Gay alien Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⣀⡀⠀⠀⢸⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡴⠉⠳⡇⢸⠀⠀⢸⠀⢫⡀⢀⠀⣿⢣⡇⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠈⢉⡇⠀⢰⠛⢺⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠳⠦⠖⠿⠘⠛⠉⠈⠁⠈⠙⠋⠀⠉⠈⠁⠰⣄⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠈⠛⠉⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠶⠒⣆⠀⠀⠀⠀⣀⣀⣤⣤⠶⠞⣛⢷⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢸⡀⢀⣼⡶⠶⠟⠛⢉⠉⠀⠐⠒⠉⠀⠘⡇⠀⠀⠀⣼⢀⡤⠦⢤⡀⠀⠀⠀⠀⣠⠤⣄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⣧⠈⣷⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡇⣾⠀⠀⠀⢱⡀⠀⢀⡞⠁⠀⠈⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⢹⡄⠀⠀⠀⠀⢀⣀⣠⣤⡶⠶⠋⢹⡆⠀⢸⠁⠸⣄⠀⠀⢨⡇⠀⣼⠀⠀⠀⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⣇⠶⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠈⣷⠀⢸⡀⠀⠙⠶⠤⠞⠁⠀⠙⠦⠤⠴⠞⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⣀⣨⣼⠇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⡇⢀⣀⣀⣤⣤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠛⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠋⠀⠀⠀⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡄⢿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠤⠧⣬⣃⠀⠙⢦⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣄⣀⣀⣨⡗⢀⠀⠙⢦⡀⠀⠀⢸⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣠⠴⣿⣸⢧⡀⠀⠙⢦⡀⣾⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⡶⠚⠙⡇⠀⠙⢦⡀⠀⠙⢧⡀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣠⡷⠀⠀⠀⠉⠳⣄⠀⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡼⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠓⠀⠛⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡆⢾⠆⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢾⠉⢑⡆⡾⠉⡇⠀⠀⠀⢠⠞⠉⠓⠀⠚⠙⣆⠘⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣀⡄⢸⠃⢰⠀⢸⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸⠐⠿⡄⣧⠞⠁⠀⠀⠀⣏⠀⣀⣀⣀⠀⠀⢸⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠟⠀⠸⠀⠸⠶⠖⠀⠘⠛⠂⠀⠀⠀⠀⢸⣆⡤⠇⠹⠶⠞⠁⠀⠀⠘⣆⣉⣹⠃⣞⣉⡽⠇⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⢠⠀⠀⣤⠀⠀⢠⠴⢄⠀⡀⠀⢠⠀⢀⠤⣍⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠁⠀⠀⠈⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠛⠶⣄⠀⠀⠀⠀⣠⠶⠛⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢤⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣾⠛⠳⠶⣤⣄⣀⠀⠀⢀⠀⠀⡀⠀⠀⣀⣠⣤⠶⠞⠛⣷⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡏⠀⠀⠀⣠⣬⡉⠙⠛⣿⠀⠀⣿⠛⠋⢉⣥⣄⠀⠀⠀⢹⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀⠀⠀⠻⠟⠃⠀⢰⡏⠀⠀⢹⡆⠀⠘⠿⠟⠀⠀⢀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣦⣄⣀⣀⣠⣴⠟⠀⠀⠀⠀⠻⣦⣄⣀⣀⣠⣴⠞⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠙⠐⠒⠶⠶⠶⠶⠒⠂⠃⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣴⠟⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠻⣦⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⢹⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡏⠉⠙⢳⡄
⠀⠀⣠⡶⠚⠛⠛⠋⢹⡆⠀⠀⠘⢧⠀⠀⠀⠻⣦⡀⠀⠀⢀⣴⠟⠀⠀⠀⣼⠃⠀⠀⢰⡏⠙⠛⠛⠳⢶⣄
⠀⣼⠋⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⠀⠁⠀⠀⠀⠈⠙⠓⠚⠋⠁⠀⠀⠀⠈⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠙⣧
⠀⣿⠀⠀⢀⣀⠀⠀⠀⣾⠀⢀⡤⣄⠀⠀⠓⠶⢦⣤⣤⣤⣤⡴⠶⠚⠀⠀⣠⢤⡀⠀⣷⠀⠀⠀⣀⡀⠀⠀⣿
⢠⡏⠀⠀⠀⡀⠀⠀⠀⢻⡄⠹⠶⠟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⠶⠏⢠⡟⠀⠀⠀⠀⠀⠀⠀⢻
⢸⡇⠀⠀⢰⡇⠀⠀⠀⠀⠙⠳⠶⠶⠖⠋⠙⠳⠶⣤⣤⣤⣤⠶⠞⠋⠙⠲⠶⠶⠞⠋⠀⠀⠀⠀⢸⡆⠀⠀⢸
⢸⠇⠀⠀⢸⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠸
⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⠊⠁⠈⠉⠀⠉⢢⠀⠀⠀⠀⠀⣠⣤⠴⢶⣦⣴⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠂⠀⡙⠁⠐⠂⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠖⣛⣋⣛⣓⣮⣕⢦
⠀⠀⠀⠀⠀⠘⢧⣤⡀⢀⣠⣤⢛⠀⠀⠀⡞⠐⠂⠀⠀⠠⠄⠠⠀⠀⠀⠐⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⣎⣾⣷⣿⣿⣿⣿⣿⣛⣛⡃⣷
⠀⠀⠀⠀⠀⠀⠲⡍⠁⠀⠉⢵⠊⠀⠀⠀⡇⠀⠀⠀⢀⣠⠭⠤⣀⡀⠀⠀⠀⣿⠀⠀⣠⠤⢒⣚⣋⣩⣭⠭⠭⠤⠤⠤⠤⠤⡭⠭⠭⣭⣍⣛⣓⡲⠤⣀
⠀⠀⠀⠀⠀⠀⠘⢠⠀⠀⢀⠌⠀⠀⠀⠀⢳⣬⣀⠀⡀⢄⠀⠀⡠⠂⠀⣀⣧⡇⠀⢾⡟⢉⠉⠠⠶⠆⢈⣠⠤⠿⠶⠲⠒⠲⠿⠤⣆⠀⠴⠶⠈⠉⠙⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⡂⠀⠀⠀⠀⠀⢸⠋⣶⢒⣶⣄⠀⠀⣤⢖⣶⣮⢹⡀⠀⠀⠉⠓⠲⠬⣤⣄⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣠⡤⠥⠖⠛⠁
⠀⠀⠀⠀⠀⡎⠉⠉⠀⠀⠈⠉⠙⡆⠀⠀⠘⣦⡙⠛⠿⠟⠁⡘⠻⠿⠛⣃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⡶⠶⠶⠶⠶⢶⣼⠃
⠀⠀⠀⠀⣜⠁⣀⡀⠀⠂⠀⣀⠀⠙⡀⠀⠀⠈⣿⠳⡄⢠⠁⠩⠄⡴⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⡼⠀⠛⡇⠀⠀⠀⡹⢃⠹⢄⠀⠀⠀⢻⡀⠀⠆⠀⡀⠀⠀⣠⠇⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣤⠤⠴⠒⠒⠒⠾⠿⣷⣄
⠀⠀⠀⠰⢀⠌⠀⡃⠀⠇⠀⡇⠈⢆⠸⡀⠀⠀⠀⠉⢻⡀⠙⠋⢠⠟⠁⠀⠀⠀⢺⡿⠀⢺⠇⠐⣿⠃⠀⠀⠰⡿⢾⣯⣿⣷⣶⣶⣶⣶⣶⣤⣠⣴⢾⡿
⠀⠀⠀⡆⢈⠀⠜⠉⠀⠀⠈⠙⠄⠈⠸⡁⠀⠀⠀⠀⠀⠓⠶⠶⠋⠀⠀⠀⠀⠀⣼⣧⣼⣿⣿⣤⣿⡄⠀⠀⠀⠀⠀⠉⠿⠉⠙⠛⢻⠿⢿⢿⣟⠚⢧
⠀⠀⠀⠁⡘⠀⡆⠀⠶⠶⠦⠠⡄⠘⠀⡇⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⡿⢷⣳⡟⣷⣧⠿⣟⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠈⠁⠀⠒⠻⡆⠈⢦
⠀⠀⠀⡤⠃⢰⡇⠰⠀⠀⠀⠀⡇⡀⠳⡀⠀⠀⠀⢠⠋⠉⠉⢻⣿⣿⣻⡦⠀⠀⠇⢰⢸⠇⢸⠰⠀⠃⠀⠀⠀⠀⠀⡠⠎⢠⢎⡢⣄⠀⠀⠀⠀⢧⣤⠾⠃
⠀⠀⠰⠃⠈⢹⠀⠆⠀⠀⠀⡀⠁⠋⠀⠳⠀⢠⣾⣫⣠⣤⣴⡶⠿⣿⠁⠀⠀⠀⠁⠈⠴⠀⠰⠌⠀⠁⠀⠀⠀⡠⠊⠀⢴⣿⣿⡉⠈⠳⣄
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠈⠉⠙⠄⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣠⡮⣿⡿⠀⣠⣟⡬⠳⡀
⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣢⡾⣦⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡰⡾⢋⣤⣼⣤⣞⡿⠋⢠⠜⠁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣽⣯⣶⣶⣶⣾⣿⡝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡋⣻⣯⡜⠋⢠⠞⠁
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠤⢤⣒⣚⣋⠭⣍⡩⢩⠭⢉⠭⢥⣛⣒⣢⠤⢄⡀⠀⠀⠀⠀⠀⠙⢮⡋⢀⠞⠁⠀⠀⢠⣶⡄
⠀⠀⠀⢀⡔⢁⠞⠆⠀⠀⠀⠺⢆⠑⣄⠀⠀⠸⣏⡉⠀⠴⠆⢀⠤⠜⠒⠒⠒⠚⠤⢄⠀⠴⠆⠈⢉⡿⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣭
⠀⠀⠀⠘⠃⠁⠀⠀⣀⠀⠀⠀⠀⠁⠛⠀⠀⠀⠀⠉⠐⠒⠠⠼⡇⠀⣀⣀⣀⡀⠀⡾⠤⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣶⢀⡄
⠀⠀⠀⠀⠀⠀⡠⠞⣩⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠭⢭⡭⠽⠿⠃⠀⠀⣠⣤⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠻⣿⠟⠁⠀⡀
⠀⠀⠀⠀⡀⠊⠀⢰⣶⡆⠀⠈⢳⣶⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⢳⣴⣟⣿⣛⣦⡞
⠀⠀⠀⠀⠀⢀⠀⠸⠿⠟⠀⠸⠟⠛⠛⠻⠿⠿⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡏⠉⠉⠽⣿⠉⠙⠿⡆⠀⠀⠀⠀⠀⠋⢠⡿⢿⠿⡀⠱
⠀⠀⠀⠀⢠⣾⣿⣷⣶⣶⣿⣿⣶⣶⣦⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠀⠀⠐⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⢸⠁⣶⡆⣠⡈⠋⠨⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⡀⠉⠁⠿⢧⡰⢆⣆⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⠀⠀⠀⣤⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄
⠀⠀⠀⠀⠠⠤⠦⠤⠄⠤⠸⠧⠤⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣖⣒⣒⣒⣚⣛⡛⠛⠓⠶⣤⡞⢳⡴⠚⢛⣋⣉⣉⣉⣉⣉⣛⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡭⠟⣋⡭⠟⢛⡛⢦⣙⣇⣸⣁⣼⠟⠛⢷⣍⡙⠛⠯⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠖⣺⠟⢉⡴⠋⣩⠟⢉⣩⠭⣭⡉⠛⢾⡛⠲⣌⠻⣷⡶⢤⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡴⠋⠀⠀⢯⠴⠋⠀⢀⠀⠙⡲⠴⠟⠀⠈⠳⣌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠛⠁⠀⠀⠀⠀⠀⠘⢤⠀⠨⠄⡰⠁⠀⠀⠀⠀⠀⠈⠓⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠶⠶⣶⣄⡀⠈⡅⢘⠀⡅⠀⢀⣤⠶⠚⠛⠛⠻⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢁⣠⣤⣤⣄⡀⠙⣿⣶⣿⣼⣴⣧⣴⡏⢀⣠⡴⠶⠶⠦⣄⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣴⠋⠁⣀⣠⣽⣿⡿⠿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣦⣄⣀⡀⠀⠱⡄⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣾⠃⣰⡟⠉⠹⣿⠃⣶⢓⡆⠀⣾⡅⠀⢠⡖⢢⠙⣿⡏⠉⢻⣆⠀⢹⡄⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡿⠀⣿⠁⠀⠀⢿⣦⣈⣉⠀⠀⠈⠀⠀⠈⠛⣋⣠⣿⠃⠀⠀⣿⠀⠈⣷⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⡄⠀⠀⠈⠉⠉⠛⣿⣄⡀⡀⢰⡿⠛⠉⠉⠁⠀⠀⠀⣿⠀⢀⣿⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣧⠀⢸⣇⠀⠀⠀⠀⠀⠀⣸⣧⣍⣡⣿⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⣸⡇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢻⡄⠀⠋⠀⠀⠀⠀⣀⡴⠿⣿⣿⣿⡿⠿⣦⣄⠀⠀⠀⠀⠈⠀⢠⡟⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠁⠀⠀⢤⡀⣠⡾⠋⠀⣴⣿⠟⠛⢷⣄⠀⠙⢷⣄⣀⡤⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠈⢳⣤⣿⠟⠀⣠⡾⠋⠀⣀⣀⡀⠙⠷⣦⡀⠙⢿⣷⣾⣁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⡙⠛⠋⠀⣠⡾⠋⢀⣴⠟⠋⠉⠻⣦⡀⠈⠙⣦⡀⠙⠛⢛⣉⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⣛⡉⠛⠿⣦⠀⢸⣟⠀⠀⡟⠁⢠⣾⣷⠀⢈⡷⠀⣠⣿⠃⣠⣾⠿⠛⣛⠻⠷⣦⣤⣀⡀
⠀⢀⣠⣴⣶⠿⢛⣩⡤⣠⣾⠋⣠⣤⣤⡈⢷⡘⢿⣆⠀⠻⣄⡀⠙⠋⢀⡾⠃⣴⡟⢡⡾⢋⣥⣶⣶⡝⢷⣤⠠⣬⣙⠻⢷⣶⣤⣀
⠚⠛⠉⢩⣴⣿⠟⢋⣾⡟⠁⣼⡿⠋⠙⠻⢦⠙⣦⡙⢷⡄⠈⠙⠲⠖⠋⠀⣼⡟⠰⠋⠰⠛⣉⡉⠻⣿⡆⠙⣷⣌⠻⢿⣷⣦⠉⠉⠉
⠀⠀⠀⠈⠉⠀⠀⠟⠋⠀⢸⣿⠃⢰⣿⡿⣶⣤⣈⡛⠀⣿⠀⠀⠀⠀⠀⠀⢻⣷⣤⣴⡶⠟⠛⣿⠀⢻⣿⠀⠈⠛⠷⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠹⣆⠀⠈⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⡟⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠀⠀⠀⠈⠉⠉⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⢰⠁⠀⠀⣠⠴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠦⣄⠀⠀⠀⢇⠀⣀⣠⣤⣤⣀⡀
⠀⡴⠛⣉⣀⡀⠀⠈⠉⠓⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠛⠉⠀⠀⢀⣀⡉⠢
⢘⢠⣿⡿⣿⢿⣳⣄⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⡀⠀⣠⠞⠉⠐⠙⡇
⠈⡀⠉⠀⠀⠀⠙⢿⣆⠀⡇⠀⠀⢀⣔⣯⣭⣭⣍⡓⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣉⣭⣭⣭⣶⣄⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀
⠀⠱⡀⠀⠀⠀⠀⣤⣿⡄⡇⠀⢀⣿⠋⢁⣠⣤⣤⣿⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠊⣴⣿⣵⣦⣤⣀⠙⢿⡄⠀⢸⢀⣿⡄⠀⠀⠀⢀⠎
⠀⠀⠙⢄⠀⠀⠀⢿⣿⣷⢃⠀⢸⡇⣰⢟⡁⢘⣿⣿⣿⣷⡈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢹⣿⣷⣝⢧⠘⣷⠀⠸⣼⣿⡯⠀⠀⢠⠎
⠀⠀⠀⠈⠳⣄⡀⠀⠙⠛⢸⠀⢸⡇⠏⢸⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠸⠀⡟⠀⡇⠙⠋⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⣸⠀⠀⠳⡘⠌⠻⣿⣿⡿⢟⡿⢿⠄⠀⠀⠀⠀⠀⠀⢸⠻⣝⠿⣿⣿⠿⠋⠀⡼⠁⠀⢇⣀⡰⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠢⢄⡀⠄⠐⠋⣀⡼⠀⠀⠀⠀⠀⠀⠀⠺⣄⡈⠓⠀⢄⣀⠤⠊⢁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠐⠂⠀⠀⠀⠁⠀⣀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠉⠂⣀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣀⣀⠀⠈⠛⠿⠛⠿⠛⠁⠀⠀⣀⣠⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡭⣷⣦⣄⡀⠀⠀⢀⣤⣶⠮⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠸⣏⠛⠿⠿⠿⠟⢻⠏⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀⡀⠈⠑⠠⠤⠤⠒⠁⢀⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⢠⡎⢸⡟⠐⠀⠀⠀⠀⠀⠂⢻⡇⠹⡆⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡸⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⢀⠔⠉⡇⠀⠀⠀⠀⠀⠀⠀⠸⠙⢦⠈⢳⡄⠀⠈⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢨⡇⠀⡞⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢇⢸⡇⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣠⡀⠀⣀⡀⠘⠇⢸⡇⠀⠀⠈⣆⠀⠀⠀⠀⠀⡼⠀⠀⠀⢸⡼⠁⢀⣀⠀⢠⣄⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠉⣇⠰⡏⠙⠶⠀⠘⡇⠀⠀⠀⣿⠷⣤⣀⣤⢾⣧⠀⠀⠀⢸⠃⠲⠋⢹⡇⡸⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠇⠀⠀⠀⠀⢳⠀⠀⠀⡾⠀⠀⠉⠀⠘⣇⠀⠀⢀⠇⠀⠀⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⢰⠇⠀⠀⠀⠀⠀⢸⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⢀⣀⣸⠇⠀⠀⠀⠀⠀⠘⣇⣀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣄⣴⡁⣀⣴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⣀⢀⣤⣠⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠐⠂⠀⠀⠳⠤⣤⣀⣀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡠⠀⠀⠈⢻⣿⣦⣀⡀⢄
⠀⠀⡀⠀⠀⠀⠀⠀⢸⡄⠈⠀⠒⠒⠶⠶⠶⠶⠶⠶⠒⠋⠉⠀⠠⡀⠀⠀⠁⠀⢀⡇⠀⠀⠸⠦⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠋⠀⡇
⠀⠀⢡⣦⣄⠀⢀⣠⣶⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡦⢠⣾⡿⠇⠀⠀⠀⠁⠰⠷⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠈⠙⠋⠀⠘⢛⡉⠁⠀⠀⠀⠀⠜⠁⠀⠀⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⠆⠀⠀⢠⠀⠀⠀⠁⠒⠤⠤⠤⠤⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢂⠀⠀⡠⠄⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠟⠒⠂⠀⣶⡂⠂⣹
⠀⠀⠀⠀⠀⣀⠔⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣤⣤⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠠⡄⠧⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠙⠷⢦⣬⡀
⠀⠀⠒⠛⠿⣷⣶⣶⣶⣶⣶⣿⠿⠟⠒⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠋⠉⠙⠃⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠂⠀⠀⡄⠀⡄⠀⠀⠁⠐⣄⠀⠀⠀⠲⠶⠶⣤⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠤⣤⠤⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⣂⡀⠀⠀⢀⣀⠷⠀⠀⠰⣴⣦⣶⡤⠶⠒⠒⠟⠷
⠀⠀⠀⠀⠻⠂⠺⠃⠀⠀⠀⠀⡿⠿⠆⠰⠾⢿⠇⠀⠀⠀⢼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⣠⡎⠉⠁⠈⠈⠀⡇⡆
⠀⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⡐⠁⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣲⣒⠞⠋⠃⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣙⡢⣤⣤⣀⡀⠀⠀⠀⢤⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⢀⠄⠒⠒⠒⠢⢀
⠀⠀⠀⠸⠀⠀⠀⡸⠀⠀⠀⠀⠇⠀⣷⠀⠀⢀⠀⠀⠂⠀⠀⠀⠰⣨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠐⠛⠀⠠⠄⢀⢱⡀
⠀⠀⠀⠁⠀⠀⠀⡁⠀⠀⠀⠀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠠⠄⠀⣠⡝⠀⠀⠀⠀⣀⣀⣀⠀⠀⣈⠁⢀⣀⣀⡀⠀⠀⠸⢀⡀⠉⠀⠀⠖⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠴⠀⠁⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠈⠒⠤⣤⡶⠾⠛⠁⠀⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠈⠈⠁⠀⠁⠀⢂⣤⣿⣿⠏
⠀⠀⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢀⡇⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢈⣿⠁⢸⡄⠀⠀⢷⣿⣦⠀⢠⣾⣿⡟⠀⠀⠀⠀⠙⢲⠶⠖⠡⠾⠟⠶⠗⠂⣡⣶⡗⠒⠲⣶⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠺⠉⠈⢻⠀⡼⠀⠀⠀⠈⠉⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠐⢤⣀⣀⣀⣠⣤⡴⠿⠿⠿⠿⠤⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⣿⣿⣿⠀⠀⣿⣿
⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠢
⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣶⣄
⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣆⠀⠘⣷⣿⣷⣄
⣿⣿⣿⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣾⣿⣿⣿⣿⣦⡀
⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣃⣰⡟⠀⠀⣸⣿⣿⣿⣿⣿⣮⣽⣶⡀
⣿⣿⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠼⠏⣿⠅⠀⠀⣹⣿⠛⠻⣿⣿⡿⠟⠻⢍
⣿⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢻⡇⠀⠀⠸⠃⠀⠀⠀⠀⣴⡟⣿⣟⠀⠐⠾⣿⣿⡂⠀⢾⣟⢧⣠⡴⡾⡁
⣿⣿⣿⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠒⡿⠃⠙⢦⠀⠀⠀⠀⠀⠀⠀⠛⠋⣿⣵⡆⠀⢾⣿⣯⡻⣶⣿⣿⣦⣳⣷⡜⠟⠈⠳⡀
⡿⠿⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣤⣤⣤⢶⣷⣿⣤⡀⠀⠀⠀⠀⠀⢀⣴⣆⣤⠟⠁⠀⠸⢿⣯⣙⣻⣿⣾⣿⠟⠿⠏⠋⠄⠀⠀⠙⣆
⣀⣀⢀⣤⣴⣶⠶⠶⠶⢶⠒⠙⠃⠛⠉⠀⠀⠀⠀⢀⡿⣿⣿⡟⠙⢦⡤⠀⢠⣴⣿⠶⠉⠃⠒⠀⣧⡴⠤⠿⠿⠛⠉⠉⢀⣀⠀⢀⡀⠀⡄⣄⠟⡾
⣿⣿⣿⠀⠀⣸⠂⠀⠀⡀⠙⠀⢠⡀⠀⠀⠰⣆⠀⠸⣸⡈⠋⠁⠀⢀⠄⠀⠒⠀⢈⣀⡀⠀⣤⢀⡁⠀⠐⠀⠀⡀⠀⠀⠀⣀⡄⠀⢐⢰⡧⣤⠾⠁
⣿⣿⣿⠀⣠⣿⠀⠀⠀⢀⠲⣠⠟⠁⠠⠄⠛⠛⠂⠀⡅⠀⣇⣿⣿⣿⣱⣶⣶⣴⣿⣿⣱⣿⠋⢘⣡⣾⣄⣰⣤⣠⣤⣤⣈⣙⣿⠟⢿⣿⣯⡽⠓⠀⠀⠀⣄
⣿⣿⣿⣴⠃⢼⠀⠀⠀⠈⠛⠻⠃⠀⠀⠀⠀⠀⠀⢠⡇⠀⢹⣿⣿⣿⣿⣷⣿⣿⡿⣿⡟⠋⠁⠈⢩⣿⣿⣿⣿⣿⣿⢿⣿⡿⢏⣴⡿⠟⠃⠀⠀⠀⠀⣠⣿⣦⣄
⣿⣿⣿⠁⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⢀⠀⢿⡧⠛⢉⣛⠀⠀⠀⣤⣤⡠⣤⣀⠈⠻⢛⠉⡉⣀⣴⣖⣌⣠⡬⠏⠲⠒⠒⣠⠴⠞⠛⠉⠙⣿⣇
⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠂⠱⠦⣴⣶⣿⣿⣆⠀⠈⣹⢿⡿⠀⡈⠁⠀⠉⣰⠏⠉⠉⠀⣈⣀⣤⡤⡄⠺⠻⠿⠶⢤⠰⡶⣦⣾⣿
⣿⣿⣿⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢱⡀⠀⣴⢠⠛⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣠⠞⠁⠐⠛⢀⣼⣿⣷⣀⣠⡇⢈⣦⣶⢦⠀⠀⢹⢹⣿⢿
⣿⣿⣿⠀⠀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠉⠀⠀⠡⡀⠀⠈⢀⡛⠀⡠⠞⠋⠀⠀⠀⠀⢈⣞⡟⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣇⠀⠀⣾⣶⣽⣿
⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⠈⠃⡀⠀⠀⠉⠑⠂⠈⢁⡤⠀⣴⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠛⠉⠉⠀⠉⠈⣿⣿⣿⣿⢿⡅⣿⣦⣸⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠈⠁⠀⠀⠀⠀⠀⢀⢻⣤⣾⠉⢰⡯⠉⠐⢲⡧⠐⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⣿⣿⣿⣾⣷⣿⣿⡏⣿⣿⣿⣿
⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡜⠁⠻⠛⠿⠃⠀⠀⠀⠀⣾⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣩⡻⣿⣿⣿⡟⣿⣿⣿⣽⣿⣿⣿⡟
⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠂⠘⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣥⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⠀⠐⠶⠾⠿⠾⠿⠿⠶⠖⠀⠀⣀⠀⠀⢠⡇⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣅⢀⡀
⠀⠠⣤⠀⢀⣼⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠷⠶⠟⠁⢀⠀⣀⠀⠉⠙⠛⠛⠉⠈⠿⠍⠀⣀
⠀⠀⠃⠀⠀⠃⠀⢠⠔⠒⠉⠁⠀⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠦⠴⠶⠤⠶⠖⠋⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠐⠒⠠⠤⣤⣤⡼⠟⠓⠒⠂
⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⣄⣀⣤⡿⠀⠀⠀⠀⣤⡀⠀⣠⣰⠀⠀⠀⢠⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⡿
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠘⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠐⠚⠋⠁
⠀⢀⡤⠀⠀⠁⠤⠭⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠴
⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠁⠀⠘⠓⠶⢶⣶⣶⣶⣶⡶⠾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⠀⠀⠎⠀⠀⠀⠀⢠⣀⡀
⠀⠰⠚⠷⢤⣤⣽⣀⣉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⠗
⠀⠀⠀⠀⣼⡟⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣤⣤⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠂⠀⠃
⠀⠀⠘⠛⠛⠃⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣾⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠀⠀⠀⠁⠄⢰⣷⠉⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⣿⣿⡗⠔⠄⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠙⡿⠯⠑⠁⠘⠠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠙⠆⠀⣠⣄⣴⣦⣼⣠⡏⠙⡷⠂⠀⠀⡀⠀⣄⠀⠀⠈⠒⠢⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠄⣀⠀⠀⠁⠀⠀⢿⣍⣟⢡⡿⡏⠻⠞⠛⠃⠀⠀⠁⠖⠀⠀⠀⠀⠨⠂⠀⢄⡼⠀⠀⠀⠐⠟
⠀⠀⠀⠀⢀⡀⠀⠀⠐⠓⠀⠉⠀⠀⠀⠀⠀⠛⠁⠉⠀⠀⠀⡀⠠⠀⠀⠙⠄⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠆⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠄⠀⢀⠀⠀⠀⠀⠒⠐⠖⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⠎⢆⠠⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠂⠀⠈⡀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠢⠀⣉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⢀⣠⡤⠀⠈
⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃⠚⢛⣛⡠⠀⠀⠸⠿⣷⣦⣤⣤⣾⣶
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⢀⠂⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠘⢶⣳⠔⢾⣉⡿⠀⠀⠀⠔⠀⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⠟⠃⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⢋⣴⣫⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⢛⡝⣿⠃
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢟⠄⣸⣾⡋
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⡌⣀⣿⢸⣧⢀⠀⠀⠀⠀⣀⡤⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣟⣧⣾⣿⣿⣿⢻⣁⣈⢡⣤⠘⣦
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠸⢿⣿⣿⠏⢿⡾⢛⡵⢿⣷⣝⡷⠪⠀⢠⣄⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡖⢾⣇⠋⢀⣼⢶⣿⣿⣿⣿⣿⡇⣴⣾⣀⣩⡄⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠿⠻⣿⡿⢿⣿⡇⠀⣬⠿⠛⠙⣹⣿⣿⡟⣸⠋⣿⣿⡙⢿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⠟⠁⠀⣹⢀⠀⣴⣿⣿⣟⢿⣿⢾⣿⢿⣇⠨⣽⣮⠙⡛⢦⡀⠂⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠛⣿⣿⣻⣧⣿⣷⣿⣿⣾⣷⣿⡏⣴⠞⠛⠷⡽⢾⡇⠸⡏⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣫⣿⡟⣿⣿⣷⣿⢾⢋⣡⣤⠉⠐⠀⣤⠹⣶⣵⠀⠁⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣿⢇⣿⠇⠘⢿⣻⣾⣷⢿⡟⡾⢿⡏⠀⡝⠟⠁⠀⢻⣿⡒⠂⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡻⣻⣿⠁⠀⠀⠀⢻⣿⣯⢺⣿⡟⣻⣶⡇⠀⡐⠀⠀⢨⣽⠃⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢀⣠⠾⠛⠛⠉⣹⣿⢣⠋⣿⡲⣤⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⣿⠆⠓⢠⣄⠘⣿⡆
⠀⠀⢀⡴⠋⠀⠀⢀⣠⡾⣹⣱⡟⠁⠈⡇⠈⣿⠀⠀⠀⠀⠼⢋⣿⡯⣍⠿⢷⡄⠀⢹⣇⢿⡇⣾⣄⣠⡀
⠀⠀⠞⠀⠀⠀⠰⣿⢫⡟⠉⠀⠀⠀⠀⠀⠀⣿⠁⣠⣾⣷⣶⣿⣍⣾⣾⣷⣆⡉⣄⢰⣯⣿⣿⢿⠧⣌⣷⡞
⠀⠀⠀⠀⠀⣴⣾⣣⡟⠀⠀⠀⠀⠀⠀⢀⣴⠏⣴⣿⣿⠟⠛⢀⢰⣍⠿⣿⣯⡉⠉⠛⢿⣷⡁⣀⠑⢦⣿⠆
⠀⠀⠀⢀⣼⡿⠻⢇⡀⠀⠀⠀⠀⠀⣰⡾⢁⣸⣿⠗⢩⡀⣰⣿⣿⣻⠆⣿⣿⣷⠀⠀⠘⣿⠻⡇⠀⠀⠁⠀⢀
⠀⠀⠀⣸⠠⠃⠀⠈⠻⠀⠀⠀⠀⠠⣿⠃⠚⣉⣥⣾⢛⣾⣏⣀⠈⠋⣸⣿⣿⣧⡴⠂⣸⡿⣻⣟⠀⠀⠀⣸⣿
⠀⠀⢺⣽⣧⣀⣀⡀⠀⠀⠀⠀⠀⠰⠟⣡⣾⡿⣤⣿⠿⠟⠉⣋⠀⢰⡿⢾⣿⣏⢀⣴⣟⠀⣹⣯⠶⠀⢠⣿⣥
⠀⠐⣹⠷⣌⡉⠉⠀⠀⠀⠀⠀⠀⢐⡾⢩⣼⣿⢋⣵⣾⣿⣿⣿⠟⡸⢷⡼⢥⣶⡿⣷⢻⡏⠱⠛⣀⠾⣟⠁⢻
⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⣴⣷⣎⣔⢴⣅⣼⣿⡏⠀⠿⠟⢩⠀⠀⠀⣠⣾⢿⣤⣬⣾⠃⠀⠘⣁⡴⣋⡰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠛⢤⡞⢛⣟⣯⠅⠈⠀⠀⠀⠀⢀⠄⢱⣬⣶⣿⣿⣥⡀⠀⠀⠁⢜⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠱⣿⠶⠿⠋⠉⠻⣹⣆⠀⠀⠀⣠⠄⠈⣤⠞⠹⣿⡿⣧⡙⣷⡄⠀⠰⠿⢾⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⢿⣿⣶⣄⠀⠈⠿⣵⠀⠈⠁⢠⡼⠁⠀⠀⠈⢿⣿⣮⡌⣡⡀⣀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡻⢽⣿⣷⠀⠀⠙⠾⣤⡀⣈⡁⠀⠀⠀⠀⠈⠻⣿⣜⠯⠑⣬⡉⠛⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⢦⣭⢻⠂⠀⠀⠀⠉⢸⡿⣿⣤⣤⣤⣦⣤⡤⣽⠻⣆⢸⡟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠉⠙⠟⠻⠗⠿⠋⠻⠇⢀⣤⡹⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣏⣤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢛⣿⠟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣠⢾⡷⠋⠉⠀⠀⠀⠀⠀⠀⢠⣀⣰⣦⣤⣾⣿⡿⣿⠏⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠷
⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣀⣠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⣤⡄⠀⠀⠀⠀⢠⣄
⠀⠀⠀⣠⡀⠈⣧⣳⠀⢀⡟⣾⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⡀⢀⣤⣴⣶⣿⣿⣿⣿⣷⣶⣦⣀⣀⣴⣿⣿⣿⣿⡇⠀⡶⣦⠀⢰⣿⠀⠀⣠⣤
⠀⠀⠀⢰⡙⣆⢹⡏⡄⣸⠇⡏⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠁⠀⠹⡹⢇⣸⢿⠀⢰⢃⡿
⠀⠀⠀⠀⢧⡸⣟⢁⡽⢫⣤⣧⣴⢞⡇⠀⠀⠘⢿⣿⣟⣽⣿⣿⡟⠛⢿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣇⣽⣿⡟⠁⢠⢤⠴⢧⣌⣵⣸⣶⠃⠾⠁
⠀⠀⠀⠀⢸⡇⠹⢯⣶⠛⠘⣏⡦⠊⠀⠀⠀⠀⣸⣧⣿⣿⡿⣿⣆⠀⠀⢸⣿⣿⣿⠄⠀⢠⣿⣿⣿⣿⣿⡄⠀⠈⠓⠛⠵⣏⣛⣱⣿⣼⡆
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣟⡟⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠙⣛⣉⣤⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣯⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣻⣦⣀⣀⣠⣿⣿⣿⣿⣿⣿⣤⣿⣿⣩⣿⣿⡛⣻⣿⣏⣹⣿⣇⣸⣿⣿⣿⢿⣿⡀⠀⢀⣠⢮⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣀⣿⣿⣇⣹⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣿⣿⣽⣿⣿⢿⡏⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⣺⣿⣿⡟⠿⢿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⠿⣿⢻⢉⣿⠻⣦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠲⠍⢩⡖⢚⣿⡷⠶⣿⣟⣾⢉⡽⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡴⡴⣿⣾⣿⣄⠴⣉⢹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠛⣙⣷⡿⠴⣃⠬⣽⡟⣪⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣡⢿⠜⡹⢿⡾⣽⣐⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢫⣗⡯⠆⣱⢿⠞⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢦⡱⣝⢎⡳⣍⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣞⠟⣃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡃⢿⡙⣞⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠟⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡠⣄⠀⠀⠀⣄⠀⠀⣤⢠⠀⣀⡀⠀⠀⡄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠐⠒⠂⠂⠘⠂⠀⠃⠊⠀⠀⠁⠈⠀⠀⠀⠀⠀⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⣤⠀⢠⣤⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠂⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠙⠀⠀⠀⠀⠀⢠⣨⣤⡬⢠⡄⠀⠀⠀⠀⠐⠉⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠐⠋⡁⠁⠀⡙⠛⠃⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢟⣀⡀⣠⣤⣐⠀⠀⠀⠀⡆⠀⣿⣷⣦⣾⣿⢷⠀⠀⠀⠀⠀⠀⣆⣤⣄⣀⡈⠻⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠛⢻⣹⣿⣷⠀⠀⠀⢰⡁⣼⣯⣿⣿⣿⣯⣼⡄⠸⠀⠀⠀⠀⣿⣿⣏⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⣿⣿⣿⣿⡇⠀⠀⢀⣁⣬⣛⡛⠛⠟⢛⣻⣥⡧⣠⣤⣤⣼⣿⣿⣿⣿⠀⠀⠠
⠀⠀⠀⠀⢰⠀⠀⠁⢀⣼⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠶⢾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⡿⣿⣿⣧⡀⠀⠀⠐⡆
⠀⠀⠀⠀⢸⠀⣀⣴⣿⣿⣿⣧⡼⣼⣿⣿⡿⠛⠙⡍⠹⣏⡛⠀⠈⢿⣻⠟⢩⠀⠈⠉⠛⠋⠀⢣⣼⣿⣿⣿⣦⣀⠀⡀
⠀⠀⠀⠀⠀⣹⠛⠿⢿⠋⠹⣿⡇⡁⠀⠉⢀⠀⢀⣁⠀⠀⠁⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⢀⣨⣿⡏⠙⡿⠿⢛⣧⣄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⣸⣿⡟⠘⠒⢀⡀⠛⣹⣿⣶⣄⠀⠀⢠⣾⣿⣿⡀⢀⠀⢀⡁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⣿⡿⣇⢰⣶⠟⠁⣾⣿⣿⣿⣿⡶⠛⣿⣿⣿⣿⣷⣄⠀⣰⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣧⠹⢰⡄⢸⣿⡄⠀⠻⢿⣿⣿⣿⣷⢰⣿⣿⣿⡿⠟⠁⠀⠋⣾⣿⣿⠏⢰⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠘⠛⠛⠛⠛⠀⠀⠀⠙⠛⠛⠛⠘⠛⠛⠋⠀⠀⠀⠙⠒⠛⠛⠋⠀⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣷⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡀⣾⣶⡆⣤⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣄⠀⢠⣄⡀⠘⠛⠀⣿⠿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠋⠈⠃⠿⠄⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣩⣄⠛⠉⠃⠀⠀⠁⠋⠙⠃⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣹⣿⡏⠀⠐⠀⠀⠀⣠⢼⡄⠀⠀⠸⣄
⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⣭⡾⢁⣀⣀⠪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⡿⠀⢿⠀⠀⠀⠃⢠⣿⣧⣤⣬⣥⣤⣿⣆⠀⢀⣶⣶⣶⣶⣤⣤⣶⣤⣴⣶⡶⠋⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣈⣿⣟⣧⣿⣯⣽⣬⣏⣘⠀⠻⠿⠿⠿⠿⠛⠙⠛⠋⠀⠀⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⢿⣿⣿⣿⣿⣿⣿⠉⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠚⠛⠛⠛⠛⠛⠛⠀⠘⠀⠀⠀⠀⠀⠀⠘⠛⠃⠐⠂⠀⠀⠘⠛

⣾⠾⣶⡟⢶⣶⡤⣤⣤⠤⠦⠄⣀⣠⣀⣀⡀⠀⠀⠀⠈⠀⠀⠈⠀⠨⠔⠃⠀⡀⣤⡐⡾⡤⠥⠙⠃⠁
⠀⠀⡨⠒⠀⣠⣦⣤⣴⣿⣶⣶⣞⣤⣶⣶⣾⣭⣿⣳⣖⣶⠦⠄⡄⡀⠀⠀⠀⠉⠅⡀⠠⠔⢒⡀⠅⠄⢠⡄⠀⢠⡤
⣶⣿⣧⡈⠀⡈⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣍⡶⢦⠀⠀⠀⠈⠚⢈⢡⡗⠋⠁⠀⣀⣤⠴⠖⠒⠒⠂⠈⠉⠉⠑⠐⠢
⠈⠁⠙⠛⠛⠿⠶⢦⣀⣶⣸⣿⣅⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠶⠀⠀⠀⠈⠀⠀⡀⠕⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⢽⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢀⠄⠈
⣾⣿⣿⡟⡿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣄⣀⣀⠀⠉⠉⠲⠼⢿⡛⣛⠻⢿⡿⢋⠙⠁⠀⠁⡤⠈
⣿⣿⣿⡇⠃⣼⣿⣿⣿⡿⠿⠼⠿⠿⢿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⡘⠀⠁⢈⠀⠂⢀⠌⠀⢀⠴⣺⣿⣿⣶⣦⣀
⣿⣿⣿⡧⢤⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⢿⣿⣿⢿⣷⣦⣀⠀⠀⢱⡞⣡⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢹⣿⡟⡻⣟⣿⣿⡷⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢻⣿⡇⠁⠙⠛⠚⠛⢾⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣰⣾⣉⠀⡀
⠀⠀⣿⣵⡀⠀⠀⠀⢠⣾⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠂⠘⠀⢁⠀⠻⣿⣿⣃⣵⠛⠂⠈⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣝⠗
⠀⢠⢡⡽⠿⡄⠀⠀⣿⠘⠻⠟⠟⠻⣻⠟⠁⠀⠀⣴⣇⡀⢨⢃⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⣿⡟⠁⠀⠀⠀⠀⠀⣀⣴⣿⠋⣿⣿⣿⣿⣿⣿
⠀⠆⢸⣇⡀⡇⠀⠀⢿⣄⣀⣠⣴⣾⠋⠀⠀⣠⣾⣿⣿⡇⡼⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠃⠀⢀⣤⣴⣾⣿⣿⠁⠀⠸⣿⣿⣿⣿⣿
⠀⠸⠀⠉⠿⠃⠀⠀⠀⠙⠿⣿⡟⠁⢀⣀⣼⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠋⠁⠀⠀⠀⣿⣿⡿⠉⠉
⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠲⣴⣿⣿⣿⠇⠻⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢀⡀⠀⠀⢠⡿⠟⠛⠉⠛⠓⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠘⢆⠀⢠⣴⠆⠀⠀⣸⣛⠋⠙⣓⠄⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡛⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡈
⠀⠀⠀⠀⠼⡄⠀⠋⠀⠀⠀⠁⠌⠀⠀⡟⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏
⠀⠀⠀⠀⠀⣣⡤⠶⠦⠤⣄⠀⢣⠀⡌⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠁⠀⣴⣥⣦⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣿⡙⠂⠀⠀⠀⠀⢠⣿⣿⣿⣤
⠀⠀⠀⢀⠀⠀⢣⠀⠈⠉⠀⣀⣾⣿⣿⣿⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣿⣶
⠀⠀⠀⠀⠘⠋⠈⠳⠶⢶⠊⠹⡿⣿⣿⣿⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡠⠞⡡⠀⠄⠀⣿⣿⠇⠸⡄⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⣶⠟⠁⠀⠀⠀⠀⢸⢿⣿⣧
⠀⣀⠠⠤⠔⠒⠉⠀⠚⠁⠀⠀⠀⢸⣿⠀⠀⠁⠀⠀⠀⠀⠑⠒⠒⠤⢀⡀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠋⡏⢠⡀
⠂⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠈⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⡇