Dog breed Emojis & Symbols

⠀⠀⠀⠀⢀⠀⠀⠀⡐⢄
⠀⠀⠀⠀⠀⣆⠀⠀⠇⠀⣠⠇⢀
⠀⠨⡅⠀⠀⢀⣀⡀⢦⠔⢫⡆⠀⠠⣤⣀
⠀⠀⠀⢘⣃⠙⠊⠁⠀⠀⣸⠅⠀⡴⠋⣸⣇⠹⣶⣶⣖⠲⠖⣛⣓⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢹⠀⠀⠀⠀⢻⡏⠀⢻⠋⠀⡿⠋⠏⠋⠉⠀⢀⡄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡎⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠎⠀⠀⠈⢁⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣬⡃⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣆⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣽⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠘⢷⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣿⣿⣄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡟⠈⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠒⢡⣒⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠟⠀⣄⣒⠄

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡭⠂
⠀⠀⠀⠀⠀⠉⠁⠈⠁⠈⠀⠀⠀⠀⢀⠀⠀⠀⠠⢈⠀⠀⠀⠚⢱⠀⠤⠀⠀⠀⠀⠀⠁⢽⠉⠈⡇⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠠⠤
⠀⡄⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠉⠀⠀⠀⠁⠀⢀⠀⢄⠀⠀⠴⡀⠍⠨⣁⠀⠀⡀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠁⠀⠈⠀⡄⠀⠀⠀⠀⠀⠄⠀⢀⡄⠈⠀⠀⢸⠅⠀⠀⡠⠚⠑⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠘
⠀⠀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⣀⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠂⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠠⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠈⠀⡼⠃
⠀⠀⠀⠁⡁⠀⠀⠒⠤⠀⠀⠀⠀⠈⢀⠀⠢⠔⠀⠄⠀⠀⠀⠀⣸⣀⡼⢸⣩⡧⣞⣽⢘⣯⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⡁⢠⢀⡠⢠⠀⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠋⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂
⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⢠⣰⣦⠀⠀⠀⢀⡀
⢀⠠⠀⠀⠐⠀⠀⠀⠠⡈⠀⠀⠀⢀⡐⠀⠀⠀⡀⢀⠃⠀⠀⠀⣡⠁⡀⠀⠀⠀⠀⠸⠀⠠⢠⠀⡄⠀⠈⡀
⠀⠙⠁⠀⠀⡀⠰⡀⠀⡁⠀⠀⠠⠈⠀⡀⠸⠀⠐⠀⠀⠀⠀⠐⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠚⠀⠃⠀⠀⠀⠰⠊⠀⠀⠀⠀⠅⠈
⠀⣀⠂⠨⠁⠀⠀⠈⠂⠀⠀⠀⠁⠀⠊⠈⠀⢀⠐⠀⠀⠀⠀⠀⢠⠀⠡⠘⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠰⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂⠒
⠀⡁⠀⠖⠒⢠⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠱⠈⠶⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⢀
⠀⠀⡁⠀⠁⠞⠀⠀⠀⠀⠀⡆⠘⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠥⢀⠉⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⡄⠀⣠⠂⠈⡏⠻⠄⠀⠀⠀⠀⢠⠇⠂⢀⢀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠡⠄⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⡄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣶⡶⢖⡤⠀⢢⠒⢶⡒⢄⡲⠍⢪⡙⠙⢿⣦⡸⣿⡓⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⣰⣏⢋⡖⡡⡊⣀⢵⡇⣧⡸⠮⣔⠈⠢⣄⠈⣢⡹⣿⣿⣷⣦⡀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣿⣾⡿⣩⠋⠼⠈⠊⢐⠲⡄⢏⡖⡩⠀⠀⠀⠀⠀⠀⠛⣮⠻⠿⣿⠛⣎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⡏⣵⠋⠀⠁⣡⢶⡆⠁⣧⢸⠀⠸⣟⣳⡦⢄⠀⠀⠀⠈⢳⡽⠃⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⢀⣤⣺⣿⣿⣅⡴⢿⢹⣦⣤⣿⠋⣷⠿⢶⣾⣆⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡿⣾⣿⣟⣹⡿⣋⠕⠚⣀⣒⡁⠒⢅⠃⠘⠂⢸⠛⠆⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⣌⣼⡴⣣⣶⡖⡋⠙⠲⣍⠢⠙⣆⠶⠿⠀⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡟⣿⣿⣰⣿⣯⣿⣧⠻⠖⠘⠷⣌⣌⢆⢘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣧⣿⣿⠧⢻⣮⣛⣯⣿⠎⠀⣑⠲⢼⡈⡌⣆⢻⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢞⡽⢿⡌⣸⣞⢧⡀⠪⠍⠡⢧⢿⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⡼⣎⣿⡽⣏⠻⣧⡈⢅⢲⣂⠜⣿⣸⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣼⣹⣷⣾⣿⣷⣿⣿⣄⣉⡁⣼⣿⠟⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣛⣿⣿⣷⣞⣿⣯⣿⣿⣦⣤⡽⠃⠀⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⢿⣿⠿⣿⣿⣿⣿⣿⡛⣿⡏⢹⠏⠀⠀⠀⢈⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⡆⢻⣆⡰⠈⣿⡍⢱⡇⢹⠇⠘⠇⠀⠀⠀⡌⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡆⠸⣿⡀⠙⣿⣶⠴⣧⣄⣠⣴⠷⠶⠀⠀⠀⡐⠁⢀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠱⡤⠘⣿⡄⠸⣧⠄⠉⡽⠇⠁⠀⣶⡅⠀⡼⢁⡀⠉⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣷⠀⠙⢇⡨⢿⡦⠙⣿⠇⠀⢸⡀⠀⡟⠀⣴⠄⠈⢁⣴⠁⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠹⣧⣀⠈⠷⢦⣤⡞⠀⣶⠀⠀⢁⡼⢁⣈⠁⢀⣰⣿⠃⠐⢡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣧⠀⠉⠛⣣⣄⡈⠁⠀⡀⠙⣿⡴⠟⠀⠘⠁⢀⣼⠋⠀⠀⣴⣛⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠘⣦⣄⠀⠙⠻⢿⣦⠀⠻⡄⠸⠁⠀⠀⠀⣠⣎⠉⠀⢀⡾⠾⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣧⠀⠈⠉⠳⠦⠀⠀⠹⢧⣄⠉⠂⠀⠀⠀⣴⠁⠀⠀⠀⠚⠳⠐⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠻⠐⠇⠀⠒⠒⠒⠒⠒⠀⠛⠚⠃⠂⠒⠛⠛⠒⠒⠒⠒⠒⠂⠀⠂⠻⠟

⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠔⠁⣀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠆⢉⠀⠤⠀⠀⢨⢢⠀⠀⠀⠀⠀⠄⢈⠁⠀⠀⠀⢠⠐⡀
⠀⠀⠀⢸⠀⠚⢁⣀⣀⠉⠀⡥⠈⡄⠀⠀⠄⠀⠀⡃⢤⡴⠁⠸⠂⠀⠁⠀⠀⢐⠉⡔⠀⣀⡀⠀⣀⡀⠀⠈⡀
⠀⠠⠀⠘⠀⠀⠈⠻⡋⠀⠀⠀⠀⠁⠀⠰⠀⠀⠸⡁⠴⠀⢠⣤⡄⠈⢾⠀⠀⡅⠀⢆⠐⠉⣀⣀⠈⠑⡀⠀⠈
⠀⠀⠀⠀⢶⠠⠴⣌⠋⠗⠐⠃⠚⠀⠀⠀⠰⣠⠀⣇⠀⠀⡀⠽⢅⣠⠞⠀⠀⠡⠀⢸⠀⠀⢙⡋⠀⠀⠤⠀⡠
⠀⠀⠀⠀⠀⠙⠠⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠇⠀⠄⠂⠁⠀⠀⠀⠀⠑⠢⠛⠅⢀⠀⠀⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⡈⠐⠂⡀⠃⢀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⠂⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠁⡀⣀⠈⠋⠀⣄⠀⠀⠀⠀⠐⠀⠀⠀⠿⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠋⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠖⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢁⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠇
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠘⠀⠡⠀⠀⠀⠀⠁⠑⠄⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⠀⠀⢼⠀⠀⢀⡴⠀⠠⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⠁⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠈⠃⠀⠀⠀⠀⠀⡇⠀⠀⢽⠀⣠⠀⠀⢀
⠀⠄⠀⠀⠀⠛⠀⠀⠀⠛⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠈⡁⠀⢈⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣛⠟⠋⠠⣄⠉⠉⡁⠋⠙⠛⣟⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣿⠏⢀⣵⡄⣿⣆⣾⣇⣰⣶⡞⠻⣿⡻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢈⡅⢠⣼⣿⣾⢳⠁⠁⠿⣿⣿⣮⡀⢀⠃⠹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡿⣹⣮⣥⠋⠉⣿⢁⣄⠀⠀⠰⢫⣝⡁⠙⣆⣧⠠⣤⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣱⠋⡧⣥⣶⡿⢀⣴⣶⡦⣤⡶⣄⢣⣻⢖⣿⢸⠀⠁⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⢸⠅⣽⣿⠁⣾⠿⣣⣄⣠⡽⣿⡇⢹⣷⣿⠘⡆⡐⢿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⣀⡆⣿⡟⠀⠉⣠⠨⣿⣿⠐⠄⠹⡠⣿⣿⢰⢣⡁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⣮⠷⢿⡿⠂⣼⣴⡷⢾⡅⢾⣾⣦⣧⣼⡿⠙⣼⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢠⠼⣷⠂⢿⣿⣷⣶⣤⣾⣿⣿⣿⣿⣦⢄⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡧⢿⡀⢠⡼⡿⣿⣿⣿⢋⠟⢋⠟⠹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢤⡘⢿⠺⢿⣼⣮⣿⣵⡧⢶⢛⣤⣧⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢀⡀⢻⣌⢠⡟⠀⣼⣅⠀⢁⢸⡾⡿⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡁⠀⠁⠋⠛⠡⢮⣭⣭⣾⢮⣍⠈⡢⡀⡀⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡤⢋⣴⣔⠰⢠⣧⡼⠑⡈⢮⠀⠉⠑⠈⢀⠳⡄⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⢀⢸⡛⣴⣺⠀⣁⡆⠳⢸⠈⣦⠈⣆⡏⢣⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠇⠸⣿⠈⠰⣻⠇⢏⠁⡉⠼⠷⢼⡆⠃⡗⡺⠓⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⢥⣷⢾⡎⠰⠖⠉⡄⠘⠀⠀⠀⠂⠈⠇⣼⠿⠷⢠⢀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠘⠻⠰⠀⢰⡦⢠⡈⠸⡀⣦⡿⠀⣤⡞⣉⡶⢀⡏⠃⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⡖⠋⢳⡄⢧⠀⢳⡝⠃⢀⢳⣿⣧⠈⣿⠟⢛⡃⢸⡏⣶⡶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣯⢆⠼⣷⡀⣄⠘⣿⠀⠈⠘⣼⢋⣰⣿⡄⢀⣵⣬⠀⢌⣷⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠁⠀⠺⡿⡱⣝⢦⣿⣧⣧⡴⢹⠀⣿⡿⣻⡿⡽⡀⠄⢈⣯⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⠀⣼⡗⢁⢸⣷⠻⣿⢇⡇⠀⣶⠼⣫⡟⠴⡇⠈⡄⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣀⣌⣄⣄⣸⣷⠾⢷⣷⡶⠻⢾⣿⣞⣴⣴⣦⣻⣬⣿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣉⣉⣉⣁⣈⣉⣁⣀⣀⣉⣁⣀⣈⣉⣉⣁⣉⣉⣉⣉⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣠⣶
⠀⠀⠀⠀⠀⠠⢣⠛⠛⡀⠄⠀⠀⢀⣀⣀⣤⣄⣀⣀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢼⡿⢆⠺⡶⠀⠀⠈⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠟⠿⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢸⠟⠉⠛⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠻⠭⣀⠁⠁⠀⢀⡀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢀⠐⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣆⠀⠀⠈⠈⠙⠋
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢀⠀⠀⠀⣴⣅⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠿⢷⣦⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣀⢰⠦⡀⠀⠀⠀⠀⠀⠀⣼⣬⡖⣠⠈⠆⠀⠀⣽⣿⣿⡿⣾⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛
⠀⠀⣶⣾⣿⣷⣶⣶⣦⣤⣤⣴⣌⣣⣾⣿⣻⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⠰⠆⠀⠀⠙⣿⡿⠃⠀⠦⡀⠀⠐⠀⠈⠀⡀⡀⠄
⠀⠀⣿⠻⢿⣿⣿⣿⣿⣿⣿⠟⠏⠇⠀⣠⣉⡀⠦⠀⢠⠊⠙⠉⠛⠛⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠁
⠀⠀⣠⡀⠐⠯⠽⠿⣿⣿⣧⡐⠀⡀⠐⠁⠀⠁⠀⠀⡆⠳⣤⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠒
⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠁⠑⠊⠉⠀⠀⠀⠀⠀⠀⠑⣄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉
⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣶⣶⣦⠀⠀⠀⠰⠤⠂
⠀⠀⢿⣷⡀⠀⣼⡿⣷⠀⣠⣴⣶⣿⣿⣆⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣦⢤⣴⣶⣶⣦⣤⣀⣀
⠀⠀⠈⣿⣿⣿⣿⣧⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣯⣼⢯⣔⣆⣀⣀⣀⣀⣸⣿⣫⠟⠁⠀⣿⣝⡻⣿⣼⣿⡿⢸⣿⣿⣿⣿⣶⡼⣟⠛⠛⠛⠲⠦
⠀⠀⠸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⠀⢸⣟⣅⢀⣙⣿⣿⣿⡿⣿⢝⡻⡟⠉⠀⠀⠀⠈⠉⠻⡏⣿⣿⣷⠘⢻⡿⣿⣿⡿⣿⣿⡀
⠀⠀⠐⣿⣿⣿⡿⣿⣿⣿⣿⡿⢃⣼⠃⠀⠀⠀⠀⠉⠻⠛⠛⠿⢯⡅⠈⢂⠀⠀⢸⠃⠀⠀⠀⠀⠀⣿⡟⠛⠻⣶⡎⠀⠘⢿⣧⠙⢿⣧⡀
⠀⠀⠀⠀⠉⠉⠴⠟⠈⠙⣿⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠂⠀⠀⠈⠢⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡇⠀⢀⣴⠏⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠙⠐⠁⠀⠀⠀⠀⠀⠾⠏⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠿⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣒⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⡄
⠀⢶⣯⡑⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡟⡄⡀
⠀⠀⠀⠁⠀⠀⣡⡀⠀⠀⠀⠰⣄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠁⠀⠀⠁⢰⣠⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣶⣧⣤⣶⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠲⡆⠠⠤⠤⢆⠀⠀⠀⠀⠀⣅⡀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠛⠉⠉⠉⠻⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡙⠀⠀⠀⠀⠈⡻⠁⠁⠀⠀⠰⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠼⡀⠠⠧⠀⢀⠀⠄⠀⠀⠀⠠⠀⣀⣀⣀⣀⠄⠀⠀⣀⠙⢠⡀⠀⣀⠀⠀⢷⣔⠒⠀⠀⠄⠀⠀⠉⠼⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠉⢠⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠋⠛⠉⠀⠀⠀⠀⢀⡀⠈⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⡀⢤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠙⠂
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢋⣤⠀⡠⣔⢂
⠀⠀⠀⠓⠄⠀⠈⠀⢂⠀⠀⠀⠀⢿⠶⠛⠈⠈⡃⠀⠀⢸⡟⠉⠁⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠓⠂⠘⠂⡀⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠀⠁⠀⠑⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢈⡁⠀⠐⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠠⠤⠀⠀⠀⠀⠀⢰⠜⠋⠁⠀⠶⡶⢯⠀⠂⡀⢀⡄⠂⠠⢸⡟⠉
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠚⢓⣷⡀⣮⠛⠟⠉⣺⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠻⠀⡀⠶⠔⠀⠀⠀⠆⠀⠢⣤⠀⠂⠠⠤⠤⠔⢻⣙⡝⠙⠁⠀⢴⠻⣿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⢀⡀⠘⡄⣤⣀⣿⡷⠻⢦⣄⣰⣆⣸⠟⠀⠀⡀⡒⠂⠀⣘
⠀⠀⠀⠀⠀⠀⠰⠸⣿⠂⢸⣿⠧⡼⣧⢼⠿⠋⢁⠀⠀⠈⠉⠹⢧⠀⠀⠘⠁⢀⣯⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⠘⣿⡄⠂⠙⠀⢠⠆⣾⣶⡀⠀⠀⣀⠁⠐⣾⡏⠠⠉
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣯⠀⠈⠁⠀⠀⠀⢸⡦⠈⠿⠇⣀⣤⠇⣠⣶⣿⣄
⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠈⠻⠋⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢿⠃⣾⣿⡌⠻⠟⢳⡀⠉
⠀⠀⠀⠀⠀⡝⠿⠋⠀⠀⢠⠀⠀⠀⠀⡀⣶⣤⣄⣶⣶⠁⠀⠀⢀⠬⣼⣷⣸⡆⠈⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠶⠀⡇⢼⡗⣿⣿⣿⣿⣿⠃⠀⠇⠘⣶⠟⠀⠀⠃⠀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡏⠈⠣⠘⡿⣿⢿⡇⠀⠀⠀⡀⣀⡄⣦⣆⠰⡶⠁⠤⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⣤⣤⣤⢄⣀⣀⣀⣠⣄⣀⣠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣦⢉⣽⣿⣿⣿⣿⣿⣿⣮⣻⣗⢦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣤⣭⣗⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⢿⣿⣷⢹⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣿⢇⡔⢪⡳⣤⣿⣿⣿⣿⣿⣇⣠⢚⠤⣀⢹⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡗⣿⣜⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣁⣿⣶⡿⢀⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣴⣿⣿⢹⡏⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢻⡟⣿⣿⠿⠉⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⢿⣿⢸⣧⠘⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠈⢧⡈⠁⠀⢠⣿⣿⣿⡏⠈⠀⠀⠙⠟⠁⠀⢡⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠛⠁⠀⠀⠀⠈⢧⡀⢰⣿⣿⣿⣿⣷⡄⠀⡆⠀⠀⡄⣰⣿⣿⡏⠀⠀⠘⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣯⣉⣉⣻⣿⠀⠀⢑⣴⣣⣴⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⢿⣿⣿⡿⠋⠀⢀⣼⠟⠋⣼⡿⢹⣿⣇⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠛⢷⡴⣤⠀⠀⠀⣷⢦⡽⠭⣤⡴⠶⠛⠁⠀⠀⡿⠁⣿⣿⣿⠀⠀⠀⣠⠞⣿⠋⢈⡿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣹⣦⠾⣧⣸⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⡇⠀⠀⢹⡴⠟⠓⢿⣤⠞⣷
⠀⠀⠀⠀⣤⣤⣤⣤⣷⣼⣿⣤⣤⣤⣿⣷⣤⣤⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣷⣴⣴⣿⣧⣤⣤⣤⣷⣶⣧⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⣿⡔⣶⣰⠂⣼⢳⢀⣶⣰⡟⡆⣶⢰⢢⡖⡦⡔⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠃⠙⠙⠊⠃⠘⠉⠊⠙⠈⠋⠙⠙⠚⠈⠋⠃⠙



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠶⠀⠻⠉⢂⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⢮⣍⠀⣀⢈⠵⠊⢡⣑⠠⠈⠘⠋⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠱⢆⡁⠀⠑⠁⠀⣀⣔⡏⠠⠀⠡⠊⢹⡄⣄⡁
⠀⠀⠀⠀⠀⠀⢠⢊⡴⠒⠒⣲⢚⡛⢻⡝⡄⣤⠋⠉⠉⣠⣴⠄⠽⠛⠃⠔⢱⡙⢦
⠀⠀⠀⠀⠀⠀⢸⠈⡔⠀⣀⡠⠤⣈⠢⡇⡇⢸⠀⠂⠎⢰⠏⠠⠂⠴⣀⡀⠐⠈⠆⢧⣀
⠀⠀⠀⠀⠀⠀⠈⣽⠀⠈⢃⡤⠄⠀⢀⠁⠀⠀⢀⣄⣀⣀⣠⣀⡀⣀⠀⠫⠁⠂⠀⠪⣑
⠀⠀⠀⢀⡀⠔⢻⡥⠂⠐⣭⠴⠒⠿⣿⢖⡮⠟⡄⠋⠈⠁⢻⢟⡁⠀⢀⠀⠀⢘⠀⠐⢬⢣
⠀⠀⢩⠁⡀⠐⡀⠀⡀⠀⠁⡆⠀⣀⠀⢿⡈⠀⠀⠀⠀⠀⠀⠈⠉⠓⣌⡀⢢⣀⣎⠀⠸⢸
⠀⠀⠀⡜⣴⠀⠼⠈⢆⠀⢀⡘⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⡉⠈⠐⠀⠈⠑⢦⡀
⠀⠀⠀⠘⠊⢀⢠⡀⠈⠀⠊⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡆⠀⠀⠀⠐⠀⠀⠀⠃⠀⢠⠈⡅⠂⠀⠃
⠀⠀⠀⠀⠀⠻⡀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠳⠥⠄⢌⡲
⠀⠀⠀⠀⠀⠀⠩⢄⢄⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⢠⢄⠑⠒⠒⠀⠂⠈
⠀⠀⠀⠀⠀⡆⠀⠀⠁⠂⠑⢄⠀⠀⠀⠀⠀⡠⠒⠁⠀⠈⠓⠒⠀⠨⠲⠀⠃⡀⠣
⠀⠀⠀⠀⠀⠀⢈⡶⠊⠡⠀⠈⢦⣤⣠⠔⠛⠀⠀⠀⠀⡀⣀⡀⡠⠃⠉⠂⠠⠴⠚
⠀⠀⠀⠀⠐⠀⢸⠁⢠⡈⠈⠢⠀⢄⠀⡎⠓⠐⠂⠀⠊⠁⠀⢀⠀⠂⠤⠤⡀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠓⠀⠀⠈⠀⠃⠀⢃⠀⠀⠀⠀⠓⠄⠀⠁⠀⠀⠀⠃⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⢀⣀⣀⣀
⠀⢀⣤⢸⠞⣥⡾⢣⣄⡉⠉⢂⠀⠀⠀⠀⣰⣾⣿⠏⡿⣿⡑⣄⠀⠀⠀⠀⠛⠋⢰⠤⡤⠤⡀⣠⠄⠂⠀⠉⠻⣿⣿⣿⡿⠀⣿⣿⣽⡿⢿⠃
⠰⣿⠘⠸⡘⣿⡀⢫⠏⠉⠛⣨⡄⠀⠀⠀⡿⣿⡿⣇⡘⢿⣇⡣⡀⠀⠀⠀⢣⣏⠉⣴⠂⠀⣾⠁⣠⡆⠀⣩⣽⣿⡭⠃⢀⡘⢻⣿⣿⣷⣼
⠀⠉⣀⠠⣷⣴⡘⠂⠠⢺⣤⣿⠁⠀⠀⠀⢠⣿⡆⢘⠿⠲⡿⠛⣿⡦⢀⣴⣎⣅⡾⡟⠀⠞⠟⠻⣿⡇⠀⣸⣿⣁⡀⠀⠘⠛⠛⣿⣿⣿⡟
⠀⢸⣿⠘⣿⣟⠃⠀⠀⠀⢛⡁⠁⠀⠀⣰⣾⡟⠀⠀⢹⡛⠀⠐⠋⠁⠘⠛⠟⠉⢀⠀⠀⠀⠘⢆⣿⠀⠀⣿⣧⣯⣅⣀⣀⣤⣄⢉⠸⣿⡟
⠀⠺⡟⢓⣈⢙⣷⣴⣶⠟⠏⠁⠀⠀⣾⣿⣿⠇⣠⣠⢾⣷⠀⠀⠀⠀⠀⠈⠀⠐⠘⠀⢀⣱⣤⣾⣻⠀⠀⢙⠻⠟⠙⢁⡇⠁⣠⠞⠹⣿⣿⠣⡀
⠀⠀⠀⠼⢿⣷⡾⣿⠀⠟⠀⠀⢠⣆⣿⣿⣿⣿⣯⢿⣆⣼⣧⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⡿⢛⣿⣆⠀⢋⡈⡄⢀⢼⡆⠀⣠⣦⠘⠛⢦
⠀⠀⠀⠐⠀⠈⠀⠐⠀⠀⠀⠀⠀⠙⠛⠻⠿⠴⠯⠾⠛⠋⠉⠀⠀⠀⠀⠿⠿⢿⣤⣿⣿⠿⠿⠿⠛⠉⠀⠠⣾⠙⠋⠲⢀⠀⠉⣱⡖⠠⡌⠓
⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠆⠖⠳⠆⠠⡀⣹
⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠄⣿⠉⢿⠟⢹⣷⡄⣦⡀⠀⠀⡶⠀⣤⠀⢀⡄⢠⣀⣤⣤⡠⠀⠀⠀⠀⠀⢠⣶⠉⣽⣾⡆⣀
⠀⠀⠂⢰⠉⠀⠀⠾⠗⠀⠀⠘⢃⠀⠀⣸⢿⡿⣿⡦⠀⠀⣼⠝⣱⣿⠇⠀⡸⣷⡆⠀⢠⣾⣷⣴⣿⢻⣿⣿⣆⠀⠀⠀⢸⣸⣦⣾⡍⢶⣝⢿⡇
⠀⠐⠀⠈⡀⠀⠀⠐⠁⠀⠀⢺⣶⡇⠀⢻⡞⣻⣶⡖⠀⢰⡄⠀⢉⡅⠴⠀⢱⡎⠀⠀⢠⣜⠛⠁⣬⣸⠉⣿⠿⢄⡿⣻⣟⣹⣯⠀⠀⢾⠟⢻⡟
⠀⠀⡀⢴⣧⣀⠒⣶⣤⢠⣤⣿⡛⠁⠀⠀⢿⠟⠉⣴⣶⡄⣅⠂⢈⣃⠄⠀⠰⣷⣷⣀⠈⠑⣶⣬⣿⣏⣠⠀⠀⠈⣿⣿⢿⣿⠀⢠⠅⢬⣶⢃⡗
⠀⣼⠃⠀⠐⠌⠁⠙⠻⣚⠻⠿⣗⠀⠀⠀⠐⢶⡠⣾⠿⣤⡿⠀⢈⣿⠀⠀⠀⠉⢿⠟⣳⡾⢟⣾⡟⠋⠀⠀⠀⠀⠀⠙⣠⢜⣴⢳⣴⣾⡟⡰⠛
⠀⠹⣦⡀⠀⠀⠔⠀⣸⡿⠗⣠⣿⡇⠀⠀⠲⣜⣃⡀⠀⠀⠀⠀⣿⣣⣶⡆⠀⠀⠀⢚⣿⣴⡟⠀⠁⡄⠀⠀⠀⠀⠀⠐⠛⠪⠓⠾⠟⠇
⠀⠀⠈⠓⢄⡀⠀⠀⣉⣴⣿⠿⠧⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⡿⠋⠰⠃⠀⠀⠀⠈⠻⣿⣧⣴⠿⠛⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⣨⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢨⣧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤
⠀⠀⠀⠀⣾⢛⣬⢉⣼⣷⣄⠀⠀⠀⠀⠀⠐⢰⣼⡿⣿⣿⡌⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⡄⠀⠀⠘⣿⡟⢻⣿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⡜⡈⣿⢿⣟⠘⣿⣿⠏⢷⠀⠀⠀⢠⠀⣼⡻⡏⠀⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⢀⣤⣔⠋⠴⣹⣧⠀⠀⠀⢛⢿⣿⣿⣴⣾⣿⣿⣿⣿⣿⡄
⠀⣰⢟⣴⢿⡉⢁⣀⠉⡿⣠⠸⣄⠀⠀⣿⡔⣎⠻⣆⡄⠀⠀⠀⠀⣸⣿⠁⣀⣤⢠⣾⠻⠇⠀⠐⣭⣋⣤⠀⠀⢎⣼⡟⠉⠙⠛⠋⠘⣿⣿⣿⡇
⠀⣿⣉⣽⢻⠇⣿⣿⢸⣟⣟⣷⣻⠄⣰⡇⠡⣍⣄⣿⡷⢂⣐⣀⠈⠉⠀⠀⠘⠇⠀⢥⡀⣴⣦⣤⡴⠛⡫⢻⣤⠘⣿⡁⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠘⢿⣿⢳⣾⣲⠟⡣⢞⣯⣛⣻⣿⡅⠙⢻⡆⣹⣿⠿⠀⡾⢹⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠁⠘⠁⡇⠹⣆⠉⠁⠀⠀⢠⣿⣿⠟
⠀⠛⠿⢟⣻⣿⡶⢧⡝⢿⣿⣍⣽⠃⠀⠈⠁⠹⢶⣄⠀⣷⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠂⠀⠘⠋⠁⠀⠾
⣤⡄⡴⢂⣄⠀⠀⡀⢀⡀⠀⠉⠁⠀⠀⣤⣶⡖⠒⠺⢤⠈⠁⠀⠀⠀⠀⠀⠠⠞⠟⠉⠀⠈⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣹⠑⠂⠢⡄
⠛⣡⠆⢠⠟⡞⢋⣙⢮⣻⡆⠀⢀⠤⣚⣉⡿⣻⣷⣆⠀⠠⡄⠀⠀⠀⠀⠸⠀⠰⣗⠀⠀⠸⣿⡟⡧⢤⡀⠀⠀⠀⡠⠀⠩⡍⢰⣿⠗⠂⠠⡄
⠀⠙⢺⣷⢘⢁⣯⣽⢤⣟⠀⢀⡿⢸⢋⡿⠋⠈⠉⠙⠁⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⣀⡝⠃⠀⠈⠗⠀⠀⢠⣷⠚⢁⡃⠄⠡⢤⠱⣶⠜⢦
⠀⢆⣤⣑⠊⢺⣿⣿⠊⣿⡇⢸⣱⣧⢻⣷⠀⣠⡴⠆⡀⠀⣴⣿⡸⣏⠀⣤⡀⠀⣰⣾⣟⣁⡠⠄⡠⠂⢰⡀⠀⠹⢃⠁⣿⣭⠀⠀⠀⢠⠛⡀⢶
⠀⣾⣋⣿⣷⡿⠿⢿⢃⣼⠷⠀⢸⣿⣿⣿⣿⣿⡵⣞⣿⣿⡟⠟⠁⢀⣶⢶⡀⣚⣿⢛⣨⡁⠹⠞⣷⠀⠀⢷⣶⡇⠀⣠⣀⡛⠀⠋⠁⠊⠘⢛
⢠⣾⣿⣬⣿⣦⡀⣠⣏⣽⡀⠀⠈⠉⠛⠙⣿⡿⣿⣛⠃⣤⠀⠀⠀⠈⠛⠛⢹⠛⠛⣌⠉⠀⣀⣀⣶⠾⠀⠟⢻⣧⠀⢨⡉⢿⣆⠀⢠⠀⣰⡆
⠘⢿⣿⢦⡟⣿⡟⠻⠋⣹⠇⠀⠀⠀⠛⠻⣯⣾⠋⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠰⢧⡅⢠⣶⣾⠟⠉⠀⠀⠀⠀⠻⡄⣠⡘⠧⠉⠂⠀⢠⣬
⠀⠈⠛⠊⠃⠛⠃⠁⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠻⠛

⠀⢀⣤⣤⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠐
⠀⠸⣟⠟⣿⡿⣿⣷⡄⠀⠀⠀⠀⣀⠄⠠⣤⣤⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣧⣧
⠀⢀⣿⣯⣛⣧⣷⡟⠀⠀⠀⠀⢀⣶⣿⢖⠈⡻⠁⠀⢀⠀⡆⠀⠀⢯⡃⢠⠀⠀⠀⠀⣠⠏⣭⣌⡿⣷
⠀⢸⣿⣉⣉⣻⣿⣷⣦⣄⡀⠀⢮⣰⣿⡷⠴⢿⡲⠰⡸⠣⠃⠀⣸⡀⠣⡀⠀⠀⠀⠀⠉⠛⣋⣿⣿⣿⣧
⠀⣿⣭⣿⣿⡿⣧⣿⣿⣿⣧⡀⠀⠀⠁⠀⠀⠀⠍⢀⣘⡆⠆⡞⠋⠁⠀⠈⠐⡀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣧
⠈⣏⠈⣩⣯⣙⠉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⠎⠀⠁⡠⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣏⣿⣿⡿⣿
⠀⢹⣾⣿⣿⣿⣾⣿⠛⠻⠻⣿⠀⠀⠀⠀⠀⡤⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠰⠤⢸⣿⡿⣿⣿⣿⣶⣿⣷⣿
⠀⠘⣿⡇⠀⣼⣿⡇⠀⠀⠀⠸⡇⢀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣾⣿⡏⠀⠀⣿⣿
⠀⠀⢸⠁⠀⠉⠻⠃⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⣰⡟⠟⠀⠀⠀⠀⣿⡀
⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⢐⣄⣀⣈⣄⠀⠀⠀⠀⠛⠀⠀⣀⡀⠀⠀⠌⠁
⠐⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⣴⣿⠀⠀⢸⣛⡻⠷⢾⣮⠉⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡇⣾⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⢀⡤⣶⠹⢗⣦⣄⣭⠀⠀⣨⡈⣡⠀⠠⢿⡇⠀⠈⠁⠀⠀⠀⠐⣶⣶⣦⡀
⠀⣏⢿⣶⡾⠛⢿⢻⣿⣿⣿⡟⢫⠟⠀⠘⡀⢢⣛⣿⣯⣦⠀⣸⠃⠉⣠⣶⣵⣿⣦⣀⣀⣀⣀⠀⢀⣀⣩⡿⢣
⠀⠈⠉⠉⡇⠀⣄⢸⣿⣿⡟⣰⠘⢤⡘⣧⡉⢿⣿⠿⡿⠋⠀⢿⠀⠀⠁⠿⠃⢞⣾⣿⣿⣯⣻⣝⣿⣿⠿⠅⠋
⠀⠀⠀⢀⢷⠀⠠⢃⡙⠻⣷⢾⡄⠀⣳⠘⠇⠼⠟⠀⠀⠀⠀⠰⡄⠖⠁⡄⠀⣹⣿⣿⣿⣿⠟⢸⣿⡟⡇
⠀⠀⠀⠘⠷⠄⣤⡾⠟⠓⢄⣸⠀⢛⠱⠤⠖⡼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⣈⣉⢉⣤⣤⡅⢹⣿⣿
⠀⠀⠀⠀⣀⠀⠊⠃⠀⠀⠀⠙⠶⠶⢶⡂⠰⢤⣀⢀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⠐⢌⠛
⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠒⠂⠀⠀⠀⠦⠄⠈⠉⠀⠀⠀⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠂⠀⠁⠉⠉⠉⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣈⠁⠀⠀⠀⠓⠀⠀⠄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠘⠛⡁⠀⠀⠈⠭⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢸⠀⠀⠐⠄⢀⠀⠀⠀⢀⠀⢠⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠜⣄⢣⢀⡠⠤⠤⡤⢴⠋⡠⡞⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠢⡹⠀⠀⠀⡖⡡⠊⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⡇⠀⠀⠀⡋⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡀⠀⠱⢄⡠⠔⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⡀⠀⠀⢰⠀⠀⠀⢛⠀⠀⠀⠀⠀⡜⢇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠄⠑⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⢠⠞⠀⠈⢆⠀⠀⠘⡀
⡔⠋⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢣⠀⠀⠘⡄⠀⡰⢻⠀⠀⠀⠈⢣⠀⠀⢃
⡇⢄⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠀⡟⠀⠀⠀⠀⠀⠘⡄⠀⠀⢣⠐⠁⣸⠀⠀⠀⠀⠀⢣⠀⠸⡀
⢣⠈⢦⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘⡤⢖⣁⠀⠀⠀⠀⠀⠈⢇⠀⢣
⠀⠑⢤⣈⠉⠛⠉⠉⢳⡄⠀⠀⠢⣇⣀⠀⠀⠀⠀⠀⢀⣱⠀⠀⢸⡁⠀⢙⡆⠀⠀⠀⠀⠀⢣⠈⠓⠤⢄
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠢⠼⠤⠴⠼⠀⠉⠉⠉⠉⠉⠁⠸⣀⢀⠀⢈⢻⠉⠁⠀⠀⠀⠀⠀⠀⠣⣀⣰⣀
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠑⠢⣄⢀⡤⠖⠚⠋⠉⠙⠓⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠾⠄⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⡤⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⡀⠀⠀⣀⠼⣄⣀⠀⠀⠀⠀⢀⣼⡏⣹⡅⠈⢹⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠚⠉⠁⠀⠀⠉⠉⣭⡟⢦⣬⣽⠝⢯⡿⢯⣿⠛⣾⡭⠶⠤⠞⠵⠯⠴⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⠞⣹⢟⡴⠋⢳⣞⢟⣴⡻⣽⡾⠉⢧⢯⣉⠙⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⢧⣀⣨⢗⠼⠒⠷⡼⣅⣀⣼⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⢻⢧⡼⣄⣀⡰⣣⣔⣖⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠫⡟⠧⠼⢻⡤⠗⢘⡎⢳⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⣒⠤⣴⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⡤⢾⠷⠁⠀⣀⡀⡀⠉⠀⢀⣉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠉⠁⠀⠀⠀⡠⣠⠶⠛⠉⢻⠀⢀⣴⢶⣮⡉⠛⢿⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣾⣧⣾⣷⣷⣾⠊⠁⢀⣤⡿⢸⠀⠀⠀⠀⠈⠻⣦⣽⡻⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⡏⢠⣼⣿⡿⠃⣼⣦⡀⠀⠀⠀⠀⠀⢽⣦⡲⣵⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢾⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢷⣼⣿⠇⠀⣰⣿⣟⣓⠦⠀⠀⠀⠀⣰⣿⠙⢿⣏⠑⢄
⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢋⣽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢻⣦⣾⣿⣿⣟⠻⠅⠀⠀⠀⠀⠈⠋⠃⠀⢿⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠐⠣⠄⠠⠛⠛⠀⣸⢉⠛⠙⠉⠉⣙⡻⡿⠀⠘⠿⠿⣟⡛⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠘
⠀⢀⡀⢤⣔⡊⠀⠀⠀⠀⠀⠀⠸⠅⠁⠀⠀⠐⠚⠛⠓⠹⣦⡀⢀⡀⠀⠉⠂⠐⣄⠀⠀⠀⠀⠀⢃⠀⣸⣾⠃⠀⡷
⣴⣯⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠠⠀⠀⠀⠙⠺⢟⠲⠀⠰⣄⢸⣆⡀⠀⠀⠀⢸⡆⣼⡿⠀⠀⡇
⠘⠟⢛⣀⣀⣀⣤⣤⣤⣤⣤⣀⠠⠴⠖⠋⠉⣠⠀⢠⣤⢀⡤⠂⡀⠀⠀⠘⣧⣿⢹⠹⣿⡄⠀⣦⣸⡿⠋⠀⢸⢠⡇
⠀⠀⠈⠢⠤⠾⢦⣉⠛⢿⣿⣿⣿⣦⡀⡀⠀⠀⠀⠸⢤⡿⠂⠸⣿⡏⠓⢰⠏⠃⠈⠀⠃⠸⢀⡟⢻⡇⢀⠀⣾⣾⠇
⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠙⣿⠛⣰⣿⡜⡄⠀⠊⠀⠈⠠⡑⢤⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢸⣴⠃⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⢟⡿⠀⠀⠀⠀⢴⡲⠾⡿⠀⡀⢀⡆⣴⣾⡀⠀⢠⠀⡖⣼⠇⢀⣾⢣⠀⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡙⣠⢷⡟⠀⢀⠔⠁⠀⠀⠈⡶⠆⣰⡇⣸⠿⠻⣿⡇⢀⣾⣼⠟⡑⣠⠞⠁⣞⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡿⢁⡤⠃⠀⠀⠀⠀⠀⠀⠞⠱⢚⠃⠀⠀⣼⡴⠿⠋⢉⠴⠛⠁⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⡀⠀⢸⠏⠀⠀⠀⠀⣠⠂⣠⡾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣴⠟⠀⠀⠀⣠⠂⣀⣤⣾⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⡏⣀⣤⣶⣾⡵⠞⠋⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠛⠉⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠈⠠⡀⠀⡄⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⠀⢺⠃⠀⠀⠀⠀⠀⠀⠘⡕⠀⣀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣿⣿⣿⣿⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠚⣸⣿⣿⣿⣿⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠻⠿⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠒⠲⢄⡀⠀⠀⢀⡠⠖⠒⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⢈⠻⣆⣰⠟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠖⣠⡴⠛⠻⣯⣁⣦⣿⣆⢻⡟⡰⣯⣴⣈⣽⠟⠛⢦⣄⠲⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢴⣿⡥⠀⠀⠈⠛⢿⣿⠀⢸⡇⠀⣿⡿⠛⠁⠀⠀⢨⣿⡦⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠂⠜⣻⡴⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣦⣟⠣⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⡷⢷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡾⢮⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⡄⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢠⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡘⠀⢀⠀⠀⠀⢸⡄⠀⢵⣄⣠⡮⠀⢠⡇⠀⠀⠀⡀⠀⢃⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣧⡀⠘⢿⡿⠃⢀⣼⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡇⠀⠀⠁⠻⠲⢶⣶⠖⠏⠈⠀⠀⢸⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠎⠱⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⢰⡄⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠸⠇⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢖⣨⣿⣿⣿⣷⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣞⣾⠁⡀⠀⠀⠀⠀⠙⣶⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⢛⡋⠀⠈⠃⠀⠀⠀⠀⢉⢶⡦⢤⣄⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⣤⠀⢽⣯⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠟⠛⠻⠦⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠁⠀⠀⠈⢳⡶⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣊⠂⠀⠠⠀⠀⠀⠀⠀⠀⢤⣀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⣴⣬⡁⠈⠰⠐⠶⠀⠀⢠⣀⣰⠽⠻⣯⠛⢒⡬⡓⢔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠠⣆⣲⠞⡃⠀⠀⠀⠀⠀⡀⣾⣿⢯⡀⣉⠐⠀⢤⣾⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠀⠀⠀⠀⣼⡷⠀⠀⠀⢀⣢⣾⣾⡿⣿⣹⣿⢳⡟⣧⡇⣳⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠤⢲⣿⡑⠀⢀⣦⣿⣿⢿⡟⣿⢿⣿⢮⣿⣿⣽⣧⣿⠿⡧⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡟⡅⠁⠀⣼⡟⠙⠛⢃⠉⠈⢙⣳⢿⣻⣯⢿⣿⣿⢀⡀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠈⠁⠀⣸⠟⠀⠉⠀⠀⠀⢀⢀⢠⠺⡧⡉⢺⡜⣦⢐⠣⠀⠀⡸⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⡀⠀⣀⣀⣠⣤⣤⣠⣤⣤⣤⣴⢿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠈⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣀⠄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣼⠁⠀⢀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⠀⠀⠘⠀⠀⣷⣾⣿⠈⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠿⠟⠀⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠠⡀⠀⢸⡿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⢀⣀⣤⣤⣀⠘⠀⢸⠃⠙⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣥⣶⣶⣾⡇⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠻⣿⡗⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠰⣄⠀⠀⢀⣠⠴⠒⠛⠓⢢⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⠀⠸⢻⣿⣧⣤⣶⣶⡿⠛⠉⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠧⢀⡀⠀⠀⠀⠈⠙⠉⠋⠁⢀⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠶⣄⣤⣦⣤⣤⢴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⢄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠀⢰⠀⠀⠀⡴⠁⠀⠀⠀⠈⢃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀
⠀⠀⠀⠀⢠⠀⢀⡞⠀⠁⣀⡤⠤⠶⠖⠒⠺⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇
⠀⠀⠀⠀⠈⠦⠊⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠞⠛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⡠⠴⠒⠒⠒⠒⠒⠤⠄⠀⠘⠀⡟
⠀⠀⠀⣀⠄⠈⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠐⣌⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣦⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢰⠁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠧⠞⠀⠐⠀⠀⢀⡠⠴⠒⠒⠓⠲⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢃⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠈⠀⠘⡟⠛⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⢀⣀⠀⠀⢢⠜⠙⠛⢛⠟⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⡜⢁⡄⠀⢰⠃⠀⠀⡴⢃⣀⣀⡤⠖⠀⠤⢄⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠡⡎⠀⠀⠸⣤⡤⠞⠁⠀⠈⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠑⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡤⠤⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠳⢄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠆⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠳⣄⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠄⠐⠒⠂⠠⠄⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢡⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡄⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢀⠃⠀⠀⢸⣯⠆⡠⠤⠤⡀⢯⣿⠀⠀⠀⠇⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠸⠒⠒⠒⠐⠒⢊⣤⣒⣠⣌⠑⠒⠒⠒⠐⠺⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇⠀⠀⠀⠀⠀⣀⣉⡿⣏⣁⡀⠀⠀⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠫⣀⡨⠁⠀⠀⠀⠀⠀⡰⡖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠢⠤⢀⣀⣀⣀⣀⠀⠤⠄⠲⡋⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣷⠃⠉⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢣⠀⠈⠢⣀⠀⠀⠀⢀⡠⠊⠀⢠⠃⢱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⡆⠀⠀⠈⠉⢲⠊⠁⠀⠀⠀⡜⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠂⡜⠢⠤⠤⠀⢸⠀⠀⢀⡀⠜⣄⠚⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣰⣘⣴⡀⢰⠀⣀⠼⢄⡀⢐⠀⢰⣼⣰⣀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⢤⣶⣶⡦⡤⢀
⠀⠀⠀⣴⣿⣿⠟⣱⠇⠀⠉⡽⠡⣩⣍⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢀⣤⣤⣼⣶⣬⡑⢂⢹⣦⡀
⠀⠀⠘⡟⢿⣿⠂⣟⠀⠀⢸⡗⢰⣿⡟⠃⣘⣦⠤⣶⢾⢿⢿⠿⠻⣖⠂⢉⡀⠶⢶⣭⡏⠉⠉⠛⢦⡻⣿⣿⡄
⠀⠀⠀⢣⠘⣿⣀⡡⠂⠀⣾⠃⣸⣿⡷⠾⠋⠁⠴⢁⡴⠀⣸⠇⡐⠈⠓⢦⡌⠓⢄⡙⢇⠀⠀⠀⠀⠹⡝⣿⣿
⠀⠀⠀⠀⠁⢸⣿⠀⠀⠸⠏⢠⣿⠟⠀⠀⠀⠀⠠⠏⢠⡾⠋⢠⡷⡄⠐⣦⡉⠓⢤⡙⢌⢦⠀⠀⠀⠀⠸⣽⣿
⠀⠀⠀⠀⠀⡈⣿⠃⠀⡁⠀⣾⡟⠀⠀⠄⠀⠠⠁⢠⠟⢀⣶⠟⢀⣷⠰⠘⡟⠁⠀⣀⣀⠘⢧⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⠀⢀⠉⠑⢸⠁⣸⣟⠀⠀⠀⠤⠀⠀⠀⠁⠀⢁⣠⡤⣄⠙⡆⡆⢷⡄⠘⢩⣿⣫⣍⣦
⠀⠀⠀⠀⠀⠀⢗⣻⣿⢠⣿⣿⣦⣐⠀⠀⠀⠀⣠⠖⣛⣛⣻⣷⣤⣤⡗⠁⢸⣷⣴⣾⣟⡷⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠘⣿⣿⣿⣿⣿⣟⠀⠈⣡⣾⣿⢿⡝⠻⣿⣿⣷⠀⣾⣿⣿⣿⡿⠴⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⢹⣿⡿⠀⠍⠉⣶⣄⠁⠱⢽⡯⠴⢃⣿⣿⣿⡆⠈⠻⣿⣭⡳⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠰⠂⢀⢻⣦⡀⣀⣶⡄⠈⡼⡫⣿⠇⠠⠧⠃⠀⠉⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠨⡄⠻⣿⣿⡿⢁⠎⠜⡴⠁⢀⠄⢀⡀⡀⠫⣤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⣆⠀⠀⣷⠀⢹⡟⢠⠎⢀⡾⣂⡀⠚⠀⢸⡧⢸⢀⠻⣤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡏⣿⣿⣦⡀⠈⣇⢸⢁⡞⣠⣟⡴⢛⣷⡀⠉⠑⢤⣸⢨⣞⡡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢱⢹⣿⣿⣷⠰⣹⣸⡸⢠⣿⡯⠶⢋⣹⡇⢰⠖⠁⢸⡂⠀⠛⠂⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠂⠁⠉⢻⡀⣿⢻⠇⣼⣯⠤⠶⠟⢻⡆⠈⠀⠀⡀⠷⢦⡘⠃⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠄⠀⠀⠈⡇⠟⣼⢀⣿⣷⡦⠴⠖⣻⣇⢠⠄⠃⠐⠂⠈⢷⡆⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀⠐⠐⠆⠀⠀⢳⣾⣿⢸⣿⣿⣿⣄⣀⣿⡏⠈⡄⠖⠒⠛⢋⠸⣧⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⠀⠈⠀⠀⠀⠀⠔⠀⢻⡇⣼⣿⣿⠗⠊⠙⡻⠀⣀⣤⣤⡀⠀⠀⠀⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠛⢧⣸⣶⠀⠇⠀⠌⡖⠀⡤⠀⠳⣽⣟⣧⣴⡶⢏⣵⠃⣿⣿⣿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢴⣄⣀⠈⠄⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⠀⣹⣿⡿⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠀⠀⠀⠀⠀⠰⠟⠛⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡠⠔⠒⠉⠉⠷⠿⣶⣦⣭⠭⠉⠉⠉⠙⠳⣆⠠⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣴⠶⠆⠀⠐⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢺⡏⣠⠀⢠⠂⠀⠀⠀⠀⠀⠀⠈⠀⠢⡀⠀⠀⠘⡇⠀⠄⠀⠀⠀⠀⠈⣏⢧⠸⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⣨⣴⡇⠀⡇⠀⠀⠀⢀⡀⠀⠀⣀⡆⣠⠇⠀⠀⠀⠁⢦⣠⣶⣀⠤⠀⠀⢸⣾⠀⠃⠉⠻⣄
⠀⠀⠀⠀⠀⠀⣼⢸⣿⡇⠸⣿⣿⡇⢰⡇⠀⠀⣀⡾⣿⣻⣿⣿⣆⢿⠀⠀⠀⠀⠀⠀⠻⣿⣽⣷⠄⡀⠈⣟⡇⠀⠀⠀⠿⢷
⠀⠀⠀⠀⠀⠀⢹⣆⢻⡇⠀⢻⣿⡇⢸⡇⠀⠉⠉⠁⢼⡿⠉⣿⡏⠀⠀⠀⠀⣷⠀⠀⠰⡙⠧⠀⢀⡄⠀⣯⡇⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⢿⣷⠀⡿⡄⠀⢤⣀⠀⠀⢈⣿⠆⠀⠀⣀⣸⡟⠃⠀⠀⢀⣰⠿⠋⠀⠀⣿⣇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢸⣿⡀⡇⠀⠀⠀⠙⢻⡇⠀⡏⢀⡴⠛⠉⣠⣤⣄⠐⢶⣦⠙⣦⠀⠀⠀⣿⣏⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⢸⣿⢣⣇⠀⠀⠀⠀⠊⠀⠀⠀⡜⠁⠀⠀⣭⣷⠄⣀⠸⣯⡅⠸⠀⠀⢠⣿⣿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠾⣃⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⡷⠞⠀⠀⠠⢇⠀⡿⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⢿⣿⡇⠀⠋⠘⣵⣆⠀⠀⠀⠀⡀⡀⢸⣿⣿⢈⣶⡆⠄⠀⢾⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠈⣿⣷⡀⠀⠀⠻⣿⣆⠀⠀⡄⡄⢤⠴⣿⢻⣾⣿⣷⣍⣀⠌⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⢹⠈⢳⣄⠀⠀⠘⡿⢿⣶⣤⣤⡴⣚⠛⠯⠋⠀⢹⡛⣉⠞⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡼⡆⠀⢇⠀⠉⠑⣦⡀⠈⠙⠛⠻⣏⣴⡙⠦⣀⠀⠀⠘⣿⠃⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠈⣆⠀⠀⠈⠛⠂⠰⢤⣀⠙⠻⠿⠶⠶⠖⢚⡶⠋⠀⠀⠀⣼⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠈⠀⠀⢠⢠⠀⠀⠀⠈⠑⢶⣶⣶⠃⠈⠁⠀⠀⠀⠀⡀⢸⡟⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣻⣿⠃⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⡾⣿⣿⡀⠀⠀⠀⠀⠀⢠⠀⢸⠃⠀⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠘⢱⠃⡀⠀⠀⠀⠀⠙⢿⣟⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠁⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢿⣇⣤⠀⠀⠀⠀⠀⢸⣿⡇⢀⡄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡇⠀⠀⠀⠻⡿⣆⠀⠀⠀⠀⠈⠈⢿⣿⣧⣆⠀⣠⣶⣄⠀⣀⠀⠀⠀⠠⣹⡆⠀⠀⠀⡏⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠁⠙⠻⢶⡏⠀⠉⠻⠇⠈⠁⠀⠀⢹⠃⠀⠀⡼⠃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠳⣄⢀⡀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⠛⢷⣾⣷⣄⢲⣄⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⠖⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠔⣪⠿⠋⠀⠀⠀⠀⠀⠀⣠⠄⠂⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣉⡼⢋
⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠠⠚⠁⠈⡙⠀⠀⠀⢀⡤⠔⠊⠡⠉⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢰⡆⠀⠀⠀⢼⡇⢨⣡⣶⣮⠈⠒
⢠⣾⠴⣻⠇⣸⠀⠀⠀⠀⠚⣍⡄⢦⠀⠀⠀⠄⣦⠐⠀⠀⠐⠚⢻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣧⠀⠀⣠⣿⣿⣈⣋⡼⠟⢶⠶⣶⢀⣆
⣿⡿⣊⢃⣲⣼⣇⣤⡶⠚⢈⠉⢰⢌⣁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⡆⠀⠀⣫⣜⠅⠀⡜⢛⡎⢉⣻⣀⣤⠈⢃⡀⠙⢿⣀
⣿⠞⣹⣈⡽⢌⣿⣿⡷⠂⠀⠈⡃⠀⠀⢣⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡷⠂⠘⣁⡙⢶⡀⠟⠁⡴⣄⡘⣿⡏⠳⡌⠙⠷⣾⣿
⠿⠓⣅⡟⢘⣦⣹⡿⠗⠚⠶⠖⠉⠛⠧⣌⠳⣦⣦⣴⣀⣴⣠⡠⢼⡿⢄⣀⣰⣄⣦⣦⣾⣷⣶⣏⢜⡁⢸⠞⢉⡅⢸⡡⠒⠉⠻⡀⠻⣌⣗⣦⣤⣀⠈⠻⣿
⣰⡎⠀⣿⢺⣏⣠⡤⢾⣀⣤⠾⢶⢸⡆⠘⠷⣿⣿⣿⣿⣿⣿⡗⡹⡟⢺⣿⣿⣿⡟⢹⣿⣿⣿⡥⢟⠙⠓⠛⣩⢸⢛⣀⠀⠂⣧⠘⣤⣼⣿⣇⠀⠙⠷⢴⣿
⠴⠳⣀⣿⣶⠟⠉⣀⢀⣉⣇⠀⢨⡽⡟⢦⣀⠸⣿⡟⡟⡿⡿⣉⣠⠉⢈⢻⣿⣿⡴⢊⣻⣿⠋⡠⠴⠗⠶⣦⣽⣇⣼⠡⠤⠖⠛⢿⡀⠘⢯⠉⠁⣄⠀⠀⢹
⢀⣶⡟⣹⣷⡞⠋⢀⣬⠋⠀⡖⠈⠀⢀⡀⠙⠳⣾⣿⡏⣿⠯⠎⣀⢧⡼⠨⢿⡵⡁⠊⢉⡟⢋⠀⣠⢤⠦⣀⢹⣿⣅⠀⣠⡀⠀⢹⣉⠉⠺⣆⡀⠈⠂⢤⣀
⣾⣁⣼⣿⡯⠀⠚⢻⣁⣠⡞⠀⢠⡀⠘⢳⡄⣀⠈⡿⢿⡅⠀⠈⡇⢸⠀⠀⠠⡾⠁⠲⢎⠁⣣⣤⡇⢀⡷⣄⣉⣿⣿⠜⠛⣧⠀⢠⡏⠶⣄⡘⢧⣠⠂⠀⢻
⠀⠀⡽⠃⠀⠀⣀⡤⠞⠉⠀⠀⠀⠛⣆⢨⡗⠛⠓⠇⠘⠓⠐⠋⠙⠛⠒⠀⠀⠈⠀⠀⠀⠁⠀⠀⠑⠁⠀⠘⠛⣁⠆⠀⢈⠉⠓⠃⠀⠀⠀⠙⠻⣯⠁⢀⢈
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠲⠀⠀⠀⠙⠻⠇⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⠠⠾⠴⣄⡀⠀⢠⣀⣣⡀⠈⣻⠿⠿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠛⠛⠀⠙⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠛⠹⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⢀⡤⠞⠃⠀⠀⠀⣠⠤⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠢⢤⣄⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉
⠈⢳⣤⣀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡿
⠀⠀⠉⠉⠡⣴⠶⠊⢹⡇⠀⠀⠀⠀⠀⠀⣰⡯⢶⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡤⣰⠟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣀⣤⣾⠋⠀⠀⢠⠟⠀⠀⠙⠓⠆⠒⠷⠒⠋⠀⠀⠀⠀⣸⢱⡇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠋⠉⠀⠾⢦⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢷⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣿⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣤⣭⠆⠀⠀⠀⠀⠀⠈⠓⣦⠀⠀⠘⠦⣤⡴⠞
⠀⠀⠀⠀⠀⠀⠱⣦⣄⣀⣨⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢰⣬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⡞⣍⠲⣄⣀⠀⠀⣀⣠⢞⡭⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡅⢨⣏⣽⣖⣽⣆⠀⠀⠀⠀⠀⠀⠀⣷⢺⡇⣽⣿⢿⡿⣿⣇⢼⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣄⣠⣤⣶⣾⣿⡟⠁⣼⡁⠺⢷⣤⡉⣄⠙⢳⠄⠀⠀⠀⠀⠀⡿⣿⣋⣭⣶⣾⣷⣶⣭⣛⣷⢿
⠀⠀⠀⠀⣀⣤⣴⠶⢤⣴⡦⣤⡤⣶⠶⣈⣩⠥⠬⠿⣶⣖⣒⣻⣯⣛⣷⠄⢺⠗⠶⢶⡶⠈⠀⠙⠁⠀⠀⠀⠀⠀⣼⡣⣾⣟⣭⣝⣿⣿⢫⣭⣿⣷⢜⣧
⠀⠀⢠⣾⣟⠃⡵⠶⢿⡦⡶⣋⣸⡇⣰⠏⢹⠥⢈⡷⠋⣯⢥⣤⣾⢉⣹⣶⡀⠲⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⠿⢿⡭⠉⠁⠈⠉⣽⡿⢿⣿⣿⠆
⠀⢰⢿⣿⣶⢶⣷⣦⣦⡴⠛⠋⣿⠘⣽⠖⢋⣾⣾⠗⠾⣠⡘⠛⢻⡾⠛⢛⣷⣷⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡅⢈⣀⠀⠀⠀⠀⣈⡁⢨⣿⣿⠁
⠀⠀⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⢿⣴⡘⡞⣾⢿⣿⣿⣿⡟⠛⡿⣿⣔⣒⡻⠯⡾⠭⣉⣙⣒⠄⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⠟⢻⡘⢿⡿⢃⠟⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣽⣫⡼⠟⠀⢻⣿⣿⡇⠀⠀⠉⠉⠉⠙⢒⣦⢀⠆⠀⠈⠁⡑⢤⡀⠀⠀⠀⠀⠀⠈⢻⣷⣀⠉⠛⠛⠁⣀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡤⠞⠋⠁⠀⠀⠀⠀⡟⢸⡀⠀⠀⠀⠀⠀⣶⡿⠐⠁⠀⠀⠀⠀⠈⠒⠇⠀⠀⠀⠀⠀⠀⠀⠉⢻⣇⠀⠀⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⡀⠀⠀⠀⠀⠀⠀⠙⠢⢕⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠤⠀⠤⠀⠀⠠⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠢
⠀⠀⠀⠀⠀⢀⡴⠋⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠠⡀⠈⣷⣤⣤⣶⣦⣤⣴⡏⠀⡠⢀⡄
⠀⠀⠀⠀⡴⠋⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⠀⠀⠀⢿⠀⢸⠃⠀⠀⢰⡇⠠⡇
⠀⠀⢀⡾⠁⠀⠀⠀⢰⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⠞⠃⠀⠀⠀⣾⠀⢸⡆⠀⠀⠀⠛⢶⣌
⠀⠀⣼⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⢀⠀⡀⠀⣻⠀⢸⡁⢀⡀⢀⠀⠀⢫
⠀⢠⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⣾⠉⠛⢯⡀⠉⣃⡿⠀⠸⣃⡋⠁⣨⠟⠋⢹⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠿⠀⠀⠀⠈⢹⡿⠃⠀⠀⠻⣿⠉⠁⠀⠀⢸⢧
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡿⢛⠁⠀⠀⠚⠀⣤⣤⣤⡀⠘⠃⠀⠀⠙⠺⡆
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢺⡏⠀⠈⣿⣿⣿⣿⣿⡻⠿⣿⣷⠶⠂⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠳⢬⠀⡋⠀⠀⠀⢙⣿⣟⠁⡀⠀⠀⠃⢨⠴⠃
⠀⠀⠈⢷⡀⠀⠀⢀⣠⣴⣶⣿⣅⣼⡇⠀⠀⠘⠻⣿⠍⠻⣿⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⢩⡀⠈⠉⠛⠉⠉⠀⣤⠉⢁⡜
⠀⠀⠀⠀⠳⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣶⣄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢦⣘⠳⠤⡄⡤⠴⢋⣠⢶⠟
⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⠲⣧⡷⠻⠎⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⢀⡿⠋⠉⢽⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣋⡄⠁⢻⣿⡆
⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣺⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣼⣿⡶⢀⣴⣿⡇
⠀⠀⠀⠀⠀⣸⠀⠀⢸⣿⣿⣿⡿⠛⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⠀⣀⣄⣴⣿⠟⢁⣿⠿⠋⠀⢼⣿⣿⡇
⠀⠀⠀⠀⠀⡏⠀⠀⠺⢿⡏⠁⠀⠀⠀⠀⣻⣿⣿⣧⣶⣦⣤⣤⣦⠀⣴⡿⢶⡾⣿⣶⣿⣿⠿⠃⢀⠀⠈⢹⡇⠠⣾⣿⣿⣷
⠀⠀⠀⠀⠀⡇⠀⠀⢦⣤⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠿⣿⣿⠉⠀⠉⠀⢈⣿⣿⣿⣿⣿⣄⣴⡏⠀⠀⠀⢿⢠⣿⣿⣿⣯⡀
⠀⠀⠀⠀⢳⣿⠀⠀⢌⣿⣿⡀⠀⠀⠀⠾⠋⠉⠀⣈⢃⡀⠉⢀⣶⠟⠀⠀⡾⠋⠉⢀⡼⠁⠛⠻⣤⣤⠂⢠⠇⡼⣿⣿⠟⢸⡇
⠀⠀⢀⣀⣴⡿⠀⠀⠛⢿⣿⣷⣤⣀⠀⠀⣀⡶⠛⠛⠿⠿⠷⣾⡇⠀⠀⢀⣤⣶⡞⣻⢿⠿⠻⣿⡼⠋⠀⢃⣠⣶⣿⠇⠀⠘⡇
⠀⠀⠀⣹⠋⠀⢦⣴⣿⣿⣿⠛⠁⠀⠀⢠⡿⠁⠀⠀⢀⢀⡀⠈⠿⠃⢀⣾⠛⠀⣰⣿⣦⣶⡀⣀⣠⣴⡀⠙⢿⣿⣿⣧⣤⣤⣿
⠀⠀⢰⡿⢀⣴⣾⣿⣿⠟⠉⠀⠀⠀⣤⡾⠁⠀⠀⠀⢈⣿⠛⠿⡆⠸⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡋⣀⣀⡈⠙⠿⢿⣿⣿⡇
⠀⠀⢀⣷⣶⣿⣿⣿⣷⠀⠀⠀⢀⣀⠀⣁⡜⠀⠀⠀⠀⢹⡄⠀⠀⠀⠿⠀⣰⡿⣁⢁⡉⣽⣿⣿⣿⣿⠟⠛⠛⠁⠀⠀⢿⣿⣿⠶
⠀⡠⢿⣿⣿⣿⠛⠉⣁⡤⣤⠀⠋⠤⣄⣀⣠⡴⠆⠒⠓⢄⠁⠀⠀⠀⠀⠀⠛⢸⠙⠹⣷⣀⣁⣌⢘⣛⠻⢿⣶⣶⣿⡄⠀⣽⣿⣟⠂
⠀⠀⠘⣽⣿⠁⠀⢈⣽⠃⠀⢀⡠⠚⠉⠁⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠈⠳⣾⡿⢿⣷⡀⠀⠹⣿⡿⠄
⠀⢠⣾⣿⣟⡁⠀⢴⡧⠀⠀⠈⠀⠀⠀⢶⢻⣿⠷⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⡟⢶⠆⠀⠀⠈⠓⠀⢺⡇⢀⡀⣾⣿⣦
⠀⠾⣿⡿⠋⠠⢾⣿⡅⠀⠀⣾⡁⠀⠀⠈⠢⠉⣡⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠴⢰⣧⠉⠡⠃⠀⠀⠀⣹⡆⠀⠀⢻⣾⣿⠻⢿⣶⣄
⠀⠘⣻⡿⠋⠀⣼⣿⡂⠀⠰⠟⣁⣹⠂⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⢺⣁⣹⢷⣤⠀⣶⣿⣿⡶⠄⠈
⠀⣪⣿⣿⠅⠀⠀⠾⠿⣷⣦⠀⠈⠻⣤⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶⢠⡄⠀⣠⡾⠋⠀⡿⠁⠀⠺⣿⣑⠀⣄⣰⣾⠆
⠐⠋⢽⣿⣿⣶⠶⠒⢀⣠⣿⣧⠀⠙⠛⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠾⠟⠋⠁⢐⠃⣠⠀⣲⣿⣿⠃⠀⢿⠛⠆
⠀⠠⣿⣿⣿⣧⠄⠰⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡍⠀⠀⠀⠀⠀⠈⣰⡿⠀⠈⣽⣯⠀⠀⣾⡇
⠀⢠⣿⣿⡿⢋⣤⣠⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠓⠀⣀⠤⠀⠘⣠⣿⠅⠀⠳⣿⡿⠀⠀⢼⡀
⠀⢸⣿⣿⣿⣿⡿⠷⠂⠘⠛⠛⢛⣷⡀⠀⢀⠀⢀⠀⠀⢀⡤⠶⠛⣛⡛⡓⠶⡄⠀⠀⠀⠉⠀⠀⠀⠀⠨⣿⣤⣴⣶⣿⣿⣯⠁⠀⣼⣷
⠀⣿⣿⣿⣯⣴⣶⠶⠄⠀⠀⣠⠞⠋⠑⠆⢠⡈⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸⣿⣟⠻⣿⣿⣷⣄⣴⣿⢷
⠀⣿⣿⣿⣿⡿⠁⢰⡀⢀⠾⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⡇⡋⠀⠀⠲⣿⣷⡌⠳⣿⣿⠻⣿⣿⣿⢷⠦
⠀⠀⠀⣹⡟⠁⠀⠘⣷⡄⢺⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠙⣻⣿⣿⣿⣟⣋⡀⠀⠀⢀⣨⠃⠀⠀⠀⣷⠙⢾⣷⣶⣾⣟⠁⢈⣿⠛⣧
⠀⠀⠠⠟⣿⣿⣤⠀⣸⣷⡘⠷⠀⠀⠀⠀⠀⠈⢡⡀⠀⠰⢿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠈⠀⠀⠀⠀⠐⢦⣤⣾⡿⠛⣿⡿⢀⢻⠙⠃
⠀⠀⠀⠈⠉⣻⣿⣿⠟⠉⣿⣧⡄⠀⠀⠀⠀⠀⠀⠈⠃⠠⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡟⢇⠳⣼⣿⡾
⠀⠀⠀⠀⢠⣿⣿⣁⠀⠀⠘⢙⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠸⢃⣤⡴⠖⠛⠁⠀⠀⢠⠀⠀⠀⣲⣴⣾⠿⠋⠁⠀⢀⣮⣿⡷
⠀⠀⠀⠀⠺⠉⢿⢿⣦⣦⣤⡿⠀⠙⣷⢷⣶⣤⣤⢠⣤⣄⠀⠛⢁⠀⠀⠀⠀⠀⠀⠀⣷⢦⣷⡟⠉⠀⢀⢠⣀⣤⣰⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⠛⣿⣴⣠⡀⠀⠁⠀⠀⠈⠻⠿⠿⢾⣿⠿⠃⠀⠀⠀⣹⡞⠛⠀⠀⢰⣧⣴⣿⢿⠿⠿⠳⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠛⠿⣻⠟⣿⡷⠀⠀⠀⠀⠀⢠⡗⣠⣀⣀⣤⣉⣀⣤⣤⣼⣿⠛⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢷⣷⣾⣿⣶⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠻⡿⠉⠿⠏⠘⠃⠘⠻⠏⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣃⣉⣏⣀⣏⣉⣯⣃⣭⣟⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⠉⣀⠀⠉⠐⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⢠⡙⣿⠁⣼⠟⣀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠉⠁⠃⠄⠹⠀⠋⢈⣷⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢈⣿⣷⠀⠰⢲⢳⠢⠀⢠⣿⢽⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⣿⡀⣤⢠⣇⢠⠀⢸⣿⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢧⣥⢟⡹⢦⣀⣸⣏⣷⡍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣽⠃⢲⣿⠿⠊⠑⣫⣾⣿⠇⠘⡆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⢘⡇⠀⠀⢠⣿⣿⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣾⣷⣆⣴⣿⣿⣿⠁⠀⠀⠀⣾⠁⢠⠀⢸⣄⣤⣤⠀⠀⠀⠻⠦⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⣰⣿⠀⣾⠀⢸⣿⣿⣿⣤⡀⠀⠀⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠄⠀⠀⠙⠻⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣾⡟⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣀⡀⠸⣧⣤⣀⠀⢀⣠⣤⣀⣠⣶⠃⠀⢰⣿⣿⣿⡿⠛⠛⠻⢟⡁⠙⠻⡷⣷⡀⠰⠁⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣠⡝⠁⠀⠀⠈⠛⠿⣿⣿⡿⠿⠟⠋⠁⢀⠀⠀⠛⠉⠀⠀⠀⠀⠀⣼⣿⡤⠔⣃⡼⠃⠀⠁⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡰⠋⠁⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣠⣤⠞⠋⠁⠀⠀⠀⠀⠀⠈⢌⡉⠟⠋⠀⢸⡋⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿
⠀⠀⠄⠒⠉⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒
⡤⢀⢀⡄⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⠀⠁
⠓⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢠⠀⡧

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⣭⣿⣻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⢻⠋⠉⠀⢮⣳⣞⡿⣻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠱⡀
⠀⠀⠀⠀⠀⠘⢄⡁⠀⠌⣹⣿⣾⣿⣿⣿⣿⣿⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠈⠃⣤⣿⣿⣿⣿⣿⣿⠋⠉⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⠞⠛⠲⣶⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣽⣷⣿⣽⣿⣿⣟⣻⣿⣷⣶⣦⡘⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⡟⣹⣿⣿⡿⠯⣅⡈⡛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡗⣆⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⢔⢶⡟⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⠀⠀⠀⣿⣻⣿⣿⡽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠉⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣉⣡⣵⣤⣦⣀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣆⠀⠈⡾⠻⠿⢿⣿⡯⠤⠵⠶⠖⠛⠋⠉⠀⠀⠀⠹⣿⣦⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠈⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣀⠀⢘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢹⢷⡎⠋⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⠀⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠉⡘⠀⢳⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢴⣆⣠⠟⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠠⠤⠃⠀⣸⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵⣆⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⢂⣄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⡠⡆⠀⢀⠛⠃⠀⠀⠀⠐⡀⠂⢄⠈⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠉⠀⣠⣤⣤⡄⠀⠀⠀⠡⠄⠤⡔⠀⠀⠀⣀⠹⢼⣦⡔⣤⡌⠳⣌⡇⠈⠁⠒⢼⣆⡿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣆⢰⣾⣿⣿⣿⣷⣄⡀⢀⠀⠠⠀⠀⠀⠀⠀⠙⡀⠶⠦⠿⣾⣿⠆⠈⠻⡄⠀⠛⠿⣿⡇⠈⢣⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠲⢞⣫⠉⠃⠤⣄⠀⢰⣿⠟⠁⠈⢳⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⡀⢈⠙⣿⣿⡄⢣⡀⠀⣿⡇⡀⠀⢅
⠀⠀⠀⠀⠀⠀⣀⣴⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠉⠓⠀⢀⠀⠀⢅⠠⠦⢀⡭⠙⠒⠲⢼⣿⣇⠀⣿⡀⣘⣧⡅⢠⡏
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠒⠶⢄⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡷⠿⣧⠀⢿⡆⣸⣇⡠
⠀⠀⠀⠠⣼⣿⣿⣿⡿⠛⡻⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠚⠶⠒⠲⢦⣄⣀⣀⡀⣠⣴⢶⡞⢻⣿⣿⠄⠈⣷⣾⣿⣿⡟⣀
⠀⠀⠀⠀⣻⣿⠟⠋⠀⠀⠉⠙⢻⣷⡆⠈⠙⣿⣿⢿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡶⣆⢀⣠⠜⠉⣹⡿⠛⠛⠻⠿⠷⣾⣿⣿⡀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣾⠃⠀⣀⡀⠀⠀⠀⣧⣿⣿⣦⠀⣷⣿⠿⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⣔⠒⣚⡙⢀⠀⢀⣄⠀⠀⠀⣿⢿⣷⠈⢸⣿⡿⠁
⠀⠀⠀⠘⠷⠶⠛⣷⣯⣴⣿⣿⣿⣿⡿⠟⠠⠛⢟⡄⠁⢹⣻⣿⠛⢿⡿⠿⢿⠿⠟⠛⠛⠻⠊⠒⠾⠓⠐⠂⠒⢿⣋⠘⢷⣿⡾⢿⠀⡷⠈⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣦⣤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠃⠒⠂⠀⠀⠀⣸⣽⣷⣿⣟⡇⠀⢿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⡀⢙⡹⠟⠏⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢰⣴⣶⣶⣶⣾⣿⣿⡿⠋⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⠿⢿⡷⠶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣦⣤⣤⣤⣶⣬⣾⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⠟⠉⣉⡥⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠤⣤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣽⠀⠀⢠⠄⠀⠘⠇⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡝⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠀⠀⠀⠀⠀⠠⣇⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠓⠀⠀⠄⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡗⠲⠛⠦⡀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠙⡄⠀⠘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠤⠶⢤⡀⠀⢢⠀⠀⠀⡔⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⠀⠀⠀⠀⠹⡆⠈⡄⠀⠀⡇⠀⣠⠀⠸⡇
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⠀⠀⣧⠞⠹⡄⠀⡇
⠀⠀⠀⠀⢸⡷⡄⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠀⠀⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠰⣧⠙⢦⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡠⠚⡇⠀⡇⠀⠀⢇⠀⠇
⠀⠀⠀⠀⠀⠈⣷⣄⠈⠓⠦⢄⣸⣄⣀⠀⠀⠀⢀⡤⠚⢁⣠⣖⠉⠉⠙⡇⠀⢧⠀⠀⠈⢣⠘⠂
⠀⠀⠀⠀⠀⠀⠈⠛⠢⠤⠄⠠⠤⠾⣅⣀⣀⣀⣈⣉⣉⡀⣠⡠⠏⠉⠀⠙⢄⠀⡁⣠⠀⠀⠁⠠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣉⣤⠒⠒⢲⠒⠠⢌⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡰⠋⠐⣎⢦⠀⠘⡀⠀⣠⠜⣦⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢠⠃⣼⣁⠀⡀⠈⣆⠻⠀⡦⢊⠴⠊⠀⠱⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⠂⠠⢤⣄⡉⠀⡀⠀⡋⠒⠒⠀⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣁⠀⠀⣠⣞⡵⠞⣳⡌⢫⠉⠁⠀⢐⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠻⠙⢫⠋⠁⠈⠀⡇⢿⠉⢦⡱⡀⢀⠎⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠉⠀⡀⠀⢀⡸⠀⢀⡱⠞⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠈⠈⣿⡉⢤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⠀⠀⠀⢀⣀⡀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠁⠀⠉⠉⠉⠁⠀⡀⠄⠂⠙⡗⠲⣤⣀⣀⣀⣤⠔⠚⠉⠀⠀⠀⠀⠀⠙⢆⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡄⠀⠀⠀⢀⠔⠈⠁⠀⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⠀⡈⠀⠠⠂⠁⠑⢄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠀⠀⣇⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡔⢃⠀⠀⣀⣀⣀⣀⠀⢦⠀⠀⠀⠀⢸⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠇⠀⠀⠀⠈⢠⡡⣀⠤⠒⠉⠀⡀⠀⠀⡏⠉⠉⠉⠀⠀⢱⠀⠀⠀⠿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⢈⠀⠀⢀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⡠⠉⠀⠉⠓⠴⢦⡂⠀⠀⠀⠀⠀⡕⠸⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⡄⠀⠀⠀⠀⡰⠁⠀⢠⠧⢄⡀⠀⢩⠁⠒⠒⠂⠐⠈⠁⠀⠀⡶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣁⠀⠰⠃⠀⠀⠁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡀⠀⠀⠀⠈⠢⢀⡀⠀⢀⠄⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣄⠙⠶⢤⣀⣀⣀⣀⡀⢀⣀⣀⡠⠴⠚⠋⣠⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠙⠲⠤⣤⣀⣀⣈⣉⣀⣀⣤⠤⠖⠒⠉⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠊⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⢀⡀⠿⠇⣀⡀⠛⠃⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷
⠀⠹⡿⠻⣿⣿⣿⣿⣷⣶⣿⣿⣷⣿⡁⠀⠀⠀⠀⠀⠀⠸⠇⠀⠈⢿⠟⠀⠀⠀⠀⠀⠀⠙⠻⠷⢦⣄⣀⣀⣀⣀⣠⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⠆⢀⡔⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠻⣿⡟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⡿⢹⣿⠀⠀⠙⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠡⣾⠟⠁⠀⠀⠈⣿⠻⣿
⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠼⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠿⠄⠀⠀⠀⠀⣿⡀⣿⡀
⠀⠀⠀⠀⠀⠛⠃⠸⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠹⠸⡈⠠⠹⢸⢘⠸⠰⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⣼⠇⠀⠀⢠⣾⡿⠿⢿⠿⠿⠿⠶⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠻⠼⡁
⠀⠀⠀⠀⠀⠘⡂⢀⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠻⠤⠄⢶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡨⠆
⠀⠀⠀⡀⠀⣠⠂⠀⠶⢷⡝⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣀⠴⠶⢤
⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣄⣤⣶
⠀⠀⠀⠶⠠⣰⠆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡁⠀⢄
⠀⠀⠀⠀⠔⠁⠀⠒⣀⠀⠶⣀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠁⢀
⠀⠐⠧⠄⡤⠀⠀⢀⠙⣀⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⢀⠤⠚⠐⠾
⠀⠀⠀⠀⠸⠇⠂⠉⡀⢀⡉⠹⠄⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠪⣭⣋⠠⣤⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣶⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠂⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠴⠀⢀⣠⣴⣯⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣭⣨⣸⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣼⣿⠿⠻⠧⢘⣿⡟⣹⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠘⠀⠀⠛⠀⠀⠘⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⣤⣀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠘⠿⡟⢿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣾⡿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⢈⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⢏⣿⡿⠤⢄⣠⠶⠊⠉⠀⠘⢿⣿⣿⣿⣷⣬⡛⣾⣿⣿⣿⣷⣄
⠀⢰⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠘⣇⠀⠀⠀⠀⢀⣠⣤⣴⣆⢿⣾⣷⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣤⣤⣄
⠀⠰⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣥⣶⡆⣼⣿⣿⣿⡟⠻⠿⠟⠿⢿⣾⣿⣿⠿⢣⣿⠿⠿⠟⠛⠿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠪⠿⠛⠋⠁⠈⠀⠀⠀⠰⠿⠟⠛⠉⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⣠⣤⡄⣠⣄⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣶⣿⣿⣷⣤⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡟⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤⠻⠿⠿⠿⢻⣿⣍⣿⣿⣿⢿⠿⠟⠋⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⠉⢹⣿⣻⣟⣿⣿⣿⣿⣿⣟⣟⣿⢟⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⣶⣶⣾⣿⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⡿⠛⠟⠋⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣶⣶⣶⣦⢹⣿⣿⣿⣿⠿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣆⠀⠘⣿⣿⣿⠏⣸⣿⡿⠋⠀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣽⣤⣴⣿⠟⠁⣀⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⢹⣮⣉⣠⣾⠂⠀⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣹⡇⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀⢠⣿⡇⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⡀⠀⠀⠀⢀⣼⣿⠃⠙⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠰⣿⣄⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠟⠋⠙⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠋⠱⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢀⢀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠘⠀⠉⠙⠉⢻⡄⠀⠷⠀⠀⠑⠀⠀⠐⠀⠀⠀⠁⠀⠈⠀⠉⠉⠁⣶⣦⣤⣤⣴⣶⣤⣤⣤⣤⣤⣶⣤⣶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠙⢷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⣷⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠁⢠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⡟⣿⣿⣿⣿⡄⢻⣿⠻⣿⣿⣿⣿⣯⠀⠀⠀⠀⣀⡄⠀⣾⠇⠀⠀⠀⢠⡀⠀⠀⣼⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⢿⣿⣅⣈⣉⣉⣿⣧⠸⣿⠰⣦⣍⡃⢻⣿⢀⣼⠴⠚⣉⡇⢀⡟⠀⠲⠶⠶⠿⠃⠀⣴⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣯⡉⠙⠿⣿⣿⠀⢻⣧⡾⢻⣿⣆⢇⡼⠁⠀⣄⠙⠀⣼⡇⠀⢀⣤⣶⡶⠀⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣧⣿⣷⣿⡿⢃⣴⠟⣱⡆⢿⢻⡄⠃⣆⢼⠉⢦⡈⠻⣇⠀⠈⣀⠉⠀⠀⠈⢻⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣟⠙⣿⣁⣈⣭⣴⣯⢰⣾⣿⠏⢀⠈⣿⢸⡿⣿⡀⠈⢙⡷⠘⠛⠾⠿⠆⢰⡦⢀⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣶⡿⠿⢭⣍⡉⠙⠦⠀⠹⠦⣾⡇⣟⢸⠀⢙⣡⣾⣟⣡⣶⠶⠛⣂⣀⡉⠙⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠺⢿⣯⣥⣤⡐⢾⣿⣷⡄⢠⡀⢿⣾⣿⠟⠓⣬⡀⠀⠉⣼⠟⣿⠋⠀⠀⣽⠟⠛⠓⠀⣈⣿⡇
⣿⣿⣿⣿⣿⣿⣿⠏⣴⣶⣿⡛⠛⠋⠠⠞⢋⣿⣿⠄⣿⣼⣿⠋⣴⡗⠈⢳⡄⠀⠃⢸⡇⠀⠰⣤⣙⣷⣤⣤⠄⠈⠉⢻⡄
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣭⣉⣁⠐⣾⣯⠉⠛⠀⣿⣿⣿⡜⠁⣄⢻⣶⠃⠀⠀⢸⣧⣴⡖⠈⣹⣿⠶⠖⠒⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⢠⣦⠔⣲⠿⠿⣶⣶⢶⣌⠻⣿⣷⡸⡯⢀⠏⠀⢀⡴⠋⡉⠉⢉⣀⡈⢭⣍⠙⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⣁⠈⠁⠶⢿⣿⡄⠯⡹⠳⣼⣿⠇⡟⣸⡀⠀⢋⣄⠶⣹⠇⠀⣈⣻⣿⡿⢷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣼⣿⣿⣿⠟⠋⠹⢿⣶⣦⣴⠻⣿⣴⣟⠈⠃⢀⡌⠛⠉⠁⣀⣶⣤⡀⠀⠀⠀⠻⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣀⡀⠛⢳⢈⡽⠟⣀⢲⡏⣤⣾⠿⠧⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣱⡇⢸⣿⡇⣔⢻⠁⠀⢿⠙⠇⠀⠀⠀⠀⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠙⢿⣿⣿⣿⣿⠇⣿⣿⣷⡀⠏⠀⠀⢸⡀⠀⠀⠀⠀⣴⣿⡶⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠓⠘⢛⣿⡿⠁⣸⣿⣿⣿⣿⠀⠀⠀⠀⢿⣆⠀⠠⣤⣯⣥⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⠀⢠⣿⣿⣿⣿⡷⠀⠀⠀⠀⠘⣿⡇⠀⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣧⢸⣿⡿⠛⠋⢑⣶⣤⣄⠀⠀⡿⠀⡀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡉⠸⣿⣧⠀⠀⢸⣿⣿⡟⠀⢀⣷⠞⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣦⣀⣸⠿⠟⠁⢀⠘⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣍⣉⢃⡶⠶⠿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⠲⠖⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣶⣶⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣎⠁⠈⠋⢹⠟⢘⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⢸⣏⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢺⣿⡿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣼⣿⢹⠿⢿⣿⠏⠀⠀⠀⠀⢠⣄⣀⣀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣏⠁⠀⠀⠁⠀⠀⠀⠀⢢⣶⣿⣿⣿⡇⠀⠻⢿⠿⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠿⠁⠀⠀⠀⢀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠿⣅⠀⠀⠀⠐⠂⠺⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⢀⣉⠁⣀⣤⡗⠀⠀⠀⠀⢀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⢐⣰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣟⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡙⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠻⠛⢛⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣬⣉⠙⢀⡄⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡧⠥⡬⠀⠥⠬⠼⢿⣄⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⠊⠀⠰⠀⠀⠀⠈⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢰⠞⠉⠉⠉⢳⡀⠀⠀⢀⡞⣁⣀⣀⡠⠤⠤⠖⠒⠀⠒⠢⠐⠄⠳⢤⣙⣧
⠀⡴⠖⠛⠂⠀⠀⠀⣸⡃⠀⣴⠛⠏⠠⠀⠀⡆⠀⠈⠀⠀⢘⠀⢰⠀⢠⠀⠘⡀⠉⣧
⢸⡇⠀⠀⠀⠈⢢⠀⠈⢿⡀⡏⢠⠀⢈⠀⠀⠁⠀⠀⠂⠀⠈⠀⠀⡄⠀⠀⠀⡇⠘⣸
⠀⣿⠂⠀⠀⡀⠈⠀⠀⣸⡿⠛⠀⢤⣚⣩⣭⣩⣒⡉⠉⠀⠴⠖⠒⢆⣀⡐⣖⣳⠂⠉⢳⡄
⢀⣸⡇⠀⠀⠁⠀⣤⠞⢹⠃⠀⠀⢰⠀⢀⠊⣴⡿⢷⠀⠀⠀⡴⢷⣦⠑⡄⠈⡇⠀⠀⠈⣷
⡟⠀⠀⠀⣆⠀⠀⡹⠶⠛⠠⡀⢀⡸⢠⣬⣄⣛⣿⠞⣠⣤⣄⢻⣿⠟⡠⣁⢀⡃⠀⠀⠀⣿
⠻⢤⣠⣤⠁⣀⢀⣠⡶⠓⠲⣦⣠⣾⣻⠟⠟⠩⢋⠕⠛⣏⠙⢌⠫⠑⠟⢿⢙⣷⣤⡤⠞⠁
⠀⠀⠀⠈⠉⠉⠉⠁⢀⣴⠞⠋⠉⠙⡇⠀⠀⠀⠀⠀⠚⡍⠂⠀⠀⠀⠀⠀⡋⠉⠉⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠤⠔⠊⠘⠀⠀⠀⠀⠀⠀⠜⠙⢆⠀⠀⠀⠀⠀⡈⠉⠑⠤⢤⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣀⣀⡀⢳⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⣈⣢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡸⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠄⠊⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢸⠒⠂⢲⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠤⢽⡇⠀⠐⠒⠀⠤⢼⠀⠀⠀⠀⠀⠀⡸⠄⠒⠊⣿⣤⡴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠁⠀⠐⠒⠂⢎⣰⣣⣆⣴⣰⣠⠗⠒⠈⠉⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⡽⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣛⣦⣤⣀⣀⣀⣤⣐⣿⣾⣓⣠⣄⣀⣀⣠⣴⣞⣯⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⠉⠀⠀⠀⠈⠀⣼⣿⡀⠈⠀⠀⠀⠈⠉⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿⢷⡳⢄⡀⠀⠀⠀⠀⠀⠀⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡄⠀⢠⡔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⢀⡀⣀⣠⣤⣤⠖⠉⣆⠸⠆⠁⠀⠀⠁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠛⡛⠉⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⠌⠉⠉⢽⡄⠀⠀⠀⠏⢀⡏⢠⠈⡁⣀⡀⠀⠏⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⡐⠁⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣡⡀⠀⠀⠈⢣⠀⠸⡇⠋⠉⠈⠓⠂⠀⠋⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠃⢸⣤⠀⠀⠀⠀⠀⠀⠄⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡦⠀⠀⠀⠀⢠⡽⣮⣶⣦⡀⠀⡀⣰⡛
⠀⠀⠀⠀⠀⠀⠀⡾⠰⡀⢺⣯⣰⡄⠀⠀⠀⠀⠀⠢⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠹⣎⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⢀⡾⠓⡄⠀⣼⣿⡇⢣⢀⠀⠀⠰⠀⠀⢃⠀⠏⠀⠀⠀⠀⠠⠀⠔⠁⡌⠀⠀⠀⠀⠀⣾⣝⢣⣉⠜⠂
⠀⠀⠀⠀⢀⣾⠇⠀⠁⢠⣿⣿⣿⣆⡄⡄⠀⠀⠁⠀⠶⣬⣀⠀⠀⠀⠀⠀⠀⠠⣾⠇⠀⠀⠀⢀⣶⣿⠽⠋⠁
⠀⠀⠀⠀⣼⠃⢀⢠⣤⣿⣿⣿⣿⣿⣵⡐⢀⠀⠀⠀⠀⠀⠈⠁⠓⠂⠄⠶⠠⠂⠛⢆⠀⠀⠀⢸⣿⣧
⠀⠀⠀⢰⣿⣚⡷⠞⣩⣾⣿⡻⣻⡾⠋⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠈⠉⠀⢠⢶⣿⠟⡰⠛⠁⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠿⠁⠁
⠀⠀⠀⠀⠀⠀⢸⡟⣵⠊⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⡀⠃
⠀⠀⠀⢀⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣥⡀⠈
⠀⠀⠀⠀⠀⠀⠲⡽⣄⠈⡌⠆⠀⠀⠀⠠⡙⡄⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠐⠒⠐⠒⠠⣤⣀⢡⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠀⠀⡉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢶⡀⢀⡼⣿⣬⣀⠀⣤⣈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠘⣷⡟⠸⠋⢨⠉⠿⠈⠉⠙⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢻⣤⣾⢋⡀⢡⡆⠁⠀⢀⠈⢀⡔⣰⠃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠊⠂⣬⠟⡇⢠⢊⠉⠀⡀⠀⢡⣭⡎⢳⣟⠀⠀⢷⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣤⠞⢿⣏⠀⢹⣠⣖⡀⡢⢸⡼⢏⣿⡇⠾⣧⢤⣤⣼⠷⣧
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡶⣾⢹⡆⣸⣇⣀⣸⡇⢻⣷⢃⣼⠁⣾⣿⣷⡶⠟⠻⠉⠛⢶⣏⣷⣰⡆
⠀⠀⠀⠀⠀⡰⠿⢸⢏⣤⠿⠿⠛⠿⠾⢷⣿⣷⡿⠙⣦⢿⣶⡿⠋⠁⠀⠠⠖⠃⠀⢀⠹⣮⣟⢳⡄
⠀⠀⢀⣠⣼⣅⣠⡾⠛⠰⠋⠀⠠⠄⠈⠑⠂⢄⠙⠻⣿⣯⣉⣀⠁⠘⠀⠀⠤⣄⡀⠀⠁⠬⠻⢦⣷⣄⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠒⠀⠁⠀⠀⠀⠂⠔⠀⠀⠀⠀⠀⠀⠙⠉⠀⠈⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡎⢇⠀⠀⢒⠄
⠀⠀⠀⡠⠔⠒⠒⢢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⡀⠀⠀⢀⠜⠀⠈⢆⠀⠀⠀⣀⠤⣀
⠀⠀⠀⡱⠀⠀⠀⠘⢲⠶⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢊⠀⠐⢳⠂⠁⠐⠲⡛⠀⠰⠁⠀⠈
⠀⠀⠈⢳⠀⠀⠀⠀⠀⡆⢣⣴⠃⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠐⣷⣖⡁⠀⠀⠀⠀⣑⣤⠀⠁⠒⠈
⠀⢠⠤⠶⠀⠈⠁⠈⠄⠉⠁⠈⡆⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡡⠤⠀⠄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⢇⠀⢀⡁⠀⠀⠀⠐⠀⠀⢐⡍⡂⠀⠐⠀⣊⠀⠀⠀⠀⠀⢊⠤⠀⠀⠀⠀⢈⠽⠋⠙⠀⠂⠠⠐⠀⠛⢍
⠀⢰⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠠⠀⢌⢑⡶⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠄⠀⠠⠤⠤⢤⠤⠀⠀⠤⠵⠂
⢹⠀⠀⠒⠒⠒⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠤⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠚⠀⠀⠀⡇⠀⡀⢀
⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣀⣀⠤⠀⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠁
⠀⢧⣀⠄⠀⠀⢣⣀⠄⠀⠀⠀⠳⠤⠂⠘⠦⠄⠀⠘⠦⠔⠀⠈⠳⠤⠤⠂⠈⠳⠤⠤⠔⠊⠀⠳⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⡄⠀⡀⢀⣀⡀⣀⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⣿⡟⠛⠋⠘⠻⠿⢟⠿⣾⣿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢧⡟⠁⣤⣾⣧⡀⠀⢱⣌⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣀⣞⣟⡎⣟⠟⢛⠇⡴⢾⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⠻⡟⠍⢛⡛⢻⠛⡼⠛⠽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⢿⠀⠀⠀⠙⠁⡀⠀⠛⠋⠀⠋⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠿⣦⡀⠀⠠⣶⣶⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣧⣸⣺⣄⠑⡙⠠⣿⡯⠀⣡⠖⣳⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⣿⠃⠈⠲⠉⢻⡻⠖⠋⡩⣼⢣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠋⠛⠗⣮⠁⢀⠙⣿⠛⠀⢤⠴⣾⢡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠃⠃⠈⠀⠀⠀⠚⣠⡞⠩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡈⠙⢷⡀⡀⠰⢺⣐⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⠀⠀⠀⠀⠀⣰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠈⡇⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢁⣾⠀⢱⣤⣤⣿⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⡇⠀⣿⣿⣿⣿⡻⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡇⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣆⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠉⣭⣽⣆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⢹⡿⠃⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢻⣿⣧⡀⠠⣄⡀⠀⠀⠀⠀⢹⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⢿⣿⣶⣤⣭⣷⣶⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣯⣍⠉⠛⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⠀⠀⠀⠉⠛⠿⠿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠙⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡏⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣴⠞⠋⠁⠸⠇⠀⠀⠀⠀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⢀⣤⠶⠦⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄
⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠙⣳⣤⣄⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣾⠃
⠀⠀⠈⠉⠉⠡⣤⣶⠞⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⠄⣼⠟⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⠀⢀⣾⠃⠀⠈⠻⠶⡤⠠⠴⣶⠤⠞⠁⠀⠀⠀⠀⢠⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠶⠛⠋⢹⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⢀⣴⡟⠁⠀⠀⠀⠈⠙⢷⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢹⡇⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣤⣦⡼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠹⣄⠀⠀⠀⠛⢦⣤⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⠀⢀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣦⣹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠙⠶⢶⣄⣀⠀⠀⠀⠀⣀⡶⠛⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠉⠙⠷⠲⢦⡼⢧⡀⠦⢄⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⡀⠀⠀⠀⠔⠲⡤⢄⢀⠀⠀⢀⣈⢥⠀⢈⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠈⠀⠀⢀⠉⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢠⠒⠃⠀⠀⢠⠀⠀⠀⠀⢀⣄⣼⠃⠰⠚⠁⠁⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⣀⡴⢿⣰⠀⢀⣘⣿⣄⣠⣄⠀⣀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣴⠗⠚⡅⠐⠂⢹⡆⣸⠋⠁⠀⠀⣬⡟⠉⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠀⠀⠀⠓⠋⠀⠀⢠⠄⠀⠀⠀⢻⣧⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⠀⠀⠀⠀⠀⠫⠇⠀⠀⠀⠀⠀⠀⡀⢺⡧⠤⢤⡈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣸⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⡆⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⣿⡗⠒⠚⢁⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠒⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡦⣿⡏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣑⣑⣚⣘⣃⣄⣤⣤⣤⠤⠤⠬⠶⠮⢕⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣌⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢟⣥⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢸⣷⠄⢦⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⡔⠠⣿⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣗⠀⠻⣦⡙⠷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⣴⠏⠀⣺⣿⠂⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠦⠀⠙⣿⣦⡈⠻⣦⡶⣴⣴⢶⣴⠟⢁⣴⣿⠋⠀⠴⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⡍⠀⠀⠘⣿⣷⣴⠂⠀⠀⠀⠀⠐⣦⣾⣿⠁⠀⠀⢩⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣗⡀⠀⢀⣼⠟⠁⠀⡐⠀⠀⢄⠀⠘⠻⣇⡀⠀⢀⣻⣿⣇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⣿⠛⠁⠀⠉⠀⠀⠀⣰⠇⠀⠀⠸⣄⠀⠀⠀⠉⠀⠈⠛⣿⣿⡄⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢀⣀⣀⣀⣈⠳⣄⡀⢰⠀⠀⡄⣀⣠⢞⣁⣀⣀⣀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣥⠀⠀⠀⠀⠀⠀⠉⠉⢹⡿⣿⣌⢱⡏⠀⠀⢻⡌⣡⣿⢿⡏⠉⠉⠀⠀⠀⠀⠀⢀⣬⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣥⠄⠀⠀⢽⡆⠀⠀⠀⠀⠓⠒⠻⠀⠀⠀⠀⠀⠐⠟⠒⠋⠀⠀⠀⠀⣸⠇⠀⠀⠠⣬⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣁⠀⣠⣄⡀⢻⣄⠀⠘⠶⣄⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⣠⠶⠃⠀⣰⡟⢀⣠⡀⠀⣈⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣥⠖⠀⠈⠛⢦⠻⠦⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠴⠧⡴⠋⠁⠀⢲⣬⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣤⣤⣤⣀⠀⠐⣶⣤⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢻⡄⠀⢀⣤⡶⠂⠀⣀⣤⣤⣤⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡟⠓⠀⠈⢿⣷⡀⢺⠁⠀⠀⠀⠀⠀⠀⠘⡇⢠⣿⡿⠁⠀⠛⢻⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣯⣤⡀⠈⣿⣧⡀⠀⣠⣤⣶⣦⣤⣄⠀⢀⣾⡿⠁⢠⣤⣽⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣶⣦⣼⣏⢳⣄⠹⣭⡍⢩⣭⠏⣠⡞⣹⣧⣶⣾⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠽⣿⣿⣆⠻⣷⣤⣭⣭⣴⣾⠏⣰⣿⣿⠯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣜⠛⠛⣡⠋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣉⣩⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢀⣤⣴⣶⣿⣿⣧⣼⣿⣿⣿⣿⣿⣻⣇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢟⣽⣿⣿⡄
⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⡟⣿⣿⢟⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢋⣴⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⣿⡟⠹⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢊⣿⣇⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⠾⠿⠟⠸⣫⣯⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠃⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⠩⠤⠰⢒⣲⣲⣟⣉⣡⣆⣖⣶⡶⡤⢄⣉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⣿⡷⠴⠛⠻⠿⠿⢿⢟⢻⢛⡛⠛⠃⢠⣤⣾⠃⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠃⠂⠈⠑⢾⣿⢿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣶⡤⠊⠀⡠⣿⡟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠁⠕⠶⣤⣀⡀⠙⠻⣿⣿⣿⣹⣿⣿⣿⣿⠿⠋⠀⣀⣬⣤⢟⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⡿⣿⣶⣤⣀⡉⠛⢷⣆⡈⠛⢿⣿⣽⡿⠛⢡⠴⠶⠛⢉⣩⣴⠞⠋⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⣴⣬⡿⠀⠀⠉⠛⠛⠿⢷⣬⣥⡶⢤⣽⢫⣴⢶⣀⣤⡴⠶⠛⠉⠀⠀⠈⠁⠈⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣞⣱⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⣻⡷⠊⠋⠉⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠠⠟⠻⢏⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⢎⢽⡄
⠀⠀⠀⠀⠀⠀⣗⠰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠻⡀
⠀⠀⠀⠀⠀⢸⣶⠁⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡰⠀⠀⠈⠥⠀⣧
⠀⠀⠀⠀⠀⣿⠘⠄⠄⠈⠳⢘⠲⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⠋⢻⡤⠂⠐⠠⢰⣽
⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠐⢮⢀⣦⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⠞⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⡿⠃⠁⠀⠀⠀⠀⣴⣆⣿⡜⠇⢠⡐⡠⣠⠀⠘⢁⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢻⣾⡿⠄⡖⡶⠆⠀⠀⠐⣿
⠀⠀⠀⠀⠀⣯⡆⠀⠀⠀⠀⠚⠟⢻⡿⣟⣿⣒⣛⣛⣈⣀⢀⠏⢐⢄⡟⠁⡽⠋⠉⠱⣖⠶⠺⡗⡻⢿⡇⡇⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⢇⡗⠀⠐⠠⠶⢻⣿⡝⠫⠍⠀⢹⠟⠛⠇⡮⠀⠴⠮⠒⠀⠀⠀⠀⠈⠁⠀⠀⠫⠞⢹⡗⠦⠄⠀⠀⠀⠀⢰⡾
⠀⠀⠀⠀⠀⢸⠜⠉⠀⠀⠀⠀⠸⠋⠙⠀⠁⠀⠀⠀⠀⠀⢳⣦⣾⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠐⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣥⣽⢿⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢺
⠀⠀⠀⠀⠀⠀⢻⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡑⢀⡻⣿⠛⣛⠩⣶⢤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠆
⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⡄⡀⠀⠀⡀⠄⠀⢨⡴⣟⣫⣻⡿⡖⠱⠘⠈⠁⠹⠃⢽⡠⣢⣠⣔⠀⢀⡀⠀⠀⠀⠀⣧⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣀⡲⡶⣿⡳⠛⠟⡿⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢧⡙⣲⠤⢆⣠⣤⣶⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢩⠏⠁⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠉⠉⢡⢁⣞⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠋⠄⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠈⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠈⠀⠚⠛⠛⠒⠒⠒⠠⠒⠚⠟⠉⠉⠛⠊⠉⠁⠀⠀⠀⠀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠶⠄⠄⠖⢦⠐⢶⡶⠶⣶⣠⢶⣶⣶⡶⠲⠹⠟⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⣿⠆⠀⠀⠀⣠⣴⣾⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡏⣇⠀⣸⣶⣝⣠⢴⣾⡿⠛⠁⠀⠀⠀⠀⠀⣀⢠⠖⠈⠁⠀⠀⠲⣻⡶⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⡰⢧⠀⢠⡀⠀⣄
⠀⠀⠀⡀⠀⠀⠀⣦⡀⣀⠀⢞⠛⠋⡼⢡⠿⣞⣏⠌⢉⡅⠀⠀⠀⢀⣤⠆⠉⠁⠂⠀⢸⡧⠀⠀⣿⢉⣦⡄⠀⠀⠰⢿⠆⠀⠀⠀⣝⡄⠶⣷⡀⡶⣷⢴⣿
⢠⣦⣸⣷⠀⣶⣜⣍⣁⣿⣶⣯⠼⣷⢶⢿⡀⢈⠛⠁⠈⠀⠠⠔⠪⢿⠇⠀⠀⠀⠀⠀⣻⡟⠄⠘⣻⣾⢧⣀⠀⠀⠶⢻⣼⢠⡄⢸⣏⣹⢼⡀⢻⢧⣼⣌⣿
⢸⣿⣵⢾⣿⣯⠼⡯⣤⢿⣃⡞⠀⣿⠂⡸⣧⣰⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢤⡇⠿⠠⠶⣿⣌⡟⠀⠰⡶⣿⣄⠚⠄⠚⣿⣥⡾⠷⠾⣧⣏⢸⣹
⢸⣿⢿⡤⣿⣁⡠⢆⣦⣤⣿⣧⣾⣿⡿⢀⣾⣷⡀⢦⣠⣀⡆⠀⡀⡀⠀⠀⠀⠀⠐⣸⠟⣿⢼⣤⠚⢻⠉⠉⠀⠠⠖⠻⠎⢃⡄⠘⠻⣯⡴⣦⡀⢹⣽⢻⣿
⢸⣷⣿⣿⡀⣠⠀⣈⣧⣀⠙⣿⣿⣿⣽⣿⡏⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⠶⣾⣶⣋⢼⡴⢿⠶⣴⣦⣼⣤⣤⢺⣧⣤⡖⣲⠃⠑⣊⠻⣿⣾⣿⣿⣿⣷⣼⣿
⢸⣿⣿⡿⠉⢉⡶⠏⠈⢻⡟⢻⣿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢷⣷⣯⣿⣿⣿⡵⢚⣇⢘⠧⣜⣦⣿⡿⡄⣩⡐⢿⣋⠉⡇⢸⡅⢙⣻⣿⣿⣿⣿⣿⣿⣿
⢸⡿⣿⡿⠑⢺⡀⠈⡧⣀⣷⡖⠟⠘⠁⠹⡇⠁⠈⠋⠛⠁⠀⠀⠀⠉⠙⠛⢻⡡⠒⠻⠋⠀⠴⠗⠀⣿⠁⢯⠡⠅⠐⠵⡎⢁⣏⠙⠦⢭⢹⠟⠛⠉⠀⠙⠻
⠀⠀⡈⢛⠚⠉⡉⢁⣄⠀⠈⠿⠒⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠘⠃⠀⠚⠂⠉⠁⠀⠀⠀⠐⠈⠘⠃⠋⠸⠀⠆⠀⠦⠴
⠀⠀⠉⠉⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢷⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣟⣘⡾⠾⣼⣼⣰⢢⢄⠀⠀⠀⠀⠀⠈⡈⠁⠀⠄⠀⠠⠀⠁⠀⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⢀⠈⠻⡇⢠⣴⠀⠈⠉⠛⠺⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠷⠶⢤⣄⣑⡆⠙⠂⠕⠚⣣⡰⠟⣠⠋⠀⠀⠀⠀⠰⠁⠀⠄⠀⠀⡀⡐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠉⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠐⢠⡄⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢸⠃⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠘⠆
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠓⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡐⠒⠅⠀⠀⡒⠲⡁⠈⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠦⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠒⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡤⢀⠴⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡾⠛⠉⠠⠤⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠳⣤⣤⣤⡤⠴⠚⢁
⠀⠀⠀⢠⠁⠀⠈⠁⠀⠀⢀⣀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠟⠛⠀⠑⠒⠒⠒⠛⠋⠉⡠⣄
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠒⠚⠉⠁⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡤⠶⠶⠖⠒⠒⠒⠒⠶⠤⢬⣽⠓⠦⢤⣤⣀⣀⣀⣀⣀⣤⠴⠶⠛⡏
⠀⠀⠀⢰⠀⠀⠀⠀⠈⠁⠀⣤⠀⠹⠓⠒⠶⠦⠤⠤⠤⠤⠶⠒⠚⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢠⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠶⠀⠀⠀⠀⠿⠀⠀⠀⠘⠃⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠰⠆⠀⠠⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠛⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣟⣻⣿⣛⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠄⠀⣀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠁⠀⠀⠐⠉⠉⠀⠀⠈⠁⠀⠀⠐⠀⠒⠒⠂⠶⡶⢄⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢀⣿⡏⠠⠂⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀
⠀⠀⠀⠀⡀⢀⠀⠀⠀⢰⡆⠀⠀⣤⠏⡤⠀⠀⠀⠐⠂⡰⠦⠀⠀⠀⠄⠂⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⠛⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄⢀⣴⣏⣜⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢳⢦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣡⡄⠀⠀⣀⣤⣔⢄⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡆⢿⠘⢠⠁⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⣼⣟⣵⠶⠓⢠⣿⣿⣧⣿⡌⠹⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⢷⣶⡀⠀⠈⠛⢾⡇⠀⡇⠀⠀⠀⢉⠀⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠉⣿⣿⡿⣀⠀⠀⠑⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠺⠻⣟⡽⠳⠀⣸⠸⣿⠁⠀⠀⠀⠀⠀⠈⢸⠃
⠀⠀⠀⠀⠰⡟⡀⠀⠀⠀⡟⢰⣿⣿⠀⠈⠹⣿⣶⠀⠀⠀⠀⢀⣤⡄⠠⠀⡀⣀⠀⠀⠀⠣⡀⠀⢀⣤⠀⠘⡓⢿⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠈⠻⣆⠀⢀⠁⣾⠏⡿⠀⠀⣀⢹⣿⡀⠀⠀⣰⡿⣋⡀⠀⠌⠁⠈⠻⣄⠀⠀⠐⣶⣿⡏⠀⠀⣿⣿⢸⣇⠀⠀⠀⢰⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢇⡜⢴⣿⢸⡇⠀⠀⠛⡿⡭⠁⠀⢠⣿⣶⣿⣿⠁⡀⢺⣿⣷⣼⡄⠀⠀⠻⣿⠀⠀⠀⣽⣿⡘⢿⡀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣼⡇⣸⠗⠋⠁⠈⠀⠃⠀⠀⠀⠑⣧⡈⢡⣼⣗⣠⠉⣻⠿⠇⠀⠀⠀⠉⠲⣀⢀⡿⣹⣇⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⢃⣿⢀⡴⣶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢠⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⡿⣿⠐⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣻⡯⠸⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠈⣧⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣿⠚⣧⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣤⣿⣦⣡⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⡼⢏⣼⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠸⡇⢻⣿⣿⣤⣄⣀⣠⣴⡿⣿⣟⣙⣧⣀⠀⠀⠀⠀⢠⠎⠁⠔⠃⠛⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣇⣿⣿⣿⣿⠗⠒⠂⢺⣿⡋⠀⠿⣷⣶⣶⣶⡿⠐⠀⠀⠛⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡷⠞⣨⠛⠁⠀⠀⠀⠙⠋⠁⠀⠀⠸⣯⣽⣟⠓⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠹⠿⣿⡿⠿⠛⣷⡶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡺⠑⠤⢲⡞⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖⠒⢤⣐⡊⠁⠠⠀⠀⠀⠉⢽⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣽⠁⠞⠀⠀⠀⠀⠀⢠⢜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠁⠝⠛⠛⠛⠋⠀⠀⠀⢠⠄⠐⠂⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸⡅⡜⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠼⢶⠤⠔⠋⠙⠁⠀⣇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⡘⠀⠀⠈⠙⢦⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣏⣉⠉⠒⠒⣚⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠐⠣⠋⠉⠉⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠘⠳⢤⡀⠀⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠸⠞⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⣦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠸⡄⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⢸⠀⠀⡇⣠⠖⠚⠛⠓⠲⢄⡠⠁⠹⢄⠀⠀⠀⢳⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠙⣇⠀⢻⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢳⡀⢠⠏⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠸⡄⢸⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠜⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡄⣀⡬⠽⢧⣸⡆⢀⡵⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢧⡰⠂⠀⠀⢀⣾⠀⢀⠀⠀⣠⣀⡀⠀⠀⢀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠉⠈⠙⠛⠒⠚⠁⠀⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠋⠀⣴⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣪⢁⣠⠄⢼⡿⢩⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣪⣤⡭⠀⠟⢁⣻⠋⡐⠛⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡿⣻⣡⣤⠀⣴⠁⣾⠃⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⡖⠉⠁⢹⣿⡙⢃⣾⣾⡏⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣥⣶⣿⣾⡆⣀⣋⠙⠿⣟⡹⢀⢰⣹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⣤⣀⡼⡵⣞⣉⣉⢻⡜⣶⣝⠄⣿⡧⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋⡞⢱⣿⠋⠻⠰⢃⣿⣿⠀⣩⡧⢈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠘⢿⣧⡐⠚⢛⣿⣿⣀⠉⣅⣶⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⣤⣤⣤⣝⡛⢻⣿⣿⠟⠛⣷⡌⢧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣀⣼⠇⣄⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣦⣉⠡⢾⡛⢧⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠹⣿⣿⣿⡿⠛⠙⠻⣮⢳⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⡄⠀⠀⢹⣿⣿⡇⠀⣦⠀⢹⡇⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢷⡀⠀⣸⣿⣿⣿⣶⣿⣷⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⢸⣿⠿⠟⢹⣿⡟⠉⠙⢿⣇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠻⣧⡀⠘⣿⡇⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠙⢿⣦⣻⣧⠀⠀⡼⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣀⠀⠀⠀⠀⢰⢀⡶⢈⡥⡟⣸⡄⠧⢌⠐⣦⢠⠄⠀⠀⠀⠀⣠⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡹⣿⣿⣷⣭⣐⣦⡤⣿⣷⠃⣴⠁⡘⢁⢰⣄⢳⣿⡧⣤⣾⣈⣵⣾⣿⡿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣏⢹⡗⠉⢾⣌⣻⣿⡝⢷⢿⣿⠏⠀⢻⡇⣾⠃⠀⢹⣿⣷⠟⢻⣻⣋⣴⠟⠁⣿⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⢤⣀⠀⢽⣿⣎⣻⣤⢸⣇⡤⡀⠠⣦⣤⠀⣠⢤⣹⡇⣬⣏⣽⣟⡅⢀⣤⢅⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣠⣽⣶⣾⣿⣿⣿⣇⣾⠁⢠⡇⠀⠸⡇⠀⣧⡀⢸⣇⣿⣿⣿⣿⣶⣾⣵⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣻⣿⡟⡏⠈⣿⣿⣿⣿⢁⡟⣡⡐⠾⠧⢢⣝⢧⢸⣿⣿⢿⡏⠈⡿⣹⣿⣏⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠤⢸⡟⢌⣿⡓⣴⣶⣿⡿⣿⢿⣼⣿⡿⣯⣍⣭⡷⢻⣿⣼⣿⣿⢸⣿⣶⡴⣻⣏⠜⢿⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠃⣿⡴⠲⣛⣉⠿⠿⢵⣤⣘⡺⣿⣯⣀⢰⡤⣾⠁⣨⣿⡿⢖⣁⣤⠭⡿⢯⡙⣻⠶⣼⡧⠋
⠀⠀⠀⠀⠀⠐⠦⣾⣏⣯⢳⣼⣾⣷⣿⣟⣛⣙⡻⣆⢉⠯⢹⣟⣿⣌⠛⠏⡴⢛⣛⣙⣻⣿⣿⢽⣥⠏⣟⣻⡷⠶
⠀⠀⠀⠀⠀⠠⣀⣘⠿⡶⠯⢩⡼⢟⣿⣿⣿⣏⡙⢿⣿⣾⣿⡓⢺⣿⣿⣼⡟⣋⣻⢿⣿⣟⠻⢮⠉⠷⣦⢟⣂⣀
⠀⠀⠀⠀⠀⢀⣀⣩⣮⡥⠚⠁⢀⣾⣿⣥⣸⣟⠶⣿⣿⣿⣏⡀⢏⢿⣿⣿⡿⠞⣿⣡⣬⣿⣧⡀⠉⠲⣬⣫⣍⣀⡀
⠀⠀⠀⠀⠈⣉⣭⣽⠧⠀⣶⣾⣿⣿⡿⣟⠙⠻⣦⡒⣿⣿⢨⠁⢀⡘⣿⣷⣂⣴⠟⢉⣽⣯⢿⣿⣷⣦⠠⢿⣭⣭⡉
⠀⠀⠀⠀⠰⢋⠀⡠⢴⣾⣿⣿⣽⡾⣿⣥⢷⡄⢹⣿⣿⠃⡟⠀⠈⣇⠻⣿⣿⠇⣤⡳⣽⡿⣸⣝⣿⣿⣶⠤⣄⢈⠛
⠀⠀⠀⠈⠳⠄⢠⣜⡷⢻⢻⣿⣽⣠⡟⣿⣯⣶⣿⣿⠇⠀⠁⠀⠀⠈⠀⢻⣿⣼⣮⣿⠟⢷⣘⣿⣿⢻⠳⣞⣠⠀⠵⠋⠁
⠀⠀⠀⠀⠟⢰⣦⡟⠁⣸⣾⣿⣿⣷⡾⣁⣛⣻⣿⠁⠀⣴⣿⣛⣻⣿⡆⠀⢹⣿⣿⣻⡙⣶⣿⣿⢿⣼⢆⠉⣧⣶⠈⠆
⠀⠀⠀⠀⠀⢸⠃⠀⣾⠹⢿⣿⣟⣿⡟⣿⣻⣿⢿⡄⠀⢹⣿⣿⣿⣿⠇⠀⢨⠿⣿⣿⡿⢿⣟⣿⣿⠿⢼⡇⠁⢹⡇
⠀⠀⠀⠀⠀⠈⢠⠇⢾⠀⡾⣿⣿⣵⠀⣾⣿⣿⡸⠇⡀⠀⠙⠛⠛⠋⠀⢀⠟⠲⣿⣿⡅⢠⣯⣿⡿⠆⢸⡇⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⡇⣧⣿⣾⡄⣿⣿⣸⡷⡶⣤⣭⣙⡛⠛⣛⣡⣤⣼⣿⢻⣿⡇⣼⣻⣿⡗⣧⣾⣯⠄
⠀⠀⠀⠀⠀⠠⠾⠋⠙⠋⢠⡿⠁⣽⣇⣿⣸⣿⢿⡄⣻⣿⢿⣿⣿⢹⢹⢛⣿⣿⣸⢷⣧⣾⠍⠸⣿⠈⠛⠹⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠀⠀⡾⠛⣿⣼⡧⠘⠧⢿⣿⢈⠁⣿⠀⠘⢸⠿⣿⣿⣼⡿⠹⡇⠀⠈⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⠀⠀⣀⠈⢻⣇⠲⢰⣿⣿⠇⢿⠙⠀⢰⣾⣻⠃⣿⠋⢀⡀⠀⢰⠁⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⠀⡟⠀⠈⣿⢰⡞⣿⣿⡞⣿⠀⢇⠸⡏⣿⠸⡏⠀⠈⡇⠀⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⠀⠘⣿⡇⠟⢰⠈⠆⡀⠘⠂⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⢾⣠⠟⣷⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡠⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⢶⣶⢶⢶⡶⠿⣯⣍⠻⢿⣦⠙⣿⣟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣦⡴⠾⠻⠉⠁⠠⠀⠈⡜⠉⠈⠁⠀⠠⠙⣷⣄⠻⣦⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣶⠟⠿⢻⣽⣿⠏⠀⠀⠀⠀⠀⣧⡀⠀⢠⣥⢀⣄⠀⢀⠀⠹⣿⣦⠀⢲⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡋⢸⠁⠀⠀⣾⣿⠏⠀⠀⠀⠤⢴⣾⣾⣧⠀⢠⣿⣿⡿⣧⣾⣿⣤⣤⣿⣷⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣤⠾⠿⢿⣿⣆⢸⣿⠁⠀⠀⣿⡿⢬⠉⠻⣿⠟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢠⣿⣿⠀⠀⠐⣼⣧⡀⠀⠀⣿⣿⠈⢿⣷⣦⣾⣿⣷⢶⣼⣿⣿⡆⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣸⣿⣿⠀⠀⠈⢡⢴⣾⡓⢸⡿⠛⡆⢀⡛⢯⣼⣧⣵⠞⣼⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⠏⢸⣷⣠⣶⡞⠻⢌⡙⠷⣾⡁⠠⠐⠀⠉⠘⠙⢷⣶⣾⣿⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢚⡟⠁⠀⢐⣦⣀⣀⣠⠏⠀⢰⣶⣦⠀⠀⠀⠀⠈⠉⠹⠇⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠐⠛⠿⠛⠃⠀⠀⣈⡉⠀⠐⣲⣶⣤⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠁⣴⣾⣿⣿⠗⠀⠀⠀⣼⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡷⢿⣿⣶⣦⡀⠀⠀⠀⠀⠐⣼⣿⢻⠿⣖⣆⠀⠀⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣴⣽⣿⣿⣷⡄⡀⠀⠀⢸⣵⣧⡼⠦⠀⢉⣴⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠼⢿⣿⣿⣿⣿⣿⣉⠐⠛⢀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢈⡋⠈⣩⣾⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣀⣉⠽⣿⣿⣿⣿⢿⡇⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⠋⠀⠘⠲⠿⠞⢻⣏⣾⣸⠃⠹⣿⢳⣿⡿⣏⠻⠿⠛⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⡄⢀⣤⠀⠀⠀⠈⠙⠁⠀⠀⠀⠊⠋⠉⠀⠀⠀⢀⣀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠛⢿⣿⣷⣶⣖⣫⣴⣸⡀⠀⠀⠀⠀⠀⢀⣾⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠄⠚⠛⠻⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠘⣿⠏⢙⡿⢿⣿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⡿⠛⠿⠷⠿⠳⠖⠚⢿⡀⠛⠀⠀⠀⠀⠉⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢰⡆⠀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠀⠀⠆⠀⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⠀⠀⠰⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠃⠀⢸⠀⠁⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⡰⣿⢶⣄⣸⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⠀⣿⣄⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣾⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣾⣿⡿⠏⡁⢉⣿⣿⡟⠋⠉⠉⣈⣁⠙⢻⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠟⠛⣛⠉⠙⠙⠻⠿⢿⣿⠁⣼⠃⣸⡿⠁⠀⣤⠾⠟⠉⠉⣁⣠⣿⡿⢿⣦⡀
⠀⣾⣶⣶⣤⣀⣀⠀⣀⣀⣴⡾⠋⠁⢀⡄⣸⠏⠁⠀⠀⠀⠀⠈⣧⣸⡇⠀⣿⢁⡄⢰⠇⣿⣟⡒⠛⠛⠉⠀⠀⠀⢨⣳⣄
⠀⠙⣧⠉⠀⠙⠛⠛⠋⢛⡯⠀⠀⣴⣿⠁⡯⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠟⣼⠀⢸⠀⢹⣯⢉⣷⢤⡾⠀⠀⣾⠀⢻⣿⣷⣶⣤⡆
⠀⠀⠙⣷⣦⣄⣀⣀⣴⣾⣿⡤⠀⣿⣿⡀⢀⠀⠀⠀⠀⠀⣼⠀⠀⣿⡆⠀⠀⢿⣧⠘⣿⣤⠟⠉⠁⢠⠀⠀⡀⠈⠀⠈⣿⣏⣵⠟
⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⣿⡇⠀⠈⣿⣇⠘⣧⡀⠀⠀⠀⠹⡆⠀⢿⣷⠀⠀⠘⢿⣶⣿⠃⢠⡄⢸⡌⢷⠊⢀⢀⣄⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠱⣌⠘⣷⡄⠁⠀⠀⠀⠀⠛⢸⠈⣉⣠⡀⠀⠸⣿⣿⣧⡈⠳⡄⠛⠀⠀⡤⠈⢡⡿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡀⠈⠁⢸⣷⣤⣄⣀⠀⠀⠀⡾⠐⠛⢻⣿⢀⣴⣿⠻⠿⢿⣦⡘⣠⠁⡙⣆⢰⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠁⣀⣠⣿⢿⣿⣿⣿⣿⣿⡿⣷⠀⠀⠸⣿⣿⡿⣿⣶⡶⠶⣾⣿⡘⣦⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⣿⠟⠁⢸⣿⣿⣿⡿⠋⠀⣿⠀⠀⠀⢹⠁⠀⠀⠙⠛⢷⣾⣿⢿⣛⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣿⡇⠀⢠⣿⣿⣿⠟⠁⠀⠀⠘⢇⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⣩⠃⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⠙⠄⢻⣿⣿⡏⠀⠀⠀⠀⠀⠘⡖⠀⠀⡇⠀⠀⠀⠀⠀⣴⠇⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⢂⢻⠿⢷⡀⠀⠀⠀⠀⠀⠇⠀⠀⢳⠀⠀⠀⠀⣼⢁⠄⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⢆⢣⠀⠱⣄⠀⠀⠀⠀⢸⠀⠀⠸⡆⠀⠀⠀⠿⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠴⠎⠀⠣⡀⢀⡈⣱⡀⠀⠈⢶⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢱⡀⠀⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣠⡀⢡⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠖⠛⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠙⠒⠒⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠚⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠉⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⣠⣶⡟⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡀⠀⠀⠈⢧⠀⠰⡄⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⡠⠀⠀⢀⣐⣾⠛⠀⠀⠀⠘⠀⠀⠃⠀⠀⢠⡌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠐⠀⣰⣾⣿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣦⡘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⣿⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⡟⣳⡘⣿⡀
⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠉⠉⠉⠁⠘⠁⠀⠀⠀⠀⠀⠄⠀⠀⠤⠍⠻⢿⣇⣿⣧
⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⢙⠶⢤⣄⡀
⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢿⣧⡀⢂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣷⣤⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⠟⠋⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣮⣆⠡⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡜⠄⠀⠀⠀⠀⢠⣿⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⡀⠀⠀⢀⣾⡯⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⣿⣿⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣿⡏⠁⠐⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣪⣴⣿⣿⣿⣿⣿⣿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠠⡪⠀⠀⠀⢀⣴⣶⣶⣶⣦⣤⣴⣶⣤⣶⡶⢿⣿⣿⣿⣿⣿⣿⣿⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢋⠃⠀⠸⣇⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠰⣬⣻⣿⣿⣿⣻⡿⠿⢛⣯⣷⣿⣿⣿⣿⣿⣿⡟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⡟⠉⠁⡠⡾⡿⣿⡟⠁⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢹⡄⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠊⠀⠊⡜⡑⢑⣿⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡆⢳⡀⠀⠀⠀⠀⠑⡀⠀⠠⡐⢄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⠁⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢳⡀⠀⠀⠀⠀⠈⠀⠀⠘⢮⠣⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠜⢀⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⢀⠎⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢸⣿⣷⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⢸⣿⣿⡇⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⣼⣿⣿⣿⡀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣵⣾⣿⣿⣿⣿⣷⣤⡀⠀⣸⣧⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠙⢿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠛⠉⠉⠙⠻⣿⡟⠻⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⠋⠉⠉⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠠⣤⣤⣀⠀⠘⣿⠀⠀⠻⣿⣿⣿⣿⠀⠀⢸⣏⠀⠲⣶⣶⣦⡀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⣿⣷⣦⡀⠀⠹⠏⠀⣰⣿⠀⢀⠀⠘⣿⣿⡏⠀⠀⣿⡿⢷⣦⣀⠉⠻⣷⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠉⣀⣀⡀⠈⢿⡄⠀⠀⣴⣿⡟⠀⣸⡄⠀⠘⣿⠃⠀⢠⣿⣥⣀⠈⠛⢷⣦⡀⠀⣾⠹⣷⡀
⠀⠀⠀⠀⢀⣴⠾⣿⣿⣿⣿⣇⠀⢻⣿⣿⠀⠀⣿⠀⠀⠙⠻⣿⣦⣿⣷⠀⠀⠉⠀⢀⣾⣿⣿⡿⠙⢶⣄⠙⢿⣶⣿⠀⣼⡇
⠀⣠⣴⣿⣿⡁⠒⠉⣉⡉⠛⣿⡀⠘⠿⠿⠇⢠⣿⡆⠀⡄⠀⠘⢿⣿⣿⣇⠀⠀⢀⣾⣿⣷⠙⢿⣦⡀⠙⢿⣦⡈⠻⢠⣿⠇
⠐⢿⣿⣿⣿⣿⣦⣀⣙⣡⣴⣿⣿⣦⣤⣤⣴⣿⣿⡇⠀⣿⡄⠀⠈⣿⣿⣿⠀⠀⣾⣿⣿⣿⣧⡀⠙⢿⣦⡀⠹⣷⣄⣾⡏
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⡇⠐⣿⣿⡄⠀⠸⣿⣿⡇⣼⡟⠋⠻⢿⣿⣿⣦⡀⠹⣿⣄⠈⣿⡇
⠀⠀⠀⠀⠀⠈⠻⣿⡈⠁⠀⠈⠀⠀⢀⣠⣿⣿⣿⡇⢀⣿⣿⣷⠀⠀⢻⣿⣷⣿⣿⣶⣤⠀⠙⢿⠈⣅⡀⠈⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡄⠀⠈⠻⢿⣿⡿⠋⣿⣧⡀⠀⠀⣿⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢺⣿⣿⣿⣿⡿⠛⠉⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣿⣿⣷⣤⣤⣿⡿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣿⣿⣿⡿⠋⠀⠀⢠⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠁⠀⠀⠰⠄⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠆⠀⠀⡤
⠀⢀⡄⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⡠⠀⠠⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⠉⣄⠑⠀⠁⢀⠀⠀⠀⠀⢀⣿⠀⠐⠀⠀⠀⠺⠀⠀⠐⠀⠀⢢⠀⣰⡄⠊⠀⠠⠀⠈
⠀⠀⠀⠈⢀⢃⠈⠀⣠⣤⣤⣵⠀⠀⠖⠢⠂⠒⠆⠀⡌⣂⠀⣐⠩⠁⢀⢠⣆⠰⢃⠱⡀⠤⣼⡇
⠠⣾⡀⠀⠐⠐⠰⠛⠛⠛⠃⠌⠶⠒⠀⠓⠐⠃⠘⠘⡖⠿⠀⠿⠀⠗⠀⣤⠈⠻⠫⠛⢋⠈⢀⠃⣠⣤⡀
⠈⣾⡅⣠⠨⠺⠀⠰⠂⠗⠀⡂⡄⠚⢀⠄⠄⠄⠘⠃⡇⠀⣏⡅⠀⠀⣶⠀⣶⠀⠿⠿⠀⢠⡄⢘⢁⣤⠉
⠐⠛⠂⢸⠐⠾⠀⠐⠂⠂⢸⠽⠃⠀⠀⠂⡀⠂⠀⠰⡇⠰⠃⢧⠈⠘⠛⠀⠛⠂⠿⠽⡄⠘⠃⢸⠀⠅⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢀⣠⣴⣶⣶⣶⣶⣿⣿⣿⠛⠉⠁⠉⠀⠀⠈⠹⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡴⢋⣵⣿⣿⣿⢏⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⠳⣄⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣴⡏⠀⣼⣿⣿⣿⡟⣸⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠒⠲⢿⣿⣿⣿⣿⡇⢻⣷⡄⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⣿⡇⠀⣼⣿⣿⣿⡇⣿⣿⣿⣫⣭⣭⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡗⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢿⣿⣿⡄⢹⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠃⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠻⣿⣿⣆⣿⣿⣿⡇⣿⣿⢿⣿⣿⣽⡿⠃⠀⠀⠀⠘⢿⣿⣿⣻⠛⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡇⣿⣿⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⢧⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣤⣤⣄⠀⠸⠃⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠙⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣤⣾⠷⠤⠤⠚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢸⣿⣿⡟⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠈⣿⣿⣿⣌⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡙⠻⢿⣦⣌⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣉⣙⠂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢃⡈⢉⠈⠀⠀⢄⠀⢱⣆⣐⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢢⣌⠀⠀⠀⢋⣁⠼⠒⡉⠤⠖⠨⡑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢁⠀⠀⢰⡈⠠⡴⠂⠉⢀⠀⠀⠈⠙⠳⡤⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⢠⣔⣢⡄⢈⠁⢩⠀⠀⠀⢆⠀⠅
⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⣄⠀⠠⠀⠀⠐⠁⠈⡀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠂⠐⠒⠒⠂⠒⠀⠂
⠀⠀⠀⠀⠐⠠⠀⢀⠀⠀⣀⡔⠀⢈⠂⠀⠀⡠⠈⠁⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠈⣀⠉⠀⣈⠈⠹⠀⡴⠁⡂⠀⠀⠀⢀⡀⠘⡄
⠀⠀⠀⠀⠀⢣⡈⠀⠀⠉⡀⡀⠉⠀⠉⠀⠆⢊⠐⠋⡂⠀⠈⠒⠀⠅⠀⠀⢀⠄⠀⠤⡀
⠀⠀⠀⠀⠀⡀⢱⢔⣄⣀⣀⡀⠀⠀⠀⠀⢃⠀⠀⠈⠃⠀⠰⠆⠀⠀⠀⣰⠃⠀⠀⠀⢈⡄⡀
⠀⠀⠀⠾⠀⠀⠤⠱⠤⡄⢼⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠍⠀⠀⡰⢃⠊⢐⡀⠠⠁⠂⡍⠂⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⢋⣖⠀⠀⠀⠀⠀⠰⠨⠬⠉⣂⢝⠡⡄⠸⣄⡐⠭⠔⢀⣀⠂⠀⢀⠀⠀⠄
⠀⠀⠀⣠⢀⠅⠄⠉⠈⠗⡧⡅⠀⠀⠀⠀⢀⣣⠁⠀⠤⢄⢀⢑⣷⡴⠤⠈⠀⢠⠤⠤⢆⡠⠶⠤⠘
⠀⠀⠰⠧⠀⠀⠑⠂⠈⠠⠁⣈⣄⠀⠀⠀⠀⠉⡄⠀⠀⠊⡀⠀⠈⠀⠀⠐⣠⢦⡤⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠂⠀⠀⠀⠀⠀⢨⡉⣩⣉⡅⠀⠠⡀⠀⠁⠀⠉⣕⣾⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠿⠄⠇⠀⠀⢀⢠⠀⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⠀⠀⢀⡼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣆⠈⣦⠲⠾⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣧⡾⠛⠅⠀⠀⣆⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⢻⣿⡿⠵⠀⠀⠀⡀⠀⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⡀⠁⠀⠀⠀⠻⠆⠙⠊⠟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⢯⠵⠍⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠋⠹⢏⣰⣦⣶⠄⠀⠙⠿⣿⡏⠓⠤⠸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⢶⡶⠲⠶⠖⠚⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⢴⣾⣷⣶⣴⠀⢀⢀⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣻⡗⣮⣿⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠍⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⣴⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣶⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣿⣿⣠⠀⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠠⣷⣾⡯⠀⢈⣧⠀⠀⠀⠀⠀⠀⣼⠆⠀⠀⠐⠀⠀⠀⠀⠀⢠⠀⣽⣷⣾⣿⡿⢿⡿⣷⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡰⠀⠈⣿⡷⠀⠀⠀⠀⠐⣿⠇⣠⣴⣤⣄⠻⠔⢀⣤⣦⣾⣿⣿⣿⣿⡇⢼⠐⣻⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠰⣻⣧⠀⠀⠀⠀⣾⠟⣼⠟⠛⠛⠛⠿⣾⡿⠿⠛⠛⠛⢿⡟⣿⡃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣣⠆⣉⢻⣿⣿⡀⣠⡜⠃⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣿⡇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⣸⣿⣿⡟⠃⠀⠀⣠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⢃⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣍⡤⣾⣿⣿⠁⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠀⠄
⠀⠀⠀⠀⢀⡠⠀⣿⣿⣿⠿⣿⣿⡿⣡⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⢠⡏⡀⣼⣿⣿⢧⣺⣿⣿⠀⠃⡔⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⣸⠓⣿⣿⣿⣿⣿⣽⣿⣿⡷⠆⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠠⠀⠀⠀⢀⡀⣿⠿⣿⠉⠉⣻⣿⡿⠿
⠀⠀⢠⡟⢰⣿⣿⣿⣿⣿⣿⣿⠿⣇⠐⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣤⢄⣶⣶⣶⣶⣾⡾⠍⠉⠙⠐⠂⠐⠂⡠⠴⢲⡾⠇⠐⠁⢔⣿⣿⡿⠄⠒
⠀⢠⣿⣃⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⠀⢃⠤⣀⣀⣤⣤⡔⠺⠿⠈⠋⠁⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠋⠁⠀⢀⣤⣿⡿⠛⠁
⠀⢸⣿⣛⣻⣿⣿⣿⣿⡟⢛⣧⠀⢷⣄⠠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⡀⠀⠀⠀⢠⣿⠟⠋⠁
⠀⠈⠉⠉⠀⠻⣿⢿⡿⢁⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⠀⠀⠀⠀⠈⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡃⠀⠈⠀⠀⠀⠀⢀⠀⣶⣠⣄⢀⡀⢒⣐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠲⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠂⠀⢾⠋⠀⢀⣀⠈⠒⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢳⡄⢀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠄⠀⠀⠀⣶⡎⠀⠀⢠⣴⣌⠀⡀⠀⠀⠀⠀⠀⠀⣤⠦⣄⠀⠀⣿⣦⡀⠀⠀⠈⢧
⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⡇⢠⠀⠻⠿⠛⠐⠀⠀⠀⠀⠀⠰⡎⠻⠿⠟⠁⠀⢻⣿⡇⠀⡆⠀⠀⠑
⠀⠀⠀⢀⡞⣤⡆⠀⠀⣿⡇⠀⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠋⠀⢿⣇⠀⠃⠀⠀⠀⠀⠆
⠀⠀⠀⣰⣿⡁⠀⠀⠀⢻⡇⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠨⡁⣻⣿⡄⣀⠀⠀⠀⡈⠋⠣
⠀⠀⠀⢻⢿⣿⣾⣄⣄⢸⡇⡏⠔⡠⠀⠀⢠⣿⣿⣿⣿⣿⣷⡄⠰⠀⠀⣦⣤⢸⣏⣿⣇⢿⣿⣄⣸⡟⣾⡟
⠀⠀⠀⢸⣿⢿⡏⣽⣽⡇⣏⢧⡀⢿⠢⠀⠈⠛⢿⣿⣿⣿⠛⠀⠀⠁⣴⠟⢁⣾⡷⣿⣿⢸⣿⣯⠁⣴⡏
⠀⠀⠀⠀⠙⢿⣿⣿⣏⢰⣿⠀⠁⠈⣇⠀⠀⠀⢀⣈⠡⠀⠀⠀⠀⣠⠃⠀⢀⣈⠀⣸⣿⡸⣿⣫⡸⢢⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣏⣞⣤⠗⠀⣀⠻⣷⣤⣶⡶⠿⣿⣶⣶⣤⡶⡫⠟⠀⠁⠈⠀⢻⣻⣇⢿⣿⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢚⠇⠀⡀⠀⠙⠃⠘⢻⣧⠀⠀⠁⠀⣨⣿⠎⠀⠀⠀⠀⠢⠀⢀⣡⣿⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣶⠟⠁⠀⠀⠀⡀⠀⢆⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢷⡄⢃⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢯⠀⢨⣶⣾⢿⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠋⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡀⠉⠈⠁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⠳⣶⣄⢰⡆⣀⠀⣄⣠⣅⠀⠿⠂⠁⠀⠀⠀⠙⠂⢈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠙⠛⠙⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢘⣿⣻⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡃⠀⡄⠀⢠⣯⠄⠀⠀⠀⠀⣸⠀⠀⢀⠀⠀⠀⠀⣨⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠠⣿⣿⠿⣿⣄⡀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢢⢠⣇⠀⣰⣿⡇⢰⠀⠀⣴⣿⡷⠀⢀⣆⢰⣿⣇⠀⣾⠀⠀⡀⠀⣼⡆⢀⠀⠀⢀⣼⣧
⠀⠢⢼⣿⣿⣶⣉⡶⢿⣤⠀⠀⣼⣿⣇⠀⢰⠀⠠⣿⠀⠨⠀⢠⣿⣾⣿⣤⣼⣿⣿⣿⠀⢴⣾⣿⡟⠂⢼⣿⣿⣿⣿⣿⣿⣦⣠⡆⠀⣼⣧⣾⡆⠀⢠⣿⣿⠄⢰
⢠⣾⣾⣿⡿⢿⠯⢹⣿⣿⣷⣾⣿⣿⣿⣶⣿⣶⣼⣿⣦⣾⣄⣸⣿⣿⣿⣾⣿⣿⣿⣿⣀⣿⣿⣏⣼⣷⣿⣿⡿⠟⢟⡛⢿⣿⢿⣿⢈⣿⣿⣿⡇⠀⣼⣿⣿⣇⣾
⠘⢿⣿⣿⡿⣌⣴⣿⠿⠉⣿⡿⠿⠿⠟⠛⠙⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⢿⠟⠓⠚⠛⣵⡎⢿⣾⣿⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠛⠻⠿⣤⣿⣿⢡⠤⡤⠠⠀⡦⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠉⠀⠂⠀⠀⠀⠀⠀⠉⠋⠉⠉⠙⠛⠛⠿
⠀⢺⠙⠇⠉⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣤⣤⣀⣀⣠⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡄⠤⠀⠀⠦⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣶⣶⣤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠠⢄⡠⠐⠨⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠑⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠂⠀⠀⠀⠀⠀⠰⡀⢰⠁⠀⠀⠀⠀⠈⠄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⣀⡀⠀⠀⢧⡞⠀⠀⠀⠀⠉⠲⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠄⠀⠀⠀⠀⠈⢠⣬⠀⠂⠸⡇⠀⢀⣭⡍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⡆⠀⠀⢢⠀⠉⠁⠀⠀⠀⠀⠈⠉⢀⠆⠀⢀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠀⠀⠈⠢⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡴⠊⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣤⡄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⣣⠀⠀⠀⠓⠀⠀⠀⣴⣶⣶⣦⠀⠀⠁⠊⠀⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡏⠏⢣⠀⠀⠀⡀⠀⠉⣿⣿⠍⠀⣠⠀⠀⠀⠀⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡀⡄⠃⠀⠀⠈⠓⢶⡒⢓⡲⠚⠁⠀⠀⠀⡰⠄⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠟⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⢡⢦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⠀⢀⡀⠀⠀⠀⠀⠀⡀⢰⢧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⢆⠁⢀⠀⠀⡤⢀⠰⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢇⡄⠐⢀⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣀⢣⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢀⣤⣴⣶⣤⣄
⠀⠀⠀⠀⠀⢀⣀⣀⣼⠿⣤⣾⡿⢿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⡀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠻⢝⣲⡤⣤⣤⠼⠉⢹⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⡆⠀⠀⡆⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣅⣠⠀⠀⢸⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⣧⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣦⢻⣿⣿⣿⣿⣿⣿⣯⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢿⣟⢛⣱⠋⢈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⡆⣫⡁⠀⠀⢈⣧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⣦⣈⢿⣦⢶⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢾⣿⠻⣿⣾⡆⠀⢻⣿⣿⣿⣿⠋⡟⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⣿⣆⠘⢻⣷⡀⠀⠹⡝⢿⡇⢰⠁⠈⢿⣿⣿⣿⣿⠟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣿⡄⠘⢿⣷⡀⠀⠀⠈⢳⠃⠀⠀⠈⠉⠛⠻⢷⣤⠄⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣦⡀⢸⡇⠀⡀⢀⢸⠀⠀⠀⠉⠀⣴⡾⠶⠧⣤⣝⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡺⠛⣿⡇⠙⢿⠀⢡⣘⣮⡀⠀⠀⢀⡴⠁⠀⢠⣴⣶⣾⣿⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣃⠹⣷⠀⠀⡇⠠⢹⣻⡁⠈⡆⣼⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣇⣿⡄⠀⡇⠹⣼⣿⣿⣷⣼⣿⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⣿⡇⠀⢈⠘⣿⡯⠙⣿⣿⣿⣇⠀⠸⣿⣿⣿⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡛⢿⠇⠀⠘⣤⣿⣇⣄⣈⣻⣿⣿⣦⠀⠈⠻⠿⣿⡞⠁⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⢶⡯⢆⣤⣿⠀⠀⡾⢠⢻⣿⣿⣿⣿⣿⣿⠾⣷⣄⠀⠰⢽⣿⣶⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠿⠤⠟⠓⠁⢠⣞⡴⣡⠋⣿⠀⢰⣣⢋⡵⢞⣻⣶⣶⠾⠿⠟⠛⠛⠛⣻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠀⠘⠛⠛⠷⠾⠛⠧⠀⠀⠒⠒⠒⠒⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠓⠀⠀⠰⣶⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⡀⠀⢀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠐⠗⠀⢀⣀⠀⢹⠟⠀⠀⠀⠀⠀⢀⢸⡿⠃⠄⢀⣿⣄⠲⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠄⠿⠀⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠉⠀⣼⠀⠀⠀⠀⠀⣴⣿⠛⠳⣆⠀⠀⠉⠃⠀⣴⣆⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣶⣦⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⣆⠀⠀⣀⣄⡝⠀⠀⠀⠀⠀⠸⣿⢄⠣⢄⡀⠀⢶⣀⣀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⢥⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠀⢩⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢻⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⢒⡤⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠲⢀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣂⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⣴⢰⡆⠛⠀⠈⠓⣿⢺
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⡙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⡀⣀⡰⠿⠁⠀⠀⠀⠀⠀⢻⠀⣷⣄⣀⢀⢸⣏⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⠐⢿⣏⢈⣿⣿⡇⠀⠀⠀⠀⠀⠐⢄⠀⠈⣿⡇⢉⣛⣛⡛⠟⠀⠀⠀⠀⠀⠀⢀⡀⢋⠀⢼⣧⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠐⠛⠙⠉⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠑⠊⢛⡀⢸⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀⢘⠳⣄⠲⠸⠷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠰⠄⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡼⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⢄⠐⡆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠀⠀⢠⣄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠶⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⡇⠛⠀⠀⠛⢸⠁⠡⠀⠀⠀⠀⠀⠀⣠⡶⣿⣅⠈⠁⠚⠻⠀⠐⣄⠀⠀⠀⠀⠀⠀⠈⠠⡆⠀⠀⠂⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣅⠈⢻⠟⠀⣨⠷⠂⠀⠀⠀⠀⠀⠘⣿⣇⠳⠈⠂⠀⢂⡀⠀⢸⣿⠂⠀⠀⠀⠀⢠⡇⠀⢿⣄⠲⠶⡦⣭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢿⣾⣷⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠁⠈⠳⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠲⠺⣇⠘⡟⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣲⣥⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢰⠏⠂
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠂⠀⠀⠠⠒⠀⠚⠀⠀⢀⡠⠀⠂⠃⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⢸⡆⣰⣧⣆⠒
⣴⣧⣿⣇⡆⠀⠀⠘⣯⠐⠂⠀⠀⢲⡄⠀⠀⠂⠻⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢰⢷⠀⢠⣾⢷⣭⠌⠛⢶⠒⢠⡆
⣻⡟⢫⣿⣧⣷⣏⡠⠀⠔⠐⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡔⢯⡀⢘⡁⢂⠪⡦⠴⡘⢦⣝⢳
⠚⣯⡶⢹⣿⣿⠋⠂⠀⠂⠐⡈⢺⣶⣆⣤⣀⣤⢀⠀⠀⠀⢀⡀⣤⢀⣠⡊⠃⣴⠞⠃⢜⡺⠤⠉⠱⣿⠀⠈⠀⠙⢿
⢈⠁⠖⢸⣉⡤⠎⣠⠆⠀⠀⠐⠲⣿⣿⡿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠈⠈⠺⣂⠘⣯⡤⠒⣀⡠⣜⡀⠀⠈⠶⢾
⠸⠄⢠⣟⡉⠠⠠⠶⢀⣰⢿⠑⢠⣙⣯⢓⣹⣭⠟⣋⡁⠀⠀⠀⠙⢿⠀⠈⠙⠳⣎⢢⡟⠒⠉⠈⠣⠌⡂⠀⠠⡀
⠀⠀⢠⡏⠠⢰⠂⢠⠊⠙⢄⣯⡀⠀⠉⠁⠀⢄⣪⣷⣻⣓⣦⣴⡶⠂⠀⡀⠁⣌⠚⢿⣗⠄⣇⠀⢰⡆⠈⠲⡀⡀⠑
⠀⡰⠋⠀⢀⡬⣟⠀⠀⠀⢣⣀⠧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⡋⠀⠀⠉⠐⠉⠄⠀⠁⢿⡁⣀
⠀⠀⠀⠈⠀⠀⠀⠙⠊⠀⠊⠁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠘⠉⠀⠄⠐⠤⠦⠀⠽⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟