Eco Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣀⠀⠀⠀⠀⢀⣴⣿⡿⢛⣽⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡄⠀⢠⣿⠟⣡⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡜⣿⣿⣿⡄⡾⢃⣾⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣌⠻⣿⡇⡰⠿⠿⠛⠛⠉⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠈⢣⠃⠀⠀⠀⢰⣏⡁⣰⠋⠉⢠⡏⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⣧⡤⠹⢤⣤⠘⠧⣤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠒⠀⡖⠁⡆⣴⠩⠆⡖⠉⡆⡜⠉⠃⠘⠐⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠈⠒⠀⠁⠀⠁⠈⠂⠁⠈⢀⡜




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠲⠐⡀⠆⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡁⢙⠁⠁⠀⠈⡔⠊⠀⠀⠀⠀⠀⠀⠐⠀⢐⡀⠉⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣾⣩⣏⠠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠥⠄⠠⠄⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢐⠀⡠⠂⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠐⠚⠌⣲⡀⣱⠀⠀⡀⡀⣀⠀⠀⠐⠲⠶⠒⢶⠃⠀⠀⠃⠀⠀⠀⠀⠀⡀⢀⠀⠔⠀⢀⠀⡊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠠⠠⠄⠃⠀⠀⠀⠀⠈⠒⠾⡟⣁⡴⠐⠙⠉⢉⠶⠠⡀⠀⠀⠘⢸⠀⠀⠀⠠⡀⠀⢀⡀⠀⠀⠀⡀⠀⠀⡠⠊⢀⠀⠄⠀⠤⠈
⠀⠀⠀⠀⠀⢰⠀⠈⣳⠀⠀⠀⠀⠀⠀⢠⡴⠟⢋⡡⠀⠀⠂⣀⡤⣀⠈⠛⢄⡀⢸⠀⠀⠀⠀⠄⠀⠀⠈⠁⠒⢈⡈⢁⣈⡀⠀⠐⠀⠠⢠⠄
⠀⠀⠀⠀⠀⠈⠞⢻⡷⠀⠀⠀⠶⡾⠋⠁⡄⠂⠀⢈⣠⠔⠋⠀⠀⠈⠙⠢⣄⠈⠻⢇⡀⠀⠀⠈⠢⡁⠀⠄⠐⢮⠹⠉⣏⣜⢹⣓⠶⠂⠁
⠀⠀⠀⠀⠀⠀⢀⠀⢷⠀⠀⠈⢿⣡⠗⠂⣁⡤⠖⠋⣀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠲⢤⣈⠑⠢⢄⡀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⡄⠈⢧⠀⢐⢈⡀⠔⡊⠁⠀⠀⢊⠀⡀⠀⠀⠀⢀⠄⠠⠑⠀⠀⠀⠙⠉⠲⠤⣸⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠑⢤⣁⠀⠀⠁⠀⠀⠀⢠⠿⠟⠀⠀⠀⢠⡸⢗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠢⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣈⡉⠒⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠓⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⢠⣯⣁⣒⢒⡲⠶⠠⠤⡀⠀⣴⠠⡶⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢀⠀⠘⠀⠀⠀⠀⠉⠑⠒⠒⠒⠀⠉⠀⠀⠀⠀⠨⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁⠤⠠⠦⠇
⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠄⠂⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⡦⡶⢲⠀⠀⠀⠀⠀⠀⠀⠤⠢⡀⠀⠀⠠⠀⡖⡖⠠⠖⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠁⠄⣠⠀⠘⠀⠒⠈⠀⠀⠐⣠⢤⠤⠐⠀⠀⣿⣤⣧⢼⢾⠀⠠⠠⠀⠀⠀⡀⠀⠀⢦⡀⠀⠖⠀⠆⣏⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠰⣼⢁⡀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢸⠀⠀⠠⠰⠀⠀⠀⠀⠈⠉⠀⠀⡅⢫⠀⠀⠢⢠⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠁⠹⢤⡀⠰⣿⣾⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢸⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡃⠸⣀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠋⠙⠉⠛⠉⠚⠉⠛⠓⠋⠒⠐⠒⠚⠒⠊⠒⠁⠀⠀⠐⠀⠐⠘⠃⠀⠄⠄⠉⠤⠢⠒⠀⠀⠤⠠⠔⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠌⠇
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠗
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣪⡖⣀⡙⠛⡆⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠏⣿⡏⠀⠐⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠈⠉⠓⠯⠽⠿⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡆⠲⡄
⠀⠀⠀⠀⠐⡀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠁⠂⠀⠀⣼⣿⣷⣾⣿⣶⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⠂⠀⠐⠐⠀⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠛⠛⢹⡏⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⢀⣲⢒⡒⡖⣆⠀⠀⢈⢠⠄⠆⠀⠠⠒⠄⠀⠔⠢⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄
⠀⣞⣖⣰⣂⣰⣸⡆⠀⠈⠘⠄⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠇⠈⠂⠀⠠⢊⠀⠐
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣟⠋⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⢀⢀⡀⢀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⡀⠘⣄⢉⡄⠁⠉⠀⠀⠐⡉⠀⠀⠀⠅⠐⠸⠁⠃⠀⠚⠈⡄⠀⡱⣁⡀⠐⡀⠀⠀⠀⢠⠂⠀⢓⠠⠀⣘⠀⠀⢹⠀⡂⠨⠔⠁
⠀⠀⣤⢀⡤⠈⠃⠠⠟⡼⠢⠁⠈⡆⢲⠎⠀⠐⢸⠤⠂⡸⠂⠠⠳⡀⢁⠀⠀⢀⠄⠀⠀⢀⠸⠀⠀⠈⠒⢄⠈⠢⠤⠊⠤⣲⠀⢀⣄
⠀⠀⣀⢈⡰⠒⣀⠐⢤⡥⠔⢀⡀⡇⠠⠁⠀⠀⡀⠄⠀⢓⠐⠂⠐⠁⠀⠑⢠⠊⠀⠼⠀⡇⠀⠇⠀⠀⠀⠸⠀⠰⢤⠀⢢⠆⠂⠄⠋
⠀⠘⠀⠀⢸⠐⠁⡀⢀⠂⠐⠃⠀⠈⠤⠤⠤⢄⢠⢠⠀⡠⡪⠀⠂⠈⠂⢀⠚⠀⠀⣆⡄⠈⠰⠀⠀⢀⠀⠀⡀⠰⠦⠀⠐⠀⠰⢀
⠀⢸⠀⠃⢸⠐⠐⣁⠤⠦⢀⡑⠂⠉⠛⣻⡛⠛⠀⠘⠀⠐⠁⠁⠀⠀⣐⠄⡀⠠⣊⡀⡇⢀⠀⠢⠀⠊⠀⢀⠹⠀⠘⠣⠄⠠⠱⡦
⠀⠐⠀⠀⢸⠀⠌⠄⡂⠀⢢⣈⠂⠀⢀⠃⡄⠀⠀⠟⠀⠂⡄⠀⠀⠀⠀⢉⡇⢈⣒⠀⡆⡁⠋⡁⠀⠀⢆⡣⣚⠄⠈⢦⣀⣠⠜⠋
⠀⢰⠤⢐⢸⠀⠀⢢⠆⠉⢳⠋⠨⠀⠀⠢⠁⠀⠀⠆⠁⡐⡀⠀⠀⠀⠀⡨⠀⢐⣊⠌⢃⠈⠊⡔⡎⢷⣦⠄⡀⠀⠠⠔⠬⠁⠀⠐
⠀⢠⠀⠃⢰⢸⠋⠚⠂⠀⠓⠋⠁⢠⠲⢠⠀⠀⠀⡇⠀⠀⢀⢢⠀⠀⠂⠀⠀⢐⣶⠁⠈⠀⢀⠀⣇⢠⡟⠀⠃⣠⢀⣒⣀⣠⣀⡅
⠀⢘⠀⠠⠂⠀⡁⠀⠀⠛⠀⢀⡂⠈⠟⠚⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣿⣘⣆⠀⡤⠦⠂⠇⢠⣤⡤⡇
⠀⠀⠉⠉⠁⠀⢠⣍⣭⣭⣥⣀⣤⢤⠈⠀⠀⠀⠈⢭⠉⡁⠈⢩⡭⠂⢩⠍⣂⠂⠭⠐⠀⠀⢸⣈⣹⣙⣼⠀⡈⢀⠄⠒⠠⢉⠁⢀
⠀⠀⠘⠶⢖⠀⠹⣄⣀⣀⣀⣀⠀⢹⡇⠀⠀⠀⡐⠑⠊⠠⠄⠐⠊⠀⠠⠌⡄⠈⠀⢁⠁⠀⠈⠈⡿⠉⠸⠀⢠⡃⠀⠀⠀⠐⢉⡆⠁
⠀⠀⢈⡆⢨⠀⢢⡽⠰⡎⢀⣡⠀⠉⠃⠀⠀⠀⡈⠀⢀⡁⠈⠀⡁⠀⡁⢌⢀⠀⠉⡀⢀⠀⠘⡉⠧⠁⢙⠀⢂⠈⠀⠀⠀⠀⣠⡀⠆
⠀⠈⠈⢀⡘⠀⡮⠲⠮⠥⠉⠉⠀⠌⡐⠀⠀⠄⣁⠤⢠⠀⠠⢕⠊⡄⡄⡌⠡⠠⠹⢐⠁⠀⡠⠀⠀⠀⠂⠘⠀⠀⠉⠍⠩⠉⠄
⠀⢀⣢⠀⠀⠀⠈⠀⡰⠀⢀⠀⣀⠈⠀⠀⠀⢄⡠⠢⠁⠐⠣⠊⠦⡣⠡⠃⠠⠄⠇⠁⠆⠀⠘⠀⣠⠂⠔⣤⡀⠀⡀⠁⢀⠀⡄
⠀⢨⠼⣎⠆⠝⠕⡜⠁⠄⠀⡾⣄⡽⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠉⣢⠃⠈⡄⠐⡄⠀⡎⠀⢡
⠀⠀⡔⠚⢸⠀⢤⠑⠐⡆⠈⠁⠀⠀⡁⠁⠀⠀⢘⣂⠠⢨⡱⢍⡆⡆⡧⠄⠀⠞⠐⠀⡀⠀⢀⠐⠮⣋⠁⢀⠴⢓⡔⢰⠀⠃⠀⠰
⠀⠀⠃⠀⠨⢀⠀⠀⠀⣢⠀⢋⠀⢈⠀⡰⠦⢀⡁⠁⠪⠓⠀⢂⠋⠀⠑⡱⢀⠔⠒⠢⢤⠀⠀⠉⠐⠂⢀⣄⡀⢒⠊⠉⢰⠀⠀⡇
⠀⠀⠄⠀⠀⠀⢜⡀⠀⠙⠀⠤⣄⠀⢨⠊⠀⡀⢳⡀⠀⠄⢂⡸⠀⠁⡌⠀⡺⠀⠀⠀⠀⡆⠀⠀⠀⠘⢷⠀⡅⣹⠷⠀⠀⠈⡆⠐⠄
⠀⠀⡁⠀⠀⠁⠊⠓⠀⡅⠀⠅⠂⠐⢨⡀⠀⠀⠀⣣⠀⠀⠘⠡⠐⠠⠀⠀⢪⠀⢸⠄⠀⡇⠐⡈⢃⠂⠀⠁⠉⠡⠘⢅⠈⠀⢅⡀
⠀⠀⠀⠁⡀⠈⠉⠉⠈⡀⠂⢀⢰⠆⠸⠧⠐⠂⠉⢤⠀⢈⠤⢔⡰⢰⠄⢄⠈⠁⠚⢐⠚⢁⠐⠤⠦⠊⠀⠔⢤⠀⠀⠹⠂⣄⠀⠀⠄
⠀⠀⢀⡖⢣⠥⠂⡀⠀⡸⠠⢎⡰⠀⠁⠀⡀⠴⣓⠏⢠⣮⢴⢀⣀⡀⠂⠍⣯⡄⠐⠀⠀⢁⠔⠀⠰⡄⠀⠖⢁⠔⢄⠀⠘⣛⣺⣛⡄
⠀⠀⠸⠞⠋⡀⠀⠀⠊⠠⣄⡀⢡⠀⠔⠁⡈⠀⢩⠀⠈⠏⠚⢀⡀⡀⠀⠂⠍⠀⠀⠀⠀⠮⠤⠤⠀⠙⠂⠐⠩⠭⠩⠂⠈⠳⢏⡓
⠀⠠⠁⠠⠀⠁⡁⠀⠀⠠⣈⠩⠂⠀⠑⠪⡀⡀⠀⠀⡀⢸⠀⠈⠈⠀⠈⢐⡆⠀⢠⢤⠀⡈⠞⠓⠓⠛⠀⠈⠉⠉⠉⢀⢔⠡⢢⡀⠂
⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠈⠀⠀⠁⠀⠉⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠐⠀⠁⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠁⠢⡀⠤⠄⡀
⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠄
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠈⠀⠀⡀⣀⢆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢑
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⠄⢂⣿⡄⠀⣘⡐⢢⣀⠄⠄⡈⠄⠀⢨⢀⡄⠴⠀⠀⠀⠉⠉⠈⠦⠤⠆⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠇⠀⠀⢠⠇⠁⠈⠃⢠⣿⡄⠠⠢⠸⠿⡃⢠⠂⢋⠻⠀⢈⠀⣓⠫⡇⠀⠣⣾⣷⡄⠀⠀⡀⢸⣷⡆⠀⠌⠁⠓⢢⠠⠂
⠀⠀⠀⠀⠰⠀⠀⠈⠲⡀⠀⠂⠼⠟⠁⢀⠀⠀⡰⠀⡠⠄⠤⠜⠂⠓⠚⠠⠜⢄⠀⠀⠨⠙⠃⠀⠈⠀⡀⠙⠃⠈⠀⢀⠋
⠀⠀⣠⠆⠴⣆⡀⢀⣀⣨⠦⠀⠀⠀⠀⢀⡠⠊⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⡡⠊⠀⠀⠀⠦⠰⣤
⠀⠀⠿⠀⠴⡀⠉⠈⠀⠀⠀⠀⠈⠉⠁⠀⡓⢄⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠼⠙⠂⠰⠂⠀⢉⠑⠂⠠⠔⢀⠠⠤⠛
⠀⠀⠀⠀⠀⠈⠀⠒⢐⠆⠀⠀⠀⠀⠀⠀⡇⠀⠈⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠒⠒⡁⠀⡄⠀⠀⠀⠀⠀⠐⣀⣀⡀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠀⠪⣑⣤⣀⡀⠀⣀⠠⠖⠧⠈⠀⠀⠡⢤⠁⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠒⣤⣀⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⡁⠀⠀⠀⡀⠠⠀⠀⠣⠀⠉⢱⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠉⢀⠀⠒⠲⠊⠀⠃⣀⢀⣀⠁⠀⢀⠒⠚⠈⢆⠁⠑⠄⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠠⢹⠀⠀⠀⠀⢀⠠⠠⡀⠀⠀⠀⡀⡃⡀⠀⠠⢁⠋⢢⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡈⠀⠀⢠⠃⢸⠀⠀⢀⠀⢅⣀⡠⠃⠶⡀⡐⠈⢆⢉⡠⠅⠔⢂⣘⠁⡠⠁⠀⠀⠀⠀⠁⠐⡀
⠀⠀⠀⠀⠀⢰⢀⠀⢠⠃⠀⢸⠀⠀⠈⠀⠀⣀⣀⣤⠀⠘⡆⠀⠀⡇⠀⡠⠎⢳⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠐⡀⠀⢰
⠀⠀⠀⠀⠀⠦⣄⣈⣓⣤⠀⢸⣉⣉⣙⣢⡑⠤⢀⣈⠢⠤⠈⠂⠤⠇⠊⠁⣇⣜⣉⠭⢣⣴⣓⣒⣒⡆⠀⢀⣔⣋⣁⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠐⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠠⢀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⢘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢈⠀⠠⢄⣒⠢⡶⢀⣂⠤⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠀⠀⢀⠔⠈⠐⠀⠑⠈⠀⠐⡄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠑⡀⠇⠀⢡⠀⢀⠎⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠐⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠙⠀⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⡔⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠈⠁⠀⠀⠀⠀⠀⠴⠶⢦⣀⣤⡄⡤⡄⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠠⠂⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢀⠀⠀⢧⠀⠀⠀⢀⡴⠋⢸⣀⠀⣇⠇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⢤⠄⠀⠈⢣⡀⢰⣏⣀⡄⠸⣤⠄⠏⢦⠸⣤⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⣀⣀⢀⣀⠀⠀⠀⠀⠀⡀⠀⡀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠸⠂⠀⠀⠀⠂⠀⠐
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠆⠀⠀⣧⡀⢠⡎⣇⢯⠀⢹⡏⢹⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠸⣿⡌⡟⢻⠈⣣⠘⡇⢸⣏⠀⢀⠆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠐⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠐⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⣠⣴⣾⣿⣿⣷⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣠⣤⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢐⣯⣶⣿⣿⣿⣿⠟⠱⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠰⢟⣫⣿⣿⣿⣿⡿⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠉⣳⣿⣟⣛⣛⣛⢭⠀⠀⠀⣐⣿⣦⠀⠀⠀⠀⠀⠀⠘⠻⣯⡾⠿⠿⠿⠿⠟⣫⣶⣶⣝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⠿⠟⠀⠀⠀⠀⣼⣯⣌⣽⣧⠀⠀⠀⠀⠀⠀⢰⢏⡀⠀⠀⣀⣴⣿⣿⣿⠏⠰⠦⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢾⠀⠈⠃⠦⣠⣄⡀⠀⠸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣦⣟⡿⠿⣿⣿⣏⠀⡀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⢿⣿⣿⡖⠀⠀⠀⣻⣿⡿⠀⠀⠀⠀⠀⠀⢿⢸⣿⣿⣿⣅⠀⠀⢉⣿⣿⣿⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⣿⡟⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠘⣆⢻⣿⣿⣿⡀⢀⣾⣿⣿⣿⠇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⣻⣀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡻⢿⣧⣿⣿⠿⢟⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⣠⣶⣿⣿⣿⣿⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢘⣵⣾⣿⣿⣿⡿⢋⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠋⠉⠛⠛⢉⣉⣶⣿⣿⠟⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⢀⣤⣴⣿⣿⣿⡿⠃⠉⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣼⠛⠛⢿⣿⣇⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⡆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣮⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⢀⣴⡆⠀⠀⠀⠀⠀⢤⣾⠿⢿⣤⠀⠀⠀⠀⠀⠰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡖⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⢀⣾⡯⠁⠨⣛⡁⠀⠀⠀⠀⠀⠸⣷⣤⣼⠷⠀⠀⠀⠀⠀⠀⢻⣿⣿⣲⣾⠟⠀⠀⠀⠀⢀⣤⣬⣃⢿⣿⣇⡀⠀⠀⠀⠀⢹⣿⣿⣿⣤⡄
⠀⠀⠸⡔⢦⡄⠘⣻⠃⠀⠀⠀⠀⠀⠀⣈⣹⣉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣃⣉⡀⠀⠀⠀⠀⠘⠻⢿⣿⡏⠙⠛⠁⠀⠀⠀⠀⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠈⠛⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢀⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠐⣿⠢⠟⠁⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣦⠀⠠⡄⠀⠀⠀⠀⠀⢠⡙⡴⠒⡲⣔⢡⠀⠀⠀⠀⢸⠷⠶⠾⠆⠶⢿⡄
⠀⠀⢰⣤⠐⣿⡃⠀⠀⠀⠀⠀⠀⢤⠸⣆⣿⣤⡞⢀⠀⠀⠀⡞⠁⠘⣀⣄⠀⠛⠄⠙⡄⠀⠀⢒⡸⡅⠀⠘⣸⢐⠂⠀⠀⠀⢸⣛⣛⣛⣓⣛⣛⡇
⠀⠀⠀⠙⢃⣿⡇⠀⠀⠀⠀⠀⠀⠸⡷⢿⡿⠿⠧⡟⠀⠀⠀⠙⠦⠔⠁⠁⠀⠑⠤⠞⠁⠀⠀⠀⠔⣩⢓⠛⡑⠆⠀⠀⠀⠀⠀⠉⢩⣽⣯⡍⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⣆⡼⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⣼⡋⠛⠛⣴⠂⠀⠀⠀⠀⠀⠀⡿⠿⣿⡃⠀⠀⠀⠀⠀⢈⢱⡃⣴⡀⣳⣉⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣦⣦
⠀⠀⠘⠀⡧⠶⠴⣏⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⠀⠀⠀⠀⠀⠀⠀⠔⢳⡙⣱⠓⠄⠀⠀⠀⠀⠀⢰⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⢸⡉⠁⠈⣻⠃
⠀⠀⠀⢸⡇⠀⢸⡟⠆⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠴⠋⠀⠀⠀⠀⠀⠀⠀⠓⠶⠖⠃

⠀⠀⢀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢸⠥⠶⠌⣇⠙⣷⠀⠀⠀⠀⠀⢮⡹⣄⡜⣡⠂⠀⠀⠀⠀⠀⡤⢼⠤⢼⠤⡄⠀⠀⠀⠀⠀⢐⣾⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣷⠂
⠀⠀⢸⣷⣶⢶⣿⠀⢸⠀⠀⠀⠀⠀⢰⠙⣦⡊⢱⠀⠀⠀⠀⠀⠀⡇⠈⢀⣬⠀⡇⠀⠀⠀⠀⠀⢸⡟⢤⠜⢿⠀⠀⠀⠀⠀⢸⣿⣧⠀⢀⣀⠑⡀
⠀⠀⣸⣿⣤⣾⣟⠢⠜⠀⠀⠀⠀⠀⡨⢎⣀⣙⢮⡀⠀⠀⠀⠀⠀⣇⠀⠛⠋⢀⡇⠀⠀⠀⠀⠀⠸⣷⣶⣶⡿⠀⠀⠀⠀⠀⠘⠟⠀⠀⢿⣿⠟⠁
⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠠⠤⢤⡄⠀⠀⠀⠀⠀⠀⣀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠸⡭⠭⠭⢵⠀⠀⠀⠀⠀⠀⠀⢸⠴⠒⠀⠀⠀⠀⠀⢑⣖⠢⠾⢿⡃⠀⠀⠀⠀⠀⠀⡔⠁⠈⢂
⠀⠀⡇⠀⠀⡈⠀⠀⠀⠀⠀⠀⡠⠸⠤⡄⠀⠀⠀⠀⣼⡫⠏⣷⢾⣷⣿⠙⡆⠀⠀⠀⢰⠈⢷⡞⠀⠁
⠀⠀⢡⣀⣀⠇⠀⠀⠀⠀⠀⠀⢇⣀⣀⡇⠀⠀⠀⠀⠈⠛⠚⠋⠀⠉⠓⠛⠁⠀⠀⠀⠘⢄⣀⣀⡸⠁

⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠒⢄⠀⡀⠀⠀⠀⠀⢀⠠⠤⣀
⠀⠀⣀⣼⡄⡀⠀⠀⠀⠀⠘⡄⡈⠤⠤⢆⢀⠇⠀⠀⠀⠀⡆⠤⣀⡨⢳⠀⠀⠀⠀⠀⠀⡠⠔⣒⣠⠖
⠀⠚⠊⢸⠉⠲⠀⠀⠀⠀⠎⡰⠁⠰⠶⠊⢣⢱⠀⠀⠀⠀⠐⠄⠉⠠⠃⠀⠀⠀⠀⠀⣠⠖⠛⠁⠀⢀⠃
⠀⠀⠀⠎⠆⠀⠀⠀⠀⠀⠁⡗⢹⠀⡄⢸⢩⠉⠀⠀⠀⠀⠀⢛⣁⡘⠀⠀⠀⠀⠀⠸⠃⠀⠒⠒⠂⠁
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⣠⢤⡠⢤⡄⠀⠀⠀⠀⠀⠀⡠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢢⢀⣅⠀⠀⠀⠀⡠⡤⡀⡠⢄⠀⡠⠤
⡞⢁⣀⠁⠈⢉⠑⡄⠀⠀⠀⠰⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢰⡭⠀⠀⠈⢳⡀⠀⢸⣾⣿⣿⣿⢿⣿⠺⢇
⠉⠳⠟⠉⠙⠒⠉⠁⠀⠀⠀⠀⠓⠄⠠⠔⠁⠀⠀⠀⠀⡒⠛⡖⡅⣥⢨⠈⠀⠀⠈⠉⠉⠉⠛⠛⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠁

⡰⠊⠉⠑⠖⠉⠑⡄⠀⠀⢀⠠⠀⡆⠐⠂⠄⡀⠀⠀⠀⠀⢀⠔⢁⠑⣄⠀⠀⠀⠀⠀⢀⠆⢉⠄⠁⠄
⢇⠀⠉⢷⣞⡉⢀⠇⠀⠀⠣⠒⠁⠐⣦⢤⠀⣵⠀⠀⠀⣀⠼⡖⠁⠣⣤⡁⠀⠀⠀⢀⣨⡀⠜⠠⠘⡸
⠀⠑⢄⠀⢀⠤⠊⠀⠀⠠⠤⠀⠀⠀⠈⠈⠑⠁⠀⠀⠀⡎⠐⢣⡤⠮⠀⢸⠀⠀⠀⠀⢄⠙⡳⡶⣊⠠

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠛⠒⠮⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⡴⠋⠁⠀⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣴⡟⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢦⠀⠀⠙⢿⣿⣿⡿⢻⢹⣽⡻⣿⣿⣿⣿⠿⠁⠈⠉⢙⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣿⠇⠀⠀⢰⣿⣿⣿⣿⠿⢿⣟⣛⠿⠭⣿⡏⠉⠛⠻⢄⡱⡄⠀⠀⠹⣟⢎⠎⠓⢗⠥⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⡀⢸⣿⠀⠀⠀⣸⣿⠟⠁⢀⣀⣉⠨⠯⣤⢄⣀⡀⠀⠀⠀⠀⡝⠙⣄⠀⠀⠘⣮⠃⢋⢹⠡⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⣿⣯⣻⡇⠀⠀⠀⣿⢃⠔⠊⠁⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⣀⠎⠀⠰⠿⣆⠀⠀⠈⢷⠚⠛⠉⠙⠳⣄⠀⠀⠀⢠⣤⣶⣾⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠁⠈⠁⡇⠀⠀⠀⡿⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⣯⣔⡼⡄⠀⠀⠈⢧⣄⠀⠀⠀⠈⢻⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡔⠀⠀⠀⣾⡗⠉⠀⠸⡄⠀⠀⠘⡆⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠋⠓⢄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠌⠀⠀⢠⠞⠁⠘⠦⡀⠀⢳⠀⠀⠀⠸⡀⣀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⠙⠢⢄⡀⠀⠀⢣⠀⠀⠀⠸⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠌⠀⠀⡴⠳⣄⠀⠀⠀⠀⠀⢈⣧⠴⠖⠚⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⢳⠖⠾⠤⠤⠤⣤⣇⣀⣀⣀⣀⣀⣀⣀⣚⣌⣀⣀⣞⣀⡀⠬⠷⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡋⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢈⡷⢤⡀⠀⠓⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⣠⠊⠀⠰⠯⠤⣄⣼⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠰⡋⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡣⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡹⠖⠉⢹⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡘⠒⠒⠲⠦⠤⠤⡄⠀⢀⠞⠈⠉⠀⠀⣀⠤⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠧⣀⣀⣀⠀⠀⠀⢥⠀⠙⠢⣄⡖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⢳⡀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒⠒⠄⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣒⣒⣒⣓⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣯⠈⣽⣿⠿⠋⠀⠀⢀⣤⣬⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣤⣾⣷⠀⠉⠀⠀⠀⢠⣀⣟⣸⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠋⠈⠀⠀⠀⠀⠀⣴⠿⠻⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣷⣤⣤⡾⣿⣿⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢶⡀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡿⠟⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⣿⣿⣷⣄⡀⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⡟⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠂⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠠⠀⠀⡠⠄⠀⡄⠄⡄⠀⠀⠀⠀⠄⠀⠀⡀⢀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠄⡀⡀⠀⢀⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢤⠼⡗
⠀⠀⠀⠁⠈⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⠠⠀⠤⡀⠄⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠐⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⠄⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠀⠂⠐⠂⠉⠀⠆⠘⠀⠂⠐⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠂⠀⠂⠀⠈⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠐⣀⠀⢇⡂⠘⠉⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠐⠛⣁⠀⠀⠀⠁⠀⢠⣦⡄⠉⠀⢸⢀⠀⠈⢠⣤⡁⠀⠀⠀⠈⡀⠐⠀⠀⠆⡀⠀⠉⠃⢠⡴⠂⢤⡔
⠀⠀⠀⠀⠀⠀⠲⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠆⣀⡃⢰⠈⢈⢀⠀⠀⠀⠘⠃⠀⠼⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠺⠂⠠⣤⢀⡀
⠀⠀⠀⠀⠨⠂⢀⡼⣷⡀⠀⠑⠰⠀⠀⠀⢀⠈⢠⣸⣆⣀⠀⡵⢸⠀⠄⢄⠦⠀⠀⠀⠀⠀⢀⡄⠀⠀⡄⡆⠀⠸⠞⠀⠘⠃⢠⣿⣷⣿⠀⠳
⠀⠀⠀⢀⠀⠀⠈⢏⣀⣠⡀⡂⠀⣀⡆⢠⣾⣌⡄⣘⣿⣹⣶⡇⣬⣰⡤⠘⣫⣅⣄⣴⣠⣦⣤⡷⡖⠀⣽⣷⣗⣴⣴⢶⣔⡄⠀⣩⢸⣿⡇⣡⡦⡄⡀
⠀⠀⠀⠈⠾⠰⠿⠾⠷⠿⠷⠿⠿⠿⠧⠿⠿⠿⠷⠿⠿⠽⠿⠷⠿⠿⠿⠿⠿⠿⠏⠭⠿⠿⠿⠷⠿⠻⠟⠿⠿⠿⠿⠼⠿⠧⠧⠿⠿⠿⠿⠿⠧⠧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡿⠋⠉⠹⣿⣿⣿⣿⣶⣦⣄⣠⣴⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣿⡄⢀⡴⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣤⣤⣴⣾⣿⣿⣿⣿⣷⣤⠀⠀⢸⡀⠐⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⣴⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣷⡀⢸⡅⠀⢀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢛⡻⠋⠱⠀⠀⠀⠀⢹⣿⣿⡇⠘⣇⠀⢀⠀⢁⡈⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⢳⠀⠀⠀⠀⠀⠀⣸⢯⣿⡇⠀⠻⠂⣸⣤⡶⠀⠀⣘⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣶⠋⣿⣿⠉⠇⠀⣶⣾⡋⠀⢠⠚⡿⠧⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠘⠃⠀⠀⠀⣀⠠⠀⠘⠷⠀⠀⣤⡾⢋⣼⣿⠃⠘⠆⠐⣻⠿⠃⠀⣸⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⣤⣀⢻⠃⣠⣾⣿⣿⡆⣦⢀⡄⢻⡗⠀⠀⢉⣩⢠⡾⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠉⢹⡀⠉⢹⣷⡾⠟⠉⠻⢿⣿⡀⢹⣤⠴⡃⣰⣇⣈⣧⣿⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠀⠀⠀⠂⠀⣾⠇⠀⠋⠁⠀⠀⠀⠀⠀⠈⠀⠈⢧⡴⠇⢿⣀⣩⡶⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢾⣆⠀⠀⠀⠀⠀⣀⣄⡀⢀⣿⣇⣀⣀⣹⣍⣀⣩⡿⠋
⠀⠀⠀⠀⠀⠀⢠⣼⣧⠀⢄⠀⠀⠘⠀⠀⠀⢀⣀⣴⣿⡄⠀⠀⢀⣾⣿⣿⢷⡟⠋⠙⠋⠹⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢾⡇⠀⠀⠀⢂⠀⠂⣙⣿⣿⡇⠀⠀⣼⣿⣿⡉⠀⠀⠼⠄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣷⡀⠱⢣⣏⣤⣾⡿⣿⣿⠁⠀⠀⣿⣿⣏⠁⠈⠀⢤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣛⣿⡗⣿⣫⣽⣿⣿⡿⠃⠀⠀⠀⣿⣿⡿⠇⠀⢸⠘⢖⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣵⠀⣾⣇⣸⣗⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡐⠞⠷⢶⣤⣀⣠⣤⣤⣴⣿⣿⡿⠿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠋⠀⡀⢻⠠⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣆⣀⠐⢡⣀⣤⣼⠏⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣿⡿⠋⠀⠀⠀⠀⢿⣧⠀⠀⠠⠄⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠤⣄⠀⠀⠀⠀⠀⡠⠔⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠔⠒⢒⡬⠖⠒⠒⠒⠾⣵⠒⠒⢄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡀⣠⠋⠀⠀⠀⠀⠀⠀⠈⠳⡄⢨⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⢠⣤⡀⠀⣀⠀⢠⣤⡀⢹⠋⠀⢸⣳⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠚⠁⡜⠈⡇⠈⠛⠁⢸⠀⠀⣠⡏⢞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠹⣤⠃⣠⠖⢳⠊⠀⠀⡇⠙⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡑⠒⠒⣾⠁⣀⠏⠀⠀⠀⠳⢤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⢺⣀⡵⡄⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢸⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠋⠉⢢⡀⢸⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢦⡀⠀⠀⠀⠈⠉⠒⠒⠲⡄⠀⠉⠒⠲⠤⠒⠊⣡⠜⢢⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⣄⠈⠓⢤⡀⠀⠀⠀⠀⠀⠳⡀⢀⠀⠀⢀⡴⠊⠁⢀⡜⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠢⡄⠀⠉⢦⠀⠀⠀⠀⠀⠈⠛⠀⡴⠋⠀⠀⡴⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠇⠠⡡⠰⡹⠀⠠⠀⡎⠐⠁⢺⠰⠈⠉⢢⠂⠀⠰⡱⢘⠅⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠆⢰⠶⠔⠂⠢⠖⠶⠀⠆⠐⠢⠰⠰⠴⠄⠶⠆⠆⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠚⠉⠉⠛⢦⠉⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⠃⠀⠀⠀⠀⣠⠞⠉⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢠⡴⠚⠛⠃⠀⠀⠀⠀⠀⠀⠸⣦⣍⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⢀⡴⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣴⠃⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠉⠙⠳⡴⠖⠒⠦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡼⠋⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⣦⠀⢸⡇⠀⠀⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠶⣠⠞⠉⠽⢤⠀⠀⢀⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢘⣧⢸⠃⠠⣄⣿⠀⠀⢸⡇
⠀⠀⠀⠀⡴⠚⠋⠁⢠⡤⠶⠛⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⠘⢧⡟⠀⠀⠈⣿⠀⠀⠀⢳⡀
⠀⠀⠀⡼⠁⠀⠃⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⣯⠀⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷
⠀⠀⠀⠳⢤⢤⡄⠀⠀⠀⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣿⠐⡇⠀⠀⠀⠀⣿⠀⣠⠆⠀⣸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠶⠆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣿⠀⢻⡀⠀⠀⠀⣿⠞⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠈⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠂⣿⠰⠶⠻⢦⣀⠀⣿⢀⣀⡴⠋
⠀⠀⠀⠀⠀⢀⡿⠀⡖⠘⢦⣄⣀⠀⣠⠶⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀⣀⣀⣀⣈⡁⣿⠈⠁
⠀⠀⠀⠀⠰⠯⠥⠞⠁⠰⠯⠭⠥⠤⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠉⠉⠉⠁⠀⠀⠉⠁⠟⠘⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠠⣤⠀⣤⡄⠠⡤⠘⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠦⣤⠴⠒⠀⢲⡶⢄⠀⠯⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢀⣤⡀⠀⠀⢸⡇⣸⠃⠀⠀⣠⡔⢲⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠉⠙⠛⠛⠉⠀⠀⠀⠘⠧⠞⠉⣖⢻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⡆⠀⠀⠀⠀⠀⠀⠀⠰⠆⠠⣀⠀⠀⠀⠀⠀⠈⠓⠶⠃
⠀⠀⠀⠀⠀⠀⢠⡏⠀⡀⠀⢠⡇⠀⣀⣴⠄⠀⣀⣤⣤⣤⣀⠈⠙⢦⡀⠠⣀⠴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠈⣧⣎⢀⣠⠞⠀⠈⡽⠹⢠⠾⣵⣧⣼⣬⣯⠷⣄⠀⢳⠐⣿⠀⠀⠴⠓⢒⡶⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⢠⡇⠀⣯⣤⣯⣤⣼⣤⣼⣤⣼⠀⠘⡇⠸⠄⠀⠀⢰⡋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣣⣀⣜⠀⡀⣇⠀⢳⣀⣿⣀⣼⣀⣼⣀⡼⣀⢸⠃⠀⠈⢓⣶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡾⠭⣤⠭⣶⠃⠘⣆⠀⠙⢬⣧⣽⣰⡧⠟⠁⣿⡯⠆⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⡖⣇⠁⣿⠈⣸⢲⠀⠈⠓⢤⡀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⣦⢤⡖
⠀⠀⠀⠀⠀⠀⠀⠁⣼⠓⠿⠚⣧⠈⠀⢀⠤⢄⡀⢈⣁⣀⠀⣠⠤⣄⢀⡜⠉⣽⣹⣏⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⠞⠉⣉⣩⣉⠉⠓⣄⡿⠀⠐⠛⢳⣰⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡞⣵⠒⣺⢳⡀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢧⣈⣻⣁⣸⠃⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠈⠉⠉⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢿⣦⠀⢀⣴⣿⣿⣿⣿⣿⣶⣤⡀⣤⣶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠈⣿⠀⣸⣿⣿⠉⢿⣿⣿⣿⣿⣿⣾⣿⣿⠁⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠃⠀⢻⡿⣿⣄⠈⣿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⡏⠉⠛⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣯⣍⡛⠷⠋⢻⣿⣿⣿⣿⣧⡀⠀⠸⣧⣀⣀⣿⡿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠌⢹⣿⣉⠙⠓⢺⠛⠻⣿⣿⣿⣿⣷⡀⠀⠈⢿⠛⠋⠐⠶⠶⢀⣠⣾⡆
⠀⠀⠀⢠⡀⡀⣤⣦⡄⣀⣤⡤⡲⣧⣿⣾⣟⡖⣿⣿⣤⠄⣠⣖⠴⠋⢻⣿⣿⣿⣧⣀⣯⣐⣆⣀⣐⣰⣼⣿⣾⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣷⣤⣿⣿⡿⢛⣛⣿⣿⣿⣧⡿⠿⠶⠒⠛⠁⠀⠀⠀⠛⠻⢿⣿⣷⣿⣿⣋⡭⣁⠙⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣿⣿⣷⣽⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣴⣤⣤⣤⣶⣦⣠⣶⣤⣤⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠙⠆⠀⠀⠹⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⢠⠶⡄⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠂⠀⠂⠐⠀⠀⠀⢠⠋⠀⠹⣄⣭⣀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠹⡄⠀⠀⠈⠀⠁⠄⠁⠄⠀⠀⠀⠀⢻⡀⠴⢃⡟⠀⠈⢳⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣰⣂⡏⠀⠀⠐⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠉⠛⡙⢤⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢢⡀⢹⠉⠀⣠⠤⣦⠀⠀⠁⣀⣤⢤⣤⣤⣀⠀⠀⠚⠁⠀⣤⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣙⣶⡃⢸⠀⣾⢡⠀⣼⠀⣠⠮⣵⣇⣸⣇⣹⣬⠷⡄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠀⣸⠳⠚⠁⢰⡇⠀⣟⠀⢸⠃⠀⣧⠀⢹⠀⢸⠓⠦⣄⣀⣀⣀⡤⠖⢻⠂
⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⣤⣽⣾⣥⣤⣤⠀⠸⡏⠉⣏⠉⢹⡏⠉⡿⠉⢹⠁⢸⣀⡴⠋⠀⠀⠈⠙⢆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠻⡖⢺⡗⢲⠗⣶⠏⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠋⢩⠍⠩⠉⣧⠀⠀⠈⠓⠻⠾⠷⠟⠋⠁⠀⠐⢷⠦⢤⣈⣀⣀⣀⣠⡤⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠈⠓⠦⣤⣿⣬⣯⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢶⡶⣄⠀⠀⠀⣹⡟⠁⠀⢈⣧⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡵⠚⣧⠞⣇⠀⠀⠀⣇⠀⠀⠉⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣋⣹⠆⠀⠘⢀⡀⠀⠀⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣉⣻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⢱⠀⠀⠀⠄⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠁⠀⠀⠐⠢⣀⠊⠀⠀⠈⠀⠘⡤⠀⠐⠠⠬⢀⠀⠈⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⠐⠂⠈⠀⢂⠀⠈⠂⠦⠀⣂⠀⠔⠀⠀⠘⠑⠰⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠈⡀⠀⠀⠀⠃⡀⠀⠴⣦⣸⠀⠀⢀⡜⢀⠀⠂⢀⠀⡠⠔⠂
⠀⠀⠀⠀⠀⢀⠘⠦⣤⣄⠀⠀⠀⠀⡀⠀⠄⠘⡺⠠⠜⠖⠈⠉⠀⠐⢂⡐⠀⢣⠌⣁⠈⠂
⠀⠀⠔⠢⢀⡠⢄⠀⠄⠊⠱⣔⠀⠁⠠⠐⠀⠁⡔⠒⠀⠁⠀⡆⠤⠀⠀⠧⡔⠁⠀⠀⢀⡡⠠⠄⠀⠄
⠀⠀⠀⠀⠑⠀⢂⠰⠒⠒⡠⡏⠀⢅⠀⡠⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠦⡚⠋⡡⠀⠈⢀⡀⠀⠀⡄
⠀⠀⠀⢀⠀⠀⠇⢀⣀⡠⠓⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠤⠀⠔⢉⠈⠙⢂
⠀⠀⢨⠀⡰⠲⠴⠶⠘⠀⠀⠀⠔⠀⠀⠀⠒⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⠀⠘⠀⠄⢁⣉⡉⠲⡀⠀⠀⠀⠔⠈⣈⣉⠳⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠈⠀⣿⣿⣿⡆⢰⠀⠀⠘⠀⣿⣿⣿⡇⢐⠀⠁⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠄⠀⡀⠁⠀⠙⢄⠙⠛⠛⠁⠂⠀⠐⠈⢄⠙⠛⠛⢁⠈⠈⠐⠤⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠇⢠⠀⠲⠈⡀⠀⠀⠀⠀⡈⠉⠀⠈⠀⡀⠸⠐⠀⠐⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢄⠀⡨⣅⠂⠀⠀⠀⠑⠄⠀⠀⠄⠀⠀⠀⠀⢪⡥⡀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠢⢀⡀⠀⠀⠀⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠡⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠄⠁⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢨⡀⠀⠀⠀⡠⠎⠀⠂⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠏⠲⠇⠱⣄
⠀⠀⢀⡤⠒⠒⠤⡀⠀⠀⢀⡇⠀⢀⠀⠀⠀⠈⢑⠒⠦⢄⡀⠀⠀⢀⠤⠒⠒⢤⡀
⠀⠀⡎⢰⠋⠉⠲⣌⡦⠊⠁⠲⠀⠈⠀⢠⠀⢀⠈⢠⠀⣀⠈⠓⢴⣡⠞⠉⠙⡆⢱
⠀⠀⢳⡘⢄⠀⡠⠊⠀⠀⠐⠀⢀⠈⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⡠⢃⠞⠀⠀⠀⠀⢀⣠⠤⠴⢒⣆⣤⠤⢤
⠀⠀⠀⠙⠢⡝⠁⣠⠤⠤⠤⣄⠀⠄⠀⢁⠀⠐⠀⠀⢀⡠⠤⠤⠤⣀⠈⢫⠔⠉⠀⣠⠴⠒⠉⢁⠀⠈⠀⠀⠀⠄⠀⠛⠒⣤
⠀⠀⠀⠀⡜⢀⠎⣠⣶⣿⣷⣦⡱⡄⠠⠈⠀⠄⠘⢠⢋⣴⣿⣿⣶⡌⢳⠀⢳⠒⠉⠀⠂⠀⠀⠁⠀⠀⡀⠀⠀⣀⠀⠀⠀⡑⠦⡀
⠀⠀⠀⢸⠁⢸⠀⣿⣿⣿⣿⣿⣧⠷⡖⠉⠉⠉⢲⠦⣾⣿⣿⣿⣿⣿⢀⠇⠸⡀⠀⠠⠄⠀⠈⠁⠀⠀⠠⠀⢀⡀⠀⠀⣀⠀⠀⠈⢫⡒⠢⣄
⠀⠀⠀⡇⠀⠈⢣⡙⢿⣿⣿⡟⠁⠀⠑⠒⣤⠖⠊⠀⠈⢻⣿⣿⠿⣃⠞⠀⠀⡇⠠⠄⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⡀⠀⠱⡀
⠀⠀⢸⠀⠀⠀⠀⠈⠙⠒⢺⠀⠀⠀⠓⠖⠛⠲⠚⠀⠀⠀⡗⠒⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠈⠁⠀⢀⠒⠀⠀⠀⠀⢳⣀⣀⠇
⠀⠀⠸⠖⡆⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢠⠓⠃⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠊⢀⡴⠊⠁⠀⠀⠀⠈⠀⠈⡆
⠀⠀⠀⠀⢸⡀⣀⡄⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⣀⠀⡜⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⣧
⠀⠀⠀⠀⠀⠉⠀⠘⠖⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣆⠜⠉⠛⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⡖⠲⣖⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠓⢤⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢹⠒⠤⣠⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⡸⠀⠀⠀⠀⠀⢠⣇⣀⣀⣀⣀⠤⠤⢤⠖⠚⠉⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⠀⢀⡴⠋⠀⠀⡰⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠸⠻⢄⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠑⠒⠒⠒⠉⠀⠀⠀⠰⡁⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣀⣀⣀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠓⠗⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡁⠀⠔⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⡘⠀⠀⠉
⠀⠀⣀⣤⠴⠶⠦⢼⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠙⢄⠇
⠀⠀⠈⠳⢄⡀⠀⣸⠳⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜⠀⠀⠈⡎
⠀⠀⠀⠀⠀⠀⠉⠐⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠤⠄⠒⠒⠀⠉⠀⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠑⠂⠤⠄⣀⣀⣀⡀⠤⠔⠒⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⢠⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢿⣿⣿⣿⠀⠀⠀⢠⠏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠙⣛⠟⠀⠀⡰⠋⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠋⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠜⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⢧⣄⣠⣤⡴⠛⠁⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠂⠤⠤⠤⠀⠄⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠊⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⢰⣾⣦
⠀⠀⠀⠀⠀⠀⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣿⣿⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⣿⣿⡿
⠀⠛⡁⢀⡐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⣹⡏⠃
⠀⠈⠡⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠉⠈⠉⠉⢉⠉⠐⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⣤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣺⡞⢯⣭⣷⣐⡲⠤⣄
⠀⠁⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⣎⢧⡀⡀⠀⠀⠁⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠁⠠⢝⠢⢉⡳⣯⡛⡶⢾⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠘⣧⢻⡄⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⠫⠟⢆⣁⡘⠿⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣷⣿⣆⠀⠀⠀⠀⠀⠀⠲⢤⡤⠤⠂⠀⠀⠢⢄⠉⠁⠀⠀⠙⠲⠞⠄⠋
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⡿⢿⣄⡆⠀⠀⠀⠀⠐⠄⠛⠀⡘⠃⠀⢀⠀⠀⠈⠀⢠⡀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠦⢊⣟⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⢀⣼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠉⠁⠀⢻⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠠⠀⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠃
⠀⠀⠀⢀⣾⡿⢿⣿⠁⠀⠀⠀⣿⡏⣹⡿⠀⠀⠀⠀⠈⠁⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢻⡇⠀⠙⢷⣄⠀⠀⣽⡇⢿⡇⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠟⠀⠀⠀⢤⡄⠀⢠⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⣄⣄⡀
⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠁⠀⠀⠀⠐⠾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠊⠀⠀⠈⠑⠄⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⢠⠀⠜⠢⣀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡸⢂⠂⠀⠀⠀⠀⠀⡈⠒⠐⠄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢾⣿⡆⠀⠀⠄⢸⣿⡆⠀⠀⠙⢉⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠉⠁⠀⠀⠀⠀⠉⠁⠁⠀⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠈⠈⠂⠤⠤⠒⠂⠈⠀⠉⠁⠚⠉⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠔⠃⠂⠄⠠⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⡀⡠⡅⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡑⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⠉⠀⠈⠉⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠡⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣱⠄⢀⠠⠄⡠⠀⢀⠤⠈⣙⢠⠴
⠀⠈⢤⠀⠠⢦⠀⠀⠨⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠋⡉⡖⠁⠦⣨⠃⠉⠑⠀⠀⡰⢀⠌
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸⠀⢰⠰⣰⠀⠄⡠⣀⣄⠄⠂⢠⠀⠀⡀⠀⠈⠉⠉⠁⠀⠀⠈⠀⠀⠀⠡⡉⠀⠈⠈⠁⠐⠒⠊⠁⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠘⠠⠙⠀⠄⠓⠙⠇⠄⠂⠈⠀⠀⡇⠀⠀⠀⠲⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠤⡀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡈⠉⠁⠀⠃⠀⠀⠁⠀⠀⠠⠀⠰⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠡⡀⢀⢠⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⢄⠀⠀⠂⠀⠀⠀⠆⠀⠀⠐⠀⠐⠀⠀⢀⠂⠀⣤⣚⣃⣀⣰⠀⠀⢠⣒⣃⣀⠴⠂⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠀⣠⡴⢤⡀⣠⡴⣤⡀⢠⡤⠦⡄⢤⡀⣠⡄⣠⡤⢤⡄⠤⣤⡤⠄⣤⠤⠄⢠⣤⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠀⣿⠀⠀⠸⣿⠀⢸⡇⠘⠳⢶⡄⠈⢿⡟⠀⠙⠷⢶⡄⠀⣿⠀⠀⣿⠒⠂⢸⡟⣷⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠉⠛⠛⠁⠙⠛⠋⠁⠘⠛⠛⠁⠀⠘⠃⠀⠙⠛⠋⠁⠀⠛⠀⠀⠛⠛⠃⠘⠃⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠫⠝⡇⠀⠸⣋⡣⠀⠀⠀⠠⠂⡰⠁⣤⠀⢀⠀⠀⠀⠀⠐⠑⢨⢂⣀⣀⠀⠀⠀⠀⣠⠈⠫⡭⢙⠀⡄⠀⠀⠀⠀⠀⢻⣀⣞
⠀⠀⠀⠀⠀⠘⠁⠊⡡⡒⡄⠁⠘⠀⠀⠀⢀⠀⠠⠆⠀⠄⢁⠀⠀⠀⢠⡜⡃⠰⡀⠓⢐⣤⠀⠀⢐⢠⠜⡒⠒⠨⢥⣀⠀⠀⠀⡆⡛⡿⠵⢹⠟⠈
⠀⠀⠀⠀⠀⢰⠠⠀⡈⠒⠡⠀⠠⠀⠀⠀⠀⠂⢀⠀⢀⠈⠀⠂⠀⠀⡅⠀⢈⠢⠀⢀⡋⠀⠀⠀⠘⡀⠖⣱⢔⡃⡖⡀⠀⠀⠀⠃⡁⠷⠭⠾⢆⡰⠂
⠀⠀⠀⠀⠀⠘⠳⠤⠇⠀⠸⠎⠈⠀⠀⠀⠈⠂⠈⠓⠋⠄⠂⠀⠀⠀⠈⠃⠀⠀⠀⠯⠏⠀⠀⠀⠀⠉⠠⢄⣀⠤⠐⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠄

⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠤⠠⠀⠀⠀⡠⠀⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠓⠈⢠
⠀⠀⠀⠀⠀⠀⡌⠉⠤⠀⠁⠊⢀⠀⠀⠀⡂⡉⢰⠒⠑⠊⠛⡄⠀⠀⠐⠀⠒⠂⠂⠀⠂⠂⠀⠀⠐⡀⠘⠛⡤⠀⡐⠀⠀⠀⠀⡐⠗⠀⠘⠤⠄⠰⡆
⠀⠀⠀⠀⠀⠈⢓⠲⠀⡌⡔⡀⠘⠀⠀⠀⠀⢀⢦⢛⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣸⠀⣿⡞⠀⠀⠀⢇⠠⠆⠀⢀⢴⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠰⡬⠏⠉⠀⠀⠀⠀⠀⠈⢧⣣⡜⠆⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠔⠘⠉⠉⠄⠐⠀⠀⠀⠈⠠⠤⣀⡈⠳⠂

⠀⠀⠀⠀⠀⠐⢀⠤⠀⠀⡀⠂⠠⠀⠀⠀⡔⠀⢀⠀⠢⢀⢀⠀⠀⠀⢀⢀⠢⠄⠄⠄⠀⢠⠀⠀⠀⠄⢄⠐⠀⠄⠐⠀⠀⠀⠀⢀⠀⣠⣴⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠡⠀⠔⠒⠬⠁⠁⠀⠀⠀⠀⠈⠠⠐⠠⠁⠀⡁⠀⠀⠁⠀⠁⠒⠒⠉⠍⠁⠀⠀⠀⠼⠤⠒⠒⢌⠸⠅⠀⠀⠀⠀⠀⠈⣀⡃⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠒⡤⠊⠀⠀⠀⠀⠀⠠⠆⠐⢴⠔⡘⢠⠄⠀⠀⢆⡆⠀⢠⡔⣠⢶⣆⠀⠀⠀⠁⠈⠣⡬⠊⠀⠈⠀⠀⠀⡀⠀⡘⢿⠗⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁⠀⠀⠈⠉⠀⠈⠁⠉⠀⠁⠀⠀⠀⠀⠐⠈⠃⠐⠀⠀⠀⠀⠀⠀⠅⡀⠀⢐⣰⣆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢤⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠄⣈⢣⡟⠾⡁⢄⠀⠀⠀⠠⠀⢤⢬⣤⠄⠠⠀⠀⠀⢠⡴⢉⣀⡁⠈⢢⡄⠀⠀⠀⠀⡄⡤⠥⡄⡄⡀⠀⠀⠀⠀⠀⣖⣹⣸⡃
⠀⠀⠀⠀⠀⠠⡤⣭⢃⠜⣑⢷⢤⠀⠀⠀⠀⠶⠚⡧⠈⠰⠇⠀⠀⠀⢰⡀⠀⠋⠨⠀⢀⡅⠀⠀⠈⠀⣸⡀⣗⣸⡀⠠⠀⠀⠀⠀⢀⣈⢹⡭⣀
⠀⠀⠀⠀⠀⠀⡄⠹⠮⠵⠄⡇⠰⠀⠀⠀⠀⢀⠀⢀⠠⢁⠀⠀⠀⠀⠀⠘⠔⡤⢤⠂⠃⠀⠀⠀⠀⠀⡁⠈⠎⠁⠀⠀⠀⠀⠀⠀⠇⡸⢫⡁⠈⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣚⣉⡉⠚⣿⢿⣛⣿⣭⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣼⣿⣷⠈⡦⢸⠈⢻⣿⣿⡭⢅⡀
⠀⠀⠀⠀⠀⣀⡤⠴⠒⢒⣒⣒⣒⣒⣉⣁⠠⠴⠀⠻⣿⣟⣠⢏⡎⠀⢸⣿⣯⣍⡀
⠀⠀⠀⣴⡿⠿⠭⠽⠗⠒⠒⠚⠛⠛⠛⠓⠒⠦⡀⠀⠀⠀⢀⠞⠀⠀⡾⡝⢝⢮⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣠⠔⠁⠀⠀⢸⠁⠘⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠉⠀⠀⠀⠀⠠⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠴⠀⠀⡀⡉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠉⠀⠀⡄⢀⡤⠬⠥⣄⡀⠘⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠃⢀⠀⠢⠂⠈⠲⡄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠚⠀⠀⠀⠴⠀⠈⢦⠁⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡇⠠⠆⠀⢠⠀⠀⠀⡄⠀⢣⠒⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢧⠀⠀⠁⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡇⠠⣰⠀⢹⠀⠙⠀⠀⠈⠃⠘⡆⠄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢳⠀⠀⠀⠘⡆⠀⠀⢠⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠘⢆⠀⠀⠀⢱⡀⠀⠈⡆⠀⠀⠸⡄⠀⠀⢰⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣬⣷⣄⣀⢀⣳⡀⠀⣸⢄⡀⣠⠃⠀⢃⠀⢇⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠈⢻⡟⠁⠉⠉⠁⠀⠉⠙⡄⠀⢸⠀⠸⡄⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⡇⠀⢧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠭⢟⣛⣫⣥⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠸⡄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠩⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣇⠀⠀⡇⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣄⢀⡟⠦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠁⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢏⣿⢰⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⣿⣿⡿⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⠷⠀⢸⠀⠀⣴⣾⡇⠀⠀⠀⣠⢆⣴⢰⣦⠰⣄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢦⢸⠀⠀⡫⠾⠃⠀⢀⣶⡆⣴⣭⢠⣭⡆⢶⣶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣠⠞⠀⠀⠀⠀⢘⣛⡃⣛⣉⢀⣉⣁⢘⣛⡁⠀⠸⣿⡷⣀⣤⣤⣤⡐⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠈⠀⠀⠀⠈⢿⠧⠻⠿⠘⠿⠏⠾⡿⠁⠀⠀⢋⣾⣿⣿⣿⣿⣿⣦⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠻⠎⢿⢸⡟⠱⠓⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣯⡽⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣭⣍⢛⣛⢛⣭⣥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⡀⠀⠀⠀⠀⠈⠉⠁⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⢰⣤⠀⠀⠀⠀⠂⣿⣿⡿⢟⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢵⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠀⠀⠀⠀⠛⠿⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⡇⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢄⣤⡤⣤⣤⣤⣌⣀⠀⠀⡾⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣡⣿⢏⣴⣎⢿⣿⣿⣿⣿⣶⣄⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⣼⣿⣏⢾⣿⣿⢎⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⡻⠿⣿⡟⣼⣿⢿⣿⣮⡛⣫⣾⣿⢿⣿⣿⣿⡿⣿⣿⣷⡀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡖⣤⣭⣍⢰⣮⣙⠇⢟⣩⣶⣞⣿⣶⣦⣾⣿⣿⣿⣿⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢣⣿⣿⣿⡸⣿⣿⡇⣾⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣶⣭⡆⣮⣵⣾⣿⣿⣿⣿⣟⡛⢛⣽⣿⣿⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⢛⣡⣌⡛⢟⣫⣬⣛⠿⣛⣥⣝⡛
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⢿⣿⠿⠿⠿⠿⠇⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣛⣭⣥⡔⣶⣾⣿⣿⣿⡇⣩⣴⣭⣛⣩⣶⣝⣛⣭⣦⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣜⢿⣿⣿⣿⡇⣿⣿⢿⣿⣿⡿⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡻⣿⣿⡇⣭⣵⣶⣭⣭⣴⡦⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠊⠻⠇⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⢴⢖⣴⣶⠀⠀⠒⠀⠀⠀⢀⣀
⣠⣤⣴⣦⡾⣆⢻⠟⠀⠀⣠⣤⣬⣶⣿⣿⣿⣶⣶⣤⠄
⠉⠙⡿⠿⣦⡷⠄⠀⠀⣤⣽⣿⣿⣿⣿⣿⣿⡯⠙⠁
⠀⠀⠙⠿⠛⠀⠀⠀⢠⣿⣶⣿⡿⢿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠸⣟⣢⠀⠀⠉⣿⣿⠁⠀⠀⠑⢂⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠙⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠒⠂⠀⠀⠀⠀⠀⢀⣀⢀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠉
⠀⠀⠀⠀⠀⢀⡀⢀⣄⣀⢀⡀
⠀⠀⠀⠀⠀⠾⠿⢽⠷⠿⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡆⠀⠀⠀⣀⣀⣀⣀⣀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢪⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲⠤⠀⣒⡣⠀⢐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡻⠇⠀⠈⠭⣓⠀⡩
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠃⠁⠀⢻⣏⠀⢀⣿⠀⠀⠀⢉⣿⣶⡖⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠚⠋⠹⠀⠀⠀⠀⢿⣿⡀⠀⢻⡀⠀⠀⢀⣀⣈⠙⠇⢼⣷⠄⠀⠃⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣓⡀⠀⢀⣠⠸⣶⣦⡜⣩⣷⣸⣏⠃⢀⡔⡏⠉⢋⠆⠀⠘⣁⣄⠀⢀⣷⡜⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐⠿⠿⠂⠚⠑⢻⡀⣄⡠⠿⢿⣿⡿⣦⣩⡀⠀⣠⣿⣧⣤⣼⣿⣿⣷⣟⠁⠀⠀⠁⣀⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠿⣦⣀⣻⣃⡠⠞⠉⠁⠀⠀⠀⠀⠀⠉⠀⠘⠛⠳⣽⠆⢈⢿⡍⠻⣿⣿⠧⢤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠁⠀⠀⠀⢠⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣯⣇⠼⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠸⠷⠚⠉⠀⢀⣠⣴⣇⣤⣀⠀⠀⠀⠀⠘⣭⣙⢦⣾⠿⠛⢇
⠀⠀⠀⠀⠀⠰⢛⣻⣷⣶⡶⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠏⢀⡀⠀⠈⠀⠀⠀⢁⡴⢌⣀⣀⠐⠆⠱⠄
⠀⠀⠀⣤⡀⠀⢘⣿⣿⣭⡤⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠐⠀⢀⠤⠓⠒⠛⠋⠉⠓⠀⡀⠰⠆
⠀⠀⠀⠈⠃⠀⣄⣙⣫⠽⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣀⣤⠦⣄⠈⠁⠀⠀⠀⠀⠀⢰⠀⢠⡴
⠀⠀⠀⠀⣀⡀⠁⢰⣶⢆⣸⠿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⡯⠐⠙⠓⠈
⠀⠀⠀⠀⠈⠁⠀⡈⢻⣿⣿⣄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⣞⠀⠀⠀⠀⠀⢀⡼⠄⠀⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢠⣇⡀⠸⠿⢿⠷⡷⡄⠀⠀⠀⠻⠀⠀⠘⠀⠀⠀⠀⠻⡄⠀⠀⠀⢀⣼⣷⠚⢻⣟⣡⡶⠉
⠀⠀⠀⠀⠀⠀⠋⢯⡀⠀⠺⢺⣧⣨⠟⣦⣤⡤⠽⢾⣿⣶⣇⡀⠀⡀⠀⠀⠀⣆⠳⠚⢿⠹⣷⠿⠛⢉⡀⣴
⠀⠀⠀⠀⠀⠀⢷⣄⠀⠐⠢⡶⢿⢿⣿⣧⣈⣷⢲⣬⠡⠤⣀⣋⢀⣀⣗⡴⠊⠀⠀⠠⠆⠀⠸⡄⠀⠡⠙⠛
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣤⡼⡺⢼⠛⢿⣿⣇⠀⠀⠀⠀⠡⠟⢐⣾⣿⠈⡠⣶⣿⠀⠀⠀⢠⠛⠉⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣤⣠⡓⠚⠋⠁⢻⣆⠂⠀⠀⠆⠋⠀⠰⠚⠛⠋⢙⠀⠀⠠⠀⠂⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣟⣿⣿⣷⣄⣀⠀⢹⠠⢤⡄⢠⣴⡶⠀⠀⠐⠒⠁⠀⠀⠀⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠈⠇⠘⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢠⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⡇⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣎⣤⠀⠀⢾⣿⢿⣿⣿⣿⡟⣩⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⣿⡷⠆⠁⠀⣼⣿⣿⠉⡁⢩⣿⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠓⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣄⡀⣿⠙⠛⠀⠀⣾⡿⠉⠂
⠀⠀⠀⠀⠀⠀⠰⠆⠶⠴⠰⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣻⣤⣤⡀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢻⣿⢿⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⢿⠏⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢂⠀⠀⠐⠁⢠⠀⠲⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣠⠀⠀⠀⠀⠀⢀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⡀⠀⠀⠀⠗⠀⠀⠀⡈⠀⠀⢀⠀⠀⣀⠀⠀⠄⠀⣀⣀⠉⠆⠓⠀⢈⠀⡀⠀⠰⠄⢠⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢁⠀⠀⠀⠈⠀⠄⢠⣄⡀⠠⠊⠀⢀⠤⠂⠁⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠂⠄⡀⠈⢣⠊⠀⡠⠁⢃⠀⠀⠀⠔⠁⠀⠀⠆⢀
⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠈⠆⠊⠐⢄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠂⠀⠀⠀⠀⠈⡦⠆⠀⠰⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠠⡀⠀⠀⣠⠀⠔⠁⠀⠀⠀⠑⠄⢁⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⣀⠀⢀⠔⠀⠈⠢⠀⠀⠀⠀⠀⡀⠔⠓⢄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠠⡀⠀⠇⠀⠀⠀⠀⢢⠃⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠔⠃⠀⠈⠀⠁⠀⠀⠀⠀⢀⠀⠀⠱⡀⠀⡴⠈⠤⠀⠀⢀
⠀⠀⠀⠀⡀⡀⠀⣀⠀⠤⠀⠆⠐⠀⢄⠀⠀⠂⠀⠀⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠠⠋
⠀⠀⠀⠀⠄⠸⠄⠡⡄⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠈⡀⣀⣀⠀⠀⠐⠁⠀⠐⠂
⠀⠀⠀⢀⠤⢤⠐⠀⠈⠀⢄⠀⠀⠀⠀⠀⣨⠐⢄⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠈⢂⠀⡗⠀⠄⢀⠊⠀⠈⢂⡀⡀
⠀⠀⠀⠘⠤⠔⠀⠀⠠⠀⢀⡈⠅⡀⢈⠠⠸⠀⠀⠁⠀⠀⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠄⠘⠀⠀⡐⠊⠉⠀⡠⠀⠀⠀⠀⠃
⠀⠀⠀⡰⢢⠀⠀⠂⠀⠀⠀⠀⠀⠈⠅⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠨⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠘⠁⠈⠀⠂⠀⠐⠉⢑⠀⠘⠄⢀⢀⠐⡀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣤⡀⠹⡃⠀⢈⡁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠁⠀⠀⡀⠀⠀⠀⠲⣄⠀⠈⠄⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠉⠓⠊⡓⠀⠀⠀⣐⠗⠉⠘⠃⠀⠉⠛⠋⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐⠀⠊⠀⠀⠄⠀⠀⠈⢶⠒⠨⡄⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢠⡋⠐⢱⠞⠁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠑⢄⠀⠁⠂⠄⠀⠀⠀⠀⠀⠀⢀⠔⠚⠁⢀⠠⠊⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠂⠐⠒⡒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡆⠀⠘⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡤⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢻⣷⠈⢿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⢺⡀⠀⠀⣿⠟⠁⠘⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⢸⡇⠀⣀⠀⠀⡀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣀⠀⠀⠠⣿⣿⣿⡿⠀⠸⢇⣀⣿⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⢿⣿⣿⣧⢰⡿⠞⠛⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣶⠀⢸⣿⣿⣇⠘⠁⣠⠖⠈⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⡤⠀⠻⣿⣿⣶⣶⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣴⣿⣿⣿⣧⣿⣸⣤⣾⠿⠋⠉⠁⣾⠿⠿⠃⠀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣼⡟⠃⣿⠇⠐⠟⠃⠀⠀⢀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠈⢻⣿⣷⣾⣄⢁⡀⠲⠀⠿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⠀⣱⡟⠃⠉⠉⢙⣤⠜⢺⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡿⠷⠾⣷⣆⣹⣧⣼⣿⣿⣿⡿⠿⠟⠛⠃
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠘⠟⠙⢣⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⢸⡇⢠⣾⡅
⠀⠳⣄⡀⢸⣿⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⢸⣿⣾⠟⠁⢀⡄⠀⣠⡆
⠀⠀⣿⡇⠘⣿⡁⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣀⣽⣧⡴⠞⠋⢀⣶⡟
⠀⠀⠉⢁⡴⠈⠉⠀⠀⠁⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠻⣿⣿⣿⣿⡟⠉⠁⣠⠶⣠⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠑⣄⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢿⣆⠈⠻⣿⣿⣷⣮⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⠃⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⣿⡇⠀⣹⠿⠟⠋⠉⠀⠀⡀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠘⠃⠀⠀⣶⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡜⢷⢀⣿⠀⠀⢠⡤⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⢁⣴⡗⠉⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⡀⠉⠀⠀⠀⠠⣤⡀⠀⢸⣿⣿⠉⢿⣿⣯⡘⠻⣧⣴⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣼⡿⣨⢻⣶⣌⣿⠃⠀⠀⠹⠁⣠⡾⢛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⣿⣠⣆⠀⠀⠿⠄⢹⣿⡏⠀⠆⠀⠀⣴⣟⣵⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣆⡀⠀⣤⡀⢻⣿⠀⢺⡆⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠻⣿⠉⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⡟⠉⠉⠉⠉⠀⠹⣿⡾⣿⣇⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⢰⣦⣤⣄⠀⠈⠁⢸⣿⣤⣿⠇⠀⠀⢀⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣰⠁⣀⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⢻⣿⣿⣷⣤⡀⠈⠻⣿⠇⢀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡇⢰⡿⠻⣿⣿⡿⢡⠀⣿⢠⡜⢣⣾⠏⠀⠀⠀⠀⠀⢠⣄⡀⠀⠐⠀⠀⠺⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠜⠁⠀⠘⢿⠇⢸⡄⠸⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⠈⠁⠀⣴⠁⠈⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⢠⠆⠀⢀⣤⡀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡌⠙⢧⡀⢰⣈⣷⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⣾⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣶⣼⣿⠊⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠟⠀⠀⠀⠺⣿⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣏⠈⣿⣿⣇⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡀⠈⣤⠀⢀⣴⡀⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⡀⢃⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠛⢷⣄⡹⡀⢸⣿⠇⢻⣿⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠘⡷⠗⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣤⠀⠀⠀⣉⠛⣿⠈⠻⠀⢈⡟⠀⠀⠀⠀⠿⠃⢠⠀⣀⠀⠀⠾⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣘⠿⣤⡄⠀⠀⠸⠟⠀⠀⠀⠀⠀⡂⠁⢠⣿⡆⠘⣀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⣿⣷⣽⣿⣴⡀⢰⡆⠀⠀⠀⢠⣾⣿⣿⠀⢻⣿⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠈⠻⣿⣿⣿⠀⢸⡇⢠⡆⢠⡿⠋⠈⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠈⠻⣿⣤⣤⡆⢀⣶⠏⠀⣶⣾⣿⡀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠈⠙⣿⠁⠈⣡⡄⠘⣿⡇⢀⠁⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠸⡀⢀⣿⡇⢸⣿⣇⡈⣡⡭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⢰⣧⠘⣿⡇⠈⢻⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣄⠀⢸⣿⠀⠸⠇⠀⠏⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿⢈⣿⠀⠀⠀⠀⢸⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⢻⣿⣇⠈⠸⠿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣌⢹⣿⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⣼⣿⡀⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣴⣦⣽⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠁⠘⠛⠻⣿⣿⣿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⡜⣿⣿⣷⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⡦⠼⠗⠉⣀⠉⠓⠌⣙⢣⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⣈⣭⣥⡄⠀⠿⠿⡛⠆⢤⡉⠉⠙⢻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠐⢊⣿⣿⡄⢠⡀⠈⠳⠀⠀⠀⠺⢿⣿⣿⡇
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣹⠿⢁⣿⣷⡀⠀⠀⠀⠀⢀⣼⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠚⠁⠀⡸⢹⠟⠰⣧⠀⠓⠈⠀⠀⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⣈⣁⣀⣤⣴⣿⢿⣿⣾⢟⡛⠾⠦⠄
⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣻⣿⣿⠟⣫⣕⣿⡿⣻⣿⣷⣈⣂⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠁⠀⠈⢙⣿⣿⣿⣟⣉⢙⣋⣉⣿⣿⣷⣿⣿⣿⣿⣧⣿⣿⣿⡟⢿⣧⣼⡾⠛⠙⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠵⢚⣩⣭⣿⣿⢿⡿⢟⣿⠿⠛⠙⠛⠉⠃⠈⢡⡤⠈⠙⢧⡀⠄⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢊⡽⠁⡠⠶⠒⠀⠁⠀⠀⠁⠀⢀⡴⢂⣆⡤⣧⣞⡀⠀⠀⠀⠙⠦⣔⠀⠀⠀⠀⢝⠢⠀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠏⢤⠈⠀⠲⡄⠀⠒⢿⣶⣿⣷⣿⣾⣯⣽⣿⠏⠈⡇⠀⠀⠀⠀⠀⠙⢳⣤⡀⠀⠈⢦⠀⠙⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢳⡤⣿⣀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠛⠋⠀⠈⣯⣠⡿⠶⡄⠀⠰⢦⣴⢛⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠙⠓⣶⠀⠀⠀⠀⠀⠈⠻⠶⠶⠃⠀⠐⢻⡇⠀⠁⣠⡼⠷⠒⠒⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣀⣤⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢷⡛⠉⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠠⠤⠄⢀⣀⠀⠀⠀⠉⢀⡀⠀⠀⠘⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠒⠒⠚⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠉⢻⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢳⡀⠀⠀⠀⠀⣤⢶⣿⡇⠀⢀⡤⢶⡿⢻⠛⢷⠶⣄⠀⠀⠙⣦⠀⠙⠟⠃⠀⠀⢀⡞⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⡀⢻⡄⠀⠀⠀⢀⡟⠸⠇⣴⠿⢦⣿⣤⣼⣤⣬⣷⠼⠷⡄⠀⠈⣧⠀⠀⠀⠀⠠⠟⢀⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠘⠃⠀⠹⣄⠀⠀⢸⠁⠀⢰⡇⠀⢸⠃⠀⢸⡀⠀⢸⡄⠀⢻⠀⠀⢸⡆⠀⠀⣠⠆⠀⠘⠃⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠐⠂⠀⠀⠙⣆⠀⢸⠀⠀⢸⡟⠛⢻⠛⠛⢻⠛⠛⢻⡟⠛⢻⠀⠀⢸⡇⠀⣰⠋⠀⠀⠐⠂⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠸⣇⠀⠈⢧⣀⣼⣧⡤⣼⡦⢤⣾⣄⣠⡟⢠⠀⣼⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠻⢦⣹⣄⢸⣃⣴⣣⡼⠋⠀⣾⣼⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣳⣤⣴⡃⢀⡀⠘⢷⣄⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠛⠋⠁⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣭⣥⣭⣿⡾⠂⠀⠀⠈⠛⠶⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡗⠲⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠂⢸⠐⠂⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⢉⡟⢙⡏⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣳⣄⣼⣠⣼⡃⠘⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠘⢦⡤⢾⡉⠉⣹⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠉⠁⠸⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠸⡇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠠⠄⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⠃⠀⠰
⠀⠀⠀⠀⠀⢠⠀⣠⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢰⣿⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⢺⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡴⠊⠁
⠀⠀⠀⠀⣰⠏⠀⠆⠀⠀⠀⠀⠀⠀⠀⣠⠾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣤⡿⠏
⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠨⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⢡⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠰⣀⣿⠿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⣿⣯⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⢷⣦⣄⡁
⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣧
⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠘⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡤⣶⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠒⠂⠉⠉⠉⠉⠉⠈⡱⠒⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⣤⡠⢱⠀⠄⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⠉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠢⡀⠀⠀⡠⠊⠀⠀⠀⠘⡄⣇⠄⠜⠀⠀⠀⢚⠂⣌⠑⡄⠀⠀⢀⡔⠉⠢⠻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⡎⣀⠤⢄⠀⠀⠀⠈⠒⠄⡠⢪⠇⠀⠀⠉⠁⠀⠈⠆⠀⢸⠀⡠⠐⠑⠳⣜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠘⢌⠈⢚⡀⣠⣴⣆⡀⠈⡕⠛⠂⠀⠀⠀⠀⠀⠀⠒⠒⠁⠈⠆⢸⢈⣐⠳⠹⣦
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⢫⣛⠉⠸⣇⡀⢰⠚⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠢⠘⠫⠀⢢⠘⠨⣄⢥
⠙⡉⠒⠠⢀⡀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠡⡃⠁⠀⠈⠑⢷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢄⡀⠀⠀⢀⢀⠇⠀⠈⠉
⠀⠰⡀⠀⠀⠈⠑⠠⣀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠱⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⡀⠀⠐⠁
⠀⠀⢃⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⡆⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠘⠀⠀⠀⠢⡀⠀⠀⠀⠈⠢⣠⠇⠀⠀⠀⠀⠀⡄⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠰⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣀
⠀⠀⠀⠆⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠐⡄⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢄⠀⠇⠀⣠⣀⢤
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡑⠒⠂⠁⠀⠀⠀⠀⠀⢀⠤⠤⠠⠔⠉⠉⠀⠀⠱⡤⣔⠭⠤⠎⣀⠜⠘⢁⠂
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⢣⡀⠀⠀⢀⠴⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⢀⡹⢶⡈⠉⠢⡙⢦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠉⠓⢦⣌⡂⢝⢦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢷⣤⡀⠀⠀⠈⠆⠀⢀⠃⠀⠀⢀⡀⠤⠒⠁
⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣶⣶⣾⣶⣾⣶⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡟⣛⢻⡿⣿⠻⡿⢿⣿⢻⡿⣿⡿⢻⣿⡟⢻⣿⢿⡟⣿⢿⡿⣿⠿⡟⣿⡟⣛⡟⣿⣿⢿⠟⣿⢿⠻⢿⡿⢿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⢿⢀⢨⢼⢸⢺⠀⠀⠀⢸⠄⢸⢸⣿⢐⡘⠃⡆⡇⠀⡆⡇⠓⡇⡅⣿⡷⡌⠃⡱⡇⡥⡄⠰⡶⢰⡆⢨⠤⢌⢺⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣿⣶⣾⣶⣶⣾⣿⣾⣷⣾⣶⣾⣿⣾⣷⣾⣷⣷⣿⣷⣿⣷⣶⣷⣿⣷⣶⣷⣿⣷⣾⣷⣷⣾⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣇⣀⣀⣿⣃⣈⣇⣇⣼⣌⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢹⡿⠍⠉⠉⡏⠉⠉⠉⣩⠍⠉⡉⠉⠙⠋⠉⠍⠉⠉⠉⢹⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⣮⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⢞⣃⠀⠀⡇⠀⠀⢰⣷⣖⠲⣧⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠶⠿⠂⠀⠄
⠀⠀⢘⠓⢰⡆⠈⠁⠀⠀⢀⡀⠐⢪⣙⠀⠀⡇⠀⠀⠈⠉⣻⢰⣿⡄⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⣤⣤⣤⠄⣀⢰⣇
⠀⠀⠀⠀⠀⢻⡄⠀⣄⣼⢩⠖⠂⣨⡿⠀⠀⡇⠀⠀⠀⢀⣻⢮⣭⣉⠻⣷⣄⠀⢀⡀⠀⠀⢸⠀⠠⠁⠒⠲⠿⢧⠴⠎⠋⠐⣾⣆⣨⢿⡀
⠀⠀⠀⠀⠙⠈⢻⣄⢻⠇⠈⠀⠚⠋⠄⠀⠀⡇⠀⠀⠀⠸⣷⠬⣹⣿⣷⣜⣿⡆⡞⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⢾⠏⠁⠉
⠀⠀⠀⠀⠂⠀⠘⠇⠀⠀⠀⠀⠐⠛⠀⠀⠀⡇⠀⠀⠀⠀⠙⣿⡿⠾⠛⠋⠉⣀⠀⠀⠀⠀⢸⡤⠶⠒⠋⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⡀⠈⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⣇⠀⠀⠀⣀⡀⠀⠙⢳⣤⣀⡀⠀⡶⣦⠀⠀⢸⠀⢀⠀⣀⠀⣠⢀⡈⢱⣄⠀⠀⠀⠀⠀⣘
⠉⠉⠉⠉⠉⡉⠉⢉⣉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⣉⡍⢩⠉⣉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⢉⢉⣉⣿⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠋⢾⣿⣮⡳⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⡀⠂⠘⠉⠰⣤⣀⠀⠀⠀⠀⢸⠀⢀⣯⣭⣍⣛⠀⠀⠁⣄
⠀⠀⣰⣾⡀⠿⢯⣾⣿⣄⣴⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣘⡻⣏⣹⣧⣤⣄⡜⠓⢠⡢⠄⠀⢸⠀⢸⣷⣈⣉⣽⡷⠈⠀⠘⣷⡄
⠀⠀⠧⠸⡀⠄⠀⢀⣅⣘⡿⠀⠀⠀⠀⠀⠀⡇⠀⠖⠺⡟⠀⢈⠹⣿⣷⠋⠁⠀⠐⠂⠀⠀⢸⠀⡾⣯⣩⣿⣿⡧⣠⣶⠿⣿⣿⣦⡀
⠀⣇⡇⠀⠁⠀⠀⠀⢉⡉⣵⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⣷⠈⠀⠘⠃⠀⠀⠀⠀⣰⡇⠀⢸⠀⠀⠉⢿⣿⣿⠁⠏⠃⠀⠀⢿⣿⢧⠀⢲
⢸⣅⠉⠢⠀⠀⠀⠖⠀⠂⠹⡃⣤⣄⡀⠀⠀⡇⠀⠀⠀⢻⡘⠃⠀⠈⠀⠀⠀⠀⠈⣭⣢⠀⢸⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣸⡏⣠⣤
⠸⠐⠆⠀⠀⠀⠠⠆⠈⠀⠀⢠⡟⣀⡻⣦⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣧⣣⣼⠀⠀⣶⣇⠀⢸⠆⠀⠀⠀⠀⢹⢃⣿⣯⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⡛⠿⠆⢀⣀⢀⡀⠀⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⠛⠇⠀⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠉⠉⠛⠉⣩⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣄⣀⣀
⠀⠀⠀⠀⢰⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⠋⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣬⣭⣭⣭⡄
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⢀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠁⠀⠈⢿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣻⣿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢧⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠙⠋⠁⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⣠⣤⠀⠀⠀⠀⠀⠀⠻⣿⣧⣭⣭⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⡀⠀⠀⢀⣠⣀⣀⣀⣀⣸⣿⣿⡇⠀⠀⠀⠀⢀⣠⣌⡛⠛⠛⣋⣡⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⣿⣿⣿⡿⢋⣭⣭⣿⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠙⠿⣿⣿⣿⡿⠋⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠋⠀⠀⠠⠴⠶⠾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡢⠀⠀⠀⠐⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣸⡁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠛⠻⣯⡁⠀⠀⠀⠈⠀⠉⠓⢦⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠈⢟⢆⠀⠀⠀⢀⡀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣀⠀⠀⠀⠀⡸⠈⡆⠀⠀⡎⠛⡂⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠈⠀⠀⠀⠀⢀⡜⠀⠀⠘⣆⢀⠃⠀⠡⠀⠀⠀⠈⠗⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⣁⣼⡅⠀⠙⠀⠀⠀⠘⢾⠀⠀⠄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⡄⠀⠉⠟⠒⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠲⢖⠚⠛⠉⠉⠉⠉⣇⠸⠂⠴⠐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢆
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠀⢰⠁⠀⠀⢀⠂⠀⠀⠀⢠⠎⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠄⠆⠈⠀⠄⠈⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⢀⣼⠆
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⢀⢿⠀⡀⠠⡀⠀⠈⢦⡀⠀⠀⠘⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⢎⠔⠒⠒⠂⠒⠒⠀⣦⠡⠀⠄⠀⠀⡴⠃⠘⠤⠤⠤⠴⠤⠤⠤⠥⠝⠛⠓⢀⠆⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣎⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠂⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢽⢆⠀⠀⠠⠀⡀⠀⠀⡄⠀⠀⠀⠈⢧⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⡴⢯⡖⠀⠀⠀⠀⠀⢀⢍⡶⠰⠢⣀
⠀⠀⠀⠀⡀⠀⠀⠀⠚⠁⠂⠀⠙⠂⠀⠂⠁⠀⠀⠀⢰⡄⠀⠀⠀⠙⢄⢠⡧⠤⠤⠤⢴⠖⠚⣉⣴⡡⠽⣿⡀⠀⠀⠔⡰⣡⣧⣰⣆⠨⢳
⣈⠁⠀⢤⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣦⣦⠀⠈⠢⣀⠀⠀⠀⢻⠇⠀⠀⠀⢳⠀⣺⢿⠿⡿⣾⣳⢠⡘⠀⠘⢏⠛⣯⣿⣷⠒⣸
⠉⠒⠂⠈⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠑⠦⢬⠤⠔⠊⠀⠀⠓⠀⠀⠈⠣⢤⣉⣤⠴⠃
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢛⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⢳⡀⠀⠀⠀⠀⢀⡾⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠚⣇⠀⠀⠀⠀⢸⡃⢠⣴⡞⣆
⠀⠀⠀⠀⠀⢠⡞⢛⡷⢄⠀⠀⠀⠀⠀⠘⣧⣿⣄⠀⠹⡀⠀⠀⠀⢸⡇⠛⢀⣱⣿
⠀⠀⠀⠀⠀⠘⡄⠀⠑⠈⢆⠀⠀⠀⠀⠀⢻⠇⢁⡶⢿⣇⠀⠀⠀⠘⡇⠀⠚⢉⣽⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠂⠀⣪⣢⠀⠀⠀⠀⠘⡆⠈⠀⠀⠈⡄⠀⠀⠀⣷⣯⡀⣿⡿⣇
⠀⠀⠀⠀⠀⠀⠀⢳⡸⠆⠀⠄⢣⡀⠀⠀⠀⠉⠀⠀⠀⠀⢺⡀⠀⠀⠟⠀⣰⣟⠃⢛
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⠀⠀⠀⢳⡀⠀⠀⢨⠀⠀⡠⠖⠚⣇⠀⠀⡄⠰⠋⠉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠠⠻⣄⠀⠈⣇⢠⠀⠀⠀⢹⠀⢠⡅⠀⠓⠀⠐⠺⡆
⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡴⠎⠲⠌⢆⠀⠸⡀⣆⠀⠀⠘⡇⠘⡇⠀⡀⠠⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛
⡟⠡⠈⡓⢄⠀⠀⠀⠀⠀⠈⢶⠁⠠⠂⠂⠸⣄⢀⠃⠈⠙⠛⠋⠙⠚⠁⠊⢦⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠃⠂⣔⢀⡴
⠹⣤⣤⣤⣶⣷⣄⡀⠀⠀⠀⠘⣧⠀⠐⠠⠀⠘⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢿⣄⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⡆⢀⣤⢄⡞
⠀⠈⠲⣀⠩⠉⠉⠙⠲⣄⡀⠀⠈⣧⠀⠸⣧⣄⠀⠀⠀⠟⠁⡀⠀⠀⢤⡄⣴⣂⣠⣾⣿⡀⠀⠀⠀⠀⠀⠀⡼⠣⠝⣿⠿⡿⡾
⠀⠀⠀⠈⠳⢆⠀⢰⣿⣀⢛⡶⠤⠞⠀⣄⣂⠀⠀⠀⠀⣠⣾⣿⣿⡦⠿⠃⢿⡿⢿⠀⠠⣿⣦⠀⠀⠀⠀⣸⠡⠾⠊⢍⡀⣾⠃
⠀⠀⠀⠀⠀⠀⠳⣟⠉⠀⢂⠠⢀⣴⠄⠉⠀⢠⡆⣀⡼⠟⢫⣥⣠⣀⠦⠀⢿⣵⠊⡷⢠⡷⠢⠷⣄⣀⣼⠏⠠⢘⠀⠝⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠁⠀⠀⠀⠠⡀⢀⠈⠁⠉⠀⠀⠀⢉⡿⠟⡷⣟⣶⡑⡓⢡⠟⣿⣠⠶⠈⠉⠉⡉⠐⣨⡋⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⢢⣐⠁⠀⠀⠀⠈⢀⠀⠀⣴⣦⡀⠀⣾⠟⠃⠦⠁⠼⠃⡯⢵⠄⣆⢰⣦⡀⢰⣎⣡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⠛⠟⢀⠐⠊⠓⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⢶⣽⡄⢀⣒⣋⢴⣓⠋⠉⠀⢺⣄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣤⣴⣾⣿⣿⠶⠀⠀⠀⠚⠀⣿⡿⠀⠀⠀⠉⠁⠨⠈⣉⠀⣹⢻⡟⠀⢩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⡟⡿⡆⢰⠀⠀⠀⠀⠈⠁⠐⠒⠀⢳⡻⣄⣿⠇⠀⢠⣄⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠈⠃⢀⠀⠘⡆⠀⠀⠀⢠⣀⡀⠀⡀⠉⠂⢝⣯⢀⣶⣾⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡠⠇⠉⠀⠀⠙⠒⠀⢀⡀⢉⠛⠃⠀⡀⠀⢀⣳⣌⡙⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣐⣒⣶⣂⣈⣉⠉⠉⣭⠀⠤⢅⣀⡀⠉⠉⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡠⣴⡯⣤⣀⠀⠰⠶⢿⠿⠂⠈⠀⠈⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣤⡄⠀⠤⠤⠄⠀⠸⣿⠏⠡⠶⠶⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡌⠉⡄⢆⡶⣴⣶⡦⠀⢀⠀⠇⠐⠟⢻⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠷⢶⣼⢃⣄⢠⡄⠀⣾⢠⢆⡄⢀⣾⠸⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣴⣵⣶⣿⣼⣼⣮⣤⣼⣿⣼⣼⣼⣮⣧⣶⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣟⠙⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣏⠏⣡⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠙⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡄⠀⠀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣸⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣵⡿⣿⣿⣿⣿⣿⣫⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⠆⢻⣿⣿⣿⣿⣿⣾⣿⣽⣽⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢛⣿⣿⣿⣿⣿⣿⣿⣴⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⣿⣿⠻⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⡞⠽⢽⠿⢿⣿⣿⣿⣿⣿⣿⣼⣯⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⣿⡿⢹⣿⡿⢿⣿⢿⣾⠟⣙⡻⣿⣿⣿⣿⡏
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠻⢷⠛⣿⡟⠺⠒⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣧⣿⣼⡇⠀⢾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠂⢺⣿⣏⢰⣦⣬⣿⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⣿⣝⣿⣿⣿⣿⣧⡀⢛⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣤⣿⡿⣿⣿⣿⣷⣾⣾⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣯⡽⢽⡟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⣿⣯⠹⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢁⣿⣹⣧⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⢿⣿⣿⣻⠋⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠁⣿⣿⣆⣻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⣸⣷⣿⣼⣴⡿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠠⣠⣿⢻⣿⡏⠸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⡿⢿⢹⡟⠳⣿⠸⡟⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣸⣿⣿⣿⣿⡟⣿⣇⣾⠠⠀⣤⣿⠨⢾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡖⢸⣷⠀⣟⡄⣷⣿⣿⣿⣿⣿⣿⣿⠹⡿⢿⣿⣿⣿⠁⣿⠯⣿⣿⣿⢠⣿⠋⡄⢠⠀⣿⣷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⣯⣧⠙⣻⣿⣿⣿⣿⣿⣿⡇⢿⠸⣿⣿⣿⣧⣿⡌⢿⣿⡇⡜⣿⠉⣇⠸⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠏⢻⣿⣿⣻⣿⣋⣷⠘⡄⢯⠘⣿⢻⣿⠃⡎⢻⡷⠃⠿⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠸⠯⠰⣿⠀⡇⠀⠄⢿⠀⠿⠐⠛⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛
⠀⠀⠀⠀⠀⠀⢀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠴⣦⢴⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠂⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠋⠄⡿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠂⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢿⣆⠀⢸⣆⠘⠋⣀⠀⠀⠀⣷⡆⢀⠀⢠⣄⠀⠰⠀⠀⠀⢀⠘⠇⠀⠀⠀⢠⣄⠁⣀⠀⠀⠠⣤⣁⣼⠂⠀⠀⢀⠛⢀⠂
⠀⠀⠈⠻⠆⠈⡛⠀⠾⠋⠀⠀⠀⠈⠁⡿⠁⠀⠁⠲⠀⠀⠀⢀⡘⢧⡶⠂⠀⠀⠀⣉⠾⠋⠀⠀⠀⣬⡙⠁⣀⠀⠀⠈⣈⠺⠈
⠀⠀⢶⣦⡀⣰⠆⢀⣴⡶⠀⠀⠀⠀⠃⠀⠀⠀⠰⡀⢀⡀⠀⠈⣿⣆⣴⡇⠀⠀⠈⢻⣧⡶⠀⠀⠀⠉⠛⣿⡟⠀⠀⠀⠉⠲
⠀⠀⠀⠉⠀⡿⠀⠈⠁⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⡹⠈⠁⠀⠀⠈⠉⠋⠀⠀⠀⠸⣇⣡⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢈⡙⡔⠗
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⠰⣶⡄⢠⡄⠀⠰⢾⣶⢄⢿⠄⠀⠀⠸⣶⣾⣯⡔⠀⠀⢀⡀⠀⡄⣧⡀⠀⢰⣿⠀⠀⡀⠀⠀⢠⡄⠀⠀⡀
⠀⠀⢈⡄⠈⠀⠃⣀⠀⠀⢠⣌⠃⢸⠇⢀⡀⠀⠺⠃⠙⢇⣴⡆⠀⠀⠁⠀⠀⠀⠰⣌⢰⣧⡿⠆⠀⢠⣜⣡⠀⠀⠙⠳⠀⠘⠃⠀⢚⡁
⠀⠀⢀⠀⡄⠀⠀⣨⠀⢰⣬⡛⠀⡆⢰⣿⠃⠀⠀⠀⠶⢌⣾⠀⠀⠀⣠⠀⠀⠀⢳⣶⡧⠍⠀⠀⠀⢦⡟⢋⠀⠀⢠⣤⣦⣶⣤⠛⠉⠁
⠀⠀⠉⠀⠀⠐⠀⠀⠀⠘⠿⣷⠀⠄⠈⣁⣀⠀⠀⠀⠀⠀⠁⠀⠐⢶⣿⣶⠆⠀⢸⠃⠀⠀⠀⠀⠠⣤⣷⣿⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠐⠛⠛⠛⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠁

⣿⠿⢿⢿⡿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠰⠦⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣋⣃⠑⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣾⣿⣯⡳⠄⠂⠀⠀⠀⠀⠈⠉⠀⠀⠁⠒⠁⣱⣿⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡿⣡⡦⢏⠤⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠉⠸⣿⣧⣶⡆⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠻⠋⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠿⡁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠰⣿⣿⡾⡃⠀⠀⠀⠀⠀⠐⢿⡻⠷⠀⠀⠀⠀⠀⠀⠀⠀⢴⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠿⡟⠁⠀⠀⠀⠀⠀⠈⠓⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢠⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣢⠀⠀⠀⢠⠸⣿⣾⣧⣾⣟⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠄⢰⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠁⠀⠀⠀⠠⠀⠈⠓⢮⠋⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⡀⠳⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⢀⠀⠀⠀⠁⢠⣀⣬⠷⠦⠤⠤⠴⣋⠀⠀⠀⠖⠀⡇⢠⠙⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠂⠠⠄⣀⢀⡀⠀⠤⠚⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⢸⣿⠀⠐⣿⠀⠙⠋⢁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠙⠢⠄⠀⠸⠇⠀⠀⠿⠀⢰⡄⠀⢀⠠⠁⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣰⣿⣿⣿⣿⣿⠶⣤⣠⣷⡾⠛⠋⠛⠻⠶⠿⠇⣠⠞⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣀⢸⣷⡿⠻⡿⠂⠚⠁⠀⠀⠀⠀⠀⠈⠀⠐⢸⣿⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⢯⣹⣿⣿⡿⠇⣠⣤⣄⢀⠴⠴⠄⢰⡀⠀⠀⠀⠺⢿⣿⣦⣁⣀⡽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣄⡀⢠⣿⣿⣿⠗⠊⠉⠻⠿⠿⠶⠆⠀⠈⠁⠀⠀⠀⠀⠸⡟⠛⠋⠉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠃⣶⣦⠀⣀⢱⣶⡬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⣿⣿⣿⣶⣿⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡷⠀⠀⣾⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠺⢩⡾⠿⣿⣿⣿⣿⡗⠀⠀⠀⢀⡿⢻⣿⣿⣿⣿⡀⠀⡀⠰⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⡄⠺⣦⠟⣿⣿⣿⣿⣆⣀⣠⣿⣷⣿⣿⢟⠁⠉⡻⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣷⡆⠁⠀⣈⠀⠌⠍⠿⣿⡿⠏⠫⣥⣼⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠈⠁⠀⠈⠀⠈⠉⠑⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠘⠁⠼⢀⡀⠀⠀⠀⠀⠀⠃⠒⡆⠀⠀⠀⠀⢸⣿⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡁⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠉⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠀⠀⠀⠀⢀⠵⠂⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠷⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢠⡀⡀⣄⣤⣠⡄⠀⠀⠀⠀⠀⢀⣄⣠⣠⢀⠀⡠⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠂⠀⠀⠈⠐⠠⣀⠀⠀⢀⡈⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠐⢆⠿⠿⠛⠿⠛⢷⠇⠀⠀⠀⠘⡾⠙⠿⠋⡿⠻⡱⠂⠀⡠⠔⠁⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣙⠮⡅⠀⠒⠀⡦⠄⠉⣈⠉⣁⠉⠠⣤⠂⠒⡄⢈⠵⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠨⣖⠀⠀⢑⣼⣶⡐⢄⠀⠉⢀⣴⣶⠂⡱⡌⠀⠀⢲⠅⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠐⠚⢃⣶⠠⡎⢿⣿⡇⡠⠀⣀⡘⣿⣿⢃⠆⠰⠄⢲⡘⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⢇⠀⣩⡀⠆⠉⣠⠁⠙⠁⣤⠀⡸⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠂⠀⠀⠀⠐⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠲⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡘⠀⠀⠀⠀⠓⠀⠂⠐⠂⠀⡖⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⠀⠀⠠⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⣢⣀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣆⡌⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣛⣲⣤⣄⣀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡆⠁⠑⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⡱⠿⠃⠷⣰⣿⣿⣷⣤⡜⢦⢀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠒⢙⣱⠆⢳⣤⣍⣙⡿⢹⣽⢺⡟⡾⣮⢰⡞⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣹⡬⠟⠣⡤⣷⣙⢛⡀⣠⡙⠻⣾⣶⣄⡰⡛⣋⣹⠟⡶⣖⣫⣾⣧⣴⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⠶⢹⣿⣿⡞⣷⣖⡴⣿⢽⣴⣿⣎⢇⣼⣄⣡⣬⢓⣾⣿⡟⣿⣿⢿⠿⣿⢛⣸⢘⡀
⠀⠀⠀⠀⠀⠀⢸⣦⠡⠤⣄⢬⣉⠋⡵⢶⣸⡇⣠⣼⢎⡛⢡⣆⢿⣯⣿⣁⣼⠛⢻⣯⣷⣷⣼⣄⠁⢿⢿⣼⣿⢀
⠀⠀⠀⠀⠀⣀⡳⣿⠦⣸⣏⣿⣼⡟⢿⠜⠻⡯⣶⠤⡶⠧⣞⣷⢜⡙⡛⢽⣿⠛⢹⣿⢹⣦⣶⣟⠆⣿⣻⢛⢃⣙⣠⡄
⠀⠀⠀⠀⢀⡻⡕⡇⣴⢦⠸⡿⢟⡲⢖⣾⣷⣿⢿⡿⣁⣷⣿⣷⢏⢿⣮⣾⣯⢶⣼⣟⣸⣯⣽⣉⡋⣿⢻⣏⢩⣭⡛⢊⡧⠄
⠀⠀⠀⢤⡌⣵⠑⡾⢾⡞⣶⣿⣏⣻⡿⠎⣵⣶⢧⣯⣻⣭⡥⣍⣸⠼⡿⠷⠿⣈⣍⣉⠻⠶⢾⣛⣩⣹⣘⣹⡟⢈⣭⣿⣧⣼⡇
⠀⠐⢲⣢⣗⣭⣿⣥⠸⢾⣿⣷⡄⠆⡿⢰⣯⣬⠻⠿⣇⠿⢘⣯⣉⣛⡿⣰⣆⣿⣿⡏⡷⣷⣍⣩⣿⢡⣌⢻⣿⣻⣍⣤⣤⡔⣣⡀
⠀⠰⣆⣽⢅⡋⠏⢶⣿⢰⣶⣶⣶⢷⣴⣼⡙⣡⣖⠷⣶⣶⡏⣬⣭⣭⡭⡙⢁⣼⣯⣀⣷⣿⣦⣝⠋⡼⢡⣻⣿⣷⠙⡛⠉⣅⣿⡅
⠀⣼⣿⣿⣿⣿⣧⡻⢡⢼⣙⣗⢡⣾⡩⣹⡶⠿⡿⢣⣾⣷⡾⣾⣍⢹⣄⢿⣶⣭⣽⠶⢅⣻⣿⢇⣴⡧⢼⣷⣉⣴⡾⢛⣧⣬⣽⣦⡀
⠀⠛⠛⣻⣟⣽⡻⣿⣌⣿⣿⡼⡛⢎⣷⡬⣛⡿⣦⠚⣇⣸⣙⣹⡟⢧⠿⣿⣿⣳⣙⢿⣶⡴⣋⣽⣹⠟⣞⣹⡢⢻⠧⠾⢫⡿⣛⣹⡋
⠀⠀⠀⠀⠀⢰⢆⡾⠹⠿⣩⣿⣿⣿⣄⡶⢫⢸⣿⠏⢟⠻⠛⣷⣾⣿⣿⣮⣿⢻⣿⣇⣶⣺⠿⣿⡿⣇⣦⣽⣿⣿⣭⣍⣋⡛⣿⣾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⢽⠿⠟⠛⣊⣛⣻⣈⣏⡒⣷⣆⡞⣭⣛⢻⣻⣯⣹⠾⣷⡋⣛⢡⡞⣯⣽⡤⠉⣿⣛⠿⢻⡆⣿⢧⣛⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉⠛⠛⠋⠉⠈⠀⠘⢳⣼⣷⣴⣣⡾⠉⠂⠉⠁⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢦⣄⣉⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣌⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢺⣿⣿⣿⣿⠉⣹⣿⣿⣿⣿⣿⣍⠲⢄⠀⠀⠀⠀⠀⠹⣷⣄⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⣴⣾⣿⣿⣡⣶⣿⣿⣿⡏⣬⠋⠀⠀⠀⠑⣄⠀⠀⠀⠀⠈⢿⣦⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠸⠋⠈⣿⣿⣿⣿⣿⣿⣿⣷⠾⠇⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢻⣧⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣄⠀⣶⡤⠀⠀⠈⢇⠀⠀⠀⠀⠀⢿⡆⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢹⡇⣠⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠾⠿⣿⣿⣷⡆⠀⣀⠀⡾⠙⣆⠀⠀⠀⠘⣿⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠁⠀⠸⣆⠉⣿⡇⠀⡟⡆⠀⠀⠀⣿⡀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡿⠀⢠⣧⠇⠀⠀⠀⢸⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠘⣿⡿⠈⠉⠻⣿⣿⣿⣿⣿⣿⣄⡀⣀⣀⠀⠀⠀⠀⢀⣾⠇⠀⢸⡟⠀⠀⠀⠀⢸⠀⣿⣿⡇
⠀⠀⠈⠣⡀⠉⠉⠉⠒⠢⢤⡀⠀⠀⠀⠸⣿⠀⠀⢹⣿⡄⠀⠀⠘⠻⢿⠏⠘⣿⡏⠹⣿⣿⣇⠀⠀⠀⣾⡏⠀⠀⣼⠃⠀⠀⠀⠀⡞⢸⣿⣿
⠀⠀⠀⠀⢱⠀⠀⠀⠀⢄⠀⠈⠢⡀⠀⠀⠙⡆⠀⠀⢿⣿⣦⠀⠀⠀⣸⠀⢠⣿⡇⠀⢿⣿⡏⠀⢀⣼⡿⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⣄⠀⠱⡀⠀⠀⢻⡀⠀⠀⠉⠛⠣⣄⡼⠋⠀⢸⣿⡇⠀⠘⢿⣧⠴⠛⠉⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠘⢧⡀⡧⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠘⢷⡇⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢰⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⣠⠤⠚⢿⣦⡀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣠⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡇⠀⢠⡇⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⡇⠀⠀⠀⠀⠀⡇⠀⢸⠃⠀⠀⠀⠀⣸⣧⣴⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣶⣤⣷⣤⣾⣶⣶⣶⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢀⡠⠔⠀⡀⠀⠀⠀⠀⠣⢸⠆⠀⠀⠀⠑⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣰⠀⣁⠁⠀⢀⡴⠚⣁⡤⠒⠉⠀⠀⠀⠀⠀⣠⠏⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠇⠰⣂⡦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⢀⡞⠈⣰⠎⠐⢀⠝⣠⠞⢉⡴⠚⠉⠀⠀⠀⠈⠉⠁⡹⠚⢁⡐⠁⠀⠀⡀⣀⡀⠠⠴⣠⡤⠀⠀⠀⣹⢠⡆
⠀⠀⠀⠀⠀⠀⢀⠤⠶⡅⣸⠅⠀⠀⢰⠏⢀⣾⠗⢠⡼⠃⣴⢁⠔⠋⠉⠃⠀⠉⠀⠀⠱⠞⠁⣀⠔⠋⠀⢀⡴⠋⠉⠀⢀⡴⠞⠉⠀⢀⣤⡞⠷⠋
⠀⠀⠀⠀⠠⠖⡖⢑⡎⡃⠘⠀⠀⠀⠸⠆⠘⣷⣫⠎⠀⠀⢰⣯⡒⠦⠠⠤⠄⡶⠖⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⠝⠉⠀⠀⠀⠀⠫⡄⣿⠤⣀⡀
⠀⠀⢀⡀⢠⠚⡇⣩⣇⣬⠀⠀⠀⠀⠘⢆⠐⣟⠃⠀⠀⠀⠘⠆⣁⣀⣠⠄⠊⢁⡤⠊⠀⠀⣠⣤⠀⠲⠋⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠁⠀⠠⣝⡳⢦⡀
⠀⠀⠀⠰⡿⠛⣿⣩⣏⡼⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⡠⠞⠁⡠⠾⣁⠀⠀⠐⠋⠐⠂⠢⡀⠀⠀⠈⠉⣙⣛⣗⣂⡼⠛⠉⠀⠀⠀⠀⠀⠀⠁⠉⢳⡀
⠀⠀⠈⣠⢾⡾⢛⣯⣿⡇⠀⠀⠀⠀⠀⠀⣀⡴⣷⠀⠀⠀⠀⠀⢀⡤⡌⢶⡄⣀⡉⠲⢄⡀⠀⠀⠀⢻⢟⣻⣏⠀⠉⠉⠙⠛⠢⢤⠀⠀⠀⠀⢀⣀⣤⡔⣦⠼⠁
⠀⠀⠀⠘⠄⢀⣎⠟⠁⠀⠀⠀⠀⠀⠀⠰⠃⠠⢼⡅⠀⠀⠀⣰⢈⠀⣀⠀⠀⠀⠀⢠⣀⠉⠓⠄⡀⠀⠈⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⢻⠭⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢠⠤⠞⠈⠀⣾⣧⠀⠀⠀⣤⠻⢟⡛⠛⠉⠉⠉⠉⠉⠛⠉⠻⣅⠘⢆⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠪⡾⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢦⠤⣻⠴⢾⢟⣧⡄⠀⠀⠀⠈⠧⣀⡻⠾⢿⡛⠛⠻⠟⠉⠋⠉⠉⠛⣹⠀⠀⠀⠃⢀⠤⠄⠀⠀⠀⠀⡤⠴⠁⠈⠠
⠀⠀⠀⠀⢀⣀⣄⣀⡀⢈⣙⣶⡾⣭⣦⣼⡒⠁⠀⠀⠀⠀⢀⡀⠀⠉⠲⢀⡹⠦⢤⡤⠶⠶⠶⢦⡼⠋⠀⠠⠦⡄⠀⠲⠀⠀⣀⣀⣤⠶⠖⠃⠀⠀⠀⢀⢠⡄
⠀⠀⠀⢸⠿⣥⠌⡁⢛⣥⢶⡋⣠⣋⡼⠿⠛⠀⠀⡀⠀⠀⣷⡞⢣⠀⠀⠀⠉⠓⢄⡸⢷⡶⠞⠉⣠⠞⠀⠀⠀⠀⠉⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠰⠆⠩⡝
⠀⠀⠀⠀⢀⠀⠠⣟⡭⢰⣦⣍⡁⠀⠀⠀⠀⠀⠀⠀⠣⠜⢀⣦⣄⠉⡼⠖⠂⠀⣀⠝⠋⢀⣤⡞⠳⡄⠀⠀⠀⠀⣀⣀⠀⠐⠒⠒⠒⠀⠀⣈⠉⠁⠀⣲⠁
⠀⢠⣴⡓⣊⣍⣰⢿⣧⠎⡘⠋⠁⠀⠀⡄⠂⠚⣁⡸⠖⠈⣉⠁⡜⠈⠁⣀⠴⠊⢁⡠⠶⠿⠾⠿⢶⢿⡄⢠⡶⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⡋⠁
⠀⠀⠀⠁⡭⣘⡡⢺⣁⡀⠀⠀⠀⠀⠠⠃⠜⠋⢀⡀⠄⡆⠀⠈⢁⡠⠊⢁⣠⣶⣭⣤⣤⣤⡤⡤⢴⡟⠃⠘⠀⠀⠀⠀⠀⠀⠠⢶⣷⣧⣠⣄⣤⠆
⠀⠀⢰⠶⠀⣿⣧⠉⣟⠿⠂⠀⡨⠦⢠⠅⠀⡌⠀⠁⢸⠁⠀⡴⠋⣀⣴⣋⣀⣀⣀⣀⣀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⢈⣫⠾⠟⠋⠁
⠀⠈⠻⡦⡿⠹⠇⠙⠀⠀⠀⠀⠐⠓⠁⠀⠀⠁⠀⠀⠀⠀⠈⢀⡞⠉⠉⠉⠉⣉⢉⣩⠝⠋⣀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⢀⢚⡇⠀⡞⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⣿⠂⠀⠈⢈⡹⠟⠉⣠⠔⢊⡁⠤⠂⣁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠳⠈⠉⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠀⠀⠀⠀⠹⠟⡷⠞⠁⡀⠀⠈⣡⠔⠹⠃⠀⠀⠀⠑⠠⠀⠀⠀⠀⢠⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⢚⠁⠀⠀⠀⠀⢀⠈⢀⠖⠛⠢⢄⡀⠉⠈⠉⠀⠀⠑⠂⡀⠀⠀⠀⠀⢠⠇⠀⠀⢠⠀⠀⠂⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠿⢊⡁⠀⠀⠀⠀⠀⠀⡰⠛⠛⠛⠾⢧⡈⠀⠀⠀⡀⠀⠀⢀⡿⣣⣦⣤⣴⠂⠀⢀⡴⠊⠳⠄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠈⡄⠀⠀⠀⣾⠏⠁⠀⠀⠀⠀⠀⠀⢰⡄⠰⠦⠄⠠⠶⠽⠇⠤⣗⠈⠳⢄⠈⠆⠙⠃⠈⢇⠀⢠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡷⢰⠄⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣤⡀⠀⣠⣶⡶⡤⠤⠬⡳⠤⡘⣧⠀⠀⠀⠀⠈⢆⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⢼⠀⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⢄⡈⢹⣦⣄⠀⣤⣤⣤⠤⡄⣰⢿⠀⠀⠀⠀⠀⢸⠆⣸⠇
⠀⠀⠀⠀⠀⠰⡿⠀⠀⡷⢣⠂⠀⠃⠂⠀⠀⠀⠀⠤⡀⠀⣠⣶⡀⠛⠉⠓⢥⡈⠛⣦⡀⠀⣀⡔⢋⡜⠀⠀⠀⠀⠀⣫⣾⡏
⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡈⢙⠷⢉⠀⠀⠀⠀⠀⠈⠒⢌⡩⠟⢉⡠⠋⠀⠀⣠⠴⢆⡸⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠬⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣠⠾⠁⠉⠀⠐⠛⠀⠀⠈⠀⠀⠙⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠈⠑⢦⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⡆⠀⢀⡠⠼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠤⠊⠈⠁⠉⠦⣀⣠⠰⢅⡴⠁⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢠⣤⣤⢊⠀⠀⠀⠀⠀⡠⠂⣱⣦⡸⣙⠻⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⣄⣀⠞⠔⠁⣰⣿⣆⠀⣀⠀⡀⠀⢿⣿⢿⠇⠈⠀⠀⠲⣀⡰⢂⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣰⡉⠑⠀⠀⢆⠀⠻⣿⠏⠀⠠⠇⠈⠒⠒⠉⢸⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⠀⠀⡈⠭⡀⠀⠐⠂⠊⠀⠁⠀⡼⠃⠀⠀⠀⠀⣰⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠀⠂⠀⠀⠀⠀⢀⣀⣴⣊⣀⣀⣀⣀⠤⠒⠁⢻⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠒⠲⢈⡩⠝⠀⠀⠀⠀⠀⠈⡇⢀⡠⠖⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣹⠁⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⠉⠊⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠁⢀⣣⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⡼⠉⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡰⡇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡰⠁⠰⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠁⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠤⠤⣴⠁⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣍⣉⡦⠀⠀⠀⣏⣭⣭⣭⣍⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠖⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠂⢁⡀⠀⠀⠤⠈⠀⠛⠿⠿⠶⣶⠶⢤⡂⠀⠂⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⣠⣀⠀⢦⣶⠀⣸⣤⣶⣶⣶⣾⠷⣿⣿⣭⡿⣿⡆⢇⠐⣶⢧⣢⣤⣄⠒⢠⠤⣤⠠⠄⠀⠀⠩⢆
⠀⠀⠀⠀⠀⡐⠁⠢⣤⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣻⣉⣉⣀⣈⡉⠓⢦⣾⣧⣾⣿⣿⣿⡿⣶⣾⣧
⠀⠀⠀⠀⣠⣡⣾⣶⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⢠⣿⣿⣿⣭⣿⣶⣿⣿⣿⣿⣾⣿⣿⣧⣼⣿⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠿⢿⣿⣾⣶⣶⣮⣿⣿⣿⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣈⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣥⣼⣯⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⢉⣭⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠈⠿⠟⢿⣿⣿⣿⣿⠟⠇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠛⠛⠻⢿⠿⠻⠛⠛⠛⢻⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠠⠶⣿⣿⣧⠼⠄⠀⠻⣿⣿⣿⣶⣶⣴⣶⣶⠼⠾⠟⠿⠿⣿⣿⣷⣤⣀⠀⠀⠀⢀⠀⠈⠉⠉⢋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣽⣿⣿⠟⢿⣷⣶⠀⠀⠀⠀⠀⣤⣿⣿⠟⠉⠛⠿⠀⡄⣿⢿⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣡⠀⠈⠻⣿⣆⠀⠀⠀⠀⠉⠉⠀⠀⠐⠦⣄⡀⣷⣾⡿⣳⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣴⣿⣤⣀⣀⣌⣿⡶⣢⣤⣤⣴⣦⣤⣤⣴⣤⣼⣿⣿⣿⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣟⡿⠛⠋⠀⠀⢢⠈⢻⣧⣿⣽⣻⡏⠀⠀⡀⠉⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹⢤⣬⣿⣿⣿⣯⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⣶⡀⢀⣽⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⡀⠀⠀⠀⠀⠀⣿⡇⠂⠈⣿⠁⠀⠉⠀⠀⡀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠋⠙⠶⢤⡀⠀⢠⢿⠀⠀⠀⡿⡆⠀⣴⡀⠃⢠⢄⡤⠉⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣾⣿⣿⣿⣿⣶⣤⡀⠀⢰⣦⣼⣴⠶⠶⠶⢷⣦⣤⣿⠇⠀⣠⠧⢀⢂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢱⣿⣿⣿⣿⡿⠛⢻⣌⣻⣿⣿⣿⣋⢀⣾⠁⠀⠈⠀⠀⠈⠉⠻⠇⠀⡀⢰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⣸⣿⣿⣻⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⢠⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠻⣦⣼⣿⣿⣿⠟⢀⣤⣄⣢⡀⡀⠾⠾⠦⠀⢶⡀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣄⣀⣴⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣀⣀⠀⠀⣸⣿⣿⣿⡷⠐⠋⠉⠻⢿⡷⢿⣶⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⠛⠛⠛⠉⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⣿⣿⠛⠓⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠘⠦⣄⣀⠀⠀⠀⢦⣬⡄⢘⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠶⠔⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⣀⣤⣾⣿⣧⢠⣶⡌⠛⠻⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⣿⣿⣿⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣾⣿⠁⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡟⠀⠀⣼⡿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠟⢠⣺⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠰⠟⣡⣾⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣏⠀⠀⠀⡀⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠉⣦⣀⣹⢿⣿⣿⣿⣿⣆⠀⠀⢀⣼⣿⣴⣿⣿⣿⠟⠛⠻⢷⣼⣭⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣷⣧⡀⡨⠟⠁⠺⠿⠛⠿⢿⣿⣶⣶⣿⣿⣿⠿⠛⢻⣴⡀⠀⠰⢊⠁⠉⠙⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣆⡀⣀⢰⣄⡀⠉⠳⠘⢟⣿⣟⠛⠀⢳⣷⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠈⠛⠛⠁⠀⠀⠘⢿⠟⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⡦⣄⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡿⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⡀⣹⣿⣿⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣧⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣱⣿⣿⣿⡏⢻⢯⡙⢗⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⣬⣿⣷⣅⠘⢃⣹⣿⡏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠀⣄⠀⠀⣴⣿⣾⣿⣿⣿⣶⢟⣹⣿⣿⣷⡆⠠⣾⣷⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡉⢹⡟⢻⡿⢿⢿⣿⣿⣿⣿⣿⠛⠛⠛⢛⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣿⡟⣁⣼⣷⣿⣟⣿⣿⣿⣿⣿⡅⢬⠅⣼⣿⣿⠟⣭⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣀⡼⠉⠻⣴⣾⣿⣿⠿⡟⢿⣿⣿⡿⠹⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡿⣿⠰⢣⠀⠀⣿⣷⡿⣿⣶⣯⠀⠘⢿⣷⣹⣿⣻⡶⣿⣿⣿⣿⣿⡿⢻⡇
⠀⠀⠀⠀⠀⠾⠍⠁⠀⠀⠀⠀⠉⠈⠀⠀⠀⣄⢨⡿⣷⠛⠟⠚⢿⠀⠈⢸⣿⣻⣿⣷⣬⡟⢹⡿⠋⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⣤⣰⣿⣿⣿⣇⠀⠀⢀⡎⠀⠀⠀⢸⣿⣿⣿⠟⠗⠓⠿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣍⣿⡉⣿⣆⠀⣭⠁⠀⠀⠀⢸⣿⣿⡟⠀⢰⠷⡄⠛⠙
⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⢰⠈⣿⣿⣿⠿⣋⣉⣸⣛⠃⠀⠛⠀⠀⠀⠀⣿⡏⣼⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡄⠻⢿⣠⣾⣆⣿⠻⡇⣠⣾⠿⣿⣋⠁⠶⠒⠀⣠⣶⣷⠛⠛⠠⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣀⡀⠀⠀⠒⠶⢿⣭⣿⣧⣤⡷⠎⣿⣾⠿⢿⣿⣿⣶⣿⣿⣏⡷⣀⠚⠢⡄⠀⠀⠀⠸⠏
⠀⠀⠘⢿⣿⣤⡀⠀⠼⠿⠿⢾⣗⠦⠁⠀⣉⠉⠐⠦⢤⣀⣽⣟⣿⣎⣷⡄⠀⠀⣁
⠀⠀⠀⠀⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣴⣆⠀⠋⠁⠁⠁⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠶⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣇⡀⠀⠀⠀⣠⣴⠦⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠁⢉⡺⡉⠓⠀⢀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠆⠀⠈⠛⠿⠿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠰⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⡒⠁⠀⠀⠀⠢⠼⢆⠀⢠⠎⠀⠀⠀⠀⠣⣀⣬⠇⣀⠀⠀⣴⢉⣀⣉⠀⠈⠉⠈⠉⠉⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣀⡠⠜⢢⠀⠀⠀⢠⡀⢀⠀⠑⢮⡀⠀⠀⠀⡄⠀⠀⠀⣰⢇⡉⣲⠀⠀⠀⠀⠉⠑⢄⡀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢑⡆⠀⢺⠉⠀⠀⠀⢀⢣⡀⠀⠀⠙⠒⠷⠤⢄⣡⣀⡰⠟⠀⠀⠀⡰⠁⠁⢀⡇⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠀⠀⠸⠄⠀⠀⠈⠀⠀⠳⡀⠀⠀⢀⣠⣤⣀⣹⡤⠤⠄⠀⠀⡰⠁⠀⠀⠸⠀⢠⠃⠀⡇⣀⣴⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢆⡠⡞⠉⠧⣺⢸⢀⣠⣉⠦⠚⡅⢠⠆⢀⠃⠀⡷⠀⣠⠏⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠽⠶⢤⣬⣀⡄⠀⠀⡇⠀⠀⣀⡠⠤⠒⠊⠉⣙⠟⠢⠔⢹⠛⠁⠀⠀⠀⠀⠈⠛⣄⡌⠀⠈⢱⠾⢥⣀⡀⠘⠀⠉
⠀⠀⠀⣠⠤⣄⠀⠀⢀⠀⠀⠀⢀⡤⠜⠻⣄⢰⠓⠂⠉⣀⣠⠤⠒⠊⠉⣠⠤⠤⠤⠚⠓⠒⠢⣄⣀⣀⠀⠀⢸⣁⠀⡔⠁⠀⠀⠃⠈⠉⠉⣀⡀⢀⣠⣀
⠀⠀⠘⠢⠴⠚⡰⠒⠁⠉⣧⠀⣁⡀⠀⢀⣸⡞⠒⣈⠥⠤⠉⠢⠀⠀⠀⠑⠤⣄⠀⠀⠀⠀⡰⠀⠀⠀⠈⠉⠉⠀⠙⣄⡠⣤⠀⠀⠀⣖⠉⠀⠈⠁⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠈⠛⠒⠉⣡⠚⡁⠈⠋⡥⠦⡧⠀⠑⡄⠀⢀⠔⠀⠀⠀⠀⠀⠀⠳⠀⠀⡜⠁⠀⠀⠀⠀⠀⠘⠻⢍⠋⠁⣨⠶⠀⠀⠸⣀⣀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⡱⠈⠀⢀⡷⠶⠃⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡇⠀⠀⠀⣀⡀⠀⠀⣠⠞⢉⡭⠧⠷⡄⠀⠀⠀⠀⠉⠊⠁⠈⠁
⠀⠀⠀⠀⡤⠴⠋⠉⢂⢱⡁⡴⠲⡶⠋⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠙⠢⠔⠊⠀⠀⠉⠉⠀⠀⡌⠀⠀⠀⠘⣄
⠀⠀⠀⠀⡧⠀⢀⠍⠾⠄⠟⡷⠚⠁⠀⠀⠀⠀⡔⠋⠀⠀⠀⡈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⡄
⠀⠀⠀⠈⠣⡼⠁⠀⠀⠀⢠⠃⠀⠀⢀⣠⠄⡼⠀⢠⣠⠞⠒⠋⠒⠣⣴⠀⠀⠀⠀⠀⠀⢠⡤⠚⠒⠛⠒⠦⣤⠀⢀⠔⠃⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢠⠋⠀⠀⠀⠀⡜⠁⣠⣴⣶⣶⣄⠀⠳⠀⠀⠀⠀⢠⠊⠀⣠⣶⣶⣦⡄⠈⢆⠘⢦⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣄⠀⠸⡀⠀⠀⠀⠰⠀⠀⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⠀⢸⠀⠀⠈⠙⠢⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠈⠢⣀⠈⠒⠂⠒⠚⢇⠀⠹⢿⣿⣿⠟⠁⣠⢁⡤⠒⢄⠘⡄⠈⠻⣿⣿⡿⠏⠀⡜⠉⠒⢤⡀⢀⡅⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠢⡀⠈⡆⠀⠀⢀⣀⠈⠳⢄⣀⠀⣀⡠⠞⠁⠈⠀⠀⠀⠀⠘⣦⢄⡀⠀⣀⠤⠊⠀⢀⣀⡀⠈⠉⠀⣠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠒⠧⠤⠔⠉⠮⠤⢠⡄⠀⠛⢄⣀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢠⡤⠤⠗⠉⠓⠒⠋⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠤⣄⢀⡀⠀⠀⢀⣛⢃⡄⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣍⣛⡀⠀⠀⡠⠔⠒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⢦⡀⣆⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠰⠯⢐⣇⠜⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠢⢄⣀⣀⠠⢄⠀⠀⠀⠁⠀⠀⡰⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣘⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣀⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠒⠂⠠⠄⠀⠐⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⢌⠎⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰
⠀⠀⠀⠀⠁⠀⢸⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣷⣣⠂
⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠄⠜⢂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥
⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⢀⡀⠉⣀⣼⢏⡴⠒
⠀⠀⠀⠀⢡⠈⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡌⠀⠆⠀⠀⠀⠀⠀⢀⡡⣼⣿⣷⡈
⠀⠀⠀⠀⠀⢣⡉⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠐⠀⠀⠀⠀⢀⣵⡿⠉⡄
⠀⠀⠀⠀⠀⠀⠳⡀⢣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⢹⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡁⠈
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂