Template Emojis & Symbols

⠀⠀⠀⠀⠀⢰⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠢⠀⢀⡀⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡠⠔⠒⢨⠓⠐⢤⣀⡋⢀⠌⠸⠱⠀⠃
⠀⠀⠀⢀⡀⢰⠀⠘⠀⢠⡌⠀⢀⠀⠀⡑⠬⡺⢿⠇⣀⣱⡀
⠀⢔⠈⠀⡀⠀⠑⢄⠡⢰⠀⡠⠀⠀⡐⢙⠈⠠⠦⡂⡀
⠀⠀⠁⠢⡀⣁⡀⠀⣿⣿⣞⠂⠀⠈⠁⠢⡀⠀⠀⠈
⠀⠀⢠⠊⠀⠀⢀⠔⢻⠝⠣⡁⠒⠀⠀⠀⠈⢢
⠀⠀⡄⠀⠐⠈⠀⡠⠂⠘⠀⠐⠂⠀⠐⠐⠂⠉
⠀⠀⣓⠀⠀⢈⡈⠁⠀⠀⠃⠀⠅
⠀⠨⠀⡑⡖⠅⡀⠈⠢⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰
⡠⠂⠁⣳⣿⡆⢀⠤⠂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉
⠈⠁⠒⠨⠩⡐⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠠⠄⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣠⢊⠉
⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⣨⣦⡐⠂⠠
⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢄⡀⠚⢀⡀⡛⡛⠖⠖⠈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠢⠀⡀⠔⠑⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⢀⠤⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠀⠀⠀⠐⢄⠰⢀⠂⢀⠤⠐⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠐⠠⣿⣯⣖⠁⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⡀⢈⠐⡢⠀⠐⡘⢻⢿⢇⠀⠂⠄⡈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⢂⡋⠀⡐⠌⠀⡠⠊⠀⣘⠈⠆⠑⢄⠀⣀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⢨⢄⣿⣿⠊⠕⢄⠀⠀⠀⡠⠉⡀⠘⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠔⠠⠁⠀⠆⠀⠙⠀⠮⠐⠀⠁⠀⠀⠑⠄⡀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣈⣦⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠰⣤⡀
⠀⠀⠀⠠⠶⡤⢘⣶⡄⠰⠴⠙⠀⣄⠀⡀⠀⣀⠤⠀⡷⠆⠴⣀⣣⣀⢠⢀⡔⠖⣋⣮⡇⠀⢀⡤⠄⠀⠀⣠
⠀⠀⠀⡄⠀⢠⢿⠁⠠⣉⡔⠄⠈⣏⣀⡀⠀⣱⣀⡴⠉⠀⢲⡼⠐⠀⣴⣞⣷⠞⢥⠞⢰⣆⠀⢊⢪⠄⠚⢥⡐⠛⠋⢀⡀⠀⢀
⠈⠛⠁⡽⠖⢐⢐⠀⣴⠉⠀⠀⣄⠈⠀⣀⠽⣫⠜⠓⠀⣤⣜⣅⠀⠀⣌⡀⡛⠁⢹⣄⣠⣷⣶⣮⠥⠆⠀⠀⠑⣄⠀⠅⠄⢠⣞⠐⠶
⠀⠀⠀⠀⠀⠀⡖⠛⠛⠛⣿⣛⣿⢿⣻⣅⡲⢛⡄⢀⠄⣿⣿⡿⠒⠾⡉⣻⡏⠒⠚⣋⣫⠽⢛⣛⣛⡛⠛⠛⠛⠛⠛⣦⠁⠀⠈
⠀⠀⠀⠀⣀⣠⡇⠀⣴⣶⣶⠟⣿⡩⣥⣖⣛⠾⣶⠁⠀⠠⣣⡀⠀⠀⣆⡙⣀⠶⢶⣙⢶⡶⢾⣶⢮⣯⣶⢶⣶⣄⠀⡇
⠀⠀⠀⣠⣽⣿⡗⣶⣿⢀⣀⣈⣹⣺⣿⠎⣯⡘⣿⠂⠀⠶⠉⡅⠒⠉⢣⠁⠀⢀⡑⢼⣶⣵⡀⠈⣿⡆⠛⣿⣿⣁⠀⡇
⠀⠀⠀⠉⠁⠀⡿⠋⣿⣨⣿⡟⢹⡏⠁⠈⡿⠂⠈⠀⠸⠀⠴⡇⠒⢊⠥⠁⢈⣻⡿⢢⣴⠉⠉⠀⠻⣯⠀⠙⢻⠛⠛⡇
⠀⠀⠀⠶⠶⠾⡇⠀⣿⠉⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠁⠀⠈⠙⠋⠁⠸⠋⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⡏⠛⠛⠂
⠀⢀⠴⡀⠠⣂⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡧⡰⢰⠜⠢
⠀⠈⠁⠂⠶⠡⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡗⠘⣂⠁
⠀⠀⢀⡾⢧⢀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⡰⠛⢦
⠀⠀⠀⢀⡆⠉⣷⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣶⣾⡇⠀⣧
⠀⠀⠀⠈⠃⠀⡿⠟⣿⠔⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣺⣏⠛⡇⠀⠁
⠀⠀⠀⠀⠀⠠⣵⠞⣿⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢸⣏⢻⡏
⠀⠀⠀⠀⠀⠀⡇⣿⣿⡄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿⠻⣧⡇
⠀⠀⠀⣠⣤⠴⡏⠁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠈⡗⠴⠶⠄
⠀⢀⣀⠀⢀⢀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⢠⢀⠠⢄
⠀⠘⠀⠇⡥⢊⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡧⠑⠆⠂⠈
⠀⠀⠀⣴⣆⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⢠⠾⣆
⠀⠀⠘⢁⡌⠚⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠉⣆⠈
⠀⠀⠀⠸⠇⠀⡇⠀⠻⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠀⠀⡇⠀⠛
⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇

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

⠀⠀⠀⢾⠀⠀⣹
⠀⠀⠀⠈⠛⠚⠁⠀⠀⢀⠤⠤⢄
⠀⠀⠀⠀⣴⣶⡄⢠⠋⠉⢻⡉⠳⣝⡄
⡆⠀⠀⠀⠛⡟⠡⠊⣗⠒⣿⣿⠂⣽⢸
⢇⢀⡀⢄⠀⠀⠀⠘⢜⢦⣤⣤⠶⡣⢃⡠⢀
⠀⣿⣿⡇⡃⠀⠀⣀⠀⠑⠈⠐⡛⣿⣏⠀⢀⠇
⡐⣌⣩⠜⠁⠀⠈⠛⠀⠀⠀⠀⠇⠻⠿⢯⠗⢦
⠱⣬⠔⠣⣤⣄⠀⠀⠀⠀⠀⣰⡋⣷⠈⠉⠓⠋
⣴⢉⣼⣇⣙⠢⣷⠢⣀⡠⠴⠻⣿⠃⣇⠠⡔⣒⠦⢰⠋⢉⣦⣀
⠛⢨⠛⢃⣈⣙⣞⢤⢪⡾⠛⢳⡌⡆⢻⡷⢸⢿⡗⡨⢫⡵⠶⣍⢣
⠞⢘⢦⠸⡿⣵⠒⠚⢜⢷⣤⡼⣣⡗⢫⠖⠑⠓⠒⡇⣿⠀⠀⢸⣇
⢞⣍⡵⢃⡗⠛⣿⠗⢸⠇⢲⡎⠫⣙⢎⣄⡠⡀⠀⢸⣮⡛⠚⡫⠊⠳⡄
⡸⡯⡪⢕⡲⢶⡄⡔⡥⢶⣿⣿⣶⡌⢧⢂⢙⣨⣭⡻⡏⡵⢫⠀⠨⣢⡥⢤⡔⣠⡄
⠑⢸⡞⠳⡝⡆⡇⡏⠴⣄⠻⣿⡿⠇⡼⠸⢸⡁⢀⡿⠐⠑⠿⡃⠆⣏⠀⠀⣹⠌⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠫⡈⠁⠀⣡⠄⠑⡄⠀⡀⠋⠣⣔⣂⣤⣤⣤⡀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣀⠀⠀⠙⢂⠶⠄⠘⠇⠀⠀⠀⠉⠀⠉⠉⠻⣆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⠀⢀⣀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠹⣇⠉⣠⠀⠀⢀⠀⣀⠀⠀⠸⡟⠉⢀⣄⡠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣷⣄⢸⣿⡇⢸⣿⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣍⣛⠁⠀⠀⣸⠷⡘⢦⠀⠸⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡟⢿⣿⣿⡇⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣁⠠⠤⠚⠠⢠⠏⠀⠁⢆⠀⣆⠹⣿⡻⣾⣏⡉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⣿⠇⠈⠻⣿⠇⢸⡿⠀⠹⣿⡄⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠶⠖⢀⡴⣡⠆⢀⡼⠓⠈⠳⣍⣠⣿⡧⠻⣌⡩⠭
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⢠⣤⠦⣠⣴⡄⣤⠀⣤⢤⡄⣤⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⢋⠔⢁⣴⡿⢡⣄⠀⢡⠈⠉⠉⠁⠀⣀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡿⢸⣟⣃⣨⣻⡦⣿⡺⣧⣰⣦⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠊⣡⡾⠟⠋⢀⡟⠙⡄⢀⢳⣄⠀⠀⢀⡿⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠉⠀⠈⠀⠈⠉⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⡾⠁⠀⠘⣄⠀⠙⠿⠾⠟⠁⠀⣌
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⣶⠾⠛⢀⣴⠿⢷⣌⠳⢄⠠⣀⣠⡾⠐⢡
⠀⠀⠀⠀⠀⠀⠀⠹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠳⠄⠀⠀⠁⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠒





⠀⠀⠀⠀⠀⠀⠠⣦




⠀⣀
⢶⣾⣶⣦⣤⣀⡀⠀⠠⣀⣤⣄⣀
⣀⠀⠀⠀⠉⠉⠉⠓⠂⠈⠪⠁⠈⠉⠓⢦⣤⡀
⣿⣿⣿⠶⠛⣍⢒⡂⠀⢀⠀⣀⣴⠞⣧⠀⠈⠛⢷⣦⣄
⡛⠭⠒⠊⠓⠺⢿⡁⠆⠸⠋⠁⣰⠀⢹⣧⠀⠀⠀⠙⠻⣿⡾⠓
⠄⠀⠀⣴⠟⢻⠀⣇⠀⢠⣾⠁⢿⡀⠀⢻⣷⣄⠀⠀⠀⠀⣠⠞⣡⠂
⠲⢄⡼⠃⢀⡗⠀⡩⠄⠙⠛⢆⡈⢿⣄⠀⠙⠿⣷⣶⣶⠞⢋⡴⢁⣴⡇
⠴⠋⠀⣰⠃⣉⡩⠀⠠⠒⠲⢶⣽⡂⠙⢶⣄⡀⠀⠀⣀⣤⠞⣠⣾⡿⠁⠀⢻⡄
⣾⣆⠰⣇⠀⠉⢀⡄⠀⠀⠀⠀⠈⠻⣦⡀⠈⠉⠛⠛⢉⣤⠞⠋⣿⠃⣠⣄⢸⠁
⠁⠘⠳⣌⡓⠒⠋⣠⣴⣶⣦⣄⡀⠀⠙⢿⣷⣄⠀⠀⠀⠀⢀⣾⣿⠟⠉⠉⣿⢀⣾⠂
⠀⠀⠀⠈⠛⠿⠛⠛⠻⣿⣿⣿⣿⣦⣄⠈⢻⡏⠀⠀⠀⠀⠀⣉⣥⠶⢻⡇⡇⣼⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⠙⠶⠦⠴⠖⠛⠉⠀⢀⣾⠙⠃⢻⡀⢸⡇
⡀⠀⠀⠀⣴⣶⡶⠟⠚⠒⢒⠒⠂⠤⣭⡭⠁⠀⣀⣿⠿⠋⠁⣠⠔⠋⢸⡇⠰⣤⣣⠈⠳⠄
⣠⠀⠀⠀⠹⣿⠀⠀⠐⠁⣛⣫⣤⡶⠶⠆⠚⠋⠁⣀⣤⣶⣟⣁⠀⠀⠀⠙⡃⠀⠁⠉⠁
⣁⢣⡀⠰⣶⣿⣆⠀⠀⡜⠉⠁⠀⠀⠀⠀⠀⠠⠾⠿⠛⠛⡉⠉⢉⣀⠀⠿⢛⣛⠋⠁
⠻⡆⠱⡄⠘⣿⣿⡄⢠⣇⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢰⣏⣁⠀⠈⠁⠒⠀⠨⠉⠉⠉⢉⠁
⣆⠀⠀⢹⡆⠘⣿⣿⡌⢿⣦⡸⣟⠉⠉⠙⠛⠿⠷⠤⠤⠬⠭⠵⠶⠂⠈⠀⠐⠒⠀⠀⠤

⠀⡈⠀⡆
⠀⠉⠀⡄
⠀⠒⠀⡀
⠀⠆⠀⠁
⠀⢄⠀⠉⢀
⢀⣄⠀⠃⠀⣀
⠈⠉⠀⠔⠀⡈
⠀⠉⠀⡄⠐⠉⠀⡠
⠀⠏⠀⣀⠀⠓⠀⢀⠀⢀
⠀⠂⠀⡀⠀⠶⠀⠈⠀⠢
⠀⡆⠀⠃⠀⢄⠀⠉⠀⣤⠄⠈
⠀⡀⠀⠂⠀⣀⠄⠘⠀⣀⠀⠒⠀⣀⡠
⠀⣀⠀⠆⠀⠉⠀⠔⠂⣀⠀⠰⠀⡉⠁⠤⠐⢀⡀
⠊⠁⠀⠤⠀⠉⠀⠀⠀⠉⠁⠠⠀⠈⠂⠠⠀⠈⠃⠀⠄
⠀⠀⠀⡀⠈⠋⠁⣀⠀⠒⠀⢠⠀⠛⠀⢂⡀⠐⠂⢀⠀⠘⠓⠀⣀
⠀⠶⠀⠁⠀⠢⠀⠠⠀⠲⠀⠈⠀⠰⠄⠀⠀⠴⠆⠀⠀⠐⠄⠀⠀⠐⠶
⠡⢄⠀⠁⠀⡤⢀⠌⠀⢄⠀⠉⠀⣤⠄⠈⠀⠠⡀⠈⠁⢠⡤⠀⠃⠠⡄⠀⠉⠠⣤⠀⠀⠀⢤
⣀⣄⣀⣃⣀⣀⣐⣂⣀⣀⣀⣘⣀⣀⣀⣐⣀⣀⣀⣐⣀⣂⣀⣐⣂⣀⣀⣀⣇⣀⣀⣀⣒⣀⣀⣀⣘⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤
⠀⠀⠀⠀⠀⣾⣿⣤⣤⡉⠻⣿⣷⣤⣤⣤⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣤⣾⣿⠟⢉⣤⣤⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣠⣾⠟⠋⠉⣩⢵⣾⣿⣿⣿⣿⣷⠮⣍⠉⠙⠻⣷⣄⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣧⣾⡟⠁⡀⠀⠊⣵⣟⣯⠭⣉⣈⠭⣽⣻⣮⡑⠀⢀⠈⢻⣷⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠀⣼⠀⠀⢺⣿⢋⣴⡿⠛⠛⢿⣦⡙⣿⡗⠀⠀⣧⠀⢻⣿⣿⡟⠁
⠀⠀⠀⠀⣠⣴⣿⣿⡿⠀⠀⢿⣦⣤⣿⡇⣼⠋⠀⠀⠀⠀⠙⣧⢸⣿⣤⣴⡿⠀⠀⢿⣿⣿⣦⣄
⠀⠀⠀⣴⣿⣿⢣⣿⡇⢠⠀⠀⣤⣤⣬⣁⠙⠀⠀⠀⠀⠀⠀⠋⣈⣥⣤⣤⠀⠀⡄⢸⣿⡈⣿⣿⣦
⠀⠀⢸⠏⣿⡇⢸⣿⠀⣿⡃⠀⠻⡝⢜⣿⣿⣄⠀⠀⠀⠀⣠⣿⣿⡣⢫⠟⠀⢈⣿⠀⣿⡇⢸⣿⠹⡇
⠀⠀⠈⢸⣿⠀⢸⡟⠀⣿⣆⡐⠒⢚⣦⠄⣿⠃⠀⠀⠀⠀⠘⣿⠠⣴⡓⠒⢂⣰⣿⠠⢻⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠈⣷⠀⢿⣟⡀⠀⠉⠀⠀⡞⠀⠀⠀⠀⠀⠀⢳⠀⠀⠉⠀⢀⣻⡿⠀⣾⠁⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⢻⡧⡈⢿⡟⠀⢀⠀⢰⣧⠆⠀⠀⠀⠀⠰⣼⡆⠀⡀⠀⢻⡿⢁⢼⡟⠀⠀⣿⡇
⠀⠀⠀⠈⣿⣿⡆⠈⢷⡀⠀⠁⣰⡇⠀⠘⢿⣦⣀⣤⣤⣀⣴⡿⠃⠀⢸⣆⠈⠀⢀⡾⠁⢸⣿⣿⠁
⠀⠀⠀⠀⢹⣿⣿⡄⠈⠻⣦⡀⣿⡉⠓⠂⠀⠈⠙⢻⡟⠋⠁⠀⠐⠚⢉⣿⢀⣴⠟⠁⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠻⡟⣿⣆⠀⠈⠛⢿⣏⡛⠒⢀⡀⠀⣼⣧⠀⢀⡀⠒⢛⣹⡿⠛⠁⠀⣰⣿⢻⠟
⠀⠀⠀⠀⠀⠀⠁⠘⢿⣷⣼⡄⠀⠙⠿⣿⣥⣴⡾⠿⠿⢷⣶⣬⣿⠿⠋⠀⢠⣧⣾⡿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣿⡽⠚⠁⠀⠀⠈⠓⢯⣿⣤⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣏⣀⡀⠤⢤⡤⠤⢀⣀⣹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠷⠞⠛⠛⠛⠛

⢝⢧⡀⠀⢹⣷⡀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢸⡏⠀⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡼⠁⢀⡼⠋⠀⢀⡴⠋
⠀⠀⠙⢦⡀⢻⣿⣄⠀⣄⠀⢠⣇⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠞⠀⠀⡠⠋⠀⣠⡾
⡀⠀⢤⣄⡙⠮⣿⣿⣶⣿⣦⣾⡇⢀⣠⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⠀⣠⠞⠉⡠
⣀⠀⠀⠙⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢈⠴
⣠⣥⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠂⠁
⣬⣵⣦⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡻
⠀⠂⢠⣾⠟⠛⠉⣿⠟⣿⣿⠋⠃⠉⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠚⠁⣀
⠲⢦⣅⣀⠀⠀⠀⠟⠀⠘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠐⠚⠉
⢄⢂⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⢂⢀⢀
⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⣿⠛⠛⠻⠷⠶⠶⠶⠶⠶⠶⠶⠦⠴⣶
⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⢩⣤⣀⠀⠀⣀⠀⠀⠀⠀⣤⡄⢀⣠⣤⠀⣤⣤⠀⠀⢀⡀⠀⠀⠀⢠⣿⡄
⣺⣿⣿⢠⣼⣿⣇⣠⡆⠀⣿⣧⢸⣿⣿⣤⣿⣿⡇⣤⣼⣿⣆⣴⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠓⠒⠛⠻⡛⠛⠻⡛⠛⠛⠟⠛⢟
⠔⠁⣠⠞⠁⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⢢⡀⠀⠀⠢
⣴⠟⠁⠀⡠⠂⠀⢠⠞⣹⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢳⡄⠀⠙⢦⡀
⠁⠀⣠⠊⠀⢀⣴⠏⠀⣿⠃⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠘⣆⠀⠠⡀⠀⠙⣦⡀⠀⠙⢦

⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⡀⣀⠀⡀⠀⢀⣀⣀⠀⢀⡀⢀⠀⣀⢀⠀⠀⠀⠀⡀⢀⡀⣀⠀⢀⣀⣀⡀⠀⡀⢀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸
⠀⣿⠀⠀⢰⠂⠉⡑⡀⠀⠐⠀⠀⠈⠂⠉⢀⣿⡿⣿⣄⠈⠀⠊⠐⠁⠐⠀⡄⠀⠂⠑⠈⠁⠈⠀⣼⡿⢯⣧⡀⠁⠀⠀⠊⠐⠀⠀⠠⡄⠉⠊⡃⠀⢸
⠀⣿⠀⠀⠀⢒⡴⠀⠁⠀⢀⠀⣂⠰⡀⢀⠀⠿⠿⠿⠀⡐⢀⡡⠈⡄⢈⠀⠀⢀⠀⢎⠀⡄⠠⡀⠸⠟⠻⠇⢀⠄⣀⠀⡡⠀⠀⠀⠐⢤⠀⡚⠅⠀⢸
⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⢸
⠀⣿⠀⢀⣠⠀⠀⣀⡁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣁⡄⠀⢂⣄⠀⢸
⠀⣿⠀⢀⢄⠀⠈⣤⡀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⡌⠀⢁⡄⠀⢸
⠀⣿⠀⢀⢠⠁⠈⣄⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⡌⠀⢁⣄⠀⢸
⠀⣿⠀⠀⣀⣀⣆⣠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⣶⣀⡀⠀⢸
⠀⣿⠀⠀⣝⢿⡻⣏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢈⡻⣟⢿⡃⠀⢸
⠀⣿⠀⠀⠋⠙⠏⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠻⠉⠁⠀⢸
⠀⣿⠀⠀⠛⡀⠀⠛⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠂⠀⡘⠒⠀⢸
⠀⣿⠀⠈⠛⠀⠀⠋⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢃⠀⡈⠋⠀⢸
⠀⣿⠀⠈⠋⡀⢀⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢁⠀⡈⠃⠀⢸
⠀⣿⠀⠀⠀⢠⡄⠁⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣤⠀⠁⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠂⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠄⠀⡠⠠⠀⢸
⠀⣿⠀⠐⠒⠄⠀⠒⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⠂⠀⡐⠂⠀⢸
⠀⣿⠀⠀⠓⠀⠠⠒⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠢⠀⠔⠃⠀⢸
⠀⣿⠀⠀⠓⠀⠀⠓⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠖⠂⠀⠐⠂⠀⢸
⠀⣿⠀⠀⢶⣼⣧⣴⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⣤⣿⣴⡆⠀⢸
⠀⣿⠀⠀⢻⢿⡮⢿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠯⣷⢽⡇⠀⢸
⠀⣿⠀⢀⣀⠀⠁⣀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠈⢀⣀⠀⢸
⠀⣿⠀⠠⣤⠀⠀⣤⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⡔⠀⢢⡤⠀⢸
⠀⣿⠀⠀⡤⠂⠀⢤⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠠⡤⠀⠠⡄⠀⢸
⠀⣿⠀⠠⠀⠂⠐⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠐⠀⠂⠀⠀⢸
⠀⣿⠀⠀⠀⠐⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⠀⠀⠀⢸
⠀⣿⠀⠈⣈⠀⠀⣁⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢋⡁⠀⢈⡉⠀⢸
⠀⣿⠀⠈⣍⠀⠀⣉⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⡁⠀⢊⡉⠀⢸
⠀⣿⠀⠀⣄⠉⠈⣁⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡈⠁⢉⡄⠀⢸
⠀⣿⠀⠀⢀⢀⡄⣀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⣤⢀⠀⠀⢸
⠀⣿⠀⠀⣿⣿⢻⣟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠿⣿⢿⡇⠀⢸
⠀⣿⠀⠀⠙⠻⠟⠛⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠛⠿⠛⠃⠀⢸
⠀⣿⠀⠀⠖⠀⠀⠒⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠂⠀⡐⠖⠀⢸
⠀⣿⠀⠀⠒⠁⠀⠒⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠂⠀⡐⠂⠀⢸
⠀⣿⠀⠈⠙⡁⠀⠛⡁⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠉⠂⠀⡘⠋⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⢸
⠀⣿⠀⠀⢠⠆⠰⣄⡀⠀⢀⠀⡁⠢⠀⠤⠀⣦⣠⣴⠀⠠⠀⡰⢀⠖⠀⠀⠀⠀⠀⢆⠰⡁⠰⠀⢰⡆⣴⡄⠀⠄⠈⠆⡰⠀⠀⠀⢠⠄⠶⠀⡄⠀⢸
⠀⣿⠀⠀⠐⠀⢀⢍⠅⠀⡠⢀⡄⢀⠀⣀⠐⣿⣯⣿⠒⢀⠀⣄⠠⡀⠀⠀⠂⠀⠀⣠⢀⡀⢀⠀⢺⣷⣽⡟⠀⡀⢀⠀⢄⠀⡀⠀⠰⢆⠀⢈⡄⠀⢸
⠀⣿⠀⠀⠈⠀⠃⠈⠀⠀⠀⠈⠂⠙⠂⠑⠀⠉⠈⠉⠀⠀⠁⠊⠀⠃⠐⠀⠀⠀⠀⠁⠈⠂⠘⠀⠈⠉⠈⠁⠀⠁⠐⠁⠊⠀⠂⠀⠀⠉⠁⠃⠀⠀⣸
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉

⡇⠿⡽⠇⢠⣾⡇⠀⢸⣷⡀⠸⣯⠷⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠾⡵⠇⢠⣾⡇⠀⢸⣦⡀⠹⣯⠧
⣀⠀⠀⠀⣾⣿⠁⠀⠈⣿⣧⠀⠀⠀⣈⣫⠘⠿⣦⠀⠀⠀⢀⣴⠿⠃⣝⣀⠀⠀⠀⣾⣿⠁⠀⠈⣿⣧⠀⠀⠀⡀
⣿⣿⣿⠈⠉⠁⠀⠀⠀⠈⠉⠁⣿⣿⣿⡟⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⢻⣿⣿⣿⠈⠉⠁⠀⠀⠀⠈⠉⠁⣿⣿⡇
⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠉⠀⠰⠀⠀⠀⠀⠀⠆⠀⠉

⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡆
⠻⠿⣿⣿⠀⠀⠀⢌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⢀⣿⣿⠿⠇
⠀⠀⠀⡙⡆⣀⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⣀⡀⡰⢋
⠀⠀⠀⢻⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⡟
⠀⠀⢠⣾⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄
⡿⠃⡾⣫⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣿⢧⠘⠇
⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠛⢿⣷⡀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⢀⣾⡿⠃
⠀⠀⠉⠃⠀⢀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠉⡀⠀⠚⠉
⠀⠀⠀⠚⠉⠂⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠐⠈⠓
⠀⠀⠀⠙⠒⠣⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠏⠒⠋
⣀⣠⣶⠏⠀⠀⠶⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠖⠀⠀⠹⣶⣄⡀
⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇
⣍⠀⣤⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣤⢀⡁
⠛⠃⢸⣿⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣳⣿⡇⠘⠃
⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠟⡏⠻⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠻⠟⢿⠻
⣀⣤⣴⣾⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⣷⣤⣤⡀
⣿⣿⡿⠏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠹⡿⢿⡇
⠁
⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⡄
⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣆⠀⠀⠀⠀⠆⠐⠀⠀⠀⠀⣰⣿⣾⣟⡀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣷⡇
⠛⠉⠉⠈⣿⣷⠀⠀⠀⣾⡿⠁⠉⠉⠛⡛⢀⣤⡾⠀⠀⠀⠀⢷⣤⡀⢛⠛⠉⠉⠈⢿⣷⠀⠀⠀⣾⡿⠁⠉⠉⠃
⡆⣴⢶⡄⠘⣿⡇⠀⢸⡿⠃⢠⡶⣤⢸⣿⣾⡟⠀⠀⠀⠀⠀⠀⢻⣷⣿⡆⣴⢶⡄⠘⢿⡇⠀⢸⡿⠃⣠⡶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠠⣤⠖⣚⠭⣖⡒⠦
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠲⠤⣀⢀⣤⠶⣛⣭⠭⢴⣖⣒⣒⣒⣒⣲⣒⢖⡦⣻⣕⡯⢗⣚⠯⡳⣝⢦⡙⢮⡙⢦⣝⠳
⡿⣖⢤⡦⣺⢗⡭⣖⠯⢭⣍⣛⠲⢮⣙⢶⣩⣗⣺⠭⢝⡒⠾⠿⡻⢶⢜⡵⣫⠾⢿⣓⣫⣭⠭⣭⣺⢮⡳⣝⠦⣝⠲⣌⡓
⣫⢗⣫⣞⠵⠭⣭⣍⣛⡲⠦⢭⣝⡳⣬⣟⠭⢖⣛⣛⣓⣦⣞⠵⣚⢵⣏⡾⠭⠭⠭⠵⠶⢒⣒⣒⣺⡽⣿⣮⣓⠮⢭⣶⣾
⣭⣓⠲⠭⣭⣛⡒⠶⠬⠭⠭⣷⡒⡼⠋⠓⠉⠉⠍⠯⠤⢶⠚⠛⠾⣽⡲⠭⣝⣛⣛⣛⣛⣭⠭⠵⣞⣿⣿⣯⣻⣿⣗⣒⣚
⠶⢬⣙⡓⠶⢬⣭⣭⣩⡭⠽⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠬⣭⡭⠵⠖⠋⠉⠁⠀⠀⠀⠈⠉⠙⠻⢷
⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣛⣩⣭⣴⣶⣶⣶⣶⣦⣭⣍⡙⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⣥⣶⣿⣿⣿⡿⢿⣿⡿⠛⢿⣿⣿⣿⣿⣷⣄⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⣡⣴⣿⣿⣿⣿⡇⢹⠁⠀⠉⠀⠀⠈⠉⣿⣿⣿⣿⣿⣷⡄⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣼⣿⣿⣿⣿⣿⣿⣿⡘⣤⣄⢈⣟⡩⢶⡄⠈⢹⣿⣿⣿⣿⣿⡄⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣿⣿⣿⣿⣿⣿⣟⠉⠉⠁⠙⠈⠙⢲⣳⣋⡄⠀⠀⢉⣿⣿⣿⣿⣷⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠠⢤⠞⠀⠈⢇⠀⠀⠐⣾⣿⣿⣿⣿⣿⢻⡄⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣀⣬⠀⠀⢨⡛⠤⠤⣤⣼⣿⣿⣿⣿⡟⢨⡇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣆⢠⣾⣿⣷⣦⣾⣿⣿⣿⡿⠋⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣿⣿⣿⣿⣿⣿⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢻⣿⣿⣿⣿⡇⣿⠁⠀⠀⠀⠀⣀⣘⣛⣷⣦⣸⣿⣷⣀⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣵⣾⣿⠟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⢰⠀⠀⠀⠀⣶⣦⣆⠀⠀⠀⠀⠀⠀⠀⢻⡌⢿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣾⣿⣏⣭⣥⠻⣿⣾⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⢀⡾⠁
⠀⢸⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⣿⣿⣇⠀⠀⠀⠀⠈⣽⣿⡏⢴⣦⡟⣶⣝⣈⣏⠉⠁⠀⠀⠀⠀⠀⣰⠟⠁
⢀⡇⠀⠀⠀⠀⡿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢿⣆⠀⠀⠀⠀⠈⢹⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⢀⣠⠞⠁
⣾⣶⡄⠠⡄⠀⣷⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣀⠀⠀⠀⠀⠀⠉⠹⡿⠋⠈⠻⠇⠉⠁⣀⣤⠶⠛⠁
⣿⣿⡂⠀⣧⢠⣿⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠛⠉⠁
⣿⣿⡇⠀⡿⢸⣧⡄⢠
⣿⣿⣷⣾⡇⢸⣿⣯⢠⡇
⣻⣿⣿⣿⡁⣸⣿⣿⣸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡅⠀⠿⠿⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⣸⡇⠀⠀⠀⠀⢨

⡅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢻⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠉⠁⠒⠀⠂⠤⠄⣀⡀⢀⡤⠒⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠤⠒⠉⡏⢣⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⢀⠔⠁⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⠣⡀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡜⠀⠀⠀⠱⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠁⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡇⠀⡘⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⡇⠀⠅⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠓⠒⠒⠒⢖⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⣲⠖⠒⢺⠒⠒⠒⠒⠒⠒⠲⡒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⡗⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⠀⠀⠀⠀⠀⠀⠀⡷⠐⠒⠒⠲⡄⠐⠀⠒⠒⠒⠀⠀⠀⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢖⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠊⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⡇⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡇⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⡤⠤⠤⠴⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠽⠦⠤⡷⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠐⢄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⢢⡀⠀⠀⠀⡷⣄
⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡇⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇⠀⠀⠀⠀⠙⢄⠀⠀⠀⢀⡠⠚⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⢄⠔⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢰⡿⠛⠻⣿⣿⡛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⡛⢛⣿⣿⠟⠛⢷⡆
⠀⠀⠘⠷⠿⠀⢸⣿⣷⣵⣄⢀⣈⣝⠷⣤⡀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⢀⣤⠞⣫⣀⡀⣠⣯⣾⣿⡇⠀⠿⠾⠃
⠀⠀⠀⠀⠀⣤⣾⣿⣧⣘⠙⡷⡦⠬⢵⡝⣝⢷⣄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⣾⡻⢣⡮⠥⣴⢾⢻⣁⣼⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠙⢿⣿⣿⡈⠑⣧⠯⣦⡀⢡⠘⡇⢛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡛⢸⠁⡎⢀⣼⠽⣼⠋⢁⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣀⣿⣿⡟⢲⡁⡴⠶⠽⣜⠦⣸⡈⣸⠙⣧⡀⠀⣴⣆⠀⢀⣼⠋⢣⢀⣇⠴⣡⠯⠖⢦⢈⡖⣻⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⠷⣷⠄⣀⡈⢷⣄⠑⢾⡀⠘⣿⣔⣿⣿⣢⣿⠁⢠⡷⠊⣠⡾⢁⣀⢀⣿⠾⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣦⣤⣽⡶⣦⣀⣌⣑⡢⣝⣲⣾⣿⣿⣿⣿⣷⣖⣫⣔⣋⣥⣀⡴⢶⣯⣤⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣷⣶⣶⡶⠾⣿⠟⠛⠟⠋⣼⣿⣿⣧⠙⠻⣟⡿⡿⠷⢶⣶⣶⣾⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⡫⠁⡠⠞⠡⢠⠀⢀⣼⣿⡻⢿⣿⣧⡀⠀⡝⡌⠳⠄⠈⢝⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠋⡰⣋⣠⠤⣧⣾⠶⠋⣸⢿⣿⣿⡿⣇⠛⢶⣷⡜⢤⣄⡙⢆⠙⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡾⢋⠎⠀⡰⢁⠃⣀⡴⢻⠟⣿⣿⠛⡟⢦⡀⠙⡘⢆⠀⠱⡙⢷⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣞⠀⡰⠀⣸⠔⢁⠁⣸⠀⠻⠟⠀⣇⠈⡌⢢⣇⠈⣆⠀⣷⣾⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣴⡇⢠⡟⠠⢹⢀⡟⠀⠀⠀⠀⢻⡀⡇⠄⢻⡄⢸⣦⣿⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣶⣿⠞⠀⠀⠀⠀⠀⠈⢳⣿⣶⣼⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡆⠀⢸⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡇⠀⢰⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⡶⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢶⡦⠶⠋

⠀⠀⢐⠂⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⠖⡀⠶⠂
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠩⠔⣊⡅
⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡂
⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠅
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅
⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠌⠇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠒⠈⠁⠀⠤⠀⠂
⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠁
⠀⠀⢨⠄⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠂⠀⠁⠀⠀⠀⠂⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⢊⠀⣠⢀⡤⠠⠀⠚⠀⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠃⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠰⠀⠉⠐⠲⠀⡖⠒⠒⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⡄⠀⠀⣠⡒⠀⠀⢎⠀⠀⣠⠀⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠐⠂⠠⠄⠀⠠⠄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠂⢀⠀⠀⠐⠀⠀⠀⠀⠐⠒⠂⠀⠀⠒⠒⠃⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠁⠀⠀⡈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⢀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠈⠈⠉⠁⠈⠉⠁⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠉⠀⠁⠉⠉⠁⠀⠈⠀⠀⠀⠀⠁⠀⠉⠉⠀⠈⠉⠉⠈⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠘⢩⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⡐⠀⠣⠀⠀⠀⠰⠘⢃⡀⠀⠀⢉⠖⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷
⠀⠀⢴⠌⠁⠀⢀⠁⠀⡃⠀⠀⠀⠀⠇⡀⢡⡀⠀⠀⠀⠁⠞⡀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠘⡏⢀⣴⠆
⠰⣙⠂⠀⠀⠀⠠⠀⡐⠅⠀⠀⠀⠀⠈⡥⠨⡅⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢄⡇⠘⠋⣀
⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠴⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⡇⠀⣾⠟
⠀⢀⡄⠶⠃⡛⢐⡋⢐⠃⠰⠆⠀⠀⠀⠒⠰⠆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢷⠊⠁⣤
⠚⡀⢤⡘⠂⠙⠀⠁⠈⠀⠺⠉⠀⠀⠚⡷⠲⠀⠀⠀⠀⢸⣿⡆⠀⣴⡇⠀⠀⠀⠀⠀⣤⡀⠀⠘⡄⣸⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣶⡙⠓⢸⡿⠃⠀⠀⠀⠀⠀⠈⠉⠁⠒⢺⠁⢠⣾
⠄⣀⠀⠀⠀⠀⠀⠈⠳⣾⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠊⠀⢀⡀⠀⠀⠀⠀⠀⠰⣶⣄⣀⣣⡜⠁
⣀⠀⠈⠜⠑⢂⡄⠀⠀⠀⠉⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠰⣦⣄⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠹⣄⡼
⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⢰⡄⢀⣿⠟⠀⠀⠀⠀⠀⠀⠉⠛⢃⡼⠋⠀⠀⠀⢘⣷⠶⠃⠀⠙⠛⠋⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢿⣷⣯⡄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣴⡿⠀⠀⠛⠁
⠀⠀⠀⠀⠀⢀⣄⠀⢸⣿⣔⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡀⠀⠛⠁
⠀⠀⠀⢠⡀⠘⣿⣠⡊⠛⠛⠋⠀⠀⠀⣦⠗⠀⠀⠀⠀⣶⣄⠀⠘⠁⢀⣤⠄
⢀⡄⠀⢸⣇⣔⠛⠻⠟⠁⠀⠀⠀⠀⠛⠈⡶⠁⠀⠀⠀⠘⠻⢧⠀⢰⡿⠟⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠
⢸⣇⡤⠊⠙⠛⠛⠀⠀⠀⠀⣀⢀⠀⠀⠳⡆⠀⠀⠀⢲⣦⡀⠀⠛⢁⣤⡦⠀⠀⠀⠀⠀⠀⠈⠠⢠⠄⠄⡀⠅
⠚⠻⠿⣷⠆⠀⠀⠀⠀⠀⢠⡹⠟⣀⠀⠀⠀⠀⣀⠀⠈⠻⡗⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡈⠁⠀⠀⠀⠀⢹⣷⡄⠀⠐⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⠀⠉⠃⠀⢀⣴⣾⠗⠀⠀⠠⣄⠆⢀⡀⢀⠠⡄⠤⠈⠃⢠⡆
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢿⣦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠂⠤⠃⡬⠀⡤⠰⠆⠘
⠀⠀⣠⡿⡀⠻⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠀⠀⣬
⠀⠀⠹⠁⠐⣤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⡀⠀⠀⠀⠀⠤⡝⠂
⠀⠀⠀⢀⣴⡀⠳⢟⠛⠓⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⡁⠀⠀⢠⠜⠃
⠀⠀⠀⠸⠟⠁⠀⠀⠑⠦⣔⠶⠿⠖⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠆⡀⠀⠀⠀⠀⠀⢬⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⠑⠒⢤⣤⣄⠀⠀⠀⠀⠀⠀⠠⡅⠀⠄⠀⠀⠀⠀⡀⠦⠠⠆⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠂⠠⢂⠀⠀⠀⢠⠙⠀⠖⠀⠀⠀⡄⢦⠉

⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠈⠻⣿⣿⣿⣿
⠙⢿⣿⣷⣄⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⡀⠀⠈⠻⣿⠟
⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠋⠀⠀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣠⣶⠄⠀⠈⠻⣿⣿⣿⢟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⠀⠀⠀⠺⠟⠁⠀⠀⠀⠀⠈⢛⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⠀⠀⠀⠀⡴⠋⠀⣀⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⢀⠀⠀⠀⠀⢴⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⠀⠀⠀⠀⡀⠀⠀⠙⢿⣿⣿⣿⣦⣔⣄⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠟⠁⠀⠀⢀⣴⣿⣷⣄⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⢰⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠆⠈⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⣿⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⢸⡆⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠈⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⣿⢠⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿




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

⠀⠀⠀⠀⢠⡟⠿⢻
⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⢸⡇⠀⢸⡀
⠀⠀⠀⠀⢸⡇⣶⠿⠯⠭⠭⠽⠿⣆
⠀⠀⠀⠀⢸⡇⢻⣤⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⣠⣿⣿⠟⠻⠛⠛⠻⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡴⠒⢺⢛⣡⢄⠀⠈⠀⠀⠀⠈⠁⠀⣠⠈⡛⣗⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠉⠙⠻⣿⣿⠟⠿⢿⣿⣿⡄
⢧⡀⢻⠀⠉⠉⠀⠀⠢⠄⠠⠔⠁⠀⠈⠉⠁⣽⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣇⠀⠰⠀⠀⠀⠰⠆⠀⠘⠷⢀⣀⣿⠿⣿⠃
⠀⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡁⠀⠐⠤⠔⠀⠀⠘⠑⠀⠀⠁⠀⠀⢸⠆
⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣤⣾⣄
⠀⠀⠀⠀⠐⡿⢻⠛⡖⠒⠒⣲⠛⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣛⡖⠒⠒⠒⢛⡏⠛⣿⣿⡿⠟⠛
⠀⠀⠀⠀⢰⠃⡞⠀⠘⠒⠒⠁⠀⢻⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠈⢳⡙⣟⠿⢿⠋⠙⠦⡀⢸⡿⠿⠄
⠀⠀⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⢘⡇⢸⠀⠀⠀⠀⠀⠸⡆⢧
⠀⠀⠀⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⡼⢁⠞⠀⠀⠀⠀⠀⠀⣇⠘⡄
⠀⠀⣠⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢶⠿⡖⠉⠀⠀⠀⠀⠀⠀⠀⢹⠀⠳⡀
⠀⠀⠙⠒⢺⡗⡶⢶⡦⠤⠴⢶⡶⢶⡞⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⠀⣷⡶⣶⠤⠤⠴⢶⡶⢶⠛⠒⠚⠁
⠀⠀⠀⠀⢸⡇⢧⠀⠈⡗⢺⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⢹⡒⢺⡅⠀⢸
⠀⠀⠀⠀⢸⡇⢸⡄⠀⡇⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢻⠀⢸⡇⠀⡇⠀⢸
⠀⠀⠀⠀⢸⡇⢈⣇⠀⣇⣸⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⡆⠀⡇⠀⣧⠀⣸
⠀⠀⠀⣴⠚⠉⠉⣽⣀⡿⢹⣀⣺⠉⠉⠛⣢⠀⠀⠀⠀⠐⠒⠀⠒⠘⠛⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⡗⠛⣇⣀⡏⠉⣿⣀⡸⠓⠒⠢⣄
⠀⠀⠀⡏⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡗⠒⠒⠲⠶⠶⠶⠒⠒⠒⠚⠉⣿

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⢰⣿⣭⣤⣉⠛⢿⣿⣦⣀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⣀⣴⣿⡿⠛⣉⣤⣭⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⣠⣿⠟⠛⠛⣋⣭⣿⣿⣿⣿⣿⣿⣭⣙⠛⠛⠻⣿⣄⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⡿⣠⣾⠟⠁⠀⠀⠚⣡⡾⣛⣛⠉⠉⣛⣛⢷⣌⠓⠀⠀⠈⠻⣷⣄⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⡞⠀⠀⢾⣿⠟⣡⣶⡿⢿⣶⣌⠻⣿⡷⠀⠀⢳⡀⠹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣠⣴⣿⣿⡏⠀⢸⣇⣀⣀⣿⠇⣼⠏⠁⠀⠀⠈⠹⣧⠸⣿⣀⣀⣸⡇⠀⢹⣿⣿⣦⣄
⠀⠀⠀⢀⣾⣿⡟⣹⣿⠀⡀⠀⠉⢉⡙⠛⠀⡟⠀⠀⠀⠀⠀⠀⢻⠀⠛⢋⡉⠉⠀⢀⠀⣿⣏⢻⣿⣷⡀
⠀⠀⢀⡿⢻⣿⠀⣿⡏⢰⡧⠀⠸⣿⣟⢿⢷⣦⠀⠀⠀⠀⠀⠀⣴⡾⡿⣻⣿⠇⠀⢼⡆⢸⣿⠀⣿⡟⢿⡀
⠀⠀⠘⠁⣿⡇⠀⣿⡇⣾⣟⠀⣀⣙⣪⠉⠛⣿⠃⠀⠀⠀⠀⠘⣿⠟⠉⣕⣋⣀⠀⣻⣧⢸⣿⠀⢸⣿⠈⠃
⠀⠀⠀⢸⣿⡇⠀⣿⠀⢹⣿⡖⠀⠠⠼⠛⠑⡿⠀⠀⠀⠀⠀⠀⢿⠋⠛⠧⠄⠀⢲⣿⡏⠀⣿⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⢹⣧⠈⣿⣦⣄⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣠⣴⣿⠁⣼⡏⠀⢸⣿⡇
⠀⠀⠀⠈⣿⡇⡄⠈⣯⠃⠈⠻⡀⢀⠔⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⠠⡀⢀⠟⠁⠘⣽⠁⢠⢸⣿⠁
⠀⠀⠀⠀⢻⣿⣿⡀⠘⢷⡀⠀⢀⡿⣄⡀⠈⠛⠷⣶⣶⣶⣶⠾⠛⠁⢀⣠⢿⡀⠀⢀⡾⠃⢀⣿⣿⡟
⠀⠀⠀⠀⠈⢿⣿⣷⡀⠈⠻⣦⣼⣧⣄⣉⠉⠀⠀⠀⢹⡏⠀⠀⠀⠉⣉⣠⣼⣣⣴⠟⠁⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢯⢻⣷⣄⠀⡈⠙⢻⣦⣉⣉⡤⠀⢀⣾⣷⡀⠠⢤⣉⣉⣵⡟⠋⢁⠀⣠⣾⡟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣷⡄⠀⠉⠛⣷⣶⠾⡟⠛⠛⢻⠷⣶⣾⠛⠉⠀⢠⣾⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣾⣿⠞⠉⠀⠀⠀⠀⠉⠳⢿⣷⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣀⡠⠤⠤⢆⣀⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠟⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⡖⠋⠙⠉⢛⠻⢛⡻⠛⠓⢮⣿⠉⠉⠉⠙⣉⠩⠒⠊⡐⠋⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠋⢳
⠀⠀⠀⠀⠀⠀⡇⠀⢀⣐⡠⠗⠈⠀⠈⠈⡒⣿⠐⠂⣠⣼⣧⣤⠤⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠑⠉⠒⢲⠄⠀⠀⣊⣠⣯⠗⣩⣿⠋⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣷⣾⣟⢦⠀⢠⡜⠐⠙⡽⠋⡹⢢⠼⠏⠀⠀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠐⠻⢋⡀⠤⠝⣷⣅⡀⠀⡞⢁⠞⡴⠃⠀⠀⠀⣉⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⣒⠒⢠⠊⠁⠀⠀⡘⠀⣿⢳⣼⢁⡌⡼⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⢹⠇⠀⠀⢀⡴⣡⣞⡵⢟⠁⠈⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⣙⡫⠴⠲⡎⠁⢨⡟⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠂⠃⠉⠀⡟⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡈⠓⢾⠀⠤⢢⣐
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢀⣠⣾⢕⡥⠜⠓⠋⡽⠦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠌⣰⡾⣩⠞⢡⠋⠀⠀⠀⡸⠧⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣠⢏⡌⢠⠏⢳⣿⣀⠆⠀⢀⡀⠔⠁⠒⠚⠆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠤⠀⠀⠀⡴⢋⠞⢠⠎⠀⢀⡈⠻⣮⣉⣀⣴⠷⠂
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠁⠀⠀⣼⣏⢑⣧⣴⣯⠦⡂⠋⡁⠀⠙⠾⠟⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⣠⣴⣿⠥⠺⣿⣁⠔⠀⠀⠈⠓⢒⣴⡀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠉⣽⠏⠅⠒⠀⣿⠒⠀⠄⢀⡀⠺⡁⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠓⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠲⠔⠒⠤⠤⠤⠤⠤⠤⠿⣟⣲⠶⠗⠦⠶⠶⠤⠤⠤⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⠤⠶⠶⠶⠶⠶⠦⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣚⣻⡍⠉⠁⠀⠲⠖⠒⠛⠓⠀⠀⠀⠀⠀⠲⠶⠦⣭⡉⠙⠓⠦⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠻⢯⣍⠉⠉⠉⠛⠛⠶⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣤⣤⣤⡤⠴⠶⠶⠖⠛⠛⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣧⡆⠀⠰⠖⠛⠛⢻⡆⠀⠀⠀⠀⠀⢀⡏⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣻⣏⣀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⣀⣸⡇⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠉⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⣸⠃⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢀⣄⣀⣤⣤⣼⡇⠀⠀⠀⠀⢀⡟⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣌⣽⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⠛⣻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣼⠁⠀⠀⠀⠀⣼⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡟⠀⠘⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⣿⠄⢠⣤⣤⣤⡤⣿⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠶⣿⠒⠀⠀⠀⠀⠀⠾⠧⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣿⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⣁⡀⠀⠀⠀⠀⠀⣼⡇⠀⠴⠶⠶⠚⠋⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⣤⣴⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠒⠲⠶⠶⠶⠶⠶⠖⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⢀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⣤⡿⠛⠾⣯⡅⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠱⣄⠀⠀⠀⠶⢶⣬⣆⢰⡎⢃⣮⠁⣀⠀⣷⢇⣴⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠎⣲⠦⡄⠀⢘⢭⠋⠻⠆⠸⠋⠞⣙⡚⣴⡞⡋⠸⢿⣯⣷⢤
⠀⠀⠀⠀⠀⠀⢰⠂⢀⣰⡆⠀⣧⠀⠂⠘⠹⠄⠋⢀⣉⠀⠀⠀⠰⠻⣿⣁⠨⢔⡅⢀⣀⣍⡯⢿⠁
⠀⠀⠀⢀⡠⠀⡠⠄⠘⠉⣠⣼⣛⠃⡠⠀⣀⠀⠀⡼⠨⣍⢀⣠⠀⡾⣿⡇⢀⣤⡄⠸⣿⣭⢑⠋
⠀⠀⠀⠈⠳⢄⠠⠀⠘⠻⠟⡹⢏⠆⠇⠈⣠⡶⢀⡀⢠⡈⠊⠀⠀⢹⣿⣣⢾⠛⣿⣦⣸⣿⢽⠇
⠀⠀⠀⠀⠀⠀⢵⣂⡁⠀⠠⠒⠒⠁⢰⡞⡩⣠⡾⢷⡴⣣⠜⠂⠀⠈⠉⠛⠊⠑⢯⣟⡻⠈⡺
⠀⠀⠀⠀⠀⠀⠈⠙⠯⠀⠐⠊⣰⡿⠻⠛⣆⣤⣄⣜⠻⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡇⠈⣹⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⢿⣟⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠙⠳⠆⠀⠈⠀⠀⢉⣻⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠷⠄⠀⠀⠀⣀⣴⠿⠛⣋⣉⣉⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠀⠀⠀⢀⣼⠟⣡⡾⠟⢛⣙⠛⠿⣶⡌⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⠀⠀⢀⣾⠃⣾⠏⣴⡾⠛⠛⢿⣦⠘⣿⡀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠲⠀⠀⢸⡏⢸⡏⢸⡏⠀⠀⠀⠀⢻⡇⣹⡇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⡶⠶⢶⣶⠶⠶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠙⢷⣦⡀⢸⡇⢸⣇⠸⣷⣄⠀⠀⢀⣾⢃⣿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⢿⡄⠀⠉⠳⠀⠀⠙⠃⠀⠈⠙⠂⠈⠻⠟⠛⢿⠶⣶⣤⣤⣭⣿⣿⣿⡄⠻⣷⣬⣉⣠⣴⠟⣡⡾⢃⡾⠃
⠀⠀⠀⠀⠀⣀⣤⣶⡟⠋⠉⠙⠷⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⡙⠊⠉⠻⠍⠙⠿⣶⣬⣉⣉⣩⣥⡾⢋⣴⠟⠁
⠀⠀⠀⠀⠺⣿⡁⠘⠿⠆⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢷⣶⣤⣤⣄⣀⣉⣉⣉⣩⣥⡶⠟⠁
⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⢀⣠⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣛⣿⣷⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢻⣿⣿⣿⣿⡿⠛⢉⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠋⣠⠾⠋⣁⣠⣄⣀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣿⣿⣿⡟⢀⡾⠃⣰⠞⢋⣉⡉⠙⢻⣄⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⠁⣼⠃⣼⠃⣰⣿⣿⣿⣷⠀⢻⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⣿⠀⣿⠀⢻⣿⣿⣿⣿⠃⣼⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠐⢶⣶⣦⡐⣶⣶⣄⠠⣤⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢻⡄⠘⢷⣄⣸⣿⡿⠋⣰⠏⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠲⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⣾⣿⣦⣶⣦⣀⢤⣀⠀⣀⣀⠈⠻⣦⣄⣉⣉⣁⣤⠞⢁⡴⠋
⠀⠀⠀⠀⢀⣠⡀⠘⢿⣿⣿⣶⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢿⣾⣿⣷⣦⣀⣉⣉⣉⣉⣤⡶⠛⠁
⠀⠀⠀⠀⠈⢻⣿⣶⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠙⣿⡿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣄⣴⡆⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⢰⣦⢠⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⢻⠃⠿⢌⣥⢺⡇⠀⠀⠀⠀⠀⠀⢹⡗⣬⡡⠿⠘⡿⢿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠉⠁⠹⡄⠀⠀⣳⣯⣇⣤⣶⡚⢓⣦⣤⣸⣽⣎⠀⠀⢠⠇⠈⠉⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠄⢀⣲⣽⣻⡎⠀⠀⡡⠤⠤⠶⠶⠤⠥⣌⠀⠀⢱⣞⣯⣆⡀⠜⢭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⣾⡈⠈⡌⠛⠙⠒⠤⡄⡴⡆⢇⡰⢑⢆⢠⠤⠒⠋⠛⢡⠉⢑⣶⣤⡈
⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⢠⢫⣟⢀⡠⠀⠀⣻⠤⣅⠐⠁⠂⠐⠈⠂⣨⢤⣟⠀⠀⢆⠐⣻⡽⡈⠉⠓⠦⣄⣀
⠀⢀⣠⡴⡺⠋⠁⠀⢀⠆⣠⠿⠛⠁⠚⠘⠦⠘⠱⣧⠈⠀⠀⠀⠀⠀⠀⠁⣾⠎⠃⠔⠁⠓⠈⠛⢷⡄⢠⠀⠀⠉⠻⡶⢤⣄⡀
⠀⣼⢻⣇⠰⠆⢐⣾⠋⡼⠃⠀⠀⠀⡠⢄⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡠⠄⠀⠀⠀⠹⣧⠓⣲⡆⣠⠄⣽⡿⡇
⠀⣿⠀⠙⠧⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠉⠀⠀⡰⠟⠀⡇
⠀⣿⣠⣦⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣤⣄⡇
⠴⣿⣩⠈⢦⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡠⠋⣝⡿
⠀⣿⣅⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⢠⣹⡇
⠀⣾⠉⢧⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡸⡙⡇
⠀⣿⠘⠰⠈⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⡄⠆⡇
⠀⣿⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠿⣀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠉⠓⠦⣤⣀⠂⢻⣼⣟⣷⠀⠀⠀⢘⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡃⠀⠀⠐⣮⣻⣧⠗⠐⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣌⡋⠳⢤⡄⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡴⠋⢘⣥⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠀⠀⠉⠻⠶⢭⣛⠶⢤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣠⡤⢖⣋⡥⢶⠟⠉⠀⠀⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣶⠀⢠⠖⠙⠈⠙⠛⠖⠦⣍⣉⠉⠉⠉⠉⣉⣭⠴⠺⠛⠉⡡⠋⠢⡄⠀⣾⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠛⠇⠀⠀⠀⣀⠀⠀⠀⠀⣉⠹⠶⠶⢋⣁⠀⠈⠀⠀⣈⠀⠀⠀⢹⠛⠛⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠀⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠐
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠦⣄⠀⠀⢀⣠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠱⠔⠉⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠢⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⡀
⠀⠀⠀⠀⠀⠀⡎⠀⢠⠶⡄⠀⠰⣏⡳⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⢰⠄⠀⠈⠛⠁⢀⡄⠀⠀⠀⠀⠀⠪⡬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢇⠀⣴⡦⠀⠈⠁⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⣎⣱⠀⠀⠑⠊⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣀⠀⠀⣀⣀⣀⣀⡤⠤⠔⠒⢚⠉⠉⠉⠉⠉⠉⠉⡏⠉⠛⠒⠒⠒⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠁⠈⡇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴⠒⠛⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡔⠉⠛⠉⢣⠀⠀⠀⢀⠴⠧⡀⠀⠀⢣⡀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠑⡄⠀⠀⠀⡇⠀⠀⠀⠀⠘⣄⠀⣠⠎⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠙⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⡰⠃⠀⢠⠖⠓⡄⠀⠀⠀⠀⠈⢓⠁⠀⠀⠀⠀⠈⠲⡖⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠹⣀⣀⠆⠀⠀⢀⡤⠤⠼⠤⢄⠀⠀⠀⢀⠔⠳⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⢦⠀⠀⠀⡤⠧⡀⠀⠀⠘⣄⠀⠀⠀⣰⠃⠀⠀⠘⠦⡤⠃⠀⠀⠀⡰⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⠞⠀⠀⠘⣦⣤⢇⠀⠀⠀⠈⠳⡤⠞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡟⡎⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢱⡀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠁⢡⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠃⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠫⡈⠁⠀⣡⠌⠑⡄⢀⠀⠉⠪⣖⣊⣤⣤⣄⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⠀⠀⠙⠢⠶⠂⠘⠃⠀⠀⠀⢀⡈⠉⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⣀⣀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣇⣉⡠⠀⠀⢀⠀⡀⠀⠀⢻⡋⠁⢠⣄⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣷⡄⢿⣿⠀⣿⣧⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⣭⣭⠭⠭⠁⠈⠀⡾⢣⠙⡆⠀⠻⣧⢠⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠛⣿⣿⣿⠀⣿⡿⢿⣦⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠥⡤⠤⠔⠒⠉⡀⢰⠁⢀⡐⢤⠀⡆⢹⣯⠷⣿⣤⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠘⠿⠃⠈⠻⠿⠀⠿⠇⠈⠻⠷⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠞⠛⣠⠞⡰⠃⣠⠟⠁⠈⠻⢤⣼⣿⠎⠳⡬⠭
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⣄⢶⣖⠂⣴⡶⢠⡆⣠⠶⠶⢰⣦⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⢚⡡⢊⣠⣾⠏⣰⣆⠀⢠⡀⠀⠀⠀⢠⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⠏⠼⣯⠄⢬⡿⠺⡯⠻⣦⠿⠸⠏⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⢁⣴⠟⠉⠁⢰⠏⠸⣆⠄⠳⣄⡀⣀⣼⠃
⠀⠀⠀⠀⠀⢠⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⣀⣠⠏⢀⣄⠘⢆⠀⠉⠛⠛⠁⡠⢰
⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⠁⣠⠟⠉⠻⣦⡙⠢⡰⠶⠾⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⣀⣀⣙⠂⠀⠀⠀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠋⠁




⣤⣼⣤⣄⣀⠀⠀⠀⢀⢀⣀⡀
⠀⠉⠉⠉⠛⠛⠓⠦⠄⠉⠙⠉⠙⠳⢦⣄⡀
⣿⣶⣶⡶⢖⡒⠤⠄⠀⡀⠀⣀⣤⢰⡀⠈⠛⢷⣤⣀
⠿⣋⠵⠜⠲⠿⣿⠃⠀⣿⠞⠉⡌⠈⣿⡄⠀⠀⠉⠻⣿⣶⡶
⡁⠀⠀⣴⠞⢷⠈⡃⠀⣠⣾⠀⣇⠀⠸⣿⣦⠀⠀⠀⠈⠁⣠⢊⡔
⠲⢄⡼⠋⢀⡦⠀⡫⠒⠛⠻⣀⠹⣧⡀⠈⠻⢿⣦⣤⡴⠞⣡⠏⣠⣶
⠴⠋⠀⣴⠋⣉⡉⠀⠠⠶⠶⣮⣕⠈⠳⣦⣀⠀⠀⠀⣀⡴⢃⣼⣿⠏⠀⢸⡆
⣾⣆⠸⣇⠀⠉⢀⠌⠀⠀⠀⠀⠙⢷⣄⠀⠉⠛⠛⠋⣡⡴⠋⣹⡟⣀⣤⢰⠃
⠁⠙⢷⣍⡓⠒⢋⣠⣴⣶⣤⣄⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⣰⣿⠟⠉⠉⢻⠀⣴⠆
⠀⠀⠀⠈⠛⠛⠛⠛⠻⢿⣿⣿⣿⣦⡀⠘⢿⠁⠀⠀⠀⠀⢈⣡⠴⢺⡇⡜⢸⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠈⠓⢶⣶⣶⣚⠉⠀⢀⡼⡇⠃⠸⡇⢸⡇
⡀⠀⠀⢠⣶⣾⠿⠛⠉⢀⣐⡒⠀⠤⣬⠍⠀⣀⣼⠿⠛⠁⣀⡴⠊⠰⣧⠐⢦⣹⢄⡙⠆
⡠⠀⠀⠀⠙⣿⠀⠀⠊⢁⣩⡵⠶⠗⠒⠂⠉⠁⣀⣤⣶⣿⣁⣀⡀⠀⢈⣁⣂⣀⡉
⣁⠱⡀⠘⣶⣿⡆⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⢉⣉⠁⢀⣤⠀⠘⢋⣭⣉⣀⣀⡀
⠹⠆⠹⣄⠘⢿⣿⡄⢼⣆⠀⣀⣠⣤⣤⣤⣤⣄⠀⠀⠯⣤⣀⠀⠁⠐⠀⠀⠠⠤⠭⠭⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⡄⠒⠀⠀⠀⢀⡀⠀⠀⠺⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠇⢘⡶⢧⡔⠁⠀⠀⠀⠂⠀⠀⠀⠀⠠⡆⠀⠀⠀⣄⡃⡴⠀⠠⢆⠀⢀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠁⠈⠢⠈⠀⠀⠀⠀⠉⠀⠉⠀⠐⢄⡤⠀⠀⠀⠀⠛⢻⠕⠁⠀⠈⠁⠀⠀⠃⢈⡈⠁⠀⠧⠔⠃
⠀⠀⠀⠀⠀⠀⠀⢰⢳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⢀⠀⢀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠰⠁⢉⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠬⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⠻⠇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⢁⡐⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠉⢘⡊⠀⠀⠠
⠀⠀⠀⣅⠠⠄⠀⠀⠀⠀⠀⢕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠈⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠣⢖⠿⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠎⢀⠠⠖
⠀⠀⠀⠀⠀⠀⢐⡂⠀⠙⠓⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣀⠀⠀⠓⠁⠀⢠⣁
⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⡀⠀⠐⠄⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⡼⢤⠀⠀⠀⠀⠀⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠂⠄⢂⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇⣂⠖⠀⠐⠂⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠃⢰⠂⢀⠈⡃⠀⠀⣠⠀⠀⠀⡁⢀⠀⢀⠄⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⣈⠁⠚⠀⠠⣧⠀⠀⠀⠉⠀⠐⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰⠂⣤⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣀⡠⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠱⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⢠⠆⠀⠀⠀⠀⠀⠰⣿⠰⢓⠣⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣈⢏⡐⢟⣀⣤⠀⠀⠀⠀⠀⡘⠃⣿⡃⠾⠉⠀⠀⠀⠀⣶⠆⣄⠰⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡅⢿⣋⣈⠋⠀⣀⠀⠀⠀⠀⠐⠒⠟⠃⠐⠆⠀⠀⠀⠀⠀⢀⡛⣾⠃⣀⠐⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣌⡣⢆⣴⠀⠀⢀⡀⣀⣀⠁⠘⠂⠈⠤⢐⠀⠉⣁⢀⡐⣀⠢⠀⢶⠀⠀⢀⡠⠂⠁⣉⢠⠛⡁⠶⡀⠛⠀⡀⠀⣀⢙⣤⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⡀⠿⢣⣤⠁⠀⢈⠁⣈⠻⢶⡤⡐⠚⠀⡶⢹⢷⡏⠁⡴⢀⡄⣤⢥⠈⠁⠀⣠⣁⣈⣀⣀⣤⣈⣀⡉⣠⡶⠀⣿⣴⠋⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣉⠙⠪⠁⣁⡀⠹⠧⠈⡆⢆⠳⡈⢆⡞⣠⠃⡏⣼⢋⠌⢼⡹⠁⣀⣰⡶⢾⡏⢹⠏⠹⠯⠉⠟⠙⣿⣀⡠⠈⢡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣥⣤⣐⣚⡓⢖⢘⠀⢳⡎⣰⠁⣸⡗⢄⠃⣨⠃⡄⣼⣏⠙⠒⠈⢡⣄⢀⣦⣀⣆⣀⣤⠋⠉⠁⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠋⡀⠀⠈⠉⠹⢍⡙⢻⠘⡄⣈⣠⣶⣶⣿⣷⣜⣼⢃⠔⡰⠟⠁⢴⣬⡷⢾⡛⢛⠉⠛⠛⣉⠁⡀⠀⢀⣀⠉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⡶⠟⠷⣦⣦⣄⠓⢳⣿⠟⠛⠃⠀⡉⠄⠙⠃⠼⠈⣤⣸⡷⠿⠉⠁⠀⠆⡄⣿⠓⠈⢀⠉⠀⠠⠀⠀⠀⣉⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣾⠛⠛⢛⣀⣁⠀⣤⡅⡈⢋⣽⡧⠀⠀⠲⣀⡃⣰⠂⡀⠀⢧⡾⠏⣖⠄⠀⠆⣰⡷⠰⣶⢀⡐⡮⠐⣀⠀⣧⡀⢰⠟⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⡀⡀⢩⣴⣈⠿⠿⢀⣦⣼⣯⠰⡁⠐⠂⠀⠀⠀⢺⣉⠀⠀⡔⣠⠍⡀⠀⠇⢩⣶⡄⣤⠛⠇⡐⢂⠛⢷⣿⡟⠉⠴⠛⠐⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡿⠁⠀⡟⣴⡤⠉⠁⠀⠀⡐⠉⢣⣿⠃⠀⢉⡠⢄⣀⠠⣌⠁⢀⠁⡄⠑⣱⠦⣄⢀⡌⠰⣦⠉⠁⢲⠀⠀⠘⣿⠯⣄⡠⣜⠛⠾⢲⠆
⠀⠀⠀⠀⠌⠀⣅⠴⠆⢿⣇⠂⣠⢸⣤⠀⠀⠀⠀⠀⢈⠀⠀⠻⣶⡄⠈⠁⠞⠘⠆⠈⠀⣠⡾⠦⢜⣛⠲⣦⣉⠲⡜⠛⢂⠀⣸⠀⢀⠶⠁⠀⢸⡇⠘⢃⣤
⠀⠀⠀⠀⠀⠀⠻⠆⠀⠈⠋⠄⠁⣠⡅⡀⠀⠀⠘⠄⠀⠀⡄⠀⠸⣷⣦⣦⡀⢀⣤⣄⣠⣿⠛⢶⣄⡈⠗⢀⡛⢣⡈⠇⢀⣌⠁⠀⠀⠀⠀⠀⠰⡶⠀⠀⠉
⠀⠀⠀⠀⠀⠠⣶⠀⢘⣄⣦⡦⣰⡉⢉⣄⠀⠂⠀⠂⠀⠈⠀⢀⢄⡺⠳⢽⢟⡛⠯⣽⡉⡷⡜⢣⠎⠿⢶⣅⡵⠘⣃⡀⠚⡋⠀⠢⢠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⡀⢈⣿⠏⠄⡇⠁⣙⠟⣠⣅⠀⠀⠀⢀⡠⡅⣮⢡⡄⢸⡏⡀⢠⠘⣷⠒⠴⢲⣅⠸⢦⠙⢳⣶⡋⣥⡸⣇⣠⠶⠃⢐⠀⣀
⠀⠀⠀⠀⠀⠀⠘⣧⣾⠃⠀⠂⠈⢁⠽⠃⠈⣥⡚⠛⣐⣛⣳⢰⡄⠈⡆⢽⠊⣷⠘⠒⡘⠇⢘⢁⠻⠏⠶⠆⣭⣍⣍⡈⣫⠀⠈⠴⠶⠧⠘⠛⠁
⠀⠀⠀⠀⠀⡤⢰⣿⢃⠠⠀⠁⠠⠀⣴⠟⣲⢈⣷⣤⠄⠉⠙⢠⡤⢰⠂⣽⢇⠸⣆⢠⣄⠘⡄⠺⠸⠷⢰⡖⡶⠀⢐⣬⢁⢀⡐⠲⢶⠀⣤⡄
⠀⠀⠀⠀⠀⢱⣾⠏⣄⠀⠀⡐⢠⡾⠓⡀⢰⠿⣧⣭⠀⠀⠀⢃⠾⡈⢁⣾⡸⠄⠿⠂⡁⢌⡷⣶⠸⡗⣼⠁⣥⣤⠛⠁⣼⡀⢹⡆⠀⠇⠉⠁
⠀⠀⠀⠀⢰⢸⣿⢰⠈⠂⠀⢀⣿⢀⡀⣼⠶⢰⡏⣉⣄⠀⠀⠀⣚⠷⡸⣿⢃⡛⢧⣜⢃⣤⡙⠯⣴⡆⣿⣆⠈⠁⡀⢠⣼⠀⠀⠰⣶⠆
⠀⠀⠀⠀⠀⠹⣿⠀⠁⠀⠀⣾⢁⡈⡐⣀⡠⠚⠛⢈⡋⢸⡿⡈⣿⣮⢛⣉⠘⣃⣱⣿⢷⡭⠘⠓⠆⠀⢙⠻⣧⡐⠃⠈⠉
⠀⠀⠀⠀⠘⠂⣿⣦⡀⠀⢸⡏⠀⢡⣄⠈⠉⣖⠐⠻⡍⠙⠿⢉⡹⠁⡀⠘⠀⢨⣯⣤⡼⣿⠞⢠⢢⠠⣢⢤⣿⣇⠀⠀⠰⣶
⠀⠀⠀⠀⠈⠀⢹⣿⣇⡀⣾⠃⠚⢈⣁⣝⠉⠛⠓⠀⠺⢷⢰⠟⠁⠒⣽⠦⣦⢲⣦⡉⢃⣿⠈⢣⠘⠎⣡⢨⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⣭⣝⢇⣿⠂⠆⢡⡈⠉⡃⠰⢮⢹⡶⠊⢡⡈⢉⣶⣋⡘⠟⣀⣋⣵⠿⠁⢏⡀⠖⢙⡀⣽⣿⡟⠀⠀⠀⠷⠁
⠀⠀⠀⠀⠀⠀⢿⡘⣋⣾⡿⠈⠦⢸⠏⡚⠛⠓⣤⠋⢐⣁⡍⠁⡌⠉⠟⢙⡻⠋⣙⠁⣲⠀⢨⠄⠲⢙⢸⣿⢿⣇⠲⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣶⡄⢠⡄⠞⠛⢚⣧⣩⠀⢎⠺⡟⡾⡆⠶⢺⡛⢁⡜⠃⠠⠇⠀⠴⠀⠚⣤⣾⣿⠰⠌⠂⠀⡂
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠻⣿⡀⢀⡘⢷⢈⣅⠸⠷⢌⡁⠴⢷⠃⡤⣠⣁⠚⠀⢀⡘⠁⠴⢂⣀⢴⡿⣇⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡹⣿⣆⡠⠦⠉⠡⢶⢆⣻⡧⠜⣃⠰⠠⠖⣡⣀⡀⣹⣆⡤⠔⠉⠗⠀⠃⠈⠁⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⢀⠿⣿⣦⣐⡛⠀⠶⠀⢒⡀⣡⣶⠟⠁⠠⡀⠀⢁⣀⠰⠶⢀⡌⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠈⠁⠙⠿⢿⢾⣿⠷⢿⠿⠛⠉⠨⣄⠄⢠⣤⠀⠈⢒⠖⠁⢇⠐⠦⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⡄⠀⠈⢶⠀⠀⠀⠁⠀⠌⠡⠀⣸⣨⠆⢶⠌⠓⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠿⠟⠂⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⡠⡉⠀⠀⠌⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢰⠒⠶⠶⠶⠤⠄⠀⠀⠒⠀⠀⠀⠠⠄⠠⠤⠤⠤⠶⠲⠒⠒⠒⢲⠶⠶⠶⠒⠒⠂⠀⠀⠀⡐⡆
⠀⠀⠀⢸⠀⠐⢦⠀⠀⠆⡀⠀⠐⠃⠀⣠⠀⠚⠀⣀⠀⠀⠛⠀⣀⠀⠀⠉⢀⡄⠀⠘⠁⡀⠀⠘⠁⠃⡇
⠀⠀⠀⢸⠀⠀⢀⡀⡄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠒⠒⠒⠀⠀⠀⠀⠳⠀⢀⡄⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡆⡇
⠀⠀⠀⢸⠘⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡇⡇
⠀⠀⠀⢸⠀⠀⠠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇⡇
⠀⠀⠀⢸⠠⠦⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡇⡇
⠀⠀⠀⠸⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡄⡇
⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⡇
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⡆
⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠁⠀⠃
⠀⠀⠀⠀⡆⠁⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠁⠀⠀⡂
⠀⠀⠀⢠⠁⠀⠁⢈⡂⠐⠒⢂⣔⠒⠒⠒⠒⣲⡒⠒⠂⠀⢠⡀⠂⠒⠒⣒⠒⠒⠒⣒⠒⠒⠀⠐⠃⡇⡇
⠀⠀⠀⠀⡆⠶⠀⠀⠁⠤⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠶⠀⠀⠀⠠⡄⠀⠀⠀⣠⠀⠉⠀⠘⠂⠠⠄⡇⡇
⠀⠀⠀⠠⠭⠤⠤⠤⠅⠤⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⢤⣰⢶⣲⡆⣴⣲⢖⣠⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣺⣽⣾⣊⣿⣬⣽⠻⠿⠇⠿⠿⢻⣭⣼⣏⣺⣾⣭⣲⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣧⡹⣄⡷⠳⣋⣭⠴⠖⠒⠚⠋⢛⠛⠛⠒⠒⠶⢬⣝⡓⠳⣇⡼⣡⢷⡦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⢿⣌⣯⡷⣛⡬⠚⠉⠁⠈⠀⠀⠀⠄⠠⢭⠥⠀⠀⠀⠀⠈⠀⠉⠙⠪⣜⡳⣯⣏⣼⠷⣄
⠀⠀⠀⠀⠀⡠⣺⣿⣴⠟⡩⠞⢁⡀⠀⠀⢀⠀⣽⣦⣉⡒⠃⢜⠄⠓⣊⣡⣾⡁⢀⠀⠀⠀⣠⠙⠮⡙⢧⣾⣯⡣⡀
⠀⠀⠀⠀⣀⠓⢭⡳⣫⠞⠁⠀⠈⠴⢧⠡⠀⡴⠛⣿⡄⠉⠙⣶⡞⠁⠁⣼⡟⠳⡄⠠⢡⠷⠄⠀⠀⠘⢦⡳⣫⠗⢃⡀
⠀⠀⠀⣞⠮⣝⠚⡵⠅⠀⠀⠀⠤⠙⣀⣀⣼⡀⠀⣸⠛⠦⣄⠠⢀⡤⠚⢻⡀⠀⣸⣄⣀⠘⠡⠄⠀⠀⠀⠵⡝⢚⣭⢞⡆
⠀⠀⣜⠺⣻⡞⡼⠁⠀⠀⠻⣶⣶⡋⠁⠀⡉⠀⠠⡏⠀⣄⢈⢷⣏⢀⡄⠈⡧⠀⠈⠁⠀⠉⣳⣶⡾⠃⠀⠀⠹⡜⣾⡻⣚⡄
⠀⢰⣛⠻⡿⢰⠃⠀⠀⢈⠆⢸⠉⠛⣿⠛⠛⠙⠻⢟⡌⢹⢤⡙⣡⢼⠉⣜⠟⠛⠙⠓⢻⡟⠉⢹⠀⢏⠀⠀⠀⢳⠸⡿⢛⢳
⠀⢸⣛⣟⡇⡏⠒⠶⠰⠤⠅⠘⣆⡀⠘⢧⡀⠹⠳⡤⠤⣧⣤⣽⣥⣤⠧⠤⡴⠻⠁⣠⠟⠀⣀⡞⠐⠤⢶⠰⠆⠊⡇⣿⣿⣿
⠀⠳⠾⠿⡅⡇⠀⠀⠀⢲⢁⡞⠉⠁⣈⡤⠿⠫⠂⣱⢶⡿⠁⠀⠀⢹⣷⢾⡁⠮⠻⠧⣌⡀⠉⠙⣆⠱⠀⠀⠀⠀⡇⡽⠿⠶⠂
⠀⢚⣻⣿⡁⡇⠀⠀⠀⣁⣾⣄⣤⣶⡉⠀⠶⠗⠚⠤⣬⢿⣄⣀⣀⣼⣿⡤⠜⢒⠷⠄⠈⣱⣦⣄⣽⣆⡁⠀⠀⠀⡇⣹⣿⣛⠆
⠀⢸⢷⠿⡇⢷⠒⠀⠉⢙⠛⣏⠀⠨⠙⠓⠶⣶⠟⢀⣇⡠⢿⠙⢹⠧⣀⡇⠙⢷⡖⠖⠛⠉⠈⢨⡿⠋⠙⠁⠀⢲⠇⡷⢷⢿
⠀⠘⣶⠾⣿⡘⡆⠀⠀⠈⡑⠄⠙⢶⠦⠀⢸⡃⠠⠟⢀⣰⢄⣱⣁⢔⣀⠘⠧⠀⣿⠀⠰⢶⢖⠁⠐⡉⠀⠀⠀⡜⣸⡿⣶⡞
⠀⠀⠱⣾⡾⣳⠹⡄⠀⣄⠲⢊⣂⠘⡀⠀⣸⣦⠴⠖⠋⢻⡄⠙⠀⣼⠋⠗⠶⢤⣾⡀⠀⣸⠀⡈⢲⢂⡀⠀⡼⢱⣻⣾⣲⠁
⠀⠀⠀⠳⣫⠵⢲⡙⣎⠈⠀⠀⠨⠀⣷⣾⡋⠀⠀⣠⡄⠀⠻⣤⡼⠃⠀⣤⡀⠀⣈⣻⣶⡇⠸⠀⠀⠈⢉⡞⣱⠲⢽⡳⠃
⠀⠀⠀⠀⠠⡖⣫⣞⣎⠳⣀⠀⠀⠲⠋⠁⡬⢅⠉⢍⠳⢄⡀⣿⡇⣀⠴⢋⠍⣁⠩⡌⠉⠷⠂⠀⠀⡰⢋⣞⣮⡓⡦
⠀⠀⠀⠀⠀⠈⢾⡿⢛⣷⣬⡳⣇⡀⠀⠀⠀⠈⠴⡁⠕⢢⠙⢿⠏⢡⠒⠅⡵⠌⠀⠀⠀⠀⣈⡶⣫⣴⣟⠻⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠙⠿⡡⣿⣏⡶⣹⡲⢤⣀⣘⠓⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢋⣀⣠⠴⣚⡱⣮⣯⡧⡹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⡼⢁⣟⣶⣶⣭⣍⣒⠲⡲⠦⠾⠦⠶⣒⢒⣚⣭⣵⣖⡞⣇⠹⣜⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⢽⣿⢪⣿⢫⣽⣯⣿⡇⣿⣿⣿⣭⢻⣯⢺⣻⠿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠛⠚⠚⠃⠛⠚⠒⠓⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⣤⡤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒⠀⠉⠁⠀⠀⠀⠀⠀⠙⠁⠓⣤⠄⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠸⡶⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⢠⣄⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰⣾⣿⣶⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠁⢶⣄⡀⠂⢀⡀⠀⣀⣠⡄⠀⠀⠀⠠⠄⣀⠀⢀⣀⣠⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡟⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠃⠐⣤⠉⠻⠓⣤⡤⣤⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⠻⢿⣏⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⠁⠤⢺⡿
⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠉⠀⡄⠀⣄⠀⠰⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⣀⣰⠦⠘⠛⠃⣼⣧⢀⣄⠂⠀⣼⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣶⣦⣄⣀⣀⠀⠀⠀⠁⠀⢠⡚⠉⠀⠄⠀⠀⠀⠀⠀⠀⢸⢿⣶⠉⣉⠉⠁⠸⠻⢆
⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠙⠲⠶⠦⣤⣼⣅⣂⣴⣾⣿⣦⠒⠀⣠⣿⡯⠛⠁⠾⠛⢠⠆⠰⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐⣶⣥⡄⠋⠹⠿⢿⣿⣿⣥⠞⣋⣁⡀⠀⠀⠀⠀⢁⣴⣦⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣿⠷⠄⠀⠀⢉⠳⣶⣿⣿⣿⣧⠙⠁⠀⠀⣘⠋⢀⣴⠞
⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠁⣴⡟⠻⣷⣌⠀⠈⠛⣿⣿⣿⢀⣤⣾⣷⣾⠟⠙⣉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣄⠙⠃⣠⣿⢋⣴⡀⠀⠜⠻⣿⣉⣤⡀⠀⠀⠀⠘⢻⡇⠈⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣀⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠉⠉⣉⡙⠛⡛⠷⢾⣿⣿⡄⠈⠄⠹⣿⣿⣿⡄⠃⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠁⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠻⣿⣁⠟⢢⣌⠙⠻⠂⠀⠂⡹⡿⠋⠀⠀⠐⠀⠾⠟⢢⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠘⠏⣀⡄⠀⠑⢦⡀⠀⠀⠠⢿⣀⣀⣀⣀⠀⠠⣬⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⢤⣀⡀⠀⠀⠀⠲⠄⠙⠶⣶⣿⣦⣸⣦⡀⠀⠸⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣀⠀⠀⢠⣴⣿⢿⡟⢉⡙⢷⡈⢻⣭⡔⠒⠒⢤⣤⣀⠀⠀⠀⠈⠛⠿⣷⡄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣀⠀⢈⠙⠿⡆⢿⣅⣼⡿⢀⠘⣅⠚⢧⣀⡐⠛⣧⡀⠀⠀⠀⠀⠈⢻⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠦⠄⢀⡀⠈⠛⠛⠰⢿⣷⣄⡉⠶⠋⣡⣶⢄⣙⣤⢀⠀⠀⠀⠀⠑⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⠇⠀⠀⠀⢻⣷⣤⣄⣀⣀⣌⠀⠀⠀⠀⠈⠙⠋⠙⠟⠳⠦⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⡄⠀⠀⠀⠀⣧⣿⣿⠿⣿⡿⠷⠚⠛⠻⣯⡄⢠⡶⠂⠴⠤⠄⠀⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠸⢸⣿⠀⣿⢁⡀⠀⠀⠀⠈⣄⣴⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⠃⠀⠀⢀⠀⠠⢶⡚⢿⣷⣿⠎⢡⠀⠀⠀⠀⠈⠃⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠃⠀⠀⠀⡀⠂⣈⣿⣸⣿⣿⢠⡆⣤⠂⠀⠀⠀⠈⡴⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⠋⠀⠀⠈⠠⠈⠓⠀⠉⠹⣿⣿⡀⠀⠁⠞⢉⠀⠰⠀⠰⢆⡀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⣿⣟⠁⠀⠀⠀⠉⠀⠂⠀⠀⠈⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣦⠀⠀⠀⠀⠀⠒⢯⡄⢀⠀⣿⣿⠀⠀⠀⢇⡈⠀⠀⠀⠀⠀⣥⡄⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣠⣤⣿⣷⡀⠀⠀⠀⠀⠁⣰⠋⢶⣿⣿⡸⠇⠳⠀⠡⠄⠀⠀⠀⢸⣿⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠉⢡⣿⣡⣿⣿⡦⠀⠀⠀⠠⠀⠀⠴⣿⣿⡄⠞⠀⠀⠀⠀⠀⠀⣰⣿⣏⣹⣿⢠⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣸⣿⠿⠋⠉⠀⠈⠁⠀⠀⠀⠁⠀⣿⣿⠇⡀⠈⠀⠀⠀⠀⠚⠛⠛⠿⢿⣿⣏⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠸⠃⢀⠄⣀⣀⣤⣤⣼⣿⣿⣆⣁⣤⣀⡀⠛⠀⠀⠀⢤⡀⠀⠈⠛⢣⣄⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡇⠀⠀⠐⡄⠀⠀⢠⣶⡿⠛⠉⠉⠉⣿⡿⣿⠋⠉⠙⠛⠷⣷⣀⡀⠀⠹⠃⡄⠀⠀⢨⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⢊⠀⠀⠀⡄⠀⠀⢰⣿⠃⠀⠈⢀⠀⠰⣿⠀⢻⣆⠀⡀⠁⠦⠈⢿⣄⠠⠀⠀⠐⢄⠀⠀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠁⠀⠠⣿⠇⠀⠀⠠⠈⠀⠀⡏⠀⠘⡇⠀⠳⢆⡀⠀⠀⣿⣄⠀⠀⡇⠘⠀⠀⠻⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡆⠀⠃⠀⠀⠈⢠⣿⠀⠀⠀⠠⠄⠀⣦⡀⠀⠀⣤⡀⠀⣈⠀⠀⠀⢿⣯⠀⠀⡇⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⡀⠀⡀⠀⠀⣿⡄⠈⠀⢀⠈⠀⠀⡾⠀⢸⣇⠀⠀⠉⠠⠀⠀⣿⡏⠀⠀⡆⠀⠀⠀⣿⠾⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⠀⡀⠳⡀⠁⠸⢿⣆⡀⠀⠀⠀⠀⢳⣄⡰⠏⠀⠀⠀⠀⢀⣼⡿⠄⠀⠀⠃⠾⠀⠀⣈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠉⢀⠀⠁⠀⢣⡀⠀⠈⢻⣿⣦⣀⠀⠀⠈⠀⠀⠀⠀⢀⣴⣾⣿⠿⠁⠀⢀⠈⢠⠂⠀⢠⣼⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⡄⠀⠀⠀⠀⡄⠀⠀⠙⢻⡟⣷⣄⠀⠀⠀⠀⣴⣿⣤⡿⠇⠀⠀⡰⠆⠀⠈⠀⠠⡌⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢀⠁⢄⡀⠀⡀⠀⢆⡀⠀⠀⢻⣿⠙⣧⡄⠀⣿⣏⣸⡟⠛⠀⢀⠐⠀⣠⠂⠀⢀⢷⣦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠳⠄⠘⠠⠼⠃⠀⠀⠈⢽⣿⠟⠷⢴⡍⢻⣿⠁⠀⠀⠠⠦⠄⠁⢀⡰⠄⠀⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡤⠀⣥⡄⡀⠀⠀⠀⠉⣼⣿⠀⠀⠀⡀⢸⣿⣵⠀⠀⠀⠀⢠⠀⠾⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠈⠁⠴⣉⣁⣾⠟⠙⣷⣦⣤⣴⣿⠛⢿⠇⣀⠒⢰⣧⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣿⡏⠁⠀⢰⡿⠋⠉⠉⣩⡟⠓⠒⢾⣧⠠⠄⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⢽⡟⠀⠁⠂⣿⠇⠐⠀⠈⠟

⣿⣿⣿⣦⠀⠀⠀⠈⢿⣿⣿⣿⡀⠀⠀⠸⣿⣿⣧⠀⠀⠸⣿⣿⡇⠀⠀⣿⣿⡇⠀⢀⣾⣿⡿⠁⠀⠀⣠⣾⣿⣿⡿⠟⠋⠉
⣿⣿⣿⣿⣧⡀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠹⣿⣿⡆⠀⠀⣿⣿⡇⠀⠀⣿⣿⠀⠀⣼⣿⡟⠀⠀⣠⣾⣿⡿⠟⠉⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠈⢻⣿⣿⣿⣷⡄⠀⠀⠀⠻⣿⣿⣿⣄⠀⠀⠹⣿⣿⡄⠀⠸⣿⣷⠀⠀⣿⡏⠀⢰⣿⡟⠀⢀⣼⣿⡿⠋⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠙⣿⣿⡄⠀⢻⣿⡄⠀⣿⡇⠀⣾⡿⠀⢠⣿⡿⠋⠀⣀⣴⣾⣿⣿⠿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣄⠀⠈⢻⣿⣄⠀⢻⣧⠀⢻⡇⠀⣿⠃⢠⣿⠋⠀⣠⣾⡿⠟⠋⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⣶⣄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣄⠀⠀⠈⠻⣿⣷⣤⡀⠙⢿⣦⡀⢻⣇⠸⣇⢸⡟⢠⡿⠁⣠⡾⠟⠉⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤
⣿⣿⣷⣦⣀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⣄⡀⠀⠙⠻⣿⣦⣀⠙⢷⣄⠹⣆⢻⢸⡇⡾⢡⡾⢋⣠⣴⡾⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣦⣤⣀⠉⠛⠷⣦⣌⡳⣜⢮⢿⢘⡵⣫⠶⢛⣉⣠⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠙⠻
⠀⠈⠛⠿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠉⠙⠛⠛⠿⠷⠶⠦⠬⠭⢷⣻⣿⣾⣟⣶⣭⣭⣉⣉⣉⣉⡉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⠶⠶⠖⣚⡽⡪⠣⢽⣕⢭⡲⢦⣬⣉⠙⠛⠿⣿⣷⣶⣤⣄⡀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣷⣦⣀
⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢀⣀⣤⣴⡶⠛⣡⠞⣱⢳⡜⡎⢧⡙⢶⣌⠙⢿⣶⣄⡀⠈⠙⠻⣿⣿⣿⣶⣄⡀⠀⠀⠀⠉⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣴⣶⣶⣶⣶⣿⣿⠿⠟⠋⢁⣤⡾⠋⣰⠏⣸⠇⣿⡈⢷⡄⠻⣷⣄⠈⠻⣿⣷⣄⡀⠀⠉⠻⣿⣿⣿⣷⣤⡀⠀⠀⠀⠙⠻⣿
⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠀⢀⣤⣶⡿⠋⢀⣼⡟⠀⣿⠀⢹⡇⠘⣿⡄⠘⢿⣷⡀⠈⠻⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠋⠀⣠⣾⡟⠀⣸⣿⠀⢸⣷⠀⢹⣿⡄⠈⢻⣿⣆⠀⠈⠻⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣿⣷⡀
⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⠿⠛⠁⠀⣠⣾⣿⠏⠀⢰⣿⡇⠀⢸⣿⠀⠈⣿⣷⠀⠀⢻⣿⣧⡀⠀⠙⢿⣿⣿⣆⠀⠀⠀⠙⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⣠⣾⣿⡿⠃⠀⢠⣿⣿⠁⠀⣿⣿⠀⠀⢹⣿⣇⠀⠀⢿⣿⣷⡀⠀⠈⢻⣿⣿⣷⡀⠀⠀⠈⢻⣿⣿⣿⣷
⠿⢿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⠟⠀⠀⣠⣿⣿⠇⠀⢠⣿⣿⠀⠀⢸⣿⣿⡀⠀⠘⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠛⢛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣤⠶⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⢜⣼⠃⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⢉⣹⠶⡟⠉⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢛⣩⡤⠶⣦⠀⠀⠀⠀⠀⣠⣾⣇⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⣴⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣡⣶⠋⠁⢀⡴⠋⠀⠀⢀⣤⠾⡟⢠⠿⣆⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢧⣤⡤⠞⠁⠀⢀⣤⠴⠶⠶⣾⡁
⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢀⣾⣿⢃⣠⠴⠋⠀⠀⣠⡴⠟⠁⣼⠵⠁⠀⣹⣆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣠⠾⠋⢻
⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠈⠙⠋⠉⠀⠀⣠⡴⠞⠋⠀⣠⠞⠁⠀⣠⠞⢡⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⠀⡼
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⣀⣤⡶⢛⡭⢖⡩⢶⠟⠁⢀⡤⠚⡵⣠⢋⢞⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⢾⣁⠢⢐⣂⣠⣤⠶⠛⠫⢑⡪⠵⢊⡡⢞⣁⠴⢊⣡⡤⣪⢞⡵⢋⠞⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠉⠛⠉⠉⠉⢻⣖⠚⣉⣁⣤⠶⠛⢊⣉⠤⢚⣵⣾⡿⠕⠉⡠⠋⡠⢋⠎⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠭⠥⢤⣴⣭⣥⠤⠖⢛⣉⠁⠀⣠⣾⠔⠋⡰⢫⠎⢸⡼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣉⡉⠃⠀⠒⠒⣋⣉⣤⠴⠚⡩⢔⡠⢊⠔⢁⣠⠏⢀⠜⣷⣤⣤⣤⣄⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠩⠽⣉⡩⠴⢋⡡⢄⡠⠔⡫⠔⣡⠔⢋⣾⢔⢧⡜⢉⣯⠀⠲⢈⡷⠀⠀⠀⠀⠈⠓⠒⠒⠛⠉⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣉⠉⢤⣐⣪⠥⠒⣩⣔⠭⠒⢉⡠⣴⢏⠔⣡⡮⢔⣽⠇⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣒⣒⣒⣊⣉⠭⠤⠒⠋⣩⣖⡡⢵⢞⡩⢖⡽⠋⣀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡖⠤⠤⠤⠒⠒⢒⡾⠛⠉⣀⡴⠟⣉⡴⢋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⠤⠔⠒⢋⣡⠤⣶⢟⣩⡴⢞⣩⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣷⣭⣭⣥⠴⠾⠛⣋⣥⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢦⠀⠀⢀⣀⣠⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠛⠉⠉

⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⣶⣷⣶⣷⣦⣷⡔⠒⢲⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡶⣻⠇⠀⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣩⣿⢿⣿⢱⠋⠀⠀⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠈⢣⠀⠀⠀⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢣⠀⠀⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢆⠀⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢿⣄⠀⠘⡄⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠻⣦⠀⢱⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠈⣬⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡿⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣦⣤⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⡿⣿⣿⣿⣟⢷⣼
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡺⢿⣿⣿⢟⣫⠟
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠹⠑⡉
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣷⣶⣄⢀⠀⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⢻⣿⣿⣿⣯⣻⣾⠀⠘⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⣛⢿⣟⣭⠞⠋⠀⢦⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⠿⠿⠿⣶⣤⡀⠀⠈⢸⠈⠀⠀⠀⢠⢱⠀⡇
⠀⠀⢸⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣠⣶⣶⣾⣶⣶⣦⣄⠉⠻⣦⡀⢸⠀⠀⠀⠀⠎⢸⠀⡇
⠀⠀⢸⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⡿⠟⠛⠉⠉⠉⠉⠛⢿⣷⡄⠈⣷⡸⠀⠀⠀⡜⠀⢸⠀⡇
⠀⠰⢸⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣉⠳⣤⣀⣠⡴⣋⣁⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⢸⡇⠀⠀⡐⠀⠀⢸⠀⡇
⠀⢨⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣍⣉⣽⣉⣉⣉⣉⣀⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣽⣭⣭⣯⣬⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠷⠍⠉⠒⢄⡠⠒⠉⠩⠾⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠄⣀⡇⠀⢀⡶⣠⢠⣨⣅⡄⣄⣶⡀⠀⢹⣀⠠⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠏⠀⠀⢀⣳⡼⡲⣼⠾⣇⣺⣗⣸⠷⣭⢖⢧⣞⡀⠀⠀⠩⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣻⢚⣾⣑⣵⠶⠿⠶⠟⣁⣈⠻⠶⠿⠶⣯⣊⣷⡓⣟⠀⠀⠡
⠀⠀⠀⠀⠀⢀⡤⠼⢤⣰⢞⢻⣅⣽⠃⡴⣖⣦⣼⣭⣽⣧⣴⣲⢦⠘⣯⣨⡟⡳⣆⡤⠧⠤⡀
⠀⠀⠀⢠⢴⡇⠀⢀⢺⡫⢱⡟⢉⡤⣤⡿⣛⣫⣲⣾⣷⣶⣝⣟⢿⣤⢤⡉⢻⡟⢝⡖⡀⠀⢸⡦⡄
⠀⠀⠀⠈⡇⠁⠘⣫⣲⡟⢻⡇⠸⣽⡿⣰⣴⣿⡿⣿⣿⢿⣿⣦⣗⢿⣯⠇⢸⡟⢻⣔⣝⠃⠈⢸⠁
⠀⠀⠀⠀⠘⢄⡀⣲⣩⣹⠟⢡⠖⣿⣨⣾⣿⣯⣿⡿⢿⣿⣽⣿⣷⣅⣿⣲⡌⠻⣏⣍⣖⢀⡠⠃
⠀⠀⠀⠀⢠⠊⠁⠽⣙⣹⣦⡘⠧⣿⢹⢿⣿⣟⣿⣷⣾⣿⣿⣿⡿⡋⣿⠽⢃⣴⣏⣋⠯⠈⠑⡄
⠀⠀⠀⢀⡇⡀⢠⣝⡝⣧⣼⡇⢰⣻⣷⢽⠻⣿⣷⣿⣾⣾⣿⠟⡯⣾⣟⡆⢸⣧⣼⢫⣫⡄⢠⢸⡀
⠀⠀⠀⠘⠺⡇⠀⠈⢼⣕⡼⣧⣈⠓⠛⣷⣽⣝⠝⢿⡿⠫⣫⣯⣾⠛⠚⣁⣼⢧⣪⠯⠁⠀⢸⠗⠃
⠀⠀⠀⠀⠀⠈⠒⢲⠚⠹⢮⣼⡋⣻⡄⠳⠯⠟⢻⣛⣟⡟⠻⠽⠞⢠⣟⢙⣧⡵⠏⠓⡖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣽⢬⢿⡩⣻⠶⣶⠶⣦⡉⢉⣴⠶⣶⠶⣟⢍⡿⡥⣯⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢘⣧⣂⠀⠀⠈⡽⢳⠵⣻⢶⡏⢽⡯⢹⡶⡟⠮⡞⢯⠁⠀⠀⣐⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠉⡇⠀⠈⠿⠙⠘⢙⡋⠃⠋⠾⠁⠀⣸⠉⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡶⣂⣀⠤⠊⠑⠤⣀⣐⢶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠤⡀⠀⢀⠒⠄⠀⠰⢢⡀⠀⢀⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢀⠂⠶⠄⠀⢀⢀⡀⠀⠠⠆⠄⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠲⠀⠠⡀⠈⠛⠋⠋⠀⣀⠄⠐⠆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⠀⡄⠀⢪⣷⢦⢡⢴⣾⡎⠀⡠⠈⠐⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⠀⠀⠀⠈⠅⡾⠿⣆⠩⠀⠀⠀⠘⠇⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠈⠉⠢⢼⠸⡠⠞⠉⠁⡀⢠⣬⡋⣶⠄⣮⢻⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠯⠴⡄⡀⠀⠀⠀⡀⠀⠈⢵⡎⠛⣡⣄⠴⠄⢆⢌⠱⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⢀⠀⠀⠀⠀⣧⠀⠈⠈⠀⠀⣀⠛⣀⠺⣿⠨⣕⡲⣮⣉⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠨⢷⠀⠀⠠⠖⠀⠀⠀⠀⠀⠌⣠⠙⡅⠿⠇⠿⠇⣶⡶⠙⠻
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢉⡀⣛⠃⠀⠠⠀⡎⢰⡇⠀⠀⠀⠰⡐⠂⠈⢠⣄⠿⠒⠿⢢⡦⠰⠿⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠈⠃⠉⠀⡀⡴⠘⢧⡣⠙⠀⠀⠀⠀⠱⡀⢠⣬⠉⣐⢂⠀⠀⠸⠗⠺⠷⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠄⠠⠀⠴⠂⠀⠀⠀⢿⠀⠀⡤⠀⠀⠀⡐⢰⡅⡄⠩⢌⠐⠊⢛⣐⠿⢞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠖⠻⠓⠀⠀⢤⡀⢀⡘⠓⠽⠃⠀⠘⢛⣴⣀⠙⠀⠆⢹⣕⠿⣘⣟
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈⠀⠁⠀⢀⠁⠰⣆⠸⡇⣴⠙⠘⠮⣓⣘⡋⠐⠶⣄⡀⠈⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠻⢡⡆⠁⠀⢨⡀⡀⠈⣁⣘⡦⡤⠤⠀⠩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⡧⠁⡈⠀⠘⠁⠿⠘⠉⢀⣥⠖⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠠⢀⠀⠈⠀⠀⠀⠀⠀⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠖⠂⠖⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡟⠒⠢⢠⣤⣄⣐⣒⣒⣂⣠⣤⠠⠚⠚⣧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣽⠷⠚⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠙⠒⢫⡉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢢⣧⡀
⠀⠀⠀⠀⠀⠰⠴⠦⣤⡴⠁⠿⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⠀⠱⣤⡤⢶⠶⠂
⠀⠀⠀⢀⣰⡶⠖⣸⡽⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⣽⡔⠶⣶⣀
⠀⠀⠀⠀⠀⢀⣼⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢆
⠀⠀⠒⠶⢤⣼⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣶⠞⠻⠃
⣠⣶⠶⠂⣼⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠄⠙⠾⢦
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⣠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡀
⠀⠰⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡱
⠀⠀⠱⣼⠀⠀⠀⠀⠀⠀⢀⠶⠂⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⢸⡴⠁
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⢹⣄⠀⠐⣆⢀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢠⠄⠀⢀⣼⠁
⠀⠀⠀⠀⠀⢎⢆⢀⡌⠃⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠩⢁⠀⢀⢎⠆
⠀⠀⠀⠀⠀⠈⢦⢫⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠘⢡⢋⠎
⠀⠀⠀⠀⠀⠀⠀⠣⣳⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⡣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⡍⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡿⣏⠏⢂⠀⠀⡠⢄⡀⠡⠀⠀⠎⠁⠀⣀⢹⡤⠀⠄⠀⡐⡺⢸⡷⡟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣟⠛⣻⢤⠊⢰⠇⡎⣲⢉⠟⣳⣄⣸⡑⠎⢰⠀⠈⣠⣿⠛⢟⡸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⡞⠋⠀⡷⠒⠀⣄⠀⠀⢫⢄⠤⠊⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣁⠘⠛⡚⠀⠐⠎⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠄
⠀⠀⢀⡤⣀⢀⣵⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡾⠄⡆
⠀⠀⠈⠒⠉⣻⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡋⠋
⠀⠀⠀⠀⢀⢻⡀⠀⣀⣀⣸⢄⡠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⣘⣄⡀
⠀⠀⠀⠀⠀⣇⢷⡜⡟⠉⢻⡏⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⣹⠋⠋⠁
⠀⠀⠀⠀⠀⠘⡄⠙⡇⠀⠀⠓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⡀⠀⢀⢼⠃⠀⠀⣀⡀
⠀⠰⣻⣤⣭⠀⡏⡤⢹⠰⣮⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⢼⡿⢵⣲⡎⢾⠀⣀⠤⠿⡟⠁
⠀⢀⣼⠽⡍⢳⡏⠀⢸⣤⣿⣟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠘⣞⢱⠎⠉⠛
⠀⠈⠁⠀⠘⡾⠁⠀⣽⠚⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠙⣾
⠀⠀⠀⠀⠀⡇⠀⢀⠇⠀⠀⢀⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠹⡄⠰⠙⣆⠀⠂
⠀⠀⠀⠀⢸⠇⡀⢸⠀⠀⠀⠁⢭⣷⣾⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣿⣿⣶⡻⡄⠀⢻⣰⣿⠀⠘
⠀⠀⠀⠀⠀⡇⠃⠘⡆⠀⢀⠞⣩⠟⠻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡛⠃⠀⠘⡇⠸⣿⠔⠛⠇
⠀⠄⣈⣾⡢⠻⡤⠰⠘⢄⣾⢲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠒⣹
⢀⠈⡹⠋⣉⡑⠻⡑⢄⠈⠻⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡁⣦⡇
⠀⠹⣽⠁⠀⠈⠓⢼⣆⠠⠀⣈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⠎⠀⠀⡼⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠈⠑⢤⣌⠁⠀⠈⠉⠙⠒⠲⠒⠶⠒⠒⠒⠒⠲⠏⠉⠉⢉⣉⡁⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠤⣄⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠛⠻⠾⢤⣄⣀⣁⣀⣀⣀⣀⣒⣦⡤⠤⠭⠤⠴⠦⠤⠤⢤⣀⡀⠀⠔⠂⠐⠂⣀⠀⠢⠉⠢⡀
⠀⠀⠀⠀⠀⢀⡤⠚⠉⠂⠠⠶⠂⢀⡠⠀⠓⢀⣁⣠⠀⠭⠤⠀⣀⣁⣀⣀⣀⢀⣤⡶⢀⣀⣀⡨⠷⢤⡀⠀⠀⠈⠀⠀⠀⢠⡌⢆
⣀⣀⣀⣠⣔⣁⣄⣠⣠⣤⣀⣴⣠⣄⣉⣤⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣹⣤⣀⣀⣄⣸⣄⣀⣌⣮⣄⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⢀
⠀⠀⠀⠀⠸⡔⠓⠃⠘⠚⠎⠇⠀⠀⡉⠁⠉⠉⠉⢉⠀⠀⠋⠉⠉⠉⠉⠉⠉⠃⠀⢘⡭⠋⠉⠉⠯⡇
⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠠⡅⠀⢀⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠐⡃⠀⠈⠁⠀⠀⠀⠀⢈⠀⠀⠦⡤⠤⣤⣤⠤⡤⠄⠀⢸⣓⢤⣀⣤⣊⡇
⠀⠀⠀⠀⢰⠣⠤⡄⢠⠤⠂⡆⠀⠀⠄⠀⣠⣄⠀⠦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣈⠁⠀⠀⠀⣠⠤⠤⠤⠄⠤⣄⠀⠀⠈⠀⠀⢸⠀⢸⠋⠉⠉⡇⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠋⠉⠉⠉⣷⠀⠀⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⡷⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢱⡀⠀⠀⠀⡿⠁⠀⡂⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢸⠀⢸⣄⣀⣠⡇⠀⡗⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣉⣙⣋⣉⠁⠀⠀⠳⠤⠤⠤⠤⠤⠖⠀⠀⠘⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠁⠲⠶⠶⠊⠁
⠀⠀⠀⠀⡏⠃⠀⠀⡟⠁⠀⢠⡖⠂⠀⠀⢰⣦⠀⠀⡴⠒⠒⠛⠒⠒⢦⠀⠀⠟⠁⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⢧⣆⣀⣀⣧⠄⠀⠘⣇⠄⠀⠀⠰⡿⠀⠀⠳⠄⠀⣀⠄⠀⠞⠀⠀⣆⣀⠀⠀⠀⠀⠀⣀⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣧⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠦⠾⣽⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠃⠠⠄⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣤⠁⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⣺⣿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠒⠋⢋⠉⠄⠰⠿⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣉⢠⡤⠀⠆⣒⣂⣩⡤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡫⣶⢀⣃⡴⠴⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣾⣟⣷⣶⣶⣶⣶⡶⡶⡖⣖⣒⣚⣛⣟⣋⣭⡩⡴⠦⠶⠒⡛⢋⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠟⠛⢛⡛⢉⡉⢉⡉⢩⡅⢡⡅⠠⣄⠀⡆⠰⠇⠘⣃⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⡄⠰⠆⠘⣁⣘⣃⣀⣥⣬⣥⣤⠥⠬⠥⠶⠶⠖⠒⠚⠋⠉⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣶⣾⣿⣿⣿⣯⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠖⡒⠋⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠿⠿⠛⠛⢛⡋⠉⡭⠉⢩⠉⠁⠄⠀⢰⠀⠀⠇⠀⣓⣀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢩⠄⠀⡆⠀⠩⢀⢀⡃⣀⣁⣀⣨⣡⣤⣤⠤⠴⠴⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣂⣠⠤⠶⠒⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣷⣤⣤⣤⣤⣤⣤⡤⡤⢤⠤⠤⠤⠴⢶⢶⣶⣶⡶⢶⣶⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣷⡿⣶⣺⢹⣦⣞⣼⣣⣷⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠓⠛⠛⠛⠚⠓⠓⠚⠛⠛⠛⣛⣛⣉⣩⡭⠿⠿⣛⠻⢴⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠶⢖⠒⢋⢉⣩⠉⠤⡀⡶⠀⠿⢀⣚⡤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢐⠹⢂⣚⣡⣭⠴⠴⠴⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⡛⡟⣻⠟⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⣠⠳⢀⣆⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣌⠽⣟⠏⠐⢩⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⡀⡒⠂⠒⠐⢂⠀⠊⠀⡀⣉⢀⠀⠀⠈⢤⠄⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⢨⢁⠮⣴⡂⡾⠁⠒⠚⠀⠐⠒⠋⠁⠀⠀⠈⠶⠢⣍⠃⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠶⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢋⠝⣈⣹⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠆⠀⠀⠀⠉⠀⢀⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠘⢴⠂⠀⠉
⠀⠀⠀⠀⠀⠆⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠈⣀⠒⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⡀⠀⣼⡛⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠿⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⣎⡀
⠀⠀⠀⠀⠀⠀⢀⠘⠐⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡒⠥⢀⠀⡑⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⡀⠀⡀⠁
⠀⠀⠀⠀⠀⢀⠀⢀⡄⠋⠈⠶⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡖⠒⠁⠘⣿⠃⠣
⠀⠀⠘⠁⠀⠉⠀⠀⠀⠀⠀⠅⣀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⡤⠀⢀⠌⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠋⠐⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⡀⡿⢀⣄⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠈⠂⠤⠀⡴⣚⣀⢀⡀⢃⠀⠀⣹⡀⠐⠀⠀⠘⠈⠈⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⣠⠖⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠜⢋⣡⣴⡾⠁⣠⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⢀⣾⡟⣽⡟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠋⠀⢀⣴⡿⠋⣼⢋⣼⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣴⣾⡿⢛⣤⣾⣷⡿⢃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠘⢿⣿⣿⣿⣿⠋⠐⠄⠀⠀⠀⠀⠀⠀⠁⢀⣴⣿⠟⠋⢉⣠⡿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⡉⠉⠉⠀⢀⣶⡇⠀⠀⠀⠀⠀⠠⠞⠛⠋⠁⠀⣰⣿⠏⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⠋⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⢸⡿⠋⠉⠉⣉⣤⣾⣿⠇⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⡼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⡋⣹⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢰⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⡿⣿⠋⣠⡞⣡⡿⢡⡟⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠁⢸⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⠇⡼⢋⣴⡿⠁⣾⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢨⣾⣿⣿⡇⠀⠀⠀⠀⠀⠰⠏⣀⣴⡿⠋⢀⣼⣿⣤⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣽⣏⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⢀⣾⡿⠛⠉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡿⢁⣠⣶⠿⠋⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣱⡿⠋⠀⣠⣾⠟⠁⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣣⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⡿⠁⢀⣼⡿⠁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣷⣾⡿⠋⢀⣼⣿⠋⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠉⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⣉⣡⣤⣴⣿⠟⢁⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠉⠠⠶⠟⠁⠀⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣶⣤⢠⣴⣤⣆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠀⠀⠀⠀⡔⡂⢹⣿⣿⣿⢿⣿⣿⡿⢐⣢⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠄⡄⠀⣀⣴⣾⣦⣒⣶⡴⣞⠁⠀⠘⠋⠍⠌⠍⠋⠀⠨⣴⣤⣴⣦⣤⣷⣦⣠⢀⢠⠤
⠀⠀⠀⠀⠀⠁⠙⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠋⠈
⠀⠀⠀⠀⠀⠐⣠⣿⣿⣿⡋⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⢙⣿⣿⣿⣔
⠀⠀⠄⣦⢠⣴⣻⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣄⠄⣴⠠
⠀⠀⠀⠁⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡌⠀⠉
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠂
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡑⠁
⠀⠀⠀⠀⠀⠀⠘⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠐⢌⣁⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡄⠀⡠⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⡓⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣗⡤⠄⢊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⡖⣦⡀⠀⠀⣰⡦⢶⣾⡅⠠⠐⠀⠁
⠀⠀⣤⡀⢷⡄⣂⣄⢂⣤⠳⣦⡤⠀⠛⣿⣿⣿⣷⣏⣿⣯⣿⡣⢤⣴⠞⣤⡐⣠⡀⢠⡾⢀⣤
⠀⠀⠋⠉⢥⠷⠊⠩⡷⢲⡯⡿⠁⠀⠰⢴⣿⣯⣿⣿⣿⣿⣿⣇⠸⢿⢹⡖⢿⠍⠐⠾⡤⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠛⠛⣿⠿⠋
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠤⠤⣤⠤⠐⠒⠒⠒⢲⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠐⠁⠉⠉⠀⠀⣿⡇⠀⠀⠠⠀⣿⠀⠀⢀⣄⠀⢸⠀⡇⠀⢀⣀⣀⠈⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⣿⡄⠠⠶⠆⠀⣿⠀⠀⠚⠃⠀⢸⠀⡇⠀⢨⣿⣻⣯⣿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⣱⣿⠀⣿⠐⠤⠤⠤⠐⠛⠐⠒⠒⠒⠒⠚⠀⡇⠀⢸⣯⣿⠛⠏⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⣿⠀⠐⠒⠒⠀⠀⠀⠉⠉⠉⢹⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⠒⠦⠀⠀⣶⠀⢸⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠠⠠⠤⠤⢤⡄⠀⠀⠀⠀⢀⡴⣆⠺⠗⠀⢸⡇⠀⠀⢠⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⢰⣿⠄⢸⡇⠀⢠⠀⢀⡈⠻⣿⠇⠶⠀⢸⡇⠀⠀⢸⠀⡠⠀⢠⡄⢸
⠀⠀⠀⠀⠀⠀⠘⠿⠇⢸⡇⠀⢸⠀⠘⠛⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠐⠃⠀⢹⡇⢸
⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠁⠀⠈⠒⠒⠒⠒⠀⠤⠤⠤⠼⠃⠀⠀⢸⣀⣀⣀⣀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⠄⠀⣠⣤⣤⣤⣄⡀⢺⣽⠇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣧⣌⣿⣶⣿⡛⠻⣿⣿⣿⣿⣾⣿⣄⡰⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⣶⡪⣷⢬⡟⡿⣿⣿⡿⣝⡆⢹⡟⢙⡿⣻⣷⡽⢁⣿⡡⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡿⣿⣄⣼⢸⣿⣿⣧⣷⣴⣿⣷⣯⣔⣿⣿⣶⡉⣯⣶⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣌⢳⣽⣾⣿⣿⣿⠿⢿⣿⣿⣿⡟⠔⡎⠋⢀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠄⢻⣾⣿⣿⣿⢋⡶⢛⣛⢮⢻⣿⣧⢈⠀⣯⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣨⣧⣿⣷⣿⣿⣿⡿⡇⣿⣇⢿⢤⢟⣼⣿⣿⣿⠧⣉⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢹⣿⣿⣽⢹⣻⠻⣿⣨⣿⡿⢶⣿⣿⡿⠁⠀⡞⠉⢻⣇⣴⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢀⣹⣷⢟⢿⡟⡟⣼⡿⢃⡁⡁⢻⢷⠙⢃⡶⣻⣶⣿⣿⣿⣁⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠙⡸⡗⣮⣻⣿⣿⣇⢼⣾⣼⢤⣿⣟⣭⣾⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠑⢡⠴⠋⣉⣿⣾⣷⣿⣿⣿⣾⣿⣷⣿⣿⣾⣻⠿⢿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣼⡫⢀⡼⢁⣶⣿⡿⣛⣿⣟⡻⣿⣿⣿⣿⣿⡟⣼⣿⡿⣫⣾⠁⠁⡄⠉⠉⠻⣆
⠀⠀⠀⠀⠀⣺⠧⠈⠼⢠⣿⡿⣣⣾⢿⣏⣭⠟⣿⣿⢿⣿⣞⣙⣿⠟⢳⣇⣈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣿⠅⠨⠇⣼⣿⡇⣿⣻⣟⣻⣷⠿⣝⣾⡿⠯⣠⢿⠿⡛⠉⠉⠙⢶⡄
⠀⠀⠀⠀⠀⣻⡓⢺⠀⢹⣿⡅⣿⣿⣿⡻⣮⣽⣟⣏⡱⢖⣵⣇⣺⠂⠐⠀⠃⢸⣇
⠀⠀⠀⠀⠀⢚⣯⢜⡇⠸⣿⣧⢻⣟⡾⣽⣿⣿⣦⡀⠀⠀⣿⣿⣿⣧⣄⣀⣴⡾⠁
⠀⠀⠀⠀⠀⠀⢻⣗⣩⣦⡿⠏⠷⡺⡟⡉⢌⢹⣟⣷⣀⣴⣿⣽⠋⠀⠉⠉⠁
⠀⠀⠀⣠⣾⣿⣶⡿⠝⠀⠀⢀⣶⣾⣧⣄⣋⣠⣿⣿⣟⣻⠟⠁
⠀⠀⠀⠻⣿⣿⣿⢇⠀⠀⠀⢼⠴⠴⢸⣿⢿⠿⠛⠋⠉
⠀⠀⠀⠀⠈⠉⠉⠙⠚⠷⠻⣾⡆⠀⣾⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀⣀⣃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣙⣧⡙⡇⢴⣿⠿⠟⠃⠀⠘⠖⠤⣐⠤⢀⡀⠀⠉⡠
⠀⠀⠀⠀⢈⣭⣇⣛⢰⣶⣄⠀⠀⠚⠀⠀⠀⠀⠉⠀⠀⠩⠿⠃
⠀⠀⠀⠀⡾⠟⠅⠟⡠⠙⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠄⠶⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⣤⡾⠁
⠀⠀⠀⠀⢰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣤
⠀⠀⠀⣰⣧⠁⢠⢠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠
⠀⠀⠀⠈⢁⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠿⠤
⠀⠀⠀⠀⠈⣄⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⡟⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠠⠀⠄⢀⣀⡀⠀⠀⢀⠀⣰⣷⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢁⡀⠀⠀⠀⠀⠀⠠⠽⣿⣷⣦⣼⣓⣿⣧⡊⠀⡼
⠀⠀⠀⠀⠀⠤⠀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⣀⠀⠓⠀⠀⠀⠁⠀⠀⠀⠈⠉⣩⢜⡛⣙⡻⡥⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠂⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡷⠋⠻⠈⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

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

⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠀⠀⠓⠈⠅⠀⠀⢰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠍⣾⠈⠙⠒⠒⠒⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⡀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡄⠀⡥⠀⠀⠀⣰⠊⠁⠈⠻⣆
⠀⠀⠀⠀⠤⠤⠤⣤⡤⠴⣦⣤⡤⠤⢆⠄⡀⠀⠰⣄⣀⣀⡈⡟⠉⣍⠂⡺⢀⡀⠀⠀⢠⣴⠇⠀⠀⠀⠀⠈⠉⠳⢦
⠀⠀⠀⣀⣀⢀⣌⠁⠀⠘⢻⣿⡿⠆⠈⠃⣄⣀⡤⠻⣿⣿⡐⡟⠀⡈⣠⠇⠀⢉⡆⠀⠈⢿⣆⠀⠀⡀
⠀⠀⠀⠀⠀⢺⣤⡀⣶⣿⣿⠆⠠⢀⠀⠀⠸⠀⠀⠇⢸⢸⣽⣷⣰⡷⢺⠀⠀⢸⢁⠀⠀⠀⠉⠳⠮⠤⠖⢂⣢⡀
⠀⠀⠀⠀⠀⠘⢿⣿⠟⠸⠉⠀⠀⡀⠀⠀⠘⠢⣂⡀⠀⢘⢻⣇⣻⡷⠞⠅⠀⠈⠈⠑⠠⡀⢀⣀⣣⣼⡿⠿⣯⣙⠓
⠀⠀⠀⠀⠀⠀⠘⢯⠀⠀⢀⡀⠀⡠⠀⠀⠀⠀⠀⠉⠓⠺⠞⠋⠘⣏⠔⠁⠀⢂⡀⠀⠀⠀⢸⡄⠁⠀⠀⠀⠈⠛⠕
⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠚⣮⡉⠉⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠘⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡹⣧⠀⠀⠶⠀⢺⣦⠤⢤⠤⠶⠶⠛⠛
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⢧⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢰⠀⠀⢀⠀⡅⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣆⢡⠀⠀⠀⠀⠀⠠⣠⡴⠞
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⠳⣥⣀⣀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢷⡙⢏⠛⠛⠯⣉⠁
⠀⠀⠀⠀⠀⠀⢁⠀⡀⠀⠀⠁⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣌⣳⣄⢀⠄⠉
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢤⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠟⣯⠁⠠
⠀⠀⠀⠀⠀⠀⢀⡯⡁⠀⠈⠈⠉⠉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡻⡇⣿⡀⠁
⠀⠀⠀⠀⠀⠀⣟⠁⠚⡇⠀⠀⠆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡕⢄⠨⠫⢸⠄
⠀⠀⠀⠀⠀⠰⣧⠀⠨⠇⠀⠀⢈⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⡄⠈
⣶⣶⠶⠶⠶⣶⣿⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣶⣷⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠛⠶⣤⡀⠀⠀⠀⠀⣀⣤⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣠⣤⠶⠶⠶⠦⣬⡻⣦⠀⣠⠞⣩⣤⣤⣄⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⠞⠉⠀⠀⠈⠻⣦⡀⠀⠛⢶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢉⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣄⣀⣉⠉⠙⠛⢶⡄
⠀⠀⠀⠀⠀⠀⣼⠃⢠⡾⠋⠁⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠉⠉⠛⠷⣄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣿⢠⡟⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⢠⡞⢻⣷⠀⠀⠀⣿⠀⠀⣴⡿⠳⣆⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠸⣧⣸⠇
⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠘⣧⠈⠉⠀⠀⠀⣿⠀⠀⠙⠃⠀⣿⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣿⡟
⠀⢀⡴⠞⠛⣛⣛⣿⣷⡀⠀⠀⠀⠐⣿⣄⡀⠙⢷⣄⢹⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡿⠀⣴⠏⠠⣼⡟⠀⠀⠀⠀⣼⣟⣀⣀⣀
⣰⠏⣠⡶⠛⠉⠉⠉⠙⠛⠳⠶⣤⣀⠈⠉⠀⠀⠀⠻⣦⢻⡄⠀⠀⠀⣿⠀⠀⠀⠀⣼⢇⡾⠃⠀⠀⠀⠀⠀⢀⣠⠾⠛⠛⠛⠿⣭⡛⢶⡄
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⠙⣿⣷⣤⣄⠀⣿⠀⣠⣤⣴⣿⡟⠁⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠈⣷⡀⢻
⢻⡀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⢰⡏⠀⠀⠉⢷⣾⡿⠁⠀⠀⢹⡆⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸
⠸⣧⠘⣧⠀⠀⠀⠀⠀⣾⡿⡷⠀⠀⠀⠀⠀⠀⠀⠙⣾⣧⡀⠀⠀⠈⣿⡇⠀⠀⠀⣼⠟⠋⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⢠⡾⢡⡟
⠀⣿⠀⣿⠀⠀⠀⠀⠀⠻⠷⣤⣤⣀⣀⡀⠀⠀⣠⡴⠾⠿⣿⣦⣤⣶⣿⣧⣀⣴⡾⠷⠶⢦⣄⠀⠀⠀⢀⣀⣠⣤⠟⠁⠀⠀⢠⡿⠀⣿
⠀⡿⠀⢹⠀⠀⣾⣿⠆⠀⠀⣀⣈⣩⣭⣽⣿⣿⡏⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢹⣶⣟⣛⣋⣉⠁⠀⠀⠠⣾⣷⠘⣧⠀⣷
⢸⡇⠀⢸⡆⠀⠈⠁⢀⡴⠛⠉⠉⠉⠀⠀⠀⠘⢷⣄⣀⣠⣴⡾⠟⠿⣿⠛⠻⢶⣤⣤⣠⡴⠟⠉⠉⠉⠉⠉⠙⠻⣦⠀⠉⠁⠀⢻⡀⢻⡆
⢸⡇⠀⢸⡇⠀⠀⠀⠘⢷⣴⡶⠀⠀⠀⠀⠀⠀⣀⣤⠿⣿⠋⠀⠀⠀⣿⠀⠀⠀⠈⢿⡟⠳⠶⣤⣄⣀⠀⠀⣴⣤⣼⠇⠀⠀⠀⢸⡇⠈⣷
⠈⣷⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠋⠁⠀⣧⠀⠀⠀⣸⣿⣧⡀⠀⠀⣸⠇⠀⠀⠀⠈⠉⠛⠶⣌⠉⠁⠀⠀⠀⣀⣼⠃⢠⡟
⠀⠘⢷⣄⠀⠙⠷⢦⣤⣤⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⣠⣿⠷⠶⠾⠋⢸⡏⠙⠛⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣶⣿⣯⣤⡶⠟
⠀⠀⠀⠙⠛⠶⠶⢶⣿⡏⠀⠀⠀⠀⠀⣀⡀⠀⣠⡾⣻⠏⠀⠀⠀⠀⣸⠃⠀⠀⠀⢿⡝⣧⡀⠰⢶⡄⠀⠀⠀⠀⢻⡎⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣿⢹⣇⠀⠀⠀⠀⠸⣯⣡⡾⠋⣰⠏⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⡈⣷⠈⠛⠶⠞⠁⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠙⢶⣄⣀⠀⠀⠀⢀⡀⠀⣿⣀⣶⡄⠀⠀⢸⡇⠀⠀⠀⠻⣷⡿⠀⢴⣶⠀⠀⠀⠀⠀⢀⡾⠁⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠈⠉⠛⠷⣦⡿⠿⠀⠘⠻⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣡⡴⠶⠶⠶⠶⠟⠁⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣀⣤⡴⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠈⢷⡄⠀⠀⠀⠀⠀⣠⣾⣿⡿⣦⣀⣀⣤⡾⠃⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠙⠷⢦⡴⠶⠛⣡⠟⠀⠹⣦⣉⣉⣁⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⡴⠞⠋⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⣴⡘⠃⣴⣧⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣴⡇⢿⣦⠀⣿⣃⡄⠛⢘⣡⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⣴⡇⠻⠀⣉⠉⠁⠀⠉⠋⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⠃⠠⠏⠁⢀⠠⠀⠀⠀⠆⡀⢀⠆⢠⠀⠧⡠⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⠠⠀⠀⠀⠉⠀⣤⡄⠀⠀⠁⢀⠀⠆⠄⠙⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠄⡤⠀⠴⠆⠀⠀⠈⠐⠃⠄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠠⠀⡀⢠⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⠀⣀⢀⠀⢀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣾⢃⣠⣀⣀⡸⠗⣟⠀⠀⠘⠀⠐⠂⠒⢣⠈⠯⠄⢤⠜⡈⣩⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠚⠋⢁⣴⠄⠈⣉⠁⠸⠁⠰⠌⠂⠶⠣⠔⠠⡤⡀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠐⠛⠋⣴⠂⠉⠀⣀⠘⢀⠈⢲⠕⠦⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁⡐⠀⢀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢴⠧⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠭⠍⠑⠀⠈⠊⢫⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣳⠀⠰⣄⠀⠀⠐⣒⠈⠅⠒⠂⠑⡦⠈
⠀⠀⠀⠀⠀⠀⢰⣶⢰⣶⡄⢰⣶⢰⣶⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠧⠐⣌⠳⣄⡉⠀⠀⠀⠁⠤⠁⠎⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⢿⣾⣿⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠢⢄⣸⣆⠲⣭⡑⠀⡈⠙⢂⡖⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠸⠟⠘⠟⠀⠙⠟⠘⠿⠀⠛⠷⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠾⠋⠀⠁⢀⣜⣵⠟⠁
⠀⠀⠀⠀⠀⠀⢸⠛⣦⣾⡏⢰⣿⣸⣧⡞⢛⣸⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⣛⡛⢂⣀⠠⠀⢙⣩⣴⡞⠁⣰
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠙⠛⠘⠛⠉⠃⠙⠛⠉⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠉⠁⠀⠐⠘⢉⠽⠋⢠⠞⠁
⠀⠀⠀⠀⠘⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣀⣀⡀⠀⠈⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣄⣤⠾⠋




⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈



⠀⠀⠘⠛⠻⠶⢦⣄⣒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣭⣳⣦⣀
⠀⠀⣀⠀⠀⠤⣄⡀⠁⣦⡀⢂⠝⡻⣿⣷⣦⡀
⠀⠸⣿⡟⠛⠲⠦⠉⠻⢷⣭⡳⢕⡮⡈⢻⢿⡻⣷⣄
⠦⣄⠙⢷⣄⠀⠀⠀⠀⠠⢙⠻⣦⡙⢮⡲⡕⠻⢾⢿⣷⡀
⠢⠤⠀⠀⠙⢷⣄⠐⣶⣤⣌⠳⣌⡳⡄⠙⢮⠳⡈⠂⠻⣿⢆
⠛⣛⣓⠦⢄⠀⠉⠳⣌⢿⡛⠻⢦⡻⣌⠀⠀⠳⡱⡣⡄⠹⡇⠱
⠋⠉⣉⣉⣀⡀⠀⠀⠈⢦⢻⡄⠀⠙⣮⠳⡀⠱⡘⣴⢹⡄⢻⡄⠠
⠛⣋⣥⡤⢤⣉⠳⣌⢥⡀⠁⢳⠀⠀⠈⢧⠀⠀⢳⠸⡆⢷⠈⣷
⠉⣁⣀⣠⠤⣤⡙⢌⢫⠆⠆⠀⠆⢸⣦⠈⡇⠀⠸⡇⣷⢸⡆⢹⡄
⣉⣉⡡⠤⢤⣄⠹⢨⠈⠀⠀⠀⠀⣿⣿⡇⠁⠀⠀⡇⣿⠘⠃⠈⡇
⣤⣤⣤⣤⡀⢹⠀⡞⠀⠀⠃⢀⣾⠏⢹⡇⠀⡇⡇⡇⡇

⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⢀⣀⣆⢰⡀⢰⡾⠋⢹⡔⠶⡄⢀⡰⢀⡔⠛⢢⡀⢆⡀⢠⡶⢦⡞⠻⢷⡄⢀⡆⣰
⢤⡀⠀⠀⠀⠉⠉⠛⠦⣧⣠⠳⢴⣾⣦⠀⠿⠯⠴⠿⢅⡀⣠⠿⠬⠽⢿⠀⢠⣷⣦⠴⣀⣌⠠⠟⠃⠉⠀⠀⠀⠀⣠
⠈⠣⠰⣄⡀⠀⠀⠀⡀⠈⢧⣤⣈⠛⣁⣀⣀⣀⡸⠀⠀⣬⠁⠀⣖⣀⣀⣀⢉⠛⣁⣠⡼⠃⢀⠀⠀⠀⠀⣠⠞⠐⠃
⠀⠀⠀⣸⠷⠄⠐⣾⣥⣀⡀⠀⢀⣼⣭⣭⠽⢛⣁⣀⠀⠞⢀⣀⣈⠻⢿⣉⣉⣦⡀⠀⠀⣀⣨⣶⠒⠀⠾⢏
⠀⠀⠀⠀⠀⠠⠖⠋⠻⣍⡛⡖⢡⠇⣼⡧⣦⣤⣌⠚⠀⡅⡑⠒⣩⣤⣴⢽⣇⢹⡌⢲⠟⣫⡿⠉⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠚⠛⠓⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠒⠛⠓⠓⠚⠋⠁










⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⠀⡄⢤⣶⠶⠒⠒⡒⠒⡶⣶⠒⢒⠒⠒⠶⣶⡤⢤⠄⣤⣄⡀
⠀⠀⠀⢀⠀⠀⠒⢤⣴⣯⣴⠟⢦⢻⣈⣿⡙⠏⣉⡥⢴⠄⠅⣠⣌⡉⠩⢝⣿⣁⡟⡐⢳⣬⣻⣦⡴⠒⠀⢀
⠀⠀⠀⢩⡿⠃⠐⠺⣫⠁⠀⣀⣀⡙⢯⣭⣽⣷⣄⠀⠀⢰⠆⠈⠀⣡⣶⣯⣭⡽⢋⡀⡀⠀⠉⡻⠓⠀⠻⣯⠁
⢀⡶⠰⠋⠁⠀⠀⠀⠀⢀⣾⠉⢁⣴⣦⠀⡀⠀⠀⠇⠀⣸⣁⡀⠼⠁⠉⠉⢀⣰⣭⠉⢙⣇⡀⠀⠀⠀⠀⠈⠳⠀⣦
⠘⠁⠀⠀⠀⢠⣄⢴⡞⣿⠁⣱⠊⠻⡟⠀⢸⠿⣌⠻⣍⠁⠈⣰⠟⣓⢾⡃⠘⢻⠟⠳⣌⠙⡝⢲⣄⣠⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠇⠀⠻⢷⡤⠋⠚⠋⠀⠈⠃⠈⢴⡦⠁⠘⠁⠀⠙⠗⠫⣤⣾⠟⠀⠸⠘⢣
⣀⣀⣀⣀⣀⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣊⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣤⢤⡴⢦⣔⠢⡤⠤⠤⠤⠤⠤⣤⢄⢤⡤⢤⣀⣤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣳⣞⣶⣶⠟⠙⠻⠋⠀⠀⠀⠀⠀⠘⠻⠛⢷⣶⣾⣷⣏⡽
⠀⠀⠀⠀⣿⢉⡓⠺⣛⣹⣏⠁⠙⣙⢻⣇⣼⡛⣋⠋⢌⣿⣏⣻⠖⢛⡩⡇⠀⠀⠀⢀⠷⢹⡎⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⢻⡏⣿⡕⢧
⠀⠀⠀⠀⣿⠈⠈⠤⣻⣤⣍⣏⣼⣾⣭⣿⣿⣭⣷⣡⣛⣩⣴⡃⠄⠉⠁⡇⠀⠀⠀⠨⢷⡏⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣷⢿
⠀⠀⠀⠀⢿⠀⠀⠀⢿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠁⠀⠀⠀⡇⠀⠀⠀⠘⡮⠗⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠿⡼
⠀⠀⠀⠀⢸⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠘⣆⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇
⠀⠀⠀⠀⢠⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢸⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⢸⠂⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⢸⣇⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠘⢸⠀⠀⠀⠀⢰⢻⣶⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣴⡧
⠀⠀⠀⠀⢸⢠⣀⠠⣸⠟⢛⡟⢻⣿⣻⣿⣿⣛⡿⡛⣟⡛⠻⣥⠀⢸⢸⠀⠀⠀⠀⢸⠾⣧⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣨⡿⣟
⠀⠀⠀⠀⣼⣛⣧⣤⣟⣺⡏⠁⣀⣫⣙⠟⢿⣉⣋⡀⠈⣿⣛⣳⣤⣜⣘⣆⠀⠀⠀⠸⣖⣿⣧⣿⡤⠤⢤⣤⠤⢤⣤⡴⣶⡶⠶⣶⣶⣶⣾⣿⣿⡰⡎
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠙⠛⠉⠉⠉⠛⠛⠉⠉⠙⠛⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⣃⢿⡷⢟⠿⣦⣴⣶⠄⠀⠀⠀⠀⠀⣤⣴⣠⡾⠿⢿⡿⣍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠉⠉⠒⠛⠒⠚⠁⠀⠀⠀⠀⠈⠓⠒⠚⠓⠋⠉⠑⠙⠃
⠀⠀⠀⠀⠀⡞⣛⣿⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣾⣟⢳⡀
⠀⠀⠀⠀⠀⣿⢿⣁⢻⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣟⢌⣹⢿⠀⠀⠀⠀⠀⡖⡒⠒⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠲
⠀⠀⠀⠀⠀⣿⠀⠝⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠋⠀⣿⠀⠀⠀⠀⠀⡇⠀⠾⣀⡠⢀⠀⡴⠤⠤⠶⠤⠤⠤⠤⠤⠤⠤⠶⠀⡠⢄⣈⠷⡢⢰
⠀⠀⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠄⠀⢨
⠀⠀⠀⠀⢠⠧⡐⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠒⠸⡄⠀⠀⠀⠀⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⢈
⠀⠀⠀⠀⢸⠗⠐⢢⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⡔⠒⠐⣇⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢘
⠀⠀⠀⠀⠈⡏⠐⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⠒⢸⠁⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠸
⠀⠀⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⣸⠀⠀⠀⠀⠀⡇⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸
⠀⠀⠀⠀⠀⣿⢀⣷⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⢷⣀⢿⠀⠀⠀⠀⠀⡇⢀⢀⣧⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⡼⡀⠀⠸
⠀⠀⠀⠀⠀⣿⣯⣄⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢷⣢⣼⢿⡀⠀⠀⠀⠀⡇⠀⠛⠄⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠠⠛⠁⢰
⠀⠀⠀⠀⠀⠷⠶⠿⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠿⠷⠾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠿⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡀⣀⣠⣴⣦⠶⠖⠚⠛⠛⠻⢷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣾⣿⣿⡯⢥⡶⠄⠢⠀⠀⠀⠀⠀⠀⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣀⡀⠀⠔⠒⠄⠀⠀⠀⠀⠀⠀⢻⡇⠀⠐⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣇⡾⠃⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣿⠁⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠒⠀⠀⠀⠀⠠⢄⠀⢸⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠴⢒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣼⠃⠀⠀⢀⣀⠈⠀⣤⠀⠀⠀⠀⠀⠀⠈⠻⡧⣄⡀⠀⢀⣀⡀
⠀⠀⠀⣠⣤⡄⣀⣀⣀⣀⣿⠀⡠⣚⠉⠁⠀⠠⣼⣄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠉⠉⠉
⠀⣠⣾⠋⣱⠋⠁⠀⠀⠈⢿⣿⠧⣄⠀⠀⠀⠀⠘⠀⠀⠀⡞⠉⠁⠀⠀⢸⡇⠀⠀⢀⡶
⢰⠏⠁⠀⠀⠀⢀⠀⠀⠀⢸⡇⠀⠈⠻⣦⠀⠀⠀⣠⢄⣀⡀⠀⠀⠰⠇⢸⠁⠀⠀⢸⠃
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣆⠁⠀⠀⠸⣷⡀⠄⣠⠀⡀⠀⠐⣴⠓⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠘⣇⠀⠀⠀⡅⢀⣼⠁⠉⠀⠘⠇⠀⠀⠀⠀⠀⢀⠤⠤⠤⣀⠉
⠀⠀⠈⠛⠒⠒⠀⠀⠰⠀⠀⠀⠀⢻⡄⠀⠀⣆⢹⠀⠀⢆⣄⡞⣁⠠⠤⣔⡁⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢻⣆⠀⠙⠸⡇⠀⣼⣾⡞⠃⠀⠀⠈⠉⠁⠀⠀⠀⠘⣏⠀⠀⠔⠛⠁⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣦⣙⣦⡀⠀⢳⠀⣿⡿⢐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣆⡈⢧⢹⣷⠉⠁⣀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣳⣿⣦⠀⠀⠀⠀⠁⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣀⠀⠀⠀⠀⣠⢃⣠⠄⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠾⢍⣁⣁⣁⡤⠤⠴⠚⠉

⣿⠙⠉⠙⠋⠛⠋⠙⠛⠛⠋⠛⠛⠋⠉⠉⠙⠛⠙⠛⠙⠉⠛⠛⠙⠋⠛⠛⠉⠛⠉⠛⠋⠋⠋⠙⠛⠉⠉
⣧⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⡏⠀⠀⢸⢠⣶⠶⢦⠀⡂⠴⢢⢒⣠⣤⠀⢢⠞⠉⠀⠀⠈⠻⡄⠂⣤⣌⠒⡴⠦⢄⠀⣵⣦⢶⡄⡇
⣇⠀⠀⢸⡸⣷⣆⣻⢀⣀⣛⣈⣉⣙⣋⣀⡏⠀⠀⠀⠀⠀⠀⢹⣀⣙⣋⣉⣁⣛⣀⡀⣟⣦⣽⠆⡇
⣟⠀⠀⢸⠰⠀⠴⢰⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⡆⠦⠀⠂⡇
⡿⠀⠀⢸⠴⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣿⠆⡇
⡿⠀⠀⢸⢀⡀⡛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢟⢐⠀⡇
⣷⠀⠀⢸⠈⣡⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⣌⠁⡇
⣿⠀⠀⢸⠀⠛⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⠛⠀⡇
⡿⠀⠀⢸⠤⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢮⠄⡇
⣿⠀⠀⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇
⣿⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣯⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡗⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐
⣧⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⣏⠀⠀⢸⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡇
⣯⠀⠀⢸⠉⢝⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡥⠁⡇
⣟⠀⠀⢸⠀⣶⣦⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣶⠀⡇
⣟⠀⠀⢸⢠⢌⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽⠣⡄⡇
⡿⠀⠀⢸⠀⣢⡶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢶⣐⠀⡇
⡷⠀⠀⢸⠘⠿⠗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠼⠿⠃⡇
⣷⠀⠀⢸⡘⣠⣙⣘⢻⣆⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⡟⣃⣋⣀⠁⡇
⡇⠀⠀⢸⢸⡯⡁⢺⠀⡔⠶⢠⠤⣴⣦⠀⢧⠀⠀⠀⠀⠀⠀⣼⠀⣴⣦⡤⡄⠶⢄⠀⣷⡁⣽⡃⡇
⣿⠀⠀⢸⣈⣙⣛⣋⣀⣊⣙⣙⣒⣉⣉⣐⣈⣳⣤⣀⣀⣠⣾⣁⣂⣉⣡⣒⣛⣛⣲⣀⣙⣟⣓⣁⡇
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⣹⣿⣿⣿⣿⣿⣿⠟⠂
⣷⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⣍⠀⢀⣴⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣦
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠉⣿⣿⣿⣿⣿⣿⣟⠉⠉
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣶⡿⠿⠛⠴⣿⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠁
⣽⣿⣿⣿⣿⣿⠟⠋⠁
⣉⣹⣿⣿⠿⠇
⡿⢻⣿⡎⠀⠀⠀⠀⠀⢠⣴⣦⣶⣿⣿⣭⣄⡀
⣅⢸⣿⣇⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛
⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠹⣿⣸⣄⠀⠠
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠉⢿⣿⣦⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠉⠛⠛⠿⣿⣿⣿⣿⣏⠀⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀
⢀⡀⠀⠀⠀⠀⠀⠀⣀⣬⠟⣿⣿⣿⣿⣿⠟⠇
⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠅⠀⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡀⠀⠢⠲⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠆⠲⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⠉⠉⠉⠰⣄
⠀⠀⠀⡀⠁⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⡦⠐⠀⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⣀⣀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡼⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠴⠀⠀⠒⠚⠛⠒⠦⠀⢉⡄⠀⠀⠀⠀⢌⠁⢠⠶⠀⠉⠁⠐⢦⡀⠈⠰⠤⠤⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠩⠉⠀⠀⢀⡄⠀⠀⠀⠀⠀⣄⠀⠀⠈⠁⠊⠁⠀⠀⣠⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠈⡀⠀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠖⠒⠓⠛⠒⠒⠀⠀⠈⠲⢦⣤⠶⠉⠀⢠⣀⠀⢠⡄⠀⡠⠄⠀⠃⠀⣄⣤⠀⠛⠀⠘⡶⠚⠋⠁⠛⠒⣿
⠀⠀⢸⡇⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣻
⠀⠀⢰⡇⠀⠀⠀⠀⢸⠀⠀⢠⠆⠒⣒⠒⡦⠀⠘⠂⠀⠀⠀⠀⠀⠃⠀⡄⡤⠀⠆⢠⢤⠀⢠⠇⠀⠀⠀⠀⠀⣯
⠀⠀⠘⡃⠀⠀⠀⠀⢘⠃⠀⢸⠀⠀⠀⠀⠁⠀⢠⠐⠀⠰⡆⠀⢣⡄⠀⠃⠉⠀⠀⠈⠉⠂⠈⣗⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠉⠉⠃⠜⠉⠉⠀⠀⢷⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡁⠘⠯⠽⠎⠯⠾⠭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⣀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠲⠖⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠒⠆⠚⠚

⠀⠀⠀⠀⢀⣀⢀⣀⢀⣀⠀⠀⠀⡀⠀⣀⡀⠀⡀⠀⠀⢀⠀⣀⣀⠀⡀⠀⠀⢀⡀⣀⣀⢀⣀
⠀⠀⠀⠀⣣⠊⠉⠈⠉⢣⡃⠀⠀⠉⠀⠀⠀⠈⠁⠀⠘⠉⠉⠉⠉⠉⠉⠃⠀⢹⠝⠉⠉⠙⣿
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠸⢆⠀⢠⡆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢽⠀⠀⠀⠀⢸⠅⠀⠀⠅⠀⠀⠀⠀⠅⠀⠘⠲⠒⠶⠶⠒⠖⠂⠀⠾⠕⠦⠤⠮⠿
⠀⠀⠀⠀⠯⠵⠲⡰⠶⠮⠅⠀⠀⠓⠒⠶⠖⠒⠂⠀⡄⠀⠠⠀⢀⣀⣤⣀⡀⠀⡠⠶⠶⠦⣀
⠀⠀⠀⠀⢠⡤⠴⠤⣄⠀⠀⠰⠒⠒⠐⠂⠰⠆⠀⠀⡇⠀⠀⠀⢈⡅⠀⠈⡇⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠀⢘⠇⠀⠀⡇⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠹⠤⢤⠤⠜⠁⠀⢀⠀⠀⠀⠀⢀⡂⠀⠀⡇⠀⢀⡀⠈⠓⠒⠚⠃⠘⠇⣀⣀⣀⠟
⠀⠀⠀⠀⣶⠶⠶⢶⡆⠀⠀⣠⡉⠉⠉⣩⡉⠀⠀⣀⠀⠤⠄⠀⣀⠀⠀⡤⠄⠀⠀⠉⠉⠡⢤
⠀⠀⠀⠀⣸⣀⠀⣸⡃⠀⠐⣿⡀⠀⠀⣸⡗⠀⠸⣀⠀⠀⠀⠀⣸⠂⠀⡁⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠆⠻⠂⣤⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣠⣤⡀⠀⠴⠂⠀⠀⠀⢀⡜⡿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠖⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴
⠶⣶⣿⣕⣽⣿⠀⠒⠋⠀⠀⢠⢏⡾⢡⢫⡟⡴⡦⠀⠀⠀⠀⠀⢀⣴⡿⠛⣿⠟⢀⣴⠾⣿⣿⣿⠇⠀⠀⠀⣀⣠⣤⣴⢶⣶⠾⠟⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠉⣿⣿⡟⠀⠀⠀⠀⡰⣣⡟⡱⣱⢏⢞⡽⢡⢶⠀⠀⠀⣠⠞⠋⠓⢚⣩⠾⢿⣁⣀⡼⠟⣋⣤⣴⣾⣿⣿⡿⠋⠀⢸⣏⠀⠀⣠⣿⣿⣿⡿⠋
⠀⠀⠀⣿⣿⠁⠀⠀⢀⡜⣵⣟⢜⡼⣣⣫⡞⡱⢣⠟⣰⣶⠰⠋⠀⣠⡴⠋⠀⠀⣀⣬⣴⣾⣿⠿⠿⠿⠿⠿⠿⠷⠼⣀⣀⣙⣛⣛⣛⣉⣉⣀⣠⣤⣴
⠀⠀⢰⣿⡇⠀⠀⢀⢞⣾⢯⣪⢟⣵⣽⢋⢜⡵⣫⣪⣾⠋⣀⡠⠞⠁⢀⣠⡶⠟⠛⠉⠁⠀⢀⣀⣤⣤⣶⣶⣿⣿⠟⠉⢉⣿⠋⠉⠉⣿⣿⣿⣿⡿⠋
⠀⠀⣾⣿⠀⠀⢠⣿⣿⣳⡿⢫⣮⡿⣵⣵⣫⢞⣿⢟⡵⣫⡿⠃⠠⠞⠉⠁⠀⠀⣀⣤⣶⣿⡿⠿⠿⠿⠿⢿⣿⣧⣐⡆⠈⠿⣷⣶⣾⣿⠿⠟⠋
⠀⢠⣿⠇⠀⣰⡏⢙⡻⢿⣷⣿⣯⣫⣿⣿⡿⣻⢕⣥⠾⣋⣤⣤⠀⠀⢀⣤⠶⠛⠋⠉⠀⠀⠀⠀⢀⣀⣀⣀⣤⣭⣭⣤⣤⣤⣤⢤⣤⣤⣶⣶⣶⣶⡶
⠀⣼⡿⠀⢰⣿⣿⣿⣷⣶⡙⢿⣿⣿⢿⢯⣪⡶⣋⢵⣺⡿⣟⣡⣄⠚⠉⠁⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⣁⠀⢾⣧⣀⢀⣽⣿⣿⣿⡿⠋
⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣯⣤⠹⣿⣷⣯⣷⡯⣟⡯⢗⣫⡵⠞⠁⢀⣤⠶⠛⠋⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⣙⣛⣋⣀⣀⣙⣛⣛⣛⣛⣋⣉⣀⣀⣀
⢰⣿⣇⠀⢸⣿⣿⢋⣍⢻⣿⣷⡆⢿⣟⣯⣷⣯⣷⠾⢯⣷⣾⡿⠂⠈⠀⢀⣀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⢛⠉⣹⣿⠛⠙⠻⣿⣿⣿⣿⣿⣿⡟
⣸⣿⣿⣄⠈⢻⣿⣦⡼⢸⣿⣿⠆⣸⣿⣯⣭⣴⡖⠛⠯⣭⣤⡄⠠⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⢈⠉⠙⠛⠻⠼⠃⠛⠿⣦⣤⣶⣿⣿⣿⣿⠿⠋
⢿⣿⣿⣿⣷⣤⣬⣭⣴⣿⣿⣿⠄⣿⣿⣷⣶⠶⠿⠿⠟⣍⡉⢀⣠⡤⠴⠶⠶⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢙⣿⣷⣶⣶⣶⣬⣥⣉⣀⡀
⢸⣿⣿⣿⣿⣿⡏⡛⠿⠟⠿⢀⣾⣿⣿⣛⣛⣛⠿⢿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣇⢲⡄⢸⣿⠉⠈⠉⢻⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠻⣿⣿⣿⣿⣇⢹⣶⣶⣿⣿⣿⡿⣿⣭⣛⣩⣭⠙⠉⠈⠉⠉⠙⠛⠛⠛⠻⠿⣿⣶⣶⣶⣶⣦⣤⣤⣍⣉⠀⠈⠻⢷⣶⣴⣾⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠈⠛⠻⠿⠿⣿⣿⡿⣿⣿⢯⣟⠶⠿⠆⢩⣥⠤⠤⠶⠶⣶⣶⣶⣤⣤⣤⣄⣀⡈⠉⠛⠿⣿⡟⣍⠉⣽⣿⠿⠷⣶⣤⣭⣉⡉⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣶⣦⣬⣙⠛⠀⢿⣧⡀⠀⠀⢹⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠩⡈⢿⣿⣶⣤⡙⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⣠⣾⣿⡿⠋⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⣠⣾⣿⠿⠃⠀⠀⢹⣿⣷⡀⠀⢹⣿⣿⡀⠀⠸⣿⣿⡄⠀⠸⣿⣿⡄⠀⠘
⣿⡿⠋⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⣠⠾⠛⠉⠀⠀⢀⣀⠀⠀⢿⣿⣇⠀⠀⢿⣿⣧⠀⠀⢻⣿⣷⠀⠀⢻⣿⣷
⠋⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠄⠀⠘⣿⣿⡄⠀⠘⣿⣿⡆⠀⠈⣿⣿⣇⠀⠈⣿⣿⣇
⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⣀⣠⣶⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⢹⣿⣿⡀⠀⢹⣿⣿⡀⠀⠸⣿⣿⡄⠀⠸⠿⠋
⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⣀⣤⣶⣿⣿⣿⠿⠛⠉⠀⠀⣀⣤⣶⣿⣇⠀⠀⢿⣿⣧⠀⠀⢿⣿⣧⠀⠀⢻⣿⣷⠀⠀⠀⢀⣴
⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⣠⣾⣿⡿⠿⠛⠉⠀⠀⣀⣤⣶⣿⣿⡿⠟⠋⠁⠀⠀⠘⣿⣿⡄⠀⠘⣿⣿⡆⠀⠈⠋⠀⠀⣠⣴⣿⣿
⠀⢀⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⢠⡾⠟⠋⠉⠀⠀⣀⣤⣶⣿⣿⡿⠟⠋⠁⠀⠀⣀⣤⣶⠀⠀⢹⣿⣿⡀⠀⢹⣿⠟⠀⠀⢀⣤⣾⣿⡿⠛⠁
⣴⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⣀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡿⠟⠋⠁⠀⠀⣀⣤⣶⣿⣿⡿⠟⠃⠀⠀⢿⣿⣧⠀⠀⠁⠀⣀⣴⣿⣿⠟⠋⠀⠀⣠
⣿⠟⠁⠀⢀⣴⣿⣿⠟⠁⠀⠀⣾⣿⣿⣦⣄⡀⠀⠀⠉⠋⠁⠀⠀⣀⣤⣶⣿⣿⡿⠟⠋⠁⠀⠀⣠⡄⠀⠘⠟⠋⠀⠀⣠⣾⣿⡿⠟⠁⠀⢀⣴⣿⣿
⠁⠀⢀⣴⣿⣿⠟⠁⠀⣀⣀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠀⠉⠛⠿⠟⠋⠁⠀⢀⣠⣤⣾⣿⣿⡷⠀⠀⠀⢀⣴⣿⣿⠿⠋⠀⠀⣠⣶⣿⣿⠟⠁
⢀⣴⣿⣿⠟⠁⠀⠀⠺⢿⣿⣿⣶⣤⣀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠰⢾⣿⣿⡿⠟⠋⠁⠀⠀⣠⣾⣿⣿⠟⠁⠀⢀⣴⣾⣿⡿⠋⠀⠀⣠
⣿⣿⠟⠁⠀⣠⣤⣀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠈⠁⠀⠀⠀⢀⣴⣾⣿⡿⠋⠀⠀⣠⣴⣿⣿⠟⠉⠀⢀⣠⣾⣿
⠟⠁⠀⠀⠘⠻⢿⣿⣿⣶⣤⣀⠀⠀⠈⠙⠻⣿⣿⣿⣶⣄⡀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠀⠙⠻⠟⠉⠀⢀⣤⣾⣿⡿⠛⠁⠀⣀⣴⣿⣿⠿⠋
⠀⣠⣶⣦⣄⡀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠀⠙⠛⢿⣿⣿⣶⣤⣀⠀⠀⠀⠐⠻⢿⠟⠋⠀⠀⣠⣾⣿⡿⠟⠁⠀⢀
⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠀⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠰⢿⣿⡿⠋⠀⠀⣠⣶⣿
⣦⣄⡀⠀⠀⠉⠛⢿⣿⣿⣷⣦⣀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠁⠀⠀⣤⣾⣿⡿⠋
⠿⣿⣿⣷⣦⣄⡀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣄⡀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠉⠉
⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⠀⠀⠉⠛⠿⣿⣿⣷⣦⣄⡀⠀⠀⠉⠛⢿⣿⣿⣷⣦⣀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣪⣵⡾⠷⢶⡭⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣹⡟⠁⠀⠀⠀⠙⡌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣏⣓⢦⡀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⡷⠿⣻⣿⣸⠛⣇⠀⢀⣟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣽⠞⠉⠀⠀⢈⠝⣡⣾⣿⡤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠖⠋⠀⠀⢀⡤⣚⡵⠞⣽⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣭⠞⠁⠀⢀⡠⢖⣽⠞⠉⢀⢾⠏⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠵⠋⠀⠀⣠⣖⣭⠞⣻⠏⠀⢀⣾⡟⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⣠⣔⡿⠞⠉⠀⣸⠏⠀⢀⣮⡟⡇⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⣠⣴⡿⠞⠉⠀⠀⠀⣴⠏⠀⢀⢮⠟⠘⡇⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣾⠟⠁⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⣸⠏⠀⢠⢫⠏⠀⡆⡇⠀⡇⡇
⠀⠀⠀⠀⠀⠀⣀⣴⣾⡯⠵⠒⠲⣼⡿⣅⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⣰⢣⠏⠀⠀⢱⡇⠀⣧⡇
⠀⠀⠀⠀⣠⣞⡵⠛⠁⠀⠀⠀⠀⡸⢠⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⣣⠏⠀⠀⠀⢸⡇⢠⢻⠃
⠀⠀⢀⢞⡵⠋⠀⠀⠀⠀⠀⠀⢰⠃⡞⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣰⣳⠏⠀⠀⠀⠀⢸⡇⢸⢸
⠀⢀⣏⡞⠀⠀⠀⠀⠀⠀⠀⣰⢃⡜⢁⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⠷⢷⣴⣿⠏⠀⠀⠀⠀⠀⢸⡇⢸⢸
⠀⢰⡿⠀⠀⠀⠀⠀⠀⢀⠔⡡⠋⡠⣿⡟⠀⠀⠀⠀⠀⢀⡴⣫⠴⠚⢯⢹⣿⣆⠀⠀⠀⠀⠀⢸⡇⢸⣿
⠀⠈⢿⣄⠀⠀⣀⡠⢖⣵⣪⠴⣫⡾⠋⠀⠀⠀⠀⠀⢀⣞⡼⠁⠀⠀⢸⢀⡇⢻⡆⠀⠀⠀⠀⢸⡇⠸⣿
⠀⠀⠀⠙⠛⠿⠿⠿⠭⠥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⡼⣸⠁⠘⡇⠀⠀⠀⢠⣾⠽⢿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⣰⣷⠇⠀⣸⠃⠀⠀⢠⣿⠃⠀⠈⣿⡜⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⠀⢀⡴⡿⠋⢀⣴⠃⠀⠀⠀⢸⣿⠀⠀⠀⢹⡇⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣽⠮⢴⣺⠟⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⣸⠃⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢧⣣⣀⣴⣟⣴⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣉⣁⣀⣀⣀⣀⣀
⣿⣿⠋⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣬⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢻⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⠛⠙⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣄⠀⠀⠀⠃⢹⡀⠚⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣤⡤⡀⠀⠄⢀⡀⣄⡃⠀⠈⠔⠛⣴⣎⡠⢚⣇⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠉⠀⠀⠀⠈⡄⠘⡄⠈⠃⠁⠀⠀⣇⣀⣰⠙⠁⢘⣥⠀⣠⠃⠀⠀⠒⡟⠁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠙⠀⠨⢶⡷⢆⠀⢹⣿⠑⠈⠃⣦⣨⣟⠲⢯⡀⠀⠠⢜⠀⢠⠄⠀⠀⠂⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢧⢀⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⣼⣆⠀⣠⡇⠀⡅⠈⠸⢡⠾⠇⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⢯⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢭⣧⣝⣇⠀⢁⣀⣶⡟⣀⣤⡆⠀⠀⠀⠀⡄⣥⠉⠀⠀⡾⠀⢠⠃
⠀⠀⠀⠀⠀⢀⡠⢤⣌⢧⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⠛⠻⢷⣾⣿⣿⡤⠤⠤⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⡞⢀⡀
⠀⠀⠀⠀⢠⠎⠀⢛⠀⠈⢳⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⣇⣀⡴⣀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⢸⠀⠀⠈⠲⠤⣀⣹⣆⠢⡀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⡰⠋⢀⡀⠀⠀⠀⠀⠀⠀⢤⣱⣤⣿⣿⢿⡿⣡⠦⣤⡀
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠢⣩⠐⢌⡂⠀⣀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠲⣤⠛⠙⢿⣥⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢌
⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠈⢧⡀⠙⠢⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⡿⠻⢿⠃⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠻⡄⠀⢙⣦⡙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠈⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠖⠉⠉⠀⠀⠀⢠⠟⠂⠀⠈⠑⢦⣈⠉⠙⠃⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡀⠀⢤⡀⠀⠀⠀⢠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠄⡀⠈⠓⢤⠀⣀⠔⠁⠀⠀⠀⠀⠑⠦⣈⣙⣶⠦⠶⠶⠶⠛⠒⠒⠒⠒⠒⠲⢴⠀⠀⠀⠀⢀⠔⠉⢷⡀⢀⣵⡄⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠓⠌⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⠎⠁⣄⣀⡀⠀⠀⠐⠒⠒⠒⠠⢤⡴⠃⢀⠀⢀⡔⠃⠀⠀⣿⣩⣏⣑⣷⢠⠀⠰⠂
⠀⠀⠀⠢⠴⠦⠄⠠⠦⣀⡀⠠⠀⠂⢀⠄⡔⠀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠚⠀⠈⠉⠉⠙⠒⠾⢁⠀⠹⢯⠿⣼⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠉⠚⠑⠂⠌⠾⠶⠍⠛⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⡮⠀⠀⠈⢶⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠆⠄⠀⠀⠀⠀⠀⣉⠉⠉⠁⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⢀⡀⠤⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⡿⠁⠀⠀⠉⠉⠜⠉⠉⣩⠟⠛⠛⢛⠗⠒⠒⠲⠖⠺⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣀⡠⠀⠰⠁⠀⠀⠀⣼⢻⡈⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡩⠋⠀⠀⠀⠀⢀⢀⠀⢷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠘⣆⣂⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⡜⠁⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⡄⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣠⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⣄⠀⠀⠀⣾⡆⠙⠁⣼⡿⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣧⣾⡇⢿⣷⡄⠀⣿⡇⢀⡀⠛⠁⢛⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢏⠋⣠⡎⠻⡇⠀⠹⠻⠛⠁⢂⠾⠿⠿⠋⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⡀⠀⢀⡿⠇⠀⠁⠀⠒⠃⠉⠀⠀⠀⠀⠀⠀⠠⠀⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⠁⠀⠒⠀⠀⢀⡤⠑⠀⠀⠀⠀⠀⣀⠀⠈⠃⠀⠆⠀⡗⠀⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊⠀⠄⠀⠀⠀⠈⠁⠀⣠⣄⠀⠀⠀⠁⠀⠀⠀⠆⠤⠔⠉⠓⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠁⠀⠀⠘⠋⣴⠂⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠆⠀⠐⠀⠂⠀⠆⠀⠦⠀⠀⠀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⣵⠄⠀⠀⠀⠀⠰⣿⢰⡟⠀⠀⠀⢹⠀⠀⢤⠌⠤⠖⠀⠒⣞⡁⠀⠁⠸⠁⠃⠃⢉⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠂⠀⠉⠙⠰⢿⠿⠛⢿⡦⠁⠈⢓⡀⡀⠀⡆⢀⠀⠂⠀⠀⠂⠃⠀⠉⠱⠀⠉⢵⠖⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⣀⣤⡀⠂⡘⢀⠀⠋⠀⠀⡐⠃⢁⠓⢠⡳⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠛⠉⢠⡼⠂⠈⠀⠀⡀⠀⠁⡀⠈⢚⡇⠸⡦⡄⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠨⠉⠀⠄⠀⠀⠈⠘⢃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠃⡀⡰⡈⠂⠀⠈⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠈⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢐⡓⠆⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣆⣶⣠⣿⣿⡰⣇⢀⣄⣶⣦⠀⣄⢀⠀⣎⣾⡇⠲⠄⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠿⡟⠛⠅⢹⢻⡄⠓⣻⡇⡘⢳⣶⣿⡆⣼⡟⣻⡷⠦⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣦⡆⠄⠻⠃⠑⠤⠉⢘⣯⡹⠧⣿⣁⠉⠟⣹⡄⠛⠿⣿⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠙⠂⠅⡀⠘⠃⢰⡀⣤⢾⣿⣿⢣⡏⣄⠀⣾⡞⠋⣄⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣤⡤⢌⡙⠸⠇⠹⣾⣿⡟⢾⠃⣿⠠⡟⣉⠚⣹⠋⢙⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠗⢛⣋⡀⢷⡘⠋⢻⡆⠀⠀⣸⢃⡾⢁⡩⣴⠶⣶⢶⣶⣿⣉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠂⠀⠈⠉⠻⡿⣿⣟⠛⣧⠀⠀⢙⣼⣇⣾⣧⣬⣴⣫⣴⣧⠜⠿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠲⠤⠄⠀⠀⠶⢻⣿⣿⣿⡄⠀⠈⣽⣿⣿⣶⣿⣿⣟⣿⢤⣸⣿⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣀⡀⠀⠀⠀⠶⠟⠳⠻⠇⣠⣠⢿⣿⣿⣿⣎⠹⡾⢯⣡⣥⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⣥⣄⠀⠀⠀⠀⠀⠀⠈⢹⡿⠋⠉⠉⣹⣿⢶⣤⣩⣭⣿⣿⣛⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠆⠀⠀⠀⠀⠀⠤⣶⣄⡀⠀⠀⠀⠀⣴⣽⣿⣿⣟⣷⣾⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⢙⣷⣤⡄⠀⠀⠀⠀⠀⠈⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠉⠿⣷⣶⣤⣤⡴⢾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡿⣾⣿⣿⣿⣿⣵⣟⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣹⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⢠⡞⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⢸⣅⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢩⠟⠁⣿⣿⣿⣯⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡇⠀⠀⠀⣾⣿⢿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⡯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⢶⢿⣿⣼⣿⣿⠟⢛⣏⣿⣿⣾⢿⡏⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠋⠉⠋⢹⠶⠿⠿⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⣀⡠⠔⠒⣒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⢐⢊⡭⠭⣉⡩⠖⠺⠝⠏⡀⠘⠈⠀⡀⠉⠓⢶⡉⠉⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣬⠃⡴⠋⠀⢀⠒⣂⠀⠳⠀⠀⢸⡌⠆⠀⠀⠙⣆⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣁⣠⠄⠘⣌⡻⠀⠀⣀⣀⠈⠢⠂⠀⠉⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣚⡣⢴⠂⠀⠀⢄⠉⠀⢁⡕⠀⠀⠙⠫⣭⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢧⣶⣡⠀⠀⣄⠈⢁⡶⢉⣀⠤⠃⣀⣑⣭⠛⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⠴⠚⠛⢛⣚⢳⡦⠒⠒⠦⡍⠁⠀⠀⢀⡴⠋⠀⢀⡈⢻⣁⣀⣀⣈⣙⣲⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡔⣋⠉⠉⠙⠲⣄
⠀⠀⠀⢠⠎⠀⣠⠖⠋⠉⠉⡏⠀⡆⢠⡄⢘⣟⣋⣉⣭⢧⣠⠷⠼⠓⠞⠉⠉⠉⠉⠉⠉⠉⠉⠛⠯⢭⣍⣉⣉⣭⡭⠽⠋⠉⠉⠉⠉⠓⢦⡀⠈⢦
⠀⠀⠀⢿⠀⢰⡇⠀⠀⠀⠀⠈⠚⠉⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⣇
⠀⠀⠀⠈⢧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⠃
⠀⠀⠀⠀⠀⢸⡇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡴⠃
⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⢸⡇⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢼
⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿
⠀⠀⠀⠀⢰⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢿
⠀⠀⠀⠀⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣻
⠀⠀⠀⠀⢻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠈⣻⢇⡀
⠀⠀⠀⠀⠀⠙⢿⡛⠛⠛⠛⠛⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠚⠛⠓⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠈⣹⠿⣄⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠶⠶⠶⠾⠷⢶⡶⠶⠶⠶⠶⠶⣶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⢶⡶⠶⠶⠶⢶⡾⠷⠶⠶⠶⠶⠶⠚⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠠⠆⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⢢⡌⠙⢠⣶⡄⢀⣳⣄⢚⢫⡄⠢⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠦⠕⣫⠼⠋⠀⠈⠙⠷⣜⠚⠴⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠒⠀⠀⡷⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠘⠿⠀⠐⣉⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⠋⢀⡦⢴⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡒⢦⠀⠙⠽⡆
⠀⠀⠀⠤⠀⠀⠀⠀⢘⢦⣶⡿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⡧⢞⠅⠀⠀⠀⠀⠤
⠀⠀⡀⠈⠳⠆⠀⠀⠈⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠰⠖⠁⢀
⠐⠐⣣⠀⠠⣶⡁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⣶⠄⠀⣞⠒
⠀⡴⢠⡙⡆⠘⠞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠳⠃⢰⢋⡄⢦
⠀⢱⡘⠋⣶⡧⡴⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢦⢼⣶⠙⣃⡎
⠀⠀⣻⠠⠛⢡⠑⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠊⡌⠻⠄⣟⠄
⠀⠂⣀⠅⠒⢀⠐⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠂⡀⠒⠸⣀⠐
⠀⠀⣺⠉⣶⡌⡔⠅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣢⢡⣶⠉⣗
⠀⡘⢤⣦⠙⢿⣛⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣛⣿⠋⣴⡤⢃
⠀⠙⣂⡤⠃⢠⣲⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣖⡄⠘⢤⡐⠋
⠀⠐⠞⠀⠐⠻⡁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⠟⠂⠀⢳
⠀⠀⠀⠀⠔⠇⠀⠀⢀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠸⠦
⠀⠀⠀⠂⠀⠀⠀⠀⢸⠞⠿⢿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⡗⢮⡄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢱⣆⠀⠟⠺⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢪⠕⠎⠀⣠⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠄⠀⢀⡗⠂⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠠⢶⠀⠐⡈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠖⡢⣍⢲⣆⠀⢀⣠⡖⢩⢀⡒⠄⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠈⢫⣤⠘⠻⠉⠉⠽⠋⢤⣌⠃⠌⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⡇⠀⠀⠀⠙⠃
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠖⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠴⠚⠤⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠙⠋⠲⠶⣦⣄⣀
⠀⡠⠠⣭⡀⠀⠀⠀⠀⠄⠠⣀⠀⠈⠀⠛⠁⠠⠠⣦⣤⡀⠀⠉⣡⣶⡀
⠀⢀⣤⣴⣶⣶⣶⣤⣤⣤⣀⣲⡤⢌⣉⡐⠒⠢⢄⠀⡌⣫⡔⠛⠋⠹⣿⡄
⠀⢸⣿⣿⠟⠛⠻⠿⠿⠿⢿⡿⠿⣿⣷⣾⣭⣓⢶⣴⡜⠇⠀⠀⠆⠀⠹⣿
⠂⣾⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠿⠿⣿⣧⡹⣿⣎⠀⠀⠀⢀⣀⠀⠠
⡀⡇⠀⠀⠀⢀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⢹⡟⠀⠀⣴⢻⡿⠀⠀⠄
⡀⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢿⣦⡀⢹⣆⣧⢀⢠⡄
⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡿⠇⢀⡿⠈⠰⡌⡇
⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢁⢻⠀⢸⡗⡀⠀⢹⡟
⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠘⠛⡄⡜⡇⠇⠀⣼⠁
⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣠⠙⢱⡇⣆⠔⠁
⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⡅⠈⣸⣿⣿⣆
⠀⠠⢌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣠⡶⠟⢝⡯
⠀⠀⠀⠀⠉⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣦⠔⠁⠀⠈⠁⠒⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢙⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⣀⠀⠀⠸⣿⣿⠗⠲⠤⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀⠶⠀⠀⠀⢁⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁

⣌⠳⡄⠻⣦⡹⣄⠈⢈⢣⡀⠃⠱⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠁⠸⠁⠀⠀⠀⢀⠞⠠⠃⡰⢁⠞⠁⠔⣡⠾⢃
⣌⠳⣌⠀⠈⠳⣌⠳⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡰⠋⠀⢀⡼⠉⡰⠋
⣌⠳⢌⠓⢄⠀⠈⠳⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠴⠃⡠⠋⠀⢈
⡈⠓⢤⡑⠀⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡠⠖⣩
⡙⠢⣄⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉
⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⡠⠔⠉
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤
⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁






⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠶⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛

⠀⢀⠄⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠚⣁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠙⠢
⠟⣻⣿⣿⣤⣤⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢠⣤⣤⣿⣿⣿⠀⢰⣾⣿⣿⣤⣤⠀⠀⠀⢠⣤⣤⣄⠀⡀⠀⠀⠀⠀⢀⣿⣿
⣞⣻⣿⣿⣿⣿⠴⣧⣤⣼⣿⣿⣿⣀⣠⣶⣷⠀⠀⢸⣿⣿⣷⡆⢸⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⠀⣤⣤⣼⣿⣿⣿⣇⣈⣶⣶⠀⠑⢮⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⠀⠀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢥⣿⣷⣾⣿⡼⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡀⡇⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⠆⠀⡇⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⢰⠀⣤⣤⣤⣤⣤⣤⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠃⠀⡇⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⡛⣛⣁⣑⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡋⢸⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⢸⠀⠀⢸⣿⠉⢿⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⣴⣄⡀⠰⠀⣤⠀⠀⠀⣿⡇⠀⠿⠿⠿⠿⠿⠿⠟⠀⢸
⠀⠀⢸⠀⠀⢸⣿⣦⣽⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣼⣿⡇⠀⠀⣿⠧⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼
⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⡖⠒⠒⠒⠒⢲
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣼⣿⡟⣋⣿⣿⣿⡿⠁⠀⠀⠀⣿⡇⠀⣿⣏⠀⢸
⠀⠀⠈⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⡁⠄⠀⠀⣸⣿⣿⢸⣿⢹⣿⣿⣃⣾⡇⠀⠀⣿⡇⠀⠛⠛⠀⢸
⠀⠀⠀⠀⠀⡇⠀⢀⣀⣤⣄⠀⠀⡇⠀⠀⠀⠉⠁⢀⣹⣿⣾⣿⣿⣿⣿⡇⠀⠀⡿⠉⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⡧⠀⠀⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡏
⠀⠀⠀⠀⠀⡇⠀⠸⠿⠿⠟⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠇⣀⣀⣀⠀⠀⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠻⣍⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠒⠒⠒⠒⠒⠛⣶⣦
⠀⠀⠀⠀⠀⠀⣾⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣷⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡼⢦⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠾⣇⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃



⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⢃⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡿⡹⠂⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⡠⠀⠀⠀⠀⣀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⡡⢀⠀⠀⠀⠀⡅⠑⠄⠈⡿⢋⡠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣟⣂⡁⠀⠀⣦⣄⠱⡀⢨⡔⢠⡁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⡿⢐⡀⠀⠀⣿⣿⡆⠈⢹⠗⢁⣀⡀⠀⠀⢀⠠⠴⠀⠀⡀⠌⢒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠧⣀⠀⠰⣦⠀⠀⠀⠀⢐⣿⠄⡃⠀⠀⢈⠙⢇⠀⡎⣴⣿⣿⠀⢀⠒⡁⠀⣠⠔⢁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣑⢄⠀⠆⠀⢠⣄⠘⢽⡆⡈⠀⠀⢀⠉⢢⢱⣸⣿⠟⠁⢀⠂⠀⠀⣰⠕⠊⠁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠳⣜⠀⢘⠋⠀⡒⣶⡡⠀⠀⠀⢱⠞⠚⠓⠠⠄⣀⣌⠀⠀⡞⠁⣀⣀⡔⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡀⠀⠈⢃⠠⠀⢰⣶⠻⣌⠅⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠑⢞⠁⠀⡠⠊⠀⠠⠊⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠁⠐⠚⢳⡀⠀⣆⠬⠛⠞⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠇⠛⠤⡀⠀⣃⣠⢊⣀⡔⠈⠉⢁⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠙⠡⢄⡀⠀⠀⢣⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠈⠂⣀⠄⠀⠀⠀⠙⠻⢤⠀⠠⣁⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡉⠐⠄⡈⠉⡰⠋⠀⠀⠀⡠⠒⠉⠉⠉⠀⠒⠇⢀⠤⠤⡀⠀⠈⠂⠀⠀⠀⠀⠀⠃⠱⢄⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣀⢘⡏⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⡠⠴⢁⠀⠀⠈⠆⠀⢸⠃⠢⢄⠀⠀⠘⠐⢖⠒⢤
⠀⠀⠀⠀⠀⣀⠄⠐⠐⢒⠀⠒⠨⢟⡁⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡎⠀⠀⠀⢡⠀⠀⠸⢀⠾⠀⠀⠀⠑⣀⢏⠑⠌⠑⠀⠃
⠀⠀⣠⠖⠁⠈⠢⣀⠀⠀⠱⣀⠀⠀⠈⠑⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⡀⠀⠙⠁⠀⠠⠋⠁⠀⡇⠀⠀⠀⠘⠀⠑⠼
⠀⠜⡡⠔⠒⠈⢉⣉⡭⠭⠒⠒⠳⢤⣤⡀⠵⠀⠀⠀⠀⢂⠀⠀⠀⢀⠔⠚⢄⠀⡠⠊⠀⠀⠀⢠⠁⠀⠀⠀⠀⡗⠀⠀⣀
⡼⠬⠄⠀⠠⠖⣉⠀⠀⠀⢀⠤⠂⠀⠀⠀⣀⠕⣄⠀⠀⣀⠟⠐⠂⠉⠣⡀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠘⠀⣤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠃⠀⠀⠀⠐⠈⣔⣪⡗⠟⣍⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠄⠤⠊⠁⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣲⠾⢭⠆⠈⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡨⠟⡈⠄⠀⠀⡠⠒⠉⠑⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢾⠑⠐⠁⠀⢠⠊⢀⡀⠤⣲⠋⠀⠈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⠿⢠⠁⠀⠀⢰⠋⠁⠀⢀⠜⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡗⠄⠉⠀⠀⠀⡌⠀⡀⠰⠃⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢔⣸⡗⡄⠀⠀⠀⠀⠀⡏⠁⠀⠏⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⢠⣫⡟⠉⠁⠀⠀⠀⠀⠀⠃⠀⠰⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠠⣈⠌⠁⠀⠀⠀⠀⠀⠀⠈⠀⡆⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠉⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢇
⠀⠀⠀⠀⠀⢀⣎⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣆
⠀⠀⠀⠀⠀⢰⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳
⠀⠀⠀⠀⠀⢘⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡞
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢸⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⢘⣾⢦⣤⡤⡤⢤⠤⠤⣤⢤⣤⡤⠤⡤⠾⢞⣀⣀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣉⣉⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣴⣦⠘⢷⣤⣀⣀⣠⠀⣴⠏⠀⠀⣼⣆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⣆⣾⡿⣿⣷⠀⠀⠀⠈⠓⠀⣙⣁⠩⠥⠬⠭⢭⣭⣅⠻⣇⠀⢾⣿⡿⣘⠋⢙⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠸⣯⣻⣄⣠⡿⢀⡴⠚⠀⣀⠀⣠⡖⠀⠀⣴⠂⠀⠀⠉⣿⣾⠷⠈⠋⢤⢻⣿⡿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢶⣬⡿⠉⣻⣳⠟⠀⠀⠀⠉⠀⢿⣆⠀⢸⣷⡀⠀⠀⠀⣴⡀⠀⢈⣽⣲⡜⣿⠁⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢻⡏⢀⣠⡄⣴⢴⣿⢸⣿⠀⠀⠉⠁⠀⡀⠀⢙⡛⠷⠐⠲⠿⣦⡈⠀⢈⣽⣶⣦⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⣠⡾⢫⣴⣿⠿⣶⣄⣬⠿⣿⡿⣠⣽⡯⠀⠈⠓⠒⠛⠁⠀⠀⠀⠘⠉⢄⣪⣥⣤⣤⣄⡀⠠⣄⣙⡄⣿⡟⠋⠁⣠⡤⣤⠉
⠀⠀⠀⠀⠀⢰⣿⢣⣿⠏⠸⡿⣏⢿⠼⠀⢀⡷⠿⣿⠖⠂⠀⠀⠀⠀⠀⠀⣰⠚⣟⢠⡟⠋⠉⠉⠉⠉⠙⠳⣮⡙⢷⡏⠀⠀⣾⠁⣴⣮⡇
⠀⠀⠀⠀⠀⠘⢿⣇⣻⠀⠀⠀⠘⢈⡴⠛⣫⣭⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠘⢮⣧⠄⠀⠀⠀⠀⢀⡄⢀⣉⠊⠻⡄⠀⠃⢠⡌⠉
⠀⠀⠀⠀⠀⠺⣿⡿⠿⢿⣶⣤⡀⣨⡾⠋⣩⡏⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠋⠉⠀⠀⠙⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⣿⠃⢸⣶⠶⣝⢮⠋⠀⠘⠉⠛⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣌⣳⡀⣦
⠀⠀⠀⠀⠀⠀⠙⠃⠀⢀⠀⠀⣆⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⢀⠂⢀⠂⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠉⠁⠠⣬⢻⡅⣽
⠀⠀⠀⣤⡀⠀⡀⠀⢸⣇⠀⠀⣿⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⡌⠀⠁⠎⠁⠀⠰⠠⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠤⣤⣌⢷⠇⢁⡄
⠀⠀⠀⡸⣷⣸⡇⠀⠀⠉⠓⠄⣿⠀⠀⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡙⢶⣆⠀⠀⠙⣿⠇⣸⠇
⠀⠀⠀⢳⡻⣿⡇⠀⢠⡎⠁⠁⢹⣠⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠙⢷⣿⠀⠰⡄⠟⠀⠁
⠀⠀⠀⠀⠙⠿⡧⠀⠈⠧⣶⡀⠈⠃⢀⡾⠁⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠠⣤⣶⠀⠀⠈⣿⠀⣰⡧⠶⠶⣦
⠀⠀⠀⠀⠀⣀⣤⡀⢄⡀⠤⠍⠁⠀⢸⡇⠀⢿⡟⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⢿⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⢀⡨⠤⠤⠤⢄⡀⢳⡀⠈⠃⠀⠰⠛⠿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣠⠃⠀⠀⠈⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠢⣙⢄⡀⠀⠀⠀⠀⠀⣸⡟⠀⢤⡀⠀⢠⣶⣦⠀⠀⢀⣤⠀⠀⣀⡴⠁⣀⠀⠀⠴⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠁⠻⢷⣤⡀⣆⠘⢉⠔⠂⠀⠙⠂⠈⠉⠀⠀⣰⣿⡏⠀⠘⠉⠈⠡⣶⣶⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡀⣀⣀⣀⡈⠙⠪⠣⠀⠀⠀⠀⠀⠀⠀⠀⠜⠴⠃⠀⠀⠈⠙⢶⡄⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠂⢸⠀⠎⠈⠉⠉⠉⠀⠀⠀⠀⢀⡤⡈⠢⠷⠖⠀⠀⠀⢲⣍⠉⠂⣼⠂⠘⠃⢀⡇⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢤⣀⠀⠀⠀⠀⠀⢀⣀⣼⣿⠟⠁⠀⣠⡀⣼⠟⠀⠀⠁⠀⠀⠀⠉⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣈⣙⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠿⠻⡿⠛⠟⢿⠿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣴⣾⢷⣄⡀⠀⠀⢀⣠⣾⣷⣦⣤⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠙⠷⣶⣶⣿⣷⠖⣫⢿⣿⣿⣿⢏⣽⣿⢿⡿⡇⢸⢿⡿⣿⣯⡹⣿⣻⡟⠿⢟⠳⢾⣿⣶⣶⠾⠋
⠀⠀⠀⠀⢀⡴⣾⠟⢀⢞⣵⠿⢿⣿⣿⣿⣧⣽⣿⣧⣧⣼⣽⣿⣧⣼⣿⣿⣿⡿⠾⣶⡱⡄⠹⣷⡦⡀
⠀⠀⠀⢠⢏⢞⡏⠀⣼⠏⠈⢣⣘⠘⠻⣿⣿⣿⡿⠿⠋⠙⠿⢿⣿⣿⣿⠟⠋⡃⡜⠀⠙⣷⠀⠹⡵⡙⡄
⠰⣦⢴⡾⣾⠎⠀⠀⠉⠀⠀⠀⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠑⢵⢷⡦⣴
⣷⡄⣠⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣄⢠
⠙⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿
⢈⣻⣗⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣾⣟
⠀⢭⡯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢽⡭
⢀⡲⡷⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢾⢖
⠀⣙⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣋
⢈⡵⣾⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣷⢮
⠀⢚⣗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣺⡓
⢘⣽⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⣯
⢈⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷
⡿⠇⠑⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠋⠸
⠡⠟⠺⢷⢷⢆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⣠⣾⠾⠗⠻
⠀⠀⠀⠘⣌⢎⣆⠀⢻⣄⢀⡘⣉⢠⣴⣾⣿⣿⣷⣶⣄⣠⣶⣾⣿⣿⣷⣦⣄⡉⢃⠀⣠⡿⠀⣰⡳⢣⠃
⠀⠀⠀⠀⠈⠳⢿⣆⠈⢮⢿⡶⣿⣿⣿⣿⡟⣻⣿⡟⡟⢻⣻⣿⡟⢻⣿⣿⣿⣷⢴⡾⡳⠃⣰⡿⠗⠁
⠀⠀⠀⣠⡶⠾⠷⢿⣷⣦⣕⣾⣿⣿⣿⣜⣻⣿⣿⣷⡇⢸⣾⣿⣿⣟⣳⣿⣽⣿⣿⣪⣵⣾⣿⠾⠷⢶⣄
⠀⠀⠀⠉⠉⠋⠉⠁⠀⠀⠀⠀⠁⠙⠛⠻⢿⡿⠋⠉⠀⠀⠉⠙⢿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁
⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠄⢀⠀⡀⠀⢀⣤⡀⠀⠠⣀⠀⢀⠤⠀⠀⠤⡀⠀⣀⢄⠀⢀⣤⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠐⠘⠂⠀⠀⠁⠁⠀⠀⠄⠀⠀⡠⠀⠀⠀⠤⠀⢀⡋⠀⡠⠒⠀⠀⠒⢄⠀⢙⡀⠀⠤⠀⠀⠀⢀⠀⠈⠀⠀⢀⠈⠂⢀⠀⠀⠁⠂
⠀⢀⠀⡁⠀⠠⠀⠀⠀⠀⠐⡄⠂⠘⠃⠀⠀⠰⠒⠒⠛⠀⠀⠀⠀⠀⠐⠄⠀⢂⠀⠓⠐⠒⠆⠀⠀⠸⠂⠐⣀⠂⠀⠄⠀⠀⠴⠀⢈⠈⡄
⠀⠈⠀⠙⠂⠀⣈⠀⠀⠼⠉⠀⡈⡄⠐⢀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠀⠀⡠⠂⠀⢁⠀⠙⠧⠄⠀⣁⠠⠐⠊⠀⠁
⠀⠠⠓⠂⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⢠⡠⠐⠚⡄
⠀⠀⠀⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⢀
⠀⠘⠷⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⠀⠁⠼⠃
⠀⠀⠀⠄⣀⡁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢈⣀⠠
⠀⠀⠄⠀⠈⡃⢠⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡄⢘⠁
⠀⠀⠂⠐⠀⠔⢤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠸⠀⠀⠁⠆
⠀⠀⠀⠠⠀⢀⠘⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⡀⠐
⠀⠀⠈⠀⠀⠈⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠁⠠⠀⠉
⠀⠠⠀⠠⠀⡆⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢰⠀⠄⢀⠄
⠀⠀⠀⠀⢀⡅⠐⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢨⡀⠀⠀⠂
⠀⠀⠀⠀⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡈⠉⠀⠈
⠀⠀⠀⠂⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠶⡄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⡦
⠀⢀⡠⠀⠐⡄⠐⠨⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⢠⠂⠀⠄⡀
⠀⠈⠀⠀⠈⠃⢵⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠘⠁⠀⠀⠁
⠀⠀⠐⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁⠂
⠀⠀⠀⠈⠀⡀⢐⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡆⢀⠈⠁
⠀⠀⠀⠀⠀⠉⢁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡈⠺⠀⠀⠀⠁
⠀⠀⠄⠀⢠⠆⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡦
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⡁
⠀⠘⠏⢠⠄⠖⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠄⠸⠃
⠀⢀⠄⠀⢀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⠀⠀⡄
⠀⠀⠚⠁⠁⠀⢄⠄⠂⠀⠀⠀⡄⡀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠨⠀⠈⠈⠛
⠀⢠⠆⡔⠁⠀⠀⠀⠀⠹⠢⠄⠐⠁⠈⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠁⠀⠂⠠⠔⠇⡀⠀⠀⠀⠈⢢⠀⡄
⠀⠀⠀⠄⠀⠈⠀⠀⠀⡄⠘⡋⠀⠙⠇⠀⠀⢘⡁⠀⠻⡀⠀⣀⠈⠀⠈⠀⣀⠀⢀⠟⠁⢘⠃⠀⠀⠼⠂⠈⠙⠁⠀⠀⠀⢀⠈⠀⠀⠄
⠀⠀⠐⠲⠂⢀⡀⠀⠐⠀⠀⡠⢀⠀⠀⠀⠀⣤⡉⠁⠀⡦⠀⣈⡊⣀⣀⢘⣁⠀⠴⢀⠈⢡⣤⠀⠀⡀⠀⠀⢀⠀⠀⠒⠀⠀⡀⠀⠒⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⡄⣏⠐⠂⢀⡭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠒⣦⡀⢰⣶⠀⠀⡤⠒⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠆⡄⢀⠄⠠⠈⡇
⠀⠀⠀⠀⠀⢸⡇⠘⣂⠃⢈⣤⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣭⣤⣤⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⡀⠀⢀⡀⠑⠆⠼⠤⠊⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠻⠔⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡇⠛⡀⢒⡀⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠈⠁⣧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠃⢀⢆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⡠⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠍⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⠄⠀⢿
⠀⠀⠀⠀⠀⢸⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠈
⠀⠀⠀⠀⠀⢸⠀⢊⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⡏⢀
⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠳⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⢸⢠⠤⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠤⠴⠀⣺
⠀⠀⠀⠀⠀⣾⠈⠃⠚⠂⠺⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣼⠴⠤⠖⠀⣿
⠀⠀⠀⠀⠀⡿⠀⡖⢉⠋⡘⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠰⢄⣀⠀⢀⣀⠀⠀⣀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠘⠂⢠⠀⣿
⠀⠀⠀⠀⠀⣇⠈⠉⠀⠀⠑⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁⠀⠀⠘⠛⠀⠀⠉⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠄⠀⠂⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⠶⠶⠶⠶⠤⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠄⠔⠂⠈⠀⠈⠈⠇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠐⢈⣀⣥⠴⠒⢚⢈⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠂⠤⠤⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⠤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠢⢄⣀⣀
⠤⠤⠔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢤⠦⣤⠄⠀⠀⠀⠀⠀⠐⠤⠠⠤
⣀⡀⠥⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⢔⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠤⠤⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠵⡪⠔⠁⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⠞⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠀⢸
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠁⠀⠀⢀⣉⣉⣀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⠸⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠤⠀⠀⠀⠰⠀⠀⠀⠀⠠⢄⣀⡀⠀⠀⠀⣀⡤⠆⠀⠀⠀⠀⠀⢀⡦⠀⢀⠀⠀⠀⠀⠀⡐⠈⠀⠀⢂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⢰⠀⠀⡄⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠚⠛⠚⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⢀⣀⠤⠊
⠀⠀⠁⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢚⠀⠀⠀⠀⠀⠀⠐⢄⠈⠉⠉⠉⠉⠁⣀⡠⠔⡀⠀⠀⠀⠀⠀⠈⠂⠤⠄⢀⣀⣀⡠⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣢⠄⡀⠀⠀⠀⠀⠐⠀⠈⠩⠭⠭⠭⠭⠤⠐⢈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠔⢁⠃⠀⠀⠀⠀⠀⡁⠀⠐⠒⠒⠒⠚⠛⠉⠁⡠⠀⠀⠀⠀⠀⠀⠰⣀⣀⣄⣀⣀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢐⠒⠈⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡈⠀⠐⠀⡀⠁⠘⡂
⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⡂⠂⠀⠁⢣⠀⡀

⠀⣠⡤⠤⢤⡀⠀⢀⣀⣤⣤⣤⣤⠞⣉⣹⠲⣄⠀⠀⣀⠤⠤⠤⣄⠀⠀⣀⠤⠤⠤⣠⠊⠉⢉⠑⢢
⡾⢁⣶⣦⣤⠙⠶⣿⣂⠀⠀⠀⢘⡷⣏⠉⣧⣿⠀⡰⠁⠠⣤⣀⠈⠓⠉⠀⠀⠀⠀⠀⠐⢎⠁⠁
⣧⠘⣧⠀⢙⡆⠀⠀⣿⢱⣶⣶⣿⠙⡽⣞⣡⠏⠀⢧⠀⠠⡀⠈⡆⠀⠀⢸⠁⣴⣦⠸⡏⠈⢶⠁⡈
⠈⠻⢮⣝⣺⡇⠀⠀⠙⡊⢻⣟⠈⣚⠁⡟⠁⠀⠀⠈⠓⠤⣈⢒⡇⠀⠀⠀⠀⠈⣛⠀⢀⠀⢸⠁
⠀⠀⠀⠀⠁⠹⣄⠀⠈⠻⣿⣻⡟⠋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠁⠑⢄⠀⠀⠘⠌⠉⠕⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢈⡑⣦⠄⣤⣠⣤⡞⢁⣤⢞⣽⡄⠀⠀⠀⠀⠀⠀⢀⡑⡄⠀⢀⣀⣀⡴⢋⣠⠖⠉⢆
⠀⠀⠀⢀⠀⠂⠀⠈⠈⠳⣄⡴⡛⠁⠀⣻⠿⣵⣻⠀⠀⠀⠀⡠⠀⠀⠈⠉⠐⠄⠠⠺⠃⠀⠘⠖⠤⢊⠆
⠀⠀⠀⢠⣧⣀⡀⠀⠀⠀⠨⠔⠀⠀⠀⢹⣻⠞⠁⠀⠀⠀⢀⠖⣄⣀⠀⠀⠀⠀⠕⠁⠀⠀⠀⡀⡲⠁
⠀⠀⠀⠘⣌⢽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⢄⠀⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠘⠦⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣿⡟⠉⠓⢤⣀⡀⠀⠀⠀⠀⣀⡴⠚⠻⣿⣶⡄⠐⠋⠈⠁⠉⠠⢄⡀⠀⠀⠀⠀⢀⠀⠊⠛⢯⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⢒⡛⠭⠉⢂⣀⠒⠠⠤⠶⣤⡖⣂⡀⠉⠭⠝⣒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⠩⢔⡂⠭⣐⣂⣭⣑⣦⣶⣶⣗⣚⣛⣛⣓⣚⡾⢿⣷⣥⣶⢬⣕⣪⢙⠲⣄
⠀⠀⠀⠀⠀⠀⢀⡴⢋⠕⡪⢔⡨⣐⡬⣟⣿⠿⠛⡋⠋⠙⠉⠙⡏⠛⠻⠛⠿⣯⣭⣛⠲⢭⣛⠦⣍⠳⣝⠢⡙⢦
⠀⠀⠀⠀⠀⡴⢋⠚⡡⡪⢊⢵⠟⣡⠞⡏⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠋⡹⢶⠈⠳⣌⢧⡈⢷⡌⢎⢧
⠀⠀⠀⠀⣼⢡⠃⡔⡱⠱⢱⠁⣼⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣟⠀⠀⠸⣾⠡⠈⠘⠀⡊⡇
⠀⠀⠀⠀⣿⢀⠘⠀⡇⠀⢸⢠⡏⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠶⠦⠤⣤⣀⡀⠀⠀⠇⣼⠉⠳⡄⣰⢃⠎⡜⢠⢀⣵⡇
⠀⠀⠀⠀⣿⡜⡀⢄⢇⠰⢰⠈⣧⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣤⠇⠀⣠⣿⠗⡡⢊⠔⡡⣫⠏⡇
⠀⠀⠀⠀⡇⣿⡐⡌⢎⢢⠑⡕⢌⠳⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡖⢟⡫⢔⡨⢒⡥⣪⠞⠁⠀⡇
⠀⠀⠀⠀⣧⠉⠻⣌⠢⡱⢕⢬⡑⠬⢚⣽⣓⣶⢤⣤⣤⣤⣤⣤⣴⠶⠶⠞⢛⡋⠭⢐⠪⠅⡒⠥⣢⣵⣯⡥⠴⢶⠖⠟⠒⠶⠒⠖⠲⠶⠒⠲⢦⢤
⠀⠀⠀⠀⣿⠀⠸⠋⢻⢮⣑⠩⣙⠲⠦⣤⣉⣉⣀⣀⣈⣉⣉⠀⠀⠴⠆⠑⣂⠠⣉⣂⣬⣵⠞⢻⠉⠉⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇⣼
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢹⠛⠶⢬⣍⣙⡛⠒⠖⠒⠒⠒⠀⢒⣈⣃⣽⣾⠿⠻⠋⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠇
⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⠀⠀⠀⠁⢹⠉⠙⠛⠛⠛⡏⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡞
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠖⠚⠋⠉
⠀⠁
⠀⠁

⠀⢰⢲⣖⣀⣶⣖⣀⣶⣖⣠⣶⣆⣠⢒⡆⠀⣢⣶⢶⣶⢦⡴⢶⡶⢶⡴⢶⡶⣶⣴⠀⢰⣤⣤⣦⣤⣤⣴⣤⣴⣤⣶⣤⣦⣴
⠀⢈⢹⠰⡦⠶⠴⠦⠶⠴⠦⠶⠴⡆⣩⠃⠀⣿⡍⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⢩⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠸⢿⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡇⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢰⣼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡄⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⢹⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠁⠀⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⢻⠰⣇⠀⠀⠀⠀⠀⠀⠀⣀⡇⠸⡇⠀⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢰⡼⣬⡍⣉⣉⡉⣉⣩⢉⣉⣩⠡⡞⡆⠀⣿⣴⣠⣄⣠⣄⣠⣄⣠⢄⣠⣄⣢⣿⠀⢸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿
⠀⠈⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠐⣶⣖⢴⡦⠤⠤⠀⠠⠤⠶⣶⢴⣶⡆⠀⣠⣤⡀⠀⣄⠠⣶⣶⠄⡠⠀⢀⣤⣄⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡇⠀⠛⠿⡟⠓⠒⠛⠛⠛⠛⠒⠚⢻⠿⠹
⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣾⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷
⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠈⠛⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⠛
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠥⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈
⠀⠀⣶⡆⣀⣀⣀⣀⠀⢀⣀⣀⣀⢰⣶⡇⠀⣷⣿⡿⠛⡩⢟⢿⡿⡻⢍⠛⢿⣿⡾⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠈⠉⠁⠀⠈⠉⠀⠉⠀⠉⠛⠛⠁⠀⠈⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡀⠀⠐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐⠈⢼⣡⠄⠐⢀⠀⣧⠤⠔⠁⠀⠠⢀⢸⠃⢀⠀⠁⠈
⠀⢀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠘⠊⠌⠀⢀⠀⢀⠀⠕⢀⠰⡗⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⣀⡄⠀⢲⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠒⠂⠣⠬
⠀⠀⠀⢠⣀⡀⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠴⠂⠀⢀⠘⢄⡀⢁⡀⣤⠂
⠀⠀⠀⡋⠀⠀⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢀⠂
⠀⠀⠈⠄⠀⠀⠂⠀⠀⠀⣀⡴⠒⠛⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠄⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢘⠗⠠⠁⠜⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠒⢄⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠁⠀⠈⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠂⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠜⠉⠀⠀⠈⠀⠀⠈⠀⠐⢠⡀⠑⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⣆⢱⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⠀⢠⢡⠀⠀⢻⣰⠀⡇
⣤⣄⡪⠎⠉⠑⢒⠒⠒⠠⠤⠄⢀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠛⠁⠀⠁⡼⠀⠀⣽⢸⢀⡇
⠘⠋⠉⠋⠙⠓⠒⠶⠦⠤⢬⣄⣐⠀⠀⠉⠡⡀⡀⠀⠀⠙⠒⠒⠒⠊⢠⠔⠾⠗⠯⠴⠦⠀⠀⡀⠀⠀⢀⢄⣤⢄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠆⠈⡢⣄⣀⡀⠀⢀⣀⣬⡴⠒⣀⣞⣛⢳⡶⠴⡖⠀⠠⠮⠾⣫⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠓⠀⠀⠀⠰⠃⠘⠛⡏⣟⠐⠛⠖⣺⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢞⣡⠗⠖⠖⠚⠁