Wedding anniversary Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢲⡟⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣄⢀⡀⠀⢢⠀⠀⠀⠀⠀⢻⡆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢸⡇⠀⣀⠄⡀⠀⠀⠁⢹⡄⠀⠀⠈⡿⣇⠀⢸⡇⠀⠀⠀⠀⢸⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⣇⢰⡇⣸⣡⢺⣤⣀⡼⠁⣷⢤⡴⠗⠻⠴⢸⡇⡔⠀⠀⠀⢸⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠿⠤⠛⠉⠁⢸⡇⠁⠀⠀⣷⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢠⡟⡸⢁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⡴⢞⠛⢦⡀⠀⠀⠀⡀⠰⡇⠀⠠⠀⣿⠀⠀⣀⠴⢚⡟⠀⠀⠀⣰⠏⠈⢐⣩⡴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣰⠏⠀⢸⡇⠀⠀⢰⠁⢠⡇⢠⠃⠀⣿⢠⡞⠁⣠⡾⠁⢀⡴⠊⠁⠀⠊⣉⣐⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠢⠙⠀⠀⠀⣠⡞⢁⣼⠏⠀⢀⡾⠁⠀⠀⡇⠀⢸⠇⣾⠀⢀⡟⠀⠙⠋⠁⠀⠊⠁⣀⣢⣬⠭⠷⠶⠾⠟⠛⠿⠷⠶⣭
⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⣼⠟⢠⣾⣯⣤⠞⠫⠐⠀⠀⠀⠧⠴⠋⠀⠘⠒⠋⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣻⡿⠛⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⣀⡀⡠⠖⡄⢰⡷⢲⢴⢏⠇⣠⠔⣠⠀⡼⣲⢲⡇⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠁⣰⡿⠃⢀⢀⠖⣷⢠⡀⠔⣹⢠⠀⢸⡇⡼⢁⡟⠀⠊⣰⠏⡴⠋⠸⣇⣼⠃⢰⡏⣰⢱⠁⣸⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠃⠀⣰⡿⠁⠀⣿⠋⣼⠃⢸⠇⣰⠃⣿⢀⢼⡿⠁⢸⡇⢀⣴⠋⠈⠇⢀⢀⣽⢻⣤⠾⡶⠃⠈⠀⠘⣻⣏⠴⠊
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣰⡿⠁⠀⢠⠏⢰⠃⢀⠞⠀⣇⣸⢷⣊⣈⣁⠀⠀⠛⠛⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡤⠴⠖⣾⠏
⠀⠐⠤⠤⠚⠁⠀⠀⠀⠀⣿⣁⣀⣀⣀⣀⣈⣤⣤⣤⡴⠶⢶⡿⠷⠶⣎⠛⠦⣄⡀⠀⠀⠀⣀⡠⠔⠂⠁⠀⠀⠹⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠙⠶⠶⠋⠀⠀⠀⠉⠉⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⣀⣤⢼⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⠏⠀⣸⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢰⡏⢀⡟⠀⡰⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡿⠀⣾⠠⠊⢁⡤⣤⡄⠀⣠⣠⣶⡀⢀⡀⣠⡀⠀⡀⠀⢀⡀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠇⠀⣰⠏⢠⡟⠀⢸⡟⠁⣼⢃⡿⠊⢹⡇⣾⠁⢠⡿⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣿⠀⢰⡏⡠⣿⠁⢐⡿⠀⢠⠏⣸⠇⠀⡼⣻⠇⡴⣻⠇⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠒⠒⠒⠶⢤⣄⡀⠀⠈⠀⠀⠘⠛⠀⠸⠋⠀⠿⠊⣼⠇⠀⠁⢤⠿⠄⠊⠁⠛⠋⣰⠟
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠰⠋⠀⢀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠊⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠀⠰⠆⠀⠀⢾⡆⢠⣇⣀⡤⠊⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣠⣴⣯⣤⡄⢰⡏⡠⣾⠠⢰⡏⡴⡿⠀⣴⢀⡾⠀⢸⠇⣠⣿⠃⣘⡁⠙⢃⡄⠿⠀⡄⠛⣾⢣⣾⠾⢧⡶⢀⣾⠃
⠀⠀⠀⠀⠀⢀⡤⠔⣺⠉⠁⠀⣿⠀⠀⠁⣿⠏⢰⡇⢠⣿⠎⣸⠃⢰⡇⢸⡇⢀⡞⣾⠋⠀⣰⡟⠁⠀⠙⣓⢀⡛⢠⣾⢇⣿⠋⢠⣿⢁⣾⡏
⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠿⠄⠀⠸⠇⠀⠿⠂⠸⠃⠠⡿⠀⠺⠃⠘⠷⠊⠰⣯⡠⢘⡟⠀⠦⣄⡠⠟⢹⠟⠩⡿⠺⠋⠀⠸⠟⢁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠁⠀⠀⠀⠀⢀⠔⠁⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⢠⣀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠁⠀⠀⠀⠐⠤⠀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⢀⡴⣾⠀⠀⠀⠀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⡿⠖⠋⠠⣇⠀⠀⠀⣼⡡⡶⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡗⠀⠀⢀⡼⠃⠀⡤⠟⠄⠱⣼⠀⠠⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣀⡀⡖⠚⠁⠀⠀⣗⠀⠀⠀⣈⡳⠀⢸⠔⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡞⣦⣄⡉⢳⡭⣗⣬⣦⢢⠍⡇⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠓⢦⣀⠀⠀⠀⣸⡟⠉⢹⡉⢋⠲⢬⢢⡶⢊⢠⠓⡪⢯⣧⠀⢸⠀⠀⠀⣀⡴⢺⡇
⠀⠀⠀⢠⡤⠤⠼⠆⠀⠈⠙⠲⢤⡇⣇⠀⠀⢇⠮⡩⣧⣵⣋⣵⠃⢸⠃⠀⣿⢀⣮⠤⠖⠋⠁⠀⠸⠤⢶⡖
⠀⠀⠀⠀⠳⣄⡀⠀⣰⠾⣛⠓⢺⠀⢸⡀⠀⠸⡔⠛⣛⣻⠇⢹⡀⣸⠀⢸⠟⡏⠉⢉⡽⠶⡄⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠈⠙⢲⠏⠀⠈⠙⠻⢤⣄⣇⣀⡜⠀⣠⢿⡏⠀⠀⣇⣏⣀⣸⡤⠷⠚⠉⠀⠀⢳⡤⠞⠁
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠶⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠒⠤⠀⢀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢄⣰⢎⠀⡰⢃⢀⠄⣠⢶⣄⡠⢲⢀⡄⣤
⠀⢠⠀⠀⠀⢀⠤⠊⠁⢸⡞⠁⢈⠈⣰⠋⠉⡼⢉⠁⠀⢡⠋
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⡠⢀⡏⠀⠁⠀⠀⠐⠁⠀⠀⠃
⠀⠀⠀⠀⡞⠀⠀⠂⢚⡾⢥⡞⡴⢰⢠⠆⡆⡌⢠⡆⡄⣤⠀⢶⠀⡰⣄⣀⡆⠰⡆⢠⡆⡄
⠀⠀⠀⠀⠑⠀⠠⠖⠋⠀⠘⠄⢠⡇⠀⡼⠀⠅⠀⠁⠀⠈⠀⠈⠀⠀⠀⠁⢀⠠⠅⠠⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⢠⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⣄⠀⠀⠀⠀⠛⢸⡧⢸⣿⠀⢆⣶⡄⣶⠒⣦⢰⡖⢲⡔⣶⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠷⠀⠀⠀⠀⢸⡇⠸⣿⠐⠯⠾⠇⣿⠤⠟⢸⡧⠾⠃⠸⡷⠁
⠀⠀⠀⠀⢀⠠⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠀⠐⠛⠳⠤⣤⣤⣤⡴⠃⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠠⠀⠐⠀⠀⣞⡉⢿⣆⠀⣶⡆⠀⢸⠃⠀⣀⠀⠀⠀⣹⣧⠀⠀⢉⣿⡄⠰⠗⠀⠀⠀⡀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠸⣿⡄⡼⣿⡀⡞⢰⣟⡹⠗⢰⡿⠉⣿⢄⣾⠋⢻⡇⢹⣿⠈⣿⡏⢻⡇⢰⡏⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⢻⣿⠁⠸⣿⣀⡀⠸⣷⣠⡿⠈⢿⣄⣼⠇⢸⣿⠀⣿⡇⣸⡇⢈⣗⡞⠋
⠀⠀⠀⠀⠁⠐⢄⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠁⠀⠈⠐⠋⠀⢼⡛⠛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠶⠶⠦⢤⣀⣠⣾⢋⣶⡖⣰⣶⠆⡴⢰⢦⣤⠆⢰⡄⢸⣀⡖⡶⢰⡄⣰⣰⠆⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠁⠿⠘⠉⠃⠛⠘⠈⠃⠙⠀⠙⠀⠘⠀⠛⠘⠊⠃⠈⠃⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡠⡄⡴⡄
⠀⠀⠀⠀⠀⠀⣠⣾⡏⣖⣠⣦⣶⣿⡗⣧⣇⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⢀⢸⢀⡍⠠⢧⠸⣁
⠀⠀⠀⠀⠀⠰⡝⢅⣉⣁⣸⠈⠸⣀⢈⡾⣳⡂⠀⠀⠀⠠⢠⡄⠐⠚⠚⠊⠛⢂⠘⠀⢀⠁⡀⡀⡀
⠀⠀⠀⠀⠀⠘⠙⢛⡏⢿⡸⣷⣏⢣⡟⢎⠾⡇⠀⠀⠀⢖⡿⡧⢿⠿⠿⠷⠟⠯⢿⠸⠾⢾⡇⢳⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠉⠁⠁⠉⠈⠀⠉⠁⠀⠀⠀⠉⠀⠈⠀⠀⠈⠉⠉⠁⠋⠈⠁⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣸⣧⡟⣡⠀⢠⣀⢠⣄⣠⢠⠄⠀⠀⠀⠀⠀⢇⢈⡂⢠⡄⢰⡤⢴⠐⠖⢠⠃
⠀⠀⠀⠀⠀⠨⠼⠘⠃⠷⣧⡯⡾⡿⠞⢙⣾⠀⠀⠀⠀⠀⠀⠎⠘⠉⠊⠛⠋⠘⠁⠐⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠠⠇⠀⠘⠁⠀⠀⠀⠀⠰⡆⡀⠀⡇⢸⠁⣸⠀⣴⢸⢠⣆⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠻⠸⠇⢺⠀⢿⠀⡛⣘⠘⠋⠓
⠀⠀⠀⠀⠀⠀⡄⣄⣄⠀⣀⣄⣠⠀⢠⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣇⢻⡏
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠁⠉⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠙⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡄⡄⡰⠀⡂⢔⡠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⠀⠀⠁⠈⠁⠁⠀⠈⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⡴⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⣀⠀⠀⠐⠄⣸⠁⣿⠀⠠⢶⡤⠀⣶⢰⡴⠀⣦⠀⣤⠀⢰⡄⢯⣣⢀⡤⡄⠙⠧⣄⠀⢀⢿⣄⠀⣴⠒⣀⠙⡧⣄⠀⣤⠀⢰⡆⠀⢸⠀⠀⢸
⠀⠀⣼⠁⠀⠑⠀⢠⠏⠀⢿⡄⠀⢼⡇⢸⡇⢸⡇⢰⡏⠀⣿⣀⡼⣧⠀⡟⢸⡏⢀⡜⠀⣿⠀⣘⡼⣿⠐⣿⣀⣿⠀⠇⣿⠀⣿⢀⣼⡇⠀⢾⠂⠀⢸
⠀⠀⠹⣄⡀⢀⡠⠏⠀⠀⠸⣇⠀⠀⠀⠘⢧⠈⠀⠘⠧⠜⠁⠁⠀⠛⠒⠁⠀⠉⠉⠀⠀⠛⠖⢹⠀⣿⠀⠀⠀⠙⠞⠀⠻⠄⠈⠁⢼⠇⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠋⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⠤⣀⠀⡇⠀⠠⡄⡠⠠⡀⡠⠠⡀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠤⠌⢿⡅⠣⠴⠧⡧⠤⠁⡧⠤⠁⠀⠣⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠔⠒⠂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠸⠄⠈
⠀⠀⢠⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡆⠀⠀⠀⢠⡇⠠⡄⠠⠀⢠⡄⢄⠀⡄⠠⡄⢤⠀⠀⠄⠠⡄⠀⢤⠀⠀⢢⠀⠤⡄⠠⡄⠀⡄
⠀⠀⠱⣄⣀⡠⠚⣆⠄⠇⠀⠤⠀⠀⠘⠜⠣⠀⠣⠄⠉⠦⠄⠀⠣⠲⠤⠀⠣⠜⠄⠀⠧⠀⠣⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠘

⣿⡿⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⠂⠀⠀⠀⢀⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⣠⠤⢠⡟⠀⠀⠀⢀⡤⢄⢠⠏⠀⠀⢠⡞⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⡏⠀⣾⠁⢂⡄⠀⢾⡁⢀⣟⠀⠈⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠈⠀⣀⠈⠁⣸⡇⢀⠀⣾⡇⢲⣀⡶⠀⣴⢀⠠⣄⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⡄⢸⡇⣺⠇⣿⠃⣼⠋⣿⢀⣾⢹⡇⠘⣿⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸⡇⡺⠄⢻⢠⣿⠘⠋⠀⣿⠙⠋⠀⠁⠜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠁⢠⠄⠀⣿⠀⣀⠀⡿⠀⢀⠀⡘⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠀⠋⠀⠀⢩⡎⠈⠈⣷⠀⠈⡇⠃⠜⠁⢤⠀⠀⡔⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣾⠁⠀⢰⡇⠀⢀⡀⠀⠀⣾⠁⢀⡀⣿⠂⠈⡄⢀⣀⠂⣾⠀⢠⠖⣤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⢠⣿⠀⣾⠈⣷⢰⡟⢀⡞⠹⣿⠀⣿⠀⣿⠀⢸⠇⡀⣿⠀⣿⠀⣿⠀⣿⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠻⡄⠈⠙⢇⠘⢇⠰⣿⠀⣧⠀⢿⠀⡘⠆⠀⠛⠀⡇⠘⠛⠊⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⡈⢃⠀⠀⣰⠛⠀⠛⠀⠄⢿⢸⣧⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⠀⠀⢀⢤⠀⠀⠉⠒⠤⢤⠄⠴⢻⠏⠇⠀⢹⣦⠀⠀⠀⠄⠋⡸⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠁⠈⣷⠀⣀⡀⣼⠀⢐⠀⣄⠀⢀⡤⡄⢹⣆⠀⠀⠀⢿⣆⠀⣠⢄⣀⠀⠙⢧⡄⣠⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢘⡇⠀⣿⠀⡇⠀⣿⠀⣿⠀⣿⢠⣇⠀⡿⠀⠀⠀⣿⢃⠂⢹⡆⢿⢰⡏⢸⡇⠀⠀⣿⢠⣏⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠌⠓⠂⠙⠀⡇⠀⠙⠀⣿⠀⠳⠌⠻⠀⠳⠀⠀⠀⢿⠀⢆⠈⢁⡿⠈⠓⠉⠃⠊⠀⠻⠊⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠛⠁⠀⠀⠻⠂⠀⠀⢀⢀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠐⢙⡷⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⣿⠄⢀⠀⢀⣀⡴⠞⠁⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠜⠀⠀⠀⠀⠀⢀⡴⠋⠀⡨⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⣰⠏⢀⡴⡶⢀⣿⠃⠀⡠⠊⠀⠀⣤⠖⡆⣠⡟⠀⠀⡔⢁⣴⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠫⠀⣿⠇⠀⣸⡟⡠⠀⡁⠀⠀⣼⠇⡰⢡⡿⠀⡠⠊⢀⣾⡇⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣿⡏⠀⠸⡇⠀⠀⠘⠇⠀⣾⡗⠀⠈⠀⣸⡿⣀⣀⠀⢀⡄⠀⣀⠀⠀⠀⢠⠄⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣀⠀⠀⣠⠖⣆⡀⢀⣿⡕⠲⣆⢠⣿⡟⠀⣿⢴⣿⠀⢠⣿⢀⠔⢸⣷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⣿⠀⢠⡿⠀⣹⡇⢸⣿⠀⣸⡟⢸⣿⢁⣴⣿⢸⡇⡰⢹⣿⠁⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⣿⡀⢸⣇⡰⢿⠁⣼⣿⠸⠟⠁⢸⣿⠸⠟⠃⠀⠉⢀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡏⠈⠀⠈⠓⢹⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⠏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⡞⠁⠀⢸⡿⣠⠄⡄⡨⣟⠀⠀⢠⡄⡼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡄⠀⢀⣀⠀⠀⠀⢇⠀⠀⠀⣰⡏⠔⠀⠁⣿⡆⠀⢸⡇⠙⠐⠋⢀⢲⡆⠀⠀⡴⠋⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢀⣀⢰⡟⠰⠁⠀⣾⢁⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣿⡗⠐⠉⠄⠀⢀⠀⠃⢸⡇⠀⢀⡤⢤⣠⠀⠀⡃
⠀⠀⠀⠀⠀⣿⠄⣿⡗⠁⣰⡆⣿⡸⠀⣼⠋⠃⣴⢲⣼⡟⠀⣰⡏⢠⣿⡇⠀⣴⡇⠀⢹⣿⠀⣾⡇⠀⣿⠃⢸⣿⠀⡰⠁
⠀⠀⠀⠓⠀⠙⠀⣿⡇⠀⣿⡇⠸⣇⣸⡟⠀⢸⡇⠀⣹⡇⠀⣿⠁⠀⣿⡇⠀⣿⠀⡌⢸⡟⠀⣿⠃⢸⣿⢀⡼⣿⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣇⢀⠿⣇⠠⠁⠀⢷⡠⠙⢇⢠⢻⣇⠀⢿⡄⠀⢻⡇⢰⠙⠖⠁⠈⠃⠀⣿⠀⠆⠙⠊⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⣈⠁⠀⣀⡀⠀⠀⠀⠀⠈⠻⠜⠀⠉⢀⠈⠓⠁⠀⠀⢠⡾⠱⠀⠻⠎⢀⠖⣹⡆⢻⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⡀⠀⠉⠐⠢⢤⣀⠀⠀⡰⠁⣠⢇⡶⢳⠀⠀⢸⣧⠰⠀⠀⠀⠸⠸⡸⠇⣾⣾⠃⡇
⠀⠀⠀⠀⠀⠠⠞⢁⢴⡄⠀⠀⠀⡔⢹⡄⠀⠀⠀⠀⠀⠉⡝⠛⠉⠁⣼⡇⠌⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠴⠃⣿⣀⠃
⢀⡴⢄⣀⠀⠀⠀⡌⢸⡇⠀⣄⢰⠁⣾⠁⠀⣛⠀⣠⠀⠐⢀⡴⢲⠄⠹⣷⡀⠀⠀⠀⡜⢿⣆⠀⢀⡴⢢⣠⡄⠀⢈⢿⣶⠀⣴⠄⣠
⣿⠁⠘⣿⠀⡰⣶⠃⢸⡇⢠⢹⡇⠀⣿⠀⢸⡏⠀⣿⢀⢣⣿⠡⠊⠀⠔⣸⡟⢠⠋⠸⣷⠈⣿⡄⣾⠇⢺⣿⠀⠀⡎⣼⡇⢸⣿⢠⣿
⢿⡀⣸⢻⣀⠇⢾⠀⢸⡇⡈⠸⡇⠀⣿⠀⣼⡇⡰⢿⡎⠸⣯⠀⢀⠌⠀⣿⠃⢘⡐⠁⠿⠁⣿⠃⢿⣠⠚⣿⢀⠎⠀⢿⣁⠏⠛⢻⣿
⠈⠁⠁⠀⠁⠀⠀⠀⢸⣇⡇⡀⠀⠀⣿⢰⠀⠉⠁⠀⠁⠀⠉⠀⠁⠀⠀⠙⠆⠊⠣⠄⠀⠴⠋⠀⠀⢀⢤⣈⠁⠀⠀⠈⠁⠀⠀⢸⡿
⠀⠀⠀⣠⠴⠒⠂⠉⠀⠉⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⡤⠤⠐⠂⠈⠉⠉⠙⢲⣄⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⠆⠀⠀⠀⠀⠀⠀⣼⠃
⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⠀⠀⠀⠀⠈⠀⠂⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢀⣵⡿⠋⠀⠀⠀⠀⠀⢀⡼⠃
⠘⢿⣄⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠈⠉⠀⠐⠂⠉⠉⠀⠀⠂⠀⠀⠀⠀⠐⠉
⣤⣤⣭⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴⠃⠀⠐⠀⠰⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢰⠁⠀⢰⡏⠀⣼⠃⠀⠀⠐⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⠠⠔⠒⠦⡄
⠀⠀⠀⠀⠀⠀⢢⣄⠀⠃⢒⣁⣈⣡⢤⣿⣄⣰⡏⢀⡀⠀⢀⡀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⡀⠈⠀⠀⠻⠯⠴⣲⠞⠉⠀⣼⠃⠈⣿⣰⢋⡟⣰⠃⣝⡞⢨⢣⢇⣼⠁⠀⠀⠀⠀⠀⠁⠀⠊
⠀⠀⠀⠈⠒⠶⠶⠖⠒⠉⠀⠀⠀⠀⠉⠀⠈⠁⠈⠉⢻⠋⠋⡼⠉⠁⠈⢹⠇
⠀⠀⢀⡤⣤⢀⣤⡄⢠⣤⠀⡅⣄⣠⢀⢤⢴⣤⡄⢿⡀⣀⢤⡄⢰⣤⢀⡟⢠⠄
⠀⠀⢾⡴⣇⡼⢸⣡⡏⣾⢸⡇⢿⠎⢻⡁⠀⣞⠀⠀⡿⣧⢾⡁⢰⣇⢾⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣄⠀⠀⠀⠀⠀⢠⢏⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠀⠀⠀⣰⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣄⠀⠀⠀⢀⣔⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢹⡄⠀⢀⠞⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⣠⠤⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠀⣸⠁⢀⠏⠀⠀⠀⠈⠂⠀⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⡜⠀⠀⢠⠂⣠⢀⡖⢀⠄⡴⠀⢀⡔⢠⠆⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠊⠀⠀⠀⠑⠀⠀⠃⠐⠃⢼⠂⠈⢠⠗⠊⠘⠀⡏⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⢀⡄⢲⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡸⠀⠀⠀⠀⠀⠖⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡾⠀⢀⡇⠀⢄⠀⠀⠀⠠⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢠⠲⠇⠀⠸⠠⡀⣠⢀⡄⣠⢀⡌⡀⣠⢀⣤⠘⣠⠀⣶⠀⠀⢀⠐⣡⢀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡔⠁⢸⠀⡠⠁⡰⢳⡃⣸⢣⢇⡞⣰⡡⠉⡟⠀⢰⠃⠖⠸⠴⣦⣏⣴⣇⣾⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⣀⣀⣈⡀⠀⢀⠀⠀⠉⠀⠁⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⡁⠀⠀⠠⠇⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠙⡆⠀⠀⢀⡴⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠀⢠⡇⠀⢀⡞⠀⠀⠀⠀⠙⠤⠀⠀⣀⣠⠤⠶⠚⠉⠁⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠁⠀⡜⠀⠀⡾⠀⠀⠈⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⣀⠀⣀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⣀⠀⠀⠀⠐⡇⠀⠀⢀⠏⢀⡾⢀⡞⠁⡸⠀⡾⠁⡠⢰⠃⢠⠏⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠊⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠘⠃⢺⠓⠀⠀⢰⡇⠋⠁⠙⠀⡿⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⣠⠈⢢⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⡴⠒⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢰⡏⠀⠈⡇⠀⢐⠁⠀⠀⠀⠀⢀⠀⠀⢐⠀⡠⠃⠀⠀⠁⠈⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡠⣿⠁⠀⢸⠃⠀⠈⠢⠀⠀⠀⠀⠁⠴⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⠀⠀⠉⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡜⢁⠋⠀⠀⡞⠐⣲⢰⡆⣠⡶⢰⠆⣴⠆⡴⢠⡖⣠⠖⠊⣱⠖⢀⢿⠀⠀⢀⡖⠈⣼⠂⣴⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⡠⠊⠀⢸⡀⢀⠎⠀⣰⠃⣞⠔⣼⢃⡏⢰⣃⣼⡠⠀⠸⡁⠀⢠⡏⣼⠃⡼⢴⣄⢼⡃⢺⠃⢸⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠉⠉⡏⠉⠀⠀⢈⡆⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⠁⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠓⢦⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠉⠉⠉⠉⠛⠓⠲⠶⣤⣄⣀⡀⠀⠀⠈⠃⣀⣠⡞⠀⠀⢠⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⢀⡴⠋⠄⢀⡀⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠈⠁⠀⠀⢹⠀⠀⠀⠸⠇⠀⠀⠞⠉
⠀⠀⢠⠎⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠠⣤⣤⠀⢠⣤⡤⠀⠠⣤⣤⣤⠀⠀⢠⣤⣤⣤⣤⡀⢠⣤⣤⣤⣄⠀⠠⣤⣤⠀⠠⣤⠄
⠀⠀⡾⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⠹⣿⣆⣸⠇
⠀⠀⣇⣾⠀⠀⠀⣴⡟⠛⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⣿⣀⣸⣿⡇⠀⠀⣸⠹⣿⡆⠀⠀⣿⣿⣀⣿⡇⠀⣿⣟⣀⣿⠇⠀⠀⢻⣿⡟
⠀⠀⢻⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣿⣿⠉⢹⣿⡇⠀⢠⡿⠛⣿⣇⠀⠀⣿⣿⠉⠁⠀⠀⣿⡟⠉⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢻⣆⠀⠀⠈⠻⠦⣤⣀⣀⡤⠞⠁⠀⠀⢀⣿⡇⠀⣸⣿⣇⠀⣼⠃⠀⣿⣿⣄⠀⣿⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⣠⡄⠀⠀⣠⣤⠀⠀⠀⠀⣿⠉⡿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⠉⡿
⠀⠀⣠⡶⢶⣾⠆⢰⡆⣰⢞⣦⢰⡦⢠⠞⣶⢀⣬⢁⣀⠐⣿⡼⠀⣴⡟⣳⠙⣶⡃⠀⢰⣿⠉⠁⢀⣴⠶⣴⡗⠙⣾⡃⠀⢰⡗⠀⣼⡇
⠀⠀⣿⢡⠞⣿⠀⣿⣧⠏⣸⡏⣸⣧⡟⢰⡿⢸⡏⢸⣿⠀⢹⠷⠶⣿⠞⠁⣰⠃⣽⠆⣸⢿⣶⠖⣾⣇⡼⣿⠃⣰⢃⣿⠆⣸⡇⣰⢻⡇
⠀⠀⠛⠋⠀⠙⠞⠹⡿⠀⢿⣡⠛⢿⠀⢸⣧⠟⠷⠏⠹⢷⠏⠀⠀⠛⠷⠶⠃⢸⣏⣰⢣⡏⢹⣷⠙⠛⠀⠘⠳⠃⢸⣏⡴⠋⠛⣡⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡤⠭⠤⠤⠤⠤⢤⣤⣤⣄⣀⣀⡀⠀⠈⠉⠁⠘⠧⠼⠋⠀⠀⣀⣤⣤⣄⠈⠉⠁⠀⣾⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠉⠉⠉⠛⠓⠒⠶⠦⠤⠀⠀⠀⠋⠀⠀⠈⣷⠀⠀⠘⣇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠷⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠶⠶⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⢠⡏⠀⠀⠀⠀⠀⠀⡴⠋⢀⠃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢰⡏⠁⣿⠀⠀⠀⢠⡞⠉⣼⠁⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡏⠀⠋⠀⠘⠃⢰⡟⠀⠀⣾⡇⣄⢀⡄⢀⡄⠀⣀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣦⠀⡾⢱⡆⣸⠇⣸⠖⣿⢁⣿⣿⠀⢾⡗⠁⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⢰⣇⢺⡇⣿⠰⠟⠀⡿⠺⠃⠉⢁⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⡀⠁⣿⠀⠀⠀⡇⠀⠀⢀⠂⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠘⡀⠀⢉⡞⠈⠈⣷⠀⢸⠀⠤⠋⢠⡄⠀⡴⠂⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣿⠸⣀⣾⢸⢀⣄⠈⡁⣼⠅⢠⣤⣿⠂⢉⡀⣤⡔⢸⡇⢠⡖⣦⠄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠰⡏⠀⣿⠹⣇⣿⠁⣾⠙⣿⠀⣿⠈⣿⠀⣿⠀⢸⡇⣼⠃⣾⠃⣿⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠻⠄⠁⠹⠄⠻⠀⢿⠀⠷⠀⢻⡀⠙⠂⢈⠁⢿⠀⠉⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⠀⠀⠀⠀⡀⠈⠁⠀⢀⣄⡤⠀⠀⣏⠀⠈⠁⡂⣸⢾⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢡⡄⠀⠀⠜⡇⠀⠀⠀⠉⠐⠃⠉⣼⠀⠀⠀⢻⡆⠀⠀⠁⠀⠞⢿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠰⡦⠀⣤⢀⡇⢰⡎⢰⡇⢠⡄⣶⠀⣴⠋⠃⠙⣧⢀⠀⣌⢻⡄⣴⠋⣶⠀⠀⣿⢃⡞⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢧⠈⠿⢸⡇⠀⠇⢸⡇⣼⡀⢿⡄⣿⠀⠀⢠⡏⢨⠀⠹⢸⡇⢿⠔⣇⠠⠀⣿⡘⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠧⠀⠀⠸⡧⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⠀⠀⠊⠀⠀⠀⣦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⣴⣶⣶⣶⣶⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⠿⠿⠿⢷⣄⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡾⠟⠻⠿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠟⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠠⢿⣿⣟⡇⠀⣼⣿⣿⣧⣘⣳⠆⠀⢀⣀⡀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡆⠀⠉⠉⠁⠀⠀⠀⠈⠉⠹⠛⠛⠃⠀⠸⣿⣮⣷⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣀⣤⣤⣤⣶⡀⣴⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⢺⠿⠭⠉⣩⠟⣿⣿⠨⣍⢒⣒⡤⠀⠀⣼⣿⢟⣵⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⣀⠉⠉⣰⡿⠁⠀⠈⠉⠁⠀⢀⣰⣿⣿⡛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⡿⠋⠀⠀⢠⣶⣶⣶⡞⡹⢿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⠉⠋⡏⠀⠛⠛⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢤⡆⠐⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣠⣦⠀⠀⢻⠇⠦⠀⠀⠀⠀⡄⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡮⠉⠉⣁⣄⠀⢀⡟⠁⠂⠀⠀⠀⠀⠀⠐⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠄⢤⠀⣂⠠⠐⠀⠀⡀⠀⠀⠄⠰⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠶⠃⣠⣶⣶⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⣿⡇⠀⢰⣿⣥⠟⠁⠀⠐⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡄⠀⢠⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣿⡷⠶⣿⡏⠁⠀⣠⣶⠶⠀⠀⠀⣼⣿⣤⣄⠀⠀⢰⣿⣴⢶⣄⢠⣿⠇⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢉⣿⠇⠰⣿⡇⠀⣸⣿⠁⣴⣷⠀⢠⣿⠋⠉⣿⣇⣠⣿⡏⠀⣠⣿⢾⣿⣀⣰⣿⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⣼⡟⠀⠀⢿⣧⣠⢿⣿⣼⣿⡇⢀⣿⡿⣠⠞⣿⡏⣼⣿⢠⣟⣽⠇⠈⠛⢛⣹⣿⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣧⣾⢿⡇⢻⣶⠟⣰⢿⡿⠈⠛⠁⢀⠀⣴⠋⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠲⠇⠀⢀⡀⠀⢠⡏⣾⡇⠀⠀⢠⡏⣿⡇⠀⠀⢀⠀⠸⣇⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠌⠁⠀⠀⢠⠀⠀⠀⠘⠿⠀⢸⡇⣿⠀⠀⠀⢸⣰⡿⠀⠀⠐⠝⠠⢀⠉⠉⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⠐⠀⠀⠐⠒⠂⠐⠀⠘⠿⠃⠀⠀⠀⠈⠋⠀⠀⠒⠐⠒⠀⠐⠀⠀⢠⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠖⠀⣰⠀⢰⠀⡔⠀⠈⢸⠉⠑⡄⡋⠑⢆⢸⠀⢰⡄⢸⠀⡔⠂⠦⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠏⡄⡇⠀⠗⠂⠃⢸⠀⠀⡇⡇⠀⡸⢸⠀⠈⢃⠸⢸⠀⢠⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡌⠀⢷⠁⠸⡠⠤⠄⠸⠤⠞⠠⠧⠚⠁⣸⠀⣀⠈⡆⠸⣄⣀⠌⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠤⠥⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠚⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⡆⠀⣶⡀⣾⢰⣆⢸⠆⡗⢸⡆⣸⢰⡏⠉⢠⡟⡆⢠⡞⠂⢀⣷⠀⢸⢳⡄⣧⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⣷⠀⡟⣧⡏⣼⢻⣼⢀⡇⠈⣧⡏⢸⡏⠉⢸⣿⡁⠈⠳⡄⣸⣿⡆⣾⣏⠀⢸⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠃⠘⠃⠛⠀⠛⠘⠃⠀⠙⠀⠘⠛⠓⠘⠀⠙⠘⠛⠁⠋⠀⠃⠛⠘⠂⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠋⠹⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡳⣞⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠖⢿⣤⣉⣉⣤⣿⠲⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠉⣀⣤⣀⠀⠀⣸⢧⡈⠓⠤⣏⠀⠀⣀⣤⣀⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠐⡇⠀⠈⠉⠉⠹⣆⠉⠲⢤⡏⠉⠉⠁⠀⢸⡂⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡖⠒⠋⠀⠀⠀⠀⠀⠀⢯⣑⣂⡼⠀⠀⠀⠀⠀⠀⠙⠒⢲⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠉⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠙⢦⣄⠀⠀⠈⠧⠤⠴⠒⠒⢦⠀⠀⠀⠀⡴⠒⠒⠦⠤⠼⠁⠀⠀⣠⡴⠋⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣇⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠈⠑⠶⠖⠋⠁⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⣸⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⡟⠓⠚⠙⣆⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣰⠛⠓⠚⢻⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢿⡀⠀⠀⠘⣆⢀⡴⠛⢦⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⡴⠛⢦⡀⣰⠃⠀⠀⢀⡿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠉⠁⠀⠘⢧⣀⣠⡞⠁⠀⢳⣄⣀⡼⠃⠀⠈⠉⠁⠀⠀⣠⡾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣆⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⢤⣤⠤⠤⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢦⣀⣀⣤⣄⠀⠀⠀⠉⠉⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⠀⠀⠀⣠⣤⣀⣀⡴⣇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⣧⠀⠀⣰⠞⠛⣦⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣴⠛⠳⣆⠀⠀⡼⠃⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠈⠓⠞⠃⠀⠀⠸⣆⠀⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠘⠳⠚⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠋⠀⠀⠀⠀⠙⠶⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⡄⠀⠀⢀⣾⠻⣧⡀⠀⠀⣠⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢈⣿⠀⠀⢸⣇⣀⣽⠇⠀⠠⣿⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⢀⣉⣛⣉⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣧⠀⠀⢸⣿⠉⣿⠀⠀⠀⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣯⣀⣠⣼⣿⠀⣿⣤⣄⣀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⢿⣇⣸⣿⠉⠉⠹⣿⣤⣿⠉⠉⠉⣿⣄⣸⡟⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣌⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣡⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣯⠉⠛⠛⢻⣿⠛⠻⠿⠟⢻⣿⡟⠛⠛⢉⣿⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠙⠷⣦⣴⠟⠻⣷⣤⣀⣤⡾⠛⠷⣦⣴⠾⠃⠈⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⡈⠉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠉⣁⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡟⠛⠿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠟⠛⢻⣯⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠾⠛⣷⡀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⠀⢠⣾⠻⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⠷⠶⠾⠋⠈⠻⣶⣤⣤⣤⡾⠟⠈⠛⠷⠶⠾⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⡀⠀⠀⣀⡀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⢸⣧⣼⠀⣼⣷⠀⣿⢹⡆⣿⢹⡎⢷⣴⠏⠀⠀⣿⣽⡇⣿⢸⡏⣷⠉⣿⠋⢸⣧⣼⡇⡟⢻⡆⣸⣷⡙⣧⡾⠁
⠀⠀⠸⠇⠹⠰⠟⠛⠇⠿⠋⠁⠿⠋⠁⠀⠿⠀⠀⠀⠿⠾⠇⠿⠸⠟⠿⠀⠿⠀⠸⠇⠹⠃⠷⠾⠳⠟⠛⠧⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠦⡄⠀⠀⠀⠀⠀⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⢀⡟⠀⠀⠀⠀⠘⠄⣀⣴⠇⠀⠀⠀⠀⠠⡊⠉⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢠⢥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⣧⠀⠀⢃⢾⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠄⢺⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡟⠀⠀⢣⣾⠟⠿⠶⣶⡀
⠀⠀⠀⠀⢀⡴⠛⠁⠀⠈⠠⣒⣦⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠢⠀⠐⠂⠉⠀⠀⠀⠀⠀⢁⠤⠖⠛⠁⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠍⠻⠿⡁⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠄⠀⠐⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⢸⡧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠊⠀⡅
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠒⠂⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣼
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠰⡄⡐⠘⡄⠀⠸⣿
⠀⠀⠀⣇⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢸
⠀⠀⠀⢹⣶⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠊⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡤⠋
⠀⠀⠀⠈⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⣼
⠀⠀⠀⠀⡟⠔⠀⠀⠂⢦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⣰⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠀⠐⠀⢀⣀⡀⠄⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢩⡟
⠀⠀⠀⠀⠸⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⠔⠂⠁⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⡏⠛⠐
⠁⠀⠀⠀⠀⠀⠺⠗⣣⠘⢸⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠞⠉
⠀⠀⠀⠀⠰⠀⠀⠀⠈⠛⠢⢄⡁⠙⠛⠳⠶⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠈⠉⠒⠲⠤⣄⠀⠈⠈⠉⠉⠑⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣈⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⠤⠤⠤⡀⢠⠔⠒⠒⢤⡀⡠⠤⠠⢤⡀⠀⣀⣀⣀
⠀⠀⠀⠀⣀⡤⢄⡀⣰⣋⣀⡤⠽⠖⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠓⠾⠥⢄⣈⣱⡄⣀⠤⢄⡀
⠀⠀⠀⡞⠁⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⠀⠘⡆
⠀⠀⠀⣧⠒⠋⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠓⢦⡇
⠀⠀⠀⡇⠀⠀⠀⠀⣷⠊⠉⠉⠑⣄⣠⠔⠒⠦⡀⠀⣠⠤⢤⡀⢀⡤⠖⠒⢤⣀⡔⠉⠉⠉⢲⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⣀⣀⠴⣇⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⡏⠀⠀⠀⠈⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡷⢄⣀⣀⠔⠁
⠀⠀⠀⠀⠐⡅⠀⠀⠈⠢⠤⠤⠖⠙⢆⡀⠀⣀⡼⢧⠀⠀⠀⣠⠿⣄⠀⠀⣠⠞⠑⠤⠤⠴⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠳⡄⠀⠀⠀⠉⠉⠁⠀⠀⠉⢒⠊⠁⠀⠀⠉⠉⠀⠀⠀⢀⡴⠳⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡗⠒⠊⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠙⠒⠒⡇
⠀⠀⠀⠀⠀⡟⠢⢄⣀⠀⠀⠀⠀⠉⠲⠤⠤⠤⠖⠉⠀⠀⠀⠈⠑⠦⠤⠤⠴⠊⠀⠀⠀⠀⢀⣀⠤⠚⡇
⠀⠀⠀⠀⣠⡏⠒⠤⣈⡉⠓⠒⠦⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠖⠒⠋⣉⡠⠔⠊⣧⡀
⠀⠀⠀⢰⠁⡇⠀⠀⠀⠉⠉⠒⠒⠦⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠖⠒⠊⠉⠁⠀⠀⠀⡇⢹
⠀⠀⠀⠈⠢⣈⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⢊⡡⠊
⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠚⢉⣉⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⣖⣒⣶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⣖⣒⡶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠭⢿⠉⠉⠉⢹⠯⠭⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠿⠿⠟⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⠶⢶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢨⠄⢠⣤⠀⠠⠤⠌⠁⢆⡀
⠀⠀⠂⠀⠀⠀⠈⢀⡽⠃⠈⠩⣥⠀⠀⠀⠐⠀⠀⠀⠰⢎⠀⠀⠀⠈⢁⡸⠟⠀⠉⢧⡄⠀⠀⠀⣹⠶⠀⠀⠀⠀⡀⠂⠀⠠⢚⣩⠠⡀⢈⠿⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠐⠃⠃⠐⡋⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠙⠀⠊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠒⠀⠂⠐⠒⠒⠀⠀⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⡀⠀⣤⣤⣦⣶⣿⣷⣤⣦⣤⠀⢀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠉⣁⣀⡀⣀⠀⣄⡈⡉⠁⠀⠀⠀⠀⠀⠀⢠⣦⠶⠸⠇⠻⠅⠻⠁⠸⠭⠔⠶⢶⡖⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣉⠂
⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠁⠉⠉⠃⠒⠀⠀⠀⠀⠈⠀⢀⡀⠀⡀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠦⠀⠐⢂⣴⡿⣛⠻⣿⠟⠛⣻⣄⠀⠀⠠⡆
⠀⠀⠀⠐⠐⠈⢀⠀⣉⢈⡁⣀⠁⠁⠘⠂⠀⠀⠀⠀⠀⢠⣋⡈⡣⠀⢹⠀⢹⢂⡠⢹⡀⡧⡇⡙⡆⠀⠀⢀⠀⠀⠀⣾⣿⣷⠟⣠⣿⣨⡛⢿⣿⡆⠀⠂
⠀⠀⠀⠒⠀⠀⠸⠟⠼⠻⠜⠈⠲⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢀⡈⠀⢿⣿⣃⡚⢛⣇⠾⣃⣾⣿⡇⠀⢀⠈
⠀⠠⢄⣁⠀⠀⠃⠲⠐⠆⠲⠀⠐⠀⠃⢃⣀⠄⠀⠀⠀⠐⠋⠠⠶⠶⠶⣖⠂⣶⣖⡲⠀⠐⠿⠛⠀⠀⠀⠀⠶⠀⠠⠘⢿⣿⠛⣛⣛⣿⣻⣿⠟⠀⠂⠠⠆
⠀⠀⠈⠀⡀⠈⠁⠀⠀⠀⠀⠀⠈⠁⢐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠛⠿⠿⠟⠛⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⢠⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠾⣿⣿⣻⣓⣒⣒⣚⣒⣒⣓⠘⣧⣤
⠀⠀⠀⠀⡀⠀⠀⢀⣉⣉⣉⢁⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠶⠔⡿⠻⠛⠟⠛⠻⠿⠟⠛⢐⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⢀⡀⠀⣀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢴⣦⢶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢀⡼⠋⠀⠐⢲⡄⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⢉⡉⡆⢉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⠐⠼⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⡀⡀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡷⠖⠀⠀⠀⠀⠰⢾⡟
⢀⠀⢀⠀⢀⠀⠀⡀⠀⢀⣀⣀⠀⣀⠀⢀⡀⠀⣀⠀⠀⡄⠀⠄⢠⠀⣄⠀⡄⡄⠀⡤⢀⠄⠠⡄⡄⡄⠀⠀⢀⠠⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⢠⠀⡄⢠⠀⡄⣄⣠⠀⠄⣤⢠⡀⡄⢠⣴⠀⠐⢯⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⡀⢨⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣧⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣅⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠭⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠷⠶⢤⣤⣤⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣧⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⣠⡞⠉⠉⠻⣦⡀⢀⣴⠞⠛⠛⢶⡀⠀⠀⠐⠀⣠⡶⠛⠋⠙⠳⣦⡀⠀⠀⠠⠀⣠⣤⢤⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢷⠶⠟⠉⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠙⠶⣤⠴⠞⠉⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠛⠉⠀⠀⠈⠻⢦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⠶⠛⠛⠛⠉⠉⠉⠉⠉⡉⡉⠛⠛⠛⠓⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣀
⠀⢸⡇⠠⠄⠀⠀⠀⠀⣀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⢷⡀
⠀⠘⢷⣀⠀⢀⣀⣴⠟⠉⠉⠉⠻⢦⣄⣀⣤⡴⠖⠛⠲⢶⣄⡀⠀⠀⣀⣠⣤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠖⢀⣀⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠷⣤⣤⣤⣤⠶⠞⠋⠉⠀⠈⠙⠳⠶⣶⠞⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣴⠞⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦
⣼⣿⠀⠀⠀⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁⠀⢸
⣿⠙⠷⣤⣀⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⣾
⠘⠷⣤⣀⠈⠙⠛⠶⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⢛⣩⠞
⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠈⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⢤⣤⠤⠦⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⢉⣉⣡⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠉⠉⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⢸⢚⡲⠄⡄⣄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠙⡟⠂⢠⣀⢂⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣤⣀⣀⣀⣀⣈⣀⣀⣭⡶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠉⢉⡉⠉⠉⠉⠁⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠁⠠⠤⠀⠀⠀⠤⠄⠐⣀⠀⠀⠂⠐⠀⠀⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠈⠁⠀⣀⠀⠀⠄⠀⠐⢄⢖⡠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣧⣴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⣁⣀⣀⣤⣤⠶⠞⠛⡃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣤⣤⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⡀⠄⢂⠀⠡⠂⠄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠍⠀⠀⠈⢵⡄⠈⠐⠢⢦⣶⣄⣀⣀⢀⡀⠀⠀⣀⢀⣀⠀⣤⠴⣖⡞⢀⠀⠀⠀⠀⠘⣡⠀⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠂⠀⠱⠀⣀⣋⠀⢠⢙⠃⢠⠀⢼⠉⠷⢶⠀⡀⠠⢐⠃⠀⠊⠙⠂⢠⠀⠐⠤⠌⠀⢀⠀⣀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡷⠧⠉⠒⠄⠁⣄⡀⠂⠈⠀⠠⠀⠀⠂⠀⠙⠀⠁⠀⠈⠀⠀⠀⠁⠀⡀⠀⠀⠂⡙⠃⠢⠐⢉⡂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣇⡀⠀⠀⢀⠐⠒⠄⠈⠁⢀⠐⡀⢠⠀⠀⠀⠐⠀⠐⠀⠀⠀⢤⠦⠀⡄⠀⠀⠀⢐⣤⣶⣶⣿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⠛⠻⣶⣦⣤⣤⣄⡂⠀⠀⠀⠀⡉⠀⠑⠂⠀⠀⠀⢈⠀⠀⠀⣀⣠⣤⣦⣴⣶⣿⡿⠛⠋⠁⡐
⡇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠑⠀⢬⡀⠀⠍⠉⠛⠻⠿⢿⠿⠿⢶⣶⣶⣶⣶⣶⣿⣿⡿⠿⡿⠟⠛⠛⠉⠉⢁⠀⢈⠀⠄⠊⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠈⢻⡀⣀⠀⠀⠀⠀⠉⠒⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⣈⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠤⠾
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⣤⡤⣆⠀⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠒⠃⠀⠀⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⢠⡖⠟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢧⡤⢤⣀⣠⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⢀⣀⢀⡦⣄⡞⠲⠾⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠒⠈⠉⠉⢛⠋⠉⠷⢞⢹⡶⠎⠳⢶⠉⢲⠋⡙⠛⢋⠛⠁⠉⠠⠤⠤⠤⠤⠀⣀
⡇⠀⣀⠠⠀⠀⠒⠈⠉⠉⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⣀⠄⠂⠘⢀⠀⢀⡘⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⢠⢀
⡇⠁⠀⠀⡤⠀⠀⠀⠀⠤⠀⠀⠀⠤⡦⠀⠀⠀⠀⢠⠄⠰⡀⠀⠀⠩⠄⡆⠠⠣⠈⡃⠀⠐⠀⡠⠀⠀⣀⠐⡄⠀⠶⣀⠀⣀⢀⠀⢀⡀⢀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡂⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠂⠀⠤⠬⢀⠤⠄⠀⠀⠐⠁⠀⠀⢀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠐⣨⠂⠀⠘⣈⠂⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⠀⠘⠠⠒⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑
⠏⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠙⢄⣠⠴⠚⢉⡀⠙⠒⢦⣀⡠⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄⡞⢁⣤⣶⣄⠀⠙⣦⣾⣿⣿⣷⣆⡜⠁⣠⣤⡀⠈⠳⣀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⡰⠃⠈⣵⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣦⠞⠉⢀⡴⠈⠳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢋⡱⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠉⢀⠔⠋⢠⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠒⢋⡔⣈⢦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠏⡀⢠⠎⢸⠄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠤⠖⡉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⠲⢤⣁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠈⡞⠁⠤⠚⢡⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠁⠀⡇⢲⠀⠈⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⡿⡀⣇⠀⣀⡤⠊⠀⢀⠜⠋⡰⠉⠻⢿⡿⠿⣿⡿⠛⢿⣿⢿⡿⣿⠟⠋⠰⢈⠙⢧⠀⠊⢀⡜⠀⠀⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠘⢾⡦⣄⣀⢀⣰⠃⢀⡴⠃⡟⠀⠀⢻⠞⠁⢠⠏⠀⠙⢦⡾⠁⢀⡰⠃⢸⠀⠀⣇⣀⠀⣀⡠⠞⣡⠋⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⢬⣁⠹⣄⠀⢀⠔⠁⠀⢀⣾⠐⠚⠁⠠⠃⠀⠀⣧⡀⠈⠀⠰⠃⠀⣠⠏⠉⠉⢁⡠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠠⣄⡀⠀⠀⠈⠑⠺⠷⣶⣶⠖⠒⠋⠘⠦⣀⣀⣀⣀⡤⠞⠀⠉⠒⠲⠶⠖⠚⢁⣠⠤⠒⠉⠀⢀⡠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠖⠒⠒⠚⠋⠉⠁⢀⡴⠒⠒⢀⣞⢀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠈⠙⠒⠒⠒⣞⠉⠉⠓⠦⡀⢀⣀⣠⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠖⠒⠂⠀⣮⣀⣀⡠⠞⠀⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⠙⠲⠤⠤⠖⠻⣄⡀⠀⠉⢓⣠⠖⠉⠉⠉⠃⣀⠜⠡⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠓⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⢹⠁⠀⠀⠀⡏⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡠⢄⠀⠀⡠⠤⠀⢀⡀⢀⡀⠀⠀⢀⠀⣠⠲⡄⡠⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣠⠇⢸⠀⢰⠃⠀⠒⠋⡇⡏⠘⠀⠀⡏⠉⠁⠀⠧⠇⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⢤⠼⠀⠀⠀⢠⠃⢹⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠘⣤⠎⠀⠳⠴⠃⠀⠀⠀⠀⠀⠀⡏⠉⠓⠦⣀
⠀⠀⠀⠀⠀⢀⣞⠁⢰⠉⡳⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⢞⠉⡦⠈⡳⡀
⠀⠀⠀⠀⠀⠸⡌⠂⠀⠀⠀⠀⠀⠀⠀⠉⠩⡙⠓⠒⠒⠒⠒⠒⠒⠒⢋⠍⠉⠀⠀⠀⠀⠀⠈⡠⠚⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⡀⢢⠀⠀⠀⡀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢠⠇⡜⠁⢸⠀⠀⠀⠈⠋⠀⢱⠀⠀⠀⠀⢰⠙⢦⡀⠀⠀⢀⠀⠀⠀⣼⠵⠤⣄⠀⣴⡸⡀
⠀⠀⠀⠀⠀⠈⢲⠃⠀⠸⡄⢀⠆⠀⠀⠀⣼⠀⠀⢀⡀⢸⠀⠀⡇⠀⠰⠛⣆⠀⢀⡇⠀⠀⠘⠚⢹⠃⢣
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠑⠊⠀⠀⠀⠀⢹⠀⠀⣼⠐⠁⠀⠀⢧⣠⠇⠀⣿⠀⠈⡇⠀⠀⠀⠀⠸⣆⡼
⠀⠀⠀⡠⠤⡴⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠀⢈⡗⢦⠤⣄
⢀⣠⠞⠧⠴⠃⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠘⠦⠼⠳⣄
⡏⢯⠀⠀⠀⠀⠀⠀⣙⣒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣒⣋⠀⠀⠀⠀⠀⠀⡽
⠘⢆⡓⢤⣀⠀⠀⠐⢅⡨⠂⠀⠈⠉⠉⠓⠒⢒⣶⠶⠶⠶⠶⠶⠶⣶⡒⠒⠚⠋⠉⠁⠀⠐⢅⡨⠂⠀⠀⣀⡤⢚⡱
⠀⠀⠙⠲⢬⣙⠓⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⢧⣠⠇⠀⠀⠀⠀⠸⣤⡼⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⣋⡥⠖⠋
⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⢤⣉⣉⡉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⢉⣉⣉⡤⠤⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⣀⢛⡦⢄⠀⣀⣀⣀⡳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠚⠛⢇⣀⣭⠙⠤⡶⠆⠸⢉⣵⡐⠲⠗⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⠖⣂⠄⠀⢁⡀⠀⡀⢀⠀⡀⣤⠄⡤⠤⣢⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠤⢬⡕⣴⣆⡿⠁⢈⢰⠴⡇⣉⣣⣇⣰⠀⡷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠶⡒⣄⡀⣫⠈⢉⢁⢸⣆⣀⣏⣉⣉⣀⣤⣭⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣁⠒⠤⠤⣌⣉⣈⣂⠉⡙⠉⠉⠈⠉⣉⣉⣠⣥⠴⠞⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣉⡸⣂⠤⣠⡄⢤⣈⡩⣉⣉⣉⢉⣉⣠⢁⠄⢰⡆⠚⢠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⡌⢒⠛⠛⠲⠨⢤⣼⣤⣙⣁⣼⣀⣹⣌⣧⣭⣭⣲⠟⢟⢛⣹
⠀⠀⠀⠀⠀⠀⣀⣠⣸⠧⣄⠉⠃⠙⠓⠖⠶⢲⡤⡬⣀⣩⣭⣥⣤⣤⣽⡴⠶⠶⢛⢋⣩⣀
⠀⠠⡀⠒⠐⢅⠀⠀⠙⠲⢄⣁⠘⠙⠼⠶⠤⢤⣤⣨⣄⣄⡤⣤⣤⣤⣔⣦⢴⠶⠟⣋⣹⠏⠉⢓⠅⣀⠂⠄
⠀⠀⠀⠁⠐⠀⠠⠄⠀⠀⠀⠀⠉⠀⠂⠠⠄⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠶⠒⠒⠉⠁⠀⠀⠀⠁⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣛⣫⣭⣭⣭⣝⣓⠶⣄⡀⠀⠀⠀⢀⡾⠁⣿⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡵⠛⠉⠀⠀⠀⠀⠀⠉⠻⢮⡻⣦⠀⣠⠟⠀⠀⢸⣦⡴⠚⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⣷⠋⣀⡤⠞⠋⣿⠉⢛⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠿⠭⣤⣤⣤⣼⣶⣯⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡷⢦⣄⠀⠀⠈⣧⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠞⣋⣩⣭⣭⣭⣍⣛⠶⣤⡀⠀⠀⠀⠀⣼⢱⡇⠀⠈⠛⠶⣄⣹⣄⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠶⢻⡙⣦⠀⠀⠀⠈⠉⠛⢦⡙⢦⡀⢀⣴⢣⡟⠀⠀⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡾⠁⠀⠀⠻⣮⡳⢦⣀⡀⠀⠀⠀⢙⣦⠻⣟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⢰⡇⡾⠁⠀⠀⠀⠀⠈⠙⠲⢬⣝⣛⣛⣛⣭⡽⣇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡛⢦⣄⣀⣀⣀⣀⣀⣤⠶⢋⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣭⣭⣭⣭⡭⠶⠚⠋




⣏⠉⣹⣛⣛⣟⣛⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣿⣿⣛⣛⣻⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣀⠀⠀⣠⣶⣾⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠀⠀⢹⣿⣿⣿⣿⣿⠋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣿⣿⣟⠉⣹⣿⠋⠁⣰⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠏⣠⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠟⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⡀⠀⠀⣀⣠⣤⣴⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣠⣄⣀⣤⣿⣿⣿⣿⣿⣿⣛⢛⣿⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⡡⠿⢿⡇⣸⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣿⣿⣽⠛⠛⠋⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀


⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠛⠻⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣍⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⣹⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠆⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢹⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣯⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣤⣴⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⢈⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣷⡄⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⡀⠀⣿⡏⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⣠⡄⣤⢤⡀⠀⠀⠀⠀⠀⣠⣄⡀⠀⡠⣄⠀⠀⠀⠀⠀⢀⢤⡀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⢀⣿⠁⡏⠀⡇⠀⠀⠀⠀⢸⣴⣄⡷⣸⠁⢸⡇⠀⠀⠀⠀⢳⣶⠏⣸⣥⣼⡇
⠀⠀⠀⠀⠀⠀⢀⣸⣇⢻⣠⠇⠀⠀⠀⠀⣠⣾⠛⡁⢿⡀⢸⡗⠀⠀⠀⠀⣜⣯⢳⣿⠛⢻⠇
⠀⠀⠀⠀⠀⣠⢈⣉⡉⡉⢁⠄⠀⠀⠀⠀⢻⠶⠾⠟⢈⡧⠚⠁⠀⠀⠀⠊⠳⠶⠋⠈⠳⠮
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠋

⠀⠀⣰⠇⣄⣰⠋⢲⡀⠀⠀⠀⢰⡾⠷⠖⣰⡆⢲⡄⠀⠀⠀⠀⠀⠦⠀⠀⠐⠂⠀⠀⠀⣄⣁⡄⣰⠂⣠⠀⢦
⠀⢀⣟⣀⣿⣿⣦⣾⡇⠀⠀⠀⠸⠒⢶⣄⣿⡇⢸⡇⠀⠀⠀⣠⠀⠀⠀⠀⠀⣔⠀⠀⠀⠉⠰⠀⣻⢀⣇⠀⡿
⠀⠀⠀⠉⡟⢻⡉⣸⠇⠀⠀⠀⠘⠃⡾⠇⠘⠃⠾⠃⠀⠀⢘⠁⠀⠀⣠⠄⠀⠙⠂⠀⠀⠀⢆⣰⠟⣼⣁⣸⡃
⠀⠀⣄⣤⡁⠆⣩⠁⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠀⠀⠀⠘⠲⠚⠀⠀⠓⠀⠀⠀⠀⠁⠉⠉⠈⠁⠁⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠻⢻⠀⣾⠃⣼⡆⠀⠀⠀⢰⠁⢀⡆⡘⠀⠈⠀⠀⠀⠀⢘⠁⠀⢠⠀⠎⢲⠔⠂
⠀⠀⠀⠀⠀⠀⠰⡟⢪⣶⣿⠀⣿⡇⠀⠀⠀⠈⠀⣸⠃⠁⠀⡀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢤⠻⢹⠇⠸⢆⠾⠀⠀⠀⣼⣡⣴⣅⣴⡴⠼⢤⣤⠀⠀⠠⣾⠺⣄⠆⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⢀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡎⠀⠇⠀⢀⠔⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⡌⠙⠒⢼⠠⠐⠛⠠⡟⢀⣔⡿⠒⠒⡤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠡⡀⠀⣠⠏⠸⠁⢈⡒⢢⡀⠘⣄⠀⠁⠀⠀⠀⠀⠘⢏⠉⠁⢈⡸⠁⠑⣏⠈⣧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣣⣱⡯⠣⢴⡆⠙⡤⠸⠊⢙⣶⣿⣷⣶⣄⠀⠈⠀⠀⠸⠶⣈⣁⠴⡄⢴⠁⠈⢦⢠⡯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢤⣾⠑⢦⢸⠀⠋⢁⡔⠛⣾⡿⣺⣘⠽⢼⡽⣦⣄⢤⡧⢊⡥⢖⠛⠃⠀⠱⠀⠣⡀⣁⠸⣆⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⡇⠀⠀⠀⠀⠀⡰⢻⡿⠒⣤⢞⣿⢿⢷⣷⣲⣏⢏⢱⣳⡿⠼⠒⠛⠲⠧⢄⣠⠁⠉⡤⠐⢇⠈⡦⢜⠉⠓⢤
⠀⠀⠀⠀⣠⠊⠁⠐⠀⠱⡀⠀⠀⠀⢠⡀⠀⠀⣼⣯⠮⣗⣏⠿⣻⣟⣿⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠓⡄⠸⠣⣀⡸⠈⠃⠀⠱⡀
⠀⠀⠀⡸⠁⠀⠀⠀⣀⡀⠈⠑⠒⠒⠟⠳⢄⣀⣿⣟⣿⣿⢎⣸⣛⣿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠛⠶⠚⠁⠀⠀⠀⣀⠀⠇
⠀⠀⠀⡇⠀⠀⠃⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⢿⣻⣮⣾⣿⠿⠃⠸⣏⡒⠄⢒⣒⣒⠦⣄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠪⠤⠷⠀⠀⠀⡄
⠀⠀⠀⡼⣄⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⡈⠉⠉⠀⠈⠀⠉⠢⣕⠢⣄⠀⠀⢠⡇⠀⠀⠤⠄⠀⠀⢀⠔⡇
⠀⠀⠀⡇⠈⠳⡌⠀⠄⠀⠠⠤⠀⠀⢀⣀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠙⠲⠭⠿⠟⠁⠀⠀⠀⠀⠀⢠⠃⢀⠇
⠀⠀⠀⡇⠀⠀⠈⢦⡀⣀⢀⡀⠀⠠⠌⢉⡀⡀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠶⠶⠄⠀⠀⠀⡰⠆⠠⠀⠀⠈⠁⣀⠤⠒⠒⠊⠁⣰⢻
⠀⠀⠀⠘⣄⣀⡀⠀⠀⠀⠀⠈⠒⠒⠒⠦⡀⣁⣉⣀⣁⢀⣀⠈⠀⠉⠀⠁⠒⠂⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣴⡿⢦⡀⣰⠿⠛⠛⠉⠨⡇
⠀⠀⠀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠀⠀⠄⠊⠁⠈⠁⠀⠉⠀⠀⢀⡾⠁⠠⠀⡇⢻⡀⠄⢀⠔⠁⣧⣀
⠀⠀⣠⢴⠈⠣⣉⡇⠀⣀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⢒⢶⣄⣀⣀⣀⠀⠀⣾⠀⠀⠀⠀⡇⢸⣢⠐⠀⠀⠀⡧⠈⠓⣄
⢀⡔⠁⣸⠀⠀⠈⡇⠠⡟⢘⠥⡂⢙⢿⣷⣄⠀⠀⠀⠀⠀⣠⠖⠏⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⡧⠀⢿⠀⠀⣀⠠⡷⡏⠀⠀⠀⢀⣠⠃⠀⠀⠈⢦
⡜⠀⠀⠈⣦⣄⠀⠑⠚⠀⠉⠀⠛⠐⠀⠨⢿⡆⠀⠀⠀⢸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠃⣿⢠⠞⠛⠉⣻⠀⠀⠀⠀⠈
⡇⠀⠀⠀⡯⠘⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡎⠀⠀⠀⢀⣇⣸⠎⠀⠀⠀⣹
⢳⠀⠀⠀⠓⢦⡀⠙⢿⣦⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⡇⢀⣠⠞⠉⠉⠁⠀⠀⢀⡴⠉⠀⠀⠀⠀⡸
⠀⠳⡀⠀⠀⠑⠉⠢⣀⠉⠛⠿⠷⣦⡤⠒⠶⣾⠀⠀⢷⣤⣤⣤⣤⡀⠀⠀⣀⣤⣤⡤⠞⠋⠉⠓⣏⠀⡸⠁⠁⠀⠀⠀⠀⢀⠴⡪⠊⠀⠀⠀⢀⡔⠁
⠀⠀⠈⠢⣄⠀⠀⠀⠀⠉⡒⠤⣀⠀⠀⠀⠀⢸⡀⢀⡎⠀⠉⠉⠙⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡀⠄⡪⠁⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠁⠀⠉⠔⠒⠠⢬⡅⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠆⠁⠀⠁⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢄⣀⡀⠀⠀⢸⠁⠀⡧⠋⠁⠈⠩⠟⠭⠬⠬⠛⠋⠀⠈⠙⠀⠀⠁⠀⠀⠀⢀⣀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⡏⠀⠀⢸⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠜⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠄⠀⠤⢀⣶⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣫⣭⡶⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣵⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠙⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⣦⣤⣤⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠁⡴⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣤⠙⠋⠋⣴⢾⡠⠼⠐⡀⠀⠀⢠⡄⠒⠁⡇⠀⢹⢨⡟⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⠰⠀⣀⠀⠀⢿⣷⣮⣻⣖⢶⣀⠂⣸⠁⢀⠰⠁⠀⣼⢾⡅⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢢⠖⠋⠁⠀⠀⠀⠉⠳⡝⢿⣷⣯⣶⣿⣤⣎⣤⣆⡤⢖⣘⣾⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⣿⠿⠿⠛⣉⠉⠉⠁⠀⠀⠀⣀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⡄⣄⡀⠀⢀⡠⠰⢸⣿⡟⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⡇⠁⠚⠣⣀⠜⠣⠀⣹⡿⠃⠀⠀⠀⠀⣡⠀⠀⠂⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⡆⣀⠀⠀⠀⢀⠸⡿⣷⡆⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠃⣟⠀⠀⠀⢸⠀⠗⣿⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡞⢘⣉⢈⠉⠉⢈⡁⠙⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⡇⠉⠁⡑⠊⠓⠉⢺⠉⠀⣿⣸⣧⠀⠀⢠⠀⠀⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠸⠁⠀⠀⡀⠀⠀⠀⢸⠀⠀⠸⣿⠈⠒⣄⠏⠀⠀⠀⠀⠀⠀⡸⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢃⠀⠀⠘⠂⠀⠸⣈⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⢀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠑⠒⠒⠄⠀⢀⣀⠀⠀⠀⣀⣀⡀⠀⠄⠒⠒⠉⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠒⠄⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢄⠠⠊⠀⠠⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠁⠠⠐⣂⠠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣉⡀⢀⢈⠉⣀⡠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁⠃⠉⠀⠀⢀⢠⢄⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⡐⢀⠁⢀⠥⠼⡁⢄⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⡗⡌⢄⡤⢾⢉⠉⠉⠑⡓⠀⠀⠘⡦⢀⣲⠃⠀⠀⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠀⠈⣉⣁⣈⣂⣀⣀⣒⡀⠀⠀⠀⠉⠠⠀⠀⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠠⠤⡀⠀⠀⠀⠠⡀⢀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠒⠤⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠤⠐⠈⠁⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠐⠒⠂⠀⠤⠤⠀⠀⠀⠤⠤⠀⠒⠒⠒⠂⠉⠉⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡀⠀⠀⢠⣓⡄⠀⠀⢀⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠇⠀⠀⣿⣩⡇⠀⠀⢿⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣭⡇⠀⠀⣟⢩⡇⠀⠀⣟⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣵⡇⠀⠀⣟⢥⡇⠀⠀⣟⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇⠀⠀⣿⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣴⡇⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠆⠒⠛⠛⠓⠀⠉⠉⠉⠉⠉⠁⠉⠛⠓⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡖⠉⢢⢀⡴⡄⡎⢸⠀⢸⠁⢸⠀⡇⢡⠀⡎⠀⢱⢠⠒⠀⢴⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠁⠀⢸⠈⡇⠓⠂⢸⠀⠸⠀⢼⠀⢃⠼⠀⡇⠀⣆⢈⠀⠓⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠒⠁⠀⠀⢨⠀⣸⠃⠈⠒⠂⡇⠀⢸⠀⠈⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠤⠤⠆⠒⠒⠒⠚⠛⠉⠀⠉⠉⠈⠁⠒⠚⠒⠂⠤⠤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠒⢤⠀⢀⣀⢀⡊⢦⠀⡰⠋⢱⡀⡎⠱⠀⢠⠊⠑⡄⢀⢤⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠇⠀⢰⠀⢂⠸⣠⠆⠘⠀⢃⠀⢘⠃⢣⢀⠀⢣⠀⠀⡇⢸⠐⠤⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⣄⡸⠀⠀⠀⡇⠀⠸⠀⠹⣀⡸⢸⠀⠈⡄⠀⠣⠞⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⡄⠀⠀⠀⠀⠀⠀⠀⠳⠤⠚⠀⠀⠀⠀⣈⠀⠀⡇⠀⠀⠀⠀⢠⠧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⢠⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⡜⠒⡄⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠈⠲⠤⠍⣐⣒⠒⠐⠲⠆⠀⠀⠤⠤⠤⠄⠀⠀⠐⠶⠒⠒⣒⣒⡩⠤⠖⠁⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠬⠭⠍⣉⣉⣁⣀⣀⣀⣀⣈⣉⣉⠉⠭⠥⠤⠤⠐⠒⠂⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⡄⠀⠀⠀⠀⢠⠃⢆⢣⠀⠀⠀⢀⠇⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡆⢱⠀⠀⠀⠀⢯⢸⢸⢸⠀⠀⠀⢸⢠⠱⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣄⣄⡜⠀⠀⠀⠀⠈⣻⣿⢿⡄⠀⠀⠘⣼⣾⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⣯⢲⡀⠀⠀⠀⡞⠛⢩⣼⠃⠀⠀⡴⠻⠛⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⢸⡇⠀⠀⢸⣴⣿⡗⣿⠀⠀⠀⣷⣰⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢚⣿⡇⣀⡀⢈⣿⠦⣌⣏⠀⣀⠀⢸⣿⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⠶⣤⣶⣾⣿⣻⡏⠭⠛⣿⣿⣭⣿⡯⣑⠢⣿⣿⣭⣿⣿⠿⣋⣿⣷⣶⣶⡴⢶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⢾⣿⣷⣿⣛⣛⠋⠉⠉⠉⣸⡧⢐⣫⣧⠀⠀⢰⡗⠠⢍⣿⠀⠀⠀⣿⣈⠤⣿⠉⠙⠛⠛⠛⣷⣶⣽⣟⣛⣳⣆
⠀⠀⠀⠀⠀⢾⣷⢻⣽⣶⣿⣭⣭⣿⣶⡞⠲⣮⣩⣭⣭⣥⣤⡶⢮⣭⣛⣋⣭⣴⡶⢦⣭⡿⡿⢭⣴⡞⣛⣛⠺⣿⣷⣴⡟⣿⢻⡿
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣯⣚⣿⡸⣿⣿⣿⣿⣾⣽⣶⢶⣾⣿⣿⣶⣮⣻⢯⣯⣭⣿⣶⣿⣯⣿⣷⣭⣿⡿⣿⠿⢿⣿⣿⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡯⣽⣽⠿⣿⣿⣿⣮⣿⣯⣿⣾⣿⣯⣽⣿⣽⣿⣿⣟⣟⣫⣾⣯⣿⣷⣿⣷⣷⣿⡿⣿⣻⣿⣟⡾⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡷⡏⣵⠟⣿⣿⣿⣞⣭⡭⢿⣟⣯⣿⣿⣟⣯⣭⢯⣟⣿⣯⣷⣿⣿⣷⡿⠞⢾⣿⢿⣿⢫⡷⣿⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⣸⠇⠀⢹⡟⣿⠉⣿⡝⣹⠟⠉⣿⣯⡿⠁⠹⣟⣿⣿⠿⣿⡿⢡⡟⠀⠀⠀⢻⣏⢃⡾⠀⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡋⠀⠀⠘⣷⣻⡿⠃⣴⠏⠀⠀⠉⠉⠁⠀⠀⢿⣭⣿⣠⣿⠇⣼⠃⠀⠀⠀⠀⠙⠛⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣘⣻⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⠟⢁⣴⡟⠀⣀⣀⣀⣠⣤⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣭⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⣫⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠩⠻⣯⡛⠿⠗⢒⣺⣾⠶⢾⣖⠾⣿⣿⠿⢟⣫⡶⠞⠛⠻⢮⣟⣟⣩⡴⠞⠉⠉⣇⡀
⠀⠀⠀⠀⠀⣀⣀⣠⠶⣻⣄⣀⡀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠉⠓⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣠⡶⠿⣟⣷⣄⣀⡀
⢀⣠⠴⠞⠋⠉⠉⢿⡟⣽⢿⣯⣟⢛⣶⡶⢦⣤⣤⣄⣤⣤⣀⣤⣤⣤⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣶⣶⣿⣻⣭⣽⣿⣿⣿⡿⠋⠉⠉⠛⠶⢤⣀
⣾⣧⣄⡀⠀⠀⠀⠈⠻⠾⢿⣽⣿⡿⡷⣿⣿⣷⣷⣿⢿⣿⣫⣴⣶⣮⣿⣿⣛⣿⣭⣴⣦⣽⣷⡾⠿⣶⣾⢿⣻⣿⣵⠟⠋⠀⠀⠀⠀⠀⠀⣀⣽
⠈⠛⠿⣿⣷⣶⣦⣤⣄⣀⣀⣀⠈⠛⠿⠿⠻⠷⡿⠿⣿⣯⣿⢾⣿⣿⠿⣯⣭⣽⡽⠿⣿⡿⠟⠛⠛⠛⠛⠛⠉⠀⢀⣀⣀⣀⣤⣤⣶⣶⡿⠟⠋
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⢀⣴⣶⣶⣦⣄⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋
⠀⠀⣴⣿⣿⣿⣿⣦
⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⡀
⠀⠀⠰⢻⣿⣿⣿⣿⣿⣿⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⡿⢈⣿⣿⣿⣿⠀⠀⠙⠛⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠈⠛⢻⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡄
⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣽⣿⣷⡀⠀⠀⣼⣿⣿⣿⣿⣿⣷
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿
⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⡏⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡿⢁⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿
⠀⠀⠀⢻⣿⡇⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⣼⣿⣿⣿⡿
⠀⠀⠀⠈⣿⡇⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣠⣤⣤
⠀⠀⠀⢀⣿⡇⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⢿⣿⡀⠘⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢻⣿
⠀⠀⠀⠘⠈⠿⠷⠂⠀⠻⠿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠻⠛⠃⠀⠀⠘⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⣤⣶⡆⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⣿⣿⢇⣿⣮⡻⣿⢹⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣝⠿⠸⠿⢟⣛⡀⣬⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢚⣫⣭⣵⣶⡘⣿⣿⣿⠇⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⡌⢿⣿⠀⣿⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣄⠛⠀⡟⠁⣼⣿⣿⣿⣶⣦⣄⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣦⣄⠙⠂⠀⠁⠈⠉⠛⠛⠻⠿⢋⣵⣾⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⢟⣩⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠋⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⢀⣤⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣈⣋⣭⣵⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠺⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠀⠐⠳⠂⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡈⠒⠠⠀⠄⠂⢉⡳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢖⠛⡟⠀⣀⣤⣤⣤⣤⣄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⡩⢔⠊⡣⢸⢃⡾⢹⣯⡿⣗⠿⠍⡉⠩⡗⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣋⠕⠚⠟⠀⠀⠠⠀⢸⣸⣧⠀⢋⠂⠘⢯⡽⠿⣶⠷⡸⢿⣧⠉⠲⢄⡢⢀⠀⠀⠀⠀⠀⠀⠈⠣⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠵⠊⠀⠀⠀⠀⠀⠀⠐⣪⣼⣇⢯⡂⢡⠡⡁⠀⠻⣴⠋⡰⠉⡸⣏⣇⠀⠀⠉⠳⢍⡢⠀⠀⠀⠀⠀⠑⢝⢎⢷⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠹⣌⢇⠳⠁⠀⣠⠞⠁⠀⠀⢀⢄⡿⡿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠢⢪⣣⣳⡀
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠙⣦⣁⡤⠚⠁⠀⠀⠀⠀⠀⠲⣱⣇⠀⠀⠀⠀⠀⠀⠀⠈⢣⡁⣄⠀⣀⠑⡱⣵⢷
⠀⠀⠀⠀⢸⢰⠀⠀⢀⣀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⠶⣋⠥⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡪⢝⠢⣤⣀⠀⠀⠀⠀⠀⠙⢮⢳⡙⢎⢮⣽⣾⡆
⠀⠀⠀⠀⢿⠈⢦⡐⠧⣣⠟⠁⠀⠀⠀⠀⣀⡠⠴⣚⡩⡖⠋⠉⠂⠀⠀⠀⠀⠀⠀⣠⢚⠠⠞⢉⣆⠀⠠⠉⠟⠶⣤⣀⠀⠀⠈⣳⡙⠈⣿⣿⣸⠁
⠀⠀⠀⠀⠸⣆⠀⠉⠒⠷⠤⠴⠖⠒⠋⠉⠠⠀⠈⠁⠉⠰⢕⠉⠀⠀⠀⠀⢀⣤⣮⡡⢔⠉⣒⠀⠀⠀⠀⠀⠀⠀⠀⠊⠩⠙⠛⠹⡏⠈⣼⢣⡏
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠈⠙⠳⣦⣄⡠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⡷⣳⠏
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⠀⠀⠀⠀⢀⠤⠞⣱⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠶⠶⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠲⠖⠒⠛⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣰⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠙⠻⠿⠿⠿⣿⣿⠿⠿⠿⢿⣿⡿⠿⠻⠿⠟⠛⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣷⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠋⠉⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠸⣿⣿⣏⠘⢿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⠿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⡟⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠙⢿⣄⢠⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠈⠻⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⡴⠿⠟⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣭⡉⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⣤⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣁⣸⣷⣏⣹⣾⣇⣈⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡙⢦⡀⢹⡆⢰⠏⢀⡴⢋⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⢦⡙⢦⣿⣿⡴⢋⡴⢋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠙⢦⡙⢋⡴⠋⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠙⠋⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⣤⠶⠚⠛⠛⠛⠛⠓⠶⣤⣀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣝⡲⢦⣤⣀⣀⣀⣀⣤⠴⢖⣋⡵⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠒⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡾⣹⣫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣻⡹⡶⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣥⣿⣛⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣞⣻⣧⣽⢻⣆
⠀⠀⠀⠀⠀⠀⢀⣿⢻⣼⠿⣶⠛⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣤⠤⣤⡀⠘⢳⡤⢿⣼⢻⣇
⠀⠀⠀⠀⠀⠀⣿⠻⣼⠟⢺⠇⠀⠀⣠⠞⣩⣭⠉⠻⣆⢠⠞⠁⣴⢶⠀⠹⡆⠈⢿⠚⢿⡼⢻⡇
⠀⠀⠀⠀⠀⢰⡿⣦⣿⠞⣻⠀⠀⠀⣯⡀⣻⣼⠃⢀⣿⡏⠀⢸⡏⢸⡄⠀⣿⠀⢸⡛⢾⣧⡾⣷
⠀⠀⠀⠀⠀⢘⣷⣌⣿⠞⣻⠀⠀⠀⠈⠹⣟⡁⠐⠿⣿⠀⠀⣿⠀⢸⠃⠀⣿⠀⢸⡛⢾⣏⣴⣟
⠀⠀⠀⠀⠀⠸⣯⠙⢿⣦⠟⣇⠀⢠⠖⢛⣻⣿⡄⠀⢹⠀⠀⢿⠀⡼⠀⢰⡏⢀⡟⢧⣾⠟⢩⡿
⠀⠀⠀⠀⠀⠰⣿⠳⢿⣧⣰⠏⣇⣿⠀⢸⣏⡼⠁⢀⡿⣇⠀⠘⠗⠁⣰⡟⣀⡏⢷⣠⣿⠷⢻⡷
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣾⣿⣄⡟⢹⣷⣤⣤⣤⣶⡛⠁⠈⢓⣶⡶⣿⣥⣴⠛⣇⣼⣿⣦⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠉⣛⣧⣠⡷⢻⢡⡏⡾⡛⡿⣩⢹⣧⢹⠳⠜⣿⣦⣟⡋⢉⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠟⠛⢛⣛⣾⡘⢁⣷⣬⠷⠶⠶⣿⣿⣿⣿⣛⠛⠛⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠻⠦⠾⢿⣵⡲⢶⣽⠟⠛⠙⠳⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠖⠋⠓⢮⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠟⠻⡛⣛⡻⠟⠛⠛⠿⣟⣛⢛⡿⠛⠿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⡏⠀⢀⣠⠤⠒⡟⠓⢤⡀⠀⠀⢀⡠⠞⠻⡲⠤⣄⡀⠀⢹⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⠒⠻⣾⠿⠷⠶⢾⡒⠒⠒⠚⢳⡞⠛⠒⠒⠒⡿⠶⠾⠿⣷⠟⢒⡿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣕⢄⠙⣧⡀⠀⠀⢳⠀⠀⠀⡼⢣⠀⠀⠀⡼⠁⠀⢠⡾⠋⡠⣫⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣷⣌⢿⡢⡀⠈⢇⠀⠀⡇⢸⠀⠀⣰⠃⢀⢔⡟⣡⣾⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣵⡝⢦⡈⣆⠀⡇⢸⠀⢰⢃⡴⣣⣮⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠙⢼⣼⠇⠸⣧⡷⠋⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠳⣦⡹⡄⢀⢏⣤⠞⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⢈⣻⣷⣾⣟⡁⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⣤⡶⠞⠛⠋⠉⠉⠉⠉⠙⠛⠳⢶⣤⡀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡌⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣋⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣛⢶⣤⣄⣀⠀⠀⠀⠀⣀⣀⣤⠶⣛⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠿⣿⣿⣿⣿⣿⣿⠿⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢱⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣫⣍⡀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣥⡀⠀⠀⠀⠀⠀⠀⣀⣩⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠑⠚⢿⠀⠀⠀⠀⠀⠀⣯⠉⠉⠙⡏⠀⠀⠀⠀⠀⠀⣻⠳⠾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠶⢾⠀⠀⠀⠀⠀⠀⡏⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⣿⠲⠦⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣄⣀⣸⠀⠀⠀⠀⠀⠀⡿⠢⣄⣀⣯⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⣿⠀⠉⠒⢿
⠀⠀⠀⠀⠀⢀⡴⠢⣤⣀⠀⠀⠀⣀⣀⣀⣿⣦⣄⣀⣸⣄⣤⣤⣤⣄⠀⡿⢢⣤⣤⠷⠤⣤⣀⠀⠀⣀⣿⣄⡀⠀⣸⠀⣀⣀⣤⣀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠉⢳⣴⠛⠉⠉⠉⠉⠑⣦⡝⠋⠁⠀⠀⠀⠈⢻⣧⡞⠉⠀⠀⠀⠀⠉⢧⡞⠉⠀⠈⠙⢿⣿⡞⠉⠁⠀⠈⠙⣦⠞⠉⠉⠉⣷
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⣷⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠷⣄⣀⣀⣀⣾⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠀⠉⠛⠲⠤⠴⠚⠋⠉⠓⠤⠤⢄⣤⠤⠞⠋⠙⢦⣀⣀⣀⣀⡤⠞⠻⢤⣀⣀⣠⠞⠉⠓⠦⠤⠴⠋⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⣄⡀⠀⡇⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡼⠋⠀⠀⠉⠛⢧⣤⠞⠁⠀⠀⠀⠀⠈⠻⣄⣠⠶⠛⠋⠉⠉⠉⠛⢶⡄⢀⡴⠚⠋⠁⠀⠈⠉⠻⣆⣠⠶⠊⠙⠋⠑⠶⣄⣠⠶⠚⠛⠛⠛⠛⢶⣜⡶⠞⠋⠙⠶
⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠟
⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣼
⠀⠀⣟⠉⠉⠓⠚⠋⠙⠶⢤⣤⣤⣤⣤⡤⠖⠲⢦⣤⡀⠀⠀⠀⣀⣤⡴⠖⢶⣀⠀⠀⠀⠀⠀⣀⡤⠾⣄⡀⠀⠀⠀⣠⠞⠳⣤⣄⣀⣠⣴⠏⠀⠙⠒⠒⠚⠉⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠑⠒⠶⠖⠊⠉⠀⠀⠈⠉⠓⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡞⠛⠛⠳⢦⡀⠀⢀⣀⠤⠤⠦⠤⣤⡀⠀⢀⣀⠴⠶⠶⠖⠶⠦⣄⠀⠀⣀⡴⠆⠛⠛⠓⠶⢦⡀⠀⣠⡤⠤⠤⢄⡀⠀⠀⢀⡤⠶⠶⠶⠦⣄⠀⢀⡤⠦⠤⣮
⣯⠀⠀⠀⠀⠀⠙⣶⠋⠁⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⠋⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠀⠙⣦⡼⠋⠀⠀⠀⠀⠀⠘⣷⠋⠀⠀⠀⠈
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠈⠛⠲⠶⠤⠤⠶⢦⣄⡀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⢀⡜⠛⠶⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠉⠛⠓⠶⠶⠶⠞⠛⠁⠀⠈⠳⠆⣀⣠⣠⡴⠞⠋⠈⠛⠶⠦⠤⠶⠛⠁⠀⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⢀⠀⠀⠁⠀⠀⠸⡢⠀⡼⠁⢀
⠀⠀⠀⠀⠀⠀⢀⠀⡟⣀⣋⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⢍⡿⣅⡴⠃⠀⠀⠁⠎
⠀⠀⠀⠀⠀⠀⠣⣱⠈⣼⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⡰⡀⠀⡤⢀⡾⢇⣰⠞⠁
⠀⠀⠀⠀⠀⢐⣠⡄⢂⠴⠴⠒⠀⠀⠀⠠⢤⣄⡄⠀⠀⠀⠀⡅⠀⠀⠀⢸⢸⠁⠀⠀⠀⢁⠅⠀⠰⢄⡤⢜⠃⢀⠀⠠
⠀⠀⠀⠀⡄⠀⠀⡀⣁⠜⠛⡁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⢸⢸⠀⠀⠀⠀⢠⢸⠀⢰⢦⣤⠺⠊⡉⠀⠀⠐
⠀⠀⠀⠀⢈⠐⠊⢀⠃⡰⠊⣡⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠸⠸⠄⠀⠀⠀⡘⡀⠀⠱⠷⡸⠒⠉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠂⠾⠐⠈⠆⢠⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠁⠸⢭⠂⠆⢴⠊⠁⠐⠈⠀⠀⠁
⠀⠀⠈⠀⠀⠈⠲⠔⠸⠦⡁⣢⠀⡴⠅⢀⡀⠀⠀⠀⠀⠀⢰⡼⠀⠀⠀⠀⠀⠀⠀⣠⡣⠂⠀⠰⣇⠀⡆⢸⡇⡀
⠀⠀⠀⠀⠄⠀⠀⠤⢀⡤⠉⠘⠀⠈⠁⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠩⠤⢦⠠⣤⣬⡴⠃⠐⠣⠒⠄⠀⠠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠤⢀⢀⣀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢢⡀⠒⠀⠂⠀⠀⠀⢸⠁⢀⡀⣀⠀⢀⠄⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⢠⠂⠀⠀⢨
⠀⠀⠀⠀⠀⢠⣤⣀⠀⠸⠾⣯⠘⠉⠈⠉⠈⠈⠐⢒⣴⠂⠀⠄⡄⠠⡤⠤⠤⢀⡀⣀⠀⠀⠀⡀⡀⣠⠀⠀⠀⢸⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠃⠛⠋⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⡐⠁⠀⢀⡢⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠉⠀⠀⣖⡾⠃⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⡟⢸⡇⠈⡇⠀⠀⠀⠀⠀⢋⣉⢹⡆⣼⠁⢹⡄⠀⠀⠀⠀⠰⣡⢹⠂⣸⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠉⣇⠸⡇⠀⡇⠀⠀⠀⠀⠀⢁⣨⡞⢁⣿⠀⢈⡇⠀⠀⠀⠀⠀⠒⠳⣄⡿⠐⣻
⠀⠀⠀⠀⠀⠀⠒⠛⠦⠽⠊⠄⠀⠀⠀⠀⢰⢋⣁⣴⡦⠻⠀⠸⠃⠀⠀⠀⠀⢾⣚⣣⡿⠻⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠀⠀⠀⠀⠈⣛⣉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⣥⡀⠀⡬⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⣰⠇⢀⢠⠏⠘⣆⠀⠀⠀⠀⢰⡞⠛⠚⢰⡷⠐⣆⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠓⠀⠀⠀⠀⣁⡤⠄⢰⠇⢠⠆⠘
⢠⣿⣀⣸⢸⠆⠀⢽⠀⠀⠀⠀⠐⠚⢳⣤⢸⡇⠀⠯⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⢸⠀⣾⠀⢸
⠀⠁⠉⣿⠹⡆⠁⡾⠀⠀⠀⠀⠚⠃⢘⠞⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠈⠃⠀⠀⠀⠀⠆⠀⠟⢠⣏⠠⣞
⠀⢀⣀⡉⢀⢈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠉⠊⠉⠋
⠀⠉⠉⠁⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢤⣾⣧⠀⣠⠆⢳⡀⠀⠀⠀⠀⡠⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⣠⡄⢷⠀⣼⠀⠘⡇⠀⠀⠀⠀⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠈⢹⡀⢿⠆⢻⠀⢸⠇⠀⠀⠀⡀⠀⠀⠋⠀⡀⢀⠀⠀⠀⠀⠀⠀⣐⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡐⠌⢃⠚⡀⠘⠡⠛⡀⠀⠀⢸⠡⠶⠕⠶⠳⠙⠒⠒⣶⠀⠀⠀⢻⠏⠱⠔⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣟⣛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢀⣼⣿⡿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⣿⡇⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⣤⣤⣼⣷⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⣀⣀⣠⣤⡿⠛⠛⢿⣦⣴⡟⠉⠙⢻⣦⣄⣀⣀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠉⠉⢹⣇⡀⢀⣼⡏⢿⣆⠀⠀⣸⡿⠉⠉⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣤⣽⣿⣿⣋⣀⣈⣻⣿⣿⣿⣥⣤⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⡿⠿⠟⠋⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠁⠙⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠛⣿⣿⣶⣶⣶⣿⣿⠏⠈⠻⣿⣿⣶⣶⣶⣶⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⢸⣿⣿
⠀⠀⠀⠀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀
⠀⠀⣠⣾⣿⡿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⢿⣿⣷⡄
⠀⠀⣿⣿⡃⠀⠀⠙⠿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⠿⠋⠀⠀⢹⣿⣿
⠀⠀⠻⣿⣷⣤⣀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⣀⣤⣾⣿⠏
⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉

⠀⠀⡀⠀⠀⠀⢀⠀⡀⢀⡀⠀⠀⢀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣯⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⢻⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠀⠞⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠍⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡀⢀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⣀⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣿⣻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⡿⠤⣴⣏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣸⠏⣠⠶⠦⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡿⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢻⠀⡇⠀⠀⣧⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣧⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢱⠀⠀⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡆⠀⢸⣄⠀⣸⠁⠀⣀⣀⡀⣀⡀⠀⠀⣿⣸⡿⢘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢳⣀⣈⣁⣉⣉⣉⣉⠥⠬⣽⣧⣙⡖⡒⢫⣥⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⠉⠉⢹⡇⠀⠀⠀⠀⠘⢦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠛⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡘⠀⠀⢸⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡇⠀⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⠃⠀⠀⢸⠃⠀⠀⡿⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡟⢀⠀⠀⡾⠀⡀⠀⡇⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡈⠀⢠⡇⠀⠁⠀⡇⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⠀⠀⡸⠀⢸⠀⢸⠃⠀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⠇⠀⢀⠇⠀⡇⠀⡸⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠎⢠⠀⡸⠀⢰⠇⠀⡇⠀⣼⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠇⠀⡈⢀⡎⠀⠃⠀⣼⠀⠀⠀⠀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⢀⡞⠀⠈⠀⢠⡇⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠉⠉⠉⠉⠀⠀⠀⢀⡾⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣤⣿⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠓⠲⠶⠶⠶⣦⣤⣀⣀⣀⣀⣾⣃⠒⠒⠐⣰⣿⣤⣤⣆⡴⠟⠓⠒⠒⠚⠃⠂⠀⠀⠀⠀⠀⠛⠶⠶⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠡⡀⠀⠀⢀⠜⠣⡀⠀⠀⢀⠜⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠘⢆⠠⠊⠀⠀⠱⡀⡰⠃⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠈⠟⠀⠀⠀⠀⠻⠁⠀⠀⠀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠘⡀⠀⠀⢀⠃⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢣⠀⠀⡜⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠘⠒⠚⠒⠒⠓⠒⠃⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⡠⠔⠒⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠒⠢⢄⡀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠉⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠈⠉⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⣀⣀⣀⣀⣀⣀⠠⠤⠐⠊⠁


⣀⣀⣀⡀⡀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠁⠀⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⢀⣠⣶⢻⡄⠀⠀⠀⢀⡠⠴⣚⣛⣛⡃⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢀⣰⡾⢳⡼⠙⠋⠀⠀⢀⡨⠔⠒⠉⡸⠹⢹⢙⢷⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡔⢠⠤⣿⡌⠛⠁⠀⠀⡠⠔⠊⣁⣀⠠⠤⠴⠥⢠⣃⣈⡏⠀⠇
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠻⠿⣏⠓⠃⠀⠀⣀⠔⠋⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠄⣀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⡜⡠⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢸⢰⣿⢏⠀⠀⠀⠀⠀⠀⡨⣩⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⢁⠀⠀⠀⠀⡠⣢⠊⠀⠀⠀⠀⠀⠠⢺⡈⢏⢣⡳⢄⠀⠀⡠⢊⠜⠁⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⡾⡄⠀⠀⡰⡵⠁⠀⢀⡠⠔⠂⠀⠀⠀⢣⠈⠀⠙⠦⡙⠮⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠱⡁⠀⠸⣱⢷⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠘⢄⠁⡯⣍⣉⣁⠠⠀⠀⠀⠀⠀⢀⢀⡤⠚⠑⠤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⠤⠤⣄⣀⡤⢾⣤⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡘⠒⠂⠀⠀⠀⠀⢀⡰⠌⠊⠁⠀⠀⠀⠀⠀⠉⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣋⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠄⣀⣀⣀⣀⣀⡀⠼⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠀⢚⣦⠀⠀⠀⠀⠀⣴⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⣀⠀⣿⠛⠛⠛⠁⣰⠇⣸⢃⡴⣠⢀⡴
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⡇⠀⠀⢀⡟⡰⢃⡾⢉⠇⢠⡿⢠⡏⣾⢳⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢸⡇⠀⡈⠿⠉⠀⠸⠇⡾⢰⡏⠈⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⠃⠀⢸⣦⡄⠀⢀⣀⣀⣘⡁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠋⣴⠗⠋⠉⢉⡉⠉⠙⠋⣴⠗⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⢶⣄⠀⠀⡀⠀⡀⣽⠈⡆⡃⣼⠃⣸⠇⣰⠏⣀⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠹⣇⢸⡇⢸⡇⣼⠀⡷⠁⡿⢠⠟⣰⠏⢰⠏⣸⠤⣶⣆⡔⣤
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠙⢦⡀⢹⢸⡇⠸⡀⢸⡇⠳⠘⠁⠸⠃⠿⠀⣿⣰⠏⣰⠋⣿⡠⠛
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⢻⣼⠘⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡧⠐⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠐⠢⢄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣦⡀⠀⠀⠐⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠠⠀⠀⠘⠻⣷⣄⠀⠀⠀⠉⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⣄⣠⣀⡴⠚⠳⠆⠀⠀⠠⠈⢽⣷⣄⠀⡠⠄⠀⠉⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⢻⡽⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡂⢤⣀⠀⠀⠀⠀⠀⠀⣤⣦⣘⣧⣹⣿⣿⣦⡀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠻⣿⠀⠀⠀⠀⠀⠀⠀⠙⣉⠙⠉⠃⠙⠻⣿⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠘⠁⠀⠀⠈⠁⠉⣶⣉⢶⠄⠀⠀⠀⠀⠀⣿⣷⣜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⠀⢿⠂⡀⠀⢀⠌⠉⢲⣒⣛⠷⠀⠀⢰⠿⠟⢿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠈⣷⠀⣤⠁⡄⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠏⠀⠀⠄⣹⡄⠀⠸⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢷⡄⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠐⣿⣯⠀⠉⢑⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠠⠿⠂⠀⠀⠀⠀⠚⠀⠀⡀⠀⠀⣶⡆⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠹⠀⣯⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠠⡆⠟⠲⠚⡃
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⣮⠆
⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⣦⣤⣤⡄⠀⠀⠀⣀⠀⠀⠀⡌⠁
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠻⠿⠿⠟⠉⠀⠀⠒⠀⠀⠀⠀⠐⠚