Tous Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠄⢠⠀⠀⠀⠀⡄⠀⠀⠀⠢⢃⠀⠀⠀⠀⠀⢀⠁⡀⠈⠰⡀⠀⡄⡄
⠀⠀⠀⠀⠀⠀⠤⠀⠁⠘⣧⣀⠤⢀⠀⠀⢀⠼⠀⠀⠀⠘⢆⠀⢀⡀⠀⠃⢂⣁⠒⠐⠀⢀⢀⠀⢠⠀⠁⢁⢊⣄
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢛⣿⡦⡆⠀⢰⠆⢰⣢⡀⡸⢠⠀⢥⣀⢢⣀⣌⢀⡐⡄⠀⠁⢄⠀⠁⢘⢰⡆⠀⠂⠰
⠀⠀⠀⠈⠀⡷⡑⣀⢀⢨⠅⣔⠒⠛⢢⠀⠰⣋⣠⢃⠀⢤⠉⢭⠀⠈⠼⠁⠑⠂⢷⠆⠀⡀⣀⡀⠩⠁⡀
⠀⠀⠀⠀⠐⠉⠍⠡⠓⣴⠠⡄⠁⠨⠋⠀⠀⠹⢼⠈⠣⠌⠐⡻⠅⢀⠀⠢⠀⠀⠀⢀⣀⠃⡁⠰⠟⠉⠀⣠⢄
⠀⠀⠀⠀⠢⢼⠀⠦⠬⠎⢹⠹⡒⢝⣧⢀⣑⠀⢘⣻⡤⢬⡚⠃⠀⢀⡘⢫⢷⡖⢀⠀⡀⠈⢤⠀⠀⠀⢀⠡⢤
⠀⠀⠀⠘⠝⣐⠄⢠⣤⡰⣄⠠⠴⠞⠁⠀⠢⠁⡘⢦⠒⢎⠁⡀⠄⠈⡟⢻⡿⢆⠀⠀⣀⢀⣾⠱⣀⠤⠲⠈⠂⠈⠂⠀⡄
⠀⣀⠀⢠⠀⡰⠀⠀⠉⠍⠋⣼⠁⠀⠄⠀⠀⡒⠓⢺⠢⣝⡿⠋⠉⠉⠑⠪⡥⠂⠉⠿⠀⠂⡘⠉⠀⠀⠀⠀⠀⠀⠈⠢
⠀⢁⠔⠁⢊⢀⡠⢀⡀⢠⠄⠈⡙⣠⠤⢤⣄⡱⠄⠖⡁⠹⠁⠀⠀⠀⠀⠀⠰⠀⢠⣒⠃⠀⢁⡄⠰⣀⣀⢀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠂⠪⠤⠄⢺⣀⠁⠀⠀⠀⠀⠣⣴⠁⠈⢄⠀⠀⢀⡠⠔⠾⢖⠻⠕⠊⠝⠂⠃⡐⠏⢉⠈⠉⠒⡀
⠀⠀⠰⠄⠢⠤⠊⠻⡆⣄⠒⠀⠰⠄⠀⠄⠀⠐⠀⢘⡆⠀⠀⠀⢰⠏⠀⣌⡀⠢⡤⠀⣨⠀⠀⠀⠈⣱⠈⠀⢀⠀⡇
⠀⠀⠀⡀⡀⡨⠆⠀⠘⡭⠰⠴⠃⢩⣄⢀⡀⣀⡠⢄⡸⠀⠀⠠⣘⠰⠞⣀⠍⠄⢑⢲⡔⣢⢴⠂⠭⠄⠙⠈⠁⡔⠠⢀⠒
⠀⠀⢘⡁⠉⠀⠀⠀⢀⠖⠨⠳⢦⣾⡞⣔⠂⠀⠀⠀⠀⢠⢊⣭⡙⠉⠙⠟⠂⣄⠨⠕⡊⠀⠆⡿⢀⠐⠄⠀⠀⠀⠀⠨⠄
⠀⠀⡀⠈⠲⢠⡄⢆⡏⣂⠆⠀⠀⠈⠠⡙⠂⠖⠂⠲⠄⠈⢁⡸⠾⠤⡴⢧⡞⠣⠁⣼⢂⢁⡞⣀⠂⠱⠀⡂⠀⢀
⠀⠀⠀⠀⠀⠋⠰⠆⠃⠥⠰⠂⠁⠀⠠⣀⡩⣆⣉⠀⢶⣀⠯⣽⡄⠉⠴⠂⡰⢶⠰⠥⠬⠃⠐⠀⠀⢀⠌⢁⠐⠂
⠀⠀⠈⠀⠀⠀⢀⢂⠉⠈⣅⣠⠲⠂⠀⢈⠁⢸⢸⣠⢂⠤⠰⠞⠁⢐⠾⢈⡅⠀⠙⢢⡄⠀⠁⡌⠈⠉⠀⣋⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠚⠀⣠⡀⠘⠁⠙⠲⣄⠐⠒⠀⣀⠀⠈⣪⣀⡥⡀⠀⠀⠘⠠⣐⣁⣀⡀⡠⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠳⠔⢀⡡⡇⠀⠀⠀⠀⢸⠑⢢⠔⠃⠘⠳⠂⢉⡆⢰⣄⢄⣤⢊⠀⡀⣀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠭⠔⢣⣀⠀⠀⣀⠎⢠⠀⠄⡢⠘⠉⠑⡦⠰⠥⢐⡆⢰⡊⢀⣡⡄⠄⢐⠈⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠠⠮⡫⡉⠡⠀⢀⠁⢀⢣⠀⠀⢀⢴⠀⠈⠆⡤⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⡡⠘⠃⠱⠬⣅⣀⡈⡀⠨⠓⠈⠀⠐⠁⠈⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⡀⠀⠀⠀⠀⣄⠠⣤⠀⠀⢠⡄⠀⠤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣴⠀⠀⠀⠀⢈⠁⠀⠀⠀⢀⢀⣀⣠⣀⡍⠀⡦⡆⠆⠰⠸⣀⠠⠐⠀⢀⠀⢀⣶⡦⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⠀⠀⠂⠁⠈⠀⠀⠀⠊⠛⠀⠘⣩⣅⣁⣥⣄⣄⣤⠀⠀⠈⠢⣴⢠⠴⡇⠈⠛⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣶⠄⠀⠀⠀⠀⠠⠆⠠⠀⠀⠀⣠⣿⢻⣿⣿⣯⠻⣷⣥⣷⡆⣿⣗⣾⠃⠆⠰⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣠⠀⠳⡄⠁⠀⠀⠀⠘⠛⠟⠛⡻⠿⠿⠛⠛⠻⠟⠃⣿⣿⣿⡷⠒⠒⠒⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢶⣦⣄⠈⠆⠀⡑⠀⢠⡆⢀⣀⠀⣄⣯⣅⠀⢀⣤⣾⡷⠀⠀⠻⠿⣿⣿⡆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⡰⣬⡍⠀⠢⠄⠈⠁⠀⣤⣄⠀⢠⣾⣿⣯⢰⣿⠏⠛⡤⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⡷⠀⢾⡟⠀⣠⣄⣤⠌⠁⣠⠀⠙⠛⠃⠀⠁⠀⠀⠳⠚⠀⣀⣄⡀⠀⠀⠀⠀⠀⠰⠏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⡤⠀⢠⣀⡄⠉⣀⡀⠈⠋⠁⠀⠀⠀⠀⠘⣦⡏⠀⠬⠀⠼⡹⠯⠛⠀⠀⠀⣶⡆⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠘⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⡄⠏⢰⠂⠀⠀⡀⡄⣤⠀⢠⢀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠓⠘⠀⠀⣶⣿⣷⢖⣶⣷⣿⣻⠄⠀⠠⠒⢠⠛⠁⠉⣀⠠⣀⣀⡄⠾⠄⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⣀⣿⣿⣿⠛⣛⣿⣻⢹⠁⠀⠀⠀⠘⠋⢛⠉⠋⠀⠀⠀⠀⠀⠀⣀⠛⠻⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠗⠀⢀⣿⣿⣿⣿⣿⠉⠿⢿⣿⡟⡷⠀⠀⢀⠀⠻⠟⠶⡄⣠⠂⣀⣀⠀⠚⠉⢠⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠀⠁⢾⡿⠷⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⢰⡠⠀⠛⢃⠂⠈⢠⡯⠅⠀⠈⠉⠀⢀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣶⣶⣤⡀⠀⢰⣖⠀⠁⠀⠀⡀⠒⠉⠁⠀⠛⣤⣀⡺⠁⠀⠀⠉⠒⠮⠵⠀⠀⢀⣙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⢠⣿⢰⠴⠴⠊⠀⠀⠀⠀⠀⠖⠛⠛⠟⠒⠀⠀⠀⣤⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⡿⣿⢠⣼⣿⠀⢠⠁⠀⠀⠀⢠⠺⡖⢠⡔⠊⠠⠀⠀⡴⡄⠀⠀⠀⠀⠈⡿⡅⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣼⣿⠀⢀⠄⠀⠐⠀⠈⠒⠀⠀⠐⢠⣾⣦⠀⠀⠁⠀⠊⣠⣴⣆⠀⢁⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠏⠉⠈⢻⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⡆⠀⠘⠀⠀⠉⠙⠋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⢰⡀⠀⢀⡈⡀⠈⠉⠀⣶⢦⡀⠀⠀⠀⢠⠀⣷⢿⡇⠀⠀⠀⠀⠀⠀⢀⡀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠀⣤⣠⣤⣄⣨⡀⠀⠀⠀⠀⣹⠶⠛⠁⠀⠀⢺⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣷⡦⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢀⢠⠀⠀⣴⣶⣾⣿⣿⣄⠀⢠⣴⡶⢲⣶⢛⢍⡾⢷⣾⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠿⠿⠿⠿⠿⠿⠿⠤⠀⠈⠥⠤⠥⠤⠿⠷⠿⠿⠿⠿⠆⠀⠤⠶⠾⠀⠾⠝⠃⠴⠇⠀⠃

⠀⠀⠀⠀⣶⠀⡤⠀⠲⠶⠀⠀⢀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠐⠀⠠⠤⡤
⠀⠀⠀⠀⣿⠀⠐⠶⣆⠓⣘⡉⡉⠁⠣⣀⡨⠄⠛⠀⠀⠆⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⣿⠀⠀⣸⣿⣿⣿⣻⣯⣶⢸⣷⣇⣀⣋⠉⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⣿⠀⠈⠛⡉⠝⠛⢉⣍⠉⢼⣿⣿⡀⠀⢀⠁⠀⢀⣥⠇
⠀⠀⠀⠀⣿⠀⠒⢸⣿⡇⣴⡿⣏⠀⠀⠈⠉⠀⠀⠈⣤⣠⣠⠀⢢⠀⠀⠘
⠀⠀⠀⠀⣿⠀⡂⠘⠛⠁⠉⡀⢐⠃⣤⣤⡀⠀⢠⠀⠑⠀⠉⠀⠉⡤
⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠟⠆⡀⠀⠉⢁⠀⣄⣉⣀⡀⢀⡀⠠⡦⠀⠀⢇
⠀⠀⠀⠀⣿⠀⣄⠀⢀⢀⠖⠒⣀⠀⡀⠰⠂⢀⣤⡄⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⣿⠀⣟⠀⠀⠀⢋⡉⠉⠀⠀⠀⡠⠀⠀⠀⠠⠀⠀⠀⢠
⠀⠀⠀⠀⢹⠀⠿⠂⠀⡌⠩⡭⠅⠂⣖⠀⠐⠀⢀⣀⣤⡀⠀⠀⢄
⠀⠀⠀⠀⢸⢀⠠⠄⠀⠱⣄⡐⠁⠀⠉⠐⠃⠀⢰⣿⣿⢠⡤⠦⡌⠄⠀⠂
⠀⠀⠀⠀⢸⢈⠀⠀⡀⠚⢉⠉⠀⢀⡀⠀⠀⠀⢎⢩⡅⠀⠔⡀⠈
⠀⠀⠀⠀⢸⢸⡁⠀⠝⠘⠀⣴⡄⠈⠁⠀⣴⣦⠀⠆⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⣿⣿⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⢸⢰⡶⣄⠀⠀⣄⡟⠉⠀⠀⠀⢀⣈⡿⣖⡅⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠸⠰⢋⠁⢠⣤⣿⣿⡄⠠⢾⣛⢫⡦⠹⠯⠕
⠀⠀⠀⠀⠀⠘⠇⠀⠚⠛⠛⠋⠉⠀⠁

⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠄⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠙⠄⡀⠂⠂⢀
⠀⠀⠀⠀⠀⠈⢊⠀⢆⠛⠁⠈⠄⠀⠈⢂⡀⠒⢀⠊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡑⣄⠀⡀⢀⣄⠀⠀⠀⢙
⠀⠀⠀⠂⠁⠂⠈⠂⢉⠦⡄⣤⡒⠄⠢⣤⠝⠀⠁⠀⠀⠢⠄⠀⠀⠇⠐⢀⣠⠀⠀⠰⠀⠘⠃⡀⠀⠁⠀⠋
⠀⠀⠀⠈⠆⠁⠂⠑⠢⢤⡀⠀⡂⠀⠀⠇⠐⢠⠀⠠⠾⡅⠀⠀⡠⠒⠂⠨⣦⣄⠴⠀⡀⠀⠂⡐⢆⡐
⠀⠀⢠⠂⠠⣀⡄⢂⡀⠀⠈⡐⠋⢉⡵⣌⢎⡀⠀⠈⠠⠔⠀⠀⠣⠐⠀⡊⠽⢉⠰⠑⠂⠀⠀⠛⣿⠁⡀⡠⠀⠀⡀
⠀⠀⠌⡇⠀⡄⣈⢲⠘⠖⣘⢣⠄⢹⣯⡀⣈⣇⠀⠀⠀⠀⠀⠀⠀⣸⡅⡠⢠⠁⠠⠀⠀⡜⢁⠈⠈⢣⣏⠰⠈⠄⡁
⠀⠘⠉⠐⢆⡀⣁⡚⠂⠀⠉⠘⡆⠀⠸⠑⢉⣶⡆⣀⡀⢀⠐⠀⠐⠁⠀⠀⡊⠀⠔⠂⢄⠀⠠⠀⠀⠙⠉⠒⠒⠢⠐⠦
⠀⠐⠞⢀⠀⠙⠃⡀⡳⠄⠀⢸⠩⠘⠺⡂⠘⠀⣈⠈⢁⠆⠐⠂⠉⠐⠠⠴⠁⠂⠀⠀⠈⡀⠀⠀⢰⡂⠠⠂⠀⠀⠦⡠⠄
⠀⠀⠀⠙⠤⠠⠞⠗⠀⡉⠀⠀⠀⠇⣂⡀⢠⠀⠂⠀⠈⠤⠂⡄⠀⠀⠀⣬⠀⠀⠒⠊⠀⠀⠀⠀⠘⠘⡎⠶⡆
⠀⠀⠀⠀⠀⢀⠐⠀⡬⠀⠈⡀⠓⠂⠀⠀⠀⠰⠒⠀⠀⠠⠁⠁⠀⡱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⢠⠰⢤⡀⠀⠀⠙⠂⠀⠀⠀⢭⡉⠢⠉⠀⠀⠢⠈⠙⠿⣿⡿⠁⠀⠀⠉⠉⠋
⠀⠀⠀⠁⠀⠊⢏⠹⠼⠘⠚⠀⠉⠀⠀⠠⣔⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢤⠀⣴⣗
⠀⠀⠀⠀⠀⠀⡠⢤⠀⠠⠀⠆⠖⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣤⣄⣰⢤⣀⣠⠄⠀⠘⠁⢠⠀⠄⢺⠀⠈⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠑⠐⠃⠀⠀⠀⡋⠑⠂⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠎⣿⣏⡈⠷⢦⣤⣦⢸⣏⠰⡞⠸⠀⠶⠓⠉⠁
⢀⡴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠛⠿⠛⠛⠿⠾⠿⠛⠛⠿⠇⢸⣿⣾⣿⠚⠒⠋⠀⠀⢄
⠈⢤⣴⠇⠀⠀⠀⠀⠀⠀⠛⢿⣷⣶⢾⣶⣦⣦⣄⠈⠆⠀⠀⠀⠀⠄⠀⠀⠀⢀⣰⣀⠀⠀⢀⣴⣷⠆⠀⠺⠿⣿⣿⣰⠀⠀⠀⣀
⠉⠃⢠⣄⠀⠀⠀⠀⠀⢰⣿⣼⣴⣶⣶⡆⠠⣈⡉⠀⠀⠀⠀⠂⠀⢠⡄⠀⠀⣼⣿⣿⠡⣾⣿⠹⢧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃
⠶⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠃⠽⠛⢦⠀⣴⡖⠀⢀⣀⣀⡈⠛⠀⠀⠙⠛⠋⠀⠈⠀⠀⠸⠤⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠠⢤⣤⣤⣀⠀⢀⠁⡀⠘⠋⠉⠀⠖⠉⠀⠀⠀⠀⠀⢆⣰⠀⢀⠀⠠⡟⣻⠵⠒⠀⠀⢀⣶
⠀⠀⠀⠠⠀⠀⠀⠀⢰⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠁⠰⠁⣰⠀⠀⠀⠀⠐⠀⠀⠀⠉⢙⠀⡄⠀⠀⠀⠀⠀⡀⠠⡀⠈⠉
⠀⠀⠈⠂⠀⠀⠀⠀⠃⢠⠃⠀⠀⠀⠀⡀⠠⠠⠄⠀⣄⣤⣤⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠰⠐⠰⠀⠀⠀⠁⠑⢀⣂⠀⠁⠁⠈⠈⠈
⠀⠀⠀⠂⠀⠒⠖⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⣿⣶⣷⠆⠾⠶⠷⠶⠀⠀⠈⠀⠈⡧⠶⠦⠼⠆⠉⠉⠉⠈⠀⠀⠀⠶⠂⠁
⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⡄⠈⠀⣿⣷⣶⣶⡶⠀⢰⢠⣦⣴⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂
⠀⠀⠀⠠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⣹⣿⣟⠀⠀⠀⠀⠈⠓⠂⠈⠀⠀⠀⠀⠀⢠⣤⢀⠐⠂⡀⠢⠀⠀⠄⠀⠃
⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢁⣀⡀⠙⠛⠉⣀⡀⠈⠰⠀⠀⠀⢀⡀⠄⠐⢀⠀⠀⢀⡌⠀⠀⠲⣑⡀⠠⡀⠀⠀⠀⣤⣤
⢀⣀⡄⠀⠑⠀⠀⠀⢀⠀⠀⢸⣄⠽⣽⣾⣻⣿⣷⠀⠀⢯⡄⠀⠀⠀⣀⠐⠁⠀⠀⠀⢈⣹⣦⣬⡁⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣾⣿
⠛⠉⠁⠂⢀⠀⠀⠀⠈⠐⠀⢨⡏⣹⢸⡞⢿⣿⢸⡄⠀⣿⡇⠘⠛⠛⠁⠀⠀⠀⢠⠂⠍⠉⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣉⡸⡵⢺⣿⣸⣗⠲⣭⠄⠀⠀⠀⠀⠀⠀⢀⢈⠏⠀⠆⠀⢀⢀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠱⠀⠈
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡿⠇⣿⣻⣿⣿⣿⠶⡞⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⣷⡆⠀⠀⡀⠈⢠⣶⣿⡄⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⠹⠳⡻⠿⠋⠀⠀⠀⠇⠀⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡿⣿⣷⠀⠀⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⣰⡦⠀⠀⠀⠀⠀⢀⡉⠀⠈⠁⢀⢀⡀⠀⠀⠀⠄⠀⠀⠈⠀⢯⡑⣦⡀⠀⠀⠀⠀⢿⡼⠿⠀⠀⠀⠀⠀⠀⠀⣤⢰⠆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣀⡀⣠⢀⣤⣄⠀⠀⠀⠠⠛⠁⠀⠀⠀⢸⣆⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠾⣿⠓⢠⣆⣾⣿⣿⣿⣬⣿⣿⠁⠀⠀⠀⠰⠀⠀⢰⣶⣾⣟⢶⣇⠀⠀⡠⠴⠤⢤⡚⠩⠁⠒⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠿⣿⣿⠀⠀⠀⠀⠠⠄⢤⣬⡶⣿⣿⣿⣿⣷⠀⠀⠴⠐⠀⠀⠎⡍⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠰⢈⠆⠀⠰⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠁⢀⡀⠀⡀⠂⠁⠀⢀⡀⠀⠈⡁⠀⠀⠀⠀⠒⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⠄⠠⣀⠄⠁⢀⠂⠀⠀⡠⠒⠆⠈⢁⠚⠃⠀⠀⠀⠠⠀⢨⠋⠉⠁⡀⢀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢂⠀⠀⠛⠀⠁⠠⡀⠀⠌⠀⡀⠘⢳⠋⠀⠀⠀⢠⣀⢀⣀⠀⠀⠁⢦⠰⢥⠀⠄⠄
⠀⠀⠀⠂⢀⠀⠀⠀⠀⡀⣠⠉⠂⠐⠢⣌⡰⠊⠁⠀⠀⢀⢼⠀⠈⠐⡀⠔⢂⠝⠚⠀⢿⡆⢡⡀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢦⡄⠀⠸⠀⠀⢈⢀⠔⠡⢸⡀⠀⡀⠁⡠⢛⠀⠉⠀⢀⡐⠃⠈⠐⠆⠘⢂⡉⠈⠲⣀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠘⠀⠘⠀⠀⠀⠀⠁⠐⡠⠮⠐⠀⠉⠚⡁⠰⠇⠛⢦⠌⠀⠀⠀⠈⢢⣏⡀⢤⠰⠀⠀⡌⠂
⠀⠀⠀⢠⠶⠈⠀⠑⢄⣀⢀⡠⠂⠀⡼⠀⠀⢀⠀⠄⠚⠁⢢⣀⠂⠄⠠⠀⠀⠀⢀⣤⠀⠀⠀⢀⠰⠃⠀⡀⠀⠉⡢⠠⠊
⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⢐⠒⢈⡩⠓⣛⠁⠀⠀⢀⠀⠄⢫⣀⣀⣰⡇⠐⢢⣏⠀⢀⡇⠀⠀⠈⠐⠦⣀⠀⠀⠜⠀⠒⠁⠓⠢
⠀⠀⠀⡈⠀⢀⠀⠄⡅⢀⠤⠒⠁⠀⠀⢀⠵⠀⠈⠀⠀⠜⢁⣇⠘⠂⠀⠈⢧⠙⡃⠐⢄⡀⠀⠀⠀⠀⠈⡑⠢⡀⠀⠀⠀⠀⢑
⠀⠀⠀⢅⣀⠂⠀⢸⠀⡋⠀⠀⢄⡠⠀⠁⠀⡄⣀⡠⠂⣎⠩⡽⠀⢤⠀⠀⠈⡇⢷⢀⠞⠀⠀⠀⠀⢠⠌⠁⠀⠀⠑⠦⠀⢀⠅
⠀⢀⡄⠀⠈⠑⠢⠌⠀⠁⠀⢰⠀⠀⠈⠄⠎⢰⢏⠻⡀⢣⠀⠀⡀⠀⠀⠀⢰⠇⣼⠃⠀⠀⠀⠀⡐⠢⣄⠀⠂⢀⡜⠀⠀⠈
⠀⠈⠉⠀⠀⠔⠁⠀⠀⢀⠖⠑⣄⣴⠉⠦⡴⠘⣦⠃⠑⠀⡦⠘⠁⠀⠀⢀⠾⣍⢣⠑⡦⣀⢠⠎⠁⠀⠀⠙⡠⠋⠁⠀⠀⠐⠊⠄
⠀⠀⠀⠀⠟⠀⠀⠒⠶⠋⠌⣠⠋⠉⠀⠁⠹⡀⠘⠆⠚⠉⠀⠀⠀⠀⠀⠰⠀⠣⡹⣤⡀⠉⠑⢄⡀⠀⢀⠴⠀⡀⠄⠒⡜⢀⢠
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⠁⠃⣀⠀⡄⣁⡱⡀⠐⢶⠁⠁⡸⠡⡈⠀⠢⡐⠀⠤⠐⠊⢡⠀⣰⠈⢲⠊⠠⠀⠂⠉⢀⠀⠖⠂
⠀⠀⠀⠀⡝⠄⠀⠀⠠⣏⠈⠛⡄⠉⢄⠀⠉⠒⡡⢦⠔⠋⠉⡉⠎⢰⣃⠄⡍⠄⠀⠀⡠⢪⠀⠈⠓⢍⠐⠖⠂⢁⡌⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠀⠀⠀⣀⣈⡉⠠⠀⠀⠀⠝⠀⠉⠁⠂⠀⡀⠀⠀⠀⠂⠠⠞⠠⡘⠀⠸⢀⡠⣀⠀⡀⠀⡜⢣⠇⠤⢠⡀
⠀⠀⠀⠀⠀⢀⠔⠉⢀⠂⠀⣠⠞⠈⠈⠁⠢⡋⠉⡀⠀⠁⠀⠠⠀⣀⣀⣶⣂⡟⠀⢀⠉⢠⡩⢄⣀⠀⠀⢟⡀⠤⠁⠙
⠀⠀⠀⠀⠀⢂⡀⠊⡀⠌⢰⠃⠀⢀⣄⠀⠀⠠⠀⠙⢄⡀⠐⠄⠀⣀⢼⣄⣈⡑⠂⠶⠈⣀⠀⠀⠁⢀⠂⡜⠙⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠙⢔⡀⠐⢈⢦⠀⠐⠗⠠⢀⠐⠀⠠⢚⠀⠀⠰⢏⡈⠁⠘⠉⠉⠶⠒⢶⠖⡄⠂⡡⡎⠌⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⢀⠄⠗⠀⠀⠀⠁⠀⠀⠐⡆⠆⢀⠀⠀⠉⠛⢡⡀⠀⠀⣩⠁⠍⠘⠁⠀⠆⠡⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⣇⠀⢈⠀⠈⠐⡉⠙⠢⠌⡀⠐⠀⡑⠀⡏⠢⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠃⣃⠀⠀⠐⠀⠊⠓⠒⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⠾⠍⠋⠀⠀⠀⠉⠈⡃⠀⠀⡬⠵⢒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⣾⡅⠀⠈⡄⠀⠐⠄⢐⣒⣀⣀⡓⠀⠤⠀⠀⠠⠁⠀⣽⡶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⠊⠈⣿⡄⣂⡥⠖⠚⠉⣩⣵⣷⣾⣬⡉⠙⠒⠦⢅⡢⣼⡏⠈⠪⡵⣄
⠀⠀⠀⠀⠀⠀⣠⣊⠀⠀⢐⢄⣿⡏⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠉⣿⣇⢠⠂⠀⠈⢢⡀
⠀⠀⠀⠀⠀⡰⡕⠀⠁⠒⡡⢺⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⠢⡑⠔⠈⠑⡵⡀
⠀⠀⠀⣀⣴⣥⣁⠂⠄⡼⠁⢸⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣾⣿⠀⠙⡄⢀⢄⣊⣵⣄⡀
⠀⠀⠈⢯⢯⠭⢻⣿⡼⠀⠀⠈⢿⣿⣦⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣤⣾⣿⠏⠀⠀⠸⣼⣿⢋⣉⢯⠏
⠀⠀⠀⢸⡇⠀⠀⢹⣿⡄⠀⠀⠀⠙⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠟⠁⠀⠀⠀⣼⣿⠁⠀⠈⣿
⠀⠀⠀⣸⠀⠈⢹⢸⠻⣿⣦⣄⣀⣀⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣀⣀⣀⣤⣾⡿⣿⢰⠀⠀⢹
⠀⠀⠀⢸⡀⠀⠘⢸⠄⠈⠻⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠿⠋⠀⢼⠸⠤⠀⣸
⠀⠀⠀⢸⣃⣀⣀⡈⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⡇⣀⣀⣀⢻
⠀⠀⠀⣴⢟⠛⠛⢻⣿⣦⣤⣀⣤⣤⣾⣿⠿⠋⢸⣿⣿⠋⢻⣿⣿⠈⠻⢿⣿⣦⣤⣄⣠⣤⣾⡿⠛⠛⢛⢷⡄
⠀⠀⠀⠙⠺⡤⡂⠁⠀⠹⣛⠻⠿⠛⠋⠁⠀⢀⣿⣿⠟⠀⠘⢿⣿⣇⠀⠀⠉⠛⠻⠿⢛⡻⠁⠁⠂⣄⡼⠚⠁
⠀⠀⠀⠀⠀⠘⣷⡄⠐⠑⠜⢦⡀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⣠⢎⠔⠢⢀⣴⡝
⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⣬⣤⣿⣶⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣾⣧⣧⣀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢑⣿⡯⣀⠌⠁⠢⠍⠓⠦⠤⢄⣀⣀⣀⣀⠤⠤⠖⠊⡥⠊⠁⡀⣨⣿⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠳⢄⡀⣌⠀⠀⡘⠀⠐⠆⠀⠠⠂⠀⠃⠀⠀⢡⠀⣀⠼⠚⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⢥⣀⣀⢤⠠⣤⢀⣀⣀⠶⠾⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠠⢖⠉⠀⢀⠸⠢⣀⠀⠀⢸⣿⣿⡿⠟⠻⢡⣉⣿⣿⣿⢨⠁⠀⠀⠀⢀⠉⠃⠀⠀⠀⠉⠉⠉⠳⢦⡀
⠀⠀⠀⡀⠀⠀⣆⡀⠨⠨⠑⠀⠀⠀⣿⡷⣺⠲⡊⠐⠁⠋⠉⡶⠂⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠐⢀⡂⠎⢁
⠀⠀⠀⠀⠀⣠⠀⠀⠐⠁⡗⠁⠀⢀⣿⣷⣬⣌⠀⠀⠀⢀⠌⠀⠀⡴⠂⢈⠀⢰⠀⠀⠀⠀⠈⢣⡠⢂⠊⠀⠘
⠀⠀⠀⣦⣤⡇⠀⠀⣂⡈⠀⠀⠀⠈⣉⣉⠀⠀⠁⠀⠐⠃⠸⠥⡄⠁⢰⠘⠙⠃⠀⠀⠀⠀⠀⠈⢏⠂⠠⠔⠨
⠀⠀⠸⣿⣿⣿⡀⡍⠀⠀⠀⠀⢠⠊⣁⡘⠲⠀⠀⠀⠀⠀⠀⢄⢀⠀⡄⢀⠀⣀⡠⠀⠐⠰⠛⠋⠉⠀⠀⠀⠠
⠀⠀⠀⡿⠿⠛⢃⠀⠀⡀⠤⠒⠃⠀⠈⠳⠀⠈⣠⠀⠀⠀⠀⠊⠍⠇⠀⠀⠈⠉⡇⠀⠀⣦⠀⠀⣀⠀⠀⠓
⠀⠀⠀⡀⠠⠂⠈⠀⠋⠀⡀⠂⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠂⠀⢀⠀⢀⠀⠀⡜⠈⠛⠛⠛⠂⠀⠂⣠
⠀⠀⠀⡄⠄⠈⠉⠰⠀⢰⠐⠂⠀⠀⠀⠀⠚⠃⠀⠀⢀⣶⡇⠀⠀⣀⣀⠀⠀⠼⠀⡐⠀⠀⣤⠄⠀⠀⠀⠀⠿
⠀⠀⠀⡔⠂⠀⢀⣠⣦⠈⡒⠠⠄⡉⠐⠀⠐⢁⣄⣀⢀⣁⠀⠄⠘⠛⠟⠀⠠⡯⣭⠁⠰⢄⠉⠄⠀⠀⠿⠀⠔
⠀⠀⠀⣦⠔⠋⠁⠠⠄⡀⠀⠀⣆⠂⠀⠀⠀⠈⠉⠉⠉⠛⠃⣀⡀⡀⠀⠀⠀⠀⠀⢰⠅⠀⢠⣀⡀⠈⠒⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠰⣂⢀⣤⡀⡀⠈⠠⠄⢐⠒⠀⠍⡁⠀⠴⠖⠂⠠⠀⠀⠑⠈⠐⣉⡀
⠀⠀⠀⡁⣀⠀⢀⠀⠀⠠⠉⠅⠊⠀⠀⠐⠀⡃⢴⠀⠊⠐⠑⠩⠆⢰⠀⣄⠀⠀⠀⢠⡌⠉⠐⠰⠉⠀⠀⠀⡔
⠀⠀⠀⠏⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠩⢂⠠⠦⠀⠂⠀⠖⠀⠛⣄⠀⣤⠀⠸⣏⠀⢢⣄⠀⠀⠀⠂⢠⡅
⠀⠀⠀⠀⠠⠿⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠐⠛⠋⠀⠀⠀⠒⠟⠒⠒⠚⠉⠉⠈⠉⠉⠉⠉⠊⠛⠛⠛⡀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠉⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡎⠂⣾⡁⢸⠤⣤⠖⢂
⠀⠀⢀⠴⠒⠂⠠⢀⡀⢀⠔⠁⢀⡤⠖⠒⢤⠀⢹⠀⠀⠀⠀⣀⠉⢳⡼⠀⢸⣷⣀⠓⣇⠀⠀⠊⠠⠁
⠀⢠⡏⠀⣀⣀⣀⠀⠈⠃⠀⡰⠋⠀⠀⠀⠈⡇⢸⡇⠀⡠⢼⣄⠑⠌⠑⠂⠀⡿⣷⠀⠈⡄⠀⠀⢦
⠀⢸⡀⠐⡅⠀⠈⠉⢻⠀⠰⠁⡄⠀⠀⠀⢰⠁⢸⠇⠀⠑⢦⡙⠇⠀⠀⠀⠀⠐⡽⠄⠀⠀⠀⠀⠈⡄
⠀⠈⣇⠀⠰⡀⠀⠀⠘⡄⠀⢠⡀⠀⠀⠀⡌⠀⣸⠀⠀⠀⠀⠉⢢⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠘⢆⠀⠹⣄⢠⠖⠀⣠⡂⠉⠒⢄⡰⠁⢠⠇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡆
⠀⠀⠀⠈⠳⡀⠈⠁⠀⡴⠁⠈⠢⡀⠀⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠘⢆⣠⠊⠑⠢⠤⠖⠉⢂⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣀⡠⠤⠴⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⢀⡠⠄⠲⠊⠉⠉⠉⠩⠉⠉⠛⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡴⠊⠉⠉⠉⠉⠉⠉⠉⠑⠒⠤⣀⡀
⠀⠀⢠⠏⠉⠈⠉⠈⠉⠁⠁⠈⠉⠉⠉⠈⠉⠁⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⢨⠧⢀⠄⠀⠀⠀⢀⠀⠀⣀⠀⢀⡀⣀⣀⠀⠀⢺⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠠⠤⠀⠀⠀⠈⢧
⠀⠠⡚⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠀⠀⠀⢹⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠧⡄⢀⡠⠬⡈⢀⡀⠀⠀⠁⣀⣁⢈⣐⠀⣠⠌⣹⠋⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠑⠤⣀⣀⣀⠀⠀⡀⠀⠊⠀⠀⢀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⡀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡠⠖⡛⠉⠅⠀⠐⢀⠱⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⠀⠀⠀⢑⠀⢪⡂
⠀⠀⠀⠀⢰⠈⠀⠔⠂⠀⠰⠃⠁⠀⠀⠀⠀⠀⢈⡀⣀⡀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠂⠁⠑⠣⣑⣠
⠀⠀⠀⠀⠘⡆⠆⣄⣀⠀⠠⠖⣚⣤⠢⡀⠀⠀⠈⠁⠐⠄⡀⠀⠀⠀⣀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠳⡀⢀⢲⡐⣟⢯⡳⡽⢷⣮⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣒⠒⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠈⠪⡪⠫⡹⣮⠣⢁⠢⠀⢄⠀⠀⢑⡄⠀⡠⡐⣬⡵⠖⡘⠀⠀⠈⠀⡀⡉⠀⠀⠐⠂⠠⠃
⠀⠀⠀⠀⠱⠵⠀⠐⢔⢄⠀⠀⠀⢐⣀⣥⡶⠌⠂⠀⠀⠉⠚⠡⠱⠈⠁⠀⠀⣆⠀⠉⠀⠉⠁⠐⠃⢠
⠀⠀⠀⠀⠡⡘⠀⠀⠀⠑⠍⠩⠀⠂⠉⠀⡀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠠⡀⠀⠀⠀⠁⠀⠒⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠂⢄⠀⠀⠀⠀⡈⢀⠤⡘⠀⠄⠀⠀⠈⡐⢨⠭⣙⢅⠁⠀⠀⢠⠐⠀⠀⣂
⠀⠀⠀⠀⠀⢰⠋⢅⡀⢀⡜⠃⠀⠀⠠⠀⠨⠀⠁⠀⠊⠀⠀⠀⢀⠀⠂⠒⠈⠐⠀⠀⠸⡬⡀⡂⠘
⠀⠀⠀⠀⠀⠀⣤⡁⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⠄⡀⠀⠗⠂⠔⠚⠉⠀⠀⠘⣏⠈⠔⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠚⠙⠀⠚⠀⠀⠀⠀⠔⠂⠐⢄⠀⢹⡆⢨⡖⣘
⠀⠀⠀⢠⡴⠖⠒⠃⠀⠀⠀⠈⠁⠀⢀⡀⠈⡄⠀⠀⣀⡤⠤⢄⠀⠀⠀⠸⠀⠭⠏⢀⠀⠈⠛⠋⠉⠁
⠀⠀⠀⠘⠣⠀⠀⠀⠒⠀⢈⢁⢀⣀⣀⡀⠀⠀⠀⠀⠕⠤⠀⡊⠄⠀⠀⠀⠰⠒⠂⠁⠀⠀⠠⢄
⠀⠀⠀⠀⠐⠀⠂⠉⠘⡀⣐⠈⠥⠀⠀⠀⡀⢀⠀⠀⠰⡸⠌⣀⠄⠀⠀⠀⢀⢄⠀⠀⡀⢠⠃⡐⠄
⠀⠀⠀⠀⠆⡀⢀⠀⠀⠀⡅⠀⣀⠀⠀⠤⠓⠚⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠻⡔⣣⠀⠀⠘⠀⠡⠂
⠀⠀⠀⠀⠰⠡⠘⠒⠂⠉⠈⠀⠖⣀⡀⠠⠀⠊⠀⠌⠠⢄⠀⠀⠀⢰⢂⠀⡀⠹⠤⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⣎⡉⠀⠀⢦⠀⠀⠀⠀⠂⠀⠉⡈⠀⠀⠀⠉⠙⠷⠀⠀⠀⠀⠀⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠡⠀⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠁⠀⠀⠐⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠰⠦⠶⠴⠆⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠆⠀⠀⣀⣀⡀⠀⠠
⠀⣠⣴⣾⠟⣿⡇⠀⠀⠀⠈⠀⠀⠆⠀⠑⠒⠚⠂⠚⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐
⠀⣿⣬⡼⠶⠛⠃⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢀⣠⣞⡇⠈⠀⠫⠩⠥⠼⠃⡀⠀⣶⣳⠐⠂
⠀⠉⠁⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠔⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣣⠟⠁⠀⠀⠀⠰⠇⠀⠀⠀⠀⠘⠋
⠀⢀⠀⠀⠀⢀⡀⠀⠀⣰⣂⣂⣲⣀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⢸⠟⢁⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠻⠭⠿⠭⠝⠇⠀⠰⡏⣋⣹⣷⣽⠇⠀⠀⠀⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠉⠁⠐⠀⢀⠀⠀⠀⢀⠀⠀⠦⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠩⢐⠀⠀⢨⠀⠀⠀⠀⠸
⠀⠀⠴⠀⠀⠀⣈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⢨⣲⠀⢨⠀⠀⢄⣀⠈
⠀⠠⠀⠀⠀⠀⢀⣈⠔⠀⠀⠀⢰⡶⠶⠄⠀⠀⠀⠀⠀⢠⡤⣤⣤⠀⠀⠀⠁⠀⠈⣤⡤⠆⠀⠀⠀⠀⠀⠈⠐⠀⠐⠌
⠀⠀⠀⠀⠀⠁⢉⠄⠐⠀⠀⠀⣼⣇⠀⠲⠤⠤⠄⠀⠤⠘⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣽⣉⣁⣄⣀⣀⣀⣀⣀⣁⣀⣀⣙⠀⠀⠀⠀⠀⠀⡈⢲⣠⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⡏⣠⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠤⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⢿⡟⠃⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⡶⡢⡀⠀⠁⠂⠐⠒⠀⠀⢀⢀⠀⠀⠀⡀⡀⡀⠀⣰⠖⠀⠒⠀⠐⠐
⠀⠈⠀⠀⠀⠝⠂⠀⠀⠀⠀⠀⠀⡎⣭⢉⣑⢂⣜⣣⡥⠏⠀⡄⡀⠀⠀⠘⠀⠛⠘⠀⠂⠀⠃⠓⠃⣼⡏
⠀⡀⠀⠀⠀⠀⠀⠁⠀⢀⡆⠀⠀⠛⠾⠿⠿⠛⠋⣽⣀⣠⠀⡁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀
⠀⣀⠀⣀⣀⣀⣐⣒⣀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢡⠐⡴⣆⠀⠍⠠⢂⢠⠀⠀⠀⠀⠀⠀⠀⠇⠇⠀⠄⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⡂⡤⡒⠂⠀⠂⠄⠀⢂⢢⠀⠂⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠈⠐⠀⠠⠀⠀⠀⠤
⠀⠀⠀⠀⢠⡀⠤⠀⠀⠀⠀⠀⣀⠁⠀⠁⠁⠀⠁⠀⠀⠁⢀⡀⠀⠈⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠓⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⠶⢶⡄⠆
⠀⠀⠀⠠⢠⠀⠀⡠⠀⠀⠀⠀⠀⠀⣾⣿⣭⣽⣽⣽⣿⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠂
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⡀⢀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠐⠀⠀⠁⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⢸⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⣿⣇⣀⣀⠀⢸⣿⣿⣿⣿⠀⢰⣶⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡟⠀⠈⠻⡦⢰⡟⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠉⠑⠛⠛⠛⠛⠛⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣇⠀⢀⠀⠀⣾⣟⣿⠀⠀⢠⣤⣤⢲⡟⠛⠛⢻⣦⣤⣤⠀⠀⢸⣠⣤⣤⡇
⠀⠀⠀⠀⢰⣿⡟⠛⠁⠘⠛⢿⣿⠀⠈⠀⠀⣿⣐⣽⠀⠀⠘⠛⠛⢼⣧⣤⣤⣼⠟⠛⠛⠀⠀⢸⣿⣿⣿⡇⠀⠠
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠻⠃
⠀⠀⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⢤⠀⠀⡆⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⢰
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠊⠀⠀⡇⠀⢸⠀⠀⠐⠆⠀⠀⡇⠀⢸
⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⣘⣷⣶⣶⣶⣶⣶⣶⣶⣦⣿⡀⢀⡀⠀⠀⠀⠃⢠⣼⣤⣤⣤⣤⣤⣤⣧⡄⠘
⠀⠀⠈⠉⠉⠉⢩⣽⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠁⢀⣤⣤⣄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⢀⣀⠀⠈⠉⣉⣉⡁⠀⠀⠚⠀⠀⣠⡿⠃⣿⣿⣿⣿⣿⣧⠻⣧⣄⠀⢰⣿⡿⢿⣿⣧⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠘⠟⠀⡴⠋⠀⠀⠈⠳⡄⠀⠀⠀⠿⠇⠀⠻⠿⠿⠿⠿⠃⠀⠿⠟⠀⠘⢿⣿⣿⣿⠏⠀⣄⠄⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣏⣀⠀⠀⠁⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⣰⣿⠀⠀⠛⠀⢰⣿⣿⣿⣿⣿⣟⣧⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣇⣀⣀⣀⣼
⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠿⠟⠀⠀⠀⠀⢠⣿⣿⣿⣤⣿⣿⡇⠀⠀⢀⠀⠀⡞⠛⠓⠒⠒⢲⠀⢀⣀⣈⡉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣤⣤⣄⠀⠀⢉⠉⠉⠉⠉⠉⠁⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢸⡿⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⣼⣿⠀⠈⠛⠃⠀⠀⣀⣀⣀⣀⠁⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠘⠷⠵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠿⠟⠀⠀⠀⠀⠀⢸⣿⠟⠛⣿⡇⠀⠀⠀⣇⠀⡀⢀⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠈⠀⠀⣾⣷⢸⣿⣿⣿⣿⡇⣾⣷⠀⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠘⠿⠿⠿⠿⠇⢿⡿

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⡀⢠⠀⠀⢄⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠠⠐⠀⣀⢡⡀⠆⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⡄⠀⠸⠀⠔⠘⠘⠊⠄⠀⠉⠀⠀⠡⠀⠀⠀⠀⠀⡀⡀⣧⡄⣧⡗⡠⡐⠳⡘⠆⡅⠄⣦⢄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡈⠁⠀⠀⠀⠀⠀⠁⠆⠋⣁⠘⡰⢇⠉⠆⠙⢸⠀⠄⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⠾⣄⣅⠣⠈⣤⠆⣻⡼⢢⡄⢠⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⡀⢠⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠴⠥⡌⠀⠄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣷⠀⠀⠀⠀⢸⠀⠐⠠⠄⠀⠔⣠⠀⡄⣶⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠀⠐⠲⠶⠶⠞⠴⠟
⠀⠀⠀⡈⠓⠠⠤⢄⠀⣀⣀⣀⠀⠀⠰⠞⠃⣈⣾⠀⠀⠀⠀⠀⢇⠀⠁⠀⠁⠈⠉⠉⠁⠒⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⡖⠒⢤⣀⡀⢀⡀⠀⠀⠀⠀⢀⡄⠉⠭⣲⠆⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢠⠉⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣰
⠀⠀⠀⡗⢦⡈⠉⡀⠀⠀⠁⠈⠉⠊⠉⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⢀⠘⠷⠤⠀⠀⠀⠠⠴⠔⠒⠀⡠⠖⠁⠀⠀⠀⠀⠀⡄⠈⡀⠀⠀⠄⣄⠀⠠⠃⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠠⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠃⠂⠘⠂⠒⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠄⣠⣄⠐⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢀⠙⠲⠄⠀⠢⠴⠀⠀⢫⣙⢃⠀⠑⠒⠶⠆⠀⠀⠢⠐⣦⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠓⠋
⠀⠀⠀⠀⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠂⠈⠠⠔⠠⠄⠩⠗⠠⠔⠰⠒⢠⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠊⠀⠒
⠀⠀⠀⠀⠀⠀⠉⠾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠐⠁⠀⠀⠀⠠⠘⠁⠀⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣿⣛⠲⣄
⠀⠀⠀⠀⡴⢋⠩⢉⠍⡉⠍⠙⢦⠀⠀⠀⠀⠀⣠⣖⣛⣛⣛⣳⡀⠀⠀⠀⠀⠀⢀⡇⠘⡇⠀⠀⠀⠀⠀⢠⠖⣫⡥⢾⢳⣗⣯⣙⣮⡇
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠥⠤⠤⢼⡇⠀⠀⠀⠀⢧⡤⠤⠤⠤⢤⡟⠀⠀⠀⠀⠀⣼⣉⠉⢻⡀⠀⠀⠀⢠⠏⡾⡥⣌⢸⢸⠿⣚⣭⢶⡀
⠀⠀⠀⢸⡗⠚⠒⣖⣛⣲⠒⠓⢺⠅⠀⠀⠀⠀⠸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣏⢈⡇⢸⡇⠀⠀⠀⢸⠸⡇⢓⡛⠾⠖⣫⣅⢸⢸⡇
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡿⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢹⠉⠀⢸⠀⠀⠀⠀⠘⣇⠳⣜⠿⢊⣤⣙⣡⢏⡼
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣰⡇⠀⠀⠀⠀⠀⠀⣟⠀⠀⢸⡄⠀⠀⠀⠀⠈⠳⢬⣛⣛⣚⣋⡵⠚
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⣠⣖⢳⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣟⢦⡀
⠀⠀⠀⢸⠷⠾⢦⣷⣯⠼⠶⢻⠂⠀⠀⠀⠀⠀⣠⣤⣭⣼⣤⣤⠀⠀⠀⠀⠀⢀⡴⠋⡁⠂⠐⢈⠙⠦⡄⠀⠀⠀⠀⢀⡞⡁⢈⠀⡉⢺⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠋⣳⠀⠀⠀⠘⢶⠒⢶⠖⠒⣶⠒⡶⠃⠀⠀⠀⠀⣸⡀⠄⠠⢀⡠⠏
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣻⣀⣀⣀⣀⣿⣛⣁⠀⠀⠀⠀⠘⡇⢸⡆⢀⡏⢰⠇⠀⠀⢀⣠⡴⣋⡽⠶⠚⠋
⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠼⠁⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣀⣀⣠⠽⠁⠀⠀⠀⠀⠹⢤⣧⣼⡧⠟⠀⠀⠀⠈⠳⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣙⣦⡀
⠀⠀⠀⠀⠀⢀⣀⡤⠞⢧⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⢦⠀⠀⠀⢠⣯⣤⣬⣷⣬⣷⡀
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢿⡀⠀⠀⠀⢰⠏⠁⠀⠟⠁⠀⠿⠁⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠓⠺⡆⠀⠀⠈⢷⠛⢓⣺⠷⡾⠁
⠀⠀⠀⠀⣷⠶⣤⠴⢤⡴⢶⡏⠀⠀⠀⣞⣶⡒⣲⣒⣒⣖⢒⣖⣒⣲⣺⡆⠀⠀⠀⠀⢀⣴⠋⠉⠳⢤⣠⠇⠀⠀⠀⠸⡖⢋⣥⢶⠇
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠁⣸⠃⠀⠀⠀⢿⠲⠭⣽⠮⠥⣬⠭⢾⡭⠵⣻⠇⠀⠀⣀⣴⡏⠉⠳⡄⠀⠀⡽⠀⠀⠀⠀⠀⢻⣉⡤⡞
⠀⠀⠀⠀⠈⣧⣸⣆⣸⣀⡏⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠚⠛⠉⠉⠀⠀⠈⠳⢤⣽⣄⣀⡽⠶⠚⠁⠀⠀⠀⠀⠀⠈⣇⣸⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢶⣤⣄⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⠀⣰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢺⠶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⢧⡼⣷⣦⢷⡄⠀⠀⣠⠏⢠⠙⢶⠏⢠⠙⢦⠀⠀⠀⠈⣿⠉⡏⠘⣷⠶⡿⠀⠀⠀⠀⠀⠀⢀⡴⣳⢛⡞⠁⠙⣦
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣸⠦⢾⣹⠏⠀⠀⠀⡇⠀⡼⠃⢸⡇⡼⠃⢸⡇⠀⠀⠀⡿⠀⣧⡞⠃⠀⠛⡆⠀⠀⢀⣠⢖⣫⣞⡵⠋⠀⠀⢠⡟
⠀⠀⠀⣰⠋⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠻⣄⠓⢀⡼⡄⠓⢀⡾⠀⠀⠀⣾⠁⠀⠈⡇⠀⠀⠀⡇⠀⠀⢸⡖⣻⠖⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋⠀⠘⠶⠋⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠙⢧⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠳⠶⠒⠶⠃⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⣀⡸⠀⠀⠀⠀⠀⠀⠀⢎⡀⡱⠀⢀⣄
⠀⠀⠀⠀⠀⠀⡃⠈⡄⠀⠖⠲⠀⠀⢀⠴⡄⠀⠀⢠⠀⠄⠀⡌⠀⡂
⠀⠀⠀⠀⠀⠀⡭⢭⠀⠀⠀⢸⠀⠀⠨⣀⠸⠀⠀⠐⠀⠀⠀⢨⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢰⠀⢦⠀⠀⠸⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠊⠉⠑⢄
⠀⠀⠀⠀⠀⢀⡄⠠⠒⠒⠀⢸⠉⠉⢹⠀⢘⠉⠉⠙⠀⠒⠂⢆⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⠀⠸⠀⠀⠈⠉⠁⠀⢐⠀⡇⠈⠢⡀⠀⠀⢀⣤⣤⣒⡀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠷⢀⠀⠐⠚⠀⠀⠀⠀⠀⠀⢸⠀⣨⠀⠀⠀⠀⠀⠀⠘⠒⠃⢀⠴⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠒⠂⠀⠐⠒⠒⠂⡞⠅
⠀⠀⠀⡂⠀⠁⠒⠀⠤⠤⠀⣀⣀⣀⣈⣉⣁⣀⣀⣀⡀⠠⠤⠄⠐⠊⠁⠀⡇⠀⠀⠰⠆⠀⠀⠀⠤⠤⠄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡆
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠐⠒⡏⠄
⠀⠀⠀⣉⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢈⠀⠀⠀⢐⠒⠂⠀⠠⠤⠤⠤⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆
⠀⠀⠀⠈⠉⠒⠠⠤⢀⣈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠈⢉⣀⠠⠤⠒⠈⠨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠉⠁⡏
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠠⠤⠄⠄⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠆
⠀⠀⠀⠈⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠒⠒⠂⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠒⠒⠒⠒⠒⠒⠂⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣄⠤⢀⡤⠠⢄⡠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⡠⠔⢒⡠⠶⠺⣦⠴⠦⣴⠳⠶⢄⠀⠩⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⠊⡠⠊⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠑⣄⠈⠢⡱⡀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⡀
⠀⠀⠀⢠⠃⡔⠁⠀⢀⠃⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠈⠆⠀⠑⡘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⢀⠆⡜⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠐⡈⠆⠀⠀⠰⡁⠑⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢁⠇
⠀⠀⠎⡜⠀⠀⠀⢠⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠐⡈⠄⠀⠀⠋⢲⡐⠢⠤⠬⣉⣉⠈⠉⠀⠁⣉⣀⣀⡉⣁⠠⠀⢐⡴⠙⠆
⠀⠈⡶⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡀⠀⠀⠰⡆⠀⠀⠁⠦⠌⣁⠐⠂⠀⠄⠀⠠⠨⠤⠀⠀⠠⠀⠀⠒⣈⣁⣰⠋
⠀⢰⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢁⠀⠀⠀⠈⠒⠤⡉⢈⡁⠀⠐⠒⠀⠀⠀⠈⠉⢉⣀⣁⠤⠒⠁
⠀⠈⠒⠀⠄⠀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠰⠂⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠂⠉⠂⠤⢀⣀⠠⠔⠊⠁⠒⠒⠒⠒⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⢠⡏⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⣶⢠
⠀⠀⣷⣶⣾⣴⠚⠓⠛⠛⠛⣶⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢸
⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⣸⣿⠶⣦⣴⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢸
⠀⠀⣿⣿⣿⠻⠦⠤⠤⠤⠤⠟⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣿⠼⠀⠀⠀⠀⠀⠀⢠⣿⣯⣟⡻⡿⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⣶⣴⣿⢸
⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠯⠿⠟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣾⡟⠛⠛⠛⠛⠛⠛⢿⡇⠀⠀⠀⠀⢀⣀⣀⣉⣉⣂⣤⣄⡀⠀⠀⢠⣿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢿⡟⡻⢦
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣉⣉⣉⣉⣹⣏⢶⣿⠀⠀⠀⠙⠛⠛⢿⣷⢤⡀⠀⠀⠀⠀⠀⢠⣴⡞⠋⠁⠀⠈⢦⣭⣿
⠀⠀⣿⡇⠀⣀⢀⡀⡀⠀⣸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣄⠀⠀⠀⣿⠉⢛⡄⠀⣀⡤⠞⠋⠁
⠀⣀⣝⣛⡛⠛⠟⠟⠻⣛⣛⣣⡀⠀⠀⠀⢿⣿⣿⣭⣽⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠈⠻⠾⠿⠛⠉
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⢀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡄
⠀⢰⣋⣉⣀⣶⣿⢿⣿⣏⣦⠀⠀⠀⠀⠀⠀⣀⣈⢻⡿⠛⠀⠀⠀⢰⣾⠿⠛⠛⠛⠻⢿⣿⣿⣶⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡧
⠀⢸⣿⣿⣿⡏⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⣾⣷⣷⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣠⣾⣷⣶⣶⣶⣶⣶⣿⣆
⠀⢸⣿⣿⣿⣿⣦⣤⣾⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣯⣿⠀⠀⠀⠀⢿⣿⣿⣏⣿⣿⣅⣀⣀⣽⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⠿⠿⣾⣶⣶⣾⣿⣿⠿⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣶⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⢤⣀⣀
⠀⠀⢸⣟⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡳⢀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⣛⣛⠷⣶⣦⠀⠀⠀⠀⠀⠀⢰⣇⣀⠤⢠⡈⡿
⠀⢠⣾⡟⢻⣷⡶⠶⠶⣶⡄⠀⠀⠀⠀⠀⣸⠀⢸⣿⡿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣱⣿⣿⣿⣿⣎⢿⡄⠀⠀⠀⠀⠀⡾⣾⣫⡿⣷⣺⠇
⠀⢸⣿⢽⢿⢿⣧⡤⢤⣿⡇⠀⠀⠀⠐⠚⠁⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣧⢻⣿⣿⣿⣿⡿⣸⡇⠀⠀⠀⠀⢸⢧⣞⡾⣭⠗⡟
⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣦⣛⠿⠿⣛⣵⣟⠀⠀⠀⠀⠀⠻⢼⣱⣗⡏⢸⠃
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠖⠉⠢⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⣀⠠⠤⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣀⣀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⡀⢀⡜⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⡠⠖⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢶⣘⣇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠊⠛⡄⠛⠁⡘⢦⡀⠀⠀⠀⢀⠤⠖⠁⠀⠀⠁⢰⠀⠀⡀⠀⠀⠀⢀⡔⠀⠀⠀⢂⡛⢉⡡⠞
⠀⠀⠀⠀⢀⠠⠌⠀⠀⠀⠀⠀⠈⠢⣠⠁⠀⠉⢉⣁⠦⠥⠤⠠⡄⠀⠀⠀⠆⠀⠀⠛⠃⢀⠴⠃⠘⡏⠉⠀⠉⠑⢤⡀
⠀⠀⠀⠠⠋⠀⠀⢀⠔⡒⡀⢀⡤⠒⠀⠤⣀⣀⡃⠀⠀⠀⠀⠀⢠⠀⢀⡮⢀⡀⠀⢀⠊⠀⠀⠀⠀⠉⢢⠋⢃⣀⠀⠁⠈⠱⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣡⡴⠋⠛⡄⢀⠲⠄⣄⠀⠙⣀⠀⠀⣄⣤⠚⠀⡞⢊⡰⢈⣱⠇⠀⠀⠀⢠⡔⢦⡾⠊⠀⠸⡆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠢⢄⡀⠰⡁⠰⣿⡆⢰⣌⠀⠦⣉⠀⠀⠈⠑⠃⠀⣠⣉⣩⣆⡥⠙⠷⠏⣀⠀⠀⠀⠈⣁⣈⣡⣧⠀⠀⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠣⢀⣡⣄⣨⠗⠊⠉⠐⢐⡄⠈⡆⠀⠀⠀⠀⢿⠉⠁⠀⠀⠉⠉⠉⢻⡀⠀⠀⠀⠀⠀⢀⠀⡉⠛⠃⠈⠉⠀⠀⠇⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠘⠂⠠⠬⠀⠀⠀⣦⠌⠉⠉⠉⠉⢉⣹⠀⠀⢸⠃⠀⠀⠀⠀⢀⣧⡄⠚⡄⣠⠀⡤⠰⠆⢸⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠦⣀⠀⠀⠀⠀⠀⣠⡷⠄⣦⠀⠀⠰⠀⢸⠀⠀⠈⣨⡀⠠⠔⠂⢉⣠⠧⠘⠣⣀⣀⠄⠐⠂⢉⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡇⠀⢰⠛⠅⠀⠀⢀⡿⠀⠀⠀⠀⣼⠤⠐⠈⠁⢀⡠⠐⠉⠀⠞⠂⠤⠄⣀⣈⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣤⣤⡔⠉⠰⠖⣻⠃⠀⣠⣼⡟⠚⠓⠛⢟⡁⠤⠄⠒⠉⣀⠈⢑⡤⢠⡃⣠⠮⠭⠉⠉⣉⢵⠉⡖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡛⠁⠀⢇⠑⣎⡰⠼⠃⠀⠀⠀⢀⢠⠄⠠⠔⠁⠀⠉⠁⠀⠀⠈⢳⣔⠲⠢⡈⠉⢰⠀⡇⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠡⠸⠀⠀⣀⣈⣉⣀⠀⢀⣀⡼⠁⠀⠀⠀⠀⡔⢁⠔⠒⠈⡂⠀⠀⢆⠈⢣⢁⣬⣀⠸⠚⠁⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⣶⣿⣿⣿⡿⠿⢿⠁⠀⠀⠀⠀⠀⠀⠀⣄⠧⠤⠺⡠⠁⢀⡀⡈⠓⠞⠛⠤⠤⣀⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡀⠀⠤⢸⡁⠀⠀⠀⠀⠸⠀⠀⠀⣠⣀⣀⣀⠀⠈⠁⠀⠀⠀⢀⠌⠀⣠⣉⡁⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠶⠀⢀⠇⠀⠀⠉⠙⢳⠄⠀⠀⠀⠐⢄⣀⡘⠉⠁⣰⠖⠉⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠁⠀⠀⠀⣆⠀⠀⢀⣀⣼⠦⢼⡦⠀⢀⣀⠀⣸⠀⣀⠠⠤⠴⡌⠀⢀⠗⠒⢉⡗⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡤⠄⠒⠂⠉⠁⠙⣶⣿⠿⠛⠋⠀⠀⠈⠻⡀⢲⡚⠉⠁⠀⠀⡀⠀⢠⡀⠜⠰⢂⡉⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠔⠂⠀⠀⠈⠁⠀⠀⠀⠋⣩⠀⠙⠋⠙⢧⠀⠀⠀⠐⠀⠀⣈⡁⠀⠘⠛⠧⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠶⠆⠀⠀⠀⢃⢀⣀⠤⠔⠊⠁⠱⠀⠀⢀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠼⡄⢀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣈⣀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣀⠀⠀⠄⡄⢀⠀⠀⠀⠈⠀⠐⠀⠂⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠐⢂⡀⣄⠀⣐⠻⠚⡷⢾⡐⠂⢘⣂⣐⡂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣤⡤⢀⠀⡀⠴⠉⠈⠁⠈⠉⡑⠀⠈⠶⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠐⠡⠤⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠀⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠒⠒⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⡆⢀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠑⠒⠰⠀⠄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠁⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠠⠤⠀⠀⠐⠀⠀⠀⠀⠀⠄⠐⠢⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠄⢀⠀⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢂⠘⠢⠊⠠⠀⠀⠁⠲⢆⡶⠜⠛⠁⠀⠀⠀⠀⠀⠀⠒⠀⢨⠀⡀⠂⠀⠀⢀⡀
⠀⠨⣀⠀⣀⠀⠠⠄⠒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠃⠀⢒⡤⠈⠁⠀⡀⡀⠀⠀⠀⠀⠀⢀⡘⠡⣏⠟⠉⣢⠀⠃⠁⠈⠊
⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠁⠀⢀⠈⠁⢂⠘⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠀⡄
⠀⠀⠈⠁⠀⠀⠀⠀⡘⠡⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠊⠃⠄⠀⠁⠀⠀⠀⠀⠐⠀⠁⠀⠀⠄⠀⠀⠀⠀⠅
⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠈⢀⣀⣀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⡠⠚⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢒⠀⠀⡊⢀⠀⠀⠀⣰⣾⣿⣿⣏⣉⣉⣙⣿⣿⣿⣿⣦⠀⠀⠀⠁⠀⢄⠀⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠅⠀⠀⠀⠠⠀⢰⣿⢩⠛⡏⣯⢩⣿⡩⠍⠛⠙⠉⢿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⢠⠀⢠⣠⡤⠠⣄⠀⠠⠤
⠀⠀⢂⢰⠀⠀⠀⠀⠈⣿⢰⣀⠷⢹⢸⣿⢰⡀⠀⠄⠘⣸⠇⠀⠀⠀⠀⠁⠀⠀⡀⠘⠀⠀⠠⠀⠀⠀⠀⠁⠀⢂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⡀⠀⠀⠔⢀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣷⣿⠾⠟⠋⠀⡄⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠄⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⢠⠠⠰⠄⠘⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠄⡢⠂⠉⠁⠂⠀⠀⠐⠐⠄⠀⠀⠁⠉⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠄⡀⠀⠀⡐⠀⠀⠀⠐⠢⠀⠀⠄⠀⠀⡀⠀⠀⠑⠞⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠁⠀⠀⠀⠈⠄
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠠⣀⢀⠼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⢀⠀⠠⠤⢀⢀⠀⠀⠀⠀⠐⢀⡀⢀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠅⠀⠀⠀⢠
⠀⠉⠀⠔⠀⠂⠈⠈⠠⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⡄⠀⠀⠀⠁⠀⠈⠑⢧⠋⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠰⡀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⢀⠀⡈⠁⢀⢁⢄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⡄⠐⠈⠀⠀⠀⠁⠠⠀⠑⠢⠄⠐⠀⠀⢠⢰⠚⢣⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⣀⡀⠀⠐⠃⠀⠊⠡
⠀⣀⠀⢂⠠⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠐⠀⢀⠀⠉⠑⠰⠼⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⢀⠐⠀⠀⠁⠄⠀⠁⠀⠀⠖
⠀⠀⠀⠈⠀⠀⠤⠄⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈

⠀⠀⠀⠉⢑⠒⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠀⠘⠇⠀⣸⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢹⠀⠀⢀⣶⢻⡛⠿⣷⡄⠀⠀⠀⠀⢠⡄
⡀⣺⣟⣿⣷⣦⣄⡟⠀⠀⢀⣶⣿⣷⣾⢿⠂⠀⠀⠀⠿⣿⣦⡀⠀⡿⠀⠀⢸⢉⠮⣬⢉⡩⣞⠀⠀⠀⠀⢸⣷
⠉⠻⢍⡀⣹⠞⠋⠀⠀⠀⠀⠛⠟⢋⠞⠁⠀⠀⠀⠀⠀⡐⠚⠭⠓⠇⠀⠀⠈⢿⢢⠆⡼⡤⠋⠀⠀⢀⠲⣶⠜
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠶⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⢰⣇⠀⢀⡏⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠠⣤⣤⣤⠄⠀⠀⠀⠀⠐⠁⢹⡀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠎⢙⠒⡼⠀⣠⠀⠀⠀⢰⣿⡀⢀⣤⡄⠀⠀⠀⠀⠀⠜⣿⠯⠀⠀⠀⠀⠀⠀⠀⠂⣇⠀⠀⠀⠀⠀⠛⠋⡏
⠀⠀⠀⡐⠁⠀⠀⠒⠀⠀⠘⠟⠁⠸⡿⠃⠀⠀⠀⠀⠀⢤⣾⡶⠀⠀⠀⠀⠀⠀⠴⠒⡟⠂⠀⠀⠀⠀⢶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢰⣋⣷⠀⣤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⢀⡀⠀⠀⠀⠘⣾⠇⠀⠀⠀⠀⢠⣴⣪⣭
⣠⠟⠛⠚⠷⠞⡇⠀⠀⠀⠂⣿⣄⠀⠀⠠⣵⠀⠀⠀⠀⡼⢠⣤⢴⢩⡇⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠉⠑⠀⢹⠇⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠾⣮⣤⣤⡾⠀⠀⠀⠀⠀⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⡤⠤⠄⢀⣀⠀⡸⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠈⡉⠉⠉⠁⠀⠀⠒⠂⠐⠈⠉⠉⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⠤⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠃⠘⠉⠭⠽⠟⠛⠛⠛⠋⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠻⠛⠛⠓⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⠤⣄
⠀⠀⠀⠀⠀⢀⡴⢚⠁⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢦⡀⠀⢀⣠⡤⠖⠛⣉⠥⠄⠠⠜⠻⣦⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠉⠀⠀⠀⠁⠀⠔⠊⠉⠴⠊⠩⡝⢳⣄⡀
⠠⢶⠤⣰⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⢣⡺⡤⣿⣌⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣠⢼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡲⠤⣄⣀
⡠⢀⠙⠺⠻⣷⣶⡤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣩⡾⡃⣀⣚⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣤⣽⣦⣀⠤⢶⢺
⠀⠐⠣⡅⣙⢄⣋⣭⣛⣓⣶⠶⢶⣤⡤⣤⡴⠶⠶⠶⠶⠚⡟⠛⠶⠿⢱⣚⡏⠩⠈⠓⢄⡀⠀⠀⠀⠀⣀⣤⣤⣶⡶⢿⢿⠿⠿⠟⠛⠉⠉⢀⣀⣼⠿
⠀⠀⣾⣷⡔⠀⢨⠃⠂⠘⠑⠷⢶⣧⣲⡖⠃⢂⡵⠷⠒⠛⣓⣲⡒⠄⡽⣿⡀⠀⠀⠀⠀⠙⠢⣀⣴⡟⠛⢿⡟⠀⣠⣲⣷⣲⠶⢶⣒⠚⠿⢍⡳⢤⣤
⠀⠀⡟⠬⡙⠗⠦⣤⣀⠀⠀⣀⣀⠀⠀⣙⡉⠀⢀⠭⠒⣈⠡⠖⠴⠼⢂⣿⡁⢠⢠⡔⠀⠀⢠⣾⡇⠘⡳⡖⠀⡴⣱⡁⢸⡌⠉⢳⢦⣍⡒⠤⣉⣲⠖
⠀⢀⠛⣦⡘⠀⢀⡈⠉⠛⠖⠀⣀⣀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣠⠎⢱⠙⢦⡸⢃⠄⠀⣾⣿⡇⠀⣷⡉⢙⡴⣝⢧⡀⣷⠀⠈⣶⣄⣹⣲⣇⡰
⠀⠐⡀⠈⠀⠩⠴⠿⠧⠤⠤⢤⣁⣉⣥⣌⡱⣶⡴⠭⢄⣒⣂⠭⠔⠋⠀⡸⠀⠀⠙⢼⠃⢠⡟⣿⣿⠀⠸⣿⡋⠵⢾⣭⣏⣻⡖⠐⡧⣄⣈⣉⣏⣹
⠀⠀⠑⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠙⢮⡇⠈⢻⠇⠀⢳⡉⠲⣤⣄⠤⣞⠛⢟⠿⣓⠊
⠀⠀⠀⠀⠈⠉⠒⠛⠛⠉⠁⠲⠶⠶⠶⠦⠤⠤⠄⠀⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢿⠭⡛⡘⣤⡉⢉⠇⠈⠑⢤⣙⡚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣈⣆⠱⣸⣌⣄⠉⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡶⠖⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠖⠛⣏⠉⠙⣇⣀⣀⣷⣤⠴⠿⣦⡀
⠀⠀⢀⣀⣤⢶⡞⠛⢻⠁⠀⢹⣀⣤⠼⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠙⣦⡀
⢰⡟⠋⢯⠀⢀⣧⣤⠼⠗⠛⠋⠁⠀⠀⠀⠀⠀⡀⣄⠰⣄⠀⠀⠀⠀⠈⠻⣄
⠈⣷⡴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠉⠈⠂⢀⣀⡤⠴⠒⠛⣦
⢰⠿⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠸⣆
⣿⠀⣿⠈⢳⡄⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣿⠀⠸⡇⠀⢻⣄⡠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣿⠀⠀⢿⠀⠀⢷⠀⢠⠞⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣧
⢸⡄⠀⠸⡇⠀⠘⣧⠀⠚⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⡀⢹⡄
⠈⣧⠀⠀⢿⡀⠀⢹⡆⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢷⣤⠀⣿⣁⠀⢷⡀
⠀⢹⡆⠀⠘⣇⠀⠀⢿⡀⠀⣟⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⠏⠁⠈⣿⣦⠀⢉⡇⠘⣧
⠀⠀⢷⠀⠀⢻⡄⠀⠈⣧⠀⠈⠓⢦⣄⠀⠀⢀⡀⠀⣼⠋⢹⣆⠘⠷⠤⠆⠈⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠸⣇⠀⠈⣷⠀⠀⠸⡆⠀⠀⠀⠉⢷⢹⡏⠻⣆⠻⠦⠾⠙⠀⠀⠀⣀⣠⠴⠒⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢻⡀⠀⢸⡆⠀⠀⢻⡀⠀⠀⠀⣸⠇⠓⠀⠙⠀⢀⣀⡤⠖⠚⠉⠁⠀⢀⡀⢠⠀⠀⠀⠈⣧
⠀⠀⠀⠈⣧⠀⠀⢻⡀⠀⠈⣧⠀⠈⠛⠉⠀⠠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⢸⠇⠀⠀⠸⡆
⠀⠀⠀⠀⢸⡆⠀⠈⣧⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠘⣇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠹⡇
⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹⡆⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢻⡀⠀⢻⡀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⣷⠀⠘⣧⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠸⣇⠀⢻⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⡖⠛⣏⢁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢻⡄⢸⡇⠀⣓⢌⠑⠆⠀⠀⠀⣀⣀⣤⢶⡞⠛⠹⡅⢀⣠⣷⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⣷⢸⡇⠀⠈⢁⣠⣤⢶⠞⠛⠙⣇⠀⢀⣧⣤⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡤⢶⡟⠙⡇⠀⠀⣧⣠⡤⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣠⣷⠴⠾⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠀⠀⠀⠀⠀⡠⠆⠤⡀⠀⠀⠀⠀⠀⣀⢤⡤⢠⣆⣠⠤⡄
⠀⠀⠀⠀⠀⡔⠋⠀⠄⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⣠⣖⣛⣒⣲⣀⡀⠀⠀⠀⣔⡉⢉⣎⣑⡄⠀⠀⠀⠀⣨⠞⢀⡎⠲⣁⡞⢻⣉⠆
⠀⠀⠀⠀⢸⡤⠤⠤⠤⢤⠤⢤⠤⢤⡇⠀⠀⠀⠀⠨⣅⣀⣀⣀⡀⣠⠇⠀⠀⠀⢳⣾⣛⡳⠶⡇⠀⠀⠀⠀⠹⡓⠾⠽⠤⠿⠚⠉⢩⠃
⠀⠀⠀⠀⠀⣿⣉⣩⣭⣭⠽⢭⣙⣲⠎⠀⠀⠀⠀⠀⢡⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢟⣉⠷⡾⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠘⢤⣀⣀⣙⣇⢛⡧⠇⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣍⣴⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⡠⠊⡡⢤⠤⠤⣌⣱⣠⠖⢆⠀⠀⠀⠀⣠⠊⠉⠈⠙⢦⠀⠀⠀⡔⠱⠆⢠⡍⠰⠗⠄⠀⠀⠀⠀⣀⠤⢄⡀⠀⢀⣀⢀
⠀⠀⠀⠀⡜⢰⠛⣲⣁⢀⠴⣿⠿⠃⢱⠸⠀⠀⠀⠀⡇⠀⡀⠁⡁⢈⠆⠀⠀⢳⠲⡖⠦⡲⠖⠲⠇⠀⠀⢐⢉⡿⠿⣶⠾⡽⢷⣶⢾⡛⡂
⠀⠀⠀⠀⢇⢸⠈⠔⠁⠉⢁⡞⢻⠾⠍⠉⠀⠀⠀⠀⠃⡀⠀⠀⠄⡜⠀⠀⠀⠀⡇⢱⠀⡃⡸⢸⠀⠀⠀⠀⢻⠀⠂⠀⠉⠀⠉⠀⡁⢹⠁
⠀⠀⠀⠀⠘⣌⠻⣅⣠⣱⣀⡰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠑⢴⠒⡼⠁⠀⠀⠀⠀⠑⠠⢄⠵⠒⠃⠀⠀⠀⠀⠘⠦⣈⣀⣀⣀⣀⡠⠔⠃
⠀⠀⠀⠀⠀⠈⠑⠢⠤⠭⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠺⡭⣭⠎⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣞⣋⣹⠀⠀⠀⠀⠀⢀⡀⠀⢀⡰⢄
⠀⠀⠀⠀⠀⢠⣾⠥⣄⡴⢮⡱⢄⠀⠀⠀⠀⠀⠀⡴⠶⠶⠷⠾⠷⠖⣦⢤⠀⠀⠀⢀⡼⢀⠟⠁⠈⠦⢤⠀⠀⢠⠧⡌⠛⢧⡀⡆⠙⢦
⠀⠀⠀⠀⢀⡏⡰⠋⠀⠉⠑⠂⠺⡓⡆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣰⡿⠵⠃⠀⠀⢩⠀⠘⡄⠀⠀⠀⢸⠀⠀⡇⠀⡟⠀⠀⢃⢱⠀⠀⡇
⠀⠀⠀⠀⢸⡴⠃⠀⠀⡀⠀⡀⠂⠙⡗⠀⠀⠀⠰⣚⠓⠒⠈⢉⣉⣉⣉⠏⠀⠀⠀⢺⠀⠀⡇⠀⠀⠀⠈⡇⠀⠑⠤⢝⡂⣠⢧⣈⡴⠊
⠀⠀⠀⠀⠸⡤⠤⠤⠄⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠈⠉⠉⢀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠒⠒⢧⠠⠤⠄⠀⠁⠀⠀⠀⠀⠙⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠤⡔⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⣿⡿⡇⠀⠀⠀⠀⠀⠀⢰⠒⠟⣻⣓⡆
⠀⠀⠀⠀⠀⡔⠉⠀⠀⠘⣄⠘⡄⠈⢢⠀⠀⠀⠀⠀⡟⡇⣣⠀⠀⠀⠀⠀⠀⢘⢁⠿⡵⠉⢹⠀⠀⠀⠀⡴⠒⢤⠔⠒⢲⠔⠲⡤⢲⢦
⠀⠀⠀⠀⡰⠻⣄⠀⠀⠀⢈⡏⠉⠓⠋⠀⠀⠀⠀⢜⣉⣉⠈⠑⡆⠀⠀⠀⠀⢸⠀⡜⠀⣀⢸⠀⠀⠀⢀⣇⣀⣁⠤⠤⣁⡠⠤⢤⠤⣴⡄
⠀⠀⠀⠀⡟⠦⣈⡱⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢈⠆⡜⠀⠀⠀⠀⠀⠘⡞⠠⠀⠀⠀⡇⠀⠀⢮⣵⣒⡬⣉⡡⢔⣂⠭⠭⡭⢧⠜
⠀⠀⠀⠀⠸⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠀⢇⠀⠀⠀⠀⠀⠀⡃⠀⠰⠀⠄⢱⠀⠀⠀⠲⠤⠒⠒⠒⠒⠒⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⣠⡨⠇⠀⠀⠀⠀⠀⠧⠤⠒⠒⠒⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢰⠖⠒⠒⠒⠒⠒⡆⠀⠀⠀⠀⠀⢸⣿⣻⣟⣿⡇⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠦⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⡟⢻⣿⡇⠀⠀⠀⠀⢱⣶⣶⣶⣶⣶⡶⢶⡇
⠀⠀⠀⠀⠸⠦⠤⢤⣤⠤⠴⠇⠀⠀⠀⠀⠀⢸⣇⣿⣿⣽⡇⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠷⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠶⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄
⠀⠀⠀⠀⠸⠛⠛⠛⡟⠛⠛⠃⠀⠀⠀⠀⠀⣾⣿⡿⢿⣤⣽⡄⠀⠀⠀⠀⠀⣰⠁⣾⣷⡎⣧⡀
⠀⠀⠀⠀⠰⣤⣤⣴⣧⣤⣤⡆⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⠁⠀⠀⠀⠀⠘⢿⠀⣿⣿⠇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇


⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⡴⠬⣿⣿⣥⣀⡄
⠀⠀⠀⠀⠀⠀⠘⢿⡿⠇⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠧⠤⠿⠿⠿⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢴⠄⠀⠀⢶⠿⠂⢸⠀⠀⠀⠀⠀⡄⠀⢰⡄⠀⣤⠀⢰⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡎⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠂⢻⡇⠙⠇⢈⣳⣿⡋
⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠀⠀⠀⠈⠿⡏⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠼⠃⠀⠀⠉⣿⣉⡀
⠀⠈⠒⠬⣍⡉⢉⡁⠤⠀⠐⠈⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡔⠋⠀⠀⠈⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⢰⣧⠀⠀⠀⠀⣠⢼⠄⠀⠀⠀⠀⠀⠀⠀⠐⣤⠤⠀⠀⠀⠈⠁⢸⡇
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⡈⢷⣧⠀⣼⡏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠮⠛⠁⠛⠴⠃⠀⠀⡆⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡇
⠀⠀⠈⠉⠉⠉⠉⢩⡏⠉⠉⠉⠉⠁⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠐⠆⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠅⠀⠀⠀⠀⠙⠛⠳⠃⠀⠀⠀⢠⣦⠀⠀⠀⠠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠴⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠢⡁⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠉⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠛⡇⠀⠀⠁⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⢠⠒⠐⠒⠲⠢
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠀⡇⠠⠀⡇⠀⠀⠀⢠⢠⣤⠀⢣⠞⣛⣶⣤⡀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡃⠀⠀⠀⢰⠶⠏⠀⠼⣶⣿⣿⠿⠃⢸⠀⠀⠀⠀⢸
⠀⠀⢀⠌⠉⣤⣠⣀⣀⣀⣀⣀⡎⠉⠀⠀⠀⠀⣇⣀⣀⡃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠈⠀⠀⢸⠤⠤⡤⢤⡼
⠀⢠⡇⠐⠀⠀⢡⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠣⣀⠀⢠⠝⠀⠘⢂⡀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢀⢃
⠀⢀⠀⠀⡰⠳⠤⠴⠂⠘⠧⠤⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠚⠂
⣀⣀⣑⣂⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣃⢸⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⡏⠀⠀⠀⠀⢀⡠⢄⢴⠊⠉⢱⡀⡏⠉⠀⣁⢀⠖⠤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠰⡁⠀⠈⢎⡆⠀⠀⢣⠡⠀⠀⢠⡌⠀⠀⡰⡰⠁⠉⢢
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣼⠀⣧⣤⣤⣤⣀⣱⡀⢺⠁⠘⡀⠀⠀⣾⠀⠀⢸⠁⠀⢠⠛⠳⡄⢀⠎
⠀⠀⠀⢰⡉⢖⠉⠉⠀⠀⠀⠘⠤⠃⠀⠀⠀⠉⢁⡣⢉⣇⠀⢇⠀⠀⢹⠀⠀⡍⠀⠀⠸⠀⡸⠀⡎
⠀⠀⠀⢸⠪⠭⢉⣛⣒⣛⠛⠚⠶⠚⠛⣛⣚⣛⡉⠭⠑⡟⡀⢸⠀⠀⢸⠀⠀⠇⠀⠀⡇⠀⠇⣼
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠧⣀⡇⠀⠸⠀⢸⠀⠀⠀⣃⡴⠊⠸
⠀⠀⠀⠀⡇⠀⠀⠀⣼⢷⡀⠀⠀⠀⢠⡾⣦⠀⠀⠀⢸⡀⠀⠈⠉⠒⠓⠒⠚⠒⠒⠉⠁⠀⠀⡇
⠀⠀⠀⠀⢡⠀⠀⠈⠁⠀⢁⣴⣶⣦⡉⠀⠈⠁⠀⠀⡏⡇⠀⠞⠋⠳⠀⠀⠀⠀⠞⠉⠳⠀⢰
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⣿⡟⣻⠁⠀⠀⠀⠀⢠⠄⢻⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠁⢀⣀⠀⣀⠀⢼⢀⣸⡀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⡴⠋⠒⡝⡤⠖⢀⣉⣛⠫⠽⠿⣓⠒⠶⣶⣶⣶⣶⣤⣬⡿⣍⡓⠛⣉⣐⡶⣚⠭⠭⠓⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⡴⠛⢒⡒⢛⡒⠢⠤⠤⠒⢬⠲⣦⣄⣢⣶⠖⠥⠦⠶⠶⠛⠛⠛⠚⠲⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠉⢲⠋⠀⠀⠰⠃⠈⠁⠺⡄⠘⣀⠘⢣⡄⠰⠂⣰⠂⡤⢸⡇⣨⡃⠘⠁⠀⠀⠀⠱⡖⠁
⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠆⠤⠤⠤⢀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⡀⠤⠤⠄⠒⠒⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡆⠀⠀⢸⣿⢸⣿⠀⠀⠀⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣴⡆⣿⣿⢸⣿⣿⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⣄⣴⣿⣿⣸⣿⣿⡷⠶⠾⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣏⣽⣿⣯⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣰⣿⣼⡟⣿⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⣺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣷⡖⣻⣿⡇⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⡇⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡖⣶⣼⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⣿⣶⣯⣿⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⢸⣏⣻⣿⣟⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡶⠛⠸⣿⣿⢹⣿⣿⡷⠶⢶⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠻⠇⣿⣿⢸⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠃⠀⠀⢸⣿⢸⣿⠀⠀⠈⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢀⡤⠦⠴⣤⡀⠀⠀⠀⢰⠶⠶⠶⠶⠶⠶⠶⣆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⡏⠀⠀⠀⠀⣿⠀⠀⠀⢠⠋⠀⠀⠀⠀⠳⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣾⠿⣿⣿⡿⡻⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡏⠀⠀⠀⠀⣿⠀⠀⠀⢸⣟⠀⠀⠀⠈⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣾⡿⠿⣿⣾⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣷⣤⣤⣤⣤⣿⠀⠀⠀⠀⠙⠀⢀⡀⠈⠋⠀⠀⠀⠈⠉⠉⢩⣿⡏⠉⠉⠁⠀⠀⠘⠿⠟⠁⠀⠘⠿⠟⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠦



⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⢰⣂⣀⡆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢰⡞⠒⠒⠒⠒⠒⠒⠒⣶⠀⠀⠀⠀⣶⣶⣶⣶⣦
⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣶⣿⣾⢟⣻⢿⣿⣶⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⡯
⠀⠀⠀⣿⣿⣽⣺⣿⡇⠀⠀⠀⢹⣿⣇⢿⣿⣺⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢸⣇⣀⣀⣀⢀⣀⣀⣀⣿⠀⠀⠀⠀⡟⣿⣿⡿⠃
⠀⠀⠀⠻⠿⠿⠿⠿⠇⠀⠀⠀⠙⠛⠛⠓⠚⠛⠛⠛⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠉⠉⠉⣩⣿⡉⠉⠉⠉⠀⠀⠀⠀⠧⠿⠿⠧⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⢀⣾⣿⣇⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⣿⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⣦⣄⡀⠀⠀⠀⡾⠛⠛⠛⠛⠛⣷
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⣶⠲⣶⣰⣿⣿⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿
⠀⢧⣤⣤⣤⣤⣤⣤⣤⣤⡿⠀⠀⠀⠸⣤⣤⣤⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠈⠀⢹⣿⣿⠏⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠐⠒⠚⠓⠒⠂⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠀⠀⠀⠀⠈⠉⠉⠉⠻⠿⠏⠀⠀⠀⠀⠀⠻⠟⠛⠛⠛⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠤⠶⠴⠤⠶⠴⠴⠶⡄
⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⢠⡤⠤⠤⠤⠤⠼⢥⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⡟⠛⠛⢻⡆⠀⠀⠀⠀⠀⣠⣇⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠛⠛⠛⣳⣀⠀⠀⢀⣰⡟⠛⠛⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⢸⣇⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠷⠶⠶⠾⠃⠤⠼⠧⠄⠀⠷⠶⠆⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠤⠀⠰⠿⠧⠀⠸⠶⠶⠶⠶⠶⠀⠀⠰⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠉⠀⠀⠀⣠⠤⠀⠀⠐⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠐⠒⠤⡄⠴⡴⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠞⠣⠒⠗⠒⠀⠀⠀⢄⢠⠤⠄⠤⣤⠲⠈⠀⡠⠶⠈⠑⠀⠤⣥⡔⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣁⣂⣀⠁⠀⠈⠀⠀⠀⠀⠀⢂⠤⣎⣁⠠⠄
⠀⠣⠀⠐⠠⠄⠀⠀⠀⠤⠀⠀⠀⢠⠞⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠐⠁⠀⢠⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠄⠊⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠓⠦⢀⡀⠀⡠⠖⡩⠄⠀⠀⠀⢸⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⠈⠀⠈⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠭⠔⠉⠀⠀⠀⠀⠀⠘⡇⡞⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠄⢠⡄⠀⠒⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⡀⠀⠀⠀⠄⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠈⠀⢠⠘⣠⠀⠅⠤⠀⠃
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⢀⡌⠀⠈⠀⠸⠁⠐⠀⠀⢀⠁⠉⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠠⠴⠄⠊⠀⢀⠘⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡜⠚⠀⠁⠂⠀⠀⢄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⣴⠄⢀⡀⠙⠂⡀⢀⡀⠀⠀⠐⠧⡄⠣⡀⠀⠀⠀⠀⠀⠛⡠⠄⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⢠⣄⣀⠀⠀⠀⢀⠀⠐⠠⠤⠀⠉⠈⠒⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠠⢌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⠀⡐⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠈⠀⢀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⢆⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠨⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀
⠰⢦⡀⠴⠄⠦⠔⠃⠀⠀⣀⠤⢠⡄⡶⠠⢄⠀⡆⠀⠀⠀⡀⠀⡝⠤⢀⡀⢠⡄⢤⣤⠀⣀⡠⠄⠀⡢⠄⠠⠄⠀⠀⣀⠤⠀⢨⣅⡰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⡥⠀⣶⠀⠀⠀⠀⠀⠀⠀⠁⢀⢈⣛⡀⠀⢠⠀⠀⠘⠡⡤⠀⠁⠀⠕⠀⢀⡀⣤⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠆⠀⠀⠐⠈⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢩⠁⠀⣠⡀⠑⠓⠐⠆⠀⠀⠀⠀⠈⠉⠀⠉⠀⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⣀⣀⣈⡀⠴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢬⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠁⠀⠈⠁⠉⠀⠦⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠷⠀⠀⠐⡶⠀⡀⠀⠀⣀⡀⠀⠁⠀⠄⠀⠺⢷⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠔⠀⠀⠠⠤⠀⡀⠠
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠌⠓⠀⠀⠁⠀⠒⠀⠀⠀⠑⠠⠌⠂⠉⠐⠂⠉⠀⠀⠀⠀⠔⠀⠑⠒⠂⢀⣁⡀⠀⠈⠁⡠⠀⠀⠀⠄
⠀⣤⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠆⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⡀⠀⠀⠀⢈⠄⠠⠐
⡇⠀⠀⠁⢄⠘⠦⣄⢠⡄⠔⠀⠘⣰⠀⠀⠀⣀⣦⠄⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠡⠀⠀⣤⠀⠀⠀⢠⠁⠀⢠⡏⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠄⡀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⡀⠘⢇⣀⠀⣀⠀⠔⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢋⡤⠀⠀⠀⠀⠐⢀⠁⠀⠀⠠⠒⠈⠉⠉⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠇⠀⠀⠀⠀⢀⠄⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠤⡀⠀⢀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⣦⠀⠀⠀⢰⠀⠀⠃⢄⣀⡀⢀⣀⡰⠞⠀⡈⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠊⠔⣈⠉⠋⣀⠲⠀⠀⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣊⠤⠖⠶⠤⡑⠀⠀⠡⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⣀⡀⣀⣀⠈⠁⠈⠣⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡧⠼⣀⠀⠀⠀⠀⠀⠆⠀⠴⠀⠀⢀⠤
⠀⠀⠀⠀⠓⠈⠜⢉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣰⠁⠀⠀⠀⠀⢠⠈⠁⠜⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⠀⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⣈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡂⢄⠀⡀
⠀⠀⠀⠆⠀⠀⠀⠠⠆⢩⠁⠀⠀⠀⢠⣴⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡤⢀⠈⡄⠀⠀⠀⠠⢠⣉⣩⠝⠀⣤⠤⠛⠂⡀
⠀⠀⠀⠈⠃⠁⠀⠀⠀⠗⠀⠁⠀⠀⠀⠙⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠻⣶⣦⣟⣀⣴⡾⠃⠀⠀⠤⠾⢖⡽⠇⠀⠌⠇⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃

⠀⢀⣤⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣡
⠀⠈⢯⣽⣿⠏⣹⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣤⡁⣤⠀⣴⡀⢠⡤⣄⢠⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢫⠸⠀⣾⣿⡏
⠀⠀⠈⢻⠙⠛⠓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⡷⣿⠻⣿⣰⠿⢷⠻⣤⡤⢸⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢹⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢺⢿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⡀
⠀⠀⠀⠀⠈⠁⣀⣀⢤⣶⣀⠀⠀⠂⢀⡤⠀⠐⢯⠿⠀⠶⡆⠀⠀⠀⠘⠛⠈⠉⠉⠃⡀⠈⠓⠢⠬⠅⠀⠀⠠⠄⠐⠀⡀
⠀⠀⠀⠀⢸⠯⠛⢟⠋⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂
⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⠀⣠⣤
⠀⠀⠀⠀⠘⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠄⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢘⡃⠃⠙⠈
⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡤⣠⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣍⣀⣀⣩⡄
⠀⠀⠀⠂⠀⠓⠒⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠘⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢀⡉⣤⣄⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂

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

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠐⠀⠐⠆⠀⠀⠀⢐⠁⠀⠈⣡⠕⠀⠀⠀⠸⢏⣙⡆⠀⠀⠀⠀⠀⢠⡆⠤⠀⠀⢤⠀⠀⠀⢀⡠⠜⠿⢦
⠀⠀⣈⠙⠓⣾⣛⣷⠀⢰⣿⡿⢿⣂⣸⡄⠀⠀⡀⠀⠀⠀⣸⣄⠀⠀⠠⣷⣦⣽⣷⢆⣰⡆⠀⠀⠀⣾⡟⠒⠚⠈⢰
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠰⢸⢸⣿⢯⡇⠀⠃⠀⠀⠹⠿⠀⠀⠻⠆⢄⡤⠀⢸⡷⣦⡄⠀⣼
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠊⠁⠀⠐⠀⠀⢀⣀⡀⠀⢠⣤⣤⡤⠀⢸⣄⣈⡁⠀⣈
⠀⠀⠀⠀⢀⢀⠀⠤⢀⡢⠀⠀⠀⢠⣾⣛⣛⡿⠞⠀⠀⠀⠀⠀⠀⠀⠤⡅⠈⠧⠺⠖⠶⠶⠶⠖⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢸⣿⣟⡶⣶⢤⣌⡀⠀⠀⠐⠀⠤⢍⣙⣷⠀⠀⠠⠔⠀⠀⣤⣶⣢⠀⠀⠀⠀⠀⢀⣚⣁⠚⠻⢶⢂⣰⠄
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⡟⠀⠀⠯⣉⡓⠢⢤⣙⠀⠀⠁⠀⠀⠀⡠⣾⡏⠀⠀⠀⣄⡀⣉⣉⠉⢀⢠⠼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠈⠑⠺⠗⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠙⠂⠐
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⡜⠹⠋⠟⡆⠀⠀⢠⣉⣀⣀⠀⠀⠀⢀⣀⣀⣀⢁⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠄⠀⠀⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣢⡈⢂⠀⠀⢀⠃⠀⠠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠅⠀⠀⠀⡴⠟⠁⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⣀⡴⠊⠀⢁⠐⢎⡠⠚⠀⢀⠈⡇⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⡀⠐⠀⡸
⠀⡠⢔⣂⠍⠁⢀⡤⠆⠈⡔⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⠀⠁⠀⠄⠀⠀⣀⡀⠀⡄⠀⠀⠀⠀⢼⠿⣶⣶⠤⣀⣤⢀⣀⣀⢠⡤⣔⠚⡄
⠘⠐⣈⡄⠖⡀⠩⡀⢀⠀⡃⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢻⡤⠤⠤⠤⠤⠒⠁⠀⢀⠁⠀⠀⠀⠀⣾⢦⠥⢌⣾⠛⠛⠀⠀⣢⡀⠀⠨⠼⣧⠄
⡸⠋⠀⠰⠈⠁⠀⠀⠀⠊⠀⠀⠀⠈⠀⡰⠁⠀⠀⠀⠀⠀⢸⠀⢀⣀⡤⠄⠀⠤⠖⠩⠀⠀⠀⠀⣀⠧⢈⠉⠣⠜⠓⠨⠭⣽⣚⡤⠎⠔⡨⠟
⢫⣄⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⡁⠈⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠘⠠⣄⠄⡀⢈⣁⡀⡠⠞⠡⠤⠄⠂⠀⠀⢠⠐
⠀⠁⠒⠒⠑⠢⠭⣉⣉⡀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣂⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠀⠈⠒⠳⠭⠤⣄⡀⣀⡀⣀⠀⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀
⠀⠀⠀⣀⠜⠁⠀⠀⡀⠢⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣗⡈⠉⠀⠀⣞⣽⣷⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠗⠀⡄
⢀⠔⢪⡀⠀⠀⠆⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡑⠦⠌⠭⠉⠉⠩⠍⠄⠀⠉⡀⠀⠀⠀⠀⠀⠀⢠⠆⠁⢀⠄⠀⠀⢀⠠⠗
⠘⠀⠗⡹⢄⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠠⠄⡌
⠀⠀⠀⠀⠈⡆⠀⣴⠃⠉⠀⠁⠠⣀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠢⠀⠂⠀⢀⠀⠀⢀⠄
⠸⡦⡀⠀⢠⣧⠞⠁⠈⠲⢄⡀⠀⠠⡑⠄⡀⠀⠀⠀⠀⡟⠉⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢀⡈⠇⣀⠂⠆
⠀⠘⡊⢗⢍⠡⠀⠀⠀⠀⠀⠈⠢⣄⠔⢀⣼⠀⠀⠀⠀⣻⡀⠀⠀⠠⠐⠊⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⢔⠉⡰
⠀⠀⠑⢀⠙⠫⡂⠀⠀⠀⠀⠠⠀⡠⣔⡝⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠤⢉⠃
⠀⠀⠀⠀⠁⠠⡀⠀⠀⡂⠤⢐⠬⠊⠜⠀⠀⠀⠀⠀⠀⠸⡓⠀⠀⠀⡀⠄⠂⠁⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷

⠀⣈⣢⣀⣈⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄
⢸⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⣯⣭⣭⣭⣭⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿
⠸⣤⣤⣤⣼⣽⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⣤⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⠇⠉⠉


⠀⠀⠀⢀⣄
⠀⢀⣴⠟⠁⢑⣄⠀⠀⠀⠀⢰⠛⢛⠛⠛⣿⣳⠀⠀⠀⠀⢠⣤⣄⣰⡞⠛⢲⠀⠀⠀⠀⠀⠀⠀⡿⠷⡄
⢴⠟⠉⢑⣴⠟⠁⠀⠀⠀⠀⢸⢀⣾⣷⣷⡉⢸⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⣀⣀⡇
⠀⠑⢴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠓⠚⠛⠓⠊⠀⠀⠀⠀⠈⠉⠉⠹⠷⠤⠾⠀⠀⠀⠀⠘⠿⠿⠇


⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⡤⠤⠤⡄⡀⡀
⠀⢤⣿⣿⡇⡄⠀⠀⠀⠀⠀⢠⣤⣶⣿⡇⡾⣳⠀⠀⠀⠀⠀⣤⣶⣿⢷⠋⠀⠀⠀⠀⠀⣧⣤⣤⡇⠁⠁
⠀⠘⠾⣿⠕⠁⠀⠀⠀⠀⠀⠘⠛⠿⢿⡗⢽⡝⠀⠀⠀⠀⠀⣻⠟⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⠀⠀⠒⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⢙⣿⣿⡋⣿⠀⠀⠀⢠⠤⠤⠤⠤⣴⣿⣿
⣿⣭⣿⣿⣿⣯⣿⡇⠀⠀⠀⠐⠤⠤⡤⠤⠼⠀⠀⠀⠀⠀⣿⢿⣿⣿⡿⣿⠀⠀⠀⢸⠀⠸⠆⠀⣿⣿⣿

⢴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠖⠀⠀⠀⢨⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠂⠀⠀⠀⠑⠀⠒⠀⠀⠇⠿⠸⠀⠇⠿⠸⠐⠇⠀⠀⠠⠀⡄⠈⠀⠀⠠⠀⠁⠀⠐⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠂
⠐⠀⡀⠀⠀⠉⢈⡀⡀⠀⠀⠐⠄⠀⠈⠤⠈⠀⠀⠇⠛⠸⠀⠇⠛⠸⠐⠇⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠒⠀⠒
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠀⡀⠀⠀⠠⠀⠀⢀⠔⠁
⠀⠀⡀⠀⠀⢠⡀⠀⠠⠠⠀⠀⠠⠀⢠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠔⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠄⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠄⢠⡀⡀⠀⠀⠀⠀⠰⠇⠂⠰⢂⠠⠀⠀⠀⠀⠀⠄⠀⠀⠁
⠀⠀⡀⠀⠀⠀⡀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⢂⢐⠂⠀⠂⠘⠃⠀⠘⡁⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠄⠀⠀⠠⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⠄⠀⠀⢠⡄
⠀⠀⠀⠄⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢺⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⠅
⠐⠀⠈⠀⠀⡀⠀⡀⠀⠉⠉⠉⠉⠉⠋⢀⡀⠠⠀⠀⠰⠀⠀⠈⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢀⠀⠀⠈⠀⠀⠃⠈⠀⠀⠄⠤⠀⠀⠀⠄
⠀⠀⠀⠀⠊⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⢀⣈⠀⠐⢈⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⢼⡅⠀⠀⡈⠀⠀⠠⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠄⠐⠀⠀⠂⠐⠀⠀⠀⠀⠈⠁⠀⠉
⠀⠀⡁⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠒⠂⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠈⠀⠐⠂⠠⠀⠀⠀⢀⢈⠀⡁⠈⢈⠀⡀⠀⠀⠀⠀⢀⢀⠀⢀⠀⡀
⠀⠀⠁⠀⠰⠆⠰⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠉⠁⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⢈⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠐⠇⠗⠀⢈⡁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠐
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠂⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⡉⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢠⡀
⠓⠀⡀⠁⠈⠀⢠⢀⠙⠍⠃⠀⠀⠀⠀⢈⡀⠀⠂⠈⠀⡁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠈⠀⠀⠀⢀⠀⡀⠀⠃⡁⠀⠁⠀⢀⠉⠈⠁⠀⠀⠂
⡈⠀⢂⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⠒⠀⠖⠀⠒⠀⠠⠀⠀⠰⠀⠀⠁⠀⠀⠀⠡⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⣛⣛⣛⣛⣛⣻⣿⡟⢻⣿⡛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⢡⣬⣙⠻⢿⣿⣿⣿⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣷⣦⠙⣿⣿⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⠸⡿⠟⣉⣴⣾⣿⣿⣿⣿⠷⠞⣛⣡⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣶⣶⣿⠟⢩⣭⣭⣭⡅⢰⣶⣿⣿⣿⣿⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⡟⣠⡆⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣧⡙⠇⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣧⣘⠛⣛⡛⠃⠘⠿⣿⣿⣿⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⡀⢻⣿⡀⠀⠀⠀⠈⠙⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⡌⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠁

⢀⡀⠀⠠⠅⠀⠀⡠⠂⠈⠢⡈⠁⠠⠄⠄⠀⠂⠀⢀⠴⠀⠐⠛⠻⠀⠸⠇⠄⠄⢄⠀⠀⠊⠅⠀⠀⡠⠊⠉⠠⢀⠇⠘⡄⢀⠀⠀⠀⢀⠴⠀⠐⠛⠳⠁⠸⠔⠠
⠀⠀⠈⠀⠐⠀⠂⠁⠀⠀⢀⠜⠀⠀⠖⠀⠨⠀⠠⡀⠀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠑⠄⠀⢀⠘⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠠⠊⠀⡀
⠺⠂⠳⣀⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠠⠀⠠⠃⠀⠈⠠⠈⠀⡔⠓⡜⢂⠀⣾⠃⠺⢆⠽⣠⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠂⠔⢂⠀⣺
⠀⠘⠂⠁⠀⠀⡠⠐⠀⠁⠐⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠈⠲⢪⡖⡛⠀⢙⠒⠂⠛⠛⠏⠀⠀⠠⠐⠀⠀⠐⠢⠀⠀⠀⠀⠌⠀⠀⠀⢀⠀⠈⠶⢢⠔⡛⠀⢛
⠀⠀⠀⠀⠀⠀⡶⠤⣂⢴⡤⢴⡆⠀⡏⠀⠄⢩⠂⠀⠀⠆⠐⠈⡧⢾⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠄⣂⢠⡆⢶⡆⠀⡍⠀⠈⢩⠂⢰⠀⠀⠀⠈⡳⢮⠃⠀⠈
⠀⠀⠉⠀⠀⠀⠉⠉⠷⠘⣣⠍⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠆⠀⠐⠂⣀⢀⡀⠁⠀⠀⠉⠀⠀⠀⠉⠉⠳⡜⣫⠝⠁⠀⢠⠀⠀⡀⠀⠀⠑⠀⠆⠀⠐⠂⢀⢀⡀
⠀⢀⠊⠀⠈⢢⠀⠀⠀⠈⠁⠀⠀⠀⠸⠄⠀⠄⠀⠀⢀⣲⠦⠀⠀⡁⠀⠀⡀⣥⠀⠠⠈⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⣀⣶⠦⡀⠰⡉⠀⢀⡀
⠀⢨⠀⠀⡠⠂⢀⢀⣑⠄⢀⣴⠤⠂⠀⠀⠀⣦⣡⡾⠟⠁⠀⡀⠀⠀⠂⠀⠀⡀⠀⢀⡀⠀⡀⠂⠀⢂⡐⠄⢀⡕⠴⠠⠀⠀⠀⣤⣱⡾⠟⠋⠀⠀⠀⠁
⡄⢢⠘⠈⠀⠀⢈⠠⡔⠲⠵⠷⣄⠒⠀⠀⠈⢜⠁⠀⠀⠠⠊⠀⠀⠀⠒⠐⠀⠀⠄⠡⠚⠈⠀⠀⠄⠀⡴⠲⠾⠶⣄⠂⠀⠀⠀⢎⠀⠀⠀⠠⠊⠀⠀⠈⠂
⢀⡁⠀⣀⠀⠀⠈⢐⠂⠠⠄⢂⠄⢀⠀⢠⣂⠀⠀⠀⠀⠀⠘⠀⠇⡈⣄⠀⠀⠀⢀⡀⠀⣀⠀⠀⠐⢐⠂⠠⠄⢂⠄⠀⠀⣘⣀⢀⠀⠀⠀⠀⠸⠁⠇⡘⡀
⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡯⠇⠀⠀⢀⠀⡰⠂⠺⠀⠀⠠⠀⠌⠢⠰⠁⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⣠⡿⠇⠀⠀⢀⠀⡯⠒⠲⡀
⠀⠃⢀⠀⠀⠀⣠⠄⠒⠀⠲⠀⠐⠂⠁⠂⠈⠁⠐⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⢀⠀⠃⠀⢠⢄⡒⣀⢶⣄⠐⠂⠑⠐⠈⠁⠐
⠀⠂⠁⠐⠊⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⡀⡀⡀⠀⠄⢀⡀⠀⠀⢀⠀⠀⠀⠒⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⡀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⡆⣀⠠⠀⠒⣀⠁⠀⠦⢷⠀⠘⡉⠁⡙⠀⠀⠀⠉⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⣂⣀⠠⠀⠒⡀⠁⠀⢨⠷⠄⠘⠃⠉⠛⠀⠀⠀⠉⠀⠀⠉
⠉⠀⠉⢉⡄⠀⠀⠀⠀⢀⠨⠀⠁⢀⣀⡀⠄⠀⠠⠀⠀⡀⠴⣀⢦⠀⢀⡁⠉⠀⠉⠀⠋⢉⡆⠀⠀⠀⠀⠀⡤⠀⡃⠀⢌⡄⣄⠀⠃⠀⠂⠠⠴⣐⢦⠀⢀⡀⠉
⢉⣑⠈⢛⠄⠀⠀⡠⠊⠈⠐⡈⠃⠀⠖⠀⢀⠂⠀⣀⠖⠐⠒⠋⠺⠀⠰⡃⣀⣄⢢⣄⠨⢋⠖⠀⠀⡀⠊⠈⠀⢀⠃⠐⡔⠀⠀⠀⠀⠀⠔⠐⠒⠉⡳⠁⠘⡏⣑
⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⢀⠘⠀⠀⠔⠀⠰⠀⠨⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢋⠐⠀⠀⢀⠜⠀⠀⠆⠂⢀⠀⠈⡀⠀⠀⡠⠈
⠿⣆⡵⣠⠀⠀⠈⠃⠈⠃⠀⠀⠀⠀⠂⠀⠀⠃⠀⠈⠂⠊⠀⡐⡁⣜⢂⠀⣷⢃⡿⢂⠵⣠⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈⠂⠂⢀⡜⡁⣄⢂⠀⣾
⠒⠛⠈⠁⠀⠀⡀⠂⠁⠀⠁⠢⠀⠀⢀⣀⣃⣀⠀⠀⠤⠀⡀⠒⠢⢔⡚⠁⠙⠐⠓⠛⠋⠇⠀⠀⠀⠀⠉⠉⠁⠢⠀⠀⢀⣀⣂⣀⠀⠀⠤⠄⡈⠖⠢⢔⡺⠀⢋
⠀⠀⢀⠀⠀⠀⡷⢒⣒⢒⡒⢶⡇⠐⡅⠀⠀⢨⠂⢀⠀⠆⠀⠈⡗⠺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣶⢒⣂⢒⡒⢶⡆⠐⠍⠀⠀⢨⠂⢰⠀⠀⢐⠈⡷⢮⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠌⠶⡜⣣⠍⠀⠀⢀⠀⠀⠈⠀⠀⠁⠒⠒⠀⠐⢂⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠙⠌⠷⠜⣯⠈⠁⠀⠀⠀⠀⡀⠀⠀⠁⠒⠂⠀⠐⠂⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⠆⠀⠀⣐⣶⠶⡄⢠⣁⡀⣀⡀⡤⠀⠠⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣶⠶⡀⠰⣁⠀⣀⣀
⠀⢠⠀⠀⡀⠂⢀⢀⡠⠄⠠⡔⠴⠂⠀⠀⠀⣤⣦⡿⠟⠁⠀⠈⠀⠀⠂⠀⠀⡀⠀⢠⠀⠀⡠⠂⠀⢀⡈⠄⠨⡔⢤⠢⠀⠀⢠⣔⣤⡿⠟⠁⠀⠄⠀⠁
⡔⢢⠊⠀⠀⠀⠀⠀⠌⠒⣋⠶⡴⠒⠀⠀⠈⢊⠀⠀⢀⠄⠊⢀⡀⢈⠁⠂⠉⠀⣔⠠⠈⠁⠀⠀⠁⠀⡌⠒⣟⠧⢴⠒⠀⠀⠀⢎⠀⠀⠀⠠⠊⣀⡀⢈⠁⠂⠉
⢀⡁⠀⣀⠀⠀⠈⠜⠂⠰⠄⢀⠄⠀⠀⢠⡇⠀⠉⠁⠀⠀⠘⠒⠃⡌⣄⠀⠀⠀⢀⡁⠀⣀⠀⠀⠀⠈⠊⠡⠤⢈⠄⠀⠀⢘⡄⠀⠉⠉⠀⠀⠘⠒⠂⡬⣄
⠁⠈⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣨⠯⠇⠀⠀⢀⠀⡸⠂⠸⠀⠀⠠⠁⡀⠃⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⡀⠀⠀⣨⡿⠅⠀⠀⢠⠀⡯⠂⠒
⠀⠁⠀⠀⠀⠄⣠⢀⡔⠭⣳⠄⠘⠄⣉⣀⢈⡁⠜⠀⠀⠀⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⠃⠄⣠⢆⡔⢭⣳⢄⠘⠆⣉⣀⣈⡁⠜⠀⠀⠀⠁
⠀⠂⠀⠐⠀⠀⠁⠂⠀⠀⠀⠐⠇⠀⠀⡀⠂⠀⣀⣀⡀⠀⠄⢠⡀⠀⠀⢰⠀⠀⠀⠂⠀⠑⠀⠀⠡⠀⠀⠀⠀⠈⡆⠀⠀⠠⠂⠀⣀⣀⣀⠀⢀⢠⡀
⠀⣀⠀⠀⠀⠀⣎⠀⠄⠀⠀⢈⠀⠀⠲⢿⠀⠘⠅⠀⠜⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⣀⠀⠀⠀⠀⣂⠀⠄⠐⠀⣀⠀⠀⢰⡷⠀⠸⠁⠀⠘⠀⠀⠀⠀⠀⠈⢀
⣁⣀⣉⣈⡀⠀⠀⠀⠀⠀⡈⣀⣁⢀⣀⣀⣄⠀⠠⠠⠀⣀⡒⣑⢢⡀⢀⣀⣁⣀⣉⣀⣃⣀⡂⠀⠀⠀⠀⢀⡤⣀⣃⢀⣌⣄⣀⠀⠃⠀⠂⣀⠐⣑⣦⡀⢀⣀⣁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠔⠂⠈⠉⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⠶⣋⢛⢦⡀
⠀⡃⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠃⠘⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠸⠪⠝⣃⡥⢚⡡⠖⠛⢇
⠀⡉⠀⡀⠉⠉⠀⠀⣀⣉⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠘⢈⡀⢈⣉⡩⠤⠒⠉⠀⠀⠀⡜
⠘⠒⠢⠂⠄⠐⠐⠤⠠⢶⠂⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠍⣉⣀⣐⠒⢒⣒⣒⡾⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠂⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠐⠀⠐⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡔⢪⠔⠒⡶⡄
⠀⠀⠀⠀⡔⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠐⢉⡉⠀⠁⢑⣻⡇
⠀⠀⠀⢀⠗⢐⠢⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠃⠀⠁⡥⠜⠉⠤⠌⢣
⠀⠀⢀⠞⠐⠀⠇⠈⠆⠈⢇⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠒⠒⠒⠒⠒⠒⢺⢁⡤
⠀⢀⠞⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠀⠀⠀⠀⠀⠄⠐⠐
⢀⠚⠁⢪⣹⡠⠮⠒⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠆⠀⠀⠀⣸
⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠈⠒⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣠⠴⠊⠽⢣⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⢄⡀
⢀⣴⣋⣀⣀⠀⠠⢥⠤⠤⠤⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢐⡀⠥⠭⠤⢐⠙⢦⡀
⠈⡤⠤⠄⠤⣀⡠⠔⠢⠤⠴⡇⠀⠀⠀⠀⠀⠀⡠⠔⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠖⠁⠀⠀⠀⠀⠀⠈⢺⡇
⠀⠧⠀⢀⣀⣀⣀⣀⣀⣀⠠⠇⠀⠀⠀⠀⠐⣊⣀⣀⠀⠠⠀⠀⠀⠀⠤⢝⠢⠀⠀⠀⠀⠀⠈⠁⠀⠠⠤⠤⠤⠤⠤⠄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠉⠀⠐
⠀⠀⠀⠀⢀⠆⡐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣯⡀
⠀⣠⠀⢀⣀⡀⠐⢒⡒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡄
⠀⠘⡉⠁⠀⠒⠒⠂⠀⣻⠯⣱⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⢀⡀⠱⣤⢀⣀⣀⡀⣴⢉⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠒⠒⠁⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠉⠀⠀⠀⢁⠆⢀
⠘⠠⣤⣤⡤⠤⠤⠤⠤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠂⡀⠈⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠠⠈⠰⠋
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢿⡿⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢻⠳⢤⣖⠉⠀⠠⡇⠀⠉⣲⠤⠚⡟⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⢸⠀⠀⠈⢱⠀⠈⡇⠀⡏⠀⠀⠀⡇⠀⣤⣀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⣿⣿⣿⣦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⣇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠢⣄⡀⢸⠀⢀⡇⠀⡇⠀⣀⠼⠿⠧⡈⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠔⠊⠀⠀⠀⠀⠀⢉⠿⠀⣨⣏⠰⣷⣉⠀⠀⠀⠀⠀⠑⠠⢄⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢁⠀⠀⠀⠀⢀⡠⠔⠊⠀⣠⠔⠻⠟⠢⣄⠈⠑⠢⣄⡀⠀⠀⠀⠀⡨⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠤⠒⠁⢀⡠⠖⠉⠀⣀⢴⣦⣀⠀⠉⠲⢤⣀⠉⠲⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠄⠊⠁⢀⡠⠔⠈⠀⠐⡇⠈⠙⠢⢄⡀⠈⠑⠦⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡉⠀⠀⢠⠂⠁⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠉⠲⡄⠀⠀⢙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢼⠀⠀⠀⡠⠔⠊⠉⠉⠙⠢⢄⡀⠀⠀⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢀⠠⠐⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⢶⣶⠶⠶⣶⠶⠶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠚⢯⢻⡀⠀⠀⠀⠀⠀⠀⢸⡟⡛⣿⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣷⣲⡇
⠀⠀⠀⠀⠀⠀⠸⢿⡞⠦⠾⠿⠀⠀⠀⠀⠀⠀⠀⠸⠷⠵⠟⠀⠀⠀⠀⠀⠀⠀⠾⠿⠻⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⢧⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠃⠀⠀⠀⠀⠀⢸⠀⠈⠈⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⢠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⣲⣶⡒⠚⠀⠀⠀⠀⠀⠠⠤⠤⠤⢤⠤⠤⠄⠀⠀⠀⠀⠀⠺⡿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠮⡀⠀⠙⠂⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⡤⢤⠀⠀⠀⠀⠀⠀⣴⠶⠶⢶⡶⡆⠀⠀⠀⠀⢸⣤⣿⠀⠀⢸⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣯⡇⠀⠀⠀⠀⢸⣉⣿⣤⣤⣼⣏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⢠⣤⣤⡤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⠆⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⣟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠰⠆⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠻⡇
⠀⠀⠀⠀⠀⠘⠿⠟⠉⢭⡿⠭⠉⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡒⠢⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡼⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡦⢐⣀⢈⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠶⣶⡄⠀⠀⠀⠀⣤⣤⣤⣤⣤⢤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢧⣹⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠈⣴⣷⣾⣦⠁⠀⠀⠀⠰⣏⣛⣛⣛⣟⣹⣿⣫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠒⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠶⠯⡇⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠖⠂⠐⠂⢤⡀⠀⠤⠤⣀
⠀⠠⡀⣀⠀⠀⢀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡋⠄⠀⠀⠁⠀⠀⠀⢰⠈⠈⡄⠀⠀⡙⢂
⠀⠀⣄⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠋⠁⠘⠀⠂⠈⠠⠔⠉⣀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⢀
⠀⠀⠛⠊⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡀⠀⠊⠉⡉⠘⣂⠀⠀⠀⠀⠙⠢⡀⠠⠋⠀⠀⠀⠀⠘⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⡀⢀⠂⠀⠀⡈⠁⠀⠀⠀⠀⢀⠀⢰⠯⠑⢦⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡂⢇⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⢸⡀⠀⡜⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠒⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⠔⠋
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠄⠆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠈⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡣⠀⠀⠀⠀⠀⠀⠈⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠐⡊⠄⡢⠌⡁⠀⠀⠁
⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀
⠀⠀⠀⠀⠈⠐⠒⠒⠒⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⣴⣂⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⣀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠐⠢⠀⠀⢉⣩⣴⠀⠀⠠⡠⠖⠉⠀⢀⠀⠀⠄⡈⠀⢈⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠀⡈⠁⠀⢀⢀⡉⠉⠈⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⢢⡄⠀⠀⠀⠀⠀⠀⣠⡄⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⣨⠀⠁⣄⡀⠀⠀⠀⠀⠀⠈⠁⠂⠤⣅⢀⠤⢀⠀⠀⣀⠤⣘⠵⠊⠁
⠀⢀⣀⡤⠄⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡦⠔
⠀⠈⠉⠠⠂⣀⠀⠀⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠃⠀⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⣀⠀⠀⠀⢀⡠⠔⠊⠀⡀⢰⣄⠝⠺⣄⡴
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠁⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢴⣤⠆⡈⠣⡀⠀⠀⠀⠀⠐⠤⡟⠹⣤⡝⠚⡧⢜⠑⡦⠔⠀⠈
⠀⠀⠀⠠⠴⠚⠁⠀⠁⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠠⣀⣼⠾⣉⠷⣋⣠⠘⢀⠀⠀⠀⠀⠀⠈⠙⠢⢜⠉⡦⠜⠉
⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⠀⠀⠤⠀⠀⠀⠀⣶⠀⢀⡀⠀⠀⠀⢡⠀⠈⠱⡞⢉⠶⡛⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠠⠀⠀⠠⠐⢀⠠⢂⠁⠢⠌⠒⠄⠈⠀⠀⣿⠄⣿⠃⠀⠀⠀⠀⠑⢄⠀⠈⠫⠔⠈⠀⠀⠠⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡉⠀⠀⠀⠀⠀⠀⠀⣞⣦⡿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⡈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠥⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⢴⠀⡦⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠂⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⠰⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠨⠉⠉⠁⠒⣒⣒⣒⠒⠀⠉⠉⠁⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⢀⡼⢷⡀⠀⠀⠀⢀⡼⢷⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢁⣴⣶⣦⡈⠁⠈⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠙⠀⠐⠈⠉⠁⠀⠤⠀⠀⠀⠀⠀⠘⣿⡟⢻⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠁⣀⠀⠀⠡⠀⠀⠀⢀⡌⠀⠀⡈⠀⠁⠀⠄⠈⠓⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠂⠀⠀⢢⠀⠀⠘⠁⠀⢠⠒⢠⠀⢀⠠⠐⠀⠠⠀⠂⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠘⠀⠀⢸⡆⠀⠀⠀⠀⠆⠀⠀⢀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢠⣶⡄⠀⠀⢠⣶⡄⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠄⣀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠀⠁⠀⠀⠀⠀⠈⠛⢡⣶⣶⡌⠛⠁⠀⠀⠀⠀⠀⠘⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣈⠉⠀⠈⠁⢁⣀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠃⢀⡀⠀⠋⠈⠉⠀⣐⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠂⠁⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠄⠀⠀⠀⠀⠄⠱⠄⠀⠀⠀⠀⠀⠠⣤⠒⠉⠉⠉⠁⠀⠀⣀⠀⠄⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢀⠃⠀⠀⠑⠚⠉⠁⠀⠀⠉⠀⠙⠀⠘⠋⠁⠀⠀⠀⢰⡆⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠉⠁⠨⠍⠁⠉⠉⠉⠉⠉⡉⠉⢉⠉⠉⠉⠉⠉⠻⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠀⠉⠉⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠂⠈⠁⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠂⠀⠒⠒⠒⠒⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡀⠀⠀⠀⠰⡆⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠀⡗⠀⠀⡇⠀⢸⠂⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠳⡈⢢⠀⡇⡴⠋⡔⠋⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡔⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣟⡍⣭⢹⣭⡍⣭⣩⣩⡝⣿⣿⣀⣀⣀⣀⣀⡤⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⣀⣀⣀⣿⣿⣯⣥⣭⣬⣭⣥⣭⣭⣬⡅⣿⣿⣀⣀⣀⣀⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠉⠉⠉⠉⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠜⠀⡇⠳⣄⠣⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣇⠀⡧⠀⠀⡇⠀⢸⠄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠈⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⣈⣈⣁⣄⢀⢠⠀⠀⡀⠀⠀⠀⠄⡀⠠⠤⠀⢀⠦⠀⠆⣴⠂⠄⠠⠀⡀⠀⠀⠠⠰⠂⠆⠠⠀⠀⠀⠀⠆⠢⠀⢰⡀⢀⠄⠆⠀⠀⠀⠰⠀⠲⠐⠆
⠀⣿⣯⣿⣿⠀⢸⠀⠀⠅⠀⠀⠑⠤⠂⠘⢁⢊⠂⠀⠀⡁⠂⠀⠀⠀⠀⠓⣒⢀⣒⡀⠀⠀⢀⠀⠀⠄⠄⠀⠐⠒⢂⠀⢂⡀⢀⠀⠄⡄⣿⣿⣿⣿⣷
⠀⠀⠀⡄⠀⠀⠠⠆⠀⠁⠂⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠀⠒⠙⠁⠂⠄⠄⡁⠀⠀⠀⠁⠁⠀⠘⠀⡜⠁⣿⣾⣿⣿⣿
⠈⠀⠀⡀⠒⠒⢢⠰⠅⠤⠠⠄⠤⠠⠀⡤⢠⠢⠤⠡⠠⠀⠀⠤⢢⠔⠍⠩⠍⠁⠀⠀⠠⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⢀⣶⣶⣮⠸⢹⠁⠙⠛⠛⠛⠋⠀⣀
⠀⡂⠀⠀⠀⠀⢸⠀⠂⠐⠀⠀⠇⢸⡀⠇⠰⡁⠇⠒⠐⠀⠀⠐⢸⠀⡇⢸⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢾⣿⠀⠀⠀⠀⠀⠀⠀⠄⠐⠄
⠀⡅⠀⠂⠂⠒⢸⠠⠀⠀⠀⠀⠁⠘⠀⠁⠘⠁⠃⠀⠀⠀⠀⠀⠘⠀⡃⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠈⠑⠊⣭⣀⠸
⠀⡇⠀⠀⠉⠭⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢈⠀⣠⣮⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⠉⠀⠀⡀⣀⠀⢀⡀
⠀⡇⠀⠄⠐⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⠠⠀⠈⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠉⠀⢁⣤⣤⣤⡈
⠀⡇⠀⠅⠸⠀⣟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢼⠰⠀⠀⢠⡰⠆⠖⣀⠠⠤⠀⠐⠀⢐⣐⣂⣒⣐⣂⡀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⡇⠀⠀⠀⠐⢻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡅⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡇⢸⡄⠀⠀⠁⡋⠉⠁⡇⢀
⠀⡇⠀⠀⠀⠀⣴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠙⠊⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠄⠀⠀⠈⠂⠈⠈⠀⠀⠘⠁⠁⠥⠠⠠⠇⣀⢸
⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠰⠉⠀⠈⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠂⠀⢀⠈⢀⢸
⠀⡇⠀⡀⠀⠀⠙⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠈
⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⠀⡆⠠⠁⢌⠀⠀⠀⠀⠀⠐⠀⠆⢰⢀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠀⢀
⠀⡇⠀⠀⠀⠀⠰⠲⠂⠐⠀⠀⠂⠸⠀⡃⠘⠀⠂⠂⠐⠀⠀⠒⠐⠀⠃⣘⠈⢀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡄
⠀⡇⠀⠀⠔⠶⢂⠀⠀⠀⠏⢀⣀⠀⣀⠀⠉⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠃⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠠⠁
⠀⠃⠀⠓⠂⠀⢸⠀⠀⠀⠁⠀⠤⠤⠤⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐
⠀⠄⠀⠀⢀⠀⠘⠀⠀⠀⠀⠐⡆⠀⠀⠖⠳⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⡄⢱⣶⣶⠀⠀⠀⠀⠠⠤⠀⠘⠃⠀⠀⠀⢀⣀⣀⣀⡀⣶⡀⠀⢸⠀⠚⢀⠰⢆⠀⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠇⢸⣿⣟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢻⠇⠈⠀⠁⠁⢸⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⢀
⠀⠈⠉⠉⠀⢀⠠⡀⢠⠀⠃⡠⢤⡀⠘⠁⠹⠿⠾⠿⠇⠹⠁⠐⠀⠃⠃⠘⠠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⢠⠀⡄⣤⡌⠀⠀⢰⣿⣇⠀⣟⠀⣿⠐
⠀⠀⠀⡀⠋⠥⠀⠂⠘⠀⠀⠙⠛⠃⢒⡁⢤⡀⠀⠀⡶⠖⠀⠀⠀⠰⠀⠀⠠⠄⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠉⠓⠤⠁⠀⠀⠤
⣤⣤⣤⣤⣤⣤⣤⣽⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣼⣭⣿⣽⣯⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⣎⣉⣳⡀⠀⠀⠀⠀⡤⡤⠒⡶⣠⠒⡦⡀
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⢠⠮⠭⠭⠭⠽⠄⠀⠀⠀⣸⠥⠄⠬⠦⠨⣆⠀⠀⠀⣜⠁⣼⡙⣧⢎⢫⣾
⠀⠀⠀⢠⡗⡒⡒⢖⠠⣒⡲⣶⠾⡀⠀⠀⠀⠘⡎⠉⠉⠉⢹⠁⠀⠀⠀⠙⣟⢻⡭⡛⢹⠁⠀⠀⠀⢹⠙⠓⠓⠚⠚⢉⡇
⠀⠀⠀⠀⢹⠒⠾⡉⣘⢿⠓⠞⡟⠀⠀⠀⠀⠀⢣⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⡟⢤⣺⠃⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠉⠁⠘⠳⣰⠞⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡁⡝⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠄⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡤⢒⣂⡉⣐⠲⡄⣠⢤⠀⠀⠀⠀⠀⣀⠤⢤⠒⠢⡄⠤⡀⠀⠀⢀⡠⠔⠒⠒⠠⢄⠀⠀⠀⠀⠀⢀⠤⠒⠢⢄
⠀⠀⠀⢠⢋⠖⠧⠎⢀⡠⡫⠞⠹⡆⠇⠀⠀⢠⠞⠁⠀⠀⠣⡀⢣⣀⣈⠆⠀⣎⣀⣀⣀⣀⣀⣠⡕⠀⠀⠀⢠⠋⠀⠀⠀⠀⢣
⠀⠀⠀⢸⠈⠆⠏⠋⠻⠒⡿⢭⢅⠙⠂⠀⠀⡜⠣⡀⠀⠀⢀⡝⠁⠀⠀⠀⠀⠈⡄⢠⠈⡄⠰⢠⠁⠀⠀⠀⠸⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⢆⠳⢖⢐⢢⣀⡰⢋⡞⠀⠀⠀⠀⡗⢄⣈⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⢡⣘⠀⢃⣃⠎⠀⠀⠀⠀⡼⢑⣤⠴⠊
⠀⠀⠀⠀⠀⠑⠢⠤⠭⠤⠒⠋⠀⠀⠀⠀⠀⢇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⢭⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⣔⣒⣢⢠⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⢖⣂⠴⡒⣒⣄⠀⠀⠀⠀⠀⡤⠤⠤⠧⠧⠤⣄⣀⡀⠀⠀⠀⢸⠀⣇⠾⠼⠄⠀⠀⠀⢀⡔⡢⣄⡠⢚⠦⡀
⠀⠀⠀⠀⡎⡡⠒⠉⠒⠒⠒⢝⢦⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⣯⣗⠅⠀⠀⠀⡸⠀⡧⠋⠈⠣⡄⠀⢠⠊⠀⢱⠈⢳⠸⡄⠈⠆
⠀⠀⠀⢸⡴⠁⠀⠀⠀⠀⠀⠈⢿⠂⠀⠠⡆⠀⠷⠤⠄⠖⠋⠃⡲⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠸⡀⢀⠇⠀⢸⠀⡇⠀⡄
⠀⠀⠀⠸⠤⠤⠤⠀⠒⠀⠀⠤⠊⠀⠀⠀⠈⠑⠒⠒⠒⠒⠂⠉⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠀⠑⢤⣃⠴⠛⢄⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠤⠤⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⡀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀
⠀⠀⠀⠀⠀⠀⣀⠀⣞⣵⣵⠗⠺⡄⠀⠀⠀⢠⠃⠘⡀⠀⠀⠀⠀⠀⠀⣠⠊⠱⢼⢌⢷⠀⠀⠀⣠⣀⡠⠤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⢰⣊⠭⣔⡺⣽⠝⠁⠀⠀⡇⠀⠀⠀⡞⣚⠓⠙⡆⠀⠀⠀⠀⣴⠥⠔⠚⠉⢉⡏⠀⠀⢸⠀⠘⠀⣀⠈⠀⠀⠋⠀⢹
⠀⠀⠀⢎⣪⠛⠊⠉⠀⠀⠀⣠⠎⠀⠀⠀⠀⠹⠀⡇⢰⠃⠀⠀⡠⠊⠀⠀⠀⠀⡠⠋⠀⠀⠀⣞⡋⢛⡓⠒⡞⠉⣖⡛⢳⣋⡢
⠀⠀⠀⠈⠡⡀⠀⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠸⠋⠁⠸⡄⠀⠀⠣⢄⡀⠀⠀⡔⠁⠀⠀⠀⠀⠘⠬⠅⠈⠫⠬⠍⠤⠬⠥⠜
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡄⠠⠃⠀⠀⠀⠀⠈⠢⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⢀⠠⠄⢀
⠀⠀⠀⡀⠀⠀⠀⡀⠀⠠⠀⢉⠑⢆⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡁⠀⢁⠀⢀⠀⢠⡀⠠⠀⠈⠁⢆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠢
⠀⠀⠀⠘⠀⠈⠀⠀⡀⠠⠀⠐⠄⠁⡀⢨⡀⠀⠀⠀⣄⠀⠈⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠸⢀⠈⠀⢀⣀⢀⣠⠊⠓⢀⠀⠜⠁⠀⠀⠀⠈⠂⢀⡀⠁⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠈⠀⠉⠀⠉⢄⡀⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⢄⡂⠐⣈⣖⡓⢼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠉
⠀⠀⠐⠀⠀⠒⠀⣱⠠⢆⡡⢉⣡⡀⠃⡴⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠁⠈⠀⠈⡉⠂⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⢈⠂⠀⡘⠁⠀⠀⠹⠄⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠼⠄⣀⣀⡠⡀⠀⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠈⠉⢀⠣⡀⠀⠒⠂⠀⠀⠀⠃⠠⠆⠀⣠⣬⡄⠀⢥⣶⠆⡞
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣅⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠁⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠔⣀⡀⢈⣙⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠺⠶⠷⠶⠤⠿⠤⠀⠔⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⢸⠀⠀⠀⠀⠀⢈⠕⢢⡀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢡⠀⠀⠀⡀⠀⠐⢹⠄⠀⠀⠀⠀⠀⠀⡠⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠢⠀⠀⡄⠀⠂⠁⠀⠀⠀⠀⠀⠀⢰⠐⣐⠨⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢈⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠖⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠂⡠⡇⡄⣤⠀⡤⠀⠀⣅⡄⢀⢠⠄⠀⠇⢦⣤⣤⡀⢴⢠⡀⢠
⠀⠀⠀⢀⠀⣁⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠁⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠉
⠀⠀⠀⢅⣀⣀⣀⡍⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣆⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⣨
⠀⠀⠀⢀⠘⠿⠃⡀⠀⠀⠀⡉⠛⠧⠁⠀⠀⠀⠂⠀⠠⠄⠠⠄⡁⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠂⠀⠀⠀⠀⠀⢀⠠⠀⠀⠞⣱⢄
⠀⠀⡐⠁⠀⠀⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠊⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢉⠀⠀⠀⠁⠀⠂⠀⠠⢟⣵⠟⠁⠤
⢀⠐⠆⠁⠀⠀⠀⡊⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⡁⠀⠺⠈⠀⠀⠀⠀⠠⠈
⠀⠈⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠰⡋⠈⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠁⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⣀⠠⠀⠀⠀⣤⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠉⠂⠀⠀⠀⠁⠀⠀⠀⠘⠁⠀⢀⣀⡀⣀⠀⠀⠀⠉⠀⠐⠆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣰⢱⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠤⠀⠀⠀⠂⠀⠀⠠⠀⣀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢉⠀⠀⠈
⠀⠀⠀⢀⣠⢀⠀⠀⠠⠀⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠍⡑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⣴⠏⠡⢀⡤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠂⠡⠎⠀⠀⠀⠀⠈⠁⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠂⠀⠀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠂⠀⠀⠠⡀⢀⡀
⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⡬⠧⠀⠀⠀⠀⠀⠀⣀⠕⠁⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠄⢠
⠀⠠⠀⠀⡔⢀⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⡀⢌⡈⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠰⣶⠆⠈⢯⡽⠁⠀⢯⡟⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠁⠀⠀⢀⠠⠤⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠤⡀⢤⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠦⠤⠐⠀⠈⠀⠠⠀⡀⣤⠀⠤⢤⡌⠛⠂⠀⠤⠆⠉⠉⠁⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⣀⣡⡒⠦⠤
⠀⠂⠀⠀⠢⠄⠀⠀⠀⠄⠀⠀⠀⡀⠞⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠐⠀⠀⠀⢀⣀⠀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠁⠒⠦⢀⡀⢀⡤⢊⠡⠀⠀⠀⠀⢠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠔⠈⠀⠀⠀⠂⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠥⠖⠁⠀⠀⠀⠀⠀⠸⡄⠃⠀⠄⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠄⠤⠀⢤⠄⠀⢂⠀⡰
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡆⠀⠀⠄⠂⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⠄⠃⡤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠌⠀⢀⠀⠘⠀⠐⠄⠀⠀⠁⠀⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⠀⠀⠀⡐⠁⢠⡕⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠇
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀⠂⢀⠀⠙⠂⠀⡀⠀⠀⠀⠑⢧⠘⠀⠀⠀⠀⠀⠀⠐⢁⠤⠀⠀⠘⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⣀⠀⠈⠀⠀⠀⠀⠢⠤⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠈⠠⢌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠁⠀⡄⠀⠊⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠦⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢀⠀⣀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠘⠲⡀⠶⠄⠦⠐⠃⠀⠀⡀⠀⢠⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠁⠤⠄⠀⠀⠀⠤⠄⠀⢀⡀⠀⢀⠠⠐⠠⠀⠀⠀⠠⠄⠀⠀⢀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣁⡀⠠⠄⠄⠀⠈⠠⠄⠈⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠠⢤⠄⠙⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠠⠤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⠀⠀⠨⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠉⠉⠀⠦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠖⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠐⠈⠁⠀⠂⠀⠀⠀⠀⠐⠒⠈⣀⣁⠀⠀⠀⡁⠀⠀⠀⠀⠃
⢀⠤⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⢀⠀⠀⢀⠀⠀⠐⠢⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠈⢂⠘⠢⠄⠀⠠⠒⠀⠈⡠⠀⠀⢀⡄⠆⠆⠀⠙⣂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠰⠀⠂⠀⠀⠀⠀⠁⠂
⠀⢀⠀⠀⠀⠱⡀⠀⠄⠒⠀⠀⢰⠁⠀⢰⠑⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠊
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⢆⣀⣀⡀⠀⠂⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠥⠄⠀⠀⠀⠀⡀⠀⠀⠀⠄⠐⠈⠉⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⢀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠓⢠⠄⠀⠀⣤⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠢⠄⡈⠣⡙⠃⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠔⠒⣉⡐⠒⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⣤
⠀⠂⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡀⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠶⠾⡄⠀⠁⠀⢂⠐⠃⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠑⠀⠈⣉⠲⠀⠀⠀⠀⠀⠀⢀⡉⠀⠭⠭⣝⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣑⣤⣤⡤⠖

⢸⣶⢺⣶⣷⣮⣶⣶⣷⣮⣶⣬⣺⣵⣷⣵⣶⣶⣭⡾⡗⢉⡉⢺⠉⠉⠉⢳⣦⡶⢶⣷⡶⣶⣷⣞⣶⣶⣶
⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⡿⣿⣿⠀⢀⡄⠘⠀⠄⠀⣼⣟⣷⣾⣿⠷⠟⠛⠙⠋⠻⠿
⠯⠤⠄⠄⠥⠿⠿⠿⠧⠄⠤⠄⠀⠤⠤⠼⠿⠿⠿⠿⠧⠀⠀⠴⠄⠁⠴⠽⠿⠿⠿⠿⠟⠻⠟⠿⠿⠷⠿
⠀⣆⣀⡀⠀⠀⣠⢤⡠⠀⣤⠀⢠⡄⢀⠀⠀⡀⢀⣴⠶⣦⠀⠀⢤⠂⠀⠀⣀⢀⠀⢠⡤⠐⠂⠀⠒⣤⣤
⠀⡟⠛⠃⠀⠀⠙⠚⠁⠀⠛⠓⠚⠃⠸⠷⡷⡇⠈⠿⡶⠟⠀⠸⠿⠿⠀⠉⠙⠛⠀⠸⠿⠿⠿⠀⠀⠟⠉
⠀⡟⠛⠃⠀⠀⣤⣤⣠⡀⣤⠤⠤⡄⠀⢰⡆⠀⠀⠀⠂⠀⠀⣶⣆⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⡿⠿⠇⠀⠀⠤⠥⠥⠀⢹⡥⢭⠇⠀⢸⡇⠀⠀⠇⠀⠗⠀⣿⡏⠀⠀⠐⠑⠁⠁⢀⣀⢀⡀⠸⠿⠤⠿
⠀⡷⠶⠆⠀⠀⣀⣀⣀⠀⠀⠀⢀⡀⠀⢠⣤⡀⠀⠀⣤⠀⠀⢠⣤⣄⠀⠀⠀⢀⡀⢀⣀⣀⡀⠀⠀⣤
⠀⣷⣶⡆⠀⠀⢿⣿⡿⠇⠀⠴⠋⠀⠰⣶⣭⠁⠀⠀⠛⠀⠀⠈⠀⠁⠀⢠⢴⠾⡇⠸⠯⠭⠯⠀⠀⠉
⠀⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⡀⠀⢀⣥⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⡀⣀
⠀⣧⣤⡄⠀⠀⣴⣄⣶⠀⠛⡟⠿⠇⢸⣿⣿⡿⠀⢸⣿⠀⠀⠲⠿⠀⠀⠀⠘⠂⠀⠘⢿⡿⠟⠀⠧⣤⠜
⠀⣏⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⣏⣉⡁⠀⠀⠀⠀⢰⠀⠀⣤⠤⠀⠀⠀⡀⡀⠰⡖⠀⣶⠀⠀⠀⣿⡇⠠⠐⣠⠀⢀⣤⣤⣄⢸⠓⠒⢻
⠀⡟⠛⠃⠀⠀⠑⠛⠛⠀⢀⣁⣀⠀⠀⠀⠁⠁⠀⢀⣀⠀⠀⠀⠁⠈⠀⠀⠛⠃⠀⠈⠉⡉⠉⠈⠂⠀⠘
⠀⡟⠛⠃⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣤⡀⠀⣤⣤⣤⡄⠀⣾⣿⡆
⠀⡿⠿⠇⠀⠀⠁⠛⠀⠀⠘⠂⠘⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠛⠃⠀⠙⠛⠛⠁⠀⠘⠛
⠀⡷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠸⠛⡆⠀⢨⣤⡤⠀⣻⣿⣿⡇⢀⣀⣀⣀⠀⠀⠀⣲
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠰⠤⠃⠀⠘⠇⠄⠀⠺⠛⠻⠇⠘⠛⠛⠛⠀⠀⠉⠘
⠀⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⣤⡄⠀⢰⣿⠀⠀⣠⣤⠀⠀⣀⣤⡄⠀⠀⢀⠲⠀⠀⠀⠀⠄
⠀⠷⠶⠂⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠸⠿⠀⠀⠉⠛⠀⠀⠉⠙⠃⠀⠀⠿⠇

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠂⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠤⠤⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⣀⣀⣀⡒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠶⡆⠀⠀⠀⠀⢺⡇
⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠄⠤⠤⠤⠄⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⢾⣇
⠀⢸⣿⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠋⠉⢻⣶⠀⠀⠀⠀⠀⠀⢀⡶⠂⠀⠀⠀⠀⠀⠀⠚⠋⠀⢀⠀⠀⠀⠀⣿
⠀⠸⠋⢁⠀⠀⠁⠀⡀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢸⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢬⣑⢱⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠙⠦⣄⣋⣢⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠑⢿⢾⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⡀⠀⠤⠤⢄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠘⠃⠀⠀⠙⢵⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡤⠼⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠁⠉⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠈⠨⠀⠀⠀⢸⡄⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠗⠀⠀⣿
⠀⠀⠀⠀⠠⢨⠀⠀⠀⠸⠃⢀⢀⣀⣀⣀⣉⣯⣨⣄⣔⣀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⣇⣀⣀⠒⠀⢀⣿
⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⣭⣤⣤⡀⠹
⠂⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉
⣿⣿⢿⠿⢛⠿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⣤⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣴⠃⠐⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠝⢱⠀⠼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠍⠱⠀⠼⢉⡀
⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡀⠀⠀⠀⠀⡴⠋⡏⡩⠦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡴⠫⡎
⠙⢣⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠆⠅⠜⢃⡶⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠐⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠰⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠰⠤⠒
⡄⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠖⡼⣿⡆⢊⠀⠀⠀⠌⠄⢉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⣖⣾⣻⡆⠊⠀⠀⠀⠌⠆⢙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠀⠀⠀⠀⠶⢋⠘⠃⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠀⠀⠶⠛⠘⠇⢦⡴⠂
⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠨⣁⠀⡤⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣀⠂⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠀⡠⠦⡴⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡁⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡠⠢⡤⠀⠀⠀⠀⠆
⠀⠀⠈⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃
⠀⠀⠀⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⢀⠉⡰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡰⠉⠆
⠀⠀⠀⠀⡶⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠃⠠⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠜⠹⠀⠼⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠱⠀⠍⠹⠀⠨⢡⡀
⠦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠐⠀⠀⠀⣴⠁⡏⠩⡦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡰⠉⡏
⠙⡃⡶⠀⠀⠔⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁⠜⠃⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠒
⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆
⣗⠺⣻⡆⢂⠀⠀⠀⠌⠂⢉⠿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡷⣊⣖⢾⣹⡖⠊⠀⠀⠀⠈⠂⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠖⢋⠘⠃⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡴⠀⠀⠀⠀⠷⢛⠘⠃⢢⠴
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣁⠐⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣁⠂⠤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡰⠦⠶⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡤⠲⡴⠐⠀⠀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠈⠀⠉⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃⠀⠀⢀
⠀⠀⠀⠀⢀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠈⠉⠰⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠃⠀⠊⠀⠀⠈⠀⠐⠀⠓⠀⠀⠀⠂⠐⠀⠀⠀⠐⠈⠒⠒⠀⠁⠁⠘⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⠆⡈⠀⠀⠀⠀⠀⣈⠑⡒⡂⠒⠐⠒⠳⠉⡁⢄⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠈⢀⠀⢀
⠀⠀⠀⣀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⢀⠀⠘⠤⢁⣂⡉⠀⠈⢁⣂⠘⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠢⡑⠇⠐⠂⠒⠀⢀⠀⢈
⠀⠀⠈⠤⠃⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠉⠀⠀⠉⠭⠀⠀⠀⠀⡂⠀⠀⢀⣀⣀⣀⣀⣀⠀⠂⠀⠂⠀⠈⠈⣠⠀⠀⠀⢀⡈
⠀⠀⠄⠠⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠄⠠⠂⠀⠐⠄⣀⠠⠂⠀⠀⠀⠀⠀⠀⠢⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⡀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣀⣀⣀⣀⣀⣠⢤⡄⠀⠀⠀⠀⠀⠃⢀⠘⠐⠂⠒⠀⠂⠀⠀⢀⠐⠀⡀⠀⠀⠀⢠⠄⠄⠒
⠀⠀⡰⠊⠁⡄⠀⠀⠀⠀⠀⠀⢰⠈⠁⠦⠀⠀⠀⠀⠀⠤⡄⠐⠒⠒⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠬⠄⠰⠀⠃⠉
⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠣⠀⡠⠁⠂⠀⠀⠂⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠐⠀⠐⠂
⠀⠀⢐⡂⡂⠁⠀⠀⠀⠀⠀⠀⠘⠠⣲⠄⠀⠀⠀⠐⠄⢀⡤⠀⠒⠂⠒⠂⠀⣄⢀⠀⠁⠀⠀⠀⠀⠉⠈⠉⠉⠡⠁⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠰⠀⠆⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠁⢀⠄⢀⠀⡁⠀⠈⠃⢀⣄⡀
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠁⠠⠀⠀⠀⠠⠀⠩⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠂⠀⠀⠃⠐⢌⠀⠀⠋⠀⠙⡀⠑⢂⠂
⠀⠀⡄⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⡐⠲⠂⡄⠀⠀⠀⢈⠀⠉⠂⠂⠆⠆⠀⠂⠀⠀⠱⠀⠀⠀⠀⠊⢙⠆⠀⠆⡡⠄⠁⠀⠐⠂⠀⠀⠐⠛⠛⠛⠃⠀⠀⠀⠐
⠀⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠃⠄⠀⢠⠈⠀⠀⠀⠈⢠⠀⠀⠄⠃⠀⠀⠀⠈⠉⡄⠠⠄⠁⠀⡀⠀⢀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⠛⠂⠐⠀⠐⠚⠒⠁⠀⠀⠀⠔⠠⡀⠀⠀⠀⠀⣀⠂
⠀⠀⠀⠦⠆⠁⠀⠀⠀⠀⠀⠀⠀⠁⠶⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⢒⠂⠀⠀⠀⠀⠂⠐⠀⠠⠄⠤⠀⠉⠰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢌⠑⠂⠀⠀⠀⠀⠒⢈⡌⠘⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⣄
⠀⠀⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡠⠃⢀⠲⠆⠶⢰⠀⠪⡌⠂⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠂
⠀⠀⠐⢀⡑⠆⠀⠀⠀⠀⠀⠀⠀⠐⢈⠒⠀⠀⠸⠀⠀⠀⠀⠚⠀⠀⠀⠐⠃⠀⠀⠀⠈⠀⠀⠀⢈⠀⡀⠀⡅⣉⠀⠀⠀⠀⠠⠂⠓⠀⢀⠀⢀⠀⠐⠂⠒
⠀⠀⠀⠠⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠰⠀⠀⠀⠰⠀⠂⠀⠄⠤⠀⠀⠀⠀⠀⠑⠃⠀⠁⠀⠈⠀⡈⠁⠁
⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠈

⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠿⠟⠉⠉⢡⠶⠶⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣀⠤⠒⠂⠈⠉⠀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠰⡗⠒⠀⠚⠇⠀⠀⠀⠀⠀⠀⣞⠀⠁⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠛⢱⠒⠛⠉⠥⡐⠶⠉
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⢸⠛⠋⠛⢻⠋⠉⢹⠋⠙⢻⠲⡇⢀⠀⠀⠀⠀⣧
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠀⠀⢸⠀⠀⠀⠖⠀⠀⢸⠀⠀⢸⠀⡇⠈⠉⠑⠒⠒⠛⠀⡀⠠⢐⠍⠁⠀⠀⠠⠄⠲⠀⠀⢀⡀
⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠛⡀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢰⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⣀⣠⣀⣦⣤⣤⠼⠆⡀⠺⠖⠶⠾⠶⠷⣤⣤⡄⠠⢤⣼⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣻⠉⠈⠀⠀⠀⠀⡰⠊⠉⠉⠲⣄⠀⡴⠋⠀⠀⠙⢦⠀⣿⠄⠼⠤⠤⠤⠤⠤⠤⠀⢀⣀⡀⠀⠏
⠀⠀⠀⠀⠀⠉⠰⢄⡠⣄⡀⠴⠞⠋⠀⠀⠀⠀⡠⠀⢼⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⣉⡈⣋⠀⠀⠄⠀⣼⠀⠉⠀⠀⠀⠀⠐⠂⠀⠀⠁⠈⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠊⠡⠀⠀⠀⠀⠀⠀⢰⣠⠊⡴⢤⠮⠄⠀⠀⠀⠀⠀⠻⣤⣀⣠⡴⠋⠀⠘⠷⣤⣭⠿⠃⠀⠀⠢⠠⠄⠃⠀⠠⠀⠀⡀⢀⠰
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⡴⣦⠉⠁⠀⠈⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⠶⠚⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢠⠓⠤⣀⠀⠀⠉⠂⠄⠀⠳⣄⠀⠀⢀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢀⢿⣀⠶⡁⠀⠀⠈⠛⢦⡀⠀⠀⠑⠄⠘⢆⠀⢸⡇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠻⠖⠛⠋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠢⢀⠀⠀⠀⠙⢆⠀⠀⠈⡄⢸⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠈⠲⡀⠀⠀⠈⠳⡀⠀⠁⢈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢃⠀⠀⠀⠀⠈⠣⡀⠀⠀⠹⡀⢀⡿⠀⠀⢸⡆⠀⠀⣤⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⢢⡀⠀⠀⠀⠀⠙⢄⠀⠀⢱⡾⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⣤⠾⠓⢶⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠙⠦⣀⠀⠀⠀⠈⢣⣤⠟⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⡤⢭⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⢻⡄⠀⠘⢧⠴⠶⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠄⠉⠙⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡤⠴⠖⠛⠁⠀⡀⢀⣀⠠⠤⠄⣀⡤⠂⢄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣁⡞⠀⠀⠀⠀⠁⠙⢣⡜⠁
⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠂⡀⠀⠙⢇⠀⠸⠿⠛⠀⠀⠀⡇⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢃⠀⠀⡈⠶⣄⠀⠀⠀⣠⡴⠁⠀⠆⠈
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⡱⠏⠀⠀⠀⠈⠀⠀⠈⢣⡄⠊⠀⡠
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠊
⠀⢀⠔⠂⠐⠀⠓⠆⠀⠀⠀⠀⡀⠀⢀⡀⠀⠶⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠃⠀⠐⠶⢤⡀⠁⠐⠀⠀⠉⠛⠃⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠆⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠐⠶⠶⠦⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠠⠀⠀⢀⡀⣀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠡⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣖
⠀⠀⠀⠀⠒⠲⠄⠋⠀⠁⠀⠠⣟⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣠⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢈⡛⠛⠒⠤⠤⢴⠖⠚⠉⠉⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠈⠙⠻⣤⠁⣀⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠲⠀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠠⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡆⠀⡆⠀⡷⠀⣦⠀⢴⠀⠸⠂⢰⡄⠀⠄⠀⠆⠀⣶⢀⣆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣉⣁⣀⢀⣀⢀⣀⣀⣀⣀⣀⣸⣿⣏⣀⣀⣠⣤⣀⣄⣀⣐⣀⣠⣤⣴⣇⣠⡀⣴⣶⣀⣴⠀⣸⣿⣇⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣿⣿⣿⣿⣟⢛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣭⣭⣯⣭⣭⣥⣭⣭⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣶⣶⣾⣿⣷⣴⣿⣷⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠒⠀⠂⠂⠀⠀⠘⠀⠀⠀⠁⠀⠘⠀⠀⠀⠠⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⠦⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠋⠀⠀⠰
⠀⠀⠀⠀⠀⣀⠄⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠙⠀⠀⠈⠁⠀⠀⠄⠀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠠⣰⡄
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚
⠀⠀⠀⠀⠀⠈⠃⠀⠐⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂
⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠀⠂⠀⠀⠀⠀⡀⠈⠀⠀⡕⢈⠀⠀⠀⠀⠀⡲⠤⣤⡀⢀⣀⠀⠀⠀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠔⠀⠀⠀⠀⠉⢀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠀⠈
⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠴⠒⣲⠀⠀⠒⠂⢊⣚⠓⡄
⠀⠀⠀⡀⣶⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠀⠃⢟⢂⡏⣇⠀⠀⢠⣾⣿⣆⠀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡇⢩⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠂⠀⠃⠐⠃⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣧⣀⠤⠤⠤⣤⣄⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠤⠄⠀⠀⢴⠆
⠀⠀⠀⠀⠀⣀⣀⡀⢘⣦⣄⣉⠉⠛⠀⠀⠐⢳⡀⠀⠀⠀⡄⠘⡆⠀⠀⢀⠀⠀⢡⣤⢠⡄⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⡄⠀⠀⠀⢰⢠⠀⠀⣴⠏⣽⠤⡶⣶⢹⡏⢳⢀⡾⢻⢴⡾⠖⢹⡇⣞⠳⠀⠀⠀⢰⡀
⠀⠀⠀⢳⡄⠀⠀⠈⠛⠀⠀⣿⣴⢶⣶⣇⣿⢸⡟⣿⢺⣷⣶⣾⡷⠄⢸⢃⡈⢻⡆⠀⠀⠀⠄⠒⠒⠤⠛
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠶⠟⠸⠁⠻⠺⠧⠟⠈⠳⠾⠹⠷⠶⠸⠊⠳⠾⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠠⣠⡀⠠⠤⢀⡀
⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠃⠈⠀⠈⠉⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⢢⠃⠀⠀⠀⠀⠑⠻⡆
⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠐⠁⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠉⠈⠉⠉⠉⠁⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠲⡂⠰⢬⡇⠀⠀⠀⠠⢀⣀⣀⠠⠄⠀⠀⢠⡀⠠⠀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⠀⠀⠀⠐⠒⠂⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢙⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠒⠈⠉⠁⢀⣈⣢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡶⠿⠋⣉⣭⠶⠛⣋⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⠉⠛⢛⠟⠛⠭⢠⡄
⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⣢⣀⠀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠓⠒⠦⢤⣄⡀
⠀⠀⢀⠴⠊⠉⠀⢔⣮⡅⠻⢮⣿⣿⣿⡶⢤⣤⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣌⣬⣵⢦⠄⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⣶⣾⣿⣭⠵⠶⠛⠋⣉⣉⣿⠿⠿⢿⣯⣯⣷⣒⣶⣧⣄⣀⣀⣿⠛⠉⠁
⠀⠀⠈⠢⢄⡀⠀⠈⠐⠀⠀⢴⣿⠿⠖⠒⠛⣩⣽⣛⡥⠴⠟⠛⠙⠛⠓⠒⠋⠀⠀⠀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣤⣀⣀⣀⣀⣀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⡄
⠀⠁⠀⠀⠀⢈⠀⠀⠀⠀⡄⠀⠠⠀⠰⠟⠛⠚⠆⠀⠀⠀⠀⠠⠅⠀⡤⠈⠀⠐⠤⠀⠀⠀⠀⠀⠠⠆⠁
⠀⣤⣶⢿⢻⣻⠀⠀⠀⠀⠉⠑⠚⠀⠘⠛⠛⠃⠛⠀⠀⠀⠎⠀⠀⡀⠈⠀⢀⡀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠠⡶
⠀⣿⡮⠿⠛⠛⠀⠀⡈⠁⠀⠀⠀⠀⠀⣀⢀⠀⡀⠈⠀⠀⠀⠀⠀⠀⣠⡶⣿⡇⠁⠉⠃⢻⠿⠋⠀⠀⣼⣽⡀⠂
⠀⠁⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠰⠀⠇⠐⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⠾⠋⠀⠀⠀⠈⠛⠄⠀⠀⠀⠉⠉⠀⠐
⠀⣤⣀⣀⣀⣠⠀⠀⢠⣯⣿⣿⢧⡄⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠘⠁⠴⠄⠀⠀⠂⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰
⠀⠉⠚⠛⠒⠹⠀⠀⠻⣽⣷⣿⣿⠟⠀⠀⠀⠚⠉⠀⠁⠀⠀⠠⡀⠀⢀⠠⠀⠀⢀⠀⠀⢀⢤⡀⠀⠀⡄⠀⠀⠀⢈
⠀⠀⠀⠀⢀⠤⠰⠀⠂⠄⠀⠀⠠⠐⠀⠂⠄⠀⠀⠠⠂⠀⠉⠐⠀⠦⠀⠀⠀⠄⠂⠄⡀⠀⠣⠅⠀⠰⠀⠀⠀⠀⠘
⠀⠀⠉⢀⠀⠄⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠄⠀⢀⡀⠀⠈⠭⠂⠰⣲⠉⢑⢠
⠀⠘⠐⠀⠠⠀⠴⠞⡈⠀⠀⢨⡿⠉⢙⠀⠀⠀⠀⠀⢸⠛⢿⣿⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠁⠁⠉⡀
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠸⡿⠤⠈⠉⠉⠉⠀⠉⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠜⡑⠐⠀⠖⠀⠤⠠⠤⠠⠄⠐⡇
⠀⠀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠘⠓⠖⠚⠒⠒⠒⠒⠒⠶⠳⠒⠂⠀⠀⢀⡀⠀⠐⠀⠳⠋⠀⠀⢄⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⣾⣥⠋⢀⠀⠀⠆⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⡄⠀⡀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⣀⠠
⠀⠠⠀⠀⢀⣿⠡⠐⠀⠀⠀⠃⢠⢳⠻⠛⡝⠫⢯⠖⡷⠀⡃⠀⠀⠀⢐⠰⡆⠄⢠⠀⢸⠰⡸⢀⣾⠋
⠀⠠⡄⢠⠀⠠⠀⠄⠀⢠⠀⡀⠹⣭⣶⣾⣶⠿⢟⣋⣁⠀⡇⠂⠒⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠒
⠀⠅⠦⠀⠀⠤⠴⠤⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⢃⠠⣭⡢⠖⡲⣠⡆⡆⠀⠀⠀⠀⠀⠀⢌⣒⠀⢱⢱
⠀⠋⠉⠉⠉⠉⠉⠉⠉⠓⠀⢀⠠⢀⠠⢄⠀⡤⠀⠐⠤⢄⠈⠄⠙⠛⠐⠛⠒⢁⠃⡀⠀⠀⠐⠂⠄⢀⡀⠁⠀⣀
⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠈⠈⠀⠈⠊⠀⠑⠑⠀⠊⠈⠀⠀⠐⠄⣀⡠⠒⠁⠨⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠌⠈⠤⠀⠀⠀⠀⠈⠉⠁⢀⣀⣀⣀⣀⡀⠀⠈⠁⠀⠧⠀⠀⡀⢴⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⡤⣤⣄⡄
⠀⠀⠀⢄⡀⢀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣟⣽⣻⣭⣿⠀⠀⠀⠀⡄⠁⠀⠁⠐⠀⠀⠀⠀⡀⠀⠀⡀⡎⠛⠶⠞⠃⠂
⠀⡀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⢀⠄⠀⡀⢀⣛⠃⢰⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠀⠀⢀⡅
⠀⠣⠤⠤⠤⠤⠤⠤⠤⠽⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠃⠀⠀⠄⠀⠄⠊⠀⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠄⠄⠀⡐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠰⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠉⠙⠓⠒⠒⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠛⠉⠙⠒⠲⢤⡀⠀⠀⠀⢀⣸⠤⠔⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠖⠋⠁⠀⠠⠖⠡⠟⡷⣄⡀
⠀⠀⠀⠀⠀⠐⡒⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⡈⠹⠿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⢟⣹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣉⣲⣄⣀⢤⠄
⠀⠀⠀⠀⠀⠀⢁⣮⠆⢽⡍⢿⣖⢶⠶⢶⠒⣒⣚⣹⠉⠞⣳⡽⠉⠈⠢⣀⠀⣀⣤⣴⡶⢛⣟⢛⡛⣉⣁⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠸⢛⠦⢄⣀⠀⠈⠉⠙⡓⠀⣉⠀⠘⠋⡥⢎⡟⢠⢀⠀⠀⣽⠉⢤⡏⠀⡎⢻⠛⢯⣄⡈⢙⣭⠗
⠀⠀⠀⠀⠀⠀⠘⠦⢀⣠⡌⠛⠁⠤⢄⢠⣈⣁⡀⠀⡀⣠⠎⠁⠣⣌⠄⢸⣿⡄⢸⣬⣖⡽⠄⣇⢀⠦⠽⢾⡜
⠀⠀⠀⠀⠀⠀⠐⢄⢀⠈⠉⠁⠈⠀⠈⠁⠉⠉⠉⠁⠈⢀⠄⠁⠀⠈⠢⣥⠙⣧⠈⣟⠬⣉⣁⡟⢴⣟⠓⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠐⠒⠒⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠙⡓⡁⢶⠨⠇⠈⠂⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠱⠘⠏⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣄⣀⣀⠀⢀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣯⡶⠿⢾⣝⢿⠠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠰⣷⠀⣿⢾⣷⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⢦⣤⡼⣿⣾⠁⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠻⣿⠛⠉⣋⡼⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡃⢶⠄⣄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣷⣶⣾⡿⠂⢄⠀⠀⠙⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠁⠄⠀⠘⢦⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⠄⠐⢃⣀⠭⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠚⡈⠁⠀⠐⠢⣶⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠄⠁⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡩⢣⠀⣤⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠓⣀⢦⠠⠤⡏⠇⠰⠰⡅⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⢆⡰⢌⡄⠹⡤⠿⠲⠁⣎⡹⠆⠡⠀⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣄⢀⡸⠒⠎⠘⡀⡠⠞⢢⠀⠨⠁⠈⡀⢂⠈⠎⠖⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢹⠇⣤⠋⢄⠀⠑⢻⠲⠉⢇⠀⠁⠡⠐⠀⣃⣸⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣶⠀⠀⠀⠀⠀⣀⡇⠀⠈⢆⠈⡆⠀⠈⠓⠋⢇⢃⠘⡆⠀⠀⣣⡶⠟⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣰⠃⠀⠀⠀⠀⢸⡗⠶⠦⢤⣬⣤⣽⣄⣦⣤⣥⣸⣬⣤⡴⣶⠞⠉⠀⠀⠀⠀⠀⡇
⠀⠀⣠⡤⠔⠒⠂⠀⣈⡧⡤⠓⠒⠤⢤⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⣤⣤⣤⣤⣧⣤⣀⣀
⠀⣼⣏⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⣀⢟⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠁⢀⠀⠀⠉⠉⠉⠛⠻⢷⣦⣤⡀
⠀⡷⠬⣍⣛⣒⠚⠛⠒⠒⠒⣒⣚⡉⠥⠚⡇⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⢉⡁⡄⠀⠀⠠⠀⠂⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⡏⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠈⠀⡇⠀⠸⡆⠀⠀⣀⣴⠾⠋⠁⡠⢰⠄⠉⠀⠂⢂⣠⠤⠖⠒⡈⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢿⣷
⢠⡇⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀⡀⠀⠀⢀⡇⠀⠀⣇⣠⡾⠋⠁⠀⠀⢀⣈⣀⣤⠤⣤⠴⠿⠤⠤⣤⣉⣀⠀⢴⡴⠀⠉⠉⠠⡠⠆⠀⠀⠀⠈⣿
⢸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⢀⣴⠟⠁⠀⢀⠀⠐⠊⠉⠁⣠⠔⠋⠀⠀⡄⠀⣀⠀⠈⠉⠛⠲⣄⠀⣆⠜⠀⠀⠀⠀⠀⠀⣸⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⢸⣷⠟⠁⠀⠀⠺⠈⢀⡠⠂⣤⠞⠁⠀⢀⡀⠉⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃
⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠄⡆⠀⣠⠞⠁⠐⠁⠐⠒⠁⢠⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢻⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣰⡟⠀⠀⠀⠀⠀⠀⠋⠀⡴⠃⠀⠀⠸⠥⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⢀⣤⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⣀⣤⠞⠋⣠⡇
⢸⡇⠀⠀⠁⠀⠀⠀⠀⡜⠀⠀⢨⣿⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠛⠉⣀⣤⠶⠛⠉⢀⣤⠞⠉⡷⢤⡀
⣿⡇⠀⠀⠀⠀⠀⢠⠎⢀⡀⠔⠉⠳⣍⡛⠿⢿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠿⠟⠛⢉⣁⣤⠴⠞⠋⠉⠀⣀⣤⠾⠋⠁⣀⡼⠃⠀⣿
⣿⠇⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠸⣇⠙⠓⠦⢤⣈⣉⡉⠉⠉⠉⠉⠉⢉⣉⣁⣠⣤⠴⠖⠚⠋⠁⠀⢀⣠⣤⠶⠛⠉⠀⣀⣴⠞⠋⠀⠀⢠⣿
⣿⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⢦⣄⣀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⢀⣀⣤⠶⠛⠉⠀⠀⠀⢀⣴⡿⠁
⣿⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦⣌⠉⠙⠛⠓⠒⠲⠶⠶⠶⠖⠒⠛⠛⠋⠉⠁⢀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡿⠋
⣿⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠲⠶⠤⢤⣤⣤⣤⣤⠤⠴⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁
⠘⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⢛⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⢿⣝⡛⠻⠷⠶⠿⠿⠟⢛⣋⣩⡴⠖⠛⠁⠀⠉⠛⠷⠶⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⣴⠶⠶⠟⠛⠋⠁
⣤⣤⣬⣭⣿⣿⣷⣾⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣏⣼⣉⣯⣩⣿⣹⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⡃⠀⠀⠠⠀⠈⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣰⢦
⠀⠀⠀⠰⠀⠂⠀⠀⠐⠀⠄⢠⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢇⠀⠉⢀⣇
⠀⠀⠀⠀⢣⠀⢰⠉⠂⠚⠀⠀⠃⠔⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠉⠉⠁⠈⠣⡀
⠀⠀⠀⠀⠀⢆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⡴⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢔⠞⠝⠀⠣⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠠⠃⡌⠀⠀⠣⡈⠁⠒⢽⢄⡠⡀⣀⡀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣀⣤⠁⠀⠃⠀⡇⠀⠀⠀⠘⡄⠀⠀⠣⢕⠁⡇⠓⢖⠊⡦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠈⠩⠀⡸⠆⣀⢃⠀⠐⣄⠀⠀⢀⣄⣀⠴⣗⢤⠭⠑⢆⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠬⠉⡾⠥⢓⣄⡠⠢⣉⠔⠫⣉⠜⢅⠔⢀⣀⢴⡤⠵⢤⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⢹⠒⠆⠨⠇⠀⢠⠀⠀⡄⠀⠰⠀⢠⡡⠔⠈⠉⠀⠀⠀⠉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡆⠘⡀⠸⠀⠈⡀⠀⠄⠀⡄⢀⠊⠀⢀⠀⢠⠦⣔⡑⠤⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣘⠀⢀⡀⢸⡤⠓⠠⣇⠀⠃⠀⠀⠀⠇⡆⠠⠀⡀⠱⡋⠀⠀⠀⡈⠃⠀⢀⡀⢐
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⠀⠈⠂⠀⠁⠀⠀⢸⡀⠐⠀⠀⡐⠀⣧⠲⠠⢄⠀⠈⠙⠉⠁⠀⠀⡠⠁⢈⠇
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢀⠇⣀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠓⠊⠑⠤⠊⠉⠈⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠄⠒⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠊⠓⠁⠀⠘⠃⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠠⠀⢀⠀⠀⡄⠘⠔⠀⠀⡠⠒⠐⠂⠄⠀⣀⠀⠀⠀⡀⠀⠠⢒⠄⠀⠀⠀⠀⠀⠚
⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⡄⠀⠀⠀⠰⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠀⠂⠂⠀⡀⠀⠀⠠
⠀⠁⠀⠀⣠⢂⢶⡀⠀⠀⠀⠀⠀⠀⠈⠐⠔⠀⠁⠀⠀⠄⠈⢀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈
⠀⠀⠀⠀⠅⠬⠋⠀⠀⠀⠀⠄⢀⡀⠠⡀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠁⡂
⠀⠀⢀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠚⠀⠂⠀⢠⠉⡄⠠⠀⠀⠀⠀⠂⠁⠠⠀⠐⣢⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⢴⠰⡄⢀⡐⠀⠀⠈⠀⠀⠀⠀⠀⡀⢤⡶⠄⠘⢊⣁⠠
⠀⠀⠀⠂⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠁⠉⠀⠀⡀⠤⢀⠀⠀⣼⡟⠁⠀⠀⠀⠈⠀⠠⡴⢡⢿⡄⠈⠂
⠀⠀⠀⠀⠐⠀⠧⠰⢺⠀⠀⢀⡀⠀⠐⠀⠀⠀⡊⠀⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠁⠀⠀⣀
⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣮⣹⣲⣲⠀⠀⠱⢄⣀⡠⠜⠀⠀⠄⠃⠀⣯⣩⡣⢭⠀⠀⠀⡀⠄
⠀⠢⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⡨⠟⠀⠀⠄⠀⠀⠀⣀⠰⢆⠠⡀⠠⠀⠀⠀⠀⠀⠀⠀⢨⠁⢀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣇⠊⠀⠀⠀⠀⠀⡀⠀⠃⠀⠈⠀⠃⠀⠀⡄⡐⡠⠀⠀⢁⠈⠀⡌
⠀⠀⠠⠀⠀⢰⠃⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡆⠀⠄⠐⠀⠘⠒⠓⡇
⠀⡄⠀⠐⠤⠤⢴⠂⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀
⡐⢀⡂⠀⢠⣀⣼⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠂⠂⠀⢬⡣⣁⣸⠀⠀⠐⠀⡂⠀⠀⠐⠂⠀⣘
⣿⡫⠁⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡻⣥⡆⠀⠀⠅⠀⠀⠀⠀⠀⠀⠄⠸
⠎⠋⢀⣴⠿⠝⠛⠁⠀⠀⢀⠀⠀⢀⣾⣦⡄⠀⠀⢨⢀⠠⠶⠀⠀⠉⠊⠀⣀⣀
⣄⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⡂⠀⣾⣿⡿⠟⠁⠀⠈⠠⠄⠊⠀⠀⠀⠰⠎⢲⡻⠄⠀⠀⠠⠠⠀⠀⠠
⠄⠀⠀⠆⠀⠀⠀⠀⣏⡀⠐⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢄⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠐⠂⠀⠀⠀⠀⠤⠀⠀⠀⠉⠀⠨⠁⠸⠆⠀⠀⠀⠰⠂⠠⠀⠀⠡⠀⠄⠀⠀⠀⠔⠂

⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠤⠤⠶⢶⣖⣒⣒⣒⣒⣒⣒⣚⢿⠯⢭⡑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⡞⣡⠖⠒⠒⠒⠒⠒⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⢂⠢⠤⠍⢐⣒⠀⠄⡀
⠀⠀⣧⢹⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⡌⠀⠀⠀⠀⠀⠀⢩⣆⡗
⠀⠀⢸⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡇⡾⠀⠀⠀⠀⠀⠀⠀⢸⢣⠅⠀⠀⠀⠀⠀⠀⣽⣸⠃
⠀⠀⠀⢧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⡇⡇⠀⠀⠀⠀⠀⠀⠀⡟⡜⠀⠀⠀⠀⠀⠀⠀⢇⡏
⠀⠀⠀⠸⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⡇⠀⠀⠀⠀⠀⠀⢸⢓⣡⠆⠀⠀⠀⠀⠀⡘⣼⠁
⠀⠀⠀⠀⢳⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⡾⣸⠇⠀⠀⠀⠀⠀⠀⢃⡏
⠀⠀⠀⠀⠘⡆⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠇⡇⠀⠀⠀⠀⠀⢠⡇⡟⠀⢀⠀⠀⠀⠀⡰⣼
⠀⠀⠀⠀⠀⢳⠘⠮⠶⠶⠶⠶⠖⢒⣒⣒⣒⣒⣒⡉⠭⠭⠭⠱⠒⠒⠚⢣⡀⠀⠀⠀⠀⠘⠇⢀⡠⠀⢶⢀⠀⠽⢳⡇
⠀⠀⠀⠀⠀⡰⠋⢨⠠⠉⠉⠳⠀⠀⠀⠀⠖⠂⠈⠀⠀⠀⠀⢠⡂⠞⢀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠂⠤⠞
⠀⠀⠀⢀⠎⠀⠠⠃⠀⠤⠀⠀⠙⠁⠘⠂⠑⠒⠋⣀⣁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⡀⠀⠀⢀⣈⣀⣀⣀⣠⣤⣠⣤⠴⠶⠶⠖
⠀⠀⠳⠄⠀⠀⠐⠂⠒⠒⠒⠈⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⢍⡒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡔⠁⡘⠉⠓⠦⣭⣓⠦⢤⣀
⠀⠀⠀⠀⠀⡴⢒⠒⠛⠋⠋⠷⠶⠤⢤⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⠋⠀⣀⡂⠀⠀⠀⠀⠈⣩⠖⣨⠃
⠀⠀⠀⠀⢀⡇⢀⡀⠀⠀⠀⠀⠀⢠⣾⡔⢉⣭⣉⢘⣧⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡡⠊⠀⠀⠀⠘⠋⠀⠀⠀⢀⡜⢁⠞⠁
⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠂⠀⠀⠀⡏⡇⢸⣿⣿⣼⡏⣼⠀⠀⠀⠀⠀⠀⠀⣰⢋⡔⠁⠀⠀⠀⠀⠀⡀⠀⠀⡠⢋⡴⠃
⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠧⠅⣀⣙⣋⣭⣃⡟⠀⠀⠀⠀⠀⠀⣼⡁⠈⠓⢦⣀⠀⠀⠀⠀⠀⢀⠞⣡⠎
⠀⠀⠀⠀⢸⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡽⠃⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣻⡾⠍⠒⠦⣤⡴⢃⡴⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠒⠶⠶⠶⠤⢤⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣮⣄⡀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠉⠉⠙⢿⣷⣤⣴⣶⣶⣶⣶⣶⣶⣤⣴⣿⠛⠉⠉⠉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣀⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣤⡀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡟⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠐⣿⣿⡷⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠈⠉⣀⣠⣤⣤⣤⣤⣀⡈⠉⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣴⠟⠉⢠⣴⣶⣶⣤⠈⠙⢶⡄⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⢸⠇⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⢿⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣧⡀⢸⡆⠀⢤⣀⠀⢸⠀⢀⣠⠄⠀⣾⠀⣠⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠉⠀⢙⣿⣶⣿⣆⡀⠉⠙⠛⠛⠉⠁⣀⣾⣷⣾⣟⠁⠈⠙⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⣰⣿⠟⠉⠛⠿⢿⣶⣶⣶⣶⣶⡾⠿⠟⠋⠙⢿⣷⡀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣤⣶⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⣦⣤⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣡⣴⣿⠿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣤⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⣀⣀⣀⣀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠛⠛⠛⠛⠛⠛⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣄⣀⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣄⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠈⠑⠂⠁⠀⠈⠂⠀⢀
⠀⠀⠀⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠐⠈⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠦⠀⠀⠈⣐⠁
⠀⠀⠀⣏⠀⠟⠀⢠⢨⡁⠀⠀⠀⠈⠒⠁⠀⠀⠈⡈⠀⠀⠘⡐⢂⠀⠀⠐⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠓⠀⠀⠀⠓⠉⠢⡀⠀⠀⠈⠀⠀⠀⠠⠦⠄⢀⣨⠠⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡆⠀⠀⠀⠀⠸⠆⣄⠀⠀⡀⠀⢀⠀⠀⠤⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⡄⢀⣒⣼⡓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠰⠿⠀⢈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⡁⠄⠀⠀⠀⠀⢅⠁⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⣄⠉⠡⠋⠘⠌
⠀⠀⠀⠀⠉⠂⠂⠚⠀⠀⠀⠀⠊⠀⠰⠈⡄⠀⠀⠀⠀⠉⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⡅⠀⠠⣶⠆⠀⠢⠤⠀⠀⠀⠀⡐⠁⠀⠀⠐⠂⠠⠀⢀⠁⠀⢀⡀⠀⠀⠐⠄⠐⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠀⠀⠠⠚⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠊⠁⠀⠀⡀⠀⠀⠀⠀⠇⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡐⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠐⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⡈⠢⡡⠀⠀⠀⠠⣹⠓⠂⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠱⠄⠀⠀⠀⠀⡅⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⢠⠀⠠⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢖⣈⠶⢌⠀⠀⠀⠈⠂
⠀⠀⠀⣂⡠⠐⠀⠃⢀⠚⠀⠀⠀⠀⠀⢈⠂⠒⠁⠀⠀⠀⢈⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣀
⠀⠀⠈⠚⠢⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠄⠤

⠀⠀⠀⠀⠀⠠
⠀⠀⠦⢄⢀⠘⠂⠀⠀⠐⠀⣈⡭⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤⢐⣢⡄⠀⠀⠀⠐⠀⢠
⢀⠀⠀⠀⣙⡀⠈⠀⠀⠀⠂⠀⠀⠀⠃⠀⠈⠀⠁⠀⠀⠀⠀⢚⡩⣥⡶⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⣒⡀
⠙⠛⠤⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠐⠀⠀⢀⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣉⠀⠐⠤⢐⡀⢠⡆⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⠀⠀⠀⠀⠀⠂⡤⠀⠀⠀⠀⠉⠛⠓⠲⠾⠭⠦⠀⠀⠘⠤⢄⣀⣀⡇
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⢀
⠀⠀⠘⠀⠀⢈⡁⠀⠩⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣟⣿⣿⡂⠀⢦
⠀⠀⠁⠀⠸⠋⠙⢛⠛⢤⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠘⠛⠉⠁⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣮⣆⣠⠤⡎⠀⢀⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⢃
⠀⠄⠀⡇⠀⠀⠀⠈⢉⢲⠄⠀⠒⠠⠰⠖⠁⠀⠀⠀⠀⣠⠀⡀⠀⠄⠀⢀⠀⠀⠀⠐⡀⢸⠀⠀⠒⠀⠈⠆
⠀⠀⠀⣷⣀⣀⣀⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠢⢌⣉⠙⠰⠂⠦⢤⡀⠀⠀⠉⢺⠀⠀⠀⠀⠀⠀⣀
⠀⠠⣀⡍⠠⠄⣀⣉⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠱⠂⠀⠉⢕⣒⡒⠡⢬⠀⠀⠀⠀⠱⠶⠶⠶⠒⠛⠉
⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠴⠬⣄⣉⣡⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⣤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡏⠓⠒⠯⠝⢻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠆⠀⠀⠹⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢉⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣥⣤⡀⡥⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⠞⡃⠠⡠⢹⣦⣾⣟⣽⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣻⣿⣿⣻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⠙⢋⡿⠣⣮⣉⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣏⡉⠙⠁⠀⠀⠒⠦⠈⠉⠉⠉⠿⣿⣿⣿⣿⡟⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠻⠛⠲⠶⠶⣄⣲⣀⡀⡒⠒⠺⠽⠛⠛⢋⣼⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣛⣉⣤⣶⣶⣮⠙⠉⠉⠉⠉⠉⠉⢉⣭⣶⣶⣤⣀⣾⣿⣿⠏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡿⣭⣙⡻⣿⣿⣿⣷⡄⠀⠀⢀⣴⣿⢿⡟⣛⣹⣿⣿⣿⣿⢾⣾⡏⠎⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠆⣈⡴⣋⠿⡝⢁⣙⠳⢶⡟⡇⠈⠀⢽⠋⡛⠞⢻⠁⢀⣰⡗⣵⠐⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡔⢡⠗⡂⣨⣍⠳⢮⠀⣀⣚⠋⠘⠀⠀⠀⢡⣴⣿⣉⣸⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣏⡟⠳⠓⠜⠉⠉⠐⠚⠛⠿⢆⠍⣀⣎⣹⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠶⠤⠤⠤⠄⠒⠂⠉⠉⠉

⢠⠤⠤⠤⠤⠤⠄⠄⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⡠⠄⠀⠀⠀⢄⠀⠀⠀⠀⠤⠤⢤⠀⠀⠀⠀⣠⠤⠤⠤⠤⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⢸⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣿⣿⣿⡁⠀⠀⠀⠧⠤⠤⠤⠤⠼⠀⠀⠀⠀⠋⠉⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠉⠉⠽⠿⠍⠉⠁⠀⠀⠀⠿⠿⠿⠂⠀⠀⠶⠶⠶⠦⠴⠶⠶⠶⠀⠀⠀⠦⠤⠼⠀⠀⠀⠀⠻⠶⠶⠶⠾⠃
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠰⠋⠀⠀⠈⢳⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⢰⡟⠉⠙⢷⡄
⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⣴⡶⣶⢶⡶⡶⣶⣦⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠸⣦⣀⣀⣾⠃
⠀⠘⠿⠀⠀⠸⠟⠀⠀⠀⠀⠻⣿⠿⠁⠀⠀⢷⣭⣭⣭⣥⣿⣧⡽⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢠⣬⣿⣯⣤

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢰⠒⠛⠛⠛⠛⠒⡆⠀⠀⠀⢿⣿⠗⠀⠀⠀⠀⣠⣴⠂⢲⣶⡂
⢀⠴⢿⣯⣨⣿⠷⣄⠀⠀⠀⢸⠟⠿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣽⣿⣽⠀⠀⠀⠀⣇⣨⣷⣯⣀⡵
⠀⠺⠂⠿⠿⠕⠿⠊⠀⠀⠀⢸⣦⣗⠀⠀⠀⠸⣷⣶⣶⣶⣶⣾⠇⠀⠀⠀⢉⣟⠉⠀⠀⠀⠀⠻⣀⣸⣄⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣤⣠⠀⠀⠀⠀⠀⠀⠤⠀⠒⢲⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠒⡀⠀⢀⠀⠀⣴⣶⣶⣶⣦⡀
⢸⣯⣿⣿⠛⠛⠻⣿⠀⠀⡄⠀⠀⠸⠀⠀⠀⠖⠒⠲⠒⠒⠖⠒⠲⠀⠀⣿⣦⣶⡇⠀⢸⠇⠀⡿⠿⠿⠿⠿⡇
⢸⣿⣿⣿⣀⢀⣠⣿⠀⠀⢧⣤⣤⣴⣄⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢀⡠⠔⠂⠁⠀⠀⠀⢠⡶⠶⣦⠀⠀⠀⠀⠀⠀⢀
⠀⣤⣴⣿⡇⡀⡕⡄⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢿⣠⣆⣆⣴⣠⠀⠀⠀⢸⣧⣀⣼⠀⠀⠀⢠⣤⣾⣿
⠀⠿⣿⣿⡏⢊⢄⡆⠀⠀⢠⣤⡇⣠⣼⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⢸⡏⠍⢻⠀⠀⠀⠸⠿⣿⢿⠃
⠀⠀⠀⠙⠃⠀⠉⠀⠀⠀⠈⠛⠁⠛⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠘⠛⠒⠛⠀⠀⠀⠀⠀⠑⠛
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⢿⡾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡃⡼⠃⠀⠀⠀⠀⣴⣶⣶⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢤⠀⠀⠀⠀⠈⢃⣀⣀⡸⢱⣀⠤⠙⠛⠛⠛⠿⣿⣿⡿⠃⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢠⣄⣀⣠⠊⠁⠀⠐⢁⠜⢣⠀⢸⣏⣶⣤⡀⠘⣿⣿⣷⡄⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠈⠒⢤⠤⠀⠠⠀⠘⠀⢀⠀⠆⢠⣉⡙⠻⠛⢹⡏⠉⠉⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⢏⠤⠒⠚⢄⠀⠢⠴⢶⡊⠁⠀⢰⠀⡏⢙⡀⠀⠠⡀⠀⠀⣴⠟⣻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠱⣁⣀⢶⣾⠂⢣⡀⠀⠸⣨⠗⠈⠙⠚⠀⠛⠳⡦⡁⠇⠀⠠⠵⣾⣿⣝⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠀⠐⡇⠛⠿⣤⣽⣿⣿⣇⣀⣰⠁⠀⣀⣀⠀⠠⢆⡀⠀⠙⣄⠀⠀⠀⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢠⣀⡇⠀⠒⢃⠜⠋⢡⣂⡄⠀⣉⠲⠄⠋⢀⣠⣴⠀⣀⠤⡀⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡡⠨⢳⡀⠀⡏⠀⠀⢨⡽⢗⠻⠀⠀⡎⠁⡪⠽⠋⠰⠥⡀⡨⢰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠰⡅⡀⡇⠙⠂⠖⠂⠘⠁⢀⣎⠀⣀⠔⠋⠉⠑⠢⣾⠼⣀⣈⢣⠸⣌⠆⡀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠳⢌⣘⡦⡄⣠⡀⠀⣤⠈⠈⢶⠁⠠⡄⣠⣶⣴⠈⡞⠀⡏⡆⣠⠃⠊⠐⠂⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠕⠠⢊⠼⢿⠀⠉⣀⣀⣄⠀⠀⠸⠀⠀⢀⠁⢀⡀⠀⢰⠊⠀⠀⢹⠍⠉⡓⣎⠔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠡⡐⠆⠆⠀⠻⠽⠟⠀⠀⠀⡆⠧⡸⠀⠿⠃⠀⠸⠀⠀⠇⢸⠈⢑⠈⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⠖⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⣶⣶⣶⣿⡖⠒⠒⠚⠧⠁⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠈⠛⠟⠛⠁⠀⠀⣠⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣤⣀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢀⣀⡀⠀⠀⠀⣰⣶⣶⣦⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⣀⠉⠑⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⣀⢠⠂⠁⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠈⣄⠘⠛⠁⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠨⡇⠀⠰⢀⡐⠀⠘⠀⡰⡄⠂⠀⠀⠀⢊⠁⢀⠀⢀⣀⡆⠀⢠⠔⠉⠑⠂⠀⠺⣀⠀⠀⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠊⡜⠁⠀⣀⢀⠀⠧⢴⣀⡀⠈⠁⠀⠘⢀⡁⠀⠀⠀⢀⠀⡈⡔⣡⣶⠀⣴⡄⢆⠁⠀⠀⠀⠀⠀⠀⠘⠔⢈⡀⡔⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠉⠣⡀⠑⠂⢈⡠⢷⠚⠠⢄⠀⠀⠀⠀⠀⠈⢏⠐⠂⠀⠡⠈⡇⠈⠉⣂⡉⠁⢨⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠙⢩⠦⠤⣧⣤⣆⡠
⠀⠀⠀⠀⢀⠌⠉⠉⠙⠦⠜⣤⡀⠀⠁⡄⠀⠀⡀⠀⠸⠄⢀⠀⠀⠀⠈⠂⠄⠉⠠⠔⠁⠡⠒⢀⠄⠒⢀⠀⠀⡼⠋⠁
⠀⠀⡀⠂⡌⠀⠀⠀⠀⠀⢦⠉⢈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄⠀⠀⠸⠄⠀⠋⠀⠀⠀⠈⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠸⣄⣠⠅⠌⠀⠀⠈⠀⠸⡵⠶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠠⠔⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⣀⠆⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠸⠀⠡⠀⠀⠈⠀⠀⠄⡀⠠⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣂⠀⠀⢠⠂⠩⠀⠁⠘⠂⠀⠀⡀⠀⠙⠢⠤⡀⣀⠀⠀⠀⣀⡀⠔⠁
⠀⠀⢔⠀⠁⢠⠤⠤⠴⠺⠄⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠈⠀⠁⠈⠀⡃⠀⠠⠄⠀⠠⠀⠀⠄⠀⠀⠑⠤⣄⣀⠤⠂⠀⢀⠏⠁⠀⠄
⠀⠀⠀⠉⠉⠁⠠⣀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠠⠤⠸⠀⢐⡃⠀⠀⠀⠀⠂⡀⣀⣠⡄⣀⢠⠀⠀⠃⠀⠀⠔⠃⢀⠰⠆⠀⠀⠈⠳⠶⠆⠶⠎
⠀⡐⠁⠀⢀⡠⠐⠂⡀⡀⠀⠀⠀⠀⠁⠀⠣⢔⠃⠁⠀⠀⢰⠐⠒⠆⠀⠐⢃⡀⡀⢀⠀⡠⠀⠀⡅⠀⢘⡄⠰⠾⠀⢰⣷⠀⠠⠄⠠⠀⡀
⠰⠀⠀⡠⠋⠀⠀⠀⠀⠰⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠉⠀⠉⠁⠀⠀⠈⠣⣀⣴⣄⠨⡵⠤⠤⢴⣠⠄⠀⠀⠀⠄⡠
⠈⣄⡐⠀⡠⠂⠀⢀⠀⠘⠂⠀⠀⠀⠀⠀⡀⠀⠠⠠⠀⠰⠁⠀⠀⠠⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠒⢀⠀⠐⢢⡀
⠀⠘⢦⣀⠀⠀⠄⢂⠔⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠈⠎⠄

⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤
⠀⢨⣿⣿⢟⢿⣿⣧⠀⠀⠀⣰⣞⡛⣳⣦⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠶⢤⠁⠆⠰⠆
⠀⠸⣿⣯⠈⠠⣿⡗⠀⠀⢠⡟⠛⠁⠙⠛⡇⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢿⣤⣬⣇⠁⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⢶⢆⣶⣶⣇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄
⠀⠀⠀⠤⠤⠤⠆⠀⠀⠂⠀⠉⠉⠈⠉⠈⠀⠀⠀⠠⠄⠀⠤⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠻⡿⠿⠃
⠀⠀⠀⠀⢀⢀⠀⠀⣈⠥⠀⠀⠰⣠⡆⣴⢰⣴⢰⠀⣤⣤⢀⡆⣦⢰⠀⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠐⠻⠳⠀⠀⠉⠁⠀⠀⠈⠁⠀⠈⠈⠈⡈⡀⣁⡈⡀⡅⠀⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⡄
⠀⠀⢠⡀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿⡶⣾⣏
⠀⠀⠀⠁⠈⠁⠁⠀⠀⣶⡄⠀⠀⢠⣶⠀⠀⣀⣻⠟⢉⠙⢿⣃⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣿⠙⢹⣿
⠀⠀⠀⠏⠀⢒⣛⠀⠀⠘⡇⠀⠀⢸⠇⠀⠀⣭⣿⠀⠀⠀⢈⣯⡅⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣿⠀⢸⡟
⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢹⡷⣶⣶⣿⡍⠁⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⢸⣶⣾
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣍⠀⠀⠀⠀⠶⠖⠀⣬⣿⡄⠘⠿⠗⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⣿⣥⠽⠬⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠻⢶⣴⠿⢿⣄⠀⠀⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣶⣦⣶⡞⠁⠀⠀⢈⣷⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠖⠋⠉⠻⢿⣧⣬⣁⣠⣼⣿⠁⢀⣀⣸⡃
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠴⠉⠩⠭⢌⢻⣿⣿⡿⢿⡉⢉⣿⣃
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠒⠖⠃⠀⠀⠀⠀⠀⠁⣗⣀⣶⡆⢛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣸⠂⠀⠀⠀⠀⠀⠠⣿⠅⣿⠇⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠤⠤⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⣆⠀⠀⠀⠀⠀⢀⣽⣸⡟⢠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⣤⠴⢒⣾⡷⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣤⡙⣿⣿⣤⣤⣀⣴⣿⣿⣿⣵⠿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠋⠁⠒⠻⡿⠿⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⣿⣿⣿⣿⣿⣿⠿⠛⠑⠉⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⣄⡀⠀⣾⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⡗⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣗⢶⡖⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣴⣷⡄⢛⣿⣿⣿⣖⣦⣼⣀⡀⠀⠀⢹⠀⠀⠀⣥⣾⡗⠆⠀⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⠿⢟⠛⠉⣉⣤⣶⣛⣻⡿⣿⠿⢿⣿⣿⣶⣦⣤⡏⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠎⣸⢀⣆⠠⣤⣀⡀⠀⠀⠀⠀⠀⠈⠒⠰⠤⢄⣀⣀⠙⠉⠁⠀⠐⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⣴⣯⣀⢨⣦⢈⣁⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢿⣖⠲⣶⡤⣀⡈⠛⠛⣩⣟⣛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠺⠾⢇⣀⣿⣶⡙⢦⠛⣿⡶⢆⠉⠉⠁⠀⡈⠳⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠁⠀⠀⠀⠀⠀⠀⠙⢀⣬⣏⣆⣀⡠⠥⣦⠷⣦⡄⢠⠀⠀⢽⡇⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣁⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣨⣟⣁⡙⣿⣳⢶⣿⢻⠘⠀⠀⢸⡇⠠⡅⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⣭⣿⠛⠿⢾⣿⣦⣭⡿⢀⡁⣰⣿⣿⣿⣧⣌⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣂⣾⣿⣿⡶⠶⣞⣿⠷⠉⢙⣲⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠈⠀⠸⠿⣓⡲⠶⠶⠾⠟⠻⠉⠉⢠⣶⡿⠿⠷⠞⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠄⣀⣀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉

⠀⠀⠀⡠⠀⠠⡀⠀⠀⠀⢀⣤⠤⣄⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⢰⡀⠀⠀⣘⠀⠀⠀⣎⣹⣶⣉⡇⠀⠀⢸⣿⢩⡍⣿⡃⠀⠀⠈⠢⡶⠕⠁⠀⠀⠀⠀⣇⣀⡇
⠀⠀⠘⠟⠀⠘⠏⠀⠀⠀⠈⠻⠤⠛⠁⠀⠀⠘⠛⠓⠚⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⠼⠇

⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⣾⠻⢻⣦⠀⠀⠀⢠⣤⣤⣤⣄⠀⠀⠀⡠⡖⡷⣦⡀
⠀⠀⠸⣿⣄⣼⡿⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⣿⠚⠚⣷⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢇⣇⣇⣇⠇
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠘⠛⠛⠛⠋⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡏⠀⠈⡇⠀⠀⠀⢸⣿⣿⣶⠀⠀⠀⠀⢠⣶⣦⣀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⣷⣶⣶⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠐⠿⠿⠿⠿⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠘⣿⣿⡏
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢸⣟⣻⣛⣿⠀⠀⠀⠀⠀⠈⡎⠀⠀⠀⢀⣞⠁⠈⣳⠀⠀⠀⢸⣻⣟⣟⡷⠀⠀⠀⠸⢿⣿⣦⠄
⠀⠀⠘⠋⠉⠉⠛⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠸⠿⠿⠿⠿⠂⠀⠀⠀⠟⠛⠋⠁⠀⠀⠀⠆⠂⠀⠉

⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⠀⠀⡆⠀⠀⢠⡄
⠀⠀⠘⣯⡀⢀⡀⠀⠀⠀⡃⠀⠀⠀⡃⠀⠀⠸⣿⣟⣻⣿⠆⠀⠀⠸⣿⡇⠊⠐⠀⠀⠀⡟⠛⠛⠛⡇
⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠈⠉⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠃⠀⠀⠐⠃

⠀⢀⣶⣾⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⢠⣶⠶⠶⣶⡄⠀⠀⣼⣽⣯⠷⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⢶⡆
⠀⢸⡏⠈⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⣷⣤⣤⣿⠀⠀⠀⣿⣿⢱⣿⣿⢷⠀⠀⠀⠀⢸⣇⣀⣀⣸⡇
⠀⢸⣇⣀⠀⠀⠤⠤⠤⠿⠿⠿⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢸⣿⣌⡻⠿⣋⣾⠀⠀⠀⠀⢹⣿⣿⡏⠁
⠀⠈⠿⠿⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣁⡀⠀⠀⠀⢸⣿⣿⡇
⠀⣠⣤⣀⠀⠀⠀⢰⣿⣷⣶⣾⠟⠉⠙⣻⣦⠀⠀⢀⣤⣼⣧⣤⣤⣤⣤⣤⣤⣿⣤⣄
⣾⡿⠛⣿⣧⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣸⣿⠀⠀⢸⠏⠀⠀⠹⡇⠀⠀⡿⠁⠀⠈⢿
⠻⣿⣾⡿⠏⠀⠀⠸⣿⠿⠿⠿⠷⣦⣾⠿⠟⠀⠀⢸⣧⣀⣀⣴⣿⣿⣿⣷⣄⣀⣠⣾
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⠉⠉⠙⠆⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⡤⠤⠤⠤⢤⡀⠀⣀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⢤⢴⡇⠀⠀⠀⣇⣀⣀⣀⣼⠀⠀⡷⢤⠤⡤⢼⡇⠀⡇⠀⠀⠸
⠀⢠⣤⣠⣤⠀⠀⠀⠀⢸⢽⢽⢽⡇⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⡗⢺⠒⡗⢺⡇⠀⣷⣤⣴⣶⠀⠀⡀⢀
⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠛⠛⠻⠛⠛⠀⠀⣏⣹⣉⣏⣹⠇⠀⣿⣿⣿⣿⠄⠠⣧⢸
⢀⣠⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⣿⣾⣿⣾⣿⣿⣿⣿⠀⠀⠀⣞⣛⣻⣿⣿⡇⠀⠀⣴⡾⢷⡿⠟⠻⣿⣦⠀⠀⢰⣯⡽⣇⡤⡀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠿⠟⠛⠁⠀⠀⣿⣿⣿⡁⠀⠀⢸⣿⠀⠀⢸⣿⢸⣿⣿⣸⣿⣿⣿⣾
⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠻⠿⠿⠿⠶⠶⠿⠟⠀⠀⠈⠻⠛⠾⠚⠛⠉⠉⠉⠁
⢀⡤⠤⠤⠤⠤⠤⠤⠤⣤⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣽⡆⠀⠀⠀⣀⣄⣀⣠⣄⣀⣠⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⣟⣿⣿⡇⠀⠀⢰⣏⢈⣻⠿⠿⣟⣷⣟⡇⠀⣿⣿⣦⣾⣿⣿⣿⡇
⣼⣷⣴⣶⣦⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣭⣤⣤⣬⣷⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣧
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿