Love love rose cute Emojis & Symbols

⠀⠠⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡠
⠀⠂⣡⢤⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⡏⣉⡀⢬⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠠⣤⡁⠂
⠀⠈⠉⠈⠐⠠⠀⢽⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡅⠉⠛⣭⠟⢀⢏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⠄⠠⡂⠈⠈⠉
⠀⠀⠀⠀⠀⠱⠀⡀⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠙⢷⣤⡀⣼⣂⠞⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⢆⡀⠐
⠀⠀⠀⠀⠀⠀⠚⢷⣶⠦⣀⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⣶⡴⠄⠠⢽⣍⣉⠠⣴⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⣤⡠⢶⣾⠟⠂
⠀⠀⢀⡤⠖⠋⠒⠲⠾⢝⡻⠃⣢⣶⠶⠦⠛⣷⠖⠂⠹⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⠁⠒⢲⡟⠣⠶⢶⣶⡂⢻⣛⠽⠶⠒⠊⠓⠦⣄
⣠⠖⣻⡶⠖⢚⣓⣦⣄⠀⡿⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢾⡇⢀⣤⣖⣛⠒⠶⣟⡓⢦
⢣⡞⠁⢀⡀⢩⠚⠁⠔⣿⡏⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢉⣿⡗⠄⠙⢮⠁⣀⠀⠙⣦
⢸⡦⡞⢹⣏⣟⠀⠀⠞⣼⣿⠦⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⢾⣿⡝⠆⠀⢸⣏⣿⠻⡶⣿
⠘⣇⢣⡀⠹⠿⣀⣠⢞⡽⣿⡀⣀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⣸⠻⡝⢦⣀⡸⠿⠁⡰⢃⡏
⠀⠈⠒⠳⢤⡴⠯⢴⠊⠀⣹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠈⢲⠬⠳⣤⠴⠓⠊
⠀⠀⠀⠀⠘⠦⣄⡤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⢄⣤⠀⠄⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠼⣶⠀⣏⠁
⠀⠀⠀⠀⢀⡴⠒⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠲⣄
⠀⠀⣀⣤⠼⢦⡦⢴⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣴⠤⣤⠾⢤⣄⡀
⢀⡎⡰⠃⣠⣤⠛⠲⣌⢦⣿⠊⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢺⣤⢏⠴⠚⢣⣤⡀⠣⡘⣆
⢸⡧⢧⢸⡟⣟⠀⠀⣌⢿⣿⠴⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠲⣼⣿⢋⡄⠀⢸⡟⣿⣠⠧⣿
⡼⣆⠀⠉⠉⠹⣄⠀⢬⣿⡏⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⣿⣯⠄⢀⡼⠉⠉⠁⢀⡿
⠱⣌⣱⡦⣄⣙⣚⠿⠖⠉⣯⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢽⡏⠑⠾⣟⣚⣁⡤⣖⣉⡼
⠀⠀⠈⠧⢤⣈⣁⡠⢤⣒⣫⣀⣻⠷⠤⠤⣴⣷⣄⣀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣀⣴⣦⠤⠤⠶⠟⣀⣬⣓⡦⠤⣀⣁⣠⠤⠋
⠀⠀⠀⠀⠀⠉⣀⣴⡿⠽⠛⠃⠀⠀⠀⠘⠛⠁⠀⠀⠉⣿⠷⠒⠈⢶⠶⠀⠴⠿⡍⠀⠀⠀⠙⠓⠀⠀⠀⠀⠛⠫⢿⣷⣄⡈⠁
⠀⠀⠀⠀⠀⢀⠈⠃⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠔⢺⠋⠻⢷⣆⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡌⠃⢠
⠀⠀⠀⠀⠀⠱⠀⠶⠈⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡍⢀⣜⣆⡀⠀⡏⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⢸⠀⠰⠁
⠀⡌⡹⠾⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠍⡉⢉⡗⠃⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠨⠾⡁⠄
⠀⠀⠣⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠣
⣶⣶⡿⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⡄⢠⡄⢠⣄⢠⣄⢀⣤⢀⣤⠀⣤⠀⣤⠀⣤⡀⣤⡀⣠⡄⣠⡄⢠⡄⢠⡄⢠⣄⢠⣤⢀⣤⠀⣤⠀⣤⠀⣤⠀⣤⡀⣤⡄⢠⡄⢠⡄⢠⡄⢠⡄
⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⣶⣿⠀⠀⢀⡤⠤⡴⠋⠺⠉⡷⠛⠛⣶⠚⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⠠⠀⠳⠀⠀⣠⠤⠤⠴⠋⠰⡌⢮⣛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡏⣸⠓⠲⠤⢠⢎⠀⢀⣠⡤⠴⠚⠁⠀⠀⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠸⣇⠿⣄⡀⠀⠁⣁⡴⠋⢀⡔⡴⢁⣤⠶⠶⠶⠾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠘⢄⣀⣡⣤⣌⡁⣀⣒⡭⠚⠐⠩⠒⠋⠉⠀⣠⡟⠀⠀⠀⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢢⣀⡀⢀⣴⠟⠁⠀⠀⠹⢤⣄⡀⠀⠀⣀⣠⣴⠶⠛⠉⠀⠀⠀⠀⠈⠉⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣥
⠀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠻⠶⡴⠶⠛⠁⣐⣒⣂⠤⠀⢀⣼⡟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⣍
⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠷⠀⠀⠀⠀⠙⠶⠞⠛⠉⠉⠙⠛⠛⠋⢀⡧⣤⠖⠶⢤⡀⠀⠀⠀⠀⠀⠹⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⣉⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠒⠲⣄⠀⣼⠃⢯⡙⠂⠀⠳⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠾⣴⠏⠀⠀⠙⠛⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋
⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣯⢔⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛
⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠤⠤⣹⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠊⠉⢻⣆⠀⣀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⢅⣀⣈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡴⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣠⠴⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠙⠃⠘⠃⠘⠋⠘⠋⠈⠛⠈⠛⠀⠛⠀⠛⠀⠛⠁⠛⠁⠙⠃⠙⠃⠘⠃⠘⠃⠘⠋⠘⠛⠈⠛⠀⠛⠀⠛⠀⠛⠀⠛⠁⠛⠃⠘⠃⠘⠃⠘⠃⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⣠⠶⠂⠀⠲⣏⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣾⠀⢸⡃⠀⠀⣦⠀⢸⢷⡀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠸⡄⠀⠑⠒⠒⠁⢀⡞⠀⢷⡠⠚⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⠀⠀⠀⠀⠀⢴⡒⠒⠲⡏⠀⠀⠀⠀⠘⢶⠦⠤⠴⠒⠉⠀⠀⢸⠁⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡀⠀⡇⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣧⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢻⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡾⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⣆⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢧⡀⠀⠈⠳⣄⡀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢀⡜⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠙⠲⣄⡀⠀⢉⣳⠶⠶⣏⡁⠀⢀⣠⠖⠉⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠉⠛⠯⢤⣤⣤⡤⠽⠛⠉⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣦⠟⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢬⣚⡷⡖⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠰⣯⡦⢘⠲⢤⠀⠀⠀⠀⠀⠀⣰⡉⣯⣖⠉⢙⣷⣧⣶
⠀⠀⠀⠀⢠⢏⠏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠙⣆⢳⡀⠀⠀⠀⠀⠀⠀⢸⣀⣈⠧⡔⢚⡭⢴⠋⠀⠀⠀⠀⠀⠚⡯⠙⠳⣕⡉⢽⡟⠁⣧
⠀⠀⠀⠀⠘⢮⡀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠜⣸⠃⠀⠀⠀⠀⠀⠀⠀⠸⡝⠤⠘⠋⠀⣸⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠺⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀
⠀⠀⢀⡴⠚⢉⣩⣥⣭⡓⠦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⣍⣿⠀⢸⠦⡄⠀⠀⠀⠀⣰⢫⠿⣒⣒⣲⡤⣉⣆⠀⠀⠀⠀⠀⠀⣠⢾⠉⣹⣷⣮⠳⣄
⠀⠀⢠⠷⡄⠂⣏⠁⢸⣷⡀⢣⡀⠀⠀⠀⠀⢀⡜⡕⢿⠡⠞⠹⣠⣯⢰⡇⠀⠀⠀⡞⠁⣻⢼⢿⣉⣏⣷⠈⣿⢳⡀⠀⠀⠀⣞⢁⠸⡞⠯⡒⠃⡷⡎⢳⡀
⠀⠀⠘⣇⠙⢄⡈⠩⢭⣴⣃⣠⠗⠀⠀⠀⠠⣏⠘⠷⠶⠷⠾⠖⣋⠟⣸⠁⠀⠀⠀⠙⣄⡱⢌⡓⠌⢋⣴⡵⢃⣠⠇⠀⠀⠀⠈⢞⢧⠙⢀⣒⣮⢡⠷⡼⠃
⠀⠀⠀⠈⠳⠄⠁⢀⣀⡬⠟⠁⠀⠀⠀⠀⠀⠈⠛⢦⣑⣲⣖⣛⡥⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⠙⠚⠉⣨⣧⠏⠀⠀⠀⠀⠀⠀⠘⣎⣙⣉⣩⣁⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⢀⡤⠤⣤⡖⠒⢶⡀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣴⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠖⠒⣦⣀
⠀⠀⠀⢀⡞⣠⢾⣭⣍⡛⢶⡷⣄⠀⠀⠀⠀⢠⠿⢠⣿⡿⣯⠳⡏⢳⡀⠀⠀⠀⠀⣠⠞⠉⣹⣴⣞⣓⢮⣗⠓⡆⠀⠀⠀⠀⢠⠞⠶⢒⣚⢫⡉⣯⠷⣄
⠀⠀⢰⠃⣹⣇⢺⣀⣢⢹⣾⠇⢸⠄⠀⠀⠀⡟⠀⠊⠈⠙⠃⡴⢣⡀⣳⠀⠀⠀⠀⠻⡄⣾⢻⠙⠦⠬⣾⢿⠇⢻⡀⠀⠀⢀⣿⡞⠹⣏⣀⣙⡷⣌⢲⡈⣷
⠀⠀⠸⡄⠹⣌⣻⡶⠶⣚⣽⡤⠞⠀⠀⠀⠀⡷⠴⣌⠲⢤⠤⠄⣘⠁⢹⠆⠀⠀⠀⠀⡟⠻⢬⣳⣄⣊⠥⠞⠶⣞⠁⠀⠀⠘⢾⣧⡘⢲⣭⣭⠶⠋⣸⢿⠁
⠀⠀⠀⠙⠚⢦⡀⠈⠉⢁⡼⠁⠀⠀⠀⠀⠀⠹⣤⣈⣳⣦⡶⠚⣁⣤⠟⠀⠀⠀⠀⠀⠘⢦⣀⣀⡬⢦⣀⡴⠚⠁⠀⠀⠀⠀⠀⢧⠙⠢⠙⣳⣒⣚⢋⡞
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠈⠀⠀⠀⠀⠀⠠⢄⡐⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠆⠀⠀⢠⠐⠂⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡤⠀⠀⠀⠀⠓⣠⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⡀⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠂⠠⠀⠊⠈⠀⠀⠸⡀⠀⢠⡥⣌⠀⡂⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠠⡄⠀⠃⡀⠐⠓⠐⠂⠠⠄⠀⠈⢀⡂⣀⠐⠒⠀⠀⠀⠀⠐⡈⠁⡀⣠⠆⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⢌⠄⣠⠉⠉⡉⠀⠀⡀⠀⠀⠀⠑⠦⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠄⠀⠀⠀⡀⠠⠀⠀⠀⠀⠁⠀⠀⠉⠁⠂⠀⠀⠀⠁⠂⠀⠀⡖⠠⠀⠀⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠐⡀⠀⠈⠀⠈⠊⠁⠀⠀⠠⠐⠐⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠃⢀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠃
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠚⠒⠁⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⢀⠂⢶⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠈⠛⠁⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠁⠌⠁⠀⠐⠀⠄⡄⠀⡀⠤⢈⡌⠈⠁⠁⠀⠀⠀⠀⡀⠀⠀⡴⠃⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠛⠀⠀⡀⠀⠐⠀⢀⠀⠶⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠋⠀⠀⠐⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣄⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠄⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⢆⣴⣿⡿⠟⠛⠛⠛⣛⣛⣛⣿⣿⣷⣤⡀⠀⠀⠀⣠⣴⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣴⣿⢋⣾⣿⠏⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⣁⣤⣤⣶⣶⣶⣶⣶⣶⣭⡛⢿⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣾⣿⠇⣼⣿⡟⠀⣼⣿⣿⣿⠟⠋⣉⣭⣤⣤⣤⣬⣍⠛⣠⠾⢟⣛⣛⣛⣛⠻⢿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣇
⠀⠀⠀⣾⣿⣿⠀⣿⣿⣧⠀⣿⣿⡟⠁⣠⡿⠛⣹⣿⣿⣿⡿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣷⠀⠙⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡀
⠀⠀⢰⣿⣿⡇⢸⣿⣿⣿⡄⣿⣿⠀⠀⣋⡄⣼⣿⣿⣿⣿⣿⣷⣌⢻⣿⠿⣿⣿⣿⣿⠏⠀⡆⢸⣿⣿⣿⡟⢸⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⡇⠘⣿⣿⣿⣷⡸⣿⡄⣼⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣷⢹⣿⣟⣁⠀⣸⡇⢸⣿⣿⣿⠇⣼⣿⣿⣿⣿⡅
⠀⠀⠈⣿⣿⡇⢧⠹⣿⣿⣿⣷⡹⣷⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⢸⣿⣿⡿⣰⡿⢀⣿⣿⣿⢏⣼⣿⣿⣿⡿⣿⠃
⠀⠀⠀⠸⣿⣿⢸⣧⠙⣿⣿⣿⣿⣝⣿⣿⣆⢿⣯⢻⣿⣿⣿⠿⢘⣸⣿⣯⣾⣿⡿⣱⣿⢃⣾⣿⡿⣡⣾⣿⣿⣿⣟⣾⠋
⠀⠀⠀⠀⠙⣿⡆⢿⣧⡈⠻⣿⣿⣿⣮⡇⠻⣧⡻⣷⣝⠻⣿⣿⣿⣿⣿⣿⣿⢟⣼⡿⣡⣾⣿⢋⣼⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⢿⡜⣿⣷⣄⠘⢿⣿⣿⣷⣄⠙⢿⣎⡻⣿⣶⣿⣿⣿⣿⣫⣴⣿⢟⣴⣿⠟⣵⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⢄⠹⣎⢿⣿⣷⣄⠙⠻⣿⣿⣷⣌⡻⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⢟⣫⡵
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡂⠻⣿⣿⣷⣄⡈⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣺⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⣙⢿⣿⣿⣶⣤⣝⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣏⣭⣿⣽⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣯⣾⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣟⣛⣋⣙⣯⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢒⡶⡄⠀⢠⣦⡀⠀⢀⠤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⠘⠒⠁⠀⢸⠹⡍⠲⡅⠰⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⣤⣯⡀⢸⠚⠦⣜⣆⠙⡇⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠫⠤⠤⢭⣙⡄⣠⠌⢻⠆⢥⡀⡤⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠤⣀⠀⠀⠀⠀⠀⠉⠲⣄⣀⠤⠽⢾⣾⠚⢾⣊⣴⡆⠒⠒⠂⠩⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⢀⣔⠁⠐⠯⢘⠝⠷⣿⢗⢢⡉⠲⣶⣶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢠⡾⠉⢉⠖⢒⢿⠀⠶⢹⡦⢍⣀⣀⣭⢹⡝⢿⣿⣏⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠏⠀⠀⠸⣂⣊⡼⢧⡤⡟⠘⡄⠙⠆⠀⠀⠀⣈⡎⢿⣧⠱⡀
⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠹⡄⡇⢸⠀⣎⠙⠀⠈⠀⠈⣿⡇⢣
⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣰⠆⠀⡩⠖⢤⠀⠀⠦⢿⣿⢸⣀
⢰⣇⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢸⠀⢶⠴⠁⠀⠀⢸⠿⣄⠁
⢸⣝⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⣠⢎⠀⢈⠂
⡶⣿⣿⣵⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⠖⣻⡀⢇⠘⣄
⣁⣸⠟⢷⣼⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡄⡀⡀⠠⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣯⣤⠞⣠⣷⣌⢢⡸⡄⢀⣄
⣍⠹⣶⡞⣷⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⡟⡰⢻⠣⢢⡟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣽⣿⠹⢿⡇⠉⠛⠂⠊
⠉⠓⢿⣷⣾⠀⣼⣿⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⣿⡝⠃
⣀⡀⠀⠈⠹⡇⣿⣿⣇⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠸⡕⠼⠂⣔⡓
⣻⣍⠓⣦⡀⢻⣿⣿⣫⣼⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠘⠦⣀⣉⡠
⠟⢩⡟⢻⠟⣲⣿⡿⣡⠟⢀⣀⡀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⣠⠋⣠⣾⣾⡟⢻⣟⣡⠞⠋⣉⣿⡶⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠉⠉⠉⢡⣿⣶⣿⠋⣹⢧⣿⢻⡼⣱⣿⣹⠆⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋
⡶⢦⠀⣾⢿⣼⠇⣰⢿⣾⣇⡼⠻⣿⢋⣉⣙⠲⣤⡟⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁
⠙⠛⠓⠮⣤⠟⢿⡝⢦⣿⣇⠀⠀⢿⣯⣉⣩⡇⠈⣇⣠⣾⠉⠛⣦⣄⡀⠀⠀⣀⣴⡾⠋⠁
⡿⠶⠶⣶⠏⠀⢠⡿⠞⠿⠿⣦⣤⣼⠷⠤⣼⣧⠾⠋⣹⠇⢀⣼⠇⣨⢟⣷⠿⢫⡿⠁⣀⣤⣶⡇⢀⣠⣶
⣠⣤⠞⠙⢦⡀⢻⣀⡀⠀⠀⠈⠻⣄⡀⠀⠀⢀⣠⡾⠛⢿⠛⣧⣾⡷⢋⣁⡴⣿⠶⣫⠟⢋⣼⡿⢫⠟⣽⠀⢀⣀⣤⣤⣄⡀
⠷⠛⠀⠀⠀⠙⣦⡉⠙⠛⠛⠓⣶⣬⣉⠛⠛⠋⠁⠀⢀⡼⠀⣿⠛⠋⠉⢁⣾⣷⣚⣡⡴⠋⣿⣶⡿⠞⢁⣴⣯⡥⠶⣺⡿⠃
⠀⠀⠀⠀⠀⢰⠏⣻⠶⠶⣞⠛⠉⠳⣍⠛⠛⠶⣤⠴⣟⣤⣞⠛⠻⢶⣶⠿⠭⣭⣭⣤⣤⣴⣯⠤⢶⣖⣛⣻⠷⠶⠛⠉
⣀⣀⣀⣀⣀⣘⣿⣁⣠⣔⣋⣹⣷⣾⣛⣓⣶⣶⣶⣟⣉⣀⣹⣧⣄⣀⣹⣷⣦⣤⣀⣙⣷⣶⣶⣶⣤⣈⣿⣿⣝⣓⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣄⣀⢀⣾⣿⠀⣠⣤⣿⡏⠹⣼⢔⠁⠀⣹⠶⢣⠙⠢⢬⠛⠉⣀⡠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠾⡟⡛⢿⠤⠿⠯⣿⣷⢄⡈⢱⠶⠝⢃⣺⠵⠀⡀⢈⡳⡔⠁⠀⠀⣴⣫⢾
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⣷⢤⠻⢟⣉⠆⢶⣾⣿⠓⠊⠀⠀⠀⠈⠍⢁⣼⡇⠙⡆⡈⢫⡃⢀⣀⠿⠷⣿
⠀⠀⠀⠀⠀⠀⣉⢏⢞⡅⣿⣿⠽⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢠⢿⢄⣠⠷⠋⢲⠉⢫⣿⣿⣄⠈
⠀⠀⠀⠀⢠⡜⠇⣎⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡛⢓⡖⠳⣅⠀⢀⣽⠛⠻⠆
⠀⠀⠀⠀⠀⠰⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢄⢱⠵⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠬⣶⡬⢿⣲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⡼⣦⣞⠻⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⣱⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡤⠀⣀⢠⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡰⡸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⣡⢷⡇⠞⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⡡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢦⠚⡁
⡐⠠⣀⠊⣡⢛⠀⠀⠀⣰⢤⠀⡘⠋
⣫⣲⣨⠞⠁⠒⠀⢠⢪⡟⠰⠃⠸⡴⠀⢠⡆⢀⢒⡓⠆
⠀⢠⣽⣴⣄⣠⠴⣯⣰⠓⠛⠳⣘⢃⡠⠟⠀⣀⡅⢘⠁⣠⣤⠶
⠲⠚⠻⠿⠟⠠⠈⢯⡉⠚⢤⣠⡤⠀⠀⠀⠀⠐⢯⠤⠀⠈⣷⠆⠶⢶⡄
⣘⣤⣄⣰⣷⣒⣒⣙⣲⣰⣷⣌⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀⣘⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡞⠉⠳⣖⣲⠾⣷⣾⣉⠉⠉⣻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠁⠀⠀⠈⠳⡄⠈⢻⡻⣧⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⢳⠘⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠀⢀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⡀⠀⣠⠀⡞⠀⣸⠀⠀⠀⣇⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣝⢷⣤⡿⢤⣇⣠⣏⣀⣴⣿⠟⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣏⣹⣧⠀⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⢿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠙⠲⣼⢺⡿⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠼⣆⡀⠀⢸⣿⣃⠞⠁⣹⡤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠉⠳⣼⣿⢃⡴⠋⠁⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡾⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣦⠀⠀⠀⠀⢻⣿⡛⠳⠶⣤⣤⣤⣤⡶⠶⠛⣻⡿⠀⠀⠀⠀⠈⠷⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡴⠟⠀⠀⠀⠀⢹⡏⠛⢶⣄⠀⠀⠀⠀⠀⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢧⡀⠀⠀⢀⡾⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠈⢻⣄⣴⠟⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴⢿⡁⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⡶⠟⠋⠀⠘⠇⠀⠀⢀⣿⠀⠀⠀⣴⠟⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⣿⠀⠀⠸⠿⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⣦⠀⠀⠀⠀⠀⠙⠻⠶⢶⡶⠞⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⣤⡶⣶⠀⠀⠛⠛⠛⠲⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠾⠛⠀⠀⠀⣿⠻⢶⡄⠀⠀⣿⠀⢠⣿⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣿⠀⠀⡿⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉




⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄⠀⠠⡄⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣤⣀⣤⡄⠰
⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣢⠜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠉⣦⠺⡅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠛⢤⠔⡁⢏⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠻⢤⢞⡰⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠳⡤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢻⡾⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤
⣿⣿⣤⣥⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⡠⣊⣽⣏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣧⠀⢰⣶⢄⡀⢰⣿⡿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡦⢀⡗⠀⢸⣿⣾⡅⢸⣿⣿⣤⣤⣤⠀⠀⠀⠀⠀⠀⡄⢠⡶⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣟⠁⠀⢸⣿⣿⢁⣿⣿⡿⢋⣴⡇⠀⠀⠀⠀⠀⢼⠧⣤⡤⠆
⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠘⢿⠟⠋⠉⢊⡀⡛⠙⠃⠍⠁⡠⠀⠢⣈⠣⡀⠀⢠⣇⠴⠶⠒
⠀⠀⠀⠀⠀⠀⠹⡟⠫⢍⣷⠃⠀⠀⢀⣼⠏⣼⢠⣶⡶⠄⢱⣦⣄⠈⠡⢈⣆⢸⣧⡶
⠀⠀⠀⠀⠀⠀⠀⣧⣀⠈⡟⠀⢀⣴⡿⠋⢸⠟⠘⣛⠳⡤⣷⡄⠙⣧⠀⣿⣿⣦⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣩⣀⣾⡟⠀⠀⢸⣆⠘⢿⣶⡷⠸⠷⠀⠃⡰⣿⠒⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⠀⣄⢸⡿⠓⣀⣠⣴⣾⣟⡄⠈⠉⠳⣾⡿⠃⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠻⣿⣦⣽⣿⣥⣾⣿⡿⠛⠻⢛⣁⣤⠤⣶⣟⠁⠀⣦⡾
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣨⡿⠋⠙⠛⠿⠛⠂⠀⠀⣸⡿⣁⣜⡛⠟⠁⣸⠟⢡⣶⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠉⣧⡀⠀⠀⠀⠀⢀⣀⠀⢿⡆⣿⠿⠋⠀⣼⡃⠀⠸⣇⡈⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢤⠖⠒⢁⠶⠦⣴⣿⡁⣷⢰⡦⢸⣿⣿⠠⣌⣳⣀⡀⠁⢈⣿⣿⣮⣵⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢄⡈⣿⣷⣷⠾⣧⣼⣭⣵⣄⣿⣿⡿⠈⢀⣿⣿⠿⠋⠁⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⠈⢷⣾⢋⣴⠈⣿⠟⠻⣿⡧⠼⣿⣷⣦⣼⡛⠁⠀⢀⡶⢋⣉⣩⣽⢽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣿⣿⣿⣖⠛⣾⣿⣿⣗⣠⣿⣿⣿⣿⣿⣆⢰⣿⣴⣿⣿⣿⣿⣸⠇
⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⣿⣍⣹⣿⡿⣿⣿⣦⠎⠙⠿⠛⠧⠈⠉⠀⠘⣿⣿⣿⣼⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡟⢿⣿⠿⠛⣃⢴⣶⠦⠀⠿⠛⢿⣆⠈⣿⣿⣿⣭⣿⣿⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠾⠁⢠⣾⠃⣾⢡⠶⢾⡆⠀⠘⠛⠀⠙⠻⣿⣿⣿⣿⣿⣷⣌⡳
⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡿⢳⡄⠀⣿⠇⠀⠙⢿⣿⣶⣿⡄⣴⣦⡀⠀⠀⠊⠻⣿⣿⣿⣿⣿⡿⠃⣠
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠋⠀⢸⣧⠘⡿⠀⠀⢦⣈⡿⠟⠛⢃⣸⣿⠷⠀⠀⠉⠀⠀⠉⣉⣩⣿⣀⡿⠻⠶⠦
⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣧⠀⠈⢿⣷⣾⡀⠀⠘⠁⢀⣴⠞⠋⠁⠀⣤⣾⡗⠀⢀⣷⣶⡿⢿⣥⡙⠻⠦⠄⠀⠀⢀⣀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢄⡀⢲⣍⠻⣿⡀⠀⢸⣿⣿⣿⣄⣰⣿⠏⠁⢀⣀⣤⣾⣿⡿⠓⠀⢙⣟⣉⣻⣷⣌⠉⣁⣠⡄⢠⠖⠉⠀⠀⠀⢠⠍
⠀⠀⠀⣀⣤⣄⣘⢿⣜⣿⣇⣿⣷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠿⣎⣁⡀⣀⠴⠃
⠀⠀⠀⠈⠉⢙⣿⡿⠿⢛⠿⠛⠋⣿⣦⣤⣤⣿⣿⡿⠿⠿⠿⠟⠋⠀⠀⠀⠀⣠⣤⡘⣿⠿⠿⠿⢿⣿⠛⠁⠄⢀⠀⠉⠑
⠀⠀⠀⠀⣰⣟⡿⢟⠛⠋⠀⠀⠀⢿⣿⣿⠿⠛⣡⠿⣄⠀⠀⠀⠀⢀⣤⡄⢈⣿⡿⠿⠦⢶⣦⣤⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢂
⠀⠀⠀⠀⠉⠉⠙⠳⠲⠚⠂⠀⠀⠀⠀⢀⣴⣾⣿⣷⣻⣿⣶⣶⡾⠛⠛⣩⡞⠁⢀⡠⠖⠒⠻⠟⢂⡀⣀⠀⠘⠒⠒⠐⠒⠂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⠇⠀⣺⣿⣿⣄⡀⣠⣶⠂⣰⣿⣍⠻⣉⠓⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣷⣾⣏⣽⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⠛⢿⠀⠀⠿⣿⣿⣇⠀⠀⠩⣾⣿⣾⣿⣦⠟⠀⠙
⠀⠀⠀⠀⠀⠀⢾⠷⠿⠿⠛⠋⣸⣿⣿⣿⣿⡇⢛⣿⣿⣹⣿⣿⣷⠄⠀⠛⠻⣷⡀⠀⣀⡈⠻⣿⣧⡽⠛⣠⠰⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠈⣀⠻⣻⡿⣽⡇⢸⣿⣏⣙⡿⠿⢷⡄⠲⣮⣆⠹⢿⣿⣿⣿⣷⠨⠷⣶⣂⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣷⠟⠉⣰⠋⢧⡈⣿⣿⠏⠁⠄⣨⣿⣿⡍⢩⣄⣀⠀⠀⠀⠀⢀⡤⣾⣯⠖⢀⣀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠻⠀⠈⠳⢾⡇⢀⣀⠀⠹⣿⡟⠛⣧⠻⣏⡀⡀⠀⠀⠘⠀⠘⠁⠄⠈⠙⢟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣿⣿⡆⢠⣿⣯⣤⢼⣷⡈⠳⣄⠀⠀⠀⠘⢀⡐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠈⢹⡟⠶⠆⠉⠳⠀⠘⢧⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠻⡷⠀⠀⠀⢹⡄⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡗⠐⠋⣠⠀⣀⣤⣤⣤⣌⠙⠻⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⣠⣶⡿⢡⣾⣿⣿⣿⠿⢿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠀⣼⣿⡿⢀⣿⡿⢋⣥⡶⠶⣶⠆⠙⠇⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⣿⣿⣷⢸⣿⠁⣾⡟⠐⠺⢯⣳⡄⢠⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣷⡈⢿⣿⣆⢻⠀⣿⡇⢹⣿⡈⣳⠇⠘⣿⣿⣿⣿⡟⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡙⢿⣿⣆⠙⢿⣦⠰⣿⣿⣦⣬⡍⠁⣤⡀⢹⣿⣿⠋⡀⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣌⠻⣿⡇⠰⣭⣀⣉⣉⣉⣡⣴⣾⣿⣷⠀⠻⢃⣾⡇⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠘⢃⣀⡈⠻⠿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣿⡿⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢰⣿⣿⣿⣿⣶⣦⣭⣍⣉⣉⣡⣴⣾⣿⡿⠁⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⣀⣤⣤⣤⣬⣭⡛⠻⠿⠿⠿⠿⠿⠋⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠛⠿⣦⡐⢶⣶⣶⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⠿⠟⣋⣤⡈⠀⢠⣬⣭⣝⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⢉⣴⣦⣿⣿⡇⣿⣷⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⢁⣶⣼⣿⣿⣿⣿⡇⢿⣿⣿⣿⣦⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠏⢠⣻⣿⣿⣿⣿⣿⡿⠁⠈⠻⣿⣿⣿⣧⡘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠛⠿⢿⣬⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢁⣴⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⡴⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠊⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠛⢃⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣏⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣽⢛⣿⠀⠀⠠⠆⠀⠀⢀⠀⠈⡀⢀⠀⠀⠘⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠋⣥⠀⣄⡖⠃⠀⠀⠁⠀⠀⠀⣾⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⢀⣀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢾⠖⢠⡆⠀⢰⡾⠁⠀⣼⠀⣠⡷⢠⢤⣤⣤⡤⠀⣤⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⢦⡘⢿⠀⣸⠙⢤⣿⣷⣮⣿⢋⣼⣿⣷⣧⣾⣿⡟⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠻⠟⠿⢿⣿⣿⣌⢷⣴⣤⣾⣿⡿⠟⠁⢉⣿⣿⡟⠉⠁⠀⠀⣀
⠀⠀⠀⠀⠄⣀⣀⣀⣈⣰⣤⣤⣤⣤⣼⣿⣿⣿⡆⢿⣽⠃⠀⠀⠀⣠⠊⠁⠈⠛⠋⠳⣶⠊⠀⠛⢲⡞
⠀⠀⠀⠀⠀⣈⠉⠉⢉⣽⠟⠛⠙⠏⠉⣿⠟⡻⣦⡰⠿⠋⣹⠾⠛⢻⣶⣤⣤⣄⣀⠀⠈⣷⠀⠀⠀⡻⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠔⠁⠀⠐⠇⠀⠀⠉⠀⣴⡶⠾⢉⣀⡌⣩⣽⡿⠛⢿⣦⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⣀⣶⠀⢸⠛⢁⡴⢛⣼⣽⣶⣿⢦⡴⠀⠀⢻⢿⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠂⢠⡄⠒⢦⡄⣻⡞⠉⢳⡀⣿⣄⣼⢷⢸⣭⣿⡏⢻⡏⠐⠓⢻⠟⠀⢻⢿⡆⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠺⠛⢛⣶⣷⣿⠂⠀⠈⢿⣿⢻⡏⢾⣼⣽⡿⢅⣏⠛⠁⠀⠃⠀⠀⣷⠸⣿⡄⠀⣀⡞⡠
⠀⠀⠀⠀⠀⢘⣦⣀⣞⠀⢀⣤⣤⡼⠇⠈⠉⣆⠀⠀⢸⡣⡘⢷⠒⠭⠾⠓⢀⣁⠀⠀⣸⠄⠀⡐⠁⠀⠻⣿⢶⣿⣿⠁
⠀⠀⠀⠀⠀⠁⢺⣿⣿⠀⣿⣾⠋⠀⠀⢠⠞⠛⠁⠀⢸⡇⠈⢦⣧⣀⣀⡀⣿⡟⠁⠁⠀⠀⢰⠇⠀⠀⣼⡿⣿⣿⣷⠶⢶⣤⠀⡾
⠀⠀⠀⠐⢉⠛⠉⣡⣬⢷⣿⠉⠁⢂⡀⠈⠛⠲⣤⠀⠻⢷⣄⠀⣶⠈⠙⠛⠳⣤⡀⠀⠀⢠⣿⠀⣴⣼⣿⡽⠋⠀⠀⠀⠀⠘⡟⠁
⠀⢀⡀⠂⠀⠠⢞⡿⢳⠀⠉⠳⡄⠀⠀⠀⠀⠀⠈⢧⡀⠀⠹⣶⣬⠿⠿⠿⠛⠉⠛⠷⣤⣼⡟⢀⣿⣿⣿⡷⠄⠰⣴⣶⠶⠚⠁⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠰⢿⠃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⡤⠠⡤⠄
⠀⠀⠀⠀⠀⠀⣆⠀⣆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠷⠶⣶⣦⣴⣶⣾⣶⣶⠾⣿⡿⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣠⡘⣧⡤
⠀⠀⠀⠀⠀⠀⣿⡟⠋⣀⣀⡀⢠⣤⣤⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠉⠛⠁⠙⠿⣶⣶⣌⠀⠀⣀⢀⣠⡴⠋⠀⠀⠀⢀⡀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠠⠜⡛⠄⠂⣉⣤⣬⣹⣿⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉⠙⠛⠳⢶⣶⠮⣉⠡⢶⣶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠴⢾⣶⢆⣿⣿⠯⢺⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠙⢆⠈⠃⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠉⠉⣽⡶⣛⣻⣿⣿⣷⠠⠤⢴⡀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠁⠀⢁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⠐⠢⣀⠀⠠⣤⡘⣦⣀⣿⣿⣿⣿⣿⠙⣿⡄⠀⠀⠙⠳⣄⠀⠀⣀⡄⢁⡀⠀⠀⣀⡤⢘⡩⢉⠛⠀⡀⠀⠀⠀⠀⠀⠣⡈⣧⡀
⠀⠀⠀⠀⠀⢀⣠⠒⠺⠋⠀⡴⠎⠉⡉⣹⣿⣿⣿⠸⣧⣿⣿⣦⠀⠀⠀⠀⠈⣴⠟⠁⣼⣿⡷⣾⣿⠞⠛⣯⠙⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣠⠋⡌⢀⣤⠀⠖⠀⠀⢲⣿⣿⣿⣿⠿⠖⠻⢿⡿⠀⢀⣁⣡⠤⢶⣧⣄⡀⢱⣿⣿⣯⠛⢧⡉⠉⠀⠉⠁⡀⡴⢆⣀⣴⣦⣤⣤⣀
⠀⠀⠀⣾⠃⠚⠁⠉⠀⠀⠀⠀⠀⣿⣿⣿⠟⢻⡦⠀⠀⠈⠳⣦⣉⣽⠄⢀⡼⢿⣿⣁⠞⢻⡇⠀⢳⡄⠙⢦⡀⣠⣾⣶⣴⠟⠋⢉⡁⠉⠀⠀⢱
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⡏⠠⠿⠃⣀⠀⠀⠀⠉⠀⠀⠀⢸⡇⠈⢻⣿⠀⠞⣿⣄⠈⠀⠀⠈⠻⡈⠙⠻⠷⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⠁⠀⢰⡏⠢⢄⣀⡀⠀⠀⠀⢮⠙⠄⠀⠉⠀⠀⠈⠏⢻⡆⠀⠀⠀⢹⣆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠰⣤⣄⣙⠋⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠲⢰⣼⠇⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡿⣉⣩⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⠌⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⢰⠃⡞⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠟⠈⡱⠋⠀⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠘⠰⠁⠀⠀⢸⡇⠁⢀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⠔⠊⠉⠉⠉⠙⢭⡉⠑⢦⡇⠀⢀⠀⠀⠀⠀⢠⣃⠴⠓⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⡠⠚⠉⢀⡀⠴⠥⢄⣀⣀⡀⠀⠀⠀⠙⡄⠀⠹⣄⠘⠶⠤⠤⠰⠋⠤⣖⠉
⠀⠀⠀⠀⠀⠰⡎⠉⠀⠀⠀⠀⠀⠀⠉⢢⠞⠁⠀⢠⠋⠀⠔⠀⠉⡀⠀⡀⠈⠤⡀⠀⠘⡄⠀⠱⣉⡶⠒⠒⠒⠲⢤⡀⠃
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠐⠢⢤⣀⣹⡄⠀⠀⠈⠀⣠⢆⢀⢪⠄⠀⢈⡆⠀⠘⠆⠀⡇⠀⠀⠏⠉⠒⢤⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⣠⠔⠋⠀⢡⠀⠀⠀⠰⡏⢆⠙⠤⠤⠖⢈⣃⠄⢈⠀⣠⠃⠀⠀⢰⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⢑⡞⠁⠀⠀⠀⠀⡆⠀⠀⢀⠆⠈⠢⡀⢀⠀⠈⠁⠀⢸⡜⠁⠀⠀⠀⡎⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⡄⢠⠖⠉⠀⠀⠙⣄⠀⠸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡃⠀⣀⢠⡌⠀⠀⠀⠀⠀⢰⣆⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠦⢤⣄⣀⣀⣱⠁⠀⠀⠀⠀⠀⢈⠳⣬⡄⠀⠀⠀⠡⠀⠀⠀⢀⡠⠖⢋⠔⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠧⠒⠢⡀⠀⠀⠰⠛⠓⠲⣄⠀⠀⠈⠁⠓⠂⠉⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣼⣡⣔⠈⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⣀⣀⣃⠀⠀⠀⠀⠀⠀⠈⠻⢔⡂⠤⠤⢀⣲⡞⠉⠀⠀⠀⠀⠀⣀⡤⡶⠋⠀⠀⠈⠙⢦⣠⠞
⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⢈⠟⠈⠒⠒⠒⠛⠉⠁⣴⠛⠒⠄⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⡀⢀⡤⠔⠒⢺⣷⠤⢄⣀⣀⣀⣀⣀⠠⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠋⠀⠀⡴⠃⠈⡄⠀⠀⠋⠀⠀⢸⠓⠦⢤⣀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠓⢤⣀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠜⠁⠀⠀⣿⢄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣰⠇⠀⠉⠓⠶⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣨⣤⣙⣶⣴⣾⣿⣿⣿⣿⣯⣿⣯⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡇⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣅⢸⣿⠀⠀⠀⣠⣾⣿⢟⡿⠟⣿⣿⣿⣿⡿⠿⢿⣿⣿⣼⣿⢏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⣠⣿⣿⣷⣿⡵⠿⠟⠉⠻⣅⣉⣴⢸⣿⣿⢹⠏⣾⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢇⠀⢠⣧⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⢎⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣠⡴⣿⣿⣼⣄⣾⣿⣷⣄⠀⠘⢷⣦⣄⡀⠀⠀⠀⣀⣀⣤⢻⣿⣿⠿⠛⠿⢟⣽⣿⣿⣿⡿
⠀⠀⠀⠸⡀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣆⡀⠘⢻⣿⣿⣶⣾⣿⡿⣱⡿⠋⠁⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⣦⣀⠙⡻⢿⣿⣿⡟⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣀⣀⠀⣀⠀⠈⣉⣫⡽⠟⠛⠛⠛⠿⠷⣶⣾⠿⠿⠿⣿⣿⣿⣿⣿⣁⣀
⠀⠀⠀⢀⣤⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⡏⠀⠀⠀⣀⣠⣴⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣿⣿⣿⡿⠿⡿⠦⣀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠉⠁⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡷⣄⢀⣠⣴⣾⣿⢿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢠⠿⠛⠛⠻⠿⠿⡿⠿⠿⠛⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡿⠋⠁⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⠛⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⢳⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⣿⢸⠇⠔⣽⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡓⢄⠀⢹⣿⠋⣀⢸⣿⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⢟⣫⠴⠶⠶⢷⣍⠈⢷⣀⢡⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⢀⡾⢁⣤⡤⡒⡠⣟⢦⡀⠈⡎⠹⣏⡀
⠀⠀⠀⠀⢠⣤⢞⡵⢇⣧⡘⢩⣿⠀⡇⣁⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠘⢿⠁⠀⠀⣌⠃⢺⠏⡸⢁⠿⢺⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠈⣵⢤⣊⡉⠉⣀⡴⢃⡎⢠⡟⢀⠊⡣⠀⡀
⠀⠀⠀⠀⠀⠐⡇⠀⠀⣹⡟⠛⠉⣉⣤⠟⠉⢉⡼⣡⢾⣿⡄
⠀⠀⠀⢀⣴⣣⡱⣄⠀⠈⠉⢉⠟⠀⠀⢀⣀⡿⢰⢃⣿⣿⣧
⠀⠀⠀⠘⠛⠿⠿⠾⠵⠒⣂⠓⣒⣦⠥⠤⠤⠅⠇⢠⣿⣿⡏⡠⢤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣧⠙⠿⣻⣾⠿⠿⠶⢌⣻⡟⠀⢴⣿⡿⠁
⠀⢀⣠⣤⠴⠶⠤⠤⣄⠁⢿⣯⠤⡼⠯⣤⣀⠀⠀⠀⠈⠉⢹⠚⠋
⠀⠀⠙⣿⣿⣿⣷⣦⣠⢠⡟⠁⠀⣠⠦⠤⢌⣙⣶⡖⠦⣄⠀⠙⢦⡀⠀⢀⠴⣲⣿⡇
⠀⠀⠀⠀⠙⠿⢿⣿⣿⣽⣧⠖⡿⢁⡴⣾⡛⣝⢯⣿⣄⠈⢳⡤⢤⡷⠐⢃⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡠⠋⣸⡇⢸⡇⣯⡾⣿⢿⣿⣾⠏⡟⠀⠀⣿⠈⢿⠀⢼⡿⠟⠁⠀⠀⠀⠀⢀⡴⢦⢤⢄⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⢿⢳⣴⡗⣸⡿⠵⢋⣼⢋⡴⣧⣀⡴⡿⠀⢸⡄⣀⡀⢤⣀⡀⣀⣀⠤⠾⢦⣖⣚⣪⠅
⠀⠀⠀⠀⠀⠀⢸⣆⠀⢸⡀⠈⢷⣀⣈⠿⠉⣰⠟⢀⡿⠀⣰⠃⠀⣼⢁⣴⣶⣿⡿⣱⠯⣧⠤⠴⢶⣤⣬⢯⠶⠆⠠⢄⣠⣤
⠀⠀⢀⣤⣖⣈⣜⣧⠀⠀⠙⢦⣤⠬⠤⠶⠛⢁⣠⠞⣡⠞⠁⣠⣾⡟⠾⠿⣟⡋⢰⣿⡶⢯⡼⣀⡾⢕⣢⠌⣷⢠⣶⣿⠟⠃
⠀⠀⠀⠙⠻⢿⣿⣮⠳⡀⠀⠘⠳⣶⣶⣶⡾⠿⠗⠋⠁⠀⢀⣿⣿⣤⡤⣄⠈⠙⢦⡉⠑⠺⡛⠓⠺⡉⢀⣛⣁⡉⠛⠲⢄⡀
⠀⠀⠀⠀⠀⣠⠞⣀⣤⣴⡀⠒⣏⠀⠀⠙⢻⡷⠶⠴⠶⢒⣽⡜⣿⣿⣿⣿⣿⣦⣄⠹⣆⠈⢿⣿⣶⣜⢎⢿⣿⣿⣿⣷⣦⣽⣄
⠀⠀⠀⠀⣴⣡⣾⣿⣿⠟⡇⣾⣾⠲⢤⣤⡿⠀⠀⢠⢱⣿⡿⠁⠈⠻⢿⣿⣿⣿⣿⣷⣼⣇⠀⠙⠻⠿⠿⠄⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠱⡿⠋⠀⠀⠀⠀⠀⠀⠘⡿⠋⠁⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠐⠒⢦⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢼⠁⠀⡀⠀⠀⢀⡠⠂⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⢰⠀⢷⠀⠀⢀⡎⠀⠒⢋⡡⠔⠂⠓⠀⠀⢠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⠀⠀⡆⡼⣠⡏⠀⠀⠈⠀⢀⡀⠁⡀⣀⡀⠀⠀⠀⠢⠳⢄⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠛⣿⡦⠀⢰⠂⢸⡀⠀⠊⣳⡀⠈⠴⢆⠤⣀⠀⠈⠉⠀⡣⠠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠀⢹⠀⢳⡷⡡⠈⢆⡸⢷⡀⢣⣿⢣⡀⠐⠒⠲⡄⢡⠀⠀⡆⠘⣀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⣿⣿⠻⡀⠀⢿⠹⣆⠈⢷⣤⣥⡈⣿⣶⡙⣶⣗⠀⠈⠉⠀⠀⠁⠀⠈⠙⢢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠈⢙⣿⣶⠀⠀⠈⠓⠿⣦⡈⢯⡛⠭⠛⠻⢿⣾⠾⢷⣼⣠⣇⡀⣀⣀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡴⣻⠁⢻⣦⣄⠀⠀⠀⠀⠙⠮⣧⣶⣤⣦⢀⣉⣁⣂⢀⠈⣭⣽⣿⡏⠀⠀⠸⠀⠀⢸⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⣿⣾⠀⠀⣿⣯⣿⢦⣕⣒⣄⠀⠉⠻⢷⣄⡀⠢⢤⣄⠈⢈⠈⢉⣁⣠⣴⣿⠄⠀⢀⡿⠁⠉⠉⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⢿⣿⡀⠀⠘⣿⣿⡇⠈⣁⣽⢷⣤⣤⣤⣈⠉⠛⠦⣄⣀⠀⢏⣿⣿⣿⣻⠋⠀⠀⠊⠁⠀⠀⠉⠀⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢈⣿⠏⢸⡿⣇⠀⠀⠈⠻⣗⣀⣿⣿⣤⡀⠈⠙⡟⠛⠒⠲⡾⣯⣟⣿⡿⠿⠛⠁⠀⠀⡀⠀⠀⠀⣸⡦⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⡟⣏⡔⠀⣾⣿⣷⣄⣀⠀⠈⠻⣟⣋⣹⣛⠻⠶⠾⠿⠤⠧⠿⠽⠿⠞⠛⠛⠁⠀⠀⠈⣥⠀⠀⢰⣧⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡏⠙⢻⣷⣔⡝⠹⣻⠛⡿⣿⣿⣶⣄⡉⠻⢯⣍⠒⠤⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⢴⣶⣶⠏⣱⠚⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⡇⠀⠈⢻⣿⣿⣦⣻⣔⣏⡿⣿⣿⣿⣿⣿⣷⠎⡇⠀⢹⣶⣤⢏⣿⣿⣿⣿⣿⡷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣶⣶⡀⠻⡏⠉⠍⣹⢿⣏⣿⣿⣿⣿⣿⢿⠀⣷⠀⠠⣸⣏⣾⡿⠿⠛⠋⡉⠈⠁⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣾⡄⠀⠴⠊⣿⣿⣿⡟⣵⣷⣿⣆⠸⣤⡶⠛⣩⡶⠶⠖⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⣷⠙⡆⠀⢠⣿⣿⣟⢟⣻⣧⡿⠿⠤⢟⣒⡉⠁⠀⢀⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡟⣼⣶⣤⣘⣿⣿⡶⠚⠉⠀⠀⢠⣶⣟⣿⣿⣶⣾⣿⠯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠈⢏⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠠⠶⢶⣶⡶⠶⠿⣿⣿⡿⡿⠿⠟⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣀⣸⡷⣶⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⣀⣀⣠⣾⣿⠿⠋⣽⠏⠙⣿⠟⠻⠿⣿⣿⣿⣧⣽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⣼⠏⠁⡸⠃⠀⠀⠀⠀⠀⠀⠈⢻⡍⢿⠸⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣧⢻⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠙⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⢀⠂⠀⠒⠁⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣀⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠓⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠁⠫⠀⠸⠀⣦⠀⢀⡥⠀⠈⠀⠀⠀⠀⡀⠀⠀⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡖⠀⠘⡔⠄⠸⣄⣁⣸⣧⡑⣤⠀⠀⠂⠀⠀⠀⠒⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⣹⢷⠀⠀⠈⠚⢦⡹⡝⠉⠛⠳⢆⠳⠶⢴⣄⣠⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣮⣣⠈⢿⠦⣄⠀⣀⠉⠳⣶⡒⠂⠀⠐⠀⠰⠶⠟⠁⣠⡀⠀⢠⡆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣯⢿⡇⠀⠸⣇⣦⠙⠉⠧⣄⣀⠉⠓⠤⢉⡀⠀⢲⣾⡟⠚⠀⠀⠋⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⡏⠨⢻⡄⠀⠘⢷⣀⣴⣠⣀⡀⠉⠃⠀⠰⣻⡿⢿⢛⠁⠀⠀⠀⠀⠀⡴⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⢧⡄⠀⠸⠿⡶⣤⣤⣉⠣⢴⡋⠉⠉⠛⠚⠈⠈⠉⠉⠁⠀⣀⣀⠦⣀⢸⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠹⣷⣄⣀⡀⢇⢿⣿⣷⣶⣮⢳⠀⢠⢈⡐⢲⣶⣶⣶⣮⠾⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⣶⣆⠸⠏⠉⠙⢿⣰⣿⡿⢿⢿⠀⡆⠈⣼⡰⠿⠛⠋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⣟⣿⣿⡻⣄⠀⢸⣿⣿⠡⡿⢿⣆⢱⡞⠡⠔⠊⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⠇⡈⣀⢸⣿⣧⠖⠋⠉⢁⡴⣿⢦⣤⢾⠯⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣷⣭⣿⣇⠹⠀⢀⠀⠀⣿⢟⢻⣿⡿⠃
⠀⠀⠚⠛⠁⠁⠉⠛⠚⠓⠉⢁⣾⣿⢿⡿⣿⣿⣿⡲⣦⣾⠛⣿⣿⣷⡿⠛⠁
⠀⠀⠀⠀⠀⢤⣶⠶⠴⠖⠚⠋⠉⢀⡾⠀⡜⠁⠈⠉⠉⠛⠻⡟⣏⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠌⠀⠀⠀⠀⠀⠀⠀⠙⣼⣜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⢂⠢⠤⠤⢄⣀⢤⣤⣶⠶⢷⣶⣶⡶⢦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⡸⠁⠀⠸⣧⠀⠀⠀⠹⣭⣪⣤⡴⠟⠉⠉⠉⠙⠳⠭⠿⡂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢀⣠⡇⠀⢀⣤⡿⠁⠀⢀⣴⢋⣀⣀⣠⣤⢤⡀⠀⠀⠀⠀⠀⠈⢦⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⢠⠋⠈⣿⡀⣯⣿⣧⢠⣤⡼⢹⡅⢾⣿⣯⣽⣷⡗⢤⣤⣤⡀⢀⠀⠀⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢴⡁⠀⠀⠘⣇⢻⡗⣼⠀⢷⡶⠋⠈⣿⣿⣽⣻⡏⣿⡌⣿⠁⠉⠛⠛⠢⣸⣷⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣧⠀⠀⠀⡏⣸⠇⢿⣦⠀⠙⣦⠀⠈⠙⣏⣟⠹⣿⢃⡿⠀⠀⠀⠀⣰⢿⠋⠀⠀⠀⠀⢸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢿⡀⠀⢰⡇⠀⠀⠀⢰⣿⣇⠀⠙⣆⠀⢸⣧⣀⠠⣿⢸⣠⣿⣾⣁⡀⠀⣠⣦⢿⡞⠀⠀⠀⢀⡤⠊⠱⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⢷⡄⠀⠻⣄⣀⣀⠀⠙⢿⣷⣦⠈⠓⠒⠛⠿⠶⠖⠛⠋⢉⡉⣈⠇⢠⣿⣿⣿⡇⠀⠀⡴⠛⠀⠀⡴⠃
⠀⠀⠀⠀⠀⣀⡸⠦⠤⠀⠀⢀⣀⣿⣦⠄⣀⠈⠙⣿⠑⣦⠈⢻⣆⣀⣀⣀⡀⢀⠠⢐⣬⣶⣶⡶⣶⣿⠿⠟⠋⠀⠀⣼⠃⠀⠀⣸
⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢸⣁⠀⠀⠀⣀⣤⣷⣦⣿⣧⣼⣷⣄⣟⡽⠛⠋⠛⠿⠿⠛⣡⡾⢋⡾⠋⠀⠀⠀⢀⣤⠾⠁⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠸⠭⣤⣤⡉⠙⠛⠀⠀⢀⠀⠀⠀⣠⣿⡡⠋⠀⣀⣠⣴⠾⠟⠁⢀⣠⡴⠚⠛⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠈⢳⡆⠀⠀⠀⠈⠻⣿⣷⣦⡀⠀⠀⠀⠙⠢⣄⣀⠀⠱⢦⡭⠿⡿⠿⠯⠤⠚⢻⣿⣿⠶⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣠⣼⠛⠛⠻⣦⡀⠀⠀⠀⠀⠉⠛⠻⠶⣶⣶⣾⣷⣦⣄⡀⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⣧⣠⡞⠛⠻⣦⣄⡀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠙⠶⣤⡼⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠙⠿⠿⣿⡿⠿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣶⠶⠶⠶⠤⠤⢤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠚⠛⠛⠛⠶⠶⠶⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣷⣬⣿⣿⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣟⠛⠛⠻⠛⢟⡋⠉⠉⠛⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣌⣷⣴⣦⣜⣥⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣾⣟⣖⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢠⣶⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⢄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⡿⣿⣿⣿⣿⡿⠿⠟⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠿⠿⠟⠟⠉⠈⠋⠋⠒⠀⠙⠣⠉⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠉⠀⠀⠉⠙⠻⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠀⢀⣠⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠋⠁⢨⣿⣁⣴⣿⢿⣿⣿⠿⠟⠛⠛⠿⢿⣶⣤⡀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣷⣦⣀
⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⣠⣿⡿⠟⠉⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄
⠀⠀⠀⣴⣿⡟⠉⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣴⡿⠁⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⣼⣿⠁⠀⢀⣴⡿⠟⠉⢉⣀⣀⣹⣿⣷⣌⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⣾⠏⠀⢀⣾⠿⠏⢤⣍⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠈⣿⡄⠀⠀⠀⢸⣇⠀⢸⣿⠀⠀⢸⡿⠻⢷⣄⢹⡇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏
⠀⠀⠀⢠⣿⣿⣿⣧⡀⠀⠀⠘⢿⣦⡀⠀⠀⢻⣆⠸⣿⠀⠀⢻⣇⠀⠀⢿⣾⠇⢠⣿⣇⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣿⣦
⠀⠀⠀⣾⣿⠀⠈⠛⢿⣦⡀⠀⠀⠻⣿⣆⠀⠀⠻⣿⡟⠀⠀⠘⢿⣶⣤⣤⣥⣶⣿⣿⣿⡄⠀⠀⠀⢀⣴⣿⣿⠃⠀⠹⣿⣷⡀
⠀⠀⠀⢿⣿⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⢿⣷⣤⡀⢹⣷⠀⠀⠀⠀⢀⣀⣼⣿⠟⠁⠘⣿⣷⠀⠀⢀⣾⠟⢹⡟⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⢻⣧⡀⠀⠈⣿⡏⠙⠻⠿⢿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⢸⣿⣧⣠⣿⠋⠀⣼⡇⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿⣄⣀⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⢠⣿⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠙⠛⠻⠿⣶⣤⣄⣀⡀⠀⠀⠀⣀⣠⣴⣿⡿⠋⠀⠀⢀⣾⡇⠀⠀⠀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠛⠋⠁⠀⠀⠀⢠⣾⡿⠁⠀⠀⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠹⣿⣶⣾⣿⣿⠿⠿⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡷⠶⣶⣶⣶⣿⡿⠟⠋⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣤⣤⣄⣤⣤⣤⣶⣶⣶⣤⡀⠘⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠟⠛⠉⠉⠁⣀⠀⠀⢀⣩⣭⣿⢿⣷⣿⣿⣿⡷⣶⣤⣤⣤⣤⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⢿⡏⠁⠀⠘⣿⡟⠛⢶⣤⡄⠀⠀⠀⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠠⠤⢤⣴⡿⠋⠀⠈⣧⠀⠀⠀⣿⠀⠀⠐⠈⠙⣷⣄⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢷⠀⠀⠀⠉⠀⠀⠀⣿⡄⠀⠀⠀⠀⠃⠙⣦⡤⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠉⠉⢳⣿⡟⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠤⠤⣴⣿⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣦⡀⠀⠀⠀⠀⠉⢿⣦⠀⠀⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣾⡿⢻⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠙⠻⣿⣷⣦⣄⣀⠀⠀⠹⢷⡀⠸⣿⣧
⠀⠀⠀⠀⣼⣿⠁⠀⠀⢩⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣶⣤⣽⣦⣽⣿⠇
⠀⠀⠀⢠⣿⡟⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠁
⠀⠀⢰⣿⡟⢁⣠⡾⠋⠀⢀⣀⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠸⢿⣿⣿⣿⣶⣿⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣤⣄⡀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⠀⠀⣀⣤⣴⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣇⠀⠀⣾⡦⠀⣤⣼⣿⣿⡿⠿⠿⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣬⡿⠟⢿⡆⢰⣿⡇⣠⣿⣿⠟⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠘⣿⣿⠗⡂⠚⠓⢾⠟⠱⠿⠟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⢻⡟⠀⡔⠀⠄⢳⠈⡄⠸⠀⡵⢊⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⣼⣿⣿⣿⣿⣧⡱⠊⠠⣄⣠⢂⡝⠠⠀⠂⠰⠋⠈⠁⠀⠤⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢀⡐⣴⣰⢃⡴⢠⣴⣿⣿⣄⣀⠀⡄⠀⢀⣴⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠐⠦⠙⢬⢣⣟⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠃⣙⡛⠛⠆⡟⡤⢸⣿⣿⣿⣟⠉⠛⠏⠉⠉⠉⠉⠉⠻⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⣀⣨⢵⠸⡆⢧⢸⣿⣿⣿⣿⣷⣤⣤⣤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠋⡄⣓⠐⢨⣿⣿⠿⠿⠿⠛⣡⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠄⠈⠀⠀⠀⠤⠂⠠⠖⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⢌⠁⠄⠀⠈⠯⠐⠒⠒⠀⠒⠛⠂⢀⢀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⡈⣙⠷⣤⣀⣤⣤⣄⠺⢿⣿⠃⠙⠰⠎⠁⠉⠀⠀⣀⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢳⡙⠷⠦⠉⠛⠿⠛⣛⠀⠴⢛⣥⠀⣠⡦⠰⠟⠋⠋⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⢀⣈⣓⠐⠦⢤⣙⣛⣓⠲⠖⠚⠭⠒⡛⠁⢀⣀⣀⣤⠠⠶⠂⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠠⠄⠠⢒⣛⣂⡠⣤⣭⣍⣁⠀⣂⡈⠁⠀⠀⠀⠄⠴⢀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⣈⠛⠷⣿⣿⣽⣭⣥⣤⠄⢩⣭⣬⡭⣭⣍⣉⠶⠶⢾⠿⣛⣁⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠟⠳⠶⠊⠉⠭⠉⠐⠚⠛⣛⣛⡘⠛⠛⠛⠛⠑⢚⣋⠤⠉⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣀⣀⣀⣀⣠⡬⢠⣶⢀⣴⣶⡶⠛⠟⠩⠶⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠭⠿⠍⠩⠄⠤⠤⠄⠉⠑⠒⢀⣉⣀⣴⠄⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠰⣦⣥⣈⠠⠐⠂⠀⠠⠤⠭⢉⣉⡭⠍⠁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠛⣙⡛⠞⣛⡛⢛⣯⣝⣁⣀⣐⡂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⡀⠀⠉⡉⢈⣑⣚⣛⣯⠭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⠶⠶⢛⣻⡭⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⠶⠖⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠒⠒⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⢀⡀⠒⠂⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⢀⣴⡆⢀⣴⠋⠁⣤⣬⣹⣿⣄⡄⢠⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢇⠀⠍⢱⣬⡵⢾⠟⠛⢿⣿⣿⣇⢻⣾⠟⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠆⢈⠈⢭⠓⠂⠀⠴⣿⣿⣴⣿⢛⣥⢾⣿⡆⠀⠒⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⡀⢠⣿⡆⠀⠀⠀⠀⣂⡈⣓⠺⣧⣀⣠⣦⣬⣭⣍⣽⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣷⣤⣄⡀⠀⠈⢳⣽⣿⣤⣤⣬⣉⣛⠻⢿⣿⣿⣿⠟⠁⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⢉⡙⠻⣿⣧⡀⠀⣀⣙⡛⢿⣿⣿⣿⣋⣿⣿⣿⣿⣵⣶⣿⠛⣿⣟⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢿⣿⠿⣿⢿⣿⡿⠋⢉⣿⣿⢿⣿⣿⣿⣿⣿⡏⠉⠻⣼⡁⠉⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣈⣀⡡⠉⠉⠀⠀⠀⠀⠛⠋⠁⠈⠿⣿⣷⣷⡀⠀⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣉⠀⠄⠀⠀⠀⠀⠀⢀⣠⣾⢿⣦⣾⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡻⣿⣦⠀⠀⠀⠀⢐⢋⣶⣿⣺⣿⣿⠶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠹⡟⠛⠉⡻⣧⣀⣀⠈⢨⣿⡍⣿⡿⢿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣶⣬⣛⣶⣬⣿⣿⣿⣦⠈⣿⡏⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⢁⠋⠀⢱⣤⠇⠀⠀⣀⣴⡆⠀⠀⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠃⠀⢀⣾⣿⡿⠿⢤⣾⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡔⠀⣴⣿⣿⣿⠋⢸⣠⡿⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣾⣿⣿⣿⢀⣁⣸⣿⣧⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡹⠿⣿⠿⣿⣿⣿⣿⡦⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠠⣴⣿⡷⢶⣮⠭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠿⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡐⡀⠠
⠀⠀⠀⠀⠀⣀⠀⡄⢰⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢀⠀⠥⠂⠐⢈⠀⡀
⠀⠀⠀⠠⠆⠰⣤⠷⣧⡠⢶⠉⠀⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠂⠂⣉⡣⡄⡖⢘⢩⠄⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⣤⣀
⠀⠈⠙⠂⣐⣲⣼⣿⣵⣼⣖⡛⠉⠁⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠈⠢⢤⣧⠕⢤⠙⠢⡀⠂⠀⠀⣤⣾⣿⣿⣿⣿⣿⠛⠉
⠀⡤⠚⣧⣿⠟⠋⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠃⠀⠀⠀⢀⠀⠀⣼⠁⠀⠁⠀⠁⠀⢠⣾⢟⣵⣿⣿⣿⠏⠉⠁
⠀⠠⠖⣹⠃⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢀⣴⣷⣀⠈⣏⠀⠀⠀⠀⡾⣦⣰⠃⠀⠀⠀⠀⢀⣼⡟⣵⣿⣿⡏⠉⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣿⣿⣿⡇⠹⣄⠀⠀⠠⣿⢈⣿⣶⣦⠀⠀⢀⣿⡟⣼⡿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⣿⡟⣿⡇⠀⠑⠄⠀⠀⠈⣿⡇⠻⣿⣷⠀⢿⡿⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣾⣿⣷⢻⣷⡄⠀⠀⠀⠠⡀⣾⢹⣧⣹⣿⣧⣾⣳⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣷⣦⣄⡀⠀⠈⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⣷⠄⣿⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⣌⣹⡿⢿⣿⣿⣿⣿⣿⣷⣿⡄⣿⣿⣿⣿⣿⠿⠛⠁⠿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠛⠻⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠾⣿⢿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⢄⣤⣴⣾⠿⢿⠟⠙⢿⠉⠛⠿⠿⢿⣿⣿⣿⠿⠿⢷⣶⣾⣽⣷⣶⣤⣾⣿⢹⣧⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⣧⣾⡿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠃⠀⠀⠀⠙⠛⠻⣿⣿⣧⣼⣤⠻⣷⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡾⠒⠳⣽⡿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⢐⣀⣀⣀⣤⣤⣭⣭⣥⣤⣤⣤⣤⣭⣥⣤⣤⣀⣀⣐⠂⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⣩⣴⣶⡾⠿⢛⠉⢰⣶⣶⣿⣿⣯⡉⠉⠉⠉⠉⠙⠛⠛⠓⠒⢒⣿⠭⢽⣗⣲⣤⣍⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡔⢡⣾⡿⢋⠉⠀⠀⠀⣐⣾⠿⠿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠬⠭⣓⡾⣍⡛⢿⣷⡌⢆
⠀⠀⠀⠀⠀⠀⢸⡄⢻⣯⠠⡘⠦⣄⣈⠓⠶⠬⠭⠭⠭⠽⠿⠟⠋⠀⠀⢤⣭⣿⣿⣿⣷⡄⠀⠀⠈⠱⠎⣻⢎⣿⠄⣿⠇⢸
⠀⠀⠀⠀⠀⠀⠀⢿⢢⡉⠓⠮⣵⣒⣯⠭⣽⣖⣒⣀⣀⡀⠀⠀⠐⠨⠥⢾⣿⣿⣿⠿⢛⣁⣀⣀⣤⣤⣿⣶⣯⠵⠚⣁⢴⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢹⣗⠶⠤⣈⡉⠛⠛⠒⠶⠿⠯⠭⣭⣭⣭⣭⣽⣯⣽⣯⡭⠭⠿⠿⠗⠛⠛⠋⣉⣡⣤⣶⡛⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⡯⠀⠀⠀⠉⠉⠑⢒⣒⡲⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⡯⠁⣼⢁⠀⠀⠀⠀⠀⢀⠄⣨⠔⠂
⠀⠀⠀⠀⠀⠀⡠⠔⢒⡩⢦⠹⣕⡂⠀⠀⠀⠀⣀⣀⠤⣭⠭⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢀⣾⣿⣿⣿⣶⡤⡀⠀⣡⣾⡇⠤⣀⠀⣠⠆
⠀⠀⠀⠀⠀⠁⠔⢊⠡⠐⠊⢳⡝⢶⡀⠀⠀⠀⠒⣒⣨⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣠⣾⣿⣿⣿⣿⢿⣿⢾⠁⣿⣿⣷⣭⣶⣾⣷⢟⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣽⣷⣦⣤⣤⣴⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣡⣾⣿⣿⠿⣽⢷⣝⣷⣽⠿⠂⠻⠿⣿⣿⣿⣯⣵⠟⠁
⠀⢠⠀⣠⣤⣤⣴⢦⣄⣴⣾⡾⣷⣶⣮⠙⠻⢷⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠿⠋⣉⡴⣟⣼⠟⢋⣤⣾⣿⢿⡿⠛⠛⠛⠉
⠀⣸⡿⣛⣯⢨⣶⣠⣦⣬⣴⣷⣻⡿⣗⣒⣶⣄⡀⣉⣉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣉⣉⣭⠥⢴⣖⣚⣭⣷⡾⢋⡵⣡⡾⣿⣿⢏⣼⠇
⣰⣿⣾⣿⣿⣿⣿⠷⡖⠢⣮⣟⣿⣶⣭⢋⡩⣿⣿⣖⠶⠶⠭⠭⠭⠭⠭⠭⠭⠭⠽⠶⣶⣶⣒⣿⣿⣯⢽⣷⠞⢉⡴⣪⣾⣿⠿⣫⣴⡿⠋
⠀⠀⠀⠉⠉⢻⣾⡿⠣⣿⣞⣿⣿⣿⣿⣾⣿⣷⣿⣿⣭⣉⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡭⠽⠶⣶⡾⠋⠀⣤⢋⣾⣿⣭⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠈⣷⡟⣾⣾⣿⡿⢿⣿⣿⣿⣿⣛⣛⣛⡓⠶⠶⠾⠿⠿⠿⠶⠶⠶⠶⠶⢞⣛⡿⠟⠁⠀⣤⢞⣵⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠹⣷⡿⠛⠁⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠟⠋⠀⡠⣢⢞⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠁⢀⡤⣪⠞⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡐⠾⠿⣛⣥⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⡀⢀
⠀⠀⠀⠀⠀⠀⣘⣙⣃⠟⠉⠈
⠀⠀⠀⠀⠀⠂⠀⠀⠈⠙⠲⣤
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡾⡀⠐⠢⣄⣀⡀⢠⡉⢄
⠀⠀⠀⠀⠀⠀⠀⢘⢷⣶⣶⣿⣷⣾⢿⣿⠿⠦⠌⠩⠦⡢
⠀⠀⠀⠀⠀⣀⣀⡊⠀⠹⣿⣿⢛⣴⣿⢏⠷⠶⠶⢶⣄⠈⠒⣄
⠀⠀⠠⢾⣿⣿⣛⡿⠿⣦⢸⠷⣿⠟⠁⠀⡀⠀⠀⠐⠻⠷⠄⠀⠑⣄⡀
⠀⠀⠀⠈⠈⠛⠿⠿⣿⣾⢾⣀⡀⠐⢀⣁⣤⡶⠶⢶⣦⣤⣀⡀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠧⠒⠚⠏⠉⠀⠀⠀⠀⠁⣯⡿⡇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠑⡦⢤⣦⣀⠀⠀⠀⠀⠀⣀⣩⡜⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⣾⣟⣛⣭⣭⣿⡞⡇⠀⠈⠙⠛⢤⣤⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠰⠻⠛⠿⠟⠛⠋⠉⢀⡇⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠀⠀⠀⠀⠙⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣀⡴⢚⣉⣁⡀⠁⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⠴⠃⣠⠞⢁⡞⠋⠀⢀⡔⢋⠉⠀⠠⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⢣⠀⢸⡆⠀⠀⡸⢠⡎⠉⠢⠀⠈⢣⡄⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⣠⠏⢀⣾⡇⢆⡇⢡⠘⢌⢂⣰⢱⢀⠀⡥⢆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣼⡏⢀⡞⠁⠘⢦⠱⣀⠀⣠⣤⣥⡖⣚⣐⣡⠇⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⡎⠀⠀⠀⠈⢆⣀⣉⠢⡀⠤⠒⠋⠉⠁⢀⡞⠁⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠒⠢⢄⠀⠀⠀⣀⣀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠳⣌⠢⢄⡉⠐⢲⠞⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠙⠄⠀⠀⠉⢻⡇⠀⠀⠀⠀⠛⣀⡠⠤⠶⠶⠤⢄⡠⢀⣨⠷⠖⠒⠛⠉⠀⢰⠖⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⡀⠀⠈⡄⠀⢀⡼⢷⡀⠀⢠⡖⠛⠓⠤⣀⢀⣠⣤⡀⠈⠋⢁⣀⡀⠀⣿⠛⠒⠋⠀⢨
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠢⣰⠀⣸⠁⡜⠁⠀⠀⣙⡷⣾⠁⠀⠀⠀⠈⠉⠁⠀⠀⠑⠢⠞⣹⠟⠊⠁⠀⢀⡶⢤⠎
⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⡇⣸⢁⡠⠖⠋⢁⡞⢉⣷⣤⣄⣀⣀⡀⠀⠀⣀⣀⡤⢞⣁⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠉⠉⠁⠒⠠⠈⠟⣁⣁⣀⣀⡼⠉⡴⠋⠁⢡⠉⠉⠉⠉⠛⠿⣟⡶⠾⠛⠉⠉⠑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⣀⣤⢸⠀⠀⣠⠟⣠⠊⠀⣀⠤⢼⡴⠂⠤⠤⢤⣀⠀⠙⢄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠈⣇⢀⠔⢡⠼⠁⠀⡼⠁⠀⠈⠀⠀⠀⠀⢠⠟⠀⠀⠈⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⡴⠃⠀⢀⡼⢁⣠⠔⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⣓⣒⣀⡛⠻⢭⡐⠢⢄⣀⣠⠔⠛⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠖⠉⠀⠀⠈⠙⢦⠀⠈⠢⡀⠈⠳⡒⠤⠄⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡄⠀⢳⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠷⠦⠤⠤⠤⠶⠒⠒⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⢠⢊⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡇⢸⠃⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢢⣼⡡⠞⡰⠖⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢹⡀⡜⠁⠀⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠤⢤⣀⠀⡁⠀⠈⠁⡇⠀⠀⠀⢳⠀⣀⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⢒⡶⠋⠀⠀⠀⠀⠈⠉⠢⡀⠈⠳⣇⠀⢰⠂⠀⠀⠀⢀⡮⠞⢋⠨⠵⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠄⠀⠤⠤⣄⡀⠀⣠⠊⠁⠀⡤⠒⠋⢐⣲⡤⠤⠤⠄⡀⠀⠀⠘⡆⠀⠘⡧⣌⡙⠓⠒⠚⠉⠀⠚⢥
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠸⠀⢠⠊⠀⢀⠤⠠⢤⠀⠘⠦⡀⠀⠸⠀⠀⠘⣄⣜⠉⠉⠉⠉⠓⢦⡀⠇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠒⠦⣄⣨⢧⠀⠀⠀⠰⠀⣼⢆⠠⣡⠖⠀⠒⣿⠀⠀⣸⠀⠀⡇⠀⠀⢁⠈⠉⠲⣄⠀⠀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⠀⠀⣠⠖⠋⠁⠘⡆⠀⠀⠀⠱⠝⣄⠙⠢⠤⠖⠊⣛⡤⠊⡌⢀⡴⠁⠀⠀⢸⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢑⠞⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⠆⠈⠢⡀⠀⠠⠀⠉⠀⠀⣧⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠊⠹⡀⢀⡴⠊⠉⠉⠙⢆⠀⠀⡎⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠲⢄⣀⡀⠀⠀⣳⠋⠀⠀⠀⠀⠀⠀⠑⢦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⢊⠝⠋⠁⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠭⣧⠤⢤⡀⠀⠀⠀⡴⠿⠶⣤⡈⠉⠀⠒⠠⠶⠶⠒⠒⠉⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡤⠂⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⢀⣀⣀⣀⠠⣤⡴⠋⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⠙⠳⢦⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠒⠒⠒⠒⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠒⠚⢻⠤⠤⣤⡤⠤⠴⠶⠒⠈⠿⠄⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⣀⣀⣘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠐⠢⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠶⠋⠉⠀⡴⠛⡏⠉⠓⠲⡖⠒⠒⣶⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⠞⠁⠀⢰⡄⠀⠀⠁⠀⠀⣿⠀⠉⠛⠲⠦⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠙⠲⢤⣤⣀⣀⣀⠤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠊⠀⠀⠀⢸⠛⠦⣄⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠉⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⡠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣐⡂⡀⢀⢐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠤⠒⠀⠃⠁⠈⢠⠁⠈⡀⠁⠉⠘⠀⠒⠠⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠓⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡀⠂⢁⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠰⢀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⠁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠂⠈⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢑⡐
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠆⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠰
⠀⠀⠀⢀⠐⠠⡁⠀⠀⡀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⢈⡔⠂
⠀⠀⠀⣈⠀⠀⠄⠐⠀⠀⠀⠀⠀⢈⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⡁⠀⠀⡁⠀⠀⠀⠀⠀⠂⠠⠀⠀⡁
⠀⠀⠀⠀⠰⠐⡂⠄⠀⠁⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⢠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⢐⠂⠆
⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⡜⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⢠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠤⡀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠤⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⢀⠐⠠⠂⡀⢀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠐⠀⠂⣀⡰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠉⠐⠆⠆⠠⠈⡀⣀⠁⡈⣀⢀⡁⠄⠰⠠⠂⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠁⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿⣿⣿⠇⣰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⢠⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠃
⠀⠀⠀⠀⢸⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢹⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣧⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣿⣷⣾⣽⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡸⣿⣟⣿⣿⢍⢻⣿⣿⡿⢿⡻⣟⣻⢟⡿⢿⣿⣿⡟⡩⣿⣿⣻⣿⢏⣿⣦
⠀⠀⠀⠀⠀⠀⢠⢞⣱⡟⣷⣌⠻⣻⣿⡷⢟⣋⣉⣙⡲⡝⣾⣷⢫⠞⣋⣍⣙⡻⢾⣿⣟⠟⣡⣾⣹⣎⡳⡀
⠀⠀⠀⠀⠀⢠⢏⣿⣿⣿⡻⣿⣷⡾⣫⣾⠟⣩⡭⢭⣛⢬⣸⣧⡱⣫⡭⢭⣍⠻⣶⣝⢷⣿⣿⢏⣿⣿⣿⠹⡄
⠀⠀⠀⠀⢠⠏⣿⡋⢁⣚⠿⠾⣿⣾⡿⣡⠿⢛⣷⠀⢹⡎⢹⣿⢱⡇⠀⣾⡛⠿⣌⣿⣷⣟⠷⠟⣓⡈⢹⣷⠹⡄
⠀⠀⠀⠀⣾⡞⣹⣯⣿⢿⣿⣿⡿⠻⡵⣿⢾⣿⣿⣆⣼⡡⠛⠟⠘⣧⣰⣿⣿⡷⢿⢮⠙⠿⣿⣿⡿⣿⣿⣝⢻⣷
⠀⠀⠀⢀⡏⣼⣿⡿⠋⢠⣾⣫⣷⣿⣧⠹⣦⡉⠉⢿⡟⠁⠀⠀⠈⢿⡿⠋⢉⣴⠟⣼⣿⣾⡿⣷⡄⠙⢿⣿⡧⢹⡀
⠀⠀⠀⢸⣧⠟⢁⣠⣴⡿⠋⣿⡟⢿⡟⠇⠀⣿⢀⡞⠀⠀⠀⠀⠀⠀⢳⡀⣿⠁⠸⢻⣿⢻⣷⡘⢿⣦⣄⡈⠻⣼⡇
⠀⠀⠀⠈⡏⢰⣿⣿⡏⠀⡼⣿⣧⠸⣿⣶⣖⣿⡟⠀⢀⣤⣤⣤⣤⡀⠀⢿⣾⣳⣶⣿⠇⣼⣿⢧⠀⢹⣿⣿⡄⢹⠁
⠀⠀⠀⠀⣷⡿⢉⡿⠏⢀⣴⣿⣿⣦⠹⣯⣙⣿⠁⠀⢺⣷⣶⣶⣿⡗⠀⠈⣿⣫⣿⠏⣼⣿⡿⣆⡀⠸⢿⡉⢿⣾
⠀⠀⠀⠀⠸⣇⣎⣴⣿⡿⢁⡼⠃⢿⣷⣿⣿⡇⠀⠀⠈⢻⣿⣿⡟⠁⠀⠀⢸⣿⣿⣾⡟⠘⣟⠈⣿⣷⣦⣱⣸⠇
⠀⠀⠀⠀⠀⠹⣿⠃⣾⡇⣾⡅⢠⡿⣿⣿⣿⣇⠀⠀⣠⣿⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⡳⡄⠘⣧⢸⣿⡘⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣖⣿⣇⢿⣷⣿⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡆⣿⣷⡿⣸⣿⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣇⣿⢻⡟⣿⡿⣿⣹⣿⠻⣿⡿⣿⣧⣿⣿⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣸⣿⣷⣿⣿⣿⣯⣻⣿⣽⣷⣿⣿⣾⣿⣧⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣮⣿⣟⣵⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠟⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠰⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣽⣾⣷⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠛⠍⢙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡀⣰⢀⠁⠁⠘⢧⠴⢦⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⠟⣄⠠⠁⢠⠀⣠⠃⠀⠙⣴⣯⣾⣷⣡⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣽⠷⠾⠓⠠⠼⣋⣁⣁⠠⠔⠉⠹⢿⠛⠭⡛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⢀⠄⣀⡀⠀⣻⣗⣀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠱⡐⠋⠉⠠⠆⠉⠿⢿⣃⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⢿⣀⠀⠈⣁⣠⡶⣶⣶⣏⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡽⠿⠋⠻⣽⣟⣽⣠⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠲⣤⣶⠘⠟⣧⣷⣚⠁⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⡿⣭⣀⡀⠀⠀⠈⢻⡄⠆⢹⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠄⣈⡁⠒⢦⣆⣻⠈⠀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠛⣷⣰⣿⣷⠶⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⣽⣿⡽⠐⡏⠉⠃⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡻⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠉⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠴⠶⠶⣤⡎⠈⠋⠀⠀⠀⠓⠂⠈⣀⡤⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣠⠔⡖⠙⣄⠀⠀⠀⠀⠀⠀⣠⠗⣢⣠⣄⠀⠈⠱⣍⠢
⠀⠀⠀⠀⠀⢰⡡⠖⠁⠀⢰⣫⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⣙⠆⠀⠈⠑⢼⡀
⠀⠀⠀⠀⢀⡏⠁⠀⢠⠚⢦⡈⠓⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠀⢀⡴⢲⡀⠈⣧
⠀⠀⠀⠀⠘⡀⠀⠘⡀⠀⠀⠧⠛⢴⣄⡀⠀⠀⠀⠐⠀⡀⠀⢀⣀⣤⣴⠎⠙⣾⠀⠀⢹⣀⡏
⠀⠀⠀⠀⠐⡃⠲⣏⠉⠀⠀⠀⠀⢸⣠⢌⡤⠀⠐⠲⡝⠄⠃⠰⢛⣄⡸⠀⠀⠀⠀⠀⢀⣹⣀⢀
⠀⠀⠀⠰⡖⠴⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠈⣿⡋⠀⠀⠀⠀⠰⠛⠁⠀⢸⣀
⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠰⠀⠀⠓⢀⣀⣠⡇⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠑⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠢⠛⠉⠉⠢⢀⡤⠄⠈⠉⠉⣳⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠌
⠀⠀⠀⠀⢹⠁⠀⢀⣴⠆⠈⢀⠀⠀⠀⢄⠀⠀⠀⠰⡇⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠰⢦⡄⠀⢖⠚
⠀⠀⠀⠀⠀⣶⠚⣏⡀⠀⠀⠀⠀⢰⠱⣄⠡⣆⣀⠜⢳⠖⣀⠤⣮⠟⡧⠀⠀⠀⠀⠀⣀⣱⠠⠤⠄
⠀⠀⠀⠀⠀⡇⠀⢼⣁⠀⣀⡿⣤⠞⠁⠉⠀⠀⠀⠐⠁⠀⠀⠀⠉⠀⠹⡦⢾⠂⠀⠀⣿⠍⣇
⠀⠀⠀⠀⠀⠧⠀⠀⠹⠶⠃⣰⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢧⡈⠙⣥⠎⠁⠀⡏
⠀⠀⠀⠀⠀⠈⢄⠒⢄⡀⠘⢧⡀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣹⠆⠀⠀⠄⡾
⠀⠀⠀⠀⠀⠀⠀⠑⠦⠑⢆⠀⠈⠉⣻⡴⠚⠁⠀⠀⠀⠀⠀⠙⢦⡴⠉⠋⠀⠀⣀⡣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠤⠤⠦⠀⠀⠀⠀⠠⢄⡸⠒⠲⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠣⣀⣀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⡋⣾⣿⣿⣿⠿⠿⠛⠛⠟⠿⠿⢿⣿⣿⣶⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠉⠻⣿⣷⣽⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠻⢿⠆⠀⠀⠀⣀⣀⣀⣀⣈⣿⣷⡶⣦⣶⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠟⠀⠠⣅⣠⣾⣿⣿⣷⣿⣿⢿⣿⣿⡶⢃⣿⣞⣿⢿⣿⣿⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⡀⠐⣻⣿⣝⣿⠿⠿⣿⣿⣿⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣶⡩⣿⣿⡿⣛⢿⣯⡿⠿⣿⣻⣯⣝⣏⣍⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾⣥⣽⣿⣿⣿⣿⣿⣿⣴⣶⣶⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⡟⣘⣿⣿⣿⣿⣩⢟⡛⣿⠿⣿⣿⣿⣯⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⣿⣿⣿⣿⡿⣿⣷⢞⣡⢿⣼⢻⡿⣇⣿⣿⣻⡿⠿⠿⢿⣯⠽⣿⢷⡞⠻⢿⠿⠿⠿⠻⠟⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣼⣿⣦⣤⣿⣿⣧⣴⣦⣄⣶⠾⠷⣶⣍⣳⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠿⠿⣯⣷⣿⡿⠿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠉⠈⠉⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣤⠀⢹⡇⠀⠀⢈⣀⠀⠀⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡼⠃⢀⣀⠈⣿⠀⡀⢀⣌⢹⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣧⠠⡿⢰⣄⣿⣶⡋⠿⣍⢸⡇⣷⢸⠇⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⢷⣟⣸⠇⠙⠈⢷⡶⠋⠈⠃⣿⠘⠃⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⢠⡀⡀⠀⢤⢠⠀⠠⡈⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠉⠈⠀⠈⠁⠁⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠁⠉⠉⠒⠂⠄⠀⣀⡀⠠⠠⠐⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠒⠄⢀⣀⣀⣠⠤⠤⠔⠲⡄⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠤⠀⣠⠊⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⡔⠁⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠉⠁⠒⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⠎⢀⠀⠀⠀⠀⡀⠒⣊⠉⠉⠉⠲⣄⠈⢳⠀⠀⠀⠉⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⠀⡊⠀⠀⠐⠈⠔⠀⢀⡉⠂⢄⠀⠀⡇⠈⡆⠀⠀⠀⠀⢷⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠂⢹⠀⠂⠀⡀⡄⠀⡈⠉⠓⠀⠁⠠⠇⢀⠇⠀⠀⠀⠀⢸⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠑⢀⣰⠛⡁⠘⠀⠰⠮⢾⡠⠀⠀⡼⠀⠀⠀⠀⠀⡜⠀⠀⠀⣸⢀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢰⠀⠀⠀⠀⠀⢤⡀⠀⠀⡇⣰⢷⠀⠈⠑⠀⠀⠀⠀⠀⠐⠋⠀⠀⣰⠁⠀⠀⠀⠀⡜⠁⠀⠀⣰⠁⠀⢡
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠟⠀⠱⠀⠀⠀⠁⠀⠀⠀⠀⡠⢂⠔⣹⡀⠀⠀⡠⠊⠀⠀⢀⠴⡁⠀⠀⢸
⠀⠀⠀⠀⢀⠀⠙⢄⠀⠀⠀⠆⠀⠀⠀⠀⠀⡇⠀⠀⡷⣤⡀⠀⠈⠂⠄⠀⣀⣀⡀⠾⠐⣁⡴⠋⠀⠠⠔⡀⣀⠄⠊⠁⠀⠘⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠈⢦⡀⠀⠀⠀⢇⠀⠀⠐⣼⣬⡁⠐⠒⠒⠒⠀⠀⠀⠚⢉⣡⠄⠂⣁⡼⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⡈
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠑⠀⢀⡙⢦⡀⠀⠈⠳⢄⣀⠈⠳⠀⠉⠉⠉⠀⠀⠈⠁⠠⠋⠤⠲⠋⠁⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠘⠄⠙⢦⡀⠀⠀⠈⠉⠙⠂⠒⢎⡉⠉⠀⠀⠁⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⢆⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠃⠀⢀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⣀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⡀⠀⠀⠉⠈⠉⠉⠉⠁⠀⠀⠀⢀⣀⡤⠔⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠘⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠻⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠄⠤⠠⠔⠉⠀⡔⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠈⠉⠉⠝⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣀⡠⠤⠐⠉⠂⠄⠀⠀⠤⠔⠒⠂⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠂⠀⠀⠀⠀⠀⢀⠀⠀⣰⣿⣿⣿⣆⡀⠀⠀⣶⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠙⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣛⠛⠉⠀⠀⠈⠀⠒⣨⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠖⠂⠀⢰⣾⣿⣿⣿⣿⣿⣆⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣿⢿⣿⣟⡿⣿⣿⣿⣦⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⣄⣹⣿⣦⣠⣤⣿⣷⣦⡄⠀⠀⠐⣤⠿⣩⠉⠙⣿⡿⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠾⠛⠉⠠⣀⣙⢫⣿⢛⣿⡔⢣⣄⣀⡀⠀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⣠⣴⣦⣤⣤⣄⣼⣿⣿⣿⣮⠵⠿⣶⣯⣿⣷⣘⣻⣿⣶⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣶⣷⡋⣸⣟⠋⠉⠙⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠅⠘⠿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⢽⡷⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠙⠛⢻⣿⣧⣿⣿⣿⣿⣿⡿⠈⠀⠹⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⣿⣶⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣇⣸⣿⣿⣼⣿⣿⣿⣾⣿⣯⡄⠀⣀⡠
⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣥⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣄⠀⢠⡄⢀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⠗⣾⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣀⡀⠉⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠹⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣶⣭⣿⢻⣿⣷⣿⣿⣿⣿⣿⣧⢾⣹⠂
⠀⠀⠀⠀⠀⠀⠀⣄⣤⣦⡀⠀⢢⡄⣠⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣮⣍⣛⠿⣿⣿⣿⣿⣿⡄⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣟⣷⣿⣿⣾⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣍⣛⠿⣿⡍⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⣭⣽⣿⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡉⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡐⢻⣿⢰⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⠹⣿⣿⠿⢿⣿⢿⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⢹⡟⠁⣿⠛⠛⠀⣟⠀⣿⠉⠀⠈⢹⢾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⠀⠀⠀⣏⠀⣿⠀⠀⠀⠰⠸⠈
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⣿⠀⠀⠀⠀⠀⠸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡏⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠂⢁⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠆⠀⠀⡀⠀⡀⢰⣾⣷⣦⣤⡄⠀⠀⠀⠀⣀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⠀⠀⠐⠀⠈⢸⠀⢿⣿⡿⠛⠀⠁⠀⠀⠘⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⢸⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⣀⣸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⢶⣶⣶⣏⠉⠉⠉⠉⣷⣶⣶⠦⢌⣀⡀⠠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡻⠿⣿⣽⣿⣯⣥⣴⣿⣿⣆⠀⠀⠀⢀⣾⣿⠿⠿⣿⣿⣿⠛⠊⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠓⠤⠢⢔⠝⣿⠿⣷⣶⣶⣿⣿⣶⣦⠀⡀⠒⢠⠀⣸⡗
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⠟⣈⣹⣯⡹⣙⣽⣿⠀⠩⠭⠜⠁⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠙⠛⠛⠛⠛⠛⠛⠛⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔⠒⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣠⠀⠀⠉⢛⡀⠀⠚⠶⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠰⣂⠫⣀⠀⠸⠢⠁⡄⠀⠀⠀⠀⡀⠀⠙⠋⠀⠀⣶⢯⣤⡤⠤⡀⠈⣤
⠀⠀⠀⠀⠀⠀⠰⢇⢪⡏⠀⣀⡄⠾⠛⡯⢱⠀⡸⢀⠀⠀⠀⠀⠙⣿⣦⣄⡾⠀⢀⢴⡎⠁⠳⣔⠏⢠⠸
⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⣦⡌⣆⠳⠔⣡⡎⠀⠁⢀⠻⠀⠀⠀⢀⠈⢡⣾⠇⢰⣿⡀⠓⢀⢀⣼⠃⠸⠇⣠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠦⠙⢃⠤⠼⠭⠐⠋⠀⣠⣎⠄⠀⠀⢀⡴⠞⠋⢝⢌⡐⠻⠳⠒⣻⠗⠁⢀⣔⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠈⠉⠑⠠⡄⠹⣦⡀⡠⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠍⠢⠛⠉⠁⠐⠀⠀⠨⠁
⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣤⣈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠀⡦⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢐⣠⡍⠁⠚⠉⠁
⠀⠀⠀⠚⠋⠁⠘⠛⢂⡠⠌⠙⠛⠆⠀⠀⠀⠃⠯⠊⠛⠛⠛⠚⠛⡟⠛⠁⠀⠀⣰⡟⠁⠀⠉⣉⣻⣾⠀⡀⠤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⣶⣯⣤⡖⠶⣤⡀⠀⠀⠀⠀⢠⢖⣅⢔⣀⡄⣀⡀⠀⠀⠀⠀⡍⠀⣠⣞⡑⡟⠓⣒⡦⣌⠃⠹⣾⣄
⠀⠀⠀⠀⣠⠊⠂⣡⣞⠉⠑⠮⣛⠀⣦⠀⠀⠀⠀⠘⠣⣜⡁⠋⠃⠋⠀⠀⠀⠀⢿⢰⠈⢋⡞⠁⠀⠨⠃⣹⣿⠀⡞⡳⡀
⠀⠀⠀⢸⣿⠀⣴⡆⠙⠀⡀⢠⡿⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠸⡇⠈⠻⣶⣰⣦⡶⠼⠟⢊⡴⡱⠁
⠀⠀⠀⠈⣏⠂⠘⣿⠤⠶⣻⠏⠀⠀⠀⠀⢀⠄⡀⠘⠣⠄⠀⠄⠀⠀⢀⣀⠀⠀⠙⠦⢰⣦⢀⠀⠉⠓⠶⠶⢖⠞⠰⠁
⠀⠀⠀⠈⠛⠕⡒⢄⠶⠚⠁⠀⠀⠀⠀⠐⢀⡘⠋⣀⣠⠂⣄⠀⠁⠻⠋⠀⠀⠀⠀⠀⠙⠉⢀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⢄⠈⠆⢸⢹⠛⡯⣀⠀⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣷⡤⠀⢀⣤⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⣤⠴⣧⣠⠀⠀⠼⠌⡒⢪⠝⣠⠀⣇⠜⠃⡀⠀⠀⠀⠀⣠⡴⠶⠙⣿⢀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠹⣂⠞⢃⡴⠁⢰⣿⠁⠀⠀⠀⠐⠉⠀⠀⠀⢈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⠀⠀⠀⠀⠀⠁⠐⠚⢃⠀⠐⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠶⠖⠛⠛⠉⠉⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⡀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠿⠴⠶⠶⠦⠤⠤⠬⣭⣙⣺⢄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄⡀
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⣠⠞⣁⢔⡢⢬⠽⠿⠿⠶⣴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢦⡀
⠀⠀⠀⠀⣿⠁⠀⠀⠀⣠⠖⠚⣇⠀⠀⠀⢠⡿⣡⠞⡱⣫⠞⠁⠀⠀⠀⠀⠈⠑⢄⠁⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠙⢦⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠹⣄⠀⠀⣼⡷⠁⡼⢰⠃⠂⡀⠠⢀⣂⠀⠒⠒⠈⢣⠀⢱⠈⠙⢦⡀⠀⠀⠀⠀⠀⢿⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧⠀⠀⠀⠙⣆⠀⣿⠇⢀⡇⡟⢰⠋⣠⡖⣋⠉⠁⠘⠟⡓⠚⠢⢤⡇⠀⠀⠱⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡆⠀⠀⠀⠘⣆⢻⠀⠀⡇⠇⢨⠀⡧⣪⣥⢍⠓⢄⠀⠻⢀⠀⠃⠈⢆⠀⠀⠘⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⢎⢧⡀⣿⠀⠈⢆⠈⠛⠄⠈⠀⢠⡄⢀⡜⡀⠀⠀⠈⡄⠀⠀⠸⡄⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⠀⠀⠱⡕⢿⠀⠀⠈⠑⠢⠤⠐⠂⢁⠄⡪⠊⢡⠀⠀⣸⠀⠀⠀⠀⢷⠀⢀⡏⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠱⡹⣄⠀⠀⠀⠀⠘⢆⠑⢤⡀⠀⣀⣠⠤⠖⠑⠈⠀⢀⠌⣠⠞⠁⠀⠀⠀⠀⢸⡄⣸⠁⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠱⠘⢦⠀⠀⠀⠀⠀⠑⠤⢈⠣⢀⠀⠀⢀⣀⣤⡴⠿⠋⠁⡐⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢡⡀⠙⠛⠛⠓⠒⠒⠶⠤⠬⠭⠽⠛⠋⠉⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠙⢷⡢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⠳⢤⡉⠉⠛⠒⠶⠶⠤⠤⠤⠴⠖⠋⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣀⣀⣀⣀⣀⣤⣤⡤⠶⠒⠛⠋⠉⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣀⣀⡤⠤⠴⠶⠾⠯⣥⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢡⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠄⠀⠀⠀⢀⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡀⡠⣴⠃⠀⠐⡋⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢰⡃⠀⠀⠀⠀⠁⡀⠒⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡆⢇⠠⠚⠒⡀⠀⠁⠀⠀⠉⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠀⠙⠺⠄⠀⠀⠀⠀⠀⠈⠉⠀⠉⠖⡂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠍⠀⠀⠀⠠⠄⠀⠬⠈⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⢫⡑⠢⡀
⠀⠀⠀⠀⠀⠀⣀⠤⣺⢀⡀⠀⠀⠀⠀⢨⡑⠒⠂⠢⠬⠤⠤⠤⠤⠤⠤⠔⠠⠒⠚⠋⡅⠀⠀⠀⠀⢠⢊⠄⠒⠀⠈⠁⠀⠉
⠀⠀⠀⠀⣠⡎⡄⠊⠀⠀⢀⢀⣓⠀⠄⠈⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠁⠀⠀⠀⠀⠈⠨
⠀⠀⠀⡼⠀⠑⣀⡀⠀⠀⠀⠄⠀⠀⠀⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡠⠄⠐⠂⠰⢄⡀
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡄⠀⡆⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⡰⠁⠀⠀⠀⠀⠀⠠⠉⢆
⠀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢸⠀⠀⡇⠀⣠⠖⡋⠉⠉⠙⡳⢤⠀⢰⠁⠀⡇⠀⠀⠁⠀⠀⠀⠘⠀⠀⡆
⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⢸⡷⠀⠀⢸⣷⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⡆⠀⠀⣀⠀⠀⠀⠀⠈⡿⠀⠀⡇⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠑⡶⠢⠤⠤⡤⠤⢤⠤⠤⡤⠂
⠀⠀⠀⠘⡄⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⠳⢤⣀⣀⣀⣀⣠⠔⢋⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢁⠀⠀⠀⠈⠉⠀⠀⠀⢸⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢆⣀⣀⣀⣀⡀⠤⠔⠚⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠸⠤⣄⣀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠀⢀⡴⢠⡀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠀⠀⠀⠏⠀⠀⠉⢠⠀⡀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⡃⢿⡀⠀⠀⠀⡄⠀⠀⠀⡄⢡⠀⠀⠀⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠐⠤⢄⣀⠁⠌⠁⠀⠀⠀⠓⠂⠀⠁⠙⠚⠟⠒⠀⣀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⡀⢸⡀⠂⠀⠀⠀⢀⣀⠀⠀⠀⠔⠀⠀⢀⡠⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠙⠛⠀⢀⡜⠊⠀⠀⠀⠀⠀⠠⠴⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠠⠐⠈⢱⠄⠀⠀⠀⠈⠀⠀⢀⣀⣈⣲⡒⠀⠶⠓⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⢀⠟⠢⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣤⠄⠀⠀⠀⠀⠐⠉⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠂⠛⠁⠀⠀⠀⠀⠀⠓⠒⠛⠓⠲⠶⡒⡟⠀⠈⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠛⠒⠒⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠻⡀⠎⠀⠀⠀⠀⠀⠉⠉⠓⠐⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣶⠶⣦⡀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣆⠀⠀⠴⠟⣉⠉⠉⠃⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠈⠳⡶⢶⣤⣤⠅⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⠀⠀⠀⠀⠀⠀⠈⢀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⢳⣤⣤⣤⣤⠄⠀⠈⢀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⣙⣷⣿⠁⣠⡴⠶⠋⠉⣉⣯⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠉⠻⣅⣾⣥⡴⠂⠀⢉⣉⣤⣤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⡘⣿⡏⠀⠐⡛⠉⠁⠀⢠⣶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣶⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⢄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠀⠀⢠⡟⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡖⣠⠞⠀⣠⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣈⠻⣦⣤⣤⣦⣴⣤⡶⠋⠀⣸⣟⣁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣯⣭⣤⣴⣦⣀⣠⣾⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣲⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠻⣿⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢣⣿⢵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠈⠱⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡔⠁⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠏⠀⠀⣠⢰⣿⣏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡻⠀⢀⣼⢣⣿⡿⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣗⣅⣠⣿⣟⣿⣿⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣄⠀⢈⠻⣶⡀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣿⣿⣟⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠟⠛⠳⢄⠀⠀⠀⠈⡇⠀⠀⠀⠘⢻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢠⡇⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣐⠀⣀⠀⠀⠀⠀⠀⠀⠘⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠛⢿⣿⣦⣿⣤⣤⣀⠀⠀⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣆⠈⠉⠙⠻⢿⣿⣿⣷⡄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣭⣄⡀⠀⠀⠀⠀⠉⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡿⣥⣄⣤⣀⠀⠀⠀⠈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⠚⠛⠂⠼⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡆⠀⢠⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢻⡤⠀⠀⢸⠃⠰⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⠀⢾⠀⠀⢰⡆⠀⠻⢦⣴⡀⢠⠄⠀⣧⡜⠀⢀⠀⣼⢀⠀⠈⢳⡀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⡀⠄⠀⢹⡀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠉⢷⠾⣿⣷⣿⠀⠀⢸⡷⠟⠉⠀⠀⠀⢣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠉⠻⣶⣤⡳⣄⠠⠷⢀⣾⠀⠀⢀⠀⠀⠀⠀⣹⢿⠛⢷⣤⡈⠀⠀⠀⠀⠀⠀⢸⠷⠖⠒⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡢⡀⠀⠘⣿⠶⠶⠦⣄⠀⠀⣙⠾⢿⠁⠀⠀⠀⣿⣈⣧⠀⠹⢇⢀⣤⣄⠀⠀⠀⣈⡠⠄⠒⠊⠈⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⢷⡈⠲⢶⣿⡄⠀⠀⣈⠻⣶⠇⠀⠸⣄⡀⣸⣾⣿⣿⣿⡁⣠⠊⡿⠋⠀⠀⠀⢀⣯⣀⣀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠙⢦⡀⠙⢷⣤⠞⠁⠀⢸⠀⠀⠀⠜⢧⠙⠿⣿⣿⣿⠟⠁⢀⡁⢀⠠⠒⠉⠀⠀⠀⠈⠉⠙⠂⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢽⣶⣤⠾⢿⣦⠞⡇⠀⠀⠀⠈⣇⠀⠀⠀⢻⠀⠀⠙⢿⡃⠀⠀⣸⡏⠁⠀⠀⠀⠀⠀⡠⠴⠤⢴⡞⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠖⠉⠁⠀⣠⠴⠋⠀⠀⠊⠀⠀⠘⠀⠀⠀⠀⠈⣷⣿⠀⠸⣇⠀⢀⣈⠋⠉⠙⠻⣧⡀⠀⠀⠀⠴⠿⡀⢀⣴⠏⠀⠀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡥⠴⠒⠒⠒⠤⣤⣀⣀⣠⣶⣤⠴⢾⣿⣧⣠⠞⢿⡷⢻⣿⡇⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠠⣍⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠰⠖⠛⠁⠀⠀⡀⠀⣀⣀⣨⠿⠿⡿⠉⠀⠀⠀⠀⠈⣿⠀⠀⣣⣼⠟⠀⡀⠄⠀⣦⠀⠹⡤⠴⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣵⣤⡄⠀⠠⣤⢤⣇⣠⣾⠷⢤⣤⣾⣦⣄⡠⠇⠀⠀⠱⣤⣤⣤⣤⣥⣤⡤⠤⠴⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣰⠃⡈⠁⠸⡇⠀⠀⠸⠋⠀⠈⠳⣄⡀⠀⠀⠈⠦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠲⣤⣼⠗⠀⠀⠀⣠⣿⡀⢀⣶⣄⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠉⠉⠙⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⢀⣀⣠⠖⠛⠛⠳⢼⠀⠉⠛⠶⢤⣄⡁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⢸⠁⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠑⠂⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⣿⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢋⡟⢻⢽⣶⡄⠀⠀⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⢰⠒⠊⡇⣰⡟⢧⡘⡴⠃⢹⣄⠀⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⢯⣵⣼⠀⠀⣷⢳⠇⠀⠙⢷⡶⠟⠘⡇⠀⠀⠀⠃⠀⡀⠀⣠⠴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠋⠛⣏⠓⢦⣿⣖⠒⢒⣶⣿⣶⡖⢻⡅⠀⠀⣀⠀⠀⢿⡞⢹⡄⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⣿⣠⣾⢯⣉⢱⡄⣏⠻⡍⠉⠉⠉⠉⢁⡜⢀⡠⠔⢹⡀⠀⣿⡇⣼⠃⣸⣷⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣾⠀⣿⡇⢧⣾⠟⡟⢿⡟⠀⢹⠿⣯⣍⠉⠉⡰⠋⠀⠀⠈⡽⠀⣿⣿⣿⣾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⢀⡟⠈⢣⣽⣧⣀⣹⡾⠷⢻⠃⣠⢯⠀⠈⣯⢻⣴⡇⢀⣼⠃⣸⢧⣠⠟⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠈⠳⣤⣀⣀⣀⣠⣿⠞⠁⢸⡇⢀⣿⣼⡇⢳⣾⡷⣾⣵⣯⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠠⡤⣤⣐⠒⢤⡀⢸⠀⠙⠶⢤⣀⣈⣻⡿⠟⠋⠁⠀⢀⡼⠀⣸⣭⣭⣿⠁⠒⠻⣥⣀⠙⠛⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠑⠦⣬⣭⡱⢾⣘⣦⣀⠀⠀⠊⠉⠛⠛⠛⠒⢲⣶⣯⣥⣤⡟⠉⣧⠹⣤⠀⠢⣈⢿⢮⠀⢄
⠀⠀⠀⠀⠀⡠⠊⡩⠁⠀⣼⡟⠻⣶⣌⠙⠦⣄⠀⠀⠀⠀⣠⠞⢿⣿⣯⠀⠀⠐⢬⡳⡈⠻⠷⢬⡙⣮⢣⡀⠑⢄⢲⡄⠀⣠
⠀⠀⠀⠀⠀⢀⠎⢀⡼⠆⢿⣽⡀⢠⣽⠀⣦⣬⣿⣶⣶⣾⡿⢳⡀⠙⠿⠷⣤⣦⣀⣱⣇⠀⠀⠀⠈⢺⡇⠉⠒⠒⠋⠁⠉⠁
⠀⠀⠀⠠⠴⠧⠶⠟⠁⠀⠈⢧⡇⣸⢇⣴⡿⠋⣸⠁⠀⠙⡇⠘⢇⠀⠀⠀⠈⠀⠀⠉⠻⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⣡⣿⠋⠀⠀⢹⣦⠀⠀⢻⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠁⠀⠀⠀⠀⠉⠻⢦⣸⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⣾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣀⣼⠁⢠⡀⠢⠶⣠⡁⠀⡀⣤⣀⣶⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠙⢿⠀⢸⡇⠀⠀⠁⡈⡀⠑⢛⣿⣿⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣧⡒⠂⠛⠢⣀⠀⠀⠀⠣⠀⡍⢩⠟⡀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠠⡺⡄⠸⡄⠀⠹⣿⣷⡀⠈⠉⠀⠀⠀⠀⠠⣀⣀⠀⠁⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣽⣦⡀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⢀⣼⠿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠄⠈⠙⠻⣽⡟⢿⣾⣷⣦⠀⠀⠈⠀⠀⣀⡤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⣀⠀⠉⠻⣿⣯⣄⡀⠀⠀⠤⠾⣿⡟⠀⣠⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠢⣄⠈⠙⣿⢿⣶⣦⣤⣾⠋⠴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡀⠀⠘⢿⠿⠛⠁⠚⠛⠉⠉⠁⠀⣔⡴⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢋⣁⣀⣀⠀⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⠛⠋⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣉⠳⢦⣄⡀⠀⠀⠀⠘⣷⡀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⣀⣭⠥⣄⣬⣥⣄⣉⠻⣦⠀⠀⠀⢸⡇⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰⣤⡿⠋⠀⢠⠞⣁⣐⣛⣛⠛⠻⠟⠿⣿⣿⣧⢦⠀⠀⣷⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣾⡟⠁⠀⢠⢃⣾⣿⢟⣵⣿⢾⢿⣶⢠⡘⣿⣿⣼⡇⠀⡏⢠⡀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⣼⡟⠀⠀⢠⡿⠘⡿⣱⣿⠃⢿⣤⣤⡿⣹⡇⣿⠏⣿⠇⢰⡇⣸⣧⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⣰⠃⠈⢧⠀⠉⠉⠁⠀⣠⣿⣧⠀⢰⣿⣿⠀⠀⠙⠿⣿⣿⢣⠏⣠⠏⠀⣼⣷⣿⣿⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢨⡃⠀⠀⠀⢿⣿⣿⣿⣆⠀⢻⣿⣆⣀⣠⣤⣶⠗⢃⡼⠃⢠⣾⣿⣿⣿⣿⠁⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⢸⠀⠀⠸⣷⡀⠀⠀⠸⣿⣿⣿⣿⣆⠈⣿⣿⣿⡿⠛⢁⣴⡿⢁⣴⠿⠛⠛⢻⣿⠏⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⣷⡀⠀⠀⢯⡙⠿⢿⣿⡶⠟⢋⣡⣤⣾⣿⠿⠛⠉⠀⠀⢠⣴⡿⠁⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⣿⣿⣦⡀⠀⠻⣶⣶⣦⣤⣉⡉⠉⠉⠉⠀⠀⠀⠀⣰⠶⠓⠁⠀⢀⣴⣿⣿⡿
⠀⠀⠀⠀⠘⣿⣄⠀⠀⠉⠛⢿⣿⣿⣶⡀⠀⠙⠻⠿⢿⣿⣷⣶⡶⠞⢋⣁⠀⠁⢀⣀⣤⣾⣿⠟⣹⡟⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣀⠀⠙⣿⣿⣷⣶⣶⣦⣤⠤⠤⠤⠤⠶⠾⠿⠿⣿⣿⣿⣿⣿⡟⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠈⠛⠿⠟⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢦⣤⣭⣭⡭⠶⠞⠛⠛⠛⠻⠶⠶⠶⢤⣤⣤⣤⣶⡿⠃

⣷⣿⠟⠁⣠⣿⢿⣇⠈⢿⣿⣌⢻⣿⣦⠐⠀⠀⣠⡾⠟⠉⢀⠤⢿⣿⣿⠟⠁
⠉⢀⣤⣾⡿⠃⣸⡿⠀⠈⣿⣿⡝⢻⣿⣧⣤⡾⠋⠀⠀⢀⣠⣶⡿⣛⠋⠛⠢
⣾⣿⡿⠋⢀⣴⣿⢇⡄⠀⣿⣿⣿⣸⣿⣿⡏⠀⣠⠴⣾⣿⣿⢿⣿⠁⠀⣠⠶⠀⡆
⣿⠇⣴⣾⠿⠛⢡⠞⢀⣼⣿⠿⢣⣿⣿⣿⣿⣿⡶⠟⢉⣾⢳⣿⡇⠀⠊⠀⣴⡀⠈⠀⠀⣀⣀⣀
⣤⣤⣽⣷⣤⡶⣣⣴⠿⠛⣡⣶⣿⣿⣿⣿⣿⣯⡀⠀⣿⡇⠸⠿⣷⣄⠀⠀⠁⠁⠀⠀⠀⠉⡟⠻
⠛⠋⠉⠉⠀⢉⣉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣯⣟⠶⠌⣙⣲⣤⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⠛⡛⠛⠻⠟⠛⠛⠻⢿⣷⣜⢮⠙⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣤
⠀⢀⣦⡼⣿⣿⢏⡨⠐⣨⣤⣶⣾⣿⣿⣷⣮⣄⠄⠉⠻⣷⣧⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⡄⣾⣿⣱⡿⠑⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⣽⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠆
⣻⣿⣿⣿⠃⢀⣾⣿⠏⡴⣒⣛⣿⣿⣹⣿⣿⡞⣿⣇⢠⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⡤⠴⠚⢉⡠⠊
⣿⣿⣿⣿⠀⣸⣿⣿⡸⡸⡁⢠⣿⣿⣿⣿⣿⡇⢹⣿⣿⡿⠟⠉⣭⠿⠍⠻⠿⠿⠛⠋⠁⢀⡴⠊
⣿⣿⣿⣿⠀⢻⢻⣿⣕⣯⣿⣿⣿⣿⣿⣿⡿⢀⣾⣿⠏⠀⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⣰⡟
⢻⣿⣿⣿⡄⠀⢳⣝⢿⣿⣽⣿⣿⢙⣿⣿⡃⣼⣿⡟⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⣿⠁
⠈⢿⣿⣿⣷⡀⢻⣿⣷⣮⣟⢿⣿⣾⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠲⢄⠀⡀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⢀⡤⠤⠖⠦⢌⣿⡄⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣠⣤⠴⣿⣤⣤⣀⠀⠀⠙⣿⣆⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡎⣠⠤⣤⡾⢁⣿⠳⢄⣈⠙⣿⡇⠀⠀⠸⣿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣸⠞⠁⠀⣿⢡⢾⢿⡇⠀⠈⠙⢾⡇⠀⠀⠀⣿⠀⠀⠀⣸
⠀⠀⠀⠀⣠⢾⡏⠀⠀⣸⣷⢋⡞⠈⢿⣦⡀⠀⢸⡧⠀⠀⢸⡏⠀⠀⠀⣿⢦
⠀⠀⢠⠞⠁⣾⠁⠀⠀⣿⣯⣼⠷⠶⠚⠛⢿⣦⠞⠀⢀⣠⡿⠁⠀⠀⣸⡿⠀⢧⠀⢰⣆
⠀⣰⠃⠀⠀⣿⠀⠀⠀⢸⣏⠠⠤⠄⠐⠀⢰⠏⢀⡴⢿⣿⠃⠀⠀⣰⡟⠁⠀⠸⡇⡘⣿⡆
⢰⠇⠀⠀⢠⠻⣧⣀⠀⠀⢻⡄⠀⠀⠀⢀⡏⢰⣿⠖⢻⠃⠀⠀⡼⠋⠀⠀⠀⠀⣷⠃⣿⣷
⣾⠀⠀⠀⣼⠀⣿⢿⣿⠲⢄⢻⣄⠀⢀⣼⡷⠛⠁⢀⡞⠀⠀⠈⠀⠀⠀⠀⠀⢸⡟⢠⡏⣽
⣟⠀⠀⠀⢹⡀⣯⠀⠉⠓⠾⠷⠿⠛⠉⠁⠀⣀⡴⢛⡅⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⠏⢀⡟
⢻⠀⠀⠀⠀⠳⣽⣧⣄⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⡁⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⣠⠞
⠈⡄⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⡟⠛⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡾⢋⡴⠚⠁
⠀⠈⠢⣀⣀⣀⣀⣀⣀⣠⣠⣄⣀⠉⠢⡀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣠⣿⣴⠋
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⢭⣉⠓⢤⣙⣦⣀⡀⢀⣠⣼⠿⣶⠿⠹⠏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠉⣛⣻⣿⣿⣭⣥⣴⣋⠉⣀⣠⡼⣇⡤⢒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⠊⠁⠀⠀⠀⠈⠛⠉⠈⠛⠛⢧⣀⠀⠑⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣋⡙⢦⡀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣆⠹⣆⡠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⢼⣆⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠙⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠀⠀⠰⠖⠆⠰⠀⠠⠤⢀⣀⠀⠀⣠⡄⢤⠄⢤⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣦⣿⣿⣋⣀⣤⣤⣤⣤⣧⣤⣤⣠⣀⣀⣀⡀⠈⠑⠓⠿⡞⢿⡛⣷⠺⣶⠷⠾⡄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡶⣤⣀⠀⣝⣯⣙⣏⣙⣟⢻⡛⣄
⠠⡤⠄⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⣟⣿⣿⣿⢏⠿⠀⠙⣷⣿⣿⣿⣩⣭⣽⣏⣹⣉⣆
⢂⠣⠀⠀⠀⠈⠙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣴⣶⣮⣶⣴⢟⠟⠋⢻⣿⣴⣤⠼⣦⣽⣌⣦
⠈⢦⠠⠉⠈⠁⠀⠈⠿⣆⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣯⡷⠣⢊⣤⣾⣿⣿⣿⣷⡾⣦⠬⣤⣱⡀
⠀⠀⢢⠐⠀⠆⠀⠤⠠⣼⣷⣤⡀⠀⠀⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⢁⣴⣷⠯⠂⠀⣈⠀⠀⠻⣿⣿⡿⣿⠿⣦⠤⣦⡼⣄
⠀⠀⠀⠉⠉⠛⠳⣿⡛⠛⠋⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣯⣄⣀⣀⣀⣻⣆⠀⣚⣛⣭⡾⠿⡦⠼⢦⠤⢦⡬⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠤⠀⠀⠀⠀⠀⠈⢉⣠⣶⣶⠾⠿⠛⠛⠛⠉⠭⢒⡩⠔⠊⠀⠀⢡⠿⣖⣻⣖⢻⣖⠚⢶⠖⢶⡖⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣾⣻⣿⠿⠿⠉⠀⠀⠀⠠⠤⠤⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢶⣶⣏⠉⣉⣉⣩⡘⣿⡷⠊⠓⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⡍⢠⠙⠒⠉⡏⠀⠉⠈⠙⣅⢾⠁⠀⡰⢦⠈⠋⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠙⠫⢿⣤⠀⣠⡶⠶⣄⡰⢟⣷⡟⢋⣦⢼⣄⣀⠁⠲⢤⡿⠿⢦
⠀⠀⠀⠀⠀⠀⠀⣠⣼⢳⠄⠀⣀⣤⢿⡏⠑⠀⢉⣁⣈⣛⡀⠉⠀⢠⠏⠙⣷⣿⠂⡀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⢀⠼⠛⠞⠓⠀⣀⣿⣽⣆⢀⡴⠟⠓⠀⠀⠀⠚⠁⠢⡀⠀⠘⠛⡹⣿⣄⢈⠀⢉⢙⡆
⠀⠀⠀⠀⠀⢰⣦⠤⠀⠀⠒⢙⣷⠄⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣤⠚⠁⢨⣏⠉⠀⠰⠘⢧
⠀⠀⠀⠀⠀⣿⠟⠋⢀⠀⣼⢧⣽⣤⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⠸⢿⣭⡤⣧⠀⠀⣛
⠀⠀⠀⠀⠀⡏⠀⠶⠋⠐⢧⡄⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⠶⠛⡇⠀⡅⠀⠀⡾
⠀⠀⠀⠀⠀⢻⣆⣀⠠⢠⠖⣃⣲⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡼⠆⢠⣤⣤⣇⣀⣿⠀⠀⢹
⠀⠀⠀⠀⠀⢸⣿⠿⢀⠸⣆⢉⣀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠀⠀⣡⡞⠳⡶⠀⣸⠏⢹⠋⠁⠀⣴⠃
⠀⠀⠀⠀⠀⠀⢹⣶⡤⢄⠈⠙⢿⣡⣤⠖⠀⠟⢲⡖⠠⠶⠶⠋⣿⠁⠀⣀⡀⣿⣄⢹⠀⠀⢶⠟
⠀⠀⠀⠀⠀⠀⠈⠉⣷⠈⠀⠀⠙⠶⣬⡄⣠⡄⣾⣷⠀⠀⠀⠀⠸⣦⡞⠿⡟⠀⢀⡜⠀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣹⣤⡀⠀⠀⠉⠻⣥⣿⣿⡀⠀⠀⠀⠀⠟⠙⡞⠙⠶⣣⣤⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣀⡀⢠⠀⢠⣿⠏⣻⡇⠀⠀⠀⠀⢸⣦⣳⣶⣤⡼⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⣿⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠀⠀⣷⠀⠀⠀⠀⠀⢹⣼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢹⡄⠀⠀⠀⠀⢸⡇⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢘⣇⠀⠀⠀⠀⠈⡇⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢠⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡅⠈⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣰⡏⢡⠀⠀⠀⠀⢸⣿⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⠘⣿⠠⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⠀⢸⡇⠀⠈⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢸⠇⠀⠀⠛⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⡿⠀⠀⠀⢸⡀⠀⠀⠀⢸⡄⢃⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠐⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠸⡇⠙⡄⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠐⠀⠐⢀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⠀⢡⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢹⡀⠈⠆⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⡇⠀⠸⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣶⠀⠀⢃⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠸⡄⠀⠈⣇⢀⠀⠀⠀⠀⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡇⠀⠀⠉⡄⠀⢀⡴⠆⠋⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠤⠶⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡰⠛⠲⢄⣸⠀⠀⠀⠹⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⣿⡿⠿⣿⣿⡿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣶⣼⣧⣴⣦⣦⣿⣤⣾⣯⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠦⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠰⠂⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠎⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠆⠀⠀⠀⢀⡀⠀⠀⠀⢀⡐⠂⠀⢄⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⡀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⡄
⠀⠀⠀⠀⠀⠀⠀⢈⠻⡄⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠚⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠲⢤⣀⡀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠊⠋⠁⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠒⠒⠛⠒⠚⠛⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⢋⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⡆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣃⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠰⡆⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⡀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⡏⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠃⠀⠀⠋⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⢄⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣦⣤⣼⠄⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣫⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠃⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣹⣍⡄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣏⣿⣿⣿⣧⣸⣿⣿⣯⣿⡀⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣿⣷⣶⣦⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢲⠖⣶⣦⡄⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠤⣀⠀⡖⠂⡇⣰⠛⣄⣣⠋⢹⣄⠈⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⣳⣷⣇⠀⣿⠹⠀⠈⣻⡾⢋⣸⠀⠀⠀⠁⢠⡄⣠⠔⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⣠⠼⢦⡑⣾⣯⠭⠭⠿⠿⠏⡸⠀⢀⢰⠀⠀⣿⢁⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⡇⢸⡞⣏⣽⣶⣷⣼⠈⣶⣤⡖⠒⠖⡡⠚⠁⠈⢷⠰⣿⣾⣧⡾⠛⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢠⠏⠣⣸⣇⣈⣣⣾⢼⡇⣠⡇⠈⢿⢶⣰⠇⢀⡖⢀⢇⣨⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠻⣬⣁⣀⣀⣼⠞⠁⢸⠀⣼⣾⡏⣷⣿⣶⣿⣮⣥⣤⣄
⠀⠀⠀⠀⠐⡶⠦⣔⣢⢄⢸⠀⠙⠲⢤⣤⣽⣟⡋⠁⠀⣠⠏⢠⣧⡶⣿⠀⠙⠳⣤⡙⠋⠀⠈
⠀⠀⠀⠀⠀⣨⠷⠞⠺⣿⣼⡷⢦⣀⠀⠀⠈⠉⠉⢩⣿⣷⡶⠞⠀⠳⡜⢦⣈⡒⢽⡵⡀⠀⠀⢀
⠀⠀⠀⠀⠂⡰⢀⣤⢸⣳⠈⠛⣆⢈⢓⣦⣄⣠⣴⣧⠘⢿⣿⣀⢀⠘⢮⡄⠈⠉⠂⢳⡙⠦⠬⠴⠇⠄⠂
⠀⠀⢀⣠⣎⢤⠞⠁⠈⢯⡇⣸⢁⣼⠟⢻⠋⠙⢿⠀⢇⠀⠀⠉⠋⠉⠛⢧⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣱⡿⠁⠀⢹⣆⡄⠸⡄⣾⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠉⠛⣤⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠾⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⡐⢦⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⠀⡴⣶⣾⣄⠹⣾⣷⢉⣤⣤⡀⢀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⣘⠿⠿⣿⣿⣿⣾⣿⡸⣿⣿⣷⠚⣉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢀⣠⣀⠰⠾⠿⣛⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣧⡜⠀⣀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⣳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣋⡐⠛⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣤⡴⢬⣭⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢥⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⡟⢻⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⣶⡶⢂⠈⠉⠁⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⣡⡤⢻⣿⣿⡇⣿⡿⣿⣿⣿⣿⣶⡌⣟⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠀⠈⠛⠛⣡⢿⡿⣦⢙⡟⠿⠛⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠳⠈⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣶⣿⣿⣿⣷⣿⢀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣎⣴⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠂⠈⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⣤⡄⠈⠋⢹⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠂⠉⠀⠀⠰⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠉⠑⢀⠔⠻⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⡤⣦⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⡏⢠⠏⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡵⡴⠃⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡼⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⠇⢄⡞⢁⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡤⠤⠒⠒⠈⠉⠛⠛⠉⠉⠉⠉⠉⠉⢁⡟⢀⠞⠙⠛⠛⠓⠒⠒⠒⠒⠒⠈⠉⢙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣠⢖⠭⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡜⠀⡞⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡇
⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢀⣠⠤⠀⠒⠂⠉⢉⠁⠀⠀⢠⣀⠀⠸⠄⠜⠃⠀⠀⢀⣀⠀⠉⢀⣈⣀⠲⢤⢤⣀⡠⢣⡇
⠀⠀⠀⠀⠀⠀⠈⢳⢽⣶⣤⡮⠁⢀⣀⣀⣘⠂⠀⠙⣋⣀⣀⣀⣀⡀⠀⠀⠀⠤⣶⣄⣀⣀⣤⣤⣤⣀⣀⣀⠠⠭⠕⠂⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠉⠉⠉⠀⠀⠒⠒⠒⠒⠒⠀⠤⠤⠀⠀⠀⠀⠐⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⣀⢀⡀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣀⠀⢠⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠏⠹⠿⠶⠶⠶⠶⠖⠒⠒⠊⠉⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⣛⣒⣦⡀⠀⣠⣴⡂⠥⣠⣖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠟⠟⠉⠈⠉⡙⣄⣴⠋⠀⠁⠒⠈⠙⠳⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠘⠏⢿⠃⠀⠁⠀⠀⠀⠀⠀⣛⠀⠠⠀⠀⠀⠀⠀⠃⠠⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⡴⠊⠘⠛⠂⠀⠀⠀⠀⠀⠁⠀⡄⢿⡀⢀⠂⢂⠄⠀⠀⠀⠁⠀⠀⠈⠳⢂
⠀⠀⠀⠀⠀⠀⠀⢠⣣⠏⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⢀⢾⣟⠛⠀⠈⠀⠀⠐⢀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠂⠀⠀⠀⠠⡀⠀⠀⠀⣤⣤⠗⣿⣿⣏⠻⢶⣶⣀⣠⡆⠀⡱⢀⠀⠀⣠⡾⠳⣶⢲⣄
⠀⠀⠀⠀⠀⢀⣴⠶⠟⠲⠦⢀⣀⢾⡤⣀⣹⡿⠟⠛⠂⠀⠀⠀⠀⠀⠀⠙⠿⣯⣄⠀⣴⣶⠞⠋⠀⠀⠀⠀⠉⢿⡄
⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠘⠋⠻⠧⣿⡟⠁⠀⣤⣶⣶⢶⣿⣷⣮⣤⡄⠀⢛⣩⣿⠍⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠐⠀⠀⠀⣷⡟⠁⢀⣾⡿⠋⠁⠀⠀⠈⠉⠻⣿⡖⠀⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⢎⣿
⠀⠀⠀⠀⢹⣧⡀⠀⠀⠈⠍⠀⠀⣹⣿⡇⢨⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⢀⡀⣠⠀⠀⠀⠀⠀⠴⠀⣋⣽⡃
⠀⠀⠀⠀⢈⡾⠀⠀⠀⠀⠐⠂⢀⣀⣿⡇⡞⢽⣿⡇⠀⠀⠀⠀⠀⠀⢀⢸⠿⢃⡈⢓⣿⠋⠀⣀⠀⠀⠀⠀⠻⢯⢳⡄
⠀⠀⠀⠀⣿⡇⠄⠀⠀⠀⠐⠀⢼⣏⣙⣳⠠⠀⢻⣷⣅⣀⠀⠀⠀⣤⣾⣻⠂⠁⢴⣿⣟⠀⠀⠠⠀⠀⠀⠀⠀⢸⣸⡇
⠀⠀⠀⠀⢻⣷⡤⡄⠀⠀⠁⣠⠟⡛⠻⢿⢿⡀⡄⠘⠿⢿⣿⣾⣿⠿⠋⣀⠀⠰⣦⡿⢟⠻⣷⣤⡄⠀⠀⢠⣤⣾⡟⠁
⠀⠀⠀⠀⠀⠉⠻⠶⠄⠔⠟⠁⠌⠀⠀⡠⠃⣿⢠⣴⣆⣀⣀⠀⠀⢄⣈⡥⢒⣕⠝⠀⢄⠐⢗⠈⢻⡟⠢⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠁⠈⠁⠛⠃⢸⡿⢶⢻⣿⣿⠿⠞⠃⠀⠀⡀⡂⠁⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠔⡠⠀⠀⠀⠈⢈⡸⡷⡇⠉⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢜⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⠐⠁⠡⠃⠄⠨⢨⡟⠀⠈⠆⠉⠁⠀⠀⢂⢀⣉⣤⣰⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠺⠀⢚⣤⠀⢀⠆⠀⡂⠟⠋⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠓⢀⠀⠀⢀⡰⠃⠀⠀⠙⠫⢴⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠚⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠈⢀⣀⡈⠉⠑⠒⠒⠶⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣚⣭⣴⣶⣿⣿⠅⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⢫⣽⡓⠦⣄⡀⠀⠀⠀⢠⣶⣪⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣞⣵⣾⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠿⣿⣻⣶⣝⢢⣤⣶⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⠿⠋⠁⢠⣄⠀⣠⠦⠀⠈⠉⠉⠛⢳⠐⠿⠇⠀⠁⠈⠉⠁⡄⠀⡀⠉⡹⢿⣿⡿⡏
⠀⠀⠀⠀⠀⠀⠀⣏⠾⡿⠁⠀⢀⠀⠉⠁⣾⢁⣴⡶⢄⠀⢴⣮⣿⣿⠓⣦⡁⠀⠀⣐⣭⠂⢠⣄⣥⠞⠋⢡⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣮⡂⠀⠀⠄⠡⠀⠀⠙⠀⢠⡶⠊⠉⠾⠏⠀⠻⢧⠀⢸⣇⠀⠀⢛⠷⠂⠐⠛⠁⢀⣴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠂⠀⠀⠀⠀⠀⠐⠛⠋⠁⠐⠐⠀⠀⠠⢤⠮⠂⠀⠢⠶⠄⠂⠀⠀⣀⣤⣶⣿⢃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⡫⠍⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⡯⢂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣭⣠⠞⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⣟⣥⠾⠋⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠳⠶⠶⠤⠦⠴⣶⣶⣶⣾⣿⢟⣡⣿⣴⣶⣤⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⢤⣀⣀⣀⣀⣭⣭⣽⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣾⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⢽⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⡠⢀⣼⣿⣻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⣯⣿⣿⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢛⣛⣛⣛⣻⣿⣿⣿⡿⠿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣽⣦⣭⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣿⣿⣶⣶⣶⣾

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠉⠉⠈⠉⠈⠉⠛⠉⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠐⣢⣴⠼⠿⢿⣶⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡝⢾⣟⣠⠶⠲⢶⡾⣿⣇⣶⣠⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠻⣅⠀⠀⠘⠓⠻⠻⣿⣿⠇⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠇⡈⢣⡈⠁⠂⠤⠀⠈⠙⣄⣀⣀⠀⠀⠀⠀⠀⠘⢦⠙⡛⠉⠊⠀⠠⢾⡿⡏⡠⠰⣦⣬⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠘⢦⣄⡀⠄⠰⠿⠿⣭⣙⣛⣳⣖⣣⣔⠤⠈⣧⠹⠓⠄⠀⠀⠁⠀⠉⠑⢀⡾⡌⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡴⣒⣒⠶⠌⠉⢈⡉⠉⣳⡨⠤⣄⠻⡆⠱⡆⢠⣄⠀⢀⣠⣤⡾⠁⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⢋⣛⠟⠻⠉⢀⣌⠭⣷⣾⣷⣌⢀⣷⣾⣏⣭⡴⢶⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣾⣿⣿⢘⣿⣿⣿⣶⣿⣴⣦⣄⣿⡿⢿⣏⡿⣿⣿⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⠿⣿⡿⢻⣽⣿⡇⢸⡏⣍⣋⣍⠻⠳⣬⠍⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠁⣾⣿⡇⠰⡀⢻⡄⢭⣭⣷⣤⠿⠚⣳⡀⠀⠰⠎⠹⣟⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⡿⢯⣋⣙⠺⢦⣬⣿⣾⣶⣦⡀⠈⠛⢷⣤⣾⡇⠁⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠁⠀⣼⣿⣧⣙⣛⣷⣤⠴⣶⣦⡄⠉⠛⣂⠀⠀⠙⣿⣧⡇
⠀⠀⠀⠀⠀⠠⠶⢿⣛⣧⠀⠀⠀⠁⠀⠀⠀⣠⣽⣿⣿⣿⣭⣭⣴⣾⡿⣻⣿⣶⡄⠈⢷⡤⣀⠹⣟⣇
⠀⠀⠀⠀⣤⠀⣴⡿⠫⡙⣇⠀⠀⢰⡀⠀⣿⣻⣿⣿⡿⣿⠿⣯⡀⠉⠛⠛⠷⡿⣷⠀⣨⣇⠻⣶⠙⠏
⠀⠀⠀⠐⠉⣾⡟⠀⠀⠀⡹⠀⠀⠀⠻⣄⣈⡽⠟⠋⠀⣸⠀⢈⢻⡄⠈⢦⠀⠙⠀⡇⢙⡌⣃⢹⠀⠀⢈⣚⡃
⠀⠀⠀⠀⢀⠉⡇⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⣰⡌⠀⢧⠀⢸⡇⢰⠀⣷⠸⠇⠀⠰⢿⣷⣾⠋
⠀⠀⠀⠀⠈⢧⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣩⣾⠟⠀⣠⢿⡿⣠⠿⠀⠀⢀⣇⣾⡿⡀⢠⠆
⠀⠀⠀⠀⠀⡈⠹⢄⠀⠀⠀⠀⠀⠀⠴⡿⢛⠉⠀⣐⣮⣿⣷⣿⠋⠀⠀⢀⣾⠙⡿⢳⡼⡁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠛⣿⣷⣼⡿⢁⠔⡊⠍⢀⣤⣤⠶⠒⢁⠔⡙⠋⠀⢷⡀⢣⠼⠃⠐⠍⠀⢠⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣤⡄⢰⡧⢫⣾⣿⠟⠋⢠⡄⡴⢫⠞⠁⠀⠀⠈⢿⡆⢀⠂⠀⢀⠀⡀⢀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠀⣾⣧⢏⣾⠁⠀⠳⣾⣼⢇⠛⣠⠀⠀⠀⠀⠀⠉⠈⠙⢒⣛⠂⢈⡁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸⣷⠀⠀⠀⢸⣿⡷⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⢀⠀⠀⢸⠟⠚⠖⠈
⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠈⠸⣧⣄⣆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⢹⠷⡾⠦⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿
⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⢀⠀⠀⠐⠂⠀⠄⡀⠠⣀⠀⠀⢀⡐⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣦⠀⠀⠈⠁⢀⠀⠃⠀⢀⡄⠠⠀⡀⠀⠀⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡗⠀⠰⠂⠈⠂⢉⠠⠀⠀⠁⠀⠀⠀⠈⢁⠒⠀⣀⠓⡀
⠀⠀⠀⠀⠀⠀⡠⠐⠒⠠⢸⡆⠀⠈⠐⠓⠖⠀⠀⠠⠵⠀⠔⠲⠖⠁⠀⠲⡀⠼⠃⣢⠎
⠀⠀⠀⠀⠠⠋⠀⠐⠀⠀⠀⠀⠁⠒⠄⠀⠄⣀⣠⠀⢂⠀⢂⣀⡸⠀⠴⠀⠈⠀⢉⠏
⠀⠀⠀⢀⠀⢐⠚⢆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠉⠉⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡆⠐⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡀⠀⠀⠀⠀⠀⠀⢉⡀⠂
⠀⠀⠀⠀⠠⡀⠉⠠⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢈⡡⠴⠂⡀⠀⣁⣀⣄⠀⠠⠄
⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢤⠆⢄⠉⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠂⡈⠉⢁⠀⠀⡴⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣦⣴⠛⢳⡜⣻⠟⣴⠟⢳⡄⡇⠀⣾⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠙⠶⠟⠱⠿⠶⠙⠷⠞⠁⠿⠖⠻⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠐⠒⠘⠉⠀⠀⢀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢈⣠⠂⣼⠿⠷⡆⠀⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠚⡀⣸⠉⠀⣏⠀⠀⠁⣠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⣣⡇⢿⠀⠀⢹⡄⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⣿⣽⣿⣤⣼⣤⡤⠦⡇⢸⠷⠒⠒⠒⠒⠒⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⡸⠁⠉⣹⣿⠛⠁⠀⣼⣿⣾⠟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠘⠉⠉⠀⠀⠀⣿⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⣀⣠⣿⣿⣦⣾⡆
⠀⠀⠀⠀⠀⠀⢀⠄⠂⢈⣛⣿⠷⠾⣿⣶⣴⣾⣻⠛⣹⣿⣿⣿⣾⣥⣤⣴⡆
⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠏⣡⣾⠟⢋⣴⠿⢿⣿⣿⣿⣷⠀⠈⠀⣀⡀
⠀⠀⠀⡔⠁⠀⣠⣶⣶⣶⣶⣶⣤⣤⣀⣤⣴⡛⣉⣡⣦⣤⣶⡈⢼⡿⣿⡿⣉⡄⠤⠔⣨⠇
⠀⢀⠌⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉⠉⠁⠀⠀⠉⠳⢟⠛⠚⡇⠙⠂⣐⡛
⠀⠂⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣻⡾⠙⢦⡀⠐⠺⠓
⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠟⠋⠀⠀⠀⠉⢲⣶⢄
⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣬⡛⠆
⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡶⠚⢙⡉⡉⢹⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡰⠀⣼⢹⠓⢶⡏⢖⣹⠇⡻⢿⡆⠀⣎⡈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣏⠀⠐⢿⣞⣆⡀⢻⣈⣭⢎⣵⣿⣶⣤⠼⠋⡸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠲⢬⣦⡀⣿⡟⢀⣽⣷⣻⠕⠉⣼⢋⠤⠄⣤⡜⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠓⠲⣼⣿⣾⣿⡞⢩⡉⠁⠤⢚⠝⠁⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⣀⣤⣤⣄⣀⡴⠉⠁⠀⠀⣠⣿⡅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠋⠁⠀⠛⡻⣿⣧⣤⣆⣀⣴⠟⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠙⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣄⡀⠀⠀⠀⠀⠁⠀⠀⠹⡧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡘⢦⢄⠀⠀⠀⠀⠀⢠⡄⢀⠄⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢻⡦⡀⠀⠀⠀⠀⠁⠋⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢤⠀⠀⡀⠁⣧⠀⣾⠀⠁⠀⡔⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠁⣀⡟⠀⡇⠀⢀⠀⡀⠀⠠⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠘⠅⠀⠁⣀⠯⠄⢀⣤⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢦⣽⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⣶⠒⠐⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠚⠋⠐⠄⠀⠘⣄⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠴⠄⠘⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⠃⠈⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢾



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⣿⣿⠷⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⡿⣽⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⢻⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣄
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣽⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣼⣷⣿⣷⡞

⠀⠀⠀⠀⠀⠀⠀⠸⡁⢿⡿⠀⣈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠘⠃⠀⡇⠀⡁⠀⠀⠀⠀⢸⡏⠴⡟⠃⠀⠃⠈⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣇⠀⢗⠀⠀⠀⣠⠏⠀⠀⠁⣠⡖⠀⠀⠀⣀
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⢀⣘⡷⡤⢦⡀⠀⠀⢿⡃⣤⣿⣛⣭
⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⡿⠛⠉⠙⢿⡷⠼⣶⠀⢰⣿⠛⠀⠉⠛
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡀⢰⠣⢭⣤⠀⠀⠀⠀⠀⠀⠉⠘⣏⠀⠉⠛⠶⣦⣈⡙⣿⣟⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠪⢥⡀⠀⠀⠛⠐⣄⠺⢿⣦⣄⡀⠀⠀⠈⠑⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡤⠁⢔⠈⠃⠀⡏⢡⡄⣹⢿⡿⣿⣶⠿⠿⠛⠛⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠖⡇⣼⠧⠔⠉⣠⠏⠀⠣⣄⡀⡠⠞⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠴⠃⠈⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢴⣄⠋⠀⠀⠀⠀⠀⠁⢀⣿⣡⣤⣤⡀⠀⡄⠠⠔⠊⠉⢀⠆⢈⣏⡄⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠀⠀⠀⢺⣿⠋⠁⠀⠀⠉⠢⡀⣆⡀⠀⠀⠈⣀⣼⠃⣰⣿⣯⠇
⠄⠠⣄⡀⠀⠀⠀⠸⣇⠀⠀⠀⣀⣼⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢘⠀⡅⠂⠐⢠⡿⢹⣿⡟⠛⢁⣠
⣷⢾⡿⣿⡄⠀⠀⠀⢹⣄⣠⣟⣉⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⢀⣦⠐⣿⢀⡴⣡⣿⠀⢿⠙⡄⢿⣿
⠦⠤⠶⠛⠀⠀⠀⠀⢀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡽⠷⠾⣶⣤⠀⢀⡤⠒⠀⠱⢤⠀⠀⣁⣹⡼⠟⠸⣻⣿⡿⢀⠸⠀⢸⠈⠙
⠀⠀⠀⠀⢠⠆⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣈⣶⣾⣾⣗⡢⣍⠱⠆⢤⣔⠠⣶⠀⠠⣀⣠⠴⠃⠀⠀⠙⠋⠀⠀⠑⢶⡟
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠉⠛⠂⠀⠉⠫⠙⠋⠛⡻⠟⢇⣤⠮⣹⣆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⡔⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢴⣾⡾⡿⣧⡉⣎⢦⣹
⠀⠀⠀⠀⠀⠀⡀⠰⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡃⠀⣴⠞⠀⠀⠀⠀⠀⠀⡾⢲⣿⠃⠘⣿⣗⠏⠈⠉
⠀⠀⠀⠚⠓⠉⢁⡙⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡞⠃⠀⠀⠀⠀⠀⠀⠀⢆⢘⡏⠀⠠⠈⠻
⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠄⠀⢠⠀⡤⣶⣶⣮⡴⠂⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠆
⠀⠀⠀⠀⣀⡀⠀⠈⠳⡄⠁⠀⡀⣤⠀⢳⣿⠟⡷⡝⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⢠⡾⠏⠀⠀⠂⠈⠀⢧⢀⠸⣯⡄⢚⣹⠗⠋⠘⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠨⢹
⠀⠀⠚⠀⠈⠀⠟⠁⠀⠀⠀⠈⡄⠀⠿⣩⡕⠚⠆⠀⡴⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⢗⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠀⠀⠀⠀⠀⠀⠿⣶⣤⠋⢁⡴⠃⠀⠀⠀⣠⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣤⡀⠀⠀⠀⠀⢈⣷⠞⠉⠀⢆⠀⢠⠉⣀⣴⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠈⠹⠦⠆⠁⠁⠙⠛⠛⣻⣤⣤⣱⠾⣿⣋⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡴⢓⡄⠐⢤⣂⣼⡎⢳⣄⣀
⠀⠀⣠⣮⠿⠶⠿⠿⠦⢀⠂⣠⣀⠦⣄⡀⠀⠀⠀⢜⣭⣶⣿⠋⣸⣿⡟⠿⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⢀⠙⢷⡂⢉⡇⢐⣬⣾⣿⣆
⠀⠘⠛⣥⣖⣿⣿⣵⣶⣼⢀⣨⣛⣷⡉⠱⡄⠀⠀⠙⠋⠉⡇⠰⠁⢸⢰⣶⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠛⡄⠀⠀⠈⢳⣶⣷⠘⣷⣊⣀⢀⣿⣫
⠀⠀⠘⠛⠛⠋⠉⠋⢋⣠⣽⣷⣮⠁⣎⢲⣷⠀⠀⠀⠀⠀⢣⣀⣠⠃⢸⠟⢿⣷⣈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢠⠃⠀⠀⠀⠀⢬⡘⢧⡈⠋⢉⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⡎⠉⢿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠳⣄⡙⠻⣿⡇⠀⠀⠀⠀⢀⠆⠀⠀⠹⡾⠀⠀⢀⣠⢴⣊⣦⡙⠻⠿⠶⠿⣿⣏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠒⢒⡻⠿⠛⠓⠾⣍⣉⡙⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⣤⡴⠊⠀⣠⣤⣴⠤⣤⡙⣆⡠⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡿⠉⢸⠁⢰⣿⠳⣤⢞⡿⣶⣷⠘⡯⣉⠻⣄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢸⡁⢀⢸⢰⡼⠙⠲⠬⢽⣶⣉⡘⣾⢣⡏⠀⠘⣆⣹⣄
⠀⠀⠀⠀⠀⠀⠀⢴⡁⠀⢸⡁⢸⡌⢷⡧⠴⠖⠒⠒⣒⠒⣋⠥⢞⡷⠂⣰⡷⠃⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠻⢄⠹⣯⡀⠀⠀⠀⠀⠀⢉⣡⠔⠋⣀⣴⠋⡀⠀⠀⣈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⡀⠀⣳⠤⣝⠳⢤⣀⣠⠞⠉⢀⣿⡿⣅⠈⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠭⢭⢟⣽⡏⠀⠈⠳⣤⣬⣷⣤⠶⠋⠀⠀⠸⣟⡻⣟⣫⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⠤⠟⢦⡐⠠⠈⠀⠁⠀⠀⠀⠀⢀⡼⠧⠬⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⡠⠖⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣧⢒⡒⣽⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠟⣫⣥⡶⣶⣭⣻⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣶⣦⣭⣛⠿⠟⣿⢋⣾⣯⣿⣷⣿⣏⣽⡟⠛⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⢸⣟⣻⣿⡱⢊⣿⣟⣻⢮⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣫⣭⣍⣛⡻⠿⠿⠿⠿⢋⣼⣿⠜⣿⣋⣿⡿⣿⣯⣻⡟⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡸⠮⢛⠿⠷⠿⢟⡋⠾⢢⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⠘⢿⣿⣿⣿⡿⣿⣿⡿⠿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣮⣙⣛⣥⣾⣿⠇⠀⠀⠉⠉⠁⠀⠈⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣭⣶⣮⡝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡏⣼⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣼⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣭⡍⣼⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⢈⣭⣭⣭⣭⡁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂