Doctor of divinity d Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠁⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⣿⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡄
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇⠀⠀⠀⠀⠙⠳⣌⠻⣿⣿⠿⣀⡀⣿⣿⣿⣿⡇
⠀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⡟⠇⠃⠀⢀⣠⣤⡿⠳⡌⠉⠙⠟⢛⣿⣿⣿⣿⡇
⠀⠈⠺⠿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⢋⡤⠙⠛⡟⠿⠟⠁⣸⠃⠀⠀⠀⢳⡀⠀⠀⢺⢿⡏⠻⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⡇⣾⡿⠷⠀⠀⠀⢹⣤⣤⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠔⠋
⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠁⣇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠟⠛⠃⠈⠻⠟⠋⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣈⢳⡀⠀⠀⣸⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢠⡇⢀⣠⣤⣖⣒⣯⣽⠿⠟⣹⠃⠀⢀⣇⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⢧⡛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡀⠀⠀⠈⠙⠂⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠟⠁⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⣿⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⢠⣀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣶⡛⢣⡀⠀⠀⠀⠀⢠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣾⣿⣯⣽⣷⣾⣿⣿⣣⣰⣶⣿⣽⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣗⡀⠈⠛⢿⠿⠋⢻⣟⣿⣿⣿⡽⢿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠛⠿⣷⣦⣤⣠⣄⣠⣾⢿⠍⣽⣿⡟⢿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣞⣶⣬⡏⢩⡏⠛⠁⠀⠀⠀⠀⠀⠐⣿⢿⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⢛⣿⣽⣿⣿⣶⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣷⡿⡿⠿⣿⣿⢭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣷⡾⣷⡄⣿⣮⡇⠀⠴⠒⠒⠒⠀⠀⠀⠐⠚⠓⢸⣿⠞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣜⣿⣯⣿⣾⢷⣾⠁⠀⠀⠘⠁⠀⠀⠀⠀⠈⠋⠁⣼⣿⣦⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣍⣻⣿⣏⢀⣷⣋⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⣯⣿⣿⢻⡿⠀⠀⠀⠀⠀⠀⠐⠂⠠⢶⡂⠀⣿⣿⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣯⣿⣿⣿⣿⣿⣿⠛⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣿⣧⣬⣀⣨⣴⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣛⢽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⠾⣿⣿⣯⣿⣤⣌⢿⡆⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⠿⣿⠃⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⣿⣧⣽⣿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣠⣀⣤⣤⣤⣬⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⡿⠿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢹⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠛⠅⠉⠛⠟⠛⠛⠀⠀⠙⠛⠙⠛⠛⠛⠉⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠁⡀⠠⡀⠂⡀
⠀⠀⠀⠀⠀⠀⡀⣠⣀⣀⡀⣀⣀⣤⣀⡄⠂⢠⣄⣤⢤⡤⠤⣾⠶⠶⠀⠈⠁⠀⠐⠚⠛⠚⠉⠙⠀⠀⠈⣄⣀⡀
⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⡦⠀⠁⠀⠀⠀⠀⠀⠀⠸⣙⣉⡹⠀⠀⠀⠀⠀⣀⣀⣀⣙⣄⣡⡏
⠀⠀⠀⣠⣦⡁⡀⣀⡀⣀⣠⣠⣤⠤⠤⠷⠘⠷⠶⠶⠆⠶⠠⠒⠛⠙⢛⡉⠉⠋⠀⠀⠀⠀⠀⢠⠖⡉⠚⡏⢹
⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠈⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⡀⠀⠀⠠⣄⠀⠘⢅⣤⣬⡇⢸
⠀⠀⠀⢘⠀⠂⠀⠀⠐⢂⠀⠀⡀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢄⡀⢈⠘⣣⡂⠀⠀⠀⣶⣾
⠀⠀⠀⢨⠆⠀⠐⢠⣯⣤⣏⠀⠐⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⢶⢾⣿⠃⠀⠀⠀⠉⢿⠟⢻⠃⠀⠀⠘⢛⣹
⠀⠀⠇⢸⠀⠀⠀⢦⠄⣝⠉⢀⠔⠶⠀⡇⠀⠀⣴⣶⠀⠀⠀⠘⠛⢄⢻⠇⢀⠀⢀⣾⡖⠂⣠⣴⣴⡾⣿⢋⣫⢆
⠀⠀⠁⠸⠀⠀⠀⠀⠀⠠⠯⢀⣈⠐⢣⣷⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⢇⣶⣆⣽⡮⠉⢷⡟⠥⣤⠖
⠀⠀⠀⢠⡄⠀⠀⠀⠀⢗⠀⠈⡄⠁⠀⠆⠀⢀⣄⡤⡀⠈⠛⠀⠀⠀⢠⡆⠀⠀⠘⠻⣛⣿⢥⠀⢐⣩⡳⠀⢸
⠀⠀⠀⢨⡄⢀⠟⠂⠤⠅⢾⡂⠀⠀⠀⠆⠀⠭⣯⡀⠹⢄⠄⠀⠀⠀⠠⡄⠈⢡⣤⢸⣿⣯⣌⢛⡿⡾⢷⠀⢸
⠀⠀⠀⢨⣵⣿⡜⠂⠀⠀⢀⠈⠣⠀⠀⠄⠀⢀⠙⢿⣷⡆⠸⠀⣀⠒⢠⠀⠀⠰⠋⢠⣙⣾⣿⣬⣷⡻⣼⠀⢸
⠀⠀⠀⠀⠻⡛⠛⠿⠟⢑⢺⠁⠘⠀⠀⠀⠀⡐⡆⠀⢻⣷⣄⣤⣤⠀⣨⠀⠀⢀⠀⠀⠲⠰⣪⡟⠋⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠈⢉⠀⢰⠀⠀⢀⠀⣠⢹⠀⠀⠐⢻⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⠀⠠⠠⣄⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⡀⠑⢺⠀⠈⠀⠀⠰⢀⡏⠘⠀⡐⠉⠀⠁⠸⠄
⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⢀⡀⠀⠀⠀⡀⢠⠄⠙⠒⠂⠀⠀⢾⠀⠀⠐⡄⠀⠃⢵⡢⠂⠀⠀⠀⠀⠸⠆
⠀⢀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠘⠃⠈⠂⠂⠄⠀⡂⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠐⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⢀⢀⣀⣀⡀⡀⢀⡀⣀⣀⣀⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡆⠀⢀⣠⣶⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡂⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠃⠐⢿⣿⣿⣧⢸⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆⠀⠀⢀⡆⡇
⠀⠀⠀⠀⠀⠀⢠⣤⣄⠈⠛⠁⢹⣿⠀⠀⠀⣤⣤⣄⠀⠀⠀⠢⠠⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⢐⣇⡰⡃⡇
⠀⠀⠄⠀⠀⠐⠿⠏⠹⡷⢠⢀⢸⣿⠀⠀⣸⡿⠉⢷⡇⠀⠀⠀⠀⢠⡄⡆⠀⢀⣺⠛⠉⣷⡿⠘⠩⢓⠁⡇
⠀⠀⠀⠸⡇⢺⣷⠆⠈⢻⣄⠠⣿⣿⡶⠀⡿⣓⣤⡟⠃⠀⠄⠀⠀⠸⣏⣂⣤⠋⢟⠀⣰⣿⢁⣗⡠⠆⢸⡇
⠀⠀⠶⢠⢷⣟⣯⠀⠀⡜⡥⢬⡹⣿⡏⣽⣷⣽⢀⢷⡀⠀⠀⠐⣠⠶⢿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣀⡼⢻⡇
⠀⠀⠈⢴⣦⣿⣿⢄⢂⡇⠑⠀⣯⢿⡁⠉⡍⠉⠉⠁⠀⠀⠠⠀⠇⠀⠀⠉⠙⢿⣿⣿⠋⢠⣴⣾⡿⣿⣿⡇
⠀⠀⠀⠙⠛⣿⣿⣽⣶⣥⠀⠀⢹⣿⣿⣤⡄⣰⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣿⣿⣿⣿⠛⠡⣧
⠀⠀⠀⠀⢴⣿⣿⠿⣿⡭⡇⡀⡌⣿⣿⣿⣿⣿⣃⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠈⣿⣿⠘⠀⢩
⠀⠀⠀⠀⠀⡽⠋⡟⡿⢀⢛⣱⣃⣼⢽⣿⣌⡉⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠘⣿⡀
⠀⠀⠀⠀⠀⢧⢞⣜⡁⠁⢸⡟⠛⢳⢸⠛⢂⢻⡗⢁⣧⠀⡀⠀⠀⠀⠀⠇⣿⣿⣏⣿⠋⠀⢠⠀⢿⡷
⠀⠀⠀⢀⣾⡼⠀⠙⠳⠄⢸⡟⢀⣸⢸⣷⠴⡟⢡⢮⣅⢀⡁⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠀⠐⢀
⠀⠀⢠⠈⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⠸⠶⢾⣷⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠛⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠙⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠋⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣏⠁⠑⢄⠙⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠟⠋⡠⠀⠈⣹⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠆⠀⢌⠋⠀⠈⠻⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠟⠁⠀⠘⡅⠀⠰⢻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠘⠂⠀⠀⠀⠈⠙⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠃⠁⠀⠀⠀⠐⠁⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⠐⠄⠀⠀⠀⠁⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⢀⠀⠀⠠⠂⣁⣾⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⣿⡀⠀⠀⢀⣿⡟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠓⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠚⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣋⣈⠀⠀⠀⠐⠀⠀⠀⠀⢀⣠⣿⡇⠀⠀⢸⣿⣄⡀⠀⠀⠀⠀⠂⠀⠀⠀⣁⣹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠤⠤⠒⠀⠀⠠⠀⠀⠀⠈⠻⣿⣆⠀⠀⣰⣿⠟⠁⠀⠀⠀⠄⠀⠀⠒⠤⠤⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣖⣊⣠⠄⠀⠀⠀⠀⠀⠀⠸⣿⡄⢠⣿⠇⠀⠀⠀⠀⠀⠀⠠⣄⣑⣲⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣧⣶⠒⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⠒⣶⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣯⣴⠀⣠⠀⡀⠀⠈⣿⣿⠁⡀⢀⠀⣄⠀⣦⣽⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢿⣿⣷⣿⣶⣿⣿⣶⣿⣾⣿⣿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⢇⡙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣄⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⢈⣷⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⢆⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠈⠉⠁⠀⠙⠂⠀⡀⠀⠀⠀⢙⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⢠⣀⠘⠁⠆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡈⠀⣀⣨⣶⣶⣿⣿⡿⣽⠿⣿⣿⣿⣿⣿⣤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠉⢰⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣿⣿⣿⣟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣰⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⡿⠛⠿⣿⣿⣿⣿⣇⣠⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣴⠀⠀⠰⣦⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠈⠻⠶⠀⠀⠀⠀⣀⡉⠻⠟⠛⠛⠻⠿⠟⠚⠛⠛⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⢻⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣃⡇⠀⢘⡇⣰⣺⠀⠀⢸⠚⠶⠮⣤⣡⣵⣄⠀⢰⣦⠀⡄⠀⠘⣐⠖⡄
⠠⠶⣄⣤⣶⡀⠀⠸⢗⣢⣿⠃⣴⣠⣯⣤⡄⠀⠀⢹⡧⠖⣶⣾⡇⠀⠀⠀⣶⢩⡈⣟⠀⢠⣿⣼⡺⠃⠀⣾⣿⡇
⠶⠋⠁⠻⠾⢣⣷⠀⠁⠛⢻⡤⠛⠓⢶⡄⠀⠀⠀⣼⡅⣲⣿⡀⡙⣤⠀⠀⠀⣠⡔⠚⠡⣄⡏⠛⠉⠀⢠⡈⣽⢋⣤⡄⢀
⢀⣰⣦⡀⠐⣾⣼⠂⢸⡄⡞⣰⢃⡰⠀⠀⠀⠀⠀⢀⣸⣧⠠⡇⠈⢻⠀⠀⠀⠈⠀⢐⠄⣂⠷⠀⡄⢀⣿⣷⣋⠙⡿⠟⠺
⠈⠿⡾⠓⣤⡈⠉⠲⠜⢿⣿⠉⠻⣭⠛⠁⠀⠀⠀⠨⣹⡇⢠⣽⡄⡏⠀⠀⠀⠰⠵⢛⡽⢨⡔⣱⣋⡛⠞⠛⠧⣀⣀⡀
⠀⣠⣄⣊⠚⠛⡾⠑⢴⣦⣵⠬⠂⠀⢀⣀⡀⠀⡀⣀⢘⣧⢀⣙⢷⠁⠀⠀⠀⠀⠀⠀⢴⣶⢼⢉⣀⢱⣷⣶⡂⢺⣯⡿
⠀⢿⣾⠏⠀⠈⠀⠠⣤⡼⢤⡠⠻⡻⢵⣦⣤⣽⣭⣭⣭⣭⣭⡭⣭⣭⣿⣯⣭⣬⣵⠄⢀⠈⣹⠜⣉⠀⠙⠃⢉⣠⣄
⠀⠀⠁⠀⠀⠀⠀⠐⣛⣁⣈⣣⣄⣻⡆⢸⣿⣽⣾⣭⣿⠉⣩⣵⣿⡟⣭⢯⣹⡏⢱⡅⢈⠵⠉⠹⠼⠅⠀⠘⠉⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣫⠿⠁⠈⣙⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣾⣾⢾⣿⡿⢮⠓⠋⢳⣷⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠗⠈⢻⣟⣟⣿⣷⣺⣟⣟⣵⢲⣷⠺⣹⣽⡾⠉⠽⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠿⠟⡊⣏⣻⢷⣷⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡓⢠⣞⡿⣿⡟⢇⠠⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠁⢉⠼⣻⡜⠂⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⡊⣃⠤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣰⡖⠓
⣤⣶⣤⣤⣦⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣴⣴⣤⣤⣤⣤⣴⣦⣴⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣦⣦⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠁⠘⠉⠆⠈⠒⠓⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠙⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣡⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡤⣤⢟⣛⣯⠿⠻⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣯⣵⡿⢿⣟⣉⠈⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⡀
⠀⠀⠀⠀⠀⢀⣤⣀⢰⡿⠿⣿⡶⣾⣽⡗⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠹⣿⣅⣀⠠⡄
⠀⠀⠀⢀⣀⣈⡘⢍⣻⣶⣉⡐⢠⣾⡟⢉⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠋⣬⣒⡄
⠀⠀⢀⠘⠡⣟⠛⠛⠿⢡⢈⠀⠁⣩⠟⠃⣶⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡟⢸⡿⡓⡄⢤
⠀⢀⣤⠻⠿⠿⠟⢛⡉⡾⣿⠒⠿⣉⣢⣿⠌⠁⠀⠀⠀⢀⣀⡀⣤⡴⠶⠶⢶⣤⡀⣀⣀⡠⢤⡤⣤⣀⡀⠹⡿⠳⢬⡟⠀⣄⣉⣤⣀⣀⡀
⠀⠼⣧⣴⣶⡖⣛⣙⠿⣤⡌⠂⡔⠉⣯⢋⡀⠀⠐⠛⠋⠛⠉⠏⠀⠐⠀⠀⠀⢸⠏⠀⡍⠂⠀⠀⠈⢻⠇⠀⠣⢼⡘⡧⠿⢇⠁⢻⣦⣦⡍
⠀⠑⠦⣩⣷⡁⠋⠛⢁⣴⣶⣿⠷⢰⢃⡦⣤⠀⠀⠀⠀⠀⠀⠸⢆⣀⣀⣠⠴⠔⠀⠀⠻⡄⠀⢀⣴⠗⠀⣨⣿⠋⠙⠻⣆⣸⡳⠄⠉⠘⢛⠶⢶
⠀⠀⠀⠀⠫⠷⣟⣀⡉⣥⠾⢉⡶⣿⡏⢰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣏⣀⠉⠀⠀⠘⣷⠘⡇⠈⠉⢹⡘⠃⢰⡇⣈⣩⢔⡿⠁
⠀⠀⠀⢀⣔⣀⠀⠻⡶⢠⡶⠞⠀⡈⣛⣷⠊⣿⣼⣗⣀⡄⠀⠀⠀⠀⠀⣠⣤⣨⣤⢤⣴⡡⢿⢷⣢⠤⠐⣜⠻⣧⡗⠳⡏⣙⠉⢾⢑⣭⠀⣸⠞⢦⡤⡆
⠀⠀⠀⢦⡟⣛⢲⠀⢸⣿⣁⣵⠾⠛⡻⣽⣿⣯⣞⣿⣿⢁⠀⠀⠀⣀⣤⣿⠋⣿⡗⠀⠡⠀⠂⠈⡡⠾⢼⠋⢧⡌⠳⣆⢠⠝⣢⣏⡭⢸⣿⣍⡤⡾⠃
⠀⠀⠀⢾⣏⠹⡐⢳⡞⠛⡿⣂⡧⣽⣉⡗⢿⣿⢺⣽⠿⣿⡀⠁⠦⢥⣿⣿⠉⣽⣥⡀⠰⠹⡄⣖⢱⣯⡏⣀⠖⢹⠆⠙⠿⣿⡉⠉⢷⠄⢠⡭⠀⡤⠄
⠀⠀⠀⠀⡗⠐⠇⠈⣧⣾⣧⠉⡼⣧⡏⣸⡇⣾⡡⠬⣰⠁⡤⣀⠒⡁⢸⠘⢾⠞⡿⠃⠒⡤⣾⠋⣤⣷⣱⡮⡛⡅⠀⣻⢋⡀⠸⠑⢠⠖⢧⠀⠌
⠀⠀⠀⠠⠀⠀⠂⣴⠋⣿⣶⠂⠀⣥⡤⠾⡥⣿⢋⡾⢡⣆⢾⣿⠇⠚⢰⠗⠀⠈⠁⢣⣾⠷⣼⣧⠈⠿⣿⠳⣷⣵⣤⣿⣭⡽⡷⡆⣼⣇⠠
⠀⠀⠀⠀⠀⡀⠀⠉⠙⢿⣷⡀⠁⢱⡁⠦⡴⡶⠫⣞⣰⠁⠟⠡⠶⣹⣧⢆⣼⣯⢒⣸⣶⡁⢈⢱⠟⢀⢛⣼⣯⣹⡟⡟⢲⣬⢹⠁⢀⣿⣲⠄
⠀⠀⠀⠀⠀⠆⠈⠡⡄⠀⠃⠀⠂⢸⣿⣆⡱⢃⣾⡏⠟⣡⣼⠆⠀⠀⢹⡄⢈⣽⣏⢀⡷⠼⠀⣩⡀⡜⡆⣷⡶⣿⡇⢛⡸⡟⢁⠜⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢤⠋⠀⡠⠤⡷⠯⠹⣻⠒⠋⢹⠀⠺⣠⢾⣼⣀⡉⡱⠉⡇⢰⣴⣉⠙⠋⣡⡸⡇⠳⣏⡽⠁⠂⣹⡏⡐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⠠⣤⡆⠀⡻⢆⠀⣡⡄⠹⣶⠀⣶⠋⣹⡆⠶⠀⡾⡧⢨⣃⡦⢽⠇⣼⣴⢿⡿⡿⠋⠻⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢃⡿⣤⣄⢙⢋⠴⠈⣁⣀⡍⠀⣀⡾⣋⣽⣃⢤⡔⣷⣅⣠⡇⠺⢶⡟⠻⢻⠗⢻⣹⡶⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⢤⠀⣜⡁⣁⠜⣇⣨⡏⣐⠀⢸⡄⠸⡟⠡⣾⡏⢹⣿⣭⣳⠚⢚⡇⢄⠺⢀⡞⢙⡒⠃⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⠀⠢⠀⡍⠐⠃⡥⠚⠀⠠⠋⢀⣞⠉⣆⠈⡼⠋⠙⢷⡤⠀⡟⣉⢟⡔⠈⡡⠆⢀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠆⡤⢿⠀⠣⢿⡼⠃⠀⣞⠉⡲⢾⡅⠀⡹⠿⢼⡃⠀⢰⠎⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠂⠋⠀⠀⠠⡀⠀⠐⠀⠰⠚⢻⠿⠧⠁⠰⠀⠁⢀⠸⠄⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠁⠀⠀⠉⢭⠓⡀⠀⠀⠠⡘⠇⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠁⢨⣉⣉⣉⣉⣉⠉⢉⣉⣉⣉⣉⢉⣉⢉⡉⠉⡉⠉⣉⣉⢉⣉⡉⠉⣉⣉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⢉⠀⠀⠀⡈⠁⠁⠀⠈⠈⠀⠀⠁⢀⠁⠉⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢶⣤⣦⢀⣠⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣶⣿⣿⣾⣿⠟⠀⠀⠸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠛⢿⡟⢃⠙⢿⠅⠀⠀⠀⢀⣐⠀⢤⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠿⢿⡇⠘⣳⣄⡈⠠⠔⠂⠀⠁⠀⢸⡇⠀⠀⠀⠀⠀⢙⣿⣿⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠛⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣴⣿⣿⣿⣿⡏⠀⠠⠀⢠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠐⠶⠂⠈⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣿⠿⢿⣿⣿⣿⣿⠷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡿⠋⠀⠀⢀⡀⢀⣀⣤⠠⠬⠀⠀⠀⠀⠉⠉⠉⠀⠛⠉⠉⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⡾⢷⡼⠛⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠒⠠⢦⡄⠀⢄⣀⠄⣤⢠⣄⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠋⠙⠂⠀⠤⠠⠄⠐⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠈⠩⠁⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠉⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢤⣄⣀⡈⣿⣿⢷⡀⠀⠀⠀⠀⠐⠛⠛⠛⠋⠀⠘⣿⣿⣻⡆⠀⢂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠋⠉⠻⣷⣾⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⣿⣤⡀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠲⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠴⠶⠦⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⢠⠔⠒⠒⠦⡒⠢⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢎⣐⡁⣶⣶⣠⣶⣦⣴⣶⣦⣀⣬⣟⠻⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⡻⠞⠩⠟⠀⠀⠘⢾⡧⠼⣿⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠤⢤⣤⣤⡤⠴⠶⠶⠦⢬⣭⣥⠾⠿⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠤⡄⠀⡀⠀⡀⢄⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⣾⣄⣀⡝⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠂⠀⠀⢠⠞⠀⡏⠀⠈⠁⣼⠟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠓⢠⡇⠀⠀⡇⠀⠀⢰⡇⠀⢳⡌⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠀⠀⡇⠀⣠⠞⠁⠀⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠙⠂⣟⣰⣃⠠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠞⡿⡟⠟⢿⡉⠢⡲⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡇⠀⠀⠙⢢⡔⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⢄⠸⡆⠀⠀⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢀⣠⢅⢣⡀⠀⡇⠀⠀⠀⠄⠻⣄⢀⡤⣈⠳⠤⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠀⣀⠱⡀⠀⠀⠘⢀⡙⠯⡀⠀⠉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⠀⠉⠉⠀⠀⠙⠉⠀⠙⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣧⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⡋⠙⣿⣟⠛⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣄⡀⠀⡙⢷⣄⠈⠻⣶⣧⣻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡕⢄⠀⠚⢿⣆⠀⣌⢻⣿⣏⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠻⣶⣿⣿⣟⣿⣏⢻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⠀⢠⠹⣿⣿⣿⡾⣿⣧⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣇⠈⢷⡹⣿⣿⡇⣿⣿⡄⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⡀⢸⣇⠸⣿⣷⣼⣿⣿⣌⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣧⣸⣿⠀⣿⣿⡿⣿⣿⡀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆⣿⡇⢻⣿⡇⢻⣿⣧⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠄⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣷⠘⣿⣷⣘⣷⢺⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⡀⡇⣿⣿⣿⣾⣿⣿⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣹⣿⣇⢻⢹⣿⣿⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⠸⡇⢻⣿⡹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⡆⣷⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠁⣿⢿⣿⣀⣿⣿⣗⢻⣇⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠙⠀⡙⢻⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠹⠰⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⣿⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡄⠀⠸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⠀⢸⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⠈⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⡇⠀⠀⠀⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣧⠀⠀⠀⢸⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⠀⠀⢸⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡀⠀⠀⢸⣿⣽⣷⠀⠘⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⡇⠀⠀⠀⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡀⠀⠀⢿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⣿⣿⢿⡿⠿⠿⠂⠀⠾⠿⠿⠻⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠇⠁⠀⠀⠈⣑⡆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⣆⡆⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠂⠀⠐⢠⠂⠀⠀⠀⠀⠀⠈⠂⠒⢀⠸⢁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠂⡀⠀⠀⢠⠉⠴⢱⣴⠁⠀⠐⠠⢤⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⢠⡀⠀⡞⠈⠀⡼⡇⠀⠀⠂⠦⣿⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠇⢹⡾⠁⡀⢘⣯⠁⠀⢀⠁⢸⣇⣿⡇⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⡈⣿⡷⠋⠀⠈⣠⠀⠀⠀⠀⢿⡒⡟⡳⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠻⠃⠀⠀⠀⠸⣿⡆⠀⠀⠀⠐⢪⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣖⡂⠄⠀⠂⠀⠀⠀⠂⢻⣏⠇⣬⢌⢁⡺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠾⠿⠞⡩⠄⠂⢡⣴⢾⣶⣦⣤⣼⡖⠂⡟⠀⢳⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⣸⡇⠹⠻⢿⣥⣞⡷⠺⡇⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⣿⠇⠀⢨⠂⣴⣿⣧⡀⠇⣜⢲⠶⢦
⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠓⢳⡄⣹⡼⠣⠏⠉⡤⠀⡍⣈⠑⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠒⠈⣽⢟⢹⣗⣡⢯⠏⡳⠀⠀⠀⠀⣧⠀⠀⢰
⠀⠀⠀⠀⠀⣴⣿⣿⠿⠒⡄⠀⠀⡀⢒⣴⢿⠁⣀⣭⣶⣾⡅⠀⠀⠀⢠⠇⣀⣀⡈⢇
⠀⠀⠀⠀⣴⣧⣿⡿⠀⠉⠓⠢⠞⠋⠉⠀⣛⡉⠙⠁⠤⠘⠉⠀⠀⠀⠀⣿⠷⢿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡴⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠀⣀⣀⡠⠊⠀⠀⠉⠰⠊⠀⠀⠀⠀⠈⠢⠘⡋⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠳⣄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠇⠀⠀⢠⠀⠈⠛⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⠀⠆⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⣄⠀⢀⡀⠤⠤⣀⠀⠀⠉⣀⡠⠤⣀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢁⡠⠔⠃⠐⠒⠒⠒⠀⠠⠤⠎⠀⠀⠈⠁⠈⠀⠀⠀⠈⠓⠒⠊⠁⠀⠀⠈⠀⠒⢤⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡌⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣆⠈⡄
⠀⠀⠀⠀⠀⠀⢀⠃⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢃
⠀⠀⠀⠀⠀⢠⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⣧
⠀⠀⠀⠀⠀⠘⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠝
⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠤⢀⣀⣀⠀⠀⠀⠤⠀⠤⠄⢀⣀⡀⢠⡤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣴⠄⢀⣈⡁⠀⠀⠒⠒⠛⠓⠀⢀⣉⣁⢠⣤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣴⠀⠀⠀⠉⠀⢹⡇⠀⠀⠀⢺⠁⠉⠀⠁⠀⣘⣦⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣀⠃⠈⠑⢤⡀⠀⢸⡇⠀⠀⠀⢸⠀⠀⢀⣠⠞⠉⠱⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢠⠁⠀⠀⠀⠀⡹⠂⢸⡇⠀⠀⠀⢸⠀⠰⡈⠀⠀⠀⠀⢣⡀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠠⠆⠀⠀⠀⢠⡖⠁⠀⢸⡇⠀⠀⠀⢸⠀⠀⠙⢆⠀⠀⠀⠀⢴⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠑⣄⠀⢸⠇⠀⠀⠀⢸⠀⠀⡠⠊⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⠣⣸⠀⠀⠀⠀⢨⣀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠶⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⣠⠶⠆⣩⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢠⡍⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠙⠦⠔⢛⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢩⡄
⠀⠀⠀⢀⠴⠉⠀⠙⠶⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠴⠊⠁⠑⢄⡀
⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠙⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢤⣶⠋⠀⠀⠀⠀⠀⠀⠈⠳⢦
⠳⢄⡤⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⢀⣠⠶⠛⠛⠻⠶⣦⣤⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠸⣀⣴⠗⠀⣀⠀⠀⠐⠛⡇⠙⡄⠀⣾⠃⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⠀⡷⠀⠀⠀⣀⠀⢰⣄⣈⠇
⠀⠀⠀⠙⢀⠰⢏⣀⠘⠻⣤⢷⠔⡟⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⣀⣶⣠⡀⠀⢸⣿⡀⠰⡖⢃⡀⣹⢆⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⠂⠻⣆⣀⡀⠀⠀⢀⣴⠏⡇⠀⢸⡇⠀⠀⣇⠀⠀⠀⣴⠁⠘⢿⣷⠀⡿⠤⣶⢀⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⣖⠸⠟⠛⠛⠿⢿⡶⠚⠿⠃⢤⡇⠀⢸⡇⠀⠀⣿⠀⠀⠀⠈⠢⣤⣼⣷⣼⠃⠺⠇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡿⠦⠾⠿⠿⠖⠛⣇⠀⠓⠤⠚⡇⠀⢸⡇⠀⠀⣏⠀⠀⠀⠀⢠⠾⠤⠼⠿⠦⠛⠲⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡏⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⢀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠑⠒⠒⠂⠒⠊⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠒⠂⠒⠂⠒⠊⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⠶⠶⠶⠶⠖⠶⠶⠶⠶⠶⠖⠲⠶⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢤⣶⣞⣛⣋⣉⣉⡛⢻⠗⢰⡷⠙⣿⣛⣛⣛⣛⣛⣻⢷⡶⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠰⠎⠉⠛⠉⠉⠛⠛⠻⠂⣸⡇⠰⠎⠛⠉⠉⠙⢉⣉⣠⡦⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠠⢀⣀⠀⠀⠀⠀⣀⡀⠄⡹⢎⠰⢀⣀⠀⠀⠀⠀⠀⣀⠠⣞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣠⠀⡀⢠⣠⡄⡀⢰⡄⣤⡄⠀⠠⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡤⠒⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠘⠂⠙⠈⠸⠆⠑⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⣄⠸⣵⠤⠚⡀⠀⠀⣠⠊⠑⣤⠀⡾⠁⠈⢀⠌⠀⠀⣸⠀⢠⢶⣄
⠀⠀⠘⢇⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⡼⠾⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢅⡀⣀⣨⠴⠃⠀⡏⣸⠁⠀⠀⠀⣠
⠀⠀⡀⠘⣆⠇⠀⠀⠀⣰⢆⣠⠊⠀⠀⠰⠛⢧⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠒⡉⠋⠉⠛⠻⣏⠉⠁⠀⠀⠀⠀⢇⠸⣀⣀⠴⠻⣮
⠀⠀⠙⢦⢹⡃⠀⠀⣶⠁⠀⠙⠷⠀⠀⠀⠀⠀⠀⣠⠝⠒⠒⠒⠠⠖⠷⠆⠾⠃⠀⠀⢘⠠⠁⠀⢅⠀⠈⡀⠈⡇⠀⠀⠀⠀⠀⠘⢦⣀⣀⠤⠚⠁
⠀⠀⠀⠀⢻⡅⠀⢀⡼⢦⣀⣠⡷⠀⠀⢠⣲⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⢇⠂⠁⠂⠌⡀⢀⡴⠃⡠⣲⠶⠄⣠⡀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⣀⣾⠞⢀⡴⠖⠒⠒⠚⡓⢖⠚⠒⠚⠉⠀⡎⡞⠀⠀⡴⢱⢃⢞⡆⢀⣀⡀
⠀⠀⠀⢀⠀⢱⡸⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠀⢹⠀⠀⠁⠀⠀⠂⠈⣳⠀⠀⠀⠀⢇⣉⡽⢾⢁⡈⠉⡼⠀⢸⣿⣟
⠀⠀⠀⠉⢣⢸⡇⠀⢠⠒⠒⠒⣦⢞⡉⠂⡇⠀⡀⢀⣠⡴⠖⠲⠒⠶⠖⠤⣬⣯⣀⣀⣀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠛⠁⢟⡴⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢿⠀⠀⠘⣦⠀⣴⢃⣄⠉⢲⣇⠀⠁⠉⠑⠀⠀⢀⠀⠁⠀⠐⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⠉⡇
⠀⠀⠀⠀⠀⢸⠁⠀⢀⠈⡻⣅⠀⠉⢠⠟⠈⢣⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⣠⠴⠋⠀⠀⠀⠀⠐⡿⠷⠀⡿⢻⠀⠐⡾⡖⠀⠀⢸⢸⢀⡇⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠉⢀⡇⠀⣉⡶⠧⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⣿⣾⠀⠀⡇⡇⠀⠀⢸⠰⢨
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⠀⠀⡶⡄⠀⠀⢀⡔⠢⡀⠀⠀⣿⡇⠀⣿⣿⠀⠀⣧⡇⠀⠀⢸⠈⢸
⠀⠀⠀⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠤⠃⡇⠀⠀⢸⡘⢳⢣⠀⠀⢿⠇⠀⠿⠿⠀⠀⢿⠇⠀⠀⢸⡀⢸⠀⡀
⠀⠀⠀⠀⠉⠀⡇⠄⠘⠂⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⢸⠀⡤⠦⡀⡇⢀⡀⢸⡐⠞⡜⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠘⡇⠀⠀⠀⣇⠇⠀⠱⠇⢠⡇⠀⠑⠊⠀⠀⠀⢀⡜⠁⠀⠀⢀⣠⣶⣄⠀⣠⠚⠛⢤⡀
⠀⠀⠀⠀⠀⠀⣹⡃⠀⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠲⢖⡖⠉⠀⠀⠈⠿⠁⢀⡀⠀⠙⠇
⠀⠀⠀⠀⢀⣔⣁⠳⡀⠀⠀⠀⠀⠀⠀⡮⠀⣰⠀⠀⢳⠀⠀⠀⠸⠇⢶⠀⠀⠉⢉⡉⢹⡀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⡞⠑⠸⠟⢧⠀⠀⠀⠀⠀⣸⣷⣶⣾⣷⣶⣾⣇⠀⠀⠀⠀⢽⠀⠀⠀⢸⡇⠀⣉⠉⠉⣭⠉⠉⠙⣄⣀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⣇⠀⠀⠀⡸⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⠠⢼⠀⠀⠀⢸⡇⠀⢸⠀⠀⣾⠀⢀⣄⠀⠀⠈⣭⡍⠉⢹⡅⠀⠀⠉
⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⡀⠐⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⢸⠀⠀⠀⢸⠁⠠⢸⠀⠀⣿⠀⢸⣾⠀⠀⠀⡏⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⢈⣿⣆⣀⣠⢿⣦⡤⠤⠄⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⢸⢰⠀⡏⠀⠀⣿⠀⢸⡏⠀⠀⠀⡇⡇⠀⢸⣧⠀⠀⢤⡀
⠀⠀⠀⢀⣤⣤⠴⠛⢻⡿⠁⠀⠾⠎⠀⠐⠗⠁⠀⠀⠀⠀⢠⣀⠠⠤⣼⠤⠤⠤⠾⠼⠼⠷⠦⠤⠿⠤⠴⠧⠧⠤⢤⡷⠷⠶⠾⠷⢼⡆⠚⠁
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⠃⠁⠀⠉⠉⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢀⡀⠀⢀⠄⠀⠰⢤⠀⠔⠃⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⡀⠀⠤⣬⠝⢫⣴⠊⢉⢰⠀⠴⠒⠚⠍⣤⠄⠀⠝⠀⠀⠠⠄⠀⠀⢤⣦
⠀⠀⠀⠀⠀⠀⢀⡾⠃⡤⠄⠀⠀⠐⠂⠠⠉⠨⠀⠀⠀⠀⢬⠴⠀⠄⠘⠈⠏⢨⡁⠀⠐⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢀⣴⠶⠷⠐⠀⡖⠒⣆⠴⠀⠉⠊⠚⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢜⢢⡄⠀⠀⠀⠀⠀⣿⠷⡄
⠀⠀⠀⠰⠏⠀⡤⢤⡀⠀⣁⡴⢉⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⢀⠀⠘⠐⣀⣀⠀⠄⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡿⠀⠀⣐⠀⠀⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠩⡄⢍⣷⡁⢾⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠃⣰⠋⠹⢏⣤⣒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠅⣸⠀⢀⣌⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢋⠅⢠⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⡁⡟⢴⡄⠛⠅
⠀⠀⠀⢀⣀⠀⡀⢠⡞⢶⣇⣴⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢸⠻⡎⢷⠂
⠀⠀⠀⠀⡀⠀⣠⡏⣵⣙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠣⣾⠀⠀⣸
⠀⠀⠀⠀⠳⣴⣿⣶⣝⣿⣿⣿⠿⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⠀⠀⠐⠀⣠⡊⠈⠓⠚⠃
⠀⠀⠀⠀⣠⣿⣿⣾⡿⢿⠟⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢺⡄⠰⢆⠀⢠⡜⠃
⠀⠀⢀⡄⣙⡿⠛⣩⣛⠿⠆⠀⠲⡀⠑⡀⠀⢀⡀⢠⠀⡀⠀⠀⠀⠠⡀⠉⠡⣁⠈⠁⢞⡁⠠
⠀⠀⠐⡻⠋⠐⡹⣵⠿⠇⠀⠀⠀⣅⣤⢈⣀⠄⠉⢀⡀⣀⡀⣀⡘⠀⠀⢳⡀⠈⠽⠯⡁⠁⢦⠰⡿⠈
⠀⠀⠈⣄⢨⠙⣠⣿⣠⡆⠀⠀⠀⠸⠓⠸⠋⣢⢀⡁⡀⠉⠁⠀⠈⠉⠒⠈⢤⠠⠀⠈⢳⡤⠈⠇⠄
⠀⢀⣀⡀⠠⣼⠋⢉⣉⡀⠀⠀⠀⠀⠀⣰⣞⡻⠯⠉⠀⠒⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠈⠄⣠⠹⡏⡇⢸⢶⡧⠀⢀⠀⢰⡷⡿⢿⡅⠢⠀⠀⠀⠀⠀⣤⠀⠠⢠⡂⡀⠀⠀⠀⠀⢀⢠⡶⢀
⠀⠀⢠⠃⠀⣱⣿⣶⣻⣿⣄⡏⣄⢾⣿⠇⠈⡠⢀⠀⠀⠀⠀⡀⠀⠁⡰⠁⠈⠀⠂⠀⠀⠀⠠⠎⠀⠀⠀⣠
⠀⠀⠰⠆⠀⠒⠒⢒⣾⣩⡏⠀⠿⠓⠋⢀⠈⠀⠈⠁⠀⢀⠈⣀⠀⡗⠁⡈⠁⡀⢀⣨⣀⣶⡅⠡⠆⣤⠊⣉⠅
⠀⠀⠀⠓⠀⡀⢀⣿⣰⢿⠫⡆⡀⣑⡴⠈⢠⡄⢤⡥⠀⢬⣤⡴⢸⣧⡀⠀⢒⢻⣄⣠⡹⣽⠾⣱⢦⣼⣇⡀
⠀⠀⡃⠘⠃⣤⢤⡈⠋⠸⡟⠗⠃⢘⢣⣌⣿⣉⢳⣶⣖⣆⡽⡃⠾⠀⣝⠶⣯⣤⣼⠚⠏⢹⡳⣴⣿⣿⡘⠳
⠀⠀⢃⣐⢤⡍⠀⠀⠀⠐⡇⡦⠐⠺⠺⠙⠟⠹⠛⠉⢉⠁⠀⠉⠉⠋⠛⠷⢭⣦⡿⠀⠀⠀⠀⠎⢼⠋⣃
⠀⠄⠀⠿⠛⢿⠀⠀⠀⢀⣹⣄⠀⠀⠈⢀⠈⠤⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⢀⣌⠈⣰⠓⢽⠂
⠀⡂⠀⢠⠐⡎⢃⠀⣰⣾⡛⠋⠃⠀⠀⠀⠁⠀⠤⠀⠠⢀⠀⠀⠁⠀⠀⠀⠛⠿⣴⣆⡄⠟⠛⣇⣹⠉⠫⠁
⠀⠀⠀⠤⠄⠼⠈⣦⠋⠨⡅⠀⡄⠀⠀⠀⣰⣳⢘⡞⢓⣞⢻⡦⠄⠀⠀⡀⠘⡄⠸⣿⡗⣼⠋⢀⣛⠠
⠀⡆⠀⠀⠻⠶⠓⠚⢂⣠⢦⠀⠤⡐⠉⣡⠺⠷⢭⠞⠛⠟⠫⡔⠻⢊⣿⣲⣞⣹⣅⣾⡱⢦⢮⣟⠉
⠀⡄⠀⠀⢀⠠⡌⠉⣂⣋⢈⠀⡘⠛⠀⠩⠋⢙⠷⠉⠀⠀⠠⠷⠷⠟⠶⠿⡯⡏⠉⢶⠆⠀⠈
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⡀
⠀⠀⠀⠈⠃⠂⠀⡀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡢⠀⠀⢂⣤⠔⠛⠛⠁
⠀⠀⠀⠀⢒⣌⡳⣾⣄⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⡄
⠀⠀⠀⠀⠈⢉⣿⣿⣷⣮⣶⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠐⠊⠀⠑⠀⣀⠄⠀⠀⠀⠀⠀⠈⡠⣦⡀⠶⡤⠄
⠀⠀⠀⠀⠀⠰⢻⠛⢳⡦⣿⢀⡀⢈⢤⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠘⠉⠀⠀⠀⠀⠀⠐⠚⠁⣄⡁⠀⢀
⠀⠀⠀⠀⠀⠀⢈⣹⣭⣽⣆⠄⠀⠀⠎⠠⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠂⠀⠀⠀⠀⠀⣠⣤⠀⠰⠷⠅⠊⠐
⠀⠀⠀⠀⠐⠀⠀⠙⢿⣧⣟⡊⠀⢲⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠩⣶⠥⠀⢉⣯⠐⡀⠀⠀⠀⠀⠐⢠⢁⡔⠀⠀⠀⠀⠐⠀⠀⠈⠀⡼⢂⠐⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠈⠽⠃⠐⠀⠀⡆⠀⠀⠈⠀⠉⢀⠀⠀⠀⠀⠀⢀⡀⠌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠈⠑⣤⣤⡤⠤⠤⠂⠁⠀⠄⡘⣀⡃⢼⠆⠈⠑⢏⠁⠂⠠⡬⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠀⠀⠀⠀⠓⠒⠀⢀⡠⠀⠋⢰⣋⣠⣉⡁⠘⢄⠠⣀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⢀⠔⠊⠁⠀⠀⠀⠁⡠⢉⡃⢴⡄⠈⢃⠀⠑⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⣛⡚⢛⢹⡇⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠲⡿⠥⣈⠛⠏⠩⠀⢠⠎⠀⠀⣤⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠷⢶⠒⠘⠆⠘⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡤⠤⠤⠔⢛⣂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠆⠀⢱⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠘⢠⡟⠲⣄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡤⠀⠀⢹⡀⠀⠻⠇⢠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡤⠀⠀⠸⡆⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⡇⠀⠀⢸⣥⠀⠀⣿⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⠀⠠⠄⠶⠂⠾⢀⠇⠀⠀⠸⡇⠀⠀⠈⡷⠀⠀⢻⠀⠠⠄⠺⠇⠠⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⡀⢀⣰⡆⠀⠀⡠⠟⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡡⠁⠀⠀⢠⠀⢆⠀⠀⠀⠀⣀⡄⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⡁⠂⠔⠁⠁⡂⠀⠂⠉⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢢⠀⠀⠀⠀⠀⠀⠊⠀⠀⠆⠀⠀⠀⠄⠘⠀⠈⠡⠀⠋⠀⡀⠀⠀⠄⠄
⠀⠄⠀⠀⠀⣠⠀⠀⠀⣀⠈⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⣤
⠀⢀⠀⠀⠀⠐⠁⠀⠈⣿⠀⢠⡄⠀⠈⠁⠁⠒⠈⠉⠃⠄⡈⠡⠀⠠⠤⠀⠊⠑⠦⠀⠀⠀⢠⣄⠀⢸⡏⠀⠀⠑
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀⡀⠶⢶⠀⠀⠀⠀⠈⠀⠐⠀⠁⠀⠁⠀⠀⢰⠶⠆⣀⡀⠹
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇
⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢳⠎⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢶⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡖⡇⠸⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⡗⠆
⠀⠀⠀⠀⠀⠀⢀⡄⠱⡀⢃⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠃⡰⠁⣄
⠀⠀⠀⠀⠀⠀⠘⡙⢄⠑⡄⢦⠸⡄⠀⠀⠀⠀⠀⣠⢶⠒⢄⠀⠀⠀⠀⠀⠀⢀⡼⢠⠆⠔⢁⠜⡙
⠀⠀⠀⠀⠀⠀⠐⡙⠦⣝⡢⠀⠁⠈⠢⣤⣀⠀⠈⠓⠄⠀⢸⠀⠀⠀⢀⣠⡤⠊⠀⠁⠠⢒⡥⠞⡕
⠀⠀⠀⠀⠀⠀⠀⢾⡓⠦⠬⠀⠀⠀⠀⠀⠈⢆⠀⢀⡄⠀⠀⡄⠀⢀⠎⠀⠀⠀⠀⠀⠨⠤⠖⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⢉⣉⡁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣉⣉⠉⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⣁⡤⠊⡰⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠰⡈⠢⣄⡉⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣠⠞⢡⠎⣰⡃⣇⣠⡀⠀⠀⣰⣀⡇⣳⡘⢆⠙⢦⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⠉⠙⠋⠁⣀⡠⠊⠁⠀⠘⠉⠢⣀⡀⠉⠛⠉⠉⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢢⠃⠀⠀⠀⢐⣉⣁⠠⠀⠀⠀⠀⠀⠀⠀⠠⣀⡉⣑⠀⠀⠀⠀⢣⢢
⠀⠀⠀⠀⠀⠀⠀⢠⢧⠇⠀⠀⠀⠀⠀⢅⡠⠔⠂⡠⢀⠀⣀⠠⡈⠓⢤⣄⠅⠀⠀⠀⠀⠀⢧⢧
⠀⠀⠀⠀⠀⠀⢠⣏⡞⠀⠀⠀⠀⠀⠀⠘⢦⣤⠊⠀⢸⠀⢸⠀⠈⢢⣤⠞⠀⠀⠀⠀⠀⠀⠘⡎⣧
⠀⠀⠀⠀⠀⢀⡞⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠻⢄⠼⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣆
⠀⠀⠀⠀⢀⡾⣽⠁⠀⠀⠀⠀⢀⣀⠠⠤⠶⠐⠦⢤⡀⢸⠀⣠⠤⠶⠶⠦⠤⣄⣀⠀⠀⠀⠀⠀⠱⡹⡆
⠀⠀⠀⠀⣼⣳⠇⠤⠤⠐⠚⠉⠉⠀⠀⠀⢀⣀⡀⠀⢈⣻⡊⠀⠀⣀⣀⡀⠀⠀⠈⠉⠑⠒⠠⠤⢤⣷⣻⡄
⠀⠀⠀⣼⣿⣁⣀⣀⣀⣤⣤⣴⣶⣦⣭⣭⣭⣿⣿⣷⣍⣀⣈⣵⣿⣿⣿⣭⣭⣽⣶⣶⣤⣤⣄⣀⣀⣀⣹⣿⡄
⠀⠀⢸⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠉⠛⠛⠛⠋⠁⠈⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠄⠒⠀⠀⠈⠃⠐
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠀⢀⢀⣀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠄⠀⢸⠞⠉⢆⠀⠀⠀⢀⠉⠀⢀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡀⢀⠈⠙⠖⡋⠘⠂⠂⠀⠚⢂⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠄⠉⠐⡀⠚⡅⠛⠐⠧⡤⠀⢶⠀⠆⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠸⠖⠌⠀⠸⠧⡇⠀⡀⠠⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⠷⡀⡁⠞⠀⠀⠀⠀⢀⠀⠆⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠐⡄⠀⡐⠂⠄⠈⠙⢱⠾⠶⣁⠀⠀⠒⣈⠦⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠘⠛⠲⣄⢸⡆⢠⡄⣵⢀⡔⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠀⠈⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠠⠀⠀⠀⠀⢀⠊⠘⡁⡀⠀⠀⢀⣸⠀⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠸⠷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠞⠀⠀⠀⢱⠈⠑⠔⠀⡆⢥⡀⠀⠀⠀⠻⣄⠀⠀⡾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠙⢄⠁⠀⠀⠀⠄⠀⠀⠀⠀⠁⢀⢧⠀⠀⠀⠀⠈⠀⠀⠙⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠟⠴⡆⣿⢳⡄⠧⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⢀⣬⠀⠀⠀⢿⠠⠃⢰⠀⢀⠀⠀⠀⠐⠶⠄⠀⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣁⠛⢢⡀⠀⠸⣧⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣍⡄⠀⠳⠀⠀⡿⣇⢰⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣧⡟⢰⡗⠀⣰⠇⣇⣿⠀⢀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠁⠀⠀⠈⠀⢀⣤⡠⠞⡩⠀⡞⠀⡐⠛⣠⣿⠟⠀⠸⣁⠉⣠⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂⠂⠀⠴⠦⡈⠀⠄⠀⠊⢀⣼⠁⠐⣇⠀⢼⡸⣟⡄⠁⠀⠀⢨⣄⠠⠀⠀⢤⡀
⠀⡀⠀⠀⠀⠀⠀⠘⣃⡀⠀⢄⡑⠆⠀⠑⠲⡆⠰⠶⠋⠉⠃⢰⡿⠄⠀⠓⠿⠄⠒⠀⡴⠕⠘⠧⠀⣀⠀⠀⠀⢀⡀
⠀⠅⠀⠀⠀⡠⠄⠀⠈⠀⠘⠉⣔⠊⡇⠀⠀⠱⠀⢢⡀⠁⠸⠸⠫⢶⡀⢢⣴⠲⠶⢏⡁⠀⠈⠦⠘⠋⡈⢰⠐⠊
⠀⠂⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠈⡠⠇⣘⠂⢀⡲⡦⢄⢠⡴⢐⠁⢺⠀⣠⠀⠀⠐⢀⠱⠀⠁⠀⠆⠀⠐⢣⣄⠀⡁
⠀⠀⠀⠀⠀⠀⠘⡂⠀⠘⠑⠄⠘⣠⠠⣀⡼⠏⠀⠀⠀⡈⢤⢀⣀⠈⠻⠑⡀⢠⠀⢀⠠⠃⠂⠉⠤⡷⠄⠀⠀⠈⠉
⠀⠃⠀⠀⠀⠈⠒⠓⠖⣠⡄⠐⠀⡠⠏⠈⠀⠚⠀⠀⠀⠈⠠⠠⠈⡼⠀⢈⠲⢈⡕⠠⠆⠠⡄⠹⠏⠀⠉⠁⠠⠐⠐⠒
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠃⠀⠘⠂⠀⠀⠀⠀⠀⠚⠒⠈⠁⠀⠁⠀⠉
⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢘⠈⡰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠉⠂⠊⢐⠟⠉⠁⠢⡀⣀⡀⠀⠈⠂⠄⠺⣄
⠀⠀⠀⠀⠀⠀⢠⡎⠉⢳⣴⠋⠉⣦⠀⣼⣷⣿⣶⣤⠇⠛⠃⠐⠒⠂⠀⠀⠙⢷⠄⣶⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠰⠗⠶⠋⠈⠓⠖⠧⠀⢻⣿⣿⣿⡇⠀⠀⠀⠈⠒⢦⡀⠰⠆⠆⠶⠠⠈⢀⣀⠴⠷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣖⠒⡸⠀⠀⠀⠀⠀⠈⠿⠿⠷⠼⠤⠛⠠⠼⠀⠙⣦⠀⠀⠀⠀⠀⠈⠁⢀⣠⡬⠭⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄⠀⠰⠆⠀⠘⣿⡆⠀⠀⠀⠀⢀⣤⣞⠀⠈⣧⢀⣤⠀⢀⡴⠞⣩⡅
⠀⠀⠀⠀⠀⣀⡀⠘⢎⣉⡀⠁⢾⣿⣿⣿⡗⢿⣿⠀⠀⠀⠀⠺⣿⡿⠀⠀⢹⡄⠉⣴⠋⠀⠀⠻⠃⠴⣒⠁⠀⡀
⠀⠀⠀⠀⠀⠉⠀⢰⠃⠤⠹⡄⠰⣿⣿⣿⣿⠻⣿⠇⠘⠟⠀⠀⠰⠀⠂⠀⢸⡇⣼⡇⢰⣶⡆⠀⠀⠀⠋⠁⠈⠛
⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠒⠲⢤⣀⠈⢀⠀⡀⠁⣾⢣⣿⠀⢸⣿⡇⢀⡛⠀⠀⠀⠀⠀⠘
⠀⠾⠶⣤⠈⢁⠐⠀⠀⠊⡠⠀⠀⣷⠀⠰⠀⠀⠀⠀⠀⠀⠈⢷⡌⠀⠀⢰⡿⣸⡇⠀⠀⣬⣶⣼⣇⠀⡦⠀⠠⡆
⠀⠀⡼⠁⠐⠒⠀⠀⠀⠀⠒⠀⠀⣿⢰⣿⣿⣇⠀⠀⠐⠀⠀⠀⣿⡆⣠⣿⢣⣿⢁⡄⠀⠛⠛⠋⢛⣀⣤⣤⣤⣤⡀
⠀⠀⣀⡀⠀⠁⠀⣀⣀⠀⠨⢦⠀⣿⠀⣉⣩⣥⣤⣀⠀⠀⠀⠀⣼⣿⣿⣷⣿⠏⠺⠛⣫⢁⠀⠘⠛⠛⠛⠛⢋⠁⠂
⠀⠾⠋⠀⢶⣶⠀⠙⠟⠀⠀⠋⠀⣿⠈⠙⣿⣿⣿⡟⠛⠀⠀⢠⣿⣿⣿⡿⠃⠀⢲⣶⡁⠷⣤⠀⠀⠀⠈
⠀⠠⣶⣤⠈⠏⠀⠀⠀⣸⣧⡴⡀⢻⣆⠀⠀⠉⣩⣴⠀⠀⢠⣿⣿⠟⣁⡤⠀⠀⠈⢉⠁⠐⠁⠀⠄⢐⠀⠀⠀⡌
⠀⠀⠀⠀⠀⢀⣄⣀⠀⣀⣠⠏⠀⠀⠛⢿⣶⣤⣙⠋⠀⣰⣿⠟⢁⠀⠀⠀⢀⠀⢸⣿⠀⠀⠀⠀⢂⠉⠐
⠀⠀⠀⠀⠀⢰⣿⣿⠀⠸⠷⠄⠀⠀⠀⠀⠉⠻⣿⣿⣾⣿⡏⡰⠀⡐⠁⡤⠁⢰⡄⠀⠀⠆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⢠⣼⣍⠀⠀⢡⠀⠀⣸⣿⣿⣿⣷⡀⠀⣿⠀⠀⠀⣼⠇⡤⠘⠛⢠⡄⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠈⣠⣾⣿⣿⣿⣿⣿⠿⠷⠦⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⣼⣿⣿⣿⣿⣿⡟⢁⣠⠤⠖⠒⠚⠛⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡼⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⢀⣾⠴⠒⠋⠉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠓⠲⢤⣸⡇⢀⣠⠤⠖⢒⣛⣋⣉⣉⣉⣉⣉⣛⣒⣲⣦⣼⣆
⠀⠀⢀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠲⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡄
⠀⣠⣺⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣶⣶⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀
⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣷⣬⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣷⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢔⢶⣪⣧⣵⣥⣭⣏⣜⡰⠢⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⣤⣲⡽⠞⠛⠉⣽⣿⣿⣿⡟⣿⣿⡉⠙⠳⢭⣗⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠈⠙⢿⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠨⡑⠦⣄⣀⠈⢿⣿⣿⣿⣿⣟⣹⠃⠀⢀⣀⡤⢖⡫⠒⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠴⢂⢌⣉⡛⠛⠿⠿⠿⠿⠗⠒⢋⡩⡵⢮⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠜⠙⠑⢰⠐⠺⡙⠌⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠶⠶⠲⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠀⠀⢀⣀⣀⣀⣀⠀⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⢷⣶⣶⣶⣶⡯⠶⢤⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢷⣶⣶⣶⣶⡶⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠼⣿⣿⣿⡿⠁⠀⠀⠁⠀⠀⠈⡄⠀⠀⠀⠆⠀⠀⠈⠀⠀⠌⣿⣿⣿⣿⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠠⠦⠤⠐⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠄⢀⣀⠄⠀⠀⠀⠀⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⢀⣀⣀⣀⠀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠈⠙⠢


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠄⣀⣀⠀⠀⠀⣀⠤⠖⠊⠉⠓⠦⢤⣀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⢋⣠⠤⠤⠄⢀⡀⠉⠉⠉⢀⣀⠤⠖⠒⠒⠤⢄⣀⣀⡀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣀⡤⠴⠤⢄⣀⠈⠉⠉⢁⣠⠴⠖⠒⠲⠤⣄⣀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠃⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠛⠁⠀⠀⡀⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢻⡛⠶⣄⣀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠘⠿⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⢃⣀⣠⣬⠿⠻⢯⣉⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⢻⡟⠙⠛⠋⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⢹⣿⣿⣿⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⣴⣦⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠙⢧⣀⣠⠴⠤⣤⡀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣿⠰⣿⡿⠋⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿⣿⣿⣧⠀⣀⡤⠞⠙⡇⠀⠀⠀⠙⢦⡀⠀⣀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢼⡟⠋⣹⣿⡏⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢦⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢁⠀⠀⠀⠀⣇⠀⠀⣀⠼⣗⠉⠀⢻⡇⠀⠀⠀⠀⣿⠀⠀⠀⣶⣷⡄⠀⢹⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠎⠀⠀⠀⠀⠈⠓⠉⠀⠀⢹⡀⠀⠸⡇⠀⠀⠀⠀⠛⢷⣄⡀⠸⠿⠃⢠⡟⠀⠈⠳⢀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⢻⣤⠴⠛⠁⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠻⣶⣶⣶⡟⠀⠀⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣏⠀⠈⠁⠀⣠⣴⠊⠁⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠒⠒⠤⣤⡀⠀⠀⠀⢸⡆⢠⡤⠤⠤⠤⠤⠤⢼⣿⣿⣇⣀⡀⡀⠀⠀⠀⢹
⠤⠄⠀⠀⠀⠉⣹⡟⠉⢹⣿⠉⣀⣴⠛⠁⠀⠀⠀⠈⠉⠉⠲⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢰⡤⠤⠦⢰⣦⣶⠤⣿⣿⡧⢄⣀⣀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⣿⡁⠀⢀⣿⠞⠋⠈⠉⠙⠲⢦⣀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠠⠖⠒⢤⠀⠀⠈⡇⠀⠀⢀⡿⠀⢠⣶⣿⡿⣿⣿⣿⣿⠃⠀⠀⢹⠄⠀⣰⠃
⠀⠀⠀⠀⢀⡾⣟⣠⠖⠋⢻⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⡇⠀⠀⢸⡇⠀⠈⣿⠃⠀⠈⢿⣿⡿⠀⠀⠀⢸⡀⢠⠏
⠀⠀⠀⠀⣿⣴⡟⢡⣶⣦⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠙⠳⢦⣀⠀⠀⢀⣤⠞⠀⠀⣸⠇⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢈⣿⠃⠀⠀⠀⡯⢀⠎
⠀⠀⢀⡴⠛⣿⡇⠘⣿⣿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠉⠉⠉⠀⠀⣀⠔⠃⠀⠀⠸⣏⠀⠀⠀⠀⣷⠀⠀⢸⡟⠀⠀⠀⠀⣃⡌
⢀⡼⠋⠀⠀⠘⣿⣦⣌⡁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠉⠓⠦⠤⡤⠤⠔⠚⣉⠀⠀⠀⢀⡀⠈⠲⣄⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⡟
⢸⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⠂⠀⠀⢀⣀⣀⣀⠤⠤⠶⠶⠒⠓⠚⠛⠓⠃⠈⠉⠉⠉⢉⡉⡛⠲⢦⣇⡀⢸⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⠁
⢸⠀⠀⠚⠈⠈⢀⣿⣿⣿⣿⡿⢷⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄⢠⠎⡪⠀⠀⠀⠈⠓⢾⠀⠀⣴⠟⠁
⢸⠀⠀⢠⡞⢉⣼⣿⣿⣿⣿⡇⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠙⠋⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⢸⠀⠀⡾⠀⢺⣿⠋⠉⢹⣿⠇⠀⠀⠈⠙⠛⠶⠶⠤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢀⣀⡤⣾⠟⠀⠀⠀⠀⠀⠘⠛
⠸⡀⣼⠃⠀⠈⣿⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠙⢻⣿⣿⣿⡿⠛⠛⠛⠛⠉⠁⠀⠋
⠀⣧⡏⠀⠀⠀⠸⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃
⠀⣿⠁⠀⠀⠀⠀⢿⡆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠃
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠛⣩⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣉⣉⣏⣨⣉⣩⣝⣉⣽⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢤⡀⣀⣀⠀⠀⣠⣔⠒⠉⠁⠀⠨⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠓⠦⡀⠀⢠⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠋⡀⢢⣀⣀⣀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢘⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⢸⠗⢤⣀⡜⢸⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡊
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢇⠀⠉⠐⠊⠓⠒⠠⠤⠤⠴⢒⠒⠲⠖⠉
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠤⠀⠀⠀⠀⣀⠬⠤⠶⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣠⡄⠀⢰⡎⠘⡇⢀⣀⠀⠀⠀⣇⣤⡶⠛⠉⠉⠉⡿⢻⡅⠀⠤⠀⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠃⠘⠁⠑⢼⢰⡉⠳⠼⠁⠀⠻⡀⠀⠃⣠⠇⠀⢙⠦⠤⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠥⡀⠀⠀⠀⠀⠉⠙⠉⠁⠉⠚⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠤⣤⣄⢀⣀⣀⢤⠤⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠐⠢⢧⡐⣰⣇⣀⠇⡅⠀⠠⡒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠙⠳⡃⠀⣿⣉⣆⡴⢓⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠘⠋⠁⠀⢸⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠓⣤⣀⠀⠀⠀⠀⠀⠸⣤⡴⠚⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢠⠈⠉⠒⠒⠒⠒⣿⠁⠀⠀⠀⢱⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠄⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡟⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠘⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⢳⠤⠤⠔⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⠀⢀⡇⢀⢀⣀⣠⠤⠒⠋⠀⠀⠨⡍⠁⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⢟⠁⠉⢉⢉⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢡⠀⠀⠀⢀⠔⢡⠀⠀⠓⠤⢤⡞⠉⠒⠒⣹⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠂⠀⢰⠁⠀⠀⠈⡖⠶⠶⢶⡉⠐⢆⡉⢀⡟⠢⡀⠀⡠⠊⠀⠀⠈⠒⡄⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠰⠀⢸⡀⠀⠀⠀⠱⢤⡠⠜⢡⠀⠀⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠣⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⢀⣠⠜⠁⠀⢆⠀⠀⠀⠀⠀⡜⠀⡄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠓⠒⠒⠒⠂⠁⠀⠀⠓⢤⣀⣀⣀⣀⡤⠊⠀⠉⠉⠀⠀⠀⠀⠀⠀⠑⠠⠦⠐⠋⠀⠀⠁

⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠶⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢷⠃⡏⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⢢⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⠀⠁⣤⠀⠀⣤⣠⠄⠀⠰⠬⠀⠀⠄⠀⢙⡿
⠀⠀⠀⠀⠀⠀⠀⠉⢻⠄⡟⠀⠀⠀⡄⠀⠀⠀⠀⠠⡄⢛⠂⠘⠴⢆⠙⠆⡀⠀⠁⠀⠀⠀⠇⠀⠀⠘⡄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⠀⠀⠀⠀⠘⠀⡒⠙⠂⠀⠀⠀⠄⠠⡙⠛⠀⠀⠀⠀⠀⠀⠐⡀⠀⠰⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠀⠆⠡⠀⠀⡄⠘⠀⠄⡀⠀⠻⣨⠆⠀⠴⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠁⢀⡄⠀⠀⢂⠀⠀⠀⠁⠂⡀⠀⢈⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣘⡣⠀⠠⣅⠀⠒⠀⠂⢰⡫⠀⠀⢈⡅⠌⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⢂⠈⠁⢀⠀⠑⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠈⠀⠈⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠄⠀⠂⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣩⠀⠀⡄⠀⡀⠀⠞⠀⠀⠰⠀⠀⠁⠀⠂⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠒⠀⠀⠰⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠠⠠⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⢀⠀⠀⠀⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠀⠶⠚⠚⠀⡂⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⠀⡘⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠁⠀⠀⠀⠀⠂⠀⠀⠐⠰⠄⠀⠀⠀⡀⠄⠀⠀⠈⠀⠀⢀⡠⠁⠂⠀⠀⠀⢰⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠀⡠⠀⠀⠀⠀⠂⠠⠈⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠙⠃⡄
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢄⡀⠀⡐⠀⠀⠄⣀⠴⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⡠⠀⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡘⠀⢀⠈⠘⠧⣄⠀⠘⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⢀⡽⣀⠀⠀⠀⠀⣠⡴⠂⣀⠄⠁⠀⢩⠄⢀⡀⠁⠄⠀⠈⠰⣄⡈⢷⡄⠀⠀⠀⣰⠠⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢠⣦⠀⠀⠀⣿⠠⡈⢿⣄⡀⠤⠀⠀⠀⠁⠀⠀⠀⠒⣤⠋⠁⠨⣇⠀⠀⠠⠔⠋⠀⠈⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢃⠀⠀⢹⡀⠈⠀⣈⡗⢂⠀⠀⠀⠀⠀⠀⠠⡀⠒⠖⠀⢸⠇⢀⣴⠎⠁⠀⠀⠀⣀
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡶⠀⠀⠃⢀⣀⡬⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠑⣀⡔⠋⣁⠐⠀⠀⠀⠀⠀⠀⠁
⠀⡘⠀⠀⠀⠰⠁⠀⠀⠀⠀⡘⠀⠀⠁⢐⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢚⠣⠀⠴⠫⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠄⠒⠂⠀⠀⠀⠂⠀⢀⠀⣀⠀⠀⠂⠢⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⠀⠀⠈⠀⣀
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠂⡃⠀⠀⠀⠀⠀⢀⡅⠂⡱⠀⠄⠀⠀⠐⠑⠀⠀⢀⡀⠈⠑
⠀⢉⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠲⠁⠈⠀⠠⠉⢀⠀⠀⠸⠀⠀⠀⠁
⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀⠀⠀⠀⠀⢀⠔⣒⡶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⡤⣶⣶⣷⡄⠀⢠⡷⠞⣉⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡃⠀⠀⡔⠁⢰⡾⠇⠈⠀⢠⠀⠀⠈⠒⠉⠀⠑⣄⠀⠀⠘⢄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘⠁⡌⠀⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡟⣀⡷⠀⣀⡈⢆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⡉⢀⠁⠀⠀⠀⠈⠘⢆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠂⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⢸⠐⠂⠀⢈⡔⡀⠐⠃⠈⠒⠂⠩⠄⠀⠀⡰⠀⠀⠀⠀⡸⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠈⢆⠀⢀⠃⠀⢠⢀⡰⠂⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠃⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢡⡀⠀⠀⠑⠤⢕⣒⣺⣉⡀⠀⠐⠈⠀⣠⠞⠀⠀⠀⠀⡀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠢⢄⣀⡤⠀⠀⠀⣀⣸⠦⠤⠖⠋⠀⠀⠀⣀⠔⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠠⠸⠀⠀⠀⢀⣀⠤⠒⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠒⠒⢐⠊⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸


⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠄⠒⠒⠒⠒⠂⠉⠉⠉⠉⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⢰⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠈⡀⠡⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡆⠘⠀⢄⡀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡀⠀⢰⠂⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠄⠀⠥⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠄⠀⠐⣂⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠠⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⣁⣒⣒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢣⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣥⣴⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠘⣧⠀⠀⢸⡇⠀⠀⣼⠃⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⢻⡇⠀⢻⡇⠀⣸⡟⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠻⣧⠀⠀⠛⠀⠘⠁⠀⠋⠀⠀⣼⠏⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⢷⣦⠈⠃⣠⡾⠟⠛⠛⠻⢦⡀⠈⢁⣴⠾⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠈⠙⠳⣶⣤⡀⠁⣼⠋⠀⠀⠀⠀⠀⠀⠹⡄⠈⢀⣤⡶⠞⠋⠁⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠙⠻⢷⣤⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⠿⠛⠉⢿
⣾⠛⠒⠶⠶⠶⠤⣤⣏⣀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡴⠟⠉⠀⠀⠀⢀⣈⣧⡤⠴⠶⠶⠒⠒⢻
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⡀⠀⠈⠻⣆⠀⠙⠳⠤⣤⡤⠴⠊⠁⢀⡾⠋⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⠷⠶⠾⠿⠿⠿⠿⠿⠶⠶⠶⣦⣤⣄⣀⠀⠈⠒⢄⠈⢆⠀⠀⠀⠀⠎⢀⠔⠋⠀⢀⣀⣤⣤⡴⠶⠶⠾⠿⠿⠿⠿⠿⠿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠤⡀⠁⠀⠀⠀⠀⠀⠀⠁⡠⠴⠚⠉⠁
⣶⣶⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⠤⠄⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠶⢧⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣤⡀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠶⣴⣿⣷⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋⠛⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⠀⠀⢸⣶⣞⢬⣷⣶⣾⠠⠀⡐⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢿⣡⠄⡀⢠⣼⣏⣷⣝⣿⣤⠀⡀⢤⣹⢿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠁⠀⠉⢲⣾⠟⣿⡟⢻⣶⠊⠁⠀⣽⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢻⡇⠀⠀⠘⡇⠄⠈⠀⢄⠏⠀⠀⠀⡿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠂⠃⠀⠀⠀⠘⡂⢈⠀⡊⠀⠀⠀⠀⠃⢊⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⢁⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠋⠁⠀⠀⡀⢀⠀⢈⢋⡃⠀⠀⢀⡀⠀⠀⠉⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠀⠀⠀⠿⡀⡄⢬⡁⣩⢄⡄⣸⠃⠀⠀⠀⠠⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⡴⠛⠁⠀⠠⣤⡐⠂⠄⠮⢮⣟⣧⠾⢆⡠⠚⣠⣤⠀⠀⠙⠳⣜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁⢀⡘⠃⠚⠉⡄⢶⡀⡀⢴⡶⣿⡷⣶⢄⡀⣱⠖⡌⠙⠀⠋⣀⠁⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⢲⠏⠀⠐⢶⣆⠀⠘⣧⠀⢠⠴⠻⠳⢄⠀⢸⡟⠄⢀⣶⠦⠀⠈⢶⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⠀⠈⠋⠁⣀⣩⣱⢂⡗⢰⡀⣰⢐⣇⢳⡩⣁⡀⠙⠁⠀⢀⣨⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠋⡩⠛⠻⢂⣶⣀⣷⡏⠘⠋⠚⠷⠟⠎⠛⠈⣷⣆⣘⣆⠚⠛⠫⡈⠣⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠐⠂⠂⠓⠁⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠙⠂⠂⠒⠈⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢰⠀⠀⣤⠀⢀⠀⠀⢰⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠁⠒⠣⠀⠓⠀⠉⠘⠁⠘⠚⠀⠀⠈⠉⢨⠀⠃⠀⠈⠁⠓⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣿⣿⣷⣾⣯⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣏⢁⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⡟⠛⠋⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣾⣿⣿⡛⣾⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡈⢿⣿⠟⠃⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣠⣴⣖⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⡦⠄⠀⣤⣴⣿⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣾⣷⣿⣿⣟⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣾⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⣿⣏⣿⣽⡏⢉⢁⣀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣷⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿⣧⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠛⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡟
⠀⠀⠛⣲⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠓⠞⢻⡏⠉⠉⠉⠉⠉⠉⠉⠉⡻⠗⠛⠚⠳⠒⠛⠛⠛⠚⠒⠚⠒⠒⠒⡋⢹⠛
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⠂⠀⠐⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘
⢠⠶⣸⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⠀⢈⡄⠀⠀⠀⢠⠚⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠱⣖⢩⡇⠀⠀⠀⢸⠒⢤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡁⢸⡆⠀⠠⡏⠑⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢼⢃⡀⣴⡀⣤⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢛⢨⠀⠀⠀⠉⠀⢹⠀⣞⣷⣔⢷⣶⠄⢀⣤⣤⢀⣤⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠜⠀⠀⠀⠀⠀⠀⢸⡀⠋⠁⠈⠀⢉⡆⢨⡿⠛⠚⠓⢿⠀⠈⣿⠿⣼⣽⣿⠀⣴⣶⣖⣶⣦⡄⠀⢀⣤⣤⣤⣄⡀⠀⢸
⠀⡿⠛⠒⠀⠠⠤⠤⠼⠦⡄⣀⣀⣀⣨⡇⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠈⠀⡼⠋⠉⠉⠉⡇⠀⢸⠿⠛⠚⠻⠏⠀⢸
⠀⢥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠛⠛⠒⠚⠂⠾⠦⠤⠀⢀⣠⣀⣥⣀⠀⠀⠀⣟⠀⢈⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠒⠦⠶⠦⠀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠀⠒⠶⠶⠾⠄⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠉⡘⠀⠀⠀⠀⠉⠉⣛⠉⠑⣶⠒⠲⠖⠒⠠⣤⣤⣤⡤⡀⠀⢀⣀⣀⠀⣸⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡜⢠⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢸⠀⠀⠸⢠⡄⠀⠀⠀⠈⠉⠉⠁⠉⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢰⢡⠌⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢿⡀⠀⠀⡇⠀⠀⠏⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⢠⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠸⠂⠀⠸⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⢲⠀⠀⠸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡜⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠀⣠⢁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢰⠆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠇⠀⠀⠟⢰
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⣨⠁⠀⠀⡘⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢰⠄
⠀⠀⠀⠀⠀⢠⠁⠀⠀⣠⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠇⢰
⠀⠀⠀⠀⠀⠆⠀⠀⢰⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⠀⡆
⠀⠀⠀⠀⠚⠒⠒⠒⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢶⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⡆⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⢸⣰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⡌⠳⠀⠤⣀⣙⢳⡄⠀⠀⠀⠀⠀⢠⠖⠦⠀⠀⠀⠀⠀⣠⠞⠁⣀⠀⣴⠖⣡⠄
⠀⠀⠀⠀⠐⢯⠝⠳⠶⢤⣼⣿⣝⠻⣦⡀⠀⠀⠀⠸⢤⠐⠂⠀⠀⡠⣾⠛⠋⠹⣇⠤⠔⣛⣠⡤⠂
⠀⠀⠀⠀⠐⠒⠻⡿⢛⣓⣿⡯⣽⠁⠈⢌⠂⠀⢠⠎⠀⠀⢳⠀⠈⡰⠃⠈⠓⠘⢓⣲⡯⢭⠼⠢
⠀⢀⠀⠀⠀⠀⠉⢉⣡⣬⡵⠿⠗⣳⡂⣈⡓⠚⠃⠀⠀⠀⠀⠓⠋⠀⡀⢠⡤⠦⣌⣁⣚⠓⠤⠀⠀⠀⠀⠀⡀
⢒⡿⠿⠿⠿⠿⠛⠛⠀⠀⢀⡴⠾⠻⣻⣿⠿⠿⡆⠀⠀⠀⢠⡷⡴⣦⣘⣙⣾⣔⠶⠏⠉⠓⠚⠛⠻⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⡀⠀⠸⠐⠀⠛⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡜⢁⣀⡠⠀⡀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⡈⠀⠘⠀⠄⠀⠱⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠈⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠣⠓⢘⠀⠂⠀⠀⠘⠃⠀⠀⠀⠀⣠⠀⡆⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡁⠁⠀⢠⣪⣈⠀⠀⠀⠀⠘⠦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⡆⢀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠙⠉⠈⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠙⠁⠀⠐⠁⠀⠈⠙⢍⡆⠀⠴⠃⠠⡠⠡⠁⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠘⠄⠀⠀⠀⣐⡀⠀⠀⠀⠒⢼⣉⠇⡀⣠⣌⡀⠀⠀⣀⠆⠐⠆⠀⢀⣀⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⢠⣴⣦⠀⠴⠺⣇⡒⠴⡂⠙⠋⠃⠀⢀⢄⠸⠄⠼⣤⠠⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠠⡀⠀⠎⠙⠂⡀⠈⠁⢿⠁⠀⣻⠊⠀⠁⠀⠀⡂⠀⠀⣤⣀⡠⠄⠈⠉⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠀⠀⣌⠄⠐⠀⠈⠳⡀⣿⠔⠺⣄⠀⠀⠀⠀⡀⠙⠋⠁⠰⠂⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⡀⠀⠄⢀⡆⡹⠲⠷⣀⡿⢥⣀⠠⠎⠁⠠⣄⠀⠈⠰⠀⡤⠁⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠙⣑⣾⡁⠁⠀⠀⣀⣹⠀⣀⠰⣾⣷⠆⠀⢢⠶⡄⠀⣠⠁⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠛⢡⠔⠳⣄⣰⡆⠀⢹⠀⠅⠈⡆⠀⢐⠢⢿⠴⠒⠋⠑⡄⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣽⢿⡇⠀⠀⠀⠀⠓⠛⠳⣤⣿⠘⠶⣴⡥⠦⣤⡼⠛⠳⠤⠐⠐⠁⠈⠩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠛⠀⠀⠀⠀⢠⠖⠀⠀⠙⣿⣷⣾⠃⠀⡀⠈⢓⠀⠀⠀⢰⣶⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠘⣿⣿⡄⠐⠻⢷⠦⠌⡑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠤⠴⡛⢛⠻⣦⡄⢀⣀⣀⣀⣀⣀⣐⣀⣀⠀⠀⠀⣈⠡⣤⡰⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠾⣯⣥⣴⣿⠃⠀⠀⠀⠀⠀⠒⠒⠒⣒⣂⣈⣉⣉⣉⠀⡂⣀⣀⡀
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠉⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠉⠉⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢱⣤⣿⣇⣼⣀⡔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡄⠀⠀⢤⣹⣿⣿⣿⢥⣬⣽⣿⣾⣥⠤⠀⠀⢰⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣟⠃⠐⠺⢿⣯⣝⣻⠾⠿⣋⣠⣿⠷⠶⠄⢉⡿⢯⡁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⣷⡶⠀⠈⠀⠈⠀⠀⠚⢙⣽⣿⢿⣯⣽⣿⣿⠻⢦⠀⠀⠀⠀⠀⠀⠐⣲⣮⠤
⠀⠀⠀⠀⠀⠀⠀⠰⠏⠙⠀⠀⠀⠀⠀⠀⠂⠈⠹⠾⡛⠹⠛⠿⠙⠀⠀⡠⠊⠀⠀⠀⠀⠈⠁⠙⠆⢀⡀⢀⡀
⠀⠀⠀⣈⣣⣞⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⡄⠘⣴⣾⣷⡄⢀⠁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢿⡯⡤
⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠎⢈⣿⣆⣾⣧⣿⣔⠍⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣿⣿⣿⣿⣿⣿⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⡀
⠀⠀⠀⠀⣑⣾⡴⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠧
⠀⠀⠀⠀⠀⠘⠇⠀⡀⠀⠀⢀⠔⠒⡤⡴⣾⣿⣝⣛⣛⣻⣏⣿⣿⣿⠟⢿⠒⢀⠔⣦⡀⢠⡀⡤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⢽⣾⣃⠀⠛⠶⠶⣤⣤⣬⢟⣩⡍⣿⣍⣽⣡⠰⠄⠄⢦⡽⠚⠛⠁⠶⢿⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠙⣿⣽⠉⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡴⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠳⣤⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⢸⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠘⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡄⠹⡄⠹⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡸⠁⡼⠁⣼⡄
⠀⠀⠀⠀⠀⠀⠀⢳⡙⢦⡘⢆⠹⡄⢳⡀⠀⠀⠀⠀⠀⢀⡔⢻⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡴⢁⠞⣠⠞⣱⠃
⠀⠀⠀⠀⠀⠀⠀⢯⠙⠦⣙⠢⢅⠈⠀⠙⠦⣄⣀⠀⠀⠉⠳⡄⠀⢨⡇⠀⠀⠀⢀⣀⡤⠞⠁⠈⠀⠥⢚⡡⠞⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠠⡗⠦⢤⣉⡀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⡇⠀⠀⣇⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣈⣡⠤⠖⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠈⠓⠶⠚⠀⠀⠀⠘⠲⠖⠋⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡶⠖⠚⢁⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣄⠙⠒⠶⣶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⡤⠞⠁⣠⠏⣰⠀⡆⢸⠀⡀⠀⠀⠀⠀⡄⢸⠀⡆⢰⡈⢧⡀⠙⠦⣤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠴⣾⣁⣴⢃⡴⣇⡼⠤⣷⡀⠀⠀⣰⡧⠼⣄⡷⣄⢳⣄⣹⡶⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠉⠉⠉⠉⠉⣀⣀⡤⠖⠁⠉⠀⠈⠀⠓⠦⣄⣀⡈⠉⠉⠉⠉⠙⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⠏⠀⠀⠀⠀⣎⠉⣉⣠⠴⠂⠀⠀⠀⠀⠀⠀⠲⢄⣈⡉⢉⡆⠀⠀⠀⠈⢯⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⡟⠀⠀⠀⠀⠀⢸⡋⣉⣠⠔⠁⡀⠀⠀⠀⠀⡀⠑⢤⣈⠉⡻⠀⠀⠀⠀⠀⠘⣇⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⡾⠀⠀⠀⠀⠀⠀⠀⠸⡍⢀⣠⠞⠀⢸⠀⢸⠀⠘⢦⣀⠈⣽⠀⠀⠀⠀⠀⠀⠀⠘⡎⣧
⠀⠀⠀⠀⠀⠀⢠⡟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢇⣀⣠⣟⠀⢘⣧⣀⣀⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⣧
⠀⠀⠀⠀⠀⢀⡾⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⣆
⠀⠀⠀⠀⢀⣾⢱⠏⠀⠀⠀⠀⣀⣀⡤⠴⠖⠚⠋⠉⠉⠓⠲⣄⢸⣀⡴⠒⠋⠉⠉⠛⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⢷⢻⣆
⠀⠀⠀⠀⣼⣧⠿⠤⠴⠖⠚⠉⠉⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣈⣿⣏⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠼⢧⣿⡄
⠀⠀⠀⣼⣿⢃⣀⣀⣀⣀⣠⣤⣴⣶⣖⣻⣭⣭⣥⣶⣾⣿⣿⣁⣀⣀⣹⣿⣿⣶⣦⣭⣭⣽⣓⣲⣦⣤⣤⣀⣀⣀⣀⡀⢻⣿⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠛⠿⠿⠿⠟⠋⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠠⠤⠀⢀⣤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠸⠶⢤⡄
⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢛⣧⣖⡯⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⡅⠀⠀⠀⣻⡇
⠀⠀⠘⠇⠠⠀⡀⠀⠀⠀⢠⣠⣴⡶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠈⠉⠲⡆⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣴⣿⠇
⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⣷⠀⠒⠲⠎⢹⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⢈⠒⠶⣤⣤⣤⣀⣀⣀⣠⣴⣾⠿⣛⣫⡽⠂⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠈⠙⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣈⠓⠦⠀⠉⣑⢲⣚⠩⠕⢚⣩⠵⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠉⠢⢄⣐⣄⡭⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⣶⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠘⠗⣱⡄⠀⠀⠀⠀⠨⣥⣟⠀⠠
⠀⠀⠀⠀⢔⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢨⣔⣀⣀⣠⣤⡴⠞⠛⠉⠀⠀⣀⠄⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡆⠸⣷⢰⡆⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠃⡳⢚⣷⣌⠐⣄⣀⠄⠊⠀⠀⣀
⠀⠀⠀⣿⣠⣿⣾⠀⢄⡄⠀⠀⠀⠄⠀⠀⢀⣾⡄⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⣠⢴⣾⠋⠀⠀⣠⠀⠀⠀⠂⠀⣤⣠⣤⣠⠤⢀⠀⠢
⠀⠀⠀⠸⡏⢻⣿⡗⣼⠀⠀⠀⠀⠻⢇⣀⢸⡆⣉⠛⠶⣶⣤⡄⣀⡀⣀⡠⠔⣚⡭⠊⠀⠐⣪⢽⠁⠀⠀⠒⠡⠤⠊⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⣿⠀⠀⠈⠓⠀⠀⠀⠀⠀⠢⣽⣼⣇⣄⠀⠰⣇⡈⠻⠷⣤⡐⠈⡁⠦⣬⡥⠔⠋⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠳⠶⠶⠦⠿⠷⠚⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⣦⡀
⠀⠀⠀⠀⢸⡄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠈⠛⢤
⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⡀⠀⠀⠀⠀⠉⣉⣉⣀⣀⢀⣀⣀⢀⢈⡉⡉⠉⠉⠁⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⣣⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠐⠒⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢳
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⢄⠀⠀⠀⠀⠀⠀⡠⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠻⡆⠀⠀⠀⠀⠀⠀⢀⠁⠈⣿⠋⠸
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣠⣔⡉⢸⣵⢄⠀⠀⢠⣈⣠⠠⠄⡀⠑⠄⠀⢰⣖⡀⠀⠀⢀⣧⠀⠠⣳⣄⠀⠀⠀⠀⠀⠇⢀⣼⠇⢠⠓
⠀⠀⠀⠈⠂⠀⠀⠀⠰⠊⢤⣀⣷⢟⠁⢀⠰⠀⠞⠁⠀⠀⠀⠀⠐⠋⠀⠈⢁⠠⠀⡠⠀⢀⠀⠀⠈⣻⡳⣦⣠⣤⢶⠶⡞⢁⢀⠐⠁
⠀⠀⠀⠀⠀⠁⢼⡁⠐⣤⡾⠋⠄⠠⠂⠀⠀⠀⠀⠀⠠⣄⠀⠀⣀⠀⠀⠀⢭⠩⡉⡏⡍⢽⠀⠀⠀⠉⠛⠿⢿⣽⡷⠦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢾⡋⢰⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⡿⠃⠀⠀⡺⣐⢓⠅⠂⣢⠀⠀⠀⠀⠀⠀⠐⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠊⠉⠀⠀⠀⠀⠨⠠⠠⠥⠀⠜⠀⠀⠀⠈⠙⠀⠄⠤⠠⠛⠋

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠉⠀⢀⠈⠀⡁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⡀⠄⠈⠀⠀⢠⡄⠀⡌⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠶⠀⢀⣠⣅⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠀⡀⠩⢄⣩⠥⣔⠃⠀⢠⣀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢡⠀⠈⢠⡖⣤⢰⡆⣁⢀⡄⢀⠠⠂⡄⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢐⣤⡑⠀⢰⣇⠃⠀⠅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠋⠈⣴⠀⡦⠈⢡⠞⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⣀⠶⠀⠄⠚⠠⡶⢶⡉⠁⠀⢂⡢⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠁⠈⠓⠒⢤⠸⡏⢠⠈⣧⢠⠖⠉⠁⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠐⠀⠀⠀⠢⠀⡆⠀⠀⠀⠉⣠⠀⠤⠁⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠐⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⠸⠟⠸⠁⠀⠀⠀⢀⠀⠀⠈⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⣀⢞⠁⠀⠀⢠⠁⠈⠀⠀⠀⢳⠀⠀⠀⠈⠳⡄⠀⣟⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⡂⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣤⠀⣀⣠⡀⢸⡀⠀⠀⠀⠀⢰⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⢸⠃⠈⠙⡏⢙⠁⡃⠀⠀⠀⠀⠀⣄⡀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⢻⣄⠀⠀⢿⣨⡀⡇⠀⠂⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⠈⢦⠀⠈⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡚⡽⠢⡶⠀⣸⠀⣛⡇⠀⢀⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠆⠀⣀⢄⡴⢛⠃⡜⠀⡰⠃⣰⣿⠇⡀⢏⠉⢁⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠃⠡⠀⠴⠦⠀⢀⠀⠐⢁⣨⡃⠐⡇⠀⣿⢸⣣⠀⠀⠁⠸⣇⠠⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⢃⠀⠐⣤⠔⢂⠁⠛⣪⠀⠖⠋⠉⠁⢰⡿⠄⠈⠚⠃⠒⠂⡰⠓⠘⠣⠀⡄⠀⠀⠀⣠
⠀⠀⠀⠀⠠⠆⠀⠀⠀⠈⠁⢾⠉⡇⠀⡀⠂⠐⠤⠄⠘⢘⠛⣿⠀⠶⠖⠚⠻⣅⠀⠈⠳⠉⢡⠄⡂⠉⠁
⠀⠀⠀⠀⠀⠀⡂⠐⠀⡀⠀⢠⠜⠁⡌⣡⡬⠿⢲⠲⠖⡰⠀⢻⣰⠖⠀⠀⠀⠄⡆⠀⣄⢂⡀⠈⠶⠤⣠⠐
⠀⠀⠀⠀⠀⢄⢡⡀⠀⠀⢃⠀⢲⡤⠴⢋⡔⠀⠀⠨⠐⠤⠤⠀⠉⢅⠀⢆⠀⢂⠙⠁⣤⡀⢋⣀⠀⠀⡡⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠘⠇⠀⠠⠪⠁⠀⠈⠄⠀⠀⡄⠈⠂⠀⢋⠀⣎⠁⡴⠉⠉⠀⠦⠈⠁⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣦⣤⣶⣶⣶⣶⣶⣶
⣿⡿⡉⠿⣯⡿⢽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢀⡴⠖⠛⠛⠶⢦⡀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⢻⣆⢰⡟⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⢻⡄⠈⢛⡟⢻⡟⠁⣠⡟⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢰⡇⢸⡇⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠀⠀⠀⠀⢻⣴⣧⣼⣦⡟⠀⠀⠀⠀⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢦⣄⡀⠀⠀⣹⠶⠶⠶⢶⣏⠀⠀⢀⣠⡴⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠶⣤⣌⡛⢶⣄⠈⠹⣟⣻⠛⠁⣠⡶⢛⣡⣤⠶⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠶⠶⠶⢤⣬⣙⡳⣽⣷⡀⠈⠁⢀⣾⣯⢞⣋⣥⡤⠶⠶⠶⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⠶⠶⠾⢿⣿⣿⣿⣆⣰⣿⣿⣿⡯⠷⠶⠶⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⢶⡉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣆⡀⢀⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⢰⢆⡆⡖⢢⢆⢦⡄⡆⠀⡆⢰⠒⣤⠒⡀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠁⠁⠉⠈⠈⠁⠁⠀⠁⠈⠉⠀⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡏⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⣭⡇
⠀⠀⢠⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢾⡿⠋⢡
⠀⠀⢀⠳⣀⠤⠤⠤⣂⠬⠄⣂⡄⠀⠀⠀⠀⣛⣛⢛⣛⡛⠀⠀⠀⠀⠘⠠⠀⠀⣀⠀⠀⠠⠘⠀⠀⠀⢰⣦⣤⣤⣀⡄⡀
⠀⠈⢄⣒⡪⠭⠭⢙⠵⠊⠁⠀⠀⠀⠀⠀⣾⡿⠿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢺⣷⢀⡄
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣙⣺⣹⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⡏⣿⡭⢿⠺
⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠀⠀⠰⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠈⠋⠉⠁⠉⠀⣿⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣴⣿⣷⡦⢸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣷⡆⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣯⣿⣿⡇⠛⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣨⣵⣒⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠉⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢩⡄
⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠿⡶⠿⠷⠶⡿⢶⠾⢾⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣙⣛⢛⣉⣤⣤
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠒⢳⠒⡗⠒⠗⢺⠒⡺⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣫⣭⣿
⠐⠀⠀⠐⣿⣿⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⣫⣛⣹⡹⣋⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⠿⠟
⣤⣤⣤⣤⣽⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠖⠚⠛⠛⠛⠒⢢⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⢀⡴⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠇⠀⠀⢀⣎⠄⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⡿⠿⡇⠀⠀⠀⠙⢔⠃⠈⠢⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢐⠾⠁⠀⢰⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⡧⠆⡇⠀⠀⠀⠀⠀⠑⣄⣠⣾⣦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠲⠄⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠁⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⣥⣤⣤⣤⣤⣤⡼⠀⠀⠀⠀⠀⠳⣄⡉⢀⣠⠞⠀⠀⠀⠀⠘⣇⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠋⠀⠀⠀⠀⢸⡋⡉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠚⠁⣂⣄⣃⠙⠆⠀⠀⠀⣠⡾⠶⢿⣤⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣞⡄⠀⠀⠀⢰⠋⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⠇⠀⠄
⠀⠀⢴⠈⢼⢡⣶⢹⠌⢑⠄⠀⠀⢼⣇⣛⣸⣷⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⠇⠀⠀⠀⠸⣖⠤⠀⣠⡿⠀⠀⠀⠀⠀⠈⣠⣤⣬⢏⣤⣀⡈
⠀⠀⠀⣈⠁⡓⠖⣋⢈⡅⠀⠀⠀⠀⠙⠉⠋⢰⣯⣷⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠈⠙⠛⠉⢿⣦⡀⠀⠀⠀⠈⢙⢿⠏⠈⣿⢟⠈
⠀⠀⠀⠈⠀⠑⠖⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⠀⢀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠝⡻⣦⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠴⢶⣾⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⠛⢠⣾⣿⣿⣷⡖⢒⡶⠀⠀⠀⠀⢠⡶⣿⣿⠾⠟⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⡆⠀⠀⠸⠟⠛⠛⠿⠟⠛⠉⠉⠀⠀⢸⠀⢸⠀⠀⢀⣤⠚⢹⣿⣿⣟⣫⠟⡉⠀⠀⠀⠀⣴⢶⣿⣶⠿⠁⠀⠀⠀⠀⣾⡏⠀⠀⣿⣿⡆
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⠀⠀⠀⠉⠉⠁⠈⠉⠉⠁⠘⠛⠀⠀⠀⣀⣿⣕⣪⣷⠀⠀⠀⠀⠀⠀⢿⣧⣠⣤⣥⡅
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⠉⠁⠀⠀⠀⠀⠀⠀⠼⠿⠷⠬⠍⡥⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡄⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠂⠀⠀⢱⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⣀⢀⠀⠀⠀⢐⠃⠈⠀⡀⠐⢂⠒⢂⣀⡀
⠀⠀⠀⠀⠀⠀⣴⢢⣨⣓⡩⠄⠂⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⡀⠀⠀⠀⠀⠁⢹⡷⢤⣀⡟⢀⣶⣴⣮⢖⡋⠴⠞⠋⠁
⠀⠀⠀⠀⢀⣼⣥⣾⣉⣥⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡿⠊⠉⠉⠋⠀⡀⠀⠈⢀⣤⡀⡿⠛⠛⠛⠻⠾⢽
⠀⠀⠀⠉⠀⠀⠀⠀⣠⣤⣤⠀⠀⢸⠀⠀⠀⠀⣠⡤⢀⡀⠀⠀⠀⠐⣦⠈⠲⠂⢱⣯⡅⠁⠀⠚⠷⣶⣤⣈⡤⠴⠤
⠀⠀⠀⠀⠀⠀⢧⣠⣼⡏⢸⡰⣤⣤⡄⠀⢠⣤⡜⠀⢸⣇⣀⡀⠀⠀⠈⠳⠒⠚⠛⠉⠻⣦⣄⡀⣼⠏⡁⠉⠀⠀⠀⠀⠀⠠⠉⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠱⠘⠺⠇⢀⡤⠊⠔⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡶⡀⠀⠀⠀⠙⠛⠧⣄⣀⣀⠈⠉⠛⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡄⠰⡀⠀⠀⠠⠤⠔⢊⢆⠞⠀⢰⠀⣀⠀⠀⢀⣎⡗⠐⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋
⠀⠀⠀⢀⣄⡄⠀⠀⡇⠁⠻⣄⡈⠲⠤⠄⠠⠼⣫⠞⢸⡆⠈⣇⠉⠀⠠⠞⠾⣇⠀⢰
⠀⠀⠀⠼⢉⠃⠀⠀⡧⠀⠀⡏⠃⢰⣶⣶⡆⠀⣏⡀⣸⠁⠀⠘⣆⢠⢠⠀⢠⡙⢧⣤⠀⠀⠀⣀⡤
⠀⠀⠀⠀⣾⡆⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⡃⠀⠈⠁⠀⠀⠀⠀⠀⠙⠳⢴⢷⣿⠶⠀⠀⠀⣺⠁⠀⠀⠀⠀⠀⣠⢀⣄⠀⣀⣄⣢⡄
⠀⠀⠀⠀⠞⡉⠂⢧⡀⢄⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⣿⡉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠞⢁⡉⠢⡽⠂⡄⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢤⣉⠘⢻⠿⠁⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⠂⠢⠀⢂⣸⠃
⠀⠀⠀⠀⠐⠛⠛⠶⠁⠀⡥⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⡤⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠹⢦⣬⣤⡴⠃
⠀⠀⠀⠀⠀⡀⠀⡘⣦⣼⠃⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⢎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡀⠀⠀⠀⠀⠀⠘⣿⠾⠃
⠀⠀⠀⠀⠀⡁⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠁⠀⠀⢀⣘⢾⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢋⣥⣴⡀⠀⠀⠀⠀⠀⢹⠃
⠀⠀⠀⠀⣴⡁⡐⢤⣤⣿⡷⠄⠀⢸⠀⠀⠀⠀⠀⣴⠟⡛⠲⠿⢿⣿⣷⣄⠀⢀⡠⠊⠁⠒⣈⣉⣉⣙⣃⠀⠀⠀⠀⢖⡫⠘⣖⠂
⠀⠀⠀⠀⠁⠛⠛⢃⣬⠏⠀⠀⠀⢸⠀⠀⡆⠀⣰⣿⣷⣿⣭⣭⠭⢽⣶⢭⣵⣆⣤⣴⣶⣿⣿⣿⣷⣾⣿⣧⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠸⢂⠄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠄⠒⠑⣆⡞⠀⠀⠨⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠢⢄⡠⢿⠀⠀⠀⠀⠙⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠀⠀⠘⠄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⠀⠈⢎⠂⠀⠉⠲⣄⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⢧⠀⣦⡃⠀⠀⠀⠈⢣⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⡀⠠⠄⢠⠜⠀⡇⠑⠐⠂⠀⠀⠀⢳⡀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠘⠡⠈⠢⠒⠁⠀⠀⠘⢆⠀⠀⠄⠀⠀⠀⢳⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠎⢰⢰⡸⡀⠀⠀⠀⢷⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⢸⠀⢇⢧⠀⠀⠀⢸⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⠆⠀⠀⡇⢣⠀⠀⠀⠀⢻⣸⠀⢸⡸⡄⠀⠀⠀⣷⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠸⡀⠀⠀⠃⠘⡄⠀⠀⠀⣼⡿⠀⠀⣇⢧⠀⠀⢀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢧⠀⡠⠊⠑⢄⠀⠀⠀⣸⠃⠀⠀⢹⢸⡀⠀⣸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⢧⠳⣄⡀⠈⠀⠢⡄⠃⡀⠀⠀⠘⡎⡇⢀⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠳⣄⠢⣔⠒⠉⢀⠠⠈⠐⣄⠀⢇⢧⣼⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠳⣄⠀⠀⠀⠙⠺⢤⣄⣀⣀⣀⡀⠇⠀⢈⣼⠏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠈⠳⣤⡀⠀⠀⠀⠈⠀⠀⠀⣀⣠⠴⠟⠁⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠙⠂⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠢⡄⠐⠒⠒⠊⠥⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠰⠊⢀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠑⢄⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠰⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠂⠁⢨⠉⠢⠔⠸⡑⠤⡀⢀⡀⠀⠀⠀⢀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⣼⠀⠀⠀⠀⢣⠀⠀⠁⣀⠉⠉⠈⢁⣂⣸⣄
⠀⠀⠀⠀⠀⠀⣇⡄⠀⣄⠈⡄⣀⠀⠀⢸⣀⣤⠖⠒⠒⢶⢺⠁⢠⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠈⠁⠐⢆⡎⠑⠊⠀⠘⣄⣈⣠⢏⢀⠑⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⠀⠀⠀⢉⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠍⣟⠈⣜⢙⣝⠀⠀⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠛⢏⠈⣯⢡⡤⢳⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠢⣀⠀⠀⠀⠁⠀⠀⡄⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡗⠢⠤⢀⡀⣤⠿⠋⠀⠣⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠐⢃⠀⠀⠀⠀⠘⡂⠀⠀⢸⢻
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠀⠀⢀⠃⠀⠀⠈⢸⠀⠀⠀⠀⠀⢹⡖⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠢⢤⡀⠤⠴⢦⠄⠐⡖⠉⠁⠀⠀⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡠⢔⠁⠣⢄⣀⠞⠠⠤⣃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⡌⠀⠀⢰⠒⠀⢾⠁⠲⡈⡉⠓⠄⠀⠔⠁⠀⠈⠢
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⡀⢃⠀⠀⠀⠓⠀⠊⢆⠀⠀⠀⠀⡸⠰⠀⠀⠀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠀⠈⠢⡀⠀⠀⠀⢀⠜⠂⠀⠐⠈⠀⠀⠂⢄⣀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⡿⠿⢛⣫⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⢿⣿⣿⠿⢛⣋⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣶⣤⣍⣙⠛⠿⢿⡿⠿⠛⣋⣩⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡃⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣿⡇⢉⣛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣛⣉⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣉⠸⣿⡇⢸⣿⣿⣿⣶⣬⣉⠻⢿⡿⠟⣉⣥⣶⣿⣿⣿⣿⠿⠛⠉⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢶⣶⣶⣦⣤⣉⡙⠛⠿⢿⣿⣦⣴⣿⣿⣿⡿⠟⠋⠁⢀⣠⣴⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⣤⣉⡙⠻⠿⢿⣿⣶⣶⣬⣍⡙⠛⠉⠁⣀⣤⡶⠾⠛⠉⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣉⠛⠻⠿⣿⣿⣶⣦⣬⣉⡛⠻⠿⣿⣤⡶⠟⠋⣥⣶⣿⣦⠶⠟⠋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣷⣶⣤⣌⣉⠛⠻⠿⣿⣿⣶⣦⠀⣀⣠⣶⠶⠛⣿⣿⣧⣠⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣶⣦⣬⣉⡛⠛⠋⠁⢀⣠⣴⠽⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣤⡶⠟⠋⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠑⠢⡄⠀⠀⠀⢀⡔⢁⣤⠾⠋⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⣤⣾⣿⣿⣿⣿⠆⠀⠀⢸⠿⠋⣁⣄⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠂⠀⠀⢠⠎⠀⢠⣶⡿⠀⠀⠀⠀⣠⠀⠀⠀⠉⠒⠉⠀⠀⠑⣄⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠉⠃⠄⢠⠃⠀⣴⠾⠋⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⠋⠳⣄⠀⠀⠀⠳⡀⠀⠀⠐⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⢀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠿⠋⡴⢚⠃⠉⠑⠂⠄⣱⡀⠀⠀⠌⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢦⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣤⡀⢤⠀⠈⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⠀⢀⠄⠀⠀⠀⠀⠀⢻⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠏⠀⠀⠀⠇⠤⠤⠄⠀⠀⢊⡡⠊⠀⠶⠀⠠⠤⠠⠴⢋⡀⠁⠀⠀⢀⠂⠀⠀⠀⠀⠀⡇⠀⡀⠈⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⡰⠛⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢰⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠳⡀⠀⢸⠁⠀⠀⣠⢀⡴⠋⠉⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢀⠎⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠈⠲⢌⣓⡒⠲⢷⡁⠀⠀⠀⠘⠀⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⣠⠉⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⠦⡀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠙⣦⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⢀⡠⠚⡇⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠲⠶⠀⠀⠀⠀⠀⢶⠚⠛⠛⠉⠁⠀⠀⠀⠀⢀⡠⠔⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡄⠀⠀⠀⠀⣀⠤⠔⠊⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⢚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⣀⣿⠀⣆⠀⠘⡄⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠀⢧⠀⠈⡇⠀⢹⠁⠀⣰⠁⣠⠤⠤⢄⡀⢀⡇⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣤⢀⡈⢣⠈⢳⡀⢱⠀⢸⠀⡔⠁⡞⢀⡀⣤⠀⠙⣾⠀⠀⠀⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠻⠉⢹⠀⡸⠀⠀⡷⢺⠆⢺⠶⠁⠀⡇⢈⠋⢙⠞⢀⡇⠀⠀⣸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢳⣈⣄⡇⠀⠀⣏⣡⠖⢁⣴⠀⠀⢹⣸⢀⡎⡤⢺⠁⠀⣰⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⡡⢃⣧⠤⠤⠽⢯⣉⡭⠿⠶⠤⣿⡹⡝⢿⣅⣸⡀⣰⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⠙⠯⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠽⠃⠀⣨⡟⠻⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠉⠛⠻⠿⠿⠿⠛⠛⠋⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⣿⡇⢀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢈⡿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠿⠃⣼⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣿⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠁⠀⢠⠇⠀⠑⢦⡀⠀⠀⠀⣀⡤⠞⠁⠀⢹⠀⠀⠉⠉⠙⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣩⠗⠒⠯⣅⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣠⠖⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⢀⡀⠀⢀⣠⠴⠖⢚⠛⠋⠩⠍⢁⠐⠂⠤⢀⠀⠀⡠⠤⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⣀⢼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠑⠂⢄⡀⠉⠢⢄⣀⡀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⡌⠀⠀⡔⠈⢀⠊⠀⢰⠙⣆⠉⠒⠠⢀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠈⠐⠤⣀⠉⠢⢑⠀⠀⠀⢂
⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⡰⠁⠀⢀⠄⠀⠈⡳⣄⢀⠀⠈⠐⠀⠀⠄⢀⡀⠀⠈⠁⠂⠀⠀⣈⣤⠶⣿⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡔⠀⠀⡠⠊⠀⡠⠊⠀⠀⠉⠪⠁⠒⠠⠤⠀⢀⡀⠉⠉⠄⠹⠟⠋⣠⡴⣂⣽⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⢴⣉⣀⠔⠈⣀⠴⠎⠠⠀⠀⢀⣠⠖⠒⠠⠛⠒⢦⠤⠶⠶⠤⠒⠲⠂⣉⠈⢀⣈⣹⠂⠀⠘
⠀⠀⠀⠀⠀⡆⠀⠀⡌⢡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣭⠜⡋⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢀⠁⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠃⠀⠀⠆
⠀⠀⠀⣠⠂⠀⠀⠌⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠐⡀⠀⠘⡄
⡔⠂⠈⠀⠀⡠⠊⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠑⠄⠀⠈⠑⠂
⠈⠐⠒⠂⠉⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⣀⣄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢄⡀⠀⠌⠄⠲⡁⠀⠈⠙⠢⢌⣁⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣍⡉⠌⠀⠀⠀⠉⠒⠄⡀⠀⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡾⡄⠀⢀⡀⠀⠀⠠⠄⡀⢀⠁⠂⠞⢢⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡐⢠⣡⠔⠉⢸⠀⠀⡄⠂⣹⡇⠑⠄⣠⡳⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠉⠁⠏⠀⠀⠀⠀⣀⣤⣈⣏⡐⠁⠀⠀⠀⢑⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠤⣣⣤⡄⠀⠀⠀⠀⠸⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⣀⠰⠄⣀⠀⠀⠰⠆⠛⠠⠆⠀⠀⣀⣠⣁⡀⣀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⠦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⡚⠛⠳⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡀⠉⠒⠤⣀⠀⠀⠀⠀⠀⡘⠌⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⠀⡟⠀⢔⠒⢽⠲⣤⢄⣘⡬⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⢻⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⢰⠊⡦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠳⣦⣴⣾⣻⢀⡀⠄⣀⢾⠀⢸⠀⢸⠂⠀⠀⢀⣀⣀⣎⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠁⠀⠀⠈⠀⢸⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠢⣀⣀⣀⡠⠂⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠐⢄⣀⣀⣀⠌⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⢔⣒⣒⣶⣶⠶⠖⣾⠲⠞⣓⣛⣛⣒⣶⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡋⠉⠓⠒⠂⠉⡡⣏⢌⠋⠉⠀⠀⠉⠙⣠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠂⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠒⠒⣒⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠉⠀⠀⠀⣀⢀⣤⣤⣶⡶⠶⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠉⣠⡶⢲⣶⠷⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣞⠏⠋
⠀⠀⠀⠀⠀⠀⠀⢴⣶⣴⣶⣶⣶⡿⠤⠾⠷⠶⣄⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡇⠀⢠⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡇⠀⠀⢧⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁⠉⠁⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠑⣦⡉⠻⣿⣿⡟⠋⠉⠉⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⠶⡖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⠙⢦⡈⠻⠁⠀⠁⣶⣶⠾⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠒⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⡟⠀⢀⣿⣷⣄⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠤⠤⣀⣛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢠⡞⢻⠇⠀⣼⢫⣽⣿⣿⣦⣘⣂⣤⣤⣤⣤⣤⣬⣿⣷⣶⣶⣚⣿⣿⠟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⣿⣿⠀⣠⣿⡾⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣹⣿⠀⠻⠿⢤⣤⣤⣀⣀⣀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣳⣄⣀⡸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢴⣾⣿⣿⠶⠒⠒⠒⠒⠒⠀⠈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠏⠀⠻⠟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠤⣀⣀⣊⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣖⣻⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⢟⡭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣋⣉⣀⣤⡤⠤⠴⠶⠶⠒⠒⠒⠒⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣵⣷⣾⣷⡝⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⠋⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡔⣬⣭⢆⣤⣤⣤⡀⢸⣿⣿⣿⣿⣿⣿⠿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢿⣎⢫⣾⠿⠿⣿⣿⡜⣿⣿⣿⣿⠿⠏⣾⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⠻⣿⣿⡸⢟⣫⣶⣷⡕⢉⢡⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢸⣿⣿⣿⠀⢹⣿⣿⣿⣿⠿⠋⠁⠈⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢸⣿⣿⣿⠀⠀⠉⠛⠛⠁⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⢠⣤⣤⣴⣿⣿⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠉⠛




⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣿⣛⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠸⣿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣻⣵⢟⣛⣾⣽⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣮⣭⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⣦⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣇⠈⠿⠿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣌⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⡛⢩⠟⠉⠉⢻⣿⡿⠿⣿⣿⠟⢿⣿⣿⣿⣿⣿⠋⣤⢹⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠗⣸⣿⣿⣿⣿⣿⠀⠀⢀⣾⡿⠀⠀⠈⡷⠀⣸⣿⠾⡿⣿⣿⣷⣴⣾⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⡟⠉⠉⢿⣷⣦⣾⣿⣴⣾⣶⣾⣷⣾⠿⠃⢀⠴⢊⣽⣿⣿⡿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣁⣀⠴⠚⠻⣿⣿⣿⣿⣿⣿⣦⣤⣤⠶⠛⠛⠛⢩⣿⣿⣿⡑⢆⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠁⠉⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣾⣿⣿⣿⣶⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠞⠛⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠛⠻⠿⡦

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠀⠉⠁
⡇⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⡇
⡇⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠉⠁⠀⠈⠁
⡇⠀⠀⠀⠀⠀⠘⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣇⣀⣀⡤⠴⠦⢄⡀
⡇⠀⠀⠀⠉⠳⢦⣼⠿⣷⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠉⠁⠀⡏⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⡆⣼⡖
⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣴⣿⣶⣶⡿⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⠀⠀⠀⠀⢀⣸⣿⣾⣿⣿⣷⣿⣀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⣿⣿⣿⣿⣇⠐⠀⠀⠀⠀⠀⡄⠀⡇⡜⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⠥
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣂⣧⠤⠵⠦⠤⢀⣤⣤⡮⠬⠟⢨⠟⡿⡟⢻⡅
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⣆⢀⡀⣰⠀⡤⠒⠀⠀⠒⣄⠀⡆⠀⠀⠐⢄⡠⠖⠀⠀⠀⢦⠀⣠⢦⡀⣰⠂⢰⡂⣀⡀⢰⡆⡀⡀⢰⣆⠄⠂⠀⢸
⠀⠀⠇⠀⠀⠸⠀⠙⠂⠤⠤⠐⠋⠀⠇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠛⠁⠀⠙⠃⠀⠸⠤⠄⠀⠘⠇⠄⠄⠘⠃⠑⠢⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠐⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣠⠁⡞⠀⠀⡴⠚⠉⢳⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣝⠸⠇⠀⢸⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠧⢠⡔⠁
⠀⠀⠀⠀⠀⢂⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠉⠢⡀⠧⡄⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠃⠈⠁⠀⠀⠀⠀⠀⡀⢶⣿⢟⣧⡦⡀⠀⠠⠃⠀⢐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡑⢯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⢁⠀⠀⠄⠀⠀⡀⠀⢠⣀
⠀⠀⡞⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢂⠄⠀⠀⠉⠂⠈⠀⢀⠀⠀⠀⠁⠐⠀⠀⠁⢀⠀⠀⠀⠠⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠈⠀⠀⠀⠂⠠⡔⠀⠀⠀⠀⠁⠀⠀⣠⠀⠀⠐⠀⠀⠀⠀⠁⠐⠊⠀⠀⠀⠀⠪⢤⣀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⡤⣄⡀⠀⠐⠱⡄⠀⠘⠋
⠀⠀⠪⠀⢠⠭⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠐⠉⠓⡂
⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⣤⠆⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠌⠐⠄⠀⠄⠁⠀⠀⠁⠀⠀⡀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀
⠀⢂⢠⠤⠔⠊⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠐⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠂⠀⠀⠀⠀⠇⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠄
⠀⠀⡠⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⠤⠗⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠫⠨⠁⠀⠀⠀⠘⠤⠋⠀⠀⠀⢀⠀⡇
⠀⠀⡀⠀⠀⠀⠠⡀⠀⠈⠓⢄⣠⠞⠁⠀⣀⡄⠀⠀⠀⡤⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⡂⠀⠠⠀⢀⡜⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠋⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠺⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣀⣀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡞⣩⡍⢳⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢺⡀⠀⠳⢥⡤⠟⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠁⠀⢣⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡧⣼⣿⡧⡉⠁⢩⡅
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡙⢰⣿⠟⢹⡜⠀⡲⠁
⠀⠀⠀⠀⠀⠀⡿⢟⣵⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠿⢋⠔⠿⠒⠉⠀⣀⠠⠄⠐⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠙⣟⠵⡉⢢⠣⡀⠀⣀⠀⠀⠀⠀⢀⡌⢀⠔⠁⠀⣠⠔⠂⠉⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡑⢄⠑⡌⢾⡇⠀⠀⠀⠀⠰⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠣⡈⠢⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡜⢄⠑⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠱⡀⠢⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢌⢦⠔⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠑⠤⡀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠄⠠⠾⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠒⠈⠁⠀⠀⠉⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠟⠻⠉⠉⡿⢻⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠙⠃

⠀⠀⠀⠀⠀⠀⠐⢶⢶⡶⠶⡶⠀⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡤⠤⣀⣀⡠⠤⢄⠀⠀⠀⠸⣵⠤⠤⠒⠉⢄
⠀⠀⠀⠀⠒⠀⠀⢈⡖⠀⠀⡇⠀⠈⠀⠀⠀⠀⢠⠋⠑⢦⠒⠀⠀⠀⠀⣆⣀⣨⣟⣦⡀⠈⡆⠀⡠⠔⠁⠀⢠⠊⢱⡄
⠀⠀⠀⠀⠀⠚⠀⣼⣀⠀⠀⡇⠈⠃⠀⡀⣀⣴⡿⡆⠀⠀⣡⠀⠀⠠⡊⠉⢣⡏⠀⢀⡙⢯⡟⠲⢶⡄⠀⠀⣈⠒⠐⢁⡀
⠀⠀⠀⠀⠀⠀⡰⠁⢩⠀⠀⠸⡀⠀⢞⢉⡟⠁⠀⠱⣶⣾⣧⠀⠀⠀⠙⠲⣤⣑⢄⡘⠋⢘⠿⡀⠀⡸⠀⠘⠼⢃⡴⢋⡿
⠀⠀⠀⢠⡤⢰⣧⣴⣿⣶⣾⣷⣷⡀⠀⢿⠹⡄⠀⠀⣸⣭⡅⠀⠀⠀⠀⠲⡌⣇⠈⠉⢳⢟⣉⡿⠁⠀⠈⠀⣠⢊⡴⠋
⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⠹⡀⢸⣄⠹⣄⣄⣒⣒⣚⣣⡀⠀⠐⠶⡁⠈⠒⠚⠁⠀⢀⣀⣀⣀⣤⣾⡴⠋⠠⠒⣶⢤
⠀⠀⠀⠀⠘⢌⡻⠿⠿⠿⠿⢛⣋⠴⠧⠼⡏⠉⠩⠍⠉⠉⠉⠅⡵⠀⠀⠀⠀⠀⠀⠀⣰⡾⢓⣀⡒⠪⡙⢿⠀⠀⢰⠀⣿⢦
⠀⠀⠀⠀⡴⣦⠀⠁⠀⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠈⠉⡉⠉⠁⠀⠀⠲⡿⠀⠀⢸⠋⣜⢁⢍⢨⢆⢹⠀⢇⠀⢸⠀⡾⠦
⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠃⠀⣀⠀⡀⠀⡐⡀⠀⠀⠐⠉⠙⠂⠚⠀⠀⠀⠀⠀⠀⢸⡀⠻⣠⡍⣈⠎⡜⠀⡅⠀⢸⢐⣾⠂
⠀⠀⠀⠀⠸⠇⡴⠋⠉⢳⡀⠀⠉⠙⠙⠂⠁⠀⠀⠀⠐⠉⠑⠢⠒⠁⠀⢠⢤⣂⢰⡄⠣⣤⡀⡩⠀⢊⡠⠊⠀⠀⠸⠼⠏
⠀⠀⠀⠀⠀⠀⣇⠁⠀⠀⠁⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢠⡖⢒⠒⠒
⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⠀⠀⣠⢞⠛⠓⣆⠀⠀⣶⠈⠙⠀⡶⠶⠶⠆⠈⢀⡀⠀⠀⢠⡀⠀⣠⠤⢤⡒⠀⢸⣇⣀⣒⡀
⠀⠀⠀⠀⠀⢦⡀⠀⠀⢸⡇⢰⡇⠀⠀⠀⠘⠀⠀⣿⠀⠀⠀⡏⣀⠀⠀⠀⢸⢻⡄⠀⣾⠁⣸⠣⠈⠘⠃⠀⢸⡏⠉
⠀⠀⠀⠀⠀⢈⠳⠶⠶⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⡗⠒⠒⠂⠀⣾⢂⢳⡐⣿⠀⣿⠀⠀⠀⠀⠀⠸⣧⡶⠶⠶
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡘⣇⠀⠀⠄⣀⠀⠀⣿⠃⠰⠀⡿⢀⣀⣀⢀⡏⠀⠊⢷⡇⠀⠻⣌⣀⣬⠞⠁⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠚⠋⠁⠀⠐⠛⠀⠀⠀⠉⠉⠉⢉⠀⠀⠀⠀⠀⠀⢀⢀⣀⣁⠀⠀⢀⡤⢒⣉⠑⢦⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⡄⠀⠀⢠⡆⠀⢶⠦⡀⢠⡤⣀⡀⢠⠃⡤⡦⡤⡆⠀⠀⠓⠚⠉⠒⠁⣴⣉⠔⠉⠈⢣⠀⡇⠀⡀
⠀⠀⠀⠀⠐⠿⠂⣠⠤⡀⢀⡬⡋⠀⣠⣄⠀⠀⠀⠑⣤⠋⠀⠀⠈⠉⠒⣤⠀⠀⠀⠀⠠⡇⠐⢂⣇⡼⠛⠋⠀⠀⣠⠃⢨⠃⣾⡿
⠀⠀⠀⠀⢀⣀⣀⣯⣩⣧⢼⡭⣧⢤⣯⣽⣠⡀⠀⣴⠁⠊⠀⠀⡈⠀⠀⠀⠀⢷⣾⠃⢀⡙⢦⣰⢣⠀⠀⠀⠀⢘⠻⠷⢡⣄⡏
⠀⠀⠀⠀⠈⣿⡗⢺⠒⡟⢻⣋⡏⠉⣏⣻⡏⠁⠀⠈⢆⠀⠀⠁⠀⠀⠀⢰⠀⠀⠁⠀⢈⡴⠋⠈⠓⢤⡀⠀⠀⠚⠀⠀⠈⢻⣷⠆
⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⢸⣿⡇⠀⣿⣿⡇⠀⢀⡤⠊⠑⣄⣀⠨⠥⠄⠾⠀⠀⡀⣰⠃⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠸⣦⣞⡁
⠀⠀⠀⠀⢀⣿⡇⢸⣿⣃⣘⣛⣃⣀⣛⣿⣇⣀⢠⣀⡄⣄⠉⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠏⠃⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠷⠿⠾⠶⠗⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⡠⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠁⠀⠀⡇⠀⠀⠀⢀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⢤⠧⠤⢼⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠃⠀⠐⠆⢠⠟⠀⠀⠸⣄⠀⠀⡘⠀⠀⠎⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢸⠀⠀⠀⣴⠃⠾⠀⠀⠀⡍⢦⠀⠇⠀⠐⠆⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢸⠀⠀⢀⡅⠀⢸⠀⠀⠠⡇⠈⠿⠀⠀⠀⣁⠊⠀⣠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠒⠂⠷⠀⠀⠀⠀⠀⡇⠀⡄⠀⣀⣠⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⣤⠀⠀⠀⠀⠀⠇⢠⠁⠐⠰⠹⠀⢀⠀⠠⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⢤⡀⠀⠀⠀⠀⠀⢀⡾⠈⢂⠀⢛⢀⡇⠀⠀⢀⢀⡏⠀⡰⢁⠻⣄⠆⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⣄⠀⠀⠐⢠⠎⢰⠀⠀⢫⠉⠉⠀⠀⠉⠉⠋⠀⣔⠀⠎⠀⡜⢀⠠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⣸⡀⠀⢠⠋⠀⢸⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠌⠀⠙⠲⠎⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⢆⣰⠃⠀⠀⡜⠀⠀⠀⢀⠵⡴⠶⠶⢦⣮⣄⠀⠀⠀⠀⠀⡾⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢨⢧⡀⢀⣼⠄⠀⠀⣀⣬⡶⠟⢛⡛⢿⣦⣎⡑⠆⠀⠀⠀⡇⠀⠈⢣⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠀⠈⠙⠓⠀⢀⡔⠋⠀⡇⢰⣿⣿⠆⡋⠙⠻⣧⡄⠀⢠⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢶⣶⣭⣥⢶⡷⠖⠚⠁⠀⠀⢸⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⢄⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡑⠛⠒⠟⠘⢇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠁⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡆⠢⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠌⠀⠀⠀⠀⡀⠀⠀⠀⠹⠀⠁⣰⠃⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠞⠁⠀⢀⣠⠞⣀⠀⠀⠀⠀⠀⢰⠓⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⡇⠛⠋⠉⠀⠈⠩⠥⢄⣀⡉⢉⣹⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡩⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢻⠉⠉⠉⢍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⢺⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡗⠒⠒⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⣻⡿⠛⠋⢩⡏⠙⠛⢿⣿⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠉⠁⢀⡾⠁⠀⡀⠀⢸⣇⠀⢀⡀⠈⢷⡀⠈⠉⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⣶⣤⣀⣾⠁⠀⠀⠹⣷⣾⣿⣶⠏⠀⠀⠈⣷⣀⣤⣶⣿⣿⠿⣿⣦⡀
⠀⠀⠀⠀⣰⣿⣿⣁⣀⣀⣈⣙⣛⢿⣿⠒⠚⠻⠿⣿⣿⣿⣿⠿⠿⠖⠒⣿⡿⣛⣉⣁⣀⣀⣈⣿⣿⣆
⠀⠀⠀⣼⣿⠟⠛⠛⠛⠛⠛⣛⣉⣭⣿⡀⠀⢀⡼⠛⢻⡿⠻⢧⠀⠀⢀⣿⣭⣙⣛⠛⠛⠛⠛⠛⠻⣿⣧
⠀⠀⣼⣿⣏⣤⣤⣶⣶⣿⠿⠛⣋⣥⡾⣿⣄⠀⠀⠀⢸⡇⠀⠀⠀⣠⣿⢷⣬⣙⠛⠿⣿⣶⣶⣤⣤⣹⣿⣧
⠀⢰⣿⣿⡿⠿⠛⠉⢁⣠⣴⡿⠟⣩⣾⠟⣻⣿⣶⣤⣼⣥⣤⣶⣿⣟⠻⣶⣝⠻⣿⣦⣄⡈⠉⠛⠿⢿⣿⣿⡆
⠀⣿⣿⠁⠀⣀⣤⣾⡿⠟⠋⣠⣾⡿⢋⣼⣿⣿⢁⣸⣿⣿⣅⡈⣿⣿⣧⡙⢿⣷⣄⠙⠻⣿⣷⣤⣀⠀⠈⣿⣿
⢰⣿⣧⣴⣿⣿⠟⠋⢀⣤⣾⡿⠋⢠⣾⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣷⡀⠙⢿⣷⣤⡀⠙⠻⣿⣿⣦⣼⣿
⢸⣿⣿⠟⠋⠀⢀⣴⣿⡿⠋⠀⣰⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡄⠀⠙⢿⣿⣦⡀⠀⠙⠻⣿⣿
⠸⣿⡇⠀⢀⣴⣿⡿⠋⠀⠀⣰⣿⣿⣿⠟⢁⣤⣶⣿⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠀⠀⠙⢿⣿⣦⡀⠀⢸⣿
⠀⣿⣿⣾⣿⣿⠏⠀⠀⢀⣴⣿⣿⠛⢁⣴⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣦⠀⠀⠀⠹⣿⣿⣷⣿⣿
⠀⢸⣿⣿⠟⠁⠀⢀⣴⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⣷⣤⡀⣶⣿⣦⣀⠀⠀⠀⢻⣿⣿⣷⣦⡀⠀⠈⠻⣿⣿⡏
⠀⠀⢻⣿⡄⢀⣴⣿⠟⠉⣿⣿⡇⢸⣿⣿⣿⡿⣿⣿⠇⠀⠈⠛⣿⣿⣷⣄⠀⢸⣿⣿⠉⠻⣿⣦⡀⢠⣿⡟
⠀⠀⠀⢻⣿⣿⠋⠀⠀⠀⠸⣿⡇⢸⣿⣿⣿⡇⠈⠁⠀⠀⠰⣶⣿⣿⣿⣿⡇⢸⣿⠇⠀⠀⠀⠙⣿⣿⡟
⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⢻⣿⠘⣿⣿⣿⣇⠀⢀⣤⣤⣄⠻⠟⣿⣿⣿⠇⣿⡟⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⢸⣿⡄⣿⣿⣿⣿⡄⢿⣿⣹⣿⠇⣴⣿⣿⣟⢰⣿⡇⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢈⡿⢻⡏⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣻⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⠤⢤⣄⡀⣀⡀⣀⡤⣴⢂⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣤⡴⣂⡈⠉⠉⠉⠀⢤⠀⠁⠉⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠱⠀⠀⠀⠙⣶⢤⡴⠶⠦⠤⢤⣀⡀⡸⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⢉⡴⠃⠸⡅⠀⠀⣀⠀⢹⠿⡷⠄⠀⠀⣀⣴⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠉⠉⣄⠀⠀⣳⣄⣀⣀⣠⠏⠀⢇⣠⠴⠋⣉⢼⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠⡄⠀⠀⠀⠀⠑⠦⣈⡛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣊⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣰⡻⣄⡀⠀⠀⠀⠀⠀⡴⠛⢳⡶⠒⠲⢶⠖⢛⠏⢍⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣯⠱⡄⢙⠒⠤⣀⣀⠔⢃⠀⢸⠈⠁⢉⠋⣴⠊⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡵⠠⣄⡼⠀⠀⠈⠁⠀⣸⠀⡌⠀⠀⠘⢰⢹⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⢣⡀⠀⠀⠀⢀⠙⣠⠁⠀⠀⢰⡆⠀⡄⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⡇⠈⠑⠒⠒⠺⢠⠃⠀⠀⠀⠀⠇⠀⣡⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠤⠚⠢⢄⠀⠀⠀⢀⠎⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡙⠂⢄⣸⠖⠀⠀⠀⡱⠤⠒⠁⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠃⠀⠀⠉⡿⠤⠶⢊⠁⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣡⡏⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⡇⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⡠⠄⠤⠤⡀⠀⠀⠀⣔⢒⣒⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠐⠠⠀⠀⢠⡇⠀⠀⠉⠁⠒⠒⠒⠀⢫⠉⠀⠀⠈⠁⠉⡉⠀⠀⠀⠀⢸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠓⠲⠤⠄⣀⡸⠃⠀⠀⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠈⠀⠀⠂⠀⠠⡇⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⡘⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠑⠦⡤⢄⣀⡠⢴⠀⠈⠉⠓⠲⠤⢤⡄⣀⣀⣀⡇⢠⠊⠀⠀⠀⠀⠈⢂⠀⠠⡁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡆⠀⡎⠁⠀⠈⠈⠐⡆⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠀⠐⠀⠀⠀⠀⠀⠀⢴⠀⡜⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⡃⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠁⠀⠀⠀⠈⠢⡀⠀⠀⢀⡠⠊⠰⠁⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⣶⣶⣶⣾⣶⡷⢷⣾⣾⣿⣶⣿⣿⣿⣶⣷⣶⣿⣷⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⡾⣿⠶⠷⠷⠾⣶⣿⠶⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠜⢉⡙⢳⠉⠀⢀⣀⠐⠀⢄⠀⠁⠲⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢤⡀⠈⣄⡀⠉⠉⠂⠃⡁⠀⠀⠂⢀⠘⠀⣸⡀⠈⠰⠀⡀⠃⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢳⠀⠀⠒⠈⠉⠀⠈⠀⠀⡀⡔⠠⡌⠳⢀⣀⣠⢴⠁⠈⠉⠱⣔⢀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⣀⣄⢠⣀⣂⠌⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⢠⠂⣉⠆⡀⠀⠈⢿⠈⠉⠗⠀⡜⠈⠐⠤⢤⠎⢉⣍⠓⠄
⠀⠀⠐⠃⠉⠀⠈⠉⠙⠦⡘⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠈⠀⠀⠀⠀⠈⠲⠤⠤⠒⠀⠀⠀⠀⠴⠄⠷⠌⠓⠛⠒⢤⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠣
⡆⠀⠀⠀⠀⠀⠀⠀⢠⡆⢰⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠉
⠘⢄⠀⠀⠀⠀⠀⠒⠠⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⠤⠀⠂⠁
⠀⠀⠙⠲⠤⠤⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠐⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠲⢂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠀⠀⠂⠀⡇
⠀⠀⠀⠄⠀⠰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰
⠀⠀⠀⡀
⣀⣀⣀⣈⣀⣀⣀⣀⣀⣲⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠶⠂⠉⠈⢉⠍⢳⡈⠁⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⡔⠉⠳⡀⠠⠆⣄⠀⢐⠹⡉⠉⠉⠉⠈⠁⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠚⠄⢀⠐⠁⢀⡄⠸⠂⠈⢠⣅⣀⠀⣀⣀⣀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⢸⠄⠀⢨⠃⠄⢠⠔⠈⠐⠺⡅⢇⠀⠀⠀⠀⢀⣉⣀⣀⣈⣣⡀
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢿⠀⠀⠃⠀⢆⠙⠀⠀⠀⠀⡟⠊⠀⠈⠈⡉⠀⠉⠉⠋⢉⠜⠑⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⠶⠄⠠⣒⣬⠕⠓⠤⠤⠊⠀⠈⠀⠈⠁⠉⠀⠑⢀⢀⠂⠀⠀⢰⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠣⡠⠖⠉⢦⠀⠀⠀⠑⠀⢀⣳⣀⣠⡀⠈⠠⠄⠸⠏⡄⠀⠀⠀⢇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣤⡀⠓⠢⡀⠠⣄⠀⠀⠈⡍⠁⠀⠒⠒⣼⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠚⠢⠤⢴⠄⠄⠙⢆⠀⠀⢠⠁⠀⠀⠀⠘⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡠⠍⠄⡈⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠝⢠⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⣀⠀⠀⠀⠀⠀⠘⡞⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠥⠌⠓⢜⡆⠀⠀⠀⠀⠀⠇⠀⠀⠆⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⡈⠞⠁⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢌⡯⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⢀⡀⠀⠀⠀⣀⣠⠴⠬⠛⠊⠁