Butterly Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢋⡿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣿⢻⡷⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⣧⣾⠷⣿⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠻⢡⠋⢀⡠⠛⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡧⠶⣇⠔⠋⢀⡴⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⡟⠀⢸⢃⡠⠖⠁⢀⣠⣾⠟⠁
⠀⠀⠀⣴⣶⣶⡦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡞⠉⠀⢀⣴⣿⠟⣁⣀⣤⣀⡀
⠀⠀⠀⠘⢿⣿⡙⣾⡛⠫⣿⣿⣷⣦⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡰⠁⢀⣴⣿⣿⠿⠋⢉⡹⠿⢿⣿⣧
⠀⠀⠀⠀⠀⠙⢾⣿⣭⣽⠯⢅⣊⡽⠻⢿⣷⣮⣄⡀⠀⠀⠀⠀⠀⢸⡇⢠⣃⣴⡿⢿⣟⡡⠔⢊⣁⠤⠐⠚⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⡤⠵⠦⢄⣀⠉⠛⠻⢷⣤⣀⢠⣶⣼⣥⡾⠟⣫⠞⠉⠙⠒⠚⢓⣤⡔⠒⠂⢉⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡤⠄⠒⠋⠉⠁⠒⠒⢒⣻⣿⣿⣿⣷⣴⠯⠤⠤⠴⠶⠶⢏⣁⠀⠉⠙⠒⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣤⣤⣤⣶⣶⣿⡿⠟⣫⠜⣿⣿⣿⡯⣓⠦⠤⣀⡀⠀⠀⠉⠓⢦⣼⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠛⠛⣳⡖⠉⠀⡸⠀⡝⡟⢿⡎⠕⣦⣀⠉⠙⠒⠦⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡎⢀⡾⠀⢰⠃⠀⢧⠘⡜⣿⣄⠀⠈⠑⠲⠴⠾⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡀⡟⢏⠣⡀⠘⡀⠱⣏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣦⣑⣄⢁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠋

⣶⣶⣶⣶⡶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⢶⣶⣶⠶⠶⡶⢶

⠀⣠⡤⣤⣄⣀⡀
⠀⣧⣿⡿⣷⣶⣤⡉⠳⠶⣠
⠀⠻⣷⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣦⣀⡀
⠀⠀⠸⣿⣤⣿⣿⣏⣉⣻⣾⠿⠿⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⢽⣿⣽⣙⣷⠤⠼⣿⠀⠀⣠⣾⣿⢯⣷⣄⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣹⣏⣉⣿⣗⠒⠛⣣⣀⠿⡿⠉⠀⣩⣮⣳⣄⡀
⠀⠀⠀⠀⠈⣻⣏⣛⣿⣏⠁⢈⣉⣓⣦⣀⠺⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤
⠀⠀⠀⠀⠀⢈⢫⣩⣽⣿⣁⠀⠀⠉⣁⣿⣿⣶⣭⡃⠈⢿⣿⡄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠫⣿⣭⣼⣏⣀⠀⢀⣉⣹⣿⣿⣇⠈⠱⢦⣻⣿⡀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⢀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣶⣾⡧⠥⠿⣤⣤⡤⠤⠤⠤⠬⠍⢙⣓⡻⢿⣿⣿⣿⣶⣿⣿⣠⣤⣤⢴⠶⠾⠿⠿⣿⣿⣿⣟⣛⣓⠲⠾⢭⣽⣛⠲⢦⣄
⠀⠀⠀⠀⠀⡿⣧⣬⡷⠒⢻⠋⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⢿⣾⡿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⡀⢰⣿⣿⠀⠸⣿⣽⠉⠙⢶⣮⣭⣟⣾⣟⡿⢷⣄⡀
⠀⠀⠀⠀⠀⣿⣏⣱⣿⠆⢙⣦⣀⡀⠀⣀⣤⠞⠋⠁⢀⡠⣺⣿⣛⣿⣿⡷⠪⠙⠳⢄⡀⠀⣠⣿⣿⣿⡦⣄⣻⡟⠁⠀⣀⡼⠣⣄⣹⣿⣻⣿⣿⣟⠹
⠀⠀⠀⠀⠘⣿⡟⣍⣿⣶⠁⢠⠏⠙⢋⡻⠋⠀⠀⣰⠟⣰⣿⣳⣾⠏⠈⢰⡄⠀⠑⠦⡉⠻⣿⣿⡿⠋⠙⠁⠉⠋⠉⠛⣭⣑⣦⣾⠿⣍⣙⢿⣆⡿⠟
⠀⠀⠀⠀⢶⣟⢛⣋⣿⣿⣾⣿⣀⣄⣭⡀⠀⣠⣾⠋⣰⣿⣿⡿⢃⡼⠀⠀⣧⠀⠀⠀⠹⣷⢄⣹⣷⣬⣦⡀⢰⣤⣤⣶⡿⢯⡝⣹⣧⣼⠟⠛⠚
⠀⠀⠀⠀⢀⣿⣿⠻⡉⣫⣿⠿⣿⣿⣛⣿⡶⣥⠃⢰⣿⡿⠟⢠⠞⠁⠀⢈⡟⢧⡀⠀⢀⠿⣆⣹⣾⣿⢿⣿⣿⣭⣿⣼⣿⡟⠛⠏
⠀⠀⠀⠀⣼⢃⠐⠀⢼⡻⠛⢺⣿⠙⠛⡟⣭⠋⠀⠛⠋⢀⢐⡿⢶⣤⠀⢸⠃⢸⠋⠒⠘⣆⣹⣽⣼⣿⠀⠈⠉⠈⠁⠀⠈
⠀⠀⢀⣼⡖⠁⠀⠀⠀⠀⠀⠘⠛⠀⠀⠉⠁⠀⠀⠀⠀⣴⠹⣿⢇⣿⣇⣜⠀⣸⣄⣸⣶⡟⠿⣤⣿⡇
⠀⠀⠞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣤⣾⣿⣿⣿⣶⣿⡿⣿⡍⢻⣶⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣃⣿⠿⣿⣯⣿⣥⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⡛⣶⣿⣿⣿⠿⣿⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⢀⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠹⠄⠀⠈⠙⠀⠉⢻⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠴⠉⠑⡆⠀⣤⠀⠀⠠⠛⠉⢳⡄⠀⠀⠀⠀⠀⢸⣄⠀⡀⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣌⠑⠆⠠⠴⠃⠀⠈⢷⣄⡀⠀⠀⠈⡧⠀⠀⣾⣦⣴⣦⠈⠉⠈⢦⣀⡤⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⡰⡁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢸⡏⡼⠏⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣠⡄⠰⠚⠲⢤⡀⠀⠀⠈⣴⠀⢀⡴⠋⠛⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢰⠃⠀⠀⡀⠀⠀⠙⠲⣄⠀⠘⠶⠉⠀⠀⢀⡟⠀⣰⠟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⢄⡠⠂⠀⢸⡇⠀⡼⠀⠀⠀⠷⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠉⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣷⠀⠐⠛⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡽⢆⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⢠⡀⣠⠇⠀⠀⢀⡄⠀⣤⠀⠀⠀⠀⣼⠃⠸⣿⣇⠀⠀⠀⢹⡀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠀⠀⠉⠁⠂⢀⣀⡞⠀⠙⠀⠀⠀⠀⠘⣷⡐⠢⠿⠿⣿⠖⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⠀⠀⠈⠁⠁⠀⠀⢀⡀⠀⢠⣊⣀⣤⣬⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⠹⡄⠈⠉⠋⠁⠀⠀⠀⠀⢠⣄⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣭⣿⢻⡆⠀⠈⠓⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⡺⠈⣿⣤⠀⠀⠀⠀⠀⣠⡶⠀⠀⠈⠳⡄⠀⢠⡷⠤⠀⠀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠈⢻⣆⠀⠀⠀⠀⠈⠉⠲⠦⡀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠐⠒⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠏⠀⠀⠀⠀⠒⠚⠳

⢼⣶⠆⡀⠀⠀⠀⠀⣀⠰⣾⡧⠀⢸⡿⢖⣀⠀⠀⠀⠀⠀⢀⡴⢶⣶⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣿⣷⣦⡀⠀⠀⢀⢴⣾⣿
⢸⠿⣛⣛⣥⡀⢀⣬⣉⣛⠻⡇⠀⠈⣿⠛⠻⢷⡄⠀⢀⡴⠿⠟⢾⡏⠀⠘⣭⠚⣱⣿⣶⣄⣴⣤⣴⣾⣌⠓⡽⠀⠀⢹⣿⡇⠈⣦⣠⠀⠀⣿⡟
⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠡⢀⠄⠀⠙⣶⠞⠀⠀⠀⠨⠁⠀⠀⠀⢨⠛⠿⠛⣻⣿⣿⠛⠿⢛⠄⠀⠀⠀⠀⣸⠿⠋⠹⠛⠉⠻⣧
⠀⠉⢿⣿⠏⠸⠇⠹⣿⣿⠁⠀⠀⠀⢰⠁⠀⠀⠀⢻⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⠟⠀⠠⠁⠀⠀⠀⠀⠀⠻⣦⣀⡄⠀⣄⣠⡿
⠀⠀⠀⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠘⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠈⠉⡇
⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡿⠛⠉⠀⣀⠀⠀⣀⠀⠉⠉⠻⡄⠀⠸⣿⡗⣦⡀⠀⠀⠀⠀⣠⢾⠛⡟⠁⠀⠀⠀⠈⢢⠀⠀⢀⠀⠀⠀⠀⠀⣸⠿⠛⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠁⢠⣾⣏⠁⢠⡀⠀⣹⣿⡦⠀⠀⠀⠀⢳⣷⣻⣿⣦⠀⢀⣼⡿⠁⣷⠃⠀⠀⠀⠀⠀⣤⣗⣄⣦⡄⠀⠀⠀⠀⠉⢀⣤⣶⠊⠀⡀⠈⢳⣶⣆
⢠⢾⣿⣟⢀⣼⣧⡀⢹⣿⡇⡆⠀⠀⠀⢈⡝⠋⠈⢿⢿⢿⠎⠉⠜⣌⠀⠀⠀⠀⢠⡟⢿⠟⠟⣿⠻⣦⠀⠀⠀⠀⣼⣿⣿⠂⣨⣇⡀⢺⣿⣷⢀
⠈⠀⠙⠻⠿⠉⠋⢻⡿⠋⠀⠁⠀⠀⠀⠀⢢⢈⣱⡦⠈⠠⣴⡍⢁⠊⠀⠀⠀⠀⠘⢷⡆⠀⠀⢰⣶⠏⠀⠀⠀⠀⠂⠙⢿⣿⠏⠏⢿⡾⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡾⣻⣴⠦⠀⠀⠀⠀⠀⠠⠶⣮⣝⠇⠀⠉⠰⣄⠀⠀⠀⠀⠀⢀⡤⠒⠀⠀⢶⡴⣤⡀⠀⠀⠀⠀⢀⣠⣴⡶⠀⣟⠒⢀⠀⠀⠀⠀⠀⠀⠀⠐⢚
⣿⠋⢀⣠⣤⣠⣠⣠⣠⣤⣀⡀⢙⡇⠀⢀⣀⣿⣷⡀⠀⠀⣠⣾⣗⣀⡀⠀⠸⣿⡙⢯⣆⠀⢀⣴⡽⢫⣿⠃⠀⠹⣮⢿⣷⣄⠀⠀⢀⣴⣿⢦⡾
⠘⢓⢛⡿⡝⣯⣿⣏⡿⣽⣿⢛⡛⠁⠀⠸⣿⣁⣹⣿⣤⣴⣿⣁⣹⡿⠁⠀⠀⠙⣣⠘⢻⣿⣾⠛⢠⡛⠁⠀⠀⠀⠻⡇⢙⣿⣦⣤⣾⡟⠡⡿⠃
⠀⢾⣼⣿⣿⣿⢸⠹⣷⣿⡿⣼⠇⠀⠀⠀⣴⣿⣿⡿⣿⡿⣿⣿⢷⡄⠀⠀⠀⠐⣿⡄⠞⠸⠘⣇⣬⡗⠀⠀⠀⠀⠀⣶⣿⠛⠛⡏⠙⡟⣶
⠀⠈⠛⠾⠟⠁⠈⠀⠈⠒⠛⠋⠀⠀⠀⠀⢿⣦⠿⠀⢩⠁⠸⢷⡾⠇⠀⠀⠀⠠⠙⠇⠀⠀⠀⠈⠟⢢⠀⠀⠀⠀⠀⠈⠻⠃⠀⠃⠘⠿⠉
⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠁⠈⠱⠗⣄⠀⠀⣠⠐⠆⠃⠂⠀⠀⠘⣿⠿⠶⡄⠀⠀⠠⠾⠿⡿⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⠀⢿⣿⢟⣥⠄⠀⠀⠀⢠⣔⢻⣿
⠀⠀⠀⣀⠀⣿⣿⡄⣀⠀⠀⠀⠀⠀⠀⣯⡦⠀⣀⣰⣆⣄⠀⠀⡱⠀⠀⠀⠄⠀⠀⠀⢰⡖⠀⠀⠀⠀⠃⠀⠀⠈⢿⣸⣁⣀⡠⣿⢀⣀⣹⢣⡟
⠀⠀⠔⠈⠀⢹⡏⠁⠛⠦⠂⠀⠀⠀⠀⢠⣼⠛⢙⢻⡟⡏⠛⣷⡄⠀⠀⠀⢀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁⠀⡏⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⠞⠉⠉⢳⡤⠛⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠳⢤⡄⠀⠁⠠⣤⠴⠃

⣴⠉⡟⢓⣶⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣖⠛⡏⢱
⣿⣿⡻⣿⣿⢿⣍⣻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣋⣽⢿⣿⡿⣻⣿
⠹⣿⣬⣿⣿⡿⣏⠉⠉⠁⣈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡀⠉⠉⣉⣿⣿⣿⣯⣼⡿
⠀⠸⣿⣿⠿⣃⠐⢫⣿⣿⠛⣿⣏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣿⡟⢻⣿⣯⠓⢀⣻⢿⣿⡿
⠀⠀⠹⣿⡤⠾⣿⣿⣿⠟⠛⢿⠋⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⢻⠟⠛⢿⣿⣿⡿⠦⣼⡿⠁
⠀⠀⠀⢻⣿⣼⡟⠉⠀⠀⠀⠀⠑⢄⠀⠙⢿⣷⣄⠀⠀⠀⢀⣴⣿⠟⠁⢀⠐⠁⠀⠀⠀⠈⠙⣿⣼⣿⠃
⠀⠀⠀⠘⣟⢻⡽⠒⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⣿⣦⣶⣦⣾⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠐⠺⣽⢛⡟
⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣈⣿⣿⣿⣏⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠈⠛⠿⢿⣿⢿⡿⠿⠿⠿⢿⠿⠛⠉⠁⠀⣿⡇⠀⠉⠙⠻⢿⠿⠿⠿⠿⣿⢿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠠⢿⠇⠊⠈⠀⠀⠶⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠱⠆⠀⠈⠈⠒⢿⠧
⠀⠀⠀⠀⠀⠀⣾⠙⡧⠀⠀⠀⠠⠟⠒⠂⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠒⠚⠧⠀⠀⠀⠠⡝⢹⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣙⡇⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠉⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣹⣇⣀⡀⣂⣀⡤⠂⠀⠀⠀⠀⠀⠀⠢⣄⣀⡂⣀⣀⣿⡩⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡤⣤⡀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⣤⡄
⠺⡄⠀⠀⢰⣦⣄⠀⠀⣠⣴⡶⠀⠀⢀⡗⠘⠇⠀⠀⠀⢠⡄⠀⠀⠀⠸⠃⠀⠀⠹⣦⠀⢳⣄⠀⣴⠇⢀⣼⠃⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠈⠓⢤⡀⢈⣩⣽⣟⣍⡁⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⠻⣿⠋⢠⣾⠁⠀⠀⠀⠀⠀⠀⠰⣟⢹⣄
⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠘⢦⣀⠈⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⢿⡷⠆⠇⠰⣿⠟⠀⠀⠀⠀⠀⠈⠳⠞⣣⣮⡿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⣄⡁⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⢠⣤⡄⠀⠀⢀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠹⣟⣷⣄⠀⠀⣠⣾⣻⠏⠀⠀⠀⠀⢻⣯⣷⣄⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠉⠳⡤⣠⡼⡧⣤⡠⡞⠉⠀⠀⠀⠀⠀⠻⠿⠿⢷⡾⠿⠿⠟⠀⠀⠀⠀⠀⠀⢹⣾⡏⡟⢽⣿⠃⠀⠀⠀⠀⠀⠠⠀⡀⠈⡃
⠀⠀⠀⠀⠀⠷⡶⠂⠑⢶⡾⠃⠀⠀⠀⠀⠀⠀⠰⠀⠠⢚⡗⠄⠀⠆⠀⠀⠀⠀⠀⢀⣨⠟⠃⠃⠙⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡷
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⠛⠉
⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⣰⠖⠀⠀⠀⠻⣟⢷⣦⣀⠀⠀⣀⣴⡾⣿⠟⠀⣶⡲⣦⣄⡀⠀⠀⠀⢀⣤⡶⣲⡆⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠘⣧⠀⢀⡄⠀⣴⠏⠀⠀⠀⠀⠀⠘⢷⡝⠻⢷⡶⠟⢫⡾⠃⠀⠀⠈⢿⠊⠻⣷⠄⡀⢴⡿⠋⢚⡟⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠸⣇⠀⠹⠏⠀⣠⡇⠀⠀⠀⠀⠀⠀⠸⣿⣄⠸⠇⣠⣿⠇⠀⠀⠀⠀⠈⢳⣤⣘⢶⣷⢞⣡⣴⡏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠘⣟⡾⠀⠀⠸⢗⡿⠁⠀⠀⠀⠀⠀⠀⠳⠞⠁⠐
⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠈⠹⣿⣿⣷⡄⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣴⣶⣶⠂⠀⠀⠀⠀⣀⠂⡀
⠀⠀⠀⠀⠙⡟⢻⣿⡿⣟⢻⠛⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠃⠀⠀⢰⠀⠀⠀⠀⠀⠀⣤⠈⠀⠇⠈⢠⡄⠀⠀⠀⠀⠀⠙⠳⣦⣶⣟⢇
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠘

⣶⣿⣿⣿⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⣺⣿⣿⣿⠷
⢻⡼⣿⣿⣿⠳⠀⣿⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⣿⣷⠀⢸⣿⣿⣿⣼
⠀⢳⡼⣿⣿⣷⡜⢿⣿⠀⠉⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⢿⡟⣚⣿⣿⡿⣾⠃
⠀⠀⠳⣼⣿⣷⣦⣜⠛⠂⢸⣿⣿⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⢿⣿⣦⠔⠈⢉⣹⣿⡿⢶⡏
⠀⠀⠀⢻⡽⣿⣧⣈⣒⠀⠀⢻⡏⠀⣼⣿⣿⣷⣄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⡾⣿⣿⡇⠀⢘⣿⠅⠁⠶⣿⣿⣿⢗⡿
⠀⠀⠀⠀⢧⡿⣿⣿⡉⠀⠀⠨⠿⠄⣿⣿⠅⠈⢻⣷⣄⠀⡀⠙⠄⠀⠀⠀⠀⢀⠜⢀⠀⣠⣾⡋⠀⠘⢿⣷⠀⠛⠀⠀⠐⣲⣾⣿⡟⣾⠃
⠀⠀⠀⠀⠘⣇⣿⣿⣿⡎⠛⢂⢀⡀⣹⣿⢀⠀⣼⣿⡿⢷⣌⠁⡌⠒⣤⣤⠔⢁⠔⣪⣾⣿⣿⣗⠀⠀⠸⡿⠀⠄⠀⠀⢉⣿⣿⣿⢷⡇
⠀⠀⠀⠀⠀⠸⣇⢹⣿⣿⡾⠶⠒⠀⡹⠁⠀⠀⣿⣿⡃⣈⢿⣷⣜⢜⢟⣿⢿⣮⣾⡟⠁⠘⣿⣿⠀⠁⠴⠀⠀⠀⡀⢾⣿⣿⡿⣳⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣙⢿⣷⣶⣦⡤⠀⠀⢀⢀⣿⡏⠀⠐⢿⣿⣿⣾⣿⣿⣟⣿⣿⢃⢀⣀⣸⣿⣇⡀⠀⠀⠐⢶⣶⣾⣿⣿⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠧⠶⠦⢭⠄⠛⠋⠐⣶⡀⡈⠨⣿⣿⣿⣿⣿⣿⡆⠈⢻⣿⠀⠈⠉⣿⣅⡲⠶⠾⠿⠿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⡶⢀⢠⠂⠘⣇⠀⠀⠉⡘⣿⣿⡿⡟⠆⠀⢸⡏⠀⢘⢦⣽⣟⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⣿⡟⠁⠀⠘⠀⠀⠹⡄⠈⢠⢱⢿⣿⠇⣧⠐⠀⢸⠃⠀⠀⣦⣨⣿⣿⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣾⣿⣿⡗⡐⠻⣆⠀⠀⡗⠀⠘⠸⢸⣿⡖⠟⡆⠀⡞⠀⠀⣸⠇⢼⣿⢡⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠙⣿⣿⣧⣤⠀⡠⠀⠀⣿⠀⡆⣿⠸⣿⠂⡗⡄⢠⡇⠀⠾⠉⣤⣠⣿⣾⡟⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣿⣿⣿⡏⢠⣤⠀⠀⣿⠀⠇⠀⠀⠀⢠⡗⡇⣸⠁⠀⣆⠀⠈⣿⢣⣾⣷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢹⣿⣿⣿⡟⢀⠀⣹⡀⢚⡒⠀⠀⠘⣃⠁⣿⣇⡀⠉⣿⣿⣿⡞⣡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⣟⢻⣿⡿⣿⠟⢿⣛⡃⠀⠀⢈⣟⣴⣿⣿⡿⣾⣯⠶⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⣻⣏⣬⣿⣤⣿⡏⠁⠀⠀⠀⢨⣋⣘⣿⣀⣸⣧⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⡟⢉⣻⣫⣼⠃⠀⠀⠀⠀⠘⣿⣝⣟⠛⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⢷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧

⠀⣠⣤⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣤⣄
⠀⣿⡑⢀⢤⣬⣙⡓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣋⣤⡤⡀⢊⣿
⠀⠘⡦⢷⡕⣊⠅⢉⢛⣾⣗⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⣷⡛⡉⠨⣑⢫⡾⣴⠃
⠀⠀⠘⣎⠿⣇⠲⡂⠒⠈⢹⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⡏⠁⠒⢐⠖⣸⡿⣱⠃
⠀⠀⠀⠸⡎⣮⠑⠀⠵⠢⢠⢀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠟⠋⡀⣀⠐⠬⢄⢊⣵⢱⠇
⠀⠀⠀⠀⣗⢹⣝⠒⠈⠤⠀⠭⠙⠲⢌⢻⣿⢦⡀⠀⠀⠀⠀⢀⣴⢿⣟⡡⠔⠋⠅⠀⠴⠁⢒⣩⡇⣺
⠀⠀⠀⠀⢻⢸⢫⠥⠀⠄⠠⠄⣙⠒⠀⣉⠻⣟⢷⡀⣠⣄⢀⡾⣻⠟⣉⠔⠐⡋⠠⠄⠠⠀⠬⡙⡇⡏
⠀⠀⠀⠀⠈⠫⡮⣗⠚⠒⠐⠒⠚⠰⠦⣍⣀⠈⢻⣷⣿⣟⣿⡟⠁⣀⣥⠴⠆⠓⠒⠂⠲⠓⣺⢷⠝⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣤⣠⣤⣀⣀⣈⣓⣦⣿⣿⣿⣿⣴⣚⣁⣀⣀⣤⣄⣤⣤⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠅⠡⡏⢸⢹⠉⠉⢿⣿⣾⢿⡿⣷⣿⠿⠉⠉⡏⡇⢹⠀⠩⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠀⢇⠸⡘⢎⢀⠈⠉⡟⢸⡇⢻⠉⠁⡀⡵⢃⠇⡼⠀⡄⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⡁⠀⠹⡄⠱⣜⠒⣄⣢⠁⢸⡇⠘⣔⣠⠒⣣⠎⢠⠏⠀⠊⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⡀⠇⠄⠙⡢⣈⢑⡺⠃⠀⢸⡇⠀⠘⢖⡊⣁⢔⠋⠠⠸⣀⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢁⠑⢠⣭⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣭⡄⠊⡈⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚

⠀⠀⠰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⣠⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⢶⢢⡤⠀⠀⠀⠀⠀⠀⠠⣦⢰⠆⢰⣶⠒⠠⡀⠀⠀⠀⡀⠄⢒⣶⠄
⠀⠀⠀⠈⢧⡀⠀⠀⣤⠀⠀⢀⡼⠁⠀⠀⢠⡟⣠⢒⡀⠀⡐⢦⠸⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢻⡄⠀⠈⣢⣠⡊⠀⠀⢠⠏
⠀⠀⠀⠀⢀⡍⠉⠀⣿⠀⠈⢩⡀⠀⠀⠀⠘⠃⡇⢸⣸⣇⡗⢸⡘⠃⠀⠀⠀⠀⠁⠀⠀⠀⡿⠀⠀⢀⠉⠀⠀⠀⠘⢧⣤⢀⣨⣿⣄⢠⣤⠞
⠀⠀⠀⠀⠘⣧⣀⣀⣙⣀⣀⣼⠇⠀⠀⠀⠀⢻⣿⡄⠙⡟⢀⣼⡾⠀⠀⠀⠀⠀⢾⣧⡀⠀⠃⠀⣠⣾⠇⠀⠀⠀⠀⢸⡁⡿⡃⠃⡹⡗⢸⠆
⠀⠀⠀⠀⠀⣸⠋⠉⠉⠉⠙⣇⠀⠀⠀⠀⠀⠀⠙⠾⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⢉⡟⠛⠀⠛⢟⠁⠀⠀⠀⠀⠀⠀⠙⡶⠇⠀⠻⣴⠋
⠀⠀⠀⡀⠘⠋⠀⠀⠀⠀⠀⠘⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⢼⡈⣋⣶⢄⠀⢀⢴⡎⡉⣨⠇⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢳⣀⡀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⢱⣄⠀⠀⠀⣷⠀⠀⠀⣠⡏⠀⠀⠀⣷⠙⠉⣈⢿⠏⡈⠉⢱⡇⠀⠀⠘⡇⠀⠀⠀⢰⠄⠀⠀⠀⣿⠀⠀⠀⠘⠗⠛⠀⣿⠀⠛⠿
⠀⠀⠀⠀⢹⣇⠀⠀⠟⠀⠀⣸⡏⠀⠀⠀⠀⢸⡙⢆⡈⠺⠊⣁⡼⣹⠁⠀⠀⠀⠛⡆⠀⠀⢸⠁⠀⠀⡶⠃⠀⠀⠀⢺⠀⠀⠀⠋⠀⠀⢀⠆
⠀⠀⠀⠀⠈⠻⠷⠦⠀⠶⠾⠟⠁⠀⠀⠀⠀⠀⠙⢦⡭⠀⠨⣭⠞⠁⠀⠀⠀⠀⠀⠙⠦⡤⠀⠀⡤⠴⠃⠀⠀⠀⠀⠈⠷⣦⡄⠀⢠⣴⠟
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢿⡀⠡⠂⠀⠀⠀⠲⠝⢠⡟⠀⠀⠀⠀⠀⠀⠠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⡰⠀⠀⠠⡠⡄⠠⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠻⡄⠀⠀⣿⠀⠀⠰⠏⠀⠀⠀⠰⣇⠀⠀⠀⢻⠃⠀⠀⢀⣽⠀⠀⠀⠀⠀⡧⠀⢰⣷⠀⠠⡇⠀⠀⠀⠀⠀⠀⠶⣬⢿⣤⠆
⠀⠀⠀⠀⠘⣆⡀⡀⠟⢀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠓⠀⢂⠛⠀⠀⠀⠀⣠⣻⠷⢶⣶⡶⢾⣷⡄
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠉⠁⠀⠘⠓⠒⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠒⠛⠀⠀⠈⢷⠀⠀⢐⠛⠀⠀⠀⠀⠘⠟⠋⣿⣷⣿⣿⡯⢹⡿
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢿⠟⢡⣶⠆⠀⠀⠀⠰⣶⡍⢻⡗⠀⠰⡿⢧⡶⢤⡀⠀⣠⠴⣎⢿⡷⠀⠀⣿⠿⠗⠄⠀⠀⡠⠺⢻⡟⠀⠐⢻⣗⠄⠀⠀⠀⠀⠀⠄⣾⠟⠂
⠀⠀⠘⡀⠸⣇⠀⠀⣶⠀⠀⣸⠃⠸⠁⠀⠀⢻⠀⢠⣍⠙⡟⢉⡥⠀⣸⠃⠀⠀⢹⠀⠀⠈⢦⡜⠀⠀⢸⡇⠀⠀⠀⢿⡀⠀⠀⣶⠀⠀⢸⡟
⠀⠀⠀⠀⢀⠻⣦⣀⣿⣀⣴⠋⡀⠁⠀⠀⠀⠈⣓⠘⠇⠀⠃⠈⠟⢐⡋⠀⠀⠀⠘⡶⠒⠀⢸⠃⠐⠲⢞⠀⠀⠀⠀⠈⣿⠂⠀⡿⠀⢸⡏
⠀⠀⠀⠀⠸⣷⣌⡉⠀⢉⣡⣾⠃⠀⠀⠀⠀⠀⠹⣦⣤⠀⠀⢠⣤⡾⠁⠀⠀⠀⠀⢧⣠⡖⠈⠀⢦⣠⡟⠀⠀⠀⠀⠀⠹⣦⣼⠹⣆⣴⠃
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈

⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⡀
⠀⠀⠀⢠⣿⣿⣻⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣛⣿⣿⡄
⠀⠀⠀⢸⣿⣟⣻⣿⣿⣿⣿⣿⠛⢻⣏⣹⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣟⣩⡟⠛⣿⣿⣿⣿⣿⣟⣻⣿⡇
⠀⠀⠀⠀⢻⣿⣟⣿⣿⠉⠉⣿⣷⣿⡿⣏⡉⣻⡟⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢻⣟⢉⣹⢿⣿⣾⣿⠉⠉⣿⣿⣹⣿⡟
⠀⠀⠀⠀⠀⠙⢿⣿⡿⣿⣿⠛⠛⠛⠷⢶⡿⠛⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠛⢿⡶⠾⠛⠛⠛⣿⣿⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣦⣤⣤⣀⣀⣳⡀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢀⣞⣀⣀⣤⣤⣴⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠖⠶⠶⠶⠒⠒⠒⠚⠛⠲⢤⣀⠀⠈⠻⣦⠀⣼⣇⠀⣴⠟⠁⠀⣀⡤⠖⠛⠓⠒⠒⠒⠶⠶⠶⠶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡈⢳⣿⣿⡞⢁⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣉⣿⣿⣿⣿⣉⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⡿⠿⠛⠛⠛⠻⢿⣋⡩⠭⠿⠿⠻⣿⣿⣿⣿⠛⠿⠿⠭⢍⣙⡿⠟⠛⠛⠛⠿⢿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣏⣤⠤⠴⠶⢒⡶⠃⠀⠀⠀⣀⡴⠋⣼⣿⣿⣧⠙⠦⡀⠀⠀⠀⠘⢶⡒⠶⠦⠤⣄⣹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⣀⡠⠴⣶⠋⠀⠀⠀⣠⠞⠁⢀⠞⣽⣿⣿⣯⠳⡀⠈⠳⣄⠀⠀⠀⠙⣖⠦⢄⣀⠀⠙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠚⠉⠁⣀⠴⣅⡠⠤⢶⠞⠁⠀⣰⠋⡸⢁⣿⣿⡈⢇⠙⣆⠀⠈⠳⡶⠤⣄⣨⠦⣀⠈⠉⠓⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣀⠴⠋⠁⣰⠃⠀⢀⠏⠀⢀⡜⠁⣰⢃⠈⣿⣿⠁⠈⣆⠈⢣⡀⠀⠹⡀⠀⠘⣆⠈⠙⠦⣀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣿⡄⠀⣰⠃⠀⢀⡎⠀⢀⠞⠀⢠⠃⠂⠀⣿⣿⠀⠐⡘⡄⠀⠳⡄⠀⢱⡀⠀⠘⣆⠀⣠⣿⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣻⢧⣀⣠⣞⠀⢠⠎⠀⢠⡿⠁⠀⠀⢻⡟⠀⠀⠈⢿⡄⠀⠹⡄⠀⣳⣄⣀⣼⣟⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⣶⢿⣄⣠⠟⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠻⣄⣠⣿⣶⣿⣷⣿⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠾⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠷⠿⠟⠋⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣀
⠀⠀⢠⣾⡿⠙⣷⣿⡉⠙⠻⠍⠙⠛⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⠚⠋⠉⠑⠂⠀⠚⣿⣿⠁⠙⣿⢦
⠀⠀⢺⣿⢆⣰⣟⣉⣉⡉⠀⠀⢀⣀⣻⣿⠒⠼⠭⣒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡺⠹⠓⠊⢿⣧⡤⠠⠀⠤⠤⠤⠬⢽⡏⢐⣿⡏
⠀⠀⠘⢿⣷⣈⡵⢂⣀⡤⠠⠀⠀⠛⠫⢄⡀⠀⣠⣄⣴⣯⠳⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⡻⣿⣿⣤⣦⡀⢂⡠⠚⠉⠀⠀⠐⠲⠦⠙⣳⣦⢿⡟⠁
⠀⠀⠀⠈⠱⢟⣿⣤⣖⣛⣡⣤⠔⠀⠀⣤⣾⡟⢛⣯⣉⡛⠀⡲⢝⢄⠀⣤⣀⠀⣴⣿⣊⠴⣋⡡⠬⢛⣿⣿⡦⠈⠁⠐⠶⠎⢙⣳⡶⢯⡽⠋
⠀⠀⠀⠀⠀⠀⠱⡾⣻⡡⠔⠚⣃⡤⠄⠒⣿⣿⣦⣀⣀⣉⡛⠶⣦⣝⣷⡄⢸⣾⣯⠶⠞⠋⠤⠤⠤⢴⣿⣯⡐⠒⠤⣌⡓⣒⢤⣏⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⠿⣏⣠⠴⠟⢈⡻⠿⠗⠒⣒⣀⠬⠉⡭⠞⡽⢿⡿⢯⠐⠀⠉⠭⠅⣀⠒⠒⠻⠭⢉⡙⢷⣤⣬⠛⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢽⡷⡯⣁⠒⠂⢉⡉⠁⠀⠀⠀⠴⠊⣸⢩⠙⠀⠑⠦⡀⠄⡁⠐⠪⢀⠉⠁⠖⣿⣻⡏⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡽⠛⠂⢀⠞⠀⠁⠀⢀⠔⠀⠀⡜⠈⢰⠀⢃⢠⠠⡈⠢⣈⠂⠄⡀⠙⡄⠀⣙⠳⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣾⠽⠒⢙⠆⢥⠔⠊⠁⢠⠂⡜⠠⠀⢈⠀⠈⡄⢣⠱⡀⠈⡁⠒⡤⠴⣏⠑⠺⢽⡿⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣡⠆⡴⠃⠀⡆⠀⢸⢀⡎⢰⢁⠀⠀⠈⠀⠀⠘⡀⠆⢱⡀⠃⠀⠸⡄⠈⢢⡐⢆⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⢳⡞⢠⠇⡼⢰⠀⡇⣸⢀⠇⡌⠀⠀⠀⠀⠀⠀⠠⠈⡀⢧⠸⡀⣦⢱⡘⣇⢙⣿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⣱⠿⣶⣁⣞⣸⣣⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢸⣆⣇⣹⣄⢿⡟⢿⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠏⠼⠏⠿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠨⠿⠜⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⠿⢻⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⠀⠀⢸⠟⠻⡟⠙⢿⠻⣏⣵⣼⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠻⡉⢻⠙⣿⣦⣿⡇⠀⡇⠀⠎⢀⢿⣧⢽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡋⠓⢄⠀⣈⡃⠡⢸⣿⠁⠀⠁⢀⠶⠚⣻⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⠲⢦⣝⡇⠙⠦⣼⣿⠀⠀⡴⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣉⠓⠦⣌⠻⣄⠀⢿⡇⠀⠘⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠑⢈⣳⣼⣇⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠒⠶⢿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠂⣠⠔⣨⠞⢿⡏⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠤⠒⢋⣥⡞⠁⢀⣿⡇⠀⢠⡀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠴⠚⢋⢴⣀⡴⠋⢿⣇⠀⠀⠳⡀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⠚⢁⠌⢰⠀⡆⣼⣿⠀⠀⠀⠘⠲⣤⡝⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣮⣤⣯⣼⠿⠋⣿⠀⢸⠀⠀⡆⢰⣾⣛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢿⣦⣾⣦⣴⣷⣾⡉⡏⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣷⣧⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⠛⠛⠲⣄⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣦⡀⢀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡈⢿⣦⣰⡏⣠⢻⣿⣿⣿⣿⠏
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣿⣿⣿⣿⡟⠁
⠀⠀⣼⣿⣿⣿⣝⣭⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣯⠻⣿⣿⡿⣯⡀⠉⠙⣿⣿⣿⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣇⠈⠻⢗⢪⣙⠲⣴⣿⣿⣿⣷⡀
⠀⣿⠃⠙⡿⠛⢻⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠀⠉⠙⠀⠀⠀⠙⠾⢳⣾⣿⣿⣿⣿⡇
⠀⣿⠀⠐⠇⠀⢸⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡃⢻⣄⣤⣤⡇⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉
⠀⠸⣷⣾⣷⣶⣾⣿⣿⣿⣿⠿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠃

⢰⣶⡶⠖⠛⠛⠒⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠒⠛⠓⠶⣶⣶
⣿⡋⡉⠀⠀⠀⠀⠔⠂⠀⠀⠈⠙⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠒⠄⠀⠀⠀⠈⡉⣻
⢻⣀⡀⠠⠄⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠤⠀⢀⣸
⠀⠛⢦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⢠⣴⣤⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠞⠃
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣀⠠⠀⠀⠉⠐⠀⠤⢀⣀⣙⣷⣴⣿⣷⣴⣟⣁⣀⠠⠄⠀⠈⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⢶⡖⠒⠉⠁⠀⠀⠀⠀⢀⣠⡤⠖⠚⠛⠛⠻⣻⣿⣿⠛⠏⠛⠛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠉⠑⠒⣶⠎
⠀⠀⠀⠀⠀⠀⠳⣦⣀⠀⠀⢀⣠⡶⠋⠁⡀⠄⠤⠀⠀⢀⡞⣿⡟⣆⠀⠀⠠⠄⠄⠀⠉⠳⣦⣀⠀⠀⢀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡟⠉⠀⠀⠀⠀⠄⠀⠀⢀⣾⠐⣿⡇⢸⣆⠀⠀⠀⠄⠀⠀⠀⠀⠙⢿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠃⠀⠠⠂⠀⠀⠀⠄⢸⣿⠀⢿⠇⢸⣿⠁⠄⠀⠀⠀⠢⠀⠀⠱⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⡠⠁⢀⠀⠀⠀⠀⠀⢻⠀⠘⠀⢸⠇⠀⠀⠀⠀⠀⠀⠱⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡐⠀⢀⠂⠀⠀⠀⠀⠀⠈⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⢣⠀⠐⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢀⠆⠀⠀⠀⡆⠀⢀⠀⣃⠀⢀⡇⠀⠀⠀⠆⠀⠀⠀⢂⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡜⠀⠰⠀⠀⠆⠀⢸⣠⡏⠀⠈⣧⣸⠀⠀⠂⠀⠘⡀⠈⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡇⠀⢠⠀⢀⣼⠋⠀⠀⠀⠈⢻⣄⠀⢰⠀⠀⢇⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⢾⡿⠛⠛⠀⠀⠀⠀⠀⠘⠛⠻⣿⠾⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢛⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⡙⠼⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⣕⢢⠉⢢⠀⠀⢳⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣄⠒⠊⠀⠀⠀⠥⠋⡇⠀⠃⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢯⡒⢄⠁⠀⠀⠀⠀⠈⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡾⠈⠑⠊⠀⠀⠀⠀⠀⠀⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠏⣱⣄⠀⣯⢧⠶⣱⠀⠀⠀⣀⣠⡶⠿⠟⠛⠁⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡜⣟⠿⣏⣆⠘⢾⣄⣀⠤⠒⠉⠾⠋⠀⠀⠀⠀⣰⢿⣃⠐⢻⡄
⠀⠀⠀⠀⠀⣰⡟⢩⣤⣿⠻⡏⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣎⡽⣂⠩⣿⡄
⠀⠀⠀⠀⠀⣿⡿⢈⣳⠍⢧⢳⣾⣼⠀⢆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠼⡽⣿⢞⣽⡔⠹⣿⡄
⠀⠀⠀⠀⠀⠻⣇⣾⡿⠏⠀⠻⡿⢿⡇⠀⠀⠀⠁⠀⠀⡄⠀⠀⠟⢻⢽⣜⡥⠈⣳⠔⠡⡇
⠀⢀⣤⣶⣶⠶⣶⢿⣧⣄⣄⡀⠉⣸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠉⢋⣿⣞⣡⠤⢏⠀⠉⠱⣄
⠀⣞⣾⢡⣭⢣⡟⠋⠓⠯⣿⣯⣦⣻⣧⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠛⣿⡤⠒⠉⣻⣄⠤⠾⢄
⠀⠹⡺⣄⢛⣤⣩⣛⡶⠿⠿⢟⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⣀⠀⠹⣮⣳⡀⠀⢻⣂⠀⣙⣠⣤⣄⡀
⠀⠀⠈⠙⠛⠋⠉⠁⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣟⠛⠚⠳⢷⣖⣚⠷⣬⢯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⠀⠀⠀⠀⠉⠓⠛⠊⠁
⡀⠀⣀⠀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⡀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣽⣿⣿⣿⣿

⠀⠀⢀⣠⡄⠀⠀⠈⢛⣉⣀⡀⢐⣒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢒⡂⢀⣀⡈⠛⠁⠀⠀⠠⣄⡀
⠀⠀⢸⣶⡟⠲⣤⡀⠀⢎⠀⠀⠘⡟⠀⡶⢦⡄⠀⠀⡀⠀⣶⣶⠀⢀⠄⠀⢠⡴⢶⠀⢻⢋⠀⠀⡱⠀⢀⣤⡶⣺⣾⡇
⠀⠀⠀⠉⠻⢷⣆⠙⢆⡀⠙⠒⠿⠷⢴⠷⢾⠄⠀⠀⣾⣶⣿⣸⣶⡿⠀⠀⠠⡷⠾⡤⠾⠿⠒⠋⢀⡰⢋⣰⡾⠟⠉
⠀⠀⠀⠀⠀⠈⠛⣟⣦⡑⢤⣄⠀⠀⠈⠒⠞⠂⠀⠔⠺⢿⡟⢻⡿⠗⠂⠀⠐⠳⠞⠁⠀⠀⢠⡤⢊⣴⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣌⡓⣆⡀⠔⠀⠀⠀⠀⢀⣞⡧⢼⣷⠀⠀⠀⠀⠀⠢⣀⣰⢞⣡⣾⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣟⠁⠂⠀⠀⠀⠀⠀⢸⠀⡇⣸⠀⡇⠀⠀⠀⠀⠀⡐⠉⣻⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⣾⣶⢀⠁⠀⠀⢀⣀⠸⠀⢳⡾⠀⠇⣀⠀⠀⠀⠈⡀⣶⡷⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡈⠷⢻⡆⣿⢰⡿⡝⢐⡀⠈⠁⢀⡂⢯⢿⡆⣿⢰⡟⠯⢁⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⠊⣉⣻⠚⢧⡔⠁⠀⠀⠀⠀⠈⢢⡼⠓⣻⣉⠅⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣼⡿⢚⣿⣟⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⡖⣏⣷⢿⣿⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣯⣿⣿⣿⣿⣦⡀⠀⠙⢄⠀⠀⡰⠋⠀⣀⣴⣿⣿⠿⠟⢻⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣽⣅⣈⣉⣿⡁⠉⠻⣦⡀⠈⠆⠰⠁⢀⡴⠟⠉⢀⠾⠐⠒⠚⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣅⣀⣀⣀⠭⠶⢄⡈⠻⣄⢰⣆⣠⠏⠀⣀⠴⠥⠤⠄⠤⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣀⣀⣀⣀⣀⣉⣲⣿⣾⣽⣧⣴⣎⣡⣤⣤⣤⣤⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⠿⠿⠿⣿⠿⠛⢻⢿⣹⣿⡟⠛⠛⠻⡟⠛⠛⠻⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠤⠐⣂⠘⠁⢀⡠⠋⢸⡿⣿⠆⠠⣀⠀⠘⣍⣁⠐⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠐⣨⠜⠆⠔⠉⠀⠀⣿⣿⡿⡆⢀⠈⢣⠐⢎⠢⡉⢘⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡔⢁⡄⠐⠀⡠⠀⣸⠃⣿⡇⠱⡄⢢⠀⢣⠈⣦⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣴⣤⡴⠃⠀⠙⠁⠀⠙⣦⣵⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⣶⡶⢦⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡰⢶⣶
⠀⣿⡗⣿⡍⠬⢿⣟⠳⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⠞⣻⡿⠥⢬⣟⢺⣿
⠀⠹⣾⢛⣶⠒⠛⣧⣜⠻⣿⣭⡲⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⢖⣭⣿⠟⣣⣼⠛⠒⣶⡟⣷⠏
⠀⠀⠹⣿⣷⡗⢺⡟⠉⠉⠉⠉⠉⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠉⠉⠉⠉⢻⡗⢺⣾⣿⠏
⠀⠀⠀⠈⣿⣷⢾⣧⣄⠀⠠⠶⢄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡠⠶⠄⠀⣠⣼⡷⣾⣿⠁
⠀⠀⠀⠀⢹⣿⣋⣻⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠙⣄⠀⠀⠀⠀⣠⠋⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣟⣙⣿⡏
⠀⠀⠀⠀⠈⣿⣿⣽⡗⠂⠈⠉⠉⠀⠀⠈⠀⠠⣀⠈⠳⣾⣷⠞⠁⣀⠄⠀⠁⠀⠀⠉⠉⠁⠐⢺⣯⣿⣿⠁
⠀⠀⠀⠀⠀⢸⣯⣽⣧⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣁⣠⣿⣿⣄⣈⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣼⣯⣽⡇
⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠛⠉⠉⠉⠹⠋⠉⠉⠉⢉⠿⣿⣿⠿⡉⠉⠉⠉⠙⢏⠉⠉⠉⠛⠻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣸⡶⣿⠶⠂⠒⠒⡘⠀⠀⠀⣠⠔⠉⠘⣸⣇⠃⠉⠢⣄⠀⠀⠀⠃⠒⠒⠒⠶⣿⢶⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠠⠞⠠⠴⠒⠋⠀⠀⠄⢀⢻⡟⠀⠠⠀⠀⠙⠒⠦⠄⠳⠄⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⢽⣿⣿⡋⠀⡠⠊⠀⠀⠀⠀⠀⠀⣤⠃⢸⡇⠘⣄⠀⠀⠀⠀⠀⠀⠑⢄⡀⢹⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣄⡀⣀⡄⠀⡠⠀⣰⠃⠀⠀⠀⠀⠘⣆⠀⢄⠀⢠⣀⢀⣠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣿⣽⣟⣷⣺⣇⡴⠃⠀⠀⠀⠀⠀⠀⠘⢦⣸⣷⣾⣻⣯⣿⣯⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉

⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢿⡃⠉⠲⣄⠀⠀⠀⣠⠖⠉⢘⡿⠀⠀⠀⢿⡇⣴⣦⡄⠀⠀⠀⠀⠀⣤⣶⡈⣿⠂⠀⠀⠛⣿⢷⣦⡀⠀⠀⠀⠀⢀⣴⡞⣿⡙
⠀⠀⢠⣈⠁⠀⠈⠠⣶⠄⠁⠀⠈⣁⡄⠀⠀⠀⠈⣿⡙⠛⣦⣧⣀⣄⣠⣧⠟⠛⣼⡏⠀⠀⠀⠘⠿⣟⣿⠃⣀⣸⣇⡠⠘⣟⣼⠯⠁
⠀⠀⠀⢙⡓⠒⠒⣺⣿⡗⠒⠒⠞⡋⠀⠀⠀⠀⠀⠈⣻⣿⢉⠉⣽⣿⡍⢉⢹⣿⡋⠀⠀⠀⠀⠀⠈⢻⣏⡁⢠⢿⡿⡄⣈⣹⡟⠁
⠀⠀⠀⠨⡀⠰⠂⠰⠿⠆⠑⠆⢠⠅⠀⠀⠀⠀⠀⠀⣿⣿⡘⠛⠋⠃⠟⢛⣸⣿⠇⠀⠀⠀⠀⠀⣼⣿⡿⣷⠀⠘⠁⠰⡾⢿⣿⣧
⠀⠀⠀⠀⣻⣠⡔⠁⠀⠀⢠⣀⡏⠀⠀⠀⠀⠀⠀⠀⠉⡿⡿⠟⠁⠀⠹⠿⡿⡏⠁⠀⠀⠀⠀⠀⣣⣬⡷⠟⠀⠀⠀⠀⠿⣮⡥⡝
⠀⣀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠻⣿⡿⢖⢄⡠⠀⠀⠀⢄⡠⡲⢿⣿⠟⠀⠀⢳⡤⠺⣿⠒⢤⡀⡀⣠⠔⢻⡿⠠⣴⠃
⠀⠀⣿⣇⠀⣀⠑⢄⣀⡠⠋⣀⠃⣸⣿⠀⠀⠀⠀⠹⣿⣆⣀⣠⣿⣿⢇⣀⣀⣾⡿⠁⠀⠀⢀⡄⠀⠀⢀⡀⢀⣴⣦⡀⠀⠀⠀⠀⢠
⠀⠀⠸⣿⠦⠴⠶⠶⣿⠷⠶⠶⠴⣿⠇⠀⠀⠀⠀⠀⢹⡏⠉⡦⠾⡿⡦⡄⠙⣿⠀⠀⠀⠀⠈⠛⡅⠀⠀⡀⠈⣿⣿⠁⣀⠀⠀⣬⠋
⠀⠀⢘⣯⠀⠤⠖⢰⣿⡆⠲⠠⠀⣽⡇⠀⠀⠀⠀⠀⠀⢻⣄⣠⠄⠀⢦⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⢾⡇⠀⠀⠛⠂
⠀⠀⠀⠻⢿⣶⡦⠂⠀⠐⢴⣶⡿⠟⠀⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠀⠉⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠈⠁⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⢀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⡀⠀⠀⡴⠦⠀⠑⠢⣀⠀⡀⢀⡠⠒⠁⠠⠶⡄⠀⠘⣟⣯⡽⣖⢄⡀⠀⠀⢀⡀⣲⢯⣝⡿
⠀⢯⣀⠉⠉⠈⠀⡉⣿⢁⠀⠈⠉⠉⣀⡽⠂⠀⠱⣄⣀⣀⣀⣈⣿⣿⣏⣀⣀⣀⣀⡤⠀⠀⠀⢹⡄⠀⠀⠀⠑⣄⣠⠋⠀⠀⠀⢨⡇
⠀⠀⠳⠆⠀⠚⠋⠀⣚⠀⠙⠓⠄⠰⠞⠀⠀⠀⠀⢠⠞⠁⢀⠁⣿⣿⡇⠁⠀⠑⢆⠀⠀⠀⠀⠀⣱⠟⠙⠟⠚⣿⣟⠓⠻⠛⠻⣍
⠀⠀⠀⠰⡀⠀⢀⡔⠉⠢⡀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠈⠁⡜⠉⠉⠙⣄⠉⢰⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⢺⡷⡄⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠐⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠈⠻⠶⠶⠀⠀⠀⠀⠶⠶⠛⠁
⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⢠⣾⣶⡦⡀⠀⠀⠀⠀⢀⣀⣶⣾⣦⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦
⠈⣿⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⣾⠁⠀⠘⣿⡟⠄⠈⠠⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⢻⣿⡿⣽⠷⣄⠀⠀⣠⢺⣭⢿⣿⡟
⠀⠈⠶⠀⠄⠈⠢⠀⣤⢀⠜⠁⠠⠄⠖⠁⠀⠀⠀⠹⣷⣆⡀⠴⢤⣦⠤⠄⣀⣶⡿⠁⠀⠀⠀⠈⢿⣷⣌⢻⣿⣷⣾⣿⡟⣡⣿⡟⠁
⠀⠀⠑⠠⢀⣀⣀⣠⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠼⡿⠄⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢹⣿⡈⣁⣿⣿⡈⢁⣿⡏
⠀⠀⠀⢰⠏⠀⠀⠈⣿⠇⠀⠀⠉⡆⠀⠀⠀⠀⠀⠘⢷⣤⣤⡴⠀⠃⠰⣤⣤⣼⠏⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⠛⢙⣷⣿⣿⠇
⠀⠀⠀⠈⠂⠥⠄⠀⠁⠀⠠⠬⠐⠁⠀⠀⠀⠀⠀⠀⠀⣩⠃⠀⠀⠀⠀⠀⢫⡁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠉⠀⠀⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠘⣿⣿⣆⠀⢀⣼⣿⣿⠀⠀⠀⠀⣶⡶⢤⣀⠀⠀⣠⡤⢶⣶⠀⠀⠐⡏⡵⢆⡀⠀⠀⠀⡠⢮⢹⠇⠀⠀⣿⣿⣤⡀⠀⠀⠀⣤⣾⣿⠇
⠀⠀⠀⠀⠀⢛⡇⠿⣿⡿⠧⢜⠋⠀⠀⠀⠀⠻⢇⣄⣘⣶⣿⣁⣀⠸⠏⠀⠀⠀⠻⠿⣾⣗⣦⣤⣖⣷⠾⠿⠀⠀⠀⠸⣿⣿⣿⣦⣤⣾⣿⣿⠿
⠀⠀⠀⠀⠀⣿⠁⡖⠹⠉⢦⢸⣷⠀⠀⠀⠀⢀⣿⠷⣻⠟⠿⣻⠾⣿⡀⠀⠀⠀⠀⣶⣿⣶⣽⡯⣱⣿⣶⡄⠀⠀⠀⠀⣾⣿⣌⠻⠻⣃⣾⣿⡆
⠀⠀⠀⠀⢀⠿⡿⠀⠀⠀⠐⠿⢧⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠙⠿⠏⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠙⠿⠟


⠀⠀⠀⠀⣶⢶⣤⡀⠀⠀⢠⣄⢶⡧⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⣿⠟⠤⠀⠀⠀⢀⠤⠚⣿
⠀⠀⠀⠀⠹⣿⣷⣿⣶⣴⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠄⠂⠁⠀⠀⠀⠻⠆⣀⣈⣶⣶⣅⣀⠠⠿⠀⠀⠀⡔⠈⠙⠛⢳⣶⠺⠛⠁⠢⡀
⠀⠀⠀⠀⢠⣿⣿⡞⠻⠟⢾⣷⣷⠀⠀⠀⠀⠀⢠⠂⠀⢹⡏⠀⠠⡄⠀⠀⠀⠀⢠⣞⠁⣼⡿⣿⣧⠈⢻⡆⠀⠀⠀⠙⢳⣾⠾⢿⡿⢷⣶⡶⠚⠁
⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠹⡷⠟⠁⠃⠻⢶⡿⠀⠀⠀⠀⠀⠀⠑⠒⠋⠈⠒⠚⠁


⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⣀⣀⡀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⢻⡉⠘⢷⣴⣴⡟⠇⣻⠇⠀⠀⠘⠥⡉⠀⠛⢾⡿⠋⠀⢉⠼⠃⠀⠀⠀⠀⠀⠐⣤⣤⠂⠀⠀⠀⠀⠀⠀⠡⣰⣿⣷⣶⣶⢾⣿⣶⠨
⠀⠀⠀⠀⠈⣷⢤⣴⢿⠿⣤⢴⡏⠀⠀⠀⠀⠀⠈⢷⣤⡞⢷⣤⡿⠁⠀⠀⠀⠀⠀⠀⢀⣤⠀⠃⡤⡀⠀⠀⠀⠀⠀⠀⢸⣿⡹⢿⣿⠗⣿⡿
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠙⠿⠛⠁

⠀⠀⡶⣤⢄⠀⠀⣀⣤⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⡘⠉⠳⣴⣦⠞⠉⢓⡲⠆⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⣿⣟⣷⣶⣻⣿⠛⠀⠈⢷⣿⣶⣤⣴⡾⣷⠏⠀⠀⠉⢶⣀⣼⢣⣀⣶⠉⠀⠀⠙⢃⢼⡿⢾⡾⣿⢆⠑
⠀⠀⠀⢿⣿⠕⠃⢟⣿⠂⠀⠀⠀⢌⣙⡛⣛⣁⠄⠀⠀⠀⠀⠨⠛⠁⠈⠛⠇⠀⠀⠀⠀⠈⠻⠯⠁⠩⠿⠋
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠠⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⣠⣴⣄⠀⠀⢀⣤⣤⣄⣤⣤⣄⣤⣤⢤⣤⣤⠀⠸⣿⣿⠓⢠⡄⠚⣿⣿⠇
⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⣀⣴⣺⣿⣿⣿⣟⣢⣄⠉⠛⠻⣿⢿⠿⡿⣿⠛⠋⠉⠀⠀⠈⢻⣆⡘⢃⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠿⣯⠿⢯⠿⠛⠋⠁⠀⠀⠑⠚⠀⠓⠈⠀⠀⠀⠀⠀⠀⢨⠛⠋⠙⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⢄⠒⢠⣤⠐⠀⡔⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⣿⠿⡿⠃⡀
⠀⠀⠀⠠⠤⠃⠤⠀⠀⢠⡄⠀⣠⠀⠀⠀⠄⠡⠄⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠙⠺⠻⠚⠁⠀⠀⠀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢰⡿⠛⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⡀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⣹⣤⣼⡇
⠀⠀⠀⠀⢹⣷⣴⣿⣿⠟⠁⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠊⣤⡀⠀⠀⠀⠚⣿⣯⣽⠇
⠀⠀⠀⠀⠸⣿⣤⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠐⣪⣬⣭⣿
⠀⠀⠀⠀⠀⠻⣿⣽⣯⣅⣀⠀⠀⠀⠀⠀⠓⢴⣶⣤⣤⣾⣿⣁⡤⠴⠂⠀⠀⠀⠈⠙⢙⣋⠏
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠖⠛⠛⠒⠒⠒⠒⠲⣿⣿⣿⣿⣿⣿⡷⠤⠤⠀⠀⠀⠀⠀⠒⠊
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣴⣧⡴⠋⠀⠀⠀⠀⢰⡿⣷⣿⢿⢻⣿⢻⠘⠿⣿⡀⠀⠀⠀⠀⠀⠈⢑⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣧⡦⡘⠀⠐⠋⢀⡵⠋⠀⠸⠟⠀⠀⠀⠉⠀⠀⠀⠀⣈⠲⢦⣬⣿⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡃⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣠⣄⣠⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉

⣠⣤⣄⡀⠀⠀⠀⠀⠀⣀⣤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣦⣄⠀⠀⠀⢤⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠
⠈⠳⣝⠿⣦⣄⠀⣠⣾⢿⡿⠃⠘⣿⡖⣤⡀⠀⢀⢤⣐⡿⠃⠘⡟⠀⣵⣤⡾⡀⢻⠁⠐⣖⣂⡀⠀⠀⢀⣀⣴⠀⠈⠻⣧⢼⠆⡻⠏
⠀⠀⠙⠷⣨⠻⣿⠿⣵⠟⠁⠀⠀⠈⠿⣽⣿⣿⢿⢷⠟⠁⠀⠀⢀⠀⠁⠋⠀⠀⡄⠀⠀⠘⠌⠉⢳⠞⠉⠱⠁⠀⠀⠀⠀⠈
⢰⠦⣤⡀⠙⠗⠉⠘⢃⣤⣖⡗⠀⠀⠐⡇⠀⠀⠈⠸⠃⠀⠀⠀⠈⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⢰⠞⠳⠀⠀⠀⠀⢀⢠⢼⢤⠄⡀⠉
⠀⠐⢿⡛⠷⣤⣤⡾⠛⣩⠎⠀⠀⠀⠠⠑⠁⠀⠙⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⢠⣴⡖⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠙⣾⡏⠟⣽⡿⠃⠀⠀⢀⣤⡴⠂⢠⡀⠤⣠⣀⠀⣴⡶⣤⣄⣠⣶⠖⣶⠆⠀⠀⠘⣷⡽⣡⡞⠀⠀⠻⢾⣤⣄⣀⣠⣴⡶⠖
⠀⢶⣓⣦⡈⠀⠀⢈⣴⣒⠆⠀⠀⠉⠻⢦⠼⣤⡶⠛⠉⠀⠈⠳⡝⢿⡿⢫⡞⠁⠀⠀⠀⠀⠻⠃⠟⠃⠀⠀⠀⠀⠋⠁⣯⠉⠋
⠀⠀⢻⡙⢿⣄⣤⡿⢛⡟⠀⠀⠀⡤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⡹⠓⠚⢏⠀⠀⠀⠠⣖⡤⢀⠀⠀⠀⠀⣄⢤
⠀⠀⠀⢠⣌⠹⡟⣁⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢶⡶⠂⡀⠀⠀⡠⠐⢲⡶⠀⠹⢵⠋⠠⠶⠈⢧⢹⠃⠀⢤⡀⠀⠷⠀⣀⠖
⠀⠀⠀⠘⠿⠇⠙⠻⠃⠀⠀⠀⠀⠀⣄⠀⠀⢀⣰⠀⠀⠈⡇⠀⠈⢢⡄⠀⠀⣸⠁⠀⠀⠀⣦⣀⠦⣠⣤⠀⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠰⡦⠘⠀⠀⠀⠀⠡⢶⠀⠀⠀⡀⠉⠁⠀⠈⠁⠀⢀⠀⢩⠀⠀⢸⣇⠀⠀⡅⠀⠀⠀⠀⠐⠁⠀⠑⠁⠀⠀⠀⠀⢃⢶⣄⢦⠌
⠀⠀⠃⠈⠁⠀⠀⠈⠀⠁⠀⠀⠀⠳⣤⣄⣤⣤⣤⣤⠞⠁⠈⠳⠠⠞⠙⠤⠔⠁⠀⠀⢰⣶⣤⣄⠀⠀⠀⣠⣤⣶⡆⠐⡧⠛⣾
⠀⠀⠀⠒⠀⣶⡆⠀⠶⠀⠀⠀⠀⠀⠈⠉⠘⡇⠈⠁⠀⠀⠀⣾⠗⠀⠀⠀⠀⠂⠸⣿⡄⢻⣿⡉⢣⣤⠞⠁⣼⡟
⠀⠀⠀⠀⠘⠀⠘⠄⠀⠀⠻⣿⣻⣶⣦⡀⠀⠀⣠⣤⡖⣺⡿⠊⣄⠀⠀⡦⠀⠀⢠⠃⠀⠀⢛⡗⠈⠟⠐⢶⠛⢁⣤⡴⢶⡶⣦⣄
⠀⠀⢀⣤⠀⢀⡀⠀⣤⠀⠀⠀⠙⠻⠋⠿⣦⣤⠷⠽⠟⠉⠀⠀⠀⠁⢀⠀⡀⢐⠀⠀⠀⠀⠈⠻⡶⠐⣶⠞⠀⠛⠛⣿⡏⢹⡿⠿⠷
⠀⠀⠀⠈⢀⡀⠁⠔⠁⠀⠀⠀⠀⠀⣎⣂⡘⢧⣠⡗⠀⠀⠀⠀⠀⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⠀⠀⠠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣽⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣯⣭⣿⣿

⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣤⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣦⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣯⠛⠁⠀⠀⠈⠀⠦⡽⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⢸⣿⣶⡄⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⣠⠒⠉⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⣼⣟⡻⠟⠀⠀⠀⠀⠀⠀⠘⣿⣯⡉⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⠖⠀⠀⠘⠉⠉⠉⣡⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⢽⡷⢌⡛⢷⡀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣝⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠳⣭⣬⣿⣦⣀⢀⣿⣿⣿⣣⣀⠀⠀⠐⠀⠀⠀⠀⠀⢴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣛⡛⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠒⠿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠁⠨⠀⠀⠀⠀⠀⣀⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠀⠀⣠⣀⣠⣤⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢶⣦⣤⣀⠀⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠁⠀⠀⠈⠁⣨⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠟⠠⣌⢱⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⢠⠀⠋⠉⠁⠀⠀⠀⠀⣩⣿⣿⣿⡟⠂⠀⠀⠉⠉⠉⠉⠀⠀⠀⢸⣾⣄⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⢀⣀⡀⠀⠀⠀⠀⠠⠂⢀⠄⠀⠀⠀⣿⡇⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠘⠿⠟⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⣿⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣤⣄⡁⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠈⠙⢄⠀⠀⠀⠀⠀⠛⠋⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡀⠘⠿⢂⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣚⣻⣿⠷⢿⣿⠿⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣼⣿⣿⣤⡤⠶⠖⠛⠛⠛⠙⠛⠛⠻⢿⣿⠾⢿⣿⣛⣲⣦⣤⣀⡀
⠀⠀⢀⣠⢶⣿⠿⠟⡫⠀⠉⡁⠴⢒⣿⡁⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⣤⣿⣿⠘⣧⠀⠀⠂⠀⠀⣀⠀⣀⣀⡀⠀⣻⣗⠢⢄⡉⠁⠬⡛⠿⢿⡷⢦⡀
⠀⢠⣾⣁⡟⠁⠀⠀⢀⠔⠉⡠⠞⠉⠀⢀⠔⠋⠀⢀⠌⠀⠀⠀⠀⣰⣿⣿⣿⠀⢹⣷⡀⠀⠀⠀⠐⠄⠀⠈⠲⣄⠀⠈⠓⢄⠈⠐⢄⠀⠀⡀⠹⣏⣹⣦
⠀⢿⣹⣅⣻⣎⢀⡔⠁⢀⡄⠀⠀⣠⠞⠁⠀⠀⡠⠂⠀⠀⢀⣴⣾⡿⠁⣿⣿⠃⡀⢻⣿⣦⣄⠀⠀⠈⠢⡀⠀⠀⠑⢄⠀⠀⠑⣄⠀⠱⡀⢸⣾⣋⣿⣺
⠀⠈⠷⢿⣷⣾⡏⡿⢤⣏⣹⣟⣻⣇⠀⠀⡠⠊⠀⠀⢀⣴⣿⠟⢁⠂⠀⠹⣿⠀⠁⠀⠈⠙⢿⣷⣄⠀⠀⠈⢦⡀⠀⢀⣿⣛⣿⣉⣧⠿⡩⣟⣶⣯⠾⠋
⠀⠀⠀⠀⠉⠉⠉⠙⠛⠳⠿⣿⣦⣿⣻⣿⡁⠀⢀⣾⣿⠟⠁⡠⠘⠀⠀⢰⣿⢀⠀⠀⠈⠠⡀⠙⢿⣷⣄⠀⠀⣿⣿⣻⣦⣿⡿⠗⠛⠋⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣇⣼⢛⣶⣿⠟⠁⠂⠂⠀⢰⠀⠀⣾⣿⠀⡇⠀⣶⠀⠀⠂⠂⠙⢿⣷⡞⢿⣨⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⣽⢯⠉⠁⠠⠀⠀⠀⠀⠸⠀⠀⢹⣿⠀⠇⠀⠙⠀⠀⠀⠀⢀⠀⠉⠭⣯⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣟⣠⡠⡆⠀⠀⡇⠀⠀⣀⠀⢸⠛⡋⠀⢀⡀⠀⠀⠀⠀⢀⡄⣤⢘⣭⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣾⣹⡯⢽⡯⣟⣲⣞⣫⣿⣿⠀⢻⣿⣿⣛⣶⣚⡯⣿⢭⣟⢹⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠓⠿⠻⠗⠟⠛⠋⠀⠘⠛⠻⠷⠿⠿⠓⠛⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢱⣇⣀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣥⡀⠀⠐⠟⢛⣿⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠙⠳⢤⣤⣽⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⠄⠀⠀⠀⠈⣙⣛⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠷⢣⠀⠀⢠⠞⠋⠀⠙⢛⠟⠃⠲⣷⠀⠀⠿⠇⢹⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⢁⡴⠋⠀⠀⢦⣴⣻⡄⠀⠀⠀⠀⠨⣦⠉⣟⡉
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⠾⠀⠀⠀⣀⡿⢟⣏⠁⠀⢰⣄⣰⣦⣍⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢠⣿⡀⠀⠀⣶⠈⠀⠀⠉⠒⠚⠻⣿⣿⣭⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⣿⡿⢃⠞⠃⠰⢦⣤⠄⣀⣀⠀⠀⠈⢛⣻⣃⣙⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣈⢁⣿⣧⠞⠁⠀⠀⠤⠶⠾⡶⠄⠀⠀⢠⣬⣭⣋⡀⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡆⠒⠒⠀⠀⠀⠒⠒⠀⠀⠐⢸⣯⣟⣡⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠻⣦⠀⠂⢄⡀⠀⠀⠀⠀⣷⣾⣝⠋⣹⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠒⢤⣀⣴⣿⣟⣻⣷⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠻⠟⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠖⠀⠀⠄⠴⠶⣾⣿⣿⣿⣷⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠭⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠧⢼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡞⠛⠛⠣⣼⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢿⣿⡤⠛⠛⠛⣾⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣯⠉⠉⠛⣿⠃⠀⣠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡀⠀⢻⡟⠉⠉⢩⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣉⣉⣙⣇⣸⣿⡿⢉⣿⣷⡀⠀⠃⠀⠀⠃⠀⣰⣿⣏⠹⣿⣿⣀⣟⣉⣉⣉⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠉⣀⣀⣍⣿⣿⡀⢸⣿⣿⢿⡄⢡⡀⡠⠁⣼⢿⣿⣿⠀⣸⣿⣯⣅⣀⡀⢹⣟⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣀⣀⣀⣤⠿⠿⢿⣿⣧⣈⣿⣘⣿⣟⣸⣏⣠⢿⣿⠿⠿⢷⣤⣀⣀⣰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣇⣠⠤⠤⠶⠒⢾⣿⠦⠬⣭⣿⠁⢹⣯⡭⠴⢾⣿⠗⠒⠦⠤⠤⣀⣿⣽⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣦⡤⠴⠶⠒⠚⢻⣶⣶⢾⣿⠁⢸⣿⢶⣶⣾⠛⠒⠒⠶⠦⣤⣾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⠴⢒⠞⠉⣿⠃⢀⡾⣿⣗⣿⡿⣆⠀⢻⡏⠙⢖⠲⠤⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣼⣃⣤⡏⠀⠀⣿⢠⡞⢰⠏⣗⡏⢷⠘⣦⣸⡇⠀⠈⣧⣄⣻⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⠻⡅⣸⣇⣀⣠⣿⣻⢀⡞⠀⠻⠃⠘⣆⢸⣽⣧⣀⣀⣿⡀⡽⢻⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⢾⣾⣷⠁⡜⠉⡏⠈⣿⣽⠃⠀⠀⠀⠀⢻⣭⡏⠈⡏⠙⡄⢹⣿⣿⠿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⣿⣼⣿⠷⣴⡷⢾⣷⣿⠀⠀⠀⠀⠀⢸⣷⣿⠶⣧⡴⢿⣿⣼⣿⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⢹⣿⣿⣲⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣯⣿⣷⣿⣿⣿⢡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣶⣽⡿⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⣿⣵⡾⣿⠿⠁

⠀⠀⠀⢰⣶⣄⠀⢀⣴⡶⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⢠⢤⡀⠀⠀⠀⢀⡠⡄⠀⢠⣤⡀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⢿⠹⣶⡾⢹⠃⠀⠀⠀⠿⣈⣱⣴⣞⣁⠽⠃⠀⠈⠿⣼⣦⣤⣴⣧⡿⠃⠀⠘⣿⣿⣦⣀⣴⣿⡿⠁
⠀⠀⠀⠰⣏⡖⠙⠑⣚⡇⠀⠀⠀⢸⣟⣿⠛⢿⣛⡧⠀⠀⠀⢰⣿⡮⠿⢵⣿⡆⠀⠀⠀⢾⣿⣜⠛⣣⣿⡇
⠀⠀⠀⠘⠙⠁⠀⠀⠙⠑⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⣶⣶⢄⠀⢀⢴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠠⠀⠀⠀⠆⢻⡇⠀⠀⠀⣀⡀⠀⢀⣀
⠀⠀⠀⢈⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⣈⠀⣿⠀⢀⠁⠀⠀⠀⣉⠤⢸⣿⡧⠠⣌⠀⠀⠰⣤⣀⣭⣿⣍⣁⣠⠆
⠀⠀⠀⠘⢿⠗⠈⠸⢿⠏⠀⠀⠀⠀⠁⠀⠙⠀⠀⠁⠀⠀⠀⠹⣦⠟⠙⠻⣴⠏⠀⠀⠀⠀⠋⠝⠙⠭⠙


⠀⠀⠀⢾⠒⢦⣤⣤⠖⢺⠆⠀⠰⣖⠋⠲⣴⠶⠊⢒⠖⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⢡⣶⣦⣤⣴⣶⡌
⠀⠀⠀⠈⣷⡦⠿⢧⢴⠏⠀⠀⠀⠀⠹⣶⠟⣦⡞⠀⠀⠀⠀⠀⠀⣤⠈⣠⡄⠀⠀⠀⠀⠘⣿⣛⣿⣛⣿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧⣤⣤⡄
⠀⠀⠀⠀⣿⡟⠛⣿⠛⢻⣿⡆⠀⠀⠀⠀⠀⣾⡟⢻⣿⣿⠻⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣋⣿⠛⢻⣿⣧⠀⠀⠀⠀⢠⣿⣿⠛⣿⡟⠻⣿⣿⡄
⠀⠀⠀⠀⣿⣿⡿⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⠻⠿⠷⠿⠟⣹⣿⡿⠀⠀⠀⠀⠀⢾⣿⣦⣙⠛⠟⡋⣹⣿⡆⠀⠀⠀⢸⣿⣿⣼⣟⣧⡼⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⣷⣶⣤⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠘⢿⣿⣦⣥⣤⣾⣿⠿⠃
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣤⣤⣠⣾⣿⣄⣄⡀⠀⠀⠀⠀⠀⣠⣤⣠⣶⣿⣇⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⣠⣄⣾⣿⣠⣀
⠀⠀⠀⢸⣿⡿⠛⣿⠟⢻⣿⣿⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⡿⢛⣿⣟⡛⣿⣧⠀⠀⠀⠀⠀⣼⣿⣟⢻⣿⡛⣿⣦
⠀⠀⠀⢸⣿⡳⣶⣿⣦⠔⣿⣿⠀⠀⠀⠀⢿⣿⣅⣼⣿⣿⣿⣇⣸⣿⡿⠀⠀⠀⠀⢰⣿⣿⠉⠿⠟⠉⣿⣿⡆⠀⠀⠀⠀⣿⣿⠛⠿⠿⠛⣿⣿⡆
⠀⠀⠀⠈⣿⣷⣦⣤⣴⣾⡿⠃⠀⠀⠀⠀⠘⢿⣿⣷⣮⣥⣴⣾⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣶⣤⣴⣾⣿⣿⡗⠀⠀⠀⠀⠻⣿⣶⣶⣶⣶⣿⠟
⠀⠀⠀⠀⠈⠛⠛⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⢠⣴⣤⣿⣶⣦⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣾⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣷⣆⠀⠀⠀⠀⢀⣤⣤⣶⣾⣿⣤⣴⣤⡀
⠀⠀⠀⠀⣿⣯⣼⣿⣿⣤⣿⡇⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣭⣿⡷⠀⠀⠀⠀⠀⠀⠀⣾⡁⣿⣿⣏⢸⣿⠀⠀⠀⠀⣼⣿⣋⣹⣿⣿⣏⣸⣿⣿
⠀⠀⠀⠀⢿⣧⣉⣉⣉⣡⣿⠇⠀⠀⠀⠀⠀⠸⣷⣌⡀⠈⣉⣩⣿⠇⠀⠀⠀⠀⠀⠀⢀⣿⡋⣙⣛⣉⣹⡏⠀⠀⠀⠀⢹⣿⣯⡛⠛⠛⣫⣿⣿⠇
⠀⠀⠀⠀⠀⠘⠻⠟⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠛⠟⠿⣿⡿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠟⠛⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠷⣄⠛⢢⢤⣤⣠⠴⠲⢃⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠀⠀⠀⠀⠀⠐⠋⣼⠁
⠀⠀⠙⢷⡄⠸⢻⠙⠄⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⠀⠀⠀⠀⠧⠀⡀⠀⢐⠀⠀⢀⠀⠝
⠀⠀⠀⠈⢧⣄⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠀⠄⠀⠀⠀⠀⠀⢤⠀⠀⠈⢈⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠂⠈⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⢀⣤⠜
⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤
⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠙⢷⣟⠛⠉⠂⠀⢀⠀⠐⠋⠙⢻⣷⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢷⣀⣠⣤⠴⢿⠶⣤⣤⣀⣸⠃⠀⠑⢄⠀⠀⠀⢰⡄⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢸⠀⠀⠈⢷⡄⠀⠀⠀⠀⠃⡀⠀⢸⠇⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⠘⣄⣀⣠⡜⠀⠀⠀⠀⠀⠀⠐⠤⠔⠦⠴⠃
⠀⢶⣶⠒⠤⠀⠀⠀⠀⠠⠔⢲⣶⠂⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢻⣆⠀⠀⠀⡄⠀⠀⢀⣾⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠫⣖⣤⡀⠀⠀⣠⣴⡾⢫⣿
⠀⠀⠈⢩⠀⠀⠀⠇⠀⠀⢈⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⠿⣦⡈⠹⢞⣾⡞⠾⢁⣠⡿⠇
⠀⠀⠀⠸⣆⣠⠀⠀⣄⣀⡾⠀⠀⠀⠀⠳⣤⠀⠀⠠⠀⠀⢠⡤⠇⠀⠀⠀⢰⣿⠀⢸⠸⢸⠀⣸⡇
⠀⠀⠀⢀⠏⠉⠀⠀⠈⠉⢇⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠻⣷⡎⠀⠀⣶⡿⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁
⠀⠀⢀⠁⠀⢀⠀⠀⠀⡀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⢀⣴⣶⡖⣴⣶⣤⣦⣶⢶⡶⣦⣦⡀⠀⠀⣿⠒⠀⠂⠂⠀⢠
⠀⠀⠀⠀⠂⠀⠀⣁⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣌⢹⡟⣡⣶⣼⠟⠋⠁⠀⠀⢧⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠁⢀⡅⡀⠀⠁⠀⠀⠀⠀⠀⠈⢯⣟⡿⢻⣛⡽⠃⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⡶⣶⡦⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⠁⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢺⣏⢹⡇⣩⣿⣫⡾⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣋⠈⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⣀⣠⣴⣿⣿⡔⠋⢀⣼⣿⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣗⠙⢷⠆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⣿⢿⠇⠀⢠⣾⣿⡷⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⣌⣀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣿⣿⣟⢿⣿⣌⠂⠀⢠⢸⣿⣘⠇
⠀⠀⠀⠀⢀⣠⢺⣿⣿⣿⡄⣷⣿⣿⣧⡽⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣆⡹⠟⠛⠻⠈⠃⢿⣿⡧⠀⣠⣿⣿⠧⠃
⠀⠀⠀⢠⣜⣿⣿⣿⡟⠁⠘⠋⠹⣿⣿⢇⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⠿⠦⢉⣁⣀⣠⣀⠠⠄⢀⣉⣟⠞⢻⣿⡟⣺⡀
⠀⠀⠀⢘⡉⢿⣿⣿⣷⡶⢀⣠⣤⣬⣽⣿⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⡶⡿⢿⢿⣿⣟⢿⣿⣿⣿⣿⣦⡀⠀⠗⠉⠀⠓⠄
⠀⠀⠀⠀⠁⠈⠛⠉⠟⠃⠻⠿⠿⠟⠫⠌⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠷⠛⠛⠉⠉⠁⠈⠋⠖⠋⠽⣉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣬⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢿⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠳⠾⠁⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠉⠁⢑⣶⠄⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣶⣌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢋⡀⢁⡂⠀⠀⢀⠀⠀⣠⡀⠀⠒⣀⠘⢛⡿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⠥⢠⣶⣿⡃⠀⠀⢥⣄⢺⠭⠞⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣛⡷
⠀⠀⣾⣿⡟⢶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⢀⠀⠱⠀⠵⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠟⣡⣿⠐⡟
⠀⠀⠙⣿⣿⣴⠿⠿⠟⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⠇⣾⣿⣹⠇
⠀⠀⠀⠘⣿⣷⠒⠒⠂⠀⠄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣭⡛⢲⡿⣧⣼
⠀⠀⠀⠀⠘⣿⡏⠉⣁⣠⣤⣤⣤⣀⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⣷⣶⣷⣤⣿⡈⣿⢤⣄
⠀⠀⠀⠀⠀⣿⡛⠻⠟⠉⠍⠉⣡⣾⣿⣿⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣈⠿⢹⢿⣿⣿⣷⣤⡟⣿⠟⠛⠋
⠀⠀⠀⠀⠀⢻⣧⡀⠀⠞⠀⣾⣿⡿⠁⢿⡆⠀⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣾⠀⢶⣿⣿⣿⣗⣿
⠀⠀⠀⠀⠀⠀⠹⠿⣷⡶⣾⡟⠁⣀⠂⢸⡇⠀⠁⢀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠈⠁⠐⢿⡇⢰⠀⢾⠘⣽⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⢿⣿⡿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣦⣼⣷⣾⣦⣾⣾⣯⡍⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠠⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠻⢿⣿⠟

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢻⡛⠦⣀⣀⡴⠛⡿⠀⠀⡤⢀⠄⠀⠀⠀⠠⣄⢠⡄⠀⢸⣷⣄⠀⠀⢀⣴⣿⠀⠀⠀⣶⣶⣦⡀⠀⢀⣴⣶⣶⠀⠀⢻⣶⣄⠀⠀⠀⠀⡠⣶⡟
⠀⠀⠀⠈⠃⠀⠸⢇⠀⢐⠃⠀⠀⠱⠁⠀⠀⣴⡀⠀⠀⠛⠁⠀⠀⣿⢻⣧⣠⣿⣳⡇⠀⠀⠀⢾⣟⣹⣿⣴⣿⣏⣻⡗⠀⠀⠈⣷⣿⣷⣄⣠⣾⣿⣾⠁
⠀⠀⠀⠀⢹⣤⠂⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢈⣯⣿⢿⣯⣏⠀⠀⠀⠀⠠⣿⣬⡿⠿⣿⣭⣿⠀⠀⠀⠀⠈⣽⣿⠟⠻⣿⣯⠁
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠹⡟⠀⠀⠀⠀⠀⠙⠛⠇⠀⠸⠛⠋⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⢠⣴⡆⠀⣤⠤⢄⠀⠀⠀⠀⢀⠤⢤⡄⠀⣶⣤⡀⠀⠀⠀⢀⣴⣶⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⣿⣿⢗⣤⣴⣦⣤⡲⢿⣿⠀⠀⢫⣴⣾⣤⣾⣶⣌⠇⠀⠀⣀⠀⠹⣄⣀⡶⠁⠀⡀⠀⠀⠘⣿⢿⣆⣀⣰⡿⣿⠇⠀⠀⢸⡿⢷⢀⠀⠀⣀⡾⢿⡇
⠀⠀⠈⢷⣸⣿⣿⣿⣿⣟⡼⠃⠀⠀⠈⢉⣿⢿⢿⡏⠉⠀⠀⠀⢀⠐⠀⢈⣏⠀⠐⢀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⢉⢊⣉⣿⣿⣃⡙⠈
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠀⠀⠀⠀⢦⠀⡞⠹⡄⢠⠆⠀⠀⠀⠀⣿⣿⠉⠀⠉⣿⣿⠀⠀⠀⠀⢸⡸⠿⠁⠀⠿⠇⡆
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠉⠉⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉
⠀⠘⣇⠉⠀⠄⠀⠀⢀⠔⠉⢠⠇⣶⣦⣄⠀⠀⠀⢠⣴⣶⠄⠸⡟⡷⢀⠀⠀⢀⢸⡟⡿⠀⠰⡾⠂⠀⠀⠀⢀⠠⠐⣿⠄⠀⣤⠄⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠈⢦⣴⣾⣦⣰⣿⣶⡴⠋⠀⢸⡟⢹⣷⡤⣼⣿⠙⣿⠀⠀⠃⠀⡜⢱⣶⠙⡄⠀⠁⠀⠀⠅⠀⠒⠃⣴⠘⠓⠀⠨⠀⠀⠁⢠⠀⠀⢰⡆⠀⠀⡄⠘
⠀⠀⠀⢀⣼⣿⡿⢿⣿⣧⡄⠀⠀⠀⢴⠈⠿⠻⠻⠇⢰⠀⠀⠀⠠⡀⠀⠈⠏⠀⠀⡰⠀⠀⠀⠀⠈⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠈⡿⠞⠁⠀⠁⢺⠅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⢰⣤⡀⠀⠀⠀⠀⣠⣶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⢤⢤⣄⠀⠀⠀⠀⣠⡤⣤
⠀⠀⠘⣿⣋⣴⣄⢠⣴⣝⣿⡇⠀⠘⣿⢚⣦⣀⣠⡟⣽⡇⠀⠀⡇⣧⠀⠀⠀⠀⢠⡇⡇⠈⢻⡿⣷⣄⠀⠀⠀⣠⣾⢿⡟⠀⠘⡍⠈⢳⡄⢠⣾⠁⢉⠇
⠀⠀⠀⢻⡟⠛⠻⡿⠛⠻⣿⠀⠀⠀⣡⣾⣿⢿⣿⣿⣬⠀⠀⠀⠁⠸⡿⢷⣷⡿⡿⠀⠁⠀⠀⠻⠌⣻⣷⢶⣾⣟⠡⠟⠀⠀⠀⠘⣡⣿⣿⣿⣷⣌⠃
⠀⠀⠀⠘⠷⣤⠂⠐⣤⡾⠃⠀⠀⠀⢹⢉⡛⠀⠘⣃⣻⠀⠀⠀⠐⣄⠃⠁⠂⠀⢃⡔⠀⠀⠀⠀⢾⣅⡉⠚⢉⣩⡷⠀⠀⠀⠀⠈⠢⠝⠀⠀⠫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢻⡇⠀⠀⠀⡾⣿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠃⠀⡻⠀⠀⠀⠀⡅⠀⠀⠈⢿⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⣸⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣠⠴⠋⠁⠻⡆⠀⢣⢱⠀⠀⠀⠴⠛⠉⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⠀⠀⢀⠔⠊⢉⠟⢦⡄⠀⠀⣰⠏⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⢀⣶⣄⢀⣤⡈⠙⠛⠋⢰⡀⠀⠀⡰⠒⠋⠉⠉
⠀⠀⠀⠀⣴⡿⠄⠀⡼⠂⠀⠀⡀⠉⠁⠀⠀⠀⠀⠉⠙⠓⠀⠠⢠⣄⣼⠃⠀⠀⣾⡟⢹⡿⠟⣷⡀⠀⠀⠀⠙⠲⠚⠁
⠀⠀⠀⠸⠿⠶⠴⠄⢣⣀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⢱⡟⠱⠀⠘⣻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠟⠛⠳⢦⡀⠀⠀⠀⠀⢹⣸⠀⠀⣠⠞⠁⠛⢷⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣾⠃⠀⠀⡀⠀⠀⠀⠙⠲⢤⡀⠀⠀⢿⣤⡎⠉⡀⠀⠀⣰⡇⠀⢠⡿⠋⠻⠋⠣
⠀⠀⣀⣤⠤⠀⢀⠀⠀⢀⠔⠁⠈⣿⠃⠀⠸⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠁⠀⠀⠀⠒⠋⠀⢀⡾⠁
⠀⠀⠙⣿⡀⠀⠈⠑⢤⡏⠀⠀⠠⡿⠀⠀⣼⠁⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⢰⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠘⢷⡤⠄⠀⢸⡇⠀⠈⠉⠳⡄⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠩⠞⣣⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠀⢞⠀⠀⠀⠀⠁⢀⠀⠀⣼⠃⠀⠈⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⣼⡇⠀⢼⣿⣧⡀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠰⠋⠁
⠀⠀⠀⠀⠈⠷⣤⣠⠇⠀⠈⠓⠚⠃⡀⠀⠀⠀⡿⠁⢰⠟⠁⠀⠀⠀⠀⢸⣿⠀⣠⠀⣿⣿⣷⣦⣄⡀⠀⠙⠓
⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⡞⠁⠀⠀⣤⠀⡀⠀⠀⠀⠀⠛⠇⠀⠘⣩⠉⠙⠛⢡⡞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣄⠀⠀⣦⣥⣀⣤⡦⣦⣼⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠹⣄⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⢀⣤⣠⣶⡄
⠀⠀⠀⠀⠀⠀⣰⣛⣿⢶⣿⡄⠀⠀⠛⠦⠌⠀⠀⢠⠶⠟⠂⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⣿⢻⡇
⠀⠀⠀⠀⠀⢰⣯⣽⣙⡓⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⢀⣀⡾⠁
⠀⠀⠀⠀⠀⢸⣴⣥⣌⠃⠀⢿⣿⣤⠀⠀⠀⠀⠀⠀⢴⣿⡃⠀⠀⠀⠀⠙⠆⠀⠀⠰⠟⠓⠂⠀⢀⣴⣿⠽⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠙⣿⡅⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢻⣿⠃⠀⠀⠀⢀⣠⡧
⠀⠀⠀⠀⠀⠀⠾⠿⢿⠂⠰⠦⠀⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⡿⠀⠀⠀⠀⠀⠠⠤⠾⢷⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⢀⣤⡤⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣤⣤⡤⣤⡀
⠀⠀⠘⣿⡇⣿⣿⢸⣏⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠰⡍⡇⢹⣿⡧⣿⠇
⠀⠀⠀⠹⣯⣾⣷⣀⣹⠤⣃⣀⡾⠋⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠑⢷⣄⣈⢤⣇⣁⣾⣿⣼⡟
⠀⠀⠀⠀⠹⣧⣾⣿⡤⠔⠚⢻⣤⣤⣾⣿⡟⢦⡀⠀⠀⠀⠀⢀⣴⢟⣿⣷⣤⣠⡟⠛⠒⢤⣽⣟⣾⠏
⠀⠀⠀⠀⠀⠙⣿⢻⣷⠖⠉⢁⣀⠹⠿⣿⣿⣿⣿⣦⣴⣶⣠⣿⣷⣿⣿⠿⠯⣀⡈⠉⠓⢶⡿⣾⠟
⠀⠀⠀⠀⠀⠀⠹⣯⣿⠞⠉⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠓⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃⣠⣤⡤⠶⠒⡛⠛⠻⣿⣿⡿⢿⣿⣿⡟⠛⢛⠒⠶⢦⣤⣄⡐⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⢻⣯⠀⡀⠴⠁⢀⣴⡟⠙⡿⢺⠏⢹⣦⡀⠀⠦⢀⠀⣿⡟⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⡟⣷⠚⣿⡁⠐⠣⠔⡋⢸⠀⠀⡇⢸⠀⢀⡇⠉⠲⠔⠂⣌⣿⠓⣾⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠹⡶⢿⣅⡀⡆⠀⡇⡞⢀⠀⢧⢸⠀⠠⢧⢘⠀⠐⣀⣸⡿⢷⠏⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⣼⠛⢿⣷⣸⣄⣧⡈⠀⠈⠀⠀⢀⣼⣨⣆⣶⣿⠛⣧⣼⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣛⣿⣦⣄⣋⣻⣩⣧⠀⠀⠀⠀⣼⣏⣛⣉⣠⣼⢿⣻⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣝⣻⣝⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⢀⠀⠀⢀⡀⠄⢀⡄⠄⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⣟⣤⣾⣥⣴⣿⣤⣤⣾⠤⣴⣾⢷⣤⠞⢳⠾⢛⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡯⣅⣴⠭⣤⠾⢅⣴⠏⢤⡴⠧⣠⡾⠲⡶⠗⢲⡟⠈⣿⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢥⣤⠯⢤⡼⠥⣤⡮⢄⣠⡯⢄⣴⠅⢤⡮⢀⣴⣿⡇⠀⣿⣗⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣉⣀⣈⣁⣀⣁⢀⣰⡉⢀⡀⠁⣀⠈⠀⡐⡁⢠⡴⠛⣛⡏⠀⣛⣛⣓⣌⢿⣦
⠀⠀⠀⠀⠀⢀⡼⠉⠡⠋⠁⡼⠉⢠⠿⠉⢉⡟⠉⡸⠋⠉⠟⠉⢉⣿⡙⣿⣿⢀⠀⣿⣿⡋⣾⣌⠳⣇
⠀⠀⠀⠀⠰⣧⠒⣤⠰⣴⣴⠶⣤⣤⣤⣀⣤⢤⣢⣦⣀⣶⣦⣴⣿⣴⣶⡖⢶⡶⠀⣶⡆⣶⣶⣶⣷⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢿⡇⣿⢻⠃⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠑⡌⢶⠀⠛⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡁⠿⠤⠄⠀⠀⡠⠤⠤⠤⠄⠠⠀⠠⠤⢽⣿⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢰⡆⠀⠀⠠⡄⠀⠰⢠⡀⡦⠀⠀⢰⠀⢸⡇⡴⢮⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣬⣷⣤⣤⣴⣾⣦⣤⣤⣴⣇⣶⣴⣾⣧⣼⢻⠀⡇⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⡇⠀⠘⡄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⣤⠆⠀⠶⢦⢀⠀⢀⠤⢀⠀⢀⡀⢈⢸⠀⠃⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠋⢉⣿⡿⠈⠀⠀⢰⣞⣶⣦⣶⣆⣴⣀⣠⣬⢸⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠐⠉⣿⣡⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⣿⠨⠀⢠⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⣇⣸⣷⠤⠤⠴⣾⣃⣽⢩⠁⠀⠠⠠⠴⢶⢰⠀⢰⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⡗⠾⣯⣹⣛⠛⠳⠲⣿⠖⣿⡶⠶⠶⡶⠖⠒⢿⢿⠓⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⢷⣨⡈⠙⠓⠶⠴⡧⠰⡯⠤⢤⢤⠢⠤⠔⢿⣾⡄⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡾⡅⠙⠿⡤⡄⢠⣷⣴⠇⠀⣺⠀⠀⢀⣀⣼⣿⡧⢾⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⢷⣶⣄⣧⡀⠈⠈⢩⢁⡉⠈⣧⡉⢀⣼⣿⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠐⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢉⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄
⠀⠀⢻⣧⣏⡗⠚⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠟⠲⣏⣯⣿⠁
⠀⠀⠈⣽⢤⣿⣋⣈⣽⡇⢨⣿⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣯⠰⣿⣉⣉⣹⣥⣿⡇
⠀⠀⠀⠹⣯⣼⣯⣀⣨⣛⡧⠤⡿⠷⠮⢷⣄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣠⣴⠯⠶⠿⡯⠴⣟⡯⣀⣨⣟⣼⡟
⠀⠀⠀⠀⠘⢿⣾⡉⡱⡗⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⢀⣼⣿⡉⣳⣿⠏
⠀⠀⠀⠀⠀⠠⡿⣫⢽⣿⠛⠂⠀⠉⠒⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠔⠋⠁⠀⠛⢾⣻⡽⣧⡟
⠀⠀⠀⠀⠀⠀⢹⣿⣤⢷⣀⠀⣀⣀⠤⠴⠦⠄⠀⠀⠈⠳⡀⢀⣀⢀⡴⠋⠀⠀⡀⠠⠶⠤⠄⢀⡀⢀⣸⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠘⣾⣿⠎⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣤⣶⣶⣶⣶⠒⠒⠤⣤⢤⣼⣿⣿⣷⣤⣤⠀⢀⣶⣶⣶⣶⣶⣤⣤⣴⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠞⢿⣿⡟⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡽⠓⠂⠀⠀⠉⠀⠀⣀⡤⠊⠁⠄⢸⣿⠀⡀⠙⠢⣀⠀⠀⠈⠀⠀⠀⠒⠻⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣻⣄⣀⠀⠰⢊⠠⠒⠋⠁⠀⠀⠜⠀⢹⣿⢠⠘⠄⠀⠀⠉⠒⠦⠘⠲⠀⣀⣀⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡅⢀⡔⠁⠀⠀⠀⠀⠀⠀⣤⠃⠸⡟⠈⢷⡀⢀⠀⠀⠀⠀⠀⠱⣄⠀⣵⣹⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⣟⣿⣄⣀⣠⡆⠀⡰⠁⣰⠃⠀⠀⠀⠀⠈⢧⠀⢣⡀⠈⣦⣀⣀⣼⣛⡟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣻⣽⣿⣷⣺⣇⡴⠃⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⣲⣯⣿⣽⣿⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣾⠀⢀⡏⡹⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢾⡿⢖⠂⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠀⠃⠲⡛⠿⣦⣤⠄⠀⠀⠀⠀⠀⠀⢀⠴⠻⣶⠾⠳⢽⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⣲⠀⠀⠀⠙⣆⠀⠙⢷⡀⠀⠀⠀⢀⠔⠁⢀⠼⠓⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣃⠈⢀⣀⣉⣕⣦⣄⡙⢦⣶⡷⠃⣀⣒⣉⣀⣀⣀⢀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢛⢻⠿⠟⢉⡙⠫⡭⣿⣿⣷⣯⣋⡉⠉⠛⠿⣿⣟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣉⠀⠀⡐⠊⡠⠂⠐⠸⣿⠘⠂⠠⡈⠲⠀⠀⠘⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠁⠒⠀⡐⠀⢀⣿⠀⠠⠠⠈⠒⢤⠀⠀⢐⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢢⡄⡀⠀⠀⠠⠀⠄⠈⣿⠀⢀⠂⠡⠀⢂⠁⣈⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢇⣞⣦⣷⡾⠀⠀⠁⠀⠀⠺⢦⣷⣾⣿⠿⠋

⠀⣶⣦⡀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⣶⡶⠄⠀⠀⠀⠀⣀⡴⣶⡆⠀⠀⠀⣠⡶⣶⡀
⠈⣿⣭⣷⣄⠀⠀⠀⠘⣈⠑⠶⠀⠼⡤⠠⢟⣀⠃⠀⠀⠸⣇⠀⠐⣶⣶⡞⠋⣁⡿⠁⠀⠀⠰⣅⢰⡹⣧
⠀⣽⠿⣿⣿⣆⠀⠀⠀⠻⠶⠂⠀⠀⠀⠐⠺⠟⠁⠀⠀⠀⢾⣿⣆⣿⡏⠹⠜⣫⠇⠀⠀⠸⣷⡈⣷⢻⣧⡀
⠀⠹⣄⠈⠙⣿⣦⠲⡷⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠁⠀⠈⠁⠀⢸⢿⣧⣼⣿⣿⡇⣻⣷
⠀⠀⠈⠁⡼⣽⣧⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⡄⠐⣶⠦⠤⠄⠀⣀⠀⠲⡄⠙⣼⣿⣶⣿⣿⣟⠟⢠⠿⠃
⠀⠀⠀⣾⣾⠟⠋⣁⠬⠻⣿⣿⡿⢲⣦⡀⠀⠀⠀⠀⠏⠀⠀⠀⠸⣦⣄⢢⣯⣟⠻⣿⡿⠿⠈⠛⠂
⠀⠀⠀⡉⠀⠀⠄⡍⠓⠲⠾⠛⠛⠛⠛⠋⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠉⠉⠉⠻⣷⣶⣶⠾⠃
⠀⠰⢩⠀⠀⠛⡰⠁⠀⢀⣀⠀⢿⡇⠒⢤⡀⠀⠉⠉⠍⠉⠉⠀⢀⡤⣒⣼⡷⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠘⠷⠿⠂⠀⠀⡰⣿⣿⡆⠈⢿⣷⢊⡻⠦⡀⢀⠀⠔⢀⠴⢷⠛⢲⣿⠁⢸⣿⣿⡄⠀⠀⠀⢀⡰⠉
⠀⠀⠀⡀⠀⠀⠀⣸⣿⣧⣿⣧⡀⠐⢻⣧⣅⡈⠝⡆⢸⣶⣌⡂⢌⣼⣿⠇⠀⣸⡿⢹⣿⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⢴⣖⠠⠀⢀⡟⢻⡿⠁⢀⡀⢠⡦⠀⠀⣻⠗⣿⣿⡇⠀⠀⡤⢀
⠀⠰⣶⣄⡀⠀⣸⡛⠏⠉⠁⡐⡄⠀⠈⢻⣆⡿⡁⠈⠛⠉⠄⢯⡱⡟⠁⠀⠰⣿⠂⣿⣿⣿⠀⠀⠀⠈⠁
⠀⠀⠘⢿⣿⣆⠸⣟⣾⠀⠀⠁⡗⠰⠀⢠⣿⠙⠀⠀⠀⠀⠈⠻⣿⡀⠀⠠⢽⣿⣸⣿⠟⠁⠀⠀⠳⣿⣆
⠀⠀⣀⣤⠀⠀⠀⠈⠙⠿⠶⠤⠅⢀⠠⠊⠁⠀⠀⢀⣤⡀⠀⠀⠉⠱⣄⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢻⣿⣿⣤⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠺⢿⣿⣦⣄⡀⠀⠀⢠⣾⣶⣆⣀⠀⠀⠀⠀⣤⣛⣿⣿
⠀⠀⣼⣿⣿⣿⣿⡄⣀⣠⣶⣷⣿⣿⠿⠂⠀⠀⠀⠒⠤⢤⣤⡈⠹⣷⠀⠀⣿⢙⣿⣿⣷⣄⣤⣾⣿⣿⣣⣿⠂
⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⠋⠀⠀⠙⣻⢪⣿⣿⣿⣿⢿⣿⣿⢿⣧
⠀⠀⢿⣿⣿⣿⡟⣿⢻⣿⣿⣿⣿⠉⠀⣀⡀⠀⠀⠑⠐⠂⠒⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠛⠹⢿⣷⣿⡿
⠀⠀⠀⠙⠛⠉⠀⠁⠘⢿⣿⡿⠏⠀⠀⡿⢣⣶⣄⡀⠀⠀⠀⠀⣀⢠⣤⠀⠀⠉⠛⠿⠏⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⡀⠀⠀⠠⣀⠈⠁⠀⣀⡀⠀⢨⣷⢯⣯⣵⣶⣦⣘⣞⣿⣋⡟⠀⢰⣶⣀⡀⠐⠆⠀⠐⠂
⠀⠀⠀⠀⢘⣦⣴⠿⠛⠋⠀⣠⣿⣿⡄⠀⠛⠿⠿⠙⣾⠏⣿⣿⣿⡗⢀⣠⣿⣿⣿⠿
⠀⠀⢠⡶⠂⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣾⣿⠿⡍⢾⡏⠀⠶⠀⠀⠀⡔⣷⣷
⠀⠨⠊⠀⢀⣠⡶⣤⠀⠀⠀⢘⡿⣿⣿⣿⣄⣀⠀⠀⠀⠀⢀⣴⣶⡾⢻⣵⣾⣷⣿⠁⢀⠖⠄⠀⠀⠄⠹⣿⡀
⠀⠀⢰⣦⣻⣿⠟⠉⠀⠀⠀⢸⣷⣄⣿⣿⣿⣿⡇⠀⠀⢰⣿⡿⢡⡌⣻⢿⣿⣸⡇⠀⠉⠀⠀⠀⢠⣵⣤⣿
⠀⠀⠘⠿⠏⠁⠀⠀⠀⠀⣰⣿⣿⣿⠿⢿⣿⣿⠇⠀⠀⢸⣯⣴⣿⠿⠟⠙⢟⣋⣤⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⡀⢤⣶⡶⣦⣟⣿⣿⣿⡗⠏⢧⡀⠀⠁⠀⠀⡠⢤⣤⣀⣀⡀⠀⠛⠉⡿⣿⣭⣛⡶⠦⣤⣄⡀⠈⠁
⠀⠀⠐⢽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣠⠔⣓⣦⣴⠞⠛⠋⠉⣠⣴⣿⣏⠙⡿⠿⠟⣛⣳⣬⣥⣾⡗
⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣯⣿⣿⠟⢁⣼⣿⡿⠋⠉⠉⠀⠀⠀⠀⢯⣥⣴⣮⣴⣶⠟⠻⠿⠿⠛⠛⠻⠧⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢧⣍⠻⢿⣶⣤⣀⣀⣤⣤⠶⠶⠶⠶⣤⣀⠀⠀⣠⣤⠶⠶⠶⠦⣤⣤⣀⣀⣤⣴⡿⠟⣩⡼⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠉⠻⡶⢦⣭⣉⣿⡍⣠⠶⠟⣛⣛⣻⣿⣿⣾⣿⣿⣛⣛⠛⠶⣄⢨⣯⣉⣭⡴⢶⠟⠉⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⢀⣀⣤⠟⠉⠈⠀⠐⠋⡉⠉⠉⠉⠛⠟⠉⠉⠉⢉⠉⠂⠀⠁⠈⠻⣤⣀⡀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠶⡿⠋⠀⣠⡄⠀⠀⢰⠟⢳⠆⢰⡖⢢⡔⢲⡆⠰⡞⠻⡄⠀⠀⢤⣄⠀⠙⢿⠲⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡴⢿⣿⠀⠶⠧⡘⠄⠋⠀⢸⢃⡾⢷⡘⡇⠀⠹⠠⢃⠼⠶⠀⣿⡿⢄⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡀⠀⡀⠀⡀⡸⢛⡓⢦⡶⠄⠄⠀⠀⠹⠋⠀⠀⠙⠇⠀⠀⠀⠴⢦⠴⢚⡛⢇⢀⠀⢄⠀⢀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡟⢠⡞⠁⣰⠃⠁⠈⠛⢆⣄⣙⣠⣷⠀⠀⡀⠀⠀⠀⡀⠀⣾⣄⣋⡼⡠⡛⠁⠈⠈⣆⠈⢷⡄⢻⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣽⠁⣰⡇⠀⢀⡴⣻⡿⠿⠿⠛⠓⠠⠐⠂⠀⠀⠐⠂⠄⠘⠛⠻⡿⢿⣟⢦⡀⠀⢸⡆⠈⣏⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⣿⡆⢸⢀⠀⠈⠰⠋⢠⣀⣰⢏⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⡹⣆⣀⡄⠙⠆⠡⠀⡈⡇⢰⣿⢀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠀⢹⡇⠘⣿⠀⠀⠀⠀⣦⣯⡙⠇⠐⢤⡄⠄⠀⠀⠀⢠⡤⠊⠸⢋⣿⣴⠀⠀⠀⠀⡿⠃⢸⡏⠀⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣸⣇⠀⠸⣦⠀⠀⠰⣿⣮⡙⠦⠀⠀⠰⡄⠀⠀⣠⠆⠀⠀⠔⢋⣵⣿⠆⠀⠀⣴⠇⠀⣸⣇⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠙⠛⠷⣦⡉⠳⡀⠀⣿⣯⡙⠀⠀⠀⠀⠈⢠⡄⠃⠀⠀⠀⠐⢋⣽⣿⠀⢀⠞⢉⣴⠾⠛⠋⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣥⣀⣀⠘⠛⠿⣿⣄⡈⠀⢾⣿⣷⡆⠀⢠⠀⠴⠾⠷⠦⢠⡄⠀⣰⣾⣿⡷⠀⢀⣠⣿⠿⠛⠃⣀⣀⣬⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣛⡀⠀⠈⠙⢿⣦⡀⢹⣿⡿⠀⡿⠶⠧⢦⡴⠼⠶⢿⠀⢻⣿⡏⢀⣴⡿⠋⠁⠀⢀⣛⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠷⠆⠀⠀⣈⣷⡄⢻⡇⣰⡇⠀⠀⠀⠀⠀⠀⢨⣄⢾⡿⢠⣾⣉⠀⠀⠰⢾⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⣦⣀⠀⠉⠸⣷⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⣼⠇⠉⠀⣀⡴⠖⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣿⣿⠙⠃⠀⠀⠀⠀⠘⠋⣿⣿⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢿⣿⡧⣤⣤⡶⠶⣄⣤⣼⣿⡿⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠾⢦⣄⣠⡴⠷⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠰⢢⡶⠀⠀⠀⠀⠀⠀⠰⣆⠶⠀⣶⠒⠂⢀⠀⠀⠀⠠⡐⢰⡶
⠀⠀⠀⠈⢧⣀⡀⢰⡆⢀⣀⡼⠁⠀⠀⢰⡇⡶⢡⢀⢠⡱⡆⣷⠀⠀⠀⠈⡷⠀⠀⢀⡀⠀⠀⢸⡇⠀⠀⠘⡆⠀⠀⢥⣤⠄⠀⠀⣾⠁
⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⡆⠀⠀⠀⠈⣡⡇⠻⣼⣼⠃⣧⡉⠀⠀⠀⠀⢀⡄⠀⠈⡇⠀⠀⣄⠀⠀⠀⠀⠙⡶⢠⡴⡿⣦⡐⢶⠃
⠀⠀⠀⠀⠘⢷⣤⡤⢤⣤⡾⠃⠀⠀⠀⠀⠹⣿⡄⠸⠁⣼⡿⠃⠀⠀⠀⠀⠙⢷⣤⣄⢁⣤⣼⠟⠀⠀⠀⠀⠘⢧⡛⡧⠁⣜⢃⡼
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠉⠧⠀⠀⠀⠀⠀⡀⠈⠛⠁⠀⠉⠋⠀⢀
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⣠⠠⡄⡀⠀⠀⠀⣀⠤⠄⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠘⣇⠀⠀⠀⢠⡀⠀⠀⠀⡼⠁⠀⠙⣆⠦⠏⠶⣤⠞⠻⠶⣴⠃⠀⠸⡇⠀⠀⠀⣀⠀⠀⠀⢠⡗⠀⠀⠈⣷⢦⠀⣤⠠⢾⡾
⠀⠀⠀⠙⣷⠀⠀⢸⠇⠀⠠⡾⠃⠀⠀⠀⢻⢤⡀⠦⡿⠞⢀⠴⡟⠀⠀⠀⢷⡄⠀⠀⢿⠀⠀⢀⡼⠃⠀⠀⢠⠀⠀⠀⠟⠀⠀⢠⡀
⠀⠀⠀⠀⠹⣷⣄⡈⢠⣰⣾⠇⠀⠀⠀⠀⠈⠳⣙⡆⠀⢒⣫⠞⠁⠀⠀⠀⠀⠳⣀⡀⠈⢀⣀⡼⠁⠀⠀⠀⠈⢧⣀⡀⠀⣀⣠⡞
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⠉⠁⠀⠈⠉
⠀⠀⠘⣧⠐⡢⠀⠀⠀⠠⠔⢂⡼⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠀⠀⢄⢠⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠈⢧⡀⠀⢸⡆⠀⢠⠞⠁⠀⠀⢰⣆⠀⠀⠘⣿⠁⠀⠀⣰⡆⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠴⣬⣿⣱⠆
⠀⠀⠀⠀⢺⣄⣀⠸⢁⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠁⠀⣰⠃⠀⠀⠀⢠⣘⠷⠶⢢⠴⢾⣣
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠈⠛⠒⠂⠀⠀⠀⠀⠦⠀⠀⠀⠀⠐⠒⠛⠀⠀⠈⠧⠀⠀⠼⠁⠀⠀⠀⠀⠿⠆⠽⠵⠿⠮⠏⠸⠗
⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢿⠃⣼⡗⠀⠀⠀⠀⢻⡆⠹⡟⠀⠸⡟⠳⠗⣦⣀⣠⣔⠻⠛⡿⠀⠀⢿⠛⠓⢄⠀⠀⠚⠛⣿⠃⠀⠛⣿⠂⠀⠀⠀⠀⠀⢺⡿⠋
⠀⠀⠈⠀⢸⣆⠀⢸⡇⠀⣸⠇⠀⠀⠀⠀⢻⡀⣰⡆⢸⠁⢼⡀⣰⠇⠀⠀⢸⡁⠀⠀⣶⠃⠀⠀⡿⠀⠀⠀⠹⣇⡀⠀⣿⠀⢀⡼⠃
⠀⠀⠀⠀⣄⠙⠶⠜⠷⠾⢋⡄⠀⠀⠀⠀⠀⣧⠈⠀⠈⠀⠈⢀⡇⠀⠀⠀⠀⡏⠉⠀⠹⠀⠈⢉⡇⠀⠀⠀⠀⢼⡃⢀⣧⡀⢸⡇
⠀⠀⠀⠀⠘⠿⠶⠀⠐⠶⠟⠁⠀⠀⠀⠀⠀⠸⠛⠃⠀⠀⠛⠻⠁⠀⠀⠀⠀⠹⢾⠃⠀⠀⢷⠞⠁⠀⠀⠀⠀⠈⠻⠞⠈⠷⠛

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⣦⣄⠀⢀⣴⡶⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⢠⢤⡀⠀⠀⠀⢀⡤⡄⠀⢠⣤⡀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⢿⠹⣶⡾⢹⠃⠀⠀⠀⠿⣈⣑⣴⣞⣁⠹⠃⠀⠈⠾⣬⣢⣤⣴⣧⠿⠃⠀⠘⣿⣿⣦⣀⣼⣿⡿
⠀⠀⠀⠰⣏⡖⠙⠑⣊⡇⠀⠀⠀⢸⣟⣻⠛⢿⣛⡷⠀⠀⠀⢰⣿⡮⠿⢵⣿⡆⠀⠀⠀⢾⣿⡜⠛⣣⣿⡇
⠀⠀⠀⠐⠙⠁⠀⠀⠙⠑⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⣶⣶⢄⠀⢀⢴⣶⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠠⠀⠀⠀⠆⢻⡇⠀⠀⠀⣀⡀⠀⢀⣀
⠀⠀⠀⠈⣿⣟⣿⣟⣿⡏⠀⠀⠀⠀⣀⠀⢿⠀⢀⠀⠀⠀⠀⣁⠤⢸⣿⡇⠠⣌⠀⠀⠰⣄⣀⣭⣿⣍⣀⣠⠆
⠀⠀⠀⠈⢿⠟⠈⠘⢿⠟⠀⠀⠀⠀⠁⠀⠘⠀⠀⠁⠀⠀⠀⠹⣦⠟⠉⠻⣴⠏⠀⠀⠀⠀⠋⠝⠙⠭⠉


⠀⠀⠀⢾⠒⢦⣤⣤⠆⢺⠆⠀⠰⢖⠋⠲⣴⠶⠊⢒⠶⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣴⣦⡈
⠀⠀⠀⠈⣷⡤⠿⢧⢴⠏⠀⠀⠀⠀⠹⣶⠟⢦⡞⠀⠀⠀⠀⠀⠀⣤⠈⣠⡀⠀⠀⠀⠀⠸⣿⣛⣿⣋⣿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢐⣾⣻⣻⣿⠖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⣿⣟⣟⣶⡂
⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⢰⣟⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⣻⡆⠀⠙⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣶⣛⣻⣍⠙⠛⢷⡄⠀⠀⠀⠀⢠⡾⠛⠋⣩⣟⣛⣶⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣉⣠⡤⠬⠷⠦⣄⡹⣆⢀⡀⣰⢏⣠⠴⠾⠥⢤⣄⣉⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⣁⣀⣠⣤⣤⣤⣤⡭⢻⣿⣿⡟⢭⣤⣤⣤⣤⣤⣀⣈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣍⠻⡿⠛⢋⡝⢿⡿⢫⡙⠛⢿⠟⣩⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣏⠽⢗⡚⢀⣴⠋⠀⢨⡅⠀⠙⣦⡀⢓⡚⠯⣹⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⠴⢫⠏⡽⠁⠈⠀⢨⠅⠀⠠⠈⢯⠹⡝⠦⣌⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⠋⣼⠁⢌⠄⠀⠈⠁⠀⢠⡡⠈⣧⠙⣦⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣷⣾⡞⠀⠀⠀⠀⠀⠀⢳⣷⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⡿⠿⣿⠿⠛⠓⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⢿⠿⠋⠁⠸⡷⠿⠟⡀⣠⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣾⣿⣿⡿⣛⣭⡶⠃⠀⢰⠁⠀⠀⢠⣎⡴⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⣿⣿⣿⣿⣿⡿⢟⣵⣺⠽⢾⠁⠀⢠⡇⠀⠀⠀⠀⠉⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣫⡶⠛⢉⣠⠄⠀⠑⠤⡈⠳⠤⠤⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢟⠕⠁⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⡣⠋⠀⣈⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⡑⠁⠀⣰⢻⠀⠀⠀⠀⢀⣠⡶⠋⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⢠⡶⠃⠀⢀⣠⠴⠚⡹⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⢀⣠⡴⠚⠉⠀⣠⠞⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣠⠾⠿⣿⠀⢀⣄⠘⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣖⠺⠿⠉⠀⢠⣿⢀⡾⠁⠀⠀⠀⠀⢸⠟⠀⠀⠸⣡⣶⠀⠀⠉⠙⠿⠟⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⣒⠷⡾⠷⠶⠤⠤⠤⠤⠤⠤⠤⠤⠶⠿⠷⠶⠒⣒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠉⠛⠳⠶⠶⠶⠟⠛⠛⠻⢶⣄⠀⠀⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣰⣿⣶⣾⣶⣶⣤⡀⢠⣀⣴⣄⠹⣆⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⡇⢨⡟⠀⠀⠙⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡇⠀⠀⠙⠛⠿⣿⢿⣿⣿⣿⣿⣿⣧⢸⡇⠀⠀⠀⠀⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡛⠋⣙⣛⣻⡟⢀⣤⣾⣦⣤⣤⣀⡀⠀⠙⣿⣿⣿⣿⣿⣇⠀⢀⣠⣶⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠿⢟⣛⣩⣿⣄⣛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠙⠷⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⠙⠳⣮⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠉⠛⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⣦⣶⣦⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⠻⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⡀⠀⣀⣠⣤⣾⣿⣿⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣾⣿⣍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡾⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣮⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠞⠛⢋⣩⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣠⠾⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠿⢿⣿⡿⢿⠿⣿⢿⣿⣿⣟⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢦⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⢠⡈⢻⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣳⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠿⣿⣿⣟⠿⣿⡿⣿⣆⣾⣿⣆⠉⠛⠻⠟⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⠂⠈⠛⠌⠻⣿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⠷⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠀⢹⠃⠀⠀⠈⢿⠈⠙⢿⠻⣿⡛⢿⡛⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⡐⠒⠤⢀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣿⣿⡔⣤⠀⠀⠈⠒⢤⡀
⠀⠀⠀⣪⣾⡷⠅⠐⠢⢄⡆⠹⣿⣿⣿⣷⣦⣄⡀⠀⣸⡿⠲⣽⠆
⠀⠀⢰⢿⣿⣷⡄⠀⠀⠀⠉⠓⣼⣟⡛⠿⣿⣿⣿⣋⢛⣩⣽⡞⣧⣄
⠀⠀⠀⠈⣿⣿⣛⣳⣶⣄⡀⢠⡏⠀⠹⢳⣼⡟⢦⣀⠉⠻⢏⣰⠏⣞⡦⣄⡀
⠀⠀⡆⠀⠈⢿⣿⣿⣿⣿⣟⣩⠙⡷⠊⣎⢻⣷⡊⠁⢰⡂⢈⣉⡭⣿⣤⣾⢻⠕⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠻⢴⡌⠙⣍⣉⣽⢟⣿⣷⣆⠀⠀⠫⠄⣀⠰⠿⢷⣮⢛⣷⢬⣛⣦⣄
⠀⠀⠀⢂⠠⠀⠀⠀⠀⠉⠉⢠⡤⠘⠟⠱⣿⢋⣼⣻⣿⡀⠀⠀⠓⠠⠒⢉⡽⠋⣠⡾⠥⠈⠛⠻⣆
⠀⠀⠀⠀⠑⢔⠄⠀⠀⠀⠀⠀⠉⡔⠛⠛⣻⣻⠟⢱⣏⣙⣷⣄⠀⠀⠉⠸⠤⠘⡅⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠪⡢⡀⠀⠀⠀⠀⠈⠡⠐⠈⠉⣉⡋⢀⡾⢦⡟⢿⣦⡀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⡀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠄⢄⠀⠀⠀⠀⠀⢩⠔⠊⢉⠝⠉⣠⣾⠭⢀⡛⠿⠷⠦⣼⣤⣤⣤⣤⣤⣤⠾⣲⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⠀⠀⠀⠀⠀⠈⠔⡁⢴⠞⠋⠁⠀⠀⠀⠘⣿⣦⣀⣀⡀⠀⠀⠀⠄⣺⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠂⠀⠀⠀⠀⠈⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⠉⠛⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠁⠂⢤⣀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢀⣀⠀⠀⢀⣀⡠⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⣄⣁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣵⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠁⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣱⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⢀⡴⠛⠛⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠘⠋⠀⠀⠴⠚⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠄⢀⣰⣆⣼⣿⣿⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⡇
⠀⠀⠀⠀⠀⢀⣠⣤⠤⢴⣶⠾⠟⠛⠋⠉⠉⠁⠈⠉⠙⠛⠛⠛⣛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣏
⠀⠀⠀⣴⡾⢛⠩⠀⠲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡿
⠀⠀⠰⣿⣖⠃⣴⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠃
⠀⠀⠀⠹⢿⣿⣧⣤⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡿⠛⢻⣿⣿⣿⣿⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿
⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⠻⣷⡀⠈⠙⠢⠀⠀⠀⠀⠀⠀⢈⡿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣤⣤⣴⠇⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠹⣿⡄⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢥⣄⣠⣾⡴⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⡇⠀⣼⠀⠀⢠⠀⠀⠀⠀⢠⡀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣦⣤⣾⣇⣀⣦⣤⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⡶⢶⣶⠶⢶⡶⠶⣶

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⠞⢻⣭⠭⢽⡓⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⡯⠭⣭⡟⠳⡄
⠀⠀⠀⠀⣿⠀⠻⠿⠁⣀⣈⠑⢄⠙⠻⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠿⠋⡠⠊⣁⣀⠀⠿⠟⠀⣿
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠻⠟⠁⠀⠑⣄⠈⠢⡑⢄⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⡠⢊⠔⠁⣠⠊⠀⠈⠻⠟⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠹⡄⠀⣤⣤⠀⠀⠔⠋⠀⢱⣄⠈⢆⡑⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣠⢊⡴⠁⣠⡎⠁⠉⠢⡀⠀⣤⣤⠀⢀⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠛⠛⠀⡌⠀⣀⣠⠃⠈⠳⣜⠛⢌⠳⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠜⡡⠛⣣⠞⢁⠘⣄⣀⠀⢡⠀⠙⠛⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⣴⣤⡅⠘⠿⠟⠀⠋⠀⠈⢳⣄⠱⣝⢄⠀⠀⠱⡀⠀⠀⠀⠀⢀⠎⠀⠀⡠⣋⠎⢠⡞⠁⠀⠙⠀⠹⠿⠃⢈⣤⣦⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠙⠋⠁⢀⣤⣤⠀⠀⠀⡰⢅⣈⠳⣌⠁⢧⡀⠀⠱⠀⢀⡀⠀⠎⠀⢀⡼⠛⣩⠞⣁⡈⠆⠀⠀⠀⣠⣤⡀⠸⠙⠋⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡘⡈⠛⠛⡀⠀⠀⡇⠀⠋⠙⠪⣑⠦⣙⢦⡀⣨⣿⣿⣅⢀⡴⣋⠴⣊⠔⠊⠙⠁⢸⠀⠀⢀⠛⠛⢃⢂⣀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠇⠀⡀⠀⠡⣾⣿⠧⣀⣉⠉⣁⡲⣵⣬⣓⢿⣿⢻⡟⣿⡿⣞⣥⣮⣴⣊⡉⣉⣀⠸⣿⣷⡌⠀⢀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⡈⠄⠀⢣⣠⠤⠷⢒⠒⡉⠩⣿⣭⣍⣛⣿⣿⣿⣿⣛⣩⣭⡿⠍⢉⠐⡒⠾⠤⣤⡜⠀⠠⢃⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠟⠋⠁⣀⣠⣤⣈⡑⠾⢦⠶⢾⣿⣻⣿⣿⣿⣿⣿⣿⡷⢶⡴⠷⠊⣁⣤⣄⣀⠈⠙⠻⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠊⠍⣙⡽⢃⠠⢀⣶⢶⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⡶⢦⡀⠄⡘⢯⣋⠩⠙⢦⡀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⣺⢟⣪⠴⠛⠉⢀⣠⣶⣫⣽⠿⣻⡿⠃⣸⣿⣿⣇⠈⢿⣯⠻⣼⣝⡶⣄⡀⠉⠛⠦⣕⡻⣗⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⢉⠁⠀⠀⡀⠘⠋⢉⠔⠁⡼⢻⠁⣠⢿⣿⣿⡿⣆⠈⡛⢷⠈⠢⡉⠙⠓⢄⠀⠁⠈⡉⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠔⠁⠀⢀⢸⣿⠀⣐⠁⢠⠟⠄⡄⢠⠇⢸⣽⣯⡇⠸⡄⢡⠠⠻⡄⠈⣂⠀⣿⡇⠀⠀⠈⠢⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠁⢸⡏⣸⡿⠀⣟⡜⡐⢀⡎⠀⢸⢾⡷⡇⠀⠱⡀⢂⢳⣳⠀⢿⣧⢹⡇⠈⠄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣄⠂⠀⠈⢰⡿⠁⠀⠟⡰⠁⡸⠀⠀⠘⣿⣿⠇⠀⠀⢧⠈⢆⠻⠀⠈⢿⡆⠁⠀⠘⣀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢦⡀⠀⠆⠀⠀⠀⡰⢁⣶⠇⠀⠀⠀⠛⠛⠀⠀⠀⠘⣶⡈⢆⠀⠀⠀⠐⠀⢀⡴⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠳⠴⡀⠀⣀⣠⡷⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢾⣄⣀⠀⢀⡦⠞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠙⠊⠉⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠉⠉⠑⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⣤⡄
⠰⣄⠀⠀⢰⣦⣄⠀⠀⣠⣴⡶⠀⠀⢀⡷⠘⠇⠀⠀⠀⢀⡄⠀⠀⠀⠸⠃⠀⠀⠹⣦⠀⢳⣄⠀⣴⠇⢀⣼⠃⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠈⠓⢤⡀⢈⣩⣽⣿⣍⡁⠀⡠⠖⠉⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠙⣧⡈⢻⣿⠋⢠⣾⠁⠀⠀⠀⠀⠀⠀⠰⣟⢻⣄
⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢦⣀⠈⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⢿⣷⠆⠇⠴⣿⡟⠀⠀⠀⠀⠀⠈⠷⠞⣃⣮⡿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⣄⡁⠀⠀⠀⠀⠀⣑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃
⠀⠀⢠⣤⡄⠀⠀⠀⡀⠀⠀⠠⣤⡄⠀⠀⠀⠸⣟⣷⣄⠀⠀⣠⣾⣻⠏⠀⠀⠀⠀⢻⣯⣷⣄⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠻⡤⣠⡼⣧⣤⡠⡞⠋⠀⠀⠀⠀⠀⠻⡿⠿⢷⡶⠿⠿⠿⠀⠀⠀⠀⠀⠀⢹⣿⡏⡟⢽⣿⠃⠀⠀⠀⠀⠀⢠⠀⡀⢈⡃
⠀⠀⠀⠀⠀⠷⡶⠆⠑⢶⡾⠇⠀⠀⠀⠀⠀⠀⠰⠀⠠⢚⡟⠄⠀⠆⠀⠀⠀⠀⠀⠀⣨⠿⠃⠃⠛⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡷
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠾⠛⠉
⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠻⣿⢷⣦⣀⠀⠀⢀⣴⡾⣿⠟⠀⣶⡲⣦⣄⡀⠀⠀⠀⢀⣤⡶⣲⡦⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠘⣧⠀⢠⡄⠀⣰⠏⠀⠀⠀⠀⠀⠙⢷⡝⠿⢶⡶⠿⢫⡾⠋⠀⠀⠘⢿⠊⠻⣷⡄⠀⢰⡿⠋⢘⡟⠁⠀⠀⠀⠄⠂⠐
⠀⠀⠀⠀⠰⣇⠀⠙⡟⠁⣠⡇⠀⠀⠀⠀⠀⠀⠸⣿⣅⠸⠇⣠⣿⠇⠀⠀⠀⠀⠈⢳⣤⣘⢶⣷⢞⡡⣤⡏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠘⣟⡿⠁⠀⠸⣗⡿⠁⠀⠀⠀⠀⠀⠀⠳⠾⠅⠐
⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠈⠹⣿⣿⣷⡄⢀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣶⣴⣶⣶⠆⠀⠀⠀⠀⣀⠂⡀⠁⠄
⠀⠀⠀⠀⠙⡟⢻⣿⣿⣟⢻⠛⠁⠀⠀⠀⠀⠀⡆⠀⠀⠘⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⣤⠈⠀⠏⠈⢠⡄⠀⠀⠀⠀⠀⠹⠷⣆⣶⣗⢇
⠀⠀⠀⠀⠀⠹⠤⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠠⠖⠃⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠘

⠀⠀⣀⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠈⠏⠀⠑⠀⢀⠀⠔⠁⠀⠟⠀⠀⠘⣇⢾⣶⢀⠀⠀⢠⢰⣾⢸⡏⠀⠀⠨⣯⢥⠆⠀⢀⠀⠠⣮⣹⠅
⠀⠀⠲⠦⠤⠤⣽⡧⠤⠤⠴⠃⠀⠀⠀⠘⢦⡜⠛⢲⣷⠚⠳⣴⠟⠀⠀⠀⠀⠸⡮⠂⢒⣿⡖⠐⢳⠏
⠀⠀⠀⠀⠠⠀⠿⠇⠠⠄⡀⠀⠀⠀⠀⠀⣿⣇⠓⠏⠛⠗⢢⣿⠇⠀⠀⠀⠀⡖⣾⠣⠀⠘⠀⠜⢿⡶
⠀⠀⠀⠨⠤⠀⠀⠀⠠⠤⡁⠀⠀⠀⠀⠀⢩⠿⠛⠁⠀⠙⠿⢏⠀⠀⠀⠀⠀⠤⠵⠎⠀⠀⠀⠸⠮⠠⡀
⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣡⣤⡤⠀⢀⠀⢨⣀⡀⠀⠀⠀⣀⡌⠀⢠
⠀⢹⣯⠁⠑⢄⠀⢀⠔⠁⠩⣿⠁⠀⠀⢳⣦⠁⠈⣲⣶⠈⠀⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⢿⡤⠬⠤⣿⡧⠤⠥⢼⡏⠀⠀⠀⠀⢹⠋⠩⠸⡿⠍⠙⣿⠁⠀⠀⠈⠲⡀⠀⠀⠀⣿⡇⢀⠀⠀⠖
⠀⠀⢽⣀⠀⠂⠾⠇⠒⠀⣸⡇⠀⠀⠀⠀⠈⢧⣤⠆⠀⢦⣴⠃⠀⠀⠀⠀⠀⠀⠊⠀⠀⣛⠀⠀⠉
⠀⠀⠈⠛⠛⠂⠀⠀⠚⠛⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡀⠀⠀⠀⡀⠀⢀⡄⠀⠀⡿⣖⣤⠀⠀⠀⠀⠀⢤⣲⢿
⠀⣇⡈⠒⠒⠀⢸⠆⠐⠒⠊⣀⡵⠀⠘⢀⣀⣀⡈⣰⣷⡈⣀⣀⣀⠈⠀⠀⢻⠉⠈⠈⠣⣀⠜⠁⠁⠉⡝
⠀⠈⠒⠀⠊⠁⢸⡀⠉⠒⠐⠚⠀⠀⠀⠠⠊⢀⠀⣸⣿⡀⢀⠈⠂⠀⠀⠀⠀⡜⠉⠋⠙⣿⠋⠙⠉⢳⡀
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⢧⣀⣀⠘⠙⠁⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣀⠉⠉⠀⠀⠀⠈⠉⢀⣀
⠰⡇⠈⠢⡀⠀⠀⠀⠀⡠⠊⠁⡿⠀⠀⣿⡏⠈⠀⠀⠀⠀⠈⠘⣿⠇⠀⠀⢿⣿⢯⡦⡀⠀⢀⠴⡽⢿⡿
⠀⠘⠂⠀⠈⠀⢠⠀⠊⠀⠀⠒⠀⠀⠀⠘⢷⠤⠀⢰⣶⠀⠠⢴⠏⠀⠀⠀⠈⢿⣦⠹⢿⣶⡿⡏⣵⡿⠃
⠀⠀⠀⡠⠂⠀⢾⡗⠀⠰⠀⠀⠀⠀⠀⠠⡇⠀⠀⡘⠏⡀⠀⢀⡇⠀⠀⠀⠀⠀⣿⣄⣰⢿⣧⣠⣿
⠀⠀⠈⠇⣀⠀⠘⠁⠀⡀⠘⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠙⠻⠛⠁⠀⠀⠀⠀⠀⢙⠿⠓⠀⠚⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃

⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⡶⢀⠀⠀⢀⠐⡆⠀⠀⠛⣴⠂⠀⠀⠀⠀⠀⣲⠘⠀⢻⠉⠀⢄⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠘⡢⠄⢸⡇⠠⠔⠃⠀⠀⠸⡧⡇⡖⡔⡆⡣⢽⠀⠀⠀⠘⠀⠀⠠⡆⠀⠀⠛⠀⠀⠈⣇⠀⠀⢲⡇⠀⢀⡟
⠀⠀⠀⠐⣇⠀⠘⠃⠀⣸⠂⠀⠀⠀⢾⣇⠙⡿⢁⣾⡆⠀⠀⠀⠠⣦⡀⠀⠃⠀⣰⡆⠀⠀⠀⢨⠋⣾⠹⠹⡮⢹
⠀⠀⠀⠀⣸⠛⠉⠉⠛⣇⠀⠀⠀⠀⠈⠻⠄⠁⠸⠋⠀⠀⠀⠀⠀⠈⡿⠓⠘⠻⡋⠀⠀⠀⠀⠀⠳⡼⠁⠸⢶⠋
⠀⠀⣀⡀⠁⠀⠀⠀⠀⠈⢀⣀⠀⢀⢀⡀⠀⠀⠀⠀⢀⡀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣆⠀⠀⠀⠀⠀⠀⡶
⠀⠀⢻⡀⠀⠀⢀⡀⠀⠀⢀⠏⠀⠸⡄⡼⠷⣄⡤⠻⠤⣴⠃⠀⢿⠀⠀⠀⣀⠀⠀⠀⣼⠀⠀⠸⣶⡄⢠⠀⣴⣾⠁
⠀⠀⠀⢳⡄⠀⢸⠃⠀⢰⡟⠀⠀⠀⢳⢤⠐⢼⠵⢀⡄⡏⠀⠀⠸⣄⠀⠀⢿⠀⠀⣠⠇⠀⠀⢠⠁⠀⠸⠀⠀⢁
⠀⠀⠀⠈⠿⣦⡄⢠⡴⠟⠀⠀⠀⠀⠈⠻⣙⠀⢐⣫⠎⠀⠀⠀⠀⠘⢤⡀⠀⢀⡤⠃⠀⠀⠀⠈⢧⣤⠀⢠⣤⠞
⠀⠀⢠⠀⡀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠘⢦⠑⠁⢠⡀⠘⢊⡼⠁⠀⢀⡀⠀⠀⣾⡗⠀⠀⢀⡀⠀⠀⠀⡖⠐⢀⡀⠂⡆⠀⠀⠀⠀⠀⡀⣾⡇⡀
⠀⠀⠀⠨⡇⠀⢸⠇⠀⢨⠀⠀⠀⠘⠂⠀⠀⠸⠁⠀⠀⠚⠁⠀⠀⠀⡍⠀⠸⠃⠀⡡⠀⠀⠀⠀⣤⣙⣊⣛⣡⡄
⠀⠀⠀⠀⠙⠒⠀⠐⠖⠋⠀⠶⠤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠤⠆⠀⠘⣆⠀⠀⡴⠁⠀⠀⠀⣼⠓⣮⣵⣯⡔⢻⡆
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠘⡿⢡⡶⠀⠀⠀⠐⣷⠈⣿⠀⠸⡟⠳⢢⣄⣀⣤⠲⠛⡗⠀⢸⡟⠓⢀⠀⠠⠚⢻⡇⠀⠛⣿⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠈⣧⠀⢸⡇⢀⡾⠀⠀⠀⠀⢻⡀⣾⠈⡇⢸⡆⡸⠃⠀⠀⣇⠀⠀⣶⠀⠀⣸⠃⠀⠀⠹⣇⠀⢸⠇⢀⡼⠃
⠀⠀⠀⠰⣌⠓⠚⠓⢛⣠⠀⠀⠀⠀⠀⣦⣀⠀⠀⢀⣠⡆⠀⠀⠀⢸⠁⡀⠙⢀⡀⣽⠀⠀⠀⠀⢿⡀⡼⣄⣨⡇
⠀⠀⠀⠀⠉⠛⠀⠈⠛⠉⠀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠙⠀⠀⠀⠀⠈⠛⠁⠀⠀⠛⠁⠀⠀⠀⠀⠈⠉⠁⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿