Super strong Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⢀⡀⣲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠧⠞⠟⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠹⣿⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⣿⣿⡿⣦⣄⢀⣀⢀⣠⣴⣶⢰⡀⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡿⠓⣾⡟⠉⣿⡟⠫⢿⣷⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡰⣆⠀⠀⠋⠁⠀⠙⠁⠀⢸⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠿⢻⣆⡀⠀⢼⣃⡀⠀⣠⣞⡾⠃⠉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀⠀⠀⠀⠀⢤⠠⢼⣿⠑⣤⣉⣁⣤⣾⠁⠈⠃⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠻⣿⣿⣷⣦⣤⣤⣤⣤⣴⣿⡌⣿⠉⣽⡏⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣀⣼⣿⣿⣿⠿⠿⢿⣿⣿⣿⣷⢁⣾⡟⣀⣿⣦⣈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⠻⠿⠹⣿⣷⣿⣿⣿⣿⣷⣄⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⠟⠉⠉⠉⢻⣿⡿⢶⣆⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠿⢛⣿⣿⣿⠿⣋⢹⣿⣿⣿⣶⣶⣶⣤⣀⢻⡅⠀⠀⠀⠀⠀⠙⡇⠈⣿⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣿⣿⠛⢵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣸⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣿⣿⠃⣾⠛⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣾⣿⡟⣸⠃⠀⢹⣿⠟⠻⢿⣧⣄⣀⣀⣀⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣸⣿⣿⢁⠇⠀⠀⠀⢿⣦⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⡿⠿⢿⣿⡆⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⣿⣿⠃⡘⠀⠀⠀⠀⠘⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡏⠀⠀⣿⣿⣧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣸⣿⡇⣸⠃⠀⠀⠀⠀⠀⢣⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⠁⠀⠀⢸⡟⣿⡆⢸⡆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣤⣿⠏⢠⡿⠀⠀⠀⠀⠀⠀⠈⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⡏⠀⠀⠀⠸⡇⢻⣿⠀⢻⡄
⠀⠀⠀⠀⠀⢠⡟⠀⢀⣾⣿⣧⠀⣼⠇⠀⠀⠀⠀⠀⠀⢠⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⡇⠀⠀⠀⠀⢡⣸⣿⡀⠀⢻⡀
⠀⠀⠀⠀⠀⡸⠁⢠⣿⣿⣿⠇⢠⡿⠀⠀⠀⠀⠀⠀⣰⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡄⠀⠀⠀⠸⣿⣿⡇⠀⡄⢳⡀
⠀⠀⠀⠀⠀⡇⠀⢸⣟⣿⡿⠀⣸⠃⠀⠀⠀⠀⠀⣰⠃⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣆⠹⣦⡀⠀⠀⣿⣿⣷⢸⣇⠀⢰
⠀⠀⠀⠀⢀⠇⠀⠀⣼⣿⠇⣰⠏⠀⠀⠀⠀⠀⣼⢃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣷⡀⠀⢿⡸⣿⣿⣿⡄⢸⡇
⠀⠀⠀⠀⢸⠀⠀⢠⣿⡿⣰⠏⠀⠀⠀⠀⠀⡼⠁⠎⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣧⠀⠈⢷⡘⢿⣿⣧⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣳⠏⠀⠀⠀⠀⠀⣸⠁⡴⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⢣⠀⠈⣿⡀⠀⠈⢷⡘⣿⣿⡀⢻
⠀⠀⠀⠀⠀⠀⣴⣼⣿⠏⠀⠀⠀⠀⠀⢰⡟⣸⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣸⡄⠀⠹⣷⡀⠀⠈⢷⣸⣿⡇⠸⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⢠⡿⢱⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⡾⠀⠀⣿⣿⡄⠀⠹⣧⠀⠀⠈⢿⣿⣷⠀⡇
⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⢠⡟⢠⠃⠀⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣁⡀⢸⣿⣿⣷⡀⠀⢹⣧⠀⠀⠈⣿⣿⡄⠁
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⡾⠀⠃⠀⣼⣯⣾⣿⣿⣿⣿⣿⣿⠛⠛⣛⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣇⠀⠀⢻⣆⠀⠀⠘⣿⣧⠘
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⡼⡔⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⢿⡼⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡀⠀⠘⣿⡄⠀⠰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣸⢳⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⡇⢸⣗⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣧⠀⡸⠃⢸⣇⡅
⠀⠀⠀⡆⠀⣀⠀⢰⣿⠀⢰⡟⡞⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠇⣰⡿⠀⠀⣿⢻⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠀⠀⢹⣿⢰⣧⣴⡿⠋⡇
⠀⠀⠀⠹⡆⠛⢳⡀⢹⡆⣾⠃⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⠁⠀⠀⢿⣾⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡀⠀⢸⣿⠈⣿⣽⢃⣴⠇
⠀⠀⠀⠀⠱⢤⡈⠑⡾⢰⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⠃⠀⠀⠀⢸⡟⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠈⣿⠀⠻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⠇⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠇⣼⠏⠀⠀⠀⠀⠸⣧⢻⣿⣇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⢰⡟⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠛⠻⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⢀⡀⠀⠀⣀⠀⣄⠀⡴⠀⠀⠀⠀⠀⠁⡈⣶⡶⣶⣾⣿⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⡶⡉⠀⠀⠀⡿⠃⣠⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢫⣄⠁⠀⢐⠀⠴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠘⠰⣄⠁⢉⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠒⠢⣽⡀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠙⠷⠶⠤⠀⠀⣀⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠀⢸⡉⢷⣄⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠰⠶⠾⠿⠏⢠⡄⠆⠀⠘⠰⣿⡀⠀⠀⢤⣤⣾⣇⡀⠀⠀⠀⣼⡗⠀⠉⠁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠈⠙⣆⠀⠀⠙⠛⠻⣿⣶⠶⠾⠿⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠰⣾⣉⣀⣀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋⠁⠈⢧⣀⢀⣴⣷⣤⣤⣴⣷⡄⡀⠀⠀⠀⠀⠀⠘⢯⠄⠀⠛⠛⠿⠿⠿⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠈⠉⠹⣿⣿⣟⣡⠄⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⣠⢰⡟⡄⠀⠀⠀⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⣸⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠀⣼⠀⢷⣀⠀⠀⣿⣿⣿⡿⣿⣿⣷⡶⢦⡔⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠼⠁⠀⢾⣿⡄⣼⡿⣷⡟⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣦⡀⠀⠀⢻⣿⢿⠁⠄⠃⢀⢀⣠⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡇⠘⢻⣶⡐⢈⣧⠀⠀⠀⠀⢺⣟⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠃⢸⣁⠘⠻⣤⠦⠄⠀⠈⢫⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⣿⠀⢨⠹⣖⠀⠈⠓⠺⠿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⣿⣄⣈⠀⢻⡄
⠀⠀⠀⠀⠀⢠⣼⣇⡀⠀⣤⣀⣴⢿⣿⣿⣿⣿⣿⣿⣷⣄⡁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⢰⡾⢯⣍⣙⣿⠿⣄⣀⣼⣿⣿⣿⣿⣿⣿⠇⠀⣡⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠈⠃
⠀⠀⢀⢸⡿⠳⠶⣤⣽⡋⠲⢦⣼⡟⢲⣿⣿⠛⣋⣴⣧⣴⣿⣦⠀⠀⠀⠀⠘⠿⣦⡄
⠀⠀⣈⣽⣉⡓⠲⣾⠯⣉⣑⣾⠯⣼⣿⡿⢁⠈⠁⠘⣿⣿⣿⠉⢷⣄⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠼⣯⣉⣙⣿⠛⠶⢤⣽⣟⣰⣿⡟⠑⠂⠀⠀⠀⢹⣿⣿⣄⠀⠙⢷⣄⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠉⠉⠛⢻⡶⠾⣿⣬⣿⣿⠣⠂⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⣀⣹⣿⣷⣶⣤⣤⣿⣦⡀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡿⠋⠉⠉⠉⠉⠛⠻⣶⣤⣾⡉
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⣀⣤⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⠶⠿⠿⣿⠋⠉⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠋⠀⣀⣴⠎
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢟⣿⠟⢀⣤⣾⣛⠷⠦⣄⢀
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣛⠁⠐⠋⠠⠖⠋⠀⢹⡿⠿⣶⣄⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⢳⡄⢠⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⣾⣄⡀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣀⣠⣤⣴⣦⢰⡄⠀⠀⠀⠀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣠⣴⣿⠛⠛⢦⡙⣄
⠀⠀⠀⣀⣤⣤⠶⣾⠛⣋⣻⣧⡼⢿⣿⡽⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⠳⠦⣄⠁⠈⢷⣦⡀
⠀⠀⠈⣽⣧⠴⠖⢻⣏⡉⠤⠿⣷⣈⣿⣿⣎⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠄
⠀⠀⠀⠠⠿⡖⠛⣋⣹⣷⠖⠛⣻⣿⡜⢻⣿⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠘⢻⣟⣩⡤⠿⣿⣉⣤⠾⣿⡉⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢆
⠀⠀⠀⠀⠀⠉⣹⣧⡴⠖⠛⣯⠠⣴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠁⠘⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠉⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢸⣿⣤⣀⣀⠀⣀⣤⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠁⢴⣤⣤⣴⣿⠿⡆⣩⠉⣸⣭⣥⠞⢡⣦⣤⣤⣖⣀⣤⠄
⠀⠀⠀⠀⠀⢠⡎⠀⠀⠹⠀⠀⠀⠘⠋⠀⠉⠻⢿⣷⣼⠇⠤⢭⣵⣿⣟⡇⠙⠋⠈⠉⠉⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⢸⣇⠀⢠⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣾⣿⣿⡏⠀⠠⣀⡀⠀⡀⠀⠀⠀⠀⠀⣴⣿⣇
⠀⠀⠀⠀⠀⠘⢿⣷⣿⣧⣴⣿⣦⣴⣤⣴⠎⠀⠀⣀⣤⠀⢙⣛⠻⠿⠓⢀⣀⣙⣿⣷⣶⣠⣦⠀⣤⣾⡿⠛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⢻⠛⢿⡏⢉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⢩⡟⠁⡇⠀⠉⠁⠈⠉⠁⡀⠀⠀⢘
⠀⠀⠀⣤⠀⠀⢠⣆⠀⠀⠀⠀⣠⠇⠀⠀⣱⣄⠀⠀⠀⠀⢠⠆⠀⢀⠀⠀⣸⡀⠀⢹⡀⡀⠀⢀⠂⢾⣇⠀⢀⣼⡆
⠀⠀⠀⢹⣦⠀⠈⡙⠂⠀⠵⠾⠣⠤⣤⣴⣿⣿⣿⣶⠄⣀⡴⠂⢴⡛⠳⣾⣿⣿⣷⠶⠛⠋⠉⠉⠀⠀⡘⡄⣸⣿
⠀⠀⠀⠀⢻⣞⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠙⠻⠟⣁⣀⠭⠴⢞⣛⠇⢀⣈⠙⠋⠁⠀⠀⠀⣀⣴⣶⣶⣿⡿⣿⠇
⠀⠀⠀⠀⠀⣿⣦⣤⣤⣤⡥⠤⠖⡂⠀⠨⠖⢂⣀⡁⠟⠛⢛⢉⣁⣠⣤⢍⣀⣀⡀⠀⠐⠾⠿⠿⠿⢿⣿⣶⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⠶⠶⠒⠚⢂⣥⣼⣿⣿⡿⣞⢛⡛⠛⣉⣀⣤⣼⣿⣿⢛⡉⣀⣤⣤⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣿⣷⣾⣿⣿⣿⣛⣷⣚⡛⠛⢛⣭⣥⣤⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⣿⣿⣿⣿⣿⣿⣮⣭⣥⣾⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⠟⠿⠛⠿⡿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⢦⡀⠀⠀⠀⠀⣠⢾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠫⡀⠹⢦⣤⣤⠾⠁⠈⡿⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠛⠉⠁⢸⣠⠖⢛⡆⠀⠀⠀⢀⡴⢻⡀⢰⠉⠙⠓⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⢁⡴⠛⠚⠽⠿⠯⠝⠛⢮⡉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠐⠀⡀⢐⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡤⠀⠀⠎⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⢀⣴⣥⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢦⣀⡄⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⣰⢃⣀⣀⣀⣀⣀⣤⣼⣿⣬⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣧⣤⠄⠀⠀⠀⠀⠈⢧
⠀⠀⠀⡰⠋⠉⠁⠀⠀⠀⢠⠏⠁⠀⠠⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠛⠛⠿⡛⠛⠋⠉⠉⠉⠙⠢⡀
⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢐⠠⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠒⠈⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠳⣄⡀⠀⢠⡀⡀⢹⣀⠀⠀⢨⢐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠐⠀⠀⠀⢸⢀⡀⡄⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠈⠉⠙⠛⠳⠿⠾⠿⢿⣻⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣹⣶⣾⡤⡴⠾⠿⠶⠞⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠋⢳⡹⢷⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠙⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠉⠢⠉⠛⠦⣄⡀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⠀⠉⠲⣀⠞⠁⠀⢀⠔⠀⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⠀⠀⠀⡀⠀⢀⣯⠀⠀⠀⠁⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⠂⠉⢸⠀⠀⠀⠀⠀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠒⠒⠠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠔⢊⣉⠤⠔⠒⠊⠉⠉⠉⠉⠓⠒⠢⠬⣉⠐⠢⢄⣀⣀⡀
⠀⢀⣠⡀⠀⠀⠀⠀⠀⢰⠛⠋⡗⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠁⢎⠙⢻⠀⠀⠀⠀⠀⠀⣀⣄
⠀⣸⣿⡈⠢⡀⠀⢀⠔⠉⡾⠛⠃⠂⠀⠀⠀⠀⠀⠀⣠⣤⢶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠁⠘⠛⢆⠙⠢⡀⠀⢀⠜⢠⣿⣇
⠘⢿⠈⠳⡀⠘⢴⠁⡰⠊⠀⡄⠀⢰⠀⠀⠀⠀⠠⣎⣧⣇⣰⣄⣥⣿⣳⠀⠀⠀⠀⠀⠃⠀⢰⠀⠑⢄⠙⡖⠁⢠⠞⢀⡿
⢰⡟⠣⡀⠈⢦⠀⠙⡄⠀⠀⠃⡀⠀⢆⠀⠀⠀⢸⡏⠀⠌⠉⠉⠀⠀⢹⡇⠀⠀⠀⡜⠀⠀⢸⠀⠀⡠⠋⢀⡔⠁⢀⠎⣻
⠀⠱⡀⠈⢢⠀⠑⣄⠈⠢⡀⡀⠁⠀⠸⢆⠀⠀⣿⠀⠈⠛⠀⠀⠛⠁⢈⣏⠀⠀⠸⠀⠀⠀⢰⢀⠜⠀⡠⠊⢀⠔⠁⢠⠋
⠀⠀⡟⢢⡀⠑⢆⣈⠳⡤⣌⣾⠀⠀⠀⠀⠱⠿⣿⣿⡇⢐⠄⢀⡂⢸⣿⣿⠷⠎⠀⡀⠀⠀⣷⣡⢴⠎⣀⡴⠋⢀⡔⣳
⠀⠀⠈⠃⠘⠿⠏⠙⠛⠉⠈⠉⡗⠦⣦⠀⠀⠀⠈⠻⠣⡙⣝⣹⢃⠜⠟⠀⠀⠀⠀⣥⠔⢘⠉⠁⠉⠛⠋⠻⠟⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢣⡔⠀⠀⠀⠢⠘⠋⠙⠃⠀⠀⠀⠀⣤⠞⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠢⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠜⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠀⠌⠐⠂⠔⠛⠓⠠⠐⠂⠡⠀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠢⠀⠀⠀⢸⠆⠀⠁⠀⠔⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢸⠆⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠜⠢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⢟⡿⢿⠟⢻⡟⠻⠿⢟⡿⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠊⠈⠑⠤⡈⢁⠄⠊⠁⠑⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⠃⠱⡄⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠿⣿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢁⠀⠀⢀⣽⣟⠲⠦⢀⡶⠞⣿⢁⠀⠀⣀⡄
⠀⠀⠀⠀⠀⣠⠂⠀⢾⠀⠀⠀⠮⠛⠻⣿⣿⣝⣶⢁⡖⣛⣿⣴⠸⡿⠛⠛⠚⠛⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢠⣿⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣬⣿⣿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇
⠀⠀⠀⠀⠘⢿⣧⣾⣤⣤⣷⣤⣤⣤⠖⠀⢀⣀⡤⠙⢿⠿⠿⢧⣀⣘⣿⣶⣴⣠⡤⢀⣤⣿⠟⠿⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠻⡟⠿⡟⠩⠉⠉⠁⠈⠉⠀⠠⠀⠌⣿⠋⢿⠀⠙⠁⠉⠉⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⣦⠀⠀⠀⢀⠜⠀⠀⣰⣄⡀⠀⠀⠀⠆⠀⢠⠀⢀⣧⡀⠸⣄⣀⣀⡀⠰⢿⡀⢀⣼
⠀⠀⠀⢿⣄⡀⠨⠁⠀⠓⠋⠒⠲⠾⣿⣿⣿⠗⢠⠶⢋⣼⡍⠙⢿⣿⡿⠛⠉⠉⠀⠀⣀⣠⣷⣸⡿
⠀⠀⠀⠈⢿⡄⠀⠐⠶⠅⢀⣀⡀⠠⢀⡉⠡⠤⣌⣿⣭⠿⠁⠰⠆⠁⠀⠀⠀⣠⣶⣿⣿⣿⣟⡿⠃
⠀⠀⠀⠀⠸⣿⣿⣛⣛⣉⣉⡰⠄⠌⢡⣶⣶⣮⣤⣴⣶⠶⠚⠋⣰⣶⣶⠤⠌⠉⣉⣩⣭⣿⡿⠁
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣭⣤⣤⣤⣿⣿⣿⢿⡥⠶⠶⠶⣚⣛⣉⣿⣿⣷⣶⣶⣿⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣤⣞⣋⣿⣿⣿⣿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⠎⠁⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⣠⣄⣸⣿⠀⢀⣴⣷⡄⠀⢀⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡼⢻⣽⠏⠘⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢨⠉⠉⣿⡟⣿⣿⣿⣿⣿⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣥⣄⠀⠀⠸⣟⣷⣿⡇⠙⠋⣩⣵⣶⢀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⢀⣬⣿⠟⠁⠀⠀⣿⣿⣿⣿⣷⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡶⢾⣿⣥⡟⠀⠤⠀⠀⣿⣿⣿⣿⣿⡆⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠁⠀⠀⠀⠀⠻⣿⣿⠛⣿⣿⡄⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠠⣤⠀⠀⠀⠀⠀⠉⠀⠹⣿⠃⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠔⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠘⣿⡀⠀⣤⣀⡀⠀⠀⠀⠉⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢹⣇⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢿⣧⣤⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣮⣴⣿⣶⣶⣦⣶⣾⠏⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⣼⡟⢿⣧⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⠀⣠⠞⠋⠀⠉⠉⢻⣿⣿⣿⡏⢀⡄⠀⢰⣿⡏⢹⡇⠀⠀⢰⣿⡇⢸⡿⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⡛⠛⠁⠀⠀⢸⣿⠇⢸⠇⠀⠀⣾⣿⠇⢸⡇⠀⠀⣴⠇⠀⠀⣠⣿⣿⣿⡿⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠁⠀⠀⠀⠀⣸⡟⠀⠁⠀⠀⢰⣾⣿⠀⢀⠀⠀⠘⣿⣤⢒⣾⣿⣿⠃⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣠⡴⠂⠀⠀⠀⠀⡄⠀⣼⡟⠁⠀⠀⣀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣿⣿⠃⢀⣿⣷⡶⠟⠋⢡⣾⣿⣿⣿⠀⠀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⡿⠀⠀⢀⣠⣼⣿⡟⣰⡿⠀⠀⠀⠀⠘⡿⠟⠁⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⣴⣿⡟⠈⢿⣿⠀⢸⠿⢿⣦⡸⣧
⠀⠀⠀⠀⠀⡴⠋⠀⣠⠞⡃⠀⡴⠛⠉⠉⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⢀⣾⠟⠉⢷⡀⢸⣿⠀⠀⠀⠀⣿⣧⠹⣧
⠀⠀⠀⢠⠎⠀⠀⠘⠁⣸⡇⠘⠀⠀⠀⠀⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠈⠻⣿⣿⡆⠀⠀⠀⣿⡄⠀⢻⣷⡀
⠀⠀⠀⡟⠀⠀⠀⠀⣰⠏⠀⠀⠀⣀⣤⣾⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣿⣿⠀⠀⠀⠀⢀⡄⢰⡟⠀⠀⠀⠀⠀⠀⢹⣿⣷⣄⠀⠀⣿⡇⠀⠀⠘⢿⡄
⠀⠀⠀⡇⠀⠀⠀⠐⠁⠀⠀⠀⣼⠋⠀⠀⣠⣿⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠁⣿⡏⠀⠀⠀⣠⡞⠁⣾⡇⠀⠀⠀⠀⠀⠀⠘⣿⠛⢿⣦⡀⣹⣿⠀⠀⠁⠘⣿
⠀⠀⢰⡟⠀⣤⡀⠀⠀⠀⢀⡜⠁⠀⢀⣴⢿⡅⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣀⣿⣇⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⣼⠛⢿⡶⠶⠦⢀⣀⣠⣿⡟⠙⠲⠀⠀⢰⡿⠛⠠⠦⠶⠄⠀⠒⠛⠛⠛⠛⠋⠙⣿⠉⠁⠀⣏⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣿⣿⣷⡄⠀⠀⣿
⠀⠀⢸⡇⠀⣿⢠⣿⠃⠀⢠⣾⡿⠋⣼⠃⠀⠸⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡀⢿⣿⣿⣧⠴⣾⣿
⠀⠀⢸⡇⠀⣿⣿⡏⠀⣰⣿⡟⠀⢠⡏⠙⠛⠛⠷⠶⠾⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠾⠟⠻⠟⠉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⢸⣿⡇⢰⡿⣿
⠀⠀⢸⡇⠀⣿⣿⠇⣰⣿⠋⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠈⣿⣷⣸⡇⣿
⠀⠀⠸⡇⢸⣿⢯⣾⣿⠃⠀⠀⣰⠇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢻⣿⣿⠃⣿
⠀⣀⠁⠀⢸⣿⣿⣿⡇⠀⠀⢀⡟⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⢾⡀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⢀⣤⠴⢿⣧⢸⠸⣿⣿⠀⣿
⠀⣯⣴⡇⢾⣿⣿⣿⣷⣄⠀⡾⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⣧⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⣸⡁⢀⠘⣿⣿⡀⣿⠇⡀⢹
⠀⡌⠉⠀⠀⢹⣿⣿⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣶⠞⣫⣿⣧⠀⠀⠀⢀⡴⠋⠹⣿⠗⢾⣿⣧⣿⠰⣧⣸
⠀⣿⠀⠀⠀⣾⣿⣯⣼⣿⡏⠀⠀⠀⠈⠙⢶⣤⡀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠡⠘⠁⢸⣿⡄⠀⠀⠀⠳⡶⠀⢘⠏⢙⣿⣿⠁⠀⠹⠃
⠀⣿⠀⠀⢸⡿⠿⣏⢻⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠐⣶⠞⠊⠁⡈⢻⣆⡀⠈
⠀⢿⣠⡀⠟⠳⢠⡏⣿⡇⢠⠀⠀⠀⠀⠀⠀⢠⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠘⢦⣰⠋⠀⢈⠿⠀⠠
⠀⠀⠉⠓⠂⠠⠾⠛⢻⢡⡏⠀⠀⠀⠀⠀⢀⣾⠃⠀⢸⣿⣿⣿⣿⣿⣇⢿⣿⣿⠟⣾⣿⣿⢸⣧⠀⠀⠀⠀⠀⢘⣿⢿⣿⡆⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⣼⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⣿⡟⣸⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠃⣠⠔⠀⠀⠀⠀⠀⠀⢸⣇⠀⢘⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⢰⠟⠀⠀⠀⠀⠀⠀⢀⣸⣿⣦⣨⣿⣿⣇⣀⣀⡀
⠀⠀⠀⠀⠀⣴⢿⣶⣤⣼⣿⣿⣿⣿⣿⣿⡟⠿⣷⣄⠀⠀⠀⢻⡆⠀⣀⣠⠀⠀⠀⠀⠀⢀⣴⢶⣿⡿⠿⣿⣿⣿⣿⣤⣴⣾⡟⠳⣦
⠀⠀⣀⣤⣾⠃⣾⣯⠛⠁⠀⢿⣿⣿⢿⣿⣿⣷⣤⣉⣻⣦⡀⢙⣷⣾⣹⣟⣶⣀⠀⣠⠶⣋⣵⣿⠟⠁⢠⣿⣿⣿⡇⠈⠻⣷⣷⠀⢻⣄
⠀⣰⡿⡿⠃⠀⣿⡟⠀⠀⠀⣿⣿⣿⣆⡙⠻⠿⢿⣿⣿⣿⣿⣿⠛⠿⠹⠿⠿⡿⢿⣿⣿⣿⣟⠁⠀⣠⣿⣿⣿⣿⣿⠀⠀⠈⣿⡆⠀⠛⠿⠛⠛
⣰⠏⡼⠁⠀⠀⣿⡇⠀⠀⠀⣿⢻⣿⣿⣏⠓⠢⠤⣾⣿⣿⡷⠿⠃⠀⠀⠀⠰⢁⣼⣿⣿⡿⠟⠃⣸⣿⣿⠟⣹⣿⣿⠀⠀⠀⢹⡇⠀⠀⠈
⠃⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿⡀⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⣼⣿⠟⠁⢀⣿⣿⣿⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣷⡀⢹⣿⣷⠀⣤⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⠀⢀⣾⣿⢿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⣿⠀⠀⠀⠈⠁⠀⣄⡀⣀⡆⠘⠀⠀⠀⠸⠃⢸⡟⢠⣿⣿⡟⣼⡇⠀⢀⣾⣿⡇⠀⠀⠀⠀⣨
⡇⠀⠀⠀⠀⠀⢸⡀⠀⣸⡎⣿⣿⡜⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡿⢡⣿⣧⣰⣿⣿⣿⡇⠀⠀⠀⢀⡻
⢿⡄⢠⠀⠀⠀⣼⡇⢸⣿⡇⢻⣿⣿⡌⢿⣿⣿⢿⡄⠀⠀⢀⣉⣭⣭⣥⣤⣤⣤⣤⣅⣀⡀⠀⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⣿
⣼⣿⣼⣧⠀⠀⣿⣷⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣶⣾⣿⠿⠋⠉⠉⠙⠉⠙⠛⠋⠛⠀⢰⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⡇⠀⣠⠀⢀⣽⣧
⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⠁⣼⡧⠀⣾⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣶⠿⠋⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⢇⣾⣿⠁⣼⣿⣿⣾
⢹⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠁⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⡿⣟⣿⣛
⣈⣿⣷⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣯⠹⣿⣿⣿⣿⣷⣾⣿⣿⠁⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⡿⠿
⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣆⠹⣿⣿⣟⢿⣿⣿⠇⣠⣀⠂⢸⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⡟⣿⣿⣿⡄⠹⣿⣿⣿⣿⣟⣰⡳⠈⠀⣸⣿⡇⣿⡃⣸⣿⣿⣿⡿⠿⡋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣤⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢆⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣷⣾⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠉⠉⠁⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠳⠖⢰⡶⠟⡀⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢁⢿⣿⠀⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄⣠⣤⣶⡤⢋⣾⢃⣰⠇⠀⠀⠰⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⣳⣌⢩⠻⢋⣤⠾⠃⠉⠁⠀⢀⢀⣤⣶⣶⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠈⠀⠀⠀⠀⢀⣠⣽⣦⡘⠁⠐⣆⣠⠀⣠⣰⣯⣾⡿⠛⠛⠛⢋⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢹⣿⣿⣾⣦⣴⣾⠟⠉⢀⣼⣗⣼⣦⣙⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⡠⠞⠙⡿⠿⢿⣿⣷⠂⠉⢀⡆⢉⣙⣛⣻⡿⢊⠿⠛⠹⣧⣄⠀⠀⠀⣀⣼⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠀⢀⠚⠁⠀⠀⣿⣿⣦⣤⣼⣿⣶⣬⣿⣿⢁⠋⠀⠀⠀⠚⠈⠑⠀⠀⢻⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⣶⣌⢳⣦⣤⣴⡿⣿⣿⣿⣿⠿⣿⠿⣿⣿⣦⣿⣶⠆⠁⣀⣠⣤⣄⣰⣤⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣅⠙⠆⠛⣿⣷⠀⠈⠛⠻⠉⢉⣹⣁⣉⣉⣻⣿⣿⠀⠈⣀⡤⠿⢛⣿⢟⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣄⠀⠀⠻⣿⡀⠀⠀⠠⠇⠀⠘⠉⠀⣹⣋⣽⠏⠀⠊⢉⣤⠶⣛⣵⢟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣦⡄⠀⠀⠀⠺⠆⠀⠀⠀⠀⠈⠉⠁⢀⣠⠀⣈⣭⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⡆⠀⠈⠓⣀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣽⡿⠿⠏⠁
⠀⢀⡀⠀⢀⢀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠈⠋⠓⠋⠑⠂⠐⠈⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⢟⠻⣛⠛⢿⠟⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠈⠛⠁⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⣠⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⢀⡀⠀⢀⣠⣾⣯⠛⠿⠶⢠⡾⠟⣫⠏⣀⢀⡀⣀⣠
⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⣾⠀⠀⠀⢁⣬⠛⠻⢿⣿⣿⣜⢳⠞⢁⡾⢟⣻⣣⣴⢻⣿⠿⠿⠷⠾⠛⠁⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⣿⠃⠂⢀⢸⡄⠀⠀⠈⠀⠀⠀⠀⠙⢛⢿⣯⣉⣈⢛⣿⣿⣿⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⣿⣧⠀⣾⠀⠀⣤⡐⢀⠀⠀⢀⡀⠀⠀⠂⠉⠻⣿⣿⣿⣿⣧⠀⠀⢢⣤⣤⡐⢀⠀⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣏⣀⣀⣠⣴⡶⠀⢨⣭⠉⠛⠉⠭⢴⣤⣽⢿⡿⠿⣴⡿⢀⣶⣿⠿⠋⠉⠻⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢹⠍⠟⢿⠁⠄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠐⠊⣾⠁⠐⡇⠀⠈⡀⠀⠀⠀⣀⠀⠀⠀⣧
⠀⠀⠀⢸⠀⢀⠀⢴⡇⠀⠀⠀⠀⣠⠏⠀⠀⢈⣧⣀⠀⠀⠀⠀⢠⠇⠀⠀⡄⠀⢀⣿⠀⠀⢷⠀⡀⠁⢀⡉⠶⣿⡀⠀⣠⣿
⠀⠀⠀⠸⣷⡀⠀⢈⡙⠂⣠⠷⠾⠧⠤⢤⣴⣿⣿⣿⣿⣶⠀⣀⡴⠒⢲⣚⠳⢾⣿⣿⣿⣷⠿⢛⡋⠉⠉⠀⠀⢀⢣⢀⣿⡟
⠀⠀⠀⠀⠹⣷⡇⠀⠀⢀⡀⠤⠤⠀⠀⠀⠈⠉⠻⠿⠟⠁⠈⣯⣤⠶⢛⡟⠀⣀⡙⠟⠋⡀⠀⠸⠀⢀⣴⣶⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣧⣄⣀⣉⣉⣉⣠⡤⠶⠂⢀⣣⠶⠀⠘⢉⡵⠶⠛⠚⠋⢀⣨⡍⠁⠀⢀⡀⠀⢠⣷⣿⣿⣿⢿⣿⣧⣾⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣯⣭⣭⣤⣤⡤⠽⠤⣒⣀⣾⣿⣿⣧⡼⠶⠾⠿⠟⠋⢉⣁⣿⣿⣿⠷⠖⠒⡀⣐⣥⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣯⣥⣶⣤⣤⣿⣿⣿⣿⢿⣭⢷⠶⠶⠶⠞⡛⢋⣹⣿⣿⣷⣾⣶⣾⣿⣿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣖⣲⠶⠟⢻⣽⣿⣿⣿⣿⣿⣿⣿⡟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡞⣿⡟⣳⣦⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⣾⣿⣿⣿⣧⣼⣿⣏⣹⣿⣥⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠐⡬⣼⠀⠈⢻⡏⠉⠉⠉⠁⠀⠈⢻⣷⢾⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠿⠙⠋⠀⠋⠁⠀⠀⢀⣃⣀⠀⣠⣴⠖⠂⠈⢻⣿⣷⣼⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣆⠉⠔⠹⠷⠂⢹⠛⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⠃⠀⠀⠀⠀⠀⠀⣨⢴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⣘⣃⠀⠀⠀⠀⢀⣷⣮⣿⠅
⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠇⠀⠀⠀⣀⣴⠟⣿⢇⠿⣿⣢
⠀⠀⠀⠀⠋⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⡿⠋⠀⠀⢷⣸⠷⣟⣿
⠀⠀⠀⢸⡀⠀⠀⠠⠘⠷⠶⠶⠒⠛⠛⠛⠲⢦⣴⠶⢶⠟⠛⠛⣶⣤⣴⣿⡁⠀⠀⠀⠀⠈⠻⣿⣟⠃
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡞⡆⠀⠀⢿⣿⣿⠿⣿⣆⠀⠀⠀⠀⢠⡏⠙⣦⡀
⠀⠀⠀⠙⠳⢶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢀⡿⠀⠀⠀⠙⠋⠀⣠⡘⣆⢀⣠⠴⠋⠀⡼⠁⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣤⣤⣀⣀⡀⢲⣿⣿⠟⠸⠁⣄⠀⠀⠐⠟⠛⠉⣿⣹⣯⠗⢲⡄⢸⡇⠀⢀⠀⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣧⡿⣠⡟⠀⠀⠀⠀⠀⠀⠙⡿⠃⠀⠈⠳⣼⠁⡴⠋⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⢻⡟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⢈⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠰⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠄⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠘⠂⡀⢠⣿⣀⣠⡤⠶⠦⣄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢑⡾⠹⠿⠛⢛⣛⣓⠢⠄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⣆⢹⡇⠀⠀⠀⠀⠀⠀⢠⡿⠠⣷⡶⠶⠿⠿⢶⣯⡒⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠲⣄⠙⡘⡇⠀⠀⠀⠀⠀⠀⣸⠷⠚⠉⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⢀⡘⠦⠙⢣⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⠙⣂⣀⣈⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠉⠉⠀⠀⠀⢀⢀⣠⡤⠤⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣿⡄⣸⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠞⠁⠟⠹⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠞⠀⠀⠂⠀⠀⠀⠀⠃⠉⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣶⢦⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠶⡡⢿⡞⡏⠀⠀⠀⠀⢰⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡂⢀⠟⡉⠀⠁⣘⢳⢿⡄⢸⠀⠀⢨⠻⠻⣤⣇⢀⣖⠦
⠀⠀⠀⠀⠀⠀⣴⣥⠄⡀⠀⣹⡗⣡⣾⣿⠃⣰⡇⡸⠀⣿⠿⣄⣠⣿⢣⡀⠈⠹⣾⠁⠀⠈
⠀⠀⠀⠀⠀⠠⠋⠉⠛⠳⢾⣯⣾⣻⢳⠃⢠⣿⠇⡇⠀⢿⣾⡘⡈⢻⣇⢻⣤⠬⢶⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠉⠭⠙⠒⠋⠛⢻⣿⡄⠚⠛⠓⠓⠘⠻⡏⢁⡤⠔⠈⣷⣀⠄
⠀⠀⠀⠀⠀⠢⡀⠀⠀⡀⠘⠇⠀⠀⠀⠀⠀⠀⢸⢸⡇⠖⠂⠀⠀⠀⠀⣹⣀⠀⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠤⠷⠞⢀⣀⠀⠀⠀⠀⠀⡄⢸⠃⠀⠀⠀⠀⢀⠌⠀⢠⠋⠱⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠉⠀⠉⠉⢉⡉⠉⢩⡀⠴⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⠀⠀⠀⢀⠀⢐⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣝⡀⠀⢀⠁⡊⠀⠀⠈⢻⢦⠀⠴⢂⡿⡄⠀⠀⠹⡦⡐⠐
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠈⠓⢍⠓⢤⣁⠀⠀⠀⠀⡟⢀⠀⢀⠞⠀⡟⠀⠀⢠⠀⠹⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⢧⠀⠈⠳⡀⠐⣦⡙⢮⠢⢸⠁⢠⠃⠀⡠⠋⠀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢖⠈⣀⣀⡀⠀⠀⢸⡤⠀⠀⢧⢠⣇⠹⡌⢳⠘⣆⡿⢀⡞⠁⠀⠀⢀⠆⢀⠎⢣⠀⡀
⠀⠀⠀⠀⠀⠈⠀⣈⠉⢳⡎⢢⡀⢸⠀⠶⡀⠈⠻⠂⠀⢱⠀⠀⡿⢽⣼⠀⢠⠀⢀⡌⢀⠠⡀⡏⠐⠁
⠀⠀⠀⠀⠀⠀⠈⢹⠙⠸⡇⢀⠱⣾⡄⢁⠈⠢⡀⢠⡄⡞⠀⢀⠇⡄⠋⡠⢁⢣⠏⠀⢸⢣⢰⠇⢀⢦
⠀⠀⠀⠀⠀⢀⣆⢺⡊⠀⠹⣇⠰⠠⢄⠀⠂⠀⠰⠂⢠⠃⢀⡞⡐⢸⠐⠀⢠⠃⠀⡰⠃⣸⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠘⡏⢦⣀⠀⠀⠈⠳⣝⢤⡈⠲⠀⠀⡄⢸⢠⠟⠐⠀⢾⠀⠂⡇⣠⠏⠀⣀⡎⠀⣠⢀⡸
⠀⠀⠀⠀⠀⠀⠱⣄⠈⠑⠢⢤⡀⠘⡄⠱⠀⠀⠀⠆⠈⠿⠀⠀⠀⠀⠀⡆⢹⠇⡄⢠⠎⢀⡰⣻
⠀⠀⠀⠀⠈⢻⠆⠈⠲⢄⠀⣄⡙⠶⣗⠀⠁⠀⠀⠘⢄⠈⠂⠰⠀⠀⠀⠐⡤⠊⢄⣮⠖⢋⡜⠁⣦⡀
⠀⠀⠀⠀⠀⠘⠒⠠⠱⠀⠱⡀⠂⠑⠄⠀⡄⠀⠀⠀⠀⠉⠂⣤⠀⠀⠀⠀⠄⠐⠎⠥⢈⠏⡀⠀⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⡀⡇⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢐⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠓⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⠀⡀⠁⠀⠔⠀⡀⠀⡀⠀⠀⢐⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠐⠀⠀⠈⠈⠀⠀⠁⠀⠈⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢯⣽⡶⠀⠀⡀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⣦⡀⠀⠀⡄⣼⣤⣄⢌⢱⣆⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠙⡄⠤⠄⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣿⣷⡀⠦⠳⣿⡥⠛⠙⢉⣋⡭⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣜⠀⠀⠀⠈⠁⠀⠀⠀⢢
⠀⠀⠀⠀⣼⣿⣿⣧⢠⣁⡼⠇⢩⣱⣿⣁⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢓⠶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡦⠈
⠀⠀⠀⠀⢿⣿⡟⣏⢪⡿⣶⡳⠰⣶⣆⣥⣾⠏⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⢻⣞⠃⢿⣏⣿⣿⢾⣒⡙⣿⣏⠻⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠠⣄⠀⠀⠀⠀⠀⠤⠀⢸⠁⠀⠠⡀⠠⠴
⠀⠀⠀⠀⠀⢻⣄⠈⠉⢩⣯⣢⡙⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠱⢀⠀⠀⠀⠀⡇⢸⠓⣦⠁⠤⠖⢂⠄
⠀⠀⠀⠀⢀⣼⡿⣦⣄⠀⠻⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣤⣄⠀⠀⠄⠀⣠⣦⣿⢀⣽⡇⢀⡏⣾⠂
⠀⠀⠀⣠⣾⣿⡛⢿⣍⡻⢻⡟⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠠⠤⢴⣿⣿⣿⣟⠘⢠⣿⢋⣩⡤
⠀⠀⠀⣿⣿⣿⣷⣄⠀⣽⣾⣿⠘⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⢀⣀⢄⠀⠀⠙⠟⠛⣋⠘⠏⡁⠁⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣆⠈⣿⣿⠈⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠉⢁⣤⣤⣤⣤⣤⣴⡞⢋⡀⠀⠌⠂
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣮⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠻⣾⣿⣷⣤⡄⢉⠻⠿⠡⠒⢊⢀⣀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠷⠌⠒⠉⠻⠿⠿⠛⠛⠒⠒⠀⠐⠂⠀⠙
⠀⠀⠀⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠣

⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠘⣇⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠰⠋⡇⣦⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠰⡆⣨⢛⢥⡶⠀⠀⠀⠀⠀⠀⢸⢸⣄⣧⣠⠀⠀⠀⠀⠀⢀⠀⣲⠛⡏⠀⠀⠀⠀⠀⠀⡾⡿⠜⡄
⠀⠀⠀⣷⣼⢀⡾⣤⠦⡼⠀⠀⠀⠀⢸⣾⠈⡟⠙⢻⠀⠀⠀⠀⠀⠘⢟⢫⣿⣀⡀⠀⠀⠀⢀⠠⢇⠠⣤⢷⡄
⠀⠀⠀⠘⠦⠾⠇⠘⠃⠁⠀⠀⠀⠀⠀⠁⠰⠛⠖⠁⠀⠀⠀⠀⠀⠀⠀⠱⠐⢯⠃⠀⠀⠀⠘⣷⠛⠘⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡀
⠀⠀⠀⠀⠘⡿⡏⡅⠀⠀⠀⠀⠀⢀⢀⠀⣿⢣⣀⡀⠀⠀⠀⠀⠀⠀⠎⣼⣿⢰⡀⠀⠀⠀⠀⠀⡄⣾⡼⣃⡋
⠀⠀⠀⠀⠸⣧⠛⣇⠀⠀⠀⠀⠀⠈⠉⢷⠾⡌⠛⢛⡁⠀⠀⠀⠀⢰⣜⣇⢹⡾⣧⡀⠀⠀⠀⠀⡁⢏⢁⢹⠠⠇
⠀⠀⠀⠸⣆⣿⢶⣼⠀⠀⠀⠀⠀⠀⣻⡛⠀⡿⣆⠛⠇⠀⠀⠀⠀⠸⣿⠹⢰⡀⠻⠀⠀⠀⠀⠠⣼⡾⢿⡘⢾
⠀⠀⠀⠀⠀⠰⠏⠋⠀⠀⠀⠀⠀⠀⠈⠃⠻⠅⠙⠋⠀⠀⠀⠀⠀⠀⠙⠘⠋⠃⠀⠀⠀⠀⠀⠀⠈⠃⡎⠻⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⣀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠈⢢⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⣬⢣⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡠⢒⡭⣻⠘⡆⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⠊⠁⠀⠀⠀⣿⠀⠀⠀⠀⢿⣆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⣠⣴⣿⡿⡄⠳⣄⣤⠠⢺⠀⠀⠀⠀⠘⠻⣿⡲⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⣿⠛⢿⢻⡅⠐⣙⡟⠰⢸⠀⠀⠀⠀⠀⣄⠈⢷⣌⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣤⠄⡼⣿⠆⠀⠀⠙⠶⣾⣿⣶⢸⠀⠀⠀⠀⠀⣿⠻⣦⠙⠷⣼⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠏⢡⡞⠁⠸⣇⠲⡄⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⠻⣧⢻⢳⣀⣀⣹⡛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡏⠀⠀⠀⢹⣷⣜⣦⡠⣤⣀⣒⣧⢳⡀⠀⠀⢠⠁⣿⢺⠈⣷⠈⠉⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠠⣇⠀⠀⠀⠀⣿⣿⣿⣿⣎⢻⣿⣿⢸⠁⠀⠀⠁⢠⡏⡜⠀⣹⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣌⣾⠄⠀⠀⠙⢆⠀⠀⠀⣿⡿⣿⣿⣿⣆⢿⣿⣇⡇⠀⠀⠀⢸⠸⠀⠀⢿⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⢘⠄⠀⠀⡏⡇⣿⣿⣿⣿⡸⣿⣿⣿⣆⠀⠀⢸⡀⠀⠀⡆⠀⠀⠀⠀⣸⠇⠘
⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⢠⡄⠀⠊⠀⠀⠀⢣⢧⣿⣿⣿⣿⣷⣿⣿⣿⡝⠳⠤⠔⢷⣄⠀⠁⠀⠀⠀⣠⠃⠀⡇
⠀⠀⠀⠀⠀⣠⡾⠟⠀⠤⠀⣸⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠁⠀⠀⠃
⠀⠀⠀⠀⣰⡏⠀⠀⠀⢀⠀⡟⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⡼⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢹⡟⣹⣿⣿⣿⣿⣏⢧⠑⣌⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⢹⢿⡟⣿⣿⢈⠇⠘⢆⠠⡀⠀⠐⠀⠀⠀⠀⢀⠎
⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣀⣠⣴⠏⠀⠀⣾⢸⣿⢸⡗⠊⠀⠀⠀⠱⣌⠐⠀⠀⠀⠀⢠⣾⡿⣻⢖⣂⠀⠀⠀⠀⠤⠀⡀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⡤⢴⠒⠋⠉⠀⠀⠠⠀⠀⠈⣾⠏⠈⠀⠀⠀⠀⠀⠀⠈⠳⢔⠢⢤⣴⣿⣷⡾⠛⣉⠤⠀⠀⡀⢀⡤⠀⠀⠈⠐
⢸⡏⠀⠀⠀⠀⠀⠀⡰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣵⣿⡿⠷⢶⠟⠓⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠂
⣾⡷⠀⠀⠀⠀⢒⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡟⠉⠋⠴⠀⠀⠀⠀⠀⡀
⣿⣡⠖⠐⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠛⠻⠿⡿⠟⠛⠉⠒⢦⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠙⣧⡈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠒⠛⠉⠁⠈⣷⠀⠀⠀⢀⠀⠀⠀⠀⠈⡇⠈⠐⠀⠀⠀⠀⢀⣀⣀⣠⠤⠴⠒⠈⠁
⠀⠈⠛⠓⠲⠷⠦⠤⠄⠐⠂⠐⠒⠒⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⣰⡀⢰⠤⠄⠀⠰⠥⠀⠐⠂⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠘⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⢺⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠻⣿⡄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⡀⣰⣿⡿⠃⠀⢠⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡼⣿⠁⠀⠀⠸⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⣿⣷⠈⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣦⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⢤⡀⠀⢀⣿⣷⡀⠀⠀⣸⣿⣿⡟⠀⢤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⡇⠀⠀⠀⢱
⠀⠀⠀⢤⡀⠀⣴⡿⠀⡀⠙⣿⣿⣿⣿⡆⠀⠀⢸⣷⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⠁⠀⠈⣿⣷⡄⠀⠀⠙⠻⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣷⣤⣀⣤⣿
⠀⠀⠀⠈⣿⣶⠟⠀⠀⣿⣦⣾⣿⣿⣿⠇⢀⣴⣿⠟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠉⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣇⠀⢀⣿⣿⠀⡀⠀⠘⢿⣿⣿⣿⢟⣴⣿⣿⠋⠀⢠⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⠀⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣇⣀⣽⣷⡀⠈⠙⠿⢋⢸⣿⣿⣿⣷⣤⣾⡇⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⣿⣌⣿⣿⣿⣿⣿⡿⢡⣾⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⢠⠀⠙⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⡟⠀⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣷⣶⣿⣿⣿⣿⡟⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣘⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⡟⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠿⠃⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⢤⠉⠐⠄⠀⠀⠀⠀⢌⢉⠁⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴
⠀⠀⠀⠔⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⡍⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⢀
⠀⠀⠱⠦⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠠⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠛⠉⠀⠈⠄
⠀⠀⠀⠀⠶⣠⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀
⠀⠀⠞⠀⠴⠿⢋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⢣⠀⠛⠀⣦⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣤⡈⠉⠐⠂⠀⠀⠀⠀⠐⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠁
⠀⠀⠘⠃⠀⠀⠀⠟⣤⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡷⠶⣄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⣀⠀⠀⣰⣾⣿⣦⠀⠀⠀⠀⠀⣰⣶⣮⡉
⠀⠀⠰⠒⠀⠀⢀⣴⣽⣧⠀⠀⢀⣿⣿⣿⣿⣿⣿⢀⣧⡿⠷⡀⠀⠀⢀⣬⣭⣭⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⠋
⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣧⠀⣼⣿⡿⠛⣿⣿⡇⠌⢩⠀⠀⠈⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⡅
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠋⠀⢸⣿⣿⠰⢒⡟⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⠻⢿⡿⠀⠀⢀⣿⣿⣿⣿⣿⣄⠀⠀⠀⣰⠁
⠀⢘⣿⣿⣿⣿⣿⣯⣭⠉⠛⠛⠀⠀⢠⣿⣿⡇⢂⢀⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠁⢀⣰⣿⡁
⠀⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠻⠿⣿⠠⣅⣪⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠋⠀⠀⠀⣼⢷⣿⡃
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠌⢀⠒⠒⠓⠂⠀⠚⠑⠂⠂⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⢀⣾⢻⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⢀⠞⡈⣧⣿⣿⡇
⠀⠀⠀⠀⠀⣦⠐⢀⠄⠀⠉⠀⠰⠂⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⢀⡎⠀⢱⣿⣿⣿⡇
⠀⠀⠀⠰⠜⠋⠀⠈⢁⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢠⡀⠀⠘⠛⠛⠫⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⢠⢎⠈⢲⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣤⠄⠚⠁⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣦⣄⡀⠀⠀⠀⢀⣿⣿⣿⠃⠀⣰⣿⣄⣳⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢾⡀⣀⣠⣆⡙⡀⠀⣠⠀⠀⠐⠀⠀⠀⠀⠀⣀⣀⠠⠆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣤⣀⣸⣿⣿⣿⠀⢠⠫⡝⣯⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠀⣀⠉⣶⠘⠓⠀⡀⠛⠋⠤⠤⠚⠋⣻⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⠋⡀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢺⠀⢰⣧⣾⣿⣤⣋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡚⠀⢸⣿⣿⣿⣿⣿⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⡈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣰⣿⡷⠺⢿⣿⣿⣿⣿⢰⣿⡿⡟⠻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢰⣿⣿⣏⣉⠁⠤⢾⣧⣿⣿⣿⢠⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠉⠉⠀⣿⣿⣿⣿⣿⡿⢸⠽⣻⡇⠀⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⢸⠘⠋⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠻⢿⡿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠛⠻⠇⠘⠐⠚⠀⠘⠹⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠿⠿⠿⠟⠛⠻⠚⠛⠿⠟⠻⠳⠛⠚⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣝⢷⣄
⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣧⠹⣷
⢀⠀⣰⣿⣿⣿⢿⣿⣿⣿⣿⡄⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡳⣦⡀
⠙⠒⢤⣬⣭⡅⢀⢈⣿⣿⣿⡇⢸⡿⠉⢢⢤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣯⣿⣿⣿⣿⣷⡘⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡇⠀⠇⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠿⠷⢾⠇⠙⡿⠛⢻⣿⣿⡇⣿⣆⡀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⢏⣼⡟⠑⠀⠰⡀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠈⢷⠀⢹⣶⣾⣿⣿⣇⣿⠛⠛
⠀⠀⠀⠈⠻⢿⣿⣿⣛⣵⡿⠋⠀⠀⡆⠀⠱⡄⠀⠀⠀⣼⣿⡿⢋⡙⢇⠀⠀⠀⢸⠆⠀⣿⣿⣿⢟⣾⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢹⡄⠀⠹⣄⠀⠀⣿⠛⠀⠈⠀⢸⠀⠀⠀⣎⡀⠀⡿⠿⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠱⣄⡙⠂⢀⣀⠀⢸⣄⡤⠋⠀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣠⣀⠉⠑⠢⣌⠙⠻⢦⡀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⠉⠂⠀⠀⢹⣧⡀⠀⢳⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠠⢄⣸⣿⣿⣷⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⣼⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠛⠋⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠉⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⡤⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣠⣿⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡆⢢⡄⣀⣀⠀⢠⠋⠙⠊⠉⠁⠐⡇⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣦⣻⡀⠀⠈⠓⠁⠀⠀⠀⢀⡠⠚⢏⣁⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣾⣁⣀⣉⣳⣤⣀⠀⠀⣠⣴⣋⣀⣀⣼⣿⣿⣷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣠⡇⠀⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠋⠀⢀⣾⠟⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣴⣿⡏⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⢳⣿⢀⠠⠾⢻⣿⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⣿⡿⣱⣿⡿⠃⠀⠀⣼⣿⣼⠠⠄⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣽⣿⣿⣿⣿⣆⣠⣾⣿⢿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣿⡿⣿⣿⣿⣿⣿⢣⣼⣿⡎⢷⣇⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⢏⣾⡟⣸⣿⣿⣿⣿⡇⡾⣿⣿⢻⡌⠻⣆⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⢠⠁⣿⠟⣿⡿⣰⣿⣿⣿⣿⣿⡘⣇⢸⣿⣿⣿⠀⠙⣷⣄⠠⡱⣄
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣾⣿⡇⣿⢸⣿⣿⣿⡿⠧⠀⣼⡈⣿⣿⡇⢢⠘⣿⣧⠙⣿⣦
⠀⠀⠀⠀⠀⠀⢸⡀⣼⢿⣿⣿⠀⣿⣼⠳⠏⢠⣷⢀⣼⣿⠃⣸⢹⡇⣸⡄⠸⣿⡇⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠘⣧⢹⡜⣿⣿⡄⢹⣿⠀⠀⢸⣾⡈⠻⣿⢀⡟⣹⠇⣿⣥⠀⣿⣷⠀⢻⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠹⣿⣿⣿⣦⡿⣷⣄⡈⠻⠏⠀⡹⣾⣱⠏⣼⣿⣧⠀⣿⣿⠀⢸⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣻⣯⣛⣿⣿⡝⢷⣂⠠⣼⣷⣿⢏⠼⠁⢸⡇⢰⣿⡟⠀⣸⢄
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠈⠋⣉⣿⣿⣿⣷⡙⠿⠿⠯⠁⠀⢀⠴⠋⣴⣿⠟⠁⣰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⣷⣦⣤⣤⣤⣷⣼⣿⣿⠗⢀⡴⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⣿⣿⣿⣿⣿⣿⣿⠿⢛⣡⠴⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣧⣴⣿⡭⠤⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠿⠟⢻⠟⢿⠿⢻⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣵⣀⡀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠉⢦⠈⢷⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⡴⠚⠳⣬⡽⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣫⠴⠛⢆⠈⢳⡀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⣾⢳⡶⠦⣌⠙⠢⣅⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠚⠁⢀⠀⠀⠳⣄⣿⣾⠏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡼⢣⡏⣴⡀⠀⠉⠒⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠀⢀⣴⣿⣷⣤⣤⣿⡟⢹⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣞⣧⡟⠀⢸⣿⣄⣀⣀⡀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⣼⣿⣿⣏⠟⣽⣼⡿⠏⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠛⣿⣧⣸⡋⠙⣿⣿⣧⠆⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢽⣿⣿⡸⠛⠋⢻⣿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠙⠿⣿⣄⣠⡟⠉⠉⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠿⣿⡦⠀⠀⠘⡇⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢛⡛⡀⠀⠀⠀⠀⢀⣶⡟⠁⠀⠀⠀⠀⠀⠀⢈⠳⠀⠀⠀⠀⠀⠹⡄⢰⣶⣤⡀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢤⣄⠀⣀⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠀⠀⠀⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣄⣽⣿⠿⠟⢻⠇⠀⠀⠀⠀⠀⠀⣠⠄⣰⡈⠻⣄⠀⠀⠀⠀⠀⠹⡟⣿⡷⢤⡤⠰⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⢡⣿⡿⣿⠶⠄⢀⡿⢄⠀⠀⠀⠀⠀⢼⠃⠀⠃⠳⣤⣿⣄⠀⠀⠀⠀⣠⣿⡾⣿⡂⠀⠀⠀⠀⠙⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⠏⠀⠈⠏⠀⠀⠀⠀⣼⡗⠈⡁⠀⡆⡔⠀⣸⠏⠀⠀⠀⠈⠳⣄⣹⣤⡆⠀⠁⠘⣧⢙⡁⠀⠀⠀⠀⠀⠈⠿⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠑⢶⣶⡄⠀⠀⠀⠀⣰⠟⠁⠘⠃⢰⠯⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢇⣀⣀⣘⢿⣦⢉⣀⡀⠀⠀⠤⢀⣱⠏⠳⣄
⠀⠀⠀⠀⠀⠀⣰⠟⠹⣶⣤⣀⡉⠉⠉⠉⣁⣠⣤⡶⠰⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣦⣁⣀⣀⡀⣤⣄⣦⠝⠁⠀⠀⠙⢧⡀
⠀⠀⠀⠀⣠⠞⠁⠠⣷⠀⠉⠉⠛⠻⠿⠿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠺⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠌⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠐⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣥⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢇⣤⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⢠⠟⠙⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⡀⢠⡆⠀⠀⠀⠈⣧⠄⠐⠸⠀⡤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠀⡰⠉⠷⠀⠐⠑⠀⠃⠀⣤⡠⠞⡷⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠸⢤⡇⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠐⡁⠘⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠈⠁⡐⠂⡰⠁⠀⠀⠀⠤⠂⡳⠀⠇⠆⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣦⡱⡄⠲⠇⠘⠀⠀⠀⠀⠀⠀⢀⠀⠞⠀⠔⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠌⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠊⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠈⡤⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢥⡀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠮⠴⠖⠖⢤⣼⢶⡿⣷⣾⣷⠋⢻⣿⣷⡖⠦⢤⡄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣤⣤⣴⠞⠋⠀⣸⠁⢀⣿⢻⣆⠀⠙⢯⣟⠉⣷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣁⣀⣠⣶⡇⠀⠸⣿⠄⣻⡆⠀⠈⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠈⣿⠷⠏⠛⠉⠘⠶⠶⠞

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠉⠉⠉⠙⠛⠒⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠴⣶⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠄⠀⠀⠎⠀⠀⠀⢊⠔⠁⢀⡀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠂⣠⣾⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡧⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⣃⡤⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠃⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡆⠀⠀⠘⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠀⠂⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠿⠀⠀⢈⣛⠀⠀⢶⡶⣤⣉⠳⢦⣀⠀⠀⠀⠀⠀⠀⣠⠖⣁⣤⢦⡶⠀⠠⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠁⡸⡇⠀⠀⠙⠦⣍⡙⠲⠉⠃⠀⠀⠀⠀⠾⣻⢚⣫⡴⠟⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠐⢀⡇⠀⠘⡰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢨⠓⠢⢃⠹⡙⠳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠀⠀⠀⣠⢎⠟⠀⣰⠂⢁⠀⠀⠉⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠲⣄⠀⠠⠴⠶⠚⠶⠖⠒⢶⣤⠀⣠⣾⠁⠄⠀⢠⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⠒⠲⠒⠒⠊⣡⣾⣿⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢻⣷⣦⣤⣤⣴⣾⡿⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⠸⣿⣷⡞⠋⣽⣿⠃⠀⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⣘⣿⣿⡀⢻⣿⣿⣾⣿⡟⠀⢰⣿⣿⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣦⣄⡈⠀⠐⠠⢄⣀
⠀⠀⢀⣀⣤⠶⢚⣋⡁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣀⡀
⠖⠛⠉⢁⣤⣾⣿⣿⣿⣆⠀⠀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡄⢀⠀⣴⠤⠤⠔⠐⠒⠒⠀⠈⠉
⣶⣾⣿⣿⣿⣿⣷⣶⣶⣿⡆⠀⠀⣶⣦⣤⣤⣤⣀⣈⠉⠉⠻⣿⣿⣥⣶⣤⣤⣴⣿⣿⣿⣿⡇⠀⢠⣿⣷⣶⣶⣤⣤⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠛⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢻
⠀⣠⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠁⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣰⡆⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣤⣿⣿⣤⣶⣶⣶⣯⣴⣷⣭⣿⡆⠀⠛⢲⡀⢛⣒⣶
⠀⠀⢀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⡏⢿⣿⣿⠀⢀⢀⡐⢾⢈⣦⣠⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣰⣶⠟⣤⢿⡏⢈⡷
⠀⢀⣾⣿⣿⣧⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠋⠀⢀⡌⣦⣠⢷⣏⣿⣯⣯⣧⡐⠀⠀⠉⢈⣍⣉⣩⣍⣭⣥⣤⡄⠀⣜⣿⣶⣼⠟⢹⣏⣸⡅
⠀⣼⣿⠏⠀⢿⣿⣇⠀⠀⠸⣿⣿⢿⢿⣿⣿⠃⠀⠀⢀⣜⣾⣷⣿⣿⣿⣛⣿⣿⣼⣿⣿⣷⣦⡰⣼⣿⣍⠓⢺⣟⡋⠉⠉⠀⠘⠿⠞⢿⣶⣿⠿⠛⠁
⠀⠻⢧⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⣁⣸⣿⣿⡟⠛⠈⠑⠀⠀⠀⠀⡀⠀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡀⣴⢠⡀⠀⠀⠀⠀⠀⠀⠆⡐⠂⡆⠐⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⣸⢼⣠⢧⣟⣳⢼⡰⣅⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠉⠁⡄⣑⣘⣄⠀⣀⣙⣦⡴⣃⠀⠀⠀⢠⡀
⠀⠀⠀⢸⡆⠀⠀⣯⣻⣾⣾⣿⣿⣿⣾⣷⣿⣷⣿⡄⠀⠀⠀⠀⠀⢀⣼⣧⣶⡤⣄⠀⠀⠀⠀⢀⠙⠐⠀⠑⠿⠟⠀⢠⣞⣿⡻⣞⡽⠁⠀⢠⣤⣽⠆
⠀⣰⢠⡿⢁⡀⠀⠈⠛⠛⢉⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⢠⣼⣽⣿⣿⣿⣿⣿⣤⠀⠀⣀⡴⠛⢦⡞⠀⠀⠀⠀⠀⣹⣟⣿⣏⠀⠀⢰⣛⣦⣹⣦
⠀⢿⡈⢷⣼⣄⠀⠀⠀⣠⢿⣆⣤⠀⠀⠀⠀⣦⣷⡄⢣⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣞⠀⡄⡟⢷⡜⣮⣷⣴⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⢈⣽⣿⠁
⠀⢸⡿⢸⣿⣿⠇⠀⣰⣯⢾⣿⣏⣦⠀⠀⠲⣬⡟⣷⣦⡙⣷⠀⠁⢸⣿⣿⣿⣿⡟⠃⠸⣧⣿⣿⣵⣿⣟⣿⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⣿⡟⠋
⠀⣾⣷⣾⣿⣿⠀⠀⣿⡇⠀⠋⢹⡿⠀⠈⣧⣿⣷⣿⣼⣷⣡⣧⠀⠻⣿⡟⢽⣿⡅⠀⠀⣽⣯⣿⣿⣿⣿⣻⡇⠀⠀⣀⣤⣴⣆⡀⠀⠀⠀⠉⢻⣿⣦
⠀⠈⠛⠛⠛⠋⠀⠀⠈⠛⠀⠐⠋⠁⠀⠀⠙⠛⠉⠋⠋⠙⠛⠋⠀⠀⠘⠀⠘⠋⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠃⠀⠾⠿⠿⠿⠿⠟⠛⠗⠀⠚⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠣⡀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠓⠀⠸⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠈⠳⠦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⢿⣯⣶⢀⡀⠰⠶⣾⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣝⢷⣦⡄⠙⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⣀⣤⠶⠾⠛⠛⠻⠿⣿⣿⣦⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡄⠀⠀⠀⠀⠠⠤⠤⠊⠀⢀⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡂⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠃⠀⠀⡐⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⢀⣾⣿⡄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣰⣿⣿⣿⣿⣄⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⢻⣿⣿⣿⣿⣷⡀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⢻⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣷⡄⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠈⢿⣿⣿⣿⣿⣿⡄⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠈⢿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⢻⣄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⠀⠈⢿⣿⣿⣿⣿⣻⡄⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⣿⣿⣆⠀⢿⣆⠀⠀⠀⠀⡀⠈⢿⣿⣿⣿⡄⠀⠈⢻⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠘⣿⣧⠀⠀⡀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠘⣿⣷⣄⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⢻⣿⣿⣿⢸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⠘⡿⠿⠦⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠙⠿⠘⡄⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠴⣀⡤⣔⣤⣶⣮⣶⣾⣷⣾⣿⣾⣿⣷⣿⡦⠀⠀⠀⢡⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠚⠩⠞⡻⠿⣻⠿⢿⠿⠟⠻⠛⠋⠙⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣤⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⢰⣷⣿⠇⠀⢻⣷⡆⠀⠀⢰⣷⣿⠿⣿⣿⣆⡄⠀⠀⠀⠀⢻⣿⣿⣿⣶⣇⠀⠀⠀⠀⢸⣿⣿⠻⣿⣶⠀⠀⠀⠀⡄⣿⣿⠏⢿⣿⡆
⠀⠀⠸⣿⠁⣰⣦⠈⣿⡇⠀⠀⢸⣿⠿⠀⠘⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⣶⡿⠁⡀⠛⣿⠀⠀⠀⠀⣿⡿⠁⠀⢸⢿⡿
⠀⠀⠀⠙⠦⡙⢛⠴⠋⠀⠀⠀⠀⠻⠄⠀⠀⠠⠟⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠹⠄⢾⡿⠀⠋⠀⠀⠀⠀⠙⠧⠀⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⣆⢸⣿⡄⡄⠀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⢠⡄⣾⣿⢿⣿⣀⡄⠀⠀⠀⠀⣶⣻⣿⣷⢀⡄
⠀⠀⠀⢸⣿⣿⣿⣇⣷⠀⠀⠀⢈⣿⣿⠏⠻⣿⣿⣶⠀⠀⠀⣼⣿⣿⠋⢻⣿⣧⠀⠀⠀⣿⣿⣿⠟⠈⣿⣿⣿⠀⠀⢰⣦⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡇⢀⣦⠀⣿⠇⠀⠀⠀⢻⣿⠁⠀⣼⢿⡟⠀⠀⠀⠸⣿⠉⢀⣆⠉⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠈⠁⠘⠟⠁⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠛⠟⠀⠉⠀⠀⠀⠀⠈⠙⠚⠛⠛⠋

⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⢀⢀⣼⣿⣷⡄⠀⠀⠀⠀⡀⠈⣿⣧⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠀⡀
⠀⠀⢀⣿⣿⣿⢿⣿⣿⡄⠀⠀⢀⣿⣄⣽⣿⡟⢀⡀⠀⠀⠀⡀⢻⣿⠛⢿⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⣿⣿⣿⣾⣿
⠀⠀⠸⣿⡟⠉⠀⠹⣿⡇⠀⠀⢸⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⣿⣾⠋⢠⡀⢻⣿⠀⠀⠀⢠⣸⣿⡏⠿⣷⣾⡆⠀⠀⢸⣿⣿⣿⠛⢿⣿⣿
⠀⠀⠀⠻⣧⡀⠀⣰⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⢿⣄⣿⣧⡼⠃⠀⠀⠀⠀⠻⡏⠁⠐⢻⡟⠀⠀⠀⠈⢿⡿⠷⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢦⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⡯⠙⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣸⣿⣿⣿⣏⣤⣿⣆⠀⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣏⢷⡿⠏⠲⣤⠙⣆⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢺⠿⠛⣿⣿⣿⣿⣿⡷⠀⠀⠀⠈⠃⢹⠂⠄⢠⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⣀⣴⠶⠋⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⢿⢸⠀⣼⣿⡟⠁⠙⠿⢆⣄
⠀⠀⠀⠀⠀⢰⣿⣿⠛⢿⣿⠻⣿⠋⠀⠀⠀⠀⠠⠿⠿⢿⣟⣛⣂⣠⣤⡤⠤⠴⣾⢸⡆⢻⣿⡇⠘⠟⣿⡟⠋
⠀⠀⠀⡄⠀⢸⣿⡇⢰⣂⢥⣼⠷⠶⠒⠒⠚⢛⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⣧⣷⡜⣿⣿⣦⣴⣿⠇
⠀⠀⠀⢣⢠⠸⣿⣿⣄⣴⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠣⣧⣙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠐⢿⣿⣿⡿⣟⠛⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⠘⠁⣿⠇⢻⡄⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣸⡏⠀⠀⣇⡰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢹⣷⠀⠀⠈⠃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣇⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣾⣿⣇⠀⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠁⠀⠓⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠉⠉⠀⠐⠂⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠤⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⢀⣧⡄⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⢶⡀⠛⠃⠀⠀⠀⠘⠻⠋⠲⠂⠄⠀⡀⠀⠀⠠⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠀⠀⠁⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠣⠀⠀⠀⠂⠰⠀⠀⠀⢀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣠⠀⠐⠀⠀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠁⢤⠈⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠤⠀⠀⠀⠀⠀⠀⡈⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⡀⠀⠀⠀⢉⡆⠀⢀⠀⠈⠣⠀⠀⠀⠀⠀⠈⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢠⠾⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠂⠀⠀⢸⡇⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡠⠀⠇⠈⡀⠀⠀⠀⠀⠀⠁⠺⠇⠀⠀⠀⠈⢁⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠰⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠄⠀⠀⠀⠤⠀⠀⣤⠀⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠵⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠄⡀⠀⠀⢀⠄⠀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢄⡀⠀⠀⠀⢀⡠⢞⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠀⠉⠁⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣹⣟⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠈⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⢀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠰⠳⣄⡎⠀⠀⠁⠠⠀⡜⢆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠈⠆⠀⠀⢀⠀⠰⠁⢸⠈⠰⠃⢰⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡏⠲⢦⠀⠀⠀⠀⠀⠈⢄⠁⠀⢸⠀⠀⠀⡌⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⡘⠘⡐⢚⡇⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⡀⠀⠳⠉⠀⠌⡰⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣄⡀⠀⠀⠀⠀⠂⠄⠐⠂⠀⠀⠁⠄⠂⠀⠀⠤⠊⠉⠈
⠀⠀⠀⠀⠀⣼⠹⣭⢍⣠⢴⠚⢠⣀⣤⡤⡖⠢⣤⢼⣐⠒⣦⠀⢲⢢⡀⠘⠛⣻⣻⡄⢠
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠻⠼⠛⠛⠊⠳⣾⡴⠃⠰⣌⣠⡼⠷⣤⣸⡖⠲⠮⠯⠟⠛⠛⠃

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠆
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⢀⣠⣿⣿⡿⠏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⡀⢸⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠈⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⣿⣷⣬⣉⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣩⣭⣶⣿⣿⠁⣑⣬⣉⣓⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣾⣿⣿⡷⣿⡛⠿⣿⢸⠿⠹⠋⢟⣻⣿⣶⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣿⡏⠀⢫⠌⠀⠀⢰⣿⡿⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣔⠟⠃⢀⣴⣿⢹⡇⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣷⢾⠻⢿⡟⣸⠁⢁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣽⣾⣿⣿⣿⠀⣠⣴⣧⢣⣾⣯⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡈⠁⢠⣿⡷⠋⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⠁⠙⠿⣷⣦⠿⠋⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣦⡀⠀⣀⣁⣀⣀⠀⠀⢀⡀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⣿⠿⠛⠛⠻⢿⣿⣿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣶⣶⠶⠦⡄⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⣠⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠉⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⢿⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⢦⣌⢷⣄⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⣆⠙⠷⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⡓⠦⡀⠈⢷⡀⠀⠀⠀⣿⠀⠀⠘⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡄⠀⠻⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡆⠀⣠⠟⠀⠀⠀⠹⣄⡀⢻⠀⠸⣇⠀⠀⠀⠀⠀⢰⡇⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⠟⢰⡏⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠘⢷⣄⠀⠀⠀⠀⠻⣄⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⡉⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠳⢦⣄⠀⠀⠈⠳⡄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡀⠀⠀⠀⠈⠉⢻⠓⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠃⠀⠀⠀⠀⢠⣸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢠⡞⠀⠀⠀⢀⣤⠟⣿⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠀⠀⢹⡆⢀⡤⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢁⡖⠉⠀⣀⡴⠞⠋⠀⣰⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠘⡇⢸⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠘⢧⣠⠞⠁⠀⠀⠀⠘⠁⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⠇⢸⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⢠⢀⠞⠁⠀⣰⠋⣠⡾⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠃⢀⣠⠄⣀⣴⠆⢀⠀⠀⠀⠞⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠰⣶⣤⣛⠀⠈⢁⣾⣿⣷⣿⣿⠃⠀⠀⣀⠀⠖⢀⣀⡀⠀⠀⠀⠀⠀⣰⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣍⣻⣦⣄⡀⠀⣀⠐⣀⣈⠛⠻⣟⣻⣿⣿⡿⠟⣋⠀⠀⣠⣤⣤⣤⡶⠿⠛⠁⠀⠀⠀⣀⡼⠯⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠴⠶⠛⠻⢶⣤⣄⣈⣁⣰⣿⡿⣯⣥⣤⣀⡛⣿⣿⣶⣬⣍⠀⠻⠷⠶⢶⣆⣤⣴⣾⣿⣶⣶⣶⠤⠴⠶⠖⣶
⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣤⡤⠤⠶⠶⠚⠋⠉⠉⠉⠉⠁⣀⡤⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⠲⠶⣿⣿⣭⢤⣭⣍⣛⡛⠛⠶⠦⢤⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠋⢑⣻⡿⠟⠋⢁⣀⡈⠉⠉⠉⠋⠉⠛⠒⠾⠭⣅⣀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⣯⣉⣀⠤⠖⠚⠉⠉⠀⠠⠖⠛⢉⣀⡙⠚⠙⠛⠶⠶⢦⣄⣠⣤⡴⠶⠯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠉⠉⠉⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠒⢤⡀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⣿⠀⠈⣷⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡄⠘⠿⠋⠀⢠⡿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢦⣄⣠⣴⠟⠁⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠋⢿⡄⠈⠻⣿⣦⡀⠀⠀⢀⣠⣤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣿⣿⣿⠿⠛⠉⢿⣿⠀⠈⠛⠀⠀⠀⠙⢿⣶⣜⠉⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣆⠀⠀⢠⠀⢀⣴⣶⣿⡟⠉⠛⠳⡄⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⢱⣾⣿⣿⣿⣿⠀⢀⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢹⣿⣿⣿⠈⠉⠀⠀⠁⢀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠉⣯⣈⡅⡀⠀⠀⠠⠆⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠉⣀⣤⠀⠀⠉⢤⣷⣶⡶⠶⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠸⣿⠀⠀⢸⡆⢹⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠀⠀⠀⠃⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢀⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⠔⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⣷⣦⣤⠴⠖⠁⠀⠀⠀⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⣀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣿⠟⠋⠉⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠐⠢⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠂⠀⠀⠀⠀⢈⣷⣄⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠀⢀⣠⣴⡿⠁⠀⠀⡠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⣠⣿⣷⣦⣤⣶⣶⣿⣿⣿⣿⡇⠀⠀⢰⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⠀⠀⠀⢀⣼⣿⣿⠃⣀⣠⣴⡿⠿⠿⠟⠛⠛⠋⠉⠀⢸⣿⡇⠀⠀⠉⠆
⣠⣴⣦⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠊⠀⢠⣿⣾⣿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠸
⣿⣿⣿⠀⣤⣀⣀⠀⠈⠑⣦⣤⡤⢾⡇⢀⡅⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠇
⢹⣿⣿⣷⠟⠛⠿⣷⣤⣤⡇⠀⠀⠈⢻⣏⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⠀⠺⠇
⢻⣿⣿⡇⠀⠀⠀⠀⠙⢿⡇⣀⠀⠀⠀⠙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣠⡄
⠘⠿⢿⣷⠄⠀⠀⠀⠀⠀⠻⠼⠗⠢⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣄⣀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠛⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⢀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⣿⠁⠀⠀⠀⠀⣠⠎⠑⢦⡀⠀⠀⠀⠘⣿⡀
⠀⠀⢰⣿⡆⠀⡄⠐⠈⠁⠀⠀⠀⠀⠉⠙⡆⢀⠟⣷⡀
⠀⠀⢸⡇⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡩⠀⠘⢷⡀
⠀⠀⢸⡇⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⢻⣆
⠀⠀⢸⣷⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⣿⡀⠀⠈⠣⣀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⣀
⠀⠀⠀⠸⣧⠀⠀⠀⠈⣷⠂⠰⡖⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⣦⣤⣄⣀
⠀⠀⠀⠀⢻⣦⡴⠶⢾⣏⣀⢀⣹⡃⠈⣥⡖⠂⠠⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⣄
⠀⠀⠀⢀⣿⠏⠀⠀⠀⠈⠉⠉⠁⠈⠀⠀⡿⡀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⣾⠇⢸⠀⣤⢴⡿⢟⡻⢿⠶⣤⡀⡇⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⢄⣀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢰⡿⠀⢸⠀⢿⣎⠀⠈⠁⠀⢳⡼⠁⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⣧⡀
⠀⠀⣼⠇⠀⢸⠀⠘⣿⡠⡀⣠⢜⣾⠃⢠⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠘⣷
⠀⢀⣿⠀⠀⣿⠀⠀⠈⠛⠿⠿⠛⠁⠀⠸⢧⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣦⣦⡶⠟⠋⠀⠀⠀⠀⢸
⠀⢸⠇⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇
⠀⣿⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⣿⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⣿⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⣿⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⢀⣿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠉
⢸⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⣼⡇⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⣿⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡾⠋
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠉⠁
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡟⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠉⠙⠛⠛⢶⡶⠒⠒⢲⣶⣶⡖⠒⠒⣶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣄⣀⣀⣹⣧
⠀⠀⠀⠀⠀⢈⣿⠀⠀⢸⡇⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⡇⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠃⢸⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣿⡆⠀⣿⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠘⣿⠀⢸⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠀⠀⣿⡀⢸⡇
⠀⠀⠀⢀⣤⡶⠟⢁⡜⢻⡆⣰⡟⢧⡈⠻⢶⣤⡀
⠀⣠⣾⡟⢁⡀⠔⣉⣤⡾⠃⠘⢷⣤⣉⠢⢀⡈⠻⣷⣄
⠘⢿⣤⣤⣶⠾⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠷⣶⣤⣤⡿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠻⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢣⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣶⣶⣦⣤⣤⣄⡠⢄⡬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⡀⠀⠀⢇
⠀⢠⣦⢶⠒⣀⣤⡀⢐⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡯⣶⡵⣂⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣶⣬⣓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⠀⠀⠀⠀⢀⣤⣀⡀⠄
⠀⠀⠀⠀⠀⡐⡰⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣿⣿⠿⣻⠂
⠀⠀⠀⢀⢠⣷⣻⣿⡿⢿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣽⢷⣶⡔
⠀⠀⠀⠶⠿⠿⠛⣧⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⠻⣿⣿⣿⣿⣯⣟⣿⡿⠻⠛⠛⢉⣥⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⡹⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠙⢻⣿⣿⡅⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿⣿⣿⡿⣿⠏⠀⠀⠀⠀⣽⣿⡷⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⡯⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠭⣽⣿⣿⣿⣿⣟⠭⠊⠁⠀⠀⠀⠀⠀⣽⣿⡗⠀⠀⠀⠀⠀⠀⠀⠉⠚⠩⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⣞⡽⣻⠽⡫⠅⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠩⠛⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣴⣶⣶⣿⣿⣶⠄⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡑⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣻⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡝⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡷⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠵⠫⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣟⣿⣿⣟⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠿⠿⠛⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢿⡿⠿⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠀⠰⠶⠶⠰⠿⠁⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠏⢹⡀⠀⠀⠀⠀⢀⣀⢀⣥⣞⠉⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣾⣷⣄⠀⠀⠂⠟⢫⣿⣿⣿⣿⣦⡙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠠⢠⢄⢤⣿⡿⢋⣠⣿⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⠋⢀⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣽⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⢉⠸⣧⢻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣸⢿⣿⣿⣿⣽⣿⣿⣿⠟⠀⠀⠀⠀⣾⡄⠙⠒⠈⠀⠆⠀⡀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⣴⣾⣿⢻⣿⠋⠉⠀⠀⠀⠀⢀⡰⢻⣿⡄⡀⠀⠀⠀⢠⡐
⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠸⠏⣼⣿⣿⡟⣼⡇⠀⣠⡤⣤⣶⣾⠋⠀⠀⠙⢯⣷⠀⠀⠀⠘⢿⣾
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡠⠐⠀⠀⠈⠛⢿⠿⣿⣿⣷⠿⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠙⢧⠠⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠊⠀⠀⠀⠀⠀⣴⠋⣼⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⡤⠀⠀⢀⣲⠁⣠⡏⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠃⢠⣾⣿⠃⣰⡟⠀⠀⠀⠒⠠⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣭⣢⣼⣛⣀⡤⢤⢄⣀⣠⣄⣀⣰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣯⣴⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠉⣦⣅⢈⠿⢋⢘⣿⣿⣿⣿⣿⣟⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡛⣴⣼⣿⣿⣮⡇⣼⣿⣿⣿⣿⣿⡝⠿⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠏⠻⣮⣻⣿⣿⣿⠿⠻⠿⠋⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠙⠋⠁⠤⣽⣶⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠐⠲⣾⡏⠀⠘⢦⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠞⡀⠖⠀⡠⣀⣾⠿⠇⣤⣤⣤⡈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠁⠊⡀⠐⠊⣉⣼⠋⠀⠔⠉⠀⠸⣧⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠚⠉⠀⠒⣉⣤⣶⣾⣿⢧⣀⠀⠀⢀⣠⠄⢻⣆⢀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⡥⠔⠚⠋⠁⠀⠐⢊⣩⠞⢉⣾⣿⠷⠏⠁⠀⠘⢿⣿⠾⣿⣧⠂⠸⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠋⠉⣀⠀⠀⣀⣀⣥⡴⠶⢋⣡⢾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡻⢼⡄⣧
⠀⠀⠀⠠⠔⢋⣁⡤⠦⢶⣿⣿⠿⣿⠿⣿⣿⣶⣶⣿⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡈⢷⣿
⠔⢊⠖⢁⠔⠋⡄⠀⣀⠶⠋⠀⠀⠡⠚⠵⣣⣿⡟⣿⢟⣿⢻⣿⣄⠀⠀⠐⠒⠒⠲⠀⢠⣿⣿⣿⣿⡄⠻⡄
⢴⠃⢀⠀⠈⠀⠀⢚⡡⠄⠀⠀⢉⣀⠴⠚⢁⡾⢡⣟⣼⠃⢸⡟⠈⠳⣄⡀⠀⠀⠁⣴⣿⣿⣿⡿⡟⣧⠀⢹⡀
⣎⢰⡯⠀⣠⣦⣰⣶⠶⣶⡿⠉⠉⠁⡀⣴⣟⣡⠾⠛⢁⣴⣿⣿⣿⣦⠈⠙⠒⠒⠈⠹⣿⡿⣸⣷⠛⡹⡀⢸⡇
⣿⣼⠃⢰⣿⡿⣹⣿⣼⡟⢀⣀⣤⣷⠾⠟⠛⠷⢛⠻⣿⠋⠻⠟⢿⣿⠀⠀⠀⡅⢠⡔⣿⣿⣿⣇⡆⣧⣟⡸⠃
⠁⠙⣧⣈⣿⠁⢸⣿⣿⡟⠛⢉⣟⣤⠶⠤⡤⠀⣈⠑⢦⡑⢦⡄⠀⠀⠀⠀⢰⣿⣬⡆⠈⠹⢿⣿⣿⣼⡟⠁
⠀⠀⠹⣟⣿⣇⢠⣿⣿⣴⣾⢿⣿⠀⠀⠀⠀⠀⠀⠙⠲⢶⣄⣻⡄⠀⠀⠙⠁⠡⡉⠛⠄⠘⠸⠧⡈⢩⠀⠑⣄
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⣸⠇⠀⠀⠀⠀⠀⢤⣀⣑⣠⣬⣥⠷⠠⠄⠀⠤⠀⠈⠉⠓⢄⠀⠀⠈⠿⣄⠄⢈⣹
⣠⠐⣤⣤⣾⣱⣿⣿⣿⣿⣃⢸⣦⡀⠀⠀⠀⠀⠈⣉⣩⡭⠤⠤⠘⠢⢤⣀⠐⠀⠀⠀⠀⠀⠁⠘⠁⠀⠉⢻⣇⠄⢡
⢻⠀⠀⠙⠉⣉⢹⠇⢸⣿⢿⡄⠿⠟⠁⣀⡴⠞⢛⠍⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⠉⠻⣄⠀⡆
⢇⠻⣶⣾⣟⠇⢁⣠⣾⡏⢲⣀⣠⣶⣿⠁⠀⠀⣿⣴⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠂⢄⠃⢀⠃⠀⠀⠈⢿⡇
⠀⠐⠠⢉⣙⣛⣻⣿⡿⠀⣼⠛⣱⡿⠃⠀⠀⠀⣿⣿⣿⡁⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠁⡟⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠉⠉⠉⢙⠃⢰⠁⢀⣿⠁⠀⠀⠀⢸⣿⣿⣿⣦⠸⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠃⠀⣿⣿⠀⠀⠀⠀⣾⢧⠙⣿⣿⣦⠻⣿⣿⡿⠛⣧⣀⣀⣀⢰⠌⡇⠀⡷⣤⣤⣟⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠁⢸⠀⠸⣿⠸⠀⠀⠀⣰⠇⠈⢣⢻⣟⢿⣷⣌⠉⠉⠛⠏⠉⠉⠉⠀⠘⣤⡸⠀⠈⠉⠛⣧⢸
⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⠀⠛⠄⠀⠀⣰⠏⠀⠀⠀⢆⢻⣷⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⡟⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠀⠛⠆⡀⢠⡟⠀⠀⠀⠀⠈⢆⢻⣿⣷⣤⣀⠀⡘⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⢈⢹⡇⠀⠀⠀⠀⠀⠈⣆⠙⢷⣤⠙⠣⠳⢰⡄⠀⠀⠀⠀⠇⠀⠀⢀⣿⡇⢸⣄
⠀⠀⠀⠀⠀⠀⢰⠀⢰⣿⠀⠀⠀⠀⡎⡇⠀⠀⠀⠀⠀⠀⠘⡆⠳⣽⡃⠀⠀⠜⠀⠀⠀⠀⢸⠀⠀⢀⡿⣿⡗⠹⡏⢦
⠀⠀⠀⠀⠀⠀⠈⢆⣿⡿⠉⠀⠀⢀⠇⢁⠀⠀⠀⠀⠀⠀⣰⢩⣿⣾⡋⠀⠀⠀⠂⠀⠀⠀⠸⠀⠀⢸⡏⠙⣷⠀⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠈⢀⣸⠆⠀⠀⠀⢀⡰⠁⠸⡛⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⣦⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣸⣤⣿⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⠎⣱⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⡦⠋⣹⣿⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠜⡹⣿⣿⠀⠀⠀⠀⢠⡇⠀⠀⠀⡼⢰⣿⣿⣿⠋⡟⠉⠶⠶⣤⣀⣀⠀⠀⠂⠉⠒⡄⣀⣤⠚⠉⣿⣇⠀⣷
⠀⠀⠀⠀⢠⠊⠠⠁⣼⣏⠀⠀⠀⠀⢸⠃⠀⠀⢨⡗⣽⣿⣿⣿⢀⠁⠀⠀⠀⠇⠉⠈⠳⠁⠀⠀⠀⢘⠀⣿⡆⠀⣸⣿⠀⢻
⠀⠀⠀⠀⠁⢠⠁⡀⢻⣿⡀⠀⠀⠀⣸⠀⠀⠀⣀⣧⣿⡿⢿⣿⣾⣷⣶⣦⣤⠀⠄⠀⡜⠀⠀⠀⠀⢸⠳⣿⣯⣷⣿⠀⠀⢸⡆
⠀⠀⠰⠆⢠⠃⡔⠀⠀⢿⡇⠀⠀⠀⣿⠀⠀⢀⣽⡟⠉⠻⠶⠄⠀⠀⠀⡈⠉⠙⠢⢄⡑⣀⠀⢀⣴⣿⠿⠟⢻⠀⣿⡄⠀⠘⡇
⠀⠀⠀⠰⠃⠜⠀⠀⠀⢸⣇⠀⠀⠀⡿⠀⢠⣪⣥⡀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⠈⠙⠻⠞⠋⠁⠀⠀⢀⡇⣼⣧⠀⠀⣿
⠀⠀⠀⣠⠈⠀⠀⠀⠀⢸⠿⠒⠒⠲⣦⠀⣠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⣿⠀⠀⢻
⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢤⣿⣿⣟⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⣿⡗⠂⢹⡄
⠀⠀⣇⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⠀⢀⡀⠛⢮⡛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⢠⣆⣤⡶⡶⢊⡀⠀⠀⡆⣿⡃⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⢠⣤⣾⠛⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢛⣷⣤⡄
⠀⠀⠀⠀⠀⢸⡇⢸⠀⣿⢸⡇⠀⠀⢠⣤⣤⣤⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠻⣮⠙⠷⣤⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⠀⠀⢸⡇⣿⢸⡇⢸⡇
⠀⠀⠀⠀⢸⣿⡇⢸⠀⣿⢸⣷⣶⣶⣾⣇⡀⢀⣼⣷⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣿⣶⣶⣶⣶⣾⣧⡀⢀⣸⣷⣶⣶⣾⡇⣿⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⢹⡇⢸⠀⣿⢸⡇⠀⠀⠀⠉⢻⣏⠙⢧⡀⠀⠀⠀⢹⣣⡟⠳⠶⣤⣤⣤⣤⣤⠀⣿⠀⠀⠀⢠⡾⠉⣹⡟⠁⠀⠀⠀⢸⡇⣿⢸⡇⢸⡏
⠀⠀⠀⠀⠀⠸⠷⣾⣀⣿⢸⡇⠀⠀⠀⠀⠀⢹⣄⠈⢻⣄⠀⠀⢹⣿⡃⠲⠶⠀⠀⠾⠆⢸⡆⣿⠀⠀⣰⠟⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⣿⣨⡷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠾⠇⠀⠀⠀⠀⠀⠀⠻⣆⠀⠹⣦⣄⠘⢿⣇⠀⢀⣀⣀⠀⢀⣾⣿⠃⣠⡼⠋⠀⣰⠏⠀⠀⠀⠀⠀⠀⠸⠷⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⠳⣌⠙⢦⣀⣉⣉⣠⠾⢋⣵⠞⠉⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠘⢷⣴⣟⠉⠉⣿⣤⡾⠁⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣠⡟⠁⠙⠛⠛⠋⠈⢷⣄⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⣤⡄⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢹⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⡇⢹⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⣾⠀⠈⣷⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢰⡏⠀⠀⢻⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣼⠁⠀⠀⠘⣧⣤⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁

⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⡟⣉⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣬⣴⣢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣴⣿⣿⣿⣿⣿⣷⣦⣍⠒⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣴⠟⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣦⣄⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠚⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡉⠉⠛⠛⠶⣄⡀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣴⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡙⠿⣿⣿⣿⣿⢿⣷⣦⣤⣀⠀⠙⠢⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⡾⠿⠿⠛⠉⣁⣴⣿⣿⠟⣽⡟⠈⠻⣆⠈⠙⠛⠿⠷⣦⣄⣀⣉⣁⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠐⢉⣀⣠⣤⣶⣶⣿⣿⠿⣛⣥⣾⡏⠀⠀⢀⣩⣿⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠉⠉⠢⣄⠀⢃
⠀⠀⠀⠀⠀⣠⠃⠀⢠⣶⣿⠿⣟⣛⣩⣭⣭⣶⡾⢛⣿⣿⣿⣿⠀⣿⣿⣿⠛⣿⣿⡿⢻⠿⣿⣿⣿⣿⣦⣄⠀⠀⠈⢣⠘⡆
⠀⠀⠀⠀⢠⡇⠀⡴⢛⣽⣾⣿⣿⣿⣿⠟⣸⣿⡅⠘⠛⠹⣿⣿⠀⣿⠏⠛⠀⡸⠃⢰⠛⢰⣦⣙⠻⣿⣿⣿⣷⡀⠀⠘⡄⢸
⠀⠀⠀⠀⡜⠀⠀⣴⣿⣿⢟⣿⣿⣿⣷⣌⣹⣿⣿⠗⠀⠀⣿⡿⠀⠛⠀⠀⠀⠀⠀⣼⣴⣿⣿⣿⣿⣮⣿⣿⣿⣿⡄⠀⡇
⠀⠀⠀⠀⡇⠀⣼⣿⣿⢏⣾⢧⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠹⣦⠶⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠿⣿⣿⣿⡿⠏⠀⠀⡇⢠
⠀⠀⠀⠀⡇⠀⣿⣿⡿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⣤⣴⣶⡶⠆⠀⠀⠀⢀⣾⣿⡏⣿⡟⠀⠀⠀⠉⠉⠀⠀⠀⠠⢀⠎
⠀⠀⠀⠀⢣⠀⣿⣿⣧⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⠛⠈⠂⠀⠀⣀⣴⣿⣿⣿⠁⣿⡇⠀⢠⠎⠁⠉⠉⠐⠇⠛⠁
⠀⠀⠀⠀⠘⡄⢻⣿⣿⡸⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣦⣄⣠⣴⣾⣿⣿⣿⣿⡿⠀⣿⠇⠀⠘⡄⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠘⢎⢿⣿⣷⣿⣧⡻⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⠟⣿⠁⠿⢿⣿⣿⠃⢠⡟⣰⠀⡀⢣⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣎⠻⣭⡙⣯⣶⣿⣧⣿⣿⣿⢠⡏⠀⠀⠀⣈⣽⠋⠸⠟⢀⣴⡶⠾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⣠⣼⣿⣿⣧⡻⣷⡙⣿⣿⣿⣿⣿⣿⠈⠁⣠⣴⣿⣿⢣⣾⠇⣰⣿⣿⣷⣦⡀⠙⢦
⠀⠀⠀⠀⠀⠀⡰⠁⢀⣾⣿⣿⣿⣿⣿⣷⣝⣷⡸⣿⣿⣏⠉⠻⡧⠀⠉⢀⣿⣿⣿⢃⣾⠟⠁⠀⣿⣿⣿⣆⠀⢣
⠀⠀⠀⠀⠀⢠⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⡿⣵⡿⠃⠀⠀⠀⣿⣿⣿⣿⡄⠀⡆
⠀⠀⠀⠀⠀⢸⠀⣼⣿⣿⣿⣿⢹⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⣸⡇⠀⣸⣿⣿⡾⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠃
⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⢃⣿⣿⣿⣿⠀⠀⠀⠉⠻⢿⣿⣿⣿⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⠀⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⡿⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢍⡻⠿⠿⣿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣶⣶⣶⣾⣿⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠉⠉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠿⢿⣶⣄⡀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠈⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠟⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣟⣙⣽⣯⣥⣍⣹⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣭⣭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠔⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣾⣿⡀⢰⢁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡆⠀⣰⣾⣿⣳⣿⣿⣿⣿⣿⣿⣻⣿⣉⣻⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣚⡂⠠⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠘⠉⢹⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁⠀⣈⡉⠁⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⢡⡄⠀⢀⣀⣠⣤⣶⣾⣿⡿⢱⠄⢀⠀⣾⠠⠄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡄⠀⠀⢀⡇⠀⠰⠀⣀⠀⠀⠒⣀⠲⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⡇⠀⢠⣿⡀⠚⡍⠛⠢
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⣴⣷⠔⠉⢛⡥⡤⣀⠀⣛⠒⠋⠉⡜⠛⣒⠿⠛⠋⠉⠌⡁⠩⠩⣠⠄⡈⠉⡓⠴⠸⢿⡇⠛⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⣿⠧⠘⠉⠁⢀⠔⡅⢀⠈⠁⠀⠁⠀⠸⠓⠒⠉⠀⢀⠄⠘⠆⢀⣿⠀⠀⡀⠉⠈⠑⡷⢤⠀⠀⠈⡖⠉
⠀⠀⠀⠀⠀⠄⠀⠙⠤⠊⠁⠀⡀⠂⠀⣼⢰⡄⠘⠃⠀⠀⠀⢠⡀⠂⢀⠀⠀⣿⢸⣿⡄⣀⣀⠀⢀⠀⠂⠀⡆⠀⠀⠇
⠀⠀⡆⠀⠂⠀⠀⠠⢀⣀⠀⢀⣤⣤⡤⣭⡁⠀⠰⠆⠀⣠⡄⣾⡇⠲⠵⠄⠜⠛⠛⠉⠉⠀⠄⠈⠀⠀⠈⠀⡇
⠀⠀⠁⠨⠁⠠⢈⠀⢀⠀⣀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠀⠒⠠⠅⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⠿⡷⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠃⢂⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣤⣶⣚⣋⣭⣬⠹⣆⡀
⠀⠀⠀⠀⠀⣿⠏⠉⠡⠤⠬⣿⡏⣿
⠀⠀⠀⠀⢸⡇⢋⣀⠠⠤⠤⣼⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠖⠒⠒⠒⠀⢀⣠⠄
⠀⠀⠀⠀⢸⠀⠈⠀⣐⣶⠤⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠒⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⡶⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢿⠀⣯⣀⣀⣠⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣀⣀⣀⡠⣄
⠀⠀⠀⠀⠘⣆⠀⠉⠭⡵⡞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠰⣡⠚⠷⠚
⠀⠀⠀⠀⠀⢻⡀⢄⠀⠈⠙⣆⠹⣆⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠉⠙⠛⢿⣿⢶⡄⠠⣤⡀
⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠀⠈⠃⠙⣦⡀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠹⣆⠈⠻⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣆⠀⠀⠀⠀⠈⠛⢦⣼⢇⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠙⢷⣤⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠻⣮⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢀⠉⠙⢦⡈⠙⠛⠳⠶⠶⠶
⠀⠀⠀⠀⠀⠸⡇⢄⠀⢸⡳⣄⠀⠀⠀⠀⠀⠀⠘⣟⢻⡄⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⢿⡨⣂⠸⡟⢾⣶⣲⠤⠀⠀⠀⠀⣻⣤⡇⣀⣀⡀⢀⣀⣴⠟⠁⣠⠄⠀⢸⣤⡇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣷⡀⠀⠀⠀⠀⢀⣀⣠⠟⢿⠑⠀⠉⠉⠉⠉⡁⠀⣞⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠻⠶⢤⣤⣤⣤⠅⠀⠀⠸⠀⣤⠀⠀⠀⠐⢬⣊⣸⠄⠀⠀⣾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠘⢦⡀⠀⠀⠀⠀⠀⣠⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠁⣠⡾⠃⠈⠻⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡙⠲⠤⠴⠀⠈⢀⣀⣠⣤⣀⣀⣤⣤⣤⡴⠾⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⡴⠞⠛⠉⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⣤⠴⠞⣛⣉⡙⣦⡀
⠀⠀⠀⠀⠀⣾⡟⠛⠉⣉⣉⣻⣾⠹⡆
⠀⠀⠀⠀⢀⡟⠴⠂⠀⣀⣀⣈⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠄⠀⠀⣀
⠀⠀⠀⠀⢸⡇⠐⠋⠡⣤⣀⡈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠀⠠⣤⣤⣤⣤⡴⠞⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⣯⣴⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢸⠀⣰⠀⠀⠀⣸⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠸⣇⠘⠓⢶⣚⣫⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠞⣳⣒⡫⠍⠂
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠙⠽⣄⠻⣄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠖⠺⠿⢶⣤⣾⣤⣄
⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠀⠘⢦⠙⣦⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣌⢳⡄⠙⢶⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠹⣆⠀⠀⠀⠀⠈⢷⣄⠀⣸⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⣄⠀⠻⣦⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠻⣿⢠⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠳⢦⣈⠻⢶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢰⠀⢀⠈⢷⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⠰⣄⠈⣿⡷⣄⢀⣀⠀⠀⠀⠀⠸⣇⠹⡆⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠈⡇⣸⠀⠘
⠀⠀⠀⠀⠀⠀⠸⣇⠚⠀⣿⠈⠚⠛⠒⠂⠀⠀⠀⠀⣿⡿⡅⠦⣤⣤⣤⣴⠾⠋⢀⣴⡣⠀⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠸⣦⡀⠀⠀⠀⠀⠤⠤⠞⠁⣧⠀⠀⠀⠀⠀⣀⢄⣀⢯⠏⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⡛⠛⠶⠶⠶⠖⠂⠀⠀⠏⢀⡆⠀⠀⠀⠈⠳⠥⠬⡇⠀⠀⣾⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢦⡀⠀⠀⠀⠀⢠⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⠈⠻⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣙⠓⠒⠒⠀⢀⣠⣤⣤⣤⣤⣤⣤⣶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⢸⠇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠿⠀⠀⠀⠀⡆⢸⠇⠀⠀⢠⡀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠀⠀⠀⢰⠃⠉⠀⡼⠀⠀⣇⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠁⠀⢠⡏⠀⠙⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⣶⠀⠀⢰⡀⠈⠁⢠⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⡟⠀⠀⠈⣷⠀⠀⢸⡄⠀⠇⠀⠀⣀⢠⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠸⠇⢄⠀⡄⠀⠀⠀⠈⠁⠀⠀⢠⠀⠛⠈⠀⣧⣰⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⢀⠈⠀⠁⡀⠀⠀⠚⠀⠀⣆⠛⠀⠀⡇⢸⢿⠋⠀⡀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⠋⢸⠃⠀⠀⠃⠀⢰⣆⠑⡆⣼⠘⠀⠀⠙⠀⠀⠄⢠⠀⠈⠀⠠⡇⠸⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠈⣷⢈⡁⡀⠀⠀⢀⠘⠛⠀⠁⠻⠀⠀⢠⡀⠀⠀⣄⠀⠰⠀⠀⠀⠃⡿⠀⣆⠸⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⠀⠐⡋⢻⠃⣷⠀⠀⠚⡀⠀⠀⠀⠀⠀⢰⡌⡅⠏⢠⠟⡄⠀⠄⡀⠀⠀⣀⠠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡸⠇⠑⠴⡄⢡⣲⠐⣄⡇⠀⢀⠀⡄⢈⠀⡀⠿⠀⡾⠠⣠⡇⠸⠇⢀⡜⠃⠀⠀⢰⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⠂⠓⡆⣠⡄⠀⢧⣴⣾⡿⣶⡔⡌⠇⠀⠘⢠⡇⠀⠀⠀⠀⠋⡠⡖⣠⣸⣧⡘⠁⠀⠈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡦⠘⣄⠀⠈⠛⠈⠃⠙⢟⠃⣿⠿⣦⠀⠶⠀⠈⠓⣦⠀⠀⠐⠈⣷⠏⣻⢁⣼⡿⠋⢀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣤⣌⠀⡮⡄⢈⣗⣦⡼⢆⢠⡄⠻⠃⠀⠀⠊⡰⣿⠄⠈⠀⠰⢷⠠⠉⠈⠈⣴⢒⡊⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢈⣛⣠⠤⣿⣄⡧⢴⣾⣿⡹⠇⢸⣧⢱⣄⡶⠀⠆⠁⠁⠁⢠⣄⠀⢁⣈⡀⢻⣧⢀⣿⡌⠃⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠁⠀⠀⠀⢹⣿⣆⡈⠯⠀⣀⣀⠀⠈⠛⢡⣿⣧⠤⠓⠠⢾⣿⣦⡈⠿⠃⢘⠡⢜⣿⡛⠁⠀⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣀⣀⣠⣾⡾⠁⠀⠀⠀⣨⡿⠂⠒⠒⢿⠏⠀⠀⠀⠀⠀⠙⢿⡟⠈⠁⠙⣄⠀⠈⠙⢿⣯⡭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⡽⠯⠽⠿⣵⣠⢤⣄⣾⡿⣇⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⣠⣿⣷⣤⣠⢔⣿⡆⠀⣠⡴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠐⠾⠶⠛⠿⠧⢯⡥⠿⣿⣓⠠⠄⠂⠾⠛⣋⠿⠷⠿⠿⠳⢿⠶⠾⠾⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⢱⡀
⠀⠀⠀⠀⢀⣤⣸⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⢢
⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⢸⡏⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣿⣿⡎⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢹⣿⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠈⠻⣿⣆⡀⠀⠀⠀⢠⣿⣿⣷⡄⠰⠃⡤⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣜⠦⢀⣀⣸⣿⣿⣿⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣾⣯⣿⣿⣿⣧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣡⣿⣿⣿⣿⣿⣿⡿⣻⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠋⠉⠉⠉⢉⣼⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢰⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠉⢉⣽⣿⣿⣷⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣼⣿⣿⣿⡿⠋⠁⠀⠀⣴⣿⣿⣿⣏⣭⣿⣯⣝⠻⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣉⠙⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠁⠀⠀⢀⣴⣾⣿⣿⡟⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⢠⣾⣿⣿⡿⠛⠉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣾⣿⣿⡟⠁⠀⠀⠀⠈⠀⠉⠛⢶⡀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⢠⣤⠙⠋⠉⠀⠀⠀⠀⠀⢶⣶⡶⢦⡀⠀⠀⠀⡴⠶⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠁⠀⠀⢸⣷⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⢟⡼⣿⠇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠏⢸⡇⣿⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⣴⠋⠀⠸⣅⡿⠀⠀⠀⠘⠳⣤⡀⠀⠀⠀⠀⠀⠀⠠⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠥⠀⠐⠛⠁⠀⢀⣠⢿⡇⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣀⣀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠛⣋⣠⣧⡀⠀⠀⠀⠀⠀⠀⣸⠋⣿⣟⣹⣷⣶⡆⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢈⣟⣻⣿⡿⢿⣏⠙⢷⣄⠀⠀⠀⠀⠀⢸⣟⣿⣿⣶⣿⣿⡿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⠿⣿⣷⣄⣿⣿⡿⢻⣧⢀⡀⠀⢀⡾⢿⣧⣿⣷⣾⡿⠆⢀⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢨⡏⠁⠀⠄⡁⠀⢸⣄⣼⣷⣿⣏⠻⣧⣠⣿⣿⡟⢀⣾⣇⠘⣿⠉⣿⠏⢠⣠⡿⠃⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣾⣶⣿⠿⠿⣷⣾⣿⣶⣿⡿⠛⠙⣧⠙⣶⣿⣿⢁⣹⣧⣼⣧⣰⣦⣿⣴⡏⠀⠈⠉⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⢀⡿⠋⠁⠀⢘⣀⡀⠀⠉⠧⠀⢰⣗⠀⣠⣿⣿⡿⢿⣿⠟⠛⢿⡇⠘⣿⣻⣏⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀
⠀⠀⠀⠀⠀⣸⣧⣴⣿⣿⣿⠿⠿⣷⣾⣿⣷⣿⣿⡿⢿⠋⢹⡂⣀⣿⣦⣤⣼⣷⡶⣿⠿⡿⠻⡟⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⣿⡟⠛⡉⢀⣸⣶⣤⣀⣤⣶⣆⣀⣽⣷⣾⣧⣼⣿⠟⠛⣫⠀⠈⣿⠀⢸⣤⣷⣾⠃⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠸⣷⣤⣿⣿⣿⡟⠉⠉⢉⣉⡉⢛⡉⠉⣂⣿⠉⣇⣠⣾⣿⣷⢾⣿⡷⣿⣏⠛⠁⠀⠀⠀⠀⠀⣠⡿⠉⣿⣄
⠀⠀⠀⠀⠀⠀⣿⢛⣿⠟⢁⣴⡾⠟⢻⢿⣿⣿⠿⠻⣿⣿⣶⣿⡟⠉⣿⣧⣤⣼⡀⠚⠃⠀⠀⠀⠀⠀⣠⣴⣿⣷⡾⣿⡟
⠀⠀⠀⠀⠀⠀⣿⡿⠃⣠⡾⠋⠀⣀⡼⠟⠋⠀⠀⠀⢸⣿⣄⣾⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⢀⣼⣏⣽⣤⣿⠀⢸⣧
⠀⠀⠀⠀⠀⢀⣿⠀⢰⡏⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⢿⡿⠻⣿⣿⡿⢿⣿⠆
⠀⠀⠀⠀⠀⠸⣿⣷⡿⢡⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣿⣧⣀⣿⣿⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠸⣿⡇⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣭⣀⣿⣟⣛⣿⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠛⠻⠏⠙⠻⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢤⣀⠾⠃

⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤
⠀⢀⣸⣿⣿⣿⣷⣀⣄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣠⣄⣰⣿⣿⣿⣿⣀⡀⢀⣰⣿⣿⣿⣿⣠⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⢤⣿⣿⣿⣿⣄⡀
⠀⠈⠹⣿⣿⣿⣿⠈⢿⣤⡀⠀⠀⣀⣀⠀⠀⢀⣤⡾⠃⠸⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⠀⠻⣦⣄⠀⠀⣠⣄⠀⠀⢀⣴⡾⠃⠀⣿⣿⣿⣿
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⣿⣦⣄⣿⣿⣀⣴⣿⠋⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⢿⣷⣤⣿⣿⣤⣴⣿⠏⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠀⠀⠀⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⠒⠒⠒⠲⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⡰⢋⡼⠙⠉⠣⡀⢄⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⢀⡠⠘⠀⠀⠀⠀⡰⠋⣀⣤⣶⣂⣩⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⠖⠀⠐⠀⠀⠀⠀⠀⠀⠁⠐⣁⣬⡿⠿⠿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠆⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣷⡄⠀⠀⠀⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠇⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠄⠘⠳⠀⠀⢤⣤⣄⣉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⣠⣤⣤⠀⢀⠀⠀⠀⠀⠠⢠⡇
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠊⢹⡆⠀⠈⠙⢮⣙⠛⠶⣬⠻⠆⠀⠀⠀⠀⢠⡾⣯⡶⢏⣣⠿⠁⠀⠀⠀⠀⠀⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠚⠋⠁⠀⠀⠀⠀⣄⠀⠀⠆⡐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠰⠁⠈
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢡⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⢶⣄⠀⡄⢬⣿⣧⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⡀⢢⠰⠉⠳⣤⡑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠈⠐⠠⡈⠆⠉⠡⣀⠀⠀⠀⠀⠀⠀⢀⡀⢊⠀⠀⠀⠀⠀⠀⣀⠜⠡⡋⠀⣸⠃⠀⢆⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠒⠚⠋⠉⠙⠋⠉⠙⣷⠆⣠⣾⡿⠀⠈⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⣄⠀⠙⠛⠛⠛⠋⣡⣾⡿⣿⡟⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⡶⣤⣤⣴⣾⣿⠏⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣇⢸⣿⣿⣞⠋⣹⣿⡟⠀⢸⣿⡿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⢀⢻⣿⣿⠀⢿⣿⣿⣦⣿⣿⠃⠀⣸⣿⣿⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⣀⣴⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣶⣤⣀⠈⠀⠢⠤⣀⡀
⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢉⠛⠒⠦⣤⣄⣀
⣤⡴⠶⠛⠋⣡⣴⣾⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣌⣀⣀⣀⣀⣨⡍⠙⠓⠶
⣠⣤⣤⣴⣿⣿⣿⣋⣉⣹⣷⡀⠀⠀⣤⣀⣉⠉⠙⠛⠛⠛⠻⠿⢿⣿⣿⡟⣁⡀⠈⢉⣛⣿⣿⣿⣿⣇⠀⠀⢸⣯⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤
⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⢀⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⣀⠰⡄⢱⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠚⠐⢭⣠⣇⣼⡴⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⠀⣠⠞⠋⠉⠓⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠠⠋⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⣤⡴⠶⠶⠶⣤⣀⠀⢀⣤⣴⠚⠋⠉⠉⠉⠒
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠁⠀⠈⠉⠉⠁⠈⠙⠻⠋⠁
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠒⠋⡉
⠀⠀⠀⠀⠀⠹⣇⠓⠀⠀⠀⠀⣤⡴⠞⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠷⣶⣶⠦⠄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣔⣒⣒⣒⣲⣤⣤⣶⡶⠾⠟⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢧


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⠶⣄⣢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣻⣤⠲⣤⣩⣿⣾⣧⣾⣧⣾⣀⣄⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⣿⣿⠛⠉⠁⠀⠙⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠇⢀⠀⠀⠠⠤⠈⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⡄⠀⠀⠀⠀⢾⠿⠉⠁⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⢣⣤⡤⠂⠀⠀⢀⡴⠚⠁⢨⣙⠛⠉⠙⠂⠀⡀
⢰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⠄⠀⠠⡀⠀⠈⠀⠀⠀⠀⠈⢻⡶⢶⣿⣿⣧⣤⣠⡆⠠⢘⠖⠀⢀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⣠⡁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⡷⠀⠉⠉⠁⠀⣧⠆⢠⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⣀⢨⣥⣾⣿⡟⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣄⠠⠙⠋⠁⠀⠀⠀⠀⢀⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣯⣽⡏⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡿⢀⣄
⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠳⡀⠀⠀⠀⣻⣿⣿⡆⠀⢸⡀⠀⠀⢀⡀⣀⣤⠛⠙⠛⢶⣿⣿⢸⣧⣸⣿⣿⠆
⠀⠀⠀⠀⠀⣰⣿⡇⢀⣤⣠⣷⣶⣶⣭⣽⢀⠀⢠⣄⣸⠛⠛⠛⠛⠋⠉⠉⠛⣿⡆⢠⠈⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠘⠛⣿⣿⣾⠏⢨⡇⢀⣴⠋⠁⠀⠀⠀⠹⠧⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⡇⠀⠈⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠛⣴⡿⠃⢀⡖⠀⠀⠀⣀⠀⠀⠀⠀⢦⣀⡀⢀⣼⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢠⡁⠀⠀⠀⠉⠉⠃⠀⠀⠈⠣⠄⠙⠃⠈⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢤⠀⠀⠀⠀⠰⣶⣶⣄⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠰⣿⠋⣸⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡄⠀⠀⠀⢀⡼⠋⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣀⠀⠉⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣤⣌⣁⣠⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⢿⣿⡿⠟⠛⠛⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠹⡇⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⢠⡇⠀⠀⠀⠀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣠⠋⢹⣄⡀⠀⢀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣀⠁⠀⠀⣿⡧⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠏⠀⠀⠀⠇⠀⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣀⠀⠀⠀⡘⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢰⠇⠀⠀⠀⢷⡔⠆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡾⠀⠀⠀⠀⠈⢿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣵⣄⡀⠀⠀⠀⠸⡇⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠛⠁⠀⠀⠀⠀⣿⣤⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⢀⣶
⣿⣿⣦⣶⣦⣤⣄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⣿⣿⣿⣿⣟⣽⣿⣿⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣰⣿
⠉⠛⣿⡿⢿⠏⠀⢻⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿
⠀⠀⠹⣷⠀⠀⠀⢸⣿⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣦⣿
⠀⠀⠀⢸⣶⠀⢀⣬⣿⣏⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣤⣌⣿⡟
⠀⢀⣿⣿⣿⣿⣏⠉⢸⣿⣿⣇⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠶⢾⣿⣄⣾⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⠀⠀⠙⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⣿⣿⣿⡿⠃
⢀⣴⣿⣿⣿⣿⡏⠀⠀⠀⠈⠻⢿⣟⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣗
⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠶⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠉⢯⢢
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠙⡜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣘⠀⢀⡴⣦⡀⠈⡆⢃
⠀⠀⠀⠀⠀⢀⣆⣀⢔⠺⡆⠀⠀⢁⠸⣖⣾⡋⢶⠤⠭⠭⠭⠭⠭⠑⠺⣯⢽⡥⠤⠨⣗⣼⠇⠀⡇⢸⠗
⠀⠀⠀⠀⠀⠙⡖⠂⠻⠶⠃⠀⠀⡈⢠⠀⠀⢣⠈⢆⠀⢀⣠⢤⡴⣤⡠⠋⠻⠘⣄⠀⠀⠀⠀⣰⢁⠆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⢃⠎⠀⠀⠘⡄⠈⣴⠋⢁⣀⣀⣸⠃⢠⠃⠀⠈⠢⠤⠤⠴⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠴⠞⠓⠉⠀⠀⠀⠀⠘⡄⠹⣦⡏⢙⢷⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢹⢿⡻⠿⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠁⠀⠙⢒⡃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⣀⢀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⢺⡎⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠺⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⢭⡥⢒⡚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⡨⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣘⣤⣸⠈⡒⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢻⠑⢺⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣅⣀⠔⠛⢩⠄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠟⠢⡄⠸⠄⠉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠈⠸⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠉⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡆
⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠹⣿⣿⡀
⠀⠀⠀⣼⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠛⠶
⠀⠀⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣼⣿⣷⡀⠀⠀⡀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡿⣷⣄⠀⠏⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⣿⠈⢿⣆⢠⣿⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡿⢿⡄⣾⣿⠘⣿⣿⣿⣧⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣸⢠⡿⠁⢸⡇⢸⣿⡀⣿⢸⣿⢻⣧⠀⠀⢠⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢠⣿⣾⠃⡠⠀⠀⢸⣿⣴⠏⠸⣿⢸⡿⢠⠇⣾⣿⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⠀⣠⣿⡿⠃⠰⢃⡄⡄⣸⡿⢋⡀⠐⣣⣿⣷⣿⣿⠏⢸⣧⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⣿⠀⢀⣼⡿⠋⢀⠀⢀⡾⠈⢡⡟⢡⠎⢀⣴⣿⠟⠁⠀⢀⡞⣼⡏⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣾⡟⣰⣿⢋⡄⠀⠉⣰⡿⠁⢀⡟⢠⡏⠀⣾⣿⣯⡶⢒⣠⣀⡾⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⣿⣿⣿⡿⠋⠀⠀⣼⡿⠁⡴⠘⠁⣸⠀⡆⣿⣿⣿⢠⡿⢛⣭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⡟⠀⠀⠀⢰⣿⡇⢠⣇⠀⡄⠁⠀⢣⠸⣿⣿⣾⢁⡾⠁⣠⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢸⣿⣿⡟⠀⣠⠀⠀⢸⣿⡇⠀⢿⠀⡀⢠⡀⠢⠀⠹⣿⣿⣿⡇⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣿⣿⡇⠀⠉⢸⢸⡆⢿⣷⡀⠀⡀⣧⠀⠳⡄⠀⢤⠘⣿⣿⣧⢀⡄⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣿⣿⣇⠀⠀⢸⡄⠇⠈⢿⣧⠀⡹⣾⡆⡄⢻⡄⢸⡆⡟⣿⡇⠈⣴⣿⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢻⣆⠀⠀⢿⡄⠀⢄⠙⣧⠀⢹⣿⠀⢸⡇⢸⣧⡇⣿⣇⣼⣿⣿⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣷⡙⠋⠳⡄⠈⢿⣄⡈⢧⠹⠀⠘⣿⠂⣼⡇⢸⡟⢠⣿⡿⢿⢻⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡱⣆⠙⠧⠀⢲⡄⠀⠀⢻⣿⣦⡀⢰⢰⣿⢰⣿⠃⠈⣰⠟⠉⣀⠄⣼⣿⢁⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡙⠷⠀⠃⣀⠩⣌⣳⡠⣻⡏⣿⡀⣾⣷⣿⠋⢀⡨⠁⠀⣈⣥⣾⡿⠃⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣶⣬⣓⠈⢿⣿⢹⣿⣾⣿⣿⠟⣡⡞⣉⣴⣾⡿⠟⠛⠉⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷⣼⣿⣿⣿⣿⣿⢋⣾⣿⣰⣿⠟⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢿⣼⡿⠿⢿⣧⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⠄⠀⡆⢠⠀⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣀⣀⣰⠧⣤⣊⣡⣊⣐⣣⠞
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡼⠛⠳⠶⠴⢧⣠⣤⠼⠃
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠷⢶⣦⣄⠀⠀⢀⣠⡴⠆
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠘⠁⢿⣤⡴⠶⠶⠲⠶⢦⣤⣀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⣾⠟⠉
⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠈⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⢦⡀
⠀⠈⠷⣤⣤⣤⣤⣤⠤⠤⠄⠈⠙⠛⠒⠶⠾⠛⠛⠻⣦⡀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣤⣤⣀⣀⣀⡀⣀⣀⣀⣤⣬⡿⠷⣦⣬⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠁⢸⣧⠀⠀⠉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠰⣄⠀⠀⣜⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⠻⢦⣼⣆⠙⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡐⠦⣽⣷⣄⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆