Taco Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⣛⣿⣍⣉⣿⠛⢛⣻⣿⣭⣿⣷⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣡⣶⡿⠛⣿⠟⢉⣵⠾⠛⠉⠉⠁⠀⠀⠉⠉⠛⠻⣧⣄
⠀⠀⠀⠀⠀⠀⢠⡾⠋⣤⣾⠿⣶⣴⠶⢟⣴⠟⠁⠀⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢠⡿⢁⣾⠟⠀⢀⣸⡏⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠠⡄⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣾⠃⣰⡿⠶⢾⡟⠉⣰⡟⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢰⡟⢸⣏⠀⢠⣼⠇⣴⠟⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠰⠂⠀⠀⢹⡇
⠀⠀⠀⠀⢸⡇⣿⡅⠀⢻⡇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢸⣿⡏⠁⣴⠟⣽⠏⠀⠀⠘⠃⠀⠀⠐⠇⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⣇⣀⣿⣾⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠾⠏
⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢰⣿⣿⠂⠀⠀⢀⡄⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡧⠛⢞⢩⢿⣿⣿⣏⣓⣶⡶⠓⣇⣀⣈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣤⣾⠛⣭⣀⠇⢀⣠⡁⢸⣿⣿⣓⣁⣾⣄⣠⣋⡉⣓⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠿⣿⣷⣴⠒⣿⣷⢲⣷⡾⠟⢛⣛⡭⠁⠄⠖⢀⠐⠛⠻⣿⣿⡿⣧⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⡄⢸⢿⣿⣷⡽⠟⠉⠙⠃⠄⠘⠚⠀⠀⠂⠐⠀⠀⠻⠀⢉⠛⢿⠺⣝⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡛⠓⠒⠷⣏⣧⣿⡏⠒⠀⠀⠀⠁⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠐⠀⡈⠀⠂⠈⡳⣽⣄
⠀⠀⠀⠀⢰⠿⢆⣾⣳⡤⢤⣦⠞⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣸⣶⣤⠀⢘⡆
⠀⠀⠀⠀⠈⠓⡾⠋⢽⣶⣶⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⠀⠀⠐⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⣠⣾⣥⣤⣬⣿⣿⡄⠀⠈⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢀⣼⠵⠚⠉⠁
⠀⠀⣠⣾⣿⣿⠿⠟⣿⣿⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣀⣤⠶⠚⠉
⠀⠐⣿⣿⣟⠁⢾⣿⣿⠉⡤⢀⠀⠀⠀⠀⠁⠀⠄⠀⣀⡤⠖⣻⡿⠖⠋⠁
⠀⢠⣴⢧⢨⣟⡥⢾⣿⡄⠀⠄⠀⠀⢀⣯⣯⠀⢒⣫⡵⠞⠋⠁
⠀⠘⠮⠥⠜⢣⢠⣿⢹⠃⠀⠀⠀⠠⢀⣨⠴⠚⠉
⠀⠀⠀⠀⢀⣧⣿⣿⣿⣖⣶⡤⠷⠛⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠤⣀⠀⢠⣄⣰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠳⣀⢂⣝⡅⠀⠠⢚⣩⣥⠶⣶⠶⠾⠶⠶⣦⠌⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⣧⠂⢉⢃⠮⢎⡤⣲⠜⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⠁⠲⠛⠒⠠⣠⢆⣲⢞⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡈⠄⠒⠒⡆⢤⣨⢞⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡐⠀⡠⠔⠠⠀⢔⠔⡱⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⢰⠒⠰⠀⠀⣇⡤⠂⢜⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠏⡀⠃⡴⠋⡇⢀⢪⠞⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⡠⢤⣄⠂⠀⠄⣀⣀⣠⣤⠤⠤⠖⠚⠁
⠀⠀⠀⠀⠀⡸⠅⠠⠎⠀⠥⡠⣣⠋⠀⠀⠀⠀⠀⢀⡠⠄⣒⠢⠍⣒⣂⡭⠥⠖⠒⠛⠉⠉
⠀⠀⠀⠀⢀⠗⠀⢄⣀⠚⡴⡵⠃⠀⠀⠀⠀⠀⠀⣀⣨⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠈⣆⠈⣀⣊⢌⠞⠁⠀⣀⣠⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠘⣝⣒⣵⡥⠴⠚⠋⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⡀⠀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠀⠀⢀
⠀⠀⠀⠲⡄⠈⢧⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⡠⢀⠀⠀⡠⢦⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡠⠋⠀⣀
⠀⠀⣄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⢄⡠⠁⠈⠳⠔⠁⠀⠣⠐⠉⠀⠸⠀⢀⡠⢦⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⢀
⠀⡀⠈⠃⠀⠀⠀⠀⢰⠆⠠⢄⣠⡀⢄⠀⠀⠀⠀⠀⡠⠄⠒⠀⠀⡂⠀⠀⠃⢁⡀⠼⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠈⠁⠀⣀⡀⠤⢤⠀⠀⠊⠁⠀⠀⠀⢂⠀⠀⢀⠎⠀⠀⢀⡀⠀⠇⢀⡴⠋⠀⠀⠀⠀⠈⢫⡇⠀⠀⡤⠠⢀⠀⠚
⡠⠄⠂⠉⠀⠀⠀⠈⡜⡀⠀⠀⠀⣇⠀⠈⠆⠀⣼⠀⠀⠀⣿⠀⡴⢀⢺⠁⠀⢠⠎⠑⢆⠀⠀⢣⣀⡾⠀⠀⠀⡹⠈
⠘⡀⠀⠀⠀⠀⢰⠂⠑⣴⡄⠀⠀⠉⠀⠀⠘⣄⠿⡀⠀⠀⠓⠀⢰⡇⢸⠀⠀⠈⠈⢂⡘⠀⠀⣸⣱⠁⠀⠀⡐⠁
⠀⠑⠮⣉⡄⠀⠈⡇⡆⠀⡇⠀⠀⢲⠳⡄⠀⠘⣇⠑⢄⡀⠀⠀⠈⡇⠘⡄⠀⠈⠒⠋⠀⠀⣠⢧⠃⠀⢀⡜
⠀⠀⣀⠠⠴⠀⠀⠸⡰⠀⠇⠀⢀⣸⠦⢗⠔⠂⢹⣄⣀⣈⣉⠉⣹⢣⡀⠈⠢⢤⣤⣤⢤⠞⣿⠵⠬⡕⢀⡽⠃
⠀⠉⠢⡀⠀⢧⢀⣀⠵⢇⠘⢉⡁⣠⣶⢾⡓⣛⠿⢉⠟⣻⣅⣛⢿⣽⣍⡳⢤⡄⠐⠀⠀⡼⠙⢤⡤⠾⢉⡀
⠀⠀⠀⡈⠓⠈⠉⠂⠐⡈⣠⣮⣵⠷⠾⠷⠶⠿⠶⢾⣮⣜⡡⡯⠹⠿⣶⢻⣶⣬⠷⣄⡀⠈⠀⠈⠀⠀⠀⢈⡳⠂
⠀⠤⣊⠀⠀⠀⠀⢀⡾⠛⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠩⢈⠙⠶⣄⣀⠻⡐⢻⠰⣇⠘⣿⢦⡀⠀⠀⢠⠖⠉
⠀⠀⠀⠈⡑⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠪⡳⣌⠺⢟⡓⢾⠦⡛⢛⣿⣦⠀⠀⠉⠢⡀
⠀⠀⢠⠎⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠳⣍⢙⣧⢴⣽⣈⣆⣻⣳⣀⠤⠒⠁
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢊⢷⡇⣤⢜⣽⠋⣃⣿⣷⢄
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⡼⢑⠶⠞⠉⢿⡎⡏⠁
⠀⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠻⣆⠀⠉⢀⣰⢇⡇
⠀⣀⠀⠀⠉⠓⠲⠦⠤⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⢳⡾⢟⣫⡾⠁⠀⠀⠀⣄
⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠤⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⡖⠒⠲⠶⠞⠛⠉⠁⠀⠀⠀⠰⣄
⠀⠉⠀⣠⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢇⠀⡠⠖⢀⠀⠀⡰⠀⡀⠀⢰⠁⠢⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⠁
⠀⠀⠘⠁⢀⡔⠀⢀⡄⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠢⠊⠀⠀⠙⢦⠃⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠸⣄⠀⠳
⠀⠀⠀⠀⠉⠀⠀⠛⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡴⠒⣒⠒⣆⣀⣴⢲⣟⣿⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣳⡯⣽⢋⣭⠭⣟⣾⡋⣥⣴⣿⣶⣮⣹⢯⢵⡚⠳⣶⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣚⠽⠖⠻⠵⠋⠠⠾⠽⠛⠧⣑⠦⣽⣟⡚⠻⢿⡇⢠⣠⢰⣶⡇⣠⢜⣴⡫⠿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣞⣽⣷⡶⠬⣟⢿⡼⡿⢚⣠⣴⣿⡇⠀⠀⡈⣽⣂⣤
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⣿⢿⣩⢤⡖⢲⡛⠀⠹⡍⠉⢭⣏⣿⢻⡚⠘⢩⢟⡿⡗⡶⠂
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣀⣀⣀⣹⣦⡙⠻⣖⡓⠚⠾⠶⠿⠮⡭⣝⢯⣱⠹⣽⣳⣆⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠛⠋⠉⢿⡶⣤⣍⡛⢿⣖⣒⡚⣅⣞⢿⡛⠃⣮⠔⢻⡽⠻⣦⡀
⠀⠀⠀⠀⡼⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢧⣷⣏⡛⠛⢷⡦⣏⠘⣎⢦⡑⢄⠪⣵⡌⢩⣭⠴⠃
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠕⠛⢿⡯⣗⣌⠢⡱⣿⣞⠙⢲⣧⣮⡛⡶⣾⢵⡆
⠀⠀⠀⢰⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠷⢻⠳⣭⣒⣿⣮⡪⣴⣷⡛⣿⡙⣟⡟⣆
⠀⠀⠀⠸⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣝⣒⣶⠀⢩⠍⣤⠣⣬⣟⡻⣷⢿⡀
⠀⠀⠀⢠⠇⡆⡆⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣹⣜⡶⢃⣜⣁⠹⢼⡼⣩⠏⣩⡛
⠀⠀⠀⢸⡄⡇⡇⡇⢸⢸⢸⠰⡄⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⢹⠘⠲⣟⢮⡛⣟⣫⡞⢧⣀⡞⡇
⠀⠀⠀⢸⠛⢇⠇⡇⣸⢸⢸⠀⡗⢇⢸⠘⡆⢰⢰⢠⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠙⠚⣧⣳⣬⣿⡠⠄⠊⢹⣸⣍⠦⣹
⠀⠀⠀⠈⢧⡀⠀⠁⠙⠈⠘⠃⢧⢸⣸⠀⡇⢸⠘⣬⡆⡇⢸⠀⡏⠘⡆⡆⢠⠀⡄⡀⢀⠀⠀⠀⠀⠀⢸⡉⠙⢯⡷⢀⣤⣎⠙⢺⢳⢺⠃
⠀⠀⠀⠀⠀⠉⠓⠲⠮⠤⢤⣀⣀⠀⠉⠃⠳⠈⠇⢧⢧⢻⠘⡆⢳⠀⢇⢹⠸⡄⡇⢳⠸⡄⡇⡄⠀⠀⠀⢿⢳⠦⠽⢤⡞⣽⣇⣨⣿⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢤⣀⡀⠀⠈⠘⠂⠳⠘⡆⢸⡸⡄⣇⢱⢸⡀⡇⢹⢹⠈⡆⢧⠘⡿⣰⣆⠈⢷⣖⠥⣌⠻⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣤⣀⠀⠀⡀⠁⠓⠸⠜⡆⡇⢹⡈⡇⣇⢻⢸⡀⢳⣈⢻⠀⢳⡙⢄⠨⣝⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣀⡀⠀⠃⠀⠃⠹⠘⡌⣆⣇⠀⢷⡀⢾⢨⣇⢸⡀⠹⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⣀⠀⠀⠀⢘⠀⠸⣷⡎⡃⢹⣾⣟⡸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠬⣄⠀⠹⣧⣿⡦⣽⡿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣉⡭⠥⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠿⠿⠿⠿⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣋⣡⣶⣷⠾⠻⣾⠿⣦⣤⣤⣌⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⣿⣋⣁⣈⣛⡋⠉⠻⣦⣤⣤⣾⠋⠈⠉⠻⢿⣦⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣶⠿⠛⠛⠉⠉⠙⠛⠻⠷⣾⣥⡀⠹⣷⣴⣶⣴⠾⠻⠿⣶⡌⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⠁⠈⠁⠀⠀⠈⢁⣀⣀⣀⣂⡀⠉⠛⢷⣦⡀⠈⢿⣤⣄⠀⠘⠿⣦⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⣀⣤⣴⠾⡟⢛⣛⠛⣛⠛⠛⠿⢶⣤⣈⠙⢷⣦⣉⠹⣷⣀⠀⠛⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢀⣣⣴⡿⢿⣭⣴⣿⣿⠛⠛⠿⢛⣷⢶⣶⣦⣈⠛⢷⣦⡈⠛⢷⣿⡛⢿⣄⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢻⣿⣥⣤⣤⣭⣥⣀⡙⢷⣶⠶⣿⡁⠀⠀⠙⢻⣷⣀⠙⢿⣦⢀⡍⠻⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⠿⠛⠉⠉⠀⠀⠈⠉⠉⠛⠷⣦⣄⡘⠿⠶⢷⣾⠟⠛⠛⢿⣆⠙⣷⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠋⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠻⣶⣤⡀⠈⠛⣷⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡘⣿⣄⡀⠉⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠉⠻⣾⣍⣻⣧⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣴⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠙⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰⠆⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠶⠂⠀⠀⠀⢀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⡶⠟⠋⠉









⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⣿⣿⣿⢿⣿⠿⢻⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣀⣀⡀⣀⣤⠤⠤⠤⠶⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠒⠉⠀⠤⠠⠤⠤⢀⠀⡀⠤⠐⠒⠒⠀⠐⠂⠷⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠁⠀⡸⠀⣀⣠⡎⣁⣀⠀⣀⡀⡠⠋⠀⣀⠤⠒⡒⠶⠶⢦⣄⠀⠙⢕⠦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡡⠔⠋⠀⠂⢛⠣⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⢤⡖⠀⠒⠾⠀⠀⠀⠀⠈⠥⣤⣀⣳⠉⠉⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡨⣠⠔⠊⢁⠞⠁⠀⡤⣖⣉⡍⠄⠠⡜⠋⠐⠂⠔⠊⠀⢀⣠⣀⠀⠄⠄⠤⠤⠤⠈⣁⣀⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡅⠂⠁⠘⠡⡡⠀⢀⠂⠀⠠⠺⣜⠁⠀⠁⠲⢞⠀⠀⢀⣠⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠐⠠⡄⠘⢣⡀
⠀⠀⠀⠀⠀⠀⢠⠋⢸⠀⠀⠀⣠⠐⣇⠀⠆⠀⠀⠛⣆⠉⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣱
⠀⠀⠀⠀⠀⢀⠃⢀⡸⢄⡀⠴⠃⠀⢛⢸⠀⠀⠀⡎⠈⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⢇
⠀⠀⠀⠀⢀⠆⠀⡙⠀⡎⠀⠀⠀⠀⠈⠾⡄⠀⠀⡀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⡜⠀⣺⠄⠒⠛⠒⠒⠀⠀⢠⣀⠇⣀⡧⠂⢀⠎⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠱
⠀⠀⠀⢰⠁⠀⠃⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢀⠔⠁⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⡎⠀⠀⡄⠀⠀⠀⠀⡠⠤⠷⠀⠤⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⢠⡔⠁⠀⠀⠀⠀⡇⠀⠀⠀⣀⠞⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢱⠀⢆⠀⠀⠀⠀⢠⠄⠀⣀⠞⠁⢀⡴⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠘⣆⠈⠳⢄⣀⣤⡩⠴⠛⠁⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡼⠁
⠀⠀⠀⠀⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠤⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠳⣄⠁⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠴⠖⠒⠒⠒⠚⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠖⠒⠒⠊⠋⠉






⣿⣿⡿⠿⣿⡿⢿⠿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠞⣉⠻⣟⠲⢶⣒⣲⣦⠄⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣤⣿⣿⣭⣭⣝⣛⣳⠮⠤⠬⢭⠷⠞⣛⠉⠉⠛⢦⡇⣸⠗⢦⡀⠀⠀⠀⢀⡀
⠀⠀⠀⢤⢤⣀⣀⣠⡿⢒⡭⢕⣚⡽⢖⣛⡭⣤⢶⡶⠖⣫⣴⠞⢉⣍⡛⣯⣡⡬⢇⡿⢋⣝⣿⣶⣶⠿⡟⣀⡀⣠⡤
⠀⠀⠀⠘⠒⣦⣬⠭⠿⠟⣛⣓⣛⡚⡓⠢⠬⣴⣉⣴⣞⡓⣻⠟⠁⠳⡙⠿⡏⢸⢹⡶⣿⠿⠟⣛⣻⣤⣭⢁⡖⠁
⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⠍⣛⠻⢅⡀⠀⠀⢧⠀⡏⡞⢸⡼⠃⡼⢋⡡⠒⠉⣼⣛⣓⣒⣒⡒⢲⠆
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⡓⢦⣼⣷⡿⠁⠛⠳⠦⠿⣟⣲⣿⣿⣿⣿⡷⠼⠬⣍⣁⣀
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢌⠻⣥⡠⠤⠄⠒⠂⢠⣿⣿⣷⣶⣶⣶⣶⣦⢤⡤⡜
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡙⢦⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢣
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢧
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡆
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿
⠀⠈⠓⠲⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡝⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠢⠻⣿⣿⣿⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⢦⣤⣄⣈⣙⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⡀⠀⠘⣧⠀⠀⠻⠀⠀⠓⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡾⠃⠀⠀⣰⠗
⠀⠀⠀⠀⠈⢻⡄⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠓⢄⠀⠀⢀⠞⠙⣆⠀⠀⢀⡠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠞⠁⠀⢀⡶⠄
⠀⠀⢠⣄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠑⠦⣄⢠⠁⠀⠀⠑⠶⠁⠀⠀⠘⠦⠐⠁⠀⠀⠸⡆⠀⢀⣠⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⡀
⠀⠀⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠂⢠⠀⠀⠀⠷⠒⠉⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠽⠓⠋⠉⠉⢆⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠑⠢⣤⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⢀⣠⠤⠖⠒⠙⢦⢀⡇⠏⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢠⠃⠀⠀⠀⢀⡤⠒⠒⠎⠀⣠⡾⠁⠀⠀⠀⡀⠀⠀⠀⠈⢻⠁⠀⠀⢠⡞⠙⠲⢤⡀⠀⢀
⢀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠘⡌⠃⠀⠀⠀⠀⢸⣇⠀⠀⠘⡆⠀⠀⡎⠀⠀⠀⢠⠇⡀⠀⡸⠀⡌⣽⠁⠀⠀⢠⠞⠉⠑⡆⠀⠀⠀⢧⢀⡴⡟⠀⠀⠀⠀⢨⠃⠉
⠘⡄⠀⠀⠀⠀⠀⠀⢀⡤⠔⠳⣸⢴⠀⠀⠀⠘⠛⠀⠀⠀⠘⡄⢘⣧⠀⠀⠀⠈⠯⣁⣀⣁⡜⠁⡎⠀⠀⠀⡏⠘⢢⠀⣸⠀⠀⠀⣸⠋⡼⠁⠀⠀⠀⡰⠃
⠀⢹⡀⣀⠤⠄⠀⠀⠈⡷⢄⡀⠜⢻⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⣼⠘⢆⠀⠀⠀⠀⠀⠀⠸⡇⠀⣥⠀⠀⠀⢇⠀⣰⡧⠃⠀⠀⢀⡟⡸⠁⠀⠀⠀⡰⠁
⠀⠀⠙⠠⢤⢸⡀⠀⠀⠸⡀⢅⠀⠸⡀⠀⠀⠀⣻⠈⢧⠀⠀⠀⠙⣄⠈⠳⣤⣀⠀⠀⠀⢀⡇⠀⠘⣆⠀⠀⠀⠉⠁⠀⠀⠀⢀⡞⣱⣃⠀⠀⢀⣜⡀
⠀⠀⠀⠀⣀⡠⢵⠀⠀⠀⢳⠘⡀⠀⡂⠀⠀⠀⣙⢣⣸⡧⠐⠂⠚⣻⡀⠀⠀⢉⠙⢙⠉⢩⢣⡀⠀⠈⠳⢄⣀⣀⣀⣀⣤⡶⢻⣽⠤⠬⣉⠗⠁⢈⠝
⠀⠐⢎⡉⠀⠀⠈⡆⠀⠀⠈⢧⢁⠀⠧⠄⠒⠊⢡⣠⣀⣻⣤⢤⣤⢟⠿⢟⣻⣿⡎⢠⢽⣿⠶⠗⠦⣤⠀⠀⠀⠀⣁⠕⠈⢠⠛⢇⠀⠀⢈⣦⠞⠁
⠀⠀⠀⠈⠲⣄⠀⢹⣤⠴⠒⠉⠀⡦⠈⢢⣴⠀⣾⢿⣋⠷⠀⢵⠖⠋⢲⡈⡠⢾⠿⠭⣦⣽⡿⠿⠚⣍⢛⠳⣬⡉⠀⠀⠀⠺⣀⠈⢙⠟⠉⠙⠒⠦⣄
⠀⠀⠀⠀⣀⠜⠁⠀⠀⠉⠐⠀⠡⢒⣲⣥⣶⡿⠿⠿⠛⠛⠛⠛⠻⠛⢺⠿⣤⣉⡀⢾⠧⠉⠾⢟⡛⢙⠷⢶⣤⠛⢶⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣈⠽⠃
⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⢀⣦⡿⠟⠉⠈⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠈⠐⠨⠛⠶⣤⠐⠂⠚⣧⠲⠞⡅⢠⡃⡀⢿⡗⢦⡀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠁⠙⠒⠢⠄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡔⠈⡻⢦⡃⢤⣦⣤⣧⣄⢹⡄⢘⣿⡲⡙⣆⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⡠⠂⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠦⡙⢧⡀⢹⣤⡈⣯⠛⢣⡂⢄⡼⢮⣷⡄⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢠⠞⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⡢⠹⣧⡀⢈⣧⡤⣮⣽⣀⣘⣂⣷⡹⣄⣠⠴⠚⠁
⠀⠀⠀⠉⠐⠒⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠑⢌⢻⣍⠏⢀⣀⠹⣋⡷⠛⡏⢳⢹⣦⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠹⣧⡨⠥⢖⢊⣃⣴⠲⡿⣇⢻⡝⠦
⠀⠀⠀⠀⠀⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⣧⡃⢨⠏⢛⡠⠀⠸⢿⢸⡇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠱⡘⣿⣄⡀⢡⡀⠄⣀⣿⢸⡇
⠀⠘⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⢌⡻⣤⣤⣰⣼⠿⢣⣾⠁
⠀⠰⠖⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠛⠛⠓⠒⠒⠲⠶⠶⠶⠶⠴⠤⢤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣈⣐⣪⣭⣴⡾⠟⠁⠀⠀⠀⠀⠀⠙⠶
⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠤⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠉⣹⠉⠉⠙⠛⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀
⠀⠈⠋⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⢧⠀⠀⢀⡴⠂⡀⠀⠀⠀⡴⢄⠀⠀⠀⠀⡌⠑⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠛
⠀⠀⠀⢴⠟⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠔⠉⠀⠀⠑⡄⢀⠞⠀⠀⠑⢄⠀⡸⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢻⣄
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣴⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢰⡄⠀⢱⡄⠀⠸⣧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣷⣾⣷⣶⣾⣷⢷⣿⣶⣿⣾⣷⣷⣾⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡷⡷⢾⡷⠾⢶⣶⠶⠿⠶⠾⢿

⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠸⣇⠀⠠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⢠⡶⠀⠀⠀⣠
⠀⠀⠀⠀⢾⣄⠀⠈⢷⡀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⢶⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠞⠁⠀⢀⡾⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠂⢄⠀⠀⠀⠎⠀⠑⢄⣀⡔⠁⠀⢳⡀⢀⠴⠊⠁⢰⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣴⠟⠁
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠢⠜⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣇⢀⡤⠚⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⡤
⠀⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢐⡗⠒⠢⢤⣀⡧⡤⢤⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠉⠉⠉⢸⠀⠀⠀⠈⠁⣀⢠⡤⠧⢤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠈⠓⠀⠀⠀⠀⢀⣀⣤⡀⠀⠁⡔⠊⠉⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠈⠳⣏⡇⠀⠀⠀⢀⢀⣀⠀⠀⠀⠚
⠀⠀⢀⡠⠴⠒⠉⠉⠀⠀⢧⢠⡄⡇⠀⠀⠀⢠⡀⠀⠀⢣⠀⠀⠀⣼⠀⠀⠀⠀⡴⠛⡉⢉⠁⢀⢼⡏⠀⠀⠀⣠⠤⢄⡀⠀⠀⠈⢇⠀⠀⣰⠏⠀⠀⠉⠲⣄⠠
⢖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢅⠁⠀⠀⠀⢸⣧⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀⠀⣇⠧⠤⠞⢀⡎⣾⠀⠀⠀⣰⢃⠀⠀⢱⠀⠀⠀⢸⣤⢞⡟⠀⠀⠀⠀⣠⠃
⠘⡄⠀⠀⠀⠀⠀⠀⢰⡃⠁⠘⢴⣰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢰⢿⡀⠀⠀⠀⠑⠒⠒⢲⡎⠀⢿⠀⠀⠀⠂⠀⠘⡆⡸⠀⠀⠀⢸⠁⡼⠀⠀⠀⠀⡰⠁
⠀⠻⡤⠖⠚⡀⠀⠀⠈⣯⠢⠄⠊⢸⠀⠀⠀⠀⣤⢶⡄⠀⠀⠈⢾⠀⠳⣄⠀⠀⠀⠀⠀⠈⡇⠀⢹⡀⠀⠀⠰⠄⠴⠟⠁⠀⠀⢀⡏⡼⠁⠀⠀⢀⡜⠁
⠀⠀⠀⠈⠓⠸⡀⠀⠀⠘⡄⢃⠀⢸⠀⠀⠀⠀⢫⠂⢻⡀⠀⠀⣈⣧⠀⠈⠓⠦⢤⣀⣀⣠⡗⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⣠⣟⠔⠣⠤⣀⡠⠾⢤⡀
⠀⢀⣀⡤⠤⠒⢣⠀⠀⠀⢳⠸⡀⠈⡄⠀⣀⣠⡤⠳⠘⣅⠉⠁⠀⣼⣤⣠⣤⡰⠀⡠⢄⣰⡁⣄⠀⠀⠈⠒⠦⠤⠤⠴⣒⠟⢹⡾⠚⠓⠲⡌⢀⣠⠊
⠀⠈⠓⢄⠀⠀⠈⡆⠀⠀⢀⣷⢠⠀⠣⠋⠁⠀⢠⣼⣤⡼⠶⠞⠻⣯⡋⠱⠞⢛⡏⠹⣛⣿⣛⣉⡉⢶⣇⣀⠀⠠⠔⠊⠁⢠⠇⠳⢄⣀⣠⣿⡋
⠀⠀⠀⠀⠑⢦⡀⠸⠖⢊⡁⢀⠌⠃⢀⡵⠺⣬⣟⣻⣬⣩⣥⣹⣃⣀⣸⣄⠔⣹⠛⢛⡿⢶⣞⣻⣭⣦⣄⠈⠒⢦⡀⠀⠀⠘⠢⠠⠤⠊⠀⠀⠈⠙⠲⣤⣀
⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⣀⣼⣭⣷⠞⠟⠛⠋⠛⠉⡉⢉⠉⠉⠉⠹⣟⠳⢦⣌⡙⠛⢒⡋⢻⡌⢈⢟⣿⠿⣍⠹⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠰⢚⣁⠀⠀⠀⠀⠀⠀⣸⡾⠛⠋⠀⠄⠀⠀⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠄⠁⠪⠙⢶⣍⠁⡈⠷⡙⢫⡵⠀⢧⡤⠘⣿⡻⣆⠀⠀⠀⠀⢠⡞⠋
⠀⠀⠀⠀⠉⠒⡂⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠎⢰⢌⠳⣄⡐⠴⣾⠷⢶⣤⣧⡀⠿⢝⢮⡳⣄⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⣠⠎⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠑⢈⠳⣆⡠⠖⢦⡰⠋⠑⣦⠠⢦⡙⣟⣦⠀⠀⠀⠀⣈⠦
⠀⠀⠀⡔⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⢈⢳⣄⣠⣣⠖⠿⢼⣤⣬⢇⣸⣎⢷⡤⠒⠉
⠀⠀⠀⠀⠀⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⡙⣧⡟⢀⡤⠜⢣⡿⠉⠳⢸⡎⣷⣄
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⡌⢿⡄⢖⢈⣅⣧⡼⠙⢟⣻⡘⡧⠓
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡌⢿⣝⠀⠊⢩⡄⠀⠀⢻⡇⣿
⠀⣀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⢄⢻⣇⠄⠐⠄⠀⣤⣿⢃⡟
⠀⠉⠀⠀⠀⠈⠛⠲⢦⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢝⠳⢤⣮⣷⠟⣡⣾⠃⠀⠀⠀⠀⢀
⠀⠚⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⢹⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣉⣺⣦⡶⠾⠛⠁⠀⠀⠀⢀⠀⠈⠛
⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡠⠔⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⠁⠀⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡀
⠀⠈⠁⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢷⠀⠀⣠⠔⠐⡄⠀⠀⢀⡴⠢⡀⠀⠀⠀⡎⠉⠢⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠁
⠀⠀⠀⠾⠋⠀⢀⡴⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠚⠁⠀⠀⠘⣄⣠⠎⠀⠀⠈⢦⡀⡸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⣧⡀
⠀⠀⠀⠀⠀⢰⡟⠁⠀⢀⣾⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡦⠀⠘⣆⠀⠈⢿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡤⠤⢄⡀⢀⡠⢎⠉⠳⣄⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠁⠈⢳⢤⡤⠃⡠⠴⡌⠭⠀⠈⠂⠀⢈⠭⣓⣂⣚⢳⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠉⠉⢆⠀⠀⢦⠃⠀⠘⡀⣀⣱⠰⡶⠧⠴⢊⡵⠮⢭⢤⣍⣿⢀⠎⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠲⠤⣀⠀⢦⡱⣀⠮⠁⠀⣊⣉⠭⢵⣿⣭⠥⠤⠽⢊⣉⣠⠤⢾⠋⠉⠑⢤⣀⣠⢷⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣇⠀⠀⢲⠤⠞⣓⡩⠭⠭⠝⣒⣦⣀⣹⡀⣁⣠⠤⠔⠚⠛⢛⣛⣛⣛⣛⣒⠲⠦⢄⡀⠀⢃⠄⢀⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠤⠤⢩⠖⣡⣶⠋⣠⡂⠤⠔⡺⠉⢉⡥⠖⠉⢁⣠⠴⠒⠚⠉⠉⠁⠀⠀⠀⠉⠉⠙⠒⠮⣕⡺⡀⠁⠈⠉⡧
⠀⠀⠀⠀⢀⡖⠉⢱⠀⠙⠲⢡⢞⣥⣶⠦⢤⣛⡏⢈⡱⠚⠁⣠⠴⣚⠥⠂⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠲⢍⠻⣦⡀⠘⢑
⠀⠀⠀⠀⠀⡇⢀⡴⣒⣤⢣⣣⠟⠋⠘⡄⠀⢜⡵⠋⢀⡴⢋⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢷⡔⠋
⠀⠀⠀⣠⠚⠉⡰⡪⠃⣟⢿⣧⠀⠀⡠⣇⡴⠋⢀⠔⢩⠞⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢷
⠀⠀⠀⢇⠀⡰⠃⠀⣸⡟⢀⡾⣖⠊⢠⠎⢀⡴⠃⠔⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡆
⠀⠀⠀⣸⠙⠁⢅⠮⠊⡠⢪⡄⠀⡴⠃⣠⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢰⠃⢠⡌⡆⠠⡪⡾⠛⠃⡜⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⢀⡏⠀⢾⡀⠀⡇⡇⠳⢄⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤
⠀⡼⠀⠖⠀⢨⠂⢄⠀⠀⡜⢀⡞⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⠁
⢠⠇⡆⠠⣀⡴⠒⢲⠁⡼⢀⡞⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠤⢒⣊⠭⠐⣂⡥⠴⠒⠉⠁
⣸⢰⠉⡀⢀⠀⠐⠊⡼⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢒⣊⠥⠖⠊⠉
⡇⠘⢀⠀⠘⢰⠄⡰⠁⣰⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀
⡇⡇⠈⠓⢚⣜⡼⠁⣰⠃⠀⠀⢀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠉⢻⡏⠉⠀⣸⣧⠀⠀⣴⠟⠋⠙⠁⣴⠟⠉⠛⢷⡄⢼⡏⠉⠋
⢻⡿⣌⣩⠥⠊⢀⣜⣡⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⣯⣼⣇⠀⣿⡀⠀⠀⠐⣿⠀⠀⠀⢸⡇⠈⠙⠻⣦
⠀⠙⠒⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠠⠟⠀⠀⠹⠆⠘⠻⠶⠶⠆⠙⠳⠶⠶⠋⠀⠲⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀⠀⣐⠀⠀⠀⢀⠀⢠⠂⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣭⣶⣖⣒⣀⣀⣀⣚⣒⡒⠲⠂⠨⡍⠙⠻⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠟⠛⣉⣉⣉⣉⣉⣉⡙⠛⠻⠿⣿⣟⡛⠛⠿⠶⣦⣤⣈⠳⢦⣍⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⣩⣴⡶⠿⠛⠛⠉⠉⠉⠉⠛⠛⠻⠶⣦⣤⣉⠛⠷⣦⣀⠀⢉⡙⠻⢶⣬⡙⠦⣍⠻⣷⣦⡀
⠀⠀⠀⠀⠀⣰⡿⣫⣴⠟⠋⠁⢀⣠⣤⣤⣶⠶⠶⣶⣤⣤⣄⣀⠀⠉⠛⠷⣦⣈⠙⢿⣟⠛⢻⣆⠉⠻⢷⣌⣷⠈⠻⣿⣆
⠀⠀⠀⠀⣼⣿⡿⠋⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄⡀⠈⠙⢷⣄⠙⢷⣬⣿⣀⡀⠀⠙⢿⠳⠦⣌⠻⣷⡄
⠀⠀⠀⣼⣿⠟⠀⣠⡾⠋⠁⠀⠀⠀⠈⠀⠀⠀⠞⠋⠀⠀⠀⠀⢠⡄⠉⠻⣶⣄⠀⠙⢷⣄⠙⣿⡍⠻⣧⠀⢸⡄⣼⣟⡇⠙⣿⣆
⠀⠀⣰⣿⠋⢠⣾⠋⠀⠀⢀⡄⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠈⠙⣷⣄⠀⠹⣷⡈⢻⣆⣿⣦⣤⡙⢦⣽⣇⢠⡈⢿⣧
⠀⢠⣿⠇⢠⡿⠁⠀⠀⠀⠈⠓⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠻⣦⡀⠘⢿⡄⠹⣯⠁⠈⠻⣦⠈⢻⣆⠻⡌⢿⣧
⠀⣿⡏⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⣷⡄⠈⢿⣆⠹⣧⣀⠀⣿⠀⠀⢻⣇⢻⡌⢿⣧
⢸⣿⠁⣾⠃⠐⠖⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠈⠋⠀⠀⠠⠄⠀⠈⢿⡄⠈⢿⡄⢹⣿⢿⣿⡀⠀⠀⢻⣆⠁⠘⣿⡆
⣾⡟⢸⡟⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⣿⡄⢻⣆⢹⣿⣆⣀⡀⢿⡄⠇⢸⣿⡀
⣿⡇⢸⡇⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠳⠀⠘⣷⡀⠘⣷⡈⢿⡾⠿⠛⢻⣧⠸⣷⠀⡄⢿⣇
⣿⡇⢸⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡆⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠹⣧⠘⣷⣖⣛⣩⣿⠆⢻⡇⣷⢸⣿
⣿⣇⢸⡇⠀⠋⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣇⠀⢻⣆⠸⣿⠿⢹⡇⠀⢸⣧⢸⡈⣿
⠘⣿⣾⣿⠀⠤⣤⣄⠀⢀⡀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠄⠀⠛⠋⠀⠀⡄⠀⠀⢿⡆⠀⢿⡄⢻⣿⠽⣷⠀⠈⣿⠈⠁⣿
⠀⠈⠛⠿⣿⣶⣶⣶⣤⣬⣥⣀⣘⣛⡒⠲⠶⠦⠄⠀⠀⣀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠘⣿⡀⢿⣞⣿⠀⢰⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣷⣶⣶⣦⣤⣭⣭⣁⣈⣓⡀⠀⠶⠤⢤⣤⣄⣀⣀⡀⠀⠀⠘⣷⡀⠘⢷⣄⠻⢿⣴⠿⠁⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣷⣶⣶⣶⣤⣭⣭⣉⣁⣀⡈⢿⣦⡈⠻⢷⣤⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣷⣶⣾⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣶⣶⣶⣶⣶⣶⣶⡖⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣿⣿⣿⣿⣿⣿⣾⣽⣿⣽⣿⣿⠿⠟⠛
⠀⠀⠀⠁⠰⠄⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠿⣿⠿⠿⠿⠿⠿⠛⢛⠛⠂
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⣀⠀⠠⠀⠀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡦⠤⠴⠦⠤⠤⠤⣧⣀⡘⣷⠠⠟⠁⠀⠀⠳⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⡐⢂⣇⣒⣹⣴⡎⠑⠀⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠭⣄⠰⣄⣭⡷⢴⡟⠿⡔⣢⢀⠁⠒⣄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⣤⠀⣉⢀⢷⣆⡁⡸⡿⣡⢣⢶⡐⢄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠌⠳⣌⣾⢃⣾⣷⣧⠴⠃⠎⠀⡧⣘⡆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⠀⠫⣥⣚⡠⢀⡜⣱⢃⡀⠙⠯
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣤⣀⠙⣿⠿⠓⢉⠙⠳⣷⣀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⢃⠈⣿⠿⣈⠀⣶⣤⡁⠺⠷⢀
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣶⡦⠀⠉⢳⠀⠨⣃⡘⠓⢀⡀⢀⠂
⠀⠀⠑⠦⢤⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣷⣲⣤⠖⣄⣶⠛⢻⡄⠸⢃⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢦⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⢻⣏⠙⠛⢳⠾⡟⢿⣻⡟⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⣧⣉⠁⠠⠟⣮⢱⣎⢹⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣬⣖⣄⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠈⠀⢿⣮⣉⣷⣡⡼⢧⣜⠳⣞⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⢦⡙⣿⣟⠡⠆⢼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢤⣀⣀⠀⠀⠠⠙⢧⣌⣿⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠓⠒⠒⠚⠉⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠈⠉⠲⠈⠩⠖⢎⣑⠤⠤⣀⣀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠔⠉⠻⡋⢠⠘⠢⡄⢀⡐⠉⣑⠮⠋⠉⠇⠠⡁⢰⡘⠉⢚⠡⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠐⠷⠒⠓⠤⠀⢒⣣⡘⢀⠤⠷⠾⠆⠀⢀⣡⡯⣶⡼⠲⠏⠉⠁⠉⠙⠢⣱⢱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢠⠠⢇⠀⢀⠤⣞⢠⠀⠈⠕⠀⢂⡶⣢⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢷⣄
⠀⠀⠀⠠⣔⢈⣉⠉⠩⣢⠀⠈⠑⡕⢁⠤⠤⠁⠀⠈⢂⠘⣒⣛⡻⢅⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢿⠯⡀
⠀⠀⠀⠀⠐⡩⠤⣀⠀⠢⡀⠤⠐⡁⠠⡠⠀⠀⠢⡤⠂⣿⠟⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠛
⠀⠀⢀⠔⠻⠵⠂⠚⠀⠠⠜⠀⡎⠀⢖⠒⡢⡈⠆⣧⡾⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠰⣀⠀⢣⡀⠱⠌⢦⠢⢴⠎⠁⡀⢢⠀⠙⣉⡙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢣⠃⠀⡏⠀⢀⠔⠉⠁⠀⠀⢋⣇⣠⡞⠁⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠰⠂⠉⠀⡹⠂⠻⡸⡉⠐⢌⡋⠉⣠⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢰
⠀⠀⢞⠀⡜⢀⡨⠂⠀⡍⠑⠪⡈⢐⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⡹⣷⠙⢒⢤⡬⠖⠠⡃⠸⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢷⠥⠥⣺⠮⣠⢮⠉⠀⣥⠁⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠃
⠀⠀⠰⡸⠒⡉⢉⡀⠤⢬⡑⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⡄⡖⢊⠉⡩⠒⡠⠥⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠀⠉
⠀⠀⣧⣁⡴⠂⡗⠀⡡⠀⢎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠉⠁
⠀⠀⢶⡡⠈⠐⡊⠘⡆⣬⠎⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⢀⡀⠤⠒⠊⠉
⠀⠀⢨⢋⠀⣔⠉⠫⣠⡏⠀⠀⠀⢀⣀⠠⠄⠒⠒⠊⠉⠁
⠀⠀⠀⠣⣙⢄⡧⣔⣕⡁⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢰⡆⠀⡐⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧⡤⢧⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣇⢠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⢺⡄⠀⠠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠟⠛⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠓⠒⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠛⠛⢩⠉⠁⢀⣀⣠⣤⣴⣾⠏⡄⠀⠀⣤⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠀⢠⠀⠀⠀⣆⠀⠰⠀⡀⠀⠐⣀⠰⢶⣾⣾⣿⣿⣿⣿⣿⡿⠋⢸⣷⠀⢠⣿⠀⢚⠛⠃
⠀⠀⠀⠀⠀⠀⣸⡇⢰⣼⠧⠊⢙⠯⢆⡄⢘⡓⠊⡉⠄⢛⠸⠛⠋⠉⠀⢁⠈⠥⠦⣀⡈⢉⠒⠼⠿⡆⠋
⠀⠀⠀⠀⠀⠀⣿⠓⢈⠀⠀⠔⠃⢠⠀⠀⢀⡀⠀⠋⠉⠁⠀⠄⠂⢉⡀⣿⠀⠠⠄⠀⠈⠿⠲⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡜⠂⢀⠀⠀⠀⢰⡆⣀⠄⠁⣸⣧⡿⠧⠠⠖⠀⠀⠀⠀⠆⠀⠸
⠀⠐⠀⠤⢀⠀⠀⠀⠐⠀⠺⠿⠯⠿⠆⠀⠉⠁⠐⠃⠸⠧⠈⡉⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠈⠰⣶⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠲⢢⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠀⠀⠀⠀⠒⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠲⠴⠿⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡝⠋⢙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡄⠀⠀⠑⣾⠃⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠎⡀⢰⠄⢸⠿⠛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢢⡀⠀⣆⡀⠀⠀⠀⠀⠒⠀⣺⠏⠀⡉⡉⣁⠀⢠⣤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡌⢠⣡⠜⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⡶⢀⡹⢷⡀⢻⡇⠀⠀⣀⣤⣤⣄⡉⣤⣼⣿⣡⣿⣰⣾⠁⣤⣄⣀⡀⣷⢾⣤⠀⠀⣠⡿⠈⣁⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠆⠙⢬⣥⠀⠀⠀⢠⠿⣯⣽⣯⣿⢸⡟⠛⢻⣿⣿⠛⠛⡟⢙⡏⢹⣿⣷⣾⣶⢀⡿⠀⠂⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣤⡄⠀⣠⡄⠈⠃⠁⢠⠉⠉⣁⡴⣠⣷⠀⣿⠟⠁⢹⣷⣤⣴⡟⠿⠆⢀⣵⣤⡵⣿⣿⣟⣿⢋⣼⣷⣿⠞⠋⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠛⠒⠀⢷⡌⠠⣽⡇⠘⠉⠠⣾⡿⠇⣿⠟⢠⡉⣿⣶⣶⢻⡟⠉⠀⠀⢾⡉⠙⠿⢿⣿⣾⣿⣭⣿⣍⣆⣴⠄⠀⠀⠀⢀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠄⠠⠀⠀⠛⣶⣿⣽⡾⣿⡿⣾⠀⠀⠈⢲⣦⡿⠿⠿⣿⣶⣿⢦⣶⣶⢿⣿⣶⣿⣿⣿⡏⠛⠛⣿⣿⣟⣭⣤⣴⠆⣼⠋
⠀⠀⠀⠀⠈⠁⠀⠈⡉⠀⠀⠰⡄⣠⢆⠡⢈⣿⣿⣿⣿⡞⣧⣀⢠⣾⣁⡀⢀⡀⢉⣻⡇⠘⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠶⣤⠀⠄
⠀⠀⠀⣤⣴⣿⣿⣶⠈⠠⢉⡀⠠⠛⠛⣦⣜⠛⣿⣿⣋⠀⠛⣿⠀⠙⠉⣹⣾⣷⣶⡿⢃⣠⣾⣿⠛⢿⣿⣗⣾⡟⣼⣏⣛⣿⣿⣿⣿⣧⣤⠲⣏⠠⡄
⠀⠀⣾⡗⠿⠺⠿⣏⠀⠠⣿⣷⣤⣈⣷⣾⠷⣿⣿⣿⡇⠀⢰⡖⠀⠈⠢⡘⢿⢿⣟⣳⣾⡁⠉⠀⣀⣾⠟⠿⠿⠊⢘⣿⣿⣿⠿⡛⠿⠿⣿⡷⢾⡇
⠀⠀⢻⣾⣿⣶⠀⠹⣷⡀⠁⢀⣼⡏⠀⠰⠤⣾⡿⠿⢧⡀⠀⢰⠀⠀⠁⠐⣦⠐⠛⣋⣽⣿⣿⣿⣿⡇⠀⠐⠀⢈⣿⡟⠁⣤⣶⣴⣷⣤⠌⡥⠨⠇
⠀⠀⠈⠙⠛⠁⠤⠐⣿⡴⣶⣾⣿⡿⠃⠠⠀⠀⣄⡀⠀⠙⢶⡄⠀⠀⠀⠀⠀⢶⣾⠟⢀⣿⣭⣿⣿⣦⠀⠀⠀⣨⡿⣦⣼⣏⣀⣽⣿⢦⠈⣇⣀⣴⠇⠀⠀⠂
⠀⠀⠀⢀⠄⠀⠀⢰⣿⢧⡩⠶⡟⠠⠏⡄⠀⠀⠨⠛⠻⣧⠀⠁⠀⢀⣠⡄⠚⠁⠀⠀⡼⢋⡉⠉⠉⠹⣿⣿⣿⣿⣧⣼⠛⠛⠛⠛⢻⠟⣠⡿⠿⠷⢀⡀
⠀⠀⠀⠆⠀⠰⠶⠂⣹⣬⠀⢠⣿⡷⣦⡖⠀⣀⠖⣻⣷⠈⣥⠙⣤⡀⣈⣻⡶⠂⡶⠛⣦⡠⣤⣴⣶⣶⠾⣀⡼⢿⣿⣿⣶⣤⣬⣤⣤⣾⣿⢿⠷⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠲⠟⣿⣿⠀⣾⣿⠠⣿⣿⣿⢋⣰⢻⡿⣄⣠⣶⣻⣿⣿⣿⡁⢸⠀⢀⣯⡀⢰⠿⠟⢧⣀⣍⣡⣚⣿⣿⣿⣿⠛⣶⣿⣿⣿⣿⡶⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⡉⢱⣠⣿⣯⡶⣀⣈⡉⠘⢛⡌⠁⣸⢏⡿⠉⡉⠙⢿⣷⠄⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠁⣼⡉⠛⠞⢉⣴⠿⠿⣿⢧⣤⣤⠐⠚⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣤⣤⣶⣄⣹⣷⣾⣿⣿⣿⠋⣽⠗⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣄⣸⠷⠈⠉⣻⡿⣿⠏⣰⣆⣼⡇⠀⠀⣈⣤⠀⠀⠀⣀⣤⣶⣻⠉⠀⠀⢉⠉⠉⢨⣿⣿⣿⠟⣻⣿⣿⣿⣿⡵⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢞⣿⣿⣿⡂⠀⢀⣿⡷⣽⣶⣿⡿⠋⠁⠚⠛⠻⠟⣠⣴⣿⣿⠻⢿⣿⣄⣀⣴⣿⣦⡀⠀⣿⣿⣏⣼⣿⣍⣁⠄⢸⣿⣿⣷⣄⣼⡇⢘
⠀⠀⠀⠀⠀⠀⣡⣴⣿⠁⢻⣯⡓⢀⣾⣿⡇⢄⡸⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⡿⢁⣾⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣉⣠⣤⣿⣉⣉⡉⠙⢳⢈⡁
⠀⠀⠀⠀⠀⠉⠹⠿⢉⡇⠈⠿⣧⡾⠉⢿⡷⠊⠀⠀⠀⠀⢀⣴⠟⠛⣽⣿⡇⢸⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⠿⢿⡿⠃⠀⢻⡿⢿⣿⣿⣿⣯⣤⣴⠀⢴⠃
⠀⠀⠀⠀⠀⠠⣄⠲⣎⡀⢤⠄⢀⣵⠆⠁⠀⠀⠀⠀⣠⣶⣿⣏⡤⠿⠟⠻⣿⣿⡿⠟⠉⠙⡛⣿⣿⣿⠋⠁⠀⠀⢨⣿⡄⣤⣿⠃⣸⣿⣿⣿⣏⠻⣿⣿⠈⡇
⠀⠀⠀⠀⠁⣀⡶⢚⡇⢲⣀⡴⠊⠁⠀⠀⠀⠀⣠⣾⣿⣿⣙⣋⠁⠈⠀⠓⠀⠷⣆⠐⠊⠉⠙⣿⠯⣤⣀⣠⣄⣠⡿⠋⠀⢈⣷⣼⣿⠋⣹⣿⣿⣷⣬⣿⡗⢷
⠀⠀⠀⠀⠈⠉⠑⠛⠳⢯⣥⣄⡀⠀⢀⣤⣶⡿⢟⠃⠘⠣⣬⣍⣙⠛⠚⠳⠖⢶⠷⣤⣤⣴⣶⣿⣤⡜⠉⠏⠀⠈⣷⣤⣤⣾⡟⠀⣿⣶⣿⣿⣿⣿⣿⣿⡅⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠋⠈⠙⠁⢀⣼⣷⣦⠀⠈⠉⠉⢳⡆⣹⣟⣶⠶⠛⠉⠉⠙⠛⠛⠳⣶⠟⠰⠾⠟⠁⠀⢨⣷⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠍⠃⣠⡄⠀⠀⠺⠿⠧⠋⠀⠀⠀⠀⣾⣿⣿⡟⠁⣀⣠⠆⠀⠀⠀⠀⢀⣿⣷⣄⣠⠷⣤⢴⣿⠟⠀⢀⣾⣿⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡿⠶⠋⠒⠈⠵⠷⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⣴⣿⡿⢿⣯⣀⣀⢀⡀⠀⠀⣿⠉⢻⣦⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠀⠀⠀⠀⢀⡄⠀⢀⣿⣿⣿⣽⣆⡈⢿⡇⠀⣶⣦⣀⣀⣿⣿⣿⠟⠛⣬⣿⣿⣷⣤⣴⣿⢤⣾⠟⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⣦⣠⣤⣶⠟⣠⣴⣿⣿⣿⣿⣿⢿⣿⠿⠿⣤⣄⣘⣿⣿⣿⠿⣻⣿⣧⣾⣿⣿⣉⠻⣧⣤⡴⠛⢶⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⡿⠿⢿⡿⠿⠿⠙⠛⠋⠉⠌⢿⡂⠀⠠⢉⣉⣉⣽⠋⢺⣯⣿⣿⠟⠡⠌⢻⣴⠿⠋⠐⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣱⠞⢶⡶⣦⣤⣄⣤⡶⠾⢻⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠋⠑⠻⠟⠛⠯⣹⣿⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢿⠏⠩⠁⠀⠀⠀⠀⠤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⢠⠄⡄⠀⠂⠈⣄⡉⠉⠫⠿⠫⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡠⠄⠰⢏⣟⣯⣒⣂⣀⡀⠘⠃⠤⢠⣤⡤⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠒⠊⠉⢠⠤⣞⣠⢟⣎⣞⣿⣶⡶⢄⠂⣠⠀⢀⠀⠀⠌⡀⠹⢎⣳⡽⢂⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢀⣀⠐⠄⠿⠟⣻⡿⡿⡿⢿⣞⢴⣏⠀⢣⢀⡒⣆⢠⢦⠁⢀⠀⢁⡵⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢠⣾⣽⣿⣷⡁⢪⢼⡟⣙⣗⣯⣿⣄⠛⢀⡀⢾⠘⠢⠌⠻⣃⠂⢉⠟⠒⣚⢁⢀⣠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣭⣾⣼⣿⢾⡿⠿⣷⡽⢃⢋⡟⣉⡤⢻⠧⠈⢳⣄⣠⡀⣥⡄⠁⠀⠀⣁⣠⢿⠁⢐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⡹⡾⣿⣾⣏⣯⠸⣿⣣⢁⣸⡟⠡⠆⠀⠲⡀⢸⠛⠾⣛⠚⣷⢀⡀⢦⠘⣧⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⡿⣷⣿⣷⡿⣳⣾⢋⡔⢁⣀⠤⠒⠒⠒⠶⣭⣿⠀⣃⣼⣙⣿⠟⢦⣈⡿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⢷⣺⢹⠟⣷⣿⡷⣯⣴⣿⠁⠀⠀⠀⠀⠀⠘⣷⣦⣮⡘⠺⣏⡔⡐⣾⣛⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡭⢽⣋⠿⣬⣻⠿⣿⣽⡿⠀⠒⠀⠀⠀⠀⠀⢻⢋⣢⡑⢾⡋⠞⢻⠯⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣿⢿⣿⣿⠾⣾⢽⡼⣿⡏⠁⠀⠁⠀⠀⠀⠀⢀⣿⡘⠷⣻⠮⢯⡟⢛⠒⣅⣐⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣟⣿⣟⣛⡾⢺⣿⠇⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⣻⠆⡜⣦⣌⡿⢉⠀⢿⣧⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⠀⠀⠟⡷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣼⡅⢾⣷⢄⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠿⣾⡇⢆⣱⢸⣿⠀⠀⠀⠀⠀⡠⠂⠀⠐⠿⢿⣿⣾⣻⡫⠫⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⢟⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣷⡿⣿⣧⠧⢘⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠸⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣏⣔⣁⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣻⡟⠦⣄⣀⠀⠀⠀⢀⣷⡀⣀⠔⢹⢹⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢄⡿⣉⣙⣿⣙⡿⢋⣻⣿⠤⠧⢜⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡟⠁⣠⠸⢿⡮⣌⠈⠑⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠁⠄⣮⡀⠁⠳⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠉⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠄⠒⠊⠉⣿⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⢀⣀⣠⡅⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣡⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠟⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣻⣿⣿⣿⣷⣾⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠉⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠿⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⣹⣁⣼⢿⣿⡿⠛⢩⢿⠟⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠻⠿⣅⣛⣋⡹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⡟⠁⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⣴⣿⠫⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀⠀⠀⠀⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⠀⣿⣬⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣯⣀⣀⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠃⠀⠀⠀⠀⢀⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣖⡒⠛⢻⣿⣿⣷⣼⣷⣶⣶⣶⣶⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣧⡄⠤⡄⠀⠀⠀⢨⣭⣿⣿⡟⠀⠀⠈⠉⢉⣿⣛⡙⠿⠛⢿⣿⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣴⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣇⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠾⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⣽⠟⠛⠛⢿⣿⡿⠛⠉⠙⢿⣿⡿⠛⠋⠉⠛⢿⣯⡀⢀⠈⣿⣾⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣦⢳⣄⣾⣿⠨⣿⣤⡄⢻⣿⡄⢺⣤⡄⠀⣾⣿⣷⣥⣼⣿⠿⣏⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣾⣯⠉⠉⢻⣿⣷⣿⣿⣿⣧⣷⣿⣷⣿⣿⣿⣦⣭⣤⣾⣿⣿⣿⡿⢿⡁⠀⠘⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⣿⣂⣤⣿⣯⡉⠉⠀⢻⡟⢻⡿⠟⠋⠉⠉⢻⡟⠋⠉⢹⡏⠀⠀⠀⣿⣤⣾⡟⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣾⣷⣤⡀⣀⣀⣼⣷⣤⣴⣾⣿⣦⣶⣼⣿⣷⡿⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⠟⠿⣿⠿⡿⢿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠙⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠠⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀⡀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣾⣿⣿⣿⣿⣿⠟⣻⢿⣿⣿⣶⡐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣬⡟⠻⣬⣶⢳⣿⣿⣿⣿⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣀⠀⢸⣿⣿⣿⣿⣿⡷⢠⣼⡿⣻⣿⣿⣿⣿⠇⢨⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠆⡼⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣷⡹⣿⠟⢛⣉⠉⠉⠯⠉⠛⠻⢿⡿⣣⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣏⣅⡀⠉⠀⠈⠁⠀⠀⠙⠛⠂⠒⠉⠀⠈⠙⢉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡙⢿⣿⠓⠶⣤⣀⣀⠀⠀⠀⢀⣀⣂⣴⠴⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⣬⣿⣶⣶⣦⣬⣭⣤⣤⣬⣥⣤⣶⣾⣿⡁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠧⠤⠌⠻⠋⠅⠈⣿⣿⣿⣿⣿⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣄⠀⠻⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⢸⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⡿⠿⠿⠟⠻⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡖⠂⠀⠀⠈⠀⠠⠉⠓⠠⣀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣄⠉⠉⠙⠻⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⡏⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠉⠙⠻⠿⠇⣠⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠀⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡿⠛⢿⡿⠿⢿⣿⣿⣷⡿⠿⠟⣳⠀⠈⠉⠀⢠⣆⣂⠀⠀⠀⡔⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢠⡀⢀⠇⠃⠈⠩⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠛⠋⠀⢠⠞⠅⠸⡇
⠀⠀⠀⠀⢀⣀⡀⠀⠐⠖⢻⡌⢷⣾⡼⣷⢠⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠈⠻⠗⠙⠁⠠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠸⣃⡇⠀⢃⣞⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⠘
⠀⠀⠀⠀⢀⡀⡀⢀⣾⣀⠀⣶⠀⠀⠋⠄⠀⠰⡄⠻⣃⠛⣧⣶⠀⣴⠴⣹⢀⡸⣶⠃
⠀⠀⠀⢀⣾⠏⠀⣿⡿⢁⣾⡏⠀⠀⠀⠀⠀⠀⠁⢨⠋⠉⠁⠀⠾⠉⠋⠃⠀⠈
⠀⠀⢀⣿⠏⠀⣸⣿⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⣿⣦⢠⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⣄⠀⣿⣿⣿⠿⣿⣿⡆⠸⣿⡀⠀⠀⠀⠀⠘⣆⠐⠒⢤⣀⠀⠀⠀⠀⠀⠀⠁
⢻⣇⢻⣿⣿⣦⣿⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⣤⣀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⡀⣈⡉⠻⣄⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠆
⠀⠀⠀⣸⣧⠀⠻⣿⢋⣉⣩⠽⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠮⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣿⣿⡇⣶⣫⢘⣟⢒⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢩⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢿⠛⣷⣿⡿⣆⣻⣏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠄⠀⠀⠀⠠⠀⣀⠀⠠⠈
⠀⠀⠀⢈⣧⡀⠘⡗⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⡀⠀⠀⠀⣁⡌⢱⡄⠩⣐
⠀⠀⣠⣿⡗⢿⡳⢿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠂⠤⢼⣿⣿⡛⣡⠗⡣
⠀⠀⣿⣿⣿⣄⠸⣿⠢⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠴⠖⢀⠀⠉⣉⣨⠅
⠀⠀⣿⣿⣿⣿⣦⣿⣧⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣶⣯⣍⡙⠿⠃⠂⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣃⣠⣤⣀⢀⠀⡀⣖⣿⣭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣷⣶⣮⡝⣧⢾⣱⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠛⣿⡮⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣽⣟⣴⣿⢷⡿⠿⠋⡏⠈⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣏⠉⠉⢁⣤⣶⣤⡀⡇⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⣿⣿⡄⠀⢿⣷⣷⣿⡟⡃⠀⣸⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⣤⠁⢸⣍⣻⣦⣌⠙⠋⠁⢀⣧⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣤⠾⣻⣇⠘⡿⢷⣴⠖⠿⡏⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣋⠠⡿⢺⣾⣁⠀⠀⠀⢠⡇⢀⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⠟⣩⣧⣥⣬⣤⡔⠀⢀⡊⣃⡤⠋⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⡿⢿⣿⡷⠀⣸⣿⣿⣟⣦⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣟⣿⡟⠻⠿⢯⡿⠿⠶⠄⠿⠝⠿⠷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⢀⣀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠀⣈⢰⠦⢶⠋⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣀⠀⢀⠁⣾⢀⡴⢋⢀⠀⠠⠀⠐⣮⠛⢶⣦⣿⡉⢿⠁⢸⣇⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢿⣿⠀⠀⠀⢰⣾⣱⣸⣿⣆⠀⠀⠘⢿⢦⣈⣿⣛⣿⢯⡵⠎⠉⣤⠥⡼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣇⠀⢡⣌⣿⡻⣿⣿⠏⠀⠀⠀⢘⣦⣴⡎⠉⢳⠀⣖⡀⠈⠀⠸⠯⣬⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠨⡭⠝⣻⣦⡀⠓⠌⠛⠾⠿⠿⠀⠀⣠⣾⢿⠷⢾⠲⣦⣤⠃⠋⠀⠀⠰⢇⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢈⠀⠀⢀⡴⢋⣿⡟⠦⣄⣀⣀⣠⠤⠔⠚⠁⠀⠀⠀⠀⢱⢦⣿⡆⢳⡀⠗⣀⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢴⣍⣠⡤⣂⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡽⠈⢠⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠉⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡈⠁⠐⢁⡐⠃⠀⠀⠀⣀⣀⣀⠀⣶⠀⠀⠻⠇⠀⠀⢘⣤⣬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠏⠀⠀⠀⠀⢏⠙⠦⠴⠿⠉⠀⠀⠀⠀⠀⠀⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢁⡄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠞⡀⢀⣀⣀⠀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⢰⠋⢠⡎⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣨⣄⠘⠁⣊⠳⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⣀⣀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠩⠿⢳⣽⡷⠀⠁⠄⠀⠐⢶⣤⠀⠀⣀⠀⠘⠛⠋⠁⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣥⡀⣖⢘⣧⣉⠁⠘⢷⡄⠀⡀⢹⠀⠘⡿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠿⠋⢹⠆⠊⢻⡶⠺⠫⣴⠀⣤⡤⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⢠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠌⠀⠀⢄⠸⠋⠑⠆⡐⠂⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣱⠂⡤⠠⢣⠀⠲⠀⠈⠘⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⡾⠁⠀⢰⠀⡿⡷⠦⠖⢶⠦⠀⠴⡀⠀⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣤⡆⣼⠆⠠⠆⠈⠉⠄⣀⣨⠟⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣈⡝⠀⣤⠄⠴⠛⢤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠤⣄⣤⣀⡤⢤⠀⢀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣯⡈⠛⣦⣉⣣⠘⣇⣼⢳⠈⠒⣉⡿⠴⢟⣒⣒⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣒⣓⣾⣿⣿⠈⠧⣈⠭⣤⣙⣻⡾⠛⣛⡥⠖⠛⠉⠛⠣⠍⠙⡚⠭⢷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣾⣿⣿⡿⣫⢟⣻⣿⣶⣦⣼⣿⡿⢋⣠⡜⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢶⠱⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣾⠛⣭⣭⣭⣗⣓⠿⣿⣿⣿⣿⠟⣡⠶⢛⣡⣤⠦⠄⠀⠀⠀⠀⣤⣤⡀⠈⠻⣈⠷⢸⡿⣄
⠀⠀⠀⠀⠀⠀⠀⢧⣀⣰⣟⣻⠿⣭⣿⣿⣷⡌⣿⣿⢏⡜⠁⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⡀⠈⠉⢦⠓⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢧⣤⣚⡡⠖⠉⠉⠉⠉⠛⢿⣿⣫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⢆⠀⣿
⠀⠀⠀⠀⠀⢀⡴⠻⠋⠈⠳⢄⣤⣤⣴⣶⣤⡿⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡀⢣⣿
⠀⠀⠀⠀⠀⠀⣿⠓⠲⠴⢚⣿⠿⣿⣿⣿⡿⣹⣁⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⡄⠉⢁⣼⡟
⠀⠀⠀⠀⠀⢀⣘⣦⣠⣾⢻⣸⡇⡏⢸⣿⣿⠉⠈⠓⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠟⠛⠁
⠀⠀⠀⠀⠀⢯⣿⢁⣿⣿⣿⣿⣧⣿⣿⢳⠇⠀⠀⠀⠀⣀⡀⠀⠀⠈⠍⠁⠀⣀⣠⣤⠶⠞⠛⠋⠉
⠀⠀⠀⠀⠀⡼⢿⣿⢿⣿⢿⡟⢿⣿⢿⡿⠖⠢⠄⠈⠉⠉⠁⢀⣀⣤⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⣧⠀⣿⡆⢻⡌⣷⣼⣏⣾⣋⣀⡤⣰⣦⣤⡶⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠹⠤⣿⣽⣾⣷⣿⣫⣿⣿⡷⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢰⣿⠁⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠟⠁⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠋⠀⠀⠀⠀⠀⠛⡛⠛⠃⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣈⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠿⠇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡴⢾⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣇⡏⠘⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⢸⠛⣦⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠷⣿⡴⠏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣀⠀⠀⠐⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠀⠀⠀⠀⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⢰⡀⠀⠀⠀⠀⠀⠶⢇⠆⠀⠀⠀⡇⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡂⠀⠀⠀⢀⡀⠠⡜⠀⠀⠀⡌⠁⠀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠂⡇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⠀⠀⠈⠧⢤⠀⠀⠀⠀⢀⠂⠀⠀⠠⢻⡆⠀⠀⠂⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢐⠳⠋⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠂⠀⠀⡀⠀⠀⠀⠀⠛⠁⠀⠂⠀⠀⠀⠁⠀⢠⢠⠀⠀⠀⡄⠨⢧
⠀⠀⠀⢀⠀⠀⠀⣸⠀⡄⠀⠀⠀⣮⢀⠀⠀⠀⠘⠀⠀⠀⠑⠂⠀⠀⢠⡐⠂⢠⢸⠀⠀⢀⠀⠀⠈⣸⠀⠀⠀⠁⡀⢹⡇
⠀⠀⠈⠀⠆⠀⠰⠉⠀⢀⠀⠀⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠒⠟⠉⠙⠁⠉⠀⠀⠀⠛⠀⠀⠀⢈⡄⠺⣷⠀⠀⠀⢸⠿⡆
⠀⠀⠀⠠⢭⣶⣶⣂⣀⢾⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢫⣿⣄⠀⠀⠸⡦
⠀⠀⠀⠐⢉⠛⠻⡉⠫⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⡇⠀⠀⠀⡃⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⣘⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠅⠀⠀⠀⢇⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠈⡩⡟⢿⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡄⠀⠀⠀⢀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠀⠉⠍⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄⢱⠀⠐⠈⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⣱⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠍⠁⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠝⠛⢄⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣰⣇⠀⠒⠀⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠻⢛⠛⠻⠀⢀⡄⠛⢰⠹⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡅⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠈⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠶⠀⠁⠀⠘⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡠⠌⠁⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠠⡄⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⢆⠀⠀⠀⠆⠀⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢥⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⣤⠸⠃⠀⢀⣀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⠈⠋⠈⢆⢰⠠⠆⠀⣎⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⡄⠐⠂⠀⠈⠝⣢⡀⢹⣆⢻⡀⠀⠀⠀⠀⠘⢻⡤⠌⠐⢧⡄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠌⠀⠀⠠⠀⢀⣀⠉⠙⠶⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⡠⠀⠘⣟⣧⡆⡀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠘⠱⠂⠈⠹⡿⠱⠄⠀⠐⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣷⣿⣿⣶⣶⣶⣤⣲⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡾⡻⣿⡁⢿⣿⣿⣿⠿⡌⠙⠉⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⣤⣠⣏⣳⣾⣇⠈⠁⠱⢷⣶⠃⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⡇⠻⢿⣿⣿⣷⣵⣤⣀⣀⠀⣴⣿⣿⣿⣿⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠢⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣄⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⠛⡿⣿⣿⣷⡄⠀⠀⠈⠛⠻⢿⠿⠿⣿⠘⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠘⠀⠀⢸⣿⣿⣿⣶⣷⣶⣿⡆⣠⣶⣾⣿⠰⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠉⠁⠀⠛⠈⠉⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣷⠟⠷⣿⣿⣯⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢸⡟⡿⠿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⠀⢘⡀⢠⣴⠟⠋⠀⠑⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⣿⣷⣄⣈⣛⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠒⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠂⡀⠰⠀⠀⠀⠀⢰⠁⣴⣿⣿⣯⡙⠿⠿⣻⣤⣙⣲⣦⣄⡀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠂⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⡿⢛⣦⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢷⢽⣿⢇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠋⠀⠀⠹⠠⠄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢘⢉⡉⣻⣟⠉⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⢿⡷⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣐⠛⠿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠂⠀⢀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⠿⠟⠁⠳⠶⢶⣀⡤⠀⠀⠛⢷⣦⣭⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠴⢧⠠⣤⠀⢸⣷⣽⣿⣿⣿⣷⡀⢃⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⠷⠢⠀⠀⠠⠿⠶⠼⠿⠿⢿⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠈⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⡀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢉⠀⠀⠜⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣨⠤⠉⠐⠊
⠀⠀⠀⠀⠀⢇⠂⠔⠊⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣀⠀⠀⠀⠀⠀⠀⠀⠎⢦⣀
⠀⠀⠀⢀⡀⠊⠀⠀⠐⠣⣀⠀⠀⣀⠏⠂⠐⡦⠀⠀⠤⢊⠀⠠⣫⠀⠀⠀⠀⠀⠰⢥⢀⣐⣱⠄
⠀⠀⠀⠀⠀⠀⠱⡄⠌⠀⠉⠀⠀⠉⢢⡀⡼⠅⠀⠀⠀⠸⠎⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⠀⠀⠀⠀⠀⠉⠀⡀⠤⠄⠠⠄⡀⠀⠀⠀⢰⠲⢄⢀⣤⠆⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡰⠘⠀⠰⡄⠀⢀⠔⠁⠐⠀⠀⠀⠀⠈⢦⠀⠀⠀⠄⠀⠁⠮⢀⠀⠀⡀⠜⠀⠱⢤
⠀⠀⣀⠀⠀⠀⠈⠓⢦⠀⠀⡞⠀⠀⠆⠀⠀⢀⡠⠖⠲⠤⡀⠀⢳⠰⠧⠠⠀⡠⠄⠒⠃⠈⠑⡆⢠⡈⣘
⢀⠼⠁⠓⡖⠀⠀⠀⠸⠴⠉⠓⠀⠀⠀⠀⢀⡞⠀⣀⣀⣀⣸⠀⠀⡀⠀⠀⠢⠁⠀⠀⠀⠀⠀⠖⠈⠀⠈
⠉⢰⠐⠒⠚⢀⠔⠒⠂⠐⠒⠒⠃⠈⠁⠀⠘⠉⠉⠉⠉⠉⠉⠄⠀⠉⠓⠒⠒⠀⠀⠄⠤⠀⠀⠀⡖⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⠀⠀⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔

⣿⣿⣿⣷⢻⣎⠻⣮⣿⣆⠳⣌⠛⠷⣶⣶⣽⣿⣿⣿⣾⣿⢃⣴⣿⡿⢟⣫⣾⣧⣾⣿⢟⣠⣿⣵⠏⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡄⢻⣧⡀⠹⣿⣿⣿⣿⣶⣄⡈⠙⣿⡎⢻⣿⣿⣾⣿⣯⡾⣫⣭⣿⣿⣿⣿⣿⣿⠏⣠⣶⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⢻⣷⠀⣿⢇⣤⣌⡙⠻⢿⣦⣹⣧⣾⣿⣿⣿⣿⣿⣴⣿⡿⠛⢉⣡⣤⣸⣿⣾⡿⠋⣠⡿⢣⣿⣹⣿
⣿⣿⣿⣿⢿⣷⡀⢻⣷⣿⣸⢳⣎⣙⢦⡀⠙⠿⠛⠋⠉⠉⠉⠙⠛⠿⠋⢀⡔⣋⣥⠸⡇⣿⡟⣠⣾⠟⠁⣼⢣⣿⣿
⣿⣯⢻⡟⣧⡹⣿⣌⣿⣏⣿⢸⣙⡾⣧⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡰⣿⣿⡃⡇⣿⣿⠟⠁⣠⣾⣿⡿⣿⣿
⣿⣿⣎⢿⣌⠻⣿⣿⣿⣿⣾⡘⣛⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⢣⣷⣿⣯⣴⣿⣿⢟⣩⣾⣿⣿
⣿⣷⣿⣾⣿⣦⣌⣻⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢟⣿⣿⣯⣶⣿⢟⣱⣿⣿
⣿⠶⢈⣙⣻⣿⣯⡉⠉⠁⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠈⠉⣉⣽⣿⣿⣿⡿⠛⢻
⣿⣫⣭⣭⣿⣟⣛⣛⡶⡄⠀⠀⠀⠀⡞⠀⢰⡏⠳⡄⠀⠀⠀⢠⠞⣽⠀⠈⡧⠀⠀⠀⠀⠀⢾⣛⣿⣿⣿⣿⣿⣿⣻
⣿⡿⢟⣿⣿⣫⣭⠍⠁⠀⠀⠀⠀⠀⠸⡄⢸⡇⠀⡇⠀⠀⠀⢸⠀⢿⡇⣠⠃⠀⠀⠀⠀⠀⠈⠭⣭⣛⣿⣯⣟⡻⢿
⣿⣴⢟⣿⣿⠟⠁⢀⣀⣀⣀⠀⠀⠀⠀⠈⠚⠓⠊⠀⠀⡤⠀⠈⠑⠚⠛⠁⠀⠀⠀⠀⣀⣀⣀⡀⠈⠻⣿⣿⣷⣭⣻
⣿⣶⣿⣿⢇⡴⢋⣭⠿⠛⠉⣿⡷⢦⣄⡀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⠉⠙⠻⣍⠛⢦⣹⣿⡿⣿⣿
⣿⣾⣿⣿⡟⢀⡾⠁⠀⢠⠾⢫⡇⠀⠈⠙⠳⠦⠤⣤⢰⣿⣂⡤⠤⠴⠚⠋⠁⠀⢸⡙⠧⡀⠀⠈⠳⠀⢿⣿⣿⣿⢻
⣿⣿⡇⢹⣧⠸⠁⠀⠀⠀⠀⢚⣇⠀⠀⠀⠀⠀⠀⢀⡏⡇⢯⡀⠀⠀⠀⠀⠀⢠⣼⡃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣾
⣿⣿⣧⠈⢿⡄⢤⠀⠀⣀⡤⢟⣿⠀⠀⠀⠀⠀⢀⡞⣠⣿⡌⢧⠀⠀⠀⠀⠀⢸⣿⠳⢤⡀⠀⠀⡄⢠⡟⠟⢸⣿⣿
⣿⣿⣿⣷⡈⠳⠸⡷⠤⣤⣴⡿⢻⣷⠀⠀⠀⢀⡞⣰⠃⡇⠹⣌⢧⠀⠀⠀⢸⣾⠟⢷⣤⣤⠴⣾⠇⠟⠀⣠⣿⣿⣿
⣿⣿⣿⡿⢿⣷⣶⣿⣷⡿⢯⣤⡀⢿⣴⠀⠀⣼⡼⠁⠀⡇⢀⠘⢮⣧⠀⠈⣾⡟⢀⣤⡽⣿⣾⣷⣶⣶⡾⢿⣿⣿⣿
⣿⣮⠻⣷⡀⢠⣾⣿⣿⣿⣶⣌⢻⡌⣿⡀⠀⣿⣇⠀⡀⠟⠀⠀⣼⡿⠀⢀⣿⢠⡟⣡⣾⣿⣿⣿⣷⡄⢠⣿⢏⣵⣿
⣿⣿⣧⠘⣷⣿⣿⡸⣿⣼⣿⢿⣾⣇⣿⠙⢆⢸⣿⠀⠀⣤⠀⢀⣿⠇⡴⠋⣿⣾⣾⡿⣿⣷⣿⢡⣿⣿⣾⠃⣾⣿⣿
⣿⣿⣿⠀⢸⣿⠹⣿⣿⢿⣿⣸⣿⣿⠇⠀⠈⢿⣿⡆⡦⠀⠄⢸⣿⡾⠀⠀⢻⣿⣿⣅⣿⡿⣿⣿⠫⣿⡇⢠⣿⣿⢻
⣿⢻⣿⣇⠈⣿⣷⡿⣃⠘⣭⣿⣿⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⣸⣿⠁⠀⠀⠀⣿⣿⣿⣭⠁⡛⣿⣾⡿⠀⣼⣿⠏⣸
⣿⣶⣿⣿⣷⣬⣝⣛⣻⠿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣷⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⣿⣿⡿⠿⣛⣋⣭⣤⣾⣿⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢰⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡸⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⣀⠔⠈
⠀⠀⠀⠀⠀⠀⠤⢔⡳⠶⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⠀⡤⠚⠁
⠀⠀⠀⢀⢶⠂⠀⠀⠀⠀⠙⠂⡹⠋⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠒⠂⠸⢤⠴⠀⠀⠀⠀⠀⠁⠀⠀⠋⠁⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠷⠃⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⢰⣮⠃⠀⠀⠀⠀⠀⢀⢾⠁⢆⣀⡀⠀⠀⣠⠅⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠒⠦⠠⡔⠀⠀⡰⢀⡈⠆⠃⠀⠀⠀⠀⠀⠀⠐⣦⠎⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠓⠀⠀⠀⠈⠀⠔⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠁⠀⢀⠠⠐⠊⡅⠀⠠⡤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠠⡆⠀⠠⠴⡅⠀⠀⠀⠀⢀⠁⡉⠒⠢⠄⢧⢴⠂⠕⠁⣃⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠁⠀⠀⠀⠀⠠⢶⡀⠀⠙⠄⠁⠂⠀⠶⠊⡙⡆⠀⠀⢀⠄⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⢰⠊⠀⠀⠨⠁⠀⠀⠀⠢⡄⠀⠀⠀⣈⠩⠀⢦⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⢀⡟⢀⠄⠀⠊⠢⠄⠀⠰⠄⠘⠀⢒⡎⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡄⠀⣆⣤⠋⡀⠀⡀⠠⠨⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣭⣤⣍⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⡉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠠⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠒⠤⣄
⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡄
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡇
⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠈⢳⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢤⣲⡺⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠤⣤⣶⣒⡪⠭⠽⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠊⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⣋⣩⣵⣶⣦⣤⣾⠏⠁⣉⣭⣭⣵⣶⣿⣿⣿⣿⣭⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢡⣴⣾⡿⠛⢻⣿⠋⢉⣡⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣀⣴⣿⣧⣌⣡⣤⣾⠟⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢀⣾⡟⠛⠀⠉⣹⡿⠉⢡⣾⠟⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣿⣟⠁⠀⣠⣤⣿⠇⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡿⠀⣠⣿⠿⠿⢿⣿⠁⠀⣼⡟⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠁⠀⢀⣼⡿⠀⣼⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⢠⣿⠁⣾⡟⠀⠀⣿⡏⢀⣾⡟⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣠⣿⠇⠀⣀⣿⣇⣾⡟⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⣠⡀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢰⣿⢉⣾⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣄⣀⣼⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡿⢻⡿⠀⠀⠀⠀⠀⣀⠀⣠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢧⠚⠁⢠⢄⠀⠐⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢢⠉⠀⠀⠀⡠⠔⠒⢂⠎⣸⡖⠁⣴⢦⣄⠈⠙⣿⣿⣤⡀⠀⡌⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠩⣐⣚⡁⠀⡀⠠⠘⠁⠘⡄⠙⠚⠿⣿⠦⣼⠛⠿⠛⠀⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣹⠇⡀⠄⢇⠀⢠⡁⣤⠔⠊⠀⢡⠈⡟⢂⠀⠀⡉⠀⠀⢠⡾⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⡻⢃⡀⣴⡆⠱⡀⠀⠸⣉⠦⠒⠋⠺⠁⠺⣦⡐⠸⠀⢀⣩⣴⣿⣛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⠆⠻⢯⣬⣿⣾⣏⢀⣀⠃⠀⡀⡀⠀⢠⡀⠈⠈⢇⠀⠀⠀⠈⠻⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣂⢠⣠⡄⠐⠒⢩⠛⠉⣔⡄⠀⣉⠲⡄⠃⣀⣠⣤⠀⡠⢀⠉⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡁⡨⢣⡀⢰⠁⠀⠀⡽⠧⠛⠃⠀⡎⢁⡮⠛⠃⠪⢄⣨⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠨⠅⠀⡋⠉⠲⠏⠉⠋⠀⣼⡀⡠⠒⠉⠉⠁⠲⡷⢃⢠⡕⡀⣧⠕⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⡀⠙⠢⢭⣳⠀⡄⠀⠰⠆⠀⢹⠀⠰⡆⡴⠶⠖⠘⠇⡸⠱⢡⣏⣀⡊⠑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠂⢐⡡⠚⡇⠀⢠⣤⣴⡄⠀⠀⡀⠄⠠⠀⣤⠀⠀⡟⠀⢀⠸⡃⡐⢍⢣⡊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢔⣈⣏⣀⣈⣑⣉⣀⣀⣀⣇⣑⣘⣘⣛⣀⣀⣃⣀⣈⣀⣇⠠⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢸⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣀⣀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⠈⠁⠀⠀⢀⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⠀⠘⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠐⠒⠒⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢉⠀⠀⠜⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣨⠴⠋⠐⠊
⠀⠀⠀⠀⠀⢇⠀⠔⠈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣀⠀⠀⠀⠀⠀⠀⢀⠎⢦⣀
⠀⠀⠀⢀⡀⠊⠀⠀⠐⠧⣀⠀⠀⣀⠏⠂⠰⡦⠀⠀⠤⢊⠀⠠⣫⠀⠀⠀⠀⠀⠰⢥⢀⣀⣱⠄
⠀⠀⠀⠀⠀⠀⠙⡄⠌⠀⠉⠀⠀⠉⢲⡀⡼⠅⠀⠀⠀⠸⠊⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠉⠀⡀⠤⠤⠠⠄⡀⠀⠀⠀⢰⠒⢄⢀⣤⠆⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠰⠘⠀⠰⡄⠀⢀⠔⠁⠐⠀⠀⠀⠀⠉⢦⠀⠀⢀⠄⠀⠁⠮⢀⠀⠀⡀⠜⠀⠱⢤
⠀⠀⣀⠀⠀⠀⠈⠓⢦⠀⢀⡎⠀⠀⠆⠀⠀⢀⡤⠖⠒⠤⡀⠀⢳⠰⠧⠠⠀⡤⠄⠒⠃⠈⠑⡆⢠⣌⣈
⠀⠘⠁⠓⣖⠀⠀⠀⠸⠴⠉⠛⠀⠀⠀⠀⢀⡞⢀⣀⣀⣀⣸⠀⠀⡀⠀⠀⠢⠁⠀⠀⠀⠀⠀⠒⠉⠀⠈
⠉⢰⠔⠒⠚⢀⠔⠒⠀⠒⠒⠒⠃⠈⠁⠀⠘⠉⠉⠉⠉⠉⠉⠄⠀⠁⠓⠒⠒⠂⠀⠠⠤⠀⠀⠀⠖⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⠀⡀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣤⣿⣯⣶⣿⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣶⣤⣦⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢿⠂⠀⢀⠀⢰⣿⡛⣷⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠸⡿⠀⠀⠾⡗⠿⠻⢶⡆⣄⡀⠀⠀⡄⡅⠀⢹⡟⠀⠀⠐⠚⠻⡿⠭⠻⠏⠙⢺⣿⡅⢱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣧⠀⠀⠀⠀⢀⣤⡈⠉⠀⠁⠀⠀⡀⢡⠀⢸⣇⠀⠀⠀⠀⠀⠁⠀⢀⠀⠂⠈⠛⠘⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⣹⣿⣿⣈⣀⣤⢾⠣⠀⠀⠀⠀⠀⡓⡀⡇⠈⣿⣦⣀⣀⣀⢀⡀⠀⠐⠾⠿⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⢿⣿⣿⣿⣏⠙⣶⠀⠀⠀⠀⠀⠀⣒⢨⢿⣀⣻⣿⣿⣿⡇⡽⢁⣀⣴⣶⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢐⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣤⡉⠁⠺
⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣀⠀⢹⣷⡹⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⠘⢿⣿⣿⣿⣿⣿⣿⣤⡈⣻⡟⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⢷⡽⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡹⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⣿⣧⡘⢿⣿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠹⣿⣷⡌⣿⣿⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⢀⣠⣄⣀⣀⡀⠀⠀⠘⣷⠀⠀⠀⠀⢈⠉⠉⠛⠛⠳⠶⢶⣤⣤⣀⣀
⠀⠀⠀⠀⢸⣏⠉⠉⠉⠛⠛⠛⠻⢿⡆⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⣦⣤⡀
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠰⡶⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠒⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠠⡦⠀⠀⠀⠀⠙⠋⠀⠀⣠⡾⣯⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠻⠂⠀⠀⠓⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠈⠉⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠐⠆⠀⠀⢀⣴⠟⠁⠀⠀⠓⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠰⣿⠆⠀⠀⣸⣧⠀⠀⠀⢀⣴⠟⠁⠶⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣴⠏⢻⡆⢀⣴⠟⠁⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⣴⣿⡁⠀⠀⠛⠛⠁⠀⢤⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠁⠸⣧⠀⠀⡀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⠤⠤⠶⠒⣒⣒⠒⠒⠶⠤⠤⠤⠤⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠛⠓⠀⠀⠐⠪⠭⠭⠍⣑⣒⡒⠒⠛⠛⠛⠋⠭⠒⠀⠀⠀⠀⠉⠉⠑⡶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⣠⡾⢛⡡⠄⠀⠀⠀⠀⢀⠄⡀⠀⠀⣉⠭⠤⠤⢔⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠫⢝⠯⡪⣕⢄
⠀⠀⠀⠀⡼⢡⠞⡡⠂⢁⠀⠔⡐⡡⢁⠌⠀⠀⠀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠉⠪⡪⣣⠑⡄
⠀⠀⠀⢸⢱⢃⠎⠀⠐⢡⢊⠜⠔⡠⠂⠀⠀⠀⠠⠁⠁⠀⠀⠀⣀⠼⢓⣄⡀⡀⠀⠀⠀⠀⠀⠊⡐⢁⠄⡠⠂⠀⠀⠀⠆⡇⡷
⠀⠀⠀⣿⠸⢸⠀⠀⠀⠀⢊⠊⠔⡡⢂⠀⠀⠀⠀⠀⠀⠀⠀⣴⡣⢠⠘⢁⠱⣖⣀⡀⠀⠀⠀⠈⠀⠂⠔⠁⠀⠀⠀⢈⠜⣸⠵
⠀⠀⢸⡟⣧⡈⠀⢀⢀⠀⠠⢊⠔⡠⠁⠀⠀⠀⠀⠀⠀⠐⡿⡗⠁⢸⡀⠯⣇⠨⡳⣖⣒⠀⠠⠀⠀⠈⠔⠠⠀⢐⣀⠥⠚⢁⢼
⠀⠀⢸⣿⣎⠻⣖⡦⢅⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡞⠋⣰⡗⢸⠇⣈⣡⠤⡙⠪⠳⣤⣤⠤⠴⠤⠔⠲⠊⠁⠀⠀⣊⠔⣻
⠀⠀⠀⢻⣕⢝⠢⠌⠁⠘⠉⠙⢛⠉⠒⠒⠒⣒⣚⢲⣿⠀⡡⡄⠀⢺⡇⠻⢟⡳⢃⠐⠿⠗⢒⡒⠀⠀⠀⠠⠀⠀⠀⠀⠐⠈⡞
⠀⠀⠀⠀⠻⡳⢕⠂⠀⠀⠀⡀⠁⠀⠀⠀⣐⠀⠀⢼⡏⠨⠯⠊⢄⣯⡁⠶⢤⢰⡦⣄⢸⠭⠠⠀⠂⠀⠀⠀⠂⠀⠀⢀⠈⣸⠃
⠀⠀⠀⠀⠀⠙⢆⣤⡀⠀⠀⠊⠀⠀⠀⠀⠀⣀⢀⢹⡇⢡⢦⢠⠎⠀⠈⠲⣄⠀⢈⡁⢸⠃⠈⠀⠀⠀⠀⠐⡀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠯⣀⠀⠈⠁⠀⠀⠀⠀⣐⡀⢸⣗⠚⡳⠁⠀⠀⠀⠀⠈⠳⣌⢋⣼⠂⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣴⣀⠀⠀⠀⢀⣺⣣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣽⣤⣀⣀⣖⡲⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠⠤⠤⠀⠈⠁⢠⣶⣤⣀⡀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⢀⣈⣉⣉⣀⣠⣤⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡶⣶⡖⣦⣤⠖⠲⢶⡏⠸⢿⡿⠃⡼⠛⠋⠙⣾⡦⠙⢋⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⣻⣿⠉⠃⠈⠉⠔⠉⠀⠀⠸⣿⠍⠂⠀⠀⠀⣰⣧⠈⢧⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢆⠀⠀⠻⣿⡧⠈⠀⠀⠀⠈⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣨⠀⠀⠀⠀⠀⠀⠰⠆⠀⢼⣿⣿⣦⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠃⣦⠐⢿⣿⣆⣴⣆⠠⠀⠀⠀⠀⠀⠀⠐⢠⠄⣠⣀⣤⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠣⡀⣨⠞⠙⢿⣯⠔⠀⠀⠀⣀⣀⣀⣀⠏⠉⠙⠛⠿⠷⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠿⠥⠬⠭⠴⠀⠀⠒⠒⠉⠉⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⡟⢿⣿⡿⣿⢿⢿⣿⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣾⣷⣿⣶⣾⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠒⠀⠃⠀⠠⠘⠃⠒⠶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⢠⡀⠀⠀⠒⢄⡀⠀⠐⢂⡀⢀⣀⠀⠉⠉⠂⠠⣄⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠀⡀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠈⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠈⠁⠀⠀⠀⣠⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠀⠀⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠂⠀⢄⣰⣣⢿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠙⢄⠀⠢⣀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠁⠀⢀⡀⠀⣀⣴⡞⠺⣹⢗⣿⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡙⠂⢌⣛⣒⠠⠤⠤⠤⢄⣀⣀⣀⡠⠤⣴⢾⣋⣁⣴⡞⣻⣥⡿⠉⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠐⠦⠬⣍⣙⣓⡒⠲⠦⠵⠴⠤⠤⠤⠴⢾⣿⣭⠿⠿⠋⠉⠁⣠⣶⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡱⠖⡀⠤⠀⠀⢀⠉⠉⠉⢉⣀⡀⠈⠛⠋⠉⠁⣀⣀⣠⡤⠶⠋⣩⠟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢶⡆⢄⣀⣈⣉⣙⡠⠉⢉⠘⠛⠒⠋⠁⠡⠁⠂⣡⠞⢃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠅⣀⣛⠚⠐⣲⠶⠤⠤⠶⠶⣞⣋⠥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠼⣆⣄⣿⣿⣿⡏⣿⣽⣿⣿⣿⣷⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿
⢀⣿⣹⣿⣿⣿⣿⣿⣿⣿⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣸⠃⢹⣿⣿⣿⣿⣿⣿⣏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿
⠟⢀⣾⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⢋⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⣛⡛⠻⢿⣿⣿⣿⣿⣿⣯
⠏⣿⣿⣿⣿⣿⣿⣿⣾⣇⣠⣤⣶⣾⣷⣦⣤⡀⣀⣀⣀⣀⣀⠔⢋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿
⠀⣿⣿⣿⣿⣿⣿⣿⠿⣋⣩⣭⣤⣬⡉⠛⣿⣿⣏⢀⣀⡹⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠀⣹⣿⠉⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿
⣸⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⡀⡹⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿
⢾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⠃⣿⣿⡿⠷⢿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿
⠼⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⠄⣼⣿⣿⣴⣤⣾⣿⣿⣷⣭⣝⣻⣿⢋⣩⡴⠿⣿⣿⣿⣿⣿
⠠⣶⣿⣄⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠟⣃⣼⣿⣿⣿⣿⣿⣿⠟⣿⣿⠏⠈⢈⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠁⡟⢱⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⣾⠿⠛⢷⡿⠇⠈⠉⢉⠀⠈⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠰⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⢀⣠⣬⣽⣶⣦⣤⡀⠀⢸⡇⠀⠀⠀⣺⣿⣿⣿⣿⣿
⠀⠀⠎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⣰⣿⣿⠿⠿⠛⣛⣿⣿⣷⣸⡇⠀⠀⠀⡼⣿⣿⣿⣿⡿
⠀⠀⠀⠈⢿⣿⡹⢟⠛⣿⣿⣿⣿⣧⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⣰⣿⠿⣿⡟
⠀⠀⠀⠀⢠⠿⢀⡤⠈⠉⡿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠛⠁⢸⡇⢀⡀⣨⣾⡏⠉⠀⠸⡗
⠀⡀⠀⠱⣤⡀⣴⠀⠀⠀⣥⣟⠈⠻⣿⣶⣤⣄⠀⠀⠀⣴⠛⠛⠉⠀⠀⠀⢸⡇⣩⣾⣿⣽⠁⠀⠀⠀⠐
⠔⠀⠀⢆⣼⣿⣿⠀⠀⢰⣿⣿⣷⣶⡾⠿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⡀⣀⣼⣷⣿⠋⠟⠁
⠀⠀⠀⣼⣿⣿⠏⣀⡀⣼⡿⡿⢻⣿⡇⠀⠈⣿⣿⣿⣯⣄⣀⣀⣠⣴⣾⣿⢿⡏⠁⠀⠀⣾⡀
⠀⠀⠀⣿⠛⠈⣾⣿⣿⡏⠀⣧⣼⡿⣷⠀⠀⠘⠟⠉⠛⣿⣿⣯⣥⠠⠞⠁⢸⡇⠀⠀⢀⣿⣷⣀⡀
⠀⠀⠀⠀⠤⠺⣿⣿⠏⠀⠀⣿⢿⣤⢽⡀⣾⣾⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣿⣿⣿⡟⢂
⠀⠀⠀⠀⠠⠂⡜⣡⣶⡄⠉⣿⠪⢤⣼⡿⣿⡷⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⢰⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⡿⡡⠋⣿⠀⠈⠛⢀⡙⠁⠀⠀⢰⣤⡄⠀⠀⠀⢀⣿⢻⡇⠠⠀⠸⣿⠿⣷⣞⠳⠄
⢉⡉⠛⠉⢙⡒⠟⢋⣀⣠⣴⣿⣴⣶⣾⣿⡿⢿⣷⣛⢋⡉⠀⠀⠀⠀⣈⡁⢸⣇⣴⣶⠞⠋⣀⠿⡛⣿⣤
⣦⣷⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⣿⣿⣿⣷⣄⠀⠀⠀⣹⣿⣿⢾⣿⣟⣿⣶⡀⢇⢸⣿⡏⢻
⢿⣿⣿⣾⣿⣿⡿⣿⡟⣉⢻⣿⢹⣿⡛⠹⣛⣯⣽⣿⣿⡿⠀⠀⢆⣹⣿⡿⢿⣿⣧⣧⣘⡿⣦⠺⣿⣿⣿
⡸⠙⢘⣿⣟⣿⡿⣟⣷⡿⢸⡿⣸⣿⡿⠰⣶⣿⣿⣏⡁⠀⠀⠀⣾⣿⡷⢶⣿⣿⣿⡋⠘⢿⡿⠛⠛⠛⠛
⠁⠀⣿⣧⡬⣿⣿⣾⠉⠛⠺⣏⢹⣧⢴⣿⣿⣿⣯⣅⣿⣾⣆⠰⠽⣿⣿⡔⠿⡿⢿⡿⣾⣷⡶

⣿⣿⣷⣿⣿⣿⣿⣿⡿⣷⣖⣯⣿⣿⣿⣽⣿⣿⣯⣷⣿⣷⣟⣻⡿⣿⣿⣿⣿⣷⣻⣽⣷⣾⣿⣿⣷⣟⢳⣿⣿
⢿⣿⢿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣻⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⢿⣿⣿⡷⣧
⣟⡿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣟⣿
⠇⣾⣻⣽⣿⣽⣿⣿⣿⣿⣿⣻⣿⣿⣷⣻⡟⣿⣧⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣳⣷⣏⣽⣹⠷⢽⣿⣹⣻⣦⡟
⢄⢻⣽⣼⣿⣝⡿⣯⢿⣿⣿⢿⣷⡿⣭⢿⢟⣿⣯⣿⣿⣿⢿⣿⣿⡶⣿⣿⢿⣤⣖⣶⢏⣹⢶⣟⣏⡟⠘⡋
⠡⠌⠒⣺⡟⣟⠷⣳⠌⣞⡿⠠⠽⣿⢯⣏⣾⣟⡟⣻⡾⢛⣿⡛⣯⣿⣹⣿⣭⣷⣿⢶⣾⣿⣿⢟⣳⣾⡿⠃⣄
⣀⢄⢊⣌⣡⠐⠇⡻⣽⠞⠱⢧⣭⣤⣶⡷⣯⣍⢹⣯⡟⣺⣿⠾⡛⡿⢟⡻⡿⠿⣿⠿⠿⠀⠗⠿⢗⢨⡐⣵
⡁⠛⠚⣃⣚⠖⣚⢀⡛⠆⡣⣄⢦⡰⠹⣶⠟⢥⣾⣴⣦⣶⣷⢊⢹⠚⢿⡇⠦⠄⡉⣠⠀⢈⡀⢂⠞⡄⠈⡹⠃
⡤⣀⢴⡆⠠⢞⡠⠬⢂⢀⠀⠒⢈⠡⠂⢿⡽⠩⠆⡈⠂⢉⢰⢙⠜⢢⡾⣯⣎⣈⣽⠏⣫⠠⡟⣴⠠⡆⢲⣓⣖
⠈⠂⠍⢱⠳⣔⣲⢅⡴⡦⠘⠁⠠⢠⠀⠰⢤⠚⡥⢂⢅⣺⠤⡜⠻⢶⢃⢿⠃⣑⡆⢀⠛⣃⡇⢠⠌⠄⠈⠏⠴
⠁⠀⠈⠄⠠⠩⠄⠨⠠⠔⠃⢺⠈⠄⠈⠀⢀⣀⠀⡀⠀⢑⠂⡔⢘⣃⡯⠲⠈⣿⢃⠀⠒⠉⠏⠀⡲⠄⠲⠆
⠀⠀⠈⠀⠐⠄⠜⠀⢢⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠘⠡⠀⠒⠄⠈⠘⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠐⢀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠂




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⠤⡒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠊⡽⢃⣤⠗⠚⠉⠉⠉⠑⠚⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⢷⡔⡉⠉⣷⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢥⣲⡇⡈⢠⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣴⣩⠤⠃⢇⡼⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣸⣨⠋⢣⢀⡼⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡎⠉⠈⠀⢸⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡁⢀⣀⣤⠚⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡗⣡⠖⠞⢈⡇⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⢣⠀⠚⢩⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡸⣶⢿⠂⢺⠀⡇⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⢮⣛⣧⡼⣰⠁⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠥⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣾⣿⣷⡀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣯⣴⣿⠛⠟⠛⠁⠒⠀⢀⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⠀⠀⠀⠀⠀⠀⣀⡒⣒⠚⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠤⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣀⣀⣠⡄⠀⠀⠀⠨⣥⡄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⣤⠀⠀⠁⠈⠀⠀⠒⣂⣿⡇⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠂⠀⠀⠀⠀⢦⣹⣃⠀⠀⠀⠀⣠⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡌⠀⠠⠀⠐⢾⣻⡷⠀⠀⠄⠰⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⡄⢀⠀⠀⢙⣷⣄⡀⠄⠀⣹⣿⡇⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠙⢄⠀⠶⠻⣿⣿⡆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠆⠻⢶⣿⣿⣿⠃⢀⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⡀⠈⠉⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⠓⠚⡶⠿⢋⡶⣯⣷⣟⣣
⠒⠒⡾⠿⠿⠻⠿⠻⠿⠻⢟⠳⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡄⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⢐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠰⠞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣻⠃⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠢⡀
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠈⠁⠐⢄
⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠂⠁⠠⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢦⡀
⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠑⢦⣄⡂⠤⠀⠀⠠⠄⢀⢀⣀⣀⣠⡤⢤⢖⡶⢌⠆
⠀⠀⠈⢄⠠⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠽⡹⢿⣿⣿⡯⠸⠳⠉⠚⠹⡘⡸
⠀⠀⠀⠀⠀⠨⡀⢒⠢⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠤⢀⠀⠀⠀⠠⠄⣠⣄⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢺⡄⠀⢠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣰⡖⠀⠀⢀⣄
⠀⠀⠀⠀⢿⡄⠀⠘⢧⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⢠⠾⡄⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⣠⠟⠁⠀⣀
⠀⠀⢀⠀⠀⠙⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡖⠠⣀⠀⠀⡰⠁⠈⠢⣀⡰⠃⠀⠹⣄⣀⠔⠋⠁⠸⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⡾⠋
⠀⠀⠻⢷⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠖⠁⠀⠀⠀⠈⠀⠀⠀⣀⣈⣀⢀⠀⠀⠀⣇⡀⠔⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡴
⠀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠉⠐⢒⣤⠼⠤⠄⢆⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⢸⠀⠀⠀⠈⣀⡀⠤⠤⠷⠤⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠉⠀⠀⠀⢀⣀⠤⢦⡀⢸⠀⠊⠁⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⣀⣀⣸⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⣭⠃⠀⠀⠀⡤⠤⢄⡀⠀⠘
⠀⣀⠠⠔⠚⠉⠁⠀⠀⠈⣧⠺⠀⡆⠀⠀⠀⣦⠀⠀⠈⣆⠀⠀⢰⠃⠀⠀⠀⡴⠉⠀⢠⠀⠀⢺⠏⠀⠀⠀⡤⠒⠦⡀⠀⠀⠈⣆⠀⢀⣾⠁⠀⠀⠈⢳⠄
⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⢆⠁⠀⠀⠀⠿⠆⠀⠀⠘⡆⠀⣿⠀⠀⠀⠀⢷⠛⠒⠚⢠⠇⢽⠀⠀⠀⠼⠠⣄⠀⢹⠀⠀⠀⢹⡖⢩⠃⠀⠀⠀⢀⠎
⠘⣆⠀⠀⣀⠀⠀⠀⢻⣁⠀⠈⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡟⣆⠀⠀⠀⠀⠉⠉⠙⡏⠀⢻⠀⠀⠀⠇⠀⠈⣆⠜⠀⠀⠀⡾⢠⠃⠀⠀⠀⢠⠃
⠀⠘⠾⢋⡈⡆⠀⠀⠀⢇⢑⠀⠀⡇⠀⠀⠀⢰⡞⢷⡀⠀⠀⠸⣇⠈⠳⣄⠀⠀⠀⠀⠀⢧⠀⠘⡆⠀⠀⠈⠒⠚⠁⠀⠀⠀⡰⢣⡏⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠉⢘⡄⠀⠀⠸⡆⡆⠀⢠⠀⠀⠀⠀⢮⠈⣷⣀⣠⠤⠼⡄⠀⠈⠙⠒⠶⠖⢒⣏⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⣤⠾⣳⣉⣑⠒⡤⠊⠙⡲
⠀⢠⡔⠒⠉⠁⢱⠀⠀⠀⢻⡘⠄⢸⣀⡠⠤⠚⡃⡁⠱⣄⣀⣀⣼⣷⡶⢶⣮⣧⢒⣓⣾⣦⡷⣤⣀⡀⠉⠉⠉⠋⡋⠝⠁⠾⡏⠀⠀⠙⣄⡴⠊
⠀⠀⠈⠲⣄⠀⠘⣇⢀⡠⠔⠛⢱⡀⠁⣀⡀⢤⣿⡿⠻⠍⢉⣍⠑⠣⡔⢉⡬⣷⣄⣴⣛⣶⣦⠤⡛⠳⢶⡐⠂⠉⠀⠀⢸⠀⠈⠲⡶⠚⠛⠤⣄
⠀⠀⠀⠀⢀⠵⠀⠈⠁⠐⠀⠐⡠⢤⣖⣩⣵⣾⣶⡿⠶⠶⠶⠶⠶⠦⣷⣎⡐⠁⢤⣮⣙⡯⣶⠶⠻⣶⣤⣌⠽⣦⡀⠀⠀⠁⠒⠊⠀⠀⠀⠀⠀⠙⣲⠆
⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⢠⣲⣷⠟⠋⠉⠀⠠⠀⠀⠔⠰⠂⠀⠀⢀⠙⠊⠍⢻⢦⣄⠠⠄⠨⣇⢰⡵⢟⠉⡖⢈⢿⡷⣄⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠈⠐⠒⠤⣀⠀⠀⠀⣠⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⡁⠉⠳⣦⡒⢉⢠⣸⣏⣀⠙⡇⠘⣿⢬⡳⣄⠀⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⡠⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠁⠪⠻⢦⡈⠛⣤⡙⣛⠟⢮⡉⢑⡙⢮⣧⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⠎⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⢪⠻⣮⠁⠙⣆⣠⣴⣹⠉⢱⠊⢯⠳⡄⣀⡤⠖⠊⠁
⠀⠀⠀⠃⠠⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢌⢳⣏⡾⠀⣉⣹⢛⡿⠻⡏⢣⢻⣅
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠢⠹⣦⠘⣭⠐⠊⡃⣠⢦⡾⡆⢻⣑⡄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠣⠘⣧⠲⢈⠟⢋⠩⠀⠸⢿⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⡘⣷⡄⡀⢨⠀⠀⣀⣾⢸⡇
⠀⠛⠀⠀⠈⠛⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢌⡻⣤⣠⣴⣮⡿⢣⣾⠃
⠀⠴⠂⠀⠀⠀⠀⠀⠘⠛⠉⠉⠛⠛⠛⠓⠒⠲⠶⠶⠶⠶⠦⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⣒⣺⣉⣥⡶⠟⠁⠀⠀⠀⠀⠀⠙
⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⠋⠉⠙⠛⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀
⠀⠘⠁⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠸⡄⠀⠀⣠⠖⠄⠀⠀⠀⣠⠆⡀⠀⠀⠀⡜⠑⢦⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠋
⠀⠀⠠⡾⠋⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡴⠋⠀⠀⠈⢆⢀⠔⠁⠀⠙⢦⡀⢰⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢻⣄
⠀⠀⠀⠀⠀⣰⠟⠁⠀⢠⡾⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠰⡆⠀⢸⡄⠀⠘⣧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⡟⢰⡿⠛⡛⠛⣿⣿⣿⣿⣯⣩⠙⢿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠠⣿⣿⣿⣿⣂⡼⡛⠹⣿⣿⣿⣯⣾⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢾⣿⣿⣿⣿⣿⣿⣤⡀⢿⣿⣿⣿⣿⡿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⡶⠾⠿⠿⠿⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠙⢋⣴⣟⢫⢻⠀⡏⣸⠋⣽⣦⣀⡁⠁⠙⠋⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠋⠁⠀⠀⣿⣷⢰⡿⣿⣸⢧⠏⣸⠏⢘⣿⡄⠀⠀⠀⠉⠀⠉⠛⢿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⡁⣠⡶⠿⠛⠁⠀⠀⠀⠄⠀⣿⣿⣾⢳⣷⣿⠟⣴⠋⣴⠟⣽⣿⠂⠀⠀⠀⢄⡀⠀⠀⠚⠛⠷⣦⠐⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠟⠄⠀⠀⢄⠁⠀⠀⢀⣿⣿⣿⣿⡿⣫⡞⣱⢞⣥⣼⡿⢿⣄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠞⢯⡟⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠏⠀⣀⣈⢈⣀⣀⣀⣀⣀⡑⠲⣶⣾⣟⠿⣽⣿⣿⣿⣿⣡⠾⣛⣽⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣦⢀⠘⠿⣿⣿⣿⣿
⣿⣿⣿⣍⢀⣴⡟⠀⠀⠀⡀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣷⠀⣶⣿⣦⣄⠀⠀⠀⠑⠀⠀⠀⠀⠈⣷⡄⢈⣽⣿⣿
⣿⣿⠏⠊⡍⠋⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡏⠀⣠⡿⠸⣿⣿⣶⣄⡀⠀⠀⠀⠢⠀⠈⠉⠫⡈⠋⢿⣿
⠿⢿⣤⣾⡀⣀⡀⠊⠀⠰⣤⣴⣄⠴⣵⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠉⠀⠀⣿⡇⢰⣿⣯⣙⡿⣿⣦⡀⠀⠀⠈⢂⣀⡀⣸⣦⣼⠿
⠐⠉⠉⠉⠚⠛⠑⠀⠀⠀⢸⠿⠏⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⡇⢀⣤⣿⣿⢁⣾⣿⣛⣿⣷⣶⣽⣿⣶⣄⠀⠀⠉⠛⠋⠉⠉⠰
⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠆⢀⣠⣶⣾⣿⣇⢿⡿⠿⢿⣿⣿⣿⣷⣿⣿⣟⠀⠀⣿⣿⠟⣾⣿⣿⡿⠛⠁⠀⠈⠉⣿⣼⣷⣤⡀
⠀⠉⠒⠠⠀⠀⣀⣴⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣻⣿⣤⣀⣿⠇⣠⣾⣿⣇⣀⣀⡦⣶⣶⣧⣿⣿⢛⣙⢻⣄⠀⠐⠚⠁
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⢟⣉⣨⣿⡄
⠀⠰⢾⣻⣉⣁⣀⡀⡀⠀⠀⠀⣿⣁⣀⡀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣧⣼⡿⠋⣙⡇⠀⠐
⠀⢰⠌⣉⣥⣤⣤⠼⣤⠤⠀⢀⠹⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⣻⣿⡟⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⠟⣿⣿⣿⣧
⠀⠘⣷⣬⣼⣶⠿⢿⣿⣿⣯⣠⣴⡖⠉⠉⢸⣷⡀⠀⠀⢀⣠⣾⣿⣿⡃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣥⡾⣯⣶⣿⣿⣿⣿⣬⣦⣀
⠀⣨⡿⣽⣿⣁⣀⣀⣾⣟⣃⣼⣿⡇⠀⠀⠀⢿⢷⡀⠰⣟⣿⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⠿⠟
⠀⠹⣿⣓⣛⣚⣛⣛⣛⣚⣓⣳⣷⣶⠀⠀⠀⠈⠃⠁⠀⠀⠉⠉⣡⡿⣯⣯⣝⣿⣿⠀⠀⠀⠈⠹⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⢀⡀⠀⢤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣤⠀⠀⢀
⠀⠀⠀⠰⡄⠀⢳⡀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⡤⡀⠀⠀⣠⢦⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠈⠀⠸⠁⠀⡴⠋⠀⣀
⠀⠀⣄⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠘⠐⠄⡀⠰⠀⠈⠢⠔⠁⠀⢣⠠⠊⠁⠘⡄⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠉⠣⠀⠀⠀⠀⠀⡤⠀⠀⡀⣀⣀⡀⠈⠀⠀⠀⠀⢀⠤⠄⠀⠀⢀⠀⠀⠓⠊⠁⣀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋
⠀⠙⠂⠀⠀⢀⣀⢤⠀⡇⠔⠂⠉⠀⠀⠐⡀⠀⠀⢀⠜⠁⠀⠀⠀⠀⡥⠀⣀⠔⠋⠀⠀⠀⠈⠲⣾⠀⠀⠀⡀⢀⡀⠀⠒
⢀⡠⠄⠒⠉⠀⠀⠀⢗⠇⠇⠀⠀⢰⡀⠀⠱⡀⠀⡼⠀⠀⠀⡞⡉⢠⠃⢔⠏⠀⠀⡠⠒⢢⠀⠀⠘⡄⢀⡾⠀⠀⠈⢲⠐
⠸⠀⠀⠀⠀⠀⢠⠤⠚⢀⡄⠀⠀⠘⠋⠀⠀⢣⠀⣷⠀⠀⠀⠯⢡⢅⡜⢸⠀⠀⢰⠁⠢⢀⠇⠀⠀⡟⡹⠁⠀⠀⡰⠁
⠀⠣⡤⠒⠄⠀⠀⢗⠠⠈⢹⠀⠀⠀⡤⣄⠀⠀⢳⡌⠦⡀⠀⠀⠀⠈⡇⠘⡄⠀⠈⠄⠴⠋⠀⠀⣰⣳⠁⠀⠀⠐
⠀⠀⠀⠉⢑⡀⠀⠸⡸⡀⢸⠀⠀⠀⡧⢘⣆⠠⠤⢷⠀⠉⠒⠲⠤⠐⠇⠀⠙⢄⡀⠀⠀⢀⣠⣴⣓⣑⡒⠤⠚⣲
⠀⠰⢈⠉⠀⢃⠀⠀⢱⣥⠀⡤⠔⠊⢇⣅⣳⣤⣤⣿⠷⣿⢿⡖⡥⣾⠾⠷⢤⡄⠈⠉⡉⠝⢁⡼⢇⠀⢈⣦⠚⠁
⠀⠀⠀⠑⢤⠈⠦⢒⡉⠌⠃⡀⠖⣨⣟⣯⣋⣴⣦⣍⣳⡠⠻⠛⣺⠿⣟⣿⣧⣍⡑⢠⡀⠀⠈⠣⠠⠝⠁⠉⠑⠢⣄⡀
⠀⠀⡠⠒⠁⠀⠀⠀⢠⣴⡴⠟⠋⠉⠉⠁⠀⠀⠀⠈⠉⠛⠳⢮⣉⡀⠭⢷⣠⣹⠛⡧⠙⣶⣄⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠈⠒⠀⠤⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡳⣶⡊⢡⣼⣤⣙⡆⢸⣮⣷⣄⠀⠀⠘⢄⡀
⠀⠀⠀⢀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡙⢦⡹⠦⡹⠋⢳⡤⢞⢺⣧⡀⠀⠀⡹⠆
⠀⠀⠰⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⡳⣤⢾⠚⠛⡷⢾⢦⠷⣳⡖⠉
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⢷⡘⡯⠜⣏⡴⣼⣧⢻⣢
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢷⡇⠝⣩⠄⠀⢻⣸⡆
⠀⠤⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢊⠻⣄⠀⡀⣴⡾⣸⠁
⠀⠤⠀⠀⠀⠈⠉⠛⠒⠒⠲⠶⠶⠤⠤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠚⣻⣛⣭⡾⠋⠀⠀⠀⠀⠦
⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠔⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠉⠉⡍⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡆⢀⠔⠋⢀⠀⢀⠜⠢⡀⠀⢠⠁⠑⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⡀⠈⠁
⠀⠀⠈⠁⣠⡞⠁⢀⡴⠀⢀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠓⠁⠀⠀⠈⠢⠃⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⣄⠀⢹⡄⠈⠛
⠀⠀⠀⠀⠈⠀⠀⠘⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁
⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡠⠔⠢⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠱⡀⠀⠀⠉⠀⠀⢀⡜⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⣀⠀⠀⠱⡦⠦⣀⠀⣠⠎⠠⣇⡀⢀⠠⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⢀⡠⠔⠈⠀⠀⢀⡀⡖⢼⠄⠁⠀⠀⢣⠀⠈⠻⣄⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢐⠈⠀⢀⡀⠀⠀⢐⠐⠬⠈⠁⠀⠀⠀⣀⠤⠃⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢃⠀⠘⠑⡢⠀⠈⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢆⠀⠈⠁⢀⡠⠔⠈⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⢦⠄⠺⠁⠀⠀⠀⠀⠀⢀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠤⢄⣀⣀⠆⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠧⠤⠒⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠒⠒⠐⠒⠂⠈⠀⠀⠉⠁⠐⠒⠒⠂⠁

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⢀⡇⢠⡎⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠤⠶⠄⠀⠀⠀⠺⠃⠊⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⠀⠀⠀⢠⣦⢀⠀⡤⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣉⣉⣀⢀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⢭⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⢀⡀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠐⣯⠙⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⢢⣬⠗⠀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⣤⣄⣁⡀⣸⣿⣿⣿⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⣿⣿⣿⣿⣷⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠂⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢸⡆⠀⠀⢻⠀⠀⢀⡾⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢦⠘⣠⠌⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⣄⠸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠙⠀⠀⠈⠀⠀⠘⠁⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⢠⡃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠒⢂⠀⢀⠒⠂⠀⠀⠀⠀⠀⠰⠆⠀⡀⠀⠀⠉⠂⢀⠀⠀⠀⣾⡀⠀⠀⢀⠀⠋⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⡀⠈⠀⠈⠀⠀⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠆⠀⠀⠙⢷⣄⠀⢿⠀⢀⣼⠟⠀⠀⠠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⡀⠀⠀⣀⣀⣀⠙⠂⠈⠀⠋⢁⣀⣀⡀⠀⠀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⠈⠛⠋⠉⢉⡀⠀⠀⡈⠉⠙⠛⠉⠀⠈⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⢠⣴⠏⠀⣼⠀⠙⢷⣄⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠉⠀⠀⢀⡀⠉⠁⠀⠀⣿⠆⠀⠀⠉⠀⣀⠀⠀⠈⠁⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⠀⠀⠈⠀⠀⢠⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⣰⠇⠀⠀⣼⠀⠀⠈⣷⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠙⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡆⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠐⠆⠀⠁⠀⡀⠀⠁⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡀⠀⢀⠃
⠀⠀⠀⠀⠒⠆⠀⠰⢦⠀⡇⣠⠖⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣄⡈⢷⢠⠟⢀⣀⢠⠄
⠀⠀⠀⠠⠦⠀⠰⠶⠤⠁⠀⠡⠴⠦⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠀⠀⢘⡉⠁
⠀⠀⠀⠀⠤⠄⠀⢠⠞⠁⡆⠱⣦⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⢠⡎⢸⡄⠉⠓⠰
⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠃⠀⡀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠇⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠤⠴⠶⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠒⠫⠩⠍⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠒⣄⣀⡀⠉⠙⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠲⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠊⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠉⢆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠒⠐⠂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠑⠤⠔⠂⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀
⠀⠀⠀⢀⣀⡠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⣀⣀⣀
⠠⠖⠋⠁⠀⠀⠈⠒⠦⠤⠤⠤⠤⠤⣤⣀⡔⠉⠉⢣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠙
⠣⣀⠀⠀⠈⠁⠀⠒⠒⠠⠤⠤⠀⣀⣀⣀⣀⣀⠀⠀⠉⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠠⠤⠄⠈⠛⠛⠓⠒⠚⠁⢀⣠⠴⠊
⠀⠀⠉⠉⠒⠦⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⣀⣀⡤⠶⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣚⣛⣒⣓⣶⣶⣶⣶⣴⣶⣶⣦⣄⣀⣀⣀⣠⣤⣥⣤⣴⣖⣒⣒⣒⣚⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠷⣴⢴⡡⠀⠒⠊
⠀⠀⠀⠀⠀⠀⡰⠃⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠻⡒⠀⠀⣀⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠙⣄⠀⠀⠈⠉⠁
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⢦
⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠹⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠟
⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡆⠀⠀⠀⠀⠇⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⡄⠀⠀⡎⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢣⠀⢰⠁⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⡀⡎⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⠟⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢄⢠⡄⢠⣤⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠁⠀⣶⡾⢠⠀⠀⠀⠶⣆⣱⠿⠈⢛⢱⡄⡠⠀⠾⠋⡋⢁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠄⠀⣠⡙⠋⠀⢀⢉⠑⠋⢁⠬⠂⠂⠄⠀⠀⠉⠙⠲⢨⣿⡁⣾⡘⠛⡀⣾⡥⠀⠀⡐⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⡟⢿⠈⣿⣧⠢⣬⡡⠀⠀⠃⠤⠀⠀⠀⠀⠋⠙⣉⠁⣀⡨⡏⢠⣤⡄⢘⠀⠈⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠫⢬⡄⣥⡴⢇⠨⣤⣶⣄⠻⠄⠛⠆⢀⠀⠀⠀⠈⠑⠅⢁⠇⠟⣡⢉⢀⢄⣀⣀⣀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠡⣀⠀⣘⠀⡟⠁⣎⢥⣤⣤⡼⢟⡆⠀⠀⣄⠀⠀⠙⠣⣄⡘⣒⡀⠯⣨⣿⣧⣚⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⣍⠏⢻⣅⣇⠻⢁⠋⠉⠓⠈⠡⣀⠀⢹⣇⠀⠀⠀⠉⠻⡏⡿⠋⠁⡉⣌⢃⢭⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡟⣯⠉⣦⣔⢻⣶⡠⡔⢂⡿⡔⠘⣿⣆⠀⠀⠀⠀⠙⣿⣄⠀⢀⡍⢁⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢭⣘⣏⠂⠀⠠⠠⣿⠫⣾⣷⡀⠹⣿⣔⠀⠀⠀⠀⠀⠹⠛⢿⣴⡿⠷⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠠⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⢿⠿⢷⣄⣐⡠⠄⣤⠐⠻⣷⠄⣿⣿⣶⡄⠀⠀⠀⠈⠢⣼⣯⠀⢦⣤⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡞⠉⢿⣷⡶⣷⠾⣿⣿⡀⢸⣿⣿⣿⣁⠀⢀⠀⠀⠙⠙⣾⣷⡶⠆⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣤⣤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣼⣯⡁⢠⣄⣈⠻⣇⠀⠀⠉⠛⠿⢿⣶⣦⣤⣀⣳⡄⣿⣵⣔⣗⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠛⠻⠿⣶⣤⣄⡀⠀⠀⠀⠈⠨⢽⣧⣶⣯⣅⠀⢻⡄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠮⣏⠉⠈
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣦⣤⣽⣄⢹⣿⣻⡀⢸⡛
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣝⡿⠛⠇⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⣤⠴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢠⣤⠀⡈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⣤⡮⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⣠⣾⡫⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠦⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢔⠃⠁⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁⠼⢀⠈⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⢢⡐⠈⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠎⢲⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡏⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡅⣄⠡⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⣀⠤⢂⢅⠟⠁
⠀⠀⠀⠀⠀⠀⡀⡗⡘⢆⠱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠚⠅⢚⠔⠏
⠀⠀⠀⢀⠀⡨⠳⣄⣌⠢⠀⠀⢉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⠤⡀⠆⡑⠨⠁⡒⠌⡤⠊
⠀⠀⠸⠷⣤⣤⡄⠀⠽⠛⢦⣈⠑⡠⢅⣂⠈⠐⠦⠦⠤⠤⠤⡤⠠⠀⠀⠀⠐⠬⠭⠉⠙⡫⠉⢁⣀⣢⣤⣴⣶⣶⠖⠒⠁
⠀⠀⠀⠇⡈⠇⠉⠩⠉⠲⡒⠬⡬⡏⣛⠒⠂⠂⢈⠉⠀⠀⠉⠉⠉⠙⢈⣀⣀⣬⣥⠤⠴⠖⠟⢛⡽⢋⣷⢿⠏⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠡⣀⠈⠫⢯⠲⠒⠤⣉⡈⠁⠀⠉⠀⠠⠨⠐⠈⠀⢀⠀⢂⡄⣡⢾⠟⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢓⡐⠒⠤⠄⣀⣀⣀⣀⣴⣇⣵⡃⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⢈⢀⡌⠉⠹⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠠⠀⡀⡀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣼⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆
⠀⠀⠀⠀⠀⢰⣿⡟⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⠋⠀⠀⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣽⣆⡀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⢺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣿⣧⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢹⡾⣿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣗⡿⣾⣿⣄⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣿⡿⣿⣆⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠈⠛⣷⣞⣛⣿⣿⣿⣛⣶⣤⡀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠻⣷⣄⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠈⠀⠉⠀⠈⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡗⠄⠀⠀⠒⠀⠒⠀⠀⠀⠀⠀⢘⢙⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣧⠐⠂⠀⠀⠀⠀⠀⠀⠀⠃⠂⠂⣳⣿⠿⠛⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⢠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣀⢤⢠⣤⣤⢼⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⠆⠀⠀⠀⢸⣿⣷⣿⣿⣾⣷⣿⣽⣞⣾⣯⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣀⣌⣿⣟⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⣴⡶⠛⠉⠀⢾⠟⢦⠀⠀⠀⣨⠛⡟⠛⠻⣿⣋⡀⠀⠈⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠾⣅⠀⠀⠀⠀⢸⢰⡌⡇⠀⢠⢧⣆⣽⠀⠀⠀⠙⢿⣀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠘⠚⠛⠓⠀⠘⠛⠓⠇⠀⠀⠀⠀⠈⠻⡇⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠐⠶⣾⣿⡿⠿⢿⣿⣷⠶⠂⠀⠀⠀⠀⠴⢫⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠤⠤⠤⠤⣤⣀⣀⣈⡛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⣰⠞⠉⠉⠁⠉⠉⣿⠓⠒⠲⠤⠤⣄⣀⣀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡾⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠓⠒⠒⠶⠤⠤⣤⣄⣀⡀
⠀⢀⣠⠴⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠚⠐⠡⠊⠥⣪⠔⣋⠴⡠⣴⢤⡀⠈⠉⠙⠲⣄
⢠⣯⣗⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠁⠉⠘⠱⠂⢀⣞⣹
⢸⡟⠀⠉⠓⠮⣝⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⢾⣿⡇
⢸⡇⠀⠀⠀⠀⠀⠉⠑⠢⢽⣲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⡟⠸⣿⡇
⢸⡁⠀⠀⠀⠀⠀⣴⢶⣦⡀⠈⠙⠒⠯⣕⡲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣵⡇⡇⡇⣿⡇
⢘⣷⠀⣠⣄⠀⠀⢻⣇⠧⠛⡆⠀⠀⠀⠀⠈⠙⠒⠭⢵⣒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢠⢎⣾⣿⢳⢣⡆⡇⡇
⠈⣿⠀⠙⠟⠀⠀⠀⠳⣄⣀⡟⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⠉⠓⠪⢭⣒⡢⢤⣀⠀⣠⢃⡾⡘⣽⢯⠙⣿⣧⣷
⢀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⣀⢤⢤⣄⡀⠉⠑⠲⢭⡷⣿⡆⢿⣿⣟⢀⡿⣽⣿
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡟⡗⡦⡄⠀⠀⠀⠀⣴⣏⠮⠋⠃⢻⡄⠀⠀⠀⣶⡙⡸⡸⢷⢥⢾⡿⣸⣷⡀⣀⣀⣀⣀⣀
⢸⣿⠀⢀⣾⢿⢷⢦⠀⠀⠀⣟⢜⠝⠙⠑⣸⠀⠀⠀⠀⢿⣻⠇⠀⠀⢠⠁⠀⠀⠀⣷⣷⢧⡇⡇⡌⣌⣇⣿⣿⣛⣛⣛⣒⣒⣒⣒⣒⣒⣒⣂⣀
⢸⢻⠀⢸⣿⣷⠟⠓⢧⠀⠀⠘⢧⣀⣀⡠⠃⠀⠀⠀⠀⠀⠓⠦⠤⠖⠁⠀⢀⣴⢾⡻⠗⢸⣤⢡⢁⢺⠙⣇⣟⠒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠒
⠀⡞⡀⠀⠻⠧⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⢮⣒⡬⠀⣸⣿⣼⢼⡇⣷⣧⣏⣀⣐⣐⣒⣒⣒⡐⠤⠤⠈
⠙⠳⣝⡲⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⡟⡝⡝⡶⡄⠀⠀⠀⠹⢿⣽⠁⣠⢃⡿⠭⣰⣳⣼⡿⠭⠤⠤⠤⠤⠤⠬⠭⠁
⠀⠀⠈⠙⠶⣍⡒⢤⣀⠀⠀⠀⢸⡟⢳⠀⠀⠀⠀⣿⣽⡕⠕⠉⠙⡀⠀⠀⠀⠀⠉⢹⡱⡹⢻⣟⡟⣹⡿⠭⠭⠭⠭⠭⠍⣉⡙
⠀⠀⠀⠀⠀⠀⠛⠳⠮⣗⢤⣀⠀⠙⠋⠀⠀⠀⠀⠈⠫⡃⠀⢀⡼⠀⠀⠀⠀⠀⠀⢸⢧⢇⠇⣿⣷⣿⣓⣋⣉⣉⣀⣒⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢺⣗⡦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⡞⡘⢼⡿⠓⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣝⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⢞⢯⠏⣿⢃⣾⠯⠭⠭⠭⠭⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢓⣭⣲⢤⡀⠀⠀⠀⢺⣛⡧⠀⠸⣿⣁⣴⣿⣾⣟⣛⣒⣒⣒⣐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢓⣮⡳⢤⡀⠀⠉⠀⠀⠀⠀⣿⢧⣟⣟⡒⠒⠒⠒⠲⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠵⢮⣲⣄⠀⠀⠀⠀⡏⣸⡟⠭⠭⠩⠭⠬⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⣭⡲⢄⡀⣷⣿⠭⠭⠭⠭⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣿⣿⣿⠭⠭⠭⠭⠅

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣛⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣩⣿⣿⣹⣿⣿⡿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⡿⣝⣿⠿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⢻⣿⣿⣿⣿
⠟⢽⡛⢫⣟⣿⢻⣯⣟⣻⣾⡵⣉⣿⡿⣿⣟⡀⢙⠛⠿⣿⣾⡿⢛⣿⡫⣽⡚⢿⣿⡷⢹⣿⠽⡿⣽⢿⠻⡛⣿⣿⣻⣹⣻⠙⠻
⠹⡶⣿⡜⣧⠸⣟⣯⠝⠯⠹⢿⢾⡴⢿⣘⡿⣬⠚⣫⣿⡆⢿⣋⢿⠼⢧⣎⠧⠿⣩⢷⣿⡏⢢⣱⠘⣷⢇⢀⠜⢿⣭⣥⢿⣁⠗
⠀⠛⠤⠚⡁⠁⠰⠋⠀⠠⠖⠃⠁⠀⠐⢡⠁⠉⠗⠹⠍⠘⢂⡝⠆⠐⠀⠀⡠⠀⠁⠩⠌⠁⠀⠝⠨⠸⠒⠚⠙⠋⠉⠙⠛⠉⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤⠀⠀⢀⠄⠒⣀⠀⠀⠀⠀⠖
⢀⢠⡌⠀⡻⠀⡀⡑⠀⢀⣀⣤⠖⢠⡷⣀⢠⢀⠤⠀⣀⢸⡤⡄⠀⠠⠀⣀⣠⢠⠧⠐⢀⠀⣔⣠⣐⣤⡀⠔⡀⣀⠠⢄⡀⠀⠖
⡹⠾⢧⣴⣗⢖⡒⣿⡻⢗⡘⣯⣶⠲⣶⣶⡼⢻⣾⡍⢻⣦⡟⣥⣿⣕⣲⣌⢝⣀⡻⣶⣽⢈⡟⣉⡘⡸⠶⠊⢮⡌⡖⣷⣼⠉⣫
⣄⢩⠽⣿⣪⣿⣤⣷⣿⣿⣟⣝⣧⣫⣷⣝⠽⢼⣀⡳⣶⣜⣻⣿⣭⠛⠋⢻⣤⣽⣇⡾⣧⣾⣧⣸⣑⣿⣚⣾⣿⣾⣷⣿⣏⣾⢗
⣿⣾⣿⣿⣿⣿⣿⣿⡿⣯⣿⣾⣿⡿⣿⣟⣿⣯⣿⣿⣿⣻⣿⣿⣿⣾⣿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢀⣤⣤⡀⠀⠀⠀⠀⢀⣶⠿⢶⣤⡴⠟⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠻⣿⡿⣿⣶⣄⣠⡶⠟⣉⣉⣉⣉⠛⠿⣿⠙⠳⣤⡴⠛⠲⠟⠁⠀⠀⠹⠁⠀⠀⣴⣋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠐⣿⡟⠛⠛⠋⠀⠀⢹⣿⠏⣰⡾⠛⠉⠉⠉⠳⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣶⣾⣿⣶
⠀⠀⠀⠀⠀⠀⣾⣟⠉⠉⠉⠛⠛⠻⠆⠀⠀⠀⠀⣼⠏⣼⣿⠟⠛⠛⢷⣶⣄⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢠⣿
⠀⠀⠀⢀⣠⣤⣌⣹⡿⠀⠀⠀⣀⣤⣶⣦⣤⡀⢸⣿⣠⣿⣷⣤⣤⠶⠶⠿⣍⡀⠀⠈⢻⣷⠀⠀⠀⢀⡾⠁⠀⠈⢻⣶⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⢰⣿⣏⡀⠈⠀⠀⠀⠀⣾⣏⡀⠀⠀⠈⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡤⠾⠛⠒⠒⠒⠾⠷⣤⡀⢀⣼⡿⠦⡴⢿⣷⠀⢰⣟⠉
⠀⠀⠀⠉⠉⢻⡄⠀⠀⠀⠀⠈⠙⢿⣷⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⣤⣴⣶⡾⠿⠛⠛⠳⠖⠀⠙⣿⡿⠃⠀⢀⡼⠃⠀⣀⠿
⠀⢀⣴⣾⠓⠉⠀⠀⠀⠀⢠⣴⣤⣄⣹⠟⢁⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣤⣾⣿⠟⢋⣁⠀⠀⢀⣤⣄⣀⡤⢤⡟⠀⠀⠀⠘⠣⣤⡄⠙⣦
⠀⣠⡬⠛⠁⠀⠀⢠⣴⣤⣀⣿⠁⠙⠿⡴⠻⢷⡼⠿⣧⠀⠀⢠⡞⠁⣾⣿⡟⠁⢰⣿⠛⠛⠢⠾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⡅⢰⡇
⠀⠛⠿⣶⠊⢀⣤⣾⣿⣁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢷⣤⣤⣾⣅⣼⣿⣿⠀⠀⠈⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠿⠾⣿⡿⠃
⠀⣤⠞⠁⠀⠈⣉⣿⢷⣦⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⣉⣁⣤⣤⣄⡀⠈⠙⠢⣄⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣸⡇⣠⣄⣀⣾⠃⠀⣼⣿⣆⠀⠀⠀⠀⢠⡞⢁⣴⠾⠛⠋⢹⣿⠛⣿⣷⣶⣤⣤⡿⠿⠂⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⣿
⠿⠟⠛⠻⣿⡿⠀⠀⣿⣿⢿⣷⡀⠀⠀⢿⣴⠟⠁⠀⠀⠀⢸⣿⠀⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣿⠿⠟⠶⠄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⢻⣿⣦⣄⠀⠀⠀⠀⢀⣤⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠿⣿⣿⣦⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⡀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣤⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡄⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠰⠆⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⣰⣿⣧⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣶⣶⣿⣿⡿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢈⡙⣿⣿⣿⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠶⠶⠖⠛⠛⠋⠉⠉⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣏⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠙⢷⡀⠀⢸⡇⠀⠀⠀⢀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⢻⡄⠈⣇⠀⢼⣁⡟⢹⡗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⢻⠀⣿⠀⠀⠉⠀⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠶⠿⠶⠶⠶⠶⠶⠶⠾⢧⣄⡀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠞⠋⠙⠛⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠚⠛⠛⠛⠿⠿⢿⣿⣟⣛⣳⡶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣯⣛⠙⢮⡍⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠀⣀⣄⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠾⠛⠦⡀⠀⠀⠙⢿⣏⠉⣿⣬⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠊⢁⡈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠁⠀⠈⢳⡐⠦⣬⣷⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣰⠞⠉⣉⡻⣆⠀⠀⠀⠀⠀⠀⠀⢰⢋⡤⡄⠈⢻⠀⠀⠀⠀⠀⠻⣷⠿⢙⣆⠘⣷
⠀⠠⣄⠀⢀⡀⠀⠀⣠⠏⠀⠀⠁⠀⣏⠀⢸⣧⣷⣹⠀⠀⠀⠀⠀⠀⠀⢸⡸⣷⡇⠀⣸⠁⠀⠀⠀⠀⠀⢻⡄⢒⣿⡆⢹⣇⢤⠀⣠⠶⢀
⠛⠲⣮⣷⣾⠁⠀⢰⡟⠀⠀⠀⠀⠀⠙⢦⣬⣙⡥⣋⣀⠀⠀⠀⠀⠀⢀⡠⣽⡒⠒⠚⠁⠀⠀⠃⠀⠀⢀⠸⣿⣚⠉⢷⠘⣿⢸⣿⣿⣞⣋
⠚⠛⠻⠿⠟⠶⠶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣭⣿⢒⣶⢲⣞⣹⣶⣾⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⠛⣿⠟⣿⠋⠛⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠿⣿⣿⠛⠻⢛⣻⣿⠿⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠁⣄⠀⡀⠀⠀⠀⢀⠀⠀⠀⠈⠩⠭⠭⢉⣀⣀⣀⣀⣀⣀⣄⣀⣀⣤⣴⡤⠴⠾⠦⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⢉⣿⠛⠛⠛⠛⠋⠉⠉⠉⠉⢿⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣶⣶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠶⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠒⠒⠦⠤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠙⠻⣟⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠈⢀⠀⠙⠲⣌⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢵⡄⠀⠈⠙⠶⣤⡙⢷⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠄⠀⠀⠈⠻⣦⣿⣄
⠀⠀⠀⠀⡴⠃⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠙⢿⣷⡄
⠀⠀⠀⡼⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢳⡀
⠀⢰⠃⠀⣾⣿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢾⣷⡉⣷
⠀⣿⠀⡄⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠉⢿⣼⡇
⢀⡇⢰⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⢹⣷
⢸⡇⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⢘⡄⠃⣿
⢸⡃⢁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⢈⢇⠀⣿
⢸⡇⢰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡿⠀⡟
⠈⣇⢘⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⢠⠀⠀⠀⠀⠌⢠⢶⡇⢸⡇
⠀⢹⣎⢷⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡦⡞⠁⣼⠁
⠀⠈⢿⣮⣎⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠄⠀⠀⠀⠀⣤⡄⡀⢠⠏
⠀⠀⠈⢿⣆⠺⡯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⣾⠏⠀⢠⠏
⠀⠀⠀⠈⢿⣦⡉⠻⣼⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠱⠀⣰⡏
⠀⠀⠀⠀⠀⠹⣿⢦⡸⣧⣶⠀⣀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠘⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣏⡷⢿⠟⢧⡀⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⠐⠀⠀⠀⢀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡛⠷⢯⣄⣶⣷⣾⣿⢦⡀⣅⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⢠⠆⠀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⢬⣍⣛⠻⢭⣂⣓⡬⠅⠁⣠⡀⢠⡒⠁⠊⠀⠉⢁⣠⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠽⠷⣤⣤⣬⠤⠤⠴⠶⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢶⡖⢐⢲⣊⠭⣷⡯⢉⣲⢒⠐⣶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⠷⢼⣰⣛⣛⣻⣯⣾⣯⣭⣭⣷⣮⣿⣛⣛⣢⣺⠼⣿⣷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣯⡷⣿⣤⠾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢦⣼⡷⣯⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠷⠷⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⡷⠷⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡞⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢋⠁⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠛⣞⢧⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡬⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢯⡼⣧⠀⠀⠀⢸⠀⠱⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠊⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡠⡄⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⢿⡆⠀⠠⠚⠀⣇⠠⣀
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠑⠈⠁⠈⠐⠊⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢙⣧⠀⠀⠑⠆⢠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⣤⣤⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢈⣿⣀⡠⠊⣠⠊
⠀⠀⠀⡠⠒⣉⠥⢿⡃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢻⠖⠐⠊
⠀⠀⡜⠀⡌⠀⠀⢸⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠻⠛⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢸⣇⣿
⢠⠎⠁⠀⢁⠀⠀⠈⢧⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃
⠇⡐⠉⠂⠤⠃⠀⠀⠀⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⡶⡖⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡇⡇⡇⡇⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠈⠙⠃⣇⡇⠋⠉⠀⠀⠀⠉⢢
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠉⠉⠉⠁⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠉⡠⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢧⡀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠓⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠙⠒⠲⠤⠤⣄⣑⡢⢤
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⣠⠆⠈⠀⠀⢹⡖⢦⣄
⠀⠀⠀⠀⠐⡇⠀⠀⠈⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣰⠋⢄⠠⠂⣱⠂⠀⠀⡧⠹⢦⡀
⠀⠀⠀⠀⠀⣧⠀⠀⢀⡀⡀⠐⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡀⠂⠀⡀⠐⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢀⡇⡤⠗⠀⢀⠯⡤⠆⠀⢣⠔⢄⡃
⠀⠀⠀⠀⠀⢸⡀⠂⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠸⡇⠀⠄⠈⠀⠃⠀⡆⠲⡁⠀⠀⢇
⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢧⡀⠀⠠⠀⠁⠀⢀⠀⠘⠳⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⡄⣀⠨⡄⠺⠄⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣁⡀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠻⣄⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢀⡤⣪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠒⠶⠤⣤⣤⣀⣀⣀⣀⣠⣤⣤⡤⠤⠴⠚⣡⠖⠉⣚⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣬⣉⠁⠒⠂⠤⠤⢤⣤⣤⣤⡤⠶⢶⣖⣲⡿⠧⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠳⠛⠻⠿⠿⠷⠒⠒⠚⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⡤⠀⠀⣀⢰⣄⠀⠀⣼⡦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠠⡦⣸⠷⡘⠈⠘⣇⠨⠟⢡⠟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣠⡆⠑⠛⠹⠾⠗⠚⠓⠛⠳⢦⣇⡶⣏⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠴⠦⢤⣀⡞⠀⠈⢳⡀⡴⠚⠒⢦
⠀⠀⠀⢠⠎⠉⢢⡞⠁⠙⡦⠒⠲⣄⠀⠀⠀⠀⠀⢠⡟⠉⠉⢻⡆⠀⠀⠀⢰⡇⠀⠀⠀⠉⠁⠀⠀⠀⠻⠁⠀⠀⠀⢣
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓⡄⠀⠀⠘⢷⣤⣤⠟⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢉⡤⠦⠄⠀⡄⠀⢠⠀⣠⣤⣤⠀⢰⣦⠀⠀⣴⠲⢤⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⠀⠀⣇⣀⣸⠀⣿⠀⠀⠀⣸⠘⣇⠀⣿⠀⣸⠇⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣇⠀⠀⠀⠀⡏⠉⢹⠀⣿⠓⠀⠀⣿⣤⣿⠀⢸⠛⠁⠀⠀⠀⠀⢀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠦⣤⡄⠀⠇⠀⠸⠀⣿⣠⣤⠀⡇⠀⠸⠇⠸⠀⠀⠀⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣤⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣀⣴⠾⠋⠉⢰⠶⠄⢠⡀⠀⡤⠀⡶⢤⡀⢰⠶⠦⠀⣄⠀⢠⡄⢠⠶⠀⢰⡆⢠⠀⠀⡤⢠⡶⠆⠀⠀⣿
⠀⠀⠀⠠⣾⡋⠀⠀⠀⠀⢸⣀⡀⠀⢳⡾⠁⠀⣇⣀⡷⢸⣤⠄⠀⣿⡄⢸⡇⠸⣄⠀⢸⡇⢸⡀⢰⠇⢸⣇⡀⠀⠀⣿
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢾⠉⠁⠀⡼⢳⡄⠀⣏⠉⠀⢹⠀⠀⠀⣧⠹⣼⡇⠀⠘⡇⢸⡇⠈⣇⣾⠀⢸⡏⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠿⠤⠦⠸⠃⠀⠛⠀⠋⠀⠀⠘⠒⠒⠀⠛⠀⠘⠃⠐⠚⠁⠘⠇⠀⠘⠇⠀⠸⠧⠤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇

⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿