Sandy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⡙⠻⣶⣶⠿⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣉⣭⣽⣿⣶⣿⣷⠶⠷⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⠉⢉⣽⣿⡛⠻⢷⣤⣀⣭⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣴⣿⠁⢻⣧⠀⠀⢻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣠⣿⣿⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⣄⠀⠀⠀⠹⡿⠟⠙⣿⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢫⣿⠉⢿⡟⠿⣦⣄⠀⠀⠀⣠⣴⠾⠛⣩⡿⠉⣿⡿⣷⣄⠀⠀⠀⠀⠀⢿⡇⢹⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣟⣁⣠⣿⣇⣤⣨⣿⣄⣨⣹⣷⠀⠘⠿⣷⣶⣴⣿⣥⣄⣹⣧⣈⠻⣷⣄⠀⠀⠀⢸⣇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣽⡏⠉⠛⠛⠛⠿⠋⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣤⣤⣴⣿⣦⣤⣦⣴⣤⣤⣤⣦⣤⣤⣤⣴⣴⣿⣧⣴⣤⣦⣦⣤⣦⣴⣴⣤⣾⣿⣀⣿⣷⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡟⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠿⠀⠈⣿⡶⠶⠶⢶⣦⠀⠈⠁⠀⠿⠇⠀⢹⣿⠶⠶⠶⢶⣆⠀⠀⠰⠆⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⠀⠈⠋⠀⣀⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠘⠃⢀⣀⠀⠈⠋⠀⢀⣀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠶⠶⢶⣦⣤⣶⠶⠶⢶⣦⣤⣶⠶⠶⣶⣦⣴⡶⠶⠶⣶⣤⣴⡶⠶⠶⣦⣤⣶⡶⠶⢶⣦⣤⣶⠶⠶⡶
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠛⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠛⠛⠛⠛⠉⠉⠛⠛⠛⠋⠉⠙⠛⠀⠀⠀⠀⠙⠛⠛⠛⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣤⣶⠶⢶⣦⣤⣤⡄⠀⠀⢠⣄⣀⣀⣠⣤⣤⣄⣀⣀⣠⣤⣤⣀⣀⣀⣤⣤⣄⣀⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠉⠉⠛⠋⠉⠉⠉⠙⠛⠋⠉⠉⠉⠙⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣞⠙⠛⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⣯⡁⠀⣀⠉⢿⣙⠓⢮⡉⠉⠙⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠙⢿⡁⠀⠀⢉⡉⠉⠀⠘⠳⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠛⠳⢦⣤⡴⠞⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡾⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡸⠀⢀⡏⠀⠀⢰⠞⠳⢤⠤⠶⠖⠒⠒⠶⠦⠞⠁⣹⡆⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢷⣤⠞⠁⠀⠀⠘⠷⡄⠀⠀⣦⣴⣴⣂⣶⠿⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠁⣤⠈⣿⢠⣄⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠼⠿⠌⠉⠉⠛⠶⣄⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣸⡶⠿⠴⠛⠻⠧⠞⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢾⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡷⣄⠘⣇⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠀⠀⠀⠰⣏⣉⣩⠟⠀⢠⡘⣆⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⡄⠀⠀⠀⠀⠀⢿⡀⠘⠛⠢⠤⢤⣀⣠⣭⡥⣴⠞⠋⣠⠏⠀⠀⠀⠀⢠⠏
⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢦⡀⠀⠀⠀⣀⣹⣦⣤⣀⣀⣀⣸⡇⠈⣀⣿⣴⣞⣁⣀⠀⠀⠀⣴⠏
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢱⣶⣚⣋⣉⣡⣤⡤⠬⠭⢿⠋⠉⢻⡯⠥⣤⣄⣈⡉⣉⣻⣿⠁
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡀⠈⠉⠛⠓⠶⠦⠤⠤⣾⣤⣤⡼⠦⠴⠶⠖⠛⠋⠉⠀⣿⣀
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⢷⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢾⠋⠉⠛⠲⣤⡀
⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⢦⡀⠀⣠⠖⠛⠳⣄⠀⠀⠀⢸⡄⠀⠈⠉⠙⠓⠒⠒⠲⢶⣶⣶⠖⠒⠚⠉⠉⠀⠀⢸⠀⠀⠀⠀⢸⡏⠳⣤⡀
⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⣹⠟⠁⣀⣀⣀⣈⡆⠀⠀⢰⠇⡞⠒⣲⡤⠤⣤⠀⠀⢰⠏⢻⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠀⠀⠈⣿⣄
⠀⠀⠈⠛⢶⣤⣀⣀⠀⢀⣀⣠⡾⠋⠀⠀⠀⢰⡏⡴⠋⢁⡴⠋⢉⡿⠖⠛⠛⠳⢷⣾⣍⣛⣶⣼⠆⠀⠘⣻⠛⠁⠀⠀⠀⠀⠀⠀⣾⣄⣀⣠⠞⠁⠀⣠⡾⠁⠘
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠸⣾⠃⠀⢸⠀⢠⡏⠀⠀⠀⠀⠀⠀⠙⢦⣼⠇⢸⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⠛⢶⣖⣻⡥⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣘⣆⠘⣆⣄⠀⠀⠀⠀⠀⠀⢸⣿⣀⡼⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣀⣼⠯⠤⣤⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠛⢳⣄⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⠞⠉⠀⠀⠀⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⡇⠀⢾⠀⠀⠀⠀⠀⢀⡤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⢳⣶⠶⢶⣾⣭⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡃⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣇⡀⠉⠙⠳⣶⣤⣤⣤⣤⣤⣤⣤⠴⠞⠋⠁⣹⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠓⠒⠛⠋⣷⠀⠀⠀⠀⣰⠻⣄⣀⣠⠴⠃⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⣆⢹⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠸⣿⢸⡀⠀⠀⠀⠀⠹⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢞⡇⠀⠀⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠙⠓⠶⢤⡀⠀⠀⢀⡴⣣⠎⠀⠀⠀⠀⠀⠀⠀⢿⣶⣄⠀⠀⢠⠎⠀⠀⠀⢀⣠⠞⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣄⡀⠀⠀⠀⠹⡆⣠⢞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⢤⡈⠆⢀⣠⠴⢋⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢭⣙⣒⠢⠤⠴⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣭⣉⣉⣤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⣶⢰⣤⢰⢲⠐⡔⠀⡔⠂⡦⡆⡶⢰⡶⢰⣔⠰⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠈⠉⠀⠀⠀⠈⠁⠁⠀⠉⠀⠉⠈⠀⠈⠁

⠀⠀⢰⠀⠡⠀⠒⠀⠒⠂⠔⠀⡂⠀⠀⠀⡊⠌⠆⠐⠂⠐⠂⠠⠊⢀⠀⠀⠀⠐⠈⠢⠀⠒⠒⠂⠀⠜⠍⡂⠀⠀⠀⠈⠌⠦⠐⠀⠀⠒⠠⠊⢈⠄
⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠈⡇⣠⠂⢢⡔⠀⢢⠈⠀⠀⠀⠀⠀⠑⢠⣖⠐⣤⣂⢲⡄⡉⠀⠀⠀⠀⠀⠁⢴⣂⠐⣔⡀⢲⠘⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠑⠀⠊⠀⠀⠀⠀⠀⠀⠂⠈⠋⠀⠋⠋⠐⠁⠐⠄⠀⠀⠀⠀⠊⠉⠃⣐⢙⠁⠚⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠐⠀⠤⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠠⡐⠛⠂⠀⠀⠀⠀⠀⠀⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢐⠉⣨⠈⢀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⢀
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠐⠂⠁⠀⠈⠀⠒⢀⠐⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠠⡀⠐⠂⠀⠁⠀⠐⠒⢀⡁⠀⠐⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡀⢲⣎⠀⣆⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⢠⣆⡀⢶⣂⠐⡆⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠊⠀⠉⠒⡍⠅⠐⠁⠈⠢⠀⠀⠀⢀⠁⠀⠀⠈⡀⠀⠀⠀⠠⠈⠁⠙⠐⡉⡉⠐⠁⠉⠢⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠂⠒⠂⢌⠀⠀⠀⠀⠀⠃⠀⢀⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠂⠒⠤⣌⠀⠀⠀⠀⢀⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠑⠠⠈⣈⠀⠁⢀⠠⠐⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠂⠄⠈⠈⠀⠁⠀⠀⠔⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢀⣁⠀⣅⡀⠀⠀⠂

⠀⠀⠀⠀⠀⣠⣽⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠂
⣶⠀⢀⡀⠀⠿⣿⣿⣿⡓⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠘⠀⠙⠃⠀⠀⠀⠏⢸⣷⡀⢼⡟⠀⢀⠀⠻⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠤⠀⡀
⠀⢔⠀⣷⣶⣦⣤⣤⣀⣽⣯⣋⢣⣶⣿⣥⣤⣤⣭⡀
⠀⠘⢶⣤⣈⣻⣿⡇⠀⠈⠉⠉⠀⠈⠉⠉⢛⣉⣍⠩⡄⠤⠤⠄
⠶⣼⣿⣿⣾⣝⡛⠛⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣠⣆⠀⡉⠉⠛⠛⠳⠶⣤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣶⣤⢤
⠀⠉⠉⠻⠄⠀⠀⠀⠀⠺⠯⠙⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⢀⣴⣾⣋⣀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠘⠿⢿⣿⠿⠟⠷⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢅⣀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠚⠛⠻⠶⣦⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠶⠛⠛⠳⣆⡠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠁⠀⠉⢁⡤⠔⠲⡄⠋⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠺⠶⠖⠛⠁⠰⣶⠶⠚⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁⠀⠀⠀⢀⣷⡀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠙⠦⠤⠖⠋⠀⠙⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⠦⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⠀⠀⠀⠀⠐⡏⢦⡀⠀⠀⠀⠀⢳⠈⢷⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠾⠒⠒⠒⠒⠲⠦⢬⡇⠀⠀⠀⠀⠈⢷⣈⡇⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣄⣠⣧⣤⠀⣦⠼⠿⣇⠀⠀⠀⠀⠀⠈⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡾⠉⠀⢀⣈⠹⠁⣀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣧⡀⠀⠸⠿⣳⣅⣿⣃⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⠙⠒⠒⢋⣁⣨⡭⢽⠗⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣴⡒⠀⠀⠀⠘⢯⣄⡀⢀⡞⠀⠐⢿⡆⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠳⢤⣀⠀⠀⠀⠈⠉⠉⠀⣠⠴⡿⠃⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠈⠉⠙⡗⠒⢲⠚⣿⠵⠋⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢉⣙⡗⠚⠛⢻⡀⠀⣀⣽⡀⡀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣞⡛⠉⠉⠉⠉⢹⣇⠀⠀⢀⡟⠉⠉⠈⠉⠉⣉⡿⠚⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⢴⡋⠉⠓⢲⡶⠶⠯⠭⣭⣭⠥⠤⠶⣶⠋⠉⠁⠘⢃⣧⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⢅⡀⠀⠹⡏⠛⠛⠓⠒⠶⠦⠽⠤⠶⠶⣶⣶⠒⠚⠛⠛⡏⠈⢷⠈⠉⢻⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠉⠳⣄⠀⠹⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⣧⠀⠈⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠉⠲⣄⠀⠀⠹⡄⠀⡗⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢈⣇⠀⣾⢹⡇⠀⣰⠃⠀⢀⡇⠀⠀⡸⠈⣳⢦⣄
⠀⠀⠀⠀⢀⣠⠖⠚⠉⠉⠙⢦⡀⠀⠀⠘⡆⠀⢠⣇⡰⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡄⠀⢸⠀⡷⢾⣁⣀⣠⠞⠀⣀⡴⠃⣰⠇⠀⠈⠓⢦⡄
⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠹⡆⠀⣀⡧⠖⠋⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⢸⠀⡇⠀⠉⠙⠓⠶⠿⣁⣀⡴⠃⠀⠀⠀⢸⡀⠙⡆
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠊⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠘⠓⣿⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣆⠀⠈⣇⠀⠹⡄
⠀⢸⡇⠀⠀⠀⠀⠀⣠⢾⠀⠀⠀⡾⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⢧⣠⠟⠀⠀⣇
⠀⠀⠛⢦⣀⣀⡤⠞⠁⢸⠀⢀⣼⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠛⠒⠲⡶⠒⠒⠒⠛⡟⠉⠉⠁⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢦⣀⣀⣀⣰⠇⠀⠀⢠⠃⢣⣤⢤⡤⠴⠛⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡠⢄⠀⠀⠈⠉⠁⠀⠀⢡⡎⡜⠉⢱⠀⣀⣀⣤⣤⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠆⠀⠀⠚⣛⡩⠿⠻⠧⣤⣀⡞⠀⠡⠖⠋⠁⠀⢀⣈⣉⣹⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠓⠋⠀⠀⠀⠀⠉⠀⣀⣀⠤⣤⡙⣧⠀⠀⠀⠀⣴⠊⠉⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠳⢤⣄⣀⡀⠀⡴⠋⠁⢀⣀⠀⠀⠘⡷⠤⠤⢄⣁⠀⠀⠀⠀⣀⣀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⠽⠿⠷⠿⠯⠭⠬⠿⠿⣿⠟⠒⠒⠒⠒⠿⠭⠭⠷⠒⠛⠛⠃

⠀⠀⠀⠀⣠⣶⡤
⠀⠀⣀⠀⠿⣿⠻⠅
⣄⡛⣏⠀⡈⠀⠀⣠⠀⠀⠀⣀⡀
⣶⣙⣄⣼⣇⠀⠠⢉⠐⠂⠀⠛⠁
⠀⠀⢁⣼⠚⠧⣌⠁⠀⢀⡦⣀
⣶⣤⢀⣿⣧⠀⠘⠷⣤⡀⣋⢀⣐⣦⣤⣄⡀
⣿⡏⢻⣿⣿⣤⣠⣤⣀⠙⠋⠉⠉⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠛⠓⠾⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠂⠤⠤⠄⢀⣀
⠀⢀⣢⣄⣀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠶⣤⣤⣀⣀⡈⠀⠙⠛⠓⠶⠦⠄⢠⡄
⠀⠘⠛⠟⠛⠉⠓⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣟⣛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣽⣯⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⠀⠘⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢀⠠⢄⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⣀⡀⠀⠀⠨⢩⡿⡓⣎⣱⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⡸⠅⠀⠀⠀⠄⠀⠈⠀⢄⠈⠀⠀⠘⣌⠛⢻⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠂⠈⠁⠀⠀⠀⠀⠠⠌⠉⠒⢒⠀⣴⢨⣶⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠀⠀⠀⠠⢀⠀⠀⠀⠠⠓⠀⠐⡀⠀⣀⠄⠀⠀⠀⠀⠀⠈⠐⠂⠀⠢
⠀⠀⠀⠀⠐⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠠⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠤⠀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠀⠐⠒⠂⠀⠀⢀⠀⠀⡐⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⡆⠀⡬⠀⡁⡄⣀⢰⠀⠁⢠⠃⠰⠃⢀⠀⠲⡅⠁⢸⠀⠁⢀⠀⠁⢰⠀⢰⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠁⠈⠁⠀⠘⠂⠀⠃⠀⠘⠀⠐⠀⠇⠈⠀⠂⠀⠀⠃⠀⠂⠐⠒⠸⠀⠐⠘⠇⠈⠃⠢⠠

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠉⠉⠈⠙⠛⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣦⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⡀⠀⣴⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣰⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠋⠉
⠀⠀⠀⠰⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠠⢤⡄⠀⠶⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉

⠁⢀⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢼⠃⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠠⠐⢻⡦⢠
⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠈⣁⢡⡄
⣰⣆⡀⠀⠉⠀⢠⣱⡟⠎⠀⠀⠀⠀⠀⠑⠂⠘⠋⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣼⡏⠁⡴⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠹⠏⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⢁⡤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣢
⠀⠀⡀⠀⠀⠀⠀⠀⠆⢠⡆⡄⠀⠀⠀⠀⢁⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠻
⠀⢐⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⢀⠀⠆⠁⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⣀⣾⣲⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢡⠆⠀⠀⢠⣶⡆⠀⠚⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⣿⣿⣷⠀⠀⣀⡀⠃⠀⣴⡄⠀⠀⠀⢈⠀⠀⠀⠊⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠧⣤⣿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣤⡄⠀⣤⡄⠀⠀⢠⣀⠀⠴⠖⢀⡀⢠⣤⣤⡀⠀⠀⠀⠀⢠⣄⣀⣀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠈⠠⠖⡀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠉⠀⠐⠛⠁⠶⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁





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

⡀⠀⠁⠈⠀⠀⢀⠀⠁⠈⠀⠀⡀⠀⠁⠁⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠀⡀⢀⠀⠁⠈
⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠀⠀⢉⡖⠀⠀⠁⠁⠐⠂⠤⣀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠀⠀⠈⠊⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠉⡦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠤⠦⡠⠖⠁⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⠐⠒⠒⠠⠄⠐⣉⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠂⢂⠂⡌⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⠉⠂⠤⣁⠀⣈⡀⠱⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢄⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠃⠀⠠⠀⠈⠀⠸⡀⢀⠐⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢒⣀⡤⠤⣤⣦⣭⣤⣿⠲⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠁⠚⠻⠿⠿⠧⠄⠸⠛⠋⠁⠀⠐⡇⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠠⢜⠉⠀⠖⠀⠀⠀⠀⠐⡤⠀⠀⠀⠀⢣⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠉⠀⠀⠀⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⣿⢡⡀⠀⠀⠘
⠀⠀⠂⠀⠀⠀⠀⠀⠈⢧⣀⡤⢎⡁⠀⠑⡀⠀⣀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠀⠀⡤⠒⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⡀⠞
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢀⡶⢋⠀⠈⢳⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠎⠀⠀⠳⠤⡤⢇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡠⠂⠀⠀⠀⠀⠀⠀⠈⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡤⢄⣀⣀⣀⣀⠠⠔⠈⠠⠔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠭⡀⠀⠀⠈⠀⠀⠀⠀⢣⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢱⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠄⠀⠀⠀⠀⠆⠀⠀⢃⠀⠀⠁⠀⠀⠀⠀⠄⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⠠⠀⠀⠰⠀⠀⠈⠄⠀⠀⠈⠀⠠⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠈⠀⠠⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⡀⢀⠀⠁⠀⠀⡀⠀⠀⠁⠁⠀⡀⠀⠀⠉⠀⠀⠀⢀⠀⠉⠀⠀⡀⠀⠀⠉⠀⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣠⠖⠀⠀⠀⢠⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣟⣿⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡷⠀⠀⡉⠀⠀⠀⠓⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣀⠁⠙⠁⠶⠀⠀⠀⡇⠀⢠⣤⠀⢈⢠⡄⣉⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣤⣠⠀⢤⢴⢦⠄⠀⠀⠁⠉⠙⠋⠐⠘⠠⣶⡤⠾⠿⢿⣿⣿⡿⢣⠦⠼⢷⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠂⠸⠄⠀⠀⡈⢰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣧⠖⠂⢛⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠸⣏⠿⠏⠙⠋⡉⡏⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣈⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢂⡠⢀⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣹⣿⣿⣿⣯⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⠛⣿⣅⣤⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠲⠉⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠙⡧⣘⣃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⢍⠂⠉⢑⠂⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠉⠘⠁⣠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠉⠙⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣴⣴⡆⠀⠈⢂⣠⣔⣤⣤⡤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠀⠉⠉⠉⠉⠁⠉⠉⢉⣁⣀⣀⡼⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠋⠉⠁⠀⠘⡌⠉⠉⠉⠉⠉⠉⠉⣿⠉⠀⠘⡇⠀⠀⠈⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣀⠊⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢰⠀⡆⠀⡆⡇⠀⠀⠀⠀⠀⠀⠈⣄
⠀⢀⡤⠒⠉⠁⠉⠑⣄⠀⠀⢀⣠⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⡇⣿⠦⢤⣄⠀⠀⠀⡰⠁⠈⠢
⢠⠋⠀⠀⠀⠀⠀⠀⢸⠔⠋⠉⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠁⢹⠀⠀⠈⠑⠲⣏⠀⢠⠀⠱
⢄⠀⠀⠀⢀⢐⠆⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢦⠈⠣⡰
⠈⠲⠤⠖⠁⠸⠄⠤⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠑⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢀⣀⣀⣠⣄⠀⠀⠠⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⡀⠀⠀⢨⢧⡀⡴⣧⣀⣀⡠⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠉⠈⠀⠀⣿⠁⠀⠀⠀⠀⠠⢼⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠂⠙⠓⠦⣄⠀⠀⠀⠀⠠⠄⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠀⢀⠀⠀⠀⠀⢀⠤⠐⠀⠈⣧⠀⠀⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢍⣐⠀⠀⠄⠀⠀⠀⠀⣿⠲⠭⠭⠭⠵⠶⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⡄⣚⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠁
⠀⠀⠀⠀⠚⢙⣿⣿⣯⣜⡟⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⠩⣦⠁⠁⠀⣴⣗⢂⣠⣦⠄
⠀⠀⠀⠀⠀⡾⠁⠋⢡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠝⠀⡀⠈⠀⠙⢇⠉⠘
⠀⠀⠀⠀⡐⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡀⠑⠠⡀
⠀⠀⣠⠞⠀⣠⠊⠀⠐⠀⠴⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢄⡀
⠀⠘⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⠀⠀⠰⡞⠀⠀⠀⠀⠀⠀⡺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡞⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢍⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢫⠞⡣⣀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⠰⣟⠳⢅⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⢃⣴⠋⠅⣚⣥⠶⠦⠔⠀⢶⡓⢬⡑⠦⡙⣷⢬⡿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡟⡅⣰⡿⢋⣴⠞⠋⢂⡄⢸⣟⢦⡻⡄⢹⡎⣧⢳⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣾⣼⢳⡿⢃⣼⡥⠞⣛⠡⠖⢧⡻⣦⣻⣏⢸⡇⠹⣧⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⣤⣥⣿⢱⢫⣫⠔⣫⣵⠠⢶⣦⡹⣾⢿⠛⠈⣷⣐⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣠⠶⢾⠞⠓⠉⠙⣻⡇⠙⢯⡉⠉⠸⢿⣆⣩⣭⣭⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣝⡛⠃⠀⠀⠲⠞⠉⠀⠀⠛⠈⠆⠀⠀⠙⠶⢯⡻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣵⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣯⣵⠷⣾⠷⣤⢤⡰⣆⡶⢠⣄⡤⠶⢭⣭⣿⣰⣿⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⣴⠶⢞⣉⣛⣻⣆⡳⣬⣛⣿⡭⠖⠲⠶⠶⢿⣿⢸⡗⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢋⣡⣾⣟⣩⣭⣭⣭⣙⠛⠳⠮⣭⣙⣋⣛⣵⣀⠐⣌⣸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣫⢗⣋⣩⣵⠞⣻⣟⣋⣭⠽⢒⣢⡽⠛⢷⣤⣈⣷⡙⠿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠭⠷⠶⠛⣋⣤⣭⣀⠚⣭⡀⢂⡙⠒⠾⣝⡳⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣛⣛⡯⠶⢭⣛⣛⣭⣭⢭⣿⣦⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣟⢷⠾⣻⣯⡩⣽⣷⡶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣺⠟⣓⣻⣯⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢛⣛⣹⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠱⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⢀⠠⢀
⠀⠀⠀⠀⡠⠒⠢⠀⠚⠁⠀⠀⠀⠀⠈⡁⠈⠑⠺⡒⢄
⠀⠀⠀⠀⢅⠠⣅⣤⡊⠀⠀⠀⠀⠀⠀⣈⡑⠦⡀⠈⢢⠣⡀
⠀⠀⠸⢀⠘⠀⠀⢀⡷⢄⣀⠀⠤⠤⠤⠀⡸⠀⠀⠢⠤⠀⠁
⠀⠀⠀⡏⠀⠰⠒⠉⠂⢄⠐⠒⠠⠋⠉⠪⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⠀⡀⠤⠒⢒⣆
⠀⠀⠀⠑⠒⠁⠀⠀⢀⠼⢠⡄⢀⣴⡆⠘⠀⡉⠂⠀⠀⠀⠀⠀⠀⠀⢀⠋⠐⠃⠀⠀⣠⠖⠦⡉⠑⠢⡀
⠀⠀⠀⠀⠆⠀⠀⢰⠁⣀⠈⠁⠤⠒⠠⢀⡴⠁⠄⠀⠀⠀⠀⠄⠀⠀⡌⠀⠀⠀⠀⢠⠃⢠⠀⠹⡄⠀⠘⡆
⠀⠀⠀⠀⠘⡀⠀⠈⠢⡈⢃⠐⢢⠒⠂⢃⣀⠊⠀⠀⠀⠀⠀⠀⣸⠙⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠹⡀⠀⢹
⠀⠀⠀⠀⠀⠑⠄⠀⠀⠈⢢⢢⡤⠶⢈⢽⡇⠤⠤⠀⢀⡀⠁⠀⢹⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⢧⣠⠏
⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⡑⢔⣬⣴⡋⢻⣾⡶⠖⣪⠦⣀⠀⠘⡇⠀⠀⠀⠀⢸⠀⣶⣶⡆⠀⠀⣼⣇
⠀⢀⣠⠴⢐⠂⠈⠉⢩⠉⢹⠐⢛⣛⣛⡁⠤⠵⠒⡚⠀⣀⡈⢣⠀⢱⠀⠀⠀⠀⠆⠀⡀⢀⠀⠀⠀⠉⡟
⠀⡏⢠⠔⠀⢰⠄⠤⢀⡁⠘⡀⠀⠀⣈⢀⠀⢀⢀⡞⠉⠀⠈⠙⡆⠸⡄⠀⠀⡘⢀⣦⣄⠀⠱⣄⡈⠉⢳
⠀⢳⡁⠀⡰⢇⠒⠀⠬⣉⠉⢣⢀⠒⠉⠉⠉⠉⠙⡇⣀⣀⡀⠀⢺⠀⡇⠀⢰⠃⡜⠿⠏⠀⢀⣿⡿⠀⠀⡇
⠀⠀⠑⢤⡀⠂⠀⠀⠀⠀⠉⣆⡎⠀⠀⠀⠀⠀⡗⠉⠀⠀⠈⠳⣼⡞⠀⢠⠃⡄⢃⠀⠀⠀⡌⠉⠀⠀⢠⠁
⠀⠀⠀⠀⠈⡷⠤⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⢀⠹⡀⠀⠀⠀⠀⡟⠸⡤⠃⠌⠐⢌⠓⠐⠊⠡⡀⢀⡠⡇
⠀⠀⠀⠀⠀⠙⠢⠄⣄⠠⠖⢁⣧⠀⠀⠀⠀⠀⠀⠱⡄⢀⡤⠊⢀⠔⠁⠈⠀⠀⠈⠂⢄⠀⣀⡈⡁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⡄⠀⠀⠀⠀⠀⠀⠘⢿⠲⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠈⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢣⣀⠀⠀⠀⠀⡔⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⣠⠖⠊⠋⠛⠓⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⢑⣀⠴⠊⠀⠀⢰⠃⢀⣀⠀⢀
⠀⠀⠀⣀⡀⠀⠀⠀⠸⠄⡰⠁⡀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡎⡰⠋⠀⠉⠻⣷⡀
⠀⠀⡘⠀⠙⢦⠶⠓⡆⠐⠀⢀⣵⠺⠿⠏⠉⠚⠚⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡄⠀⠸⡄⠀⠹⢷⡀
⠀⠀⢀⠀⢀⠃⠊⠢⣇⠀⢀⡾⠁⠀⠀⠐⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠇⠀⠙⣄⠀⠈⠂⠀⣉⡇
⠀⠀⠸⡄⡌⠀⠀⠐⠸⡀⡾⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⢢⠀⢠⣾⠏
⠀⠀⠀⠑⣇⠐⠂⠜⠀⢻⠁⠀⠀⠀⠀⡰⠃⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡀⠀⠀⠀⠀⠙⣗⠁
⠀⠀⠀⠀⠘⣄⠠⠂⠀⠈⠑⠒⠒⠞⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⢽⡳⣄⡀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠈⠒⠚⠛⠋⠛⠢⣄⣀⠵⠿⣦⣄⡀⠀⠀⡀⢀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠙⠏⠛⠲⣤⡀⠀⠀⠀⠈⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠭⣭⣥⣶⣽⡷⠮⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣆⠀⠀⠀⠀⠀⠀⣰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⡃⠀⠀⠀⠀⠀⠀⠀⢺⡿⢿⣿⠀⠀⠀⠀⠀⢰⡽⣿⣧⠀⠀⢀⣰⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⢠⣤⣾⣾⡄⠀⠈⠛⢿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⣷⡌⣧⠀⠀⠀⠀⠻⣿⣿⠿⡇⠀⠀⣀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⡀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢻⠀⠀⠀⠀⠀⣼⠀⠀⣷⠀⠘⢻⠟⡍⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠘⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⠀⠀⠀⠀⠀⡟⠀⠀⣿⡀⢰⣾⣿⣿⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⢹⡿⠛⠀⠀⠀⠀⢀⣀⣠⡆⠈⠀⠋⣼⣧⣿⡇⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠹⣿⣿⠀⠀⠴⢴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣻⡇⠀⠀⠀⠀⣿⣿⠀⠠⠦⢬⣽⣭⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⠀⠀⣀⢠⡀⣀⣀⠀⣿⢹⡇⠀⠀⠄⠀⡀⠀⠘⢸⠃⠀⠀⠀⠀⣿⡿⠀⠀⣀⣹⣟⢶⣶⡄
⠀⠀⠀⠐⠰⢶⣶⣾⣶⣷⢿⣽⣟⠀⢿⣿⣀⢸⠲⠂⠀⠉⠉⠀⢸⣼⠀⠠⠢⢄⢉⡑⣀⡀⣿⣀⣐⣀⣀⠀⢿⣿⠤⣨⡿⠕⣿⡋⠛⠁
⠀⠀⠀⠐⠀⣀⣠⣬⣥⣾⣯⣽⣆⡁⢸⣯⣭⣉⣋⣙⣛⠒⢖⠲⢸⣿⣧⣤⣤⣴⣛⣛⣻⣿⣿⣿⣿⣛⣿⣁⣿⣿⣿⣟⣴⣶⣿⣽⢯⣐
⠀⠀⠀⢀⠲⢜⣿⣽⢿⣹⢿⣶⠷⣄⣾⣏⣥⣯⣍⣽⣿⣿⡿⢃⣼⣿⣿⣷⣴⣦⣤⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠺⣭
⠀⠀⠀⡄⢘⠙⣛⣻⣿⣷⣾⣵⣶⣶⣾⣿⣷⣞⣿⣯⣽⣿⣇⣾⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⡛⠛
⠀⠀⠀⠛⢛⣓⣻⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣤⣶⣿⣗⢿⣿⣿⣿⣿⣿⣧⣴⣿⣷⡄⠀⠶⡿⠟⣿⣿⣿⣏⠉⣝⣿⣟⠛⣿⡵⢯
⠀⠀⠀⠛⠃⠀⠙⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠉⠉⠋⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠈⠁⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠁
⠀⠀⠀⠀⢀⡁⠀⠀⠀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀
⠀⢠⠀⢀⠄⠀⠀⢠⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠀⠀⠀⠐⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⡤⠀⢉⠐⢦⠤⠄⠀⠀⠰⡀
⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠑⠀⠀⠀⠀⡄⠀⠠⠀⠋⠿⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡠⠀⢹⠦⢀⡄⢙⠆⠃⢀⠐
⠀⠀⠀⠀⠀⠀⠊⠸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠞⠀⠀⠠⠢⠌⠉⣿⠒⢊⡼⠉
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠶⠂⣠⣈⠙⠆⠀⠀⢀⠀⠈⠉⡷⠄⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠄⡀⠊⠹⠈⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⠋⠻⠒⢏⠗⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⢆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⣥⠰⠀⣠⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠘⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠐⢀⠀⢠⢠⠀⠁⢐
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠘⠒⠀⠠⠀⠀⡀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠐⠂
⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡀⠈⠉⠡⠤⠄⠀⠀⢀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠓⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠤⣄⣀⡀
⠀⠠⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠤⠄⠀⠀⠀⠀⠉⠀⠂
⢀⣀⡄⠀⠀⠀⠀⠐⠶⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠉⠉⠙⠂⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⢠⣀⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠁
⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⢄⡀⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠻⠛⢉⠙⠳⣿⣾⠟⠁⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣴⠟⡩⠄⠒⢿⣷⣿⣿⡯⢅⡈⢀
⠀⠀⠀⠀⡀⠀⢠⠆⢀⡀⠀⠟⡙⠡⡈⢀⣾⡾⣿⡿⣟⢶⣄⠻⣬⡀
⠀⠀⣀⣤⣼⣿⣿⡿⢦⣤⠀⢀⠊⢰⣷⣿⢿⢳⡟⢧⠸⡖⢿⣷
⠀⢰⠏⢠⢈⣼⠻⢵⣎⢿⣦⡆⠐⡿⢫⡟⣼⣼⠀⠈⠀⡰⠮⣿⠆
⠀⠘⠀⠀⢸⣿⡘⠘⠏⠀⠋⠈⠀⢠⡟⠀⠃⠸⠀⠀⠈⠀⠀⢸⠂
⠀⠀⠀⠀⠈⠘⣷⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠻⢆⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⣀⣀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⢣⠀⢀⣀⠈⣀⣋⣈⣉⡉⣋⠀⡀⣋⣈⣉⣃⡉⣁⣙⠈⢛⣉⣉⣐⣠⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⢸⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⠟⠛⠛⠛⠉⠙⠙⠋⠉⠉⠁
⠀⠀⠠⠀⠀⠀⢸⡧⠀⠀⣾⢸⠀⠀⢀⡄⢀⡠⢀⢄⠀⠀⠀⠀⢠⡏⠠⠠⠤⠀⠀⡀⠀⠀⠀⠄⡠⠀⠄⠀⠀⠄⠀⢤⢀⡄⠄
⠀⠀⠐⢠⠄⠀⢸⡇⠐⠄⣗⢸⠴⣞⣂⣐⣭⡭⠤⢒⡀⠈⣁⣀⡹⡇⠍⣉⣩⣤⠤⠀⣀⣈⠉⠧⠄⠒⠒⣛⣩⣤⡒⢒⣠⣤
⠀⠀⠐⠒⠒⠀⢻⡟⠛⠛⡟⢸⠃⠀⠒⠒⠀⠉⠓⠣⡈⠉⢂⠬⠽⣧⣴⣶⣾⣿⣭⣍⣽⣷⣶⠶⠶⠖⠈⠉⠛⠓⠠⠤⠤⠦⠄
⠀⠀⠀⠀⠀⠢⣜⠃⠀⠀⢡⢸⡀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠚⢡⡟⢦⡀⠈⢆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣸⣧⡦⠀⠀⠀⠀⠀⠀⠀⣣⣄⣘⣯⡇⠈⣷⠹⡞⣮⡁⡀⠔⠚⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠉⠙⡇⠐⢺⣧⣼⣾⣿⣶⠞⠋⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⡤⠀⠀⠧⠀⠉⠀⠀⠈⠙⠉⠒⠲⢤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⢤⡀

⣿⣿⣿⣿⣿⣾⡟⣡⣾⣸⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠇⠀⠀⣠⠇⠀⠀⠀⠀⡤⠄⢠⢬⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⢠⡗⢀⣆⡀⣼⠀⣼⣡⡄⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠿⣶⢻⣴⣿⡢⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡾⠇⠚⠋⠛⠿⠿⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⣀⣠⣶⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡖⡶⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣦⣁⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣛⣛⣉⣈⣻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡺⢿⣿⣤⣤⣀⣆⣴⣴⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠹⣿⣿⣿⣿⣿⣿⣿⠻⠿⣷⣄⡈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⣼⡆⣿⣿⣿⣿⣿⣿⣿⣟⣷⣦⢘⡿⠟⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⣹⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⣴⠆⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣴⠋⠀⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⣼⣿⣿⣿⣿⣿
⣿⠟⠀⢠⡀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠞⠋⠀⠈⢻⣿⣿⡻⣿
⡟⢠⣾⡿⣷⡀⣀⠁⣠⡌⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠘⢫⡿⣿⣿⣿⣿⠛⢣⡀⠀⠀⠶⠝⠿⣿⣿
⢠⣿⣿⣆⣿⣯⣥⣴⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣧⡴⠛⣀⠀⠀⠐⣒⣒⣞⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⠀⢰⣾⣧⣿⣿⣿⣿⣿⠀⠀⠀⢀⣨⣯⣿⣿⣿⣠⣾⣏⠀⢀⣘⣿⣿⣿⣿
⣯⣿⣿⣿⣿⣿⣿⣿⡏⠙⠃⡰⠤⢤⣤⣼⣿⣿⣿⡟⠀⠀⠀⠈⢙⠛⠛⢛⣿⣿⣿⣿⡇⠀⠉⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣴⣷⣿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⣙⣛⣛⣛⣻⣛⣛⣛⣻⠀⠀⢘⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⡿⠀⠀⠀⠀⠀⢤⣌⣛⢿⣿⣿⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⡀⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣆⢀⣤⣤⣴⣦⣤⣈⠉⠙⠛⠿⢿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠈⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⢿⣿⣷⣶⣦⣤⣄⣁⠀⠀⠸⠿⢿⣿⣿⠟⠻⢿⣿⣿⣿⠿⠀⣀
⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣆⣤⣀⡀⢀⣀⣀⣀⣴⣾⣴⣷⣾⣿
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠙⠟⠛⠛⠚⠿⠿⠿⢿⣿⣿⣿⣿⣿
⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⢿⢶⣶⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣠⣴⣿⣿⡟⠛⠛⠋⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠖⠾⢿⡖⢤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣷⣶⣶⡤⣾⠤⣶⡷⠀⠗⠀⣲⣿⣿⣿⣿⣷⣿⣿⣿⣿⣉⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣭⠿⠿⠟⠃⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡏⣥⣀⠀⠀⠨⠰⠀⠀⠀⠈⠙⢯⡿⢽⣟⣿⣿⡿⠿⠿⠿⠿⠟⠃⠋⠘⠋⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⡐⢩⠑⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿
⠿⠿⠘⠛⠉⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⢿⡿⢻⢿⣿⡛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣀⣄⣠⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣧⣞⣷⠾⢿⠁⣇⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⡿⢻⣿⣿⡿⣿⣿⣿⣿⡟⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠋⡛⠋⠉⠿⠟⢿⣿⣩⣿⣉⡙⠙⣛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠛⠿⠭⣿⣿⣿⣮⠿⣿⡕⠻⡽⣤⣴⣶⣆⣀⣀⠀⠀⠁⣶⣶⡍⠙⠙⠛⠿⢦⣤⡉⣰⠦⠀⠀⠉⣉⠙⠛⠿⠿
⠉⣿⡿⢛⣓⠛⠙⠁⠋⠁⠤⡦⠤⢬⢴⡆⠀⠀⠉⠉⠛⠿⢛⡛⠻⠿⢿⢿⣿⡾⠋⠵⣶⣖⣂⡐⠀⠀⠀⠀⠀⠀⠐⢀⠙⠻⠿⣶⣴⣀
⠈⢉⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠔⠂⠃⢶⣶⣾⣾⣼⡏⣶⠦⡙⢿⣷⣖⡰⠂⠀⠀⠖⠀⠀⠀⠀⠄⠀⠉⠻⣷⣆⡆⣤
⠀⡀⠀⠈⠁⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣟⠥⠔⢊⡏⠀⠀⠄⢝⣋⣭⣼⢟⣩⠎⡠⠤⣿⣿⣿⡿⡜⠃⠁⠀⣀⣴⡆⠀⠀⢰⡤⣀⣼⣷⣉⡉⠁
⠀⡂⠀⠀⠄⢀⠀⠀⠈⠁⠀⠀⠈⠻⣛⣛⡿⢋⣄⡤⠶⠶⠆⠸⣿⣯⣭⣩⣽⢋⠁⢈⣭⣶⣿⡿⠛⣤⣵⣾⣿⡀⢉⡉⠀⠀⠀⠉⠀⠀⢹⡟⠛⠒⠈
⠀⠀⠀⠀⠘⢓⠂⠀⠒⠀⢐⣾⢛⣛⣏⣩⢬⡳⠋⣾⠏⣴⡼⣫⣽⣿⣿⣃⣽⣷⠞⠿⠛⠷⡾⠲⠰⠶⠃⠀⡀⠀⠚⠓⠀⢀⠀⣂⣴⡿⢛⠉⠓⣀⡃
⢀⣠⣈⢉⡙⠛⢋⣬⣥⣾⠗⠲⣿⣶⣶⣛⡛⢿⡿⢟⣉⣿⣿⣿⣿⣍⣹⡶⣇⢀⠀⢀⡀⢈⡈⢤⡔⣂⠰⠐⠆⠀⠐⠛⣡⣤⡾⠋⠭⢛⠛⣻⣭⡈⠆
⠈⠁⠁⠀⣀⣄⡈⠛⠡⣥⡤⠶⢿⣿⣿⣿⣯⣿⣯⢿⣿⣿⢿⣿⣽⣟⠿⠿⠴⠙⢯⡍⢩⣭⠉⡄⠜⠀⠀⠜⢶⣶⣶⢟⡩⣿⢿⣇⣂⣤⣌⢋⢋⣁⡀
⠜⠣⠤⢩⢏⣭⣿⡟⠲⡜⡷⣛⡺⢙⣩⣽⡆⢨⣥⣦⣼⡦⠨⡟⡛⢻⠗⢆⡙⣳⠦⣤⡈⠂⠀⣥⣤⣨⠟⢻⠛⢦⣛⠺⢥⠒⠀⠘⠋⠻⠁⠈⠉⠀⡀
⣀⣂⣄⣀⣤⣑⣚⣀⣙⣂⣐⣒⣃⣼⣯⣛⣛⣟⣛⣛⣋⣐⣁⣐⣀⣒⣂⣀⣀⣀⣀⣀⣁⣸⣂⣙⣉⣐⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣮⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⢸⠀⠀⠀⠀⠠⠆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠊⠁⡀⠀⠀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣰⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠇⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣤⢰⣾⣿⣿⣿⠗⠀⢀⠠⠒⠁⠢⡄
⠀⠀⠀⢰⠂⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢹⣿⣾⣄⠄⠁⠀⠀⠀⠀⠈⣀⣠⠶⣦⠀⠀⠀⠀⠄
⠀⠀⠀⠜⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣷⣾⡿⠆
⠀⠀⠀⠪⢤⣀⣀⣤⡿⢿⣦⡀⢀⣄⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⣀⡀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠈⠛⠳⢦⡀⢈⠛⢶⣶⣦⣄⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⣰⠋⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠉⠙⠛⠿⢿⣷⣶⣾⣷⡄⠻⠰⠶⠾⠿⠟⠁⠀⡰⠁⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠒⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣆⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⢰⠛⣆⠀⠀⢠⠞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⡜⠀⠸⡄⠀⡏⠀⠸⠀⠀⠀⠀⠈⠀⠈⠵⡀⠀⠀⠀⡌⠀⠀⠰⠀⠀⠀⠀⠀⢰⣾⣄⠀⠀⣤⢿⡇
⠀⠀⠀⢀⡰⠧⠀⣀⡷⢼⣀⠀⠠⠦⢀⡀⠀⠀⢁⠀⠀⠱⢄⡠⠔⠁⠀⠠⠁⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠈⢟⠂
⠀⠀⠘⠀⠀⠀⠀⢄⠀⠀⠠⠀⠀⠀⠀⠀⡆⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠠⠀⠀⡀⢀⠀⠕⠒⠠⢀⡀⠀⣀⠠⠀⠀⠘⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢀⠄⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠠⡂⠀⠀⠀⠉⠉⠀⠀⠉⠁⠀⠀⠀⣠⡡⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠠⢀
⠀⠀⠈⠙⢾⠀⠀⠀⠀⠐⠀⠒⠀⢁⠝⠁⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⡤⠒⠁⠀⠐⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⡠⠃⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠉⠙⠂⠂⠀⠀⠀⠀⠀⢁⠔⠈
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⠰⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠐⢗⠆⣠⠔⠓⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⡰⠢⠊⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠃⠈⠉⠀⠀⠀⡴⡄⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠉⠄⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠃⢙⣒⠒⢄⡠⢤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡈⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡰⠒⠣⢄⡁⢸⠉⡱⡞⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢣⠈⠗⠄⡙⣎⡻⢖⠳⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠳⣘⢖⠇⣩⡥⢉⠜⠀⢀⠎⢀⠴⠚⠛⠉⠓⠒⠲⢦⡀
⠉⠉⠉⠉⠉⠉⠉⠀⠀⠐⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠄⠤⠷⣤⣒⣊⡉⡗⢲⢖⣊⣓⡦⡔⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⡀⠀⡀⠤⠀⠐⠂⠈⡸⠁⠀⠀⠀⠀⡗⠒⢬⡭⠭⠭⠭⠥⢴⠒⠓⠾⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇
⠄⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠠⠄⠐⠂⠀⠉⠀⠀⠀⣠⠒⠉⠉⢇⠀⠀⡴⠒⠂⡆⠀⠒⠃⠀⢀⠐⡄⠣⡀⣀⠀⠘⢤⠒⠉⠉⢯⡀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣀⣈⢓⠞⠀⠀⠀⢃⠀⠀⡔⠉⠉⠉⠓⣖⠉⠀⠀⠀⡨⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢇⡾⠀⠀⠀⠀⠸⡀⠀⠢⣄⠠⢴⡁⣠⣂⠠⡶⢉⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠁⠈⠈⠀⠀⢀⡼⡴⠊⠉⠁⠀⢳⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠒⢦⡤⠤⠄⢶⠊⠉⠾⠑⢎⠆⠀⠄⠘⣆
⠀⠀⠀⠐⠂⡀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠭⠥⠍⠉⠢⣀⠔⠋⠉⠑⣤⠋⠀⠀⠀⠈⢣⣀⡠⢤⣊⣀⠄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠀⢣
⠀⠀⠀⠀⡠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⡀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⣠⠼⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠄⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠤⠴⠇

⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢠⡤⠄
⣶⣆⣄⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢲⠴⠄⣤⣶⡅⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠈⣿⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⢤⣿⠁
⢀⣾⣷⠞⠉⠀⠤⠑⢾⣿⡁⣲⠀⠄⠀⢀⣂⣰⣶⠿⠂⠠⠀⠈⢳⣼⣿⠍⠀⠠⠴⠤⠴⣶⡀⠄
⢈⣿⣟⠁⠀⡀⣀⠀⠀⠙⠻⣽⡄⠀⠀⣻⡿⠗⠚⠁⣀⡄⡀⠀⣹⡿⢿⠉⠀⠀⣀⠀⠉⠓⢿⣷⠀⠀⠀⠐
⣏⣶⣺⣧⣶⡮⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠁⢨⣶⣶⣿⣶⣠⣿⣾⡦⠀⠀⠀⠀⠀⠈⠁
⣿⠃⢠⣻⠷⢅⢄⢀⢀⠲⣄⠀⠀⠀⠀⠀⣀⠔⢂⢠⢄⣴⣿⣿⣿⠀⣿⡿⣿⠳⢄⢠⡀⠀⠲⣄⠀⠀⠀⠀⠀⠐
⣿⢡⠸⣿⠀⠀⠁⠁⠋⠷⣉⠿⣆⡀⢠⡾⢣⡢⡞⠋⠉⢺⣿⡟⢻⡄⡿⠛⢸⡇⠀⠁⠉⠞⠢⣚⢷⣄⣀⠀⠀⠀⡴⠄
⠁⡸⠒⣯⠀⠀⠀⠀⠀⠀⠉⠈⢈⣷⠏⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⠀⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠄
⡔⠁⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡔⠀⠀⠸⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⡇⡦⠶⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠤⢸⡇⡄⠀⢀⡧⣿⡧⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⢀⢠
⣿⢁⢾⡏⠀⠀⠀⡎⠀⡢⢤⡀⠐⡄⢰⢁⠝⠃⣤⣀⣅⠀⠀⢰⣼⡇⡧⠆⠚⡇⠿⡀⠀⢀⢤⠒⠐⡊⠁⣠⠋⡑⠠⣆⣲
⠸⣜⠀⡅⠀⣀⠠⡍⠈⠤⠃⠐⠉⢳⢈⠁⠖⠁⣀⡁⠙⠏⠋⢉⢸⡃⣷⠀⢸⢃⠦⠉⠈⠀⢰⠄⢁⡁⠀⢳⢆⡀⠀⣀⠁
⠀⣿⠀⡇⠷⠀⢀⡄⠀⡧⠀⠘⠁⢀⡃⢴⢁⠀⢈⠀⠐⠆⠀⠉⣹⠀⠶⢨⠃⠎⢕⠀⠉⡁⢨⣇⠀⣠⠠⠞⡼⠧⣀⡆
⡴⡇⠀⡁⠀⡀⠀⠤⠤⠋⠂⠓⠎⠈⢀⠆⠀⠈⠈⠈⠀⠀⠉⠈⣽⡌⠤⠌⢠⠀⠀⠷⠴⠈⠁⠀⢄⣁⠀⡼⢁⣀⡈
⠀⠁⠠⠄⠀⠉⠈⢁⣀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⣀⠐⠒⠂⠀⣿⠀⠈⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⣀⣀⣀⣀
⠀⢀⠈⠦⠁⠀⠀⣐⠂⠀⠀⠀⠀⠉⠀⡀⠐⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡇⠒⠒⠒⢦⣁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡠⠥⠮⠅⠀⠰⢒⣋⠁⣀⡀⣖⡒⠂⠀⠈⠛⠀⠌⠉⠐⠚⠀⣈⠀⢰⠀⠀⠠⠄⠤⠤⠤⢋⠈⠉⠤⡄⠀⠀⠀⠈⠭
⠒⠈⡠⠂⠒⠀⠠⡄⠀⠀⠂⠀⠀⠈⠉⠁⠂⠤⠀⠀⠁⠀⢨⣁⠂⠀⠐⡍⠁⠀⠐⠀⠀⠄⣀⠂⠀⠀⠀⠢⡄⠁⠚⠉⠍
⣉⣁⠀⡃⠠⠀⠂⢁⡀⠠⠤⠬⠀⠂⠂⣈⠀⡀⡀⠀⠄⠀⠀⠂⠨⠉⠅⠚⠀⢀⡢⠀⠀⠔⠁⠀⠀⠀⡄⠐⢁⢀⠠⠐
⠀⠁⠍⢄⡀⠀⠐⢐⠒⠒⠒⠀⡒⠈⠀⠠⠄⣐⣀⠀⠀⠈⢢⠐⠀⠒⠀⠅⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⠤⠀⠐⠂
⠀⠠⠀⡘⠂⣀⣀⣐⢒⣈⠭⠥⠭⠩⠭⣐⠬⠁⠀⠰⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠥⢐⠀⠀⠠⠭⠤⠀⢀
⠓⠒⠊⠓⠀⡀⢂⠀⠐⠀⡀⠆⠀⠀⠉⠉⠀⠈⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠐⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⢠⣾⣶⣄⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⠀⠀⠀⠀⣰⣿⣷⡀
⣿⣿⣿⣿⣷⡀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⡀⠀⣰⣿⣿⣿⣧
⠛⠛⠛⠛⠛⠁⠈⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠗⠒⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣰⣿⣿⣦⡀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣤⣤⣤⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡇
⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣀⠀⠀⣠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⣤⣤⣤⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣤⣄⣀⣠⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⡠⠄⡆⠀⡄⠀⡄⢠⢀⢠⠀⡤⠀⢰⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣞⢿⠀⡇⢰⢳⣸⣿⠸⣼⣼⠀⡇⠀⡝⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠟⠸⠀⠧⠸⠀⠃⢸⠀⠏⠿⠀⢧⠰⠉⠇⠌⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⠿⠿⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠛⢿⣿⣿⠿⠿⢿⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆




⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⢀⠠⣤⣤⣤⣤⠤⠤⠤⢴⣄⠀⠀⠀⣾⣿⣷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⢀⣀⣠⢤⠈⠉⢹⣿⠟⠛⠉⠁⠀⠈⢉⠟⠀⠀⠀⠀⠠⣿⣦⣤⣤⣬⣋⣉⡀⠉⢉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢻⠁⢹⣷⡢⣤⣀⢠⠂⠀⠀⣼⡤⠴⠞⠋⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠙⠈⠛⠿⢿⣭⣿⣷⡿⠶
⢀⡀⣠⣤⣤⣤⠀⣨⣿⣷⣉⣤⣶⣿⢇⣼⣿⣾⣀⣀⣸⠁⣀⣀⣀⣠⣤⠴⠖⠒⠚⠛⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣬⣿⣿⡇
⢀⣀⠀⣀⡐⣛⣛⣿⣿⣿⠿⠿⠿⠟⠛⠿⠿⣿⣿⣿⣯⣿⣿⣀⡀⢠⡶⣀⡔⠀⠀⠀⢹⣿⣿⣿⡄⢠⠄⣠⣀⠀⠀⣼⡏⠉⠻⢿⣥
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠶⠺⠷⢶⣦⣘⣉⠉⠩⢍⣛⡛⠿⢿⣿⢿⣿⣿⣿⣿⡿⠿⠿⢿⠟⠿⠿⠿⣿⣿⣿⣅⣀
⢸⣿⡛⣛⠟⡛⠘⠛⠘⠻⡿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⡿⠿⠿⠶⠶⢦⣞⣿⣿⣿⣀⣀⡀⠘⣇⡀⠀⠀⣯⡉⠉⠙⣍⠛⠶⣶
⢠⣤⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢫⣤⣭⢿⣿⣿⣿⣿⣶⣦⣄⣩⣿⠓⠢⠬⣭⣉⡉⣛⠛⠻⠿⠿⢷⣄⣀⠈⣳⣄⡀
⠐⠂⣀⡒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠻⠿⠭⠿⣟⡿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠜⢹⣷⣄⣀⠀⠈⠉⠉⠛⠛⠿
⢸⣿⡿⠭⠩⠅⠠⠤⠤⠤⠤⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡿⣿⡿⣿⣿⣿⣷⣻⣿⣿⣿⣻⣿⣶⣬⣙⢳⣶⡦⣄⣀⡀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⣤⣥⡴⠶⠿⠿⣿⡷⠼⣿⣿⣿⣯⣥⣎⣻⡿⣿⣿⣿⡿⣿⣿⣷⣶⣭⣿
⠸⠷⠶⠖⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠹⣿⣧⠤⠼⠿⠛⠻⣿⣿⣭⣟⣙⣷⡷⢿⣽⣽⡾⣽⢿⣻
⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠟⠿⠿⠿⠷⠛⢻⡃⠀⠀⠀⠀⣾⣿⣿⣇⣩⣟⣙⣿⣿⣿⢶⣏⣽⣞⣷
⠰⠶⠶⠶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⠶⠶⠶⠟⠛⠛⠛⢿⣿⠃⠀⠈⠈⠙⢿⠿⠟⠟
⠐⠒⠒⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣼⣄⠀⠀⠀⢀⣏⣀⡀⡀
⠘⠓⠀⣀⣠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠙⠓⢤⠀⠀⠑⢤⣀⣼⣯⣇⣱⡟
⢠⣤⣤⠤⠤⠤⠀⠨⠿⠿⠿⠿⠿⠿⠿⠷⠶⠤⠤⠤⠤⠤⠄⠐⠒⠒⠶⠶⠶⠶⣶⣶⣷⠀⣀⣀⣤⢄⣠⢳⢦⡄⠀⡙⣿⠟⠛⠋
⣴⣴⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣴⣶⣶⣶⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣽⣭⣽⣯⣿⣭⣥⣥⣤⣥⣧⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⣀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⢉⡷⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠓⠤⠄⠈⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠂⢙⡂⠐⢶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡶⠊⠑⠚⠉⠀⢀⣀⠀⠀⢀⣀⣀⣀⣴⠋⣳⠀⠈⠢⠤⠄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⠴⠶⢤⣀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣏⠈⠳⢛⣉⡁⢀⡤⡄⢸⠇⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠋⠉⠁⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢳⠀⠋⠉⣽⡏⠀⠶⣽⣆⡀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⠀⠀⠀⠀⠀⢀⡠⠼⠆⠳⠤⣴⠿⠶⡖⠁⠀⠈⠱⡄⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⣆⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⠑⠊⢀⠀⡶⠀⢠⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠹⣆⠀⠀⠀⢳⡀⠀⠛⣃⠒⢲⠘⠃⢋⡐⢀⡴⠋⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢹⡶⠚⠒⠲⣄⠀⢀⣆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⣦⡤⠤⠤⠽⠷⠦⣌⡳⢏⠐⣈⢟⡵⠋⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⠔⠋⠉⠉⠲
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠻⡉⢹⣀⣀⣀⣀⣀⣀⣆⠀⠀⣰⠧⡙⠲⢶⣶⣶⣾⠇⢹⣶⣶⡖⠛⠲⢄⡀⠀⣠⡴⠋⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢹⠋⠉⢫⡈⠁⠙⢏⠁⠙⣇⠉⢦⠈⠐⠂⠈⠙⠻⠶⠴⢿⣿⣿⣿⣶⡤⣿⣿⡥⠤⢤⡴⠶⠶⠶⠖⢇⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⡇⠀⠀⠆⠀⠀⣸⠀⠀⢸⠀⠐⡆⠀⠀⠀⠀⠀⠀⠠⡤⠄⠀⠀⠠⢰⡏⠈⡆⠀⠀⢃⠀⠀⠘⡀⠘⡄⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠰⣇⠀⣰⠀⢀⣠⣋⣀⣠⡏⣀⠞⠀⠀⠀⠀⠀⠀⢀⡌⣹⠀⠀⣀⢀⣼⠁⢀⠇⠀⠀⡸⠀⠀⢀⠃⠀⡇⢀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⢸⠉⢿⠉⠉⠉⡏⢀⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠜⠀⠀⠰⠠⣼⠗⠒⠛⠒⠒⠒⠛⠒⠒⠛⠉⠉⠉⠉⠳⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⣧⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠧⢰⡇
⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⡜
⠀⣶⠿⠿⠶⠶⡒⢞⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⢠⠁
⠀⠹⡀⠀⠀⠀⠀⡌⡆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡼
⠀⠀⢳⡄⠀⠀⡀⢠⠸⡆⠀⠹⡖⠛⠉⠉⠲⣖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠈⣧⠀⠀⠀⠀⢃⢻⡀⠀⠀⠀⠀⢀⣀⠈⣦⠀⢀⣠⠤⠖⠚⠂⠤⢤⣀⣀⣀⣀⣤⡤⠔⠋
⠀⠀⠀⠘⣇⠐⠒⠀⠀⠌⢧⠀⠀⠀⠰⣿⡿⠃⣸⠋⠉⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢱⡄
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡸⣇⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⡞⠙⠣⢀⣀⢀⡤⢾
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠁⢻⡄⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⡄⠀⠀⠈⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠄⠤⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⡗⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠀⠀⠀⠀⠚⠋⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⠌⠛⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡠⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠤⡀⠄⠀⢀⠀⢠⣄⡀⠤⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⢀⡀⠀⠀⡀⠀⢀⡀⣀⣤⣴⡄
⠀⠀⡀⡀⠀⡄⠀⡀⠄⢄⣦⡵⠊⠉⠉⠉⠁⠒⢄⠒⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⣀⠈⠰⣷⡅⢈⣁⣠⢀⡀⢀⠈⠀⠠⡀
⠀⠀⠃⣹⣾⠗⠀⠀⠀⣠⠟⣶⢖⡴⢿⡢⠐⠀⠀⠀⠐⠓⢀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣠⣿⣶⣲⣿⣏⠀⢀⠉⠚⠅⠛⠁⢠⠀⠉
⠀⠀⢰⡝⡏⠀⣀⢄⠘⠻⠉⢿⡀⠻⡾⠀⠉⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠟⠚⠁⢙⡵⠻⡏⢻⣁⡤⠀⠈⠀⠀⠀⠒⠠⡀
⠀⠀⠸⠉⠁⠀⠉⠆⠀⠀⢀⣿⡏⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⡟⠁⠀⣿⡭⢹⣋⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠘⠷⠗⠚⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠀⠀⠨⠁⠀⠀⡽⠓⠴⠋⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⣠⣦⡴⠀⠀⠘⠀⠀⠐⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠠⠄⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠞⠃⠐⠣⠈⠁⠀⠀⠀⠄⠀⠀⠄⠀⠀⠄⠀⠀⠀⣀⣠⣡⠀⠘⣆⠀⠀⠀⠀⠀⠁⠒⠀⢀⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠁⠀⠈⠟⡇⠈⠙⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠦⠔⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣎⠘⢻
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠔⠃⠀⠀⠀⠀⠠⣴⣤⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠉⠉⢳⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠛⠀⣀⣠⠞⠋⠙⢲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⣤⣤⣤⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⣰⠋⡽⠟⠁⠀⠀⠀⠀⢸⠇⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢿⡀⠙⠒⡶⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠉⣛⠉⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⡋⠙⠓⠿⣄⠈⢧⣀⡤⠴⠒⠒⣒⣦⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⣘⣆⢸⣧⡶⠒⠾⠯⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣹⠾⢤⣍⠉⠳⢦⠤⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡼⠁⠀⠀⠈⠙⠲⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⡾⠁⠀⡤⠚⠉⣩⣷⡀⠉⠀⣠⠖⠋⣩⣷⡄⠀⠀⢠⠖⠉⢉⡭⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣰⠃⠀⡼⠁⠀⠘⣇⠈⠀⢀⣰⠃⠀⠀⢧⡀⠁⠀⣠⠏⠀⠀⠸⣄⡀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡿⠐⠋⠁⠀⠀⠀⠈⠉⠛⠉⠁⠀⢀⠀⠀⠉⠛⠛⠁⢀⣀⣀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠒⡇⠀⠠⠞⠋⣉⣳⡄⠀⠀⢠⠞⠉⢉⠭⣦⠀⠀⢀⡞⠉⢀⡼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⢇⡈⠁⠀⣠⠏⠀⠀⠹⣄⡀⠀⣠⠞⠀⠀⠘⢦⣀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠤⠴⣇⣀⣀⣀⣀⣀⣉⡛⠋⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⣚⣛⣋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠶⠶⠶⠦⠤⠴⢶⣟⣉⠉⠉⠉⠉⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⢢⠀⢰⠀⣒⠀⣦⠀⠀⠐⠀⠀⢆⠐⠂⢰⡂⡔⠐⢠⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠈⠈⠀⠀⠂⠈⠂⠐⠀⠀⠂⠀⠀⠀⠀⠀⠊⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠢⡞⠉⠉⠁⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠁⢦⠤⠔⠺⡅⠀⠀⠀⠀⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠒⠀⠀⠀⡠⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠈⠀⠘⡦⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠤⠖⣇⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡰⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠒⢤⣀⡠⠒⠒⡄⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡞⠀⠀⠀⠉⠉⢂⠠⠤⣆⠈⡴⠒⠊⠀⠀⠸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠢⢀⡀⠛⠀⡀⠰⠆⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡀⠀⠀⢾⣄⠀⠀⠙⠲⠀⠠⢤⣀⠀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠱⡀⠀⢸⣿⣷⣤⣀⠀⠃⠀⠀⠉⠀⡀⠙⢆⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⢄⠀⢿⠿⠿⠏⠀⠃⢰⣶⣶⡾⠃⢀⡘⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣀⡀⠀⠤⢥⡄⠢⣀⠀⠀⠀⠛⠿⢋⣠⠔⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⢀⡿⠃⠠⣤⣤⣴⣶⣶⣶⠦⠤⠤⣤⣴⣌⣉⡓⠲⠦⣄⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠃⠀⣀⢈⣧⣤⢀⠀⠉⠛⠻⠿⠿⠀⠀⠀⣿⣿⣿⣿⠿⠿⠖⠋⢹⣁⡀
⠀⠀⡤⠂⠲⡀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠥⠶⡔⠋⠀⠉⢄⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠘⡏⠈⠉⠳⢦⡀
⠀⢨⠀⠀⠀⣇⡀⢀⣀⡤⠖⠋⠉⠑⢄⠀⠀⠈⡆⠀⠀⠈⡇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠈⣥⡅⠀⠀⠀⠀⠀⢠⡇⠀⡠⠀⠀⠙⢦
⠀⠈⠣⡀⠀⠈⠉⠉⠉⠐⢢⡀⠀⠀⠈⡄⠀⠀⠐⠀⠀⣠⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⠰⠀⠐⠀⢀⠀⢠⣇⡀⠀⠀⠀⠀⠈
⠀⠀⢠⠃⠀⢀⠔⠈⠀⠀⠀⢹⠀⠀⠀⣁⣠⡤⠶⠚⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⠀⠀⢀⠰⠄⠈⣿⠏⢹
⠀⡰⠁⠀⠀⠈⠀⠀⠀⠀⠀⢰⣤⡴⠚⢉⣁⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠀⠀⠀⣿⡴⠃
⠠⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⡄⠀⠀⠀⢹⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠒⠀⠀⡟⠠⡀⠀⠀⠀⢀⡜
⠀⢧⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠙⢦⣀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⠀⢀⡤⠋
⠀⠈⠛⠦⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⠐⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⣼⠛⠶⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠛⠲⡶⠤⠤⠤⠤⠤⡔⠒⠊⠁⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⠤⠤⠰⣇⠀⠀⠀⠀⠀⡷⠀⠈⠉⠉⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⣴⡌⡇⠀⠀⠀⢸⣴⣷⡄⠀⠀⠀⠐⠋⠀⠐⠲⢤⡀
⢀⣀⡀⢀⡀⢀⠀⠀⢀⣀⣀⡔⠊⠉⠁⠀⣠⠚⣉⣠⠠⠄⢀⡀⠀⠸⣿⡇⠀⠀⠀⠀⢸⡟⣿⡇⠀⢠⠂⠁⠀⠀⠀⠀⠈⢻⡀
⠘⡿⣿⣋⠁⢰⠒⠀⢸⣯⢉⣿⠇⠀⠀⠀⢐⣿⠋⢹⡷⠀⠀⠹⡆⠀⠉⠁⠁⠀⠀⠀⠘⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠘⠛⠉⠋⠁⠈⠀⠀⠈⠛⠉⠁⠀⠒⠀⣀⠀⠉⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠀⠀⠈⠉⠈⠀⠀⠀⢀⣀⣀⣀⣈⠂⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠒⠒⠒⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⢸⡄
⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣶⣿⣿⠆⠀⠀⢻⣿⣦⣶⣿⡇⠀⠀⠸⣿⣆⢀⣼⣿⠀⠀⠀⢿⣿⡶⣿⣿⡇⠀⠀⢸⣿⣦⣠⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣦⣀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠉⢻⡿⠋⠁⠀⠀⠸⠿⢿⣿⣿⠿⠿⠀⠀⠉⠛⢿⡿⠛⠉⠀⠀⠀⠉⠻⣿⠟⠁⠀⠀⠈⠙⠻⣿⡿⠋⠉⠀⠀⠈⠛⢿⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠃⢀
⠀⠀⠀⢀⣀⡄⢀⣄⣀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⢀⣆⠀⠀⣴⠀⠀⠀⢀⣄⠀⠀⢀⣤⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⢠⣿⡀⠀⣼⣆
⠀⠁⠀⠘⠿⠟⠺⠿⠟⠀⠀⠀⠿⠿⠿⠿⠿⠁⠀⠀⠸⠿⠇⠸⠿⠇⠀⠀⠘⠿⠷⡰⠿⠟⠀⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⠘⠿⢷⡴⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠄⠀⡤⣤⣤⣤⣤⣤⡄⠀⠐⢶⣶⣶⣶⡶⠆⠀⠀⠤⣤⣤⣤⣤⠤⠀⠀⠤⣴⣾⣿⣶⡦⠄⠀⢠⣤⣤⣤⣤⣤⣤⠀⠐⠀⣀⣀⣀⣀⡀⠐
⠀⠀⠀⠁⠈⠻⠟⠁⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠈⠻⠏⠁⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⠉⠛⠿⠟⠋⠉⠀⠀⠀⠈⠻⠟⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠈⠙⠛⠣⠤⠌⠈⠁⢤⣶⠲⠀⠀⠀⠀⠙⠻⠿⣿⣛⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⡿⡿⠋⠉⠙⠛⠛⠛⠛⠛⠃⠀⠀⠠⣤⣄⣀⠀⠀⠀⠐⠖⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠉⠀⠀⠀⠸⠿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣠⠀⠀⠀⠀⠉⠉⢩⣭⠔⢲⣶⣶⣶⠶⠶⠶⣶⡶⣒⣲⣶⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣻⣷⣤⣤⣤⠤⠤⠤⠐⠒⠒⣊⣀⠀⠀⣠⡀⣾⣯⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿
⣥⣴⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⢿⣋⣉⣀⣐⠶⠒⠚⠛⠉⢻⡇⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣭⣥⠶⢿⣯⣿
⠿⠿⠿⢛⡛⢛⣛⣟⣽⣷⡾⠝⠛⠛⠉⠉⠀⠀⠀⠀⢀⣀⣿⡇⡆⡍⣿⣇⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⣿
⣶⣶⠾⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣤⣴⣿⡏⣿⡇⠃⣦⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣻⣿⣿⣿
⣿⡿⠗⠒⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⡟⣿⣿⣿⣿⣿⣿⣗⣺⣿⣿⣿⣿⣿⣍⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣯⣿⣟⣹⣻⣤⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠁⠀⠀⠰⣖⢸⣷⢀⣀⡻⢋⡀⠀⣇⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣧⠀⠀⠀⠀⣹⣯⠁⠈⢹⣧⣾⣶⠹⣿⣁⡞⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⢴⣇⠀⠀⢻⣿⡀⠀⢘⣿⣟⣛⠀⠘⣿⣷⣞⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣅⡟⠀⠀⠀⢛⠁⠀⢹⣿⣿⡆⠀⠀⣽⣿⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⡖⠆⠀⠀⣀⣤⣼⣿⡟⠃⠀⠀⠀⢸⠀⠀⢀⣿⡟⠛⠀⠐⢿⡟⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣆⢘⣸⠉⣇⡄⢀⣇⣸⣇⢀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⠟⢻⣿⣧⣤⣼⣿⡇⠀⠀⢹⡼⠇⡀⣿⡇⣸⣿⠁⠸⠾
⠀⠀⠀⠐⠦⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠵⣿⠃⢸⣿⣿⣿⣿⣿⠃⠀⠀⣼⢿⠀⠤⢸⣷⢹⣁⠀⢈⣤⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠋⣠⣮⣭⡛⢁⣴⣶⣶⣿⣿⡙⠀⠀⠀⠀⢿⡿⠀⠀⠈⣿⢸⡇⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⢿⡆⢹⣿⣷⡮⣾⣵⡜⠇⠀⠀⠀⢡⠈⠁⠀⠀⠇
⠀⣠⠶⠶⣶⣶⣴⣿⡿⠁⠀⠀⠀⢠⣼⢋⣛⢘⣿⣿⣿⡬⣿⣼⣿⣿⣿⣿⣿⡇
⣼⣇⣠⣶⣿⣿⣿⡟⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⡻⣿⣟⣟⣣⣰⡇⠀⠀⢀⡀
⠘⣿⣿⡿⣿⣿⣟⠓⠀⠀⠀⢸⠁⠈⢹⣿⣿⣿⣿⡾⠻⢿⣿⣿⣿⣹⢿⣯⣯⠄⠀⠈⠉⠙⠿⣿⣿⣒⡢⢤⣀⡀
⠀⠈⠛⠿⠿⣿⣯⠀⠀⠀⠀⠰⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠻⢿⣿⣿⣿⣿⡿⣶⣤⡤⣑⠓⠲⠛⠛⠻⠿⠿⠿⠿⠿⣶⣂⠰⣮
⠀⠀⠀⠀⠀⠘⢿⣿⣦⣤⣀⣴⣋⣤⣶⢿⣿⠟⠀⠀⠀⠀⠀⠀⠙⣿⣿⣯⡽⣾⣶⣤⣠⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢓⣶⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣿⠿⠿⠿⠽⠷⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠹⠆⢀⣀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⣶⣀⣬⣅⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢲⠀⠂⠀⠀⠀⠈⢳⠀⠘⠁⠀⢢⠀⡚⠉⠐⡖⠀⠀⠀⠒⠂⢤⠀⡐⠀⠘⡆⠠⠠⠤
⠀⠀⠀⠀⠀⡴⠒⠠⠄⣸⠀⠇⡄⠀⡔⠂⠈⡄⠠⠀⠀⠈⢇⠁⠀⢰⠁⠀⠀⡔⠒⢠⠸⠀⡅⠀⢀⠃⠰
⠀⠀⠀⠈⠄⡈⠐⠢⢄⡀⠀⢠⠁⠀⡇⢘⠀⡇⠰⠀⢸⠀⠈⠃⠀⢸⠀⠀⠀⡇⠀⠀⠀⡆⡇⠀⠸⠀⠀⠀⢠
⠀⠀⠀⢠⠀⣀⣉⡲⠀⠙⡄⡄⠀⠀⠀⠀⠀⢱⠈⠀⢸⠐⠀⠀⠀⢸⠀⠀⠀⡇⠀⠂⠀⡇⢀⠀⠐⠤⠐⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⠀⢀⡏⠉⠀⠀⢸⡀⠀⢸⠀⠡⠀⠀⢸⢐⠀⠀⢉⣉⣀⠠⠃⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠈⠀⠉⠉⠁⠉⠀⠈⠉⠉⠀⠀⠁⠉⠈⠉⠀⠉⠀⠀⠁⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⡀
⡀⠀⠀⠀⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠻⠠⠶⠀⠈⠹⢛⣆⠀⣴⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡆⠴⣤⣤⣤⣀⣿⣇⡛⢴⣿⣤⣤⣍⡀
⠀⣑⣶⣬⣿⣿⡀⠀⠈⠁⠀⠀⠉⠥⠬⠱⠐⠒⠂
⢙⠛⠻⠿⣾⣭⣉⡓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⡀
⠙⠓⠲⡄⠀⠀⠈⠽⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠉
⠀⠀⠀⢀⣠⣶⣞⣀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⡄
⠀⠀⠀⠈⢛⠿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠓⠶⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣀⠤⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠇⠠⢯⠀⠀⠀⠀⠀⢰⡀⠩⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣀⣇⣸⠋⠀⠀⠀⠀⠀⠠⣍⠢⡈⠂⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⢤⣀⠀⠀⢠⠃⠀⠀⠠⡊⠲⣒⡉⡩⢁⡎⠀⠈⠁⠀⢧
⠀⠀⠀⠀⠀⣰⠾⠉⠁⠉⠀⠀⠈⠳⡀⢸⠀⠀⠀⠀⢸⣊⡀⣺⣄⡻⠓⢤⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡄⠀⠀⠜⠀⣀⡀⠙⣘⡀⡦⢀⠇⠀⠀⡼
⠀⠀⠀⠀⠈⢧⡤⢤⣀⠀⣤⠀⠀⠀⠘⡇⠙⣄⣀⣸⣤⣌⣠⡥⠀⣷⠗⠁⠀⠀⡼⠁⠀⠀⣀⠤⠶⢤
⠀⠀⠀⠀⠀⠸⡀⠀⠈⢻⣹⢤⠤⢤⣤⣇⣤⡟⢷⣮⣁⣺⠈⠂⠺⢕⠢⣀⡤⠊⠀⣀⣀⡼⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⡦⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠉⠘⠉⠭⣻⠛⠛⢽⠋⠉⠉⠉⠉⠁⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢄⡄⢣⢤⡤⠤⡤⣤⠤⠞⠀⠀⠀⠀⢪⠇⠀⠒⣞⣀⣆⣀⣤⣀⣤⡤⠤⣈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠘⡆⠀⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠬⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣠⣶⣶⢶⡶⢤⡀⠀⠀⠀⠘⢦⣼⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⡏
⠀⠀⢫⠁⠈⠑⣡⠀⢳⣀⣀⣀⠀⣀⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠈⢧⠀⠀⠫⠆⠀⠻⠀⢈⠻⡁⢀⣀⣤⢤⣄⣀⣀⣀⣀⡠⠃
⠀⠀⠀⠘⣆⠀⠐⢊⠄⠀⠀⠀⢀⠟⠉⠀⠀⠀⣀⡹⠌⠉⢹⠆
⠀⠀⠀⠀⠘⣆⠀⠘⢶⣀⡤⠚⠁⠀⠀⠀⠀⢰⡇⠉⠒⠒⢹
⠀⠀⠀⠀⠀⠙⠒⠲⠾⠋⠀⠀⠀⠀⠀⠀⠀⢸⠡⠄⠀⠀⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡈⠱⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠈⠀⢀⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡡⠒⠓⡄⠰⡗⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠓⠒⢋⡠⠞⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⠙⠖⠒⠉⠀⡀⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢘⡄⢇⣀⣀⠀⠀⠀⠀⠀⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣄⡜⢀⠔⢤⣈⡑⢐⣉⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡎⠀⢠⠙⠶⣬⣤⡓⢨⡏⠀⠀⠀⠐⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⢦⢸⠙⢢⣜⣤⠝⢉⠑⡆⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠤⠤⠿⣯⡛⠤⣼⣥⣫⠔⠃⠀⢀⡞⠁
⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣠⢤⣞⣓⣾⣍⠻⢿⣿⣿⠛⢻⣿⣯⣕⣲⣤⠞⠋
⠀⠀⠀⠀⢏⠀⢧⣀⣠⠤⠖⠚⠋⠉⠁⠀⠀⠀⣻⠒⠢⠬⠭⣭⡍⠭⠥⠴⡞⠳⣤⡀
⠀⠀⠀⠀⢈⡇⢀⠄⠀⠙⡄⠀⠀⢀⣀⣠⡤⠖⠁⠀⠀⠀⠀⠘⠀⡠⠤⢐⡇⠀⠀⢻⡄
⠀⠀⠀⢠⡞⠀⠈⠀⠀⣠⢷⠚⠩⢍⠀⢰⡇⠀⠀⠀⠀⠀⠈⠐⠁⡇⠂⣸⣹⠇⠀⠈⡇
⠀⠀⠀⠈⣧⡀⠀⣠⠋⠀⠈⢧⡀⢸⠂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⡿⢤⠀⠀⣸⠃
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠹⢦⡟⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢠⡇⢸⠷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣈⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠦⣤⣀⣀⣀⣀⣀⣤⣾⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠲⢾⡄⠉⢉⡿⠓⠒⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣥⡀⢀⠠⣇⠀⢸⡇⠀⠀⣠⠿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⢲⠘⠜⡇⠀⢸⡗⠂⠔⠉⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠴⣧⠀⢨⡷⠖⢒⠒⠒⠒⣒⣺⡄⠀⠀⠀⣀⡀⠀⢀⡀⡤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠈⠁⠉⠀⠀⠉