Patient Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡞⠁⠁⠀⠀⠀⠀⠀⠀⠈⣟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢐⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠄⢈⡄⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠈⠑⠢⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠥⠀⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣿⢧⠻⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⡀⠀⠀⣈⠁⡲⠠⠈⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⣤⠍⠁⣨⠖⡱⠇⡈⠚⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠉⠀⠐⠂⠒⡲⠒⠂⠠⠔⠁⠚⢧⠒⠀⠁⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠀⠘⠁⠀⠀⠀⠀⠀⠂⠀⠂⠁⢀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⡉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⢀⡞
⠀⠀⠀⠀⠀⢀⠀⢠⠀⣀⡀⠀⠀⠀⢀⡀⠠⣶⠖⠋⡚⠂⠠⠄⠀⠀⠄⠐⡇⠀⠠⠁⠀⡞
⠀⠀⠀⠀⠀⠘⠂⠈⠉⠁⠍⡁⠰⡗⠁⠀⠀⠓⠂⡐⠈⠂⠀⠀⠰⠀⠀⠀⠀⠀⠂⢀⡍⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠂⠀⡈⠀⠖
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡄⠘⠀⢀⡄
⠀⠀⠀⠀⠀⢸⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠃⠀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠤⠄⠀⠀⠀⠒⠠⠅⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⡏⢱
⡀⠀⣤⡤⠀⠀⠀⢀⡃⢐⢀⣒⣒⣒⡒⢠⣤⢄
⠳⠅⠡⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣦⠆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠙⠋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢠⠒⡋⠋⠉⡏⠛⠐⢢⢤⡀⠈⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⢳⠄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠣⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠥⠅⠄⠘⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⣀⢀⠀⠀⠀⡀⠀⠀⠀⠓⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡖⠆⠐⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣬⣹⣯⡢⢴⣧⡄⠀⠀⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⣀⠬⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⡄⢐⢰⠈⠑⢮⣝⠂⠉⠈⢢⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣍⣸⣀⡆⠸⢸⠀⣆⡀⠀⢹⠇⡶⠀⠹⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⠐⠒⠠⣍⣉⠞⠉⠀⢱⡠⠎⣸⠇⠼⠒⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⣀⣀⣀⣀⡘⠀⢷⣉⠀⠛⡘⠏⠀⠒⡴⠋⢠⡞⡉⠙⠒⠤⣀⢸⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠉⢉⡉⠟⠁⠱⠤⠴⠊⠁⠐⠫⠵⠆⢉⠂⠀⠈⢋⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠈⠑⠒⡶⠒⢂⠟⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠂⠔⠂⠁⠀⢠⠞⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⢰⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡰⠓⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣆⢀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡔⠑⠄⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠒⠚⠋⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠜⠂⢄⣰⠇
⢀⠠⢀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢡⢀⠀⠀⣤⣄⣠⠴⠤⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠦⠀⠀⠀⠜⠂⠄⣠⡛
⡇⢠⡖⡀⠹⣏⣉⡦⣦⣄⣀⠀⢀⡄⣄⠶⠆⣒⢛⡟⠗⠒⡶⢆⠀⠉⠁⠒⠒⠒⠒⠈⠉⠀⡇⠀⠀⠘⠠⢄⡀⣵
⡇⢰⡇⠃⠀⠉⠉⠁⢢⢸⡀⠈⢿⡉⠐⠀⢀⠀⠘⡟⠄⣉⢆⠈⡑⠤⡀⠀⠐⠖⠀⠀⠀⡐⠀⠀⠐⠃⠄⣀⠉⢸⠀⠘
⡇⢸⡇⠀⠀⠀⠀⠄⠘⠀⠈⠆⠀⠁⠀⠀⠀⠈⠐⠈⡉⠀⠀⠀⠈⠑⠪⢑⠨⣧⢤⣤⣤⠁⠀⢀⠓⠠⡤⡓⠁⠘⠀⠘
⡇⢸⡇⡀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠉⠢⢔⡰⠀⠀⠀⡘⠂⡴⠚⠀⠀⡇
⡇⢸⡇⡗⠀⠙⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⡀⠀⠀⠀⠀⠑⢤⡀⠀⢳⠊⣜⠒⠠⢄⡇
⠃⢸⣧⣬⣀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⡇⠈⠀⠐⠤⠕⠀⠀⡇⠀⠄
⠀⠘⠃⠈⡈⠷⡦⣠⢀⠑⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠠⠤⠤⠤⠀⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⣀⡀⠤⠤⠐⢺
⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠤⠤⠐⠒⠀⣃⡠⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⣿⣿⣿⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠦⣀⡀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⡇⣿⣿⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡟⢲⣄⣄⣀⣀⠀⢨⠆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡔⢩⡇⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠛⠛⢹⣿⣧⡹⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢡⡇⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣈⠙⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⣷⡄⣶⡀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣧⢠⡇⣿⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢻⡴⠛⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢽
⣿⣿⣿⣧⠀⠀⠀⣀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠚⠒⢤⠀⢹⡄
⣿⣿⣿⣿⣷⡄⢰⣿⣴⣷⣿⣿⣿⣿⣿⣿⡇⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⣧⠈⢻⡀
⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣶⣾⣿⠀⠀⠀⠀⢸⠀⠸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⣿⠀⠀⠀⢠⣒⣒⣾⠹⢾⢿⣧⡾⣿⡆⢀⣀⣀⠸⡆⠀⢿⡀
⣿⣿⢟⡽⣫⢟⡽⣫⣿⣿⣿⣿⣿⣿⣿⣿⡇⡏⠀⠀⠀⣿⠄⣀⡤⠺⡀⢀⡼⢠⣶⣎⠽⠊⣉⣷⡏⠁⠉⢹⡇⠀⠘⣇
⠟⣡⢞⡵⢫⠞⣵⣿⣿⡖⠛⠺⣝⣿⣿⣿⡇⡇⠀⠀⠀⣿⠥⢈⠉⠙⠻⠶⠶⠶⠾⣯⣍⣉⣉⣉⣁⣀⣀⣸⠃⠀⠀⠸⡄
⢔⣡⠼⠒⠋⠉⢿⣿⡷⠿⠀⠐⠛⢺⣿⣿⡇⡇⠀⠀⠀⣿⡫⠔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⠋⠀⠀⠀⠀⢻⡀
⠉⠀⠀⠀⠀⠀⠈⢿⣷⠄⠀⡀⠀⠚⣮⣿⡇⠀⠀⠀⠀⣿⣚⠥⢂⠡⠀⠀⠀⠀⢀⣀⣠⢤⣤⠆⠀⣿⣿⣆⠀⠀⠀⠀⠀⢧
⣀⡤⡊⠅⠀⠀⠀⠀⣯⢀⣀⠬⠷⠯⣿⣿⡇⠀⠀⠀⠀⣿⢕⣪⠕⡪⢐⣠⠴⠶⣏⢀⣀⠵⠋⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠸⡄
⣗⡭⡀⠀⠀⠀⠐⠢⣟⡡⠒⠉⠙⠒⠦⣌⡙⠶⠤⠤⣤⣿⣭⣶⠟⠚⠉⠀⠀⠀⠘⣯⣤⡤⠤⠤⠼⠿⠿⠿⣿⣷⣤⣀⣀⡀⣷
⣗⡯⠂⠀⠀⠀⠀⠀⠈⠳⡰⣄⡀⠀⠀⠀⠙⠲⠲⠖⠶⠛⠉⢀⡤⡪⢀⠀⠀⣀⡤⠏⠀⠀⠀⠀⠀⠀⠀⠐⢉⣿⣿⣿⣿⣿⣿⣿⣶
⢕⡪⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣏⣤⣦⣤⣤⣤⣠⣠⡤⣠⣾⣿⣯⣾⠷⠛⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣉⢽⣿⣿⣿⣿⣿⣿
⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠷⠿⠿⠿⠿⠿⠿⢿⠶⣦⣤⣶⡶⡶⠾⡿⢿⢿⢿⠟⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠛⠷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⢦⠐⠂⠀⢸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣗⢃⡤⠈⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢹⡆⢀⠔⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⣿⣗⠀⠈⠁⢘⢻⠀⠀⠀⢀⠀⣀⠀⢀⣀⠀⠀⠀⠀⢰⠇⠀⠘⣇⠊⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠠⣾⣭⡿⡆⠀⡒⢋⡜⠀⠀⠀⣌⢣⠿⡿⠒⠢⠘⡆⠀⠀⠎⠠⡆⠀⠀⠈⠛⡆⠀⠀⢀⣿
⡆⢠⠂⠉⢙⣍⠉⢰⠣⡀⠸⠉⡖⠤⣀⠀⠘⡆⢰⡇⠀⠀⢸⠇⠀⠀⠀⠀⣧⡀⠰⣷⣿⠓⠒⠶⣾⡇
⢣⠈⣆⣰⠋⣼⠀⢸⠄⠻⣦⡇⠋⠀⡈⢷⣰⠁⢸⡇⠐⢠⡏⠀⠀⡘⠀⣸⠃⠙⡗⠦⠤⡆⠀⢰⡏⢷
⠈⢧⠘⣇⢀⣿⠀⢸⡇⠀⠈⠀⠀⠱⣧⠔⠉⠀⢸⡇⢠⡟⠀⠀⢰⠁⢠⡏⠀⠀⠳⣀⠜⠁⢀⡞⢀⣼⡇
⠀⠀⢧⡈⢯⣿⠀⠀⡇⠀⠀⠀⠀⠀⣹⡆⠀⠀⢸⣇⡾⠀⠀⠀⠃⠀⡾⠀⣠⠔⠊⠀⢀⣠⠞⠤⠴⠚⣧
⠀⠀⢸⢳⡈⢻⡄⢰⣧⢀⡤⢄⣢⢴⡟⠀⠢⣤⡟⣿⠁⠀⠀⣠⠀⠚⠓⠉⢀⣀⡤⢖⠋⣥⡂⠀⠀⠀⣿
⠀⠀⠸⡆⠹⡄⢻⡞⠁⠀⣈⡥⠤⢼⣇⢀⣀⡀⠀⠿⠒⠒⢶⣥⠀⣢⠴⠚⠉⢁⠔⠁⠀⠀⠀⠀⢀⡾⠉⢞⡒⠒⢲⣄
⠀⠀⠀⣇⢰⡟⢆⣻⡄⢈⡠⠴⠒⠋⠉⠉⠉⠙⣆⠀⠀⠀⠀⡍⠉⣧⠀⠀⡰⠁⠀⠀⠀⠀⢀⡴⠋⠉⠉⢧⠉⠛⠤⢤⣭
⢀⡀⠀⣿⢸⣇⠼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡄⢀⡀⠀⡇⠂⢹⡆⠈⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⣀⡼⠞⠛⠋⠉⠁
⠘⠋⠓⢾⡘⣇⠀⢹⡵⣤⠀⠀⠀⢀⡇⠀⡇⣇⢹⣧⡴⢿⠀⣿⢰⠈⢿⠀⠀⠀⠠⠚⠁⠀⢀⣠⠶⠛⠉
⠀⠀⠀⠀⡙⠿⡇⣸⠂⡈⢳⣄⣠⠾⡇⠀⡇⢹⠈⣿⡀⢸⡆⢹⠘⡀⠈⢧⡤⠀⣄⠀⠀⠚⠉
⠀⠀⠀⠀⠈⠢⣄⠽⣶⡺⢄⠙⣧⠀⡇⠀⡇⠈⠃⢘⢧⡔⠛⣲⠀⣠⢂⢼⡇⠀⡿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠙⢦⣣⡈⠳⣄⠀⠠⣀⡴⠁⠎⡇⠀⣼⠀⠃⣈⡾⠤⠚⠁⣐⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡉⠻⣄⠙⣧⠐⠑⠁⡌⣼⣃⡴⠇⢚⠩⢀⣠⡵⠖⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢌⠓⣾⡅⠣⠔⠚⠩⢀⣢⡥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢀⣶⣦⠶⠚⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠸⣿⣿⡿⣡⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣦⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣛⣛⣛⣛⣛⣛⣋⣀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⣭⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡧⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⠟⣷⡹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢱⡟⢿⡎⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⢿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠳⢦⡄⠀⢰⡶⠿⢶⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢠⡶⠛⠋⠙⠻⣦⡀⠀⠀⠀⠀⠀⢻⡄⢸⡇⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣤⢶⣿⠀⠀⠀⠀⠀⠈⣷⣤⣄⠀⠀⠀⢸⡇⢸⣧⣤⣾⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠀⠈⣿⡀⠀⠀⠀⠀⢠⡿⠀⢸⡇⠀⠀⢸⡇⠀⢸⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣸⣇⠀⠀⢈⣻⣶⣤⣤⣶⣟⠀⠀⣸⣇⣀⣀⣸⡇⣠⡿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠉⠙⣻⡿⠛⠉⠀⠀⠀⠀⠉⠻⢿⡋⠉⠉⣉⣹⣿⡋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣀⣀⣀⣴⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣟⣛⣋⣁⣘⣷⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣾⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣏⣉⣉⣉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣉⣉⣉⣹⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣺⣇⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠊⠁⠀⠻⣄⣡⡞⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠆⠄⡀⠀⠈⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁



⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⢤⡀
⠀⡔⠚⠉⠉⠁⡀⠀⠀⠀⢠⠔⠒⠈⠃
⠀⡇⠀⠀⠀⣰⣄⠀⠀⠀⡅⠀⠀⢱⠀⢀⡑⠄
⠀⠙⠶⢤⣺⠤⣽⣦⣀⠀⣙⣢⠄⠀⠀⠀⡨⠛⠀⠈⠀⠀⢀⣀⣤⣀
⠐⠒⠒⠛⣿⡀⠀⠉⠻⡉⠀⢃⠀⠀⠀⡜⠡⠊⢀⠂⠀⠀⠀⠀⠀⠀⢉⡉⠳⠦⠤⠀⠀⠀⠀⢀⣀⡠⠤⠴⠒⠚⢳
⠀⠀⠀⢸⡇⠙⢦⣀⠀⠈⠑⢼⡄⠘⣛⠇⠀⠔⠁⣀⠔⠀⠀⠀⠀⠀⠀⠈⢉⡠⠶⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠠⠤⠖⢺⣧⣤⣀⣈⠓⠦⡀⠀⠈⢂⣸⠂⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⡄⣀⣀⠉⠉⠙⠛⠳⠦⡌⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠐⠒⠘⠀⠀⠀⠈⠉⠐⠒⠀⠤⢼⠀⠀⡀⠀⠘⠀⠀⠀⠈⢰⣀⣀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⢀⠾⢀⣀⣉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⡀⢀⣀⣀⡴⠃⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⡆⢸⠯⡀⠀⣙⡤⠀⠀⠀⠀⠠⣄⣀⣤⣀⣀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣇⣿⣿⣤⢸⣞⠆⠆⣹⡇⠀⠀⠀⠀⠀⠹⣟⡻⢾⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⢀⣴⣌⣿⣟⣛⣩⠟⣾⡤⠖⠒⠓⠯⣌⠀⢀⠀⣼⣣⣿⣽⣿⣿⠄⠀⢐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣧⣿⣼⡿⢿⣿⡻⣶⣶⡗⠚⠂⡆⢀⠲⢶⣿⣿⣿⢿⣽⣿⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⠀⣠⠤⣶⣿⣿⣿⣆⣀⣽⠛⠉⠉⢯⠹⠁⠓⡲⠖⠏⢴⠞⢃⡼⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡶⠟⠲⢭⡿⠋⣹⣿⣿⠂⠀⢠⣶⣾⣶⣦⣤⣄⣨⡤⠤⠴⣿⡀⣱⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡞⣿⣔⢙⣀⣨⣼⠛⠋⣹⣷⠖⠉⠁⠈⠹⣏⠻⣿⡇⠀⠀⠀⣀⡼⣿⣿⠟⠂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣃⢹⣍⣿⣭⣤⠟⠢⢀⣿⡅⠀⢸⡇⠀⠀⢹⣆⣯⣤⡴⠶⢾⡁⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣯⢘⣿⡇⠤⠄⠀⣀⠞⢿⡧⠹⣿⡇⠀⠀⢸⠟⠉⠀⠀⠀⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠃⠀⠀⠀⢀⣾⢇⠘⣏⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⡿⣸⠄⠙⣤⣤⠀⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢁⡾⠀⢷⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠟⢋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡙⠓
⠀⠀⠀⠀⠀⠀⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠿⢺⢾⣏⢸⡹⢺⢸⣉⠰⢧⢸⡀⠀⡯⡇⣿⡰⣍⠰⣉⠇⡯⡇⣏⠇⣻⠄⢸⢺⣉⢾⣹⢸⢲⠇


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠉⠉⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣆⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡷⠀⠀⠠⣴⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣶⣤⣀⣤⣾⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠿⢿⣿⣿⣿⣿⣿⣦⣠⠤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠛⢿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⢤⣀⠀⠀⠉⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⠁⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡾⠛⠛⠛⠛⠛⠛⣇⠈⠉⠉⠉⠉⠉⠁⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⡇⢀⣀⣀⣀⣀⣀⣉⠉⠉⣉⡉⢉⡉⠉⣉⡉⡉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠁⢸⠏⢉⡭⡍⠉⣿⠈⢿⣿⣿⣾⣷⣾⣿⠿⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⣿⢀⡼⠛⢧⢀⡟⠀⠀⢠⣾⣽⢿⡧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣯⣬⣶⣶⣮⣼⡇⠀⠀⠀⢾⣿⠇⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣆⣤⢠⢴⢀⣠⡄⢤⣐⡇⢠⢄⣤⣠⢄⡠⡄⡄⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠟⠥⠸⠼⠸⠳⠄⠾⠷⠇⠸⠈⠧⠻⠄⠣⠗⠇⠣⠞




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣾⣿⠀⣿⡟⠛⠃⢸⡟⠛⢷⡄⠘⣿⡟⠀⣴⠟⠛⠇⠀⣸⣿⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠿⢹⣿⠀⣿⡏⠙⠁⢸⡇⢀⣼⡇⠀⣿⡇⠈⣿⣀⠀⡀⢰⣿⣼⣿⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠋⠀⠙⠛⠛⠁⠘⠛⠛⠉⠀⠘⠛⠛⠀⠈⠛⠛⠁⠙⠁⠀⠈⠃⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⠀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢉⣿⠀⢸⣏⣉⡉⢰⡿⠉⠙⠃⣾⠏⠉⢻⡆⢸⣟⢉⣿⠆⢸⡟⠉⢻⣆⢰⣿⣉⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣧⡀⢸⣏⣉⡀⠸⣷⣄⣠⡄⢿⣆⣀⣼⠇⢸⣟⠻⣧⡀⢸⣧⣀⣼⠏⢠⣉⣉⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠈⠉⠉⠁⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠁⠀⠈⠁⠀⠉⠉⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣤⣀⣤⠶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡾⠁⢀⡄⠀⠙⠁⡀⠀⠀⢻⡀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣉⣉⡉⠀⣤⣿⣤⡾⢻⡄⣤⡾⠳⣤⣤⣾⣤⠄⠉⣉⣉⣉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⡀⢀⠀⠀⠙⢦⡀⢿⠇⠀⢀⣴⠟⠀⢀⣀⣀⣀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢈⠀⢁⠈⠁⠀⠀⠀⠙⣦⣀⣴⠟⠁⠀⠀⠻⣥⣤⠿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠅⣿⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠰⠶⠶⠶⠶⠶⠖⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣿⠀⣾⠀⣾⠀⣀⠀⣀⠀⠀⠀⠘⢛⣛⣀⣛⣛⡓⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⠀⠀⢀⣈⣉⣉⣉⣉⣉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠂⣿⠀⠹⠦⠿⢤⠿⢤⠿⠦⠿⠤⠿⠀⠀⠀⠠⠤⢤⡤⠤⠤⠀⠀⢸⡇⠶⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇⠀⠈⠙⠳⣦⣀
⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣥⣤⣤⣤⣤⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠈⢃⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣬⠁
⣤⡤⠤⠤⠤⣶⠶⠟⠠⠄⠙⠶⣶⡦⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣦⣀⣀⣸⡏⠉⠉⠉⠉⢹⡇⠀⠀⠀⣿⡦⠶⠶⠶⠶⣶
⣿⢰⡶⠶⠶⢿⢤⡤⣤⠴⠦⡤⡿⠶⠶⢶⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⢹⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⢻
⣿⢸⡇⢀⡴⠦⢦⡀⠰⠶⠆⠰⠶⠶⠄⢸⡇⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⢀⣀⣀⡀⢸⡇⠀⠀⠀⣸⡄⠀⠀⠀⠀⢸⡇
⣿⢸⡇⠈⠳⠶⠞⠃⠰⠶⠶⠶⠶⠶⠆⢸⡇⢸⠀⠀⡾⢷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⢈⣭⣭⡁⢸⣧⣤⣤⣤⣿⡇⢠⡞⢻⡆⢸⡇
⣿⢸⡇⠀⣤⢤⣤⠤⠦⠤⣤⠦⠤⢤⡄⢸⡇⢸⠀⢐⡷⣾⠀⠀⠀⠀⠀⢸⡇⣤⠀⠀⢸⡇⢸⡇⢸⡇⢸⡧⠤⠤⠤⣿⣧⠀⣿⠈⣷⠈⣇
⣿⢸⡇⠀⣿⠲⡿⠶⠶⠲⡷⠖⠶⢾⡇⢸⡇⢺⠀⠘⣧⣼⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⡇⢸⡇⢸⡇⢸⡇⢠⡄⠀⣾⣿⠀⣿⠀⣿⠀⣿
⣿⢸⡇⠀⣿⢴⣿⠦⠶⢶⣷⠶⠶⣾⡇⢸⡇⢸⠀⢸⡇⢸⠀⠀⠀⠀⠀⢸⡇⣿⢠⡄⢸⡇⢸⡇⢸⡇⢸⡇⠸⡇⠀⣿⣿⡀⢿⠀⣿⠀⣿
⣿⢸⡇⠀⠿⠶⠷⠶⠶⠶⠷⠶⠶⠾⠃⢸⡇⢸⠀⢸⡇⢸⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇⢸⡇⢸⣇⣸⡇⢸⡇⢠⡆⠀⣿⢻⡇⢸⡇⢸⡆⢸
⣿⢸⡇⠠⠶⠶⠶⠶⠄⠤⠴⠀⠀⠀⠀⢸⡇⢸⠀⢸⡇⢸⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇⢸⣧⣬⣭⣭⣥⣼⡇⠸⠇⠀⣿⢸⡇⢸⡇⢸⡇⢸
⣿⢸⡇⠐⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⢸⡇⢸⠀⢸⡇⢸⠈⠳⣄⠀⣀⢸⡇⠿⠸⠇⢸⡇⢀⡴⢤⡀⢸⡇⠐⠆⠀⣿⠈⣇⠈⠛⠛⠁⢸
⣿⢸⡇⠈⠛⠛⠛⠛⠛⠁⠈⠃⠉⠀⠃⢸⡇⢸⠀⢸⡇⢸⠀⠀⠙⠷⠋⢸⡷⠶⠶⠶⢾⡇⠘⠷⠾⠃⢸⡗⠒⠒⠒⣿⠀⣿⢛⣛⣛⣛⣙
⣿⠘⠟⠲⠶⠒⠒⠒⠚⠲⠚⠒⠶⠓⠖⠺⠃⣸⠀⠘⣧⣼⠀⠀⠀⠀⠀⢸⡗⠒⠒⠒⢾⡿⠒⠒⠒⠓⢿⡟⠛⠛⠛⣿⠀⣿⡋⣉⣉⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶
⣿⣿⣿⠁⠉⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⣠⠤⠤
⠀⠀⠀⠀⠂⠀⠀⠀⠘⡀⠀⠘⠀⠀⠀⠀⠀⠈⠁⠐⠀⠂⠀⠄⠀⠵⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠁⠤⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⢤⠀⠀⣀⠀⠀⠀⠀⡀⣠⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣷⣶⣠⣠⡟⣂⣤⢀⣀⣿⠎⢸⡟⢹⣦⣤⢄⣸⣿⣧⣇⡤⠀⢀⠆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠟⣿⠷⠿⡿⠿⡥⠿⣿⢧⠀⠸⣇⡾⠿⢿⠿⠿⡿⡾⢿⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⠆⠶⠶⠶⠰⠴⠶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠛⠋⠈⠛⠈⠛⠛⠃⠀⠛⠘⠁⠘⠛⠁⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠀⠐⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠛⠉⠤⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠚⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⣦⠖⠁⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐
⡏⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⠠⣴⣧⠖⠀⠀⠀⠀⠠⠘
⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠘⢿⠏
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠒⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠁⠀⠀⣠⣆⡠⠀⠀⠀⠀⠀⠈⠄⠁⠀⠀⢀⠀⠀⠀⠀⣴⣧⠖⠁⠀⠈⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⡸⣿⡿⠀⠀⠀⠈⡀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠠⠊⠿⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⢹⠀⠀⠀⠀⠀⠘⠐⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠊
⠀⠀⠀⢸⣷⣶⣦⡀⢀⢰⣿⣷⠀⢰⣿⣿⣿⣷⠀⣿⣷⢰⣿⣿⣷⠀⣾⣷⡄⣾⣿⡄⠈⣴⣿⡆⢀⣾⣿⣶⠄⢀
⠀⠰⠀⢸⣿⣿⣿⣷⠀⣸⣿⣿⡇⠘⠛⣿⣿⠛⠀⣿⣿⢸⣿⣏⡁⠄⣿⣿⣷⣿⣿⡇⣸⡿⠛⠁⢸⣿⡟⠋
⠀⠀⠀⠸⣿⣿⣿⠏⠀⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⢸⣿⣿⠇⠀⣿⣿⣿⣿⣿⡇⣿⡇⠐⠀⢸⣿⣿⡇
⠀⠠⠀⠀⣿⣿⠁⢀⢸⣿⣿⣿⣿⡇⠀⣿⣿⠐⠀⣿⣿⢸⣿⣷⣤⡀⣿⣿⡿⣿⣿⡇⢿⣷⣸⣷⢸⣿⣷⣤⡀
⠀⠀⠀⠀⠻⠿⠃⠉⠸⠿⠁⠹⠿⠇⠀⠿⠟⡀⠀⠿⠟⠘⠿⠛⠛⠁⠿⠿⠃⠻⠿⠃⠈⠿⡿⠟⠘⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢂⠀⡀⠀⠐⠂
⣧⠔⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⣀⣷⣀⠔⠀⠀⠀⠀⢡⡀⠁⠀⠠⠯⠶⡀⠠⠻⠇⡔⣲⠆⡔⠓⢼
⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⣿⠇⠀⠀⠀⠀⠀⠺⠀⠒⠂⠀⠀⠂⠂⠀⠖⠊⠉⠁⠀⠃⠠⠛
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⡀⠀⠀⣀⠂⠈⡀⠀⠂⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠘⣿⠟⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠⠘⠀⠀⠀⠀⠀⠐⠀⣤⣧⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠐⠀⠀⠠⠘⢿⠟
⢀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⣤⣧⡔⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄⠬⠀⠀⠈⣷⡄⠀⠀⠻⠉⠉⠀⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣾⣏⣀⠐⠀⠀⢻⣇⠀⢰⡄⢃⠀⠀⢦⣠⣿⠷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣦⣼⣿⣿⡏⠘⢀⢋⠀⣾⣿⠀⠈⡇⠈⢀⠀⣾⣿⣇⢀⣾⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠻⣿⣿⣵⠃⢸⢸⠀⣿⣿⠶⠐⡇⠨⢸⠀⣿⣿⣿⣿⡇⣼⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠖⠈⠳⣽⠀⠀⣼⠀⣿⣿⠄⠀⡧⠀⡏⠀⡟⢛⣿⠿⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⠉⠲⣌⠙⠄⢿⣀⣿⣿⣆⠀⠇⠀⡄⠐⢀⡼⠛⠒⢶⠾⠿⣾⣇
⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠁⠈⠙⣦⡜⣿⣿⣿⢻⣿⣇⠀⡁⡀⠈⠀⠀⠀⠀⠀⠀⠹⣏
⠀⠀⠀⠀⡀⠐⠆⠠⠞⠓⠀⡀⠒⠒⠀⣿⡷⠒⢸⣻⣾⠿⣿⣦⣿⠀⠰⠀⠀⠈⠀⠀⠄⡀⢹⣷⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡄⠀⢸⣿⠇⠠⡾⠛⢛⠳⠮⡙⣿⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⢻⢳⡀
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⣿⡿⠂⠀⢹⡟⢓⠻⠕⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠄⠀⢰⣿⣧⣀⣴⡀⢹⡇⠘⣷⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⡆⠀⠛⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠟⣿⡍⢱⠋⠀⢸⡇⠐⠹⣿⠈⡙⠁⠀⠠⠀⢨⠀⠐⠃⠀⠀⣏⠘⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠉⢐⣩⠞⠋⠔⠁⠀⢰⠘⠇⠀⢰⣮⣶⣿⡶⣥⡀⢀⠀⠀⢀⠀⠀⣴⡏⢠⡇
⠀⠀⠀⠀⢱⠀⠈⠀⢀⣠⡶⣛⣀⣀⣰⣖⢠⠤⡜⠒⠂⠠⢿⡛⠋⣫⡛⠄⠙⢾⣄⠀⠈⢁⣲⣿⣦⣾⠁
⠀⠀⠀⣄⡸⠀⣰⣾⡿⠛⠛⣇⠙⠛⢿⠌⠃⠴⢦⠀⠂⠰⢼⡟⠉⢠⡿⡆⠑⠒⢮⠷⣤⣀⣨⣿⣿⡿
⠀⠀⠀⠘⣄⣼⣽⡿⠀⠀⠘⠅⠀⢠⣄⢱⣜⢞⠻⠀⠀⢶⣾⢫⣾⡿⢁⢀⠆⡀⢘⠀⢠⢛⣛⣿⣿⠁
⠀⠀⠀⠀⠘⣿⣿⣷⠀⡴⣄⠀⠘⢤⣿⣿⣿⡦⠀⠀⠀⣼⣧⣿⣿⣴⡯⢀⡝⠁⡬⠀⣼⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠙⢾⣿⡗⣼⣬⣦⣄⡀⢙⡻⣿⣿⡆⠀⣤⣿⣿⣿⣯⣭⠴⠟⢀⡾⠁⢰⡿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣗⢿⣿⣿⣿⣿⣶⣿⣷⣮⣵⣿⣿⣿⣿⡶⠮⠶⠋⡀⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣮⣭⣙⣿⣿⣿⣿⡿⢿⣿⣿⣯⣥⣄⣤⣴⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠿⠿⣿⠿⠟⠁⠘⠻⢬⣿⡿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡽⠂⠀⠸⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⢻⠀⠀⠀⠀⠀⠀⢰⢻⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡈⡇⠀⠀⠀⠀⠀⢸⣸⠃⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠙⠁⠀⠀⠀⠀⠀⠘⠃⠀⣠⠃
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣤⡀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠚⠁

⠀⠀⠀⠀⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⣺⣼⡀⠀⠀⠀⠀⠀⢀⣿⡀⡏⠩⠉⢹
⠀⠀⠀⣠⠙⢋⣄⠀⠀⠀⠀⠀⠀⣀⣽⡯⣄⠀⠀⠀⠀⠀⠀⣀⡙⠋⣀⠀⠀⠀⠀⢠⣿⣿⠛⡯⠠⠀⠸
⠀⢠⣾⣿⡿⢿⣿⣷⡀⠀⠀⢀⣼⣿⠀⠀⣽⣷⡄⠀⠀⠀⣴⣿⣷⣷⣿⣿⣿⠀⠀⠀⢸⣿⠀⡏⠩⠀⢸
⠀⠐⠛⠒⠒⠒⠚⠛⠂⠀⠀⠐⠒⠚⠓⠛⠓⠒⠂⠀⠀⠀⠛⠓⠚⠛⠛⠛⠓⠀⠀⠀⠘⠛⠀⠛⠛⠛⠛

⠀⠀⢸⠉⣩⣉⣉⠀⠀⠀⠀⠀⢠⡏⢉⢉⠉⠉⠀⠀⠀⠀⠠⢸⠉⣉⡭⣝⡀⠀⠀⠀⢠⠈⠉⠉⡩⢭
⠀⠀⢸⠈⠉⢹⠉⠉⠀⠀⠀⠀⢸⡇⠘⠣⡀⢀⠀⠀⠀⠀⢰⢸⠀⢻⠭⣿⠁⠀⠀⠀⢸⠀⠀⢠⣷⢺⡆
⠀⠀⠸⠀⠀⠈⠠⠀⠀⠀⠀⠀⢸⠇⠀⠀⠁⠬⠀⠀⠀⠀⢸⠸⠀⠀⠙⠱⠀⠀⠀⠀⢸⠠⠀⠈⠉⠩⠁
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⢀⡀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⣊⣁⣒⣨⣭⣑⠀⠀⠀⠀⡄⠀⠀⠀⡄⢁⢸⡀⠀⠀⠀⡔⢒⣒⣒⠲⡀⠀⠀⠀⠀⡏⢀⣀⣀⢸
⠀⢸⣿⡿⡯⢽⢿⣿⡇⠀⠀⠀⡇⢠⣷⡀⣷⢸⢸⠃⠀⠀⣜⣀⣀⣘⣀⡠⢆⠀⠀⠀⠀⡏⠈⠪⠂⢸
⠀⢸⣿⣷⣗⣺⣾⣿⡇⠀⠀⠀⡇⠈⠈⠁⡏⠄⠘⠀⠀⠀⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⣷⣤⣄⣤⣼
⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀
⠴⠁⣈⢱⢔⣂⣀⣀⠀⠀⠀⠒⣤⡄⠂⢉⣑⣀⡀⠀⠀⠀⠀⠀⢠⡤⣤⡄⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈
⠐⠢⡥⠊⠀⠀⣠⡸⢲⠀⠀⠀⠀⠠⣀⠸⢿⠾⠆⠀⠀⠀⠀⠀⢸⣷⣾⡇⡀⠈⠁⠀⠀⠀⠀⡳⠤⠤⠚
⠀⠀⠷⠶⣶⣶⠶⠾⠁⠀⠀⠀⠀⠀⠠⢈⣽⣭⡅⠀⠀⠙⠛⠁⢸⡟⠻⡇⠀⠈⠁⠀⠀⢀⣾⠇
⠀⠀⠀⠘⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠚⠘⠃⠘⠃⠀⠀⠀⠀⠀⠈⠓⠚⠃⠀⠈⠉⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⠶⢶⣯⣭⣭⣤⣤⠤⠔⠒⢒⣂⣐⣒⣦⣤⣤⣤⠤⠦⠤⢴⣖⣒⣂⣀⣀⡀⣀⣤⠤⠤⠄
⠀⠀⠀⠀⣴⣯⡹⡏⠁⠰⠶⠚⠛⠛⠛⠉⠉⠉⠉⠙⠉⠐⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠠⠤⠶⣶⠂
⠀⠀⠀⠀⣿⢹⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡀⠀⣀⣠⣶⠄⢠⠀⠀⢀⠀⠀⣰⣿⡀⢠⣶⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣿⣻⡟⡇⠀⠀⠀⠀⠀⠀⢠⡄⡾⣇⠀⢀⣿⡄⣴⣿⡿⠋⢿⡁⠀⣿⠟⠁⠀⢸⣇⠀⢸⡆⢠⡏⠘⠁⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⢿⣿⣇⠃⠀⠀⠀⠀⠀⠀⢸⣿⠁⡿⠀⣼⣿⡇⠉⣿⡇⠀⢸⡇⠀⣿⠀⠀⠀⣿⣿⡀⢸⡇⢸⠁⠀⠀⢸⣧⣴⠄⠀⠀⠀⠀⠀⠀⠈⣿⣽
⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⡇⠀⣿⢹⣿⠀⢹⡇⠀⢸⡇⢀⣿⡿⠃⠀⢻⡻⣧⢸⡇⢸⠀⠀⠀⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡇⢻⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⢸⣿⣾⣿⡇⢸⡇⠀⢸⡇⠈⣿⠀⠀⠀⢸⡇⢻⣾⡇⢸⡀⢰⡆⢸⡇⢀⣀⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡏⠁⣿⡇⢸⡇⠀⢸⣇⠀⣿⣠⣶⡶⢸⡇⠀⢻⡇⢸⣧⣾⠇⢠⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢽⠁⠀⢸⡇⠀⠃⠀⣼⠟⠁⣿⠿⠛⠁⠘⠁⠀⠈⠃⠀⠙⠋⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠇⣧⡸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠶⣶⠿⠶⠲⣾⠿⠟⠉⠉⣷⣧
⠀⠀⠀⠀⠰⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠉⠉⠁⠐⠛⠋⠀⠉⠉⠛⠒⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠷⣄⣀⣀⣀⣀⣀⡶⠖⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠛⢲⣦⡀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣙⡄⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⢠⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣏⠁⠀⠀⠹⣷⡀⠼⣣⠴⠃⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣰⠏⢠⣿⠀⠀⠀⠀⣿⡇⠀⣀⣤⣶⡶⠾⠿⠟⠛⠛⠛⠉⠉⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⡏⠀⢸⡟⠀⠀⠀⢀⣿⡷⠚⠉⢹⡇⠀⡄⠀⠀⠀⠀⢀⣄⢀⡾⢿⣾⢫⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⡟⠀⠀⠀⣾⠃⣰⢆⡞⡗⣸⣇⢾⡟⣼⠃⣸⣿⢋⡦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⣀⣾⢟⣠⣄⡀⢠⡿⢠⣿⢸⡟⢡⢻⡟⠸⡷⠻⠶⠋⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠋⣱⡿⢉⣿⠇⣸⣧⠎⠷⠏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣣⠎⠹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠁⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⡀⠀⠀⠠⠀⢄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠇⠐⠀⡈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠘⢐⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠖⠦⠠⠀⠀⠚⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⣀⠄⠀⠡⣀⠐⠂⠂⠀⠠⣀⡟⠁⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠐⠈⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡆⢀⠢⠀⠉⠑⠂⡽⠛⡋⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢸⠀⠀⠀⠀⠀⠈⠀⡂⠈⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠁⠀⠀⢀⠇⠀⠇⠀⠀⠁⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠄⣠⠔⠋⠀⢸⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠈⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠐⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠐⡒⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠁⠀⠀⠀⢀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠠⠒⠀⠀⠀⠀⠀⢀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠆⠠⠀⠐⠀⡃⠠⠀⡓⠂⠰
⠀⠀⠀⠀⠐⡦⡀⠀⠱⠀⠀⠀⡁⠀⠁⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠄⠀⠈⠀⠉⠀⠀⡀⠉⠁⠀⠀⡆
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠢⢀⠀⠁⠤⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⡀⠡⡀⠀⠀⠀⡃⠀⡃⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠚⣋⠀⠄⠆⡈⢿⠉⠂⠀⠀⠀⠀⠀⠀⠐⠀⠘⠂⠀⠀⠈⡀⠤⠄⡈⣁⣀⠄⠤⠈⣀
⠀⠀⠀⠀⠈⠄⠀⠀⠀⢠⠋⠙⣆⠈⠀⢀⣼⠀⠀⠈⠢⡀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠈⢀⢀⡠⠌⠳⠀⠃⠀⠀⠙⠈⠘⢢⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠁⠀⠀⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⡇
⠀⠀⠀⠀⣀⣀⣀⣼⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⢠⠞⠉⠉⠉⠁⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⡄⠀⠀⣿⠀⠀⠀⡇
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣿⠀⠀⠀⡇
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣿⠀⠀⠀⡇
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠀⠀⡇
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠖⠶⠖⢶⡀⠀⠀⠀⠀⠰⡶⠶⠲⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡇
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠙⠒⠒⠚⢷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠳⣄⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠬⠷⡄⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠢⡀⠀⠀⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣈⣲⣄⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣈⡍⠉⠉⢹⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⢸⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠧⠼⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣼⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠭⠭⠍⠁⠀⠀⢿⣀⣀⠀⢀⣀⣸⠇⠀⠀⠉⠭⠭⠭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣀⣺⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⠹⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⣠⣴⣤⣶⣦⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢰⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣴⣤⡿⠟⠁⠀⠀⠤⠀⠀⣀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠚⠟⠀⠀⠸⠋⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠠⡤⠄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣹⣿⣿⡇⠻⢶⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣵⠆⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡄⣼⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⢇⠙⢏⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⠖⢉⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠈⠁⠀⠀⠀⠙⠂⠉⠂⢀⠀⠀⠀⠃⠀⢄⠀⠀⠀⠀⠀⠀⣺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠘⠁⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡄⠀⣨⠀⠀⢠
⠀⠀⠀⠀⣠⠚⢤⡀⠀⠀⠀⠀⠀⠀⠀⣸⣡⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⣧⡟⠀⠀⠀⡄
⠀⠀⢀⠞⠁⠀⠀⠈⠑⣄⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡸⠁⠀⠀⠀⡇
⠀⢀⠎⠀⠀⠀⠀⡠⢾⣿⣷⢠⡴⠃⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠁⡆⠀⠀⠀⡇
⠀⠊⠀⠀⠀⠀⠈⠠⡀⠙⠻⠏⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⢀⡇⢀⣇⠀⢷⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠛⢧⠈⠁⠀⠘
⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘
⠀⠀⠀⠀⠀⠈⠙⠒⠦⣤⣀⠀⠀⠉⠒⠄⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⡀⠀⠈⠒⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠥⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣡⣤⡄⡀⢠⡤⢄⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠃⠀⠐⠀⢀⠀⠀⠀⠀⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡇⠈⠉⠀⠸⠀⠈⠉⠀⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⢢⣀⣀⣀⣤⠚⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠙⢦⠀⢠⠞⠁⠀⢀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠘⠲⢄⣳⣃⠴⠚⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢰⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣰⡇⠀⠀⡀⠀⠀⢸⠀⠀⠀⣀⠀⠀⣷⡀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⣰⢿⢀⡤⠊⠁⠉⠉⠹⠉⠉⠁⠉⠢⣀⢸⢷⡀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⢄⡀⠀⠀⠀⣰⣃⣾⣼⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⣸⣇⣳⡀⠀⠀⠀⣀⠤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠥⣀⠀⠙⣄⡠⠚⠉⠁⠀⠀⠈⠑⠒⠦⠤⠼⠤⠤⠖⠒⠉⠀⠀⠀⠉⠙⠦⣀⡜⠁⢀⡠⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠱⡔⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡑⡴⠁⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣜⢰⢁⡶⢠⠇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠢⣤⠒⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢧⠰⡄⢱⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⣠⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠶⠔⠂⠁⠲⢄⠀⠀⠀⠀⠀⠈⠒⢡⡀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡆⠀⠀⠀⠀⠀⠙⠒⠤⣀⠀⠀⠀⠀⢉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠿⠤⠤⠷⠤⠤⠴⠶⠶⠶⠦⠤⠴⠷⠶⠖⠒⠉



⣿⠿⠿⠿⡿⣟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣿⣟⣻⣿⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⢀⣴⠀⠀⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢺⡀⠀⢸⢹⣈⡃⣀⣷⠀⠨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣜⠷⣟⡬⣃⣼⣿⣿⣿⣻⣽⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡯⣭⢞⢽⢳⣷⣿⣿⣿⣿⣿⡿⣿⣽⡀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⢬⣾⣿⣿⠿⠿⠛⢿⣿⣿⣦⣿⣽⡄⠀⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠉⠻⣿⣿⣿⠃⢀⠀⠀⠀⢈⠛⠿⣿⣿⣿⣦⣇⡐⣀⢡⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢴⣂⡈⠁⠠⣿⣿⠁⠀⠈⠉⠀⠈⠁⠀⠀⠈⣿⣿⣿⣻⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⠉⠉⠁⠀⢾⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⢉⣹⠈⢠⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡧⠂⠾⠿⢠⣾⣿⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣿⡁⣨⡀⠘⠇⠀⠳⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠹⢟⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢈⣧⡄⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⢹⡏⠩⠙⢳⡄⡨⢁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⠈⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠈⢌⠸⠋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡛⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⡄⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠘⣿⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠐⣦⠀⢀⠀⠀⠀⠀⠀⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣿⣤⣤⣤⣤⣴⣯⠀⠀⠀⠀⢀⣿⣿⠿⢿⣿⣷⣤⢸⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣻⣿⣿⣿⣿⣿⣉⣩⣿⣿⣿⣀⣀⢘⣿⣿⣿⣏⡀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢻⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠿⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠭⠉⠉⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢇⣼⡟⢛⣿⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣷⣠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⡟⠀⠈⠀⣄⠨⣿⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡇⠀⣾⡄⢰⣄⣨⣝⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⢀⠟⡷⣡⣾⢿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⢘⠀⢰⣿⠁⢠⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⠀⢀⣿⣿⠀⠀⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⣿⣿⣿⣿⣿⣶⣴⣮⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣤⣿⣿⣇⢻⣿⣏⠀⢀⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⠿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⣿⣿⡜⣿⣿⣄⢰⣿⣿⡇⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡴⡟⢿⣿⣿⣿⠛⠑⠋⠱⣏⠙⠋⠛⠙⠙⠛⠛⠉⠁⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⣰⠀⢁⡀⠀⠀⠀⠀⠀⠘⡓⢦⣀⣀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⣿⠆⡉⠀⠀⠀⠀⠀⠘⠀⣏⡨⠁⠘⡋⠙⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣧⢹⣆⢷⣄⣐⣀⣠⠄⠀⠀⣭⣷⣦⣌⣁⣀⣀⣂⣀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⠙⣆⠻⣄⡙⡿⠛⠀⠀⠀⢀⣿⣌⣨⡉⠙⠛⠛⠛⢻⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⡟⠉⠉⠀⠠⣐⢦⣙⠛⢒⠆⣀⣡⡾⢛⠉⠉⡑⣀⣤⣤⣚⢿⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⡟⣱⡥⠾⢴⣿⢹⣶⣶⣝⣿⣷⢹⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠿⠿⠟⠥⠛⣉⣠⠬⢻⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠁⠈⢳⣦⡌⠀⣾⢠⣭⣡⠶⣼⠇⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢷⡘⠁⠸⠚⠁⠀⠙⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣄⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⣿⠀⣶⣾⣿⣷⣶⡆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣈⣿⣋⡀⠀⠀⠀⠀⣿⠀⠛⢻⣿⡟⠛⠁⠀⢰⠆⠠⠤⠤⠤⠤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⣿⣿⣿⣿⡄⠀⠀⠀⣿⠀⠀⠈⠉⠁⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠟⣿⣿⣿⡟⢿⣄⠀⠀⣿⠀⢀⡀⣀⣀⡀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠋⠀⣿⣿⣿⡇⠈⠉⠀⠀⣯⠀⠀⠀⠀⠉⠁⠀⠀⠸⠇⠐⠒⠒⠒⠒⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⣿⠀⠠⠴⠤⠶⠄⠀⠀⢰⡆⠠⠤⠤⠤⠤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⣿⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⠇⢹⡿⠀⠀⠀⠀⣿⠀⠈⠉⠉⠉⠁⠀⠀⠈⠁⠈⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣤⣤⣤⣤⣤⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠦⣀⡀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⣼⢸⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⡞⠙⣦⣤⣤⣀⠀⡜⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢊⢾⢸⣿⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⠦⠈⠉⢸⣿⣇⠇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⢺⢸⣿⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣄⢈⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣶⣷⡀⠀⠀⠀⠀⠀⢠⣦⣾⣿⣧⣼⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣹⣋⣤⣀⠈⠲⡀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣷⡄⠀⣴⣄⣄⣿⣿⣿⣿⣿⣿⢸⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠈⢣⠀⣿⡀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣼⣇⠀⠀⠀⠈⡇⠸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⢸⠀⠀⠀⣠⠄⢠⣖⣽⣶⣯⣽⣿⡀⠀⣀⠀⡇⠀⢻⡄
⣿⣿⢟⡿⣿⢿⢟⣽⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⢸⠄⣀⡴⢯⣉⣩⢇⣴⢾⡭⠛⠙⣷⡋⠉⠙⡞⠀⠘⣇
⠟⡡⢋⠞⡵⣫⣾⡿⣗⠒⠻⣿⣿⣿⣿⢸⠀⠀⠀⢸⠅⡈⠉⠙⠶⠶⠶⠶⠿⣍⣉⣉⣉⣁⣀⣀⡇⠀⠀⠘⡆
⣘⠥⠓⠊⠉⠹⣿⡿⠿⠁⠘⠙⢻⣿⣿⠸⠀⠀⠀⢸⠭⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⢹⡄
⠁⠀⢀⠀⠀⠀⠙⣿⠆⠀⢄⡀⣩⣿⣿⠀⠀⠀⠀⢸⡭⣒⠤⠀⠀⠀⠀⣀⡤⠄⢲⡶⠂⢘⣿⣿⣆⠀⠀⠀⠈⣷
⣴⡪⠕⠀⠀⠀⠀⢹⡤⢔⣒⣛⡛⠻⢿⡀⠀⠀⠀⢸⡫⢔⣩⣢⠴⠚⠛⢧⡤⠴⠛⠁⠀⢸⣿⣿⣿⣆⠀⠀⠀⠸⡄
⣟⡪⠀⠀⠀⠀⠈⠛⣞⠁⠀⠀⠈⠑⠦⣌⣉⢙⣒⣾⠾⠛⢉⡠⠀⠀⠀⠀⣷⠒⠒⠒⠛⠛⠛⠛⠿⣿⣶⣶⣦⣤⣷⣀⣀
⣗⠍⠀⠀⠀⠀⠀⠀⠈⢯⢷⡆⢀⢀⠀⠀⠉⠉⠈⠀⣠⣴⣿⣮⣢⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿
⣳⠅⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⠿⠾⠿⠿⠛⠛⠻⠶⢤⣤⣴⣶⣶⣶⣶⣤⣄⣀⣀⣤⣤⣭⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⡏⠩⠿⠿⠿⠿⠄⠀⠀⠀⠠⠶⠒⠒⠶⠄⢸⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣄⠘⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢇⣠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣄⠀⠀⠀⠉⠍⠍⠀⠀⠀⣠⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢀⠈⢉⠛⠛⠛⠷⣤⡀⠀⠀⠀⢀⣤⠞⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⡌⠱⡏⢣⠋⢣⠀⠀⠀⠈⠙⠻⠶⠟⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠉⠓⢄⠀⢨⠀⠸⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⢸⣿⣵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢓⡂⢀⣿⣻⣦⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠲⢦⣄⡈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣂⣉⣉⣁⠟⠫⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠙⢸⣈⠔⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡾⠉⠹⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⡴⠖⠛⠛⠛⢻⣄⣀⣀⣀⣀⣀⣀⡽⠛⠛⠛⠓⢶⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠆⠀⠤⠤⠤⠤⠤⠀⠀⣠⠖⠛⠉⠛⠳⢦⣀⡴⠞⠛⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣶⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠶⠃⠀⠒⠒⠒⠒⠒⠀⢸⡄⠀⢠⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣸⢻⣀⣿⠀⣤⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠁⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠿⢸⣿⠻⣷⠋⠉⠉⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠁⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⠀⢶⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢀⣤⣤⡌⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢠⣀⣠⠀⡄⠀⣄⣀⡄⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠢⠤⠴⠂⠀⣠⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣏⣀⣀⣀⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡆⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢻⣸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣠⠇⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⡀⠀⠀⠙⢦⣀⢀⣀⣀⣀⠀⢀⡼⠋⠀⠀⣠⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠀⠀⠙⢦⣀⠀⠀⢉⣙⠒⣄⠉⠛⠉⠀⠀⣀⡴⠃⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠙⠓⠲⠦⣄⣈⠛⠒⠯⣌⣉⣁⣀⣠⡤⠶⢚⣁⣠⠤⠴⠖⠒⠂⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⢀⣠⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠷⠶⠤⠤⠤⠶⠶⠖⠚⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⣿⡿⠀⠀⢠⣾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠾⠟⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢶⣄⣀⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡀⠀⣀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⡀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⠉⠑⠀⠀⠘⠿⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⠛⠋⣽⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢁⡈⢹⡄⣀⡴⠊⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠁⣰⠛⢻⡛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠋⢁⣀⡀⠈⢳⠐⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠈⠋⠁⠀⠈⢙⣶⡇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣀⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡠⠀⠀⠀⣌⡿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡉⠉⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡘⠂⠀⡠⣼⣿⠕⠉⠧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢊⡟⠁⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠒⠻⡏⠉⢛⣻⡿⠋⢁⡠⠊⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠓⠀⠀⢀⡝⠀⠀⠀⠀⠀⢀⡴⢹⢀⡟⠀⠀⢻⡀⣼⠏⠉⠉⠁⢀⠖⢀⡠⠖⠁⠀⢹⣆
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣀⡠⢤⣀⡝⢤⣠⣤⠞⠑⠚⠁⠘⣜⣰⠇⠀⠀⢸⣷⡏⠀⠀⠀⢀⠎⠐⣯⡴⠶⠻⠻⠻⣿⡄
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠡⠄⡠⢤⣄⣀⣀⣨⡏⠀⠀⢠⡟⣿⠏⠀⠀⢀⢎⡞⣸⠃⢀⠀⠀⢀⡄⣸⠇
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢸⠉⠓⠦⣄⣀⣤⠶⠖⠶⢦⣭⣩⣺⡇⢀⣠⢟⣼⠏⠀⠀⠠⢂⠎⢠⡇⠐⢁⡠⠔⠋⣰⣿
⠀⠀⠀⡾⠀⠀⠀⠈⡇⠀⠀⢸⣦⣤⣞⡯⢁⣈⠉⢲⡛⠛⠉⠉⢻⠻⠿⠿⢛⠏⠀⠀⠀⣠⢋⡔⠉⠁⠉⠁⠀⠀⣰⡟⣾
⠀⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⢸⡋⠁⠈⠳⣵⣤⡀⠀⠑⠶⢤⣤⣟⣀⣀⣠⣏⣀⣀⣀⣴⣥⣾⣀⠀⠀⠀⠀⣠⣾⣟⢴⣏⡀
⠀⠀⡟⠀⠀⠀⠀⠀⢿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⠦⢤⣤⣸⢰⠇⠈⠉⠁⠀⠀⠀⠉⠁⠀⠙⢮⡛⠀⠠⠚⣱⡟⠁⣼⠀⠉⠛⠲⣄
⠀⠘⣧⣀⠀⠐⣒⡀⢸⡀⠠⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⣼⠏⢠⠞⠁⠀⠀⠀⢰⡏
⠀⢰⠿⠀⠤⠤⠬⢷⠤⠑⣄⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣀⡼⠋⠉⠀⠈⠉⠉⠉⠛⠒⠲⠶⠶⠶⠶⠶⠾⠃⡀⣸⡀⠀⠀⠀⢀⡿
⠀⢸⡆⠴⠒⠂⠀⠈⢣⡀⠈⠑⣦⡀⠈⢳⣀⡠⠖⠶⠋⠁⠉⠓⢤⣐⠦⢤⡤⢤⣤⣤⠄⢀⣀⠤⠐⠈⠀⣰⠓⣿⠉⠳⡶⢤⡾⠁
⠀⠘⠃⠀⠀⠠⠴⠆⠰⠷⣒⠞⠁⠉⠳⢤⣈⠁⠒⣦⣀⠀⠈⠑⠒⠀⠛⠉⠐⠒⠒⠀⠉⠀⠀⠀⠀⢠⠜⠁⠀⢸⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⠀⠀⠀⠈⠉⠓⠛⠉⢷⡀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠉⠉⠀⠐⠂⠤⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠶⣖⠒⠂⠤⠄⢀⣠⠄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⢀⡾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⣤⠝⠋⠁⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⢀⣾⣇⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠚⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⢷⡀⠙⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠉⢠
⠈⢳⣄⠀⠀⠀⠉⠙⠛⠛⠶⠾⠟⠛⠛⠋⠉⠉⠁⠀⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⡀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠚⠛⠛⠉⠀⠀⠀⣠⠞
⠀⢴⡋⠳⢶⣤⣤⣀⣀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠟⢹⣦
⠀⠈⢿⣄⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠠⡎⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣤⡿⠁
⠀⠀⠀⠉⣿⣶⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠙⢦⡀⠀⢀⣤⣤⡀⠀⢀⣴⠏⣴⠃⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣴⢶⣟⠉
⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣽⠟⠁⠀⠀⠈⠻⣋⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣀⣀⣀⣠⣤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⢤⣤⣀⣀⣀⣤⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⡉⠉⠁⠀⠀⠀⢀⣀⣤⠒⠉⠀⠀⣀⣀⣈⣳⣄⣀⣀⣠⣞⣁⣀⣀⠀⠀⠀⠒⢤⣀⠀⠀⠀⠀⠀⠉⢉⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⠶⠶⠞⠋⠉⠀⣀⡤⠖⠋⠉⠉⠉⠉⠻⡏⢹⠟⠉⠉⠉⠉⠙⠲⣤⣀⠀⠉⠑⠒⠶⠶⣶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣶⡶⠶⠛⢋⣴⣶⣾⣿⣷⣦⡀⠀⡇⢸⠀⢀⣴⢶⣿⣿⣷⣦⡉⠛⠶⢶⣶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⣷⣾⣿⣆⡇⢸⣰⣿⣷⣾⠿⠿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⡀⠀⠉⠛⠋⡇⢸⠙⠛⠉⠀⢀⣠⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⣀⡇⢸⣀⣠⣴⣶⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⣿⣿⣧⣼⣿⣿⣿⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠁⠀⡇⢸⠀⠈⠛⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⡇⢸⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣄⠀⡇⢸⠀⣠⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣧⣼⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⡇⢸⠛⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⡇⢸⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⡇⢸⠀⠀⢨⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⡇⢸⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⡇⢸⠈⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⡇⢸⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⡇⢸⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⡏⢹⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⡇⢸⠀⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⡇⢸⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⡇⢸⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠛⡏⢹⠛⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡇⢸⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⡇⢸⠀⠀⢀⡼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣤⣤⣀⣤⣷⣾⣀⣀⣤⣄⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⣿⣿⠿⠿⠿⠿⠋⠿⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⢻⡿⢿⣿⣿⠿⠿⢿⣿⠿⠿⣿
⣿⣶⣿⣷⣶⣶⣶⣶⣿⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠘⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡆⠀⠘⠂⠀⢠⡇⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠁⢀⠀⢹⡄⠀⡇⠀⡼⠀⢀⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠈⠓⠀⠁⠀⣀⣀⠁⠐⠋⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⢀⡀⠀⠀⠠⠿⣫⣭⠄⠀⠀⠀⣼⠟⠉⢀⡄⣀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠉⠉⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣿⣿⠁⠀⠀⢠⣿⠇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠛⠀⠀⠸⣇⡿⠀⠀⢠⡺⢦⠀⠀⢠⣶⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠛⠁⢠⣿⡏⠀⠀⠀⠘⢿⠄⠀⠀⢀⣴⣿⠿⢿⡄⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⣼⣿⠃⠀⠀⠀⣠⠀⠀⠀⢀⣿⡟⠁⠀⣼⡇⠀⢰⣿⡇⠀⢀⣴⣿⠃⠀⢀⣾⡇⠀⠀⣠⣶⣿⣿⣿⡇
⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⢰⣿⠀⠀⠀⣼⣿⠁⢀⣾⣿⠁⠀⣿⣿⠀⢠⢟⣿⡟⠀⣠⢿⣿⠇⢀⣾⣿⠋⠀⣼⣿⠁⠀⠀⣠⠖
⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⡿⠀⠀⣰⠋⢿⣶⠞⣿⣿⠀⠀⠹⣷⣰⠏⢸⣿⠁⢰⠏⢸⣿⢀⡞⢻⣿⠀⣴⢿⡿⠀⢠⡞⠁
⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⢸⣇⠀⣰⠃⠀⠀⠀⢀⣿⡇⠀⠀⠀⠈⠁⠀⠘⣿⣠⠏⠀⠈⠿⠞⠀⠘⢿⠾⠃⢸⣇⣰⠏
⠀⠀⠀⠹⠧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⣸⡿⠛⠛⠉⠙⠂⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠶⣄⠴⠶⣄⠠⠶⡶⠶⠀⢰⠖⠂⠀⣦⠀⣰⢀⡾⢻⡆⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⣿⡤⠟⣠⠶⢿⡀⢀⡇⢰⡆⣼⠤⠄⢀⡟⣇⡿⢸⡇⢀⡀⡿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣶⣶⣶⠾⠋⠀⠀⠀⠏⠀⠘⠷⠞⠹⠇⠸⠇⠸⠇⠿⠶⠶⠘⠇⠹⠇⠈⠳⠞⠀⠳⠒⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣐⣃⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⡀⢀⠀⡀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⠀⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠉⠀⠀⠀⠉⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠂⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠰⠷⠶⠾⠾⠿⠿⠆⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣀⣿⡇⢠⠴⠤⠀⠀⠀⠀⠀⠀⠰⠄⢦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⡅⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⢙⣿⡇⠀⠰⡷⠀⠀⠀⠀⠐⣶⣤⠀⢐⠀⠀⠀⠀⠀⠀⠀⠊⣾⡧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠿⣿⡇⢐⠀⠀⠀⠀⠀⠂⠀⠀⣿⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⡆⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠲⠂⠒⠒⠒⠒⠒⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠠⠀⠈⠉⠁⠀⡁⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⣠⠀⠂⣈⢂⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⠀⠒⢀⠀⠒⠀⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢢⡀⠠⠄⢀⡌⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡊⠀⠺⡀⢀⠗⠀⢑⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠐⢰⡦⠂⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⡜⣏⠄⠂⠀⠘⠃⠀⠐⢄⢹⢧⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠢⡀⢀⠼⠔⠓⠢⠄⡀⠀⠀⢀⠠⠔⠚⠢⠧⡀⠀⠐⠘⢧
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠑⠤⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠤⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢸⡇⠄⢆⠂⠀⠀⠀⠀⠀⠀⠀⠉⠐⡌⢁⢀⡀⡀⠀⠀⠀⠀⠐⣰⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⠠⢀⠀⠀⠀⢙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠐⠒⠒⠒⠒⠚⠒⠚⠂⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡠⠄⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠐⡄⢲⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⢂⠀⠀⠘⡤⠐⠀⠀⡈⠓⢦⡁⠀⠀⠈
⠀⠀⠀⢀⠀⠈⠀⠀⠀⠐⠛⠂⠘⠢⠬⠖⠃⠓⠂⠀⠀⠀⠀⠀⢀⢀⡐⠡⡀⢁⠀⠀⠀⠀⠀⠀⡔⠀⠀⠒⠀⢀⠀⠀⠀⠀⠀⢀⠈⣀⠀⠀⠀⠀⠀⠀⠠⢐
⡀⠀⢀⠎⠀⠠⠁⠀⠑⠤⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠚⢀⠀⠀⠀⠀⠀⠀⠱⠍⠁⠀⠈⠡⠂⠀⠈⠃⠀⢰⡃⡴⠃⠀⠀⠀⠠⡀⠀⠀⠁⠐
⠈⠂⠈⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡠⠀⢠⠀⡒⢀⡀⠀⠀⠀⠀⠀⠠⠝⠉⠀⢠⠊⠉⠁⠐⢄⠁⠀⠀⠄
⠄⡀⠡⡀⠀⡄⠀⠀⠂⠀⠀⠀⠘⠐⠤⡈⠠⠀⠈⠀⠀⠐⠈⠙⠉⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠠⣁⡈⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⠐⢄
⢉⠀⠀⠘⡄⠑⠒⠀⠉⠀⠀⠀⠀⠀⠀⠈⢦⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠐⠔⠀⠀⠀⡈⣢⠔⢉⣠⠀⠀⠀⢀
⠈⡆⠀⠀⢱⠀⠀⠙⠒⠆⠀⠀⠀⡐⢂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢠⢁⢁⠀⠀⠀⠀⠀⠀⠋⠐⢀⠠⠐⠁
⠀⠸⠠⠔⠚⠀⠦⠦⣤⡀⡠⠠⢄⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠘⠸⠈⠀⠐⠀⠦⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢇⠀⢸⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⡇⠀⠠⠀⠀⠄⠀⠂⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡱⠂⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⢰⠁⠀⠀⡀⠀⠀⠀⠀⠀⠈⢀⠔⠁
⠂⠀⠐⠀⠀⠀⠀⡀⠀⠈⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⡜⠀⠀⠄⠀⡔⠒⣦⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⡹⠽⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁⠀⠀⠀⡀⠰⠐⠊⠀⠀⣰⠀⠈⠒
⠀⡀⠁⡄⠀⠉⠀⣆⠀⣀⡄⠀⠄⠂⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠢⣀⠀⠀⠀⠀⠀⠀⡂⠁
⠀⠐⠄⠁⠀⠀⢀⠇⠀⢹⠀⠀⠀⠄⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⡀⠀⠠⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠉⡐⢀⠀⠐⠆⣀
⠀⠈⠀⠀⠘⢠⠤⠂⠀⠤⠀⠀⠠⠀⠀⠠⠄⠐⠠⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡁⠀⠂⢀⠀⠀⡠⠈⠃⠀⠠
⠀⠀⠀⠀⠀⠌⢁⣁⠀⠚⡠⠂⡀⠀⠀⡀⡄⠀⡅⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠘⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠰⠷⠤⠤⠣⠷⢠⠇⠀⠀⠀⠘⢀⠀⠀⢒⠐⡒⢒⠶⠲⠀⠀⠀⠠⠄⣀⣀⠀⠀⢄⠀⡀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠀⣠⡆⠀⠀⡠
⠀⠀⠁⠀⠈⡐⠀⠀⠁⠀⠀⠀⠰⠠⢄⠀⠀⠀⠄⠀⠀⡠⠃⠀⠢⠤⠶⠐⠒⠒⠓⠚⠀⠐⠂⠀⠀⠀⠠⠀⠀⡀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠤⡀⠈⢀⠔⠁
⠞⢀⠟⠀⠀⢈⣀⠀⢠⠠⠀⠀⢄⠑⣀⠔⠁⠀⠈⠯⠋⠀⠀⠀⠒⢂⠀⢰⠉⠉⠢⠒⠀⠄⠀⠀⠄⠑⠄⠀⠀⡂⡀⠀⠀⠀⡐⢄⠀⠀⠀⠀⠀⠁⠀⠀⠐⡀⠇
⡴⠃⠀⡖⠈⠁⠀⠀⠈⡀⠁⠀⠀⠀⠁⠘⠁⠀⠀⠠⠀⡀⠀⠀⠐⠈⠀⠘⠄⠀⠀⠀⢀⠄⠀⠀⠀⠰⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠈⠀⠀⠀⠁⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⡀⢀⡄⠀⣤⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠈⢃⡴⢛⡛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠺⡟⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣼⠖⠒⠛⠛⠛⠓⠒⠾⣄⠹⡆⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠁⠀⠀⢠⡄⢀⣠⠟⢦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡆⢀⣴⡏⠛⢋⣁⡀⠈⢿⠂⡟⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⣟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃⡴⠋⠀⠀⠀⠀⠉⠻⣆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⣤⣀⣠⡄⠀⣼⠟⠁⢸⡃⠀⠀⢀⣠⡴⠶⢤⣹⡄⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠙⠷⣤⣉⣁⡤⠞⣡⣄⡀⠸⣏⠘⣛⡉⠁⣀⡀⠀⣹⠇⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠰⡟⠳⣄⠀⠀⠉⠀⠀⢀⡴⠛⡇⠀⢹⡄⠉⠁⠀⠉⠁⢰⠇⠀⠖
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢷⠀⠈⠳⣤⡀⢀⡴⠋⠀⢸⡇⠀⠀⠻⣄⡛⠒⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⡴⠚⠳⣄⠀⠀⠙⠋⠀⢀⣀⣾⠀⣠⡴⠶⣌⡉⠉⢉⣠⡶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⣥⠀⢠⣼⠆⠀⠀⠀⠀⣿⠁⠀⣼⠃⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⠛⠀⠘⠛⠀⠀⠀⠀⠀⠙⠓⢸⠏⠛⢳⠀⠀⠀⠀⠀⠀⠀⣶⠛⠋⣷
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡿⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠲⢤⣀⣀⣀⣠⠔⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⢉⣹⡏⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⣿⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⢠⡾⠛⠉⠙⠳⣆⠀⠙⣄⠀⠀⠀⠀⢀⡼⠁⠀⠀⣿⠀⠀⠀⠀⠀⠉⢣⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡆⠀⠈⠳⡄⠀⣠⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠶⠃⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢿⡆⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⢷⣤⡄⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣈⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⡇⢸⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣉⡁⢈⣉⣉⣽⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⢸⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢀⡞⠡⠀⣠⠖⠆⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣾⠁⠀⠀⣷⠈⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠈⠀⢐⡿⠀⡀⠀⣀⣄⠀⡀⠀⢶⠀⢠⡤⡄⣤⠒⢆⡤⡀⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣾⡇⢹⡆⣾⠁⡿⢸⡇⢰⡏⢸⠏⠀⠌⣿⠂⣿⢀⡿⠀⣸⡏⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⣿⠀⣸⠃⢯⠘⣇⢾⡇⢾⣇⠿⣄⠐⠀⠿⠀⣿⢠⠧⢐⡈⠃⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠄⢀⣤⠀⠸⣧⠁⠉⠀⠀⠀⢀⣶⠂⣿⠄⢰⡏⡘⠀⠀⠀⡠⣦⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠃⢈⣧⠀⠀⢠⡖⣶⠄⠀⠀⣸⠏⠀⠀⢀⢸⡆⠀⠀⢴⡄⢀⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⠼⡃⣸⠀⠀⢺⡀⢿⡰⠀⡠⣿⠀⣡⡶⠰⠉⣹⠏⠘⢸⡇⠘⠃⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⠀⢹⣁⠌⠀⢻⡀⠂⠈⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⢠⠞⡡⠀⠀⠀⠀⠈⣿⣢⣠⠤⠤⠔⠒⠒⠒⠀⠀⠀⠐⣿⠇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⣟⢘⢀⣠⠤⠶⠒⠋⠹⣍⢤⡖⠀⠀⢀⠀⢀⠈⢲⠄⠀⢻⡀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠙⠄⠀⠀⠀⠀⠀⠀⡀⠀⣾⠃⠠⢄⡇⠀⠀⣦⣄⠔⣦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡤⠡⠀⣾⠃⠀⠀⠀⣴⠟⣷⢀⡾⠙⠀⣿⠀⣼⠇⢰⡏⢘⠁⣿⠀⣿⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⢰⠊⣿⠀⡠⠀⠀⣿⢠⣿⢸⡇⠀⡜⣿⠀⢿⣀⠾⡇⠌⠘⠃⠀⣿⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣿⠜⠁⠀⠀⠈⠁⠉⠈⠃⠘⠀⢿⡜⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠜⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉




⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠻⠂⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠐⠃⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⡻⠃⠀⠠⠄⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠛⠉⠁⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⢀⠀⠐⠠⠶⠖⠐⠛⠂⠒⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢠⡘⠷⣄⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠐⠀⠀⡠⠀⠀⠄⡶⠄⠷⠒⠀⠶⠂⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⡑⠷⣦⡄⠀⠄⢀⢀⣀⣀⣀⣀⣀⣨⡆
⠀⠀⠀⠀⠡⠀⠀⠀⣀⢀⠀⢀⣀⡀⣷⠦⠤⢀⣀⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⡀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠙⡄
⠀⠀⠀⠀⣄⠐⠈⠀⢀⣀⣀⢼⣶⣷⣿⣶⣄⢀⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣤⣀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⢓
⠀⠀⠀⠀⠀⠠⠖⠒⠋⠉⣡⣈⠀⢈⣀⣻⣯⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣮⣝⣓⣀⣀⣈⣁⠀⠀⠀⠐⠀⠈⡀
⠀⠀⠀⠀⠀⠀⡠⢤⢖⡙⠀⠀⠀⠿⠤⠀⠸⣿⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣈⣍⣃⣀⣈⣉⣉⠀⠀⠀⠠⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠐⠐⠂⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣧⡙⠛⣿⣄⣉⠉⠁⠀⠒⣊⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠈⢈⣉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢱⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣶⣶⣦⣄⣠⣴⠀⣠⣴⡆⣼⣿⡎⢈⡿⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⢁⣾⠏⣾⡇⣿⣿⠷⡎⠀⠀⣷⠀⠀⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢹⡟⣾⡟⣰⢿⡇⣿⣇⠀⡿⠀⢸⡿⠀⣼⠏
⠀⠀⠀⠀⠀⠀⢀⠙⠀⠑⡀⠀⠀⠀⢀⡞⠁⢠⡿⠁⠻⠧⠃⠘⠧⠞⠿⠴⠃⠀⣿⣇⡼⠃⠀⠀⠀⠐⠁⠈⢁
⠀⠀⠀⠀⠀⠀⠸⡄⠨⠎⣀⠀⠀⠀⣾⢁⡴⠋⠀⠀⠀⠀⢀⡠⡆⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⢀⡈⠪⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠶⠇⠓⠿⠀⠓⠗⠀⠷⠽⠣⠾⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣄⠀⠚⠀⠀⠀⠀⠀⢐⡆⣤⢰⡂⢰⣄⣦⣶⠀⣤⣴⡶⠀⠀⠀⠀⠀⠘⠂⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⡁⠉⠀⠈⠀⠙⠉⠀⠀⡀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢅⢐⡔⣥⡆⠐⡄⢸⣳⠦⠏⡇⠀⣶⠶⢿⠳⣧⡸⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣸⡧⠀⠀⠀⠘⠜⠙⠙⠛⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⡇⣠⠴⡄⠀⣠⣄⡟⢦⢀⡀⢀⣤⠀⣧⡃⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⣷⠇⢀⣿⢰⡟⣻⠀⣿⡼⣷⡏⢸⡇⡝⠿⣶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠎⠸⣿⠀⢸⣿⠘⣷⠏⠰⡿⠁⠛⠁⠸⠿⠀⠀⢏⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⢠⡤⣤⢤⣠⣠⠤⠀⣤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠘⠗⠻⠚⠙⠙⠶⠚⠛⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣾⡧⣞⣓⣾⢛⣶⣿⢶⣟⡶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠈⠁⠈⠉⠈⠀⠁⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠯⢿⠉⢹⢛⢳⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣒⢻⠀⢸⠀⢸⢸⢸⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸⠀⢸⢸⢸⠀⢸⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠚⠋⣿⡄⢸⡤⣼⠀⢸⠸⢸⠀⢸⢸⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡷⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⢀⣀⣀⣘⣛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡭⠿⠤⠤⠤⠼⠯⡍⡇⠀⠀⢀⡄⣾⠛⢛⣛⠛⠛⡇⣘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠒⠂⠨⠭⠬⠀⡇⡇⠀⠀⢸⠀⣿⠠⣞⢉⣳⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠒⠂⠠⢬⡍⠀⡇⡇⠀⠠⢾⠀⣿⢀⢈⣛⣁⢠⣧⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠰⠆⢸⣿⡛⠀⡇⡇⠀⠀⢸⠀⣿⢀⢐⣒⡐⢸⢸⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠤⠄⢐⣒⡒⠀⡇⡇⠀⠀⠘⠃⢿⣤⣬⣭⣤⢾⠸⠘⠹⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣳⣶⣶⣶⣶⣶⣶⣃⡀⣀⣀⣠⡴⠂⠀⠀⠀⢸⡘⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⢋⣉⡙⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⡞⠉⠉⣙⢳⡀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⡶⠶⠚⠙⢻⡇⠀⠀⠸⡆
⠀⠀⣠⣤⡀⠀⠀⢀⡴⠶⣿⠳⠶⠞⣻⠶⢦⡄⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣈⣷⣀⠀⣠⣾⡁⠀⠀⠀⣿
⠀⠀⢻⠀⢻⡀⠀⣿⠀⠀⠈⠳⣤⡼⠋⠀⠀⣿⠀⠀⡿⠀⡿⠀⠀⠀⠀⠀⠀⠀⢿⠀⣰⠋⠉⠁⠉⠉⠉⠈⠉⠻⡆⢠⡏
⠀⠀⠸⡇⢸⡷⠶⣝⠲⠤⣤⣤⣤⣤⣤⡤⠶⣫⠶⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢧⡻⠶⠶⠶⠶⠶⠶⠶⠶⠶⢧⡾⠁
⠀⠀⠀⢿⡈⠻⣄⠈⠳⣤⡀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁⡾⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⢩⡴⠚⠛⠲⠶⠶⠶⣄⠰⣋⣤⠤⢤⡀
⠀⠀⠀⠈⠳⣄⠈⠁⠀⠈⣷⠀⠀⠀⣾⠁⠀⠈⠁⣠⡞⠁⠀⠀⠀⠀⠀⢿⠉⠉⣿⠒⠛⠀⠀⣤⠤⠴⠶⠶⠾⠋⢉⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠘⣦⣀⣀⣤⣿⣤⠀⣤⣿⣤⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⣀⣀⣀⣀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢿⣭⣤⣤⣤⣿⠀⣿⣤⣤⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣈⡟⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⣤⣤⣄⠙⠳⢦⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⣉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⠳⢦⡄⠉⠛⢺⡍⣿⠀⠀⠀⠀⢀⣰⢶⡄⠀⠀⢸⡷⠶⠞⠋⠓⢾⡇⠀⠀⣠⢶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣙⢦⣀⠀⢀⣀⣸⡆⣿⠀⠀⠀⠀⣿⢹⡆⡟⣷⠀⠘⣧⠀⠀⠀⢀⡾⠁⢀⡞⣿⢸⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠙⡆⠉⠉⠉⠉⠹⠶⠿⠀⠀⠀⠀⡏⢸⡇⡇⣿⣀⣠⡼⠷⠶⠶⠿⣥⣄⣸⡇⣿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⠛⢧⣼⠋⠈⠳⢤⣄⣤⡴⠟⠈⢹⣧⡟⢻⡆⢹
⠀⠀⢀⣀⣀⠀⠀⠀⣠⠴⠿⠦⣤⡴⠿⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⢷⡀⠻⢤⣄⠀⠀⠀⠀⠀⢀⣠⡴⠏⢠⡞⢁⡾
⠀⠀⢸⡇⢹⠛⠛⠛⠛⠲⣄⣀⣀⣀⣀⣀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠁⠀⠀⠈⢷⡤⣤⡤⢤⡟⠁⠀⠀⠈⢀⡾⠁
⠀⠀⢸⡇⢸⣀⠀⠀⢤⣄⡉⠻⣍⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣄⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⣤⠶⠛⠁
⠀⠀⠘⠷⠚⠉⠛⠦⣄⡈⠙⢦⠿⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠶⠶⠾⠷⡆⣴⠾⠷⠶⠾⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⠠⠤⠒⠋⠀⠳⡀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣠⠚⠙⠓⠂⠀⠀⠐⠒⠂⠘⡶⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⣽⠀⠈⠉⠁⣸⠀⠈⠉⠁⢠⣳⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⢧⠀⠀⠀⠁⠀⠀⠀⠀⡜⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣨⠷⣄⠀⠉⠉⢀⣠⠾⣄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⠋⠀⠐⠾⡉⠑⠂⢉⠗⠂⠀⠙⡆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠚⠂⠀⢄⡀⠘⣆⣰⠃⢀⡀⠀⠐⠓⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠑⠾⠧⠊⠁⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡞⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢳⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢀⡞⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢳⡀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠒⢤⡀⠀⠀⣠⣮⠤⠶⠓⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠶⠤⣵⣄⠀⠀⢀⡴⠒⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢠⠿⠲⢤⡀⠀⢹⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡏⠀⢀⡤⠖⠿⡄
⠀⠀⠀⠀⠀⣰⢃⠀⠀⠀⠘⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠃⠀⠀⠀⡙⣆
⠀⠀⠀⠀⠀⡏⡎⣸⢁⡶⢠⠇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠲⢤⠖⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠸⡆⢶⡈⣇⢱⢹
⠀⠀⠀⠀⠀⢳⡄⡇⢸⠱⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠛⠓⡦⠴⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠳⠎⡇⢸⢠⡞
⠀⠀⠀⠀⠀⠀⠉⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⠀⠀⠀⠈⠑⠢⣄⣀⠀⠀⠀⠀⠀⠈⢊⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣈⣵⣤⣤⣤⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠳⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠷⣄⣀⣀⣀⣀⣀⣀⣀⣀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠋⠙⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡴⠶⠿⠀⠀⠿⠶⢦⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠛⣷⠀⠀⣾⠛⠛⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⢠⣤⣠⢴⢰⣠⠄⣠⡄⡆⠀⡤⣤⣄⡤⢀⠤⣀⡄⡤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠈⠉⠈⠈⠃⠉⠁⠁⠀⠁⠉⠁⠙⠈⠉⠉⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠚⠙⠃⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⡟⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⠀⠙⠚⠁⣸⠀⠙⠚⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣀⣀⠄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣏⠀⢀⡠⢟⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠈⠉⠙⠋⠉⠀⠀⠉⠻⢿⣿⣿⣾⣿⣦⣛⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⢸⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠃⣇⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢧⡝⠀⠀⠀⠀⠀⠀⠀⢸⣴⠃⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣀⣤⠴⠷⡄⠀⠀⠙⢦⣄⡤⠤⢤⣀⣠⠞⠁⠀⢀⡼⢧⣀⡀
⠀⠀⠀⢀⡴⠋⠉⣀⣀⠀⠙⠲⣄⣀⣠⠤⢍⠵⠀⠀⠀⠀⣀⡴⠋⠀⠀⢈⠙⠳⣄
⠀⠀⢠⠏⠀⠀⠀⠀⠉⠙⠛⠲⢤⣌⡉⠓⠶⠶⠶⠖⢚⣋⡥⠴⠒⠛⠋⠉⠁⠀⠈⣧
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠙⠲⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⣀⠀⢀⣀⣀⣀⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⣧⡄⠀⠀⣠⠂⠀⠀⠀⠉⢙⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠿⠅⠈⠛⠁⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡚⠉⠀⢿⡇⠀⠙⢦⡀⠀⢤⡀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠉⠉⠛⠒⣮⢿⡄⠀⠀⠙⢦⡀⠙⢳⡾⡁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠒⢦⡀⠀⠀⠀⢰⡇⠘⣿⣄⣤⠴⠒⠙⣾⢹⣵⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠱⡄⠀⠀⠈⠓⢦⣸⡇⠈⢣⠀⢸⠁⢸⡿⠉⠙⢧⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠙⢻⣄⠀⢣⢸⡄⣿⣷⠀⠀⠈⢧⠀⣧
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⣯⣳⣄⢻⣇⡏⢸⡀⠀⠀⠈⢇⢸⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠮⢻⠞⢮⣿⡇⠈⢧⣠⡄⠀⡈⣾⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠛⠉⠀⠈⢿⠀⠀⠀⠈⠁⠈⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠘⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠻⡀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠙⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠳⢤⣀⣀⣀⠴⠊⠁⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠾⣄⡠⠤⠒⠒⠚⠉⠭⢙⣲⣴⠽⢛⣥⡴⢦⣰⠛⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡿⠀⠀⠀⣀⣐⣛⣶⡶⠛⠁⢸⡏⢆⠳⣀⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠛⠳⢶⣤⣀⠀⠀⢠⣏⣸⡧⠤⠖⠋⣁⡴⠛⠁⣀⣴⠚⠳⣤⠴⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠼⠁⠹⠀⠀⠰⠾⠥⠤⠖⠋⢹⠓⠷⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⢸⠃⡀⠀⢌⡆⠀⠀⠀⠀⠀⢤⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡆⣿⡏⣤⢸⡜⠄⡔⠈⡂⠀⠀⠀⠀⠀⠘⢟⢛⠷⢾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡙⣿⡗⣛⡠⠟⠴⣠⠴⠲⠄⠠⣀⠀⠀⠀⠠⣟⣼⣿⣻⣿⡆⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⣿⣇⣟⣼⣿⣿⣟⢫⣱⣦⠷⠶⠂⢤⠀⠠⠤⣾⣭⣭⠿⣿⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣤⡿⣏⡻⡄⠈⣩⠷⠛⠛⢻⠚⠒⠸⠤⡤⠴⢁⡤⠎⢁⣾⡟⣿⡅
⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⣤⠿⣔⣛⢂⠂⢳⣵⡿⠍⠀⠀⣠⣴⣦⣄⣀⡀⢀⣂⣀⣁⣴⡏⠐⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⠴⡟⠡⠂⠄⠙⣵⠶⠟⠻⣟⡀⠐⠈⠙⠻⣟⢻⣿⡟⠉⠁⠀⠀⢈⣿⣶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠓⡲⢛⣉⡧⠄⠀⣾⠋⠁⢠⡆⠀⠀⢹⡆⢸⠃⢀⣀⣀⡔⠋⠘⠩⠅
⠀⠀⠀⠀⠀⠀⠀⣱⠂⢸⣿⡋⠋⠉⠀⠀⣰⢿⣇⢲⣤⡧⠀⠀⠀⣷⠖⠛⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠁⠈⠳⠶⠋⠢⠉⠁⠈⠊⠁⣸⡟⠰⡿⡟⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⢡⡀⢡⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠟⣫⠞⣀⠀⠺⠛⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠏⢀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣁⠤⠤⠤⠤⠤⠤⠤⢄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠒⠆⠀⠀⠀⠀⠖⠆⠀⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠒⠒⠀⡆⠀⠐⠒⠂⠀⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣧⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠂⠂⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⣦⢄⣀⣀⢴⡊⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⠀⠀⠈⠙⢄⠀⢀⠜⠉⠀⠀⢀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠲⢤⡈⢦⠏⣠⠴⠂⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣴⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⡄⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠙⠢⡄⠀⠀⢀⣾⠥⠖⠓⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠒⠓⠶⢽⣆⠀⠀⠀⡤⠚⠉⠹⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠒⠤⣀⠀⢸⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣸⠀⢀⡤⠔⠚⢧⡀
⠀⠀⠀⠀⠀⠀⣼⢃⠀⠀⠀⠈⢶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠎⠀⠀⠀⢀⢹⡄
⠀⠀⠀⠀⠀⢰⡇⡏⣸⠁⣴⠂⡜⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠦⣤⠖⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠘⡄⢲⡄⢹⡈⡆⣷
⠀⠀⠀⠀⠀⠘⢷⡀⡇⢸⠙⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠶⢤⣄⡤⠴⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠱⠜⢹⠀⡇⣰⠟
⠀⠀⠀⠀⠀⠀⠀⢻⡓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠁⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠈⠒⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⠀⠀⣀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣄⣀⢀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣮⡛⣶⡂⠈⣵⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠈⡻⣿⣿⣾⣥⣾⣿⣿⣿⢟⠿⠿⣿⣿⣿⣇⣠⠂⠁⠀⠀⠀⠀⠀⠫⣽⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣧⡘⠀⠙⣿⣯⣿⣿⣿⣿⠭⠤⢼⡗⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠼⢻⣿⣶⣦⡄
⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣿⣿⣿⣿⣶⡄⢹⣿⣽⣾⣿⣏⢳⡄⡈⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⣿⣿⢸⡄
⠀⠀⠀⠀⢀⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣻⣿⡿⣿⣿⣼⣿⣿⣿⡟⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⢿⣟⠀⣳
⠀⠀⠀⠀⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⢷⡿⠿⠿⠿⠿⠋⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠄⣼⠏⢰⡏
⠀⠀⠀⠀⠀⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢰⣶⣄⡈⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣾⣿⣿⣫⣾⣿⢆⡾⠁
⠀⠀⠀⠀⠀⠀⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣌⣻⠋⠀⠀⠈⠉⠛⠛⠿⢷⣾⣶⣄⣶⣦⣾⣹⠿⠞⣻⣩⣾⣿⡧⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣿⣿⣿⣿⠁⠀⠀⡇⠀⠀⠀⠠⡀⠠⠆⠂⣼⣿⣿⣿⣿⠟⠛⠛⠛⠿⠋⠉⠋⢿⣃⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠙⠟⠋⠄⠀⠀⢰⣶⣀⠀⢇⠀⠄⣨⣤⣿⠟⠋⠀⣀⣼⣆⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠈⠀⠀⠈⠻⣿⣷⣾⣿⣿⡿⠋⠁⢀⡠⠊⠙⠿⠛⠁⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠀⣿⣿⣷⡀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠋⠁⠐⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢹⠈⠫⣀⣀⠀⠀⠀⠀⠐⠀⢀⠤⠶⠦⠟⠋⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⠏⠉⡿
⠀⠀⠀⠀⠈⠉⠀⠰⠀⠀⠀⣷⠀⠀⠉⢻⣦⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣄⡴⠀⣿⣷⣿⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⣏⠀⠀⠰⡿⠛⠛⠛⠻⣤⣤⣠⣄⡀⣀⣴⣦⡴⠟⠶⣷⣾⡿⠁⠀⠙⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠼⠀⠤⣀⣇⣀⢈⣶⣦⣿⣬⡟⣻⣿⣿⠿⠛⢃⡠⠿⠷⣿⠇⠀⠀⠀⠀⠈⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠉⠙⢻⣯⣿⣉⢳⠞⠁⠉⢿⠋⢠⣸⠟⢷⣶⡘⢻⡆⠀⠀⢆⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⡿⠉⠁⢠⡶⠚⠒⠛⠛⢾⡿⠿⠻⡿⣷⢰⣾⣏⡰⢲⣾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡄⢺⣿⣷⣷⠞⠓⣼⣷⣲⠾⠗⠾⠛⠛⠶⠾⢿⣿⢼⡟⢉⢧⡟⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣤⣦⣤⣜⡻⢿⣿⡇⣵⠟⠛⣶⣶⣾⡶⠻⡗⠒⠶⠀⠛⠛⠀⠈⠛⠳⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⠟⠋⠉⡩⠉⣇⠹⣷⡎⠀⠀⣿⠟⠛⠻⢿⣿⠦⠀⣴⠀⠀⠀⠀⠀⢀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢃⣄⣶⣿⠷⠿⣷⣼⣿⠁⣠⣾⡅⠠⣾⣿⣿⣿⢣⣼⡿⣣⠀⠀⠀⠀⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠞⣿⣻⣿⠟⢻⠿⠟⢼⣧⠀⠈⣧⠀⣻⣿⣿⡿⠛⡛⡍⠁⠀⠀⠀⣾⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣀⣋⣀⣀⠃⢀⣴⣿⠿⠛⠀⣨⣯⣿⡿⠉⢠⠎⢡⠗⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢋⣤⣾⣿⡅⢰⣾⣿⡿⠃⠀⡠⢌⠳⣂⣦⣶⣿⡀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⣀⣾⡿⠛⠉⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣾⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣼⣿⠰⣿⣛⡃⣿⠛⢳⡆⣿⢠⡾⠛⠳⠀⣼⢿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⢻⠏⣿⠸⣿⣭⠅⢿⣤⡾⠃⢿⠈⠷⣤⡶⢰⡿⠾⢿⠸⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⡀⠀⣀⡀⠀⠀⣀⡀⠀⢀⣀⡀⠀⣀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣿⢸⣯⣭⣁⣾⠉⠙⢢⡟⠉⢹⡆⣿⣏⣽⠆⣿⠉⢻⡆⢿⣭⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⠧⠸⠷⠶⠆⠻⠶⠾⠊⠻⠶⠾⠃⠻⠉⠿⠀⠿⠶⠟⠁⠶⠶⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣉⣉⣹⡏⠉⠉⣿⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⢹⡇⠀⠀⣿⢰⡆⢸⣷⣴⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠻⣿⠀⠀⢸⡇⠀⠀⣿⢸⡇⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠓⠀⣿⠀⠀⢸⡇⠀⠀⣿⢸⡇⢸⡇⠀⠀⢸⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⢸⡇⢸⡇⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⣤⣀⣴⣶⠄⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⢸⡗⢸⡇⠀⠀⢸⡇⣿⠀⠶⣷⣤⣤⡀
⠀⠀⢠⣶⠞⠋⠉⠀⠀⠀⣿⠶⠦⠈⣿⠶⠶⢾⡇⠀⠀⡿⠘⠇⢸⡇⠀⠀⢸⡇⣿⠀⠀⠀⠈⠉⠛⠿⣧⣀
⠀⣿⠏⠀⠀⠀⠀⠀⠀⢰⡿⠶⠶⠾⠿⠶⠶⠾⠷⠶⠶⠷⠶⠶⠾⠷⠶⠶⠾⠷⠿⣷⠀⠀⠀⠀⠀⠀⠈⢻⣄
⢺⡏⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⢶⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⢠⣥⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⢦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣰⡿⠆
⣸⡁⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⢸⡧⠀⠀⠀⠀⠀⣀⣀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⢀⣋⡀
⢹⡇⣿⠀⠀⠀⠀⠀⢠⣤⣤⡄⠠⠄⠀⣿⢰⣧⠀⠀⠀⠀⢸⡟⠉⠀⣿⠀⠀⣀⣼⠟⣿⣀⠀⠀⢸⡇⠈⢹⡇
⢸⡇⣿⠀⠘⠛⠛⠀⠰⣶⣶⣶⣶⠄⠀⣿⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⣿⣉⠀⣈⣹⡇⠀⢸⡇⠀⢸⡇
⢸⡇⣿⠀⢀⣀⣀⠀⠰⠄⠴⠶⠶⠆⠀⣿⢸⣏⠀⠀⠀⢀⣸⣷⠀⠀⣿⠀⠀⠉⠻⣦⡿⠉⠁⠀⢸⡇⠀⢸⣧⡀
⢺⠃⣿⠀⠈⠉⠉⠀⠰⠶⠶⠶⠆⠀⠀⣿⢸⣏⠀⠀⠀⠘⢻⣶⠀⠀⣿⠀⣄⠀⣤⣤⣤⣤⡄⢰⡾⢷⡄⢰⡿⠋
⢸⡄⣿⠀⢀⣀⣀⠀⠰⠶⠶⠶⠶⠆⠀⣿⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⣤⠀⣤⣤⡄⢠⡄⢸⡇⢸⡇⢸⡇
⢸⡇⣿⠀⠈⠉⠉⠀⠘⠿⠿⠗⠀⠀⠀⣿⢸⡧⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⡤⠀⣤⣤⣤⡄⠀⢸⡇⢸⡿⢾⣷⣄⣀
⢸⡇⣿⠀⢠⣤⣤⠀⠘⠛⠛⠛⠛⠃⠀⣿⢸⣿⠀⠀⠀⠀⠈⠛⠛⠀⣿⣀⣀⣀⣀⣀⣀⢀⣤⣼⡇⢸⡇⢿⠅⣿⠋
⢸⠇⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⣿⠘⠗⠀⠀⠀⠀⠀⠀⠀⣀⠙⠛⠛⠛⠛⠛⠛⢻⡇⢸⡇⠀⠀⠀⠀⠉
⢹⠇⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠀⠆⢀⣀⡀⣀⣀⣤⡾⠻⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁
⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠈⠋⠙⠿⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢠
⣶⣶⣶⠶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣾⠉⡶⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⣀⣹⠀⡇⠀⠙⢦⠀⢰⠋⡿⠲⣄⠀⡞⠿⠈⢲⡀
⠀⠀⠀⠀⣞⢴⠃⠘⠀⠑⠂⢄⡀⠑⠬⣆⠀⠀⠈⠳⣇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠳⣀⠖⠦⠎⠲⢌⢢⡀⠈⠳⣄⠀⠀⠘⣆⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣦⠀⠈⠓⠤⠀⣿⣀⣀⣀⣀⣤⠤⠴⠒⠒⠉⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢿⡇⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⢛⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠒⠒⠒⠒⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢶⡂⢺⠀⠀⠀⠀⠀⡠⠄⠒⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠌⣙⠒⠠⢠⣶⡽⠖⠆⡤⣀⣀⣠⢼⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡮⡉⠑⠂⠄⣉⠑⠒⠇⠀⢰⠇⢼⡄⣴⠤⠤⣤⣆⠠⢀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒⠉⠀⠈⢢⠀⠀⠀⠉⠒⠧⡴⠁⠑⠾⢀⠴⡊⠐⠓⣛⣺⢻⣉⣀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣶⡀⡠⠒⠥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣎⣀⢀⡴⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠺⢔⢯⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠆
⠀⠀⠀⠀⣴⣤⡠⢬⡧⢀⣀⡀⠀⢉⣿⣷⡶⢤⣀⢀⣀⣀⢀⣀⡀⠤⠄⠐⢶⢲⠉⢁⡎
⠀⠀⠀⠲⠚⠟⠀⣯⢤⣀⠠⠈⢿⡻⠊⢁⣴⠷⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠆⠃⢀⠎⠃⠂
⠀⠀⠀⠀⠀⠀⢠⣶⢩⡹⠲⠟⣾⠍⣏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣸⣠⠏
⠀⠀⠀⠀⠀⠠⠾⠍⠀⢁⣶⢾⡇⢹⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⡏⢉⣸⣠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⢖⣹⡯⠕⠒⠒⠀⠤⠤⠤⠤⠤⠖⠒⠊⠉⠁⠚⠓⠀⠁
⠀⠀⠀⠀⠀⠉⠉⠁⠘⠶⠶⠂

⠀⠀⢸⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣽⣿⣿⣿⣷
⠀⠀⢸⣿⡇⠀⣀⠉⠉⠑⢢⣤⣤⠒⠉⠉⠁⢀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⡈⠉⠙⠲⣄⣠⡔⠚⠉⠉⢀⠀⣸⣿⡇
⠀⠀⢸⣿⡇⠠⠉⠉⠠⠈⠈⠁⠀⠈⠀⠀⠁⠡⠀⣿⣿⠀⠀⠀⠀⠀⢠⣿⡏⢀⠉⠉⠩⠄⠀⠁⠀⠈⠁⠀⠁⢥⠀⣿⣿⠇
⠀⠀⢸⣿⡇⠨⠀⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠨⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠨⠉⠈⢹⠉⠁⠉⠉⠉⠉⠉⠁⠍⢠⣿⣿
⠀⠀⢸⣿⡇⢈⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⡌⠈⠀⢩⡌⠀⠀⢡⠩⠀⠁⠨⠁⢸⣿⡟
⠀⠀⢸⣿⡇⠈⠀⠀⠀⠉⠀⠀⠀⠁⠀⢠⡄⠈⠀⣿⣿⠀⠀⠀⠀⠀⣿⡟⢀⠁⠀⠀⠈⠀⠀⠀⠈⠁⢠⡄⠈⠀⣾⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⣧⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇⠠⠀⠠⠀⠤⠀⠀⠄⠄⢀⣾⣧⠀⠀⣿⣿⠃
⠀⠀⢸⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠁⡸⣹⣿⢣⠀⣿⣿⠀⠀⠀⠀⣸⣿⠃⡄⠠⠤⠤⠤⠤⠤⠀⠡⢪⣿⡏⠄⢸⣿⣿
⠀⠀⢸⣿⡇⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣸⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⣿⣿⠀⠀⠀⢰⣿⡏⢠⡀⠀⠀⠀⠀⡀⡀⡀⠀⣾⡟⠀⠀⣿⣿⠇
⠀⠀⢸⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠂⠀⣿⣿⠀⠀⠀⢸⣿⡇⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠂⢰⣿⣿
⠀⠀⢸⣿⣇⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣿⣿⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡿
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⠀⠤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠾⠟⠿⠿⠿⠿⠿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠈⠉⠀⠈⠀⠀⠀⠀⠁⠀⠁⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⢀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠟⠛⠇⠀⠄⠈⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⣃⠀⡃⣀⠀⣈⣀⣀⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠧⠤⠤⠤⠤⠤⠀⠄⢀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠨⠀⠤⠤⠀⡇⣶⡆⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠈⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⡀⢀⠀⠀⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡏⠉⣿⡄⢀⡀⢀⣀⣠⠶⠛⠉⠀⣀⠀⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⣸⠏⢸⡇⠀⣿⠁⠀⠙⣿⠋⠡⠀⠀⠀⠀⠙⠛⣋⡁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⣾⡇⣸⢣⡾⣦⢀⡿⢰⠇⣾⡇⣼⣰⡟⣼⠉⣿⡽⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠁⣾⡠⣿⠸⣇⣾⡼⠧⠎⠟⠘⠟⠳⠚⢯⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠁⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠱⣿⠀⠀⠀⣸⡄⣠⡾⢁⡾⡻⢠⡟⢀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⣻⣶⠂⠀⣿⣿⠉⠀⣸⣏⡵⠻⠷⠋⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡿⠀⠠⣿⠈⠳⠛⣁⣭⣤⣄⣀⣠⣿⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣰⡾⠋⠁⠀⠉⢉⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⢻⣿⣧⠀⠀⠀⠐⠀⣂⡀⠐⠀⠀⠀⠀⢸⡿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠹⠿⠀⠀⢀⣤⣤⣬⣤⣤⣆⠀⠀⠀⢸⠀⠀⠀⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⢀⣾⡿⠛⠋⠈⢿⣿⣆⠀⠀⠀⣠⣀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⢸⡋⠀⠀⠀⠀⠀⠉⣻⠀⠀⠀⢻⣯⡉⢉⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣆⠀⡕⢸⣿⡁⢸⣿⣧⠀⠀⠀⢠⣾⣿⠀⠀⠀⡤⢝⠛⢛⡯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠀⠻⠄⠀⠙⢿⢷⠀⢰⠿⡛⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⢃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠈⡅⡿⠀⠀⠀⡄⠀⠀⠀⠐⠄⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠀⠂⠂⠀⠀⠱⠇⠀⠀⠂⡇⠀⠘⡟⢸⠆⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠀⠠⠀⠀⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⠀⠀⠀⠀⠀⢀⠅⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠀⠀⠈⠀⠀⠈⠁⠘⠀⠄⠀⠀⠂⠒⠀⠀⠄⢁
⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠤⠤⠤⠴⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣤⡀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⠁⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣤⡿⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠉⢉⣀⣤⣤⡤⠤⣿⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⠾⠿⠛⠉⠀⠀⢠⡿⠀⠀⣤⣤⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣠⡴⠖⣤⠀⠀⢸⡇⠀⠀⢛⡋⠀⢠⡞⢱⠀⢠⣄⡴⣦⠀⢀⡴⠿⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠏⠀⢰⡟⠀⠀⣿⠁⠀⠀⣸⡇⠀⣿⡠⠋⠀⣸⣿⠀⢹⡆⣿⠁⢠⣿⢠⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣄⣠⠋⣇⢀⣼⡏⠀⠀⠀⡿⣇⣠⢿⣅⠀⡸⠀⣿⠀⢸⣧⠻⢄⡸⣿⢁⡠
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⠀⠀⠀⢸⠀⠉⠋⠁⠀⠀⠁⢸⡇⠀⠀⢰⠀⠀⠀⠀⠉⠉⠀⣀⡉⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠠⡦⠀⠀⢠⣤⠀⠤⢴⢼⡧⠴⢶⡗⠒⠈⠛⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⣤⡀⠀⠀⣀⣤⣶⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣦⣿⣿⣿⣿⡄⣰⣿⣿⣿⣥⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣀⠻⣿⣿⣿⣿⣷⡌⣿⣿⣿⣿⡇⠻⠿⠿⠿⠋⢴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢠⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⣾⣿⣧⡹⢿⣿⣿⣿⣧⠻⢿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⢏⣶⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⢿⣿⣿⣟⣛⣩⣴⣿⣿⣿⡇
⠀⠀⠀⠀⢹⣿⡿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⢩⣴⣿⣿⣿⣿⣎⡻⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣩⣍⢋⣴⣷⣆⢀⣤⡄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢋⣶⣿⣿⣿⡆⣿⣿⢿⣿⣿⣿⠛⢿⢡⣿⡏⣾⣿⣿⣿⣇⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣾⣿⣿⣿⣿⡇⣩⣵⣿⣿⣿⡇⣿⣦⡘⢿⡁⣿⢟⣉⠻⣿⢸⡿⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⣿⣿⡆⣿⣿⣿⣦⡀⢡⣾⣿⣷⡉⣠⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠈⠙⠛⢉⣁⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⡛⠿⣿⣿⣿⠿⣿⣿⡿⠿⣋⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠶⠶⠒⠀⠒⠶⠶⠿⠟⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⢷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠈⣷⡀⠀⣼⣿⣿⠰⣂
⠀⠀⠀⠀⠀⠀⠀⣼⡏⢡⠀⢹⣧⠀⢿⣿⣿⡆⣿⣆⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢡⡿⠀⢸⣇⠸⣿⡄⢸⣿⣿⡇⢸⣧⣅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⡃⠀⠛⠻⡀⢸⣷⣼⣿⣿⣯⠠⠻⣿⣷⠈⣼⣿⣿⡿⢛⠲⡄
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⣷⠀⢻⣿⣿⣿⣿⠌⠢⠤⠘⠀⢹⡿⡡⡇⣿⡇⣧
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⣸⣿⣧⠀⢿⣿⣿⣿⣆⠀⠁⠀⡀⣹⠗⡷⠛⣎⣥⢉⣠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣷⠘⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣘⣧⣴⣮⣝⢾⣏⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣤⣿⣿⣿⣿⢿⠟⠿⠋⠋⠙⢮⡻⣿⣿⣿⣿⡿⣿⡄⠐⠂⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⣿⣿⣿⡿⠛⠉⠀⢀⠠⠄⠀⣐⣬⣽⣷⣿⣿⡏⠙⢿⣮⡙⢦⡙⠧⣍⣳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⢸⣿⣏⠀⠄⣤⠚⠉⢄⣴⣾⣿⣿⣿⡿⢙⡿⣇⣀⣀⡙⢿⣦⡈⠒⢿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⡄⢾⡿⢹⣿⡟⢆⠀⠀⠈⠉⠻⠿⣭⡁⠀⠈⠀⠀⡟⢹⡇⠈⠈⢿⣦⣀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠈⢻⣧⠸⡆⠀⠀⠀⠀⠠⠹⣿⠀⠐⠀⠀⠧⠸⠇⠀⠀⠀⠻⣿⣷⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⣼⣿⡀⡇⠀⠀⠀⠀⠀⠡⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⣾⣿⠟⠃⠇⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈