Fest Emojis & Symbols

⠀⠀⠀⢀⣶⡔⣾⠇⣠⡀⠀⠀⢀⢴⣖⣽⣷⣢⡄⠀⠀⠀⣴⣶⣺⣷⣦⡄
⠀⠀⠐⡿⠦⢛⣌⢚⣫⣆⠀⠀⡾⣾⢿⡿⣿⣿⣻⠀⠀⣾⢷⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⢷⡀⡴⢦⣾⣿⣶⠶⣄⢰⢿
⠀⠀⠐⢿⢛⡶⣩⢺⣭⡋⠀⠀⢻⢿⣿⣻⡿⢟⣩⠀⠀⢻⣿⣿⣿⣿⣿⡽⠁⠀⠀⢠⣶⣿⣿⠝⣧⣬⢿⣿⢿⣤⡿⢼⣿⣿⣦⡀
⠀⠀⠀⠀⠛⠃⠻⠇⠉⠀⠀⠀⠀⠙⠃⠥⠷⠚⠁⠀⠀⠀⠙⠛⠺⠿⠋⠁⠀⢠⣦⡙⢿⣿⣽⢚⣿⣿⣿⣽⢾⣿⣟⢿⣿⣿⡟⢁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢾⣿⣷⢾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠶⠿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣠⣿⣿⣷⠦⣿⣿⢾⣿⢾⣿⡷⠶⣿⡟⢃⡀⠛
⠀⠀⠀⠀⢀⠄⢂⣡⠆⡀⡄⡆⢠⠀⠀⠀⠀⠀⡇⡀⢠⣀⢀⡀⠀⣬⠀⡂⠀⠀⠀⠈⠻⣿⣿⣧⡏⢹⣾⣿⣾⠉⡷⢻⣵⡻⠟⠁
⠀⠀⠀⠐⠁⡀⠘⠀⠀⠐⠀⠆⠀⠀⠀⠀⠰⡇⡇⠇⢸⠸⠈⠃⠇⡏⠰⠅⠀⠀⠀⠀⠀⠸⡿⠀⠙⠛⠿⠿⠟⠒⠁⠸⠿
⠀⠀⠀⠁⠀⠹⠂⠄⠦⠘⠘⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⢠⣤⡀⠀⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⡼⣿⡶⢴⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠛⢣⠜⠲⣍⣩⣷⢾⡆⠀⠀⠀⢀⣾⠠⠀⣀⠀⢴⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣤⠾⢿⡷⢾⡿⢏⣿⡟⠁⠀⠀⠀⠀⠸⠟⠿⠃⢉⠘⠃⣸⢠⣽⣆⡀⠀⢰⠶⣾⡷⢤⣶⣿⡶⡖⣿⠃⠄⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢉⣬⡟⣻⣭⠸⠋⠀⠀⠐⠀⠀⠀⠀⢠⣬⡿⣁⣭⢉⣧⣼⠋⠿⠃⠀⠀⠀⣜⣿⣽⡃⢛⣚⡿⣜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⠼⡄⠀⠀⠀⠀⠉⠀⢾⣿⠉⠱⠿⠂⠀⠀⠀⣠⠊⢈⠙⢋⣴⢻⠟⠊⢨⡈⢁
⠀⠀⠀⠀⢰⠃⡐⢀⠀⡌⢀⢀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢄⡄⢸⣿⢺⣟⠀⢣⠃⠰⡷
⠀⠀⠀⢀⠘⡖⠃⢾⠁⠗⠂⠈⠃⠀⠀⠀⠀⡆⠀⣠⠃⠀⢀⠀⠇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠄⠾⡆⣸⠀⡸⠛⡟⢻⡀⢸⣄⣴⡁
⠀⠀⢀⣸⢠⢠⠀⢩⠀⣸⢀⠄⠀⠀⠀⠀⠀⢁⠸⠓⠠⠉⣀⣈⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠐⠙⠇⠉⠈⢿⣯⣿⣋⡐⣀⢨⣽⡿⠏⠙⠉
⠀⠀⠘⢺⠀⠘⠈⠀⠈⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢠⣦⡀⠀⠀⠀⠀⠀⠁⠷⣭⠿⡶⢻⡟⣶⠦⢬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⣽⢧⣿⣿⣗⣴⣶⠀⠀⠀⠀⠀⣿⠀⡇⢻⡃⢉⣧⠀⡟⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠐⠀⠐⠾⣻⣟⡿⠋⠉⠙⣿⣿⣛⡂⠀⠀⠀⢤⡾⣇⠁⠸⣷⠈⢯⠁
⠀⠀⠀⠀⠀⡇⠀⢳⡀⠀⠀⠀⢰⠇⠒⠁⠀⠀⠀⢀⠄⠘⠃⡄⠀⠀⣷⣾⣿⣇⠀⠓⠀⣽⣿⢿⠿⠂⠀⠀⠀⢀⣿⡇⠀⣿⡧⠀⠀⠀⣠
⠀⠀⠀⠓⠀⡇⠀⢸⣇⡄⢰⠀⣼⢈⡦⡇⡆⡇⠇⠘⠐⠘⠂⠀⠀⠈⠛⢋⣹⣿⣷⣶⣿⢿⣷⣬⠁⠀⠀⠀⠀⢠⡿⢰⣦⣿⣧⠁⠀⠀⠉
⠀⠀⠀⠀⠀⡇⠀⡾⠘⠂⠈⠀⣟⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠿⠟⠐⢿⣿⠘⠉⠉⠀⠀⢰⡆⠀⠀⠀⠀⢼⠀⢨⡄⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠃⠉⠉⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠐⢂⠀⠂⠂⣠⠀⡀⠀⣄⣠⠴⢶⡇⠀⠀⠀⢤⠴⠆⠀⠀⠀⠀⣀⠀⣰⠶⡆⠀⠠⠀⠁⡔⠲⠀⠀⠀⣀⠀⡀⠀⣠
⢠⠐⠀⢀⡀⠀⠄⣠⠤⠁⠀⠀⠀⠉⠘⠋⠉⠁⠀⠀⠀⠀⠠⠄⠀⠀⠲⢛⠉⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢀⡀⠀⠀⠀⠀⠀⡄⠘⢦⣤⠰⡆⠋⢠⡄⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣾⡇

⠀⢁⣀⠄⠀⣸⣣⡤⠾⡇⠀⠰⣁⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠛⡿⠿⢨⠀⠁⣚⣫⠂⣸⠇⢠⡟⣻⣾⠟⣁⣴⣟⡒⣲⣾
⢀⡩⠋⠀⠀⠛⠉⠲⡈⢧⠀⠀⠐⢈⠌⠀⠀⠀⠀⡀⠀⠀⠀⠀⡴⠀⠀⠀⣼⠟⠀⠈⠋⠀⠘⠻⠿⢿⣿⡟⣿⣷⣾⣿⣳
⠉⢑⡴⢘⣷⠀⠀⣴⠃⠸⡆⠀⢈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡟⣽⣿⣿⣭⣟
⢠⠍⢂⣨⣄⣧⡠⠯⣴⡤⠇⠀⠁⠀⠀⠀⠈⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣛⣿⣿⠟⢻⣿⣿⣾
⠴⠗⠚⠋⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠍⠉⠐⠂⠀⠐⠈⠉⠛⠳⠶⣄⡀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠈⠻⠋⠉
⠀⠂⠠⣀⠀⠀⢠⣄⢠⣤⣤⣤⣤⡴⠟⠕⠉⠀⠀⢠⡄⢰⣶⡆⢲⣦⠀⣀⠀⠀⠊⠻⢦⣤⣤⣤⣤⡄⣠⡄⠀⠀⡡⠀⠙
⢀⣆⠀⠉⡱⠀⢠⡴⢟⠔⠉⡁⠈⠈⠀⢀⠐⢿⣿⡄⢷⠰⠿⠇⠸⠇⣼⣿⣾⠆⠀⠀⠁⠈⢉⠉⠠⡿⢦⡄⠀⠠⠀⠀⠜
⡛⢱⠍⠷⠁⠀⢸⡇⠁⢀⣘⣽⠇⠀⠰⣬⡷⢌⠓⠀⠀⣀⣠⣄⣀⡀⠈⠙⠷⣶⣿⠂⠀⠸⣯⣃⡀⠈⢸⡇⠀⠒⠘⠛⠛
⡹⢦⠀⠀⠃⠀⢸⡇⠀⢀⣿⡇⠀⣾⠃⣬⠑⢀⡤⢰⡿⣿⢿⡿⣿⣿⡆⢤⡀⠘⣧⣾⣷⠀⢸⣿⠀⠀⢸⡇⠀⠀⠁⠄
⠀⠈⠄⠀⠀⠀⢸⡇⠀⠈⠁⠀⠀⠈⠙⠋⠀⠈⠛⠋⠁⠉⠀⠀⠉⠈⠙⠛⠁⠀⠉⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⢌
⡄⠀⠀⠀⠀⠀⢸⡇⠀⠐⣿⠿⢦⣿⣛⠓⢴⣾⡻⠆⢻⣿⡛⢲⣿⠼⣷⢀⣿⠄⣿⣿⡄⠰⣷⠄⠀⠀⢸⡇⠀⠸⡀⢀
⢄⡀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠶⡄⣿⣛⣃⢠⣍⣻⣇⠀⣿⡇⢀⣿⠀⢻⣿⡏⢰⣿⣿⣧⠀⣿⠀⠀⠀⢸⡇⠀⠀⢃⣥⢸
⢞⢛⠀⢀⢄⠀⢸⡇⠀⠰⢿⡁⠀⠻⠛⠛⠂⠉⠋⠉⠀⢈⠁⠀⡉⠁⠈⠉⠁⠈⠓⠈⠻⠘⠿⢾⡇⠀⢸⡇⠀⠠⢌⠉⠉
⠁⠉⠣⣀⠊⠀⢸⡇⠀⠀⠀⡤⠠⣤⡴⠶⣦⣴⢾⢿⠿⣿⠻⠟⣿⠿⡿⡷⣶⣴⠦⢶⣤⠄⢠⠀⠀⠀⢸⡇⠀⠀⠀⠀⠄
⣢⡀⠀⢨⠂⠀⢸⡇⠀⠀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⢸⡇⠀⣀⡀⢠⣀
⣡⣬⡟⠁⠀⠀⢸⡇⠀⠀⣷⣿⣿⣻⣟⣻⣟⣟⢻⡟⣻⣏⣻⣟⣟⣟⣟⣻⣟⣻⣏⣿⣟⣿⣿⣿⠀⠀⢸⡇⠈⢻⡏⠉⠁
⠀⠉⠁⠀⠀⠀⢸⡇⠀⠀⠡⠿⠿⠛⠟⠿⠟⠟⠛⠟⠻⠟⠻⠛⠻⠿⠻⠿⠿⠻⠿⠿⠛⠿⠻⠎⠀⠀⢸⡇⠀⠀⠃⢨⡦
⠀⢠⣴⠀⠀⠀⢸⡇⠀⢠⡤⢠⣤⡄⣄⡄⣤⡤⡄⠀⣤⡄⢠⠤⢀⢤⠀⣤⠠⣤⠤⣤⠠⣤⡄⣤⡄⠀⢸⡇⠀⠀⢱⡞⠃
⠀⢀⣁⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⡀⢀⣀⣠⠀⣠⠀⣄⣠⠀⢠⡄⢠⣀⢠⣠⡀⢀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠈⠏⠣
⣴⣾⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠁⠉⠉⠀⠀⠁⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀
⠿⠛⠃⠀⠀⠀⢸⡇⠀⠀⠃⠃⠛⠘⠃⠘⠓⠘⠘⠀⠋⠋⠊⠘⠃⠘⠘⠃⠃⠈⠚⠃⠀⠛⠛⠘⠀⠀⢸⡇⠀⢠⣴⣟⣯
⠀⠐⠢⠀⠀⠀⢸⡇⠀⠀⡄⠤⠠⠄⢰⠄⠠⡤⠠⢠⠄⠄⢠⠀⡄⢤⠀⠀⠀⠠⠤⠤⠀⡄⠠⠀⠀⠀⢸⡇⠀⠘⢿⣿⢑
⠐⠒⠄⠀⠀⠀⢸⡇⠀⠀⡀⠀⣀⠀⡀⠀⣀⠀⠀⢀⡀⡀⢀⡀⢀⠀⡀⠀⡀⢀⢀⡀⣀⢀⠀⢀⠀⠀⢸⡇⠀⠀⠈⣹⡿
⠀⠀⠀⠰⠄⠀⢸⡇⠀⠀⠁⠀⠈⠀⠁⠀⠉⠀⠀⠀⠁⠁⠈⠁⠈⠀⠁⠀⠁⠀⠈⠁⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⢼⡿⠟
⢽⡆⠀⠀⠀⠀⢸⡇⠀⢀⣤⢶⣶⡞⠁⡀⠀⠠⣟⢳⣧⣿⣴⣦⣿⣼⡞⣻⠆⠀⠀⠀⢳⣶⡶⣤⡀⠀⢸⡇⠀⠀⠻⠿⠿
⠀⡿⢂⣠⠔⠀⢸⣇⡂⠈⠓⠋⠛⠀⠀⠡⠦⣀⠀⠈⠛⠛⢻⡟⠛⠛⠁⠀⠀⡴⠗⠀⠀⠛⠙⠚⢁⢄⣸⡇⠀⠀⠀⠀⠤
⢣⡛⢿⡁⠀⠀⢠⡬⢻⣬⣶⣶⣶⣔⡀⡀⠀⠁⠚⠀⣤⢠⢀⣠⢀⢰⡔⠦⠁⠁⢀⢀⣢⣴⣴⣶⣤⡟⢡⡄⢠⣀⡀⣠⠂
⠟⠉⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣔⣠⠀⡀⠀⠈⠀⠉⠀⠀⢀⠀⢀⣠⡵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡩⠎⠁
⣰⠶⣦⡀⠀⢀⣴⣶⣶⠀⠑⠐⠄⠀⠀⠀⠈⠙⠳⠶⠶⢤⣭⣬⣥⠴⠶⠞⠋⠁⠀⢀⠠⠀⡀⢠⠄⡀⠀⠀⠀⠉⠒⠆⣀
⣿⣶⣿⣷⣄⣿⣟⣾⣿⣤⣴⣶⣆⠈⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠑⡄⠀⠂⠀⡴⠂⢄⠈
⣿⣾⡯⠛⣿⣿⡿⣿⣿⣏⡿⣿⣷⠁⠀⢂⣀⡀⠀⠀⡀⠈⠉⢻⣿⣄⠀⠀⠀⠰⠀⢁⠐⠂⡤⠀⢬⠀⡈⠊⢉⠀⠀⢀⡀
⣿⡿⠠⠹⢿⣷⣷⣾⣿⡿⣿⡟⠁⠀⠈⠼⠿⠓⠃⣜⠀⠀⠀⠈⣿⣿⡇⠀⠀⡠⢀⠀⠒⠨⣅⢡⠊⡆⠀⠄⠠⡜⢸⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡴⠖⢪⠋⠉⠛⡉⠛⠶⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡱⠋⠀⠠⠇⠀⠀⠀⠘⡀⠀⠈⠢⡈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡜⠀⠀⠀⠴⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠘⡀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠘⠀⢀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣾⣶⣦⣤⣤⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⢁⣀⣥⠤⠤⠤⠤⠤⠤⠴⠤⠤⠤⢈⣉⡟⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡩⠤⢗⠊⠉⠁⠀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠉⠉⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⡄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡌⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠘⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⡰⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠘⡄⠀⠀⢩⠀⠀⠀⠀⠀⠇⠀⠀⡰⠁⣠⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⠦⡈⠢⡀⠀⢁⠀⠀⠀⡘⠀⢀⠜⡠⠚⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠐⠨⢦⣌⣢⡀⣠⣡⡴⠓⠈⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠀⠀⠀⠀⡆⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠾⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠶⣴⡇⠀⠀⠀⠀⢰⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣸⠀⠀⠀⠀⠀⠀⣇⢰⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢈⠉⠐⠶⠀⠤⠤⠤⠤⠤⡤⠤⠤⠄⠐⡒⠈⠙⠀⠓⠛⠒⠒⠂⠀⠀⠀⠉⢹⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⡌⠀⢀⡀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⢃⠀⠀⢂⠰⣴⠀⢰⡒⠒⣖⠒⢲⡎⠀⠀⢀⣾⣦
⠀⠀⠀⠀⢀⠜⠀⠀⡴⠀⠀⡄⠀⢸⠀⠀⢰⠀⠈⡄⠀⠈⡄⠀⠈⢆⡿⠀⠘⠃⠈⠛⠀⠙⡇⠀⢠⢾⣿⣿⠧⡀
⠀⠀⢀⠔⠁⠀⢀⠜⠀⠀⠰⠀⠀⠘⠀⠀⠸⠀⠀⠱⠀⠀⠈⢆⠀⠀⠑⣤⡀⠀⠀⠀⠀⠐⠃⡔⠡⢳⠙⠋⠛⠐⠄
⣤⣮⣥⣤⣤⣴⣥⣤⣤⣤⣧⣤⣤⣧⣤⣤⣤⣧⣤⣤⣵⣤⣤⣤⣵⣤⣤⣤⣬⣶⡄⠀⠀⡠⠊⡠⠁⠆⡄⠀⢠⠀⡀⠢⡀
⠈⠉⢩⠉⠀⠋⠀⠉⠀⠉⠁⠈⠉⡍⠉⠀⠉⡍⠉⠀⠉⠁⠈⠁⠈⠁⠈⢩⠉⠉⠀⡠⠎⠀⡐⠁⡘⠀⠃⢸⠀⠆⠘⣄⠈⠢⡀
⠀⠀⠈⡄⠀⢸⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⢀⠤⠊⠀⢀⠎⠀⡰⠀⢸⠀⠈⡀⠈⡀⠈⢂⡀⠈⠒⢄
⠀⠀⠀⠃⠀⠀⡄⠀⠀⠀⡟⡽⠋⠛⢯⣭⡟⠛⠉⣝⡿⠀⠀⠀⠰⠀⠀⣞⣁⣀⣀⣴⣁⣀⣴⣁⣀⣌⣀⣀⣅⣀⣸⣄⣀⣙⣤⣀⣀⣉⣢
⠀⠀⠀⠸⠀⠀⠃⠀⠀⠀⣷⡇⠀⠀⢸⣿⡇⠀⠀⡧⡇⠀⠀⠀⠀⠀⠘⠁⠈⡁⠉⡇⠉⠈⢉⠈⠁⡏⠁⠈⠉⠉⠀⡉⠀⠁⡎⠁⡌⠁⠈
⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⣿⡇⠀⢀⣿⣿⣷⢠⠀⡿⡇⠀⠀⠀⡇⠀⠶⠀⠀⢡⠀⢠⠀⠀⢸⣤⣤⣧⣤⣤⣦⣤⣴⠁⠀⢰⠀⢠
⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⣿⡅⢸⡇⣿⣿⣧⣾⡄⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠀⠀⠸⣿⠀⠀⣿⣷⠀⠀⣿⠀⠀⠈⠀⡌
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡇⣼⢷⣿⣿⣿⢹⡇⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⣿⢀⣷⣿⣿⣦⠀⣿⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢟⣾⣿⣿⣿⣧⢷⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣾⣿⣿⣿⣿⣇⡏⠀⠀⠃
⣀⣀⣀⣀⣤⣀⣠⣤⣤⣤⣿⣵⣾⣿⣿⣿⣿⣿⣧⣧⣧⣤⣤⣤⣤⣤⣄⣀⣀⣀⣠⣤⣧⣠⣤⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣠⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⢀⣠⡀⢀⣀⣴⡀⡢⠠⠆⠀⠐⠂⡤
⠀⠀⠀⢠⡞⠃⠹⡌⢛⣾⣿⣷⣿⣿⣶⠗⠰⠄⠂
⠀⠀⣴⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠒⠈⡄⣀
⠀⠚⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠗⠉⠃⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⡿⠎⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⢀⠄⠀⠀⠀⢀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⡀⠀⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠾⠉⠁⡄⠀⢀⡐⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠸⢠⡟⢭⡿⠇⠀⡜⠁
⠀⢀⠀⠀⠀⠈⠀⠀⢰⡄⠀⠀⠀⢀⠀⠀⠀⠐⠚⠉⠁⠀⠐⣦⠀⠀⣠⠀⠀⡀⠀⠁⠠⠀⡀⠀⠀⠀⠀⠀⠈⠀⠂⠀⢀⠀⢠⡞⠁⣾⣿⣆
⠀⡈⠓⡆⠀⠀⠀⠀⣼⡆⠀⠀⠀⢈⡷⠀⠀⢠⣿⠀⡸⠷⠐⡁⠈⠀⠀⣀⡠⠃⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⣧⡾⢃⣸⣿⣿⣿⣿⠇
⢀⠿⢆⠀⠂⠀⠀⢀⢩⠃⠀⠀⠉⣉⠀⠀⢀⣽⣿⡟⠡⣤⡀⠁⠀⠐⠀⠀⠀⠀⠀⢘⣻⣯⡀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠁⣷⣶⢟⣻⣿⣿⡇⠤
⠈⠀⠀⠀⣀⡤⠴⠊⢿⣷⡄⠀⠀⠨⣷⡄⢠⢄⣛⠀⠀⠈⢹⠀⠀⢰⡆⠀⠀⠀⠠⢩⣿⢿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠈⠀⢿⣿⠖
⠀⠀⠲⠟⠉⠀⠀⠀⠀⠈⠁⠀⡀⢸⣿⠃⢘⡈⣷⣧⠀⠰⣾⡄⠀⠸⠷⠀⠀⣶⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⡏
⠀⢰⡆⠁⠀⠀⠀⢀⠀⠠⠀⠀⣂⣸⣿⡄⣼⣷⣾⠏⠀⠀⡄⠁⢀⣈⣽⠂⠀⣿⣿⣿⣿⣿⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡇
⢠⣶⠗⡀⠀⠀⠀⠄⠀⠰⠂⠀⠀⢿⠿⣿⣯⠉⡏⠀⠀⠀⠃⠀⠀⠉⣤⠀⣄⢐⢿⣏⢉⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠐⣠⡀⣠⠄⡀⠀⠀⡀⡇
⠈⡅⠀⣳⣶⣒⢻⣶⠄⠀⠀⠀⠀⠀⠀⣹⣿⣷⠃⠀⠀⠀⠀⠀⠸⣀⣿⠅⢉⠁⠀⠀⡀⠁⢿⣿⣿⡄⣤⠀⢀⠀⠀⠀⢹⣀⣿⡤⠸⣿⣿⠆
⠀⠁⠀⠀⠉⠋⠙⢁⡀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⠿⢄⣼⣅⣸⣤⣧⣾⣾⣿⣿⣷⡀⠀⠀⠀⣴⣲⣶⡀⠀⠀⠀⠛⠛⠛⠃⠀⣀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣿⣿⣿⣿⡇⠀⠰⣄⠀⡄⠀⢈⣿⣿⣿⣿⣻⣿⣿⣯⣾⣿⣿⣿⡇⡀⠀⠀⠉⣉⣯⣥⡀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⣿⣿⣿⣆⣀⣀⠀⠀⠀⠘⢃⣀⠀⣸⣿⠿⠈⠁⠀⠀⠛⣿⡇⣾⣼⣿⣿⣽⣏⣽⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⢰⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠉
⠰⣮⣥⣈⣩⣿⣿⡛⣵⣄⡀⢈⣩⠀⠈⢛⡀⣀⡀⣀⣀⣀⡀⠐⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠛⠻⠿⣻⠿⣿⣷⣫⡵⠿⠛⠛⠙⠋⠛⠛⠛⠋⠁⠀⠀⠀⠀⢸⢿⣷⠆⠚⠛⠛⢿⠁⢸⣿⠉⠁⠙⠟⢻⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠬⠄⢉⣿⡶⠒⠂⠒⠀⠀⠉⠈⠛⠛⠋⠉⠋⠟⠛⠛⠉

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⡇⠊⠀⠀⢀⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⢼⣧⣀⣤⡄⣼⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣹⠈⡇⢽⣹⣿⢹⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢉⠀⠑⠊⠑⠊⠁⠈⢉⡉⠉⠉⠉⠁⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢡⡞⠀⣶⠀⣰⡗⠀⢨⡅⣴⠀⡄⣠⠄⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠼⣯⡠⢸⣷⢸⣧⡄⣿⡇⣿⣇⠙⣿⡼⣇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠈⠁⠀⠀⠀⠉⠀⠈⠋⠈⠉⠀⠈⠀⠉⠙⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠂⢀⡿⣰⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣤⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢸⣿⣷⢘⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣅⣸⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡶⠠⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠲⡤⠀⠀⢀⡾⢟⣿⣿⣼⡟⠲⣝⢿⣛⣿⣷⣿⣿⢿⣷⣦⣄⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣴⠟⢁⡿⠈⣷⠀⢸⣾⣿⣿⢏⣾⢯⢸⣷⢻⡟⣷⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠰⠚⠋⠀⠀⢏⣾⠏⠀⣼⠁⢀⣿⠀⣼⣿⣿⢇⣿⡟⠸⢸⡿⢀⣿⣿⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣸⠇⠀⣼⠏⣰⡿⠛⣿⣸⣿⠁⣠⡿⢃⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠛⠛⠋⠛⠉⠀⠀⠀⠉⠛⠚⠛⠙⠋⠉

⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡅⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⠠⠄⠀⡇⢠⢄⠀⠠⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢀⢀⠈⢷⠀⢠⠀⡇⠀⡄⢀⡏⠠⠂⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠢⠠⠈⣆⠈⠀⡇⢰⢀⡞⣀⠑⢀⡴⠃⡀⠀⠀⠀⠀⠀⠰⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠐⠈⠀⢈⠳⣄⢣⡸⣾⣇⣧⡇⡼⡰⢂⡴⠋⢀⠁⠊⢀⢀⡀⠤⠀⣰⠛⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣅⣓⢮⣳⣷⣼⣿⣿⣿⣿⣵⡯⠞⣉⣤⠴⠚⠋⡁⠀⠀⣴⣿⣶⡖⠈⡓⣤⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠤⢬⣙⣛⣿⣿⣿⣿⣿⣿⣿⣾⡯⠥⠄⠂⠀⠀⠁⢀⡞⠉⡿⠛⠓⠼⣉⡽⠈⠑⠢⢤⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠋⠉⢉⣉⣭⣿⣿⣿⣿⣼⣿⣿⣿⡿⠯⣛⣉⠉⠉⢉⣱⣏⡄⠀⠀⣤⠴⡆⠉⠀⣶⣾⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣀⣡⠴⠚⣩⢷⣿⣿⣿⣿⣿⣿⣟⠯⣓⠦⣄⣈⠀⣲⡟⠀⣙⠦⠀⠧⢄⡜⠃⠀⠛⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠒⠉⢀⠀⡢⢋⡴⢫⢾⡏⣿⡟⡿⡌⢯⡳⣌⠓⠀⢈⣽⠉⠉⠙⠃⠀⠀⠀⠈⠀⠰⡖⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢈⡴⠋⠐⠁⡞⠰⠞⡇⠺⠹⡄⢂⢈⠳⢤⣽⣽⣿⣯⠀⠀⠀⣶⣿⣤⠀⠘⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠈⢀⠀⠂⡼⠁⠂⠀⡇⢀⠁⠱⡀⠡⣰⣯⡄⠈⠋⢉⡀⠀⠀⠉⠻⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠸⠁⠐⡰⠀⡇⠘⡀⠀⠡⡰⠳⡴⠃⠀⠠⣞⠉⢏⠀⣠⠞⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⡇⠀⠀⠀⣜⠁⠀⠀⢀⣀⡀⠘⠋⠉⠀⠈⡷⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⣏⠙⠢⣄⠾⣿⠧⠀⢐⠖⢶⡜⠁⢸⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⢄⡙⠳⢄⡀⠈⢱⣿⠈⡁⢸⠀⠩⠀⡼⠀⠄⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠟⠒⢤⣉⡶⠧⠘⣆⢱⢸⡄⠇⣼⢁⠕⢁⠾⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣰⢇⢄⡘⠀⠈⡙⢮⣳⡘⣿⣾⣿⣸⣧⢣⡔⣫⠠⠈⢀⡠⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡴⠁⠀⡀⣉⠓⠲⢬⣶⣽⣿⣿⣿⣿⣿⣷⡿⣊⡥⠖⣚⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠞⢀⣀⣀⣁⣀⣈⣉⣶⣾⣿⣿⣿⡿⣿⣿⣿⣿⣟⣋⣁⣀⣉⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣠⠏⠀⠀⠀⠀⡄⠀⠐⢔⣺⡿⣿⣿⣿⣿⣿⣿⣿⣯⣝⡛⠢⠄⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡰⠃⠀⠀⠀⢀⢀⡤⠔⠚⣉⡤⢺⠿⣿⡿⣿⣿⡟⢿⣯⡻⢍⢓⠲⢤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡜⠁⠀⠀⠀⠀⠈⠁⠀⠐⠨⣈⠜⠣⡊⡿⠹⢿⠙⡽⡌⠣⠙⢦⡁⠠⠂⠈⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢀⠈⣸⠁⠸⢸⠀⠡⠹⡄⠊⡂⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢨⠃⠀⠄⢸⠀⠢⠀⢱⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠁⠀⠀⠀⠉⠢⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⢣⡇⠀⡇⠀⢈⠆⠀⠀⢤⢠⡄⠀⠀⠀⠰⠞⣉⠇
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣄⠀⠀⠀⢠⠒⠔⠡⠘⣤⠊⠀⠐⡁⠤⠤⠄⡀⠀⠀⠀⠀⢀⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⢺⠉⠒⠚⠂⢀⡶⠊⠀⡠⠪⠮⣀⠄⠒⠂⠸⣉⠉⠉⠚⢅⠀⠀⠉⠢⡀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠿⡋⢉⡸⠶⠁⠀⢀⢜⣇⡒⢢⠀⠱⣀⠤⠠⠬⣆⡠⠤⠼⢤⡊⠁⠒⠣⢄⠈⠐
⠀⠀⠀⠀⠀⠀⢠⡂⢦⠀⢰⠋⠀⠈⠁⠀⢃⠀⣰⠙⡛⢿⣿⡆⠛⠒⠳⡆⢣⡰⡀⠑⢶⣄⠀⠈⡄⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢠⡇⠚⢃⠇⠀⠀⠀⠀⠀⠀⡝⠂⠉⢉⠨⠟⠊⢴⢄⠀⢈⠦⠐⠘⠤⢧⢊⠭⠀⠉⠒⢅⠀⠈⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢰⢒⢂⠉⠰⠀⠒⠀⠈⠥⡝⡠⠒⣏⣰⡄⠀⠙⢄⢉⣛⠢⡄⣇⡴⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⣀⣀⣀⠀⠀⣀⠖⠚⢎⠀⣇⠀⢔⠠⡄⠀⢱⠁⠐⠈⠡⠉⠚⡆⢸⡡⢒⢆⢠⡀⠉⠻⡼
⠀⠀⠀⠀⠀⡄⠀⠀⠐⢤⡋⠸⣀⣀⠍⡜⠀⠀⠀⠙⢌⡶⠠⡉⠀⣀⠼⡀⠠⠤⠤⠀⠀⡄⢸⠁⠄⠀⠁⠘⠦⡀⢡
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠃⠀⠀⠀⠰⠉⠑⣄⠀⡀⠜⢀⠔⠓⠣⠬⣶⣍⣂⠅⠈⢀⠔⠁⠆⠀⢠⠄⡀⠁⠀⠦⣘
⠀⠀⠀⠀⠀⡇⠀⠀⢠⠂⠀⠀⠀⡠⠃⠀⠀⡇⠉⠢⠔⠓⠠⠄⠒⠈⠈⣧⣿⠋⢢⢜⠖⠲⣞⣢⣈⠢⠂⣀⠔⠚⠹
⠀⠀⠀⠀⠀⡇⠀⡐⠁⠀⠀⠀⡔⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠢⠤⣌⠀⢀⠃⠀⣭⣡⣔⡧⢄⠀⡆
⠀⠀⠀⠀⠀⡇⢠⠉⠉⠐⠲⠎⡀⠀⠀⠀⠀⠈⠑⠒⠤⢀⣀⣀⡠⠔⠊⠀⠀⠀⠀⠀⠈⠙⠂⠬⣼⣏⠀⠇⠀⡇⡇
⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠰⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠀⠀⠂⠀⠀⠀⠀⠱⠀⠀⠀⡐⠈⠀⠀⠀⠑⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⠀⠂⠀⠋⢢⠀⣀⡀⠀⠐⢠⡄⡴⠓⣀⡀⠀⠀⠀⠀⠀⠀⡀⣀⠄⡀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⣠⡄⠊⣦⠚⢄⡅⠀⠀⠀⠀⠀⡀⣼⠃⠀⠀⠀⣏⠈⠲⠦⢤⠖⠺⡆⠈⠄⢀⣡⠤⠶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠖⠒⠒⠢⣞⠇⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⠀⠛⠀⠀⠀⠀⠀⠀⡇⢠⢠⠟⠉⠉⠁⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⠖⠒⠒⢲⡉⠀⣀⠀⢀⣀⠀⠀⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⢍⠉⣾⢠⠀⠀⠀⠀⠉⠑⠀⢠⢠⠂⠀⢀⠀⠀⢀⡠⠤⠄⠀⠛⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠲⠤⣤⠤⠔⠦⡀⠁⣟⠰⠤⠀⠀⠀⠠⡠⠟⢸⠀⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⣄⠸⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠑⠶⢤⣤⣀⣠⣭⠴⢿⠀⠀⠀⣧⡈⠷⠀⠀⠀⢀⢛⡠⣇⠀⠜⠉⠒⠒⠒⠒⠊⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠢⠴⢶⣷⠼⠴⠃⠀⠀⠀⢇⡹⢟⣟⣛⡛⢋⣋⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⣀⡃⠘⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠙⠟⠁⠀⠀⠀⣠⣴⡆⠀⠀⠀⠠⠶⡄⠀⠀⠸⠁⠀⠀⣦⡶⠉⠛⠳
⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠠⠄⠀⣠⣹⡄⠀⠀⠀⠠⠠⠆⠁⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀
⣶⣄⠀⠀⢀⣀⡀⠀⠀⠀⠁⣠⣾⡿⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠠⡖⠀⠀⠀⠀⠀⢠
⠻⠿⠀⠀⠙⣻⣗⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢘⠻⡿⠀⠀⠈⠉⠛⢻⡄⠀⠈⠁⠀⠀⢶⣤⣀⡀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⡥⡄⠀⣀⠀⠀⠀⠀⢀⡀
⠙⢷⣤⣰⠀⠀⠀⠀⠀⠀⠿⠐⠒⠃⠀⢠⡾⠋⠙⠀⠀⠀⠀⠀⠀⠀⣦⢲⠀⢃⠀⠀⣿⠀⠀⠀⠀⠈⠩
⠀⠈⠉⠽⠦⠀⣀⣀⡚⢦⠀⢀⠠⡟⠓⣌⣥⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡃⢀⣀⣈⣉⠁⠀⠀⠀⠀⣸
⣠⣄⡀⠈⠛⠋⠉⠙⣿⡦⠀⠂⠀⠒⠻⣮⠈⣤⠀⠀⠠⢶⣤⢺⡇⠑⠆⢹⣧⡀⠛⠿⠻⣦⠀⠀⠀⠀⠉
⣿⣿⡗⠀⠀⠀⠀⠀⢸⣧⢀⡀⡀⠀⠀⠉⠀⠈⡆⠀⠀⣀⣸⣧⣿⡷⢀⠈⠀⡿⢻⡄⠀⠶
⣿⣿⣇⠀⠘⣦⣀⣤⡿⣿⣾⣿⣿⣶⣲⠂⠀⢠⣿⠀⢰⣿⣷⣾⣿⣷⣾⣅⡖⠀⠈⣼⡆⢙⣆⠀⠀⢀⣤
⢽⣿⡿⠀⠈⠻⠏⠀⠈⣤⣉⠛⠁⠉⠉⠀⠀⢨⣿⠀⣸⣿⣿⠟⠛⠻⣿⣿⡇⠀⠀⠩⣭⡛⠁⠀⠠⣿⡅
⣀⣠⣤⣀⡀⠀⢤⠀⢀⣿⣯⣤⠀⠀⠀⠀⠀⠈⠛⠀⢙⠏⠀⢀⠠⠀⠀⠈⡷⣸⣆⠀⠀⣷⠀⢴⠀⣿⣷
⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠘⣴⢟⣻⣦⡀⠈⠀⢠⣿⣿⣷⣄⢻⠄⠀⠀⠀⢻
⠹⢿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣇⣴⣿⣷⣿⣿⣦⡀⠀⠀⠁⡜⢁⣠⣂⠘⠟⢡⡍⣹⣿⣦⡤⡀⠀⣀
⠀⠀⠉⠈⢹⣿⡏⠀⠈⠛⠛⠒⢀⣿⣿⣿⠟⠹⠟⠁⠛⠀⢀⠀⠀⠙⠃⠉⠁⠀⣀⣠⣿⣿⣿⡇⠀⠀⣤
⠀⡆⠶⠂⠈⠉⠀⠀⠤⠄⠠⣄⠐⣿⣿⠿⠀⠀⠄⠀⠀⠀⠘⠃⠀⠀⠀⠀⢠⣶⡌⣹⠛⠻⠿⢷⣄⣀⡀
⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡋⠁⠉⣠⢤⣤⡴⢳⣤⠤⣀⠀⠀⠀⠀⠈⠉⣰⣿⡆⢰⣶⣿⣿⠛⠛
⠈⠻⢿⡆⠀⠀⠀⠀⠀⣿⣟⠀⢹⡄⠀⠀⢧⠀⠹⠑⠛⠳⠀⢁⣠⣾⡟⢻⠀⢀⣼⣶⣇⢈⣫⣽⣿⣶⣿
⣈⣥⣤⣷⠀⠀⠀⠀⠀⢸⣿⠀⠈⠀⣤⢴⣤⣀⣠⡄⢰⣶⣶⠟⣿⣿⣧⣾⠒⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣷⣾⣿⣶⣶⣾⣿⣷⣿⣿⣷⣦⠈⣿⣿⣿⣤⣿⣧⠘⠿⣿⣿⣭⡄⠘⢦⣤⣥⡽⠿⢿⡿⢻⣿

⠀⠀⠀⠀⠔⠀⡤⢀⠄⠀⣐⢄⠀⢤⠐⠖⢄⣀⢠⠄⠄⠄⣀⠐⠀⡀⢠⢀⠐⠀⠄⠠⠀⡀⡂⠀⠠
⠀⠀⠀⠀⠁⢊⡴⠡⠀⡶⢄⠉⠚⢛⠀⢁⠈⠩⠉⠩⠐⠁⢀⠠⠐⡑⡊⡆⢡⡠⠱⣄⠏⢹⣤⠆⡀
⠀⠀⠀⣰⢟⠛⣀⡡⠂⠀⠒⡦⠈⠌⠀⣚⢸⢸⠀⠀⠀⠂⢠⡄⢨⡃⣀⣀⢸⠆⢃⠈⡄⠀⠁⡢⢲
⠀⠀⠀⠄⡀⡑⡘⠒⠈⢫⠜⢊⡑⡡⢈⠖⠀⢰⣀⡀⠢⠔⠁⡂⠙⡁⢙⢉⣁⣀⣈⠠⠀⢄⠤⢁⡁
⠀⠀⠀⠃⠆⠒⠡⠚⠀⢨⠢⣑⠊⠊⠠⡄⢃⠀⠠⠢⠛⠈⠍⠀⢃⣓⣀⣳⡕⠓⠃⢐⠁⠸⠛⠠⠡
⠀⠀⠀⠀⠀⡀⠁⡑⠒⠀⢒⠲⢥⠀⠂⠔⡂⠂⠀⠀⠀⠁⠄⢀⠨⠇⡄⠠⣄⠀⡦⢀⡏⠀⠂⠀⠈⠁
⠀⠀⠀⠄⢠⠉⢘⢱⠜⠄⠉⠢⡄⠄⠈⠀⡀⠄⠠⠠⠨⠀⠊⠁⠉⠀⠀⠨⠀⠀⡈⡁⢡⠀⠖⠉⠐
⠀⠀⠀⡀⠅⢎⢀⡁⠰⠒⠠⠀⠀⠀⠠⠀⠁⢀⠰⠰⠀⠀⠸⠀⠌⠀⠌⠀⠉⢐⡂⠀⠄⡀⠱⠠⢂
⠀⠀⠀⠉⡂⠀⠈⠀⡠⠀⣀⠠⠄⠃⡠⡋⡀⠌⠀⠀⠈⠘⠀⠀⠅⠅⠀⠁⠀⡬⠀⠀⢠⠀⠀⠀⡈⠂
⠀⠀⠐⠏⣉⠞⣡⢆⠈⠂⠄⠰⠀⠀⠿⠃⢁⡀⠀⣊⣴⠀⠠⠀⡀⡀⠃⡐⢂⡀⠢⠀⠄⠆⠀⠀⠑⠂
⠀⠀⢀⣧⡆⠀⡡⡐⠈⠐⢥⠑⠀⠆⢢⢢⣤⠨⣇⣘⠀⠤⢐⢂⠆⠔⠹⠈⣉⠁⠀⠀⣄⡀
⠀⠀⠠⠃⠌⠁⢀⢄⡀⡦⠂⠀⠈⠠⠰⡐⠆⠀⠀⠇⠐⢒⡈⡈⠀⣵⠀⠈⠂⠀⢀⡈⡀⠀⠁⠠⠄
⠀⠀⠠⠜⠦⠊⠠⠀⡀⠐⡀⠉⡀⠠⢀⠀⡄⡔⠅⠀⠛⠔⠁⠂⠀⠡⢈⢅⠰⠈⣱⠉⣟⠐⠥⠀⠠
⠀⠀⠀⢁⣁⣌⡰⣩⡴⠶⠀⢠⢆⡠⠀⠀⡉⡈⠁⢠⡦⢂⠂⠀⢰⠀⠀⠀⠁⡀⠐⠘⠊⠈⠂⣂⠌
⠀⠀⠀⠀⡀⠍⡚⠘⠐⢡⢅⡤⠀⠀⠈⣀⡁⠡⠀⡁⢂⠀⠀⠀⡖⠀⠈⠀⠈⠁⠈⡀⠈⠕⠠⠆⠀⡄
⠀⠀⢀⠄⠀⣄⠉⡂⢐⠀⡀⠂⠴⠄⣤⣴⠠⠇⣐⢀⡀⠐⠀⠔⠀⠀⢰⢉⠂⡈⠂⢬⠀⢀⢞⠅⠈⠂
⠀⠀⠘⠀⡐⠔⢐⡇⠠⣀⠓⠐⠒⠄⠀⠐⠂⠀⢪⠀⣂⠀⠋⠀⢄⢆⠲⢣⠄⠒⢆⣘⠐⠶⣶⡆⢶
⠀⠀⠀⠘⠠⠴⠚⠀⠀⠠⠒⠘⠤⠐⠀⠀⠂⠕⠠⠁⠂⠙⠚⠀⠀⠀⠈⠂⠁⠑⠢⠙⠁⠁⠈⠁⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡒⣿⡟⢗⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢒⠁⠊⡴⠁⡇⠀⠑⢄⠙⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⡠⠔⠁⠀⡼⠁⠀⢡⠀⠀⠀⠑⢤⡀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⡟⣲⠄⢀⠠⠀⠀⠁⠀⡀⠔⠊⠀⠀⠀⡰⠁⠀⠀⠈⡆⠀⠀⠀⠀⠈⠒⢄⠀⠀⠉⠓⠦⢄⡀⠀⣧⠤⠛
⠀⠀⠀⠀⠀⣿⠂⠀⠄⠀⠀⢠⣶⠩⠤⠤⠀⠀⢀⣴⠥⠤⠀⠀⠀⢱⡄⠀⠀⠀⠠⠤⠤⣵⡄⠀⠀⠀⠀⠘⣻⢿
⠀⠀⠀⠀⠀⡏⠑⠠⡤⠤⠒⠁⢸⠑⠒⠠⡤⠔⠋⢸⠉⠒⠠⣤⡔⠊⠈⡖⠤⠤⠤⡔⠊⠁⢸⠒⠤⠄⡖⠈⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡄⠀⠀⢰⠁⠀⠀⣸⠀⠀⢠⡿⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⢠⢻⠁⡇⢇⠀⡇⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⢸⠃⠀⠀⡇⠀⠀⢀⠇⠀⠀⡜⠀⠀⠀⡇⡰⢃⠇⠀⢱⠈⢆⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠈⡆
⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢠⠟⠁⡞⠀⠀⠸⡀⠀⢣⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢣
⠀⠀⠀⠀⡞⠀⠀⢰⠁⠀⠀⢸⠀⠀⢀⠇⢀⡴⠋⠀⢰⠀⠀⠀⠀⢇⠀⠀⠱⡄⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠘⡆
⠀⠀⠀⢰⠁⠀⠀⣸⠀⠀⠀⡇⠀⠀⢸⡴⠋⠀⠀⢠⠃⠀⠀⠀⠀⠘⡄⠀⠀⠈⢲⡄⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⢱
⠀⠀⢀⡏⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⡌⠱⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠐⡇⠀⠀⢸⡄⠀⠀⠀⢠⠀⠀⠀⠀⢇
⠀⠀⡜⠀⠀⠀⡸⠀⠀⠀⡜⠀⠀⠀⠇⠀⢱⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠌⠀⡇⠀⠀⠀⡇⠀⠀⠀⠘⡀⠀⠀⠀⠘⡆
⠀⠚⠀⠀⠀⠐⠓⠒⠒⠒⠓⠒⠒⠚⠃⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠂⠓⠐⠒⠒⠓⠒⠀⠒⠐⠓⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠶⠏⠀⠀⠀⠀⠀⠽⠿⠿⠿⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄⠛⠀⢺⣦⣾⡆⠚⠀⢸⣧⣼⡃⠘⠃⢰⣷⣴⡇⠐⠃⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⢠⣿⣿⣿⠁⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣿⡄⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠸⢿⣶⡆⠀⠀⠀⠀⢀⣤⣾⡿⠃⠀⠀⠰⢿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠘⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⡂
⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣠⣤⣾⣿⣿⣋⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⢿⡿⢻⡿⢻⣿⠻⣿⠻⣿⠿⣿⠿⣿⡟⣿⠟⣿⡟⣿⡟⣿⡿⢿⡿⢿⡿⢻⣿⢻⣿⠻⣿⠻⣿⢿⣿⠿⣿⠟⣿⠟⣿⡟⢿⡟⢿⡿⢿⣿
⠀⠀⠀⠀⠀⡆⠁⠀⠁⠀⠁⢰⡇⠀⠁⠀⠉⠀⢈⣧⠈⠀⠈⠀⠈⠀⣿⠀⠀⢁⡈⠁⠀⣿⠀⠁⠀⠁⠀⠁⣼⡉⠀⠉⠀⠈⠀⣸⡄⠈⠀⠈⠀⠈⢱
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⢸⣿⣄⣴⣺⣇⣦⢰⣿⡇⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⢣⣿⣿⡜⣷⣭⡓⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⠀⠀⣴⣾⣿⡿⢋⣾⣿⣿⣷⡙⢿⣿⣷⣦⠀⠀⣿⣿⣿⡆⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠙⠋⢀⣾⣿⣿⣿⣿⣷⡀⠙⠋⠀⠀⢰⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿
⠀⠀⠀⢰⣿⣿⠉⡇⠀⢰⠇⣿⣿⠃⣇⠀⢠⡇⣿⣿⡇⣧⠀⣴⠁⠐⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣦⠀⡾⢸⣿⡿⢸⡀⠀⣸⠸⣿⣿⠸⡆⠀⢸⠙⣿⣿⡇
⠀⠀⠀⣾⣿⡟⠀⢿⠀⣼⠀⢹⣿⠀⢹⠀⣸⠀⢸⣿⠀⢸⣾⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣷⡀⠀⣿⡇⠈⣇⢀⡏⠀⣿⡇⠀⣧⠀⡟⠀⢿⣿⣿⡀
⠀⣀⣼⣿⣿⣇⣀⣸⣆⣇⣀⣘⣇⣀⣘⣇⣏⣀⣈⣏⣀⣸⣿⣿⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣿⣿⣇⣀⣹⣀⣀⣻⣸⣃⣀⣸⣃⣀⣸⣰⣇⣀⣸⣿⣿⣧⡀
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⢀⡴⠒⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠀⠀⠠⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠄
⠀⠀⠀⡎⠤⠠⠂⠲⠅⠀⣧⠀⠀⠀⠀⠐⣿⠽⠯⠿⠽⢿⡇⠀⠀⠀⠀⠀⠐⣏⠴⣠⣄⣰⡿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠘⠢⢴⡁⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⠡⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣰⠁
⠀⠀⠀⠈⠓⠧⣤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⠖⡛⠉⠉⢉⡉⡙⢦⠀⠀⠀⠀⠀⠀⢀⣖⢒⣆⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠓⠲⣄⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⡶⡄
⠀⠀⠘⣎⡔⠜⠓⢼⠵⢈⠟⠀⠀⠀⠀⠀⢰⡉⠤⡠⠭⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⢿⣯⢿⢹⢻⣽⠇
⠀⠀⠀⠘⣄⣸⡃⣭⣰⠏⠀⠀⠀⠀⠀⠀⢸⠄⣀⡼⡀⣼⠂⠀⠀⠀⠀⠀⣷⣦⣤⣼⣧⣤⣴⡇⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡗
⠀⠀⠀⠀⠘⣏⡵⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠜⠁⠀⠀⠀⠀⠀⠈⠲⣀⣓⠉⢀⢛⡸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠂⠀⠀⠀⠀⢠⠋⣿⢁⣾⡇⢳⠀⠀⠀⠀⠀⡶⢷⣾⡶⣄
⠀⠀⢠⢴⠞⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟⠻⣴⡇⠘⡇⠀⠀⠀⠀⡏⢦⢻⣿⣿⣆
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢴⡖⠚⣛⣛⡒⢲⡆⠀⠀⠀⠀⠀⣧⠀⣫⡴⢛⡆⠀⡇⠀⠀⠀⠀⡇⠀⠱⡻⣿⣿⣄
⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⣤⣀⣀⡀⣀⣸⠃⠀⠀⠀⠀⠀⢣⠀⢿⠙⢺⡇⢠⠃⠀⠀⠀⠀⡇⠀⠀⠙⢝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡏⠛⠛⠻⠟⢻⠀⠀⠀⠀⠀⠀⠘⣄⣸⣞⢋⣧⡼⠀⠀⠀⠀⠀⠧⠤⣤⣄⣈⣮⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡏⠉⢳⠏⠉⢷⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢱
⠀⠀⠀⢠⣇⡀⣀⢆⣀⣾⠀⠀⠀⠀⢀⡤⠚⠉⠁⠆⠉⠑⢦⡀⠀⠀⠀⠀⣀⢔⠚⠿⠟⢷⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡾⡛⠁⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⣸
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠀⠀⠀⠸⣽⡀⠀⠀⠀⠀⠀⠀⢀⣞⡶⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠸⡀⠀⡸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⣖⡒⠒⣲⠾⠛⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠓⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⠈⢷⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣴⣦⣀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣀⣀⣀⡁⢤⠀⡄⢠⠀⠀⠒⢠⣄⢠⠀⠂⠀⠀⠀⠀⣿⠀⢹⡆⠘⢧⡀⠀⠠⠛⠶⠀⠀⠀⠂⠀⠀⠀⣠⠶⣥⣛⠶⣮⠃⠀⠀⠀⠀⠀⠀⢀⣰⢶⣄
⠀⠀⠉⠙⠉⠁⠘⣄⠏⠸⠀⠀⠰⠶⠶⠶⠶⠛⠀⠀⠀⠀⠻⠇⠈⠁⠀⣰⠇⠀⠀⠤⠰⠶⠔⢠⠀⠀⠀⠰⢫⣾⢱⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⣾⡗⣬⠟
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⠶⠞⠉⠀⠀⠀⠀⠀⠀⢄⠶⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠢⡀
⠀⠀⠀⠸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣄⠾⠂⢠⠀⠀⠀⠷⣿⣷⣿⠿⠃⠀⠀⠀⠴⠀⠉⠒⢄⢀⡀⠀⠀⠀⢰⣶⣶⣶⣾⣧
⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⢠⠖⠐⣮⠙⠃⠀⠀⠀⠀⢷⡆⠉⠀⡠⠋⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣾⠃⣀⡀⠙⠷⠀⠀⠀⠈⠉⣙⠿⡇
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢰⠈⠁⠈⢁⡀⠐⠀⠀⠀⢀⡀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠶⠀⠰⠏⠁⣀⣉⣁⡀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠉⠛⠉⠉⠉
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠰⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠉⠁⠂⠀⠀⠀⢠⡀⠀⢛⠿⠀⣀⠀⠀⠀⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⢴⠁⠐⠀⠀⠀⠀⢸⡇⠀⠀⠙⠂⠀⠐⠀⠈⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⢉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠉⠁
⠀⠀⠀⠀⠀⢨⣯⡹⡭⠀⠀⠀⠁⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠟⡷
⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢐⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣦⠀⠀⠀⠀⠀⢀⡀⠲⡀⠚⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠛⠃⠀⡘⠛⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⢁⡇⠀⠀⠀⠄⠘⠃⢀⡵⠚⠃⠀⠤⠀⠀⠈⠂⠀⠃⠀⠀⠀⡟⠻⠿⠿⠛⢋⢳⡆
⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⡄⠀⠀⣤⠀⠀⠀⠀⠀⢤⡄⠀⠠⢦⣤⠇⠀⠐⠲⠖⠲⠟⠁⠀⠀⠀⠀⠲⠐⠆⠀⢠⡤⠄⠀⠀⠀⠈⠢⠄⠀⠴⠋⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⣮⠀⠀⠀⠀⠀⠈⢀⠀⠐⠀⠀⠀⠀⠀⢀⠄⠴⣿⡟⠀⠀⢀⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠒⢠⡆⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠠⠀⢀⡤⠈⠀⠀⠀⠈⠀⣄⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⣄
⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⠀⠠⢾⣥⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠊⠀⠀⠀⠀⠀⠀⠉⠉⡆⠀⠀⠉⠀⠀⠀⠈⠀⠂⠰⣆⣶⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠘⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠊
⠀⠀⠀⠀⠸⠷⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢟⡻⢿⣧⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠰⠾⠦⠀⠀⠀⢰⠆⢀⡛⡄⠀⡀⠀⠀⠀⣠⣶⣶⣴⡆⠐⠓
⠀⠘⢶⣶⣄⣤⣴⣶⡞⠀⠀⠈⠛⢧⣼⣿⡶⠟⠀⠀⠀⡀⠈⠁⠈⠀⡀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠂⠀⠰⠃⣠⢻⡿⠓⢾⠉⢓⡄⠘⠿⠶⣤⡞
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠞⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⢾⣤⠴⠛⠓⠋

⠀⠀⠀⢀⣤⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠤⣴⡄⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢷⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖⢠⡀⠀⠀⠀⠀⠀⠂⠀⡈⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠄⢀⡤⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢲⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠓⠇⠀⠀⠄⠀⠀⠀⠙⠷⣶⣶⠶⠟⠁
⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠆⠈⠄⠀⠑⠄⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠀⠀⠀⣤⣙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣧⡄⠀⢀
⠀⠀⠀⠴⠆⠀⣤⣾⠃⠀⠀⠤⠤⠤⠌⠉⢫⠀⠀⠀⠀⣤⣹⣿⣧⣄⠉⠀⠀⠀⠀⠀⢠⡄⠐⢳⡄⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢠⡤⠲⡦⠴⠶⠀⠀⠂
⠀⠀⠀⠤⠄⠻⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⠋⣻⡑⢫⣧⠀⠀⠀⠀⠤⠸⠃⠶⠊⠀⠀⠀⠀⠿⠟⠀⣀⢠⣦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠂⠐⠛⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠉⠀⠀⠀⠈⠤⢀⣀⣀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠉⠉
⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡦⠄⠀⠀⠀⣀⠐⠂⠀⢠⡤⠀⠀⠀⠀⠠⠶⠶⠦⠀⢀⠀⠀⠀⠀⠛⠏⠀⠀⣤⢶⠒⣄
⠀⠀⠀⣤⣴⣶⡆⠀⠀⠀⠀⠰⠀⠀⠀⠹⠀⠀⠀⠀⣴⠿⠛⠉⠀⠀⠀⠘⠀⠀⠁⠀⣄⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡌⠄⠀⠀⠀⠁⠂⠂⠀⠐⠫⠜⠋
⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠟⠃⠀⠀⠀⢈⣿⡷⠲⠶⠿⠓⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⡿⢿⣿⡿⠛⢿⡿⣿⡿⣿⠿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣥⣤⣼⣷⣠⣾⣠⣴⣷⣬⣴⣿⣥⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠉⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢆⡀⠀⠀⠀⠀⠀⢀⡠⡰⣿⣿⢆⢄⡀⠀⠀⠀⠀⠀⠀⡰⣆⡀
⠀⠀⠀⠀⢀⡀⣠⢮⠟⡟⢷⠻⡷⢄⡠⢔⡴⢋⡾⢡⡇⢸⡎⢷⡙⢧⡢⢄⡠⢮⠟⡾⢻⠻⡱⢄⢄⡀
⠀⠀⠐⢺⡗⣾⢓⡿⢺⣷⣾⣇⠉⣿⠋⣿⠋⣿⠏⣿⢻⡟⣿⠹⣿⠙⣿⠙⣿⠉⢸⣷⣾⡗⢿⡚⣷⢸⡗⠂
⠀⠀⠀⣿⢠⠇⣼⢃⡿⣼⣷⠏⢰⡟⢰⡏⢰⡟⢰⣏⣾⣷⣹⡆⢻⡆⢹⡆⢻⡆⠹⣼⣧⢿⡘⣧⢸⡄⣿
⠀⠀⢠⡇⡾⢰⠏⣼⢡⣿⣿⡇⣼⢃⡿⠀⡾⢡⣟⣾⣿⣿⣷⣻⡌⢷⠀⢿⡘⣧⢸⣿⣿⡌⣧⠹⡆⢷⢸⡄
⠀⠀⠘⠚⠑⠋⠘⠑⠛⠛⠛⠃⠋⠚⠁⠚⠁⠛⠚⠛⠛⠛⠛⠓⠛⠈⠓⠈⠓⠙⠘⠛⠛⠛⠊⠃⠙⠊⠃⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣯⣓⢦⡀
⠀⠀⠀⢀⡴⢋⠡⠈⠄⡀⠍⠙⣦⠀⠀⠀⠀⠀⣰⣒⣚⣛⣛⣶⡀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣠⢞⣩⠴⣿⣼⣚⣍⣳⣽
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠤⠤⠤⣼⠆⠀⠀⠀⠘⣧⡤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⣞⡉⠉⣧⠀⠀⠀⠀⣼⢡⢏⠤⡅⡏⠿⢟⣫⡵⣆
⠀⠀⠀⢸⡗⠛⢒⣒⣛⣒⠒⠓⢺⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡇⢹⡇⣸⠀⠀⠀⠀⣇⢸⠘⢒⠋⠷⢚⣭⡀⡇⣿
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡟⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡟⠉⠀⣿⠀⠀⠀⠀⠹⡜⢧⡻⠗⣡⣌⣋⡼⣡⠏
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃⠀⠀⠀⠀⠀⢠⣇⣀⣀⣻⠀⠀⠀⠀⠀⠙⠦⣍⣛⣓⣛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣞⢻⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⡳⣄
⠀⠀⠀⢸⠷⠾⠮⠷⠧⠾⠶⣿⠀⠀⠀⠀⠀⠀⣤⣤⣯⣯⣤⣄⠀⠀⠀⠀⠀⣠⠖⠋⡀⢀⠐⡈⠓⢦⡀⠀⠀⠀⠀⣰⢋⠀⡁⢈⠙⣿
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⢛⡧⠀⠀⠀⠙⣶⠓⡶⠚⠲⡖⢳⡞⠁⠀⠀⠀⠀⣏⠠⠀⠄⣠⡼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣿⣀⣀⣀⣀⣟⣋⣀⠀⠀⠀⠀⢸⡄⢹⠀⢸⠃⣼⠀⠀⠀⢀⣤⠞⣩⠷⠖⠛⠁
⠀⠀⠀⠀⠸⢤⡤⠤⠤⢤⠼⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠳⣼⣧⡾⡴⠃⠀⠀⠀⠘⢦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣳⣆
⠀⠀⠀⠀⠀⢀⣀⡤⠞⣧⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⠀⠀⠀⣸⣥⣤⣽⣧⣬⣧
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢷⡀⠀⠀⠀⣰⠋⠀⠀⠏⠀⠀⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⡏⠙⠓⢿⠀⠀⠀⠹⡞⠛⢚⣷⢶⡏
⠀⠀⠀⠀⡷⠶⣤⠴⢤⡴⢶⡇⠀⠀⠀⣟⣶⣒⣲⣒⣲⣒⣒⣖⣒⣶⣻⠀⠀⠀⠀⠀⢀⡞⠉⠙⠦⣄⣸⠁⠀⠀⠀⢻⣚⣩⡴⡾
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠀⣸⠁⠀⠀⠀⣿⠦⠭⡽⠯⢥⡬⠵⠮⡭⠴⣻⠀⠀⢀⣠⢾⡉⠙⢦⡀⠀⢈⡗⠀⠀⠀⠀⠈⣏⣡⢴⠃
⠀⠀⠀⠀⠈⣧⣸⣄⣼⣠⡇⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⠘⠲⢤⣷⣀⣠⠿⠖⠋⠀⠀⠀⠀⠀⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⢶⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⡾⡶⣴⢧⡀⠀⠀⣴⠋⣄⠙⣶⠋⣄⠙⣆⠀⠀⠀⠈⡏⠉⡇⠸⡷⢾⡇⠀⠀⠀⠀⠀⠀⣠⢞⡼⣳⠋⠈⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠶⢿⣹⠋⠀⠀⠰⡇⢀⡼⠀⢸⢀⡞⠀⢸⠀⠀⠀⢀⡇⠸⣧⡞⠁⠈⢳⡆⠀⠀⢀⡴⢞⡵⣫⠟⠁⠀⠀⣸⠃
⠀⠀⠀⣴⠋⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⢳⡈⠃⣠⢾⡈⠇⣠⠟⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢿⢚⡿⠞⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠙⠶⠃⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠻⣄⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠓⠒⠶⠚⠃⠀⠀⠀⠀⠈⠉⠉

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

⣞⣟⣉⣉⣉⣉⣉⠉⠉⠉⠙⣶⣶⡄
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⡏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⣛⣙⣿⣻⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣟⠋⢹⣏⠉⢉⣿⠳⣮⣛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⣿⠀⣼⠃⣠⠞⠛⣯⡻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⠤⠤⠼⠦⠼⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠧⠿⠶⠧⠾⣧⣤⡴⠛⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣥⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢦⣄⣀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⡞⠁⠙⣿⣦⡈⠙⢻⡿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡴⠋⠀⠀⠀⠈⢧⣙⣶⢟⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⠎⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢿⣿⣿⣿⣿⡿⠋⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠛⠛⠛⠛⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⠀⠀⣿⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠉⠉⠀⠀⢹⡀⢀⣿⠀⠀⠉⠉⠉⠙⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣄⣀⣀⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⣀⣀⣤⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠈⣿⠿⠈⠃⠁⠀⠃⠋⡿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠙⠌⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠟⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣴⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣟⢀⡄⣠⣠⢀⡀⡆⡀⡀⢰⣄⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠂⠀⠠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠐⠞⠃⠐⠷⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠤⢀⠜
⠀⠀⠀⠰⢀⠀⣀⡀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⡀⣰⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠢⠤⠄
⠀⠀⠀⠀⠠⠉⠠⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠹⡀⡜⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠤⠄⢀⡀⠀⠂
⠀⢰⠒⢰⢠⠀⠀⠀⡀⢀⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠄⠀⠁
⠀⠘⠄⠘⠂⠀⠈⠁⠀⠏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣿⡄⠈⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠗⠀⠀⠀⠀⠘⠒⠤⠒⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠒
⠀⠀⠃⠂⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢰⠐⠀⠇⠐⠂⠀⡆⡄⠀⠀⡀⠀⠀⠀⠀⢠⡥⠤⠊⣿⠃⠄⢠⣬
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢂⣞⣘⠁⣀⠢⢚⢠⠴⡁⣨⡽⠁⠀⠀⠀⠀⢚⠻⠀⠀⠋⠀⠀⠈⠙⠆
⣦⣀⡀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠀⠀⠠⠄⠀⠀⠀⠈⠈⠛⠺⠁⠀⠀⠀⠴⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠈⠦
⠙⢿⣧⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣬⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡢⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠂⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⢝⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠛⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⣦⠄⠀⠀⠨
⠀⠀⡂⠀⠀⠀⠀⢠⣤⡄⢴⠀⠀⢸⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⡀⠀⢸⣿⡇⠘⢧⣘⣿⣇⣰⠏⠀⣤⠀⠀⢠⠀⠀⣠⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⣶⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⠀⠀⢼⣷⠀⣰⠇⠀⠀⠀⢹⣿⣿⠁⠀⠀⠸⣆⠰⣾⠆⣠⡟⠀⠀⢻⡀⢲⣶⠂⠀⠀⠀⠻⣄⠰⣷⠆⣰⠇⠀⠀⢾⣷⠀⢀⡶⠀⠲⣦⣀⠀⢿⡷⢀⡼⠃
⠀⠀⢠⡶⣶⣶⡞⠁⠀⠀⠀⠀⣸⡿⣿⡀⠀⠀⠀⠈⢻⣿⣿⠉⠀⠀⠀⠀⠙⣿⣿⡟⠛⠲⡄⠀⠈⠻⣿⣿⠁⠀⠀⣠⢶⣿⣿⠉⠁⠀⠀⠀⠉⣻⣿⣶⠋⠁
⠀⠀⠈⢷⣿⣿⡇⠀⠀⠀⠀⣴⠏⠀⠈⢷⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⣧⠈⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠰⠂
⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠾⠃⠀⠀⠀⠀⠻⠆⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠚⣿⢿⡟⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿⠈⣷⠀⠀⠀⠀⠚⣿⢿⡿⠃
⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢀⡿⢀⣿⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠘⠠⠆
⠀⠀⠀⠀⠀⣼⢻⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣶⣄⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⢻⡟⢹⠟⠉⠋⠀⠀⠀⠀⠀⠀⠀⣿⣽⣟⢻⣿⠙⠛⠁⢠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠳⠀⠸⠀⢠⣚
⠀⠀⠀⠀⠀⠀⢸⣧⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⡛⠿⣦⡀⠀⢠⠀⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⣿⠀⡀⠀⣀⣄⡀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠛⢶⠀⠸⣿⣿⣷⣶⣶⣾⠇⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠿⠁⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢰⡟⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⣠⣻⣿⠀⠀⢈⡘⢶⣄⣬⢩⣿⣿⣿⠉⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⡄⠀⠻⣿⡿⠇⣀⢠⢷⡀⢹⣿⣧⢿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⣿⣿⣷⣴⣶⣿⠟⣴⣶⣵⣼⣷⡟⣾⣇⠘⠻⢟⣁⣀⣤⡾⠟⠉
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣽⣛⣻⣿⣿⣿⣆⣙⣻⣛⣹⣿⣿⣿⡙⣿⣿⣿⣿⡏⠉
⠀⠀⠀⢸⣿⡷⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣿⢿⣾⡛⣿⣿⣿⣿⣿⢹⣿⠃⣿⣿⣿⣿⣷
⠀⠀⠀⢠⣾⣆⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⣿⡷⣿⣷⣿⣿⣿⣿⣿⢸⣿⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⡟⠛⠛⠛⠃⠀⠀⠘⠛⠛⠛⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⡇⣿⡇⣸⡷⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠛⣿⡿⣿⡇⣿⡇⣿⣷⣿⣿⢹⣿⠉⠈⠋⠈⠉⣿⡇⢸⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡟⠛⠃⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢸⣿⠃⠀⠀⣿⡇⢿⡿⣿⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⢸⣿⠀⠀⠀⠈⠀⠈⠁⣿⣿⢸⣿⠀⠀⠀⠀⠀⠻⠃⠸⠟
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠻⠟⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⡸⢣⢇⢔⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢱⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⠀⠈⠀⢀⠴⠙⢻⣶⠖⠀⠀⠀⠀⠐⠀⢀⠀⠀⢉⢶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠓⠀⠀⠀⠀⢠⢡⣛⠻⠿⣧⠀⠀⠀⠀⠸⠋⠘⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢀⠐⠿⣳⡆⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣢⠇⢰⡄⠀⠀⢩⠶⣝⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠌⠀⠀⠀⣠⠀⡌⠣⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡴⣰⢰⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⡀⠀⠀⠀⠈⠀⠠⢦⣄⠉⠀⠂⠀⠁⣊⢞⢔⣭⣠⠄
⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠒⠲⢿⡢⠀⠀⠀⠜⠁⠄⡽⠷⠭⠤⠀⠄
⠀⠀⠰⠄⠀⠈⡹⢦⠀⠀⠀⢀⠀⠄⠀⠋⠸⣄⡄⠂⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠨⠙⢒⣨⣍⡙⠃
⠀⠀⠀⣤⢀⠀⢨⠷⠠⠀⠀⠐⠻⠀⠀⠀⠁⡤⢿⣥⠀⠀⠀⠨⠀⠀⠠⠄⢀⠀⢀⠀⠀⠲⡤⡙⢾⣛⠅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠶⡶⠀⠄⠀⠀⠠⠂⢴⡧⡎⠀⠸⠀⠁⠀⢘⡛⠓⠭⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠓⠁⠃⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⣶⠀⣤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⢠⡞⢭⣱⠀⠀⠀⠀⠀⠀⡍⠒⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⢃⡤⠦⠀⠀⠀⠀⢀⡴⢯⣅⡢⠁⠀⠀⠀⠀⠐⠚⠲⡀⠄⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠞⠢⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣶⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⡈⠳⠃⠀⠀⢀⠤⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠏⠳⠎⠀⠀⠀⠀⢀⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠈⠀⠀⠀⢎⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡔⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣀⡞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣄⠀⠀⠀⠀⠀⣤⠠⠃⠑⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠱⡀⠀⠈⠢⣀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⣔⠲⠈⢃⡿⠘⠀⠀⠀⠀⠀⢘⣀⠤⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠓⢄⠀⠀⢈⠀⠀⢸⠀⠀⠀⢀⡤⢄⠀⠙⣠⠗⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢠⠁⠀⠈⠢⡀⠀⠑⠒⠙⢄⣀⠀⡈⠳⢨⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⡴⢸⠙⢬⡯⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢠⠃⠀⠀⠀⡠⠛⢦⡀⠀⠀⠀⠙⡆⡹⠶⠋⠀⠀⠀⢀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠴⠟⠫⣚⡰⠀⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡠⠁⠀⠀⢀⠜⠁⠀⠀⠙⣢⡀⠰⢭⠟⠣⡀⠀⠀⠀⠀⢆⠀⠀⡄⠀⠀⠀⠀⠘⠾⠖
⠀⠀⠀⠀⠀⠀⠀⢀⠂⡰⠁⠀⢀⡴⠁⠀⠀⢀⡠⠊⠁⠈⠢⢄⠀⠀⠘⢄⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⡎⡰⠁⠀⣠⠊⠀⠀⣀⠔⠉⠀⠀⠀⢀⠠⠒⠉⠢⢄⣨
⠀⠀⠀⠀⠀⠀⡘⡐⠁⢀⠞⠀⢀⡠⠊⠁⠀⢀⡠⠖⠉⠀⣀⠤⠐⠀⠁
⠀⠀⠀⠀⠀⢠⡑⠀⡔⠁⢀⠔⠉⠀⡠⠔⠊⢁⡠⠔⠂⠉
⠀⠀⠀⠀⢠⡟⡠⢊⡠⠊⣁⠤⣒⠩⠄⠒⠉
⠀⠀⠀⢀⣿⣌⣔⣩⡶⠝⠂⠉
⠀⠀⠀⣾⠿⠛⠉


⣿⣿⣶⣶⣷⡿⢾⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣾⡿⣾⠿⠶⠶⢶⣿⡶⠶⠶⠶⢾⠶⢶⡶⠶⠾⠶⠾⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⣰⠋⢳⡄
⠀⠀⠀⠀⢀⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⣩⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⣤⠐⠿⡞⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞⠛⣡⢼⡛⠷⢯⣷⡀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠒⠚⠉⠀⠀⢸⡆
⢀⡞⣹⠷⠒⠿⣄⠀⠀⠈⠓⠦⢤⣄⣀⡄⠀⠀⠀⣸⣴⣣⢾⠷⠶⢿⢻⡞⠁⢧⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡴⠛⠛⠳⣄⠀⠳⣄
⠉⠉⢻⠀⠀⠀⠈⠳⢦⣄⣀⣀⣀⣀⠿⣽⠀⠀⠀⢻⠙⠛⠻⠶⠶⢾⠏⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡼⠀⢸⠀⠀⠀⠀⣹⠀⠀⠈⢳⡀
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠉⠛⠛⢦⣴⡆⠀⠀⠀⠈⢦⠀⠈⠁⣰⠋⠈⠀⠀⠀⢻⡀⠀⠀⠀⣰⠋⠀⠀⠈⠳⢤⣤⠴⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣤⣤⠤⢿⣸⠇⠀⠀⠀⠀⠈⢧⡀⣰⠃⠀⠀⠘⠀⠠⠈⣇⠀⠀⠀⢿⡀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⢀⠀⠀⠀⢸⡆⠀⠀⠀⠙⠓⠚⠉⠀⠀⠀⠀⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠤⠀⠈⠀⠀⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠙⢦⣀⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢰⢡⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣾⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⣠⠤⡎⢉⡆
⠀⠀⠀⠀⠀⠀⠀⡟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⣀⠀⠀⢀⡞⣠⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠙⣦⠟⠳⣦⡟⣏⠹⣞⣦
⠀⢠⠶⠶⠶⠶⠚⠓⠓⠒⠒⠒⢲⡄⠀⠀⠀⠀⠀⣞⣛⣛⣛⣛⡇⠀⠈⢇⢹⢀⣤⣄⣠⡿⠋⠀⠀⠀⣏⣛⠛⢦⣞⢹⢠⡿⣆⠘⢧
⠀⠉⢻⠉⠉⠉⠉⠉⠉⠉⠉⢉⡏⠁⠀⠀⠀⠀⡴⠛⠉⠉⠉⠉⠑⢦⠀⠞⢀⢸⣄⠈⢹⡇⠀⠀⠀⠀⢀⣈⡟⣆⠈⢻⣸⠃⣼⣄⣨⣷
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⣞⠉⠙⢿⡳⠞⠁⠀⠀⠀⠀⠀⢻⠉⠉⠙⠛⠛⠉⠉⠁⢠⡇
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠶⢿⡶⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣤⣀⣷⣠⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢰⡏⠐⠈⠙⣏⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠒⠒⠒⠶⠟
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠻⠶⠶⣶⡿⢦⣧⡴⠋
⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠓⠲⠶⢤⣄⡀
⠀⠀⠀⣰⠿⢞⠳⠮⣍⡹⣯⣽⣇⣤⣀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠶⠒⠒⣖⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣀⡀⣠⠀⠈⠉⠳⢤⡀
⠀⢀⡞⠁⠀⠈⠀⡄⠀⠙⢦⡸⢭⣳⣈⠱⡄⠀⠀⠀⠀⣴⢋⡀⠳⠀⠶⠀⠡⠆⢈⠳⡄⠀⠀⠀⠀⠀⢸⡷⣤⡈⠉⠓⠦⣤⡄⠀⠀⠙⢦
⠀⠸⡆⠠⠀⠀⠀⠀⠀⠂⠀⠹⡄⢿⣽⣇⢹⠀⠀⠀⠀⢷⣌⣁⣀⣀⣀⣖⣀⣈⣋⣁⣹⠀⠀⠀⠀⠀⢸⡷⢈⡇⢀⣩⡤⣤⣙⠶⣞⠀⣈
⠀⠀⠘⠦⣀⠈⠁⠀⢀⠀⠈⠃⠹⡄⣹⢾⣼⠀⠀⠀⠀⣸⣭⣭⠭⣍⣉⣩⠽⢯⣍⣩⠿⡄⠀⠀⠀⠀⢸⠟⠋⢠⣯⡴⡖⣟⣮⠷⠞⠋⠉
⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠠⠄⠀⢷⡷⢺⠃⠀⠀⠀⠀⠹⣦⠤⠶⠶⠿⢶⣶⠶⠶⠖⢺⠁⠀⠀⠀⠀⢸⠶⣄⢘⣦⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣄⣸⡴⠃⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⣀⣈⣹⣦⡴⠋⠀⠀⠀⠀⠀⢾⠴⠛⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣄⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣛⠃
⠀⠀⠀⠀⠀⠀⡌⣁⣈⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⣟⣿⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⡷
⠀⠀⠀⠀⠀⠀⠈⣹⣿⡉⣀⣈⠿⠿⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢟⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢒⣒⣒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣍
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠘⣍⣉⣏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣿
⠀⠀⠀⠀⠀⠀⣧⡉⠐⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⣬⣤⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⢟⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠖⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠾⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠠⠾⠷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠈⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣶⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣰⣃⣠⡄
⠀⠀⠀⠀⠶⣿⡄⢈⣏⠰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⡷⢄
⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠙⠋⠁

⣿⠿⠿⠿⠿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣛⣿⣟⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⢀⣀⠸⡄⠀⣰⡆⢸⠀⣴⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⡆⡴⡄⢀⡖⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⢀⠀⡔⡴⠁
⠀⠀⠀⠀⣤⣙⡳⠅⣰⠃⠸⡄⠾⠵⠋⠁⠀⠀⠀⠀⠀⣀⠀⠀⠑⠄⠂⣸⠁⠸⡈⠖⠰⠂⠀⢀⡀⠀⠀⠀⠢⠀⠘⢶⡌⣡⠻⡄⢠⠞⠀⠀⠀⡀
⠀⠀⠀⠀⠠⣶⠖⠒⠁⠀⠀⠛⠛⢛⣰⢆⡀⡀⠀⠀⠀⠈⠁⠰⣏⠉⠉⠁⠀⠀⠉⠉⣉⠗⠈⠉⠀⠀⠀⠀⠀⠀⠤⠤⢴⠿⠶⢷⠶⢶⡶⠄⠉
⠀⠀⠀⠚⣒⣀⠉⡆⠀⠀⠀⠀⢰⠋⣄⣉⣁⠀⠀⠀⠀⠀⠶⠒⢨⠕⡆⠀⠀⠀⢰⡋⠅⠒⠆⠀⠀⠀⠀⢀⣀⣤⣤⠑⡾⡀⠀⣨⣷⠁⣀⠀⠒⠒
⠀⠀⠘⠛⠉⡴⢸⢃⣠⠖⠳⣄⠸⡔⢦⡈⠉⠁⠀⠀⠰⠂⠉⢤⠖⢰⠁⣠⠞⠢⣄⢳⠰⡌⠁⠐⠀⠀⠀⠀⠈⠡⠀⣼⣡⠞⠛⠠⢘⡆⠩⣙⠛
⠀⠀⠀⠀⠘⠁⠛⠋⢠⢰⠀⢦⡙⠇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠋⣧⠈⠈⠆⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣆⠠⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘

⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⡀⠐⣎⢳⠀⣴⠻⣆⠀⣾⣡⠞⠁⠀⠀⠀⠀⠀⠀⠙⢧⡘⣧⠀⣴⠀⠀⡞⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡶⣄⢠⡀
⠀⠀⠀⠈⠙⠛⠊⢁⣰⡏⠁⠿⣄⠁⠵⠞⠃⠀⠀⠀⠀⠀⠻⠶⢬⡗⠉⣸⣿⣇⠀⠁⠫⠤⠶⠂⠀⠀⠀⠀⠀⠠⠤⠴⣣⠏⠀⠹⣌⠳⠶⠂
⠀⠀⠀⠀⠛⢯⡛⢉⠉⠶⠀⠀⠏⠉⣛⠟⠃⠀⠀⠀⠀⠀⠀⢠⣦⢰⣶⣿⣿⣿⣷⣤⣤⡤⠀⠀⠀⠀⠀⠀⠐⢶⡛⠉⠁⠀⠀⠀⠉⠉⢙⡷
⠀⠀⠈⣛⣛⡶⠙⡶⠁⢀⡀⢁⡂⣾⢁⢾⣭⣄⡀⠀⠀⣀⣀⣀⠙⢸⣿⣿⣿⣿⣿⡿⠋⣀⣤⣄⠀⠀⠀⠀⠀⢤⣙⢳⡄⠀⠀⠀⠀⣴⢫⠔
⠀⠀⠉⠉⣡⡾⢸⣗⣰⠞⠳⣤⡄⣿⠈⠳⠀⠈⠀⠀⠀⠉⣉⡴⠂⢸⣿⡿⠛⠟⣿⠆⢤⡳⢶⣤⠀⠀⠀⠀⠀⠀⠹⢸⠇⣠⠞⢦⣀⣿⢹⠄
⠀⠀⠀⠀⠁⠀⢸⠟⢡⡆⣷⢮⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⠁⣰⢲⡄⠙⠂⠈⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠟⠵⠛⠳⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⢄⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡐⡄⢀⡞⢳⠀⠇⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⢀⠀⢠⠀⡀
⠀⠀⠀⣀⠀⠀⠘⣷⢠⠇⠈⢇⢰⡯⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⢂⡼⠀⠀⢧⡐⠁⠚⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⡠⠄⡌⠁⠂⠎⣐
⠀⠀⠀⠀⠠⡖⠒⠒⠋⣤⣆⡈⠒⠒⢒⠄⠲⠀⠀⠀⠀⠀⠀⠲⢏⡉⠉⠀⠀⠀⠈⠉⢉⡽⠃⠀⠀⠀⠀⠀⠉⠓⢂⡘⠁⢤⣀⣰⠀⠚⣡⠄
⠀⠀⠀⠘⠂⣩⢢⠀⠈⠟⠁⡀⠀⡴⣋⡐⠂⠀⠀⠀⠀⣀⣀⡥⠄⢉⠆⠀⠀⠀⠀⢰⠋⢄⡓⠀⠀⠀⠀⠀⣈⡡⠤⠑⢢⠴⢿⠿⠦⠂⠶⠾⠆
⠀⠀⠀⠀⠘⡃⡌⠀⢀⠔⠢⣀⠀⠆⣙⠃⠀⠀⠀⠀⠀⠀⠀⠐⠃⡞⣀⠴⠊⠓⢤⡈⡇⠰⠍⠃⠀⠀⠀⠀⠀⢐⠉⣀⡌⠀⠘⠣⠀⡀⠢⢍
⠀⠀⠀⠀⠚⠁⠃⣺⠁⢺⡆⠠⡑⠊⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠔⢸⠀⡄⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠘⡡⣀⢰⠂⣈⡑⡈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠙⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠉

⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⡀⠀⠀⠀⢠⠀⣥⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢰⣧⣄⣷⣶⠀⠀⠀⠀⠀⠁⠐⠂⠜⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⠠⣤⣄
⠀⠀⠀⠀⠀⠈⠀⠑⠒⣿⠀⠀⠀⠀⠀⠆⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠀⠀⠀⠀⢰⠀⠀⠀⠀⠹⣶
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠰⠀⠓⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠦⠈⠾⠃⠀⠀⠀⠀⠀⠣⠀⠠⠾⠃⠀⠀⠀⠸⠆⠀⠶⠃⠀⠀⠀⠀⠠⠄⠠⠶⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠴⠟

⠀⠀⠀⠀⣀⡀⠀⢠⣰⢄⡀⠀⠀⠀⡤⠄⠀⠠⠀⢤⠀⠀⢠⠂⠐⠒⠂⢲⡄⠀⠀⣠⡤⢀⠀⣤⣤⣄
⠀⠀⠀⠀⠹⡄⠀⠈⢹⠟⠀⠀⠀⠀⢂⠀⠀⠀⠀⠘⠀⠀⠀⢂⠀⠀⢀⠞⠀⠀⠀⠣⠀⠀⠀⠀⠀⠉⠀⠀⢠⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠙⢻⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡟
⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠘⠀⠀⠀⠐⠋

⠀⠀⠀⠀⣀⡀⠤⠄⠀⢀⡀⠀⠀⠀⠀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢏⠀⡀⢀⡀⢻⡇⠀⠀⠀⠘⠓⠛⠛⢛⡗⠀⠀⠀⠂⠀⠈⠀⡶⠀⠀⠀⠀⠃⠀⠀⢹⡇⠀⠀⠀⠐⠗⢒⣆⣰⠛⣿
⠀⠀⠀⠀⠘⡀⠀⣀⢀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⢄⡋⢿⢛⡇⣿
⠀⠀⠀⠀⠀⢟⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠁⠀⠀⠀⢀⠐⠀⢀⡀⠀⠀⠀⠀⢸⠀⠀⠐⡇⠀⠀⠀⢀⡁⠀⠒⠊⠀⡁
⠀⠀⠀⠀⠀⠘⠃⠀⠚⠃⠀⠀⠀⠀⠀⠙⠀⠒⠛⠀⠀⠀⠀⠘⠀⠐⠛⠁⠀⠀⠀⠀⠀⠂⠀⠚⠀⠀⠀⠀⠈⠓⠂⠀⠈⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⣧⢸⣸⡸⡰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⣀⣈⣤⠀⢀⠀⠀⠀⢬⣓⣬⣾⣿⣿⣟⣥⣐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡆
⠀⠐⠀⠀⠁⢡⣙⠃⠒⠤⠀⠀⠀⡦⠶⣿⣿⣿⣿⣿⣿⡭⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠠⠀⠀⠀⠄⠁⠀⡀⠀⠀⠀⠐⢛⡩⢻⢿⢿⢟⢮⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⠀⠀⠀⠈⠐⠻⠸⠸⠘⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠐⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⡈⣐⡚⣼⣄⣤⠁⠀⠠⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠄⠪
⠀⠀⠀⠀⠀⠀⠀⠂⡩⠙⣿⣿⡁⠖⠀⠠⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠄⡡⠢⢓⠉⠀⠂⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠐⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡠⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⣀⠀⠀⠀⠈⠈⠀⠀⠔⠀⠀⠀⠰⠀⠀⠈⢢⡀⠀⠀⠀⢠⡞⠠⠐⠠⠁⠀⠐⠚⠷⠀⠛⠁⡀⠀⠀⢀⠁⣸⠊⠑⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠶⠀⠀⠀⠀⠘⠐⠂⠈⠁⠀⠀⠃⠀⠀⠁⠀⠨⢠⡞⠀⠀⠀⠀⠀⠀⠠⠶⠀⢾⠷⠈⠛⠁⠀⢘⣦⠰⡄⡠⢯
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⢰⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⠁⠶⠄⠘⠷⠀⠀⠀⠀⠙⠛⠐⠙⠃
⠀⠀⢀⠀⠀⠀⠀⠀⠈⣵⠀⠘⠀⡀⣰⡄⠀⠀⠣⡀⠀⠈⠀⠐⠀⢀⠄⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠀⠀⠀⠀⠈⠐⠂⠐⠒⠊⠁⠀⠀⠀⠀⢀⡀⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠁⠐⠀⠢⠐
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⠳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⢯⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠀⠀⠘
⠀⠀⠀⠀⠀⣀⠀⠀⢈⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠃⠠⠀⠀⠀⠐⠀⣾⠒⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⠀⠅⠀⣆⠔⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣼⠒⠀⠀⠀⠐⠀⠂⠀⣰⠃⠀⠀⠀⡀⣀⠀⠀⠀⠈⡄
⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠌⠀⠀⠀⠐⠃⡼⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠰⡴⠁⠀⠀⠀⡃⠤⠀⠑⡀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠋⠀⠄⠰⠄⢀⠀⠀⠀⡨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⡇⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠔⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢦⠀⠀⡐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⡀⠀⠘⢎⡀⢀⣄⣦⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡠⠊⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠚⢋⡁⠊⠒⢄⠀⠀⠀⠀⠀⠤⠈⠀⠀⠐⠉⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡋⠌⠀⡠⠃⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⢢⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠰⠁⠠⠤⢱⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠑⠤⠁⣀⡄⠃⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠷⢀⣀⠁⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠁⠉⠀⡄
⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⡀⠀⣠⡀⠙⠾⡀⠀⠸⠆⢡⠔⢀⠲⠀⠀⠀⠉⠁⠀⣠⡿⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⡈⠉⠓⠢⡀⢸⠀⠙⠊⠀⠀⠀⠀⠀⠀⠘⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢾⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⡄⢀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠀⠢⡘⠀⠈⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣀⠓⠀⠈⣶⠀⢀⣤⠃⠀⠀⠀⠀⠀⠀⢇⠺⢃⠀⠀⢰⠀⠴⠃⢤⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠛⢷⣯⣭⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⢆⠇⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠴⠛⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠
⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠛⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡁⠀⠀⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠐⠒
⠀⡀⠀⠀⠀⠈⠤⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠉⠁⠀⠀⠀⣤
⠀⢁⠀⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⢀⡂⠀⠀⠀⠀⡅⠀⢀⡀⢀⡤⢠⠠⠀⠁
⠀⠈⠀⠬⠀⠈⠀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠘⡀⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠄⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⢀⡀⠀⣁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠆⠘⠃⠂⢂⠄⠀⠀⠀⠀⠀⠤⠄⢙⣐⣒⣉⠠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠠⠤⢀
⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠸⡀⢆⢀⣄⠲⠀⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠲⠂⠀⠀⠀⠀⠀⢀⠈⠀⣀⡀⠁⡁⣀⣀⢱
⠀⠀⠀⠀⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡠⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⢀⠠⢐⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⣀⣢⢠⣈⣀⣥⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡿⠂⠀⠀⡐⢁⢲⡀⠀⠸⠀⠀⠀⠀⣠⠤⠶⠶⠿⠿⢶⡄
⠀⠘⠈⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠾⠀⠀⠀⠀⠀⠛⢾⡡⠀⢁⡆⠀⠀⠀⢹⠀⠀⠀⠄
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠠⠀⠀⠀⠀⣶⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡄⠀⠀⠐⠀⠀⠀⠐⠒⠘


⠀⠀⠀⠀⢤⠉⠀⠀⠀⠀⠀⢀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢘⠆⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠰⣆⠀⡀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⡄⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠠⠂⠀⠀⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠲⢎⠣⣄⠀⠀⠈⠀⡃⠈⠠⠈⠀⠠⠀⠑⠠⠀⠀⠀⢀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⢙⡧⠄⠀⠀⠀⠀⠐⠨⠤⠒⠀⠡⠀⠀⠀⠀⡁⢈⠀⠠⠋
⠀⠀⠈⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣠⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⠊⠀⣀⣤⣤⣀⡈⠀⠀⠀⠀⣿⢿⡄⢸⣟⠖⠁⠀⠀⠀⠀⢀⡨⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄
⠐⠀⠂⠀⡰⢛⡅⠈⠀⠁⠀⠀⠰⠀⠀⢨⠉⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⢋⣀⣠⡠
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠨⡀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠠⡬⠀⠀⠀⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢀⠀⠀⠀⠀⠀⢀⣠⠄⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⢀⠂⠈⠂⠀⠀⠀⢠⡏⠃⠀⠀⠀⠙⡆⠀⠀⠀⡀⠔⠒⠂⠀⡀⢀⠠⠀⠀⢀⠔⠀⠀⠀⠑⠄
⠀⣀⠀⠀⠐⠚⠛⠛⢲⠇⠀⠀⢀⠈⠀⠂⠂⠀⠁⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⢈⠀⠀⠒⡄⠶⠀⠒⢄⡜⢂
⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢆⠤⠁⠔⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠈⠘

⠀⣀⠀⠀⠀⠀⡀
⢀⠀⠀⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⣰⣤⣤
⠀⠀⡀⠙⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠃
⠀⠀⡇⠀⢣⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⡜⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠦⡀
⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠶⠒⠃
⠀⠀⢀⠀⠸⠀⠀⠠⠀⠘⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠄⠄⠤⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⡄⢀⠐⠁⠔⢸⡄⠀⠀⠀⠀⠀⠀⠁⠀⣵
⠀⠀⠀⢀⡠⠈⠋⠆⢰⠆⣝⠀⠀⠀⠐⠐⠶⠚⠙⠿⠿⣖⡂⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⡼⠎⠀⠀⡀
⠀⠀⠈⠐⠂⠀⡧⠐⠒⡠⠡⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠚⣿⡷⠀⣤⢠⠌⣍⢀⣀⣈⣉⡀⢀⡀⠀⠀⠈⠙⠒⠒
⠀⠀⠀⠤⡀⢶⠸⠟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣴⣿⡇⠀⠈⠻⠴⣧⣰⣄⣤⣠⡷⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠃⠀⢰⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣷⣄⣤⣾⣿⣿⡿⠀⠀⢀⡀⠡⠔⠤⠀⠀⠀⡇⠀⠀⠀⠐⠒⠀⠡⡀
⠀⠀⠀⠀⠀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠙⠁⠀⠀⠀⢀⣀⠀⢐⠇⠀⢠⠃⠀⣄⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠸⠀⠀⠹⡇⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⣀⣴⠋⠀⠀⠘⢄⣀⢀⣠⣠⣶⡞
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⢘⣁⠀⠀⠀⠀⠻⣷⣶⣾⣿⢃⡖⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠨⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠖⠋⠀⠀⠀⠔⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⡀⡇⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣸⡀⠀⠀⠀⠀⠀⠀⢂⣿
⠀⠀⠀⠀⠀⠑⠀⡾⠀⠀⠐⢦⣀⣧⣀⣴⡷⠃⠠⢂⣱⣯⢧⠷⠾⣷⣄⠀⢐⠀⣏⠀⠀⠈⠻⣤⣀⣀⣀⣰⣦⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠃⠁⠈⠉⠆⠀⠀⠈⢻⡆⠀⠀⢹⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠡⠀⠀⠀⢴⡇⠀⠈⠒⢤⣄⣠⣼⣶⠿⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣤⣀⣠⡶⡀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⣾⣎⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣄⠀⠀⠏⠀⠀⠀⠀⠠⠟⠃⠙⠁⡧⠠⠄
⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣟⠓⠀⠈⠳⣦⣄⣀⣀⣀⣀⣀⣴⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣾⣄⣀⡀⠀⠀⢀⣀⣀⣀⣠⣿⣧⠀⠀⠀⠀⠠⠾⣿⠧
⠀⠀⠀⠘⢿⣿⣿⣏⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⣤⡄⠀⠀⣺⣿⠆
⠀⠀⠀⠀⠘⠟⠉⠙⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠛⠻⣿⣿⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠋⠉⠁⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⣿⣦⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⣶⣶⡤⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⣿⠃⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⠿⢿⣿⣿⣿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣧⡀
⠀⠹⢿⡏⠀⠀⠀⠨⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠶⣾⣿⣿⣿⡿⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡀⣠⣾⣿⣷⠀⠀⠀⠀⠀⢸⣿⠿⣿⣇⠀⠀⠰⣶⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠾⠿⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡿⠉⠁⠀⠀⠀⠀⠀⠀⠰⠿⠿⠛⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⢸⣿⣿⣦⣠⣤⣤⡄⠀⠀⠀⣤⣤⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣦⣶⣶⣶⠆
⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀
⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢲⣶⣿⣤⡀
⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣠⡄⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⡀⠀⠸⠛⢿⠁
⠀⠀⠀⠀⡿⠋⠁⠀⠀⠀⠈⠀⢀⣴⡀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀⠀⠘⠟⠃⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣿⣧⣀⡀⠀⠈⠉⠙⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣷⣶⡶⠀⠀⠼⣿⠇
⠀⠀⠀⠀⠰⣾⣿⡶⠄⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠛⠉⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡷⠆⠀⠀⠀⢀⣿⠟⠛⠻⠿⠀⠀⣠⣤⣿⣦⣀⡀
⠀⠀⠀⠀⢀⣰⣆⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⢈⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣴⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢈⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣛⠂⠀⢀⣠⢶⣀⡀⢀⣄⠛⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠁⠀⡄⡇⡄⡀⠂⠶⣠⠸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠞⠙⢿⡉⠉⠉⠩⠩⠩⠩⠩⠍⢹⠃⠀⠁⠸⠭⠄⠀⠀⠀⠡⠂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢧⠀⠘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢲⠖⡐⡒⠀⢓⣃⠱⢇⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠣⠻⣉⡦⣎⠙⠃⠀⠉⠁⠑⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠆⠈⢘⢭⠀⠠⠄⡀⠀⠰⠣⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠠⠀⡴⣎⢨⢦⠀⠄⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠃⢨⠀⠈⣿⡗⢡⡏⠀⠀⢣⡀⠀⠀⢏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⡣⢬⠁⠄⡬⠋⠀⠠
⠀⠀⠀⠀⣤⠀⠁⣉⡀⠀⢘⡇⠀⢠⢿⣴⢬⠷⡀⠀⠈⡇⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠘⠓⠀⠀⠀⢀⠰⣄
⠀⠀⠀⣠⡄⠈⡁⠈⣽⣄⡼⣇⡀⢂⠄⠈⠖⠠⢄⢀⣰⠿⡄⣴⡄⡄⠀⠀⠀⢠⠁⡀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘
⠀⠀⠀⠉⠁⠀⠀⢀⠸⢷⣆⠌⡝⢁⠀⠁⣀⡁⣠⡡⡐⠶⠀⠉⠀⠀⠀⠀⢀⠘⠌⠃⡫⠨⠈⠀⠃⠀⠀⠀⠀⠀⠸⠀⢀⡖⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠥⠘⢛⣛⣭⡤⢷⢶⢬⣭⣐⣀⠂⠀⠀⠁⠀⠀⢼⠀⢐⠀⠅⡠⡆⡀⠀⠀⠀⠀⠀⠀⠉⢐⠾⠀⡀⠂⠁⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⡍⠀⢑⠀⣖⡆⠐⢇⡄⠉⠙⣅⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣃⠀⢿⠀⣛⣇⠀⠠⠖⡀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣸⡄⠈⠄⢹⡽⡄⠸⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⡶⣤⠀⠀⣆⣥⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢱⡄⠀⠀⠀⠠⡦⠤⠂⠀⠀⠀⠀⡀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠃⠿⠀⠀⣧⣿⠗⡄⠀⠀⠀⢠⣤⠀⠀⠸⠀⢸⠀⠈⡇⡀⢀⠄⢸⠂⡆⡆⡤⣃⢤⠘⠇⠆⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⠀⣮⣀⣿⣼⣠⠝⠀⡀⠀⠀⠉⠀⠀⠀⠀⢸⠀⣸⠓⠇⠘⠂⢸⠀⠁⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢁⡛⠀⠘⡮⣙⣿⣟⠰⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠏⠑⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⢡⣦⠈⡿⠃⠈⠶⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣯⡞⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣰⠘⣆⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⣠⢞⡾⢸⣇⢳⡑⢆⡄⡀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠇⣶⢤⡀
⠀⠀⠀⠀⠀⣠⡶⠋⣴⡏⠀⣿⡆⠙⣦⡄⢀⣠⠴⢊⣵⠟⢡⣿⠁⣾⣿⠀⢿⣆⠙⢮⡑⠢⣄⡀⢀⣴⠏⢰⣿⠀⢸⣧⠙⢷⣄
⠀⠀⠀⠀⠀⠙⠉⠋⠙⠉⠛⠙⠋⠛⠙⠋⠙⠉⠋⠙⠉⠋⠙⠋⠛⠙⠋⠙⠉⠋⠙⠉⠋⠙⠉⠛⠙⠋⠛⠉⠋⠙⠉⠋⠙⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠙⠇⠈⣿⡇⠀⢹⡏⠀⠙⣷⠀⢀⣶⠋⠀⠈⠻⠀⢹⡏⠀⠀⠙⠏⢠⡆⠀⠙⠇
⠀⠀⠀⠀⠀⠰⡽⠂⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⢸⡷⠠⣞⠋⠀⢺⣿⠀⠀⠀⠀⠀⢺⡗⠀⠀⠐⠇⠀⠙⠻⠷⣦⠀⠰⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⡠⠄⢀⣿⡇⠀⣸⣧⠀⠙⢷⡄⠈⠻⣦⣀⣀⠔⠀⠘⢧⣀⣀⠀⠀⠨⡧⡀⢀⠜
⠀⠀⠀⠀⠀⣤⣀⣄⢠⡄⣤⢠⡄⣤⢠⡄⣤⣀⣄⣠⡀⣤⢠⡄⣤⢠⣄⣤⢠⡄⣠⣀⣄⢠⡄⣤⢠⡄⣤⢠⡄⣠⣀⣄⢠⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠄⠠⡀⢀⠆⠀⢄⠀⡄⠀⠀⡄⢠⢀⡀⠀⠄⠄⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁⠁⠓⠀⠀⠀⠁⠑⠊⠀⠊⠈⠀⠈⠒⠀⠘⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠠⠤⠤⠤⠄⠀⠀⠀⠠⠄⠤⠄⣤⠤⠀⡘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣾⡗⠒⠒⠒⠲⠒⠒⠒⠒⠲⠶⠒⠒⠖⠿⠖⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢸⣾⠇⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠧⠀⠀⠀⠀⠤⠶⠒⢢⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠷⠶⣴⠤⠤⠤⠤⠴⠤⠦⠤⠤⠤⠤⠶⠤⠤⠤⠴⢦⡼⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣤⣤⣤⣴⣶⣶⣶⣦⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⣤⣤⣤⣦⣤⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠽⠶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠤⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣧⣀⣠⣤⣤⣤⣤⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣐
⠀⠀⠀⠀⠀⠀⢁⠤⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠒⠀⠒⠒⠂⠀⠀⠀⠂⠒⠀⠀⠀⢲⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠤⠤⠶⠤⠦⠤⠶⠶⠦⠶⠶⠶⠶⠶⠶⠧

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠉⠀⠀⠀⣈⣙⡦⠀⠀⠀⠀⠀⠀⠀⡔⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡏⠉⢢⡐⢋⡥⣄⠀⠈⠂⠘⠀⠀⠀⠀⠀⢐⠌⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠙⠒⠷⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠉⠐⠒
⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⢜⡠⠀⠀⠀⠀⠈⣄⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠈⠊
⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠓⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡔⠈⠹⠄⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠘⠢⠤⠤⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠃⠀⠀⠀⣈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠰⠀⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀
⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠤⠀⠀⢠⡎⠁⠀⠀⠀⢑⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠒⠶⠶⠚⠋⠀⠀⠀⠀⠁⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣝⣁⣀⣀⡀
⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠈⢁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠧⢤⡤⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠶⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡔⠂⠐⡄⠀⠀⣿⡣⠄⠙⠀⠈⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⢘⣃⡀⡀⠀⠀⢘⣖⣟⡠⠂⠀⠀⣿⡠⢄⠀⠲⢘⠀⠀⠀⠀⠀⠻⣷⠄⢀⡉⠁⠟
⠀⠀⠀⠀⢸⣥⣅⢛⣄⠀⠈⣼⠋⠀⠀⠀⠀⢸⠟⢢⠒⠂⠈⠀⠀⠀⠀⠀⠀⠘⣷⠄⡒⠊
⠀⠀⠀⠀⠀⣿⡯⠉⢩⡙⠡⠸⠀⠀⠀⠀⠀⢿⣦⠿⠰⡏⢰⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢹⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠿⠓⢄⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡦⢠⠛⢸⠀⠀⠀⠀⠀⠀⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠢⠴⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠖⠀⠁⣄⠁⠈
⠀⠀⠀⠀⠀⠀⢸⣿⢧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠐⣠⠶⣌⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣾⣦⠤⠦⣻⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣭⡏⠀⠩⠃
⠀⠀⠀⠀⠀⠀⠘⠛⠿⢀⡀⠀⠀⠀⠀⠀⠀⣯⣁⠌⠂⠒⢙⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⣧⢄⠀⢀⢘⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢁⢨⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⡀⠀⠀⠀⠀⣿⠟⠶⠄⠛⠛⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢣⠀⢠⠀⢠⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠂⢸⠀⠂⢀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠀⢉⣀⡀⠀⠀⠐⠈
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣼⡿⠛⣷⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⡀⡼⣿⣦⣤⣝⠂⠐⠀⠀⠐⠠⠄⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠔⠈⡀⠐⠁⡉⠀⠑⢀⠁⠈⠀⢀⠐⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠄⠀⠀⠁⠠⠀⠡⠀⠀⠀⠑⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂⢠⠀⠀⠀⠈⠀⠀⠁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠠⠀⢠⠃⠀⠀⠂⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠄⠂⠠⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈


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

⠀⣀⡜⣆⣀⠀⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⢠⡆
⠙⣤⠁⠡⡜⠁⠀⠀⠈⠳⠀⠀⣩⠋⠀⠀⠀⠉⢛⡽⡻⠋⠀⠀⠀⠀⢩⠰⠆⠅⠁⠀⠀⠀⠑⠀⠀⡈⠉⠀⠀⠀⠘⢻⡭⠶⠉⠁⠀⠀⠈⠻⡭⠀⠈
⠀⠷⠊⠑⠇⠀⠀⠀⠀⠸⠊⠁⠺⠀⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠀⠀⠀⠀⠀⠛⠁⠙⠂⠀⠀⠀⠀⠘⠃⠈⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠠⢢
⠀⢖⢣⢗⠆⠀⠀⠀⠀⠛⣟⠙⡴⠂⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠀⠘⣭⠁⠈⣭⠃⠀⠀⠀⠒⠆⠉⠲⠂⠀⠀⠀⠐⠖⠈⠐⠛⠂⠀⠀⠘⢭⠁⠀⢩
⠀⠘⠁⠑⠀⠀⠀⠀⠀⠸⠃⠛⠆⠀⠀⠀⠀⠀⠶⠀⠸⠀⠀⠀⠀⠀⠻⠖⠲⠟⠀⠀⠀⠀⠀⠟⠈⠳⠀⠀⠀⠀⠀⠴⠃⠸⠇⠀⠀⠀⠀⠠⠕⠒⠭

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⢖⣚⣓⠖⠀⠀⠀⠀⢶⣾⣿⣶⠆⠀⠀⠀⢈⠉⠀⠈⡡⠀⠀⠀⠠⣄⠁⠀⠒⠂⠀⠀⠀⠠⣤⠻⡤⠀⠀⠀⠀⠰⣖⠋⢓⡶⠀⠀⠀⠰⢦⠈⠀⠒
⠀⠘⠛⠛⠀⠀⠀⠀⠀⠰⠿⠻⠧⠀⠀⠀⠀⠀⠡⠤⠄⠃⠀⠀⠀⠀⢀⠤⠀⢣⠀⠀⠀⠀⠀⠛⠛⢃⠀⠀⠀⠀⠀⠺⠖⠾⠆⠀⠀⠀⠀⢠⠔⠀⢷

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⣄⠊⠂⣤⠄⠀⠀⠠⡆⠀⠈⠀⡦⠀⠀⠀⢤⠐⠁⠓⣠⠀⠀⠀⢰⣟⠃⠘⢻⡆⠀⠀⠀⢤⡀⠃⢤⠄⠀⠀⠀⠤⠀⠀⣀⠠⠄⠀⠀⠠⣤⠘⠑⢤
⠀⣸⠴⢮⡅⠀⠀⠀⠀⢰⡀⠀⣀⠀⠀⠀⠀⠀⣇⠤⣘⡅⠀⠀⠀⠘⢿⣤⣤⡿⠃⠀⠀⠀⠀⡤⠀⢦⠀⠀⠀⠀⠀⡁⢲⣿⡗⠀⠀⠀⠀⢨⡤⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⣀⡀⡀⠀⠀⠀⠀⣀⡠⠧⣀⡀⠀⠀⠀⣀⠴⠋⠢⢀⠀⠀⠀⢀⣀⣰⣀⠀⠀⠀⠀⢀⡠⠞⠀⠳⢆⠀⠀⠀⣀⠠⠇⠤⢤⠀⠀⠀⠀⠚⠁⠁⠙
⠀⠠⠛⢏⠀⠀⠀⠀⠀⠈⡧⢠⡍⠀⠀⠀⠀⠀⢆⣀⣰⠃⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⢹⠀⣀⠐⡏⠀⠀⠀⠈⠓⣠⠐⡆⠀⠀⠀⠘⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉

⣀⠤⠎⠣⠤⡀⠀⠀⠀⣀⣰⢧⣀⡀⠀⠀⠀⢀⣀⣾⣄⣀⠀⠀⠀⠀⠤⠎⠱⠤⠀⠀⠀⠀⣀⠀⡗⢀⡀⠀⠀⠀⣀⠠⠏⠡⢀⡀⠀⠀⠀⡀⢠⢇⣀
⠘⡆⠀⠀⡖⠁⠀⠀⠀⠙⣆⡀⣞⠁⠀⠀⠀⠈⣿⣥⣿⠋⠀⠀⠀⠈⡢⠀⠀⢔⠁⠀⠀⠀⠉⣃⠀⣍⠁⠀⠀⠀⠉⣷⢀⡀⡞⠁⠀⠀⠀⠙⢊⡺⡍
⠀⠓⠉⠑⠂⠀⠀⠀⠀⠘⠉⠈⠉⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠀⠙⠋⠉⠊⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⠀⠛⠉⠙⠃⠀⠀⠀⠀⠘⠉⠀⠉

⠀⠀⡀⣀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡰⢳⣀
⠀⠨⠀⠈⡄⠀⠀⠀⢠⠀⣻⢿⠃⡠⠀⠀⠀⠑⠄⠀⠀⠌⠀⠀⠀⠈⢫⠀⢈⡝⠁⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠈⢣⠰⠷⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠦⢯⠀⠀⡎⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠸⠀⢀⣀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡀⠀⠀⠀⡆⠀⠋⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⢡⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠁⠀⠘⡄⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢱⠀⠀⠲⣏⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⡏⠀⠀⠀⡇⠀⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠈⡆⠀⠀⣽⠀⠀⡼⠋⡉⠙⢦⠀⣠⠶⠷⠦⡀⠀⡇⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠀⢳⠀⢾⣁⡴⠛⠃⠀⠀⠀⣀⣻⠁⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢸⠀⣸⠋⢀⠀⠀⠀⠀⠉⢁⡽⠒⠀⠀⠀⠀⡸⠀⠀⠀⠈⣦⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡖⠀⢸⡀⠙⡆⣾⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢠⠃⠀⠀⠀⣠⣟⠁⠀⡀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣈⣇⠀⢸⡀⣰⠇⠜⠓⡦⠀⢠⠀⠈⢳⡤⠀⠀⢠⠃⠀⠈⣟⠉⠁⠘⠀⠐⠀⠼⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⠟⠁⢀⡠⠤⠷⣀⠀⠂⢰⡏⠀⠀⢰⠃⡀⣀⣴⠏⠀⠀⡠⠊⠀⠀⠀⣹
⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠫⡉⠉⠉⠉⠉⠓⡄⠀⠀⠰⢏⣀⣀⣀⠥⡀⠈⢈⣧⣀⢠⠃⠀⠀⡽⠀⢀⠄⠊⠀⠀⠀⣰⠀⠁
⠀⠀⡴⢧⡀⠈⠢⣄⠀⠀⠀⠀⠀⠙⢄⡀⠈⠑⠒⠀⠒⠊⠀⢀⣀⡀⠀⠀⠀⠀⢰⡇⠀⢹⡁⢀⠇⠀⠐⣎⡡⠂⢁⣀⣠⡟⠒⠚⠁⣠⡶⠟⠂
⠀⢰⠦⣄⣉⠓⢦⣈⠑⢄⡀⠀⠀⠀⠀⠉⠒⠤⠤⠀⠠⠄⠒⡭⣿⣿⣦⣄⡀⠈⠉⢹⢀⡞⠃⡜⠀⢀⣠⠏⠀⡤⠒⠉⠁⠀⠀⠀⣾⠁
⠀⢾⣤⣄⣈⡙⠲⢬⣑⠢⡙⠦⡀⠀⠀⠀⢀⠤⢄⡀⠀⠀⠀⣍⢻⣿⡙⠿⣿⣿⣶⣦⣙⡄⢀⠃⠀⢸⣆⠖⠚⠁⠀⠀⠀⠀⠀⠀⠙⠳⣤
⠀⢸⣀⣀⣈⣉⣛⠒⠒⠭⠄⣒⣼⣷⣄⢰⡧⠖⠢⣍⠈⣰⡄⢻⡘⣿⣧⠀⠀⠉⠙⠻⣿⣦⣾⣆⣠⣭⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠘⡁⢀⣈⣉⣉⣉⣭⣭⠭⢄⡺⣿⣿⣿⡄⠀⠀⠀⠉⠉⠀⠐⣦⠸⣿⣷⣄⠀⠀⠀⢹⣿⣿⡿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣶⣦⣼⠁
⠀⠀⢻⠉⠉⠉⣁⣠⡤⠖⢊⡭⢚⢝⢿⡿⣿⡄⠀⢠⣶⠶⠦⢤⡈⢶⡈⠻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣴⣿⠟⡵⠃⠈⢧⡀
⠀⠀⠀⢳⠞⠛⠉⢀⣤⠞⢉⡴⢫⠎⡆⡇⡏⡜⣆⠀⠀⠀⠀⣸⠇⠀⠙⠲⣤⣉⣉⣁⣀⠈⠻⣿⣿⣶⣶⣶⣿⡿⠟⣡⠜⠁⠀⠀⣸⣧
⠀⠀⠀⠀⠱⣤⠞⠋⢀⣴⠋⢠⠏⣸⠀⡇⡄⡌⡌⢆⠀⠀⠸⣧⣀⣀⣀⠀⠀⠀⠀⠀⠈⠳⢤⣈⣉⣙⣉⣉⣥⠖⠋⣁⣀⣤⣶⣿⣿⢻
⠀⠀⠀⠀⠀⠈⠂⣠⠞⠁⢠⡟⢀⡟⢸⠂⣧⢱⠘⡌⢣⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣠⣾⣿⣿⠿⠛⢉⣿⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡟⠀⣸⠃⢸⠀⢻⠈⣇⢹⡄⠣⡀⠀⠀⠀⢾⡀⠀⠀⣀⣀⣤⣴⣶⣶⣤⣄⣀⣼⣿⠟⠉⠀⠀⢀⣾⣿⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣟⠀⢸⠀⢸⡄⢹⡀⢳⡀⣱⠀⠀⠀⠮⢻⣿⣿⠿⠿⠟⠛⠛⠛⠛⠻⣿⣿⣇⣀⣀⣀⣤⣾⡿⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠘⠧⠼⠓⠚⠉⠀⠀⠀⠀⠈⢳⣝⢿⣷⣤⣀⠀⠀⠀⣀⣴⣿⡿⠿⣿⣿⣿⠿⠛⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⠻⠿⣿⣿⣿⣿⡿⠋⢀⡤⢤⣤⡤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣬⣍⣤⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⢀⠀⢀⠀⠀⣀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⢀⠄⠀⡀⠈⠀⠠⠀⠁⢁⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⡖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣭⠀⠀⠀⠀⠀⠢⣤⣥⡤⠂
⠀⠉⠠⠀⠀⠀⠀⠀⠁⠀⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠈⣻⣿⣾⠟⠁⢠⡀⠀⠂⠐⠆
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⣤⢿⡤⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠚⠀⠠⠟⠋⠛⢇⠀⠙⠛⠀⠠
⠀⠀⠈⠀⣄⠀⠀⠁⠀⣣⢬⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠞⠙⠇⠀⠀⠀⠀⠀⣀⣀⣠⠃⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠠⣤⠞⠘⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠉⠲⡔⠀⠀⣠⠊⠀⠀⠴⠆⢠⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⢨⣃⣤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⠈⠀⠀⢸⣥⠖⠦⣸⡀⠀⠀⣤⣤⣾⣧⣤⡤
⠀⠀⢈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣰⢇⠀⠀⠐⠐⠀⠐⠀⠀⠀⠈⠀⠀⠀⠈⠡⠀⠀⠀⣹⣿⣿⡏
⠀⠀⠈⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⣤⣾⣿⣏⣤⣤⣄⡄⠀⠀⢶⣶⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠋⠁⠈⠓⠀⠀⠈⣇
⠀⠀⠀⠐⠀⢀⡾⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠠⣄⠀⠋⠀⠐⠦⡤⠀⠀⠀⠀⠈⠛⠻⣦⣯⣤⠔⠂
⠀⠀⠲⢶⠶⢋⡴⠟⣻⣶⣦⠶⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⢸⣿⡿⠿⣿⣷⠀⠀⢀⣀⣼⣧⣀⡀⠈⠁⠀⠀⢠⡀⠀⠀⢤⣦⡤⠀⢀⡿⠁⢷⡀
⠀⠀⡀⠈⢶⡿⢁⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠛⠁⠀⠀⠈⠙⠂⠀⠀⢹⣿⢿⡏⠀⠀⠖⠉⠀⠐⠇⠀⠀⠘⠉⠃⠀⠈⠀⠀⠀⠉
⠀⠘⠋⠀⢨⢶⠿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠂⢀⣀⡰⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⢧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⡆⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠂
⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠠⣤⠤⠶⠞⢀⠈⠳⠦⠤⣤⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠸⠛⠉⠛⠇⠠⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠀⢀⡄
⠀⠲⣶⣶⣿⣿⣷⣶⠖⠀⠀⠄⠀⠈⠳⡄⠘⣿⣿⠂⡴⠊⠀⠀⣤⠀⠀⠰⣶⣶⡿⠧⢀⡄⠀⠀⠀⣀⣴⣆⣀⠀⠀⠁⠀⠀⠀⠀⣀⡤⠞⠙⠤⢀⡀
⠀⠀⠈⣿⣿⣿⣿⠁⠀⠂⠀⠀⠐⠂⠀⡇⠀⣁⣉⠀⢧⠀⠐⣾⣿⡶⠂⠀⠈⣹⣮⣶⡏⠀⡀⠀⠀⢙⣿⣿⡁⠀⠀⠀⠀⠀⠐⠀⠈⢲⠀⠀⢰⠋
⠀⠀⠸⠛⠁⠈⠛⠇⠀⠀⠂⠀⠃⠀⠸⠗⠉⠀⠈⠙⠻⠀⠀⠋⠉⠓⠀⠀⠀⠉⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠟⠊⠙⠺⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⠶⣄⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⡀⢈⡆⠀⣠⠾⣻⠟⠋⢀⣀⣀⣀⣀⣀⡤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⡦⠾⣁⠈⣻⠛⠻⣟⣡⢾⡗⠋⠸⠛⢚⣿⣶⠶⣾⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⣾⠁⠀⢹⣟⣻⣦⣤⡿⠛⠿⣿⣿⡛⢿⣯⠛⠉⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢷⣤⣤⣾⡟⠋⠛⣿⠋⠁⢀⡷⣤⣤⡼⢿⣗⡤⢽⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⠚⠿⠛⣄⣒⣴⡿⠿⠿⢿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⣷⣤⣾⣿⠿⢿⡉⠳⣤⡠⠈⠙⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢬⣿⠟⣱⢻⡧⢀⣸⡇⠀⠀⢹⡶⣆⠒⠂⠀⠀⠘⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡾⠟⢰⢋⣽⣫⣾⡇⠜⠓⢶⡿⣷⡀⡆⠀⠃⢈⡳⣞⠃⠀⠀⠈⠙⢓⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡯⣔⠀⣿⡿⠋⠁⡇⠙⣦⠀⠁⠂⢸⡻⣧⠀⠀⠈⣇⠈⢻⣌⠉⠀⠀⠀⠉⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡘⣡⣾⢿⡇⠀⠀⣇⠀⣯⡀⠀⣠⠧⢋⢻⣦⡠⠀⠀⠀⠀⣏⠿⣟⠓⠒⠀⠀⠘⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡿⠃⢸⡁⠀⡆⣽⡀⠀⣹⠆⣠⠂⠘⢾⡇⠙⢦⡀⠀⠀⠙⢸⠀⠳⣖⠒⠀⠀⠐⠺⣆
⠀⠀⠀⠀⠀⠀⢀⡤⠾⣿⠙⣇⠀⠀⣇⠀⠰⢻⣏⠘⠧⡜⠁⠀⠐⠈⣝⣆⠀⢳⣄⣀⣤⡀⠀⠀⠩⠳⣦⡰⠂⠀⣘⣆
⠀⠀⠀⠀⠀⢰⢏⡄⠠⣿⠀⠘⢦⠀⠈⣷⡀⠀⠸⣷⠄⣿⣤⣐⡿⠀⣈⢻⡀⠀⠈⠉⠉⠉⠳⣄⠈⠀⠈⠙⠦⣄⠉⠹⡆
⠀⠀⠀⠀⠀⢸⢸⠃⢰⣿⠀⠐⠘⣆⠀⠀⠹⣴⡀⠟⣷⣌⢧⡘⢦⣤⣇⣆⠹⡄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠒⠚⠿⣦⣿⡄
⠀⠀⠀⠀⠀⠸⣆⠀⠘⠉⣦⠀⢀⠘⢦⡀⠀⠀⠛⠦⠼⣽⣎⣧⠀⠈⠉⠙⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣿⣧⡀⠀⠂⠹⡄⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢳⡴⠀⠙⠉⢳⡄⠈⣄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⣴⠀⣿⡄⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⢷⡸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢿⣿⡄⠀⠀⠀⣰⠞⠛⢿⣤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠾⠟⠛⠛⠋

⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠁
⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⡀⠀⠂⠀⣠⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠽⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠿
⠀⠀⠀⢰⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠈⠁⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿
⡀⠀⠀⠀⠠⠀⠀⠀⢹⡿⣿⡁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⢻⡿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣶⠀⠀⠀⢴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⢴⡦⠀⠀⠠⣼⣷⠄
⠀⠀⠀⠤⣽⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⢀⠀⠀⠀⠰⣾⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠃
⠃⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠟⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⢀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠠⣦⠄⠀⠀⢸⣿⡷⠄⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⣻⣿⡶
⠿⡗⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⠀⠀⠸⢿⠂⠀⠀⠨⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡦
⠀⠿⠆⠀⠀⠀⠀⠂⠀⠀⠛⠙⠂⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠠⣼⣧⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡀
⡦⠀⠀⠀⠀⠈⠛⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⢲⣿⠄⠀⠀⠀⠀⠘⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⣶
⠁⠀⠀⢀⣠⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⢀⣤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠻⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠀⠀⢀⣄⠀⠀⠀⢀⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠀⠀⢠⣄⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⢰⣀⡀⠀⠐⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⡿⠿⠄
⡦⠀⠀⠈⠝⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⣴⣄
⣴⡄⠀⠀⠐⣾⣷⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠚⠛⠏⠀⠀⠀⢠⣴⡀⠀⠀⠰⣿⣗⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠛⠻⠇
⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⣀⣶⣄⣀⣀⣀⣀⣀⣀⣈⣿⣿⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣦⣀⣀⣀⣀⣀⣀⣀⣈⣿⣯⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠁⠀⢸⠃⠀⢀⡎⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡄⠀⠀⠀⢠⣿⠀⠀⠘⠁⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢱⣄⠀⠀⢀⣼⣧⡀⣀⡴⠋⢿⣄⠀⣀⠀⠀⢀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⢻⠳⠶⠟⠃⠈⠉⠉⠀⠀⠀⠉⢹⡏⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣤⡼⠃⢀⣤⠶⠒⠛⠛⠒⠶⣤⡀⠀⠛⠶⠶⠶⢒⡿⠋⠁⠀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⣀⣼⠇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣾⠁⠀⠀⢉⡥
⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠈⢻⡉⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠠⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⣄⠀⠀⠈⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⢦⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⣠⠶⠒⠻⠿⠦⣄
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⣸⠃⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⢠⡶⠿⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠈⠙⠛⠓⠚⠛⠋⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢠⣾⡤⠶⠒⠲⣆⠀⠀⠀⠀⣀⣀⡀⣠⡤⣄⡀⢹⡀⠀⠀⠀⠈⠱⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠛⠛⢷⣀⡾⠉⠀⠙⠃⠀⠀⠙⠿⣧⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⢀⠀⠀⠀⢲⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠘⠇⠀⠀⣾⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠸⠏⠀⠀⠀⠛⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣂⠀⠀⠀⠀⠐⣆⠀⠀⠸⣦⣄⣠⣾⠃⠀⠀⠰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣼⡆⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠰⢿⣾⠃⠀⠀⣀
⠀⠀⠀⠀⣼⣿⡆⠀⠀⠁⠀⠻⠷⠀⢀⣀⣀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣶⣦⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⢠⣦⣅⡀
⠀⠀⠀⠰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢿⣿⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣹⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢻⡇
⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡿⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠸⡇
⠀⠀⠀⠀⠀⠰⠄⠀⠠⠒⠀⠀⠠⠀⠹⠀⠸⠧⠀⠘⠉⠩⠅⠀⠀⠠⠄⠄⠀⠀⠠⠄⠀⠀⠠⠤⠀⠠⠄⠠⠄⠀⠛⠀⠀⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⡜⠻⠄
⠀⠀⠀⠀⠠⠔⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠀⣴⡴⠂⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠸⢀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⡼⡿⠿⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠸⢰⣿⡿⣿⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠄⠒⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣾⠟⠏⠈⢣⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣤⣯⠤⡀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣰⠃
⠀⠀⠀⠀⢀⡙⠻⠿⠷⠾⠿⣫⡄⠀⠀⠀⠀⠀⠀⠈⠲⢼⡷⠀⠀⠀⢠⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⢤⠇
⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣁⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠂⠒⠚⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠢⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⡇⠀⠛⣿⡿⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠲⠤⡌⣉⠀⡤⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⣼⡄⠀⠀⠘⠙⠓⠒⠒⣒⣲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠺⣿⣧⡠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⢻⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣷⣂⡀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣿⠧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣿⣷⣦⠀⣡⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥
⠀⠀⠀⠀⠀⢀⣿⣻⣛⡓⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠲⠤⠭⠭⠙⠂⠈⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠲⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖
⠀⠀⠀⠙⠻⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⢀⣠⣾⣷⣄⡀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⣠⣴⣿⣿⠟⠻⣿⣿⣦⣄⠀⠀⠀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢀⣴⣾⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣷⣦⡀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⡸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢠⢰⣖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣤⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⡀⠀⠀⠀⢽⣦⠄⠀⠘⢉⣿⣖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢢⣌⠈⠀⢁⠝⠳⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠂⣸⢰⣾⢏⡞⣼⣷⠀⡠⠀⠖⠀⠀⠀⠀⢉⢿⣭⡅⠀⡀⠀⡀⢠⢠⢠⡆⡀⠀⢀⣉⠋⠁⠀⠀⠐⠿⣝⠿⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡙⢦⠡⣔⠈⡏⡾⠐⡿⣫⠞⣠⠾⡃⣷⡟⠰⠀⠈⢷⠿⠷⢤⡈⠃⠳⠈⠋⣘⢿⢔⣅⣤⡄⢆⣠⠀⡀⠀⢦⣛⢿⡃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⠌⢀⠁⠘⠀⠃⠀⣠⠖⡡⠎⣲⡿⢷⣛⡯⠀⢰⠁⠎⠀⠒⠾⢿⠎⠀⠀⠐⢁⠤⠿⠿⢾⢵⠟⠇⠌⠃⣀⠘⢏⠛
⠀⠀⠀⠀⠀⠐⠛⠛⢺⣿⡢⠶⠁⠀⠀⠀⠔⠁⠀⢴⣩⣵⣾⣯⣶⣤⣤⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠐⠉⢹⣥⣭⣉⠀⠀⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⣂⣀⠀⠈⠉⢀⠀⠉⠀⠀⠀⢐⣚⣢⣬⣤⠤⠶⠶⠶⠶⠤⠀⠀⠀⠀⡀⢚⣤⡆⢠⡀⠀⠙⢦⣍⢾⣕
⠀⠀⠀⠀⢀⣩⠴⠒⠂⢀⡠⠄⠀⠀⠈⠀⠀⠀⢈⠄⠀⠤⣽⡿⢶⣦⣤⡀⠀⠀⠀⠈⠐⡿⡻⣠⠈⠇⢀⠀⠸⣌⠛⠂
⠀⠀⠀⠀⠀⠔⠪⠀⠀⠜⡴⡀⣢⡄⠄⣀⠀⠀⠀⠑⢧⣤⡉⢙⣯⣓⠶⠄⠀⠀⠀⢠⠀⡇⣥⡟⣦⣶⣿⢿⡷⠈⡀
⠀⠀⠀⠀⠀⠠⢒⡥⢆⣴⡾⣣⣾⠃⠀⢿⡄⠘⠀⠀⢀⢰⡾⣷⢭⡛⠗⠀⠙⢦⣄⠲⡙⡆⢸⠛⣽⢃⣿⡿⣠⠞⢁⣤
⠀⠀⠀⠃⠀⠀⢉⠔⠹⣿⡟⣹⠏⢠⠀⠉⡇⠀⡐⠀⠀⢳⣧⡀⠑⢽⣲⢦⣐⠢⠙⠧⠙⡆⢸⠀⠁⠐⢋⡼⣫⢖⣫⣤⣀⣠⠤
⠀⠀⠀⠀⠠⠀⠀⠀⠔⠙⠰⡝⠰⢀⠇⠀⠅⠠⣧⠂⢈⣆⠉⢳⣀⣤⣄⣙⣶⡕⠠⠦⡀⠀⠈⠀⢀⠼⠋⠜⣉⠵⢚⣫⡭⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠆⠄⠀⡆⡆⣴⣿⣄⠘⡜⠃⠀⠉⠰⠾⠻⠿⣍⠺⠃⢀⡀⠀⠐⠋⠀⢀⠚⣶⠾⠿⠿⠿⠿⠶⠶
⠀⠀⠠⡀⡀⠶⢲⣧⡀⠀⡀⠈⠳⣅⢘⠏⡏⠏⣽⣣⢊⡤⠀⢀⣀⡩⠤⠀⠀⠀⠀⠤⠀⠀⠐⠈⠀⠨⣍⡽⠶⠶⣖⣚⠛⠛⠛⠻⠆⠀⢠
⠠⠭⣧⡄⠀⠀⠚⣉⣿⣞⣛⢳⡄⢈⠀⠃⠁⢠⠖⠕⡹⢾⡶⢯⡤⠖⡛⠋⢉⡠⠄⠀⠀⠀⠁⠀⠀⠀⢀⠠⡀⠰⢶⣽⠻⠷⣶⣤⡄
⠀⠴⠀⠀⠀⠀⠈⠛⢪⣭⣛⠛⠿⠃⠠⠀⠀⠁⢠⣓⡚⣛⣛⣳⣖⠩⢒⠀⡴⡠⠂⢘⣔⠠⠂⡆⠀⠀⠀⠙⢮⣦⣄⠩⣻⢭⣓⢶⣄⢀
⠀⡀⣺⣴⠂⡆⠀⠙⣾⣿⡿⠂⢀⠀⠀⠀⠀⠀⠙⠈⠩⣵⢶⣤⣩⢖⣥⠖⣠⣶⢏⣼⡿⠀⠀⣷⠀⠘⠆⠀⢀⠨⣪⣷⣮⣝⠿⡿⠋⡛⢦⣆⡀
⠀⠀⠋⠃⠀⠀⣰⠠⡙⠊⠃⠰⢶⡀⣦⠀⣄⠀⡀⠙⢶⣌⡹⣿⡓⠙⡡⢊⣿⣵⢏⡿⠁⠀⠀⢻⡇⠀⠀⡀⠀⠱⣽⡈⠛⢿⡳⠆⠈⢠⣞⡿⣷
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠊⢴⣿⢺⠃⠀⢻⠀⠀⠀⢸⣏⠻⡪⠁⠈⠀⡠⠫⢃⢮⢃⠆⢣⠀⠈⡇⠀⣇⠇⠀⣦⠙⠻⣏⡀⢀⠀⠀⠀⣄⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠎⠂⡇⠀⠀⣿⠀⣦⠙⢆⠀⠀⡀⠀⠁⠀⠈⢎⢊⢀⠊⢠⠀⠁⣰⣿⠀⠈⡞⡧⠐⠻⣿⡟⠐⡇⠀⠨⡟⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⡘⠀⢸⢸⠀⠹⠁⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠇⠸⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠎⠈⢻⣿⡄⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠒⢡⣶⣤⣤⣾⣿⣿⡆⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠈⠊⠋⡟⣿⢿⣿⣿⡄⠀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠃⠀⠌⢠⠀⣿⠸⣏⢿⣿⣿⡃⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⢁⡔⢁⡌⢀⠋⠀⠿⠀⣿⡈⣿⣿⣿⣞⠃
⠀⠀⠀⠀⠀⠀⣆⣀⣠⠐⠺⠇⠔⡠⠊⠐⡜⢀⣾⠁⢀⣺⠀⢻⣇⠸⣿⣎⢿⣷⣤⡟⠂⣄⣀⢰
⠀⠀⠀⠀⠀⠀⠃⠈⠻⠀⢀⡴⠒⢁⣔⠞⠀⣼⢿⣴⣾⣿⡄⢸⡿⡆⠹⣿⣦⡙⢿⣿⣦⣽⠁
⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶⠗⠀⢴⠿⠋⠀⣴⣿⣿⠟⣛⣷⣧⣀⢿⡱⡄⠘⣿⣷⣌⠛⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠐⣦⣀⣠⣏⡁⢀⣨⣍⠁⠀⢈⡟⠉⠹⣿⠋⠋⠛⡟⠘⠓⠳⡀⠈⠻⠛⣗⠐⢛⣿⣭⡿⠟
⠀⠀⠀⠀⠀⣿⡏⠈⣹⡿⠻⠋⣿⣿⠿⠛⡷⢁⣼⣿⣄⣦⣦⠿⢷⠶⣿⣿⣶⣶⢾⣿⡟⠻⣿⣿⣷
⠀⠀⠀⠀⢀⣷⠀⢀⣿⠇⠀⢰⣿⡇⠀⢜⣵⣾⣿⣿⡏⡜⣿⡆⠀⠀⣿⣿⡀⠁⠸⣿⣷⠀⢹⣿⣿⡄
⠀⠀⠀⠀⣼⡇⠀⣼⡟⠀⢀⣿⠿⣒⣴⠟⣰⣿⣿⣿⣿⣾⣿⢻⠀⠀⢹⣽⡇⠀⠀⣿⣿⡆⣈⣿⣿⣷⡀
⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⢾⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣄⣀⣸⣿⣿⣤⣴⣾⣿⣿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠐⠊⠈⠁⠁⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠙⠉⠉⠉⠉⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⢄⠀⠠⠀⠂⢀
⠀⠀⠀⠀⠂⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠈⠀⠈⠀⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢣⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⡒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠢⠀⡀⠁⠈⢈⠀⠀⠀⢀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠄⢀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠄⡃⠰⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠺⠄⢳⡀⡿⠣⢀⣗⠅⡀
⠀⠀⠀⠀⠂⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⢒⡙⠦⠤⠅⠀⠐⡡⠴⠃⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢋⠛⠇⠀⢀⢩⣐⢒⡖⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡟⣤⠊⡠⢸⣀⣈⣳⡈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢁⡜⢣⢘⠁⣯⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠆
⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⣰⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠀⢈⡿⣦
⠀⠀⢀⣹⣟⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠶⢶⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⡄⣼⠆⠀⡄⠀⠀⠀⠀⠀⠈⠟⠀⣾⠡⣼⡀
⠀⠀⠈⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠅⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⠘⠋⡀
⠀⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⢠⡟
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣿⣆⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢸⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⠏⢿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣁⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠈⣿⣿⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢠⣀
⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻
⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠚⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⢀⠀⠀⠀⠀⢈⡷⢤⣀⠀⠀⠀⠀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡜⣁⡤⠴⠾⠷⣤⣤⣴⢋⡴⣿⣫⣳⣄⠀⠀⣿⢸⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠶⢦⣤⣀⡀⠰⠿⢷⣓⣦⣠⢤⣴⣿⣿⣣⡆⠀⠀⠀⠀⠙⢯⠈⡇⠐⣼⡿⢍⡑⣄⣽⠾⠁⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠍⠀⠀⠀⠠⣀⣈⣿⣿⣦⠀⠀⠀⠁⠀⠀⢸⣿⡇⠛⠿⠃⠀⠀⠀⠀⠈⣇⣿⠐⣼⣿⡆⠘⣏⠀⣠⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠓⠀⠀⠀⠀⠈⠀⠀⢹⣿⣿⣧⡤⠚⠋⠉⠉⢹⡏⠉⢤⡀⠀⠀⠀⠀⠀⠀⣿⣌⢁⣿⣿⠃⠀⢿⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣄⡀⢀⣠⠀⠀⠀⠀⠀⣹⣿⠏⠀⠀⠀⠀⣀⡼⠃⠀⣀⣹⣿⣶⣦⣤⣀⣀⣈⠻⠿⢛⣁⣀⣤⣟⣈⣿⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⠉⠛⠻⣿⣦⣀⠀⠀⣿⠏⠀⠀⠀⣴⠟⠉⠷⣾⡋⠉⠁⠀⡽⢻⡟⠛⠻⣿⣿⡛⠛⠛⠿⠍⠉⠉⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣷⣼⠏⠀⠀⢀⣾⠃⠀⠀⠀⢸⣟⠂⢀⣰⠀⢸⡇⠀⠀⠙⢟⢮⠃⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠻⣶⡀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⣼⡟⠀⠀⠀⠀⣼⠉⠛⣿⣟⠀⣾⠁⠀⠀⠀⠸⡆⠀⠀⠀⢠⣷⡾⠃
⠀⠀⠀⢀⡄⠀⢸⡇⠀⠀⠀⠈⠻⣤⠀⠤⠊⢹⠃⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠇⠀⢀⣿⣿⢰⠇⠀⠀⠀⠀⢰⣧⣤⡶⠿⠛⠉
⠀⠀⠀⢸⣿⣦⣿⠁⠀⠀⠀⠀⠀⢫⠀⠀⠀⣸⣧⣤⣆⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡟⠀⠀⠀⠀⢀⡟⠉
⠀⠀⡠⣾⠋⠀⠙⠤⣼⠿⠷⠾⣦⣼⣇⠀⠀⣉⠻⣿⣿⣿⠏⠀⢀⡀⡀⡄⠀⣆⢸⡿⠈⠟⠀⠀⠀⢀⡤⠋
⠀⢰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡻⢿⣺⡃⠀⠋⠀⠀⣿⣿⣿⣿⣿⣾⣧⣧⣀⣀⣑⣒⣿⠟
⠀⡇⠀⢰⠀⠀⠀⠰⡀⠀⠀⠀⣸⠀⠀⢻⡇⠀⠙⠇⠀⠀⠀⣼⡿⠟⠻⢿⣥⣀⠀⠉⠙⠛⠉⡙⠁
⠀⡇⠀⢸⡇⢰⡀⠀⠹⣦⡀⢠⡟⠀⠀⠈⠁⠀⠀⢸⡂⠈⣿⠏⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠋⠁
⠀⢻⢆⢸⡇⠈⣿⡶⢦⣼⣿⣾⣇⠀⠀⠀⠀⣀⣴⠯⠄⠊⠁
⠀⡀⢠⣿⡇⠀⡟⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁
⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

⡿⢿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⡿⣿⣿⢿

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠠⡏⠀⠀⠀⠀⠈⠉⠑⢆⠀⠋⢰⠋⡠⠄⠀⠓⣄⠀⠀⠀⢘⠁⣀⠥⠀⠀⣌⢮⠑⠁⢀⠀⠀⠀⠊⢄⡊⠀⠠⠀⠁⠄⢱⠀⢛⣌⠂⠀⢀⡠⠤⣤⣄⡁
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢤⣋⠃⠀⠘⡄⠈⠂⡄⡀⠈⠆⠀⢠⠁⠀⣁⠀⡸⠀⠀⠀⠐⡂⠀⠐⠀⠠⠀⠀⠀⠆⠀⠀⠐⢀⠆⠀⣀⠑⠃⠰⡯⡤⠄⡹⢺⠁
⠀⠀⠀⠌⡄⠡⠀⠀⠔⡠⠌⡳⠀⠀⠘⢆⡀⠠⣈⠢⣘⠀⠀⠙⡝⡣⢬⠁⠀⠀⠀⠠⠅⠀⠀⠸⠀⠀⠠⠁⠀⠀⠑⡠⠋⠀⠀⠉⠓⢄⠀⡄⠀⠀⠀⢸
⠀⢀⡀⠰⣉⣉⡀⠤⠂⠂⠉⣀⣀⢀⣀⡀⠈⠒⠈⠔⠀⢠⢶⠀⢛⠽⣳⠀⠀⠀⠡⡡⠊⠘⢄⢀⠰⢀⠅⡀⠀⢂⠜⠁⠈⠦⢇⣀⣀⡘⠀⠃⠠⠤⠔⠈
⠀⠈⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⠃⠌⠠⠉⢲⡀⠀⠀⣿⠙⠀⠈⣞⡜⠀⠠⠬⡶⠁⠀⠀⣸⡀⢀⠐⢄⡩⠔⢁⠄⡀⠀⣀⠀⣀⠌⠀⠄⢠⡀⠀⠀⢒⠄
⠀⠀⢀⣄⡀⠁⠀⡈⢁⣀⣎⡀⠦⠬⠐⡦⣮⠵⡎⠀⣀⣤⣄⢀⠀⢻⡃⠀⠀⠀⠙⡂⠐⡦⠛⠬⠂⠀⠀⠀⠀⠌⡔⢀⣀⠀⠉⠉⠀⠐⠂⠁⠀⠆
⠀⠀⢿⠀⢹⡄⠘⠰⠒⠠⠐⠚⠒⠒⣉⣀⡤⠞⠀⢘⠇⠀⠀⢉⡗⠀⢠⠄⢠⠀⠀⡀⠼⠀⠀⠀⠀⢀⣤⣄⣤⣎⠀⠈⠋⠀⠊⠑⠀⠀⠈⠀⣀⡀⣀⠂
⠀⠀⢸⢀⠤⠑⡄⠀⠉⠓⠃⠉⠉⠉⠉⠀⠀⠀⠐⡼⠀⠀⠀⢸⡇⠀⢠⠰⠀⠀⠎⠁⠃⠀⠀⠠⣿⣿⣝⣿⣵⣿⣷⠀⢠⠄⠀⠀⡆⠀⠤⣼⡁⢠⠍
⠀⠀⢱⡈⠒⢀⡇⠀⠀⠀⢳⠚⠒⠀⠤⠄⠒⢶⠂⠈⠃⠒⠶⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡼⡅⠀⠀⠀⠀⢃⠀⢄⣀⡠⠃⠀⠀⠉⠉
⠀⠀⠀⠙⠙⠋⢀⠴⡀⡀⢄⠉⠀⠐⠒⠒⠊⠁⠀⢀⢠⡠⢂⡀⠀⠀⣀⠁⠀⠀⠒⠒⡶⢦⠀⠉⠉⠀⠀⢘⠻⠀⠉⠁⠀⢀⠇⠀⠀⠀⡀⠀⢣⠈⠂⢢
⠀⣰⠂⢐⠀⢠⠃⠀⠉⠁⢈⠀⠀⠀⠠⠄⠤⡄⡖⣆⡿⠿⢉⡕⢀⡔⢱⠊⠉⠌⠉⠉⠐⠁⠀⠈⠒⠀⠤⠀⠀⠐⠀⢠⠌⠁⠀⠁⠀⠞⠁⠀⢀⠗⠲⣎⠄
⠀⠈⠉⠀⢀⠆⠀⠀⠀⠀⠄⢠⢤⠀⢲⠒⠀⠛⠁⣀⠠⠔⢋⡔⠹⠃⠈⣰⣹⠟⠉⠀⠒⠀⠒⡄⠀⠶⠀⠀⣠⣀⡀⣠⡄⠀⣀⠀⢰⠁⠂⣰⠁
⠀⠀⠀⢀⠎⠀⠀⠐⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⢉⡀⠀⣠⣈⡥⠴⠖⠚⠋⣡⣄⢠⠀⠀⠀⢀⠇⠀⠀⣤⢒⠇⠨⠄⠤⠀⠅⠘⠠⡀⠙⢁⠼⠂⡀⣀
⠀⢀⠀⠰⢈⠋⠣⣀⠄⠀⠀⢀⡂⠀⠤⠄⠀⠀⠙⠁⠀⠁⠀⣤⠀⠀⠀⢞⣭⠍⢸⡀⣀⠔⠁⣀⠀⠀⡀⠀⠠⡈⠉⠉⠁⠉⠉⠁⡁⠀⠀⠀⡘⠀⠀⢁
⠀⠘⢤⡀⠀⠈⠁⣁⡀⠀⠀⠰⠺⣾⠪⠀⠁⢠⣶⠶⠒⠒⠠⢟⡦⣄⡀⠘⠁⡠⠀⠉⠀⠀⠈⠊⠀⠀⡆⠁⠀⠀⠀⠉⠀⠁⠀⢹⠁⠀⠀⠀⠇⠀⢀⡘
⠀⠀⡀⠄⠲⢈⠜⠁⢀⠀⠀⠀⠀⠑⠄⠀⠠⠋⠀⠀⠀⠀⠂⡈⠉⠉⠀⠐⠏⠄⢀⠀⠄⠠⠔⢈⣆⠈⠑⠂⠠⠤⠤⠤⠤⠤⠔⢚⠳⠀⠀⠰⠈⠀⠁⡇
⠀⢨⠁⠙⠀⡁⠆⠀⡠⢀⡠⠄⠤⢄⠀⠀⠁⠀⠀⠀⠀⢈⡄⠀⠔⠈⠉⢂⠀⠈⠁⠐⠀⠄⠂⠉⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠈⠀⢀⣎⡆⠐⠤⢤⠰
⠀⠀⢅⢐⡂⠠⠔⠁⠠⡃⣰⠉⢱⠀⢧⠀⠛⠀⠀⠐⠚⠛⠁⠜⠀⠀⠐⠸⡄⠐⡄⠠⠜⠀⢂⠉⠆⠀⠏⠐⡀⠄⠀⠀⣀⠐⠠⠀⠀⠓⠇⠀⡇⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢁⢀⡠⠃⣾⠑⠒⠒⠄⠠⠊⠈⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠼⠒⠀⠀⠒⠺⡀⠀⠀⣈⡆⠀⠀⠀⠀⡀
⠀⠀⡁⢨⠽⢹⣀⢓⡀⠈⠢⠚⠁⠀⠀⢰⠁⣀⡤⠊⠀⡇⡀⠰⠿⠀⠃⢸⠀⠈⠄⠉⡁⠀⠀⢀⠴⠊⠁⠀⠀⢀⠔⠂⠀⠉⡹⠊⠀⠀⠀⢾⣟⣀⠤⠂
⠀⠈⠁⠀⠠⡀⠸⢘⡀⠀⠰⣉⣈⡳⠀⠀⠁⠘⠘⡄⠀⠡⡐⠀⠀⢈⣠⠎⠀⠀⠀⠈⠁⢀⠄⢃⠀⠀⠀⠤⢀⠀⠀⠀⢀⡼⠡⡮⠀⠀⠒⠊⠉
⠀⠀⠀⠓⠀⠃⣉⠉⠁⠀⠀⠁⠀⢠⠄⠀⡄⠀⠤⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠨⠦⠀⣑⠬⠤⣉⣒⣒⠚⣥⢊⡛⠋⠥⠐⠊⠁⡄⠄⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠁⢈⠀⠀⠀⡉⡕⢀⠈⠒⠬⠀⢀⣤⡀⢰⡋⠉⠉⣷⠀⠉⢱⠀⠀⠃⠀⠀⠀⡀⠀⠀⢀⡠⣤⠀⡠⢦⡀⣀⠤⡀⢀⠉⠀⠀⠀⠀⠀⠈⠖
⠀⢠⠀⡀⠢⠀⠠⠐⠀⠀⠱⢡⠞⠁⠀⠀⠀⠱⡤⠜⠀⠇⠀⢸⠇⠀⠀⡆⠀⠈⠢⠀⣠⡔⠁⠀⠀⠈⠠⠋⠈⠄⠎⠀⠅⠠⠁⠀⣴⣤⢂⡘⠃⠁⢆⣀⡄
⠀⠀⠉⣀⣤⠐⠤⡀⠀⠀⢀⢰⠀⠀⡠⠒⠒⡄⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⠠⠤⠀⠀⠀⠀⣠⠃
⠀⠀⣼⢳⣽⣐⡟⠉⠀⠼⠄⢈⠔⠉⠀⠀⠂⡄⠀⢀⠔⢁⡀⠤⠵⠆⠀⠄⠠⠄⠂⡚⠀⠀⠀⡀⠔⠈⠈⠉⡶⠻⡿⠥⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠔⠁
⠀⠂⢻⡶⠒⠉⠀⠀⡄⠀⠀⠸⢀⠀⣀⡠⠊⣤⠀⡇⡰⠋⠀⢠⢤⠀⠑⠒⠒⠒⠊⠀⠀⠐⠀⣀⣀⠤⠤⠔⠁⠀⠈⠢⣀⠀⡀⠀⠠⠄⠁⠀⠀⣀⣀⢺⠃
⠀⠀⠀⠈⠐⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⣠⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⣿⡿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣤⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣃⠀⠈⠀⠀⢾⣷⠀⠀⠀⠀⠀⠀⡀⣸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣅⡄
⠀⠀⠞⣱⡿⠛⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠳⠒⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣭⢹⣀⣀⣸⡀⠀⠀⠀⠀⠀⢠⣴⣄⣰⣿⣦⢾⡿⣷⠰⠶
⠀⠀⢀⣿⣧⠀⠘⠓⢲⣮⣁⠀⠀⠀⠀⠀⠘⠛⣿⣿⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣟⣿⠀⠀⠀⠀⠀⠰⠾⣞⠿⠶⣿⣾⠟⠛
⠀⠀⣼⠃⠸⡇⠠⠴⠟⡆⠉⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣤⣴⣦⣦⣬⠉⠀⠀⠀⠀⠀⠀⠉⠉⢀⣤⣬⣿⣤⣤⡀
⠀⠈⠃⠀⠀⠛⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⣀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣰⠎⠉⡀⠄⠠⠉⢰⠀⠀⠀⠀⠀⠀⠰⠛⠋⠉⠉⠛⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⢠⡤⡶⣦
⠀⠰⠂⠄⠁⢀⣀⠀⠈⠄⠸⡄⠀⠀⠀⠀⠐⢄⠀⣀⣤⣤⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣰⣴⣾⣿⣿⣿⣶⡴⡀⠀⠀⠀⡘⠀⠀⠈⢣⡠⠤⢤⡀⠀⣀⣤⡀
⠀⢗⠀⡃⠀⣻⠿⡃⠀⡀⠀⠇⠀⠀⠀⠰⠂⣝⢉⡉⣿⣿⡟⢲⡎⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⡟⠛⠛⠋⠀⠀⠀⢁⠀⢀⡀⠊⠱⡀⠀⠳⠔⠁⠀⢸
⠀⠘⢇⠀⣲⠃⡀⢹⡔⢀⠜⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡏⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⡀⣿⣿⠇⣆⣀⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠱⢄⠀⠀⢀⡠⠊
⠀⠀⠈⡽⠧⠤⡤⠠⠿⡌⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣿⣧⣤⣤⣄⠀⠀⠀⠀⠀⢀⣈⣩⣤⣽⣿⣦⣬⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⠆
⠀⠀⢸⣸⠃⠀⠀⠠⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣦⡝⢿⠏⡀
⠀⠀⢸⣿⣷⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⢎⣫⣖⡻⢿⣛⡛
⠀⠀⢸⠀⠈⠧⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⣼⣋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡄⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⣟⠥⣊⠥⠒
⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢠⣿⠃⠉⠳⠄⠀⣀⡀⢿⠀⠀⠀⠀⠀⠀⣿⣷⣟⢿⡏⣱⣶⣄⠀⠀⠀⠀⠀⠀⠾⠡⠊⡡⠊⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⠟⠈⡷⠀⠀⠀⢀⣽⣅⣿⡀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣀⡀⠀⠀⠀⠀⠀⡁⠀⠀⣼⠀⠀⠀⠁
⣤⠀⢶⡆⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⣀⣀⠰⡶⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢠⣦⣀⣀⣀⣽⣿⡟⠉⠀⠀⠀⠀⠀⠀⡁⠀⠀⠙
⠈⠓⣻⣿⣉⣉⣁⣀⣀⣀⣂⡀⠀⠀⠘⠉⣽⡿⣆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠸⣿⣿⡁⡄⡝⣿⣿⠀⠀⠀⠀⠀⠀⠀⣥⡄⠀⢀⣄⢀⣤⡀
⠀⠀⠉⣿⣇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⢿⡄⠙⠒⠂⠀⠀⣀⣀⣸⣿⣿⡇⠀⠀⠀⠀⠙⠿⠦⣤⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⠁
⠀⠀⣴⠏⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⢠⡇⠰⣶⣶⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣠⡀⣠⣼⣤⡀⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠛⠛⠻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠘⣿⣿⡀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⢀⣼⠛⣿⣿⠁⠀⠀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣄⣀⡀⣹⣿⠷⢤⣀⡀⢀⣼⣿⣦⠀⠀⠀⢠⡟⠁⢀⡿⠿⣄⣀⣤⣶⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠉⠉⠛⣻⣧⣀⠀⠀⠙⠻⣿⡿⠉⢷⡀⢠⣿⣷⣴⠋⠀⠀⢸⠿⠛⠋⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣿⣿⣿⡿⠛⠲⢤⣄⣈⢧⡀⠈⢷⡞⢹⡟⣁⣠⣤⣶⣇⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⢤⣄⣉⠙⢻⡦⢸⡇⢿⣿⣅⣠⡴⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠿⣿⣿⠉⠋⠉⠉⠉⢻⠋⠉⠉⠉⠛⠛⠓⠒⠒⠲⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⣀⣀⣠⣤⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⡇⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣶⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠦⢤⣤⣤⣤⡼⠷⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⣿⣷⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⣼⢏⣿⡜⣧⡀⠁⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⣴⣿⠋⣼⡿⣷⡘⢿⣦⡀⠀⠁⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠘⢀⣀⣤⣾⠿⠛⢁⣾⣿⠃⢻⣷⣄⠙⠿⣷⣤⣀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠴⠶⠟⠛⠋⠉⠀⠀⠀⠈⠉⠋⠤⠈⠿⠿⠷⠤⠬⠝⠻⠿⠷⠶⠤⠬⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⣿⣿⣿⠋⠉⢩⣿⣿⡟⠛⠛⣿⣿⡟⠛⠻⣿⣿⡿⠛⠿⢿⣿⣿⠿⠿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⢀⣼⣿⣿⠃⠀⠀⣾⣿⣿⠇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⡀⠀⠈⢿⣿⣧⡀⠀⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣶⡶⠛⠛⠃⠂⠐⠛⠛⠛⠃⠀⠀⠘⠛⠛⠛⠀⠀⠈⠉⠉⠁⠀⠀⠈⠛⠙⠃⠀⠀⠈⠛⠛⠛⠀⠀⠘⠛⠛⢲⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣴⡇⠑⠀⣿⣧⣤⡴⠃⠱⢤⣤⣿⡄⠤⠚⢄⡀⠀⣠⠓⠤⣤⣿⣤⡤⠞⠈⢦⣠⣼⡇⠒⠀⣿⣦⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⢀⢪⣿⣿⠑⢂⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⢸⣿⣿⣿⠁⠀⠀⣸⣿⣿⡇⠰⠈⢸⣿⣿⠀⠉⠰⣻⣿⣿⡇⠀⠀⠸⣿⣿⣿⠀⠀⠸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⣼⣿⣿⡿⠀⠀⠀⣿⡟⣷⡟⠀⢀⣼⣿⣿⢧⡀⠀⢹⣶⠟⡇⠀⠀⠀⣿⣿⣿⡄⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⢀⣿⣿⣿⡇⠀⢠⢰⣼⣿⣿⣇⣠⡾⢡⣿⣿⡌⠻⣦⣸⣿⣿⣿⠐⢠⠀⢻⣿⣿⣇⠀⠀⠸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⣸⣿⣿⢿⠰⠆⠈⢸⣿⣿⣿⡿⠋⢠⣾⣿⣿⣧⢀⠙⠻⣿⣿⣿⡄⠈⠀⠾⣿⢿⣿⡄⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⡀⣿⣹⣿⡆⠀⢠⣤⣿⠿⠛⠁⠀⣰⣿⣿⣿⣿⣿⠀⢦⠀⠈⠙⠿⣷⣦⡄⠀⢿⣾⣿⣡⠀⡀⠈⢿⣿⣿⣧⡀
⠀⠀⠀⢠⣾⣿⣿⣿⡄⠸⠀⣷⣿⣿⣿⠀⠀⠀⠻⣇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠀⠈⢷⡀⠀⠀⣰⡟⠀⠀⠸⣿⣿⣿⣆⠀⠲⠘⡿⣿⣿⣷⣄
⢀⣠⣴⣿⢻⣿⣌⣀⣀⣀⣼⣿⣿⣿⣇⣀⣀⣀⣄⡙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠘⢿⣷⡿⠋⣀⣀⣀⣀⣿⣿⣿⣿⣄⣀⣀⣈⣿⣼⣿⢻⣷⣄
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣭⣤⣤⣅⠀⣦⢱⢂⢞⣵⡶
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⡾⠛⠉⠀⠀⣹⢆⡿⡞⢠⡾⠉⢀⢀⣀⣠⠴⣖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠙⠁⠀⠠⠖⠋⣼⣡⡄⣨⠀⣶⢈⣽⢏⣴⡿⢋⣽⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠶⣤⣤⣤⣄⠀⠋⣸⡇⡿⠂⣿⢫⡏⣾⡟⠛⠉⠁⣰⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢋⡴⢖⣒⣒⠂⠈⢻⡀⠹⠇⠂⠀⠀⠀⠰⢿⣧⣄⣮⣾⠟⠁⣠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⢋⣾⠟⠉⠉⠁⢀⡾⢀⣶⡶⣷⣬⣕⣒⠦⠤⠉⠉⠉⣀⣤⣾⡏⢜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⢹⡈⢿⣤⣠⣤⡴⠟⣡⣾⡟⣶⡿⣩⡿⡿⣛⣿⣷⣞⡻⢟⣿⣋⣀⣈⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠚⠯⢭⣛⡻⢧⣿⣼⣷⡟⡞⡞⢛⠓⣿⢟⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣝⣻⠾⣿⣿⣭⣧⣽⣿⡿⠏⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣭⣭⣁⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡍⣅⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢜⡿⡦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣠⣄⡤⠊⢴⠏⠐⡇⠘⠧⠙⡂⢄⣠⣤⡀⣠⠄
⠀⠀⠀⠀⠀⢈⢇⣿⠸⡑⡇⣿⢋⠀⠀⠀⣀⢠⡔⣼⢳⢠⣀⡀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣾⣾⣷⣿⣾⣷⣷⣿⣾⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠸⢸⠇⢠⣧⠹⢸⡌⡀⠀⠀⡌⣼⠃⣱⡼⡞⣇⠆⠀⠀⠀⠀⠀⠙⠙⠙⠛⠋⠋⣿⣿⣿⣿⣿⣿⡟⠉⠋⢻⠋⠋⠛
⠀⠀⠀⠀⠠⠣⠋⠠⠿⠿⠷⠀⠳⠅⠀⠜⠐⠃⠴⠿⠿⠄⠘⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣶⣿⣿⡁⣿⣿⣿⣿⠟⠛⢇⣤⣀⣸⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⣀⣬⣧⣄⡀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⡏⠉⢿⠃⠛⠻⠿⠃⠀⣴⡇⠿⣹⠟⠛⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠐⣶⡾⣟⠋⠉⠉⡏⠉⠉⢓⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡿⢠⣤⡄⣼⡇⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠤⢤⣀⡴⠋⠀⣨⢷⠚⠙⡏⠙⢲⣾⡁⠈⠳⣄⡤⠤⠄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣿⣿⣾⣿⣷⣿⣧⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠰⣶⣶⡿⠛⢢⣾⡁⠈⢧⠠⡇⢠⠟⠀⣹⣶⠚⠹⣶⣶⠆⠀⠀⠀⠀⠷⠾⠶⠷⠾⠷⠿⠾⠷⠾⠶⠷⠾⠶⠿⠾⠷⠿⠶
⠀⠀⠀⠀⠀⢰⡇⠀⣸⠀⠉⡓⢦⠗⠓⢅⢖⣋⣁⣘⣆⣀⣷⣀⡀
⠀⠀⢀⢉⣉⢹⡏⠉⢻⠉⠉⡩⠝⡦⡠⡊⡽⣉⠉⢩⠋⠉⡿⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄
⠀⠀⠘⠛⠋⠀⢷⢀⣨⢶⢛⢿⡿⠁⡇⠹⣯⠏⢑⠾⣄⣰⠇⠙⠛⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⠟
⠀⠀⠀⠀⣀⣤⠞⢿⡀⠀⡿⣽⣅⣀⣇⣀⣹⡽⡃⠀⣴⠋⠳⠦⠀⠀⠀⠀⠀⢀⣴⣷⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⢹⡄
⠀⠀⠀⠀⣤⣤⠄⠀⠙⢲⢷⣇⠀⠈⡇⠀⣀⣯⢷⠛⠁⠀⢶⣶⠆⠀⠰⠶⢷⢿⠾⣷⠷⢿⠶⠶⠀⠀⠀⠀⣠⠞⠀⠀⠘⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣟⡟⠉⠉⠙⡟⠉⠉⠘⡭⡦⠀⠀⠀⠀⠀⢀⣄⣠⠀⡈⠀⣿⡀⢸⣄⠀⣀⠀⣤⣔⡁⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣴⢿⠃⠀⠀⠘⠛⠀⠀⠀⢯⢵⡆⠀⠀⠀⠀⠘⠋⣿⡀⡧⢸⣿⢷⠆⢻⣆⠛⠃⠈⠻⣿⣭⣕⣒⡆⠀⣅⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣎⡎⠀⠀⠀⠛⠛⠃⠀⠀⠘⡭⡆⠀⠀⠀⠀⠀⠀⠈⠀⠙⣺⣿⡀⠛⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⡇⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⣸⣳⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣳⡀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⣀⣀⣇⣀⣇⣀⣀
⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠀⠟⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡶⠶⣄⠘⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⡿⡄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠉⠋⠀⣘⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⠆⠀⠀⡴⠉⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢶⣦⢰⣶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠉⡙⠻⣤⣠⣤⣤⣠⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢲⣶⠚⣿⠉⠙⠋⣿⡇⠈⠋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⢠⠀⣉⠀⠋⡤⢠⡞⠁⣘⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⢻⣦⣀⣀⠜⢠⣾⣿⣟⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⡀⠀⠙⢷⣦⣿⠛⠟⣉⠀⠀⣤⡜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⠻⠂⠘⠃⢾⡆⠀⠀⠘⢿⣦⣭⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢁⣼⠟⠛⢷⣶⠀⠀⠀⠀⣶⣉⡉⢹⡄⢰⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⢸⡃⠀⠀⢀⡽⢇⠀⠀⣿⠀⠙⣁⢸⣧⠈⠁⠿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣸⢷⣄⠀⡼⠃⣾⠀⣾⠀⠀⣤⠟⠋⠀⠙⢻⣦⠙⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠉⠀⠀⠸⢆⣿⠀⣼⠋⠀⢰⡞⠁⠀⣿⡇⠛⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠀⣿⠀⠀⠸⢷⣴⠾⣏⡀⠶⠀⠀⠀⠀⢾⡟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢻⡶⠶⣤⡹⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢁⡸⠇⢠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡜⢻⡖⢻⣿⠿⣿⡀⠀⡀⠀⠀⠀⢀⣠⣤⡀⠀⠀⣀⠐⠛⠛⢷⣤⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣧⠘⢻⣾⠿⠛⣷⣾⣿⡍⢉⠛⣤⣤⣀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⣏⣠⡞⢣⣤⣿⣷⣞⠛⣷⠶⢻⡟⠀⠀⢶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠻⢿⡿⠇⡸⠃⠠⠼⣿⣀⣿⣄⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠱⡀⣠⠗⠂⠀⠈⠿⠧⣱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⢰⣿⣦⣄⣼⠃⠀⣠⠐⣤⠀⢀⡅⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣿⡟⠛⠙⠛⢿⣿⣿⣶⣤⠔⠋⠁⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣶⢠⣿⠘⢧⡀⠃⠚⣁⣼⠿⣷⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠗⢉⣀⣉⡀⠹⣷⣄⠹⠶⠚⠛⢉⣴⣿⠈⠉⠁⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⣴⡞⢋⡉⠻⢶⣄⠉⢳⣶⠶⠿⠟⠉⣿⢀⣴⣿⣻⣶⠛⢁⡀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡶⣏⠀⠈⣉⠀⠀⢹⣷⠀⠀⣠⣤⠀⠀⣿⠈⠛⠛⢋⡀⠠⣿⠃⠀⠛⠁⠀⢲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠻⠟⠃⠀⠀⢈⣿⢠⡼⢃⣽⠃⠀⣿⠀⠀⢀⠸⠷⡀⠛⠂⠚⠃⣤⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠶⣢⣤⡀⠀⢸⡟⢸⣿⢻⣿⠀⣶⣅⣠⣼⠟⢀⣤⠟⢣⣴⣶⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⢀⣴⢿⠟⢷⡄⠀⣸⡟⠙⣿⡀⢸⡇⠸⣿⡟⣣⡿⠉⠛⠋⢉⣠⡾⠻⠤⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣼⣿⢈⣁⣨⡿⠀⠘⠿⢿⣿⣧⡈⠇⣀⣠⡾⠋⣀⣀⠿⣦⠙⣿⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⣿⣎⠉⠉⠀⠀⠀⠀⠀⠀⣉⣡⣄⣽⣯⣴⠄⠛⢋⣤⡌⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠠⠀⠈⢹⡇⠀⢀⣾⣦⣤⣤⡾⠟⣉⠙⠻⣯⡁⠻⠷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠁⢀⡁⣠⡿⠋⣩⠉⣩⠿⢶⣄⠐⢀⣼⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⣿⣧⠼⣀⣠⣤⣶⣦⣜⠳⣾⣿⠉⣤⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢀⡄⢻⡏⠀⣼⡿⠛⠿⠉⠙⢻⡇⢸⡿⣦⡀⠙⠣⣄⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⢨⣇⣸⣇⠀⢿⣿⠛⠶⠃⠀⠀⠀⠾⠃⠈⣳⡀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⢉⡹⢿⣷⣀⠙⠷⣤⣄⠀⠑⣾⡆⠀⢰⣿⣠⣾⠇⠀⢠⣾⠁⠀⠀⢠⡘⠿⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢸⡇⢸⡇⠀⠀⠀⠉⠉⠻⠿⡈⠀⢠⣾⣿⣿⣥⣴⣾⡿⠁⠀⠀⠀⠈⠁⠀⠲⣮⠋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⢸⡇⠈⢿⣧⡐⣤⠀⠀⠀⡰⠟⢰⠟⢻⡈⣿⡏⠉⠁⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⢺⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣦⣄⡈⠻⣦⣄⠙⣿⣿⣿⡷⠿⢣⡄⠀⣠⠎⢠⣿⠇⢀⣴⠟⠋⠁⠀⠀⠀⠉⠻⣿⣷⡀⠘⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠛⢿⣷⣦⡀⠈⠉⣥⣿⠙⢷⣦⣀⣠⡾⠃⣠⣿⡿⣶⡟⠁⠀⠀⠀⢀⣀⡀⠀⠀⠙⣿⣿⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⢷⣄⠉⠻⠿⣿⠿⠟⢿⣦⣄⡈⠙⠋⣠⣾⣿⠟⣿⠏⠀⠀⠀⠀⢰⡞⠉⠁⠀⠀⠀⣿⣿⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡹⢷⡄⠀⠀⠀⠀⠀⠛⣿⣿⠿⢿⣿⡟⠁⣾⡇⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⣰⣿⡟⠀⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠓⣆⣱⠂⠀⠀⠀⣴⠟⠉⣿⠀⠀⠈⠁⣴⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣿⡿⠋⠀⠰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢴⣿⣿⡆⠀⠀⢰⠁⢸⡿⢩⡇⠀⠀⣾⡟⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡾⠿⠟⠁⠀⠀⠀⢠⣶⡇⠸⠇⠀⢠⣿⠃⠀⢿⡏⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠀⠀⢿⣿⡿⠀⠀⠀⢸⡟⠀⠀⠀⢀⣼⠟⠀⢴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠙⣿⡿⣿⣷⣶⡄⠀⠈⠛⣀⠀⠀⢀⣾⣇⠰⠶⠶⠿⣧⣀⠳⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣌⡛⢿⣿⣿⡿⠇⠀⠚⢿⣆⠀⣸⡟⠁⠀⠀⠀⣀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⣧⣰⡿⠀⠀⠀⠀⢾⡀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠿⠟⠛⠿⠟⠛⠿⠟⠛⣼⠟⠛⠻⠿⠟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣿⣏⣉⣉⣉⣉⣉⣩⣏⣿⣿⣿⣟⣛⡛⠛⠛⠛⠛⢛⣛⣻⣿
⣿⣿⣶⣿⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠈⠉⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣠⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁
⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠈⠁

⠀⠀⢼⡿⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⠃
⢀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠻⠂⠀⠀⠀⠀⣲⣿⡥⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠐⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠁⠀⠀⠀⣄⣠⠀⠀⠐⠀⠠⣴⣄⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⢻⠟⠂⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠠⣶
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢿⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟
⠀⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡧⠀⠀⠀⠀⠀⣺⣷⡥⠀⠀⠀⠀⢀⣠⡄
⣶⡇⠀⠀⠀⠀⠀⠀⠄⢠⣷⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠄⠀⠀⠘⠻⠋
⠛⠉⠀⠀⠀⠀⠀⠃⠀⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⣽⣯⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠋
⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⠄⠀⠀⠀⠀⠀⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠜⡿⠏⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⢀⠀⠐⠂⠀⠁⠀⢀⣄⠀⠀⠀⠀⠀⠚⠟⠃⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⢠⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣾⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠁⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠃⠀⠀⠀⠀⠀⠛⠟⠃
⠀⠀⢠⣶⣦⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⣹⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠉⠈⠃⠀⠀⠀⠀⠀⢀⣤⣶⣶⠀⠀⠘⢿⣿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⢶⣤⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠀⠼⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣶⣶⣤⡀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠐⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⣄⠀⠀⠀⢸⡆⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣧⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠿⠿⠿
⠀⠀⢠⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⢤⣀⠀⠀⠀⠈⠃⠀⠘⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣤⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣄⠀⠀⠀⠀⢠⣤
⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⡀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠀⣤⣦⣀
⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣽⣿⡟⠋⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣧⣀⠀⠀⠀⠀⢠⣠
⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣶⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠛⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠐⠿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀