Wavy Emojis & Symbols

⠀⠀⠀⠠⠂
⠀⠀⠀⠀⡀⢀⣭⠃⠀⠀⠠
⠀⠀⠀⢀⠀⠁⠁⠠⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢄⡦⡄⠀⠀⠈⡇⢀⠔⢡⠄⠉⠀⢀⣴⣶⠁
⠀⢠⠀⠀⠀⢠⠃⠀⢀⣻⡷⢃⣵⠿⠿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠆⢄⠄⠀⢀⣆⡁⠤⣰⣯⡶⠋⢁⡠⠤⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⢠⠏⠀⠌⡼⠙⠈⣴⢡⠏⠀⠀⡏⠀⣤⡝⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⢠

⡼⠀⠀⣜⠁⠀⣸⠡⡟⠀⠀⠀⠣⠀⠓⠒⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠴⠦⣄⠈
⡇⠀⠘⠡⠀⠀⠋⠂⢻⠀⠀⠀⠀⠁⠐⠒⠹⠻⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⢀⡴⠃⠙⠀⢀⣤⡄⠈⡇
⡁⡀⠀⠇⠀⢠⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡚⠉⠁⠀⣄⢀⠙⠉⠉⠀⠢⢄⠀⠘⢥
⡟⠈⡰⠀⠀⠸⡄⠀⠀⠈⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠴⠚⠑⠂⣔⢀⢸⡃⠀⠀⠀⠀⣤⢀⡇⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⢳⠑⠀⠀⠁⠀⠑⠠⠤⠄⠀⣀⡠⠤⠖⠊⠁⠀⢀⠀⠀⠀⠈⣄⠚⠇
⢧⡠⠀⠀⠀⠀⠋⢧⡀⢀⡀⢀⠀⠀⠀⢀⠀⠈⠈⠀⠀⠀⠀⠀⠠⠂⣁⡀⠂⠈⠀⠀⠄
⠈⡄⠀⠀⠀⠀⠀⠀⠝⢶⡀⠀⢔⠀⣀⠀⠉⡲⠀⠀⠀⢀⢔⠀⠀⠀⠈⠙⣆⣢⠀⠀⠐⠄⠀⠀⠀⠀⠔⠚⠃
⡀⠀⡀⠀⠀⠂⠀⠀⠀⡀⠍⠛⢦⣤⣤⣄⣈⡀⣤⠔⠈⠀⠁⠀⠀⠀⢀⠀⠸⢿⠄⠀⠀⠀⠑⠂⠀⢀⣀⣀⡀
⠀⠀⢲⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡡⠁⡘⠁⠂⠀⠈⠀⠀⠀⠀⢀⠀⠀⠳⠧⠀⠀⠀⠀⣀⡲⠀⠐⠀⠀⠢
⠀⠀⠀⠻⣎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⢢⣀
⣀⠀⠀⠀⠘⠦⣄⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠱⡉⠉⠙⠉⠀⠀⠈⢳
⠀⠀⠈⠢⠠⡀⠈⠓⢤⣝⣄⣀⣐⠪⢉⣂⠤⠄⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⣤⡆⠀⠜
⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣛⣿⣛⣻

⠀⠀⠀⠀⠀⣧⠠⠀⢙⠲⠦⠭⠤⠤⠤⣤⣀⣽⣲⡁⢠⡟⡉⡈⡩⢋⠔⠡⣪⠶⠋
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠻⢿⣆⠈⠄⠐⠁⣠⠾⠓⠒⠒⠒⠒⠲⣦⣄
⠀⠀⠀⠀⠀⠸⣇⠠⢐⠀⠀⠀⣀⣀⣀⣀⢀⣀⠀⠐⠈⠝⢳⣄⣰⡟⠡⠀⠀⠐⠀⠀⠀⠄⠀⢈⡻⢦⡀
⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⡀⠠⠀⠈⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠒⢒⣒⡒⠈⠁⠢⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢊⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣲⠶⡶⠛⠟⠋⠉⠙⠻⣶⠄⠀⣿⠀⡀⠀⠁⠀⠀⠀⠄⢐⣬⣥⣬⣄⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠋⠁⠈⠔⠁⠊⠜⠀⠀⠠⢹⠀⣸⢿⣀⣀⡀⠀⡀⣀⣤⠶⠋⠉⠀⠀⠙⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡾⢂⣠⣤⣤⣤⣁⠀⠀⡈⢐⣑⣠⣎⡼⠋⠀⠈⣻⠙⠛⠋⠉⠀⠁⡀⡀⢀⣰⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠩⠁⠈⢌⠙⡻⢛⣿⠟⠉⢹⣟⢳⣄⢀⡴⠷⠾⠓⠶⠶⠶⠴⠶⢞⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠆⠀⢪⡞⢩⡏⠀⠀⣤⣯⣤⣿⣯⣄⡀⠀⠀⠀⢀⠐⠢⢌⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢘⣨⣠⣤⣿⣤⠼⠷⠗⣿⠛⠁⠀⠂⠈⠉⠙⠶⣤⡀⠀⢠⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠛⠋⠉⠁⠐⠀⠀⠀⢸⡿⠛⠉⠱⣦⠀⠀⠈⠀⠈⢻⣦⠟⠁
⠀⠀⠀⠀⠀⢀⣴⡿⡷⢶⣤⣄⠀⠈⠀⠀⠀⠀⠘⣇⠂⠀⠄⢸⡇⠈⠀⠈⠈⠀⠹⡆
⠀⠀⠀⠀⣴⢟⠡⠀⠀⠀⠀⡈⠛⣦⣄⡀⠀⠀⠀⠙⢦⠨⠢⢘⣧⠀⠂⠁⠀⠀⠀⡇⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢀⣿⠘⠐⠀⠀⠸⠀⡀⢸⡃⠈⠛⣧⣤⣀⣀⣨⢷⡐⠁⢿⡄⢃⠀⠀⠀⠀⡇⠸⢯⠉⠈⠉⠛⢦⡀
⠀⠀⠀⠈⡇⢂⠡⠀⡀⠁⢀⣬⣾⣷⠀⢠⡇⡈⠈⠉⠀⣼⢻⣌⠌⢿⣾⡠⠀⠀⢰⡇⠀⣸⠀⠀⠀⢀⠘⣧
⠀⠀⠀⠀⠙⢦⡁⠌⠂⢊⠴⣶⡿⢃⡴⣿⠁⠠⠀⠀⣰⠃⢈⣿⣆⢱⢹⠿⣆⡆⠘⣷⠚⠁⠈⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⢉⡴⠋⠁⣇⢁⢡⢀⣾⠷⠚⣻⠇⢙⠻⢾⣦⣈⡛⠶⣬⣷⣄⣀⠀⣀⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢂⠻⣾⣬⣿⣧⣤⣤⡟⠀⠀⠀⠀⣀⠀⠉⠙⢲⡌⠉⠉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡀⠀⠀⠀⣽⡟⠩⢂⠡⠙⢻⡻⣦⣄⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠄⠠⣿⠀⠀⠁⣠⣤⣼⡇⠀⠙⢷⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣘⣦⡀⠀⢀⠻⣧⣷⣰⣿⢹⡿⠁⠀⠐⢈⢻⡄⠀⠂⢀⡿
⠀⠀⠀⠀⠀⣠⡞⢋⣀⡀⠀⠈⠉⠙⢳⣄⠁⠈⠛⢻⣷⠞⡀⡠⠀⠀⠈⡘⣿⣀⣡⣞⣁
⠀⠀⠀⠀⢠⡿⣀⠲⠐⠂⠐⢀⠀⠀⠀⡙⢷⡄⢁⡾⠁⠊⠔⠁⢂⠀⡐⡈⣿⡉⠁⡈⠉⠻⣦⡀
⠀⠀⠀⠀⠈⣿⡟⠛⠳⣌⠀⠠⡁⡐⢌⠠⠀⢻⣾⠐⠁⠊⠔⡠⠀⠈⠄⣐⡿⢀⠁⠀⠀⢀⡘⢿⡄
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⣳⡐⠐⠌⠢⠈⠀⢸⡏⠐⠁⢂⠄⠔⠡⠂⢀⡾⡁⠡⣪⡴⠟⡋⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠹⣦⡀⠅⠂⠄⢹⡇⠀⠠⠀⠊⠀⠐⣵⢋⠡⠀⣴⠋⠐⠐⡀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⣠⡽⢦⣤⡀⠊⠙⠳⢦⣤⣼⣿⡠⠁⢀⠂⢢⠞⠁⠄⠀⢴⡏⠊⢈⠔⡀⣠⠟
⠀⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⡹⣤⣀⠀⠀⠀⠀⠸⣷⡀⠂⠀⡏⠀⠀⠘⢌⡾⠀⠄⡠⢊⡴⠋
⠀⠀⠀⠀⠀⣿⣘⣧⣠⡶⢾⣸⡇⠈⠉⠒⢮⣀⣀⢈⣻⣷⣴⣿⣤⣮⣶⢋⢔⡁⢊⡴⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⣠⣤⠤⠀⣐⣤⠠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠆⡔⠡⠯⠤⠬⢁⢄⠀⣀⠀⢒⠤⠇⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠂⡖⣡⢤⡀⠀⠡⠀⠀⠀⠀⠀⡄⣄⣙⡓⢲⢀⠤⡜⠌⡸⡀⠈⡆⢳⣠⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⢰⢡⢣⡹⠤⠃⠀⠀⠀⠀⠀⠀⠀⡆⢀⡤⡝⠀⢡⠚⠢⡀⠀⠉⠚⡡⣾⡏⡜
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⡀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠤⠲⡸⠀⣌⡀⠀⠂⢰⠆⠄⠀⠀⠐⠊⠣⠃
⠖⣂⠀⠀⠀⠀⠀⠀⠀⡀⢀⢄⡄⣠⠄⣤⢠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠳⣕⠄⠱⢽⠄⠀⠈⠘⠡⠂⠠⢀⠀⠀⡠⢄
⠍⠂⠁⣀⡀⢠⠠⡄⢉⣀⣙⠮⡓⢬⣉⣡⠎⠀⣩⠭⠤⡔⡄⢢⠄⠉⠀⢈⣑⠕⠑⠪⠡⠀⠀⠀⠀⠀⠀⢡⠛⠙⢦⢣⢨⢊⠢
⣠⠖⠁⡠⠋⠈⢈⡬⠒⢲⡌⢳⡌⠦⠤⠤⠤⡀⣇⠀⡰⠑⢕⠕⠊⠉⠑⢆⢻⢉⠄⠀⠀⠀⠀⠀⠀⠠⠂⠻⣤⣤⡼⠃⡇⠃⢣
⠁⣠⢪⠢⣄⠣⠬⠉⠉⢍⡀⣠⠍⠁⠀⢀⠁⢈⢎⠛⢰⢠⠸⣀⣀⣀⣀⡼⢀⠀⠀⠀⠀⣀⠀⠀⠈⡆⢠⠶⠶⠶⠶⠞⢁⡇⠸
⡞⠁⠘⡓⠒⠠⠔⠀⣀⠑⠁⠁⢀⣖⡆⠁⠁⠈⢊⣤⡀⠳⢕⡒⠤⠤⠤⡴⠎⡄⠀⠀⠘⠷⠇⠀⢠⠁⠏⠖⡩⠭⢭⡉⢻⠛⣓
⣇⠀⡞⡔⡥⠬⢭⡉⢎⠀⠀⢀⡊⠁⠀⠀⠀⠠⢄⡢⣉⣓⣒⡂⢭⡓⢄⣀⣸⢸⢠⢢⡀⠀⠀⠀⠆⠀⠀⠸⡐⠓⠐⠁⠁⢉⣒
⣜⠶⡇⢇⠣⢄⡤⢋⠀⢀⢠⣓⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠐⠂⠥⠈⠐⠍⠿⠂⠁⠀⠈⠓⠀⠀⠘⡄⠀⠀⠀⠀⠀⡀⠤⠒⢶
⠈⠑⠤⣀⠉⠒⢪⠖⡔⢼⣀⡴⡀⠀⠀⠀⣰⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⢀⠠⠦⠰⢆⠄⠀⠀⠀⠀⠈⢢⣭⡔⠂⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠑⠲⢌⡳⠕⠢⠭⠔⣣⡇⢢⡀⠘⠢⠤⠤⠚⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⠀⣀⠀⠀⠀⠀⠀⣸⢿⣇⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠽⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⣀⠀⠙⠒⠀⠀⠀⠀⢠⣇⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣤⢤⡀⠀⠀⣠⡖⢄⣀⡖⡾⢆⠀⠀⠀⣤⢠⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢠⢶⣤⣀⠀⢀⡠⣤⣀⠀⢀⣴⠦⣤⣀⡀
⠀⠀⠀⣴⢽⠝⠽⡛⣯⣭⡻⣛⢙⢾⡫⡟⡅⣠⣾⣵⣪⢞⣿⠶⢦⡤⢶⣷⣃⢺⠵⠿⠷⣝⡲⢯⣭⢎⠖⣻⡿⣛⠵⣛⣿⢶⣙
⢀⢴⣸⣶⢳⣫⠭⠾⣫⢽⡶⣛⣗⣭⡚⢞⢬⡿⢽⡯⢖⣷⡟⣩⡕⣟⡫⡲⠬⡿⠛⡼⠷⠦⣹⡶⢭⡻⣚⡥⢂⡒⣎⢳⣑⣿⣦
⣱⢩⢏⣙⠭⢣⣚⣛⡱⢓⡮⠗⠛⢇⠿⢲⢵⣚⣭⣭⣽⠟⣚⣡⢮⢵⡮⢜⡲⣍⣛⡺⢽⣛⣻⠯⠷⢿⢶⣻⣫⣬⣫⡳⢞⡵⢚
⣖⣣⢞⣵⢝⡷⠗⠒⠶⠃⠀⠀⠀⠹⣛⣋⡭⢟⣾⣿⡷⠁⠀⠂⠀⠰⠴⠓⢮⣲⠟⠀⠀⠛⢭⡭⠽⠛⠿⠿⠷⢦⠳⣭⢵⡵⠋
⠛⠻⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣈⠁⢤⡀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣅⠠⠐⠄⢧⣼⠗⠊⡀⠀⢀⣤⠅⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⣾⣗⡵⣪⡶⣫⢵⣢⣤⣬⣀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⡷⣾⣾⣾⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⠟⢉⣭⡁⠈⠀⠒
⠀⠀⠀⠠⠀⣠⡊⠀⠀⠛⠚⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣵⣶⠖⣀⣀⣀
⠀⠁⠀⣠⠐⣟⣥⣤⢂⡤⠤⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣭⡉⠉⠀⠆
⠀⠀⠀⠈⠁⠀⠀⠙⣿⠏⠀⠙⢷⣦⡬⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⣿⣿⣤⣴⣤⡀
⢎⣡⣠⣄⣀⠲⣦⡲⣌⢻⣦⣌⢲⣴⣶⡂⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡼⠛⢿⣿⣴⠗⠳⢄
⠬⠿⠿⠿⢿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣭⣻⣧⣠⡀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⣻⣿⠃⠀⢤
⠀⢀⣀⡀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣠⡘⣿⣿⣿⣿⣿⡾⡄⠀⠀⠀⠀⠀⠘⠋⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠈⠙⢷⣤⣢⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⡝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡯⢖⡀
⠀⠘⣦⣔⢦⣨⡛⢭⠁⠀⠠⣙⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣮⡳⢄⠀⠀⠀⠀⢀⢀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣟⣴⠂
⠀⠀⠸⣿⣿⣿⣿⣦⣻⣦⣳⣮⡻⣄⣿⣦⣀⠹⠿⣿⣿⣿⣿⣿⣾⠿⣿⣿⣽⣿⣦⡉⠓⢿⣿⣿⣿⣦⣾⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡯⠉⢀⠠⣐⢬⡋⠉⠙⠿⣿⣷⣎⡻⢿⣿⣿⣿⣷⣦⣀⣉⠙⡛⣛⢻⣿⣿⣛⣛⣭⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣮⣷⣽⣷⣶⣤⣈⣛⢿⣿⣷⣭⣛⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣋⣥⣤⠶⣶⣒⣒⣒⣒⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣽⣾⣿⣿⣿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢭⣭⣽⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣛⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠶⢦
⣦⡈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣰⠋⣀⡙⠄⠀⠀⠀⠀⠀⢀⡴⣫⡴⠟⢋⡙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣛⠛⠷⣤
⠙⢿⣦⡈⠛⠲⠦⢤⡤⢔⣥⣤⣍⡂⠀⡰⣡⡾⠛⠻⣆⠀⠀⠀⠀⡰⢋⡾⠋⣠⡾⠟⠛⠳⡵⣄⠀⠀⠀⠀⠀⢀⠴⣚⣉⡙⠻⣦⣈
⣄⡀⠙⠿⣷⣶⣶⣤⣶⠟⣁⣀⣉⣙⣋⡴⢋⣴⣶⣶⡸⡄⠀⠀⡼⣱⠏⣠⡾⠋⣠⣶⠿⠷⣌⠪⣕⣒⣒⢶⣺⢕⣫⣭⣉⠛⢶⣌⠙
⢿⣿⣦⣄⣀⣀⣀⣀⣠⡾⠟⠛⠛⠛⢋⣴⠟⢉⣀⡈⢻⡡⡀⢜⡼⢃⣾⠋⣠⣾⠛⢁⣤⣶⣬⣙⠒⣒⣺⢽⣚⣭⣤⣤⡙⢷⣄⠙⠷
⠀⠉⠛⠿⠿⠿⠿⠿⠋⣠⣤⣶⣶⠿⠟⣡⡶⠟⠛⠻⣦⢧⢌⠛⣡⡟⢁⣼⠟⢁⣴⠟⢉⣠⣤⣭⡭⣝⡪⠭⠶⠶⢦⣌⠻⣆⡙⠻⣦
⣷⣦⣄⡀⢀⣀⣀⣠⣾⠟⠉⢁⣠⣴⠞⣋⣴⠶⠿⣦⡘⡎⣎⠛⠋⣠⡿⠁⣴⡿⠁⣴⡟⢡⠴⠒⠊⠁⠈⠉⠙⠓⢦⡙⣦⡘⠻⣦⣄
⠙⠿⣿⣿⣿⡿⠿⠟⢁⣴⡾⠟⢋⣥⠞⡉⠤⠀⠀⠈⢳⡹⣪⠳⣾⠟⢠⣾⠋⣠⡾⢋⡴⢫⠎⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⠻⣦⣄⡉
⡀⠀⠀⠀⠀⢀⣠⣴⠟⢉⣠⠾⢋⠄⠈⠀⠀⠀⠀⠀⠀⢧⢏⢧⣤⣴⡟⢁⣴⠟⠠⠾⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡙⠛
⣿⣿⣶⣾⣿⡿⠟⢁⡴⠟⣡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⣎⠛⠉⣠⡿⠃⣴⠟⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿
⠉⠉⠉⠉⠀⣠⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡹⢷⡾⠟⣠⡾⠋⣼⠋
⣤⣤⣴⣶⡿⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣠⣴⠟⢠⡾⠃
⠿⠟⠋⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢁⣴⠟
⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣟⣻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣌⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣀
⠀⠀⠀⠚⠛⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡶⠂
⠀⠀⠀⠀⠀⢀⣴⣾⣶⣿⣿⣿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣶⣏⠝⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣻⣿⣇⠀⠀⢀⡀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠂⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠁⠒⠈⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠻⣿⡟⠟⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣷⣶⣤⡀⠀⠀⠀⠋⣀⠀⢠⣼⣦⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣭⣥⠈⠉⠁⠀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣭⡆⠈⠁⠀⠀⠀⠘⢿⡏⠃⠀⠉⠀⠈⠉
⠀⠀⠀⠰⠾⠿⠿⠻⠿⠛⠟⠛⠛⠉⠛⠞⠻⠶⠆⠀⠀⠴⠻⠿⠷⠿⠿⠿⠟⠿⠞⠖⠒⠒⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡶⢶⣶⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢟⣟⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢤⣤⣴⣶⠿⣿⣿⣿⣧⣼⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⡍⠛⠀⠀⠀⢀⣤⣤⡄⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⣿⣿⡅⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⣀⣴⣿⣿⣿⡌⠧⡀⠀⠀⣄⠀⠀⠀⠀⢀⡴⠟⢛⣿⣧⣀⣀⣠⣴⣂⣀⣀⡀
⠀⠀⠀⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣴⣾⣶⠀⠀⠀⠀⠀⠀⢁⣾⣿⠇⠀⢀⣼⡟⡋⠁
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣛⠓⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⠁⣀⣴⣿⡿⣿⡀⠀⠀⢀⡀⠀⠀⠈⢿⠁⣤⣾⣾⣿⣻⣷⠖
⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣍⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣵⣿⣿⣿⣿⣷⣿⣷⣤⣾⣿⣏⠀⠀⠀⠀⠐⠿⣿⣿⠾⠛⠁
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁
⣟⣿⣿⣻⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣻⣻⣿⣻⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠉⢛⡒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⢭⣣⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⡎⠁⣨⠇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣦⣉⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠸⡇⠀⠧⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣩⡽⠿⠛⠛⠛⢛⣛⠻⣧⣤⡀⢻⡀⠀⢀⠔⣉⣤⢬⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡾⠛⠁⠀⠀⠀⠀⣁⣀⢀⠀⠀⠀⠉⠳⣿⣦⡏⠀⡟⠀⣞⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠊⠀⠀⠀⢔⣀⣭⠤⠤⠤⠤⣤⣀⠁⠐⠠⢈⠻⣧⠼⢛⣉⣉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠐⠁⠀⣠⠶⢛⡝⠉⣀⣤⣤⣄⠀⠀⠈⠙⠲⡄⠀⢹⠏⣰⡏⠉⠉⠓⣦⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣰⠟⠁⠀⡎⢠⠋⠁⠀⠀⠈⠙⢦⡀⠀⠀⠙⣄⠸⣧⡘⠋⣹⠀⠀⢸⣧⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣰⠁⠀⠀⠀⢇⢻⠀⠀⣀⡀⠀⠀⠀⢹⡆⠀⡀⠘⡆⠀⠈⠙⣷⠀⠀⣸⢻⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢿⡀⠀⠀⡀⣈⠢⢉⣉⣠⠆⠀⠀⠀⠀⣧⠀⠀⠀⣿⣀⣰⠤⠿⠦⣴⣯⣼⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠻⠶⠞⠁⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠋⠁⠀⠀⠀⠀⠀⠈⠛⢷⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡞⠀⢀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠁⢰⠃⢠⠀⠈⣿⣷⡄⠀⠑⠠⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⢆⠘⠆⡼⠊⢙⣿⣿⡈⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⠂⢸⠋⠒⠖⠒⣿⡟⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⠎⢠⡏⢀⣀⣀⣼⡿⠀⠀⡇
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⢀⣎⣤⠿⢋⡉⠄⠉⠉⠙⠳⣾
⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⠖⠲⠒⠲⠿⢧⣶⣶⠾⠛⡉⠔⠈⡀⠤⠒⠒⠒⠀⢠⡏
⠀⠀⠀⠉⠙⠓⠶⠤⣄⣀⣀⣠⣤⠶⠛⠉⠀⢀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠙⠻⠷⣶⣶⡤⠶⠒⠛⠛⠛⢛⡾⠀⠀⠀⠀⠀⠀⢰
⣶⣤⣄⣀⣀⣀⣠⣴⡶⠟⠛⠉⠀⠀⠂⠀⠂⢀⣀⣀⣠⣤⣌⣢⣀⣀⣠⣤⠶⠚⠉⠑⢈⠀⠄⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢠⠏
⢦⣌⠉⠉⠉⠉⠉⠀⢀⣠⠤⣄⡁⢀⠀⡠⠞⠋⠉⠀⠉⠁⠀⠈⠉⠛⠿⣦⣾⣁⡐⠈⠀⠀⠁⠀⢠⡟⠁⠀⠀⠀⠀⢀⣴⠋
⠀⠙⢷⣄⠀⠀⠀⠀⠿⠴⢒⡆⠘⣇⡞⣴⠟⠛⠙⠛⠲⣤⣀⠀⠀⠀⠁⠀⠈⠙⠻⠿⠶⢷⢶⣶⠋⠀⠀⠀⠀⠀⣠⡞⡡⠀⡴
⢤⡀⠀⠈⠙⠳⠤⢤⣤⠤⠞⠁⣠⠟⡇⢇⡀⣠⢶⡆⠀⠀⠉⠛⠶⣦⣤⣀⣀⣀⠀⠀⢀⣴⠞⠁⢀⡴⠁⠀⣠⡾⠋⠔⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣒⡲⠭⠿⠟⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣒⣚⣋⣛⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠭⠮⣗⣒⣒⣛⣉⣉⠛⠛⠿⣷
⠠⢤⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣚⣉⣭⣭⣍⡙⢧⠳⡤⣀⠤⣤⣐⣚⣛⣚⣚⣛⣫⣭⣭⣭⣭⣉⡉⠙⠛⠿⣶⣤⡀
⠭⠽⢟⣛⣚⣹⣕⣤⠀⠀⠀⢀⣠⣴⣺⠵⠚⣋⣉⣉⣉⣉⡉⠻⣼⠃⣧⡈⠳⠶⠦⣤⡤⠤⠤⠤⣤⣤⣤⣀⡉⠙⠻⢿⣦⣄⠈⠙⢿
⣩⡭⠭⠭⠽⢖⣒⣺⠭⣚⢕⡿⢟⣫⠴⠞⠛⢋⣉⣉⠉⠙⠻⢷⣼⣧⣈⠛⠓⠒⠒⠒⠒⠶⠶⣶⣤⣄⡉⠛⠿⣷⣦⣀⠉⠻⣿⣦⡀
⢖⣒⣛⣛⣩⡭⠵⢖⡫⢗⡭⣚⣭⡴⠶⠟⠛⠛⠛⠛⠻⠿⠶⣦⣍⠪⣭⡭⢭⣭⣍⣙⡛⠳⢶⣤⣈⠙⠻⢷⣤⡀⠙⠻⣷⣤⡀⠙⠿
⠭⠥⣶⣒⣒⣚⡭⢽⣺⠵⣚⣩⣤⣴⡶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣉⡛⠾⣭⡽⡖⡲⠭⣝⡳⢦⣌⡙⠻⣦⣄⡉⠻⢷⣤⡈⠙⠿⣶⣄
⠭⣭⡿⢓⠶⣺⣝⡭⠖⣋⣉⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣉⣉⠛⠛⠶⢬⣟⣙⣉⣱⣭⣷⣬⡙⢶⣤⡙⠻⢶⣄⡉⠛⢷⣦⣈⠙
⣚⣶⡭⠶⠿⠾⠶⠶⠿⠭⢭⣍⣛⠡⠤⣀⣀⢀⣈⣉⣉⣉⣉⣉⠛⠛⠛⠳⠶⠦⢬⣭⣑⣒⡺⠶⠶⣒⣒⣛⣒⣒⣛⣛⣓⣂⣈⣙⣿
⠵⠶⢚⣛⣛⣋⣙⣛⣛⣓⠲⠦⣭⣙⠓⠶⣭⣛⠲⢭⣙⠻⢿⣛⡛⠛⡛⠻⠶⠶⠶⠶⠤⣬⣭⣭⣙⣛⣒⣒⣒⠲⠶⠶⠶⠶⠶⠶⠶
⠞⢛⣉⣭⣭⣤⠤⠤⠭⣭⣭⣓⡲⠬⣝⡳⢦⣍⠛⢦⣍⡛⠶⣬⡙⠳⢦⣍⡓⠶⢶⣒⡶⠶⣶⡶⠦⠤⠬⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭
⠛⣋⣩⣤⡴⠶⠶⠶⠶⠶⠶⠶⠭⣭⣒⡯⢕⡪⢝⡲⣬⡙⠶⣬⡙⠷⣦⣈⠛⠷⣦⣌⡙⠳⢦⣭⣙⠒⠶⢤⣖⣒⠲⠶⣶⣒⣒⡒⠒
⠛⣉⣡⣤⠶⠶⠞⠛⢛⣛⣛⣛⣛⠒⠶⠭⢽⣚⡷⣯⣗⣭⡳⢬⡙⠷⣤⡙⠻⣦⣌⡙⠻⢶⣤⣈⠙⠻⢶⣤⣌⡉⠛⠷⢶⣦⣬⣉⡙
⠛⣋⣡⣴⠶⠞⠛⢛⣋⣉⣉⣉⣉⣉⣙⣛⡒⠲⠭⣝⣛⠿⣊⢗⠯⣳⢬⡙⠷⣤⡙⠻⢶⣄⡉⠛⠿⣶⣤⣈⠙⠻⠷⣶⣤⣀⡉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⢠⢀⡀⡀⡄

⠀⠀⣀⣀⣀⣀
⣴⣿⣿⠿⢿⣿⣷⣄
⠋⢁⣀⣀⠀⠀⠙⢿⣷⡀
⣿⠿⠿⣿⣿⣷⣤⡀⠙⢿⣆⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⣤⣤⣄⣀⠈⠙⠿⣿⣦⡈⠻⣧⡀⠀⣰⣿⠟⠋⢉⣁⣨⣭⠁
⠿⠿⣿⣿⣿⣦⣄⠈⠻⣿⣦⡈⢿⣾⠟⠁⣠⣾⡿⠋⣡⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⣤⣄⡀⠉⠛⢿⣿⣷⣤⡈⠻⣿⣶⣝⢷⣾⡿⠋⣠⣾⡟⢁⣴⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢋⣉⣤
⠙⠻⢿⣷⣤⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠟⢠⡾⢁⡼⢁⠎⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣨⢵⣒⣛⣩⣭⣵
⣷⣦⡀⠙⠻⣿⣦⣀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⢁⣾⢁⣾⣴⣷⣧⣤⣄⣀⣀⣀⣠⣤⣤⣬⣾⣟⣛⣛⣩⣽⣿⠟
⡈⠙⢿⣦⣄⠈⠻⣿⣷⣄⡀⠀⠉⠉⠉⠉⢉⣩⣭⢟⣻⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣟⣚⣛⣶⣶⣶⣿⡿⠟⠁⣴
⢿⣦⡀⠙⢿⣷⣄⠈⠛⢿⣿⣷⣶⣶⣶⣿⡿⠋⣱⣿⠟⠋⠁⢀⣀⣀⡀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⡿⠿⠛⠉⠀⣠⣾⠟
⣦⠙⢿⣦⡀⠙⢿⣷⣤⡀⠈⠉⠉⠉⠉⢁⣤⡾⢋⣡⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⢋⡞
⠙⣷⣄⠙⢿⣦⡀⠙⠻⣿⣷⣶⣶⣶⡾⣛⡵⠾⣛⣉⣁⣤⣄⣀⡀⠈⠉⠙⠻⢿⣿⣿⣿⣷⣶⡶⠖⣋⣉⣤⣤⣤⣤⣤⣀
⢷⡌⠻⣧⡀⠙⢿⣶⣄⣀⣬⣿⣿⣷⣿⣷⣾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣤⡀⠀⢈⠙⢛⣫⡵⠶⠛⠛⠉⠉⠉⠉⠉⠙⠛
⣌⢻⣦⣙⣿⣦⣴⣿⣿⣿⣿⣿⣟⣛⣒⠲⠶⠶⢶⣶⣤⣤⣀⠈⠙⠻⢿⣿⠿⣋⡴⢞⣫⣥⡶⠶⠿⠛⠛⠛⠻⠿⠿⣷⣶
⣿⣶⣿⣿⡿⠿⠿⣿⣿⡯⢽⣓⡲⢮⣍⡛⠻⢶⣤⣄⡉⠛⠿⣿⣦⣄⣠⢴⣫⠵⢚⣋⣥⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⡈
⣿⡿⠋⢀⣠⣤⣶⠶⠮⠭⣷⣮⣝⣷⣬⣙⣷⣦⣈⠙⢿⣶⡄⣨⢕⡫⢖⣫⡵⠞⣋⣉⣥⣤⣤⣤⣤⣤⣄⣀⡈⠉⠙⠻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠤⠠⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠈⠁⠁⠉⠂⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠄⠀⠀⣀⣶⣶⡆⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⢀⣮⡅⠀⠳⣿⣇⡀⣀⣹⣿⣷⢝⢻⡉⠁⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣾⣿⣿⣤⠀⠀⠈⢻⠛⢯⣿⡟⠙⢦⠱⡱⠀⠱⡀⣆⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠐⠿⠿⢿⣿⣿⡀⣤⣴⣤⡋⠀⠀⢻⡀⠈⠀⢹⠃⠀⠇⢻⣆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠀⠀⠨⠈⠁⠀⠙⣿⣿⣿⣿⣿⡄⠀⠀⡇⠀⠀⠸⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠀⠴⠁⠀⠀⠀⢸⢹⣿⣿⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀⣸⢸⣿
⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠘⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⢻⣿⣿⠃⠀⢀⠁⠀⠀⠀⠀⠀⡇⢸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣊⣰⣿⢿⣿⠏⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣿⣳⣿
⠀⠀⠀⠀⣂⠀⠈⠀⠀⣤⣰⣴⣖⠂⠀⠀⠀⠁⡤⣤⣴⣾⣿⣿⣿⣷⡿⠋⠔⠀⠀⠀⠀⢠⠀⠀⣰⠃⣼⣿⣿⡟
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠛⣃⣾⣯⣀⠠⠋⠀⠀⠀⠀⢙⢿⣿⠿⢛⡩⠀⠀⠀⠀⠀⠀⡰⠃⢀⡼⠁⣼⣿⣿⠟
⠀⠀⠀⡀⠁⠀⠀⣴⣤⣿⢹⣿⣿⠀⠒⣂⣀⠀⠐⢷⠧⠛⠒⠉⠁⠀⠀⠀⠀⠀⢀⠜⣡⡶⠋⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⢸⣻⣿⣦⡈⢯⢿⣅⠀⠈⣷⠄⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⢋⣠⣾⣿⡯⠋
⠀⠀⣠⠀⠂⠀⠀⢀⣤⠀⠈⢻⣿⢿⣿⣦⣙⠫⣽⣁⣀⣀⣀⣠⣤⣴⣾⢿⣛⣩⣴⡾⢟⣫⡷⠋
⠀⠀⠀⠐⠃⠀⠀⠘⠃⡄⠀⠀⠻⢆⠙⢿⣿⣿⣶⣯⣽⣿⣛⣛⣿⣛⣛⣿⣯⠽⣖⣻⠟⠋
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠱⠆⠂⠁⠒⠄⠀⡈⠛⠻⠿⢿⣷⣶⣶⣶⣶⣦⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠐⠀⠐⠉⠉⠉⠙⠛⠛⠋⠉⠉⠁


⣿⣿⠛⠿⢻⠿⡿⢻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣤⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣖⠾⣖⢄
⣿⣿⣿⡯⡲⡵⠀⠀⠀⠀⢀⣠⣶⣻⠵⣟⡫⢕⡮⣲⢄⠀⠀⠀⢀⣀⣴⢶⣿⣿⣽⣒⡯⣓⢕⣷⣄⠀⠀⣀⣠⣤⣤
⣻⣿⢟⢝⣞⣮⣀⣀⣤⣖⣫⣿⣿⣿⣯⣗⣯⣗⣯⢾⡵⢿⣿⣿⣭⣿⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣻⠯⣭⣿⣿⠷
⣿⣯⣿⣿⣿⠾⣟⣯⣷⢾⠿⣗⣺⣶⣶⣶⣶⣚⣿⡗⣯⣿⣿⣿⣿⣿⣟⣛⣛⣷⣻⣏⡶⢿⣿⣿⣿⣷⣽⣭⣯⣿⣻
⣿⣿⣷⣒⣚⡯⡿⡿⡏⡟⣾⣵⣷⣶⣟⢿⣿⣿⣶⣽⢿⣻⣿⣟⣛⣒⣒⣲⣶⣶⣶⣾⣿⣯⣽⣾⣽⣿⣿⣏⣿⢿⣿
⣻⡯⠯⢿⣾⣻⣾⠽⣵⣷⢿⣿⣿⣷⢾⣿⣿⡿⠛⠛⠿⡾⣶⣿⢗⣒⣒⣒⣒⣛⣯⠭⢽⣿⠿⣽⣛⣿⣝⣛⡻⢿⣿
⠉⠛⠻⠿⣶⣿⣿⣭⣽⣷⣿⣿⡟⠉⠉⠉⠚⠀⠀⠀⠀⠘⢮⣺⠭⣖⣒⣒⣒⣒⣚⡯⠵⣚⣭⠵⠖⠒⠛⠛⠛⠻⢿
⠀⠀⠀⠀⠀⠉⠛⠿⢾⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡵⠚⠉⣡⡤⠄⠠⠭⢍⡓⠦⣆⡄⡀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠱⣿⣤⣤⣤⣤⣉⣉⣒⠂⠤⣀⡑⠢⣉⠺⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠥⠴⠖⠒⠀⠀⠀⠐⠚⠭⣗⡦⣍⠲⣌⠓⢌⠳⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⡳⣌⢣⠀⠑⢌⢫⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡆⠇⢀⣀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⢸⣽⣷⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠀⣾⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡼⠃⢀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⠜⠁⠨⠥⡁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⠴⠋⠀⠀⠀⠀⠀⢸⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣾⣷⠀⣠⠆⢄⣀⣠⣾⠻⣷⠀⠀⠀⠀⠀⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢹⣶⣼⣿⡛⣾⣿⣄⠈⢿⣿⣿⡇⣿⣶⣦⣀⠀⠀⢀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣀⡄⣀⣀⣾⣿⡛⠉⠳⡌⠿⠃⢀⣻⣿⣿⣿⣼⣿⣇⣿⣧⡔⠫⠀⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠻⠆⠀⠀⠠⡘⡄⠀⠈⡏⢹⡗⠛⡿⢿⣿⣿⣿⣧⣤⣰⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠘⠛⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠃⠈⠁⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡘⣸⠀⣿⢠⣿⣿⣦⣄⠄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⢀⣴⣒⣠⣶⡿⠟⠻⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⣸⣧⣿⣿⣿⣿⣿⡀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠛⠋⠋⠛⠛⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡟⠠⢱⣿⣿⣿⣿⣿⣿⣿⣦⡞⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠈⢀⠀⠀⣴⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠈⠀⠀⢿⡟⢏⣿⣿⣿⣍⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠠⠿⠖⠚⠛⠛⠛⠛⠻⣿⡶⠶⢿⣥⣤⠀⠀⣀⣠⣤⠀⠀⠀⢚⣿⡿⠃⠀⠀⠀⠀⢀⡀⠀⣠⠔⠀⣰⡿⠻⣿⣿⠟
⠀⠀⠀⠠⠔⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⣀⣀⣒⣀⡀⠀⠐⢶⣬⠁⠀⠀⠉⢹⣤⣶⠉⠉⠉⢴⣦⠖⠁⢀⠔⠛⠻⠟⢛⠶⡟⠋⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠤⢤⣀⡀⠉⠉⠉⠉⠀⠀⠀⠀⢀⣉⡿⠛⠀⠀⠉⠥⢀⣀⣠⡶⠤⢀⣾⠗⣀⡤⢀⠀⠠⣾⣿⣴⣶⡟⠁
⠀⠀⠀⠀⠀⢠⣤⡾⠋⠁⠀⠠⣄⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠀⠀⠈⠁⢀⣬⣭⠤⣤⣤⣤⣭⣤⣤⣶⣯⣵⣿⣿⣿⣿⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⣿⣅⡀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠉⠉⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡠⠖⠋⠉⠉⠙⠲⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡞⠀⡴⠊⠉⠉⠑⢄⠀⢣⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢰⠀⠀⠀⠀⠀⠈⡆⠈⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡆⠀⢆⡔⠊⠐⢲⠉⠁⠲⡁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠦⣀⠀⠀⠀⠈⡆⠀⠀⢣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡈⠀⠀⠀⠀⣏⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣸⣆⠀⡏⠀⠀⠰⠋⠉⠉⠉⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⢹⠉⠀⠀⢰⡀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠐⠂⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠓⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠇⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⠛⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠎⠩⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠜⠀⢀⡀⠀⠧⠤⢄
⠀⠀⠀⠀⡠⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠰⣾⣷⠄⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⢄
⠀⠀⢀⠞⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢤⠀⢸⡇⠀⡤⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠣⡀
⠀⢀⠎⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢪⠀⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠱⡀
⠀⡜⠀⣰⡆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢸⠀⣼⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⣆⠀⢣
⠸⠀⢀⣿⣿⡄⠀⠣⡠⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢰⢠⣿⣿⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠜⠀⢠⣿⣿⡄
⡇⠀⣸⣿⣿⣿⡆⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⣾⣿⣿⣧⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢰⣿⣿⣿⡇
⡇⠀⠈⠉⠻⣿⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢰⣹⣿⣿⣿⣿⣆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠀⢀⣿⠟⠉⠁
⠰⣀⠔⠢⡀⠈⠁⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⣸⣿⣿⣿⣿⣿⣿⣆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠀⠀⠁⢀⠔⠢⣀
⠀⠀⠀⠀⠈⠦⡀⠀⠀⠈⠑⠢⠤⠄⢀⣀⠀⠤⠤⠒⠙⢄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠑⠒⠤⠤⠀⣀⡀⠠⠤⠔⠊⠁⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣶⣿⣄⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣄⡀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⣀⠠⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⠤⣀⡀⠈⠙⠻⢿⣧⣄⠀⠀⠀⠈⠹⢿⣿⠟⠋⠁⢀⡀⠤⠔⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠉⠻⢿⣆⡀⠀⠀⠀⠀⠋⡱⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠙⠋⠐⡢⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛⠶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠛⠛⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⢿⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣿⠀⠘⣇⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⠀⠀⢻⡀⢻⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠀⠀⠸⡇⠈⢧⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿⠀⠀⠀⣧⠀⠸⡆⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢻⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⡇⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣧⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡏⠀⠀⠀⣿⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠇⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣀⣀⣠⠄⠀⢀⣀⣧⣿⣿⠴⠶⠶⢤⣤⣀⣀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣯⠭⢷⣶⣾⣿⠯⠽⠶⠿⠚⠛⠛⠛⠉⠉⠉⣉⣹⣿⣿⣿⣿⡿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠶⠒⠋⠉⠁⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⠿⠟⠛⠉⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣶⣶⣶⣾⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⣀⣀⣀⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠉⠉⠉⠉⠉⢀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠴⠶⠶⠒⠚⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠋⢠⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⣉⠘⠀⡰⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⢡⠀⠀⠀⠀⠀⠀⡎⠰⠁⠐⠐⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡠⠀⢀⡜⣆⣰⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡐⠁⢀⠊⢇⠳⡈⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠐⠀⠀⠀⠀⢀⡜⠀⢠⠃⡰⢈⠜⡸⠆⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡰⠁⠀⡇⢸⠘⣀⠇⠀⢀⠔⠁⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⡠⠃⠀⡔⠁⠀⢰⡉⡞⢀⠇⢀⠴⠃⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⡐⠁⢀⠜⠀⠀⠀⡎⢸⣠⡎⠠⠁⠀⠀⠈⠀⡌
⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⢀⠜⠀⢀⠎⠀⠀⠀⠀⢇⠸⠉⢃⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠸⡀⠈⡄⠀⠀⢀⠊⠀⠠⠃⠀⠀⠀⠀⠀⢨⢜⠇⢸⢀
⠀⠀⠀⠀⠀⠀⠣⠀⠈⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣀⡳⠟⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠒⠒⢈⣁⠴⢺⣍⢦⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠤⠤⠤⠤⠄⠒⠊⠁⠀⠀⠀⠛⠛⠲⣶⢝⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠈⠐⠀⠀⠀⠊⠀⠀⠀⠀⠒⠖⠂⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⣀⠠⢤⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⠔⠋⠀⠀⠸⠈⠉⠀⢀⡴⠋⠐⡷⠋⠉⠀⢀⠴⡃⢸⠖⠉⠃⠀⢀⣤⠊⡹⠋⠉⠀⠀⠀⢀⠴⣾⡿⠋⠙
⠀⠀⠀⡏⠀⠀⠀⠀⠘⠤⣠⠴⣻⠓⠰⡈⣇⣀⣠⠔⣏⢦⡇⢻⣀⣀⡠⣴⠉⡀⠀⠳⣄⣀⣀⡠⠖⠇⢨⢳⠷⣀⣀⣀⡄
⠀⠀⠀⡇⠠⠀⢘⠰⠆⡀⠐⠈⢿⣧⠗⠢⠧⣠⠃⡰⣿⣿⠇⠘⣿⢠⡧⠛⠲⠇⡄⠠⠒⢼⡄⠠⠀⢀⢾⢀⡶⠊⣩⡷⡀
⠀⠀⠀⠇⠀⠀⠠⠀⠈⠀⠀⢀⠸⠃⠀⠍⠷⠁⠀⠤⠟⠁⠠⣅⠿⠊⠀⢸⣸⠄⠃⠀⢀⠘⠔⠀⠀⢿⡠⠊⠀⠰⣼⡧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠂⠀⠄⠂⣴⣂⠀⠂⣠⠄⠐⡠⢀⢀⠀⠀⠀⡀⡀⢀⡄⠀⢠⠀⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠂⠚⠘⠀⠀⠁⠈⠀⠃⠀⠀⢓⠟⠀⠀⠀⠀⠂⠃⠈⠐⠃⠈⠘⠐⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡿⠟⠻⢿⣿⣮⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡏⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢻⡷⠔⠒⢖⢲⣞⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⣤⡗⠛⣯⢹⣿⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⠛⡇⢰⣿⣾⢻⡅⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⡗⠺⣴⡇⠀⣿⣿⣦⡇⢸⠁⢀⡤⠤⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣹⠶⠶⠶⢶⣒⣋⣹⣄⡹⢧⣀⣿⣿⣦⣏⢻⣷⣿⣿⣷⠐⣷⣏⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⣮⣉⠛⣿⣟⡧⢽⡶⢳⣼⣿⣼⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢙⣿⣶⡏⠻⡧⠶⠞⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣿⡇⣿⡆⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⣿⡇⣿⣱⠞
⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠀⢘⣿⡇⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀
⠀⠀⠀⠀⣠⢋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣴⡟⠀⢸⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣄
⠀⠀⢀⣼⠇⣼⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣐⣳⣇⡀⠸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢳⣜⢧⡀
⠀⢀⣾⠏⢰⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⡋⢙⠿⢿⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣎⢷⡀
⠀⣼⡏⠀⣼⣿⣿⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠻⣷⣿⢦⣞⡉⣣⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⣿⣿⣿⣧
⢰⡟⠀⢀⣿⣿⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢨⣿⣿⠀⣏⣿⣹⠆⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⣿⣿⣿⣿⣿
⡼⢀⣴⠿⡿⣿⣿⡛⠷⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⣿⣿⡆⣿⣡⠏⠀⠀⠀⠀⠀⠀⢠⡾⠷⢛⡿⣹⢻⠿⣟⠻
⡷⠋⠁⠀⢳⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡏⠸⠦⠐⣿⣿⣿⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣰⡿⡟⠀⠈⠙
⠀⠀⠀⠀⠘⣆⢈⡻⢿⣿⣶⣤⣄⣀⣀⣠⠞⣧⡞⠀⠀⠀⡼⢿⣿⣿⣧⡑⠦⢤⣀⣀⣀⣤⠤⠖⠉⣠⣾⡿⣱⠃
⠀⠀⠀⠀⠀⠘⣞⣿⣷⣍⡛⠿⠿⣿⣿⡟⢤⣿⣖⣀⠤⠚⠀⠀⠙⠿⣿⣿⣷⣶⣤⣤⣤⣴⣶⣷⣿⣿⢟⣴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣝⡛⠛⠁⠀⠀⠀⣷⢬⡏⠉⠙⠲⡄⠀⠀⢠⠴⠛⠛⣻⣿⣿⣿⣿⣿⡿⢟⣫⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣹⡦⣽⡀⢀⣠⣾⣆⢰⠃⠀⠀⠐⠛⣛⣫⣭⣿⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠼⡗⠿⢿⣿⣿⡇⣀⡤⠶⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠢⡇⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢰⢄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠁⠀⠀⢀⢑⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠄⢂⠀⠀⠀⠐⡀⢂⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⢠⠀⠸⢢⡀⠀⠿⡄⠠⠀⠀⠀⠀⠀⠀⠈⠠⡁⢀⢢⠠⠀⠐⢦⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠄⠀⠀⠃⠀⢀⠇⠀⠀⡄⠀⠀⠀⠀⠘⠄⠀⠠⠂⢇⠀⠀⠊⠀⠀⠴⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣾⣁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡈⠀⢠⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡄⠀⢢⠎⠀⠰⣸⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⣿⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄⢰⣡⣘⣈⠞⡡⠀⠐⠠⠆⠀⠀⠀⢄⠀⠠⣀⠄⠀⠮⡀⢲⣷⣶⣆⠐⡀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣯⠀⡼⣿⡦⠀⠀⠀⠀⠀⠀⠈⠢⢽⠶⠭⣿⠿⠊⢃⠂⠲⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⢦⣴⣶⣿⣿⣿⡧⠔⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠚⠡⡎⡀⠐⢢⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠋⠀⠈⠉⢉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠛⣦⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠚⠁⠀⠘⡆⠀⠀⠀⢤⣠⠀⣄⢠⡤⢠⢠⡀⢤⠀⢠⡄⡄⠀⣆⠠⣀⠠⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠀⠀⠀⠀⠈⠀⠈⠈⠉⠈⠀⠁⠈⠀⠈⠀⠁⠈⠈⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⣗⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀
⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⠆⣦
⠀⠀⠀⢇⡚⠛⢧⢹⠀⢀⠒⡒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡆⠀⠈⠁
⠀⠀⠀⠀⠀⢰⡟⢹⠟⠉⡘⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠝⢝⠢⢄⡀⠀⠀⠀⡀⠠⡀⠀⠈⣶⣿⣿⣷⡦⢴⣷⡁
⠀⠀⠀⠀⠀⠀⣷⡿⠀⠀⠀⠀⠀⠀⣰⠊⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⢃⠀⠀⠀⢀⢒⡒⠘⣋⡿⢿⡙⠷⣾⢷⣞⣿⠓⢀
⠀⠀⠀⠀⢀⠄⠃⣇⠀⡀⠀⠀⡀⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢇⠀⠲⣦⡀⠀⠀⡿⠹⠀⠀⠀⠻⠀⠈⢉⠄⠀⢂⠁⡀⣉⠈⡉⢀⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠈⢂⠑⡝⢸⠀⠀⠸⢱⡇⠀⠀⠀⠀⠀⠠⠐⢰⢦⣀⠀⡎⠐⠀⠀⢸⣤⣠⢄⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠱⡀⢢⠀⠰
⠀⠀⠀⠀⠀⠰⡀⣩⡈⠲⢘⠆⢠⠻⡄⠀⠀⠀⠀⠈⢳⣄⡠⢹⡏⢉⡁⠀⢠⣾⣟⠄⣫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣀⢈⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣙⡒⠙⣝⡄⠀⠀⠀⠀⢈⣃⠀⣼⡃⢡⢰⣺⢋⢷⢕⢏⡜⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⡄⢀⠀⠻⢇⣸⣿⢋⡿⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠢⣄⠛⠘⣿⣜⠀⣌⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠉⠃⠋⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣆⣼⣏⣝⣻⣶⣄⣶⣤⣴⣦⠀⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⣿⣯⣿⣿⣿⣿⣿⣽⣿⣧⠿⠃
⠀⠀⠀⢀⠊⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⠃
⣢⡬⠞⠉⠀⠀⠀⠀⠸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣥⡴⠃⠀⠀⠀⠀⠀⢠⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⡇
⠁⠀⠀⠀⠀⠀⠀⠂⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠹⣷⣀⡀⡒⣴⣿⣻⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠃⠀⢀⢄
⠀⠔⢸⣖⣷⣻⣍⢻⣿⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⣀⠃⠀⠀⠀⠈⠱⠀⠄⠂⠀⠂⠨⠒
⣤⣤⣼⣿⣽⣧⣿⣟⣿⣾⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⡄⣀⣸⣿⣿⢻⣿⣿⣶⣴⣶⣶⣤⡆⢶⡆
⣿⣾⣿⣽⣿⠽⠗⠛⠛⠛⠉⠛⠛⠛⠿⣿⣿⣿⠟⠁⠀⠀⠀⠄⠀⢀⢀⡹⣿⣿⣿⣿⣿⣻⣿⣿⣟⡿⠟⠉⠁⠈⠀⠁⠀⠀⠈
⣿⡯⠝⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⢉⠀⠀⠀⢤⡀⢦⣀⢀⣄⢳⣻⣿⣿⣿⣿⢿⣷⣷⡟⠁
⠋⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⡘⢤⣰⣀⡀⠴⠄⢀⡀⠰⣦⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⡷⣿⡇
⠀⠀⠀⡀⠀⠒⢑⣆⣾⡟⣿⣿⣿⣿⣿⣿⣷⣀⣨⣽⣷⣿⣿⣿⣿⢿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡦⡀
⢀⣀⢀⡁⠀⠀⠒⣌⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣷⠦⠄⠀⠀⠀⣠⣤
⢷⣿⣿⣿⣷⠎⣯⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠙⠙⠛⠛⠛⠛⠻⠟⣋⡉⢉⣀⣀⣉⣩⣅⣀⡀⢶⣦⣐⠷⣶⣮⣽
⣿⣿⣻⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⣀⣤⣴⣦⣄⡀⣷⣶⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣦⣭⣻⣿⣿⣿⣿⣿⣿⣮⣝⡛⢶⣭⡙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⡇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠈⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⢀⡼⣃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇⢀⠀⠀⣠⣾⠿⠋⠁⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢠⡟⣠⡾⠋⠁⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣼⡟⢀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⠜⡿⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⡼⠁⠈⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⡾⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⡾⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⢉⣴⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠉⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⡀⣰⠏⠀⠀⠀⠀⠀⢀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⣀⣴⣋⣡⡤⠀⠀⠀⢀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠘⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⣠⣾⣿⣿⣿⡷⠶⠶⠚⠛⣹⠿⣷⣶⣶⣦⣤⣤⣤⣤⣴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁
⠀⠀⠚⠛⠋⠡⠤⠤⢤⣤⣤⣤⣾⣥⣤⣤⡤⠤⠤⢶⠒⠒⡆⢿⣋⠛⠒⠒⠒⠀⠀⠠⠤⠤⠤⢤⣤⣴⣶⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡹⠯⠛⠻⣷⣦⣤⣅⣈⣁⠘⠳⠦⠬⢥⣤⣀⣀⣀⣀⣀⣐⠺⠗⠀⣀⡵⠀⠀⡈⠉⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡟⠋⡉⠙⠛⠿⣿⣟⡛⠛⠲⠶⢶⣶⣶⣶⣶⣶⣶⣖⣚⣋⣉⣠⣤⠞⠀⠤⢒⣋⣭⣤⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠈⠻⣿⣦⣄⡀⠋⢀⡀⠈⠹⣿⢿⣿⣿⣛⣛⣉⣁⣤⣴⠾⠛⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⠀⠀⠈⠙⠿⣯⣍⣉⣀⣠⣴⠟⠀⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢾⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⡏⢹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢸⡇⣰⠌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢸⡏⠁⠨⠶⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣾⠇⠀⠀⢸⡇⠀⠀⢐⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢠⣿⠀⠀⠀⢸⣿⢶⣞⣯⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⣿⠀⠀⠀⢸⡇⢻⡅⠞⠃⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢸⣿⡀⠀⠀⢸⡇⠀⢂⣠⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢸⣿⠁⠀⠀⢸⣗⡀⠈⣿⡯⠖⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠈⡶⣒⣈⠄⠀⠈⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠸⣟⢿⡄⠀⢸⣯⣀⣤⠀⠺⡿⠂⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠄⠀⠀⠀⠀⠀⠀⣿⢘⣷⡀⢸⣿⣫⣥⡀⠀⠸⠀⠀⠀⠀⠀⢀⣱⡀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠡⠀⠀⠀⠀⠀⠀⠠⠈⢿⣿⣷⣸⣿⣿⣿⡁⠀⠀⣡⣤⣶⠾⠛⠋⠙⠉⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⡷⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠐⢒⣖⠠⣤⢠⣿⣿⣤⣶⠾⠿⠟⠛⠛⠛⠛⠉⠉⡉⠉⢻⣿⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⠀⠀⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⠾⠶⠶⠶⠶⠶⠶⠷⠾⣿⠿⠿⠿⠿⠿⠶⠶⠷⠟⠿⠿⡟⠿⠷⠶⢶⡶⠶⣿⠷⣦⠔⠃
⠀⠀⠀⠀⠀⠠⠤⢤⣤⣵⣤⠈⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠛⠒⠒⠀⠀⠙⠛⠋⠀⠀⠛⠛⠓⠈⠛⠛⠛⠾⠟⠛⢋⣷⣤⣤⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣷⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠤⠤⠴⠶⡾⠿⠯⠥⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠬⠉⠙⠛⠖⢛⣻⣿⣟⣙⠛⢻⣯⣭⣄⣉⡙⢛⣯⣭⣥⣭⣭⣥⠶⠾⠟⠛⠛⠛⠛⠒⠶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢉⡙⣛⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣄⣘⡛⠻⠿⢿⣿⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⢉⣉⠁⠀⠤⠖⠒⠒⠛⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣤⣤⣶⣶⣶⣾⣻⣂⣀⣀⣀⠀⠄⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠉⠉⠉⠉⠉⠉⠥⠤⣤⡀⠉⠑⠓⠲⣶⢶⣶⣶⡶⣶⣶⣶⣦⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⠖⢛⣩⠤⠀⠀⠐⠀⠐⠛⠛⠛⠛⠛⠛⠉⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠉⣀⡀⢀⣀⠈⠃⣀⡉⠀⠀⠀⠀⠒⠒⠂⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠿⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡷⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠘⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣰⠲⠶⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⢦⠠⠋⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢶⣤⣄⣀⠀⢰⣟⣻⣟⣿⣶⣶⣶⣤⣼⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⣼⣩⡙⠲⢾⣽⡏⢉⣛⣿⣿⣏⡙⢻⠿⡇⣤⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠿⣿⣿⣎⠁⠀⠀⠾⠯⠉⢻⠿⠿⢿⣯⣿⣿⣿⣷⣷⠀⠀⠈⢇⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣶⣿⣖⠤⢤⣀⠀⠀⠀⠁⠒⠦⠤⢭⣭⣽⣿⡿⠶⠶⠛⣾⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢻⣿⣿⣿⣿⣯⡀⠀⠀⠈⠀⠐⢢⠤⢤⣒⣤⡿⠶⣿⣿⣶⣾⣏⣩⣝⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠁⣀⡘⣿⣿⣿⣿⣷⠦⠤⢀⡒⢠⠄⢤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠀⠀⡠⢶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⡟⣶⣶⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⣤⡀⠻⣿⣿⣿⠃⢀⠴⠳⠾⠛⠿⢿⣿⡿⣽⣿⣿⣿⣿⡿⢟⣿⢲⣿⣿⣿⠃⣠⣶⣶⣾⣷⣤⣤⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢙⣆⠘⣯⠁⣀⠀⣠⣶⡷⢎⣀⡀⢰⣶⣷⣤⣈⠻⠿⠿⢿⣯⣤⣶⡇⠈⣠⣽⣿⣿⣿⣷⣭⣭⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⣴⣶⣿⣷⢶⣶⣤⣄⠀⠀⠀⣀⣠⣴⣾⣿⣤⡏⠰⣿⣿⣿⣿⠀⢦⣭⣥⣾⣯⡙⠿⣿⣯⣝⣿⣿⣿⣿⠿⠠⣽⣿⣿⣟⣯⣥⣶⣶⣭⣭⣥
⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⡿⠶⣶⣿⣿⣿⣿⣿⣿⠇⣴⣿⣿⣿⣿⡷⠘⠿⠟⠛⠿⣟⣶⣮⣭⣭⣽⣿⣭⣤⣶⢤⣬⣽⣿⣿⣿⡿⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡿⠏⣠⣔⣶⣿⣟⣿⣿⣿⠋⠀⢿⣿⣿⣿⣿⣐⣒⡓⠀⠀⠀⠀⠈⠉⠙⠛⠛⠟⠛⠋⠁⠀⠀⠁⠀⠉
⠀⠀⢀⣤⣤⣤⣼⣯⣭⣭⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⠀⢻⣿⣿⣿⣿⣿⣛⡂
⠀⠀⠀⠉⠉⠉⠉⠛⠛⢿⣿⣿⡿⠟⣋⣝⠻⠋⠉⠀⠀⠀⠀⠀⠙⠻⢿⡿⢿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠻⣦⡀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢀⣠⣴⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠙⣷⡄⠀⠀⠀⠀⢸⣧⣠⡿⠀⠀⠀⠀⣴⠟⠋⢀⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣼⡟⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠻⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠿⠿⠿⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣴⣶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠉⣁⣀⣼⡇⠀⠀⠀⠀⢰⣟⠋⠉⠉⠉⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠟⠛⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣶⠶⠿⠛⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣴⡾⠋⢀⣴⡿⠀⠀⢀⣤⣤⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠻⣦⣄⠀⠀⠸⣯⣀⣴⠟⠋⠀⠀⢰⣿⠉⢁⣀⣠⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡈⠛⣷⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣉⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣿⠋⠛⠻⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⣹⣿⠶⠿⠟⠛⠛⠿⢷⣶⠿⠛⣿⡄⠀⠀⠙⠿⢶⣦⣤⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⣴⠟⠁⣠⣾⠟⠻⢷⣤⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⡾⠛⠁⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣤⣤⣴⣦⣄⠀⠀⠐⣿⡀⠙⣷⣄⠀⠀⠀⣾⡋⠉⠛⠻⠷⣦⡀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⢁⣀⣀⣼⡿⠀⠀⠀⠘⢿⣄⠈⢻⡆⠀⠀⠙⠛⠿⠶⣶⣤⡿⠃⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠻⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⢛⡀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣹⡁⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢙⡃⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⣿⡄⠀⠀⠀⠀⣩⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⣸⡏⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢹⣇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠘⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⡿⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡏⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢸⣷⠀⠀⠀⠀⣿⡆⠀⠀⠀⣿⡇⠀⠀⠀⣼⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⠁⠀⠀⠀⣼⡏⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢹⣧⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢰⣿⠀⠀⠀⢀⣿⠁⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠈⣿⠀⠀⠀⠀⣿⠀⠀⠀⢿⠇⠀⠀⢸⡏⠀⠀⠀⢸⡟⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⣛⣛⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⣿⣿⡏⠁⠀⠉⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣄⠀⢀⣤⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⣡⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣠⣾⣿⣷⣶⣖⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⢙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣲⣿⣿⣷⣄
⠀⠰⣿⣯⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⠆
⠀⠀⠈⠻⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⡇⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⣿⣿⡄
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⣿⡇⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⣿⣧⣿⣮⡻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢻⣿⣿⣿⣿
⢹⡟⠉⢻⣿⣿⣦⡙⢷⣤⡀⠀⠀⠀⠀⠀⣿⠇⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣤⠾⢋⣴⣿⣿⡟⠉⠻
⠀⠀⠀⠀⠻⣿⣿⣿⣶⣌⡙⠳⠶⣤⣶⡾⠟⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣟⣋⣥⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣭⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣬⣙⠻⠟⣡⣴⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⢎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠀⠀⡀
⠀⢀⠀⠀⠉⠒⠠⡬⣍⣉⢤⠀⠀⠀⠀⠀⠘⡌⢦⡙⢲⢤⣀⣀⣀⣠⡞⠋⣰⠏⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣰⡟⠉⠈⠉⠢⠀⠈⠐⢆
⠀⣼⠀⢠⠀⠀⠀⠲⠄⢄⠠⠆⠀⠀⠀⠀⠀⠹⣆⠹⣦⡀⠒⠋⠛⠀⠀⣴⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⣿⡄⠈⠦⠴⠀⠈⢓⡀⠀⠠⢄
⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⡀⠐⢄⠀⠀⠀⠀⠀⢻⢠⠈⠻⣄⡀⠀⢀⡾⠁⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠈⣿⡄⠀⠘⠄
⠀⠸⠀⠋⠀⡜⠀⠠⡶⡚⢡⠄⡈⠀⠀⠀⠀⠀⣸⠸⠀⠀⠈⢻⣤⣞⠁⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠻
⠀⠀⠃⠀⠀⠀⣴⣢⣿⣽⠋⠀⠀⠀⠀⠀⠀⣴⠇⠀⢀⣤⠴⠛⢻⡏⠛⠳⠶⠦⠤⢤⣤⣀⣀⣉⡙⠂⠀⠀⠈⠢⣀⠐⠄⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠘⠀⠐⠐⣿⣿⡿⠎⠁⠀⠊⠀⢀⡰⠚⡡⠴⠚⠉⠀⠀⠀⠈⣧⠀⢀⠄⠀⣐⣠⡤⠴⠶⠒⠂⠀⠀⠀⠀⠀⠈⠙⠒⢒⣶⣤⣴⣾⠟⠛⠁
⠀⠀⠀⡅⠀⢰⡿⠋⠀⢀⡴⠁⠀⠐⠁⣀⡡⠤⠶⠖⠶⢤⡀⡀⠀⢻⠀⢠⣪⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠺⠇⢸⠀⠈⠘⢯⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⡻⠁⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠀⢸⡄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠈
⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠹⡀⠀⡤⠂
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠊
⠀⢰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒
⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⣦⠑⢠⠇⠀⠀⠠⠂⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠁⠆⠈⢠⠀⠐
⠀⠀⠂⠀⠀⡄⠀⠀⠀⠓⠀⠉⠀⠀⠀⠀⠀⠠⣄⢀⡀⠋⠀⠁⣀⠉⠘⢃⡀⢘⢂⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢠⠂⠀⠀⠀⠀⠂⠀⠐
⠀⢀⠛⠂⠄⢁⢀⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠛⠁⡄⠘⠋⢈⠁⠁⣀⣤⠀⠄⠀⠐⠀⠀⠀⠀⠀⣦⠀⠂
⠀⠂⠀⢀⠒⠀⠀⠆⣄⠀⠉⢱⢤⠀⠠⠀⠀⠘⠀⠤⡽⠀⠀⠐⠈⢨⠂⠀⢀⠀⠱⠚⠅⠠⠄⢄⠀⠐⠘⠀⠀⠀⠀⢸⠢⡁⠀⠠⡆⠀⢰⠁⠀⠀⠰⠁
⠀⠅⠀⠐⠀⠂⠠⠀⠀⠀⠒⠀⠀⡁⠄⠂⠉⠉⠀⠀⢤⠄⠠⡴⠀⢠⠏⠀⠤⠀⠐⠀⠠⠀⠑⠀⠂⠀⠠⠀⠀⠰⠄⠀⠄⠈⢤⡃⠠⠀⠘
⠄⠀⠂⠀⠈⠀⠀⣀⠤⢀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡠⠂⠄⠠⡆⠀⢀⠉⠀⢠⠀⠀⠀⠀⣼⡄⠀⠀⠀⢀⠀⠄⠀⠘⠧⠠⠀⠅⠀⠀⠀⠀⡁
⠀⠀⠀⠀⡂⠀⠄⠀⠀⠀⠉⠀⠠⠀⠂⠀⠀⠀⠀⠀⠂⠈⠁⠑⠘⠇⠰⠇⠀⠀⠀⠄⠀⠁⡆⠀⠀⠀⠀⠀⠀⢃⠀⠠⠀⠀⠠⠁⠩⡔⠀⠀⠀⢀⠀⠃⢈
⠀⠀⠀⠲⠐⠂⠀⠀⠀⢀⠂⢀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡑⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠀⠀⠉⠲⡉⠀⣉⡈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⡄⠀⠀⠀⠀⢾⡀⠀⠀⢀⣠⣃
⠀⠀⠀⠀⠐⠂⠢⡀⠒⢁⠀⠲⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠢⡀⠄⠀⠐⠑⡘⢀⡄⠀⠈⠁⠆
⠀⠀⠀⠀⠁⠒⣀⣀⠀⠘⠀⠀⠙⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡑⢀⣷⢼⠆⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡙⡞⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣅⣩⣚⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣳⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣩⣾⣿⣫⣽⣭⡽⠁⢻⣿⣿⢷⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⣿⣿⠓⠋⢥⣁⢠⣲⣮⣭⣟⡋⠙⠾⣯⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣿⡿⢡⣬⣻⣿⣿⣿⣿⠋⠁⠀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣠⣾⣟⡵⢈⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣯⣿⠏⠀⠾⢽⣿⣿⣿⣿⠀⣠⣴⣶⡲⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣠⣿⣿⣗⠀⠉⣤⣿⣿⣿⣿⡻⡿⠛⠋⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⠔⠉⠤⣲⡞⠿⠛⠉⠀⣄⢀⢶⣿⣿⡿⢇⣁⠤⠤⠴⣿⣿⣿⣷⡀⠠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⢀⠀⢶⣎⣷⣿⣿⣿⣿⡏⡓⠀⠀⠀⠀⠀⢨⣭⣻⣿⣿⣷⣶⣶⠟⢛⡿⢟⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⡧⢋⠠⠀⠀⢼⣿⣧⣶⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠈⠝⢋⣤
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣯⣭⣽⣿⣷⣶⣟⣃⡉⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⡿⠷⠉⠉⠀⠀⠀⠤⠶⣺⣿⠟
⠀⠀⠀⠀⠀⠈⢻⡿⠿⢿⣛⣿⡿⣿⠿⣥⡐⠀⠀⠀⠈⢻⣿⣿⣾⢿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⣴⣶⣦⣀⠀⠀⠨⠈⠃⠀⠀⢀⢠⡄⢀⢰⣶⣿⣿⣿⣟⠷⠉⠻⠿⣖⠀⠀⠀⠀⠀⢀⣤⣴⣿⠇
⠀⠀⠀⢸⣿⣿⣿⣿⣯⠄⡤⣸⣖⣶⣦⣼⣿⣿⣼⣷⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠠⠖⣛⡛⠉
⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠻⠍⠛⠛⠛⠓⠒⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠿⠿⠿⠿⠿⠟⠋⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠞⢉⠋⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣦⣄
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣀⣠⠄⠐⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠂⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣠⡶⣶⣶⣶⣶⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠴⢔⡴⠚⣉⣀⡀⠀⠉⠓⠵⡽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠻⣿⡟⠀⠘⡏⠽⡙⠣⠀⠀⠀⡇⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⢌⠻⢍⠢⠄⠠⠀⠁⠀⢰⠀⢠⠁⠀⠀⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⣾⡿⣷⡶⠛⣁⠄⢁⣴⣏⠫⠀⠀⠀⠂⠤
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠬⠭⠤⢤⣤⣬⣭⠴⠞⠑⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣤⡤⣄⠀⠀⢡
⠀⠀⠀⠀⣀⣤⡴⠶⠶⠒⠲⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠚⠡⡀⠄⢈⠀⠀⢀⠀⠀⠀⡌⠂⠄⡈⠠⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣤⠾⠵⠀⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⢤⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣄⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠀⠀⠀⠀⡠⣴⡿⠋⠉⠉⠙⣷⡝⣦⡟⢹⣸⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢇⡠⠔⠩⠚⠛⢀⠄⠒⢦⡀⣜⠟⢻⣇⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣋⠉⠗⠂⠉⠠⣴⣶⢟⣻⠼⡀⠐⠚⠛⠋⢀⡮⠄⠭⠭⠭⠉⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢤⡄⠀⠀⢨⠄⠀⠈⠒⠤⠤⠒⠉⠶⢶⣶⣦⠐⠛⠁⢀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠄⡈⠁⠁⠀⠒⣀⠀⠀⠀⡀⣀⠀⠀⠀⠠⠀⠄⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠦⠤⠤⠄⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠗⠠⠞⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠒⠷⠧⠤⣤⡶⠶⠷⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠷⢧⣤⣤⣶⠶⠷⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⣇
⠀⠀⠀⠀⠀⡏⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠀⢀⠀⠉⡏⠙⢶⡀⢀⡔⡇
⠀⠀⠀⠀⠀⠳⡉⠀⠀⠀⠀⠀⠳⠀⠀⠀⢈⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⠀⠰⡏⠀⠀⠻⠀⢸⠇⢈⡽⠃
⠀⠀⠀⠀⠀⠀⠙⢦⣥⣀⣀⠀⢀⣁⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⢋⣀⠀⢀⣉⣯⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢴⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⣷⣟⡿
⠀⠀⠀⠀⠀⠀⠰⠾⠶⠶⢌⠉⣹⠦⠶⢦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⣌⠉⣹⠷⠶⢦⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⡇
⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⣿⣟⠳⣤⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠛⣏⠀⠀⠀⠐⠈⢿⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⠀⢰⠞⠀⠘⠿⠀⢸⡇⠈⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢧⣤⣀⣤⠤⡦⣐⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣜⣃⣠⠤⣦⣐⣛⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢰⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢰⡿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣸⣿⣿⣟⣛⣉⣭⣤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠾⠟⠛⠛⣛⠒⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠒⠒⠒⠉




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣍⣤⣬⣽⣏⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣴⡶⠀⣿⡇⠀⠀⠘⠛⠛⠛⠛⠛⠋⠉⢻⣷⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⣿⡇⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⣿⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⢸⣿⠁⠀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣾⣟⣋⣀⣠
⠀⠀⢺⡿⠀⠀⠈⠙⢿⣷⣄⠀⣤⣴⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⣿⡏⠀⠘⠋⠀⠀⠀⠀⠀⠸⠿⠀⠀⠾⠿⠿⠿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⣾⡟⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠈⠛⠁⠀⠀⠈⠙⠛⠻⠿⣷⣶⣤⣿⡇
⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣾⠿⠿⠿⢛⣻⣶⣾⠷⠀⠀⠀⠀⠀⠀⠰⠿⠃⠀⠐⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠃⠀⠀⠀⠀⠀⣠⣴⡦
⠀⢰⣶⣄⡀⠀⠉⠁⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⢀⣠⣶⡿⠟⠉
⠀⠀⠈⠻⢿⣦⣄⠀⠀⠀⠀⠙⠉⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⢾⠿⠛⠁
⠀⠀⠀⠀⠀⠙⠻⣷⡦⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠘⠿⠿⢿⣷⣶⣦⣤⣝⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢀⣈⣉⣉⣛⣻⣇⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄⠀⣠
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠻⠟⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⣠⣾⡿
⠀⠘⠛⠿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢀⣴⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠋⠀⠀⠐⠿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⡿⠿⠛⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⢻⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠈⠻⣿⣦⣀⠀⠀⢸⣿⡟⠿⣷
⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠙⠿⣷⣦⡀⢿⡇
⠀⠀⠀⠉⠛⠻⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣤⣤⣈⡙⠿⣷⡄
⣾⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣦⣤
⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠇⠀⠀⠀⠉⠉
⠀⠀⠀⠀⢀⣤⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣶⣦⠀⠀⢰⣶⡀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⢻⣧⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⣧⠀⠀⠀⠀⠙⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠈⢿⣧⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢠⣦
⠀⠈⢿⣧⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠻
⠀⠀⠈⠿⠇⠀⠀⣿⡇⠀⠀⠀⣾⡏⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠃⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⡿⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠂
⣿⣿⣿⡿⢿⣿⠿⢿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣦⣽⣤⣧⣤⣿⣬⣼⣯⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢉⡁⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠉⠉⠉⠁
⠀⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠀⠠⠤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠔⠊⡛⢻⣷⣦⣰⣄⡀⢠⣀⠀⠀⠀⠀⢀⣀⡀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠡⠠⠼⠂⠀⠐⣂⡐⢀⠴⠄⠀⢠⣄⣤⣤⠧⢙⣵⢿⡿⣻⣿⣿⣿⣶⠈⠳⠀⠀⠀⠀⠉⠁⠤⣤⣶⣶⣤⣴⣿⣦⣄⣴⣦⡈⣩⣥⣆⡀⣀
⢤⣴⣶⣶⣷⡴⠈⣤⣤⣶⣴⣦⣤⣠⣼⡽⠁⡡⢖⣫⣾⣿⠟⣫⣿⣷⠀⠈⠲⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣛⡏⡠⣊⣝⠙
⠀⠈⠁⢀⣠⣤⣄⣀⠙⢁⠉⠙⠉⣁⠤⢚⡩⠔⣪⡷⣛⣵⣾⣿⣿⣿⣿⡄⠀⠀⢮⣧⣀⣦⣳⣰⣤⣀⣠⡀⠈⢉⣙⡛⠛⠛⠛⠛⠛⠛⠋
⠤⠤⢒⣛⠩⠥⢚⣛⣭⡅⠤⣒⣩⠔⢊⣭⠶⣛⣵⣾⣿⣿⡿⣿⣿⣿⣿⢃⠄⠀⠀⠒⠯⠹⠧⣦⡂⢥⣠⡬⠍⡉⠈⠍⠋⣠⢾⣤⡦⡤⡚
⣂⣉⠡⠴⢒⣛⣭⣴⠴⠞⣋⣥⠴⣚⡭⢖⣫⢗⣫⠟⣛⣥⢞⣫⣟⡿⣻⣷⣙⠏⠢⡀⠀⠈⠁⠪⠉⠉⠉⠚⡉⠍⠓⠈⠙⠁⠀⠀⢛⡯⠭
⠵⢖⣚⣛⠯⣉⣠⠤⢒⣫⣽⣶⣿⠵⣚⡿⢞⡋⣀⢜⣫⣕⡿⣛⣵⣿⢟⣻⣿⣿⣿⣈⣀⠈⠷⠀⢀⣀⢒⣀⠒⣓⠒⠢⠠⠤⠤⣠⣤⣤⡴
⡭⠿⣒⣛⣭⠷⠖⣛⡭⢖⣛⠭⠖⡫⠁⠾⠋⢝⣒⡽⠚⢁⣮⠟⣫⣵⠿⣫⣿⡿⢋⣽⣿⠟⣿⢿⣿⡿⢟⣿⣿⣿⣷⣾⣷⣷⣿⣿⣡⡟⣰
⠘⠋⢉⠡⢐⣂⡥⠔⣚⡭⢗⣢⡴⣖⣡⣴⠾⢋⣡⣴⠞⠋⣰⠞⣩⣵⡻⠛⣡⣶⠿⢋⡠⢊⡥⠞⣩⠞⣡⣿⣿⣯⣞⣿⣿⠟⢩⡾⠉⣡⣯
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧
⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣄⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀
⠟⠁⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⣦⡀
⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠛⠃
⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢀⣴
⣤⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀
⠀⠀⠀⠘⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢴⣆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠴⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣠⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⣤⡀⠀⠀⠀⠀⠐⠻⠿⠇⠀⠀⠀⠻⢶⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⣀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠖⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⢀⣤
⠀⠀⢼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠁⠀⠀⠀⠐⠋⠀⠀⠈⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠺⠋⠀⠀⢀⣤⡤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⢀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣃⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣴⣂⣀⣀⣀⣀⣦⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠭⢉⡁⠀⠀⠀⡀
⠀⠠⣂⠁⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣢⣄⣰⣤⢻⣿⣴⣶⡴⡀⠴⠀⠀⠠⠐
⠀⣲⠿⣗⠁⠀⠀⠄⠀⡠⠀⠀⡀⢯⡻⣽⡿⢏⣵⣬⠏⠙⠁⠐⠈⠄⠀⠀⠈
⣾⠁⣶⡹⣦⣀⠂⠀⠈⠀⠀⠸⡏⣮⡇⡷⠃⢈⢱⡇⠌⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⣐⢀⠠⠈⠠
⠙⠞⢿⣿⡿⠟⠋⣠⠤⢤⣿⡁⢿⡟⢧⣇⢰⣾⡀⠸⡦⠀⠠⠀⠂⣤⠐⣄⠀⡀⠀⢠⣶⠆⢛⠣⠀⠀⠐
⠀⠀⠀⠈⠰⣖⠊⠁⠀⢩⠧⠍⠰⠂⠉⣅⢨⡀⢄⣲⣽⢷⡴⣷⣤⣿⣻⠿⠋⠀⠀⡟⢁⠘⢿⡷⣇⣮⣁⣀⢀⠀⠠⠑⢄⠈⠀⠠⡀
⠀⡀⢀⣻⡦⢌⣙⣒⠒⠛⠒⠁⠄⠠⣦⢽⣞⠓⠈⣮⣿⡶⠀⠈⡫⠅⢠⣖⣤⣤⠜⠀⠹⢿⣶⣯⣦⣭⣭⡅⢠⡗⣠⣦⣅⣩⣷⣴⡿⠿⠄
⠀⠈⠀⠉⢉⠉⣉⠉⠆⡀⣮⠹⣀⣶⣿⢺⣍⣙⣒⣪⢞⠁⣶⣄⠻⢷⡬⣭⣥⡄⠠⡤⠴⠶⢶⠓⠷⠶⠶⠦⠫⠶⣜⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⢠⠸⡦⣹⠳⣔⣦⢮⠙⠛⠛⣋⣉⣉⠫⢅⡐⣯⣳⣬⡿⡏⣲⡉⡓⠈⡓⣤⡤⠶⣞⢿⠻⣿⠗⠊⢰⢶⣻⡛⣻⡛⢏⠛⠛⠁
⠀⠀⠀⠀⠀⠉⠓⠦⣄⠸⣷⣦⣌⣛⠓⠲⠮⣽⡲⠿⠲⡿⣮⣻⣤⠽⡿⣿⣒⠛⠾⠿⠖⠚⠛⠉⠠⡖⢄⣈⠲⢶⡐⢄⠝⠾⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠖⠉⠉⠁⠀⠀⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠁⡉⠙⠷⠖⠒⠒⠲⢶⢻⣯⣹⠯⠭⠓⠀⠉

⠀⠀⠀⠀⠄⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⢦⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠶⠶⠤⢀⠀⠀⣶⡦⠄⠀⢀⣴⣿⣿⣷⣶⠂⠀⠀⠐⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣾⣿⣿⣦⡀⠀⠀⠠⣤⣀⣤⡤⠀⠀⢀⢠⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⠆⠀⠈⠁⠘⠏⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠈⠙⢿⣿⣷⣄⡀⠀⣠⠉⠉⠀⠀⠀⠁⡞⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠉⢶⠄⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⢿⣿⡿⠿⠛⠁⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⠀⠀⣀⠀⠀⠈⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠐⠆⠀⠀⠀⢀⣀⣤⠀⢀⣿⣿⣿⠀⠀⠀⡀⢸⡇⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣀⣤⣄⠀⠀⠀⠈⠙⠣⣤⣾⣿⠿⡇⠀⠀⠀⠁⠘⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢜⠿⠛⠟⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡷⠀⠀⣾⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠖⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠈⠛⠛⠛⠻⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠿⣷
⠀⠀⠀⠀⣄⣀⡀⣐⡗⠀⠀⣠⣾⣿⠟⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠠⢶⠖⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣿⣄⡀
⠀⠀⠀⠀⠀⠉⠉⢉⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⢡⣶⣶⣶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣦⠀⠀⠀⠀⠀⠀⠀⣴⣆⡘⠀⠀⠁⠀⠘⠃
⠀⠀⠀⢀⣰⣀⠀⠀⠙⠻⣿⣿⠟⢁⣀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠸⠀⠀⠐⢿⡈⢣⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠋⠓⠀⠀⠀⢀⣿⠞⠀⠀⠛⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠀⠀⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣭⠏⠀⠀⠚⠋⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⢀⠞⠀⠀⠀⢀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢀⡀
⠀⠀⠀⠘⠀⢸⠀⠀⠐⣼⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡾⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⣄⠀⠈⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠲⠦⠤⠤⠤⠤⢴⡶⢀⣀⣀⡏⠉⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⡀⢀⣧⣀⣤⣤⣶⣾⣿⣿⠇
⠀⠀⠠⠄⡀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣯⠀⠀⠀⠀⠀⠀⢄⠀⢀⣀⡀
⠀⠠⠌⠀⣀⣛⣒⣶⣤⣤⣽⣟⣿⣿⣽⣿⠿⣿⣿⢿⣿⣿⣟⣫⣭⣥⣶⣿⣿⣿⣿⣶⣄⠀⠀⠤⠤⠬⠭
⠀⢀⣬⣭⣍⣉⣙⣿⣷⣶⣾⣿⣿⣿⣿⡳⠾⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣭⡤⠤⠄⠒⠒
⠉⠉⣍⣉⣛⣋⠋⠛⠦⣤⣀⣨⡍⠉⢿⣿⣏⣉⢾⣿⣿⠗⠛⠛⠀⠀⠀⠛⣟⣛⣻⣿⣇
⠀⠀⠀⠀⠉⠀⠀⠙⠓⠲⠦⠤⠤⠀⣀⣀⣀⠒⠒⢺⣿⠂⠀⠈⣉⡉⠉⠭⠤⠴⠒⣀⣀⡀⠉⣉⣉⡉⠑⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠙⠛⠁⠀⠀⠀⠀⢼⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⢶⣶⣤⡀
⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠸⠿⠋⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⣴⣄
⣶⡄⠀⠀⠀⠀⠀⠀⢾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠙⠛⠁⠀⢠⣶⡀⠀⠀⠀⠀⣠⡄⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⢰⣶⣤⡀⠀⠀⠙⠿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⢿⣿⠀⠀⠀⢠⣤⡀⠀⠀⣀⠀⠀⠀⠉⠛⠁
⠀⢀⣤⣶⡦⠀⠀⠀⢰⣶⣄⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⢿⡿⠀⣾⣿⠁⠀⠀⠀⠀⣿⣦
⣄⠈⠛⠉⠀⠀⠀⠀⠀⠙⠻⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠙⠛⠀⠀⢠
⠿⠃⠀⠀⣰⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠃⠀⠀⠀⠛⠋⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⢰⣿⠇
⢀⣤⠀⠀⠛⠋⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠄⠀⠀⠈⠛⠃⠀⠀⠙⠋⠀⠀⠀⣴⣤⡀
⣾⡿⠀⠀⠀⠀⠀⠾⡿⠋⠀⠀⠀⠀⠀⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⡀⠀⠀⠀⣶⣦⡀⠀⠀⠈⠛⠟
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣶⡷⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠈⠙⣿⣦⠀⠀⠀⠀⢀⡀
⣾⣿⠆⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠛⠋⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠸⢿
⢀⣀⣤⡀⠀⠀⠀⠻⠟⠋⠀⠀⠀⠀⢴⣦⣄⠀⠀⠈⠿⠃⠀⠀⠀⠀⢀⣴⠀⠀⠙⠻⠿⠂⠀⢴⣦⣄⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⣿⣦
⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⡀
⣼⡇⠀⠀⢀⣀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣴⣿⡿⠂
⠿⠃⠀⠀⠘⠿⣷⠄⠀⠀⠉⠀⠀⠀⢿⣿⡶⠀⠀⢀⣶⡆⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠰⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⢀⣴⣾⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃
⠀⠀⠰⣿⡿⠓⠀⠀⠀⢰⣿⡀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⠙⠛⠻⠿⠟⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣤⣶⡷⠀⣴⣦⡀
⣴⣶⠆⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠉⠀⠀⠈⠻⠷
⠉⠁⠀⠀⠀⠀⣾⡆⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⢀⣀⠀⠀⠀⣼⣿⠀⠀⢀⣀⣀
⢀⣀⡀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠉⠁⠀⠀⠈⠻⢿⡇
⠿⠛⠋⠀⠀⠀⠀⠀⠀⣤⣶⡷⠀⠀⠀⠈⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⣠⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠁⠀⠀⠀⠉
⠀⠀⠀⠰⠿⠟⠁⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⡀⠀⠀⠙⠛⠛⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⣦
⣦⣤⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢻⣿⠄⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⣶⣤⡀⠀⠀⠀⠀⠰⣿⠟⠀⠀⠀⣰⣦⠀⠀⠸⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⡿⢿⣿⣿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠉⠉⠉⠙⣫⣶⣶⡸⢗⣴⡶⢟⣷⣮⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⠿⠿⠿⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠄⠀⠀⠀⠀⢠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠳⣄⠀⠈⠛⠋⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡿⢻⣿⣿⣿⣿⣿⣿⣶⣘⢛⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⣛⢻⣿⣿⣶⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣭⣼⣿⣿⣛⣿⣿⢋⣭⢻⣿⣿⣷⣍⣿⣿⣭⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⢟⡛⣛⠿⣿⣿⣷⣵⣾⣿⠿⠛⣛⣛⠿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣵⣾⣿⣿⢸⣷⣮⣽⡛⣛⣭⣵⣾⢱⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡎⣿⣿⣿⡇⣿⣿⣿⡟⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⢻⣿⣿⡇⣿⣿⣿⠇⣿⣿⣿⠏

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣰⣶⣦⡀⠠⠄
⠰⠶⠲⠤⠤⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡖⠐⠒⠂⠈⠉⠉
⠀⠤⠀⠀⠀⠀⠀⠠⠤⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠢⠽⠿⠟⠁⠀⠀⠀⠀⠀⠠⠤⠮⠤⠄⠀⠀⠀⠀⠀⠀⠤⡤⢤
⣤⣤⣤⣤⣄⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⡀⢀⠀⠀⣤⣤⡄⠀⣤⣤⣤⣤
⣿⣿⣿⣿⣶⣿⣿⣷⣶⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠄⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣤⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠹⣷⣤⣾⢿⠯⠿⠛⣿⣯⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⡒⡺⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠴⣚⠶⠿⢦⣶⣮⣽⣿⣿⣿⣿⣿⣛⢛⣿⣶⣦⣌⣛⢷⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣯⣛⣻⠿⣿⣟⣛⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠒⠶⠒⠶⢶⣦⣴⡶⢦⣍⠉⢿⣿⣿⣿⡿⣛⢛⠉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣛⣫⣾⣻⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠤⠥⢤⣄⣿⣷⣮⡥⢶⣶⣤⣬⣹⣿⣿⣿⠷⠖⠂⠙⢿⣿⣷⣶⣮⣝⡛⠿⢿⣿⣧⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀⣀⣀⣤⣤⣍⣙⣛⣛⡛⠛⠀⠀⠀⣊⣉⣙⡛⠛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠛⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⣴⡶⠷⠶⠦⣄⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⠏⠀⠀⠀⠀⠈⣧⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣀⣠⠤⠤⢤⣀⠟⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠛⢰⡇⠀⠀⢸⣿⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢽⠿⡇⠀⠀⢸⣿⠟⠋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⢲⣳⡟⠊⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠶⢰⣯⣀⡀⢀⣀⣀⣀⡀⢀⠀⠀⠀⡀⣄⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣴⣾⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢻⡜⣿⠛⢻⠻⢿⣿⣿⡛⠋⠉⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⣦⣸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣿⡟⠳⣟⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⣿⡇⠀⠈⢧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⡀
⠀⢸⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣠⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⢹⣧
⠀⣾⣇⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⢻⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣽⢁⣎⣿
⠀⣿⣿⡈⢻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⣄⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣾⠃⣸⣯⣿
⠀⣿⣿⣷⡌⢿⣧⡵⠶⠀⠀⠀⠀⠀⠀⠀⢀⡠⣣⠴⠊⣵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠃⣰⣿⣹⡿
⠀⠸⡿⣿⣿⣆⠳⣄⠀⠀⠀⠀⠀⠀⢀⣔⣣⠿⣇⡤⠆⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠙⢿⠃
⠀⠀⠹⠏⠘⢿⣧⡀⠑⠦⣀⠀⢀⡔⣣⠟⢁⡜⠉⠀⠀⢸⣧⣿⣿⣦⡀⠀⠀⢀⡀⠄⠂⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠉⠉⠙⠓⠊⠁⠀⠀⠀⠀⢸⣿⡟⠝⠛⠉⠀⠉⠁⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣷⣶⣤⣀⠀⠀⠀⠀⢸⣿⡫⣴⣦⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⠀⠀⠉⠛⠿⣿⣶⣤⡀⣸⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠷⠀⠀⠀⠀⠀⠉⠻⣿⣷⣿⡿⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠈⠀⠂
⠀⠀⠀⠀⠶⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠻
⠀⠀⠀⠀⠀⠙⠂⠈⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⠀⣠⠖⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠈
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠈⡇⠠⣄⠆⠀⠈⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⡠⠆⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄⢀⠇
⠀⠀⠀⠀⠀⠀⠰⡄⠘⠃⢀⡐⢄⠀⠀⠀⣠⣯⠟⢉⠀⠀⠁⠀⠀⠀⠀⡀⡀⠀⡀⡀⠀⠀⠀⠎⡀⠀⢸⠃⣠⠌
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄⢉⣉⠉⠬⡇⠀⢺⣯⠐⠳⡀⠒⠀⠀⠀⠀⠐⣱⣃⠚⠉⠀⠀⠀⠀⠀⠄⠀⢸⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠇⠐⠀⠀⠀⠀⠈⡄⠙⠆⢀⣈⢦⡆⠀⡀⡀⠂⠉⢻⣢⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠈⠡⠄⡃⠀⠈⠉⠉⠉⠁⠀⠈⠀⠀⣿⣓⠒⠂⠈⠀⠆⠄
⠀⠀⠀⠃⠀⠀⠠⠄⠀⠀⠈⠆⠀⠀⠀⠀⡇⠰⣌⠂⠀⠀⠀⠀⠤⠀⠀⠀⠸⠋⠉⣀⠄⠐⠁⠀⠀⠀⡀⣂⡥
⠀⠀⠀⠀⠀⡾⠃⠀⣀⠤⡀⠀⠈⡒⠤⣀⣸⡇⠈⠀⠀⠀⠀⠀⠀⢀⡤⣊⠁⣻⡟⠩⡒⢄⣀⢀⢀⡄⠋⠉⢹⡄
⠀⠀⠀⠀⠑⠀⠀⠀⠉⠲⣤⠀⠀⠈⢆⠀⢁⣘⣦⣒⡉⠈⢖⡀⣋⡭⠸⠁⢠⢆⠃⠀⠈⠀⢨⠩⠖⠀⠀⠀⠀⠡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠑⠦⠤⣰⡿⠛⢫⠥⠴⢉⠛⠃⡨⠥⠜⠒⠢⠃⡟⢁⢀⠈⠋⢀⠤⢖⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡽⠃⠀⣾⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠁⠀⠊⠉⡂⠀⠈
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⣏⠀⠀⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢁⣀⣠⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣐⣾⣄⣷⣾⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣾⣾⣾⣷⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⡉⢻⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠋⣿⣟⠿⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣸⣦⠀⠘⣇⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⡈⠻⠃⣠⠟⣯⣴⣶⣄⣶⣦⡶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢿⣿⣧⢠⣿⣿⣿⣇⡀⣀⡀⠀⠀⠠⠾⠿⢟⠋⡙⠻⢿⣿⠷⢾⣷⣾⣿⠋⢿⢟⡹⢿⢄⡸
⠀⠀⠀⠀⠀⣠⣀⠀⠀⣠⣤⡂⢀⠀⠻⣟⣾⢈⣏⣉⠙⠻⣿⣿⣆⠀⠀⠴⢂⣭⣤⣹⣦⣄⣻⣿⣒⣲⣶⡗⠲⠆⠙⣀⣴⣤⣄⢀
⠀⠀⠀⠀⠐⠛⠟⠂⠀⠉⢟⣽⠿⣷⡄⣿⢿⣾⣿⣿⣷⣤⡋⢹⠟⠀⠀⠚⠈⠛⠂⠉⠛⠙⠛⠿⢮⣥⣵⣶⣦⡶⠾⠋⠛⢹⡿⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠛⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋

⠀⠀⠀⠀⠀⠀⢀⣠⣦⣴⣶⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣦⣤⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠁⠀⠉⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⢟⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣷⣾⣶⣿⡿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⡇⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⢻⡏⠻⠟⣷⣦⣤⣦⣧⡶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣠⡀⢀⠐⠆⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡮⣼⣧⣄⣼⡟⣿⣿⣿⣤⣤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠻⡿⢷⣬⠆⠃⣹⣿⡏
⠀⠀⠀⠀⠀⠀⡀⢺⠁⠀⣄⠀⡈⠻⢿⣴⣆⣿⢹⡟⠹⣟⠋⡙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠼⠟⠁⠚⠁⢋⡟⠠⠃⠿⣿⠁
⠀⠀⠀⠀⠀⣤⡤⠿⠿⠛⠛⠹⢻⡷⠞⣽⣛⣿⣛⡷⠞⢃⣟⠓⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠿⡻⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⠉⣨⣴⣿⣿⣿⣿⣿⡟⢿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣶⣼⣾⣷⡟⢩⣿⣿⣿⣛⢛⣭⣿⠎⣉⡠⢧⡃⠉⢻⡆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⣟⣟⣭⣭⣽⢻⣬⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣭⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠞⠁⢁⣬⣶⣿⣿⣿⣿⣿⢿⣯⢿⣿⢿⣿⣿⣦⡥⢿⣿⢿⣿⣿⣿⡿⠒⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡟⣼⣿⣿⢿⣹⣿⣟⣻⣿⢹⢿⣿⣿⣿⣿⢸⢻⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠷⣼⣿⣿⣿⣆⣻⣿⣿⣖⢿⡜⠘⠏⢹⣿⣿⣌⡀⠀⠹⠛
⠀⠀⠀⠀⠀⣼⠿⠟⠏⠈⢠⣿⣿⡝⠯⡧⢹⣿⣯⡓⠸⣷⠀⠀⠏⢿⢿⡓⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡿⡝⠆⠀⢸⣿⣦⡉⠀⣿⢀⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠑⠈⠀⠀⠀⠻⠇⣩⣶⣿⡝⢿⣿⡿⣶⣤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡿⣫⠵⢿⣹⡇⠀⠀⠹⡄⢹⠷⠄⠀⣀⣙⠿⣔⣲⣤⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠛⠛⣿⣷⣾⣖⣲⣤⣄⣿⡗⠛⠛⠓⠂⢲⣶⡼⠶⢦⣸⣷⣶⡿⠿⠿⠿⠛⠛⠛⠻
⠀⠀⠀⠀⠛⠉⠛⠒⠒⠒⠚⣁⣤⣤⠤⠤⠌⠈⠉⠒⠒⣿⡇⠉⢁⣷⡆⢠⠈⣡⠈⣋⣉⣣⠤⠴⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡾⢸⢻⢃⣮⢞⢥⠀⠠⠤⠭⣭⣿⣿⣯⣈⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣬⡏⢀⡟⣯⣈⣬⡃⢻⣾⣯⣀⠀⠐⣾⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠒⠊⠉⢛⡽⠋⠋⠀⠸⠘⠹⠉⠳⠈⠙⠛⠿⠿⢽⣿⠿⠿⠓⠒⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠑⠢⣼⣆⣀⣀⣀⠀⠀⠀⠀⠀⣄⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀⠁⠲⠢⠬⣦⡀⠘⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠀⠑⠐⠒⠓⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣱⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠉⣉⣉⣉⣉⣙⣛⡲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣈⣦⠖⠋
⠀⠀⠀⠀⠀⠉⠀⠀⠔⠚⠉⣉⡠⠤⠤⠤⠬⠭⣽⣓⡻⠽⣟⣓⡶⠶⠶⠶⠶⠶⠛⣋⣩⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠪⠭⢭⣙⣛⣛⣋⣉⣡⠤⠔⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠂
⠀⠀⠀⠀⠀⠲⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣌⠢⡀⠀⠀⡾⢶⣤⡀⠀⢸⠀⠀⠀⠀⠀⡠⠔⠈⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⡇⠚⢉⣁⡀⠈⣢⣞⣀⣠⢤⣁⣀⠀⠣⣀⠠⠐⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠙⠒⠢⠤⠤⢃⡜⠉⠀⠀⠉⠳⣴⠋⠀⠀⠀⠈⢻⡙⠒⢤⡀⠀⠀⢠⠃⠀⠀⠀⣀⠤⠐⠒⠈⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⢀⡴⢻⠁⠀⠀⠀⠀⠀⠘⡄⢀⣀⠀⠀⠀⢣⠀⠀⠈⠳⣄⠺⠤⠐⠂⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢠⠎⠀⢸⡀⠀⠀⣖⣆⠀⠀⢳⢰⣿⡆⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕⢠⠇⠀⠀⠀⢣⡀⠀⢿⡿⠀⠀⣾⡀⠛⠁⠀⣀⠞⠀⠀⠀⠀⠀⡄⢣⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠶⣒⡈⠉⠁⠀⠀⡸⠀⢤⠀⠀⠀⠙⠦⣤⣤⠴⠚⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⢀⠘⠀⠀⡇⠑⠢⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠀⠀⠀⢀⣀⠬⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢡⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⢸⢠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠸⡀⠀⠀⠸⡀⠀⠒⠀⠤⠤⠠⠤⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠖⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⣀⠔⠊⠁⢀⣀⣀⠤⠤⠤⠀⠒⣦⠈⢧⠀⠀⠀⠀⠀⠁⠀⠦⠀⣀⡀⠴⠔⠊⠁⠀⠀⠀⠀⠀⢀⡴⢁⠤⠀⣀⡀⠀⠀⠀⠀⠑⠢⣀
⠀⠰⠞⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⢆⠀⠀⠀⠉⠉⠁⠒⠂⠤⠤⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠠⠄⠒⢌⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢁⡤⢄⣀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⠊⠉⠀⠀⠀⠀⡆⠀⠀⠈⠉⠓⣒⠲⠲⠶⠖⠒⣋⡉⠀⠀⠀⠀⡁⠀⠀⠉⠒⠤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡴⠋⠀⢇⠀⠀⢀⠜⠀⠙⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡴⠋⠀⠀⠀⠘⡀⢀⠎⠀⠀⠀⠈⢢⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡠⠊⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠱⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⣠⠴⠒⡉⠐⠒⢄⡀⠈⠀⠂⠀⠀⠀⠤⠀⠂⠒⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠁⠀⠀⠀⠱⡄⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠠⣂⣄⠀⠀⠀⠀⠀⠰⠄⡷⠀⡀⠀⠀⠈⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢇⠀⢀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠠⠀⣠⠤⠄
⠀⠀⠀⠀⠀⢈⡦⢄⣀⢙⣀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢈⠹⠠⠏⠔⢡⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠈⡉⠁⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠠⠤⠠⣂⠀⠀⠈⠁⡀⠄
⠀⠀⠀⠀⡠⢂⠀⠀⠈⠡⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡄⢚⡀⢩⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠈⠀⠐⠈⠄⠀⠀⠃⠂⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠀⢀⠀⡤⡶⠖⢺⠐⠆⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠄
⠀⠀⠈⢇⡂⠤⠀⠀⢀⣀⠀⡀⠐⠀⠄⠀⠀⢀⠀⠄⠀⠀⠑⠐⠀⢀
⠀⠀⠀⠀⠀⠲⠿⠃⠾⢁⢉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠈⡐⠂⠀⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢩⣤⡤⢄⡻⣵⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⣁⣸⡊⠧⢨⠋⠀⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⡠⠀⡀⠀⠈⠈⠉⠀⠰⠀⠈⠀⠐⠀⠀⠐⠒⠛⠂⠁⠁⠀⠀⠀⠄⢤⠀⠤
⠀⠀⠀⠀⠀⠀⡅⠠⠅⠀⠂⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠉⠠⠇⠀⠀⠀⠀⠀⠀⠃⠠⠄⠈⠁
⠀⠀⡀⠀⡐⠘⠂⠀⣤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⢰⠀⠀⠐⠀⠸⣄⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠎⠀⠄⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⡀⠀⠹⠃⠀⠄⠀⠀⠒⠟⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠀⠀⠀⠔⠂⠁⠀⠀⠀⠀⡂⠘⠇⠀⠐⠀⠄⠀⠂⠀⠀⠀⢀⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠃

⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣭⣭⣭⣭⣍⣉⡉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣫⠥⣶⣶⣶⣾⡯⢭⣙⠓⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣶⣟⡛⠉⠉⢙⣛⣻⢯⣗⠦⣙⠷⢄⡈⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢢⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣟⡉⠉⢹⡄⢴⣟⣿⣟⢷⣮⠙⠪⣻⢦⣙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⢰⢲⠇⠈⠀⠁⠈⠀⠀⢀⣴⣶⣶⣦⣄⡀⠀⠀⠈⠛⠋⠀⢠⡇⡸⣿⣾⢡⡆⠹⣵⣄⠈⠳⣮⠑⢦⣉
⠀⠀⠀⠀⠀⠄⠀⡱⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⣭⣄⡀⠉⠛⠻⣷⣦⡀⠀⠀⢀⡼⠀⢉⡩⢪⡞⣀⣉⣉⣿⣷⣤⣌⣳⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠿⡤⠈⠹⡄⠀⠀⠀⠈⠛⠶⣦⠞⣡⣔⣩⣾⠿⣻⣿⣿⣥⠤⣄⠉⠛⡝⠻⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡒⠝⢧⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⣾⣷⠾⣛⠿⣫⡵⣻⠟⣫⠽⣿⣿⡌⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣞⠀⢀⡀⠙⢷⣤⣤⠏⠀⣀⣤⡾⠿⠛⣉⠤⢊⠵⢋⠔⡽⠁⢸⠁⣻⣿⣾⠷⢁⡴⢁⠜⡠
⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⡻⣝⠛⠛⠿⢿⣶⣿⡿⠷⠿⠛⢛⣛⣩⠥⠔⢒⣩⠴⢚⢁⡴⢋⡜⠁⣰⡞⢦⣙⢿⣍⣛⣛⣊⣡⣖⣥
⠀⠀⣠⣴⡿⡻⠝⣚⣉⡙⠊⣿⠢⢭⣑⣲⣶⣬⣿⣿⣿⣿⣯⣭⣴⣶⣒⣩⣩⣤⣴⣴⣯⠶⠿⢶⣿⣿⣧⣤⣭⣳⣿⣷⣶⣾⣟⡛⠫
⠰⠟⣱⢋⠊⠔⠉⣁⣍⣉⣴⣿⠴⠚⠉⠉⠥⢖⣛⣩⣙⣛⣿⣿⣯⣭⣭⣭⣄⣤⣤⠤⠶⠶⠖⠲⠤⠤⢄⣀⠀⠉⠉⠙⠛⠛⠿⠿⠷
⢀⢰⠃⠔⠈⠀⠀⣯⣿⠿⠟⡁⠄⣢⠴⠚⢋⣉⣡⣤⣤⣶⣶⠖⠛⠛⠟⠿⠟⣛⣛⣛⡛⠿⠟⠻⠿⢶⣶⣤⡭⢽⣶⣶⣶⣤⣤⣤⣤
⠈⢸⠀⠐⡐⢄⡁⠒⣂⣈⣤⠶⣚⣁⣤⡴⢞⣿⣭⣽⣿⣿⣿⢿⣷⣶⣦⣤⣄⣀⣈⣉⣉⣉⣉⣉⣭⣭⣤⣤⣭⣐⣒⠦⢄⣀⣀⣀⣀
⢈⠸⣇⠀⠉⠦⢍⡉⣉⣥⡴⠿⢛⣩⡵⠾⠛⠉⡉⠁⢀⣀⣠⣴⣶⣶⣿⣿⣿⣷⣤⣤⣤⣴⣞⠫⣅⣶⣶⠦⣌⠙⢧⡈⠍⠐⠛⠟⠟
⠐⠀⢙⣷⣤⣤⠶⠛⠉⢀⣠⡶⠛⠉⠀⢐⣨⣴⣒⠋⠩⠁⢈⠔⠑⠡⣟⡿⡯⠛⢦⣙⠻⢯⣈⠥⠚⢹⡀⣾⣼⡁⠀⢳⡀⠁
⠘⠛⠛⠉⠁⠀⢀⣠⠶⢟⠉⢐⣠⣴⣊⣉⣀⣬⣍⣁⣒⣮⣀⣤⣀⡬⠜⠋⠁⠀⠀⠙⠻⣔⡛⠶⣄⠀⠙⢮⣳⢶⣮⡤⠛⢦⡀
⠈⢀⣀⣀⣤⢖⣋⣁⡤⠴⠚⠋⡉⠩⠄⠀⠒⠐⠒⠒⠒⠬⣭⣍⣉⡛⠛⠶⠦⣤⣀⡀⠀⠀⠉⠙⠛⠻⢦⡀⢌⡙⠛⠻⠷⢶⢿⣷⣶
⠸⠿⠟⠛⠛⠛⠋⢉⣭⣭⣉⣙⠛⠒⠲⠶⠤⠤⠤⠴⠖⠒⠒⠒⠛⠛⢛⣛⠋⠭⠽⠿⠷⠶⣶⣤⣀⡀⠀⠉⠳⣽⣧⣅⡠⠄
⠠⡤⡤⠴⠶⠚⣋⣉⣉⣉⣉⣉⣉⣛⣒⡒⠶⢤⣤⣤⠴⣖⣒⣂⣉⣡⣤⣤⡤⢤⠤⠄⣒⣒⡈⢛⠿⣯⣿⡛⢲⣶⣿⣿⣿⣮⡄⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣴⢟⣿⣶⣃⣠⠀⠀⠀⠀⠀⠀⣰⣯⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⣼⢡⡞⣱⢟⣿⢷⣾⣁⡠⠀⣠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡞⣼⢣⣟⣼⢣⡞⣱⢏⡽⣻⢷⣾⣿⣿⡿⣫⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢯⣿⣽⣷⣿⣾⣷⣿⣾⣵⣯⣾⣵⣯⣿⣿⣿⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢁⡯⠞⠛⠛⠛⠛⠛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣭⣶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣻⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⢒⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⣫⣿⣿⣿⣿⣗⡩⠙⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠠⢟⣿⣿⣿⣿⣟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⡝⣧⠀⠀⠀⠀⠀⣀⠴⣺⣿⠃⠀⠀⢊⢿⣿⣿⣿⣯⣭⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣰⣯⠖⠛⢿⣮⣷⣄⠀⢀⠀⠀⢀⡿⢸⣧⠰⣤⡶⣛⡵⣿⣿⡏⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣟⣿⡧
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠠⣿⣿⢿⣿⢇⣿⣿⣿⠀⠈⠀⠀⠈⣳⣤⣿⡆⢟⡾⣫⣾⣴⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣀⣾⡃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡾⡷⠋⠀⠀⠀⠀⠀⠈⣿⣿⡟⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⢾⣭⣍⣉⠙⠒⠶⢤⣄⡀⠈⠉⢉⠉⠀⢀⠀⠀⠀⠀⠀⠀⢰⣽⣿⠃⣿⣿⣻⣿⣿⣿⣿⣶⣤⡀⠀⣸⣿⣿⣿⣿⣾⠏
⠀⠀⠀⢀⣹⣿⣿⣿⣷⣦⣄⠈⡛⢦⡑⣤⣠⣀⠀⠀⠀⠈⠀⠀⢀⠞⣿⡟⣸⣿⣿⡿⣵⣿⣿⠿⠛⠉⢀⣰⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠸⢭⣛⣛⣉⣉⣛⣛⣛⣦⣈⣿⣎⣿⣿⣆⡀⠐⣈⣀⢁⣡⣾⡟⣡⣿⣿⣿⣾⡿⠿⠿⠒⠀⠀⣼⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠙⠻⠿⢯⣭⣍⣉⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⣿⡿⠿⢻⠍⠄⠀⠀⢀⣠⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣾⣯⣭⣭⣵⣶⣿⠿⠋⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⠿⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣿⡟⠻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⡄⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡦⠀⠀⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⣄⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠤⠤⠴⠿⡿⠷⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠷⠶⠤⣶⣶⣶⣶⡶⠴⠶⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣶⣶⣶⣴⣦⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢦⠀⠀⠀⠀⠀⠀⠀⡇⣸⡇⠀⠀⠀⠀⠀⠀⢠⢦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⣸⠀⢧⡀⠀⠀⠀⠀⠀⡇⢹⣷⠀⠀⠀⠀⠀⢠⠏⢸⡆⠀⠀⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿
⠀⣿⡄⠉⣳⡄⠀⠀⠀⢀⡇⢸⣿⠀⠀⠀⠀⣰⡋⠀⣼⡇⠀⠀⣿⣿⣿⡆⠀⣹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡋⠀⣸⣿
⠀⠻⠻⣄⠈⠦⣀⠀⢀⣸⠃⣼⣿⣄⠀⢀⣠⠞⢁⣾⠻⠃⠀⠀⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿
⠀⠀⠀⠙⢷⣄⡈⠛⠛⠁⠀⣿⣿⣿⣭⣭⣤⣶⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⡈⠛⠛⠁⠀⣿⣿⣿⣭⣩⣤⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⡠⠐⣲⣷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⠭⠁
⠀⠀⠀⠀⡴⠛⣻⣟⣿⣡⢾⠏⠚⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⠏⣯⡉⠀⠀⣠⣶⡒⣂⣤⣤⡀
⠀⠀⠀⠀⠀⢸⠟⠹⠓⡹⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⡙⢀⠀⠀⠋⠘⢷⠈⠋⠗
⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⡀⠀⠑⠠⡀
⠀⠀⠀⡠⠃⠀⡠⠋⠀⠤⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠑⠀⡀
⠀⠰⠞⢁⣴⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠗
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⢿⠿⡿⡿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⡠⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡁⠀⠀⠀⠀⣰⠥⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠂⣀⠔⠀⠀⠀⣠⠎⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡸⠁⠀⠀⠀⠀⠀⡰⢡⠎⠀⠀⠀⠀⡰⢻⠀⢀⠤⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⢠⡰⠁⠀⠀⠀⠀⠰⠁⠀⡔⢁⡴⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢃⡰⢾⠒⢩⢔⠜⠉⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⠜⠀⠆⢰⠁⠆⠀⠀⠀⠀⠀⡠⢊⠔
⠀⠀⠀⠀⠀⠹⡦⡄⠀⠀⢃⢰⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠸⢀⡌⠀⢠⠀⡜⠀⠀⠀⡠⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠘⡌⡆⠀⠈⢻⣀⠀⠀⠀⠀⠀⢄⣣⡀⠀⠀⢀⡇⡏⠠⠀⢠⠋⠀⠀⠀⠊⡰⠃
⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠈⠦⡁⠄⠀⠀⠀⠀⠈⠑⡦⡄⠀⠃⢃⡰⢀⠆⡀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⠀⠀⠈⠢⣱⠀⠀⠀⠀⢀⠖⣼⠎⠀⢨⠓⣼⠀⡇⠔⠉⠇⠀⣠⡴⠂⠀⠀⠀⢀⠜⡜
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⢠⣟⠀⠀⠠⡄⡿⡸⡌⢀⠜⢔⠟⠉⠀⠀⢀⣤⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⢠⡸⡌⢃⠀⣠⢃⡧⢰⡴⢃⡞⠁⠀⠀⠀⡴⡱⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢎⠲⢄⠀⠀⠀⠀⠑⢴⡀⠀⠀⠀⢹⠸⣀⠟⢡⣎⠔⡏⢠⠻⠀⠀⠀⠀⠀⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠠⣤⣀⣀⠈⠣⣄⡀⠀⠸⢀⡧⣦⡋⠤⠊⠀⢸⡘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠙⢦⢜⣌⢣⣦⢈⠜⠇⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⣠⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡎⣇⠎⡘⢀⡠⢤⠶⠚⢛⠟⠲⠖⠾⠭⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠺⠋⡜⠰⡡⠊⢀⠠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⠀⡄⢷⡡⢊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢴⣴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢦⣤⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣽⣿⠿⠓⠛⠃⠀⠸⢝⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢀⣤⣀⠀⠀⠀⠐⠲⢦⣤⡉⠁⠐⢮⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠁⣠⣞⢻⣤⣿⣷⣶⣤⡈⠳⢄⡈⠻⣷⣤⢄⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡇⠀⣿⣿⠟⠋⠉⠉⠙⢿⣿⣿⣦⡀⠻⣆⢪⣻⣎⢧⡀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⠷⢾⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣾⣆⢳⣿⡎⣷⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠘⣿⡇⣿⡇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣤⣀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣿⣿⣿⣿⣿⣿⡿⢠⣿⢿⣿⠃⣸⢇⡄
⠀⠀⣠⠴⠞⠛⠛⢛⣛⣻⣿⣿⣷⣦⣄⠈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⢛⣥⣾⣿⣿⣿⣿⣿⡿⢁⣼⢯⣿⠋⣰⢏⠞⣼⣷⣤⠀⡰⠃
⠀⠉⠀⣀⠤⠖⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣦⣄⠀⠉⠉⠙⠛⣛⣛⣛⣋⣩⣥⣶⣾⣿⡿⢟⣿⣿⣿⠿⢋⣤⡾⠫⠟⣡⠜⠵⣫⣾⣿⡿⣣⠞⡡⢊⡀
⠀⠀⠀⠀⠠⠴⠒⣚⣛⣛⣛⣛⣳⠶⢤⣍⡙⠻⢿⣦⣄⡀⠤⣬⣭⣭⣭⣭⣍⡉⠥⢶⣞⣛⣋⣭⣴⠾⠛⠉⠀⠀⠀⣀⣤⣾⡿⢛⣡⣾⢕⣪⠞⠋
⠀⠀⠀⠀⠀⠈⠉⢉⣩⣭⣭⣭⣭⣝⣛⣿⠿⣷⣤⣈⠙⠻⢷⣦⣌⡙⠻⢿⣿⣿⣦⣌⠉⠉⠁⠀⠀⠤⠤⠴⠖⠚⣛⣋⣩⡴⠾⣛⣩⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠶⠶⣶⣾⣿⣿⣷⣾⣭⣝⣂⠀⠉⠛⠻⢿⣶⣬⣭⣛⠻⠿⢶⣦⣤⣄⣀⣀⣀⣀⣀⣨⣥⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⣭⣭⣛⣒⠂⠀⠀⠉⠉⠛⠛⠿⠶⠶⠶⠬⠭⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⠒⠛⠛⠋⣉⠉⠩⠉⠉⠙⠛⣛⢛⡒⠶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠙⡀⠥⠀⠐⠀⡉⠠⠀⠀⠐⢀⠈⠅⠀⡀⠠⠀⢀⡉⠡⠬⠍⠛⠳⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⡩⠄⠂⢁⡠⠄⠒⠈⢁⠠⠀⠐⢈⡡⠄⠐⢈⠡⠐⠂⠉⣀⠠⠄⠐⠂⡈⠭⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠅⠈⣀⠄⠂⠁⡀⠄⠐⠉⠀⡠⠔⠊⠁⣀⠔⠊⠀⠀⡠⠒⠈⠀⡠⠄⠂⠁⢀⠠⠐⢂⠩⠍⠩⢿⣆
⠀⠀⠀⠀⠀⠀⠀⡿⠁⡠⠊⠀⡠⠔⠈⠀⠀⡠⠔⠉⠀⢀⠄⠊⠀⠀⢀⠔⠉⠀⡀⠔⠉⠀⠀⡠⠒⢁⠔⠊⠀⢀⠠⠀⠠⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣇⠌⠀⡠⠊⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⡠⠂⠁⠀⡠⠊⠀⠀⠀⡠⠊⢀⠔⠁⠀⢀⠔⠁⡠⠒⢐⢺⡇
⠀⠀⠀⠀⠀⠀⠈⣯⠀⡐⠁⠀⠀⡠⠊⠀⠀⠀⠔⠁⠀⠀⢀⠆⠀⠀⢀⠌⠀⠀⠀⡠⠊⠀⠠⠃⠀⠀⠠⠃⠀⠌⠀⠄⠀⡠⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣤⠀⠀⠀⡐⠀⠀⠀⢀⠊⠀⠀⠀⡔⠁⠀⠀⠠⠂⠀⠀⠀⠔⠀⠀⡰⠁⠀⠀⢠⠁⠀⠰⠀⢠⠀⢀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡀⢠⠁⠀⠀⠠⠃⠀⠀⢀⠎⠀⠀⠀⢀⠁⠀⠀⠀⠎⠀⠀⢀⠁⠀⠀⠀⠃⠀⠀⡆⠀⠈⠀⢸⠀⠰⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡞⠙⠲⣄⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠆⠀⠀⠀⡌⠀⠀⠀⠆⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⢄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠈⠙⠢⣦⡀⡀⠠⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⠀⠀⢂⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠢⡀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣡⣀⣀⡀⢃⠀⠀⠀⠘⡄⠀⣀⣀⣱⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢛⣛⣛⡿⠿⣛⣿⠿⣟⣩⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣽⣷⣒⣶⡦⢤⠤⢤⠤⢤⣤⣤⣤⣶⣶⣒⣒⣿⠭⠷⠖⣛⣫⣥⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠯⢭⣉⣫⣉⣉⣙⣍⣉⣩⣍⣤⣤⠴⠷⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣘⣷⣤⣧⣾⡻⠋⠉⠙⠛⠲⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣣⠅⠼⠘⠞⠒⠝⠸⠞⢀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣬⣭⣻⣿⣿⠵⠾⠿⠿⠒⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⢾⡿⢛⡿⣯⣛⠟⠻⣶⣤⡈⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠞⣵⣿⡆⣇⠙⣦⡀⠈⠙⠆⠙⠅⠀⠀⠀⠀⣠⣼⣷⡛⣚⠷⠦⠀⢀⣳⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⡄⣤⢻⣿⡄⠹⢶⣽⣿⣄⠀⠀⠀⠐⡀⠀⠐⣣⢞⢿⣷⣬⠈⢳⢤⣴⠞⣻⣿⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢡⠻⠘⣿⡇⠘⠀⢹⡷⠙⠐⠆⠀⠀⠀⠀⣸⠧⠈⠈⣿⣟⢷⡀⢸⡏⢺⡏⢌⠓⣆⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⢠⡀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠸⣿⡁⠀⠀⠀⠁⠂⠰⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⣄⡀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠠⡀⠀⠈⠙⢦⣀⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠤⠬⠯⠿⠿⠤⠴⠖⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣆⣤⡀⠀⠀⠹⣿⡄⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢈⣉⡀⣠⣤⠴⠚⠋⠀⠀⢠⢴⠖⠈⠀⠀⠤⠐⠂⠙⢿⣯⢦⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⡤⠶⠶⠶⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠈⠐⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣯⣷⡀⠀⠈⠳
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠤⢤⠤⣤⡤⠂⢀⡤⠖⠲⠿⠟⠛⠋⢀⡾⠀⠀⠀⠀⠀⢀⣤⠖⠒⠈⠁⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⢞⣋⣩⣥⣤⡤⣶⢶⡶⠶⢶⣦⣤⣄⣀⣀⣀⣠⣤⡤⡶⠚⠋⠀⠀⣀⣀⠤⠚⢉⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠠⠤⠤⠤⠤⠴⠶⠖⠒⠒⠂⠉⠉⠉⠉⠀⣀⣀⡤⠨⠀⠀⠴⠒⠊⠁⢀⡀⠄⠚⠁⠈⠀⠀⢀⣜⠛⣋⣲⣆⣤⡤⠟⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢉⣉⠥⠀⠀⠀⠀⣀⠠⠄⠀⠲⠉⠀⠀⠀⠀⠀⣠⡖⣥⣦⡾⢸⡞⠈⢙⡓⠢⠄⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠚⠉⠀⣠⠴⠒⠋⠉⠀⠐⠂⠀⠠⠂⠀⢀⠤⠐⠛⠱⠋⠽⠇⠀⠙⠋⠙⠛⠑⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠙⡆⠀⢀⡀⠀⢸⢸⠀⠀⢠⠃⢀⡏⠀⠊⠀⠀⠀⠀⠁⠀⠀⠊⠀⠀⡇⠀⠘⡆⠀⠀⣇⠀⢀⡀⠀⠀⡔⠁
⠀⢀⠇⠀⠀⠀⠀⢀⣾⠀⠀⢸⠀⢸⣠⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡀⠀⡽⠀⢰⠁⠀⠀⣏⠑⡄⠀⠀⠀⢧
⠊⠁⠰⠀⠀⠈⢂⣇⡎⠀⠀⢸⠁⠀⢯⢄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⢠⠇⢀⡞⠀⠀⠀⠸⡴⠃⠀⠀⣀⠀⠉
⠀⢠⡀⠀⢀⠖⣫⠎⠀⠀⠀⠀⠳⡀⠈⠣⣕⡦⠤⠀⠀⢀⣀⣀⣀⡴⠃⢰⡜⠀⠀⠀⠀⠀⢇⠱⡀
⠀⠀⣀⡠⠞⠊⠁⠀⠀⠀⠉⠀⠀⠈⠓⠤⣀⣉⡉⢉⠉⠉⠉⠀⢀⣠⠜⠋⠀⠀⠀⠰⠀⠀⠀⠑⠬⣒⠄⠀⢤
⠉⠉⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠤⠤⣄⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡤⠔⢒⣒⣲⢤⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⣠⠤⠤
⠦⠤⠥⣄⡙⠲⣄⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠉⠀⠀⠀⠉⠉⠙⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⡠⠚⢁⡤⢔⣒
⠀⠀⠐⠂⠈⢆⠘⠳⡀⠀⠀⠀⡜⠁⠀⠀⠃⠀⠀⠘⠁⠀⠀⠈⠀⠀⠀⢳⡹⡄⠀⠀⠀⢀⠾⢁⡔⠁⠊⠁
⡄⠀⠀⡀⠀⢸⡀⠀⢱⠀⠀⠰⡅⠀⠀⠀⠀⠀⡴⠊⠉⠙⢢⡀⠀⠀⠀⠀⢧⢳⠀⠀⠀⡎⠀⡼⠀⡀
⠀⠀⠀⠁⠀⠀⡇⠀⢸⠀⠀⠀⡟⢦⡉⠁⠀⠸⡅⠀⠀⠀⢀⠇⠀⠉⠀⠀⢈⡞⠀⠀⢸⠀⢰⠃⠀⠁
⠀⠀⠀⠐⠄⠀⡇⠀⣸⠀⠀⠀⢧⣠⠃⠀⠀⡀⠈⠲⠤⠖⠋⡄⠀⠀⠰⠀⣏⡇⠀⠀⣿⡀⠸⡰⠀⠀⠀⠁
⠀⠃⠀⠀⠀⡼⠀⢠⠃⠀⠀⠀⠸⡇⢆⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⢀⡴⢊⠞⠀⠀⠀⠸⡀⠀⢳⡢⣀
⠤⠤⠤⠔⠊⢠⡸⠃⠀⠀⣀⠀⠀⠙⠮⣓⢤⡀⢀⣀⠀⠀⠈⠀⣀⡾⠖⠁⠀⠀⠀⠀⠀⠙⢦⡀⠙⠪⢭⣓⣀
⣀⣀⡤⠤⠒⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠒⠲⠬⠶⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠓⠢⠤⣆⣤
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣒⢖⡲⣤⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡤⠒⢋⣉⣀⣀⣀⡈⠋⠑⠢⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠔⢒⠩⠭
⠀⠀⢩⠁⠀⠈⡓⢄⠀⠀⠀⠀⠀⣰⠏⣠⠞⠭⠒⠚⠉⠀⠉⢉⠍⠳⡄⢹⢆⠀⠀⠈⠀⠀⡴⠋⠀⡀
⣀⠀⠀⠀⠀⠀⠘⡌⢇⠀⠀⠀⡰⠁⢰⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⠈⢣⠀⠀⠀⡜⠀⠀⠀⠁⠀⠀⢈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣠⠶⠒⠒⠲⢤⡀⠀⠀⣀⣤⣄⡀⢘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠒⠋⠁⠀⠀⠉⠛⠋⠙⠻⣿⣿⣿⣄⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⣀⡞⠙⢦⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⡴⠋⠉⠙⠳⣄⡼⠁⠀⠀⠀⠙⠓⠲⡄⠉⠙⠲⣤⠀⠀⠰⠿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠐⢦⠴⠃⠀⠀⡴⠋⠁⣀⣠⣤⣤⣤⠄⠀⠀⣿⠀⠀⠀⠈⢳⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⣠⠞⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⢧⣠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⠿⣍⣛⣉⣁⡴⠊⠀⣀⣀⣀⣀⣀⣤⠖⠋⠁⠀⡴⠚⠲⣄⠀⢀⣽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⡿⠟
⠀⢀⣨⣭⣤⣤⠴⠚⠉⠀⠀⠀⠀⠈⠙⢦⡀⠈⢧⣀⡀⣈⣩⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⡴⠒⠒⠦⣀⠀⠈⠳⢤⣀⣀
⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠙⢄⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠈⠳⠦⣤⣤⠤⣴
⠀⢀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⠟⠛⠛⠶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣷⣶⣤⣤⣶⣿⣿
⠀⢸⣷⣶⣶⣶⠾⠟⣋⣡⣴⣶⣶⣿⣷⣶⣶⣤⣄⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⠿⠛⢉⣡⣤⣤⣤⣤⣤⣌⣉⠙
⠀⠀⠉⣉⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⢯⣭⣭⣤⣬⣥⣤⣤⣄⡉⠛⠻⠿⠿⠿⠟⠛⠉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠘⠟⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡿⠿⠿⠿⠿⢿⣿⠷⠶⠛⣣⣴⣿⣿⣿⣿⣿⣿⣦⠤⠤⠶⠿⠿⠟
⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠙⠷⣶⣶⣶⣶⣶⣶⠶⠾⠿⠿⠿⠿⣿⠿⠛⣉⣤⣤⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⣷⣦⣄⠀⠰⣶⣶⣶⣶⣶⣶⣶⠶⠟⣁⣤⣶⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢳⣴⠶⠶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣭⣭⣭⣭⣤⣶⣿⣿⣿⣿⣿⣿⠟⢛⣉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⣤⣤⣀⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠳⠦⠄⠉⠛⠻⠿⠿⢿⣿⣿⠿⠿⠟⢛⣉⣤⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣾⣿⣷⣦⣀⠛⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠥⢒⡄⠀⠀⠁⠀⠠⣤⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠙⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⣀⣤⡴⠋⠁⠀⠀⡀⠀⠈⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠲⠀⠀⠀⡤⠔⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠀⠀⠘⠠⣄⡸⠁⠀⠁⠀⠀⠀⢀⡠⠊⠑⠦⡄⠀⠀⠀⠐⠂⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠈⠆⠀⣿⠁⠀⠀⠀⠀⣀⠘⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠦⢄⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⢠⡤⠃⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⠀⠀⠀⠀⠀⡢⠈⠀⢆⣀⡔⠉⠓⠀⡄⠀⢀⠤⠤⠔⠀⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⡀⠉⠀⠀⢀⡀⣈⠗⠈⠄⣀⣀⡀⠀⠀⠙⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠘⠂⠀⠀⠀⠁⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠔⠈⠁⠢⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡐⠂⠒⠓⠀⠬⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠒⠵⠤⠄⠀⣀⡐⠁⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠒⢁⠶⢀⢀⡠⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄⠂⠀⠐⠐⠀⢦⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⢅⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠊⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠋⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠁⠀⠀⡄⠂⠁
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⡠⠐⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡔⠀⢷⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡘⠀⠀⠈⠕⠄⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⠂⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌
⠰⠁⠀⠀⠀⠈⢆⠂⡀⠀⡇⠀⠰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡰⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠜⠀⢀⠌
⡀⠀⡀⠀⠀⢔⢦⠓⠁⠀⢁⠀⠀⠂⢀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠊⠤⡤⠀⠀⠀⠀⡃⠀⠀⠀⠀⡠⠂⠀⠠⠂
⠗⠈⠱⠀⠀⠀⠢⡑⢄⠀⠀⠄⠀⢈⡎⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⡠⢀⠔⠁⠀⠀⠉⠐⠂⠀⠀⡠⠊⠀⢀⠔⠁
⠀⠀⠀⠱⡀⠀⠀⠈⠐⠬⠀⠈⠗⠋⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⠀⠥⠒⠁⠀⠀⠀⠌⠀⠀⢀⠠⠊⠀⢀⠀⠁
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠠⠄⠊⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⠤⠤⠓⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠰⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠄⡷⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢼⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⢸⠁⠀⢀⣀⣠⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣠⡤⠴⡟⠛⠉⠉⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⠉⠁⠀⠀⢰⠇⠀⠀⠀⠀⡁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡾⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣤⠔⠛⢲⠏⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡠⠤⠔⢺⠉⠉⣀⣡⣥⡛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠁⠒⠉⠹⡀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣚⣨⣤⣾⣿⣿⡿⠻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠈⣛⢛⠛⢛⣻⣭⢛⣻⣷⠆⣟⣿⡍⢻⣿⣿⡟⠳⢶⣶⣷⣶⣋⣀
⠀⠀⠀⠈⠉⠀⠀⣄⣉⣉⣼⠯⣬⣿⣿⣞⣛⣯⣴⣾⣿⣿⠛⢋⣭⣶⠉⠨⣽⣋⣉⠛⠿⡿⠷⠾⢿⣿⡏⠁⠤
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠴⠶⠀⠽⠯⠍⠀⠐⠊⣉⣉⣁⡒⠁⠴⣟⡏⠀⠘⢶⣼⣷⠤⠒⠲⣿⣷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⠀⡏⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠁⣀⣀⣀⡀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠊⠀⠀⠀⠈⢢⠀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠀⠀⣀⡀⠀⡸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠉⠑⠤⠤⡑⠤⠤⠤⠖⠁⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⢀⠤⠠⢀⠔⠚⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⠢⠖⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠲⢤⠞⠁⣀⠴⠒⠒⠒⠲⢀⡴⠚⠉⠀⠈⠉⠓⢄⠱⠤⠠⠤⣄⠀⠀⡀⠠⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠁⠉
⠀⠀⠀⢀⡴⠒⠒⠀⠀⢀⡤⣖⠋⠩⡍⠉⠉⠓⠲⣤⡀⢀⠔⠋⠁⠀⠀⠈⠙⠦⣄
⠀⠀⢠⠏⠀⠂⠀⠀⡰⠋⠀⠃⠘⠐⣇⠀⠀⠀⣍⠁⠛⣎⠀⠀⢀⠄⠚⢆⡀⠀⠘⣦
⠀⠀⢸⠀⠀⠀⠀⠰⠁⠀⠀⠐⠐⠉⠁⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈⠢⣉⠔⠁⢀⠀⢸
⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⣀⠀⡀⠀⠸⡄⡄⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⡼
⠀⠀⠀⠙⢦⣄⡀⠸⡄⠀⡆⢂⡑⠀⠀⠣⠂⠈⠁⠀⠀⡼⠀⢤⣀⣀⣘⣑⣠⡶⠚⠁
⠀⠀⠀⠀⠀⠀⣄⠀⡙⢦⡙⠃⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⢰⠀⢈⡭⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠃⡴⠈⣝⠒⠒⠒⠒⠂⡀⠀⠀⠀⠀⢱⠈⢠⡎
⠀⠀⠀⠀⠀⠀⢀⡇⢰⡇⠀⠈⢦⠀⡏⢠⠞⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⡸⠀⢸⠇⠀⠀⢸⠀⢰⠋⠀⠀⠀⠀⠀⠀⢰⠃⢸
⠀⠀⠀⠀⡤⠖⠒⠒⠶⢄⠀⠀⢸⠀⢸⢀⣄⣀⡀⢀⡤⠤⡼⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠀⢸⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠃⠀⠘

⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⡀⠀⠀⠀⢀⡄⠀⠀⣠⠀⠀⠀⢀⡤⠀⣀⡀⠀⠀⡄⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡗⠀⠿⠀⡚⠀⠀⠸⣿⣿⡆⢀⣴⣿⠁⠀⣽⣿⠦⠀⠀⢀⣁⣀⣈⣀⡀⠀⠀⠀⠸⠿⠿⠿⠻⠇⠀⠀⣶⣿⣿⣿⣿⣷⣄
⠀⠀⠩⠀⠀⠜⠁⠀⠀⠀⡈⠁⠀⠀⠈⠛⡀⠀⠀⠈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⣀⠀⠙⠛⠻⠟⠛⠏⠁⠀⠀⠀⠀⠀⣠⡀⣀⣠
⠀⠀⡞⡐⠋⠀⠰⠾⠿⣿⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣀⣀⡀⠀⠀⢀⠀⣠⠄⠆⠀⠀⣧⢸⡏⣿
⠀⢐⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡀⣠⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⡟⠿⠿⠟⠛⠛⠛⠿⣾⡷⠖⠋⠀⠀⣀⢸⣸⢸⠔⠀⠀⠀⠉⠈⠁⠉
⠀⠘⠶⣂⠀⠀⠠⣸⢠⠀⠀⠈⠀⠌⡀⡀⠠⠛⠿⠷⠀⠀⠘⠛⠛⠛⠋⠉⠉⠁⠈⠀⠀⣀⣀⠀⠀⠀⢯⣇⠀⠀⠀⠀⠻⣾⠚⠁⠀⠀⠀⠀⣀⢀⢀⢀⡀
⠀⠀⣀⣤⣄⠀⢸⣿⡯⠂⠀⠀⢰⣿⠖⠀⠀⠀⠀⠀⢀⠀⡀⠀⡴⠃⠀⠀⣤⠀⠀⠀⠸⠿⣿⠇⠀⠀⠈⣃⣠⡄⠀⠀⠀⢈⠀⠀⡄⠀⠀⠈⣿⢈⡏⢸⡀
⠀⠀⣿⣿⢿⡦⠀⢙⠋⠀⠀⠀⠈⠉⠀⣤⠀⠀⠀⢱⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠄⠀⠀⠀⠀⣠⣶⡿⠟⠻⡇⠀⠀⠀⠀⠀⡰⣆⡀⠀⠈⠋⠈⠈⠈⠁
⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠛⠃⠀⢀⠀⣿⡇⠀⠀⠘⠈⠑⡄⡠⠀⢄⡀⣀⠙⠉⠉⠀⣰⠀⠀⠀⠛⠿⣿⣦⣤⡇⠈⠀⠀⠀⢐⣿⣿⠄⠀⠀⣀⠀⡀⢀
⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣦⠀⠀⣿⡆⢿⣷⠀⠰⣀⣀⠠⠁⠓⠘⠚⠐⠁⠀⠀⠐⠊⠘⠀⠐⠗⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠛⡟⠀⠀⠀⣇⠸⣿⢻⡀
⠀⠀⢸⡇⠀⣤⡀⠀⠀⠀⢿⣷⡀⣿⣧⢸⣿⠀⠀⠀⠀⠀⠀⢀⠅⣘⠀⠀⠈⠀⠅⡅⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠓⠈⠃⠛⠁
⠀⠋⠈⠛⠶⠖⣣⣶⡆⠀⠸⣿⣧⢹⣿⣺⡿⠀⠠⣶⣶⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠘⠛⢻⠻⢿⠀⠀⠈⠒⠀⠀⠀⠀⣧⡀
⠀⠀⢻⣷⢶⣤⣟⡾⠀⠀⠀⠙⢿⣿⣿⡿⠁⠀⠀⠉⠉⠀⠀⠀⡂⢠⡆⡆⡦⠆⠀⠀⠀⣠⠀⠉⢀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠈⣇⠀⠀⠀⣿⣶⣴⡾⡄
⠀⠀⠀⠉⠛⢿⣿⠁⠀⠀⡤⠀⠀⠉⣡⣶⣾⣿⡿⡆⠀⠀⠀⠀⠁⠈⠁⠁⠁⠀⠀⠀⠐⠉⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣴⢿⠀⠀⠀⠛⠘⠻⠳⠃
⠀⠀⠀⠀⠀⣿⣿⣷⣄⡀⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⣄⡀⠀⠋⠀⢀⡀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠙⣾⡇
⠀⠀⠢⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⠀⠸⣿⣿⣿⡇⠄⠘⢈⠐⠠⠁⠦⡀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣴⣦⡀⣿⠁⠀⠀⢰⢰⣆⣾⡀
⠀⠀⠋⠀⠀⠀⢿⣟⢿⣿⡿⢛⡉⢹⠿⠋⠁⠀⢀⠂⠀⠀⠈⢉⣿⣿⣦⡐⠀⠀⠐⠀⠈⡀⠀⠀⠀⠀⣿⢫⡟⣿⢿⣿⢿⣿⠙⣿⠀⠀⡀⠀⢾⠸⠋⠿
⠀⠀⠀⢀⣀⣀⠀⠓⢄⡜⠠⡗⠁⠁⠀⠀⢀⡔⠁⢰⣠⠀⠀⢸⡟⢻⣿⡏⠀⠀⢧⣤⢴⣶⡄⠀⠶⠴⠟⣸⡇⣿⢸⡏⢸⡟⠀⠻⢷⡶⠃
⠀⠀⠀⠈⢿⣿⡷⠀⠀⠁⠀⠐⠒⠒⠀⠘⠛⠀⠀⠀⠛⠀⠀⠈⠀⠈⢿⡇⠀⠀⠘⠋⠀⠙⠟⠀⠀⠐⠶⣛⣰⡟⠸⣧⡘⠷⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠈⡄⠀⠀⠠⠀⡠⠆⢀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠀⠀⠀⠈⠊⠀⠘⠁⠐⠀⠀⠀⢈⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡖⠠⠤⠀⠠⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠢⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡀⠘⠂⣾⣿⣿⣿⣿⣿⣶⠀⠂⢂⣤⣤⣤⣀⡒⠀⠀⢁⠂⠄⡀⠀⠘⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡠⠲⣹⣿⣿⣿⣿⣿⡿⣠⡀⣾⣿⣿⣿⣿⣿⣿⣶⢀⡟⠀⠌⠂⡀⠀⠀⠀⡠⢁
⠀⠀⠀⠀⠀⠀⠒⡂⠀⠂⠀⠠⠊⠀⠀⠙⠿⣿⣿⡟⠉⠀⠁⠁⠻⣿⣿⣿⣿⣿⣿⢋⠞⠙⠢⢄⡀⠈⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠠⠈⠀⠀⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠮⠭⠿⠭⠖⠁⠀⠀⠀⠀⠉⠲⢄⣀⣤⠁⠀⣀
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠁⠋
⠀⠀⠠⢆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠐⢄⠀⡀
⠀⠀⠄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⢂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⢠⠊⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠠⠄
⠀⠀⠠⠀⠁⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠑⠀⢀⠃⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢀⠀⢨⠀⠀⠠⠌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢠⠀⠀⠀⢀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂⢀⠠⠇⠀⠠⠒⡀⠀⠀⠜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠈⠐⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠛⠒⠪⢥⣂⢄⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⠀⣿⠿⠶⢮⣑⠮⣒⢄⡀⠀⠀⠀⠀⠀⢀⣤⠶⠒⣒⣒⡒⠤⢄⣀
⢉⣉⣉⣉⡓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⢸⡆⢿⡀⣴⣶⣬⣙⠮⣓⢭⡲⠤⣤⣤⡴⠟⢁⣴⡿⠋⢉⣉⣉⣓⠲⢭⣓⡲⠤⣤⣀⣀⣀⣀⣀
⠛⠋⠉⠉⠙⠛⢦⣑⢄⠀⠀⠀⠀⠀⣼⠃⣠⣾⠇⢸⡇⢹⣿⠟⠛⠷⣮⡓⢬⣓⠶⢤⣤⣶⠿⠟⠀⣰⡿⠋⣩⣭⣙⡓⠦⣍⡓⠶⢤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠷⢦⣌⠳⣕⢤⡀⠀⣰⠇⣸⠏⢁⣠⣾⡇⢸⣿⠀⢠⣶⣤⣙⠳⣬⣛⠶⣤⣤⣤⣤⣾⡿⠃⣸⣿⠛⠛⠛⠷⣦⣍⡓⠶⣤⣤⣤⣤
⣶⣶⣶⣶⣴⣶⣦⣬⡓⢮⡳⢬⣙⣉⣰⡟⢠⡿⠋⣁⣤⣾⡿⠀⣼⣿⡟⠛⠿⣦⣝⠻⢶⣤⣬⣥⣤⣤⣾⣿⠃⣠⣾⣶⣶⣤⣉⠻⢷⣦⣬⣭⣭
⣤⣤⣀⣉⣉⣉⣉⣉⡙⠳⣭⡳⢬⣉⡋⢀⣾⠃⣾⡿⠋⢉⣀⣴⣿⡟⢀⣴⣶⣦⣙⠻⢶⣤⣍⣉⣉⣉⣉⣀⣴⣿⠟⠋⠉⠛⠿⢷⣦⣤⣉⣉⣉
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⣭⡓⢮⣝⣛⣃⣼⡿⠀⣾⣿⠿⠛⠋⣠⣾⣿⡿⠿⠿⢿⣦⣍⣙⣛⣛⣛⠛⠛⠛⢉⣠⣶⣿⣷⣶⣤⣌⣙⠛⠛⠛
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣦⣭⡓⢮⣝⣛⠛⢁⣼⡿⢁⣴⣾⣿⠿⠟⠋⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠛⠛⠻⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⣙⠳⢮⣭⣛⡛⠛⣁⣾⡟⠉⣀⣤⣤⣴⣶⣾⣿⣿⣿⣷⣦⣤⣴⣶⣶⣶⣶⣤⣤⣤⣶⣶⣶⣶⣦⣤⣤⣤⣤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠶⣦⣍⣙⠛⠛⢋⣠⣾⠟⠛⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣭⡛⢶⣄⣠⠾⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢿⣿⣿⠶⠋⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⡾⠃⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⢷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⡿⠛⠋⠀⣠⣏⣀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣱⣾⣯⣭⣭⣤⣴⠟⠉⠀⣠⣤⣶⣿⣯⣭⣭⣭⣭⣛⣶⣿⣿⣌⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠿⢿⣿⣿⡿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⠁⢠⡞⢹⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠰⡇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣿⣿⣿⣿⣿⡷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠙⢲⡄⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣇⠀⢷⡀⠀⠀⠀⠀⢀⣤⠞⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠈⢓⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠸⡆⠀⣷⠀⣀⣤⣾⡛⢁⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⡧⠀⢸⠀⠈⠉⢉⣽⣿⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⡷⠀⢸⠂⢀⣴⣾⣿⠟⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⢦⣀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⡇⠀⠀⠀⣰⠃⠀⣼⠖⣻⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣌⠳⢤⣠⠞⠋⠉⡉⠉⠙⠛⠿⠷⢤⠴⠞⠁⢀⣼⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣉⠓⠾⣏⣻⣿⣷⣶⣤⣤⣠⣤⣤⣶⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⠛⠁⣠⡼⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠦⠶⠛⠉⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠁⢈⠟
⠀⠀⠀⠀⠀⠀⢀⢀⠄⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡠⠒⠠⠖⡠⠒⠈⠉⢀⣴⠕⠉
⠀⣘⠣⡀⠀⠀⠀⡎⠀⠈⢀⣈⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠔⠈⠀⠀⠀⢀⠁⠀⠀⠀⠈⠀⠐
⠀⠁⡀⠈⠢⣤⣀⢀⡴⣲⠿⠛⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡦⠀⠀⡄⠀⠀⠀⢀⠄⠂⠀⠀⠈⠀⠀⠀⢠⠎
⠀⠐⢌⠂⠀⢀⣀⢻⡿⠁⠀⠈⣠⠁⠉⠒⡉⠂⠀⠀⠀⠀⠙⠆⠀⠛⠀⢂⠙⠀⠀⠀⡠⠠⠀⢀⠤⠂⢐⠀⣰⠋
⠀⠀⠀⠈⠐⠂⠉⢻⡗⠀⢀⡄⠧⠀⠀⠀⠈⢧⡄⠀⠀⠀⠀⠀⣀⠀⠄⠁⠀⠀⢀⠜⢡⠀⠀⣨⡾⠋⠁⡰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡄⢰⠀⠀⠀⠀⠀⠀⢬⠒⠖⠒⣉⠝⠚⠁⠠⠔⠁⠀⠀⢰⠃⠀⠀⡟⢀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⠥⠔⠂⠀⠀⠀⠀⠀⠀⡌⠀⡆⢸⠖⠩⠄⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠐⢸⡔⠀⢄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠆⠀⡰
⠀⠀⠀⢠⡾⠤⣌⢀⠀⠀⠸⣤⠸⠦⣐⣤⣀⠀⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢊⣥⡆⠀⠀⠀⣰⠁
⠀⠀⠐⠜⠀⠀⠹⠢⣉⡀⠀⠀⠁⠒⠠⢌⡩⠬⠅⠀⣤⣀⣀⣀⣤⣤⠤⡴⠖⠹⢀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢥⣀⠀⢈⠁⠠⣐⢚⡥⠾⠃⠀⡆⠠⠤⠖⠪⠀⠀⡆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠠⣉⠈⠉⠐⠁⠀⠀⠀⠀⠀⢠⠀⢀⣤⣤⠤⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀⠀⠀⠀⢀⠇⠸⡀⠀⠀⠀⢀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢄⠀⠀⡼⠀⠀⢧⠀⠀⡰⠋⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡒⠤⣀⠀⠀⠸⠀⠀⠈⠳⣠⠃⠀⠀⠘⣤⠎⠀⠀⢠⠁⠀⠀⣀⠤⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠔⠋⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⢀⠎
⠀⠘⠳⣒⠒⠒⠒⠂⠤⠵⠀⠀⣠⠞⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠮⠔⠒⠒⠒⠒⣨⠟⠁
⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⢘⣢⠀⠀⣸⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣔⡁
⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠒⠒⠤⢄
⠈⠉⠑⠒⠤⢤⣀⡀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠛⢄
⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠔⠥⠤⠤⠒⠒⠒⡲⠀⠀⠈⠢⣑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢖⠒⠒⠒⠒⠤⠬⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⠈⠑⠲⠭⠍⣉⣀⠠⠤⠖⠊⠁⢀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⡤⠒⠉⡇⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠒⢤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⡼⠔⠊⠁⠀⠀⢠⠁⠀⢀⡔⠙⡄⠀⠀⢠⠋⠢⡀⠀⠀⡆⠀⠀⠈⠑⠢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠋⠀⠀⢱⠀⠀⡎⠀⠀⠙⢆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠱⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣯⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⣿⣿⡿⠷⢦⣕⠀⣀⣿⣿⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠇⠈⡿⠀⠀⠘⠆⢰⠟⢡⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠰⡀⠀⠀⠈⠀⢸⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣤⣿⡾⠦⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠟⠉⠓⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣼⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⢀⣀⣄⣀⣻⣤⣴⣶⣿⣿⡿⣿⣷⣯⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣲⣦⣶⣿⣷⣾⣿⣾⣿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠁⠉⠲⠿⠿⠦⠬⠭⡍⢉⣉⣉⠉⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠔⠒⠀⠀⢀⣠⣤⡴⠂⠄⠀⠀⢀⣀⡠⠭⠄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡀⠁⠠⠤⠀⣀⣐⣲⣦⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣶⠶⠿⠛⠁⣠⢄⠀⠀⠀⠪⠹⠭
⠀⠀⠀⠀⣀⣀⢀⣀⣀⡠⠭⠵⠶⠶⢚⢛⡛⠛⠽⠟⠛⠋⠉⠉⠉⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⣷⠶⢦⠀⠀⠐⠄
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣖⣲⡶⡺⠿⠿⠟⠛⠋⠀⢀⡞⠀⠀⠀⠀⠄⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠛⢛⣉⣁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠞⢫⡀⠀⠀⠀⢀⡠⠔⠋⡀
⠀⠀⠐⠒⢀⣉⣉⣉⣙⣉⣉⣭⠤⠤⠶⠟⠛⠛⠋⠉⠉⠈⠃⠛⣉⣀⢀⣙⣩⠽⠛⠛⠛⠛⢛⣫⠭⠉⠓⠋⠉⠒⠻⠧⠒⣒⠉⠁⠀⢀⣀⣱⠄
⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠖⠒⡋⠉⠅⠐⠊⠉⠀⠀⢉⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢸⣶⣶⢷⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠀⠀⠀⢀⣠⡤⠤⠒⢈⠄⠙⠂⠀⠀⠀⠀⠀⠀⢀⡤⢮⣱⣎⡿⢟⣓⣿⠉⢀⣉⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠒⠒⠒⠛⠛⠉⠁⠀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠐⠀⠂⠉⠰⠏⣥⠼⠃⠀⠉⠉⠁⠘⢋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣤⣤⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⢹⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠲⠖⠋⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⢶⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⡀⣀⣸⡇⢸⣇⣀⢀⣀⣴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣀⣀⣠⣭⣭⣍⣹⡇⢸⡏⣉⣭⣭⣅⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢹⡇⢸⡏⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄
⠀⠀⠀⠀⠀⢀⡎⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠸⡄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢷
⠀⠀⠀⠀⢀⡟⠀⠀⢄⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⠀⠀⢸⡆
⠀⠀⠀⠀⢸⡇⢀⡄⠘⣧⡴⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⣴⠏⠀⠀⠘⡇
⠀⠀⠀⠀⢸⣧⠞⣧⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣸⠓⢦⡇
⠀⠀⠀⠀⠈⠀⠀⠘⣧⡀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣠⡴⠟⠉⠀⠀⣰⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⠁⠀⠀⠀⣧⣤⡴⠶⠾⠛⠋⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⡀⠀⠀⠀⡞⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣥⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣷⣶⣾⣿⣿⣶⣶⣶⣶⣾⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠿⠛⠁⠀⠈⡻⢷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⣠⣀⣤⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠉⠉⠀⢀⣤⣴⡿⢿⣟⣿⣭⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠓⠈⣨⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⡿⣬⢹⢿⣿⡿⠋⢋⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⠿⠛⡟⠉⠀⠀⠑⢭⣦⠴⠟⡼⢡⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⡿⠟⠛⠛⠛⠛⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⠖⠊⣩⠉⠂⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠸⡿⣆⠀⠀⠀⡀⠈⠢⠄⠀⠀⠐⠊⠀⠀⠊⢁⡠⠜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣷⣌⠲⣄⣠⡈⠲⠤⠤⠀⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⡿⠃⠀⠀⢠⣴⣾⠿⣛⠛⠊⢉⣿⣿⠛⠳⠦⢬⣍⣙⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣭⡾⠃⠀⠀⢀⣠⣴⣾⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣀⣤⠶⠚⢿⣿⡿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠈⢷⣇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣄⣈⢹⣿⣷⡀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⣀⣀⣠⣤⣤⣬⠻⣾⣶⣿⣷⢀⣀⡀⠀⡀
⠀⠀⢠⠊⠀⢀⢠⠻⣍⣀⠄⠈⠉⠒⠛⢿⣿⣦⡀⠀⠀⠀⢿⣀⣠⣼⣿⡿⠿⢛⣻⣿⠏⠀⢈⣹⣛⣧⡤⠥⠚⠇⠀⣢⠀⣢⡄
⠀⠀⠸⣇⢸⣬⣿⣷⣌⣻⣶⣤⣐⣲⠶⠦⠽⠿⣷⣦⣤⣀⢀⣿⣿⣿⣿⣋⣭⣽⣿⣿⡶⣛⣫⣭⡭⠁⢀⣀⡔⡼⢠⢇⡖⠉
⠀⠀⠀⠙⢌⢮⣝⣷⣽⣿⣿⣷⣌⡋⠙⠲⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⢧⣾⠿⢛⣉⣁⣈⣃⣩⣴⢟⣵⡋⠉
⠀⠀⠀⠀⠀⠉⠚⢿⢿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣶⣿⣵⣿⣿⣿⣿⣟⡪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠉⠋⠙⢿⣿⣷⣶⣦⣭⣽⣿⣿⣿⣭⡿⠿⠾⠟⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠿⠀⠀⠀⠀⠀⢤
⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠶
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⣴⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⣠⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠋
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠘⠖⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀⢤
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠾
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⡠
⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠁
⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠖⡀⠀⠐⠂⠤⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠉⠁⠀⠀⠈⠁⠀⠓⠠⢤⠂⠀⠈⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡐
⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡠⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠑⢄⠔
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⡰⠟⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠻⢦⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠃⠂⠉⠁⠢⡀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⡀⠀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢡⠀⠁⠂⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠱⡀⠈⠀⠀⠀⣤⣾⣿⢫⠃⣰⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⡏⡏⢉⣷⣦⡀⠀⠀⠃⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢻⣏⠇⢠⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡿⡜⠀⣾⣿⠉⠀⠀⠀⢠⠀⢀⠠⠐⠁
⠀⠀⠀⠀⢀⠠⠄⡇⠀⠀⠀⠀⠈⠻⣄⣾⣿⣿⣿⡿⠋⠀⠀⠈⠿⣿⣿⣹⠁⣼⡿⠃⠀⠀⠀⠀⠸⠉
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢂
⠀⡔⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠰⣶⣦⡐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⣠⣶⡞⠀⠀⠀⠀⢀⠂⠀⠡
⠈⢀⠂⠈⠁⠐⠢⠀⢱⡀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⡶⠶⠶⠶⢶⣶⣾⣿⠿⠋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠑⠂⠄⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠉⠛⠡⠤⠀⠀⠠⠤⠘⠋⠁⠀⠀⠀⠀⠀⢠⠮⢀⡀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠤⠀⠀⠂⠁⠉⠐⠂⠀⠠⠤⠤⠄⠠⠀⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢
⠀⠀⠀⠀⢘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠪⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⣄⠀⠀⠀⢀⡀
⠀⠘⠷⣄⠂⠈⢽⣇⡕⠏⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠲⠄
⠀⢠⣄⠙⢻⡀⠱⢃⣴⣤⣧⣦⣶⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⣀⡀
⠀⠀⠨⢧⠈⢥⣠⢀⣌⡀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠑⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠈⣣⠜⣉⡁⠙⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡜⢲⠟⠛⠷⢧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⡆⠃⢀⢠⠇⡄⢠⠃⡄⢀⠄⠀⠀⠀⠀⠂⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡰⣌⢆⠣⢱⣠⣘⣘⡰⠡⢃⠎⡰⢋⠀⠀⣀⠀⠀⠀⢀⠀⡀⠀⢀
⠀⠀⠀⠠⠔⠀⢀⠀⠈⣇⠀⠀⠀⠐⠦⣄⡐⠦⣀⠦⡑⢌⠾⠋⠉⠀⠀⠀⠉⠓⢮⢊⠴⣋⠴⠊⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⢈⠳⠀⡿⠒⠒⠒⠠⠤⣀⣉⠓⠬⡑⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠵⢚⣁
⠀⠀⠀⠀⠁⠀⠈⠂⢧⢈⡉⠓⠶⠆⠀⠠⠬⢭⡑⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠭⠤⠒⠒⠉⠁
⠀⠀⠀⠛⠀⠀⠀⠨⠶⢦⡉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈
⠀⠀⠐⠂⠀⠈

⠀⠀⡀⡀
⣤⣤⣉⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⢤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠋⠁⠀⠀⣨⠖⠋⠉⠉⠉⠉⠙⠫⣟⡳⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⢀⣀⣁⣠⠴⠋⠁⠀⠀⠀⠀⠀⢀⡜⢉⡆⠙⢯⡉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⠔⠚⢛⠉⠉⠩⠄⠀⠀⠀⠀⡤⣄⠀⠀⠀⡞⢀⠎⠀⠀⠀⢱⡀⠀⠘⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢱⠃⠀⠀⠘⠶⠶⠖⠚⠁⠀⠀⠀⢃⠘⢦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠑⠦⣄⠀⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⡇⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⠀⠣⠴⠁⠀⠀⠀⠀⢀⣠⠴⠒⡦⠀⠈⠑⢄⡀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢂⡼⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⣠⡴⠶⠦⣄⣀⠀⠀⠀⠀⠺⡤⠔⠊⠀⠀⠀⠀⢀⣩⡓⠺⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡿⣀⡴⣋⣠⠴⢢⠀⠀⠀⠘⠥⠄⢀⣴⠾⠋⣀⣀⣤⣄⣉⡉⠛⠒⢦⡄⠀⠀⣠⣀⠀⠀⠀⢸⠁⡇⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠸⣍⠤⠒⠊⠀⠀⠀⠀⢀⡴⠛⢁⣤⠞⠋⠉⠉⠉⠉⠛⢷⣄⠀⢹⡀⠀⢧⠘⡆⠀⠀⢎⣠⠇⠀⢰⢿⡆
⠀⠀⠀⠀⠀⠀⢀⡟⢧⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡿⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⢷⡄⠈⢧⡼⠀⡀⠀⠀⠀⡴⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡗⠘⢦⣀⠀⢸⡉⢳⠀⠀⠀⣼⠃⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢷⠀⠀⠀⢸⠉⢃⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⢳⡀⢳⡀⡇⠀⠀⠸⣧⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢸⠀⠀⠀⠘⣇⢸⠀⠀⢹⠀⠃⣿
⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⠈⠈⡇⠀⠉⠁⠀⠀⢀⣿⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣠⠟⠀⠀⠀⠀⠈⠉⠀⠀⢸⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⡇⡰⢲⠀⠀⠀⠈⢷⣀⠀⠈⠻⢶⣤⣀⣀⣀⣠⣴⠟⠋⣠⡾⠋⠀⠀⠀⡴⠒⠖⠒⡄⠀⢸⡇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⡀⣸⠀⡇⢰⠀⠀⠀⠀⠀⠉⠛⠶⠤⣤⣈⠉⠉⠉⠉⣠⠾⠛⠉⠀⠀⠀⠀⠀⠙⠒⠚⠉⠁⠀⡼⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢀⠇⠀⠳⠜⠀⠀⠀⠀⠀⠀⢠⠠⣄⠀⠈⠙⠲⠖⠛⡡⠒⠒⠛⣢⠀⠀⠀⡴⢦⣀⠀⠀⠀⠀⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⣀⣤⣤⣤⡀⠈⢦⡈⢣⡀⠀⠀⠀⠀⠙⠚⠋⠉⠁⠀⠀⠀⠑⢤⣈⢳⠄⣀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⢄⡀⠘⠧⠤⠤⠴⠃⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⠀⠀⢀⣤⠤⠬⠟⢋⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⡓⠤⡤⠤⠤⠤⢤⣄⡀⠀⡠⠔⠚⣉⡇⠀⠀⢸⠃⣼⠀⣰⡋⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠈⠳⣗⠒⠋⠁⠀⠀⠀⠘⠓⠃⣰⠋⢀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣤⣄⣀⠈⠓⠦⠤⣄⣀⣀⣠⣴⣋⣥⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠒⠛⠛⠋⠉⠈⠉



⣿⠿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣻⣿⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢤
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠈⣒⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢀⡀⠉⠑⠂⠁⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⡙⠄⠉⣠⠀⢀⠀⠀⠀⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠀⠀⢫⠀⣛⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⡿⢲⡄⠀⠁⠠⣦⣘⠈⢣⠀⠀⢀⠡⠄⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠈⠀⠀⠀⠘⠀⠈⠀⠀⠙⠛⠉⠛⡃⠀⠈⠁⠀⠀⠀⠀⠁⠀⢀⡴⠠⠄
⠀⠀⠀⠀⠀⠈⠛⠀⢀⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⢼⢀⡄⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠀⠀⠀⠀⠚⠀⠀⠀⠀⠠⠓⢆⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⡆⣨⠒⠀⠒⠃⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡘⠁⠉⠀⠒⡈⠄⠀⠸⡑⠂⠀⠀⠀⠰⠀⠀⠀⢀⠈⠄⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⡀⠀⠈⠀⠸⠀⠀⠀⠀⠖⠁⢀⠐⠂⠄⠀⡀⠀⠁⢀⠀⠂⠀⠀⡀⠀⢀⡀⠄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡒⢀⡀⠀⠀⠀⠀⠚⠿⢏⡀⢾⡿⠆⡀⠀⠀⠐⢀⠙⠁⡀⢤⠀⠐⠀⠈⠀⢀⠤
⠀⠀⠁⠀⠀⠀⠀⣠⡀⠀⠈⠄⢰⠊⠉⢦⠀⠀⢀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠀⠀⣾⠳⠀⠀⠀⠋⠀⠀⠀⣤⠀⠀⠀⠘⠃⡀⠺⢄⠀⠀⠈⠀⠄⠀⠐⠀⠀⠀⠀⠂⣶⠠⡀
⠀⠀⠀⠀⠀⠄⠈⠀⠀⠉⠀⠉⠀⠀⠀⣤⠃⠀⠀⠀⠀⢐⣹⡃⠀⠀⠀⠉⠀⡴⢚⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠈⠀⠀⢸⣧⡇⠀⠀⣠⠀⠰⠘⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠄⠀⠀⠀⠀⡠⠦⠤⠤⠎
⠀⠀⠀⠀⠀⠀⠀⢸⠾⡇⣀⢠⠃⠀⠀⣄⠳⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⢸⡇⠐⢲⠤
⠀⠀⠀⠀⠀⣦⣀⠸⣟⡴⢋⠎⠠⡄⠀⢙⡷⠉⠀⠁⠀⠀⠀⠀⡀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⣜⠁⠒⠋⠀⠡
⠀⠀⠀⠀⠀⠁⠈⡖⠀⠀⠂⠀⠀⠀⡀⠇⠀⠀⠀⢠⠄⡀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠀⢐⠈
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⣈⠃⡂⠛⠀⠀⠀⠀⠸⠀⠫⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⢠⡏⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠘⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⣼⠉⠉
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠜⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡉
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠂⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠃⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⠉⠙⢻⣿⣿⣿⡏⠙⠟⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠿⠽⠿⠛⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣸⠟⣿⡿⠋⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⠉⠉⢀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣧⣬⣜⣓⠤⡦⠶⠶⠤⣄⣚⣶⠈⠹⠹
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡤⠈⠙⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿