Insect Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠀⠀⠈⠁⠒⠒⠤⣄⣀⣴⣦⣀⡤⠔⠒⠂⠉⠀⠀⠠⠀⠀⠀⣀⡀
⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⡠⠄⠰⠒⢽⣿⣿⣿⣿⠕⠒⠀⠤⡀⠀⠀⠀⠀⠀⢰⣿⣿⣄
⠀⠀⠀⠈⠻⣿⣿⣷⠀⠀⠀⣷⡆⠀⠀⠐⠀⡼⣿⣿⣿⡿⡆⠐⠀⠀⠀⢶⡇⠀⠀⢰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⢿⣧⡀⠀⠀⠀⢠⣶⢠⠎⠀⢿⣿⣿⡇⠘⢦⢰⣦⠀⠀⠀⠀⣠⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠈⠀⠈⣠⠋⠀⠀⢸⣿⣿⠐⠀⠈⢣⡈⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⡤⠊⣌⠔⠃⠈⢸⣿⣿⠘⠀⠓⢌⡌⠢⡴⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⢀⠀⠀⠀⢀⠆⢆⠀⠀⠀⢀⠀⠈⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠁⠀⠀⠁⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⢠⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠒⢐⣶⣶⡿⣷⣒⡆⠐⠂⠀⠀⠐⠀⠀⠐⠒⠂
⠀⠀⠑⢠⡄⠀⠼⡇⢸⡷⠀⠀⡄⠈⠀⠀⢀⠀⡼⠀⠀⠀⠀⠀⠐⠀⠘⠉⢿⠈⠉⠀⠂⠀⠀⠀⠀⠀⡸⠦⣤⠴⢇
⠀⠀⠀⠀⠐⠒⠓⠉⠋⠚⠃⠂⠀⠀⠀⠀⠘⣄⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠈⠀⠐⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢀⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⢀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠐⣀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠁⢂⣰⠉⢧⣀⠈⠀⠀⠀⠀⠐⢄⡁⠶⢈⡠⠄⠀⠀⠠⠀⠀⠀⠀⢸⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⢠⠘⠧⡙⠂⢛⡠⠃⡠⠀⠀⠀⠀⡀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠰⣞⣆⡈⢿⠁⣰⣳⠆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠙⠒⠀⠈⠀⠐⠊⠁⠀⠀⠀⠀⠀⠑⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠂⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⣀⡀⢀⢠⢠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⢠⠠⢤
⠀⠀⠀⠀⠈⠀⡿⠩⡇⠈⠀⠀⠀⠀⠀⠀⠐⢀⡠⠧⠀⠆⠀⠀⠀⠀⠈⡇⠀⠀⣀⣀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡆⢸
⠀⠀⠀⠀⠀⢠⡚⠚⢢⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠬⠁⠀⠀⠀⠀⠀⢸⡄⣐⣿⣿⢂⢀⡟⠀⠀⠀⠀⠀⢸⡧⡞
⠀⠀⠀⠀⠀⠘⠄⠀⠜⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⢂⠀⠀⠀⠈⠸⣇⠈⠛⠟⠁⣰⠗⠃⠀⠀⠀⠀⢸⡓⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⡇⠀⠀⠀⠀⠈⠀⠘⠂⠀⠀⠐⠃⠀⠁⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠂
⠀⠀⠀⠀⠢⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠄⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⢀⠯⠼⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠒⣋⠉⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠊⠇⠀⠀⠀⢤⡀⠐⠒⠀⣠⠄
⠀⠀⠀⠀⠎⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠠⠀⢀⠘⠶⠃⡀⠀⡄⠀⠀⠀⠀⠀⠚⠑⠂⠱⠂⠀⠀⠐⠐⠀⠋⢈⠁⠀⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁⣈⠁⢁⠈⢠⠇⠀⠀⠀⠀⠀⢠⠀⠀⠰⠈⠀⠀⠀⡀⢂⠀⠊⠀⠂
⠀⠀⠀⠀⠀⠦⢤⠤⢚⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠰⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡁
⠀⠀⠀⠀⠀⠈⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⢰⡄⢀⢉⠛⠋⣉⡀⢰⠆⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⡄⠀⠀⠀⠀⠀⠑⢤⣆⠀⠀⣰⡤⠊⠀⠀⠀⠀⠀⢠⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⡸⡯⣴⣦⡽⢇⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⣠⢶⢟⣶⣾⡿⣿⣶⣾⡳⡦⣄⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⡁⢰⡿⣷⣿⡇⢸⣿⡾⢿⡅⢸⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡇⢸⠁⣿⣿⡇⢸⣿⡿⢈⡅⢸⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣩⣿⣽⣇⠸⣿⡇⣾⣿⠇⣸⣷⣿⣉⡙⢷⣄
⠀⠀⠀⠀⠀⣀⣀⡠⠤⠴⠾⠟⠁⢠⣯⣤⡄⠉⠙⢿⡦⡤⢤⢴⠿⠋⠁⢠⣬⣽⠀⠙⠿⠷⠦⠤⠄⣄⡀
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⣷⢴⣾⡦⡿⣱⣮⢞⣰⠷⡖⢿⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢘⡯⣯⡽⣷⣌⢡⡆⢰⣾⢞⣳⣿⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢚⠛⣛⣿⣽⣯⢸⡆⣿⣗⣿⢹⠧⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣀⣃⣻⢤⣻⣹⡷⣏⡖⣟⣭⣤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⣙⣶⡢⡿⢸⡇⢺⢳⡇⡅⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡉⡍⠫⠃⢸⡇⠙⠫⣵⢛⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠙⠛⠓⠒⠛⠓⠒⠚⠛⠋⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⢰⣿⡆⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢶⣢⣶⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣖⣶⠄⡀
⠀⠠⢀⡐⣒⠚⠍⠁⠀⠁⢳⣿⡞⠀⠀⠉⠹⠓⣀⢀⡀⠄⠀⠈⢧⣕⣿⣯⣃⣹⢁⣸⠗⠠⢶⠂⠚⣏⡀⣏⣘⣽⣿⣚⣵
⠀⠀⣀⣀⠈⠁⠐⠄⠀⠂⢾⢛⡇⠐⠀⠠⠂⠉⠁⣀⡀⠀⠀⠀⠀⠀⣿⣿⣖⡠⣶⣪⣿⣷⣈⣼⣿⣯⣲⢄⣰⣿⣿⠃
⠘⠓⠒⠂⠀⠀⠀⣀⣁⡤⠜⣍⠢⢤⣈⣀⠀⠀⠀⠐⠲⠚⠀⠀⠀⠀⠉⠻⢿⢷⠏⢡⡟⣯⣟⣯⡟⡄⠙⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡄⠑⠊⢀⡟⡄⠙⠒⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢶⢄⠃⠀⠀⠈⠻⡶⣶⠞⠁⠻⣶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠤⠄⢀⣑⣾⣭⣿⣊⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹⢿⣤⡿⠏⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⠇⢨⣿⡇⠘⣾⢃⠀⠀⠀⠀⠀⠸⣄⡀
⠀⠀⠀⠀⠀⢠⠀⡏⠀⠀⠀⢸⠀⣆⠀⠀⠀⠀⠀⠀⠁⠃⠃⢸⣿⣇⠈⠈⠈⠀⢸⠀⠀⢠⣄⠀⡇⠀⣰⠏⠙⠒⠂⢄
⠀⠀⠀⢀⣠⡤⠑⢮⡀⣶⣀⠥⠊⠠⣄⡀⠀⠀⠀⠀⠀⢀⡜⢻⣿⡟⢢⡀⠀⠀⠸⡗⠀⣼⣿⣿⣷⣶⣇⣠⠴⠓⠒⢤⡀
⠀⠀⠀⠀⠤⡤⠀⣀⣻⠭⣿⣁⠀⠤⠤⠀⠀⠀⠀⠈⠓⠋⠀⠀⠉⠀⠀⠙⠚⠁⠀⣈⡛⢻⣿⣟⢟⣿⣽⡷⠚⢧⡀⠀⠈
⠀⠀⠀⠀⢠⠘⠋⣩⣤⠛⣡⣍⠙⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠈⢉⣻⡿⣿⠿⠇⠀⠀⢱
⠀⠀⠀⠀⠘⠰⡄⠙⢿⣶⠿⠋⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⣰⡏⠘⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣿⣿⣿⣿⣛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣻⣿⣛

⣀⡀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀⡀⠴
⢩⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣫⣁
⠈⠉⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⣿⠞⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡙⠈⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡿⠇
⠀⢀⠠⠒⣀⡰⡖⠀⠀⠘⡀⠀⠰⢦⣀⠐⠢⠀⠀⠀⠀⠀⠊⣌⠋⣬⠁⠀⠀⠀⢀⠠⠒⣀⡐⡖⠀⠀⠈⠀⠀⠲⢦
⠀⠁⠀⠀⠀⠀⠀⠐⡇⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⣀⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣄⡀⠀⢀⠀⡀⠀⠀⣀⣤⣤⣦⡄
⣩⡽⣻⣿⠟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡽⣦⣍⡓⢄⢤⡤⣒⣩⡽⣻⣿⠟⠀⠀⠀⠀⡀⠄⢀
⣦⣼⡿⠃⠀⠀⠀⠀⠀⣤⡀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣶⠛⣩⢤⡙⠳⣦⣼⡿⠃⠀⠀⠀⠀⠀⣤⡀⢠⣄
⣤⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡞⠹⡜⡌⣦⣮⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃⠸⣟
⠾⠋⠀⠀⠀⠀⠀⠀⠀⠠⠃⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠩⠃⠘⠏

⣀⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⡀⠘
⢵⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣰⢵⣥
⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠿⠋⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡌⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠢⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⢀⢨⢿⠠⠶⣾⣁⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣼⣿⡎⠀⠀⠀⠐⣿⣿⡄⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢆⠀⣿⣿⣷⢀⢀⠀⣨⣿⣿⡇⠀⠀⢀⡴⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⡆⠈⢛⣾⣾⣾⣷⣿⣭⣤⣁⡀⢀⢾⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠟⠙⠛⠉⠁⠉⠉⠙⠹⣿⣻⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢊⣶⠔⢀⡀⠀⠀⠀⠀⠀⣀⢠⣿⣤⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⣤⡴⠊⡐⡂⣺⢿⣿⣾⣤⣴⣆⡄⣄⣮⣷⣿⣭⠭⢳⠀⠈⠳⣤⣄⣄⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠚⠓⢚⠍⠁⠀⡰⠃⠉⢉⣹⣿⠻⠿⡏⡿⣟⠿⢻⣙⣓⠚⠃⢣⠀⠀⠈⠛⠒⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⢁⣞⣯⣽⡃⠀⠀⠁⠀⠈⠁⣀⣠⡏⠿⣭⣛⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠈⢠⡙⣆⠋⠹⠓⠶⠠⠖⠒⠚⠛⠉⠁⠘⠄⢀⡀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢠⠁⠀⠈⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠇⠀⠰⠀⠘⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠞⣽⠟⠒⠀⠄⠄⠀⠀⠤⠠⠐⠊⠈⠙⠀⢲⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⢇⡾⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣧⠀⠀⠻⣝⡂⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠿⠾⠧⡀⠀⠀⠀⠀⣀⣀⡥⠘⠏⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢀⡰⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⠶⠤⢄⡀⣄⠤⡤⠾⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋

⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⡅⠀⠀⢀⡗⠀⠀⠀⣠⡤⢠⢀⢄⣠⣀⢄⢠⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢢⠀⢻⢛⡛⢿⠃⡀⠀⠀⠙⢦⡀⢢⣾⡷⣿⣦⠂⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏
⠀⠀⠣⢼⣯⣽⡯⠔⠁⠀⠀⠀⠀⠹⣦⣀⣹⣋⣠⡼⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢎⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠀⢀⣺⣿⣷⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠸⣶⣧⡶⠄⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡠⣼⠿⢿⢤⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣯⡧⠀⠀⠀⠀⠀⠈⡜⢹⣄⣸⢱⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠈⠁⠈⠻⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣽⣷⣇⠀⠀⠀⠀⠀⢐⣛⡂
⠀⠀⠸⣿⠇⠀⠀⠀⢀⣿⣷⣾⣧⠀⠀⢀⡜⠻⡿⠛⡀⠀⠀⠀⣿⣽⣿⣯⡟⠀⠀⠀⠀⠹⣿⣿⡐⠄
⠀⠀⠀⣉⠀⠀⠀⠀⢸⢀⢠⢇⣭⡇⠀⠀⣵⣦⣶⣶⡉⠀⠀⠪⡇⠈⠛⢀⣶⡅⠀⠀⠈⠁⢸⡏
⠀⠀⠀⠉⠀⠀⠀⠀⠰⠻⠾⠾⠣⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠰⡹⣴⣶⣿⢿⠃⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣟⣛⣛⣛⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠄⠀⠀⠀⣤⡤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠤⣶⠄⠀⠀⢀⠊
⠀⠀⠘⡂⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠄⣀⠀⠀⠀⠀⣠⡴⣦⡄⠀⠀⠀⣀⡤⠔⠂⢀⣯⡄⡀⠀⠀⠠⠦⠀⠀⠀⡠⠃
⠀⠀⠀⠈⢆⡀⠀⠀⠐⠀⠀⠻⠱⡂⣄⡀⠂⠨⢉⣓⣼⣏⣥⣼⣧⣉⣾⣴⡫⢛⠀⠀⠰⠬⠛⠊⠀⠀⠠⠀⠁⠀⠠⠔
⠀⠀⠀⠀⠀⠱⠄⢆⠀⠀⠀⠀⣠⣀⣀⣀⣀⣈⡠⠾⣤⣘⣿⣷⣿⣟⣃⣽⠷⣤⢤⢄⣠⣤⣄⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠙⢢⣿⣿⣿⡛⢻⣿⣿⣿⠂⠁⠉⠁⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣿⡿⣿⣿⣟⢿⢿⡋⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢣⣿⠿⣿⡿⢿⡗⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⠛⠂⣽⡀⠙⡑⠏⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⡿⠿⢿⣋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠑⣒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⢆⣤⣐⢒⠂⣠⣺⣟⢙⣷⣷⣶⢶⣤⠀⠀⠀⡀⣤⣴⣶⣞⡟⡟⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠲⠋⣻⡉⠁⠚⢀⠛⠀⠀⢦⣁⠛⢓⣼⣿⣯⣿⣷⡿⢿⣻⡍⠂⠀⣰⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠐⠛⢻⠶⣯⣯⡀⣼⡤⣶⣽⡿⣿⣷⡝⠻⣉⣵⣿⣟⢹⣧⡗⢡⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠃⠈⠓⠛⠛⠛⠀⢒⣾⠓⠖⠚⢿⠝⣪⠟⠛⠘⠷⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠄⠂⠛⠀⠀⠀⠀⠀⠀⢀⡴⠋⣇⠀⠀⠠⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠈⠙⠆⠘⠉⢿⣿⠚⣖⣖
⠀⠀⠀⠀⠀⠀⠀⢉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⣀⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤
⠀⢣⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⡀
⠀⠀⢑⡆⠀⠀⠀⠠⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⢐⡊
⠀⠀⠈⢷⡀⠀⠉⠀⠈⠦⣀⣙⢦⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣶⠆⠀⠀⠀⠀⠰⣾⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⡴⣋⢀⠴⠁⠀⠉⠀⢀⡾⠁
⠀⠀⠀⠈⢿⠤⠀⠲⠦⣄⣘⠛⢣⡷⣄⠀⠀⠀⢠⠞⠀⠈⠉⠑⣤⣶⣶⣶⣶⡴⠊⠉⠁⠀⠳⡄⠀⠀⠀⣠⢾⡜⠻⣓⣠⠴⠖⠀⠠⡿⠁
⠀⠀⠀⠀⠘⣀⣀⠀⠀⠀⠀⠤⡆⠐⢌⢣⡀⠀⠸⣄⡀⠀⠀⣠⡿⣿⣿⣿⣿⢿⣄⠀⠀⢀⣠⠇⠀⢀⠜⡩⠂⢰⠤⠀⠀⠀⠀⣀⣄⠃
⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠐⠋⠃⠀⠀⡀⠙⢦⡀⢸⣿⢀⣾⢽⣾⣿⣿⣾⣿⣷⡯⣷⡀⣿⡇⢀⡴⠋⢀⠀⠀⠈⠙⠂⠀⠀⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠙⣦⡹⢿⣿⣤⣿⣿⣿⣿⣿⣿⣤⣿⡿⣏⣴⠋⣠⠖⠁⠀⠁⠀⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⠀⠴⠶⠿⢿⣷⣾⣿⡛⡿⠟⢛⣿⣿⣿⣿⡛⠻⠿⢛⣿⣷⣾⡿⠟⠶⠦⠀⠀⠀⠰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠔⠉⠛⣿⣿⡿⡀⠀⢘⣷⣿⣿⣾⡃⠀⢀⢿⣿⣿⠛⠉⠢⠄⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⢀⠈⣸⣿⡇⡀⠀⡚⣿⢿⡷⣿⢃⠀⢈⢸⣿⣎⠁⡀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠈⣸⢻⡇⠀⠠⠋⢻⣼⣇⡗⠙⠄⠀⢸⡟⣇⠑⢀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⣼⣿⣿⡇⠀⠀⠼⢻⣻⣟⡿⠇⠀⠀⢸⣿⣿⣧⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣷⡇⣿⣇⠂⢀⠀⡐⣿⣿⢂⠀⠀⠈⣸⣿⢸⣾⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢻⣿⣾⣄⠓⢿⣿⣿⡿⠚⣠⣷⣿⡟⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠉⠻⠶⠶⠟⠉⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣤⣤⣴⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠻⣿⣿⣿⡟⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⡀⠀⠀⢀⣀⣀⠀⠀⢠⠛⠀⠀⠀⢀⣼⣿⣿⣿⣀⠅⠀⠀⠙⣦⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣦⣴⣿⠟⠙⢿⣦⡹⢿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⠾⢁⡤⣶⠟⠻⠷⣶⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⣱⣿⠟⠛⠛⠛⠛⠻⠿⢿⣯⣁⣰⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣄⢀⣀⡀⠀⠀⣈⣳⠝⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠿⠿⠛⠛⠻⠿⣿⣿⣤⣏
⠀⠀⠀⠀⠠⠶⠟⠛⠛⠛⠻⣶⣄⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣴⣿⠿⢋⣽⡟⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⡀⠙⢿⣿⣿⣶⣄⣀⣤⣶⠟⠛⠉⠙⠳⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣿⡏⢠⢸⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⣸⢏⣼⢧⠸⠈⢏⠻⣎⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠳⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⢿⢧⣿⣾⡿⣷⣬⣄⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⣼⠁⠰⠀⣾⣿⣿⣿⣿⣿⠿⠿⠿⢾⣯⣷⣿⣿⡈⢷⢰⠙⣿⣷⣌⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⢣⠞⠁⠀⡆⢸⣿⣿⣿⣿⣿⣿⣄⠀⢀⣀⣿⣿⣯⢿⡇⢸⡄⢇⠈⠻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢃⡾⣷⠋⠀⠀⢰⠀⢿⣽⣿⠿⢿⣿⣿⣽⣿⣿⣿⡿⠟⠉⣈⣧⣼⡇⠈⢦⠀⠀⠙⣿⣷⡄
⠀⠀⣀⠀⠀⢀⣤⣤⣤⠴⠊⠛⠁⣾⢡⠇⠀⠇⠀⡇⠀⢸⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⡀⠈⠳⡀⠀⢸⠈⣿⣀⡀
⠀⠀⠙⠓⠛⠛⠛⠋⠀⠀⠀⠀⣼⠃⠾⠀⠸⠀⠸⠁⠀⢸⣿⣿⣿⣿⣿⢿⣿⡟⡿⠻⢻⡟⠛⠻⡟⠟⠀⠱⡀⠀⠙⢦⣸⡄⠘⣿⠛⠿⣶⣶⣦⣶⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣠⠃⢠⠃⠀⡇⠀⠀⠸⣿⢸⣿⣿⣿⠿⠸⠇⠃⠀⠀⢱⠘⠂⣷⠁⠀⠀⠡⠀⠀⠀⠙⢷⡀⢸⡇⠀⠀⠈⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡔⠁⢤⠃⠀⠀⠀⠀⠀⠀⢻⣾⣟⡿⠟⠀⠀⠀⠀⠀⠀⠸⣆⣰⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⢹⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠌⠀⠀⠀⡄⠀⠀⠀⠈⢻⣿⣿⣶⣤⣤⣤⣤⣤⣶⣾⣿⡟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢳⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠊⠀⠀⠀⠀⠐⠀⠀⠀⡰⠈⠻⣿⣿⣿⣻⡧⠻⣿⡟⢿⡟⠙⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠻⣍⡁⠁⠀⢘⣠⠞⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠋⠁⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢄⡀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠘⠁



⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⢘⢯⣭⠿⠂⠀⠀⢀⣦⡀⠀⠀⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⢰⣶⠀⠀⠀⠰⣿⡇⠀⢠⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⠃⠀⠈⠻⠽⠟⠀⠀⠠⣿⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣰⣶⣄⠀⠀⢦⣀⡀⠁⢀⠀⠀⣀⢀⣀⠀⠀⠎⡟⠀⠀⠀⣀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⢼⣿⡧⠀⠀⠀⢈⢏⠃⠀⠀⠀⠏⠀⠀⠀⠀⠀⠁⠠⠀⣰⢓⣶⡤⣄⠀⢸⣿⠀⠀⠀⠗
⠀⠀⠀⠈⠟⠁⠀⠀⠀⢸⣻⣴⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡴⠏⣿⣿⣏⠂⠀⠘⠑⠀⠀⠀⣁
⠀⠸⣷⣆⠀⢀⢠⣶⡇⠀⠉⠁⢀⡀⠀⠀⠀⠠⡍⠄⠀⠀⠀⠉⠉⠉⠉⠁⠀⣤
⠀⠀⢹⣞⢻⣿⢻⣿⠀⠀⠀⢠⠻⡟⠄⠀⠀⠀⠉⠀⠀⢠⠀⡄⡀⠀⠀⠀⠘⠾⠃
⠀⠀⠈⠛⠁⠀⠛⠃⠀⠀⠀⠈⠺⠖⠁⠀⢀⣀⠀⠀⠀⠈⠒⡓⠂⠀⠀⠀⠹⠿⠁
⠀⠀⠐⣦⡄⠰⢤⣤⣤⣿⣤⣴⡶⠂⠀⠀⣾⣿⡀⠀⠀⠀⢸⣇⠀⠀⠀⣠⡄⠀⠀⡀⠀⠉⠐⠓⠀⠁
⠀⠀⠀⠐⡀⠈⠉⠉⠉⠉⠙⠛⠉⠁⠀⠈⣿⣟⡇⠀⠀⠀⢸⠁⠀⠀⠀⣿⡇⠀⠀⡇
⠀⠀⠀⠈⠨⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠃⠀⠀⠀⠻⠋
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠸⣿⡿⠀⠇⠇⠜⠆⠈⠂⠸⠬⠂⠀⠅⠃⠟⠅⠜⠆⠻⠇⠠⠳⠀⠀⠿⠀⠧⠁⠣⠄⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠂⠐⠛⠛⠛⠂⠰⠛⠛⠛⠃⠀⠛⠛⠛⠀⠘⠛⠛⠃

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⢄⣤⢄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⡼⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠁
⠀⠠⣇⡞⠀⠀⠸⠇⣀⡄⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣦⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣑⢤⡵⣧⣖⣀⣠⠔⠁⠀⡀⢀⣀⠠⠴⣶⣾⣶⠀⠀⡡
⠀⠀⠀⣉⠀⠀⠀⠀⢡⣤⣀⠀⠈⠀⠀⠄⠀⢀⣽⢿⣼⣿⡄⠒⠀⢂⡀⠐⠀⠀⠀⢀⡤⠶⠾⢱⣄⡜⢇⠉⠀⢀⠀⠊⢀⠾⣃⡀⢰⠿⠉⠛⣇⠉
⠀⠀⠏⣹⡄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠊⠃⠀⢣⢛⡟⢠⠃⠀⠀⠀⠀⠀⠀⠂⡐⠋⠀⢀⣼⡿⢡⡜⡎⠃⠒⠁⠀⠀⣦⠀⠉⢁⢁⣤⠀⣤⠀⢄
⠀⠀⠀⢿⡀⠀⠀⠀⠀⣀⠘⠀⠀⠀⠀⠀⠀⡠⢪⢹⡟⡈⠓⠀⠀⠀⠀⠀⠀⡄⠛⠀⠀⠾⣟⡤⠋⢹⠀⠀⠀⠀⠀⡴⠋⠘⠃⠀⠈⠉⠀⣉⠄⠠⠁
⠀⠀⠀⠀⠉⠀⠈⠑⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠄⠰⡆⠀⢀⣀⠟⠀⠀⠀⠀⢀⡆⠀⠂⢠⡀⢛⡃⠐⠍
⠀⠀⠀⠀⣀⡠⢤⡀⢶⢈⡀⠀⠀⠀⢀⠠⠀⠀⠀⢘⡃⠀⠀⢀⠀⠑⠤⡏⢻⣐⣁⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄
⠀⠀⠀⠀⢀⣤⠄⠁⣼⡉⠀⣒⠀⣨⡁⠀⠀⠀⠀⢸⡆⠀⠇⡀⢀⠐⢠⠾⢾⡛⢍⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⡀⠁⡂⠀⡠⠊⠄⣰
⠀⠀⢠⠎⠁⠞⠀⢸⣨⠝⢁⣌⡉⠀⠉⠂⠀⠀⠀⢨⡇⠀⠀⠈⠁⠀⢸⢤⠀⠳⠀⠣⠈⠂⠀⠀⠀⠀⡠⡄⢀⠀⠀⠢⣀⠇⠈⢁⢨⡄⠈⠀⢀⡠⠂
⠀⠀⡎⠀⠀⢀⡀⣀⣠⣴⠋⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡇⠀⠀⠀⢀⣤⣰⣀⣀⠄⠄⠀⠀⠐⠑⠒⡆⢧⠀⠠⣛⡯⠁⠈⢠
⠀⠀⠀⠀⠀⠀⠈⠀⢀⡟⠈⠁⠀⠀⠀⠘⡃⠀⢀⢀⣠⢄⠀⣠⠦⠀⠀⣠⠤⡀⢀⡴⠀⠀⣾⠀⢠⡤⡀⠐⠢⠔⠂⠠⢈⣷⣴⡶⠟⣛⡦⣀⠁
⠀⠀⠀⠀⠀⠀⠒⠚⠉⠀⣠⠄⠀⠀⠀⢸⡇⠀⢸⡟⠁⣾⠀⠙⢤⡠⣾⡧⠴⠃⣾⠀⠀⢰⡏⠀⠘⠦⡁⠀⠀⠉⠂⢰⠏⢿⡶⠶⠟⣋⠱⡌⠆
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠐⠀⠀⠀⠀⡅⢸⣧⠔⣿⠀⠀⢯⡔⢦⣠⡿⠻⠧⠤⠖⠻⢦⠴⠻⠧⠴⢄⣠⡿⠀⠀⠀⠀⡂⢸⠀⠶⠖⣛⡏⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢠⣆⠀⠀⠤⠁⠀⠀⠀⠀⡀⣳⠀⢀⠀⠀⢀⠀⠀⢀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⡙⠉⠀⡀
⠀⠀⠀⠦⣄⣀⣀⡠⢜⠰⢬⡁⠤⠄⠴⠂⠀⠀⢸⠀⣹⢰⡁⢸⢸⡁⢸⢰⡃⢸⠀⢸⠰⡇⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⣄⣄⠀⡔
⠀⢤⣀⡀⠤⠄⡶⠁⡄⠁⢙⡧⣀⣀⣀⠀⠀⢄⠀⠁⠈⠀⠁⠁⠀⠁⠁⠀⠉⠈⠁⠉⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠙⢤⣧⣫⠞
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠠⠊⠣⡀⠀⠉⠀⠀⠀⠤⠒⠞⢳⣋⡡⢔⠢⢄⠀⠀⢀⠀⡄⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠄⢸⣷⣿⢀⡒⠀⠂
⠀⢀⡠⠔⠊⠁⠀⠀⠀⢠⠀⠀⠙⠀⠀⠀⠀⠐⠀⠀⠐⠊⢬⢥⣀⣨⣽⠇⠀⠈⠸⠛⣶⠖⠷⢦⣀⣤⠤⠤⣀⠀⠀⠀⠀⠘⢡⢚⣒⣚⠷⡀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⢞⠁⡀⠈⠓⣌⠉⢳⠄⠀⠀⠀⠤⠋⠀⠀⠀⠈⠁⠂⢄⠀⠉⠉⠐⠀⣠⠃⢨⣭⡥⢖⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠄⠈⠀⠀⠐⠀⡀⠈⠛⠁⠀⠀⠈⠀⠀⠀⣀⠀⠢⠀⣀⣀⠔⢀⠄⠀⠀⠀⠁⠀⢀⠀⣬⡁⠀⠀⢖⣛⠃⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠐⠈⠀⠀⢀⡴⣳⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠳⣄⣾⡷⣿⣦⠇⠀⠀⠀⠀⠀⣀⡘⣟⠿⣌⠲⢦⡄⠁⠤⡄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠄⠰⡶⠀⢸⠁⠃⠀⠀⠀⢀⣤⡶⠀⠀⢀⠀⠀⠨⡅⠀⠀⢼⢀⡀⠄⡀⠺⢁⠤⢤⠸⡄⠘⢷⣦⣁⣌⣈⣄⠀⠀⠎
⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⠁⠀⠈⠳⣄⡘⣯⠕⠀⠀⠁⠈⠑⣦⣧⠀⠀⣼⠌⠄⠀⠀⠀⠀⠀⠀⢠⡿⠀⡤⠋⠈⠀⠻⠈⠓
⠀⠀⠀⠤⣄⠀⠀⠐⠀⠀⠲⠤⡀⠀⠀⠀⠀⠀⠀⢀⠾⣿⣿⠗⠢⢄⠀⠀⠀⡥⠠⠅⠀⠀⠘⡆⡁⠐⢀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡰
⠀⠀⠀⠀⠈⠉⠓⠶⠄⠒⠤⢄⠚⠦⢀⠀⠀⠀⠀⢂⠊⣹⡯⠃⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠐⠉⡀⠐⠁⠀⠀⠀⢀⢀⠀⠉⠸⡽⠯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⢊⠀⠈⠓⠀⠈⠚⠋⠀⠀⠀⠀⠨⠀⣩⠴⠀⠈⢄⢀⠂⠀⠀⠐⠀⠀⠀⠈⠉⠉⠀⢀⡄⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⣴⣿⣆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣅⣽⠀⢀
⠀⠀⠀⠀⠀⠓⠜⡋⠙⣿⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡼⠿⣿⡄⠊
⠀⠀⠀⠀⢠⠖⣮⡍⣟⢩⢰⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢻⣿⣄
⠀⠀⠀⠐⠁⡴⢿⣿⣿⣼⡶⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⣸⣿⡀⠆
⠀⠀⠀⠀⣸⠁⠈⠛⠛⠛⠁⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡹⠿⠟⡁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⡀⠀⢀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⣧⣧⣼⣤⣤⠇⡇
⠀⠀⠀⠀⢀⡠⠤⠄⣴⣶⡤⠤⣀⠐⠐⠄⡑⣾⣭⣿⣿⣿⣊⡤⠒⠂⢀⣀⠤⣤⣤⠤⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠡⠝⠿⢶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣶⠾⠏⣉⣉⣀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠃⠀⠠⠇⣼⣿⣿⡽⠈⡿⠌⣷⠤⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⣸⡘⠀⣠⣾⣿⣿⣿⣿⣄⠀⣶⣟⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⡝⢿⣿⣿⣿⡿⠋⡗⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠉⠛⠋⠀⠀⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣃⡟⣣⣙
⠀⠀⠀⠀⠀⢀⠈⠩⠾⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣭⣿⣯⣥⡀⢁
⠀⠀⠀⠀⠐⠙⠡⡆⠀⠴⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⣄⠸⠂⣄⢠⠈
⠀⠀⠀⠀⠀⡐⢤⡀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢉⢹⠃⢹⠏⡉
⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠓⠋⢸

⠀⠀⠀⣾⣿⣦⠀⠀⢀⣴⣾⣿⣶⡄⠀⢀⣀⣤⣤⣶⣶⣶⣷⣶⣶⣦⣤⣄⣀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣷⣶⣶⣶⣤⣤⣀⠀⠀⠀⢠⣾⣦
⠀⠀⠀⢿⣿⡿⠀⠀⠛⠛⠛⠻⠻⠇⠀⠻⠿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠿⠃⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣽⠟⠉⢿⣽⠿⠃⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡟⠉⢿⣿⠿⠃⠀⠀⠀⠀⠘⢿⣿⣿⠏
⠀⠀⠂⣴⣦⡀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣿⣗⠀⠠⣾⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣾
⠀⠀⠊⠻⠿⠛⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⠄⠀⠀⠀⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠙⢿⣿⡿⠃
⠀⠀⠀⠈⣢⣦⠊⠀⠀⠀⠀⠠⡄⣀⣠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢈⣿⣿⣏⠀⠀⠀⠀⠡⣽⣿⣧⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢠⣴⣶⣤⣄
⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⢰⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠁⠶⠂⠀⠀⠈⠹⠿⢻⣿⡆
⠀⠀⠀⠻⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⣠⣀⠀⠠⠀⠀⣤⣴⣾⣿⠇
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⢿⣿⠟⠁⠀⠀⢀⣤⣶⣶⣶⣾⣿⠟⠛⠉⠀⠀⣠⣶⣶⣶⣾⣿⡿⠟⠛⠁⠀⠀⠈⠛⠃⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡏⠐⠤⣄⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠴⡦⢀⠀⠀⠀⡀⣴⢖⣶⠂⠘⣿⣿⣷⣦⡀⢀⢀⣴⣾⣿⣿
⠀⠀⠤⠔⡲⠂⠀⠀⠉⠙⠛⠿⠿⠛⠂⠀⠀⠐⠓⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠹⢷⣿⠾⠃⢀⡾⠃⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⠀⠬⡿⢿⣿⣿⣿⣦⡤⠀⠠⣷⡀⠇⠟⠱⣀⣿⠀⠀⠀⠀⠀⠸⣿⣿⡇⠛⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠝⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠛⠛⠁⠀⠈⠟⠃⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⣤
⠀⠀⠐⣿⡆⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤
⠀⠀⠈⣿⡇⠀⠀⠀⠀⠄⣿⣿⠠⠀⠀⠀⠀⠀⠀⠐⡶⣿⣶⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⠋⠉⠉⠉⢀⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠐⠲⣦⣄⣀⣀⠀⠀⡀⠀⠀⠀⠻⠿⣷⣦⣤⣤⣤⣤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠛⠛⠛⠙⠋⠙⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⢲⣄⣀⡴⠚⠉⠀⠀⢀⡤⠆
⠀⠀⠀⠀⠀⠀⡀⠤⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣴⡛⠬⠨⠝⣳⡄⢀⣶⠋⠀⠀⠀⠀⠀⠀⡀⡀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠘⡄⠀⢠⠁⣀⠐⠍⠓⠢⢄⡀⠀⠀⠀⠸⣇⣹⣿⣦⣷⣿⣿⣁⣼⠏⠀⠀⢀⣀⠤⠖⠉⠀⠐⠀⣀⠀⡀⣵
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠂⢤⣀⣸⣿⣵⡟⠿⠽⢙⣿⢁⣠⠴⠚⠉⢀⠄⠰⡀⠈⠁⠉⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣁⢀⠄⠄⠐⠀⠀⢀⡀⠠⢬⣿⣿⣷⣂⣠⣨⡅⠨⠦⢀⣀⠀⠀⠠⠀⠠⠐⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣌⡁⡀⢀⣀⣁⣨⠴⢞⣿⣿⣿⣭⣯⣿⢗⠢⣴⣄⡀⠀⠈⠉⠍⢀⡩⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣤⠿⠁⣤⣴⣿⣿⣿⣷⢿⣿⣷⣤⡙⢧⣈⠉⠘⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠃⠀⣼⡏⣾⣿⣏⣿⣿⣿⣿⣿⡎⡿⡄⠙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢸⣽⠀⢿⣿⣿⣗⣶⣆⣾⣿⠇⠰⣶⡀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠸⣿⣷⣟⣿⣖⣿⡿⠀⠀⠹⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⠹⣿⣿⣷⣿⡿⠃⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠄⢠⣤⣤⡤⣀⡀
⠀⠀⣴⡿⠃⢹⣿⣇⢀⠛⠂⠉⠉⣙⣒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣋⡉⠁⠐⠀⠀⠈⠿⣿⣁⠙⣿⡆
⠀⠀⢿⣿⡂⠿⠥⠄⠀⠀⠀⠀⣤⡿⠏⠉⠓⠪⠑⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠙⠈⠉⠘⠿⣶⣆⠀⠀⠀⠐⢒⡸⠇⣼⣿⠃
⠀⠀⠈⠫⢷⣾⡍⢀⣶⡀⠀⠀⠀⠀⢦⣤⣠⣶⠾⣿⡊⣳⢄⠀⠀⠀⠀⠀⣠⢞⠝⣻⠿⠻⣷⣤⣴⠊⠄⣀⣀⡀⢭⣏⢐⡾⢿⡷⠁
⠀⠀⠀⠀⠉⠲⣛⣿⡷⢐⣛⡅⠀⢀⡻⣿⣇⠚⠒⠶⢤⣈⡓⢷⡔⠆⣆⣴⢿⣳⡬⠔⠒⠛⢐⣿⡿⢃⣀⠀⢬⣉⠐⠾⣯⠝⠋
⠀⠀⠀⠀⠀⠀⠉⠶⣛⣷⡄⠒⣩⡅⠰⢿⣟⣛⠛⠁⠰⠭⡿⠟⣿⣧⣿⡟⠋⣩⠤⠌⠉⠩⢙⣿⠿⠂⢬⡉⠒⣶⣎⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⢿⢾⣥⣔⠊⠭⠠⠐⠒⠉⠁⠀⢁⠔⣡⢻⠧⠑⢄⠀⡀⠁⠠⠔⠂⠠⢍⠵⣶⣿⠻⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⠧⠍⢠⠆⠐⠀⠀⡠⠀⠀⡰⠛⠨⠐⡀⡀⡑⠢⡁⠀⠀⠀⠢⠈⠐⠿⣍⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣔⡦⠔⢣⠀⡠⠔⠊⠀⠄⡰⠁⠀⠘⠀⢡⠐⡘⡄⠈⡂⠠⡌⢠⡃⠲⢥⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣾⣡⢄⡔⠁⢠⠀⢀⠁⡘⢠⠃⠀⠀⠈⠀⠀⠂⠠⠘⡄⠁⠀⠰⡀⠙⢄⠢⣸⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⣳⡋⣰⢃⠇⡄⢸⢠⠃⠆⡌⠀⠀⠀⠀⠀⠀⠄⠂⢱⠘⡄⣆⢳⠹⡆⣻⡟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⣿⢳⣾⣰⣃⣇⣾⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⣧⣧⣸⡤⢿⠛⣧⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠿⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠛⠚⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⡇⠀⠀⢨⣌⣠⡄⠀⠀⢄⠀⠒⠀⠀⠀⡸⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣱⣄⠀⡠⢼⣁⠀⣀⣀⣈⣋⡛⠁⠀⢰⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡖⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢤⡄⣢⠼⠶⠦⢤⣀⣀⣀⣀⡀⣀⣀⣸⠁
⠀⠀⠀⠀⠀⣀⣸⠈⡡⠔⠊⠁⢙⠃⠀⠀⠀⠀⠣⣀⣀⠏⠀⠀⠀⠈⢳⣝⢗⡲⠤⣄
⠀⡠⢰⠶⠿⠛⠛⠋⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⣇⠀⠈⠲⣄⣹⢦
⠎⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢣⠈⠻⣢⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣹⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠎⠸⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⢿⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⡸⠀⠀⠙⠄⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠋⠀⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢘⣦⣄⠇⠀⠀⠀⠀⠙⠿⣆⣺⣑⡒⡦⠶⠋⠀⠀⠀⢰⠀⢱
⠀⠀⠀⠀⠀⠀⢀⣰⠍⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⡆⢶⡃
⠀⠀⠀⠀⠀⢠⣲⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢐⣣
⠀⠀⠀⠀⣰⢁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢧
⠀⠀⠀⢠⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


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

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

⠀⠀⠀⣾⣧⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣤⣼⣿⣿⣧
⠀⠀⢠⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣠⣤⣿⣿⣿⣿⣿⡦
⠀⡔⢹⣿⣿⣿⣿⣥⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠣⢸⣿⣿⣿⣿⣿⣴⣀⣰⣿⣿⣿⣿⣿⠋⠀⠈⢻⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛
⠀⢠⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠹⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣀⢌⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣤⣀⣀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⣁⣩⣽⣿⣿⣿⠖⠋⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⣿⣿⣟⣿⠻⠃⠀⠀⠘⢿⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣷⣭
⡴⡳⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠣⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣈⢁⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠋⠀⠸⣧⣈⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠰⢶⣛⠛⠛⠛⠖⠀⢀⣼⣿⣿⣿⣏⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⣿⡿⠿⠟⣿⣷⣦⣀⠀⠀⠀⠛⠛⠛⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴
⠀⠀⠀⠀⠀⢰⣿⡇⣿⣿⢛⠁⠀⠀⠀⠉⠻⢿⣿⣷⣦⣤⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠘⢧
⠀⠀⠀⠀⠀⠸⣯⣿⠟⣱⠃⠀⠀⠀⠀⠀⠀⢀⠙⠻⢿⣿⡙⠁⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡹⣇⠀⠀⠸
⠀⠀⠀⠀⠀⢨⡿⠁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠈⢏⠛⠛⡇⠈⢻⣿⣆⠙⢏⣿⢻⣿⣧⡟⢷⡄
⠀⠀⠀⠀⠀⡸⠁⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠷⠄⠀⠈⠻⣧⡈⢡⣿⣿⣿⠁⠀⡟
⠀⠀⠀⠀⠰⠁⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠹⣧⢿⣀⠠⡃
⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⢿⣶⣿⡀⣠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⠐⣦⠀⢀⢈⠙⠛⢉⢀⠀⢰⡞⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣀⠀⠀⠀⠀⠀⠀⠈⠢⣘⡎⠀⠀⠈⣞⡠⠎⠀⠀⠀⠀⠀⠀⠀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢼⡟⣀⣄⡘⣿⠅⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⣠⣴⣉⣩⣿⢸⣏⣉⣳⣤⣀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⢀⡴⠫⢏⣾⢟⣿⡿⠸⣿⣟⣿⣝⢏⠳⣄⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⣿⢟⣿⣿⡧⢰⣿⣿⡟⢿⡆⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣇⢀⣏⠘⣿⣿⡇⠀⣿⣿⡟⢈⣅⢀⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⣋⣿⣮⣿⡀⢻⣿⣷⢸⣿⣿⠃⣸⣯⣾⣍⡉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠟⠁⢠⢞⣉⡉⠙⠛⢿⣶⣍⣉⣈⣉⣵⣾⠟⠛⠉⣉⢙⢷⠈⠻⣿⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢠⠚⠋⠉⠉⠉⠈⠉⠁⠀⠀⢸⡸⣿⣿⡀⣀⢠⠈⣧⢳⢰⢯⡎⢀⡆⣠⣤⣿⡿⢻⠀⠀⠈⠉⠀⠀⠉⠉⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⣿⢡⠿⣿⡋⢏⠏⢇⠋⡖⡻⣁⣗⢹⣿⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢨⣿⣾⣶⣎⡿⣦⡘⡬⢠⣸⡟⣡⣼⣿⢟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢘⠉⢯⡽⣟⣼⣷⣀⡗⢰⣛⣏⣿⢐⡟⠺⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣀⣚⣘⡯⣤⢾⣉⡷⢾⣱⡖⣟⣨⣤⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠉⠣⡤⢭⣟⢀⡯⠨⡿⢧⡇⡫⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠼⢮⣛⢎⡏⠠⡿⠰⠷⡞⣷⠼⢄⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣾⣧⣀⣀⣠⣷⣀⠀⣬⣿⣶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠉⠁⠀⠁⠀⠉⠉⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠲⣤⣀⣄⣠⡴⠒⠦⠠⣤
⠀⠀⠹⣯⠿⣱⣆⣀⣠⣮⣽⣮⡟⠀⢰⡔⣠⣄⡀⠀⢀⣠⣄⢲⡆⠀⠙⠲⣄⡀⠈⢉⣿⠉⠀⣀⡴⠚⠁⠀⢶⡶⢢⣤⣤⣠⣠⣤⡄⠲⠆
⠀⠀⠀⢉⣟⣿⡽⣿⢻⣽⣫⡍⠀⠀⠀⠻⠟⣿⣿⣿⣿⣿⠻⠟⠀⠀⠀⠀⠈⢿⣶⡾⠙⣶⣶⡏⠀⠀⠀⠀⠈⠠⣻⣿⣋⢻⣋⣻⣟⡦⠉
⠀⠀⠀⠘⣿⣿⠇⠛⠰⣯⣿⠃⠀⠀⠀⠀⢢⣌⣙⠙⣋⣠⡴⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠈⠙⠄⠀⠀⠀⠀⠀⠀⠙⠿⠍⠀⠨⠽⠛⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⢀⣀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⢰⣶⣶⡶⠤⢀⡀⠴⢶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠂⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣦⣀⠀⠘⠿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣽⣿⠿⠃⠀⠀⠹⢿⣧⠀⢸⡇⠀⣜⡿⠋
⠀⠀⠀⠀⠀⠀⠜⠿⠇⠀⠀⠀⠀⢠⣶⣿⣼⣿⣿⣿⣿⣿⣾⣿⣦⡀⠀⠈⢹⡟⢛⠛⣟⠛⡿⠁⠀⠀⠀⠀⠀⠀⠘⣷⣶⡎⣴⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠛⠻⠿⠾⠿⠶⠿⠋⠙⠁⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠁⠈⠉⠣

⠀⠀⢠⠀⠤⠀⡀⡀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⡟
⠀⠀⠈⠓⠀⠀⢻⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⢷⣨⣿⣿⣰⠏⠀⠈
⠀⠀⠀⠀⠘⠙⠀⠙⠁⠀⠀⠈⠗⢠⣄⠺⠁⠀⠀⠘⠃⠀⠋⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠈⠿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⣰⠉⢳⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠁⠤⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠺⠰⠉⠆⠀⠀⠀⠀⠀⣶⣏⣳⡖⠀⠀⠀⠀⠀⢀⣘⣁⠀⠀⠀⠀⠀⠀⠹⠺⠈⠁⠀⠀⠀⠀⠀⢨⡀⠗⣈⠂
⠀⠀⠀⠐⠿⠗⠃⠀⠀⠀⠀⠀⠁⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠺⠏⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢘⣏⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡉⣯⠩⠀⠀⠀⠀⠀⠀⡑⣇⣿⡋⠀⠀⠀⠀⠀⣾⠃⢷⡄⠀⠀⠀⠀⠀⢸⠦⠿⠀⠀⠀⠀⠀⠀⠠⠛⡈⠓⠆
⠀⠀⠀⢓⣿⡀⠂⠀⠀⠀⠀⠨⠃⣇⡿⢡⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀⠀⠀⠀⡅⠀⠀⣏⠀⠀⠀⠀⠀⢐⠀⠁⠘⡂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⢸⣁⡿⠀⠀⠀⠀⠀⠀⠹⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠴⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠰⣤⣤⡔⠢⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡀⠀⠀⠀⠀⠐⢀⡊⣒⠀⠀⠀⠀⠀⠀⠀⡤⢢⠄
⠀⠀⠀⢐⢠⢰⠂⠀⠀⠀⠀⠀⡜⠀⠂⠀⠀⠀⠀⢀⢀⡻⠻⡟⡀⠀⠀⠀⠀⠀⠈⠀⠃⠔⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⠈⢹⡸⢀⠁⠀⠀⠀⠀⠐⠢⢝⢡⠃⠀⠀⠀⠀⠀⢿⡘⣿⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠘⢖⣲⠗
⠀⠀⠀⢻⣒⣚⡗⠂⠀⠀⠀⠀⢶⣌⣰⠦⠀⠀⠀⢀⠁⠪⡄⠼⠉⠀⠀⠀⠀⠀⠀⢇⡼⢀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢨⣡
⠀⠀⠐⡘⠁⠋⠪⠀⠀⠀⠀⠀⢈⠇⣺⠀⠀⠀⠀⠀⠀⠒⠐⠀⠠⠀⠀⠀⠀⠀⠼⠃⠷⠀⠀⠀⠀⠀⠀⠀⠚⠳
⠀⠘⠒⠄⠀⠀⠔⠀⠀⠀⠀⠀⣰⠐⡰⠀⠀⠀⠀⠀⠬⠀⠀⠈⠤⠀⠀⠀⠀⠈⢦⣛⣠⠆⠀⠀⠀⠀⠀⠀⠂⠘⠂
⠀⠈⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢤⠔⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⠘⠆⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣶⣤⡴⡇⠀⠀⠀⠀⠀⠘⢡⠛⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡆⣖⠀⠀⠀⠀⠀⠠⠌⠀⠀⠠⠄
⠀⠀⠠⠄⣿⠅⠃⠀⠀⠀⠀⠀⢂⠸⠀⡂⠀⠀⠀⠄⠀⡌⠈⣄⠀⠀⠀⠀⠀⠀⣠⡞⠤⠀⠀⠀⠀⠀⠀⢴⡄⠀⣼
⠀⠀⠀⠶⠊⠛⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠑⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⢀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡄
⠀⠀⠀⠀⠀⢀⢸⣷⢀⠀⠀⠀⠙⣧⠰⣟⠳⡄⠀⢀⠴⢻⡇⣰⠟⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠸⣧⠇
⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀⠘⢧⣊⣭⢾⣶⡾⢮⣕⣰⠋⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⣦⣼⣴⠆
⠀⠀⠀⠀⠀⠁⣿⣿⡇⠁⠀⠀⠀⠀⠀⡄⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⢺⣿⣟
⠀⠀⠀⠀⠀⠀⡟⠹⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟
⠀⠀⠀⠀⠀⠀⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢴⣶⣶⣤⣤⣤⣤⢷⣤⣤⣤⣤⣶⣶⠆
⠀⠀⠺⣽⣷⢦⣄⣀⣤⣶⣿⡽⠂⠀⠀⠀⠰⣿⣿⠀⠀⠀⠀⠈⠉⣛⣿⣿⡿⣾⣿⣿⣟⣋⠉
⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⡘⠁⠀⠀⠀⠐⢸⣷⣿⠁⠀⠀⠀⠐⠟⠛⠛⠉⠀⡇⠈⠙⠛⠛⠷⠀⠀⢠⣴⣤
⠀⠀⠀⠀⠙⠿⠋⠈⠻⠛⠁⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣄⣤⣄⣀⠀⣀⠀⢀⣠⣤⣄⡄
⠀⠀⠀⠀⠀⠀⡸⡿⡀⠀⠀⠀⠀⠀⣠⣾⡿⠡⠭⠻⣿⣦⡀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠈⠛⢻⣿⣿⣧⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠈⠉⠁⠀⠰⠇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠈⠉⠉⣿⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⣿⣿⡟⠢⠀⠀⡰⠛⣿⣿⠏⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢠⣼⣿⣤⠀⠀⠀⠀⠹⢟⣇⣀⣠⣦⣀⣠⣟⠟⠀⠀⠀⠀⢀⣮⠍⣦⠀⠀⠀⠀⠀⠀⢀⣶⣆
⠀⠀⠀⠀⢀⣾⡿⠿⣿⡆⠀⠀⠀⢐⣿⠋⠀⠘⠇⠀⠙⢻⡆⠀⠀⠀⠀⢸⣿⣾⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢸⡿⢙⣚⠹⣿⠀⠀⠀⠀⢻⣷⡴⠀⠀⠢⣶⣿⠁⠀⠀⠀⠀⠀⢻⣿⠏⠂⠀⠀⠀⠸⠛⠉⠿⠋⠙⠿
⠀⠀⠀⠀⠈⠁⠈⠉⠀⠉⠀⠀⠀⠰⠃⠈⠀⠀⠀⠀⠉⠈⠦

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠿⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠞⠛⠋⠙⠛⠒⢺⣿⢥⣀⡀⠀⠀⢀⣀⡤⠜⡗⠒⠛⠉⠙⠛⠳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡩⠗⠺⢍⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢣⣄⠀⠀⠀⠀⢰⣿⠧⠊⠁⠀⠀⠀⠀⠈⠑⠤⣀⡆⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣿⡇⠀⢀⡤⢺⣿⠀⠀⠀⠀⠀⢲⣦⣄⠀⠀⠈⡗⢤⡀⠀⣤⣀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⣷⣴⠉⠀⢸⣿⠀⠀⣷⣀⣀⣰⣿⣿⡆⠀⠀⡇⠀⠉⣢⣾⠟⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠻⣷⣤⣸⣿⠀⠀⢻⣿⣿⣿⣿⡿⠃⠀⠀⣇⣤⣾⠟⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠛⢿⣿⣄⡀⠀⠉⠛⠛⠋⠀⢀⣠⣶⡿⠛⠁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣶⣤⣀⣀⣤⣶⡿⠛⢉⠇⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣼⣿⡿⢿⣿⣥⣄⣀⣸⠀⠀⠀⠀⠀⠀⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⣶⣶⡾⠿⢿⣿⡋⠉⠁⠀⠀⠀⠉⠙⢻⡿⠿⣿⣶⣶⣾⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⣿⡃⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣦⡶⠛

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

⠀⠀⠀⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⣤⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣤⣾⣿⣿⣿⡏⣧
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⡟⢿⣿⣿⣿⣿⠓⠙⠛⢿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿⣿⢿⣿⡅⠀⠹⣷
⠀⠀⠀⡇⠉⠛⠛⠋⠀⠀⠀⠀⠀⠙⣿⣿⡋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠀⠰⣿⣷⠀⠙⣿⡆⠀⠈⣧
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣟⢷⣦⠀⠀⠀⠀⠀⣹⡿⢿⡄⠸⠏⠙⢳⣶⡾⠇⠀⠀⢸⣦
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣇⠀⠀⠛⠛⠋⠀⠈⣷⡀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠐
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠙⠃

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⢀⣀⠀⠄⡀
⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠒⠒⠒⠒⠒⠒⠀⠄⠀⠀⠀⠀⢀⡠⢆⣈⣁⠀⠁⠐⢤⣦⡉⠁⠀⠀⢄
⠀⠀⡀⢐⡉⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⢠⣤⠀⠀⠀⠠⠞⠉⢀⠄⠈⣉⠀⠈⠻⠇⡙⣄⠀⢠⣀⠀⠀⠀⡀
⠀⠈⠀⠘⣷⡀⡄⣿⢰⢶⣆⣿⣰⣸⠃⣾⠃⠀⠀⠀⢰⠐⡄⠋⠀⠀⠘⢷⣷⡶⠂⢑⠈⣷⣄⢻⢷⣶⡀⠈⢂
⠀⠀⠀⠀⠘⣷⣿⡏⢻⣀⡿⢹⢿⡏⠸⠃⠀⠀⠀⢠⠄⣸⡿⠓⢜⠶⠛⠈⢯⡁⠀⢈⠀⣬⣻⣏⠁⡝⠋⢲⣄
⠀⠀⠀⠀⠀⠘⠇⠁⠈⠉⠁⠀⠀⠐⠂⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠑⠶⠴⠖⠕⢺⣿⡷⣿⣭⣍⣓⡮⢲⣬⣿⣇
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠻⢿⠄⣀⠀⠉⠀⠀⣠⠖⠛⠉⠑⠂⠳⣝⣦⣄⡤⣽⡿⠷⢍⢳⣽⣿⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢠⢀⣻⣶⣧⠉⠛⠋⡀⣷⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣀⠠⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⠀⢣⢠⢻⡎⢿⣿⢧⠀⠀⣸⢏⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠎⣐⠀⠀⠀⠀⠈⠠⠄⠀⠁⠀⠀⠀⠀⢈⡀⢸⡇⠀⣿⡷⢲⣮⣽⠎⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢰⡏⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣞⡆⣆⣿⡿⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠟⠳⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠘⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡖⣠⣽⡿⢿⣤⡀⢀⡀⠀⠀⣀⡴⠂⠀⠀⠀⠀⢀⡞⢹⣾⠱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣈⠸⠁⣸⣄⢬⣿⣿⣦⡙⣿⢿⠉⠁⠇⠀⠀⠀⣠⡟⠐⣿⣿⠠⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢤⡿⢻⣦⠀⠛⢁⡹⠽⠿⣹⣷⣌⢛⣒⣁⠄⠀⠀⣴⠏⠀⠀⠿⠿⠦⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⠧⠀⠈⣓⣶⡿⠋⠞⢻⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠦⣀⠀⢘⣴⡤⢤⡶⢦⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡿⢟⠎⠝⠃⢒⡉⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⡇⠀⢸⣀⠐⣿⡇⣿⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⡀⢀⠄⢀⡠⠉⠀⣿⡇⣿⡞⠋⠁⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⠤⠠⠢⠀⠉⠀⡥⢀⣿⣧⠟⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠸⠀⡀⡄⠀⢄⠀⠘⠀⡅⠛⠁⠀⣤⠔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠴⠀⠀⠀⢄⠀⠐⠄⢈⡠⠗⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⣄⠀⡀⢀⡉⠀⠀⠀⠂⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⡿⡇
⠀⠀⠀⢰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣴⣇
⠀⠀⠀⠀⠙⣿⣿⣿⣽⣿⣶⣤⣀⢀⠰⠃⠘⠆⠀⢀⣤⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣙⣻⣿⣿⣿⣿⣿⣷⡇⠡⠄⠸⣾⣿⣿⣿⣿⣿⣟⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠉⣵⣿⣿⣿⡽⣛⢵⡂⠙⠋⢐⡪⣝⢯⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠷⠀⠀⡀⢀⣰⡄⠀⣸⢿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢰⢹⣿⣾⣿⣿⡏⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠂⠁⣠⣴⣿⠿⠋⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⠭⠭⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣵⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠸⢿⠿⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢢⢂
⠀⠀⠀⠈⠖⡼⢀⣃⡤⢠⡄⣀⠀⢄⡘⠃⠘⠃⣀⠀⢀⠠⡄⢰⣔⣇⢧⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⡧⠀⡄
⠀⠀⠀⠀⠘⡍⣑⡒⠽⡶⠳⢺⢧⣦⡍⠁⠈⢉⣴⡤⣟⠺⢳⡮⠔⡚⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠮⢷⠢⠌
⠀⠀⠀⠀⠀⠀⠨⠦⠎⠑⠘⠋⢋⣹⡄⠀⠀⢠⣏⠙⠋⠋⠚⠹⠴⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣮⡯⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣴⣤⣤⣤⣶⣦⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⡀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣛⡻⠿⠿⠿⢛⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠀⢠⣀⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢩⣙⣛⣛⣋⡭⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢻⣛⣩⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣾⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠿⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢋⣽⠟⠋⠉⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠿⢿⣭⡙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⢿⣆⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠀⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣀⡀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠏⣿⠀⢸⡿⣿⠻⣦⣄⡀⠀⠀⠀⢀⣠⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣍⠛⠛⠛⣿⣿⡏⠉⢀⣾⠏⠀⣿⠀⢸⡇⠹⣧⠀⢩⣿⣿⠛⠛⢛⣹⡿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠙⠿⣦⣄⣈⣛⣡⣴⠟⠁⠀⠀⣿⠀⢸⡇⠀⠙⢷⣤⣙⣋⣠⣴⠟⠋⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⣸⡏⠀⠈⣿⠀⠀⠀⠉⠉⠉⠉⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⣀⣠⣤⠤⠤⠶⠤⢤⣤⣌⣉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⢷⠀⠀⠀⠀⠀⡜⠀⠉⠙⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣆⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠇⠀⠀⠀⢀⣼⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣷⣤⣤⣤⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣀⣀⣀⠀⣀⡀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢰⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡎⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠘⢿⣦⣀⢰⣾⣿⣿⣶⢀⣠⣾⠟⠀⠀⠀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣄⠀⠀⠈⢿⣿⡿⣿⣿⣿⡿⣿⣿⠏⠀⠀⢀⣼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣾⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠋⠁⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠉⠳⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣸⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠉⠛⠋⠛⠋⠁⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠒⠒⠒⠂⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⠠⠀⠀⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡇⣼⠀⣀⡀⠰⠀⠀⠀⠀⠀⠀⠀⣴⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⡆⠀⠀⠀⠀⠒⠐⠁⢈⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⢀⡈⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡈⠆⡀⠈⠂⠔⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣧⡤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢛⡿⠄⠤⠢⣔⠀⠈⠉⠑⠓⠉⠺⠄⡛⠃⠚⠀⠀⠂⠀⠂⠀⣀⡀
⠀⠀⠀⠀⠀⣠⠀⡀⡀⠀⠈⠀⡀⠀⠀⠀⠀⠰⠒⠂⠀⠀⠀⠀⠀⠀⠢⠐⠇⣀⠐⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⢄⠓⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠍⠀⠠⣀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠁⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⠀⣅⠠⠂⠒
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢲⠒⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠛⠻⣟⠛⠟⠿⠾⠛⣻⣏⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣿⣿⡷⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢾⣿⣿⣿⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⣿⣿⡀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣉⡀⠀⠀⣿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⣀⣠⣾⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣦⣀⠀⠀⠀⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣀⣰⣿⣿⡿⣋⠹⡏⣼⢹⣿⡄⠀⠀⠀⠀⣰⡿⣿⣮⡿⠩⣿⣿⣿⣧⣀⣀⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⣿⣿⣟⠁⡁⢙⡀⠄⠠⠎⠞⠛⢦⣾⣆⣼⢋⣇⡱⠀⠀⢰⡋⢈⠙⣿⣿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⣿⣿⠄⠓⠸⠧⠀⠀⠂⣆⡄⠈⣿⣿⣰⣄⡏⡃⡀⠀⠞⠁⠄⠰⠿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⠲⣶⣾⣶⡷⡖⠒⢦⣿⣟⡻⢿⣶⣶⣶⣻⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣟⠻⢿⣷⣿⢿⡇⢑⠍⣉⠀⣿⡏⠐⣻⣿⠉⣹⠿⣷⣾⣿⢿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡉⢶⣊⠁⠉⠒⠀⡍⠀⠀⠀⢽⡇⠀⠀⢷⣧⠐⠊⠉⠙⣻⣾⣸⣳⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢷⣟⠲⠍⣀⠖⠀⣤⢀⠀⠀⠀⠸⠃⠀⠀⢀⡆⣤⠑⢟⣈⡹⢟⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢿⣿⣶⢾⣥⢴⣆⠤⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⢿⣬⣶⣶⣯⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠏⠉⠙

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

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⠛⠛⠛⠱⣼⠀⠀⠀⠀⠀⠈⠱⣦⡀⠀⣠⣤⣤⣄⠀⢀⣤⠏⠁⠀⠀⠀⠀⢠⣇⡎⠛⠛⠛⠿⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠟⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⡴⠫⠈⣩⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠱⣄⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣿⣥⣤⣾⠿⠅⠹⠇⠻⠏⣋⠁⡿⣘⣻⣿⣦⠶⣿⣿⣤⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⣶⣾⣧⣦⣿⣴⣷⣀⣴⣿⣶⣿⣿⣿⣳⣿⣷⣬⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⣉⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠪⠉⡉⠉⠉⠉⠉⠉⠛⣛⣿⣿⣟⡛⠛⠉⡉⢩⠁⣤⠀⠀⠢⢦⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⡄⠀⠀⠀⢂⠐⣰⣾⣿⣿⣿⣿⣿⣶⣄⠡⡜⠇⠀⠀⠀⠀⠀⠛⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠊⠀⠄⠐⠀⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⠉⠇⠁⠀⠀⠀⠀⡀⠀⠀⡀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣶⠁⠀⠈⠔⠀⠀⠂⠀⠀⠀⠈⠻⢿⡏⠛⡍⠥⠡⠈⠀⠀⢆⠀⠄⠠⠀⠀⡀⠄⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣯⠀⠀⠈⠎⡀⠀⠀⠀⠀⠀⣀⡙⠾⠁⠤⢱⡚⡆⢣⠀⠀⠈⡄⠠⠀⠂⠀⠀⣠⡎⣿⡆
⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣿⣿⢸⣿⡇⠂⠈⠰⢀⠀⠀⠀⡠⠳⣲⢳⣻⠠⠘⡀⢣⢭⠀⠀⠀⠀⠱⠀⠀⠠⠀⢸⣿⡧⢹⣿⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠋⠉⠉⠙⠿⣦⣸⣿⣧⠜⠟⠁⡢⠈⠃⣌⠠⠀⠠⣻⢧⣟⢾⣿⠀⠠⣹⡌⡂⠂⠈⠀⢀⡀⠠⠆⠀⠄⠄⠛⠃⢸⣿⣇⣶⡿⠋⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⡐⠁⠋⣠⣽⣿⣿⣿⣧⡺⡿⣿⣾⠀⠱⣼⣧⣀⣴⣶⣿⣿⣿⣷⣦⣇⠘⡌⠀⠁⢸⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⡛⢸⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠌⡰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣦⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠣⡈⡆⠁⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁⠍⡙⠛⠿⠟⠻⣿⠟⠠⠷⣿⠸⣌⣟⢼⠋⡟⠛⠋⣩⢩⠉⡔⣆⢩⠐⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠈⠀⠀⠂⡖⡲⠆⠀⠴⣗⡳⢽⢪⠐⢩⣾⡿⡇⢩⠀⢣⠤⠄⢤⠤⡸⡀⠆⠰⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⡄⣄⠀⢀⠁⠄⠂⢠⡄⢨⢐⢨⠰⠀⢺⡇⠀⢁⠀⡀⡰⢦⢱⠐⡀⢀⣱⣘⢂⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠻⣿⣧⣌⠀⡃⠍⢉⡴⢸⠚⢰⢸⢩⣿⢁⠀⠈⣀⠳⢨⣏⡐⣦⣿⣿⣿⣯⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠙⣿⣿⣷⡀⠂⣡⠜⢹⢾⠨⣽⠓⡏⢸⠀⡇⢯⠸⠄⡄⢡⣿⣿⣿⡿⢃⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠈⠻⣋⠡⡄⡁⠈⢹⢘⠀⡇⡀⡇⡘⠄⠹⢨⠙⠆⣡⢨⠝⣣⠞⠁⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⠀⠀⠈⠳⢍⡁⠠⣿⢸⡀⣧⡅⠂⡋⣆⢸⠄⠲⣷⢪⡠⠞⠁⠀⠸⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠒⠿⣼⣃⡘⡇⢁⡁⠥⠘⣁⠤⠚⠉⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⢶⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠀⣾⣟⠻⣦⠀⣿⠉⠛⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣄⠰⣧⠀⣿⠀⣿⡇⠀⠀⠀⢸⣿⣷⡟⠀⠙⠿⣷⣦⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡶⠀⢶⣟⠛⣦⠀⣿⠀⠈⣿⠀⢻⣆⣿⠀⢨⣷⠶⠂⠀⠀⣿⠘⣧⠀⠀⣤⣈⣿⠄⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⡄⠐⣷⣄⠘⣿⠀⠉⢻⡆⠀⠘⣿⣷⡿⠀⢹⡇⠀⢹⡇⠈⢿⣿⠀⠈⣿⡄⠀⣀⡀⢸⣇⠘⣧⠀⠛⠛⠋
⠀⠀⢰⡟⠛⢷⠀⣿⠀⠈⣿⠀⢿⣿⣦⣻⡇⠀⠘⣧⠀⠀⢿⡈⢷⡀⠈⣷⠀⢘⣷⠀⠘⣿⡄⠀⠸⠛⠛⠛⠁
⠀⠀⠘⣧⠀⠀⠀⢹⡆⠀⢹⡇⢸⣿⠙⣿⣷⠀⠀⢻⡄⠀⢸⣧⠈⢷⠀⠙⠻⠛⠃
⠀⠀⠀⢿⠀⠀⠀⠈⣷⠀⢘⣷⠀⣿⡄⠘⠿⠄⠀⠘⠃⠀⠀⠁
⠀⠀⠀⠸⣧⣤⡿⠀⠙⠻⠟⠃⠀⠈

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠢⢤⡀⠀⠀⠀⢀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⣠⠒⢛⣛⡒⠢⢄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⡄⠀⡴⠋⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⣇⠀⡏⠀⠉⠑⠦⣈⠳⢄⠀⠀⠀⠀⠣⡀⢀⡆⠀⠀⢱⣸⠁⠀⢰⠀⠀⢠⠇⠀⠀⠀⡠⠖⣋⠥⠒⠒⢢⠀⢘⡄
⠀⠀⠀⠀⠀⠘⢦⡙⢄⡀⠀⠀⠈⠑⠦⡙⢦⡀⠀⠀⠈⠉⠀⠀⢀⣸⣇⠀⠀⠈⠓⠒⠋⠀⣀⠔⣫⠔⠋⠀⠀⠀⢀⠞⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣍⠒⠤⣀⠀⠀⠈⠲⣝⠦⡀⠀⠀⠀⡴⠋⠆⠰⠑⡄⠀⠀⠀⣠⢞⡥⠊⠁⠀⠀⣀⡤⠒⣁⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢬⡙⠢⢄⡀⠈⠑⣍⢦⡀⠀⣇⠀⠑⠃⢀⡇⠀⡠⢊⠔⠉⠀⢀⡠⠔⢋⡡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣌⡓⠢⢌⣷⠙⢦⡈⡷⠠⢶⢋⡤⠊⡔⣁⣠⠴⢊⣡⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣤⠀⠀⢹⠓⠒⢾⠋⠀⢀⣩⠥⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣋⡭⠤⡄⢀⣧⣤⣀⣸⡀⠀⣀⣉⡙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠊⣁⠴⠚⠉⢀⡴⠊⢀⣼⠀⠀⠀⠈⡟⢆⠑⢄⡈⠑⠲⢤⡉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⡠⠔⠋⠀⠀⣠⠔⠉⢀⠔⠁⡏⠉⠉⠉⠙⡇⠀⠱⣄⠙⠦⡀⠀⠈⠑⠦⣈⠙⠢⣄
⠀⠀⠀⠀⠀⣠⠞⠁⣀⠔⠋⠀⠀⢀⡤⠊⠁⡠⠞⠁⠀⢸⠷⠤⠤⠤⢤⡇⠀⠀⠈⠑⢄⠈⠓⢄⡀⠀⠀⠑⠦⡀⠙⢦⡀
⠀⠀⠀⠀⡴⠁⢀⠞⠁⠀⣀⠤⠚⢁⡠⠔⠋⠀⠀⠀⠀⢸⣄⣀⣀⣀⣰⠁⠀⠀⠀⠀⠀⠙⠦⣀⠉⠲⢄⡀⠀⠈⠢⡀⠙⢦
⠀⠀⠀⢰⡁⠀⠘⠒⠒⣉⣡⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡈⠓⠢⠤⠜⠀⠈⡆
⠀⠀⠀⠀⠑⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠛⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠦⠤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⡿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠁⠀⢀⡀⠠⣄⠀⠀⠀⠸⢿⣿⡟⢼⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣤⣶⣶⣿⣿⠿⠿⣷⣶⣄⣦⡠⠙⠁⠀⠆⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢾⣿⣿⣿⡟⠁⠀⠀⠙⣿⣿⣿⣷⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⡟⢠⣾⣿⣷⡀⢙⣿⣿⣿⢫⣵⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣫⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢝⣿⣿⣿⣿⣿⣿⣿⠟⠉⣾⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⣿⣿⣿⣿⣿⣿⡿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢺⣿⣶⡎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⡲⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡋
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢸⠆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠈⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⡟⠀⠀⠀⠙⢻⣿⣿⡟⠙⠋⠉⠁⠀⠀⠀⠀⠀⠈⠈⠉⠉⠙⠛⠋⠀⠀⠀⠐⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣆⣤⣶⡄

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

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

⢐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡄
⢸⣿⣿⣿⣿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣠⣤⣤⣤⡤⠤⣀⣴⠀⠀⠀⠀⢀⠀⢸⣿⣿⡇
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⣠⣿⣿⠀⢻⣿⣶⣤⣤⣤⣹⣧⢸⣿⣿⡇
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⣻⣟⠉⠉⠉⠉⠉⢹⡏⢩⣿⡿⠈⣯⢸⣿⣿⡇
⢸⣿⣿⣿⣿⠀⠀⠀⠀⢠⣄⢀⡼⠁⠀⣰⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠿⠗⠀⠘⢾⣿⣿⡇
⠸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⣿⡁⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣷⡄⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⢸⡟⠀⡟⢹⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣿⣼⣧⣤⣧⣼⣄⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠀⠠⠤⠤⠤⠀⠤⠤⢄⡀⢸⣿⣿⡇
⠀⣿⣿⣿⣿⠀⢀⣴⡎⣡⣸⡏⠻⣏⠉⠉⠉⠉⢉⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⣿⣿⡇
⠀⣿⣿⣿⣿⠀⢺⣿⣿⣿⣿⠈⢲⣸⣧⣀⣀⣠⣾⣥⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣿⣿⡇
⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⣿⣿⡇
⠀⣿⣿⣿⣿⠁⠈⠉⠉⢹⣿⣿⣿⣿⡟⠁⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣿⣿⡇
⠀⣿⣿⣿⣿⠐⠄⠀⠀⣿⣿⠿⠯⠙⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⡇
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠄⠈⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠉⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣿⣿⣿⣿⣤⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣧
⠀⣿⣿⣿⣿⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿
⠀⣿⣿⣿⣿⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⠀⣿⣿⣿⣿⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⣿⣿⣿
⠀⣿⣿⣿⣿⢠⣿⠃⠀⡀⠀⠀⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⣿⣿⣇⠀⠀⣿⣿⣿
⠀⣿⣿⣿⣿⠈⣿⡆⣸⣿⡄⣼⡏⣿⣧⣤⡀⣠⣦⣤⡄⣼⣷⠀⢡⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⣿⣿⣿
⠀⣿⣿⣿⣿⠀⠸⣿⣿⠻⣿⡟⠀⣿⡇⢸⡿⣿⣤⣿⡇⢸⣷⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠙⣿⣿⣿⣿⣿⣿⣟⠀⣿⣿⣿
⠀⣿⣿⣿⣿⠀⠀⢈⣥⣶⣍⣷⡆⠈⠀⠈⠁⠀⠁⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿
⠀⣿⣿⣿⣿⠀⠀⣿⡏⠀⠉⣿⡷⣷⣤⣶⠶⣶⣶⡶⢶⡆⣴⡶⣶⣆⣴⣶⣦⣠⣶⣶⣿⠀⢠⣀⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠹⠿⣶⠖⣿⠀⢿⠿⢿⣶⣿⠿⡇⠸⡟⢿⣶⣾⡟⢿⣭⡿⠻⣷⣴⣿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⣄⠴⣶⢲⡆⢤⣴⣤⠄⣰⢲⡶⢂⣤⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠻⣧⣄⠀⠹⠀⣽⡇⠰⠉⠀⣠⣾⠋⠀⠀⠀⠀⢠⣾⠏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢻⣿⡄⠁⠏⢀⠁⣰⡿⠉⠀⠀⠀⠀⠀⠀⢊⣽⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⡿⠞⠀⠈⠻⣏⠀⠀⠀⠀⠀⣴⣶⣶⡽⢻⡿⡿⢻⣹⣾⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⣤⣄⡘⢿⣿⠇⠀⢇⠃⠀⣿⣿⠋⣀⣴⡄⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡠⠀⠀⢠⠤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢧⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡶⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢶⣦⠆⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡾⣏⡙⣃⢈⡄⠀⠀⠤⠄⢀⠀⠀⡀⢠⣶⡄⢀⡀⠀⠀⡠⠤⠀⠀⠀⢈⣠⣼⣧⣄⡃
⠀⠀⠀⠀⠀⠀⣨⣭⣿⣿⣟⣯⡭⡄⠀⠀⠀⠀⠀⠈⣓⢉⣿⣿⣿⡉⢉⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⣿⣋⣀⡀
⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⡇⢇⠰⠀⠀⠈⠙⠱⠋⠁⠞⠈⣿⠉⠣⠀⠙⠟⠛⠁⠀⠀⠎⠀⣿⣿⣿⣿⠁⠰⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⣿⣿⡷⠦
⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⡟⢸⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⠇⠹⣷⣿⣍⣠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠉⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⡑
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠇⠰⣲
⠀⠀⠀⠈⢃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣷⣆⠀⠔⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠉⠙⠥⢔⣀⠀⠀⠀⣀⣴⣠⣴⡾⠛⠉⢻⣿⣦⣀⡀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢿⣿⡋⠀⠀⣠⣾⣿⣿⣿⣷⣀⣀⢴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠿⣿⣙⣻⣿⠁⢈⣏⣰⣿⣻⡟⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⣠⠄⠀⠂⠈⢹⣿⡿⣋⠛⠀⣣⡾⢻⠶⢋⡟⠻⡉⠙⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠦⡀⠀⠈⠙⢿⣏⣦⣾⣫⣔⣧⣚⣇⠈⢶⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣠⣼⠟⡿⢛⣡⠾⣻⣿⣿⡟⠁⠀⡌⠀⢤⣤⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣟⣦⡼⠿⢿⣷⣎⠁⠀⢀⡨⠀⠹⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⢿⣷⣤⡶⠟⠻⣿⣿⡜⠊⠃⡀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⣿⣿⣶⠶⠛⠿⣿⣾⡌⠁⠀⠀⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠸⣇⠈⠛⠿⣶⣿⣯⣻⡧⠀⠀⠀⠀⠘⠄⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠳⣄⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠈⠉⠒⠴⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⠀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠐⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡴⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⠀⠀⣀⠤⡶⠦⠒⠾⠯⠖⠊⠙⠺⠥⢖⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⡔⢦⣀⣀⠀⠈⢿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⡇⣠⢖⣋⡉⢹⠀⠀⠙⠒⠒⠛⠻⣦⢸⣆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⡷⠟⠁⢰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠘⣏⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⡇⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⡀⠀⠀⠀⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣧⠀⠀⢀⠀⠀⢉⣉⠭⠤⠤⡜⢄⠀⢸⣏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡄⠀⡌⡠⠞⠓⡒⡚⠫⣉⢹⡜⡄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢣⣇⠔⠚⡄⠈⠀⢸⠉⠁⢇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⠦⠤⠚⢀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠲⠦⠴⠖⠚⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⣿⡍⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣼⡿⠉⠉⠒⠦⣄⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠸⡕⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣻⠃⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠮⣑⠤⣄⣀⣀⢀⣀⣀⠴⣊⠵⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠺⠯⠭⠗⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠰⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠞
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⢧⣀⣤⣀⠟⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢷⠀⠀⠀⠀⠀⠀⢀⠞⠉⠲⡀⠀⠀⠀⠀⠀⠀⡴⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⣇⠀⠀⡴⠂⢀⡙⠚⠓⠚⠉⣉⠉⠢⡀⠀⣠⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⡄⢸⡁⣾⣿⣿⣿⠀⢸⣿⣿⣿⠀⡇⢠⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⣇⠙⢿⣿⣿⠀⢸⣿⣿⠿⢠⢏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠘⣿⡄⢸⣿⠁⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠊⣩⠶⠿⣷⡿⠿⣭⡁⠉⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⢁⣴⣾⣿⣧⠀⠀⢿⡇⠀⣰⣿⣿⣷⡄⠈⣟⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⢚⠇⢸⣿⣿⣿⣿⠀⠀⢸⡇⠀⢻⣿⣿⣿⡏⠀⠸⡈⠹⢆
⠀⠀⠀⠀⠀⠀⠀⡐⡘⠀⡼⠀⠀⠙⠛⠛⠁⣠⣾⣿⣿⣷⣄⠉⠉⠉⠀⠀⠀⢧⠀⢆⢣
⠀⠀⠀⠀⠀⠀⣸⢰⠃⢠⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⡀⠈⡄⢣
⠀⠀⠀⠀⠀⢠⣳⠃⠀⡜⠀⠀⣀⣀⣀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⣀⣀⣀⠀⠈⠇⠀⠈⢴⣇
⠀⠀⠀⠀⣠⠞⠁⠀⢀⡇⢠⣿⣿⣿⣿⣿⣷⣄⠉⢹⡟⠉⣠⣾⣿⣿⣿⣿⣧⠀⢸⠀⠀⠀⠘⢦⣀
⠀⠀⣠⡼⠁⠀⠀⠀⢸⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⠟⠀⠈⡄⠀⠀⠀⠀⠹⠕
⠀⠈⠑⠁⠀⠀⠀⠀⢸⠀⠀⠈⠙⠿⢿⡿⠟⢁⣀⣼⣧⣀⠈⠻⠿⠿⠛⠁⠀⠀⠐⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⣇⢣
⠀⠀⠀⠀⠀⠀⢰⡁⢾⣠⣴⣶⣆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣤⣤⡀⡇⢉⠄
⠀⠀⠀⠀⠀⠀⣼⡅⠘⣿⣿⣿⣿⠀⠀⠀⠙⠿⠿⣿⣿⣿⠿⠟⠁⠀⠀⣿⣿⣿⣿⠁⠘⡘⡄
⠀⠀⠀⠀⠀⢀⢃⠃⠀⢻⣿⣿⡟⠀⠀⣠⣤⣄⠀⠀⡇⠀⣠⣤⣤⡀⠀⠹⣿⣿⡿⠀⠀⡇⢱
⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⢿⡟⠀⠀⣼⣿⣿⣿⡇⠀⡇⠀⣿⣿⣿⣿⠀⠀⠈⣿⠃⠀⠀⠸⡀⢃
⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠱⣄⠀⣿⣿⣿⣿⠇⠀⡇⠀⣿⣿⣿⣿⠇⠀⡰⠃⠀⠀⠀⠀⠳⣿⡀
⠀⠀⠀⠀⣠⠟⠃⠀⠀⠀⠀⠀⠈⠳⢝⡻⠿⠋⠀⠀⡇⠀⠈⠛⠛⢋⡠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠓⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠄⠀⠠⠤⠀⠀⠀⠀⠉⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠛⠿⠿⠷⠤⣤⣦⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣉⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⡐⠀⠀⠀⠀⠀⡀⠀⠲⣴⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠖⠛⠀⠀⠀⢸⡿⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⣀⠀⢠⠀⠀⠀⣰⡿⠃⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡿⣃⣞⣠⡤⠾⢋⣠⣾⠿⠉⠇⠀⠀⠀⠀⠀⠀⠒⢟⠀⠀⠀⠀⠀⠀⢠⠝⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⢉⣉⣩⣶⣾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡜⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⠀⠀⡰⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠿⣿⣿⡟⢻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⢤⡿⠁⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢾⡿⣿⣷⡀⠘⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⠀⠀⠀⣾⣟⡆⠀⠀⠀⠀⠀⢪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠹⢏⣿⣆⠀⠩⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡐⡀⣰⣿⠗⠀⠀⠀⠀⠠⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⣿⣿⣆⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣯⣿⠇⠀⠀⠀⠀⢀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢘⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠺⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠁⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⣠⣿⢯⠀⣿⡟⢸⣷⠀⠀⠀⠠⡀⢴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⢠⡵⡿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⡁⠞⠁⠀⠀⠀⠀⠁⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠛⠒⠒⠛⠁⠀⣤⢀⣄⣠⢀⣀⣴⣦⠼⠋⠉⠉⠉⠁⠾⠳⠆⠲⠖⠐⠾⠓⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠈⠒⢄⠀⡀⠤⠤⠀⠀⠰⢀⠎⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⡦⠒⠁⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠆⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣮⠴⠀⠀⠀⠚⠛⠒⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡡⠠⡀⠀⠀⠖⣠⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢗⣿⠏⠀⠀⠦⠿⠻⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡘⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⠁⠉⡉⢢⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡇⠀⠀⠀⡀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠄⠰⣜⠜⠀⢀⠔⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠎⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠺⣁⣤⣒⠡⣖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢢⡀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠠⢧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠋⢂⠀⠀⠀⠑⡀⠀⠀⠀⢀⠆⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠐⠶⠀⡠⠃⠀⠘⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠀⠀⠀⠀⠋⠀⠀⠀⡔⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⠀⠀⠀⠀⠀⠀⢾⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢳⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠢⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠐
⠀⠤⣄⡀⠷⠄⣷⣀⠃⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠃
⠴⠒⠃⠀⡠⠀⠤⣈⠑⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠈⡌⠦⠀⠀⠀⠀⠀⠀⠇⡐⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⣰⠄⣀⡀
⠀⠀⢂⠐⡀⠀⠀⠀⠑⢄⠑⡄⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠰⡀⡁⣄⡀⠀⣠⠛⣠⠁⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⡀⠄⠚⢉⠈⡈⠙⣏
⠀⠀⠀⠣⡑⠤⡀⠀⠀⠈⡂⠘⡀⠀⣀⠤⠀⠀⠚⠄⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⡐⠃⠄⡀⠀⠀⡀⠊⡠⠐⠈⠀⠀⡁⠠⠁
⠀⠀⠀⠀⠈⠂⢌⡁⠒⠒⠁⢀⠗⠈⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⣀⠱⠀⠀⠀⠋⡀⠀⠀⠀⡀⢠⣀⠄⠀⠈⠢⡌⠀⠘⠀⠀⠀⠀⢐⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠐⢰⡇⢸⡄⢸⡆⠻⡅⠀⠀⠀⠑⡿⠨⡧⠠⣷⠐⡇⠀⠀⠀⠀⠐⠄⣈⣉⡉⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠩⠉
⠀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠰⣧
⠀⠀⣠⣾⣥⣤⣿⣿⣿⣿⣿⣦⠐⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⣷⢿⡄⢠
⠀⢰⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣰⢂⣠⣴⠶⡆⡀⣀⠀⠘⣗⡀
⠀⠸⣯⣹⣿⣻⣯⠷⡝⢋⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣾⣿⣯⠀⠀⠀⢠⢸⠃⠀⣿⠁
⠀⠀⣿⣿⣿⣿⡿⠂⠻⣿⣿⣯⣿⡇⠀⠠⠀⠀⡈⢀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⢀⣾⣿⣋⠓⠀⠁⠈⣠⠊⠀⢠⡟
⠀⠀⢻⣿⣿⣿⡟⠒⠒⠇⣽⣏⣿⣷⣄⠐⠂⢀⡷⢈⠀⠉⠂⠂⠀⠰⡄⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⠀⠁⠀⠀⠀⠉⠀⠀⣾⠅
⠀⠀⠀⢻⣿⣿⣧⣶⢤⠀⠓⢉⣿⣿⣿⣗⣤⣤⠀⠈⠓⠀⠀⠀⠀⠀⠁⢄⠀⠀⢠⡄⠰⠖⠀⡆⡠⣰⣿⣿⣿⡅⠀⠀⠀⣰⡄⠜⣰⡿
⠀⠀⠀⠀⠙⢿⣿⣿⣾⣦⣤⣾⣿⡏⢼⡟⠛⠛⠓⠀⢊⡦⠀⠌⠡⠀⠀⠈⢇⠀⠷⠂⠘⠟⠛⠁⣱⣿⣿⣿⣿⠇⠐⠀⡀⠀⣀⣴⡟⠓
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣧⢸⡃⠂⡀⠀⠀⡻⣇⢀⣻⡆⠀⡳⠶⠈⣳⠀⠀⠘⡁⢈⣟⣿⣿⣿⢻⡗⠈⢀⡄⠀⣸⣿⣿⡏⡁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⢓⣾⣿⣸⣷⣾⡿⡄⢀⡘⠐⢀⣤⣿⠟⣀⢀⣤⣴⣷⢻⣿⣷⣋⠀⠀⠾⠃⢀⣴⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⣿⣿⣿⣯⣿⣯⣹⣿⣿⣿⣿⡿⣯⡾⠒⡙⢡⡽⠿⡓⣿⣾⣿⣿⣿⣿⣿⢿⣷⡴⠀⠀⢀⣾⣿⣿⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢻⣿⣿⣿⣿⣷⣿⣿⣿⣷⠏⣴⣵⣷⣿⣮⡇⢘⣿⢻⣿⣿⣿⣟⠉⢁⢉⠀⠀⠀⣸⣿⡿⢩⠏⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⣿⡋⢾⢳⣿⣿⣾⣿⡂⢐⣿⣿⣷⣿⣿⠂⢀⠆⠀⠀⠀⢰⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡧⣏⣿⡿⠁⢀⣿⣿⣿⣷⠆⠀⠶⠀⠀⠀⢠⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣇⣿⡟⠁⣼⣿⣿⣿⠃⠠⠀⡤⠀⠀⠀⢸⣿⣿⠋⠁⠀⢀⠀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣰⠟⠻⡿⢧⣤⡀⠀⠂⠀⢀⣤⡾⠋⠁⢠⠞⣀⢴⡤⠗⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⡏⠀⠸⣿⣦⣿⣇⠀⢀⣰⣾⠯⠀⠀⢰⣱⡀⢉⠔⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⢧⡙⢋⣿⣿⣏⠁⠀⢀⡾⣿⠿⣿⠷⠲⠔⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣿⣿⣿⣿⣿⢿⡿⣿⣾⠿⣿⣧⡀⠈⠀⠙⠛⡟⢋⣹⢤⣚⣽⠟⠃⠀⡀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣻⡿⣯⣿⡿⣿⡄⢽⢱⡿⣠⠀⠈⠙⠒⣤⠀⡠⣬⣻⠗⠌⠉⢃⣤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣻⣶⢻⣿⣷⡟⣀⢀⣾⣅⠑⢀⣘⣵⠼⣿⣶⠷⠟⡣⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠌⠛⠞⠓⢻⣿⣇⣿⢸⣿⣿⡿⠾⡝⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣼⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠢⡤⠤⡤⠤⣠⣀⣀⡀⣸⣴⣿⢹⣷⣼⠄⣀⡀⣠⡠⠤⡠⢦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠘⣦⣽⣿⣿⣻⣭⡍⡏⠈⡏⢩⢙⡹⠻⠙⣣⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⢀⣠⠄⠀⠰⠁
⠀⢂⡛⣯⠛⠘⠫⠝⣿⡛⠅⠣⠀⠓⠘⣛⣚⠠⠛⠈⠋⡏⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢠⠀⢀⠀⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠉⠈⠂⠀⠈⠁⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⣀⠠⣤⠀⠀⠀⣤⢄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⠁⠀⠀⠀⠉⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠴⠀⠂⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠢⠀⠀⠠⠊⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂⠀⠉⠀⠁⠂⠺⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡤⠀⢄⡀⠸
⠀⠀⠂⢬⠓⠉⠀⠄⠐⢒⡏⠈⠈⠀⢟⠒⠀⠀⠀⠑⢫⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠻⠈⠀⠠⠟⢃⡀
⠀⠀⠀⠀⢣⡖⠢⡍⠙⡻⢃⠀⠀⠀⠚⢛⠁⡥⠒⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠠⠃⣀⠘⠄⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⣰⡇⠀⠀⠀⢳⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡀⠀⠀⠀⣸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢣⡀⠀⢀⠃⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠠⠀⠀⠀⠀⠀⢄⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠁⠇⠀⠀⠀⠀⠀⠰⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢠⢠⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠤⠀⠀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠆⠉⡞⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠓⠀⢃⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠣⡀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢈⠀⠀⠀⠉⠀⠉⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⠎⠁⢱⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠀⠐⢤⠊⠁⠀⠉⠓⠴⡀⠀⠒⣁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⢴⡃⠀⠀⠀⢘⡆⠌⢀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠆⠀⠀⠀⠀⠀⢆⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢈⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠜⠁⢂⠘⡀⠀⠀⠀⠘⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⢲⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡤⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⢀⠠⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣠⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣄⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣇⠀⠀⣠⣿⣽⡆⢰⣯⣿⣄⡀⠀⣸⣽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠿⠋⣿⠁⠀⠀⠠⣾⠙⠿⢷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣏⡀⢀⣠⣷⢀⣼⣧⠀⣿⣆⡀⢀⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠻⢿⣿⣿⡿⡞⢿⡿⢳⢿⣿⣿⡿⠟⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⣀⣀⣠⠄⢼⣿⣿⡿⢿⣿⣿⣇⣤⣄⣀⣀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⡛⠿⣿⣿⠿⠿⠟⠁⠘⠻⠿⣿⢿⣿⠿⢛⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⣇⠀⣧⣭⣄⣄⣀⡀⢀⣀⣠⣤⣴⣿⠀⢸⡇⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣿⣆⢿⡿⠛⠛⡛⠃⠙⠟⠻⠟⣿⡿⣰⣿⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣸⠇⢼⣷⣤⣤⣤⡇⢠⣴⣤⣴⣿⣏⠸⣇⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⣜⡿⠀⣸⠿⢿⡿⢿⡄⢰⡿⢿⣿⣿⣇⠀⢿⣣⡀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⠏⡀⣾⣿⣤⣠⠀⠀⠀⡀⠀⠀⣄⣦⣿⣶⣄⠩⠅⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣦⡼⠋⢹⣿⣿⣾⣿⣾⣷⣿⣿⣿⣿⡏⠙⢿⣶⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣧⠀⠀⠘⣇⠀⠀⠈⢸⡇⠁⠀⢀⣼⠃⠀⠀⣼⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⢷⡀⠀⢿⣿⣿⣷⢾⣷⣾⣿⣿⡿⠀⢀⡾⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⣿⡄⠘⣧⣀⣉⣼⣇⣁⣀⣼⠃⢠⣿⠁⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⣷⠀⠘⢿⣿⣿⣿⠿⡿⠃⠀⣾⠁⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠀⠀⠀⠰⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠂⠀⠀⠀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇

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

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

⣴⣶⣶⠀⢰⣤⣶⣆⡲⣂⣶⠂⠂⠀⠂⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠒⠒⠒⣲⡒⠀⠒⠂⠀⠐⢲⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣶⡀⠀⠀⠀⠀⠀⢰⣾⣤⣿⣿⣷⣆⣀⣉⠀⢼⣿⣿⣿⣿⢠⠀⠀⡀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡠⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⢿⣿⣿⣿⣷⠃⣠⣿⣤⣼⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⡋⠉⠉⠉⠘⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣴⣿⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠂⠛⠛⠛⠋⢻⣿⣿⣛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣷⡿⠇⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⡆⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡿⠛⠛⠙⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⡇⠀⠀⠀⠈⢙⡇⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣻⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠒⠲⠶⠿⠟⠻⠿⠿⠷⠶⠶⠶⠗⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇⠀⠘⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣦⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠉⠀⠀⠀⠉⠛⢷⣦⡀⠀⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠘⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠻⠶⠶⠾⠟⠋⠉⠁⠛⠀⢰⡧⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡈⢻⣿⡟⣁⣀⣀⣀⣀⣀⣀⣀⣼⡏⢀⣀⣀⣀⣈⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠃




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠄⠀⠀⠀⠀⠀⠠⠞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡖⠀⠀⠀⠀⠀⠀⠀⠐⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢠⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢻⣷⣤⣀⡀⡄⡀⢀⣠⣴⣿⠃⠀⠀⢀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⠉⠀⠀⠈⣻⣿⣿⣿⣷⣾⣿⣿⣿⠋⠀⠀⠀⠀⣠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡴⢚⣿⣗⣻⣶⣶⣦⣤⣌⣹⣿⣿⠿⢿⣿⣿⣉⣠⣤⠶⠶⠻⢒⣶⡶⠖⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣬⣤⣄⣀⠀⠈⣨⣿⣿⡿⢻⣿⣿⣿⣰⣾⣿⣿⣿⣿⣿⣿⣿⣷⠿⠛⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢀⣠⡤⠜⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣂⣀⣀⣤⣤⠶⣮⣍⣀⡀
⠀⠀⠀⢀⣴⣾⣿⣷⣦⣰⣞⣂⣀⣀⣈⣉⣛⠛⠻⢿⣿⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣉⢉⣙⣿⣇⣤⣭⣭⣿⣷⣤⡀
⠀⠀⠰⠛⠉⠈⢉⠽⠛⢿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⡻⣿⣛⠉⠙⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⡿⣿⣿⣿⣿⣿⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡟⠻⠿⣿⣻⣯⡻⠙⠢⠁⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⢠⣿⠋⠀⢻⣿⣻⣿⣿⠛⢻⣿⣿⣿⣧⡿⠀⠘⢿⡀⠀⠈⠙⠗⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡴⠟⢻⣼⣿⣿⡁⢹⣿⣿⣿⠉⠻⡆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⣾⣿⣿⡇⣸⣿⣿⠏⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡀⠀⠈⠻⣿⣷⣿⡿⠋⠀⠀⢸⠇⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡈⡡⠀⠧⠤⢀⢀⠀⠀⠀⠀⠀⠀⠠⠂⠤⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢢⡄⠀⡐⠉⠑⠢⢢⢐⠠⠠⡂⠀⠀⠀⠀⠀⠀⠂⠀⡠⠀⡠⠤⠀⠀⠀⠀⠀⠑⡄⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡄⠴⠁⠁⠀⠀⠀⠀⠈⡌⢢⡀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠘⠄⢆⠀⠀⠀⠀⠀⠘⡑⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠎⠸⠀⠀⠀⠀⠀⠀⠀⢀⡆⠐⡀⠀⠀⠀⢀⢈⠰⠀⠀⠀⠀⠘⢁⠢⠀⠀⠀⠀⡰⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡄⢂⠰⡀⠀⠀⠀⡠⠊⢅⠀⠂⠈⢂⠐⡀⠁⣈⢺⠀⠀⠀⠀⣸⠈⠀⠑⠐⢣⢸⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⢠⠁⠆⠉⠀⠈⠀⠀⠄⢀⠀⠄⠂⢰⠐⠨⠐⢒⠐⠈⠀⠀⠀⠀⠀⠀⡆⣧⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢝⠁⠂⢱⢰⠈⠁⠀⠘⠐⣦⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⣤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢃⠸⠐⡶⡆⠀⠀⠀⢸⠀⠀⣸⢸⠀⢀⠄⠌⢠⢰⡄⠀⠀⠀⠀⠀⠈⠀⡇⡓⠸⠁⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⡌⡆⢸⠀⠀⠘⢰⠁⠀⠘⢸⠀⠜⡀⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠇⡱⠁⡜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⡇⢰⠀⠀⠂⡙⣄⠀⠀⡇⡄⠀⠃⡄⠀⠀⡀⠀⠀⠀⠀⠀⠘⡄⠐⠁⢀⠂⢸
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠈⠏⠀⡄⠀⠐⠀⢱⠀⠀⡇⠀⠁⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠢⠈⠀⠀⠈⡀⠀⡇⠈⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⡇⠀⢠⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠇⠂⠀⠀⢀⠑⢀⡇⠰⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠁⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠁⠂⠀⠀⠀⠰⠋⡇⠀⠀⠼⡀⠀⡇⢀⠀⠀⠀⠀⠀⢸⠀⡰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⠁⠀⠀⠀⠀⠐⠆⠃⠀⠀⠀⠛⠸⠁⠠⠀⠀⠀⠀⠀⢪⠀⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠆⠀⠀⠀⠀⠀⠀⢈⣘⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣀⣤⡌⠁⠀⠀⠀⠙⠿⠟⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠉⠉⠙⠒⢀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠒⢦⣤⣴⣿⣟⣿⣶⣄⣀⠒⠀⡈⠉⠰⠶⠶⠶⢶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣰⣶⠞⠛⠋⠁⠀⠀⠈⠛⠻⣶⣾⣁⣠⠤⠄⠀⠀⠾⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣦⣄⣀⡀⠀⠉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠙⠛⠛⢷⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣦⡀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⣴⡿⢧⡀⠀⠀⠤⣤⣤⣤⣤⠤⠀⠀⠀⣰⣿⣧⣀⡈⢻⡦⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⣿⣄⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⢿⣷⣄⠙⢷⡀⠀⠛⠛⠛⠃⢰⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠙⠻⣷⣄⠙⣆⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⣤⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⣶⡶⠾⠿⢿⣿⣷⣶⣶⣶⣿⢿⣿⣿⣿⠿⠿⠿⠿⣶⣶⣶⣶⢶⣶⣶⡦⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠙⣷⣄⠀⠀⠀⠘⠿⠿⢆⣰⣾⠋⠀⢿⣄⡀⠀⠀⠀⠻⠿⠿⢆⣸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠛⢷⣶⣤⣤⡤⣴⣾⡟⠁⠀⠀⠀⠙⠻⣶⣶⣤⣀⣴⣶⠞⠋⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡾⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⡄
⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠈⢧⣤⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣤⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣦⣤⣴⣶⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣠⡴⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠾⠿⠿⠟⠛⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⡋⠉⠉⠉⠉⢻⠟⠛⠛⠛⠛⢻⡿⠛⠋⢻⣿⠏⠉⠉⠉⠻⣏⡉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣿⠋⣽⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡿⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠃⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⢀⣧⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣧
⠀⠀⠀⠀⠀⢰⡎⠀⢠⡇⠀⠀⠀⠀⣿⣀⣠⣶⠆⠀⠀⠀⠛⠀⢸⣿⠀⠀⠀⠀⢴⣶⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠘⠃⠀⠸⠟⠀⠀⠀⠀⣿⠛⣿⡄⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⣴⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣆⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠉⣷⡄⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠠⠤⠤⠤⣾⣿⠀⠀⠀⢿⡇
⠀⣀⡄⠛⣻⡿⠛⠀⣠⣶⣾⣷⡀⠀⠀⠀⠀⠉⣷⡄⠀⠀⢸⣿⠁⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⠀⠀⠀⢸⣇
⠀⠻⣧⡾⠋⠀⢀⣼⠟⠉⢀⣼⣿⠀⠀⠀⠀⠀⠈⢻⡆⠀⢸⣿⠀⢀⣠⣴⣿⣤⣤⣤⣤⣤⣤⣤⣴⠛⠋⠉⠉⢹⣿⠀⠀⠀⠈⣿⡗⠐⠒⠀⡀
⠀⣼⡏⠁⠀⣠⡾⠃⠀⣰⡿⠙⢿⣦⡀⣀⣄⣀⠴⠿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⣉⣭⡿⠿⠷⠾⠿⠷⢿⣿⠀⠀⠀⠀⣿⡷⠲⠷⠾⢧⣀
⣶⠉⠀⢀⣴⠏⠁⢀⡸⠋⠀⠀⣼⠟⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⣿⡷⠰⢦⣀⣈⡛
⠙⢶⣤⣿⠇⠀⢀⣜⠃⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣶⣶⣿⣿⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿⡷⠀⠀⠉⠻⢿⡄
⠀⠀⣿⠇⠈⣴⡾⠋⠀⣠⣾⣿⣶⣶⣶⣶⣶⣶⠾⠛⠛⠛⢻⡟⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠷⠾⠾⣿⣧⠀⠑⣶⣀⣀⡟
⠀⠀⣿⣆⡀⢛⣷⣦⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠱⣦⣼⠿⠟⠁
⠀⠀⠀⠛⠻⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⡀⠈⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⠁
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣿⣦⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⡿⠿⠿⢿⣿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡏⠉⠉⠉⢻⡟⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⡏⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣆⠀⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⡄⠻⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠉⠋⠉⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠉⠹⠿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠿⠋⠁⠀⢀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⣤⣄⠀⠀⠀⠈⠉⠙⠿⠷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⣀⣀⡰⠶⠞⠉⠁⠀⠀⣀⣠⣶⠿⣧⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣨⡛⠛⢷⣶⣀⣀⣀⠀⠀⠀⠈⠉⠉⠛⣶⣶⣦
⠀⠠⣶⣶⣄⣉⣉⣀⣀⣀⡤⢶⣶⠾⠛⠋⠀⠀⠛⠛⠲⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠉⠛⠛⠛⠲⠶⠶⠶⠶⠶⠈⠛⠋
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣦⣤⣤⣤⣤⣴⣶⣶
⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⢀⠀⡀⠀⣠⣿⣄⠀⢀⠀⠀⠀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣄⠈⢲⣷⣶⠿⠿⠿⣿⣿⡶⠁⣠⠶⠁⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠂⠉⠉⠁⠉⢉⣛⣿⣿⣶⣤⣄⣀⡈⢓⣿⣿⣿⣧⣰⣤⣿⣿⣿⣛⣁⣤⡴⠶⠟⠻⠿⠍⣉⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⣀⣤⣎⣁⣈⣹⣿⠟⠙⢻⣿⣿⡿⣿⣿⡿⠋⠻⠍⠲⣤⣤⣤⠷⠦⢄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠉⠀⠀⡤⢻⠛⠀⠀⠀⠀⢸⣿⣟⣛⣿⣿⣷⡀⠀⠀⠀⠈⢦⠉⠲⣄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣟⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠢⣀⠀⠀⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠖⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠈⠛⠶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠻⣿⣿⣿⡿⠛⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⢿⣿⣿⠓⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⢶⣶⣿⢿⣿⣯⣽⡆
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣷⠘⢿⡛⠉⢹⣿⡿⠉⠙⢿⣿⠶⣤⣀⠀⠀⠀⠀⣰⣧⡀⠀⠀⠀⣀⣤⢶⣾⠟⠛⢻⣿⣿⠛⠻⢿⡿⢸⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⢿⣶⡿⣿⣏⡋⢁⣠⡾⡿⢦⣀⠀⠈⠻⠀⠈⠙⠿⣶⣄⣠⣿⣿⣇⣠⣶⠟⠋⠁⢸⠏⠀⠀⣀⣽⣿⣄⠀⠙⢒⣿⣿⣧⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣟⠉⠁⠀⢀⡀⠤⠘⢛⣓⡶⠖⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣷⠶⠶⠶⢶⣖⠒⠾⢍⣀⠀⠈⠉⠙⠛⣿⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡶⠒⠉⢀⣠⠴⠒⠉⣁⡤⠖⠛⢉⣩⣤⢾⣿⣿⣿⣿⣥⣉⠙⠒⠦⣤⣈⠙⠒⠤⣄⡀⠁⠒⢤⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡚⠉⢀⡠⠖⠋⣁⣤⣶⡯⢭⣤⠶⢺⣷⣿⣿⣿⠦⣭⣍⢓⣦⣄⡈⠙⠦⢤⡈⠉⠓⢦⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣾⣧⢴⣶⡛⠉⢻⣿⣿⠏⣠⡾⡿⣿⣿⣿⡿⡷⣄⡙⣾⣿⣿⠛⠓⢶⣦⣬⣷⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣿⣿⣿⣿⣁⠞⣿⠏⡝⣹⠁⣿⣿⣿⡇⢳⠹⡙⢾⡿⢌⣳⣾⣿⣿⣦⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣿⣿⢼⠋⡜⢰⠇⢸⣿⣶⣾⣷⠈⢧⠱⡈⢷⣼⣿⣿⣿⣿⡏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣍⣻⢿⡿⢿⠃⡼⠁⡼⠀⠘⠹⣿⡿⠙⠀⢸⡆⢱⡈⢺⢿⣿⣿⢟⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⢳⠇⣠⠇⠀⡇⠀⣠⢰⡟⣧⢀⡀⠀⡇⠀⣧⠈⣷⠷⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣤⣾⢧⣼⣷⣥⣿⣾⡆⢿⣼⣯⣢⣿⣀⣾⣇⣸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠉⠙⠛⠉⠀⠀⠀⠀⠉⠈⠉⠉⠻⠟⠛⠛⠳⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣭⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣍
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡟⠛⠛⠋⠉⠉⢸⣇⣠⡊⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠉⢉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣭⣉⠲⣄⠀⣬⡤⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣉⠂⠀⡀⠈⢣
⠀⠀⢤⣤⣄⡁⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠎⣵⠀⢈
⠀⠀⠀⠉⠳⢭⣵⣶⡄⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠘⢀⠀⠠⠱⡶⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠆⡀⠀⣠⡤⢤⡌⢠⠀⠀⡈⢀⠠⠆⠰⠚⠶⠦⣄⡀⣀⣀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⢄⢜⡔⠈⠒⢀⣄⣤⡐⢤⣠⡖⣢⣤⣥⡔⠒⡍⣑⠄⠉⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡷⣌⠄⠀⡄⣨⡅⣁⣄⣤⣿⣤⣽⡙⢪⣇⢀⠩⡉⠃⣶⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠼⣦⠶⠞⣭⣿⣿⡿⢯⣽⡦⠙⢿⣟⣁⠠⣅⢀⠢⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡹⣧⣼⢏⡿⣻⣇⣴⣯⡄⠀⠀⠹⣯⠀⢩⡟⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⢰⣿⣿⣿⣿⢹⡾⠋⠀⠀⠀⠀⣿⡚⠟⢢⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⣿⣿⣿⣿⣇⣀⣠⣄⡀⣀⣀⣿⣶⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⢾⣾⣭⣽⣷⢶⣄⣉⣉⣿⣿⣟⣟⣿⣟⣯⣭⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠿⣷⣯⡿⠿⠋⠉⠉⣿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⡙⠛⠛⠿⢻⣿⠿⢿⡿⠶⠿⣿⣿⡿⠿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠈⠉⠛⠶⣤⣿⣄⢀⣼⣧⠴⠛⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣠⣼⠿⣍⣿⣩⡟⠛⢿⠷⠶⣤⣤⣄⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⣖⣋⣁⣀⣀⣉⣉⣉⣤⣤⣼⣤⣤⣴⠶⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠙⣩⡍⠉⠉⣾⣿⣾⣅⣄⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣶⣦⣴⣶⡿⠿⠟⠀⡠⠉⣉⣻⣿⣿⣾⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⠿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠀⠀⠀⠀⢸⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⣶⡶⠷⣦⣌⠛⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⣴⣦⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣿⣿⣿⣏⣹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢻⠏⠙⢿⣿⠿⠛⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣤⣤

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

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


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

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

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

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

⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⡝⢦⡀⣼⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⢛⣛⣒⣶⣂⠀⠀⠀⠀⢀⠬⠁⡇⢱⡀⠈⢿⣿⣿⠟
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⠔⠁⠀⠀⡇⠀⢣⡀⠀⠈⠁⠀⣀⣒⣀
⠀⠀⠀⠐⠛⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡇⠀⠀⠻⠂⠤⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⣄⠀⠈⠻⠿⠟
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⢹⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡍⠑⢄⣀⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⣠⡀⠀⢰⡦⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⢉⣠⠴⢄⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⡇⠀⠠⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⢸⣾⣿⣿⡆⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢠⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠈⠻⣿⠿⠃⠒⠀⠖⠀⠙⠀⠀⠀⠀⢠⡶⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣋⣉⠐⠠⠀⠀⠀⠀⠀⢠⡔⠂⠀⠀⡈⠀⠰⡀⠀⠀⠘⢧⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡤⠄⠙⠛⠂⠀⠃⠀⠀⠀⡐⠀⠀⠀⠑⡀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⣯⠅⠀⠀⢀⣴⣾⣶⣄⠀⡐⠀⠀⠀⠀⠀⣸⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⣿⣿⣿⣯⡶⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⠋⢠⠀⠀⠀⠀⢠⠸⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣮⣽⣂⡄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢸⠀⠀⠀⠀⢸⡄⢹⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⡠⠂⠀⠀⠠⠚⡄⠀⠀⣠⡶⢦⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⡠⠈⠀⠀⠀⢠⠀⠀⢠⠀⢴⣯⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⠋⠀⠀⢀⡄⠚⠀⠀⠀⣀⣄⣤⡀⠀⠀⢂⢀⡙⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⡄⠀⢘⣳⣿⣿⣿⡆⣠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣤⣤⣀⠠⠊⠀⠀⠀⠀⢠⠀⠀⠈⠙⠛⠛⠛⠀⠷⣟⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣷⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡝⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡄⠀⠀⠀⠀⠀⢰⠎⠙⠻⣿⣿⣿⠟⠁⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⠁⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣀⡀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠃⠀⠈⠀⠀⠀⠀⠀⠻⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⠿⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠘⠁⠀⢀⡀⠀⠀⠀⢀⣀⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣤⠀⠀⠛⠃⢀⣤⡀⣀⡬⣈⠀⠀⠀⠀⠚⠋⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠅⢀⠈⠀⠀⠀⠉⠀⠁⠀⠈⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣾⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣨⠟⣩⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢻⡿⢻⡿⢛⡿⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣿⣤⣿⣴⣾⣿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⠟⣹⠋⠁⢀⡿⣾⣻⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⣘⣰⠃⣠⠔⠋⠀⣸⣿⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠉⡷⠊⠁⢀⡴⠚⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢸⣿⠇⠀⢰⢃⣠⠖⠉⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣸⡟⠀⠀⡾⠉⠀⠀⢀⣴⣿⡿⠋⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠻⣿⢿⡛⢦⣿⠿⢭⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢰⠃⠀⢀⣴⣿⣿⣿⠿⠛⠙⢻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠈⠻⣟⣾⣿⠲⢶⣿⠿⠝⡛⣿⣿⣷⣦⣄⡓⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⢠⠇⢀⣴⣿⣿⡿⠋⢁⡠⠖⠊⢁⣀⡬⠷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣿⣿⡉⠉⠒⠺⣇⠈⠉⠛⠿⢿⣷⣦⣄⠀⠀⡀⠀⡀⠀⡟⠀⣾⣶⡿⢟⣡⠿⣴⣊⣁⣤⠖⠊⠉⣀⣀⠠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⡶⠖⠒⠚⠛⠲⢦⣄⣀⡀⠉⠛⠿⢶⣄⣹⣿⣿⣷⠿⠛⣉⠴⠋⠀⠀⠀⠀⢀⣈⠽⠿⣉⡀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⠖⠒⠚⠉⠁⠀⠈⠉⠙⠛⣛⣿⣿⣿⣿⡻⣷⣿⠷⠒⠒⠒⠒⠒⠛⠭⢄⣀⠀⠀⠉⠙⡺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⣤⣴⣶⣾⣿⡿⠟⣉⠴⣻⣿⣾⣿⣝⡓⠦⢤⣀⡀⠀⠀⠀⠈⠙⠲⣤⣴⡷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⠿⠿⢯⣥⠖⠊⠁⢠⠃⢙⢿⢿⣷⣭⣒⢤⡀⠉⠙⠒⠦⢤⣀⣠⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡤⠊⢹⡄⠀⢀⡏⠀⢸⠈⢆⢻⣷⡀⠉⠙⠳⢤⣀⣀⣠⣾⣯⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣠⠟⢣⣀⡾⡄⠀⠘⡇⠘⡆⣿⣿⣄⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢸⡉⢆⠘⣄⠀⢱⠀⠘⣿⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣬⣧⣈⣣⡀⣃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣻⣿⣫⣻⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣿⣿⣯⣿⣽⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢧⠀⠰⠂⠐⠤⠤⣴⡦⠤⢤⡀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠠⣥⢀⠀⠁⠀⠐⠒⠂⠲⠂⠲⠖⠁⠀⠈⠀⣠⠈⢀⣴⡀
⠀⠀⠀⠀⣀⠀⠀⢸⣿⣷⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣇⠀⠀⢀⣴⣤
⠀⠀⢠⣿⣿⣇⣴⣿⣿⣿⣔⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⢰⣾⣿⣿⣿⣷⣀⣬⣿⣿⡀
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠀⠀⢀⠀⢛⠀⣘⡁⠀⣇⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠠⠀⠀⠀⢤⢧⠂⠤⣅⢂⢬⠏⡐⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠹⣿⣿⣿⠏⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠛⠀⠀⢀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⡿⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⣿⣿⡇⢸⣿⡿⢻⣿⡆⠀⠀⣀⣀⣀⣀⣀⡀⣀⡀⢀⠀⢀⠀⠀⠀⣀⠀⣿⣿⣿⡏⠙⢿⣿⠿
⠀⠀⣿⣿⡇⢸⣿⡇⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢻⣷⢀⣸⣿⡄
⠀⠰⠿⠿⠓⢺⣿⡇⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠈⠉⠛⠃
⠀⠀⠀⠀⠀⢸⡿⠆⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⠍⠉⢩⣭⠍⠁⢀
⠀⠀⠀⠀⠀⠀⠠⠂⠐⠀⠀⠄⢾⠃⠀⣀⠁⠐⡂⣤⡀
⠀⠀⠀⠀⢠⡂⠀⠀⠀⢀⠐⠁⠈⠀⢰⣏⡰⠟⢋⣠⠤
⠀⠀⠀⠈⠸⡀⠀⠐⠄⠀⠀⠀⡀⠀⢀⡌⣡⣤⣶⣶⡻⠗
⡀⠄⠀⠀⢀⢄⠔⠁⠀⠀⠀⢀⠃⠀⠈⠳⠋⠈⣁⣀⣠⡴
⡇⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⣀⣠⣤
⡇⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣏⣴⠷⢻⢿⠿⠟⠛
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣄⠐⣉⠁⢀⣀⣀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠩⠍⠥⠀⠁⠀⠀⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠠⣿⣃⣤⣀⢀⣤⣤⣤⡖⢀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡀⠀⠘⠛⠉⠉⠙⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣤⡶⠦⢰⣿⠿⠻⠛⠀⢰⡆⢧⢈⡑⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠐⠀⠀⠘⠁⠀⠠⠐⠒⠒⢉⣥⠀⢰⣤⣬⡓⣅⣨⣀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⠆⠀⠀⠀⠀⠀⣤⣶⢟⡩⢀⡀⢼⡳⠦⢜⠣⠿⢷⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡎⠁⠀⠀⢸⣇⣼⠛⣡⡶⠛⣡⡶⣫⠹⣼⡳⢶⣦⡀⠠⡌⠳⣤⠅
⠀⠀⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠈⠉⠁⣠⠎⠀⡾⣿⢱⢿⡇⠹⠿⢷⡖⠒⠒⠒⠂⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠋⠁⠀⣾⠀⣿⢸⣜⢟⢦⣄⢌⡛⠷⠀⠀⠀⠀⠸⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠄⠸⣇⡿⠀⣿⢈⡻⠌⢳⡿⠶⠍⠓⠂⠀⣄⠘⠛⠀⠘⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⡀⠀⠉⠃⠸⡇⠌⠛⠆⠀⠱⢄⠀⠀⠶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡅⠀⠀⠀⠀⠈⠀⠀⠤⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⠀⠀⠀⠀⢤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⠀⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣤⣴⡶⠶⠶⢿⣻⡇⣼⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣿⣿⣟⠉⠀⠀⠀⠀⠀⠉⢸⣿⣦⣼⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠘⠿⣿⣿⣷⣦⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣷⣴⣿⣤⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⣠⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⠀⠀⠀⠙⠶⠤⢤⣈⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⣷⠀⠀⠀⠀⢠⣴⣶⠾⠿⠿⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣦⣄⡈⠛⢿⣿⣿⣿⣿⣿⡇⠀⠈⠙⢻⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⣿⠟⠛⠛⠲⢤⣈⠙⠿⣿⣿⣇⠀⠀⠀⠈⣿⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣫⣾⣿⣧⠀⠀⠀⠀⠈⠑⢦⡈⠻⣿⣦⡀⠀⠀⣿⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣫⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣶⡤⢸⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠉⢀⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣶⠟⠹⠟⠁⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠙⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠂⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣄⡀
⠀⢀⣤⣴⣾⡿⠃⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛
⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠻⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⢹⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣄
⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⡿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠾⠟⢿⡟⠛⢻⠛⠛⠛⢻⣿
⠀⢸⣿⠉⠉⢹⠉⠉⠉⠛⢿⣿⠉⠉⢹⣀⣀⣀⣿⡇⠀⠸⣇⣀⠀⠈⠹⣿⣿⣿⠁⠀⠀⠀⢻⣧⣤⣤⡤⠤⠤⣤⣴⣾⡇⠀⠸⣶⣶⣶⣾⣿
⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⠿⠃⠀⢀⣿⣿⡏⠀⢀⣇⠀⠈⣿⣿⣿⡇⠀⠘⣿⣿⣿⡇⠀⠀⡏⠉⠉⢻⣿
⠀⢸⣿⠀⠀⢸⣿⣿⡄⠀⠘⣿⠀⠀⢸⣀⣀⣀⣿⡇⠀⠀⣧⣤⡀⠀⠙⣿⣿⠁⠀⣸⠿⠀⠀⠸⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿
⠀⢸⣿⠀⠀⢸⣿⣿⠇⠀⠀⣿⡆⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⠿⠟⠀⠀⣼⡏⠀⢀⣧⣤⣤⠀⠀⢻⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⡟⠉⠉⢹⣿⡀
⠀⠸⣿⡄⠀⢸⡉⢁⣀⣠⣼⣿⣇⣀⣀⣄⣀⣀⣸⣧⣀⣀⣧⣤⣤⣤⣾⣿⣥⣤⣼⣿⣿⣿⣦⣴⣾⣿⣷⣶⣶⣿⣿⣿⣷⣶⣶⣷⣶⣾⣿⣿⠇
⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠋⠀⠀⠉⠀⠙⠛⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⡼⢦⣤⠶⠶⢦⣤⣤⡀⠀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣶⣶⣶⣶⢶⡾⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣋⣥⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⠉⠉⠉⢹⡷⣏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣛⣩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠄⠀⠀⡀⢸⡇⠙⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠾⠿⠷⠷⠶⠶⠶⠶⠶⠶⠶⣶⠀⠀⠀⠀⢸⠶⠶⠀⣿⣹⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠶⠶⠶⣶⢶⡶⠶⠶⠶⠶⡞⠁⠀⠀⠀⣠⠾⠛⠂⠀⠀⠀⠘⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⢤⣤⣹⣎⣧⠀⠀⠤⢴⡇⠀⠀⢠⡞⠁⠀⠀⢀⣤⣄⠀⠀⠀⣈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣿⠂⢙⠛⠛⠛⠋⠩⢿⡇⠀⠀⣾⠀⠀⠀⠀⠘⠧⠟⠀⠀⠀⣏⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣏⣹⠆⠀⠀⣤⣴⡇⠀⠀⣿⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠉⠁⠀⠀⠀⠀⣸⠇⠀⠀⠹⡄⢈⡗⠀⠀⠀⣴⠛⣷⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢤⣤⣤⠤⣤⠴⢾⡏⠀⠀⠀⠀⠙⢿⣁⠀⠀⠀⠈⠛⠉⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠶⠶⠶⠶⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠖⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⡇⢾⢸⠅⢸⣤⡇⡇⡎⠁⣼⣆⡇⠀⢸⢭⠂⡏⢀⣿⣰⡉⠀⠉⢸⢰⡋⡇⡿⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠁⠈⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣷⣤⠭⠙⠓⠦⣄⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⡤⠖⠛⠩⢥⣴⡇
⠀⠀⠀⠀⢹⣿⡗⢦⠀⠀⠲⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠱⠂⠀⢠⠖⣿⣿⠁
⠀⠀⠀⠀⠀⢻⣏⣻⣾⢓⢲⢦⣀⠈⠻⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠋⢀⣠⣶⢒⢻⣾⣋⣿⠃
⠀⠀⠀⠀⠀⠈⣏⢉⣙⣛⣷⣭⡼⠿⣦⣄⠘⢦⡀⠀⣀⣀⠀⣠⠞⢀⣤⡾⠿⣭⣵⣟⣛⣊⢉⡏
⠀⠀⠀⠀⠀⠀⠈⣧⠙⠯⠿⠒⢟⣛⣲⣿⣿⣤⣙⣦⣿⣿⣞⣡⣴⣿⣵⣚⣛⠗⠺⠭⠟⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠒⠰⠍⠛⠛⠆⠚⢻⣿⣿⣿⣿⣿⣻⠛⠂⠞⠛⠋⠵⠐⠂⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⣰⡞⢉⠉⠠⠐⢊⣿⣿⣿⣏⠐⠠⠈⢉⠙⣶⡐⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠐⠀⠀⠀⢀⢔⣿⣧⣉⣹⣿⣗⢄⠀⠀⠀⠐⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣃⢀⠀⠠⠁⣼⣿⢿⣀⣸⢿⣿⡄⠡⡀⢀⢀⡣⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡔⠎⠀⠀⣼⣿⠏⢸⣀⡄⠈⢿⣿⡀⠀⠈⠖⣄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢀⡼⠟⠁⠀⢸⣦⡇⠀⠀⠙⠿⣄⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁

⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣶⢶⡄⠀⢀
⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣄⣿⣿⣿⣠⡆⠀⠀⠠
⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣊⠉⣃⣱⣬⣭⣿⣍⡴⠙⣆⡔⡀
⠀⠀⠀⠀⢀⠀⠀⢀⢂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡕⢢⣘⣷⡧⠴⣾⣟⣡⠒⡄⢀⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⢈⣠⠵⢟⢋⣻⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠹⣴⠂⠈⢻⠥⡦⣤⣴⣿⡃⠀⢧⠎⠀⠀⠀⠀⢀⡚⢳⡞⣡⡖⣦⠹⡆
⠀⠀⠀⢠⣾⠫⣶⣼⢹⣧⠢⡌⠉⣝⣿⣤⡀⠀⠀⠀⠀⠈⠀⠀⢳⡤⠷⢴⣧⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⣸⣇⠱⠞⣻⣿⡏
⠀⠀⢰⣙⣆⣹⣿⠗⠉⠉⢳⡔⠂⡙⣺⡿⠁⠄⠀⠀⠀⠀⠀⠀⣶⢾⣟⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⣟⡻⣿⣿⡄
⠀⠀⣄⣳⣿⣿⠏⠀⣼⣿⣿⠯⠃⠰⣸⡿⠆⠙⠀⠀⠀⠀⠀⠀⣶⣬⣻⡞⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⣷⢹⣷⣼⣿⡇
⠀⠀⠘⢻⡿⣿⡄⠀⠠⠉⠁⠀⠐⢀⣼⣏⠀⠀⢠⠀⠀⠀⠀⠀⡿⣶⣯⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣿⣵⣟⠟⢫⣿⡆
⠀⠀⠐⠬⣧⣾⣷⣬⣷⣀⣒⣠⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⡺⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠻⣿⣟⣛⣿⠇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠍⠛⠛⠿⢯⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⣋⢉⡽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⢿⣬⣿⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣯⣻⢾⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠐⣦⠳⠯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢻⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⢶⠦⠶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣯⡿⠋
⠀⠀⠀⣠⡤⣦⠶⡶⡶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣽⠏⢃⡟⠠⣷⡐⢏⡞⡻⣷⣆⠀⠀⠀⠀⣀⣠⡤⢤⡦⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⢰⣻⣿⣾⣿⣿⣷⡯⣽⣣⡔⢿⣻⣿⣧⠀⠀⢀⣿⠠⠁⡟⣰⣷⠺⣋⣟⣵⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣂⣹⠧⣿
⠀⠛⠟⢀⣼⣻⢷⡷⠀⠙⢖⣈⣽⣻⣿⡆⠀⠈⠡⠼⠿⡻⠷⢯⣼⣡⠋⠾⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡬⠏⣼⣦⣿⠃
⠀⠀⠀⠈⠈⠉⠛⠁⠀⠀⣴⠄⡴⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠖⠀⢡⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⣹⣶⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠘⢦⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠷⠀⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⣿⣿⠟
⠀⣠⡤⠂⢤⡖⠂⣀⠰⠀⣤⣿⣿⡿⠁⠀⠀⢀⣴⠖⠋⠙⡾⠟⣣⣜⣬⠄⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣸⣿⠟⠋⠀⠀⠀⣀⣀⣠⣤⣄
⠘⣷⠀⢀⢸⣇⣴⣽⣷⣶⣾⡽⠋⠀⠀⠀⠀⢸⣧⣄⣠⣾⣷⣉⣥⡜⣷⣽⣿⡟⠁⠀⠀⠀⠀⠀⢀⠀⢶⣰⣿⡟⠋⠀⠀⠀⠀⣸⠃⠀⠀⠙⣿
⠀⠘⠿⢷⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⣠⠀⣿⣾⣿⡿⠋⠀⠀⠀⠀⣠⠞⢋⣴⣶⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠⢄⣰⣿⣾⡿⠟⠁⠀⠀⠀⢀⣴⠟⢡⣴⣶⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⣠⣾⡿⠛⠋⠀⠀⣠⠔⠲⣏⣀⠀⣶⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⣤⠒⢒⠂⢲⠉⢲⡗⢲⠒⣶⢦⣤⣄⠀⠀⠀⣜⣷⣾⠏⠁⠀⠀⠀⣰⢟⡉⢀⣦⣸⣿⡿⠟⠛⠁
⠀⠀⣀⡄⡖⠚⣍⠹⡄⢱⡀⢸⡦⢸⣇⣸⣧⣼⣧⣼⣧⡿⠾⠿⠛⠃⠀⢰⣿⡟⠁⠀⠀⠀⠀⣎⠀⠺⣿⣿⡿⠛⠁
⠀⢸⠾⣷⢿⡴⢿⡾⠿⠜⠿⠟⠛⠊⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢉⣙⣿⠿⠁
⣤⣤⣬⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠛⠋⠉⠛⠛⠛⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⢴⣦⡀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⠀⣀⣴⣷⠀⠘⣿⣇
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠙⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⠁⠀⠀⢿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠉⠉⠉⠉⠛⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⣴⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⣼⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣧⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠉⠉⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⣶⡿⠋⠀⠉⠉⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣄⣿⣿⠀⠀⢰⣷⣄⣸⣿⠇⠀⠀⣀⣴⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡆⠀⣼⣿⣿⣿⣿⣶⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣿⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣷⣦⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⡟⠿⠿⠿⢿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⢸⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠙⢿⣧⠀⠀⠀⠈⢿⣿⣿⡿⠿⣿⣷
⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⢹⣿⣿⣿⣿⡅⠀⠀⢨⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠈⡿⠀⠀⠀⢀⣠⣿⣿⠃⠀⠈⣿
⠀⠀⠀⠀⠻⢿⠦⠀⠀⠀⠀⠛⠛⠛⠿⠿⠂⠀⠀⠉⠀⠀⠀⠀⢀⣦⣤⣤⣤⣦⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠉⠉⠁⠀⣀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⡀⣶⣄⠀⠀⠀⢀⣉⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀⣘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠸⠋⠛⣻⣻⡟⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣻⣿⡀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⢠⣶⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⢿⣿⣿⠟⠻⣿⣿⡿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⠿⠿⣿⣿⣿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠋⠀⠀⣘⣿⣧⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢙⣿⣟⣿⡄⠀⠀⠀⠀⢘⣿⣯⠀⠀⢹⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⢭⠆⠢⢤⣀⠀⡠⠤⠊⢠⣄⠀⠱⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⠎⠀⠻⣥⡹⠀⠀⢠⢳⡄⠷⢤⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠣⠼⢤⣤⣼⡀⣶⢠⢢⠀⠀⠀⡘⠘⠁⠀⠀⠹⣄⣀⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠋⠀⣀⠔⣠⡅⠂⠀⠀⠀⢻⣀⡼⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠹⠈⠁⠀⠀⠀⠀⠀⠚⠤⢦⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣤⡤⠖⠃⠀⠀⠀⠀⢀⣤⡴⡞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⣠⠗⠒⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡠⠀⠀⠀⠀⠀⠀⣠⠾⠔⡇⢰⠃⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠽⠆⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣠⠿⠤⠂⠀⠀⠀⠀⠀⠀⢺⡗⠃⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢀⣀⣴⠋⠧⣀⡠⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⠀⠀⢷⠘⡀⠀⠀⢢⠀⠀⠀⠀⠀⢰⠤⠌
⠀⢠⠖⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡤⢴⡋⡣⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠣⡀⠀⠀⠀⠀⢳⡀
⢰⡃⢀⡴⠀⠀⠀⠀⢠⡀⢀⣀⠠⡤⢮⣙⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢷⡀⠀⠀⠀⢄⠀⠀⠀⠀⢳
⡏⠉⠁⠀⠀⠀⠀⠀⣸⣃⠆⠈⣛⡁⠀⠀⠀⠀⢠⢄⠀⢀⢤⠀⠀⢸⠀⠀⠃⠙⢦⡀⠀⠀⠠⠀⠀⠀⠈
⢧⠀⠀⠀⠀⠀⠀⠰⠯⣴⠒⣆⡥⠿⢼⢙⡤⢤⡼⠚⠳⠁⣼⣀⠤⣼⠀⢠⠀⠀⠀⠙⠢⣀⠀⢂
⠈⠧⣄⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣶⣿⠀⢸⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣸
⠀⠀⠈⢹⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀⢄⢁⠀⠀⢠⢿⡞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠃
⠀⠀⠀⠈⠻⣤⣀⣹⠀⠀⠀⣀⢦⣤⣥⣤⠶⠋⠉⡟⠀⠀⠀⠀⢸⡓⣦⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢧⢠⠀⠀⠀⣸⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡤⠞⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠸⣷⡀⠠⣘⡛⠁⠠⠤⢴⣿⣿⣧⡀⠁⠉⠀⠀⠀⠀⠀⣿⠿⠟⠃⠀⠀⢠⣿⡀⠘⢿⣷⣦⡀⠀⠈⠳⣔⣩⣭⣭⣞⣉⣁⡼⠷⣾
⠀⠀⢸⣿⠟⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣵⣖⣤⣀⣀⣀⣴⣇⡐⠃⠀⠀⠀⢉⣽⣟⣢⣤⣬⣿⣿⣷⣶⣶⣿⣿⣿⣥⣼⣿⣿⣷⣿⣿
⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣈⠫⠉⠉⠉⠀⠀⢀⣴⣿⣿⣶⣾⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣴⡆⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⣴⣿⠟⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣻⡏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢘⡿⣯⣜⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⡇⠀⠙⠛⠷⡾⠿⠱⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣶⣶⣤⣀⡶⠎⠉⠉⠉⠁⠀⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠿⣿⣭⣉⡙⠛⠿⠟⠷⠄⢀⡤⠂⠈⠓⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠀⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣷⣾⡟⠛⠛⠛⠛⠛⠛⠛⣷⣷⠛⠛⠛⠛⣷⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡟⠛⠛⣷
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣷⣾⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⡏⠏⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⣿⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⢻⣶⣦⣶⣶⣶⣤⣆⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⣿
⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠒⠂⠀⠀⠀⣿
⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⠤⠀⠀⠀⠀⠀⡠⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⣿⣿⣿⣷⣶⣤⣤⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⣀⣀⡀⠀⠈
⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣾⣿⣿⣶⣦⣴⣢⣾⡃
⠀⠀⠄⠁⠰⢀⡘⢆⡄⢃⡀⢿⣿⣿⣿⣿⣿⣷⢀⣀⠀⣤⣀⢀⣠⣆⣠⣶⣲⣠⣆⣤⣸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡀
⠀⣤⠤⠿⠗⠛⠛⠛⠋⠉⠉⠁⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠈⠈⠉⠙⠓⠚⠓⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣯⣿⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣋⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡖⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢔⡴⣪⠆⠀⠀⠀⠀⠀⠀⣨⣍⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⣈⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⣁⠬⣴⢁⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠰⡾⠓⢢⣴⢏⡆⡦⡄⢠⡟⣭⠌⠀⠀⠀⢀⣀⣀⠤⠶⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠈⡀⡐⠠⠎⢹⣧⣣⣔⣯⣵⣿⣧⣵⡿⣿⣿⣶⣶⣶⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⣿⣿⣦⢰⡿⣩⣵⣿⣟⡿⢿⠻⣧⣿⣿⣿⡿⢛⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢛⣭⣿⣿⣿⣧⡘⠿⢿⢫⡖⡿⣿⣿⣿⣿⡟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢨⢁⢟⣿⣿⣿⣿⣶⣦⣹⣧⣳⣿⣿⠛⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠼⢛⣿⣿⣿⣿⣿⣿⣿⡿⠋⣡⣶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣿⣯⣿⡟⠐⡄⠾⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⡶⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠻⣿⣿⣿⡷⠀⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠀⠀⠀⠀⣴⠀⠀⣉⣿⣯⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠴⠏⠀⠙⠻⠟⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣠⣴⡿⠁⠀⣾⢿⣿⣿⣿⡏⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠉⠉⠁⠀⣀⣼⡏⢸⣿⣿⣿⣧⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠀⠀⢠⡶⠟⠋⠀⠸⣿⣿⣿⣿⠆⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠹⣿⡇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⡇
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡿⠟⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠀⠹⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣡
⠉⠻⠿⢿⣶⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠘⠿⠶⠆⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡿⠿⠟⠁
⠀⠀⠀⠀⠊⠉⠉⠉⠻⢿⣿⣷⣤⣤⣦⣀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣀⣤⣤⣤⣿⡿⠟⠉⠉⠁⠑⠀⡀
⠀⠀⠀⠁⠀⠀⠀⢉⠀⠀⠀⠘⠿⢿⣿⣿⣶⣧⣤⣉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣤⣷⣾⣿⡿⠿⠃⠀⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒⠀⠉⠉⠛⢻⣿⣿⣿⣶⣤⣤⣶⡖⠒⠊⠁⠀⠉⠒⢲⣦⣤⣤⣶⣿⣿⡿⠛⠋⠉⠀⠒⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠋⠉⠉⠉⠉⠙⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠟⠉⠉⠉⠉⠙⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣀⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠊⠉⠁⠀⠀⠀⠉⠑⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⡰⠃
⠀⠀⠹⣿⣿⣦⣀⠀⠀⡰⢆⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⠻⣁⡐⠙⠆⠓⠈⣇⣀⣀⣼⣇⣀⣈⠧⠀⠠⠐⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⢀⠀⠤⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⢠⣴⠖⠋⠉⠙⠄⠈⠀⡄⠀⠁⠒⠂⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠉⠁⠀⠀⠀⡀⣠⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⠀⣀⢤⡆⠀⠅⠂⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠽⠍⠙⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠂⠀⠀⠐⠂⢄⡀
⠀⠀⠀⣠⣴⣶⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠉⢓⡐⠒⠂⠀⠀⠈⠉⠻⣦
⠀⡴⣾⠿⠿⡶⡤⣄⠈⠀⣖⢲⡖⢲⣴⣤⣄⠀⠀⠀⢀⠀⠴⢶⠋⢻⡀⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⢀⣻⠄
⠀⠀⣙⠻⡱⣓⡗⠀⠘⢼⠃⣜⠣⡞⠥⠗⢽⣳⠄⠀⠀⠀⠀⠘⢷⠮⢶⣦⣤⣸⣷⣤⣶⣷⣶⣶⡶⠿⠛
⠀⠀⠈⠋⠀⠈⠈⠱⠤⢥⠔⢤⠞⣥⠖⠀⠲⠟⠁⠀⠀⠀⠀⠀⠘⠀⣀⡿⠙⢇⠈⠉⠉⠉⠉⠙⠶⠶⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣴⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠡⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢀⠀⣰⡓⣐⣄⣶⣷⣰⣄⠀⠙⠻⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⠳⣄⡀⠀⠀⠀⠀⠈
⠀⢀⡏⣴⣆⡀⣿⣿⣍⣽⣿⠏⡷⢧⣀⡄⢋⠁⠦⠀⠀⠀⠀⠀⣀⣤⣠⣴⣤⠴⠊⢉⣿⢟⡶⣺⢿⣷⣾⠉⠈
⠀⠘⢦⡟⠁⠀⠉⡿⠛⠁⠉⠙⠃⠀⠺⢣⣄⠱⠀⡁⠀⠀⣠⣾⣿⣿⡇⣼⡿⢿⢸⢧⡿⣻⠟⢯⡞⠙⡾
⠀⠀⠀⠑⢰⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢠⠄⠀⠈⠙⠛⠉⠉⠁⠁⠀⠀⠉⠉⠉⠑⡄⠀⠀⠠⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂