢶⠾⡷⠒⠀⣁⠂⠘⠀⠀⠂⠉⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⡄⡄⠀⢠⠀⢸⣿⢀⡮⠍⠃⣀⠁⠐⣀⠀⠄⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁
⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠃⠀⣀⡼⢠⠄⠀⠀⣉⡹⡗⣢⡱⠀⣈⠀⠨⠤⠀⢀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⠀⠀⢀⡀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⠘⠀⡈⠒⢈⠈⠉⢲⠆⠙⠂⠀⠀⠀⠀⠀⢀⢊⠀⡄⠠⡄⠠⠺⣌⠀⡍⠀⠀⠀⠁⢈⠉
⠀⠀⠀⠀⠂⠀⠀⠓⠀⠀⢀⡶⠀⠀⠐⠒⠁⠂⠀⠀⠀⠀⠠⠶⣫⡄⠀⠉⠠⠄⠀⠒⠂⠀⢀⡄⠺⠀⠀⠀⣀⠀⠐⠃⠀⡉⠟⣢⡖⠬⠁⠀⠐⣘⣄⣈⡭⠃⠄
⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠤⠾⠃⠁⠀⠀⠀⠀⠀⠀⠐⠦⢬⡨⠁⠀⠀⠲⡀⠜⠀⠀⠀⠻⠶⠦⠀⠈⠀⠈⢁⣰⡥⠀⠀⠁⠈
⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠐⠆⢀⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠳⠋⠠⠀⣸⢁⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠐⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣁⣀⡀⢀⡤⠬⣁⣬⡆⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁⠐⠋⠉⠉⠉⠈⠀⠀⢈⣉⣀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡼⠀⠀⠠⠒⠁⠀⠀⢄⡉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⡙⠇⠀⠀⢀⡠⠔⠀⣀⣠⠄⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⢐⣒⣒⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⢢⠆⠀⠀⠐⠋⠰⣄⣭⣤⣤⢤⣶⠆⠀⠀⣬⢿⠞⣶⢼⣿⢛⣧⣻⣻⣿⢱⠏⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⣈⡤⠀⠀⠀⠀⠙⠻⢟⠋⠉⠈⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⢲⡖⠒⠐⠛⠂⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⢉⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣗⡄⠀⠀⠀⢠⡟⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠁⣀⠔⠀⠀⠀⠀⠀⠀⠀⣠⠘⢍⠙⢿⠁⠘⠀⠀⢀⣀⠀⡀⠈⠁⠀⢀⡰⠋⠙⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠧⠤⠄⠁⠊⠀⠀⠀⠀⠂⠁⢀⠈⠑⠒⡒⠋⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠃⢀⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠁⠉⠩⠥⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⢉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⣶⠶⠶⠃⠈⠉⡇⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠒⠂⠀⠤⠄⠤⡤⠄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⠔⠹⣦⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⡰⠃⠀⠀⠹⣧⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣀⣀⡄⠶⠊⠀⠀⠀⠀⠀⠉⠛⠛⠉⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⡄⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⡛⠶⣶⠀⢻⡟⠀⣶⠶⢛⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠖⠂⠀⡈⠀⠘⠃⠀⢁⠀⠐⠲⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠶⠆⠐⣟⢣⠀⠀⠀⠀⡜⣳⠂⠰⠶⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣤⣤⠄⠀⠘⠓⠀⠐⠂⠀⡛⠂⠀⠠⣤⣤⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠔⠈⠀⠁⠂⢤⣀⣀⣀⣀⡤⠐⠈⠀⠀⠢⡀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠢⡀⠀⠀⢀⡀⣀⠜⠢⣀⢀⡀⠀⠀⠀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⢄⣀⠀⠀⠀⠀⠀⠀⣀⡠⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠈⢀⣑⡀⠀⠀⢀⣊⡀⢁⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢁⠀⢸⣿⣿⡷⢾⣿⣿⡇⠀⡈⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⡌⠀⠘⠛⠋⠀⠀⠙⠛⠃⠀⢡⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠴⠶⠈⠉⠛⠛⠋⠁⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡇⠀⠘⡇⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⡖⠻⡄⠀⣧⠀⠀⠀⣇⠀⠀⢸⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⣰⠋⠀⠀⣧⠀⠹⡄⠀⠀⠸⡆⠀⠈⣧⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠏⠀⠀⠀⠹⡆⠀⢳⡄⠀⠀⢿⡀⠀⠘⢧⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠀⠀⠀⣧⠀⠀⠀⠀⠀⠸⣄⠀⠹⣤⠀⠀⠻⣄⠀⠈⠳⣄⠀⠀⠀⠉⠳⠆⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⠆⠈⠛⠶⠄⠈⠙⠂⠀⠈⠛⠶⣄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢇⠀⠀⠀⠚⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠛⠀⠀⠀⡇⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡄⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⡗⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸⡇⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⣧⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠻⣆⠀⠀⠀⠀⢠⡄⠤⠤⠤⠄⠤⢠⡄⠀⠀⠀⠀⢀⡼⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠳⣄⠀⠀⠈⢷⣄⠀⠀⠀⣠⡾⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⠳⢦⣀⠀⠈⠙⠛⠋⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡿⠛⠢⢤⠤⡤⠤⠖⠛⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⠶⠚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣛⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠠⠤⣀⣀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠈⠓⠒⠢⣬⣹⠧⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⡰⠖⠀⠈⣡⠔⠂⢉⣩⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠰⠆⠉⣀⡀⠀⠈⣷⠦⢤⣀⡠⣶⣎⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠚⢋⠀⠈⠳⠤⠛⠐⢦⣀⢄⣀⣀⣀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠙⠛⠫⠭⠭⠜⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⣤⣄⡘⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠳⢄⣀⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣴⠀⠀⠀⠀⠈⠙⠛⠛⠛⡿⠀⠀⠀⡠⠖⠛⠋⣠⠤⠤⠤⠤⠤⠤⠦⠤⣈⡉⠛⠲⣏⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣰⠁⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⡟⠠⣶⣏⣁⠀⠀⠀⠀⠀⠐⠓⢀⣈⡹⠶⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⡟⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠹⣆⠀⠈⠉⠑⠒⠚⠛⠛⠒⠒⠈⠉⠀⠀⡸⠣⣄⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⣼⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⣸⠇⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢳⣆⣀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠋⠀⠀⠀⢃⠠⣄⠀⠀⠀⠀⠀⠀⣷
⠀⠀⣠⠇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣤⣉⣙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⢀⡼⠃⣄⠀⠀⠀⠀⠸⡇
⠀⢠⡟⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠙⠓⢦⣄⡀⠀⠀⠀⣠⡞⠁⠀⠘⢧⡀⠀⠀⠀⢸
⢀⡜⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠙⣆⣠⠖⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⣧
⡘⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠹⡀
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠳⣄⠀⠀⠀⠀⠀⣠⠾⠉
⠀⠀⠀⠈⠳⠦⠀⠠⠤⠶⠚⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⠙⠶⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡀⠠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⣴⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠠⠋⠀⠀⠤⠀⡢⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⠡⠀⠀⠀⡐⠀⣀⡀⠉⠀⠉⠙⠛⢳⡶⠶⠶⠀⠀⠕⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠁⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠐⠈⢄⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁⠀⠀⠀⡁⠀⡁⠀⠀⠠⢂⡀⠀⠀⠀⠀⠠⢂⠂⡀⠀⠀⠁⠀⡀⠀⠡⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠆⡠⠃⠀⠀⠀⠙⣄⠄⠀⠀⠐⠌⠁⠁⠀⠀⠀⠐⠌⠅⠁⠀⠀⠰⠜⠈⡀⠀⠐⠞⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⡆⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠⠊⠁⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡲⠠⡀⠀⠢⡀⠀⠈⠈⠣⠀⠀⠀⠀⢃⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠊⠈⠀⠀⡠⠈⠀⠠⠠⡘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠜⠀⠀⠀⢄⠀⠈⠂⢄⡀⡀⠑⠀⠀⠀⠀⠑⠁⠅⠘⠁⠀⠀⠀⡠⠀⠀⢀⠄⠈⠀⠀⠊⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡠⠊⡠⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠄⠊⡀⠢⡈⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡡⠊⠀⠀⠀⠀⠑⠀⠠⡍⠀⠈⠁⡧⠄⠠⠊⠀⠀⠈⠢⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⢇⢀⢀⠀⡑⠀⣠⡀⠀⠀⠀⡠⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⢠⡀⣀⠀⡔⠩⠉⡘⢠⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠀⠀⠀⠀⣦⠀⠀⢷⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⡀⣤⡄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⣀⠀⣤⠀⠀⢿⠀⠀⡈⢷⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⣿⠤⠙⢷⠀⠛⠧⡀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠒⠿⠐⠀⠐⢄⠀⠀⠈⠢⡀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠛⡄⠀⠀⠈⠁⠂⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠚⢦⡀⠀⠀⢀⠔⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣠⠁⢠⣻⠂⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠉⠛⠳⠤⢀⢀⣀⡀⠋⠀⣀⡀⠀⣀⣀⣔⣀⣀⡤⠶⠿⠓⠋⠁⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠤⠄⠀⠈⠉⠀⠉⠥⠤⠤⠀⠀⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⣤⠤⠴⠂⠉⠉⠉⠉⠓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠤⡴⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠎⠀⠀⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢀⣤⡀⠀⠹⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠠⠤⠤⠂⠀⠀⠀⣀⠀⠤⠄⠐⠂⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠛⢦⡀⠀⠀⠀⢀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⡞⠉⠙⠓⠶⠤⠤⠤⠤⠶⠚⠉⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢻⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠈⢧⠀⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠃⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠓⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢀⠠⡒⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠢⠤⣀⡀⠀⠀⠀⠀⢸⠀⢀⡴⠋⡐⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣀⣸⡔⣋⣀⠰⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠂⠀⠀⠀⠀⠀⢠⠁⠀⠈⠉⠲⣄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠈⢣⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠳⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡀⠀⡠⠂⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱
⠀⠀⠀⣄⢰⡆⡖⠀⡀⠀⢸⠀⠀⠀⢤⣀⠘⢰⡆⢲⣄⠀⣠⠆⠀⠠⣄⠄⠘⣁⠀⡀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠸⢀⡀⠀⠀⢃⡀⢇⠀⠐⠂⠀⠠⠔⢂⣀
⠀⠀⠀⠈⢛⠡⠤⠤⢀⣀⡄⠀⠀⠉⠂⠈⠳⠌⠉⠀⠀⠉⠉⠁⠉⠀⢀⠈⠁⠀⠈⠁⠀⠈⠀⠀⠀⠘⠒⠀⠀⠘⠉⠀⠀⠀⠈⠐⠈⢦⣐⠒⠒⠲⢤⡁
⢦⡀⢠⠀⠳⢤⣀⣀⡀⠤⢃⢤⠄⠀⠀⢤⡀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠈⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⠁⠄⠠⣔
⠘⠷⠎⠳⠓⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠻⠿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠿⣿⣿⠿⠋⠀⠀⠀⠀⣀⣀⣠⣤⠴⠂⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⡆⣶⣶⡌⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣛⠆⠀⠀⠀⠀⠀⣴⠾⣿⣿⣿⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⢧⣍⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠶⠿⠿⠿⢿⣿⣿⣿⣇⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠤⠤⠶⠶⠚⠋⠁

⣿⡇⡆⣿⣿⡿⢣⣾⣿⣿⣿⡇⡿⢾⡿⣿⡿⣩⡥⣬⣴⡇⠐⢾⣿⡋⣻⢿⢿⠬⠉⢠⠄⠡⣤⣥⣤⢠⡴⣷⣤⣼⣧
⢊⡶⢶⢈⡝⠙⢿⣾⡽⣿⣶⡯⠾⡷⠟⠛⢷⣎⣿⠘⠛⢓⣿⣧⣴⣷⣷⣚⠀⠈⣭⣤⡇⢤⡭⢽⣷⣿⣟⣿⣿⣿⡟
⡏⣥⠁⢙⠋⠸⡂⢹⣿⡿⣼⣿⣿⡇⢀⣀⣤⠈⠁⠼⡁⠐⠞⡿⠋⢄⣼⣿⡶⣤⣿⣿⣡⢼⠶⢻⡿⣿⠟⢸⣿⣾⣶
⠁⢀⡀⠀⠀⠠⠃⠠⠘⠑⠛⠀⡈⠁⠈⠋⠁⡀⠀⠀⠉⠀⠀⠘⠀⢻⣭⣼⠁⢾⡿⣔⣦⠏⣿⠟⣿⠃⣠⣾⣿⣿⣿
⡨⣭⠣⣾⠄⠀⠀⠀⠈⠀⠀⡈⢷⣠⣀⠈⢰⣦⠇⠀⢀⠂⠙⠀⠘⠄⠉⠟⠙⠉⠀⠀⠀⠀⡍⠰⠈⠷⠿⠉⠛⠿⠿
⣴⣦⢵⣿⣾⡧⢀⠀⠂⠘⢹⡿⣽⠈⢯⠔⣋⠄⡨⢔⠟⢶⣏⢁⣤⡄⠀⠀⠆⢈⠟⡛⣁⠀⢤⣦⡄⢀⣀⣤
⠟⢃⡛⠋⠀⠃⠞⠞⠙⠀⠀⠀⠀⢀⡀⢀⡁⢨⠘⠺⢂⣤⡄⠈⡿⣾⣶⣜⣤⣶⣘⠂⠀⢠⣶⣲⡄⢘⣉⡀
⣂⡉⣿⣆⠀⠀⠆⠀⢀⣤⠀⠘⠉⠈⠉⠀⠃⠀⠀⠀⠀⠼⣳⣼⡟⠿⣿⢿⠝⣿⠏⡀⠀⠘⠻⠿⠃⠘⠉⠁
⠘⠁⠋⡟⢂⣼⣾⠲⠀⠟⠀⠀⡾⢆⣠⣭⣤⠀⢀⣀⣸⡃⢸⢛⡆⠰⠃⠎⠈⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⠄⡁⠠⠆⠈⠅⠀⢸⣧⣶⠆⠠⣼⣿⣿⡏⢠⣿⡿⣿⡥⣾⢟⠠⣶⡮⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⣿⣿⠻⠃⠀⠉⠙⠐⠚⢟⠺⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠑⢀⠀⠀⠀⠀⠀⢀⠀⡒⠀⠀⠀⠀⠀⡀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠄⠀⠀⢀⣭⠏⠰
⠀⠀⠀⠀⣤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠠⠘⠷⢠⣬⣥
⠰⠿⠃⠈⠨⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠎⠳⠎⠁⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠉⠰⠋⢁⠀⠀⠠⠠⠀⢀
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠀⠠⠀⠀⠀⢀⡈⠀⠀⠀⠂⠈⠀⢘⡃⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠐⠄⠂⠀⠈⠏⠀⠂⣀⠺⠂⠸⣟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⣠⠄⠠⠤⠀⠀⠀⢀⣀⠀⠀⠀⢈⠸⠆⣨⣄⡀⠚⠗⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣀⡀⢤⠀⠋⠀⠀⣦⡀⠀⠚⠀⠰⢠⠀⢥⡢⠈⠐⠎⠈⠚⠛⠈⠀⠀⡴⠀⠈
⡀⠀⠀⠀⠀⠀⠰⠦⡈⠁⠀⡸⢿⣌⡅⠼⠀⠀⢀⡀⠁⢀⣤⠈⠀⠆⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⣀
⣅⣿⣦⣰⣶⣿⣷⣖⠇⠀⡀⠀⠀⠉⠀⢲⠄⠤⠈⠁⠀⠀⠀⠀⠈⢠⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡄⠺⠈⠜⡃
⢿⡟⢿⣽⣭⡍⠀⠋⠀⠰⠁⠀⠀⠀⠀⠀⡀⠀⠐⠀⡀⠠⠂⠀⠀⠠⠀⡀⠀⠀⠃⠀⢀⠀⠀⠀⣠⠠⠆⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⣙⠢⡀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢠⠆⠀⠉⠁⢈⣄⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠏⠀⣄⠶⣮⠠⠇⠉⢶⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠃⡀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⡍⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠐⠡⠤⠀⢠⠇⠀⠀⣀
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣠⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠓⢆⠁⢀⡎⠀⠀⠐⠉⠑⢄
⠀⠀⠀⠀⠀⡧⠌⠀⠀⢰⠁⠿⠆⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠃⠈⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⡖⠊⠀⠀⠈⠉⠁⠀⢙⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠹⡄
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢢⠀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠄⡄⠀⠀⠇⠀⠀⠀⠀⠀⠀⢣⠀⠘⣆
⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠈⢀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠃⠀⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢦⠀⠘⡆
⡔⠀⠀⠀⡴⠛⠢⢤⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⠀⠀⡇⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠸⡄
⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠥⠬⢩⣀⣈⣁⣍⡁⠐⣄⠀⠀⠀⠀⠀⣀⡀⢀⡷⠀⠘⡄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⠞⠓⠠⠄
⠈⠀⢸⠀⠀⠂⠄⠀⠀⠀⢀⠊⢈⡲⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠠⠤⠒⠁⠀⢀⠀⠀⠀⡠⠎⢀⡠⠚⠁
⠀⠀⠘⡄⠀⠘⡈⢂⡠⠔⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⡄⡀⠉⠐⢊⠠⠊⠁
⠀⠀⠀⢱⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠡
⣶⣶⠶⠶⠶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠞⠙⠳⠞⠉⠛⠖⠛⠙⠳⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠇⠀⠀⠀⠀⣰⠶⠞⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠋⠻⣄⡀⢀⡀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣀⣀⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠳⢤⣤⣴⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠻⣦⡴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠀⠀⠀⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢹⡆
⠀⠀⠀⠀⠀⠀⢰⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠃
⠀⠀⠀⠀⠀⠀⢻⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣀⠀⠀⢀⣼⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣚⣭⣭⣿⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⢸⣿⣳⠿⣿⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⠀⠀⢸⠻⣿⣯⣭⣵⡞⡇⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣟⠓⠾⣇⠀⠀⠀⠀⣰⠷⠖⠛⠋⠁⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢹⠏⠙⠓⠾⠷⡄⢠⡾⣥⠤⠴⠶⠚⠋⠙⣏⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⡿⠀⠀⠀⠀⠀⣏⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢰⡇⠀⣀⣤⡤⠶⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠙⠛⢻⡟⠉⠀⠀⠀⠿⠾⢶⡄⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠴⠾⢷⡆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣤⣶⣾⣁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢶⣤⣤⣼⣧⣄⣤⢤⣤⣤⣾⠁⠀⢹⣧⣀⣀⣤⣄⣀⡀⠘⡇⢀⡴⢶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣤⣾⣤⡤⣶⡶⣿⠀⠀⢸⡇⠙⠶⠶⠞⠁⢨⡿⠛⠻⣯⠙⢷⣿⣿⣁⣼⠋⣧⡀
⠀⠀⠀⠀⠀⣰⠏⠉⠉⣉⡽⠿⢷⡾⢯⣿⠞⠋⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠸⣧⣀⣀⡿⠀⠀⢹⡿⢻⣿⡛⠿⢯⣉⠉⠉⠉⢻⡄
⠀⠀⠀⠀⢰⠏⠀⣠⠞⠉⠀⢠⣶⣿⣞⢻⣦⣤⡤⠞⣷⠀⠀⠀⣠⣤⣤⡀⠀⠀⠈⣩⣥⣄⣠⠞⠋⣀⣾⣽⠷⢶⡄⠉⠳⡄⠀⠀⢿⡀
⠀⠀⠀⢠⡟⠀⠀⣿⠀⠀⠀⢸⣏⠻⢯⣛⡻⠶⠶⠾⣿⣦⣤⣶⡯⠬⠿⠿⠳⠶⠛⠉⠀⣈⣩⡴⠞⢉⡾⣧⡴⠟⠀⠀⠀⣿⠀⠀⠈⣷
⠀⠀⢀⡟⠀⠀⠀⠙⢧⣀⠀⠀⠙⠷⣤⣈⠙⠛⠲⠶⠦⠤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠚⠛⠉⣁⣤⠶⠛⠳⣼⠇⠀⠀⣠⡼⠃⠀⠀⠀⠘⣧
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⠉⠙⠓⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠛⠋⠉⠀⠀⠀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠸⣆
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣸⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠈⠋⠛⠈⠀⠀⠀⢑⣺⡿⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠘⠠⢣⠈⠐⠀⠀⠀⡀⢠⠀⠀⠀⠈⠁⠱⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠁⠀⠈⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⣋⠐
⠂⠀⢠⠀⠀⡀⠀⠀⠀⠂⠀⠀⠉⠉⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⠂⠛⠀⠀⠀⠘⡀⠠⠀⠀⠀⠀⢁⠐⠀⠀⠀⠀⠀⠀⠈⠙⠑⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⡉⠀⠀⠀⢀⠀⠂⠤⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠐⠀⠀⠀⠀⠠⠂
⠀⠖⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠂⠈⠶⢑⣂⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐
⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠰⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠂⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠐⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠈⠄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠐⠐⠆⠀⠈⡈⠀⠅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣧⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣮⣯⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠒⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠠⠀⣦⡀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠈⠀⠀⢹⠀⣡⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠀⡒⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢢⡀⠀⠠⢡⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠀⢃⠀⠀⠀⠀⠛⠖⠒⠂⢆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠂⠀⠀⢀⠠⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⡀⡐⣶⢾⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢡⠀⠉⠈⠀⠉⢉⠳⠛
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠀⠀⠀⠑⢌⢁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠁⠀⠀⠀⢀⠀⠡⣼
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡁⠀⠀⠠⠄⠀⠆⠀⡐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⡀⠀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⡄⣨⣤
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠈⢻⠂
⡄⡈⠰⠂⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠞⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣄⠂⠛
⠁⠋⠂⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀⡙⠢
⠠⠄⠀⠀⠹⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠀⢀
⢀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠊⡁⡀⠈⠠⠲⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠂⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠒⠚⠛⠛⠋⠉⠉⠛⠛⠛⠒⠶⠦⣤⣀⡀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢿⡌⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠠⢶⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣞⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⢤⣄⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠩⣿⣗⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣀⣭⣏⠛⠓⠲⠶⢤⣤⣀⣀⡙⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣠⡴⠚⠁⠀⠈⠙⠲⣄⠀⠀⢤⡈⠉⠉⠛⠛⠲⠶⠦⣤⣄⣀⡀⠀⠀⠀⠀⣿⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠲⡏⠁⠀⠀⠀⠀⠀⠀⠀⠘⣦⠶⠚⠛⢦⡀⠀⠀⠀⠀⠀⠶⣯⠄⠀⠀⠀⠀⠀⢉⣭⣉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢻⡄⠀⠀⠀⠀⠀⠠⣶⣾⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⡌⠳⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⣿⣿⢼⠃⠀⠀⣾⠁⢀⡤⠴⠶⠤⣤⣄⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣰⠒⠢⣍⠛⠒⠶⠶⠒⢷⡀⠀⠀⠀⠈⣡⠟⠀⠀⠀⠉⠉⠉⠑⠲⡄⠀⠀⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠹⣄⠀⢈⠂⠀⠀⠀⠀⠀⠻⡗⠲⠖⠛⠁⠀⠀⠀⠀⠘⢿⣳⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡵⢤⣀⣀⣉⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠲⣏⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠲⢦⠀⠀⠀⠀⠀⣀⣤⠶⡿⠁⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠦⣤⣀⣤⣤⠴⠖⠋⠉⠀⣸⠃⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⢶⣶⣶⡶⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡤⢤⣤⣤⣤⣤⣤⣤⣤⠤⠤⢼⠀⢸⠶⠶⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠛⠓⠛⢂⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢿⣦⢼⣧⠀⠀⠀⠀⠀⢀⣠⠴⢫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⣉⢽⡶⣤⠖⠚⢷⡦⣤⣤⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠧⠀⣵⣇⡀⣸⠉⢳⠘⣇⢹⣉⣉⣉⣙⣒⣲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠈⠻⠭⠭⠩⠭⠭⠭⠭⠥⠤⠴⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⠿⠿⠟⠁⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⢠⠆⠀⠀⠀⠦⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⡀⠀⠠⢀⡀⠀⢳⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⡝⢿⡄⠀⠀⠈⢀⠀⢸⠀⠀⠀⢸⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⡆⠀⠀⣠⡇⠀⠉⠋⠀⡀⠀⣸⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⣤⡒⠒⠢⢿⡄⠀⠀⠈⠓⠒⠒⠊⠁⢀⡏⠀⠀⠀⣧⢄
⠀⠀⠀⠀⠀⠀⣤⡊⢙⡶⠏⡟⢶⣄⡀⠀⠀⠦⣀⣠⡎⠀⠀⠀⢸⡿⢾⡀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡟⣁⡂⠇⠀⢈⡏⢻⠙⢏⠙⠆⢟⢦⡀⠀⢊⡻⠄⣩⠆
⠀⠀⠀⠀⠀⠀⡼⠝⡏⠉⡟⣧⣠⡟⠀⠂⠀⠈⡰⡄⡜⢇⣓⡄⠀⡇⡎
⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⡇⡇⣿⠀⠀⠸⡡⠔⠘⢑⡇⡈⢫⡀⢠⠃⢡
⠀⠀⠀⠀⢠⡇⡇⣧⠀⠀⣇⣤⡾⠃⠀⡆⡇⠀⣠⠴⠊⠀⢸⣇⡎⠀⢸
⠀⠀⠀⠀⣸⡇⡇⡟⣧⣶⡋⠀⠸⡤⢼⣳⢃⣾⣤⢾⡟⢯⡁⠈⢁⢀⣮⡀
⠀⠀⠀⠀⣽⠃⡇⡇⡇⡏⣷⡀⠀⢻⠞⠁⣜⢰⢸⣿⠀⠀⢹⠊⠥⠄⠀⢈⡁⢒⣤⣄⣀⡀
⠀⠀⠀⠀⢸⠷⢷⣧⣧⣅⣆⣷⡄⠀⠀⢰⣃⣸⣼⣏⣤⣴⠾⡍⠀⠂⠉⠁⠀⡸⢻⣿⣿⣿⣿⣶⣶⣤⣤⡀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠉⠙⢦⣴⣯⣿⣿⣿⣿⣿⣿⣄⣈⠒⠐⠐⠒⢉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠉⠉⠛⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠙⠻⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣀⣀⣤⣼⣿⣀⠀⠀⠈⢧⡀⣿⢉⣿⣿⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠳⣄⠀⠀⣳⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷⣾⣿⣿⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣫⣶⣦⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠹⢿⣿⡿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡴⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠀⠀⠀⢠⣤⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⡟⠋⠉⢻⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠐⠦⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢀⠀⣀⣀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠄⠒⠒⠚⠦⠤⣄⡀⠀⠀⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⣀⠄⠈⠑⢦⡘⠿⠿⢿⡿⠟⠛⠿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠈⠀⠀⠐⠀⠀⠈⠀⠀⠀⢀⡀⠐⠀⠙⡄⠀⠐⢀⡠⠔⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠐⠀⠀⠔⠀⠀⢠⠴⣄⠀⠀⠀⠀⠀⠄⠀⠀⠀⡖⢺⡁⠉⠈⠁⣀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⢀⠎⢀⠄⠀⠀⠀⠀⠐⠐⠒⠊⢀⡠⠔⠀⠀⠄⡀⠀⢀⡴⣤⢱⣼⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⢀⠎⢀⠀⠀⠀⠃⠀⠀⠀⠐⠒⠈⢁⠀⠀⡠⠀⠀⠀⠀⠸⣄⠉⢛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⡜⠀⠂⠀⡀⠀⠠⠀⠀⠀⠠⠂⠀⡀⠀⠀⠁⢠⠋⠉⠳⣀⣸⡴⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⢷⡀⠀⠀⠈⠀⢀⡀⠀⠀⣀⣀⠀⢀⡀⠀⣠⠇⠀⢀⣠⠜⠉⠀⠀⠈⠙⠓⠒⠒⠒⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠈⠛⢶⣊⠉⠲⢄⣀⠤⠊⠁⠀⠉⠒⠒⢋⣁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠫⢄⣀⣀⣀⣀⣀⠤⠤⠒⠊⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠴⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠉⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣤⣀⣙⣿⣿⣿⣀⣀⣤⣤⣤⣶⣶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣶⣿⣿⣿⣿⡿⢿⡿⠿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠿⠿⠛⠋⠉⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣶⣦⣦⣶⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⠠⠄⠀⠀⠀⠀⠀⠀⢀⣄⣰⡄⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠐⠿⣦⡀⡀⠀⠃⢀⠘⣻⣿⠃⠘⠛⠻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢳⣶⣦⣤⣠⣼⣿⣠⠆⡀⠛⠘⠛⠛⠚⠓⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣇⠈⠹⠻⣿⣿⣿⣿⣧⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⠀⡈⢻⣿⣿⣿⣿⣿⣿⣰⣾⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠈⠁⠏⠐⠀⠀⣹⠟⠛⠿⢿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⡄⠀⠀⢠⡾⠃⠀⠀⠀⠀⠈⠉⠛⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠀⠀⠋⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠘⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢿⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⣆⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⡿⣏⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢧⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⢯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠛⠙⠿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡟⢿⣛⣽⢦⡙⡹⢿⣿⣿⠿⣋⣫⡈⠙⡿⢏⡛⠉⠇⠀⠀⣻⠙⢦⠄⣄⠀⢠⠴⢀⣾⣶⣴⣿⠘⠚⠀⡄⢠⠱⣷⣍⢃⠻⠒⢋⡙⠿
⢿⣿⣽⣾⣮⣏⡎⠹⠁⠀⠀⠀⠰⠋⠐⠈⠀⠀⠞⠃⣤⡄⢠⣀⡹⣷⠆⠂⡀⠀⢌⡰⣊⣬⣺⣿⣷⣔⢃⠊⣩⣸⣿⣿⣷⣀⣀⣠⡄⣼⣿
⠀⠁⠋⠩⠿⢀⣠⠁⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⡹⠋⠿⠿⠃⡀⠀⢈⣁⣜⠊⠘⣿⣿⣿⣿⣿⣫⣿⣷⢟⣗⢻⣮⣿⣿⣩⡻⣗⣻⡊
⠀⠀⠀⠀⣧⢾⡿⣁⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠭⠛⠀⠀⢾⣿⣿⢽⣿⣿⣿⣿⡲⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⢂⣼⣿⣴⠻⣧⠏⠐⠀⣀⠂⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⢏⠉⠀⠁⠙⠻⡿⢿⣿⣿⣿⣿⣿⡟⢛⢿
⠀⠀⠀⠐⠳⠄⠛⠙⠇⠎⠀⢀⣴⣦⡔⠀⣀⣴⡖⣷⣼⣀⡀⠀⢀⠀⠀⠀⣤⣄⣴⣶⣶⣶⣶⣿⣿⣷⣦⠀⢠⠿⣿⡷⠏⠻⣿⣿⣻⣭⣼
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠘⠿⠛⠰⠘⢿⣯⡀⠛⢫⡽⠟⠐⠈⠀⠀⢀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠄⠊⠁⢹⣿⣮⣻⣿
⠀⠀⠄⢀⠀⠀⠀⠀⠈⠀⠠⠀⢠⠀⠀⠁⠞⣿⠁⠐⠆⠃⠹⠣⠀⠈⠀⠠⠀⠀⠀⠈⠃⠙⠉⠈⠙⡏⠁⠀⠀⠀⠀⠙⣃⡀⢼⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠀⠒⢀⠀⠀⠀⢠⠙⣳⡏⠀⠐⣦⢇⠰⠈⠀⠀⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⢿⣿⣿⣿
⢺⣤⠁⠹⠁⠀⠈⠀⠀⠀⠔⣬⣛⣷⢷⡠⣶⡝⣹⠀⢀⣁⠲⢌⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠘⢿⣿⣿⣿⣿
⣶⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠃⡼⠃⣯⢳⢛⣋⣖⡾⣿⠜⡑⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠹⠏⠉
⡞⠓⠀⠀⢠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠀⠯⡷⡜⠫⣉⠄⠈⣃⢯⣹⣆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢁
⠏⠂⠀⠓⠂⠀⠀⠀⠀⢀⠀⢀⡀⠄⠀⠀⠲⠁⡀⢀⡸⢧⠰⡇⠀⠈⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠂⠀⠰
⡛⠂⠀⠀⠁⠀⠀⠀⠀⠉⠨⠅⠁⠀⠀⠀⢺⠲⠀⢀⡀⢮⡐⣯⢧⣢⡀⠂⠂⠰⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀
⣁⣠⠀⠀⡀⢀⠀⠀⠠⠀⠀⠀⡰⠀⠀⣀⡀⠀⠀⠀⡛⢃⡅⣿⢻⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐
⣿⠘⣿⡥⣠⣈⡀⠢⢀⡀⠀⠀⠀⠀⠠⣿⣀⠀⠛⠃⢁⢋⢣⠁⠄⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁
⣏⢀⡙⣿⡽⢷⠖⠺⠁⠰⢿⡄⢠⢤⣤⠞⠟⣤⣲⣬⣀⠈⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠷⠹⣧⣨⣹⠸⠿⠷⢄⠣⣰⢆⠈⠀⠉⠀⠀⠈⠛⠙⠻⢴⠁⠀⢠⢀⠀⠀⡀⠈⠀⠑⠀⡁
⣛⣱⣾⡶⠿⣦⡴⡮⣻⡖⠧⢦⡀⣞⠧⠀⠐⠀⠀⠀⠣⠔⠀⠀⠀⠰⠄⠀⢲⣲⣶⣇⡖⠁⢠⣈⡀⢀⠀⠀⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⢶⠟⠛⠳⠟⠉⠛⠶⠛⠛⠳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣤⣤⠞⠛⠛⠛⠉⠀⠉⠉⠈⠛⠒⠶⠞⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢠⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠶⣄⣀⣠⡼⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⣀⣼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⡼⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣼
⠀⠀⠀⠀⠀⠀⢸⡃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁
⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⢤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣄⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡶⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⢸⣷⣭⣭⡭⠵⣺⡇⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⣀⣸⠘⠛⠛⠛⠛⠋⡇⢀⣀⣤⠴⢶⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣼⣧⣍⡙⣦⡀⠀⠀⢀⡼⠋⠉⠁⢀⣀⣼⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⣿⠀⠈⠉⠙⠛⡆⢰⠟⠒⠒⠛⠋⠉⠁⠀⢿⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣀⣿⠀⣠⣤⠶⠞⠻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠉⠉⣻⠃⠀⠀⠀⠀⠿⠞⢳⡆⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠶⠟⢛⡆⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣶⢦⣤⣼⣦⣤⠶⠶⣤⡴⣿⠀⠀⢘⣧⣤⣤⣤⣤⣄⣀⠀⢿⠀⣠⠞⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢠⡶⢦⣴⣧⣤⡴⣶⠾⣇⠀⠀⢸⡆⠙⠶⠶⠞⠁⢀⡾⠛⠛⢧⠉⠻⣿⣿⣅⣠⡟⢹⣆⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⡟⠉⠉⢉⣭⠿⠿⣶⠿⣽⣷⠛⠁⠀⠙⠓⠚⠋⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⡼⠀⠀⠈⣿⠟⣿⣟⠻⠿⣍⡉⠉⠉⠉⢷⡀
⠀⠀⠀⠀⢠⡟⠀⢀⡴⠋⠀⠀⣴⣼⣷⠛⢻⣄⣠⡴⠞⣦⠀⠀⠀⣀⣤⣤⡀⠀⠀⠈⣩⣭⣄⣀⡶⠛⢁⣰⣯⡿⠶⣦⠈⠙⢦⡀⠀⠈⣧
⠀⠀⠀⢀⡾⠀⠀⣾⠁⠀⠀⠀⣿⠛⠿⣝⡻⠷⠴⣶⣿⣿⣤⣤⣾⣯⣭⠽⠿⠶⠶⠞⠋⠁⠈⣉⣥⠶⠛⣹⢿⣤⠶⠋⠀⠀⢈⡧⠀⠀⠘⣇
⠀⠀⠀⡾⠁⠀⠀⠘⢷⣄⠀⠀⠈⠳⣤⣈⠉⠛⠲⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠛⠛⢉⣀⡴⠞⠻⢦⣿⠀⠀⠀⣠⡾⠁⠀⠀⠀⠹⣆
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠉⠛⠳⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠛⠋⠉⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⢹⡄
⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣌⣉⣉⣉⣉⣉⣁⣀⣀⣀⣠⣤⣤⡤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠲⢽⣿⣿⣿⡧⣤⣀⣈⠛⠛⠛⠻⠿⣿⠷⢭⣙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠰⢸⣿⣿⠋⠀⠀⠈⠉⠉⠀⠀⠚⠺⢆⡛⠢⡌⢣⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣾⣿⣿⠀⠙⠳⠶⠒⠀⠠⠀⠰⣤⡄⡑⠀⠀⠜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠁⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣾⣿⣿⣿⣷⣄⠸⣿⣿⡀⠀⠀⠀⡀⠀⠀⠀⢀⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠉⣀⣠⣴⠊⠀⡆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠰⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠇⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⠹⡻⠟⢁⡠⠒⠈⠉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢀⠔⠁⡠⠂⠀⠀⠀⠀⠈⠄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡠⡁⢀⡜⠁⠀⠀⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⡞⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿
⡿⠿⠿⢿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣦⡀⣀⣤⣴⣦⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⡀⠈⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⣀⠀⠒⠒⠶⠶⠶⠶⠾⠟⠛⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠈⠀⠀⠀⠀⠀⠾⠗⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠐⠂⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠸⣧⣀⡀⢀⣠⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⢉⣉⢉⡁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠙⠋⠉⠉⠙⠀⣾⠁⠀⠀⢀⣠⣴⡶⠶⠟⢉⣉⣓⣒⡒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢀⡴⠋⣰⢏⣴⠶⢛⠉⣉⣉⡉⢩⠙⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣠⣿⡟⠁⣠⡴⣿⣉⡉⠉⠛⠳⢦⣄⡿
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠉⠛⠲⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⢰⡏⢡⡟⠐⠀⣷⣄⣀⠈⠙⠳⢦⣀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⡇⣸⠃⠀⠘⣧⡈⠉⠻⢦⣄⠀⠉⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⠃⣿⠀⠛⠀⠈⠙⣦⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⣿⡀⠀⠀⠀⢸⡏⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡜⢧⡀⠉⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣙⡓⠶⠶⢶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠋⠉⠉⠉⠉⠀⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠋⠀⠀⠀⠉⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢀⡽⢿⣿⠁⠀⠐⠒⠀⢰⠑⠂⠀⢷⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠈⢧⣣⡙⠃⠀⣠⠀⠒⠼⠀⠀⠀⣼⠀⠰⣿⡇
⠀⠀⠀⠀⠀⢀⡠⠤⢄⣷⡀⠀⠉⠒⠤⠤⠔⠂⢀⠇⠀⠀⢹⣀
⠀⠀⠀⠀⠀⢈⡜⠓⣦⠞⡗⣤⡀⠀⠀⠤⠄⣠⡎⠀⠀⠀⣾⢷⡁⣀
⠀⠀⠀⠀⠀⠈⢠⡟⣁⡀⠃⠀⣹⢛⠛⢻⠙⠎⣟⢆⠀⠐⡙⠇⣸⠗
⠀⠀⠀⠀⠀⣰⠏⡏⠀⡟⣧⣼⠃⠈⡀⠈⣔⡔⡜⢮⣱⠀⢠⢸⠁
⠀⠀⠀⠀⢠⡟⡇⠇⠀⡇⠇⣇⠀⠈⢏⠖⠈⠡⢇⠌⢣⠀⡎⠸
⠀⠀⠀⠀⣾⡇⢻⡆⣀⡧⠞⡋⠀⣸⡸⢀⠔⢚⣅⣀⠞⣼⠀⢠
⠀⠀⠀⠀⣿⠃⠀⡟⠻⡄⠀⠹⣛⡿⠁⢟⢻⣿⠃⠓⢄⠠⠄⠚⠢⠄⡀
⠀⠀⠀⠀⣧⣠⡀⡇⠀⠛⣄⠀⠋⠀⡼⠸⢸⡟⠀⣀⣮⠌⠁⠀⠰⠂⢸⢿⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⣯⠉⠙⠛⠛⠓⠻⢦⡀⣰⣷⣿⣿⣿⣿⣏⠈⠢⢀⣀⠠⠔⢃⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠐⠚⠓⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠻⣝⠻⢿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣤⣤⣤⣤⣿⣀⡀⠀⠈⢦⢸⣏⣹⣿⡟⠁⢸⡇⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢦⡀⢈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⣿⡿⠿⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠿⣯⣾⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢻⣿⣿⠿⠿⠟⠛⠋⠉⠉⠉⠉⠈⠙⠻⠿⠿⠿⠿⡿⠊⠉⠉⠋⠀⠀⠉⠉⠉⠁⠈⠈⠈⠺⠹⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡿⠟⠛⠻⠛⠿⣿
⣿⣿⢸⣧⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⣿⣿⢺⢿⡗⢠⠖⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⣿⣿⢸⣯⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⢿⣾⡿⠗⣤⠀⠈⠀⠀⠀⠀⠀⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣾⣿⣿⠖⠠⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣷⡎⠃
⣿⣿⣿⣿⣿⡗
⣿⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣥⣯⣤⣤⡄⠀⠀⠀⠀⠀⠀⣤
⣿⡟⣽⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠰⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣷⠄⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣽⣫⣷⣿⣿⣿⣿⣿⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡅⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⡁⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣾⡏⠀⠀⢱⣦⠰⠄⠀⢠⣿⣿⡶⠀⢀⣴⣦⡐⠀⢲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠟⢫⣌⡁⢱⡂⠘⠿⢀⣿⣾⣿⣿⡿⣧⣿⣿⣻⣿⣿⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣄⣀⣶⢰⡒⢀
⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣼⣿⡏⣿⣿⡇⠀⠀⡈⣻⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢀⡄⢀⣤⣀⣤⣦⣴⢤⣾⣿⣶⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⣾⣷⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿