Pirate treasure Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠲⠦⠤⠤⠤⠤⠤⠤⠶⠲⠦⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠶⠤⢤⣤⡤⠤⠤⡤⠤⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⡿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠒⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠈⠉⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⡀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠈⠁⠀⣧
⠀⠀⠀⠀⠀⠀⢸⠤⠤⢤⡤⠄⠠⠦⠤⡠⢄⡤⠀⣠⢤⠤⠤⠤⠤⠤⠤⠤⠬⠤⢤⣤⠤⠤⠤⠤⢤⡤⠤⢤⠤⡀⡤⠤⣤⠤⠥⠤⠤⠤⢤⡬⡤⡇
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁⠉⠉⠉⠉⠉⠉⠁⠀⢸⠉⠉⠉⠉⠉⠉⢹⠉⢩⡍⠈⡏⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⠀⠘⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠂⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⢀⠀⠀⣀⢀⡄⣈⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⣃⣃⣀⣀⣠⣄⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣄⣀⣀⣘⣀⣂⣀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣰⣀⠀⡀⠀⠀⠀⠀⢄⢀⢸⠀⠀⠀⠀⠀⠀⢰⣒⠄⠀⠀⠀⠀⢢⠄⢠
⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡟⢧⣸⡨⢻⡄⠀⠀⠤⠴⢮⣇⡾⣤⠂⠀⠀⠀⠀⠰⣿⠂⠀⠀⠀⠀⠨⢣⢪
⡀⡀⠀⠀⢀⠀⡀⢀⠀⠀⠈⠹⣏⡹⢿⢯⣹⠏⠁⠀⠀⠴⢲⡏⣷⠶⠶⠦⠀⣀⠀⠀⣿⠀⠀⡀⠀⠀⢀⢣⠣
⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠠⠛⠳⢾⠖⠛⠆⠀⠀⠀⠀⢸⠃⠈⠃⠀⠀⠀⠙⢦⣤⣿⣤⠾⠁⠀⠀⢰⡁⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⢀
⢀⣠⣴⣶⠿⠛⠃⠀⠀⢨⢸⠖⠒⠒⠒⣒⠰⠁⡇⠀⠀⢰⡄⠁⠀⠀⠑⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠋⠁⢹⠇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠛⠃⠀⡇⠀⠀⠀⠙⢦⣶⡾⠟⠋⣛⣢⡄⠀⠀⠀⢈⣇⢠⣾⣦⢀⣿
⠀⠀⣸⡅⠀⠀⠀⠀⠀⢸⢸⠀⠈⠀⠀⠀⠀⡤⡇⠀⠀⠀⠀⠐⠈⠙⣾⣿⣿⣿⡇⠀⠀⢰⣿⡉⣿⣗⣿⡇⣙
⠀⠐⠉⠉⠂⠀⠀⠀⠀⠘⠒⠂⠉⠀⠈⠉⠒⠒⠁⠀⠀⠀⠀⠈⠢⢀⣿⡿⠿⠛⠁⠀⠀⠀⠙⠛⠉⠛⠛⠙⠛

⢧⣤⣤⣤⠴⣶⣶⡄⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄
⢸⣿⣿⣷⡀⣿⣿⣿⠀⠀⠀⣀⣿⣏⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⡻⣙⡟
⠀⣿⢿⣿⡵⠾⠿⠿⠆⠀⠀⣟⣛⣛⣻⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⢐⣻⣓⣻⣷⡀⠀⠀⠀⢀⡀⢽⣷⣿⢀
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣶⡾⠀⠀⠐⢿⣿⣷⠀⠀⠀⢿⣷⣿⣭⣧⣭⣿⣿⣿⠟⠀⠘⠛⣳⡿⣗⡛
⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⣈⣡⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀
⢴⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⢀⣴⣾⣿⡿⠿⠿⠿⠻⠇⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠻⢷⣤⣀⣠⣴⠾⠋
⠀⠈⠉⣵⣿⣿⣷⡄⠀⠀⠀⠀⢼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠠⣄⣲⠊⠉⠉⠳⣖⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⠶⠒⠒⠒⠒⠒⠒⠤⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠜⠉⠀⠀⠀⠀⢀⠖⡫⠭⠭⢕⡢⡄⠀⠀⠀⠀⠀⠀⠀⣉⠝⡫⢛⣛⣑⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣁⣘⣒⣒⣒⣒⣒⠒⠣⠾⠤⠬⠭⠤⠽⣈⣆⣀⣀⣀⣀⣀⡰⢣⢎⠴⡁⠀⠀⡈⢻⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠐⠀⠀⠈⡈⢹⠉⠍⠉⠉⠁⠒⠒⢒⣒⠒⠒⠒⠂⠠⢎⢸⡀⠀⠀⠀⠈⠂⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠨⠄⡠⣔⠧⠀⠀⣀⡀⠀⣀⠀⠀⠀⢎⡡⠀⢀⠀⠈⠱⣝⢄⠀⠑⢄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⠣⠕⡛⠀⣠⠔⠒⠲⠊⠉⡀⠉⠣⠽⠧⣠⠾⠚⢰⣒⠎⠢⡑⣄⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡳⢆⡻⠉⢡⠅⠀⣄⡀⢀⠀⠀⠁⣰⠃⠞⢠⠗⡸⢇⠀⢀⣀⠈⢮⠣⣠⣿
⠀⠀⠀⠀⠀⢀⠄⠠⢀⡀⠀⡉⠀⢀⣀⠀⡠⣄⠤⠄⠀⠊⠀⣀⢀⡈⠳⠐⠒⠚⠀⠈⠁⠂⣄⣀⣀⣑⣤⠃
⠀⠀⠀⠂⠘⡬⠶⠦⠤⠬⠭⢥⣄⣀⣈⣁⠄⢡⣀⡀⠀⣀⠈⠣⠔⠓⠀⠀⠘⠃⢄⠄⢀⣩⠭⢓⣚⣭⡝
⠀⠀⠀⢹⣈⡉⠉⠉⠉⠉⠙⠒⠒⣖⢶⠘⠦⠴⠤⠍⣲⣭⠭⢍⣉⣙⢅⣜⡓⢲⠚⣩⠥⠒⠋⠁⠀⡆⡇
⠀⠀⠀⠈⡁⡨⢄⣀⡀⠀⢀⢀⠔⢆⠠⣛⠤⠤⢴⣺⢉⣅⠀⠀⠀⠥⠔⠀⡇⢸⠀⡇⠀⠀⠀⠠⢰⢹
⠀⠀⠀⠀⣇⢳⠸⠁⢱⠘⡇⠀⠃⠉⠀⠈⠉⠉⠉⠀⠒⠤⠃⢒⢉⠶⠀⠀⡇⢸⠀⡇⢀⣜⠐⣢⣸⠸
⠀⠀⠀⠀⢸⠸⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⠀⠂⡆⠄⠘⡟⡇
⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡇⢸⢸⠚⡄⠣⠀⠔⢡⠃
⠀⠀⠀⠀⠀⢣⢹⠐⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⡈⠖⢒⠾⣹
⠀⠀⠀⠀⠀⠸⡘⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⢁⡤⢚⠥⠊⠁
⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠨⠭⠭⠭⠭⢉⣐⣒⣒⣒⣒⡒⠒⠢⠤⠤⠤⠤⠇⢸⢘⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠓⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⣀⣤⠤⠤⣀⠀⠀⠀⠤⠄⠴⠒⢶⣏⠁⠺⡛⠻⣆⠐⠢⡀
⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠙⣆⠀⠙⡄⠈⠻⣧⡀⣈⣦⠀⠀⠀⢀⣄⡀⠀⠹⣧⠰⠘⡄⠹⣧⠀⠹⡆
⠀⠀⠀⠀⢰⠃⣠⡾⠋⠙⡄⠙⣇⠀⠸⡄⠀⠸⣷⠀⠈⣆⠀⣀⣿⠁⠉⣦⢀⠹⣧⠀⢹⡄⠹⣇⠀⢹⡄
⠀⠀⠀⠠⡇⢰⣿⠀⠀⠀⠸⡄⢽⡄⠀⢳⠀⠀⢻⣇⠲⢸⡞⢧⡀⠀⠶⠀⢰⠉⡾⡌⠁⢧⠀⣿⡄⠀⣇
⠀⠀⠀⠀⣅⡀⠉⠙⠷⣦⡄⣧⠈⡇⠀⠸⡆⠀⢸⢿⠀⠀⣇⣀⣷⠀⠀⠀⠸⠶⠶⠃⠀⠘⠋⠉⠁⢀⣹
⠀⠀⠀⠀⣧⣨⣑⠢⢄⡀⠈⠋⠀⣿⠆⠀⠳⠚⠚⠛⠀⠀⠉⠀⣴⣖⣰⣄⣽⡷⠤⠐⠒⠒⣲⠬⡍⢨⢇
⠀⠀⠀⠀⣭⢸⡏⠙⠲⢬⣑⠢⢄⣾⣀⣀⠤⠤⢤⣖⠒⠒⢢⡭⢽⡇⢰⣂⢲⣏⣉⣯⠘⠛⡄⠀⣿⠈⡇
⠀⠀⠀⠀⣋⢸⡇⣴⢚⢶⠈⢳⢀⡇⠀⠀⣞⠉⠉⣿⠐⠟⢸⣤⠞⡟⢁⡼⢸⣆⠹⣿⣦⡄⡇⠀⣿⠘⡏
⠀⠀⠀⠀⡟⢻⣿⡟⠛⣇⡇⢠⠹⡞⠀⠀⣿⠀⠀⣿⡇⣤⣼⠘⠺⡇⢾⡉⢉⠼⣧⢿⣇⣄⡇⠀⣿⠘⡝
⠀⠀⠀⢀⠇⠻⣷⣑⣖⡼⠀⣼⢸⢣⠀⠀⣿⠀⠀⣿⡇⠀⢸⠀⠸⣽⡿⠒⢲⣏⠀⠘⣧⠁⢧⠤⠟⢀⣳
⠀⠀⠀⠸⣄⣑⠪⡑⢭⡢⣀⣻⢈⣇⠀⠀⡟⠀⠀⣿⡟⠛⢸⣀⣠⢹⠁⠀⠈⣏⠄⠀⣼⠦⣒⣒⣭⣍⣈⡆
⠀⠀⠀⠀⠀⠈⠣⣈⠢⣉⠢⣿⠸⡞⠀⠀⣇⣀⣠⣿⠇⠀⠘⣛⠭⠿⢧⣔⣀⣤⠴⠚⠋⠉⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡑⠦⡀⡇⠀⣀⣉⠭⠤⠐⣒⣉⡭⠤⠶⢦⡤⠭⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⡇⠈⢀⠤⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠒⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢯⣍⣉⠙⠩⡓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠛⠶⣶⣀⠉⠻⣷⡄⢈⣦⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⠋⡉⠙⠻⣦⣠⠤⢬⡻⣿⡀⠜⢛⣩⠴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⢭⣄⣀⠈⠙⢧⣄⡀⢸⡁⢠⣄⠹⡥⠶⣫⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠷⣽⡻⣦⡈⢿⣷⢀⣠⡿⢟⣫⢿⣄⣥⡔⡑⠋⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡡⡶⢿⡿⢿⣻⣟⣻⡤⢟⣻⣵⣾⠿⠾⠿⠛⢓⣤⣽⢲⠾⢷⡎⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡁⠹⣦⠙⣶⡟⣹⢇⣶⠟⢇⡁⡠⢧⣄⣲⡧⣾⠋⠉⢣⣀⣾⣏⡉⣸⡵⢂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠙⣆⣸⡿⢫⠞⢁⠀⠵⣠⢼⡍⠤⠊⣽⡏⢁⡛⠦⢴⡿⣏⣸⣶⣺⠿⣻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡾⢋⡴⢉⢒⣨⣿⡻⠉⠈⡿⣶⡖⣻⣿⡢⠙⢢⣼⠷⠒⠛⠉⠀⢘⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣯⣼⣩⠟⢿⢿⣋⣘⣿⡻⠛⢓⢝⠉⢑⣾⣏⣧⣤⣴⣶⣶⣿⢿⣻⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⠿⠿⢿⣦⣇⣈⡟⠉⢳⠊⠙⠒⢾⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⡄⡇⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣦⣤⡀⠈⠉⣷⠊⢉⢳⣧⢤⣾⡋⠻⣿⣿⣿⡿⢻⣇⠘⡇⣧⡇⣴⠁⡴⢾⡃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢘⢿⣿⣿⣷⣶⣾⠓⠀⠠⠧⣀⡸⡇⠈⣿⠛⠙⠀⠀⣿⣤⣷⣧⡗⢰⣘⠀⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⣿⠁⠛⢿⣿⣿⣿⢼⡗⡦⢄⡤⠃⡅⠀⢻⣠⣴⠶⣿⣿⡿⠋⢩⡟⠉⣨⣤⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠍⠉⢛⣿⣦⣇⡈⡟⢿⣿⢸⡇⡇⢸⣀⣠⠵⢞⣫⣿⣿⢿⣉⡟⠉⢢⣏⠉⠉⠉⠀⠀⠈⠻⣎⡶⢀⠀⢰⣶⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣋⠀⠁⠘⢻⣿⣿⣿⣯⣗⣾⣻⣞⢷⣛⣫⡵⢖⣻⣟⢛⡤⠐⣯⡀⣸⠷⣾⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣅⣬⡟⢿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⢾⣿⡼⠶⢧⠁⠿⣿⣃⡇⠀⡝⠿⠿⠟⣿⠋⠉⣏⠛⣿⠋⠘⠦⠲⡇⢈⠁⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢆⣹⡞⡁
⠀⠀⠀⠀⠀⠀⠀⣦⣴⡫⠀⢹⡆⠐⠊⢨⡿⠟⠛⠉⠙⠨⠐⠀⠒⠈⠀⠀⠿⡾⣿⢠⣾⡒⢠⣧⢀⠀⠀⠀⠀⠙⢿⠤⢄⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣠⣿⠍⠀⠀⠈⣷⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣙⢿⣦⡷⢞⠧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡷⢀⠀⠀⠀⠀⠀⠈⣷⣆
⠀⠀⠀⠀⠀⣿⣭⠅⠀⠀⠀⠀⣹⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠦⣴⡆⠀⠀⠁⠀⠀⢠⠒⡤⠃⢀⡀⠀⠀⠀⠀⠀⠈⠛⠛⢆⠀⠀⠀⠀⠀⠀⠹⢧⡀
⠀⠀⠀⠀⢂⠿⠁⠀⠀⠀⢀⡐⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⡀⢾⡹⠃⠙⠾⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠸⣷⡄
⠀⠀⠈⡠⠁⠀⠀⢀⣤⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⠻⠮⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⡼⠶⣶⣴⣎⣀
⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠈⠱⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣀⣀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⡤⠤⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡻⠟⠛⠉⠉⠙⠛⠛⠛⠓⠒⠒⠒⠲⠶⠶⠶⠤⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠁⠒⠒⠒⠒⠒⠀⠤⠤⣤⠴⠖⠒⠒⠒⠦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⣳⠶⢒⣶⠶⠶⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣡⠴⠛⣉⣉⣉⠓⢦⡉⠻⡍⠁⠉⠉⠉⠉⠉⠁⠐⠒⠒⠒⣶⠋⣡⠞⢉⡤⠶⢶⠲⠦⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⣈⠙⠛⠛⠛⠓⠒⠶⠶⠶⠾⠧⠴⠧⠤⢤⣤⣭⣉⣀⣀⣿⣀⣹⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡼⢁⡼⡁⠀⠀⠈⠳⡀⠈⠳⡜⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠉⠉⠉⠻⡉⠛⠛⠛⢳⡒⠒⢲⡶⠶⠶⠶⠶⠤⠤⠤⣤⣤⣤⣭⣭⣉⣉⣉⣉⣙⣛⣛⠒⠚⠀⡼⠁⡾⠀⠈⢢⡀⠀⠀⠈⢦⡀⢹⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠹⡄⠀⠀⠀⢱⡀⢸⠉⠉⠁⠒⠒⠒⠒⠒⠠⠤⠤⠤⠤⠄⣀⣀⣉⣉⣉⣉⡉⠉⠉⠳⡌⠳⣄⠀⠀⠙⢄⠀⠀⠀⠑⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠘⣄⠤⢄⣀⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⡦⠀⠀⠀⣉⡉⠉⠙⢦⡘⢦⡀⠀⠀⠑⢄⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠠⣦⢤⠴⡎⢹⡼⠁⠉⠉⠉⠉⣁⡒⠒⣂⠶⠶⠶⠶⠤⣤⠤⠭⣾⡁⣀⣀⣺⣀⣹⠀⢀⣀⠙⢦⠙⢦⠀⠀⠈⠳⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⢙⠷⢚⣉⡑⠢⡄⣠⠚⠉⠉⠉⠙⠁⠀⢀⣀⡀⠀⠘⠓⣺⢉⡷⣤⠞⡿⠁⠀⣹⣇⣈⠟⠈⠳⣌⠳⣄⠀⠀⠈⢲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣸⢠⣿⡝⠋⠳⣘⡃⠀⠀⣀⠀⣀⡀⠀⠉⠉⠉⠓⠀⣰⠃⢸⡗⠁⣼⡥⠖⣻⠋⠀⠀⠀⠀⠀⠈⢳⡈⠳⡄⠀⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠲⠤⣄⡤⠏⠘⠚⠲⢄⠀⠐⠋⠁⠀⠘⡓⠤⢄⣈⡆⠀⠀⠀⠐⠺⢥⡀⠈⠀⠀⠋⢀⡞⠁⠙⣆⠒⠒⠒⠒⠒⠠⠽⢦⡙⠶⢣⠏
⠀⠀⠀⠀⢀⠤⠀⠴⠁⣠⠀⠀⠠⡀⠀⠀⣀⣀⢀⠔⠀⣂⣦⣀⣤⠤⠄⠁⠒⠛⠀⠀⢀⣀⣀⡀⠀⢳⠒⠋⠉⠛⠛⠆⠀⠉⠉⠉⠙⢢⣀⣀⣀⣀⣀⣙⣤⡞
⡠⠔⠴⣖⣓⣤⢠⣀⠀⠉⠙⠛⠒⠟⠀⠀⠀⠈⠛⢶⠋⠉⠞⠉⠀⠀⠀⠀⠀⠐⠒⠶⣝⠉⢀⣿⣄⠀⠀⠀⠀⠮⣉⠑⠢⡀⠀⠤⠖⠚⠓⣦⣤⡤⠟⠛⢹
⢇⡀⣀⣭⣉⣉⣉⣉⣉⡙⠛⠓⠒⠒⠒⠒⠶⠶⠶⠤⢴⠋⠈⢳⣬⣦⣀⡔⠐⣖⣢⣀⣀⣛⠁⠀⠀⡠⢄⣀⡀⠑⠨⠉⣲⣃⣠⡤⠖⠚⢉⣁⡤⠴⢺⡇⡿
⠸⡏⠉⡣⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⣶⠒⣶⠚⠙⡦⠤⠾⠤⢤⡖⠙⣞⣁⣉⣉⣉⣉⡉⠉⢻⣄⢀⠟⠛⠒⢲⡞⠋⢉⣠⡤⠖⠛⠉⠁⠀⠀⢸⢀⡇
⠀⣿⠋⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⢳⡞⠁⠀⠀⠀⢀⣵⠞⠳⡏⠀⠀⠉⠉⠉⢹⠁⠈⡟⠛⢳⠀⢸⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⠃
⠀⢹⣄⣠⡼⠢⣄⣀⣀⢀⣀⣀⡤⠤⣜⠉⢱⠦⠴⢧⣌⣙⠒⠒⣚⣉⡼⢤⡤⠧⣄⠀⠀⠀⢠⠞⠓⡎⠀⠀⢸⠀⢸⡇⢸⡇⠀⠀⠀⣀⡠⠔⠊⢉⡇⣾
⠀⠀⣇⠸⡧⠤⡏⠀⠉⡦⠒⢿⡀⠀⣸⠋⠉⠉⠉⠀⠚⠛⠛⠛⠋⠠⠤⠴⢇⣀⡼⠒⢤⠊⠉⢦⣔⢃⠀⠀⣸⠀⢸⡇⢸⣇⠤⠒⣩⠕⠒⠲⡄⢸⠃⡏
⠀⠀⢹⠀⣷⠀⠑⠤⠒⠓⠤⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠜⠓⠒⠋⠈⠉⠉⠉⣿⠀⢸⠀⢸⠁⢀⡞⣹⠂⠄⠺⣝⢿⣸⠃
⠀⠀⠘⡇⢸⡄⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸⠀⡜⠀⣧⠴⠒⠉⢸⡇⣿
⠀⠀⠀⢷⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠐⠒⠒⠒⠒⠒⠀⠤⠤⠤⠤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣿⠀⢸⠀⣸⠴⡇⠀⢇⠀⠀⢀⡼⠁⡿
⠀⠀⠀⢸⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣿⠀⠹⣄⠈⠑⠚⠉⣀⢼⠇
⠀⠀⠀⠈⣇⢸⡏⠀⠒⠒⠒⠒⠒⠀⠤⠤⠤⠤⠄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣿⠀⠀⡨⠟⠒⢚⣫⠏⣸
⠀⠀⠀⠀⢻⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠐⠒⠒⠒⠒⠒⠀⠤⠤⠤⡇⠀⣸⠀⣿⠔⠉⢀⣠⠖⢋⣠⠖⠋
⠀⠀⠀⠀⠸⡆⠹⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⣇⣠⠖⢋⣠⠖⠋
⠀⠀⠀⠀⠀⠓⠒⠲⠶⠶⠤⠤⠤⢤⣤⣭⣉⣉⣉⣉⣉⣙⡛⠛⠓⠒⠒⠒⠶⠶⠤⠤⠤⠤⣤⣤⣤⣀⣀⣀⡇⠀⣿⠀⠋⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠒⠒⠒⠲⠶⠦⠤⠤⠤⢤⣤⣀⣀⣀⣿⠴⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠂⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠖⠂
⠀⠐⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⠿⢿⣿⠟⠛⠛⠛⣿⠿⠿⠟⠛⠉⠉⠛⢻⣿⣿⠿⠛⠛⠻⠏⠉⠉⠉⠙⠋
⠀⠈⠛⠻⠟⠛⠟⠋⠡⡀⢀⡃⢀⢀⡀⠀⠰⠅⢀⣀⣀⡠⢰⣂⠀⣀⠙⠐⡞⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠄⠂
⠀⢰⡄⠈⠀⠀⠀⡀⠰⠀⠀⠀⠀⠋⠀⡄⠀⢐⡆⠀⠀⠀⠄⡀⡷⠤⠤⠤⠴⠀⡀⠀⠀⡐⠀⠀⠀⠐⡀⣀⠀⠄⣀⠈⠀⠀⠔⠀⠄
⠀⠀⠀⠀⠄⠁⠀⠃⠀⠐⠈⠑⠢⠀⠠⠁⠀⠀⠀⠉⠉⠉⠤⠀⠁⠀⠀⠀⠰⠆⠤⠤⠤⠤⠠⠷⠤⡀⠉⠀⠀⢆⠤⣁⡀⠈⠓⡐⡀⣀⠁
⠀⠀⠀⠀⠀⠆⠀⠀⠐⠳⢦⣄⡀
⠀⠃⠀⠠⠀⢠⠀⠀⠀⠀⠀⠈⠙⠛⠚⠒⠓⠚⠒⠒⠚⠛⠓⠚⠛⠛⠛⠛⠛⠛⠓⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲
⠀⠀⠈⣇⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠘⠠⠉⠳⢦⣄⡘⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇
⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢧⡀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠹⡓⠶⠶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠉⠂⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⡀
⠀⠀⠀⠀⠀⠄⠈⠀⠉⠀⠀⠒⠛⠐⠒⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⢲⣶⣶⣦⠲⠲⣶⣶⣆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠆⠀⠃⠄⠐⠀⠀⠁⠈⡂
⠀⠀⠀⠀⠀⢁⢠⡄⠤⠤⠤⠤⠤⠒⠂⠀⢀⡀⠀⠀⠀⢰⣿⣿⣦⣿⣟⡻⣿⣿⣿⡻⡫⣻⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢡⠤⣌⠀⠐⠀⠀⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠠⠄⠀⡔⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⣿⣿⠼⠿⣌⣿⣿⣾⣿⠋⢤⡶⠛⠁⠀⠀⠀⠀⠀⠀⢠⠀⢸⠕⢢⠑⠆⡇⠀⠀⠀⠒⣾
⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⠀⡆⠰⡰⣦⡚⠀⠜⠀⠀⠀⢀⡾⠿⠟⣏⠂⠢⡄⢠⢶⡿⠃⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠆⢘⣈⡥⠆⣇⢀⠀⢠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠇⠐⠘⠛⠀⠀⠀⠀⠀⠀⢸⣿⣯⣅⣠⡧⣠⡜⢿⣷⣿⣿⡿⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⠿⢿⢿⢸⣿⡇⣹⡏⣹⣿⣿⣾⣿⢬⣀⠀⠀⠀⠠⠖⢋⡀⡒⠰⠀⠀⡖⠂⠂⠠
⠀⠀⠀⠀⠐⠐⠲⣀⠈⠊⠐⠀⠭⢧⡦⠀⠀⠀⠠⣜⣻⠛⠠⠄⣀⡄⠦⢟⣧⢸⣯⣿⡟⢋⡨⠉⢺⠴⠛⢒⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠠⠄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠶⠐⡁⠀⢒⣮⠲⠃⠀⣔⠋⠉⠉⠧⠠⠚⡛⠀⢦⠜⠂⡠⠞⠁⠐⢀⠰⠂⢋⠀⢁⠀⢦⣤⣦⡀
⠀⠀⠀⠄⣀⣀⡠⠄⡀⠁⣐⠀⠦⢀⠀⠀⠀⠀⣉⣙⠶⢈⣩⡅⣘⢗⡉⣰⠛⠈⠉⠉⠉⡉⠆⠉⠑⠚⠁⠀⠂⠛⢨⢗⠾⡶⠳⣡⡰⠍⠀⠀⢰
⠀⠀⠀⠌⠁⠁⠙⡆⢈⡶⠶⡮⢲⠎⡙⠇⠀⠀⠀⠀⠀⠀⠂⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡧⠀⣰⢌⣄⢣⠁⡇⠀⠰⠄⠷⠸
⠀⠀⠀⠠⣰⡆⠎⠀⠉⠀⡨⢃⣈⣔⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⠶⡆⠉⢌⡚⠿⢥⢀⢳⡓⠰⢄⢂⠀⠤
⠀⠀⠀⠈⠓⢁⣥⠀⠀⡆⠈⣻⠯⡊⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⡌⠱⠇⡨⠍⠁⠈⢀⡀⠹⣀⠈⠵⠦⢀⡠⠄⠁⠈
⠀⠀⠀⠀⠀⠀⣐⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠒⠌⠁⠀⠁
⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠻⣟⠟⣻⡟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠤⠤⠤⢄⡀⠒⠀⠒⢖⠒⠈⣉⡉⠉⠉⠉⠉⠁⠐⠢⣄⠈⠐
⠀⠀⠀⠀⠠⠖⠚⠮⡍⠁⠉⠻⣉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠘⢦⠀⠀⠀⠙⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠱⡀
⠀⠀⠀⠐⠁⢀⠤⣀⠈⠢⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣧⠀⢀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠂⢐
⠀⠀⠀⠁⠀⠀⡠⠊⢱⡄⠀⠀⠀⠈⠤⠤⠴⠶⠖⠒⠒⠒⠋⠉⠉⠉⠁⠀⠀⠈⢒⠀⢀⡀⢉⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⡩⠛⠁
⠀⠀⠀⠀⠀⡴⠁⢀⠎⠐⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣁⣀⣀⣠⡇⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠞⠀⣠⠋⠀⠀⠈⠠⠂⠀⠀⠉⠀⣀⣀⣀⡀⠤⠤⠤⠤⠶⠒⠒⠒⠊⠉⠉⠉⠁⠀⣀⣰⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠄⣰⠃⢀⠌⠀⡐⠓⠒⠋⠉⠉⠉⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠖⠒⠒⠒⠉⠉⠁⠀⣸⢀⠀⡠⠊⠁
⠀⠀⠀⠂⢸⠁⢀⠎⠀⣄⡠⠤⠤⠤⠶⠒⠒⠒⠉⠉⠉⠀⠀⠀⢀⣀⠠⠴⠤⡤⠴⠒⠒⢒⠉⢉⣹⡔⠊
⠀⠀⠀⠐⠈⣠⠋⠀⠔⠀⠀⠀⣀⣀⡀⠤⠤⠤⠖⠒⠒⠊⠉⡉⠁⠸⠀⠀⠀⠚⠀⡱⠞⠿⠦⡀⠀⠙⡆⢀⡀⢀⡀
⠀⠀⠀⠀⠁⢡⠀⠚⠒⠉⠉⠉⠀⠀⢀⣀⣀⡤⠤⣴⣶⡲⠟⠀⠠⡴⢂⡚⠉⠂⢺⡄⢀⡤⠀⠾⠀⢔⠉⠀⠒⠠⢓⡀⠅⠤⣀⠂⠤⢀
⠀⠀⠀⠀⠀⢠⣄⣤⣤⠾⠩⡀⠿⢋⠭⠗⠛⠠⣤⠁⠀⠀⠀⠤⠐⡩⠙⠋⠛⣢⡜⠉⠉⡱⣤⡤⠀⠺⠗⠑⠒⢢⡙⠀⠀⠀⣉⡠⠤⠖⠈⠑
⠀⠀⠀⠀⠀⠈⠑⠦⣅⠀⢀⠔⢀⠉⡆⠋⠐⠂⠉⠓⡄⠀⠀⢀⠐⠄⠀⠀⠈⢀⠠⠐⠀⢤⠁⠀⠈⠓⡀⠀⠀⠠⠖⠒⠉⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠠⠀⠈⠯⠀⡀⠈⠀⢲⡄⣐⡀⢀⠖⠑⠀⠐⠌⠀⡠⠐⠀⠈⢉⡗⢀⣀⠰⠁⠐⠒⠈⠉⠀⠀⠀⢀⡀⠤⠄⠒⠉⠉⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠠⣄⠈⠀⠀⡠⠿⠑⠀⠤⠄⠚⢀⣉⠄⠀⠀⠁⠈⠁⠀⠀⠀⢀⣀⠠⠤⠐⠊⠉⠀⠀⠀⠀⠀⠀⢀⠃⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⣀⠠⠄⠚⠀⠩⠁⠀⠀⠀⠀⣀⡠⠤⠐⢒⠈⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⠀⠤⠒⠊⠉⠀⠀⠀⠀⠘⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⡀⠀⠐⡒⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠀⠃
⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠠⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⠚⣉⡷⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⣏⣉⣲⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢀⣤⢄⣀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠁⠀⢀⡼⠋⠀⠀⠀⠀⢎⣱⠀⢳⡃⢨⣽⣿⣒⠦⠭⢍⣓⠒⠦⠬⣗⣎⣦
⠀⠀⠀⠀⠀⢀⣠⠴⠒⢋⣼⣏⣽⣭⣷⠀⠀⠀⠹⣷⡀⣿⢦⡎⢣⡞⢿⣸⡏⠁⠀⠀⠤⢉⣉⠑⠒⠬⠭⣙⡒⠲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠈⢩⣯⡆⣼⣧⣀⣠⣴⡿⠃⠀⠀⠀⠘⡝⠟⠈⠃⠈⠁⠘⢱⡏⠁⠀⠀⣴⣿⣿⣷⡀⠀⠐⠠⠤⢍⡉⠒⠂⠭⢍⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠉⢻⣿⡇⠀⠀⠀⠀⠀⢹⡴⠰⠀⠷⠐⢂⣻⣤⣠⣄⣰⣯⠐⣽⣿⣿⣄⠒⠤⠤⣀⠀⠀⠀⠓⣲⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⣠⣤⣤⠴⠚⣍⡙⠭⠤⣬⠭⡗⠋⠀⠀⠀⠈⣿⠿⢿⣿⣿⣿⣦⣤⣤⣤⣤⠀⡐⢲⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡏⢠⢍⣙⡒⠲⠤⣔⣢⠦⠄⠡⣉⣠⠤⠄⠀⣟⣙⣖⡦⢝⡻⣿⣿⣿⣿⣣⣀⣠⠏⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣷⠃⡗⠢⠤⠈⠉⠒⠲⡟⠉⠓⣶⡦⢤⣞⣻⣒⢀⣐⡶⠂⣤⡟⠚⠏⡩⠀⠘⣦⣎⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⡄⠀⠀⠈⢱⣶⡱⡶⠆⠀⠀⢈⡛⢉⢽⣰⣸⣁⠒⠪⢿⣼⣓⠲⠤⣬⢧⡿⣴⠖⠒⣒⡛⣻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣟⢛⡁⢶⣷⠖⠉⣼⣿⠀⠀⠢⣤⣴⣳⣌⠶⡬⡧⠬⠀⠀⢸⢴⡯⣩⠀⡏⢸⡷⢯⡉⠁⢤⠇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣄⡰⠁⠈⡞⡯⠄⠑⢠⠋⠀⠀⢾⠃⢸⡹⠀⠀⣀⡀⡹⢶⠓⠾⢠⠇⣾⣽⠾⡤⠒⢺⢸⠃
⠀⠀⠀⠀⢀⣴⡻⠭⠷⡿⢿⡇⠈⢸⣀⡓⠤⠄⣹⡀⠋⠀⠈⡹⡷⠣⠤⠀⠀⠉⣱⠾⡦⡇⢸⠀⡧⢼⠛⡅⠂⡏⡼
⠀⡀⢠⣴⣋⠁⢧⣴⡞⠓⢼⡆⠀⢸⡀⠉⠙⠒⠬⢿⣖⣒⡩⢼⣉⠀⠀⢤⣄⡀⠙⣾⢳⡇⡟⢸⢤⣞⣻⢉⡹⠟⠳⡄
⠀⠀⠀⠉⠉⠓⢲⠗⢑⠀⠘⢣⠐⡀⠻⡗⠒⠀⡀⠀⠀⠉⠑⠒⠤⣍⡱⠛⢄⠙⣄⠙⢻⣭⣷⢺⣯⡽⠥⣾⠄⠀⠔⠉⠧⡄
⠀⠀⠀⠀⠀⠀⢯⡐⠌⡓⠓⠂⠑⢬⡂⠈⣳⣤⡉⠉⢀⠴⢞⡉⠉⠉⠣⡀⣨⢶⠯⣍⣁⣸⣉⣉⡤⢤⠶⠇⣀⡀⠐⠚⠁⢈⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠚⣩⠌⢒⡂⢨⣩⠯⣀⣀⡻⡿⢤⡈⠹⢆⠀⢀⣯⣼⣫⣤⠴⠋⠉⠁⠀⠀⣏⣠⣄⠄⡀⣀⠠⠜⢀⣀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠚⠦⢾⣉⣩⠟⠳⣄⣱⠀⢈⡶⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠮⠖⠢⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠦⠤⢄⣀⡠⠀⠀⠀⠐⠲⠶⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁
⠀⠀⠀⠀⠰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠑⠒⠠⠌⢀⡀⠀⠀⠀⠘⠶⠂
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠐⢄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⡀⠂⠀⠀⢢⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣰⢦⡀⢄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠳⠎⣜⡿⢺⣐⠾⢟⡛⢆⣀⡀⠀⠀⠀⠀⢣⠁⠀⡸
⠀⠀⠀⠀⠰⣄⠀⠀⠀⡤⠐⠁⡠⢒⢵⢓⢂⢫⢙⣂⢀⠄⡿⢳⠇⠀⡈⣦⣀⠤⠄⣄⢃⠀⢃
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠁⠐⠀⠉⣩⠉⠾⣔⣛⡯⢟⠤⣶⣲⣫⡞⡍⢍⡵⠛⣠⢤⣼⡬⣆⠘⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⢀⣩⣷⣾⡾⣕⣲⡤⢿⣝⡹⣮⢤⡼⠒⠁⡁⠇⠀⠀⢈⠀⠀⡄⠀⠀⠃⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣾⠏⠈⠁⠐⠚⠢⢯⣲⠤⠓⡡⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⠀⠀⡀⠀⢨⡗⠀⠀⠀⠀⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠒⠀⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⢿⡄⠀⠀⠀⠐⡁⠀⠀⠀⠠⠉⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠲⣄⢸⣿⡆⠀⠀⠀⠠⡣⣉⡀⢠⠀⢀⡤⣚⣥⣯⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣐⣺⠋⢥⠮⣍⡢⠄⡸⢒⣰⣀⣾⠟⣤⡯⢗⠸⠿⠤⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢤⠩⣨⢾⡕⢻⣛⠃⢸⡞⢋⠿⣀⡛⢲⣌⣷⣈⣂⠂⢈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⠺⠥⠷⡠⢒⡪⢙⣿⣤⠃⣸⠧⢬⠈⡛⣼⡒⠯⢢⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠈⠈⠉⠻⣯⡴⠶⠟⠣⠈⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠐⠦⣀⣀⡀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⠀⠀⠀⠀⢀
⠀⠀⢄⠀⠀⠀⢠⣄⣤⠤⠛⢻⠶⡛⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⣀
⠀⠀⠈⢣⡀⠀⢸⣃⣀⣀⠀⣸⠨⣁⣄⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠙⠄⠘⠛⢻⣿⣿⣿⣶⢹⣿⣧⡀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠺⣵⣶⣟⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣴⣿⣿⣧⣄⣤⡶⣿⣟⢈⠉⣄⣀⣴⣿⢦⡀⠀⢻⣿⣿⣷⣤⣟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⣻⣷⣶⣶⣷⠁⠒⣿⡿⠧⣾⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣭⣙⡡⣇⠤⠖⠺⠀⠀⠀⢀⣀⣉⣭⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⣿⣿
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⢮⣛⠉⠙⠙⣶⢻⡄⠀⣤⣤⣴⣖⣈⣻⣷⠞⠃⢹⣿⣿⣿⡙⠛⣿⣿⢻⣆⣐⣽⡿
⠀⠀⠀⢸⠛⠙⠉⣽⣿⣿⢃⣶⠈⠃⣰⡀⢿⣬⣇⣀⣿⣿⣿⣿⣏⣹⣟⡘⣉⢸⣿⣿⣿⡿⠿⢿⠃⠘⣿⣿⡏
⠀⠀⠀⠰⠀⠀⠠⣡⡞⠁⢸⣿⣄⠀⠀⠈⠺⠟⠃⢀⣠⣄⠀⠀⠀⠁⠐⠀⠀⢈⣯⣯⣏⣀⣀⣾⣇⠈⣽⣿
⠀⠀⠀⠀⠀⠀⣦⡼⠷⠿⢾⣯⠢⠄⠘⠛⠛⠈⢴⠛⢿⣿⣿⠿⠿⠿⠟⠛⣙⣸⣿⣿⡿⠿⠿⣯⢷⣶⣿⣿⡄
⠀⠀⡀⠀⠀⠀⠘⠓⠔⠒⢺⣿⣥⣀⣠⡐⠛⠛⢶⣷⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠇⣀⣠⣤⣟⢎⣿⡟⣽⣧
⠀⢰⣅⡀⠀⠀⠈⠉⠉⠛⠛⠛⡛⠛⠛⠛⠻⠶⢶⣿⣿⣿⢿⣿⣿⣶⣿⣿⣿⡿⠿⠿⣿⣿⢿⡿⠟⣿⠗⠘⣿⡀
⠀⠈⠉⠉⠁⠀⠀⠀⠈⠛⠚⠛⠛⠚⠒⠒⠒⠀⠒⠂⠚⠒⠒⠶⠂⠀⠲⠾⠋⠁⠐⠒⠲⠖⠛⠓⠚⠛⠚⠛⠛⠃
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣶⠾⣿⣖⡿⠛⢿⣶⢶⠾⣿⡿⣿⣶⠒⡶⢖⣒⣒⣒⡒⢒⢒⠆
⠀⠀⠀⠀⠀⠀⠀⢠⠯⣻⠿⢿⢿⣿⣧⣾⣶⣽⠷⠎⠓⢦⣽⠟⣾⠓⣾⣟⢿⣿⢿⡿⣿⡖
⠀⠀⠀⠀⠀⠀⢠⢟⢻⣿⣿⣿⣿⣿⣾⣿⣾⣭⣿⣿⣿⣛⣿⣤⠏⣾⣿⣿⣷⣎⣥⣺⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠘⡷⣿⣤⠬⢭⣭⡹⡏⡙⣛⡛⠛⠛⠻⢿⠥⣿⣬⣤⣤⣥⣴⣶⣶⣶⣶⡖⣶
⠀⠀⠀⠀⠀⠀⠀⢷⣿⡇⠀⢀⡀⣿⡿⣿⣟⣫⡝⣩⣿⣿⡷⣿⣇⣴⣿⡻⠟⣻⣩⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠷⣾⢧⣽⣿⣿⡚⠓⠈⢃⣬⣿⣖⣹⣿⣿⢒⣈⣁⣤⣦⣼⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⢿⣞⣻⣹⣿⢸⣇⣠⣼⣿⣿⣿⡟⠹⣿⣿⣶⣶⡫⠛⢛⣛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠩⠸⠈⠛⠓⠺⠿⠿⢿⣿⠾⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠻⠶⠾⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠄⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠥⠀⠀⣒⠀⠤⠀⢀⠀⠈⠁
⠀⠀⡠⢒⠈⢉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠶⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠌⠌⠀⠀⠀⠑⡄⠃⠀⠀⠀⠀⢀⡠⡤⠒⡊⡉⠤⠄⠀⡆⠀⠀⠀⠀⠀⠅⠀⠀⢠⠄⠰⠀⠀⠄⠀⠀⠀⡀⠑⡀⠀⠀⠈
⠀⠹⠀⠀⠀⠀⢀⣀⣘⠠⠄⡒⠩⠀⠂⠀⠀⠁⠀⠀⢰⢠⠁⠀⠒⡒⠄⠀⠄⢀⣀⣈⠁⠀⠀⠀⠀⠀⠀⢀⡀⣠⠈⡄⠊
⠀⠀⠌⡀⠀⠈⠉⢱⢰⠀⠀⠀⠀⠀⠃⢑⠀⠀⠀⠀⡈⡜⠀⠀⢉⡄⠀⠀⠀⠉⠉⠉⠛⠓⠚⠒⠀⠉⠁⠀⠀⠀⡁
⠀⠀⠘⣂⠀⠀⠀⠘⠀⡈⡀⠀⠀⠈⠀⠀⢀⠀⠀⠀⢃⠃⠀⠀⠈⡠⠀⠀⠀⠀⠈⠁⠒⠀⠀⡄
⠀⠀⠀⢹⡄⠀⠀⠀⡄⡁⠃⠀⠀⠐⠀⠉⠀⢀⠠⣐⡘⠀⠀⠀⠀⡁⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣘⠂
⠀⠀⠀⠀⠣⢐⡀⠤⠇⠇⠀⠀⠀⣀⠢⠌⠒⠀⠉⠀⠀⠀⠀⠀⠀⠁⠨⠠⠀⣐⠂⠤⠤⢀⡀⡃⠀⠀⠀⠀⡀⠙
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠄⠤⠅⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠚⣻⡿⢤⣄⠀⠈⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠒⠛⠉⠁⠀⠈⠙⠲⣟⡁⠀⢈⣙⢦⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣚⠋⠉⢈⣍⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠋⠀⠙⢦⡀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣞⣉⣁⡀⠀⠀⠉⠙⠦⣜⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⣶⡄⠹⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠈⠳⣄⢠⣶⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠀⠀⠹⡄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣀⣤⠤⠤⠤⢤⣄⡀⠀⠀⠈⠳⣄⠀⠀⠘⢦⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣾⠆⢹⡄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠈⢧⡀⠀⠈⢧⠰⣾⠆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣷⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢷⠀⠀⠈⣧⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡀⢸⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⣇⠀⠀⠸⡆⢰⣶⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⠟⠀⣇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡟⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡄⠀⠀⢻⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢰⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢧⠀⠀⠘⡇⠀⣀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠇⢸⠀⣠⣴⡟
⠀⠀⠀⠀⠀⢸⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡀⠀⠀⢷⠘⠛⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡤⣾⠋⠁⢸⡇
⠀⠀⠀⠀⠀⣼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡇⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⢀⡴⣚⣫⣝⡻⢧⡀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠸⡇⢶⡦⢸⠀⣀⣤⣏⡞⣁⡞⣼⡟⢦⣹⣿⡀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠒⠒⠲⠃⠀⠀⠀⡗⠀⠀⠀⡇⣀⡤⣾⠛⠳⢭⣭⣭⣵⣾⠵⠟⠋⠉⠀⢱⡀⢸⡇
⠀⠀⠀⠀⠀⠿⠤⢤⡤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣟⢀⡤⠶⡏⠁⠀⣿⠀⠀⢈⡟⠋⠉⠀⡴⠒⣦⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⠉⠉⠙⡟⠛⠋⠁⠀⠀⡇⠀⠀⣿⠀⠀⠀⢳⡀⠀⠀⠙⡆⠻⡄⠀⢀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠹⢦⡀⠀⠻⠚⠋⢀⡾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠳⡶⠶⠖⣿⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣤⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⢀⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣧⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢀⣿⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠒⠒⠞⠀⠀⠀⡇⠀⠀⠀⠀⢀⡧⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⢤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠲⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠘⣿⠔⠒⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⠥⣄⣀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⣠⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠈⠉⢒⠒⠤⡥⣀⣀⠀⠀⠀⠈⡙⠋⠀⠀⠁⠐⠂⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢂⠀⠀⠀⠀⠑⠀⠀⠉⠉⠓⠒⠤⠄⣀⢀⠀⠀⠠⠄⠉⠲⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠁⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⢒⢶⠁⡄⠐⠒⠈⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⣀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⢸⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⢋⣬⠝⣦⢜⡣⠄⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡀⠄⠀⢠⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡼⢴⠚⣥⢻⡞⢰⢃⠴⡶⡟⡏⡯⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠁⠐⠀⢸⠀⠁
⠀⠀⠀⠀⢀⡠⠤⠒⠐⣻⠃⣷⣀⠡⢭⠟⢶⣈⡓⠲⠐⢨⡖⣏⣴⠂⢫⠓⢆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠠⡞
⠀⠀⢸⡗⠈⠁⠀⣔⠋⣹⣻⠁⣏⣩⡊⣏⣀⡿⣀⢼⠋⡴⠙⣡⣯⢐⡂⣠⣡⣷⣢⡤⠛⠏⢰⡄⢸⡄⢀⢡
⠀⠀⠠⠀⢲⠂⠄⠉⠉⠭⠳⢴⢳⣴⢫⠛⣛⢜⠧⡤⢿⠰⢚⣛⣺⢁⣍⣩⣉⡵⢷⠛⣤⣀⣠⢗⣤⡺⣈⠄
⠀⠀⠐⠀⠸⠀⠀⠀⢘⠁⣤⣀⡁⠉⠛⠻⣭⣭⣧⣤⢯⣉⣎⠍⠳⡴⠷⠶⣏⠒⠀⠀⢻⣬⡹⠂⠉⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨⡔⠋⢠⣶⣻⢝⡿⠹⡩⠧⢤⠟⣒⠚⢳⠳⣲⠚⡶⠛⢫⠍⠀⠀⠄⡖⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣯⠝⠁⠈⠉⠀⠰⡈⡓⠴⣯⣉⡷⡤⠞⢋⣭⠀⠘⠃⠀⠀⠀⡇⢸
⠀⠀⠀⣄⠤⠂⠀⠀⠀⠀⠀⠀⡾⠷⠀⠀⠀⠀⠀⠀⠴⠊⠀⠐⠀⠨⠠⠀⠩⠄⠀⠀⠀⠀⠀⢀⡟⠇
⠀⠀⠀⠈⠀⠄⠁⠀⢐⠀⡀⠀⢻⣷⠀⠀⠀⠀⠀⠀⢰⢃⡆⠀⠀⠀⠀⠀⢸⠩⠀⠀⠀⠀⠀⢸⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠸⡅⠀⠀⠨⢯⣵⠀⠀⠀⠀⠀⠀⢭⠇⠀⠀⠀⠄⠀⡏⡘⠀⠀⠀⠀⠀⣨⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⡆⠂⡘⣿⢲⠄⠀⠀⠀⠀⠰⣊⢇⡀⠃⠀⠀⣂⡀⠀⡀⣠⠴⡺⢅⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⠙⢋⣩⣿⢽⠅⢠⣤⣤⡀⠀⡗⢋⡗⡒⡆⡤⠗⢢⣖⡟⠓⡿⢾⠗⠻⣟⡼⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣉⣉⣾⡗⠘⣶⠊⢰⣄⡩⠖⢋⣽⠀⣥⠠⣍⣠⣗⠕⠹⣖⡳⠾⢫⠹⠏⠵⠶⠾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣏⣠⢉⣉⠍⣳⣙⡤⢼⡶⠛⡗⠐⢳⡶⢻⠛⡾⡗⠐⡿⠹⣖⠛⣢⡘⠓⠖⠦⠤⠵⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣍⣉⡴⠚⣰⣉⠖⠔⢓⡶⢧⣤⢿⠒⢤⠇⢥⡞⠛⢷⠤⢯⢹⢻⡍⡟⡷⣂⠠⠛⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠭⠓⠒⠑⢋⠚⡭⢥⠒⠢⣾⣞⣷⠈⢠⢴⠛⠖⢫⡈⣋⣈⡿⣇⢉⠗⠣⣿⣉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠦⠤⠋⠈⠀⠙⢿⣿⣡⣨⡧⣾⡟⠧⠤⠅⡀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠃⠀⠀⠀⠀⠀⠀⠁⠛⠀⠉⠀⠀⠀⠀⠀⠓⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠔⠒⠒⣂⠙⠛⠿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠐⠒⠉⠉⢈⠉⠍⠙⠿⣿⣿⣅⠀⠀⠀⠀⠀⠙⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠛⠛⠛⠿⢿⣿⣶⣤⡀⠀⠉⠀⠀⠀⠀⠀⠀⠙⣿⣧⡄⠀⠀⠀⠁⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠄⠒⣄⠉⠉⠉⠒⠪⢍⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣀⠀⢀⣀⡠⠤⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⠀⠀⠈⣦⣀⠀⠀⠀⠀⠑⢜⢿⣿⡄⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⡭⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠊⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣹⣿⣿⡶⣾⣿⣿⣿⠟⢻⣿⣿⡏⠷⣠⠘⢹⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠠⢴⣤⣤⣶⣷⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡿⣫⠀⠶⡏⢶⠷⣿⣼⠐⢿⣓⣬⣟⡥⠬⠶⢌⡆
⠀⠀⠀⠀⠀⠀⠀⣬⣿⣯⣭⣻⣛⣌⣼⡯⠍⢴⠚⠛⢣⣁⠤⠥⢼⣧⠀⣿⢆⣠⣤⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⢻⠞⢿⣿⣿⣥⢄⣐⠈⠙⠧⢤⠩⡄⣒⣿⠿⠻⣽⠉⠀⣿⣿⣿⣾⣇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠈⠧⠎⠉⠉⢿⣧⢹⣿⣶⣦⣶⣲⡍⢠⡏⠀⠀⠟⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡯⠀⠰⣦⡄⠀⠀⠀⠉⢶⠮⢍⣻⣿⢯⣍⡹⠀⠀⠀⣿⡄⠀⠀⢹⣿⡅⠀⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢨⡇⠀⠀⠀⢠⣤⡓⠖⢳⣿⣷⡆⠤⠐⠀⠉⢽⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠂⢼⣧⣤⣤⠀⢨⡛⠁⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⣸⣿⡇⠂⠀⠀⠀⠀⠀⣿⠤⡄
⠀⠀⠀⠀⠀⠀⣀⢹⡟⠀⠀⠀⠈⠻⠿⠻⢞⡥⠀⠀⢸⣿⣿⡇⠀⠀⢀⠀⠜⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⢀⡠⠿⠋⠁
⠀⠀⠀⠀⠀⠁⠉⠸⠷⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢂⠉⢀⡀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠳⣦⠤⣀⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⡀⠤⠒⠉⠁⠀⣀⣀⠲⠂⠀⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣼⣿⣿⡇⠤⠔⠒⣉⣀⠀⠀⠀⠀⡀⠿⣙⣷⣿⣆⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣒⣀⠅⢀⡀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⡟⡛⣿⡛⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣏⠈⡇
⠀⠀⠀⠄⠉⠗⠒⠈⠉⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠔⠒⠂⠉⠉⠁⣰⡅⢸⠀⢱
⠀⠀⠀⡄⠀⠈⡄⠠⠀⠐⠂⠈⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⡏⢧⠀⠇⠈⡇
⠀⠁⡸⡀⠀⠈⠄⠀⠀⢀⣀⠀⠠⠄⠐⠂⠀⠈⠁⠀⠀⠀⠀⢀⢰⡆⠘⡀⢸⠀⢹⡀
⡀⢰⡀⢡⠐⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠉⠀⠀⢧⠀⠃⠀⠆⠈⣇
⡇⠀⢠⠀⠆⢀⠀⠀⠄⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠐⠈⢂⠘⡀⢸⠀⢹⡀
⠁⠀⠀⠆⠈⡄⠀⠈⠀⠀⠀⣀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⣇⠀⡆⠈⣇
⠐⡀⠡⠈⠀⠱⠐⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠤⠄⠒⠀⠉⠁⠀⣠⠴⠦⣴⠈⢀⣨⠦⣽⡠⠠⠄⢀⡀
⠀⠀⠄⠑⢧⠀⠇⢀⠀⠀⠖⠀⠀⠉⠀⠀⠀⠀⠀⢠⠔⠒⠚⣻⠁⣀⠤⡞⠉⢻⣶⢦⣄⣅⡠⢠⡄⠀⠀⢠⠄⠀⡄⠀⠀⠠⡀
⠀⠀⠀⠠⡀⠑⢨⡄⠂⠐⡠⠤⠀⠀⠀⠉⠀⢠⠖⣳⣄⣀⣠⠞⠛⡇⠀⠰⢤⡏⠀⠀⡸⢿⠀⠀⢹⠷⠖⡆⠀⢀⠟⠦⣤⣤⣿⠯⠒
⠀⠀⠀⠀⠀⠐⠄⡈⠒⠀⢀⢀⢀⠀⠑⣶⠂⢹⡞⠋⠛⣄⢀⡀⠀⣹⢆⡀⠀⠷⡶⣎⣀⣈⣳⣤⡂⠀⢀⣼⢲⣿⠴⠒⠋⢁⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠾⢃⠀⠄⠉⢳⠘⣆⡄⠀⢸⢛⠁⠀⠈⣸⣄⣀⣀⡴⠂⠩⡜⠁⡀⣙⠟⠟⠉⢁⢀⡤⠖⠊⠉⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠙⠲⢯⣤⣗⠁⢈⠓⠖⠚⢧⠀⣏⠙⢦⠴⠞⠋⠃⢉⡀⠄⠂⠛⠉⠁⡀⠄⠂⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡐⠂⠄⡀⠀⠩⠙⠷⠴⣆⠀⠨⠓⠋⠁⠈⡀⠄⡐⠬⠒⠂⢰⡆⡐⠂⠁⢀⠠⠐⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣀⠀⠈⠂⠠⢁⠀⠀⢀⠀⠆⠈⡀⠀⢐⡨⠄⠂⠁⣀⠠⠐⠊⠂⢑⠀⠐⠈⠀⠀⠀⠊⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠈⠑⠢⠄⣀⠈⠐⠠⠀⠀⠀⠖⠈⠀⣀⠤⠒⠉⠀⣀⠄⠒⠉⢀⠀⠐⠀⢀⡠⠒⠉⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡀⠉⠒⠠⢀⡀⠉⠒⠤⠄⠸⠀⠗⠚⠉⠀⡀⠤⠒⠉⠀⠠⠐⠈⢀⡠⠔⠊⠁⠀⠐⠠⠐⡁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⠑⠢⠄⡀⠈⠀⠂⠄⡄⠀⠀⢠⠤⠒⠁⢀⠠⠀⠈⢀⡀⠔⠊⠁⣀⠄⢂⠅⢂⡡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡈⠑⠂⢄⡀⠁⠀⠠⠀⡀⠀⠀⢀⠠⠐⠈⠀⣀⠤⠒⠉⢀⠠⠐⡉⠄⢈⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢉⠓⠦⣄⠀⠑⠂⠄⡀⢨⠀⠀⢀⣀⠤⠒⠉⠀⡠⠔⢊⠡⠀⡁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡙⠲⢤⡀⠀⠙⠀⠀⠈⠀⣀⠤⠒⡉⠄⢈⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠓⢶⠀⢰⠀⡋⠀⠂⣁⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⢘⠀⡠⠔⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⢀⣠⣤⣄⡀⠀⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣦⣤⡀⠲⢤⣶⠾⠟⠻⣶⣤⡉⠛⠛⠛⠛⠝⢊⡐⠛⠋⠙⠛⠛⠳⣄⠉⠉⠛⠛⠳⢄⠀⢀
⠀⠀⠀⠀⠀⠀⡐⣷⣾⣿⣿⣿⣿⣾⣷⢄⠈⠐⠂⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⠀⠀⠀⠱⡍
⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⣻⡿⢿⣿⣿⣿⣳⡀⠤⠀⠀⠀⠀⠀⠳⡄⠆⠀⠀⠴⠆⠀⠚⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠼⣿⣟⣻⢾⠉⢲⣿⣹⡻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣞⣻⠿⢷⣿⣿⣿⠟⣾⣟⢻⣿⣟⣃⠀⠀⠀⠀⠂⠀⠀⢷⠀⡀⠆⠀⡀⠈⡀⠀⠀⠀⠐⢀⣸⣆⣀⣶⣀⠀⣼⣧⣤⣤
⠀⠀⠀⠀⠀⣷⣿⣿⣷⣶⣼⢩⣙⢟⣿⠿⢿⣿⣿⡄⢀⣸⣄⠀⠒⠀⣸⣧⣤⡾⠖⠂⢰⢂⡐⡟⣀⡆⠈⠛⠋⣩⠉⠁⠀⠀⠀⠦⡆
⠀⠀⠀⠀⠀⢼⣟⣿⣿⣿⣿⣾⣿⣿⣾⣿⣳⣽⣏⡟⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠉⢍⢉⣧⡤⠤⠤⠴⠖⠒⠚⠛⠋⢯⠙
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⡏⠉⠛⠿⢿⣿⣿⣧⣭⣥⣤⠤⠤⠶⠖⠒⢒⠛⠋⠉⠻⣿⢋⡼⡘⢇⣀⣀⣠⣤⣤⣤⢤⣶⣶⡶⠎
⠀⠀⠀⠀⠀⠀⢹⡿⢿⣌⠿⣿⣿⣷⣶⣿⣿⣼⣿⡏⢶⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣶⣾⡇⢾⣟⡵⠸⠋⢹⠁⠀⠟⠡⢈⠻⡇⢢⢁⣴⠂
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠺⡿⠛⠻⣿⣧⢻⣿⣿⢿⡟⡾⢻⣿⠿⠉⡙⠉⣽⢀⠈⠀⠀⢹⡟⣧⢻⡇⢀⠀⠸⠐⢸⣣⢆⠈⢱⠀⣼⣟⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠰⣄⣄⡠⠾⠿⡅⠈⢻⣾⡅⠀⠰⣇⣟⡞⠀⠀⣿⠙⠁⠀⠂⠀⠻⡾⢸⡶⠃⢐⠇⣠⠉⠙⢶⣷⡦⢰⡿⠷⠐⠉⠁
⠀⠀⠀⠀⠀⢠⡀⢀⡖⠀⢉⠁⠁⢿⣆⠀⣢⣸⡷⡆⠀⢀⣡⠋⢠⡞⢾⣯⠀⠀⠀⡀⠂⠀⠁⠊⠡⣴⠋⢀⠁⡠⢸⢦⣼⠧⡽
⠀⠀⠀⠀⠀⡔⠀⢸⡆⠀⡾⣦⡀⣾⣽⣴⣿⣿⣿⡇⠀⢨⡯⣰⡏⣰⡏⠠⠀⠀⠀⠀⠑⠂⠀⠀⡀⢾⣄⡳⠺⢱⡧⢾⣿⣾⡇⠐
⠀⠀⠀⠀⠀⠀⠤⣺⣧⣸⣰⣽⠷⣹⣿⣿⣟⣁⡞⡇⠀⢸⣿⢮⣣⠿⣟⡏⣠⢈⠀⣤⣦⠀⢦⠄⡄⢀⣿⣣⣤⣦⣽⣿⢟⣋⣿⠐
⠀⠀⠀⠀⠀⠰⠻⠿⢿⣿⡿⣦⣾⣿⠩⣝⣿⣿⣯⡇⠀⢸⣯⣷⡝⣟⠿⣷⣤⣼⣰⣦⣈⠀⢀⣤⣤⠼⡿⣿⣟⣿⣭⣿⠟⠉⠛⠀⠓⠶⡀
⠀⠀⠀⠠⡄⠂⠀⠀⠛⢿⣿⣙⣿⡿⣧⣼⣿⣿⠿⣧⠷⠾⣷⣶⣼⣿⣿⣿⣾⠿⠿⢛⣛⣥⣬⣽⣶⣿⣿⣭⡿⢿⠗⢀⣴⠞⠁⢀⡤⢤⣼
⠀⠀⠀⠀⠮⣑⣀⣇⠀⠀⠈⠙⠿⢿⣿⣿⣿⣷⣿⠀⠰⢛⢸⣟⣯⡉⠩⠒⢤⣒⣩⠥⠵⠒⠛⠋⠉⠉⠀⠀⠦⡀⠘⢁⣄⠉⠐⢪⢄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠀⣱⣿⡌⡿⠿⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣠⠎⠀⠙⠑⠤⣤⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡿⠩⠝⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠤⠤⠤⠤⠐⠂⢀
⠀⠀⠀⠀⠤⢤⡀⠀⠲⡂⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠐⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢤⡈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠨⠄⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡀⠁⡰⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠲⠀⠂⠀⠂⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠞⠀⡜⠀⠀⠁⠀⠀⠀⠀⣀⡀⣀⣀⠀⠤⠤⠀⠒⠐⠂⠒⠈⢉⣉⠀⠀⠀⡠
⠀⠀⠀⢀⠎⠀⠀⠀⠛⠀⠉⠉⠀⣀⣀⠀⡀⠠⠤⠀⠒⠂⠐⠀⠉⢉⣀⡁⢀⠀⠊
⠀⠀⠀⠉⢠⠂⠀⠒⠂⠈⠈⠉⠁⣀⣀⠠⠄⠄⠄⡆⠈⠐⠁⠉⣥⣄⠐⠲⢅
⠀⠀⠀⠐⡃⠰⠂⠒⠂⠈⠉⣉⣀⣀⣤⣤⠶⠀⢀⠔⡐⠒⠠⡆⢀⠀⠤⠀⡜⠈⠀⠡⡀⠀⠄⠠
⠀⠀⠀⠀⢤⠤⡶⠂⠄⠛⡉⠛⠓⣠⡁⠀⠀⠀⠀⠉⠉⠉⠦⠉⠈⠰⠤⢀⠐⠀⠀⠈⠀⣀⠈⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠙⠣⡄⠂⠠⢘⡀⠈⠀⢈⠁⢀⡰⠈⠀⠀⠀⢤⠉⠁⠲⢀⠀⠤⠀⠀⠈⠁⠀⡀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠃⠀⠰⠃⠀⠄⠐⠀⢂⠀⠀⠈⠂⠁⠁⠀⢀⠀⠠⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠈⠀⠀⠀⣀⠠⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠺⢯⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⢶⡒⠲⠖⠀⠀⠬⠭⠉⡉⣉⣛⣐⣂⠀⠠⠤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠃⠀⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠍⠉⣹⣾⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡞⠀⠂⠃⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⢚⢳⣧⡟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡘⠘⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢁⡏⡜⡾⡼⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⠴⠴⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠠⢰⢷⢳⡷⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⣽⡟⢿⣄⣽⢰⣏⣁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢂⣏⣯⣿⣏⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣂⣶⣽⣍⣲⣖⣹⣾⣯⣭⠿⢽⣧⣿⡷⠾⣿⢬⣦⣀⢀⣀⠀⡠⠄⠀⠀⠀⠀⡚⡸⣿⣾⣏⣾⠏
⠀⠀⠀⢀⠠⣰⡾⢿⣰⣷⠯⠻⣛⢹⡾⠧⡄⣲⠿⣤⠧⡼⣻⣟⣞⣻⣿⠿⣶⣿⠗⣾⣐⣄⡀⠴⢐⡃⡜⣿⠯⠊
⠀⠰⢊⠤⠈⡛⠛⠷⠏⢿⡟⢛⣿⣭⠷⢶⡿⢻⣿⣿⣶⠿⣏⣩⢿⣟⣿⣾⣥⣿⠷⣾⣿⠦⡋⣽⠉⠉⠉
⠀⠀⠀⢰⡄⠧⠬⢆⣉⢂⠆⠂⠩⠍⠁⢚⡛⠿⠶⢿⣋⣛⣿⣷⢾⣓⣿⠾⠾⣒⣫⢅⣾⣥⣶⣑⡆
⠀⠀⠈⢸⡇⣀⣀⠀⠀⠈⣉⣝⣬⡆⣴⠾⠤⢄⣘⣀⠐⠔⠉⠁⢬⣥⢒⣨⣿⣶⣿⣯⣤⣾⣽⣿⡇
⠀⠀⠘⢸⡇⠈⠛⠊⠁⠀⣉⣙⣻⡇⣿⠀⠀⠀⢀⡄⠉⠉⠒⠈⢸⡆⣿⣡⣾⣇⣥⣤⣩⣿⣬⣈⡀
⠀⠀⡲⢸⡇⠀⠀⠈⠀⠐⠁⣶⠀⡆⣿⠀⠀⠀⠈⠉⠀⠀⠀⡇⠒⢟⣟⠋⢹⣦⡴⢦⢼⣾⢴⣴⣄
⠀⠀⣃⠸⠧⣄⣀⣀⠀⠈⠊⠭⠴⢃⡟⠀⠄⣤⢄⣀⠀⠀⠐⠂⠀⢿⡗⠓⠙⠩⣠⡶⢶⣾⡨⠨⡷⠉
⠀⠈⠁⠒⠖⠣⢀⣐⣉⠹⠙⣣⡀⠸⢿⡄⠀⠀⠀⠀⠀⠀⠐⢒⠀⣧⡧⢶⢟⣍⣤⠾⢻⣛⣿⡿⠧⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠃⠆⠤⠔⣀⢁⠆⠳⢖⠲⠶⠠⢰⠐⢿⢿⣞⣩⣽⠴⠋⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠲⠦⣕⣸⣺⠶⠟⠋⠉⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠶⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⠿⠟⠛⠉
⠀⠠⢤⣶⣶⣿⣿⡿⠿⠛⠛⠛⠛⠋⠉⠉⢉⢉⠄⠀⠀⠀⠊⠉⣉⠉⠀⠀⢦⠀⣐⠈⠋⠉⠉⠠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠈⠅⠀⠈⠀⠀⡐⠀⠐⠀⠐⡤⠂⠀⠈⠉⣐⠒⠒⠒⠀⠒⠲⡀⠂⠀⠀⠁⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⡀⠀⠠
⠀⠀⠛⠀⠀⢀⠀⢰⠀⠀⢀⠠⣀⡀⠀⠀⠃⠀⠀⠀⠠⠥⠄⠈⠀⢀⠛⠈⠉⠉⠉⡁⠂⠀⠀⠐⠀⢀⡀⠀⠠⠤⠐⠂⡉⠒⠄⠀⠀⣀⡀⠐⠀⠠
⠀⠂⠀⡀⠁⠀⠈⠀⠀⢐⡀⠀⠀⠉⠀⠈⠀⠈⠀⠀⠀⠀⠀⠐⠓⠂⠂⠀⠀⠀⠒⠃⠒⠒⠒⠒⠐⠚⠓⠒⠂⠀⠀⠀⠑⠐⠒⠂⠀⠀⠐⠉
⠁⡀⠀⠰⠀⠉⠀⠀⠐⠈⠙⠳⢦⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠁⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡽
⠀⠀⠀⢹⠀⢰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠁⠊⠙⠲⢤⣀⡈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⡷⠦⠤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣤⣤⠠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠲⠐⠐⠀⠊⠁⠀⠀⠀⠠⣿⣿⣿⣿⣻⣿⣟⣽⠋⣠⠄⠀⠀⠀⠀⠀⣠⡂⡅⠀⠀⠀⣐
⠀⠀⠀⠀⠶⠀⠀⠁⢤⣤⠀⠀⠀⠀⣹⠿⢟⠁⡉⡭⡿⢣⣍⡁⠀⠀⠀⠀⠀⠇⠍⣘⠄⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⣿⣧⣴⣷⡞⣿⢿⣿⣿⣯⠀⠀⠀⣀⢀⢀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⡦⠀⠀⣴⣖⠫⢍⡹⢼⣧⣿⣿⣟⡝⢻⠽⢢⡄⠉⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠄⡀⢾⠉⣄⠏⡀⠐⠨⠭⡀⠆⠠⠊⢀⡥⣀⣁⣠⢀⠖⠲⡀
⠀⠀⠘⠉⣫⣐⢤⡤⡴⠒⠀⠀⠀⠀⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣀⢄⢸⣥⣸⠀⠉⠆⠦⠄
⠀⠀⠠⠇⠄⠀⡰⢥⡶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠉⢣⠀⠽⡑⠚⢯⠐⢤⡐⢀⠠
⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡶⣖⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⢤⠄⡼⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⣧⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠘⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⢱⠀⢳⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⠁⠸⡸⠀⢸⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢰⡇⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡇⠀⠀⠀⣠⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⣀⣀⣀⡇⢸⢸⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠃⡼⡜⢀⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠿⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣸⠀⡇⠟⣩⠞⠁
⠀⠀⠀⠀⠀⠀⡴⠋⣉⡑⠦⣀⠀⠀⠀⠀⢀⣀⡀⠛⢒⣲⡒⠒⡲⡶⠒⠲⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⣤⠭⢭⣍⣉⣸⡵⠊⠁
⠀⠀⠀⠀⠀⢸⠀⣾⡤⢤⣀⠈⠓⣦⡤⠖⣫⠭⡯⠭⣿⣄⠈⠛⣟⣛⣒⣒⡒⠲⠶⠦⠤⠤⠤⣤⣤⣤⣤⣷⣤⣴⡿⠧⣤⠀⣀⡴⠋⢳
⠀⠀⠀⠀⠀⢸⠀⢻⡀⢀⡨⠗⣋⠥⠖⠋⣡⡖⡻⠋⢉⢿⣷⣤⡼⠦⠾⣍⠛⠯⣍⣩⠽⠛⢻⣉⡉⠀⠀⣀⣀⡩⣫⣾⡿⣾⠏⠀⢠⠎
⠀⠀⠀⠀⠀⠈⢇⠠⣿⣭⣐⣿⣤⣤⣴⣉⣁⣙⣷⣾⣕⣋⣹⡋⢀⣠⣞⣿⣄⣠⡋⠀⣀⣴⣿⡉⠉⢳⣏⡠⢋⣜⣿⡿⠊⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⢆⢱⡀⠀⠀⠸⣩⣉⣉⣛⡛⠛⠛⠻⠟⠲⠿⢯⠭⠭⠭⣭⠭⢭⣍⣉⣙⣛⣛⣛⠻⢯⣴⡿⠋⠁⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⢤⣄⠘⡆⠀⠀⠉⢉⣩⣍⡒⠒⠒⠒⠒⡒⠒⠒⠶⠶⠶⠶⠶⣤⠀⠀⠂⢰⣿⣇⣤⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⠀⠉⠁⠀⠀⠀⠸⡄⢠⠭⠭⠭⣝⡋⢉⣿⠀⠀⠀⠀⠀⢰⣁⣤⡄⠀⣾⣇⡼⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢧⢸⠀⢞⣳⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣽⠀⢀⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢱⠀⠀⠀⠀⠀⠀⠸⡘⣄⢬⠇⢠⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢸⡏⢀⡞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠸⠖⠚⡆⠀⠀⠀⠀⠱⢌⣓⣒⣣⠞⠀⠀⠀⠀⠀⠀⢀⣄⡀⡘⠀⣿⣧⢋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠄⠀⢸⠷⠦⠤⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠙⠿⢀⡿⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠶⠶⠤⠤⠥⢤⣤⣀⣂⣀⣉⡙⠉⠉⠉⠍⠉⠉⡟⠋⠀⠀⢸⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠒⠒⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣻⡆⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠀⠀⠀⠀⠀⠀⠒⣛⣙⣛⣛⣛⣀⣒⣂⣀⣠⠄⣤⣭⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣿⣧⠀⡶⣶⣿⣿⣟⣻⠟⣡⠽⠏⠡⠄⠠⠤⠄⠰⠖⠓⣾⣿⣿⣿⡇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢉⠞⠿⢿⡆⠙⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠻⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⠀⠀⠈⢫⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢿⡙⠀⠐⢿⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣂⠂⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⣠⡄⢻⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡀⡀⠈⡀⣻⡄⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒⠒⠀⠀⠀⠉⢳⣿⣷⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢷⣻⡄⢹⣿⣿⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⡄⣿⣿⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⡈⣙⣻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢿⣿⣿⣿⠀⣁⣤⣤⣤⠤⠦⠰⠒⢚⣛⣒⡀⡉⠩⠥⠍⠁⠀⠀⠀⠄⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣷⡉⢰⣓⣀⡈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣿⡿⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣿⣄⠁⢀⣀⣀⢠⣔⣐⠒⢡⣖⡉⠴⢺⣭⣱⣦⡘⢁⡌⠟⠻⢦⣤⣹⣷⣔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣨⠻⣟⠿⣷⣄⠛⣭⠶⣬⡉⢿⣭⠹⢧⠖⢈⣷⠦⠼⠶⡬⠒⣤⠀⡊⠀⠽⢿⣿⣷⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠑⢼⡷⢈⠿⣷⡄⠻⣏⣳⣆⣺⣶⠚⣙⣧⣨⣍⣉⣿⠉⡻⠄⠓⠚⠛⡓⣈⣉⣩⣥⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠀⠁⠀⠒⣌⠁⢿⢿⣦⡈⠲⠿⠗⠒⢛⣉⣉⣭⣤⣤⡶⠒⠒⣶⠶⠋⠉⠁⠉⠉⠁⡟⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠂⠂⠀⠀⠈⢣⡃⢈⢻⣿⣶⠚⡟⠉⠉⠉⠁⠀⠈⣿⠛⠟⡀⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣑⠛⢄⠀⠀⠀⠀⢀⣿⡿⠛⢀⠩⠅⠀⠀⢀⣀⣠⣷⠿⢶⠃⠀⠀⠀⠀⠀⠀⠀⡞⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠳⡍⠲⠈⠻⣿⡇⠀⡸⠀⠂⠈⠉⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⢶⡀⣼⢹⠃⢀⠃⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠠⠴⠒⠐⠒⠚⠛⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⡤⠄⡤⠄⣀⠀⠈⠣⡀⠀⢀⠙⣧⡾⠈⢰⡦⠴⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢴⡏⠶
⠀⠀⠀⠀⠀⠀⠀⣄⡹⢷⣜⢓⣶⠟⢿⡇⣩⣉⡖⢢⠀⠈⢦⣄⣿⢩⡇⠆⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠶⣖⠿⢍⣻⠶⣬⣍⣳⡒⣤⡐⠢⠻⠅⠀⠀⠀⠈⠫⠿⠁⠐⠒⠋⠉⠁
⠀⠀⠀⠀⠐⠊⠉⠁⠈⠉⠉⠁⠉⠈⠁⢈⣁⢀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠄⣀⢀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡜⢫⣙⠛⠓⠒⠒⠒⠒⠒⠂⠠⠭⠭⠭⠭⠍⣉⣉⣀⣐⣒⡒⠒⠒⠒⠂⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠎⠀⡄⠉⠉⠉⠙⠛⠛⠒⠒⠒⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡝⡠⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠟⡐⠀⠀⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⢀⡞⠁⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡔⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠤⠤⠴⠶⠶⠒⢲⠿⠿⣷⣿⣖⣤⠄⢀⡄⢲⠀⡀⠀⠀⠀⠀⠐⠂⠠⠤⢀⣀⠀⠀⠀⠀⠀⢠⠎⠈⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⢸⡾⠽⡻⠶⣤⣄⣀⣀⢰⡧⣤⢞⣹⣶⠖⠠⢤⣉⣉⣛⡟⢡⣿⢿⣴⣷⣤⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠌⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⢹⡟⠚⢯⣽⣮⡿⢾⡒⢲⡌⣫⣭⣿⠂⠀⠀⠘⠚⡵⢿⢋⠛⠲⠮⠭⣭⣒⣒⡂⠤⢤⡤⢁⠊⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠸⡏⠁⠀⠀⠀⠀⠀⠱⣀⠀⠈⣹⣟⠛⢿⣠⣿⣹⣿⣿⣷⢮⣴⢴⣆⢙⣿⢹⣖⢲⣤⣤⣤⣈⣹⠿⠿⢶⡖⠷⠶⠶⠞
⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⡿⣷⠈⠀⠀⠉⠀⠈⠀⠈⠙⢣⣽⣶⣿⣯⣿⣓⡾⠬⠝⣿⣂⢹⡧⠄⠀⠒⠈⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠒⠀⠀⠀⢷⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠘⠃⣸⠥⠐⠒⠈⠉⠹⡇⠀⡇⠀⢀⡀⠠⠀⢺⡇
⠀⠀⠀⠀⠀⠀⣠⡏⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠊⠁⠀⠀⢀⣀⠤⠤⣿⢸⡇⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣽⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⡀⠀⠀⠀⠀⢙⠀⠀⠘⠈⠉⠀⠀⠀⠀⢿⣼⠃⠀⠀⠀⠀⠀⢨⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣄⡀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠁⠀⠤⢀⣘⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⠙⠻⣷⣤⣀⠀⠀⠀⠀⠘⠀⠀⠘⠈⠁⠀⠀⠀⢀⡀⢄⣠⣾⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠄⠢⠽⢤⠆⠀⠉⠛⢿⣦⣄⡀⢠⠞⠢⡄⢀⣀⠤⣖⣮⠷⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡇⠀⠀⠈⠙⣿⣿⣀⡇⣹⣯⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠃⠀⠀⠀⣶⣟⣻⠧⠆⠉⠛⠉⠁⠀⠀⠀⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠨⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⣀⡀⠀⢀⠀⠴⣶⣖⠂⠀⠈⠙⣆⠀⡐⠋⢳⣍⠐⢒⠈⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣋⣍⣐⠀⠈⠦⠀⠀⠀⠀⠀⠁⠳⣄⣀⣀⣨⡏⠁⡤⠀⣈⣳⣤⣤⣠⣤⣤⣤⣽⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⠁⢝⠛⣧⠀⠀⣴⡶⠶⠒⠒⣒⡛⠛⠿⠻⠻⢷⣓⡀⠈⠏⠉⠉⠉⠉⣙⣿⡿⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⡶⠋⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⢀⠑⡒⠀⠀⠀⠀⢀⣾⢟⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠨⢹⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠜⡀⠈⠁⠐⠂⢠⡀⠀⢄⠀⠀⠐⠺⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⢻⡆⠀⠀⠀⠀⠀⢀⠀⠤⠾⠁⣐⠀⠀⠃⠀⠘⠐⠂⠁⠀⠙⠦⢠⡀⠀⠀⠈⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢿⣶⣷⣧⣶⠁⠩⠃⠀⡄⠘⠀⠒⠀⠀⠰⠈⠀⠀⠀⠀⠀⢰⠁⢁⢠⡦⠀⠀⠀⢩⡄⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢠⢿⠟⠠⠀⠀⠈⢂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠋⢉⡅⠈⠐⠂⠀⠀⢈⠗⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⢣⣼⢀⣶⠂⣀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⡤⠄⠀⠡⡤⠅⡀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⢶⡣⢹⡖⡀⡀⠀⠀⠇⠀⢠⠀⠀⡀⢡⠀⢖⠒⠃⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⠠⠀⠀⠚⢩⣿⡆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⠀⠀⠈⠓⠨⣁⠨⢨⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠳⣎⡦⠨⠀⢈⡗⠀⠇⠀⠀⠀⠠⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢿⣏⣠⡄⠀⠀⠀⣀⣱⣦⠼⢳⠓⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠚⢿⠅⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢺⣿⣯⡳⢄⡀⠀⠀⣽⣾⠀⢸⠀⠀⠀⠀⠀⣸⡇⠀⠤⠀⠀⠛⢠⠥⠈⠁⣼⡇⠀⠆⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢻⣿⠀⠈⣑⢿⡟⠐⣾⢉⠀⠸⠄⠀⠀⠀⠀⣿⡇⠀⠈⠀⡀⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⣿⡐⠀⠀⠀⠀⠀⡿⢸⠀⠠⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡇⣀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣼⣿⢻⡖⢀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠓⢧⣤⠤⠀⠠⣿⡇⠀⠂⠒⠁⠁⠘⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⡙⠯⣅⡀⠀⠓⠢⡄⣧⠀⠀⢀⠀⠀⠀⠀⠀⣿⡄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠸⠁⡀⢀⣀⣀⣤⣖⠚⣒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣳⣾⣷⡀⠀⠐⢀⡿⡦⠂⡺⠁⠀⠀⠀⠠⢼⠀⢈⠀⠀⠀⠀⠀⢀⣀⣠⠘⠒⠿⠛⠋⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣶⣽⣷⡇⠀⢡⠀⢀⣀⣀⣀⣘⡄⠠⠶⠖⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡋⠃⠒⢺⠟⠛⠋⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⣤⣤⠤⠤⠤⠦⠦⡤⢴⡶⠶⠖⠒⠒⠶⠒⣶⢶⡶⠒⠒⠒⠒⠒⠒⢒⡖⢋⠟⠛⠛⠛⠛⠛⠛⠛⡿⠻⢋⠭⠳⡄
⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⡤⢉⡔⠋⠀⠀⠀⠀⠀⢠⢎⡔⠁⠀⠀⠀⠀⠀⠀⠠⠎⢠⠇⠀⠀⠀⠀⠀⠀⠀⡞⠀⢁⠀⠀⢀⣹
⠀⣠⣿⠃⠀⠀⠀⠀⢀⡔⠀⠎⠀⠀⠀⠀⠀⠀⠰⠁⠎⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⢠
⢠⢳⠁⠀⠀⠀⠀⠀⠈⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠃⠀⠀⠀⢸
⡞⡗⠖⠀⠀⠀⠀⢐⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢠⣂⠀⠀⢀⣸
⣧⣍⠁⢀⣀⣀⣀⣀⣀⣀⠐⣃⠀⠐⠐⠂⡶⣥⢤⣔⠒⠒⠒⠒⠂⠀⠐⠘⠀⠀⠩⠦⠄⠄⠀⠀⠀⠠⠼⠆⠀⠸⠼⣒⣨⠥⡒
⣿⢠⡒⠖⠂⠄⠀⠠⠀⠀⡈⠥⢤⠥⢉⣉⡏⣬⡟⢿⣉⣉⣉⣉⣉⠉⡈⠀⠐⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡉⣤⠒⠉⠉
⣿⢸⠀⠀⠀⠀⠀⠀⠰⠀⡃⠀⠀⠀⠀⠀⡿⠻⡿⣷⠼⠀⠀⠀⠸⠀⠍⣥⠀⢈⣛⠛⠉⠛⠑⠒⠒⠒⢀⡀⠀⣲⠐⠀⠀⠀⠰
⣟⠠⠀⠄⠀⠀⢸⠀⢠⠀⡇⠀⠀⠀⢀⠖⠛⠛⠶⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⢀⣟⠀⠀⠀⠀⠈
⡟⠀⠀⠀⠀⠀⠸⠀⢸⠀⠃⠀⠀⠀⢸⠀⢠⡆⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠣⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠐
⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⣼⠀⠀⠀⠐⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⡀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⠧
⣶⠀⢀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢀⢆
⠛⠷⠤⠤⠤⣄⣉⣉⠀⠀⠒⠂⠀⠄⠀⠀⢄⡇⠀⠂⢠⠀⠀⠀⠀⠀⠀⡀⠀⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⡔⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠒⠶⠤⠤⣄⣈⣉⡐⠒⠒⠀⠀⠂⠍⠀⢉⣠⣇⠀⡀⠀⠀⠀⠂⠲⡄⠀⣷⡤⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠲⠦⠤⠤⣄⣀⣀⣈⠉⠉⠁⠀⣀⣤⣬⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣽⣿⣷⣿⣯⣤⣤⣤⣤⣤
⣿⣿⣤⣭⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢤⣀⠰⢆⠶⣖⡒⠒⠒⠒⠛⢲⢫⠻⠤⣗⡝⡆⠀⠀⠉⠙⠺⢿⠋⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡊⠁⣀⣐⣇⠀⠙⠢⣄⠓⠛⠢⡀⠀⣀⣚⣮⣗⣞⣯⣝⣉⠀⠉⠈⠭⣭⣬⣥⣽⣥⡜⡆
⠀⠀⠀⠀⠀⠀⢰⠁⣡⠋⠀⠀⠈⠑⣟⢁⠜⡥⠭⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉⠉⢩⠋⠉⠉⠀⠀⠀⢠⢊⠔
⠀⠀⠀⠀⠀⠀⡟⠀⡇⠀⠀⠀⠀⡴⣡⢫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡰⢡⠊
⠀⠀⠀⠀⠀⠀⣷⠶⡇⠀⠀⢀⠞⡴⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠁
⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⣠⢋⠎⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡠⢃⠜
⠀⠀⠀⠀⠀⠀⠀⢣⡮⠒⡡⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡄⠤⡤⢗⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡔⠁⠆⡠⢴⠶⠒⠖⢲⡤⠍⢉⣠⠤⠤⣶⣒⣒⣢⣶⠴⠴⠗⠛⠯⠀⠖⢂⡀⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡝⠟⣳⡶⠾⠖⠛⠊⠐⠐⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠨⠤⠲⣏⡛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣬⣑⠢⣉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⢤⢀⣲⡒⠿⠍⠛⣒⠒⡉⠩⠰⢲⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠈⠑⠢⢍⡒⠦⣍⣓⣂⣐⡩⠭⠭⣑⠒⠒⢋⡭⢍⣴⠀⠶⠀⢫⠉⢩⠈⠋⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇⢀⣼⣹⢷⠉⢳⠀⡇⠀⠀⣞⠋⠉⢩⡄⠿⢺⠀⣾⡇⠶⠀⠘⠙⢄⢹⡇⡦⠈⠀⢸⠀⢳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⢰⡟⢙⢻⡇⢸⠸⡽⠀⠀⣿⠀⠀⢸⡇⣀⣸⢀⡟⢀⣀⣾⣤⣦⢨⠏⡇⣀⢰⠀⢸⡔⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠳⣈⠙⣚⡼⠁⢸⢀⢧⡀⠀⢹⠀⠀⠘⡇⠉⢹⠺⣧⡜⣕⣻⢗⣎⢇⢰⡇⠉⢸⣀⠼⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠐⠌⠓⢦⡀⠀⢸⠈⢺⠁⠀⢸⠀⠀⢸⡇⠶⢸⠀⠀⣣⠫⣙⣫⢞⡼⠙⢁⣀⠤⠄⠐⠊⠉⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⡈⠢⡙⢦⣘⡀⣭⠆⠀⢸⠀⢀⣸⡇⠀⠘⠷⢓⣊⡵⠶⠖⠛⢒⣩⠤⠤⠒⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⠢⢍⡁⢸⠀⠀⠸⠛⢛⡉⠥⠤⠒⢊⣁⣀⠀⢀⣂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠉⢸⠀⠒⠊⣉⡠⠤⠖⠒⠉⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⠿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣀⠤⡤⠤⠤⢤⣠⣤⡤⠤⣤⣤⣤⣤⣶⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡴⠚⡂⠴⣋⡻⢿⣿⣿⣿⣿⣿⣿⣦⣍⠻⣿⣿⣷⣤⡐⠀⠄⠈⠛⢿⣷⣎⡹⢿⣿⣿⣿⣿⣦⣉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣶⣿⣿⣷⣶⣥⡑⠢⣉⢻⢿⣿⣿⣿⣿⣿⣷⣤⣉⠻⠿⣿⣦⣶⣤⣀⣀⢺⣿⡿⢦⠽⠛⠿⢿⠿⣿⠷⣾⢑⡦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡰⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠱⠦⡍⠉⠋⠉⠉⡉⠙⡁⠀⠀⠀⠅⠀⠁⠘⡏⠉⢓⡀⢀⣀⣀⣀⣨⣀⣡⣀⣴⡤⢤⡤⠿⠃
⠀⠀⠀⠀⠀⢀⠴⠥⠾⠛⠛⡛⠛⡉⠉⣍⣁⡤⣀⣰⡠⣤⢒⡶⠐⢢⠶⠖⡶⣒⡾⢶⣀⡟⡫⣿⡛⣃⢠⡜⠛⠿⠋⣩⡉⡉⠁
⠀⠀⠀⠀⠀⢹⠶⠃⠶⢷⢰⡿⣿⣝⣻⣭⣿⣥⣿⢞⣣⣖⣡⠔⠒⠛⡚⣘⢣⠭⢝⡡⢘⣣⣁⡠⣮⣿⡜⠃⡽⠿⣤⢸⡷⡗⢓⣿⢩⠅⠶⢶⡒⢤⡤⡄
⠀⠀⠀⠀⠀⢠⡀⣰⣦⣬⣟⣈⣠⠐⣋⠭⠍⠙⡺⠿⡷⣛⣿⣿⣍⠀⢻⣌⣻⠖⠾⣿⡚⢓⠿⢿⠒⢚⡙⠛⠍⠠⣉⣐⡀⠐⣀⣤⣥⣤⣧⣴⣶⡶⢁⠇
⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⣿⣿⣿⣿⠀⢰⣶⣦⣤⣤⣃⣀⠘⠓⠉⣉⣉⣁⣤⣬⣤⣴⢀⢸⣶⣶⣶⡆⢀⠀⢠⣿⣿⣿⢇⣱⣿⣿⣿⣿⣿⣿⣿⡇⣹
⠀⠀⠀⠀⠀⠀⢯⡸⣿⣿⣿⣿⠩⢛⣠⡸⠿⢿⣿⣿⣿⣿⠂⡇⠂⣿⣿⣿⣿⣿⣿⣿⢀⣸⣿⣿⣿⡀⢴⡷⣾⣿⣿⣿⣈⣸⣿⣿⣿⣿⣿⣿⣿⢡⡜
⠀⠀⠀⠀⠀⠀⢰⠄⠉⠙⢛⠛⢟⣸⠟⢹⣦⣤⣿⣿⣿⣿⠀⠀⢲⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⢇⠀⣣⠛⢻⣿⣿⠄⣿⣿⣿⣿⣿⣿⣿⡟⠠⡅
⠀⠀⠀⠀⠀⠀⠘⠦⢻⣶⣶⣦⣽⣧⣤⢞⣉⢉⠙⠛⠿⠿⠒⠀⢺⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣶⣾⣷⣄⣩⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⡇⢲⠁
⠀⠀⠀⠀⠀⠀⠀⡗⢺⣿⣿⣿⣿⣿⠈⢸⣿⣿⣿⣶⣶⡄⠉⠀⢺⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⠋⡛
⠀⠀⠀⠀⠀⠀⠀⢛⡙⠿⢿⣿⣿⣿⠈⢸⣿⣿⣿⣿⣿⡇⠛⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠺⠿⠟⡛⠛⡉⠹⣉⣐⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠦⠄⣈⠉⠀⠘⠿⢿⣿⣿⣿⡇⠀⠁⣿⣿⣿⣿⣿⣿⣿⠀⠺⠿⠿⠟⠛⡋⠉⠉⣁⣆⠀⠧⠤⠗⠒⠘⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣿⠒⢧⣤⣀⢩⡝⠁⠥⠨⠟⠛⡛⠉⠉⢀⣀⣰⡤⠼⠆⠐⠒⠈⠉⠉
⠀⠀⢠⣤⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣌⣓⠂⡭⠗⣚⣀⣩⡴⠠⢞⣛⠒⠈⠛⠂⢙⡀
⠀⠀⠀⠿⢯⣐⣈⠉⠀⢀⠰⠥⠀⠰⢇⡤⠤⣜⢷⡯⠶⢘⠛⢤⣙⡒⢮⣀⡵⠦⢘⠞⠒⠋⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⢠⣠⠌⠀⢉⠉⠍⠈⠭⠒⡇⢧⡘⠽⢏⡠⢑⣚⠉⣉⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠬⠖⠔⠀⢁⠀⠀⠈⠙⠦⠤⣄⠀⠀⢸⠲⠦⢏⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⢦⣤⠀⡤⢷⠰⠶⣌⡁⠀⢨⣟⣛⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠺⡉⠀⠄⠀⢁⡀⠀⡉⠻⣍⠒⠊⠀⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠓⠶⠶⠆⠀⢈⠉⠀⠀⠀⠉⢏⣁⣠⠲⠤⣖⠒⡖⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⣄⡀⠐⢆⠀⣀⣀⠀⠒⠲⠤⠿⢴⣍⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠒⠚⠛⠙⠋⠀⠀⠀⠀⠓⠺⠓⠓⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣿⡶⠶⠦⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣾⣿⣿⡝⢋⣉⣁⣠⣴⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠡
⠀⠀⠀⡀⠀⠚⠋⢀⠘⠷⠃⠰⣶⣶⣾⣿⣿⡿⢿⠿⠿⠛⠛⠉⠉⠁⠀⣿⣅⡿⣺⣿⡿⠿⢿⣿⡄
⠀⠠⠀⠀⢀⣀⠀⠈⠀⠀⢀⠀⡉⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡃⠀⠀⠀⠁⣀⣀⣤⣤⣤⣴⣶⣶⠟⠋⠃
⠀⠁⠀⣰⣿⣿⣿⣶⡄⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣾⣿⡁⠀⢠⣄⠙⢿⣿⣿⣿⣿⣿⠋⠀⠂
⠀⠀⠸⠟⠿⢿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡤⠈⢿⡁⠈⢻⣿⣿⣿⠏⠀⠂
⠀⠀⣷⡆⠀⠘⠋⠛⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣯⣭⣿⣿⣿⣿⣿⣷⣄⠈⠳⣾⡄⠙⣿⠏
⡇⠀⣿⣷⡄⠀⠀⠆⠀⠀⠀⠿⢟⣛⣛⣭⣭⣽⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣄⣀⣀⣀⣤⡎⠀⠈
⠁⠀⣿⣿⣹⣧⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣛⣿⣭⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢹⣿⣿⣿⠃⠘⠀⠀⣿⠿⣿⣟⣛⣻⣭⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣛⣛⣫⣭⣭⣿⡟
⠀⠀⢂⣽⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢟⣛⣋⣭⣭⣵⣶⣶⣿⣿⡿⠿⠿⠛⠛⠉⠁⠄
⠀⠀⠀⣹⣿⠃⠀⠀⢰⣿⠿⠿⢟⣛⣋⣭⣥⣶⣶⣶⣿⣿⣿⡿⠿⠟⠛⠛⢉⠉⠁⠀⠀⠒⠂⣀⣀⣤⡄⠀⠀⡀
⠀⠀⠀⢨⡇⠀⠀⠀⣶⣶⣾⣿⣿⣿⡿⠿⠿⠛⠛⢉⠉⠁⠤⠀⠀⠀⢀⣁⠠⡀⠀⠦⠘⠟⠛⢋⣉⣥⣴⣶⣤⣀⡁⠂
⠀⠀⠀⠈⠁⠀⠀⠰⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀⣴⡶⠶⠟⣛⣋⣭⣴⣴⣶⣶⠀⠀⠀⠈⠽⠀⠀⠈⠙⠛⠛⠷⢦⣄⡀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⣠⣤⣤⡶⠄⠒⠀⣀⣁⣠⣤⣴⣶⣿⠿⠛⠻⠃⠀⠀⠀⠀⠋⠐⠓⠘⡀⠀⡀⠀⣐⢂⣄⣄⠰⠛⠿⢷⣦⣄⡀⠒⠄⡀
⠀⠀⠀⠀⢁⡀⠲⠜⠛⢋⡉⠁⠀⠠⠶⢾⡿⠛⠋⠉⠛⡟⠉⢻⠀⠀⠀⠀⠠⠆⠠⠖⠁⠀⠂⠀⡉⠁⠀⠀⠘⡁⠀⠀⠀⢄⡤⡀⠉⠉⠉⣶⣤⡄⠁⠒
⠀⠀⠀⠀⠈⠀⢦⡀⠙⠻⣧⠀⠀⠀⠠⠈⠀⠀⢀⡠⠂⠓⠒⠄⠀⠀⠀⢠⡀⠀⠀⠀⠉⣛⠁⠀⠁⠐⢂⠀⠈⠃⠠⢤⠀⠈⠰⠤⠀⠈⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠫⢁⠀⠈⠁⠚⠉⣃⠤⢀⠀⢁⠶⠤⠀⠀⠒⣦⠀⠀⢀⡠⠤⠀⢀⣠⡥⠀⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⣤⠁⠀⠀⠑⢁⠀⠀⠀⠀⠒⠀⠉⠉⠆⠆⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⣀⣀⣤⠔⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦⣀⠸⠆⠀⠀⠀⠀⠁⠸⢷⠆⠀⠔⠚⠳⠶⠒⠀⠉⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠒⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⡀⢰⡆⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣴⣶⣾⣿⣿⣿⡟⠛⣉⠹⣿⣿⢿⣿⣿⡿⢻⡟⠋⠋⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠘⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣯⡀⠉⠀⠈⠙⠋⠁⢀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠇⠙⠿⣿⣿⣿⣿⠀⠙⠋⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢈⣷⣤⢸⣶⣤⣤⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣧⣤⣀⠀⡿⢿⡿⠀⠀⠂⠀⠀⠀⣿⣿⣿⣿⣿⡟⠛⠋⠀⠉⠉⠋⠁⠀⢀⠀⢸⢹⡿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣿⣿⣿⣄⠀⣱⠀⠀⠀⠀⠀⢰⣿⠟⠛⠉⠙⠃⠀⠀⠀⢀⣠⣴⣶⣿⡟⠱⠞⠀⠀⠛⠉⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣄⣀⣠⣤⣶⣿⣶⣾⣿⣿⣿⣿⣿⣟⠁⠀⠈⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠛⠟⠀⠀⠿⠀⢀⠀⢀⡀⠠⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⡙⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠛⠋⠉⠤⠀⠀⠀⠀⠈⠢⠄⠠⣄⠰⠒⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣷⣾⣷⡾⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾
⣿⣿⣿⣀⣀⣤⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠒⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠀⠉⠉⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠒⣒⠀⠤⠄⠀⢀⡀⠀⠀⠈⠐⠒
⠀⠀⠀⣀⠄⠤⠶⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠠⠌⠉⠀⠀⠀⠀⠀⠁
⠀⢠⢊⠔⠂⠀⠒⢄⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠚⠉⠁⡅⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡀⠀⠀⡀
⠀⢀⡄⠀⠀⠀⠀⠈⠆⢨⠀⠀⠀⣀⡠⠴⠒⠛⠁⡧⠒⠂⠉⠉⢠⠁⠀⣀⠀⠀⠀⠘⠀⠀⡀⢰⣂⠈⠡⠀⠐⠁⠀⠠⠀⠀⠀⠡⡀⢄⠐
⠀⠘⡁⡀⠐⠒⣂⣠⠦⠼⠔⡂⠩⠀⠂⠈⡀⡀⠀⠁⠀⠀⠀⡆⡼⠀⠀⢉⡍⠉⠐⠐⣀⣴⣤⣤⣄⡂⢰⡀⠀⢀⣀⡠⠤⠄⠼⢀⠲⠈
⠀⠀⢡⠁⠀⠀⠀⠀⢸⠸⠀⡄⠀⠀⠀⠀⣃⠀⠨⠀⠂⠀⢠⢁⠇⠀⠀⢠⠄⠀⠀⠀⢀⡀⠀⠉⠉⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢎⡄⠀⠀⠀⠘⠀⡄⠃⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠘⠘⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠃
⠀⠀⠀⠘⣧⠀⠀⠀⠀⡄⠇⠐⠀⠀⠀⠀⠀⠉⠀⢀⡀⠠⢂⠆⠀⠀⠀⠀⠃⠂⠀⠀⠒⠀⠠⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠸⣐⠠⠄⣀⡇⠦⢸⠀⣀⠀⠠⣐⠂⠬⠒⠂⠉⠁⠀⠀⠀⠀⠀⠱⠀⢀⣐⠂⠤⠄⢀⣀⡀⠀⢸⢠⠀⠀⠀⡀⢀⠨⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⣀⣀⠥⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠢⠬⠉⣈⠀⣐⡀⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣼⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⢋⠈⡆
⠀⠀⡀⠈⠉⡉⠁⠀⠀⠀⠀⡀⣀⠠⠤⠀⠐⠒⠈⠉⠉⠀⠀⣰⡇⠸⡀⢹
⠀⠌⠀⠆⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⡇⢸⠀⢃⠈⡆
⠈⠀⠉⠀⠀⠀⢀⠀⠠⠄⠐⠂⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠄⣇⠈⡆⠸⠀⢹
⠄⠘⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⢐⠀⠃⠈⣇
⠃⠀⠠⠀⠆⠂⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠐⠀⢹⡀
⠀⠈⠀⠀⠈⡀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠤⠐⠐⠂⣉⣀⣀⠑⠀⠃⡈⣇
⠀⠠⠀⢨⡀⠰⠀⠀⠀⢀⠀⠄⠐⠀⠀⠁⠀⠀⣀⡀⣤⢴⡞⠁⠀⡹⠠⢴⣉⣉⠙⠃⠀⠀⠂⠀⠀⡀⠀⡀⠤⠄
⠀⠀⠐⢄⠁⠄⣂⠁⠀⠄⣀⠀⠀⠀⠒⠀⢈⠴⢇⠀⠀⣨⠷⡞⠀⢁⣀⡞⠉⠉⣻⡏⠀⠙⣦⣤⡴⠀⠀⡷⣄⣀⣨⣦⡢
⠀⠀⠀⠀⠑⠀⡈⠐⠄⠀⠀⠀⠀⠀⣤⠄⣫⠞⠛⢯⡉⡁⠀⢹⣤⢀⠈⢦⡤⡊⠀⠹⣄⡀⠁⠀⢹⢶⣾⡤⠴⠛⠉⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢤⠏⠀⡀⠙⣆⢸⣀⠀⠀⡟⡋⠁⠈⢸⣅⠀⢀⡴⠈⢩⠉⠁⢉⠷⠛⠛⠈⢁⣠⠴⠚⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠓⠾⢧⣴⡊⠀⠙⠲⠒⢫⡈⣏⠛⣤⠴⠚⠛⠈⣁⠠⠀⠲⠊⠁⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠛⠶⢆⡀⠀⠓⠉⠁⠀⠀⢀⠀⠁⠁⠀⣦⠐⠂⠁⡀⠀⠂⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠦⠤⣀⠈⠐⠀⠀⠐⠀⡀⠐⠀⠀⠀⡀⠄⠂⠈⣀⠠⠐⠈⠑⡀⠀⠂⠁⠀⠀⠀⢀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠉⠒⠤⢀⡀⠀⠂⠀⠀⠏⠀⣀⠤⠒⠉⠀⡀⠄⠂⠁⡀⠀⠀⢀⡠⠔⠊⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⠉⠂⠠⠀⠈⠑⠂⠀⠀⠈⠉⢀⡠⠄⠂⠁⠀⠀⠀⢀⡠⠔⠊⠁⠠⠀⠠⠀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠁⠂⠄⢀⠀⠀⠺⠀⠀⠐⠊⠁⠀⠀⠀⠀⣀⠤⠂⠁⡀⠄⠂⠁⢀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⠁⠐⠄⢀⠀⠀⠠⠀⠀⠐⠀⠀⣀⠤⠒⠉⢀⠠⠐⠉⠀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⡙⠲⢄⡀⠀⠀⠠⠀⠠⠀⠖⠉⢀⡠⠔⠊⠄⢂⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠈⠓⠦⣄⡀⠀⠀⠤⠊⠁⠀⢀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠁⡀⠐⠈

⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠶⢚⡝⠛⠦⣤⣄⣀⣠⠤⢤⣄⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢠⣞⣉⣀⠉⣡⠋⠉⢹⠓⠒⠂⠀⠤⠐⠡⡾⠉⢀⣉⣉⣉⣉⣏⣩⠟⠛⠒⠒⠒⠶⢲⠚⠉⡓⢦⡀
⠀⠀⠀⠀⠈⢦⡲⠿⠿⠿⣭⠭⠿⠷⢶⣖⣲⣷⣶⣦⡦⠤⠤⣤⣤⣈⣀⣀⣩⡉⠉⠀⠐⠒⠚⠒⠊⠥⢁⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠙⠮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠯⠭⠭⠿⣷⣒⡒⢦⠊⢳⡜⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠮⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡱⡀⠑⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⢆⠈⢦⠀⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠆⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠈⢢⡳⡀⠱⡀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣻⣶⠂⠉⠑⠒⣺⣋⠁⠲⠦⢤⣐⡤⠤⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠑⣝⢄⠈⢷⣼
⠀⠀⠀⡀⠀⠀⢀⣀⡤⠶⣯⡝⠟⠉⠅⠉⠄⠀⠀⠀⡡⠀⣱⠁⠀⠀⠁⢀⠀⠈⠂⠁⠀⠘⣄⣼⣠⣄⣤⢂⠐⠐⠈⢮⢣⣠⠇
⠀⠀⠀⣬⠴⠚⣽⣏⣰⠉⠙⡆⠀⠀⠀⣄⡴⠢⠼⠃⠀⠀⠀⠳⣄⠀⠀⣸⠁⠈⠀⢀⣀⠴⠛⠙⠛⢽⣍⡉⠓⣲⠒⠢⣴⡏
⠀⠀⠀⣇⠉⠀⠒⠒⠠⠍⢙⣓⠓⠠⠤⣮⣀⣀⠀⠑⠄⠄⠀⣤⣉⡙⢛⡈⠶⣤⣀⠈⠛⢤⡀⠀⣀⣈⣯⠴⢛⠡⠒⠉⣠⡇
⠀⠀⠀⣟⠓⢲⡶⠤⠤⣀⣀⠀⠉⠉⠛⢳⢾⠍⡏⣙⣛⡶⠶⠧⢤⣬⣣⣀⣀⠈⠏⠄⠀⢀⣹⡿⠿⣋⠕⠊⢁⡠⢴⣟⢡⡇
⠀⠀⠀⢿⠊⠉⢁⠀⠀⠀⠀⠉⢟⠑⢂⣎⠙⠂⠓⠼⠂⠉⠉⠑⠒⠒⠠⠭⢉⣉⣛⠓⠓⠛⡩⠖⠈⢀⡠⠖⠉⡀⢨⡏⢹⡇
⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠀⠀⡇⢙⠈⢆⠀⠴⡸⠏⠐⠒⣦⠤⠤⣀⣀⡀⠀⠀⠈⠙⠋⢀⣠⡖⠉⠀⠀⠸⣤⢻⡇⢸⡇
⠂⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠜⠁⠘⠃⠈⡅⢴⠟⠀⠀⠀⠈⠫⡙⠓⠲⢶⡶⡋⣼⢱⢇⡄⠀⢀⡞⣼⡁⢸⠃
⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠞⠂⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸⠃⠤⠞⠣⠔⣻⢸⡘⠤⠤⡪⠊⣐⠁⢸⡀
⠀⠀⠀⣸⣄⣀⣐⡀⠀⠀⠀⠀⠀⣥⢤⡆⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠉⠈⠁⠀⠀⠠⣂⣸⡀
⠀⠀⠀⣿⡀⠉⠙⠱⣤⣀⡀⠀⡞⣁⣸⠣⡀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠚⠟⣩⠇⢀
⠀⠀⠀⠀⠉⠙⡲⠞⠁⠀⠈⠉⠳⢦⣘⡀⢄⡀⠀⢀⠞⢁⠘⢃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡷⠀⠀⠀⣠⠴⠛⠒⢻⠉⠀⠀⠈⠢
⠠⡀⠀⠀⢀⣤⠦⣀⠀⢀⢀⠆⠀⠀⠀⠉⠉⠉⠉⠛⠮⣄⣘⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢀⡤⠊⠁⠀⠀⠀⠈⢄⣀⠀⢀⡠
⠀⠈⠈⠈⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠲⢤⣼⠀⢀⠄⢠⢀⢻⠉⠀⠀⠐⠂⠀⡀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣀⡀⠀⠀⠎⢀⡼⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣀⠀⠀⢻⣏⢓⣔⠲⣤⠶⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⡦⣬⣍⣓⡒⠾⠧⣄⣀⣏⠑⢢⡴⠖⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⣭⡅⣿⡟⠓⠲⡦⢬⣍⣉⣑⠒⠚⠃⢉⢍⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠃⠀⠀⠀⠀⠁⠀⠁⠀⠈⠀⠉⠙⢻⠀⠀⣶⠿⣎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⢠⠚⢻⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣃⣀⠈⠑⠒⠢⠤⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⢶⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⢿⡛⢤⠠⣭⠁⣒⠂⠤⢄⡉⠉⠓⠂⠔⠢⢄⣀⡐⠀⠀⠀⠈⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠶⠾⣿⣛⡻⢩⢶⡮⠱⣞⢃⣮⢠⣯⢤⡓⢐⣄⡉⢉⡓⠲⠤⣄⣀⠨⠝⠒⠆⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⡀⢂⠉⠑⠀⠉⠙⠃⠤⠏⡛⢺⠁⣾⠯⣽⣤⡕⠚⣌⣁⠒⣴⠴⠛⠓⠂⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⣿⣶⣧⠀⣷⣶⣖⠄⠐⠂⣀⡀⠀⠈⡀⠉⠀⠓⠻⠭⠝⠉⡈⢉⣠⠧⠔⠛⢹⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣤⠀⠈⠛⠹⠆⢹⢀⡼⢯⣈⡐⠐⡦⠤⢀⠀⡆⣤⠖⠁⠉⣀⣴⡶⡞⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢼⣉⡉⠀⢸⣷⠢⠜⠦⢮⣀⠈⠈⠳⠀⣿⣶⠶⢀⡇⣩⡤⠒⠋⠁⠈⣀⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣟⣿⡇⢨⠄⠀⢀⡀⠀⠀⠈⠑⠒⠀⡀⠩⢙⡀⠁⣁⠀⣀⣤⢤⠖⠛⣋⣤⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠁⠘⠂⠀⠀⠈⠁⠲⠶⢤⣤⠀⡗⠀⠈⡟⠉⠹⠈⠉⢀⡤⠴⣻⡋⠿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢘⠀⢹⠷⣶⣦⡴⢲⠖⣈⡩⠖⠊⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠈⣀⠚⠓⠠⣤⢀⡘⠋⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠖⠀⢀⡀⠀⢹⠚⢣⠦⠨⠯⣤⣃⣠⠆⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⡀⡀⠨⠁⠐⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⡿⠖⠦⢶⣆⠀⢀⠀⠀⠀⠀⢀⡴⠻⣶⣟⠓⠾⣑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠾⠛⡥⢿⣿⣿⠟⠿⣽⣿⡰⠷⣟⡛⠋⢛⠋⠉⠉⠉⠛⢷⡟⢳⣐⠦⠤⠤⢤⣄⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢊⣡⠒⠒⠉⠉⠂⠠⢈⡢⡐⠀⠈⠙⠳⣶⠿⣷⣞⣳⡤⢀⠀⠀⠈⣷⢘⣿⠀⠀⠀⠀⠀⠉⠻⡟⠂
⠀⠀⠀⠀⠀⠀⢰⢉⠇⠀⠁⠀⠀⠀⠀⠀⢠⣵⣏⢀⠲⠀⡀⠈⠉⠻⣎⠻⢏⠘⢆⠀⠀⣿⣾⡄⣦⣤⠀⠀⠀⠀⣀⣈⣀⠃⢀
⠀⠀⠀⠀⠀⠀⠂⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⢇⢀⠐⠀⠀⠀⠈⠻⣿⣷⣎⣇⠢⣿⡇⠣⠙⢶⡵⠄⢦⡀⠀⠀⠈⢧⢠⢃
⠀⠀⠀⠀⠀⠀⢓⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⣜⡄⠀⠀⠀⠀⠀⠀⠈⢿⡍⢫⠷⣼⡿⢿⡾⡁⠀⠴⢦⡌⠢⡀⠀⠈⠆⠈⠆
⠀⠀⠀⠀⠀⠀⣤⣭⣑⡀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⣿⣣⠰⠰⠀⠀⠀⠀⠀⠀⠻⢶⡷⣾⣵⣺⣧⡈⠠⣀⠙⠹⠆⢰⠤⠄⠅⠐
⠀⠀⠀⠀⠀⠀⠃⡀⠀⠈⠉⠒⠒⠤⣤⣀⡀⠀⠀⠀⢨⡻⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠻⣯⢿⢹⣿⢿⣦⣌⣷⣤⡤⠊
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠮⣽⣟⣇⣳⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⣿⢸⡇⠙⢻⣿⡟⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⢀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣿⡍⠉⡍⠉⠉⠉⠉⠉⠉⠉⣽⣧⡍⣿⢿⣘⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀⠀⠀⠀⠲⡟⡄⠃⠀⠀⠀⠀⠀⠀⠀⢀⡧⡻⢀⠹⡄⠟⠳⡧⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠖⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣿⡇⡄⣂⠀⠀⠀⠀⠀⢀⡿⢸⣷⢏⡂⠙⣞⣆⢡⣀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⢦⡆⠀⠀⠀⠢⢤⣀⠀⠀⠀⠈⠑⠀⣝⡇⠀⡇⠀⠀⠀⠀⠀⢠⣷⡏⣉⠌⠀⠀⣼⢹⣾⡇⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠐⣧⣄⠀⠀⠀⠀⠈⠉⠲⠤⣀⡀⠀⠿⡇⠂⡇⠀⠀⠀⠀⢀⡞⣽⣡⡄⠀⠀⠀⢹⡄⣏⢱⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠛⠢⠄⣀⠀⠀⠂⠠⢄⡉⠑⡛⠇⡀⡇⠀⠀⠀⠀⣾⡧⢼⡩⠃⠀⠀⠀⠀⣿⢻⢘⡧⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠒⢄⣤⢤⣹⣛⣧⠀⠀⠁⠀⠀⠀⡼⢻⢇⡈⠁⠀⠀⠀⠀⠀⢸⣈⡿⢅⠀⠀⠀⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⣿⠘⢁⠂⢠⡶⣾⣵⣭⣯⡤⠤⠀⢀⣀⣀⣀⠸⢿⣷⢠⣄⣤⣤⣤⠤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⠛⣿⡯⢭⣿⣜⡫⠚⠁⠀⠀⠀⠀⠙⠫⣍⡺⠻⠻⠂⠰⠭⠩⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠀⢽⡗⠒⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠐⠾⠤⣄⣀⡀⠀⠀⠀⡀⠀⠀⠁⢀⡰⠲⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠐⠲⡤⠤⢄⣀⠀⠀⠠⠍⠁⠀⠀⠄⠀⠐⢀⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠑⡒⠠⠄⣀⣀⡀⠒⠀⠘⠋⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⠘⠈⡈⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡧⡀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠇⡲⡯⣿⣢⢌⡃⠰⢶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠄⢀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⡀⣠⡿⢸⠙⢍⠰⣩⢓⠸⣕⣛⢛⢳⣻⡏⢓⢠⣄⡀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⡸
⠀⠀⢠⣄⠲⠈⠀⢡⠤⣧⡽⠷⠤⡣⡭⠙⢷⠀⢩⡄⢚⢽⢒⡯⣀⠂⠨⢦⣀⠀⣠⡤⢀⡀⢳⠀⠐⠇
⠀⠀⢸⠃⣀⠀⠘⠧⠴⢷⡃⣳⣒⡶⡾⡶⣻⣗⠙⣤⢋⣤⡮⣧⢒⠴⠷⠿⣓⣿⡁⠁⠘⣻⠐⢣⠰⠘
⠀⠀⢸⠀⡇⠀⠁⠀⠮⢁⠉⠒⠛⢴⣧⡖⠲⡆⠋⡝⠼⡴⠲⣇⣸⣒⣳⢞⡩⠃⢸⡒⠾⣕⠿⢪⠖
⠀⠀⠸⠀⠃⠀⠀⠀⡆⠘⢛⠴⠄⣀⣰⣿⣿⢻⠟⣜⣓⣿⡤⠼⣥⣉⣩⣧⣴⠤⡶⠋⠁⠀⣀⠸
⠀⠀⠀⠀⡄⠀⠀⠀⠁⠀⠫⣤⣶⣿⠟⠙⠋⠈⢡⠼⣍⣠⡗⢲⣉⣉⠧⠚⠂⠈⡅⠀⠀⠀⢗⢠
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠈⣉⠒⠀⡛⠋⡎⡁⠔⣋⠁⠀⠆⠀⠀⠀⡷⡎
⠀⠀⠀⠉⠄⠀⠀⠀⠄⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠁⠀⠀⠀⡖⡂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣟⠀⠄⠀⣷⣳⡀⠀⠀⠀⠀⠈⣋⡂⠀⠀⢀⠀⢰⢂⠂⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡤⠠⢀⢻⣦⠄⠀⠀⠀⠀⠡⠚⢆⠰⠸⠀⠸⠈⠀⠀⢀⡠⠴⣋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢥⠘⠒⣈⣾⢾⡗⢀⣠⣄⠀⠀⠓⢊⠂⢦⠤⠼⠴⡤⣾⠛⢵⣿⡾⠿⣟⡸⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣉⣫⡟⠘⢶⠞⢰⣈⡩⠔⢃⡿⢸⣍⢼⣀⣽⡪⠙⣶⣓⠶⢋⠹⠏⠵⠤⢖⣚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢘⣡⠌⣉⡭⣱⣛⡤⢽⡶⠛⡇⠒⣷⠞⠟⢻⢗⠂⢺⠈⣖⠚⣲⡜⠓⠖⠦⢤⠇⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣉⡰⠊⣱⣉⠒⢐⣓⠶⣤⡬⡗⠂⡼⠠⣴⠛⠻⠤⠾⣽⠛⡍⣟⡿⡀⢐⡓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠛⠊⠑⠩⢋⠥⢤⠓⢰⣿⣹⣇⣀⠶⡎⠛⡻⣄⣩⣀⠽⢧⣈⡛⠃⡯⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠦⠔⠉⠁⠈⠙⣿⣯⣤⣿⡹⠟⠓⠤⠂⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣄⠀⠂⠂⠲⢶⠒⠒⠒⠒⠚⢛⣋⡉⠉⠁⠠⢤⡀⠁⠂⠄
⠀⠀⠀⠀⠀⡠⠤⢦⣐⠒⠐⠒⢖⠊⠉⠉⠉⣉⠉⠉⠉⠀⠀⠠⠤⠀⠀⠀⠘⠱⣄⠀⠀⠀⠙⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠐⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠣⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠘⣆⠀⠀⠀⠈⢆⣈⣁⡀⠀⠠⠤⠄⠀⠐⠒⠒⠈⠀⠠⠈
⠀⠀⠀⠐⠀⠀⠉⡩⠓⣄⠀⠀⠀⠀⠰⡀⣀⣀⣀⣀⣠⠤⠤⠤⠤⠔⠲⠖⠒⠒⠂⠛⢠⠀⠀⠀⠠⠇⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠀⠠⣠⠖⠁
⠀⠀⠀⠇⠀⠀⡴⠁⢀⡜⢆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠒⠆⠐⠗⠀⠃⠀⠈⠏⠉⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⣀⠞⠀⢠⠎⠀⠀⠰⢀⡀⠀⠠⠤⠄⠀⠒⠂⠀⠈⠉⠉⠀⠀⣀⣀⣀⣀⣀⠤⠤⠤⠔⠒⠒⠒⠺⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⡆⠉⠀⣠⠋⠀⡔⠀⢀⣊⣀⣀⠤⠤⠤⠴⠖⠒⠒⠚⠛⠋⠉⠉⠉⠁⠀⠀⢀⣀⣀⡀⠤⠤⠤⠶⡇⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠁⠀⣰⠃⢀⠌⠀⠀⠊⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠤⠤⠴⠖⠒⠒⠊⠉⠉⠁⠀⠀⢀⣀⣀⣀⣤⡇⠀⡠⠊⠁
⠀⠀⠀⠘⠘⠁⢀⠞⠀⠠⠦⠒⠒⠒⠋⠉⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀⠤⣤⠒⠋⠒⢒⡉⢉⢉⣁⡄⠐⠶⢷⣉
⠀⠀⠀⠀⠀⢢⠎⠀⡐⠁⣀⣀⣀⠤⠤⠤⠲⠒⠒⠛⠉⠉⠉⠀⣀⠔⠀⠙⠈⢀⣀⠈⠀⠄⠛⠙⠛⠢⡀⠀⢸⡆⠤⠄⠤⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠄⡐⠉⠉⠀⣀⠀⠀⣀⣀⣤⣤⠴⠶⢶⡞⣿⠙⠃⠀⠠⣞⣡⠋⠉⠉⠘⣇⣀⣤⠀⠒⠓⠰⢏⠀⡆⠉⠀⣛⠌⠂⠒⢢⡐⠒⠄⠄
⠀⠀⠀⠀⠀⠡⣼⣤⡤⡶⠟⠠⡀⠟⢉⠵⠒⠚⠒⢤⡁⠀⠀⠄⠠⠔⢊⠥⠚⠉⠉⣳⡎⠉⠀⢀⢷⠤⠄⢐⠺⠒⠉⠈⢑⠟⠂⠒⢂⣉⡀⠴⠚⠂⠈⠁
⠀⠀⠀⠀⠀⠀⡉⠲⢼⡀⠀⣠⠇⡀⠉⠖⠈⠀⠓⠉⠙⢢⠐⠐⠂⡄⠐⠀⠀⠀⠈⠀⡠⠐⠂⠠⣌⠀⠀⠙⠂⠀⠀⠀⠥⠒⠒⠉⠉⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⡀⠀⠙⣇⠀⠀⠘⠀⢾⡄⣀⡒⠀⡲⠚⠀⠀⠶⡅⠀⡠⠐⠀⠈⠉⣷⠂⣀⣐⡟⠠⠖⠂⠉⠁⠀⠀⠀⢀⣀⠠⠄⠒⠊⠉⢹⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠉⢀⣀⠈⠁⠀⢀⢴⠓⠂⠠⠤⠐⠊⠀⢁⣒⠒⠀⠁⠈⠉⠁⠀⠀⠀⠀⣀⡀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠁⠀⢀⣀⠤⠆⠐⠊⠉⠀⠀⠀⠀⠀⢀⣀⠤⠤⡄⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠉⠁⠀⠀⠀⡇⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠀⠀⢰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠊⡅⠀⠀⢸⠀⠀⣀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⣂⣨⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢒⣀⣤⣴⣾⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⣊⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣺⡏⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣏⢿⣿⣿⣿⣎⢿⣍⠉⡉⠹⠟⢡⠙⠙⠉⢈⣠⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠸⣿⡄⣿⣷⣿⢿⡿⠛⠃⠀⡔⢁⣐⣀⡴⠞⠋⣀⠆⠌⡠⠙⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠁⣸⡇⣿⣿⣿⣿⠟⠀⣤⠴⢙⡋⢀⣹⡀⢀⠁⠀⠒⢋⣁⣀⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠃⠿⠋⠉⠱⣤⠴⠷⠖⠛⡽⠟⠁⠙⠍⠧⣤⡴⠚⠛⢡⣤⣶⠷⢈⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣄⠲⣤⠤⣄⣀⣠⡶⠋⠉⣦⠴⢎⣠⡴⢻⠷⠶⠒⢛⣠⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡈⠲⠀⠉⠙⣶⡄⠀⠱⠶⠚⠤⠄⣛⣠⣴⣻⡿⢟⣿⣋⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣦⡘⠞⠛⣉⣰⡴⠖⣀⣤⣴⣾⣿⡞⢻⡀⠃⣴⢿⣿⢻⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠻⣿⣦⣉⣩⣴⣾⣿⣿⣿⣏⣏⣵⣷⣿⠿⠀⠀⠀⠹⠞⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⢛⠉⢠⣼⣻⡇⢿⣿⣿⢹⣿⣿⠻⠿⠛⠟⠿⠅⠀⣀⣤⣶⡴⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣄⣮⠢⡀⠿⣿⡇⢸⣿⣿⣿⢹⡟⠀⠰⠀⣉⣤⣶⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣷⣌⠢⡑⣧⢸⣿⣫⡿⠞⣋⣤⣶⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠿⣿⣿⣿⣷⣝⣿⢘⡋⣥⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠩⠟⠿⣿⣧⡻⠄⠀⠀⠁⠀⠀⠰⣄⡠⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣶⠶⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣶⡾⣿⣿⡝⢯⣉⣥⣴⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⠃
⠀⠀⠀⠀⠀⠈⠉⢡⠙⠛⠑⢾⣿⣿⠿⠿⠛⠛⠛⠉⠉⠈⠀⠀⢶⣦⣿⣽⠿⠛⠛⡿⠆⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⣤⣤⡀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣯⡄⠀⠀⠀⢤⣶⣶⣾⣿⣿⡿⠉
⠀⠀⠀⣴⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣷⣀⠐⣷⠀⠻⣿⣿⣿⡿⠀⠈
⠀⠀⠀⣦⠀⠹⠿⠟⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡘⢦⣦⠙⢿⡿⠁
⠀⠀⢰⣿⣤⠀⠀⠆⠀⠀⠸⠿⢟⣛⣛⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⢀⣉⣀⣬⠁
⠀⠀⠘⣿⣯⣶⡟⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⡿⣿⣿⠃⠈⠀⣸⣿⣿⣿⣭⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⢿⣟⣛⣯⣭⣷⣾⣿⠇
⠀⠀⠀⢰⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⠿⠿⢿⣛⣛⣯⣭⣭⣶⣶⣿⣿⡿⠿⠛⠛⠋⠉⠁⠀⠐
⠀⠀⠀⠀⣿⠃⠀⠀⣘⣻⣭⣽⣷⣶⣾⣿⣿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⣀⠀⣤⣤⠶⠶⢓⣈⣁⠐
⠀⠀⠀⠀⠛⠀⠀⠰⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⣈⣬⣤⠴⠶⢖⣉⣁⣤⡤⠀⠀⠘⣛⠉⡉⢛⠿⢶⣤⣁⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⣠⣤⡄⠀⠀⢀⣀⣀⣭⣴⣶⠾⠿⠟⠉⠉⠉⠡⠄⠐⠐⠀⠀⠀⠀⡄⣀⡀⠹⠿⢶⣤⣈⠐⠠⢀
⠀⠀⠀⠀⠘⠠⠄⠒⢛⣋⠉⠁⠀⠶⢶⠿⠛⠋⠛⠟⠛⠃⠀⠀⠀⢠⠆⠴⢆⡀⣄⠠⡉⠀⠁⠀⠁⠀⠀⠁⢠⠀⠊⠉⠑⣶⡤⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠁⠲⠄⠉⠻⢆⣀⢀⠠⠀⡂⣀⡤⠂⠀⠐⠀⠀⠀⢈⡄⠀⠀⠈⢹⠉⠀⠈⠐⡂⠀⠉⠐⡴⠀⠉⠆⠂⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⢀⡰⠆⠀⠀⠀⠉⠀⠄⠀⠰⠁⠵⠐⠂⠀⡼⠓⠂⢀⠈⠗⣀⣠⠄⠂⠂⠤⠶⠓⠀⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢙⣀⡀
⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⡄⠀⠀⠀⠒⠚⣦⣀⠀⢀⣄⣀⣀⡀⠬⠄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣀⣠⣤⣶⠶⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣅⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠈⠁⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⣿⣦⣀⠀⣦⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⣈⣣⣤⣴⣶⣾⣿⠿⢛⠻⣿⣿⣿⣿⣿⢿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⢿⣿⣿⣿⣷⡦⣀⠀⢘⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⡁⠋⠁⠈⠛⠉⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡙⠈⠻⠿⣿⣿⡇⠈⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠀⠀⣽⣦⢻⣷⣶⣾⣿⣿⣿⣿⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⣿⣿⣿⣶⣦⣀⠛⠻⡇⠀⠑⠀⠀⢸⣿⣿⣿⣿⠋⠉⠀⠀⠀⠃⢀⣀⣤⢸⡙⠛⣿⢿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠻⣿⣿⣿⣿⣦⣤⡇⠀⠀⠀⠀⢸⠛⠀⠀⣀⣄⣀⣠⣤⣶⣿⣿⡿⠁⠉⠄⣀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⢤⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⠉⠻⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⢋⡉⠀⠀⠀⠡⢄⣠⡀⠤⠠⠓⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⢀⡀⠤⠤⢤⣤⣀⣀⣄⣀⣀⣀⣀⢀⣀⣀⣀
⠀⠀⢀⡜⣡⠴⠚⠛⠓⠂⠙⢹⣟⣿⣿⠿⠿⠿⠿⠛⠛⠉⠉⠙⠒⠒⠒⢲⣴⡦⠤⠤⣤⣄⣀⣀⡀
⠀⠀⡜⢠⠀⠀⠀⠀⠀⠀⠘⣆⠼⢷⠒⠲⠶⠦⠤⠤⠤⣤⣤⣄⣀⣀⣀⣺⣿⠇⠀⠀⠀⠀⠀⣈⣍⣙⣷⣶⣄
⠀⠀⡇⣿⡀⠀⠀⠀⢀⡴⠊⠁⢀⡴⠃⠒⠒⠒⠒⠶⠶⠶⠦⠤⠤⠤⠤⠬⠭⠭⠭⣭⣭⣙⣛⣒⣒⣛⣻⡿⠿⢿⡄
⠀⠀⡄⢸⣷⣦⡢⠞⠁⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣩⠝⢋⡭⠟
⠀⠀⢸⣘⠟⠋⠀⣠⣴⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⠾⢋⡡⠞⠉
⠀⠀⠈⠣⣀⡤⠚⠛⢛⣛⣛⡛⠛⠒⠒⠛⢚⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣶⣶⣞⣛⣛⣻⣥⠖⠉
⠀⠀⠀⠀⢹⠿⣿⣏⡽⠿⠿⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠿⣿⡿⠿⣖⠶⠤⣄⣀⡀
⠀⠀⠀⠀⡞⠰⢬⡙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠴⠶⠾⠶⠶⠒⣚⡛⣛⣛⣛⡛⢳
⠀⠀⠀⠀⡇⡄⣀⡛⢷⢤⡉⠉⡶⠖⠛⠛⠛⠛⣛⣛⣉⣉⣉⡉⠩⠭⠥⠤⠶⠒⣒⡒⠛⠋⠉⠉⠉⠿⠉⠑⣉⣛⢻⡇⢻
⠀⠀⠀⠀⡇⠃⣿⣁⢠⡄⢶⠀⡇⢸⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠘
⠀⠀⠀⠀⡇⣆⠀⠉⠛⠁⢰⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠳⡙⢆⠀⠀⠀⢸⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠖⠒⣛⣉⡥⠼⠃
⠀⠀⠀⠀⠀⠈⠳⣕⢄⡀⣼⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠒⠚⣉⣉⣁⡤⠤⠖⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⠿⠀⡇⣼⠥⢄⣀⣀⣠⠤⠴⠒⠚⣋⣁⣤⠤⠖⠒⠚⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⡄⢉⣉⡉⠁⠤⠖⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠄⠀⠀⠠⢀
⠀⠀⠀⠀⢀⣀⡀⠀⠠⢤⠤⠤⠀⠀⠀⠒⠒⠒⠒⢀⠀⠉⠑⢤⡀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⢀
⠀⠀⠀⡐⠁⠀⠉⠢⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠐⣀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠠
⠀⠀⠀⠀⠀⢈⠑⢂⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠄⠀⠒⠒⠒⠀⠈⠑⠄⠀⡀⢘⡀⢀⣀⡀⠀⠀⠀⠀⠀⢐⡰⠊
⠀⠀⠀⠀⡠⠃⢠⠎⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠈⢁⣈⣀⣠⠁⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠸⠁⣠⠃⠀⠀⠁⠂⠀⢀⣀⣀⣀⠀⠤⠤⠤⠀⠒⠒⠒⠂⠈⠉⠉⣀⣀⣀⡄⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⡰⠁⠠⠁⠀⠉⠉⠉⠀⠀⣀⣀⣀⣀⠠⠤⠄⠒⠒⠒⠒⠈⠉⠁⣀⣀⣀⡆⢄⠤⠊
⠀⠀⠀⠈⠁⡰⠁⡀⠒⠒⠂⠉⠉⠁⠀⢀⣀⣀⡀⠤⠤⠠⠄⠉⠐⡈⠉⣁⣠⡀⠐⠳⣅
⠀⠀⠀⠀⠰⠁⡠⠤⠤⠖⠒⠒⠈⠉⠉⣀⣀⣀⣤⡄⠀⢀⡤⠠⠤⠀⣄⠉⠈⢉⣢⠀⡸⠀⠢⠐⢤⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢈⣀⣀⣠⡔⡀⢲⠖⣺⠿⠯⢉⠏⠉⠁⠀⡀⢙⠲⠖⠲⣀⠚⠒⠋⣄⣀⠈⣵⠔⠄⠄⡪⠀⠀⠘⢀⣀⠤⠐⠄
⠀⠀⠀⠀⠈⠙⢮⡅⠀⡰⠀⠘⠄⠂⠐⠚⠓⠤⠀⠠⡀⠁⠀⠀⠀⢈⠀⠄⢀⡁⠀⠐⠀⠀⠀⠠⠄⠒⠊⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠠⢀⠈⠇⢀⠈⠀⢲⠀⠀⠀⡐⠁⠀⠒⠄⢀⠀⠀⠈⡉⣂⡠⠰⠃⠒⠂⠉⠀⠀⠀⡀⠠⠀⠐⠈⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠠⠘⠁⠀⠒⢀⡁⠤⠂⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠀⠉⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠐⠀⠁⠀⠀⠀⢀⡀⠤⠐⠒⠉⠉⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠒⠁⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⡀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣒⣒⣂⠠⠠⠤⠠⠶⠶⠤⢤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠎⠙⣬⣉⣉⣉⣉⣉⠉⠉⠁⠐⠒⠒⠒⠒⠀⠠⠤⠤⠤⠍⠉⣉⣉⣉⡐⡲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠋⠀⡆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠐⠒⠒⠀⠀⠄⠀⠀⠀⠀⠀⢀⠞⡐⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠔⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣳⡁⣠⡎⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠌⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⡤⣶⣶⣖⠒⠒⠚⠋⠉⣉⠉⢉⣍⡏⠙⠛⠻⠷⣤⣥⣴⠎⣸⣤⢂⡀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠤⠀⠀⠀⣠⠃⠌⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⢿⠃⠀⠈⠙⠳⢶⣶⣆⣿⢽⣋⢶⣹⣏⣈⠸⡦⠶⣴⡁⠘⠛⢱⣻⢟⣷⣤⣐⣒⠠⠤⢀⣀⣀⠀⠀⠀⡠⢁⠂⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠻⠀⠉⡛⠖⣿⣭⣧⠘⢧⡼⡿⣿⣄⡠⢀⢀⠐⢏⡧⢶⣀⣈⠉⠙⠒⠢⣮⣬⣌⣒⣡⣂⣀⣀⠌
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢱⣦⡀⠜⠓⠢⠍⠊⠛⠺⢿⡏⢿⣉⢿⡽⡷⣜⡷⠹⢧⣿⠛⢿⡗⠒⢉⠉⠭⠻⣬⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠄⡀⠀⠀⢸⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⢻⡟⢻⠖⢘⡁⠬⠅⢿⠀⢹⡃⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⢠⡦⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡠⠎⠁⠀⠀⠀⠀⢸⡆⣼⠀⠒⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠀⠀⠀⠀⠰⠀⠀⠤⠄⠒⠀⠈⠉⠘⣇⡿⠀⠀⠀⠀⠀⠐⢷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠙⠿⢷⣦⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠙⠁⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣄⡀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠸⠀⠀⠰⠐⠀⠁⠀⠀⠀⢀⠠⣀⣤⡾⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⣩⣇⣤⠈⠙⠻⢶⣤⣀⠀⢀⡴⢄⡀⠀⢀⡠⢤⣲⡬⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⠀⠀⠉⡛⢷⣾⠀⡆⢳⣮⡵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠚⠈⠁⠀⣴⡾⢒⡯⠌⠙⠛⠛⠁⠀⠀⠀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠋⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⡀⢀⡀⣀⣤⡤⢠⣄⣀⠀⠀⢠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠩⠍⠲⢝⠩⣲⢄⠀⠀⠀⢘⠆⠱⠎⠰⠄⠤⣤⣬⣵⣀⣿⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠖⠁⠀⠑⢶⢂⢟⡤⠆⠀⠈⠉⠁⠀⠙⠛⡾⠃⠉⠀⠀⠚⠋⡘⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⡠⠣⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢲⠀⠀⠔⡕⡵⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡇⠀⠀⠀⠀⢊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢊⢎⡞⠁⠀⣀⣠⠤⠠⠀⠘⡉⠉⠑⠶⡿⠤⠀⡀⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡠⢣⣾⣴⣶⢯⡬⠗⠞⡣⣤⡀⠀⢈⣄⣠⠆⠰⠃⠛⢓⠢⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢝⠫⣏⣉⠋⢘⠶⢦⣀⠀⠀⢹⣇⣁⣠⡇⠀⡴⢣⡀⣀⣼⣳⠉⠷⠶⢒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠶⢍⡢⢍⡒⠬⣂⣰⣟⣀⣴⣈⠰⠯⠤⢟⣚⠻⠾⢖⣛⣡⡄⣀⡴⠒⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⢈⣒⠬⡙⢲⠕⠒⣲⡦⠽⡍⢉⣰⠒⡾⢃⠙⣈⣷⠀⡇⠉⡇⠀⡗⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⢰⣯⡿⠇⠾⢾⠀⠖⡇⠀⠀⡇⠀⢸⢠⡏⠉⣠⠀⡘⣆⡇⠛⡇⠀⣷⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠺⢨⠼⠉⠈⢁⡜⠉⣢⠀⣥⠀⠀⡇⠘⢹⢸⣀⡟⣿⣾⡳⠃⣇⠒⣇⣀⡿⢸⡟⠗⠶⣤⣄
⠀⠀⠀⠀⠀⣠⠄⢲⡊⠴⠉⠁⠳⠂⢦⣀⣠⠉⠈⠑⣀⣀⠦⣬⣷⠒⢧⡶⢸⠀⠉⣏⠷⡾⡳⠶⢃⡀⢭⠋⠁⠚⣧⣠⣦⠿⠸⠗⠂⢤
⠀⠀⠀⣀⡎⠀⡐⠉⠉⣦⠀⡴⠳⠀⠀⣨⠀⠉⢲⠞⠉⠨⠃⠀⣸⣻⢹⣧⠼⣞⡟⠛⠻⡟⢑⣬⠕⠶⠋⠐⡆⠠⢿⠕⠠⠐⠀⢰⣶⠾⠠⠤⡀
⠀⠰⣁⣀⣀⣿⠆⠀⢰⠀⠀⠈⠎⠳⣊⣉⡽⢾⠹⠄⣀⢀⣼⡛⠛⠡⠀⠬⠄⢼⣄⣀⣠⠿⠷⠞⠛⠆⠠⢴⣤⣤⠏⠦⢄⣠⣤⠾⠓⠤⠤⠴⠃
⠀⠀⠀⠉⠀⠘⢤⣠⡾⠲⡀⠀⠀⣰⣟⣩⢦⡄⠀⣀⡇⢀⡹⣁⡈⠀⢦⣀⣀⣠⣇⣈⣧⣤⣤⠾⢧⣀⢀⣠⠟⣇⡀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⣄⠁⠀⠈⣻⠒⣎⠁⢀⣰⣄⠁⠀⢈⡿⡏⠁⠀⠉⡾⠋⠁⠀⠈⠉⠁⠀⠰⣀⠀⣀⡼⠃⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⢩⠋⠉⠉⢱⡖⠛⠁⠙⠲⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣺⠿⠛⠋⠉⠙⠛⠛⠛⠓⠒⠒⠒⠲⠶⠶⠦⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣡⠞⠉⠉⠐⠒⠒⠒⠒⠒⢀⣤⠴⠒⢒⡒⠒⠦⣄⣀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢛⡻⠖⣒⡶⠶⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠖⠋⣭⣭⣉⠓⢦⡙⢦⡀⠀⠈⠉⠉⠉⠉⠉⠐⠒⠒⣶⠋⣠⠞⣡⠴⠒⢖⠒⠦⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣁⣀⣉⣉⣉⣉⣛⠛⠛⠒⠒⠚⠳⠶⠷⠦⠤⠤⠤⣤⣤⣤⣧⣀⣧⣀⣀⣀⣀⡀⠀⠀⠀⢀⡼⢁⡼⢁⡾⣅⠀⠀⠈⠳⡀⠈⢳⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠉⢏⠉⠉⠉⠙⡟⠛⢻⡟⠒⠒⠒⠒⠲⠶⠶⠤⠤⠤⠤⠤⣬⣭⣭⣉⣉⣉⣙⣛⣁⡾⢀⡞⠀⠈⠢⡀⠀⠀⠘⢦⠀⢧⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠈⢣⠀⠀⠀⠘⡄⢸⠁⠉⠉⠉⠉⠉⠒⠒⠒⠒⠒⠂⠤⠤⠤⢤⡤⠤⢄⣀⣉⣉⣙⣆⠙⣄⠀⠀⠈⢦⡀⠀⠀⠑⣼⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢀⠷⠔⠶⣤⢸⡏⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣹⠀⠀⢀⡤⢄⠀⠈⠳⣌⠳⣄⠀⠀⠙⢄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠳⣲⡖⢻⣸⣾⠀⠀⠀⢀⣀⣭⣍⣉⡼⠛⠛⠛⠓⠶⣖⠒⡿⡦⠤⠤⣼⡤⢼⣀⡠⢤⣈⣧⡘⢧⡀⠀⠀⠳⣄⢸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢈⠟⣉⣤⣄⡙⢦⡴⠉⠀⠀⠀⠉⠀⢀⣤⠤⣀⠀⠉⢩⠇⣿⣳⠞⡝⠀⣀⣤⠧⠴⠋⠀⠙⢦⡙⢦⠀⠀⠈⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢼⣀⡿⠟⠁⠘⣬⠥⠀⢠⣔⠒⠢⢄⠀⠀⠀⠀⠁⣰⠋⠠⠟⠁⣼⠷⢋⡽⢅⡀⠀⠀⠀⠀⠀⠳⣌⠳⣄⢠⢧⡏
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠙⠒⠖⠙⠀⠉⠉⠓⠄⢈⠁⠀⠀⠈⠉⣑⣒⣸⠀⠀⠀⠀⠈⠙⢦⡀⣀⣀⣁⣠⡞⠀⠀⠿⢬⣉⠉⠉⠉⠉⠙⢳⡈⠋⡾
⠀⠀⠀⣀⡔⠉⠁⠂⢠⣆⣉⣁⣲⡀⠀⠤⠦⣤⣎⣁⠤⢿⡴⠖⠛⠁⠀⠀⢀⠀⢀⣤⠖⢤⡀⠈⠋⠀⠀⢀⡈⢉⠀⠀⠀⠀⢀⣱⣶⠶⠶⠤⣤⣽⣾⠁
⡞⠉⠙⡧⠼⠶⣶⣤⣄⣁⣀⣀⣋⣀⣀⣀⡀⠈⠑⠂⡠⠭⣀⣀⡀⠀⢀⣀⣀⠉⠙⢧⡤⠼⠟⠤⠀⠀⠀⢙⠳⢤⣘⡆⠀⠊⢉⣀⡬⠿⠒⢋⣩⠀⡏
⢱⡤⠴⡗⠶⠶⠶⠤⠤⠤⣤⣤⣬⣉⣉⣉⣉⣉⣉⣻⡀⠀⢸⠓⠛⣲⣅⣨⠿⠷⠤⠤⠤⢤⣤⡔⠛⢲⣦⣄⣈⣁⣬⠵⠖⠛⣉⣡⠤⠖⠛⠉⣹⢰⡇
⠈⣧⡠⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠥⠿⣇⣀⠏⠉⠉⠛⠛⢇⣨⣗⡶⠲⠶⠶⠤⠤⡤⠷⢤⣮⣄⡀⠈⡇⠀⡴⠒⠋⠉⠀⠀⠀⠀⠀⡟⣸
⠀⢋⠀⠀⣱⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡀⠀⡸⠳⢤⣀⣀⣤⠴⢿⠁⢈⡆⠀⠀⠀⠀⢀⡧⣀⠜⠀⢸⡇⠀⡇⢀⡇⠀⠀⠀⠀⠀⢀⡠⢴⡇⡟
⠀⠸⡇⢺⡁⢈⠟⠒⢖⣒⣲⡎⠉⠙⣦⠴⠯⠭⠉⣳⣶⣶⣶⣶⣒⠋⢙⡋⠉⣢⣀⣀⠤⢏⡀⣸⠀⠀⢸⡇⠀⡇⢸⡇⠀⣀⠤⣒⣉⣁⠀⢸⢠⡇
⠀⠀⣧⠘⡏⠹⣄⢀⡸⣁⣈⠷⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⡇⠀⣿⣀⡠⠛⠒⠢⠤⢼⡃⠀⡇⢸⡗⠉⣠⢾⣁⣀⣸⢦⡟⢸
⠀⠀⢸⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⠃⢰⠃⡏⣀⡤⠞⢳⠙⡟
⠀⠀⠈⡇⢸⡍⠉⠉⠙⠒⠒⠒⠒⠒⠒⠠⠤⠤⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⣀⡏⠀⡏⠁⠀⠀⡸⠀⡇
⠀⠀⠀⢿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠐⠒⢺⠀⢸⡇⢸⠁⢳⡀⠙⠦⠤⠞⠁⣸⠃
⠀⠀⠀⢸⡆⢻⠤⠤⠤⠤⠄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⣸⠀⠀⠙⡦⠤⠤⢶⡏⣿
⠀⠀⠀⠀⣇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠒⠂⠤⠤⠤⠤⠤⢀⣀⣀⣀⣸⠀⢸⠀⣿⡠⠖⠉⢀⡤⠞⢉⡴⠇
⠀⠀⠀⠀⢹⠀⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣿⢀⡤⠞⢉⡤⠞⠉
⠀⠀⠀⠀⠘⠧⠤⠤⣤⣬⣍⣉⣉⣉⣉⣙⡛⠛⠓⠒⠒⠶⠶⠶⠦⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣸⠀⢸⠀⠟⢋⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠓⠒⠒⠲⠶⠦⠤⠤⠤⣤⣤⣤⣉⣉⣉⣉⣉⣀⣸⣠⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡇⠙⠃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣈⣉⠙⠒⠲⠮⣭⣟⣛⣶⣦⣿⣷⣶⣶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⣭⣛⡻⠿⢷⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠷⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣶⣶⣬⣍⣛⡛⠿⢿⣿⣿⣿⣥⣄⡈⣥⣶⣶⣶⣾⣿⡿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⡙⣿⣿⣿⡿⣣⣿⡟⣿⡟⣷⡌⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡍⣶⣿⢿⣷⢹⡇⣿⣿⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣇⣿⣿⡜⣿⡜⣿⣿⡿⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠰⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣇⣿⣧⣿⢟⣵⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⢿⣿⣿⣿⣿⣿⡏⣥⣭⡸⣿⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠦⣤⣀⠒⠛⠠⠤⢖⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠻⣿⣿⣿⣷⣿⡷⠙⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣟⠉⠑⠒⠒⠤⠤⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠰⣾⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠘⣾⢻⣿⣿⣿⣷⣤⣀⡤⣤⠀⠀⠉⠉⠒⠒⠤⠤⣠⣀⡀⠀⢀⣠⣤⣔⣲⡿⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣭⣟⡻⢀⣩⡙⣶⣶⣦⣤⣌⣙⡓⢺⡏⢉⢻⡟⣿⠏⣯⣶⣿⣿⡿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣟⣛⡻⢿⣸⣿⣧⣾⣭⣭⣛⣻⣿⣿⣿⣷⠄⢸⠿⣋⣼⣿⣿⣯⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⡿⢿⣿⣿⠃⠀⠉⢛⣿⣛⡻⠿⣿⣿⣿⣿⣿⠀⢰⣾⡇⣿⣿⡿⢟⣫⣵⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣸⣷⡒⠀⠙⢦⣉⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣇⣿⣿⣿⣿⣿⢿⠟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠲⠤⣄⣀⡀⠈⠉⠛⠛⠿⠿⣿⣿⣀⣼⣿⡿⢿⣿⣿⣿⣶⡿⢸⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢤⣍⣒⣶⠟⠉⠀⣟⣿⣶⡙⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⡽⠟⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣦⣄⡀⢤⣤⣄⢠⣴⣮⠶⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⣾⢿⠏⣽⣿⣷⣮⣝⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣶⢈⠷⣄⣴⣿⣿⣿⣿⣷⣮⡽⢸⣿⣿⣿⣿⠿⡿⣷⣬⡐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠶⠙⣯⣠⠀⡟⡻⠿⣯⣽⣿⡿⠛⢡⣾⣿⣿⣿⣿⡟⣼⣿⣿⡶⠑⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢺⣿⡍⢾⡇⣴⠞⠀⡡⠖⠀⠀⣿⣿⣿⣿⡟⢠⣿⣿⢟⢉⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡟⢃⣤⣿⣤⣾⡇⣿⢀⠞⠓⡀⣀⢻⡿⣿⡿⣿⡿⣿⣿⠫⣠⣾⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠙⠻⢉⡤⠫⠀⠀⡁⢠⠀⢾⡱⣿⠿⣾⠷⣏⣵⣾⡿⢑⣴⣿⡿⠣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢸⣷⣦⡀⠀⠲⢤⣼⡂⠠⠶⠊⠁⡤⠋⣰⣽⣿⢏⣦⠄⢟⠫⠉⠨⠐⠒⠉⠉⠙⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⡿⣛⠀⢠⣄⡉⠙⢀⡐⠀⡞⣃⡴⣟⣭⣾⣿⣿⡖⠀⠀⠀⠀⠀⠀⢠⡤⢤⡾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣶⣤⡾⠛⡷⠚⣿⣗⢠⣻⣭⣾⡿⢟⣷⣤⡻⡇⠀⣀⣰⠀⡀⡴⢧⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢼⠒⢂⣴⣞⣿⠗⠀⠜⠀⣹⣩⠑⢺⣿⣿⣯⢻⣿⡿⠛⣱⠓⣦⡞⠑⣾⢃⡤⠞⢱⣼⠇
⠀⠀⠀⠀⣀⠶⠈⠉⢀⠀⠀⢙⣮⣉⢻⡏⠭⣭⡽⢡⠇⡇⣾⡿⣿⣿⣬⣭⡶⢟⡉⢀⠁⣰⠛⢋⣹⡖⠚⠛
⠀⠀⠀⠈⣥⠤⠀⠀⢀⡰⢧⣛⣿⠋⢩⢿⠄⠈⢋⣉⡸⡇⣿⠙⡋⠉⡉⢉⡶⠞⢀⡾⠋⠉⠀⠈
⠘⠶⠖⣉⠡⠂⠈⠍⠉⡓⠛⠛⠛⠻⢌⣀⡀⢰⠟⠀⠳⢡⡸⣭⣙⠒⠋⡉⣡⢔⠆
⠀⠀⠨⣀⣠⣴⠍⠀⠛⠉⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠐⠀⠁⢨⡙⠛⠚⠚⢡⠰⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠉⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣈⡀⠀⠀⣄⠈⠀⠠⠀⠐⠀⠀⠀⠄⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⡀⠀⡀⠃⠀⠱⠊⡙⠁⠀⠙⠒⡀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠃⠀⠑⠀⠐⣀⠀⢸⠂⠐⠦⠀⢲⠀⠘⠆⠀⠁⠀⠰⠂⠀⠔⠀⠂⠀⠠⠐⠀⡠
⠀⠀⠀⠤⠤⠄⠀⠀⡂⠀⣸⡁⠀⡙⠀⠙⠂⠐⠣⠀⠐⠖⠀⠢⠔⠛⠒⡂⠈⠐⠈⢁⠄⠂⠤⠒⠤⠐⠲⠚⠒⠄⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠚⠂⠄⠚⠄⠀⢵⠤⠔⠑⠀⠈⠀⠖⠛⠶⠎⠳⠶⠣⠀⠰⠀⠀⠆⠔⠓⠀⠘⠒⠐⠃⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠀⠈⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠂⠀⠀⠀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡦⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠀⢀⣀⣀⣀⡐⣋⣉⣭⡉⠁⡠⠤⣤⢤⣤⣵⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣿⣷⠘⣻⠿⠿⠏⠛⠑⠚⠃⠐⠀⠀⠀⠉⠉⣽⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡖⡎⠈⠘⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣤⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⢀⠀⣄⣷⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣿⡷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣇⢸⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣧⣿⣿⡐⠂⣀⣀⣀⣀⡠⠤⠤⠤⠄⠀⣀⡒⠒⠚⠛⠋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢷⡉⣝⣛⣀⠂⠒⠒⠋⠉⠀⠀⠀⣀⡀⠀⠀⢀⣿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣷⣌⠀⣤⣄⠰⣀⣒⣰⣌⠑⢺⡮⠵⡎⢡⠌⠋⠳⡦⣹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢌⣯⡙⣷⣌⠺⣵⢦⡙⣶⣚⡏⡤⠯⡑⢏⠺⣅⢢⣠⣤⡚⢻⠿⠷⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠂⠙⠅⠊⢻⣧⡘⢢⣷⡞⠳⠶⠛⢛⣓⣚⣄⣩⣤⡤⠀⠒⠶⠒⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⠈⠢⡀⢘⣿⣶⠶⡖⠚⠛⠋⠉⢹⡟⠶⡐⠁⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠬⠚⢦⣀⠀⢀⣨⣿⠏⢀⠉⠀⣀⣀⡤⢼⡞⡳⠃⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⣌⠂⣹⣿⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⡀⣀⠀⠀⠑⢄⠀⠈⠳⣇⡇⠄⣇⣀⠤⠤⠐⠀⠀⠀⠉⠉⠁⠀⠀⢀⣸⢲⠆
⠀⠀⠀⠀⠀⢀⡘⢦⡙⢦⡟⢶⡃⣚⠢⢢⠈⠳⣄⣹⣻⠡⠘⠁⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣲⣞⠏⣽⠒⣯⣹⣒⢦⠑⠘⠧⠀⠀⠈⠛⠏⠀⠓⠈⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠲