Panthera tigris Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠐⢶⣖⢲⡀⢲⡖⠒⣦⠠⡤⢀⣀⣀⠀⠀⣀⢀⣤⣆⢀⠦⣤⡀⣀⣀⡀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⡍⠳⠱⠙⣦⢹⡆⠇⢸⡇⢻⢸⢆⠇⢠⢯⣧⠋⡿⢃⠞⡟⠡⠋⣾⢋⡴⠃⠰⣷⠏⣀⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠠⢧⡈⡇⣷⢠⠀⠇⢸⡈⡇⣶⠸⡇⠘⠟⡞⠀⠊⡏⢏⠀⡇⢸⠘⡿⠀⡜⠁⡟⢀⣞⠀⠛⠄⡶⢶⡉⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣤⠗⡁⠇⢸⠇⠈⢸⡇⢧⢹⡄⠃⣰⠀⠇⠀⡄⢹⢸⣄⠏⣎⢦⠳⠀⠀⠀⠇⢸⡇⡄⣶⢠⠃⠀⠀⣈⠄
⠀⠀⠀⠀⠀⠀⢰⡉⢹⡧⡹⡆⣼⠀⡌⣆⢣⠈⠀⣷⢰⠃⠀⡆⢰⡇⢁⡏⢹⠀⢹⡆⣷⠀⠀⣧⢠⢀⡡⢀⣾⠧⠄⠛⡢⠈⠁
⠀⠀⠀⠀⠀⠀⢸⠙⢯⡑⡄⠱⣿⢰⠇⠈⠣⣀⠀⢸⡍⣀⣾⣡⣿⣇⠞⠀⢸⠀⠈⣇⠿⡇⠀⠘⢦⠍⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣞⠳⡇⠰⣌⠲⠊⠛⠤⣬⣙⡛⢍⡺⠁⠀⠉⠉⠉⠓⠠⠀⠈⢀⣀⣍⠳⠙⠆⠀⠈⠄
⠀⠀⠀⠀⠀⢸⢷⡴⠀⠀⠁⠀⠀⠀⠸⣍⡉⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠧⠙⠳⣔⢦⠀⠀⠠⡀
⠀⠀⠠⣖⣾⢿⡎⠀⠀⠀⠀⠀⠀⢴⡲⢜⡛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠁⠲⢀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⡇⠀⢄⠀⠀⠀⠀⠈⢍⠙⠂⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢠⣀⠀⠀⠀⠆⡀⡄
⠀⠀⠀⠀⠀⠀⠹⠤⠤⠵⠀⠀⠀⠀⠀⠑⠤⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠂⠀⠀⠈⠑⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⡴⠀⠒⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠐⢀⠔⠈⣿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠂⠐⡆⡀⠀⠀⠉⣁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠦⠤⢠⡄⠀⠀⠀⠀⠘⠀⡐⢀⣄⢀⡡⠀⡋⠀⣈⠁⠀⠴⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢜⠷⠈⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⣏⣨⠟⠐⠀⠙⠃⠆⢉⠁⠐⢈⠁⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠒⠀⠀⠀⠀⠀⠀⠀⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⡦⠴⢖⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⠀⠄⠀⠀⠀⠻⠦⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢐⠒⢕⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢜⡍⠊⠡⠬⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠭⠉⠁⠀⢑⡢⣐
⠀⠀⠀⠀⠀⠀⠂⢠⡴⠒⠀⠤⢦⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠩⠍⠁⠀⠐⠲⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠒⠣⢄⢙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⡀⠰⠀⠠⠄⠂⠙⡈
⠀⠀⠀⠀⠀⠀⠃⠀⠀⡤⢀⠉⡀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣂⣨⡆⡐⠁⠀⠀⡀⡐
⠀⠀⠀⠀⠀⠀⡗⡄⠀⠁⣠⠊⠔⣀⠀⡴⠶⠒⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢭⣿⠏⢠⣴⡅⠓⠄⠐⠌
⠀⠀⠀⠀⠀⠀⢸⡠⠂⢨⠂⠀⠀⠀⠛⠈⠀⠠⢉⠀⢈⠀⢀⣠⠄⢀⣤⡄⠀⠀⢀⣭⣽⠯⠁⠐⡊⠀⣄⠀⠃
⠀⠀⠀⠀⠀⠀⠈⣴⣋⣁⠀⠀⢀⠀⠀⡄⠀⠀⠀⡀⠁⣼⠏⠁⠀⠶⠀⠀⠀⠀⣴⡴⣏⠷⠃⠀⢙
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡙⠂⠈⠀⡑⠞⢄⠙⠷⡇⠀⠀⢰⣄⢲⣷⠈⢱⠁⠀⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⣄⠃⠀⠁⠀⠄⠀⢠⠄⠒⠀⠀⠀⠀⠀⠀⠁⠀⠓⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠀⠀⢤⡀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠈⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢂⠀⠉⠀⠀⠀⣄⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⢹⠉⠀⠀⠠⠀⠾⣀⣠⠘⡰⢀⡀⠀⠁
⠀⠀⣴⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠊⠈⠀⠈⠢⠀⠀⠀⠀⠂⠀⠋⠁⠁
⣰⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠰⢆⠣⠣⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠃⠄⠀⠀⠀⠀⠀⠀⠀⠘
⣤⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⢤⣤⡤⡖⡼⣾⠃⠡⠀⡀⠀⢊⠀⡄⠀⠀⠀⠀⠦⠀⠀⡄⠀⠀⠀⠀⡀⢀⢀⣠⣠⠄⠀⢀⠄
⠙⢩⣤⡄⣀⡀⢀⣤⡔⣿⡴⢾⠀⠀⠎⠝⡱⡣⠁⢡⠆⡀⣎⠀⢀⠌⠀⠃⡄⠀⠈⠑⠀⠀⢠⠔⢆⣄⠠⠅⠚⠈⠁
⠀⠈⠻⠄⠿⠷⠌⠛⠉⠀⢠⠻⠀⠐⠀⠀⠐⡀⢰⠘⣸⢀⣏⠀⢺⠀⢰⠀⡸⢬⣒⣰⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠚⠀⠚⣴⡀⢀⢕⣧⠼⠏⠼⠇⠠⠼⠾⠦⠷⠈⠃⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⠀⡇⣨⣏⠯⠈⠁
⠀⠀⠀⠀⠀⠀⢄⢠⣱⡌⡯⠇⠟⠋⠁
⠀⠀⠀⠀⠀⠙⠈⠉⠁

⣀⣐⣤⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣛⣛⣙⣛⣟⣻⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⣀⣤⢤⠀⠤⠀⠀⠂⠐⡰⠢⢀⡀⠀⠀⠀⡄⠒⢂⠂⠀⠀⡒⠢⢤⡀
⠀⠀⢂⣴⡞⢿⠈⢛⡋⣄⢠⠄⠀⠀⠀⠠⠆⠀⠁⠀⠀⡀⠈⢠⠀⠈⠈⠀⠈⣴⡤⠃⢺⣆
⠀⠀⠐⠰⠥⢓⣴⢆⢳⡜⣯⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠐⠀⠳⡄⠀⠀⠀⣟⡿⡀⢛⣿⠄
⠀⢸⣸⡇⠸⢿⣧⣄⣿⢷⣿⡶⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣿⢧⡟⠹⢷
⠀⠀⠛⣆⣤⢠⣭⡏⠹⢾⣿⣷⠆⠀⠀⠀⠀⡆⠀⠀⠀⠀⢤⣝⢾⠀⠀⠀⢀⣿⣾⠃⢻⡟
⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠙⣿⣆⡠⠀⠀⠙⠙⢄⣀⠀⠰⣤⣝⠃⠀⠀⢀⢢⣧⣿⣦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣆⠀⠀⢐⣿⣿⣧⡀⣾⡝⠐⢄⠀⠐⢻⣿⣿⢇⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⣿⡽⢿⡍⠀⠀⠀⠀⠄⢠⠈⣿⠹⠿⣤⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢾⣿⠋⠀⠀⠀⠀⠀⠀⠐⡿⠋⢃⠘⣯⠲⡟⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠛⢻⡆⠘⠎⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⠟⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡀⢳⡟⠀⠀⠀⠈⠣⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠘⣁⣽⠀⠀⠀⠀⠀⡐⢀⣰⡿⠇⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠐⠶⠾⠿⠿⠟⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣤⣀⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠫⢋⣥⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣝⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠐⢫⣷⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣍⠃⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠙⣿⠟⠛⢷⣦⡄⠀⠀⠀⣀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣤⣄⠀⠀⠀⠀⡀⠀⠚⣉⣀⣤⣀⡾⠀⣿⣦⣤⣤⣤⣈⡁⠀⠈⠉⠛⢣⣤⣀⠀⢿⣿⣿⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠸⠛⣿⠟⠋⠀⣠⠆⠐⠁⠀⠀⢉⣠⣄⣀⡀⢠⡟⢷⣄⡀⠀⠉⡁⠀⠀⠀⠀⠀⢀⠉⠷⣦⡉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⢀⣀⡰⠋⠈⣠⠤⠟⢳⣿⢷⠆⠙⢿⣆⢠⡿⣦⠀⢀⠀⣶⣌⠙⠲⣄⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢴⣿⡛⠃⠀⠐⡡⠂⣴⠏⠀⠈⢷⠀⠀⡃⠀⠁⠿⠚⠻⠟⢸⠟⠀⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⢀⣧⣤⣤⣭⣄⠀⠸⠁⠀⠀⠀⠀⠀⠀⢤⣀⣡⠀⣀⣤⣤⣤⣤⣾⡆⢸⣿⡄⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⠇⠀⢠⣦⡙⠾⣿⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠿⠁⣼⣿⠾⠿⢁⣼⡟⠀⣦⢻⣷⠀⢻⡇⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⣿⠀⣄⠀⠈⠭⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⣀⣿⠀⣿⡆⠈⣿⠀⠀⠻⡗
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠉⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⠁⡟⠀⣿⡇⠀⣿⡇⠀⠐⢿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠁⢻⠀⠀⠠⠖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠲⡌⠉⡜⠁⢀⣿⠀⠀⣿⡇⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⣹⣿⠀⢘⡷⠲⠖⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡕⢦⣴⠀⠀⣼⡇⠀⠀⣿⠃⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⢀⣾⣿⡇⠸⣷⠀⠸⠋⣀⠀⠀⠀⣀⣀⣤⣀⣀⣀⣠⣤⣤⣤⠀⠀⠀⠀⡀⠈⣦⡟⠀⠀⣿⣷⠀⣸⡏
⠀⠀⠀⠀⡀⠀⠙⢿⣷⠀⠙⢆⠀⠈⠁⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡀⢀⠁⠀⠈⠀⠀⠴⠋⠛⠂⣿⡀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⣇⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⡀⠀⠛⠃⠀⠀⠀⢠⣣
⠀⠀⠀⢀⡿⠀⠀⠀⠀⢿⡟⠀⠠⣤⣌⣙⣉⣀⣀⢈⠀⠀⢹⡏⠀⢀⡀⠀⠀⠈⠋⢉⣠⠄⠀⢀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂
⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⣈⣉⣉⡁⠀⣠⣶⣿⣷⣄⡈⠙⠛⣋⣉⣉⡁⣄⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠡⠴⠾⠛⠛⠚⠛⠛⠛⠿⠦⣌⡻⣿⡝⠃⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠈⢷⠘⡷⣄⠀⠀⠀⢠⠸
⠀⠀⠀⠀⠀⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠘⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠧⠀⢀⡞
⠀⠀⠀⢀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⣤⣤⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁
⠀⣿⡄⠘⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠃⠀⢐⣠⣶⣿⠿⢛⣭⣶⠟⠋⠀⠀⠀⣀⣠⣤⡶⠾⠛⠉⠀⠀⣠⡴⠇
⠀⢻⣿⡀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉⢠⣶⡿⠋⢁⣀⣤⡶⠾⠛⠋⠉⠀⢀⣀⣠⣼⣷⠶⠏
⠀⠈⢿⣷⡀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⢀⡴⠋⣡⡴⠞⠛⠉⠀⠀⢀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠈⠻⣷⡄⠈⢻⣷⣦⣤⣄⣀⣀⣀⣠⣤⣶⣿⡿⠟⠁⠀⠀⡠⠋⣰⠟⠉⠀⠀⠀⣀⣴⡾⠛⠉⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠙⣿⣦⡀⠙⢷⣄⠉⠉⠉⠉⠙⠛⠉⠉⠀⠀⠀⣠⠞⠁⠀⠁⠀⠀⢀⣠⣾⠿⢋⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠘⣿⣿⣦⣄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣴⡿⠟⢁⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣠⣤⡾⠋⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠋⠀⠀⢀⣀⣠⠤⣤⣤⣤⣤⣶⠶⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⢤⡀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠚⢷⣶⡖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠛⠹⡿⣓⢧⣈⠟⢁⣥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⠈⡅⣰⢠⡥⢉⠸⠈⣁⢈⢉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣖⣢⠟⣩⢫⢋⡏⢸⠋⢩⢳⡃⠿⠈⡇⠓⣷⠇⠙⣜⣯⣘⢲⣿⡠⠧⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠟⠘⢂⠀⠏⠸⢡⡎⠜⣠⢀⡀⣿⠈⠃⡧⠀⠃⢠⡅⠠⠀⠈⣯⠻⡋⣻⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡆⡞⢸⡆⣰⠀⣸⢄⣰⡿⠘⢠⣟⠀⡄⠁⡄⠀⢰⠀⢰⡉⠀⢈⠃⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢰⢣⡘⣇⡟⣇⡇⣾⠘⢡⡆⡿⠇⣸⠃⢀⢧⢀⡜⠸⠀⠃⢹⣌⢲⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⢿⡌⣷⡡⡇⣙⣧⠿⠶⣝⣽⣇⣠⣏⣀⣾⣠⣨⣿⣤⠀⠀⠆⠓⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣏⠀⣿⠾⣧⢿⢟⠇⠀⠀⠀⠈⠙⠛⠓⠛⠓⠚⠉⠁⠲⠄⢀⢸⠃⠁
⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⠿⣍⣛⢌⣷⣿⣯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠸⢢
⠀⠀⠀⠀⠀⠀⣿⡧⣤⢻⢞⠁⠝⣿⣷⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣈⣿⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⡏⠀⠋⠀⠘⢣⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠒⡊⣹⡧⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⢴⣒⣦⣤⠷⡬⠥⠶⠶⠄⣠⣀⣤⣤⣀⡀⠤⠤⠴⠦⠒⠲⠶⠉⠉⠁⠀⠉
⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠋⠈
⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⠀⠴⣶⠆⠄⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡭⣤⣃⡀⠀⠀⢄⠠⣒⠠⢤⣝⢢⠁⠓⢉⠰⣆⢩⢐⠨⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢀⢄⣠⣦⠴⠵⠒⠲⣌⣓⠲⡄⠁⢁⠄⢈⣀⠎⢒⠐⢠⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠴⠡⠞⣀⠐⠲⠖⠓⠦⠤⡈⢷⣌⠀⢀⢠⠈⠍⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⢴⡥⠶⢊⡉⠛⠒⢦⡙⣦⡀⠁⠈⡀⠁⠘⠤⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣖⠚⠉⠙⠛⢶⣤⡛⠿⢙⠲⢴⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣥⡞⠛⠛⠙⠠⣌⡙⠆⠀⠙⠆⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣋⡴⠲⠶⠦⣲⡌⠑⠀⡃⠸⢾⠹⡄⠘⡆⢀⣤⡀⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣈⣉⣩⣙⠦⠝⢂⠈⠀⠐⠠⡠⠁⡇⠸⠃⡀⠀⠀⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡜⠁⢉⣀⡉⠛⠲⣄⠁⠀⠀⠀⠈⠉⠑⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢂⡞⠛⣉⣉⣓⠒⠒⠁⠀⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⠋⢠⡾⠋⣉⡉⠉⠀⢹⣶⡭⣙⠳⡌⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⢋⣤⡴⢋⣠⡼⠋⠛⠛⠿⠉⠳⣤⣈⠳⠘⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⡁⣤⠎⢀⣰⠿⠛⠛⢒⠂⠰⣀⠅⢠⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠞⣥⠞⣡⠖⢉⣥⡤⠾⠟⠉⣰⠋⠡⠞⢁⡀⠰⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠁⡸⠃⠞⠁⠴⠋⢀⠐⠂⠴⠾⠃⢙⡄⠀⠀⠀⠀⠈⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠶⠛⠁⣁⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡓⠾⠂⠁⠀⢀⣀⠀⠀⠀⠀⠀⠰⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠐⠁⠀⢸⣿⣷⠀⠀⠀⠀⠀⢂⠠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠆⠀⢀⡜⠛⠟⠀⠀⠀⠀⠀⠘⠷⠂
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠘⠁⠀⢐⠃⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⢰⣦⡴
⠀⠀⠀⠀⠀⠈⣹⠀⠀⠄⢀⠀⠁⠀⠠⠖⠂⠀⠀⠀⠀⠀⠀⢀⡂⢈⠃
⠀⠀⠀⠀⠀⠀⠉⠸⠆⠐⠁⠀⠀⠀⠀⢠⡶⢄⠀⠀⠀⢀⢠⡌⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣿⣆⢘⡷⠌⠋

⠀⠀⡄
⠀⠀⡄⠉
⠀⠀⠘⢂⣠⣴⡀
⠀⠀⠀⢈⠋⠉⠃
⠀⠀⡰⠟⢿⡶
⠀⣠⣷⣤⡴
⠀⢉⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⠔⠒⣶⣶⠶⡦⠤⢀
⠀⢸⣾⠟⠛⠄⡀⠀⠀⢀⡀⢤⣾⠋⠀⢿⣇⠀⢸⣿⠀⠀⡴⠶⠿⠿⢷⣄⡀
⠀⠀⠃⠀⢠⣾⠟⠛⣻⣟⠀⠘⢿⣦⠄⠀⠉⠁⠀⠉⢛⣦⣠⡶⠦⣤⣄⣉⡀⠓⠶⣄
⠀⠀⠀⠀⠙⠿⠄⠀⠙⠿⠷⠀⠁⠀⠀⠀⠀⠀⢀⣴⢯⡟⢁⣴⠟⣁⠀⠀⠀⠙⢢⣴⠟⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣱⠋⠀⡾⡵⠛⣁⣤⣶⠶⢶⣦⣄⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⡏⠀⣼⠛⢀⡞⠉⠀⢀⣀⣤⣤⣉⠻⣶⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣧⣼⠏⢠⡆⠀⣠⠾⠛⠉⠉⠉⠛⠂⣥⣀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢒⣤⡟⢹⡄⣿⡇⠀⠘⣧⡞⠁⠀⣀⣠⣤⣤⣤⡀⠹⠏⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠛⢣⡾⠁⣿⠇⠀⡴⢛⢀⠴⠟⠉⠉⠀⠈⠉⠛⢦⣄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⣇⢸⡇⢰⡇⠀⣾⠀⠟⠁⠀⢀⣤⣤⣤⣤⣤⣄⠀⠙⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠲⢤⣀⢙⣀⣳⣶⠀⠀⠀⣀⣴⣿⡿⠛⠛⠛⠻⠿⣤⣤⣠⣤⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠷⣦⡼⠟⠀⣽⠁⠀⢠⣾⡿⠟⠁⠀⣀⣤⣤⣀⡀⠈⢿⠋⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⠶⠖⠓⣴⠇⢀⣴⠟⠁⠀⢠⡶⠟⠉⠉⠉⠙⠻⣦⣾⡴⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢈⠉⠉⡿⠀⡼⠃⠀⠀⣴⠟⠁⠀⢀⣤⣤⣦⣤⡘⠿⠃⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠨⠃⠐⡇⠀⠁⠀⢀⡼⢁⡀⠠⠴⠛⢉⠤⢤⣀⣉⠳⢤⠶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢇⣀⣤⣜⣋⣤⠊⠁⠀⢀⣀⣠⠄⣠⣿⠭⠷⠶⠶⠶⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠈⢋⠀⢀⣀⣤⠔⣴⡻⠉⠁⠜⠁⣠⡶⠖⢋⣉⡀⠉⠛⠁⠠⣤⡀⠀⠀⠀⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠘⢁⣼⠛⠉⠁⢀⣤⣿⠇⠀⢀⣾⠏⠀⠀⡀⢠⡌⢻⣎⣻⠑⠶⠒⠞⠉⠀⠛⢤⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠃⢀⡜⣡⡾⢀⣠⡾⣏⢡⡆⠀⣼⡏⠀⣰⡆⢀⠸⣷⣰⠟⣱⡾⢀⣟⡵⠀⣹⠷⢶⡸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠘⢀⡿⠀⠉⠀⣿⠉⠀⢂⠘⡹⢦⣿⡇⢠⡟⠁⢈⡶⠛⢫⡤⣹⣇⠘⠯⣷⡄⠙⣄⠈⣤⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢷⣤⣴⣦⠀⠀⣿⢠⠙⢷⣆⠈⢿⡃⢀⠙⠧⢈⠀⢀⡞⢠⡔⣠⠄⣡⠀⢠⡖⡉⢠⣀⣭⠀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢦⣤⠶⠀⢰⡀⢻⣌⠷⣤⣿⣷⡈⢧⠈⢷⡀⠀⠀⢸⠀⣼⢀⡏⢼⡠⠖⠾⠀⠁⠀⠻⠟⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢴⠆⠀⢈⠸⣦⣽⣷⣤⣈⡉⢳⡌⢷⣤⣿⡀⢀⣸⠀⢿⠸⣿⠘⣧⡀⠀⢀⡄⣀⠄⠠⠄⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣧⠀⠈⠓⢤⣌⣉⠻⡆⢻⡄⠉⠻⢧⡈⠻⣆⠘⢷⣙⠧⡤⠩⣄⠸⠃⢿⣂⡀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠹⡄⢹⣀⡙⠫⣀⣉⡉⠛⠛⣳⣆⡉⠛⠛⠃⠉⣀⣠⣚⣉⠤⠄⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠀⢀⠠⠀⡇⠀⠀⠀⠀⠀⠛⠀⠀⠙⠃⣠⣥⠈⠉⠁⠀⢀⣤⣜⣽⣯⣿⠀⠀⠉⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⢀⡛⣨⡂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠑⢦⠈⠃⣠⡴⠖⢀⡙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢨⣇⡀⠁⠶⢛⡋⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡎⠑⢦⡀⠉⣉⠲⢲⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠀⠉⠳⣌⠛⢋⢭⣉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⢉⠀⠛⠉⠁⣈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣬⠂⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠆⠀⠀⠘⣄⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣆⢘⣧⠘⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠛⢩⡀⡄⣤⣔⠠⠴⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⣔⡞⢿⠰⣛⡭⠘⣃⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣚⡁⣼⣓⡖⣤⣙⠒⣀⣼⣡⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣴⠿⢥⣰⠯⣴⣌⣙⡃⣰⠾⠭⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢔⣡⢰⣦⣒⣹⣞⣳⠏⠉
⠀⠀⠀⠀⠀⠀⠀⡰⢷⡽⠚⣩⠿⣷⣶⣯⣝⡧⡀
⠀⠀⠀⠀⠀⠀⠀⣇⢸⠁⢜⣡⡴⠃⢠⣀⠛⠛⢳
⠀⠀⠀⠀⠀⠀⠀⡏⣾⢡⡿⢋⡴⠞⠋⣩⣭⠿⠿⠷⣄
⠀⠀⠀⠀⠀⠀⢠⡇⣿⢜⣡⡿⢀⣴⡞⢁⣶⣶⣛⣉⣉⣙⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⣏⠸⣯⡜⣸⢇⢾⡏⣰⠟⣡⠏⡿⠵⠒⠛⠛⢛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⡟⠂⢿⣅⡟⡘⢸⢠⠏⣾⢣⣾⠇⣸⠟⣻⣭⣭⣭⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡏
⠀⠀⠀⠀⠀⠀⡏⢸⠞⢟⡇⠀⣿⣾⢰⡇⡄⡏⣰⡏⣘⡿⠉⣶⢺⣿⣷⢶⣛⠿⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⡭⣇
⠀⠀⠀⠀⠀⢰⠁⢣⠌⣻⣿⡰⣿⣿⠻⣆⡇⣧⡏⣷⡿⢃⢣⣿⢟⣿⢀⡼⢡⢏⠽⡭⠭⢷⣄⠀⠀⠀⠀⠀⠀⠀⠫⣁⣼⣦⡀
⠀⠀⠀⠀⠀⣎⠀⠘⡼⠃⠀⠙⢻⣿⣌⣿⣧⣿⡅⡏⢿⣏⣾⣿⣾⠟⢸⠴⠋⣦⢖⢁⢲⠬⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠏⣢⡀
⠀⣴⢞⣉⠑⠏⢀⢠⠃⠀⠀⠀⠈⠙⠛⠛⠛⢿⣵⣽⣸⢿⢫⡟⡟⠀⡏⡀⠞⢹⠃⡏⣿⣴⢋⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡟⣳
⠀⠼⣧⣀⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣇⡏⠼⣇⢳⡀⠁⠻⣌⣿⡰⠇⣨⣿⣾⣄⣴⢿⣷⡀⠀⠀⠀⠀⠀⠀⢸⠛⢻
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⡜⣦⣟⠿⢧⢄⣐⠦⣽⣏⠙⣿⣟⡛⠻⣧⣀⣙⠧⡀⠀⠀⠀⠀⠀⡼⣗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣇⠴⠤⠳⣝⠬⢥⣬⠭⣍⣻⣭⡽⠛⠉⠉⠳⢷⣎⣛⢷⣆⡜⡷⡤⣤⡤⠞⢧⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢤⡤⣤⣘⠓⠒⠥⠐⢞⢫⡁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡛⠳⠤⢿⣧⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⢬⣈⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠒⠮⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣆⠠⠁⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⠘⠂⠀⠄⡱

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⣀⣀⠠⣤⣤⠄⣀⣀⡀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠈⠢⣸⣶⣮⡠⢖⡋⠩⠗⡒⠓⣛⣛⠚⢒⠺⠍⢙⡲⢄⣵⣶⣇⠔⠁⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠒⢶⣾⢟⡭⠂⠁⠤⣚⠫⠛⢛⣉⣉⡛⠛⠍⣓⠤⠈⠐⢍⡻⣿⡶⠒⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠺⢟⣵⢋⠔⣢⠀⢊⣡⡤⢘⣫⡥⢤⣉⡁⢤⣌⡙⠀⣔⠢⡙⣮⡻⠗⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⢯⠊⢾⠁⠰⢋⡥⢀⠉⡴⢛⣓⢤⠉⡄⢬⡙⠆⠈⡷⠑⡽⣿⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⢀⡞⠐⢑⣛⣛⣈⡁⢋⠘⢁⠀⠀⠊⠃⡝⢈⣁⣛⣛⡊⠂⢳⡀⢦⡁
⠀⠀⠀⠀⠀⠀⠀⠰⢠⣿⠇⡾⠀⡇⢀⢹⡐⠿⣻⡌⠀⠉⠀⠀⠀⠀⢡⣟⠿⢂⡏⡀⢸⠀⢷⠸⣿⡌⠆
⠀⠀⠀⠀⠀⠀⠀⠙⢼⡏⢸⡇⣆⢢⣄⣑⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣊⣡⡔⣰⢸⡇⢹⡇⢋
⠀⠀⠀⠀⠀⠀⠀⠆⢸⣷⢸⣧⠘⣦⡩⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⢍⣴⠃⣼⡇⣾⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⡈⣿⣦⠈⠳⢀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢪⡀⠞⠁⣴⣿⢁⣿⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠦⡙⣇⢤⣍⠷⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⠾⣉⡤⣸⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⢈⠈⠻⣷⣦⡽⠀⠀⠀⠢⣤⣄⡀⢀⣠⣤⠔⠀⠀⠀⢯⣴⣾⠟⢁⡁⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣁⠻⣶⣬⣽⣟⠀⠄⠀⠀⠈⠙⣿⣿⠋⠁⠀⠀⠠⠐⣻⣯⣥⣶⠟⣈⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⣉⠉⣤⣁⠀⠀⠀⡀⢀⣼⣧⡀⢀⠀⠀⡀⣈⣤⡉⣉⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠂⡖⠀⠉⠈⠉⠉⠁⠁⠀⢲⠐⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⢄⠀⠀⠀⢀⡠⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠉⠙⠛⠿⣿⣷⣤⣶⣶⣿⣿⠿⠿⠿⠿⠷⠶⠦⠄⠀⠀⠒⠋⢉⣉⣉⣉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠙⠻⢿⣿⡏⠀⠶⣤⣤⣤⣤⣤⣄⣀⠀⢀⡀⠀⠈⠉⠙⠻⣿⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣄⠀⠀⢀⣼⠇⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⣧⣄⣀⠉⠁⠸⣷⡀⠀⠀⠀⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠴⠛⢁⣤⣶⣿⠿⠿⠟⠛⠉⣿⠋⠉⠉⠙⠻⢿⣦⣄⠈⠙⠦⠄⠀⠀⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⢀⡴⠟⠋⣁⡤⠄⠀⣀⣤⣾⣿⠀⣷⣄⡀⠀⠀⠈⠙⢷⡄⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣇⠀⠉⣀⣴⠟⠁⢠⠶⠛⠉⠉⢉⣉⣀⡈⠙⠛⠷⣄⠀⣀⠀⠙⠂⠀⠙⢦⡙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⠁⣴⣿⠃⠀⠀⠀⣀⠀⠀⢰⣿⠟⠻⣿⣦⠀⢦⡀⠀⠈⢷⣄⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⢀⣴⠎⠀⠛⣁⢀⣀⣠⠀⠀⠙⢻⣿⡏⠀⠀⢻⡟⠀⠀⢿⡀⠀⢸⣿⣷⠀⠀⣠⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣰⣿⡏⢀⣴⣿⣿⠀⠻⣿⠀⠀⠀⠀⠿⠀⠀⠀⠘⠇⠀⠀⢸⣷⣷⢸⡿⠁⠀⢺⣿⡆⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⢸⣿⣿⠟⢳⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣬⣅⠘⠇⠀⠀⠘⣿⠇⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡄⠘⣿⣿⡆⢸⣿⡏⠀⠀⠙⠷⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠞⡡⠀⢀⠀⠀⢠⡟⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⠀⢻⣿⣷⡀⢻⣷⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⠊⠀⠀⣼⠀⠀⠈⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠙⢿⣷⣄⠙⢧⡀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡀⠐⠚⠛⠀⠀⣤⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠉⠛⠷⠦⠀⠀⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⣤⡾⠏⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⡄⠀⠀⢿⣿⣧⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠙⠋⠻⣿⣷⣶⣿⠟⠉⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⢙⡟⠁⠀⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠲⠶⠒⠛⠛⠓⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⠠⣠⣤⣰⠀⣌⡛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣦⠍⠐⣭⠂⠞⢙⡴⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠷⣾⠤⢍⣭⡶⡸⠭⠷⠨⣇⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠛⠤⢶⣖⣷⡻⠗⠒⠓⢗⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢾⣓⣶⣿⢮⣖⢝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡾⠛⡛⢻⡉⠳⡈⢳⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣶⡶⡾⠷⣤⡙⢷⣆⢸⡴⡇
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠛⠶⣤⣭⠙⢦⣄⠙⣧⡹⣾⡇⣇
⠀⠀⠘⢿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠿⠯⠽⣿⡛⡍⢳⣌⢻⣦⢹⡙⣞⣷⢹⡄
⠀⠀⠀⠀⠹⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣛⣛⣓⡲⢶⠘⣷⡝⢦⢻⡸⡏⠆⣇⣹⡇⠘⡇
⠀⠀⠀⠀⢰⣍⣩⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠾⣻⡶⣿⣽⢲⡍⠹⣟⢘⣧⢹⣎⣸⡆⣷⡇⠀⡟⠟⢴⠈⡇
⠀⠀⢀⡤⣯⣨⠝⠀⠀⠀⠀⠀⠀⢀⡴⠯⢭⡽⡽⡌⢧⠨⣿⢿⣧⢃⠿⣿⡏⣿⣿⣷⡟⣿⣷⢠⣿⡏⢠⠃⢣
⠀⣴⡉⣦⠞⠁⠀⠀⠀⠀⠀⠀⣠⣿⠭⢴⢊⢴⢴⡘⢺⡀⢻⣾⣿⣎⣿⢫⡇⣿⣿⣾⣡⣿⡟⠁⠀⠹⡌⠀⢸⡆
⢸⣙⡾⠁⠀⠀⠀⠀⠀⠀⢠⣴⠿⣍⢹⣼⢸⠎⣇⡑⣂⣿⠀⣯⢻⢹⡿⣼⣾⡿⠋⠉⠉⠁⠀⠀⠀⠀⢱⠀⠈⠋⠩⢝⡶
⢿⣉⡇⠀⠀⠀⠀⠀⠀⢰⡿⠻⣦⣾⣿⣧⣘⣣⣿⠴⠃⠀⣰⣣⡟⢊⢧⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡤⠤⠼⠓
⠸⡿⠛⣄⠀⠀⠀⣀⡔⠛⣤⡴⢟⣉⣭⠿⣤⣼⠷⣊⣥⠼⠛⠩⢿⠏⡟⠗⢲⣀
⠀⠙⢾⡝⢱⣶⠛⣱⣼⠞⡯⠶⠛⠉⠀⠀⠈⠙⠿⣯⣖⠓⢶⣂⣵⡞⠐⠉⣳⣏
⠀⠀⢀⠟⣛⠛⢉⡥⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠊⢇⣉⣡⠴⠚⠛⠛⠉
⠀⡴⠡⢊⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋
⢰⠓⠀⠀⡞⠛⢄⡀
⠈⠣⠥⠤⠤⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢛⢦⣄⣀⣀⣠⠠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⠀⠀⣇⣿⠁⠉⠁⠂⠛⠋⡿⠿⡦⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⢚⣿⣿⡙⣀⠂⠠⣿⡀⠠⠴⡗⠀⡊⠵⢄⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡮⢰⠿⡞⠁⢸⠃⣴⠇⡼⠉⢿⠳⢲⣤⡄⠐⣚⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣸⠁⠙⢸⠃⢠⡏⢠⡟⠰⡇⢳⡤⠔⠿⠛⠂⠀⠈⠲⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣇⠐⣿⠀⣾⡇⢀⣄⣦⡉⣴⠞⢥⣴⣾⣶⠤⣤⣴⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡘⡿⠀⣧⠀⣿⣧⢸⣿⡈⠹⣇⣴⣿⣿⣿⣟⡼⠛⠟⡝⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⠃⠘⢻⡀⠘⠿⣦⣌⣷⠀⣿⡏⠈⢻⣿⡟⠃⣀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠸⢧⣤⡌⠛⢦⣦⣤⣌⣻⡄⣿⡓⡀⠸⡇⢁⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⣄⠀⠀⠘⢯⢿⡆⢻⣧⣴⣷⡭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⠙⠳⠈⠀⠈⣷⣄⣀⣂⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠉⠉⠘⠁

⠀⠀⠀⠀⠀⠀⠀⣴⠶⠒⠲⠦⣄⡀⠀⠀⢀⣀⣀⡀⢀⣀⣀⡀⠀⠀⢀⣠⠴⠖⠒⢷⣆
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢨⠁⡠⠾⠛⠛⠛⢛⡉⠛⠛⠛⢷⣤⡈⣱⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⣇⢸⣆⣠⠖⠋⠈⠐⣲⠶⠶⠶⠋⠙⠻⠶⠶⣄⠠⣀⠘⠣⣄⣴⡞⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢮⠛⡡⠀⣾⠁⠐⢦⣤⣀⣰⠏⢸⣆⣀⣤⠬⠂⠈⣿⠀⢨⡛⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⠁⠊⣡⡶⠶⠆⡈⠏⣡⡼⢰⣌⡹⢃⡲⠶⢾⣎⠙⠲⠙⠃
⠀⠀⠀⠀⠀⠀⢀⠄⣠⠃⢸⣄⠁⣤⠶⣶⠅⢰⡃⠀⠘⠈⡇⢠⣶⠖⣤⠈⣠⡆⡀⢤⠀⣄
⠀⠀⠀⠀⠀⢰⡃⢰⡏⣿⠀⢿⣷⡄⠁⢲⢟⠈⠃⠀⠀⠀⠃⡻⣖⠈⢠⣾⡿⠀⣷⠘⣧⠈⡆
⠀⠀⠀⠀⠀⣸⠇⣾⡇⢿⣧⠀⠙⠳⠄⠀⣸⢆⠀⠀⠀⠀⡀⠛⠈⠠⠞⠋⠀⢀⡿⠀⣿⡄⣇
⠀⠀⠀⠀⢠⡏⢸⣿⡇⠘⣿⣷⣶⡶⠖⠄⠁⡌⠀⠀⠀⠀⢰⠀⠐⠤⢤⣶⣶⣿⠃⠀⣿⡇⠘⡇
⠀⠀⠀⠀⠸⡇⠀⣿⣷⡔⠚⠻⢿⣀⡀⠀⠀⠛⠿⣶⣶⠾⠟⠀⠀⠀⠀⣿⠟⠁⠀⣴⣿⠃⢰⡏
⠀⠀⠀⠀⠀⠙⢦⠹⣿⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⢈⡇⠀⠁⠀⠀⣸⠏⠀⢠⠄⠀⣽⠟⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠣⠈⠣⠀⢱⢶⠊⠙⠳⠦⠾⠐⠋⠙⠒⠤⢤⡾⠋⠀⣠⣼⠃⡼⠋⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡀⠀⠳⠄⠠⡐⠈⠀⠀⠀⠈⠀⢈⡔⠀⠉⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⢶⣦⣤⣤⡤⡶⠋⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⣤⣴⠶⠴⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠛⠛⢿⡟⠛⠉⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠻⣷⣤⣤⠀⣠⡴⠥⠒⠶⠟⠛⢻⣟⠛⠛⠓⠒⠢⠄⠑⢀⡀⢀⣀⣤⠖⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡆⠘⢿⣷⠀⠁⠀⠀⠠⠤⠤⠭⣽⣯⠉⠁⠤⢌⡀⠀⠀⠈⣁⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⠀⠉⠀⠠⠤⠾⠓⠚⣛⣳⣴⣦⣟⣛⠓⠶⠤⠤⡀⠀⠉⢡⠔⢀⡀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠄⠀⢀⣠⠄⣠⡶⠿⠋⠉⢛⡟⠉⠉⠻⢦⡀⠤⣄⠀⠀⢠⣾⡏⢠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠋⡀⠀⢿⠁⠈⢡⡶⠾⠿⠃⢻⡿⠘⠿⠷⢦⡄⠀⠹⠇⠀⠀⠻⠇⡸⢎⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⡾⠁⣠⡆⠀⠀⢀⠴⠛⢡⠶⠛⠛⠶⣄⠓⠦⡀⠀⠀⢠⡄⠐⢦⠈⣷⡀⠀⡹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣴⢟⠀⡘⢿⡇⣤⡄⠆⠀⢠⡆⠀⠀⠀⡀⢸⡆⠀⠀⣠⡄⢻⠟⠀⢠⢳⡌⢳⡄⠁⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⡏⢸⢰⣷⢴⣷⣤⡅⣀⠀⠈⠖⠁⠀⠀⠀⠳⠀⠀⣀⣡⣤⣶⢠⣷⢸⡇⣿⡆⠰⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣿⡿⠘⠸⡇⣼⠃⠘⢣⣥⣾⡄⠀⠀⠀⠀⠀⠀⢰⣦⣤⠞⡀⢹⡄⡏⢸⢹⣿⡇⠀⡆⠹⢀⠸⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣿⡁⠀⠀⡆⠹⣧⡀⠁⠀⠻⠃⠀⠀⠀⠀⠀⠀⠸⠏⠀⠈⢀⡾⠁⡄⠀⠀⢿⣿⠀⡇⠀⠘⡀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⣹⣷⣀⣶⣿⢶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡤⣶⣧⡜⣠⣿⠟⠀⠇⠀⡀⢹⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠈⠻⣿⣯⠙⢀⣘⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡄⠈⢹⣿⣿⠏⠀⣠⠆⠀⠄⢸⡇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣀⡀⠹⠿⣷⣤⣙⣦⢤⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⣾⣇⣴⣿⠟⠃⣀⠞⠉⠀⠀⠀⠘⡇⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠆⠀⠀⠈⠉⠻⢦⣀⠁⠈⠿⣦⡀⠀⣴⠾⠃⢈⣉⡠⠾⠛⠁⠁⠚⠃⠀⠀⠀⠀⠀⡄⠀⡇⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⠀⠀⠀⠘⣧⠤⠀⡁⠀⠀⠰⠖⠁⠀⣀⠀⠤⣾⠃⣀⣠⡴⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⢧⡀⠀⠀⠈⢿⣯⣤⣤⣴⠾⢷⡶⣤⣤⣽⡟⠁⡼⠟⠉⠀⠀⠀⢠⣿⠃⠀⠀⢰⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠻⣆⠀⠀⠀⢿⠉⠀⠀⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⢰⠀⠀⢀⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠈⢷⡀⠀⠀⠓⠒⠠⠄⢤⠴⠒⠊⠀⣠⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠸⣧⠀⠀⠀⠀⠹⣦⡀⠀⢀⣴⠿⠁⠀⠀⠀⡀⢀⣼⠟⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠹⣆⠀⠀⠙⢷⣀⠀⠀⠀⠈⠙⠀⠛⠁⠀⠀⢀⡠⠊⣠⡿⠃⠀⠀⠀⠀⠀⢀⡿⢁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠘⢧⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣀⣤⠞⠋⣠⠞⠉⠀⠀⠀⠀⡐⠀⢀⠾⣷⠛⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⢣⡀⠀⠀⠘⢿⣄⠀⠀⢀⡾⢋⣴⠖⠛⠁⠀⠀⠀⠀⢀⣴⠁⠀⡌⢀⣁⢴⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⢳⡄⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠰⠀⢈⣡⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠱⢄⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢣⠀⠈⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢰⠆⢰⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⠀⠉⠳⢆⠀⠀⠈⠀⠀⠀⠀⣠⣴⣾⠿⠋⠀⠀⢀⠴⠃⠀⢠⣤⣤⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠶⣦⣄⠀⢸⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣬⡑⠢⣤⠀⠀⠀⠀⠀⣀⣤⠔⠀⠀⠀⠀⠀⠀⡀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣟⣶⣶⣾⣿⠆⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⢆⠀⠰⠉⣀⠀⣀⣤⡾⣁⡤⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⢹⡋⠉⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⢈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠀⠀⠀⠀⠠⠀⠀⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠦⡀⠃⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢀⠀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠄⠀⠀⠀⠀⠀⠀⠸⢋⢉⡇⠀⠀⢀⠀⠀⠀⠰⠀⠂⠐⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠂⠀⠀⠀⠉⠂⠀⢃⡘⠀⠀⠀⣦⡀⢀⡀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑⠿⠿⠓⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢰⠀⠠⠀⠀⠋⠀⠀⠀⠀⠂⠀⠲⠄⠉⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣦⣠⣦⣀⣽⡀⠀⢀⡔⢀⠀⣰⡄⠀⣠⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠑⠒⠫⠴⠶⠾⠿⠶⠛⠡⠶⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠒⠒⢦⣤⣀⢠⠰⠖⠾⠴⣶⡾⣿⡿⣶⣶⠼⠖⠶⢠⣀⣠⣤⠖⠛⠲⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣤⣅⣈⡷⠄⢀⣠⣾⡟⣋⣩⣷⣾⣷⣯⣉⡻⣿⣤⣀⠀⠴⣋⣀⣥⡶⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠍⠅⢀⣀⡡⠤⢞⣋⣩⣴⠇⢷⣬⣍⣛⠦⠤⣁⣀⠀⠭⢽⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⢀⣠⢿⡅⠠⠞⣫⡷⣲⣾⢁⣸⣶⡲⣯⡛⠆⠀⣽⢧⣄⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⠛⣡⡿⠀⢠⡼⠀⣠⢛⡋⠀⠈⣛⢣⡄⠸⣤⠀⠸⣷⡙⢷⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⢛⡇⠶⠿⡄⢠⡏⠈⠀⠀⠀⠈⠈⣧⠀⠼⠷⠆⣟⠃⠀⢻⣧⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢸⣿⢸⡟⢸⣷⢴⣶⢦⡈⢻⣇⠀⠀⠀⢠⣿⠇⣠⠶⣶⢴⣿⠘⣿⢸⣿⠠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣼⣿⢸⡇⢆⡉⠳⡍⠹⡧⢸⣿⠂⠀⠀⢺⣿⠠⣿⠉⡵⠋⣁⠆⣿⢸⣿⣄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⢸⡄⠈⣛⡃⠀⠀⡗⣸⠃⠀⠀⠀⠀⢻⡐⡇⠀⠀⣙⡋⠀⣿⢸⣿⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⢼⣷⣶⣬⡶⢆⠔⠀⡌⠀⠀⠀⠀⠀⠈⡅⠀⢔⠶⣮⣼⣶⣿⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣼⣿⠧⣸⣧⠟⠀⠀⠄⠀⠀⠀⠀⠀⠐⠆⠀⠈⢧⣿⡰⢻⣿⣼⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣝⢛⠿⣿⠀⠀⠀⣮⡀⠀⣸⡀⠀⣠⡆⠀⠀⢸⡿⣟⣛⣿⣿⡧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⣟⣿⣿⣧⣬⣂⡐⠢⠈⠻⢶⡀⣰⠾⠋⠠⠚⣁⡪⣦⣽⣿⣟⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⣻⡉⠙⠳⠋⡭⠛⢃⠀⠀⣨⡀⠀⢈⠛⠩⡍⠳⠋⠈⣙⡟⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⢤⣠⡀⠘⣿⣦⣤⠾⣿⣿⢦⣴⣿⡟⠀⢠⣠⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡄⠀⠀⠀⢹⣿⣾⣉⠀⠀⠀⠈⠀⠀⠀⢈⣹⣾⣿⠁⠀⠀⠀⡄⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⡄⠀⠀⠈⠉⢿⣿⣶⣦⣤⣠⣠⣤⣶⣿⡿⠏⠉⠀⠀⢀⡼⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠛⠻⠟⢿⣿⣿⠟⠿⠛⠃⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



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

⠀⠀⠀⢠⠒⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠑⢢
⠀⠀⠀⡞⠀⣴⣶⣿⣶⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣴⣾⣷⣶⡄⠚⡆
⠀⠀⢸⠁⢸⣿⣿⣿⣿⣿⣦⠈⢢⡤⣤⠒⢒⣋⣙⣛⣓⣺⣳⣚⣛⣉⣓⠒⢲⣤⣴⠎⢠⣾⣿⣿⣿⣿⣿⠀⢹
⠀⠀⠀⠃⢸⣿⣿⣿⣿⡟⠟⠀⠰⠆⡠⠞⢛⣉⣩⣶⣿⡄⣽⢷⣮⣍⣙⠛⢦⠀⠧⡀⠘⠛⣿⣿⣿⣿⣿⡀⠃
⠀⠀⠀⠀⣽⣿⣿⣿⡋⢁⡄⢠⠄⠀⢠⠴⠟⠋⠁⣠⠄⡸⠶⣤⡀⠘⠛⠷⣄⠁⠀⢤⠀⡄⠈⣻⣿⣿⣿⡅
⠀⠀⠀⠀⠀⣿⠟⠋⣠⠂⣠⠃⠀⠐⠃⡤⠞⠋⠤⣤⠄⠁⠰⣶⡤⣌⠛⢦⡌⠳⠀⠈⢧⡈⢦⡈⠛⢿⡇
⠀⠀⠀⠀⠀⣷⠀⣾⠃⢠⣿⠀⠀⠀⡈⢀⡆⠀⣰⡃⡎⡆⢠⠀⣳⡀⠸⣆⠈⡀⠀⠀⢸⣧⠀⢿⡆⢰⡇
⠀⠀⠀⠀⠀⠈⢰⡇⡀⠸⢿⡀⠛⠛⠛⠆⢳⠀⠉⠱⠁⠁⠀⠀⠆⠁⠐⠃⠞⠛⠛⠓⣹⠿⠀⡈⣷⡈
⠀⠀⠀⠀⠀⢰⣿⠀⣿⠀⣼⡗⢶⡿⣿⣷⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⡷⠖⣿⡄⢸⡇⢸⣧
⠀⠀⠀⠀⠂⣾⣿⠀⣿⠀⡏⠻⣆⠙⠮⠵⣿⣷⠂⠀⠀⠀⠀⠀⠀⢰⣿⡷⠭⠞⣡⡾⠋⡇⢸⡇⢸⣿⡆⠆
⠀⠀⠀⠄⢀⣿⡟⠀⣾⠀⢷⡐⢬⠍⠃⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⡏⠉⠃⠈⠋⢭⠖⣰⠃⢸⡆⢸⣿⣇⠀⠄
⠀⠀⡀⠀⣾⣿⡇⠀⢸⢸⠈⠻⡤⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠢⡼⠃⢸⢸⠀⠀⣿⣿⡆⠀⡀
⠀⡘⠀⠀⣻⣿⣇⠀⣿⡆⣦⢷⡴⠁⣠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠵⡷⣴⣧⡆⣾⡇⢠⣿⣿⡃⠀⠘⡀
⢠⡗⠀⠀⠸⣿⣷⠀⢿⣿⠘⠆⢀⡴⠡⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠰⣄⢀⠟⢸⣿⠇⢸⣿⡿⠀⠀⠀⣧
⢈⣮⠄⠀⠀⢻⣿⣧⠀⠹⣆⡈⢾⣃⣴⠀⡀⢸⠶⠶⠤⣤⡤⠴⠶⢾⡿⡇⢰⣄⣻⡎⣠⡿⠃⣰⣿⣿⠃⠀⠀⢈⣏
⠀⢿⡆⠀⠀⠈⠻⣿⣿⣦⡈⠳⣄⠙⠷⠤⢤⡈⠻⣷⣦⠀⢠⣶⡿⠋⣡⠤⠴⠟⢋⡵⢋⣴⣾⣿⡿⠋⠀⠀⠀⣾⠇
⠀⠀⢠⣤⡀⠀⠀⠈⠙⠉⢿⣷⣦⣿⠳⠶⠤⠤⠀⠀⠙⢲⠚⠁⠀⠠⠤⠴⠖⢻⣧⣾⣿⠏⠙⠉⠀⠀⠀⣠⣦⠁
⠀⠀⠈⠻⣷⡀⡀⠀⠀⠀⠀⠻⢻⣿⣿⣃⣃⠀⠀⢀⣴⣿⣧⣄⡀⠀⢀⣃⣻⣿⣿⠿⢃⡄⠀⠀⠀⡀⣰⡿⠋
⠀⠀⠀⠀⠈⠁⣿⣶⣴⡇⠀⠀⠀⠀⢿⣿⣿⣿⠉⢃⡀⣛⣁⣠⠋⢻⣿⣿⣿⡏⢁⠘⠋⠁⣶⣴⣾⡇⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠟⢿⢆⡴⠿⠦⠶⣿⣿⣿⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠷⣦⢾⠟⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢿⢿⣿⣿⣿⣿⢿⣿⣿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⠀⠋⠁⠁⠚⠉⠃⣸⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣄⣀⠀⣀⣀⡄⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠒⣯⣹⣧⣼⣏⣽⠛⣷⢦⣄
⠀⠀⠀⠀⠀⠀⣼⢙⣻⠏⠀⠀⠀⠀⠉⠙⠳⢼⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣏⣩⠷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣏⣉⣽⠛⢲⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣤⣤⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⢉⠄⠂⣒⣦⡹⢻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡽⣼⢱⢁⡔⡢⢀⠽⣓⠼⠿⢷⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣷⡇⣧⠫⢸⠁⢁⢇⡞⡁⢀⡤⠒⡂⠀⣉⠽⢋⡭⢛⣳⡶⠶⣄
⠀⠀⠀⠀⠀⠀⣴⠋⢋⠀⡾⠸⡇⠹⠀⢈⠄⠜⠀⡾⡡⢎⢠⠞⡵⠋⡤⢂⡭⣶⣫⣤⣄⠈⢉⡱⣦⡀
⠀⠀⠀⠀⠀⣸⢯⢶⠃⢠⣧⠀⡇⠀⢸⢸⠀⡰⢰⢳⢠⢃⠃⡞⠀⣸⣡⡏⡸⣛⣭⣶⣿⣯⡂⢐⡭⢷⡄
⠀⠀⢀⡤⠶⢃⣾⠈⢀⢻⡿⢠⢷⡇⠁⡰⣸⠁⠞⡟⡈⡜⢰⡇⣰⠃⡿⣝⣿⣫⠵⣫⡥⠌⢩⣿⣿⣛⠻⢷⣦
⠀⠀⢸⡀⠀⠸⣿⢰⢿⢸⣅⣉⣾⡔⡇⣇⣻⠀⣼⢣⢣⡇⣼⠃⡏⣼⢿⡀⠸⢵⢀⣶⠰⢖⢼⢻⢁⢨⡓⠀⡽⣷⣿⣧
⠀⠀⠀⠙⠶⠦⠿⣾⣾⠿⠟⠛⠙⣷⡟⢹⠋⡼⡇⣿⢸⢣⡏⠀⣿⢸⣤⠏⢰⢠⡙⣉⣷⢀⣸⠀⢎⣯⣵⢦⣿⣉⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣯⣞⠀⠀⣿⠸⡸⡇⠀⣾⢜⣿⠂⣎⢲⠅⠀⠴⢀⠲⠹⡜⠳⡬⢩⢠⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣦⣀⣸⣶⡁⠙⣦⠻⡼⣯⠀⢿⠈⡨⡆⠲⡄⢨⣠⠃⠈⢧⠎⡬⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡤⠞⠋⣛⣷⣤⣬⣧⣙⣾⣷⣄⣡⢹⡦⢤⣜⣯⣀⣀⡀⢊⡴⣣⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢰⠇⠊⠑⠊⠉⠙⢧⡉⠀⠈⠙⣿⢸⢷⡋⠉⣹⣼⣡⣸⣽⠾⠋⢼⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⠆⡄⠀⠤⠀⠀⣀⣹⡆⠀⠀⠘⡿⠶⠿⢿⣰⡿⣏⢉⡖⡩⢡⠴⠞⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢆⢀⡐⣄⣦⡿⠛⠁⠀⠀⠀⠙⠓⠶⠶⠞⠀⢿⣼⣸⠀⡄⠔⠋⠭⠽⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣇⣀⠀⠀⡀⡄⠀⢙⠉⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡾⢿⣤⣦⣏⣠⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠏⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠞⠛⠿⢛⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⣤⡖⠂⠈⣿⣿⡃⠀⠀⣿⣿⣄⣀⡰⠋⢀⡠⣴⣶⣺⢟⣫⣽⠿⢛⣫⣽⠶⠿⠟⠛⠓⠒⠤⣄⡀
⠀⠀⢀⠔⠉⣿⣿⣧⣀⠠⠿⠟⠓⠒⠒⢚⠟⠋⢉⡒⢴⣫⣾⡿⠋⣱⣿⡟⣠⣾⡟⠉⠀⣀⣤⣶⣾⡿⠿⠿⠿⢿⣶⣄
⠀⢠⣿⡀⠀⢨⠟⠋⠀⠀⠀⠀⠀⠀⢀⣎⡤⢚⣁⡈⢿⣿⡟⠀⣴⡿⢋⣼⣿⠏⠀⣠⣾⡿⠛⠉⠀⠀⢀⣠⣤⣤⣤⣬⣑⣄
⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⡛⢿⣡⠟⠉⣹⣶⣻⣇⢸⡟⠀⣼⣿⠏⠀⣴⣿⠏⠀⠀⢀⣤⣾⡿⠛⠉⠀⣀⣀⣉⡙⢳⣄
⠀⡀⠈⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡞⢃⡶⠿⠿⠿⣿⠇⢸⡇⢰⣿⡿⠀⣼⣿⡏⠀⣴⢟⣩⠾⣫⠄⣠⣴⣿⠿⠛⠛⠛⢿⣟⣳⡀
⠀⢧⣄⣠⣼⣧⣀⡀⠀⠀⢀⣀⣴⣿⣿⣷⣮⠔⣀⣈⣻⣿⣇⣿⠁⣾⢹⡇⠀⢿⣹⡇⣸⣧⣿⡁⠚⣡⣞⣭⠭⠀⠀⠀⠀⠀⠀⠹⢿⣿⣤⡀
⠀⠈⠿⡿⠿⠃⠈⣿⣿⡇⠈⢹⣿⣿⣿⣿⣿⡾⣿⡿⢿⣿⣿⣿⠀⣿⢸⡇⡇⢸⣯⡿⡛⠀⡈⠛⣻⣿⣭⣥⣤⣶⣾⣿⣿⣿⣷⣦⡀⠉⠙⢿⡀
⠀⠀⠀⠈⠒⠠⠴⠿⠿⠣⠀⠞⠋⠉⠻⠉⡟⠀⢠⠂⠀⠀⠘⣿⣇⢻⡄⢿⣿⡞⣵⠏⣽⠿⣤⡾⢋⡽⣻⡿⠛⠉⠉⠉⠉⠉⠉⠙⢷⣄⣀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣇⡠⢘⡆⢰⡆⢠⡿⠿⣿⣿⣾⣿⢸⡏⣸⠁⣠⢀⣴⢏⡼⠋⣠⣤⣶⣶⣶⣤⣤⣄⠀⠈⠛⢿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠙⠎⠋⠛⠁⠀⠀⠙⠻⣿⣿⡇⠁⣾⡁⣾⣿⣾⠶⠛⠉⠁⠀⠀⠀⠉⢻⣿⣦⡀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣿⣿⢛⣻⣁⣠⠶⠛⠛⠛⠻⣶⡀⠀⠟⠛⢿⣷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣿⣉⠍⠳⠚⢛⣛⠳⢦⣼⣟⠻⢷⣄⠀⢿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⢿⣿⡄⠛⢫⠔⢠⠦⠤⣍⠳⠶⠦⡍⢳⡄⣻⣄⣾⣧⡾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⡇⠰⢶⣠⡐⢤⠐⡦⠈⡉⠙⢦⡀⠈⢉⠹⣯⡹⣟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⣰⢾⡶⠢⣅⣴⡦⢀⡁⠠⠛⡅⠈⡰⡆⢸⡶⠛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⠇⢸⣏⢸⣿⡴⠏⣶⠃⠀⠉⠀⣶⡄⠲⠄⣤⢀⣶⣞⣋⡉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⡀⢿⢸⣿⣿⠁⠙⣆⢠⠤⠞⣼⡄⣚⣤⢠⢠⣿⡟⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⠎⠀⢻⢁⣭⣙⡻⢤⣤⣌⣿⡾⠿⢃⣼⠃⢰⣇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡉⡾⡬⠁⠈⠹⡏⣠⠟⣫⡤⠶⠛⠁⢀⣾⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣄⠷⣶⣦⣵⢾⠡⠆⠱⠶⢶⣀⣴⣿⣯⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠛⠷⣦⣬⡥⢠⣴⡟⢛⣿⣿⡿⢛⡁⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡻⠦⣀⣀⣠⣴⠿⣿⣇⡼⠋⡽⢃⣉⠙⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠈⠛⠀⢉⡿⣤⠇⠈⠁⠈⢷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⣶⣹⣆⣷⣰⡈⣆⠜⢱⠇⠀⡀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠘⠀⠀⡸⠀⠀⠃⢠⠀⠈⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠁⠀⠓⠘⢂⠑⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠐⡤⠀⠈⠄⠀⢰⡄⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⣥⢷⡌⣠⣾⢁⡟⢻⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠊⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠠⠄⠀⠠⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠻⣿⣿⣶⣄⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠛⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣶⣶⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣶⣶⣿⣿⡿⠋⠀⣴⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⢀⣴⣿⠟⠉⠉⢉⣠⠶⣿⣿⣿⣿⣿⣿⣿⣿⠶⣄⡉⠉⠉⠻⣿⣦⡀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⣴⣿⡟⠁⠀⠀⠐⠋⣴⡿⣛⣉⡉⠉⠉⢉⣙⣛⢿⣦⠙⠀⠀⠀⠈⠻⣿⣦⣹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⣰⠃⠀⢀⢞⣵⡿⢋⣴⣾⣿⣿⣷⣦⡙⢿⣮⡳⡀⠀⠈⣆⠀⠹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠀⠀⣿⠀⠀⢀⣿⡏⢠⣿⠏⠁⠀⠀⠈⠹⣿⡄⢹⣿⡀⠀⠀⣿⠀⠀⢹⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣴⣾⣿⠟⣿⣿⠀⠀⠀⠻⠿⠿⠾⣿⡇⣸⠃⠀⠀⠀⠀⠀⠀⠘⡇⢸⣿⠷⠿⠿⠟⠀⠀⠀⣿⣿⠻⣿⣷⣦
⠀⠀⠀⢀⣾⣿⣿⡏⢸⣿⡇⢀⡆⠀⠀⣤⣶⣦⣤⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣤⣴⣶⣤⠀⠀⢰⡀⢸⣿⡇⢹⣿⣿⣷⡀
⠀⠀⠀⣼⠏⣿⡿⠀⣿⣿⠁⣼⣗⠀⠀⢻⡟⢧⣛⣹⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣏⣛⡸⢻⡟⠀⠀⣻⣧⠈⣿⣿⠀⢿⣿⠹⣧
⠀⠀⠀⠋⢸⣿⡇⠀⣿⣿⡀⣿⣟⡄⣀⣤⣭⣆⡈⡉⣿⡏⠀⠀⠀⠀⠀⠈⢹⣿⢉⢁⣰⣭⣤⣀⢠⣻⣿⢀⣿⣿⠀⢸⣿⡇⠘
⠀⠀⠀⠀⢸⣿⡇⠀⢹⡇⠁⣿⣿⡶⠀⠀⠠⠾⠋⠡⢻⠇⠀⠀⠀⠀⠀⠀⠸⡟⠎⠙⠷⠄⠀⠀⢶⣿⣿⠈⢸⡏⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠘⣿⡄⠸⣿⣧⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⣼⣿⠇⢠⣿⠃⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⢻⡿⡄⠙⣿⡏⠁⢀⡀⠀⢸⣧⡖⠀⠀⠀⠀⠀⠀⢲⣼⡇⠀⢀⡀⠈⢹⣿⠋⠠⢾⡟⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠘⣿⣧⣿⡀⠈⢷⡀⠀⠈⠃⢠⡞⠀⠀⠘⣿⣧⣀⣀⣀⣀⣀⣀⣼⣿⠃⠀⠀⢳⡄⠘⠁⠀⢀⡿⠁⢀⣿⣼⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠈⢿⣆⡀⠀⣾⠛⠶⢤⣀⠀⠉⠛⠿⣿⣿⠿⠛⠉⠀⣀⡤⠶⠛⣷⠀⢀⣰⡿⠁⠀⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠙⢿⣦⣿⣷⣤⣀⣀⡀⠀⠀⠀⢹⡏⠀⠀⠀⢀⣀⣀⣤⣾⣿⣴⡿⠋⠀⠀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⢻⡘⣿⣷⣄⠀⡀⠈⠙⢿⣤⣀⣀⣤⠄⠀⢠⣿⣿⡄⠀⠠⣤⣀⣠⣤⡿⠋⠁⢀⠀⣠⣾⣿⢃⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣷⡄⠀⠈⠙⠿⣷⣶⣶⡾⠿⠟⠻⠿⢷⣶⣶⣾⠿⠋⠁⠀⢠⣾⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣴⣿⣯⠖⠋⠁⠀⠀⠈⠑⠲⣽⣿⣦⣤⣴⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣬⣭⣝⣫⣭⣥⣶⣶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⢛⡢⠀⠀⠀⣠⠭⣭⣾⣭⣄⡀⠀⠀⠀⣈⣋⡳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣬⣻⠇⠀⠴⠶⢒⣰⣶⣀⠚⠻⠾⠟⢻⣩⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⣡⡶⠟⢫⡾⠛⣩⡻⠯⠙⣶⠘⡳⠄⠻⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢮⡾⠋⠊⠀⢠⣶⠾⠿⡹⠾⢷⡆⠀⠙⡈⢦⡀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⡿⠁⣼⡇⡄⡴⠒⣠⠞⢻⣆⠰⠆⣠⢸⣧⠀⠻⣄⠛⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢲⣿⠁⣼⣸⣇⡛⠞⢸⠇⠂⠠⠳⠀⠑⢛⣸⡇⢼⡀⢿⡆⢠⡧
⠀⠀⠀⠀⠀⠀⠀⢰⡏⢘⣿⡇⠏⢰⢾⣱⢴⡌⠀⠀⠀⠁⣰⡦⣾⠳⡇⢸⢁⣾⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣻⡧⢈⣻⣧⢣⣀⠛⠄⠈⠁⠀⠀⠀⠀⠹⠄⢁⠞⣀⡈⢨⣿⠇⠚⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡍⢻⣿⡜⠉⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣾⠟⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡉⠙⠳⣮⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠴⠻⡁⣼⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⢠⡑⠀⠐⢄⠀⢀⠔⠃⠔⢠⠚⠉⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣧⣅⡀⠀⣡⡁⠀⣀⣤⣾⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣀⠉⠉⠙⠋⢙⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⢶⠞⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⡶⢶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⡤⣴⣌⣛⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠘⠲⠶⣭⡙⠳⣄⠀⣠⠄⠊⣩⣵⡶⢴⣾⣿⣿⣤⣤⣌⡉⠒⠠⣀⣠⠀⢀⡀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣆⠀⠘⣻⣶⡾⠳⠀⢀⣚⣉⣉⣠⡄⢀⢀⡤⢤⣤⣬⣭⣐⡰⠚⠁⢠⡿⠋⠐⣻⣶⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢿⣿⣯⣿⣿⠿⠶⠶⠛⠛⠛⠉⣀⣴⣿⣿⣷⣄⣄⡉⠉⢉⣛⠀⠀⠘⢁⣴⣿⣿⡿⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣿⣿⢟⣀⣠⣿⠿⣻⣥⣾⣿⠟⠛⢻⡿⣯⣍⠙⢿⣷⣤⠙⠿⣷⣦⠈⠻⣿⠿⠀⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣉⣀⣾⡿⢛⡥⠆⡰⠟⠛⢁⣀⣴⣟⣿⣌⣩⣅⡀⠙⠋⠀⢳⣌⠹⣧⠀⠀⢴⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣹⡿⠛⠀⠋⠀⠀⠀⣠⣾⣿⣿⣿⡧⣿⠿⠿⣿⣿⣦⠀⠙⠀⠈⠧⠙⢷⣄⠀⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣠⣾⡿⠁⢠⣿⡗⠀⠀⠀⣉⣉⡅⠀⣀⣠⣿⣄⠀⠀⠀⣍⠁⢀⡀⢸⣷⡀⠀⠰⣄⠐⢌⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢰⣿⡿⠃⢀⢸⣿⡇⢰⡇⢸⢛⠉⢀⡾⠟⠁⢹⣟⢧⡄⢹⣻⡆⣾⡇⣾⣿⡇⡀⠀⠘⢷⡄⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣿⣿⠀⠀⣾⠀⣽⡇⢴⣿⡆⠛⠀⣿⠇⣾⠠⢸⡘⣷⣇⠈⣇⣿⡿⡀⢸⣧⠀⣸⡄⠀⠘⣷⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠸⣿⣷⠀⢠⣿⡾⡿⣿⢶⠶⣦⡀⠀⢏⣴⡃⡄⠈⢁⡜⡀⠀⢸⣧⢶⡾⡿⢿⡆⢻⣧⠀⠀⣿⡄⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣻⣿⡆⢸⡏⠠⣷⡿⢮⡳⣤⣿⡆⡩⠘⠁⠀⠈⠀⠸⣀⣴⣦⣤⢞⡵⢷⣿⢠⠘⣿⠀⣴⣿⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠸⣿⣿⣇⢸⡇⠀⠻⣤⡈⠻⠆⣹⡷⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠸⠟⢃⣴⠏⡼⠀⡇⢸⣿⣿⡿⠀⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠠⣌⠙⣷⠘⣧⣤⣄⠘⢓⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⢀⣛⡃⢀⣀⣰⠁⢸⣿⣿⠃⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢻⣿⣮⡀⣿⡟⢟⠚⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠌⠹⠋⢻⣿⣄⣼⣿⡇⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠘⢿⣿⣷⣮⡓⠀⣦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡆⠀⢀⣼⣿⣿⠏⠂⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⡀⠀⠉⠛⠛⢿⣶⣯⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⣾⠿⢛⡡⠀⣠⣾⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⡙⠀⠀⠀⠀⠀⢞⡿⣿⡱⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣸⣏⡋⠐⣊⣥⣶⡿⢛⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⠦⣀⠀⠀⠐⣦⡙⠲⠄⠈⠳⣤⡀⠀⠀⣠⠞⠁⠠⠔⢛⣥⡿⠋⠉⢉⣀⣠⡔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠶⠿⢿⣦⣿⣝⠳⠤⠤⠀⠈⠳⠤⠜⠁⠀⠠⠤⠖⣫⣾⡷⠿⠿⠛⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⣦⣀⣀⣠⣾⣤⣀⣠⣤⣤⣶⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠉⠙⠉⠉⠙⠛⠉⠁⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⣤⠀⠀⠀⠀⢀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣧⣴⣿⡷⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⡶⢶⣶⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡟⢰⡟⢱⣦⢻⢿⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣴⣾⣏⣿⠧⣞⠸⣃⣋⠛⠀⠃⡍⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣙⠻⠿⣤⡀⠢⣜⢧⡙⣿⠮⣿⣿⣦⣹⣧⡿⣿⣤⡽⣱⣧⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠳⢤⣈⢷⡶⢤⣉⠓⠦⣕⣷⣼⣅⡘⡷⢌⢧⠙⠻⠿⠳⣶⠈⠁
⠀⠀⠀⠀⠀⠀⣠⡿⢍⠳⣤⠉⢷⡊⠛⣯⣉⣛⠒⠬⣿⢹⠗⣵⢼⣌⠒⢄⡀⢤⣙⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢟⡯⢬⡃⡽⣧⠀⣹⣇⣯⣾⣩⡭⢵⣿⠈⣀⣘⢳⡿⣄⣮⡻⢯⡉⠉⠙⠛⠻⠶⠦⢄
⠀⠀⠀⠀⠀⠀⠻⣾⣽⡿⠿⠿⠿⠿⠿⣿⣛⣚⣹⣋⠐⠛⠛⠺⠿⠿⠿⠿⠷⡶⠴⠶⠶⠶⠦⠴⠶⠾
⠀⢠⣶⢰⡆⣰⡄⢺⣷⣌⡇⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠓⠘
⣄⠀⠉⠉⠉⠉⠉⠉⠉⠁
⣦⡑⠄
⠙⠛⠎⠁

⠀⠀⠀⠀⠀⡰⠒⠉⠙⠛⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠉⠉⠒⢆
⠀⠀⠀⠀⢠⠇⠀⠀⣠⣤⣤⣄⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢁⣠⣤⣤⣄⠀⠀⣼⡄
⠀⠀⠀⢀⡟⠀⣀⣽⣿⣿⣿⣿⣷⣆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⡶⢶⡶⠶⢆⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡖⠀⣠⣿⣿⣿⣿⣿⣿⡀⠈⢷
⠀⠀⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⢦⡤⣴⡖⠒⠛⣋⣉⣉⣉⣉⣛⢚⣛⣛⣋⣉⣉⣉⣙⠛⠛⣷⣶⣴⣶⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠣⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⡆⠀⣠⡖⠀⢀⡴⠿⠛⠛⠉⣁⣍⣟⡁⣍⣻⣩⣌⠙⠛⠛⠿⢦⡀⠀⢰⣅⠀⢸⢿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠜
⠀⠀⠀⠀⠀⠱⣽⣿⣿⣿⣿⣿⠿⠀⠀⡀⠚⠉⠀⠴⠉⢀⣴⣶⡿⠿⠛⠋⠙⢃⡘⠋⠉⠛⠛⣿⣶⣦⡀⠙⢦⠀⠉⠓⢀⠀⠀⠻⣿⣿⣿⣿⣿⣯⠎
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⣠⠎⢠⡖⠀⠀⢀⡴⠛⠋⠁⡀⠀⣤⠾⠋⡌⠛⠻⠷⣦⠀⣀⠈⠙⠻⢦⡀⠁⠀⢶⡀⠱⣄⠀⢰⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠠⣿⡿⠛⠋⢁⡜⠀⢠⡟⠀⠀⠠⠋⢀⣠⠾⠟⢉⣤⣤⣤⠆⠃⠃⢻⣷⣤⣤⡉⠻⠷⣄⡀⠛⡄⠀⠀⢻⡄⠈⢧⡌⠙⠛⢿⣷⠆
⠀⠀⠀⠀⠀⠀⠐⣯⡀⠀⣴⡟⠁⢠⣿⠀⠀⠀⠀⠀⠞⠁⣴⠀⠈⢀⡿⢡⡖⡀⠠⡈⠌⢿⡀⠁⠐⣆⠈⠓⠀⠈⠀⠀⠀⣿⡄⠈⢿⣷⠀⢀⣵⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠁⢸⡟⠀⠀⣿⣿⡆⢀⣤⣀⣤⣄⠐⣿⠀⠀⣾⡶⠸⠇⠇⠀⠓⠀⢳⢻⠀⠀⣿⠀⣠⣤⣀⣤⡀⢸⣿⣿⠀⡈⢿⡇⠩⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣰⠀⠟⢻⡅⠈⠙⠋⢙⡛⠂⠹⢆⠀⠀⠀⠟⠀⠀⠀⢀⠀⠳⠀⠀⠀⠋⠐⢛⡋⠉⠉⠉⢸⡟⠻⠀⣇⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡄⠀⣸⡿⠤⣶⡿⣿⣿⢷⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⠴⢿⣇⠀⢠⣿⠀⢿⣿⡀⡀
⠀⠀⠀⠀⠀⢠⠀⣸⣿⡇⠀⣿⠇⢰⡿⣷⣄⠈⢷⣘⠛⢛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡛⠛⣣⡾⠁⣠⣾⢿⡆⢸⣿⠀⢸⣿⣇⠐⡀
⠀⠀⠀⠀⠀⡘⢀⣿⣿⡇⠀⢸⠀⠀⡇⠈⠛⢧⣄⣉⠉⠉⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡿⠉⢉⣉⣤⡾⠋⠀⢸⠅⢘⡇⠀⢸⣿⣿⡀⠃
⠀⠀⠀⠀⡴⠀⢸⣿⣿⠃⠀⢸⠆⠀⣿⡄⠳⣤⣬⠉⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠑⠀⠈⠉⣥⣴⠎⢰⡿⠀⢸⡇⠀⢸⣿⣿⡇⠈⢆
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⢘⡇⣦⠈⢻⣆⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⣰⠟⠁⡶⢸⠃⠀⠈⣿⣿⣿⡄
⠀⠀⡰⠂⠀⢸⣿⣿⣿⠀⠀⣸⡇⠹⠀⣤⡉⢉⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠦⢣⡉⢁⣴⠀⠏⣸⡇⠀⠠⣿⣿⣿⡅⠀⠘⢆
⠀⢠⠁⠀⠀⠀⣿⣿⣷⠆⠀⢿⣿⡈⣷⡝⢷⢊⠀⣠⠞⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⠈⠓⠷⡑⠿⢣⣾⢡⣿⣗⠀⢰⣾⣿⣿⠀⠀⠀⠐⡄
⠀⣿⠂⠀⠀⠀⢿⣿⣿⡆⠀⢹⣿⡇⠘⠷⠀⠀⣴⠃⡼⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠐⣦⢀⠀⡾⠁⣼⣿⡏⠀⢸⣿⣿⡷⠀⠀⠀⠐⣷
⠀⢏⠜⠀⠀⠀⠈⣿⣿⣿⣄⠀⠻⣿⡄⠀⢦⣽⠇⢀⡴⠀⠀⠀⣦⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣿⣿⢧⠀⣤⡀⠸⣧⡜⠀⣠⣿⠟⠁⣠⣿⣿⣿⠀⠀⠀⠀⠢⡹
⠀⢿⣟⠀⠀⠀⠀⠸⣿⣿⣿⣄⣀⠈⠳⣦⡀⠙⢶⡿⠃⠐⠃⠀⢿⣁⣀⡈⠉⠛⠛⠉⢁⣀⣈⡿⡿⠘⠂⠘⣿⣶⣫⢄⣴⡟⠁⣀⣴⣿⣿⣿⠇⠀⠀⠀⠀⣳⡿
⠀⠸⢮⠇⠀⠀⠀⠀⠋⠻⣿⣿⣿⣷⣄⠈⠻⣄⠈⠙⠟⠶⠶⢄⡈⠛⢿⣿⡇⠀⠀⢼⣿⡿⠛⢁⡠⠶⠶⠻⠋⢉⣡⠟⢁⣴⣾⣿⣿⣿⠟⠙⠀⠀⠀⠀⢸⡿⠇
⠀⠀⠈⢤⣤⡀⠀⠀⠀⠀⠉⠙⠋⢹⣿⣿⣦⣬⣿⠷⢶⣶⣤⣤⣀⢀⠀⠈⠓⢶⡶⠚⠁⠀⣀⣠⣤⣤⣶⠶⢿⣿⣥⣾⣿⣿⡏⠛⠋⠉⠀⠀⠀⠀⢀⣤⡤⠁
⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡤⠄⡤⠠⠰⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠆⠄⢠⠠⣴⣾⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠻⣿⡄⣰⡀⠀⠀⢀⠀⠀⠈⠁⠹⠿⢿⣶⣤⣦⣄⣀⣀⣤⠼⠻⣿⣿⠛⠶⣤⣅⣀⣠⣶⣶⣾⣿⣿⡟⢉⣁⣾⠀⡀⠀⠀⢀⣆⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠁⢿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠱⣀⠀⠘⠃⢀⣠⠏⠈⣿⣿⣿⣿⣿⣿⠀⣀⠘⠋⠁⠀⣿⣶⣶⣿⡿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⢿⣶⡄⢀⣴⣷⣆⣤⣬⣿⣿⣿⣿⣤⣼⣯⣯⣯⣿⣽⣼⣶⣶⣿⣿⣿⣿⣿⣶⣶⣿⣷⣄⣠⣶⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠋⠀⠉⠉⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠋⠀⠙⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣝⣵⠻⣿⣟⣿⣿⠿⣟⣻⣿⠷⣮⣫⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⣏⠀⠈⠈⠃⠁⠚⠚⢁⠓⢀⣽⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠼⠷⢤⡴⠾⠦⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣄⢀⡀⣠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⢀⣤⣼⡧⠐⠼⠅⠂⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⢾⢏⡞⠱⣫⡾⢻⣝⡽⢡⢣⣶⠒⠏⢿⢀⠎⠻⠀⠰⠊⠋⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣳⣾⣦⠃⡎⡞⠀⠀⡏⠀⢸⠿⠱⣡⢻⠃⠀⡀⠸⡝⠷⡀⠲⡖⢀⠧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⣱⢧⡟⣏⠠⠁⢡⠀⠰⠁⡆⠘⢠⠐⢱⠏⠀⠀⠀⠁⢳⣔⣉⠀⠀⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡻⢞⣿⠘⡄⡴⠃⢀⡔⣠⢁⢠⡇⠀⡇⢀⠀⠀⡀⠈⡄⠘⢦⣄⡜⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢹⠓⢧⢸⠀⡗⠁⠀⡏⢸⢡⠎⢸⠀⡇⢳⠀⡆⠀⠀⠀⠉⠓⢄⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣩⠧⠀⠪⠧⢆⡇⠴⢖⠃⣺⣊⢀⠘⢞⣔⣈⢰⡻⡀⠄⠀⠀⠂⣠⠇
⣠⡀⠀⠀⠀⠀⠀⠀⣬⠉⠦⠀⠀⠐⠉⠀⡆⠀⠩⣡⠋⠉⠈⠀⠀⠀⠀⠁⠉⠘⠄⠀⠐⡇⠤⠖
⡿⠿⡄⠀⠀⠀⠀⣸⠃⢈⡢⠆⠀⠀⠀⢀⢇⠩⠭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗
⢠⣴⣷⣄⠀⣀⠔⣿⡖⠀⠚⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠙⠅⡀⣿⣦⠤⠊⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠂⠀⠈⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡐⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢿⠀⠓⣀⠀⢰⡤⣤⣀⠀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣞⠳⢺⡭⣝⠎⢿⡉⠑⢠⡟⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⡿⠃⠛⠇⠰⣾⡷⢟⢰⡘⠓⠀⠁
⠀⠀⠀⠀⠀⡠⠔⠒⢒⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠳⠄⠀⠀⠀⠀⢐⡃⣼⣹⠏⣂
⠀⠀⠀⠀⢰⡁⠀⢰⣿⡿⠋⠀⠈⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡸⣄⠀⠀⠔⠀⣁⠉⠁⠋⡠⠃
⠀⠀⠀⠀⠀⠙⠒⠛⠻⢧⡀⣠⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⠨⠱⢁⠀⠠⡖⠀⢀⡰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠉⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⢸⡦⣀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣿⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⣾⡉⣿⠸⡿⣿⡙⢾⢣⠉⠀⠀⠀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣦⡜⠀⠀⠀⠀⠀⠀⢀⢴⣾⣯⠹⣧⠹⣇⠘⡆⢁⠘⣿⡿⣌⠓⢄⢨⠑⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⠁⠀⠀⠀⢀⣴⢸⣿⢸⣿⠻⡄⠙⣇⢹⡄⢀⡾⠐⣮⢳⡈⣧⠈⠆⠐⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣶⣦⡠⠁⠀⠀⢀⡄⠻⣿⠸⣿⡄⣿⡆⢻⡄⢿⡄⠃⢸⢇⣂⣬⣤⣓⠈⢆⠀⡇⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠟⠁⠀⠀⡔⢻⣷⡀⢻⡄⠿⢀⡸⣷⠀⢿⡈⠃⠀⠀⠈⡟⠉⠉⠉⠑⠀⢣⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠿⣿⣷⠊⠀⠀⢀⠾⣿⣆⠙⢧⠀⠙⠀⠈⣷⡙⣧⠈⠃⠀⠀⠀⢠⢃⣠⣤⣄⠘⢦⣸⣷⠇
⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠇⠀⠀⢠⣾⣆⠈⠻⠆⠀⠈⠀⠒⠤⢿⣧⡈⠁⠀⠀⢀⠂⢸⠶⠄⠀⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⣼⠿⠿⡞⠀⠀⢠⣷⡈⠉⠳⢦⠀⠀⠈⠓⠶⣤⣌⣻⡷⡄⠀⠀⠂⠀⠈⣿⠛⠋⠉⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⣇⣠⣤⡇⠀⠀⣶⡉⠛⠷⠦⠀⠀⠀⠴⠶⢶⣬⣛⢿⡷⠀⡠⠀⠀⠀⡼⠻⡟⠛⠉⠷⢶⣿⡇
⠀⠀⠀⠀⠀⠀⢹⠋⠉⢇⠀⠀⣏⠻⠷⠦⠄⠀⠀⠐⠒⠶⢦⣍⡻⢿⠗⠈⠀⠀⠀⠈⠀⠀⢳⣶⠶⠆⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡾⠿⠿⡄⠀⣿⢷⣦⣀⠀⠀⠀⢀⣠⣠⣄⠙⢿⡞⠀⢀⡀⠂⠀⠀⠀⠀⣸⠶⢖⣂⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣇⣠⣶⡿⢶⣿⣶⣤⡉⠀⠀⠀⠀⣈⡙⠻⣿⣾⣴⣾⣯⣄⣀⣀⣀⣀⠀⢉⣤⣭⡥⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢸⣿⠉⠉⠛⠁⠀⠀⠀⣠⣾⠋⣩⡟⠛⠛⠛⢛⡛⠛⠿⣿⣷⠸⡉⠁⠀⠀⠈⠻⣏⣙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠳⣟⠛⠀⢀⣀⠠⠽⣿⣀⣏⣀⣀⠀⠛⠚⣧⢙⡆⠉⠀⠀⠙⢦⣀⡀⠀⠑⣎⣢⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⡡⠄⠀⠀⠐⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡴⣌⡉⠭⠬⠅⠴⢄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⢣⢀⣸⠿⢂⣀⢲⣝⡰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣿⠈⡀⠠⢶⣗⠂⢚⡿⠆⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠈⠀⠐⢠⠰⢀⠐⠘⡒⢃⢠⢀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠺⡐⢦⣄⣀⣀⣴⢖⡪⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢇⠈⣄⢠⡑⠀⠀⡟⠀⠹⡗⠠⢄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣰⡿⣦⣀⡜⠂⢇⡀⣀⠋⢀⣩⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⠧⡉⠛⢧⣀⠀⠿⠁⣀⡞⢋⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⢧⡈⠀⠀⠈⠶⡶⠞⣵⠞⢓⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠘⠳⣄⠀⢀⣀⠀⠞⠁⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢦⣄⣀⠑⠄⠉⠉⢀⣠⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡉⠀⠘⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⣀⠀⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠴⠗⠈⠀⠠


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⡀⠠⠄⠀⠛⠉⢠⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠀⠀⢅⡘⡳⠀⠀⠘⣩⡤⢬⠶⠦⣤⣆⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡴⠀⣀⠑⡉⠆⣇⡸⠃⢠⠶⠶⠒⠦⠴⢅⠰⣆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡷⡟⡤⢶⠞⠋⠴⠲⠿⣂⣤⣀⣠⣉⠉⠑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠄⠀⠰⡀⣠⣤⠴⠚⠉⣀⡀⣀⡀⢁⠒
⠀⠀⠀⠀⢀⡰⠂⠀⠀⠤⠀⠀⠀⠀⠘⠀⡇⠏⣠⣤⠵⠋⠉⠉⠉⣙⢢⡹
⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠂⠒⠐⢻⣆⡔⠐⠈⢀⡤⠤⠴⣛⡂⡚⠦⡙⡿
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠂⠇⡄⡏⠸⠁⣷⠖⠃⠴⣂⣤⣀⣄⡉⢦⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠁⠀⢀⠄⠛⡖⡩⢏⡁⠒⠀⠦⠝⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠖⠋⠉⠉⠭⠍⠙⠂⠃⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠺⠿⠶⠀⠶⠞⠛⠋⠉⣉⣅⣀⣀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣚⠉⣉⣤⠶⣶⣒⡤⠞⣩⠍⢉⣨⠵⣋⣁⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⡻⢋⡭⢉⠴⠶⢦⣄⠤⠶⠦⠖⢛⡛⢁⡐⠀⢁⠊⠚⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡜⣱⠟⠒⠁⠞⠓⣀⣀⡤⠀⠐⢓⣩⠀⢛⡀⡐⠁⠀⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⢻⡅⠀⠀⠰⠛⣉⡋⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠏⢱⢠⠀⠠⣾⢋⣥⠀⠀⠀⠀⠀⠘⠀⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠳⠀⠘⢎⡴⠛⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣆⠀⠀⠃⠀⠀⠁⠀⠾⣧⠈⣿⠖⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⠆⠠⠁⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⠃⢑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠒⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⠀⠀⠀⠐⠀⠀⠀⠀⢻⡟⠃⣀⠀⠀⠀⣀⠼⢧⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠾⣏⣈⣿⣅⡿⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠖⣶⣤⣄⣀⣀⠀⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢲⡶⣆⣤⠤⣴⣤⣤⣠⣾⣯⣽⠷⠶⣏⡉⠉⠛⠛⠛⣦⣤⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣾⣫⣴⣿⣿⣋⡴⣊⣿⣅⣙⡹⠟⢁⣐⣶⣿⣿⣿⡂⢠⠄⠋⠀⣀⠙⠱
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⣿⣿⣿⣿⣿⣿⣯⣾⣿⡈⠛⠋⢠⠼⠿⢟⣬⣗⠲⠦⠌⠫⠠⠺⣿⡏⣠⡀
⠀⠀⠀⠀⠀⠀⠀⡸⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢐⠆⠤⠖⣋⢙⣿⣉⡛⠓⠖⠢⣄⠘⢿⣇⠙⠁⢀
⠀⠀⠀⠀⠀⠀⢀⢣⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⠃⣀⢋⣽⣿⣿⡿⢯⡀⠀⢀⣦⠠⣀⠉⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣸⣿⢸⢠⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⡷⢦⠀⣴⢿⣿⣽⡄⢀⠶⠟⣺⡉⡆⠹⣇
⠀⠀⠀⠀⠀⠀⣿⡇⢸⢸⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣶⣴⣾⡄⠋⠈⡇⣠⢾⣿⡿⠷⢿⡄⢹⡆⢀
⠀⠀⠀⠀⠀⠀⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣟⣿⣿⠇⠀⣠⣼⣿⢘⣫⡼⠃⢈⡇⢸⡇⠀⢨
⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⢹⣿⣿⡀⢿⣿⢿⣿⣿⠇⠀⠀⠀⣿⡷⢬⡀⠐⠈⢹⠇⣼⠇⠀⠎⣰
⠀⠀⠀⠀⠀⠀⠸⣟⣿⡿⣿⡿⣿⣿⢸⣿⣿⣷⠈⠿⣾⣿⣿⠃⣽⣆⠀⠉⡃⣤⠙⠦⢛⣵⡾⡿⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣹⣿⢹⡿⢸⣿⣿⡿⠧⠀⠠⣿⣿⣯⣭⣡⠖⠑⠉⠀⣠⣴⡟⠁⠀⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⠀⣿⣟⠚⡿⣿⣦⠠⠄⢀⣬⣥⣀⣀⣰⣿⣿⣿⠤⢐⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣸⢿⡿⣿⣿⣷⣿⣆⠙⣿⣿⡿⠝⣿⣋⣾⠀⠀⠀⠀⠀⠘⠙⠟⠛⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⣸⣟⢿⣾⣿⣿⠹⣿⣆⣿⣉⣷⡎⠈⠿⣿⣷⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣬⣛⢷⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣇⡀⢙⡿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣬⣉⣻⣿⣿⡏⠀⠀⠀⢻⣿⣿⡎⠽⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠃
⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠻⣿⠃⠀⠀⠀⠈⣿⣿⡗⠓⠉⣷⣶⣄⠀⠀⠐⠉⢠⣤⣾⡏⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠘⢧⣤⣶⣷⣏⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⢰⣦⣼⠤⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢈⡟⠉⠙⢿⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠄⣀⠤⠟
⠀⠀⠀⠀⠀⠀⣼⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⡉
⠀⡀⠀⠀⠀⠀⠿⠿⣿⣶⣿⡹⠆⠀⠀⠀⠀⠀⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠇
⢾⣿⣦⣀⣠⣶⣤⠀⡛⣘⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠈⠻⣿⣿⣿⠿⠋⠀⠉⣵⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣀⡁⠀⠀⠀⠀⣿⣿⣿⣴⢦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠠
⠀⠀⠈⢿⣿⣿⡟⠄⠀⢠⠃⢻⣿⡇⠀⠀⠀⡀⡈⠰⢶⠁⠀⠀⠀⢈⣠⠷⡆⠠⠤⠖⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠈⠉⠁⠀⠀⠠⠄⠁⠄⠀⠀⠀⠀⠘⣀⣋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡴⣿⢉⡿⣍⣇
⠀⠀⠀⠀⠀⢀⡞⠀⣾⡇⠀⣿⣿⠏⠘⣳⡙⠽⠷⢦⡀
⠀⠀⠀⠀⠀⣿⡅⢢⠉⠻⡄⠘⠛⢀⡀⡈⣅⡐⢾⡀⢳⡀
⠀⠀⠀⠀⢦⡈⢻⡌⡇⢠⡇⠀⢄⡾⢡⡗⠠⠟⢛⠃⠀⠳⡄
⠀⠀⠰⠦⣄⡙⢦⠙⡇⣾⠀⡘⡾⠠⠞⠛⠓⠒⠤⠆⠀⠠⠈⢆
⠘⠛⣛⠦⣄⡉⠓⠄⠀⢷⡀⢷⠹⣤⡀⢠⠈⡄⣈⠀⠈⠤⠰⣿⠃
⢾⣛⣭⠤⠤⣭⣍⣑⠂⠀⠑⠀⢠⣀⠉⠲⢱⡀⠈⠿⠿⠟⣻⠁
⢹⣇⣶⡾⣛⣩⣥⡾⣃⣤⡴⠖⣂⣈⣉⣛⣀⡀⠀⠐⠒⠚⠁
⣸⡟⢻⣿⡟⢋⣥⡾⠋⢀⣴⡿⠛⣹⠃⠀⣠⡤⠶⠖⣢⠤⠀⠀⣀⣄⠀⠀⣀⣀⣤⠄⠀⠀⠀⡀⠀⠀⢀⣠⠴⠒⠂⠀⣀⡀
⠿⠁⣿⢻⡇⢀⣽⣷⣶⡿⠋⣠⣾⠃⣴⡟⠁⠀⢀⡞⠁⣠⡶⣻⠟⢁⡴⣫⡟⢋⣴⢞⣡⢶⣿⠁⠀⣴⡟⠁⢀⡴⠿⠟⠛⠛⠻⠶⠶⣤⡀
⢤⡀⠇⢸⠇⣸⡿⢉⣿⠓⣶⣿⣥⣾⠟⠀⠀⣠⡟⠀⣸⣟⣴⠟⠰⠋⣰⡏⢠⣟⣡⠞⠁⣼⠏⠀⣰⡿⠀⣴⡟⠁⣀⣠⣴⣶⣦⣤⣀⠈⠙
⡶⠳⣄⢸⡀⣿⡇⣸⡿⠀⡿⢿⡉⢀⣴⣶⠿⠛⢀⣤⣶⡿⠋⠀⠀⣴⡟⢠⣾⠋⠀⢀⣾⠃⣀⣼⡿⢁⣾⢟⡴⠛⣩⣴⡶⠶⠄⠉⠛⠿⠶
⡶⢇⡌⢦⡁⠹⣧⠻⡇⠸⣇⠘⣧⠈⣿⣄⠀⢾⣿⡋⣡⣶⡟⣠⣾⣟⣴⣿⣁⣀⣤⣿⣥⣾⣿⣧⣾⣿⣿⣯⣤⣀⣀⣤⣴⠶⠖⢚⣀⡀
⣴⡿⠃⠀⠙⠶⣬⣧⡑⢄⠀⠀⢿⡄⠈⢿⣦⠀⠹⣷⣿⣯⡉⠻⣯⠻⠟⠿⣶⡌⠙⢿⣿⣿⡿⣾⣿⣿⣿⣿⣷⣤⣉⡁⠀⠴⠟⢻⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠠⡀⢤⢀⡀⣀⣀⣀⢠⠀⣄⢤⠤⠄⠀⠤⡤⡄⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠋⣭⡝⠀⠄⡐⠉⠀⠘⠘⡆⢷⢰⠛⡜⢠⢳⠘⢇⠳⡀⢠⠰⡙⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠠⣄⡀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡌⠀⡏⠈⢧⠘⡇⠢⠸⡔⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠨⣱⠀⠘⠃⠀⠀⠐⢀⠀⠀⠀⠄⡃⠘⣼⠀⠳⠀⡸⠀⢧⢠⢠⠌⢢⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⡜⠁⠦⠁⠆⠀⠀⠀⠈⠀⢀⡆⡀⣿⡄⢹⠃⢤⠀⠧⣈⡝⠼⢩⣾⠘⠈⢞⡄⠀⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣘⠁⠰⠀⠀⠀⠸⡘⣿⣱⠃⢆⣌⣀⣀⠀⠁⠀⠐⠛⣨⢟⠀⠀⠐⠋⢰⠄⠦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠀⠀⠀⠀⠋⠉⠘⠃⠀⠋⠁⢋⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣙⣫⣍⣹⣝⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡃⠶⠌⠙⣀⢁⠸⠀⢿⡿⠷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢈⡭⣧⠈⠍⢉⡸⠂⢰⠀⠒⠁⣰⢸⠇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢡⣄⠈⠁⠘⢁⠏⠀⠀⢀⢹⡎⠂⢘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠀⠉⠉⠒⢀⡇⠈⢸⢁⢰⡘⣶⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⢊⠙⡖⢤⡞⠀⠀⠘⠘⣇⠃⡟⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⢁⣸⡷⡈⡎⠀⠀⠀⠀⣿⠀⠀⡏⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⢸⡟⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠙⣇⣄⠑⣌⠂⠀⠀⠀⠀⣷⢡⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢹⠻⠆⣧⢸⡛⡄⠹⠄⠀⠀⠀⠀⡏⠈⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⠴⣮⣉⠖⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣾⠁⣿⠀⡔⢶⡈⠀⠛⠻⡄⢆⠀⠀⠀⠀⢀⡟⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠲⣏⣹⠦⠄⠒⠉⠀⠀⠀⠀⢀⢤⡴⣶⢋⣽⠋⣿⠀⣿⠀⣿⠀⡘⡄⢻⡄⢄⢦⡀⠀⠀⠀⠀⠀⡞⣸⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣎⣉⡻⠊⠁⠀⠀⠀⠀⠀⠀⣠⢾⢃⡎⠸⣰⠃⡎⢸⠀⢂⡞⠱⢸⠛⢂⠻⣇⠀⠇⠈⠀⠙⠀⠀⠀⠀⠀⢠⠟⢃
⠀⠀⠀⠀⠀⢠⠋⣡⡝⠀⠀⠀⠀⠀⠀⣀⢤⡞⣇⣌⠈⣿⠀⣿⠀⢣⡇⠀⣼⣰⠀⠀⡄⠸⡆⠈⢳⡄⢠⠀⠀⠀⠀⠀⠀⣰⠟⣣⠟
⠀⠀⠀⠀⠀⠈⢶⡄⢸⠖⢢⡤⠰⣖⢿⣤⡎⢠⢹⡎⠆⣿⠀⠙⢆⢸⣰⠆⠇⠹⣀⠟⣔⣄⡙⢦⡈⠃⡘⠀⠀⠀⢀⣦⠞⣡⣚⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠚⠦⠤⠔⠒⠉⢀⡎⠁⢸⡀⠅⣆⠻⡄⠀⠀⠀⠛⠇⠂⠀⠹⡆⣌⡉⠑⠄⠻⠐⡇⠀⣠⠶⠋⠐⠊⣩⡅⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢧⢠⡀⢹⡄⠻⣄⠈⢂⠀⠀⠀⠀⠀⠀⠑⢦⠀⠉⠁⠀⠀⢀⡗⠋⠁⠀⡄⠘⢂⡴⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠰⣌⠈⠳⣄⠙⠂⠈⠁⠀⣠⠤⠖⠒⠒⠀⠤⠜⣂⠀⠉⠓⠂⠀⡇⠀⠀⢰⠉⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⢀⣀⣀⡀⠀⣀⡉⠴⠋⠀⠀⠀⡀⠠⠬⠶⡾⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⣠⠊⠁⠀⠀⠈⠀⠹⣄⡀⠀⠀⠀⣀⡈⠤⠒⠉⠀⠀⢃⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠉⢇⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠠⣄⠀⠀⡆⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠎⢀⡄⣄⢠⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⣸⢦⢠⡃⠠⡤⡄⢼⢢
⠀⠀⠀⠀⠀⠀⠸⣀⣶⡆⣬⡇⣸⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⢐⡶⢘⣾⣿⠆⠀⠀⠀⠀⠈⠢⣀⣸⣼⣷⢷⠷⠼⠧⠻⠚⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠁⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠟⣩⢀⠂⣤⣐⠤⠰⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢫⡰⠳⡏⠬⣛⠍⢽⣃⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡒⢨⡿⢶⠇⣌⠻⠤⣈⣿⣳⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣸⣏⣈⣭⣍⣦⡙⠻⠎⢭⡽⢉⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠞⡁⣤⣩⢝⢮⡷⣽⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣜⣕⡭⠞⣻⣿⣯⣽⣛⠿⣄
⠀⠀⠀⠀⠀⠀⠀⣾⢀⡟⢀⠞⣁⣼⠋⡉⠹⠿⠾⣇
⠀⠀⠀⠀⠀⠀⠀⣿⢨⡇⣰⡾⢛⣡⡴⠟⡷⢶⣶⣾⣄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⢇⡟⣰⡟⠁⣠⡔⠛⣭⣠⡤⠾⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠇⣿⢎⠎⣿⢀⣾⠟⣠⡾⢹⠟⣶⣚⣛⣿⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣻⡄⢹⡾⢸⡇⡏⡟⢰⠟⣴⢏⣼⡏⣤⣤⠤⠴⠶⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣩⡟⠁
⠀⠀⠀⠀⠀⠀⡿⠀⡎⣷⣾⠸⢠⣇⡟⢸⡇⢎⡟⢠⡟⢰⣾⠿⣛⣻⢽⣛⣓⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠿⢿
⠀⠀⠀⠀⠀⠀⡷⢰⠉⢬⣼⡀⣘⣿⣇⣟⢹⢸⢡⣿⡇⣧⠏⡆⣿⣵⣿⠟⢩⡗⣪⢭⠭⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠟⢧
⠀⠀⠀⠀⠀⢰⠁⢃⠇⣼⠛⠧⣿⣾⡇⢽⣾⣼⣾⢸⡟⣧⣸⢸⣿⢳⣿⠡⡏⡴⠳⢋⢳⢙⡛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠑⢶⡿⠓⣦⡀
⠀⠀⣀⣀⣀⣸⠀⠈⣸⠁⠀⠀⠈⢿⣿⣬⣿⣿⣿⡜⡇⢿⣧⣿⣿⣿⠋⣰⠏⢁⢾⣻⢢⢨⡒⣺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡁⢿⣆
⠀⢻⡣⠤⠀⠁⠠⢀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⣿⣿⡞⣿⢰⡇⣇⠀⡗⢼⠈⣸⡁⢿⠸⣾⣇⡴⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⣼
⠀⠚⠻⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⣏⠚⣧⣹⣆⠀⠘⠷⢿⣤⣋⣠⣾⣿⣷⣴⠟⠿⣧⠀⠀⠀⠀⠀⠀⠀⢸⡉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣻⡌⣷⢯⡛⢻⣢⣬⣑⣶⣧⣈⣽⢿⣭⢉⠻⣦⣠⡝⠳⣄⠀⠀⠀⠀⢀⠟⠯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣵⠚⠂⠻⢮⡒⠶⣶⠖⢦⣽⣶⠾⠋⠁⠀⠈⠛⠿⢬⣝⠿⣴⣩⠻⢒⢦⠖⢟⣷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠶⠶⠦⣍⡋⠛⠂⢐⠻⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⡛⠺⠿⠶⢾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡈⠓⠪⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠃⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠁⠜⠀⠀⠄⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠛⢶⣤⡀⠀⠀⠀⣀⣠⣤⣤⣄⠀⣠⣤⣤⣤⣀⡀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢠⡈⠁⠀⣠⡾⠿⠟⠛⠿⠛⠋⠙⠛⠛⠛⠻⢿⣷⣄⠀⠉⣰⡄⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⣰⡄⠀⠀⣀⡸⠇⠐⠋⣁⣤⣀⣠⣤⣠⣴⡟⢷⣦⣤⣄⣀⡀⠙⠉⠓⠀⠻⣇⠀⠀⢀⣀⣴⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢻⣷⣴⡾⠋⠀⣀⣠⠈⠡⠾⠛⠛⠛⠋⢉⡀⣀⠉⠉⠉⠙⠻⣦⠀⠲⣄⣀⠈⠙⣶⣾⣿⡇⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣌⠛⠋⡔⠀⢸⡿⠁⠀⠳⣦⣤⣀⠀⣰⣾⠁⢹⣷⡀⢀⣀⣤⠤⠞⠀⠘⣿⡆⠀⢮⡛⠋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠟⠀⠴⠟⣡⣤⣤⣤⡌⠉⣿⠿⠛⢁⡴⢀⡝⠛⢿⡟⠁⣠⣤⣤⣤⡙⠷⢤⣀⠹⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠆⣀⠀⡀⠀⢰⠿⠛⠛⠉⠓⢦⠉⢀⡶⠿⠃⢸⡿⣶⠈⠁⠴⠛⠉⠛⠻⢷⡄⠀⠈⠁⠀⠁⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣴⠃⠀⢿⣄⠀⢀⣤⡞⢿⣷⡆⠀⢸⠁⠀⠀⠈⠃⢹⡆⢀⢴⣾⡟⢶⣄⡀⢀⣴⡇⡀⠀⣦⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣼⠇⣿⡀⠸⣿⣷⣄⡈⠓⠤⣥⣾⠆⠸⡇⠀⠀⠀⠀⠈⡇⢸⣦⠭⠔⠋⣀⣴⣿⡿⠀⢻⡀⢸⣧⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠀⣿⣇⠀⠙⠻⣿⡇⠀⠀⡞⢡⡎⠀⠀⠀⠀⠀⠀⠀⠀⣷⡝⠇⠀⠀⣿⣿⠟⠁⠀⢸⡇⠀⣿⡀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣾⣿⠀⢻⣿⣆⠀⠀⠈⠻⠦⠀⠀⢠⠟⣡⠀⠀⠀⠀⠀⠀⡀⠘⠄⠀⠠⠾⠋⠀⠀⠀⢠⣿⠇⠀⣿⣷⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠁⢰⣿⣿⠀⠈⣿⣿⣷⣦⣤⣤⡤⢤⡀⠋⢀⠋⠀⠀⠀⠀⠀⠀⢱⠀⠀⢤⣀⣀⣠⣤⣶⣶⣿⡟⠀⠀⣿⣿⡆⠘⣷
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⣿⣿⡀⠀⠈⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣧⣄⣀⠀⢀⣀⣠⣼⠇⠀⠀⠀⠉⠙⣿⣿⣿⠏⠀⠀⢀⣿⣿⠃⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢻⣿⣿⠎⠉⠀⠙⠻⢷⣄⡄⠀⠐⠲⠤⠙⠛⠿⣿⣿⠿⠛⣉⠰⠒⠀⠀⡄⢠⡿⠟⠁⠀⠀⢰⣿⣿⡟⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿⠀⠈⠁⠀⠀⠀⠀⢹⠃⠀⠈⢁⡀⠁⠀⠀⣿⠐⠂⠀⣠⠀⠀⠀⣿⣿⠃⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⣿⣆⠀⠰⢤⣀⣀⡠⠿⣷⣄⡀⢁⡤⢀⣠⡾⢷⣄⠀⠤⠀⢉⣩⣾⠇⠀⠀⠀⣿⡄⠐⣴⠟⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠙⠦⠀⢸⠟⢿⠀⠀⠈⠙⠛⠛⢚⠉⠀⠀⠀⢀⡉⠛⠛⣛⠋⠀⠀⣠⡴⠶⠏⠀⠴⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⠀⠀⠘⠷⣄⠀⢦⡀⠋⠁⠀⠀⠀⠀⠀⠉⠀⠈⣠⠆⠀⠈⠁⠀⠀⢀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠳⠄⠀⠀⠀⠀⠀⢻⣦⣀⡀⠀⠀⠀⠀⣀⣠⣾⠋⠀⠀⠀⠀⠀⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⠿⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃

⠀⠀⠀⠀⢠⠒⠉⠉⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠉⠉⠒⡄
⠀⠀⠀⢀⡟⠀⢀⣤⣶⣦⣄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⣠⣴⣶⣦⣄⠠⢿⡀
⠀⠀⠀⡼⠀⢰⣾⣿⣿⣿⣿⣷⡄⠐⢄⠀⠀⢀⣀⣀⡤⠤⠬⣭⣯⣻⣿⣛⡥⠤⠤⢤⣄⣀⣀⠀⢀⣠⠊⢠⣾⣿⣿⣿⣿⣿⡆⠀⢧
⠀⠀⠀⢻⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠈⢛⡙⠛⢀⣤⡶⠶⠶⠲⠶⠔⠶⠶⠖⠶⠶⣶⣤⡀⠛⠛⡻⠁⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⡟
⠀⠀⠀⠀⠡⡸⣿⣿⣿⣿⣿⠏⠉⠁⠔⠛⢀⠔⠉⣠⣤⣶⡾⠿⠿⠏⠹⠟⠻⠷⣶⣤⣄⠙⢦⡀⠛⠢⠈⠉⠹⣿⣿⣿⣿⣿⢇⠌
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⠁⢀⠔⢁⡄⠀⠀⣠⠞⠛⠉⠁⢀⡤⠖⡈⠷⠶⣦⡀⠈⠙⠛⠳⣄⠀⠀⢠⡈⠢⡀⠈⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡟⠛⠋⣴⠃⢠⠏⠀⠀⠜⠁⣠⠶⠛⣡⢤⣤⠄⠃⠂⢷⣦⣤⣌⠛⠷⣄⠈⠣⠀⠀⢳⡄⠘⣦⡙⠛⢻⣿
⠀⠀⠀⠀⠀⠀⣧⡀⢠⣿⠃⢀⣿⠀⠀⠀⠀⠘⠁⣼⠀⠀⡼⠃⡖⡄⢰⡐⠘⢧⠈⠀⣧⠈⠃⠀⠀⠀⠀⣿⡀⠘⣿⡆⢀⣼
⠀⠀⠀⠀⠀⠀⠛⠀⣼⠁⠀⣿⣿⠆⠠⣦⣶⣶⡀⣿⠀⠸⠛⢀⠃⠃⠀⠁⢈⠋⠇⠀⡿⢀⣶⣶⣴⣄⢸⣿⣧⢠⠘⣷⠀⠟
⠀⠀⠀⠀⠀⠀⠀⣴⡟⢰⡇⠉⢹⣇⢀⣀⣤⣤⣄⠈⠣⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠁⣠⣤⣤⣀⠀⣸⡏⠉⢸⡄⢻⣦
⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⡧⠀⣾⣏⠉⢻⡙⢿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡿⢻⡟⢉⣽⣷⠀⣼⡇⢸⣿⡆
⠀⠀⠀⠀⠠⠀⣾⣿⡅⠘⡇⠀⡇⠙⢷⣄⡙⠒⠚⢿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡿⠒⠒⢋⣠⡾⠋⢸⠀⢹⠁⢸⣿⣿⠈⠆
⠀⠀⠀⢠⠂⢠⣿⣿⠃⠀⡇⠀⣷⡄⢦⣬⡉⠃⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠃⠀⠙⢩⣥⡔⢠⡟⠀⢼⠀⠘⣿⣿⡀⠰⡀
⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⣧⢰⠈⠳⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠟⠁⡆⣿⠀⠀⣿⣿⣷
⠀⢠⠎⠀⠠⣿⣿⡟⠀⢠⣿⠘⡀⣶⡈⠐⠐⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣘⢊⢄⢡⡶⢀⠃⣿⠀⠀⢿⣿⣿⠄⠀⠱⠄
⠀⣔⡀⠀⠀⢿⣿⣿⠀⠸⣿⣧⢻⡏⠛⠀⣠⢏⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠃⠛⢹⡟⣼⣿⡇⠈⣿⣿⡟⠀⠀⢀⣧
⠰⡿⡄⠀⠀⠘⣿⣿⡅⠀⢿⣿⠀⠉⡀⣴⠃⢈⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠘⣦⢠⠋⢀⣿⡿⠁⣸⣿⣿⠃⠀⠀⢀⢿
⢠⣾⠖⠀⠀⠀⢹⣿⣿⣇⠀⠙⢧⣄⠙⢯⣴⡿⠀⠄⠘⣟⠛⠛⠒⠶⠶⠖⠛⠛⣻⣿⠹⠀⢿⣦⣽⡋⣠⡾⠋⢀⣼⣿⣿⡏⠀⠀⠀⢠⣿
⠀⠿⣵⠀⠀⠀⠀⠛⢿⣿⣿⣦⡀⠙⢦⡀⠛⠶⢦⣤⣄⠙⢿⣿⣦⠀⠀⣴⣿⡿⠋⣠⡤⡤⠶⠛⢋⡴⠋⣠⣾⣿⣿⡿⠛⠀⠀⠀⠀⣮⠟
⠀⠀⠡⣤⡀⠀⠀⠀⠈⠉⠛⠙⣿⣷⣦⣽⡷⠶⢴⣤⣤⡀⡀⠈⠛⢶⡶⠛⠁⢀⣀⣤⣤⡦⠶⣾⣯⣴⣿⣿⠛⠛⠉⠁⠀⠀⠀⣠⣤⠉
⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡶⠄⠄⠀⠐⠀⠀⣀⣼⣧⡀⠀⢀⠂⠀⠠⠠⢶⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠈⠿⠆⣴⣄⣀⢠⠀⠀⠀⠀⠛⠛⣿⣶⣶⣦⣤⢴⠞⠙⢿⡟⠙⢳⡦⣤⣴⣿⣾⣿⡿⠟⢡⣤⠿⠀⡀⠀⣀⣦⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣀⠀⠀⣠⡀⠀⠻⢿⣿⣿⣇⠀⡷⣤⣬⣤⡴⢾⡀⣸⣿⣿⣿⣿⣃⣴⣌⠁⢀⣀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⠧⠼⠛⠟⠛⠛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠷⠾⠿⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⡿⣿⣿⢿⣿⣿⡿⣿⣿⣽⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⡓⠈⠉⠋⠋⠰⠟⠙⠁⣺⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠢⠔⠟⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣠⣄⣀⢀⢴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠙⣿⡻⢊⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢾⢏⣼⣿⣷⣽⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣥⢈⠯⠿⢿⢭⢯⣀⠸⣦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣇⣰⣯⣤⣾⣇⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⣭⢿⢿⡽⣿⣯⣭⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⢖⣻⠄⢣⡍⡴⡄⢧⡀⠈⠒⣀⡴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⣤⣶⣊⣾⠅⢐⣶⣾⠔⡟⠁⢠⡱⠘⣧⠀⠈⣀⡵⠛⡵⠟⠛⣻
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣸⣸⡟⢿⣧⠃⢠⣯⣼⣡⠎⢈⢦⣀⠙⢆⠉⠳⡼⠋⢠⡬⢤⠖⢊⣿
⠀⣠⡶⡆⣸⢯⢀⠀⢀⠀⢫⠁⠋⢦⡝⢯⡳⣜⣿⡈⣿⣯⣿⠀⠈⠛⣼⣿⣄⣵⢇⣀⡄⠋⠀⢀⣤⣶⣿
⠀⠙⠋⠙⠛⠚⠛⠋⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠃⠋⠛⠋⠀⠀⠳⣄⠉⣮⣮⡿⠋⠀⠀⣸⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠉⠀⠀⢰⠀⣥⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⡀⠀⠀⠀⠁⠈⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣁⠀⠀⠀⠀⠤⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠾⠇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣦⡀⠀⠀⠀⠀⠀⣀⣠⣤⣠⣄⣄⢠⣄⣤⣄⢀⡀⠀⠀⠀⣀⢤⣿⠅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠻⠶⠤⡞⠛⠙⠛⡉⢙⠉⠻⠛⠛⠉⠋⠉⠛⠛⠖⠒⠉⢠⡟⢻⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⣗⡄⠀⣀⡤⠶⠂⠋⠁⠉⡉⢿⠟⠋⡛⠓⠳⢶⣤⡀⠶⢶⠟⠻⠃⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠴⣾⠝⠛⢋⡔⠜⠛⠛⠛⠛⣡⣴⣌⠛⠙⠛⠶⢤⣤⣀⠀⠏⡔⠁⠤⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⠭⠃⠐⢋⡤⠀⢀⣶⣶⡿⠛⣉⠻⣷⣄⢰⣄⠀⢬⣭⣄⡈⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⣥⠝⠂⠀⣘⣱⢶⡼⠋⠀⠀⣠⣾⠉⢧⣀⣈⠁⠙⠷⠆⠙⠻⣧⠀⠀⠠⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⣀⡴⠟⣩⡀⠀⢀⣤⡾⠟⠉⠉⡆⢨⡍⠙⠿⠦⠄⠀⢸⣦⠉⠳⣄⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⡞⠁⠀⣰⡿⠁⠀⢉⣽⡆⠀⣀⡴⠳⣠⣅⠀⢰⣦⡄⠀⠀⢻⣶⠄⠈⢳⣆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠬⠀⣿⡇⣶⡄⠙⠁⣴⣄⠈⢤⠀⣈⢁⡇⢠⣼⡉⣴⠀⡄⢀⣤⡶⢤⡏⢀⣶⡄⣿⣆⠀⠂
⠀⠀⠀⠀⠀⠰⢋⠀⠈⣿⠀⢿⡇⣤⠄⠈⠙⠃⠟⢰⡏⠘⣁⠈⣿⠃⢸⡆⠋⣈⢁⡀⠀⠻⡘⣿⠃⣿⣯
⠀⠀⠀⠀⠀⠠⠛⠁⠀⣿⠀⢸⠁⡛⠠⡘⣇⣛⣢⡀⠣⠀⠈⠐⠈⠀⢈⢃⣮⣩⡼⢣⠂⢹⡆⢹⡀⢹⣿⠀⠀⢬⡀
⠀⠀⠀⠀⠀⢀⢞⡁⠀⣿⡧⠘⠀⢿⣄⡘⠚⠙⢻⡧⠐⠀⠀⠀⠀⠀⠀⠸⣿⠉⠀⠓⣠⡟⠁⣼⠀⣸⡇⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠘⢷⡀⢤⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⠁⠀⣸⠇⢰⡿⠇⠀⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⣶⣌⠳⠦⢿⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠛⠛⠉⡿⣤⣾⠄⠀⠀⠄⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠙⢿⣷⣦⣈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⡗⣾⡷⠀⠁⠀⠀⣴⠞⠃
⠀⠀⠀⠀⠄⠒⠒⠒⠺⣿⡶⠤⠤⠤⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡴⠋⠀⠀⠀⠢⠠⠁
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠼⠶⠶⠂⠀⠀⠽⣿⡃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢜⠯⠠⣀⣠⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡤⠴⠦⡷⢬⡻⣦⡄⣀⣀⣄⣠⣤⣠⠄⠈⠘⣈⣛⠛⠉⠂⠤⣀⡀⠀⠂⠄⣁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⠐⣊⠽⠗⣚⡽⣃⡦⠈⠙⠤⠴⠋⠀⠀⣀⣿⣿⠍⠂⢌⡁⠂⠤⣈⠒⢄⡀
⠀⠀⠀⠀⠀⠐⠈⠁⠀⠐⢊⡥⠖⣉⠄⡠⢂⢜⢽⣿⡷⠶⢶⠾⠿⠶⠶⢿⢿⡿⣽⠣⠀⠢⡈⠒⠄⡀⠉⠢⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⡤⠊⢠⠊⠀⠉⡌⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣧⢠⠀⠀⢀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡰⠀⠀⠈⠀⠀⠀⠖⠀⠰⠃⠀⠸⠁⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠺⠏⠓⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⣉⣙⠒
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣰⣿⣶⣤⣿⣦⣇⠈⢇⣀⣤⣤⡴⠶⠶⠾⠿⠷⠶⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠠⠾⠟⣿
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⣿⣿⣿⣍⠛⠃⠙⠂⠘⠛⠋⠁⠠⢴⣶⣶⣶⠶⠒⣂⠀⢉⡉⢙⣛⣒⡂⠀⠐⠁⠀⠀⠀⠀⠀⣰⡏⢀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠞⠉⣀⣠⣴⣶⡿⠟⠛⢶⣦⡈⢉⣽⠿⠶⣤⣀⠀⠀⠀⠐⠾⢿⣿⠋⢠⡇
⠀⠀⠀⠀⢀⣠⣶⣿⣷⡀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⣿⣿⣿⠏⢀⢀⢀⠀⠙⣿⣦⣀⠀⠀⠀⠉⠀⠀⠀⠀⣐⣻⠟⠀⢻⡇
⠀⠀⠀⠀⣛⣿⣿⣿⣿⡿⠃⣿⣿⣿⣿⠷⠀⠀⠀⠠⠶⣻⡿⠀⠀⣠⣤⣤⣶⣬⣿⠈⠣⠶⢶⣯⣝⡛⠛⠻⢷⣄⠀⠠⢿⣿⡟⠀⢠⡿⠁
⠀⠀⣠⣾⣿⣟⠁⠸⣿⡀⠀⠘⣿⡏⠉⠀⣀⠀⢀⣶⡿⠋⠀⠀⠾⠛⣛⣏⠀⠀⠹⡇⠀⠀⠀⡈⠛⠉⠓⠆⠀⢉⢳⡀⠀⠉⣉⣁⣼⡁
⠀⠈⠽⠿⣿⣿⣍⡀⠈⢷⠀⠘⠋⣀⣴⣾⠋⠀⣸⣿⠁⠀⠀⠀⣴⣾⠋⣻⣶⣶⢀⠀⠀⠀⠲⣌⣻⡀⠈⠲⣄⠘⣦⡁⠀⠀⡈⠛⢿⣿⡀
⠀⠀⢠⣾⣿⣿⣯⣄⣀⣀⡀⢀⣾⣿⡿⠁⠀⣶⡿⠁⠀⠀⠀⣀⠀⠀⠀⠈⠈⣿⣼⡇⠀⠀⠘⣌⠛⢷⠀⠀⠹⡆⣌⣿⣆⠀⠘⣆⠀⠹⣧
⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⡿⠋⠀⠀⠀⠉⣰⠂⣴⣿⣦⣿⣇⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⠘⣧⠈⠀⠀⠀⠀⠿⠃⠀⠠⡀⠘⢷⡄⢿⡆
⠀⠙⠉⢙⣿⣿⣿⠋⢀⣾⣿⡿⠁⠀⣠⣦⠀⣰⣿⡆⠉⠉⢛⣉⣈⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡄⠀⢠⣴⣶⣶⠦⠀⢄⢳⡀⢸⣷⠈⢿⡄
⠀⠀⣰⣿⣿⣿⠃⠠⠟⣹⣿⡧⠀⣼⣿⣿⠀⣿⣿⠇⠐⠺⣿⣿⣿⠿⣦⡀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠁⠀⣿⣛⣋⠎⣀⠄⠘⣮⡇⢸⡿⠀⠈⢿⣆
⠀⢠⣿⣿⣿⣿⡆⠀⢠⣿⣟⡀⠰⣿⣿⡟⠀⣿⡟⠀⠰⣄⡘⠷⠶⠾⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⠉⢠⣞⡡⡄⠀⣿⠇⢸⡇⠀⠀⠸⣿⡗
⢀⣿⡿⣻⣿⣿⣷⠀⠘⢹⣿⣃⠀⠹⣿⡇⠀⣿⡇⠀⢀⠈⠙⠒⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠁⠀⣀⣠⣿⠀⢸⠀⠀⠀⠀⣿⣷
⠘⢉⣴⣿⣿⣿⣿⡆⠀⠀⢹⣿⡀⠀⢻⣧⠀⢿⣷⣄⠹⠷⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢀⣉⣹⡇⠀⢸⡇⠀⠀⠀⣿⡿
⠀⡾⠟⣿⣿⣿⣿⠁⠀⢀⣾⣿⡇⠀⠀⠻⣆⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⡀⠹⣿⡇⢀⢸⡇⠀⠀⠘⣿⡗
⠀⠀⢀⣿⣿⣿⡟⠀⠀⣼⣿⣿⠇⠀⠀⣶⣾⣷⣶⠤⣄⡘⠿⣶⣤⣴⠇⠀⠀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⣷⡀⠈⠀⢻⡿⠿⠀⢲⣴⣿⠃
⠀⠀⣼⣿⣿⣿⠃⠀⡀⠉⢰⣿⡇⠀⠀⠈⠛⠁⠠⣤⣤⣤⣶⡿⠉⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⣷⠀⠀⣿⠃⢠⣤⣸⡿⠁
⠀⢠⣿⣿⣿⠏⢀⣴⡿⠀⠀⢸⣧⣤⡀⠀⠀⠀⠀⢾⠛⠉⠉⠀⢒⣠⣤⣴⣾⣿⠿⠀⠀⢀⣀⣀⣠⣤⣀⣀⠀⡀⠁⠹⣾⡇⣼⡟⣠⣿⣿⠋
⠀⢸⣿⣿⣿⣾⣿⣿⠇⠀⠀⡼⠟⣿⣧⠀⠀⢀⣤⣤⡄⠀⠀⠀⠉⢉⣩⣉⣻⣿⡆⠹⢾⣭⣤⣉⠉⠉⢉⣤⡶⠏⢀⣴⠿⠃⢹⣇⣿⡿⠃
⠀⠸⣿⣿⣿⠿⣿⣿⣀⣤⣤⣦⠀⠋⣽⠞⠀⠀⠈⣻⣧⠀⠀⠀⢀⣉⣉⢛⠛⠳⠶⠀⠀⠉⠙⠿⣅⣄⠾⠁⠀⠀⠈⢀⡠⠀⣾⣿⡿⠁
⠀⠀⠛⠁⠀⠀⢻⣿⣿⣿⣿⣟⡠⠀⢀⣤⠖⢀⡶⣛⡅⣀⠀⣤⠀⢉⠁⠉⠙⠛⠒⠶⠤⠄⠀⠀⠸⠃⠀⠀⠀⠉⠉⠀⠀⣠⡻⠟
⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⢁⣼⣿⠃⠀⠀⠈⠉⠘⠋⠀⣿⣷⣬⣉⣘⣁⣀⠀⠀⠀⠀⢀⣠⣴⣤⣤⡀⠀⢀⣶⠞⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢰⣿⢻⣿⣿⣟⣵⡄⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⢷⣤⣤⣴⣾⣿⠟⠛⠻⢿⢿⣿⠋⠁⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⠊⠻⢟⣵⣷⣤⣤⣄⣀⠈⢱⣿⣿⣿⣿⣿⣿⠘⣿⣿⠟⠻⡷⠀⠀⢰⠋⣸⣿⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣆⢻⣿⣿⣿⣿⣿⣦⣼⣄⣀⣀⣠⣴⣶⣷⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠹⣿⣿⣿⣿⡆⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢾⣻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⠘⣿⢯⣉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⠀⠀⠉⠛⠷⣶⣶⣤⣤⣤⣤⣤⡶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⣷⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢲⡄⠀⠈⢿⣷⡀⢻⣇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣤⡴⠶⠿⣿
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⢻⣿⣄⢻⣆⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠀⠀⡀⢂⡀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⣀⣤⣴⣿⡀
⠀⠀⠀⠀⢤⡀⠘⢿⣷⣄⠀⠹⣿⣦⣻⣿⣿⣧⡀⠀⠀⢀⠰⠖⠁⢀⡄⠀⠀⢠⡶⣻⣆⠀⠀⠀⠀⠀⠀⣠⡴⠟⣋⠵⣾⣿⡇
⠀⠀⠀⠀⠈⢻⣦⣈⠻⢿⣷⣦⣈⠛⢿⣿⣿⣿⣿⣆⠠⠎⠀⣴⠀⠀⣠⣀⠀⠀⠈⠉⠉⠐⠀⠠⣄⣴⠞⢉⡴⠚⣡⣾⣿⣿
⠀⠀⠀⢀⠀⠀⠙⠿⣷⣤⣙⠻⢿⣷⣦⣝⣿⣿⣿⣿⠀⠀⣈⣿⠦⠶⣿⠟⠂⠀⠀⠀⠀⠙⠀⠸⠏⢀⡴⠋⣠⣾⣻⣿⣿⣿
⠀⠀⠀⠈⠻⠷⣶⣤⣌⣙⠻⠿⣶⣬⣭⣿⣿⣿⣿⡿⠀⠀⣴⣷⠀⠀⠰⣆⠀⠀⠁⠀⠀⢠⣤⣀⣴⡟⣡⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⡀⠀⠉⠛⠛⠿⠿⠷⠶⠿⠿⣿⣿⣿⣿⡆⠀⣿⣮⠞⠡⣼⠏⠀⠐⠀⠀⠀⢀⣩⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠙⠛⠿⠶⠶⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣾⣿⣧⣴⣾⣿⣶⣦⠀⠀⠀⠀⢡⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⠾⢟⣛⣭⠷⣿⣫⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⡍⣶⣿⣽⣿⣿⡟⣹⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠠⢴⠶⠖⠻⠛⣩⡴⢾⣿⣿⣷⡾⣿⣿⣿⡏⣿⣿⣿⢿⣿⣿⣀⣄⢸⣿⣿⣿⣿⣿⡿⣱⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣉⡥⠾⣫⢴⣿⢿⡔⣿⣿⡏⡁⣼⢿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣊⡵⢊⠵⢮⡾⠋⡈⠀⠀⠘⢻⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⢿⣿⣿⣧⡿⢠⣿⡿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣋⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⡙⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⣶⣶⣾⠆⣽⡿⢫⡆⣠⣨⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⢛⣻⣿⣿⣿⣿⣿⡿⣫⣾⣿⣷⣿⣱⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢟⣉⠁⠒⠚⢛⣩⣽⣟⣻⡛⠟⠉⣶⣫⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣀⣤⡾⢛⣹⣿⣿⣿⠟⣴⡇⣿⣿⡿⣿⢻⡟
⠀⠀⠀⠀⠀⠸⠁⢀⣤⠾⠛⣡⣴⢟⣿⣿⣿⣿⣿⣿⣧⣿⣿⢰⣏⡼⠁
⠀⠀⠀⠀⠀⠀⡰⠋⠀⢠⡾⢋⣴⣿⢿⣿⢿⣿⡿⣿⢿⣿⡇⣿⣿⠁
⠀⠀⠀⠀⠀⣸⠇⠀⠰⠋⣰⡿⠉⢡⣿⠏⠸⡿⣡⣿⢿⣿⡇⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⢰⡟⠀⠀⣾⣿⡄⠀⢰⣿⢣⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⡏⣿⠀⠀⢸⣿⣿⣿⠈⣿⣿⣯⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⢸⠏⣿⠐⢸⡄⢿⣿⣿⠂⣿⣿⣿⣿⣷
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⠀⣿⠀⠙⠿⠟⣿⢹⡀⣿⣿⣿⣿⢿⣦⣀⣠⠏
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣀⠀⠐⣿⡈⠑⣿⡌⢿⣿⡀⠙⠟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣆⠀⠹⣧⡀⢿⣇⠀⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢿⣆⠀⠈⠛⠘⣿⡄⠀⠁⠊⠛⠂⠤⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠘⢿⣦⣀⠀⠈⠉⠉⠉⠉⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠠
⠀⠠

⠀⠀⠀⠀⠀⠀⣰⣤⠀⢀⡤⣄
⠀⠀⠀⠀⠀⣠⣼⣻⣻⣯⡀⢻⣄
⠀⠀⢀⣤⣾⣻⡷⣻⣿⣏⣿⣼⣿⣷⡀
⠀⢺⣿⣿⣿⣿⣿⠟⣿⡿⢹⣿⡽⣿⣇⢲⡀
⠀⠀⢿⣿⣿⣿⣿⣿⠟⣱⣿⡿⣡⣾⡇⣿⠇⡄
⠀⠀⠈⠿⠿⠻⣿⢿⢟⣛⠛⣰⣿⣿⣿⠟⣸⣿⢀⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣾⡿⣿⣿⣿⣿⢋⣼⣿⡟⣼⣷
⠀⠀⠀⠀⠀⠀⠸⠏⣡⣾⣿⣿⣿⣵⣿⡿⢋⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠏⢰⣿⣿⣿⣯⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⠿⣛⣩⣾⣿⣿⡿⢃⣿⣿⡟⣰⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⠃
⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⣯⣼⣿⣿⣿⣿⠟⣵⣿⣟⣫⣾⣿⣿⡿⢠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠛⢸⣿⣿⡿⢟⣿⣿⣯⣾⣿⣫⣿⡿⣻⣿⣯⣴⣿⣿⠟⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⡿⢛⣥⣤⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣿⣿⣿⣿⣿⣿⢹⣿⣷⣿⣿⣿⣷⣶⣿⣿⣿⢟⣫⣴⣶⣾⣆⠀⠀⠀⠀⠀⢠⣦⣍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢃⣿⣿⡟⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣭⠀⠀⠀⠀⠀⠸⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⢸⣿⡿⢠⣿⠿⣿⣿⣿⡿⠋⣁⣤⣶⣶⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠘⣿⡇⢀⣴⣿⣿⣛⣩⣴⣿⣿⡿⠿⠛⣛⣻⣭⣁⠀⠀⠀⠀⠈⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⠃⠀⠈⠃⣿⣿⠿⠿⣿⣿⣿⣭⣤⣶⣾⣿⣿⣿⠿⢛⣀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⢀⣠⣤⣀⣉⣴⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣫⣤⣶⣿⣿⠇⣀⠀⢀⣤⡙⠻⡇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⡿⠿⠿⠃⣼⣿⣧⠘⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠋⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠛⠛⠻⠂⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣷⣾⣷⣦⣐⣤⡉⠻⣿⣿⣿⣿⡿⠿⠟⣛⣛⣛⣛⣿⣾⣯⣭⣭⣈⠉⠙⠛⠿⣿⡿⠛⣡⡾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣷⣤⣈⣻⣿⡝⢦⠀⠙⠁⠀⠴⠶⣛⣛⣛⣛⣛⠛⣻⣟⣥⣬⣭⣓⣤⣤⠶⠂⠀⣼⢿⣶⣿⣿⣿⣿⣿⣿⠂⢨⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣍⠙⣻⣿⣿⣿⣧⡀⠀⠾⠿⠛⠛⠛⠛⠛⣻⣶⣿⣈⠉⠛⠛⠛⠻⠄⠀⠙⢻⣿⣟⣛⣿⣿⣿⣿⣿⣿⣂⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠋⣉⣤⡀⠀⠀⢀⣴⣾⠟⢻⣿⣿⣿⣟⠿⢿⣦⡀⠀⢀⣹⡆⠀⠙⢿⡛⠋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣈⣿⣿⡟⠁⠀⠾⠟⣁⣤⠟⣽⣿⣧⡉⣤⣌⡙⠿⠀⠘⣿⣿⣷⣄⣈⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢟⣵⡿⢿⣿⠟⠀⠀⣴⣿⣿⠿⠟⠿⣿⡿⠓⠻⢿⣿⣷⡀⠀⠈⢻⣿⡿⣿⣄⡀⠈⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣠⣶⡿⠋⣠⣿⠁⠀⠀⠀⠀⠀⣠⠀⢀⣰⡿⢆⡀⢀⡀⠀⢀⡀⠀⠀⠘⣿⣿⣿⠻⢿⣦⡀⢀⡿⠟⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣾⡿⠋⢠⣿⣿⡏⠀⠀⣠⣴⠶⠈⠃⢰⣟⠃⣡⣼⡏⠈⠛⠀⠈⠻⣷⠀⠀⢸⡿⠿⠀⠈⢻⣿⣿⡆⠀⠈⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣴⣿⡿⣵⣶⠈⠙⣿⣁⣠⡀⡏⢠⠂⠀⣠⣼⡿⢱⣿⣿⡍⢦⠀⠀⣦⠀⣹⣧⣶⡌⣷⡀⠀⣿⣧⡙⣿⣿⡀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⡟⢠⣿⡗⢀⣼⣿⡈⠙⠛⠿⢹⡄⢠⡟⠁⣧⣾⣿⣦⣽⣿⡀⠀⣸⠀⠉⠉⠁⣠⣿⣷⡀⢸⣿⡇⠹⣿⣷⡄⠀⠀⠈⠻⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⠁⣼⣿⠃⠞⣛⣹⡷⣶⣶⣶⣤⠀⠸⣷⣶⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⡿⢛⣏⣉⠃⠘⣿⣿⠀⠹⣿⣷⠀⠀⠀⠀⢿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⡟⠀⣿⡟⠀⣸⣿⡟⢻⣿⣿⣿⣿⣷⡀⣿⣿⣿⣏⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣷⠞⣿⣿⡀⠀⢸⣿⠀⠀⢿⣿⡆⠀⠀⠀⠈⢿
⣿⣿⣿⣿⠃⠀⠀⢀⣿⣿⠀⠀⣿⣇⠀⠘⢿⣏⠛⣿⣿⣏⠉⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡏⠀⣿⣿⡿⠠⣿⣿⠃⠀⢸⣿⠀⠀⣾⣿⡇⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠁⠀⠀⠸⣿⣿⠁⠀⢸⣿⡀⠀⠀⠻⢿⣿⣿⠟⣸⣿⣿⠃⣿⣿⠿⡟⣽⣶⣿⣿⣿⣿⡄⠛⢿⣿⠾⣿⠁⠀⠀⢾⣿⠀⠀⣿⣿⠀⠀⠸⠀⠀⢀
⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⠀⠀⣾⣿⣧⣤⣤⣤⣴⠾⢟⣠⣿⣿⠏⢠⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⢆⠲⢦⣄⠀⠀⣠⣶⣿⣿⡄⢠⣿⣿⠀⠀⢸⡀
⣿⣿⣿⡅⠀⠀⠀⢰⣿⣿⣿⠀⣿⣿⣿⠛⠿⠁⣴⣶⠟⣿⣿⡏⣰⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡁⠳⣄⡙⢳⣿⢛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⡇
⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣾⡾⠙⠿⣷⣤⣼⠿⠋⢰⣿⠛⣿⣿⡿⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠙⠛⢷⣡⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁
⣿⣿⣧⡆⠀⠀⠀⢸⣿⣿⣿⣿⣷⣼⣾⣿⣿⠀⠀⢀⣯⡁⢴⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⣩⣦⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⡇⠀⠀⠀⠈⢛⣿⣿⣿⣿⢿⡿⢿⣿⣇⠀⠘⣧⣁⠀⠘⣿⡀⠀⠀⠒⠄⠀⢀⣠⡿⠁⠈⣘⣥⣾⣿⢀⣿⣿⣿⣿⠿⢿⣿⣿⡿⠧
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⠟⠋⠁⠀⠀⢨⣿⣷⣦⣽⣦⡙⠃⠀⠈⠻⢷⣦⣼⣦⣴⡿⠋⠁⠀⠚⠛⣁⣾⠖⢰⣿⣿⣿⣿⣛⡛⠛⠁
⣿⣿⣿⣿⣷⡄⠀⠀⠰⣾⠋⠀⠀⠀⠀⠈⠛⠛⠩⠈⠛⠛⠲⠖⠂⠀⠀⠻⣿⡿⠟⠀⠀⠤⠴⠖⠛⠋⠀⠰⣿⣿⣿⣷⣂⠀⠀⠠⢀⣄⣄⠀⠀⠀⠀⠀⣰
⣿⣿⣿⣿⣿⣷⣂⣤⣾⣧⣤⣶⣾⠇⠀⠀⠀⠀⣠⡛⣴⣭⣅⣠⣀⢀⣀⣠⣾⣷⣤⣄⣶⣶⣶⣾⣿⣶⣼⣷⣍⢿⣿⠿⢛⡻⣷⣶⣾⣿⣿⠃⠀⠀⢀⣶⣿
⣿⣿⣿⣿⡿⠿⠟⠉⠀⠁⠘⠻⣯⣶⣶⣾⣦⣶⣿⣿⣿⢿⠟⠛⠛⠟⠻⠋⠀⠻⠛⢿⢻⠛⠛⢿⣿⣿⣿⣿⣿⣷⣿⣆⢬⣷⣾⣿⣿⣿⡟⠀⢀⣠⣿⣿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣿⣿⠫⠛⠍⠻⠟⠁⠀⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⡀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠑⠀⠰⣶⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡟⠋⠉⠀⠀⠈⠀⠀⠀⢠⣷⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣯⢙⣏⠈⢹⡿⠟⠿⢿⣿⣯⠋⠈⢠⠀⠀⠀⠀⠀⣴⠀⣶⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⠿⣿⣿⡆⠀⠀⠀⢠⣶⣿⣿⣿⣿⣏⣠⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣝⣿⣧⡀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣿⠟⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣤⣿
⠀⠀⠀⠀⠀⢀⡀⢠⣤⡤⠀⢰⣶⠉⠉⡩⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠰⣾⣏⠀⢸⣿⠧⠠⠼⣿⠷⠮⢡⣖⣽⡿⢋⣵⠟⣩⡶⠛⠉⣉⣤⣤⣤⣬⣶⣤⡀
⠀⣴⡇⠀⡹⠛⠉⠀⠀⠀⠀⣰⣡⢒⣈⢻⣿⡏⢠⡿⢫⣾⡟⠀⣴⡿⠛⠉⠁⢀⣠⣤⣬⣍⣢⡀
⢀⠻⣿⣿⠀⠀⠀⠀⠀⠀⣨⢙⡷⢋⣤⣿⣻⡇⣿⠀⣿⡟⢀⣾⡟⠀⣀⣤⣾⠟⠉⣀⣤⣤⣤⣙⣦⡀
⠰⡀⠀⣸⡄⠀⠀⠀⠀⣀⣿⣾⣡⡋⠉⢭⣿⣀⡟⣸⢿⠃⢸⣿⠀⣞⡵⠋⠕⣣⣾⡛⠋⠀⠀⠙⢷⣷⣄
⠀⠻⡿⠿⠋⢸⣶⡆⠹⣿⣿⣿⣿⣶⣿⢿⣿⣿⡇⣿⢸⣤⢸⣿⡖⠋⡙⠳⣿⣿⣭⣤⣶⣶⣶⣶⣤⠉⠙⢷
⠀⠀⠀⠀⠒⠚⠛⠁⠘⠉⠉⡏⠙⠀⠐⠀⠀⠘⣷⣹⣎⣿⡟⡽⣩⠟⠶⢟⡽⣻⠟⠉⠁⠀⠀⠈⠙⢷⣤⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⣤⡧⣌⠧⡼⠋⠛⠿⣿⣿⡇⢃⡴⢱⣏⣞⣡⠶⠟⠛⠻⢿⣷⡄⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣸⣷⢿⣟⢉⡤⠶⠶⠶⣤⠀⠿⠿⣶⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡏⣿⡩⠙⠒⢯⣟⠶⠼⣟⠳⣆⠘⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣿⠇⡉⠐⠁⢃⡚⠮⢭⡓⠎⠧⢽⡶⣷⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⣩⣤⢩⢊⣌⠁⠁⠰⢆⠘⣠⠰⣬⠷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⣿⣴⠹⠇⠀⠁⢠⡆⠲⢠⠀⣷⣞⣉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣄⠃⢻⡗⣅⣡⡔⠒⣹⣆⣽⠆⡆⢛⡋⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡐⣸⡐⠛⠲⡽⢻⠾⣛⣩⠾⠃⣼⣶⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠷⣦⣴⠴⠡⠀⠤⢤⣠⣾⣯⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⠛⠲⠾⣰⣾⠉⣿⣿⠏⣅⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢹⠉⠒⠐⡾⠛⢻⡞⡁⠫⠒⢦⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⣴⣆⢠⡁⣀⠘⣼⠁⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢠⠇⠀⡁⢀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⣌⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣇⢀⣰⢀⠻⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠙⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠇⢠⡀⠉⠿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠹⡄⠀⡄⠀⠙⢢⣤⣀⡵⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣇⠘⢦⡀⠙⢦⡙⠂⣠⣝⢲⣦⡴⢫⣽⣷⣀⡀
⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠙⣆⠈⢳⡀⠹⣄⡀⠁⠘⢧⣼⣟⣋⣀⣠⠟⠋⠘⢹⡆
⠀⠀⢰⣏⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣤⠤⣴⠶⢶⠒⢻⡟⣿⣏⠁⠸⣇⠘⢿⠀⠘⣦⠀⠃⠀⠹⠛⠀⣤⠸⡏⢸⠁⠀⠀⣠⠤⠤⠟⠁
⠀⠀⠈⢿⣹⢦⣤⣤⣤⠶⢶⡏⢉⣿⣀⠀⡟⠀⣿⡀⢸⡆⠘⡇⠘⣿⠀⣦⠘⣆⠸⡇⣤⢸⡆⢰⡄⢦⠀⠀⢸⠄⣇⣀⣡⠶⠋⠁
⠀⠀⠀⠀⠙⠒⠿⠶⠿⠒⠚⠉⢉⡼⠁⣠⠀⠀⢿⣧⠈⢧⠀⢻⡀⢸⠀⢿⠀⠸⠄⠀⢻⡆⠀⢀⣷⠞⠛⠓⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢿⠀⡼⠻⣆⠀⠘⢿⠀⠘⠧⠈⢃⣸⣆⣸⣇⣀⣀⣤⠤⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠉⠀⣋⡼⠁⡄⢹⡄⠀⠸⠄⣠⠴⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢠⡏⢀⡴⣚⣫⠽⠁⠀⣿⢠⡇⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢷⣸⢤⡇⠀⠀⠀⣀⣡⠤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⣴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢻⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠇⢠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢃⠈⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢷⡀⠈⡀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⣇⠀⠠⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡔⢿⣆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠻⣌⠻⡆⠣⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⢦⡘⢦⠹⡆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⡌⠂⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⡊⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠡⠞⢀⠔⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠳⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠳⣄⠈⠓⠆⠀⠀⠀⠀⠀⣠⣆⡴⠛⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣾⡟⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠲⢌⣁⠀⠀⠀⠀⠀⠀⢰⠟⠋⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⢀⡄⣼⣿⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣌⠁⣈⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠦⡀⢤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠟⠳⠶⠖⠈⠑⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣞⣁⣀⣤⠤⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠁⣠⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⢀⣠⣤⠾⠛⠉⠉⠉⠙⠙⠛⠻⢿⣿⢿⣦⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⡀⣀⣤⣠⣾⠿⢋⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠒⠂⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⣿⣟⣯⡥⢶⣟⠛⠻⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⢀⠹⣦⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡤⠖⠋⢡⢿⣿⣿⣿⡿⠁⠿⢷⣦⣭⣭⣤⣤⣤⣬⣥⡀⠈⠿⠀⠃⠀⠀⠀⠀⠀⠀⢸⣦⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣤⠔⢃⣾⡿⢻⣿⠃⠀⠀⠀⠀⠀⢠⠾⠛⠋⠹⣿⢿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣀⠀⢻⣿⣿⣿⣿⣿⠃
⠀⠀⢲⣄⡀⠀⠀⠀⠰⣤⣀⡈⠀⠉⠙⠃⠈⠛⠁⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡈⢳⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣛⣯⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠹⢿⣷⣶⣤⣀⣈⠙⠿⣿⣶⣶⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣮⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⢀⣼⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣦⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⠉⠉⠛⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⠛⣛⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠟⢿⡿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠷⣤⡀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⢀⡤⠿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣼⣿⣿⡿⠛⢛⣻⡿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡛⠛⢺⡿⢿⣦⣤⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠻⠋⠉⣽⣿⡇⣞⣧⣼⣷⠶⠿⣟⣿⣿⢻⠿⠶⣾⣯⣟⣓⠸⣿⣾⠉⠁⠀⡱⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣠⣴⣿⣿⠟⠋⠉⢩⣦⣶⣿⡿⢿⣿⢿⣿⣶⣶⡍⠉⠙⠳⣶⣿⣿⣆⠄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣾⡿⠋⠀⢠⣾⣿⠟⠛⠁⠀⠀⢰⡇⠀⠀⠘⠛⠻⣿⣷⡄⠀⠙⢻⣥⣾⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠟⠂⢸⣿⠜⠛⠋⠁⣠⣶⣶⣶⣼⣆⣴⣷⣴⣷⣷⣄⠈⠙⠛⠣⣿⡧⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣃⣀⡀⠘⣧⡀⠀⠀⠿⠛⠛⠛⡛⠛⠙⠋⠛⢛⠛⠉⠛⠿⠀⠀⢀⣽⠘⢿⣏⣉⡛⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠋⠀⢰⣿⣧⠀⠀⢠⡾⠛⠛⢡⣾⠀⠀⣷⡌⠟⠛⢷⡄⠀⠀⣾⣿⡆⠀⠙⣿⣿⣿⠛⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣱⣿⣏⣴⣿⡟⠁⣠⣄⢘⣿⣇⣰⣷⡇⣤⠀⣠⠟⣿⠀⠀⣿⠻⣄⠀⣤⢸⣿⣆⣸⣿⠃⣠⣄⠈⢻⣿⣆⠨⢿⣿⣄
⠀⠀⠀⠀⠀⢀⣴⡿⡃⢀⣹⣿⠃⣼⣿⡿⣾⡿⢆⣙⡻⣧⣿⠀⣧⣴⡥⠀⠀⢬⣶⣼⠀⣿⣼⣿⣋⡴⢿⣷⢿⣿⣧⠘⣿⣏⡀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⢋⣾⡿⠁⣨⣿⣿⠀⣿⣿⠀⢩⣶⣦⠙⡁⠛⢻⠀⣿⠛⠠⠀⠀⠄⠛⣧⠀⡟⠛⢈⡏⣴⣶⡍⠀⣿⣿⠀⣿⣿⣅⠀⠈⢾⣷
⠀⠀⠀⠀⠠⢿⣟⣀⠀⢰⣿⣿⠀⢿⡇⠀⠈⠛⠛⢷⣭⡛⢿⡇⠉⠀⠀⠀⠀⠀⠀⠉⢸⡟⢋⣭⠾⠛⠛⠁⠀⢸⡿⠀⣿⣿⠆⠀⠀⣸⣿
⠀⠀⠀⠀⠀⢾⣿⡟⠁⠀⠸⣿⡗⢸⣿⠀⠀⠛⣷⣆⠙⠋⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠻⠋⣰⣾⠟⠀⢀⣿⡇⢺⣿⠇⠀⢠⣤⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣿⣿⠇⠘⣿⣿⣷⣄⣈⣽⢞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡻⣯⣁⣠⣴⣿⣿⠁⢸⣿⣷⡄⠈⢿⡿⣿
⠀⠀⠀⠀⠀⠀⣿⢀⠀⠰⢚⣻⣿⣤⡈⠛⠈⠻⠋⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠙⠟⠁⠛⢁⣤⣿⣿⡛⠆⠈⣿⠓⢿⡇
⠀⠀⠀⠀⠀⠈⢷⣿⠀⠀⢩⢽⣿⣿⣿⣾⣿⣧⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣼⣷⣶⣿⣿⡿⠯⠉⠀⠀⣿⣷⠌⠃
⠀⠀⠀⠀⠀⠀⠽⣿⢢⠀⠀⠀⠛⢻⣿⣻⣿⣿⣧⢰⣄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣨⡆⣼⣿⣿⣿⣇⠀⠁⠀⠀⣀⡸⣽⠏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠉⠀⠛⡻⠿⠟⠐⢤⣈⠙⠆⠈⠻⢿⣶⣶⣶⣶⡿⠟⠁⠔⠋⣁⡔⢺⢿⡍⠉⠙⡇⠀⠀⢀⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠋⢾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⠛⣍⣁⣒⠲⠀⠀⠻⣿⣿⠏⠀⠀⠖⣒⣈⣩⠚⢻⠉⠁⠀⠀⠈⢠⠀⣸⡟⢻⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀⠙⣧⣬⣍⣁⣀⣀⣼⣅⣀⣀⣈⣩⣥⣼⠋⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠉⡉⠀⠀⠀⠀⢉⠁⠀⢀⡥⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠁⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣧⠀⣄⠀⠀⠀⠀⠀⠀⠈⠛⠃⠺⣤⣶⠗⠙⠛⠁⠀⠀⠀⠀⠀⢀⡀⢸⣅⣦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣧⣿⡆⠀⠰⣥⠀⠰⡀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣷⣹⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣷⣿⣦⡀⠳⠰⡀⠀⡀⠀⠀⠀⢀⡐⢀⣧⣰⣷⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡯⠻⠻⣿⣶⡐⡀⣀⠀⣀⡀⣰⢿⣇⣾⣱⣿⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⡬⣿⣷⣿⣿⣻⣾⡽⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠹⠟⠿⡿⠃⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢐⡀⠀⠀⠀⣒⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡴⠛⠁⠀⣠⡶⠖⢠⣤⠤⢠⣤⡄⢠⡤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⢠⠟⠀⠀⠈⠀⠀⢠⡾⠋⢀⡴⠋⠁⣴⠟⠁⠀⢼⠁⠈⢀⠐⢁⠀⠀⠋⠀⠀⠀⠑⠀⢀⠈⢄
⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠀⠀⠀⠀⠀⡰⠋⠀⢠⡞⠁⠀⡼⠁⢠⠆⠀⠀⠀⠀⡘⠀⠀⠛⡤⠀⠀⠀⠀⠀⣌⠇⠀⠈⡄⠀⠃
⠸⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⠀⢀⡿⠀⠀⠂⠀⠀⡇⢀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢱⡀⢹⠀⠀⡀⠀⠀⠀⢀⠀⢸⠋⣠⠁⠀⠠
⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠁⠀⠀⠙⠺⠂⠀⠙⠀⠀⡀⠁⠀⠸⠶⠁⠀⡀
⠛⠉⠁⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣤⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⠄⠀⠠⠆⡀⠀⢀⣍⡀⠀⢀⠠⠅⠒⠚
⠀⠀⣀⣄⠀⠀⠀⠀⠀⠛⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢾⣿⠟⠁⠀⠀⣀⣄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠂
⠀⠀⠑⠀⠀⠀⠀⠹⣿⣷⣦⠔⠈⠳⣄⡀⠀⠀⠀⠀⠄⠻⣷⣄⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠻⣶⣤⣀⣤⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⡄⠀⠈⠻⣶⣤⣄⡄⠀⠀⠉⠛⠷⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⡀⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠈⠉⠀⢀⣀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠈⠙⠻⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⡄⠀⣀⣠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣄⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⡀⠀⠁⡀⡄
⠀⠀⠀⠀⠈⠀⣀⠈⠀⠀⠇
⠀⠀⠀⠀⢸⠠⡛⢤⡴⡶⠃⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠄⠑⡄⠑⢄⠀⠀⠠⠐⠀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠄⠘⣌⠄⠀⠀⠀⠀⠀⠆⢣⣠⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢣⠀⢇⢡⠈⠘⠀⠀⠀⠀⠄⠀⠀⢻⠳⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠈⠻⢾⣦⠘⠂⣧⠘⠐⠀⢸⠀⠀⠀⡈⠀⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡞⠰⠀⢻⡄⢱⡿⣠⠃⢀⡀⢓⣶⣄⡆⢈⠰⠀⡌⡃⠀⠰⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠟⠁⠚⠴⠧⠏⠀⠞⠀⠈⠈⠀⠰⡿⠷⣋⢄⣔⠞⢁⠀⠀⢿⣢⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⣛⠫⣤⠚⢯⠆⠀⠈⠙⠷⣤⣬⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡋⠒⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠉⠀⠲⠴⠠⠊

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡿⠇⣦⣤⡀⠢⠖⡄⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠜⠃⢭⡀⠀⢨⣾⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⣄⣰⠟⠉⣠⠀⠁⠸⠳⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⢞⡅⢿⠀⣿⠀⣀⠀⠐⢰⡘⠀⠈⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⢛⢘⡸⢸⠏⢀⠇⠀⠂⠀⢳⢠⡀⠀⠹⡄⡀
⠀⠀⠀⠐⢲⡶⠀⠀⠄⠑⠞⠈⣹⢠⠀⠮⠀⠀⢠⡀⣠⠄⠇⠀⠀⠁⡷⢤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⡀⠀⢠⣄⣄⡀⠠⠀⠉⢀⡄⠀⢀⡾⠁⠁⡄⠀⠀⢀⠌⠘⢸⡇⢸⣇⢀⠷⣶⡌⠘⢓⠘⡤⡹⢖⣢⠈⠙⣦⣍⣻⡳
⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⠟⠁⠀⢠⡾⠇⠀⠈⣠⣴⡿⠃⠀⠀⠀⠀⠀⢞⠃⡾⡟⢸⡆⠙⣿⠐⡀⣽⠹⣌⢢⠙⣷⡌⠻⣎⠻⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠋⠂⠉⣀⣤⡶⠿⠛⣁⣠⠴⠂⠀⠀⠀⠀⡼⠀⣹⡏⢸⠁⢀⢸⠀⡇⢻⠀⢹⠀⠁⣏⡇⠀⢹⡄⢠
⠀⠀⠀⠀⠀⠀⠀⡄⠈⢧⣄⠀⢠⣾⠟⣉⠤⠖⠛⠉⠁⢀⠀⠀⠀⢠⡜⠁⣠⡿⣡⠋⠀⡼⡸⢸⠇⡞⢀⡏⠀⠀⢻⣷⠀⢸⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢧⠀⣸⡫⠊⣁⡤⠖⠋⠁⠀⠈⠳⠄⠠⢉⠄⠰⠻⢱⠃⠀⣸⠣⠃⣿⠘⡇⠸⢰⡆⠀⠀⠏⠁
⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⠃⠋⢠⠞⠁⠀⠀⠀⣀⠤⠀⢠⠖⠁⠃⠀⠀⣰⠋⠀⣼⠇⠀⠘⠛⠀⠇⠀⡾⠇
⠀⢀⠤⠂⠈⢷⡀⠀⠙⠀⠀⠀⠀⠁⠀⠀⠒⠚⠉⠁⣠⠖⠁⠰⠀⠀⢠⠞⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠸⠀⢆⠀⠀⠙⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣠⡀⠀⠀⣤
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⢻⣧⣰⣿⣿
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢆⣀⣤⣷⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣦⣀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣟⢿⣿⣄
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇⢉⠀⠉⠻
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⠟⣀⠈⠉⠻⠟⣩⣿⠿⣿⡻⢿⣿⣿⣿⣿⣿⡇⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⣿⣿⣿⣿⢏⡞⢹⣇⣴⣶⢰⣿⣿⣧⡿⣷⣾⡈⢻⣿⣿⣿⣿⣁⡀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⣿⣿⣿⣿⣿⣿⣼⣵⣟⡛⠉⣩⡾⣻⣿⡛⠛⢿⣿⢃⠀⢻⣿⣿⣿⡿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣭⣀⠀⢸⣿⣾⢷⢸⣿⡿⣿⣿⣊⠻⣿
⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢁⣼⣿⣿⣿⡿⠛⣛⣥⣾⣿⣿⣿⣿⣿⣏⠀⣰⣿⣿⡘⠸⣿⣿⡎⢿⣿⡄⠙
⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣰⣿⣿⣿⣿⣿⣷⣜⠋⣽⣿⠿⠻⠿⢸⣿⠋⠉⠙⣿⡿⣧⠘⣿⣿⡗⠀⢻⣷
⠀⡠⠆⠀⠐⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣝⣿⣫⣠⣤⣶⣶⣾⣥⡀⠀⢸⣿⠁⠀⠀⢹⡇⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣾⣿⣿⣿⡿⠄⠞⣿⣿⣿⣿⣿⣿⣿⣭⢀⣈⡻⠟⠁⠀⢈⣿⠀⠀⠀⠸⣷⠀⠀⣸⣿⡇
⣀⠼⠀⠀⠀⠀⠀⠀⠀⡻⠋⠁⢠⣬⣽⣏⣽⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣠⣿⢺⣿⣷⡄⠀⠀⣿⡇⢰⣿⣿⣷
⣁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⡔⣐⠒⠶⠾⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡄⢿⣿⡇⠀⠀⣿⠁⢾⣿⣿⣿
⢻⠀⠀⠀⠀⠀⠀⠠⠀⢸⠿⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⢻⡔⢙⣧⠂⡀⠀⠀⠀⠹⣿⣿
⣌⠀⠀⠀⠀⢠⢠⣾⡆⠸⠀⠉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⡠⢔⣶⣄⠀⠠⠟⠈⠉⠀⠁⠀⠀⣷⢰⢿⣿
⢿⡂⡆⢰⣆⠀⣼⣿⣧⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣦⣸⣅⣠⡿⠤⠛⡀⠀⢀⠀⠀⣄⢀⣠⠀⣿⣼⣿⣿
⣼⡇⣿⢈⣿⣸⣧⣿⣿⠀⡄⠎⡀⢀⣈⠉⠋⣉⣤⡀⢻⡏⢿⡌⣷⠸⣻⡇⠀⣼⡇⠀⣾⠀⣾⢳⣿⣣⠔⣿⣿⣿⣿
⡏⣿⣿⢈⣿⣿⣿⢻⣿⣿⣇⣼⣧⣿⣿⣷⣿⣿⣆⢻⣎⣿⠀⢠⣿⣧⣿⡇⣼⣿⠉⣠⣿⢀⣿⣿⣿⣏⢸⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣠⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣰⣿⣷⣦⠀⠘⠛⠳⣶⣾⠇⠀⣲⣶⣶⣶⣶⣷⣶⣷⡀⠀⢳⡴⠚⠃⠀⣾⣷⣶⣶⣦⠰⣿⣿⣿⣿⣿⣿⣿
⣠⣶⣿⣿⣿⣿⣿⣷⣶⠖⠳⢬⢻⠀⣰⣿⢿⢿⢿⣿⣟⣿⣿⡇⠀⠈⠴⣿⣿⡿⢿⣻⣷⠙⣿⡀⢽⣿⣿⣿⣿⣿⣿
⢿⣿⣿⡟⣿⣷⣇⠸⣧⠘⠀⢨⣧⡀⣿⣷⣿⣿⡿⠁⠈⠻⢿⡇⠀⠀⠁⢸⣿⠇⣼⣿⠄⠀⠹⡇⢸⣿⣿⣿⣿⣿⣿
⠀⣿⣺⣻⣿⠿⣻⣷⣌⡛⠾⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠁⣼⣷⡾⠛⢁⣾⣿⠟⣀⠀⠀⣗⢸⣿⣿⣿⣿⣿⣿
⠀⣿⣿⢻⣿⣿⣽⣿⣿⣿⣷⣌⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⣿⣿⣻⣤⣾⠟⠀⢰⠃⢠⣿⣿⣿⣿⣿⣿
⠀⠸⠃⠀⣻⡿⣿⣟⣿⣾⣭⣿⣿⣿⡿⢀⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡏⠉⢁⣄⠀⣄⣄⣀⢸⣿⣿⣿⣿⣿⣿
⢀⠀⣤⣬⣭⣽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⠻⢁⡼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠿⣿⡏⠉⠷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠘⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠛⠁⠀⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠹⣷⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣤⣤⣤⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⠇⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣨⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⡿⣷⡄⠈⠛⢿⣶⣤⠀⠉⢀⡤⠖⠁⡰⠾⢋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⡀⠀⠀⠙⢿⣦⣤⠟⠀⠀⣀⣀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣤⣈⣭⣉⣁⠀⠀⠀⠉⠀⠠⢤⣩⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠂⠀⢀⣤⣶⣿⣦⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⠒⠂⣐⣶⣶⣶⣲⣶⣤⣤⣤⣤⣤⣤⡴⢖⣶⣾⣿⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⡾⠱⡹⣫⣂⡴⣫⢊⢟⣵⣿⣯⣶⢁⣥⣿⢟⡩⡶⢛⡡⢴⣏⢒⣬⣥⣤⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⡟⠁⡐⡘⡸⢱⢏⡼⡱⡡⢊⢊⣿⢯⢇⡾⢙⡵⠁⡪⠞⣋⣠⢠⠐⠀⠰⣞⢿⡅⣢⡄⣄⢡⠌
⠀⠀⠀⠀⠀⠀⠀⢰⠰⣿⠀⢠⠇⠁⡀⣱⡞⡸⡱⠀⣎⠘⡜⡜⢰⡆⠊⠁⠀⠀⠚⠉⠈⡾⠷⢂⡴⠲⣚⣗⡃⠖⣌⢠⡌
⠀⠀⠀⠀⠀⠀⢠⣾⡇⢹⠀⢸⠀⡇⠀⣿⠁⣿⠃⣼⡇⠀⠃⠁⣿⣤⠀⢰⠃⡀⠀⠀⠔⣡⠞⣽⢀⣨⢙⡟⣍⠀⢘⡅⢤
⠀⠀⠀⠀⠀⠀⣄⠁⣷⠸⢀⠺⡀⡇⠀⣿⢠⣿⡖⢹⢡⠇⠀⣤⡏⣾⠀⠈⠀⡇⠀⠀⢠⡇⡶⡾⠦⢏⠸⠇⠘⢂⢠⣜⣾⠇⠄
⠀⠀⠀⠀⠀⠀⡉⠋⢿⠄⠘⠃⢀⠃⠀⣿⣸⣯⠇⣿⢸⡆⠀⢻⠇⠙⠃⡀⠀⡇⠀⡀⣸⡁⣇⡻⣌⠺⠇⠀⠀⠹⠛⢍⡬
⠀⠀⠀⠀⠀⠀⠙⣿⡌⡜⣄⢧⠘⡄⠀⢱⢸⡾⢀⡟⣏⡇⢠⠸⡄⠀⠀⣇⠠⡱⡄⠄⠉⠛⢥⡬⢔⡀⠀⠀⠀⠀⢀⠈⠁⠁
⠀⠀⠀⠀⠀⠘⠛⣿⠀⢹⢬⣎⢣⡑⠀⢠⡀⠳⡌⣧⠋⣆⢸⠀⠳⡠⠀⠘⠂⠑⠈⢂⠀⠀⣤⣁⡀⣿⠎⠳⡄⠂⠎⣠⡀
⠀⠀⠀⠀⠀⢠⣶⣽⠀⠨⢧⡝⣧⢳⡙⠢⠍⠠⢁⡹⣄⢸⡞⣿⡄⠀⠀⠀⢢⠀⠀⠲⣍⠀⠜⠟⠀⠀⠁⠈⠑⠀⠈⣷⠈⠂
⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⡀⢓⣌⢷⣝⣶⠄⠀⠂⠳⠙⣠⣿⣌⢃⡀⢀⡄⠀⠑⢄⡀⠈⠁⠰⠂⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠠⢤⡍⠀⢈⡉⠘⣟⠲⠷⢷⡇⠀⠀⠀⠀⠈⠉⢷⣬⣝⠘⠁⠤⠒⠰⡍⠃⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣒⣛⠁⢠⠊⣿⣻⣬⣍⣓⡲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠞⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣉⡉⠀⢄⠱⡷⠤⠶⣍⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⡔⠂
⠀⠀⠀⢀⡘⠟⠀⢾⡮⠥⠤⠀⠲⠾⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠁⠰⠇
⠾⢿⡗⡌⠋⠁⠀⠈⠁⠀⠀⠀⠓⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⠴⠦⣀⢲⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡁⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣛⣓⠒⠀⠱⡀⠰⠆⠀⠀⢀⡀⠀⠀⠠⠄⠀⠀⠈⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡴⠎⢩⡽⠿⠇⢷⣀⠈⠹⣯⡀⣀⣀⡀⠀⠀⢀⠈⠀⣡⠖⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡐⢤⣴⡏⠀⢠⠎⠀⠀⠁⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠀⠀⣀⣴⡋⣁⠀⠈⠉⠑⠢⡀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡁⠀⠛⠀⠀⠀⠀⠀⢀⡛⠂⠀⠀⠀⠠⢀⣤⣾⢤⠿⠛⠛⠉⠉⠁⠉⠘⠦⣄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢼⣧⠀⠘⢧⣄⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠈⠁⠐⢈⣂⠴⠆⠐⠲⠀⠀⠀⢸⠁⠀⠀⢹
⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠙⠴⣄⠐⠀⠠⠀⠀⠀⣒⠂⠈⢀⠠⠂⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠱⣈⠙⢦⣀⠀⠈⠑⠲⠶⠤⠐⠚⠁⠀⠀⠀⠠⠆⠀⠀⠀⡠⠖⠊⠲⠶⢆⡀⡤⠀⠟⠀⠀⠀⣼
⠀⠀⠀⠈⠀⠁⠀⠸⡌⠚⠺⣶⠤⣀⡀⠀⠀⠀⠀⠀⢀⠐⠛⠃⠨⠀⠀⡞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠠⠤⠂⠀⠀⠙⠄⠀⠏⠀⢀⠀⠁⢈⡉⢐⠄⠀⠀⠤⠐⠶⠀⠸⡇⡀⠀⠀⠀⠠⠀⠀⠀⢀⣠⠀⠈⠅
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢚⠃⠀⠀⠀⠐⣤⣿⣦⡄⠀⠀⠈⠀⠀⠀⠸⠇⢁⡀⠀⢠⠴⠆⠀⠈⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⡬⠥⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⠶⢟⣣⣽⣿⢙⣛⣻⣨⡙⢓⡶⣾⣗⣿⢋⣤⠈⡄
⠀⠀⠀⠀⠀⡠⠤⣤⣤⢤⣶⣶⢡⠞⣛⣫⣭⣭⣝⣛⣩⠴⣦⢉⡿⠌⣹⠃⠈⠿⣾⡷⢀⠁
⠀⠀⠀⠀⠀⡇⢲⣌⢻⡞⣱⣇⣾⣀⡻⣧⡼⣓⣚⣟⡷⠢⠁⢀⡴⢂⣨⠷⠷⣄⠈⣀⡈
⠀⠀⠀⠀⠀⠱⡈⠿⠟⢿⡏⠿⣸⣿⠮⣽⣿⣿⣹⣿⡁⢣⣴⡉⣄⣤⠏⣶⢣⡌⠀⠹⡤
⠀⠀⠀⠀⠀⠀⠰⣤⣃⣿⣵⣾⢟⣿⢖⣛⣹⣷⣿⣿⠟⡡⡈⡿⠄⢶⣤⡁⠀⣿⡄⢷⡀⠸⢦
⠀⠀⠀⠀⠀⠀⠐⢾⡶⢿⡏⢸⣿⣿⠟⣭⣿⣽⣿⣿⠇⣄⡠⢅⠀⠋⠼⣧⢺⡟⠁⣸⡇⠀⡘⠃
⠀⠀⠀⠀⠀⠀⢾⣣⡁⣿⣿⡈⠛⣏⠻⢶⣿⣿⣩⣍⠉⢡⡶⢊⡀⢠⣾⣿⠟⠀⣸⣿⠃⠀⢬⡇
⠀⠀⠀⠀⠀⠠⡾⢻⣧⠈⠻⣿⣷⣜⣶⠶⢾⣿⣹⠏⢳⣼⣀⣤⣠⣭⣽⠃⣤⢶⣿⠃⠀⣉⡞
⠀⠀⠀⠀⠀⠀⢑⡿⢻⣷⡄⠘⠻⠿⣿⣷⣫⡿⠿⣟⣛⣛⣯⣽⡏⢰⡏⠀⣽⠛⠉⠀⠀⣹⣇
⠀⠀⠀⠀⠀⠀⠈⠳⢾⣛⣿⣶⣶⣶⣌⣻⣿⣧⠀⢿⣿⢿⡿⠿⡇⣼⠉⠃⢁⡰⣄⣰⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣥⠶⣿⣿⣿⣧⣿⣷⣘⡀⣀⠄⢀⣤⣿⣀⠗⣸⣾⣿⠟⢠⣿⡝⢧
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠻⣿⣿⣾⣿⣿⣭⡹⡹⣿⠹⢯⣴⠶⣶⣟⢁⣿⢰⣿⠋⣠⣾⢟⣡⣴⣦⣄
⠀⠀⠀⠀⠀⠀⢠⠿⢷⣄⠙⠿⢿⣿⡻⢿⣿⣿⣯⣷⡾⠗⠚⠛⠛⠛⢱⡿⠃⣼⢋⡼⠛⠉⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠠⣋⡴⠟⠻⠷⣦⣄⡀⠑⢤⣙⣿⣿⣧⡀⠀⠀⠀⠀⣠⢋⠐⢼⡃⠋⣼⠋⠀⠛⠻⢿⣷⡄
⠀⠀⠀⠀⠀⢰⠋⢀⣾⡿⢂⣶⣟⠻⣿⣶⣽⣯⣝⢻⢿⣿⣿⠿⢛⣱⠏⢀⣤⣬⣄⠙⠀⠀⠀⠀⣀⠹⣿⡀
⠀⠀⠀⠀⠀⢀⡾⠋⢉⣤⢿⣿⣿⣧⠼⠛⢁⣤⣬⣍⡓⠆⠀⠠⢞⣵⣶⣾⡤⠈⠉⠛⣄⢰⣷⣤⣌⣛⡻⣇
⠀⠀⠀⠀⠀⡀⢠⣶⡟⢁⣾⣿⣿⣷⠀⠴⢟⣋⣙⠛⢿⣷⡄⢠⣿⠟⠋⣠⣤⣀⣤⣤⣠⣾⣿⣿⣿⣍⠛⠿⣧
⠀⠀⠀⠀⢰⢃⣿⣿⠀⣸⣿⣿⣿⠁⢠⣾⡿⢿⣿⡿⠶⣌⢻⣿⠃⢠⣾⠟⠉⠀⠀⠀⣤⠈⠙⢿⣦⡈⠳⣆⠈⠳⡀
⠀⠀⠀⢠⣿⡿⢛⣡⣆⠻⢿⣿⣿⣠⢏⣤⣶⣿⠛⠓⠤⠈⡀⠥⡴⠚⠁⠀⠀⠀⠀⠀⠀⣠⠂⠀⠙⠃⣀⢹⡇⠀⣧
⠀⠀⠀⣼⠏⠀⣈⣭⣿⣷⣦⢹⣿⠋⣉⣤⣿⣱⡆⢰⡆⢀⡄⠠⠀⠀⠊⣀⠐⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠸⠃⠀⣿
⠀⠀⢸⢏⣤⣾⡿⢋⣻⣮⣍⢻⡿⢰⣿⣿⣿⣿⣶⣴⣤⡞⠃⡄⡠⢀⠈⠈⢃⡔⠀⢠⣼⡏⠁⠀⠀⠀⠒⠀⠀⣠⣿
⠀⠀⢺⢸⡿⠁⣼⣿⡿⣿⣿⡿⣷⢸⣿⣿⣿⡟⢿⣇⠉⠙⢿⣿⣰⡿⢁⢀⣄⢀⣀⠞⢉⡛⢿⡓⠀⠀⣄⠠⠞⠋⠃
⠀⠀⢸⣸⠁⣸⣿⢋⣾⣿⣿⣶⣶⣦⣉⠙⠿⢷⣌⠻⣶⣤⡀⠨⠟⠓⢿⣿⣯⠞⠁⠀⠻⠿⣮⣝⡳⠶⠶⠶⢶⣶⣬⠁
⠀⠀⠀⢻⡀⣿⡃⢸⣿⣿⠿⣻⣿⣿⡿⣿⣿⠶⣬⣷⣄⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⢸⣧⠈⣿⣏⣴⣿⣿⣿⣿⢿⣝⠿⣮⣿⠀⠙⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⠀⣿⣿⡿⣿⣷⣿⡿⠿⣿⣳⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⣿⣿⣿⣿⣿⣷⣦⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⣱⣿⠿⣯⣽⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⢦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣍⣫⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣩⡴⢰⡴⢶⡖⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⡤⣸⣦⡍⡰⢮⡀⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⡰⣰⡏⣨⣯⣡⣙⣓⣩⠿⠩⠃
⠀⠀⠀⠀⠀⠀⢸⣷⣥⣶⣦⢽⣿⣾⠁
⠀⠀⠀⠀⠀⢰⠛⡟⣩⠞⡹⠛⠳⣿⣦
⠀⠀⠀⠀⠀⢸⢢⣆⡴⢟⣥⠾⢶⣶⣮⣦⡀
⠀⠀⠀⠀⠀⣸⣺⣽⣱⡏⣠⡖⢉⣧⣖⣚⣛⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⡇⢿⡌⡼⡰⡟⣰⢋⡜⣹⢓⣚⣛⣛⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣿⠋
⠀⠀⠀⠀⢠⠇⣜⣧⡇⢁⣧⠃⡏⢸⠏⡼⢩⡷⢶⣒⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡇
⠀⠀⠀⠀⢸⠠⡁⢴⣇⢠⣿⢸⣵⢾⡼⣧⣶⠳⣸⡽⣟⢉⠗⣬⣟⣓⣦⡀⠀⠀⠀⠀⠀⠹⡛⣳⡀
⠀⠀⠀⠀⡆⠀⢡⠏⠉⠻⣿⣜⣿⣾⡇⡟⣷⣡⣿⣿⠏⣨⠞⣩⣌⠣⡴⣿⣄⠀⠀⠀⠀⠀⠉⠫⣸⢳⡄
⠠⣖⠩⠉⠃⠀⡎⠀⠀⠀⠈⠛⠛⠛⢿⣿⣼⡟⡟⡟⢰⣧⠘⣹⢱⡿⣷⢫⠽⣦⡀⠀⠀⠀⠀⠀⠈⣿⣻
⠀⠛⠦⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣅⢻⣽⡄⠈⠓⢿⡌⣁⣾⣿⣦⡟⠿⡆⠀⠀⠀⠀⠀⣮⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⡙⣜⢟⣊⣙⣒⢮⣛⣷⠾⠛⢦⣭⡳⣶⡉⡢⣄⣀⢀⣴⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢦⣤⣜⡳⠾⠍⠬⠻⡉⠁⠀⠀⠀⠈⠉⠻⣝⡻⠦⢼⣧⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠥⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠐⠊⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢧⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠀⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣉⠃⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠄⠀⠀⢀⣠⠆⡃⣠⣀⢰⠀⠀⢈⠴⠁⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠃⠀⢰⣚⣩⠅⠀⠀⠈⠀⠄⠐⠂⠐⠁⠀⠀⠐⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠠⡤⢀⡉⠀⠒⠁⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⢀⠀⠀⠒⣢⠊⠁⠀⠈⠑⠠⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠰⠀⠐⠀⠀⠀⠀⠀⠘⠃⡖⠠⢄⡀⢀⡀⢀⣄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢩⡀⠈⢯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣃⠀⢦⣄⠀⠀⡈⠀⣄⠀⠀⠀⠀⠀⠀⠸⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠷⣄⡀⠀⠀⠧⡄⠤⣽⡿⠂⢧⣀⠘⠀⠀⠀⠀⠰⠍⠀⠤⠖⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣐⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣫⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣽⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⣾⡟⢯⡓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⢀⡀⠀⢸⣿⣿⠸⠀⠘⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠘⢧⢸⠀⠀⠈⠉⠛⠀⠀⠀⠳⣅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣈⡃⢇⠁⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⠲⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠓⠍⠈⠿⡌⣆⠀⠀⠀⠀⠈⠣⠀⡀⠀⠀⠀⡇⢼⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⡀⠀⠞⢂⡀⠠⠀⠀⠀⣬⠇⠀⠀⠘⢡⡏⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣸⣿⣿⠆⠻⣏⠀⣴⠖⠒⠋⢉⡀⠀⢀⣴⠋⠀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡤⣲⠞⢋⢁⣖⡫⠟⢁⠀⠈⢁⡤⠀⡙⠉⠉⠙⠛⢦⡘⠀⢀⡘⠈⠀⠀⣠⠎⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣯⠁⢸⡝⠀⡶⢡⡟⣉⣴⠾⣯⠖⢁⡾⠁⢰⠁⠀⠠⣤⣄⠀⠙⢷⡀⢄⠀⢠⡾⠋⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢸⣼⡘⣷⢄⠀⢷⡄⠇⢁⡞⡟⣡⡕⠁⢠⢿⠃⢀⡟⠀⠀⠀⠀⠙⠳⡀⠀⠑⠞⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣶⡆⠹⣼⣾⠀⠀⡇⢰⢸⣷⠃⡟⠀⢠⣧⠇⠀⣸⠇⡄⠘⠛⠛⠲⢄⠀⠀⠀⠀⢰⢀⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⢌⣧⢠⣽⠃⠀⣰⠇⢻⡸⡏⢠⡇⣼⠸⡏⠀⢀⡿⠀⠁⠀⠀⠀⡀⠀⠀⠀⢀⣶⣼⡞⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⠛⢟⠛⠆⠘⠃⢼⡋⠀⠘⠋⠀⠀⢳⡁⠸⣇⢹⡄⢻⡇⠈⠁⠀⠀⠀⠀⠼⠀⠀⠔⠀⠙⠛⠛⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡾⠉⠀⠀⠀⠀⠛⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⠳⡄⠙⠦⠿⠆⠳⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⣀⣠⣄⠀⢠⣤⡀⠲⡿⠿⠞⠁⠀⠀⣀⡀⠀⠀⠹⠗⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⣤⡀⠀⡀⢀⡀⡈⣠⠾⠤⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⣦⢀⣀
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⠛⠀⠪⣡⡦
⠀⠀⠴⠚⣹⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣷⣩⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠷⠦⢤⠄⠈⠀⣦⣀⠈⠲⣌⣠⠖⠂⠀⢀⣀⣀⠀⠀⠤⠐⡀⠝⠶⠦
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠆⠀⠢⠀⠀⠀⠀⠀⠀⢸⡿⣷⢖⣶⣷⣆⠀⠙⠉⢀⡀⢹⡅⠀⢀⠈⠀⠀⠈⠓⢀⡔⠁
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡅⡀⡾⢟⣿⠃⠀⠀⠀⠳⣄⡁⣆⠀⠀⠀⠀⠀⠀⠈⢣
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠓⠳⠏⠠⣄⠀⠀⣀⠀⠈⠈⣿⠛⠂⠀⠀⠀⠀⠡⠀⠀⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⡠
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡠⢐⡶⢄⣀⠀⣀⡀⠀⢠⣄⣀⡤⠔⠋⣸⡎
⠀⠀⠺⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣀⣀⢊⡸⠗⠁⠀⠀⠀⠡⠋⠀⣴⠟⡹⠁⠀⠀⣠⡡⠃
⠀⠀⠀⠻⣿⣿⡀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠿⣿⣿⣇⠀⠀⠀⠀⢯⣌⡰⠁⠀⠀⠀⠀⠀⡀⠀⠔⠉⠉⠙⠃⢀⡤⠊⠋
⠀⠀⠀⠀⠙⢿⣇⢀⠙⢿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡛⡡⠊⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠰⠿⠿⠗⠀⢙⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠘⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⣠⣤⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠼⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣀⠤⠤⠦⠤⠠⠤⠴⠶⠤⣤⠀⠀⠰⣦⡄⠀⡶⠶⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⢷⣤⠶⠶⠛⠋⣛⢶⣶⣆⡛⠶⠶⠶⠶⠦⠴⠇⠀⠀⣤⣶⡆⠀⠀⠀⣤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠉⠀⠀⢀⠀⢀⣴⡶⣻⣿⡷⣿⡿⠷⠽⢷⣶⣄⠀⢠⡄⠀⠐⠿⠋⠓⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣉⠐⠛⠉⣀⣤⣤⣤⣿⣷⣶⣤⣤⣈⠙⠃⢶⣴⣻⣧⣄⠁⣤⣀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡿⠋⠀⠠⠾⠿⠛⠛⠻⣿⡟⢛⣻⡟⠛⠛⠀⠀⠙⣿⡟⢿⣇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢰⣿⡇⠀⠀⠀⠠⢦⠾⢻⣷⣿⣿⣾⡟⠻⣶⣦⣄⠀⠀⢻⣿⡆⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⡀⠙⢋⣧⣀⡀⠞⠀⠂⢠⡏⣿⣿⣿⣿⣿⣦⠀⠀⢈⣤⣴⣼⣟⠁⣤⡘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣸⣇⠀⣸⡇⠙⠛⠃⠀⠀⢺⣿⣻⣿⣿⣽⣿⣿⣄⠀⠘⡙⠋⢈⣿⡄⣹⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣹⠇⠀⠟⢹⠛⣟⠻⢶⡀⠹⢿⣿⣿⣿⣿⣿⣿⢏⣴⡿⣻⡟⣻⣿⡧⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⠀⠀⣿⠘⣷⣌⡛⠻⣿⣆⠐⠉⣿⣿⣿⣿⣿⣾⡿⠛⣫⣾⣿⣿⡇⠀⣿⠀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⢿⡧⠀⢿⠀⠀⢻⣧⠾⣿⡿⠀⠹⠿⠀⡰⣿⣿⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⠃⠀⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⠀⠀⠀⡼⠟⣻⠟⠀⡘⠀⢠⡆⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣰⣏⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⡿⠾⠃⠈⢠⠴⠞⠁⠀⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡝⢯⡿⠻⢿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀⠙⢷⡄⠀⠐⠂⠀⠀⠀⠃⠈⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣿⢳⣄⣴⠿⠋⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣠⣬⣄⡀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⢿⣤⣿⣷⣬⣿⣿⣿⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠟⠉⠙⠃⠀⠐⠢⠀⠈⠢⣤⣠⣤⣤⣾⣿⠏⣸⡿⢫⣾⣾⠟⠋⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⡀⡀⠈⠻⣿⠿⡋⣀⣀⣭⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⡀⠀⣠⣴⣿⣶⣤⣤⣤⣶⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡉⡉⢉⢹⡏⠉⢻⣿⣿⣇⣴⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣰⣮⣰⣿⣾⡿⠋⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢿⣿⣿⣿⣿⣿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠙⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣓⠂⠄⠀⠀⠀⣀⣀⡴⣘⣑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢛⡷⠐⢸⢻⡷⡙⡋⣴⣿⣿⣗⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠱⢓⠓⣘⠶⠝⢳⣈⠻⣿⠏⣾⣦⣄⠀⠀⠀⠀⠀⣀⣀⣤⡤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡴⠂⠄⢏⠥⢘⠈⢁⠋⠃⢷⡌⢿⡳⣤⣤⠒⠿⣌⡠⡈⠉⠀⠉⠳⡌⠻⣴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡏⠀⣠⠟⠫⡉⠘⠼⣧⡀⡜⡇⢈⠿⣏⠛⠳⠀⠈⠣⠙⣆⠘⣆⢱⡀⢠⠙⡀⣍⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠈⠀⠨⡥⢐⠥⠂⣿⢱⠇⠈⢰⠈⣇⢰⡄⠀⠈⣷⠨⡀⠸⡄⠙⠀⣇⢣⢹⣾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠞⡶⠂⢖⣄⢠⣌⣠⡜⣡⠏⡰⠀⢸⢆⠋⠀⡇⢠⡀⠙⠆⢳⡀⢻⡀⡄⢸⢸⠘⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢝⣃⣉⣽⣏⠳⡍⡴⠋⣼⣣⢀⠌⡘⠀⡄⠀⢸⡇⠀⠐⠀⡇⢸⠁⠇⠀⣤⣴⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡑⢸⡧⡰⠟⣁⣠⠂⢀⡷⠁⣧⡿⢠⡆⡟⠀⠁⢀⠆⠰⢹⣲⣯⠶⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠷⡀⠀⡴⠉⢀⣠⠍⠀⠀⠹⡇⣴⠀⠁⠀⣠⣭⠄⣠⢻⡟⣿⡶⠋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠓⣦⠒⠀⡀⢦⡄⠀⠀⠀⠙⣷⣥⣦⣤⣾⡟⣡⡤⣂⣿⠀⠹⣷⡾⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠿⣿⣦⣝⣾⣠⡄⠀⠀⠀⠛⠋⠉⠈⣿⣿⡆⠈⠹⡷⡀⠀⠘⢷⣷⠋⢰⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠓⠚⠋⣿⠿⠀⠀⠀⢸⠀⠀⠀⠀⣸⣏⠉⣡⢼⠇⠀⠀⠀⠀⠈⠓⠿⢧⣞⣤⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣆⠀⠀⣿⠻⠶⠆⠀⡆⠀⠀⠀⢠⣯⡤⠀⠴⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠿⠶⣀⣿⣷⠀⠀⠸⠀⢀⡀⠐⠋⠁⢀⠀⣾⠗⠈
⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣻⣯⣤⣰⣀⡄⠀⡈⠁⠀⣏⡀⢾⣤⣶⣀⡀⣀⣼⣻⠶⠛⠉⠁
⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⢛⣷⣜⡓⢆⣚⡙⠉⠀⠀⠀⠈⠉⠉⠁⠐⠒⠀⠀⠀⠉
⠈⠀⠄⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠷
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡟⠛⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⡂⠀⣤
⠀⠀⠀⠀⢀⣤⣾⡿⠿⣿⣿⢦⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣯⡀
⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⡹⡆⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⢈⣴⣾⣿⣿⣿⡿⠛⢹⣿⣿⣆
⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⡆⢹⠀⣇⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⣾⣤⡀⠈⠉⠉⠀⠘⣿⣽⣿⣷⣴⣾⣿⣿⣿⣄
⠀⢠⣿⣿⣿⣿⣧⣤⣼⣿⣇⣘⣿⣧⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠟⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣟⡀⣽⣹⡿⢷⣿⣅⡀⠀⠀⠀⠀⢈⠟⢦⣄⡐⢀⠜⠁⠐⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠈⣿⣿⣿⣿⣿⠟⠛⠻⠿⣿⡟⣾⣿⣿⣶⣄⣠⣔⣡⢾⣷⣾⢡⠋⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⣽⡷⢿⣿⣿⣿⠟⢁⣾⡁⠈⣿⡟⠀⠀⠀⠀⣠⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⢰⣿⣿⣷⡀⠀⠠⣶⣿⣿⣿⣿⣿⢓⣤⣿⡿⠟⢖⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⣠⣿⣧⠶⠃⠀⠓⠀⣈⡽⠋⠛⢛⣽⣿⠿⢋⠂⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⣼⣯⣶⠧⠤⠚⠁⣈⣽⡟⠁⠀⣲⢿⣿⠡⣈⠤⡊⠉⠉⠉⠛⢆⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣧⣶⣷⣾⣿⣿⡟⠁⠀⠀⠲⢟⣁⣈⣶⠀⢴⡤⠶⠷⠠⠸⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠰⣿⣿⣿⣿⣿⣿⣿⢟⣴⣿⣷⠿⡿⠛⠉⣻⠁⣀⣸⠀⢀⣶⣤⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⠶⠾⢿⠿⠛⡟⣟⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣴⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉
⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠃⠈⠙⠛⠿⠿⠿⠿⠛⠁⠀⠀⠈⠉⠉⠉⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⠿⠟⠛⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⠉⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢩⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⠙⠦⣤⣀⠛⠶⠤⣤⡤⣴⣖⣲⣶⣒⣦⡤⣤⣤⠤⠞⢋⣠⣤⠞⢃⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣻⣛⣾⣿⠟⠉⠀⠑⣾⣯⣭⣭⣭⣿⣭⣭⣭⣿⡗⢊⠀⠉⢻⣿⢞⣻⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⡟⠁⢠⣶⣿⠀⠀⣉⣁⣤⣬⣿⣤⣤⣈⣉⠀⠘⣿⣦⡀⠙⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡸⢁⣴⠂⣿⣿⣧⢠⣸⢰⡨⠻⢦⣭⢶⢽⢣⢤⢁⢠⣹⣿⡏⢲⣄⢹⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡞⠁⣿⣇⣤⣄⣸⡙⢖⡻⡀⢠⣮⡾⠿⣦⣳⡀⡀⢜⠺⢹⣇⣤⣄⣿⡇⢹⠎⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠄⢿⣽⡿⣳⢣⣽⡻⣉⣿⣸⡽⢥⠀⠽⣹⢃⣿⣙⢟⣯⣾⡿⣿⢻⡇⣜⠳⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣳⠄⢸⢹⡃⠙⠷⣝⠟⠒⢿⠏⠀⠀⠀⠀⠈⢻⠿⠒⠿⠾⠿⠃⢸⢸⠀⣼⡃⢩⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⠈⣻⡆⣸⣼⠷⣤⣴⢖⡤⠀⢀⡀⠀⠀⠀⠀⠰⢀⠀⠀⣔⢤⣤⣴⢿⣾⠐⣾⡛⢸⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠜⣽⡇⢿⣅⣀⣴⣻⡎⠃⠀⠂⠘⠀⠀⠀⠀⠐⠁⠇⠀⠘⢳⡢⣄⣀⣿⠀⣿⡄⠨⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠿⣿⣎⣻⣿⣋⣻⣍⠳⣌⠀⢡⣄⡀⠠⢀⣤⡞⠀⣠⠞⣩⣇⣹⣟⣁⣾⡿⠇⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⢀⡄⢛⣿⣿⣛⣭⣿⣎⡓⢬⣑⡀⠙⢿⣾⡿⠏⢀⣪⠵⢊⣼⣧⣬⣿⣿⡟⠁⣄⠢⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⢟⠀⢀⠻⣿⣿⣧⣾⣿⣿⣶⣤⡭⣥⣬⣿⣥⡤⣭⣤⣾⣿⣿⣿⣿⣿⡟⢗⠀⡘⡿⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠆⣯⣿⣠⠋⢿⣿⣿⣿⣿⡿⣽⡄⣿⣿⣿⣿⣇⣴⡟⣿⣿⣿⣿⣿⡏⠱⣼⣷⣅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣣⡆⢸⡛⣿⣿⣿⣧⢹⡝⠿⠿⠿⠟⡟⢹⠃⣿⣿⣿⡟⢿⠃⢢⡟⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠲⣤⢫⠋⣿⣿⣿⣧⠿⢷⣶⡿⢧⣾⣿⣿⣏⢿⢡⡴⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡙⣿⡌⠹⣏⠉⢤⡤⠸⡿⠦⣤⠌⢩⣿⢹⣴⠟⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠻⣧⣀⣀⣀⣁⣀⣀⣰⡿⢃⣼⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠟⠛⠋⠙⠟⡹⠋⠐⠋

⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠛⠛⡲⢦⣀⣀⣀⣉⣛⣛⡹⠷⠶⢶⣶⣤⡀⠀⣀⣤⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠘⣇⠠⣄⡀⠀⢠⣿⢔⣛⠉⣉⣤⠶⠖⠛⠲⢶⠢⣌⠙⠛⢿⠁⠀⢀⣀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠘⢦⣹⣷⡖⠁⠀⡩⠕⢛⣡⣤⣤⣶⠏⠶⠤⢤⣌⡻⡗⠢⠁⢠⣤⣿⣇⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡩⠂⠀⣪⡾⠁⠋⢩⣥⠤⡀⢰⣄⡀⠀⠈⣉⠀⠈⢷⣄⠙⠛⠋⡎
⠀⠀⠀⠀⠀⠀⠀⡠⣊⣠⢄⣴⣿⠃⠠⠟⠛⠀⣾⡵⠲⣿⣯⠀⢿⡙⣀⠀⢸⡿⡎⢦⡀⠳⢄
⠀⠀⠀⠀⠀⣠⠀⣼⡟⢠⡞⠀⣿⠘⠛⠳⠄⣾⠉⠃⠀⢹⠎⠓⢸⠟⠉⠙⣸⣧⠀⡄⢹⡄⠀⠅
⠀⠀⠀⠀⣴⠁⢰⣿⡧⣾⡇⠀⢷⣌⢳⣿⣣⡈⠄⠀⠀⠀⠘⢂⣴⣛⡼⡡⠔⣉⠇⣿⡄⣧⢢⡈
⠀⠀⠀⠀⠇⠀⣸⣿⠃⢹⡇⢸⣦⡄⠀⠀⡿⠀⠀⠀⠀⠀⠀⡞⢻⢀⣿⡶⠾⠋⠀⣿⠇⢻⠈⣷⢰⡀
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠈⢧⡀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠘⠍⢠⣀⣀⣠⣿⠀⣸⠀⣿⡄⢷
⠀⠀⠀⠀⡆⢠⡈⢿⣧⡠⢾⣿⠟⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠹⣦⣤⣿⣿⠁⢠⣿⢠⣿⠇⣸
⠀⠀⠀⠀⣇⢸⡇⠘⣿⣿⡆⢀⣀⠅⣀⡀⢠⡀⠀⠀⠀⠀⠀⡀⠀⣴⣤⡈⢹⣟⣣⠾⠟⠁⣾⣿⠀⠁
⠀⠀⠀⠀⠹⠌⣿⣦⢹⡿⣛⣿⣿⡉⡷⢤⠀⠻⣗⠠⠤⢒⡿⠃⢀⣠⠀⠀⣾⣏⠙⠛⠛⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣟⠀⠈⠁⠈⢉⠤⠉⠓⠲⠀⠀⠳⡴⠋⠀⠄⣀⣴⣬⣾⡟⠃⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠙⢷⣦⣤⡤⠀⠚⠓⠀⠀⢦⣶⡶⠟⠛⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⣀⡀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣤⣑⢢⣀⠀⠀⠤⠶⢒⣲⡶⣶⣲⡒⠠⠀⣀⡔⣊⣭⣤⣮⠛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⣾⣿⣿⣿⡟⣉⡀⠦⠭⠭⢍⣹⠒⠿⠿⠷⠚⣁⣾⣿⣿⣿⣿⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢾⣿⣿⣿⠋⣵⣂⣀⡴⠂⣾⡹⠟⠓⢦⡀⢹⡆⠉⢛⣻⣿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣬⣽⠟⢋⡤⡾⠁⢨⣴⠶⠚⢙⠒⠳⠶⠄⠘⢻⡢⣄⡈⠉⠻⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠊⢠⡶⢋⣼⠀⠀⣠⡤⠖⠽⠹⣧⠤⢀⣤⡀⠈⢿⡎⠫⣀⡀⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣴⣟⡀⠈⡧⣤⣋⡠⢀⡼⡷⠈⢬⡦⠈⡇⣥⡤⢳⠀⢰⡌⣿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣸⠇⣞⡣⡤⣬⡉⠀⠀⠀⠀⠀⠁⢀⣥⣦⡔⠛⡣⠘⣷⠘⣷⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⡿⠀⣽⠀⢿⠘⢿⡟⢿⡀⠀⠀⠀⠀⠀⡾⠟⠻⠾⢙⣷⠀⢹⠀⢹⡀⢠⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡇⠀⢿⠀⠀⠲⠈⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠈⠀⠾⠁⢀⣾⠀⣸⠇⢸⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⡄⢸⡷⢶⠒⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠂⡴⢻⠿⢀⣿⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⣿⡀⠙⣤⠞⠁⠀⠀⡏⠀⠀⠀⠀⠸⠆⠀⠀⠈⠛⣠⣃⣤⣿⡿⠀⠈⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⠀⠸⣿⣧⡴⢿⡆⠰⢄⠀⢦⡠⣀⢀⠤⣠⠂⢀⣈⡀⢸⡿⠛⡿⠟⠁⠀⢠⡇⠀⣼⣷
⠀⠀⠀⠀⢀⣠⡾⠁⠀⠹⣷⣄⡀⠀⠉⠃⠘⢷⡰⢷⣀⡀⠙⠦⣀⠏⠁⢀⠤⣔⢀⣾⡇⠀⠀⠀⢀⣴⠟⠀⢀⣿⣿⡀
⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣄⡀⠘⣿⣦⣭⡅⠠⠴⠷⠤⠠⢠⣭⣵⣿⣿⣤⣤⣴⣾⠟⠉⠀⢠⣾⣿⠋⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠙⠿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠉⠀⠀⢠⣴⣿⡿⠃⠀⣼⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠛⠿⠶⠴⠤⣶⣶⣿⠛⠉⠙⠋⠁⠀⠀⠀⢠⣿⡿⠋⠀⠀⠞⠁⠋
⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠋
⣧⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣦⣀⣱⣄
⡿⡿⣿⣿⠿⢿⣷⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣶⣶⠶⡶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⣿⣇⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠈⠀⠀⢣⠀⠀⢈⣥⣿⣥⠄
⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⡸⣿⣿⣿⢀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⣤⠔⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣻⣿⡟⠀⠀⠀⠈⠛⣣⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠉
⠀⠀⠀⠀⡂⠀⢘⠃⠀⠀⠀⠀⠀⣨⣿⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡤⠞⠛⠒⡤⠀⠀⢿⡄
⠀⠀⠀⠐⠀⠀⣾⡺⣆⠀⠀⠀⡀⠘⢿⠆⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⠎⠀⢀⡼⢸⣇⡀⠀⠃
⠀⠀⠀⠀⠀⢀⠏⢀⣄⣤⣠⣤⣿⣷⣦⢀⠀⢰⡇⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂⣠⠎⠀⠀⠂⠀⡸⢿⣷⡿⠂
⠀⠀⠀⠀⠀⠀⠀⢨⡷⣿⣿⣿⠿⠿⢿⣻⣷⣿⠃⠀⠀⠇⢠⠀⠀⡼⠋⠀⠀⠀⠀⠀⢸⣿⣤⠃⢀⣄⢄⠀⡈⠀⠘⣯⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡅⢨⣼⡖⠶⢸⣿⣽⣿⣿⠀⠀⠀⠀⠆⠀⠀⠡⠀⠀⠀⠀⠀⠀⣈⠙⠇⣠⢿⠷⢶⡖⢁⠀⢜⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⢁⣿⢸⣿⢹⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⢸⠟⢡⠄⡠⠅⠀⠀⠀⠛⠃⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡃⢸⣿⠸⣿⢯⡅⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⢸⡟⠀⠂⠀⠀⠀⠂⠁⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⣿⢠⠏⢤⢃⡷⢾⡂⠀⠐⠦⣠⠤⠀⠸⠁⢀⡴⠀⠀⠀⠈⠀⣼⠀⠀⠀⠀⠀⠀⢸⡡⠋⢺
⠀⠀⠀⠀⠀⠒⠝⠁⣀⠘⢿⠷⣴⣤⢠⠿⠎⢷⠀⠀⠀⢈⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⣿⠉⠙⠒⠀⠀⠀⣾⡇⠆⠈
⠀⠀⠀⠀⠀⠀⢰⣾⡿⣷⡈⠀⡞⠛⠛⠂⡀⡈⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠀⠀⠀⠉⣿⠞
⠀⠀⠀⠀⠀⠀⠀⣯⣿⠈⠹⣠⣿⡿⡏⠀⠁⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣿⠹⣦⢲⢿⡇⠁⠁⢀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢿⠀⠀⡀⠀⠀⠀⠀⢸⠇⠘
⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢰⡆⠻⠂⠚⠚⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢼⠶⣯⡵⠀⢀⣀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠒⣶⣲⣟⠇⠀⠀⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⢇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿⠀⠀⠀⢸⡟⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣿⠀⠀⠀⠈⣇⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣾⣿⠀⠀⠀⢀⣿⡷⢿⡄
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠙⣷⣤⣿⠇⠀⠀⠘⢷⣀⣾⠛⣦⡀
⠀⠀⠀⠸⠁⠀⠀⠀⠐⠂⠈⠀⠀⠈⠉⠒⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⣰⣲⡴⢦⣀⡀⠀⠀⠀⢀⡤⠖⠛⠛⠋⠉⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠾⠥⣿⣀⠀⠀⠀⠀⣗⣻⣶⠛⣣⢛⡵⡄⣰⣏⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡄⠀⠉⠳⡄⠀⠀⠙⠶⣿⡀⠀⢉⡺⢷⡟⠸⣾⡇⢦⡀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡆⢸⡇⠀⠀⠀⢹⣀⠀⣠⠾⢅⠉⣷⢅⡀⢸⣁⡀⠈⠁⠀⢹⣠⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠈⠀⠐⠞⠀⠀⣸⡶⠃⠀⢀⡽⠁⠀⠙⢺⠸⠀⠀⠀⠀⠙⢿⡴⠲⡄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡴⠾⠇⠀⠀⠀⠀⡴⠋⢨⠇⠀⣠⠞⠀⣠⣠⣤⡙⣄⣀⡀⠀⠀⠀⠘⠀⣠⠃⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠣⣄⡀⠀⠀⠀⠀⠀⣠⠎⣠⣾⠷⣶⢮⡇⠀⠀⢱⠙⢆⡉⠀⠀⢀⣀⣤⠽⣴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠶⠲⣯⣤⣤⣤⣄⣤⣞⣥⣞⣁⡇⠀⠀⢨⡏⠙⠛⠛⠛⠚⠛⠛⠋⠉⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠓⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣼⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⢤⡤⠤⠤⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⠉⠉⠙⠂⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠳⡄⠀⠀⠀⠀⠀⠀⢀⡴⠛
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠋⠁⠀⠀⠀⠹⡄⢀⣀⣠⠴⠚⠉⠀⢰
⠀⠀⠀⠀⠀⠀⠸⣦⠤⠤⣴⠚⠋⠙⠒⠒⠒⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⣀⣀⡤⠴⠒⡻⠋⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢰⠋⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡟⢦⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⣰⠃⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠼⠁⠀⠀⢠⡇⠀⠙⠦⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡆⠀⠀⠀⡿⠀⠀⠀⡇⠀⠀⠀⢰⠋
⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡄⠀⠀⠘⡇⠀⠀⠀⠀⠀⢿⢞⠯⣝⢧⡀⠀⠀⡇⠀⠀⠀⢳⠀⠀⠀⠈⢧
⠀⢀⣤⡞⠁⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠫⣗⣤⡈⠉⠉⡟⠁⠀⠀⠀⠘⡇⠀⠀⠀⠈⢧
⣴⡁⠀⢻⣦⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣀⣴⠒⢦⠀⠀⠀⠀⠉⠲⢵⣴⠃⠀⠀⠀⠀⠀⢻⠀⠀⢀⣀⠼⣇
⠙⣷⡄⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣠⣾⡥⠞⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⢉⡽⠁⠀⣨⣧
⠀⠘⠿⣮⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⢀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⣷⣚⣡⠴⣒⡭⠖⠃
⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠛⠛⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⡦⢀⣆⠀⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⡹⠆⠉⠀⠁⠈⠉⠀⠙⠘⢏⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡁⡰⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⢁⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡆⣴⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠅⣠⠴⠤⣄⣈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⣚⣁⣤⡶⠶⠶⢤⡉⠓⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢁⣼⠗⣀⣀⡤⠶⢤⣒⠛⢷⡀⣦⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠹⠀⠘⢣⡾⠶⠖⡀⠒⢦⣍⠣⣄⢉⠻⣇⠳⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⡹⠈⡿⣚⣛⣉⠉⠻⢦⣈⠙⢎⠛⢧⠸⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠦⠙⣶⣋⡩⠅⣈⠻⡶⠤⡉⠻⠃⠁⠈⠃⠹⠘⣘⣄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⠯⡍⠨⣤⡄⠨⣟⢦⡀⠈⠂⠄⠠⣤⡤⢀⡼⣹⣏⠆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢍⣩⣯⣙⡒⠠⣤⣄⡰⣤⡈⠼⡄⠀⠀⠀⠁⠒⠒⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⡀⠄⢀⣓⣶⣒⡛⠶⣮⠅⠈⠲⢦⡝⠇⡘⣇⠘⠀⠰⠀⠀⠀⠀⠰⠎⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠖⠀⠀⠀⠉⠛⢠⡭⣉⠠⡄⡱⡔⠀⡆⣷⢠⡉⠘⢢⢀⠁⠀⠀⠀⠀⢰⡶⣦⠼⡦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠰⠂⠈⢄⡂⢰⢀⡈⢃⠘⡇⡄⠀⢳⠆⢳⠙⠀⠁⢰⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠆⢐⡄⠲⠁⣰⠾⠀⠀⠃⠳⠀⠀⠘⢀⠘⠰⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣾⡏⢡⠀⠉⠁⠀⠀⠈⠐⠀⠀⠠⡀⢿⡀⢠⡟⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡼⠐⣦⠚⣈⠀⠀⠀⠀⡐⡄⠀⠈⠃⠀⠷⠸⠰⠆⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⣭⡤⠞⣲⠞⠋⠁⠂⠠⠤⠄⠌⠒⠰⢄⢀⡄⢀⡴⢃⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠆⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠈⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡔
⠀⠀⠀⣠⠤⠶⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅
⠀⠀⠀⠼⣶⣄⡆⢈⠇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠒⠀⠢⣄⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡉⠁⠀⠀⠀⠀⢀⣈⠁⠢⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠖⠑⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⣄⣀⡁⠀⠁⢀⣀⠀⠘⠀⠈⠶
⠀⠀⠀⠀⠀⢀⠀⠈⠈⠠⠐⢦⣨⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡘⣆⣤⠋⡄⠐⠀⠀⠀⢌
⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠀⠀⠀⠐⠀⡀⠚⠃
⠀⠀⠈⢀⠀⠀⠀⠀⠠⠀⠀⢠⠰⠈⠀⡄⠀⠀⠀⠀⠀⠄⢀⠀⢄⠠⢰⡀⠀⠀⢀⠱⠀⠀⠀⡀⣸⠠⠤⢆⠈
⠀⠀⠀⠸⠀⠀⠀⠈⠂⠄⠀⣐⠠⠀⠟⣡⡥⠤⠂⠨⠒⠚⠀⠀⠒⠒⠀⠘⠆⠲⢀⠛⠳⠃⠒⠊⡁⠂⠐⠀⡇
⠀⠀⠀⠁⠐⠄⡠⠬⠃⠐⠊⡡⠀⠘⠋⠉⠉⠇⠀⠀⠂⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠐⠀⢀⣀⣀⠀⠀⣀⣀⡤⠤⠞⠀⠀⠀⠀⢢⠶⢀⣀⠾⠀⠀⠒⠀⠀⠈⠋⠀⢄
⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠁⠈⠁⡿⠘⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠄⠀⠢⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⣇⠈⠈⠉⠀⠀⢲⠖⠚⠳⢠⢄⠀⠀⢀⠀⢠⡨⢦⠀⠀⠀⠀⠀⣰⠀⠉⠑⠀⠐⠆⡜⠉⠉⠁
⠀⠀⠀⠀⢀⡈⠕⠀⠀⠀⠀⠈⠀⠀⠣⢇⠈⠸⠁⠨⠨⠀⠀⠀⠉⠢⠤⢔⠝⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠶⠉⡀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠟⠀⢀⠠⠟⠢⠄⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⢑⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⢊⠄⠘⠀⠀⠖⠀⢤⠎⠀⠉⠉⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠙⣿⡛⠿⣷⣦⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣾⣿⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣷⣼⣷⠀⠀⣀⡈⠉⠉⠉⠉⠙⠛⠲⢦⣤⣿⠋⠀⠰⠛⠋⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⣿⣿⣷⣄⠀⠉⠛⠛⠛⠛⠓⠀⠀⠀⠈⠛⢿⡶⢤⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢷⡀⠐⣬⣿⣿⣿⣿⣿⣷⠂⠀⢠⡴⠛⠉⠁⢀⣀⣀⣀⣿⣶⣍⣳⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠲⢿⣦⡈⠙⠿⣿⣿⣿⡇⠀⢰⡟⠀⣆⠀⠀⠀⠈⠉⠙⠛⠛⠿⣿⠉⢻⣇
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⢠⣿⣧⠀⢻⣦⣼⣶⣄⠀⠀⠀⠀⠀⠈⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠙⢓⣶⠂⠀⠀⠀⠀⠀⣴⣾⣟⣉⠀⠀⡠⠀⠠⠛⠛⣿⣧⣀⠈⠉⠛⠻⢷⡄⣼⡇⠀⠀⢀⡀⠀⢠⡙⢶⣄
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⡀⠀⠾⣿⣿⠋⠁⢠⣾⠃⠀⠀⠀⢀⣾⠟⠉⠹⣶⡶⠶⣤⣀⠘⠣⠀⢀⣼⣇⠀⠀⣿⡄⠙⣧
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⠀⠀⣿⣿⠀⠀⢸⡄⢸⠇⠀⠀⠀⠙⢧⣜⡛⠙⠳⠶⢾⣿⡿⠿⠶⠶⠿⠷⢤⣿
⠀⠀⠀⠀⢸⡇⢀⣤⡾⠁⠀⠀⣿⠀⠀⠇⠀⠀⠀⣿⣿⣆⠀⠘⣿⣾⡇⢠⣄⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⡤⠴⠶⠶⢦⣄⣈⣳⡀
⠀⠀⠀⠀⢸⣵⣿⣿⣡⡇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠹⣿⣿⢦⡀⠈⠻⣷⠘⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡈⠛⠛⢧⡀
⠀⠀⠀⠀⠸⠏⠈⢿⣿⠇⠀⠠⡘⣿⣆⠀⣦⡀⠈⠳⣮⣿⣷⣍⠁⠀⠀⠀⠈⠉⠙⠉⣀⣀⣀⣉⣉⣉⠑⠒⠦⠀⢰⡏⠀⠙⠳⣤⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⠀⠹⣿⣿⣷⣬⣿⣶⣦⣄⡉⠙⠻⢷⡀⠀⠀⠀⠈⣴⣿⡿⠿⢿⣿⣤⡤⣍⣉⣓⠀⠀⠻⣶⡄⢀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢀⣼⣃⡴⣿⠀⠀⠈⠙⠿⣿⣿⣿⣿⣍⣙⠓⠀⠀⠹⠀⠀⠀⢰⣿⣿⣿⣴⣧⣬⣿⣷⣖⠒⠚⠦⠀⠀⠈⣿⡾⠶⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿⠀⡾⠀⠀⠀⠀⠈⠉⠙⠛⣛⣿⣦⣄⠀⠀⠀⠀⢸⣟⠁⠈⠉⠻⣿⣿⡟⠉⣻⠶⠶⠴⠶⢿⣯⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡇⠀⢀⡴⠋⠁⠀⠈⠉⠉⣙⣛⣿⣧⡀⠀⠀⢸⡿⣦⠀⠑⣄⢈⣟⡠⠞⠉⠛⠒⢒⡖⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣰⣯⢶⡇⠀⣀⣴⣾⠿⢯⣭⣍⡉⠃⠀⠀⠈⢷⡘⢣⡀⡘⣯⣼⢧⠀⠀⢀⣠⡮⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠃⠸⣧⡞⠋⠀⠀⠀⠀⠀⠈⠙⢳⡄⠀⠀⠈⠛⢾⣷⠗⠋⡼⢬⣧⣤⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⠀⠻⣷⣾⣷⣶⣤⣮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣏⣀⣀⡤⠀⠘⠷⣤⣀⠀⠀⠀⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⠟⠁⠀⣀⣴⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢋⣽⣧⣤⠴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⣀⠀⠀⣀
⠀⠀⠀⢀⠠⠲⠀⠒⠑⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠁⠀⠀⣀⡀⠑⢾⡅⡀
⠀⠀⣊⠀⠀⠔⠒⠈⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠀⠀⠀⠀⠀⠀⠁⡀
⠠⡌⠀⠀⠀⡅⠀⠋⠀⢁⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⡀⠀⡃⠀⠀⠀⢀
⠘⡠⠀⠀⠀⢀⠀⠀⢀⡀⠊⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠒⣛⣯⠆⢈⠇⠀⠣⠀⠀⠠⠒
⠀⠈⡍⠀⠘⣎⠁⢟⢻⣻⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⡊⠁
⠀⠀⠀⠀⠉⠈⠐⡄⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⣦⠤⢤⡊⠔⠀⠀⠀⠀⠀⢀⠠⢊⠄⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠘⠗⠲⠒⠁⡁⠂⠤⢀⠀⠀⠀⠀⢆⣀⠑⠋⠀⢀⡀⠈⡏⠀⠀⣀⢀⡀⠅⠂⠁⡴⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠀⢹⠎⠰⠐⠢⠘⠦⣀⣍⣩⡶⠓⢻⠀⠹⠀⣀⢠⠐⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠒⠤⣀⡀⠀⠀⢸⡀⠐⢨⠄⠠⠆⠀⠀⠀⠀⡖⠃⠐⠋⠁⢀⠂⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡄⠉⠉⠉⠀⠉⠁⠀⠘⣄⠀⠀⠀⣠⠃⠀⠀⠀⢀⠌⠁⠀⠐⠚⠋⢩
⠀⠀⠀⠀⠀⠀⠀⠈⠰⡒⠒⠒⠈⠡⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⡆⠀⡱⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⠀⠀⠢⠑⡄⠀⠀⠀⠀⠀⠈⠛⠊⠈⠉⠁⠀⠀⠀⠀⠀⢸⠓⠒⠒⡖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠑⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⢪⣦⢀⡐⢤⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣴⢽⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣠⠖⠋⠀⠀⠈⢦⡇⠀⠀⠀⠀⠀⠀⠠⡌⠀⠈⠋⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠢⠌⠉⢡⢐⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠰⡲⡄⢂⠒⢣⡄⢠⢉⠩⢁⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠑⢃⠀⠈⠁⠂⡞⠀⠀⡘⣧⠂⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠉⠉⠆⢀⠀⠁⠇⠀⡜⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠘⠉⡇⢤⡏⠀⠀⠀⢇⠁⠏⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣼⡟⠘⡆⢀⠀⠀⠸⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⢺⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣏⠀⢳⣶⠘⡎⠀⠀⠀⠀⠿⠸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢂⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡇⠂⢩⡘⠈⠮⣆⢈⠀⠀⠀⠀⢃⡰⣻
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢒⣦⡙⠌⠛⠉⠀⠀⠀⢀⣠⣤⢒⡶⢸⠋⣹⠀⡃⠀⠎⠳⡀⠀⣈⠀⠁⠀⠀⠀⡜⢰⣿
⠀⠀⠀⠀⠀⢀⣔⡙⡷⠚⠉⠀⠀⠀⠀⠀⡠⡖⡸⠰⣰⢃⡎⡇⠈⡰⢫⢰⠛⠘⣾⡀⠇⠘⠈⠣⠀⠀⠀⠀⢡⠽⢁
⠀⠀⠀⠀⠀⡎⡩⡏⠀⠀⠀⠀⢀⡠⢰⢺⣥⡁⢻⠀⣿⠘⣥⠁⢸⢣⠀⠀⠀⢶⠈⢻⡄⠰⠀⠀⠀⠀⠀⣠⠞⡴⠇
⠀⠀⠀⠀⠀⠱⡄⢸⠒⠶⠂⢢⡹⢴⡇⣆⢳⠁⢸⠀⠈⠂⢣⣖⠃⠈⣠⠓⢴⣄⠓⣄⠁⡄⠀⠀⢀⡤⢞⣤⡬
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⢠⡇⠀⢣⡘⢰⡘⢧⡀⠄⠀⠙⠀⠀⡈⠃⠦⣄⠑⠈⠀⣇⣠⠔⠉⠀⡉⠴⡂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⢁⠱⠰⡀⠳⣌⠳⠄⠀⠀⠀⣀⣀⠀⠀⢡⠀⠠⢤⡀⠀⠏⠀⠀⠰⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠑⠀⠉⠀⠀⠒⢀⠔⠈⠁⠀⠀⣀⣊⣤⢆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⢀⠴⠒⠀⠑⠒⠒⣌⠀⠀⠀⠀⠈⣂⠬⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⢸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⢄⠸⠆⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠑⢤⡀⠀⠀⠀⠀⢸⡀⠀⡀⠼⢤⢜⠀⡄⣀⢒⢢
⠀⠀⠀⠀⠀⠀⢤⡿⣀⣾⢠⣧⡧⠀⠀⠀⠀⠀⠀⠀⠑⠄⠸⡂⠷⠿⠃⠀⠀⠀⠀⠙⠀⠼⠾⠞⠟⠂⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁