Grain Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⢈⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⡐⠘⠀⠀⠀⠰⢈⠘⠀⠀⠀⠀⠸⠀⠤⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠑⠆⠐⢀⠀⠀⠀⢍⢢⠘⡀⠀⢠⡈⠜⠀⠀⠀⠀⠇⡁⠜⠀⠀⢀⠰⠀⠔⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠁⣀⠁⡀⢰⡀⠀⢨⠐⡔⢀⠀⢄⠘⡐⠂⠀⠀⠀⢘⠡⠂⠀⢠⠈⠠⠊⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⣄⢸⢄⠀⠁⢂⠘⡀⡎⠱⠁⠆⠀⢠⠉⠎⣠⠀⢠⠀⣆⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠈⢦⠀⣇⠑⠠⠀⢇⠘⢀⠇⣰⠀⡈⢡⠉⡀⢰⡇⢡⠅⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠐⢴⠈⡷⠄⡃⢸⢳⡀⠆⢁⢀⠃⣰⠂⣡⠊⢁⡄⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⢄⠛⣆⠱⠋⣧⠘⡀⠞⢸⡄⣣⠊⡁⠀⡬⠂⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠘⣄⠛⠀⡅⠀⠃⠰⡇⠘⠁⠨⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠃⣌⢀⠀⠃⠀⠈⢠⠃⠄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠐⡆⠀⡄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⡀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣻⣻⣻⣻⣛⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣟⣟⣻

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡤⠑⠛⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣦⣀⡴⡤⢄⣐⣒⡒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠂⠀⠀⠐⠒⠲⢦⣤⣀⠀⠀⠀⠀⢀⣬⡉⣀⣐⣂⣐⣒⣒⡂⠀⡒⠒⠒⣒⠂
⠀⡼⠀⣿⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⣤⣀⠄⠂⠠⡀⠀⠀⡀⠲⢰⣹⣿⡆⠀⠀⠀⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⡿⣭⣭⣭⣭⣭⣉⠉⠂
⠀⠀⠀⠩⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡚⠿⠭⠿⠍⠁⠉⠁⠉⠉⠉⣹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⢰⠚⠀⡡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠁
⠀⢸⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠛⢿⢶⣶⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⣿⡄⣤⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢈⠀⠀⠀⢀
⠀⠀⢻⠁⠻⣿⣿⣿⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡇⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠉⠁⠀⠈⠉⠉⠠⢀⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡄⠀⠀⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠀⠀⢀⣀⣀⡀⠀⣀⣠⣔⣀⣀⣀⡄⠀⣀⢀⣀⣠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡄⠜
⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠰⠶⠦⢶⣀⣴⣿⣿⠿⡿⠯⣻⠿⠖⢿⢿⡽⢿⣿⡩⣖⠀⠙⠛⠈⠉⠒⢤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡚⠉⣽⠋⢉⣴⠞⢁⡾⠀⣸⠃⢺⡅⠹⡄⠓⡌⠠⠍⡠⠀⠀⠀⠀⠀⠈⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣶⠿⠋⠁⣸⠟⠁⣠⡿⠁⠀⣿⠀⣺⡇⠀⢿⡀⠹⣦⠀⠈⣤⠂⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⣴⣾⡟⠛⠁⠀⣼⣿⠋⠀⢰⣿⠁⠀⣸⡿⠀⣿⡷⠀⢻⡇⠲⣿⡮⠀⠻⠃⠤⢀⠷⠀⠙⠒
⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠛⠁⠀⠙⠓⠀⠊⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷⡀⠘⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⠁⠀⠘⢿⣦⠈⢻⡇⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣳⣄⡀⠀⠈⢷⢷⡄⠙⡄⠘⡟⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠙⢮⣿⣦⣀⢀⠙⢿⡄⠈⢂⠻⡄
⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⡉⠢⣄⡀⠠⣈⠛⠿⠧⡉⠂⠈⠂⠀⠁⠁⠀⠂⢀⣠⣶⣦⣤⡄
⠀⠀⠀⠀⣠⣯⣿⣿⡟⣧⣟⡋⠁⠀⣛⢦⡀⠉⠒⠤⢌⣐⠤⣀⠀⠀⠀⢀⣴⣿⣯⣿⣿⣿⡾⢻⣷⡐
⠀⠀⣠⣾⣿⣿⣿⣟⣟⣿⢿⠱⡂⠄⠀⣠⣼⡽⠻⡤⢀⡶⡉⠐⠙⢂⡤⣿⣻⣿⡿⢿⣿⡻⡿⣙⠾⠯⡇⣄
⢠⡿⢿⣭⣍⠿⠓⢆⡩⠻⠴⠀⢃⡤⢿⣽⡛⣷⠿⣽⠋⡓⠚⣯⢶⣿⣷⣿⣹⣿⣟⡻⣽⢠⣼⣷⣿⡟⢷⡴⣱
⠐⠋⠁⡈⠂⠡⣁⡀⠀⠉⣤⢾⣽⣿⣿⣧⣏⣹⣿⣩⠸⠄⠘⢖⠻⠾⠾⣿⣿⣿⢿⡵⢶⣦⣭⣵⣬⠻⡯⠗
⠀⠀⠀⠈⠁⠀⠀⠄⠰⠍⣿⢽⣾⢳⡾⣷⣾⣿⣿⣿⡧⠀⠢⠌⠲⣀⢀⠉⠇⠂⢬⣶⠃⠰⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠻⡏⢩⡿⣿⣎⠓⢤⡉⠯⡤⠀⢯⠀⠴⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠍⠑⠒⠻⠥⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡢⣄⡀
⠀⠀⠀⠀⢀⣰⣷⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠾⠛⠉⣉⣴⠦⠤⢄
⠀⠀⠀⢰⣋⠏⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⢚⣭⠗⠚⠁⠀⠀⠀⣀⣀⡀⠱⡀
⠀⠀⠀⠈⠻⣿⡿⠀⠀⣀⣶⠀⠀⠀⣰⡞⠁⠐⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡟⢿⡄⢳⡀
⠀⠀⠀⠀⠀⠘⣿⡤⡾⣿⡏⠁⢠⣠⣿⡴⠀⣀⣠⣦⡶⡟⢿⣿⣿⣿⣿⣿⣿⣮⢿⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠈⠳⢿⣛⣿⢠⣼⣿⣿⡍⠀⠉⢻⡿⣷⡯⣚⢯⡳⢯⠿⣟⡿⣿⣬⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣏⣿⢿⣷⣆⠄⠙⢿⣯⡇⡍⠫⣞⡙⣱⣳⢶⢻⢛⡓⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠈⠛⠻⢿⣷⣌⣦⣿⢦⠸⡱⣓⢶⡝⡾⡞⢻⠸⡽⡟⣿⢦⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠐⣂⢿⠢⣀⠀⢤⢔⡿⣾⣿⣻⣫⢃⡅⡳⣙⣯⣏⣣⣢⠧⣱⠡⠙⢾⣮⣳⣧⣯⡿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢆⡬⢲⣷⣆⠀⠀⠛⠉⠉⠹⠟⠚⠓⡿⠛⠿⢻⡋⣷⢏⣴⠟⠻⠏⣀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠽⠙⠶⠀⠄⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠀⠛⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⡇⠀⠛⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⠀⠀⠀⣧⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣇⠀⢸⡁⠙⡶⠙⡇⠀⠀⠀⠀⠀⠀⣠⠞⡇⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⢧⠀⠀⡴⢇⠀⠀⠀⠀⠀⣀⡇⠘⢋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢧⠀⠘⡟⠲⡀⠈⡇⠀⠀⠀⢰⠁⢱⠔⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡀⠸⡇⠀⣧⠀⠀⢸⠃⠀⠀⠀⢸⡄⠀⡰⠃⣀⡼⠉⠟⣦⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣻⣌⡏⠙⣄⠀⠀⠀⠀⡇⠀⠹⡄⣸⠣⣠⠟⣆⠀⠀⢰⠋⠸⠎⢹⠎⢹⣁⣤⡶⠁⠀⠀⠀⠀⣰⠋⡜⢷
⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⣇⠀⠉⠀⣸⠻⡄⠀⠀⢳⠀⠀⢱⣼⠀⠙⠀⢸⡀⠀⢾⡀⢠⠤⢟⠀⣀⡜⠀⠀⠀⠀⠀⣠⠞⡇⠀⣠⠟
⠀⠀⠀⠀⠈⢇⠳⡄⠀⠀⠈⠣⣄⡀⢃⠀⢻⣀⠀⢸⡀⠀⠀⢻⣦⡀⢀⢾⡀⠀⢠⠏⢯⠀⠹⠊⡇⠀⠀⢀⡴⡿⢀⡏⠠⠟⢹⠁
⠀⠀⠀⠀⠀⠈⢧⠙⢦⠀⠀⠀⣿⠈⠙⠂⠸⠉⢻⠀⡇⠀⠀⠀⣇⠘⡎⠀⡇⠀⢸⣤⢾⢀⢤⡞⠁⠀⣠⢋⠞⣡⠞⣇⣠⡴⠣
⠀⠀⠀⠀⠀⠀⠈⢳⡈⠳⣄⠀⠈⠳⣄⣀⢠⠀⠀⡇⢻⡀⠀⠀⢘⣆⠀⢀⣇⠀⠀⡇⠘⠁⢸⠇⢀⡜⢡⠏⢰⠃⠘⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⡀⠀⢯⡈⠙⠆⢀⠟⠻⡄⠀⠀⢸⡈⠳⠁⢘⡆⡴⢣⠀⠴⡏⣰⠏⢠⢃⡞⢹⠄⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⠢⡀⠙⣲⢄⣘⡀⠀⣷⠀⠀⠀⣳⢄⡠⠚⣶⡇⠀⠏⢠⡷⠃⢠⣯⣼⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠢⡸⣄⠈⠁⢠⡏⢻⠀⠀⣧⠀⠁⠀⣟⣇⠀⡠⢿⠁⢀⡞⠀⡴⠒⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠑⢄⠙⢮⡗⠒⠼⡇⢸⠶⡄⢸⡄⠀⣰⠃⠈⠎⢠⠏⡞⢙⢀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⠉⠳⣄⣀⣈⠱⣄⠙⣦⢄⡀⢸⠀⡇⠀⠙⣾⡽⣄⠀⡰⢻⢰⡇⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⣤⠬⢧⠈⢳⡬⢷⣼⣄⡈⠉⠀⣷⠀⠀⡿⣄⠈⠛⠀⡜⣠⠛⠉⠀⣀⣠⠤⠴⠒⠲⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⠴⠗⠀⠹⣧⡙⣟⠛⣎⣧⠀⡇⠈⢳⡴⠊⢠⠃⣠⠴⢊⡥⠖⠚⠛⠛⠓⠲⠦⣍⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡤⠴⠷⣝⣎⢦⠘⣿⡆⢧⠀⣼⠀⢠⡧⢚⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠛⠚⠻⢷⣷⡘⣿⣼⠀⡇⢠⢟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢀⣠⠤⠤⠒⠖⠒⠤⠤⣉⣳⡘⣿⡀⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⣠⠤⢤⣉⠻⣿⣷⣿⢃⣠⠤⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⢙⣿⣿⣿⣉⡀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⣩⠟⢹⣿⣿⠳⣌⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⢠⠞⣿⣿⢧⡀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢸⠙⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡄⡀⢠⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡀⠀⢠⡇⠁⠘⡆⡃⢰⠗⠁⡴⢤⠀⠱⠼⠁⡈⢦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡇⠀⠘⡇⢀⠀⢸⠃⢀⢆⠀⣷⠀⠀⠆⠀⠀⠳⡈⠀⠨
⠀⠀⠀⠀⠤⡀⠀⠀⠰⠀⠀⠀⠂⡐⡂⡀⠈⠀⣬⡇⠂⢸⠀⢐⠀⠀⠈⡄⠀⡀⢡⠇⠀⡀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢘⣰⠆⢁⠄⠈⢧⢼⠁⠆⠀⠀⠈⢻⠀⡔⠀⠀⠀⣧⠀⠀⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⢼⣿⣄⠨⣆⣾⠊⢇⠓⣘⠀⢠⣰⢛⠀⠇⠀⢠⢠⣿⢠⣀⢸⣇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠊⠙⠙⠛⠐⠛⠙⠁⠈⠁⠉⠁⠀⠉⠈⠀⠁⠈⠉⠉⠛⠉⠉⠙⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⠄
⠀⠀⠀⠀⠀⠀⠚⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠃⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡼⢻⡆⠀⣰⠃
⠀⠀⠀⠀⠀⠀⡇⢸⣷⡞⢀⠘⣷⠞⡟
⠀⠀⠀⠀⡆⠀⢇⣾⠈⢳⣾⠞⠁⢰⣧⠁
⠀⠀⠀⠀⢃⠀⢸⣿⠠⠀⣿⡴⣡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠸⡀⡎⠘⢷⣧⣿⡿⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⠔⠁⠀⠀⢀⡠⠖⠁
⠀⠀⠀⡀⠀⣧⣿⢀⠀⢿⠏⡀⢸⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⢏⣠⢶⣏⣤⠴⢶⡾⠋
⠀⠀⠀⢰⠀⣿⢿⣦⣧⣸⡞⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣀⣴⣷⢋⠁⣼⡯⢀⣰⠟⠀⢀⣀⡀
⠀⠀⡀⠀⣇⢸⠀⠙⢿⣿⡿⠋⣹⣃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡞⠋⢹⣇⡎⣠⡿⢛⠉⢉⡽⠟⠉
⠀⠀⢰⠀⢸⣾⣇⢀⠘⡿⡡⢀⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡸⢀⡴⢿⡟⡔⠀⣼⣿⣿⣿⣿⣶⡾⠿⠒⠂⠉
⠀⠀⠀⢣⠀⡏⠹⣮⣦⣿⣡⡿⢿⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣰⣷⠏⠀⢸⣷⣥⣞⡩⠀⣠⡴⢋⣡⠤
⠀⠠⠀⠘⣧⣷⡀⠘⣿⣿⠋⠀⣸⡟⠀⢀⠀⠀⠀⠀⠀⠀⣰⢃⡾⢹⡇⡌⠀⣾⣿⠿⠷⢶⣿⠟⠉⠁
⠀⠀⢇⠀⣏⠻⣷⣤⣼⣧⠄⣠⣿⡇⢀⠂⠀⠀⠀⡘⠀⣠⣷⡎⠀⠀⣧⣦⣎⠁⠀⢀⣴⠈⠤⠒⠂
⠀⠀⠈⣆⢹⡀⠈⢿⣿⣯⡴⠋⢹⢁⠎⠀⠀⠀⠀⢀⡞⠁⢸⡄⢀⣼⠿⠟⠒⠒⡿⠋⠁
⠀⠀⠀⠘⣯⣷⡐⣄⢿⡿⠁⠀⣾⡟⠀⠀⠀⠀⣼⣿⢀⠀⢨⣿⡿⠅⠒⣀⣴⡪⠤⠂⠉
⠀⠀⠀⠀⢸⡟⣿⣾⣿⣵⠃⣴⣿⡇⠀⠀⣠⡾⢻⣏⣸⣠⡿⠿⠿⠟⣿⠟⠋⢀⠄
⠀⠀⠀⠀⠀⡇⠈⢻⣿⣧⡾⠋⠀⡗⠀⣰⠋⠀⢸⣿⡿⠧⠐⢀⣠⢞⣡⠔⠊⠁
⠀⠀⠀⠀⠀⢹⡀⣄⢻⡿⢁⠀⣰⠇⠀⡏⢸⠀⣼⡿⠷⠶⠿⢿⡟⠋
⠀⠀⠀⠀⠀⠈⢻⣌⣾⣿⢋⡴⠋⠀⠀⢷⣾⡿⠿⠖⠂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠋⠀⠀⠀⢀⡾⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⣰⠃
⠀⠀⠀⢰⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡚⢦⡟⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠐⡤⠀⣤⣀⠀⠀⠀⢀⣦⡀⠟⣿⣿⠷⢴⢋⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⢠⡖⠁
⠀⠀⣴⠤⠄⡸⠣⡄⠀⢨⣄⣑⠎⢻⣿⡗⢤⡏⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢃⠂
⠀⠀⠘⢶⠒⠃⠴⠛⣦⠸⣄⣉⠾⠋⣻⡟⠢⡜⢡⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢄⡵⠂
⠀⠀⠀⠈⢻⣃⣑⢢⠋⢰⣯⣭⣑⠎⢈⣿⠑⠞⢁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠒⠀⠈⡐⠉
⠀⠀⠀⠀⠀⠙⣥⣬⡁⡏⢸⣤⣈⡓⠉⠻⠓⡼⠃⢙⡄⠀⡠⠆⠒⠤⠤⢤⠌⣴⠋⠩⠙⠆⠰
⠀⠀⠀⠀⠀⠀⠈⢦⡤⠬⣏⣤⢤⡑⡴⠺⠧⢠⠜⠉⣇⢁⡀⣠⡤⣤⣤⡖⣼⠂⠀⠀⠀⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠾⣷⡦⣜⣠⣾⣷⣬⣦⠖⣻⢻⣟⣯⢿⡼⢩⢟⣋⡳⢀⣀⡔⣰⣟⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣗⣿⣿⠫⣿⢜⣻⣾⣿⣧⡻⣏⣽⡷⢿⣯⢾⣷⣿⣾⣷⣿⣯⣣⡙⠏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠉⠐⠓⠿⠼⠾⠷⠾⠾⠿⠚⠚⠛⠚⠛⠓⠛⠋⠉⠁⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣰⣶⣆⣤⢬⡀⣁⢀⠊⠂⠐⠀⠀⠐⠀⠀⠀⠂⠂⠂⠀⠂⡀⢈⣠⣀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠑⠺⠩⠣⢼⢺⢶⡌⡟⢻⠬⠝⠿⡌⠿⠦⠙⠝⠒⠙⡨⠻⠙⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⠀⠠⠂⠄⠀⠠⠠⢂⠌⡈⠀⠀⡀⡀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢁⢀⠀⠐⠀⠀⠂⠈⠀⠄⠐⠰⠃⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⠁⢂⠀⠌⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⡠⠡⢂⠂⠌⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⡐⠠⠡⠂⢂⢊⢸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠔⠔⡁⡀⡠⢀⡞⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢀⠔⡡⠊⢈⢌⠐⡀⠁⠡⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠘⠀⠂⠄⠄⠄⠄⠔⢀⡀⣢⠤⡬⢤⠤⠡⠥⡬⢴⠵⣀⣡⣊⢐⠅⠄⡐⡐⡀⠈⠆⠠⠠⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠑⠂⠖⠀⠜⠣⠋⠄⠉⠀⠐⠀⠀⠀⠂⠔⠀⠂⠀⠂⠔⠈⠍⠩⠋⠒⠬⣌⢈⡼⠁⠡⠀⠀⠡⠪⠊⠔⠔⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣼⢣⡿⠀⠀⠀⠀⠀⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡺⣧⣄⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⠀⣽⢯⡷⠀⠀⠀⠀⠀⣾⡿⡿⠀⠀⠀⠀⠀⠀⣠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠟⣦⣀⠀⠀⠀⠀⣿⣻⡆⠀⠀⠀⢿⣞⣧⠀⠀⠀⠀⢸⣿⣾⠃⠀⠀⠀⠀⢀⣴⣟⣽⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣿⣿⡆⠀⠀⠀⢾⡽⣧⠀⠀⠸⣿⣹⣇⠀⠀⠀⠀⣿⣩⡿⠀⠀⠀⢀⣼⡿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡞⢿⣧⠀⠀⢨⣟⣿⡀⠀⢠⡿⢷⡿⠀⠀⠀⣀⡿⣽⡇⠀⠀⣀⣿⡟⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠾⢿⣧⠀⢈⣿⣼⡿⠀⠸⣿⢘⣷⠀⠀⢀⣿⡶⣯⠀⠀⣠⣿⠋⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢾⣟⣦⠘⣿⡜⣷⡆⢼⣏⣹⣏⠀⠀⣿⡏⣿⠟⠀⢸⣿⢛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⣼⣿⢀⣾⡓⣿⡃⣈⣿⣴⣿⠀⢠⣾⢇⣼⠇⢰⣿⠟⣻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣻⡏⢘⣿⣸⣿⢿⣧⠿⣧⠀⠸⣿⢾⣿⢀⣼⡿⢞⣯⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⠸⣷⡽⣧⣬⣿⣼⡟⠀⣿⢋⡾⣋⢸⣿⣵⣿⢋⣤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣽⠷⣿⡇⢻⣿⠟⠀⣿⢃⣿⠏⢰⡿⠛⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢿⣻⣷⣻⡇⢸⡇⠀⠀⢷⣾⡿⢀⡟⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⡟⢿⣿⠁⢸⡇⠀⠀⢸⠏⠀⣸⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣿⠀⢻⠀⢸⡇⠀⠀⣿⠀⢠⡟⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡇⢸⡇⢸⡇⢠⢀⡟⠀⣼⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣷⠈⡇⢸⡇⢸⢸⡇⢀⡟⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡄⣿⢸⡇⢸⣸⠁⢸⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞⣇⢹⠸⡇⢸⣿⠀⣿⣼⠀⠀⠀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣧⡇⢸⡏⢸⣿⠅⣠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⣿⡇⢸⡇⣼⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣧⢸⠇⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣾⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠀⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠈⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣲⢿⡽⢿⣿⣿⣟⣷⢨⡷⢷⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢿⣉⣯⣸⢛⠛⣋⣛⣙⢿⡻⣾⡗⠋⢿⣽⣯⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⡟⠒⠾⠋⣭⡿⡎⠶⠃⢫⠹⠏⡤⢖⣯⠱⠾⣋⡟⣻⡾⣟⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣰⣷⣿⣲⣿⣷⢯⣤⢘⠍⢾⠗⣋⣔⢿⡾⠗⢿⣿⡁⢾⠻⢱⣿⠆⣋⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣷⣿⣿⣿⣿⢷⣿⣾⣟⣴⠚⣻⣻⣿⣋⡋⡭⣶⣌⣥⡔⠶⢧⣻⣵⠶⢿⣻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠐⣊⡿⣿⣾⣯⣽⣷⣾⣿⣿⣿⡿⠿⡿⢟⣭⣼⠉⢴⣲⣦⡅⢊⣳⡘⠟⢾⣀⣩⣟⣛⢒⠛⣋⣠
⠀⠀⠀⠀⠀⡀⣠⣽⢾⣯⢹⣷⣻⣿⣽⣿⡿⣟⣿⣂⣛⣬⠛⣿⠉⢶⣾⠛⢋⠗⠋⣻⣋⣖⡈⠀⢻⣍⣈⠑⣤⣶⡮⢷⣀
⠀⠀⠀⠀⠲⠑⠤⠙⠿⣝⣭⠛⣿⢿⡝⣋⡿⢛⣓⣢⣭⣭⣉⡗⣢⣿⣶⢾⡿⢿⣿⡶⠿⡿⠷⠄⣘⠎⢙⡗⠻⢦⡷⠿⠆⢲
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠉⠡⠄⠙⠉⠛⠿⠟⠿⠿⣿⡟⢩⣿⠛⣀⣩⡷⠿⠡⠴⠯⣀⣻⣷⡿⢮⠛⠶⢦⣔⡮⠩⣴⣆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⠽⠋⠝⣋⠀⠹⠢⡉⠩⠿⠤⠭⡶⠝⠘⠻⠄⠈⠙⠃⠀⠠⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠐⠀⠴⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠈⠀⠀⠂⠀⠐⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠹⠿⠿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢨⣇⠤⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⣾⡄⠀⠀⠀⠀⠀⠁⠘⠋⠰⠃⣀
⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣸⣆⣴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡿⠀⢲⠈⠹
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⣿⡿⢷⠌⢀⣼⠁⠀⠀⠀⢸⢠⣼⣿⣿⡿⠟⠛⢻⠿⡁⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⢧⣾⣶⣬⣿⢦⠀⣀⣤⣿⢸⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠴⠀⣴⣿⡿⠟⣻⣴⠂⠀⠉⠁⠟⠛⣾⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠻⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠉⡀⠠⠿⠶⠛⠿⣿⣿⣳⠆⣾⡆⢠⠀⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⢂⡀⢾⣧⣤⣤⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⣤⣀⡈⡁⠀⢀⣿⡃⡀⢀⡀⠀⠀⢠⢇⣸⣤⣰⣶⣦⡿⠘⠿⢿⡒⠀⠉⠉⠀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⡭⠈⣴⣷⠖⢈⡛⠻⠾⢷⡆⠞⠋⠙⠟⠉⠉⠩⠉⠁⣄⢼⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠉⠀⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠤⠶⣄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠈⢄⠠⠀⣤⡶⠿⠀⣪⣍⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣱⠄⠩⣠⡀⠀⠈⠉⠓⠾⠛⠂⠀⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠉⠛⠧⡀⠀⠀⠀⠀⠀⢤⣌⣡⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢰⢤⣴⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠺⢷⣌⠻⢷⣦⣬⣀⠀⠀⠀⢁⢀⠸⠀⠀⠀⠙⠛⣿⣿⢿⢻⣳⠂⣾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠓⢹⣿⠛⠛⠛⠛⠒⠂⠉⠹⠀⠀⠀⠀⡀⡙⣿⣅⣾⢱⣼⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⢰⠰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠶⠛⠁⠀⠀⠀⢶⣶⡄⡄⣄⢠⡠⡀⣈⢑⣂⣛⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣦⠤⢮⢹⡜⣿⣺⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠯⠽⠞⠓⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠰⠋⠀⣰⣶⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣧⣂⠄⡀⠀⠁⣀⠀⢾⡆⢸⣿⢷⢽⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣖⠴⠆⣤⡹⡏⠀⠣⣸⠿⠍⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢊⠱⡟⠠⣤⣵⡇⣼⣠⠜⡓⠚⠁⣂⠡⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠟⠛⣬⢙⢏⠃⡄⣽⣿⢰⡟⡡⢆⣠⣀⠺⠙⠉
⠀⠀⠀⠀⠀⠀⣤⣠⣸⡋⠴⠶⢦⣷⣦⣳⢲⡈⢿⣿⣾⣣⡖⠁⠉⢀⠀⡠⠦⠤⡤
⠀⠀⠀⠀⢤⣷⠀⢿⣧⣠⠂⠬⠭⢟⡋⡙⢿⡇⣴⢮⡱⣏⣠⠞⠡⡽⠋
⠀⠀⢀⣶⣦⣌⣷⣿⡿⡿⡦⠶⠀⢻⡏⠊⠘⢿⣿⣿⡷⠸⢟⣊⠔
⠀⠀⠟⠋⣻⡷⣾⣯⣽⠟⠀⠄⠲⠄⢣⢑⣴⣼⢉⣿⡧⣟⢀⡺⢮⣁⣀⠄
⠀⠀⠀⠀⢶⡿⠿⢿⡿⡴⠒⠀⠀⠀⠀⢹⠟⢿⣸⣦⠙⠚⢋⣠⠆⠘⠁
⠀⠀⠀⠀⢲⠿⣶⢫⣿⣦⠃⠀⠀⠀⢈⢇⣿⣸⣿⢻⣇⣣⡹⣻⡂⣠⣆
⠀⠀⠀⠘⣾⣸⣿⣼⣿⢻⣋⠁⠀⠀⠈⠣⣸⣷⣯⠀⢻⡿⣷⣯⣎⠙⠃
⠀⠀⠀⣴⡿⡿⣷⣽⣿⣿⣯⢀⣀⣠⡞⠩⡷⢿⣿⡕⣾⣿⠟⢏⣽⠇
⠀⢠⡾⠿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠈⠉⢛⣿⣶⣿⣿⢸⣿⠘⠌⣽⣀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢴⣍⡏⣿⣿⡿⣻⡆⠘⣸⠀⢿⡏⠡⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⢲⠇⣿⡟⣽⣤⢸⢱⡆⠁⣷⣙⣧⡄⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⡾⡖⡿⡃⢹⢿⠄⢾⡇⢜⢹⣿⢿⣷⣿⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣸⡿⣶⣧⡿⣈⢀⣻⣼⡏⡟⡞⣿⣿⢟⡍⢿⢿⡀
⠀⠀⠀⢀⢄⣀⡀⢀⠤⣤⣄⡴⣿⣇⣿⣿⢱⣿⣦⣘⢿⣷⣿⣇⣿⡟⣾⣷⣾⣾⡧
⠀⠀⠀⠀⢾⡎⠄⡴⢂⡘⠳⢿⢟⠻⡳⣷⣿⢸⣿⣿⢨⢟⡿⢿⣿⣿⣿⣿⣿⣿⠷⠓⠒⠶⢶⣶⢷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄
⠀⠀⠀⠀⠸⣿⡞⢰⠏⠀⠀⣸⢨⡇⣰⢸⣏⠙⢿⣿⣾⡾⣬⡘⣿⢻⠹⣿⣿⠋⢠⠄⢀⠆⠀⠈⡏⢃⠉⠙⡆⠀⠀⠀⠀⠀⡀⠀⡔
⠀⠀⠀⠐⠀⠉⢅⣽⠀⣰⡾⠟⠚⠛⢳⠏⠱⣦⣴⣆⢛⣿⢻⣿⣝⣷⣿⣿⣿⡄⣼⢀⡆⠀⠀⣼⠃⣼⢸⣧⣿⢀⣶⣤⣴⡯⠈⣶⣼
⠀⠀⠀⠀⢀⣴⡶⣿⠗⢯⡶⠛⠃⣄⠁⢆⠠⠿⠛⠽⡟⠟⠢⠹⣿⣻⠹⢏⡭⡝⠛⠁⣥⡾⠿⢉⣾⣿⣿⣿⣋⢙⣓⠑⢤⢻⡇
⠀⠀⠀⠀⠀⠛⠲⠁⡄⢼⠀⡄⠀⠈⣧⣸⣿⡿⠓⠲⠲⠤⡆⢤⣤⣁⢚⡻⠆⠀⠉⠁⠻⡂⣬⠙⣽⣝⣉⣝⠛⠓⠛⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢆⠷⣼⣦⡘⢶⡶⠿⣦⢸⡿⣧⡴⠞⠓⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠛⠙⠀⠘⠛⠞⠁⠈

⠈⠻⠿⠿⠾⠓⠤⠀⢀⠀⠀⣠⡜⠋⠀⠈⠀⠉⠉⠙⠓⠲⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠿⡶⠾⠿⠟⠒⠲⣶⣧⣴⣶⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠑⠈⠀⠀⠀⠀⠠⠀⠀⠀⠐⡀⠀⠈⠙⠓⠦⣄⣀⡀⠀⠀⠐⠂⠉⠁⠀⠀⠈⠑⠀⣀⣀⣺⣯⢱⡛⠽⣿⢻⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣤⡄⠀⠈⠉⠀⡀⠐⠀⠈⠈⠀⡀⠈⠐⠔⣩⣿⣄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣏⣊⣧⣖⢫⣿⣿⣿⠄
⢀⡀⣀⣤⣴⠎⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣛⠲⠶⠶⠶⣾⢤⠤⣤⣤⣶⣤⠤⡾⠾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠚⠿⠿⠟⠛⠛⠉
⣿⠿⡁⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣴
⣄⣈⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⣠⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⠧⠒⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠞⣡
⡿⠟⠁⠀⠀⠀⢀⣀⠀⢀⠀⠂⢒⣂⣀⡾⢃⢴⡡⠞⠋⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣿⣃⣴⠏⠀⠀⠀⠀⠀⠀⢠⢟⣠⠾⠋⠄⢈⠟⢋
⠶⠂⠀⣠⣴⣿⣿⣿⢷⣾⡿⠋⠉⠉⠛⡻⠛⠛⠓⣠⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢸⡏⢀⠀⠀⠀⠀⠀⠀⣠⡿⠛⡙⠛⣀⢠⣥⣴⡿
⠀⢠⣾⣟⣧⢽⠛⡉⣏⢭⣿⣤⡤⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠈⣧⢀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢈⡇⢸⠀⠀⠀⠀⣀⣼⢃⠴⣇⡀⠊⣠⡿⠛⠁
⠀⣿⣿⡿⣿⢫⣴⡌⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡁⣟⣿⠀⠀⠀⠀⠀⠀⠀⣼⣧⣦⣾⣇⠈⠀⠀⠀⠰⣟⠘⣁⠔⢠⣴⠾⠛⠨⠄
⠀⠈⠙⠛⠳⠻⠶⠞⠛⠁⠀⠀⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠛⢻⣆⠀⠀⠀⢀⣼⡿⢯⠁⣼⣿⣅⠀⠀⠀⠀⣀⠹⠯⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣻⡇⣤⣬⠠⣇⠸⠀⠀⢸⣏⣮⠇⣁⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠁⡌⠩⠙⣦⠀⠀⠀⠀⠀⠀⠀⠙⣿⡁⢘⠛⠄⣿⠀⠀⠀⠸⡿⢛⣼⣿⣻⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣹⠗⠀⠀⠀⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⢀⠀⡃⣼⡇⠂⠀⠈⣿⣿⣿⣶⡿⠋⠀⠀⠀⢀⣀⡀⠁⠄⠀⠀⠀⢀⣾⣿⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠲⣿⢻⠀⠀⠀⠀⠀⠀⠀⣽⡏⠸⠀⢷⢾⡇⣶⠁⠀⠘⠿⠿⠛⠀⠀⢀⣴⣞⠋⠉⠝⠺⡄⠀⠀⠀⢸⣿⡛⡆⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠅⠀⡂⠀⢀⡟⡘⠀⠀⠀⠀⠀⠘⠀⣾⡇⠐⠀⣺⢈⣷⠃⠀⠀⠀⠀⠀⠀⠀⡰⣻⠿⠇⠀⠀⠂⠀⢻⡀⠀⠀⠈⢧⣭⣸⣾⣿⠇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⡐⠘⠠⠁⣸⠁⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⡓⢺⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⠀⡞⠙⢻⡿
⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠁⢠⣰⡏⠀⠀⠀⢀⣶⣶⣦⣀⠀⢸⣧⣤⡆⢰⢸⣧⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠠⠁⠂⠀⢀⡞⠁⠀⠀⠀⠈⠁⢀⡼⢁⠄
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⢟⣿⣿⢿⣧⡀⠙⢿⣳⣤⡿⠃⠀⠀⠀⠀⣠⠀⢠⣿⠆⠀⠀⢂⠀⢀⡾⠁⠀⠀⠀⠀⠀⣧⣾⡃⠈
⠀⠀⠀⠀⠄⢽⠀⠠⠁⠀⢠⣿⡀⠀⡇⠀⠀⣿⣮⡜⢿⡧⣿⣿⡄⠀⢩⡀⠀⠀⠀⠀⠀⠈⠀⢀⣾⠁⠀⢀⠀⢀⢀⡞⠀⠀⠀⠀⠀⡄⣸⣟⠈⢿
⠀⠀⠀⠊⠀⣿⠀⠌⡀⢠⡿⠙⡇⠀⠀⠀⠀⣿⣽⠗⢀⣘⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣿⠃⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠁⢀⡁⢰⠄
⠁⠀⠀⠀⠀⣿⢠⠀⣤⡿⠁⠠⠀⠀⠀⠀⠀⠘⢿⣧⠆⣉⣏⣽⣃⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠀⠀⠈⠉
⠀⠀⠄⠀⠀⢻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠟⠻⣯⠀⡀⠀⠀⠎⠀⠀⠀⠀⣼⣦⠀⠈⣠⠎⠀⠀⠀⠀⠘⢶⡤⣤⣀⣦
⠀⠀⠆⠠⠀⠈⠛⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⣽⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡾⠁⠀⠈⠀⠀⠀⠀⣈⣿⡆⠙⠻⣿⠿⢶⣈⡂
⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠙⢻⣦⣑⡦⣀⣶⣌⠻⣦⣄
⠶⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠌⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠙⠂⠀⠀⠀⠀⠙⠻⢷⣌⠙⢅⡉⠢⢉
⠰⣄⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢎⠒⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠻⢶⣶⣎⠒⠄
⠰⠞⠙⠢⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢷⠘⣇⠀⠀⠀⡄⠀⠀⠤⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣀
⠷⠄⠸⠦⠤⠾⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠦⠘⠄⠙⠷⠀⠐⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⢀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⡀⠀⢀⣿⣄⣀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣐⠶⠤⠤⡀⠀⠈⠁⠐⠄⠀⡀
⠛⠓⠣⠼⢀⣹⣿⡆⠀⠀⣿⣻⡧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠄⠈⣏⠉⠉⠉⠙⠓⠀⠀⣴⠀⠀⡄⠐⠄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠀⠉⠙⠓⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⠀⠨⠀⠀⢤⡀⠙⢮⣷⣿⠀⠀⣿⠀⣆
⠀⢀⡀⠠⠄⡄⠀⠀⠀⢄⠀⠀⠄⢐⠠⠀⡀⠀⠀⠉⠉⠋⠿⣷⣶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⣷⡀⠀⢻⣦⠈⢿⡇⠀⣸⣿⠀⣿⠐⢒⠒⠚⠓
⢀⠀⡀⠄⠀⠄⠀⠀⠀⢀⡉⠒⢄⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣷⢾⡇⠀⠀⢸⡂⠀⠀⢹⣷⠀⠈⣿⡇⢸⡏⢠⣿⡏⣸⡏⠀⠀⠂⢁
⠡⠐⠂⡂⠂⠅⠏⣠⡒⢆⠀⢀⠄⠉⠢⣄⠀⠈⠀⣀⣠⠤⠶⠒⠛⠉⠉⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠘⣿⡇⠀⢹⣿⢸⠟⠋⠙⠲⠟⣀⣠⡀⠀⠈
⠁⠐⠠⢅⠁⢎⠐⠢⠁⠬⠡⠃⢴⣃⣤⠼⠗⠛⠉⠁⠐⠀⡀⠒⠀⡀⠀⠠⣴⣆⠘⡄⠀⠀⢻⠀⠀⠀⢾⣧⠰⠈⠉⢻⡆⠀⠀⠈⠺⠿⠋⠀⠀⠠
⠸⢁⡇⠀⠐⠂⡠⠚⣀⣤⠷⠚⠋⠡⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⢴⡁⠐⠖⠒⠶⢤⣌⣦⡀⠈⠦⠀⠀⠺⣿⣥⠄⠀⠀⠠⠀⠀⠤⠀⡀⠀⠈⠀⣀⠐
⢤⢉⠹⢐⣪⡴⠞⠋⠁⠠⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠁⠐⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠉⠅⠀⠂⠠⠖⠀⠀⠀⠀⠋⠁⠀⠀⠀⠁
⣠⡵⠞⠋⠁⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠹⠶⠷⠿⠶⠄⠀⢀⠀⠀⠀⠁⠀⠤⠀⠀⢀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠈⠀⠀⠀⡀⠀⠈⠁⠈⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠒⠉⢉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠙⠻⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠓⢢⣄⠀⠈⠑⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠉⠲⢤⡀⠈⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⢀⡀⠁⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠉⠁⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠶⠶⠛⠛⠉⠉⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠘⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡐⠲⠃⡠⠀⠀⠀⢹⠇
⠀⠀⣦⣄⠀⠀⠀⠉⠙⠛⠫⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠐⠀⠀⠀⣀⠤⠚⠀⣀⢸⠀⠀⠸⠗⠀⠀⠀⣾
⠀⢄⡉⠛⠋⠶⠴⣦⠀⣿⠒⠒⠞⠋⠀⠀⠀⣀⣀⡀⠉⠂⠀⠀⠀⡀⠤⠒⠉⠀⠀⠀⡜⠉⠀⠳⣴⠁⠀⠀⠀⡔⠁
⠀⠈⠛⠷⠶⢠⣤⣄⠠⠏⠀⠀⠀⠀⠀⠒⠂⠀⠀⢁⣀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⢀⡤⠈⠀⠀⠐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢹⣆⠻⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠉⠀⠀⠀⢀⠀⠀⠀⠐⠒⠤⠄⡀⠀⠀⠀⠀⢡⣾⡏⠁⠀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠓⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⢻⣿⣿⣿⠷⢤⣀⠀⠀⢀⠀⠀⢚⡄⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠛⠿⣶⣬⡟⠃⣀⡠⠤⠟⠀⠀⠀⡠⠀⢌⡁⠀⠀⠀⠘⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠠⠛⢛⡶⢶⡊⠀⢹⡄
⠀⠀⠘⢦⣀⣀⣀⡀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣠⠀⠀⠀⠘⡏⠀⠀⣸⠁
⠀⠀⠀⠀⠉⠙⠛⠓⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠹⢄⣄⣀⣤⡑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠟⠀⠀⠀⠀⠀⢀⠠⣂⡜⢣⠀⠣⡀⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠄⢣⠴⠀⡘⠈⠂⡠⢤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠐⡀⠀⠀⢠⠁⠠⠀⠀⠀⠡⠀⢡⠄⠂⣠⡉⠈⠂⠐⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠐⠁⢀⠔⠉⢡⡔⠈⠠⠄⠀⠈⢲⠈⡱⢅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠊⢀⠄⠒⢀⣰⠁⢈⠶⢀⠀⠈⡶⢁⡬⣀⡐⠀⠄⠀⠂⢈⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⢁⠠⠁⠀⡀⡊⠀⡸⢅⠀⠀⢑⠒⢀⡈⠀⠘⠂⠀⠈⡀⠐⠁⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠁⠀⢀⡊⠀⠀⠃⠀⠀⠑⠄⠂⣀⠈⠀⡃⠀⢀⠄⠊⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠁⢈⠖⠈⠒⢄⣀⠔⢄⠠⠃⢄⠔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⠀⠀⠀⠀⠰⠁⠁⡤⢆⠀⠀⠀⡠⠀⠀⡜⠀⢀⠄⢀⠊⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⢦⠂⠀⢀⠁⠀⠑⠁⡠⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⡯⠁⡀⠀⠀⡠⠁⠈⢲⠅⠀⠠⢀⠔⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⢢⠺⢀⠀⡠⠂⠀⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠐⠉⡈⠌⠉⠁⠐⠒⠃⠀⠎⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠐⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢀⠨⠉⠁
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⡀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢀⠐⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠀⠊⠀⢀⠐⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠐⡀⠠⠋⠀⢀⠀⠂⠁⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠑⠠⠄⠈⠐⠠⠀⠀⠠⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠙⠛⠛⠛⠛⠻⠿⢿⣿⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡭⠶⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠉⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠉⠁⠀⠀⠀⠛⠛⠛⠲⠶⠶⣤⣤⣀⣀⠢⣄⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣁⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠉⠁⠀⠐⠒⠛⠲⠶⢦⣤⣈⣉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢼⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠉⣭⣉⣙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣬⣍⣛⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠉
⠀⠀⠀⠀⠰⠋⠠⠖⠚⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣶⡄⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⢀⠀⠀⠀⠘⠓⠶⣤⣀⠈⠙⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠷⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⢦⢸⡰⢁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣷⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡾⡽⣷⢿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⢯⣿⣟⣿⣹⣥⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢤⣟⣿⢺⠧⢿⣤⣷⠶⢻⠀⠀⣴⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⠀⢠⠓⡾⢤⣏⣹⣗⣻⣗⣛⣖⣩⣧⠞⢡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⣦⠀⣼⣩⡗⢺⡟⢾⢦⣼⣯⣩⣯⣠⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⢳⡗⢼⣍⣹⡇⠈⣧⠾⡦⠴⣷⠤⠾⡆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⢳⡀⢸⣝⣻⠤⢼⠇⠀⢸⣞⣟⠒⢻⡖⢺⣷⡷⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢻⡇⢸⠦⣿⣉⡿⠀⠀⢸⣯⣿⣒⣺⣏⣩⣿⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⣾⣓⣳⣼⠃⠀⠀⢸⠷⣿⢬⣽⡧⢤⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⡬⣿⡏⠀⠀⠀⣾⣉⣹⠒⠚⣟⡾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢷⢻⠇⠀⠀⠀⣿⢭⢿⡉⢉⡿⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⣿⠀⠀⠀⠀⣿⠲⢾⡽⠋⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⡆⠀⠀⠀⢹⣽⠏⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢳⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡀⠀⠀⢸⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣭⣷⠤⣾⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣤⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠹⣿⣿⣷⣼⣾⣼⣾⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⢀⡀⠱⠜⣾⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⢀⠀⠀⠙⠪⢢⣎⣿⣿⣿⣿⣿⣿⣿⣏⠵⠓
⠀⠀⠀⠀⠀⠀⢤⣿⣩⣴⣷⣿⡷⢄⣿⠅⣀⠇⢽⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣿⣿⣤⣤⡁⢠⣐⢄⣸⣿⣿⣽⣽⣯⡇⠐⣄⠉⠀⣠⡄⢐⡤⠛⠛⠁⡂
⠀⠀⠀⠀⠀⠀⠄⠓⠿⢻⢯⣉⣹⠟⠿⡟⢻⢾⣿⣿⣿⣿⣿⣿⣄⢀⣈⣠⠄⣈⠉⠁⠀⣱⣸⡔⡇
⠀⠀⠀⠀⠀⠰⣤⣤⣀⣀⣾⣿⣿⣿⣄⣉⠘⣽⣿⣿⣿⣾⢻⣿⣿⡉⣍⠉⠉⡉⢩⣾⣺⣴⢿⣻⣶⣷⡀
⠀⠀⠀⠀⠀⢢⣸⣿⣿⡿⣿⣿⣿⡌⣿⣿⣴⣿⣿⣽⣿⣿⣿⣿⣿⣧⢀⣿⣿⣷⣷⣿⢿⣻⣿⣟⣿⢽⣿
⠀⠀⠀⠀⡀⠘⣽⣿⣿⣿⣿⣿⡏⠙⢿⣿⣽⣿⡟⡛⢿⠿⠛⠟⠛⠛⠐⠿⣿⣿⣿⣿⣯⢻⣞⣿⣾⣿⢿⣃⡄
⠀⠀⠀⣌⢱⣼⣾⣿⣿⣿⠿⡿⠛⡠⠿⠿⠿⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠙⠁
⠀⠀⠀⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣦⢲⠆⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠙⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⢄⣀⣓⣠⢂⣘⣀⠂⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠘⢧⡀⠀⠰⠄⠀⠀⠀⢥⠁⡔⠊⢀⠄⠀⠀⠀⠘⣣⡔⠀⠀⣀⢄⡟⠂⣄⠀⠈⠁⠀⢹⡋⠀⠀⡈⠉⠁⠀⢙⡇
⠀⠀⠀⠀⢘⠃⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠖⢀⠞⠁⢀⡄⠊⠀⠀⠀⠀⠀⠠⣡⠜⢧⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣼⠁⣀
⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⢀⠌⠈⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠠⣔⣄⣶⠨⠍⡠⠖⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠐⢤⡆⠀⢧⠀⠂⠀⠀⠄⠀⡅⢤⣥⠔⠚⢀⡠⠆⠀⠀⠀⠙⠠⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⢤⠀⠀⣀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢗⣸⢩⡍⢮⡛⠀⠀⣄⢶⠆⠀⠀⣀⠀⠀⢦⣆⡄⠈
⠀⠀⠀⠀⡶⠚⠁⢃⣀⣀⠀⣀⠀⠀⠘⢡⠾⣼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠷⡉⠀⠀⠀⠀⠁⠀⠀⠀⢊⢱⡆
⠀⠀⠀⠀⠀⠀⡞⠋⢀⡠⠴⠬⢤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⡦⡀
⠀⠀⠀⠀⠀⠀⠻⣶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡄⢐⢰⠀⡄⢀⠇⠀⠂⢰⠀⠰⣀⠂⡦⢀⠀⠀⠀⠀⠀⠘⢼⣁⠄⡓⣧⢂
⠀⠀⠀⠀⠋⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠳⠁⠬⠸⠄⠇⠨⠤⠀⠀⠇⠱⠐⠻⠀⠗⠀⠇⠁⠀⢲⡦⡄⢩⢽⣶⠲⠨⠇⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠠⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠹⢾⣤⡜⠿⢭⠘⣧
⠀⠀⠀⠀⣠⠀⠀⠢⡇⡀⣀⠀⣠⠅⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠎⠃⠀⠀⣄⠀⠀⠀⠀⠘⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠠⠎⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⢠⡄
⠀⠀⠀⢠⠀⡈⠀⠀⠀⢠⡀⢠⠔⠀⠀⠀⢄⠀⠀⠁⠀⠀⠁⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⢻⣿⣧
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠉⠲⠀⠀⠀⠀⠘⠀⣴⡀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠻⡿⢤⠂⠀⢠⣿⣿⠃⢠
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠎⠁⡀⠀⠰⠄⠀⢡⣹⠓⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣦⣟⠁⠀⠀⠂⠀⡜⠀⠀⠀⠀⠾⠋⠐⠀⡀
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠙⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢰⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠂⣆⡀⢀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣟⢽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣰⠭⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⡄⠀⢨⡯⠿⢹⡅⠀⢠⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⢿⣿⡗⣺⣒⡖⢺⣿⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣚⣃⣛⣘⣃⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡈⣿⠥⠽⠤⡧⢼⡟⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⢽⠥⣭⢬⡧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⡒⣛⠒⡓⢺⠃⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⡓⣿⢚⢃⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⣇⣭⣉⡭⡼⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡩⣿⢍⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⣭⣥⡀⠉⣤⢰⡶⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⢢⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠠⠖⠿⢗⠀⠀⡐⠀⠂⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠤⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⡀⠀⠀⠕⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁⠈⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢀⠀⠀⠈⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡸⠄
⠀⠀⠀⠣⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠤⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠟⠃
⠀⠀⠀⢆⠈⠂⠤⣀⠀⠀⠀⠉⠐⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠆⠊⠁
⠀⠀⠀⠀⠑⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢤⠖⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠈⠁⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⣠⡤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⠤⣤⣤⠤⢤⣄⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢌⣣⢄⡄
⠀⢀⣀⣀⠀⠀⠀⠀⣈⠉⢷⣿⣾⣠⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡌⠂
⠀⠠⡦⠤⡼⢢⡀⠀⣭⡱⠚⣿⡗⠦⢋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠹⣃⡁⡊⢱⣄⡦⢬⡋⡹⣯⡑⣁⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢀⠔⠁
⠀⠀⠀⠈⢶⠂⠣⣸⢻⡒⠪⡠⢾⣄⢣⠶⡀⠀⢀⡀⡀⠀⠀⠀⣠⠤⠤⠀⡁
⠀⠀⠀⠀⠈⠻⣉⣙⡼⣉⡒⢄⠤⣆⣃⠄⢟⠂⠁⣀⣀⣈⡜⡜⠁⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠈⠢⠼⣧⢬⣃⣴⣦⣭⡴⣺⣻⣟⡿⣿⢟⡟⣛⠆⣀⡘⣰⡃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠿⡟⣿⢽⣿⡿⣷⡻⣭⣿⣻⣿⣻⣿⣿⣿⣿⣭⠬⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠙⠙⠛⠋⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣠⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠛⠴⠗⢧⢰⣶⣆⣲⢶⠰⠶⢆⠶⠦⠾⠣⠛⠻⠞⢻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⣀⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡈⢁⠹⠇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠙⠐⠐⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⡴⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠪⠀⠀⠀⠀⠀⠁⠀⠀⠑⡄
⠀⠀⠀⠐⠂⠀⠀⠀⠣⢁⢀⡂⢀⡄⡤⠤⠆⠒⠐⠃⠊⠐⠒⠃⠓⠒⠴⠤⢤⢄⠀⠀⠀⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈

⡂⠙⠿⠧⠤⠀⠤⢠⣀⢹⠇⢀⠡⠀⡈⠑⠀⠐⠀⢀⠈⠱⣧⠀⠄
⠀⠔⢤⠀⠜⠳⡄⠈⣿⠢⠂⠈⠑⠁⣄⠀⠀⠀⠀⠉⢄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸⣧⣨⢤⠐⠊⠙⣆⢫⡴⢂⡀⠀⡀⠈⢿⡇⠀⠀⠀⠀⠠
⠨⠋⠀⢸⡇⡐⢾⡟⠀⠀⠀⡉⠢⣌⡐⠊⠁
⠀⠀⠀⠘⠃⠘⠀⠈⠀⠀⠀⠀⠀⣿⡇⠂⠀⠀⠀⠌
⠀⠐⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠠⣠⡾⠿⡚⢿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡄⢴⡆⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⠀⠘⡏⠀⢰⣿⠂⠀⣛⣿⠀⢀⣿
⠀⢸⡇⣤⡄⢽⠀⠀⣾⡿⢿⣇⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢐⠀⠀⠚⡟⠒⡟⢫⡟⣤⠊⣏⡄⢀⣀⣀
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠁⠈⠁⠀⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠀⠁⢘⣿⣿⣿⣧⠈⠉⠉⠉
⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⢄⡢⣀⢄⡠⣀⣁⣰⠦⠴⠒⠛⠋⡸⠀⠀⠀⠀⠁⠀⡇⢸⡇⣿⢸
⠭⣓⡪⢭⣒⠦⢄⡀⠀⠀⠀⠀⠀⠀⢈⣳⡽⠶⠓⠋⠉⠀⠀⠀⠀⠠⠘⠁⢡⡀⠀⠀⠀⠀⠀⡇⢸⢠⡇⣿⠄⡄⡠
⠭⣒⡫⢵⣒⠭⣓⡪⠅⣂⣠⠴⠒⠋⠉⠀⠀⠀⠀⠒⢷⣆⠀⠀⠠⡤⠀⠁⠠⡿⠀⠀⠀⠀⠀⠁⣉⣿⠋⠙⣘⠟⠣⢀
⣯⢕⣚⡭⢖⣫⠵⠒⠋⠅⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠋⢉⠿⡀⢠⡿⢡⡀
⢞⣫⠵⠚⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠐⠞⠃⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠃
⣿⣷⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣿⣛⣻⡿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⣭⠈⣽⠀⢸⡥⠨⣮⢹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⡦⠠⡼⠀⠘⣗⠀⣻⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⡝⢹⠧⠠⣞⠃⠙⣧⠀⣽⡋⣧⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠲⠇⢰⠆⠠⠞⠁⠘⡧⠀⢴⠆⠲⠺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢺⠆⠲⣄⣀⡜⠃⠚⢇⡀⣴⠂⠸⠇⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠻⠦⢄⠀⠀⠱⠆⠰⠄⠀⠀⠦⠴⠛⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣠⣀⡈⠁⠈⢣⡀⢠⠎⠁⠙⣄⢠⡌⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠲⣇⠀⠘⠖⠒⢆⡀⢀⡶⠂⠲⡀⢀⡽⠚⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣿⣷⢤⡏⠉⢳⣄⣠⡌⠉⠉⣡⣄⣤⠋⠉⢳⡤⣿⡇⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⣛⣛⣛⠛⠿⣿⣿⣇⢀⠷⠲⢮⠀⠀⡸⠒⠒⢃⠀⢀⠗⠒⠿⣀⣼⣿⡿⠟⢛⣛⣛⣛⠛⠿⢿⣶⣦⣄
⠀⠀⠀⠀⣠⣾⠿⢋⣥⠶⠚⢩⣭⣭⣭⣍⡓⢦⣹⡏⢉⣄⣀⣜⠉⠉⢡⠤⢤⡎⠉⠙⣤⠄⣴⠉⢹⣯⠴⢚⣩⣭⣭⣭⡍⠓⠦⣌⡛⢿⣷⣄
⠀⠀⠀⣼⡿⠡⠖⢛⣋⣛⡛⠲⢬⣙⢿⣿⣿⣶⣽⠗⠚⡀⠀⠘⠒⠒⢆⣀⣀⠐⠂⠚⣀⠀⣈⠓⢻⣧⣾⣿⣿⠟⣫⡴⠖⣛⣋⣛⡛⠢⠙⢿⣷⡀
⠀⠀⣼⣿⣴⡾⠿⠟⣻⣿⣿⣿⣦⣍⢳⡝⢿⣿⣿⡆⢼⠉⠈⢹⡤⠤⡌⠀⠈⣠⠤⢴⠉⠀⠙⠤⢼⣿⣿⡟⣡⠞⣡⣶⣿⣿⣿⡛⠿⠿⣶⣤⣿⣧
⠀⠸⠟⠋⠀⠀⣰⣾⠟⣋⡭⠤⠤⣍⡀⠹⡎⢿⣿⣀⣰⠗⠒⢷⣀⣀⡘⠋⠙⢃⣀⣀⠛⠐⠻⣀⣠⣿⡟⣴⠃⣈⣭⠤⢬⣍⡙⠿⣷⣄⠀⠙⠻⣿
⠀⠀⠀⠀⢀⣾⡟⢡⠞⣡⠖⣛⣓⠶⣍⡳⣄⠘⣿⠁⢉⣤⣤⣜⠁⠈⠱⠦⠴⠋⠁⠉⡦⠤⣴⠁⢈⡿⢁⡴⢚⡥⠖⣛⣓⠶⣝⢷⡘⢿⣧⠀⠀⠈
⠀⠀⠀⠀⣼⡟⢠⢏⣾⣥⠤⢭⣍⡛⢮⡙⣮⠳⣌⠛⠛⣀⣀⡘⠓⠘⢃⣀⣀⡞⠓⠛⣄⣀⣀⠛⠛⣡⢏⡴⢋⡴⢛⣭⡭⠤⣼⣧⢳⡈⢿⣇
⠀⠀⠀⢰⣿⠁⡟⢈⡵⠖⣛⡓⢦⡙⣦⠻⣎⢳⡜⢆⠐⠉⠉⢱⠄⠠⠎⠁⠈⠠⠀⠴⠉⠀⠉⢀⡜⢡⢏⣴⢋⡴⣫⠔⣚⣛⠲⣬⠀⣧⠸⣿⡀
⠀⠀⠀⣼⡏⢸⣧⠏⣰⡿⠟⢿⣦⢹⡌⣦⢻⣧⡹⣎⢧⡀⠐⢣⣄⣀⡌⠀⠘⣠⣀⣠⠋⠀⢠⡞⣴⢣⣾⡏⡾⣱⠋⣾⡿⠻⣷⣌⠳⣼⡀⣿⡇
⠀⠀⠀⣿⡇⢸⠏⣼⡿⠁⠀⠘⣿⡇⢷⢸⡌⣿⣷⡘⣆⢳⡀⢮⠀⠀⡱⠆⠶⠁⠀⠈⠶⢠⠏⡼⢡⣿⣿⢸⢇⡏⣸⡿⠀⠀⠘⣿⣆⢻⡇⢻⡇
⠀⠀⠀⣿⡇⡟⣰⡿⠁⠀⠀⠀⢹⣿⢸⡎⣇⢻⣿⣷⡘⣆⢳⡈⠋⠉⢣⣄⣠⠞⠉⠙⢠⠏⡼⢡⣿⣿⡇⣿⢸⢃⣿⡇⠀⠀⠀⠘⣿⡆⠇⢸⡟
⠀⠀⠀⢹⣇⢠⣿⠃⠀⠀⠀⠀⢸⣿⡄⡇⣿⢸⣿⣿⣷⡘⣎⢣⠀⠰⢆⠀⢀⡰⠄⢀⡏⣼⢡⣿⣿⣿⢃⡇⣿⢸⣿⠀⠀⠀⠀⠀⢹⣿⠀⣿⡇
⠀⠀⠀⠘⣿⣾⡟⠀⠀⠀⠀⠀⠀⣿⡇⣿⢸⡘⣿⣿⣿⣷⠹⡌⣧⠀⡌⠉⠉⢡⠀⡾⣸⢃⣿⣿⣿⣿⢸⡇⡇⣸⣿⠀⠀⠀⠀⠀⠀⣿⣶⡿⠁
⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⣿⣇⢸⢸⡇⣿⣿⣿⣿⣇⢻⡘⡆⠐⠒⠒⠀⣸⢡⠇⣾⣿⣿⣿⡿⢸⢹⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⡎⡇⢿⣿⣿⣿⣿⡎⣧⢹⠀⠤⠤⢠⠇⡞⣸⣿⣿⣿⣿⡇⣿⢸⠁⣿⡇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⡇⣿⢸⣿⣿⣿⣿⣷⠸⡄⣇⠀⠀⡞⢸⢁⣿⣿⣿⣿⣿⠇⡟⣾⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢿⢹⡌⣿⣿⣿⣿⣿⡇⣧⢹⡀⢰⠇⡏⣼⣿⣿⣿⣿⣿⢸⢇⡏⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠸⡎⣧⢻⣿⣿⣿⣿⣷⢸⡌⡇⣼⢸⢃⣿⣿⣿⣿⣿⠇⡾⣸⢃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢻⡜⣧⠻⣿⣿⣿⣿⡈⡇⣷⡇⣼⢸⣿⣿⣿⣿⢏⡼⣱⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡙⣎⠳⣌⡻⢿⣿⡇⠷⠾⠶⠇⣸⣿⡿⢛⡵⢟⡴⢃⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⡛⢮⣝⡳⠮⣭⡘⣿⡟⢣⡭⠶⢚⣩⠴⢋⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣬⣉⢻⠠⣇⣙⣃⣼⢰⠋⣩⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡘⠷⠬⠭⠭⠥⠞⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣶⣶⣶⡾⠟⠋

⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣿⣿⡿⠛⣿⣿⠛⠛⢷⠶⠶⠶⢦⣤⣀⡀
⠀⠀⣠⡶⠻⠉⠈⠀⠀⠠⠆⠁⠀⡀⣀⠉⠀⠀⡀⣿⠿⠓⠒⠶⠤⠉⠛⠷⣦⣀
⠀⣸⠟⠀⠪⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠀⠠⠨⠀⠀⢀⣤⡴⠶⠛⢛⡛⠛⠛⠛⠿⢶⣄
⠀⣿⡌⠀⠀⡁⡜⡍⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡩⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠠⠙⣧
⠀⢻⣷⣾⡆⣠⢰⢸⢰⢾⡜⡎⢀⢀⢬⠡⠠⣸⡏⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⠟⠿⢿⣿⣾⣿⣿⣿⣿⣧⣿⣾⣀⠸⣿⡇⠀⠀⠀⠀⠅⠀⠁⠀⣀⣀⣀⣀⡀⠀⣾⠃
⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣶⣿⠿⢛⡉⠉⠉⠙⠻⣄
⠀⠀⣸⠇⠂⠀⠀⠀⠀⠐⠀⠄⠐⠂⠦⠄⡈⠉⠙⢷⡰⡠⢠⣿⣿⠟⠁⠀⠀⠁⠀⠀⢀⣠⣽⡷⠟⢛⡉⠉⠩⠛⠳⣄
⠀⢀⣿⢀⡀⠰⠀⠃⠰⠀⠐⠀⠄⠀⠀⠀⠀⡄⠀⢨⣷⠀⣼⠿⡇⡄⠠⠀⠀⠀⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢂⠀⢸⡇
⠀⢼⣯⣼⡗⣆⢀⢀⠈⢡⠀⠀⠀⠀⠀⠀⢰⢀⡖⢾⢹⠀⢸⡆⢡⡱⠀⠀⠀⠀⣾⢻⡇⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠿⢿⣿⣿⣿⣷⣼⣰⡄⣴⡇⣀⠀⢸⢨⢻⣿⣿⠀⠀⠻⣿⣿⣶⣤⡐⠀⢿⡸⡄⠄⠠⠀⢀⠀⠀⠀⠀⠈⠐⠘⣇
⠀⠀⠀⠈⠉⠉⠛⢿⣟⣿⣿⣧⣿⣧⣿⣷⣧⣾⣿⣿⣯⠀⠀⠀⠈⠻⡏⠙⡇⠀⡈⠻⢿⣦⣄⡀⠀⠀⣀⠀⠁⠒⠂⢀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠩⠭⠭⠭⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⣀⣠⣿⣦⣵⢣⡀⠀⠀⢻⠛⢻⠀⠀⠒⠃⠀⠀⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠲⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣝⣂⣀⣸⣷⣼⣇⢀⠀⠀⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣛⣻⡟⠛⠛⠛⠛⠛⢻⣿⣿⣦⣓⡀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠀⠀⠀⠶⠰⠒⠆⠐⠐⠂⠐⠐⠰⠀⠀⠂⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢉⣉⣉⣉⣉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠖⠉⠈⣠⢀⣠⠨⠝⠑⢢⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⢾⠀⠘⠢⠄⠀⠀⠀⠀⠀⠠⠤⠊⠀⢸⠶⠦⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⢲⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠚⠒⠛⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢣⢳⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣅⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⢢⠣⣀⠿⡂⠀⠀⠄⡰⠀⠀⡀⠎⠀⠀⠁⠀⠀⠀⠚⡄⢸⢀⠆
⠀⠀⠀⠀⠀⠀⠐⢢⡓⠏⠒⠀⣈⠁⠟⠉⠁⠉⠢⠀⠀⣀⠆⠐⠐⠂⠕⠲⢎⠑⠤
⠀⠀⠀⠀⠀⢐⠤⠒⠒⠒⡲⣤⢂⣿⣀⠀⠀⠀⠀⡁⢀⠁⠀⠀⠀⠀⢸⣀⢢⠄⣠⢣⡄
⠀⠀⠀⠀⡔⠁⠀⠊⠀⢀⠀⠉⠉⠉⠀⢌⢑⡴⠉⠀⡠⠛⠉⠀⠑⣎⠁⠀⠈⠺⢉⡔⠉⠧⢲⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⠄
⠀⠀⠀⠀⠁⠌⠀⠀⢀⠁⠀⠀⠀⠁⠀⢰⠁⠀⢠⠈⠐⠆⠀⠀⠁⣀⡍⢂⡠⠊⠁⠹⢄⠤⣜⣉⠠⠤⢐⡀⠨⠅⠒⢀⣉⠀⠀⡀
⠀⠀⠀⢀⣦⡀⠀⢀⣨⢀⠀⠀⣀⣠⠀⣀⣦⡀⠀⠀⢠⣴⢀⣩⣬⡴⢃⣨⡅⠀⢠⠇⣊⠥⠴⢖⣚⢊⡀⠨⠭⠀⠁⠐⠒⠀⠉
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠄⠀⠲⡖⠀⠈⠁
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠠⠄⠈⠡⠤⠀⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰
⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠁⠐⠒⠒⠘⠋⠉⠁⠒⡚
⠀⠀⠀⠀⠀⠀⢀⡾⢻⣍⠹⣇⠀⢀⠀⣀⠀⠠⠤⠠⠀⠀⠒⠂⠀⠀⠀⢩⢸
⠀⠀⠀⠀⠀⠀⠘⣯⡈⡛⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⢚⠛⡦
⠀⠀⠀⠀⠀⠀⠎⠉⠉⠙⠢⢄⣀⣀⣀⣀⠀⠀⠀⠀⢀⠤⠚⠉⠐⠄⠠⠀⢀⡎
⠀⠀⠀⠀⢀⡴⠀⠀⠀⣠⡇⠀⠃⠱⠀⠈⢧⠀⡠⠚⠉⠐⠈⠀⡄⠁⠀⢀⡞
⠀⠀⠀⠀⠏⢀⣠⠞⠉⢩⠃⠀⠀⠀⠀⢀⠼⠋⠀⠀⡀⠀⠑⠊⠀⠀⣐⣏⡠⠤⠒⠊⠙⠦⠒⠒⢄
⠀⠀⠀⢰⡴⠁⠀⠀⢠⠃⠀⠀⠀⢀⡴⠋⡀⢀⠨⠀⠤⠈⠠⠀⢐⡰⠋⠀⠀⠀⡠⣤⠶⠒⠒⠒⠺⠒⣄
⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⢀⠄⡠⠎⠀⠀⠈⢈⡠⠁⠀⠂⠀⣠⠎⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣆⠜⠁⠀⠀⢀⡐⠂⠀⠀⢀⣠⣜⡡⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠏⠀⠀⠀⠠⠂⠀⢀⣠⠴⠚⠉⠁⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⢠⠋⠀⡏⠠⠀⠀⠀⣀⡤⠚⠋⣁⣀⣀⣠⣴⣞⣉⡤⠤⠤⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡌⠀⢸⠃⠀⣠⢴⣊⠥⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠒⠒⢒⠦⠴⢄
⠀⠀⠀⢀⣀⣴⣡⣆⣧⡤⠞⢋⣁⣠⠤⠴⠖⠒⠚⠛⠋⠛⠙⠙⠓⠒⠒⠶⠤⠤⠤⠤⠤⢤⣀⣸⠀⣄⣈
⠀⠛⠛⠻⠲⠶⡦⠤⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⣠⠖⠒⠛⠉
⠀⠀⠀⠀⠀⠀⢊⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠤⠒⠋⠁⢀⣀⠴⠚⠁
⠀⠀⠀⢈⣤⣤⡵⠊⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠋⠉⢁⣀⣠⠤⠖⠊⠉
⠀⠀⠀⠀⢀⡤⢭⡹⠋⣠⠤⠖⠛⠓⠒⠒⠒⠶⠶⠖⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⢰⣄⠀⠀⢀⣴⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⡀⠀⣾
⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⣿⡀⠀⣸⣿⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⢸⣧⠀⠀⠀⠀⣰⠁⠀⠈⢳⣄⠀⠀⣿⣠⣿
⠀⠀⠀⢼⣯⠀⠀⠀⠀⠀⠈⣿⡅⠀⣿⡏⠀⠀⢸⣄⠀⠀⢻⣷⡄⠀⢸⣿⠀⠀⠀⠰⠃⠀⠀⠀⢲⣽⣆⢹⣿⣿⡏⣠⠆
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣇⣰⣿⠃⠀⠀⠘⣿⣦⡀⠀⢻⣿⣄⣼⣿⡇⠀⣴⠀⠀⠀⠀⠀⠀⠻⣿⡯⣿⣿⢧⡏
⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠻⡏⢹⠛⠀⠀⠀⠀⠈⢿⣿⣷⣤⡿⣿⡟⡟⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⡎⡾⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠃⠀⠃⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡏⠡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠸⣷⢠⣤⡄⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢰⣦⣄⠀⣶⣴⣆⣰⣷⠀⣤⣾⡆⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⠿⣿⣿⣿⣿⡿⣿⢿⣻⡟⡯⣿⣿⣛⣿⣿⣻⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣻⣿⠿⡿⣿⡻⢟⡟⣪⣿⣿⣿⣿⣾⣟⣇⣷⣟⣶⣾⢾⣿⡿⢻⣿⣯⠿⣾⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠿⠿⠛⠋⠋⠙⠳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣟⣯⠵⠛⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣽⣶⣔⡦⢴⣶⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣷⣦⠔⠒⢶⠖⣍⠉⠙⢤⠀⢜⣿⣿⣌⠟⠛⠻⣿⣿⣿⣿⣿⡿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢹⡏⠀⠀⠀⢺⣿⡒⠋⠊⠀⠙⠋⣵⠉⠀⠀⢸⣿⡇⡄⢀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡦⠄⠀⣈⢣⠀⠀⠀⣿⣿⠃⠀⣀⣤⣿⡇⣿⡇⠀⠀⣸⣿⠇⢻⣿⣿⣿⠿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⡇⠀⠧⠀⠁⠛⠉⠙⡍⠉⠉⢩⠉⠉⣹⡟⠁⣴⡆⠈⡧⢸⣸⣿⣿⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣖⠚⠀⠀⠀⠀⠀⠇⠀⠀⠼⠀⣠⣿⣷⣶⣿⣷⣾⠻⢉⠸⠿⠯⠀⠚⠋⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠷⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣫⣉⠛⢛⡟⠛⠛⠛⠤⠀⣀⠀⠀⠈⣧⠀⠀⠻⣦⠘⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄⠀⠀⠀⠀⣏⠀⠀⡿⠋⠉⠀⠀⠈⠳⡐⠀⠀⠀⠀⣈⢁⠀⠀⢼⣧⠀⠀⢻⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠙⣦⡀⠈⢷⡗⠀⢸⣿⡆⠀⠘⣿⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣂⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠄⠀⠀⠀⣿⡄⠀⠘⣿⣆⠈⣿⡄⠸⣿⣷⠀⠀⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠛⠀⠀⠀⠀⠒⢿⠀⠀⠀⢀⡶⠀⠀⠀⢸⣿⡀⠀⢻⣿⡀⢸⡇⠐⣿⣿⠀⠀⣿⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡶⠤⠀⢀⠀⠀⠀⠸⡄⠀⠀⠈⣧⠀⠀⠀⠸⣿⡇⠀⠸⣿⡇⢸⠃⠀⢸⣿⠀⠀⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⡀⠀⠀⢻⠀⠀⠀⠀⣽⡇⠀⠀⣿⠇⡜⠀⠀⢸⡟⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⣇⠀⠀⠀⢸⡇⠀⠀⠿⠋⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠘⠓⠀⠁


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

⠀⠀⠀⣠⡤⠴⠖⠲⠛⠛⡻⠛⡛⠲⠶⢶⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⣤⣀⡀
⠀⣠⠚⡩⠀⠀⠀⢀⠀⡀⠄⠁⠀⠀⠀⠀⠰⠀⡉⠙⢷⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠈⠩⠛⠲⣄⡀
⡜⠁⠀⠈⠀⠀⢐⡈⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠙⣆
⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢘⡀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡞⠁⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠉⠳⣄⣸⠀⠀⠀⠀⠂⠀⠀⣀⣀⣤⡤⠴⠖⠚⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣀⣀⠈⠁⠀⠀⠈⢀⡠⠔⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⠀⠀⠀⠠⢀⠀⠀⠐⠲⠤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠒⢄⠀⠀⠉⠂⢀⠀⠀⠀⠉⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠑⢄⠀⠀⠀⠀⠲⡄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠢⡀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠘⡆⠠⢀⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢃⠀⠰⠀⡠⠧⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⣰⠃⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⣁⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⠀⣀⣀⣤⠴⠚⢋⡉⠥⠖⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠭⠥⠔⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⡄⠀⠀⢀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣶⢀⡆⣾⣟⠀⠀⠀⠀⠀⣀⢐⣆⡀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⣼⡿⢀⣤⡀⢀⡿⢁⣤⡄⠀⢀⣶⣿⠇⠏⣎⣅⢿⣧⣇⣰⡖⣰⠞⡎⠨⠉⡁⠀⠈⡟⢠⡄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣴⢠⡴⡲⣾⢰⢃⣿⣴⣧⡵⠿⣬⡼⠾⠛⠁⠀⠾⠋⢿⣶⠞⠉⠈⠃⠈⠈⠉⠉⠛⠻⠛⠶⡾⠃⠀⢧⣇⣿⢃⡴⣰⠄⣠⣄⠀⡮⣿⠄
⠀⠀⣼⣏⣾⡷⢁⣼⠋⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠾⠛⠛⠛⠿⣬⣦⣷⠙⢀⡀
⣀⣀⣈⣛⣋⣻⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣿⣁⣀⣀⣀
⣿⣿⡟⠉⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡤⠶⠒⠛⠋⠻⠟⠛⠛⠒⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⣀⣀
⢀⠞⠡⡆⠀⢀⡠⠠⠀⠈⠀⠀⠀⠀⠐⠠⠈⠹⠗⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠋⠙⠦⣄
⡄⠀⠀⠀⠀⠐⠂⠀⠠⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠈⢧⡀
⠘⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢠⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⡼⠁⠀⠀⢀⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡇
⠀⠀⠙⢦⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠙⠳⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠈⠳⢧⢀⠤⠤⠤⠤⠔⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⠀⠀⠐⠀⠀⠀⢀⣠⠴⠳⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠠⠀⠀⠑⢄⠀⠀⠀⠑⡄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠀⠀⠈⠆⠀⠀⠀⣸⡀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⢀⠠⠐⠀⢡⠆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠛⣁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⣤⣀⣠⠤⠖⢛⡉⠥⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⡄⣀⢰⣿⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⢀⣠⣿⡏⣀⢀⢂⡿⢡⣄⠀⡀⣤⣶⠾⢣⣏⣸⣏⣇⣰⡄⡴⢮⢃⠛⡃⠀⢿⣇⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢠⡆⣤⣦⠾⣸⢹⣯⣿⡭⠿⢼⠶⠛⠋⠀⠺⠋⢿⡶⠋⠉⠉⠈⠉⠉⠉⠛⠛⠣⠾⠃⠀⢮⣹⣏⣄⣰⠄⣠⡄⢀⢻⡇
⠀⠀⣿⣼⣽⣁⡶⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⠳⠾⠾⣼⣁⡄
⣶⣶⣶⣷⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⣸⣹⠇⠀⠀⠀⠀⠀⢀⣴⡧⠁⠸⣿⣎⠈⣿⡟⣧⠘⣷⡿⣶⣞⠀⠁⡚⣸⢻⣿⣿⣿⣿⡟
⠀⠀⠀⢀⠀⣠⣤⣤⠹⣿⣼⣿⣦⣰⣾⣶⣿⠂⠀⠀⠀⢻⣿⣷⠘⠏⣿⡎⣿⡇⠈⠛⢅⣿⡇⡿⣿⢿⣿⣿⡿⢦⢀⡀⠀⡀⣨
⠀⢀⣠⣾⢼⣿⣿⣿⠑⠜⢿⣿⣻⡙⢻⣿⠎⠂⠀⠀⠀⢸⠘⣿⣧⣤⢻⡷⣿⠂⠀⠀⢠⣿⢫⢷⣿⣿⣿⣿⠁⠀⢻⣷⡿⣫⠟
⣀⢀⢙⣽⣼⣿⣿⣿⡧⢀⣜⣿⡯⢿⣧⡈⠲⣤⣿⣆⠀⠘⣇⠘⢿⣿⢸⣟⣿⠀⠀⢀⠟⣿⣾⣺⡏⣿⣿⡏⠀⢼⠟⢉⠿⣷⣀
⢻⠟⣛⣩⣿⡿⣿⣿⢿⠀⢿⡾⣿⣌⣿⣷⣄⠈⠛⢿⣆⠀⢻⣤⡈⣿⣿⡇⣿⡇⠀⡼⠀⣿⣿⡟⣸⣿⠟⣒⢷⣇⡲⠁⠀⠀⠑
⣴⢺⠟⠉⠀⣿⢿⣸⡌⠃⠀⠀⠈⠙⣏⣿⣿⣷⡄⠀⠉⢳⡈⣿⣧⡈⣿⡇⣿⡇⣰⠃⢰⣿⡿⣱⣿⣿⣿⣾⣽⣿⣯⣐⣠⣀
⠈⠪⠀⢀⠀⣿⡘⣯⢧⠁⠋⣀⠠⡑⡜⣞⣿⣿⣿⡀⠀⠀⠁⠘⣿⣷⣿⣇⣿⣇⡟⠀⣸⡿⢀⣿⢷⣿⣿⣿⢋⣰⠄⣀⠉⠻⣆
⠀⠀⠀⡜⠀⢸⣷⣿⡏⣧⢰⠸⡌⢧⢱⠘⣼⣿⣿⡇⡄⠀⠀⠀⠘⢿⣿⡿⠹⣿⡇⠀⣽⢣⣿⡟⣹⣿⣿⢏⣾⢇⣾⣿⠀⠀⡼
⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⢘⡀⢫⠉⡌⢧⢹⣞⣿⣧⣿⡒⢠⣶⣶⣤⣿⣿⣿⢿⠇⠀⡟⡼⢏⡸⣿⣿⣏⣼⣏⠌⣿⣿⡀⡰⠁
⠀⠀⠀⠀⠀⠐⠋⣵⣿⣿⣇⢹⡈⡧⠼⡽⣆⢽⡞⣿⣿⣿⣿⡛⠯⠟⢛⣛⡛⠛⠃⠀⢬⣣⣼⣿⣿⣿⣿⡟⡜⠀⡿⠫⢠⠇
⠀⠀⢀⣴⠅⠀⡼⡿⣿⣿⣿⡂⠳⢘⡥⢪⠹⣊⣿⢻⣿⣻⣿⣧⠀⠀⠀⠨⣻⣿⠙⣳⡶⢿⣿⠿⢿⣿⢋⠎⠀⠀⣠⠀⡘
⠀⢰⣯⣿⢀⡾⠀⢻⡍⠟⣿⣷⡈⠄⢻⠄⠣⢰⡸⡿⣿⣟⢿⣿⡆⠀⠀⢈⣿⣿⡀⢺⡏⣾⣿⣷⣷⣵⡁⠀⣠⣾⢯⠀⡇
⠀⢸⣿⡏⣗⡇⠀⠈⣟⡜⠸⣿⣷⢩⠄⣧⠘⡭⢆⢿⢻⣿⣸⣿⣿⡀⠀⠀⣾⣿⡐⡸⣡⣿⣿⡿⠃⠈⢓⣻⣿⣿⣧⢻⠁
⠀⢸⣿⣷⣿⡇⠀⠀⠸⣷⠐⢹⣿⡎⠥⠘⡥⢻⠵⣊⢿⣿⣿⣿⣿⡇⠀⠀⢾⣿⣷⣃⣿⢿⠟⠁⠀⢠⣿⣿⣿⣏⢾⣿⠃
⠀⠐⣿⣿⣿⡇⠀⠀⠀⢹⣷⡀⢿⣷⠩⡏⢷⠈⢧⠵⡊⢿⣿⣿⣿⣿⠀⠀⡬⡿⢛⣫⠔⠁⠀⠀⢀⣾⣿⣿⣿⣟⣾⡏
⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⢻⣧⠸⣿⣇⠽⠄⢏⠉⡧⢒⡨⣿⣿⣿⣿⡇⠀⠈⣱⣿⠇⠀⠀⠀⠀⠜⡟⣱⡿⠭⡎⣼⣧⣴⠃
⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠈⢿⣵⡽⣿⣆⢯⠽⡇⢹⡄⢗⠹⣿⣿⣿⣷⠀⢀⣿⣿⠀⠀⠀⢀⠆⠀⢠⡏⠀⠀⣰⣿⣿⣿⣶⠞
⠀⠀⠀⣿⣿⢹⠀⠀⠀⠀⠀⠀⢻⣾⡝⣷⡌⢧⠸⡀⢧⡘⡏⣫⣿⣿⣿⣇⣰⣿⡇⠀⠀⠀⠂⠀⢔⠎⠀⠀⣴⡟⠁⢈⠞⠁
⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡭⢧⢻⠈⣇⠹⡺⣿⣿⣿⣿⣼⣿⡇⠀⠀⣰⣴⣿⣿⡣⢀⣼⣿⢇⡴⠃
⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣽⣂⢣⣸⡎⢣⣿⣿⣿⣿⣿⣿⠇⠀⣬⣿⣿⣿⣷⣷⣿⣿⣿⡿⠁
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣿⣮⡇⢽⣸⢽⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⡿⠁
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣝⣧⢻⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⠋⡴⠁
⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⠙⢹⠁⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣛⣛⣭⣭⣛⣛⣒⠶⢤⣄⡀⠀⠀⢀⣠⡤⠶⣒⣛⣛⣭⣭⣛⣓⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢭⣓⣚⡭⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠈⢦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⠉⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠈⠈⠀⠘⠀⠀⠀⠘⡇⣷
⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢆⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠀⠀⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠛⠀⣇⠀⠃⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣀⡔⠹⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠉⠛⠋⠉⠀⠀⠈⠙⠛⠉⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⠇⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸
⠀⠀⠀⠀⠀⣀⡤⢶⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡶⢤⣀
⠀⠀⠀⣠⠞⠁⣠⢼⠇⡇⠀⠀⠠⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡧⣄⠈⠳⣄
⠀⠀⣼⠁⢀⡞⠁⢸⢰⡇⠀⠀⠈⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⡇⠈⢳⡀⠈⣧
⠀⢠⡇⠀⢸⠀⠀⢸⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠀⢸⡄
⠀⠘⡁⠀⠸⢦⡀⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇⢀⡴⠃⠀⢈⠃
⢀⡞⠁⠀⠀⠀⢧⣀⣳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣞⣠⡼⠀⠀⠀⠈⢳
⣼⠀⢀⣴⡦⣄⣀⣠⠇⠙⢮⣑⡢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢔⣫⡵⠋⠸⣄⣀⣠⢴⣦⡀
⡇⠀⢸⠇⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⣶⠶⡶⢶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠸⡇
⠙⠲⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠈⠉⠙⠓⠿⠀⡇⢸⠀⠿⠚⠋⠉⠁⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗⢺⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡟
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠿⠿⠿⠿⠿⠿⢿⠿⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠿⢿⡿⠿⢯⡽⠿⠿⠿⠿⠿
⣿⠅⠀⠈⣃⡀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣺⠂⣀⣀⣀⡛⠚⠛⠂
⣿⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠀⠉⠈⡁
⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠇⠀⠠
⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠠⠂⠀⠐⡶⠀⠀⠀⠀⠸⠛⠛⠃
⣿⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⠆⠀⠀⠀⠀⠇⠀⠀⠀⠈⠙⠛⠛⠛
⣿⠀⢈⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠄⠀⣠⠔⣯⢗⡿⠔⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠄
⣿⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡆⠀⠀⠀⠈⣰⠻⣡⣾⢫⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀
⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣳⢎⣧⠀⠀⣴⠞⢩⡾⠏⢒⡾⠉⠐⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠤⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⣿⡽⡷⢀⡴⢣⣸⠏⠥⣽⠏⠈⠀⠀⠀⡁⠀⡀
⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣾⡵⢻⡷⡏⣴⡿⢓⣒⡾⠡⣀⣠⡶⢳⣽⣫⡟⠁
⣿⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠣⣼⢿⣟⡟⢣⣷⡟⠥⣭⣟⡵⠞⣩⣴⣿⣛⣲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀
⣿⠀⠐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡏⢢⣟⣹⠋⢣⡿⠗⠲⣶⡟⣩⣶⡿⣋⣐⣶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⢉⠉
⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣻⠃⣿⣟⣉⣩⢿⣥⡿⣛⣓⣲⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⢸⡃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⡆⠰⡅⣷⡯⢾⢶⣭⣤⣤⣿⡟⠓⠶⣤⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣷⢯⣴⣿⠋⣏⣸⠾⠭⣭⡽⠟⠉⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢠⣿⣿⡿⣁⣼⡽⠷⠾⠒⠋⢀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢠⣾⣿⢏⣴⠟⠁⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠄
⣿⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣾⣿⣿⡟⠁⣀⡠⢖⡮⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣶⠯⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠
⣿⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠰⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⡀⠀⢠⡇⠀⢀
⣿⠁⠀⠈⡆⠀⠀⢠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⢡
⣿⡀⠀⠀⠁⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠉⠀⠀⠀⠀⠘
⣿⣄⣤⣤⣀⣀⣐⣿⣇⣄⣀⣀⣀⣤⣤⣤⣤⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣄⣀⣠⣀⣀⣀⣼⣤⣤⣄⣄⣠⣄⣴⣠
⡿⣿⢿⢿⡿⡿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠲⢤⡀
⠀⠀⠀⡌⡀⠝⠲⢍⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣄⣡
⠀⠀⠀⢣⠄⠈⡠⢘⠇⠀⠀⠐⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠤⠜⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠚⠛⠙⠟⠋⠛⠂⡀
⠀⠀⢰⠊⢾⡤⠤⢾⡶⠤⠤⠤⠾⠙⢷⡀⠀⠀⠀⠀⠀⢢⣠⡠⣆⣎⠐⢲⡀⣶⡟⠀⠀⠀⠀⠀⠀⠀⢢⠄⣀⣠⠀⠀⠂⠀⡶⠓
⠀⠀⢣⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⡰⠛⠛⠣⢛⠀⠀⠉⠃⠻⠦⠀⠀⠀⠀⠀⠀⠠⢈⠀⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠞⠚⠒⠴⠧⠶⠤⠐⠲⠒⠚⠊⠀⠀⠀⠀⠀⠀⣱⡖⡐⣀⠀⠀⠀⠲⢶⣤⣖⠀⠀⠀⠀⠀⠀⠾⠯⠀⠀⠀⠀⠀⠀⢀⣀⡰⠶
⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠐⠻⡝⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢨⠁⠈⠁⠀⠀⠀⠈⠉⠀⢹⠃⠀⠀⠀⠀⠳⠤⠤⢦⣀⡄⠠⡤⢀⠄⠰⠴⠆⠀⠀⠀⠀⠓⠤⡤⠒⠀⠢⡄⠀⠈⠀⠀⠖⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢣⠀⠄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠐⠴⠄⡆⠀⡀⠀⠠⠼⠃⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠰⢅⠀⠀⢠⠀⢀⠀⠅
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠘⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠻⣄
⠀⠀⠀⠀⢀⡽⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⣠⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢈⡀⣀⠐⠓⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⣆⣻⡀⠀⢶⢾⣏⣛⡈⠈⠢⠀⠀⠀⠀⠀⠀⠊⠉⠁⠠⢶⠖⠚⠉⠉⠱
⠀⠀⠀⢀⢌⡩⠁⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣀⡀⠀⣀⢀⣀⣀⣴⡄
⠀⠀⢀⡁⠂⠂⢠⡀⠀⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⠆⠀⢠⠀⡄⢀⠀⠄⠀⠀⡀⠀⠒⠀⠀⠀⠀⠈⠑⠄⠈⠀⠉⠋⠙⠻⠉⢄⠀⠘⡀
⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⣄⣄⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠂⠀⠀⠈⣠⠀⡀
⠀⠀⢸⠷⠄⠚⠣⠀⠂⠠⠒⠀⠒⠰⠶⠀⠀⠀⠀⠃⠀⠁⠉⠂⠰⠶⠒⠂⠘⠋⠉⡝⠁⠀⠀⠀⠸⠖⠠⠷⠤⠀⡠⢦⡄⠀⢠⠷⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⠶⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠈⠀⠠⠤⡤⠦⠤⠦⠶⠢⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⢀⡀⣀⣀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡
⠀⢠⡈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠛⠉⠈⠁⠁⡀⠀⠀⠀⢀⣏⠉⠛⠑⠛⠒⠖⠒⠛⠛⠓⠐⢛⣇
⠀⠀⠷⠒⠦⢀⠀⢀⣀⣀⡠⡄⠀⠤⠊⡁⠀⠀⠀⠀⣤⣀⣤⠤⠄⠀⠀⠤⠤⣴⠞⡀⠀⠀⠀⠀⣟⣛⠛⠛⢓⠒⠒⡒⠲⢚⣛⣫⣛⡇
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠘⠁⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠈⠉⠋⠙⠀⠉⠉⢘⠅
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠂⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠊⠀⠁

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣐⣾⣷⡆⢀⠀⠀⠀⠖⢙⡀⠀⠈⠃⠁⠀⡴⠶⠀⠀⠀⢰⠶⠶⣤⠀⣀
⠀⠀⠀⠻⠿⠛⠟⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⢀⣬⣿⣿⣷⣢⡔⠂⠀⠀⣿⣾⡞⢧⡄⠀⣄⠙⠆⠀⠀⠀⠈⢁⡄⠉⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⣚⢄⣹⡇⠸⢄⠀⠀⠀⠀⠀⠀⠀⠴⠇⣰⣋⠀⠀⠀⠀⠀⣿⠋⠀⠰⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⢺⣹⢺⡛⣇⡐⢘⣤⡄⠀⠀⠀⢰⡕⠐⢲⠀⠹⠇⠀⠀⠀⠀⠀⠀⣰⠂⡌⠛⠁
⠀⠀⠀⠈⣛⡦⣀⣤⣄⠙⢿⠛⠙⠀⠀⠀⠀⠈⢕⢺⢯⡝⢩⣽⣿⡃⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⢀⠀⠀⠀⣨⣶⠉⠆
⠀⠀⠀⠹⣿⣷⢾⣿⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⣟⡻⢶⣿⣿⠋⠙⠁⠀⠀⣤⡄⠀⠀⠀⠙⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢸⣿⢾⡋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢫⣼⣿⠉⠛⠀⠀⠀⣠⡶⠿⣷⣶⣄⠀⠀⠀⠀⠤⠀⢰⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠙⠛⠁⠀⢺⣿⢻⠀⠀⠀⠀⠀⠀⠀⠔⢿⠆⠀⠀⠀⠀⣷⣷⠾⣾⣿⣿⠀⠀⠀⠘⠁⣆⣿⠀⠀⠀⠀⠐⠾⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣧⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠲⣴⣿⣟⡷
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⣩⡟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠰⠃
⠀⠀⢠⣿⣻⣿⣿⣿⡆⠀⠀⠀⣰⢾⣿⣧⡀⠀⠰⠟⠀⠛⠀⠀⠀⠀⠀⢀⡤⣤⡀⠉⠇⠀⠀⠀⠀⠋⠀⠀⡀
⠀⠀⠘⠿⢟⢿⣿⣿⠇⠀⠀⠀⡉⠀⠈⠙⢻⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣬⡾⣿⠀⢠⣄⠀⠀⠀⠘⠻⠿⠐⠁⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠛⠻⠛⠋⠀⠀⠀⠸⡿⣄⣀⣤⣼⠇⠀⠀⢀⣠⠐⣀⠀⠀⠀⠻⠅⣠⢸⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣄⡀⠀⠀⢀⣻⡿⠁⢀⣀⢤⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠘⣄⠑⡄⠀⠘⣿⣁⣄⣋⣻⣫⣥⣤⡄⠤⠄⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⡆⠑⠀⠀⠀⠀⠀⣰⠂⢨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣴⡀⡀⢠⠞⡍⢿⣻⣿⡽⣿⣍⡁⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡟⠀⢰⠀⠀⡇⠰⡇⢰⠇⢀⣼⢃⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠞⢲⣇⠐⠰⡉⠫⣚⡀⠻⡇⠦⠀⠀⠀⠀⠀⢱⠀⠀⠀⢃⠀⠀⠀⠀⣃⢰⡇⣶⠀⠾⢁⠈
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠿⢨⡏⢺⡄⢯⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢲⡈⢤⡀⠞⠁⢲⡚⢓⣥⠼⠢⢉⡤⠀⠀⠉⠁⠁⠈
⠀⠙⠆⠀⠀⠶⠤⢤⣄⡀⠀⠀⠀⠀⠘⠀⢐⡆⡦⠀⠀⠠⡆⠀⠈⠇⠀⠀⠀⠀⠀⠘⠛⠂⠤⠶⣾⣧⣸⣇⠴⠀⣿⠁⣿⡙⠃⠀⠀⠀⢀⡤⠀⠉
⠀⠀⠀⠀⠐⠢⠖⣑⣺⣃⡤⢠⡼⡢⡄⣉⣰⠇⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠒⠂⠤⠤⠐⠉⠉⠉⠉⠙⡲⢐⡏⠀⠑⠁⠀⢀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣫⣿⣎⠳⠾⢍⣻⣻⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠾⡟⠁⣈⡉⣁
⠀⠀⠀⠀⣀⣤⠆⠔⢉⡥⢊⠉⠳⣴⡀⠈⢉⡟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢼⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠆⠀⠀⠀⢀⡀⠀⢸
⠀⠀⠀⣀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⣀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁⠐⠂⢸⠀⠀⢠⠀⠁⢠⠖⠁
⠀⠀⠈⠉⣄⠀⠘⠰⣄⠷⣶⢦⡀⣰⣿⢀⣀⣴⣿⡆⣹⣾⠕⠂⢏⠉⠣⣄⠀⠀⠀⠄⠀⠠⠀⠀⠠⠀⡠⠊⠀⢀⠐⠀⠔
⠀⠀⢶⣶⡌⠡⠄⠑⢮⢶⡡⠼⢧⣋⠔⠋⠉⡻⣿⠟⠁⠀⠀⣤⡌⠑⠛⠛⠀⠀⠀⣀⡔⠀⠀⣠⠀⠀⠃⠠⠀⠀⢀⠘⠂⠒⠀⡐⠂⢠⣤⡤⠠
⠀⠀⠀⠉⠁⠀⠀⠸⣧⡎⡅⢀⣾⠉⠒⠢⣴⡿⠟⢴⠐⠲⣄⡸⠷⣦⣄⠀⠀⠀⠀⠀⠘⠳⠊⣁⣀⡀⠆⠀⠦⠀⣁⠀⡀⢀⣈⠄⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢠⣾⠋⠀⠀⢰⠋⠀⠀⠀⠀⠀⠈⠙⠓⠀⠉⠀⠀⡤⠒⠒⡖⠢⠀⡈⠭⠹⢆⠀⠈⠁⠘⡟⠫⣤⣤⡈⠉⠉⠍⢲⡤⢀⡀
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⡆⠿⠹⠀⠠⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⣁⡆⠀⠂⠸⣤⠀⢰⢿⠻⢿⡶⠛⠋⠉⠉⠙⠃
⠀⠀⠀⠀⠈⠀⠀⠐⢦⣀⣁⡈⠷⠆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠠⢃⡀⠘⡆⢥⠂⡈⡄⢃⠈⣿⡕⠐⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠋⣹⣦⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢆⡀⠊⠀⠀⠈⢠⠀⡄⠀⡄⠙⠄⢃⠸⠀⠀⣷⠘⠀⠘⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⠉⠀⠀⠀⠀⠀⠀⠑⢌⠀⠀⠀⠀⠋⣡⠀⠀⠈⠀⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠘⠃⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠠⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠙⡁⠁⠄
⠀⠀⠀⣀⠀⠀⠀⠀⣈⣶⡠⣰⠛
⠀⠀⠀⠈⠠⠔⣀⡀⣉⠻⠡⢣⠄⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡴⠚⠩⣻⡾⣿⡷⠸⣦⡀⠲⠄⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⣈⣶⡟⠁⠀⢀⠊⠡⠴⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⠡⡼⣿⠇⢀⡌⢿⣄⠈⠷⠄⢊⠆
⠀⠀⠀⠀⢨⡉⢂⠀⠀⢸⡆⠉⠀⠀⠀⢀⣡⡀⠄⢤⠖⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠍⡐⠀⡶⢲⢨⡄⠀⡅⠀⠙⣧⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠔⠉⠁⣠⣤⠙⠧⠀⣠⠴⠂⠉⠀⡀⠓⠀⠀⠀⠀⠑⡤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⡶⠀⠀⢳⡧⢻⣇⠸⡇⡀⠀⠸⣇⢸
⠀⠀⠀⠀⠌⢀⡞⠁⠘⢄⡀⠘⢇⠀⠀⠀⠀⠡⠀⠐⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⢾⠇⡬⣿⠘⡃⠁⠀⠀⠈⠻⠄
⠀⠠⠄⣪⠄⢨⡇⠀⠀⠀⢻⡾⠖⠼⠶⠤⠀⠀⠀⠀⠀⠀⠈⠲⠀⠐⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠞⢁⢰⡟⡄⠀⠁
⠀⠀⡰⠃⠐⡛⠀⢠⠀⠀⠀⢸⠁⠐⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠂⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⡘⢻⣇⡇⢸
⠀⠀⠀⡈⠀⠃⠀⠘⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⡾⠏⢣⡀⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠛⠀⠀⠈⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠶⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠴⠶⠾⢻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠒⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠠⠠⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⠂⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠉⠉⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⢰⣤⡤⣄⢀⡀⡄⣀⠀⣤⣤⡤⣄⣠⣀⣤⢶⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠛⠛⠟⠚⠟⠀⠙⠙⠀⠃⠙⠉⠉⠈⡀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠄⠘⢿⣦⠀⠀⠀⢰⡇⢂⠤⣠⣤⡴⠀⠀⠀⣰⡿⠃⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠄⠰⣶⣍⠁⠀⠀⠈⠁⠉⠉⠈⠁⠁⠀⠀⠀⢉⡾⠗⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⢄⣀⣀⣀⠀⠀⠀⠀⠀⠒⠒⠀⢀⣀⣀⡀⠤⠤⠒⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠠⢈⠓⡄⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⠀⢴⠿⣶⡀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⢠⡏⠼⣿⣿⣳⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣿⣿⡆⠁⡽⣤⣼⣽⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠇⣿⣿⠃⢘⠃⢀⣐⣗⣲⠺⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⠘⣿⡏⣤⠈⡃⢸⠁⠭⠽⣯⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢆⠀⠀⠐⣿⠧⠬⢁⡍⢉⣁⣭⣉⣟⣛⡺⣿⡇⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠡⡀⠀⠛⠐⠓⠀⠃⠐⠖⠺⡴⠧⣽⢍⣻⡇⠀⠀⠀⢀⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣄⠀⢘⡃⣘⠁⢐⣋⣉⡿⠲⠷⠶⢾⠀⠀⠀⣠⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⢨⡅⣨⠀⢈⣁⣀⣋⣈⣛⡛⢻⠀⠀⣰⣿⢿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⢠⡀⢴⠀⢠⡅⢨⣏⣉⣉⣉⣛⠀⣰⣿⡏⣼⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡴⠂⠶⠀⠰⡦⢤⣍⣤⣽⣩⣉⣳⣿⣿⠙⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠙⠀⠐⠂⠶⠦⠤⣼⠤⢯⣿⣿⣏⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠀⢚⠂⠒⠃⠐⠾⠖⠦⣿⣿⣿⣆⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣙⣉⣉⣏⣙⣺⣛⣟⣿⣿⣿⣿⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠄⢠⣯⣭⣽⣭⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⢴⠀⠰⡶⠶⢶⠶⡿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⢸⡇⠈⣟⢚⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢸⡇⠠⠧⢤⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢸⡇⢹⡏⣽⣷⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⡇⢸⣃⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣷⢸⣷⡾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣷⣿⡇⢿⠛⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠸⣷⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠉⢛⣓⣲⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⣀⣀⡤⠤⠼⠓⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠖⠋⠁⣀⣠⠤⠖⠒⠋⠉⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠛⢓⣢⣤⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠠⠾⠕⠒⠚⠉⠁⠀⠀⠀⠀⣀⡴⠖⠋⠉⠁⠀⠀⣀⣠⠴⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⢤⣀
⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣀⡠⠴⠒⠊⠉⠁⠀⠀⠀⣀⣤⠤⠖⠒⠒⠛⠛⠛⠒⠒⠮⠷⣄
⠀⠀⠀⠀⠀⢻⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠽⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⣀⣀⣠⠤⠤⠖⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠶⠶⠶⠦⠤⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣀⠤⠀⣠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢶⣇⣔⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣥⣔⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠧⣄⣤⣀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠺⠷⠶⠶⠶⠾⠗⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠒⠊⠁⠠⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢲⠁⣘⠀⠀⣀⣀⣠⡇⢉⣭⡄⠸⡄
⠀⢀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠜⠀⠀⢀⠀⠀⣀⢈⣤⡖⡦⢖⡞⠀⠇⠀⣾⠙⢯⠏⣿⣯⠽⠁⢠⣷
⠀⠈⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⡐⠁⠀⡰⠁⢰⠏⣽⠀⣽⣛⣿⢈⠃⠘⠀⠀⣧⣤⣄⣈⣀⣀⣠⠴⠫⠃
⠀⠀⠀⠀⠈⠐⠀⠂⠠⠂⠄⠀⠠⠂⠒⠀⠀⠀⢰⠁⣰⣏⡓⠯⠿⢼⡿⠐⠁⢠⠂⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⣷⣂⡃⠴⠔⠋⢀⡠⠒⠁
⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⡝⠓⠢⢀⠀⠀⠀⡜⠀⠜⠉⢁⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠠⡤⠆⠀⠀⠠
⠀⡠⠊⠁⠀⠀⠀⠀⠀⢰⡃⠀⠀⠈⠀⢌⢠⠇⡐⠂⠉⠁⠀⠀⠀⠀⠀⠀⡀⢠⣀⡆⠀⠀⠹⠅⠀⠀⠉⠀⠀⠁
⢰⣁⠀⣀⠀⠀⠀⠀⢈⡸⢻⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⠀⠀⠑⠀⠀⠀⠀⡀⠠⠄⠂
⠙⠀⠀⠀⣱⠤⠔⠊⠁⠀⢊⠀⠐⠁⠀⠀⠀⠀⢀⠄⠒⢖⡃⠀⠀⠀⠈⠀⠀⣀
⠰⡄⠀⠀⠉⠉⠁⠲⠀⠀⠀⠀⠀⡀⣀⠆⠀⠙⠽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠁⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡠⢐⣦⡴⠊⠀⡈⣯⠝⠉⠀⢈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢸⠟⠁⠀⢸⠟⠁⠀⠀⢠⣟⠭⠛⠳
⠀⠀⠀⠀⠀⣀⠠⠤⠤⠀⢀⠀⠀⠀⢀⠠⠀⢒⣀⢀⡐⠒⠀⠄⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀
⠀⠀⡠⠔⢁⣄⣈⣉⠙⠻⠦⣹⠀⡔⠁⢰⢚⣋⣸⣁⠋⣛⣻⢦⠈⠂⠈⡓⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠒⡏
⣠⡊⣐⡶⠦⢤⣌⠉⣳⠔⠋⠁⠀⠀⠀⠀⠀⠿⠠⣤⡤⠭⠓⠁⠀⠀⠀⢠⡁⠀⠀⠩⠉⠉⠉⠉⠉⠁⠄⠀⢀⡼
⢇⠶⠶⢶⡏⢢⡴⠊⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⠊⣀⠔⠁⠀⠀⠳⢮⣀⣀⠀⠀⠀⠀⠐⠀⣐⣨⠞⠁

⠀⠙⠿⠀⠀⠰⢠⣄⠹⠀⡀⠀⠈⠁⠀⠀⠀⠀⠁⣷
⢀⡒⠂⠀⠙⣆⠀⡿⠐⠀⠀⠁⠦⣀⡀⠀⠀⠀⠀⠋
⠸⡷⠊⣄⠀⢀⣧⠐⠀⠠⠀⠀⠀⡻⠃
⠈⠀⠀⠯⠀⠈⠁⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢤⠻⠂⢻⣦⠀⢀
⠀⢀⠀⠀⢀⠀⠀⢰⣟⣷⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣼⡇⢀⣬⣲⠀⢸⡇
⠀⠹⠒⡶⠚⠀⠀⢿⠉⠿⠶⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⠀⠨⠱⣏⣴⣰⠄⠤⠤⠶
⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠌⠁⠀⠀⠀⠀⠀⢰⡖⡟⣻
⣞⠴⣑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠑⢮⣪⡵⠵⠚⠚⠉⠉⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢸⠃⡇⡏
⡮⣝⡢⢍⡲⢌⡂⠄⣀⡠⠤⠒⠊⠁⠀⠀⠀⠰⣄⠀⠀⢀⡄⠀⠀⠵⠀⠀⠀⠀⠀⢘⡺⠃⠓⡺⠏
⡭⣗⡯⢕⣪⠵⠒⠩⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠐⠀⢰⠟⣤
⣫⠵⠚⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢩⡄⠀⡄⠈⣀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠁⠀⠀⣠⠆⠀⠠⠄⠀⠈⣄⣀⢀⣤⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠁⠶⠀⣠⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡄⠀⣠⠀⠀⠖⠀⠀⠀⠄⢀⡾⢂⢀⡀⡀⡂⠀⠠⠒⡁⠐⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⠀⠀⡀⠠⠈⢀⡔⠛⡒⠒⠀⠐⠀⠀⠒⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠑⠀⠐⠂⠐⠠⠄⠀⠁⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⠀⠤⣤⠀⣤⡶⢢⡆⢠⣤⢆⡶⠖⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⣸⠅⣠⠞⢣⣴⠀⢩⡖⢀⠆⢩⠇⡟⢹⣯⣴⣶⠀⣲⡏⣉⡛
⠀⠀⠀⠀⠀⠀⠀⡴⢁⣾⣄⣸⠁⣼⣡⡶⢋⣥⣶⡾⠛⠀⠲⣇⢾⣥⠾⢷⡾⠷⣘⢙⠻⡋⣿⠚
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⢏⣹⣿⠋⣹⣏⣠⣴⡌⠿⣷⣶⣉⠛⠛⠻⢿⣻⣧⣜⣽⣻⣟⣿⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠛⠉⠉⠉⠋⠙⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⣄⡁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣠⠌
⠀⠀⠀⠀⠀⠀⢾⡿⠉⡏⠉⡿⠶⢤⣀⠐⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⢤⣤⠤⠾⣿⠏⢻⣆
⠀⠀⠀⠀⠀⢰⣾⠀⠘⡀⠀⠀⠀⠀⠋⠉⡶⠶⠲⠒⠛⠁⠀⠀⠙⠀⠂⠀⠀⠀⠙⠀⠀⠈⢂
⠀⠀⠀⠀⢀⡿⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠘⠁⢀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠠⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡀⢰⡄⣺⠀⡴⠂⠁
⠀⠀⠀⠀⠀⠇⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣷⠰⡆⣹⣣⣾⡛⠻⠆
⠀⠀⠀⠀⠀⠘⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣟⣴⠔⠛⠦⠀⠃⠀⠀⠀⠀⡀⣤⣀⣠
⠀⠀⠀⠀⠀⢰⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⢯⡉⠛⠂⠀⢀⠀⢠⡀⢊⣧⣶⡍⠀⠁
⠀⠀⠀⠀⣠⠟⠷⢦⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠫⠀⠘⡁⢀⣶⣠⣿⣤⣚⢻⣏⣉⡭⠁
⠀⠀⠀⠀⡇⠀⠀⢀⡉⠓⢤⣀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⢀⡴⠁⢈⣠⣤⡞⣿⠋⠋⠰⣶⢾⡽⢷⡏⠑⡧⠀⠸⠇⠠⠖
⠀⠀⠀⠀⠓⠦⠊⠁⠀⠀⠀⠀⠉⠒⠂⠍⢓⡒⠤⠤⢤⣤⠀⠀⢠⡴⠶⠟⢓⣩⠟⢋⡤⠛⠉⠑⠋⠐⠋⣠⣂⣼⡯⠾⢷⠚⠒⢉⠛⠁⠐⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣴⣾⣟⣛⡯⣥⠴⠶⠆⠙⠓⠈⠉⠉⠁⠘⠓⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⣄⠀⠠⠴⠲⡀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠤⢄⣌⡡⠤⠾⠍⠁⠀⠘⠪⢅⠠⣘⡀⠴⠚⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⡀⠀⢀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠑⠀⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠊⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣾⠁⠀⠄⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⡑⢀⢲⣀⣀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡟⠀⠒⢀⠀⢀⡄⡤⠀⡀⢀⡤⠄⢀⣠⢌⠒⢈⠀⡀⠀⠀⠐⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠈⡆⢬⠀⠔⠒⣁⠈⠄⠀⠈⠃⠀⠀⢸⢨⠀⠀⡀⠀⢠⠃⠀⠀⠀⢰⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠆⠡⠀⠀⠂⢑⠆⠢⠤⠤⠈⠢⠤⡀⢐⢂⠤⠒⠼⠠⠀⠐⠜⠀⠸⢥⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠒⠢⠀⡀⠀⠀⠀⠀⢄⠀⠀⠁⡰⠀⢀⠀⠀⠀⠀⠀⠀⠀⡘⣺⡅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠢⠍⢀⠔⠁⠀⠀⠰⡀⠀⠀⠀⠀⢀⣿⣹⠈
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠂⠀⠀⠀⠀⠀⠘⢄⠀⠀⠠⣰⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢎⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠡⠃⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠅⠀⠀⠀⠀⠀⠀⠀⢠⠉⠃⠀⠀⠀⠀⢀⠀⠴⠂⠀⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⡄⠀⡠⠀⢀⠐⠉⠀⠀⠀⣠⠔⠀⠀⠀⠀⢄⠀⠀⢢⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⠲⣄⠀⢆⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠂⠀⠢⠀⠐⠂⠀⠀⠀⡄⢠⠇⠀⡀⠀⠐⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠂⠠⠄⢈⠁⣀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠰⡀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⢠⡉⠉⠉⠉⢀⠀⠀⠀⠀⠸⠄⠀⠀⠀⣺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⣀⠀⢀⠀⠂⠠⠆⠀⠀⠀⠀⠀⠀⠄⠈⠐⠁⢀⠀⠠⠾⠔⠤⠏⠀⠈⠉⠉⠂⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠺⢦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠠⠠⣀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠉⠛⠛⢛⠒⠢⠤⡀⠀⠀⠀⠀⠀⣠⡤⠶⠲⢤⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⣀⣠⣤⣨⡾⠳⠦⣄⠀⣏⢮⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣈⣆⠀⢀⡤⠻⢿⡄⠀⠀⢸⡿⠓⠦⡀
⠀⠀⠀⠀⠀⠀⢿⡦⡊⠁⠀⠉⠟⠛⠀⡀⢀⠸⡆⠸⣷⠇⠀⢠⣴⣟⣗⡆⠀⠀⢨⣽⣿⠋⢀⡾⠆⠀⠀⠃⠀⠀⢸⠀⠀⣠⡿⡄
⠀⠀⠀⠀⠀⠀⠈⣷⡇⠀⠀⡸⢀⠀⠀⠈⠳⣿⠂⠀⢨⠀⠀⠀⠈⠏⠁⠀⠀⠀⠀⣹⠏⠀⣎⠀⣈⡶⠤⠾⠶⠶⠛⠒⠾⢧⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣠⣜⣇⣑⣐⣀⣤⠟⠀⠀⠘⠳⢤⣤⣴⠀⢀⣀⣠⣤⡬⠏⠀⠀⠰⠜⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣴⣾⠛⢻⣿⣮⡵⣄
⠀⠀⠀⠀⠀⢀⡤⠤⡤⠀⡶⢤⣤⠖⠒⣶⢶⣶⠶⠋⢉⣩⣟⡲⠚⠉⣹⢒⣳⣶⠾⠉⠓⠒⢆⠀⢠⠓⠒⠉⠉⢻⣿⡟⠉⠙⠇⠀⢷
⠀⠀⠀⠀⠀⣏⡀⠠⠴⠋⠛⠁⠤⠒⠛⠛⠉⠀⠐⠚⠙⠉⡉⢀⣒⢉⡋⢉⡉⠀⢀⠀⣀⢄⡼⠀⠸⡀⠀⠀⠀⠟⠀⠙⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠙⠛⠛⠒⠓⠒⠓⠻⠿⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠒⠶⣤⣤⣀⣤⣤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⢒⡲⠶⠶⠖⢒⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⠤⣤⣀⣀⣀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣎⢀⣷⡦⣰⣯⣄⣀⡴⣮⢬⣉⣀⣀⣀⣱⡄⠀⠀⢀⠤⠂⠉⢡⣫⠟⠋⢁⣴⡫⠿⡋⢀⡴⡿⠟⠋⠁⠢⡀
⠀⠀⠀⠀⠀⠀⣾⢸⡟⠻⣆⠙⠽⢧⡌⠛⠷⣌⣀⠈⠳⢤⡈⠉⠙⢦⠀⢺⣠⠀⠀⠟⠁⠀⠀⣸⡿⠁⠀⠀⠚⠉⠂⠀⠀⡀⠩⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣄⣘⣤⣄⠈⠻⡀⠀⠈⠛⢅⡂⠀⣙⣦⠴⠋⠀⠀⠙⠷⣆⣀⠀⢀⣤⡅⠀⠀⢀⣀⣀⠀⣀⣤⣯⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠓⠒⠚⠑⠒⠛⠚⠉⠉⠉⠁⣀⣀⣀⣀⣠⣤⣀⡈⠉⠉⠙⠛⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⡠⠒⢗⠖⢛⠍⡭⠊⢡⠔⠂⠈⠛⡆⠀⠀⠀⠀⠀⣀⣤⡤⠀⡒⢢⣤⢄⡀
⠀⠀⠀⠀⠀⠀⣰⢇⡴⠊⠛⢄⠙⣆⠀⠀⠀⢀⠎⢰⠫⠊⡠⣣⣿⣴⠞⠁⠀⠀⠁⢠⠃⠀⠀⢀⢔⠟⢛⣽⠛⡄⡦⢠⢘⡦⠙⣆
⠀⠀⠀⠀⠀⠀⡏⣼⢇⣀⡤⠤⠶⢿⡀⠀⠀⣾⢾⡇⣾⠸⡃⡇⠘⣷⠀⠂⠀⠀⠂⠘⠀⠀⣴⠃⡆⢠⡋⣂⡬⢔⡥⠂⢼⡗⠀⢼
⠀⠀⠀⠀⠀⠀⣇⠸⡃⣌⣉⣓⣶⠶⡈⢦⠀⠹⣌⠣⡱⠄⠳⡘⢷⡝⡆⠀⠠⠀⠀⢰⠀⢸⠁⡀⠑⢀⣀⣀⣠⠵⠂⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⢦⢷⣅⠙⠈⠀⠀⢸⠋⢧⠀⠈⠱⡌⣎⢆⠘⡀⠃⡇⠀⠀⠀⢁⡎⠀⠘⣷⡈⠲⣦⣤⣤⣤⣤⡤⢴⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡁⠗⠰⠖⢁⡰⠃⠀⠀⠀⠸⣌⣘⡄⡇⡄⢿⡄⠀⡠⠊⠀⠀⠀⠈⠑⠲⠼⠿⠾⠷⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⡨⣆⡆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡲⢧⣴⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⢡⣐⡂⢂⠐⡄⠀⠀⠚⠋⠙⢤⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢠⣏⡩⠋⣑⠋⡱⢤⡧⢥⠐⡮⣙⠾⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣐⣂⣁⣚⣄⣺⣀⡜⢁⠛⡝⠂⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠴⠋⠩⠼⢉⡼⢋⣹⠓⢛⡲⠦⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠁⠀⠁⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣼⣯⣭⣭⣭⣽⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣚⡉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢃⠰⢤⡐⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣉⠛⣖⣉⠽⢦⡔⠃⣞⢈⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⡆⡩⠔⢁⠿⢤⠚⣉⠴⣥⠔⠃⣈⠒⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠂⡎⢻⣤⠂⢹⠧⣤⠋⣩⢯⡤⠛⣅⢡⣜⣒⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢻⡕⢃⡼⠈⣇⣤⠋⡹⢤⡎⣁⠼⢤⠔⠃⣄⠒⣀⡲⣔⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⢦⡤⠀⠨⠿⠭⠤⠞⣅⣜⣘⣀⡜⢉⣧⣤⢊⡩⠧⡤⠚⣠⠐⢊⣆⠉⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢩⣀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣉⣙⣉⣛⣓⠊⠽⠧⣤⠘⢂⡜⡆⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣄⡙⠢⣠⣀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠯⢔⣀⠈⠁⠐⠻⢴⡀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⣹⢉⣓⡸⠀⡭⢴⢀⣆⠽⢓⡦⠥⠾⠒⠑⠂⠲⠤⣀⠀⠉⠒⠤⠀⠀⠉⠂⢤⣀⣄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⣥⡎⢩⠗⢻⠔⣼⣡⠜⢀⠖⣠⢏⡉⢮⠔⠊⠍⠓⠲⢯⣶⣤⣀⡀⠀⠀⠀⠀⠈⠻⣷⡵⡀
⠀⠀⠀⣀⠠⠀⠀⠀⠠⢱⠠⠴⣀⠋⡻⠰⢧⣴⣁⡜⢉⡝⢺⠅⢺⣥⡞⣁⠖⣰⠯⣔⣋⠞⢙⢪⣟⣿⠶⣕⣤⡀⡠⡈⠻⣷
⠀⠀⠈⠉⠉⠉⠒⠢⢄⡀⠛⡔⡉⡕⠣⠴⡁⣼⠁⡙⢛⠖⢦⣴⣃⣰⢁⡜⢺⠧⣎⢤⡎⡩⠗⡤⠚⣷⡳⠄⠁⠻⣖⢌⢷⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡡⠔⡜⢄⠦⢨⡎⠳⠚⠤⣆⢠⠁⡹⠋⡗⢧⢴⣁⡜⢉⠗⢹⠗⢾⠤⣿⡄⠀⠀⠀⡙⢾⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⣈⣢⠧⣰⠈⣲⢣⡼⣀⡅⢙⡊⣣⣆⣰⣁⣟⣙⡖⣧⢴⣇⣴⠉⣇⢀⠀⠀⠈⢧⣻⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢻⣿⣿⣷⠦⡒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⡒⠦⢄⣠⣸⣿⣧⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠐⣊⠝⡩⠂⣁⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣝⣿⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⣢⡶⠟⠒⠐⠒⠒⠓⠒⠂⠒⠠⢌⣑⠂⠄⠦⣄⡂⢕⡢⢀⠠⡀⠀⠀⠀⠀⠀⢹⠇⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡈⠛⠷⣮⣕⣯⣶⣭⣒⣀⣠⣴⣟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠬⣖⣿⣿⣿⣿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠴⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠁⠀⠊⠀⠀⠤⠀⠀⠀⠀⠐⠀⠾⡀
⠀⠀⠀⠀⣱⠢⠄⠀⠀⠀⠤⡄⠀⠀⠀⠀⠊⠀⠂⠠⠀⠠⠀⠂⠐⡠⠀⠀⣅⡀⠀⢀⡰⠂
⠀⠀⠀⢠⡏⣈⣀⣀⣀⣀⣐⣋⠑⠀⠀⠀⡻⠔⠀⠀⠀⠀⣒⡢⠽⠁⠀⠀⠸⣵⣈⣷⣄⢤⣠⢤⡅
⠀⠀⠀⠑⠛⠠⠤⠀⠐⠊⠉⠀⠀⠀⠀⠈⠒⠤⠄⣀⣀⡀⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⢹⣭⣭⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠠⣀⣀⠀⠀⠀⠈⠉⣀⢢⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⢸⠂⠀⠀⠀⢀⠠⠊⠀⠙⢈⠖⠂⠠
⠀⢀⠀⢤⣀⣀⣉⠉⠁⢀⣀⣠⡴⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⢠⠎⠀⠀⡠⠀⠁⠀⠐⠀⠂⢀⠌⠁⠂
⠀⠀⢀⠀⡩⠉⠉⠉⠉⠉⣉⠔⠁⢀⠀⠀⠘⠙⢦⠀⢀⡠⠚⠁⠀⠀⠑⠑⠀⠀⠀⢀⠀⡰
⠀⠀⠀⠉⣤⠒⠀⡄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⣐⠔
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠘⢧⠜⡀⠀⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⢩⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢷⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡶⠛⠉⠀⠀⠁⣱⣄⣀⠀⠀⠀⠀⢸⠀⠀⣈⡻⢃⢸
⠀⠀⢄⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣝⠆⠀⠀⠀⠃⢠⠐⠘⡋⣋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢦⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠑⡄⢣⡀⠀⠀⠀⠀⣡⣼⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡴⠼⣦⡽⢉⠃⡄⠀⠀⢀⢢⣸⣿⣀⣠⠀⠀⠀⠀⠀⠀⢀⡀⢠⠚
⠀⠀⠀⠀⠀⠀⢀⠀⠐⣍⠶⣾⣿⡟⢉⢀⠀⠀⣸⡋⠻⣿⠏⢹⠀⠀⠀⠀⠀⠀⣨⠁⣦⣬⢤⠔
⠀⠀⠀⠀⠀⠀⠀⡷⢴⣟⣦⣤⣿⣷⡾⢻⢠⠀⢱⠷⣶⣿⣷⠾⡇⠀⠀⠀⢀⢸⠙⣿⣿⣤⡂
⠀⠀⠀⠀⠠⢈⣂⠷⣬⣿⣧⣀⣹⣿⣦⡼⢇⢰⣜⣄⣈⣿⡇⣠⣧⠀⠀⢠⡏⢹⣿⣿⣁⢜⡡
⠀⠀⠀⠀⠀⠀⢑⡤⠾⣿⣿⡉⠛⣿⣿⠀⣬⣇⣸⠉⠻⣿⡿⠋⢹⣰⢠⠛⣷⣾⡿⠉⡩⠃
⠀⠀⠀⠀⢊⣰⠤⣑⡶⢾⣿⡟⠲⢿⣿⡟⠉⣏⣿⠷⣶⣿⣯⡴⠿⡿⣿⣤⣾⠿⠛⡻⠋⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠈⣽⣶⠛⣷⣤⣿⣿⣦⣴⣿⣧⠾⢻⣸⣄⣈⣿⣿⢀⣼⣿⣀⣿⠿⠶⡾⠂⠀⠀⠀⠰⢶⣠⠔⠎
⠀⠀⠀⠀⠀⣠⣼⣿⡏⢳⣴⣾⣄⣈⣻⣿⣠⣾⣿⠉⠻⣿⣿⠛⢉⣿⣿⣧⣤⡮⠀⠀⢠⣇⠟⢷⣼⣧⠴⣃⡒
⠀⠀⠀⠀⠀⠈⣦⣼⣷⡏⢡⣬⣏⠉⠻⣿⡏⢸⠋⠓⠶⢿⡿⠴⣾⣿⣇⣠⡪⠀⠀⣤⡏⠘⣷⣾⠿⠷⣔⡉
⠀⠀⣀⠀⡀⠀⢘⣤⣽⣷⡏⢹⠻⣿⣟⣻⡛⣇⡄⠄⡆⣿⢿⣶⣿⠋⡩⠏⡠⢠⣿⡀⢻⣾⡿⠛⢓⡦
⠀⠀⢀⠼⣥⡖⢀⠱⠤⠾⢟⢟⡛⣿⣿⣭⣟⣿⣛⣢⠿⣿⣶⡿⠛⢛⠗⣇⠷⣇⢘⣿⣿⡛⠙⡳⠍⠂
⠀⠀⠀⠚⢩⢿⣏⣰⠄⠀⠈⣿⣉⣻⣿⣿⣬⣿⣏⣼⣆⣸⣿⠷⢶⡟⡸⢿⣄⣹⣿⣟⠉⣹⠗
⠀⠀⠀⠀⠙⠲⡛⣿⣼⠃⡀⢼⣏⣹⣿⣿⠦⣿⣧⠴⢉⡿⠃⠴⢫⠓⣧⣀⣿⣿⣉⣉⠝⡃
⠀⠀⠀⠀⠀⠀⠙⢍⣹⣾⣁⡮⢻⡬⢿⡿⠲⣿⡧⢶⣿⡇⠀⡞⢻⣤⣼⣿⣯⣀⠬⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠾⠻⣧⡔⢷⠈⡿⠛⣿⠖⡛⢸⠁⠀⠳⣤⣿⡿⣥⣠⠜⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣙⣷⡞⢃⡇⢸⡏⢸⠁⡏⠀⠀⣠⠞⠙⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢜⢛⠹⣧⢸⣧⡇⢸⠁⠀⣴⣁⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⢸⣿⢀⣏⣴⠞⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣸⣏⣼⣿⠏⣀⡤⠶⠒⠚⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠀⠀⢺⣿⣿⣿⣧⠞⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠸⣿⣿⡿⢁⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⢀⡄⡠⣠⢄⠀⡀
⠀⠀⠀⠀⠐⠳⠴⡊⠁⣀⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠲⠿⢿⢾⠾⡷⡷⡾⣾⣾⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠉⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠁⠁⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⣾⡟⠻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣍⣏⡁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⣴⡾⢿⣷⣶⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⣠⣸⣿⣇⣹⣟⠋
⠀⠀⠀⠀⠀⠀⢰⣮⣛⣴⡇⢸⣿⣧⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣘⠿⢃⡄⢰⣿⡏⢙⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣼⣟⠛⣻⣦⠀⠉⠻⠟⠋⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⢶⣿⣇⠙⠿⣿⣿⠟⢁⣠⡤⠤
⠀⠀⠀⠀⠀⠀⣻⣿⣾⣿⣏⠀⠀⠀⣠⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣾⡿⡰⠀⢈⣤⣾⠟⠉
⠀⠀⠀⠀⠀⠀⣿⣧⣠⣾⣿⠀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠉⣻⣷⢁⣴⣿⠟⠁
⠀⠀⠀⣀⣄⡀⠙⠿⠛⠿⢃⣾⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠻⣿⢿⣿⣿⣿⡿⠃
⠀⣤⣾⣿⣿⣿⣦⡀⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣦⡀⠀⣰⣿⡟⠁
⠀⠀⠈⠉⠛⢿⣿⣿⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⢀⣀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⠀⠀⠀⠀⠀⢀⠄⠀⢠⣶⢰⡿⠑⣿⣔⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢲⣿⣏⠼⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⠀⠀⠀⢀⠖⠁⠀⠀⢻⣧⣘⡿⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢿⡿⠒⠹⠿⠷
⠀⠰⣦⣀⣄⠀⠀⠀⠀⠀⣠⠀⠀⣴⠋⠀⢀⡤⠊⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡴⠛⠿⠿⠟
⠀⠀⠐⢷⣟⣷⣄⠀⠀⢰⡯⣶⣾⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣿⣿⠗
⠀⠀⠀⠈⠻⣯⣽⡇⠀⢸⡿⠃⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢻⣄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠐⢶⣤⣄⡀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣀⡀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣤⡤⠐⠒⣒⣶⣤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⡠⣺⠉⣀⠔⡪⢁⡠⢤⣤⣤⣄⣀⣀⡒⠋⢉⣉⠤⠬⢭⣶⠤⣀
⠀⠀⠀⠀⡀⣼⢃⠞⡱⠊⡔⠁⠼⡳⠄⢒⣒⣒⣚⣛⡳⠦⣄⣐⠀⠀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⢇⠀⠁⠊⠀⢸⠀⠀⠤⠒⠉⠁⠀⠀⢀⡠⠤⠤⠤⠬⠍⣒⣤⣀⠀⠀⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠸⠀⠀⠀⠀⠤⠶⠤⠤⠒⠒⠉⢉⣉⣉⠀⠠⢀⣈⡑⠦⡁
⠀⠀⠀⠀⢀⠤⢀⠔⠀⠐⠢⣀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⠤⠒⠒⠉⠉⠉⠛⠋⠺⠶⣄
⠀⠀⠀⠀⠇⢠⡁⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠈⠁⠀⠀⠀⢀⡠⠤⠀⠀⢈⣉⣁⣒⠢⢬⡳⡄
⠀⠀⠀⠀⢗⡸⣈⠑⠢⣄⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠘⠋⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠚⢆
⠀⠀⠀⠀⠀⠑⢨⡛⠓⠺⣗⠤⠤⠤⠤⣔⡇⠠⢄⡀⠀⠀⠀⠀⠀⠀⠶⠶⢀⣀⣈⣉⡁⠒⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⣟⠿⠿⢭⣴⠞⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠔⠒⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⡄⢠⡀
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⣅⠀⡇
⠀⠀⠀⠀⠰⡈⠸⢰⠰⠀⠀⠐⠈⠀⠈⢰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⡆⠋
⠀⠀⠀⠀⡆⡁⠀⠈⠀⠀⠀⡀⡇⡇⠀⠀⠀⢸⠨⠜⢸⢸⠀⠀⠀⠀⠀⠀⠀⢿⣮⠉⣴⡾
⠀⠀⠀⠀⡇⡅⡀⠀⠀⠀⠀⡇⠀⡁⠀⡇⠀⢸⠀⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⣮⡛⠘⢛⣁
⠀⠀⠀⠀⡇⢐⣻⠂⡀⠀⠀⡇⢸⣿⠀⡇⠀⢰⣦⡛⣣⣶⠀⠀⠀⠀⠀⠀⢀⠻⠷⢰⠿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⡻⣽⣩⡾⠇⠀⠀⠻⣾⣹⡾⠃⠀⢰⣝⠃⢛⣥⠀⠀⠀⠀⠀⠀⢸⣷⡄⣴⣾⠃⢀⠀⡇⣇⣆
⠀⠀⠀⠀⠻⣵⣨⣾⠇⠀⠀⠻⣾⢠⡾⠃⠀⢨⣛⠇⢿⣫⠀⠀⠀⠀⠀⠀⠀⠉⡁⠋⠁⠀⢸⠸⢳⢹⢸
⠀⠀⠀⠀⠻⣶⢠⣮⠇⠀⠀⠻⣮⢡⣾⠃⠀⢈⡻⠇⠾⢟⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠊⣴⡆⠟⡎
⠀⠀⠀⠀⢻⣪⢨⣶⠇⠀⠀⢻⣮⢩⣶⠇⠀⢘⢿⡆⣾⣟⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⢼⣢⠾⣃⡈
⠀⠀⠀⠀⢻⣪⢉⣷⠇⠀⠀⢷⣮⢩⣶⠇⠀⠸⣿⡄⣴⡿⠀⠀⠀⢀⣠⠞⠁⠀⠀⢀⣸⣫⠃⡚⡚⠁
⠀⠀⠀⠀⠀⠙⡿⠁⠀⠀⠀⠀⠙⡟⠁⠀⠀⠀⠈⢻⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡸⣵⢉⢿⡚⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⣉⢟⡋⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢹⣆⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣤⠴⠖⠋⠀⠀⠀⠀⠀⢠⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡲⢿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇
⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⠨⣯⣷⣟⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢸⣒⡿⣷⣺
⠀⠀⠀⠀⠀⠀⠀⡙⣳⢟⣶⣄⣔⣲⡟⣿⡇⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⣖⣾⣇⡆⠀⢸⣟⡟⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⡿⢟⣾⢿⣯⣁⣙⣦⣴⣋⣀⣀⣤⠀⠀⠀⠀⣯⣯⣯⡇⠀⢸⣻⡟⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣩⡵⣟⣡⠴⠛⠁⠈⠙⠦⣄⡀⠀⠀⠀⠀⠓⢷⡷⠃⠀⠀⠉⢻⠏⠁
⠀⠀⠀⠀⠀⠴⠾⢿⡿⣿⢿⢚⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠋⠚⠙⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠠⡌⢸⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠕⢧⡖⠁⠀⠀⠀⠀⠀⠀⠀⣠⣔⠂⠉⣉⣁⣠⣈⡙⠲⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⡀⠀⠀⠀⠛⠀⠒⠒⠒⠒⡰⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⢻⣆⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⡿⣿⣿⣿⣿⣿⣿⠛⠻⠛⢘⠿⢿⢦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠁⠀⠀⠀⠀⠀⠀⡘⠁⢠⣿⣿⠁⠐⠛⠻⢿⡇⠀⠀⠀⠀⠀⣘⡀⠈⠋⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣿⣿⣧⡥⠤⢄⠀⢡⠀⠀⢀⣀⠠⡈⠓⠀⢑⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⢰⡎⣠⠿⠏⠀⢀⠀⡀⢀⣃⣀⠧⣤⡅⡯⡤⢷⡀⠰⣌⢊⢢⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡇⠀⠀⠀⢸⠎⠀⠀⠀⠈⢀⠀⠀⡆⠹⠐⠳⠄⠀⠰⠎⠛⠈⢹⣯⣭⣿⣿⣦⠴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠀⢰⠀⡇⠀⠀⠠⣤⠤⣾⡞⠚⢆⡁⢀⠀⠀⠀⠀⢠⠔⢚⡁⠐⠰⠀⠈⠷⣄⠀⠀⣰⠇⢀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡇⠇⠈⠑⠀⢸⠷⣨⢇⠀⠄⣱⠊⠳⡀⠀⢠⠃⢰⠏⠀⠀⠀⠀⠀⠀⠈⠑⢣⡀⠋⢃⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡌⠒⢶⠒⢻⣿⣿⡄⡀⠀⡏⠀⣦⣑⠀⢰⡆⠄⠀⠀⠀⠀⠀⠐⡤⠀⢀⡜⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣄⠈⢆⢰⠘⢿⣧⣇⣀⠙⡀⡽⠛⠛⠻⠗⠒⢦⡀⠈⠢⡀⣰⡃⣀⣽⣠⡦⣀⡰⣄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡻⠿⠋⠉⢠⡨⢧⣺⠁⠀⠀⠀⢀⡄⠀⡟⠋⠁⠉⠉⠉⠉⠁⠀⡀⣀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠰⠃⢰⠉⠱⡄⠟⣣⡀⠀⠀⢾⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⡌⠀⢺⠀⠐⡄⢠⠟⢳⠦⠔⠃⠘⠻⠢⣄⣀⣠⣤⣤⣶⢶⣭⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢫⠀⡴⠁⢀⠯⣅⠀⠀⠀⠀⠀⠀⢸⡭⣏⠼⡁⢯⣜⣧⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠺⢄⠼⠢⠄⣀⢀⡀⠴⠋⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢠⠈⠀⠀⡇⠘⠀⣧⠸⠆⣴⡧⠁⡴⢀⠀⢡⢀⡎⢀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⡇⠈⠀⣿⢀⠀⠈⣾⠂⠃⡄⠀⣏⠈⠀⡀⠈⠀⠰⡀⠇⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⠀⠀⡃⢀⠆⠛⠀⡆⢀⣷⠀⠁⡙⠀⢉⠀⠀⠐⡈⠀⠀⠘⢠⠆⠁⠀⠀⣠⠄
⠀⠀⠀⠀⠈⠑⠀⠀⠀⡀⠀⡀⢠⢀⣎⠴⢰⠀⣤⠘⡿⢀⠂⠕⠐⠰⣤⠀⢀⠑⠀⠆⢰⠋⠀⠐⣤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢁⢸⣾⠁⠐⡌⢀⣈⣧⢣⡈⢠⠀⠀⠈⣼⠀⡞⠀⠀⠀⣸⡇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⢻⣿⣧⡀⣧⡾⡧⠈⣦⡉⣬⠀⠰⣾⢹⠀⡇⢠⣤⣧⣿⣇⣶⣦⣺⣷⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡰⠄⠂
⠀⠀⠀⠀⠀⠀⠰⠾⠁⠁⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠃⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡖⢦⡄⠀⠀⠀⠀⠀⢀⡴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣹⡳⡄⣧⠜⢹⣄⠀⠀⠀⢠⠾⠄⠐⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡌⡂⠙⢿⣴⡤⡙⡄⠀⠀⢸⡄⠀⠚⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⢪⠙⢌⢧⡁⠁⡜⢆⠀⢘⡄⢲⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢦⡴⠇⢐⢣⡍⢾⣄⠘⡗⠎⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡈⠳⠺⣯⡐⠀⡟⡆⠹⡄⠀⠀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⡝⠖⠁⠆⢊⠂⠀⣷⠀⡇⠀⠠⣹⠀⠀⢀⡴⡚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⡿⢷⡦⡈⠲⡤⠀⠀⠃⠀⡝⣇⢹⠀⠂⢹⠀⡜⣃⠜⢥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡒⡗⠼⣦⡹⣄⠀⠀⠦⠀⠘⣼⡄⠀⢸⢸⡄⠉⢆⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⣦⠀⠙⣞⣆⠀⠠⠑⡀⢹⣧⠀⢸⡟⠇⠴⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⡀⠻⣷⠄⠀⠀⡎⢣⠀⠀⣿⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠠⠘⢧⠀⠀⠈⣄⠄⢸⢹⢄⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠨⢳⡀⢀⣬⡦⢎⡿⠸⣭⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣷⣵⣾⣿⣀⡿⢶⠓⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣾⠻⡛⠉⠉⢱⡈⠙⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠐⡀⠀⠘⢹⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠂⠘⠀⠀⢀⢡⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⠄⠀⠀⢂⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⢄⠀⠈⣧⣘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣼⣆⣼⣿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠙⠷⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡜⢫⡞⠁⢗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠢⠄⣈⠧⠀⣘⠃⠯⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣚⠒⢤⠓⠤⠓⠀⣤⠶⢨⡂⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠲⠄⣸⠁⠐⠛⠀⢠⣌⠀⠢⢈⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣼⠓⠤⠣⢤⠛⠀⢤⡤⠁⣙⡃⢦⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⣙⠉⡲⠓⠤⠚⠂⠀⡴⠆⢀⣈⠁⠓⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣑⠦⢀⡘⠓⠢⠞⠢⢄⣀⠓⠂⢴⣁⡙⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠓⡶⢀⡈⠉⠲⠾⠂⠀⢀⡜⠁⠲⡆⢀⡛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢍⠧⢀⡘⠓⠠⣴⠄⠀⠀⣈⠁⠲⠶⢤⣈⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠤⢄⡠⠆⢀⣠⠄⠀⠀⢨⡇⠁⡒⠃⢤⠌⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠒⠂⢤⠆⠀⢀⡀⠀⠀⢘⡆⠀⣨⠉⢐⡞⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢉⠓⠲⡎⠁⠐⣎⠁⠀⠐⠧⠀⣀⣍⠁⠺⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠃⠚⠂⠄⠁⠐⠊⠁⠁⠐⡾⠀⢀⣭⠀⠈⠇⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠉⠛⠃⢶⡁⠀⡒⠁⠀⠠⡴⠀⢀⣨⡀⠀⡛⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢈⠓⠀⠦⠄⣠⠋⠐⠀⣴⡆⠀⠀⠥⢀⣙⠓⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⡊⠁⡲⢄⣀⡰⠄⠀⢀⠿⠀⣈⠿⠄⣤⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢤⠄⣨⠤⢀⣨⣀⠀⢀⡟⠀⠠⠜⠠⡄⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣈⡁⣀⡧⢀⣈⡁⠀⠈⣏⠀⠐⣖⠓⢠⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠴⠆⠸⠆⢠⡁⠀⠀⣫⠀⣀⠶⢀⣉⡋⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡒⠲⠖⠠⡌⠁⠀⠶⠣⣀⡛⠠⣤⠓⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡁⡘⠂⢰⠉⠁⣲⠃⠠⣬⡁⠲⠆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⡉⣉⣀⡤⠀⣈⡛⠰⠶⢄⣬⠁⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡾⠴⣇⣰⠏⣁⠉⢠⠒⢤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣬⣗⡯⢶⣭⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⠒⠮⣉⡽⢁⠜⣰⠋⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⢞⠀⡞⠀⠉⣆⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠤⠒⠀⠉⢙⠗⢖⠋⠁⠀⠀⠀⠀⠢⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡄⡰⡀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡖⠁⠀⠀⠉⡰⠖⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢷⠻⣕⣲⠔⠓⠒⠉⠉⠉⠉⠉⠘⠁⠀⠀⠒⠂⠤⠤⠤⠄⠀⣀⣠⡀⠀⠀⠁⠀⡄⠀⠳⡶⠶⡏⠈⣶⠓⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢲⣼⡦⢬⣷⣀⢰⠀⢤⣀⣀⡀⠀⣀⣠⣤⣤⣤⠤⠴⣖⠈⠉⠀⠀⠀⠀⠀⠀⢠⣔⠁⠀⢠⠛⡋⠙⣏⠁⡿⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢲⠤⡀⠀⠀⠉⠙⢦⡈⠁⠉⠉⠡⠉⠐⠀⠉⠉⠒⢤⣈⠁⠐⠂⠀⠀⣀⡀⠸⠊⣸⠦⣾⠓⡋⢻⡉⢹⣦⣼⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡈⠲⣄⠀⠀⠀⠈⠳⢤⡀⠠⠀⠀⠀⢀⠀⠄⠀⠈⠛⢿⡃⠀⠀⠀⣠⠖⠛⠛⠒⣿⡂⠙⠳⢾⣉⣤⣼⣉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⠀⠐⣄⠀⡙⢲⠤⣄⠀⠀⠑⣦⣄⣀⠀⠀⠈⡀⠀⠄⠀⠂⠙⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡧⣀⣯⠉⡤⡀
⠀⠀⠀⠀⠀⢀⡤⠶⠒⠂⢾⡖⠓⠒⠒⢾⡀⢈⠂⠐⢈⠉⠒⢤⡈⠳⡉⠓⠦⣤⢀⡤⢤⣬⣠⣐⡠⣳⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠦⢿⠄⡟⢢⡆
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠻⡗⠤⢄⣄⠨⠻⣷⠶⠶⠶⣛⡯⠭⠤⣼⣾⡇⠤⠤⣀⠀⠀⢀⡞⠁⠀⠈⠓⣏⣹
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡊⠀⢀⠂⡁⠀⠈⢳⣄⣉⠁⠀⠈⢧⠀⡜⠁⠀⠀⠀⠀⠿⠄⠀⠀⠀⢱⣴⠟
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢧⡙⢦⣄⡀⠀⠀⠀⢀⠻⣟⠛⠳⠶⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠓⠤⣌⠳⣌⠛⢶⣀⣠⠂⢁⠈⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣤⠤⣤⠴⠛⠁⠀⠀⠀⠙⠲⠼⣆⠀⠉⠙⠛⠶⠖⠞⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠞⡆⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣤⠀⢀⡏⠙⣄⣀⡄⣀⠀⣠⡎⢹⢰⠦⢎⠀⠽⣶⣦⡞⠀⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⡇⠙⣤⢧⠓⡶⠷⣀⠉⢀⣷⠉⠳⣻⠀⡰⠛⢻⠀⠃⢠⣧⡀⠁⡴⠋⢹⣅⠀⠀⠠⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⢲⡧⢴⠁⢀⣶⠀⢠⠄⠰⠞⠃⠀⡜⠁⡞⠀⠴⠿⡶⠀⢘⣇⠉⠀⢀⠴⠛⢻⠶⠙⠆⠀⠤⣄⠀⠀⠀⢠⡀⣠⠘⡇
⠀⠀⠀⠀⡟⠠⣄⣠⡄⠀⠀⠘⡋⠛⠦⠁⣨⣤⠁⢠⣧⠀⢀⣀⢆⡀⠈⠀⡰⠿⡄⣠⣮⡣⠀⢸⡟⠃⠄⠁⣠⠾⣁⠾⠲⡎⠀⢀⠜⠀⠀⣀⡆⠘⡡⠼⢤
⡀⠀⠀⢠⡽⠦⢼⠁⢰⡤⡄⠀⢹⡦⢤⣀⠉⢠⣄⠋⢹⣅⠊⢙⣻⡉⠁⠐⠀⣴⣥⢀⣼⣥⠀⡨⠱⢄⠀⠋⣠⣤⠋⣀⡼⠇⠘⡻⠀⠀⣰⠈⢃⠀⣀⣠⠊
⢟⠐⢦⡜⢷⣄⣈⣀⡘⠁⢹⣤⠈⢳⣄⢈⡀⠜⠩⡶⠇⢻⣀⠊⢩⣟⠓⠀⡜⢁⣼⠋⢩⣟⡀⢰⣄⠀⠰⠂⢁⣈⠿⣩⠟⡶⢿⠀⠀⠸⠛⠀⠘⢉⣠⠟⢀
⣾⠓⠒⠄⠸⠟⢧⣁⠉⢀⠊⠈⣇⣼⢦⣀⠉⠀⡘⠛⣧⣮⡌⠀⠜⢹⠶⢤⡀⠛⢉⡿⢿⢉⠇⣩⡈⠁⢀⠔⠛⠻⣻⡧⢾⣿⡅⠀⡛⠣⠀⠘⠁⢈⡿⠖⣁
⠈⢳⡤⠤⠴⡀⢘⠟⣅⣈⡁⣀⠉⢸⣄⣯⡁⠘⠃⠰⠛⢦⣏⠘⠂⠸⣶⣄⠃⠠⠟⢲⡾⠛⣳⡭⠷⠀⠈⣠⣤⡶⣯⣤⣾⠋⢰⠛⠇⠀⠇⠘⣻⠿⠀⠃⢈
⠀⠀⠙⣦⡤⠀⠆⠀⠸⠛⣅⠈⠀⡈⠁⠸⢿⠓⠰⠆⠀⡟⣹⡟⠰⠠⣏⠁⠘⠁⡰⠏⣹⠞⢳⡿⡄⠈⠒⠁⢀⡽⢣⣤⣼⣧⣼⠀⠰⠆⠶⡾⠃⠀⠛⠋⠟
⠀⠀⠀⠈⠲⢤⡄⠠⠆⠀⠟⠹⠀⠉⠀⠘⠸⣿⠶⢀⡈⠁⣨⠿⡆⠠⣟⠛⠢⡜⢁⣠⢟⠀⢾⠉⠉⠀⠠⠘⠫⠟⠁⢈⣿⠄⠈⢀⡠⢶⡛⠁⠘⠃⠈⠇
⠀⠀⠀⠀⠀⠈⠓⢤⡤⠀⠆⠀⡿⠛⠖⠂⠀⠾⣷⣤⠈⢀⠟⠛⡷⠦⣹⣦⣄⢀⠊⠀⣸⣀⣼⣦⡀⠀⠠⠶⣛⡖⠛⣿⠙⠃⡀⣁⣤⠚⡀⠈⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠠⡄⠀⣿⠶⡐⠆⠈⣧⣀⠙⠀⣼⠿⢆⡘⣆⡀⠈⢠⠞⠻⣁⣼⣧⡀⠋⠀⣾⢏⣰⠛⠿⡆⠈⣁⡴⠏⠐⢁⡸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠤⠤⣄⠀⣿⠶⣦⠙⢏⠁⠲⠀⢀⢾⡙⣏⠉⠀⠆⢠⣾⠋⣏⠉⡗⢰⣞⡡⣎⣼⣇⠀⠘⠈⣩⠇⠘⢀⡹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣤⠤⢠⡁⠀⣼⣀⣼⣧⠤⢀⡟⠉⣽⡻⡗⠒⠤⠀⣨⣷⠟⢷⠇⣜⠉⣩⣿⡄⢩⠤⠤⢶⡅⠂⣈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⢀⡋⠀⣭⣱⣤⠄⡁⠞⠉⣿⠻⣶⡄⢮⣁⢉⠶⣜⢀⡋⣹⢻⡄⢁⡤⠤⣶⠛⠂⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⣀⡈⠀⠁⢸⣱⣄⠈⠂⣼⠈⡆⢹⡇⢸⣄⠁⢴⡇⡸⢩⠁⠞⣧⢈⣠⠴⠋⠰⢾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠁⠠⠈⢣⠙⡆⢽⡄⢱⠘⣷⢸⠀⠀⢸⡇⡇⡆⣸⡰⢣⣟⠠⠄⠐⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡱⡀⠱⡙⡜⣷⠀⢇⣿⢸⠀⢸⣸⢱⠀⠁⣿⢡⡏⡜⠡⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢆⠹⣧⢹⣆⢸⣿⠈⣆⢸⣿⠘⠘⣸⠏⡎⡴⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠣⡹⡆⠟⡈⡏⡆⢿⣾⡇⠀⠇⠟⣸⠌⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡱⣧⠸⢡⡇⡇⢸⡏⡇⣾⡜⢰⡟⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⡆⢏⡇⡇⢸⠃⠂⣿⢃⡿⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢸⡇⢿⠸⢰⢠⡏⣼⠡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠃⣾⠀⣾⠈⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡆⡿⢠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⣳⠁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠟⡸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⢠⡇⣇⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⡇⣼⣷⠸⣆⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣾⢠⡉⣿⡆⢿⣆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⡇⣼⡇⠁⣿⠘⡟⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡐⢹⣇⣿⣷⡆⣿⢃⢹⣸⡞⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⠁⣾⢸⢿⢹⡇⢿⠈⣆⢓⠿⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⠁⢰⢧⡇⠸⢼⢧⠞⠓⠉⠚⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣆⡀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⢀⣼⡟⢳⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⢀⣾⡋⡥⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠀⢰⡆⠸⠀⠇⢸⣧⠰⠖⢚⣿⡄⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢠⣦⣀⠈⣇⠈⠇⠀⠇⠀⣿⠄⡿⠂⣻⢿⣱⠇⠀⠀⢀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠈⣿⣌⠛⣧⡈⠆⠀⠀⢸⣰⡿⣌⠛⣨⡟⢸⣿⢠⠀⣠⡟⢋⣼⣧⠀⡀⣀
⠀⠀⠀⠀⠀⢀⠀⠻⣇⢁⠀⣷⠌⣤⢙⣧⠈⢀⡀⠈⡟⢧⣘⢃⣽⠃⣼⡇⠘⢠⣿⢡⡌⢴⡇⠀⠀⠛⢀⣄
⠀⠀⠀⠀⠀⠛⢿⣦⡀⠘⡀⠹⣗⠰⡇⢸⡆⢸⡇⡄⢃⠀⣿⣿⠁⠀⡟⠀⠀⣾⠀⠷⢐⣾⠁⠀⢀⣴⡿⠋⢀⡀
⠀⠀⠀⠘⠿⣶⣄⠙⠻⡆⢱⠀⢻⣇⠛⡠⢿⢼⣧⡇⢸⢰⡇⣿⠀⣼⡇⠀⣼⠷⣘⢃⣿⠃⠀⠀⠞⢁⣠⣾⠟⠋⡀
⠀⠀⠾⣶⣤⣈⠙⠻⣦⣄⠀⢧⠈⢿⣌⣡⠞⢸⣿⠁⠀⣿⢁⣯⡼⢻⠃⠀⠙⣦⣉⣼⠏⠀⠀⣠⡶⠟⢉⣠⣴⡾⠟
⠀⣴⣤⣄⡉⠛⠻⢶⣤⣙⠳⠈⢧⠀⠀⢻⡀⢸⡿⠀⠀⣿⣼⡟⢁⣿⠀⠀⠀⣿⠋⠄⠀⠀⠐⣉⣤⠾⠛⢋⣁⣤⣶⡾
⢀⣀⡉⠙⠛⠿⠶⣦⣌⣙⠳⠦⡌⢷⣀⡾⠛⠛⠷⠶⡤⠿⠟⠛⠛⠛⠳⢶⣄⡁⠰⠂⠀⠰⢛⣉⣤⡶⠾⠛⠋⣉⣠⣤⣤
⠈⠛⠛⠛⠿⠶⢶⣤⣬⣉⣛⠳⠆⣠⡿⠁⠀⠀⣀⣀⣀⣠⣤⣤⣤⣄⣀⣀⡉⠛⢶⣤⣀⠚⣋⣭⣤⠶⠶⠟⠛⠛⠉⢉⣁
⠿⠷⠶⠶⢶⣶⣶⣤⣤⣬⣭⠁⣾⠋⣠⡶⠟⠛⠛⠉⠉⡏⠉⠉⡏⠉⢙⡛⠻⣷⣦⠀⠙⣧⠠⡤⠶⠶⠶⠶⠿⠿⠛⠛⠛
⣤⣤⣤⣤⣴⣶⣶⠶⠶⠶⠶⠆⠙⠳⣿⢠⡀⣀⣇⣠⣴⣧⣤⣴⣇⣠⣴⠅⠀⡆⣿⠂⣴⠏⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⢀⣀⣀⣤⣤⣤⣤⠶⠶⠖⢚⣛⣩⠅⢻⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠻⠿⢾⣿⣇⣿⣾⠃⣌⣙⡛⠛⠳⠶⠶⣶⣦⣤⣤⣤
⠘⠛⠋⣉⣁⣤⣤⡶⠶⢛⣋⣭⠴⠂⢿⣿⣿⠃⢀⣀⣀⣀⣀⣀⣀⣀⡀⠴⣾⣿⣿⣿⣿⣟⣛⣿⣯⠻⠶⣶⣤⣤⣄⣉⡉
⠀⠿⠟⠛⠉⣁⣤⡶⠞⢛⣩⡴⠞⡁⢸⣿⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⣿⣿⡿⣿⡿⠉⠉⢻⡏⣿⠻⢶⣤⣄⡉⠙⠛⠃
⠀⠠⣴⡾⠟⠋⣁⣤⡶⠛⣉⡴⠟⡁⢸⡟⡟⠋⠻⠉⠀⢸⠉⠁⢸⠋⠁⢿⠙⠁⣿⡇⠀⠀⢸⡇⣿⢶⣤⣈⠙⠛⠿⡶
⠀⠀⠀⣠⣶⠿⠛⢁⣴⡾⠋⣠⠞⠁⢸⡇⡇⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠈⠀⠀⣿⡇⠀⠀⢸⣧⣻⣤⣈⠙⠿⣶⡄
⠀⠀⠀⠉⢁⣠⣾⠟⢁⣴⡿⢉⣴⠇⢸⡇⡂⠀⢀⡀⡀⣠⣀⣀⣨⣀⡀⣀⠀⢀⣿⡇⠀⠀⢸⣿⣿⡈⠻⣷⣤⡈
⠀⠀⠀⠀⠈⠋⢀⣴⡿⠋⣠⡾⠋⡄⢸⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣶⣶⣿⣿⣿⢿⣦⡀⠉
⠀⠀⠀⠀⠀⠀⠙⠋⢠⣾⠟⢀⣼⠇⢸⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡟⠛⠛⠛⠛⢁⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⣾⠏⠀⢸⡟⠟⠉⠸⠁⠀⠘⠃⠀⢸⠁⠉⠛⠉⠹⢻⡇⠀⠰⣶⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣿⣛⣛⠛⠛⠛⠉⠛⠛⣛⣛⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡤⡤⠤⣀
⠀⠀⠀⠀⠀⡀⢤⠒⠋⢹⡖⠂⠈⢳⡌⢂⠙⣿⠣⡀⠀⠀⠐⡟⠡⠔⣛⣫⣶⣦⠀⠀⢀⠎⠀⣀⠤⠜⠀⠧⣀⠀⠡⡀
⠀⠀⡠⠒⣭⢄⠸⡍⠳⡈⢳⡀⠀⠀⢻⡌⡄⠘⣄⡇⠀⢸⠀⠃⢠⠊⠉⠉⢉⣈⣁⠀⣸⡀⠚⠀⠀⡄⢠⠀⠀⠱⠀⡧
⠀⠰⠁⠀⢿⠀⠂⠹⣆⢱⡈⢷⡀⠀⠘⡇⣧⣶⠟⠀⠀⠘⢧⡀⠐⠔⠒⠉⠉⢉⡟⠀⢿⣧⡀⠀⠀⠸⠂⠀⠀⣀⣴⠇
⠀⢠⡀⠀⠈⠓⠄⣦⣘⢦⣧⣀⣷⣶⡶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⠴⠚⠁⠀⠈⠻⣿⣷⣶⣶⣶⣾⣿⡿⠋
⠀⠀⠉⠛⠓⠒⠛⠛⠛⠛⠛⠋⠉⠀⡠⠒⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢉⡩⠭⠟⠫⢤⣀⣀
⠀⠀⣠⠒⠫⣅⠉⠉⠱⣶⢤⠀⠀⡌⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠀⠀⠙⡿⠉⠱⡀⠀⠀⢀⣴⡙⠀⠀⠀⠀⢨⠀⢨⣉⠵
⢀⣞⠣⠄⢈⢮⡀⠀⣠⡇⢠⠳⡄⡇⠁⠀⠀⠀⠀⠀⣸⠀⣸⠶⢦⣄⡰⠁⠀⠀⣷⠀⣰⡋⠀⠘⢎⢂⠀⠀⣸⠀⠊⠁
⠠⠁⠀⠉⣷⣿⣿⡾⠛⠶⠾⢤⠁⠘⢄⣀⣀⣀⣠⠴⠃⠀⡇⠀⠀⠘⡇⠀⠤⠞⡿⠠⠀⠬⢷⣤⠼⠿⠶⠛⠁
⠘⠦⠒⠛⣉⣁⠀⠄⡠⠠⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⣤⡀⠀⠰⣄⠀⠚⠀⠀⠀⠀⠤⠶⠾⠥⣄⡀⠈⠙⠲⣄
⠀⠀⣴⠍⠁⠀⠀⠀⠀⠀⠛⣯⠀⠀⠀⠀⠀⠀⠀⠤⡤⢤⣤⣤⣭⣉⠉⠁⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠙⢲⡀⠀⠈⡆
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⠈⠢⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢲⣧⡤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⡱⠀⠀⠠⠁⠀⢀⠀⠀⠀⠀⠀⢹⠁⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣸
⠀⠀⠀⠙⠢⠤⠴⠄⠂⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠘⠓⠢⠤⠤⣄⣀⡀⠀⡼⠖⠉
⡶⠒⢶⢶⡶⠶⠶⣶⢶⠶⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⠶⠶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⢠⠚⡀⠀⢠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⢰⣀⣸⠀⠳⠰⡦⢆⣴⠃⢱⣏⠒⡀⢙⠓⠆⢈⡤⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢼⣄⡘⠉⣯⠉⣓⣀⡴⡇⢨⠟⡴⠀⣴⣦⠀⢚⠓⠀⠁⡴⠿⡀⢠⠁⢁⡀⠀⠀⢀⠀⢀⠤
⠀⠀⠀⡶⢀⣀⣄⠀⠀⢰⠒⠘⠁⣧⡈⢹⣀⠁⣈⣄⡀⠁⢠⠷⡀⣤⡣⠀⣿⠓⠀⠉⡴⣎⠴⢤⠂⠀⡅⠀⢀⡈⠹⠡⢦
⣀⠀⠀⡞⠂⠍⠀⡶⠄⠀⡷⠢⠄⠀⣦⠉⡭⠄⢈⣯⣁⠐⢀⠾⣅⣴⣧⠀⡙⠢⠀⢁⠤⣎⣠⡞⢈⡹⠀⢀⡄⢁⣈⢠⡜
⣣⡙⡎⢹⣶⠤⠰⠀⠱⢆⠸⡆⠀⠄⠀⣯⢉⠇⠀⡸⢏⡁⠊⡴⢧⣠⡿⡀⠹⠄⠀⢡⣤⣮⣜⣩⡯⠃⣤⡇⠁⡄⠠⣞⡁
⠱⣄⣀⢀⠁⢳⠆⠒⠀⠘⠛⣸⡖⠂⠄⢠⠏⣹⠠⠀⣯⣉⠂⢀⠎⣩⠶⢥⢳⡄⠘⢀⣀⣵⣉⡽⠟⡤⡄⢠⠠⢤⡶⠉⠐
⠀⠈⢢⡄⠠⠄⠘⠛⣀⠃⢈⠋⡻⡖⠀⠄⢠⣛⡗⠠⢸⡉⠐⢀⡴⣻⠶⢺⣦⠀⠀⠉⣁⢊⣤⣽⢄⡇⠠⠄⢴⠎⠐⠀⡸
⠀⠀⠀⠑⢶⠆⠐⠀⠋⢩⣉⢀⠛⢹⡗⠀⡈⢠⣟⡂⠰⡟⠃⠌⣠⢾⡐⢻⠉⠁⠄⠊⣻⢃⣠⣷⠀⠠⠠⣶⠁⠀⣁⠝⠁
⠀⠀⠀⠀⠀⠘⢖⡀⠁⠸⠉⣧⣁⣈⠻⡖⠠⠌⢨⣟⠁⡟⠒⠄⢀⣼⡷⢻⡒⢀⠐⣻⠜⣁⣿⠀⠤⠐⡾⠡⠀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠘⠥⣈⠀⡙⢈⣤⣄⠻⠒⠠⠉⢉⡷⠾⠒⠀⠈⣠⡗⡟⢳⠀⡄⣉⣊⣇⠈⡄⠐⡯⠁⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠄⢘⠁⢨⣀⣰⢤⠀⡞⢉⣿⡖⠠⠄⣩⣧⠿⣾⢠⠉⣹⣇⠉⠄⠤⣎⠑⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣄⠀⠉⢀⠯⣶⠀⢠⠉⠻⡛⣷⠀⠥⠌⢳⡄⣌⡹⣣⠀⡄⠒⡞⠁⡨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡂⠰⠀⡷⡗⢤⠰⡇⢃⢸⠀⠓⠄⣻⢣⢀⠁⢨⢢⠖⡊⠁⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⡱⡈⢎⢣⢷⠀⡆⡇⡀⡇⣿⡈⠀⣰⢡⠉⢆⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⢄⢳⡌⢇⢸⡇⢣⡷⡏⢁⢣⡏⡋⠨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠢⠳⢙⠌⠇⢸⣷⠃⡸⠘⣰⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡹⡌⡼⣶⠸⡇⢀⣿⢠⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣧⢰⣼⡄⡁⢸⢇⡟⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢻⡇⣿⠈⡞⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⠘⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⢁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⡅⣌⠋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⢱⡟⢹⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡇⡇⡷⡆⣿⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⢿⢱⣿⡄⣿⠸⣳⣔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠂⣼⣼⢿⡇⣿⢠⠡⢿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠊⠀⣷⠀⠶⡷⠝⠊⠓⠃⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡆⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣠⡴⣫⢞⡽⠱⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣠⢿⣟⡽⣣⠞⣵⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢀⣮⡿⡻⢫⠊⣱⢏⡾⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⣰⡿⣛⠞⡳⢁⠞⡡⢗⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠘⠀⣀⣼⢯⣝⢫⠟⠩⡃⣜⣰⡟⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴⠀⢀⠿⣱⢏⡶⢁⠬⣑⠮⣝⠏⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⡐⢣⡟⣉⠮⣑⠎⣱⢮⣛⠊⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡎⠀⣿⠯⡼⢇⡹⢉⡰⢍⡲⢥⡟⠁⠀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⢰⠁⠀⣏⠶⣉⠮⣁⠾⢁⡶⡽⣹⠃⣰⠋⣩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠂⠀⣟⣤⡉⠢⠍⣰⠮⡽⣵⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⢹⢦⣜⢓⣤⡭⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣦⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠐⠾⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣤⣤⢤⣀⣖⠰⣿⣪⠷⡔⣶⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠷⢞⠺⢈⢀⠈⣳⡐⠭⣝⡍⢷⣲⡿⢭⣛⣶⣞⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢶⣋⣛⣀⣛⠛⠛⠾⠿⢽⣿⣾⣷⣾⠿⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⢤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠝⠶⣀⠀⢀⠀⢀⡀⡀⠀⠀⢀⠀⡎⣠⣔⣿⣼⣟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠂⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⠶⠞⠋⡉⠣⠻⢟⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠘⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡃⠤⠴⠒⠒⣲⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⢀⣠⡔⠚⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⣶⣴⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣿⣷⣞⡻⢻⡷⢺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⢀⠀⢃⣾⣷⣿⣿⣿⣿⣿⣾⡁
⠀⠀⠀⠀⠀⠀⢀⣶⢛⡶⣾⡿⢧⣭⢿⡿⢿⣟⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢀⢐⣸⣸⣿⣿⣧⡀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⢀⡽⢒⣯⣷⣟⣲⣋⣗⠏⣧⠾⣿⡶⣦⣲⠤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢣⢸⣿⣼⣾⣿⣇⢈⣷⡆
⠀⠀⠀⠀⠀⠐⠿⠛⣹⢋⣿⡼⣿⡽⠞⠁⢈⡤⠾⠛⠛⠛⠶⠦⣤⣀⣀⣠⣠⣠⣠⣠⣾⣴⡼⢿⠟⠛⢉⣁⡀⣈⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⣀⣤⠖⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⣥⡩⣷⠖⠛⣹⢆⣆⠀⠀⢠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡸⣦⣙⣲⣶⣙⣧⠿⣑⣢⡟⣤⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠋⠉⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣽⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣶⣿⣿⣷⣾⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⠀⠀⠀⠀⠀⠀⠀⠲⠚⠐⠛⠑⠒⠂⠀⠀⠒⠀⠈⠀⠀⠀⠀⠀⢸⣧⠶⠾⠿⠛⢙⣫⠃
⠀⠀⠀⠀⠀⠀⠀⠲⢀⣤⣞⣩⣿⡆⡰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⢷⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢾⢿⣿⣿⣿⡿⣉⣿⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡆⣰⠆⠁
⠀⠠⠊⠀⠀⢠⣶⡷⠴⡦⣴⣿⣾⣅⠻⣿⣷⡘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠠⠂⠁⢠⣿⣷⣾⣿⣿⣿⣿⠋⣆⠈⠉⠀⠀⠑⡄
⠀⠠⠃⠀⠀⠈⠛⠛⠛⠉⡃⣹⣿⣷⠈⢦
⠀⠀⠀⠀⠀⠀⠠⠤⠄⣠⠻⣿⣿⣟⠀⠀⢃⠀⠀⠀⠀⠀⣄⣀⠀⢠⣤⣤⡀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠼⣥⣤⡈⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣉⡑⢈⡿⠴⢏⠁⠐⢅⢂⠀⠀⢀⠀⠀⠀⠀⢠⡴⢻⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠠⠂⠀⢾⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⢸⡅⠀⠉⠀⠀⢸⡞⠆⠀⠈⠀⠀⠀⢰⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⢸⣯⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⣿⠀⠀⡀⢴⠷⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⡀⠉⢤⢾⠶⣅
⠀⠀⢀⠀⣠⣤⣤⣤⣶⡶⣶⣭⣀⡀⠂⠀⠀⠀⠀⢀⢆⡄⠀⠀⠀⠀⢱⠀⠘⢲⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⣰⣧⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⡷⢠⠀⠀⠀⠀⣿⣛⠁⠈⠀⠉⠉⠙⠉⠙⠛⢻⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢤⡾⠟⢂⡀
⠪⢟⡫⠿⠿⣿⣾⣿⣿⣿⣿⣿⢿⡿⠿⡛⠀⠀⠀⣿⣿⡇⡇⣸⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⢛⠂⠀⠀⡠⠀⠀⠈⠐
⠀⠀⢻⡏⠛⠒⠒⠴⠶⣶⣶⠶⣶⣶⠛⠁⠀⠀⠀⠻⣿⣧⢡⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣾⣿⣭⣿⣦⠐⣠⣶⠲⣄
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠋⢿⢀⣿⣟⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⢛⣿⣷⣿⣿⣿⣿⣧
⠀⠀⠀⠻⣀⠀⠀⠀⠀⢤⡿⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⢿⡿⠟⠛⣫⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠙⠛⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣼⣤⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣯⣥⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣤⣀⣀⡲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⡙⠈⠳⠄⠀⠀⣠⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⣮⣷⣌⣻⣿⣿⢟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣂⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀
⠀⠀⠀⢀⠔⠈⠹⣁⣀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠔⠀⢈⠚⠁⠀⠀⡢⢄
⠀⠀⠘⠁⠤⣀⣀⡀⠀⣈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠃⠀⠀⡌⠀⠀⠀⠐⠀⠀⠀⢄⠀⢠⠋⠉⡆
⠀⠀⡸⢄⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⢀⠃
⠀⢰⠒⢘⠁⠹⠉⠉⢃⠀⢹⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠁⠀⡎⣛⣟⢓
⠀⠀⢆⠈⡀⠀⡄⠀⠸⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⠉⠉⡁
⠀⠀⠈⠢⣐⡀⠰⡀⢰⢀⣃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠦⠀⣀⣀⣈⠑⣶⣻⠤⠔⠀⣉⣁⣀⠀⠈⠑⢢⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠐⠀⠀⠈⠐⠀⠠⡀⠀⠀⠀⠀⠀⠓⠋⠣⡐⠢⠄⣀⠀⠀⠀⠉⠰⢆⠀⠀⠉⠀⠀⠀⠀⡇
⠀⠀⢀⢀⡠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡀⠈⢁⠰⠃⠁⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⡂⠀⠈⠺⢤⠔⠊⠀⠀⠑⢄⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⣀⠇
⠀⠀⠘⣉⠀⠚⠾⠀⠀⡀⠄⠒⠈⠑⢄⠀⠀⠀⠢⠀⠄⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠶⠷⠆
⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠀⣱⢲⡀⠀⠀⠀⠲⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰⡟⠂⣈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰⣷⠏⣈⡰⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⡰⠆⠛⠈⢩⠉⢶⠠⡄⠀⠀⠀⠀⠀⠀⠣⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⢓⡈⣅⠠⣆⡒⠃⠁⢠⡴⠂⢄
⠀⠀⡤⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠢⡀⠀⠀⠀⠀⠀⠀⢰⠂⠏⠙⣀⢠⡔⠁⠈⠛⠋⠀⡡⠱⠣⣽⢁
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢠⢄⢀⣀⠀⠘⡆⠀⠀⠀⠀⠀⠰⣇⢙⡁⣡⡌⢀⢤⡔⢲⠎⣉⠝⠃⢜⢘⠀⠆
⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠵⠯⠴⠮⠬⠭⠄⠄⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⡴⠇⡨⠓⢤⡌⢱⠎⣠⠋⢃⠸
⠀⠙⠒⠲⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⢲⠖⢲⠶⠶⠒⠒⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣉⡰⢆⣨⢓⣤⠩⠵⠞⠢⠃
⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⣸⣿⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⡀⠤⠀⠠⠄⡀
⠀⠀⠀⢰⠀⢠⠀⡇⠀⢰⡖⢒⣒⣒⣛⣛⣓⣚⣒⣒⣒⣦⠀⢰⣲⣒⣒⣒⣒⣒⣒⣒⣲⣒⣀⣀⢀⠈⡇⠀⡰⢁⠀⠂⠀⠀⠠⠀⠑⠄
⠀⠀⠀⣸⠀⢸⠀⢇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠈⠓⠲⡀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠐⠸⠀⠄⢠⠂⠉⠁⠢⠀⠀⠈⡀
⠀⠀⢠⠃⠀⢸⠀⠘⡄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢣⠀⠀⠑⠎⠙⢄⠌⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠇
⠀⣴⠣⠤⠤⠼⠤⠤⠽⠤⠤⠤⠭⠶⠤⠤⠤⠴⠮⠥⠤⠤⡄⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠄⠈⠈⡐⠀⢒⠤⣀⠎⡘
⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠔⠁⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠑⠎⠀⠁⠁⠀⠄⠊
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣦⡄⠀⠀⠀⠀⠀⢠⣴⣿⣿⠁
⠀⠀⠀⠀⠀⣻⢾⡇⠀⠀⠀⣠⣰⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣾⢳⣆⠀⠀⠀⣰⡞⢷⠿
⠀⠀⠀⠀⠀⢼⣛⡷⠀⢠⣾⣻⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣹⣧⡀⣼⣏⣽⠏
⠀⠀⠀⠀⠀⠘⢯⡿⢸⣟⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠾⠃⠷⠾⠃
⠀⠀⠀⠀⠀⠢⢤⣀⠀⠀⠀⢰⣛⣟⣟⣷⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠉⢶⠀⠀⠀⠉⠉⠉⠙⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣦⡄⠀⠀⠀⠀⠀⢀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⢻⣆⠀⠀⠀⣀⣿⣳⡟⠂
⠀⠀⠀⠀⠰⣾⣷⢷⣤⣀⠀⣾⢷⣞⠁⣀⣄⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡿⣤⠀⣤⢿⣽⠏
⠀⠀⠀⠀⠀⠈⠛⠿⣾⣽⢳⡟⠛⣿⢾⣹⣭⡷⠟⠃⠀⠀⠀⠀⠀⠀⠐⠢⢤⡘⠷⠟⠀⠙⠶⢋⡤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠤⣍⡉⢀⠀⢈⣛⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⣳⡄⠀⢀⣶⡫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠀⠀⠒⡂⠐⠒⠦⠤⣋⣉⠉⠩⠉⠙⠒⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣚⣋⡀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⢦⣀⣀⠀⢄⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠌⠠⠒⠔⠲⠈⠍⠩⠉⠙⠛⠛⠛⠛⠒⠒⠤⣌⡀⠠⡀⠉⠁⠀⠈⠙⠲⣄⢀⠀⡴⠐⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡈⣀⢈⣥⣤⣀⡀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠼⠄⠀⠀⠀⠀⢠⡈⠛⠀⡠⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠽⠚⠁⠉⠀⠀⠐⠉⠍⠉⠉⠙⣛⠓⠚⠣⠦⣄⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⢀⠀⠀⠀⠨⢆
⠀⠀⠀⠀⠀⠀⡰⡷⠁⠀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠑⠫⣢⡀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠀⡀⠀⠅⢪⡀
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠠⠀⠤⠉⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠅⠀⠀⣀⠊⠀⢈⡹⣷⣌⠂⠄⠀⢁⠀⠀⠆⠄⠆⠀⢁⡨⠀⠀⠀⠀⣿⣓⣒⡀⡀
⠀⠀⠀⠀⢀⣀⣴⠿⠿⣦⣄⣈⡀⠀⠀⠀⠄⠠⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠻⣦⠀⡀⢂⡴⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⣴⡋⠐⠂⠠⠀⢀⡀
⠀⢀⣴⡾⠛⠉⠉⠉⠨⠉⣉⠉⠈⠛⠀⠛⠷⢶⢤⢬⣀⡀⠁⠀⠀⠠⠀⠐⠂⠀⠀⡀⢂⠂⠠⢳⡧⠐⠃⠀⠀⠐⠀⠂⠀⠀⢀⢀⡨⠞⢁⣀⠀⠐⠀⠀⠉
⢠⣨⠁⠀⡀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠅⢀⠀⠀⠨⠍⠐⠛⠿⢶⣤⡀⠀⠀⢀⠀⠀⠀⡩⠂⣾⠷⠔⠐⠶⠳⠶⠾⠶⣶⣷⣶⣾⣿⣶⣶⠶⣶⣶⣶⣷⣶⠖⠂
⢺⠉⠙⠳⢦⣤⣐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⢛⢶⡀⠈⠡⠀⠀⢀⣴⡽⠲⠲⠒⢒⠳⠶⠖⠛⠛⠻⠿⠏⢻⣿⣿⣿⣿⣿⠟⠋⠉
⠈⠉⠁⠶⢄⡀⠉⠛⠶⢤⣀⠀⠁⠀⠐⡀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠄⢳⣿⡻⣷⠖⣞⣿⢫⠾⠟⠛⠛⠿⠏⣛⣛⠛⠛⠛⠒⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠒⠲⣄⠈⠉⠓⠶⣠⡀⠀⠀⠀⠀⠀⠀⠆⠈⠤⠀⣀⣎⣼⠤⠩⠀⠀⠉⠑⠒⠒⠢⠥⠒⠒⠠⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣤⣀⣙⠣⠗⠶⠒⢒⣲⣖⣼⡿⡛⣡⡮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⠶⠤⢴⣂⣲⣧⣴⠟⠛⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠦⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠋⠡⠀⠀⠀⠀⡠⢒⠤⢈⣄⠀⢀⠐⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⡀⠀⡐⠀⠀⡀⠀⡐⠁⡱⠂⡤⢄⠀⢑⡎⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡐⠀⠀⣡⡋⠀⣸⡊⠁⠖⠄⠀⡰⢀⠘⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⢁⠈⠀⢠⠊⠀⠘⠊⣀⠘⠓⢄⣀⠝⢠⠈⠰⠁⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⡖⠁⠀⠈⠀⠰⠚⢀⡔⠉⠂⢄⡀⠉⠲⠓⢔⠂⢀⠈⠠⢀⠴⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡤⠘⠢⡀⠐⠢⡠⠘⠃⢀⠀⡘⠁⡲⠡⡠⠀⠀⢀⠠⠂⠁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠢⣀⡠⡀⠀⠀⢀⠁⠈⡖⠀⠀⠀⢀⠔⠁⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠁⠀⠀⠀⠖⠇⠀⠠⠁⠀⠀⠑⠐⠁⠰⠀⠀⡐⠁⡠⠁⠀⢀⠊
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⠑⠠⡀⠀⠊⠀⠔⠃⢄⠔⠀⠌⠀⠀⠔⠁
⠀⠀⠀⠀⡐⠁⠀⠀⡐⠁⠀⠀⠀⠀⡴⠰⠀⠀⠀⠀⠜⠠⣀⠄⠀⢀⠄⠠⠂⠀⡠
⠀⠀⠀⠌⠀⠀⢀⠈⠀⠀⠀⠀⠀⠰⠋⠉⠂⢀⣠⠊⠀⠀⠜⠁⠲⢀⠔⠁⡠⠊
⠀⠀⠌⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠼⠀⠐⠒⠊⠀⣠⣎⢁⡠⠊
⠀⡈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡬⠒⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⡀⠔⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠊⠀⠀⡠⠂⠁⠀⠀⠀⢀⠔
⡇⠀⠀⠀⠀⠀⠀⠀⠠⢁⠠⠊⠀⢀⠄⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⠀⠀⠀⡰⠂⠁⠀⠠⠂⠁⠀⠀⠀⠀⡠
⠈⠄⠀⠀⠀⢀⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⡠⠊
⠀⡈⠑⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊
⠀⠐⢄⣀⠐⠂⠀⠀⢀⣀⠀⠄⠂⠁
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣘⣄⢵⣬⠆⣌⣌⢿⣧⡾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠚⠒⠮⠿⠯⠬⠿⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⠉⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⢾⣯⣶⣄⡔⠀⠀⠀⠀⠀⣸⠁⠀⠉⠃⠠⠀⠒⠈⠋⠀⠉⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠿⠚⡥⢽⠿⣇⠒⡀⠀⠀⠀⢁⠐
⠀⠀⠀⠀⠀⠀⠸⡄⢾⣿⠛⠛⠛⢒⣮⣽⡦⠠⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⠳⠶⠟⢓⢩⠁⠃⠀⠀⠀⠀⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡿⠌⠃⢀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠊⠀⠀⠀⠀⠀⠀⠛⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢃⣤⠴⣒⣾⡿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠐⠒⠀⢐⣩⡴⡉⠉⠈⠀⠆⠿⠳⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡠⠶⠂⠀⠀⠀⠀⠀⠀⢠⣧⠆⠀⠀⠀⠀⠀⣠⠤⠀⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠈⠣⠄⠠⡆⠀⠀⠐⠀⠀⡠⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘
⠀⠀⠀⠀⠀⢠⠀⠀⠐⠦⠀⠀⣷⠀⢀⠀⠀⠘⠁⠀⠐⠋⠀⠀⠙⡆⠀⠀⠀⠀⢸⣠⠂⠀⠀⢀⠀⢀⠔⠊⠁⠸
⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⠀⠀⠛⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠐⠁⠀⢀⡀⢰
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⡀⢀⡤⠀⠀⢧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⢀⡄⡀⠀⠰⣦⡤⠊⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠻⠷⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣀⡆⠀⠀⢿⣇⣀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠻⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⢤⡠⠄⠀⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠐⢄⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠠⠀⠀⠰⠆⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡀⣠⠀⠀⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⣿⣿⢛⠿⠛⠛⢿⠟⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⣀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⣾⣿⣷⣤⣿⣿⡋⢹⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠻⠃⠀⠀⠛⠃⠀⢰⣦⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⣿⣀⣿⣿⡟⢻⣿⣉⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣤⠀⠾⠇⠀⢠⣤⠀⢶⠆⠀⠀⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣷⣾⣿⡿⠻⣿⣷⣿⣿⣿⣏⣈⣿⡿⡃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⠉⠀⠀⣤⡀⠀⠁⠀⠀⠀⠿⠂⢀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⣹⣇⣸⣷⣶⡿⣿⣿⣀⣿⡿⠿⣿⡄⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⠗⠘⠿⠀⠉⢁⡀⠀⠾⠇⠀⣠⡀⢛⣯⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣶⣶⣶⡶⠾⠏⢻⡿⠿⣿⣤⣾⣿⡿⠿⣷⠶⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠉⠉⢉⣉⣠⣧⠀⣠⡀⠛⠃⠀⠀⣀⡀⢉⣅⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠻⣿⣿⠀⠀⠀⠀⠑⠖⡻⢿⢹⣏⠷⢴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⢰⠀⠀⣸⣿⣿⣿⣷⣋⡥⣀⠆⠀⢂⡙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢱⣿⣿⡄⠀⠀⢀⠀⡀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣼⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠹⣿⠀⢠⣬⣥⣥⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢰⠀⢹⣿⠛⠚⠛⢻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠈⣿⣿⣿⡇⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⡆⢸⣿⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣷⣶⣶⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢚⡭⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⡙⠋⠁⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠋⣁⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠢⠀⠉⠙⠛⠲⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠈⠛⠛⠒⠶⠤⣤⣤⣤⣤⣄⣀⣀⡤⠚⠉⠀⠀⠀⠀⠀⢀⡤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠉⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠈⢢⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠋⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡇⠀⠀⠀⠀⠀⠉⠐⠶⠶⠦⡤⠀⠀⠀⢀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⡀⢀⡄⢠⠆⠠⠀⡩⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠈⠁⡺⠳⢤⣀⡄⠀⠀⠀⠀⢀⣈⣤⢁⣴⠡⣦⠠⢮⠐⠇⠘⠣⠘⢢⠤⠴⠧⠖⠀⠀⠀⠀⠀⠀⣀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡀⠀⠀⠉⠉⠰⠀⠠⡄⠂⣨⡣⢈⡆⠀⣓⠤⣍⣖⡟⣠⠔⣉⠔⠂⠲⠆⢠⡀⣀⣠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠒⠶⠤⠬⡙⠠⢄⡨⠀⠋⠠⡖⣉⡨⠷⠈⣄⡙⣌⠛⡐⢶⠡⡔⢁⣠⢈⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠃⣽⡄⢷⠈⡅⢳⠪⡤⠙⠉⠿⠗⠈⠣⠸⠆⠡⠈⠢⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣉⠰⢊⢙⡾⠧⢰⠈⠏⠰⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⠉⠒⠒⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿