Shrimp love Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠔⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡽⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⢛⡅⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠊⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡟⣠⠖⢩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠁⣸⢚⡕⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣫⠉⠀⠀⡵⢋⠔⣁⠔⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡰⣰⣟⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡪⠊⠁⡐⠀⠀⣠⣵⣋⣥⠴⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡵⠋⠀⠀⠀⢁⡠⢴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡅⠉⠀⠀⢀⣀⣼⢷⡶⠛⠚⠛⠋⡁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⡊⠀⢇⠀⠀⠀⣠⠏⢀⣷⣯⡤⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠋⠜⠀⠀⠈⢦⣀⡴⠗⡺⢋⣁⠤⠲⡆
⠀⠀⠀⠀⢀⡴⢧⡀⠀⠀⠀⠀⠏⠹⣡⠾⢛⡭⡄⠀⠀⠁
⠀⠀⠀⢠⢋⠄⠀⠙⠲⢄⢀⢀⣤⠟⠑⠈⠁⠀⠃
⠀⠀⢀⡇⠆⠀⠀⠀⠀⠀⠀⢈⠗⠤⡄⠀⠀⠀⠀⠀⠀⢠⡄
⠀⢀⡞⡙⠲⠤⢄⣀⣀⣀⣠⡞⠓⢄⠐⠀⠀⠀⠀⢀⢄⠌⣷
⠀⣼⠸⠀⠀⠀⠀⠀⠀⠀⢰⠦⠤⣌⠂⠀⠀⢀⡴⠡⢂⠴⡇
⠀⠻⠀⠀⠀⠀⠀⢀⣀⣤⡿⠤⣄⠈⠃⠀⣠⠎⠀⢠⢎⢞⡇
⠀⢸⠋⠛⠛⠋⢉⡉⠀⠀⠰⠤⡘⠄⢀⠞⢁⠄⡴⠃⣨⠞
⠀⢸⡄⡀⠀⠀⠀⠉⠀⣠⠞⠓⠚⠚⠁⠀⣫⠞⢁⡼⠁
⠀⠀⢧⠱⡀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⣘⢁⡴⠋
⠀⠀⠀⠁⠴⠒⠉⠀⠀⠀⠐⠀⠀⠀⢘⡵⠋
⠀⠀⠀⠀⠀⠀⠒⠤⢄⣀⣀⣐⠠⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠶⡝⢆⠀⢀⣠⡖⠉⠉⢛⢯⡝⠃⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⣶⡶⣻⡇⠀⠈⣄⠀⠀⠁⠀⠀⢀⡀⣀⢀⡀⠀⠀⠐⠋⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠟⣉⢑⢰⢏⣯⣚⠉⢀⣠⠔⠁⠀⠀⣠⠔⠿⠋⠉⠉⠁⠉⠀⠀⢡⠔⠊⡙⣆
⠀⠀⠀⠀⠀⠀⢀⠀⣼⠁⠀⠀⠀⣀⢀⣹⡷⠛⠛⠉⠉⠀⠀⠀⢀⣞⠀⠀⠤⠀⠈⠀⠀⠀⡄⠀⠤⠂⠖⡀⡨
⠀⠀⠀⠀⢠⠶⠧⠀⠠⠀⠀⠀⣠⣾⣿⣿⡯⣝⠂⠀⠀⠀⠀⠀⣈⠀⠧⠀⠀⠠⠀⠁⠀⠀⢠⣐⠀⠢⠤⠑⠃
⠀⠀⠀⢰⡇⡀⠘⠀⠀⢀⣰⣾⣿⠿⠻⠩⠓⣌⢳⡄⠀⠀⠀⠀⢿⢀⣀⡀⠘⠀⠀⠀⠀⠀⠀⢉⡀⠀⡤
⠀⠀⠀⠈⠀⠃⠀⠀⡾⡽⡋⣳⡄⠀⠀⣀⢰⡈⠀⠀⠀⠀⠀⠀⠈⡄⠉⠀⠈⣄⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⢸⡆⠂⠠⠀⢏⣟⠉⠛⠇⢀⠔⠡⢺⡟⠀⠀⠀⠀⠀⠀⠀⠘⣶⡒⢁⠀⠂
⠀⠀⠀⠀⠱⣠⡄⠀⠘⠻⣤⣄⡴⢾⣄⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⢀⣰⣄⣀
⠀⠀⠀⠀⠀⠈⠢⢄⣀⠂⠀⠀⣧⡉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⠇⠤⡿⢀⠁⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢀⠐⠂⠀⠀⣀⡤⢛⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⠀⡘⡀⠉⠀⢈⠀⠀⠆⠀⠀⠀⡼⠟⡆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠢⢠⡿⣆⠀⡀⠀⠁⢓⣆⠀⠀⠀⠀⠀⠑⠀⠀⣰⣆⠀⣶⡆⠀⠀⣴⡀
⠀⠀⠀⡖⠂⠄⠀⠀⠀⡿⠀⠆⣀⠀⠠⢃⠁⠀⠀⠀⠠⠬⣻⠀⠀⠀⣎⢳⣴⠀⠀⠘⢿⡇⣿⡇⠀⠄⢻⣧
⠀⠀⠀⠸⡀⠀⠀⠀⠠⡓⠢⠠⣬⣁⣀⣘⣦⡀⠀⠀⢠⠖⠛⢄⠤⠀⠀⠀⡏⠀⠀⣠⢠⢀⡀⣄⠀⣀⡀⢄
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠉⠀⠂⠂⠠⠉⠉⠉⠉⢛⠆⠁⠀⠀⡼⠄⢨⠀⡼⠁⠀⠀⠉⠈⠈⠁⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠦⠤⣤⡜⢁⣠⡾⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⣶⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢀⣶⣾⣿⣿⣿⣯⣷⣿⣿⣿⣟⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣁⡈⠉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣶⠯⠤⣉⡓⠢⡄⠀⠙⣷⣄
⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⡟⣿⣷⠙⠛⠛⡛⣿⣍⢿⣒⠦⢤⣄⣀⠀⠉⠙⠀⠀⠀⠈⢟⢆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⡡⠬⠥⣍⠉⠑⠂⢩⢎⢮⡳⢌⣙⠓⢶⡈⢧⡀⠀⠀⠀⠀⠀⠘⡎⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢥⣍⡑⠢⠀⠀⠀⣀⠀⣫⢣⡉⠲⡌⢧⠀⠙⣄⠙⠦⡀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠂⠀⠈⠀⠀⠀⠀⠬⣉⣡⠞⠁⠀⠘⢎⠣⡀⠈⠳⣄⠈⢷⠀⠀⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡰⠃⠀⠀⠈⠇⠀⠀⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⣀⣀⣀⣀⣀⠤⠔⢊⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠒⠒⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⣤⡶⣾⡅⠻⠆⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢋⠵⣠⠻⢛⡱⠓⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⣴⡞⠋⠠⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡉⠅⡂⢉⠀⡀⠀⠀⠁⠀⠀⠈⣿⡀
⠀⢀⡀⠀⠀⠀⠀⢥⣀⠀⠐⢢⠈⡆⠀⠀⠀⠀⢀⣀⣴⣾⣿⠧⠒⠊⠉⠈⠓⠬⣆⠀⠀⠐⠀⠀⣿
⠀⠀⠃⠢⡀⠚⠛⠛⣿⣷⣶⣾⡟⠙⢶⣶⡶⣚⣯⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⡘⠢⡀⠀⠀⠀⣿
⠀⠂⠀⠀⣨⡷⣶⣿⡟⠒⣲⠼⣟⠾⡀⠙⢿⡻⣏⠙⡻⠿⣿⣷⣄⠢⠀⠀⠀⢠⠃⠀⠙⡄⠀⢰⡇
⠀⠁⠀⠚⢁⢰⣿⡿⠥⣬⡉⠳⡾⣷⡝⣇⠀⠙⢮⡳⣦⡑⢢⠠⣎⢲⡆⠀⠀⠀⠀⠀⠀⠈⢀⡿
⠀⠀⠀⠁⡰⠋⢻⣿⣧⣤⡤⣽⠮⠈⠁⠀⠀⠀⠀⠑⣌⠱⡀⠀⢹⡘⡇⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠁⠀⡞⢟⡏⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡇⠀⠀⣿⢹⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠐⠀⠀⠐⡠⡡⡀⣈⠳⠤⣤⣤⣀⡀⣀⣀⣀⡀⡟⣟⠀⠴⠀⢂⠂⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠒⠤⠀⠉⣯⣩⣀⣿⠇⣄⣬⣿⣿⡟⠁⠁⣿⢸⣀⣀⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡟⠫⠉⠉⠛⠛⠛⠟⠋⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⢀⢶⣺⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣦⣶⢶⠰⠶⠖⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠈⠉⠁⠁⠉⠙⠋⢙⠛⠿⠉⠉⠋⠑⠈⢙⣺⣖⣓⣂⡈⡀
⠀⠀⠀⠀⢀⡴⠃⢀⣤⣤⣠⣶⣦⣼⣶⠾⣖⠂⠀⠀⠀⣀⡤⠘⠠⠀⢀⡀
⠀⠀⠀⢀⡾⠁⠴⡟⢣⠈⠩⠄⠅⡀⠻⠀⠁⠛⢫⠽⡙⠀⠒⠒⠀⠠⡀⠉
⠀⠀⠀⢘⢰⡆⠀⠁⠀⠀⠀⠀⠀⠁⠀⠑⠈⠣⠁⠐⠀⠈⣉⡁⠀⠤⠈⠦
⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠘⠀⠙⡆⠀⡅⠀⢰⠀⠀⠂
⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠃⠐⠁⠠
⠀⠀⠀⠘⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⠀⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠮⣍⡉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣴⡀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡮⠛⣦⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣿⠿⠛⠉⠈⠳⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣛⣶⣿⣿⣭⡾⠋⣵⣾⡗⠀⠀⠀⠀⢹⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣯⣍⢉⡉⢙⣽⡌⣻⡿⠃⢀⣾⣿⠟⠀⠀⠀⠀⠀⢸⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⣟⠉⠀⠀⠰⢋⡤⣿⠗⢐⣥⡶⣪⡾⠋⠁⠀⠀⠀⠀⣀⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠁⠀⠀⠀⢀⡽⠃⠔⠋⡴⣸⠰⠟⢛⣥⣾⣤⣤⣄⣤⣤⠶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣞⠛⣿⡲⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠋⠀⡏⠟⠉⠀⠀⠀⠀⠀⠀⠀⢰⢧⡀⣠⣶⣿⢫⢞⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⡟⡁⠀⠀⠀⢣⠀⠁⠀⠀⠀⠀⠀⠀⢠⢠⡾⣿⣷⣾⣿⣷⣍⠈⣉⣓⣂⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠁⠹⠿⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⢀⡴⢣⣿⡿⣯⣿⡟⣿⣿⡿⠙⢿⣌
⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⢳⠁⠀⠀⠀⠀⠄⠀⠀⣠⣖⣟⣵⣿⡟⣾⣷⢻⣞⠟⢿⢷⣣⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣿⢻⠀⣬⠀⠀⠀⢆⠀⠀⠀⠀⢀⣑⣬⣽⣻⣿⣿⣞⣷⠟⢁⡼⠁⠀⡟⠁⠙⢷⡀⠀⢻⡇
⠀⠀⠀⠀⢸⠃⠙⠀⢿⠀⢀⠀⠈⠳⠤⣤⢾⣋⣿⠿⠯⣥⣄⠀⠁⠀⡤⠞⠀⠀⠀⠀⢀⡀⠈⢋⠢⢠⠇
⠀⠀⠀⠀⢸⡀⠀⠀⠈⠣⣁⠀⠀⠀⠀⣿⠠⣼⠏⠠⠐⢬⡻⢧⡄⠀⠀⠀⠀⠀⢀⡴⠉⣽⡀⠀⢀⠄
⠀⠀⠀⠀⢸⣧⡀⢀⣆⠀⠈⠉⠉⠐⠚⣳⠞⣧⡴⣋⣁⣷⠹⣦⠱⠀⠀⠀⢀⣴⠟⠁⡰⢻⣧⣤⠄⠀⠀⠀⠀⣴⣆⠀⢰⣶⡆⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠘⢯⣏⢀⡉⠀⠀⢓⣀⠀⠜⢟⣠⢻⡏⠀⠀⠘⠙⠿⠀⠀⠀⣰⠏⠁⠄⡴⠓⣩⣾⠇⠀⠀⠀⠀⠀⠹⣿⣷⢸⣿⡇⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠸⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠋⣡⠏⠀⠀⠀⠀⠀⠀⠀⠸⠛⠘⠛⠃⠀⠈⠀⠘⠛⠓
⠀⠀⠀⠀⠀⠀⠈⢣⣀⢢⡄⠀⠀⠀⠀⠚⠉⠙⣿⣤⣤⣀⠀⢠⠶⠻⣯⣤⠄⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣶⢠⡆⣶⢰⣦⡆⢠⣤⡆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠫⠄⠀⠀⠀⢀⡀⠀⠠⠛⠛⠛⠻⡏⠋⣠⣿⣵⠷⠓⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠈⠁⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⡀⠀⠁⣤⡀⠀⠀⠐⠂⢷⡊⠉⠀⣢⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢶⣶⠂⠀⠀⠀⢀⣤⣼⠿⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠦⣄⢀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⢥⣲⣲⣄⣤⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠉⠛⠻⣿⣿⡄⣉⣈⣉⠀⠒⢀⣠⣤⣶⣶⣶⣶⣒⠠⣶⣶⠶⣶⣶⡖⢲⣾⣿⠒⠈⢻⣷⣶⣤⣀
⠀⠀⠀⠀⠀⡠⠐⠚⠙⠒⢳⣶⣾⠦⡾⡿⣶⡄⠙⠙⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⡀⢻⡇⡄⠘⢿⡟⡁⠀⠙⠻⠿⠿⣿⠶⣄⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠍⠑⠦⣦⠶⠽⠻⣦⣤⡀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁⠀⠀⢡⠀⠀⣿⡀⠀⠀⣷⡀⠀⠀⠀⢀⠀⠁⣾⣿⣆
⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣤⣤⣀⣀⣤⣀⣴⣂⣠⣤⣤⣠⠞⠀⢀⣿⡇⠀⠀⢸⡇⠀⢀⣴⠃⠀⠀⢈⠟⠛⣦
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⢿⣿⣿⣿⢿⢿⠻⠿⣶⡟⠛⢶⣶⠶⠿⣧⠶⣿⣇⠀⠀⢀⡏⠀⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠃⡸⠁⡏⢸⠸⡈⡆⢐⡞⠀⠀⡶⠃⢰⠖⠃⣠⡼⠉⡙⡿⢿⠁⢀⡴⣛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠄⠒⠉⠁⡠⠚⠁⣰⠃⡞⠸⡇⠰⣼⠀⠀⣸⠃⢠⠟⠀⡼⠋⢠⠞⠉⠀⠀⠻⡟⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡰⠞⠀⠀⣰⠁⠀⠇⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣰⠃⠀⠀⣸⠇⠀⢸⠀⠀⢳⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡇⠀⠀⢠⣿⠀⠀⢸⡀⠀⠸⡆⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢱⡄⠀⠀⠀⠉⠀⠀⠀⠀⣀⣤⡴⠂⠁⠴⢫⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⢀⣤⡂⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⢸⡇⠀⠀⣼⠏⠈⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⣭⠶⢦⣿⣧⠀⣼⠃⠀⢀⣠⡿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣤⡌⡀⠀⢂⣁⣀⣤⣄⣽⣿⣾⣿⣦⡿⠛⠁⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⢕⣤⢀⣨⡭⣿⣟⣿⢟⣽⡷⢪⣯⣠⣴⠶⠾⢿⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⡀⠒⠁⠁⠄⡠⠋⡴⢡⣿⠾⣿⢟⣺⣿⣯⣁⣀⣠⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠐⠹⡇⠜⠑⢉⡴⠋⠉⠈⠉⣙⡛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠀⠀⠀⢀⠅⠀⢀⠜⣁⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣶⣷⢿⣿⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠻⡯⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠓
⠀⠀⠀⠀⠀⠠⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠁⠀⠀⢽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠋⠉⠉⠀⠀⠈⠉⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⣠⣖⠱⣦⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡽⣺⠉⢻⣾⠟⣤⠤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⠈⠀⠀⡶⠡⣊⣥⠶⠋⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠁⠀⠈⠀⠀⠀⠀⢑⡴⠟⠉⠀⠢⠉⠀⢄⠈⣷
⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠈⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣁⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⠂⡠⠀⠀⠀⢠⠀⠠⠤⡀⡈⢣⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠥⣒⣩⠴⠠⣤⡐⢄⠀⠀⠐⡀⠀⠘⡗
⠀⠐⡮⡀⠀⣀⣤⣼⣷⣤⡀⣈⣧⣾⣄⣀⣀⣀⣠⣤⢶⡿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠐⠀⢀⡇
⠀⠀⠁⠈⠢⣄⣀⣠⣽⣟⠻⠛⢿⣅⣈⠻⣿⣝⣾⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠘⠈⢣⡀⠀⠀⢸⡇
⠀⠅⠀⠒⡶⠚⣽⣿⡯⠭⢭⣏⠛⣍⡳⣤⠈⠻⣝⢷⣔⠭⡛⠿⡻⣷⣘⡆⠀⠀⠀⠇⠀⠀⠹⡄⢀⡿
⠀⠀⠠⠍⢠⣨⣿⣿⣀⠹⠶⢬⡙⢝⢿⡼⠇⠀⠈⠳⡝⢷⡄⠱⠘⣿⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠠⠁⠼⣿⣯⣷⠿⠒⠟⠃⠀⠀⠀⠀⠀⠀⠘⢦⠘⡄⠀⠸⣆⣷⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⡀⠀⢹⠩⢿⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣇⠀⠀⣿⡈⡄⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠈⠀⡀⠈⡢⡪⢆⢀⣉⡓⠲⣴⣦⠤⢀⣤⣤⣠⡄⠟⣿⢀⠖⠃⢱⠃⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠒⠠⠄⠹⢬⣥⣼⣟⣢⣤⣬⣭⣿⣏⠀⣀⣽⣈⣀⣠⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠯⠉⠀⠈⠉⠉⠛⠿⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⣶⣶⣶⠦⢤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⡠⡲⠝⠞⡛⠉⠉⠉⠁⠘⠓⠶⢦⣬⣉⠙⠓⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡠⠖⠁
⠀⠀⠀⠀⢠⠑⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠦⢤⣌⣉⣛⣒⣶⣶⣤⣤⣤⣤⡤⠴⠖⠛⠋⠁
⠀⠀⠀⠀⠘⡁⠀⢠⣴⣶⣶⣤⣄⣤⣄⣀⣀⣀⣀⣀⣀⣤⢠⣤⣠⣄⣈⡉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢶⣤⠍⢙⠋⠭⣤⣶⣦⣭⣈⡓⠞⠶⡿⣿⠟⠓⠶⠤⢤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣍⣛⣿⣶⣆⣈⠛⠋⠚⠛⣃⣀⠀⠀⠀⠀⠀⢀⠀⢠⡄⠀⠀⠀⠉⠉⠉⠛⠳⢶⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠶⠦⢤⣜⢿⣿⢿⣿⣷⣶⣦⡀⠈⠛⠁⠀⠀⠀⠈⠉⠘⠒⠚⠉⠉⠉⠁⠐⠒⡒⢶⣤⣧⣿⠩⠽⢳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠋⣻⣶⣶⣶⣿⣥⣶⣤⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠅⠀⠈⠑⢈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⣖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠔⠀⠀⠀⠑⢉⡈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣿⣫⠞⣁⣄⣤⣼⣿⣿⣷⣝⡋⣠⣄⣠⠈⡉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⡀⣠⣾⢋⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣺⣿⣫⠞⢡⡾⢛⣿⢋⣉⣍⣭⣽⣿⣿⣶⣭⣙⡒⠷⠤⠜⠀⠠⠦⢼⣶⣿⢇⣀⢀⠀⠀⢀⠞⠉⠁⠁⠢⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⢀⣴⠟⣵⠟⣡⡾⡻⣿⢋⣭⣵⡶⠾⣿⣿⣿⡿⠿⠿⠛⠛⠛⣹⢿⣽⣷⣭⣵⣿⣺⠅⠀⠀⠀⠀⠀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠩⢺⢃⢔⣽⢟⡼⣵⣟⣿⣙⠻⢻⢿⡋⠁⠀⠀⠀⠀⣠⣾⡵⣫⣷⢾⣿⣃⣠⡴⠿⠧⣴⣅⣴⣬⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⠑⠿⢃⡷⢋⢼⣏⠕⢻⡉⠉⠹⢿⣖⣽⣿⡶⣀⠀⠀⣼⣿⣿⣾⡿⢿⣿⣯⡉⠉⠉⠐⠂⠒⠲⠲⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣷⠆⢾⣟⡙⢰⡉⡉⠙⠓⠒⠢⠭⢥⣔⣿⡟⣾⣿⣯⣽⣖⣿⢿⡉⠙⠻⣖⠤⣄⣀⠠⢒⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠃⠀⠙⠳⢷⣆⣤⣄⣈⡈⠂⠿⣇⣼⣿⠏⠁⠰⠜⠻⣧⠀⡀⠈⠻⣮⣿⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣬⣉⣉⡉⣛⣻⡿⡟⡇⠀⠀⠀⠀⠈⢳⢷⡆⠀⢄⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠚⠺⣿⣂⡤⠠⠐⠰⢾⣃⣦⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠐⠄

⠀⠀⠀⠀⢸⢻⡟⠟⣟⣻⢿⠟⢻⡇
⠀⠀⠀⠀⢸⡯⠁⠃⡿⠿⣌⡄⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⢏⠉⢹⠏⠊⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡶⠟⢉⠂⠠⠀⠘⣆⠞⠀⠁⠀⠁⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡾⠟⠉⠀⠀⢠⠔⠂⠀⠀⡏⠀⠀⠀⠀⠀⣠⠞⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠟⠋⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡇⠀⢀⡠⠒⠉⠀⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣯⡿⠀⠀⠀⠀⣀⣘⣀⡀⢀⣀⣤⣿⣻⢻⡏⠀⠀⠀⣀⣠⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠀⠄⠀⡠⠒⢈⣥⣤⣄⣤⣶⣿⠿⢛⣷⢣⣿⣿⣦⠊⠉⠀⠀⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠔⠉⠀⢚⡽⠖⣲⠋⣽⠃⠀⠀⡼⢫⡿⣿⠟⣧⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠉⠉⠒⠢⢄⡀⠀⠀⠀⠀⣠⠔⠁⠀⠔⠊⠉⢀⡜⠁⢠⡏⠀⠀⠀⠀⠏⠘⠁⡴⠋⠉⠉⡉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⢲⣤⠴⠊⠁⠀⠀⠀⠀⢀⠀⠊⠀⠀⠞⠀⠀⠀⠀⠀⠀⡠⠴⢇⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠚⠉⠁⠀⠑⠢⢀⣀⣀⡀⠔⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡜⠀⠀⠀⣨⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⠄⠀⠀⠑⠶⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠃


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣤⣴⡴⠿⠿⠿⣛⣃⡛⠒⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠔
⠀⠀⠀⠀⢌⠋⠠⠑⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⢤⣉⣉⡒⠲⠤⢤⣀⣀⣀⣀⣀⣀⣀⣤⠶⠗⠊⠁
⠀⠀⠀⠀⠃⠀⢀⣤⣤⣄⣀⣀⣀⡀⠀⠀⢀⡀⣀⣀⣈⣉⠙⠛⠒⠚⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠧⣍⠙⠛⠫⢭⣽⣮⣅⣘⠲⠿⢿⣻⠖⠶⠤⠤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⢌⣙⣿⣶⣄⡙⠋⠛⠛⣁⡀⠀⠀⠀⢀⡀⡀⡄⢀⠀⠀⠉⠉⠙⠛⢲⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠾⠿⠛⠻⠿⣿⣶⣄⢈⣁⣀⡀⡀⠀⠀⠁⠉⠉⠉⠈⠁⠉⠉⠻⣿⣿⣧⠚⠉⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣷⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠈⢕⠌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡿⣻⠟⠙⣛⣻⣿⣟⡿⠟⢉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⢐⣴⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣗⡻⠋⣵⢿⣿⢛⣛⣛⣿⣿⣶⣭⣚⠦⠦⣀⡆⠀⠤⠠⣦⣾⡃⠀⡀⠀⢀⡴⠛⠑⠻⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠉⣠⡾⣧⠟⣡⡟⢿⢟⣭⣭⠿⢿⣿⣿⡿⠿⠷⠒⠒⣻⢿⣽⣧⣭⣴⣶⠏⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⢋⢊⡣⣪⣿⣱⢿⣾⣽⣝⡛⢿⣯⡁⠀⠀⠀⢀⣼⡷⣫⣷⣾⣯⣤⣴⠟⠢⠦⠤⣦⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠙⢣⠛⢡⣹⡕⣹⣦⣀⣘⠛⠽⠿⠛⣦⣀⣠⣿⣿⢿⣟⣹⡿⣦⡀⠈⠈⠈⠉⡀⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠹⣷⠃⠳⣄⣄⡀⠈⠙⠷⡒⣿⡏⣿⣿⠟⠛⣻⣽⠆⠈⠙⢿⣳⣴⠈⢼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠳⣟⡓⠒⠶⠭⢿⣿⣿⠀⠀⠁⠈⡻⣼⣄⠈⢉⢻⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠿⠼⢾⣓⢔⠀⠤⠀⢼⣫⣽⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠉⠉

⠛⠁⢀⡞⢇⠣⡐⢺⣿⣿⣷⣿⡿⣿⠅⠀⠀⠀⠀⡤⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⡿⡿⠀⠀⠀⠀⠠⣴⡃⠀⠀⠀⠀⡀⠀⠀⠐⠂⠀⠀⠀⠂
⣄⣠⠏⠀⣸⡀⠈⢂⠻⠛⠶⠈⠁⠀⠀⠀⠀⠀⠀⠠⠽⠶⠀⠀⣰⣶⡾⠿⢷⣤⡀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠠⠧⠦⠀⠀⠾⠧⠀⠀⠀⣀⡀
⣿⢿⡄⠦⠁⢘⣰⡄⡁⠄⠒⠀⠀⠀⠀⠀⠀⠵⠄⠀⠀⠠⡀⢠⣿⣿⣷⣶⣿⣿⣗⠂⠀⠀⠀⡀⠀⢠⡷⠀⠀⡠⠄⠀⠀⠀⠀⠀⠐⢾⢿⠁
⣿⣿⣏⡑⡤⢤⡉⠸⠃⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐⠀⠁⣼⣿⣿⣿⣻⣿⣿⡿⠖⢒⡎⠀⠾⠂⣉⠀⠀⠐⠲⢤⡀⠀⡀⠂⠀⠀⠂⠀⠀⢀⠀⠀⡀
⠟⠉⠈⠠⣷⡖⢃⢉⢄⣦⣶⣿⣾⣤⣦⠀⠀⠀⢀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠀⢸⠿⢿⣷⣴⣶⣤⣤⣀⡀⠀⠀⠁⠖⠀⠀⠀⠁⠀⠀⠀⡻⠃⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⢠⣀⡤⢠⡀⠀⢿⣿⣿⣿⣿⣧⣀⠃⠀⠀⠈⠉⠙⠻⢿⡿⣿⣤⡀⠀⠀⠀⠀⢈⠀⠀⢀⠄⠀⠀⢢
⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣼⠿⠀⣾⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠉⠙⠂⢰⠞⠀⢠⣶⣶⡎⠀⠀⠀⡾⣿⣿⣿⡇
⠃⢠⠀⢴⣾⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣧⠄⠀⢁⣿⡿⣿⣿⣏⡀⠉⠈⠙⠿⠿⢶⣶⣶⣤⣄⡀⠀⠀⡰⠃⠠⠘⠿⣛⣁⣀⠂⠸⣷⣿⣿⣿⡾
⢀⡈⠐⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠇⣤⣴⣿⣿⣶⡏⠉⠉⠙⠷⢿⠁⠀⠀⠀⠈⠛⠉⠻⣿⣿⣶⢻⣤⠄⢢⡘⠻⣿⠇⠀⣾⣦⡝⠛⠉⠱
⠀⢐⡀⠀⣠⣶⣾⣿⢿⣿⣿⠀⢙⣀⠀⣭⠉⠉⠉⣬⣡⣴⣿⣿⣿⣿⣿⡀⠀⠉⠀⠀⢤⣷⣦⣀⠀⠀⣶⣄⣀⣽⡿⠁⣤⢠⡄⠀⢽⣦⡘⣿⣵⡿⠟⠋⠁⠀⠂
⣀⠘⠃⠰⢿⡿⡋⠀⠚⠻⠛⠀⠈⠁⢀⣴⠟⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠉⠙⠁⣴⣿⡔⠈⣩⣾⣿⣿⣿⣷⣾⡛⠂⠄⠀⠦
⡟⠀⠶⠀⠀⠀⠤⠐⠀⠀⣠⣶⡶⠲⣾⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠁⠀⣶⣾⣟⢉⣴⣿⣿⡿⢋⢾⡿⢹⣿⣿⡍⠉⠁
⠀⠀⠈⠤⠀⢰⡄⢰⣦⣼⣿⠀⠈⢢⠉⣀⡟⠋⠙⢀⢉⠻⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣰⣿⣿⣇⠚⠛⠋⠁⠔⠋⣼⣍⡁⠹⣿⣿⡄⢸⣿
⣶⡈⢡⡄⠀⠀⠰⢶⣿⣿⣿⣷⣤⠜⠣⠉⢤⣄⠀⠀⠋⠀⠀⠛⣿⣿⢄⠀⠂⠀⠈⠉⠙⢿⠿⠋⣿⡟⠻⣿⣿⣿⣿⣿⡟⠻⡀⠰⠂⣸⣿⣿⣿⡗⠈⠻⠷⠈⣿
⠉⠁⠀⢀⣶⠘⠃⠘⠿⣿⠿⢁⣴⣶⠶⠶⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⢰⣿⣷⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⡽⢏⠻⡛⣯⢼⣖⠋⣡⣶⡝
⠀⠀⠀⠈⢿⡇⠀⠘⢃⠞⢳⣿⠿⠿⢃⠀⠐⣶⠂⠀⢰⣆⣀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠞⢑⢄⠣⡈⢿⣿⠟⠛⠜⠛⠃
⣀⣀⣀⣀⣸⣹⣀⣀⣀⣀⣘⣿⣧⣀⣰⣶⣆⣐⣀⣚⣁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣏⣀⣰⣲⣁⣈⣂⣉⣙⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⢀⠤⠤⠤⠤⣀⣬⠄⡠⠊⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠼⠗⠐⠒⠫⠚⠓⢊⣂⠁
⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⡀⠀⠠⡂⠄⠀⣄⢠⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⡤⢁⡲⢟⣛⣛⠛⠉⠍⢉⠑⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢢⢠⡑⢃⡱⡐⢊⡭⢦⠆⡤⢄⠐⠀⠤⠀⡀⠀⡀⢀⣠⣤⡒⠩⢛⠖⠀⢠⡉⡈⠸⠛⣤⡀⠀⠈⠀⠀⠱⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠓⠈⡀⡆⠀⣃⢡⠐⠌⠡⠉⠐⢪⡁⡴⢊⡦⣨⡄⣓⠓⠚⠉⠉⠀⠀⠀⠐⠁⠠⢀⡀⠘⠚⠛⠀⠀⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⢠⠀⠀⠢⠀⢄⠐⢀⣆⡀⢲⣼⣄⠀⠀⣷⠀⢘⡷⠘⢆⠑⣦⠁⠨⣉⠓⠄⣀⠈⠉⠉⠉⠒⠢⠍⣛⡂⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠱
⠀⠀⠀⡀⣠⠁⠀⠀⢰⠀⠰⣷⠈⣏⣿⢰⣿⠟⠀⠚⠃⠀⠈⠀⠀⠀⠑⡌⠓⠄⡉⢧⡀⠀⠙⢢⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⢀⠐⠁
⠀⠀⠀⠈⠀⡆⠀⢂⠜⠀⠘⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠙⠄⠙⡄⠀⠀⠇⠀⠀⠀⠀⠀⢀⠠⠐⠊⠁
⠀⠀⢀⠀⠄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉⠀⠀⠀⠀⡘⠰⡘⡀⠀⠔
⠀⠀⢸⠀⡖⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠁⡇
⠀⠀⠘⣼⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠤⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠺⢷⣶⣶⣤⡤⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠤⣀⣄⣀⣀⣩⣟⡓⠲⢶⣤⣤⣤⣿⣿⣿⣿⣿⣦⠹⣿⠙⣿⡋⢹⣿⡟⠀⢹⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢩⣭⣭⠿⣦⣀⡉⠉⠉⠛⠛⠛⠛⠛⠛⠃⠀⠀⠉⢻⡀⠉⢱⡀⠀⠀⠀⠉⠉⣷⣆
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣄⣤⣤⣤⣤⣠⠎⠀⣼⠇⠀⢀⣿⠀⢠⡞⠀⠀⡹⠛⣦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠟⡿⡿⡟⡿⠙⢛⡿⠉⢳⡖⠛⡷⠚⢿⢤⣀⣴⠇⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠐⢉⠔⢀⠇⡅⡇⠁⣼⠀⢀⡏⢀⠟⢀⡞⢁⡤⠛⠹⣤⢞⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢠⠔⠁⢀⠎⠰⠁⢡⠈⡇⠀⠘⠀⠈⠀⠈⠀⠈⠀⠀⠀⢸⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠇⠀⢀⡟⠀⢸⠀⠸⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠃⠀⢸⠀⠀⢇⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠀⠀⢸⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀⣶⡟⠁⡀⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢡⠀⠀⠀⢸⣦⣾⣀⣠⣤⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⢼⣾⡀⠀⠀⠸⠃⣿⢩⠟⢹⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠖⠀⠔⢹⣽⣧⡄⢀⣰⣷⣿⣾⣴⣾⣿⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⣦⡀⠀⠀⠀⣢⣴⣻⣿⣿⣿⠟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⡄⠹⣾⣽⢀⡄⣾⣽⣿⣿⡿⠿⡷⣮⣌⣽⣿⣿⣯⠀⠀⠉⢀⣿⣭⡌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡠⢶⣞⠋⢡⢙⡿⠃⣤⡁⠒⠸⠀⣸⣿⣿⣍⠣⣙⣿⡀⢀⡼⣿⣿⡷⣀⡀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣴⣌⡹⠦⣼⢾⣡⡤⠻⣦⣀⢸⢠⣿⣿⣿⣿⣶⣼⣛⣷⣨⢾⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢻⡡⣍⣳⢿⡼⠏⠀⠀⠈⢹⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠈⣿⠻⣾⢹⣗⣯⣽⣾⣤⣦⣤⣤⣥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⠛⠿⡿⣿⣿⣵⡿⠧⢨⣿⣿⣿⢷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠉⢹⢟⣿⣿⡿⠾⢿⣿⣥⣿⣿⣿⣿⢠⡟⢀⢾⣷⣾⣧⢿⣽⠘⡈⣷⠈⠉⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣎⣎⣿⣿⣿⣿⠟⣿⢿⣄⣱⣿⡟⠉⠡⣤⢿⡇⡇⢻⡀⠤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡼⣾⣿⣿⣧⣀⣙⣆⣿⣼⢯⣴⣥⣶⠾⣯⡿⡇⠸⣧⣴⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣾⣿⣍⠳⣿⣿⠁⠄⠈⠁⠀⢰⠏⢹⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣵⠿⣿⣿⣿⡿⣿⡿⣿⣿⡘⠶⡿⣿⡆⢠⢸⢸⠀⠈⡑⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠙⢿⣿⣇⢻⣿⠈⣿⡗⡉⢹⡘⣇⠈⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡄⠀⠀⠀⠈⠻⡿⢦⢻⠃⠹⣷⢸⠚⠇⠀⠛⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢶⣄⣂⣂⢈⣑⡚⢲⣄⠈⠉⠉⠉⠛⠛⠋⠉⠁⠲⣤⡤⣤⠤⠤⠄⠰⠒⠲⠿⠛⠋⠙⠹⢻⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠛⠟⡛⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⠀⣿⣿⠀⠀⣿⠀⠀⠠⣧⠀⠀⠀⢰⡟⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⣉⣉⡅⡾⢧⡀⠀⠀⠀⡀⠀⠀⠀⠀⣼⢢⣿⣿⠀⠀⠸⡄⠀⠀⣿⠀⠀⠀⣾⡇⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠒⠉⣁⠠⠔⠋⠉⠛⠛⠢⣄⠠⣬⣩⣦⣤⣵⣴⣿⣽⣧⣀⣀⣠⣷⣄⣄⣿⣇⣀⣀⣿⣇⣄⣴⠟⠛⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠈⠀⠀⠀⠠⠐⠀⠁⠀⠀⠀⣀⣀⣀⣤⣶⣿⣿⣾⢿⣿⣿⢿⡟⢫⣹⠟⣟⣿⠟⡿⡿⠟⣿⣿⡿⣻⣿⣿⣿⣿⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢀⡴⢋⠽⠛⠉⣩⢟⡽⢋⣴⣟⡼⢫⡎⡼⠋⠀⡆⠋⢀⡾⠋⢀⠸⢋⠜⠉⠀⠀⣠⣜⣿⣷⣮⠟⠃⣧
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣰⣿⠖⠁⣠⠟⣿⠗⠁⡸⠫⣿⠟⢠⠟⠀⠁⠀⠀⠁⠀⠘⠀⠀⠋⠀⠈⠀⠀⠀⠞⠉⠉⠉⢹⣿⣤⡀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⢀⡔⣡⠞⠁⣰⠎⢠⡞⠁⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠛⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⢰⠋⣠⠞⠁⠀⣾⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠿⠂⠁⠀⠀⠀⡏⢩⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢰⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡿⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣨⠏⠀⣧⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⠄⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⣠⠇⠀⣈⠀⣠⠤⣀⠁⣟
⠀⠀⠀⠀⠀⠀⢀⢀⡤⣄⢠⡖⠓⠖⠃⠀⠀⠀⠖⣦⡀⠛⠁⠀⠀⠀⠀⠀⠀⠀⡎⠀⠚⠃⠀⢠⠀⠀⠀⣰⠋⠲⠢⠔⠃
⠀⠀⠀⠀⢀⣰⠋⠁⠀⠰⠈⠈⠀⠶⠖⠀⠁⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠖⠛⠂⠋⠀⠂⠀⠂⠀⠠⠀⠀⠈⠁⣀⠙⡄
⠀⠀⡆⠀⠁⢉⠀⣀⠀⠀⡀⢈⠠⠴⣿⡦⡴⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⡤⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⡀⠐⠂⠱
⠀⠀⡷⠀⠐⡊⠘⠹⠇⠀⣀⢄⣰⠤⠀⠀⢀⡠⢤⠶⠊⠉⠈⠉⠁⠗⠈⠁⠈⢉⡶⠄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠆⠀⠀⠁⠀⠀⡀⠈⠁⠀⠀⢀⣠⠞⠉⠀⠀⠀⡀⠃⠀⠀⠀⡠⠀⠀⠀⠛⠀⠀⠀⡀⠀⠐⠯⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⡀⠀⡘⢿⣀⠀⡟⠋⠀⢀⠞⠁⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⡀⠀⠨⠶⡀⠀⠀⠀⠀⢀⡄⠀⣚⠁
⠀⠀⠃⠈⠀⡀⠀⠙⠁⠀⠴⠃⠀⠀⠀⠀⠀⠀⣭⠀⠀⣀⣼⣀⡀⢀⣠⠦⡤⠀⠀⢀⢀⠀⠀⠀⠀⢠⠀⠈⢧⡀⠀⢰⠈⣇⡿⠁⡀⠀⠀⠀⠠
⠀⠀⣰⠳⠴⠁⠀⠀⡠⢊⠂⠀⠀⠀⠀⠀⠠⠚⠋⢠⢈⡀⣉⣉⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠨⠀⠀⠀⠘⡁⠄
⠀⠀⡇⠀⠀⠀⠀⡼⠃⠀⠀⠐⠂⠀⠀⢀⠀⢠⡀⠟⠀⠀⣯⣀⣤⠐⢻⣏⣹⠄⠀⢀⠁⠀⠀⡀⠀⠐⠀⡄⠀⠀⠟⠀⠂⠄⠀⢀
⠀⠀⡏⠀⠀⠀⣰⠁⠀⠀⠀⢀⣼⠀⠀⠋⠀⢸⠅⣀⠂⠉⠁⠀⠙⠉⠀⠀⠀⢀⠤⠰⠤⡶⠀⠀⣀⠄⢀⣅⠀⠀⠄⠀⠀⠐⠀⣈⠁
⠀⠀⠇⠀⠀⠠⠆⠀⠀⠀⠀⢀⣶⠀⠀⢀⣴⣨⡆⠶⠖⠒⣟⠘⣧⠔⠘⡟⠳⡆⠀⠀⠀⠀⣠⣤⠤⡤⠀⠈⠠⠀⢀⠀⠐⠀⣀⢀⢨⡇
⠀⠀⠎⠁⠀⢸⠀⠀⠀⠀⠀⠰⠋⠀⡴⠛⠀⢨⡦⢀⠤⠐⠛⠛⢻⠤⠘⠓⠚⠟⢒⢶⡶⢧⡁⠀⣴⡃⠀⠀⠀⠀⠈⠁⠀⡈⠾⣿⠆⠁
⠀⠀⠇⠀⠀⠘⠀⡀⠀⠀⠐⠀⠠⠊⠀⠘⠦⢜⣧⠼⠀⠀⣀⣀⠀⠀⠀⡀⠀⣦⠘⠚⠓⠺⢃⡴⢯⡥⠸⡇⢄⠀⠀⠀⠐⣏
⠀⠀⠀⠀⠀⣠⠀⠠⡄⠀⠀⠜⠀⠠⠂⠀⠀⠂⡗⢘⡋⢨⣯⣬⡤⠀⢘⣿⣈⡉⠀⢀⣀⣈⠀⢀⢀⡄⠀⠁⠀⠀⠀⠀⢰⡿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠩⠀⠀⠐⢀⠆⠠⠀⠀⠀⠀⠠⠤⣿⠜⠇⠀⠀⠀⠐⠀⠀⠀⠈⣀⠌⠸⢿⡿⣀⣽⡇⠄⣸⠀⠆⠀⠀⡀⢸⣃⡀⠠⠄
⠀⠀⠀⠀⠀⠘⢳⠃⠐⠖⠦⣤⣀⠀⠘⠁⠀⠀⣿⡠⢠⣤⣠⢼⣄⠀⣠⡀⠐⣇⠀⠀⠀⠏⠁⠀⢀⣀⣽⡴⢦⣀⠴⠋⣸⠏
⠀⠀⠀⠀⠀⠀⡈⡄⠀⠀⠦⣄⠉⠙⠲⡦⢤⠶⠿⡷⣶⣷⡿⠘⣇⣸⣁⣍⣷⢻⣇⣰⣤⣷⢻⢹⢿⠿⣿⣿⢛⡟⠁⢀⠟⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⢦⡀⠀⠀⣬⡈⠉⢩⡿⠧⠤⡽⠟⠻⠛⠿⠭⠯⠭⠭⠝⠛⢉⣓⢠⠖⠛⠊⠚⠀⣠⢋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣔⠡⢰⡆⠀⠀⠀⠀⠃⠀⠋⠉⠟⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠔⠒⠁⠀⠀⠻⣧⡀⠀⠀⠀⠀⡴⠃⠀⠇⢀⡀⢀⣈⡅
⠀⠀⠀⠀⠀⠁⡤⠈⠃⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⢠⡀⠈⠱⠀⠀⢳⡀⠀⠀⣀⠀⠈⠀⠀⠤⣀⡄⢀⠀⢠⠞⠁⣠⠀⠠⠋⠀⠀⠀⠂
⠀⠀⠀⢀⠠⠀⠹⠀⠀⠀⠀⡄⠀⠄⠀⠈⠉⠢⠀⠀⠙⠀⠀⠐⠄⠀⠃⠀⠀⠀⡀⠀⠆⠀⠀⠠⢰⡯⠄⠁⠀⠂⠀⣀⢠⡜
⠀⠀⠄⠀⠆⠀⠀⠀⠁⠀⡠⠄⠀⠀⠀⠂⢀⠀⠁⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠀⣀⡤⢔⡉⠁⠀⠠⠈⢧⣐⠈
⠀⠀⠊⠁⢀⠀⠀⠀⠀⠈⢀⡀⠄⠄⠀⠀⠀⠈⠁⠐⠢⠤⠀⠀⣤⣀⣀⡀⢤⠄⠀⠂⠈⠁⠀⣁⣄⠀⠀⣐⠀⠀⠁
⠀⠀⢠⠀⠁⠀⠀⠀⠆⠒⢀⡜⠰⣎⡐⠃⠀⠀⠀⠀⠐⠂⠁⠄⠀⠀⢠⡄⠉⢀⡀⠀⠀⠀⠈⠋⡉⢲⡿⠉⠟
⠀⠀⠃⠠⠇⠀⠀⢀⡆⠀⡿⠀⠀⠉⠁⠀⠀⠀⠠⠀⠐⠒⢶⡀⠀⠄⠈⢠⠴⠛⢧⡠⢤⡀⠈⡀⢏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠾⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠫
⠀⠀⠤⠂⠀⢠⠀⢠⢪⡵⠈⠁⠀⠀⠀⠌⠁⠂⠀⠰⠀⠀⠉⠀⠀⠀⠀⠎⠐⠋⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⠀⠶⠀⠀⡀
⠀⠀⠀⠂⠄⠔⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠡⢤⣀⠁⠀⠠⠓⢸⡦⢀⠒⠠⠀⠠⠈⡀⠀⠀⠀⠀⠀⠀⠀⠋⠁⡀⠃⠀⠀⠤⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠢⢀⣠⠀⠀⠀⠀⠰⠀⠀⡙⠂⠴⢀⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⠁⠃⠀⠀⠐⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⢀⠀⠘⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⡄⠀⠀⠀⠀⠀⢰⣶⡂
⠀⠀⠀⠀⠀⢀⠤⠐⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣀⡄⢶⣷⡖⣠⣉
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⢧⣀⣿⣠⡿⠿⠆
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⣿⣶⣾⡏⠈⣹⣶⣾⣿⠄⣴⣷⡆
⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠦⠤⠤⢀⣀⡀⣀⣀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡼⠦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⢤⣤⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⡀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢿⣷⣄⣠⣾⣿⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣶⣄⠀⠙⠿⠿⠿⠛⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠈⠙⢿⣷⡀⠀⣶⣾⣶⣶⣄
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⣿⡇⠀⠘⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⣀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠋⠁

⠀⠀⠀⢢⡀⠀⠀⢠⠖
⠀⠀⠀⠀⢳⠀⠀⠸
⠀⠀⠀⠀⠘⡆⠀⡏
⠀⠀⠀⠀⠀⡇⢀⠁
⠀⠀⠀⠀⠈⡇⢨⠄⣀
⠀⠀⠀⠀⠀⣷⠘⣧⣨⣵⣄⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠈⠳⣌⠻⣍⠻⢿⣖⢦⠙⠷⢥⣄⡈⠀⠀⠁⠢⠤⠤⠤⠄⠀⢀⡦⠀⢠⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠭⣥⣚⣓⠦⣵⡢⣴⢟⣿⡔⠂⠀⣀⠀⠀⠀⣀⣀⢷⣄⣀⡀⢘⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠭⣽⣛⣿⣿⣷⣧⣼⢀⠉⠻⣿⢞⣻⣿⣾⣿⣿⡧⢸⣿⣶⣦⣊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⣁⢔⢛⠛⣿⣿⣟⣛⠓⢬⣭⣂⣀⣀⣈⣩⣼⣿⡛⢁⣼⡿⢻⡿⠻⠗⠆⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢠⠎⢄⡼⢛⣯⡿⣽⣟⣿⣿⡿⠿⠿⢿⣿⣿⡿⢛⣷⢟⣋⣥⣦⣼⠃⣠⡔⠝⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠟⢡⡴⠛⠁⡰⣿⠉⣤⣤⣶⡶⢛⡿⠕⠀⢠⠞⢁⠜⠉⣠⠤⠾⣿⣹⡗⠀⡴⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠝⣺⠇⠀⢀⡔⠀⡿⠀⣥⠜⢥⡔⠉⠀⠀⣠⠃⡴⢁⡔⠉⣠⠖⠊⠉⣙⠿⢾⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠞⠀⠁⠀⠀⠌⠀⠀⣁⢠⣯⡀⠀⡇⠀⠀⠀⠁⠀⠀⠈⠀⠈⡥⠚⣉⣭⣹⣻⠀⠐⠢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠹⡎⠀⠉⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⡀⠀⠘⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣻⠟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠀⠚⠒⠒⠒⠒⠢⠤⠤⣄⣀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢄⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⢉⡥⠛⠁
⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠽⣀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⢠⠞⠁
⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠂⢀⡈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡺⠉⠀⠀⢀⠀⠄⠄⢠⠃
⢀⠔⠉⠀⠀⣤⡀⠀⠀⠀⠀⢁⠀⠘⠁⡀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠀⠀⠀⠀⢺
⢈⡷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⢧⡀⠀⠀⢀⣀⠀⠀⠘⣆
⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠠⠂⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⠁⠀⠀⠈⠙⠒⠤⣀⠀⠀⡀⠀⠘⢆
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠣⢄⡈⠀⠂⠀⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠁⠘⢦
⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡈⡄⠀⠙⢆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠣⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⢣⣤⣀⣀⣀⣀⠤⠤⠒⡎⠁⠀⠀⠀⠱⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠊⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇
⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣤⣤⣤⣄⠀⠀⢀⣀⣀⣀⣠⠄⠀⣼⣿⣿⠇
⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣶⠶⠟⠋⠁⣠⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⣁⣤⣤⣾⣿⣿⠏
⠀⠀⢹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠻⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣦⣅⠀⠀⠀⠀⠀⠀⣠⣷⣆⣰⣿⣿⣯⣿⣿⣿⣿⣿⣯⣉⡉⢉⣩⣤⣶⣾⣿⣿⣷⣶
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⣛⠋⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠤⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⣤⣤⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠀⢹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⡟⠀⠀⠀⠀⠁⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡆⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣿⣿⣿⡟⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⢸⠃
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠈
⣟⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣅
⣿⣷⡄⠑⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⡀⢀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡔⠒⠙⡏⠇⠈⠒⠶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠂⠃⠈⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠋⠁⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⡇⠀⠀⣾⠀⠀⢠⠎⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⢗⣶⡾⢿⢏⣴⢿⣧⣀⣠⠇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠕⣿⣿⠇⣠⣀⠀⣀⣠⠴⣖⣢⣬⣍⡉⠥⠒⣻⠋⡠⠊⣩⠴⣞⣛⣿⢩⠀⠔⠚⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠾⣶⠿⠟⠒⣛⠿⢟⡿⢟⣥⣾⡻⠛⠉⠁⠀⠀⠀⠃⠘⠁⢿⡷⠯⠭⠭⣽⠛⠃⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⡂⠌⠋⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⢋⡴⣟⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠊⢻⡿⠁
⠀⠀⠀⠀⠀⠈⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣸⢋⡴⢋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠻⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢋⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠩⣠⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⡀⡠⠤⠄
⠀⠦⣄⣤⡀
⠀⠀⠀⠉⠛⠶⢴⣤⣤⣤⠤⡶⣶⡖⠶⠶⠦⣤⣤⣄⣀⠀⠀⠀⢀⣀⡤⠤⢄
⠀⠀⠀⠀⠀⣀⠒⠛⠿⠿⠾⢷⣏⡀⢀⣀⣀⠀⠀⠀⠉⠙⡞⢹⠀⠈⢦⡀⢰⡀⢠⡖⢦⣄⠀⠀⣀⣀
⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⢀⣀⣈⣉⠲⢤⣬⣉⣥⠀⣠⣶⡁⣸⣀⣠⣼⢷⡾⢷⡾⠻⡖⠉⠛⠛⠻⠿⣿⣷⣶
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡠⠭⠹⠟⣩⠟⡿⠟⡛⠉⢹⡟⠉⣿⠀⢸⠇⢸⠃⠘⡇⠀⠀⠀⠀⠀⠀⠈⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⡤⠒⠉⡠⢊⠞⡹⠁⠀⠨⠇⢀⡇⠀⢸⡆⢸⠆⠀⠁
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢠⠃⣠⠊⡰⠋⡴⠁⠀⠀⠀⠀⠘⠃⠀⠀⠁
⠀⠑⠠⠀⡀⣀⡀⠀⠀⠀⠀⠀⠸⡸⣅⠘⣅⠀⠣⣄⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠺⢖⡬⢗⣒⠬⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠐⢎⣀⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢦⣤⡄⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⢸⠇⢰⠇⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢏⠀⡐⡅⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⢸⠀⢸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⣿⡇⠙⢿⣷⣦⣄⣘⠀⣂⣀⣴⣷⡀⠀⠀⠀⣀⣤⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠉⠛⠿⠿⠿⠿⠛⠉⠻⣿⣿⣿⠿⢿⣿⡟⠀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠸⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠙⢿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⠖⠛⠉⠉⠉⠓⠶⣤⣿⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠇⠀⢸⣿⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⠁⠹⣾⡣⠀⣠⣴⣶⣤⣀⣰⣟⣹⡆⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣀⣀⣤⡾⠟⠓⠒⠶⣄⣹⣯⠝⢦⡀⠀⢀⡇⠀⠀⢻⡗⣾⠋⢰⡖⠛⠉⠉⠉⣿⣷⠀⠀⣧⣀⡀
⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠉⠻⣿⡟⠁⠀⠀⣀⠀⠀⠀⠙⢿⡯⡈⠻⣄⢸⠃⠀⠀⠀⢻⣻⣄⠸⣇⣤⡄⠀⠀⡿⣿⠖⠒⢻⡀
⠀⠀⢈⡏⠀⡣⠀⠀⠀⠀⠀⢠⣿⣷⢅⣴⠿⠛⠻⢷⡄⠀⠈⣿⣔⠀⠈⠿⠀⠀⣆⠀⠈⢷⡉⠛⠛⠉⠀⢀⣼⢃⣸⣄⣀⣼⡿⠛⠓⠒⠂
⠀⠀⠈⠁⠙⠃⠀⠀⠀⠀⢀⣼⣿⣿⣺⡇⠀⠀⠀⠈⢿⠀⠀⢸⣿⣷⡄⠀⠀⢰⣿⡆⠀⠘⣷⣤⣤⣴⡶⠟⣱⠟⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⡞⠀⠀⣼⣷⣿⠻⣦⣀⣸⠀⢻⡶⠾⠿⠉⢉⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡆⠠⡄
⠀⠀⠀⠀⠐⠚⠛⠛⠛⠉⠉⣹⠿⣿⣿⣾⠉⠛⠛⠁⠀⠀⣰⣿⣿⣿⠄⠘⠛⠋⠀⠀⠀⠀⠀⠐⣤⠷⣖⠒⠒⠛⠦⠀⠀⠀⠈⢠⡤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⡰⠛⠻⣷⣧⣤⣤⣤⣴⡾⢿⣯⡁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡎⠈⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣠⠞⠁⠀⠀⠜⠋⠉⠉⠉⠀⠀⠀⠙⣷⡀⠀⠀⣠⠞⠋⠉⠉⠉⠲⣇⠀⠀⠙⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡼⠃⢀⡴⠞⠛⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠒⠈⠦⡄⠀⠀⠀⠀⠀⣿⡼⠁⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣠⣀⡎⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠃⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⢰⣶⣦⣅⠢
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠏⣴⡝⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣴⣦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀⣿⣿⠘⣡⣶⠍⣿⣿⣿⣧⠀⢀⣛⣿⣿⣿⠿⣟⣿⢿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡹⣿⣷⠿⢋⣴⣿⣿⣿⣿⠀⣼⣿⣟⠋⠀⠀⠟⢣⡟⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣉⣴⣶⣿⣿⣿⣿⣿⣿⠀⣿⢿⣿⠀⠀⠀⠤⠟⣽⣩⣾⣿⣿⣿⡻⠇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⠀⠀⠐⠒⠚⢛⣁⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣈⣉⡠⣤⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠛⣷⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⡔⣾⠿⢛⠭⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡇⠴⠛⠋⣐⠨⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠃⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠚⠋⠉⢉⣉⣉⡉⠭⠭⠭⠽⠿⠶⠶⠶⠤⠤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⢀⡤⠚⠉⣀⡤⠴⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠭⣑⡒⠢⠤⢤⣀⣀
⠀⠀⠀⣠⠋⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⡀⠀⠉⠁
⠀⠀⢠⠇⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⡉⠉⠉⠉⠑⠒⠲⢤⣀
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⡴⢊⠕⣋⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢳⠉⠢⡀
⠀⠀⠀⠀⠀⠈⠻⣏⠉⠉⠉⠁⠀⠸⡸⢧⠄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣸⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⡀⠀⠉⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⠇⠀⠀⠀⡏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡭⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⡀⠀⠀⣠⠎⠀⠀⠀⢠⠃⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⡥⠊⠉⠉⢉⣉⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠭⠤⢤⡭⠗⢲⣅⠀⠀⠀⣠⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡜⢰⢡⠤⠖⠚⣉⣁⣤⣽⡮⠽⠛⠓⢲⣦⣤⡤⠤⠤⢶⡒⣫⠝⠉⠈⣓⣒⣶⣶⣛⠯⠟⠋⢳⣄⠔⠁⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⡇⣶⠏⡳⠋⠉⢁⣞⣉⡤⠤⠒⢚⣟⢋⣉⣤⠤⠖⠒⠉⠉⠀⠀⠀⠈⠓⠤⠤⠤⠼⢒⣪⠟⠋⣹⡄⠀⠀⣠⠞⢸
⠀⠀⠀⠀⠀⠀⠀⠻⣽⠤⣇⠀⠀⡸⠀⡏⠀⠀⠀⡞⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣋⣉⣉⣩⠶⠒⣩⠞⣳⠒⠉⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⢆⠀⢧⡴⢧⠀⠀⢸⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢉⡷⠚⢹⣄⣀⡤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣓⢬⣦⠀⠳⡀⠘⡍⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠉⠁⠀⠀⣸⣄⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⢄⡈⣳⠾⣆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⢧⣼⣋⣓⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡅⢠⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡋⣡⠎⣠⠃⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢁⡴⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⡀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⢴⣶⠶⣄⠘⣧⠁⠘⠐⢼⡏⠀⢊⣿⣟⣷⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⠸⣿⣶⡿⠀⠉⠁⣀⡀⠈⠑⡀⢂⠻⢿⡿⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠑⠢⡐⡑⠀⠀⠴⠛⠉⠀⠀⠈⢦⡂⠀⠀⠀⠀⠀⠀⠒⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠼⠀⢡⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢂⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢹⢄⠀⡈⠀⠀⠘⡁⠒⠒⠂⠀⡁⠀⠀⠀⠀⠀⠀⠀⡠⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠕⣇⠀⠀⠀⠡⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢠⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠑⠠⠄⠀⠀⠀⠀⡀⠄⠈⠃⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠒⠒⠀⠀⠉⠀⠀⢀⠠⠢⠀⠀⠀⠀⠀⡜⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠠⠤⠄⠀⠂⠀⠁⠀⢀⠠⡋⠐⠀⠀⠹⠮⠔⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠑⣤⠤⠤⠤⠀⠀⠂⠈⢀⠔⠀⠀⠀⠀⡴⠀⠂⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠊⢢⣀⠀⣀⠀⠄⠊⠀⠠⠷⣴⠠⠾⣤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠁⠉⠂⠤⠤⠠⠄⠀⠊⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⠀⢠⣶⣶⣶⣦⠀⢠⣶⡶⣶⣦⠀⢠⣶⣶⢶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡌⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡠⢂⠝⢛⠟⠛⠛⡻⢷⠟⣫⠿⣛⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠁⠀⡆⠀⠀⠈⠀⠋⠸⠁⡞⢉⣬⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⠈⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠤⣀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠠⣤⣀⣀⣀⣠⡤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢹⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⡹⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣀⣠⡤⠶⠛⣁⠜⠁⠀⢀⡜⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠤⠤⠤⠤⠤⢶⠻⣿⡿⠉⡻⠉⠁⢀⣠⠔⠋⠀⢀⡴⠋⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠘⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⡶⠤⠄⠀⢐⡤⠖⠛⠷⠶⠒⠈⠁⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡞⡡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡋⠍⠐⠀⢻⡀⠔⡠⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠁⣼⠥⠀⡴⠉⠓⠦⢄⣀⣀⣀⣀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠔⠈⠀⠀⡀⠠⢸⠗⡡⠐⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣠⠞⠁⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⣀⡤⠺⢅⡀⠀⠈⠀⠀⠀⠈⠹⡏⢀⠄⠀⠀⠂⠀⠀⠐⢂⠀⢔⡠⠖⠋
⠀⠀⠀⡠⠊⠁⠀⠀⠈⣻⠀⠀⡡⠀⠀⠈⠅⢳⣅⠪⢐⠡⠀⠠⠉⠴⣢⣖⣋⣋⣛⣓⣲⢲⣖⣖⣶⣲⢤⣤⣀
⠀⠀⡰⠁⠡⢂⠀⠀⠀⢹⡅⡀⠀⠄⠀⠀⠄⡀⠉⠗⣤⣀⠅⣀⠴⠺⢧⢭⣭⣭⣭⣭⣭⣉⣉⣉⠉⠉⠉⠙⠺⣷⣄
⠀⢀⣇⠀⠂⢃⠂⠄⠀⠈⢯⠄⠀⡀⠀⠀⠠⢀⠈⠀⢀⡽⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠓⠚⠚⠧⢭⣲⣄⡀⠀⠀⠙⠷
⢀⠋⠈⠳⡦⣄⣀⠀⠀⡀⠈⠓⢎⣄⣐⣀⣠⠵⠞⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⡎⠀⠀⠐⠀⠰⠩⠻⣔⠐⠀⡀⢠⠞⠿⠶⢶⣶⣖⣶⡶⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⣀⡤⡶⠶⡦⠀⠀⠀⠀⠙⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠖⢶⢯⣵⣾⣭⢭⣥⣤⣤⣤⣤⣀⠀⠉⠳⠆⠀⢀⡤⠚⠁⢀⣐⠞⢳⠄
⢹⡀⠐⠀⠀⠠⠀⠀⢂⣀⡤⣾⠒⠒⠚⠉⠉⠉⠁⠀⠀⠈⠙⠷⣄⠀⠀⣠⠋⢀⢀⠔⢉⠁⢢⣏⡀
⠀⣿⠛⠛⠛⠛⠛⠛⠉⠀⣤⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠕⠰⠟⡡⣢⠖⠩⠋⢄⡟
⠀⠸⡄⠀⠀⢀⢀⠄⢀⡼⠃⠁⠀⢈⡿⠉⠙⡲⣤⡴⠒⠉⠉⠋⠻⣕⠠⠀⢊⣬⠾⠃⢀⣢⠖⠉
⠀⠀⠙⢤⣠⣤⣤⠶⠟⠅⠀⠀⣨⠏⠀⠀⠐⠠⣿⠀⠀⠀⠀⠁⡂⢿⡆⠀⢈⣀⠴⠚⠉
⠀⠀⠀⠀⠈⠳⣄⠂⠀⠀⠀⢀⡟⡀⠀⠀⢐⡒⣿⡀⠀⠀⠀⠀⠀⢀⡷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠛⢥⣀⣀⣀⣠⠼⢯⣐⣂⣀⣠⠤⠚⠁
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⠐⢖⡹⣿⡗⡳⢦⣤⡀⠀⠀⠀⠀⣤⠒⢢⣹⡋⡕⢴⢢⣄
⠀⠀⠀⠀⢀⣴⣞⠷⢛⣽⣷⡦⣾⣿⡞⣪⣽⢱⡤⣞⣉⣄⢹⢯⣻⠿⠿⠿⣉⣿⣽⣀
⠀⠀⠀⢀⠼⣌⡼⣯⣿⡏⣍⢩⣼⣷⣾⢅⡼⡮⣻⣥⣯⣿⠚⣦⣷⣤⣤⣾⢿⣷⡜⢤⢃
⠀⠀⠀⠐⡜⣶⡶⠧⣿⣇⣚⣸⣿⣻⣵⣿⣥⣴⢚⣟⢿⡏⠈⢹⣿⣢⠗⡔⣴⣿⣿⣮⡽⡃
⠀⠀⠀⢈⣋⢿⡰⣺⣧⠾⠻⢭⢿⣙⢏⣽⠁⠙⣾⠥⣋⢝⣖⣿⠗⠒⢞⡁⣿⡇⠩⢿⡧⠗⠀⠀⢀⢴⣶⣻⣒⡑⢦⡄
⠀⠀⠀⠸⣥⡼⣫⢵⡺⣤⣤⡼⢗⣾⢸⠉⠀⠈⢿⣶⢯⠒⢼⣷⣖⣾⣾⢚⠮⢟⡟⣪⡷⢆⠀⢰⡶⠖⠂⡀⣀⠀⠹⠝⡆
⠀⠀⠀⠀⠘⠛⠇⠨⠷⠬⠯⠮⡴⠼⠉⠀⠀⠀⠸⠿⠋⠶⠝⠬⠟⠛⠭⣭⠾⠏⠱⠿⢼⠧⠿⢿⠶⠄⠐⢷⣢⠀⠀⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡳⣤⣀⣀⠠⡒⠷⠃
⠀⠀⠀⠈⠯⡘⢿⣻⣫⠿⠗⣾⠙⣯⣝⣵⣿⡆⠀⠀⠀⢰⢷⠱⣟⣵⡾⡋⠅⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠮⠶⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣪⣽⠗⢺⡿⣝⣶⡀⠀⣀⢮⣿⣶⡜⢳⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣴⢾⣭⢻⣠⣇⠠⢷⣺⣾⡯⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⢹⣭⡵⢤⢮⢷⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣟⣽⡮⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢰⣶⣰⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣟⣵⢿⣶⣷⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣾⣿⣿⣿⢸⣿⣿⣿⣿⣼⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⢿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⠿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢻⣿⣿⣿⣾⣿⣿⣿⣿⣯⡻⢿⠿⠿⠿⠟⣛⣉⠉⠲⢦⣌⠉⠙⠛⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣏⣿⣿⣿⣷⡝⠿⠿⢟⠛⢁⠘⢿⣶⣤⣄⣈⠉⠛⠢⣄⠈⠳⡄⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣝⣿⣿⣿⡎⠟⢛⡉⠈⠓⢆⠈⠳⠀⠑⠀⠀⠀⠉⠉⠙⣧⠀⢸⡆⠀⢹⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠛⠰⠤⣄⡈⠑⢄⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⣷⠀⠀⢧⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⣛⡿⣿⡟⢤⣤⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⢀⠟⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢁⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣭⣽⣟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢫⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣟⡻⣟⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠙⠂⠙⠂⠉





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

⠀⡀⠀⢐⢂⠀⠀⠀⣠⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠒⠀⠂⠀⠀⠀⠀⠙⠁⠿⢛⣿⣿⠆
⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠈⠑⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣀⠀⠀⠐⠚⠒⠒⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣠⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠁⠂
⠀⠀⠀⠀⠀⠀⢻⣷⣶⣶⣶⣾⣧
⣀⣀⣀⣀⣀⣀⣘⣛⣛⣛⣛⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣭⣿⣿⣛⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣫⣾⣿⢿⣿⣿⣿⣿⣷⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⠙⡿⠁⢸⣿⡿⢿⣿⣿⣿⣆⣿⣷⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠐⠀⠃⠀⢿⠅⢿⣿⣿⣿⢧⣤⣬⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⡠⠀⠀⠀⠀⠀⠈⠋⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⣿⣿⣿⣿⣧⡂⠀⠀⠀⠄⢠⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣿⣿⣿⣿⡿⠛⠁⠆⠀⠀⠈⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⣉⣀⠀⠠⠤⠄
⠀⠀⠀⠀⢀⣠⠶⠟⠒⠊⠉⠉
⠀⣀⠴⡾⠋
⡴⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⣶⢢⣶⣶⣶⣶⣶⡤⣠⣀⣀
⣇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡷⣠⣀
⠹⣆⠈⢧⡀⠀⠀⠀⢀⣈⣩⣭⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣎⣿⣿⣿⣿⢹⣿⣿⣷⡄
⠀⠈⠓⠶⢽⣶⣦⣤⣤⣽⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⢏⣿⣿⣿⣿⣸⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠏⣩⠍⣙⠟⠛⠛⠛⠻⠿⠿⠟⠼⣿⡿⠟⣋⡾⣿⡿⣛⣵⣿⣿⣿⣿⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠊⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⣠⣾⡿⢋⣤⣾⢻⣿⣿⠿⣟⣧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣰⡿⠋⣰⡿⠟⣡⡶⢿⣿⣿⣿⣿⡿⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⡰⠏⢀⡾⠋⢠⡾⠋⢀⣶⣯⣭⣭⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠐⠋⠀⢀⣤⣝⡻⢿⣿⢿⣻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣭⣽⣷⣶⣶⣶⣶⣶⣾⣿⣷⣝⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡷⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⠛⣛⣛⣓⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⢀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠈⠙⠯⣍⠛⠶⢤⣀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣌⣛⣦⣄⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡞⠁⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⣀⡴⠃
⠀⠀⣤⣄⡀⠀⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⡴⢋⣉⣀⣉⡹⠖⠛⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⢳⡌⠙⠳⠦⣬⣇⡀⣾⢀⣀⠀⣀⠀⢀⡀⣼⢡⣏⣀⣿⡏⢀⡔⠚⣷⣦⡈⢗⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣄⣀
⠀⠀⠀⠙⢦⡀⠀⠀⠈⠉⠻⠛⠉⠛⠋⠛⠛⠉⠛⠒⠿⠟⠛⡀⢸⣷⣤⣿⣿⣇⡼⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⠿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣦⡀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣯⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⡠⠴⢚⣵⣿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢦⣀⠀⠀⠀⠑⠀⠺⣿⣿⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠰⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢰⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠉⠀⠀⠀⠀⠀⢀⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣲⣶⣶⣶⣖⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡞⢛⣶⣿⣦⣀⡀⠀⣀⣀⠠⠔⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⣥⠾⢋⡴⢋⡽⢛⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣫⡴⣻⠞⣻⠿⢿⣄⠀⠀⠀⠀⠀⠀⣀⡠⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣥⣾⠷⣶⣶⡏⠈⠉⠉⠉⠉⠉⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣛⣥⣾⣥⣹⡇⡀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣼⣿⡽⢻⡏⠀⠈⠉⠉⠉⠈⢩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⠤⣤⡟⠙⠢⢄⣀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⢉⣉⠤⣤⣤⠶⠄⠒⢀⡽⠦⣀⣀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⢀⣠⠴⠚⢁⣠⠴⢊⡴⠋⡀⢀⡈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠋⠀⠤⠚⠉⢀⡠⠊⢀⡜⠀⣸⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣀⣠⡴⣾⠏⠀⣠⠏⢀⡼⡻⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠚⠛⠉⢁⡼⠃⠀⠔⠁⣠⠎⠜⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢀⡠⠊⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠞⠛⠷⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⠃⠄⠉⠲⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⡃⠀⠀⠠⠀⠉⠑⠦⣄⣤⣶⣿⣿⣿⣿⣸⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡁⠀⡠⠁⠀⣀⠔⣊⢹⣿⠷⣄⠈⠻⣏⣙⣿⣿⣷⣦
⠀⠀⠀⠀⠀⣘⢩⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣱⣈⣅⣸⣀⣠⣚⣁⣀⡙⠉⠈⠓⠺⠷⣦⠿⣟⠿⠿⠿⠿⠇
⠀⠀⠀⠀⣎⠀⡀⡤⠔⠦⠐⠒⠆⠀⠘⠃⠀⠉⠁⠈⠑⢀⢋⠈⠉⢿⡿⠉⠉⡉⠛⠉⢹⡿⣷⣔⣺⡷⠮⠅⠤⠤⠤⠤
⠀⠀⠀⠀⣧⣀⠀⡁⠀⠀⠠⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⡘⠀⠀⠀⢸⣗⠀⠀⠀⠀⠀⠠⣿⣿⢿⣛⢤⣄⣀
⠀⠀⠀⠀⢸⣀⣀⠈⢽⠀⠁⠐⠂⠠⠤⠆⠀⢠⡃⣠⣄⡀⣾⣀⣀⣽⣿⣄⣀⣤⣄⣠⠴⠞⠃⠈⠋⡧⠈⢢⡀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠹⣅⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠩⡉⢯⠉⠧⣑⠢⢥⡂⡄⢀⣀⠜⠁⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡧⠀⢃⠀⠈⠉⠉⠙⢢⡴⠋⠂⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢸⡄⠀⢋⠀⠀⣀⠔⠁⠀⠉⠁⡖⡺⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣨⠀⠀⢸⡤⠚⠁⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣐⠁⣠⠖⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣣⠞⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⠶⠶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⢢⡄⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⡶⡞⠻⣽⡿⣬⠭⣤⠂
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢰⡞⣵⣡⠴⠎⡁⠀⠘⣧
⠀⠀⠀⠀⠀⡀⠛⠀⠀⠀⠈⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⢈⡵⠚⠉⠁⠰⠈⠀⠄⠸⡆
⠀⠀⡀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠁⠐⠒⠄⠀⠀⠐⠀⠀⠈⣷
⠀⢈⠐⠀⠀⠀⢸⣄⠈⠀⢰⡸⡂⠀⠀⠀⠀⣀⣠⣶⣷⡮⠖⠚⠁⠙⠢⢴⡄⠀⠈⠀⠀⣿
⠀⠠⠁⠢⣈⠉⠛⣻⡿⣶⢾⡟⠙⢶⣶⣶⣻⣿⣿⣭⣁⠀⠀⠀⠀⠀⠀⢀⠓⢄⠀⠀⠀⣿
⠀⠇⠀⢤⡼⢿⣿⣿⢛⣲⡶⢟⠻⣄⠙⢿⡿⣝⠝⡻⢿⡿⣯⠢⡀⠀⠀⠼⠀⠈⢣⠀⢰⠇
⠀⠀⠄⠁⣤⣿⣿⣀⠲⠦⣝⢿⢿⡽⠇⠀⠙⢮⠳⣤⠑⠐⣿⢻⡁⠀⠀⠀⠀⠀⠀⢡⡟
⠀⠀⠀⠠⠋⢜⣿⣿⣿⠛⠚⠋⠀⠀⠀⠀⠀⠀⠳⡌⡇⠀⠸⣼⡇⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⡠⠀⠸⡙⢿⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⣽⠀⢀⠿⣰⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠐⢄⡙⠙⠳⡴⠬⢉⣿⡟⠒⠴⣶⣶⡆⢨⢻⠠⠉⠀⢁⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠛⢿⣿⣾⣿⣟⠛⠿⠶⠾⣾⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢦⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡤⠔⠒⠒⠢⢄⡀⠑⣄⠀⠀⠀⠀⠀⣰⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡔⠁⠀⠀⠀⠀⠀⠀⠹⡄⠘⡄⠀⠀⣠⠔⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣠⠞⢁⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⣼⣞⡥⠾⠥⡶⡖⠒⠒⠲⡦⡤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠗⠊⠉⠀⠀⠀⠀⡇⡇⠀⠀⢀⣇⠇⠀⢸⢸⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡰⠋⠈⡆⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠰⠏⠀⠀⣼⠎⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢰⠉⠨⠆⠀⠀⡇⠈⠛⠁⡰⠋⠀⠀⣠⡒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢣⠀⢀⠞⠀⠀⠀⣼⣿⣿⣦⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⢂⠷⠃⠀⠀⠀⠀⠸⣿⣿⠟⠀⢀⠏⣠⠤⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣫⠟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⣀⠖⠀⠀⠀⠈⠉⠒⠉⠁⠀⢧⣀⠀⢀⡠⠃⠀⠀⠀⢀⠴⠒⠉⠉⠀⠀⠀⠘⠋⢁⣴⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⠴⠚⠁⣀⡤⢲⠖⠚⠁⣲⠶⣲⠖⠢⣤⢭⡤⣀⣀⣀⣀⡠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢧⣀⡠⢴⢞⠏⢠⠃⠀⠀⡼⣡⠞⠁⠀⡴⣱⠊⠀⠀⡴⠋⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡜⠀⡞⡎⠀⢰⠀⠀⣰⠁⣇⠀⣠⠞⠁⠣⣀⡤⠊⠀⠀⠀⠀⢠⠞⠁⢱⣄⡤⠔⠒⠤⣀⡠⠖⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⠃⢰⢹⠀⠀⠀⠉⠉⠁⠀⠈⢉⡠⠤⡤⣤⠤⣤⣀⣀⡀⠀⠀⢪⣀⠴⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢰⢁⠇⠀⡇⡟⠀⠙⡆⠀⠀⠀⡠⠖⢻⠀⠀⠀⠀⠀⠐⠶⠯⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡸⠀⢸⢸⠁⠀⢰⠃⠀⢠⠋⠀⣠⡼⠀⠀⠀⠀⠀⠀⢤⣒⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠈⡞⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⣶⠇⠀⢀⠏⠀⠀⣈⡒⠋⠀⣧⠤⠒⢢⡀⣀⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠹⡘⡄⠀⠀⠀⠀⠀⢧⠀⠀⠘⠁⠀⠛⠀⢀⠎⠀⠀⡎⠀⢹⠀⡼⠁⠀⠀⠀⠉⠉⠉⢳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡌⠀⠀⠀⠑⡝⡄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⢄⣀⡝⠁⠀⠀⠀⠰⣦⠤⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢠⠞⠙⠒⠲⠶⠒⠋⠳⣄⠀⠀⣤⣀⡀⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡀⠈⡱⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠷⠤⣄⣀⠀⣀⣀⡀⣀⡠⠔⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⣿⢿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡤⠠⠄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⢀⡀⠀⠀⣠⡙⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠀⠘⠒⠺⢿⣦⠭⣿⣟⠉⠉⠀⠀⠐⠒⠒⠀⠠⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⠀⠀⠀⠀⢀⠤⠲⠮⢹⢏⠻⣄⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠉⠙⠉⠉⠛⠀⠒⠦⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠒⢒⣠⣂⡀⠀⠈⠑⢄⣺⣯⡻⢽⣒⡳⣂⡀⢀⠐⣶⡐⠸⠂⡴⠃⠀⠀⠣⡀⠀⢆⠀⢀⡋⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡠⢲⠉⣰⡶⠋⠀⠀⡉⠛⠛⠒⢂⢸⣐⣻⠿⣿⡿⣿⣷⣮⣦⣤⣤⠐⢄⡹⢄⣒⠀⠀⡘⠀⢀⠇⠈⡅⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⣪⡾⢣⣾⣿⠀⠀⠀⢦⡤⠒⠛⠋⠁⠀⣠⠔⠂⠩⢋⠜⡟⣻⣟⣿⠃⣠⡾⠁⢀⣴⠟⢉⣹⠖⢙⣤⠀⠃⠀⣈⢳
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⡔⣵⠏⣠⣙⣿⠃⠀⠀⡆⠘⠀⠀⠀⢀⠔⢋⠄⠊⠡⢊⡔⠛⠁⣸⠻⠁⠀⠋⠀⠀⠃⠇⡐⠉⠁⡴⠛⢁⣠⠞⠒⠫⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠘⣼⠏⣼⣿⣿⠋⠀⠀⢀⡟⠶⡀⣠⠞⣡⠄⢀⠀⢀⠀⢀⠞⠀⣰⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡰⠖⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⢺⣿⡿⠃⠀⠀⠀⢸⠁⠀⡇⡏⢰⠁⠀⡇⢰⠃⠀⡇⡆⠀⡃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠠⠂⡟
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⣿⣿⣟⠁⠀⠀⠀⠀⢸⠀⠀⡇⠁⠘⠀⠀⣇⠈⡆⠀⢃⠹⡀⠱⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡤⣾⠃
⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⠏⠀⠑⢄⠀⠀⠀⢸⠀⠀⡇⢀⠀⡄⠀⠸⡄⢸⠀⠈⢆⠱⣄⠰⠌⡙⠲⠄⡤
⠀⠀⠀⠀⠀⣸⣻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠦⡀⢰⠀⠀⡆⠈⠀⢧⠀⠀⠱⡀⠣⡀⠀⠳⣈⠢⠀⠀⠙⠒
⠀⠀⠀⢀⣤⡟⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣀⣗⠀⡀⠸⡀⠀⠀⠱⡄⠱⡄⠀⠈⠂⢌⡁
⠀⠀⣰⣭⠖⢉⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⢻⡆⢱⠀⣇⠀⠀⠀⠘⢆⠈⠢⣄
⠀⠀⠻⠋⠀⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⡷⠈⠁⠛⠀⠀⠀⠀⠀⠙⠄⠈
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢮⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⢴⣶⣶⣤⡀⠀⠀⠀⢀⣤⣶⣾⣿⣶⡖⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣽⣿⣿⣿⣿⣿⣿⣿⣦⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⣿⣿⣿⢿⢻⣿⠙⠿⣿⣯⣴⣦⣿⣿⡿⠛⣯⣿⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢮⢷⡈⠀⠀⢸⣿⣿⣿⡇⠀⠀⠠⠋⣣⡟⣽⣿⣿⣿⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣏⣛⠶⠤⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠒⢋⣞⣱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣻⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣿⡇⠀⠀⠉⠛⢛⣩⣸⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣖⣬⡤⠹⢿⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⢿⡿⠁
⠀⠀⠀⣶⠀⡇⠀⢦⠔⢠⠀⠀⠠⠤⠀⠉⠻⢿⣿⣟⢻⣆⠀⢲⣶⣚⣷⣿⣿⣿⣿⣿⣿⣿⠿⠀⢀
⠀⠀⠀⢻⡀⠐⡀⢈⡠⠎⠀⠀⠀⠀⠀⠀⢤⣀⠈⠛⠨⠻⠷⠄⣰⡿⠻⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠘⠃⠀⠈⡁⣀⣠⣠⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⡾⢟⣓⠼⠟⠋⢁⡐⣄⠄⢠⠀⠄⠐⠒⢢⠴⠏
⠀⠀⠐⢄⣶⣾⢇⡟⠻⠿⠋⠘⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠐⡤⣠⠛⠛⠛⠐⡆⢒⠀⠚
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠙⠁⠈⠰⠾⠉⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣦⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣼⣩⣿⣿⣽⠿⠷⠎⠻⠟⢿⠿⣿⣿⢿⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⠿⣿⣿⣿⠞⢐⡆⠠⠖⢸⡇⡇⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣼⣶⣿⣿⣿⣿⢫⣸⣸⢇⣄⣠⣼⣇⣇⢠⢀⣀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⠁⢸⡏⠻⣿⡿⡿⠛⠛⢟⢿⣿⣟⣯⣥⣾⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠋⠉⡉⠀⠀⠀⠘⠇⠀⠸⣾⠀⠀⠀⠈⠆⢻⠿⡿⠛⢿⣇⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠐⠀⠉⠁⠌⠛⠂⠀⠀⠘⢎⠀⠈⠺⠿⢿⣿⠿⠟⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠳⢤⠀⠀⠀⠈⠉⠛⠂




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠤⣰⡠⣤⡤⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣠⠆⣤⢢⢠⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣏⡳⢫⣩⣤⣿⣃⢻⣤⣤⠷⣏⣷⣶⣄⡀⠀⠀⢀⣠⢔⡈⢿⣀⡹⣢⣉⣁⣤⣬⣬⡛⣾⠤⡦⢀
⠀⠀⠀⠀⠀⠀⡠⣯⣻⣥⣬⣛⢴⣟⡷⢲⣿⡧⠒⠄⣞⠙⡻⣣⣟⣫⠄⠰⣼⢗⣪⣿⣬⡶⠿⣤⣤⣿⠉⠉⠋⣹⢶⣫⣜⠚⣻⡄
⠀⠀⠀⠀⠀⡼⢻⣼⣿⠉⠩⢹⣎⣿⣿⣿⠟⣥⣾⡿⠛⣯⢑⣿⠛⢣⡴⡧⣟⣾⡇⣕⣸⣿⠞⣿⣬⣭⡷⢶⡾⢿⠸⣷⣾⠓⣶⠟⢣
⠀⠀⠀⠀⣴⣳⣱⣯⣿⣤⣴⡟⣨⣭⣬⡛⣓⣻⣿⣽⣴⣿⡻⣝⠃⠘⣾⡤⢤⠻⣧⣯⣴⠟⣿⣿⠻⢿⣿⡆⣳⣾⣿⣿⣦⡼⣟⢴⡞⡦
⠀⠀⠀⢐⠾⢹⣿⣃⣭⣶⡙⣾⠻⠛⠛⢻⡣⣾⡽⢿⣭⡛⣤⡏⠀⠰⡯⣀⣀⡟⣿⣽⣼⡟⣿⣿⣤⣉⡿⠣⣏⣛⣉⣉⣙⣇⡴⠶⢬⠛⡀
⠀⠀⠀⢀⡾⣏⢿⡟⣿⡷⡾⣼⠿⡿⣿⣋⠷⣟⣁⣀⢙⣷⢨⠅⠀⠀⢟⡿⣯⡑⣿⠁⢈⣿⣔⣹⠟⣿⣷⡩⣽⠿⣿⠿⣟⢹⣤⣤⣼⣷⠆
⠀⠀⠀⠈⣳⢋⡼⣽⣿⡆⡧⣿⡷⠗⣿⣿⣮⣻⣽⣿⠿⣃⣝⠀⠀⠀⢿⡃⣹⠇⠈⣻⠻⣥⣎⣽⣛⣛⠸⢶⣾⠃⢭⣮⣾⢳⣯⣭⠕⡛⠁
⠀⠀⠀⠀⠹⣤⣤⣤⣮⣳⣛⣛⡴⣯⡵⢎⣉⣿⣥⡶⢾⣵⠃⠀⣀⠀⢠⣟⡍⠀⠀⠸⣴⣏⢹⠗⠋⠉⠛⢲⠋⣁⣾⣷⣜⢏⣴⣿⣹⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣝⣿⣄⣻⢯⣦⡿⢣⠏
⠀⠀⠀⠀⠀⠀⠉⢿⢷⣏⣹⡞⡉⡞⢾⣛⢻⡛⢻⣼⠓⣄⠀⣸⢿⡇⠀⠾⠀⠀⡏⢺⡟⢯⣭⣷⣀⠄⠄⠾⢿⣾⠋⠑⣿⢻⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⣽⣿⣭⣷⠛⢘⣵⡿⠧⣟⢴⣿⡤⡟⡧⠇⠀⠐⠀⢠⣐⡬⢷⢿⠷⠾⡿⣴⠞⠓⣿⣿⢲⣶⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣤⣼⣉⢻⡟⠻⠛⣿⣹⣥⣷⡴⠶⢦⠀⠀⠀⣾⢏⡳⣽⠤⣤⠤⣤⢷⣿⣵⡬⣼⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢴⠷⡟⣟⣛⡟⠇⣈⣿⣄⣀⣸⠀⠀⢀⣥⢾⡻⣏⣠⣴⣶⢦⡶⠦⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣿⠉⢹⣦⡁⢴⣟⣭⠾⠃⠀⣸⢿⣾⢷⣾⡟⣵⠛⡯⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣯⣿⢎⣉⣷⣞⣇⠀⣃⡠⢤⠾⣒⡍⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢹⠥⣥⢽⢸⠏⢸⡯⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠔⠒⣒⣒⣒⡠⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡤⠖⠛⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠭⢝⡒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡞⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡔⠉⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⠒⠲⠤⢄⡈⠙⠢⣍⡓⠦⢄⡀⠀⠀⠀⠀⠀⡏⠀⠘⠝⡆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠏⠀⠀⠀⠀⠀⣠⠔⠉⢀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠓⣤⠤⠭⢶⣤⣉⠑⠲⢤⣀⡀⠈⠀⠀⠀⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡎⠀⠀⠀⠀⢀⠔⠁⢀⡔⣍⣶⣦⠈⠳⡄⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠙⢏⠒⠦⠤⣬⣭⡭⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⢀⡴⠋⠀⠀⢸⡅⢿⣿⡿⠃⠀⡇⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣱⣀⠴⠋⠀⠀⠀⠀⠀⠳⣄⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡞⠙⢆
⠀⠀⠀⠀⢠⣤⡤⠤⠶⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⠤⠤⠤⠴⠶⠒⠚⣭⡛⠁⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢉⠟⠉⠉⡇⠀⠀⠀⠀⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⢔⡾⠓⢶⡒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡱⢋⡤⢴⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⡡⠖⠛⠺⡝⠲⠤⢄⣀⡀⠀⠀⠀⣀⡤⠞⢩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢖⡶⠲⡖⠃⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⢄⣀⡀⣰⠋⢹⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⠳⣄⠀⠀⠀⠀⠈⠙⠒⡲⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⣠⠴⠚⠉⠉⢳⡄⠀⠀⠈⠳⢤⣀⣀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⠜⠁⠈⠳⢤⠤⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣰⠃⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⡇⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠖⠒⠒⢤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠉⠒⠠⢀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠨⢢⡀
⠀⠀⠀⠀⣴⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠈⢿⣿⣿⣿⡿⠿⢿⣷⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⢸⣿⣧⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⢿⣿⣏⢻⠹⣿⣿⢣⠃⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠘⣿⢿⣎⢧⡹⠁⠀⢈⡀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠛⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠸⡇⠻⣦⠳⡄⠈⣼⢿⡀⠀⠀⠑⠢⠤⢤⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣨⡗⠒⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠘⣗⠙⠳⡾⡀⠉⣳⣤⣀⣀⠀⠀⠙⠄⠀⠀⠀⠠⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⢁⠰⡇⡉⠀⠀⠈⠩⠩⠽⠟⠛⠚⠿⠶⢭⣄⢀⡠⠤⠤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠾⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⣾⠆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠐⠒⠖⠒⠒⠒⠒⠐⠂⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡑⠩⡖⢀⠉⠛⢶⣄
⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣁⣷⣆⣀⠉⠳⣄
⠀⢰⡇⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄⠈⢷⡀
⠀⣿⡇⠀⣿⡇⠀⠀⠀⠢⡀⠹⣄⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⣶⡿⠦⡀
⢸⣿⠆⢠⡟⡇⠀⠀⠀⠀⠈⠢⡈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠘⡆
⢸⠇⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠢⣗⢤⣀⣀⣀⠀⠀⠀⠀⢘⣿⣇⣀⣠⢗⢰⡆
⣾⠀⠁⣿⣆⠄⠀⠀⠀⠀⠀⠀⣠⠔⢿⡌⠻⣕⠚⠻⠶⣤⡀⣼⡿⠋⠉⢡⠟⡄⠹⡄
⣿⡆⠘⠿⣿⡀⠀⠀⠀⠀⠀⢰⡥⠊⢹⢿⡄⠹⣷⠦⣄⠀⢉⣿⣿⡀⢠⡿⠀⣷⢀⡇
⣿⡇⠀⠀⢲⠁⠀⠀⠀⠀⢠⠏⠀⠀⣼⣼⣧⠀⠈⢳⣌⠑⢼⣿⠉⠙⠿⣾⡀⠛⡀⣷
⢿⣷⠀⠀⣺⠀⠀⠀⠀⢠⡿⠁⠀⠀⣿⡟⢻⡆⠀⠀⠙⡆⢫⣻⢧⡔⠀⣿⠙⢿⣥⣿
⠸⣿⣦⣤⣋⠀⡀⠀⢀⡾⠁⠀⠀⠀⢇⢿⡈⠻⣄⣠⡴⢃⡞⣸⢳⡈⠲⡃⢠⡟⢬⡟⠲⢤⣀⠀⣀⢤⣤⡤
⠀⠹⣿⡿⠋⠛⠙⢦⣜⣦⣄⣠⣄⣀⣈⣮⡻⣦⣤⣤⡶⣋⡴⠁⠀⡇⠀⠹⡟⡠⣸⢡⡾⠒⠛⠙⠛⠤⠄
⠀⠀⠈⠳⢦⣤⣤⣾⡯⠉⠀⠀⢀⡤⣹⣿⣿⣶⣶⣶⣿⣿⣇⠀⠀⢻⣀⠀⢸⡿⣣⡿⠁
⠀⠀⠀⠀⠀⠀⣽⠛⢿⣿⠿⢻⣟⣛⡿⣯⣿⣧⠀⠙⢿⣯⣻⣦⣀⣈⣿⣷⣾⣷⡟⠁
⠀⠀⠀⠀⢀⡾⠁⠀⠉⡠⠖⣾⠃⠉⠻⢷⠮⣿⣷⡀⠀⠻⣷⣿⣿⣿⣿⣿⣿⣫
⠀⠀⠀⢠⠞⠀⠠⡶⠋⠀⢠⠏⠀⠀⠀⠀⢈⣈⣩⣿⣷⣤⣿⣿⣿⠟⠙⠋⣉⣉⡆
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠚⠿⠟⠛⠛⠛⠛⠋⠻⣿⣽⢧⡴⠋⣠⠔⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠉⣠⠄⠈⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⢂⡠⠄⠈⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⡠⠄⠚⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠂⠉⢋⣷⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣯⣤⣶⣏⠙⢻⣷⣭⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⣿⡏⠁⠀⣿⠀⣳⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠈⣿⠹⣿⠂⠀⢀⣾⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣁⣠⣼⡦⠾⠙⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣝⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠒⠲⠤⢄⣉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡈⠉⠲⢌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠞⡿⠉⢻⡉⠉⠉⢙⡛⠳⢦⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡋⠋⠀⣧⠀⠀⠀⢸⡇⠀⠀⠿⠇⠀⠀⠈⣹⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⠉⠀⠀⠀⢻⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠹⣦⡀⠀⠀⠀⠻⣆⢀⣀⣜⣧⣀⢀⣤⣄⣶⣤⡶⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡈⠀⠀⠈⠻⢦⣄⢀⣠⣽⢿⡻⡍⠉⠉⠛⢻⣯⢹⡇⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⠀⠀⠀⠀⠀⣽⣿⣍⠺⢷⡙⢿⠀⠀⠀⠀⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⣤⣤⣤⣤⣼⠇⠈⠙⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢆⠀⠀⢠⡸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡠⠀⠀⣠⡿⢦⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣼⡋⠀⠀⢀⣌⣈⣉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢰⣤⡍⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⡏⠛⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣄⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠁⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡠⠋⡌⢠⡄⢀⠄⠓⠬⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⡺⠁⠀⡁⠻⠅⠨⡢⡀⠀⣀⠑⡄⠀⠀⠀⠀⣠⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡐⠁⠀⠀⠃⠀⠀⠀⠁⠑⠢⠀⠀⠁⠀⠀⠁⠐⠁⠀⠂⠀⠀⠎⡆⠀⢀⢠⠠⢄⣀⡀⡄
⠀⠀⠀⠐⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠴⠒⠚⡛⡆⠀⠉
⠀⠀⢠⠀⡠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠙⢑⢐
⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡠⠒⢉⠭
⠀⠀⢀⠀⡀⢰⡄⠀⠐⠏⠉⠁⠄⠀⠀⠀⠀⠀⠀⠐⢄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣇⡠⠂
⢀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠁⠁
⠘⠀⡂⠀⠀⠾⢄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠲⠤⠴⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⡀⠀⠀⠀⢹⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣠⠴⣚⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠊⠕⠋⠀⠈⠙⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⣴⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⣿⣇⠀⢿⠀⠈⣧⣤⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠻⣿⡄⠈⢻⣄⣿⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢀⠀⠘⢷⡀⠀⠉⠉⢀⡀⠤⠐⠃⠤⠤⣀⠀⠀⠀⠀⠀⣴⣿⣷⣦⡠
⠀⢀⣶⠿⣷⣄⠀⠀⣠⠈⠛⠛⠛⣷⠀⠈⠁⢀⡠⠚⠁⠀⣴⡾⣿⢷⡄⠰⣕⢄⠀⠀⢠⢸⣿⣿⣿⡿
⣰⣿⡁⠀⠀⣹⢇⡼⣷⡀⠀⠰⣾⠇⠀⡤⠒⠁⠀⠀⠀⠀⢿⣦⣿⣾⡟⠀⠘⣿⣧⡤⡾⢃⠙⠛⠛⠱⡀
⠈⢿⣷⣤⡿⠋⠈⠀⠘⢷⡜⠀⠀⠀⠀⠁⠠⠀⡀⠀⠀⠀⣈⣹⣿⠉⠀⡆⠀⣿⣿⣌⠛⠈⡀⢶⠗⣾⣧
⠀⠀⠻⣿⣇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠀⠀⠀⢠⣿⣷⡳⠷⣀⡠⠲⣤⣰⠈
⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠒⡄⠀⠀⠀⠀⣴⠿⡟⠁⠉⣿⠿⢟⡳⣭⠄
⠀⠀⠀⠀⠀⠙⠀⣠⡤⠀⠀⣄⣀⠀⠀⠘⠉⠁⠉⣻⠦⠊⠀⠀⠀⢀⣄⠰⡿⠿⠿⡶⣿⣀⡼⢻⡎
⠀⠀⠀⠀⠀⠀⣾⢣⡾⢋⠙⠓⢾⣍⡙⡏⠙⢏⠉⠁⠒⡄⠀⠀⢀⣼⣿⡷⡗⠁⠀⠉⠛⠿⣶⣎
⠀⠀⠀⠀⠀⠸⡏⢰⣷⣾⢀⣴⠆⠉⠛⠷⣶⣾⣤⣤⣤⣤⣼⣾⡿⣟⠿⠊⠀⠀⠀⣀⢴⡟⠋⠹⣦
⠀⠀⠀⠀⠀⠀⢷⣰⣬⣟⣻⠏⠀⠀⠀⠀⠀⠈⠉⠒⠛⠛⠙⠂⠈⠁⠀⢀⣄⠀⠀⣿⣆⠻⣶⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡏⣤⣤⣶⣤⡄⠀⠀⢀⣀⣤⣤⣤⣀⢀⣤⣾⠉⢻⣷⣤⣿⢻⡄⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠛⢹⡇⠀⢸⡟⡏⠀⢸⡏⠈⠘⣿⠀⠀⢻⡄⠙⠀⢷⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠷⣶⡌⣿⣾⢿⡇⣿⣾⣿⡃⠀⠀⣸⡴⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣿⡇⣯⠀⠀⡇⢸⡇⠉⠙⠛⠈⠋

⠀⠀⠀⠀⡀⠀⡀⢀⢀⠀⣀⡀⣀⢀⣀⡀⡀⣀⢀⣀⣀⡀⣀⣀⢀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⡀⣀⣀⣀⣀⢀⡀⢀⣀⣀⡀⣀⢀⣀⣀⢀⡀
⠀⠀⠀⠀⡿⠻⢿⠿⣎⣢⡿⠥⡿⠯⠀⠏⡧⢸⡿⠋⠈⢹⡴⢟⣩⣦⣝⢺⠔⣫⣿⣍⣭⠨⠍⣿⠃⣻⢏⢽⠤⣻⣬⢖⣿⡿⠿⠿⣷⡟⠓⢻⣴⣁
⠀⠀⠀⠈⣇⣀⣀⣴⡿⢉⣷⠏⠛⢷⣼⠃⣓⣸⣄⣀⣴⡿⣓⣾⠃⢀⣤⣯⣾⡟⠿⢺⣿⡉⠇⠾⣉⡥⣨⢻⠟⠉⠙⣆⣷⣶⣶⣶⣏⣟⡹⣁⠘⠅
⠀⠀⠀⢀⡽⣟⢻⣋⡜⢸⣧⣤⣤⣤⡿⢹⠋⠉⣭⡽⢽⢦⠷⢾⠾⠿⢿⡉⢿⣿⣀⣿⣿⡿⠚⠻⡯⣠⣗⣞⢷⣖⡶⠏⢢⡍⡉⣼⣋⠀⢸⡏⢫⠄
⠀⠀⠀⠀⡻⠏⠾⣡⡵⢧⣹⠿⣿⣞⠳⣮⣟⣟⡥⡎⠼⠸⠖⣏⡧⣉⣩⡋⢄⣝⡻⢫⣤⡿⣿⡿⠃⠴⢯⡹⣧⣏⣳⣿⣻⣻⣮⣜⡶⡶⢞⢻⣫⡗
⠀⠀⠀⠈⣷⢾⣻⡏⠀⣸⡇⣼⡯⣁⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢿⡞⢲⡇⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡁⣉⢉⡿⢜⣣⣶⣜⢣⠶⣇
⠀⠀⠀⠀⠭⡹⣯⣛⣾⢛⣩⣬⣧⢼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⡭⢗⣎⠀⠉⣩⣟⣛⡇
⠀⠀⠀⠀⣶⠰⣅⣤⣇⣼⠁⠒⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣼⢏⣛⠛⣯⢽⣹⡇
⠀⠀⠀⢀⣾⠛⣢⢠⡖⢪⡓⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠯⣷⡏⣻⢹⡖⢢⠻⠆
⠀⠀⠀⠀⡷⡿⢻⣘⡴⢿⡉⠳⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣹⣏⣿⣸⣃⡎⣱⣅
⠀⠀⠀⠀⢷⢩⣟⣉⣵⣤⣿⠝⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣬⡆⣧⣀⣯⣽⡘⠁
⠀⠀⠀⠐⣏⢹⡿⠔⣛⣜⢯⣾⣿⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⢩⣹⣿⡇⢸⣿⣎⠕⡃
⠀⠀⠀⠀⣿⣶⣶⣾⡅⢨⣷⡯⢪⣀⡸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⢈⡇⢻⣿⠀⠀⣿⣟⣠⡄
⠀⠀⠀⠠⡟⢻⠜⡟⠃⠘⢻⠷⠖⢧⡞⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢿⢻⣡⡚⢙⡟⣳⣞⣻⡼⢇⠏
⠀⠀⠀⠀⣿⠁⣎⣙⣉⡭⢥⣷⡢⣿⠇⠸⣿⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣟⠻⢯⣿⣭⣽⣋⣿⣗⣬⣽⢤⠹⡆
⠀⠀⠀⢀⡾⠿⢿⢻⣿⠙⠙⢻⣷⢾⠒⠖⠺⣒⠀⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠇⠻⠟⠾⠿⠿⠿⣿⣿⣿⣟⣡⣾⣻⡟
⠀⠀⠀⠀⢳⣤⢞⣎⡻⣄⣀⣼⢋⣼⣏⠈⣹⣦⠷⣾⠋⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠆⠠⠦⣞⣥⣶⣷⣤⠀⠀⣠⣿⣴⣿⣿⣅⣿⡗
⠀⠀⠀⠀⡿⠹⡏⣰⣿⣿⣷⣮⣹⣿⡯⡀⢿⣿⡏⣧⣴⣾⢿⡗⣶⠀⠀⠀⠀⠀⠀⢀⣀⣰⣏⠁⢈⡏⢭⢹⡈⢉⡯⣽⣻⢻⡏⢿⡏⠁⢉⡿⢹⡇
⠀⠀⠀⠀⣩⣯⣰⣿⡇⠙⣻⣿⡏⡳⣤⣤⡤⢊⣽⢷⣤⡈⣨⢁⣿⣾⣷⣆⠀⠀⣰⡟⣁⠈⣿⠗⢩⣾⢻⠛⣿⡽⢺⣿⣻⣿⣓⢮⣳⢶⣞⡵⣿⡗
⠀⠀⠀⠐⢇⣡⢯⡻⣧⣶⣤⠿⡿⠉⠻⣾⠃⣿⣟⠂⣭⣹⠁⡌⢧⣶⣶⣜⠁⡙⡌⣳⠶⠿⠛⠓⢿⡟⢸⠶⣻⣿⣿⣇⠴⣀⣨⣾⡿⠯⠇⡾⠯⡧
⠀⠀⠀⢀⣶⠁⣾⣴⠗⣖⣲⣏⣿⣿⡷⢛⣦⡹⢿⣿⡿⣏⠞⠛⣢⢨⣥⡾⡘⢷⠋⠉⢱⢰⡏⢹⡎⡻⣾⠶⣿⣇⢻⣿⠰⠇⣿⡿⢃⠚⢛⡼⢿⡇
⠀⠀⠀⠈⠋⣤⡙⢧⠉⣿⡏⡇⣿⣧⣩⣿⡤⡘⠂⣷⣶⣧⡙⣻⣯⣸⢫⣾⠿⣾⡷⠶⢊⣶⣕⣿⣬⣅⢭⣚⠃⣹⣟⢩⡟⣻⡍⠷⣦⡿⣏⢴⠿⡦
⠀⠀⠀⠀⣶⣖⡿⣟⣻⣿⣧⣯⡼⣿⣗⣾⢿⣮⣤⢧⣀⣠⣻⣷⣺⠇⠺⣇⣀⡸⣯⣵⣏⣉⠿⣷⣼⡟⢾⣤⠗⣿⣦⢇⡼⢧⣴⠟⣇⢀⡽⡘⠋⡇

⠀⠀⣀⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⡟⢻⣏⣿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡀⠀⡠
⢀⣾⣿⣿⣿⣿⣿⢁⣫⣿⣿⢿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⡧⠊
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⣾⣁⡠⠔⠒⠀⠁⠀⠀⠀⠠⠄
⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣋⡟⠉
⣿⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣻⣿⣭⣿⣿⣿⣿⡇⠻⣿⣿⡇⠀⠀⠀⢀⣠⣤⣴⣿⣿⡟⠳⣦⣀⣠⡖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡿⣿⣏⣿⣿⣿⣿⣿⣦⢻⣿⣿⣇⡤⠔⠚⠉⣿⣿⣿⣿⣿⣿⣄⣠⣱⠞⠁
⣿⡿⣿⣿⣿⣿⣟⣇⣴⣿⣿⣯⣴⣿⣿⣿⣿⣽⣿⣿⣿⡿⠛⢉⣴⠶⣦⡀⠀⠙⡿⣿⣿⣿⡿⠉⠉⠁⠀⣠⠤⡀
⣿⣿⣿⣿⣾⣿⡻⣿⣿⡛⣿⣿⣾⣿⣿⣿⡟⢻⣿⡟⡵⠂⢀⣾⣆⠟⣸⡇⠀⣸⠁⢨⣿⣿⠃⠀⠀⠀⠸⡇⠑⣘⡄
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⠑⠀⠙⢺⣿⠛⠉⠀⢀⡷⠶⠿⠛⠁⠀⠀⠀⠀⠀⠡⠀⠈
⠀⠙⢿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡾⠓⠛⠓⠲⠶⠦⢤⣤⣄⣀⣀⣆⠄
⠀⣀⡤⠿⠛⢿⡿⠋⠉⠙⠛⠛⠛⢫⡏⠀⠀⠀⠀⠀⠀⠀⣠⠙⠁⣠⣴⠿⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀⣠⠭⠭⡿⡖⠂
⡟⠁⠀⠀⠀⢾⠃⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣴⠋⡰⠋⡉⠉⠉⠙⠓⠒⠶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠹⡔⡀
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠘⠃⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⡙⠲⡄⠀⠱⣴
⡔⠒⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⣸⠀⠀⢠⠀⢀⡀⢠⣑⠒⢽⠶⣀⣒⠒⠠⠔⠒⠒⠒⠉⠉⠉⠀⠀⠉⠙⠋
⣇⠀⠀⠀⠀⢀⣰⠋⣀⡀⢰⡒⣒⣚⡒⠲⠾⣆⠢⢭⣀⢰⠚⠉⠀⠐⠩⡉⢰
⠈⠀⢸⢿⡋⠉⠉⠕⢄⠀⠉⠉⠉⠙⠢⠌⢳⣿⠚⠉⠁⢸⠀⠀⠀⠀⠀⢡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠑⢍⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⠀⠈⡟⠀⠀⢸⣸⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⢀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣅⠀⠼⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣷⣷⣦⠤⣀⡀
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⠋⡏⠀⠀⠐⠀⠁⠠⣄⡀
⠀⠀⠀⠠⠚⠁⢠⠼⠴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢆
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⣀⡀⠀⠰⣾⠿⠠⣀⢀⣤⡾⠁
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡄⠀⣿⠃⠀⠀⠀⠀⠀⠀⠉⠞⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣽⣼⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⢠⣦⣿⡟⠁
⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⡇⢠⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⢺⣿⣶⣄⡀⠀⠀⢠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣶⠤⠄⠂⠀⣀⣠⡴⠞⠛⠁⠀⠹⣿⣿⡗⠙⠻⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠣⠀⡀
⠀⠀⠀⠀⠀⢿⡿⣏⣹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣄⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⣠⣶⣤⣼⡷
⠀⠀⠀⠀⠀⠈⠿⣬⡻⠗⠘⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠙⠂⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠶⢶⣦⡀⢀⠀⢐⢋⠀⢙⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠊⠻⣭⣯⡌⡓⠦⡀⢉⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡇⠸⢤⣊⣴⡿⡏⡙⣩⠉⢟⡀⠀⠀⠀⠀⣠⣴⣤⢀⠾⣿⣿⡿⢀⣧⢈⠀⣈⡡⡀⠐
⠀⠀⠀⢀⠄⠀⠀⠈⡀⣒⠚⠁⢸⠀⠈⠛⢷⡡⠀⢹⠆⡼⣽⠀⠀⣠⠄⢫⡙⡫⢽⡿⣭⣧⣷⡟⡇⠀⣴⢍⣷⣷⠲⣦
⠀⠀⠀⣄⣀⠀⠀⣀⢀⠁⣠⣄⠀⠐⠀⠀⡸⠡⢄⡰⠔⢄⣿⠄⠀⡗⠲⡋⠂⡀⣈⣠⠖⢛⣞⠑⠀⠂⠁⣸⡏⠙⠃⠸⣦
⠀⠀⠀⢬⣀⠀⠀⠀⠈⡷⠠⠞⣀⢀⠀⠙⠳⣤⣼⣇⣠⠊⡸⠀⠀⢉⣉⣉⡩⢓⣿⠃⠐⠉⠀⠀⠀⡄⢺⡿⠁⠀⠀⣜⡏⠠⡀
⠀⠀⢀⣤⣭⡙⠳⣖⣺⠉⠒⠁⠑⠤⠤⠚⠀⠀⠉⠋⠥⠕⠃⠀⠃⢸⣿⡯⠀⢋⣤⠀⠀⠀⠀⠀⠰⢯⣧⠀⠀⣀⡘⠛⠡
⠀⣀⣞⢁⣼⣷⡀⠀⠀⠀⣀⡄⢠⡠⠴⠶⠆⠉⠀⠠⢆⣤⡀⠀⢀⡀⢀⡄⢠⠀⠀⠈⣳⡄⠀⠠⢤⣘⠀⠄⠞⠉⠉⠀⢰⡄
⠸⣧⣸⣿⣿⠛⠻⣄⠀⠀⢁⡈⠀⢀⡄⠒⠒⢄⠀⢰⣋⢈⡗⠀⢤⠉⠉⠀⠀⠀⠀⠈⢉⠇⣀⡔⡫⢲⡴
⠀⠈⠉⠛⠻⢦⡀⠈⠑⠲⢿⣿⣆⢸⣆⣈⣴⡾⠄⠀⠉⠉⠀⠀⠈⠢⣀⡀⠀⡀⣀⣀⠀⠀⠙⠐⠒⠋⠀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢿⣶⡀⠀⠀⠈⠙⠣⢙⠛⠛⠁⠀⠀⠀⠐⠲⢤⡄⠀⠀⠉⠉⢉⣉⠤⣐⣊⣁⠀⣐⠒⠦⠀⠀⠀⠊⡁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠑⢤⡀⠀⢈⠐⣢⠀⠀⠳⠀⡠⠒⢐⡥⠐⠉⠁⣀⣠⣀⣤⣹⠇⠀⢺⠋⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣆⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠻⠁⠀⠂⠀⠀⠀⣹⠷⢶⣮⠛⠃⠀⠉⡨⠋⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣀⠀⠀⢀⣄⢸⠁⠀⠀⠹⣦⣀⠔⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⡷⢎⠣⡀⢸⠀⠳⣆⠀⠀⠀⢸⡇⢀⠔⠩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣀⠀⠀⠀⠀⠀⠀⢿⡞⠀⠙⣎⢡⡴⠽⣇⠀⠀⢸⡇⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⡦⠈⠀⡀⢀⣸⡄⠁⠒⠛⠂⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣠⠀⠀⠉⠒⠌⠳⡀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⣆⣀⣤⡀⡀⢻⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠷⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⢿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣃⣀⣀⡀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⢿⣶⣦⣤⣀⣿⡿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣏⡉⠉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⣴⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⡄⠀⠀⠈⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⡷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⣿⣷⡀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠁⠀⠀⢠⣾⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡿⠟⠋⠀⠀⠀⠀⣰⣿⠏⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣇⠀⠉⠙⠛⠿⠿⠿⣷⣶⣶⣶⣾⡿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⣠⣾⠟⠁⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠙⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢰⣿⡿⠈⠙⠳⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠛⠉⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣴⣿⡟
⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣬⣿⣷⣾⡿⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⢠⣿⠟⠉⠙⠛⠿⣷⣄⠀⠀⢀⣴⠟⠉⠀⠀⠀⣉⣿⣿⠟⠁⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠈⠻⣷⡄⢼⠇⠀⢀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣘⣷⣼⠶⠾⠟⠋⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⠟⠁
⠀⠀⣤⣿⠷⣤⣀⡀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⠟⠁
⢠⣾⠏⠀⠀⠈⠙⠛⠻⠟⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋
⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠿⠛⠁
⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠉⠙⠛⠳⠶⢶⣶⣶⣮⣿⣿⣷⣦⣤⣤⣤⣤⣶⣶⣶⣿⠿⠟⠛⠉
⠈⠻⣷⣤⣀⣀⣀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣴⠋⠉⠈⢻⡇⠈⠁⠈⡶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠛⠳⢤⡈⢳⡀⠀⠀⣗⠀⠀⡼⠁⠈⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣷⠀⢹⡄⣠⠯⠶⠾⣤⠴⠖⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⣠⠏⠀⣿⢀⣼⢹⠁⠜⠀⠀⠸⣤⣤⣤⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠀⣤⡄⠠⠔⠋⠁⢀⣠⠟⢻⠆⠉⠀⠀⠀⠀⢠⣃⣀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠉⠁⠀⢀⣠⢚⡟⠀⠀⠈⠀⠀⠀⠀⠀⢠⣏⠉⢙⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⡀⢤⢰⡶⠋⠉⡹⠓⠁⡇⠀⠀⠀⠀⢀⣠⠴⢊⡭⢿⠷⠊
⠀⠀⠀⠀⠀⠀⠀⡀⠠⡐⢖⣫⠵⡫⠔⠁⠀⡁⢡⡇⠀⢸⠁⠀⢰⠇⠀⢀⡤⠞⣉⠤⠊⢁⡴⠋
⠀⠀⣠⠤⠖⠒⠉⠀⠀⠒⠛⠁⠁⠀⡠⠊⠊⠀⡾⠀⠀⣿⠀⠀⠞⠀⢠⡏⢀⡚⠁⡠⠖⠁
⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⡼⠁⠀⢰⠇⠀⠀⠀⠀⠀⠈⠀⠈⠞⠁
⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉
⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠄⠀⠀⡘⠁⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⣆⣶⣋⣵⣰⣶⣦⣼⡀⣄⠀⠀⠀⠀⠀⢠⠀⠸⠀⠰⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣧⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠘⠀⠁⠀⡵⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢀⠀⠠⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢠⣿⡿⠿⣿⣿⣿⣿⣆⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣯⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠁⠀⠀⠀⠈⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣿⢿⡿⣿⣿⣿⣿⣿⢹⣿⣿⠿⠧
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠿⢿⠛⡿⣿⣿⠿⠒⣄⠀⡀⢰⠃⡘⠃⠀⠀⠰⠆⠂⢀⠀⠀⠀⠀⠀⠐⠈⠛⠄⢈⠁⠏⣿⡿⠁⠻⠘⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠦⡠⢤⠐⠏⠛⢤⡀⠋⠈⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠐⣂⣦⠀⠀⠶⣤⡀
⠀⠀⠀⠀⠀⠤⡀⠀⠙⠒⠓⠀⠀⠈⢀⠃⠀⣀⢠⣤⡀⠘⣇⠀⠀⠀⠀⠀⠀⢀⠀⠰⡇⠒⠛⠉⢉⠇⠀⢦⢿⡇
⠀⠀⠀⠀⠬⠕⠀⠀⡠⢰⠇⠀⢠⡤⠀⣴⠁⠁⠞⠁⡴⢳⠀⡀⠂⢠⡄⠀⠤⠟⠀⠀⠀⠀⠠⠴⠋⠠⡄⠈⡉⠋⠀⠂
⠀⠀⠀⠀⠀⠀⡠⢊⠔⡁⢀⠔⠁⠀⠀⡌⠂⠀⠀⠀⠀⡸⢳⣷⡆⠀⠀⠂⠀⠀⢀⠀⠀⠰⢶⣯⣍⡓⢀⠀⠀⠁⠀⠀⠠⡀
⠀⠀⠀⢉⡆⠀⠁⠀⠀⠐⠀⢠⠈⢈⣶⠈⠒⠤⠄⠒⠚⣁⣘⣷⡿⠥⣦⠀⢀⠂⠸⠀⢀⢦⣠⣿⢿⣧⡾⠀⢀⣤⠀⢀⠀⢣⡄
⠀⠀⠀⠀⠠⠀⠂⣀⣀⣬⠢⡈⠳⠿⠋⠀⠀⣄⢶⠀⢀⠁⠈⢳⣿⡳⠀⢀⡠⠆⡀⢠⣈⠆⠂⢋⡝⣳⠅⠀⠀⠿⣶⠟⣀⠀⠁
⠀⠀⠀⢀⢳⡼⠁⠀⢈⣧⡀⠨⠀⠐⠲⠤⣤⡟⠀⠀⢜⠉⡆⠀⠙⢂⠐⠈⠀⡀⠃⠸⠉⢂⣐⡿⢀⢡⢠⢰⠀⠀⠀⣊⠆
⠀⢀⡗⠈⠋⠀⢀⣠⣎⠈⠛⣄⠀⠁⠀⢠⠀⢀⢦⡤⠈⠉⠀⡔⠀⡄⠀⠀⠀⢸⠀⠂⢻⠿⠈⠤⠀⠀⠌⠈⠀⠐⣲⠃⠀⡀
⠀⠀⢷⡀⠀⠈⠁⠀⠠⢅⡀⠸⠦⠀⠄⠘⠱⡼⠎⠀⣤⠀⠀⠈⠀⡗⠀⠀⢲⠋⠀⢀⣀⡀⠀⠀⠲⠞⠁⢠⠀⠊⡵⣠⠿⠇
⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠈⢆⠀⠊⠐⠦⣄⠀⠀⠀⠀⠀⠂⠀⠀⠱⠀⠖⠡⠀⣰⠛⠤⡈⠟⢦⠀⠄⠴⠚⠀⠀⢿⠗⠂
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡘⠘⡄⠀⠀⠇⠀⠀⡴⠋⢻⡆⠀⠐⠄⠀⠀⣄⠵⠯⢥⡄⢀⡎⢛⢁⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠐⠠⢀⠠⠞⢁⠀⠀⠀⠀⢀⡄⠀⠐⠤⠾⠃⠀⠀⠀⠀⢠⠀⠆⠀⠀⠤⠬⠿⠃⠚⠀⠢⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠞⢠⡝⠀⠀⠤⠒⠾⣆⣀⠤⠤⠔⠁⣴⡒⠂⠠⣄⠀⢾⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠢⢄⠀⠠⢶⣾⣿⡿⠿⣎⠇⠀⠀⠈⠉⠱⠀⠀⠟⠆⢸⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠈⠉⠈⠀⠘⠻⢷⣏⡁⡇⢠⠠⠀⢤⡔⠚⠃⢀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠒⠂⢽⡟⠀⠀⠀⡌⠢⠀⢀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣠⠃⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣤⠶⢋⡀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⠌⠉

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢴⡆
⠀⠀⠀⢰⣦⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠒⠈⠉⠉⠉⠉⠓⠲⢄
⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡞⠿⠀⠀⠑⠒⠀⠐⠒⠂⠉⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⠤⠤⢀⣀⢳
⠀⠀⠀⠈⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⣀⣀⣀⣀⣀⠠⠤⠄⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⡀
⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⡤⠄⢀⣠⠞⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣥⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⡿⢿⣿⡇⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⢸⠏⡇⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠞⠀⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⣄⡄⠀⠀⡀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠤⠁⠀⠠⠁⠀⠀⣤⠀⠈⠃⠀⠀⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠠⠀⠀⠃⠒⠀⠀⠀⠀⠀⢠⡽⠂⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢧
⠀⠀⠀⠀⠀⣴⠀⠀⠀⢰⡅⠀⠀⠈⠀⠀⠁⠀⠀⠠⠀⣠⣇⡀⠠⠀⠀⣴⠀⠀⠁⢘⡇⠀⠀⢀⡀
⠀⠀⠀⢧⣀⡄⢠⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⢀⣀⠄⠀⠀⠀⠀⠀⠘⢨⣿⠀⠀⢸⡉
⠀⠀⠀⠙⠛⡙⢿⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⢘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠄⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠎⠇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⡼⡀⠀⢈⠁⣠⠀⠀⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢃⣠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠫⠄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡠
⠀⠀⠀⠀⠀⠀⠈⠉⠈⠓⠀⠀⠀⠀⠀⠀⠀⡠⣠⡇⠡⠀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⡀⠄⠀⠀⠀⠀⠀⠛⡏⢛⠀⠄⠁⡞⠃⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⠁⠀⣀⠁⠀⠸⢆⠀⠀⠀⠀⠀⣀⢹⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣄⠐⠔⠇⠀⣀⠀⢀⠘⡄⠀⠀⠀⠀⠘⠃⠠⡠⠠⢀⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠙⠰⠀⠁⠀⠈⠶⣌⢣⡱⡀⠀⠀⠀⠑⠂⠀⠳⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⢶⣤⠈⠉⠛⢧⠀⠀⠀⠀⠀⠀⠀⠈⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡧⠂⠓⠂⠙⠟⠂⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣼⠑⠛⡟⡤⠴⣉⣒⣾⣽⣖⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡆⢼⢻⢛⣭⣌⣹⠆⠵⠈⣳⠶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢏⣯⠤⠝⠒⠙⠈⠁⠉⠉⠉⠛⠠⠜⣴⠮⣓⣂⡀⠀⠀⠀⠀⠠⠞⠿⠆⣹⠄⠛⠋⠉⠁⠀⠉⠁⠓⠲⠶⠣⢩⡠
⠀⠀⠀⠀⠀⢠⠾⣌⢻⠛⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠈⠻⣏⡑⢋⣀⠀⠀⢎⣡⢋⠙⠊⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠙⢶⡥⢨
⠀⠀⠀⠀⠀⢹⡶⣦⠁⠀⠀⣠⠖⢯⠞⣽⠸⣍⢷⣾⢳⡦⢤⠀⠈⢮⣥⡏⣂⣛⠾⢢⠋⠀⡠⡰⠐⠯⠏⡷⠁⣬⣑⣬⠶⠆⣀⠀⠀⠑⡺⡵⣇
⠀⠀⠀⠀⣜⡺⢹⠁⢀⣠⣕⢆⣞⣛⣛⣦⢯⣿⣺⠛⡟⣥⣶⣌⢳⣈⡏⢱⣿⢛⣿⠉⣶⣎⣑⢋⣽⣞⣿⣿⣿⣦⣹⢟⣐⣨⣭⠗⣄⠀⢢⢤⣽⡀
⠀⠀⠀⠀⠿⣟⡹⠀⣿⠀⣸⡟⢧⣀⣠⢾⡞⢯⣽⠛⣦⠯⣭⡝⢻⣿⡾⣯⢻⢚⣻⣟⠿⣿⡗⣞⣻⣘⣋⣉⣈⣸⠧⣿⢉⣼⣇⠭⡍⢆⢸⠟⣙⡁
⠀⠀⠀⠀⡛⢧⠖⡰⢬⣟⣿⡟⠈⣻⣮⢹⣿⣮⠣⣾⣿⠲⢾⠉⣇⣴⣾⣿⣷⣮⢛⠿⣼⠟⡹⠛⢪⢻⣿⣿⣿⡟⣓⣙⡒⢻⠖⣆⢱⣃⢬⣧⠁⠇
⠀⠀⠀⠀⣿⠘⣒⠑⢂⣸⣿⣏⠀⣿⣿⣧⡿⠷⠷⢟⣻⣷⡞⣿⣼⣯⠉⠉⠉⢹⡧⣰⣿⣵⣱⣤⣞⡙⣷⠲⣏⣟⣙⣛⣛⣿⢀⣤⣭⡓⢾⡹⣫⠆
⠀⠀⠀⠀⠸⣽⡳⠶⣣⢬⡫⣤⣤⣤⠽⣽⣿⣿⣷⣮⡹⣿⣧⣿⣏⣹⢦⣤⡴⡟⣞⢿⣻⣎⣿⠏⠈⠻⣿⢭⣼⢧⡀⠀⢀⡿⣧⠇⠾⣼⡡⢷⡶
⠀⠀⠀⠀⠀⠻⡿⠼⣿⣴⣷⣲⣼⣏⡛⣿⡇⠉⣻⣿⣇⢊⣩⣥⣼⣴⣭⡾⠛⠓⡟⢷⠛⣭⣿⢶⣶⣆⡿⢠⠛⠛⣿⢛⡉⣛⡶⣏⡭⡸⣷⣶⠂
⠀⠀⠀⠀⠀⠈⢹⣒⣂⡛⣾⡏⣍⣠⣷⠹⢷⣶⡦⣟⡳⣾⣿⢿⡆⣼⣿⣀⢀⣴⡟⣼⣶⣶⣮⡙⣛⣿⣧⠜⡤⣤⣟⣿⣶⣾⡽⠷⠿⣕⣞⠃
⠀⠀⠀⠀⠀⠀⠀⠹⡌⢻⡽⣧⣋⡿⣯⣼⠖⢷⡒⢭⣝⣙⣯⣭⣵⠟⣩⡾⢯⣵⢸⣿⡍⠉⣽⣿⣼⠿⠮⣯⣴⠯⣿⠽⣷⢺⡅⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣾⣧⣜⢲⣿⡁⢀⡀⣽⣴⣿⣏⣡⣸⣶⠖⡿⢿⣾⣩⣿⡿⣿⣼⡿⢫⣼⠒⡖⡯⢿⠀⠀⠐⡿⠚⠙⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣿⠭⡿⣼⣶⡶⣏⣹⡾⡿⢟⣹⣿⡾⢳⣾⠧⠿⠩⠝⣾⢼⢺⣎⣽⡟⣟⣷⣆⣹⣛⣉⣞⡿⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣖⠧⣾⣷⣴⣿⣾⢃⣾⣿⠙⠛⣎⢻⣿⡈⣳⢴⣿⣿⣸⣽⠈⣛⠉⠈⢉⣿⡉⡟⠉⣻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣩⣿⠟⠫⣽⡜⣿⣳⣬⣷⡟⣚⠻⣧⣉⣼⠿⡋⠯⡩⠉⣉⢻⣇⢿⣿⠿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⡽⢩⡾⢿⢟⣩⣬⠿⢧⣶⣾⣶⣌⠳⣷⠶⡞⣶⣌⡭⢤⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣙⣻⣓⣋⢾⣿⣧⡷⣿⡏⠀⠠⣹⣿⣿⢁⡧⢿⣿⡅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣯⣿⢧⣭⡍⣼⣽⢧⣤⡼⡿⠬⠻⣶⣧⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣷⡴⢰⠛⠛⣣⣤⡗⢺⡏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣚⡓⠞⠯⣜⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡼⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠀⠀⣀⣀⣀⠰⠄⢀⣴⣃⣼⡇⢀⠤⠒⠁⠀⠀⡠
⠀⠀⠀⠀⠀⣠⣴⠂⣀⣴⣾⣿⣫⣭⣶⣾⣟⣾⣿⣽⣻⣚⡁⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⡿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇⣀⠀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⣾⣿⣩⡿⡟⠻⣿⣿⣿⡟⠛⢿⣿⠶⠾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⡀⠀⠀⠀⢂
⠀⠀⠀⠀⢰⡟⠻⣿⠀⠇⠀⣹⣿⣝⣂⣀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⠿⠟⢿⡇⢀⠈⢃
⠀⠀⠀⠀⠸⠁⠀⠈⠀⣾⣿⣯⣻⣿⣿⣻⣶⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠆⣇⠀⠀⠀⠀⠀⠲⣄⡼⣷⣟⠣⠈⡀
⠀⠀⠀⠀⠀⠀⠘⣿⢷⣿⣿⣭⣿⣿⣬⣿⣿⣿⣿⣿⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣄⠛⠁⠀⠀⠠⢄⡝⢷⣻⠿⠇⠀⠘⠃
⠀⠀⠀⠀⠀⣀⣀⠀⣿⣿⣷⣬⣿⣿⣿⣧⠀⣀⣿⣿⣷⣷⣶⣾⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠚⠁⢘⠀⠀⢁⠀⣰⡉⡀⣠⣴⠁
⠀⢠⣶⣿⣿⣿⣿⠆⢼⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠝⠁⠀⠁
⠀⠈⠿⣿⣿⣿⣿⠀⠈⠙⠿⣿⣿⣿⣿⣿⣶⣿⠿⡂⠀⠘⢿⣿⡿⠛⠛⠻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢆⢠
⠀⠀⠀⠀⠀⠙⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣦⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡆
⠀⠀⠀⠀⠀⠰⡿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⢠⠈⠘⠙⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣯⣭⣾⣷⣶⣿⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡯⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣏⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠬⡓⡀⠀⢈⡶⠞⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡌⣷⠈⣽⡄⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠙⠋⠀⠠⠤⢤⢀⠉⡍⡈⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣁⣾⣁⣹⣄⣹⣿⣄⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠃⡞⢰
⠀⠀⠀⠀⠈⠀⠀⠀⠠⡆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠄⠐⠢⣴⠄⠃⠀⠀⠀⠈⠈⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠤⠴⠞⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁⢀⣽⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡐⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢘⠋⠁⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⡤⠐⣻⢶⠂⠀⠀⠀⢃⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢬⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠊⠀⠀⠆⠀⠀⣠⠞⠅⠂
⠀⠀⠀⠀⠀⠀⠠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⣀⠀⢀⠀⠈
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠳
⠀⠀⠀⠀⠀⢀⣴⠄⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⢠⡀⢠⠀⣤⠀⡄⡄⢠⠀⡄⢠⡀⢠⢠
⠀⠀⠀⡄⠀⠀⠁⠄⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠀⠛⠀⠋⠂⠘⠀⠙⠊⠃⠘⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠙⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⣀⠀⠂⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣦⣀⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢄⣀⣀⠀⠀⠀⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⢠⠙⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠐⠈⠐⠉⠱⠀⣿⡒⠄⠀⠲⡟⠇⢀⡀⠀⠀⢀
⠀⠀⠀⠀⡌⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢀⠀⠘⠉⠃⢄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠠⢈⠎⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠚⢀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠐⠂⠁