Hello kitty! Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠙⠳⣶⡿⠋⠁⠈⢿⣆
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣤⣀⣤⣴⣶⡶⢿⡟⠀⢀⣤⣤⣼⡷⢤⣄⣤⠾⠿⢦⡀
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⢸⡇⠀⠸⣧⣾⠁⠀⠀⢹⡷⣤⠀⠈⡇
⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣤⡿⣦⣀⣠⣾⠷⠟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠙⠶⠴⠾⠻⣧
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡷⠛⠛
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣼⣧⣀⣀
⠀⠀⠀⠀⢀⣀⣿⣤⣄⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠘⠋⠉⠹⣧⣀⡀⠀⠀⠛⠛⠀⠀⠀⠀⢸⣏⣹⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⠷⠶⠄
⠀⠀⠀⠀⠀⢠⠶⠻⣿⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢿⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⡶⠟⢻⣇⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠁⢀⣤⡾⠟⣿⠟⢻⡿⠛⠛⠛⠛⠉⣿⠁⠙⣷⡀⠀⠻⣧⡀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠻⣦⣾⣯⣤⣄⡻⣦⣤⣠⣤⡾⠃⣀⣤⣬⣿⣄⣤⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠟⠋⠉⠉⠙⢻⣆⠀⠁⠀⣠⡾⠋⠉⠈⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣧⣼⡏⠀⠀⠀⠀⠀⠀⢻⡆⠀⢠⣿⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣠⣿⣀⣀⣀⢻⣆⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣤⣤⡾⠟⠛⠛⠛⠛⠛⠻⠷⣦⣤⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠶⢤⣀⡀⣠⠞⠋⠳⣄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢈⣹⡃⢀⠀⠀⢹⣦⠤⠤⠤⠤⣴⠟⠁⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠶⡾⠉⠉⠙⣯⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣔⣳⡀⠀⣀⡿⠦⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠳⡄⠈⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣧⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠠⠤⢼⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢺⡿⢭⣍⡓⢦⡀⠉⠀⠀⠀⠀⠀⠀⡔⠒⢄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢦⡷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡽⠛⠢
⠀⠀⠀⢀⣤⣄⠀⠀⠀⣠⣤⣄⠀⠀⠀⠹⣆⠀⠀⠀⢸⡷⣤⡤⣤⣞⣉⣙⠳⢦⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠿⠻⣄
⠀⠀⠀⣿⠀⠘⠗⠒⠒⠋⠀⢿⠀⠀⠀⠀⠈⠳⢦⣄⣼⠃⠀⠀⢸⡇⠀⠈⠙⣾⠟⣿⡛⠛⣿⠉⠉⠉⠁
⠀⠀⡼⠋⢀⣠⠤⠤⢤⣀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢸⠃⠉⠲⢤⣾⣀⣀⣠⠞⢁⣼⠋⠉⢣⢻⡆
⢀⡾⠁⢠⠏⢴⠆⠸⠗⢀⣽⣄⠈⢷⡀⠀⠀⠀⠀⠘⢧⣤⠴⠛⠻⣿⡿⡶⢶⡉⣧⠤⠤⢼⡆⠹⣆
⣼⠃⠀⣿⠰⠆⢰⣋⣣⢈⣁⢸⠀⠈⢷⠀⠀⣠⠤⣄⢸⡇⠀⢀⡴⣿⠁⢧⡤⣿⠁⠀⠀⢸⠃⠀⢹⡆
⣿⠀⠀⢸⠖⡆⠀⠉⠁⠈⣫⠞⠀⠀⢸⡇⠀⠹⢦⣼⣿⡷⠚⠉⠀⣿⠀⠀⠀⠈⠙⢦⣤⠞⠀⠀⣼⠷⠶⢦⡄
⠻⣤⣀⣈⣉⣉⣓⣒⣒⣋⣁⣀⣤⣤⠾⠳⠶⠶⠛⠁⠈⢿⣄⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣃⣀⣀⣀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⣶⣄⠀⠀⣀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⢷⣶⣤⣀⡀⣀⣀⣀⣤⣤⣤⣼⠟⠁⠀⠀⠀⠈⠻⣷⡿⠟⠛⠉⠉⠉⠹⣷
⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠈⠙⠛⠿⠛⠛⠋⠉⠉⣹⡟⠀⠀⠀⢀⣤⣤⣄⣿⣇⣀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢾⡁⣼⡟⠋⠉⠛⢿⣶⣶⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠾⠛⢿⣦⡀⠀⣀⣼⡏⣹⡇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⠉⠉⠉⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣦⣤⡶⠟⠉⢿⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⢀⣀⣀⣼⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣿⡿⠿⠻⠟
⠀⠈⠛⠋⠉⢹⣿⡉⠉⠁⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⢀⣿⣧⣴⡦⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠘⠛⣿⡿⠿⠷⠶⠄
⠀⠀⠀⠀⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠿⠻⢷⣦⣄
⠀⠀⠀⠀⠀⣴⠿⠋⠁⠈⠛⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡴⠋⠀⢹
⠀⠀⢀⣤⣠⣄⣠⠞⠁⠀⡁⠀⠀⠀⠀⢀⡴⠒⠉⠉⠰⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⠀⠀⠀⠸
⠀⠀⢼⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⢠⠔⠋⠁⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠘⢄⡀⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠈⢦⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣀⡾
⠀⠀⠀⠀⠈⠉⠒⠤⣤⠎⠀⠀⠀⡇⠀⠀⢠⠃⣴⠈⢢⠀⠈⢢⡀⠈⢳⠎⠀⢀⠔⣩⣤⡙⢆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡇⠀⠀⢸⠀⠉⠛⡧⣄⠀⠀⠹⡄⠀⢇⣠⠏⠀⠳⣤⠞⠈⣧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠘⡀⠀⠀⢉⣠⠀⠀⠀⢹⡄⠘⡇⠀⠀⠘⢿⠇⠀⢈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡔⢊⡉⣉⠚⠃⠀⠀⠀⠉⠀⠀⠀⠀⢱⠀⢱⠀⠀⠰⠷⠀⠀⢸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⣥⠸⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣧⠖⠂⠶⢄⡀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠘⡄⠀⠘⠝⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡍⠀⠀⠀⠀⠉⠿⣤⡧⢀⣀⡔⠊⠉⠳⡀⣠⠔⠒⢄
⠀⠀⠀⠀⠀⠠⡎⠀⢀⡠⠤⠤⠤⢴⡄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠛⠁⠀⠀⠈⣧⠀⣀
⠀⠀⠀⠀⠀⠰⡇⠀⠸⠀⡴⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⢁⡴⠂⠲⣄⣠⣐⣚⠁⠀⠈⡃
⠀⠀⠀⠀⠀⠀⢸⡀⠘⣆⠙⠒⢻⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣄⠀⢀⡧⠈⠉⠉⠓⡄⢠⠁
⠀⠀⠀⠀⠀⠴⠃⠀⢀⡌⠶⠀⠀⠀⠑⠓⠀⠀⠀⠀⠀⠀⠀⣤⡀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠈⠉⡰⠉⠉⠁⣤⣄⠀⢀⡼⠀⡎
⠀⠀⠀⠀⠀⢧⠀⢸⠁⡔⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡟⠀⠉⠉⠀⢸
⠀⠀⠀⠀⠀⠈⢧⠀⠳⡌⠛⠹⣛⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣿⠀⠀⠀⠀⠀⢦⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠚⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠢⣀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⡷⠀⠀⠀⢸⣨⠀⠀⠀⠀⢩⠏⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⠑⠶⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠉⠁⠒⠒⠠⠤⠤⣶⡬⠛⠓⢄⠀⠈⠑⡤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣈⠶⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⣴⠶⠶⠶⠃⠀⠀⠀⠈⢆⠀⠀⡰⠦⢀⣀⡀⠾⠃⣰⠶⠒⢞⠋⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣸⠆⠀⠀⠀⠀⠀⣈⣧⣴⠁⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠹⡓⠄⣀⡀⠀⢸⠉⠲⢄⣉⠛⠚⠒⢦⣀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠙⢤⣄⣈⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⡃⠉⠐⠖⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠈⠑⠤⣀⣀⣀⣀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠒⠒⠒⠂⢀⡀⢠⡄⠀⠑⣄⡀⠀⠀⠀⠀⢰⠀⠉⢉⠉⡉⡉⠁⠒⠒⠒⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠁⠀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠀⠀⠉⠒⠢⠤⠴⠃⠀⠀⠀⠀⠀⠉⠙⠢⡄⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠲⠦⢤⣄⠀⠀⠈⠉⠰⠶⠄⣤⣤⡀⡀⠀⠀⠀⠀⠀⢀⠀⣠⣤⠄⠶⠊⠋⠀⠀⠀⢀⣤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠂⠠⠤⠤⠬⠭⠭⠭⠭⠭⠥⠤⠤⠤⠄⠒⠒⠒⠋⠉⢉⡠⠖⠲⡀
⠀⠀⠀⠀⣠⠤⠤⣀⠔⠋⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠓⠲⠴⠋⠀⠀⢠
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠱⠤⣀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⣀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣤⡀⠀⠀⣀⣤⣶⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠀⠀⠉⠻⣷⣾⡿⠟⠋⠁⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣿⣷⣶⣦⣤⣀⣠⣤⣴⣶⣶⣶⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠤⠤⠀⠤⠀⠠⠄⣸⣿⠏⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠟⠛⠉⠉⠉⠉⣸⣿⠀⠠⠄⣴⡿⠿⣿⣾⠿⠿⠿⢷⣦⣴⣶⠿⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⣇⣸⡿⠁⠀⠀⠀⠀⢻⣷⣄⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⣸⡿⢙⣿⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⣶⣶⠿⠻⣷⣤⣤⣤⣾⡿⠿⡿⠟⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣷⣄⡀⠀⣀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠛⠁⢹⣿⡄
⠄⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⣴⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⢀⣀⣾⣿⣀⣀⣀
⣀⣀⣀⣤⣶⣾⠿⠿⣿⣿⠛⠛⠁⠀⠀⠀⢀⣿⣿⣿⠄⠀⡀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⢀⠀⠀⠀⠀⠿⡿⠏⠀⠀⠀⠀⠀⠈⢻⣿⡿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⢀⡀⠀⠀⠀⠀⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⣠⡾⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⢶⠾⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠿⢷⣶⣤⡄
⣀⠀⡀⢀⣀⠀⠈⠉⠁⠀⠹⣿⣦⣀⣤⡄⣀⠀⠀⢀⠀⣀⠀⣀⣠⣤⣤⣤⣤⣤⣼⣿⠿⣿⣧⠀⠀⡀⠀⠀⠄⣀⠀⢀⣴⣿⠟⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⢿⣷⣤⣀⣀⣀⣀⡀⠀⣴⣿⡟⠋⠉⠉⠙⠛⠿⠿⣼⣿⣧⣀⡀⠀⠀⣀⣠⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠛⠁⠀⠀⢉⣿⡿⠟⠛⠛⢿⣿⡟⠻⠿⣿⣷⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣾⡿⠟⠛⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⡀⠀⣿⣷⢀⡀⣿⣧⣤⣶⣾⢿⣧⠀⠀⢀⣀⣸⣿⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⣯⠛⠁⠀⠉⠉⠁⡀⠀⠹⣷⣄⣼⡿⣿⡿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢸⣿⡀⠀⢀⣤⠀⠀⠛⠀⠀⠈⠛⠋⣸⣿⠁⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠻⣿⣆⡀⠀⠀⢀⣼⡿⠋⠀⠀⠁⠀⠀⠀⢰⡆⠀⠀⠘⠛⢿⣦⣀⠀⠀⣀⣴⡿⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠈⠛⠿⢿⠿⢿⣿⠀⠀⢴⡄⠀⠙⠃⠀⠀⠀⢀⣤⠀⠀⢀⣿⡿⠿⠿⠟⠋⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠉⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠿⠀⠀⠀⠀⣠⣴⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⣀⣀⣀⣠⣴⣿⠟⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⣤⣄⣘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣀⠀⠀⠀⢀⣠⣾⡿⠛⠛⠋⠉⠉⠉⠉⠙⠛⠻⢿⣧⣀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠂⠀⠀⠀⠙⠻⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣶⣾⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⣦⣤⣀⣀⠀⠀⠀⢤⣠⡤⠶⠶⣄⠀⠀⠀⠀⠀⠀⢠⡴⠛⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠶⠖⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⠚⠛⠉⠀⠀⠀⠈⠳⣦⣴⠛⠻⠲⠶⠶⡄⠀⠀⠀⡠⠦⠦⡴⠲⡄⣀⣠⡴⠞⠋⠁⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠤⠼⠃⠒⠒⠒⠧⠤⠄⠤⠶⠃⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠻⣷⣄⠀⢀⣤⣴⣾⣿⡿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠛⠻⠿⣿⣷⣶⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣾⡟⠁⠀⠀⠀⠀⠈⢻⣿⡿⠿⠋⠉⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⣿⡏⠀⠀⠀⠀⣀⣀⡀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢠⣾⠟⠛⣿⣿⠿⠿⠿⢷⣦⣀⣠⣤⣤⣼⣿⣧⣄
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣿⣄⣾⡟⠁⠀⠀⠀⠀⠙⣿⡏⠉⠉⠀⠉⠉⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠈⠛⣿⡇⠀⠀⠀⠀⠀⠀⣿⡿⢿⣦⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣶⡶⠿⣿⣄⡀⠀⠀⣀⣴⣿⣅⣼⡿⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣏⠉⠛⠋⠁⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⣀⣀⣴⣾⣿⣆
⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⢿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣀⣀⣀⣀
⣀⣤⣤⣤⣴⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠿⠛⢻⣿⡟⠛⠛⠛⠛
⠉⠉⠉⠉⠉⢿⣿⠉⠉⠁⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣶⣦⣤⣄
⠀⠀⢠⣴⣶⠿⢿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⣿⣏
⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣯⡁⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠻⢿⣷⣤⡀
⠀⠀⠀⠀⢠⣾⠿⠋⠁⠀⠈⠻⣿⡟⠁⠀⠈⢻⣷⡾⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⠇⠀⠀⠀⠈⠁⠀⠀⢸⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡞⠙⢦⠀⠀⣠⣼⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡟⠛⠛⠻⣿⡿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⠀⠀⠓⠖⠋⠀⠀⠉⢿⡆⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⢹⣿⡄⠈⣻⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⠀⠀⠀⢀⣄⠀⠀⢀⣼⡇⠈⠻⣷⣤⣀⠀⠀⢀⣠⣴⡿⠃⠀⠀⠀⠀⠀⢻⣿⣾⡿⠋⠉⠛⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠈⢿⣦⣤⣴⣿⣟⠿⣿⣿⠋⠀⠀⠀⠈⠙⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡁⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⠉⠉⢻⣿⣆⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⢸⣿⢿⣧⡈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣴⣿⠏⠀⠹⣿⣦⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣶⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣾⣿⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⣠⣤⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠈⠻⠟⠉⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣆⣀⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⣿⠁⣀⣠⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠿⢶⣾⡿⠋⠀⠀⠙⢷⣤⣤⣤⣤⣶⣤⣤⣿⡿⠛⠉⠁⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣀⣼⣁⣠⣤⡀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⢀⣴⠿⠶⠶⢦⡞⠋⠉⠙⢿⣄⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⢸⡁⠀⢀⡴⢿⡀⠀⠀⠀⢸⣏⡁⢀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠘⣧⠀⠈⠷⠾⠿⣦⢤⠶⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⣾⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣄⣀⣀⡀
⠀⠀⠐⠶⠖⠺⣿⠷⠶⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⠀⠀⠀⠈⠉⢹⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠠⢦⣾⣧⣤⣀⠀⢀⣠⣤⠶⣤⣄
⠀⠀⠀⠐⠛⠋⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠏⠀⠀⠁⣴⠟⠁⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⢀⣠⣼⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠷⣤⡀⣸⠇⠀⠀⠀⢠⡶⣸⠇
⠀⠀⠀⠀⠀⠛⠉⠀⠈⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠛⠁⠀⠀⠀⠈⢉⣽⠆⠠⡶⠾⢋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣿⡷⠶⢶⣶⠶⠶⠶⠶⠶⠶⣿⠟⠛⢻⡟⠷⣦⣀⠀⠀⠀⢀⣴⢟⣵⠟⠳⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠟⢿⣏⣡⡿⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣽⡇⠀⠀⢻⣆⣴⠟⠛⠛⢶⣏⣵⠟⠁
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢈⡿⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠈⣿⠁⠀⠀⠀⣠⡦
⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡴⠶⢶⡶⠛⠳⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠇⠀⠀⠀⣠⣿⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⠻⣦⣤⣤⠾⠋⠀⠀⢀⣠⣿⣉⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⣴⠟⠉⠉⠉⠁⢉⣙⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⣧⣤⡶⠛⠛⠶⠿⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡴⠶⠶⠟⣻⡟⠁⠀⠘⢷⣶⠶⠾⠿⠿⠿⠿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠉⠉⠉⠉⠉⠉⠉⣿⡏⠁⠀⠀⠀⠀⣀⣠⣴⠟⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠶⠾⠿⢟⡛⠻⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⣷⣴⠶⠶⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠒⠒⠒⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢶⣤⣀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠈⠉⠻⢷⣦⡀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣾⠋⠀⠀⠀⠈⠙⢷⣄⣠⣶⠿⠛⠉⠁⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⠛⠛⢛⣿⠃⠀⠀⠀⠀⢀⣀⡈⣻⣿⣡⣀⡀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⢰⣿⠛⢻⣿⠟⠉⠉⠉⠛⢷⣤⣴⣶⡶⢶⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⣦⣿⠃⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⠀⠀⣀⣈⣻⣇⠀⠀⠀⠀⠀⢀⣿⠏⢻⣆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠙⠷⣦⣤⣤⣴⠿⢿⣶⠾⠋⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣆⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⢀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⢹⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿
⢰⣶⡶⠾⠿⠿⢻⣿⠛⠋⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⠿⠿⠿⠶⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⠀⢀⣿
⠀⠀⠀⠀⢀⣀⣼⣿⡿⠟⠋⠁⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠙⠛⠿⣾⣿⣄⣀
⠀⠀⠀⠀⠛⠋⠉⠹⣷⡀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣀⣀⣹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⣰⡿⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣴⡟⠁
⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⡶⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⣦⣄⡀⠀⠀⠀⣀⣠⣤⣶⣦⡄
⠀⠀⠀⠀⠀⢀⣾⡿⠛⠻⠿⢶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡿⠃⠀⠀⠀⠉⠻⣶⠾⠛⠋⠉⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉⢉⣿⠁⠀⠀⢀⣤⣤⡴⠿⠶⢤⣄⡀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⣾⠋⣴⣦⠀⠀⠈⢻⣶⠚⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠘⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⢀⣻⡎⠻⠛⠀⣴⣦⠀⣿⡄⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠛⠋⠛⢧⣤⣀⡀⢨⣥⣾⣿⠟⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣷⠂⠀⠀⠀⠉⠛⠛⢧⣄⡀⠀⠀⣠⣾⣏
⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⠞⢻⡏⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠈⣿⡆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣄⣀⣰⢀⡤⢴⡿⣤⣤⠀⠀⠀⠀⠒⢾⣷⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣇⣀⣀⣀⡀
⢀⣠⣤⣤⣿⣷⣤⣤⠐⢶⣏⠙⢉⠛⢋⡤⠀⠀⢉⣧⠀⠀⠀⠀⢀⡴⠻⣷⣄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠛⠛⢻⡟⠉⠙⠛⠁
⠈⠁⠀⠀⠸⣿⠀⠀⠐⣿⡯⠀⠈⢹⡿⢤⡄⢐⣬⡏⠉⠀⠀⠀⠀⣠⡴⣿⠖⠀⢸⣿⡿⠀⠀⠀⠀⠀⢀⣠⣾⣇⣀⡀
⠀⠀⠀⣀⣤⣿⣷⠖⠀⠈⡹⠾⠧⣾⣠⢀⣶⡏⠀⠉⠀⣴⠶⠶⣦⠀⠀⢻⠀⢀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢨⡿⠋⠛⠛⠃
⠀⠀⠀⠉⠁⠈⢿⣆⠀⣀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠛⠶⠶⠋⠰⢦⣸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠶⣦⣿⣃
⠀⠀⠀⠀⢀⣠⣼⠿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⠶⠄⠀⠀⠀⠀⠀⢀⣤⡟⠉⠙⠻⠶
⠀⠀⠀⠀⠛⠉⠀⠀⠈⠙⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣼⣧⠄⠀⢀⣀⣠⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⢶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣿⠷⠾⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠉⠙⢷⡶⠟⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠉⠙⠛⠶⠶⠛⠛⠛⡿⠀⠀⣠⠤⣬⠧⢤⣀⣀⣠⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠳⣾⠁⠀⠀⢹⣅⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠒⠛⢦⣀⣠⠾⠼⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡴⠞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣀⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠈⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡉⠁⠀⠀⠸⠿⠇⠀⠀⠀⢀⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠷⢶⣄⡀⠀⠀⠀⠀⠀⠻⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⣹⡿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⣡⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⢻⡇⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣤⣤⣤⣴⣶⣶⣿⡿⠋⢁⡠⠔⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⡆⠙⠦⣤⡾⣦⡀⠀⢀⣠⡿⠀⣼⠋⠀⠀⠀⠈⠉⠀⢿⣎⣁⣀⣀⣘⣿⣄⡀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢾⣏⠀⠈⢻⡟⠋⠉⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⣿⠇⠀⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠛⠷⠶⠋⣤⣤⡄⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣠⣼⠃⢀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⢻⠶⣄⠻⠟⠃⠀⢠⣤⣀⡀⠀⠀⠀⠈⢿⠀⢀⣷⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡆⠙⠷⣤⣀⣀⠈⠿⠟⠁⠀⢶⣦⣤⠸⡇⠘⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢳⡄⠀⠀⠀⠉⠻⢦⣤⣀⣀⣘⠛⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⣦⡀⠀⠀⠀⠀⠀⠀⢈⡿⠛⠲⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠳⠦⣤⣀⣠⡴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⣤⣶⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⢀⣾⡿⠋⠀⠀⠙⠻⣿⣦⣴⣶⣶⣶⣶⣶⡿⠛⠉⠉⢻⣷⣾⡿⠿⠟⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣸⣿⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣽⡟⠁⢀⣤⣤⣤⣿⣧⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢸⣇⣴⠟⠛⠻⣿⣶⣶⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣨⣿⣿⡀⠀⢀⣿⢿⣧⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠻⢿⣿⣿⣷⠶⠏⠀⢠⣿⠇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣃⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⣠⣴⣿⡏
⢀⣴⣾⠿⣷⣤⡀⠀⠀⠘⠿⣿⣿⣿⡟⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⢻⣿
⠻⣿⣅⠀⠈⠙⠿⢷⣶⣤⣤⣿⣿⣿⣧⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣼⣿⣆⣀
⠀⠈⠻⣷⣦⣄⡀⠀⠀⠈⠉⢻⣿⣿⣧⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⣹⣿⠉⠙
⠀⠀⠀⠀⠉⠛⠻⠿⣶⣶⣶⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣹⠇⠀⠀⠀⠀⠀⠙⠋⠀⠀⠘⢻⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣯⣿⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⣿⣿⣿⣿⣿⠃⠀⠈⢙⣿⡿⣿⣷⣶⣶⣶⣦⣴⣶⣶⣶⣾⣿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣛⣩⣴⣾⣿⣿⣿⣿⠇⠀⠀⢠⣿⠏⣀⣄⣀⡿⠛⣿⠉⠉⠉⣿⡏⠉⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠉⢸⣿⠇⣾⡿⣷⣤⣤⣿⠏⢸⣏⡈⣻⡷⣴⡿⠟⢷⡄⢿⣇⠀⠀⢀⣠⡿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣇⠀⢨⣿⠏⠀⠀⣹⠿⢻⣤⡾⣷⡶⠞⠁⠈⢿⣦⣴⠟⠉⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⣿⡇⣼⡟⠀⠀⠀⠻⣤⡾⢻⣄⣨⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⣠⣄⠀⠈⠉⠀⠀⠀⠀⠀⠹⢷⣶⣶⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⣿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⣤⣶⣾⣿⣇⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠻⢿⣷⣶⣶⣾⣿⣿⣶⣦⣤⣤⣤⣤⣴⣶⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⠳⡄⢀⣠⡤⠶⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⠀⠀⢹⡋⠁⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠙⠳⠶⠖⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠋⠉⠉⠑⢦⡤⠴⠶⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⡦⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠖⢧⣀⠀⠀⢀⡜⢀⡀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣇⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠋⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣀⣀⣿⣄⣤⡀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠉⠉⣿⠉⠉⠉⠉
⠀⠀⠀⠀⠉⠁⠀⠘⣧⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠠⣤⣿⣤⣄⡀
⠀⠀⠀⣤⢤⡄⣰⠶⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠠⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣧⣄⠠⠦⠄⡀
⠀⢠⠶⣼⣴⣧⠷⠘⣫⡼⢿⡿⠖⠛⠛⠲⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠋⠉⠉⠙⠦⣽⡿⠻⠷⠿⣷⣀⠐⠄
⠀⠉⢙⣻⠟⠁⠀⠚⠁⣄⡞⠀⠀⠀⠀⠀⢘⠉⠀⠉⠉⠓⠦⣄⣀⡤⠞⠋⠉⠹⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠑⣦⣈⡀
⠀⡾⢋⡉⠀⠀⣀⠀⣤⣈⣧⡀⠀⣀⡴⠒⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠛⠲⣄⣀⣠⣾⡀⠚⠀⠀⠀⠀⠀⢠⣌⢻
⠀⠻⣬⣥⣄⠀⠉⠀⠘⢹⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣧⠰⢟⠃⠴⠀⢀⡤⠴⠛
⠀⠀⠀⠀⣈⣿⠷⢾⡟⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠳⢦⣤⣤⣴⣿⡁
⠀⠀⠀⠸⣏⠀⠀⠈⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⣿⠀⠀⢈⡿
⠀⠀⠀⠀⠉⠙⠉⠋⢻⡷⢬⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣀⣾⡧⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡴⠋⠉⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢷⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠒⠛⠛⠛⠓⠒⠶⠶⠶⠶⠶⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣤⣀⢠⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⣶⣆⡚⢿⣿⣿⣿⣿⢪⡾⢿⣿⣿⣧⣶⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠰⠀⠀⠙⠿⣷⡮⠿⠋⠀⠀⠸⣷⣥⣏⡉⣹⡇⢋⠀⠈⢻⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⣍⡙⢿⡇⠺⠀⠀⠠⠀⠀⠘⠰⣄⠀⠀⠾⠿⠿⣿⣿⢛⣤⠁⠒⠀⣸⣿⡇⠘⢦⣀
⠀⠀⠀⠀⠀⠀⣠⠄⣙⣉⣁⣸⣶⣿⣇⢲⣶⡴⣧⢭⣶⣶⣮⣥⣷⠀⢀⣛⡉⠈⢉⣒⣂⠰⠿⡿⠃⠀⠺⣿⡗⡄
⠀⠀⠀⠀⠀⡴⠁⠀⣈⡟⣿⣿⣿⣿⠟⡙⢋⣥⣿⣾⣿⣿⣿⣿⡏⣿⣿⣿⣿⣷⣿⣿⣿⣿⡆⠀⠂⠀⠀⢻⡿⠃⠠
⠀⠀⠀⢀⣶⢹⣿⣾⣍⣠⠞⢁⣠⣁⡀⠀⠀⠉⣿⣿⣿⣿⠿⠿⠇⣿⣿⣟⣻⠿⣿⡋⢴⣮⠃⠀⠀⠀⠀⠈⠀⠀⢠⣶⡄
⠀⠀⢀⡬⠇⢿⣼⡿⣻⠏⢠⡟⠁⠈⠙⠷⣤⣤⣤⣀⣀⣠⣶⣶⣄⠉⣉⣉⣀⠐⠦⢉⡘⢿⣷⣾⣧⠀⠂⠀⠀⠀⢀⣿⡅⠂
⠀⠀⢺⡇⢀⣾⣷⣝⣻⠄⢸⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏⠉⠉⢹⡇⢸⣿⣿⡎⣿⣿⣿⣆⠀⠀⠠⠠⠤⠉⠁
⠀⠀⠀⠙⢿⣿⡿⠛⠟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣧⡈⠛⢻⣧⠀⣈⣻⠟⠁⠈⠀⠀⠀⠠⢠⣤⡀
⠀⠀⠀⠀⢀⠬⠖⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠻⢿⣿⣿⣿⣿⣿⠃⠸⢿⣿⡧⠉⠉⠀⠀⠀⠛⠰⠿⠁⢰⣿⣷
⠀⢠⣄⢀⠆⠀⠘⠛⢻⣷⣆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠃⠀⠀⢃⡽⠃⠀⡀⠀⠀⢠⡀⠀⠀⠀⠐⠛⠁
⠀⣈⡋⢸⠀⠀⣠⠴⣾⠁⠘⡇⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣼⣄⣈⠉⠄⠀⠀⠒⠁⠀⠀⣀⠭⠀⠀⠀⣰⣐⡆
⠘⠿⠏⠈⠀⠀⠁⠀⠈⠀⠀⠛⠶⣄⠀⠀⠀⠸⣿⡆⠀⠀⠀⠛⠁⠀⠀⣠⣿⡀⠈⣠⣿⣦⣀⠂⠀⣀⠀⠀⠑⣀⣄⢀⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠓⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⠉⠉⠀⢿⡟⠿⠿⠗⠂⣀⢀⣤⣾⣿⣿⣧⣯⡛⠇
⣸⣄⠀⠀⣀⣤⣶⣶⣾⡀⠈⠛⢋⣰⠟⠛⠒⠶⠤⠤⠤⠤⠤⠤⠶⠚⠉⠉⠓⠀⠀⠀⠈⠾⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣶⣤⣿⣿⣿⣿⣋⡉⠛⠛⠉⠀⠄⠫⡀⡕⢢⠀⠀⠀⢄⣠⣤⣦⠤⢤⡸⣿⣟⠛⠉⠿⣇⣶⣶⣦⣝⢿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⠟⠁⣐⣿⣷⠆⣶⣿⠄⠑⠒⠡⠀⠀⡏⠀⣠⣹⡧⢄⠀⢹⠙⠦⠄⠲⠂⢨⣿⣿⣿⣿⣷⢹⡿⣿⡟
⣿⣿⣿⣿⠟⠻⠇⠀⠀⠙⠋⣱⣮⣾⢟⣤⠀⠺⢂⡖⡀⣧⣄⣡⣼⣷⣤⣴⣾⡈⠿⠿⠿⢃⣾⣯⣿⣿⣿⣿⣧⡄⠈
⣿⣿⠟⠁⠀⠀⠀⠀⣄⣀⡤⣹⡙⠀⣿⣿⣿⡾⣿⣦⡁⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⠏⠁
⠟⠁⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠛⢣⣿⣿⣿⣧⣾⣿⣵⣿⣭⣿⣿⣿⣭⠝⠀⠀⠀⣀⣇⠻⠿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⣯⣿⣿⠿⡿⡿⢿⣿⣦⡓⣶⣶⣿⣿⠓⢆⠘⠋
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⡿⣿⡋⠉⣿⣿⣿⡏⠉⢻⡿⣈⡧⠤⠚⠋⠉
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠷⣶⣄⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡟⠁⠀⠀⠀⠈⠻⣷⣾⣿⠿⠛⠋⠉⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠉⠉⠉⠛⠻⠿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⡅⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢀⣴⡾⢷⣶⣴⣿⣷⣶⣦⣄⠀⢀⣀⣠⣼⣿⣇⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣏⠀⣼⡿⠋⠀⠀⠀⠉⢻⣿⡟⠛⠉⠉⠉⠙⢿⣦
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣷⣶⣄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⠀⢀⣀⣨⣿⣧⡀⠀⠀⠀⠀⣰⣿⠃⣸⣿⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠙⠿⣶⣶⣶⣾⡟⠻⠿⠟⠃⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⡀⠀⠀⣀⣼⣿⣇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⢻⣿⡄
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⠿⠿⠻⠿
⢀⣀⣠⣤⣴⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠛⠛⠋⠉⠉⢿⣿⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⣴⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠸⣿⣇⣀⣀⠀⠀⠀⠀⠀⠸⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠛⠉⠛⠛⠃
⠀⠀⠀⣠⣴⣶⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⡏
⠀⠀⠀⠉⠉⠀⠀⠹⣿⣦⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠈⠉⠛⠛⠂
⠀⠀⠀⠀⠀⣤⣾⠿⠋⠁⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⣽⣿⠟⠛⠛⠻⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⡟⠛⠛⠛⣿⣿⡛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⡟⠁⠀⢀⣼⡿⠃⠀⠀⠀⠀⠙⣷⣤⣀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠈⢿⣷⡄⠀⠉⢛⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠋⠉⠻⣿⣦⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣴⡿⠛⠉⠛⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⢀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣶⣶⣶⣿⠿⠻⣿⣦⣄⡀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠿⣿⣷⣶⣶⣶⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡍⠉⠉⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠉⠉⠉⢩⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢶⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⠛⠛⠷⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠈⠙⢷⣄⣤⡶⠟⠋⠉⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣴⠶⠶⠶⠾⠻⣿⠃⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣴⠾⢷⣶⠿⠛⠛⠶⣤⣀⣤⣤⣶⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣤⣿⠁⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣽⣇⠀⠀⠀⠀⠀⢀⣿⢦⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠻⣦⣀⠀⢀⣠⣾⣃⣸⡇⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣌⠉⠉⠀⠀⢀⣰⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠛⠉⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢾⡿⠶⠶⠶⠦
⠀⠀⠶⠾⠿⠛⢻⡟⠛⠛⠁⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⢤⣶⣿⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣀⣤⣿⡶⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠋⠁⠈⢿⡄⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣦⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠿⢶⣄
⠀⠀⠀⠀⠀⠀⣶⠟⠋⠁⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠻⢶⣄⠀⣀⣠⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⣰⡿⠛⠛⠛⠿⢶⣤⣄⣤⣤⣤⣤⣤⣾⠏⠀⠀⠀⠀⠻⣿⠟⠋⠁⠀⠀⠙⣷
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢸⡏⠀⠀⢠⡶⢶⣦⣿⣦⣄⡀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠘⢧⣾⠁⠀⠀⠈⢿⡋⠉⠉⠛⢷⡀
⠀⠀⠀⠀⠘⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⣤⡼⣿⡀⠀⠀⢀⣾⢻⡆⠀⠀⣸⡇
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⡟⠛⠛⠁⠀⣰⡟
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣴⠞⠛⣿⡄
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀
⣀⣤⣤⣼⣷⣤⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠛⢻⡿⠛⠛⠛
⠈⠀⠀⠘⣿⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⣠⣼⣇⣀⡀
⠀⠀⢠⣤⢿⣷⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⠛⠛⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠈⢻⣷⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣧⣄⡀
⠀⠀⠀⣠⡴⠟⠋⠻⢷⣤⣀⠀⠀⢀⣀⣤⡶⠟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡿⠟⣻⡟⠁⠀⠀⠐⢿⣤⣤⣤⣤⣤⣤⣶⡶⢿⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⠉⢉⣿⠁⠀⠈⢿⡄⠈⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠹⣧⡀⠀⠀⢀⣼⠿⠶⠋⠁⢀⣤⣄⠈⢿⣤⣴⠟⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⢿⡿⣿⠟⠛⠛⠋⠁⠀⠀⠀⠀⢿⡀⣸⠇⠈⣿⡁⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⣧⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠻⠟⠿⠿⠿⣿⡿⠿⠿⠿⠻⠛⠛⠛⠛⠛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⡀⠀⠀⢀⣀⣠⣿⣧⣀⡀⠀⠀⢀⣀⣀⣠⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⠀⣀⣤⣤⢤⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠉⠛⠳⢦⣄⡀⠀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣶⠶⠛⠉⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⣀⣀⣸⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠟⣧
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣀⣀⣸⣧⣤⣤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠞⠛⣿⠛⠛⠛⠂
⠀⠀⠉⠉⠉⠹⣏⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣀⣿⡀
⠀⠀⠀⠀⠀⣀⣿⡴⠶⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⣤⠶⠶⣤⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⣹⠏⠉⠛⠃
⠀⠀⠀⠀⠙⠉⠘⣧⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣴⣏⡀
⠀⠀⠀⠀⠀⢀⣠⡾⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠛⠷⠄
⠀⠀⠀⠀⠀⠛⠉⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠶⠤⣤⣤⣤⠤⠶⠶⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠶⣶⣶⣤⠶⠶⣦⣄⡀⠀⣴⠟⠁⠀⠀⠈⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⣼⠏⠀⠀⠀⠀⠉⠻⣾⠏⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠿⠿⠿⠿⠿⢿⣶⣶⣴⡾⠿⠛⠉⠁⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⡴⠞⠲⣆⠀⠀⠘⠛⠳⠶⣦⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠸⣇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⢰⣤⣤⣤⣤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠈⠛⠳⠶⠶⠾⠛⠹⣇⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠐⠛⠛⠛⠛⠻⣿⠿⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠞⢿⡿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢀⣀⣀⣠⣿⣧⣤⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣧⣀⣀⣀
⠀⠀⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⠇
⠀⠀⠀⠀⣀⣤⡶⠾⢿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠿⠶⣦⣄⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⣿⣿⣿⠷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡶⢿⣿⣿⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⢶⠿⣿⡏⠁⠀⢠⣾⠏⠀⠀⠀⢹⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⠁⠀⠀⠈⢿⣆⠀⠀⠉⣿⡿⢷⠶⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⠀⠀⠘⣿⡄⢀⣾⡏⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⣿⣆⠀⣼⡟⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠘⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠛⢷⣤⣀⣀⣀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⠘⣿⣾⡟⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠶⠶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠛⠛⠛⠻⠿⠿⠿⠷⠶⠶⣶⣶⣶⣶⣶⡶⠶⠶⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣤⣤⣤⣤⣤⣴⣾⠿⢿⣶⣤⣤⣤⣤⣤⣤⣴⡶⠾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠇⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠋⠳⠀⡖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⡞⠳⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣼⣟⣉⣩⣽⣿⡇⠠⣹⠟⠢⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⠆⠘⣿⣇⢳⣦⣤⣄
⠀⠀⠀⠀⠀⠀⣠⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⡆⢸⣿⡿⠀⣿⣬⡟⠄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⠀⣿⡇⣸⣿⣟⠀⢸⣿⣿⣶
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣾⡀⢸⣿⣿⣿
⠀⠀⠀⣸⣫⣿⣿⣿⣿⠏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿
⠀⠀⠀⢿⣽⣿⣿⣿⣿⡀⠀⢀⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⣂⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣦⡀
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣯⣻⡿⠉⠀⠀⠉⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣼⣿⡿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢀⡤⡄⠀⠀⣀⡹⣟⣫⣀⣶⣾⣶⣒⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⢯⣿⣿⣿⣿⠿⠇⠀⠐⠲⢄⣀⣀⣀⠀⠀⢸⣷⣻⣿⣟⣿⣭⡿⠋⢫⣙⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡏⣀⠀⠀⠀⠓⢪⣝⣥⣤⡴⠶⠾⣿⡹⢩⣿⣿⣇⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠓⠾⠶⠞⠉⠁⠀⠀⢀⣀⣀⡀⠀⠘⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⠀⠀⠚⠂⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣖⣠⣤⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠋⠀⠀⣼⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢶⣤⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣛⡽⠟⠛⠉⠀⠀⢻⣿⡿⠯⠕⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⢀⣀⣤⣤⣀⢀⣤⣤⣤⣀⢀⡄⠀⠀⣀⠀⠀⣤⣀⠀⢀⣤⣴⣶⣶⣦⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣀⡀⡀⣆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡇⠀⠀⠈⠙⠿⣰⣿⣿⠛⣭⣭⣿⣿⣿⡌⢲⣿⣷⡟⣠⣶⣿⣿⣿⣿⣿⣿⣌⠀⠀⠀⠀⠶⠆⡇⠢
⠀⢀⣿⣿⣿⣿⡿⢿⣏⣛⣿⣿⢇⠩⢉⣷⠠⠄⢤⠀⠀⣿⣿⣷⣿⡿⠻⠇⣮⢻⣿⢘⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣾⣦⣤⣾⢿⣶⣤⣶⣇
⠀⠸⠿⡿⠋⠀⠀⡴⠈⠉⢩⣴⣾⣿⣿⡋⡦⢀⣤⠠⡄⠟⣫⣭⣋⠔⠀⠀⠻⡸⡟⣼⣿⢇⣿⡼⠿⠿⠿⢿⡍⢛⣛⢿⣿⣇⢿⣿⣿⣿⣸⣿⣿⣿⠏
⠀⢀⡄⠢⠄⢀⡐⢀⠀⠠⠖⠉⠉⠹⣏⡁⠀⠈⠉⠸⠇⢀⣶⡆⢨⠀⠀⠀⠀⠁⢀⣭⣭⣌⡙⢓⣨⣥⡁⣀⣴⣿⡿⣨⣭⡍⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⣾⣷⣶⣶⣾⡄⣀⠙⠁⠀⠉⠁⠀⠀⠀⠈⠀⠈⠁⢸⢡⡀⠀⠀⠀⢐⡀⠛⠿⢿⣿⣿⣿⣿⡇⣿⣿⣯⡐⡿⠿⢿⠛⣫⣽⣶⣶⣮⣝⣛
⠀⢠⣿⡟⠉⣿⣟⠻⣿⣧⡈⢀⠆⠠⠀⡀⠀⠤⠀⠀⠀⢀⣡⣀⠙⢿⣿⣦⠸⢿⠇⠀⣤⡻⣿⢿⣿⣿⣷⡉⠉⠹⠿⣠⡿⢶⣾⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠈⢻⡅⠀⠀⠁⠀⠸⠛⠋⠈⠐⣿⠓⠀⠀⣿⣿⣦⣾⣿⡿⠟⠀⠀⠁⠀⠺⠆⠄⠀⢿⣷⣄⣤⡄⢿⣿⢣⣤⠀⠘⠻⣾⣽⣿⣟⡝⠙⠛⢿⣿⣿⡿
⠀⠀⡨⠥⠤⠤⣴⣶⣖⣚⣆⠠⢴⣿⣧⠤⠤⡉⣿⣿⣿⣿⣆⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⢿⣿⣿⣿⡰⠀⠈⠁⢀⣠⠀⣭⠉⠳⣽⣤⢷⡆⣾⡻⠿⠁
⠀⠀⡇⠀⠀⠀⠙⠟⠻⢿⣿⠀⡤⣽⠡⣄⠀⢸⠈⠁⠀⠚⡿⢤⠇⠀⠀⠀⢓⠂⠀⠀⠀⠘⠿⠿⣿⣷⠄⠀⠄⢞⣛⢃⡘⣳⢄⡑⣀⡀⣀⡝⠁
⠀⠠⣅⠀⠠⠀⠀⠀⠀⠀⢸⠆⢠⣾⣧⣈⣠⣾⠰⡖⢐⡂⢀⠀⣀⣀⣀⡉⠀⠀⠀⠄⠀⠠⠐⠤⡽⠃⠀⠀⠸⣿⣿⣿⣷⣄⣮⢱⣬⣥⣬⣴⣿⣶⣆
⠀⢔⠃⠁⠐⠀⣉⣠⣶⣦⣘⠀⠘⠰⣬⣽⡛⠿⣂⣉⣡⣶⡿⣴⣿⣿⣿⣿⣬⣆⠀⣦⠒⠀⠀⠀⠀⢸⣿⣧⣤⡸⣿⣿⣿⣿⠡⣾⣿⣿⣿⣿⣿⣟⠉
⠀⠀⠁⡶⠦⣾⣿⣿⣿⣿⣿⡷⠔⠃⠹⢿⣿⣿⡏⣿⣿⣿⡃⣿⣿⣿⡿⠿⠟⠑⠀⠘⠢⠀⠀⠀⠀⠈⠁⠙⠛⡀⠻⣍⡻⢋⠻⠎⢛⡛⠿⡟⣉⠛
⠀⠀⠀⣤⠀⠀⠀⠀⠈⠉⠻⢷⡄⠀⣀⢸⠏⠉⠛⠉⢬⢻⡇⠊⠛⠋⠘⠛⢫⠀⠀⠀⠀⢃⢀⠀⠀⠄⠀⠁⢠⠇⢰⣿⠇⠹⡟⣻⣿⣿⣿⣶⣿⠂
⠀⠀⢀⣿⣶⣄⡁⠀⠄⠀⢀⣤⣶⣾⣿⣷⠀⣠⣤⠤⡄⠉⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⣠⡜⠀⢷⣶⣴⣶⣦⢃⣤⣤⣍⣤⣦⣽⢻⣿⣾⣿⣿⣿⣿⠆
⠀⠐⢿⣿⠟⠛⠻⠃⡴⢾⣿⡁⢌⡿⠛⢻⡇⠀⣶⣶⡆⠀⠀⡀⠀⠀⠀⠀⠀⢰⣬⣛⠻⢿⠀⠼⠿⢿⡿⢣⣮⡀⠀⣸⡀⠀⢉⣇⢻⣿⣿⣿⣿
⠀⠀⠀⠉⠒⠀⠀⢰⣾⣦⠩⢙⣇⢶⣤⣜⣛⡀⠀⠉⠀⣀⠈⠁⠀⠀⠘⢀⡠⠈⠙⢛⣛⣠⣶⣿⣿⡷⣴⣧⣭⢹⣿⣿⣿⣿⣿⣿⠯⢟⣫⣭⣍⡀
⠀⠀⠰⠀⠀⢠⣄⣀⠉⠿⠿⠸⢟⣓⡙⣿⣿⣿⣿⡛⠿⠟⠋⠄⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡽⣷⠟⠟⠋⠀⢻⣿⣿⣿⡟⣫⣾⢟⣭⡻⣿⡇
⠀⠀⠀⠶⠖⢛⡉⠟⣣⣤⣶⣿⣿⣿⣿⡎⢿⡏⠸⠃⠀⠀⡐⠂⠄⠠⣴⣶⣒⣆⢹⣿⣯⡛⢻⠄⢀⡺⣶⣶⠖⣀⣛⠛⣛⠿⣱⡿⣀⣸⣿⣷⢸⣷⡄
⠀⠀⢰⣧⣤⣭⡉⠘⠿⣿⣿⣿⣿⠿⢿⣿⠌⠁⠀⠀⠀⠀⠇⠀⠀⠀⠛⠛⠿⠟⠀⠀⠛⠋⠰⠀⠆⠀⡀⢀⠘⠂⢺⣿⣞⣃⠹⠰⢿⣿⣿⣿⠰⣿⣿
⠀⠀⢸⣿⡿⣛⠇⣴⣦⣘⣛⣛⡃⠛⡼⠃⠀⠠⠀⠐⠀⠘⣇⠐⠀⢠⠄⠀⠀⣰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠛⠟⡁⠙⣃⡻⣿⣿⣷⣎⠋
⠀⠀⣿⢛⠆⠉⣼⣿⣿⣿⣿⣿⢋⡁⠀⠀⠀⠁⠂⠀⠀⣠⣬⢶⣏⣱⣤⣶⣖⠁⠐⣿⣿⣷⠀⠀⠀⠄⠀⠀⠀⠁⠐⠀⠈⠠⠃⢴⣮⣾⡋⠁⠘⠻
⠀⠀⢈⣬⣄⡘⠏⠀⠈⢹⢿⣧⡹⣷⣤⣤⡆⣾⣶⢖⣟⡟⣋⣊⠭⡖⣖⢮⣥⣄⠀⠸⠟⠀⣀⣀⢠⣤⣲⣼⣿⢿⣓⣾⣎⠓⣀⡴⢎⠣⠄⠠⠶
⠀⠀⠈⣥⣤⣥⣠⣥⣍⠀⠛⠿⡇⣤⣨⣿⣷⡮⣩⣾⣿⣯⣿⢓⣹⣟⠮⡧⣈⠋⣴⣶⣿⣿⣿⣿⣷⠹⣿⣿⠟⠛⢿⣽⡾⣷⡀⢳⣿⡀⣺⣷⣦
⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠸⣷⡄⠻⠍⠉⢛⢿⣮⠹⣿⢿⣿⡿⠏⠙⢛⣶⣱⠇⣹⣿⣿⣿⣿⣿⣿⣷⣌⢁⠀⠀⠀⣿⣿⣿⣯⢰⣶⣾⣿⣿⡿⠃
⠀⠀⢼⣿⣿⣿⣿⣿⣿⠀⣰⠟⠁⠀⠶⠤⠤⣾⠁⠀⡤⡀⠋⡏⠚⠛⢾⣷⡾⠸⣿⣿⣿⣿⣿⣿⣿⢙⠁⣦⣀⣀⠤⠻⠟⣛⠻⠈⢉⡿⠀⢤⣴⡄
⠀⠀⠈⣻⣿⠿⢿⣿⠟⠉⣛⠸⣷⠄⠀⠀⠀⠀⢀⣤⠘⠱⠇⢠⣀⣀⣈⡟⠀⠘⠻⣿⣿⣿⣿⣿⡿⠘⠻⠛⠉⠻⠖⣰⣿⣿⣟⣠⣿⣧⣤⣾⣿⣷
⠀⠀⠀⠛⠋⠀⠀⠋⠀⠀⠋⠑⠀⠁⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠙⠋⠉⠉⠛⠁⠀⠘⠚⠂⠒⠀⠉⠙⠿⠿⠻⠿⠿⠻⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢤⣤⣔⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢶⠤⠈⠙⡓⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠄⠀⠐⠒⠚⠣⣰⠾⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⢹⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⢐⣒⣶⠆⢠⣶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⣆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⠀⠉⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⠀⠒⢤⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡄⠀⠀⠀⠉⠛⣻⠻⣷⠦⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡀⢳⠀⠀⠀⠀⣠⣧⡀⢹⡀⠀⠀⢳
⠀⠀⠀⠀⠀⢀⡤⡒⠉⠀⠀⠀⢀⠜⠀⠀⢧⠀⠀⠀⠻⣿⠁⠀⡇⠀⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⢆⠀⠀⠀⣿⣷⠀⢳⠀⡇⢸⡈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⢆⠀⠀⢹⣿⣇⠸⢀⠁⢸⡇⠘⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡿⢛⠋⠘⠃
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠦⠀⠘⣿⣿⡆⠘⠀⠀⣷⡀⢜⣽⠟⢉⣿⠂⢀⠠⠶⡒⠛⠓⠀⠀⠑
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⡤⢟⣛⣛⣄⣀⣀⡭⣴⢿⣿⣀⣩⣷⣾⠿⠒⠀⠀⢀⠀⠂
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢠⢞⣵⣿⠟⠛⢩⣽⣿⠿⠂⠀⠈⠻⠿⠟⠋⢸⠓
⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠸⡂⠀⠀⢀⣏⣾⣿⡃⡀⠰⠛⡟⠁⠀⠀⠀⠀⡅⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⡸⠞⠛⠉⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⠅⢠⣴⡦⠞⠁
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠀⣼⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⣤⣴⣲⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠊⡌⡼⠎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠻⠰⠀⠈⠀⠀⠀⠀⢀⣠⣤⣶⣾⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⣀⠤⠐⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠚⣡⣶⣶⣿⣶⠆⢠⠄⠀⠀⠀⣸⣾⣿⣷⣶⠀⠀⠀⠀⠀⣠⡸⠿⠂⠶⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡆⠀⠀⠀⡀
⠀⣴⡿⢛⣿⠿⣿⡞⠂⠀⠀⠀⠀⢿⣤⣯⣉⣿⠠⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⡁⠀⣤⠀⠀⠀⠺⠉⠙⠁⠂
⠀⠻⡇⠈⠉⠀⣻⠛⠀⠀⠀⠀⠀⣾⠟⢻⡿⠅⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⡀⠁⠀⠀⠀⢁⡶⣶⠀⠀⣤⣤⣤⠀⠀⠀⠀⠄⢀⣦⡤⠀⠀⠁
⠀⠘⠓⠀⠀⠲⠇⠀⠀⠀⠀⠀⠀⠓⠀⠀⠛⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠂⠙⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⣤⣶⡶⢶⣶⣄⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⡷
⠀⠐⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⣾⣿⣥⡾⣿⣿⣿⣧⠀⠀⠀⣻⣿⣶⣾⣷⣦⣀⠀⠀⠀⠀⣰⣄⣡⣾⣄⣠⣄⠀⠀⠀⠀⠿⣿⣿⣿⡅
⠀⠀⠀⣃⠀⠀⢀⠄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠹⣿⣿⣤⣿⣿⡟⠀⠀⠀⠀⢿⠋⠁⠈⠙⡐⠄
⠀⠀⠀⠙⢿⠾⢿⠇⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⢿⠄⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠈⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠈⠐⠒⠒⠚⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⢀⣠⣀
⠀⣸⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⢿⣺⣿⣿⣶⣿⠀⠀⠀⠀⠀⢀⣠⣄⣤⡀⢀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣅⣠⠀⠀⠀⣀⣄⠉⢛⣿⣿⣿⣿
⠀⣽⣿⡯⠿⠻⢯⢿⠿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣽⡿⡿⡿⠁⣧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠉⠃⠀⣿⡛⠉⢛⣿⡇
⠀⠙⢋⠀⠀⠚⠀⢀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣷⣤⣿⡧⠀⠀⢾⡟⠋⣶⣿⣶⠉⢻⡷⠀⠀⠀⠀⢀⡈⢠⡀⣾⡏
⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠘⠛⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠄⠤⠤⣴⣶⣐⡀⠀⠀⠀⢠⡄⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣆⣀⡀
⠀⢠⠀⠀⠀⠉⠙⠻⢇⠀⠀⠀⢀⠊⠈⣙⣟⡁⠉⣆⠀⠀⠀⠀⢠⣽⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡀
⠀⠸⠂⡐⠀⠄⠈⠀⠎⠀⠀⠀⢨⣦⣈⣤⣷⣌⣤⡇⠀⠀⠀⢠⡼⠯⡤⠠⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠙⢻⠗
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠹⠷⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢩⡭⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⢀⡀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⢿⣿⣶⣻⣿⣿⠇⠀⠀⢀⣀⣤⣴⣾⣶⣦⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⣄⡀
⠀⠀⠀⣟⠉⠉⠡⢿⠇⠀⠀⠈⠛⠉⢿⣿⣿⣿⢿⣷⠄⠀⠈⠛⣿⣧⣼⣿⣦⣿⣧⠀⠀⠰⣿⣿⣿⣶⣶⣤⣴⡖⠀⠀⠐⣿⣿⣿⣿⣿⣺⣄
⠀⠀⠀⠀⠐⠞⠛⢈⡦⠀⠀⠀⠀⠊⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢿⡛⠀⠀⠐⢋⡟⠀⠀⠀⠈⠉⠉⠻⣿⣏⠛⠃⠀⠀⠀⠉⠘⠿⠏⠻⠋⠛⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⠦⣤⣀⣠⠞⠋⠳⣄⠀⠀⠀⠀⠀⠀⣠⠴⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣹⣇⣀⡀⠀⢹⡶⠶⠶⠶⠶⠞⠁⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠒⢺⠃⠀⠈⢷⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠰⠽⢦⣀⡤⠟⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠳⣄⣀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⢺⡗⠒⠂⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣷⠶⠦⣄⠀⠻⠇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠉⣿⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠓⢮⣳⡀⠀⠀⠀⠀⠀⠀⠣⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⢧⡀
⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⢿⡀⠀⠀⠀⣿⣄⣀⣀⡴⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⢾⡁
⠀⠀⠀⡏⠈⠷⠤⠤⠾⠁⢹⠀⠀⠀⠀⠙⢦⣄⣀⡟⠈⠁⠘⡏⠉⠉⠳⣽⢶⡶⠒⢶⡞⠛⠛⠉⠉⠀⠀⠉
⠀⢀⡼⠃⢀⣠⣤⣤⣀⠀⠈⢧⡀⠀⠀⠀⠀⠈⡿⠉⠲⢄⣼⡁⢀⣠⠾⢁⡼⠋⠳⡜⣧
⢀⡾⠁⣰⠋⠶⠀⠶⠀⣽⣆⠈⢷⡀⠀⠀⠀⠀⠻⣤⡤⠞⠻⢯⡿⡷⢶⣙⡧⠤⠤⣷⠘⣧
⣼⠁⠀⡇⠶⠀⢞⣱⠀⣉⢸⠀⠈⢷⠀⠀⡤⢤⡀⡿⠀⢀⡴⢻⠁⠧⠤⣟⠀⠀⠀⡟⠀⠸⡇
⣿⠀⠀⢿⣳⣀⠀⠁⠀⣩⠞⠀⠀⢸⠆⠀⠓⣦⡿⣿⠚⠉⠀⣼⠀⠀⠀⠈⠙⠤⠴⠃⠀⣰⠟⠓⠲⣄
⠙⠦⣤⣤⣁⣉⣉⣉⣩⣤⣤⠤⠶⠛⠛⠛⠛⠉⠀⠙⠷⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⡤⠾⢯⣤⣤⣤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⢷⠞⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠛⠻⠿⣷⣶⣴⣿⠋⠁⠀⠈⠻⣷⣄⣀⣀⣀⡀⠀⠀⠀⣀⣤⣶⣶⡿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢹⣿⠃⣀⣀⠀⠀⠀⠙⣿⡿⠿⠿⠿⠿⣿⣿⠟⠋⠉⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣦⣤⣶⡿⠿⠿⣿⣏⠹⣷⠀⠀⠀⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⢉⣿⠏⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣇⠀⠀⢰⣿⢻⣧⡀⠀⠀⢀⣿⣿⣶⣦⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⠛⠛⠛⢿⣶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⢰⣿⠿⣷⣦⣄⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⣴⣶⣶⣶⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠈⠉⠙⣿⡟⠉⠉⠛⠃
⠀⠀⣠⣤⣴⣿⣿⠶⠀⠀⠀⠀⠀⠹⣿⠟⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠀⢠⣤⣼⣿⣁
⠀⠀⠈⠁⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠛⠛
⠀⠀⠀⠀⣀⣤⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣾⣿⣇
⠀⠀⠀⠘⠛⠉⠀⠀⠙⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣠⣴⣾⠟⠉⠈⠙⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠿⠛⠛⠿⣿⣟⣫⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠏⢉⣉⣭⣭⣍⣹⣿⠁⠀⠀⠀⠀⠘⠿⠋⠉⠉⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⢰⣿⠛⠉⠉⠙⣻⣿⣶⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⣿⡇⠀⠀⠀⣰⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠸⣿⣄⠀⣰⣿⠃⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣀⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡾⢿⣿⡏⠀⠀⠀⠀⠈⠻⣷⣿⣇⠀⠀⠀⣀⣼⡟⠀⠀⣀⣴⡾⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⠛⠿⣶⣿⠛⠉⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⡀⠀⢹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⢀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠢⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⢷⣴⣯⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⣿⡟⠈⠻⡿
⠀⠀⠀⢠⠤⣖⠀⠀⣀⡴⠀⠠⠄
⠀⠀⠀⠀⠀⢘⡛⢲⣽⣷⡆
⠀⢰⣵⣦⣤⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣤⣤⢀⣀⣀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⡇⢸⣿⣿⡸⣿⢾⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠘⣿⣿⣇⢿⣧⣿⣿⣶⠿
⠀⠀⠘⠋⠉⠉⣿⣿⣿⣿⣿⣿⠙⠛⠛⠓⠢⡀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠸⠿⠿⠿⠷⠰
⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠣⣽⣿⣿⡿⠛⠛⠻⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠈⠓⠢
⠀⠀⠀⢠⣤⣤⣶⣶⣤⣤⣤⣤⠴⠦⢀⠀⠀⠀⢐⣿⣿⣿⣏⣀⣀⣠⡇⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⢿⣿⣶⣤⣀⡀⠐⠐⣶⣿⣿⣿⣿⣾⣿⣿⣥⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣼⣶⣶⣤
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣾⣟⢻⣿⣿⡏⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢀⣻⠿⢷⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⡾⠁⢦⣿⡃⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣼⣿⢴⣰⠍⠛
⠀⣤⢘⠷⣴⢦⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢻⣿⣯⡫⢠⡄⠀⠀⠀⠀⠉⣀⠴⢻⠿⣿⣿⡇⡀
⠀⣻⣷⣿⡗⠀⠘⠛⢿⣿⠟⠛⠋⢉⣻⣿⣷⡯⣿⠋⣻⠇⠹⣿⠛⢈⣄⣤⡄⠀⠀⠀⢧⣤⣤⡤⢿⡹⣳⣤⣘
⠰⣿⣿⣿⣇⠂⠤⠀⣶⠃⠀⠀⠠⣼⣿⣿⣿⣷⢿⣿⣿⡿⣿⣦⣴⣾⣿⣿⣿⠆⠀⣀⠤⠤⢼⡇⠈⠳⣿⠶⠟
⢈⣁⡽⣿⣿⣟⣶⠟⠁⠀⢠⣼⣿⣿⣿⣿⣿⣟⣿⠿⡿⠾⠻⠿⠿⠿⠛⠛⠀⠀⠘⢗⡶⠖⠒⣋⣀⠀⠘⠒⠖
⣩⣽⡀⠘⠻⣏⣁⣤⡴⠞⣿⣿⡿⠛⠉⠁⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠖⠋⠉⠁⠉⠛⠲⠶⠶
⡷⢖⣣⣤⣀⣀⣀⣠⣦⡤⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣀⠀⠀⠀⠀⠀⡀⠰⠂
⡵⠋⢀⣖⣿⣭⣿⣿⡏⠀⠀⠀⠀⠈⠄⠀⠀⠀⠙⡆⠀⠀⣤⣽⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠀⢀⣴⣶⣶⣶
⠀⣤⣸⣿⣟⣩⣽⡇⠀⠀⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⡀⠲⡄⠀⠀⠘⣿⣿⣿⣿⣿
⣀⡹⣿⣿⣿⣿⣿⡃⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⡀⢸⡟⠉⠉⠙
⣾⠂⣾⣿⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡇⠀⠀⠰
⣿⠟⠛⠙⢻⢜⡿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠘⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⡇⠀⠀⣤
⣙⠲⠶⠶⠋⢐⡇⠀⠀⠈⠀⠀⠀⠀⠙⠀⠀⠀⠈⠃⠀⠀⠀⠈⠃⠀⠀⠀⠙⠻⣿⣿⣿⡿⠟⠀⠀⡅⠀⠀⢹
⣿⣤⣶⣽⣼⣿⡇⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣁⠀⠀⠀⠀⢀⡴⠀⠀⠠
⣽⣿⣿⣿⣿⣿⣿⣶⣤⣾⠿⠿⠿⠿⠿⠛⠻⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠿⣿⣦⡀⣴⣿⣧⡶⢦⣭
⣿⣿⣿⡟⠋⠙⣿⣿⣿⠃⠀⠤⠀⠀⠀⠀⢶⣶⣶⣴⣶⣶⣤⣤⣴⣶⡄⠀⠀⠀⠠⡄⠈⣿⣷⣿⣿⣿⠃
⣿⣿⣿⣆⠁⣤⢹⣿⣿⢄⠀⠀⠀⠀⠆⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠤⠀⠀⠀⢰⣿⢹⣿⣿⣿⣧⣋⣀
⠙⣿⡿⠿⠿⠶⠾⣿⣿⡀⠀⠐⠄⠀⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⣿⡏⢸⣿⣿⣿⣽⣿⣭
⣄⣈⡙⠒⣲⠴⠦⣿⣿⡧⠀⠀⠀⠀⠒⠀⠀⠀⠐⠀⠀⠀⠀⠤⠀⠀⠀⠠⡄⠀⠈⢸⡟⠀⢸⣿⡿⠀⠉⠙⠳
⣿⣿⣿⣿⣿⣶⢦⣿⡿⣿⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⢀⠀⠐⠄⠛⠃⠀⢸⣿⠷⣿⣷⣶⣶
⣼⣿⣿⣿⣿⣿⣧⣿⣿⣼⡆⢀⣀⣀⣈⣀⣀⣀⣀⣂⣀⣀⠀⠀⠀⢀⠀⠀⠀⠢⠀⢻⣦⣄⣾⡿⣾⣽⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣷
⣿⣯⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣣⡄⠀⠀⠉⣿⣿
⠋⠁⠀⠀⢀⣀⣼⣿⣿⠿⠿⠿⠿⣿⠇⠀⠙⠿⣿⣿⣯⣽⠿⠟⠋⠁⠀⠀⠀⣀⠠⣄⣲⠞⠋⠀⣀⣠⡼⣿⣟
⣶⣾⣟⣿⣿⠏⠺⣷⣶⠶⠟⠓⠒⠚⢋⣀⠀⠀⠈⠛⠦⢤⣠⡦⢄⡶⠤⠾⣶⣿⣿⣿⣶⣦⡀⠈⢧⣀⠀⠀⠉
⠅⡼⠿⢹⣃⠀⣾⣩⣴⠶⠛⡛⢻⣛⣫⣛⠷⣶⣤⣄⣀⣀⣀⠀⢳⣄⡀⠀⠙⠦⢽⣯⡟⢿⣿⣷⣄⡈⠙⠳⠶
⣶⣾⣿⡞⡁⠀⠉⢥⢂⡀⣠⣻⣿⣿⣿⣿⣿⣧⣴⣽⠿⠍⠉⢙⠛⠿⠿⣿⡲⣶⢦⡙⣌⠳⢿⣿⣿⣿⣶⣤⣀
⡟⣿⠏⠁⢀⣌⠱⣾⣈⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠈⠀⡀⠈⢷⡌⢳⣿⡌⢳⣄⠈⠙⠛⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⠀⠀⠀⣴⠋⠻⡆⢰⡏⢙⡆⠀⠀⠈⡃⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢠⣞⣀⣧⡀⠀⠀⣿⠀⠀⡿⣠⠟⠛⣧⠀⠀⢸⡇⢸⠇⠈⡗⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⠀⠀⠈⠏⠀⠰⠄⠙⠦⠾⠃⠙⠦⠴⠏⠀⠀⠸⠇⠸⠇⠀⠇⣿⣿⣿⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠒⢤⣤⣴⣶⣆
⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⣴⣶⣶⣦⣤⣄⡀⠀⣀⣀⣠⣤⣤⣤⣤⡔⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠢⡀
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣧⣸⣿⣧⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡴⠶⠶⠶⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣧⣤⣤⣤⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⡿⣫⣿⡷
⠀⠤⠀⠴⠦⠤⠦⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣴⣴⣂⠀⠁
⠀⢰⠀⣠⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣮⢿⣿⣿⣿⣇⡄
⠀⠸⠦⣿⡄⣠⡿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⣯⣾⣾⣭⣭⣭⣭⣭⣽⣿⣾⣿⠻⣷⣿⣿⣿⣿⣿⡸⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣼⣿⣿⣾⣿⢟⣿⣿⠛⣿⣯⣹⣿⣷⣿⣿⣼⣿⣿⣿⣿⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⡹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿⣷⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⡟⢻⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠁⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠁⠀⠉⠙⠛⠛⠛⠛⠛⠉

⠁⠀⢀⡄⠀⠀⠀⠀⢀⡀⠀⢀⣀⡤⠞⠻⢿⣿⣭⣭⣭⣭⣷⣀⠐⠠⠐⠀⠀⠉⠀⢰⣏⣁⠀⠛⠁⠀⡠⢄⠀⠀⢀⣄⢠
⠀⠀⠀⠁⠀⠀⠀⠀⢈⡵⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⣞⠛⠲⣼⣇⣤⠴⠦⣄⠀⠈⠁⠀⠀⠈⠋⡏
⣠⣤⣤⣄⣀⠠⡤⠀⢸⠀⣠⠀⠀⠰⠀⠀⢀⡀⠀⠀⣀⠀⠀⢀⠀⢀⣹⣿⣟⣿⣿⣿⣿⣷⣶⣶⣿⣀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠙⢦⠀⠀⠀⢻⠃⠀⠀⠀⠀⠢⠜⢅⠄⠀⠁⠀⠀⣸⠞⣋⠁⠘⠻⠿⠛⠉⠹⢿⣿⣿⡇⠉⠙⠶⣄⠀⠀⠀⢸
⣴⣄⠀⠀⠀⢈⣧⡴⠚⠻⠛⠳⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣼⠋⠀⢀⣄⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⠈⢳⣄⣀⣤
⠉⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢉⡳⣄⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠘⠋⠀⠀⠄⠀⠀⣾⡆⠀⠸⣇⠀⣠⠼⠋⠁
⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⠋⠙⠲⣤⣤⣤⣿⣤⡶⣦⣀⣀⣀⠐⠀⠀⠀⠈⠀⠀⠀⢙⡾⠁
⣤⣾⡏⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⣰⣯⣴⣮⣿⡉⠉⣷⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠿
⠸⣿⠃⠀⠈⠁⠀⢴⡦⠀⠀⠾⠆⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣽⣿⣿⡿⣆⣠⣤⠤⢤⣄⣸⠇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡁⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣴⠟⠁⠀⠀⠀⠈⠻⠤⠶⠒⠒⠲⢤⡖
⠛⠛⠶⠶⣴⠖⢶⣤⣤⣀⠀⠀⠀⢸⡥⠖⠀⢉⣀⣀⠯⣆⡀⠀⠸⠇⠀⠐⠛⠻⡟⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⣾⣷⣿⣿⣿⡀⠈⣇⣀⣀⣸⣧⣀⣰⡋⠀⠈⠛⠉⠙⣦⠀⠀⠀⣈⢙⡞⠃⠀⠀⠀⠈⠋⠀⠀⠀⢾⡷⠀⠀⠀⣠
⠀⠀⠀⠙⠻⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠉⠉⠓⠞⢳⣄⠀⠻⣄⠀⠀⢨⡏⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣀⠀⠀⠀⣀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⢰⠻⠶⡆⣹⠀⠀⣸⡇⠀⠀⠀⠲⣤⡀⠀⠀⠀⠀⠀⢀⣾⠃
⠚⠁⠀⠀⠛⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠁⠯⡄⣠⣿⣿⠿⠟⣿⣿⣿⣷⣶⣤⣤⣽⡶⠶⠶⠶⠶⣾⡇⠀⢰⡆
⠀⠀⠀⠀⠀⢸⡀⢠⣦⡴⠦⠤⠶⣄⣤⠀⠀⠀⠀⠀⢀⣾⡟⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⣿⠁
⠶⣄⡀⠀⠀⠀⡟⠉⢠⡦⠀⠀⠀⠀⠈⠙⠻⣤⣤⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠷⠲⢤⣀⣿⡀⠀⠀⢀
⠀⠈⠻⣄⣀⣀⣿⣀⣀⣀⣀⣄⢀⡀⠀⠸⠗⠀⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠉⠉⢙⣿⢛
⡀⢀⣤⠟⠋⠉⠉⠀⠀⠈⠉⠙⠳⣄⡀⠀⠀⠀⠀⢘⣿⠟⢉⡉⠈⠉⠉⠛⠛⠿⢿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢾⣿⣿
⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣴⣶⣶⣿⣿⣤⣜⠋⠀⠀⠀⠀⠀⢠⣄⠉⢿⣟⠂⢀⣄⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣾⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣯⠙⠛⠛⠡⠞⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⣀⣀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠀⠐⠉⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣟⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠂⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣾⣿⣿⡀⠀⠀⠈⣸⠉⣧⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠈⠤⢄
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠘⣽⡅⠻⢣⠀⢠⣶⡇⠀⠈⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⣤⠀⠁⠀⢸⣷⡀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⡼⠈⠉⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⣤⡞⠁⠀⠀⠀⠀⠙⠋⠀⠀⠈⢣⡀⢀⡇⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⢠⡼⠏⠀⠀⣀⣀⠀⠀⠀⠀⢳⡀⠀⠀⠙⡼⠀⠀⠀⣸
⠀⠀⡀⠀⢀⣀⡀⢰⣿⠟⠉⠀⠉⠉⠉⠁⠀⠀⠀⠟⢟⣿⣷⠀⠀⠀⠈⣷⣆⣀⡤⠀⠀⠀⠀⡏
⠀⠸⠀⡤⣶⠿⠟⠋⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⢋⡩⠾⠟⠀⠀⠀⠀⠻⢿⣿⣇⢠⣀⠀⢸⠁
⠀⡦⢆⠄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⢀⣤⣤⡆⠀⠀⠀⠀⠙⠿⣿⣿⣧⠆
⠀⢷⠉⠀⠁⠀⠀⠀⠀⣀⡀⠀⢀⣠⡄⠀⠀⠀⠀⠀⣴⡿⠛⠋⢻⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠈⠛⠓⠚⠛⠛⠉⠉⠀⠀⠀⠀⠙⣿⡄⠀⠀⢀⣾⠋⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣷⣶⣶⡶⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠙⢷⣄⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠋⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⢦⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠾⠋⠈⢻⣦⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢰⣿⠿⠟⠻⢷⣄⠀⠀⢀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠛⠻⢦⣄⣀⣀⣠⣿⣧⣤⣤⡿⠁⠀⠀⠀⠀⠹⣷⡾⠟⠋⠉⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠁⣿⠁⠀⠀⣠⡶⠶⣄⣿⣤⣀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀⢿⣄⣼⠋⠀⠀⠈⢻⣶⠟⠛⠛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣀⣀⣹⡇⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢦⣄⣠⣴⠿⡴⠟⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣄⠀⠀⢀⣤⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣤⠶⠾⣿⡗⠒⠂⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠉⠀⣼⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⣧⣀⡀⠀⠀⠀⠻⡿⠏⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠻⡿⠏⠀⠀⠀⠀⠰⢶⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡀⢀⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠏⠀⠀⠉
⠀⠀⠀⠀⠀⣠⣤⣄⣀⣠⣤⣄⣻⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠿⠷⣤⣀
⠀⠀⠀⠀⣾⠋⠀⠈⠋⠁⠀⠙⣿⠈⠛⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠁⠀⠀⠈⠉
⠀⠀⠀⢀⣼⠇⠀⣠⠶⣄⠀⠰⣯⡀⠀⠀⠈⠉⠛⠛⠷⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠿⠿⠿⣯⡀
⠀⠀⠀⣿⠁⠀⠀⢧⣀⡼⠃⠀⠈⣿⠀⠀⠀⠀⣠⡴⢾⡿⣫⣤⣄⠀⠀⠀⠀⢸⣿⣀⣾⣿⣷⠀⠀⣴⣿⣿⣦⡀
⠀⠀⠀⠙⠷⢤⡄⠀⠀⠀⣠⣤⣴⣏⣠⣤⣴⠞⠉⣰⡟⠸⣿⣿⣿⠀⣠⣴⣤⣸⡿⣯⠻⠿⠟⠀⠀⠻⠿⠟⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠏⠀⠈⠻⣯⠀⠀⠀⢀⣟⣀⡀⠈⠉⠁⠀⢿⣿⣿⣿⠃⠹⣧⠀⢀⣤⣄⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠉⢹⡟⠀⠀⠘⢷⣿⣿⣿⡇⠀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⣸⡟⠛⠋⠀⣠⣦⣤⠀⣰⡟⠀⠀⠀⠀⠀⠙⢿⣍⡀⠀⠙⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠙⣷⠀⠀⠐⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣧⡀⢀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⡟⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠈⠙⠳⢦⣤⣄⣀⣀⣀⣀⣀⣤⣤⠶⠞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣃⣠⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⡀⢀⣤⣶⣿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⣿⠏⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠉⠛⠛⠿⢿⣿⣿⠿⠿⠟⠛⠛⢻⣿⠇⠀⢀⣴⣶⣶⣾⣿⣷⣤⣄⣀⣀⣤⣼⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⢀⣾⡟⠉⠀⠉⠻⣿⣿⣍⡀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠙⢻⣿⣇⠀⠀⠀⢠⣿⠇⢹⣷⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠾⠿⠿⠛⠻⢷⣶⣾⣿⣿⡶⠾⠏⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣠⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⢷⣶⣶⠶⠾⠶⠷⠷⠶⠶⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣾⣟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⢿⣿⡟⠙⠉⠙⣿⣿⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⣹⣿⣿⣀⣀⡀
⠀⠀⠀⠰⠾⠿⠟⣿⣿⣟⠁⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⡿⠀⢀⣀⠀⠘⣿⣆⠀⠀⠀⠛⠿⠃⠀⠀⠀⠀⢈⣿⣿⡟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⠀⠀⠀⠀⠈⠛⠋⠀⠀⢀⣼⡿⠁⣾⠋⠉⢹⡆⠈⠻⣶⣄⣀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣀
⠀⠀⠀⠀⠀⢠⣶⠿⠿⢿⣿⣦⣀⡀⠀⠀⠀⣀⣠⣴⡿⠋⠀⠀⠈⠛⠚⠋⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⣩⣿⡿⠛⠛⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡿⠿⢿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⢷⣶⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠋⠀⣿⠟⠁⠀⠀⠀⠘⣿⣿⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⣷⣿⡏⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠉⠉⠉⢹⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠶⢶⣾⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠹⣿⣿⣤⣤⣤⣤⠀⠀⠀⢠⣤⣤⣤⣼⣿⡿⠃⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣶⣶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠉⠙⠋⠉⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣦⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠊⡔⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣞⣛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠃⡀⠁⠔⠙⣦⣈⣥⠤⠶⠆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡟⠉⠉⠉⠀⠀⠀⣠⠶⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣥⣤⣄⡀⠠⡄⠀⠀⢼⠁⠀⠀⠀⠀⢼⣆⠀⡤⠰⣆⠲⡤⣴⣾⣿⠛⠀⡇⠀⠀⠀⠀⡤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠖⠠⢀⠀⠀⠀⠉⠙⢿⣆⠐⡄⠀⢸⡄⠀⢠⣄⡀⢀⠻⣷⣤⣡⣼⣳⣾⣿⠟⠙⡆⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠈⠻⣧⡈⢤⣼⠁⠀⡘⣷⣐⡿⠛⠉⠉⣻⣿⣿⡟⠹⠄⠀⠘⢀⠤⠋⠀⠀⠀⠀⠀⠀⠀⢀⠳
⠀⠀⠀⣀⡀⠀⠀⠁⠚⠲⠤⢄⡀⣀⠀⠀⣠⣄⡶⣿⡷⣾⣻⢠⡄⢙⣿⠟⠀⠀⣠⣾⣿⠟⠹⣧⣠⠶⣦⣿⣧⣦⢀⠀⠀⣀⡠⠄⠐⠈⠀⠀⠀⣤
⠀⠀⠀⣿⠈⣁⠀⠀⠀⠀⠲⠾⢿⣿⣿⣦⣟⠛⠉⠿⢣⢙⣥⠾⠷⠚⠋⠀⣾⣿⣿⣟⡁⠀⢀⣿⣿⣾⡿⠟⣉⣥⠴⡲⣾⣦⣤⣴⡶⠖⠒⠉⢀⣸⠆
⠀⠀⠀⢸⡇⢈⠉⠒⠂⠉⠉⠀⠀⠰⠿⣿⣎⠻⠇⣰⠟⠉⠀⠀⠀⠀⡀⠘⢿⡟⠛⠙⣀⣴⣾⣿⣿⣿⣷⣿⡿⣅⣂⣾⣿⣿⡖⠒⠚⠒⢀⣀⡈⢋⡃
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣐⣠⣤⠶⣿⣯⣏⡗⢲⡏⠀⠠⣄⠀⠀⠀⢀⠐⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⣿⣿⠉⠉⠉⠉⠙⠁⠀⣼⠃
⠀⠀⠀⠀⣷⠀⠃⠈⢁⡈⣭⡤⠶⠻⢕⣼⣼⣯⣻⣷⠀⠀⠈⠻⣄⡔⠁⠀⠀⢠⣿⣿⡿⢿⣿⡏⣿⣿⡽⣿⠿⣿⣻⣿⣿⡿⠒⠒⢛⣛⣙⠀⢀⡿
⠀⠀⠀⠀⣿⠀⠀⠀⣀⣠⣤⠶⢾⣿⣷⣿⡟⠿⢹⠿⣷⣄⠀⠀⠈⠳⠆⠀⠀⣼⡿⣟⣛⣓⠺⢡⡿⠿⠿⠿⠨⡿⢿⡶⣿⣤⣿⣿⣽⣿⣟⡀⣼⡇
⠀⠀⠀⠀⢿⠈⠉⢉⠉⢍⣤⠶⠛⠋⠛⣃⢻⡟⣿⠓⡈⢉⡷⢤⣀⣀⣠⣤⣾⡿⡛⠛⣡⣿⣄⣾⠙⠛⠶⣄⡒⠲⣶⠏⠉⠛⠛⠻⠿⢿⣷⣾⣿⡇
⠀⠀⠀⠀⢸⣄⣠⣤⡾⠛⠁⠀⠀⠀⠐⠛⡿⣾⢅⣠⠖⠋⠀⠀⠉⣽⣿⣋⢥⠈⠿⠻⣏⡿⣛⣅⠀⠀⠀⣽⡿⣷⣤⣏⡀⠀⢶
⠀⠀⠀⠀⠸⠿⠛⠉⠀⠀⠀⢰⣦⣖⠀⠀⢀⡴⣿⣿⣿⣦⣠⠀⠀⣿⣿⣿⣷⡀⢀⣴⣯⣷⣮⠿⠜⣀⠆⡙⣐⠻⢧⡙⣿⣄⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⡿⠁⢿⡟⣯⠋⣠⡼⣇⡌⣿⣿⣿⣿⣿⡟⢘⡕⢨⣄⢻⡽⢢⠵⣿⠜⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠃⠀⠈⠑⠿⠦⣿⠶⣹⡝⣽⣿⣽⢛⣹⡇⠘⠁⠀⠀⠉⠓⠐⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣿⣷⣛⣿⡟⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠳⢦⣄⣠⣤⡄⣴⠋⠉⠙⣧⠚⠋⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠁⠀⢸⡇⠀⣾⣳⡾⠷⣤⣤⣤⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠆⠀⠀⠀⠀⠀⠀⠘⢧⣤⣬⣿⡀⠀⣸⣧⡀⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⠛⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣉⣘⣃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⡁⠀⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⣉⣉⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣄⠀⠉⠉⠀⠀⠠⣾⣶⠄⠀⠀⠉⠉⠀⢀⣍⣉⡉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡛⠉⠁⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠎⠉⠙⣣⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠀⠹⣦⣀⠀⠈⠛⠶⣦⣤⣄⣀⣀⣀⣤⣤⠶⠟⠋⠀⢀⣠⡾⠋⠨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣄⣀⠙⠷⣤⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⣤⡶⠛⠉⣀⣀⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣉⠛⠶⣤⣀⠀⠀⢀⣠⡴⠞⠋⣡⣴⠾⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡉⠛⠶⣭⣁⠤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⢊⣙⡳⢦⣄⡉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⡶⠟⢋⣡⣴⠾⠛⠉⠀⠀⠈⠙⠳⢦⣄⡉⠛⠶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠁⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⠈⠉⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣤⣠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⣿⣤⠛⢿⣿⠿⠿⣰⡟⠿⣿⣿⡶⣠⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⢇⠀⠀⠈⠙⠻⡈⠃⠀⠀⣸⣷⣾⣦⣼⠇⠀⠀⠀⣿⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠦⠶⠊⣿⣨⡄⣀⣀⢠⡀⢄⣓⣠⠄⣍⠉⢹⡿⠇⠾⢂⡀⣠⣿⡿⠀⢨⣦⡄
⠀⠀⠀⠀⢀⠘⠁⠐⣶⣶⣿⢿⡿⠞⠟⡊⣏⣿⣿⣿⣿⡏⣴⣶⣶⣦⣴⣶⣶⣦⡈⠡⠀⠈⢻⣷⠁
⠀⠀⠀⢠⡜⡶⣶⡚⢈⡿⠋⠛⠁⠀⠘⠛⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⠟⣭⣝⠇⠀⠀⠀⠘⠀⠀⣠⣤
⠀⠀⣠⡽⠸⣽⡿⢛⡋⠄⢠⣤⣶⣴⠀⢀⡀⠉⠉⠉⠙⠸⢿⠟⠉⠁⠬⢉⠘⣿⣶⣶⡀⠁⠀⠀⠀⢹⣯
⠀⠀⢿⣀⣼⣷⣭⣒⠊⢠⣼⣿⣿⣿⠆⣼⣷⣦⣀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣼⣿⣿⣧⡀⠀⠠⠠⠈⠁
⠀⠀⠀⠙⠿⠿⠋⠛⠃⠻⣿⣿⢿⣿⣮⡿⠿⠿⣿⣿⣿⣜⠿⣟⠋⢩⣿⣏⣹⣧⢠⣬⠟⠀⠀⣀⢀⣀⠂⢴⡄
⠀⠀⠀⢀⠀⠈⠠⣀⠇⣀⣠⢅⢁⣩⣴⣶⡜⣷⣶⣭⣭⣥⣿⡿⢺⡋⠉⠉⡿⣿⠇⠀⠀⠀⠀⠉⠈⠋⠀⣿⡿
⠀⠰⠆⡀⠀⠀⡀⣉⣐⡋⠁⢻⣿⣿⣿⣿⣷⡌⡿⠛⠶⠛⣻⡇⢂⣀⣈⠤⠐⠋⠀⡔⠀⠀⠘⠦
⠰⣷⡆⢃⠀⠀⣁⠙⠻⣿⣦⣟⠉⠹⣿⣿⠻⣷⡕⢠⣤⢤⠉⢁⢿⣿⣿⣷⣧⡀⠀⠀⠀⠀⠁⠠⠀⠀⢰⡷⣾
⠀⠁⣶⢈⡀⠙⠋⠀⣼⡿⠛⠻⢿⡇⡄⠀⠀⠺⠇⠀⠀⠀⠐⡫⢾⣿⣿⣿⡿⣿⣷⠄⠀⠀⣀⣴⣿⣷⣼⡓⠟
⠀⠀⣴⣿⣿⣶⣤⡄⠜⠁⠀⢨⡟⢡⡄⠠⠀⣀⠀⠄⢀⠠⠊⠀⠀⠀⠀⠀⠑⠄⠀⠀⠈⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠉⣿⣿⡟⣭⡱⡿⠤⠵⠊⠁⠈⠀⠕⡄⠀⠀⡀⠨⣶⡦⠄⢄⢿⢿⠋⠉⢿⣶⣶⣶⣭⡻⣿⣿⣿⡿⠁
⠀⠀⠀⠙⢛⡸⠋⠁⣼⢿⠟⣼⣿⠆⠀⢈⠀⠀⡎⠀⠴⢼⡔⠆⢀⡏⣓⣆⣐⠀⣸⣿⣿⣿⣷⠹⠻⡿⠃
⠀⠀⠀⠀⠈⠓⠀⠀⠈⠀⡿⡾⢫⣶⣄⣉⣼⠀⣼⣶⣶⣾⣿⣶⣿⡇⠙⠋⠙⣼⣿⣾⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠷⠔⠑⠳⡤⣸⣿⣿⢋⣿⡶⣜⡿⢿⣿⡿⠿⠟⠁⠀⠀⡘⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⡠⣤⣄⣾⣷⠄⠉⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⢼⡿⠛⣴⣷⣷⡞⠛⣿⠎⣋⡩⠵⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠛⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⠿⠶⠖⣸⣿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠻⠟⣻⡖⣻⡿⠿⠛⠤⠝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⣹⠿⠛⣹⠏⠀⣐⢒⠎⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⡿⠋⠁⣴⣠⣿⠀⠠⠈⠋⡁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣁⣽⠶⠾⠃⠀⢰⡏⢹⡁⠀⠀⢀⣸⢃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣔⣶⣾⣿⣿⣭⣤⣄⣤⣰⣿⠅⠈⠁⠲⡄⠀⢂⣾⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠉⣰⠟⣿⣁⣼⣷⡄⠙⡀⠉⠉⣿⡋⠐⠶⠴⠤⢀⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⠃⠘⢳⡝⠃⢸⠁⣠⠁⠀⠀⠹⡇⠀⠀⡀⠀⠰⣇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠿⢟⠻⢂⡀⣾⢠⡇⠀⠀⠆⢘⣇⠀⠀⢀⡠⢀⣿⠀⠁⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣝⣣⣴⠶⣏⣿⣇⠏⠀⠁⠀⠀⢀⡿⠂⠚⠫⠂⢀⡛⠈⡇⠀⣿⢽⡄
⠀⠀⠀⠀⠀⠠⢶⣾⣯⣥⡿⠋⠀⠤⠭⠹⢿⠦⡅⠤⠶⠂⠈⢿⠆⠨⠄⠀⠘⢲⠀⡋⣸⡿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⢤⢤⣤
⢀⣄⣰⣷⣦⣤⣀⡈⠛⠳⠦⠤⢄⣤⣄⣀⠀⠀⠀⠓⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣿⡀⠀⠀⠀⠀⡀⢀⣀⣄⣠⣤⡄⣒⢳⣄⢸⣷⣶⠶⠶⠿⠿⡿⡇
⠋⠻⣿⠿⠇⠹⠻⠿⣿⣶⣶⣶⣦⣄⣀⣀⠉⠓⠆⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠼⣯⡙⠗⠆⣿⠺⣎⣿⣻⡥⠿⠿⠧⡑⠾⡟⣸⡖⠉⠙⠃⠘⠁⠙⠉
⠀⠀⢈⣷⢶⣦⣤⣤⣠⠀⠀⢉⣉⡛⢿⠋⠛⠶⣦⣈⠰⣿⣿⣶⡄⣻⠻⢏⣹⣟⣽⣹⣿⣿⣄⣓⣹⠙⠋⠉⠁⠀⠀⠀⠀⠀⣿⠧⠵⣿⠁
⠀⠀⢸⠘⠛⠎⢩⣛⠲⠶⠦⢸⣿⣖⢀⠻⢦⡀⢃⡘⢧⣸⣏⣹⡇⡸⠿⠟⠛⠋⠉⠉⡅⠸⣯⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢴⣾⠃
⠀⠀⢨⡏⠱⠀⠈⠉⠩⠶⢅⡀⣷⣏⠉⠓⠈⠻⣦⣴⣶⠿⠛⣉⠀⠁⠀⠀⠀⠀⠀⢀⠃⠀⠹⣶⡟⠀⣀⣀⣤⣤⣤⣶⣶⣮⡵⠟⠁
⠀⠀⠐⡷⠂⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⢈⠀⠀⠲⠌⠃⠐⠂⠐⢆⠀⠀⢀⣀⣤⣮⡿⠾⠶⠿⣿⡿⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⢷⠀⣀⠈⠀⠀⠀⠀⠦⠈⠉⠀⠀⣄⠢⠀⠀⣠⣾⣿⣿⡿⠆⠛⠉⠉⠀⢀⠀⠈⠓⠦⠁
⠀⠀⠀⠸⣷⣮⠳⣄⠀⢀⡶⡤⢀⠀⠀⠀⠀⠀⣀⣼⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢄⡄⠰⠿⣄
⠀⠀⠀⠀⠱⣞⡻⠦⠛⡯⢥⠲⡜⠂⡀⣠⣴⡿⠛⢁⠀⢀⡤⢀⣀⣄⡀⠀⠀⠀⠀⠸⢦⡄⡙
⠀⠀⠀⠀⠀⠈⠙⠷⠿⡶⠶⠲⠾⢯⣿⣿⠏⠄⠀⠠⠖⠻⢟⡿⠛⠉⢟⢻⣦⣤⣄⠀⠀⠉⠁⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠀⠈⠀⠀⠀⠀⠈⠻⡻⣮⣉⣮⠙⣿⣿⡛⠳⠦⣤⣀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡀⠀⠀⠀⢙⢊⣉⠛⠃⢻⡹⣷⢶⣧⢾⢻⠷⢦⣄⡈⠓⢥⡴⢄⠰⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⢰⡄⢤⣼⡀⢰⡸⣶⣎⣉⡅⢨⣅⣝⠲⣷⣯⣽⢳⣶⣿⣧⢶⣄⠀⠣⠖⡘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣄⠐⠉⡙⠇⠙⠎⠝⠟⠁⠈⠥⠌⠛⠣⠹⠏⡼⠑⠿⢿⠧⡻⢿⠦⡄⠁⠺⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⠓⠶⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢛⡛⢿⣳⡄⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⠻⣦⣀⣠⣴⣶⡿⠿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠉⠙⠛⠿⣿⣶⣤⣴⣶⣶⣶⣶⣶⣶⣶⡿⠁⠀⠀⠀⠀⠈⢿⡟⠋⠁⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢠⣿⠁⠀⠀⣠⣶⣶⣤⣼⣷⣤⣄⠀⠀⠀⣀⣹⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⣿⣀⣼⠟⠁⠀⠀⠙⢿⡾⠛⠛⠛⠛⢻⣆
⠀⠀⠀⠀⠀⠘⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⢸⡿⢶⡄⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⠶⠾⠻⣷⣄⣀⣀⣤⣿⣧⣼⠟⠀⠀⣸⡏
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⢿⣄⠉⠁⠀⢀⣼⡟
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠟⢻⣷
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣆
⣠⣤⣤⣤⣿⣧⣤⣤⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠲⠾⠿⣿⡟⠛⠛⠛
⠉⠉⠁⠀⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⣀⣸⣿⣦⣤⠄⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠛⣿⡿⠿⠷⠶⠆
⠀⠀⠚⠛⠉⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⠃
⠀⠀⠀⠀⠀⢀⣸⣿⣷⣟⠃⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠿⣶⣦⣀
⠀⠀⠀⢠⣶⠟⠋⠁⠈⠻⣿⠏⠁⠈⢻⡶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠀⠀⣀⠀⠀⠀⠀⣿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢾⣀⡷⠀⠠⣾⡏⣿⡏⠙⠛⠛⠛⠛⠋⠉⣿⠏⠉⠈⢿⣟⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡟⠀⠀⠀⡀⠀⠀⢸⡷⠸⣷⣄⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠈⢿⣧⣴⡿⠻⠿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠏⠘⢷⣄⣠⣼⡿⢶⣶⡟⠁⠀⠈⠛⠿⠶⠶⠾⠟⠋⠀⠀⠀⠀⠀⠘⣿⣟⠀⠀⠀⠀⣹⡿
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠉⠉⢹⣿⣄⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⢸⣿⢻⣦⡘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡾⠟⠃⠀⠙⠷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠟⢿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢷⣶⣶⣶⡶⠿⠿⠿⠿⠷⣶⣶⣶⡶⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠋⠈⠉⠉⠉⠉⠉⠙⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⣀⡀⠤⠀⠐⠂⠒⠒⠒⠂⠤⢄⣀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⡤⠒⠉⠀⠀⢀⡀⠤⠤⠤⠤⠤⠀⣀⠀⠀⠈⠐⠤⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠞⠁⠀⠀⠀⠈⠀⠀⢀⣀⡀⠀⢀⣀⣀⡀⠀⠉⠒⠤⡀⠀⠑⢄⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡠⠊⠀⡠⠂⠁⠀⠀⠐⠈⠀⢀⣀⡀⠀⢀⣀⣀⠉⠉⠒⠤⡀⠈⠑⢀⠀⠉⢦⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡔⠁⡠⠊⢀⠤⠊⢀⡠⠔⠊⠉⠁⠀⣀⣀⣀⠀⠀⠉⠑⠂⢄⡀⠑⢄⡀⠑⢄⠀⠱⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡜⠀⡔⠁⡠⠁⣀⠔⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⠀⠀⠈⠢⡀⠑⢄⠀⠳⡀⠱⡀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⠼⠤⠴⣀⡜⢀⣎⣀⡔⠁⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⠀⠣⠀⠱⡀⢱⠀⢰
⠀⠀⠀⠀⣀⠎⠁⠀⠀⠀⠈⠖⠋⠁⠀⠈⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢱⣀⠷⠤⠷⡀⣦⠚⠁⠒⠒⠒⠐⠢⡀
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⡠⠒⠠⠔⠚⠁
⠀⠀⠈⠒⠢⠤⠒⠉⠑⠤⠀⣀⣀⣀⡠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡀⠀⠀⢠⡀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⠠⠾⠷⠶⠶⠿⠶⠄⢠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣦⣤⣤⣿⣀⣀⣀⣀⣠⡞⠋⠙⢿⣶⠾⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⠙⠛⠛⠉⠉⢹⡟⠀⣠⣴⣬⣿⣄⡀⣀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⣾⠃⠀⠈⣿⣯⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠒⠛⠷⣤⣴⡿⠿⠃⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡧⠤⠤
⠀⠀⠀⠀⠀⠀⠀⣠⠶⢮⡉⠉⢻⡏⠁⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⢀⣼⣇⣀
⠀⠀⠀⠀⠀⣠⠞⢡⡲⣌⢳⡶⠛⢿⡋⠀⠀⠀⠁⠀⠀⠀⠸⣏⣽⠂⠀⠀⠀⠀⠀⠀⢀⣸⡟⠉⠉
⠀⠀⠀⠀⠘⠧⣜⠳⡝⠎⠁⡇⣠⡾⠿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠈⠓⠦⠶⠲⣿⢧⡀⠀⠀⠉⣻⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⣶⠶⢾⣯⡾⠁⠈⣿⣀⣀⣀⣀⣼⠇⠈⢿⣼⠟⠻⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣍⣉⠉⠉⢛⣻⣟⡛⠛⠉⣉⣩⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠉⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠛⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡴⢚⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⡤⠄⣾⣿⣞⣋⠵
⠀⠀⠀⠀⡀⠈⠋⠈⠉⠉⠓⡂⠀⢀⣀⡀⠀⠀⣰⣦⣤⡶⡶⠟⠛⠙⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢄⣀⣀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠿⠛⢻⠉⠀⢀
⠀⠀⠀⠀⠀⠉⠉⠹⣿⠶⢤⡀⢀⠠⠿⠯⣂⠀⠀⢾⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠈⠀⣠⣾⣏⠉⠙⠢⣜⣇⣠⡴
⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⣠⣾⣵⣿⣿⣷⣶⣶⣄⡙⠂
⠀⠀⠀⠀⠀⠀⠈⠙⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣈⠳⢄⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡟⠿⢿⣷⣶⠉⠀⣶⣟⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠇⠀⠀⠙⠿⠳⠾⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡮⢿⠋⣿⣇⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠈⠀⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⢻⣿⡟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⠀⢸⡇⢉⠂⢸⣿⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡇⠀⠀⠀⠿⠿⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠷⣶⣤⣀⣀⣀⣀⣤⣤⣼⡟⠁⠀⠉⢿⣶⠿⠛⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠈⠙⠛⠉⠉⠉⣹⡟⠀⠀⣴⢶⣦⣿⣤⣄⣀⣀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠳⣾⠁⠀⠀⢹⣏⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠞⠻⣦⣀⣠⣾⣿⡇⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣄⣀⣀⣴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠘⣿
⠀⠀⠀⠀⣀⣤⣤⣿⣤⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠲⠞⣿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠠⢤⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠒⠛⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⡽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠛⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠙⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠉⠻⣦⣴⠾⠛⠋⠉⠉⢷⡀
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠉⠳⠶⠛⠛⠛⠛⠛⣻⠃⠀⠀⠀⣀⡀⠘⣧⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡞⢉⡽⠛⠉⠙⠳⣦⡤⠶⠶⠿⢦⡀
⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠳⣾⠁⠀⠀⠀⠀⢸⣧⣄⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⠼⣧⡀⠀⠀⢀⣼⢁⣽⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣯⠉⠉⠁⠀⣠⡏
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⡤⠞⠉⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀
⠀⠤⠶⠶⢾⡷⠦⢤⠄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠛⠉⢹⡏⠉⠉⠛
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⣠⣀⣿⣀
⠀⠀⠀⣤⠶⠻⣟⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⡞⠉⠙⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠙⣧⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣾⣏⣀
⠀⠀⠀⠀⠀⣠⠞⠉⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠉⠛⠆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠉⠉⠉⠉⠉⠉⠁⠐⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣷⠀⣶⠀⣾⠛⠁⡆⠀⣶⠀⢠⡾⣷⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⠒⣿⠀⣿⠂⠀⣿⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠿⠀⠿⠀⠿⠖⠀⣿⡄⢿⣤⠸⣧⡾⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠤⠀⡠⠤⠤⠤⠤⠤⠤⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⣀⡠⠤⠐⢲⣶⣶⣶⣶⠒⠂⠤⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢮⣤⠑⠖⠉⠀⠀⠀⠀⠈⠈⠉⠈⠁⠀⠀⠀⠀⠈⠑⠤⢎⣤⢡
⠀⠀⠀⠀⠀⠀⢸⠈⠁⠀⠀⠀⠔⠂⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢄⠀⠁⠸⡀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⣠⣖⠂⠐⠢⡀⠀⠀⠀⠀⠀⠀⣀⡔⠒⠒⢤⡀⠀⠀⠈⢢
⠀⠀⠀⠀⠜⠢⠤⠀⠀⠠⣾⣿⣿⣷⠀⠀⢡⠀⠀⠀⠀⠀⣼⣿⣿⣦⠀⠀⢘⠄⠀⠤⠤⠷⡀
⠀⠀⠀⠎⠀⠒⠂⠀⠀⠀⠻⣿⣿⣿⠇⠀⡸⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠊⠀⠀⠐⠐⠒⠱⡀
⠀⠀⡜⠀⠉⠉⠀⠀⠀⠀⠀⠙⠻⠟⠠⠔⠁⠀⢠⡄⠀⠀⠀⠙⠿⠧⠒⠁⠀⠀⠀⠉⠑⠒⠀⢱
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢞⡱⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡄⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸
⣧⣤⣤⣤⣤⣤⣤⣬⣵⣶⣷⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣷⣶⣬⣥⣤⣤⣤⣤⣤⣤⣤⣬⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣰⢿⣿⠟⠹⠟⠛⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠈⠉⢙⡟⣇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⠋⠀⠀⠀⠀⠀⠀⢀⢧⠹⡇⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢸⣧⢿⣄⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⡠⠜⠉⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⢆⡀⠀⠩⠻⡿⠟⠀⢁⡄⠀⠑⠄
⠀⠀⠀⠐⢡⠔⠚⠛⠓⠬⣦⠶⠾⢿⣿⣿⣿⣿⠿⠓⠀⠀⠀⡀⢠⣦⣾⠾⠉
⠀⠀⠀⠐⢯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡶⣤⣀⣴⠾⣿⣿⡿⢀⡀
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠉⠀⠀⠀⠙⣿⣿⡷
⠀⠀⠀⠀⠀⠀⣿⡿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠂⠀⢀⣤⣀⠀⠀⠀⠀⢸⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⠀⠈⠉⠉⠙⠛⠿⠿⣶⡀⠀⠀⠈⣻⣿⣷⡄⡄⣤⠸⡿⡿⣦⣼⣄⣀⣀⣀⣀⣀⣀⢀⡠⣄⣄⣀⣴⢮⣤⣤⣄⣒⡀
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠤⠢⣹⣿⡿⢓⠖⣶⣶⣷⣶⣶⢒⠆⠓⠛⠛⠻⠛⠻⠿⠃⠈⠛⠟⠻⣿⡿⠿⢽⡿⠛
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⢀⠀⠙⢟⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⣀⠄⠤⢰⠞⠀⠀⠈⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣀⠀⢑⣄⡈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⣤⣤⣴⣾⣿⡿⠿⢟⣽⣿⣿⣿⣿⣯⣍⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⡅⣀⠀⠙⠻⢿⣿⣿⣿⣿⣦⣤⡦⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣛⣛⡿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣦⣤⡜⠹⠿⠛⠷⣯⣿⣿⣿⣿⣿⣿⣥⠖⠀⠘⠫⠏⢺⣿⣿⣿⣿⣧⣤⣄⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢧⡇⠀⡖⣷⣿⣿⣿⣿⣿⣹⣿⣯⣥⠲⣆⠀⠀⠀⠉⠉⠉⠻⢿⡿⣶⣶⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⣠⣿⠿⠿⠟⠛⠁⣿⣿⣿⣥⡄⠈⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣧⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⡗⢿⣛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⣛⣯⣥⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⢿⣧⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠾⢿⣻⠇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠾⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠉⠙⢋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⢛⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠻⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣀⣠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠘⣆⠀⠀⢀⣠⣤⣷⣤⣄⡀⠀⢹⣧
⠀⠀⠀⠀⠀⢰⣿⣠⡾⠟⠛⠛⠿⣶⣄⣤⣤⣼⣧⣤⣀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢸⣤⣾⠟⠉⠁⠀⠈⠙⠻⣦⡘⣿
⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠈⠛⠉⠁⠰⠶⢭⣙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣠⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣤⡀
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠙⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣭⣋⣠⣤⣶⣧⡀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠻⠷⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⠿⢿⣿⣿⣶⣤⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠉⢠⣤⠀⠀⠀⢰⣿⠄⠀⠀⢀⣤⡀⠈⠙⠻⣿⣿⣷⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣠⣾⣿⡿⠋⢁⡀⠀⠀⠈⠋⠀⠀⢀⣀⣀⣀⠀⠀⠈⠛⠁⠀⠀⣀⠈⠙⣿⣿⣧⡀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠻⠟⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠘⠿⠃⠀⠈⠻⣿⣿⣄⠀⠈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⢠⣿⣿⡟⢁⣤⡀⠀⠀⣠⠞⠉⠀⣀⣤⣶⣶⣿⣿⣶⣶⣦⣄⡀⠈⠳⣦⡀⠀⠀⣤⡄⠹⣿⣿⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⡏⠀⠀⠛⠁⢠⡞⠁⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⢿⣦⡀⠈⠳⣄⠀⠛⠁⠀⠸⣿⣿⡄⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⣤⡄⠀⣠⠏⠀⢠⣾⡟⠁⠀⣀⣤⠶⠞⠳⠶⢦⣄⠀⠀⠙⣿⣆⠀⠹⣆⠀⣠⣤⠀⢹⣿⣿⡀⠀⢀⡀
⠀⠀⠀⠻⠀⠀⢸⣿⣿⠁⠀⠙⠁⢠⡏⠀⢠⣿⠏⠀⢀⡼⠋⠀⠀⠀⢀⡀⠀⠙⢷⡄⠀⠘⣿⣇⠀⢹⡄⠘⠋⠀⠈⣿⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣀⠀⠀⣾⠀⠀⣿⡏⠀⠀⣾⠁⠀⠀⢺⣷⣿⡗⠀⠀⠀⢻⡄⠀⢸⣿⡀⠀⢷⠀⢀⣀⠀⢹⣿⣿
⠀⠀⠰⠖⠀⢀⣿⣿⡇⠘⠛⠃⢠⡇⠀⢸⣿⠁⠀⢸⡇⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⡄⠘⠟⠀⢸⣿⣿⡀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠁⠀⠘⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠃⠀⠈⠁⠀⠀⠀⠀⠛⠛






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢐⡇⠷⡀⠀⠀⠀⠀⠀⠸⠁⢣⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣤⣄⣐⣇⠱⡀⢠⣤⣤⡤⢴⣧⣤⣷⠔⠛⣰⠷⠤⢴⣧⣼⡦⠒⢋⡴⠂⢸⠀⢣⠀⣀⣤⡶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⣄⠤⠟⠿⣧⣤⣷⢼⣯⡭⠿⣾⣇⠀⣿⡔⠊⠙⠒⠒⣾⡅⢈⣷⣶⣾⣴⠶⣼⡧⣼⡿⠛⢉⡵⠂⠹⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠙⠒⠀⣴⣇⢀⣽⣿⠙⣅⢘⣁⣘⣿⣦⣭⡶⢣⣤⣾⣥⣽⣿⣀⣹⡏⠹⣦⣾⡁⣨⣷⡐⠋⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢰⣧⣬⡿⢦⣿⡀⣸⣿⠿⠛⢻⣍⠉⠃⠈⣿⠉⣉⡭⢍⡙⢛⣧⢀⣿⡶⠟⢛⣾⠵⣆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣬⡿⠆⣤⣄⣽⠋⠙⣧⡼⣿⡛⢁⣙⡿⠗⢿⢋⣁⡴⢯⣥⣬⡟⠉⢻⣄⡴⠋⠉⠑⠜⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠙⡷⠞⠙⢦⡀⠈⠉⡙⠳⣤⡼⢿⡉⠀⠀⢠⠋⠙⢶⡉⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⠀⢀⡠⠀⠀⠀⠀⠀⢀⣅⡤⠃⠈⠒⢠⡙⠀⠰⡇⢠⠈⠳⠤⣙⢆⠀⣸⣀⠌⠀⠙⠲⢴⡇⠀⠀⠀⠀⠠⣀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡟⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠚⠙⠁⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⣷⠛
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣀⣀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀
⠀⠀⠉⠉⠛⠛⠻⣿⠶⠶⠦⠀⠀⠀⠀⠀⢙⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢹⡟⠀⠀⠀⠀⠀⠠⠶⠶⢾⡟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⢀⣤⠶⠟⠻⣟⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⢆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⢻⡿⠻⠷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠷⢶⣤⣀
⠀⠀⠀⠠⠞⠋⠁⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠉⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠀⠘⢿⣯⡉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⠉⣹⣿⠏⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⣳⣄⠀⠘⢿⢿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⣿⠋⠀⣠⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠈⠻⢿⣷⡄⠈⠳⠿⠿⠿⠛⠻⠿⢶⣤⡀⣠⣴⠾⠿⠛⠻⠿⠿⠶⠃⢀⣼⣷⠟⠁⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⢿⣦⡀⣠⡴⠶⠚⠛⠛⠉⠙⠿⠛⠙⠛⠛⠛⠲⠶⣤⣀⣠⣿⠟⠁⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⢘⣿⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⠶⣦⡀⣠⠶⣶⠁⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢠⡾⣿⡖⠶⢦⣄⠀⣠⣷⡶⠙⠿⠛⠲⣾⣇⣀⢀⣤⠶⢂⣿⣿⣆⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣀⣤⣴⣿⡷⠟⠛⠋⠻⣿⣭⣭⣽⣿⣶⣦⣶⣾⣿⣭⣭⣽⡿⠋⠉⠛⢷⣿⣷⣤⣀⣠⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⢿⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠯⡥⣄⠈⢿⡄⠀⠀⠀⢀⣤⣤⠶⠶⠶⣤⡄⠀⠀⠀⢀⣤⡴⠶⠶⢤⣤⣄⡀⠈⠁⠀⣼⠋⢀⡬⢭⢟⣦⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣭⣶⣶⣶⣿⣇⠈⠙⠶⠛⠉⢉⣠⣤⠶⠶⠶⣄⠙⠳⣤⡶⠋⣠⠶⠶⠶⠦⣤⡈⠉⠛⠲⠞⠁⢠⣿⣾⣷⣾⣦⣽⣧
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⢿⣿⣏⠷⠶⣶⣶⣾⡿⠿⠛⠛⠿⢶⣌⠳⣄⣀⣠⡴⣫⣴⠿⠛⠛⠲⢿⣿⣶⣖⡶⠾⣫⣿⡿⠿⠟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⠿⣶⣭⣵⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠦⠤⣤⡤⠤⠶⠶⠶⠞⠛⠛⠋⠉⠙⠛⠷⠶⠶⠶⢤⣤⡤⠶⠶⠶⠞⠛⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠐⠢⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡤⠖⠂⠀⠘⠓⠶⡌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠉⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⣄⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠛⠿⠅⢈⡛⠋⠀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢳⠀⠀⢀⠀⡠⠁⠀⢀⠌⠀⢀⠂⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⡈⠀⠀⠈⡀⠐⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠀⠀⢢⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⡘⠃⠀⡔⠍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡀⠀⠀⠀⠁
⠀⠀⡠⠂⠀⠀⡼⠀⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠠⠑⢄⠀⠀⠀⡜⠀⠀⠤⠞⠠
⠀⠈⠀⠀⠀⡼⢁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠠⠄⡴⠁⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠋⠀⠀⡸⠁⠌⡀⠀⠀⠀⠀⠀⠄⠤⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠰⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡄⠑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⢀⢠⡴⠅⣀⠄⠀⠀⠀⠀⢀⡀⠀⠐⢀⠀⠀⠀⠀⢳⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠈⠘⣌⠸⠆⠀⠀⠿⢬⣯⡠⢄⣠⣀⣀⣤⣄⣃⣀⣀⣁⣀⣂⣀⣇⣀⣹⣀⣙⣀⣘⣀⣈⣆⣀⡠
⠀⠀⠀⢠⡀⠋⠉⠉⠏⠋⠍⠭⠻⠩⠹⠻⠉⠉⠉⠉⠋⠋⠋⠏⠛⠁⠁⠃⢈⡑⠜⠛⠚⠂⠉⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠈⠨⡷⠈⠀⠀⠀⠀⠀⠐⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠤⠀⠀⢀⡀
⠀⠀⠀⠀⡀⠀⠀⠙⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⡉⡉⢉⣁⠈⠀⠀⢀⠁⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠤⠤⠤⠤⠤⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠤⠴⠰⡀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠠⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣤⣤⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥
⣿⣿⣭⣭⣯⣬⣭⣯⣥⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠉⠐⢄⡀⠀⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⡘⠀⢀⣀⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⣀⣀⠘
⠀⠀⠀⠀⣀⡷⠛⠋⠉⠙⢠⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⡠⠊⠉⠙⠛⢷⣀
⠀⡰⠖⠛⠉⠉⠀⠀⢀⣄⡐⠋⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢂⣤⡀⠀⠀⠉⠉⠛⠲⢆
⠀⠁⠀⠀⠀⠀⢠⡞⠉⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠉⣳⠄⠀⠂⠀⠀⠈
⠀⠀⢳⡄⠀⠀⠀⢻⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⣠⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠷⣤⣤⣤⣤⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠋⠳⣤⣤⣤⣤⠾




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⠤⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠆⠀⠀⠀⠀⠓⠢⠀⡠⢄⠀⢀⣀⠀⢀⡄⠀⠀⠁⠀⠈⠂⢄⠀⠀⠀⢀⣠⠃⠀⠈⠊⠁⠀⢱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠎⠀⠈⠁⢫⠀⢆⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⢹⠙⠏⠒⢈⣤⡤⢣⣀⣂⣠⠆⠀⠀⠈⢣⣀⣴⠦⡠⠎⠀⠀⠀⠈⠢⢤⡀⠀⠀⠀⠀⠀⠀⡤⠔⠃
⠀⠀⠀⢸⣰⡴⠋⠁⠈⠛⠿⢁⣨⠕⡞⠉⠓⠢⡎⠀⠀⠃⠀⢠⠋⠉⠒⠒⡶⢋⣱⡖⠒⡎⠢⠤⠔⠁
⠀⠀⠀⢸⣬⡀⠀⠀⠀⢖⠒⠒⠒⠛⠲⡀⠀⠀⢳⠒⠒⢲⡀⡸⠃⠀⠀⠀⠑⠼⢇⣸⠏⡳
⠀⠀⠀⢸⠘⠑⢤⣀⠀⠀⢣⠠⡈⠀⠐⠐⡤⠒⠁⠑⢤⠤⠓⡇⠀⣀⠀⠀⠀⠀⠀⠑⢊⣇⡀
⠀⠀⠀⠘⠴⠀⠀⠀⠈⠉⠉⠱⡈⠂⠀⠀⡔⠀⠀⠀⠀⠀⠈⠽⣄⠀⠀⠐⠂⠀⠘⠀⣠⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠀⠀⡏⢹⠀⢀⣀⣖⡤⠛⡖⢲⠢⢤⢔⡒⠉⠁⡠⠖⠤⡀
⠀⠀⢀⣀⠀⠀⡠⠄⠠⢄⠀⡖⠶⠀⠐⢤⡀⠀⢣⣨⠞⢩⠀⠀⠙⠦⠶⠮⠤⠚⠁⠈⠉⠲⡇⠀⠀⡇
⠀⠀⠀⠀⠉⠊⠀⠀⠀⡤⣵⠃⡱⢄⣠⠋⠀⠀⢯⣸⠀⠀⠀⠀⢶⠒⠒⠒⠒⠒⢦⠀⠀⠀⣻⠛⠉⠻⣤⡠
⠀⠀⡔⢢⣠⣮⠝⠂⠄⠈⠀⠉⠑⠀⠛⡄⠀⠀⡆⢹⠳⣄⡀⠀⠀⠣⡀⡔⠁⠀⠂⢣⡤⠊⠔⠓⠤⠤⠃
⠀⠀⠈⠻⡄⠢⣀⡀⡆⠀⠀⠀⠀⠀⣔⠀⠀⠀⢧⡸⠀⠀⠉⠉⠉⠉⠱⣄⠢⠒⠂⠀⡇⠀⢄⣀⡀
⠀⠀⠀⠀⠈⠲⠁⠈⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠀⠀⠀⠀⠡⢀⡀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠸⠀⠀⢸⠀⢀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠂⢀⡠⠅⠰⠒⠀⠐⠆⠤⣈⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠓⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠈⠁⣀⡔⠊⠑⠢⠤⣀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢆⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡁⠀⠀⠏⠙⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⢱⠒⡛⠤⣀⠴⠒⠚
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠒⠒⠾⢄⡉
⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⡀⣈⢆⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⠀⠀⢫⠳⡀⢀⡜⠁⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⢊⡄⣨⠟⠁⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠈⢣⠀⡀⠄⣀
⠀⠀⠀⠀⠈⠒⠲⣀⢀⡤⠤⠊⠉⣰⡏⠀⠀⡰⠋⠀⠀⣀⠴⠒⠋⠉⠙⠒⠦⣄⠀⠀⠈⢆⠀⠀⠀⢏⠀⠀⠈⠓⠒⠖⠂⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡸⠁⠀⢀⠞⠁⣀⡠⢤⠤⠤⢄⠀⠈⠳⡀⠀⠹⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠁⠀⢠⠃⠀⡶⠋⠀⠀⠀⠀⠀⠑⡄⠀⠱⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠌⠀⠀⡌⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠠⠀⠀⡀⣀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠚⠢⠴⠣⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠧⣀⡰⢇⣀⡠⠛⠒⠊⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠀⠀⠈⢙⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀⠁⠀⠀⢉⣤⠀⠀⢠⡉⢀⡄⠀⠀⡀⢠⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠘⡀
⠀⠀⠚⠁⠀⠀⠈⠚⠋⠀⠀⠒⠒⠒⠒⠀⠀⠛⠁⠃⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠒⠓⠂⠁

⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⡀⠀⠀⠀⠐⠀⠀⠀⣂⡄⠠⡀⢀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⠀⢿⣠
⠀⠠⠄⠤⠀⠀⠀⠠⠄⠀⠀⠀⠠⡰⠀⠀⠀⠀⠀⠀⠀⢨⠿⠇⠆⠀⠀⠒⠂⠀⠀⣈⡀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠁⠀⠻⡀⡿⠃⠀⢀⣀⠀⠀⠀⠀⣀⢲⠆⠀⠀⠠⣤⠁⠀⠐⢀⡀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⡉⠀⠀⠀⠈⠙⠀⠀⡄⠈⠛⠤⠄⠀⠀⢹⠀⠀⢀⠀⠀⡤⢤⣤⢀⣻⢧⠀⠀⣤⡵⠀⠀⠀⠀⠉⠀⠀⠀⠠
⠀⠀⠛⠓⠀⠀⠀⠉⠁⠀⠀⠠⠛⠋⠘⠀⠀⠺⠘⠆⠀⠀⠨⠁⠓⠁⠈⠛⠛⠛⠀⠀⠸⠁⠀⠀⠀⠀⠘⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶
⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⢀⠀⠀⠤⣄⠠⠀⠀⠠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠃⠁⠂⠀⠃

⠀⠀⠀⣀⠀⠀⠀⢀⣄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀
⠀⠀⣠⡄⠀⠀⠀⢀⠁⠀⠀⠀⣧⣈⠃⠀⠀⠀⠐⠀⠀⠀⢠⣤⠀⠀⠀⡀⠀⠀⠀⠀⢀⡈⠀⠀⠀⢀⡀⣬⠄⠀⠄⠀⠀⠈⠆
⠀⠀⠈⠁⠀⠀⠀⠙⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠠
⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠆⠀⢠⣜⣁⠀⠀⠐⠁⠀⠀⠀⠀⠐⠋⠀⠀⢀⡀⢀⣈⠁⣉
⠀⠀⠻⠀⠶⠀⠀⠰⠀⠀⠀⠀⠘⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠆⠀⠈⠿⠻⠄⠀⠀⠐⠂⠀⠀⠀⠀⠚⠇⠀⠠⠬⠬⠭⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠘⠄⠀⠃⠀⠂⠠⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⠔⠂⠈⠀⠀⠀⠈⠀⠢⡈⠠⠆⠀⡠⠠⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠠⡀⡹⠀⠀⠀⠀⠉⠀⢑
⠀⠀⠀⠀⠠⠤⣀⠁⢠⠀⢀⣄⡀⠀⠀⠀⠀⠀⠉⠈⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠈⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⢣⡀⢄⠀⢀⣀⠜⠉
⠀⠀⠀⠀⠐⠤⠤⠀⠰⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠠⠤⣀⠂⠉⠁
⠀⠀⠀⠀⢀⣀⠤⠭⠤⣣⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢀⠅⠀⠀⠀⠀⡸⠑⢠⠞⠀⠀⡠⠔⠊⠉⠉⠉⠉⠒⠤⡀⠀⠈⢢
⠀⠀⠀⠘⠤⡄⠀⣀⡠⠒⢡⠋⠀⢠⠊⠀⢀⡠⠤⠒⠦⠤⡀⠀⠈⣦⠀⠀⢱⠊⠉⠢⠤⠤⠠⠄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⠃⠀⠰⠁⠀⡔⢁⣠⠤⠄⠤⣀⠈⠢⡀⠘⣇⠀⠀⡆⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠀⡌⠀⡞⠁⠀⠀⠀⠀⢣⠀⢡⠀⠸⡀⠀⢰⠀⠀⠀⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡨⢄⣀⣇⡰⠀⠀⠀⠀⠀⠀⠀⡀⢨⡀⢀⡀⠀⡼⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢠⢤⣤⣂⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤
⠀⠀⡏⠈⠉⠂⢀⡴⣶⣦⠤⠤⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠈⠀⠀⣀
⠀⠀⠑⠀⠐⠻⠉⣱⢣⠢⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣶⡜⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃⠈⣿⡃
⡀⠂⠀⢤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⢰⣿⡇
⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠈⠄⠀⠀⠤⡄⢠⠀⠀⠀⠀⠀⢀⠠⠄⠀⠐⠏⠉⠉⠇⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢼⣿⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠔⠀⠀⠀⠀⠀⠐⠂⣀⡀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣿⡿⣁⠠
⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠭⡀⣀⣀⠯⠀⠀⠠⠄⠐⠂⠈⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⠟⠁⠆
⠀⠉⠁⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠂⢤⠀⠀⠶⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠂⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡽⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠐⠀⠀⠀⠀⠈⠐⠀⠀⠰
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠙⠀⠿⠃
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⠀⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣴⣶⣶⣦⣤⣀⠀⠠⣶⣠⠀⠀⣀⣠⣄⣀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣞⣻⣿⣿⣿⣿⣧⣽⠀⠀⠀⢉⣿⡿⠿⣿⣏⣽⣿⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡿⢛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⣿⣿⡷⠀⠸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣤⣴⣿⣿⣧⣶⣼⣿⣿⣿⣽⣶⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣤⣶⣾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠛⢷⣾⠟⠋⠁⠀⠈⣿⣆
⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⡀⣀⣠⣤⣴⣶⣶⣿⠇⠀⠀⣀⣄⣀⣿⣦⣤⣀⣀⣤⣼⣿⣤⣀
⠀⠀⠀⣸⡿⠋⠉⠉⠉⠛⠛⠿⠟⠛⠉⠉⠁⠀⣿⠀⠀⢸⡟⢹⡟⠉⠀⠈⠹⣿⣁⡀⠀⠈⣿⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠛⢿⣇⠀⠀⠀⢀⣿⣙⣿⠀⠀⣿⠁
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣴⠶⠟⠛⠷⠶⠶⣿⡛⠛⠁⠀⣼⣏
⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠟⠙⣿⡆
⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⠾⠿⠛
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠈⠉⠈⣿⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠐⢻⣿⠟⠛⠛
⢀⣤⣤⣾⣿⡶⠶⠂⠀⠀⠰⣿⣿⡆⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⣼⣿⡀
⠈⠉⠀⠀⢹⣧⣀⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢿⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠛⠛⠻⠆
⠀⠀⠀⣴⠾⠻⣿⣅⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣨⣿⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⣿⡇⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠠⡾⠋⠁⠈⢙⣻⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡾⠿⢿⡟⠛⢿⣧⠀⠀⠙⣿⣄⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⠋⢡⣿⠏⠀⠸⣿⡀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠻⣷⡀⠀⠘⢿⣦⣴⡿⠋
⠀⠀⠀⠀⠀⣿⡋⠉⠈⢻⣷⣿⣷⣶⣶⣤⣙⠻⢶⣶⣶⡶⠟⠁⣠⣴⣶⣶⣿⣷⣶⡶⠿⠛⠉
⠀⠀⠀⠀⢰⣿⠁⠀⢠⣾⠟⠉⠀⠀⠀⠉⢻⣧⡀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠻⣦⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣥⣤⣤⣤⣽⣿⣄⡀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣤⣴⣶⠿⠛⠋⠉⠉⠉⠉⠉⠙⠛⠿⣶⣶⣶⡾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣠⠤⠖⠛⠛⠲⣄⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠀⠀⠀⣠⡤⠖⠋⠉⣹⡾⠿⠛⠛⠋⠉⠹⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠚⠛⠋⠉⠉⠉⠉⠉⣿⠁⠀⣀⣀⣤⣤⣤⣴⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣀⣀⣀⣀⣀⣀⣀⣀⠀⠻⣾⣿⣿⣿⣿⣿⣿⠋⢹⣦⡀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣉⡭⠽⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠿⢿⢿⣿⠃⠀⣾⣿⣿⣿⣿⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢻⠯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣸⣿⣿⠿⠋⠁⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣄⡀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠁⢀⣀⣤⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠙⢻⣿⡟⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠉⢫⡀⠀⠀⠀⠀⠀⠀⠐⢯⣹⠆⠀⠀⠀⠻⠿⠃⠀⠀⠈⢩⠻⣟⠓⠎⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠉⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣹⠛⠦⠘⢦⣀⠀⠈⠉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢧⠘⢆⡼⠈⡏⣿⢒⣤⣤⣀⣀⠀⠀⠀⠀⢀⡤⠤⣼⠛⢧⡀⠀⠀⠀⠈⠓⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢬⣳⡼⠁⢠⡿⠛⢯⠿⠤⠶⡟⢻⡟⢿⡛⢫⠄⠀⢾⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡽⠿⣿⣟⢦⣼⠀⠀⠀⡷⠀⢷⣠⢿⡛⠲⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡇⠘⢦⠳⣄⣀⣠⣇⠤⠞⠛⢾⡗⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠸⡇⠀⢸⡷⣄⠉⠉⠳⢦⣄⢀⡾⢤⣀⡈⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣇⠀⣈⣧⠬⠷⠤⠶⠶⠚⣿⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢩⡧⠤⠤⠤⠴⠶⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠐⠒⠒⠢⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⢀⡀⠤⠐⠒⠒⠒⠒⠒⠂⠒⠒⠂⠤⢄⣀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠊⠀⠀⠀⠀⢀⡠⠤⠒⠂⠈⠉⠉⠉⠉⠉⠀⠀⠐⠒⠠⠄⡀⠀⠀⠈⠓⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⠔⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠈⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠠⠃⠀⠀⢀⠎⠀⠀⠀⢀⠔⠊⠀⠀⠀⢀⡀⠤⠄⠀⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠑⠢⣀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠁⠀⠀⡐⠁⠀⠀⠀⠘⠁⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢄⡀⠀⠀⠀⠀⣱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⡔⠀⠀⠀⠐⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡤⠖⠁
⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠇⠀⠀⠀⠀⠀⣤⣀⣄⣀⡀⠀⠀⡔⠁
⠀⠀⡴⠋⠀⠀⠀⠀⠈⠙⠢⣀⠔⠂⠁⠀⠀⠀⠀⠀⠈⢓⣬⠀⠄⣀⡀
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡗⠀⠀⠀⠈⠳⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠡⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⠁
⠀⠀⠈⡾⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠢⢀⡀⠀⢀⣂⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⡠⠤⠚⠀⠙⠢⢤⣀⡀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⢰⡀⢸⠀⣼⠀⣆⣤⠶⠛⠛⢷⡀⠀⠀⢀⣴⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣆⠸⣄⢷⡈⣇⢸⡆⣿⢸⠏⠀⠀⠀⠀⠈⢷⠀⠀⠘⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣹⣿⠟⠁⡼⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡍
⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⢀⣴⣿⠏⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠂
⠀⠀⠀⠀⠀⢻⠀⠀⠀⣠⣿⡿⠃⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠈⣧⣴⣿⡿⠋⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣧⠴⠒
⠀⠀⠀⠀⠀⠀⢸⠟⠁⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠈⢀⣿⣀⣀
⠀⠀⠀⠀⠀⠠⣯⠴⣞⠁⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢉⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠤⠶⢿⡛⠁⠀⠀⠘⠿⠃⠀⠀⠀⠀⢯⡭⠇⠀⠀⠀⠀⠀⠀⠀⢈⡿⠛⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣹⠾⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠉⠙⢛⣷⢶⠶⣟⣻⣽⣋⡽⢻⡇⠀⢀⣽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⠉⠘⣿⠀⠙⠁⠀⠙⠁⠀⠻⣶⡛⠁⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣄⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢹⣧⣄⣀⣀⣀⣀⣀⣀⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⣋⣹⣍⣛⣛⣫⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠛⠋⠁⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⡀⢀⣀⡀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠈⢻⠿⣿⣿⣇⠀⡲⠂⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⢰⣴⣦⣤⢼⣷⣤⡤⠂⠀⣼⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣶⣦⣤⣾⣦⣠⣄⣈⣙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢍⠉⠓⠶⠆⠁⠀⠀⠉⠍⠛⣿⣷⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⠃⢀⣂⣀⣐⣂⠈⠀⣄
⠀⠀⢰⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄⢘⣿⣇⢀⣰⣿⣿⣿⡿⢿⣿⣿⣆⣬⣍⣀⣀⣤⣤⡀⠈⡧
⠀⠀⠈⠇⣤⡀⠀⠀⠰⡀⠀⢠⣲⣾⣷⠐⣶⢾⣿⡟⣿⡿⡏⣧⣻⢾⣻⡟⠁⣾⣧⠸⣿⡿⠯⠤⢿⡷⢀⡀⠀⡀⠘
⠀⠀⠀⠈⠛⠳⠀⠀⢀⡄⠁⠸⢸⣿⣿⢂⠋⠉⠉⠁⠁⠁⠀⣸⣿⣼⣿⣯⠦⡉⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠦⠑⠀⠀⠐⠽⠯⠊⠀⠀⠀⠀⢀⡀⣀⣿⣿⣿⣿⣿⣆⠠⠀⠀⠈⠃⠂⠠⠴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⢀⠈⠀⠀⠀⠀⠠⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣠⣿⣷⣄⡀⠀⠀⠀⠠⢍⠛⠿⣿⣿⢿⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠛⠋⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣈⣉⣀⣙⣿⣿⣿⣿⣿⠋⠉⠢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⠟⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣷⣴⣷⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣿⣿⣷⣽⣷⡀⠀⠀⠹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢟⠻⡆⠀⠀⠘⢿⣿⡟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡋⠈⠉⠙⢿⣷⣥⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⢰⡇⠀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⡏⣩⣄⠈⣛⢀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⢸⡇⣼⣿⣿⣿⣿⣿⠛⡁⠈⣥⢹⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⡇⠙⠛⠀⠛⠘⣧⣄⡀⠀⢀⣸⡀
⠀⠀⠀⠀⠀⠀⡜⣸⣿⣿⣿⣿⣿⣿⣧⣍⣀⣱⠿⠋⢀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⠀⠀⠻⠇⠙⢿⣿⡏⣉⢰⣧
⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡉⢀⢉⡉⣉⠠⡶⢶⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣄⠀⠈⢿⣿⣄⠘⢫⣿⡛⠀⣁
⠀⠀⠀⠀⠀⠈⡄⢿⣿⣿⣿⣿⣷⠘⣿⣼⠏⡻⠓⠊⠃⠀⣿⣿⣿⣿⣿⣿⡿⣿⡿⠋⠚⠛⠒⠒⠛⠻⢿⣾⣿⣉⠉⣀⠙
⠀⠀⠀⠀⠀⠀⠹⡜⣿⣿⣿⣿⣿⣷⡀⢠⣾⣿⣿⣿⣶⣶⣿⣿⡿⠛⣋⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡋⠉⠻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⢳⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣥⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⣶⣆⢿
⠀⠀⠀⠀⠀⡀⠔⢉⣤⣉⠛⠛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡈⢁⣸
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣿⡇
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠋⣩⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠈⠛⠿⠿⠿⢾⣿⡿⠿⢭⣤⣀⣀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⣀⣀⣠⣼⣿⣧
⠀⠀⠀⠀⠈⣶⢧⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠉⠉⠀⣹⣿
⠀⠀⠀⠀⢀⣾⣷⣿⡷⠖⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⡷⠶
⠀⠀⠀⠀⢸⣻⣿⣿⣿⣄⣀⣀⡤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣤⣴⣿⠏
⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠛⠻⠆
⠀⠀⠀⠀⠀⠰⣿⣿⣾⣻⡈⠻⣿⣷⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣟⠡⠔
⠀⠀⠀⠀⠀⠀⠉⠹⣿⣼⢇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡖⠂
⠀⠀⠀⠀⠀⠀⠀⣼⣯⣴⣾⣧⡀⠈⠻⣿⣿⣿⣿⡏⠉⠛⠦⣄⣀⡉⢉⣩⠟⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣽⡄
⠀⠀⠀⠀⠀⢠⢪⣿⣿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣆⠀⠀⠀⢉⣽⣏⡀⠀⢸⣿⣿⠟⠁⣴⣿⣿⣿⣿⠟⢿⣿⣦
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⠹⣿⣿⣿⣷⣤⡀⠈⠛⢿⣿⣧⠀⠀⠠⢿⣿⠇⠀⣼⡿⠋⢀⣼⣿⣿⣿⣿⣿⣧⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣀⠀⠙⢿⣷⣤⣤⣤⣤⣤⣾⠏⣀⣴⣿⣿⣿⣛⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠻⣿⣿⣿⣿⡿⢁⣼⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⢿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉