Sweets Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠄⠀⠂⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣲⣤
⠀⠀⠀⠰⠀⠂⠀⠀⠠⠀⡔⢤⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⢇⠀⠉⢀⡄
⠀⠀⠀⠀⢃⠀⠰⠁⠢⠔⠀⠀⠣⠴⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠠⠀⠀⠈⠉⢉⠃⠈⠢
⠀⠀⠀⠀⠀⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⡤⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⢔⠞⡟⠁⡧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠂⡜⠀⠀⢣⡈⠑⠲⣑⣄⡠⡀⢀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⣠⠃⠀⡇⠀⡁⠀⠀⠀⠑⡄⠀⠈⣦⡱⠁⡯⠷⡔⠚⡢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠂⢫⠀⠸⢆⠀⢇⠀⠱⡀⠀⠀⢀⣇⣀⡠⣗⣌⠉⠵⢄⠘⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠦⠁⡶⠗⡢⡀⡨⠬⡁⡲⢯⢁⠴⢅⡠⢄⢀⢥⡠⠵⢤⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒⠖⢱⠢⠤⠩⡇⠀⢨⠀⠀⡅⠀⠠⠀⢠⢁⠜⡚⠈⠉⠉⠉⠁⠒⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⡄⠸⡀⠰⠀⠈⡄⠀⡇⠀⡈⢀⠜⠁⠀⠀⢀⠄⡔⠓⠄⡀⠁⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠀⠀⣀⣰⣀⠗⠤⣇⠀⠇⠀⠁⠀⠃⡎⠀⠀⡀⢫⠛⠉⠀⠈⢑⠇⠂⢀⠀⢰
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠛⠁⠈⠇⠀⠁⠀⠀⢸⠀⠐⠀⠀⠘⠀⢧⢤⡠⢄⠀⠉⠒⡀⠈⠁⠀⣀⠇⠉⠎
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⣄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠱⣀⠈⠢⠒⠐⠄⠔⠑⠊⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠤⠤⠤⠄⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠠⠤⠄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡉⠉⠀⢀⣀⣀⣤⡤⠽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠋⠡⣤⢶⣛⢉⣡⣴⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠉⠉⡟⠋⠑⠨⠴⡀
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⢣⣀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠙⠒⠲⠤⣤⣀
⠀⠀⠀⡠⠖⠋⠁⠠⢔⣮⡅⠻⢼⣽⣿⣿⡶⠦⣤⣠⣇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣇⣭⣵⠦⣄⠀⠈⠙⠲⢄
⠀⠀⠈⠀⠀⢠⣴⣿⣛⣻⣥⡴⠶⠛⠛⢛⣻⣿⣷⡿⣯⣿⣓⣲⡦⢤⣼⣀⣀⠀⠀⡷⠟⠛⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠦⣀⠈⠉⠉⠙⠳⠀⠀⢠⣶⣿⣯⠭⠶⠶⢒⣻⠿⣋⣉⣽⠿⠛⠷⠿⠿⠽⠇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⠀⠉⠁⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠒⠲⠶⠶⠶⠤⠤⠶⠶⠶⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠉⠉⠀⢠⡄⠀⠀⠉⠉
⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⢇⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⣇⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠎⠀⢀
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁
⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⣀⠆
⠂⠀⢐⠘⠙⢢⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢢⠆⠀⢘⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠓⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉
⠐⠄⢄⠀⠀⠀⠀⠀⠀⡬⠔⣃⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠈⡭⠔⣂⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠆⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠊⠀⢀⠀⠄
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠊⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠄⠀⢀⠆
⠀⠀⢈⠘⠙⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢀⠄⠀⢐⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠑⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⡀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣣⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢽⡓⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡖⠒⢲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠉⢻
⠀⠀⠀⠀⠀⠀⡠⠟⢤⡀⢹⠀⡜⠀⡸⠙⢆⠀⠀⠀⠀⢠⣄⠤⠖⠢⡀⠀⠀⠀⠀⠀⠀⣧⠈⠓⢾
⠀⠀⠀⠀⠀⢠⠃⢀⣀⠱⣜⣴⣁⠔⠁⣠⠎⢧⠀⠀⠀⠈⢦⢀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡟⠓⢦⣸
⠀⠀⠀⠀⠀⠸⡎⠁⢀⡽⠋⣿⠯⣐⣉⡠⠤⢺⠀⠀⠀⠀⠀⣳⣾⣎⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠙
⠀⠀⠀⠀⠀⠀⠳⣀⠎⠀⠀⡇⢆⠀⠀⠀⣠⠃⠀⠀⠀⢠⡋⠙⠀⢨⢷⠀⠀⠀⠀⠀⠀⢠⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣧⣀⣱⠶⠚⠁⠀⠀⠀⠀⡟⠋⠠⡦⠀⣀⡇⠀⠀⠀⠀⠀⢸⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⡷⠆⢀⣄⠀⠉⡇⠀⠀⠀⠀⠀⢸⣤⡀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⣀⠐⠶⡇⠀⠀⠀⠀⠀⠸⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⢀⣀⡀⠀⠀⠀⠀⢻⣁⠀⡉⢀⣼⠁⠀⠀⠀⠀⠀⠸⠶⣄⡀⠱
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢾⣶⣖⣉⣠⡼⠀⠀⠀⠀⠈⠫⢤⣫⡴⠃⠀⠀⠀⠀⠀⠀⠀⣆⡀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⣹⠛⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠷⡄⠀⠀⠀⠀⠀⠀⠀⡇⠙⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠀⡄⠀⠙⠂⠀⠀⠀⠀⠀⢀⡇⣀⠤⠼⠀⠀⠀⠀⠀⠀⠀⢸⠦⣄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣤⠤⠼⠆

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠒⠤⢀⠀⠀⠀⠀⠀⣀⣴⣎⣩⣶⣦⡀⠀⠀⠀⠀⠀⣀⢆⠁⠀⡌⢆⠀⠀⠀⠀⠀⡠⣶⣬⣿⣷⣴⣿⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠂⠁⠀⠀⠉⠛⣿⣿⡄⠀⠀⠀⢰⠌⡁⣈⢁⠡⠄⠇⠀⠀⠀⢠⣴⣿⣿⡁⠀⢀⣹⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣟⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠈⠉⠉⠙⠓⠍⣁⠀⠠⠁⠀⠀⠀⠀⠐⠤⣄⡀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠭⠹⠿⠋⠍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠈⠢⠊⡀⠤⠈⡄⠀⠀⠀⠠⠆⠀⠉⠿⠛⠁⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⠷⣽⣿⣛⣛⣛⣫⠭⠇⠀⠀⠀⠀⠀⢄⠀⠠⢄⢁⠄⠀⠁⠀⠀⠀⢸⠓⠲⠶⠤⣤⣀⣀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠠⢀⡈⠃⠀⢃⡦⠂⠀⠀⠀⠀⠘⠉⠙⠛⠒⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠤⠐⠀⠈⠀⠀⠈⠐⠄⠀⠀⠀⠀⡼⢿⡟⠁⢹⡟⠻⣷⠀⠀⠀⠀⠀⣰⣾⣿⣛⣻⣷⣶⡀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠞⠙⢢⠈⣷
⠀⠀⠀⠀⠘⠠⠶⠀⠀⡤⠀⠀⠰⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢀⠈⠙⠛⠛⠛⠛⠉⢃⠀⠀⠀⠀⠀⠀⠘⣄⠸⣦⣐⣁⣼⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⡤⡠⢤⠀⠁⠀⠀⡠⠂⡍⠀⠀⠀⠀⠀⠀⠀⠘⡅⠠⠀⠀⠀⠀⠀⠈⡷⠆⠉⠉
⠀⠀⠀⠀⠀⠢⡀⠈⠀⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠞⠀⠀⠀⠣⡀⠐⠢⠤⢤⣀⣤⠤⠴⠎⠁⡠⠀⠀⠀⠀⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠆⠙⣿⣿⣿⣿⡿⠃⡓⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠆⠀⠀⠀⠀⠀⣀⠐⠁⠑⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣋⠌⠀⠀⠀⠀⠀⢠⣾⣻⢻⣟⣞⣻⣿⢽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣿⣿⣷⣯⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⣰⢶⠇⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠁⠉⠈⠁⠀⠀⠀⠀⠀⢣⡾⢅⡠⠷⡶⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠸⠷⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠛

⠀⣀⢀⡀
⠀⡁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡏⠘⣯⡁⠂⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠣⡀⠈⠙⠲⢤⣀⠐⡸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⢱⣤⠀⢀⠀⠹⣿⣾⠇⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠤⠐⠀⣠⠃⢈⠤⠀⣀⣈⡀⠐⢿⡇⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠒⠛⠂⠙⠱⢂⠋⠁⣡⠶⠋⠀⠈⢢⠀⠀⣩⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⠃⠀⠀⠀⠀⢨⣷⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠤⠴⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⣸⠁⢸⣄⠈⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠚⣁⣀⣠⡤⠖⠋⠁⠀⢠⡧⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢦⣶⠖⠒⠶⠒⠒⠉⠓⠀⠀⢀⡴⠞⠋⠉⠉⠁⠀⢀⣀⣤⣴⣿⣿⣛⡳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠢⢤⡀⠀⠀⠀⣠⣶⡛⠁⠀⠀⣀⣀⣤⣴⣾⠿⢟⠭⠋⡙⡉⡍⢐⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠛⠟⡛⠚⡛⠟⠻⡏⢍⠁⠀⠈⠀⣾⣶⣾⣷⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⡶⣤⣄⣠⡄⠀⣀⠀⣀⢀⣄⣀⢡⣈⣠⣇⣴⣥⣼⣿⢷⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⢸⡆⠸⡏⠉⣻⠉⢿⠉⢻⡋⢻⠛⢻⠍⢉⡇⢠⣯⢸⣿⣭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡄⣷⠀⣷⠀⢹⡀⢿⠀⣼⠀⢸⠁⣸⠀⣸⡇⣸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠰⣸⡆⢻⠂⠸⣇⢼⠣⣸⡅⢸⠆⣿⢈⣿⣹⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣿⣟⣹⣧⠀⣏⣾⡇⣿⣧⣿⢐⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣻⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡼⣿⣿⣷⣿⡟⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣷⣿⣿⣷⣿⣿⣷⣿⣏⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⠿⡏⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⠿⠿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠟⠻⠿⠻⠛⠛⠛⠛⠛⠋⠛⠉⠋⠉⠉

⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⢄⡀⡚⠑⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠠⣀⡀
⠀⣂⠳⣠⡴⢯⡁⠀⣈⠆⠀⢙⡤⠞⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠃⠴⠙⡌⠄⢉⠁⠉⢳⠆⠀⡆
⡠⠊⠀⠀⢀⠝⠻⠀⠀⠠⣀⠇⣷⢴⠈⡡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⢀⡈⣣⠀⢸⠀⢸⡄⣈⡿⢗⡔⠊
⠣⠀⠖⠣⡈⢑⣔⡌⡈⢂⢐⡶⠙⠢⠤⠃⠀⠀⣠⠄⠰⠒⣒⡲⠂⠤⢄⠀⠉⣟⡴⠈⠁⠁⠋⠁⠉⠉⠉
⠀⠀⠀⠀⠈⠁⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠂⠬⠄⣋⣉⣉⣑⡍⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠘⠀⣐⠀⠀⣀⠀⢀⣇⠜⠁⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢠⠒⡋⢂
⠀⠀⠀⢀⡀⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠔⠀⠀⠆⠈⠀⢎⡀
⠀⠀⠀⠀⡓⢄⡈⠢⠄⣀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠀⠤⠜⡀⠁
⠀⠀⠀⠀⠘⢄⡈⠀⠂⠠⠀⡴⠊⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡀⠀⠠⠖⠉⠀⠀⠉⠰⠆⠀⠀⠙⠠⠠⣠⠶⠊⣑⡢
⠀⠀⠀⠀⠀⡸⠈⠗⠒⠒⠉⠀⠀⠀⠀⠀⣀⣈⠓⢆⠀⠀⠀⠀⠁⠀⠲⠄⠀⠂⠀⠀⡸⠀⠀⠀⠀⠐⠂⠑⠂⠐⡄
⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡀⠛⠶⠄⣀⣀⠤⣄⠀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢠⠃⡘⠀⠀⠀⠀⠀⠀⠣⢄⡂⣄⣀⣀⠬⠄⣀⡀⣀⠐⠉⠂⢈⡄⠈⠁⠀⠀⢀⡠⠴⠲⠶⢤⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠴⠁⠀⠀⠀⠀⠀⠀⠑⠤⣈⡀⢀⡅⠀⠀⣇⡀⢀⡁⢀⠜⠚⠀⠀⠀⢀⠞⠁⠀⢀⣀⡀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⡟⢀⣀⠔⢁⣄⢹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⠀⠢⡀⠀⠀⠀⠀⠀⢧⡀⢸⡀⡨⠶⠚⠠⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠂⠛⢍⢂⠀⢱⡄⠀⡃⠀⠀⠀⠀⠀⠀⠑⠯⣙⣦⡤⠴⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⠈⠁⠀⠀⠑⡀⠀⢀⣦⠴⠋⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠱⡀
⠀⠀⠀⠀⠑⡒⠠⠤⠀⠑⠄⠑⠠⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⡏⠀⣈⣒⡖⠊⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠪⢈⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡿⠗⠀⠀⠀⠴⣭⠪⡵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⡴⠓⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⢘⢸⡰⠭⣵⢉⠄
⠀⠀⠀⢀⣀⣤⣤⣴⣶⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⣡⣤⣬⣄⠀⠀⠀⠀⠀⢰⣿⠁⣉⣿⠏⠀⠀⠀⠀⠀⠈⠦⣙⣙⡥⠜
⠀⠀⣴⣿⣿⣿⠿⡿⣛⣹⡄⠀⠀⠀⢸⠀⠀⠀⠀⢀⢼⠿⠿⠿⡿⠻⠤⠀⠀⠀⠀⣺⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣶⣷⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⢂⠂⢠⠀⠁⢇⠁⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠢⠤⠼⠼⠌⠀⠀⠀⠛⠿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⢀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⠬⠯⠥⡞⠉⢃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢈⠖⠀⠒⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⡈
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢢⠀⠀⠀⡼⠉⡇⠀⠀⠘⠢⠤⠤⠤⠤⠗⠋
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⠚
⠀⠀⠀⠀⠀⢹⡢⣞⣢⢯⠇⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡚⢳⣤⡀
⠀⠀⠀⠀⠀⠀⣷⢾⣉⡾⠀⠀⠀⠀⢠⠞⠡⢀⠀⠈⠀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡞⠙⣦⡴⠛⢏⣠⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠸⣞⣭⠇⠀⠀⠀⠀⠇⠨⢠⢰⣿⠿⣦⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⣠⣴⠚⢣⣠⠽⢏⢉⡷⣖⢋⣱⣶⠋⣱
⠀⠀⠀⠀⠀⠀⠀⢫⡟⠀⠀⠀⠀⠀⡇⢁⠀⢘⠦⠤⠊⠈⠀⠀⡇⠀⠀⠀⠀⠀⣾⢀⡸⢶⠋⣹⣴⠚⢻⣤⠞⢻⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢳⣆⣀⠂⠄⠂⠐⢀⣀⣾⠃⠀⠀⠀⠀⠀⠙⣯⣠⠼⢻⣁⡼⢿⡉⣹⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠷⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠚⢹⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡀⠑⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠸⠀⠘⠀⠐⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢈⢩⡙⠘⠒⠁⠀⠀⠆⠈⠀⠀⠁⠁⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠘⣄⠢⡑⠀⠀⢠⠀⠀⠀⠂⠈⠀⠀⡆⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠩⡥⠀⠀⠀⠀⠁⢈⠀⠀⠸⡀⠀⠀⠀⢣⠀⠡⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣁⣨⠀⠀⢄⢡⠀⠀⢕⢄⣇⠀⣁⠀⠄⠑⣇⠠⠀⠀⠀⢀⠂⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⢀⠔⠼⠢⠠⠀⠊⠀⢣⠀⠀⠦⢻⢀⢀⠠⠌⠦⠧⢀⠀⠀⠀⠀⠀⡠⠜⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⢲⠒⣦⣀⠀⠒⠐⣬⠡⡆⢤⡾⢠⣌⣒⣐⣒⠶⡊⠭⠩⠉⣁⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑⠒⠒⠳⠤⠤⠜⠋⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠠⠀⢀⡀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢂⠀⠁⠀⠀⠐⠀⡰⠂⠀⢀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠤⢀⡀⡑⢄⠀⠀⠈⠹⠀⠀⠀⠀⡏⠁⠀⠀⢀
⠀⡎⠀⢴⡁⠉⠉⠉⢇⣀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠈⠀⠈⠀⠀⡀⠉⡀⠀⢀⡀⠁⢠⠀⠀⣠
⠀⠈⠒⠤⠤⣀⡴⠀⠀⠀⠀⠉⠉⠉⠒⠀⠀⠰⠤⠄⠀⠀⠠⡚⠀⠀⠠⢀⠁⡀⠉⠁⢠⠀⠀⠈⠐⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠧⢄⣀⠴⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠛⠛⠛⠛⠶⣾⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⡀⠑⠀⠀⠀⠀⠀⠰⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⢈⡐⠄⠅⠀⠀⠀⢀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠐⠀⠀⠀⠀⠀⢀⠰⡉⠙⠂⠈⠗⠁⡠⠄⠀⠀⢲⠶⣤⣑⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢨⠀⠀⠀⣀⠤⣰⠁⢄⠄⠑⠄⠗⠚⠉⠀⠀⠀⠀⣸⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠠⠃⠀⠀⡜⠁⢀⢜⠧⢠⢸⠐⢊⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢆⠀⠈⠁⣠⠎⠁⠀⢀⡀⠀⠈⠀⠀⣠⡟
⠀⢠⡴⢒⠒⠶⠶⠴⠋⠁⠀⢢⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠠⡏⠈⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠹⣦⡀⠁⠉⠙⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣠⡴⠞⠋
⠀⠀⢨⡇⠀⠀⠈⠂⡑⠁⠀⠀⠀⣿⠙⠓⠲⠶⠶⠶⠚⠋⠉
⠀⠀⠈⢷⡀⠀⠀⠀⡄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠉⠛⢶⡄⢇⡘⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠀⠀⠈⠢⣄⠈⠉⠓⠲⢄⡀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠙⢦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⣀⠀⠀⠀⠀⠀⡟⠓⠢⠤⣄⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣠⠖⠒⠛⠉⠉⠉⠉⠉⠉⢹⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢚⠇⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠉⠒⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠁⠀⠈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠢⣉⠒⠲⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⡀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡤⠞⠁




⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠂⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢯⢣⠈⢻⣄⠀⣀⡠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⡀⠀⠣⡑⣄⠹⡏⠀⠀⠀⠀⠀⠀⡴⣺⣛⠻⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠁⠀⠈⠁⠀⠀⠈⠪⡵⠁⠀⠀⠀⠀⠀⠈⠘⢐⡠⡁⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣧⡀⠋⠀⠀⡤⠀⠀⠙⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠽⢑⣫⣷⠶⠮⡙⢦
⠀⠀⠀⠀⠀⠀⣀⣀⠨⣧⠈⢗⡄⠀⡀⠀⠀⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡠⡤⡀⡀⡼⡄
⠀⠀⠀⠀⠰⢍⠀⠀⠀⠈⢷⣀⠪⣒⣏⠔⠊⠀⠀⠀⠀⠀⠀⡀⠠⠠⢀⠀⠀⣄⣀⣀⠀⠓⣬⡥⠞⠋⡠
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⢀⠟⠓⠉⠀⠀⢀⠔⠈⠀⠀⠀⠈⠀⠘⠛⠖⠀⠄⠠⠄⣀⣀⣀⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢈⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⣀⡥⣐⣂⠄⠶⢦⡀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁⠀⠀⠀⠀⠀⣀⠄⠂
⠀⠀⠀⠀⠰⠚⠉⠃⠀⠀⠀⡀⢀⠀⢷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡠⠂⠀⠀⢠⠖⠭⣀
⠀⠀⠀⠀⠀⣀⠠⠼⠖⠒⠈⢁⠀⠀⢸⡆⠀⠀⠀⠑⢄⠀⠀⠀⡠⠊⠀⠀⠀⡠⠁⠀⠀⠀⠉⠒⢤
⠀⠀⠀⠀⠀⢁⠀⢀⣡⠠⠤⠘⣆⠀⠩⣦⠀⠀⠀⠀⠀⠁⠲⠊⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠈⠯⠀⠠⠖⠉⠓⠁⢀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠂⠌
⠀⠀⠀⠀⠀⢀⣀⠀⠄⠐⠀⠈⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠠⠁⡌
⠀⠀⠀⠀⠀⠀⠈⡀⢀⡀⠄⠄⠄⠂⠈⠂⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠀⠀⠠⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⡰⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⢛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠆⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⢉⡉⠛⠢⡄
⠀⠀⠀⠀⠀⣠⠔⠚⠉⠀⣀⠀⠂⢀⠀⢠⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⢰⠁⠀⠂⠀⠂⠀⠠⠄⠈⠀⠀⢀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⢡⠀⠆⠀⠀⠆⠠⠄⠀⠐⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⣼⠕⢆
⠀⠀⠀⠀⠘⡆⠀⠆⠀⠀⠀⠰⠀⢀⠤⢤⡀⠀⢺⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⢹⠀⠈⠉⠀⣸
⠀⠀⠀⠀⠀⠹⡀⠄⠀⡴⠦⣄⣀⡜⠀⠀⠱⡀⢈⠆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠡⠀⠘⠑⠶⠒⠶⠁⠑⢄
⠀⠀⠀⠀⠀⠀⢣⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠰⠀⠁⢀⠁⠐⠀⠀⡈⢈⢧
⠀⠀⠀⠀⠀⠀⠈⢦⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⣤⡶⣷⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⡤⡺⢋⠟⠀⡿⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢡⠞⢡⠎⠀⠀⣇⠙⠲⢧⣀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠋⠀⡎⠀⠀⠀⠈⠢⡀⠀⠈⠙⢾⡳⣖⢒⡄⡠⣤⠀⠀⠀⣀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢣⣤⡟⠀⡷⠘⠳⣖⠋⢉⡦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠤⠔⠒⡏⠀⠈⣷⡀⠀⢰⠀⠀⠱⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡗⣄⠑⠚⣳⣄⣀⠨⢷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⣹⣄⣸⠀⠙⠲⠆⠷⢄⣀⡸⠦⣄⡀⠤⠞⠛⠒⠋⠁⢹⠈⠻⣅⠀⠈⠳⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠕⠒⠂⢸⠓⠒⠬⣑⣄⡔⠉⠳⣄⠖⠉⠢⣠⠞⠑⢦⠞⠑⢆⡤⠺⠶⡒⠚⣳⣎⣴⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⢒⡞⠉⡟⠲⢦⠤⠬⡇⠀⠀⢤⠀⠀⠠⠄⠀⠀⡶⠀⠀⡜⢀⠴⠒⠉⠉⡄⠠⠀⠀⠈⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢹⠀⠈⡆⠀⢱⠀⠀⢸⠀⠀⠀⡀⠀⠀⡇⠀⢠⠟⠁⠤⠈⠀⠀⣀⠀⡰⢦⡀⠀⠀⠂⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢇⠀⢹⡀⠀⢇⠀⠀⡇⠀⠀⡇⠀⢰⠃⢰⠃⠀⠂⠐⢠⠤⣼⠭⠙⠶⠤⢭⣙⠄⠈⠠⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣀⡇⣀⢀⣀⠠⢬⣦⠞⠉⠒⢾⡄⠀⢡⠀⠀⡇⠀⢸⢀⠇⠠⠄⠒⣀⠀⢾⡁⠀⠀⠀⠀⣀⠜⠀⠁⢀⣀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠘⠏⠀⠈⠱⡄⠀⠉⠀⠀⠀⠈⡷⠀⠸⠀⠀⠇⠀⠇⠘⢇⡤⡄⣠⣄⠐⠠⠉⠻⠒⠙⡉⠡⠀⠃⢀⡜⠀⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⠋⠉⠀⠀⠀⠈⠉⠉⠉⠉⠣⡈⠁⠈⢆⢀⡠⠤⡀⠁⣠⠤⢄⠼⠉⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⢀⡠⠚⠢⠤⠄⠠⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠁⠀⠀⠈⠛⠁⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⠤⠤⠤⠒⠊⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡀⠀⠄⢀⣀⣀⢀⡈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⢀⡠⠄⠠⡀⠀⠀⠀⠈⠃⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⠉⠀⠀⠀⠈⢢⠀⠀⢠⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣁⠈⠂⠊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⠣⡀⠀⠀⡠⠂⠐⠒⠀⠐⠁⠀⠀⠀⠃⠀⠀⠤⡀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡄⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⣀⠤⠤⣀⠀⣀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠣⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⠀⠀⠑⡀⠀⠈⢆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣎⢄⡀⠀⠀⠣⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣀⣰⠀⢀⡠⠜⠒⠒⠈⠁
⠀⠀⠀⠀⢀⠔⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠁⠀⠀⠀⡃⠈⡆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢰⠂⠐⠒⠚⠢⠔⠊⠁⢱⠀⠀⡎⠀⠈⢆⠀⠀⠀⡠⠠⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢃⠀⠀⠀⠑⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠁
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠘⣄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠒⠀⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠒⠒⠒⠒⠒⠂⠒⠒⠒⠀⠒⠒⠀⠒⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠤⠄⠠⠄⠀⠒⠒⠒⠀⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠢⠄⠔⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠶⣚⠀⠀⠀⠀⢀⢠⠀⠀⠳⠤⠤⡴⠂⠀⠀⠀⠀⣠⠀⠀⠀⡔⠹⡀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠈⠱⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡴⠋⢄⣠⠎⢀⠀⠉⢩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠜⠀⠀⠀⠐⣀⠀⠀⡸⠄⠠⢄⠀⡜⠀⠀⠀⠀⠀⠐⠀⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠤⣀⣔⠉⠉⣶⡁⠀⠀⠀⣿⠊⠉⢦⠀⠀⠀⡠⠔⠒⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠒⠚⠀⠑⠲⠐⠊⠈⠲⠰⠋⠢⣄⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⣀⠔⠊⠀⠈⠳⣄⣀⠴⠋⠀⠈⠣⡀⢀⠤⢤⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢉⣁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⡄⠀⠈⠁⠀⠀⠈⠑⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⡄⠀⠀⠀⢠⡄⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠃⠀⠀⠀⠰⠀⠀⠰⠆⠀⠀⠀⣄⠀⠀⠀⠀⠖⠀⠀⠀⣀⠀⡇
⠀⠀⠀⠀⠀⡤⠴⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠉⠀⠀⣀⣀⣀⣀⣀⣀⣉⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠉⠛⠿⢿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⡷⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣶⣶⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣤⣶⣶⣷⣿⣿⣶⣄
⠀⠀⠀⠈⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⣀⡸⠀⠀⠀⠀⠀⠀⠀⢎⡀⡱⠀⢀⣄
⠀⠀⠀⠀⠀⠀⡃⠈⡄⠀⠖⠲⠀⠀⢀⠴⡄⠀⠀⢠⠀⠄⠀⡌⠀⡂
⠀⠀⠀⠀⠀⠀⡭⢭⠀⠀⠀⢸⠀⠀⠨⣀⠸⠀⠀⠐⠀⠀⠀⢨⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢰⠀⢦⠀⠀⠸⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠊⠉⠑⢄
⠀⠀⠀⠀⠀⢀⡄⠠⠒⠒⠀⢸⠉⠉⢹⠀⢘⠉⠉⠙⠀⠒⠂⢆⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⠀⠸⠀⠀⠈⠉⠁⠀⢐⠀⡇⠈⠢⡀⠀⠀⢀⣤⣤⣒⡀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠷⢀⠀⠐⠚⠀⠀⠀⠀⠀⠀⢸⠀⣨⠀⠀⠀⠀⠀⠀⠘⠒⠃⢀⠴⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠒⠂⠀⠐⠒⠒⠂⡞⠅
⠀⠀⠀⡂⠀⠁⠒⠀⠤⠤⠀⣀⣀⣀⣈⣉⣁⣀⣀⣀⡀⠠⠤⠄⠐⠊⠁⠀⡇⠀⠀⠰⠆⠀⠀⠀⠤⠤⠄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡆
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠐⠒⡏⠄
⠀⠀⠀⣉⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢈⠀⠀⠀⢐⠒⠂⠀⠠⠤⠤⠤⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆
⠀⠀⠀⠈⠉⠒⠠⠤⢀⣈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠈⢉⣀⠠⠤⠒⠈⠨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠉⠁⡏
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠠⠤⠄⠄⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠆
⠀⠀⠀⠈⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠒⠒⠂⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠒⠒⠒⠒⠒⠒⠂⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣄⠤⢀⡤⠠⢄⡠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⡠⠔⢒⡠⠶⠺⣦⠴⠦⣴⠳⠶⢄⠀⠩⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⠊⡠⠊⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠑⣄⠈⠢⡱⡀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⡀
⠀⠀⠀⢠⠃⡔⠁⠀⢀⠃⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠈⠆⠀⠑⡘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⢀⠆⡜⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠐⡈⠆⠀⠀⠰⡁⠑⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢁⠇
⠀⠀⠎⡜⠀⠀⠀⢠⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠐⡈⠄⠀⠀⠋⢲⡐⠢⠤⠬⣉⣉⠈⠉⠀⠁⣉⣀⣀⡉⣁⠠⠀⢐⡴⠙⠆
⠀⠈⡶⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡀⠀⠀⠰⡆⠀⠀⠁⠦⠌⣁⠐⠂⠀⠄⠀⠠⠨⠤⠀⠀⠠⠀⠀⠒⣈⣁⣰⠋
⠀⢰⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢁⠀⠀⠀⠈⠒⠤⡉⢈⡁⠀⠐⠒⠀⠀⠀⠈⠉⢉⣀⣁⠤⠒⠁
⠀⠈⠒⠀⠄⠀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠰⠂⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠂⠉⠂⠤⢀⣀⠠⠔⠊⠁⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⢶⣒⡒⠶⣤⡴⠒⠒⠒⢦⡤⠖⠒⢒⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢀⣠⠤⠴⠶⠤⣬⣙⣢⡱⡄⢀⣰⡋⢀⣴⣋⣭⣤⠤⠤⣤⣉⡛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣠⠖⠉⠀⠀⣠⠖⠉⠁⠀⠉⢹⠟⠉⠀⠉⠛⢏⠀⠀⠈⠙⠦⣄⠀⠉⠳⢌⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⠞⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠳⡌⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠋⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⣆⠘⣆
⠀⠀⠀⠀⠀⢠⠏⠀⡴⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢧⠈⢧
⠀⠀⠀⠀⢀⡏⠀⡼⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⢧⠈⢣⡀
⠀⠀⠀⠀⡞⠀⡼⠁⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢧⠈⢧
⠀⠀⠀⡼⠀⡼⠁⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⢧⠈⢧
⠀⠀⠰⡇⣸⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⢧⢸⠆
⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠘⣏
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠙⠲⠶⠶⠶⠶⠒⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⠲⠖⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⢀⣀⣀⡤⠼⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠦⣄⣀⣀⠀⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠓⠶⠦⠤⠤⠴⠖⠚⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣼⠏⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⣠⣴⠾⠋⠀⠀⠀⢀⣿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⢀⣴⡿⠉⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⢀⣴⠟⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⡀⠀⣰⡿⠁⠀⠀⢀⣀⣀⡀⠀⣴⠟⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⣀⣤⣾⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠈⢻⣶⣿⣤⣴⠶⠟⠛⢻⡏⠻⢿⣯⣀⣀⣤⣴⠾⠛⢻⣿⠛⠷⢶⣶⡟⠋⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡟⠉⠁⠀⠀⠀⢸⡏⠀⠀⠀⣿⠁⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡿⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢿⡄⠀⠀⠀⠘⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠘⣷⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢹⣧⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⣼⡇⠀⢸⡏⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⢿⡆⠀⠀⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣦⣾⣧⣤⣤⣿⣄⣀⣀⣀⣴⣿⣤⣴⣿⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣶⡶⢶⠶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⣶⣶⣶⢶⣶⠶⣶

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠐⠀⠐⠆⠀⠀⠀⢐⠁⠀⠈⣡⠕⠀⠀⠀⠸⢏⣙⡆⠀⠀⠀⠀⠀⢠⡆⠤⠀⠀⢤⠀⠀⠀⢀⡠⠜⠿⢦
⠀⠀⣈⠙⠓⣾⣛⣷⠀⢰⣿⡿⢿⣂⣸⡄⠀⠀⡀⠀⠀⠀⣸⣄⠀⠀⠠⣷⣦⣽⣷⢆⣰⡆⠀⠀⠀⣾⡟⠒⠚⠈⢰
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠰⢸⢸⣿⢯⡇⠀⠃⠀⠀⠹⠿⠀⠀⠻⠆⢄⡤⠀⢸⡷⣦⡄⠀⣼
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠊⠁⠀⠐⠀⠀⢀⣀⡀⠀⢠⣤⣤⡤⠀⢸⣄⣈⡁⠀⣈
⠀⠀⠀⠀⢀⢀⠀⠤⢀⡢⠀⠀⠀⢠⣾⣛⣛⡿⠞⠀⠀⠀⠀⠀⠀⠀⠤⡅⠈⠧⠺⠖⠶⠶⠶⠖⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢸⣿⣟⡶⣶⢤⣌⡀⠀⠀⠐⠀⠤⢍⣙⣷⠀⠀⠠⠔⠀⠀⣤⣶⣢⠀⠀⠀⠀⠀⢀⣚⣁⠚⠻⢶⢂⣰⠄
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⡟⠀⠀⠯⣉⡓⠢⢤⣙⠀⠀⠁⠀⠀⠀⡠⣾⡏⠀⠀⠀⣄⡀⣉⣉⠉⢀⢠⠼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠈⠑⠺⠗⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠙⠂⠐
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⡶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉⠁⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣇⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢠⣴⣾⠏⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠙⠿⣷⣤⣤⣤⣀⣿⠃⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⣾⡏⠀⠈⣿⡿⠿⢶⡾⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣿⣿⣦⡙⢷⣶⠾⣿⣄⠀⣸⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠀⠀⠀⠙⢿⡇⠀⢈⣿⠛⠋⠀⠈⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢁⣴⢿⣇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢡⡿⠃⠘⣿⠀⠀⣠⣶⠿⠛⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢠⡿⠁⠀⢸⡟⠀⣼⡟⠁⣀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣿⠃⠀⠀⣾⠁⣸⡟⠀⠀⡏⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣾⠏⠀⠀⣼⠃⠀⣿⠃⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣄⠀⠀⠀⢰⡿⠛⢻⣆⠀⠀⠀⣴⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠁⠀⠀⢰⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠆⠀⠉⠉⢻⣏⠀⠀⠀⢸⣧⠀⠈⣿⠀⠀⠀⣿⠁⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⡟⠀⠀⣼⡇⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠈⠿⣧⡀⠀⢸⣿⠀⠀⢹⡆⠀⠀⣿⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠃⢰⡇⠀⢸⠃⠀⠀⣿⠇⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⣿⠀⠀⠘⣷⠀⠀⣿⡆⢰⠈⣿⣧⣄⡀
⠀⠀⠀⣠⣶⠿⠋⠁⣾⣿⠀⠈⠁⠀⣿⡄⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢸⣿⠀⠀⠀⠹⣧⠀⢹⣧⠀⠀⣿⡯⠉⠻⣶⣄
⠀⢀⣾⡿⠃⠀⠀⠀⣿⣿⠀⠀⠀⡀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⠀⢸⡆⠀⢻⡄⠈⢿⣦⣸⣿⡇⠀⠀⠈⢻⣧⡀
⠀⢸⣿⡇⠀⠀⠀⠀⢻⣿⣷⣄⡀⠃⠀⠀⠀⠀⠀⡄⠀⠀⣦⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⢹⡇⠀⢻⣆⠀⠃⠀⠈⣷⣤⣴⣿⣿⠟⠀⠀⠀⠀⢈⣿⡇
⠀⠘⣿⣿⡄⠀⠀⠀⠀⠉⠛⠿⠿⣿⣶⣶⣤⣤⣼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣧⣄⣨⣿⣤⣤⣶⣶⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠛⠛⠛⠉⠉⣼⡟⠁⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⣤⠀⠀⠀⠀⠻⢿⣦⣤⣤⣴⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣯⣤⣤⣴⣶⣾⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣛⣛⣛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣟⣉⣉⣙⣛⣻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡤⣤⣤⣤⢤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣌⣡⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⠿⣿⣿⠿⣛⣛⠿⣿⣿⠿⣛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣝⡛⢿⡿⣛⣫⣝⣛⢿⡿⢛⣫⣝⣛⢿⡿⢛⣋⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣝⠻⢟⣭⣭⣭⣍⡻⢟⣩⣭⣭⣍⡻⠟⣫⣭⣭⣭⡻⠟⣫⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⣽⠇
⠀⠀⠀⠀⠀⠀⡙⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢲⡤⠤⢄
⠀⠀⠀⠀⠺⢿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡴⠋⠀⠀⡜⠁⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠎⠀⠀⡠⠊⠀⠀⡠⠛⢤
⠀⠀⠀⠀⠀⡠⠒⠒⠛⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠃⠀⢠⠎⠀⢀⠔⠊⠀⠀⣸
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⢀⠔⠁⡠⠒⠁⠀⠀⣀⠜⡱
⠀⠀⠀⠀⠆⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⢃⠄⠁⠀⠀⢀⠄⢊⠴⠊
⠀⠀⠀⠀⠠⢿⠀⡿⢿⣷⣿⠀⣠⣀⣄⢀⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⡄⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠒⠁⠉⠹⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣤⡀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣭⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣄⢀⣴⡆⢀⣤⣤⣶⠀⣴⣤⡆⢀⣤⣀⣤⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣷⣾⣿⣿⣿⣼⣿⣿⣧⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⡠⠀⠤⠀⠈⠢⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠃⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⡘⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠈⠀⠋⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⣄⠀⠠⡀⠄⠀⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁⠁
⠀⠀⠀⠀⢀⠀⠄⠂⠀⠂⠠⢄⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡦⢶⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⣀⠀⠦⡀⠀⢀⢼⠦⣀⠀⡎⠯⢠⠀⠀⠀⢴⣿⣿⣜⣥⣷⣳⣽⣯⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠐
⠀⠀⠈⠙⠒⠂⢴⣡⢾⠷⣄⣱⠒⠊⠁⠀⠀⠀⠀⠈⠁⠘⠉⠁⠙⠈⠁
⠀⠀⠀⠀⠀⠀⠸⠁⠘⠳⡄⢹⠀⠀⢀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠠⡀⠀⠤⠤⠄⠠⠀⠄⠐⠆
⠀⠀⠀⠑⠢⠀⢰⠎⠀⠀⠀⠙⠤⠊⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⣀⣀⠤⠞⠋⠀⠀⠀⠀⢀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠤⢤⡀⠁
⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣚⣿⣿⠟⠂⠀⠀⠀⠀⠀⠈⠁⠈⠈⠑⠒
⠀⠀⢄⡀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠍⠀⠀⠂⠀⠀⠀⠀⠐⠶⠤⠤⠠⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠐⢈⣀⡤⠊⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠠⠄⠤⠒⠀⠚⠀⠀⠀⡀⢀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠠⠄⠙⢋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣟⣻⡽⣿⣻⣛⡀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠄⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠠⢠⡄⠀⢐⠀⢀⡀⠀⢸
⠀⠀⠀⠠⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢨⡇⠀⠀⠀⠈⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠅⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣝⣻⣦⡀⢠⣿⣿⣿⣿⣿⣧⠀⣠⣞⣿⣫⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣽⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡵⠶⢶⣦⣤⠤⠿⠿⢿⣟⠗⠿⠿⠿⠿⠟⠋⠚⠛⠛⠻⠛⠛⢟⣯⣧⣤⣤⣖⣲⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡉⠻⠗⠻⣿⣷⡦⠶⣼⣿⣿⣿⣿⣻⣿⣿⣿⡶⣶⣦⣘⠈⡿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣦⣤⣤⣒⠈⣷⠀⣀⠤⠛⡻⠛⠓⠋⠁⠀⠈⠉⢻⣿⣿⣿⣦⣌⣻⣿⣿⣿⡿
⠀⠀⠀⠀⣀⣀⣠⣶⣶⣶⢸⣶⠶⣮⣭⣛⠿⠿⠶⠶⠾⠷⠦⠤⣀⣀⣀⣠⣾⣥⣭⣉⣉⣋⠁⢦⣝⡻⣿⣿⣶⣶⣦⣀⣀⡀
⠀⠀⠀⠀⠙⢏⣿⣿⣿⣿⣇⣿⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠆⠤⠤⠤⠤⣴⡶⠶⠶⠮⢭⣛⣛⣛⣛⣻⣌⣿⣿⣿⣿⣗⠟⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⠀⠀⠲⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠉⠙⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡿⣷⠀⠀⠀⠀⣀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠈⠁⠀⠀⠀⡀⠀⢿⣿⣿⣿⡁
⠀⠀⠀⠀⢀⣤⢾⣧⣿⢿⣧⢿⡆⣶⣦⣄⣁⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀⠠⠄⠀⠈⠁⢠⣸⣿⢿⣳⣽⣦⣄
⠀⠀⠰⢶⣽⣿⢿⣿⣿⣷⡏⢸⠋⠻⣿⣿⣛⣫⣷⣶⣶⣦⣄⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣵⣿⣿⣿⣿⣟⣷⠶
⠀⠀⠀⠀⠀⠈⠙⠚⠿⣿⠀⣿⠀⠀⠄⠀⠀⠀⠉⠉⠀⠀⠀⠈⠙⠛⠾⣝⠿⠭⠿⢽⣿⣿⣿⣿⣿⠀⢸⣽⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⡀⡏⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠙⠛⠛⠟⠀⢸⣿⣮⣆
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣿⠀⠰⢬⣓⠲⠬⠭⢼⠀⠀⠀⠀⠀⠀⠣⠄⡀⠘⣯⠀⠀⠘⠃⠀⢀⠀⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⣤⠻⠿⣟⡲⢬⣉⣙⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡸⡆⠃⠀⣀⠀⠈⠀⠘⠛⠛⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠉⠛⠓⠦⣍⠲⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣷⠀⠀⠉⠀⠀⠀⢠⠲⠦⣄⠀⠙⠳⢆
⠀⠀⠀⡀⠀⢀⠀⠐⠂⠈⠀⡐⠀⠲⢤⠀⠐⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢴⣶⣖⠐⢲⣾⠂⠀⠈⠑⢄⠀⠀⢳
⠀⠀⠀⢷⡀⠈⢆⠀⠀⠀⠀⢻⠀⠈⠑⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠈⠂⠹⣿⠛⠋⠒⠒⠿⠀⠀⠀⠘⠀⠀⢸
⠀⠀⠀⠘⢿⣶⣤⣙⠶⣤⣀⠘⠳⠶⣤⡀⠀⠀⠀⠀⠀⠢⠔⠀⠒⠢⠔⠁⠀⣀⣠⠄⠋⠁⠠⣞⡢⠀⠒⠃⠀⣀⠄⠀⣀⠄⠈
⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣿⣿⣷⣶⣤⣬⣻⣶⡶⠒⠛⠳⠶⠶⠒⠛⠲⠶⠂⠀⠀⠀⠀⠀⣀⣀⣀⡤⠴⣖⣫⡥⣖⡫⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢟⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠛⠛⠛⠛⠋⠛⠛⢒⡛⠋⠟⠒⠋⠁

⠀⠀⠀⠀⢫⠐⠂⠤⠄⣀
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⡩⠒⠂⠠⢀
⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠈⢆⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣲⠄⠤⠄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠦⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⣀⠠⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠁⠃⠂⠤⠄⣀⠀⠀⠀⡠⢋⠤⢰⠖⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠉⢸⠁⢀⠔⠁⠀⠀⠀⠀⠀⡜⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠠⠠⢀⢘⡔⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠴⢮⠀⠀⠘⠒⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠤⢄
⠀⠀⠀⢠⠤⠤⠔⠁⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀
⠀⠀⠪⣀⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠉⠲⣄⠀⠀⢀⡀⠤⠀⠒⠈⠉
⠀⠀⠀⠀⢈⣦⡤⢤⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⡠⠔⠂⠉⠉⠀⠀⠀⠀⠙⢦⢀⡀⠀⢀⡠⠖⠁
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠪⠤⠄⣀⠀⠀⠀⠀⠀⠀⢀⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⡌
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢰⠁
⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⢃⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⡿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠠⠄⣀⣠⡴⠶⢞⡛⠋⠉⠁⠐⠚⣛⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⣿⠁⠒⠺⠥⡴⢒⠛⠉⣉⣭⣭⣽⣿⣿⣫⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⢻⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢽⠛⣿⡿⢭⣄⣓⠀⠌⠳⣍⠉⠙⠒⠲⠤⢤⣀
⠀⠀⢀⣤⠶⠋⠉⠀⠀⢀⣠⢴⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠇⠀⠀⠉⠀⢸⡇⠀⠀⠈⠉⠛⠒⠾⠷⣦⠀⠀⠀⠀⠀⠉⠑⠢⢤⡀
⢀⣾⠟⠁⠀⠀⠀⣠⡖⠋⠁⢸⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣤⡀
⣿⡏⠀⠀⠀⠀⣼⣟⠀⠀⠠⠊⠉⠙⠛⠛⠿⠷⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⠢⡀⠀⠈⢦⠀⠀⠀⠈⢳
⢻⣷⡀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸
⠈⠻⣿⣦⡀⠀⠀⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⣶⣶⣤⣤⣄⣸⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⣠⡿
⠀⠀⠈⠻⢿⣷⣦⣄⣀⠀⠈⠉⠛⠳⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣛⣻⣤⠴⠶⠛⠉⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠛⠯⣿⣷⠦⢤⣤⣀⣀⡀⠈⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⠋⠉⠉⠀⠀⣀⣀⣤⠴⣶⣿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠫⠭⠭⢝⣛⣓⣒⣲⡶⠶⠦⠤⠤⠤⢤⡤⠤⠤⡤⢶⡶⢒⣒⣾⣛⠯⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠘

⠀⠀⠀⢠⣴⣾⣿⣶⣼⣿⣿⡀⠀⣬⣤⢼⠿⠸⠟⣠⣤⠄⠀⠀⠀⠠
⢰⣷⣦⣿⣿⣿⣿⣿⠇⠙⠛⠃⠀⢝⠋⠿⠻⠷⢀⡉⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣄⡀
⠘⣿⡿⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠠⢸⣷⣤⣤⠻⣋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠟⠁⠈⠙⠿

⠀⠀⢀⢀⣠⠤
⠀⠀⠈⡃⢉⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠉⡄⡘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠛
⠀⣿⠋⠉⠀⠈⢀⡤⠶⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⣴⡆⣀⡀
⠀⠻⣦⣀⢀⠼⣿⣁⠀⠀⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⢤⠉⠁⠼⠳⣆⠘⠛⢿⣿⣿⣷⢀
⠀⠀⠈⠉⠁⠀⠙⠿⢿⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠠⣦⣀⠶⠂⠘⢻⡆⠀⠈⠙⠛⢻⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣧⡤⢤⡤⣤⡷⠀⠀⠀⠀⠀⠀⠀⢠⠟⠲⠤⠬⡇⠀⠀⠀⠀⠀⠀⣠⠼⠁⠀⠀⠈⠦⣄⠀⠀⠀⠀⠀⠀⡟⠲⠊⠙⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢦⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⣇⢀⣀⠀⢀⣀⠀⣸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⢛⡏⠀⠀⠀⠀⠀⠀⠈⢻⡀⡍⢩⠄⡏⠁⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣇⡖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣄⣠⢧⡀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠉⠱⡖⠁⠀⠀⠀⠀⠀⠀⢀⡤⠧⠾⢤
⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⡞⠛⠒⠛⠛⠛⠋⣻⠀⠀⠀⠀⠀⠰⣧⣠⢄⣤⣤⡷⠀⠀⠀⠀⠀⠀⠀⣸⠖⠦⠔⠺⡇
⠀⠀⠀⠀⠀⠘⠲⣍⣙⣚⣉⣙⣒⣋⡹⠚⠁⠀⠀⠀⡿⠿⠿⠿⠿⠝⠛⢿⠀⠀⠀⠀⠀⠀⠘⢦⣶⣤⡞⠀⠀⠀⠀⠀⠀⠐⢾⣛⣒⠒⠒⣓⣛⡶
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠙⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⡎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡗⢯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⡔⣩⠥⠬⣝⢦⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣯⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠎⣡⠤⣍⠓⣄⠀⢳⠀⠀⠀⠀⠀⢸⢸⠁⡏⠵⣸⢀⡇⠀⠀⠀⠀⠀⢸⡁⢀⡀⢀⡀⢀⣧⠀⠀⠀⠀⠀⠀⣿⣿⣼⣧⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⡁⣄⠈⡇⢸⡆⣸⠀⠀⠀⠀⠀⠈⢮⡳⢬⣯⡵⠾⠃⠀⠀⠀⠀⠀⣿⠙⣯⢹⡏⢹⡇⣹⠂⠀⠀⠀⠀⠀⣿⣿⣯⣍⣉⣽⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡳⣌⣙⣁⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢿⢸⡇⣼⢠⡏⠀⠀⠀⠀⠀⠐⡏⠉⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠓⠛⠛⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠠⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⢮⡹⣆⠀⠀⠀⠀⠀⠀⠀⢧⢠⡤⣸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠸⠁⠀⢀⠁⠀⢳⠀⠀⠀⠀⠀⠀⣰⢻⡄⢳⠀⡟⠋⠀⠀⠀⠀⠀⢰⡋⠚⠁⠀⠙⢋⣷⠀⠀⠀⠀⢰⢏⠀⢧⠀⠀⡼⠁⡹⡆
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠃⢀⡏⠀⠀⠀⠀⠰⣎⠳⣀⢣⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠰⡏⠀⠀⠀⠀⠀⠸⣄⢹⡚⠓⠚⢑⡟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⡖⠛⠋⠀⠀⠀⠀⠀⠀⠘⠲⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⠲⣄⠙⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠏⢷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡇⠀⠀⡇⠀⠀⠀⠳⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⡋⠩⠍⢸⣇⠀⠀⢇⠀⠀⢀⣶⣂⡀⠉⢉⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠊⢁⣀⡤⠒⠊⠉⠨⠖⠈⠁⠲⣎⠉⠀⠐⠠⣄⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⢙⠋⠀⣠⠎⠒⢲⡗⢠⠖⠐⢦⡜⠀⢀⡀⣠⢀⠑⠀⡆⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡎⢀⡼⠕⠀⠀⣾⠇⡼⠖⠀⠀⢿⡄⢺⡀⠉⠀⢩⠆⠹⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡞⠁⢸⡀⠀⠀⠠⡏⠀⠀⠀⠀⠀⢈⡇⠸⡧⠄⠀⠈⠾⡀⠿⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠃⡤⠞⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⢦⣇⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠻⡬⠃⠀⠀⠀⠀⢰⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠃⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣏⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⣼⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠂⠀⠠⠷⣦⢤⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡃⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣄⣀⡀⠀⠀⠹⠶⣶⣤⣄⣀⢀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⣀⣀⣀⡠⠞⠚⠉⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠈⠙⠉⠉⠓⠶⠶⣶⡶⠶⠶⠛⠋⠉⠙⠋⠉⢁⣤⠶⠶⠚⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠒⠉⠉⠙⢾⡀⠀⠀⣀⣀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠓⠶⠤⠉⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⠏⢠⡿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡎⢀⣾⠃⣶⠀⡆⣠⠖⢸⡇⢠⡖⢰⣿⢰⡆⣴⢀⢰⡆⣠⡖⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⣿⠀⡇⣿⠀⣾⡇⣾⠃⣼⡇⢸⡇⢿⡏⢸⡇⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠙⠛⠁⠙⠋⠸⠇⠘⠛⠙⠇⠘⠇⠘⠁⠘⠃⠙⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠁⠀⠈⠁⠁⠀⠀⠂⠀⠀⠁⠈⠀⠀⠀⠁⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⡃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⠀⠀⠀⣄⡀⠀⠀⠀⠀⢆⠀⢸⣿⣸⠄⠀⠦⢴⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠉⠛⣦⡀⠀⠋⠑⠲⢤⣾⣆⢘⠆⠉⠀⠀⣀⠀⠀⢸⣤⣼⣷⣠⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢦⠀⠀⠹⣤⡀⢄⠉⣙⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠹⢤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠡⢷⣦⡂⠀⠀⠈⢷⣄⠙⠩⠁⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠙⢿⣦⣄⠀⠀⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⣗⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠙⢿⣶⡄⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⡘⢉⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠉⠿⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⠉⠀⣀⡡⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⠿⠟⢋⣉⣽⠟⠉⢀⣾⣿⣿⣤⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣀⢀⠀⠠⠤⠤⠀⠀⠐⠂⠉⠀⠈⠀⣀⣩⠿⠟⢁⣠⡴⢛⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢨⣯⣉⣀⣀⣀⣀⡀⠤⠤⠤⠀⣀⣠⣄⣶⣾⣶⠶⠊⣙⣿⡿⠾⡿⣩⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⠉⠀⢀⣀⣤⣤⣶⡾⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠀⣀⣤⣾⣿⡿⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢦⣤⣶⣿⣿⣿⣿⡿⠿⠦⣄⣀⠀⣀⣀⣤⠤⠶⠶⠾⢿⡉⣹⣿⣿⣾⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠠⠄⢨⠅⢤⡄⠀⣤⣤⡤⠄⣤⣥⠁⣠⣄⡀⣠⣀⣀⣄⣀⢙⣿⣯⣴⠷⣶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡀⠈⡀⠀⠸⠁⠀⠀⢹⠁⠀⢸⡇⠀⢸⡇⠀⢸⡇⢸⡿⢠⡿⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⡇⠀⠀⡆⠀⠀⢸⠁⠀⢸⡇⠀⢸⠇⠀⢸⡇⢸⠃⠘⠃⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⡇⠀⠀⢸⠀⠀⠠⡇⠀⢸⡆⠀⢸⡇⢸⠇⣾⠀⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⠀⠀⢹⠀⠀⢸⠀⠀⠀⡇⠀⢸⠂⠀⢸⡇⢸⡇⣿⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⢸⠇⠀⢸⡇⢸⠃⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠘⠇⠀⠀⠁⠀⠸⠀⠀⢸⡇⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⠇⠨⠠⢇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠠⠤⠶⠒⠒⠒⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⠶⠶⠶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠁⠀⠈⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣀⡤⠖⠒⠚⠒⠲⠦⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠘⣆⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠈⢧⠀⠀⠀⠀⢸⡄⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡟⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⡆⠀⠀⠈⡇⠀⠀⠀⠀⣇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⢿⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⡿⠀⠀⠀⡿⠀⠀⠀⠀⡟⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⢠⡇⠀⠀⠀⢠⡇⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠈⠛⠲⠦⠤⠤⠶⠚⠁⠀⠀⢀⡞⠀⠀⠀⠀⣼⠁⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⣰⠃⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⣤⣤⠤⠴⠖⠛⠁⠀⠀⠀⠀⢀⡴⠃⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢉⣠⣴⡾⠋⠀⠀⠀⠀⡠⠐⠂⠀⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣦⣤⣴⣶⣶⣶⣯⣭⣴⣶⡿⠛⣿⡅⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠐⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠹⣧⠀⠘⣿⡀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠹⣷⢀⠎⠀⠀⠀⠀⠀⡠⠊⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠉⠁⠒⠢⠤⣀⢻⣆⠀⢹⣯⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣟⠒⠊⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠤⠤⠤⠐⠒⠊⠉⠀⠀⠈⣆⠀⢀⣽⣤⢀⡀⠈⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⣿⡀⠈⣿⡄⠀⠈⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠹⣷⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣠⠔⠃⠀⠀⠀⠀⢹⣧⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⣿⣿⣿⣧⣤⣶⣶⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⡔⠫⢽⡻⢴⣶⣶⣦⣌⣉⣩⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⡀⢲⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠒⠁⠀⠈⠀⣈⡹⢟⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣾⣄⡎⠙⡿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠿⠿⠶⣯⣄⣀⣺⣃⡠⠔⠊⠉⡤⠋⣩⠽⠛⠋⣉⡣⠀⠀⡨⠿⣿⣿⣿⣿⣾⠤⠼⣿⣿⣿⣿⣇
⠀⢀⣤⣤⣴⣶⣶⣿⣿⣧⢹⣿⠿⢶⣶⣮⣝⣛⠻⠿⠷⠾⠟⠛⠿⠷⣶⣶⣶⣤⣴⣶⣾⣶⣬⣥⣤⣴⣉⣀⣀⣣⣎⣙⠻⣿⣿⣿⣿⣶⣶⣦⣤⣤⡀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡼⣿⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⢿⣷⣶⣶⣶⣦⣤⣶⣶⣶⣶⣦⣬⣍⣛⣛⠻⠿⢟⣋⣥⠹⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⢉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠛⠛⣟⣳⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⢰⠄⠀⠈⠁⠀⠀⠀⢹⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠸⣿⠀⠀⠀⠀⠀⢤⠀⠀⠀⠛⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⣿⣿⣿⣿⣷⣄⡀
⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡇⢿⣷⢸⣿⣶⣤⣄⣀⣀⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠠⡤⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⢻⣿⡏⠀⢉⡉⠉⠉⣙⡿⠿⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⢸⣿⠃⠀⠈⠁⠠⠪⣥⣀⣙⡛⢓⡶⠖⠀⠀⠀⠀⠀⠉⠻⣿⡛⠛⠉⠛⠿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢾⣿⠈⠋⠀⣀⡐⠶⠤⣤⣌⢱⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣦⡄⠀⠀⠀⣉⠉⠙⠛⠁⠸⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⢸⣿⡄⠐⠾⢦⣍⡛⠒⠲⠶⣸⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⠀⠹⣆⠀⠀⠀⠉⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣠⠴⠛⠉⠁⠀⣠⣌⠿⣿⣿⡙⠦⣬⣉⣉⢛⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⢻⡀⠓⠀⠀⠀⠀⠈⠁⠀⠛⠙⠻⢿⣿⣿⣦
⠀⠀⠊⠁⠀⠀⣠⠴⠂⠙⠻⠷⠶⣿⣉⠳⢤⣈⣉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠘⣇⠀⠀⠈⠃⠀⠀⢠⡄⡶⢦⣄⡀⠀⠙⠻⢷⣄
⢀⠀⠀⠀⠀⠈⢀⣄⠰⠦⠀⢀⠔⣧⡉⠳⠦⣌⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣠⣤⣤⣄⣀⣧⠀⠈⠙⢷⣄⠀⠀⠙⢷
⢸⣆⠀⠀⣦⠀⠀⠉⠀⠀⠠⣦⠀⠳⣍⡳⠦⣄⢈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣯⣤⣬⣝⡻⢇⡄⠀⠀⠀⠙⣧⠀⠀⠈
⠸⣿⣦⡀⠘⢧⡀⠀⠀⠀⠀⢸⡁⠀⠀⠈⠳⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠞⠀⠈⢁⣙⣻⡏⠉⠉⠉⠙⢛⡋⠀⠀⠀⠀⠘
⠀⠙⢿⣿⣷⣤⣙⠷⣦⣀⡀⠈⠻⠷⣦⣤⣀⠀⠈⠉⠁⠀⠀⠲⠤⠒⠊⠒⠲⠤⠎⠀⠀⢀⣀⣠⠄⠉⠉⠁⢰⡏⣢⠀⠐⠛⠛⠀⢀⣠⠄⠀⢀⡔
⠀⠀⠀⠈⠛⢿⣿⣿⣶⣯⣿⣳⣶⣤⣤⣈⣙⢷⣦⣤⡤⠶⠶⠶⣦⣤⣤⡤⠶⠶⣦⣤⠄⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⢀⣀⣤⠴⠚⣋⣠⠴⣚⡥⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⣶⣶⣚⣻⣯⣭⠵⢶⣚⣫⡭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣯⣭⣭⡽⠶⠶⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣯⣭⣄⣀⠀⠀⠀⠀⠀⢀⣀⣈⡙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⡞⠁⠀⠀⠀⠈⠉⠓⠒⠒⠋⠉⣅⠈⠙⢆⠀⠈⠓⢤⡀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⠞⠁⠀⡼⠀⠀⠰⣾⠇⠀⠠⣀⡄⠀⠀⠙⠛⠀⠀⠈⢣⣀⡠⢾⡉⠤⠄⠚⠁⣨⡍⠢⣄
⠀⠀⠀⠀⣠⠿⠚⠋⠉⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠚⣋⠠⢶⠀⢚⠓⠘⠛⣄⡘⣁⠱⡀
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⣠⠖⣚⡿⠿⠿⠯⠭⣕⢦⡀⠘⢀⠃⠀⠉⠁⠘⠃⠈⠁⠘⠃⠀⠀⠙⠀⢱
⠀⠀⠀⡟⡇⠀⠀⠀⠈⠛⠃⠀⡼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠙⢷⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢸⡇⢳⠀⠀⠀⠀⣀⠀⣼⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠘⡇⠀⠀⠀⠹⠆⢷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄
⠀⠀⢸⡇⢠⡇⠀⠶⠚⠀⠀⠘⣾⣆⠀⠀⠀⠀⠀⠀⠀⠈⠦⢠⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠸⠂
⠀⠀⠀⣧⢸⠁⠀⠀⠀⠀⠛⠓⠈⠻⣦⣀⠀⠀⠀⠀⠀⢀⡴⠋⢰⠘⠒⠉⠙⠢⠀⠄⠀⠀⢠⠖⠢⢄⣀⠔⠁⠇
⠀⠀⠀⠘⣎⣇⠀⠀⠀⠀⠲⣄⠀⢀⡀⠉⠛⠒⠒⠒⠋⠉⢀⣤⣬⡄⠀⡀⠀⣶⡆⠈⠂⠐⠁⢰⣶⠄⠀⠀⢸
⠀⠀⠀⠀⠘⣟⢦⡀⠀⠀⠀⠀⠀⠸⠇⢀⣠⠄⠀⠀⠳⡄⠀⢸⠙⣇⠀⢃⠀⠉⠁⠀⠈⠁⠀⠈⠉⠀⢸⠀⡌
⠀⠀⠀⠀⠀⠈⢣⡉⠓⠲⠤⣄⠀⠀⠀⠈⠁⠀⠙⣆⣀⣀⢀⠏⠀⢸⣀⣨⡀⠀⡇⠀⢰⠀⠀⡄⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠈⢧⡀⠀⠀⠀⠀⠀⡞⠀⠀⠛⠒⡏⠉⠁⠀⢹⡄⠁⠀⠈⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣙⣦⢤⠤⠤⠖⠣⡀⠀⠀⣀⣇⡀⠀⢀⡼⠥⠄⠀⣀⡀⠀⠤⠤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠛⠋⠉⠉⠁⠀⠉⠉⠁



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⢺⠹⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠌⢋⠔⢀⠋⡄⠈⠮⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠁⡠⠃⠀⡜⠀⢳⠀⠀⠈⠲⡕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢌⠀⣸⠀⢠⠃⠀⢰⡇⠀⠈⣧⠤⢤⡐⠉⠛⣗⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠈⠢⡸⢤⣸⣆⠀⠀⣧⡀⣐⠱⠕⠀⣿⠰⢲⡜⠀⠀⠀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡌⠙⠲⠤⣄⣀⡀⠀⠀⠀⠈⠙⠛⠉⠉⠉⠢⠤⠖⢋⣉⣉⣠⡤⠤⠖⠋⠁⠸⡄
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠢⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠑⠐⠋⠀⠀⠀⠘⢄⠀⠀⠀⢻⡄
⠀⠀⠀⢀⡇⠀⢀⡴⠒⠢⠤⠔⠋⠀⠀⢣⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠔⠛⡇
⠀⠀⠀⡸⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⡃⠀⠀⠠⠀⠈⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣰⢦
⠀⠀⠀⠰⠀⠂⠀⠀⠐⠀⠄⢠⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢇⠀⠉⢀⣇
⠀⠀⠀⠀⢣⠀⢰⠉⠂⠚⠀⠀⠃⠔⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠉⠉⠁⠈⠣⡀
⠀⠀⠀⠀⠀⢆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⡴⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢔⠞⠝⠀⠣⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠠⠃⡌⠀⠀⠣⡈⠁⠒⢽⢄⡠⡀⣀⡀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣀⣤⠁⠀⠃⠀⡇⠀⠀⠀⠘⡄⠀⠀⠣⢕⠁⡇⠓⢖⠊⡦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠈⠩⠀⡸⠆⣀⢃⠀⠐⣄⠀⠀⢀⣄⣀⠴⣗⢤⠭⠑⢆⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠬⠉⡾⠥⢓⣄⡠⠢⣉⠔⠫⣉⠜⢅⠔⢀⣀⢴⡤⠵⢤⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⢹⠒⠆⠨⠇⠀⢠⠀⠀⡄⠀⠰⠀⢠⡡⠔⠈⠉⠀⠀⠀⠉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡆⠘⡀⠸⠀⠈⡀⠀⠄⠀⡄⢀⠊⠀⢀⠀⢠⠦⣔⡑⠤⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣘⠀⢀⡀⢸⡤⠓⠠⣇⠀⠃⠀⠀⠀⠇⡆⠠⠀⡀⠱⡋⠀⠀⠀⡈⠃⠀⢀⡀⢐
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⠀⠈⠂⠀⠁⠀⠀⢸⡀⠐⠀⠀⡐⠀⣧⠲⠠⢄⠀⠈⠙⠉⠁⠀⠀⡠⠁⢈⠇
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢀⠇⣀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠓⠊⠑⠤⠊⠉⠈⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠄⠒⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢀⠀⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣰⠃⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢀⡿⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠷⠶⣿⡆⠈⠇⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⠁⠀⠀⢀⣠⡴⠞⠋⠀⢀⣀⣠⣤⣄⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⢀⣠⠴⠚⠋⠉⢀⣠⠟⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠰⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠤⠐⠚⠉⢁⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⡄⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣤⣤⣴⡶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠈⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⣀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⡿
⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠾⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⢀⣴⡿⠛⠉⠀⢀⣀⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄⣀⡀⠀⠀⢀⣰⡿⠁
⠀⣴⠟⠁⠀⢀⡴⠚⠋⠁⠀⠀⣠⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢛⣿⡿⠋
⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⠆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋
⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⠄⠀⠸⣿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠈⠛⠿⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⣸⠁⠀⡾⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣷⡄⠀⠀⠁⠀⢸⠇⠀⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⢠⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⢿⣀⡾⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠉⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⣠⡿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡜⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⢁⠔⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠙⠢⢤⣀⣀⣠⠴⠋⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠦⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⠒⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠐⠒⠐⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡏
⠀⠀⠀⠀⠀⠀⠀⣀⣷⣄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠔⢒⠞⠛⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⣞
⠀⠀⠀⠀⢀⣴⠞⠉⠀⠈⠉⠁⠀⠉⠲⣄⡀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⣀⠔⠳⣄
⠀⠀⡀⠈⠹⠋⠓⢄⢀⡴⠋⠙⠊⠀⢠⠞⠉⠓⢖⢋⠔⠋⠙⢦⡀⡠⠒⠉⠓⣄⢀⠔⠋⠙⢯⢉⡴⠋⠉⠺⣧
⠀⠀⠀⠀⠀⠀⣄⠀⠉⠠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡇⠀⠀⠀⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡶⠾⠿⢿⠃
⠀⠀⠀⠀⠀⡀⠈⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠆⠀⣆⠀⠀⠀⡇⠈⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡆⠀⠀⠀⠇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡇⠀⠁⠀⢰⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠌⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠉⢉⡉⢈⡐⢒⠒⣒⠒⡒⠒⠒⢒⡒⢒⣒⣒⡒⣈⣉⣉⢉⡡⠠⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡉⠀⠐⠒⠒⠂⠀⠤⠨⠤⠤⠤⠤⠬⠤⠌⠀⠒⠒⠒⡀⢀⣉⣁⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠬⠭⢍⣁⣁⣈⣈⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⡩⠭⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡴⠦⠤⣄⣀⡤⠴⠶⠤⣀⣠⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠁⣀⣀⣈⣉⣉⡒⠦⣝⢦⠀⠀⣠⠋⢀⡠⠖⣛⣉⣉⣉⣙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠴⠋⠁⠀⣠⠴⠚⠛⠛⠛⢻⡶⠛⠛⠓⢾⡛⠉⠉⠛⠢⣄⠉⠉⠓⢦⣉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⠞⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠑⣄⠀⠀⠈⢦⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡴⠃⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠹⡄⠹⣄
⠀⠀⠀⠀⠀⠀⡼⠁⢀⡞⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠙⣆⠘⣆
⠀⠀⠀⠀⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠘⣆⠈⢧
⠀⠀⠀⠀⢰⠃⢀⡞⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣆⠈⢧
⠀⠀⠀⢠⠏⢀⡞⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⣆⠈⢧
⠀⠀⠀⡟⢀⡞⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⣆⠘⡇
⠀⠀⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⣤⠇
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣀⡼
⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣀⣀⣀⡤⠤⠖⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠲⠤⢤⣀⣀⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠖⠒⠋⠉





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

⠀⠀⠀⠀⠀⠠
⠀⠀⠦⢄⢀⠘⠂⠀⠀⠐⠀⣈⡭⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤⢐⣢⡄⠀⠀⠀⠐⠀⢠
⢀⠀⠀⠀⣙⡀⠈⠀⠀⠀⠂⠀⠀⠀⠃⠀⠈⠀⠁⠀⠀⠀⠀⢚⡩⣥⡶⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⣒⡀
⠙⠛⠤⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠐⠀⠀⢀⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣉⠀⠐⠤⢐⡀⢠⡆⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⠀⠀⠀⠀⠀⠂⡤⠀⠀⠀⠀⠉⠛⠓⠲⠾⠭⠦⠀⠀⠘⠤⢄⣀⣀⡇
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⢀
⠀⠀⠘⠀⠀⢈⡁⠀⠩⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣟⣿⣿⡂⠀⢦
⠀⠀⠁⠀⠸⠋⠙⢛⠛⢤⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠘⠛⠉⠁⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣮⣆⣠⠤⡎⠀⢀⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⢃
⠀⠄⠀⡇⠀⠀⠀⠈⢉⢲⠄⠀⠒⠠⠰⠖⠁⠀⠀⠀⠀⣠⠀⡀⠀⠄⠀⢀⠀⠀⠀⠐⡀⢸⠀⠀⠒⠀⠈⠆
⠀⠀⠀⣷⣀⣀⣀⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠢⢌⣉⠙⠰⠂⠦⢤⡀⠀⠀⠉⢺⠀⠀⠀⠀⠀⠀⣀
⠀⠠⣀⡍⠠⠄⣀⣉⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠱⠂⠀⠉⢕⣒⡒⠡⢬⠀⠀⠀⠀⠱⠶⠶⠶⠒⠛⠉
⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠴⠬⣄⣉⣡⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡼⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠹⢷⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⠶⣦⣼⡇⠸⠃⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠀⣠⡴⠖⠁⢀⣀⣤⢤⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠔⠚⠉⢁⡠⠖⠃⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣀⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠋⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠾⠷⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⣀⣤⠤⠖⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣄⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠚⠉⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢸⣶⠶⠶⠶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣄⡀⠀⠀⢸⠃⢠⠇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄⠀⠀⠀⣾⠀⣸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣏⢠⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠙⠋⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠋⠙⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡯⣕⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢹⡏⢠⣤⣤⣄⡀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⡍⠉⣩⠉⠉⠁⠙⡀⠸⠿⠛⠉⡵⠾⠛⠛⢛⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⡄⡷⣀⢁⣰⣇⡤⠀⢀⡶⣀⣀⣐⣈⣀⡀⠀⢙⠏⢉⣉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠂⠀⣠⣶⣶⣾⣦⡀⠀⢀⣀⣸⣅⣠⢴⠟⢿⠉⠉⢳⠉⠠⠀⣴⡆⡉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⣀⣴⣽⣿⣿⣷⡹⢷⣾⣿⣿⣿⢩⠁⡄⠀⠈⣿⢠⣆⡞⠃⠀⣾⣧⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣉⡀⠙⠛⠟⠛⣇⣀⣀⣾⡿⠛⠉⠒⠧⣀⣤⠾⠺⠴⠁⣉⠥⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢑⢲⣶⣤⠤⣤⣤⣤⢤⣤⣤⣤⣤⣴⣶⣦⣭⣅⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⢿⠛⠉⠉⠛⠶⡀⠉⣿⣺⣿⠉⠆⢽⡏⠉⠙⠛⣼⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠸⣗⣂⠰⠃⠉⠁⠀⣠⣇⢀⣈⣉⣁⣀⠒⢛⣛⣛⣉⣭⣭⠭⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣉⠁⠀⠂⠂⠐⠠⢌⢹⢿⣿⣿⣿⡍⢿⡏⠙⠛⠟⠉⠘⠛⢛⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⢂⠤⠴⠯⡁⠒⠀⠒⠒⠒⣿⠾⣿⣿⣿⣿⣷⡼⠓⠠⢠⣤⡶⠗⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠚⠶⠶⠮⠭⣤⣤⠬⠍⠉⠩⠙⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠋⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠤⠀⠀⠀⠀⢀⣠⣴⠛⠓⠒⠚⠙⠨⢧⣴⣶⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠩⠏⠟⠛⠛⠃⠬⠴⠾⠿⠛⠛⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠧⢄⡠⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢅⡨⡠⡀⠬⡠⢄⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⡆⠀⠀⠀⠀⠑⡖⣦⣤⢥⣤⣤⡶⡞⠁⠀⠀⠀⠀⠀⢀⡴⠚⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣴⢃⠀⠀⠀⠀⠀⢳⢚⣥⢚⣷⠚⣶⠃⠀⠀⠀⠀⠀⣀⣸⣴⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢛⡇⠀⠀⠀⠀⠘⣧⣼⡿⠤⣿⡝⠀⠀⠀⠀⠀⢠⢗⣊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠼⡄⠀⠀⢀⠀⡿⠋⠉⡙⢣⡇⠀⡀⠀⠀⢀⠯⢤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡔⢳⢠⣼⡟⠋⠉⢢⠀⢠⠞⠉⠛⣍⢦⢀⡾⣭⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢷⣉⠖⢯⠠⠐⠀⠀⡇⡇⠀⠀⠠⢈⠟⣾⣭⠯⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢒⠒⠶⠢⠤⠵⠶⠶⠶⢭⡵⠶⠶⠶⠥⠤⠴⢖⣒⣚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠙⠚⠒⡲⠲⠲⠶⠶⠴⠴⠶⠶⡒⠚⠋⠉⠉⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⢤⣄⣄⡴⠉⠀⠙⢦⡀⠀⠀⣠⠞⠁⠈⠱⣄⣠⣤⠜⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⢉⣴⠁⠀⠀⠀⠠⢽⠉⢹⠥⠀⠀⠀⠀⣹⢡⣒⠍⢹⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⠀⠘⠾⣳⡀⠺⡄⠀⠀⠀⠀⣺⣄⣼⡂⠀⠀⠀⠀⡛⢢⣁⡠⠞⠀⠈⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠹⠓⠲⢦⠤⠬⣉⡉⠶⠶⠖⠋⣀⠜⢆⡈⠙⠶⠶⡊⣉⡩⠤⢤⠖⠒⢻⠁⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠘⢀⠞⠁⠀⠀⠀⣠⠋⢹⠋⢹⠉⢣⡀⠀⠀⠀⠙⢆⠘⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⡇⠀⠀⡆⠾⡔⠒⣄⠀⣰⡇⠀⢸⠀⢸⠀⠀⣷⡀⠀⠔⠒⡾⠆⡇⠀⠀⡇⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠁⢹⠀⡇⠀⠀⡇⠀⡇⠀⠘⡶⠃⡇⠀⢸⠀⢸⠀⠀⡇⠳⡞⠀⠀⠇⠀⡇⠀⠀⡇⢸⠁⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢆⣇⠀⠀⡇⢠⠀⠀⠀⡇⠀⡇⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⠀⢸⠀⡇⠀⢀⣇⡞⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠈⠉⠙⠓⠺⠤⠤⣠⣇⣀⡇⠀⢸⡀⣸⠀⠀⣇⣀⣧⡠⠤⠼⠒⠛⠉⠉⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⣤⠖⢿⠉⡟⢑⠦⣄⠀⠀⠀⠀⠀⠀⠀⡖⠒⢏⠉⠓⢦⡀⠀⠀⡞⢳⠞⢳⠞⢛⠖⢛⡖⢛⡆
⠀⠀⠀⠀⢀⠾⣀⠳⣸⣼⣡⣋⠴⠚⢧⠀⠀⠀⠀⠀⢠⠟⢦⡀⠑⢄⠀⢳⠀⠀⣇⡏⢀⡎⠀⡞⠀⡞⠀⡼⡇
⠀⠀⠀⠀⢸⠦⠬⢵⣿⣿⣿⣷⣚⣉⣙⡆⠀⠀⠀⠀⠈⣇⠀⠙⢦⡀⠑⡏⠀⠀⣟⣀⣜⣀⣼⣀⣼⣁⣸⣁⡇
⠀⠀⠀⠀⠸⡖⠒⣩⢿⢿⢿⢯⠲⢤⣹⠁⠀⠀⠀⣠⢞⡽⠓⠲⠶⠛⠒⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡽⣏⣠⠏⡼⠸⡆⢳⡴⠃⠀⠀⣠⢞⡵⠋⢀⣀⠤⣀⣀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠦⣄⠀⠀⠀⢠⠒⡿⠛⠛⠓⣦
⠀⠀⢀⡴⡫⠊⠀⠉⠓⠓⠒⠋⠁⠀⠀⠀⣞⡵⠋⠀⠀⡇⠀⠀⠈⢉⠇⠀⠀⣼⠁⢠⠖⠓⠂⠀⠘⡆⠀⠀⡞⠉⠛⠓⠒⠋⢹
⢀⡴⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡜⠀⠀⠀⠹⣄⠀⠁⠀⠀⠀⡰⠃⠀⠀⣇⠀⠀⠀⠀⠀⣀
⠻⠚⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣼⡅⠀⠀⠀⠀⠈⠙⠒⠒⠒⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢶⠲⢤⠋⠉⠉⠉⠈⠈⠙⡤⠖⡆⠀⠀⠀⡼⠉⠉⠉⢧⠀⠀⠀⠀⢠⠤⣄⣀⠔⠚⠉⠓⢦⣀⣠⠤⣤
⠀⠀⠀⠀⠀⢯⢀⣸⣄⠀⠀⠀⠀⠀⢠⣇⠀⡝⠀⠀⢰⠁⠀⠀⠀⠈⣇⠀⠀⠀⢞⠀⠀⡏⠀⠀⠀⠀⠀⡯⠀⠀⣣
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠺⠤⠤⠤⠤⠤⠿⠀⠀⠀⠾⠴⠒⠛⢦⣀⣀⣀⠴⠋⠒⠮⠇
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⡅⡇⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⢸⢨⠆⠀⠀⠀⠀⡏⠀⢠⠃⠀⡼⠁⠀⡼⠁⠀⡼⠀⢈⡷⡄
⠀⠀⠀⠀⠀⠀⢘⡅⡇⠀⠀⡎⠁⠀⠀⠀⢹⠄⠀⢸⠠⡃⠀⠀⠀⠀⠈⠓⠛⠒⠚⠓⠒⠚⠓⠒⠚⠓⢲⠋⠀⢹
⠀⠀⠀⠀⠀⠀⢨⠆⡇⠀⠀⠈⠒⠶⠴⠒⠋⠀⠀⢸⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠚⠒⠋⡽
⠀⠀⠀⠀⠀⠀⠰⠷⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⣓⡦⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⣿⣥⠽⠬⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠻⢶⣴⠿⢿⣄⠀⠀⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣶⣦⣶⡞⠁⠀⠀⢈⣷⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠖⠋⠉⠻⢿⣧⣬⣁⣠⣼⣿⠁⢀⣀⣸⡃
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠴⠉⠩⠭⢌⢻⣿⣿⡿⢿⡉⢉⣿⣃
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠒⠖⠃⠀⠀⠀⠀⠀⠁⣗⣀⣶⡆⢛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣸⠂⠀⠀⠀⠀⠀⠠⣿⠅⣿⠇⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠤⠤⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⣆⠀⠀⠀⠀⠀⢀⣽⣸⡟⢠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⣤⠴⢒⣾⡷⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣤⡙⣿⣿⣤⣤⣀⣴⣿⣿⣿⣵⠿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠋⠁⠒⠻⡿⠿⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⣿⣿⣿⣿⣿⣿⠿⠛⠑⠉⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⣄⡀⠀⣾⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⡗⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣗⢶⡖⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣴⣷⡄⢛⣿⣿⣿⣖⣦⣼⣀⡀⠀⠀⢹⠀⠀⠀⣥⣾⡗⠆⠀⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⠿⢟⠛⠉⣉⣤⣶⣛⣻⡿⣿⠿⢿⣿⣿⣶⣦⣤⡏⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠎⣸⢀⣆⠠⣤⣀⡀⠀⠀⠀⠀⠀⠈⠒⠰⠤⢄⣀⣀⠙⠉⠁⠀⠐⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⣴⣯⣀⢨⣦⢈⣁⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢿⣖⠲⣶⡤⣀⡈⠛⠛⣩⣟⣛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠺⠾⢇⣀⣿⣶⡙⢦⠛⣿⡶⢆⠉⠉⠁⠀⡈⠳⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠁⠀⠀⠀⠀⠀⠀⠙⢀⣬⣏⣆⣀⡠⠥⣦⠷⣦⡄⢠⠀⠀⢽⡇⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣁⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣨⣟⣁⡙⣿⣳⢶⣿⢻⠘⠀⠀⢸⡇⠠⡅⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⣭⣿⠛⠿⢾⣿⣦⣭⡿⢀⡁⣰⣿⣿⣿⣧⣌⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣂⣾⣿⣿⡶⠶⣞⣿⠷⠉⢙⣲⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠈⠀⠸⠿⣓⡲⠶⠶⠾⠟⠻⠉⠉⢠⣶⡿⠿⠷⠞⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠄⣀⣀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠾⠟⠛⠛⠛⠛⠻⠷⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠙⠿⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠿⠋⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⣀⣤⡶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢶⣤⣀
⠀⢀⣴⠟⠋⠁⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⠙⠻⣦⡀
⣰⡟⠁⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠈⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣄⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣠⣤⣶⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠙⠛⢷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡾⠛⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣮⣍⣙⡛⠛⠿⠿⠷⢶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠾⠿⠿⠟⢛⣋⣩⣵⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣟⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⠛⠛⠋⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠀⢀⣀⡤⠴⡖⠚⠛⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⢸⠉⠘⢳⡾⠭⣩⣽⣿⠿⣟⠷⣤⠄⣀⣀
⠀⠀⠀⣀⡤⠖⠊⠉⣀⣿⡇⠀⠀⠀⠘⠀⠀⠸⠇⠀⠇⢹⡏⠑⠒⠢⠬⣷⣄⠀⠈⠉⠒⠠⢄⡀
⠀⣠⡞⠁⠀⢀⡴⠋⠁⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠤⣀⠀⠀⢄⠀⠈⠳⣄
⠀⣿⡀⠀⠀⢸⣇⠀⠊⠀⠀⠉⠉⠛⠛⠷⠶⣦⣤⣤⣀⣈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠑⠂⠀⡧⠀⠀⠘⡆
⠀⠘⢿⣦⡀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⢶⣦⣤⣼⠀⠀⢀⣠⠞⠁⠀⢀⡼⠃
⠀⠀⠀⠉⠻⢷⣦⣤⣀⡉⠙⠓⠲⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠬⠽⠒⠊⠉⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠠⣄⣼⣷⢣⠃⠀⠀⠀⠀⢀⡴⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠊⢄⠈⠂⢸⡄
⠀⠀⣠⣤⣶⠛⠋⣀⣾⣀⡀⠀⠀⡠⢿⣤⣀⣀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠐⡇⠀⠘⣄⠐⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡰⣆⣀⡤⣶⠏⠀⢀⣠⣄⡀
⠀⠀⠀⠈⠉⠉⣻⠋⢀⡼⠙⢲⣼⡥⠶⠶⠿⢯⣛⠛⡇⢠⠞⠋⠉⠙⢳⣦⡹⣄⠁⠀⠀⣀⣴⣣⠴⢲⡖⠒⢶⣤⣠⠃⠈⠁⠸⣧⣀⡴⠋⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢠⡇⡰⠋⠀⣴⠋⠁⣠⡤⠶⣤⡀⠙⢷⣷⠏⢀⣤⠶⠚⠉⠀⢻⣼⢻⠟⣫⣿⠋⠀⠀⣸⠁⠀⢸⠀⠙⣶⣤⣀⣀⣾⡟⠳⠶⣤⣀⡀⢹
⠀⠀⠀⠀⠀⠈⣟⠁⠀⣼⠃⠀⣸⠁⢀⣀⠈⢳⠀⠈⣿⠚⠉⠀⠀⢀⣠⠖⠋⢹⣞⡼⢁⣏⠀⢀⣀⣿⣀⣀⣘⣀⣀⣿⣀⣈⣽⣏⣁⣀⣀⣤⣭⣽⣿⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣿⡶⠶⠿⠶⠶⠿⠶⠟⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⡄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⢶⡆⢾⣿⣦⣄⠀⠘⢿⡇⢰⡿⠛⠿⠀⢹⣧⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⣧⠈⢻⣷⠀⢸⡇⠸⣧⠀⠀⠀⠸⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡿⢾⡏⠁⠀⢸⠇⠀⠙⠧⣤⠄⠠⠇⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⢿⡆⠛⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⡟⠀⣿⢀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣼⠃⠀⠿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡁⠀⠀⢀⣀⣀⣀⡀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣆⢾⣷⣦⣀⠀⠀⣿⠿⠿⠆⠀⢺⣿⣦⠀⠘⠋⣿⠉⠃⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⣿⠉⢻⣧⢠⣿⠋⠀⠀⠀⣾⠶⠿⡇⠀⠀⣿⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⢶⡟⠁⠀⠻⣤⡴⠀⠰⠃⠀⢠⠇⠀⠀⢸⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⠏⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣏⣀⣀⣀⣀⣀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⢈⣠⣄⠀⠈⠉⢳⡀⠀⠀⠀⠀⠀⢸⠗⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠹⣏⣁⣈⣽⠃⠀⢸⡇⠀⢀⡞⠋⠉⠉⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣶⣤⣤⣤⣼⢁⡄⠀⠙⣦⣴⣯⣴⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢻⡀⠁⠘⢠⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠋⣠⠖⠒⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠶⢤⡤⠤⠤⣤⠤⠤⠤⢤⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣧⠀⠀⣿⠀⠀⠀⢸⠃⣾⠷⠶⢶⡶⠶⠶⡶⠶⠶⠶⢶⡶⠶⢶⡶⠶⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡄⠀⢻⠀⠀⠀⣼⠀⢹⡄⠀⠈⣇⠀⠀⣧⠀⠀⠀⣸⠀⠀⣼⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⣧⠀⢸⡀⠀⠀⣿⠀⣸⢿⡀⠀⢹⡀⠀⣿⠀⠀⠀⣿⠀⢠⡇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡄⢸⡇⠀⠀⡇⠀⡟⠀⣷⠀⠈⣇⠀⢸⠀⠀⠀⡏⠀⣼⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⣧⠈⡇⠀⢰⡇⣸⠃⢰⠟⣧⠀⢹⡀⢸⡆⠀⢰⡇⢠⡇⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠘⣆⣘⣇⣸⣇⣀⣸⣇⣼⣁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⡀⠀⠀⢀⣼⣿⣿⣿⣿⣆⠀⠀⠀⣠⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⢿⣿⠶⠒⠛⠻⠿⣿⠿⠛⢛⡛⠻⢛⣛⣛⣋⣙⡛⠛⠛⠋⠙⢿⣿⣿⣶⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠨⠝⠿⢿⣷⡶⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⠀⡿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣤⣤⣤⣤⠒⠪⣷⠀⠀⣠⠜⠛⡿⠻⠿⠿⠉⠉⠉⠉⠛⣿⣿⣿⣷⣧⡜⠙⣿⣿⣿⣿⡏
⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⡜⣿⣬⣭⣭⣛⠳⢾⣶⣯⣤⣤⣾⣶⣾⣅⣀⣀⣀⣀⣠⣮⣁⣛⣉⡩⠛⠉⠡⣙⠿⢿⣿⣷⣶⣤⣄⣀⣀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⣿⡇⠀⠙⠻⠿⢷⣶⣶⣶⣶⣶⣶⣦⣬⣭⣉⣉⣩⣭⣭⣭⣭⣛⡻⠿⠿⠶⠿⠿⣂⢻⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⣄⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠉⢉⡉⠉⠉⠉⠀⠀⠉⠉⠉⠙⠛⠛⠻⣿⣳⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠄⠀⠙⠀⠀⠀⢸⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⢻⣇⠀⡀⠀⠀⠶⠀⠀⠘⠁⢀⡀⠀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣿⣿⣿⣿⣦⣄
⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡘⣿⡄⣿⣷⣶⣤⣤⣤⣀⣀⣈⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣳⣿⠁⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡇⣿⡟⠀⠐⠆⠀⠠⠖⠋⠍⣀⡀⢀⠀⠀⠉⠙⠻⢿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣼⡇⠤⠀⠀⠠⣈⠑⠒⠒⡠⠊⠁⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠈⠛⠛⠿⠿⠇⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏⣿⡇⠀⣤⣜⠲⠦⢭⣭⣅⠇⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⢻⡏⠀⠀⠐⠃⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⡠⠞⠋⠉⠁⣀⠹⣿⣶⡆⢬⣉⡓⠒⢦⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢻⡀⠆⠀⠀⠀⠀⠋⠀⢹⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠈⠀⠀⢀⠴⠂⠻⠷⠶⣿⡙⠲⢬⣉⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠘⡇⠀⠀⠚⠀⠀⠀⣄⢻⣤⣄⠀⠉⠛⢷⣄
⠀⠀⡄⠀⠀⠀⠀⢠⣄⠰⠆⠀⠠⢺⣌⠓⠦⢄⣙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣤⣤⣀⣀⣤⣤⣶⠀⠉⠙⢶⡄⠀⠙⢷⡄
⠀⠀⣿⡀⠀⢰⡀⠀⠀⠀⠀⠰⡄⠘⠈⣙⠲⠄⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠻⣿⣿⣷⣦⣬⣙⣃⡄⠀⠀⠀⠙⡄⠀⠀⡷
⠀⠀⠻⣿⣦⡀⠳⣄⡀⠀⠀⠀⣥⣀⠀⠀⠉⠠⠤⠤⠄⠀⠀⠀⠀⣀⡀⠀⠀⡠⠴⠒⠊⠀⠀⣠⣬⡿⢀⡀⠈⠉⣩⣅⠀⠀⠀⠀⠁⠀⠀⠇
⠀⠀⠀⠙⠻⣿⣷⣮⣝⡳⢦⣄⣈⠙⠛⠶⣦⣀⠀⠀⠀⢀⣈⠙⠉⠀⠈⣉⠚⠁⠀⠠⠶⠶⠂⠀⠀⠀⠿⠼⠂⠀⠉⠁⣀⡤⠂⢀⡤⢖⠅
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⣶⣦⣽⣿⣟⣛⣉⣉⡛⠓⠚⠋⠉⠛⠛⠋⠀⠀⠀⠀⣀⣀⣀⣠⣤⠤⢶⣚⣭⠥⢖⣺⠽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣞⣛⣛⣯⡭⠽⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠐⠒⠀⠀⠐⠐⠐⠐⠀⠀⠂⠀⠂⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⢦⡀⠀⠀⣠⠔⡒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠢⢤⡀⠱⡄⢀⡗⠚⡟⣡⠋⡠⠔⠂⢀⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠤⢍⣉⡓⣦⠴⡷⠲⡗⢫⠀⣠⠷⡗⢾⠒⢶⠯⠥⣤⡄⠤⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠤⠒⢻⠁⢀⡆⢀⡜⠀⡇⣨⠇⠣⣀⠳⠈⠳⠘⠢⠀⠱⠌⠙⣂⡽⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣢⡤⠤⠥⠤⠬⠤⠤⠒⠚⠉⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⢤⡈⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠬⠓⠂⢈⣑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠤⠶⠒⢚⣋⣉⠥⠤⠶⠒⠚⠋⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣩⡥⠤⠤⠶⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣠⣤⣚⣁⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠒⠒⠒⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠴⠦⠤⠤⠤⠤⠤⠤⠴⠒⠒⡻
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠤⠔⠋⠙⠒⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⢸⣀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠐⠒⠒⠒⠒⠒⠉⠉⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⠤⠤⠤⠤⠐⠁
⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠠⠥⠤⠤⠤⠔⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠙⠛⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠁




⡿⠉⠙⡟⡻⠟⠟⠛⠻⣟⠛⡟⠿⠻⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣟⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⢠⠪⠁⠀⠉⢳⡄⠀⠔⠋⢩⣟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣤⢰⡶⠛⠉⠀⡀⠉⠳⢝⡲⠤⣤⣤⡶⢋⠉⠓⢦⠀⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⢿⡿⢿⡴⠚⠉⠀⠈⠙⠦⣄⣈⣀⣠⣿⢳⡄⠳⡀⠈⢗⠈⣉⣉⠙⢦⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠹⡟⢻⣬⣔⣲⣤⣄⣀⡀⠻⠙⠦⣄⣀⡀⠀⣀⣌⠥⣪⣥⠀⢳⡀⠙⢦⣈⡳⡤⣄⠱⡜⣧⣶⡌⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⡍⠙⠿⠿⢿⣶⣦⣤⣄⣀⠀⠀⠀⠈⠻⠛⣆⡀⠙⠲⣴⡶⣿⣷⣬⣇⣷⠏⠉⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠉⢻⠛⠿⣶⣦⣤⣀⡀⠀⠉⠉⠉⣿⡆⠻⠟⠃⠉⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠈⠓⠈⠻⢿⣷⡲⢄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢇⢹⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣲⠌⢏⠳⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⢤⣄⡀⠂⠀⠀⠀⠙⢯⠙⣔⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣺⣽⣟⡻⢿⣶⣀⠁⠘⡟⠋⠀⠀⠚⠿⣟⠶⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣟⠿⣶⣦⣵⣄⠀⠠⠄⠈⢱⡼⠂⠈⢑⣒⡲⡄⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣭⡻⢿⡷⣦⣤⣀⠠⠖⠉⠀⠈⠉⢻⡌⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣬⣽⣿⢿⣿⣷⣴⣬⣀⠸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢒⣀⡥⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣯⣝⡒⠬⢕⡫⢽⣻⣷⢼⢿⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣬⣁⡒⠈⣟⡼⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⡈⠹⣄⢀⡀⡠⠂⠀⠉⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠵⡄⠥⢼⠤⣏⢙⡧⢄⣤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠘⠤⠎⠉⠀⠀⠀⢈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠄⠀⣰⠊⡆⢀⡀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⡏⢠⠃⡀⠀⡇⠀⠙⠁⠰⢰⠀⠤⠀⠃⢀⣤⠀⠀⠻⡸⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⣀⠴⠳⡎⠀⠇⢸⠃⠀⠀⠀⡀⢨⠀⠀⠀⢠⣸⠈⡇⠀⡆⣧⠗⠲⢄⡉⠲⣄
⠀⠀⠀⠀⠀⢠⠊⠀⣠⠊⠁⠀⢀⡇⢰⠀⡼⠀⠀⠀⠀⢧⣸⠀⠀⠀⠀⠁⠀⢱⠀⡇⢿⠀⠀⠀⠙⢢⡀⠳⡀
⠀⠀⠀⠀⢀⠃⠀⡰⠁⠀⠀⠀⢸⠀⠈⠛⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⠀⠀⠀⠀⠀⠱⠀⠸⡀
⠀⠀⠀⠀⢸⠀⠀⢃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠀⢧⠧⠈⢆⠀⠀⠀⠀⠈⠙⠒⠦⠤⣄⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠒⠋⠁⠀⠀⢠⠀⠀⣠⠊⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⢀⡤⠚⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠉⠒⠠⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠒⠊⠁⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣀⣀⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣀⣀⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠒⠒⠒⠊⠉⠉⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢹⠂⢠⠔⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⢊⡓⣯⣧⣯⢟⣯⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠈⠁⠉⠋⠙⠛⠉⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⣀⡀⠀⢀⠄⠀⠀⢄⠀⡠⠒⠢⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠁⠀⠸⣀⡞⠀⠀⠀⠀⢄⠇⠀⠀⠱⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣔⠀⠀⠑⠢⠤⠄⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠒⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⠤⠤⠀⠀⠀⡀⠀⠀⠀⠠⠤⠤⠤⠐⠂⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣒⣲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣿⡿⠟⢹⣻⣿⡆
⠀⠀⠀⠀⠀⠣⣀⡤⢄⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢛⡷⢺⣗⣿⡿⠒⠉⢨⣿⠓
⠀⠀⠀⠀⢠⠂⠉⠀⡞⠉⠁⢕⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣲⣯⣭⣭⣭⣙⣒⡦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣡⣿⠝⠫⠴⠤⠄⠤⣿⡄
⠀⠀⠀⠀⣾⠗⡒⠒⠘⠒⠁⠐⡑⠀⡧⠀⠀⠀⠀⠀⠀⡔⣠⣶⣞⣭⣵⣾⣷⣿⣿⣿⡽⣎⣓⡄⠀⠀⠀⠀⠀⢀⡏⢿⡇⠀⠠⠀⠀⠄⢠⣿⠃
⠀⠀⠠⡖⢧⠠⠄⠴⠶⠂⢁⣀⠡⢺⠁⠈⠆⠀⠀⠀⣜⣴⣿⡿⣿⣿⣯⣾⣿⣿⣝⢿⣿⣾⣝⣿⣆⠀⠀⠀⠀⠉⠡⠄⠁⠠⠀⡀⢀⣐⣘⠿⢎
⠀⠀⠀⣯⣐⢛⠿⠣⠤⢄⣀⡠⠔⢊⠔⢀⡄⠀⠀⢰⡅⣿⣿⣟⣿⣿⡿⣩⠭⢦⡹⣮⣿⣿⣿⣿⢸⡄⠀⠀⠀⠐⢆⠀⢀⠰⠀⠈⡡⠈⠁⢀⠎
⠀⠀⠾⢤⣉⡐⣃⠠⠴⠦⠄⠐⠋⢀⣐⡋⡅⠀⠀⠸⢶⡟⣿⣿⣇⣿⣸⠁⠀⠀⡱⣼⣿⢿⣿⡿⡄⡇⠀⠀⠀⠀⠀⢹⢉⡕⡲⢒⢶⣶⡶
⠀⠀⠀⠄⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠃⣿⢹⣿⣿⣿⡏⠣⣤⡔⣡⣿⣿⣿⢿⡳⢣⠃⠀⠀⠀⠀⠀⠀⢇⠰⡑⢎⡾⢮⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠡⡙⣾⣿⣿⣿⣽⣟⢷⣾⣿⢿⣿⣿⡟⢡⠋⠀⠀⠀⠀⠀⠀⠀⢩⡰⣹⢯⠈⡆
⠀⠀⠀⠀⢧⠀⠂⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢟⠻⢿⣟⣿⣿⣿⣿⣷⡿⠋⢉⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⣃⠣⠼
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⣀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⠭⠭⢛⣿⠿⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣤⢣⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⡏

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠐⠀⠀⠦⠀⠀⠀⢰⠁⠀⠈⢁⠔⠀⠀⠀⠈⠟⣉⡆⠀⠀⠀⠀⠀⠀⣴⠤⠀⠀⠠⠀⠀⠀⠀⡀⠔⠿⢧⠄
⠀⠀⣌⠑⠓⣾⣛⣷⠀⢰⣿⡿⢿⣆⣠⡄⠀⠀⡀⠀⠀⠀⢰⣦⠀⠀⠀⣿⣶⣬⣷⡖⣰⣆⠀⠀⠀⢰⣿⠓⠒⠊⠑⡆
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠈⠀⡈⣇⡏⡟⠀⠚⠀⠀⠘⠿⠅⠀⠙⠷⠠⣠⠄⢠⣷⢶⡤⠀⢰⡇
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠙⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠛⠛⠁⠀⠀⠂⠀⠀⣀⣀⠀⢀⣤⢤⣤⠄⢀⣇⣀⣁⠀⢈⡁
⠀⠀⠀⠀⢀⢐⠀⠠⢀⡢⠀⠀⠀⠀⣼⣟⣙⣻⠟⠁⠀⠀⠀⠀⠀⠀⠠⢭⠀⠿⠜⠶⠲⠶⠶⠶⠂⠀⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠸⣟⣟⡶⢶⠤⣥⡁⠀⠀⠐⠀⠤⠍⣉⣿⠀⠀⢀⢄⠂⠀⣠⣴⣲⠄⠀⠀⠀⠀⢀⣘⣃⡚⠛⢗⠂⣀⡆
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⣝⠀⠀⠯⣉⡓⠒⢤⣉⠁⠀⠈⠀⠀⠀⠰⣾⡟⠀⠀⠀⢠⣀⢈⣉⡉⢁⣀⡤⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠈⠙⠒⠟⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠙⠓

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠋⠉⠉⠉⠉⠓⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣄⡀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⣦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠶⣄
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠈⣷⡀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢠⡶⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⢷⡀
⠀⢀⡞⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣰⠏⠀⠀⠀⠀⠀⠀⣾⠀⠀⣼⠀⠀⠀⠀⠀⠀⣤⠖⢦⡀⠀⠀⠀⠀⠀⠘⣆⠀⠹⣄
⠀⢸⣇⠤⠤⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⡏⠀⠀⠀⠀⠀⢸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠹⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⡼⠀⠀⣸⠁⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢻
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡇⠀⠀⠀⠀⠀⢰⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⣾⠀⠀⣼⠁⠀⠀⠀⠀⠀⡼⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⡝⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡟⠀⠀⠀⠀⠀⢀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠉⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠇⠀⠀⠀⠀⠀⣼⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡿
⠀⣿⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠊⠉⠀⠀⢀⣠⡴⠚⠉⣾⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⠀⠀⠀⠀⢠⡏⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⡇
⠀⣿⣀⡤⠤⠖⠛⠋⠉⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠁⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣾
⠀⡏⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⡜⠀⠀⠀⠀⠀⢀⡟⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⠏
⠀⣇⣀⣤⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⢠⠇⠀⠀⠀⠀⠀⢸⠃⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣸
⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾⠀⠀⠀⠀⠀⠀⡏⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡇
⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⠀⠀⠀⣰⠃⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣴⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣾⠀⠀⣸⠁⠀⠀⠀⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⡟
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⡏⠀⠀⠀⠀⠀⢸⠇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣸⠃
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⢻⠃⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡿
⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠋⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡎⠀⠀⠀⠀⠀⢠⡇⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠃
⢸⣇⣀⣤⣤⠴⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢰⠋⠒⢦⣀⠀⠀⠀⠘⢧⣤⠼⠁⠀⠀⠀⠀⠀⣼⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞
⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠳⣄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢨⠇
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠳⠶⠶⠶⠛⠋⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣀⣤⡤⠶⠤⠶⠋⠳⢦⡀⠀⢀⡏⠀⠀⢰⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⠀⠀⠀⣼
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⢙⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸
⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡇
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣍⡛⠲⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣸⠃
⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⡷⠶⠶⠦⢟⣯⣷⠶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠈⠉⠛⠒⠒⢶⠖⠒⠒⠒⠲⣶⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠉⣿⠻⢭⣭⣵⡒⢒⡒⠒⠋⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣶⣾⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠂⣄⠰⠾⡂⢤⠐⠢⡀
⠀⠀⠀⠀⣀⣠⡖⢯⢤⡜⣼⠳⣤⣄⣀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠼⠁⣤⠇⠘⢁⡤⠃
⠀⣴⠚⠉⠀⡠⢿⠠⠀⠀⠀⠀⣥⠀⠀⠉⠓⢄⠀⠀⠀⠀⠈⢳⣴⠋⠀⠱⢴⠋
⠀⠳⣄⠀⠀⠑⠀⠱⠤⠄⠒⠈⠉⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⢸
⠀⠀⠀⠉⠓⠒⠲⠆⠤⠤⠤⠴⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠚⠘⠂⠀⠚⠘⠓⠀⠀⢀⣤⡖⠖⠚⠙⠛⠒⠒⢒⢤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡋⠀⠀⠀⠠⠀⢀⡀⣀⣀⡹⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠯⢑⠦⠈⢩⠮⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡻⢦⣀⣀⠀⠀⠀⠀⢀⣀⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⣼⣶⢊⡉⠓⣷⡘⣄⡸⢧⠀⠀⠀⠀⠀⠀⠀⠘⢦⡁⠪⠸⣀⠍⠉⢸⣉⡩⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⡼⢋⣍⣰⣷⣊⡈⡇⠘⠤⣿⠁⠀⠀⠀⢠⡀⠀⠀⠀⠈⠛⠒⠦⠤⠤⠤⠤⠖⠚⠁
⠀⠀⠀⠀⣀⣀⣀⡀⢀⣀⡀⠀⠹⣄⠈⠁⠙⠈⠁⠋⠀⠀⣠⠃⠀⠀⠀⠰⠁⢈⡢⠄⠐⢒
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢹⠀⠀⠈⠳⣤⣠⣤⣤⣴⡶⠞⠁⠀⠀⠀⣀⠥⠄⣌⠀⣀⡠⠞⠚
⠀⠀⡔⠒⠀⠀⠀⢀⣀⣀⣸⣦⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠁⠀⠐⣄⢢
⣠⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⢠⡀⠀⠀⠀⠀⠀⣀⣿⠀⠓⢄
⠈⠀⠄⠠⠀⢀⣀⣀⣀⠤⠬⠭⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠑⠃⠀⠀⠀⠀⠈⠉⠉⠡⠀⣸⠂
⠀⠀⠀⠀⢀⠴⠛⠁⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⡀⣀⢀⣀⠴⠊
⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠂⠈⠠⣄⠀⡄⠀⠀⡚⠁⠀⠐⠀⡨⠀⠀⠀⠀⢸⡟⠙⡆⠀⠀⠀⠀⠀⠀⢀⣦⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣠⢶⣶⣤
⠀⠀⠀⠒⡤⢤⣴⡼⣦⠀⢀⣴⣷⣶⡤⠀⢘⡀⠀⠀⠀⠀⠀⠈⠉⢡⣄⠀⠀⠀⢰⣦⣌⣛⣦⣤⠀⣤⠀⠀⠀⠀⢠⣷⡦⠤⠤⠗⢠
⠀⠀⡙⠂⠀⣴⠿⢞⣛⠀⠀⢿⡟⠉⠉⠓⠚⠃⠀⠀⠘⡄⢠⢠⡔⡾⣿⠃⢰⡀⠈⠛⢻⣿⠟⠉⠺⣯⡂⠀⠀⠀⢘⣿⣀⡀⠀⠀⢸
⠀⠀⢈⠑⠀⠶⢟⣋⡭⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣷⣇⡏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠑⠊⠀⠘⡟⠙⠿⠀⠀⠿
⠀⠀⠀⠀⠀⠛⠉⠀⢀⠀⣀⠀⠁⠀⠀⠀⢀⣀⣴⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢠⢴⢢⡄⠀⡒⠖⠒⠒⡁⠰⢿⡤⢤⣄⠀⠴
⠀⠀⠀⠀⠀⣄⣁⠀⠰⠀⠄⢂⣀⠀⠀⠰⠾⠯⠬⣝⣛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠖⠆⠀⠓⠊⠛⠙⠓⠛⠛⢙⡁
⠀⠀⠀⠀⠀⢻⣽⣟⡿⢶⠖⣦⣤⠀⠀⠀⠒⠂⠠⠤⢀⣹⣇⠀⠀⢀⢔⠂⢐⢢⢲⣾⣵⠀⠀⠀⠀⠀⠀⣀⣙⣁⡛⠛⠛⣛⣀⣼⠆
⠀⠀⠀⠀⠀⠨⠷⣷⣿⣻⣏⡹⣭⠇⠀⠰⢯⣉⡙⠒⠤⣌⣙⠀⠀⠈⠀⠀⠀⠐⡶⣿⡏⠀⠀⠀⢠⣀⡀⢈⣉⠉⣀⣀⣤⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠋⠁⠀⠀⠀⠀⠉⠐⠲⠭⠇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠙⠛⠥⠬⠥⠀⠀⠁

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣀
⠀⢀⠂⠀⠀⢱⡀⠀⡐⠀⠀⠀⠀⠀⢠⠈⠁⢀⠀⠀⠀⠀⢀⠁⢀⠀⠀⡀⠀⠀⡎⠀⣀⠀⠇
⠀⠈⢦⣀⣀⡼⠁⠀⢳⡀⠀⢀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⣠⠃⠀⠀⠀⢤⣀⠤⠂⠀⢀⡀⡀
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠙⢫⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡸⠉⠉⠀⠀⠀⠀⠀⡎⠀⠀⠀⣀⣙⣧⡼⠆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠈⠢⢤⡔⠀⠀⠀⣰⠁⠠⠀⠂⠄⠀⠀⠘⠀⣀⣄⡀⠹⣡⣏⢳⠟
⠀⠀⢀⡀⠁⠀⠀⠀⡠⠐⠠⡀⠈⠀⠀⠀⠀⠀⠇⠀⢀⠄⠠⡀⢀⠐⠗⠀⡆⠀⠀⢸⣿⣿⣿⠀⠀⠉⡇
⠀⠼⠥⠭⠦⠀⠀⠈⠀⠀⠀⠰⠀⣠⠢⠂⣠⠀⠸⡀⠀⠀⠀⢀⠀⠑⠲⠾⡁⠀⠀⢸⣿⣿⢻⠀⠀⠀⢸
⠀⢐⡒⢻⣋⡄⠀⢠⠀⠀⠀⠰⠀⢻⣤⠀⡤⠇⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠙⣄⠀⠸⣿⣾⣿⠇⠀⠀⠈
⠀⠈⢫⣥⢤⠄⠀⠀⠀⢤⠄⠁⠀⢀⠟⠛⠋⠀⠀⠀⠀⠀⠀⠰⠀⡄⠒⠒⠦⠈⠀⠀⠈⡟⠉⢀⡤⠐⠀⠄
⠀⠀⠀⢹⠁⢀⠤⢀⠀⢸⠀⠀⠀⡜⠀⢠⣲⢛⠷⡄⠀⠑⡂⠀⢸⠀⠀⠀⢐⠀⠀⠀⠀⣧⠀⢸⠀⠀⠀⠘
⠀⠀⠀⢸⠀⡏⠀⠀⠀⠸⠀⠀⠀⣁⠀⢇⠃⣍⣶⠃⠀⠀⡇⠀⠀⠓⠒⠺⡁⠀⠀⠀⠀⠸⠀⠈⠳⡤⠄⠂
⠀⠀⠀⠈⠆⡇⠀⠀⠈⠀⠀⢰⡛⢡⣁⠈⠉⢹⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠐⢦⣀⠜⠀⠀⡾⠁⠀⡨⠀⠀⠸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⣿⣀⣦⠇⠀⠀⠀⠃⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠑⠠⠔⠊⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢀⡠⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⢆⢡⠀⢀⠋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣞⠃⢐⡄
⠀⠀⠀⠀⠈⡄⣏⠉⠁⠈⢢⣀⠀⣀⢀⠀⠀⡀⣀⣠⠀⠀⠀⢀⡀⡀⠀⠤⠤⠓⠀⠀⠠⠚⣄
⠀⠀⠀⠀⢘⣄⠈⠁⠀⠀⢁⣨⠄⢀⡀⣬⣥⣤⣶⣬⣭⣬⣥⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣭⣤⣬⣴⣤
⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠉⢀⣷⡊⠙⡾⠟⠛⠛⠉⠛⠟⠋⠛⠿⠛⠉⠉⠛⠋⠉⠛⠛⠙⠛⠛⠉⢻⠁
⠀⠀⠀⠀⢫⣭⣽⣛⣛⣛⣭⣭⡝⣹⢎⡙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⢇⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢦⡜⠳⡜⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣯⡼⣿⣿⣿⣴⣿⠷⣶⣄⣠⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡼⠛⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠀⠀⠀⢹⡿⠋⠉⢹⣿⠿⠋⠙⠛⠛⠛⠛⠻⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⢨⣷⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣾⣿⣶⣦⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⣤⣿⣿⣿⠏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡈⠛⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣉⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣩⣴⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣶⣦⣭⣭⣉⣙⣛⣛⣛⣛⣋⣉⣭⣥⣤⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉