Salt Emojis & Symbols

⠀⢶⣤⣠⢤⣤⠤⢤⣤⡄⠀⠀⠀⣤⡤⠀⠒⠶⣆⠀⢂⢶⢶⣖⣀⣶⢶⣶⣆⣲⢲⡖⢂⠒⣶⡆⠀⣠⠄⠀⣲
⠀⣆⠁⠀⠀⠉⠛⠋⠀⠻⠦⣤⡶⠏⠀⠀⠀⠀⠈⠙⠓⠁⠀⠘⠙⠁⠈⠳⠯⠵⠋⠙⠃⠎⠀⠙⠲⠋⠀⠸⣿
⠀⡟⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾
⠀⣷⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡻
⠀⠣⢑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿
⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⣛⡆⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣼⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤
⠀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠈⠻⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⠖⠒⠚⠉⠉⠉⠛⠛⢚⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⢰⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢉⣙⣛⣛⣓⡚⢛⠚⣒⣙⡉⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⢸⠻⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⣯⣻⣏⣏⣿⣹⣹⣏⣿⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣦
⢨⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡉⢩⠛⠉⠉⠉⣿⡉⠉⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡶
⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⣇⠐⢳⡐⡂⣰⢻⢁⠄⡇⠐⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣦
⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡧⡬⡥⡾⡾⡶⣿⢷⣶⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿
⠀⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠑⠧⢧⣧⣧⣇⣿⣾⠿⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠸⣭
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶
⠀⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢅⢀
⠀⣮⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢿
⠀⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣬
⠀⣿⡄⠀⣠⠦⣄⠀⡠⠠⣄⣠⢖⣲⢦⡀⢀⣄⡄⠀⢀⢤⣄⡀⠀⠀⠀⠀⣰⠾⠛⠲⣦⠀⣠⣤⣀⠀⠀⢀⠹
⠀⠯⠀⠐⠋⠀⠸⠿⠤⠁⠼⠧⠿⠽⠿⠷⠿⠉⠽⠷⠷⠩⠀⠹⠶⠄⠀⠚⠛⠀⠀⠀⠘⠛⠓⠒⠛⠓⠋⠙⠶

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡤⣀⠉⠀⠀⠀⠀⢀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⠀⠀⠁⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⢠⠇⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠠⣀⣠⠖⠄⠀⢃⠀⠀⡇⠀⠀⠀⠀⠀⡠⡈⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠔⠀⠀⠀⠀⢳⠈⠀⣰⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣦⠀⠂⠁
⠀⠀⣀⠀⠀⡀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣤⡐⠀⠃⠀⠁⠀⠀⠀⡀
⠀⠀⠸⢄⠀⣀⣤⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⣀⣙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡙⠈⠉⠉⠉⠉⠀⠄
⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣻⣟⣟⣿⣿⣟⣿⣻⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂
⠀⠀⠀⢐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⣬⡉⠐⠒⠀⠀⠤⠠⠄⣀⡀⠀⢀⠁⠀⠈⠛⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠠⠤⠀⠀⠚⡗
⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⠐⠀⠀⢀⣤⣾⣿⡀
⠀⠀⠘⢿⡿⣿⣖⠀⠀⡀⠀⣀⣀⡰⠖⠉⠉⠉⠀⠀⠀⠀⢠⡀⠀⢠⡆⠀⠀⢴⠆⠀⠀⠀⠀⠂⠀⠀⢙⡌⠳⠴
⠀⠀⠀⠀⠳⢌⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠤⠻⠥⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠛
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇
⠀⢠⠂⣈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇⠀⠀⡀
⠀⠀⠘⠌⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠃⠀⠀⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣿⣟⣛⣻⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠂⠁⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣬⣵⣶⣶⣶⣤⡀⠀⠉⠋⠙⠿⠟⠉⠀⠀⠀⠀⢀⢀⣠⣠⣀⣀⣤⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠿⢟⣛⣫⣿⣿⣿⠛⠻⡹⣄⠀⠀⠀⠀⢢⡄⣀⣀⡤⠼⠛⣻⣿⣯⠿⠯⠽⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣍⣿⠶⠶⡶⠲⢶⡿⠿⠏⠁⠘⠿⠀⠀⢹⡘⣦⠀⠀⠀⢸⣿⣿⣽⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⣀⣶⡿⠁⠀⡃⠀⢂⠀⢀⠊⠀⠀⣸⠀⠀⡀⠀⠀⠟⠻⣿⠀⠀⡾⢸⠟⠉
⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⡼⠛⠋⠁⠠⡄⠀⠠⠈⠀⠐⠀⡀⠰⢧⠀⠀⠇⠀⣤⡠⠖⠉⠴⢛⣵⠋
⠀⠀⠀⠀⠀⠀⡀⠀⣰⠏⠀⠀⢠⡀⡀⠳⠄⣀⡦⠠⠀⠐⠀⢀⠠⠤⠐⠂⢉⣀⣠⣤⣴⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠃⠸⡅⠀⠝⠐⠅⠀⠈⢀⠀⣘⣂⡀⠔⠋⡩⠔⠲⠾⠞⢙⣩⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠻⣶⣶⠐⠀⠀⠀⠐⢁⠜⣁⣴⠂⠀⣠⣠⡤⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣤⠶⢋⣤⣚⣥⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠐⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠒⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠖⠀⠀⠀⢀⣿⡇⠀⠈⣷⠴⠦⡀⠀⠀⠀⠀⢰⣿⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢲⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣷⣾⣷⣄⡀⠀⠀⠀⠀⠐⢢⢠⣼⣷⣤⣀⠀⢢⣐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⡿⠿⠝⠛⢷⣦⣄⣀⢀⠀⠀⠹⡏⠈⠙⢿⣿⣆⠹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⣀⣀⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣤⡈⠂⡀⠀⠙⣿⣷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠻⢿⣷⡤⡀⠀⠈⠙⠛⠁
⠀⠀⠀⡔⠀⣀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠴⣢⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢀⣠⣶⣄⡁
⠀⠀⠀⠀⠀⠈⢩⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠠⠄⠀⠐⠄⠐⠛⢉⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠏⠠⠁
⠀⠀⠀⠀⠂⠈⠙⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠂⠹⣿⣿⣿⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠠⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠂⠿⠧⠴⢶⡶⣷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⢈⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠁
⠀⠀⠀⠈⠐⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠰⠶⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣿⣷⣠⣾⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣈⠋⠈⢛⣛⣋⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠋⠀⠈⢻⣿⠟⠛⢿⣄⡀
⠀⠀⠀⠀⠠⣷⠒⣠⣄⣀⠀⣀⡤⣢⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⠀⣀⣠⡤⠀⠀⠀⠀⢨⣿⣅⣀⡀⣈⡿⠗
⠀⠀⠀⠀⠀⠘⠆⠉⠊⢙⠛⠻⠿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠐⠛⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠚⡸⢛⣧⣴⣧⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠄⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⣉⡉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠺⠟⢀⣝⠁⠺⠗⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠶⠃⠹⣀⠀⣀⣄⡀⣺⠙⡄⠀⡠⣼⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠉⠛⠂⠀⠉⠁⠀⠙⠒⠃⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠖⢒⣲⠀⡔⢲⡀⢠⠶⡄⡔⠒⠒⠲⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠘⠦⢌⠓⣤⠁⠇⢣⢸⠀⣇⡉⡇⢸⠉⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣴⣒⣚⡠⣏⡰⢧⣈⣾⣀⣀⡙⣇⣸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠤⠤⢤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠤⠄⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠒⡒⢲⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⣸⣤⣤⠀⣉⣈⣃⣀⣤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⡄⢀⣀⣠⡩⢵⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⠧⠤⡤⠼⣿⣾⣻⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣹⠋⠁⠀⠀⠀⠀⠉⢭⣇
⠀⠀⠀⠀⠀⠀⢠⠓⡇⠀⠀⠀⠀⠀⠀⠀⠘⢟⣆
⠀⠀⠀⠀⠀⢠⠏⠀⠀⡀⠀⠀⠘⣷⡦⣤⡁⠐⠿⢄
⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢉⠉⠈⠩⢷⣦⡘⡄
⠀⠀⠀⠀⢸⣷⣤⡀⠀⠀⠀⠀⡀⡞⠀⠀⣨⣒⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠞⢼⢢⡦⢀
⠀⠀⠀⠀⠘⣿⠙⠟⠱⠶⣶⣟⣾⣟⣵⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠌⠀⠫⡀⠄⢠⣀
⠀⠀⠀⠀⢠⢗⠀⠀⠀⠀⠀⠀⡉⣛⢠⠮⣹⣿⡏⢹⣿⠀⠀⠀⠀⠀⠐⠀⠊⠁⠀⠀⠀⠀⠀⠁⠁⡀⠰⢦⣄⠀⡂⢠⡀
⠀⠀⠀⠀⠘⡜⣴⠀⠀⠈⠀⢀⣈⠉⠙⠳⣿⣻⢉⣾⠏⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠨⠨⣆⣄⠁⡀
⠀⠀⠀⠀⠀⠘⢿⣿⣆⣀⣀⣼⠡⠀⣠⣿⣿⣻⡾⠋⠀⠀⠀⠈⠀⠁⠀⠀⠄⡄⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠌⠒⡍⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡯⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠂⠠⢠⠠⠁⠀⠀⠀⠈⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣟⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⣷⡿⡿⣿⣿⣿⣻⢿⣻⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⡤⠤⠴⢖⠛⠛⢋⠙⣙⠛⠓⡂⠳⠾⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠀⣠⣄⣃⣀⣡⣈⡂⣐⣂⣀⣀⡒⣀⣡⣀⠀⠶⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣐⣈⣉⣭⠉⠋⠙⠉⠉⠭⠉⠹⠉⠀⣉⡀⠀⠀⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡏⣿⣿⡟⣿⣿⣻⣿⣿⣻⣿⣟⣿⣿⡇⠀⠀⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡏⠁⣴⠟⠛⠯⠉⠉⠉⢩⣿⣭⡍⠉⢹⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡇⠀⣘⣷⣤⡄⣠⡀⠀⣟⡿⣿⠖⠀⣼⠀⠈⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡀⣿⣾⡉⢀⣿⣼⢡⡟⣰⡟⢡⣏⢰⠇⣿⠀⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠂⣿⣈⣩⣯⣥⣬⣯⣽⣯⣽⣯⣽⣯⣤⣿⠀⠁⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢹⣿⡏⣿⣿⣇⢸⣿⣿⢸⣿⣿⢻⣿⣿⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠳⠾⢿⣿⣼⣿⣿⣼⣿⣿⣼⠿⠋⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⠀⡄⠀⠈⡀⠠⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⣀⠀⠀⠀⠓⠀⠀⠀⡀⠒⠀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠒⠒⠒⠒⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠰⠄⠈⣦
⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠠⡄⠁⠄⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⡴⠄⣼⠏
⠀⠀⠐⠀⢀⠀⡄⡀⠀⠀⠀⢿⠀⠀⠀⠀⢀⠀⠀⠈⠄⠀⠀⡀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⢡⣭⣿⠁
⠀⠀⠀⠀⠀⠀⠠⢙⠲⡀⠀⠀⠁⠀⠀⠀⠀⢇⠀⠀⠛⠄⠐⠉⠗⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⢐⠤⡀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠦⠄⠤⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⡀⠼⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⢠⠀⢱⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠰⡄⠀⠰⠀⠀⠀⠀⠀⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠗⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡟⠀⠀⠄⠠⠀⠊⠀⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠀⠀⠀⠀⢀⡻⠋⠀⠀⠠⡄⠀⠀⠀⠀⢸⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⡢⠀⢦⣤⣄⠄⠄⠀⠀⠉⠀⠀⠀⠀⠰⠍⠀⢀⣀⢠⣿⣋
⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠖⡄⠀⠀⡀⠀⠀⠐⠤⣀⠈⢀⡁⢠⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢍⣙⣒⣚⣋⠥⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠈⠀⠀⠀⠀⠉⠈⠁⠈⠁
⠀⠀⠰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢢⣦⡄⣀⡄⡀
⠀⠀⠀⠀⠀⠈⠁⠐⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⣴⣄⢂⣀⣀⢐⣤⢽⣶⠽
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⠁⠒⠲⠤⣀⠂⢠⢀⡀⣔⣶⣤⠀⠄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣎⠉⢉⣠⣤⡿⠟⠁
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈⠓⢹⣯⡈⣻⣟⢠⣑⣅⣌⣤⠸⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⠛⠌⠉⠁⡘⢳⡾⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡤⣐⠒⣍⠐⠀⣀⣁⣀⣠⣵⣶⡇
⠀⠀⠸⣿⣽⣏⣿⣽⣯⣿⣽⣯⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠀⠁⢀⡙⡀⠄⠛⢛⠘⠋⠉⠉⠉⠉
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣋⠱⢤⣈⠉⠁⠀⢀⣀⠴⠿
⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠭⠴⠚⠛⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠶⡖⠀⠀⠈⣁⣀⠀⠙⠛⣉⣉⡉⠛⠷⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠶⠖⠀⣀⡈⠀⠀⠐⠉⠁⠐⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⡄⠀⠀⠉⠉⠀⠀⠀⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣦
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⡴⠒⠒⣂⣉⣡⣤⣤⣶⣾⣿⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠒⠾⠟⠛⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣄⣀⣀⣀⣀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠉⠉⣿⣿⣿⣿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠰⣤⣿⣿⣿⣿⣿⣧⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣏⠃
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠈⢻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋⠉⠉⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢻⠅
⠀⠀⠀⠀⠀⠸⣿⣿⣿⠻⠿⣿⣿⣷⡶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⣾⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⣿⡿⠯⠀⠀⠏⣿⣿⡇⣿⡟⠉⢿⢛⠉⡏⠉⠁⢻⣿⣿⣿⡆⢹⠀⢿⣿⣿⣿⣿⣿⠀⠆
⠀⠀⠀⠀⠀⡅⣿⠇⠀⠀⠀⠀⢿⣿⠁⣿⠀⠸⠈⠀⠀⠀⠀⠀⠘⢹⡿⣿⡇⢸⡇⢸⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⢻⠀⡟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠁⣿⡇⢸⡇⠸⡇⠟⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⡟⠀⢸⡇⠀⠉⠀⣾⣿⣿⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⢸⠀⠀⠀⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠘⠀⠀⢠⡇⢿⣿⣿⡇⢸
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠈⠁⠘⢿⣿⣷⠈
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⡡⠀⠀⢀⠀⠀⠀⡆⠀⡆⣾⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠲⣄⣀⡀⠉⢀⠀⠀⢸⠀⠀⠀⠇⠀⠀⣿⣼⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣌⠀⠂⠈⠉⣛⡻⣏⠀⠀⢸⠀⣇⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢦⣄⡀⠀⢯⣙⡿⠀⠀⢸⠀⣿⠀⠄⢸⠀⠿⣿⣿⡆⡆
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠻⠶⣄⠉⠀⠀⠀⢸⠀⣿⠀⠀⢸⠀⠀⢿⣿⡇⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠚⠀⠀⢈⠙⢦⠀⠀⢸⠀⢁⠀⠀⠈⢀⡀⢸⣿⡇⡇
⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⡸⠁⠀⠀⠀⢠⠀⠀⠀⢸⡇⢸⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⣷⣼⣿⡇
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⣾⣾⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⣿⣿⣿⡷⢸
⠀⠀⠙⢿⣿⣶⣤⣄⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⡆⣿⣿⣿⡿⢣⠊
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠂⣼⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⢀⣇⣿⣿⣿⠔
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣅⣿⣷⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢈⣿⢊⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⣿⣿⣿⣿⣷⣤⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣿⢈⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⠿⣿⣿⣿⣿⣿⣷⣬⣤⣶⣤⣄⣀⣴⣇⣤⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠛⠛⠉⠉⠉⠉⠑⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠀⢀⡀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠰⠀⠈⠀⠀⡄⠀⠀⣤⠀⠈⠁⠀⠀⠆⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡤⠖⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠢⠤⠤⠤⠄⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀
⠀⠀⠀⠀⠀⡐⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡵
⠀⠀⠀⠀⠀⠁⠀⢀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡄⣤⠤⠤⠤⠶⠒⡒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢰⠇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⢠⡟⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣼⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢀⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠈⣧⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⢀⣠⣤⣤⣽⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⣤⣤⣤⣤⣀⣀
⢿⣿⣿⣿⣿⣿⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠉⠛⠿⢿⣿⣿⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣋⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠶⠄⠉⢩⠄⠈⠋⣭⡍⠙⠶⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠁⠀⠶⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠐⡋⣩⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⡛⠛⠓⠛⠒⠶⠒⠀⠀⠀⠀⠀⠐⠠⡨⠽⢚⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠴⢶⣾⣿⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠟⠉⠉⠉⢉⣹⣿⣿⣿⡉⠉⠀⢀⣐⣩⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠟⠛⠛⠛⠻⣿⣿⣿⡿⠟⠛⠛⠉⠙⢻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣦⣤⣀⣀⣶⣾⣿⣿⣷⣀⣤⣤⠴⢾⣿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⣬⣭⣭⣄⡀⠀⠀⠀⢀⣜⣀⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠻⣷⣶⡶⣶⣤⣤⣭⣭⣭⣭⣴⣶⢶⡶⣿⣿⣿⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢹⣿⢻⡟⠘⡏⠀⠃⠁⠸⣿⣿⠀⡇⢹⢿⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠛⢸⠇⠀⠀⠀⠀⠀⠀⠃⢹⠃⡇⠈⠚⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠇⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⠀⠂⠁⠠⠀⠁⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠤⣀⠀⡀⠀⠀⠀⠀⠀⠀⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠰⣄⣈⡙⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣆⠀⠀⣹⢽⡇⠀⠀⢰⠀⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠙⠷⣌⡛⠀⠀⠀⢸⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⠙⠆⠀⠀⠀⠀⠀⢀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠐⠀⠀⠈⢃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢀⣿⣿⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣾⣀⢸⣇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⢠⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣷⣿⣾⣤⣤⣀⣀⣸⣀⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠒⠒⠒⠢⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠒⣽⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣶⢄
⠀⠀⠀⠀⠀⠀⡼⠮⠉⠛⠻⠿⠗⠶⠄⢀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢊⡥⠚⡇
⠀⠀⠀⠀⠀⠀⡇⣿⡇⣶⡄⣤⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠒⠒⠒⠒⡒⢂⡀⣈⡁⣴⣸⡇⡇
⠀⠀⠀⠀⠀⠀⣇⣿⡇⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣻⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠿⠟⡁⣿⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⣿⡗⣛⢧⣫⡙⢄
⠀⠀⠀⢀⠔⣡⣿⣦⡄⠀⠉⠐⠒⠠⠤⠄⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠼⠯⠜⠓⠈⠀⠀⠙⢿⣿⣦⡑⢆
⠀⢀⠔⠁⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⢣
⢀⡎⠀⠀⠮⣛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡿⠛⠀⠀⢃
⢸⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⠤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠔⠒⠉⠁⠀⠀⠀⠀⢸
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠇⠀⠀⠀⠀⢰⡏⠑⠒⠢⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇
⡀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠁⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⡇
⡄⠀⠀⠀⠀⢸⠀⠀⡔⠉⢩⠭⣭⡙⢷⡀⠒⠒⣒⠶⢤⣀⡠⢶⡄⠀⠀⠀⠰⣯⣍⠉⠉⡩⠝⠁⠀⡇
⡇⠀⠀⠀⠀⢸⠀⠀⣧⠀⢻⣄⠈⠋⢱⡇⠀⡎⠉⣷⠀⢿⡇⠀⡇⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⡇
⡇⠀⠀⠀⠀⢸⠀⠀⠈⠳⣤⡉⠛⢶⣼⡇⠀⣧⠀⡿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡇
⡇⠀⠀⠀⠀⢸⠀⠀⠀⣠⡄⠈⣷⠈⠻⡇⠀⠈⢡⡀⠀⢨⡄⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠄
⡇⠀⠀⠀⠀⢸⡀⠀⢷⣌⣙⣂⣁⣀⠐⣇⠀⡿⠀⣧⠀⢸⡇⠀⢷⡤⠤⠤⣤⠀⠸⣧⡀⠇
⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠉⠉⠀⠀⠉⠃⠀⠀⠘⠓⠈⠛⠶⠒⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠇⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⢸⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠒⠚⠁⠀⠀⠀⠀⠀⢠
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⢳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠘⠦⣈⠉⠒⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⢉⡏
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⣀⣈⣉⠓⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠒⠒⠒⠈⣉⣀⣠⠤⠔⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⢐⣚⠿⠍⣭⡛⣫⡍⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠆⠠⠬⠉⠤⠌⠛⠛⠷⣦
⠀⠀⠀⢠⠂⠀⠉⠈⠛⠀⠘⠓⠀⠛⠁⠈⣌⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⡇
⠀⠀⢀⠼⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠼⣦⠀⠀⠀⠀⠀⠀⠀⢠⠇⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⠗⠛⡇
⠀⠀⣸⠂⢨⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⡥⠶⢟⣺⡆⠀⠀⠀⠀⠀⠀⣟⠀⠤⢤⣍⣉⣉⣉⣁⣠⠤⠤⠴⠒⣚⣭⣿
⠀⠀⣿⣀⠰⠤⠤⢤⣭⣁⣉⣩⣥⠤⠤⠶⠚⢛⣙⠇⠀⠀⠀⠀⠀⠰⣯⣀⡒⠦⠤⠤⠤⠤⠤⠤⠴⠖⠒⣋⣩⣴⣿⠁
⠀⠀⢸⠋⡿⠓⠒⢶⢶⡶⠶⠶⢶⡶⡖⠚⠛⣯⢹⡆⠀⠀⠀⠀⠀⠀⢸⠉⡟⠛⠛⡿⢲⠖⠒⠚⢻⢻⡋⠉⢹⡇⣿
⠀⠀⣸⠀⡇⠀⠀⣿⢸⡇⠀⠀⢸⡇⡇⠀⠀⢿⠘⡇⠀⠀⠀⠀⠀⠀⣾⢰⡇⠀⠀⡇⢸⣀⣀⣀⣸⢸⣇⡀⠀⣧⢸⡆
⠀⠀⡟⢸⡇⠠⣀⡿⢸⠃⣀⠴⠈⡇⣿⠀⠄⣸⡆⣷⠀⠀⠀⠀⠀⠀⡏⢸⡧⢴⣾⡇⢸⣿⣛⡿⢿⡆⣿⣛⣷⣿⡘⡇
⠀⢀⡇⢸⠡⡤⠉⡇⢸⠀⠀⠒⠂⡇⢿⠈⡁⠘⡇⢻⠀⠀⠀⠀⠀⢠⡇⢸⣿⣟⣿⡇⢸⣿⣭⣿⣿⡇⣿⣿⣽⣿⡇⣷
⠀⢸⠃⣾⠀⠀⠀⡇⢸⠀⠀⠀⠀⡇⢸⠀⠁⢀⣿⢸⡆⠀⠀⠀⠀⢸⠃⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⢿⣿⣿⣿⣧⢹⡀
⠀⣼⠀⡏⠀⠀⢠⡇⣼⠀⠀⠀⠀⡇⢸⡆⠀⢸⢸⡈⡇⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⢸⣿⣿⡟⣿⠸⡇
⠀⡟⢠⡇⠀⢠⢸⡇⣿⠀⠀⠀⠀⣿⢸⡇⠀⢸⡸⡇⣿⠀⠀⠀⠀⣿⠀⣿⣿⡿⣿⡇⣿⣿⣿⣿⣿⣇⢸⣿⣿⡇⣿⡇⣷
⢀⡇⢸⠃⠀⣼⢸⠁⡿⠀⠀⠀⠀⣿⠈⡇⠀⢸⡇⣷⢹⡀⠀⠀⠀⡏⢠⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⠈⣿⣿⡇⢹⣇⢹
⢸⠁⣸⢠⣴⡿⢸⠀⡇⠀⠀⠀⢀⣿⠀⣿⣦⣼⡇⡿⢸⡇⠀⠀⢰⡇⢸⡟⠛⠀⣿⠁⣿⣿⣿⣿⡿⣿⠀⣷⡉⠃⣸⡿⢸
⠸⣦⡻⣮⣍⡡⠊⠀⣷⣸⣶⣶⠏⡟⠀⠻⣮⣍⡠⠃⠸⠃⠀⠀⠸⣧⡸⣿⣦⣾⠏⠀⢿⣧⡉⠉⣰⡿⠀⠹⢿⣿⠿⠁⠸
⠀⠈⠛⠳⠶⢦⣤⣄⣈⣛⡳⠶⠂⠀⢀⣀⣀⣤⠤⠂⠀⠀⠀⠀⠀⠈⠻⠶⣬⣤⣀⣀⡀⠙⠻⠟⠛⠁⠀⣀⣀⡤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⢠⡄⢠⡄⠀⠀⠀⠀⢸⠀⡯⠀⠀⠀⢀⣤⣤⡤⢤⡄⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⣤⣤⣤⣤⣬⡇⠀⠀⠀⢸⣇⡇⠀⠀⠀⢿⣿⣯⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⢫⡄⠀⢼⡇⠀⠀⠀⠀⣿⠇⠀⠀⠀⣾⣿⣿⡟⢳⡆⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢸⣇⡀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣇⣸⣇⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⠃⠘⠇⠀⠻⢧⡀⠀⠀⠀⣿⠀⠀⠀⢠⣿⡿⠛⠇⠘⠃⠀⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⢸⣿⠀⠀⣰⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⢀⠀⣄⣀⠀⠀⡔⢹⠀⢸⣿⠀⢰⣹⣷⡄⠀⠀⠀⣴⡄⠀⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠱⣼⣷⣿⣿⣴⣧⡄⠈⠄⠸⣿⠀⢨⣼⠛⠁⠀⠀⠀⡀⢽⠈⠁⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠊⢛⣛⣿⣿⣭⢃⣿⣷⡀⢠⡁⠈⣿⠀⠘⠏⣶⢶⠀⠀⢀⡴⠈⠢⣤⠐⠚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡽⢿⣿⡿⣿⣿⢯⠇⠀⠀⡅⠀⣿⡂⠀⣴⣿⣤⣤⡖⡉⠀⠀⠀⠡⠉⢠⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣆⠀⠈⠘⠃⢊⢹⠰⠀⠀⠀⠇⠀⣿⡇⠀⡼⣿⣾⣾⡿⣮⣴⣦⡤⣀⣵⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣶⣤⡄⢀⡀⠈⡈⠶⠁⠀⢀⣄⣤⣿⣦⣤⣄⣿⣿⣻⣶⢟⢥⣰⡌⢸⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⡟⠻⣿⣿⣿⣿⠋⢻⣿⢉⣿⡿⠉⠀⣿⠉⠙⡟⣿⣿⣿⣻⡛⠛⡿⠙⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣷⢾⣟⢻⣿⣿⣟⣽⣴⣿⣿⠁⠄⠀⣿⠀⠀⡆⣿⣿⡾⠿⣶⠡⡀⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⣿⣿⣤⢿⢿⣿⣿⣿⣸⣿⣿⡿⠀⡆⠀⣿⠀⠀⣹⡿⠃⠀⠀⠘⠇⢠⡙⣿⣿⠟⢿⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣹⡟⡇⠈⠑⢿⣿⣿⣿⣿⣿⠋⠀⡇⠀⣿⠀⢨⢿⡇⠀⠀⠀⠀⠀⠜⠀⠀⠉⠀⢸⡅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⡅⠀⠐⠠⡙⢿⣿⠋⠈⠁⠀⣦⣤⣿⣦⣴⣸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷⣦⣤⣤⣼⣾⣷⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠚⡿⠉⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠺⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠶⠶⠶⢦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⠁⠀⠸⠇⠀⣤⡄⠘⠛⠀⠀⢉⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠛⠓⠶⠶⠾⠶⠶⠖⠛⠛⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠳⠶⢦⣤⣤⣀⣀⣀⣤⣤⣤⠶⠶⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣀⣀⡀⠀⣦⠀⣄⠈⠋⢹⡏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢾⡋⠉⠀⢸⣿⡄⣿⠀⠀⠈⣇⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠙⠷⣄⣼⠿⣧⢿⠀⢀⡀⣿⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠠⣤⡴⠾⢋⡟⠀⠻⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣬⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠚⠻⡇
⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢀⣀⣸⣻⠷⠋⠀⠀⢀⠠⠶⡒⢀⣴⣮⠤⠾⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⢀⠔⠁⠀⠀⠁
⠀⠀⠀⠀⢪⡿⠛⠁⢀⡀⣁⢿⣼⡾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠧⣝⣋⣀⣀⡴⡂⢀⠀⠀⠀⠄
⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⣀⣨⣶⣾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢶⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢼⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⣦⡤⠀⣀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠀⠀⠀⠀⠀⠁⠀⠀⠤⡀⢀⣀⠤⠞⠉⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢀⡀
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⣀⣀⣀⣠⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠐⠀⠤⠁⠂⠠
⠀⠀⠀⠀⠘⠒⠒⠀⠀⠀⠀⠻⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠉⢀⠘⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡀⡴⢊⡴⡶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢤⣴⠇
⠀⠀⠀⢀⠰⠛⠟⠙⠃⢀⣠⠴⢤⣶⡆⠀⣴⣂⣄⠀⠀⠀⠀⠀⠲⢤⣤⡦⠞⠁⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳
⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠰⣦⣌⠈⠩⠝⠡⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠿⠂⠀⠀⠀⠀⢣⠀⠀⢶⣶⣧⣀⠀⢠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣠⣉⡵⠶⠒⠉⠉⠉⠀⠀⣠⡶⠖⣒⡒⠉⣉⡩⠴⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠂⠀⠈⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡵⠿⠏⠁⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣂⠤⣄⣀⠜⠁⠀⠀⠈⠂⠀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠘⠛

⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀
⠀⠀⠀⢙⣽⣿⡗⠀⠀⠀⣠⠀⠠⢤⡼⡇⠀⠀⠀⠀⠀⠀⠀⡗⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⡷⣦⠄
⠀⠀⠀⠈⢻⡿⠀⠀⠀⠘⠁⠀⠀⢸⠃⡇⠀⠀⠀⠀⠀⣰⣧⣿⢀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢟⣃⡌⣵⣽⣶⣿⠃
⠀⠀⠀⢸⣿⡇⠀⠀⢰⣷⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡾⢯⡏⠸⡄⢻⡀⣿⠇⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠿⠟⢁⣀⠔
⠀⠀⠀⠘⣿⢧⠀⠀⢸⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠃⠀⠿⢀⣧⡇⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣤⣶⣶⣯⡇
⠀⠀⠀⠀⣿⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤⣤⡄⠀⠈⠤⢦⣅⣠⡀⡇⠀⠀⠐⣿⠀⠀⠀⢠⣿⣿⣿⡽⣿⠃
⠀⠀⠀⠀⢻⡇⠀⠀⠐⣿⠇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠁⠀⠀⢰⣿⣿⣯⣽⣿⡿
⠀⠀⠀⠀⢹⣿⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡿⠏
⠀⠀⠀⠀⠺⠹⠀⠀⢰⡇⠀⠀⠀⠀⠀⡆⠀⠀⠑⠾⠂⠀⠀⠀⠀⢸⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠁
⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⣷⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⠀⠀⢀⣀⣤⣄
⠀⠀⠀⠀⡿⡏⠀⠀⠀⣶⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣶⣇⡈⠋⠉⠉⠁⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⢸⡇⡇⠀⠀⠀⣿⠀⠀⠀⣿⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⣼⣧⣼⡁⢻⡇⠀⠀⠀⠀⠀⢴⣾⠇⠀⠙⠉
⠀⠀⠀⠘⢰⡇⠀⢠⡤⣿⡄⠀⠀⢿⣿⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢸⡇⣾⣅⠛⠛⠋⠟⠁⠀⠀⠐⣷⣿⣁⢀⣦⡀
⠀⠀⠀⠀⢸⠁⠀⠘⠃⠛⠂⠀⠀⠉⢹⡇⠀⠀⠀⠀⠛⠄⠀⠀⠀⠀⠀⠘⠃⠈⠙⠳⠀⠀⠀⠀⠀⠀⠘⠿⠋⠁⣾⣿⣿
⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⠀⠒⠀⡀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⢀⡀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠰⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⢻⠆⠀⠀⣀⠃⢀⠆⠀⠀⢰⡟⠀⠀⠈⠃⣿⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠠⣴⠇
⠀⠀⠀⠀⠈⠳⣄⡄⢻⣧⢚⣶⢀⣠⠞⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⠀⢄⣀⠀⢀⣠⣀⣤⠼⠷⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣤⣤⠀⠀⠈⣽⣿⣿⣿⣛⠛⠃⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⡀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡛
⠀⠀⠉⠉⠉⠉⠉⢢⢆⢤⡕⠌⠓⠒⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠒⠀⠀⠀⠀⠀⠀⠀⠐⢰⣄⣀⣰⠆⠴⠁
⠀⠀⠀⠀⠀⣀⣠⠋⠘⠸⡏⠂⢠⡔⠀⠀⠀⣴⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠉
⠀⠀⠀⠀⠼⠟⠁⠀⠰⠔⠃⠀⠈⠀⠀⠀⣀⣍⠁⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡦⠛⣿⣰⣿⡏⠀⠀⣤⡀⠀⠀⠀⠚⠋⠁⠀⣤⣤⣀⠀⠙⡾⠂⠀⠘⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⣖⣫⢿⠿⠃⠀⣀⣴⣦⡀⠀⠀⠀⡴⠋⠉⠀⠀⠀⢀⣴⣛⣶⣄⠀⠀⠉⠙⠒⠂⠀⠀⠀⣀⣀⡆⠠⢄⢀⣴⡿⠁
⠀⠀⠀⠰⠋⠀⣠⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⢔⠿⣓⢿⡯⣟⣶⣄⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣷⠀⢖⣻
⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠻⠡⣗⢫⠬⡝⢧⣚⠽⠀⢁⠀⠀⢠⡿⡿⠻⠟⢸⡟⢰⣯⣿⣦
⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢴⠸⣹⣷⠀⢹⣿⣗
⠀⠀⢠⢷⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣖⡰⡠⢀⢀⣀⡆⠐⣒⣦⠀⠀⡀⢀⢀⠁⠀⢀⡀⠀⠸⠈⢹⡏⠘⡿⣿⠏
⠀⠀⠠⡿⠠⠃⠰⡟⠟⠛⠓⡄⠀⠀⠰⠯⠒⠓⠛⠻⠚⠁⠀⠃⠻⡾⠻⠚⠋⠙⠀⠀⠨⠽⠃⢀⣤⡈⠇⠀⠈⠿⠄
⠀⠀⠀⠀⠀⠀⣴⢰⡄⠘⠻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠁⠀⠀⢀⡀⠀⠀⢠⡖⢄⠈⠿⠇⠀⣶⣦⠀⠀⢀
⠀⠀⠀⠺⢿⣿⣿⣿⣧⡄⠀⠘⠀⢠⠀⠀⠀⠈⣀⣀⣀⠀⠀⣼⠀⠀⠀⠀⢿⠶⣿⠇⠈⠙⠉⢀⣠⣤⣤⣄⣀⡀⠀⠻⠆
⠀⠀⠀⠐⠿⣿⣿⣿⣿⣧⠀⠀⠀⠈⢰⠀⠀⣿⠉⠉⠁⠀⠀⠁⢨⣽⣶⠀⣤⠀⣤⣄⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⡀⠀⠀⣿⠀⣽⠉⡏⠀⠀⠀⢰⠎⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⣭⡇⠀⠉⠉⠉⠁⠸⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠰⡟⠀⣿⠀⡇⠀⠀⠀⠈⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⣴⣿⠇⠀⣁⡀⢀⣀⠀⠀⠙⠉⠉⠀⠀⠃⡏⠙⡿⠁
⠀⠀⠀⠀⠀⠇⠀⣿⠀⠇⠀⢰⡀⣰⣆⡀⠀⠀⠑⠀⠀⠀⣀⠰⠾⠉⠀⠀⣿⢹⣿⣯⠀⠀⠰⢄⣀⠀⠀⠀⢀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠰⢴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠒⠚⠻⠀⠀⢐⠀⡀⢐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡢⡶⠢⣾⡆⠀⡘⠀⠿⠜⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠗⣉⣧⢻⡇⠠⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣗⠀⠀⣡⣿⡇⠀⠀⠀⠀⣦⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠨⡚⠉⡻⠛⠛⠃⠈⡀⠀⠀⢯⣴⠿
⠀⠀⠀⠀⠀⠠⠀⠂⠌⢑⠀⠠⠤⠀⠠⠀⠉⠒⠌⠁⢀⣠⣀⠀⠈⡙⠋⠀⠐⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⠀⠈⠐⠀⠀⠀⠀⠀⣼⡟⢛⢻⣾⠊⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⡀
⠀⠀⠀⠄⠠⣾⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⡀⣩⠴⣺⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡴⠟⠏⡹⢿⣿⣦⣤⡀
⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠞⢁⠞⡽⢠⣿⣿⣿⠀⠀⠀⣠⣶⠃⠀⠀⠁⣴⣣⣤⠿⢿⣿⣷
⠀⠀⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⠁⡰⠃⡜⡰⠋⣷⣿⣿⠀⠀⠀⠻⢯⣄⣀⡀⠀⢀⣿⣥⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠹⢛⡿⣿⠿⠋⠀⠀⠀⠀⠀⣧⠞⣀⠴⠀⠀⠀⣻⣿⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠘⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠀⠀⠀⠀⠀⢰⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⣿⣟⡛⢚⣭⠀⠀⠀⠀⠀⢀⣤⡤⣿⣿⣿⡿⢀⣠⣄⡀⠀⠀⠀⠀⢀⠰⢶⣶⣶⣾⡀⡰⠶
⠀⠀⠀⠀⠀⠀⢸⣟⠒⠈⠋⠀⠀⠀⠀⠀⢿⣿⡿⠋⠉⠁⠀⢾⣿⣿⡶⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣤⠄⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣶⡄⠀⠉⠉⠀⠀⠀⠀⠀⠈⢿⡷⠆⠛⠛⠁⠀⠀⡎
⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠃⢀⣾⣿⣦⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣟⡷⠾⠿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⢠⡛⠋⠉⠁⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠳⠿⠿⠵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⣽⣟⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢠⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⡄⢿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣴⣿⣿⢟⣫⣽⣶⣾⣿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠈⠉⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠉⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣯⣿⣽⡟⣿⣿⣿⠟
⠀⠀⠀⠈⠂⡀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⢀⡄⠀⠀⠀⠲⠾⣿⣿⣿⣿⣯⣿⣧⣿⣿⣿⡿⠟⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠘⣷⣿⣷⣦⣀⠀⠀⠀⠉⠉⠹⠋⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠙⠭⠽⠯⠿⠿⠛⠋⠁⠀⢀⣀⠻⠿⣿⡷⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡄⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠰⣶⣬⠙⢉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠘⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⡆⠐⠀⠀⠀⣀⠰⠀⠆⠀⠀⠀⠀⠈⠳⣌⠳⢄⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠐⠦⠈⠀⢀⡁⠀⢀⠄⠀⠀⠀⠀⠀⠱⣤⣿⣦⣹⣿⣃⣠⣴⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠒⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣟⠻⣅⠀⠀⠀⠀⠈⠛⠛⠛⣻⡿⠿⡟⠻⠏⠙⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠉⢰⠈⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠻⣝⠻⣷⣜⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⣿⠿⣿⣿⡿⡿⠟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠌⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢧⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿
⠀⠀⠀⠀⡀⠀⠈⡌⠀⣸⣯⠟⠁⠀⠀⠀⠀⠀⠀⣴⣾⢿⣿⣧⣡⣄⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣴⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠏
⠀⠀⠀⠀⠈⢼⠀⡇⢰⣟⢕⣡⡄⠀⠀⠀⠀⠀⠀⠉⢡⣾⣏⢻⣿⠻⠗⠀⠀⠀⠀⠀⠀⣿⣻⣟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣠⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠸⡆⣷⣿⣟⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣤⣶⡾⠿⠿⢛⠻⢿⠋
⠀⠀⠀⠀⠀⠀⣿⡿⠝⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⣽⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣿⣷⡆
⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠗⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠃


⠀⠀⠁⠁
⠀⠐⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠊⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠸⠆⠀⠀⠀⠀⠀⢠⠑⠶⠃⠀⠀⣳⠖⠀⣠⡄⡐⠀⠴⠉⠒⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠈⠁⠀⠀⡤⣻⠀⠀⠊⠳⣼⠀⢀⡴⢡⠞⠁⡜⠒⠁⠙⢡⣀⠀⠒⢀⡈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⣀⡄⠀⠐⠀⠀⡔⠀⠀⣰⡃⠀⢸⠀⠠⠀⠀⡘⢰⠃⣠⠞⠀⣀⡆⠂⠀⠀⢀⣀⠈⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠀⠁⠘⣆⡰⠀⣼⠀⠀⠀⢱⠃⠀⠀⡇⠀⢂⡔⠀⠈⢉⣥⠔⠈⠁⠀⠀⠀⠀⠀⠈⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠄⠀⢦⠈⠀⠴⠁⠀⠀⣠⠏⠀⠀⠀⡟⢠⢎⣠⠴⠊⠁⢠⡖⠒⠒⠒⠀⠤⣤⣀⣙⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⡀⢀⠀⠂⢀⠗⢀⡴⠊⠀⠀⠀⠀⣀⡴⠟⠋⠩⠍⣀⠐⠂⠩⠉⠉⠩⠿⠥⢤⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠱⡈⡞⡰⠋⠀⠀⠀⡠⠔⠋⠁⠀⠀⠀⠈⠢⣄⠈⠐⢀⠀⣀⣀⠀⠀⣠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠃⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⡎⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡠⠊⠀⠀⡠⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⠀⢀⡴⠊⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢤⣀⠀⠀⠐⢂⣠⣥⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢈⠑⠢⢄⣈⠁⠀⠈⢉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠸⡳⡀⠀⠙⠂⠠⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⣄⠁⠙⠓⠤⢄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⣿⠙⣷⢀⣀⡀⢀⡀⣀⢀⣀⠀⣿⡇⢀⣀⡀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠃⣸⢼⣿⢸⣿⠁⠹⣧⡁⣿⡇⣿⠜⠃⠹⣇⢸
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠛⠚⠛⠘⠛⠀⠐⠚⠃⠛⠃⠙⠓⠂⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⢀⠀⣀⣀⣀⣀⡀⣀⣀⣠⢀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠠⠄⡀⢄⠀⢀
⠀⠀⠀⠀⠠⠬⠥⠤⠖⠒⠩⠭⢍⠀⠈⠲⠖⠋⠠⠀⠆⠀⠉⠓⡜⠒⣾⣔⡾⠄⠀⠀⠀⠀⠀⠀⡀⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⡄⠂⠈⠄⠁
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⠆⠀⠀⢀⡀⠀⠀⠀⠀⢠⠤⠔⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠈⠟⠛⠁⠀⠀⠀⠠⠼⠀⠉⠀⡀⠣⠀⠐⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠋⠀⠀⠀⠀⠒⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⡀⠀⠠⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠘⠰⢄⣀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠠⢀⠀⠀⠀⠀⠈⠀⡀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠈⠉⠱⠣⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠤⠀⠀⠀⠀⠀⠀⠠⠽⠛⠀⠄⠀⠁⠈⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢄⡆⠀⠀⢘⠀⢀
⠀⠀⠠⠀⠠⢂⣀⣀⣀⠀⠈⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠀⣀⠀⠀⠀⠈⣑⡀⠇⠀⠀⠠⠄⠠⡰
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⢀⠀⠀⠀⠀⠉⠄⣊⣁⡄⠀⠉⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⡂⠁
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠙⠒⠈⠀⠀⠀⠈⠁
⠀⠀⣿⣿⢿⡿⣿⣿⡿⣿⢿⣿⡇⠀⠀⣠⣄⣤⣤⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠆⡄
⠀⠀⠘⣿⣶⣾⣷⣿⣷⣾⣾⡿⠃⠀⢿⣿⣿⣿⡿⠟⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠈⠻⠿⣿⣿⣿⠿⠛⠁⠀⠀⠈⠂⠀⠀⠂⠑⠀⠁⠀⠀⠀⠀⠀⠠⠄⠤⠁⠀⠀⠠⠤⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠸⠧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⣀⣀⢀⣁⡦⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⡁⠝⠂⠠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠰⣬⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠒⢠⡂⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⣡⡂⠀⠀⠀⠀⠀⡣⢠⡀⣄⣤⢀⡄⠘⣂⢉⣿⠁⣤⠲⠆⡾⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⢺
⠀⠀⠀⠀⠀⠉⣽⡍⠓⢀⠀⡀⠀⠀⠀⠤⠀⠠⠆⠀⠽⠇⠀⠀⠀⢀⠎⡀⠸⠶⠿⣯⣊⣁⣈⡁⠐⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠁⠴⠤⠼⡄⣠⠄⠀⠀⡀⠀⠤⣡⠉⠁⠀⠀⠀⠀⠀⠈⠓⠛⠁⠒⠯⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠀⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⡀⠤⢦⢀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣀⣀⣀⠤⠾
⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠂⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠠⠂⣀⡀⠔⠀⠍⠀⠂⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠁⠀⠉⠑⠚⣶⣷⡞⠤⠀⠀⠀⠀⠀⢀⢾⣁⠉⡀⠜⠁⠁⣠⠀⠀⠴⡌⡀⣢⢴⡇⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠘⡷⣤⣤⡀⡀⢠⣴⣶⠿⣾⣷⡀⠄⠀⠀⠀⠀⠈⠀⠈⠑⠐⠇⠤⠤⠤⠤⠼⠡⢚⡫⠕⠈⠓⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠘⣟⠁⠀⠀⠟⢱⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠀⠉⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⣄⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠋⢀⠀⠓⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠀⠀⠐⠒⠈⠁⠀⡀⠄⣀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡴⠿⠗⠀⠀⢠⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢠⡰⠃⢀⣀⡀⢠⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠛⠛⠉⠉⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⠀⠀⠀⠀⠀⠀⣬⠂⣠⠅⠀⠀⠀⠀⠀⠀⠀⢺⠀⢀⣄⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣀⠠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢤⢥⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠖⠂⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣈⠁⠈⠀⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠁⠀⠀⢀⣦⡀⠀⠀⠀⣼⢂⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠆⠀⠀⠀⠈⠳⠾⢄⣗⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠤⢤⠤⣀⠄
⠀⠀⠀⠀⢠⡀⠰⣎⡀⠂⠻⠶⡶⠚⡋⡿⠥⣠⡆⠀⠀⠀⢴⠋⠁⠀⠀⠀⢠⠌⢁⣆⠄⠀⠀⠈⣭⡩⣷⡆⠀⠀⢀⠀⠀⠀⠀⠀⠘⠁⠀⠘⢦⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠃⠍⠄⠐⠊⡝⠀⠀⠀⠀⠱⠒⠄⢐⣀⢁⠀⠉⠉⠉⢀⣀⣰⣦⠴⠟⡟⠀⠀⠀⠀⠛⠀⠰⠆⠀⠀⠀⠀⠀⠘⠙⢿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣄⠀⠀⠀⠀⢀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⣀⣤⠤⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣵⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠒⠒
⠀⠀⠀⡀⠀⠒⠀⠀⠁⠠⠀⠄⠀⠢⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠘⠱⠂⠀⠠⠄⢀⡀⡈⠒⢤⠀⠀⢤⡀⣇⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠀⢠⠆⠀⠀⠀⠈⠄⠈⠀⣆⠀⠀⠀⠀⢀⡔⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⠒⠀⠠⠀⢀⠃⠀⠀⣀⠀⠀⠀⠀⠠⠃⠀⠀⣠⠞⢁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⣂⣀⣠⡞⠄⠠⡈⠆⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠄⠀⠰⠀⠀⢸⡀⠁⠀⣠⡀⠊⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠁⠀⠀⢘⠀⢀⢨⠁⠠⡘⠛⠁
⠀⠀⠂⠀⠀⠀⠀⠀⢀⠌⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣸⠠⣮⠛⠦
⠀⠀⢱⡆⠀⠀⠒⠘⠋⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣌⠈⠀⠀⡀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠂⢠⡀
⠀⠀⠀⠳⠄⠀⠤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠂⠀⠀⠀⠘⢠⣤⡀⣀⠀⢀⣀⣀⡤⢤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠠⡘⠀⠀⠀⠈⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣛⣿⢻⡟⣿⣟⣟⢻⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠠⠖⠂
⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡉⠓⠬⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⠀⠙⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣠⣄⠈⠀⠀⠀⠀⠉⠀⢲⣦⡄
⠀⠀⢸⣏⣯⣆⠀⠀⠀⠈⠉⠁⠙⠃⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠈⠁⣀⣀⣈⡀⠀⢀⣾⡀
⠀⠀⢸⣿⣷⣿⣽⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣤⡤⡄⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠠⠂⠐⠿⠁⠀⢀⠀⠀⠰⣶⢿⣿⠧⡀
⠀⠀⠀⠹⣿⡿⣯⣿⣃⣀⣀⣀⣀⣀⡠⠤⠛⠋⠒⠋⠊⠀⠀⠀⠀⠀⢸⡄⠀⠀⣼⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⡮⣙⠖⢃⡄
⠀⠀⠰⠀⠈⠳⣌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠗⠀⠞⠿⡤⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠥⠙⡋⡄
⠀⠀⠀⡀⠆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠇⡃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠾⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠰⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣠⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠫⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⡑⢦⣉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠶⠖⠛⠛⠦⠑⠄⠀⠃⠀⢠⠀⠀⢰⠇⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠢⠙⠂⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠐⠐⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠈⠁⠀⠀⠀⠀⠈⠒⠤⠄⠀⠀⠀⣀⡀⠄⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠉⠱⣆⣀⡀⠀⠀⠀⢀⡿⠁⡝
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⢤⣤⣿⣶⡶⠀⠀⠀⢸⣿⣶⣧⡄⠀⠀⠀⠀⠀⣀⣴⣄⡀⠠⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⣾⣿⣿⡿⠃⠀⠀⠀⠸⣿⠿⠋⠙⠷⣤⣄⣀⡀⠙⠁⠙⢻⣷⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⣤⣀⠀⠘⠿⡦
⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣤⠀⠈⠀⠀⠀⠀⠀⠉⠋⠅⠀⣰⡄
⠀⠀⠀⠀⢩⣭⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠐⣂⣘⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠉⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣾⣋⣈⣻⣟⣿⡟⠂
⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢙⣿⣇
⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢹⣷⣟⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡏⠛⢦⣀
⠀⠀⠀⠘⢏⠴⠲⣤⣤⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠲⠦⣀⠀⢀⡿⠇⠤⠀⠘⠉
⠀⠀⠀⠀⠈⠀⠀⠆⠶⣍⣽⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣄⡜⢧⡄⠀⡄⢠⠈⡛⢠⢖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣏⠙⠁⡏⠁⢰⣄⢰⠃⠀⠀⠛⠃⠀⠰⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠁⠀⠚⠃⠀⠀⡄⣸⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⣌⠀⠀⠀⠀⠀⢰⡥⠃⠂⠀⠀⣾⠽⠂⢁⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⠀⠀⠀⡇⠀⠀⡴⠀⠀⠀⠀⠀⠀⠨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠆⣤⡀⠀⠀⠀⠀⠀⣵⠀⠀⢠⠀⡠⠊⠁⠀⠀⢾⡭⠄⠂⠒⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣴⣆⣘⡅⠠⠆⠙⣤⡀⠀⠀⠀⠈⠀⢀⣦⠎⠀⠀⠀⠒⠀⠀⠀⠀⠰⠒⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢏⠁⠘⢍⢡⡀⠀⠘⠃⠀⠀⠀⠀⠀⣰⢏⡀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠲⠼⠂⠀⠀⢈⢁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠘⠁⠢⣀⢀⠀⢰⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡛⠀⠀⠀⠀⠀⠀⠀⠈⡉⠘⠋⠓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⣉⡍⢩⣠⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡘⠂⠀⠀⠀⠀⠀⠉⣠⣄⢰⡀⠀⠀⠀⢠⡤⣄⡀⠀⠀⠰⡔⠉⣤⠇⠀⡠⢫⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡦⢚⡷⠀⠀⠁⢸⠁⠈⠀⠃⠀⠀⠈⢋⡄⠀⢈⠙⠓⠦⣤⣄⠀⠀⠀⠉⠀⠀⠁⠘⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡯⠀⠀⢁⡄⡆⢰⠇⠀⠀⠀⠈⠙⢤⠂⠀⢸⠃⠀⠀⠀⠁⠈⠑⠒⠀⠀⠀⠋⠁⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣶⠴⡶⠋⠿⠀⠘⣻⠀⠀⣴⣄⢰⠄⠀⠀⠰⠀⢀⣬⠂⠀⠦⠉⠂⠀⢠⣤⣅⢠⣤⣤⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠶⡆⠈⠃⠀⠀⠀⠀⣄⠸⣼⠀⠀⠀⠐⠆⠀⠈⠛⠿⠧⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢹⣰⡄⠀⢞⠰⢶⠶⡶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⣀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠁⣼⡄⣿⡇⣤⢰⣄⠠⣦⢰⣦⢰⣿⠐⣴⡤⢆⣴⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣿⡇⣿⡃⣶⣸⣿⢀⣿⢀⣿⢸⣿⠀⣿⠀⠸⣿⢨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠂⠈⠀⠉⠀⠉⠁⠉⠀⠉⠘⠁⠀⠉⠀⠉⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⢉⡇⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡀⠐⠀⠇⢀⠀⠀⢀⡀⢠⠉⠒⢁⡀⢈⡼⡃⢀⠴⣀⠂⠐⠃⠈⠁⣁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠔⣸⠀⠀⠀⠙⠾⠀⢠⠊⡴⠋⢠⠋⠁⠀⠁⠄⠄⠀⠀⣤⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢢⠴⡀⠀⠃⠀⡞⠀⠀⠴⡇⠀⠀⡆⠀⡀⢀⠌⢸⣠⠴⢁⣠⠼⠊⠀⠀⠀⠤⣄⡠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⡀⠙⠤⠀⠰⠁⠀⠀⢰⠃⠀⠀⣧⠀⢡⠊⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⢀⣀⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠚⠀⠈⠂⠀⢘⠃⠀⢀⡴⠃⠀⠀⠀⠟⣰⣥⠶⠋⠁⣀⠸⢭⣤⣤⢌⣭⠒⠶⠤⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠎⢀⠖⠁⠀⠀⠀⣠⠴⠚⠉⠀⢐⡀⠀⠀⠈⠁⠀⠀⠘⠑⠈⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠱⡜⠐⠁⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⢖⠦⠤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠔⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠔⠁⠀⣠⠖⠁⠘⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠐⠊⠀⢀⡠⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠠⢀⠀⠀⠚⠉⠁⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣦⡀⠉⠲⣄⢀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠡⡀⠀⠱⢤⣀⡀⠈⠁⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠢⠖⠢⠒⠚⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣶⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠟⢘⡩⣿⠈⣿⠉⠸⣯⠀⣿⢠⣾⠙⠋⢿⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠻⠗⠿⠀⠟⠀⠀⠾⠃⠿⠈⠻⠆⠀⠘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈

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

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂
⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢠⡤⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠇⠺
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠉⣫⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠆⠃⢄⡀
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠱⣄
⠀⠀⠀⠐⡽⣆⠀⠀⠀⠁⣄⣠⢞⠅⠀⠀⠀⠀⠀⠀⠀⡤⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠓⠒⠰⠶⠒⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠈⠳⠽⣓⣒⣚⡫⠕⠋⠀⠀⠀⠀⠠⣀⣀⣀⣁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢸⡖⠠⣤⣶⠐⣾⠀⠀⠀⠠⠀⠀⢀⡠⠞⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁
⠀⠀⠀⠀⠘⠧⠀⠘⠋⠀⠛⠀⠀⠀⠀⠐⡌⠉⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⢀⣀⡀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡦⣃⢶⡀
⠀⠀⠀⠀⠀⣶⠆⠠⠤⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠉⢹⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠉⢈⢁⡆
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⡀⠀⠀⠀⠀⠀⠁⠶⣀⣸⡞⣭⡇
⠀⠀⠀⠀⢀⣿⠦⣄⣠⢤⡇⠀⠀⠀⠀⠀⠀⠘⣇⣄⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⣆⣹⠎⠗⠂⠀⠀⠀⠐⠐⠔⠋⠉⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠸⣯⡉⣿⣿⣿⣿⣿⣿⣿⣿⠋⣩⡿⠀⠀⠀⠀⠀⢿⣉⢹⣿⣿⣿⣿⣿⣿⣿⡟⣉⣽⠇⠀⠀⠀⠀⠀⢺⣍⡉⣿⣿⣿⣿⣿⣿⣿⣿⢉⣩⡿
⠀⠀⠀⠀⠀⣠⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣧⡀⠀⠀⠀⠀⠀⢀⡼⢻⣿⣿⣿⣿⣿⣿⣿⡟⢿⣄⠀⠀⠀⠀⠀⠀⢀⣠⠟⣿⣿⣿⣿⣿⣿⣿⣿⠻⣄⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸⡇
⠀⠀⠀⠀⣿⢶⣦⣤⣴⡶⣶⡴⡖⣶⢦⣆⣴⣼⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣾⡇
⠀⠀⠀⠀⣿⢺⣏⣿⡴⣿⠾⡾⣭⣻⣻⣟⣿⢺⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣇⠀⠈⢢⣄⠀⠀⠀⠀⠀⣴⣯⣿⢻⠃
⠀⠀⠀⠀⣿⢹⠻⣾⢫⣸⡓⣻⢚⣾⢿⣼⢿⢻⠇⠀⠀⠀⢸⣷⣛⣶⣮⣼⠃⣿⢻⣟⢰⣧⡿⢶⡟⠀⠀⠀⠀⠀⣏⠻⣦⣘⣿⣷⣤⣴⣶⣿⣿⡿⠃⣸
⠀⠀⠀⠀⢸⣔⢿⠟⢛⣿⣿⣙⣞⣛⣆⢷⢏⡽⠀⠀⠀⠀⠀⣿⣯⣉⣿⣾⣯⣽⣯⣤⣿⣺⣟⣿⠇⠀⠀⠀⠀⠀⢻⡀⠈⠛⣻⣿⣛⣻⣟⣛⡉⠀⢀⡟
⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠙⠉⠉⠋⠙⠋⠁⠀⠀⠀⠀⠀⠈⠉⠙⠙⠉⠋⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠋⠋⠉⠉⠉⠉⠉⠉⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣤⡤⣤⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⢤⡄⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄
⠀⠀⠀⠀⠈⠓⣦⣿⣿⣿⣿⣿⣿⣿⣿⣦⡖⠋⠀⠀⠀⠀⠀⠛⢲⣼⣿⣿⣿⣿⣿⣿⣿⣇⣴⠚⠁⠀⠀⠀⠀⠀⠘⠳⣦⣿⣿⣿⣿⣿⣿⣿⣿⣴⠞⠋
⠀⠀⠀⠀⢠⡶⠋⠙⠛⠛⠛⠛⠛⠛⠛⠉⠛⣦⠀⠀⠀⠀⠀⣴⠛⠙⠛⠛⠛⠛⠛⠛⠛⠃⠙⢶⡄⠀⠀⠀⠀⠀⣠⠞⠃⠛⠛⠛⠛⠛⠛⠛⠛⠈⠳⣄
⠀⠀⠀⠀⣾⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢸⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣿⣋⣤⡶⣋⣿⡛⠿⣿⣫⣽⣿⡇⢹⡇⠀⠀⠀⢸⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⣿⡟⢿⣿⡏⣽⣿⣦⣹⣿⣏⢻⣧⣾⡇⠀⠀⠀⢸⣿⣭⣽⣷⣞⣿⣯⣿⣯⣹⣾⢿⣽⣿⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⣿⣿⣮⣿⣿⣿⢰⣿⢟⣽⣿⣶⢿⣿⡇⠀⠀⠀⢸⣿⣻⠿⣾⢿⣿⣵⢟⣽⣛⣿⣇⣿⣿⠀⠀⠀⠀⢘⣿⣧⠿⣶⣿⢿⣷⣾⣛⣿⣠⣼⣷⣿⡇
⠀⠀⠀⠀⣿⣿⢋⣽⣧⣹⣤⣿⣾⢿⣷⣶⡾⣿⡇⠀⠀⠀⢸⣿⣿⣻⣷⣿⣽⣿⡿⢟⣿⣧⣿⣹⣿⠀⠀⠀⠀⠀⣿⣿⣾⣛⣿⣿⣥⣼⣟⣻⣿⣧⣿⣿⠁
⠀⠀⠀⠀⢻⣿⣿⢟⣿⣿⣛⣉⣻⣧⣿⠟⢠⣿⠁⠀⠀⠀⠸⣿⣍⠻⣿⣾⣯⣙⣿⣿⣯⣽⠾⣿⡏⠀⠀⠀⠀⠀⣿⣿⣹⣿⣛⣿⣉⣽⡿⢿⣼⡟⣻⣿
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠤⣀⠀⠀⠀⠀⠀⡔⠀⢠⡄⡄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⢠⡤⢤⣔⣢⠴⠗⠂⠀⠀⠀⢇⠀⡼⡇⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡆⠧⣇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⢀⣒⣾⠀⠀⠀⠀⠊⠈⠀⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠄⠭⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠂⠀⠊⠉⠉⠉⢡⠸⡄⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢱⠊⠑⠠⠄⠀⠤⠤⢤⣀⡼⣠⣇⠀⠀⠀⠀⢀⡀⠤⢇⠀⠀⢀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠠⣰⡀⠀⠀⠀⠀⠀⠀⣀⣿⡻⣇⠉⠉⠙⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⡦⠀⡀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⢀⠜⠙⠓⠶⠂⠒⣶⣯⠝⠉⠋⢽⢳⣀⣀⣀⣀⣀⡠⠴⢻⠔⢒⣦⡀⠈⠦⠈⢓⠐⡞
⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠨⡟⠀⠀⠀⢈⠀⢣⠀⠀⠀⠀⠀⠀⠁⣰⡿⡏⣵⣀⡀⠀⠀⠷⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢠⠞⠁⠖⠀⠀⢈⣁⠀⢀⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠋⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠠⠀⠀⠀⠀⠠⠀⣸⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⣠⡷⣁⣀⣤⡀⢀⣆⣀⣀⣤⠴⠌⠁⠀⠀⠀⠀⠀⠀⣋⣴⡟⠀⠀⢠⠀⠀⠀⠐⠂⢀⠃⠀⣺
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠕⠀⠀⠈⠉⠉⠒⠋⠉⠀⠐⠀⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈⠉


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

⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⢠⣶⡄⠈⠙⡄⠀⠀⠀⠀⠠⣶⠾⣫⣵⣾⠇⠀⠀⠀⠀⢰⣿⣧⣴⡾⠀⠀⠀⠠⠀⢄⢄⠄⠠⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠹⣄⠴⠆⠀⠀⠀⠀⠀⡈⠀⢀⢹⠟⠁⠀⠀⠀⠀⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⠄⠱⢲⠂⠀⠀⠀⠀⢀⡄⡜⠲⠄
⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠀⠀⠀⠀⠐⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢘⣛⠂⠀⣛⣛⠀⠀⠀⠀⠀⠀⣀⣀⣻⣷⣷⠀⠀⠀⠀⢴⣛⡿⣿⣶⡀⠀⠀⠀⣀⢠⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀
⠀⣿⣿⠇⠀⠟⠻⠀⠀⠀⠠⣾⢟⡫⠿⠃⣫⠉⠀⠀⠀⠀⠀⠈⣿⣿⠿⠁⠀⠀⠀⣿⠅⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠿⠿⠇⠸⠀⠀⠇⠀⠀⠐⠉⣑⣐⣋⣩⠴⠃⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⢰⠺⠓⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠸⢿⡿⠀⢠⣶⡄⠀⢀⣤⣤⣄⢠⡿⢋⣵⣿⡇⠀⠀⠀⣾⠁⠀⢠⣤⠀⠀⠀⠀⣠⣤⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⠿⣷
⠀⣠⣤⣴⡆⠀⡈⠀⠀⠀⠻⣯⡿⢟⣵⣿⡿⠛⠀⠀⠀⠀⠘⠂⢠⡟⡹⠀⠀⠀⠀⣿⣿⣿⣧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢩⠉
⠀⠛⠛⠁⠀⠘⠛⠀⠀⠀⠀⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⠒⠶⠚⠫⠒⠁⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁