Rosa Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢀⣴⠀⣠⠖⠃⣠⡙⢶⣆⡀⢈⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠨⠉⣤⡭⢾⠟⠛⣿⣿⣯⢻⣾⢟⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⡁⠨⡝⠒⠐⠶⣿⣧⣾⣛⣵⣺⡿⠄⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣾⣿⠀⠀⠀⠰⣤⣨⣝⠻⠦⢴⣶⣶⣦⣼⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⠻⢿⣿⣶⡄⠀⠀⠿⣿⣷⣶⣶⣶⣯⣽⣿⣿⠿⣁⣤⣤⣴⡞⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠗⢲⣬⣿⣷⣦⣴⣶⠶⣽⣿⣿⣷⣶⣿⣿⡿⠿⣿⡳⠘⠿⠦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠈⠋⠺⠟⠁⠀⠉⠿⠟⠋⢻⣿⣿⣷⡀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⣁⠂⠀⠀⠀⠀⢀⡰⣾⣿⣶⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣷⣀⡀⠀⠀⡉⣾⣿⣽⣿⣿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣀⡫⣥⣀⢸⣷⣴⡆⠀⣿⡧⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠿⠻⣿⢛⠟⠢⣝⡇⠋⠉⠀⣀⠀⠀⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡟⠁⠀⣴⣾⣿⡄⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠌⣠⣶⣾⣿⠋⡆⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢰⣿⣿⣿⢈⣀⣿⡿⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⢛⠿⠻⢿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢺⣿⣟⣿⡗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠰⣶⡆⠀⡀⠈⠀⠀⡗⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⡄⠀⠀⡀⣀⠁⢳⢰⡇⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠂⠈⠀⡇⢻⡴⡾⢨⠋⣸⠶⣁⡠⢤⠀⠀⠐⣒⣢⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠐⠤⢢⣼⣾⡄⠷⡀⠅⠀⠋⠀⠈⢻⣭⡤⠟⠹⣄⢳⣀⠊⠉⡀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⠀⠚⠾⠏⠁⠀⠀⠙⠀⠁⠀⠀⠀⠀⠙⠂⠁⠒⠟⢿⣗⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠤⠀⣐⠠⠀⠀⢀⡀⠐⠦⠀⠀⠈⠁⣁⠀⡴⠀⠀⠀⠀⠃⠀⠌⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠰⠽⠙⣷⡟⠋⠐⣲⣟⣓⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⢸⣦⣾⣿⣿⣿⣿⡧⠐⠌⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⠁⠀⠀⠀⢈⣿⣿⣇⣼⡿⠛⠁⠾⡀⠀⠻⠖⠀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠠⠴⢿⣘⠿⠿⣿⣿⠄⠀⡀⠛⠁⢐⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣍⣁⣄⣮⣤⠤⡤⠀⠄⣘⡛⠯⢅⡄⠀⠴⠟⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢩⡿⣧⠇⡐⠃⠀⠀⠀⡀⠀⢠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡟⠥⢀⣠⡴⠞⠁⠀⠀⠀⠀⢀⢐⢙⡀⢀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠐⠋⠁⣀⡠⠤⠆⠐⠦⠂⠀⢻⣾⠟⠓⣠⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢨⣭⣄⠹⣷⣶⡆⢠⣦⠀⡈⠁⠀⠐⠉⠀⠀⡠⠐⠉⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠲⢤⡛⠈⢳⢠⣉⡋⠂⠉⢸⠃⠰⢤⠁⠠⢀⠞⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣂⢯⣀⣎⡸⣅⡑⠀⣸⠃⠀⣥⣼⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠉⠉⠉⠈⠩⠞⠛⢴⠏⢅⣊⡈⢽⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠠⢽⡥⣀⠄⠙⢭⣋⡀⠐⠂⠀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠿⢟⠂⠒⠤⠀⡈⠁⠀⠈⢁⣀⡀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⡷⠃⠀⠀⠀⠀⠁⠉⠀⠉⠐⠐⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢤⣤⣔⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⡖⢠⣶⣿⣿⣷⣶⣿⣶⣦⡐⢦⠘⣿⡖⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢸⡋⠱⣾⠋⣴⣾⡏⠴⠶⠶⣤⠀⣨⢀⣿⠇⠀⠀⢡⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣿⡟⡆⠈⠻⣦⠙⠛⠒⢒⣋⣡⣾⣿⡿⠗⠀⠀⢠⣿⠟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠸⣇⠘⣦⣀⣈⠓⠲⣾⣛⠛⠛⠉⠉⠀⠀⣀⣴⣿⣿⠇⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣌⠳⢮⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠿⢿⣿⣿⠟⠀⣼⡶
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢹⣿⣷⣶⣤⣶⢿⣿⣿⣽⡻⣿⠙⠛⠉⠀⣼⣿⠋⣠⣾⣿⠛⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸⢿⣿⣿⣦⣴⣬⣿⣿⣿⣎⠳⣀⣠⣾⣯⣵⣾⣿⣟⠁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⠟⠉⠋⠉⠋⣹⢇⣿⡿⠃
⠀⠀⠀⠀⠀⢀⡄⠀⠻⣿⣷⣴⣤⣤⣶⣶⣶⣶⣿⣿⣇⢦⡀⠀⠀⠀⢁⣼⠟⠁⠀⠀⡔
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠹⣿⣿⣿⣿⣦⣶⣽⣿⣿⣿⣆⢰⣮⡤⠔⠋⠁⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠈⠙⢻⠿⠿⠛⠛⠻⠿⠛⠛⢋⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣴⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠉⢹⠏⠀⣿⣿⣿⣿⣿⡟⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢁⣬⣿⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠘⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣤⣶⣶⣶⣄⣀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣾⣷⣧⣷⣹⡿⢷⡀⣷⠀⠀⢀⣤⣶⣾⣿⣿⠿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⣣⣛⣯⢀⣴⣿⠿⢿⣛⣯⣤⣛⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⣿⠎⣩⣶⣿⣿⣿⣮⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠻⠟⠛⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⢋⣭⡀⠁⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢙⡛⢂⣶⠟⠋⣰⡀⠀⠀⠁⢠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⣰⣷⢮⣄⠐⠒⠁⢰⠄⢸⠀⠀⡈⠃⢀⠀⠀⠙⠳⣤⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣹⣦⣴⣯⣿⠙⠋⠛⠋⢂⠲⠀⠀⣾⡆⠀⠰⡄⢈⠀⢀⠀⢰⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⡇⠀⠀⠀⣂⠒⠀⠀⠀⠹⣷⠀⠀⢱⣼⣴⡞⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⡀⠈⠻⣿⠁⠀⠀⠀⠈⠀⠀⢰⠀⠀⢻⣇⠀⠈⣿⡿⠃⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣶⣷⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⣿⣆⠀⠻⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⣤⣖⡐⢎⡉⠓⠈⠛⡿⣟⡘⢷⣄⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⣸⣿⣶⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⣟⢂⡀⠀⠈⢻⣿⣿⡇⠀⠀⠸⣧⠈⢀⠀⠀⠀⠀⠀⠰⣾⡿⠁⡜⢫⡿⢿⡿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠻⠦⣀⣿⣀⣀⠤⣡⣹⡿⠁⣼⣷⣼⣹⡾⠛⠁⠀⣀⠀⣠⣀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠻⠟⠀⣜⣽⠿⡿⡜⢡⣦⣾⠞⠛⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣦⣵⡹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡃⢠⣄⡴⢴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣸⠿⠏⠙⠚⠻⢟⣩⣗⣶⣤⣤⣀⣀⣀⠀⠀⠐⣴⠋⡾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢂⠽⣿⠟⠉⠀⢻⡏⣿⠿⠀⠀⠀⠇⠈⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠐⡇⠀⠀⠐⠊⣁⡷⠀⠀⠀⠀⠀⠂⠢⠌⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣀⡀⢀⣠⠄⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⠃⣀⣀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠁⠀⣄⣰⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠊⠀⠂⠂⢀⠀⠀⠀⡇⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠙⠀⠐⠦⣄⠀⢈⠁⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠄⠻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠇⠀⠀⠀⠀⠀⣾⣅⣴⢏⣀⣿⣧⠈⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⢻⡋⣟⢲⣄⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⣠⠀⠀⠀⣸⣏⣦⣻⠛⢻⣿⢶⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣶⠿⣿⣿⣦⠀⠀⢡⡮⣿⠋⠂⢀⣼⡇⠀⠀⣠⣿⠏⠀⠀⠀⠀⣿⣳⣷⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⣩⣌⠉⢰⣷⣼⣣⣿⠈⢠⣿⣿⡇⠀⠀⢹⣿⡄⠀⠀⠀⢰⣵⣿⣽⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⢰⣟⡛⢿⣧⠈⣿⣿⡿⡏⠀⠸⣿⠟⠀⠀⠀⠸⣿⣧⣤⣀⣼⣿⣿⡿⠥
⠀⠀⠀⠀⠀⠀⠀⠘⠁⣠⣶⢶⡆⢿⣿⣄⡈⢿⣆⠉⢁⣀⡇⠀⢸⡏⠀⠀⠀⠀⠀⣹⠿⣯⣽⣿⠿⠋⠀⣠
⠀⠀⠀⠀⠀⠀⢀⣄⣚⠛⠻⠸⡇⣸⣿⣿⣿⣷⣿⡆⢿⣯⣿⣰⣾⠀⠀⠀⠀⠀⡾⠚⣿⠿⠋⣠⣶⣶⣿⣧⣴⣶⡞
⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠀⢺⣧⠉⣿⣿⡽⢿⣿⣿⠚⠛⢿⠿⡟⠃⠀⠀⠀⢸⡇⣼⠃⠀⢠⣿⣿⣿⣟⣿⣿⣿⡿
⠀⠀⠀⢀⣀⣀⠀⢸⠄⠀⠀⠀⡹⣟⠷⣿⣳⣾⣿⡇⢀⣷⢸⡆⡇⠀⠀⠀⠀⠀⣰⠃⠀⣠⣿⡟⣿⣿⣿⢿⣿⣿⠁
⠀⠀⠀⠋⢻⣁⠀⠀⠀⠒⢢⣴⡾⣿⣦⣻⡿⠟⠋⣀⠀⢤⣾⣿⣷⣶⣶⣄⡀⢠⡏⠀⣼⣿⣿⣿⣿⣿⡿⣈⡽⠂
⠀⠀⠀⠀⠀⠛⠿⠿⢿⣖⣀⣈⠙⠻⡟⢋⣀⣾⣿⠛⢆⠘⣿⣿⣿⣿⣿⣿⣿⣯⢀⠞⢸⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⡿⠙⡟⠻⣆⠈⠆⠸⣿⣿⣿⣿⣿⣿⣿⡇⢀⣬⣿⣿⣯⣉⣥⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⢅⡀⠲⣎⡗⠀⠁⠀⠳⠀⠹⡆⠀⠀⢸⡯⠙⠛⠻⠿⠿⠴⠿⠿⠟⠓⢿⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⡔⢋⣵⡆⣀⡜⠂⣨⣿⣿⡆⢠⡄⢀⣄⣿⣶⠟⡙⢷⡶⠆⢀⣀⢲⡶⢶⣦⡰⡞⢹⣿⣿⣿⣿⣿⣧
⠀⠜⠀⠀⠠⡙⢾⣭⡗⠩⠐⠿⠃⣄⣿⣧⠀⠿⠄⠹⠟⢡⣾⡇⠀⠀⠀⢉⣉⣈⠁⣠⠑⠚⠁⠺⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠔⠆⢀⡀⠂⠀⠀⠀⠠⢫⣿⣿⡀⢀⠐⠀⢰⣿⣿⠃⠞⢰⡿⢿⣋⣥⠤⠷⢤⡗⠲⢶⡦⠠⠴⠖⢤
⠀⠀⠀⠀⢀⠻⣿⡀⠀⠀⢰⣮⠴⠛⣛⠻⣧⠸⡇⠠⡆⣼⣿⠆⣰⣧⣷⡾⡍⠁⠀⠀⠀⠻⣦⡀⠀⠲⣦⠄
⠀⠀⠀⠀⠙⠓⠛⠛⠒⡀⢋⣡⠖⠋⠁⢹⣿⡿⠁⠀⠠⠟⢁⣴⣯⡼⠏⠀⠀⠀⠠⠦⢄⡃⢉⣻⡄⠀⠀⣀⠀⢰⣶⣶⣶⡄
⠀⠀⠀⠀⠁⠀⠈⠛⠛⣰⣿⣏⣠⣤⡴⠟⠉⠀⡀⡀⠷⡄⢿⣯⣤⣠⡄⠀⠀⠰⣾⣿⢦⠄⠚⣉⡻⣅⠀⣿⠀⠈⣿⣿⡏
⠀⠠⠤⠀⡀⠀⠀⢠⠾⢛⠿⠉⠁⠀⣤⡆⠀⢾⣦⡇⠀⠀⢸⣿⡧⢻⣤⠀⢀⠳⠨⠱⠟⣙⡔⢉⠕⠉⣠⠾⠶⣠⡿⠛
⠀⠀⠀⠀⠀⠐⠀⠀⢁⠉⠀⣴⣿⣆⡹⠀⣷⣤⣉⣁⠀⠀⠀⠻⢿⣦⠛⡷⠸⢷⣈⣥⣤⠟⠠⠞⢀⣾⡟⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⣾⣿⣿⣿⣦⠀⢿⣿⣿⡏⠀⢀⣤⡶⠛⡍⠙⠿⣿⣿⣷⣶⣶⠶⠚⣠⣎⡁⢄⡐⣉⠉
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⣿⣿⣿⣤⣦⣉⡉⠁⠀⠀⠈⢀⢰⡇⠀⠀⠀⠈⠉⠡⣶⠶⠋⠉⣀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣀⢰⣿⡟⣿⣿⣿⣿⣦⢰⣄⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠀⢀⣴⣾⣿⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢀⣤⣶⡾⣻⣿⣿⠘⣏⣹⣿⣿⣿⣿⣿⣿⣿⡇⣄⢀⡤⠤⠀⢠⠶⠟⠐⠺⢻⣿⠿⠃⠀⣠⣤⣾⣿⣶⣄
⠀⠀⠀⠀⠀⣼⣟⢫⣿⡿⣿⡽⠀⠸⣿⡿⢿⣿⣿⣿⢹⡁⣿⠃⣀⢤⣦⣤⡐⣶⣶⣄⡀⠀⠘⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣼⣿⢛⣿⣿⣿⣿⠇⠀⠀⢹⣷⣿⣿⣿⡟⣿⣄⣿⣿⣿⣷⣬⣿⡇⠸⣿⣿⣿⣦⣴⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠙⠛⠿⠇⣿⢾⣿⡜⠳⠾⢿⣿⡇⠀⠘⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠙⠛⠉
⠀⠀⠀⠘⣿⣿⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠹⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⢸⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⣷
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⡆⡄
⠀⠀⠀⠀⠀⠀⠀⢧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⠙⣿⡾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣷⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⣇⣼⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣎⣿⣿⣨⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣋⠘⣻⠇⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⡏⠀⠀⠀⠀⠀⠀⠀⠰⡀⢀⠄⠈⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⢀⣀⣀⣠⣹⡿⡆
⠀⣀⣀⣤⣤⣀⡀⠡⣀⠁⠀⠲⢽⡀⠀⠀⠀⠀⢀⣶⠞⠀⠀⢠⡟⠙⠛⢿⣡⣴⣷⣶⣤⣤⡄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⢷⣄⢀⣵⣖⠀⠀⠀⣾⠋⠀⢀⣴⠟⠀⣤⣶⣼⠟⢱⣧⣘⣿⣯⠛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣿⡏⠀⠀⠸⠹⠀⠀⠘⡇⠀⢠⡿⠉⠀⠀⠀⢹⡿⠸⣿⣦⣷
⠀⠀⠀⠘⠒⢄⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⢸⡟⠀⣾⣴⠿⡀⠘⣧⠀⠀⠀⠠⠚⡶⣀⣹⣿⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⣴⢷⣮⣤⡆⠀⠈⣇⣸⠟⠁⠀⣿⠀⠸⣷⠀⢀⡠⠞⠛⠛⠙⢿⣏⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⢀⣀⣹⠏⠐⠀⣶⣷⡏⠀⠀⢀⣿⣷⢀⣧⠞⠋⠀⡀⠀⠀⢀⣤⣹⣶⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠁⠀⠀⠀⣿⣿⠂⠀⢀⣾⣉⠉⠉⠀⣠⡴⠞⠿⠲⠛⣿⣋⣴⡙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈⠀⠀⠀⣀⡀⠀⣧⣿⡀⢀⠌⠉⠘⠛⠟⠋⠉⠀⠀⠘⠓⢀⣿⡟⢉⠖⠁
⠀⠀⠀⠀⢠⠄⢰⠏⠀⠀⠀⠀⣔⣨⠉⠻⠻⠿⢿⣧⣿⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠈⠐⠊
⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢸⣿⣡⣶⠒⠂⠀⢲⡏⠹⣾⣦⣠⠄⣀⣀⣠⣤⠴⠟⠉
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠘⠛⠟⠛⠀⢠⡟⠁⠀⠹⣿⣿⢿⡟⠿⠟⢻⡆
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠠⢀⣿⣇⠀⠀⠀⣱⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠾⠛⠃⠉⠙⠁⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠘⠀⠀⠂⣀⠀⠀⠀⠀⠊⠞⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡆⠀⠀⠀⢡⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠺⠀⠀⠀⠂⠀⠀⠘⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡞⠋⠁⠀⢺⡀⠀⠀⠀⠀⠘⠅⠁⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠠⡠⠈⣹⡛⢷⣄⠀⠀⠀⠂⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠀⡠⠀⢜⢁⠀⢤⡃⠠⣜⠃⠀⠀⠀⠀⠀⠖⠀⣥⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡀⠠⡀⠑⢆⠘⠀⠀⡀⠆⠀⢀⣠⠒⢘⠁⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠋⠠⢄⢨⠀⡱⢤⣈⡳⠞⠉⠀⠀⠐⠉⠀⠠⠞⠁⢀⠀⠀⠀⠤⠂⠀⠀⠀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠶⣤⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡴⢴⡶⠁⢰⠀⠀⠀⠀⠠⠏⠀⠀⣤⠀⠀⠴⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠼⠁⠀⠀⠀⢀⡠⢶⠆⠤⠖⠁⡰⠀⠚⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⡾⠷⠶⠤⢤⠴⢶⣂⠠⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⢹⣻⠞⠁⠀⠰⠀⠀⠀⣆⡧⠦⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⠜⠁⠀⠂⠀⠀⠀⠀⠠⠋⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⢋⠓⣓⠾⠋⠁⠀⠈⠀⠀⠀⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⢀⣀⡤⠀⠀⠀⠀⠈⠉⢀⣀⣴⠶⢓⠚⠋⠁⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣀⠀⠈⠽⡁⠀⠀⠀⣠⠞⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣂⠠
⠀⠀⠀⠀⠀⠀⠀⠘⡉⠁⠀⠀⠀⠐⠉⡱⢄⡀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠠⡎⠁⠀⢣⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⡆⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⡇⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢰⠀⠀⠀⠀⢰⡇⠀⠀⣄⠐⠀⠀⠀⠀⠀⠈⡀⠀⠉⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣾⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠓⡀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡴⢹⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠠⡀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢀⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠤⠤⣀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⡠⠄⠤⢀⣀⣀⣀⣨⠭⠤⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠄⢀⠞⠁⠀⡠⠖⠋⠁⠀⠀⠀⠀⠱⣄⢀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⢠⠁⠀⢠⠊⠀⠀⠀⠀⣀⣀⣀⣀⠀⠘⣆⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⡇⠀⢠⠃⡄⠀⠀⡠⠂⠁⠠⢀⠀⠉⢢⠘⡄⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠀⠐⡇⠀⠀⠐⡇⠀⠈⠀⣀⠀⠒⠤⠈⠄⣸⠀⡇⠀⠀⠀⢸⠀⠀⠣
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⡈⠃⣠⡟⡃⠂⠀⠾⣼⡄⠁⢰⠁⠀⠀⠀⡸⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠆⠀⠀⢰⠀⠀⠀⠀⠢⡀⠀⢠⣸⢧⠀⠈⠀⡀⠀⠀⠐⠋⠀⢠⡇⠀⠀⠀⡐⠁⠀⢀⠏⠀⢱
⠀⠀⠀⠀⠠⢆⠀⠀⠸⡀⠀⠀⠀⠀⡇⠀⣼⠋⠀⠁⢀⠀⠀⠀⠀⢠⠄⠔⣹⠗⠀⡀⠊⠀⣀⠴⠛⡄⠀⠸
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠡⡀⠀⠀⠸⡄⠀⠨⣹⡛⠀⠤⠭⠕⠒⠒⠭⠖⢊⡁⠀⣨⠗⠒⠉⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠘⣄⠀⠀⠈⠢⢄⡈⠢⡀⠀⠑⢄⡀⠘⠏⠑⠒⠀⠀⠀⠒⠠⠞⡥⡴⠊⠋⠀⠀⠀⠀⠀⠀⡇⠀⡐⠁
⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠋⠉⠦⡀⠀⠈⠉⠛⠛⠊⣉⠉⠀⠈⢀⠐⠈⠀⡜⠀⠀⠀⠀⠀⠀⠀⡗⠋
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠡⠀⠈⠠⠀⡀⠀⠀⠀⠀⡀⠀⠉⠉⣠⣴⠫⠄⠀⠀⠀⠀⠀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠲⠦⠄⠀⠱⣄⡀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠚⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠈⢲⢤⣀⣀⠠⠔⠉⡄⠁⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⠀⠀⠈⠉⠙⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⠤⠒⠈⠁⠀⠄⠀⠒⠊⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⠀⣤⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠰⠶⠤⣤⡤⣈⣤⣤⣀⡀⢹⣤⡀⠘⣷⠶⠶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⡔⠃⠀⣸⡗⢠⡤⠄⢨⣥⣬⣿⣤⣿⡟⠂⠁⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⠋⢀⣐⠛⠻⣼⢋⣴⣦⡾⢁⣤⣤⣤⣙⣉⠉⠻⣿⢷⣜⢦⡈⠻⣦⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⡿⠇⡴⢃⣤⣭⣿⣷⣶⡿⠿⠿⣯⡙⠿⣦⣌⡙⢿⣷⣆⠐⢶⣌⠀⢹⡄⠘⣸⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣶⠟⢉⣷⣼⡷⠛⠛⢶⣶⣾⠿⣤⣰⡆⢈⡛⣷⡿⢿⣷⠘⣿⣿⡇⣸⢻⡆⢸⡇⢸⡷⠀⣿⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡘⢋⣽⣰⣿⠿⡃⠘⢿⣷⣶⠉⢱⣦⣸⣿⣦⣾⠫⣿⠿⣎⣿⣧⡿⠛⣴⡯⠈⣇⣸⢀⣾⡿⠀⡿⣿⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣾⠀⡃⢾⣿⡿⢁⣄⣿⡾⢃⣠⣾⢴⣾⣿⡿⣿⣿⣷⣾⣿⡷⠘⢛⣡⣴⣾⣿⡗⢸⡿⠡⠾⠛⣁⡴⢢⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡇⠘⠿⠷⣿⣿⣿⢁⣾⠟⢡⣾⡟⢳⣦⡈⣿⡏⠀⣁⣤⠾⣿⣿⣿⠿⠟⠁⣈⠤⣴⣶⡿⢋⡴⣳⣿⣿⡇⣿⣧
⠀⢀⡀⠀⠀⠀⠀⢻⠇⠈⡃⠀⠀⠀⠀⠈⠹⢿⢿⣶⣿⠿⠆⠀⢹⣿⡟⠡⠚⠉⠀⠀⠀⠉⣁⡴⢾⣫⣾⣿⠟⢋⡴⣫⣾⣿⢋⣿⣧⣿⠏
⢠⣌⣧⠀⠀⠀⠀⠈⠀⢀⠃⠀⠀⠐⡀⠀⠀⠀⠈⠉⠙⠿⣶⣶⣤⣛⠁⠀⠀⠀⠀⢀⡤⢞⣵⣾⣿⣿⠟⢁⡴⣿⣾⣿⣿⣿⣾⡿⢸⠏
⠀⠘⣷⣧⣀⣄⡀⠀⠀⠾⠾⡀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡁⠀⠀⣠⣮⣶⣿⣿⣿⡟⠁⣴⢏⣼⣿⣷⣿⣿⣻⣿⠁⣼
⢀⣴⣿⣿⣿⣿⠟⠀⠄⢶⡀⠀⠈⠉⠉⠉⠉⠉⠓⠛⠛⠒⠛⢛⣨⣙⠿⠃⡰⢋⡾⠿⠟⠉⣹⠏⢀⡾⢃⣼⠛⠿⢿⣧⡾⣿⡏⢠⣿⣴⣿⣶⣶⡶⠖
⠈⡿⣿⡿⣿⠃⢠⡇⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠈⠁⠛⢻⣿⣿⡟⠁⣠⢞⡵⠟⠁⠀⠀⡀⠁⣴⣟⡴⠟⠁⠀⠀⠸⡿⣻⡿⢀⣿⣿⣿⣿⠿⠋
⠀⣰⣿⣇⢸⣆⡸⣿⡀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⣠⠞⠁⠈⠀⠀⠀⠀⡴⢁⡾⣽⠋⠀⠀⠀⠀⠀⢀⣴⡟⢁⡼⢫⠋⠈⠁
⠀⠹⣿⣿⣿⣿⣷⣿⡟⠋⠁⠀⠀⠙⣿⣶⣶⣦⣄⣈⣶⡿⠁⠀⠁⠀⠀⠀⠀⠀⠀⢈⣴⠟⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠠⣼⣧⣤⣀⣀
⠀⠀⠀⠈⠉⠏⠁⢸⣿⡆⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⣴⡟⠋⣠⣶⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡄⠀⠀⠀⠀⣀⠛⣚⣚⣻⣤⣄⣀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⣀⣠⣴⣶⡿⠟⠁⢀⣼⣿⣿⣩⡿⣼⢏⣿⣿⣿⣿⣧⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠉⠁⠘⠿⠛⠉⠙⠙⠛⠻⠿⠿⠿⠷⠶⠶⠂⣶⣟⠉⠉⠉⠀⠀⠀⢠⣿⣿⣿⣧⣿⣷⡿⠛⠁⠄⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣴⣿⣿⣾⣾⣿⣿⣷⡀⢸⣿⣿⣿⡿⣯⠈⠁⠐⠀⠀⣾⣿⡟⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⣻⣤⣀⣾⣧⣿⣷⡌⠀⠈⢀⣄⣿⣿⠈⣿⣿⡏⣼⣿⣿⣿⣿⣿⣷⠘⢿⣿⣟⠷⣀⠈⣀⢤⣴⣿⠛⠁
⠀⠀⠀⢠⣤⣀⡀⣀⣀⡀⡆⠀⠀⠀⢊⠻⣝⢿⣿⣿⡟⠀⠀⢠⣷⣽⣿⣿⡁⣿⠛⠀⠛⠛⠛⠛⠿⣿⡿⠀⣠⠞⠁⠀⠤⠐⠟⠋⠁
⠀⠀⠀⠀⠠⠟⠛⠋⠛⣿⣿⣷⣶⣷⣠⣄⠈⡀⢙⢿⣿⠷⠛⠛⠛⠻⢿⣿⡅⠀⠀⣀⣤⣤⡶⠿⢶⢄⢡⡞⠉
⠀⠀⠁⠀⠐⣶⠆⠐⠋⠉⠈⠙⣿⣿⣿⣿⣾⣿⢸⡇⠀⠀⢀⣱⣦⣤⣄⣹⢰⡶⠊⠉⠁⠀⠀⠀⠀⠀⠠⢀⣀⣾⣿⣿⣶⡀
⠀⠀⠀⠀⠈⣥⣄⠀⠒⠀⠈⠉⠉⣻⣿⣿⣿⣿⡆⠀⡲⠟⠉⠁⠀⠀⠀⠉⠸⠁⠀⠀⠀⠀⢀⡴⢀⣤⣤⣤⣿⣿⣿⣿⣿⣛⡻⢷⣦⡀
⠀⠀⠀⠀⠀⠨⣿⣿⣋⣉⠋⠙⠛⢻⣿⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⡠⡶⠄⠀⠀⠀⢀⡜⠀⢸⠛⣿⢋⣼⢿⣿⣿⣿⠛⠿⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢻⣿⣿⣿⡿⠟⠁⠀⣀⠺⠿⢿⣿⡏⠀⠐⠉⣀⡗⠢⠄⠀⠀⠛⣠⠰⠌⢿⢃⡝⢁⣼⣿⣿⣿⣿⣷⣎⣩⣝⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡌⠳⡀⠀⠙⠁⠀⠀⠀⢠⡟⠦⡀⠀⠀⠛⠁⠀⣳⡄⠘⠉⡙⢡⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣭⣽⡿⠿⣿⠚⠙⠲⣄⠀⠀⠀⠀⠀⣿⡄⠈⠀⠀⠀⠀⠀⢸⣽⣅⠀⢀⡾⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣽⣿⠟⢻⠀⠀⢹⡀⠰⠀⠙⢆⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠈⣧⠈⢠⡿⠃⣾⠿⣿⣿⣿⣿⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠛⣛⣿⡟⢻⠀⠈⠀⠀⠸⠁⠀⠀⣀⣨⣀⣀⡀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠨⡄⠘⠀⠀⢯⢀⣾⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⢻⡁⠘⠀⠀⠀⠀⡀⠀⠀⣰⠟⠋⠉⠉⠻⣆⢀⡀⠀⢳⡀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⠋⣸⡿⢧⠀⠁⢀⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢾⣷⡄⢲⠁⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠰⣣⣾⣿⡇⠘⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠻⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣇⢻⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠟
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠛
⠀⠀⠀⠀⠀⠈⢿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣰⡤
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢠⠤⡀⢠⠈⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣼⠀⢰⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢹⠀⡠⠚⣆
⡇⠸⠇⠀⢿⡄⠘⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡘⠆⠁⣠⠋
⠃⠀⠈⠀⢀⣀⣀⣀⠛⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⠀⠘⠛⠀⣼⠁⠀⢀
⠀⢃⠀⠀⠀⠀⠀⠈⠛⢀⣤⢠⡇⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠉⠘⠂⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠘⠧⣄⠀⠹⠀⠀⠀⠀⠀⠠⠄
⠀⠈⢦⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠐⠶⠀⠀⠛⠀⠉⢈⡵⠈⠹⡆⠀⠀⠀⠀⠀⠀⠈⡇⠀⠳⣤⡀⠀⢀⡤⣤⠁
⠀⠀⠀⠉⠲⣄⠀⢾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡼⠃⠀⠈
⠀⠀⠀⠀⠀⠈⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠛⠀⠀⠀⢀⡛⠀⢠⡤⠚⠁
⠀⠀⠀⠀⠀⠀⣗⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣹⠶⠒⠋⠉⠉⠉⠉⠁⠒⠲⣤⡀⠀⠀⠀⠀⠲⡅⠀⠀⠀⠀⣴⠋⠀⢀⡎
⠀⠀⠀⠀⠀⠀⢹⡄⠀⢻⡀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠹⠆⠀⢀⡴⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⢃⠀⠘⢣⠀⢠⠞⠁⠀⠀⠀⠛⠃⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠹⡀⠀⠀⡀⠀⢀⡞⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢀⣼⠦⠶⠛⢻⠇⠀⠀⠀⠀⠀⠀⡠⠒⠲⡄⠀⠀⠀⢀⣠⠾⠀⠀⠀⢫⡀⠀⢹⣦⠛⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⢁⣼⠀⠀⠀⠘⣇⡀⢸⡟⠀⠀⢀⠾
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⠀⠀⠀⠀⢸⣿⡗⠙⠛⠛⠛⠉⠀⢀⣀⣴⣿⡟⠀⠀⠀⠀⠀⠙⡿⢦⣀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⠀⠀⠀⠸⣿⣷⣤⣤⣤⣤⡶⠛⠋⠉⢹⡟⠁⠀⠀⠀⢷⡤⠛⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣷⠀⠀⠀⠀⠹⣿⣿⣿⠿⠟⠐⠒⠒⣴⠟⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣆⠀⠀⠀⠀⠈⠻⠇⣀⣀⡠⠶⠞⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠙⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠳⠾⠙⠛⠛⠛⠋⠁⠰⠶⠶⠦⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠈⠙⠛⠛⠛⠲⠦⢤⣤⡤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠐⠛⠋⣉⣁⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠳⣤⡤⠔⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡤⠴⠶⢶⣶⠶⠖⠛⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠈⠉⠉⣿⠉⠙⠛⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⠤⣼⡁⠀⠀⠀⠀⠀⠀⡰⠓⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢘⡇⠀⠀⠀⢀⡤⠚⠀⠀⠀⢠⡇
⠀⠀⣀⠀⡀⣀⣠⡴⠖⠉⠀⠀⠀⠀⡀⠘⣧⣀⠰⠊⠉⠀⠀⠀⠀⠠⠺⡇
⠀⢘⠋⠤⠀⣀⣈⣡⡀⣀⡀⠀⢀⡠⠚⠛⠁⠉⢠⡀⠀⠀⠀⠀⡜⠁⣀⠃
⠀⠈⠑⠂⢤⣤⣤⣤⣤⣤⠀⠠⣏⠑⠂⠠⠀⠀⠀⣴⠄⢤⣤⠘⠓⢠⠌⠁
⣤⣤⣀⣤⣤⣤⣤⣤⣤⣠⣤⣤⣄⣉⣤⣤⣶⣶⣶⣤⣶⣤⣤⣌⣁⣠⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣤⣤⣤⣄⣠
⣿⣿⣿⣿⠿⠛⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐⠒⠀⠀⣀⡀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡤⠤⠔⠒⠂⢣⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠂⠀⢀⠊⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠃⠀⠰⠁⠀⠀⠀⠀⠒⠂⠀⠒⢄⠘⡄⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢨⠀⠀⠁⢨⠀⠀⠀⠀⠀⠌⡐⠀⠀⠁⠡⠀⠀⠀⢱⠀⠀⡀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡶⠃⠄⢠⣄⣄⠀⠀⡆⠀⠀⠀⡸⠀⠀⠰
⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⢄⠀⠀⣀⡶⠀⠙⠀⠀⠀⠀⠐⠃⠀⡼⠀⠀⠀⠰⠁⠀⢠⠃
⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⢸⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡷⠀⠀⠀⠀⠀⠔⠣⠀⠀⡇
⠀⠀⠀⠀⠀⠑⢀⠀⠰⡀⠀⠀⢸⠀⠀⢉⣗⠀⠠⠤⠀⠒⠀⠕⢒⡉⠀⣠⠗⠂⠁⠀⠀⢀
⠀⠀⠀⠠⣀⠀⠀⠁⠀⢈⡲⣄⠀⠑⠄⣀⠛⠀⠈⣉⡀⠀⠀⠈⠩⠐⠊⡙⠀⠀⠀⠀⠀⢸⣀⡠
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠡⡈⠢⡀⠀⠀⠈⠈⠁⠠⠀⠀⠀⡀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⣀⠠⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠲⣄⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⡠⠖⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠢⠤⢤⡤⠄⠀⠈⠁⠒⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⣀⡀⠀⠊⠀⠀⠀⠠⠄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣤⣌⣀⡀⠀⠐⠒⢭⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⣫⣭⣭⣭⣭⣇⣀⣀⣀⣐⣿⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡵⡺⠟⠟⠛⠉⠀⠉⠁⠀⠀⠀⠀⠉⠹⣟⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠏⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⢿⡆⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⢹⠆⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠀⠀⠀⢸⠱⠀⠈⠔⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠙⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠃⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠖⢣⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢦⢀⣀⢄⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡆⠀⠀⠀⠀⠀⢴⠒⠚⠉⢀⡠⡾⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⢀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⢶⠒⠚⣉⢴⠇⠀⠀⠀⠀⢀⡾⠁⠀⠀⣀⠔⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⠲⠒⠁⠀⠀⠀⢀⣴⠏⠀⢀⡤⣄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⠀⠀⢀⣀⣠⠴⡟⠴⠒⠊⣁⡠⠟
⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⢉⡩⠝⠋⢅⣀⡠⠃⡖⠂⠉⠁
⠀⠀⠀⠀⠠⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⡏⠀⠉⢉⣠⢴⠆⠀⠈⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠞⠁⠒⠒⠒⠒⠉⠑⠒⠉⠉⢀⡞⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠤⠬⣉⠑⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠉⠓⠢⠤⣈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠺⣆⠀⠀⠀⠀⠁⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣯⠙⡖⠒⠒⠃⠤⠤⠔
⠀⠠⢄⠀⠀⠀⠀⠀⢀⡔⢉⡴⠊⠉⠹⠦⠖⠒⠒⠓⠓⠂⢄⡈⠉⠉⠛⠒⠒⠒⣃⣀⠀⠀⠀⢀⠏⣸⠁
⠠⡑⢄⠀⠒⠤⣀⢠⠎⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢇⠀⠀⠀⢀⡏⣀⠠⠔⣚⠖⠁
⠀⠘⢄⠳⣀⠀⠀⠉⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⡼⠒⠒⠒⠉⠁
⠀⠀⠀⠙⠢⡑⢤⡀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⣼⣿⣿⣿⣷⣾⣿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠟⣁⠀⠀⠀⠀⠀⠀⣀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠁⠚⠉⠀⠀⠀⠀⠀⠀⠉⠃⠀⠸⣿⣿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⠋⠀⢠⣤⡀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠙⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣸⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⠀⠀⠀⠐⠀⠀⢀⢆⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠐⡶⠖⠻⠁⢀⡀⠔⠈⠀⠀⡠⠂⠀⠈⢞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣠⠄⢴⡈⠠⠠⠠⣦⠒⠁⣀⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⢿⣧⣾⡇⠀⠀⠀⢹⡖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠄⠺⣇⠀⠀⠀⠀⠋⠈⠀⠀⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠃⠈⠁⣀⠠⠄⠛⠒⢺⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠢⠐⠉⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣤⣤⣤⣤⣤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⠛⠈⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⢰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣆⣀⡇⠀⠀⠀⡀⣠⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⢯⣷⣿⠟⠀⠀⠀⠀⢿⣿⣴⣛⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡨⠊⠀⠀⠀⠀⠀⠈⢛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠁
⣿⣿⣻⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣻⣛⣿⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠒⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠚⣓⣀⣉⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣀⠞⠁⠀⠈⠀⣲⠶⠖⠒⠛⠉⠉⠁⠘⣆⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠀⠒⠂⠈⡵⠁⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠤⢀⡀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢳⡄⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡜⠀⡀⠀⠀⠀⢀⠠⠉⠩⡁⠀⠀⠉⠳⢄⠀⢻⡀⠀⠀⠀⠙⢦⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠸⠀⢐⠁⠀⢀⠔⠁⠄⠀⢀⣈⠑⠢⣄⠀⢠⡇⠀⡇⠀⠀⠀⠀⠈⣇⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠐⠈⡇⠀⠀⢀⠈⣠⠀⢈⠉⠝⠀⡈⡆⢸⠇⢀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⡁⢃⠀⣸⠻⠃⠘⠀⠀⠴⣧⣷⡠⢀⠀⣸⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡅⠀⠀⠀⠀⠠⡀⠈⠀⠀⠆⠀⣼⡀⠀⠙⠧⠀⠣⠀⠀⠀⠀⠴⠞⠁⠀⢠⠃⠀⠀⠀⠀⢀⡜⠁⠀⠀⢠⠏⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⣦⠀⢀⢸⣼⠇⠱⡄⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀⠄⡠⢻⠀⠀⠀⠀⠀⠊⠀⠀⠀⣠⠎⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠜⢇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⣼⡘⠄⠀⠈⠠⡀⠀⠀⠀⠀⠀⢤⡔⡡⠞⢀⡿⠊⠀⢀⠔⠁⠀⢀⠤⠞⠉⢳⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠂⠀⠈⠳⡀⠀⠀⠹⡄⠀⠀⠀⠀⠸⡇⠀⠀⠠⠙⡾⠥⠀⢀⣈⣙⣒⠒⠒⠒⢊⣩⠴⠖⠉⣀⠠⢂⣧⠤⠐⠊⠁⠀⠀⠀⢀⠇⠀⠀⠈⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⡀⠀⠈⠢⡀⠀⠀⠀⢳⡀⠀⠀⠱⣿⠖⢀⣀⣠⠄⠀⠀⢀⣀⠀⢠⡤⠖⠉⣀⠴⢺⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠈⠑⠠⠤⡈⢳⣄⠀⠀⠙⠲⢤⣀⣈⠓⠀⠀⣀⣀⣀⠀⠀⢀⠀⠂⠐⢋⠛⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⢦⡀⠀⠀⠀⠀⠈⠉⠉⠙⠄⣀⠀⠀⠈⠁⠀⡀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠂⠀⢀⠔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⣀⡀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠲⢄⡂⠀⠈⠉⠉⠉⠋⠉⠈⠁⠀⠀⠀⠀⢀⣀⡤⠴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠉⠁⠐⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⠏⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⢀⡠⠖⠉⢠⠈⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⣶⠶⠖⠂⠀⠁⠀⠀⠉⠉⠀⠀⠀⢀⠟⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⢀⡀⠜⠁⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠋⠁⠀⠀⠈⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣋⣭⡠⣜⣦⣄⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠁⢼⣿⡈⢷⣓⣥⣪⣿⣄⡷⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣄⠸⡏⣬⣷⡯⠈⣽⠉⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⠛⠛⠀⠂⡠⠄⠃⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠊⠙⠻⣿⣥⣄⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⣤⡀⠀⠀⠀⢠⢀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⡄⢀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠐⢀⡇⢘⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣠⠷⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣠⠀⢠⠈⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠚⠋⠀⠈⣄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠀⠂⠈⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⡜


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠙⠀⠀⠀⠛⠛⠛⠓⠲⠢⠠⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠐⢤⣀⠈⠙⠻⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⡟⠀⠀⠀⠀⢠⣏⢠⠆⠂⢀⠒⠀⠉⠀⠁⠀⣘⣮⠛⣭⠉⠙⠲⢄⠀⠀⠀⢑⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⠻⠹⠀⠀⠀⠀⠀⢨⠃⢻⣤⣾⣦⣤⣴⡀⠀⠃⠀⠙⢻⡆⠉⢲⣄⡀⠀⠁⠠⡀⠀⠆⠀⠐⠁⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⢰⠀⣄⠀⠀⢸⡀⠈⡙⠻⢿⢯⣬⡙⠳⠀⣡⣹⣆⣷⠀⣸⡿⠃⠀⠀⠀⡵⠀⠀⢀⣤⣬⡀⣄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⡆⠀⣿⣧⠀⠈⠀⠀⠀⠈⠛⠶⣿⡿⡏⠘⠋⠸⣿⣧⠀⠀⠀⠘⢇⠀⠀⣻⢿⣿⣿⣯⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⡟⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠄⠀⢿⣿⡷⠀⠀⢀⣞⡃⢠⡿⠒⠃⠘⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠄⡉⠙⠲⣶⠖⠈⡠⠀⠀⣾⠻⢣⣿⡇⠀⠀⠀⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠃⠄⠐⠀⠙⣿⣿⣿⣶⣤⢤⣤⣤⣤⡤⠄⠀⢀⣴⡊⣠⡔⠋⠀⢀⣿⡟⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠉⠉⠛⠛⠚⠛⠋⠁⠀⠀⠀⠀⠈⢠⡟⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⢀⡀⠀⠀⢀⣀⣴⡿⠀⠀⢠⣿⠟⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣷⣤⡶⠟⠁⠀⢠⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠈⢣⣀⡀⠀⢀⣤⣤⣤⣤⣤⠤⡤⠤⠤⠖⠒⠐⠉⠁⠀⠀⠀⠀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⡟⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⢀⢄⡸⠀⠐⢅⡤⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠄⠀⠀⠀⠀⠄⡻⠦⠙⠁⡠⠚⠒⡄⠈⠃⢖⢠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠑⠀⠀⣔⠦⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠪⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡮⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢕⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠉⡄⠀⢀⠀⠀⠂⠀⢢⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠆⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡂⢠⡇⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠙⠛⠶⣄⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠂⠀⠀⠀⠀⠠⠁⢈⠀⠀⠀⠀⠛⢈⠇⠀⠀⢄⠄⢀⠏⠀⠀⠀⠀⠄⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⡀⡀⠁⠐⠚⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡰⠂⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄⢴⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠈⠁⠄⠠⠀⠠⠀⠠⠤⠡⠈⢢⠈⠢⠀⠀⠄⠁⠀⠀⠊⠀⠁⠌⠑⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠤⠀⠀⠢⡀⠀⠀⠀⠔⠁⡀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠈⠲⠤⡤⠤⠴⡊⠀⠐⠂⢬⢶⢰⠎⢠⠆
⠀⠀⠀⠀⠀⠀⠀⢠⡠⠁⠀⠀⠀⠀⠙⠒⡒⠂⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠄⠀⠀⠤⠀⠈⠧⠀⠚⠏⢈⣟⠚⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⠀⠀⠀⠸⠁⠀⠁⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠄⣠⠐⠓⡂⠀⠀⢐⠀⢀⠂⠀⠀⢄⠀⠙⠃⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠃⠀⠘⠲⠄⠀⠀⠀⢀⠀⠀⢀⡤⠊⠁⠀⢀⠂⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠨⠀⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠐⠀⠃⠀⠀⠀⠀⠀⣆⠀⢀⡆⠀⠀⠀⠀⠀⠄⠀⠈⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠰⣀⠃⠀⠀⠀⠀⠀⡂⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠈⠳⠀⠀⠀⠀⠀⠶⠂⠀⠰⠤⠀⠀⠀⠀⠠⠬⠉⠀⠉⢥⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣨⣤⣙⣶⣴⣾⣿⣿⣿⣿⣯⣿⣯⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡇⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣅⢸⣿⠀⠀⠀⣠⣾⣿⢟⡿⠟⣿⣿⣿⣿⡿⠿⢿⣿⣿⣼⣿⢏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⣠⣿⣿⣷⣿⡵⠿⠟⠉⠻⣅⣉⣴⢸⣿⣿⢹⠏⣾⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢇⠀⢠⣧⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⢎⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣠⡴⣿⣿⣼⣄⣾⣿⣷⣄⠀⠘⢷⣦⣄⡀⠀⠀⠀⣀⣀⣤⢻⣿⣿⠿⠛⠿⢟⣽⣿⣿⣿⡿
⠀⠀⠀⠸⡀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣆⡀⠘⢻⣿⣿⣶⣾⣿⡿⣱⡿⠋⠁⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⣦⣀⠙⡻⢿⣿⣿⡟⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣀⣀⠀⣀⠀⠈⣉⣫⡽⠟⠛⠛⠛⠿⠷⣶⣾⠿⠿⠿⣿⣿⣿⣿⣿⣁⣀
⠀⠀⠀⢀⣤⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⡏⠀⠀⠀⣀⣠⣴⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣿⣿⣿⡿⠿⡿⠦⣀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠉⠁⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡷⣄⢀⣠⣴⣾⣿⢿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢠⠿⠛⠛⠻⠿⠿⡿⠿⠿⠛⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡿⠋⠁⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⠛⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⢳⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⣿⢸⠇⠔⣽⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡓⢄⠀⢹⣿⠋⣀⢸⣿⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⢟⣫⠴⠶⠶⢷⣍⠈⢷⣀⢡⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⢀⡾⢁⣤⡤⡒⡠⣟⢦⡀⠈⡎⠹⣏⡀
⠀⠀⠀⠀⢠⣤⢞⡵⢇⣧⡘⢩⣿⠀⡇⣁⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠘⢿⠁⠀⠀⣌⠃⢺⠏⡸⢁⠿⢺⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠈⣵⢤⣊⡉⠉⣀⡴⢃⡎⢠⡟⢀⠊⡣⠀⡀
⠀⠀⠀⠀⠀⠐⡇⠀⠀⣹⡟⠛⠉⣉⣤⠟⠉⢉⡼⣡⢾⣿⡄
⠀⠀⠀⢀⣴⣣⡱⣄⠀⠈⠉⢉⠟⠀⠀⢀⣀⡿⢰⢃⣿⣿⣧
⠀⠀⠀⠘⠛⠿⠿⠾⠵⠒⣂⠓⣒⣦⠥⠤⠤⠅⠇⢠⣿⣿⡏⡠⢤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣧⠙⠿⣻⣾⠿⠿⠶⢌⣻⡟⠀⢴⣿⡿⠁
⠀⢀⣠⣤⠴⠶⠤⠤⣄⠁⢿⣯⠤⡼⠯⣤⣀⠀⠀⠀⠈⠉⢹⠚⠋
⠀⠀⠙⣿⣿⣿⣷⣦⣠⢠⡟⠁⠀⣠⠦⠤⢌⣙⣶⡖⠦⣄⠀⠙⢦⡀⠀⢀⠴⣲⣿⡇
⠀⠀⠀⠀⠙⠿⢿⣿⣿⣽⣧⠖⡿⢁⡴⣾⡛⣝⢯⣿⣄⠈⢳⡤⢤⡷⠐⢃⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡠⠋⣸⡇⢸⡇⣯⡾⣿⢿⣿⣾⠏⡟⠀⠀⣿⠈⢿⠀⢼⡿⠟⠁⠀⠀⠀⠀⢀⡴⢦⢤⢄⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⢿⢳⣴⡗⣸⡿⠵⢋⣼⢋⡴⣧⣀⡴⡿⠀⢸⡄⣀⡀⢤⣀⡀⣀⣀⠤⠾⢦⣖⣚⣪⠅
⠀⠀⠀⠀⠀⠀⢸⣆⠀⢸⡀⠈⢷⣀⣈⠿⠉⣰⠟⢀⡿⠀⣰⠃⠀⣼⢁⣴⣶⣿⡿⣱⠯⣧⠤⠴⢶⣤⣬⢯⠶⠆⠠⢄⣠⣤
⠀⠀⢀⣤⣖⣈⣜⣧⠀⠀⠙⢦⣤⠬⠤⠶⠛⢁⣠⠞⣡⠞⠁⣠⣾⡟⠾⠿⣟⡋⢰⣿⡶⢯⡼⣀⡾⢕⣢⠌⣷⢠⣶⣿⠟⠃
⠀⠀⠀⠙⠻⢿⣿⣮⠳⡀⠀⠘⠳⣶⣶⣶⡾⠿⠗⠋⠁⠀⢀⣿⣿⣤⡤⣄⠈⠙⢦⡉⠑⠺⡛⠓⠺⡉⢀⣛⣁⡉⠛⠲⢄⡀
⠀⠀⠀⠀⠀⣠⠞⣀⣤⣴⡀⠒⣏⠀⠀⠙⢻⡷⠶⠴⠶⢒⣽⡜⣿⣿⣿⣿⣿⣦⣄⠹⣆⠈⢿⣿⣶⣜⢎⢿⣿⣿⣿⣷⣦⣽⣄
⠀⠀⠀⠀⣴⣡⣾⣿⣿⠟⡇⣾⣾⠲⢤⣤⡿⠀⠀⢠⢱⣿⡿⠁⠈⠻⢿⣿⣿⣿⣿⣷⣼⣇⠀⠙⠻⠿⠿⠄⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠱⡿⠋⠀⠀⠀⠀⠀⠀⠘⡿⠋⠁⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⡶⣋⣙⠲⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢀⡠⡶⣫⠞⠛⠳⣶⣤⢸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠒⢶⡟⠀⣠⣿⣸⠟⢉⣉⡛⣆⢸⡌⣿⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢈⣧⠀⡇⠸⣯⣰⣧⣚⡷⢋⡼⣱⢻⡇⢠⠷⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢸⠏⠻⣧⠀⠙⠿⣽⡿⢚⡭⠞⣁⣼⣵⡏⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠦⢼⡇⠀⠈⠳⢾⡛⠛⠛⣿⠛⠋⠉⠁⣸⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⠀⠈⢳⣄⠀⠀⠀⠙⣆⣀⣯⡀⠀⠀⣠⡿⠖⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠉⠳⣤⡀⠀⣿⠁⠈⠉⢛⣻⠏⠀⢀⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣄⣀⣉⣻⡿⠶⠶⣾⣏⣥⣤⠶⠋⢁⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣄⣀⠉⠉⠁⢀⣶⡀⠘⣇⠀⠀⣰⠋⣧⠚⢓⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⢄⡸⡟⣄⢀⡜⣯⢷⠀⣿⠀⣾⠁⢦⡇⢁⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣊⢳⡅⢹⡿⢣⡟⢺⢀⡿⠀⣟⠜⢋⣤⣟⣥⡤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣳⣸⣧⡏⣠⠋⣼⡷⠚⢻⣟⣶⣿⣶⠷⠶⢞⣻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣤⣄⠙⢿⡯⠞⠁⣰⠟⠀⢰⠃⢿⡍⢳⡉⠙⠚⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡞⢷⣭⠾⡽⠃⠀⠀⢷⢀⣼⠋⠀⠀⠘⣧⠼⣯⢪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠥⠗⠋⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠈⢻⣩⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠐⠒⢦⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢼⠁⠀⡀⠀⠀⢀⡠⠂⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⢰⠀⢷⠀⠀⢀⡎⠀⠒⢋⡡⠔⠂⠓⠀⠀⢠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⠀⠀⡆⡼⣠⡏⠀⠀⠈⠀⢀⡀⠁⡀⣀⡀⠀⠀⠀⠢⠳⢄⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠛⣿⡦⠀⢰⠂⢸⡀⠀⠊⣳⡀⠈⠴⢆⠤⣀⠀⠈⠉⠀⡣⠠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠀⢹⠀⢳⡷⡡⠈⢆⡸⢷⡀⢣⣿⢣⡀⠐⠒⠲⡄⢡⠀⠀⡆⠘⣀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⣿⣿⠻⡀⠀⢿⠹⣆⠈⢷⣤⣥⡈⣿⣶⡙⣶⣗⠀⠈⠉⠀⠀⠁⠀⠈⠙⢢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠈⢙⣿⣶⠀⠀⠈⠓⠿⣦⡈⢯⡛⠭⠛⠻⢿⣾⠾⢷⣼⣠⣇⡀⣀⣀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡴⣻⠁⢻⣦⣄⠀⠀⠀⠀⠙⠮⣧⣶⣤⣦⢀⣉⣁⣂⢀⠈⣭⣽⣿⡏⠀⠀⠸⠀⠀⢸⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⣿⣾⠀⠀⣿⣯⣿⢦⣕⣒⣄⠀⠉⠻⢷⣄⡀⠢⢤⣄⠈⢈⠈⢉⣁⣠⣴⣿⠄⠀⢀⡿⠁⠉⠉⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⢿⣿⡀⠀⠘⣿⣿⡇⠈⣁⣽⢷⣤⣤⣤⣈⠉⠛⠦⣄⣀⠀⢏⣿⣿⣿⣻⠋⠀⠀⠊⠁⠀⠀⠉⠀⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢈⣿⠏⢸⡿⣇⠀⠀⠈⠻⣗⣀⣿⣿⣤⡀⠈⠙⡟⠛⠒⠲⡾⣯⣟⣿⡿⠿⠛⠁⠀⠀⡀⠀⠀⠀⣸⡦⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⡟⣏⡔⠀⣾⣿⣷⣄⣀⠀⠈⠻⣟⣋⣹⣛⠻⠶⠾⠿⠤⠧⠿⠽⠿⠞⠛⠛⠁⠀⠀⠈⣥⠀⠀⢰⣧⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡏⠙⢻⣷⣔⡝⠹⣻⠛⡿⣿⣿⣶⣄⡉⠻⢯⣍⠒⠤⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⢴⣶⣶⠏⣱⠚⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⡇⠀⠈⢻⣿⣿⣦⣻⣔⣏⡿⣿⣿⣿⣿⣿⣷⠎⡇⠀⢹⣶⣤⢏⣿⣿⣿⣿⣿⡷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣶⣶⡀⠻⡏⠉⠍⣹⢿⣏⣿⣿⣿⣿⣿⢿⠀⣷⠀⠠⣸⣏⣾⡿⠿⠛⠋⡉⠈⠁⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣾⡄⠀⠴⠊⣿⣿⣿⡟⣵⣷⣿⣆⠸⣤⡶⠛⣩⡶⠶⠖⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⣷⠙⡆⠀⢠⣿⣿⣟⢟⣻⣧⡿⠿⠤⢟⣒⡉⠁⠀⢀⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡟⣼⣶⣤⣘⣿⣿⡶⠚⠉⠀⠀⢠⣶⣟⣿⣿⣶⣾⣿⠯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠈⢏⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠠⠶⢶⣶⡶⠶⠿⣿⣿⡿⡿⠿⠟⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣀⣸⡷⣶⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⣀⣀⣠⣾⣿⠿⠋⣽⠏⠙⣿⠟⠻⠿⣿⣿⣿⣧⣽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⣼⠏⠁⡸⠃⠀⠀⠀⠀⠀⠀⠈⢻⡍⢿⠸⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣧⢻⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢲⠖⣶⣦⡄⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠤⣀⠀⡖⠂⡃⣰⠛⣄⣣⠋⢹⣄⠈⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⣳⣷⣇⠀⣿⠹⠀⠈⣻⡾⢋⣸⠀⠀⠀⠁⢠⡄⣠⠔⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⣠⠼⢦⡑⣾⣯⠭⠭⠿⠿⠏⡸⠀⠀⢰⠀⠀⣿⢁⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡇⢸⡞⣏⣽⣶⣷⣼⠈⣦⣤⡖⠒⠒⣡⠒⠁⠈⢷⠰⣿⣾⣧⡾⠛⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢠⠏⠣⣸⣇⣈⣣⣾⢼⡇⣠⣇⠈⢿⢶⣰⠇⢀⡖⢀⢇⣨⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠻⣤⣁⣀⣀⣼⠞⠁⢸⠀⣼⣾⡏⣷⣿⣶⣿⣮⣥⣤⣄
⠀⠀⠀⠀⠐⡶⠦⣐⣢⢤⢸⠀⠙⠲⢤⣤⣽⣟⡋⠁⠀⣠⠏⢠⣧⡶⣿⠀⠙⠳⣤⡙⠋⠀⠈
⠀⠀⠀⠀⠀⣨⠷⠞⠺⣿⣼⡷⢤⣀⠀⠀⠉⠉⠉⢩⣿⣷⡶⠞⠀⠳⡜⢦⣀⠒⢽⡵⡀⠀⠀⢀
⠀⠀⠀⠀⠂⡰⢀⣤⢸⢳⠈⠛⣆⢈⢓⣦⣄⣠⣴⣯⠘⢿⣿⣀⢀⠘⢮⡄⠈⠉⠂⢳⡙⠦⠬⠶⠇⠄⠂
⠀⠀⢀⣠⣌⢤⠞⠁⠈⢏⡇⣸⢁⣼⠟⢻⠋⠙⢿⠐⢇⠀⠀⠉⠋⠉⠛⢧⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣹⡿⠁⠀⢸⣆⡄⠸⡄⣼⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡟⠀⠀⠀⠀⠉⠛⣤⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠁⠀⠉⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡴⢶⠀⢀⠀⡀⠠⠀⠀⠀⡀⠀⠈⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡁⠈⡄⡈⢀⠓⠀⢴⠣⡀⠀⠂⢀⠀⠀⠀⣀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⣿⡀⠀⠱⢵⡈⢷⠷⠾⢷⣌⢣⣀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⡐⡋⢳⣤⡀⠀⠈⠪⣇⣤⠤⠈⠁⠈⢉⣭⡿⠃⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡃⠈⣷⣭⠓⠚⣄⡈⠙⠲⠤⡐⠀⠀⢤⣴⡶⠏⠀⠠⠋⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢰⠇⠹⣇⠀⠘⢿⣀⣰⣀⡉⠉⠓⠂⠀⢽⣶⣾⠟⠁⠀⢀⠀⠀⢠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⢥⡄⠀⠿⣷⣤⣤⣉⠫⢽⡉⠉⠛⠓⠃⠈⠈⠈⠁⠀⣀⣰⠆⡀⠗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⠀⠻⣧⣄⣄⣌⡿⣿⣿⣶⣮⠣⠀⣄⡁⢲⣶⣶⣶⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡼⡾⣄⡻⡀⠈⠻⣶⣿⡟⣻⣿⠰⡀⣠⠧⠟⣋⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⣷⣿⣯⠱⡄⠀⣿⡿⠑⣿⡿⠇⢻⡁⠂⠉⣴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡠⣴⣬⢿⠟⠋⠀⠀⣴⣿⣏⣷⣿⠓⠁
⠀⠀⣠⣤⠀⠠⢴⣲⢟⠿⠟⣻⣿⣿⣿⣾⣿⣄⡀⣰⣤⣼⣿⣪⣿⡟⠁
⠀⠀⠀⠀⢀⣠⣀⣀⣀⡠⠾⠟⢋⡿⢉⠟⠛⠳⠿⠿⣤⢷⣿⣿⠃
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠞⠀⠈⠀⠀⠀⠀⠀⠈⢯⣧⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⠖⠒⠒⢦⣀⣀⠀⠀⠀⢀⣠⣀
⠀⢰⠁⠀⠀⡞⠁⠀⠈⠱⡄⡴⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣇⠀⠀⠱⡀⠀⠀⢀⡿⡇⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠉⠲⡄
⠀⠀⠈⠲⣄⣠⠟⠢⣤⠞⢀⣧⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⡆⢸⡄
⠀⠀⠀⠀⠀⠻⡇⠘⡟⠀⡽⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡴⠉⠀⠀⠀⠀⠀⠉⠲⡄⠀⡇⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣼⣣⠞⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⣾⠁⠀⠀⣀⠔⢁⣠⠔⠀⣹⠀⠸⡄⠀⠀⠀⠀⠆⢀⡞
⠀⠀⠀⠀⠀⡔⠲⡿⠋⢠⠔⠋⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⢴⣮⠭⣿⡖⣊⣉⡀⣈⡩⠤⠔⠊⠟⣆⠀⠘⢄⡀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢇⢀⣽⠀⡏⣠⠴⠖⠒⠒⠒⠒⠦⡀⢷⠀⠀⠀⢀⠀⠀⠀⠀⢯⡇⠠⠔⠲⠄⠀⠘⠉⠉⢸⠃⠀⠀⠀⢹⣻
⠀⠀⠀⣠⠔⣿⣿⠀⠀⣷⣟⠒⠒⠒⠒⠒⠒⠒⣇⣾⠀⠀⠀⠻⣉⡗⠀⠀⠀⠙⢄⠀⠀⠢⠤⠔⠂⣠⠏⠀⠀⠀⠀⢀⠧⣀
⠀⠀⠀⠁⠚⢹⢻⠀⠀⣿⢉⡭⡛⠒⠒⠚⠻⠥⠈⣽⡄⠀⠀⠀⠈⠳⢄⠀⠀⠀⠈⢑⡄⢤⠄⠐⠞⢹⣦⣀⣀⡠⠤⠺⣯⡼⠃
⠀⠀⠀⠀⠀⠛⠈⢧⠠⡻⡄⠀⢀⣀⠁⠀⣠⠀⣰⠃⠙⡄⠀⣠⡤⢤⠀⠙⠲⠤⣤⠚⠙⠪⡖⠐⡖⠁⠀⠙⣄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣇⠈⠒⣤⣬⣭⠥⣴⣊⣁⣀⣤⡿⠔⠓⠤⠼⠃⠀⢀⠔⢧⠀⢀⠀⡇⠀⠱⣀⡤⠴⠉⣆⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠉⠉⡇⠈⠉⠀⠈⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡉⠉⢹⠧⠤⠔⢻⣀⡴⠚⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢹⠇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⠊⠀⡀⠀⠀⢻⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣴⠛⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⢧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⠖⠋⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡦⠇⠘⠦⡤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⢀⣀⣀⣀⣀⣤⣴⠾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣇⠀⠉⠉⠉⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣵⡇⠀⠀⠀⠾⣩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⡴⠞⠉⠙⠳⢦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢉⣠⠞⣡⣴⠞⣫⣽⣟⢶⡄⠉⢻⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡏⡏⣾⢁⣿⡼⣡⣖⣻⣾⠟⢦⣀⣇⠀⠹⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢫⠷⡌⢳⣧⠙⣾⡛⠻⢿⣭⣀⣿⡥⠊⣿⠉⡧⢀⡿⢀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠏⢀⣸⡀⠻⣤⣻⣷⣸⡏⠙⢒⣀⣨⣽⠷⠛⣡⠞⠁⣼⠟⠁⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠠⢌⣻⣶⣄⠙⠻⢿⣿⣛⣋⣉⣥⡤⠖⢻⡏⣠⢾⡏⣀⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⠒⠿⣿⣮⣳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡾⠟⠁⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⠛⠛⠻⠷⣦⣀⣠⣤⣶⣫⡥⠶⠒⠛⠻⢤⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡴⠲⣤⣀⠀⠀⠉⠛⠛⠛⠒⠂⠀⠀⢀⣠⠟⠀⠀⢀⣤⡾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠿⣷⠶⣤⣄⣀⣀⣤⣤⠶⠋⢡⣀⣤⠾⠋⢉⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⢀⡀⠀⠀⠀⠳⣄⣀⣨⡴⣟⠹⠈⡟⢧⠟⠓⣦⠟⠋⣅⠀⣀⡞⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢍⡛⠛⡻⠶⣤⣦⡀⠀⠀⠙⠀⢹⡆⢰⠇⠈⣠⠞⠉⢀⠀⢹⣠⠟⣀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠙⢦⣷⠘⡌⢫⠙⢶⡀⠀⠀⠀⡇⡿⠀⣸⠃⠀⡆⠸⡄⣸⠟⠋⠁⢀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈⣉⣉⣳⣷⡘⡆⠂⢷⠀⠀⠀⣿⡇⠀⡏⢠⠀⢳⠀⣿⣥⠴⠒⠁⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢀⣈⣀⡽⠷⣿⣾⣀⣀⠀⣿⡇⠀⣷⠀⣇⢨⡟⢁⣀⡤⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠤⠔⢺⣿⢭⣍⡓⢿⡇⠀⠘⣆⣸⠟⠋⠉⠁⠀⢘⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣄⣬⠵⠃⠀⠀⠹⣮⡇⢀⣠⣾⡛⠛⠛⠉⢁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠋⠹⣍⡫⣉⣁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢲⡝⠃⠀⠀⠀⠀⢀⣷⠏⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠛⠣⡈⠇⠀⠀⠀⠀⡀⣦⠁⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠀⠀⠀⠈⠑⣆⠀⠀⡰⠳⠈⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⠋⠀⠀⠀⠀⠀⠈⣦⢂⣵⣦⠒⠈⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⠁⠀⠀⠀⠀⠀⢠⣟⣼⣻⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣇⠸⡏⠀⠀⠀⠀⠀⠀⡴⣏⣟⢻⡁⠄⠐⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡌⠀⠹⠀⠀⠀⠀⠀⡄⣠⠎⠉⢀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⠁⠀⠀⢷⠀⠀⠀⡞⠹⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣥⠻⠀⠀⠀⠀⠈⡇⣀⠘⣠⡶⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣾⣿⠱⡆⠀⠀⠀⠀⢸⡟⣤⣋⣠⡴⠖⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⠇⠀⠘⣄⠀⠀⠠⠈⡾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡄⢻⡏⠀⠀⠀⠀⠆⣴⠟⣠⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠙⠄⢃⠀⠀⠀⠀⠸⠏⣸⠟⠁⠀⠀⠒⠋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠘⣇⠀⠀⢀⠀⠐⠁⠀⠀⠀⣠⣄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠸⣄⢠⠌⣤⣴⡤⠤⠤⠊⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢠⣿⡾⣾⣿⡩⠄⠐⠒⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢸⡇⣰⠏⠀⠀⢀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢱⡿⠦⠐⠚⣻⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣡⡟⠟⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣤⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠹⣷⣿⣿⡿⠾⠿⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣶⣿⣷⣶⣶⣶⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⠟⠉⢹⣿⣷⢻⢯⣉⣹⣿⣿⣿⣿⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣶⣶⣾⣿⣯⠟⣾⢋⣻⣿⣻⣿⣽⣿⡈⣷
⠀⠀⠀⠀⠀⠀⠀⣱⣭⣝⣻⣿⠿⢛⣡⠞⠉⠉⠉⠀⣀⣀⣼⣿⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⡿⢟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡗⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡧⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣤⣄⣀⣀⣀⣀⣼⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠿⠿⠟⠛⠛⠋⠁

⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣠⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠘⡡
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⢶⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⡄⢤⠊⠀⠀⢀⡀⢰⡇⢀⠊⠀⠀⠀⠀⢠⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡘⣿⠁⠧⣀⣿⣠⣼⣠⣾⣵⣹⣿⠋⠔⠛⠋
⠀⠀⠀⠀⠀⠠⠀⠐⠾⠲⢶⣿⣜⢮⣤⣿⡿⠟⠁⣻⣿⢋⠉⠁⠀⡀
⠀⠀⠀⠠⠶⠶⢾⣶⡶⡶⢾⣿⣿⠈⣿⡥⣀⣤⣎⠀⠀⠁⠙⢯⠀⠉⢻
⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠜⠁⠨⠉⠀⠂⢡⣤⡞⣋⡙⣓⡶⠾⣇⢀⡘
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⣴⠀⣾⢁⡔⣱⣿⣾⣷⠆⣀⣹⠻⣷⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⡳⢤⣽⣼⡇⠀⣷⣿⡾⢽⣽⣿⣧⠻⠄⠈⠋⢠⡏⣧⠀⠀⡔⡀
⠀⠀⠀⠀⢧⣀⡂⢀⣤⡴⠋⠉⣄⠀⢸⡏⠳⠈⠿⠃⣈⡀⠀⡤⠀⡈⠁⢻⣷⣾⡟
⠀⠀⠀⢤⡼⠟⣇⣻⠯⠀⠀⢮⣉⠀⢼⣇⠐⡗⠦⣤⣟⠁⠀⠀⣰⠁⣀⣾⣿⠟⠛⠛⢲⡼⠁
⠀⠀⠄⠀⣴⡿⡏⠛⢄⠀⠀⠀⠈⢣⡀⠙⢦⣸⡶⠶⠜⠳⢦⣠⣿⢸⣿⣿⡅⠠⣤⣤⠜⠁
⠀⠁⠀⠀⠾⠁⠁⡀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠉⠀⠀⣀⠀⢀⣹⡟⠋⠀⠀⠀⢀⡿⠁⠀⠀⠀⢠⠀⠖
⠀⠀⠀⠀⢰⡼⠚⠁⠀⣀⣀⠀⠀⣠⠞⠉⠉⠙⠻⠿⠛⢿⣭⣛⠄⠀⠀⢀⡠⠊⠀⠀⠀⡠⠖⠊⠛
⠀⠀⠀⠀⠈⠀⠚⠉⢀⢩⣽⣷⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠓⠋⠙⠛⠷⣶⢶⡋⢵⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠣⠿⣏⣸⣿⣶⣄⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⠆⠑⠀⠡
⠀⠀⠀⠀⠀⠄⠈⢀⣀⢦⣘⣿⣿⣿⠟⣯⠈⠉⠢⣄⠀⢀⡀⠀⠀⠀⣀⢀⠛⠻⠀⠀⠀⠀⠀⢄⢣⡀
⠀⠀⠀⢀⡠⠒⠋⠀⠞⢉⣩⣿⣿⣏⣷⣿⡷⠀⢀⠀⢀⠞⠁⢿⣷⣿⣟⢛⠏⢩⡏⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⠃⠄⠐⠃⠁⠀⢸⣿⣿⢿⡉⠉⠹⣁⠐⣒⠀⣹⣷⡆⢼⡏⠳⡝⢦⡀⢀⣴⣈⡵⠞⠛⠖⠒⢄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⣿⡁⠾⢁⡀⠀⠈⠉⠁⢸⡆⠹⣯⠀⢿⣄⠁⠀⠙⠎⠛⠻⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠾⡁⠢⣤⠀⠀⢰⣌⠀⠀⠀⢀⠋⡷⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡓⡂⠀⠀⠸⠃⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡀⠀⠀⠀⠀⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⢀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠔⠆
⢀⡀⠀⠀⢠⠆⠀⠀⠀⢀⠀⠤⠀⠖⠂⠀⠀⠈⠉⠁⠒⠒⠊⠋⠁⠀⠀⠁⢸⠠⠤⠐⠒⠈⠁⠀⠁⠈
⠆⠁⠔⠀⠘⠀⢀⠠⠀⠤⠤⠤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠴
⠀⠐⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⡔⡈⠰⠄⠀⠁⠌⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠤⠤⠤⠐⠒⢒⡔⠃⠀⠈⠐⢲⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢈⠀⠸⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢈⡀⠀⡆⠀⢀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡆⠉⡋⠉⠀⠀⠈⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⣃⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠹⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⢀⠒⠈⠀⢘⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣀⡴⢚⣉⣁⡀⠁⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⠴⠃⣠⠞⢁⡞⠋⠀⢀⡔⢋⠉⠀⠠⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⢣⠀⢸⡆⠀⠀⡸⢠⡎⠉⠢⠀⠈⢣⡄⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⣠⠏⢀⣾⡇⢆⡇⢡⠘⢌⢂⣰⢱⢀⠀⡥⢆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣼⡏⢀⡞⠁⠘⢦⠱⣀⠀⣠⣤⣥⡖⣚⣐⣡⠇⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⡎⠀⠀⠀⠈⢆⣀⣉⠢⡀⠤⠒⠋⠉⠁⢀⡞⠁⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠒⠢⢄⠀⠀⠀⣀⣀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠳⣌⠢⢄⡉⠐⢲⠞⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠙⠄⠀⠀⠉⢻⡇⠀⠀⠀⠀⠛⣀⡠⠤⠶⠶⠤⢄⡠⢀⣨⠷⠖⠒⠛⠉⠀⢰⠖⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⡀⠀⠈⡄⠀⢀⡼⢷⡀⠀⢠⡖⠛⠓⠤⣀⢀⣠⣤⡀⠈⠋⢁⣀⡀⠀⣿⠛⠒⠋⠀⢨
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠢⣰⠀⣸⠁⡜⠁⠀⠀⣙⡷⣾⠁⠀⠀⠀⠈⠉⠁⠀⠀⠑⠢⠞⣹⠟⠊⠁⠀⢀⡶⢤⠎
⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⡇⣸⢁⡠⠖⠋⢁⡞⢉⣷⣤⣄⣀⣀⡀⠀⠀⣀⣀⡤⢞⣁⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠉⠉⠁⠒⠠⠈⠟⣁⣁⣀⣀⡼⠉⡴⠋⠁⢡⠉⠉⠉⠉⠛⠿⣟⡶⠾⠛⠉⠉⠑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⣀⣤⢸⠀⠀⣠⠟⣠⠊⠀⣀⠤⢼⡴⠂⠤⠤⢤⣀⠀⠙⢄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠈⣇⢀⠔⢡⠼⠁⠀⡼⠁⠀⠈⠀⠀⠀⠀⢠⠟⠀⠀⠈⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⡴⠃⠀⢀⡼⢁⣠⠔⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⣓⣒⣀⡛⠻⢭⡐⠢⢄⣀⣠⠔⠛⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠖⠉⠀⠀⠈⠙⢦⠀⠈⠢⡀⠈⠳⡒⠤⠄⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡄⠀⢳⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠷⠦⠤⠤⠤⠶⠒⠒⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⢠⢊⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡇⢸⠃⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢢⣼⡡⠞⡰⠖⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢹⡀⡜⠁⠀⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠤⢤⣀⠀⡁⠀⠈⠁⡇⠀⠀⠀⢳⠀⣀⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⢒⡶⠋⠀⠀⠀⠀⠈⠉⠢⡀⠈⠳⣇⠀⢰⠂⠀⠀⠀⢀⡮⠞⢋⠨⠵⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠄⠀⠤⠤⣄⡀⠀⣠⠊⠁⠀⡤⠒⠋⢐⣲⡤⠤⠤⠄⡀⠀⠀⠘⡆⠀⠘⡧⣌⡙⠓⠒⠚⠉⠀⠚⢥
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠸⠀⢠⠊⠀⢀⠤⠠⢤⠀⠘⠦⡀⠀⠸⠀⠀⠘⣄⣜⠉⠉⠉⠉⠓⢦⡀⠇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠒⠦⣄⣨⢧⠀⠀⠀⠰⠀⣼⢆⠠⣡⠖⠀⠒⣿⠀⠀⣸⠀⠀⡇⠀⠀⢁⠈⠉⠲⣄⠀⠀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⠀⠀⣠⠖⠋⠁⠘⡆⠀⠀⠀⠱⠝⣄⠙⠢⠤⠖⠊⣛⡤⠊⡌⢀⡴⠁⠀⠀⢸⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢑⠞⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⠆⠈⠢⡀⠀⠠⠀⠉⠀⠀⣧⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠊⠹⡀⢀⡴⠊⠉⠉⠙⢆⠀⠀⡎⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠲⢄⣀⡀⠀⠀⣳⠋⠀⠀⠀⠀⠀⠀⠑⢦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⢊⠝⠋⠁⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠭⣧⠤⢤⡀⠀⠀⠀⡴⠿⠶⣤⡈⠉⠀⠒⠠⠶⠶⠒⠒⠉⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡤⠂⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⢀⣀⣀⣀⠠⣤⡴⠋⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⠙⠳⢦⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠒⠒⠒⠒⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠒⠚⢻⠤⠤⣤⡤⠤⠴⠶⠒⠈⠿⠄⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⣀⣀⣘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠐⠢⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠶⠋⠉⠀⡴⠛⡏⠉⠓⠲⡖⠒⠒⣶⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⠞⠁⠀⢰⡄⠀⠀⠁⠀⠀⣿⠀⠉⠛⠲⠦⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠙⠲⢤⣤⣀⣀⣀⠤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠊⠀⠀⠀⢸⠛⠦⣄⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠉⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⡠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⣚⣲⣦⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠾⠋⢍⠉⠉⢁⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⠙⠾⠳⠶⠶⠂⢀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢦⡀⠀⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⠀⠙⣷⡶⣶⡶⠂⠀⢀⣠⣤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢬⣽⠿⢀⡴⠞⠋⠁⡠⠤⠗⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠠⠀⠀⢀⣀⡈⢦⣿⣶⠛⢁⣠⠤⠔⠶⠖⠈⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⠀⠀⠀⠀⠀⠈⢂⣻⡇⠀⠀⠁⠀⠀⠀⣸⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠙⢻⣄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⣀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠀⡀⠀⡾⠁⠀⣠⣴⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡄⠘⢷⡀⠀⠀⠀⢀⠀⣀⡞⠁⢠⣷⠞⢁⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣮⣿⢻⠛⣛⡉⠛⢋⣤⣤⣿⣷⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⣿⣶⣿⣿⡟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣻⣟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠘⠿⣤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢀⡀⠋⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠋⠀⠀⡀⣼⣿⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⣧⠀⠀⡸⢳⣿⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡾⡃⣠⣾⣿⣿⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣶⣄⡀⠈⠿⣧⡀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣿⣿⠿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠺⠷⠿⠷⣄⠀⠀⠀⠘⡇⠀⠀⠀⠹⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢠⡇⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣔⠂⢄⡀⠀⠀⠀⠀⠀⠘⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡝⢿⣿⣶⣼⣦⣤⣀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣗⡀⠉⠙⠛⠿⣿⣿⣷⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⣀⠀⠀⠀⠀⠈⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣦⣤⣀⠀⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠙⠃⠚⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣀⠾⡦⠀⠀⠀⠀⠀⢠⠶⣝⣦⠄⠀⠀⠀⠀⢀⠔⢻⣯⡠⢄⠀⠀⠀⠀⣔⣲⡟⢻⣷⣤
⠀⠀⠀⡞⠁⠀⡇⠀⠀⠀⠀⠀⢸⠁⠈⠃⡆⠀⠀⠀⠀⠸⣤⠳⡬⠗⡋⠀⠀⠀⠘⡏⠙⠫⣹⠃⡣
⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠈⠲⠤⠖⠁⠀⠀⠀⠀⠀⠘⠦⠤⠔⠁⠀⠀⠀⠀⠙⠢⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⡴⠂⣠⣴⠢⡄⠀⠀⠀⠀⢀⢔⣒⣆⢙⢄⠀⠀⠀⡰⡾⣧⣬⣙⣂⠀⠀⠀⠀⡠⠒⣶⣽⢦⡀
⠀⠠⡳⡈⠧⡼⣳⠑⡄⠀⠀⡠⢶⣹⣘⣹⢾⢸⠀⠀⠺⡀⡻⣿⠿⢇⡼⢱⠀⠀⠸⣀⠯⠓⡁⢳⣹
⠀⠀⠑⠌⠂⠈⠽⠋⠀⠀⠀⠙⠢⣗⣤⣒⠥⠃⠀⠀⠀⠙⢍⡒⠚⣹⠔⠁⠀⠀⠀⢸⣓⣒⣋⣁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⡠⢤⣄⠲⡄⠀⠀⠀⠀⣠⢤⣴⢤⠀⠀⠀⠀⠀⠀⣀⡤⠤⣀⠀⠀⠀⠀⠀⣠⠤⠔⣤⡀
⠀⢀⠜⡴⡗⢒⢝⡟⡆⠀⠀⡰⠁⠻⠿⢹⡈⣆⠀⠀⢰⣉⣼⢿⣛⣿⡍⣆⠀⠀⢰⡹⡽⠿⣬⢏⠲⡀
⠀⠸⡀⣯⣻⣿⣾⡥⠋⠀⠀⡷⢤⡢⠤⢀⠃⣹⠀⠀⠀⡟⠯⠦⡐⠽⠣⡞⠀⠀⠻⣄⠻⣭⠵⢣⣷⠁
⠀⠀⠈⠑⠦⠤⠔⠁⠀⠀⠀⠈⠒⠛⠛⠥⠖⠁⠀⠀⠀⠈⠲⠒⠓⠖⠉⠀⠀⠀⠀⠣⠭⠝⠛⠯⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠒⠒⠊⠁⠀⠀⠀⠀⠉⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠄⡀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡠⠂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠖⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠐⠀⠠⠁⠀⠀⠀⢠⠦⡀⠀⠐⠠⠀⡀⠀⠈⠉⠁⠀⠀⡩⠀⠀⠀⠀⠀⠰⠢⠔⠘⠐⢃⡮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⠑⠂⢄⣄⣀⣀⢀⣀⣠⡔⢺⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣠⣶⠤⢤⢀⠀⣀⣠⡛⢡⡌⢊⡷⠊⠀⣋⠏⠀⠀⠀⠀⠀⢀⠎⠀⠈⠁⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢒⢢⠤⡴⣽⠀⠶⠀⡩⠗⢀⠉⠶⡤⠤⣢⠃⠀⠀⡇⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠆⠀⠈⢓⡒⠚⠋⠀⠠⠴⠀⠀⠀⠮⠹⢀⡜⠀⠀⣀⠤⠒⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀⠧⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠪⠗⠲⡍⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣠⡜⠢⠤⣄⣀⣀⣀⡀⠤⠴⠊⢡⠃⠀⢀⡁⠘⡀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠸⢀⡀⠀⠀⠑⢄⠈⢢⠄⠲⠀⠃⡤⠔⠉⢡⠀⢃⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠆⠀⠈⡗⠂⠐⠁⠁⠺⡀⠀⡏⢠⠂⠀⠀⠀⡀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⠀⠀⠀⠀⠀⠀⠙⠢⡝⠞⡐⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠄⠀⡆⠀⠀⠀⠀⠀⠈⠄⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡰⡇⠀⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡌⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠰⠇⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⣮⢀⠀⠠⠤⠤⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠆⠰⡘⠾⠁⠀⠀⠀⠉⠀⣀⣀⡀⠷⠠⠤⠤⠀⠒⠠⠜⠒⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⣸⠀⠀⠈⢻⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢢⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠞⣰⢠⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⢄⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢱⡋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣠⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⢤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠻⣿⣧⣞⣶⡴⣀⠈⠑⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡛⣃⣴⣾⣈⠻⡥⠔⣻⠀⡆⠀⠘⢷⡄⠀⠐⢦⣄⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣿⣧⣽⣿⣿⡿⢿⠷⣦⣤⠉⢠⣷⠀⢱⡀⢹⢀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠽⣿⣿⣿⠏⠀⠀⢶⡾⠁⠀⠚⣿⣥⠀⢳⣼⣷⡟⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡄⠈⠻⡿⠀⠀⠀⠟⠀⠀⡴⠁⠞⣿⣅⠈⣿⡟⠁⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣶⣿⣏⣿⡄⠀⠀⠄⠀⠄⠀⠀⠴⠀⠊⢀⣻⣷⡄⠻⠀⢠⣟⡀⠠⡀
⠀⠀⠀⠀⠀⠲⢿⣿⣷⣜⠃⠙⠿⣿⣿⣿⡦⠀⢨⣤⢴⡪⠃⠀⠀⠀⢠⣽⣿⡗⢀⣠⣿⣿⣿⡄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡷⡀⠀⢹⣿⣿⡇⠀⠀⢻⣆⠰⣄⡀⣄⢀⣼⣿⡿⢡⣯⣾⣿⣿⡿⠟⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢿⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⡟⢠⣾⣿⣿⣿⣯⢣⣤⣶⠴⠾⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢋⣦⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⡿⠿⠛⠛⣿⣟⣿⣶⣬⣤⣀⡀⡀⠀⠐⢤⢟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⣯⣿⡿⠋⠉⢻⣿⣿⠏⠀⠀⣿⡈⠱⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣻⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠑⠒⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠚⠋⢉⠛⢱⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠑⣿⣫⡶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⡂⠐⠒⢀⡀⠀⠈⡇⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠙⠃⠚⢶⣄⠀⡙⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠞⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠄⠀⡀
⠀⠀⠘⢮⢳⡔⠢⡀
⠀⠀⠀⠈⠱⢿⣆⠀⢳⣄
⠀⠀⠀⠀⠀⢀⠙⢄⡀⣻⡆
⠀⠀⠀⠀⠀⠀⢳⣴⣿⡿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⠇⠀⢰⣾⢶⣄⣼⠧⠀⠖⡆⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢿⣇⠀⠀⣸⡇⢀⣻⣏⠀⢀⣄⠳⡆⠀⠀⣠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⠶⠞⠃⠀⠀⢽⣆⠐⣿⠇⠀⠀⠉⢙⣿⣿⡆⠘⣆⣆⡟⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⢀⣽⣿⣿⣿⣧⣠⡴⠟⠛⠿⢿⣿⠀⢹⣿⣥⠾⠷⠾⣶⠀⣽⠂⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⢄⡽⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠻⣄⢾⣿⡁⠀⠀⠀⣿⠸⡟⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢴⡾⠁⠀⠀⠀⣠⣷⣤⡤⣶⡢⣴⣆⠀⠈⠻⣿⣿⡄⠀⠀⢳⡄⢻⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡟⠀⠈⠁⣹⣟⠿⣿⠏⡿⠂⠃⠁⠃⠈⠈⠻⣤⣀⡙⢿⣿⣷⠀⢻⡇⡞⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⢤⣜⠯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡟⠛⠸⣿⡇⢘⠉⢗⡼⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠜⢉⡍
⠀⠀⠀⠀⠀⠴⠂⠒⠒⠛⠓⠈⠃⠶⢦⣤⣶⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⣉⣩⣷⣤⡀⠀⡀⢀⠀⠀⠀⣀⠤⠖
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠄⠆⠈⡼⠛⠀⠙⣿⣏⣹⣿⣷⣄
⠀⠀⣠⣷⣾⡶⠶⠶⠶⠦⣤⣀⣰⢁⣠⣶⣆⠁⠀⠀⠀⠀⢿⣿⠀⠙⠿⣿⡄
⠠⠄⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⢿⣏⣿⠂⠀⠀⠀⠀⠸⣿⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁⠀⠀⢉⡿⢤⠤⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢧⡄
⠀⠀⠀⠀⠀⠀⠐⠀⡀⣀⢠⣤⠿⠿⢠⠂⣀⣀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠈⠉⠉⠉⠀⠈⠴⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠠⠀⣤⣀⠐⠆⢄⠂⠀⠀⠀⢀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⠉⠁⠀⠑⡐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠂⠀⠈⢦⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰⣧⠀⠀⠀⢰⣦⡄⠀⠀⠀⠑⡦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠀⠀⠀⡀⠀⠀⢀⠀⢨⠀⠁⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣦⡀⠀⠀⠉⠁⢠⡄⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠙⢥⠀⠺⣶⡶⠟⠁⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⣀⠈⠉⠁⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠘⠡⠀⠤⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⣀⠤⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⠄⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⡀
⠀⠀⠀⢤⡀⠀⢀⠠⠘⠈⠀⠀⠐⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠃
⠀⠂⠐⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠂
⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠤⠄⠤⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠲⡄⠀⠀⢨⠁⠀⡅⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠰⠶⠇⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠇⠀⠀⠀⡇⠘⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢀⣠⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⡅⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⢲⠂⠋⠀⠀⠈⠳⠒⠲⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠘⠈⠁⡇⠀⠀⠀⠀⠉⠉⢋⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠎⠀⠀⢀⠀⠀⠀⣰⠀⠀⠀⡠⠀⠀⠀⠀⠈⢑⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣀⣀⣀⡀⢀⡀⣀⣠⠇⠀⢰⡋⠀⠀⠀⠀⠉⠀⣀⡠⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣴⣾⣿⣯⣶⣶⣶⣶⣷⣷⣷⣶⣿⣿⣶⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠁⠉⢉⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣾⣿⣿⣿⠾⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⣿⡿⠁⠷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣿⣿⡿⣡⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢯⣿⣿⣻⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡉⣣⣾⣿⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣛⣿⣿⠿⣷⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣶⣟⣛⣦⣀⠀⠀⠀⠀⠀⣻⣿⣿⣵⣞⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⣿⣿⡿⠊⠁⢺⡇⠀⠀⠀⢀⠟⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣿⣿⣷⡂⠀⢸⣿⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⣿⣿⣿⣿⡃⣀⠸⠿⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⠄⢸⡀⡀⢀⢀⠄⡀⠀⢀⡏⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⣀⢄⢠⢰⣉⠀⡇⢁⢘⠀⣙⢈⣢⢸⠁⢸⢸⢸⠒⠁⠀⢸⠃⠀⡇⡈⢁⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢸⠀⠘⠌⠠⠀⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠊⠈⠤⠌⠘⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡤⠤⡤⠜⠙⠉⠓⢲⣀⠀⠀⠀⠀⠰⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀⢀⠔⠃⠀⠀⠀⠀⠀⠀⡤⣀⡀⠀⠀⠋⠙⠊⠳⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣃⠔⠋⠁⠀⠀⠀⠀⢨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠠⡈⢩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠠⢌⣒⡲⠄⢺⠁⠀⠙⠀⠀⠀⣠⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣄⣀⠦⠬⠭⠹⣇⠀⠀⠀⢀⡠⠟⠁⠘⠤⡄⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣸⢸⠀⡝⣿⢿⠀⠀⠀⠸⢤⣀⡶⠞⠀⠀⠀⠀⠀⠈⠉⠓⠋⠒⠩⡃⠀⠀⠀⢦⣀⠀⠀⢀⡹
⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⡏⡼⢠⠃⠉⠀⠀⠀⠀⠀⢸⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢅⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢰⠃⡾⠀⠀⠀⠀⠀⠀⠤⡄⡄⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡆⠀⠀⠀⠀⠀⠀⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⠜⠀⠀⢴⠆⠀⠀⠀⠀⢁⠡⡀⠀⠀⠀⠠⣞⡀⠀⠀⠀⠀⣤⠀⠀⠈⢆⣀⠀⡀⢀⡖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣠⢷⢤⡀⠀⠀⠠⣀⠄⠀⠀⠀⠀⠀⠀⢀⠴⠩⢋⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢷⣦⠤⠤⠤⢤⢴⣖⠉⠁⠴⡄⠸⣗⡲⠤⠄⢤⡤⠤⠤⠤⢶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⠀⢻⡇⠀⠀⡾⠞⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠧⠴⠟⠁⠀⠀⠟⠃⠰⢷⠄⢀⡀⠀⢤⠄⢢⢄⡘⠚⠷⡀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠦⠀⣀⡀⠈⠙⠀⢸⠀⠀⠉⠉⠂⠼⠟⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠐⣠⠄⠀⠉⠀⡒⠦⢼⣀⢀⠀⡀⢀⠀⡀⠠⣐⠢⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⠩⠧⠤⠾⠦⡤⠴⠾⠳⠈⠀⠑⠚⠂⠈⠁⠈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⠀⠈⡀⠀⠀⠈⢂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡄⠌⠸⡄⡤⠂⠀⠀⠐⠤⢠⠃⠈⠢⡄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢄⠀⢠⣀⠧⡀⠀⠀⢠⠲⠴⠀⠀⡠⠆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢡⢠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡖⢸⠇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢾⠅⢊⡼⠋⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠆⡜⠀⠀⠀⣷⠐⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠲⠶⣒⠒⠢⣄⡁⠀⠀⠆⠃⠀⠀⠀⢹⢀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⣩⠋⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠻⣄⠀⣇⣀⠀⢀⡠⠞⣉⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠠⡤⠒⠂⠈⠉⠈⠈⠉⠒⢦⣀⡔⠁⠀⢠⠞⠁⡠⠄⠚⠛⠈⠀⠀⠀⠀⠀⠸⡀⠀⠹⡐⢤⡤⣤⡤⣄⣀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢄⡀⠀⠀⣏⠀⠀⠀⠈⠀⢈⠀⠀⠔⡀⠀⡲⡄⠈⠐⡄⠀⢣⠀⠀⢱⠺⠤⣀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢈⣳⠖⠙⡆⠀⠀⠈⢄⢯⠑⢼⡘⢀⣀⠴⡇⠀⡠⡁⠀⡸⠀⠀⢀⠀⠀⠈⠑⢄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠓⠦⣀⠔⠉⠀⠀⠀⢳⠀⠀⠀⠈⡂⠳⡀⠈⠉⠒⠰⠖⠁⢰⢀⠞⠁⠀⠀⢸⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠤⡞⠀⢀⡠⠄⠒⠸⡄⠀⠀⠰⠁⠀⠈⢆⠔⠁⠀⠀⠀⠀⡇⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢹⡠⠋⠀⠀⠀⠀⠈⠢⡀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⡠⠔⡴⠛⠀⠀⠀⠀⠀⠀⡿⠒⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⢒⣾⢃⣀⠀⠀⠀⠀⢀⣤⣚⡛⠃⠀⠀⢠⢈⣀⡀⠠⠠⠚⠉⡰⠋⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠉⢱⠀⠀⠀⠋⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠺⢥⣀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠠⠤⠤⠤⠤⡆⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠈⠉⠥⠾⣯⣀⣀⠀⢀⣀⣀⠤⠖⣻⡃⠀⠀⠀⠀⠈⢣⡞⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⠉⠁⠀⠀⠀⡴⠃⠈⠑⠂⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⠔⠒⠉⢉⠟⡏⠒⠢⠤⡤⠤⠤⣤⡒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠋⠀⠸⡀⠀⠀⠁⠀⠀⡏⠉⠓⠲⠤⣀⣀⣀⣀⣠⠴⠚⠁⠀⠈⠙⠦⣄⣀⣀⣀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠁⠀⠀⢀⡟⢦⣀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⠙⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⠠⠔⠚⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠲⠂⠈⠉⠉⠉⠉⠉⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡁⠀⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠸⠇⢀⠀⢀⡠⠄⢲⡾⠉⠉⠉⠉⠉⠉⠉⠀⠒⠒⠂⠠⠤⢈⣳⠀⠀⠀⠀⢄⠀⠀⠃
⠀⠀⠀⠀⠆⠀⣾⠞⠁⠀⠀⢈⡴⢂⣈⠁⠢⡀⠀⠀⠀⠀⡠⢊⣡⡌⠑⢤⡈⠑⠤⣀⠀⠀⠀⢸
⠀⢀⡤⠞⠂⢴⡇⠀⠀⠀⠰⠋⣰⣿⣯⣴⣦⣸⡆⠀⠀⢠⣧⠼⠿⠷⠷⠤⣵⠀⠀⠘⡷⠀⠀⢸
⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠙⡗⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⠸
⠀⠀⠀⢇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⢀⡏⠀⠉⢿
⠀⠀⠀⠘⢧⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠘⣏⠃⠠⠴⠦⠖⠘⢋⡼⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠈⠳⢤⣀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣐⠂⠲⡄⠀⢀⠔⠁⣠⠞⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠳⢦⣀⡀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢈⣤⡁⠀⠘⠣⠚⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⡶⠶⠶⣶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⠀⠀⠰⣉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠇⠀⠀⢷⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠈⠯⣀⠀⠀⠀⢀⣨⠋⠈⠁⠀⠙⠛⠒⢶⡆⠠⠤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢤⣤⡤⣤⠞⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠤⠤⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸⡧⣤⣤⠤⠤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠘⢄⢸⣧⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⢶⡿
⠀⠀⠀⠀⣌⠁⠀⠀⠀⠀⠈⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⢀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢤⣀⡘⠀⣴⠀⠘⣧⣈⡄⠀⠀⠀⢀⡏⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠉⠛⠦⠻⡤⠚⠀⠈⠀⠀⠀⠀⣘⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠶⠒⠀⠀⠀⡟⠀⠀⠀⢸⡄⠀⠀⠠⠴⠶⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣀⣀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣰⠇⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣇
⠀⢀⠴⠚⠓⠠⣄⠀⠀⠀⠀⠀⠀⠀⡌⠉⢻⡄⠀⠀⠀⠀⠀⢸⠇⠀⣠⣤⠤⠴⠦⠄⢈⣦
⡰⠃⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠙⢒⠦⣷⠀⠀⠀⠀⠀⢸⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣧⣀⣀⣀⣀⣀⣀⣀⣘⣁⢀⠀⠀⠀⢘⠋⠀⣼⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣽⣿⣷⣶⣶⣶⣶⣶⣾⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠀⢀⡴⢠⡀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠀⠀⠀⠏⠀⠀⠉⢠⠀⡀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⡃⢿⡀⠀⠀⠀⡄⠀⠀⠀⡄⢡⠀⠀⠀⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠐⠤⢄⣀⠁⠌⠁⠀⠀⠀⠓⠂⠀⠁⠙⠚⠟⠒⠀⣀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⡀⢸⡀⠂⠀⠀⠀⢀⣀⠀⠀⠀⠔⠀⠀⢀⡠⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠙⠛⠀⢀⡜⠊⠀⠀⠀⠀⠀⠠⠴⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠠⠐⠈⢱⠄⠀⠀⠀⠈⠀⠀⢀⣀⣈⣲⡒⠀⠶⠓⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⢀⠟⠢⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣤⠄⠀⠀⠀⠀⠐⠉⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠂⠛⠁⠀⠀⠀⠀⠀⠓⠒⠛⠓⠲⠶⡒⡟⠀⠈⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠛⠒⠒⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠻⡀⠎⠀⠀⠀⠀⠀⠉⠉⠓⠐⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠒⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⡧⣤⣤⣤⡆⡀
⠀⠀⠀⠀⠀⢀⢡⡄⣄⡠⣦⣾⡎⠀⠀⠀⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⣠⡿⢋⠷⢿⣯⠟⡀
⠀⠀⠀⠀⠰⢾⡏⠰⢾⣿⣷⣴⢰⡄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⡄⠀⠀⠤⣤⠞⠃
⠀⠀⠊⠀⠀⡼⣄⢻⣏⣟⣽⣥⠚⠛⣤⡤⢀⠆⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣿⢇⡤⠂⠈⠁⠀⠀⠸
⠀⡀⠀⠀⠀⢧⠀⠀⠀⠁⡠⠦⢦⡿⠋⢀⡌⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡿⠊⠀⠀⣠⠄⠠⠤⡀
⠀⢀⡀⠀⠀⠀⠀⠙⠶⣜⠀⠀⣈⣠⠄⠛⢣⠀⠀⠈⡆⠀⠀⠀⠀⠀⠔⠒⠒⣈⡿⠀⠀⢠⣴⣍⡛⡟⠓⠂⠁
⠀⠀⠑⣀⡀⠀⢀⠀⠒⠚⠋⠛⠋⠀⠀⢠⡴⠁⠰⠂⠀⠀⠀⢀⠄⡄⠀⣆⡼⣉⠇⠀⠀⠀⢸⠋⠀⠃⢀⡄
⠀⠀⠀⠀⠹⠀⠁⠀⠀⠀⠀⠀⣀⠀⣀⠈⠀⢀⠁⠀⠀⠀⠀⠈⢸⡧⠾⠃⣤⠏⠀⠀⡀⡐⠁⢀⠤⢀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠐⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⡾⠋⢛⣒⠚⠁⠀⠀⡀⠂⠀⠀⣁⣆⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⠀⡞⣀⣶⣋⣡⣤⣡⡴⢺⠕⠀⠀⣶⡿⠿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠋⠉⠛⠹⠭⠥⠍⠛⡝⠀⠀⡀⠛⠷⠶⠧⣤⣤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢀⠀⡀⠀⠀⠀⠀⠘⢂⡀⠀⠀⠀⠀⠀⢸⡤⠞⢩⣷⣄⡀⠀⠀⢸⣿⣿⠃⢀⠐⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞⠃⢀⡐⢲⣬⣶⣾⠋⢉⣭⣽⣿⡆⡁⠀⠀⠀⢠⡶⠃⠀⠀⣸⣿⡦⠑⣄⠀⠈⠻⢻⡿⣯⣤⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠧⢐⣶⠿⣿⠟⢹⡇⠋⢠⣬⡿⠻⠉⢻⠙⡆⠀⢰⡞⠀⠀⠀⠀⢰⡿⣧⣀⠘⠆⠀⠀⠉⠓⠟⠒⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠐⠛⠒⠈⠀⠀⣾⢹⠇⠀⢀⡞⠆⠰⡀⢻⠁⠀⠀⠀⠀⠀⠳⡟⢤⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⡛⣛⠉⣅⢲⣮⡸⠀⣀⡜⠀⠀⠐⣵⠋⠀⠀⣀⡒⣘⢂⣲⢚⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣙⠓⠻⢿⣿⡷⠾⣉⡀⠀⡇⢀⡇⢀⣠⣰⣿⣴⣿⣾⡏⢛⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⠿⠲⡄⠉⢶⢱⣎⠟⠁⣴⣿⠉⢢⠉⠻⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢤⣶⣶⡆⠹⣟⣿⣏⠐⠀⢸⡀⠀⢹⠇⠀⢸⠾⡷⠀⠀⠃⢀⣶⣿⢟⡓⢠⡀
⠀⠀⠀⠀⠀⠀⢀⢊⣀⣉⡽⠻⠟⢉⠀⢛⣿⢉⠙⠀⠠⡇⠀⣴⠀⠀⠈⢴⠻⣦⠀⠇⠈⠙⢹⠛⣦⣀⠹⡀
⠀⠀⠀⠀⠀⠀⠄⢀⡴⠟⠀⠀⢠⠜⠀⠈⠛⢿⣝⠀⡴⠁⢸⡏⢃⠀⠀⠀⢱⣴⠆⠀⠀⠑⠼⡀⣙⣛⣄⣧
⠀⠀⠀⠀⠀⠚⠒⠘⠒⠒⠓⠉⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⣸⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠟⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠄⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠁⠀⠀⠁⢃⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠊⠀⠉⠁⠀⠼⠃⠒⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⢀⠔⠈⠒⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠁⠀⡄⠀⡆⠀⠀⠀⡐⢀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡌⠀⠀⠀⢃⠀⠁⠀⠀⠈⠀⠀⠀⣀⠀⠁⠐⠀⠀⡀
⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⠢⣀⠀⠸⠑⠈⡀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⢣
⠀⠀⢀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣬⣧⡈⠣⢀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣿⣹⣿⣿⣿⣷⣶⣦⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠉⠂⠄⠀⢀⡤⠤⠤⠀⠀⠀⠀⠀⡸
⠀⠀⠈⢿⣿⣿⣿⣛⣿⣿⣟⢻⣿⣷⠤⢴⣄⡀⠀⠀⢀⣼⠋⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠙⢦⣀⣾⠃⠀⡿⠁⠈⠂⠀⠄⠀⠀⠀⠀⡀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣿⢀⡶⠛⠻⣷⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠁⠀⠀⠀⠀⠆⠢⠀⠀⠄⡀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠐⡀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠂⠀⠸⣧⠀⠀⠀⠀⠀⠸⣿⣿⣹⣿⣿⣍⣿⣿⣯⣼⣿⣿⡇
⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢻⣷⣴⡀⠀⢀⡾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠁⠰⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⣠⣤⠤⠀⠙⢿⣷⣄⣼⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁
⠀⠀⠐⠀⢠⡀⡀⠀⠀⠀⠀⠀⠆⠂⠀⠁⢀⣿⣧⠀⠀⢀⣀⣙⣿⣿⣦⡀
⠀⠀⡰⠂⠈⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢠⢾⣿⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣷⡀
⠀⠰⠁⢀⠤⠀⠤⠤⡄⠐⠈⠀⢀⠤⠒⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⡀⠀⠀⠈⠢⠀⠀⠀⡀
⠀⠐⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⣿⣿⠂⠀⠁⠀⠀⢦⠁⠠⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠃⠀⠀⠑⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣦⣷⢀⡀
⡦⠤⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⠟⠛⠛⠙⠛⠋⠿⣿⣸⣷
⡀⡀⣈⡁⠁⠀⠲⠆⢄⠀⣀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿
⡙⣿⣿⠿⠿⠎⠦⠢⢤⣀⡉⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣼⣸⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠂⠀⠀⠂
⠉⠂⠀⠀⡀⠀⣤⣄⣀⢠⠙⢦⡀⠉⠓⠶⢠⢠⣀⡀⠠⢠⠀⣀⣸⡇⡏⢸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠋⠙⠚⡾⠊⠉⠀⠀⠀⢀⡢⢌⢲⡈⠉⠙⠀⡀⠈⠈⠿⢿⡇⡇⣿⡇
⠀⢀⣀⣤⠄⠀⠀⢀⠀⠀⠀⣠⣶⡾⠷⠞⠁⠀⠀⠀⠁⠈⡀⠀⠀⠁⠃⢻⣷
⠴⠛⠛⠁⠠⣴⣜⠟⠃⠀⣀⡶⠖⢒⡒⠀⠁⠐⠶⣶⡜⢦⡱⣶⠀⠀⠀⠀⡟
⣠⠦⠙⠁⢾⢾⡧⠀⡀⠠⣰⣖⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠴⠁
⠀⡀⠐⠋⠀⠀⣠⠸⠁⠚⠋⠡⠊⠁⠀⠀⠀⠀⢠⡄⢰⠢⠀⠑⢴⢦⡀⠀⠁⠦⣀
⠒⠀⡠⣔⢾⣦⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⣿⡜⡇⠀⠢⠀⠻⡻⡼⣆⠀⠀⠠⢄⡀
⠀⠺⣿⣾⣕⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁⢀⢠⠀⠀⠃⠀⠘⠀⠂⠀⠀⠀⠦⠄
⠀⠸⢦⡈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡔⣬⠇⠇⢠⠀⠆⠀⠀⠀⠀⢤⠀⠘⠷⡄
⣌⢲⣄⡉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⢀⠀⠀⠘⠀⠀⢀⡟⠀⠀⢀⠀⠶⣆⠙⢦⡀
⣬⣐⠈⠙⠃⠀⠀⠐⣆⠀⠀⢰⡄⢦⡀⠀⠀⠀⡏⠀⠀⠀⣞⡄⠀⠀⠀⠀⢸⠇⠀⢠⠀⠀⡀⠙⠀⡀⠚⣤⡀
⠶⠍⠑⠂⠀⠀⠀⣴⡈⣦⠸⡿⣿⣌⢷⡜⣦⢀⠈⠢⠀⠀⠹⠇⠀⠀⠀⠀⡜⠀⠀⠀⠆⠀⠹⡄⠀⠀⠀⠀⢶⡇
⠀⠀⠀⠀⠀⠠⣄⠻⣷⡌⢷⠈⠀⠀⠀⠀⠈⠘⠂⠀⠡⠀⠀⠂⡾⠀⠀⠀⠀⢰⠀⠀⠂⠀⠀⠀⠑⠃⠁⠀⠸⢿⣆⡄
⠀⠀⠀⠀⠀⡙⢿⣷⣦⡙⢦⡁⢀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠘⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢸⣿⠁
⠀⠀⠀⠀⣀⣿⣷⠝⠛⠛⠀⠙⢻⣿⠟⠛⢉⣉⡉⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⣿⣿⠟⠊
⠀⠀⠀⠀⣻⠏⠁⠀⢐⡶⠀⠠⠀⢱⡀⠀⠸⠿⠿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣼⡄
⠀⠀⠀⡀⠆⠀⠀⠀⢨⣭⡀⠀⠀⠄⠳⣄⠀⠀⠀⢀⣤⢿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡇⢱⡀
⠀⠀⠀⠿⠀⠀⠀⠀⠐⣤⡁⠀⠀⠀⠄⠈⠛⠷⣿⡿⢿⣿⡿⠻⠿⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡿⢳⠈⡅
⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠘⠦⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣱⠋⠀⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⣾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣀⣼⠁⢠⡀⠢⠶⣠⡁⠀⡀⣤⣀⣶⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠙⢿⠀⢸⡇⠀⠀⠁⡈⡀⠑⢛⣿⣿⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣧⡒⠂⠛⠢⣀⠀⠀⠀⠣⠀⡍⢩⠟⡀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠠⡺⡄⠸⡄⠀⠹⣿⣷⡀⠈⠉⠀⠀⠀⠀⠠⣀⣀⠀⠁⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣽⣦⡀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⢀⣼⠿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠄⠈⠙⠻⣽⡟⢿⣾⣷⣦⠀⠀⠈⠀⠀⣀⡤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⣀⠀⠉⠻⣿⣯⣄⡀⠀⠀⠤⠾⣿⡟⠀⣠⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠢⣄⠈⠙⣿⢿⣶⣦⣤⣾⠋⠴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡀⠀⠘⢿⠿⠛⠁⠚⠛⠉⠉⠁⠀⣔⡴⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢁⡠⠠⠀⣀⢀⣄⢀⢀⠉⡉⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠠⡈⣦⣴⣷⣿⣿⣿⣿⣿⣿⣷⣮⣵⣷⡶⣊⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣦⣼⣿⠟⣹⠋⠙⣿⣏⣻⣿⡻⡍⢻⡿⢿⣿⣶⣶⢖⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣼⡞⠋⠀⢻⠀⡷⣷⣾⣾⣿⣿⣿⣷⡇⢈⡇⠀⠈⠛⢿⣷⣿⣤⠤
⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠸⡆⢣⡻⣿⣿⣿⣿⣿⣣⠃⣸⠃⠀⠀⠀⢀⡠⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠦⣀⠀⠀⠀⠙⢦⡙⠺⠭⠯⠭⠚⣁⡴⠃⠀⢀⡤⡒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢤⣭⣳⢶⣶⢶⡿⠯⠶⠒⠊⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠠⡀
⠀⢀⠢⠀⠀⠀⠀⠀⢀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢈⣩⠿⠿⢿⣅⠁⠀⠀⠈⠀⠀⠀⣿⠈⠀⠀⣀⠂⡠⠀⠂
⠀⠀⠀⠈⠦⠀⠀⠀⠈⢂⣈⡄⠀⠀⠀⠀⠀⠀⡿⠁⠀⡀⢖⡀⡀⠀⠐⣄⠀⠀⢀⢸⠇⣤⠐⠋⠁
⠀⠀⠀⠀⠀⢉⢠⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠸⠋⠉⣿⠅⠈⡾⣄⣸⠆⠀⢸⠉⢀⢑⡆
⠀⠀⠀⠀⠈⠀⠎⠁⠀⡀⠀⠀⠀⣀⣠⠄⠀⠃⠀⠀⡁⠘⠶⠤⡾⠱⠋⣹⠆⢀⡦⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⢀⣴⣿⣿⠀⠀⠀⠘⢷⡟⢶⣶⡾⠁⣰⣾⠏⠀⠏⠀⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠐⠁⠂⠀⠠⠄⠀⠀⢾⡿⢛⠙⠓⢀⣄⠀⠀⠙⢦⣈⡁⣀⣉⣁⡤⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠶⠟⠡⠎⠈⠀⠀⡄⢠⣄⣀⣀⣨⠀⠘⠿⣥⡤⠠⢲⡀⠀⠀⠀⠀⢱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠰⠀⠀⠉⠉⠈⠙⢳⡀⠀⠀⠀⠂⢈⠁⠦⡄⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣰⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠉⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡐⣠⣮⡄⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⣿⣿⢈⣧⡶⠀⠀⠀⠀⠀⠄⡒⠤⠀⠀⠂⡀⠶⠲⠦⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣦⡀⠀⣽⠙⣿⡿⠀⠀⢀⡀⠀⢦⣄⠐⠚⠢⠄⣀⣀⣀⣀⣀⠀⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⠈⡄⠛⠃⠀⠀⠀⢀⠀⠘⠿⣅⠉⠉⠀⠈⠛⠙⠋⠉⠉⣨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡃⢰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠑⠀⠀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠤⠀⢀⣀⠀⠀⠀⠀⠀⢤⣴⣦⠹⢤⣴⣃⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⣥⡞⠳⠶⣦⣽⣿⠀⣠⠀⠀⠀⢿⡏⡀⠸⠏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣾⡑⠊⠈⠉⡡⠿⠛⠂⠀⠀⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠉⠛⠛⠂⣀⡈⡡⠚⠒⠀⠀⠀⠀⢠⠇⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢠⣍⣉⡟⠉⠀⠀⠘⠃⠀⠀⠀⠀⢸⠀⢠⣴⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⣀⣀⣴⠀⠀⠀⠀⠀⠀⢸⣵⣿⣿⢿⣾⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠻⣫⠟⠛⠩⣷⣀⣀⣀⠀⠀⢸⣻⣿⣟⠷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠙⣻⣷⣯⣹⣶⡆⠉⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡄⠀⠀⢸⠀⠀⠀⠀⠈⠨⠝⡛⠿⡟⠒⠶⣾⣧⣼⣋⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣿⣅⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠉⠙⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢼⣿⢁⠆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣿⡿⠀⠀⡇⠀⠀⠀⠀⢀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠙⣁⣀⡀⣧⠀⢠⣴⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣾⣿⣿⣿⠀⣿⣯⡍⢀⠒⠋⠉⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⢿⡟⢿⠼⠋⠀⠁⢻⢻⣧⣤⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠰⠶⣶⣿⢿⡇⢸⡧⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣴⡶⣧
⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⠛⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⣿⡿⠟⠂⠁⢹
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣿⣿⣟⠰⣿⣀⡀⡀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢿⣿⠇⠀⠘⣏⠛⠶⣤⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣨⣭⡃⠄⠀⠀⡇⠀⠀⠈⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⡿⠋⠀⠀⢻⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⢸⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠒⠠⠄⠀⠀⠀⡀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⠀⣀⣀⠤⠬⠄⢢⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠀⠀⢀⠎⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠳⡄⠀⢀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢠⠃⠀⠠⠋⠀⠀⠀⠀⠤⠤⠀⠤⡀⠘⡄⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠸⠀⠀⠁⡀⠀⠀⠀⠄⠀⡐⠀⠀⠈⡆⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⢡⡀⠀⣄⡄⡀⠉⠀⠈⠀⠇⢸⠀⠀⠀⠀⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠴⠃⠄⠀⠈⢉⡿⠀⢀⠇⠀⠀⠀⡰⠁⠀⢠⠇⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢈⣾⠙⢄⠀⠀⠀⠀⠀⠀⡠⢀⣾⡠⠀⠀⠐⠀⠀⣠⡂⠀⢠
⠀⠀⠀⠀⠈⠣⡀⠀⠰⠀⠀⠀⠀⡏⠀⠘⢦⣆⡄⠐⠀⠄⣀⣠⠿⣐⡥⠟⠀⢤⣀⠠⠔⠉⠀⢱⠀⠈⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠳⡀⠀⠸⡷⠁⡉⠭⠉⠀⠀⠉⡤⠖⣁⠴⠏⠀⠀⠀⠀⠀⢸⠀⠀⠄
⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠢⠑⢆⠀⠈⠒⠦⠬⠤⡤⠄⠀⠀⠄⠈⠈⠉⠀⡄⠀⠀⠀⠀⠀⠀⢸⡤⠊
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠰⡀⠑⢄⠀⠀⠀⠀⠀⠁⠀⠀⠂⠂⠀⡠⠀⡀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠑⠤⠤⣀⣀⠀⠱⣄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⡤⠔⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⠤⠊⠉⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠉⠒⠒⢲⠖⠒⠀⠁⠀⠉⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠠⠤⠀⠁⠀⠀⠠⠄⠒⠀⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⠉⠉⠉⠀⣀⣀⣀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⢀⣀⣤⠤⠖⠚⣿⢹⠉⠉⠉⠉⢳⠀⣻
⠀⠀⠀⠀⠀⠀⣠⠚⠁⢀⡤⠶⡏⡏⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⢸⠀⣽
⠀⠀⠀⠀⠀⢰⠃⠀⡴⠋⠀⠀⡇⡇⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⢸⡀⣿
⠀⠀⠀⠀⠀⣾⠀⢰⡇⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⣻⣸⣤⣤⠶⠾⠿⣍⠛⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⡇⣇⣀⣤⡤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠈⠳⣄⠉⠲⢤⡀
⠀⠀⠀⠀⠀⡇⠀⢸⣀⣤⠴⠞⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⠀⠀⠙⣲⣤⡀
⠀⠀⠀⠀⠀⡇⠀⡿⣍⠀⠀⠀⠙⢾⡻⣝⢦⡀⠀⠀⠀⠀⠀⢀⣠⡤⠖⣋⣩⡤⠖⠛⠋⠉⠉⠙⠷⣄⡀
⠀⠀⠀⠀⠀⡇⠀⡇⠈⠑⢄⡀⠀⠀⠙⠮⣷⣷⣀⣤⠴⠒⣋⡭⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠳⣄⠀⠀⠀⠈⠙⢦⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⣤⡤⠤⣤⡀
⠀⠀⠀⠀⠀⡇⠀⣸⠀⠈⠙⢦⣀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠁⣀⡀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠷⣤⡿⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠛⠉⠁⣀⣠⡤⡶⢺⣭⣿⡟⣷⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢀⣀⡤⣶⠚⣋⣭⣴⢾⡇⢸⡏⠁⣀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠉⠻⢷⣄⡀⠀⠀⢀⡟⠀⢠⡞⣋⣽⡆⣿⠟⠋⠉⢀⣀⡇⢸⡗⠋⠁⢿⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠉⠻⢶⣤⣼⡇⠀⣼⠛⠉⢹⡇⢻⠴⠖⠚⠉⠁⣿⢸⡇⢀⣀⣼⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠉⢺⡇⠀⣿⠒⠚⢹⡇⢸⠀⠀⢀⣀⣤⠿⠼⢛⣉⣥⣴⠏⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⢸⠇⠀⣿⠀⠀⣸⣇⣼⠖⠛⣉⣥⠤⠖⠛⠉⠁⠀⢸⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣼⠀⠀⣿⠚⣉⣡⠭⠗⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⠙⠦⣀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣃⣤⣼⣯⡿⣿⣷⣾⣛⣋⣉⢀⣀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢛⣭⣿⣿⣿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣦⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠀⠀⠀⠀⠀⣀⣶⣶⠿⠛⠉⣀⠶⢶⣶⣶⣶⣿⣿⣿⠿⠿⠿⠿⣿⣿⣏⡙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣯⣶⣾⣿⣧⣦⣤⣴⣾⣿⣿⣿⣦⣀⣄⡀⠀⠀⠉⠙⢧⣀⠀⠉⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣼⣿⣿⣿⣏⣤⣶⣾⣿⣿⣿⣿⣿⣿⣟⡛⠾⣿⣿⣿⣟⠛⠉⢦⡄⠀⠉⠙⢶⣄⠘⢹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⢀⣠⣾⣿⣿⣿⣿⡿⣼⣿⣿⣿⣯⣴⣿⣿⣿⠿⠿⢿⣿⣾⣽⣿⣯⣀⣤⡸⣿⣧⠀⠀⠈⣿⣧⡀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠠⡎⣬⡄⢈⣿⣿⣿⣿⣿⠛⣇⣿⣿⣿⣿⡿⠏⢁⣸⣿⠴⣒⣭⣿⣿⣿⣍⠛⠛⠿⣿⣿⣿⡇⠀⢸⣿⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⣼⣿⣿⣿⣿⡿⠀⣿⣿⣿⡟⠁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⣻⣿⣦⡀⠈⣿⣿⣷⠀⢸⣿⡇⠘⣿⡃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣿⢿⣿⣿⣿⡇⢀⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⢿⣿⡧⠀⣿⣿⣷⠀⢸⡇
⠀⠀⠀⠀⠀⢻⡿⢻⣿⣿⣿⣇⣿⣿⡟⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣧⡟⠈⠻⣿⣀⣿⣿⣿⠆⠀⣿⡀
⠀⠀⠀⠀⠀⢺⠇⠀⣿⣿⣿⣿⣿⣟⠁⠀⠈⣿⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢹⣿⠇⠀⠀⢸⣾⣿⣿⣿⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⡹⣦⡈⠙⢿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣀⣀⣀⣾⠏⠀⣴⣿⠿⣿⣿⣿⡟⠀⠀⠀⢈⡳
⠀⠀⠀⠀⢀⠄⠀⠀⢻⣿⣿⣿⠈⠿⣿⣿⣯⡙⢿⣿⣦⣄⡤⠶⣶⣿⣿⣿⣿⣿⣿⣟⠋⢉⠟⠉⣠⣾⣿⣿⡀⢻⣿⡏⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠁⣄⠀⠀⠀⢿⣿⣿⣧⠀⠈⠙⠿⣿⣦⠉⠀⠙⠿⣦⣬⣻⣿⣿⠿⠋⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⠁⢸⡏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠐⠙⢷⣄⡀⠈⠹⢿⣿⡇⠀⠀⠀⠈⠻⢷⠀⠀⠀⠀⠉⠉⠙⠳⢤⡀⣰⣿⣿⣽⣿⣿⣿⣿⠿⠟⠀⠞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠈⠻⣇⠀⠀⠀⠀⠀⠐⣤⠀⠀⠠⢠⣴⡖⠒⠒⠻⠛⢛⣿⠿⢿⠿⢛⣀⣤⡶⢋⡤⠴⢶⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠑⢀⡈⠓⠀⡀⣀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⢲⠒⣶⠶⠶⠶⠾⢿⣿⣿⡟⠋⠉⠀⠀⡀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠳⢦⣤⣤⣾⣿⣿⣍⣡⣤⣤⣤⡀⠀⠈⠁⠉⠀⠀⠀⠀⣼⡿⠋⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡹⠟⠿⢿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠙⠛⠋⠹⠿⣻⣷⠶⠚⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣀⠀⠠⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⢠⡤⠤⠐⠒⠈⢆⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠁⠀⠡⠊⠀⡠⠚⠁⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⠁⠀⡐⠀⠀⠀⠀⠐⠂⠀⠀⠢⡀⠱⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⠀⠀⠠⢌⠀⠀⢸⠀⡇⠀⠀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⢀⠶⠀⠀⠠⣤⡀⠈⢠⠁⠀⠀⢀⠇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⣀⢧⠀⠙⠀⠀⠀⠀⠐⠀⢀⠆⠀⠀⠀⠌⠀⠀⡌⠀⢀
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡃⠀⠁⠀⠀⠀⠀⢀⡄⠀⣸⠇⠀⠀⠀⢀⠤⠚⠄⠀⠨
⠀⠀⠀⠀⠀⠑⢀⠀⠱⡀⠀⠀⢠⠀⠀⢝⣃⠀⠀⠀⠀⠀⠈⠒⣊⠁⢀⡸⠂⠈⠀⠀⠀⠘
⠀⠀⠀⠐⣄⠀⠀⠀⠀⠈⡲⣄⠀⠑⠤⣈⣃⣈⠁⠀⠀⠀⠀⠈⠑⠒⠉⠁⠀⠀⠀⠀⠀⡧⣀⠄
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠠⠈⠢⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠑⠄⣀⣀⠀⠀⠡⡀⠈⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀⡠⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠀⠀⠈⠁⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠤⠀⠃⠀⠀⠀⠄



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢲⠖⣶⣦⡄⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠤⣀⠀⡖⠂⡇⣰⠛⣄⣣⠋⢹⣄⠈⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⣳⣷⣇⠀⣿⠹⠀⠈⣻⡾⢋⣸⠀⠀⠀⠁⢠⡄⣠⠔⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⣠⠼⢦⡑⣾⣯⠭⠭⠿⠿⠏⡸⠀⢀⢰⠀⠀⣿⢁⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⡇⢸⡞⣏⣽⣶⣷⣼⠈⣶⣤⡖⠒⠖⡡⠚⠁⠈⢷⠰⣿⣾⣧⡾⠛⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢠⠏⠣⣸⣇⣈⣣⣾⢼⡇⣠⡇⠈⢿⢶⣰⠇⢀⡖⢀⢇⣨⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠻⣬⣁⣀⣀⣼⠞⠁⢸⠀⣼⣾⡏⣷⣿⣶⣿⣮⣥⣤⣄
⠀⠀⠀⠀⠐⡶⠦⣔⣢⢄⢸⠀⠙⠲⢤⣤⣽⣟⡋⠁⠀⣠⠏⢠⣧⡶⣿⠀⠙⠳⣤⡙⠋⠀⠈
⠀⠀⠀⠀⠀⣨⠷⠞⠺⣿⣼⡷⢦⣀⠀⠀⠈⠉⠉⢩⣿⣷⡶⠞⠀⠳⡜⢦⣈⡒⢽⡵⡀⠀⠀⢀
⠀⠀⠀⠀⠂⡰⢀⣤⢸⣳⠈⠛⣆⢈⢓⣦⣄⣠⣴⣧⠘⢿⣿⣀⢀⠘⢮⡄⠈⠉⠂⢳⡙⠦⠬⠴⠇⠄⠂
⠀⠀⢀⣠⣎⢤⠞⠁⠈⢯⡇⣸⢁⣼⠟⢻⠋⠙⢿⠀⢇⠀⠀⠉⠋⠉⠛⢧⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⣱⡿⠁⠀⢹⣆⡄⠸⡄⣾⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠉⠛⣤⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠈⠸⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡏⣉⣦⣰⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢻⣇⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣏⣿⠀⠀⠀⣃⠀⠀⠠⠀⠀⠀⣤⠀⠀⢈⡝⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠺⡄⢲⡟⠁⠀⠀⠀⣠⠀⠀⣿⠀⢀⡃⠀⠀⠀⠀⠀⠀⢠⣴⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠹⣾⡏⢠⢧⠀⣸⡏⢀⣰⡏⣠⣾⢃⠞⡿⣿⡟⣡⠴⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣬⣶⡹⣆⢸⠀⣹⣿⣿⣿⠏⢴⣿⣿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠒⠄⣀⠀⠉⠈⠉⣿⣿⣷⡜⣿⢿⡿⠛⠋⠁⠀⡰⠟⠿⣤⢤⣀⣀⠔⢢⣀⣠⡀
⠀⠀⠀⠀⠀⠶⠶⠶⠖⣿⣿⡿⣿⠿⢿⣿⣿⡇⢈⣿⡤⢠⣠⣶⣧⡀⠀⢀⠀⠀⠙⢣⡀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠂⠀⣠⡾⠋⠀⠀⠀⢀⡝⠁⠈⡝⠋⠁⠰⠋⢁⣠⣼⠟⠛⠻⠶⢶⣦⣼⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠋⢤⠀⠀⠀⠄⠁⠀⠈⠀⠀⣀⠀⢠⡴⠛⣩⠵⣱⣟⣥⣿⣙⡁⠀⠻⣧⣾⣇⠀⠀⠀⠀⡄⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⣀⠀⢀⡀⢦⣤⠟⢿⠀⣼⡀⣸⣇⢼⢳⣷⠿⣯⠋⠰⢤⣶⠏⢹⣿⡄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡿⠶⣦⣿⣼⡇⠀⠈⣷⣿⢿⡇⣿⣸⣻⣿⢱⠛⠔⠀⠠⠁⠀⢰⡉⣿⡄⠀⠘⣼⢀
⠀⠀⠀⠀⠀⢳⣀⠀⡆⠀⢀⣀⣠⡿⠉⠛⡁⠀⠀⢸⣏⠸⣧⠨⣻⡽⠄⠙⠁⠀⠀⣆⠀⠀⠜⠁⠻⣿⣤⣿⣷⠋
⠀⠀⠀⠀⠀⠪⢽⣿⡇⢰⣯⡟⠉⠀⠀⡰⠟⠂⠀⢸⡇⠑⣄⣆⡀⠀⡀⣿⠟⠀⠈⠁⠀⡼⠀⠀⢰⣿⣿⣿⣿⣤⣤⣄⠀⡶
⠀⠀⠀⠐⠛⠓⢋⣉⣽⣬⡟⠃⠀⢀⠀⠳⠦⣄⠀⠻⣷⡄⠀⣥⠉⠓⠶⢧⣀⠀⠀⠀⣼⡇⢠⣄⣾⣯⠟⠉⠀⠀⠀⢹⡿⠁
⠀⢀⠐⠆⠈⢠⢿⡿⡇⠈⠳⣄⠀⠀⠀⠀⠀⠘⢧⡀⠈⠻⣦⣸⡷⠶⠶⠖⠛⠷⣦⣤⣿⠃⣸⣿⣿⣿⠄⠠⣤⣴⡤⠞⠁
⠀⠈⠁⠀⠀⠴⣿⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣆⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⠞⠋⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⢀⡤⢠⡤
⠀⠀⠀⠀⠀⠰⡂⢰⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠷⠶⣶⣦⣴⣶⣶⣶⡶⠾⣿⠇⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⣠⠘⣧⡄
⠀⠀⠀⠀⠀⠀⣿⠟⢁⣀⣄⠀⣤⣤⣤⡀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠉⠋⠈⠙⠿⣶⣦⣅⢀⣀⣀⣠⡴⠋⠀⠀⢀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠁⠄⠛⠡⠒⢀⠠⣶⣭⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠉⠉⠉⠉⠙⠛⢷⣶⠾⣭⠅⢶⡶⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠚⠷⢖⣸⣿⠟⢸⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⢸⣿⡆⠈⢢⠀⠁⡀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⢼⣟⣯⣽⣿⣿⣿⠂⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠠⠉⠓⣄⡀⠲⠦⣹⣦⣼⣿⣿⣿⢿⡈⣿⣄⠀⠀⠈⠓⠤⡀⢀⣴⠀⣠⡀⠀⣠⡴⣪⣕⣠⣉⣀⡀⠀⠀⠀⠀⠀⠑⠤⣦⡀
⠀⠀⠀⠀⠀⡤⡜⠉⠋⠀⠰⠋⠀⣠⣰⣿⣿⣿⡈⣷⣿⣿⠗⢀⣀⡀⠀⢀⡞⠁⢰⢿⣿⣻⢿⡟⢉⣻⠄⢵⡏
⠀⠀⠀⣠⡞⣰⠁⠴⠖⠘⠁⠄⢈⣿⣿⣿⣿⡛⠋⠉⢻⡟⠀⣠⢤⠖⠊⣿⣷⣦⠀⣾⣿⠻⢦⠙⢦⡀⠀⠀⢠⠔⢛⣱⣴⢿⠷⡶⠖⢤⡀
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⢸⡿⠀⠀⠀⠙⡷⠶⠞⠁⢰⡉⢿⣷⡖⠉⣿⡀⠈⡇⠀⠙⣦⠴⣿⣿⣿⣋⡀⢠⠆⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⡄⠉⠁⣶⡀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠻⡇⠈⠙⢿⢆⡀⠀⠀⠈⢦⡀⡉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉⠀⠀⠸⢇⡈⠑⢶⡦⠀⠀⠀⣷⣈⠀⠀⠀⠀⢀⠘⡈⣿⠀⠀⠀⡘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⣿⠷⠶⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠁⣿⡇⠀⠀⠀⡁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢳⣾⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⣀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣂⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣁⠙⠿⣿⣿⣿⢟⣱⣤
⢀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣦⡤⠟⠋⠓⢿⣯⠝
⢉⠙⠈⣦⠀⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠊⠁⠀⣀⣤⣾⠟⢁⠼⠛⠻⢯⡀⠀⠀⠀⠀⠘⢷
⣔⣭⣦⡼⠟⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⣤⡀⠀⠀⢀⡴⠷⠀⢀⡛⠉⠉⠃⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠛⠧⣒⠰⠢⠀⠐⠲⠤⣀⠒⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡝⠂⢀⣴⠟⠁⠀⢰⠟⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣠⡀⠹⣦⡀
⠀⠀⠈⠙⠳⢤⣤⡐⠾⣿⣿⠶⢦⡤⢤⣤⢐⣿⣿⠟⠁⠀⢠⠞⠁⠀⠀⢀⣀⣜⠃⡔⢲⣆⡒⢤⣍⠉⣁⡬⠽⠧⣤⣤⠈⢻⣆
⠑⢤⡀⠀⠀⠀⠉⠙⠛⠒⠬⢅⣀⣶⡿⢳⡿⣏⣤⣤⣦⢀⣠⣄⣀⣀⣹⣿⣦⣭⣹⣷⣿⣍⣍⣁⣀⣐⣈⣓⣒⣂⣤⣶⣾⣿⡿
⠦⡿⢻⣄⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⡷⠿⣿⣭⣭⣯⣉⡛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣦
⠋⢱⢣⡍⡄⠀⠀⠀⠀⠴⣿⡿⡿⡜⠁⠀⠀⠉⠉⠙⠛⠻⠿⠿⠷⠶⣿⣯⣶⣶⣶⣄⣄⣉⣿⣿⣿⣶⣾⡿⠿⠟⠛⠉⠁⠉
⠀⠀⡹⠀⠈⢆⠀⠀⠀⠈⠙⣿⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠁⠀⠀⢘⠀⠀⠀⠀⠰⡟⡾⢳
⠀⠀⠴⠁⠀⡄⠀⠀⠀⣠⣾⠋⠀⠉
⠀⠀⠀⠐⠀⠇⢀⣤⣾⠟⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠋⠉⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠲⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠛⠛⠳⠶⢤⣀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡎⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⢸⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⣻⡶⠶⠿⠛⠛⠋⠹⣦⠀⠀⠀⠈⣷⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠓⢦⠀⠀⢸⣇⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⡀⠀⠸⡆⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠁⣠⣾⠟⠋⠁⢀⣹⡇⠀⠀⣀⠀⠀⢀⠀⠀⠀⠙⢷⣤⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⡆⠀⣼⡏⠀⠀⠀⣀⠈⣷⡌⠉⠙⢶⣄⡀⠀⢿⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠐⣿⠀⠘⢿⣦⣀⠘⢹⣿⠿⣷⡀⢠⡀⠙⢿⣦⡟⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢿⡆⠀⠀⠈⠙⠳⣼⠇⠀⠈⡗⠀⣽⡆⠀⠈⣿⠇⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠰⣔⠶⢤⣤⣼⣄⣀⠘⣁⡼⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣷⡀⠀⠉⠙⠛⠛⠷⠦⠀⠐⢋⣀⣤⣶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠛⠛⠉⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠙⢿⡀⣤⠴⠶⠶⠷⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⠀⠀⢹⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠢⢄⡀⠴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠒⠲⠶⠤⠶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠈⠀⠀⠀⠀⠀⠙⣷⣀⣤⣤⣤⣤⣶⣤⣤⡶⠶⠟⠋⠀⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠉⠓⢦⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣆⠀⠀⠀⠀⠀⠀⢸⣤⠴⠒⠚⠒⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢀⡤⠶⠖⠒⠒⠒⠶⠿⢷⣦⣄⣀⢀⣤⠖⠛⠉⠛⠻⣧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠟⠁⠀⠀⠀⠀⠀⠈⣧⣀⣀⣀⣤⣴⣞⣁⡀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⠉⠀⠀⠀⠈⠉⠳⣆
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⣀⣀⣤⡴⠖⠛⠉⠈⠛⢦⣤⣤⣤⣴⠋⠁⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠙⢿⣖⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⣤⡤⠞⠉⢷⡀⠀⠀⠀⠀⠀⡿⠉⠛⠲⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣠⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⣀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣨⣤⣽⣶⣴⣾⣿⣿⣿⣿⣯⣿⣏⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡇⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢅⢸⣿⠀⠀⠀⣰⣾⣿⢟⡿⠛⣿⣿⣿⣿⡿⠿⢿⣿⣿⣼⣿⢏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⢰⣿⣿⣷⣿⡵⠿⠟⠉⠻⣇⣉⣴⢸⣿⣿⢹⡏⣾⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢇⠀⢠⣧⠈⠉⠻⣄⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⢎⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣠⡴⣿⣿⣼⣄⣾⣿⣷⣄⠀⠘⢷⣦⣄⡀⠀⠀⠀⣀⣀⣤⢻⣿⣿⠿⠻⠿⢟⣽⣿⣿⣿⡿
⠀⠀⠀⠸⡀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣄⡀⠘⢻⣿⣿⣶⣾⣿⡿⣱⡿⠋⠁⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⣦⣀⠙⡻⢿⣿⣿⡟⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣀⣀⠀⣀⠀⠈⣉⣫⡽⠟⠛⠛⠛⠿⠷⣶⣾⠿⠿⢿⣿⣿⣿⣿⣿⣁⣀
⠀⠀⠀⢀⣤⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⡏⠀⠀⠀⣀⣠⣴⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣿⣿⣿⡿⠿⡿⠦⣀⠀⠀⠀⠀⠀⠈⠙⠾⣿⣿⣿⣿⣿⣿⣟⣛⣫⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂
⠀⠀⠀⠉⠁⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣭⣿⣭⣭⣽⡿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣄⢀⣠⣴⣾⣿⠿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢠⠿⠛⠛⠻⠿⠿⡿⠿⠿⠛⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡿⠋⠁⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⣉⣉⣭⢵⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣄⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠭⣦⣤⠤⠒⢂⣈⠴⢦⡖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣁⡤⠤⠶⠦⠶⠤⠤⣀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠱⡀⠣⣀⠿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⣯⠖⣩⠴⠒⠉⠉⣀⣀⣉⣉⠒⢬⣑⣺⠀⠀⠀⠀⠀⠀⢀⡀⠆⠃⠈⠀⡇⠀⠀⠀⠀⠀⢀⡀⠠⢄⣀⡀⠀⠀⠈⠙⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣡⠊⢁⡤⣖⣋⡩⠤⠴⠦⣀⠽⠲⡞⣇⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⠀⡠⠁⠀⣠⠴⠒⠉⠀⠀⠀⡀⠀⠈⠙⢦⠀⠀⠀⣰⢤
⠀⠀⠀⠀⠀⠀⠀⠈⣇⡾⠋⣠⠤⠄⠀⡀⠀⠚⠉⠂⠀⣷⠏⠀⣀⣀⡀⠀⠀⠀⠐⠂⣴⠞⡧⠀⢞⠁⠀⠀⠀⠀⢀⡦⠵⢄⡒⠰⣬⡇⠀⠀⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢏⢳⡀⠁⠀⠀⢀⠀⢠⠄⠀⠀⣸⠇⠀⣸⣡⡤⠟⠀⠀⠀⠀⠀⠈⠱⡇⠀⣾⠒⡲⠖⠈⠉⠀⠀⠀⠁⠈⠁⢸⣹⢤⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢄⡀⠀⠀⠉⠁⠀⣠⠴⠃⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⢿⡀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⢸⠁⠀⣸⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠙⢒⠒⡟⣯⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⠢⡑⢤⡀⠀⠀⠈⠲⠁⠀⣀⡴⢷⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠒⠼⣾⠤⠼⣦⠠⢾⣉⣉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠛⠯⣉⣱⠒⠿⠋⢯⡥⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⠀⠀⠀⠀⠀⢘⣦⡤⠼⠓⠶⠤⠤⢤⡄⠀⠀⠀⣠⣞⣉⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⡆
⠀⠀⢰⠒⢦⡀⠀⠀⠀⠈⠉⡳⠒⠂⢹⠧⣄⡀⠀⠀⠀⠀⠀⠀⡟⠒⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠦⣼⠂⠀⠀⠀⡴⠁⠀⢠⡏⠀⠀⠈⠉⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠻⡖⠛⠁
⠀⠀⠀⠀⠀⠈⠳⡀⠠⡞⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠜⢦⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡤⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢚⣯⣤⣶⠶⣿⡟⠓⢶⣬⣍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⢏⡞⣡⢲⣾⣿⡿⠖⣛⡿⣸⣇⡹⠟⣦⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣽⣇⢺⣿⣧⣿⣙⣿⣶⣛⣡⡴⢟⣫⠴⢣⣿⡾⢋⡽⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠙⣿⠿⣿⣧⠙⠻⣦⣀⣩⡴⠞⠋⠁⢠⣿⠋⣰⠟⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢬⣷⣌⡛⠷⢶⣾⣏⣁⡀⠀⠀⠀⣾⠃⢠⡏⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢻⣦⣈⠛⢿⣦⡀⠀⠀⠈⠙⠲⠦⣤⣿⣤⣾⠀⢀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠈⢻⣿⣷⣄⠙⢿⣧⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⣼⣥⠤⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣿⠀⠉⠛⢦⣙⢷⡄⠀⡀⢠⠀⣰⡿⢃⡼⠋⢀⡴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⣿⡎⡄⠀⠀⠈⠳⢿⣷⣶⣾⣿⣿⡵⠟⠀⣠⡾⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠈⠻⣿⣮⡲⣄⣀⣀⣠⡽⠟⠛⢉⣴⣤⣴⣾⣧⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣭⣿⣿⣿⣿⣶⣦⣤⣶⣟⢻⣿⣿⣿⡙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⠤⠤⣤⣀⡀⠀⠀⢀⣿⣳⢿⡿⡿⠋⢿⣿⠀⠙⢿⡏⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⣿⣿⣿⣿⣶⣿⣿⣷⣤⡸⣿⠁⢸⡟⠀⠀⢸⣿⠀⠀⠀⢻⣌⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠈⠀⠀⠀⣼⣿⠀⠀⠀⠀⠙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢿⣿⣿⣿⣿⣝⠻⣿⣿⣷⠀⠀⠀⠀⣷⡿⠁⠀⣀⣤⣤⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⠇⢠⣾⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⡻⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢸⣿⡤⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⣭⠿⠛⠋⠙⣷⣄⠀⠀⣼⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⣿⠟⠁⠙⢯⡙⠿⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣿⠀⠀⠀⠀⠉⠛⠒⠾⠿⠿⠬⢿⣝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣷⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⣴⣶⣾⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⡿⠋⠉⠀⠉⠀⠀⠀⠀⠃⠀⢰⣿⡟⠉⠉⠛⠻⠛⠛⣿⠀⠀⠀⠀⠀⢻⡿⠋⠉⠉⠀⠉⠙⢻⣿⣿⠃
⠀⠀⠀⣀⠀⠈⡝⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣿⣏
⠀⠀⠘⠋⠉⠠⣿⣄⠀⠀⠀⠉⠉⠀⠀⡈⠀⣏⡃⠀⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣠⡀⠁⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠪⠙⠻⠿⣶⠀⡶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠐⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠁⠀⠡⠘⠁⠀⠀⠀⠀⠀⠀⠀⡄⢀⠂⠊⠀⠐⠀⠀⠀⠀⠈⠀⠀⣠⠃⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡤⡄⠀⠀⠀⠀⠀⠄⠀⡈⠀⠀⠀⠀⢢⢀
⠀⠀⠀⠀⢠⢨⡇⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⢇⠀⠀⠀⡀⠀⠀⠔⠳⠀⠀⠀⠀⠊⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠔⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⡂⢐⣐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠀⠀⠀⠀⠠⠔⠃⠃⠀⠀⠀⠀⠀⠈⠙⠒⠂⠈⠛⠍

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣽⣿⣯

⠀⠀⠀⠀⢀⣰⢶⠀⠀⠀⠀⠀⠀⡠⢾⡱⣤⠀⠀⠀⠀⠀⠀⡰⢺⣯⠀⢄⡀⠀⠀⠀⢀⡄⣖⠟⢿⣦⣀
⠀⠀⠀⣜⠋⠀⢸⠀⠀⠀⠀⠀⠀⡻⠀⠙⡌⡄⠀⠀⠀⠀⠸⣤⠳⣜⡯⠞⠁⠀⠀⠀⢻⠙⠫⢍⡻⠁⡇
⠀⠀⠀⠘⠢⠴⠋⠀⠀⠀⠀⠀⠀⠱⠤⣤⠵⠁⠀⠀⠀⠀⠀⠘⢅⣈⡠⠊⠀⠀⠀⠀⠈⠢⢄⡀⠁⠔⠁

⠀⠀⣀⠤⠀⣤⢄⡀⠀⠀⠀⠀⠀⢀⡠⠤⡄⢢⡀⠀⠀⠀⢀⢤⣞⣑⡲⢤⠀⠀⠀⠀⠀⣠⠤⣔⡢⡀
⠀⠀⢧⡀⣟⢉⣧⡘⡄⠀⠀⠀⡀⡯⡞⠽⢣⣼⢸⠀⠀⢰⠋⣧⣾⣻⣫⢙⠦⡀⠀⠀⡎⢠⡾⠟⢳⣜⢢
⠀⠀⢧⡑⠄⠛⠾⡥⠚⠀⠀⠘⢤⡓⣚⣛⡫⢏⠎⠀⠀⠈⠢⡓⢅⣨⠶⣎⠴⠃⠀⠀⠉⡳⣥⠴⠆⠚⡎
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠚⠁⠈⠁⠀⠀⠀⠀⠀⠙⠲⠴⠚⠉⠀⠀⠀⠀⠀⠑⠒⠚⠑⠛⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠞⣽⣛⠤⣽⡀⠀⠀⠀⣰⢋⣿⣿⢵⢤⠀⠀⠀⢀⡤⠢⣮⣭⣷⠤⣄⠀⠀⠀⡠⡯⢯⡼⢻⣦⡀
⠀⢠⠋⣿⣸⣰⢵⡿⢸⠀⠀⢠⠃⠈⠉⠃⠜⡄⣇⠀⠀⠘⢆⡟⡝⠢⣿⣿⢸⡄⠀⢠⡷⢱⢭⣹⢿⠱⣘⠆
⠀⠈⠦⣝⠚⠯⠟⡳⠋⠀⠀⠐⣍⠣⣝⣋⠤⢁⡜⠀⠀⠀⢫⡙⠚⣲⠈⣉⠽⠀⠀⠈⢻⠢⡹⢾⣭⠼⡗
⠀⠀⠀⠀⠙⠒⠊⠀⠀⠀⠀⠀⠈⠉⠉⠁⠚⠉⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠀⠀⠀⠀⠈⠓⠛⠉⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⠀⠀⠈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡄⠀⠀⠘⢰⠀⠀⡆⠃⠀⠀⢠⠁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠀⠂⡀⢠⠀⢿⠀⠀⡿⠀⡀⢀⠔⠁⣂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡊⠐⣅⡈⠀⠸⠄⠨⠇⠀⢁⣨⠂⢑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⡈⠐⢼⣿⠀⠀⢓⡚⠀⠀⣿⡧⠂⢁⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠂⠀⠈⠳⢌⣄⠻⠀⠀⢸⡇⠀⠀⠟⣠⡣⠞⠁⠀⠐⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠐⠀⠙⢆⠀⠀⠈⠁⠀⠀⡰⠋⠀⠀⠀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⡈⠀⠈⠓⠀⠒⠀⠢⢄⠰⠆⡠⠔⠀⠒⠐⠚⠁⠀⢁⠠⠀⡄
⠀⠀⠀⠀⢔⠝⠻⠆⣿⡀⠀⠀⠄⡀⠀⠀⠈⠀⠁⢀⠀⠈⡀⠈⠀⠁⠀⠀⢀⠰⢀⠀⢀⣿⠰⠟⠫⡢
⠀⠀⠀⠀⣿⠀⢀⠀⠹⡿⣄⠉⠂⠐⠓⠁⠲⠄⡀⠀⠀⠀⠀⢀⠠⠖⠈⠚⠂⠀⠉⣰⣿⠏⠀⡀⠀⣿
⢀⣤⠀⠀⢭⣓⠄⣈⣠⢌⠠⡐⠀⡀⠀⢀⠂⠄⠀⠳⣀⣀⠎⠀⠀⠐⡀⠌⢀⠀⠂⠔⡠⣄⣁⡠⣚⠬⠀⠀⣤
⠁⠀⠀⠀⠁⠈⡉⠒⠂⡡⢘⡈⣀⢉⡀⠈⠓⠀⡀⠀⢹⡏⠀⢀⠄⠚⠁⢁⡉⣀⢀⡂⢈⠑⠒⢉⠁⠊⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⣫⡮⠥⢤⡨⡀⡁⠙⠢⡄⠈⠣⡈⢀⠜⠀⢠⠔⠋⠈⠀⣅⡤⠬⢵⣝⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠙⠀⣀⠀⠈⠓⢄⡸⢇⡠⠚⠁⠀⣀⠀⠋⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠚⢣⡜⠒⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶