Tantrum Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡐⢶⡂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠈⠀⠀⠀⠀⠈⠉⠓⠀⠀⠉⠒⢷⡐⠠⢄
⠀⠀⠀⠀⠀⠐⠋⠁⠈⠈⢈⣁⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⡂⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⣊⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠃⠀⢀⠖⠢⡀⠀⠸⠀⠀⡠⠂⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡳⠒⠤⣀⡴⠁⠀⠀⡸⠀⠀⠑⠾⠀⠊⠀⠀⠀⠀⠀⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣑⡤⣠⠜⠉⠒⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢣⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠊
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠝⠂⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣁⣀⡤⠄⢤⡄⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡤⠰⠄⢸⠒⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠈⠒⠙⢄⡑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣀⡀⠉⠣⠤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⡄⠀⠀⠐⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⢿⠄⠀⠀⠘⢄⡠⡄⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠨⠈⠀⢀⣀⠀⠀⢹⠀⠀⠀⠀⠰⢤⠤⠈⠀⠀⠀⢰⠇⠸⢕⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⡎⡉⢡⠄⠀⠠⠤⠔⠁⠰⠎⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⠊⠘⠀⠠⠐⢈⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠜⠁⢉⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⣆⣀⡴⡁⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠈⠢⠄⠀⠄⠀⠀⢀⠀⢐⡀⠀⠀⡠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠠⠀⠒⠀⠀⠀⠀⠐⠊⠡⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⣀⣀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣏⡉⠓⠒⠤⠤⠬⠤⠗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡁⠀⠀⢸⡛⣃⡀⠡⠒⠒⠂⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠬⠭⠭⠄⠐⠂⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠆⠐⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠁⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣙⡆
⠀⠀⠀⢀⣤⠤⠤⠤⠤⣄⡀⠟⠉⠁⢀⣀⡀
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠳⣄⣾⠭⣤⡽
⣰⠋⠀⠀⢠⣀⣀⣀⣤⣄⣀⣀⡘⡆⢀⣀⡤⠤⠤⢤⣀⣀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⡰
⡏⠀⠀⡀⣸⠀⢉⣉⠀⠀⠈⡉⢹⠟⠉⠀⠀⠀⠀⠀⢀⡼⠓⠲⡄⠀⣇⠀⠀⠀⠀⣶⣠⠇
⣧⠀⠀⣷⠇⠰⠚⣄⠀⠀⠾⠶⠈⣇⠀⠀⢀⡤⠖⠚⠛⠳⠤⠞⠁⢠⣼⠀⠀⢠⣤⠇⠉⠀⠀⠀⠀⠀⢠
⠘⣆⡠⣿⠀⠀⢀⣙⣀⣠⠔⢲⣄⡏⠀⠀⣞⠀⠀⠀⣠⠴⠀⠀⠀⠈⠇⠀⠀⢸⠀⠀⠀⠀⠀⡼⢆⣠⠋
⠀⠈⢣⣤⣤⡀⢯⣀⣁⣤⣖⡾⢻⠀⢶⠤⣌⠳⡀⡜⣡⢆⢰⡶⠻⣤⠀⠀⠀⠾⠀⠀⢠⠶⡼⠁⠘⠃
⠀⢠⠞⠀⠀⠉⠙⠛⠛⠯⠟⠙⠋⠀⠘⣆⠀⢀⣹⣶⣤⠋⢸⣉⡷⠿⠤⡤⢤⡀⠀⠠⠏
⢀⡏⠀⠀⣠⠔⠛⠳⣄⠀⠀⠀⠀⢀⡔⠁⠀⠘⡧⠒⠻⡤⠋⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⣠⠞⡇⠀⢀
⢸⠀⣀⣼⠁⠀⠀⠀⠘⣆⠀⠀⠀⠈⠒⢲⡆⠀⠸⡄⢰⠁⡤⢦⡳⠤⢙⠲⠤⠀⠈⡇⠀⠚⠁⠐⠓⠋⠁
⢸⠏⠉⢳⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⣠⠤⠀⠙⣾⣸⠁⢦⡐⠊⣫⡆⢸⡦⣤⡧⣄⣀
⠈⠓⠚⠁⠀⠀⠀⠀⠀⡼⠦⠤⠤⠤⣤⣤⡤⠤⠴⠶⣟⣿⠀⡭⣅⣠⠬⠽⢦⣹⢶⠃⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⢦⠀⠀⠀⠀⢀⢿⠈⠳⣷⣀⣅⣠⠤⠞⠁⢸⡟⡟⢢⣀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣰⠃⢸⠀⠀⠀⠀⢸⠼⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡅⢸⣄⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⠀⢸⠀⠀⠀⠀⡞⠀⠀⢠⣇⡀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠘⡆⠀⠀⠀⡇⠀⡴⠋⠀⠉⠙⠛⠒⠒⠒⠋⠁⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠘⡇⠀⠀⠹⡄⠀⠀⣧⠀⣇⠀⠀⡴⠛⠉⠉⠙⠲⢤⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡜⠉⠙⢋⡷⠀⠀⢀⡜⠛⠛⢙⡆⣸⠦⠤⣇⠀⠀⠀⠀⠀⠀⠙⡦⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠚⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡾⠛⢉⣡⣞⣉⣠⣬⣽⣦⣍⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣁⡨⠝⠶⠀⠀⣼⣋⣐⣿⣿⣿⡿⠟⠛⠛⠛⠻⣿⣷⣿⣾⣿⣄⠀⠀⢀⣀⠄⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⢛⣫⣿⣿⠿⢛⣻⣇⠀⠀⠀⠀⢀⣼⡛⠿⣿⣿⣿⡄⠀⠈⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣋⣭⣴⣾⣿⣿⠿⠋⣀⠀⠋⠁⠈⠁⠀⠀⠀⠋⠀⠙⠃⢈⡙⢿⣇⠀⠈⠻⡒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣶⣿⣿⣿⣿⣿⡿⠃⢴⠄⢽⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⢉⣁⠀⠹⣦⠀⠀⠉⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣶⣾⣿⣿⡟⠉⣹⡍⠉⢙⣷⣶⣄⠁⠀⠀⠸⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣻⣿⠿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣆⠀⠀⠀⣿⠙⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢿⡀⠀⠀⠘⣿⣿⠟⠋⠴⠚⠋⠉⠉⠉⠛⠦⡉⠻⣿⠀⠀⢠⡏⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠘⢷⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡾⠁⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣦⡀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⣷⣤⡀⢀⣠⡶⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣨⠆⠀⠀⠀⣠⡶⠋⢴⣶⣄⡀⠀⣠⣶⠟⠛⢷⣄
⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⢀⣾⠛⢿⡿⣿⡇⠀⠀⠀⠉⠛⠶⢦⣤⣄⣈⣁⣤⣤⠶⠛⠉⠀⠀⠈⢿⣿⠻⣿⠟⢿⣆⠀⠀⠙⢷⣤⡀
⠀⢀⣴⠶⠟⠛⠋⠁⠀⠀⢠⡿⠁⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠙⣷⡀⠀⠀⠉⠛⠛⠻⠶⣦⡀
⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢿⣄⡀⠀⠀⠀⠀⠀⡠⠀⠙⢷⡄⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⣰⡟⠁⠠⣄⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠉⠛⠷⢦⣤⣤⣼⡁⣠⣴⠟⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠃⠈⠻⣦⡀⢸⣦⣤⣤⡶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠈⠛⠻⣿⣷⣶⣶⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⣴⣶⣾⠿⠟⠛⠻⣷⣄⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠈⠉⠉⠉⠉⠙⠛⠛⣻⣿⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⣙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⣶⣶⣶⣤⣤⣄⣀⣀⢀⣿⡇⢻⣷⣀⣀⣤⣤⣶⣶⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠉⠉⢻⡟⠻⠿⠿⠀⠈⠿⠟⠛⣿⠉⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡛⢳⠒⡖⡶⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢺⡓⡖⠖⠺⡙⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡇⢜⣈⠥⣥⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⠨⣄⡇⠃⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⡠⢾⡋⠉⠉⢠⡞⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠱⡄⠉⠉⢙⡷⢦⣠⣤⡀⢀⣀⣀⣀
⠀⠀⠀⠀⣠⣴⡶⠿⠿⣛⣛⠉⠙⠲⢍⣫⠝⠶⠛⠀⠀⠈⠳⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠞⠁⠀⠀⠛⠖⠫⣾⡡⠚⠉⠉⣉⣹⢿⠿⠶⣦⣄
⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢀⣀⣀⣀⣠⣤⣤⡶⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢾⣿⠷⣦⣤⣤⣤⣀⣀⣀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣹⡶⠟⣋⣩⣭⣭⣍⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⣿⣦⣤⣤⣤⣭⣭⣭⣉⡛⠷⣾⣀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⡤⣿⣏⠛⠶⠶⣦⡶⠶⠾⠛⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣷⣬⡙⠻⠶⠶⣤⡶⠶⠟⢋⣿⣦
⠀⠙⠿⣿⣿⣶⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣴⣶⣿⠿⠋
⠀⠀⠀⠀⠈⠉⠛⠛⠿⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⡇⠀⠈⡇⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡈⠀⡔⡂⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⢡⠀⡇⢢⡀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡏⠁⠀⠉⠒⢵⣄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢱⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢃⠀⠀⠀⠀⢀⣴⣦⠀⠀⠈⢟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢦⠀⠀⠀⢸⣿⣿⣧⡀⠀⠈⠖⣛⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠳⡀⠀⠘⠛⢿⣿⣷⠀⠀⢠⠑⠛⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⢿⡇⠀⠀⠀⢢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣐⣀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⢺⣇⡇⠑⢄⠀⠀⠀⠀⠀⢸⠀⠁⡲⣽⠓⢒⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠰⣇⠀⠀⠈⣦⡀⠀⠀⢀⢎⠣⠘⠄⠼⠲⠀⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡔⠀⢉⡳⠐⢤⠄⠠⠀⠐⣇⢠⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢰⣯⠀⠐⠚⠀⠘⠀⠀⠀⠀⢀⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⣄⣀⣃⡣⠤⠒⠉⠈⣩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠁⠀⠀⠀⠀⣀⣠⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠟⢻⠍⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠘⠓⠒⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣟⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣿⣿⡇⠹⠿⣿⣶⣼⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣆⠀⠀⠀⠈⠛⠛⠷⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠰⢲⠟⢿⣿⠋⠀⣀⠐⠦⠄⠤⠀⣸⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⠨⠂⠘⠃⠀⢨⣽⡿⠓⢰⣶⣟⡏⡘⢀⡀⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⣠⣴⢶⣶⣤⣝⠉⢰⠁⠀⢏⣠⣈⠁⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣾⣿⣿⣿⣿⣿⣿⡿⣧⠇⠀⠀⠀⠀⠉⠑⠢⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢠⢋⣿⣯⣭⠅⠉⠉⠉⢉⡤⠘⣆⠀⠀⣴⢀⠒⠀⠀⢣⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡌⠸⣿⣿⣇⠀⠴⠂⣀⠀⠰⠆⠘⡖⡀⡏⠎⠀⠦⡀⢸⡄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⣿⣿⡆⠀⠋⠀⠀⠐⠀⠀⢹⠃⠈⢦⡀⠀⠈⠆⢧⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⡸⠟⠁⠀⠀⠀⠀⣤⣿⠄⢸⠀⠀⠀⠈⠀⠀⡷⠛⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠘⢌⣃⣤⣄⡀⠀⠈⠑⢂⣾⣴⣲⣾⠃⠀⠀⣇⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠘⢶⡃⠈⠀⠀⡄⢸⣿⣿⣄⣒⣊⠁⠀⣨⢵⡏⠀⠀⢰⣏⢶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠝⠀⠀⠀⠰⣸⣿⣽⠿⠿⣶⢿⣿⡅⠘⠀⠀⠀⣼⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⢀⣠⠜⠉⠀⢀⡤⣤⣤⢨⣿⡇⠀⠀⠀⣰⣫⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠙⠧⣿⣸⡏⣷⢒⣿⠟⣋⣭⠶⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⡀⢀⠀⠀⠀⠀⠤⠤⢀⣉⠂⠋⡴⢛⣥⠾⠛⡩⠞⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢳⣄⡑⠂⢀⣀⡉⠐⠒⠄⠬⠁⡛⠈⢤⠾⢋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠘⠁⠈⠑⠂⠤⣉⠙⠒⠒⡂⠀⠁⠴⠞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣤⡤⠶⠋
⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠛⠲⠶⠶⣤⣀⠘⠋⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡄⠀⣴⢛⣉⠀⢈⡧
⠀⣠⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠋⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⠏⠀⠀⠀⠀⠠⣤⣄⣀⣀⣀⣹⡶⣤⣀⣀⣀⣀⢹⡆⠀⣀⣠⣤⠶⠶⠶⠶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⣿⠀⠀⠀⠀⠀⢀⡏⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⣿⡷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⠶⠶⣦⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⡿
⣿⠀⠀⠀⢰⡆⣸⠃⠀⢀⡾⠸⠆⠀⠀⢀⡴⠃⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣏⠀⠀⢀⣼⠂⠀⠈⣷⠀⠀⠀⠀⠀⠀⣿⠙⣾⠃
⢻⡀⠀⠀⢸⣷⠋⠀⠘⠋⢡⣄⠀⠀⠀⠻⠛⠛⠁⠈⣷⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠙⠷⠶⠛⠁⠀⠰⡶⢿⠀⠀⠀⠀⣶⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠈⢧⡀⢀⣈⣇⠀⠀⠀⠀⠈⠻⠀⠀⠀⣠⡶⢶⡄⢀⡿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢰⡇⠈⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⣰⠏
⠀⠈⢳⣟⠉⠋⠀⠀⠀⣠⠶⠶⠶⠶⠛⠉⢀⣠⣿⣾⠁⠀⠀⠀⠘⢷⣄⠀⠀⢀⣴⠛⠁⠀⠀⠀⢀⣄⠀⠈⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡀⢀⡾⠀⢻⣴⠏
⠀⠀⠀⠙⣶⣴⠷⣄⡀⠻⣄⣀⣀⣤⡶⣛⣫⡿⢋⡿⠀⢸⡟⠳⢤⡄⠙⣦⠀⡞⢁⡴⢋⡀⢸⡷⠏⠻⣷⣄⠀⠀⠀⠀⠸⠃⠀⠀⠀⢠⡟⢳⡾⠁⠀⠘⠁
⠀⠀⠀⡴⠋⠀⠀⠈⠙⠛⠛⠛⠻⢿⣏⣹⠟⠳⠾⠁⠀⠀⢻⡄⠀⠀⠀⢘⣷⣤⣌⡀⠟⠁⣸⠛⠛⣶⣾⣋⣀⢀⣀⠀⠀⠀⠀⠀⣠⠟⠀⠈
⠀⢀⡾⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⢰⡾⠏⠋⢙⡿⠀⢀⡿⠞⠋⠉⠉⠉⠉⠉⠉⠙⠳⣄⠀⠀⠉⠀⠀⠀⠀⠀⣠⡄
⠀⣼⠁⠀⠀⠀⣠⡴⠛⠉⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢹⡞⠛⠉⠳⣶⠟⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣠⠞⢹⡇⠀⠀⣀
⠀⡟⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⠷⠶⢤⣤⠀⠀⠈⣧⠀⠀⣸⠃⠀⡰⣆⠘⢧⣀⡌⠻⢦⣄⣀⠀⠀⠈⣧⠀⠀⠰⠟⠁⠀⠸⠷⠶⠛⠉
⠀⣧⣠⠶⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠘⢧⡀⣿⢀⡼⠃⠈⠛⢂⠠⣤⡴⠂⠀⢭⠀⠀⠀⣿
⠀⡿⠁⠀⠀⣻⠄⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢸⣥⡴⠶⠀⠀⠈⢻⣿⣸⡃⠘⠳⣦⡈⠃⢈⣴⣛⠀⢼⣷⠶⢦⡿⠶⢦⣄⡀
⠀⠙⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣾⠟⣻⠇⠈⢉⣋⠁⠀⢨⣭⢛⣿⣤⠙⣧⣤⡷⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢹⣶⠻⣆⠐⣯⠉⠱⠶⠁⠀⠈⠁⢽⠿⠋⠹⣦⣤⣤⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣰⠿⡇⠀⠀⠀⠀⠀⠀⢀⡼⢿⡀⠈⢻⡿⢦⣤⣤⣤⣴⠶⠶⠓⠀⠀⢰⡗⢸⡆⠙⣦⣀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⣴⠏⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⣸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠁⠸⣏⠉⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠋⠉⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠙⠓⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢸⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡾⠋⠈⠉⠙⠛⠲⠶⠶⠶⠶⠶⠶⠚⠋⠁⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠸⡇⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣿⠀⢰⡏⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⣷⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣿⠀⠈⣧⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠛⠛⢻⡆⠀⠀⠀⠀⢨⡿⠛⠒⠛⠛⣦⠀⠘⣧⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢧⣤⣤⣤⠤⠴⠾⠃⠀⠀⠀⠀⢯⣤⣤⣤⣤⡤⠾⠀⣾⣭⣭⣭⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣻⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣀⡠⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⡜⠉⠀⠀⠀⠀⣀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠘⠊⠀⠀⡠⠐⠸⠀⢰⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⡴⠀⠈⡀⠀⠒⠋⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⣤⠀⠀⡼⠁⠀⠀⠀⣠⠏⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠸⣦⢻⠀⡼⠁⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢠⠘⡆⠀⠻⠘⣾⠁⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⡇⠀⠀⠀⢰⣿⣿⣿⣿⡀⢀⠀⢸⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠐⠄⠦⠀⠀⠸⠀⠀⠀⠀⠋⠀⠀⠉⠁⠀⢀⡹⠆⠓⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠔⠚⠁⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠢⠎⢀⠄⣤⣄⣈⣉⠁⠀⠀⣀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⢀⠴⠋⣰⠁⠀⠀⠈⠉⠉⠉⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠃⡄⠀⠀⠂⠀⠀⠀⠀⢁⣠⣞⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠰⠄⣀⣀⣠⠀⠀⠀⠀⠀⢫⡉⠂⡀⢈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡤⠤⡀⡏⢛⣀⣀⣀⣀⣀⣀⣀⢼⠤⡉⣹⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⠁⢑⡈⠓⢄⠸⢀⠇⠀⡇⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣟⡼⢦⡯⠤⠤⠚⡗⠚⠂⣠⢧⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣟⠺⠋⠁⠒⣒⠲⣶⡗⠋⣉⣙⣊⠧⠤⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠭⠭⠭⠭⠍⠒⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠨⣙⢳⣒⡒⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠀⠀⠉⠚⢯⡑⠒⠄⡀
⠀⠀⠀⠀⠀⠰⠛⠁⠈⠉⠉⠈⣉⡐⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠾⠓⠈⢉⡩⠜⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠥⡤⠄⠐⠒⢒⣼⣋⡀⠤⠤⠐⠂⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⢀⣀⠄⠀⠀⣀⠀⠀⠀⠀⠟⠀⠀⠀⣀⠤⢄⠀⠀⠀⢄⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡔⠀⡎⣉⠀⠀⠀⢂⡔⠉⠉⠢⡀⠀⠱⡀⢀⠎⢀⡤⠀⡇⠀⠀⠀⢳⢼
⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡀⠀⢘⠁⠑⠢⣴⡫⠀⠀⠀⣠⠃⠀⠀⠈⠋⠀⠋⠀⣰⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠁⡁⣀⠀⠀⢑⡦⠌⣒⢠⠔⠁⠉⠑⠒⠋⠀⠀⠀⠀⠀⠀⠖⠂⠒⠁⠀⢀⡀⢀⠎
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢮⠀⠀⠈⠳⡄⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠸⠗⠁
⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⢀⡱⠆⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣈⢬⣀⣘⠀⢱⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠣⠤⠔⠙⢤⠤⢿⠑⠢⣄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠐⢡⠋⠀⠨⠧⡊⢀⠅⠀⠀⠀⠀⠐⠀⢀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⢳⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠑⡲⠀⣤⠌⠅⠊⠀⡀⠀⠊⠀⡔⠁⠐⣇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣆⠀⠀⠀⢂⠀⠀⠀⠀⠀⠁⠈⡴⠁⣠⠃⠈⡀⠀⢀⡔⠢⡀⡤⣶⢀⡄⡗⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠙⢌⣻⣿⣿⣆⠀⠀⠀⢢⠀⠀⠊⠀⠰⢛⠀⡴⠁⢀⠄⠀⢠⠎⠀⠀⢹⡃⢎⠙⣈⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠙⢤⡿⢿⠀⠀⠀⠀⠑⢤⡤⡔⠁⠀⠙⢧⠢⡀⠀⣀⠇⠀⠀⠀⢐⠁⢸⡉⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡒⠂⠠⠤⠌⠉⣀⣀⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢶⡭⠴⠋⠀⠀⠀⠀⣾⠀⠸⢕⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣀⡜⠁⠙⣄⠂⠀⢀⣀⡤⠏⠐⠤⠃⠀⠀⠀⠀⠈⠀⠀⢁⠇⠀⢀⡠⢠⠇⠀⣆⠈⠍⡁⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢀⣩⠇⠘⠢⠤⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠞⠀⠀⡜⡱⠋⠀⡼⢃⠎⠀⢟⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠤⠞⠤⠈⠉⠐⠲⠒⢄⣀⠄⢆⠀⠀⠀⠀⠀⢀⠀⡫⠊⠀⢀⠞⠀⠉⠑⠺⠐⠁⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠁⠀⢁⣤⠏⠀⠀⠀⢀⡀⠵⠺⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠞⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⣣⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣄⡀⠀⠀⠀⠀⠤⠴⡒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⢥⣀⡉⠉⠓⠒⠲⠤⠶⠋⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠊⠀⠂⣨⣓⣋⡉⠥⠐⠚⢛⣃⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⡭⠭⠭⠤⠄⠐⠂⠈⠉⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⢲⡀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠸⡀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠈⠀⠙⠲⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⠏⠀⣠⣤⣄⡀⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣿⠀⢸⠃⢹⡀⠙⡦⡀⠀⠀⠀⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢈⡇⢰⡇⠈⢦⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⡏⠉⠀⠀⠈⠓⠦⣝⣆⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠉⢣⡀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠘⣎⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠘⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠘⠦⠗⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⢦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠺⣝⣦⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡈⠳⡄⡰⠋⠉⠉⠻⢿⣿⣿⡆⠀⠀⣿⢦⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠙⢄⠈⠇⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⢹⠀⠙⢶⠾⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⣿⠀⢈⡷⡄⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⢸⠀⠀⠘⣆⢸⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⣿⠲⣾⠒⡎⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠶⠤⣌⡾⢶⣤⣄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠙⢿⢤⡇⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣠⠜⡿⡯⠀⠈⠭⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⢰⣼⡆⠀⠀⠀⢀⣷⣀⠀⠀⠀⠀⢠⠆⡟⢦⠳⣄⣠⡏⠺⡶⣄⡈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡼⠈⠁⠀⠀⠀⡼⢁⢿⠓⢤⣀⡔⠁⡸⠀⡀⢱⠦⡴⢦⣄⠀⠀⠉⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⠇⠀⢀⣤⣀⠼⡁⣸⠀⠓⢫⠐⢌⠉⠁⠀⢻⠉⠐⢾⣟⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣿⣶⣤⠂⠋⢹⠀⠀⠈⡱⢍⠀⠀⠀⠀⣣⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⢸⣀⣀⠀⠓⢚⣁⡤⠔⠊⠉⠉⠉⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⣀⣀⣀⣀⣤⡴⠶⠛⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠝⠛⣻⠒⠒⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⠃⠒⠨⠽⠦⠶⠾⠭⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⠛⣆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠶⠚⠋⠉⠉⠉⠉⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⣀⡴⠃⠀⠀⠀⣀⡤⠖⣞⠉⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⠀⠀⣠⢶⠋⠀⣇⠀⣸⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣠⠾⡅⠈⣇⠀⠙⠋⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢻⠀⣠⠀⠀⢠⠟⠀⠀⠀⠀⢀⡼⠁⠀⠓⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⣿⡀⢠⡏⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⢿⠉⣇⡞⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠈⣏⠺⣇⠀⠀⠀⢸⠁⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠐⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣈⢦⡈⠀⠀⢀⡏⠀⠀⠀⠀⣾⠿⠿⠿⢿⣟⠒⠲⢤⡀⣧⣀⣀⡀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠈⠙⠗
⠀⠀⠀⠀⠀⠀⠀⠙⢌⠛⠀⠀⢸⠁⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⠤⠞⠀⠀⠀⠀⠸⣄⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡴⠩⠟⠀⡼⢲⡤⢄⣀⣉⡀⠀⠀⢀⣀⣀⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠁⢀⣠⠞⢁⡞⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⡼⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢧⢀⣬⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⣿⠛⢦⠞⡉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⢹⡷⢾⠋⠁⠀⠀⠀⠀⠀⢹⠳⡄⣸⠧⡞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣩⣵⠾⣇⢸⡖⠲⠶⡶⢶⠶⠶⡾⠛⣏⣱⠤⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⡇⠀⡬⠤⠈⢑⣄⠁⡜⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣳⡿⠦⠷⠶⠖⠋⢹⠉⠉⣀⣸⢳⡖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢼⠳⠟⠉⠉⢒⣒⣲⢶⣿⠋⢉⣁⣙⡊⣭⠤⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠭⠭⣭⣭⡭⠭⠥⠔⠒⠉⠉⠐⠒⠒⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡴⠲⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠎⣇⣮⢢⠀⠀⠀⠀⠀⠀⠇⠙⠳⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡞⢉⣠⠃⠀⠀⠀⠀⡴⠋⠃⣠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠑⠈⡇⠀⠀⠀⢸⠃⠀⢠⠏⢀⡤⠖⠛⠛⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠹⡄⠀⠀⡾⢀⡀⣾⣠⠟⠀⡀⠀⢀⣤⠀⠈⢣
⠀⠀⠀⠀⢠⢤⡤⣄⠀⠀⠀⠀⠘⣦⠀⠀⠹⣄⠀⡇⠸⢌⣉⡁⢀⡔⠳⢚⡁⠣⣤⡄⠈⢦⣤
⠀⠀⠀⠀⣟⢸⠆⢸⢤⣀⠀⠀⠀⠈⠳⣄⠀⠈⢧⣿⠀⠀⢿⠉⢹⣶⠿⠯⠀⠀⢘⣿⣿⣶⠾⠒⠛⠛⢋⣉⣉⣉⡛⠓⠦⣄
⠀⠀⠀⠀⠹⠼⠧⣎⡎⠈⠉⠓⠶⠤⢤⣌⣳⣤⡤⠾⢷⠶⠾⠷⡆⠢⠠⠈⠁⠀⣾⣝⠋⠾⣴⡖⠛⠉⠉⠁⠀⠀⣀⡤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⡀⠀⠀⢠⡴⠋⠁⠀⠉⠓⠀⠑⠤⠀⢃⢰⣾⣿⡄⢠⣨⣥⡀⠀⢹⣰⢀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠏⠙⠓⢛⣿⣭⣭⡉⢀⠀⠀⡹⣌⠓⠈⣀⡤⠿⢿⣿⡇⠀⠉⠙⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣟⠀⠀⠀⠉⣿⠀⠌⣹⠋⠉⠻⣿⣇⣀⣀⣀⣹⣦⣀⣀⣀⣈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⣹⡄⠀⠀⠀⣿⠀⣶⠋⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡎⣵⠋⠉⠩⣳⠀⡿⣸⠃⠀⣀⡠⠄⠘⠂⠀⠄⢀⠉⢿⣿⣏⠳⣄⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⣤⡲⣳⢣⡇⠀⠀⠁⠐⠈⠀⠠⠀⠀⠀⠀⠈⠉⠀⠀⠈⠳⣦⣀⣠⡴⠾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡒⠛⢰⠇⣼⡁⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠟⠁⡄⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠾⣷⣏⠣⣤⣤⣴⡶⠶⠿⠯⠙⠛⠛⠛⠉⣉⠉⣉⣀⣼⠃⢠⣼⠅⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠙⢷⡷⣤⣴⢦⣀⠀⠀⡆⡂⠀⠀⡀⠄⢚⡝⣿⠁⠀⠸⡅⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡆⡠⠙⠀⠉⠓⠄⠀⠀⠁⠀⠀⠈⠀⠀⠎⠀⠃⠀⠀⠀⣹⣄⠀⢀⣼⡆⠀⡴⢲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⡁⠀⠀⠀⠢⢄⡀⠀⠀⠀⠀⢀⡤⠖⠀⠀⠀⠀⢀⡾⠁⠹⡖⣉⣼⠃⡼⢡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⡄⠀⠀⣿⠙⢦⣀⠀⠀⠀⠈⠀⢰⡀⠐⠁⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠛⣹⠔⣫⣵⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡝⡄⠈⠿⢉⣉⡿⠀⠀⠈⠛⠲⠶⠶⠶⠾⠿⠶⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⣿⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣝⠦⠤⡞⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢲⣮⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢠⣾⡏⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣧⠀⢠⡏⠸⣆⡴⠋⠸⠤⠚⣁⢞⣀⣀⠀⠀⢀⡤⢤⣄⡀
⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠘⡟⢧⣼⠀⠀⠉⠀⠀⠀⢶⡤⠤⣍⠳⣤⠄⢠⡞⠳⢯⡴⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠀⠠⡞⣉⣽⢿⠿⠆⠀⠹⠂⠈⢧⡈⢳⡖⢛⣤⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠙⠀⠀⠀⠀⠀⠘⠁⠈⣠⣤⣴⣶⣶⣶⣤⡙⣾⢠⠏
⠀⠀⠀⠀⣤⠲⢦⣄⡀⠈⢷⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇
⠀⠀⠀⣎⡩⠽⣿⢩⣏⡓⠈⠀⠀⠀⠀⠀⠀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣤⡄
⠀⠀⠀⢿⣀⣠⣯⣙⢧⣽⣟⣀⡀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠈⣿⣿⣿⣿⡟⣾⣾⠋
⠀⠀⠀⠀⠈⠁⠀⠈⠙⠾⣽⡿⢹⢷⣄⣀⡘⣿⣿⣷⣦⣤⣤⣿⣿⣿⠟⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡇⣼⠀⣹⠷⣬⣿⣿⣿⣿⠿⠛⠛⢁⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠳⢤⣇⣀⡏⣹⢿⠶⢤⣀⣤⣾⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣯⡾⠔⣒⣩⠭⠶⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⣁⡤⠤⠶⠒⠚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣁⡤⠤⠶⠒⠒⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡠⠤⠒⠚⢉⣉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣶⣾⣿⣿⣿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣿⣿⡿⠿⠧⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠛⢻⣭⣽⣿⡿⠛⠉⠙⣦⠀⠀⠀⣼⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠤⠤⣤⣀⣀⣀⣤⠴⠏⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠬⠝⣳⣔⠒⠤⠤⣀
⠀⠀⣀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠉⠚⢏⠐⠢⢄⡀
⠀⠚⠉⠉⠉⠉⠉⣁⡒⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡆⠀⠤⣤
⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠈⠀⣀
⠀⠀⠴⠓⠈⢉⡠⠔⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠣⡀
⠀⠀⠀⠀⠾⠥⠤⠄⠐⠒⢢⣼⡋⠀⠤⠄⠐⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠉
⠀⠀⠀⠀⢀⡤⠃⠀⠀⢀⣀⠆⠀⠀⣠⠀⠀⠀⠘⡏⠀⠀⠀⡠⠤⣀⠀⠀⠠⣄⠘⡄
⠀⠀⠀⠀⣼⡖⠀⢎⣉⠀⠄⠀⢈⠔⠁⠈⢣⠀⠀⠣⡀⠠⠂⣠⠄⢘⠀⠀⠀⠘⡦⡇
⡀⣀⠀⠀⠰⡀⠀⢌⠁⠈⠲⢶⡁⠀⠀⢀⡴⠀⠀⠀⠈⠁⠈⠁⠀⡜⠀⠀⠀⠀⡇
⠉⣠⣄⠀⠀⢈⠶⠬⣕⣰⠖⠁⠈⠉⠂⠉⠀⠀⠀⠀⠀⠰⠂⠐⠈⠀⠀⢠⠀⡰⠁
⠀⠉⠀⠀⠀⢸⡀⠀⠀⠑⡄⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠔⠻⠊
⠐⠛⠀⠀⠀⢀⡽⠂⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⡀⣠⢤⡀⣀
⠀⠀⠀⢀⡔⠁⢀⣀⢠⣤⣤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡧⠠⡅⠈⡆⠄
⠀⠀⠀⠀⠈⠁⠀⠑⠦⠖⠉⠦⠴⢻⠉⠲⣄⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠰⠀⡏⢌⠀⠀⠒⢜⣀⠌⠀⠀⠀⠀⠀⠀⣂⠤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢳⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⡀⢉⠃⢠⠔⠑⠂⠀⠀⠀⠈⠄⠐⠁⠀⢱⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣆⠀⠀⠀⢀⠀⠀⠀⢀⠄⢀⡀⠃⢀⠆⠀⠀⠀⢀⡔⠐⢄⡤⢺⣆⡄⡍⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠙⢦⡽⢿⣿⡆⠀⠀⠈⢢⠀⠀⠁⠀⠋⢅⣠⠃⠀⠀⠀⢀⠞⠀⠀⠈⡇⢸⣉⠆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠙⠢⡟⡻⠀⠀⠀⠀⠑⢖⡲⠉⠀⠀⠛⠟⢢⡀⢀⡎⠀⠀⠀⠀⡇⠈⡄⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠬⣉⣀⡒⢒⠂⠀⠠⠤⠄⡀⠀⢀⠃⠀⠀⠀⠀⠘⠗⠖⢻⠀⠀⠀⠀⢸⠁⢰⠮⣵⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠤⡊⡁⢈⠦⠀⠀⡤⠤⠒⠀⠙⠞⠀⠀⠀⠀⠀⠀⠀⠄⡜⠀⠀⣴⢀⡎⠀⣬⠀⠀⣌⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠤⠼⠁⢈⡒⠒⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡜⠀⠀⡘⢱⢊⢀⡴⢡⠎⠀⠺⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣂⠯⡂⠁⠀⠉⠋⠑⠄⠤⠚⡄⠀⠀⠀⠀⠀⠀⡊⠊⠀⢀⡔⠀⠀⠀⠉⠊⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢀⡀⠠⠤⠼⠥⠤⠄⠤⠤⠐⠊⠣⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⠦⣄⣀⠀⠀⠒⠖⢻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠛⢶⢤⡄⢈⡉⢉⣉⣈⡉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢤⣁⣌⣄⠧⠭⠤⠐⢂⣉⠉⠁⠤⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢙⡆
⠀⠀⠀⠀⣀⣤⡤⠤⢤⣄⣀⠸⠟⠉⠉⠀⣀
⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠈⠙⢦⡀⣖⣋⣉⣹
⢠⠞⠁⠀⠀⡀⠀⠀⢠⣄⡀⠀⠀⢻⡁⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰
⡟⠀⠀⠀⢸⡏⠉⠛⠉⠁⠉⠛⠛⣿⡷⠚⠉⠁⠀⠀⠀⠉⢉⡷⠴⣄⠀⠸⡄⠀⠀⠀⠀⣤⠀⡏
⣇⠀⠀⣶⡼⠀⣤⠏⠃⠀⢠⣞⡁⠸⡄⠀⠀⠀⢀⣠⠤⠶⢿⣀⣠⠞⠀⣀⡇⠀⠀⢀⣀⡏⠛⠁
⠹⡄⠀⣸⠁⠀⠀⠸⠇⠀⢀⡤⣄⠀⡇⠀⠀⡴⠋⠀⠀⠀⢀⡈⠁⠀⠀⢹⡉⠀⠀⣸⠙⠀⠀⠀⠀⢠⣆⠀⣰
⠀⠙⣏⠉⡀⠀⢰⠒⠒⠚⢋⣠⣼⣾⠁⣀⡀⠙⢦⠀⢀⠞⣉⠀⣀⣠⣄⠀⠁⠀⠀⡟⠀⠀⠀⣠⣀⠏⠘⡶⠁
⠀⠀⣨⠛⠉⠳⠮⠷⠶⣾⢿⡾⢥⡞⠀⢻⡉⠓⠈⢳⣉⡚⠡⠂⡿⠥⣭⡷⠀⠀⠀⠁⠀⠀⡼⠁⠋
⠀⣰⠁⠀⠀⢀⣠⣤⡀⠈⠉⠁⠀⠀⠀⢠⠗⠀⠰⡾⣙⣻⠃⣠⠗⠚⠉⠉⠙⠉⠙⢦⡀⠈⠁⠀⠀⢀⣤
⢰⠇⠀⢀⡴⠋⠀⠀⠙⣆⠀⠀⠀⠀⢴⣃⣀⠀⠀⢻⠉⠈⡿⠁⣀⢠⡄⠀⣄⡀⠀⠀⠹⡄⠀⣀⠔⠋⣿⣀⡤
⢸⣄⠤⣼⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢸⠃⠀⠈⢧⣸⡇⡴⠉⠲⣉⣥⡤⠉⢉⠀⠀⡇
⠰⣇⣀⡸⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⠒⠛⠀⠀⣹⣯⡅⢩⠷⠈⠠⠾⣥⠺⣟⠲⡟⠒⠦⣄
⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⠋⠛⠛⠒⠒⠒⠒⠒⠒⠋⠉⢻⡼⣇⢰⠓⠦⠞⠓⠛⢳⠜⢻⣅⣀⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡼⢷⠀⠀⠀⠀⢠⡞⡇⠈⢻⠳⠴⠦⠖⠒⠋⠀⠸⣏⡏⢹⡦⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡞⠁⢸⠀⠀⠀⠀⢸⠷⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⢦⡤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⠀⣾⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠀⢀⣠⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢿⠀⠀⠘⣆⠀⠀⠀⣿⠀⣰⠋⠀⠀⠈⠉⣉⡛⠛⠋⠉⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⡄⠀⠀⠸⣄⠀⠀⢸⠀⢻⠀⠀⢠⠞⠉⠉⠉⠙⠲⢤⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠉⠉⢙⡇⠀⠀⢀⡜⠙⠛⠉⣧⢈⡷⠤⢼⡄⠀⠀⠀⠀⠀⠀⠙⡦⠤⢼⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⣦⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠉⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠞⢳⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣄⠀⢀⣄⠀⢠⡿⢦⣄⠀⠀⠀⣀⢰⡟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠙⠳⣼⡍⠻⠟⠁⠀⠉⠛⠷⣤⣿⢿⡇⠀⠉⠛⠤⣄⣀⡀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⣶⠀⢀⡟
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠰⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠆⠀⠀⠀⠀⣿⠀⣸⡇
⠀⠀⠀⠀⢹⡆⠀⢀⣀⡀⠀⣾⠇⠀⠀⠀⣤⠐⠂⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠒⢠⡀⠀⠀⢀⡏⢠⡏
⠀⠀⠀⠀⠈⣿⠾⠉⠉⠙⢶⡿⠀⠀⠀⠀⠀⢠⡄⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⠀⢱⠀⠀⢸⣄⣼⠁
⠀⠀⠀⠀⠀⡟⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠎⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⠶⠤⠴⠃⠀⢠⡞⠛⡁
⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡾⠁
⠀⠀⠀⠀⠀⠀⠉⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⢀⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠿⠋⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁
⠀⣠⡞⠳⠆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢛⣲⣶⠴⠤⠤⠤⣶⣤⡚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠞⢳⣄
⡼⠃⠈⢳⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠙⠫⣄⠀⢀⣠⠜⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⢠⡜⠁⠘
⠑⢦⣔⠋⠁⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠈⠑⢃⡴
⠀⠀⠁⠚⠳⣤⠛⠙⠧⣄⠀⠀⠀⠀⠀⣰⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣦⠀⠀⠀⠀⠀⢀⡴⠋⠛⣤⡔⠓⠋⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠱⢦⡀⢀⡶⣏⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢹⣷⡀⠀⣠⠞⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣀⠀⠀⠙⠺⣧⣀⡁⠠⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠄⢉⣠⣾⡿⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠉⢲⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⡾⠋⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⣰⠏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠱⣆⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠄⠒⠒⠒⠒⢶⠶⠒⠒⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢹⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⣾⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⠹⡇⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡟⠀⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣇⠀⡾⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢰⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⣿⢺⡇⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣶⠶⠶⠶⡶⣿⠰⡿⢶⠶⠶⢶⣾⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠤⠬⠅⠀⠀⠰⠦⣾⣾⡧⠴⠀⠀⠀⠨⠤⠌⠻⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣶⣶⣶⣶⣿⣿⣾⣶⣿⣤⣷⣶⣾⣿⣷⣶⣶⣶⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠿⠟⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡓⣔⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢍⠳⡈⠉⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠑⠀⢀⡀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠙⡄⠀⢣⠀⠀⢀⠜⠀⡈⡄⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠰⠁⢀⣸⠂⠀⠆⠀⡀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢄⠀⡋⠀⠀⢡⢀⣾⠄⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠄⠊⣾⠧⠐⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⠁⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠠⠄⠀⠀⠄⠀⠒⠘⠀⠀⡰⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⢄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⡰⢀⠂⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⢏⠁⣺⠀⢀⠦⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠠⠉⠀⠀⠀⣠⣊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡇
⠀⠀⠀⠀⢀⠔⠀⠁⠀⠀⣠⠃⠀⠀⠀⠀⠀⢀⠄⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡆⠠
⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠱⠀⠰⠀⠇⠀⣮⠀⠀⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⢟⣇⠈⣁⠇
⠀⠀⠀⠰⠞⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⠞⡰⡹⢉⠜⢂⠼⠄
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡀⠔⠂⠀⠀⠀⢸⠿⠧⢤⢠⢀⠂⠀⠀⠀⠀⠀⢀⠌⢈⠼⣠⠖⢡⣄⠄⠀⡀
⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠑⠄⠄⠉⠲⡄⣀⢐⡀⠄⠋⠁⠀⠀⠀⠀⠀⡠⠊⣀⠜⠊⠐⠶⠋⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⢣⠲⣀⠀⠀⢀⣩⠻⢴⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠡⠃⠀⠀⠀⠀⢀⠃⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⡈⠐⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢄⣴⠃⠀⠀⠀⠀⣠⠶⠚⠠⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠡⠄⡄⠀⠘⠄⠀⠀⠀⠀⠀⠀⡮⠤⠚⠶⢤⡖⠒⠙⣈⣦⣀⡎⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡁⠖⠀⠦⡂⠐⠢⡀⠀⠀⠀⠀⠀⢷⠒⣒⣒⣺⡑⠀⠀⠈⠙⠈⠸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⣀⠀⠀⠰⠊⠀⠀⠘⣄⠀⠀⠀⠀⠈⢁⠿⡧⡀⢡⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡶⠷⣿⠛⡟⠉⠉⠀⠀⠀⠀⠀⠀⢺⡰⠀⠈⡄⠈⢏
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠐⠒⠤⠂⢀⡇⠈⡥⠤⠀⢀⠀⠀⣤⠄⠀⠠⠤⠤⢶⣥⣀⡈⡀⠀⠀⠀⠒⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠠⠙⠛⠛⠛⠓⠁⠤⠤⠤⠃⠀⠀⠀⠈⠉⠉⠁⠀⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠽⠍⠀⠀⠈⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣉⣡⠤⠶⠖⠒⠒⠲⠿⠿⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣗⣋⣍⣤⠤⠤⠤⣤⡤⢔⣒⣶⡿⢿⣿⣶⣄⡀⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣻⣿⣽⣷⡀⠀⠀⠙⣻⣿⣿⡛⠁⣠⣄⠀⠠⣾⡷⠚⣩⢟⡥⢞⡽⠋⣽⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡉⠙⢿⣿⣉⢉⣿⠀⢻⣿⠟⣥⣾⠛⠛⣿⣇⣀⣠⣭⣤⣄⢿⠏⢀⣟⣠⣾⠁⢠⡿⣿⣷⣄⠀⠀⠀⠀⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣴⣾⣛⢻⣿⠋⣠⡿⠁⠐⠛⠃⠀⠀⠻⢿⡿⢿⣧⣭⣽⠇⠀⠘⠋⣡⣏⣴⠋⢀⡿⣿⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢻⡆⣻⣾⢋⣤⣶⣶⣶⣶⣶⣤⣤⣀⠃⠈⠻⠆⠁⠀⠀⢀⡾⠟⢩⡏⠀⢸⠇⣿⣧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣷⡟⣰⡟⣸⣷⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⠖⣻⠟⣰⢿⡿⢿⣥⡴⠿⢻⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠉⢽⣹⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⢿⣿⣿⣿⠀⢀⣠⣴⣿⡵⠞⢡⡾⣿⢸⣧⣀⡿⠓⠛⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠸⡏⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢰⣿⣿⣿⡇⢉⡿⢻⡟⠀⣰⡟⣀⣿⠾⠋⣈⣽⣤⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢻⡜⣿⣿⣿⣿⣿⣦⣄⣠⣴⣿⣿⣿⣿⠀⠙⣋⣿⠁⢠⣿⡟⢋⣠⣴⣿⣭⣿⣭⣙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠻⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃⡴⠞⠋⠻⣄⣿⠉⣷⠈⢸⡿⠿⣿⡟⠋⠙⠻⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠳⠦⣬⣉⡛⠛⠻⢛⣫⡵⠞⠋⠀⠀⠀⠀⠙⢋⣀⣿⡿⠿⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠉⠙⠉⠙⠉⠉⠀⠀⠀⠀⣠⣴⠶⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠂⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠤⠤⠴⠦⠤⠦⠤⠴⠼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣿⠀⠀⠀⠀⠀⢀⣼⣷⡶⣶⣴⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣿⠀⠀⠀⠀⠀⠈⠙⠉⠛⠛⠻⣶⠾⠟⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⢹⡿⠛⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⡿⠿⠿⢿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⡀
⠀⠀⠀⢀⣴⣶⣄⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⣠⣿⠟⠹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⣴⣿⠋⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⣸⣿⠃⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠈⠛⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⣰⣾⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⢻⣿⡀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠈⠻⣿⣶⣤⣤⣴⣾⠿⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⣼⣿⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠙⣿⣶⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠈⢿⣿
⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣷⣄⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣶⡿⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⣤⣴⣷⡆⠀⠀⠀⣤⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⢠⣿⣮⣿⣦⡀⠀⢠⣿⣭⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⢴⡆⠀⠀⢶⡆⠀⠻⢸⣿⣿⠺⠀⠀⠀⠈⣿⣿⡿⠟⠀⠀⣸⣿⣿⣿⡜⠀⠀⠀⠀⠰⣶⠀⣿⣸⣿⣿⣹⡆
⠀⠀⢰⣿⣿⡆⢰⡿⠛⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠉⣿⣿⡏⠁⠀⠀⠀⠀⢰⣿⠋⣿⠏⠀⠉⣿⡇
⠀⠀⠀⣿⡿⠀⠈⡇⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⢿⢿⠇⠀⠀⠀⠀⠀⠀⡿⠰⣿⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠂⠀⠀⠀⠀⠀⣀⠐⣶⣦⠂
⠀⠀⠀⠀⠀⠀⢠⠴⣿⣦⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠓⡿⡿⣶⡀⠀⠀⠀⠀⠀⠙⣿⢻⣿⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⣶⣤⣄⡀
⠀⠀⠀⠀⣀⠐⠀⣸⠁⠀⢿⣷⠀⠀⠀⢀⣀⠂⣿⣼⡏⣷⠀⠀⠀⢸⣿⡇⣠⣤⢠⣦⡄⠰⠏⠛⠷⣄
⠀⠀⠀⠀⣻⣥⠴⢯⣤⣤⣼⢼⡄⠀⠀⢘⣯⠤⣿⣿⣧⣧⠀⠀⠀⢸⣿⣧⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠐⣿⠁⠀⠀⣿⣿⡆⠈⡇⠀⠀⢺⡏⠀⣿⣿⡏⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠛⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠘⠃⠀⠛⠙⠃⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠆⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣷⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⡁⠀⠀⠀⠀⠀⣨⠙⢢⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⠉⠉⠁⠀⠀⠸⣭⣃⣾⡁
⠀⠀⠀⣤⣤⣸⣿⣇⣀⣀⣸⡿⠀⠀⠀⢰⣿⣿⣿⡏⠙⠀⠀⠀⣺⡇⠀⠀⠀⠀⣼⣿⣿⣿⣓⡀⠀⢺⣇⣀⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣬⣿⣿⣿⡇⠹⣿⠀⠀⠀⢀⣩⣿⠟⣿⡀⠀⠀⢰⣿⠉⠁⠀⠀⠀⠈⠙⢻⡿⠿⠇⠀⣾⡏⠈⣿⣿⣿⡇
⠀⠀⠀⠿⠿⠿⠿⠱⠿⠀⠀⠇⠀⠀⠀⠈⠉⠀⠀⠈⠷⠀⠘⠛⠻⠄⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠸⠇⠀⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣐⣦⣼⠭⠭⠭⣤⣴⣒⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣀⣤⢶⣾⠛⠉⠉⢹⢻⡏⠙⠓⣲⢤⣄⡀⠀⠈⠳⣶⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠖⣫⠍⠛⢉⣉⣀⣀⣀⣸⣺⣇⣀⣀⠉⠛⠴⣍⣳⣤⡀⠀⠙⢦⣄
⠀⠀⠀⢀⡟⠁⠀⣠⠞⡅⠛⠀⢠⡞⠋⠉⣿⠉⠉⠉⡟⠉⠉⢹⡏⠛⢷⡄⠙⢵⡝⢦⡀⠀⠙⢧⡀
⠀⠀⢠⠏⠀⢠⡞⠁⠀⠀⠀⢀⣟⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠙⣦⠀⠈⢷⡀
⠀⣸⡏⠀⢠⡟⠀⠀⠀⡠⠚⠉⠉⠉⠉⠛⠳⠦⠴⠋⠯⣗⠖⣉⣉⣉⣙⠳⢤⡀⠀⠀⠀⠘⣧⠀⠈⢷
⢠⡿⠀⠀⡟⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣤⣤⣭⣭⣍⣻⠓⢢⠀⠘⣧⠀⠘⣧
⣿⡇⠀⢸⠃⠀⠀⢰⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⢻⡶⠚⠀⠀⢹⡄⠀⢹
⣿⠁⠀⣾⠀⠀⠀⣾⠉⣿⣩⣍⢩⢀⣠⡤⠀⢸⡇⡤⠄⡄⢠⣄⣤⣄⡤⠄⡤⣄⠈⣧⠀⠀⠀⠘⡇⠀⢸
⣿⠀⠀⣿⠀⠀⠀⡟⠀⣿⢸⣞⢸⢸⢿⠃⠀⢸⡧⡗⢀⡿⠟⡇⡷⠋⡗⠀⡗⣏⠀⢿⡀⠀⠀⠀⡇⠀⢸
⢻⡆⠀⢸⡀⠀⠀⡇⠀⠛⠙⠘⠘⠛⠙⠃⠀⠘⠃⠛⠊⠃⠈⠉⠁⠀⠛⠋⠁⠘⠀⢸⡇⠀⠀⢰⡇⠀⢸
⠸⣧⠀⠘⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣼⠁⠀⣼
⠀⢻⡆⠀⢹⡄⠀⠷⠶⠶⠶⠶⡶⠲⠒⢶⡖⠒⠒⢲⡖⠒⠒⢲⡖⠒⠒⢶⠒⠒⠒⠚⠁⠀⣰⠏⠀⢰⠇
⠀⠀⢷⡄⠀⠻⣄⠀⠀⠀⠀⠀⣷⠀⠀⠈⡇⠀⠀⠘⡇⠀⠀⠘⡇⠀⠀⢸⡆⠀⠀⠀⠀⣰⠏⠀⢠⡏
⠀⠀⠈⢻⣄⠀⠙⢦⡀⠀⠀⠀⢹⠀⠀⠀⢳⠀⠀⠀⢳⠀⠀⠀⢳⠀⠀⠀⣧⠀⠀⢀⡜⠁⠀⣠⠟
⠀⠀⠀⠀⠹⣦⡺⢯⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣩⡽⠟⠴⠃
⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣀⡀⠀⠈⠀⣀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⡘⠈⠛⠚⠲⠟⠫⠀⠘⠋⠓⠓⠛⠊⠙⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠦⠀⠤⠤⢤⣤⣤⣤⣤⡤⠶⠖⠛⠉
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠄⢠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡄⡅⢛⡄⠒⡘⡀⠬⢤⡛⢨⢠⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣩⠐⠆⠀⠪⠇⡀⠀⢡⡁⠨⠕⠀⠰⠂⣍⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠧⡁⢼⣀⠹⣐⣍⠠⡠⡼⠁⣠⣊⠏⣀⡧⢈⠼⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠐⠃⡡⡑⣼⠷⠀⠺⣿⠀⢻⡏⠀⢿⠗⠀⠾⣧⢈⢈⠘⠂⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠌⢳⡍⠀⢊⠛⠦⣬⣇⠀⢆⣳⡄⣸⣥⠴⠛⡑⠀⢩⡞⠡⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣊⢜⣧⣤⣤⣦⣀⡀⠙⣷⡄⢸⣿⠋⢀⣀⣴⣤⣤⣼⡣⣑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠐⠁⠀⠉⠛⢷⣿⣿⣿⣿⡾⠛⠉⠀⠈⢂⠐⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⣄⣀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⣀⣠⣀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠔⠋⣉⡿⠿⠶⢿⣿⣿⣿⣿⡿⠶⠾⢿⣉⠙⠢⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⡇⠠⠞⠋⣉⡵⠟⢻⣯⣉⠙⡷⠄⢸⡦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠳⡄⠀⣿⠙⠀⠀⣀⡿⠈⣻⠀⢠⠞⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠌⠙⡓⢦⠀⢠⠗⢠⠃⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠴⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠛⠉⠉⠙⠻⣷⡀
⠀⠀⠀⠀⠀⣀⣀⣠⣤⡄⣬⣿⡇⠀⣠⣠⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⣿⣿⡅⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢐⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢰⣦⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣸⣿⣿⣿⣿⣿⣿⣷⣄⣴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢼⣿⣿⣷⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋⠝⠻⠻⡟⢉⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠀⣤⡀⢀⣀⣤⣄⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⣭⣭⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠁⠀⡀⠈⡖⠙⢶⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⣤⠀⠉⠐⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠸⠷⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣴⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡑⠀⠀⠀⠀⠀⢀⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⢖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢀⠴⠂⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣀⠀⠀⠀⠀⠀⣼⣧⠏⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣠⡄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⡇
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⠗⠂⠀⠀⠀⠀⠀⠀⠄⣀⣀⡈⣿⣇⠀⠀⠀⠀⢠
⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠻⠟⠩⠖⠂⠀⢀⡀⠀⠀⠀⠠⠤⣄⡀⠘⣿⣧⣤⡴⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⢴⡨⠖⠀⠀⠀⠋⠀⠀⢀⠀⠀⠀⠀⠀⢄⠪⡝⠛⠛⣯⢬⣭⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠉⠱⡒⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠵⠋⠀⠀⠀⠀⠀⡰⣡⣾⣆⢧⠀⠀⠀⠀⣀⣠⡤⡤⠀⢸⠀⠀⠀⠀⠐⢋⣠⣿⣿⣿⢦⠀⢦⣢⠀⠀⠀⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣷⣕⡦⠖⠚⠓⠄⣀⣀⠴⠃⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⡎⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⢀⡖⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡜⠀⠀⠀⠀⠀⠀⠁⠹⠿⠿⣿⣿⣿⡿⠁⡄⢀⡖⠋⢀⠏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣠⠄⣀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠉⡄⠐⠁⠀⠀⢨⠉⠉⠛⠛⠛⠉⠋⠁
⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢠⠀⢀⡉⠁⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣠⠃⠀⠘⠁⠀⠀⠀⡇⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣂⡄⡠⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠔⠋⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢃⠀⠀⠀⢀⣀⠀⠀⠀⢀⣇⣀⢀⡀⠡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠘⢤⡤⠚⠉⠈⠉⠒⠊⠁⠀⠉⠁⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣢⣤⣖⣚⣉⣀⣀⣀⣷⣐⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣤⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠚⠁⠈⠓⠞⠘⠀⠀⠀⠉⠓⠲⠦⠄⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠱⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⡄⠀⠀⡴⠙⣺⣿⣧⣘⣽⣦⡀⠉⠀⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠈⢦⣉⢫⣁⢨⣚⣂⡝⠻⣿⣿⣻⣯⡃⢤⣶⡂⠠⠷⡠⢄⣘⣢⢤⠀⠀⠀⠀⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣿⠛⣿⡌⢹⠀⠀⢻⣿⡟⣿⢿⡏⢹⣿⡿⡿⣿⣦⣤⣤⣉⣙⡚⠲⢤⡀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢹⡇⠈⠆⠀⠈⣿⠇⠸⠀⠆⠈⣿⡇⠇⣿⡟⢿⣿⣿⣟⢿⣶⣶⣔⡤⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢿⠇⠀⣿⠀⠸⣿⢻⣿⡸⢻⣿⣿⣿⣦⣄⠸⡝⠔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢐⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⣿⡄⠀⢿⠀⣿⡟⠀⢿⣿⣿⣿⣿⣇⠻⡄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡏⡈⠀⠀⠀⠋⠀⠀⠀⠀⠀⡿⠀⠀⢻⠃⠀⠈⠀⢸⡇⠀⠈⣿⣿⣧⢿⣿⣷⣸⡆⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠆⠡⠋⠙⠁⢀⡆⣄⠀⠀⠀⠀⠀⢀⣷⠁⠀⣼⠀⠀⠀⠃⢸⡇⠀⠀⢿⠃⢻⡘⣿⣿⣷⡅⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⡼⣳⣏⠐⠁⠀⠀⡀⠸⢿⠏⠀⠀⡼⢠⡇⢸⡏⠀⠀⠀⠀⠀⡀⠀⠠⣧⠀⠀⢸⠄⠀⡀⠘⣿⣿⣷⠀⠸⢷⠁
⠀⠀⠀⠠⠶⠋⣩⠽⠋⣁⠄⠀⢀⢄⡴⠿⠀⠀⠀⡼⠀⣸⡇⡼⢃⠀⢠⡆⠀⠀⡅⠀⢰⡇⠀⣄⣾⠀⢠⠇⠀⢿⣿⣿⠀⠀⢘⡷⡀
⠀⠀⠀⠀⠀⠉⠃⠀⠚⠓⠁⠀⣱⠟⠀⠀⡔⠀⡾⠃⢠⠋⣱⣧⢸⡄⣾⠀⠀⢰⢁⠀⠈⠀⣠⢧⡧⠀⡾⠀⠀⠸⣿⣿⡆⠀⠸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠊⣁⣠⣆⡼⣠⣾⠁⠀⠊⠀⣿⣷⣾⢣⡟⡴⠀⡿⠸⠀⠀⠐⠁⣿⠃⢸⣷⠀⠀⢰⣿⣿⡇⢠⠀⣷⡇
⠀⠀⠀⠀⠀⠀⢀⠴⠊⠑⠒⠋⠁⡰⠋⠀⠡⡧⠀⢀⠀⣴⣽⠋⠃⡞⠁⠁⢹⡇⠀⠀⠀⠀⣴⠏⠐⠁⢡⡄⠀⣾⣿⣿⠀⠀⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡮⠂⠀⠀⣾⠓⢠⠂⠀⡼⠘⠀⠀⠁⠀⢠⡾⠁⠀⠀⠀⡰⠃⡴⠀⢀⣾⠃⠀⢹⣿⡿⢀⣾⡅⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠶⠋⠀⠀⠀⠀⡞⠁⢀⠄⠀⠀⠀⠸⠃⠀⠀⠀⠘⡌⡼⠁⠀⢸⣿⢃⠄⣯⣿⠇⣸⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⢀⠌⢀⡴⠋⠀⠀⠀⠀⡀⠀⠀⢀⡀⠎⡜⠁⣴⢰⣿⡇⣾⣰⣿⠋⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠠⢊⠰⠋⠁⠀⠀⢀⡠⠊⢀⠰⠇⠘⠟⠀⠘⠁⣸⢽⠋⢰⢿⡿⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠥⠚⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣰⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡔⡹⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠀⠀⠀⠀⠀⣀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⢺⡐⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⡇
⢶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⣀⡀⠀⠀⠀⠀⠀⠀⢉⣑⠒⠘⡟⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠔⠀⠀⠀⣠⣢⠄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠁⢀⠨⡊⠑⠀⠠⣇⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⠂⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠉⠡⡂⠀⡅⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠮⠔⠃⠀⠀⠀⠀⡰⠁⠈⠌⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⠀⠀⠀⠐⣋⡴⠃⠀⠱⡀⠢⣀⠀⠀⠀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡄⠀⠈⠀⢐⠐⠊⠁⠠⠀⠄⠈⠀⡀⠔⠀⠀⠀⠀⠀⠀⢠⠹⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠇⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠈⡄⠀⠀⠀⠀⢠⢰⠀⠀⣎⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠇⠀⠀⠣⠤⠋⣀⠜⠀⠀⠀⠀⡴⡫⠃⠀⡼⠈
⣎⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠤⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡰⠀⠠⠆⠀⠀⢀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⣐⠧⠞⠁⠀⠀⠀⠀⠀⢸⡀⠀⢀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠩⠞⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⢀⣀⡀⠀⠀⢸⣄⣀⣀⠨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠑⠤⠚⠁⠀⠉⠓⠉⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡤⠀⠀⢄⠀⣸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣭⣥⣤⣤⣤⣼⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⢰⣶⡆⠀⠀⣶⡆⢰⡆⣰⣶⠀⣴⣶⡀⠀⣶⡄⢰⣦⢰⣦⠀⣶⡆⠀⣶⣶⠀⠀⠀⠀⢀⣴⣶⣶⡄⢠⣶⣶⣶⡄⢠⣦⣤⣤⡀⠀⢀⣴
⠀⢸⣿⡇⠀⠀⢹⣿⣿⣿⣿⡏⢰⣿⣿⣇⠀⣿⣿⣾⣿⢸⣿⣷⣿⡇⢸⣿⣿⣇⠀⠀⠀⢻⣿⣧⣈⠁⢸⣿⣧⣬⠀⠈⣿⣧⣤⠀⠀⣿⣿
⠀⢸⣿⡇⠀⠀⠈⣿⣿⢿⣿⠁⣼⣿⣾⣿⡄⣿⡿⣿⣿⢸⣿⢿⣿⡇⣾⣿⣾⣿⡀⠀⠀⢠⣌⣻⣿⡇⢸⣿⣏⣉⡀⠀⣿⣏⣁⡀⣸⣿⠃
⠀⠈⠛⠁⠀⠀⠀⠙⠃⠘⠃⠀⠛⠃⠀⠙⠃⠙⠁⠙⠋⠘⠛⠈⠛⢉⣛⣁⣀⡛⠃⠀⠀⠀⠙⠛⠋⠀⠈⠛⠛⠛⠁⠀⠛⠛⠛⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣶⣶⣶⣶⣤⣶⣦⣶⣽⣶⣾⣿⣿⣿⣿⠛⠛⢯⡉⢀⣄⣰⣟⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⣿⣿⡿⢿⣿⣿⠿⠿⢿⣟⠻⠿⠋⠁⠀⣦⣤⣹⣿⣿⣿⡿⠏⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣙⣽⠃⠀⠀⠀⠀⢀⣀⣘⣤⣤⣴⣶⡶⠿⠿⠛⠋⠉⠀⠀⠀⢠⡇⣀⣠⣤⡄⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠚⠿⠤⠾⠿⠿⠟⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠿⠿⠆⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⢿⣿⣿⣿⣿⣷⣦⠀⠀⢀⣤⡁
⠀⠀⠀⠀⠀⠀⠀⡤⢶⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠚⠛⢯⣿⠝⠋⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⢦⣄⠈⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣀⣀⣒⠲⠤⢀⠀⢀⡐⠚⠫⠊⢁⣤⣶⠶⣶⡀⠘⢿⣿⣿⣿⣷⣌⠳⣄
⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡴⠋⠉⠛⢿⣷⣦⣾⣧⠈⠁⣶⣤⣴⣿⡟⠁⠀⠀⠓⠀⣼⣿⣿⣿⣿⣿⣷⡈⠃
⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⣠⡤⠤⢤⡙⠿⣿⠏⠀⠉⠙⣿⣿⣿⣤⠤⢤⡀⠀⠀⢿⣿⣿⣿⣿⣿⣟⠃
⠀⣤⠞⠛⠉⠛⠶⣾⣽⣿⣿⣿⣿⡅⢀⡀⠀⠁⠚⡉⠑⢂⣾⠁⣤⡀⠀⣴⡅⢹⡌⠉⠍⣓⠻⠛⡀⢸⣿⣿⣿⣿⣴⠟⠛⠋⠉⠛⠲⣄
⢸⡏⠀⠀⠰⠶⣦⣄⠉⠻⢿⣿⣿⠇⢸⣵⡇⠘⠀⠐⣠⣾⡿⠛⠃⠀⠀⠀⠛⠛⠻⢶⣄⠀⠂⠀⠸⣶⣿⣿⣿⡟⠀⢀⣤⣴⣶⣤⠀⠈⣧
⢸⣇⠀⠀⠀⠀⠀⠻⣷⡀⠘⢿⣿⡁⠈⠋⠄⠀⠈⣵⡿⠋⢀⣤⣶⣿⣿⣿⡿⠶⣦⣄⠙⢷⡍⠄⠀⠈⠛⣿⣯⠃⣴⡿⠛⠁⠀⠀⠀⠀⣿
⠈⢿⣦⡀⠀⠀⠀⣤⠼⠿⠆⢸⠟⠀⠀⡈⠀⠈⣰⡟⢁⣴⣿⣧⣼⣿⣿⣿⣿⣤⣿⣿⣦⠈⣿⡀⠀⢳⡀⢺⣿⡼⠋⡀⠀⠀⠀⠀⣀⣼⠏
⠀⠀⠙⢿⣷⣄⠀⠙⢶⡄⠀⡀⠀⠀⣸⡇⠀⣸⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⢰⣷⠀⡧⢀⡴⠃⠀⢀⣤⣾⠿⠋
⠀⣴⣶⠏⠙⢿⣷⡄⠀⢱⣸⢳⡄⠀⠿⠇⢰⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡇⠀⠈⣻⡄⠁⣾⡅⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠈⢿⣿⡀⠘⠋⠀⣿⡀⠀⠀⣼⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡾⠀⠀⣴⣿⣧⠀⠈⠁⠀⢸⡇⠀⠀⠸⣷⡄
⠀⠀⠀⠀⣀⡄⠘⣿⣷⣤⣤⣼⣿⡇⠀⠀⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⢀⣼⠏⠸⣿⣦⣀⣀⣠⣿⠇
⠀⠀⠀⠐⠿⠁⠀⠈⠛⠿⠿⠋⠁⢿⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⡀⠀⢀⣾⡏⠀⠀⢟⠻⠿⠿⠟⠋⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⣿⣦⣧⠀⢻⡿⣿⡿⢿⣿⣿⠿⣿⣿⣿⠁⢠⣾⣡⣴⣿⠏⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⡴⠀⠀⢶⡿⠀⠀⠀⢀⡤⠖⠛⠻⢿⣦⠈⢿⣌⡓⠾⠿⠿⠶⠛⣵⡿⢠⣿⢿⡿⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⢰⣾⠃⠀⠀⠈⠀⣠⡴⠞⠉⠀⣴⣿⣷⣾⣏⢷⣌⠛⢿⣶⣶⣶⣶⣿⠟⣡⠏⣠⣾⣶⡄
⠀⠀⠁⠀⠀⢠⣶⠛⠁⠀⠀⠀⢸⡇⠙⠿⣿⣿⢿⣿⣷⣤⣀⣉⣉⣉⣤⣾⣿⣿⣿⣿⠟⠁⠀⣦
⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣽⣷⣶⣶⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢴⣦⣤⣀⣰⣶⣤⡀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣄⢠⣬⡽⠻⢿⣿⣿⣿⣿⣩⣅⣉⣻⡟⣛⡛⢠⣝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣦⣄⡀⠰⣦⣄⡀⣌⣉⠻⢿⣿⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⠾⢛⡿⢽⣿⡝⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢦⣈⡛⠿⣷⣬⣙⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣯⣵⡾⠋⣄⣴⠐⣮⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣄⣙⠻⣷⣶⣦⣽⣿⣿⣶⣦⣿⣿⣿⣿⣶⣶⣿⣿⣿⠿⣶⣿⢿⣿⣟⠅⢀⣼⢻⣮⣽⣿⣿⣹⡆
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠳⣤⣙⣿⣏⡛⢿⣿⣷⣶⣤⣽⣭⣿⣿⣿⣯⣿⣿⣿⣯⣥⣶⣿⣿⡿⠟⠉⠀⠠⠚⠁⣿⣻⣿⣿⣻⣿⡇
⠀⠀⠉⠛⠳⠶⢤⣌⡓⢦⣄⣈⡙⣿⠯⢿⣷⣛⣛⠛⠻⠿⠿⢿⣿⣛⣻⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⡟⢻⣋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠷⣶⣾⣯⣽⣿⣿⣿⡿⣿⡿⠋⣩⣭⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢶⠜⣿⠁
⠀⠀⠀⠀⠈⠙⠛⠒⠲⣶⣶⣶⣶⣿⣿⣾⣿⣿⡿⣟⣿⡷⠚⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠸⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠈⣿⣿⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⣶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⡿⢻⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠳⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠛⠛⠛⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣤⣤⣤⡴⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠓⠒⠒⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢠⠞⠳⠤⣼⣿⣶⢦⣀⢦⣄⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠙⢦⡀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣀⠀⢰⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢠⡄⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⡏⠈⣷⡟⠀⠀⠀⠀⣠⠴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⠀⠀⢻⡇⠀⠀⠀⣰⠃⠀⠀⣾⣿⠀⠀⠀⢀⡞⢛⣷⠀⡟⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣇⢀⡀⠀⠀⠀⠀⠻⠤⢤⣄⣉⡟⠀⠀⠀⣾⠀⣏⣿⠃⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠚⠛⠛⠉⠙⣌⣻⡅⠀⠀⠀⠀⠀⠀⣾⡆⠉⠀⠀⠀⠀⠧⣤⣈⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⠏⠀⠀⠀⠀⠀⢀⣀⣀⡀⠙⣇⠀⠀⠀⠀⢾⡧⠈⠀⠀⠀⠀⠀⠀⠰⣿⢨⡄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢠⡏⠀⠀⠀⠀⠀⡴⠋⠀⠀⠉⢳⡘⣦⠀⠀⠀⠀⢠⣦⣠⣴⣒⣒⣦⣄⢀⡀⠻⢟⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣧⢸⡗⢦⣦⠀⠈⠋⠁⠀⠀⠉⠉⠙⠻⣷⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠻⡜⢻⣟⠲⣤⣤⣤⣤⣤⣤⡴⠖⠋⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡼⣇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢳⡀⠀⢹⣿⣌⣉⣡⠼⠁⠀⣰⠋⢧⠀⣤⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡾⠀⠈⠳⣄⠀⠘⠲⣤⠤⠤⠤⠤⢤⡾⠃⠀⠀⠀⠀⠉⠀⠀⢀⣴⣧⣤⠼⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠀⠀⠈⠳⢤⡀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⢤⣧⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣴⢧⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢳⣀⣀⣠⡤⠖⢻⡘⣆⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠻⣄⣀⠀⠀⠀⣷⠙⣆⠀⠀⠀⠈⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⢠⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣷⣄⠀⠀⠀⠀⠈⠙⠳⣤⠏⠀⠘⢦⡀⠀⠀⠀⠉⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠉⠙⠦⣄⣀⣀⣀⣀⡤⠞⠁⠀⠈⠉⠳⠤⣤⣄⣀⣀⣴⠞⠃⠀⠀⠀⠙⢦⣸⡗⣆⣀⣀⣰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠄⠈⢹⣿⠋⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠘⠛⠻⡷⠀⣈⣉⡀⢰⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣠⣤⣶⣶⡜⠿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆⢀⣀⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣶⣄⠀⠀⠀⠘⢿⣿⣿⣿⠟⠈⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣿⣿⣿⡿⢋⣭⣍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⢋⣴⣿⣿⣟⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⡸⠿⢿⣿⣿⣿⣿⣿⣿⣟⣰⣿⡆⢿⣿⣿⢡⣿⣿⣿⡀⠀⠀⣼⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣍⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⠇⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⡇⠻⠿⠋⠀⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡏⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢫⣶⣦⡙⣿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⣿⣿⣿⣷⣌⡛⢿⣿⣷⠜⣿⣿⣿⡇⣾⣿⣿⣷⠈⠀⠀⢠⣾⣿⣿⣿⣷⣆⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣬⣭⣾⣿⣿⣿⣇⢻⣿⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣿⣿⣿⣿⠿⣿⣿⠿⠟⠃⠉⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣂⢀⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣦⣤⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠛⠛⠛⠛⠛⠛⠩⠟⢫⣷⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠉⠉⠉⠉⡿⣿⣿⣿⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⢁⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠻⠛⠛⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡠⠻⢿⠿⠿⠿⠻⡷⠻⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠂⠀⢀⠈⠀⣶⡀⢀⣄⣀⠀⠀⢀⣄⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⢰⡅⡤⡄⠀⠀⢀⠀⠀⠀⠄⠀⢐⠧⠀⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠶⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣿⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠂⠐⠈⠀⠁⠀⠄⠀⠀⠈⠀⠀⡤⠟⠉⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⠃⠀⠐⠋⠀⠀⢀⠀⠀⠀⠀⢀⡉⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⠀⢠⡈⠀⠐⠆⠀⠀⢨⡇⡀⠀⠊⠀⢠⣺⡃⠀⠀⠀⣄⣁⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠸⠋⠢⠀⣀⠀⢠⠀⠉⠙⡀⢀⠀⠞⠙⠃⠀⢠⠞⠋⠁⠀⠈⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⢆⢸⡀⠀⢀⡀⠀⠀⠀⣿⠀⠘⡇⠀⢷⡷⠧⠀⠑⠦⠔⠁⠃⠠⠀⠀⠀⢀⣰⠃⠣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⢨⢣⠀⠐⢤⡀⠀⠀⠀⠀⠸⣇⠀⠀⢀⢐⠇⡄⠀⠀⠀⠀⠀⠈⡻⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⢸⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⣌⠛⡟⠉⠋⠀⠇⠀⠀⠀⠀⢀⣴⣇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡈⡄⢼⠃⠀⠘⠁⠁⡒⠀⠀⠀⠀⣧⣀⢨⠀⠀⢀⠘⣆⠦⣤⠶⢪⠆⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⣥⣀⣿⡇⣸⡀⠀⠀⠀⢠⡀⠈⠀⠀⠀⣿⣿⢸⠀⠀⣿⠀⠙⣦⣀⠀⠀⠑⠒⠚
⠀⠀⠀⠀⠀⠀⢰⣙⣄⠀⠀⠀⠀⠉⠉⠙⠻⠿⠉⠋⠉⠉⠛⠓⣿⡇⠀⠀⠀⣼⡃⠰⡇⠀⣴⣯⣿⣿⣂⣠⡿⠂⠀⠀⠇⠡⠀⠀⡆
⠀⠀⠀⠀⠀⣦⡀⠙⠿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢰⣎⣿⣧⠀⠇⠐⠀⠀⠀⠀⠉⠉⠑⢴⡶⢂⣃⣆⠀⢀⡱⣷⠄
⠀⠀⠀⠀⠀⠙⠯⠦⣄⢵⣤⣉⣛⠓⠒⠒⠀⣁⣦⣽⣐⠄⡀⠸⠟⠻⡀⣈⣟⠿⢡⠴⣶⣺⠤⠄⡀⠀⠀⠀⠀⠈⠉⠉⠚⠥⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⢿⣿⡷⣬⣈⣛⠻⣿⠟⣛⣓⣿⣁⡈⠓⢤⢞⠢⣌⠛⡿⢧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣟⠉⢆⠀⣤⣬⠦⣤⡷⠀⠀⠀⠒⢬⡋⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⢦⣬⣧⣤⣀⣀⠀⢀⠞⡩⠀⠂⠀⠐⠋⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠷⠷⢤⣀⣀⠈⠹⣽⣖⣠⡾⣦⣰⣶⣶⣶⣦⣀⣀⠀⢀⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠶⢿⣧⣄⣸⠟⠈⠛⠉⠉⣿⣿⣀⣤⣴⣾⣷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣯⣽⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠌⣉⡁⠠⣤⠀⢠⡊⠠⢖⠀⢼⠀⣉⣦⠀⣴⠀⢠⠀⢁⣐⠂⠰⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⢰⠒⡆⠺⠇⠸⠀⠑⣂⣀⠙⠀⠈⠆⠀⠈⠀⠈⠀⠉⠁⠀⠙⠠⠜⠀⠀⢈⣀⠋⠇⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⢀⣉⠤⠶⡊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣁⠶⠊
⠀⠀⠀⠀⠀⢀⠀⣀⢀⡰⠄⡀⠌⠉⢿⣓⣲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⠂⠉⠀⠀⢢⡀⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢢⠕⠐⠢⢀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠈⠁⠀⠄⠿⣍⠤⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠐⢒⡱⠆⠠⣤⠷⣀⠜⠀⠀⠠⣀⠱⣆⠀⡰⠋⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⣀⠁⠀⠀⠐⠐⠃⡁⠀⠀⠘⣩⢿⢾⡛⣧⠀⠈⠙⠉⢃⠈⠀⠀⠀⠀⠄⠀⣇⠀⠀⠜⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠒⠀⠀⠀⠘⠃⠋⠉⣁⠀⠀⠐⠈⠈⠀⠈⠉⠀⠀⠀⠀⠀⢰⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠂⠠⠀⠆⠒⢈⡉⠆⠀⠀⠀⠘⠀⢠⠜⠇⡤⠠⠀⠄⠀⠀⡀⠀⣀⠉⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣀⡀⣀⠬⡀⠙⣳⣄⣀
⠀⠀⠀⠀⠀⠲⠀⠠⠈⠩⢁⡰⣾⣷⣄⣤⣄⢠⡼⢧⡀⣀⣀⣀⣀⣰⣏⡀⡀⠀⣱⡄⡀⠀⠀⠀⢠⠔⢉⠠⣴⣟⡛⡆⠀⠁⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠉⠡⠉⠀⠈⠉⠉⠘⡷⠀⠉⢯⣉⠉⠻⣭⠉⠍⠻⠀⠉⠣⠘⡆⢀⠜⢁⡄⠀⣎⣴⣿⠏⣷⣴⣤⣤⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣈⣥⣤⢴⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠇⠀⠀⠈⠀⢠⣸⠀⠀⠠⢤⢼⠏⢠⡋⣴⠚⣿⣃⣀⣨⠷⠾⠿⣋⠿⠆⢹⡀
⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠃⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⣆⠀⡄⠀⢜⠦⠠⠴⢀⣼⣀⣹⣿⣿⡐⠪⠙⠛⣉⣛⡛⠈⠁⠄⢐⠟⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢋⠡⠀⣠⣠⣴⠿⢇⠐⠿⣶⣴⢤⡙⢻⡿⣷⡛⠋⠛⠲⠶⣶⣿⡗⠶⣶⣤⣤⣤⣖⣤⡰⠅⠊⣹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠷⠂⠛⠛⠳⠆⠀⠤⠞⢺⠿⢦⡌⠁⠘⣓⠾⠛⠛⠁⠀⠀⠲⠀⠓⠲⠦⠤⣤⣤⣤⡤⠴⠶⠿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠉⠉⠉⠉⠛⢻⣶⣶⣿⣿⣿⣶⣾⣟⠋⠉⠉⠁⠀⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⣠⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣶⠄⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣴⠟⣿⡿⢛⣛⣃⣛⣛⣛⣛⣛⣛⣃⣛⣛⡻⣿⡟⠳⣦⡈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠙⠿⠿⠿⠿⠟⣱⣷⣜⠿⠿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣛⣛⡋⠁⠀⠀⢠⣿⢫⡍⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⢻⣿⣿⣿⢇⣤⡀⣰⣿⣿⢸⡇⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣦⣝⣛⣭⣾⡟⣱⣿⣿⣿⣬⣥⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⡑⠆⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⣿⡵⠞⠋⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠘⠋⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠙⣧⠖⠋⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠘⢦⠀⢀⣴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠲⢿⣦⠄⢀⠎⣀⣀⣸⠀⢠⡄⠀⠀⠀⠀⠀⢸⣇⣼⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠐⣻⡟⠁⠀⠉⠳⡌⠁⠀⠀⠀⠀⠀⣸⠃⠽⠀⣠⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠴⣏⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣲⣿⣀⠀⠀⠀⣠⡾⠋⠀⠀⠈⠁⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠸⣧⠀⠀⠀⠀⣠⡟⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠉⠓⠒⠒⢋⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠒⠉⠀⢸⠧⡀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣿⠀⠀⠀⢀⣤⠶⠶⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠃⠀⠀⣠⡴⠛⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⠒⢲⠏⢀⠤⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠉⠈⠁⢀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠉⢰⡋⠑⠶⢤⣀⣀⣀⢀⣀⣀⣠⣤⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠀⠀⠈⡍⠉⠉⠉⠁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠸⠧⢤⣤⣤⡔⠛⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣀⣀⣀⡟⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣸⠥⠤⠄⠙⠀⠘⣆⣀⣀⣀⣤⡤⠶⣶⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠤⢤⣴⠂⣀⣴⠏⢹⠇⡏⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡏⠀⠀⠀⠈⠉⢉⣀⣠⣏⣼⣁⡄⠀⠀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠚⢧⣬⣙⣶⣦⣄⣀⣀⠀⢉⣉⣟⣉⣀⣤⢴⣞⣱⢿⡍⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣒⠦⠷⠤⠤⠤⠤⠾⢛⣩⠽⠻⣝⣛⠷⠤⠤⠤⠤⠾⢛⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠚⠋⠉⠀⠀⠀⠀⠉⠉⠙⠛⠓⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠂⠃⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣬⣝⠒⠀⠀⣷⣤⣄⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣄⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡯⠭⠏⢙⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠈⠻⣿⣿⣿⣿⣿⡏⣷⠚⣼⣿⣿⣿⣇⡿⡤⣸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢻⣿⣿⣷⣮⡘⢫⣛⠿⣋⣬⣤⣶⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣥⣿⣷⣿⣿⣿⣿⣿⣷⣦⣴⣶⣾⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣀⣀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠀⠉⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡄⢀⡀⠨⠏⣠⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣧⣿⣿⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡋⠁⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠋⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⠁⢩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠉⠀⠀⢻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠗⢺⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣄⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣤⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⢛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⣯⣴⣶⣾⣾⣿⣿⣿⣿⣷⣿⣿⠟⠁⣿⣿⣿⡿⠃⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢘⣛⣻⣿⣿⣿⣿⣿⣿⠛⢻⣿⣯⣾⠿⠋⢡⡀⠲⣿⣿⡿⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠛⠋⠛⠙⠉⠁⠀⠀⠘⢷⠀⣿⣿⣧⣶⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⠉⣼⣷⣿⠏⢠⠈
⠀⠀⠀⠀⠀⠠⠴⠿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⣿⣿⣼⣿⡿⢁⣀⡦⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⡀⠀⢠⣹⠟⢛⣯⣭⣷⣿⣿⣿⠟⠋⠐⠒⢻⢁⡅⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣮⣄⢠⣿⡟⠛⢓⣿⡟⠀⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍⢻⡷⣝⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⣀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄
⠀⠀⠀⠀⠀⠀⢨⡿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢙⠦⠄⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡆⠀⢈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⡴⢊⠔⠈⡀⢁⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠁⠌⢠⣓⣤⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢀⣿⣿⣿⣿⣋⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⠘⡿⠟⠋⠉⠛⠉⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠁⠀⠐⠄⠓⠘⠓⠒⣚⠻⠀⠀⠀⠀⢀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠂⠀⡀⠀⠤⣚⣁⠀⠄⠀⠂⢀⣡⣄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠽⠤⠆⠀⠀⢧⡄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⠀⡠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⢀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⡄⠈⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢢⢄⡀⣀⡅⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⠀⠹⠀⢙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠴⠰⠂⠀⠀⠘⢄⡀⢠⣠⡴⠚⠉⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠈⢩⠀⡀⠀⠺⣤⠐⠁⠂⢀⠀⢤⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⢠⠗⢤⡴⠋⠋⠋⡅⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠁⠀⠀⠀⠀⡦⠠⠔
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣒⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠀⠀⠀⡂⠉⠁⠈⠁⠀⠸⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⡠⠞⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢴⠀⠀⠐⠏⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠸⡀⡠⠒⠆⠀⡠⢒⠖⢦⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⢀⡠⢄⠀⢠⠇
⠀⠀⠀⠀⠀⡇⢇⠀⢀⠔⡡⠊⢠⠃⡘⠓⠀⠀⠀⠺⡁⠱⠈⠉⢎⠉⠀⢸⠠⡇
⠀⠀⠀⠀⢠⠃⡸⣧⠃⠀⠀⠀⢁⠜⠁⠀⠀⠀⠀⠀⠱⡈⠂⠀⠈⢿⣩⠳⢀⡃
⠀⠀⣀⠤⠼⡄⣦⢨⠀⠀⠀⢀⠞⢀⠀⡀⠀⠀⠄⠀⡘⢇⠀⠀⠀⠈⡇⢫⠞⠉⠳⡀
⠀⡼⠁⠀⠀⣸⡶⠏⠀⠀⠀⡸⠀⠂⠀⠐⠒⠐⠁⠀⠁⣾⠀⠀⠀⠀⣇⣸⠄⠀⠀⢹
⠀⡇⠀⠀⠀⠜⢸⠀⠀⡤⢚⡇⠐⠀⠀⠀⠐⠀⠂⠀⠀⢿⣄⠀⠀⢸⠃⠉⠢⠀⠀⢸
⠀⠱⡀⠀⠀⠀⠀⣦⠊⠀⡸⢄⣈⢄⡀⠀⠀⠀⠀⢀⡤⠚⣄⠱⣤⠎⠀⠀⠀⠀⢠⡇
⠀⠀⢣⠀⠀⠀⠀⠘⢆⣰⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠼⠳⢥⣀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠑⠒⠶⠒⠂⠁⢘⡦⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢒⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠉⢱⠙⡖⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⢄⡀⠀⠀⠀⣀⣀⠤⠴⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣰⡇⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠒⢤⣄⣠⡇⠀⠀⠀⠀⠀⠀⠀⠋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠄⣀⡠⠤⠚⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣠⡀
⠀⠀⠀⠀⢀⣤⡴⢦⡀⣤⠀⠹⠇⠀⢀⡀⢁⡠⠀⢿⡞⢶⣤⡀⠀⢠⣤⡖⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⠛⠛⠀⠞⠛⠏⠛
⠀⠀⠀⠀⠀⠉⠀⠀⠁⢙⠀⢀⠁⠀⠈⠁⢀⡀⠀⠀⠀⠘⠿⠓⠆⠘⠛⠀⠀⠀⠀⠀⠀⠛⠷⣿⣿⠆⢀⣀⣀⠀⠀⠠⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠹⣶⣶⣶⣤⣴⠟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠒⣤⡁⢀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂
⠀⠀⠀⠀⠙⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠖
⠀⠀⠀⠀⠠⢖⡃⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⣸⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠻⠷⠍
⠐⠟⠃⠀⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠤
⠀⠀⠀⠀⠒⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠸⠟
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠠⣤⡀
⠀⠀⠀⠀⢻⣿⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⡅
⠀⠀⠀⠘⡇⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⢭
⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢠⠀⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢘⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠠⣄⢀⣠⠀⠀⠀⠄⠀⢠⣦⣤⣀⡀⠀⠀⢀⣶⣶⠄
⠀⠀⠀⠠⠈⣁⠉⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢶⣶⠄⣴⣿⠛⠛⠛⠀⠾⠻⠟⠻⠲⠄⠒⠀⠈⠛⠀⣽⣿⣄⡀⢠⠻⠟⢀⡆
⠀⠀⠀⠀⠀⠀⠀⣁⠐⠀⠾⠛⠁⠀⠀⠀⠀⠀⠈⠛⠀⣿⣿⠀⢀⣀⣀⠀⠀⠄⢠⡶⠀⠰⣄⣀⣀⣀⠀⣉⡌⠁⠸⠂
⠀⠀⠀⠀⠠⠀⠀⠁⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠛⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡶⣶⢶⠶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⢶⠶⣶⣶⢶⡶⠶⠶⠶

⠀⠀⠀⠀⠀⣀⡴⠖⡛⠉⠉⠉⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⡼⠃⡴⠋⠁⣠⠄⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢸⡇⠸⡇⠀⢸⡁⠀⠀⠈⠉⠳⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢰⠚⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠘⢧⡀⠑⢤⡀⠙⣆⠀⠀⢀⡼⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⡟
⠀⠀⠀⠀⢀⡗⠀⠀⣷⠀⡟⠀⢠⠏⠀⠀⠉⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢰⠃
⠀⠀⠀⠀⣼⠀⠀⡼⠁⣸⠁⠀⠸⣄⠀⠀⠘⣦⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡾
⠀⠀⠀⠀⣿⠀⢸⡇⠀⢻⣀⠀⠀⠈⠁⠀⢀⡼⠀⡿⠀⠀⣀⣀⣀⣀⣀⣀⣸⠇⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠘⣦⡀⠑⠦⡄⠉⠓⣄⠀⠀⠛⠉⣀⡼⠁⠀⣼⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⣄⠀⠈⡇⠀⠀⣾⠁⠀⠀⠀⣻⠦⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣇⠀⠀⠹⣄⠀⠀⠀⢿⣄⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠳⠦⠤⠌⠛⠒⣃⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠴⠖⠋⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡴⠶⣦⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠒⠒⠒⠒⠒⠒⠒⠒⠒⢿⡀⠀⠘⢷⣤⠞⠀⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠖⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣽⣿⣭⣽⣿⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⢀⣠⡴⠶⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⢉⣽⠿⠋⠁⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡅⠈⢛⣋⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠈⢻⡞⠋⠉⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣰⡟⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⡶⠂⢀⠎⣀⣤⣼⡇⢰⣦⠀⠀⠀⠀⠀⠀⢻⣤⡿⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⣹⡟⠁⠀⠈⠙⣯⡁⠀⠀⠀⠀⠀⢠⡟⠀⠇⢀⣴⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠾⣍⠀⠀⠀⠀⢀⡿⠀⠀⠀⠠⣿⣿⣇⣀⠀⠀⣀⡴⠟⠀⠀⠀⠉⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠘⣷⡀⠀⠀⠀⣠⣿⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⠀⠀⠀⠈⠛⠓⠚⢛⡽⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠓⠋⠁⠀⡿⣄⠀⠀⠀⠀⠀⢀⣤⣶⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣰⣧⠀⠀⠀⢀⣤⠶⠶⢴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠟⠀⠀⢀⣤⠾⠋⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠓⣲⠟⢀⡤⣶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠛⠉⠁⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠞⠋⢹⡏⠛⠦⣤⣀⡀⠀⠀⠀⢀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡄⠀⠈⠉⣍⠉⠛⠉⠉⠁⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⣤⣤⣤⡤⠿⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠈⣿⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣸⣯⣉⣉⠛⠂⠘⣇⠀⠀⢀⣀⣀⣠⣤⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣄⣀⣀⠤⠀⣀⡾⠛⡿⢹⠋⠉⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠙⠒⠛⠋⠀⡼⢡⡏⠀⠀⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣏⣙⠳⣤⣄⡀⠀⠀⠐⠛⠛⣻⠛⠛⢉⣀⣤⠟⣹⣟⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢄⣈⣯⣉⣛⣉⣉⣙⡷⠖⣲⣾⣿⠾⣟⣉⣉⣉⣋⣡⣿⠖⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠭⣭⠭⠥⠴⠒⠋⠉⠀⠉⠛⠒⠶⠬⠭⠭⠖⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠶⠶⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡜⠁⠀⠀⠀⠀⠀⣠⠶⢤⣀⡲⣶⣤⣀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠉⠛⠊⠙⢦⣿⡙⠲⣄⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⣶⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⢳⡀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣾⠈⠻⠀⠀⠀⠀⣠⠶⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡾⢧⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡴⠋⠙⢿⠀⠀⠀⠀⠀⡼⠁⠀⢀⣈⡇⠀⠀⠀⠀⣰⠚⠙⢦⠙⢁⣾⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⣾⢹⠆⠀⠀⠀⠀⢸⡃⠀⢰⣷⣾⠃⠀⠀⠀⢰⠇⠀⡠⢼⠂⣼⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⢧⠘⣾⡆⠀⠀⠀⠀⠀⠉⡉⠉⠉⠉⠀⠀⠀⠀⠘⠧⠼⣿⡿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠳⣌⠁⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⠀⠀⠀⠀⠀⠀⢺⡼⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢸⢧⠀⠀⠀⠀⠀⣀⣤⠤⢤⣀⠀⠀⠈⠛⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣞⣸⠀⠀⠀⠀⠛⠉⠉⠙⠛⠺⠷⠄⠀⠀⣰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠻⡶⢤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⢁⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠉⠙⣆⠀⠀⢳⡀⠀⠈⠉⠉⠉⠉⠉⠉⢹⠙⢦⡀⠸⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠉⠙⠒⠦⣄⠙⣆⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡷⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡟⠀⢀⡇⠸⡆⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠙⢦⣀⠀⠉⠓⠶⠶⠖⠋⠀⢀⡼⠁⠀⢻⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠓⠲⠤⢤⣤⠤⠴⠚⠉⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⠉⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠀⠀⠀⠀⢆⡑⠒⢎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡸⠉⠉⠉⠁⠀⡠⠂⠀⠀⠀⠀⠉⠁⡈⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠀⠀⠀⢳⠀⠀⠀⢠⠚⠉⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣉⣉⠐⠢⠎⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠃⠀⠈⠈⣹⡤⣊⢀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡈⠓⠛⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠊⢀⡝⢸⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠏⡉⢢⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⢈⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠀⢀⠏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠚⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠈⠉⠙⢃⠈⣉⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠠⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠇⠉⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠚⢁⠄⠀⢀⢀⠀⡀⠄⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀⠀⠘⡄⣉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⣉⣉⣠⢼⠦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠯⣙⣽⣭⡽⠳⣗⣓⣊⡖⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠷⠎⠓⠉⠀⠀⠀⠈⠉⠉

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



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠁⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠄⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⡀⠀⠀⠀⠀⠻⣵⢀⠔⠠⡆
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⠀⣀⠤⠴⠷⠆⠈⠛⠿⣦⡀⠀⠀⠹⣾⡠⠀⠁
⠀⠙⠿⣤⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠙⢢⣄⠈⠓⠄⠀⠀⠹⣦⢀⡀
⠀⠀⠀⠀⠉⠛⢿⣷⣦⡄⠀⠀⠀⠀⠀⠀⣀⡼⠻⢖⠀⠉⠓⢦⣠⡾⢄⠀⢹⡿⣴⣄⠀⠀⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠄⠀⣀⢀⠀⢀⡿⠷⢄⡈⠙⠲⢄⣀⣹⣷⣀⠀⠀⠻⣟⣿⣿⣷⠀⠀⠉⠉⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⣶⣿⣧⣀⡀⠉⠛⠶⣤⣼⣿⣿⣿⢦⣈⡀⠙⣏⣿⣿⡀⢀⡀⠀⠀⢦⡀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢶⣶⣿⣿⣿⣿⠃⠑⠮⡑⠀⣿⣿⣿⣦⣿⣿⣶⠀⠈⣿⣆⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⢟⠛⢻⣯⠀⠸⠛⢛⣻⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠻⣿⣿⣦⣅⠠⣭⣓⣁⣀⣰⣿⣿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣥⣛⠿⠿⢿⣧⣬⣿⣿⣿⣿⡿⠿⠗⠫⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢽⣛⠿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡑⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠦⠤⠤⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠂⢀⣰⣿⠟⢉⣭⡮⠿⠛⠁⣠⣤⡄⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢚⣥⣿⣿⠋⣠⣶⣿⠟⣠⣾⡿⠋⠀⣀⣴⡾⠛⠉⠀⠀⢠⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⣿⣿⣿⣥⣾⣿⣿⣿⣦⣽⣧⣤⣠⣾⣿⣧⣀⠀⢀⣴⣼⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣋⣽⣟⣉⣡⣿⡏⣉⣹⣿⣯⣉⣽⣿⡟⣋⣿⣿⣷⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⣿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⢀⣴⡻⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣬⡙⠻⣷⣴⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣷⣤⣙⠻⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⢶⣤⣄⡀⠀⠀⠀⠀⠐⠖⠀⢰⣿⣿⣿⣿⡆⠀⢀⡈⠋⠀⠀⠘⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣉⡹⢃⣀⡇⠀⠻⠿⠀⢠⠄
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠾⠟⠀⠀⠀⠀⠀⠉⠛⠻⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⣙⠛⣋⡴⠿
⠀⠀⠀⠀⠀⠠⡦⠀⠀⠘⡿⢿⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠛⠢⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠴⠆⠀⠀⠀⣠⣴⠛⡁⢠⣀⠀⢠⠀⣠⣖⣀⣭⣿⣷⣦⣀⡀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⠿⢿⣿⣾⣾⣿⠟⠛⠛⠛⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⢶⠆⢀⣿⡏⢻⣷⡀⠀⠻⠃⠀⢸⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⣀⣀⣠⣾⡟⠀⠀⠻⣿⣦⣤⣤⣴⣿⠏⠈⣿⡇⠀⠀⠀⠀⠒⠀⠀⠀⢹⡄⢠⠂⠁
⠀⠀⠀⣀⠙⠀⢀⠈⠋⢠⣿⠋⠻⣦⡀⠀⠀⠀⠀⠘⣿⣏⠛⠛⠿⠟⠛⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠘⡔⠢⠀⠉
⠀⠀⠘⠿⠃⠀⠄⠀⢀⣾⠏⢠⡀⠙⢿⣆⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠄⠐⠀⠀⠀⠥⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣾⣿⣦⠀⠻⢳⡀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠶⠋⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠐⣿⠋⢻⠇⠀⠈⢿⣦⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⢤⣤⣤⣤⠤⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⡄⠀⢾⡷
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣈⣃⣉⣤⣤⣤⣶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠾⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣿⠃⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠁⢸⣿⠀⠈⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠉⠛⠻⢶⣤⣀⡀⠀⠀⠀⢸⣿⢀⣠⣴⠶⠛⠋⠉⠉⠉⣹⡿⠻⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠈⠉⠛⠳⢶⣦⣼⣿⣛⠉⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⣀⣠⣤⠶⠟⠋⠙⣿⡏⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠅⠟⠃⠸⠘⠇⠇⠛⠘⠃⠀⠂⠚⠘⠉⠃⠛⠀⠘⠙⠃⠛⠀⠘⠓⠋⠛⠘⠛⠂⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠶⠶⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢴⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣖⣀⣀⡀⣸⣿⣿⣿⣿⡿⠗⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⣆⣰⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠙⠁⠀⢨⣿⠅⣾⣏⠀⠀⠀⠐⠀⣠⠘⠀⠀⠀⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⣿⣾⣿⣿⣷⣦⡀⠀⠀⠈⢰⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⠋⠹⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣀⣠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⣼⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣸⣿⣟⠹⠛⣿⠄⠀⢀⠀⠀⠀⠀⠀⢀⣼⢇⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁
⠀⠀⢠⣾⣿⠋⠑⠀⢰⢡⢺⢿⣆⣱⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡉⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠋⠁
⠀⠀⠘⠿⢿⣿⣴⣿⣿⣿⠄⣰⠾⣁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠿⡟⣂⡄
⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠐⠟⠆⣠⠣⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⡙⢧⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢽⣿⣷⠘⣿⣶⣖⣾⣟⣀⡇⠠⣾⣧⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⡿⠤⡄⠉⠳⣄⠀⠀⠙⠋
⠀⠀⠀⠀⠀⢸⣿⡏⢿⡿⠟⠉⠉⢿⣿⡄⢀⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⢚⣻⢻⣿⣿⣷⣷⣷⣶⣷⣄⠀⠈⠛⣦⡀⡄
⠀⠀⠀⠘⠀⠀⢸⠉⢶⣬⣀⠀⠀⣀⠹⠁⠘⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⢀⣂⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢠⠠⣿⣿⣿⣴⣧⣦
⠀⠀⠀⠀⠀⢸⡇⠀⡼⡇⢹⠖⢾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⡑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣿⣿⣿⣯⣿⣻
⠀⠀⠀⠀⠀⠻⠷⠒⠛⢿⡇⢰⢿⣀⡀⠀⠀⣿⠀⠀⠤⠴⠶⠆⣸⣿⣿⠋⣘⣛⣻⣿⣿⣟⠃⣿⣿⣿⠋⡙⠛⠙⠟⠻⢿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠵⠒⠶⣿⡀⠄⠀⠀⠀⢠⣿⣿⣿⢰⣿⣿⣿⣿⡿⠛⠉⢹⣿⣿⡀⠐⣳⣶⣾⣶⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⠿⠷⠾⠷⠒⠂⣰⣿⣿⠯⠤⣤⣤⠾⠋⠙⠋⠀⢸⣿⡟⣇⠀⠀⠘⠛⠿⠿⠊⠀⠀⣉⡁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⠤⣄⣀⣀⣀⡀⠀⠀⠀⠚⠛⣿⣿⣿⣿⣀⣄⣀⣀⣀⣴⣾⣯⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠻⢿⠛⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠒⠛⡓⠤⠀⠀⠀⠀⠈⠙⡛⠛⠛⢿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠙⠛⠛⠉⠛⠛⠛⠛⠛⠉⠉
⠀⠀⢀⡄⣀⠀⠠⠀⠀⡄⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠄⠠⠀⠀⠄⠀⠀⠀⠄⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠄⠀⠤⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠴⡖⢰⠀⡆⠐⠀⠀⠄⣀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠘⢄⢣⣰⣷⣼⣼⣧⣦⣦⣤⣴⣡⡞⢁⡄
⠀⠀⠀⠀⠀⢀⠠⡀⠀⠠⣤⣳⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡴⠊⡀
⠀⠀⠀⠀⠀⠀⠑⠮⣷⣬⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⢿⣿⣿⢿⣿⣈⠄
⠀⠀⠀⢀⣀⣉⣒⣤⣼⣿⣿⡿⠋⠀⢸⣿⡿⢿⣿⣿⣿⣿⣿⣷⣤⣀⡀⢸⡿⠀⠙⢿⣿⣀
⠀⠀⠀⠀⠀⠉⠩⣍⢿⣿⡟⠀⠀⠀⠀⢿⣇⠈⣻⣿⣿⣿⣿⣿⠁⠀⢠⣾⠃⠀⠀⢀⣿⣿⠿⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠠⢛⣷⣝⠻⣄⠀⠀⠀⠈⠻⣿⣿⣿⣟⠙⠙⣉⣷⣷⡿⠃⠀⣀⣴⣾⠿⠋⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠷⢦⣝⡒⠤⢄⣀⠈⠙⠻⠿⠿⠷⠿⠛⠭⣐⣲⢽⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡴⠛⢻⠶⡦⢤⠭⡥⣤⠤⢶⠖⠾⠟⠅⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢠⡆⣰⡄⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣦⡀⣩⣷⣶⣭⢻⣷⣿⣧⣾⡇⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣝⣷⣶⣿⡏⣿⣿⠱⣸⣊⢿⣿⣿⣿⣿⣿⡿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣼⣿⣿⣧⣟⣵⣿⣿⣿⣿⣮⢿⣿⣿⣿⢳⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⣿⣤⣽⢸⣿⡿⠿⡿⢿⣿⢿⣿⣿⡟⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣜⢿⣿⣯⡻⣯⣿⣿⣼⢟⣾⣿⡟⣵⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣦⣻⣿⣿⣷⡹⣿⣿⣾⣭⣽⣶⣿⡿⣫⣾⣿⣿⠏⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡙⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⢠⣄⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠛⠛⠛⠛⠲⠦⠠⠦⣄⡀
⠀⠀⠀⠀⠈⠉⠓⠷⡄⠀⠀⠀⢀⣤⠾⠛⠁⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠟⠳⣄⠀⠀⠀⠀⢀⣠⣤⣖⣋⡥⠴⠋
⠀⠀⠀⠤⠤⢤⣀⣀⡀⠀⢠⣿⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠻⣄
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⢸⡯⠀⠠⢤⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⣀⣀⣤⣤⣤⠤⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⣾⠀⠀⠛⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦
⢀⣀⣤⡤⠶⠒⠀⠀⠀⠀⣾⠉⢭⡛⠀⠀⠀⠀⣠⡴⠋⠁⠀⠛⠛⠉⣀⠀⢀⣀⠀⣨⠍⠉⠛⠛⣦⡀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠉⢁⡤⠖⠉⠁⠀⠀⠀⠀⠀⠈⠳⠟⠀⠺⠁⡞⢠⡴⠆⠀⠀⠈⠛⠲⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠞⠉⠀⠀⠀⠀⣠⠎⢻⣟⣻⠂⢀⣠⣤⣄⡀⠑⣏⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⣴⠃⠀⠀⠉⠀⠀⣾⣿⣿⣿⠏⠀⠈⠉⠁⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⣰⠇⣿⠙⠲⠤⣄⣀⣀⡀⢀⣴⠟
⠀⠀⠀⠀⢀⣠⢴⡶⠀⣾⠁⠀⠀⠀⠀⠀⣰⠏⣿⣶⣤⣀⠀⠀⢾⣙⣻⠏⠀⣀⣠⣴⠾⠋⠀⢻⠀⠀⠀⢀⣠⣤⡶⠟⠁
⠀⠀⠀⠀⢯⠖⠋⠀⠀⣿⠀⠀⠂⠀⠀⣠⠏⢰⡿⠀⠉⠙⠛⠲⠦⠤⠐⠚⠋⠉⣠⣄⣀⣀⣠⣤⡴⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⢀⣠⠴⢋⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣰⠂⠀⡿⣦
⠀⠀⠀⠀⠀⠀⢸⣏⠻⡷⠶⢤⣤⣤⡀⠀⠀⣀⣀⣀⣀⣀⣤⡴⠞⠁⠘⠁⣿⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⢧⡈⠉⢉⡉⠉⠉⠉⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹⣆
⠀⠀⠀⣴⠟⠛⠦⠆⠻⡄⠀⠀⠀⠀⠀⠙⠢⣄⠉⠛⠲⢤⣄⡀⠀⠀⢀⡿⠀⣀⡴⠻⡄
⠀⠀⠀⣿⠀⢀⣤⠞⠃⣀⣀⣀⣤⣤⣤⣤⣀⣈⣳⣄⡀⠀⠈⠙⠳⢀⣾⠷⠚⠉⠀⠀⠹⣦
⠀⠀⠀⠹⣆⢸⣷⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠘⢧⣙⠣⣤⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠷⣮⡻⢶⣄⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠙⢷⣄⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣭⣿⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⣤⣬⣄⣠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠙⠓⠶⢤⣤⣤⣤⣤⣾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⠀⢀⣠⣤⣤⣶⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣭⣭⡿⠿⠟⠛⠉⠙⠛⠻⢷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠫⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⣷⠇⠀⠀⠀⠲⠄⠀⠀⣠⠖⡀⠀⠀⢻⣟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠘⠂⠄⠚⠉⠉⠀⠀⠀⠐⠉⠉⠉⠀⠈⢹⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠄⡤⢤⠠⡀⠀⠀⠀⢀⡅
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⢂⣤⣒⣐⣤⡈⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠹⠟⡿⠿⠟⠃⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠉⡍⠁⢰
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠈⢦⡀⠀⠀⣠⠋⠀⣴⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣿⣿⣿⣿⣇⠀⠀⢉⣠⣾⠁⠀⣰⣿⣿⣿⡿⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⣿⣿⣿⣿⣧⣴⣿⣿⣿⣧⣴⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣴⣾⣶⣦⡀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⠿⣿⣿⣿⡧⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠁⠀⢀⢀⢶⢟⡽⠃⠀⢸⣿⠿⠿⠿⠿⢟⠀⠀⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠙⠳⣄⣴⣿⡏⣪⠟⠀⠀⠀⠀⣿⠶⠂⠀⠀⣾⣧⠂⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣽⣿⣦⠀⠀⢹⣏⡙⢾⣇⣀⣀⣀⠀⠀⣿⣶⣶⣶⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠊⠙⠋⠛⣿⣿⣿⡇⠀⠀⣿⣿⣄⠙⠳⣭⡉⠀⠀⢻⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣿⣿⣟⣁⣀⣼⣿⣿⣿⣷⡆⠘⣿⣷⡿⠿⣿⣿⣿⣿⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⠛⠺⣃⡌⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣏⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⡀⢶⣤⣽⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊⢁⡤⠀⠟⠣⡀⠈⠂⠉⢻⠟⠉⠡⠀⠲⠆⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣧⡬⢼⡂⢸⢁⠣⡀⢶⡀⢀⠒⠆⢀⡺⠇⠀⢠⢄⡤⠂⣉⠐⢆⡀
⠀⠀⠀⠀⠀⠀⠀⡏⢉⠘⡏⣷⡆⢸⠇⣿⣿⠟⢀⡁⠸⢿⣥⡀⣼⡿⣋⣴⣨⣷⠟⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣲⣧⣷⣿⡇⢳⣸⡿⢁⣴⠟⠛⢳⣾⣏⠙⠻⣾⣿⣷⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡻⠿⣻⡿⣼⡿⢱⡿⣿⣡⣾⣿⣿⣿⣿⣷⣯⡻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡙⢿⣿⣿⣿⣿⣿⣿⠓⣛⣟⣿⡛⠿⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⢀⣀⣀⣈⢉⣀⣠⣌⣱⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⠙⠻⠿⠿⠻⢀⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣏⣥⣀⢀⣠⠄⠀⢀⡀⣠⣴⣼⣿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣿⠟⣠⣶⢿⣯⣙⣻⣿⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⢿⣯⣭⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣡⣉⣍⣉⣩⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣟⠻⣌⠻⣿⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⢚⢿⣆⣰⣾⡿⣹⠇⠈⣿⡵⢦⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡌⢦⡙⢿⣿⢡⣷⢁⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⢇⠄⡱⣯⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⢻⡄⠘⡿⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⢻⠀⢡⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠀⠀⢸⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠘⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠻⠁
⠀⠀⠀⠀⠀⢻⠀⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⡇⢹⡀⠻⠀⠀⠀⠀⠀⠀⢠⣧⣴⠆⡀
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠟⠀⡆⠀⢀⠀⠀⠀⠀⠘⣿⣅⣿⢿⣧⢸⡇⢠⡇⠀⠀⠰⠀⠀⣸⣿⠉⣠⠃
⠀⠀⠀⠀⠀⢸⡄⠀⡿⠂⠀⠷⠀⠀⠀⠀⠀⠀⠀⣿⢹⡟⣶⣿⢛⣷⣸⣇⠀⠀⠀⠀⡀⣿⡏⢠⠇
⠀⠀⠀⠀⠀⠀⢉⣾⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⢰⣿⢸⡇⡛⢿⢇⢻⣿⣿⠀⠀⠀⠀⠙⣿⢷⡎
⠀⠀⠀⠀⠀⠀⢺⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⣷⠈⣷⠆⠂⡸⢷⡄⣏⠀⠀⠀⠀⠀⠹⣿⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣧⢨⡇⠀⠀⠀⠾⣧⢻⡆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⠀⠀⠀⢸⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿