Defecation Emojis & Symbols

⠀⠀⠀⣠⣶⣾⣷⣶⣤⣀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢸⣿⣿⣿⣿⣿⣿⣧⡜⢻⣿⣿⣿⣀⣀
⠀⠻⣿⡛⠛⠛⠛⠛⠻⣾⣿⡟⢻⠀⠉⠙⠓⠦⢄⡀
⠀⠀⠈⢹⠋⠀⠀⠀⠀⢈⡟⠀⡞⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠘⠶⣤⣖⠀⢀⣞⠓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⢀⡞⠡⠞⢛⠿⣽⠇⡏⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟
⠀⠀⠀⣾⠀⢠⡔⠉⠉⠁⢸⠇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣼⢰⡇
⠀⠀⠀⠹⣄⠀⠑⢄⡀⠀⠸⣦⢤⣀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡏⢸⡟⠉⠉⠉⠉⠉⠉⠉⠱
⠀⠀⠀⠀⠈⢦⠀⠀⠙⢦⡀⡏⠀⠈⠉⣳⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⡇⣼⡧⠤⠤⠤⠤⠤⠤⠤⠴
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⢹⠇⠀⠀⢠⠟⠉⠉⠙⣶⣉⠀⢠⠤⠤⠤⣤⠒⢘⣆⠀⠀⠀⢸⠀⣼⡇⠀⠀⢼⠛⡧
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣺⠀⠀⢀⡞⠀⢀⣀⣀⣹⣍⣂⣤⣶⣾⣭⣶⣾⣿⣿⣆⠀⠀⡞⢰⣿⡇⠀⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣶⠶⠟⠛⠛⠛⠋⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡇⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠁⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⠙⢦⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣇⣠⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠹⣌⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣁⣀⣀⣁⣹⡤⠤⠤⠤⣤⠤⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣄⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⢦⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠳⡄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠙⣆⠀⠀⢻⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢹⣦⠀⠘⡄⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡎⢿⡇⠀⢹⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠞⠀⠀⣸⠇⠀⠈⢳⣤⣤⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⢀⡼⠁⠀⠀⣠⠶⠛⢁⣠⠴⠋⠀⠀⠀⠀⣸⠟⢹⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⣾⠷⠶⠶⠶⠿⠷⠾⠷⣤⣤⡤⠶⠶⠿⣿⠋⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠸⠦⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠀⠈⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣫⣵⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠩⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠂⠸⠀⠀⠀⣯⢁⠍⠙⠛⠋⠙⠁⣦⣚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠆⠀⠀⠆⠄⣿⠁⠀⠀⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠂⠀⠀⠀⢀⣤⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠃⡆⠀⠀⠈⠂⠘⢿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⣀⣀⣀⡬⣿⣟⡛⢃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣤⣶⣶⣶⣾⣿⣦⣼⣄⡀⠠⠐⠀⠀⢠⠇⠀⣸⣷⣿⣿⣿⣿⠋⠱⢼⣿⢁⡈⠰⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣶⣾⠶⡶⣶⢿⢿⣿⣿⣿⡿⣧⡄⢾⣼⠟⣨⠉⣻⣎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⣿⣮⣷⣾⣿⣿⣾⣾⣷⣿⣿⠿⣛⣿⣬⣉⠀⢺⣿⣌⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠀⠈⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠻⡿⣿⣿⣿⣿⣯⢿⣙⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣤⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠂⠀⠀⠀⠀⢠⣀⠀⠀⢀⡀⢙⠛⠛⣎⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⠠⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠂⠀⣠⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠠⠤⠀⠈⢀⣴⣿⣿⣿⣿⣦⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠈⢀⠀⠀⠀⠓⠀⠀⠀⠀⣘⣉⢻⣿⣿⣵⣮⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡿⣦⣤⠀⠈⡁⠀⢰⣤⣄⣀⡀⠀⠙⠻⢿⣶⣬⡙⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⣉⢉⣸⠣⣀⠀⢐⡟⢿⠇⠈⠉⠀⠀⠀⣀⢈⠻⣿⣾⣻⣟⠾⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⢸⣿⣷⣴⣿⡆⠀⠀⠀⠀⠐⠶⠦⠦⢶⣷⣾⣿⡿⣶⣾⡾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠿⢟⠯⣙⣙⡆⠀⠀⠀⠀⠀⠠⣄⠈⠉⠉⠈⠓⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣤⣚⣠⣻⣤⣴⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠉⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣾⡿⢿⣿⠀⠀⠀⠀⠀⣿⣿⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⣿⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⡄⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⢠⣶⣄⣠⣾⠿⠿⠿⠛⠛⠛⠛⠛⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⢸⡇⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⣾⡇⠀⢹⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠀⢀⣀⣀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⣷⣶⣶⣾⣿⡇⠀⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢰⡏⠀⢀⣾⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⠇⠀⠀⢸⣧⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠸⣷⣀⣾⡟⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠈⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠙⢿⡟⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣄⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣴⣶⣶⣶⡾⢿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣶⣶⠿⠿⠿⠿⠛⠿⠿⣿⣿⠛⠉⠉⣿⡿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠉⠀⠀⠀⣀⣠⣤⣤⣤⣤⣾⣿⠀⠀⠀⢿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⢿⣿⣁⠀⠀⠀⠀⠀⠐⠿⠿⠛⠉⠛⠛⠛⠿⠿⢿⣶⣄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠇
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⠏⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⡶⠾⠿⠛⠉
⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢉⣩⣽⣿⣿⠿⠋⠀⠀⠀⠀⠀⠉⠛⢿⣦⠀⠀⠀⠀⠀⠀⢰⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣶⣦⣤⡀⠀⠀⢀⣤⡶⢿⣿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣷⡀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢀⣠⣴⣶⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢿⣶⣶⣾⣿⣿⠁⠀⠀⢰⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠁⠀⢀⣀⣄⣤⣤⡾⠃⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠸⢿⣷⣶⣶⣶⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣷⣄⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣸⡿⠋⢙⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⣿⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⣨⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣶⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠟⠛⠛⠛⢉⣉⣠⣤⣶⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢂⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠋⠀⠀⠀⢀⣾⢷⡄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⢹⡄⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡾⠛⠁⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠉⠁⠀⠀⠀⠀⠀⡼⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⠇
⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀⣼⣿⠄⠀⠀⠀⠀⠀⢀⡠⠞⠛⠉⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⣷⡀⠀⠀⣰⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠸⣽⠀⠀⠻⣧⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠛⠛⠛⠳⣆⠀⠀⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠈⠀⠀⢀⣼⠟⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠙⠓⠶⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣆⣀⡞⣀
⠀⠀⠀⢀⣠⡤⠶⠞⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⡉⠉⠉⠉⠉⠛⢦⡀
⠀⠀⣰⡿⠉⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣤⣤⣀⣀⣀⣤⡤⠤⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠈⣷
⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣄⣀⣀⣀⠀⠀⠀⠀⢉⣉⣹⣿⣷⣤⣀⣀⣀⣀⣠⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠟⠛⠋⠉⠙⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠨⠤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣀
⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀
⢠⠋⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⢶⣶⣄⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠈⠙⠲⢤⡀
⣼⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⡿⠀⠀⠀⠀⠀⠀⢠⠛⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⡇⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⡴⠋
⢻⠀⠀⠀⠀⠀⠀⠹⣥⣀⣀⣀⣔⣵⣿⠃⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⣠⠞⠁
⠈⢧⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣀⣀⣀⣀⣀⣠⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢈⡈⠉⠉⠉⠁⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣎⡱⠀⠀⠀⠀⢰⣊⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠝⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠔⡄⠀⠀⠀⠀⢞⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠴⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠇⠀⠀⠀⠀⠈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡔⢢⠀⠀⠓⠚⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡀⠀⠀⠀⠙⠚⠀⠀⠀⡖⡦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠤⠇⠀⠀⠀⠀⠀⠀⠀⠐⠥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⣉⠆⠀⠀⠀⠀⢰⢒⡆⠀⠀⢰⣉⠆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⣦⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠁⠀⠀⠑⠋⠀⠀⠀⠀⢠⠲⡀⠀⠀⢠⠒⡄⠀⠀⣠⢤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⣄⠀⠀⢀⠤⡄⠀⠀⠀⢀⠤⡌⠉⠀⠀⠀⠈⠉⠀⠀⠀⠙⢊⠼⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠖⠢⠬⠵⣥⣀⣀⣀⣀⣑⣁⣀⣀⣀⣀⣀⡤⠤⠤⠄⠒⣇⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠖⢯⡙⢏⡒⠒⠒⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠒⠒⣩⢟⣽⢶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠈⠲⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠵⠋⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠈⠑⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠔⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠑⢬⡳⣄⠀⠀⠀⢀⠴⣫⠖⠁⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠙⠦⡑⢤⡔⡡⠊⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⢀⡤⢊⠶⢍⠢⣀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⣠⠔⡡⠞⠁⠀⠀⠑⠮⡑⢤⡀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⣀⠴⣪⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠒⢌⡲⢄⡀⠀⢰⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣼⠴⣊⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⡲⢼⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠇

⠀⠠⢄⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠰⠠⣤⠀⠀⠀⠀⠀⣀⣤⡤
⠀⠐⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠈⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠘⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢼⣿⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠘⢐⡂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰
⢰⠀⠀⠀⠀⢾⣿⣿⣇⣀⠀⠀⠀⠀⢠⡄⠀⢰⣿⣿⣧⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄
⢸⠀⠀⠀⠀⠘⣿⣉⣿⣿⣧⡀⠀⠀⢸⡇⠀⣨⠛⠛⢹⣿⣿⣆⠀⠀⠀⢰⠀⠀⢀⣴⣾⣿⢿⣿⣿⡇
⢸⣀⣀⣀⣀⣀⡙⠋⠙⣿⣿⣧⠀⠀⢸⣇⣸⣏⣰⣶⡿⢿⣿⣿⡆⠀⠀⢸⠀⣴⣿⣿⣿⡟⢷⣼⠋
⢸⣿⣿⣿⣿⡿⠀⠀⢰⡟⢹⡇⠀⠀⠀⣿⣿⣿⣿⣿⠃⣼⠋⣿⠁⠀⠀⣸⣀⣸⣿⣿⣿⣷⣦⡅
⠈⣿⣿⣿⣿⡁⠀⢀⣼⣇⣼⣷⠀⠀⠀⣿⣿⣿⣿⡅⣠⣿⣤⣽⣆⠀⠀⢸⣿⣿⣿⣿⣿⢹⣿⣇
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⣸⣿⡛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⡿⠿⣿⣟⡋⠉⠁⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⠿⠋⠁⠀⠀⠛⠋⠀⠀⠀⠀⠀⠙⠻⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⣴⠿⠛⠿⠿⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠻⢦⡄⠀⠀⠀⢀⣤⠀⠀⠀⢀⡀⢀⡀⠀⠀⢀⠇⠀⠀⣠⣴⠟⠁⠀⣿⠆⠀⠀⠀⠀⠀⠉⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⣾⡀⠀⠀⠀⠜⣧⣤⠖⠈⠁⠀⠀⠀⠀⢸⡇⠀⣿⣆⡀⣾⣆⣀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣽⣀⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⢠⠀⠈⠀⢸⣏⣸⣇⣿⡁⠉⠉⠛⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠛⠛⠁⠉⠐⢶⣦⣤⡄⢠⣦⣤⣿⡇⣦⣶⣾⠛⣩⢹⡿⢷⡀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⣴⣦⣤⠀⠈⠁⠙⠁⢙⣿⡛⢛⣥⡈⣁⠀⡐⠋⠉⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢄⣀⠛⠿⠃⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠐⠢⠤⢄⣀⣀⡀⠄⠀⠐⢶⡀⠐⠒⢂⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡦⢄⠀⠀⠀⠉⠋⡅⠀⠀⠀⠀⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⠐⠀⠀⠠⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣽⠛⠀⠀⠀⠀⢸⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢰⢣⡞⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢱⠋⠀⠀⠀⠀⢸⣀⡤⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⡿⠻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠃⠀⠀⠀⠀⠀⠸⣯⢠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⠀⣰⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢸⠁⣿⡰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⢦⠀⠀⠠⠷⣀⠀⠀⠀⠀⠙⠳⣤⡀⠀⡸⠁⠀⠀⠀⡠⠊⠀⠀⣸⠇⠀⠀⣿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠓⣤⠀⠀⢀⣔⡁⠀⢈⣳⣄⠀⠀⠀⠀⠀⠉⡼⠃⠀⠀⠀⣰⠁⠀⠀⠀⠛⠀⠀⢠⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡿⠛⠁⠀⠞⠻⠛⠻⣿⣳⣼⡻⣙⣷⣄⠀⠀⠀⠀⢳⣄⠀⠀⠈⣃⣀⣀⣀⣀⣀⣤⣠⠎⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡤⢀⠀⠀⠀⢀⠀⠀⠈⠀⡘⢻⣿⣿⣿⣾⡿⢦⣄⠀⠀⠈⠁⠛⠛⠻⠟⠻⠷⣤⣤⣤⣤⣤⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢭⣒⠁⣰⣏⡠⠤⠀⠈⢙⠀⠐⢽⣿⣅⡀⠀⠉⠳⢦⣀⣀⣀⡴⠊⠀⠀⠀⠀⢀⣠⠜⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠙⢷⡟⢋⡀⣀⠀⢰⠇⠐⠋⠀⠙⠻⣿⣷⣤⣀⠀⠈⠉⠁⠀⠀⠀⠀⣠⠴⢋⡥⢾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⣀⠘⣿⠗⣨⣰⡆⠀⠀⠀⠀⠀⠀⠛⠀⠈⡙⠟⢿⣦⡀⠀⠀⣠⠔⣻⡟⠞⠉⠀⣇
⠀⠀⠀⠀⠀⠀⠤⣾⢷⡼⣿⣿⣮⣳⣿⠠⣧⣌⣿⣤⠔⠀⠀⠀⠀⠀⠀⠈⠡⢞⣆⠈⣳⡤⠚⣁⣴⢉⡆⢀⣤⣦⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⢿⣿⣿⣿⣿⣄⠈⠻⢿⣴⠖⣀⠀⣀⠀⢀⠀⠀⠀⠀⣿⠃⡸⠀⠛⣻⠟⡿⠱⡿⠟⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣂⠉⠛⠓⠿⣧⡘⠛⣡⠞⠡⠞⣥⣾⣕⣤⡲⢅⡂⣫⠀⠃⣤⣾⡵⢎⣿⡆⢀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠛⠛⢦⣴⣿⢿⣿⢿⣶⣶⣿⣻⠧⠾⣇⡴⠋⢾⡏⢀⠀⣤⣽⣶⠎⣼⢛⠋
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢈⣹⠞⢿⡎⢿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠀⡈⠉⢁⣨⡤⠞⢱⡏
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⣠⣴⠏⠁⠀⠘⣷⠈⠙⠋⢛⡟⠁⠀⠀⠀⠀⡼⠛⠛⡉⢁⣀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠿⠛⠋⠀⠀⠀⠀⠀⢻⣄⠀⢀⠊⣴⣧⡶⠀⠀⣼⠀⡂⢀⣈⣻⣋⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠛⣻⠁⢀⣼⢃⣼⣟⠉⢻⡷⢞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣺⠿⡀⣾⡟⠋⠀⠉⠉⠓⠚⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡌⢸⡇⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠰⠁⢸⡇⠀⠀⠀⠀⠀⣸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⢀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢉⠀⠈⠹⠛⣛⡛⠉⠉⠍⠋⠉⠉⠛⠳⠶⠟⠙⠒⢄⡀
⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⢀⡴⢚⣭⠝⣶⠀⠴⢂⡄⠀⠂⠀⣀⡐⠲⣶⢀⠈⠳⣄
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢠⣿⠞⠉⠉⠀⠀⠀⠀⠀⠀⠶⠾⠿⢶⣶⣿⡶⣶⣶⢤⠈⠱⣄
⠀⠀⢀⠜⠀⠀⠀⠀⠀⣤⣶⣶⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢢
⠀⢀⠎⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣍⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⡎⠀⠀⠀⠀⢸⣿⣿⠭⠘⠋⢨⣿⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠰⠀⠀⠀⠀⠀⠈⠿⣿⣮⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣄⢀⣤⣤⠒⠒⠓⠻⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣦⠄⠹⠿⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⣿⢟⠟⠛⠋⠱⠋⠀⠀⠀⠀⢀⣴⣤⣶⣇⡀⠀⢠⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡭⠘⢁⣠⣤⡤⢀⣠⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈
⢫⡐⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠻⢅⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠓⠓⠊⠘⠄⠀⣀⣦
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠶⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠓⠛⠒⠐⠁⠛⠓⡉⢠
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⢿⣿⣯⣿⣿⣇⠀⠀⠀⠀⢀⣀⣾⡿⠛⠁⠀⠀⠀⣀⣀⣀⡀⢀⠆
⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣤⣀⠉⠻⣿⣿⣷⣤⣦⣶⣿⣿⠋⠁⣄⡀⠒⠪⢿⣛⠳⠷⣩⠏
⠀⠀⠀⠐⢄⡀⠀⠉⠁⠀⠈⠤⠀⠀⠀⠙⠯⣼⣿⣿⣿⣝⣿⣷⣖⡤⣶⣧⣴⣋⣉⣤⣂⡿⢍⡴⠃
⠀⠀⠀⠀⠈⠣⡀⠀⠀⠲⢤⡀⠀⠉⠠⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡶⠞
⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠈⠑⠢⣄⡈⠉⠉⠻⠿⠿⢿⣶⣾⣿⠿⠿⠿⣿⢛⣻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⢀⠀⠉⠑⠦⣄⣀⡀⠀⠀⠀⠀⢀⣀⠤⠞⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣤⣬⣿⣶⣶⣧⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⣶⣶⣶⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⠿⠿⠋⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠷⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠿⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠛⠛⣿⡿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⠛⠛⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢠⣿⠃⠀⣾⡇⠀⠀⠀⢹⡏⠈⠉⠉⢹⡏⠉⣿⡏⠙⣿⡀⢹⣷⡀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣼⡿⠀⢰⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⡇⠀⣿⡇⠀⢹⣇⠀⢿⣧⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢀⣿⡇⠀⣾⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⢿⡄⠈⣿⡆⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢸⣿⠀⢠⣿⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠘⣷⡀⠘⣿⡀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣿⡏⠀⣼⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⢹⣧⠀⢹⣷⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢰⣿⠃⢀⣿⠃⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⢿⡆⠀⢿⣧⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣼⡟⠀⢸⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠈⣿⡀⠘⣿⡄⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⣿⠃⠀⣿⠃⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠸⣧⠀⠸⣿⡀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⣸⡿⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡆⠀⢹⣧⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡇⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢿⣆⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⣿⡄⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣾⡏⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠹⣷⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢰⣿⠃⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢻⣇⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣼⡟⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⡆⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⢸⡿⠀⠀⠀⢀⣿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠘⣿⡀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⣾⡇⠀⠀⠀⢸⡿⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣧⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢻⣆⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣼⡇⠀⠀⠀⢸⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⢿⡄⠀⠀⣠⡿⠋
⠀⠀⢠⣿⠀⠀⠀⠀⣿⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡘⣷⣠⣾⠟
⠀⠀⣼⡇⠀⠀⠀⢰⣿⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⠁
⠀⢠⣿⠁⠀⠀⠀⣼⡟⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇
⠀⣼⡏⠀⠀⠀⠀⣿⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇
⢀⣿⠃⠀⠀⠀⢸⣟⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇
⢸⣿⣀⣀⣀⣀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇
⠛⠛⠛⠛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣯⣽⣭⣧⣬⣭⣯⣭⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⣶⣶⣶⣤⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣾⣿⣶⣶⣦⣤⣤⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠛⡛⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠉⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠈⢿⣿⣿⣿⡇⠀⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⡴⠘⣿⣿⡿⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢿⣯⡀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠀⠀⠈⠻⣷⡆⠀⠻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠠⠤⠤⠼⠤⢄⡀⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⢰⣿⣿⣿⣿⣄⣀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠒⠒⠒⠒⠒⠀⡅⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣙⣻⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢣⣈⣉⣉⣉⣉⣉⣉⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠹⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡎⠠⠤⠤⠤⠤⠤⢤⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⢺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠒⠒⠒⡲⠒⠂⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⡀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣾⣿⣿⡿⠃⠀⠀⠀⢨⣿⣻⣿⣟⠁⠀⠀⢠⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠳⣤⡀⠀⢸⣇⣨⣿⣿⠀⠀⠀⠸⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠐⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⣀⣠⣤⣥⣤⣤⣼⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⡜⠀⠀⣄⡀⢀⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⡏⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⡀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠚⠍⠁⠀⠈⠀⠀⠀⠈⠀⠀⠂⠩⢓⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠏⠊⠀⣠⠀⠀⠀⢀⣀⣼⣧⣀⡀⠀⠀⠀⣀⠈⠑⠩⡢⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠲⣾⣿⣶⠖⠀⠀⢹⣿⣿⡏⠀⠀⠲⣶⣿⣶⠖⠀⠈⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡼⠕⠁⠀⣀⠀⠀⠿⠛⠿⠀⠀⠀⠈⣀⣀⠁⠀⠀⠀⠿⠛⠿⠀⠀⣀⠀⠈⠪⢣⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠲⣶⣿⣶⠖⠀⠀⡀⠔⠀⠁⠀⠀⠀⠀⠈⠀⠢⢀⠀⠀⠲⣶⣿⣶⠖⠀⠀⡳⡀
⠀⠀⠀⠀⡾⠌⠀⠀⠀⠿⠛⠿⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠿⠛⠿⠀⠀⠀⠡⢳
⠀⡠⠶⠶⠰⠶⠶⠴⠶⠶⠶⠦⠴⠷⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠤⠤⠶⠶⠾⠶⠶⠶⠶⠆⠶⠶⠴⠾⠷⠶⣄
⠀⡇⠀⢺⣦⠀⠀⣴⣷⠀⣾⠀⢠⡶⠿⢷⠆⠰⠿⣿⡿⠿⠀⠀⣰⣿⡆⠀⠀⣿⢀⣴⠟⠀⢸⡿⠶⠿⠇⠀⢘
⠀⡇⠀⢸⡿⣧⣼⣿⣿⠀⣿⠀⠘⠻⠿⢶⣦⠀⠀⢸⡇⠀⠀⢠⣿⣉⣿⡄⠀⣿⡿⢿⡄⠀⢸⡿⠟⠆⠀⠀⢸
⠀⡇⠀⢼⠇⠹⠏⠸⡿⠀⢿⠀⠺⢷⣶⠾⠟⠀⠀⢼⠇⠀⠠⡿⠋⠉⠙⠿⠀⡿⠀⠈⢿⡆⢸⣷⣶⡶⡦⠀⢸
⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⢲⠶⠶⠶⠶⠲⠶⠶⠶⢶⡶⠶⠋
⠀⠀⠀⠀⢧⢂⠀⠀⠀⣶⣤⣶⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⣶⣤⣶⠀⠀⠀⡐⡾
⠀⠀⠀⠀⠈⢧⢄⠀⠴⠟⢿⡿⠦⠀⠀⠁⠢⠄⣀⠀⠀⠀⠀⠀⠠⠔⠈⠀⠀⠴⢿⣿⠿⠦⠀⡀⡽⠁
⠀⠀⠀⠀⠀⠈⢣⡢⡀⠀⠀⠀⠀⣶⣤⣶⠀⠀⠀⢀⠉⠈⡁⠀⠀⠀⣶⣤⣶⠀⠀⠙⠀⠀⢔⡖
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡢⡀⠀⠐⢿⣿⡿⠆⠀⠀⣸⣿⣿⣇⠀⠀⠴⢿⣿⠿⠢⠀⢀⢄⡁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣀⠄⡀⠛⠀⠀⠀⠈⠉⢻⡟⠉⠁⠀⠀⠀⠙⠀⡠⣐⠵⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠥⢀⣀⠄⠀⡀⠀⠀⣀⠀⠀⣀⣐⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠚⠛⠋⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⣤⠖⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞
⠘⢧⠾⠻⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠹⣆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠉⠓⠒⠒⠒⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠤⠀⢀⡴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣠⣤⠶⠭⣀⡠⠒⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⣉⢳⠀⠀⡸⠓⠒⣲⡞⢑⡒⠐⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⣤⠀⠈⡇⠰⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠈⠉⠀⠀⡇⠀⠀⠉⣇⡈⠀⢀⠞⠀⡀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠱⡀⠀⠀⣠⠗⡤⡀⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡏⠀⠀⠀⠀⠀⠘⢲⣴⣚⣉⣉⣉⠥⠔⠊⡇⢠⡇⠄
⠀⠀⠀⠄⠀⠀⠀⠻⡄⠐⢷⠬⢥⣉⣁⣀⣀⡀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⢀⠄⠀⠸⣀⢈⠀⠀⢀⣀⠠⢾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⠉⠉⢉⠀⠀⠐⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠳⢤⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡟⠉⠉⠉⢻⠈⠉⢻⠀⠀⢀⡤⠒⠒⠺⣅⠀⣀⣈⣉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠐⠀⠀⠸⠋⠀⢀⠈⠱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠀⠘⢄⡀⠀⣀⣧⠀⠀⠀⠀⢠⠃⢠⠏⠀⠑⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠣⣀⠀⠀⠀⡠⠎⠈⠀⠀⠀⠈⣹⡁⠀⠑⠦⠤⠒⣁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠉⠉⢉⣀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡿⠿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢠⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠳⠦⢤⣟⡄⢀⠀⠈⢀⢈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⣦⠀⢙⡨⡁⠀⠀⠀⠀⠀⠄⠀⠀⡄⢀⠀⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠃⢠⠀⠄⠁⠀⠑⠛⡁⠐⠀⠀⠀⠀⠓⠒⠂⠀⠘⠆⠀⠙⠊⢀⠠⢄⢈⠀⠀⠀⠛⢢⡄⠀⠐⠙⢀⡠⠀⢂⡀
⠀⠀⠀⠀⠈⠁⠀⡀⠂⡀⡀⡸⣀⠂⠄⠀⠙⠀⠤⡀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠘⢄⠀⠣⠔⠁⠈⠡⠂⠈⠄⠠⢀⠀⠐
⠀⠀⠈⠀⢢⠁⠀⠠⠄⠓⠀⠁⠀⠀⠀⠀⣦⠀⢠⡿⢸⡇⠀⣀⡐⠤⠤⠀⣀⣘⠢⢤⣤⡗⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠘⠃⠀⡴⢂⡄⣀⠀⠀⠀⠀⠀⠞⠀⡞⠀⠃⣴⠀⣁⡄⠻⠛⠀⣀⣨⢹⡠⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠣⠠⠂⠈⡁⢲⠀⠀⢈⠀⡜⠠⠀⡰⢏⠀⠀⠀⠀⠉⢀⠀⢿⠀⡏⢈⡵⢢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠒⠃⠈⠀⠁⠂⡜⢀⡎⠀⠀⠀⠀⠎⣩⡇⢸⠀⡇⢸⠀⣿⠀⠐⡀⡀⠈⢑⠀⠀⣀⠄⡈⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡆⠀⠀⠀⠐⠀⠏⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠃⢘⢀⣇⠀⠀⠈⠁⢄⡉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢺⠀⠀⠀⠀⢐⡆⠀⠀⠂⠀⠀⠃⠸⠁⠀⠀⠀⢠⡈⣏⣀⠤⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⣧⠀⠀⠀⠁⡌⠀⠀⠀⠀⠀⠀⠑⠈⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠘⣆⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢫⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠒⠒⠒⠂⠀⠠⡤⠀⣀⠀⠈⠋⠐⢄⣀⣠⢄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠥⠶⠄⠀⠀⠀⠀⠀⠀⠉⠀⠂⠺⠀⠀⠁⢠⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⢀⡤⠒⢀⠆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⣠⠾⣆⠀⠀⠀⢻⡄⠀⠀⢠⢦⠀⠀⠀⠀⢃⠀⢀⡠⠐⠒⠂⢄
⡎⠀⢠⠎⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⡀⠀⡠⠞⢹⠆⠘⢧⡀⠀⢸⠙⣦⢠⡆⠀⡆⠀⠀⠀⠈⡀⠉⠁⠒⠤⢀⣀
⠁⠈⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀⠤⠒⠉⠀⠀⠠⠗⠉⠀⠀⠸⠄⠀⠀⠈⡷⢾⠄⡇⢹⣄⢀⠆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⢊⣀⠀⠀⠀⢠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢸⠀⡇⠀⠉⢹⢢⡀⠀⠀⠀⡟⠉
⠀⣠⢤⡄⠀⠉⢠⠒⠲⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠸⠀⡇⠀⠦⠸⠘⠉⢢⠀⣤⣤⠀⠀⠀⠸⠓⢄
⡎⠁⡰⠀⠀⠀⠀⠀⠀⡇⢀⠃⠀⠀⠀⠀⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠄⠀⠀⠀⠀⡆⡇⠀⠱⠀⠀⠀⠀⢈
⠑⠚⠁⠀⠀⠀⠐⢤⢤⣴⠀⠀⢀⠠⢄⠀⠖⠉⠉⠀⠀⠀⠀⡠⠀⠀⣄⠀⠀⠀⠀⠀⠉⠐⢤⡀⡠⠤⡄⠀⣷⢀⠠⠔⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠰⡈⠈⢁⠀⡆⠀⢀⡁⠀⠀⠀⠀⠀⠀⣼⠠⢀⡀⠤⣇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡸⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⣄⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠩⡤⠒⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡘⠀⡎
⠀⠀⠀⠀⠀⠀⢠⠒⠀⠙⣠⠼⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡱⠊⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠞⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠙⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠈⠛⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⢠⡆⠀⠀⠀⢀⠔⠂⠉⠉⢙⡉⠀⠒⢦⠒⠀⠀⡴⠒⢲⡏⠓⠠⡀⠀⠀⠀⠀⢸⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢠⡜⠁⠀⠀⠀⠀⠎⠉⠢⡀⡠⡂⠀⣎⡀⡠⠊⠱⡀⠀⠈⠢⡀⠀⠀⢘⠀⡎⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠇⠀⡄⠓⢄⠀⠀⠀⡼⠄⠀⠀⠀⠀⠈⠊⠀⠈⠠⠤⠄⢵⠀⠀⠀⣰⠀⠀⠸⠀⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⡌⠀⠀⠀⠙⠂⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠘⡄⠀⠀⢸⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡸⠀⠀⠀⠀⠀⠀⠭⠀⠤⠀⠀⢀⣀⠤⠀⠒⠒⠒⠀⠠⡄⢠⠀⠀⠀⠰⢀⠀⠈⣌⠁⡰⠢⡴
⠀⢀⣀⠀⣤⣀⠔⠤⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⠛
⠀⠈⠀⢙⠀⢁⡤⠀⠄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⡏⢀⠁⣀⣀⣄⠀⢀
⠀⠀⠀⠉⠙⠊⠀⠀⠀⠀⠀⠀⠟⠠⣤⢀⣀⡀⣠⠞⠉⠉⠉⠁⠲⡞⠓⠀⢤⠖⠀⠉⠀⠐⢤⡤⠐⠙⠀⠈⠀⠈⠁⠀⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠛⠒⠒⢳⠏⠀⠀⠀⠀⠀⠀⠘⠖⠒⠆⠀⠀⠀⠀⠀⠀⠱⠒⠓⠲⢆⠀⠀⠈⢥⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⠠⠄⠀⠖⢢⠄⠠⠦⣤⠤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠀⠈⠀⢰⠒⡦⠤⠀⣼⣍⠀⣀⣀⡀⢴⣸⠦⠤⠤⡃⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠉⠉⠉⠉⠀⠒⠴⠢⠤⠐⣀⣛⠁⠀⠠⠄⠀⠀⠀⠀⠀⢆⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⢄⣀⣀⣀⢀⢀⠀⣉⠄⠀⠀⠀⠀⡀⠐⠂⠒⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣨⠖⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⢀⡀⠀⢤⣤⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡈⠐⠒⠒⠒⡒⠂⠠⠤⠄⢀⣀⣀⠗⠒⠒⠀⠈⠁⠀⡰⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠡⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⡬⢁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠱⣄⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⢎⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠠⠄⠒⠂⠤⠄⠐⠊⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠄⠊

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠛⠛⠛⠛⠀⠀⠈⠛⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠶⠶⠶⠶⠶⢤⣄⡈⠃
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠆⠀⠰⢦⣤⣀⠉⠳⣦⡀
⠀⠀⠀⢰⡿⠷⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⠀⠙⣦⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣴⠋⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢰⠏⢠⡟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣆⠈⣷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⣠⡾⠋⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⢀⣤⠞⣋⠉⣥⠀⢠⡍⢙⠳⢦⣀⠀⠀⢿⠀⢹⡄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⠀⠀⠰⠟⠁⠀⠹⣆⠈⠛⠋⣠⡾⠀⠀⠙⠃⠀⢸⠂⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢿⡀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⡿⠀⣼⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⣄⢀⣴⠟⠁⠀⠀⠀⠀⠘⣧⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⠏
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⠏
⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠙⠶⣤⣀⣀⡀⢀⣀⣀⣠⡴⠞⠁⣠⡾⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣈⠉⠉⠉⠉⢉⣀⣤⠶⠛⠉⠻⣦⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠉⠉⠀⢀⡀⠀⠀⠈⠻⣦⡤⢤⣄
⠀⠀⠀⢸⡇⠀⠀⠀⠠⠞⠁⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠰⣄
⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠶⠶⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠷⣀⠀⠀⠈⢷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⣤⠞⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣼
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃
⠀⠀⠀⠀⠙⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠋



⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⣀⠀⢀⠀⠀⡀⡀⢀⠀⠀⣀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠀⠀⣀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⠀⢹⢸⠀⢉⠀⡌⣡⢨⡆⢇⢸⠀⢸⠆⠀⠀⠓⢄⠀⠛⠀⡧⢜⢰⠁⠈⡆⡷⡏⢸⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣼⣶⣧⣴⣤⣴⣴⣤⣤⣤⣶⣮⣼⣶⣾⣶⣦⣤⣶⣮⣤⣶⣤⣧⣼⣬⣷⣾⣤⣧⣼⣾⣶⣦⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠻⠿⠛⠉⠀⢹⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠦⣄⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⢤⣠⠤⠅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡖⠒⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣁⣀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣿⣥⣤⣤⣽⣦⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⣀⣤⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣄⢀⣾⣯⣤⣤⣶⣿⣽⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⢤⣤⡶⠂⠀⣿
⠀⠀⠀⠀⠀⠀⢤⠿⠶⣦⣾⣿⣩⡾⣋⣵⠟⠋⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠹⠿⠿⠿⠛⠓⠀⠀⠘⠋⠙⣂⠀⣿
⠀⠀⠀⠀⢠⠶⠚⢻⡿⠛⠷⠉⠈⠀⠉⠀⠀⢀⣀⣀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⠀⣶⣟⠉⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⣶⠾⣿⣷⣄⣰⡾⠟⣫⣿⣷⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠋⠉⠉⠉⠉⠁⠀⠀⠘⠋⠈⠁⠀⣿
⠀⠀⠀⠀⠀⠀⣾⠁⢰⡟⠀⠀⠻⢿⣿⢿⡀⠀⠙⣻⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣤⡶⠶⠶⠶⠛⠛⠛⠀⣦⣶⠛⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠷⠶⠾⢛⣁⡀⠙⠛⠛⠉⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣴⠶⠶⠾⠟⠛⠛⠛⠀⠟⠉⠓⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣴⣿⣿⠿⠀⠀⠀⢀⣼⠏⠀⠀⣠⣴⣤⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠈⠉⠀⢀⣀⣤⡶⠟⠋⠀⠀⣀⣿⣿⠿⠁⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠛⠛⠛⠛⠛⠛⠉⣿⠀⢀⣠⡴⠟⠋⠁
⠀⠀⠀⠀⢀⣴⠾⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠋⠁
⠀⠀⠀⠀⢿⣥⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠈⠛⣿⣃⣀⣀⣀⣀⣀⣤⣤⣤⣾⠷⠶⠶⠶⠶⠾⠿⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡶⠶⠿⠿⠟⠛⠿⠿⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣰⠟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠀⣾⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢤⣶⡟⠁
⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⣿⠃⠀⠀⣶⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠸⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡟⠀⠀⢠⣿⠀⠀⣿⠀⠀⠀⢸⡄⠀⠀⠘⣇⠀⠀⠀⠹⣆⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣾⡇⠀⢠⠾⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⡞⠀⣿⠀⠀⢸⡆⠀⠀⠀⢿⠀⠀⠀⠀⢷⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⢸⠇⠀⠹⣆⠀⢈⣧⠀⠀⠀⠘⣧⠀⠀⠀⠘⣧⠀⠀⠀⠀⢿⣆⠀⠀⠀⢸⡿⢦⡀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⢠
⢹⡆⠸⠀⠀⠀⠈⠓⠚⠙⣆⠀⠀⠀⢸⣧⡀⠀⠀⠈⢳⣄⡀⠀⣿⠈⢷⣄⡀⣸⡇⠈⠛⢦⣤⡟⠀⡇⠀⠀⠀⠀⠀⠀⢸
⢸⡏⠻⠄⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣼⠋⠳⢦⣤⡴⠃⠈⠛⠛⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡀⣀⠀⠀⣾
⠘⣷⣶⠀⠀⠀⠀⠉⠓⠒⣢⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠒⠋⠁⠀⠀⠀⠀⠀⣿⣠⡴⢋⠉⠉⡷⢰⣿
⠀⣼⡇⠀⠀⠘⠛⠛⠛⣋⡽⠟⠁⠀⣠⣤⣤⣦⣤⢦⣄⣤⡀⠀⠙⠿⢏⡉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣏⣠⠾⠁⣾⡇
⠀⢿⡇⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠉⠀⣁⢀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠀⠀⠀⣿⡁
⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⢀⠀⠀⢠⣄⠀⠈⣿
⠀⠀⠀⠀⣽⡟⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢁⡀⠀⠀⣻⡄⠀⠀⣹⣦⣀⣼
⠀⠀⠀⠀⣿⠁⠀⣨⡙⠛⠶⣤⣤⣀⣀⡀⣾⠻⣏⢻⡌⢳⣀⣄⣤⡴⠶⢛⣉⣠⣤⣴⣶⡾⠷⠶⠾⠋⠛⠿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠻⠷⠾⠻⣷⡾⢷⣴⣆⣉⣹⠟⠻⣦⠉⠀⠀⠈⠋⣿⢀⡿⠞⠻⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠈⠉⠻⢦⣀⠈⢷⡀⢀⣠⡶⠛⢿⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠰⣷⠀⠀⠈⠳⠋⢿⡉⠁⠀⠀⠀⠙⣦⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⢷⡄⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠁⠀⢸⡇
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⣰⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣼⣯⣄⠀⢀⣼⠋⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⢀⣾⠃
⠀⠀⢀⣼⠋⠀⢉⣿⠟⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠞⠛⠁
⠀⣴⠟⠁⠀⢀⣸⣧⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⠿⣾⣣⣟⣰⠟⠃⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢘⣿⠛⠛⢛⣷⠶⠶⠶⠶⠶⢶⡞⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣼⡇⠀⠀⠀⠀⠀⠘⣷⣤⡴⠶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⣤⣤⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣤⣴⡿⠇
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢩⡍⠻⣦⠤⠤⠤⠤⠤⠤⠤⠤⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⢻⡀⠘⡃⢀⡿⠛⠛⢻⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣀⣀⣙⣶⣶⣛⣁⣀⡀⢸⡏⠉⠉⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⡧⠤⠤⠤⠤⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠶⠶⠶⠶⠶⠶⠶⠶⠦⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⡟⠛⠓⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⠶⠶⠶⠶⠶⠶⠶⠶⠦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣫⣛⣉⣛⣟⣽⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢻⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿
⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣾⣿⣷⣴⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣤⣄
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡿⠛⠋⣩⣭⡽⢿⣿⣯⣉⣡⣬⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⢀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣭⣿⠿⠿⣿⡟⢋⣀⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢟⣽⣿⣿⣿⠿⣣⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢄
⠀⠀⠀⠀⠀⠀⠀⣹⡿⣃⣼⠿⠟⣫⣿⣶⣿⠟⢿⣿⣿⣿⣿⡿⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠻⣿⣷⣝⡿⢿⣦⠀⠀⠀⠀⠀⠘
⠀⠀⠸⣦⠀⠀⣶⣿⣿⣿⣿⣿⣿⡿⠉⢿⠃⠀⣿⣿⣿⣿⣿⣧⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠹⣿⣷⡄⠿⣷⡀⠀⠀⠀⠘
⠀⠀⠀⠈⠻⣾⣿⣿⣿⡿⠛⣻⡟⠁⠀⠀⠀⠀⢻⣿⣿⣿⡏⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⢦⣈⣷⡀
⠀⠀⠀⠀⠀⠴⢿⣿⣿⣿⡖⠌⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠈⠙⢿⣿⣿⡟⠛⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠘⠉⠙⢿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⡀⢀⡀⠀⠀⠀⠙⡄⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⣿⣿⣀⣾⣄⣴⣾⣷⠿⠋⠀⠀⢀⠀⢀⣤⣴⣶⣿⣶⣿⠿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠿⣿⣶⣶⣦⣤⣀⡀⢀⣀⣨⡉⢉⣙⣛⡉⢉⣩⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢨⡏⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⣄⠀⣄⢹⡀⣘⣁⣉⢉⣋⣉⡀⠀⣀⣀⢀⣼⣿⣿⣿⣿⣿⡟⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠻⣿⣿⣿⡿⢩⣿⣿⣷⠶⠛⢿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢺⠋⠀⠀⠀⠀⠀⠸⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠚⠀⠀⠀⠀⠀⠀⠀⠘⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⣩⠦⠔⢒⣒⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡡⠞⠉⠀⠀⠀⣭⣽⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢮⣡⠋⠀⣀⣠⠴⣶⠺⡉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠚⠛⠛⠋⠟⠁⠀⠀⡷⠶⣫⡬⣿⠒⢋⡳⠃⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠀⠀⠀⠸⠀⣀⣠⣤⠓⠂⠁⠀⡿⠒⠉⡀⣠⠊⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡶⠒⠚⠁⠀⠉⠙⣒⠾⠋⠁⠀⠀⣱⠀⠀⠀⣳⠄⠒⠈⣳⡀⠀⠀⡇
⠀⢀⡤⠖⠒⠋⠉⠉⠁⠀⠀⠀⢀⡠⢤⣚⣉⡄⠀⠀⠀⠀⠀⢾⠄⠀⣜⠁⠀⠀⣠⠾⠤⠤⠾⡁
⠀⠈⠓⠶⠤⠤⠤⠐⠒⠒⠈⠉⠁⠀⠀⠟⠛⠒⠈⠉⢉⡗⣺⠛⠀⠀⠈⠓⠛⠋⠀⠀⠀⠀⠐⠚⠋⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣉⣉⠛⠧⠞⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠈⠃⠀⠀⠀⠀⠀⠠⠔⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⢀⠤⠎⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡄⠀⠀⠘⠲⠤⠖⠒⠉⠓⢤⣀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠄⠀⠀⠀⣀⠔⠁⠀⢸⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣤⣤⣄⣀⣀⠀⠀⣀⣠⠴⠊⠁⠀⠀⠀⡆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡏⠉⢷⠤⣄⠈⠉⠉⠉⠀⠀⠀⠀⠀⡤⢌⣳⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡀⢸⠄⠀⠀⠀⣠⠤⠤⠤⠞⠀⠉⠒⠉⠀⠉⠉⠉⠉⠉⢳⣀⣠⣤⣤⠇⡀⢙⡅⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢍⡿⠛⠘⣆⣠⠴⢻⡆⠀⠀⠀⠀⣀⠀⡀⢀⠤⡀⢄⠀⠀⠈⡇⠒⠒⢲⡄⣹⢯⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡧⠴⡅⢠⡔⠊⢯⡇⠀⡀⠀⠀⡛⠢⢠⡸⣀⣄⠈⢦⠤⣀⡇⠀⠀⠀⠉⠹⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠚⢹⡖⠃⠀⠘⠷⡏⠀⢀⢄⠸⣐⠄⣎⡂⠸⠚⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢊⠉⠁⠀⠀⠀⠰⠀⠀⠘⠤⠃⠾⠀⠀⠀⠀⢀⣀⣘⡆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢰⡆⠀⢠⣇⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⡗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣸⠛⠛⠋⠉⠉⡽⢩⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣠⣤⣤⣧⣼⣤⠤⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣗⢲⠤⠤⠤⣤⣤⣇⣀⣠⢤⠴⢓⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢻⣉⠤⠒⣫⠕⠋⠪⢶⣤⣘⣉⡇⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠭⠤⠖⠚⠉⠀⠀⠀⠀⠀⠈⠙⠛⠭⠭⠝

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠙⢦⠃⠀⠀⣰⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢢⠋⢸⠀⠀⠘⣶⠶⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠀⠈⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠐⠒⢤⡀⠀⠀⣖⡩⠤⠔⠒⠉⠳⠴⣀⡀⢀⣠⠴⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡻⠁⠀⣠⠀⢄⠀⠀⠈⢟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠃⣭⣭⣁⠀⢈⣑⣒⡀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⡄⠉⠉⠁⠀⠈⠉⠉⠁⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡇⠀⠑⢄⣀⠒⠉⠳⢀⣠⠜⠁⢸⠐⡆⢴⣒⡒⠒⠒⠤⠤⠤⠤⢄⣀⣀⣠⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠆⢫⡽⡿⣍⠽⣤⡀⠀⢸⠀⠀⠀⠀⠉⠉⠒⠒⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡠⠊⠀⡇⠀⠀⡇⠒⠒⡇⠙⢦⣼⠸⠂⠀⠀⠀⠀⠀⠀⠉⢇⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠠⠤⠤⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠓⠒⠒⡇⠀⠀⠀⠀⢶⡒⠢⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠈⠑⠦⣀⠉⠁⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠘⠒⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣀⡀⣠⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⢧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⢐⠥⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣠⡄⣀⡀⠀⠀⠈⠁⠐⡆⠃⠀⠀⠀⠉⠐⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢤⢁⣩⠀⠀⠀⠛⠒⡋⠀⠇⢇⣀⢄⢀⢀⠀⠀⣠⠊
⠀⠀⡠⡂⠤⢀⣀⠀⠀⠀⢀⠂⠠⠖⢢⠄⠀⠀⣈⢁⡀⠀⠠⠀⠀⠈⠉⠓⠥⣅⣠⡧⠟⠒⠄⡀
⠀⠀⠀⠙⠮⣄⣀⠌⠄⢘⠓⠰⢞⠋⠀⠀⠤⢬⡍⠅⠀⡠⠁⠐⠀⠀⠀⠀⠀⡠⠛⠷⢬⢭⠵⠮⠷⣄
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⠤⠥⣌⣑⣤⣘⣛⡀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠐⠐⠀⢌⣸⢂
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢒⡒⣶⢤⡤⠀⣀⣀⣀⡀⠠⠊⣠⣍⠐⠂⠤⢀⠀⠀⠀⠀⠀⠁⠂⢤⠔⠁⠠
⠀⠀⠀⠀⢀⠰⠍⣀⠀⠀⠐⠈⠀⢀⣀⡒⠷⠒⠀⠀⠚⠛⠋⢀⣀⣼⡶⠤⠄⠉⡆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣈⠁⠈⢀⠔⠊⠉⠁⢈⣉⣈⠉⠒⠂⠤⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⡀⠀⠈⠒⠁⠀⠀⢀⠔⢁⠶⠤⠈⢁⣐⠒⠶⢅⠴⠍⠁⠀⣂⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣈⠉⠂⠠⢤⣐⣊⡡⠎⠙⠈⠠⠔⡩⠁⠈⢀⣾⠦⠄⠀⠈⢀⠴⠒⠉⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⢥⣀⡙⠲⣖⡡⠴⠊⠍⠀⢀⣠⠶⡹⠊⡠⠷⠂⢀⠊⢛⠶⠡⠤⣴⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠠⢌⠉⠘⠚⠹⠵⠲⠾⠟⣛⡒⠀⠠⠒⠂⠅⡠⠃⠀⠆⢐⠴⠋⠀⠐⣂⠍⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢄⡢⢕⠨⠒⢈⡐⠤⢄⠀⠀⠀⠀⠀⠈⠉⡒⠢⠤⢊⡀⠀⢀⠀⢒⠢⠀⣀⡊⠁⢀⠯⣮⣷⠡⠱
⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⠐⠠⠄⠀⢀⠠⢉⠲⠖⣒⣭⠴⠦⣄⡀⠀⠀⢇⠁⠒⠒⠠⠤⠎⣘⡚⠂⢀⣤⢐⠂⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠈⠀⠈⢠⠖⠁⠈⠙⠣⣤⣘⠙⡆⠀⠈⠳⣕⡀⡀⡠⡠⠀⢸⢀⢒⠤⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠔⠁⠀⠀⠀⠀⠀⠀⠉⠓⠃⢂⠀⠀⠀⠉⠙⠒⠲⠵⣭⣿⣅⣀⡤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠑⠡⠂⠋⠐⠕⠅⠠⠂⠄⠀⠨⠂⠀⠢⠊⠔⠀⠊⠔⠐⠁⠪⠂⠐⠅⠀⠠⠠⠠⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠉⠉⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠳⣄⡀⢀⡤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠈⠁⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡀⠘⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⡀⠈⠁⠀⢸⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠒⠒⠀⠀⠀⠀⢸⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠔⠃⠀⠀⠀⡖⢢⠀⢰⡢⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢠⠎⠑⡄⠉⠁⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠓⠚⠁⠀⠀⠀⣠⠞⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣏⠀⠉⠑⠒⠤⠤⠤⠤⠔⢊⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣄⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⡀⠀⠀⠀⠀⢠⣠⡿⢻⡿⣿⣿⡿⣻⣟⣭⠿⣛⡛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡴⠋⠒⠤⢀⣴⣿⣟⡃⢿⣽⢡⠟⣷⣿⡟⠑⠉⣀⣀⠀⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⡙⠲⢤⣀⠻⣟⠻⣵⣸⣿⣿⢀⣿⣿⣇⣰⣿⣭⢿⡋⢻⢹⡏⢿⡉⢶⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⠻⣷⣦⣍⠳⣌⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣅⠸⣇⠀⠀⣧⠘⣷⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠳⠦⡉⠛⣧⠙⢆⠈⠻⣿⣿⣿⣿⣿⡿⣇⠛⢻⣷⣌⡛⠶⣌⠓⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⣄⠈⠣⡈⠷⣤⡞⠻⣯⡉⣿⣧⣼⣿⣦⠰⣍⡻⢦⡙⣦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢆⣽⡿⢦⢀⣶⣾⣷⣦⡈⣿⣇⣨⡁⢙⣿⣷⠮⢉⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢉⡴⠞⠉⣹⢳⡟⣳⣿⣿⣼⣿⣿⣿⣏⣹⡟⣹⠎⡉⢹⣟⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡄⠻⠒⣨⣽⢿⢋⡝⠙⣿⢋⣿⢹⣿⢻⡿⣿⡿⡿⣿⣽⠛⣾⡿⢃⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠟⢁⣴⣿⣿⢳⣾⣿⠁⡾⢨⢸⡇⣸⣿⡜⡷⢹⢻⡇⠹⣿⣿⢿⣡⠞⠁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⢻⣿⣿⡏⣸⣿⣿⣤⣷⢨⣿⣇⣿⣿⣧⢧⢸⠈⣿⠀⣿⢿⣧⠙⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣸⣿⣿⡗⢸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣞⣴⣿⣇⣿⣾⣿⡄⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣷⡸⣿⡿⢿⣿⠿⠿⢿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠉⠉⠛⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣻⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⡀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡏⢹⣷⡄⠀⣀⣭⣿⣧⣈⣉⣼⡟⠻⣿⣦⡝⢊⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢁⡴⠟⢁⠎⡾⣡⣽⣟⣿⠋⠙⣿⢡⡾⢩⠅⡀⣩⠞⢰⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⢀⣰⠟⠰⠐⡁⡟⣿⠏⠀⠀⠹⡟⢡⠏⠎⡴⢃⣴⠟⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠁⣴⠃⡼⢀⡼⠋⠀⠀⠀⠀⠙⢏⣠⡾⠑⣼⠃⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠻⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⢀⠀⠀⢀⠀⠀⣀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠶⠀⣻⡀⡇⡌⠀⠀⢿⠀⡇⡜⠀⠀⢘⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡇⠀⡇⠛⡇⢧⠀⠀⠈⠻⠀⡇⠀⠀⢸⠀⡗⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠉⠁


⣤⣤⣤⣄⣤⣀⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣤⣀⣤⣀⣤⣄⣠⣄⣀⣀⣀⣀
⣿⣛⣟⢻⣛⣿⣋⣙⡛⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣛⣙⣟⣛⣻⣿⣟⣻⣿⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⣀⣠⣴⣶⡿⠛⠛⢿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⣸⡿⠟⠛⣿⣿⣿⡟⠁⠀⠈⠉⠉⠉⠙⢿⡟⠻⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⣴⠟⠉⠀⣠⣾⣿⣿⣿⠿⠶⠦⣴⣦⣸⣿⣾⣦⣽⣷⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣼⠃⠀⣠⣾⣿⣿⣿⡿⠿⣿⣶⣤⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⠃⠀⣰⠃⠀⢠⣿⣿⡿⠋⠁⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡾⢠⠇⠀⠰⠇⠀⢀⣿⠟⠋⠀⣰⣾⣿⣿⣿⣿⣿⣯⣙⡛⢿⣿⣿⣿⠻⣿⣿⣈⣛⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⠈⠁⠀⠀⣴⣿⣿⢿⡿⣻⠿⠛⠉⠉⠃⠀⠀⠈⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⠀⠀⠀⠀⠀⣸⣿⡿⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡄⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢸⠀⠀⠀⠀⠀⢸⠇⣾⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠟⠁⣠⠄⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠼⠀⠀⠀⠀⠀⢻⣤⣿⠀⢸⣿⠀⠀⢀⣴⣾⡿⠿⠷⠦⠀⠀⠀⠹⣿⡿⠀⣸⣿⣤⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣶⣶⣶⣶⠒⠀⠀⠀⠈⠀⢰⣿⠟⢻⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⢹⠇⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠈⠛⠛⠛⠿⠿⠏⠉⠙⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣰⡇⠈⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠉⣽⣿⡆
⠀⠀⠀⠀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠠⠖⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⠾⠿⣿⡇
⠀⠀⠀⢰⣿⡏⠙⣦⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⣀⣀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⢸⣷
⠀⠀⢠⣿⣿⣷⡀⠘⢷⣄⠀⠀⢀⡟⠀⢿⣿⣧⣤⣶⣿⡟⠁⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿
⠀⢀⣾⣿⣿⣿⣿⣄⠀⠙⢷⣄⣸⠃⠀⠈⢿⣿⣿⣏⣉⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠹⠆
⠀⣼⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⠻⠆⠀⠀⠘⣿⣿⡋⠉⠉⠉⠈⠉⠉⠛⢧⠀⠀⠀⠀⠀⠀⣦⡀⣀⣴⡟⠁
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠘⣿⣿⠶⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠁
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠙⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣄⡀⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠲⣤⡖⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠚⠉⠳⠀⠐⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣀⣤⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠿⣧⠀⠠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⠀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣹⣿⣏⠀⠀⣉⣉⣉⣉⣉⡉⠉⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣉⣤⡤⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠲⣤⡖⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⢠⡾⠋⠀⠀⠀⠀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠚⠉⠛⠀⠐⠒⠒⠒⠒⠒⠂⠀⢀⡟⠀⠀⠻⣦⡀⣠⠞⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠤⣤⠀⠠⠤⠤⠤⠤⠤⠤⠤⢸⡇⠀⠀⠀⣨⠿⣧⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣤⡿⠀⠠⣤⣤⣤⣤⣤⡄⠀⠀⢿⡄⠀⠞⠁⠀⠈⠻⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠙⢦⣄⣀⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣀⡀⠀⠀⠶⠉⢻⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠛⠛⠛⠛⣽⣿⢿⠝⠛⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⠇⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⡿⠛⠉⠛⠛⠓⢓⣿⣿⣿⣿
⠀⠞⠀⠀⠀⠁⠀⠀⠉⠉⠉⠉⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⠫⡤⣤⡿⠛⠁⠀⠀⢀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣀⣀⣀⡀⠀⠀⠠⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠉⠀⠁⠈⠉⢻⣯⣅⣀⡡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠉⠁⠐
⠀⠀⠚⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⡄
⠀⠀⠀⢀⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠿⠀⠀⠀⠰⠦
⠀⣀⣲⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣶⣤⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⡀⠀⠈⠉⠐⣺⣿⣿⡟⠉⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡬⠛⠉⣁⠠⠃
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⢶⠤⠄⣤⣦⣴⢶⡀⢠⣤⣤⣄
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣭⣟⣻⣶⡷⣾⣿⣹⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⢠⣼⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠸⣿⣿⣿⡙⠻⠇⠀⠀⠀⣀⣸⡿⠛⠃⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⢀⣨⣿⣿⣿⣅⡀⠀⠀⣤⣿⠋⠁⠀⢀⣤⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⣾⡿⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⡀⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠟⠀⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣠⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠸⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠈⢷⡯⡄⠂⣴⠂⡂⢰⣾⠐⣫⡯⠬⡷⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣇⡼⣤⠈⠃⡷⠟⣻⣬⡏⣤⡟⠀⡀⡶⢰⣁⣠⣄⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠍⣆⠁⠰⣰⣿⢺⢚⣠⠋⢀⡿⣉⠽⠻⡟⡟⢷⣾⠍⢩⣔⠃
⠀⠀⠀⠀⠀⠀⢰⠃⣰⡋⠒⢻⣽⢹⣼⠟⣟⣼⣇⠱⡽⣟⢦⣤⣹⡴⣟⣳⠟⣿⠁⡁
⠀⠀⠀⠀⠀⠀⣘⣶⠏⣿⣿⣞⡹⢾⣽⡿⠟⣱⡟⣺⣿⢘⢮⣟⣿⣄⡅⣀⡶⠄⠀⡗
⠀⠀⠀⠀⡜⢊⡭⠿⠺⡟⢳⡞⠿⢸⣼⣿⣟⣭⡿⣿⣿⡀⢞⣤⡿⣿⢳⣿⡻⣆⡿⢁⠆
⠀⠀⠀⡀⠀⠘⠒⠉⣎⣤⣾⣿⠘⢻⣟⢿⣯⣿⡟⣹⠸⠙⢻⣏⡰⡿⡀⣹⣏⣹⠉⠋
⠀⠀⠀⠀⢸⣧⣾⣀⠞⢻⣯⣭⠙⣗⢰⣞⣿⣷⡿⣷⢠⠳⣷⣟⣷⣿⠷⣿⣿⣃⡏⢠
⠀⠀⠀⠀⠈⡀⢫⡟⢏⣰⣞⠧⣕⣏⡹⢻⣷⣼⠀⠎⠈⠧⠹⣹⣿⣉⠦⣿⣿⣿⡿⡸
⠀⠀⠀⠀⠘⠉⠈⢹⣻⡄⣽⣶⡿⣮⢻⣯⣿⣁⣷⣠⣾⠚⣾⣏⠟⠑⢮⣼⣸⣿⣰⢧⠐
⠀⠀⠀⠀⠀⢹⣅⣡⣷⣿⢹⡿⣇⣧⣟⠃⡟⣁⡟⢉⣿⣭⣿⢿⡆⠒⣬⣿⢹⣇⣀⣟⠠⠈
⠀⠀⠀⠀⠀⠀⢾⠈⠙⢈⣿⣿⣿⠳⣿⣷⣶⠏⢹⡏⣽⡿⢙⢯⡠⣶⣻⣏⠀⣿⡊⠻⡖⠒
⠀⠀⠀⠀⠀⠀⠈⠒⢱⡜⠉⣾⣷⠖⣿⣿⣇⣸⢌⡑⢫⢹⡋⡑⠀⡽⠀⢿⣽⡿⡇⢀⡁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⣿⣭⣉⣿⣞⣡⣽⡰⢷⠈⢾⠹⠅⠒⢣⣠⣿⣅⣳⣴⡍⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡧⠁⠀⠀⠈⠈⠱⠎⠑⠀⢧⠀⢀⠀⠉⠟⣯⠙⢿⣷⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠒⣿⣋⡧⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣟⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⡄

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡒⠒⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢦⣤⡶⠐⣲⡀⣀⣨⣵⣿⣾⣿⣻⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⣠⣿⠟⣠⠄⢤⡤⠂⠀⠀⢶⣶⣤⠀⠸⣷⣤⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣩⠛⠄⠐⢯⡴⠉⠀⠀⠀⠀⠜⠿⠿⣦⠄⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠠⣾⠃⠚⠁⠀⠀⠀⠆⠘⠁⠀⢀⣴⡚⠛⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⠃⢀⣾⡀⠂⠀⠀⢀⣠⠆⠀⠀⠀⠴⠹⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣦⣶⣿⡾⠟⠀⢀⣘⠶⠻⢷⣶⣷⣿⣧⡈⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣻⣯⣆⠋⣍⣤⣶⣾⣷⣿⡿⣟⡁⣦⣬⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡦
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠈
⠀⠀⠀⠀⠀⠀⠀⠙⡍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣦⣻⡿⣿⠛⠉⠻⣿⣿⣿⣿⣏⡹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⠛⢃⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣰⣙⣶⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⡏⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣋⣶⣾⣿⣿⡏⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣁⡙⠃⠀⣀⣿⣿⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⠟⡀⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠛⠉⠩⠙⣿⣧⣿⡙⢿⣿⣿⣿⣿⣿⠇⠀⠘⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⠇⠀⠈⣯⣍⡁⠈⠉⠠⠄⠀⢰⣾⠿⠟⣡⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⡿⣿⢂⣴⣶⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⢸⣿⣾⡟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⠛⠋⠛⢻⣭⠿⣿⠾
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⠿⣇⠉⠣⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠋⠿⠃⠀⠀⠀⢈⣿⣞⣹⣆⠆
⠀⠀⠀⠀⠀⠀⢸⣿⠉⢰⡿⠿⣆⠈⠳⣤⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⡀⠀⠀⣼⡻⠏⣻⡾⠃⢠⡖
⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣧⡈⢣⣼⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⡏⢳⠀⣿⣷⡄⣸⣇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⡙⣿⣿⠟⠋⣄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢠⠇⠀⢈⣿⣿⣿⢹⣿⠀⠄
⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⡹⣏⠀⢸⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⢻⠃⡦⢸⣿⡇⠰⠟⠙⠒⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠋⠙⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡁⠀⣧⣸⣇⢼⣿⣏⠐⡆⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣶⡾⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡷⠀⣿⣿⡅⢸⣿⠏⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢠⣿⣿⠇⢸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠁⢀⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⠆⢸⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡃⢲⣿⣟⣿⣿⣿⣿⡏⣿⣿⣿⣿⠏⠛⣿⣿⠀⠀⣿⡏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⢸⠁⠸⡏⠟⣟⢿⠀⢹⣿⣿⣿⠀⠀⢼⣿⡃⠰⣿⡇⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⢸⣷⢰⡇⠀⢻⣼⣇⠸⣿⡿⡟⠀⠀⢸⣿⣷⡀⢸⡄⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣾⡗⠸⠇⠀⠀⠻⣿⣦⣿⣿⠀⠀⠀⠀⢹⣿⣧⢼⠷⠷⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠸⢿⣿⠟⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⢀⠀⠠⠀⢀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠠⠀⠂⠀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⣀⠀⠀⠲⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣄⡀⠀⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⡄⠁⠀⠂⠀⠀⠀⠁⠀⠃⢀⡰⠍⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⡄⠀⠀⡄⡁⠈⢡⠀⠀⠀⠀⠀⣄⠀⠀⠀⠘⠉⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠉⠀⠈⠉⠀⠀⠰⠀⠀⣷⠍⡐⡄⠂⠀⠉⠁⠛⠸⣦⠀⠃⠀⡘⠃⢀⡔⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠳⣄⠄⣰⠈⠀⢙⡓⠀⠓⠐⠛⠀⠁⣙⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠱⠀⠀⠀⠘⠄
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⣵⠙⢤⠀⢀⡆⠀⠀⢠⢀⠀⠀⢠⢆⡀⠑⣶⠂⣠⠂⠊⠰⡀⢰⡡⠘⠀⠀⢰⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠘⢁⠾⠳⡿⠘⠍⢸⡆⠠⣂⣍⠀⠐⣴⣃⢈⡵⣀⣿⢸⡅⠀⠘⠃⠉⠀⠀⠀⠀⠤⠜⢁⣠⣴
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣉⣠⣿⠁⣰⢐⢀⡴⢷⣮⢡⣤⣆⣩⡿⠀⣩⠃⠺⠂⠄⠙⠁⠀⠀⠀⠂⠀⠀⠀⠈⢀⠟⠂
⠀⠀⠀⠀⠀⠀⠄⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣋⡿⣿⡛⣹⢿⣶⢶⣿⢾⢟⠻⢟⡇⣀⣻⡀⠸⠧⠠⠄⠀⠀⠐⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⢀⡠⠈⠁⠀⠉⠀⢿⡇⣿⢳⣥⡠⠌⣡⣍⣴⠟⢳⡜⣷⠃⣘⡀⡠⠀⠀⠈⠀⠁
⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠈⣿⣧⠞⣴⢷⠚⠑⢸⡟⠂⢿⠓⣿⡀⠛⠁
⠀⠀⠀⠐⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⡾⠁⠀⠀⠀⢀⠀⠀⠀⠈⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠏⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠒⠂⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⢠⣄⠴⠒⠉⠉⠉⠁⠀⠐⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣴⠞⣻⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠻⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠔⠀⠀⠈⠑⠢⠄⠑⠦⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠉⠀⠦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢃⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠐⠂⠀⠀⠰⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠑⠢⠤⢀⠀⠀⠀⠀⣀⡀⠀⠀⠂⠈⠢⠄⠀⠀⠀⠀⠤⠄⠤⣋⣀⣢⡌⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂


⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⣿⣿⣿⣿⠟⡿⠟⠙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠟⠟⠿⠇⠀⠁⠀⠀⠰⠈⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⢻⡟⠁⠀⠀⠈⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠿⠟⠿⣿⡿⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⣹⠇⠈⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⣤⠴⢤⣠⠶⢶⡄⠀⣼⣧⣤⡀⠀⠀⢀⣀⡈⠛⢦⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣏⡀⠀⠤⡄⠀⠉⠀⢾⣤⡄⣠⠞⠁⢹⠀⢐⣞⠉⣷⠂⠀⢹⠖⠋⠉⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣏⠀⣹⠀⣤⠟⠉⠀⠀⢀⣾⡞⠁⠀⠰⣏⠀⠀⠙⠛⠋⠀⢠⡏⣀⣀⣀⣀⣀⣀⠘⡇
⠀⠀⠀⠀⠀⠠⡏⠁⠀⣀⡟⠀⠀⠀⠀⠾⠋⢠⠆⠤⠞⢹⠃⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠉⠙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⢹⠃⠈⡯⠀⠀⠀⢀⡀⠀⠀⣸⠆⠀⠀⡾⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠠⡟⠁⡀⠻⠀⠤⣶⠋⠉⠋⠉⠁⢀⣤⡴⠃⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠙⠚⠛⠒⠲⣤⣻⡄⠀⠀⣶⠤⠾⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⡴⠛⣇⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠹⣆⠀⠀⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⠶⠋⢀⣠⠴⠋⠀⠀⠈⠳⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠘⠃⠘⠁⠀⠀⠀⠀⠀⠀⢻⠀⡴⢚⣉⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠤⠀⠀⠀⠸⣿⠗⠋⣡⠖⠒⠒⠲⠀⠀⠀⠶⠒⠒⠲⣄⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡞⠛⠀⠀⠀⠴⣾⡷⠆⠀⠀⠀⠠⢶⣷⠶⠀⠀⢀⠘⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⢠⣄⣠⡄⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠰⡟⠁⠀⢹⡖⠀⠀⣀⣀⣀⣨⡷⣿⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠚⢳⣄⣠⡼⠓⠀⣸⠉⠉⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠁⠀⠁⣀⡴⠃⢰⠟⠉⠙⣦⠀⠈⢷⣄⠀⠀⠐⠚⠛⠓⠂⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠛⠉⠀⠀⠸⣄⣀⣠⠟⠀⠀⢸⠉⠳⣄⡀⠀⠀⠀⢀⣤⠞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣼⠀⠀⠀⠙⠲⠶⠖⠋⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠈⣉⣉⣿⣿⣿⣿⠿⠿⠛⣛⣉⣥⠴⢶⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣠⣤⣴⣶⡾⠿⠟⢛⣋⣩⡥⠶⣖⣛⣯⠽⢶⣚⣻⣭⠵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣥⣶⣶⠿⠿⠛⣛⣉⣥⠴⢶⣚⣻⡭⠵⢖⣚⣯⡭⠶⠖⠛⠉⠉⢀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⡿⠿⠟⢛⣋⣩⡥⠴⣖⣛⣯⠭⠶⣚⣻⣭⠽⠶⠚⠋⠉⠁⢀⣀⠀⢠⣶⡖⢻⣿⡟⠋⠉
⠀⠀⠀⢰⡿⠿⠛⣛⣉⣭⠤⢶⣚⣻⡭⠽⢖⣚⣯⡭⠷⠖⠛⠉⠉⢀⣀⡀⠀⣴⣶⡄⠀⠸⣿⣇⣾⣿⠁⠈⣿⣿⠿⠿
⠀⠀⠀⠀⢖⣚⣯⡭⠷⣒⣻⣭⠽⠖⠚⠋⠉⠁⠀⣀⣤⣤⣴⣶⣿⣿⡟⠛⢰⣿⡿⣿⣦⠀⢿⣿⠿⣿⣦⡀⢹⣿⣦⣶⣶⠆
⠀⠀⠀⠀⠩⠷⠖⠛⠉⠉⠀⠀⣠⣤⡀⢶⣿⡀⣾⣿⣉⡙⠀⠀⠸⣿⣇⠀⢸⣿⣷⡾⢿⣷⣸⣿⣇⠈⠻⠿⠚⠋⠉⠁⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣤⣦⣄⠀⠀⢀⣿⣿⣇⠸⣿⣧⠙⠿⠿⢿⣿⡆⠀⢻⣿⡄⣾⣿⠀⠀⠈⠛⠉⠉⠀⣀⣀⣤⠤⠶⣒⣻⣭⠽⣆
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⣼⣿⢹⣿⡄⢻⣿⡀⣶⣶⣾⡿⠃⠀⠘⠋⠁⠀⢀⣀⣠⣤⠴⢖⣚⣫⡭⠷⣒⣛⣭⠽⠶⠚⣋⣩⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣧⠙⢿⣿⠇⠀⣿⡧⠘⠟⠃⠀⠉⠀⣀⣀⣤⡤⠶⣒⣻⣭⠽⢖⣚⣫⡭⠷⠖⢛⣋⣭⣤⣶⣶⣿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⢖⣚⣯⡭⠷⣖⣛⣭⠽⠶⠚⣋⣩⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⣖⣛⣭⠽⢶⣚⣫⡭⠷⠖⢛⣉⣩⣤⣶⣶⡿⠿⠛⠛⠉⢉⣤⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠨⠷⣖⣛⣭⠽⠶⠚⣛⣉⣥⣴⣶⣾⣿⠟⠛⠋⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⡞⢙⡦⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠉⠁⠈⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠋⣹⠃⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣏⢀⡼⣇⠀⠀⠀⣿⠀⠀⠀⠀⣠⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠉⠀⠙⢦⣤⡴⠃⠀⠀⠀⢠⡇⠀⠀⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡀⠀⠀⠀⣾⠀⡀⠀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡴⠖⠳⣤⠶⠛⠁⠀⠙⢷⡀⠀⠉⠉⣿⠀⣠⠞⠁⠠⢖⣛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢠⡄⠀⠀⠹⣄⠀⢰⣧⠞⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⠀⠀⠀⠀⠹⡄⠘⠁⠀⣠⠶⠒⠛⠛⠉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⣰⠇⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⢀⣀⣀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠲⠀⠀⠀⣿⠀⣴⠋⠀⠀⠀⢠⡄⠀⠘⡇⠀⠀⡇⠀⠀⣴⠋⠀⠈⢳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠏⠀⠀⠀⢀⡿⠞⠁⠀⠀⠀⣰⠏⠀⠀⠀⡇⠀⠀⣇⠀⠀⠙⢦⠄⡶⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠚⠉⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⢠⣏⣀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⣷⡀⠀⠀⣀⣠⡴⣾⣋⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⠉⠉⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⠴⠖⠋⠉⠛⠛⠉⠉⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀⣼⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⠁⠀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⢹⡏⠛⣿⠖⠒⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⣠⣤⠤⠞⢳⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⢠⡟⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⠲⢤⡄⠸⣇⠀⠹⣤⣀⣤⣤⣤⠤⠤⠶⢰⢇⡟⣼⠃⠀⠀⠠⠶⠶⡶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠐⠲⠶⠶⠖⠛⣆⠀⠀⢈⡇⠀⠀⠀⠀⠀⣟⠸⠀⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⠛⠒⠶⠶⢤⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠳⠶⠶⠦⠤⠤⠤⠤⠤⠶⠛⠀⠀⠀⠀⢧⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠴⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠐⠲⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡅⠀⠝⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠄⠀⠤⠀⠀⠀⠀⠀⠠⠾⠥⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣈⠲
⠀⠀⠀⠀⠀⠀⠀⢄⠬⢞⣿⠀⠀⠀⠀⠀⠀⠐⠐⠀⠛⠒⠲⠤⠀⠀⠀⠀⠄⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⠛
⠀⠀⠀⢀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢒⢀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡄⣤⡀⢠⠆⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠘⠈⠁⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⡀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⡀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡠⠀⠁⠒⠄
⠀⠀⠀⠀⠰⠀⠀⠁⣁⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠁⠀⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠁⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⠠⠀⠠⠀⠀⠀⠀⠀⡀⠘⠒⠒⠀⢤⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡀⠀⠀⠀⠀⢀⣐⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⠸⢳⣆⠀⠘⠈⠙⠁⠂⣶
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡉⠀⠀⠀⠀⠈⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠘⠛⢦⣌⠁⠀⣁⠲⠖⠛⠚⠛
⠀⠀⠀⠀⠈⢁⠠⠉⠈⠉⠋⠭⠀⠀⠀⠀⠁⢠⠀⠁⠅⠀⠀⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠴⠍⠋⠁⠀⡀
⠀⠀⠠⠤⠴⠀⠠⢀⠔⠒⠉⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠂⠀⠀⠂⠀⠀⡀⠑⢤⣤⡑⣀⡍
⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣤⠀⠐⣶⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠁
⠀⣰⠖⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⠛⠃⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠨
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡄⠀⠀⠠⠒⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣠⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⢀⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠦⠀⠀⡚⠙⡁⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⠋⠁⠀⠠⠐⠠⠈⠋
⠀⠀⠀⠀⠀⠄⢆⠉⠀⠁⢈⣀⡀⠀⠀⠀⠐⠦⠚⠀⢀⡀⠦⣄⠐⠂⠀⠀⠀⠀⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠀⡀⠀⠁⣴⡆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠊⠈⠁⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢀⠀⠀⠀⠀⠀⢀⢀⡰⡔
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⣐⢂⠌⠠⡑⠮⠕⢉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢜⠓⠛⠐⠠⠝⠑⠦⠓⠆⠠⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⡿⠿⢟⣛⣹⡿⢿⣿⡿⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⡿⠿⠟⣛⣫⣭⣶⣶⣿⠿⢛⣫⣾⣷⣶⣶⣷⣌⡛⠿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⠿⠟⣛⣫⣭⡶⠖⣛⣛⣛⠿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣤⣶⡆⣿⣿⣋⣭⣴⣶⣿⣿⣿⡿⣩⣶⣿⣿⣿⣿⣿⣦⣽⢫⣾⣿⣿⣿⢟⣭⣬⣭⡻⣿⣿⣿⣷⡌⣿⣿⣇
⠀⠀⠀⠀⠀⠈⠉⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣿⡿⣩⣶⣶⣦⡙⣿⣿⡇⣿⣿⣿⣏⢸⣿⣿⣿⡷⢹⣿⣿⣿⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⡇⣸⣿⡘⢿⣿⣿⣿⣮⡛⠿⢛⣡⣿⣿⣿⡿⢃⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡘⣿⣿⣬⣛⢟⣋⣵⣿⡿⢿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣌⡻⢿⣿⣿⣿⠿⢛⣵⣿⣿⣮⣭⡛⢿⡿⠿⢿⡿⢛⣭⣵⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠂⠐⢀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠉⢠⡈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠐
⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠑⢤⠀⠈⠃⠐⠄⠀⠀⠀⠀⠀⠑⠠⠐⠐
⠀⠀⠀⠀⣀⠀⠀⠘⣃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⡾⠛⠀⠀⠀⠈
⠀⠀⢰⢔⣽⠄⢀⣼⡿⣶⡄⠀⠹⠛⠿⣷⣦⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠱⠒⠀⠀⠀⠈⢿⡽⠷⠛⠉⠀⠀⠀⠀⠀⠀⢶⣢⠀⠀⠉
⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠘⠀⠢⠄⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⡠⠖⠀⠀⠀⠀⣿⣿⣻⣿⡆⠀⠀⢀⣰⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⡄⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠼⠂
⠀⠀⠀⡀⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠬⣤⢁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠤⢄⠀⠀⠀⠐⠀⠀⠀⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⠀⡀⡤⢦⡄
⣰⠀⠌⠁⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣆⠰⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀
⠀⠖⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠊⠂⠀⠠⠀⢀⡀⠑⠕⠢⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⣲⣿⣾⢁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⡴⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠋⠚⠁⣿⣀⣠⠟⢚⡷⠶⢀⡤⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠐⠋⠤⣀⠐⠀⠀⠀⠀⣀⠠⠖⠨
⠀⠀⡄⠀⠀⠀⢀⡀⢀⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⠠⠎⠀⣰⠟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⡁⠀⠂⠀⠀⠀⠀⠐⠆
⠔⠈⠀⠀⠀⠀⢸⣥⡛⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠈⠀⠀⢀
⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣤⣤⣤⡄⠞⠃⠘⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠸⠷⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣿⣿⣯⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡀⡖⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣉⣡⠔⠂⠀⠀⠹⣿⣿
⠛⢉⡉⠉⠀⠀⠀⠜⢀⠂⠀⡄⠀⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠉⠀⠐⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⡄⠐⠀⠀⠄⠀⠀⠀⣠⠁⠀⠀⠠⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⢠⠀⢒⠀⠀⠀⠀⠐⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠠⠀⠀⠇⠀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠞⢀⠈⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠂⠸⠀⠀⠀⠄⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⡶⣆⣀⠐⠃⠀⢀⢰⣯⡴⢇⡴⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠈⠁⠓⠆⢹⠄⠀⣴⣟⣸⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⣤⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⢽⣿⣿⣿⠀⠀⢰⣿⢀⣀⣸⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣛⣁⣀⣽⣿⣿⣿⠀⠀⢸⣿⢨⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⠛⠛⠛⠛⠋⠀⠀⢸⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠘⠛⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠈⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⣴⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡦⠀⠻⠟⢀⣴⣶⣦⡀⠀⠀⠀⠀⢀⣠⣄⡀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠈⠛⣿⣿⠀⠀⠀⠀⢸⣿⣿⣤⣄⠀⠀⠀⢠⣿⡿⢿⣿⣸⣿⣷⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡄⣿⣿⣦⣦⠀⠀⢀⣙⣋⣉⣿⡆⠀⠀⠸⣿⣄⣠⣿⠋⣿⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠘⠿⠿⠏⠀⠀⠘⠻⠿⠿⠛⠀⠀⠀⠀⠙⠿⠟⠃⠀⠙⠁⠙⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡤⡧⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣇⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢺⠃⠀⡀⢀⣏⣀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣏⡽⠀⠀⡟⡿⢹⣀⣯⢿⡼⠿⣁⣸⣟⣀⠀⠀⠀⠏⡷⢳⡴⣇⣤⣳⠜⢤⠾⠿⠞⠿⠧⡴⣟⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⡿⢿⣿⣷⣶⣦⣤⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣾⣍⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⣾⡿⠁⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⡀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠘⣿⣇⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠹⣿⣦⡀⠀⠀⠀⠀⠰⠶⣶⣤⣀⠀⠀⠀⠰⣿⡇⠀⠀⠈⠻⣿⣄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣶⠛⣏⠙⣆⣈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⡶⢶⠞⢟⢛⣏⣹⣆⣽⡦⠾⠛⠋⠁⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷

⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠲⣄⢰⠀⢰⢦⠀⣶⠒⣦⢰⡖⢶⢠⡆⢀⡆⣴⠒⠂⢀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣠⠟⢸⢠⡟⠺⡇⠿⠙⢧⢸⠋⢿⠸⡏⠉⡇⢿⣍⡁⡼⠓⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⣩⣭⣭⣭⣭⣭⣙⡛⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⣀⣙⠛⠛⠛⠿⠿⠿⠿⠂⠀⢀⣈⣽⣷⠟⠛⣿⠛⠳⠶⠶⠶⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠉⣉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠘⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠆⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⣀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠟⢀⣠⣤⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠟⠋⠙⠷⠶⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠉⢿⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣟⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⢳⢾⣿⡟⠰⠀⠀⠀⡴⠃⠀⠀⠙⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠡⠟⠸⡛⣛⣯⡿⠁
⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⢿⠰⣾⡳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣛⢣⣬⣤⣂⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⡹⠟⣼⠁⢹⣆⠙⣯⠘⡿⠇⠀⠀⠀⠀⠀⠀⠈⠈⠙⠽⢿⣿⣿⣿⣿⡿⠿⠋⣀⣀⠔⠁
⠀⠀⠀⠀⠘⢿⡇⡄⠀⠀⢨⣭⣶⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⠀⠀⣿⠂⡸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⣠⣴⣶⣾⣭⡏
⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠠⣿⣿⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠘⢀⢙⡝⡃⠀⡈⢹⠀⠀⠠⠤⢴⡗⠀⠀⠀⠀⢠⣾⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠈⠙⠻⠅⢈⡉⠉⠌⠋⠓⠊⠣⡜⠀⠀⠀⠀⠾⠇⠀⠀⠀⣠⣿⣿⠿⢿⣿⣬⣿⠆
⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢸⢹⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠰⠾⠒⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⣶⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⢠⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣀⠀⢿⣿⠷⠶⠶⠀⠀⠀⠐⠺⣷⣿⣿⣄
⠀⠀⠀⠀⢀⣿⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⡿⢟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡧⢼⣿⣢⣾⡁⠈⣿⡃⠀⠀⠀⠀⠀⠠⢶⣯⣿⠁⠀⠉⠁
⠀⠀⠀⠀⠸⠁⣿⠀⠀⢀⣤⣿⣧⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢹⡇⣶⣯⡘⠛⠟⠛⠻⠏⠁⠀⠀⠀⠾⣴⣿⠃⠀⢰⣦
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠿⠏⣼⡿⠀⠀⠀⠸⠛⣻⡄⠀⠀⠀⠀⠠⠿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢁⣾⣿⣷⡀
⠀⠀⠀⠠⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢠⣤⣤⣠⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠀⠉⠀⣤⠀⠀⠀⠀⠀⢸⣿⣯⠏
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⠃⠀⢠⠄⠀⠀⠀⣶⡟⠀⠀⠀⠸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣾
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢾⣦⣠⣸⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠐⢀⠀⢀⣀⣸⣦⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣧⣬⣿⣧⣼⣿⣵⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠶⠦⢄⡓⠚⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢰⣶⣯⣀⣀⣀⣀⠗⠻⠿⣿⠷⣤⡀⠀⠀⢲⣦⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡼
⠀⠀⠀⠀⠀⠉⠁⠀⠐⣲⢇⡦⣶⡙⡀⡉⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠊⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄⣀⣀⣸⠀⠴⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡰⠋⠸⠀⢿⠓⠈⢄⣈⠄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠀⠀⡠⣿⠟⠁⠀⢠⣀⣼⠀⠀⠐⠉⠘⠀⠀⠀⠙⠛⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⢀⣀⠀⣾⣻⡆⢠⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠷⠂⠀⠀⠀⠀⠀⠠⢄⣀⣄⠀⠀⢠⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠈⢹⣯⡿⠷⠏⠀⠀⠰⣿⠆⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⠶⠶⣄⢀⣀⡽⠉⠁⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉
⡇
⠃
⡆
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣷⣦⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⢫⣿⣿⣿⣿⣏⠛⢿⣿⣶⣤⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀⠿⠿⣿⣿⠿⠿⠇⠀⠀⠙⠻⣿⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⣀⣤⣿⣿⣦⣀⠀⠀⠀⠀⠀⢿⣿⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⣀⣤⣶⣿⡿⠿⣿⣿⠿⣿⣿⣶⣤⡀⠀⠘⣿⣷⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣰⣿⣿⣶⣿⡿⠟⠋⠁⠀⠀⣿⣿⠀⠀⠉⠛⢿⣿⣷⣦⣽⣿⣧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣏⡁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣶⣿⣧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡈⠙⠛⠿⣿⣷⣶⣤⣀⠀⠀⣿⣿⠀⣀⣠⣤⣶⣾⣿⣿⠿⠟⣻⣿⡟⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣿⣿⣿⠿⠿⠟⠋⠉⠀⠀⠀⣼⣿⡟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣼⣿⠟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢀⣾⣿⠏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣡⣿⣿⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃
⡇
⡇
⡇
⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⣠⡌⠀⠀⠀⢠⣤⡀⠁⠀⠀⠀⠀⣾⣷
⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⣿⣿⣷⠈⠀⠀⠀⣰⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⣀⡀⣴⣦
⠀⠀⠀⠈⢻⣿⣿⢿⠀⠀⠀⠀⠈⢹⣿⣿⣻⠀⠀⠀⠀⠙⣿⣿⡿⠁⠀⠀⠀⠛⣿⣿⡏⠁⠀⣠⣾⣿⠋⠉⡉
⠀⠀⠀⠀⢸⣿⣿⠈⠀⠀⠀⠀⠀⢸⣿⣿⠈⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠙⢿⣿⡀⠀⢹⡀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣴⡟⠁⠀⢸⣇
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⠉⠃⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠈⠋⠀⠀⠈⠉⠉⠁
⠀⠀⠁⠈⠈⠀⠈⠈⠁⠁⠀⠀⠈⠈⠀⠉⠀⠀⠀⠀⠉⠁⠁⠀⠁⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⢠⣾⣿⣿⠋⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⠀⠀⠀⠈⢻⣿⣿⠇⠐⠒⠂⠀⠀⠀⠀⠀⣾⡿⠈⠛⠁⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢰⣶⡼⣿⣿⣤⣤⠀⠀⢰⣶⡼⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⡇⠀⠀⢸⣿⣿⣿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠋⠙⠁⠀⠀⠀⠀⠈⠋⠙⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠛⠀⠀⠀⠈⠛⠛⠛⠁⠋
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠀⠀⠈⠈⠉⠈⠈⠀⠀⠀⠀⠀⠁⠈⠉
⠀⠀⠀⠀⠀⢿⠷⠀⢀⠀⠀⠀⠀⢾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⣶⣿⣷⠶⠆⠀⠀⠀⣴⣿⣿⡿⠷⠀⠀⠀⠀⠀⢠⣶⣦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡀
⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⢀⡿⣿⣿⡇⠀⠀⠀⠀⢰⣰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠈⠀⣿⣿⡇⠀⠀⠀⠀⢸⠙⣿⣿⣯⢿⠶⠶⠾⠿⢶⠆⠀⠀⠀⠀⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⠒⢺⣿⣿⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠋⠛⠁⠀⠀⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠘⠉⠙⠋⠛⠘⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠹⣧⡀⠀⠀⠀⢀⣰⠿⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠈⢳⣼⣦⠈⠻⠷⠶⠶⣿⡟⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠃⠉⠳⡀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠠⠤⣼⡷⠦⠄⠀⠀⣼⠟⠀⠀⣰⣶⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢀⣀⣅⣀⣠⣤⣼⠏⠀⠀⢰⡿⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢰⡟⠉⠉⠉⠉⠉⠉⠀⠀⢠⡿⠁⣿⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠘⢷⣤⣤⣤⣤⣤⣤⣤⣴⣿⣡⣤⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣧⣤⣿⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣯⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢻⡇⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢸⣧⠀⠀⠙⢻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢠⣿⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢾⣿⣧⡶⠟⢋⣁⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡶⢶⣄⠘⢿⣛⣥⣤⣾⣻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣯⡿⢟⣽⣷⡄⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀
⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⣤⠖⣊⡤⢚⣩⡶⢟⣫⣵⣾⣿⢿⣿⠟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢪⣤⡾⢋⢔⣷⡿
⠀⠀⠀⠀⣀⡘⣷⠚⣛⢉⡥⢞⣵⠶⠋⣡⣶⣿⣿⢿⣯⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣊⣾⣿⢿⡿⣯⡾⠋
⠀⠀⠀⠀⢿⠉⢿⣽⠻⡧⠞⠋⣁⣴⣿⡿⢿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣾⡿⢏⡴⢫⣾⠟
⠀⠀⠀⠀⢀⣄⣀⠻⡆⣻⣶⣿⣿⠟⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⣱⣾⡿⢛⣷⢟⣵⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠃⠁⠀⠛⠻⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⠀⠀⣀⠠⣄⣾⠟⠋⣸⡿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠘⠏⢿⠿⢿⣶⣾⡿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⢹⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠰⡆⠀⠌⣩⡼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠠⠤⠌⠳⡀⣿⢀⣴⠟⠋⠀⢒⣶⡶⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠈⠱⣶⣶⣶⣽⡉⢻⡿⠷⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⣾⡿⢿⣯⢿⢯⣀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣿⡟⠛
⠀⠀⠀⠘⠃⠈⠀⠀⠀⠤⠶⠟⠛⠉⠐⢁⡏⢿⡀⠙⠙⠛⠷⠞⠓⠀⠒⠀⠀⠀⠀⠀⠘⠾⢿⠿⠿⢿⠿⠟⠟⢿⣿⣿⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠃⠘⢧⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠚⠒⠈⠻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠓⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⣨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠛⠁⠀⠀⣰⣿⣉⣹⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠛⢡⡾⠋⠀⠀⠀⠈⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠷⣤⡀⠀⢻⣄⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⢻⡄⠀⠙⠻⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢀⡄⠀⠀⠀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⣴⠶⠒⠲⢶⡄⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢸⡇⠀⠀⠀⣿⢀⣼⠃⠀⠀⣠⠟⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⣿⠀⠀⠀⢠⣿⡾⠁⠀⢠⡾⠃⢠⣾⣯⣥⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠀⠉⠀⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⠁⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⣴⠋⠛⠲⠶⣤⣄⡀⣸⠇⠀⠀⠀⣿⠀⠀⠀⠀⠈⠁⠀⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⢸⡷⠴⠦⠴⠦⠴⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠘⣧⡀⣀⡀⣸⡇⠀⣿⠀⢸⡇⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⢻⡏⠀⠀⣿⣀⣸⣇⣀⣀⣀⣙⣶⣄⣀⣀⣀⣀⣀⣳⣄⣠⣴⣏⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⣧⣀⣈⣷⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣉⣉⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣀⣤⡴⠞⠋⠁⢠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠁⠹⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣈⣷⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤
⠧⠤⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⣀⠀⠀⢀⣀⡀⠀⡀⠀⣀⢀⠀⢀⠀⠀⣀⡀⠀⢀⡀⠀⢀⣀⠀⡀⣀⠀⢀⣀⡀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⠁⠀⡧⢸⠀⢸⠀⣘⣡⠀⣯⠸⠃⢸⠀⠀⡧⠄⠀⠘⠦⡀⠀⡇⠀⡧⢬⠠⡃⠀⢹⠀⡶⡁⠰⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣦⣼⣦⣾⣥⣼⣤⣬⣤⣥⣬⣧⣷⣶⣥⣴⣦⣤⣶⣦⣤⣤⣶⣭⣤⣧⣤⣧⣬⣤⣷⣶⣯⣤⣦⣽⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣰⣾⣶⣄⠀⢨⡅⢾⣷⠀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠀⠀⠀⢿⣿⣭⡛⣷⣴⣞⡙⠛⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡟⠱⠀⢢⡆⠀⠉⣋⣉⣿⣟⠻⠇⠀⠀⠈⢳⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣯⠈⠁⠀⠀⣾⣿⢶⣌⣻⣻⡿⠃⠀⢠⡄⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣿⠀⡀⠠⠄⢿⣷⣶⣯⣿⣿⣿⣿⣶⣶⣤⡝⠓⣿⡿⠁⢒⣤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠘⢋⠚⢀⣶⣶⡀⢻⡿⠋⠙⠏⠙⢻⣿⣿⡅⢠⣴⣿⣇⣴⢿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣜⣹⡄⣾⣿⣿⣷⣿⣤⣦⠀⠘⠻⠞⠿⣯⠻⣿⠿⣿⣻⣿⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡄⢿⠟⠙⠻⣿⣿⣿⡶⣦⣴⣶⣶⣤⣀⡈⣂⣼⣹⡿⢿⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣩⣶⣤⣾⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢴⣦⠛⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⡟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣿⣿⡿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡼⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⡟⠀⢈⡝⣿⢿⣿⣿⣷⣴⣎⠈⠉⢿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣷⠚⡈⠹⣿⡎⣻⣿⣿⣿⣿⣷⠟⣶⣤⡉⡫⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠛⢿⣿⣿⣿⣧⡼⠖⣿⠀⢿⣿⣿⣿⣿⣿⠃⣹⣿⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣿⣿⣧⣼⣿⣧⣸⣿⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿⡿⠿⠶⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⠛⠆⠠⠀⠈⣿⣷⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡟⣿⣿⣿⣿⡆⠀⠀⠀⠁⠐⡜⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣤⣀⣤⣤⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣾⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣀⠀⢠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣿⢿⣿⣿⣿⣮⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠹⣿⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⣿⣹⣿⣿⣿⣿⢏⣿⣿⡟⠀⠠⣌⢿⣿⣿⣿⣿⣿⣿⠈⣿⣿⠀⠙⣿⣿⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⡁⢏⣵⠇⣸⢟⣸⣿⡏⠉⢶⣄⠈⠲⣿⣿⣿⣿⣿⣿⡇⣿⣿⡄⠀⢿⣅⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣱⣤⡴⢦⡅⠈⡿⣿⣿⡷⣀⠙⠃⠀⠀⢉⣿⣿⣿⣿⣷⡿⣿⣿⣀⣨⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣧⡰⠛⣧⠞⢳⢾⣏⠃⠈⣁⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣟⢙⠀⡿⠀⠀⣾⡿⢧⣼⣿⡇⣼⡇⢹⣿⣿⣿⣿⣿⣿⣱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⢰⣶⡆⢿⣦⡄⠙⠀⠀⣤⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠄⡸⣿⠀⠬⠙⢷⠀⢠⡤⠋⣾⣿⣽⣇⠘⠋⠙⣿⣿⢹⠟⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠃⣠⠟⠀⠀⠀⠊⠀⠈⠀⣄⡼⢿⣿⣿⣿⡐⠀⢸⣿⠉⢠⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢰⡾⠀⠀⠀⠁⡈⠙⠷⣾⣿⣿⠟⠋⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⢀⠄⠠⣷⢰⣶⣿⠿⠿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⢛⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣙⠻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⣴⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⡌⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⢡⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠟⠃⠹⣿⣿⣿⣿⠿⢂⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠺⢿⣿⣿⣿⡿⠁⠛⢿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⣀⣤⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠘⢛⣩⣤⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣬⣙⠛⠁⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣄⡀
⢀⣤⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦
⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⣉⣉⣍⣉⡙⠋⣉⣭⣉⡉⠛⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⣠⣾⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣷⡄⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣧⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣾⣿⣿⣿⣿⣿⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣷⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠛⣛⣉⣉⣉⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢉⣉⣉⣙⡛⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠠⠿⠿⠿⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠹⠿⠿⠿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⠀⡤⠀⠠⠀⠂⢀⠀⠀⠀⠀⡀⠀⠄⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠌⠀⠄⠀⠀⠀⠐⣀⠄⢰⠀⠁⠀⠀⠀⡇⢠⡄⢀⠀⠀⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⣂⢀⣀⣀⣀⣀⠀⠀⠀⣘⠀⢂⣀⣀⡀⠁⣀⠀⠀⣂⡀⣀⣀⡀⢸⣀⣀⡀
⣿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠞⠃⠞⠀⠀⠸⡀⠀⠀⠀⢀⠄⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⡌⠓⣄⠀⠀⢣⢀⠀⡰⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠧⠒⢬⠦⠀⠈⠶⠉⠱⡾⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠸⡀⣺⠧⠄⠰⠎⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠠⢉⠇⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢲⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⡀⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠽⠍⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠀⢾⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⡉⠀⠉⣇⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠑⠛⠤⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣧⢽⠀⠀⠈⡓⢨⠦⢄⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠐⠂⠤⣀⡉⠑⠒⠂⠤⠤⠄⠀⢀⠀⢣⠰⢿⡓⢊⣠⠁⠀⣠⠋⠀⠀⢨⡉⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠐⠢⠄⣀⠀⣠⠂⠑⢆⠀⠀⠉⠀⠉⡠⠊⠁⠀⠀⠀⠸⣁⠁⠢⢀⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠁⠀⠀⣈⡄⢂⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⡏⢰⢦⡀⠹⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠐⠆⠀⣀⢀⡀⠧⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠈⢻⠒⠐⡒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠧⣀⣀⣀⣀⣀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢀⡠⠀⣋⠉⠉⠩⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠻⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢓⣄⠰⠀⡏⠀⠀⠀⣶⠢⠄⠀⠀⠀⠰⢆⠆⠘⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⢸⠀⠃⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⣮⠴⠀⠐⠒⠚⠲⠡⡚⣤⡤⣤⣤⠦⠞⣰⠞⠁⠀⠀⠀⠀⠀⠀⡀⠤⠠⢄⡁⢸⢸⠀⢤⣇⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢦⡀⠀⠀⠀⠀⠀⠉⢣⣦⣟⣧⣬⣬⡁⠀⠀⠀⠀⣀⢠⠔⠁⠐⠢⠀⠀⠑⠞⣼
⠀⠀⠀⠀⠀⢀⢠⡠⢆⠀⠀⠀⠀⠈⠂⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠈⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⡄⣠⢄⣀⠕⡿
⠀⠀⣠⠔⠊⠙⠯⠈⣉⠐⣋⠸⠥⠃⠀⠀⠀⠀⢀⡀⠐⢦⠀⠐⢐⠄⡀⠀⠀⣀⠀⠀⠀⠀⠀⢤⣤⣀⣀⢀⠀⠀⠀⠈⠁⠉⠀⠀⠧⠄⠽⠊
⠐⠎⣀⣀⠤⠄⠒⠈⠉⠁⠀⠀⠀⣠⠴⣇⢠⠀⡞⠉⠐⠚⠀⠀⠀⢀⣀⠀⢀⠼⠂⠀⠀⠀⠐⠃⠀⠀⠘⢯⠷⠤⠠⠄⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠁⠀⠀⠀⠀⠀⠠⠄⠥⠊⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠿⢿⣟⡛⠛⠛⠳⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⣰⠟⠁⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣴⠶⠷⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⢹⡷⠄⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇⠀⠀⠀⣤⣤⣄⣀⣈⣻⣄⠀⠀⣀⣠⣤⣾⣁⣀⣿⣼⣟⡃⠀⠀⢠⣿⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⠁⠀⠙⣯⡉⠉⠙⢿⣅⣀⣠⡾⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⡇⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠓⠶⠶⠶⠶⣤⣠⡴⠟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⢀⣀⣀⣀⡀⣀⢀⣀⢀⣀⣀⣀⡀
⣀⣈⣁⣀⣁⣈⣁⣀⣀⣁⣀⣈⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢛⣻⣻⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⣀⣠⣀⣀⣀⡆⠀⠀⠀⢀⠀⠀⠠⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣟⣙⣿⣿⣿⣷⣤⣰⣿⣷⣼⣷⣶⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⡿⣻⣄⣻⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⣟⣿⠟⡻⣶⣯⣿⣿⡟⢿⣿⣿⣿⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⢡⣏⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠄⠀⠊⠈⠛⣿⡿⢻⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣠⣼⣷⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣦⡠⢄⢋⣹⢿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⣾⢿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⣮⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠖⠒⠒⠠⠄⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢨⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⣦⣶⠶⠶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢈⠲⠀⠀⠀⠀⠈⠀⠀⠀⠰⣏⠰⣈⣉⠑⠪⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢄⠒⠢⠛⠺⡰⡆⠀⠀⠀⢀⠀⠀⠀⠐⡈⠳⢤⡍⡉⠒⢚⣠⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⡍⠀⣀⣂⡄⠀⡴⠟⢟⠐⠒⠃⢄⡀⠀⠀⢡⡀⠀⠈⢉⣉⣉⠝⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⡁⠀⠉⠀⢀⣤⣥⡤⣌⠂⠀⠀⠀⠑⢄⠈⠓⠩⢐⡒⠉⠉⠒⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠢⣀⠠⠭⠅⠀⣀⠝⠰⠀⠀⠀⠀⠀⠑⠄⢀⡀⠈⠁⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠠⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠤⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡭⠝⠋⠙⠲⡛⠮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠢⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢤⠀⣀⣀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢰⠡⠀⢖⠀⠀⠺⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠣⣀⣄⣀⠀⠠⠄⠂⠀⠀⠐⢄⡤⠴⠛⠀⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠉⠅⠀⠀⠀⠀⠀⠀⢠⣤⣕⣂⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠒⡐⠄⠀⠀⠀⠀⠐⢁⠈⠀⠀⠀⢀⠀⠊⠀⠐⢄
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠂⡀⠀⠂⠀⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠠⡀
⠠⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⡤⠉⠐⠠⠁⠄⢐⠀⠀⠀⠄⠀⠀⢀⣀⣀⣴⣶⣶⣦⡀⠀⠀⠀⠄⠁⠂⠈⠑⢆⠀⠀⠀⠀⠀⠨⠆⠐⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠴⠂⠀⠀⠀⠀⠈⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣿⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢹⣿⠿⠛⠉⠀⡈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⣐⠁⠀⠀⢙⡇⠘⠀⠀⠀⠊⠀⣕⠀⠑⣄⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⡔⠉⡇⠀⠀⠀⠀⠀⠀⠦⣀⣴⣿⣧⡀⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠀⣀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏⠀⠀⠂⡀⠀⠀⠀⡀⠔⠀⠈⠻⣿⣿⣿⣄⠀⠀⠀⠁⠀⠄
⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⠀⠉⠀⠀⠀⠈⡅⠈⠀⠀⠀⠃⠀⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⢀⣀⣤⡔⠀⠁⠀⠁⣶⣤⣀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣥⣴⣶⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣷⣦⣄⣻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⢀⢔⡶⠞⠳⢄
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠑⠌⠳⣄
⠀⠀⠀⠀⠀⠀⠈⢃⠀⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⢦⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢅⣀⣁⣤⡼⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠿⠶⠶⠩
⠀⠀⠀⠀⠀⣠⠎⠳⡄⠘⣧⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠅⢢⡀⢈⠢⡘⣧⠀⠀⠢⡀⠀⠘⢦⡀⠀⠀⠀⠀⣰⠃⠀⠠⠀⠀⠀⠀⢳⡀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⢆⠁⠀⠱⣌⢾⣷⡄⠀⠈⠓⢦⡈⠻⣦⡀⠀⡼⡉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⢒⠚⠓⠊⠀⠀⠤⡀⠀⢀⠔⠈⠳⣄⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠘⢧⡙⢿⣆⠀⠀⠀⠙⠷⣌⡻⢦⡀⠑⠄⠀⠠⡀⠀⢀⠀⠀⠇⠀⠀⠀⢀⠔⠁⢀⠀⠘⢦⠀⠀⠐⠂⠀⠳⡄⠀⡼⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⠀⠀⠙⢦⡻⣧⡀⠀⠀⠀⠀⠙⢮⣷⣤⠀⠀⠀⠑⠀⠈⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢁⣰⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡾⠉⠉⠙⠳⣤⣀⠀⠙⢌⠻⣤⡀⠀⠀⠀⠀⠈⠻⢷⣄⡐⠆⠀⢀⡀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢷⠤⡤⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢄⡀⠀⠉⠳⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠢⡉⠻⣦⢤⣨⣤⠟⢻⡄⠀⠀⠀⠀⠀⠀⠠⠊⠀⠐⠘⠂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⢻⡀⠀⠀⠙⣆⠀⠀⠻⣆⠀⠀⠀⠈⡳⢦⡀⠀⠀⠀⠈⠀⠈⠳⢦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠶⠦⣦⣄
⠀⠀⠀⠀⡜⠀⢄⣳⡄⠀⠀⠉⠳⣄⠀⢻⣧⡀⠀⠀⠙⠦⣝⢦⡀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⠛⠖⢲⡶⠓⠛⠉⠀⠐⠒⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠐⡇⠀⠀⠱⣿⣄⡀⠀⠀⠘⣧⡾⠦⠿⣦⡀⠀⠀⠈⠳⢽⣷⣄⠐⢦⠀⠀⠀⠀⠈⠳⢦⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢻⠀⠀⠀⠈⢳⡉⠓⠒⠚⡇⠙⢦⡀⠀⠉⠓⠲⢤⡀⠀⠉⠻⢿⣦⣑⠀⠀⠀⠀⠀⠀⠙⢦⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠶⡶⠚⠉
⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠙⠲⢄⠠⡇⠀⠀⠻⣦⡀⠀⠀⠀⠳⣤⡀⠀⠀⠹⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠑
⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⢷⠀⠀⠀⠀⠙⠪⣽⣦⡀⠀⠀⠀⠀⠀⠙⢦⡑⠢⠀⠀⠀⠀⠀⣠⡿⠀⠁
⠀⠀⠀⠀⠀⣀⣠⣤⣭⡿⠶⠖⠋⡎⣷⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠉⠳⣄⠀⠀⠀⠀⠀⠙⠳⢶⣤⠤⠶⠛⠁
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⣇⠈⢧⣀⠀⠀⠀⠀⠀⠀⠙⢦⣾⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡀⠀⠀⠀⠈⢦
⠀⠀⡏⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⠙⢷⣄⠈⠙⠳⢶⣤⣠⣤⣴⠾⢿⣆⣰⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠘⡆
⢀⣠⣤⡴⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⡆⠈⠳⣤⣀⠀⠀⢀⣀⡼⢧⣤⡼⠋⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣴⡏
⠛⠛⠉⠠⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢀⡤⠤⠤⠭⠭⠭⠭⠴⠖⠋⠁⣠⠾⠋⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠉⠓⠒⠒⠛⠋⠁⢀⣰⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠁⠀⠀⠀⠙⢦⣀⣠⣤⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠟⠛⠛⠷⠶⠶⢶⣶⣶⣿⠭⠥⠤⠤⠤⠤⠶⠶⠖⠛⢉⣠⣞⣀⣀⣰⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⣤⣄⣠⣤⣤⣴⡋⠁⠀⢀⣠⣤⣤⣤⣄⠀⢀⣀⣤⠶⠋⠁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠳⠶⠤⠤⠶⠶⠶⠶⠖⠛⠉⠁