Stinky Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢒⡬⠤⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⢄⡀⠀⠀⠀⠀⠀⠀⣠⠂⢠⠬⠭⠥⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠉⠢⡀⠀⠀⠀⠈⠐⠊⠭⢒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⢠⠄⡶⠓⠊⠀⠀⠀⠀⣀⠤⠀⢖⣊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣐⠑⠁⠀⠀⠀⠈⠀⠡⣒⢤⠀⠀⠀⠈⠢⢘⡥⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢉⠱⣈⠆⠀⠀⠀⠀⠀⢀⢀⡦⠃⠀⠀⠀⣀⠤⣘⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠣⠯⠀⠀⠀⠀⠀⠃⠏
⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⣤⣤⡀⢀⡤⠤⠤⠤⠤⡄⠀⠀⢀⡤⠤⡴⠦⠤⠤⠤⡤⠤⠤⠤⢤⣠⢤⡤⢤⠤⢤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⣀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠳⢤⡔⠋⣀⠔⠁⡤⡄⠀⠀⡇⢀⢔⠁⡠⢉⢍⡠⣪⠆⠘⡡⡢⢉⢸⠃
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠘⠬⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⡀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⡇⢐⠅⡨⢒⠕⢅⡞⣱⣟⡝⣾⠔⣡⣎⡳
⠀⠀⠀⠀⠀⠈⢻⡻⡄⠀⠀⠀⠀⠀⠫⠂⠀⣦⠶⠃⠁⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡲⠷⠦⣈⢔⠕⣡⣠⠆⢿⡉⣀⠼⢖⢕⠕⡇
⠀⠀⠀⠀⠀⠀⢀⠗⡇⠀⠀⢀⡀⠀⠀⠀⠀⠑⠤⢤⡴⠞⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠻⠇⣀⣠⡧⡢⢊⠝⡺⢊⠔⡡⢀⢔⢡⠗⢁⡇
⠀⠀⠀⠀⠀⣠⣮⠜⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⠀⠀⢠⢄⠀⠀⠀⡸⢊⢈⠔⡡⢊⡰⣡⢊⢔⠕⣱⣡⣾⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠌⠊⠈⠈⢱⠀⠀⠁⠀⠀⠀⡇⠔⡡⢊⢰⡙⠝⠉⡇⡡⠪⣪⢜⢆⣳
⠀⠀⠀⠀⠘⢷⡄⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣢⠀⠀⢀⡠⡰⠀⠀⠀⢤⢶⢲⢷⣾⣴⡡⡠⠙⠒⡲⢋⢔⣟⢕⡑⡰⣹
⠀⠀⠀⠀⢠⠎⠀⠀⠻⣍⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠐⣉⠔⠁⠀⠀⢸⡦⠃⠁⠀⠀⠀⢹⡔⡡⠊⡠⣳⠛⡹⣏⡱⢈⢼
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠻⢇⣀⠐⠒⣊⢽⠖⡡⠪⣪⣪⡾⢊⢄⢔⡕⡏
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡴⡖⡶⢦⡀⠀⢾⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡹⢝⠍⠐⢡⡊⢎⠝⡠⣫⣖⣻⡼⠿⠗⣧⣤⡶⠶⠶⠶⠶⠄⣀⣀⠐
⠀⠀⠀⠀⢸⠋⠀⠀⠀⢰⢏⢜⡞⢋⣉⣱⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⡗⡧⡯⠪⣪⣪⣎⠮⠴⠯⣐⡛⠻⠿⢿⡷⠖⣲⣖⣛⡛⠓⠋
⠤⠐⢒⣒⠸⠦⠤⠶⠶⠟⣛⣛⠋⠹⠿⠽⢒⣒⠶⢿⣶⡿⠶⠖⣛⢒⠒⠶⢶⡶⣶⡶⠾⣷⢿⣿⣿⣽⣿⣟⠛⢩⣯⣬⣷⠶⠒⠒⠉⠉

⠀⠀⡀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⢀⢀⠀⢀⢀⡤⠆⠀⠐⠒⠚⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣄⡅⠰⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠀⠀⠀⢱⠶⠒⠲⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⢀⣀⡴⠊⠉⠀⠀⠀⢠⠆⠀⣰⠃⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠐⢢⠀⠀⠀⠀⠀⠀⢠⠃⣀⣀⡇⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⠀⠀⠘⠐⣆⠀⠀⠀⠘⢡⠋⠉⠉⠳⡄⣀⠀⠀⠀⢘⣇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⡀⠈⢦⡀⠀⠀⢸⡄⠀⠀⣴⣏⠉⠀⠀⣠⣾⡽⠋⠁⠀⠉⡆⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣑⣄⣱⠀⠀⠀⠙⠦⠤⣺⠏⠑⠒⠊⠉⠀⣄⣀⣀⠤⠚⠁⠀⠀⠀⠉⠐⢒⣶⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⣉⣉⡉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢰⣋⠉⣠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠛⠚⠋⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣤⠼⠓⠙⠒⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠴⠚⠉⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃⠀⠀⠀⠀⠘⢧⡀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢰⠚⠉⠉⠤⠛⠚⠙⠧⡄⠀⠀⠀⡸⢉⠂⠈⢲⡌⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢈⠇⠀⠀⠠⠀⠤⢤⡶⠃⢠⠒⠧⣍⡛⣄⠀⠘⠁⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⣯⠜⠉⠀⠉⠉⠀⠀⢸⠀⢦⣴⣿⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡹⡁⠀⠀⠀⠀⣀⡇⢸⣀⣀⣤⡀⠀⠀⢀⣀⠴⡠⣈⠀⡽⢏⠒⠄⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡄⠀⣴⠛⢻⠀⡞⠁⠀⣶⠟⠒⣋⠭⠒⠉⠀⠈⡏⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢜⡦⠃⢠⡏⢠⡃⠀⠀⣟⡏⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢉⣶⢰⠃⡜⠉⠑⠒⠿⠀⠀⠀⠀⠀⠀⢠⠞⡇⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⢠⡿⠻⡜⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠇⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢿⠝⢦⡀⡸⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠔⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠒⠒⢻⠉⣩⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠰⢾⠶⠇⢀⣇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⢻⡟⢶⠶⣲⡾⣿⣽⠿⠫⢿⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣷⣴⡶⠞⠋⠀⠈⠛⠷⠶⣴⣧⠾⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠴⠠⠒⠒⠉⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⣡⠀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠋⠀⠀⠀⢙⡶⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢠⠏⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠀⠈⠀⠈⠑⣄⢀⠀⠀⠀⠀⢇⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⠀⢣⣄⠀⠀⠀⣄⠀⠀⠬⣿⠁⠀⠀⢀⠔⠀⠋⠀⠀⠈⡷⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣦⣘⡆⠀⠀⠈⠒⠒⣒⠏⠀⠀⠀⠀⠀⣄⣀⢠⡴⠚⠁⠀⠀⠀⠈⠁⢙⡳⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢉⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠰⣏⡁⣠⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠋⠘⠉⢀⡠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡤⠶⠛⠈⠓⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠚⠉⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⡰⠃⠀⠀⠀⠀⣈⠳⣄⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡂⠀⠀⠐⠛⠋⣉⠗⣤⠀⠀⠀⣘⢉⠇⠈⠳⡄⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡶⠃⢠⠞⠓⠬⡙⣦⠀⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠸⠂⢰⡴⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠄⢠⣇⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠉⢹⠃⡜⠀⠀⣴⡜⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⣵⠂⠀⡞⢀⣇⠀⠀⢏⡏⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⢀⡵⢆⠃⣸⠀⠈⠐⠚⠁⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣄⣾⠛⠾⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠹⠘⠓⠄⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢀⣀⣀⠠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠂⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠹⡇⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡇⡜⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠈⢛⣟⣋⣀⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⢹⠿⠽⢟⣭⠿⠿⣾⣿⠗⠻⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣿⡶⠾⠛⠁⠀⠀⠈⠙⠛⠶⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠠⠀⠀⠠⠀⠀⠀⠄⠄⠄⠄⠀⠀⠀⠀⠀⠆⠆⠀⠄⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⡼⠷⡄
⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠎⠀⣠⣇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠞⢫⠟⠛⣦⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠃⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⡏⠀⢀⡿⠒⢲⠀⠀⠀⠀⢀⡟⠀⠀⠀⠠⠎⠙⠓⣲⠖⠲⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠾⠀⠐⠋⢀⠴⠚⣓⣦⣀⣴⣯⢷⣦⠀⠀⠀⠀⠐⠚⠁⣀⡴⠋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠒⠒⠚⠒⠒⠒⠒⠂⠙⣋⣿⣠⣷⠖⠛⠂⠀⠀⣀⣤⣤⣭⡥⠴⠋⠁
⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠉⢻⣀⡼⠻⠄⠀⢀⡞⠁
⠀⠀⠀⢀⡞⠀⠀⣤⣄⣴⣶⠄⠀⠈⢷⣄⠀⢠⡀⠀⠈⠉⠛⠀⠀⠀⠀⣼
⠀⠀⠀⣼⠀⠀⠀⣸⣿⣿⣷⡄⠀⠀⠀⠻⣧⠈⢻⡄⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⡇⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⢻⠀⣸⠇⠀⢤⣄⣀⣤⣤⡟
⠀⠀⠀⣧⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣾⠀⠋⠀⠀⠀⠠⣤⣀⣤⣿
⠀⠀⠀⠹⣷⣞⣋⣀⡀⠈⢻⡀⠀⠀⢀⣼⠏⠀⠀⠀⠑⣦⡀⠠⢤⠤⣾
⠀⠀⠀⠀⠀⠉⠉⠉⠉⣧⣸⠇⠀⠀⠈⠀⠀⣀⣠⢤⡞⠁⠉⠛⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠖⠒⡟⢿⡁⠰⣄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡷⠶⠚⠋

⣿⣷⠿⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣻⣄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠝⢽⠭⡢⣱⠑⠀⢤⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠒⠒⢄⠴⠊⠁⢱⠊⠀⢈⣳⣄⠔⢭⠎⣰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠭⠽⢷⡾⠦⢤⣠⠎⠀⠀⠸⢋⣉⢳⢄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠉⠉⣡⠙⠶⠊⠀⢠⣶⠆⠀⣤⣴⠿⠋⠉⢉⠐⠢⡄⠀⠀⠀⠰⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡀⠀⠀⠀⣀⠔⠁⠀⠀⢀⣔⡧⢁⣠⠴⠿⣀⠀⠀⢀⠆⠀⢀⠇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠈⠉⠉⠉⠀⠀⢀⣠⠶⣉⢎⡔⠁⠀⠀⠀⠈⠳⡄⠘⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢩⠼⠊⢁⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠶⠒⢤⣈⡬⠄⠉⠁⢇⠉⠀⠀⠀⠀⢀⣀⡠⠔⠊⠁⠀⠸⣄⣂⠀⠀⠀⠀⠀⢸⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⠁⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠿⠆⠀⠀⠀⠀⣇⢀⠎
⡠⢮⠿⣳⢊⡱⠀⠀⣃⣤⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠄⠐⠒⠚⠀⠀⠀⣸⠁⠈⡻
⢩⠁⠀⢠⢃⡠⠐⠊⠁⠀⠈⢉⣗⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠒⡶⠀⠒⠈⠁⡃⠀⢀⢃⠀⢰⡁
⢈⠃⠀⡜⠇⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠉⠙⠓⠶⠖⠠⠤⣄⣿⠀⠀⠀⡘⠀⠀⠀⠘⠅⠲⠀⢰⣺⠁⡜⠁
⠸⠀⡠⠤⣞⣀⠔⠊⠉⠚⣄⠀⠀⠉⢐⣒⣶⡖⠛⠛⠛⠛⠛⢋⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⣉⣀⣤⠇
⠈⠊⠁⠀⠉⠀⠀⠀⢠⢤⣌⡩⠍⠬⠷⠌⠙⠓⣶⠠⠤⣄⣀⠀⠀⠀⠨⠀⠀⣀⡠⠤⠐⠊⢯⣸⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣡⠤⠦⠴⠖⠒⠂⠈⠀⠀⠀⠀⠀⢉⠃⠒⠖⡚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣲⣯⠤⠶⠒⣒⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠊⠉⠀⠀⠘⠉⠉⠉⣉⣩⡭⠽⠶⠦
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠭⠝⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣞⣀⣀⠀⠀⢀⣀⣀⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣞⣉⣡⡤⠤⠤⠭⢽⡯⠤⠤⠤⠤⢵⠄
⠀⠀⠀⢀⡤⠒⠒⠢⣄⡇⠀⠀⠐⠓⡒⠒⠠⠤⠄⠒⠊⠙⠒⠒⠲⣖⡭⠖⠲⣄
⠀⠀⢀⡏⠰⠞⠓⠆⠈⡁⠀⠙⣆⢙⠦⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠀⠠⠾⣁
⠀⠀⠘⢄⠠⠤⠒⠈⠀⠈⠲⣄⠈⢿⡀⢰⠁⢠⠏⠉⡽⠉⠉⠀⠀⠀⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠉⠳⠤⠮⠤⠴⠛⠇⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⡀⠤⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠇⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⡾⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠲⢍⡑⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠳⠴⠋⠽⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠦⡀⣱⠚⠀⠰⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⡄⠉⠀⠀⡿⠧⠤⢄⣀⣀⣀⣀⣀⠀⠤⠇⠰⠋⣿⢄⠀⠀⡜⢰⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡿⠂⠀⢸⠲⢄⣀⣿⠒⠒⠒⠒⠒⠂⠀⠀⠈⢉⠁⢄⡴⡇⠀⢑⡄⢙⠎⢆⠀⠀⠠⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣳⠀⠀⠈⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠀⠀⡇⠀⢸⠀⡎⠀⠎⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠉⣿⣟⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠪⡀⠀⡇⠀⡼⠀⡇⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⡇⢻⣤⢄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣴⠇⠀⠇⠈⠁⠀⠀⠀⠀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡨⠝⠧⠼⠍⠉⡗⡶⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠂⠀⠘⡄⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⢣⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠎⡞⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠇⠀⠶⠶⢾⠾⡃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠺⡄⠀⠀⠀⠀⠀⠑⢢
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⡇⠀⠀⣮⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⣰⠇⠀⠀⠀⠀⠀⣴⢶⡢
⠀⠀⡖⠋⠉⠉⢹⣟⡟⢛⣛⡿⠿⢿⣿⣛⣛⣫⣋⠉⠉⣙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠛⠿⠶⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠓⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠆⠀⠀⠀⠀⠀⠀⠤⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡐⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣉⠛⠲⠦⣌⣢⡀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠉⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠾⠳⢦⣀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⢚⣋⣉⣀⠀⠀⠀⠀⠀⢶⡬⣷⣄⠀⠀⠀⠀⠹⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⡡⠖⠉⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠒⠒⠒⠶⠤⠈⠳⢄⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⡔⠒⢄⠈⢇⡀⠀⠀⠀⣿⠗⢃⠤⠒⠂⠈⠉⠁⠀⠀⠀⠀⢀⡽⠒⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠣⡀⠈⠃⠀⠉⠙⠛⠉⠁⠀⠉⠙⠒⠒⠤⠀⠀⠀⠀⠀⠴⣥⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⢤⠀⠀⠊⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢀⡄⡘⠀⠀⠀⠀⡎⢃⣰⣁⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣠⠎⢻⢡⠀⠀⠀⠀⢈⠎⡠⢤⡧⢀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⢀⡖⠚⠛⠓⠲⢖⠒⠒⠒⢦⣀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠲⢞⠁⠀⢸⠉⠁⠀⠀⠈⠉⠐⠧⠒⡗⠠⡎
⣀⣐⣇⠱⣀⡠⠐⢈⣉⡇⠀⠀⠀⠀⢠⠙⠢⢄⡀⠀⠀⠘⠂⠀⠀⠀⠀⣀⡀⠈⠓⠹⠦⠀⢹⡀⢈⡉⠀⠀⠀⠀⠀⠑⡤⣚⣥⠵⢥
⠑⣤⡬⠀⢀⡐⠊⠥⡄⠙⣄⣀⡠⢤⠇⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠉⠁⠈⢳⠶⠤⠤⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠣⣽⣡⣐⣚⣢
⠈⠃⠄⠊⠁⠈⠉⠉⠁⠀⠈⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠣⡑⣤⠚⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⣢⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⡤⠠⣠⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣼⠀⠀⠀⠀⠲⠓⠒⠳⠶⠆⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡹⢮⡧⡽⠒⠤⢄⣀⠄⠀⢸⡆⠀⠀⢀⣀⠴⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⢄⣐⣒⡒⠒⠀⢸⠄⠀⠀⢏⣉⠉⠉⠀⠀⠀⠈⢀⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡶⣦⠖⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⢿⡛⢯⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⢿⡉⢧⡈⣧⠈⣧⠹⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣴⣾⡿⢿⠹⡆⢻⡄⢳⡈⣧⢘⣆⣼⣶⠿⠛⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠸⣿⡏⢳⡘⣇⠹⣆⣻⣤⣷⡾⠛⠋⠉⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⢷⣼⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⢀⣄⣠⡀
⠀⠀⠀⠀⠀⠘⢯⣻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⣇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡛⢦⡈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠙⢦⣙⣷⠿⣿⣧⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡿⠋⠀⠘⣿⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠸⣿⡆⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠙⠂⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣴⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⠇⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠈⣿⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣿⢷⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢸⡷⠆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣼⣿⣿⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⡇⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣿⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣿⡟⠀⠀⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣿⡟⢀⠀⠀⣿⣿⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠉⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣸⣿⣤⣴⡶⠾⠷⢶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢻⣿⠫⠄⠐⠋⠀⠓⠀⠿⢉⡻⣷⡄⠀⠟⠀⠀⠀⢀⣾⡿⠁⠀⠾⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠁⣌⢻⣆⠀⠀⠀⢠⣿⡿⡿⠿⡿⠷⣦⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⡄⣀⣴⣿⠋⠀⠁⠀⠁⠒⢊⡻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣄⣀⣀⣀⣀⣥⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣶⣦⣤⣴⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢂⣀⣤⡤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠡⠞⠋⠉⠀⠴⠶⠿⠷⠶⠶⠦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⡛⢭⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣸⣀⣒⠶⠒⠀⠀⠐⢰⣛⠋⠉⠉⠙⡸⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡇⠀⢀⡀⢨⡥⠍⠉⠓⠊⠉⠀⠀⠈⠉⠉⠙⠣⠒⠈⠁⡲
⠀⠀⠀⢰⠁⠀⠁⠉⠀⠀⢄⡀⠀⢳⡀⡟⠲⢦⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢄⣀⠇⠀⡜⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠙⠢⠴⠧⠔⠚⠉⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢼⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠯⣉⠻⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠛⠦⠞⠩⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡀⢙⡖⠃⠀⢄⠐⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠀⠉⠉⠉⠿⠄⠀⢀⣀⠀⣀⣀⡀⠀⠀⠤⠀⠚⢻⣦⡀⠀⢀⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠀⠀⠀⠦⢀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡄⠀⠈⢂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⢶⣶⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢰⡀⠀⢠⠀⠀⡀⢸⡀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⢹⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠃⢀⣸⠀⢸⠁⠘⠁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡆⢺⢘⡏⠈⢧⣄⣀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⠁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠈⠉⠁⠀⡾⡸⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⢇⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠀⠀⠀⣀⣂⣼⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠉⠙⢹⠋⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡸⡀
⠀⠀⠀⢀⣀⠤⢤⣾⣤⣄⣀⣀⣀⣀⣏⣀⣀⣬⣦⢤⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣧⠟⠀⠀⠀⠀⠀⠀⠾⠻⠟
⠀⠀⢰⣇⣀⣀⣀⣸⣦⣟⡦⠬⠟⠋⠛⠿⢶⣮⠥⠾⣄⣀⣠⡼⠃
⠀⠀⠀⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠺⠂⠀⠀⠀⠀⠀⠀⠒⠓⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠀⠄⠠⠠⠀⠠⠐⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠂⠠⠀⠆⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠒⢂⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⠀⠀⠀⠀⠀⠠⠄⠀⠐⠲⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣏⣤⣤⣴⣶⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠛⠛⣩⣼⡿⢋⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢿⣿⠛⡻⠏⠉⠀⠈⢀⣿⣿⡿⠿⠧⢤⠀⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣗⣚⣿⣀⠀⠀⠀⠀⠐⣫⡉⠁⡀⠀⠀⠀⢙⠩⢍⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⠤⠤⠿⠟⠉⢿⡄⠀⠀⢀⣠⣞⢲⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⣿⣆⠀⡾⠟⠉⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣭⣿⣿⣿⣏⣀⡀⢠⣤⠀⣼⣿⣻⣷⡀⢶⣅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣻⣿⣿⣿⣿⣽⣿⠀⢻⠀⢹⡇⠀⢻⡁⢸⡇⢿⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣷⣿⡄⢸⡀⢸⡇⠀⣸⠁⣿⡅⣿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⢸⡇⠀⣿⠀⣿⡀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⡧⢸⡄⢸⡇⠀⣿⠀⣿⠉⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢸⡇⠸⣇⠀⣿⢀⣿⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣦⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣿⠀⣿⠀⣿⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⡗⠀⣿⠀⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠞⣹⢟⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⠀⢹⠀⣿⠰⡟⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠈⠀⠛⢸⡷⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣭⣿⣛⡟⠚⠀⠴⢀⢭⣥⡶⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣿⡂⢸⡗⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣽⣿⣿⣿⣿⣧⣤⣤⣤⣽⣷⡾⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠸⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⣀⡀⠀⠀⠀⠀⠑⠉⠁⡝⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⠲⣀⠀⣀⠀⠀⠉⠁⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⡍⠀⡱⠒⠀⠀⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣚⣛⡛⠓⠦⣄⠀⣠⠔⠋⠁⠀⢹⠀⢺⠀⢀⠖⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⠈⠉⠒⣬⣿⣧⠀⠀⠀⢀⡿⠀⡤⠃⠈⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠒⠒⠒⠒⠒⠛⠛⠂⣀⠉⠉⢇⣀⣀⡠⠔⠛⠀⠸⠒⣋⣉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠐⢲⠤⠤⡤⠔⠒⠉⣀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣤⣈⣉⠡⠔⣇⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠇⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠘⠋⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢖⣂⣉⡦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣓⠭⡎⠑⠢⠄⡈⠢⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠉⢡⡀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠸⡖⠒⠁⠀⠀⠀⠈⠒⢄⠀⠀⠠⣴⡒⣉⠀⠀⠀⠀⠀⠉⠐⠊⠁⢠⣤⣶⡏⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡈⠀⠀⠀⠀⠀⣠⣳⠀⣰⠕⢱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣦⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⣂⠴⡖⠚⢂⠖⠙⠋⣠⠔⠉⠉⠉⠉⢉⠿⠧⠄⠀⠀⠀⢰⠠⡼⠔⣣⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣗⣈⠗⠀⠀⠀⢀⡏⠙⠒⢦⣀⣮⠗⠀⠀⠈⠉⠁⠑⠤⣭⣭⡇⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⡀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠉⠓⠒⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣣⢣⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣀⠖⠊

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠤⢄⡀⢸⠵⠲
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡤⠄⠼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣣⠀⠀⡜⠉⠈⢦
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⡠⠒⡞⠁⠀⠚⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠷⡀⠑⣴⠋⠙⠣⡴⣠⣆⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣜⣄⠘⣏⠉⠉⡏⠥⡄⣀⣀⣀⠤⠴⠊⠁⠀⠀⠔⠁⠀⠉⢢⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣾⡄⠈⠒⠰⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣓⣢⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⢳⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣼⡢⢄⠠⡂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⡎⠢⡀⢳⡝⡳⠂⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡮⣹⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡶⢦⡇⠀⣸⠀⢀⠤⢦⣤⣤⡴⠶⠞⠛⠳⣋⣽⢆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠒⠢⣤⠭⠎⣀⠀⢸⠁⠀⠀⠀⠀⠀⢐⠉⠇⣤⣇⣉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠊⠈⠀⢣⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢮⡉⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣬⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡤⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡇⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡔⠒⡶⢼⠒⠙⣰⣖⡖⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠠⡈⢶⡊⠑⠂⠋⢹⠤⠤⡘⠐⠯⢝⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠪⠽⢽⣹⡞⠀⠀⠰⢲⠋⡇⠀⠉⠊⠕⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠽⠕⠒⠒⠒⠚⠪⠽⠬⠃⠀⠀⠀⠁⢎⡑⠤⠤⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣁⡠⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣿⠀⠀⠀⡄⠀⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡀⠘⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⠇⠀⡀⠀⠀⣾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⠀⠀⠀⣼⠇⠀⠀⡟⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡁⠀⠀⠀⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠈⠅⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣠⣤⣀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⠛⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠛⢙⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⣱⣾⣿⣿⣿⣿⣶⣶⡮⢻⣷⡄⠀⡀⠀⣠⣾⡿⢋⢀⣴⣿⣯⢻⡆⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣋⣴⣿⣿⣿⣿⣿⣿⡿⠋⣴⣾⣿⣷⣆⣤⣾⣿⢿⣷⣴⣿⣿⣿⣿⣿⠁⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣤⣤⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠾⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣈⠙⠛⠋⠄⡀⠀⠈⣿⣿⣿⣿⠿⣻⣧⡀⠀⠀⠈⠉⢉⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣅⡀⠀⠀⠀⣠⠄⡠⢜⣿⣿⣿⢏⡾⢿⣿⡿⣦⣄⣀⠀⠀⠀⠀⠀⢤⣙⢻⡿⣋⣥⠶⠞⢛⠟⠛⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢉⠁⠘⢿⣶⣿⣿⣧⢊⣴⠟⠋⠀⠀⢈⣠⣽⣿⣷⣶⣍⠛⠿⣶⣤⣀⣀⣠⣤⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣷⡘⠿⣧⠐⣶⣤⣤⣿⡿⠃⠀⢀⣠⣶⣿⠟⢛⣿⣷⣄⡉⠻⢦⡀⠈⢻⣿⣙⣿⣿⡿⠏⠀⠀⠀⠈⠀⢠⣿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣿⣦⡀⢉⣙⠂⠈⠷⣿⣿⣿⠏⠀⣠⣴⣿⠟⣩⠴⣟⡛⠶⣌⡙⠻⣷⣦⡈⢷⣤⣿⣿⠿⠏⢰⣧⢀⡂⠀⠀⢀⣿⡟⣸⣿⣿
⠀⠀⠀⠀⠀⢀⣤⡾⢿⣭⣁⠈⢉⣙⠀⣿⣿⣿⡶⠛⠋⣀⣴⣿⡿⢋⣵⣿⡋⠳⢬⡙⠷⣶⣤⣤⡘⢿⣿⣾⠿⠋⠀⡀⠲⣆⠛⢸⠁⠀⠀⣼⣿⣱⣿⣿⣿
⠀⠀⠀⢀⣴⣿⠉⠻⠆⠙⠻⠷⠈⣻⣿⣿⡿⠋⠀⣠⣾⣿⠟⣫⠾⣿⣿⣌⠻⣶⣤⣈⠢⣌⠻⣿⣿⠿⠋⠁⠀⢀⠀⢿⣆⠙⢷⡈⠂⡠⠀⣿⣿⡿⠛⢹⣿
⠀⠀⢠⣾⣿⣿⣷⡄⢶⣶⣦⣀⣼⣿⣿⠟⠀⢀⣴⣿⣋⣡⣾⠻⠶⣦⣤⣈⣀⠈⠛⠻⢷⣾⡿⠋⠁⠀⠀⠀⣄⠘⢷⡄⠹⣷⡀⠻⠆⠱⠘⠋⢁⣀⣴⣶⣿
⢀⣴⣿⣿⣤⣤⣤⣤⣀⣘⣿⣿⡿⠋⠠⢂⣴⣿⡟⠉⠉⠛⠻⢷⣦⣀⠉⡉⢛⣿⣮⡿⠟⠉⠀⠀⠀⠀⠘⢦⡌⠳⡄⠙⠆⠈⡀⣀⣤⣴⣶⣿⣿⣿⠏⠉⠛
⣼⣿⡇⠀⠉⠁⠺⢿⣿⣿⣿⣿⣄⣀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠌⢛⣿⣷⣽⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣠⣴⣾⣿⠋⠻⠿⠋⠀⠉⠁
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⠦⢭⣛⣿⣧⣀⡀⡀⠤⠀⠀⠀⣀⣤⣶⣿⣿⣿⡟⢿⠏⠉⠁⠀⠤⠂
⢻⣿⣿⣀⣀⣀⣀⡠⠄⢀⣀⣤⣴⣿⣿⣿⣿⠀⠀⢠⠐⠂⢀⣀⡈⠲⣮⣽⣿⣏⣠⣤⣤⣴⣶⣿⣿⢿⣿⠋⠈⠉
⠀⢹⣿⣯⣭⣭⣴⣶⣾⣿⣿⣿⣿⡿⠋⡉⢻⣦⣤⣶⣦⣬⣴⣭⣝⣻⣾⣿⣿⣿⣿⣿⡿⢿⡿⠛⠋
⠀⠀⠙⠛⠿⠿⢿⣿⠛⠛⠋⠀⠉⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⣿⡿⠿⠟⠙⠛⠀⠈⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣋⣙⣏⣈⣉⣹⣝⣫⣽⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠙⢿⠟⢿⡟⠛⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢀⣤⣄⠀⠘⠿⠗⠐⢾⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠚⠁⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠇⠀⠀⠀⠞⠁⠐⠂⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡀⠀⣠⣶⡄⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠁⠀⣿⡿⠃⠀⠀⣿⣿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⢡⣦⣉⠉⢱⡞⢉⣦⡀⠀⠀⠉⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠈⡻⠟⠙⠛⠛⠷⡄⠀⠈⠉⢁⣤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⢀⣾⣷⠤⣤⠄⢀⣀⠃⠀⠀⠉⠉⠀⠀⣦
⠀⠀⠀⠀⢻⡀⠀⢾⡇⠀⠀⠈⣻⣧⡀⠀⠀⢸⣏⠀⢀⣤⠄⠘⢻⣦⠈⣤⡄⠀⠀⠀⠀⠀⠀⣤⣤⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡷⠀⠀⠀⠘⠋⠀⠀⠙⠛⠛⠿⠟⢿⡿⢷⣤⣾⣿⡟⠃⣠⡄⠀⠄⠉⠀⣀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠘⠛⠙⠋⠀⠛⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠻⠿⠃⠀⠀⠀⠻⡇⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠘⠿⣷⣀⠀⠊⠀⠀⠀⠀⠉⠻⢷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠶⣄⠀⡀⠐⠲⣦⠉⠉⠻⠿⠷⠦⣤⣤⢤⣤⠤⠒⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⣧⠀⠿⣄⡀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠻⢷⡀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠙⠶⠛⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠹⠷⠰⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠜⢿⣧⣀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢹⡇
⠀⠀⠀⠀⢀⠀⠀⣠⠄⠠⠶⠄⠀⠀⣤⡄⠀⣾⠛⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠀⢸⡇
⠀⠀⠀⠀⣾⠄⠀⠙⢶⣤⣤⡶⢿⣷⣿⡁⠀⣿⡇⢰⣷⠀⠀⠀⠀⠀⠀⠀⢀⠛⣤⠈⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢹⠏⢻⣶⣿⡇⠈⣿⠀⠀⠀⠀⠀⠀⢀⠟⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡜⠃⠀⠈⠉⣿⣿⠆⠉⡄⠀⠀⠀⠀⢀⠟⠀⣠⠉⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠃⠀⢰⣿⠀⠀⠀⠀⡿⠀⠀⣿⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠇⠀⠸⣿⠀⠀⠀⣿⠀⠀⠀⠛⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢻⡄⠀⣶⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠛⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢻⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣨⡿⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⣻⡇⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⣀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣀⣤⣀⣀⣤⣤⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢋⣤⣄⣀⣀⣀⣼⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠋⠻⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡖⣶⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⢻⡍⢧⡘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⣠⣴⣾⡿⣿⠹⣄⢳⡄⢷⠈⢧⠘⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣴⣿⢿⠻⡍⢷⠘⢧⠘⣆⢻⣨⣷⡾⠟⠋⠉⠛⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⣆⢻⡌⣧⣼⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⢀⣤⣾⣻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣸⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⣶⣶⡦
⠀⠀⠀⠀⠀⠈⠳⠺⠿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⡇⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣏⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠳⣌⠳⣄⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⡈⣳⡾⠋⠙⣿⣆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠰⡄⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠈⣿⣇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢠⣿⡁⠉⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣧⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠆⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣥⢤⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⢸⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣰⣿⠃⠀⠀⢸⣿⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠈⠁⠀⢸⣿
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⣿⣇⣤⡶⠶⠶⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢸⣿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⢸⣿⡏⠥⠀⠋⠀⠒⠀⠯⢉⡻⣦⡀⠠⠏⠀⠀⠀⣠⣿⡏⠀⠰⠆⠀⠀⢸⣿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡌⢿⡄⠀⠀⠀⣰⣿⢿⡟⢿⠻⢶⣤⡀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣀⣠⣾⡿⠃⠈⠀⠀⠀⠓⣘⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⣄⣀⣀⣤⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⣿⣅⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣶⣶⡿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡤
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠉⠲⠶⢤⠄⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠒⠲⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠃⡀⠀⠀⠀⠀⢄⠀⠀⣠⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠐⠂⠒⠶⢤⣄
⠀⠀⠀⠀⠃⠀⠀⠀⡿⠳⠞⣿⠀⠘⡴⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡶⠖⠻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⢀⠀⠀⠀⠀⠀⡸⢷⣤⣤⠀⠀⡄⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⣶⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠰⣀⠀⠀⢰⣀⣀⢀⣼⣆⠀⠑⢄⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠟⠀⠈⡟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡀⠀⠀⠀⠈⠀⠀⠈⡟⠉⠹⣇⡁⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠒⠂⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠑⠀⠀⠀⠀⠀⢀⡀⠷⢠⣾⣿⡇⠀⡄⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠱⣆⠙⢦⠀⠀⣇⠀⠀⠒⠂⠀⠀⠀⠀⠀⠎
⡀⠀⠀⠀⠠⠘⢷⡀⠀⣼⣿⡇⢠⡄⠀⠀⠀⠘⠀⠈⢆⠀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠁⠈⠳⡄⠀⠀⠀⠀⠀⡠⠊
⠁⠀⠀⠀⠷⣦⣈⡻⠞⠁⢿⠃⣠⡼⢆⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⣤⣈⠷⣄⠀⠒⠉
⠀⢀⢰⣿⣄⣀⡙⠁⠀⠀⠈⠻⣋⢀⣬⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠶⢀⣤⡀⠀⠀⠀⠀⠀⠀⡈⠳⣄
⠆⠈⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⡋⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠂⢤⣤⣇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠙⠲⢤⣌⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠒⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠠⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣶⣶⣶
⣿⣿⣿⡿⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣴⣦⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠐⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡐⠒⢤⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠻⠿⠋⠀⠹⠋⠀⠉⠛⠙⠿⠋⠈⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠔⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⡐⠁⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡿⠁⠉⠻⡏
⠀⠀⠇⠀⣀⡀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠀⠐⠀⠀⡁
⠀⢰⠀⠘⠄⠈⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⣿⡀⠀⠠⠈⠠⠀⣶⠆⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠁
⠀⠈⠢⡀⠀⡀⠃⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢀⣼⣿⣧⡠⠃⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⣤⣶⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⠟⠀⠀⠁⠂⢀⠀⢀⠎⠀⠁⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠸⠥⠄⠀⠤⠄⠠⠀⠘⠛⠿⣿⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠄⠀⠠⠀⠀⠀⠀⠀⠈⠣
⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠁⠈⠅⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢂
⡇⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠈⡂⠎⠱⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠂⠂⠀⠀⠀⠀⠀⠈⠁⠒⠀⠈⠁⠉⠐⠄⠀⠀⠀⠀⠀⠑⠠⠀⢀⠠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢠⠴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠈⣇⠀⠀⠀⠙⠶⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⢹⠆⠀⠀⠀⢀⣤⠶⠖⢶⠖⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠛⠋⠀⠀⠀⠀⢸⡁⣀⣤⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠙⢶⡟⠁⠀⠈⢧⣰⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢰⠋⠙⡦⢤⠀⠀⠀⠀⣠⠤⣤⠞⢛⣓⠒⠶⡶⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⣀⠈⡷⢠⠖⠋⠀⠀⠀⠀⠈⢻⠁⠈⠋⠉⣀⡴⠃⠀⣠⡤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⣠⠔⠊⠙⣏⠈⠻⡇⡼⠀⠀⠀⠀⠀⠀⠀⣸⠀⣀⣀⣀⣧⣀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠓⠒⠛⠒⠒⠒⠛⠒⠚⠓⠛⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⢳⡜⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡶⠖⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠓⣶⠚⠹⣄⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣀⠀⠀⣠⢄⠀⠀⢀⡤⢤⡀⠀⢀⣀⡀⠀⢀⣀⠀⢠⡇⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠘⡀⠰⡇⠈⡆⠀⡞⠀⠀⣧⠀⠏⠀⠃⢀⠋⢸⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⡄⢃⠀⡇⠀⢡⠀⠁⠀⠀⢸⢸⠀⠀⡀⠘⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⠸⠀⡁⠀⢸⠀⠀⠀⠀⠈⣸⠀⠀⡇⡄⠀⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⡇⠃⠀⠈⡇⡀⠀⠀⠐⡿⠀⠀⡇⡇⠀⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡆⢰⢸⠀⠀⠃⠀⠀⠀⢀⠳⠀⠀⠃⡇⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢡⠘⠀⡇⠀⠀⢰⡀⠀⣸⢸⠀⢰⠀⡇⠸⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⠶⠃⠱⠤⠃⠀⠑⠶⠃⠈⠳⠋⠀⠛⠃⢸⣧⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⠴⠃⠀⠀⠿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⢻⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠁⠀⠀⠀⣀⠀⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢀⣀⣤⣤⡤⠆⠀⠀⣀⣠⣤⣤⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⡿⠟⠛⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠍⢠⣿⣿⣯⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠋⣿⡇⠡⠞⠃⠀⠀⠀⣀⣼⡿⠿⠛⠉⠛⠒⢂⣴⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣽⣿⣓⣀⣒⡂⠀⣀⣈⣉⣦⠀⠀⠀⠀⠀⠀⠨⠅⠲⣪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡶⠶⠶⠶⠶⠒⣘⣷⡀⠀⠀⠀⣠⣮⣍⡛⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣿⣿⣿⣿⣿⣟⣻⡛⠛⠛⠋⠛⠛⠹⣿⡄⠀⣾⠟⠳⠀⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣥⣟⣻⣿⣿⣦⡛⢀⡀⠀⣀⡀⢀⣿⣿⢾⣧⡀⣲⣔⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⣿⣿⣿⣿⣟⣻⣿⡉⢻⠈⠙⣷⠈⠈⣿⠉⢸⣇⢸⣿⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⡷⣶⣿⣿⣿⣻⣏⣿⡀⢸⡧⠀⣿⠀⠀⣿⠆⢸⡏⢸⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⠀⣿⠀⠀⣿⠀⢸⡇⢸⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⣿⡇⢸⡇⠀⣿⠀⠀⣿⠀⣿⡇⢾⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣟⣻⣟⢸⡇⠀⢸⠄⠀⣿⠀⣿⣇⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⠈⡇⠀⢺⡄⢠⣿⠀⣿⢉⡷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⣶⢾⣿⣿⣿⣿⣿⣿⣿⠈⣷⠀⢸⡇⠀⣿⠘⣿⢸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡎⣿⠀⢸⡇⠀⣿⠐⣿⣬⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⡠⠜⣻⢟⡿⢻⣿⣿⣿⣿⣿⣿⣿⡷⣿⡧⣿⡆⠈⡇⠀⣿⢰⣿⣏⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠁⡜⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇⠀⠇⠀⡿⢀⣷⡉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣿⢸⠃⠀⡀⠠⠄⢚⣣⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⡯⠁⠈⠉⢡⣾⠉⢻⣯⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⢿⣷⣿⣿⣿⣿⡆⠀⠀⠀⢨⣿⠄⣨⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⣿⣿⣿⣿⣿⣶⣶⣶⣾⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠒⡄⠀⠀⠯⠭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣄⣀⡷⠀⠀⢀⡴⠒⠶⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢼⡦⠒⠢⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠇⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠚⠁⠀⢀⢄⠀⠀⠀⠀⠀⠀⢠⣶⣀⣀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢰⢀⠭⠃⠀⠀⠘⡟⠁⠖⢂⡨⠁⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠐⣅⣀⡔⡊⢻⡉⣻⣸⣀⣀⣀⣀⣀⣇⣤⣤⣭⢄⡤⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣴⠒⠒⠒⠒⠶⠦⠤⠤⠤⠤⠄⠒⠒⠒⢲⠞⠳⣜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠄⢠⠒⡄⢀⠖⠲⠀⡔⠢⠀⠔⡄⣸⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡭⠠⢀⠀⢀⠸⠀⠀⡆⠁⢀⠰⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡀⡀⢸⠀⠀⠀⢣⠀⢀⡀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠁⠀⠀⠀⠀⠀⣾⠀⠈⠁⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣀⠰⠀⡆⢆⢀⠙⣀⠆⣄⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣉⣀⠉⠀⠀⠁⣀⣀⣀⣀⣀⠟⠛⢲⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣭⣭⡭⠭⠭⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡬⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣤⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠆⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢐⢀⡬⠠⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⠒⠈⠀⠉⡆⠀⠀⠀⠰⠘⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⢈⠙⢶⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⠂⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⣄⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠈⠢⡄⠑⢄⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠁⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⡘
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢣⠀⠈⠢⡀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡠⠀⠀⠀⠀⠀⠀⡐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠸⠀⠀⠀⠑⡄⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢌⣀⣀⣀⣀⠠⠔⢫
⢣⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠘⡄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠜⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆
⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡃⠀⠀⠀⠀⠀⢀⠸⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠔⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠉⠓⠂⠤⠤⠤⠐⠂⠁⠀⠑⣀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⠣⣄⣀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠉⠉⠉⠁⠀⠀⠒⠒⠒⠒⠀⠀⠤⠤⠤⠤⠤⠤⠀⠀⣀⣀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢠⠀⠀⠀⠆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⠀⠀⢰⠑⠀⢠⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠇⠘⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠱⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡆⠀⠀⠀⠀⠧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⢇⣠⡔⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠒
⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠉⠓⠢⠤⠏⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡖⠒⠒⠋⠀⣀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢳⠀⠀⢀⡎⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠠⠒⠋⠀⠀⢈⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠤⡄⢠⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⡄⠀⢰⣀⡀⠀⠀⢏⠴⠛⠐⠒⠒⠂⠀⠀⠀⠀⠢⠀⠀⠀⠀⣠⠄⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⣆⠀⢣⡀⠀⠀⡛⠐⠶⠄⠀⠀⢤⠠⠐⠀⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠨⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣞⡄⠀⠉⠒⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠐⠲⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡃⠀⠀⢧⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⣉⡀⠀⢣⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⢭⣳⡀⢳⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⡀⠙⣆⠀⢳⠃⢹⠉⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⢸⠦⣼⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⠼⣦⡇⠀⠀⠌⠀⠀⠀⠤⣆⠀⠀⢐⡲⠶⠾⠛⠛⢾⣋⣼⢣⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠓⠨⠄⢀⠈⢁⡐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⡟⡀⠱⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠃⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡈⠠⠤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠰⠖⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⡤⠇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡇⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣇⣠⠁⢀⡀⠀⢀⣠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢒⣛⠀⠀⣏⣸⡏⠀⠀⢰⡛⠭⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⣉⡁⠁⠈⠁⠀⡐⠂⠢⠴⠀⠀⠐⠭⢓⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠼⠭⠯⣿⣑⣐⠇⠀⢀⡰⠶⡞⠉⡇⠀⠉⠐⠮⢑⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣚⣹⡛⠤⠤⠀⠠⠴⢦⣚⣻⣉⣲⠄⠀⠀⠈⠒⢬⡷⠦⣄⠀⣀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠂⠈⠋⢀⣀⣤⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⢉⡠⠔⡒⠟⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠀⠀⠠⠠⠀⠠⠰⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠠⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡂⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠂⠠⢤⣢⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⣄⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠀⠘⠁⠦⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠐⣛⠭⠥⢤⣀⠀⠀⠀⠀⠲⡮⠷⣤⠀⠀⠀⠀⢳⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣠⠖⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢸⠁⠀⠀⠀⠀⣀⣠⠏⠀⠀⠈⣉⠉⠒⠂⠀⠑⠦⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠏⠉⢢⠈⠦⣄⣀⣀⡼⠟⢡⣆⣉⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⠀⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢫⠖⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣴⠁⠀⠀⠀⠣⣰⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠀⢀⡥⠧⠀⠀⠀⠠⠁⠜⠁⠀⢐⡆
⠀⠀⠀⡄⢀⠀⠀⡀⠠⠐⠀⠀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⣄⢤⡉⠳⡄⠀⠀⠐⠐⠀⠀⠀⢀⡀⣠⠇⢨⠃
⠀⠰⣁⠘⠂⠓⢉⡴⣒⠒⢇⠀⠀⠀⣀⠃⠀⠈⠑⠢⠤⢄⣄⣀⣀⠤⠔⠚⠢⣄⣀⣀⣁⣠⠝⠢⠶⠀⠀⠀⠀⠀⠀⢏⢲⠋⡀⠸⣀
⠀⠀⢞⣉⠤⠒⠒⠤⠜⠃⠀⠓⠊⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⢞⠊⣉⠝⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢢⡑⢄⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠈⡁⠉⠉⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠰⡆⠀⠳⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡕⠀⢬⠇⠀⠀⣀⡇⠀⠀⠇⠀⠀⠀⠀⠰⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠀⢀⡀⠀⣀⣀⡀⠀⠀⢆⣀⡉⠁⠀⠀⠀⠀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠋⠉⠉
⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢲⠀⠀⠸⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣄⣈⠇⠀⠀⢠⠖⠒⠖⠒⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣽⠖⠒⢢⢀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠙⠁⠀⢠⢄⡀⠀⠀⠀⠀⠀⣰⣧⣀⣀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⡀⠣⢨⠝⠀⠀⠀⠻⡏⠐⠒⣀⠜⠀⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⣖⣉⣻⣈⣳⣎⣀⣀⣀⣀⡠⠤⠤⢤⡧⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠊⠣⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠄⢰⠓⡄⢠⠊⢣⠀⠖⠆⠠⢲⠀⡏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠸⠀⠃⠘⠀⠈⢰⠀⠀⠀⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡈⠀⠀⢰⠀⠀⠀⡄⠀⡆⡅⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠆⠆⠀⢀⠀⠀⡇⠀⠃⠇⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⣠⢠⢀⠈⢄⡠⠰⣠⠀⣤⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⡼⠉⠉⢷⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠶⠦⠴⠶⠲⣶⣀⣀⣀⣀⣀⣤⣤⠤⠤⠤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠴⢩⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡄⢀⠀⣰⠇⠀⠠⠀⠄⡢⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠉⣀⣀⠐⣀⣈⠴⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡄⠉⣠⣜⣁⡰⢶⠺⠶⢖⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢉⣁⣀⡤⠤⠿⠶⠶⠶⠶⠶⠤⣤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣻⢉⣡⡀⠀⢰⠒⠛⣿⠀⡴⢒⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⣧⠀⢸⠀⠀⣿⠀⡇⠈⣸⣿⡕⠢⣀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢹⠀⢸⠀⠀⡏⢠⠇⠀⡏⠱⣤⣾⠎⠙⢍⠺⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⢸⠀⠀⡇⢸⠀⢸⠁⠀⠈⢣⣴⡿⠃⠑⢌⡆⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⠊⠉⠉⢆⡼⠀⠸⣀⢀⡇⠘⣠⢯⡄⠀⠀⠀⠙⢄⡴⣾⠆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⠭⣗⣙⠛⠒⢾⣿⣒⣋⣀⣉⣉⣙⣳⠆⠀⠀⠙⠢⣠⣶⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠐⠚⠛⠲⠀⠬⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣠⡖⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣾⢿⣿⢿⢿⡾⢿⣿⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠟⠋⢸⣯⠀⠀⠀⣉⣙⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠻⠿⣿⣾⠿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡴⠦⣌⡒⣽⣿⣆⠈⠻⣿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣴⣾⡿⠿⠶⣿⡿⢿⣿⣿⣦⠀⠈⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⢤⣤⣴⡿⠙⠟⠋⠁⠀⣤⣤⣀⣀⣠⣹⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣦⡿⡉⣷⣤⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠿⢿⠿⢿⣿⣿⣿⣿⣷⠙⣿⣿⣿⣿⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠿⠗⠛⠉⠘⠛⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⢠⣤⣤⣤⡠⣄⡄⠀⣄⣤⡠⣤⠄⢰⣠⡰⣔⠀⠀⠠⠀⠀⢰⣲⢶⢰⠀⠀⠀⠀⠀⢀⣆⡆
⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡀⠤⢀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⣿⣿⠟⠁⢻⣿⠋⠙⠿⠿⢿⣿⡿⠙⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠄⠂⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⢻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠐⠈⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢸⣿⡿⢿⣿⣿⡏
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⠋⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⡿⠃⠈⠈⠻⡇
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀
⠀⢀⠃⠀⢆⠀⠐⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⡐⠑⡄⠂⠰⣄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠁
⠀⠈⢄⠀⠀⠀⢠⠁⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⣸⣿⣧⠀⡴⠀⠀⠀⠀⠁⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣆⣤⣶⣧
⠀⠀⠀⠉⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠁⠂⠄⡀⠀⠀⠀⡰⠂⠒⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠁⠀⠀⠀⠀⠀⠑⢤⠞⠁⠀⠀⠀⠀⢀⡀⢤⣶⣿⣿⣿⣿⣿⡏⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠀⠀⠀⠉⢁⠁⠀⠀⠀⠉⠻⣿⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⠠⠊⠑⠄⡠⠁⠀⠀⠀⠀⠀⠀⠈⠄
⠠⠄⠒⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢂⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠈⠂⠈⠀⠂⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠁
⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠁⠂⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢄⢀⠀⢀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⢀⣤⣴⡾⠟⠋⢁⣀⣀⡈⠙⠻⢷⣦⣄⡀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦
⠀⠀⢻⣧⠀⠀⣀⠈⠉⠛⢿⣦⣴⡿⠋⢡⣄⠀⠀⣿⡟⢻⣿⠀⠀⣠⡌⠙⢿⣦⣴⠿⠛⠉⠁⣀⠀⠀⣼⡟
⠀⠀⠈⣿⣆⠀⠛⠿⣶⣤⡀⠈⢻⣧⠀⠈⢿⠆⠀⠙⠿⠿⠋⠀⠰⡿⠁⠀⣼⡟⠁⢀⣤⣶⠿⠛⠀⣰⣿⠁
⠀⠀⠀⠈⢿⣦⡀⠀⠈⠙⠿⠆⠀⢿⣇⢀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣄⡀⣸⡿⠀⠰⠿⠋⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⢙⣿⡿⠿⣶⣤⣄⡀⣨⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣅⢀⣠⣤⣶⠿⢿⣿⡋
⠀⠀⠀⠀⢀⣿⠏⣀⡀⠀⠉⢙⣿⡿⠁⠀⣠⣴⡾⠿⠟⠻⠿⢷⣦⣄⠀⠈⢿⣿⠋⠉⠀⢀⣀⠹⣿⡀
⠀⠀⠀⢀⣾⠏⠀⠙⠻⠗⠀⣾⡟⠀⢀⣾⠟⠁⣀⣀⠀⠀⣀⣀⠈⠻⣷⡀⠀⢻⣷⠀⠺⠟⠋⠀⠹⣷⡀
⠀⠀⢀⣾⠏⢀⣤⣤⣄⠀⢸⣿⠀⠀⣾⡏⠀⠀⠙⠛⠀⠀⠛⠋⠀⠀⢹⣷⠀⠀⣿⡇⠀⣠⣤⣤⡀⠹⣷⡀
⠀⠀⢸⣿⠀⢸⣿⣉⣿⡇⢸⣿⠀⠀⣿⡁⠰⠶⠆⠀⠶⠶⠀⠰⠶⠆⢈⣿⠀⠀⣿⡇⢸⣿⣉⣹⡇⠀⣿⡇
⠀⠀⠈⢿⣆⠈⠙⠛⠋⠀⢸⣿⠀⠀⢿⣇⠀⠀⣠⣤⠀⠀⣤⣄⠀⠀⣸⡿⠀⠀⣿⡇⠀⠙⠛⠋⠁⣰⡿⠁
⠀⠀⠀⠈⢿⣆⠀⣠⣴⡦⠀⢿⣧⠀⠈⢿⣦⡀⠉⠉⠀⠀⠉⠉⢀⣴⡿⠁⠀⣼⡟⠀⢴⣦⣄⠀⣰⡿⠁
⠀⠀⠀⠀⠈⣿⣆⠉⠁⠀⣀⣨⣿⣷⡀⠀⠙⠻⢷⣶⣦⣴⣶⡾⠟⠋⠀⢀⣾⣿⣅⣀⠀⠈⠉⣰⡿⠁
⠀⠀⠀⠀⠀⣨⣿⣷⣶⠿⠛⠋⠁⢙⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡋⠈⠙⠛⠿⣶⣾⣿⣅
⠀⠀⠀⢀⣾⠟⠁⠀⢀⣠⣶⠆⠀⣾⡏⠀⠙⠛⠿⠿⠿⠿⠿⠿⠛⠉⠁⢹⣷⠀⠰⣶⣄⡀⠀⠈⠻⣷⡀
⠀⠀⢀⣿⠏⠀⣤⣶⠿⠛⠁⢀⣼⡟⠀⢀⣾⠆⠀⣠⣶⣶⣄⠀⠰⣶⡀⠀⢻⣧⡀⠈⠛⠿⣶⣤⠀⠹⣿⡀
⠀⠀⣼⡟⠀⠀⠉⢀⣀⣤⣾⠟⠻⣷⣄⡘⠋⠀⠀⣿⣇⣼⡿⠀⠀⠙⢃⣠⣾⠟⠻⣷⣤⣀⡀⠉⠀⠀⢻⣧
⠀⠀⠻⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠈⠛⠻⢷⣦⣄⡈⠉⠉⢁⣠⣴⡾⠟⠋⠁⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⣄⣀⠤⠤⠤⠤⠴⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠒⢶⡄⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠆⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠏⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠉⢀⠒⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠁⡠⠚⠃⠘⠆⠀⠀⢱⣄⠀⠀⠀⠀⠀⠤⠤⠒⠋⠀⠀⠤⠘⠁⠀⠀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠲⣆⠀⠈⠉⠉⠹⢟⣿⡷⠶⠶⠶⠶⠂⠉⠁⠀⠀⠀⠀⣀⡰⠎
⡆⢀⡔⠒⠂⠀⠙⠃⠀⠤⠤⣤⠀⢠⣴⠆⠀⠈⠙⠛⠦⣤⣤⣤⣤⣤⣤⡤⣶⠛
⠁⠈⠳⠶⠀⣠⡄⠸⠆⠀⠠⠾⢁⡀⠀⠀⠉⠳⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⡀⠋⠁⠀⠀⣤⡀⠀⠈⢹⡿⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦
⠀⠀⠀⠀⣤⣀⡀⠴⠃⠈⠳⣄⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡄
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣷⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⢺
⠀⠀⠀⠀⠀⠀⡠⠶⢦⣀⢸⡇⠀⠔⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣿⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠘⢧⣄⠀⠉⣿⣧⡴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠏⠀⠀⠀⠀⣧
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠀⠀⠀⠀⠀⠏
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⢿⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⣰⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡠⠚⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠐⠊⠀⢀⡰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢃⣀⢀⣀⠐⠂⠀⠻⣶⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠻⣄⣀⣀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣿⠀⢨⣄⣀⣀⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣄⣈⣉⣉⣁⣀⣈⣙⣋⣡⣤⣾
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠈⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠆⠀⠀⢀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣳⡄⠀⣠⣿⣿⠟⢡⡀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⢠⣾⢟⣿⣇⣐⣻⣿⣛⣿⣿⣋⣈⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠏⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣮⣭⣽⣿⣯⣤⣤⣤⣤⣽⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⢿⣿⡿⣿⣿⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⣿⡇⣿⣿⢸⣿⠃⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢸⣿⠀⣿⡇⢸⡏⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⡀⣿⡇⣿⡇⢸⣿⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣿⡇⣿⡇⣿⡇⣸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣿⣷⣿⣷⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⣀⠀⠀⠀⠀⠀⣒⣒⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣵⣴⡶⢾⣿⡿⠿⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠿⠟⠉⠉⣴⣾⣯⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣟⣋⣹⣇⠐⠉⠀⠀⢀⡴⠟⠛⠉⠉⠉⠣⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣾⣶⣶⣀⣀⣰⣖⡚⣦⡀⠀⠀⠀⡀⠤⢕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⠿⣷⠖⠒⠒⠒⠚⣷⡀⢀⡾⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣋⣿⣷⣄⢀⣀⢀⣤⠀⣽⣗⣾⡄⢰⣄⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣙⢻⣿⣿⣯⢽⡇⢹⡄⢹⡇⠀⣿⠀⣿⢸⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣾⣾⣧⢸⡇⢸⡇⠀⣿⠀⣿⢸⣇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⣿⢸⡇⠸⡇⠀⡏⢰⣯⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣃⣿⣸⡇⠀⡇⠀⡇⢸⣇⡸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣿⣿⣿⣿⣷⣿⡆⡇⠀⡇⠀⡇⢸⡇⡶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣫⣭⣿⣿⣿⣿⣿⣿⣽⡇⣧⠀⣿⠀⣧⢸⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠴⣻⢿⢟⣿⣿⣿⣿⣿⣿⣽⣇⣿⠀⢹⠀⣿⢸⣟⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⢫⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⠀⠀⠇⣸⠌⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⣿⣿⣿⣿⣯⣿⣯⡿⠈⠀⠀⣀⠠⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⣿⣿⣧⣿⣿⣿⡏⠀⠀⠐⣻⠀⢚⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⢿⣿⣿⣶⣶⣤⣶⡿⠾⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⣤⣀⡀⠙⢬⡙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⠉⠙⠒⠿⠆⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠔⠒⠛⠉⠉⠉⠓⢄⡀⠀⠀⠀⠀⠱⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣛⠭⠔⠒⠲⠤⡄⠀⠀⠀⠀⠉⠀⠛⠂⠀⠀⠀⠀⠘⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⡠⠊⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠈⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⠁⠀⠀⠀⠀⣠⣀⡞⠀⠀⡀⠁⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠁⠉⢦⠈⠦⣄⣀⣀⡬⠟⠁⣴⣋⣁⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡲
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢛⠖⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⣰⣇⡆⠀⠀⠀⠀⠆⠡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣍⣀⠀⠀⠀⠀⠀⠁⠀⠂⠐⠀⣠
⠀⠀⢀⢄⡀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠙⠉⠉⠁⠈⠀⠤⠐⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠠⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢘⠄
⢠⡄⠸⠤⠱⠤⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠤⣄⠀⠀⠈⠁⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⣤⠶⠉⢰
⠀⢩⠖⠂⣀⠤⣉⣐⣲⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢻⠑⠂⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡨⡴⠼⢮⢷
⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠱⡈⢖⠁⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢀⠀⠤⠤⠀⠀⠀⠀⠀⠤⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⢤⠆⡀⠀⠀⠀⠛⠁⠈⢹⠃⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡟⠸⠳⠋⠁⠀⠤⣼⠀⠀⢸⣀⣀⣀⡠⠤⠚⠤⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠶⠌⠭⠭⠭⠀⠀⠹⠀⠀⠐⠤⢀⣀⣀⡀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠂⠀⠁⠂⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠔⠢⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠄⠐⠂⠤⣀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⠊⠀⠂⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⢸⠀⠀⠐⠀⠄⣀⠀⠄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠐⠈⢀⣀⣤⡼⢤⡄⠤⠤⠤⢄⣐⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠤⠒⠛⠐⠂⠐⠒⠦⠤⣀⡀
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⢀⠞⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⢀⡴⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣰⠚⠳⠒⠒⠒⠒⠤⣤⣀⠀⠀⠙⠲⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡠⠔⠒⠲⡃⠀⠀⠀⠀⣀⡀⠀⠀⠉⠙⠲⣄⠀⠈⠢⡀⠀⠀⠁⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣀⡠⠤⠶⠴⠶⠐⡿⠀⠀⠀⠀⠈⠺⢀⠄⠀⠀⠈⢉⠂⢄⠀⠀⠈⡇⠀⠀⠸⣄⠀⠡⡄⠀⠂⠀⠁
⠀⠀⠀⠀⠸⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠳⣤⣄⡀⠉⡀⠀⠀⠀⢀⡿⢀⡀⠀⢹⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠠⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠛⠠⡀⠀⠀⢀⡧⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⢱⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠂⠀⠀⠈⠑⠒⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⡟⢠⡀⠂⠀⢍⠒⢤⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠁⡀⠁⠀⡀⣠⠟⠀⠀⠉⠉⠐⠲⠤⢤⣄⣀⣀⣀⡠⠖⠋⠉⠀⠂⠈⠁⠈⡀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠄⠀⡀⣀⠀⢈⡀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠠⠀⢁⡀⠀⠱⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⡇⢰⠂⠀⠀⠀⠠⠀⠊⠀⠀⠄⠀⠀⢈⠄⢤⠀⠐⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⢱⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⣌⢦⠁⠉⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠤⠄⠠⠤⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⣀⠀⣀⠀⠀⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠀⠙⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠉⠉⠙⠛⠂⠀⠀⠘⠋⠁⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠐⠛⢿⠃⠀⠀⠀⠀⠜⢿⠋⠃⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠴⠃⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⡤⠀⢀⡔⠁⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠆⠀⠐⠁⠀⠀⠊⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣰⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣾⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠆⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠒⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣧⡌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡈⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣴⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠟⠛⠛⠉⠉⠉⠉⠉⠙⠉⠛⠛⠻⠿⢿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷
⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋
⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠅
⠉⠛⠿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠉⠻⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣷⣦⣤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⢿⣿⣿⣿⣿⣾⣾⣶⡿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠐⢠⠋⠀⠀⠁⣢⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡄⠀⠸⣄⠀⠀⡆⢺⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡐⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢳⣤⠴⠞⠿⠻⠏⠙⡟⠲⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠴⠆⠎⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⣀⣀⢩⡟⠋⢀⠀⠀⠀⢠⡀⠀⣠⡄⠁⠙⣦⣠⣤⡴⠚⠀⢀⡀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⢠⠀⠀⠀⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⡿⠀⠀⠈⠓⠈⠀⠐⠃⠀⢃⡀⠀⠀⠻⡆⠀⠀⠀⠀⠋⠀⠀⠀⠈⢢⡀⠀⢳⣀⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⡟⠀⢀⡖⠒⠀⠀⠐⠀⠀⡀⡤⠤⠀⠀⣇⣀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣽⠚⠉⢁⠀⠙⠓⢤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠾⣏⡀⠉⠀⠠⠀⠐⠋⠀⢀⡁⠀⠀⠀⣸⠋⠉⠁⠀⠀⠀⠀⠈⠙⢒⡾⠉⠀⡀⠘⠀⠀⠠⠈⢣⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠉⠀⠀⣠⠟⢦⡀⣀⠀⣴⠒⠠⡄⠀⠙⠀⠒⣲⠿⣄⠀⠀⠰⠒⠒⠀⠀⠓⡾⠀⠀⠂⠈⠀⠘⠁⠠⠔⢉⣇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠀⡴⠛⢧⣄⡀⣀⠀⠃⠀⢀⣳⣶⠋⠀⠘⣆⠀⠀⠀⠈⠉⠑⠉⣧⠀⠐⠁⠀⠀⣀⠐⠆⠀⣹⠋⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⠻⡗⠒⠻⡏⠁⢸⡀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠉⣀⠷⣄⠀⠃⠀⡉⠀⣠⣴⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠀⠀⠀⠀⠿⠀⠀⣇⠀⠀⠇⠀⠀⠓⢀⡴⠀⠀⠀⠀⠀⠀⡀⠈⠀⢀⠎⢙⡓⢺⠛⠛⢣⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠉⠳⠀⠘⠀⠈⠁
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⡀⠀⢡⣤⠲⠤⣔⠁⠀⠀⠐⠒⠁⢀⡀⠀⠀⠀⢣⠀⠀⡀⠀⣸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡲⠋⡀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈⠃⠀⢀⡀⠘⢦⣀⣧⣠⣹⣆⣀⡆⡞⠁⠀⠀⠀⢀⠀⠀⠀⡼⠉⠁⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢸⠁⠀⠄⠀⠁⠄⠈⡇⠁⠀⠀⠀⠀⠀⠤⣀⢉⡾⠉⠀⠀⠀⠈⡁⠋⠙⠷⣄⡰⠒⠚⠁⠀⠀⢰⠀⠀⠀⠀⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢧⡀⠈⠀⠀⣀⠼⠉⠂⠀⠀⠀⠀⣀⠀⢈⡟⠀⠀⠒⠂⠀⠸⠁⢠⠶⠀⠚⢧⠀⠀⠀⠀⠀⠐⠳⠤⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠙⠋⠛⠉⠂⠀⠀⠀⠀⠀⠉⠈⠉⣹⡅⠀⠀⡠⠄⠠⠀⠀⡀⠄⠀⠀⢼⠒⠦⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⣧⣀⠀⠀⡀⠀⠀⠠⡄⠀⠚⢲⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠈⣧⡀⠀⠀⠸⠃⠀⠠⣄⣠⠞⠙⠂⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⢀⠝⠙⡷⢤⣄⣀⣰⡤⠞⠙⡆⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠀⠰⠁⠀⣸⠀⢠⠃⠀⠀⠃⠀⠀⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣴⠶⠞⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠉⠉⠉⠻⡆⠀⠀⠀⠀⠸⣧⣤⣴⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠁⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣤⡀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⡿⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠛⠷⠞⠋⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⣦⣤⡙⣷⡶⠚⠛⠛⢶⡄⠀⠀⠀⠀⠀⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠈⠻⡟⠀⠀⠀⠀⠀⢻⡤⠟⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⣠⡶⠞⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠁
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⣦⣠⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠾⠶⠿⠦⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠙⢁⣼⠂⠀⠀⠀⠀⠀⠸⣯⣨⡟⠁⢠⣴⠶⡶⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢠⡏⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⢠⡶⠶⠾⠛⠉
⠀⢸⡇⠀⠀⠀⢀⣤⠶⠚⠛⢾⡅⠈⠑⢾⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⢸⣇⡀⠀⠀⢀⡾⠃
⠀⣈⣿⣤⣤⣤⣿⣤⣤⣄⣀⣼⣇⣀⣀⣼⣅⣿⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠿⠶⠾⠿⠷⠾⢿⣏⠙⢶⡞⠋⠁
⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⣧
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢻⡄
⠈⣧⣀⣀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡼⠿⣆⠈⢻⡄
⠀⠘⢻⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠙⢷⣄⣹⣦⡀
⠀⠀⠀⣿⢀⣤⡀⠀⠀⠀⣠⢤⡄⠀⠀⠀⢀⣤⠤⣤⡀⠀⠀⢀⣠⣄⠀⠀⠀⣀⣤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠙⠛⠁
⠀⠀⠀⢿⠘⡇⠹⡀⠀⢰⡇⠀⠹⡀⠀⢀⡾⠁⠀⠀⣧⠀⢀⡟⠀⠈⡇⠀⢰⠏⢸⡇⠀⢸⡇
⠀⠀⠀⢸⡇⢷⠀⠇⠀⢸⡇⠀⠀⣇⠀⢸⡇⠀⠀⠀⢸⠀⢸⠃⠀⠀⡇⠀⡏⠀⢸⡇⠀⣸⠃
⠀⠀⠀⢸⡇⢸⠀⢸⠀⢸⡇⠀⠀⢹⠀⢸⠃⠀⠀⠀⠸⡆⢸⠀⠀⠀⡇⢠⠃⠀⢸⡇⠀⣿
⠀⠀⠀⠀⣷⠀⡇⠈⡆⠘⡇⠀⠀⢸⡀⠈⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⡇⢸⠀⠀⣼⠀⢰⡇
⠀⠀⠀⠀⣿⠀⢳⠀⢷⠀⣷⠀⠀⠈⡇⠀⡀⠀⠀⠀⠀⡇⣿⠀⠀⢸⡇⢸⠀⠀⣿⠀⢸⠇
⠀⠀⠀⠀⢸⡆⠸⡀⢸⡄⢸⡀⠀⠀⣷⠀⣷⠀⠀⠀⠀⡇⣿⠀⠀⢸⠁⣼⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠘⣇⠀⡇⠈⣇⠘⡇⠀⠀⢸⠀⣿⠀⠀⠀⠀⡇⣿⠀⠀⢸⠀⡿⠀⢸⠇⢀⡟
⠀⠀⠀⠀⠀⢿⠀⢱⠀⢿⠀⣷⠀⠀⢸⠀⢻⠀⠀⠀⢰⠃⣿⠀⠀⡸⠀⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠸⡄⢸⡄⢹⡄⠀⢸⠀⠸⣇⠀⠀⣸⠀⢻⡀⢠⡇⠀⣧⢀⡟⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢿⡀⠻⠾⠁⠀⠳⣤⠟⠀⠀⠈⠳⠞⠁⠀⠈⠛⠋⠀⠀⠘⠛⠁⢠⣿⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⠀⠀⠀⢉⣹⡆
⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⠶⠳⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣳⣶⣶⣶⣶⣶⣞⣛⣛⣛⣛⣛⣛⣛⣛⣉⣉⣉⣉⣉⣉⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢠⡄⠰⠾⠛⠁⠀⠀⠀⣀⠘⠃⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⣴⠟
⠀⣠⣴⠶⠶⢶⣤⡀⠀⠀⠀⠰⠶⠶⠾⠛⠛⠉⠀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠇⠠⠶⠟⠁
⣰⡟⢀⣤⣤⣄⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠾⠛⠉⠀⢠⣿
⣿⠀⢾⡇⠀⢻⡄⢸⡷⠶⠶⠶⠶⠶⠶⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿
⢻⡄⠈⠀⠀⠈⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠘⣷⡀⠀⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡷⠶⠾⠛
⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠘⠷⣤⣀⣤⣤⣤⣀⣴⠶⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠃⠀⠀⠀⠐⢷⣄⠀⠈⠿⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢻⣄⠀⠙⠃⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠁⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⣤⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⣠⡶⠗⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠻⣧⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠐⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⢀⣴⢷⣄⡀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣤⣤⣤⠶⠟⠁⠀⠉⠁⠘⠃⠈⠁
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢐⡻⠞⠻⠾⠂⠁
⠀⠀⠀⠀⠀⠐⠒⣼⠋⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣧⣤⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡷⠦⡀
⠀⠀⠀⠀⣠⣤⡰⠷⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡧⠴⠿⠁⠀⡀⠀⠀⠀⠀⠴⠛⣀⡴⠚⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⠷⢌⡣⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡀⠀⠀⠀⠈⢡⠀⠀⢀⣴⡷⢨⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡁⠀⠀⠀⣠⣤⣀⡀
⠀⠀⠀⠀⣀⠈⢠⡞⠃⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⡟⠋⠁⠀⠀⠀⠲⠀⠀⠀⠹⠶⢈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣍⠹⠀⠩⡁⠂⠉⠙
⠀⠀⠀⠈⠛⠦⠬⢉⣀⡼⠃⠀⠰⠀⠂⢺⡇⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢲⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⡂⠀⠀⢁⣐
⠀⠀⠀⠀⠀⠀⠀⠊⣁⣀⣀⣀⣠⡦⠰⣾⠃⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⣀⣀⠀⠐⢊⠀⡇⠀⠀⠀⢸⡍⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢫⡤⠖⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢋⠉⠙⣷⣦⣄⠁⠀⠀⣟⢷⠒⣤⠂⠴⠓⠠⣾⣿⠂⠉⠁⠈⣤⣆⡀⠂⢀⡀⠀⠀⠀⠀⠸⠀⠀⣀⠀⠀⢢⣭⡄⢀⡻⠦⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠘⠲⠀⠻⢣⠟⠀⣀⢀⡻⢿⡽⠛⠛⠛⣿⣶⢏⠙⣶⣤⣼⡷⣿⠉⠙⠃⡉⢰⡆⠀⠀⠈⠀⠀⢎⠁⠀⠀⠀⠀⠈⠉⣱⠄⠛⣈⣤⠇
⠀⠀⠀⠀⠀⢀⠔⠙⠀⣷⠀⠀⠀⢹⡿⢂⢉⣉⣉⣁⣄⣀⣈⡁⢶⡟⣤⠳⠾⢡⡍⣤⠉⢹⡇⠀⠀⠙⠲⢀⠀⠰⠆⢠⡈⠂⠀⠀⠀⠀⣠⠶⣌⣡⠜⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢆⣴⠇⠀⢠⡦⢋⡴⢛⠧⠀⢧⡄⠉⢡⣼⣷⣾⠇⠀⠀⠴⠉⠀⠛⠄⢘⡇⠀⠀⠀⠀⡠⢺⣷⣤⡿⠁⡠⠄⣀⣤⠀⠉⠻⠷⢉⣷⣤⣴⢦⡀
⠀⡠⣠⡄⠀⡘⠀⠀⣁⡀⢰⠌⢀⣾⣧⣿⡀⢂⠠⢜⠷⣶⣯⣿⣁⡰⠦⠖⣦⠀⠀⠈⠒⠛⠁⠀⢠⠀⠠⣇⢀⣿⡏⠁⢀⣠⣦⡨⠋⡇⠀⣠⣤⣤⣋⡉⡀⣦⣽
⠿⣁⣿⡁⠰⣧⣤⠛⠁⠹⠃⢠⣿⣹⡷⣿⣷⡤⢷⡤⡶⢿⡿⠁⠀⠀⡀⠀⠀⣶⠀⣀⠐⠀⠀⡀⡾⠋⠙⠋⢀⣿⣇⠺⠟⢥⠈⠁⠔⠀⠀⠻⣶⡇⠀⠀⠀⠈
⠀⣀⣻⡽⠀⠉⠻⠀⠀⡄⠀⣾⠁⡈⠀⢙⡿⠷⠋⠀⢳⠈⡷⢐⡖⢠⡅⡀⠀⠛⠀⢛⡆⠀⢤⣇⡀⠀⠠⠈⣃⢸⡃⠀⠀⣄⣘⣦⠐⢦⣤⣤⣆⣼⠇
⠈⠫⠿⣤⠀⠀⠀⠂⢀⣧⠀⠻⢿⡧⠀⠈⠀⠰⠈⢀⠂⠰⡗⢨⠁⣼⣇⠑⠀⠀⠀⠀⠑⠳⠊⢁⠄⣀⡸⣆⣹⣏⣼⠟⢀⠀⠉⠿⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⡀⠀⡀⠀⢻⣆⠀⢦⠀⠀⡃⠀⡤⠀⠀⠐⠂⠿⠨⠐⣟⡹⠀⠀⣀⠐⣀⢠⣶⣼⠁⣴⣉⡟⠋⠉⡛⠃⣰⣃⠀⠉⡀⠀⠐⠐⢄⡀
⠀⠀⠀⠁⢴⡟⢲⣷⠀⢀⡙⢷⣼⠷⠚⠓⢤⣀⡂⠀⠀⠐⠀⠀⠈⢸⠁⢨⣾⠟⣿⠿⣦⣾⣿⡾⢳⠉⢀⠘⠋⠀⠒⡞⠉⠈⢹⡇⠙⠀⣷⣎⠁
⠀⠀⠀⠑⣈⠻⣿⣿⠏⠉⠙⠒⢀⡄⠐⠦⠀⠈⢳⡌⣠⡀⠀⠐⢶⣼⣷⣿⠛⠎⠀⣀⣀⣈⣽⠖⠈⠐⡍⢠⢀⡀⠀⣀⡀⠀⠛⠓⠀⠸⢷⠛⠚⠐⠢⡀
⠀⠀⠀⠀⠈⠐⣈⠻⠀⠀⠀⠀⢠⠺⠆⢼⣶⡶⣦⡉⠁⠈⠋⡙⠿⠋⢉⡙⠛⠛⠛⠛⣉⠉⢁⡀⠀⢾⡧⠈⣹⡄⣾⡌⢉⡗⠂⣠⣼⣣⡈⢴⠆⠁⠤⠉
⠀⠀⠀⠀⠀⢿⣄⡀⠀⠐⠀⠀⠶⡇⣰⣾⣏⠛⠚⣡⢮⣷⠶⠿⣿⡟⣤⡶⢺⣧⣾⣷⠿⡗⠋⣛⢷⠞⢷⣄⡀⣠⣿⣼⠋⠉⠉⠀⠀⣹⣏⢰
⠀⠀⠀⠀⠀⠈⢉⠇⠘⠀⠠⠰⣟⡦⠙⢛⣿⣗⠀⣴⢏⣹⣾⣿⠿⣿⣿⡏⠻⢿⡉⠉⣱⠀⣠⡀⢦⣤⣎⡛⢸⡇⠘⠢⠔⠉⠐⣆⠸⢌⣷⣽⠂
⠀⠀⠀⠀⠀⠰⠀⢀⠔⠀⢂⠀⠀⢀⣆⠾⢫⠛⠸⣧⣿⣦⣿⢀⡞⢻⣿⣿⡄⠀⠙⡎⢣⢀⡿⢻⣄⢹⣆⠹⡞⠛⠓⠚⠒⠛⠛⠛⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠤⢀⣼⢧⣴⣿⣩⣤⡈⠠⢀⠈⢷⣸⡁⠼⣛⡿⡿⠋⠀⠀⠀⡷⠀⠀⠀⠀⠀⠈⠉⠋⣡⣤⣤⣤⡤⠤⢀⣠⠔⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⢿⣿⣿⣿⣟⣁⣿⠀⠈⠛⠁⣀⣿⡵⠂⠀⠀⢱⠘⣷⠤⠂⢀⠀⡴⠄⠀⢸⣿⠟⠛⠁⢠⡆⠈⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠈⡉⠛⠻⠿⠿⠀⠀⠀⠾⠿⠋⠀⣠⡄⢠⠀⢴⠿⠶⣆⣠⢤⣄⠴⠘⠣⠀⠀⠈⣰⣼⡇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠢⠴⠄⢀⣐⣀⡀⠄⢀⡤⠔⠀⠞⠉⠉⠀⠀⠀⠀⠀⠈⠀⢀⣀⢦⣤⣤⠰⠖⠻⠉⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠈⠉⠙⠷⢀⣄⣤⠲⠿⠿⣶⡿⠖⠞⠲⠒⠂⠀⠙⠉⠉⠀⡀⢀⠁⢈⣦⢠⡷⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⢀⣤⠤⠖⢀⠀⠀⠀⠁⠀⠀⠁⡀⠀⢀⡀⠀⠀⠀⠐⣬⠶⠲⣄⠠⠁⢾⡉⠀⠛⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠰⢢⣄⣸⠁⡀⠀⠀⠃⠀⠀⠀⣀⢀⣾⠀⠘⠁⠈⡐⢀⡀⣰⠿⣠⠀⢈⡦⣑⣾⡉⠀⠀⠀⠀⢀⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣼⣿⣍⠁⠀⠀⠀⡿⣿⣦⠀⠉⢾⡷⠶⣾⠀⠀⣿⠼⣿⢿⣿⣧⠄⣿⣷⢿⣿⡟⢻⡇⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡏⠙⠿⠟⢣⣄⡠⣮⣼⣿⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠁⣾⣿⡏⣸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣷⣶⣦⣤⣏⣰⣏⢷⣿⡷⠀⠀⢻⡟⠛⠤⠀⠀⠻⣋⠾⣿⠦⠶⠂⣿⣿⢿⣿⣋⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⡟⢻⣿⣟⠉⠛⠻⠿⣿⣿⣦⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣄⣀⣀⠀⣤⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠈⠿⠟⠈⠁⠠⠤⡿⠛⠟⠉⠀⢛⡉⠩⠈⠀⠀⠙⠛⢹⣿⠙⠛⠈⣿⠛⢻⡟⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠀⠀⠸⠂⠁⠀⠀⠀⠈⠀⠀⠀⢠⡄⠠⠀⠀⠀⠀⠀⢘⣥⡈⠉⠀⣕⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢨⣆⡉⠁⠀⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⢠⠀⢹⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠐⣍⣉⠀⠀⣷⢈⣾⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⢸⠁⣀⠀⠀⠀⠀⠀⡄⠀⠐⠂⠐⠂⠀⠀⠀⠀⣘⢧⣈⠁⠀⣿⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⢈⠁⠀⠀⠀⠀⠀⠀⠁⠀⢘⠋⠉⠀⠀⠀⠀⠀⢨⡧⢈⠀⠀⡟⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠆⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠈⠁⠀⠀⠀⠀⢰⣧⢈⡀⠀⡿⠘⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠀⠀⠀⠀⠀⢸⡧⢀⡄⠀⢆⠰⣇⢸⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢄⠀⠑⣈⡀⠀⠰⠇⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⡧⣤⠀⢸⠃⠐⢋⣾⡁⠀⠈⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠐⠀⠈⠁⠀⠂⠀⠀⡔⠀⢸⡆⠀⠄⠀⢀⠀⠀⠸⢷⡄⣠⠮⠀⠀⡘⢡⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⠓⠒⠠⠄⠀⠀⠀⠀⠛⠂⠤⠀⠃⠀⢠⣀⣡⠘⠡⠶⡈⠢⣤⣾⠛⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠐⠂⠀⣲⣿⠛⠀⠀⠀⠈⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡴⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⢠⣤⣄⠷⢊⣉⣀⢀⡤⠐⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠶⠾⠾⠿⠛⠋⢹⡿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣍⡙⠓⠶⠤⣝⣢⡀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠉⠉⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠽⠷⣤⡀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⡉⠉⠀⠀⠀⠀⠀⢤⣝⣶⣄⠀⠀⠀⠀⠙⣆⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⡡⠔⠊⠉⠉⠉⠉⣦⠀⠀⠀⠀⠀⠑⢄⡉⠁⠀⠀⠀⠀⠘⠟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢠⠎⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠤⠤⠤⢤⣀⠙⠦⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⠤⢄⠀⢻⠀⠀⠀⠀⠰⣴⡶⠋⣀⠤⠄⠒⠒⠂⠀⠀⠀⠀⠈⢑⡤⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⡀⠀⢳⠀⠙⠲⠤⠴⠒⠉⠀⠛⠤⠤⢤⡀⠀⠀⠀⠀⠀⢠⣞⡁⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠜⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠞⠁⠀⠀⠀⢀⠀⠇⠀⠀⠀⢠⠰⠉⢹⠀⠀⠀⠀⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣠⢿⡼⡀⠀⠀⠀⠈⢢⠗⢉⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠽⠶⠤⣤⣀⣀⡀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠄⣀⡠⠞⠁⢠⡷⠇⠀⠀⠀⠤⠎⢰⢋⢽⡍⣉⠶
⠀⠀⡖⢦⠀⠀⢀⠠⠀⠇⠀⠀⠀⠀⠈⠳⢄⡀⠀⠙⠒⠉⠳⠀⠀⠀⠀⠀⠀⠀⠠⢤⡠⣄⠉⠲⡄⠸⠳⠒⠒⠒⠒⠒⠒⣌⢁⣴⠳⣨⠃
⢖⡐⠛⠂⠓⠊⡠⠔⠒⠺⡀⠀⠀⠀⢠⠇⠀⠈⠑⠲⠤⣄⣀⣀⣀⣀⡠⠤⠒⠢⣄⣀⣀⣈⣁⣀⠷⠤⠾⠀⠀⠀⠀⠀⠀⠘⡙⡾⠋⣀⣸⡀
⠀⡟⠋⣡⠴⠢⠤⠭⠗⠀⠑⠖⠒⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡗⡜⠒⡲⠺⢄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠘⣌⠫⡀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠂⠒⠒⠒⠒⢰⠖⠶⠂⠀⠀⠒⠒⠒⠒⠒⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣘⣀⣸⡀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡔⢶⢧⡀⠀⠀⠈⢹⠉⠉⢹⠙⠂⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣰⡙⠞⠓⠋⠉⠒⠦⣼⠀⠀⠸⣄⣀⣀⡤⠴⠚⠣⠤⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠲⠾⠍⠉⠀⠀⠙⠀⠀⠀⠧⠤⣀⣀⣀⡀⠀⢀⡠⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠖⠒⠒⠒⠲⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠛⠿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⣤⣄⠀⠀⠈⠻⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⠛⡡⠄⠒⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⠀⠀⢀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣆⡀⠚⠓⠂⢀⣾⣿⣿⣿⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⢘⠛⢋⠁⠈⠉⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠖⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠙⠻⠖⠀⠀⠀⠂⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⢸⡯⠅⢳⣰⠃⡯⠍⢸⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠓⠂⠈⠋⠀⠓⠒⠘⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠲⠖⠂⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠉⠉⠀⠒⢤⡀
⠀⠀⠀⠀⠀⠀⡏⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢇⠀⠉⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢾⠇⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠤⠄⠀⢄⠀⠀⠀⠀⠠⠐⠀⠔⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠰⠀⠓⠀⢀⡙⠛⠯⣀⣀⣀⣀⣀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠀⠂⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠓⠢⠄⠒⠀⠃⢤⣀⡑⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢲⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠤⠄⠂⢑⠤⠬⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠀⠁
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠑⢤⡀
⠀⠀⠀⡠⠤⣸⡇⠀⠐⠀⠀⠀⠀⠀⠀⠁⡆⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡄⢯⣈⡇⠀⠀⠀⠀⠀⠠⠁⢸⠀⠀⠈⠳⢄⠀⠀⢄
⠀⠀⠀⠑⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡘⠀⠇⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡼⠀⠦⢤⣀⡀⠀⠀⡰⠁⠀⢸⠀⠀⠀⠀⠀⠁
⠀⠰⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⢀⠁⢰⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡃⠀⡠⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠃⠀⠀⠀⠀⠀⢠⠅⠈⠠⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠀⢸⠀⠀⠀⠀⠀⡸⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⡏⠃
⠀⠀⠀⠒⠲⣀⡈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⣀⣒⣒⣒⣒⣒⣀⣀⣀⣀⣀⣒⣒⣒⣒⣖⣀⣚⣓⣚⣒⣠⣶⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣂⣒⣒⣒⣒⣒⣒⣒⣒⣒⣐⣓⣒⣚⣃⣀⣐⣒⣒⣒⣒
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠳⣔⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣉⠛⠒⠬⢷⣄⠈⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⠚⠋⠉⠳⢤⡀⠀⠀⠀⠈⢧⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣚⠭⠕⠒⠒⢤⠀⠀⠀⠀⠙⢟⠛⠦⠀⠀⠀⠀⢳⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⡠⠊⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⣀⣀⠑⠦⡀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⡴⢋⢀⡀⠰⡇⠀⠀⠀⢠⣦⡴⢃⣀⠤⠤⠤⠀⠀⠁⠀⠈⠓⣄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⡐
⠀⠀⠀⠀⠀⠀⢰⠃⢫⠀⠘⠆⠙⠒⠤⠤⠚⠉⠐⠫⠤⢤⣀⠀⠀⠀⠀⠀⣴⡋⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⢀⡀⠀⠠⠃⠀⡠
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣠⢰⠀⠀⠀⢠⠐⡁⣑⠀⠀⠀⠈⢑
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⡴⢳⢣⠀⠀⠀⠀⢱⠋⡩⣱⣀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⡴⠚⠛⠒⠲⣖⠒⠒⠲⣄⣀⢤⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⢶⡋⠀⢸⠋⠀⠀⠀⠀⠁⠸⠴⢺⠠⣜⠁
⡀⠘⣅⢣⡀⠄⢀⣁⣁⠀⠀⠀⠀⡈⠑⠢⢄⡀⠀⠀⠃⠀⠀⠀⠀⣀⡀⠉⠋⠓⠆⠘⣆⢈⡹⠀⠀⠀⠀⠈⢢⢔⣯⡵⠧⡀
⢑⡦⠤⢀⣀⡚⠑⣤⠈⢆⣠⠤⢰⠃⠀⠀⠀⠈⠉⠑⠒⠒⠒⠈⠉⠀⠈⢷⠒⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠈⢮⣇⠴⠮⣷
⠈⠑⠊⠁⠀⠈⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠋⢪⠲⡊⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠒⠒⠒⠒⢠⠠⠄⠀⠀⠀⠀⠀⠒⢲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⣸⣀⣣⣀⡀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢲⡔⣟⣤⣀⠀⠀⢁⠀⠀⡏⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣃⣒⡨⠭⠥⠤⠬⠉⣏⠀⠀⢳⠲⠖⠒⠋⠉⠉⠒⢂⡢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⣀⡀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⢉⡙⠛⠂⠀⠀⠛⢉⣀⠁⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⠀⠋⠻⠃⠀⠀⠀⠀⠹⠏⠃⢈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⢘⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠋⠐⠐⠈⡀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⠀⠀⠔⠃⠀⠞⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⡼⢹⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣷⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⣤⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠿⠿⠿⠛⠋⠉


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

⠀⠀⠀⢀⣤⣄⣰⣷⣾⡇⠀⣶⣼⣧⡄⣠⣤⡀⠀⣠⣤⣤⡄⢠⣄⣠⣤⣼⣆⡄
⠀⠀⠀⠘⠷⠿⠻⠇⠿⠀⠀⠿⠼⠿⠿⠻⠿⠄⠀⠿⠿⠿⠷⠿⠿⠿⠇⠸⠿⠧⠀⠆⠰⠰⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠠⠆
⠀⠀⠀⣶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⡖⠲⣶⡒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⣒⣒⡒⠒⢒⠒⠒⡒⠒⡒⠒⢒⡲
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⣀⢀⣌⣷⣰⣾⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠈⠁⠁⠀⠈⠈⠀⢙
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣹⣿⣾⣿⡏⠋⠸⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢷⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⠛⠀⠈⢳⣦⣄⣸⣯⠙⡷⠀⠀⠀⠀⠀⣶⢦⣀⡀⡇⣠⡸⣧
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⢰⣶⢷⠽⠛⠛⠒⠗⠀⠀⠀⠀⢀⢡⣶⣿⣷⡇⠻⠃⣿⠀⠀⠀⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣅⣼⠆⠀⠀⠀⠀⠰⠀⠀⠀⢆⠀⠉⠢⡽⢃⠀⠈⢻⣤⣄⠂
⠀⠀⠀⣿⠀⢀⠀⠈⡀⠈⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⢈⣶⣾⣾⣿⣷⡻⣦⣿⡇⣹⡇
⠀⠀⠀⣿⠀⠃⡀⠠⢿⣷⢷⣮⣤⡌⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢤⡴⣏⠉⢻⣿⣿⠵⠛⠉⠙⠛⠁
⠀⠀⠀⣿⠀⠀⡀⠴⢻⣧⣀⣘⣿⣦⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡔⠀⠀⣹⡷⠾⣏⠀⠈⠢
⠀⠀⠀⣿⠀⡐⠀⡀⢰⡿⠉⠻⣆⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠠⠸⠠⠄⢺⡏⢁⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⢀⡀⠠⠀⢾⠇⠀⢠⠈⠃⠤⣁⠀⠀⠀⠀⠀⢀⠀⠄⠀⠒⠀⠀⠀⠁⠐⠀⠀⠀⣿⠓⠉⠢⠚⠒⠒⠖⠤⠀⢀⣀⠀⡤
⠀⠀⠀⣿⠀⡤⡀⠀⣻⠀⠂⠁⠀⠀⠀⠀⠀⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣄⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⣿⠀⠠⠙⠢⣼⠀⠀⡴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠆⢠⣿⠀⠀⠀⠘⠃
⠀⠀⠀⣿⠀⢀⣰⣴⣿⣂⣤⠴⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⣸⣤⣿⣦⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⣿⠀⠛⠿⠿⣿⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠂
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠿
⠀⠀⠀⣿⠀⠀⠀⠐⠉⠁⠀⡈⢠⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠚⣴⠷⠺⣟⠾⠀⠀⠈⠁⠀⠋⡴⠴⠆⠶⡀⠦⠠⠈⠀⠀⠠
⠀⠀⠀⣿⠀⠀⡆⠸⡧⠿⠀⠀⡜⠀⠀⢀⠀⠀⢀⣾⢻⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣤⣠⢀⢤⣄⢀⠂⠀⣤⣠⣤⠀⢠⣤⡄⣠⣤⠀⣤⢠⡀⠀⠠
⠀⠀⠀⣿⠀⠀⣀⣀⠠⠔⠀⠀⠙⠂⠀⠂⣥⣠⣟⡿⠟⣿⠇⠀⠀⠀⠀⠀⠀⡆⢠⠀⠉⠉⠁⠀⠉⠉⠈⠀⠀⠈⠉⠙⠀⠀⠙⠁⠁⠉⠁⠉⠉⠉⠀⢀
⠀⠀⠀⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⢿⠿⢫⣾⣴⠏⠀⠀⠀⠀⠀⠀⠀⡇⠘⠉⠉⠀⢀⠒⡀⠐⠀⠐⠒⠀⠉⠁⠀⠈⠇⠎⠯⠿⠍
⠀⠀⠀⣿⠀⠀⠀⢠⠀⠈⠀⠀⣀⢀⠀⠀⢸⠂⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠀⠈⠄⢀⠔⠒⠦⠀⠀⠂⠀⡄⢂⡄⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⣿⠀⠀⠀⢠⣄⠀⢠⣜⠀⡸⠀⠠⠻⣆⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⣳⣶⣾⣧⡀⠀⠁⠀⠠⠄⠂
⠀⠀⠀⣿⠠⡀⠀⠀⣹⡷⠻⣯⣾⠇⠈⠁⠀⠙⢿⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⠈⠒⠐⢈⡿⣏⠉⣿⣧⣄⡀⠠⠆
⠀⠀⠀⣿⠀⠀⠀⠋⠙⣳⣦⣾⠟⠫⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠊⠀⢸⠟⠛⠻⣧⠈⠂
⠀⠀⠀⣿⠀⠈⠀⠀⣴⠟⠀⠙⣆⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢂⠀⢴⠇⠀⠀⠀⡇⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⠠⠈⠒⢐⡏⠣⡀⠀⠶⠀⠒⠀⠠⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡅⢠⡠⠤⠀⢺⠛⠈⠳⠚⠁⠀⠀⢀⠄⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣿⠐⡶⠄⢸⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠄⠀⢀⣀⣀
⠀⠀⠀⣿⠀⠀⠸⣿⠀⢀⣠⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡶⠒⡒⢺⡷⣊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⣿⢀⣽⣦⣷⣞⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠾⣿⣿⣿⣿⡷⠀⠀⠀⠀⠶⣳⣶⣤⣤⠶⢶⣿⣿⠟
⠀⠀⠀⣿⠈⠙⠿⠟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣉⣤⠿⠋⡉⠛⢻⢿⣏⣡
⠀⠀⠀⣿⢀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠟⠓⠛⠛⠢⢭⣿⡤⠼⠷⠀⠀⢈
⠀⠀⠀⣿⠘⠛⠛⠛⠀⠛⠛⠃⠙⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠈⠉⠉⢉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠇
⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⢀⣿⣿⣿⠉⠙⠀⠀⠀⠀⠀⠀⣀⠀⣸⣟⠁⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⡼⢻⢿⠂
⠀⠀⠀⠀⢿⡛⠀⠀⠀⣄⡜⠉⢻⡁⣠⣄⠀⠀⠀⠀⣶⣦⣿⣿⡟⢿⠟⠂⠐⢢⠀⠀⡘⠙⠁⠀⠀⠀⠀⢠⣤⡀⢹⠿⣿⠀⢠⠛⠠⠄
⠀⠀⠀⠀⠀⠱⣤⣤⣤⣈⡇⠀⠘⠟⣿⣿⠁⠀⠀⠀⠘⢿⠃⠉⠃⠀⠀⠀⠐⢄⠏⠃⢠⣤⡄⠀⠀⠀⠀⢸⡿⠷⠲⣄⠈⠑⠏⠀⠀⣄⣀⡀
⠀⠀⠀⣿⡟⢉⣽⣿⠿⠙⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣶⣾⣏⣐⢦⢄⠸⣄⣰⣾⣿⣿⠀⠀⢠⣶⣯⡀⠀⣤⣼⡆⠰⡖⠁⠘⣿⣿⠆
⠀⠀⠀⠀⠀⠿⢿⣿⡤⢠⡏⠐⣿⣿⠅⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠁⡤⡀⠀⢨⡟⠛⠋⠛⠁⠀⠀⠈⠙⠛⠁⢸⣿⣿⡛⢦⠃⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠸⠃⣸⡡⠴⠿⠁⣶⣿⡄⠀⠀⠀⠀⠉⠿⠃⠐⢶⣶⣽⣿⣿⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣸⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⠂
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⠳⢭⠙⠋⠙⠢⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡘⣄
⠀⠀⠀⠀⠐⠊⠉⠐⠘⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣯⣩⣤⣭⣿⣧⣿⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣀⡄⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠶⠟⠛⠛⠛⠻⠿⠶⠾⠛⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣴⡟⠛⠛⢷⣤⠄⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⣸⣧⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢠⣤⠿⠛⠻⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠷⠾⡏⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⠀⠀⠀⢀⣿⡀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠛⠋⢻⣆⠀⢀⡿⠀⠀⠀⠈⠉⣿⠶⢾⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣼⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠃⠀⣀⣀⣠⣤⠄⠀⠀⢠⣤⣄⣀⣀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠁⠀⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⢉⠙⠃⠀⠸⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠈⣷⠀⣿⠀⠀⠈⠻⠿⠛⠀⠀⠀⠐⠻⠿⠛⠀⠀⢠⡗⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠶⠶⣿⡀⠀⠀⠹⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟
⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠈⢻⡟⠃⠀⠀⢹⣇⠀⠀⠀⠀⠀⠐⠶⠶⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠻⣦⡀⠀⠀⠀⣤⠶⢶⣄⠀⠀⠀⣠⡾⠁⠀⢀⡀⢀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠈⢻⣶⣤⣴⣾⠋⠈⠀⠀⠀⠀⠀⢸⡿⣦⣀⠀⠻⠶⠶⠏⢀⣠⡾⣿⠀⢀⡰⣌⠛⠛⠛⠋⠉⠙⢷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠙⢷⣤⣀⣠⣴⠟⠁⠀⣿⠀⠈⢷⣌⡅⠀⠀⠀⠀⠚⠻⣧⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠹⣦⣀⣀⢻⣇⠀⠀⠀⠀⠀⠘⠋⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡴⠶⠾⠛⠛⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠿⣧⡀⠀⢀⣴⣦⣄⣴⠟
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠈⠛⠛⠋⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠉⠛⣷⠀⠀⠀⠀⠀⢿⣥⣠⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠃⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣀⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠿⠶⣶⠾⠷⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⠋⠻⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⢿⣦⣤⠶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⠉⠁⠈⠉⠻⣶⡟⠁⠀⠀⠀⠈⢷⣀⣴⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠉⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠛⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠈⣷⠶⢦⡀⠀⠀⠀⠀⠀⠀⣴⠶⣤⣴⠞⠛⠉⠙⠛⠳⠶⢾⡗⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⣀⣤⠾⠁⠀⠀⠀⠀⠀⠀⠻⣶⡟⠁⠐⠶⠟⠻⠏⠀⢀⣼⠃⠀⠀⠀⠀⢀⣀⣴⠿⠃
⠀⢀⣾⠟⠀⠀⠀⠀⠀⢀⣀⡀⣠⡴⣦⡀⣼⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣤⠶⠛⠁⠀⠀⢰⡿⠛⠛⠉
⠀⢸⣇⠀⠀⠀⣠⡴⠾⠋⠉⠙⣿⠀⠀⠙⣷⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣀⣠⠀⣀⣿⣤⡀⠀⠀⣠⡟⠁
⢀⣠⣿⣶⣤⣤⣿⣦⣤⣤⣤⣤⣿⣤⣤⣤⣿⣤⣿⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠛⠛⠛⠻⠿⣅⠙⣿⡛⠉
⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⣧
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠲⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢿⡄
⠘⣷⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡾⢿⣄⠈⢿⡄
⠀⠘⢻⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠻⣦⣄⣻⣦⡀
⠀⠀⠀⣿⠀⣀⣀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣠⣀⠀⠀⢸⡏⠀⠀⠀⠀⠈⠉⠛⠛⠃
⠀⠀⠀⢻⡄⣯⠹⡆⠀⠀⣾⠁⠈⣧⠀⠀⢠⡟⠁⠀⠈⣇⠀⠀⡾⠁⠈⣧⠀⢀⡾⠁⣿⠀⠀⣾⠇
⠀⠀⠀⢸⡇⢹⡀⢻⠀⠀⣿⠀⠀⢸⡆⠀⢸⠁⠀⠀⠀⢹⠀⢸⡇⠀⠀⣿⠀⣸⠁⠀⣿⠀⢀⣿
⠀⠀⠀⠈⣇⢸⡇⠈⡇⠀⣿⠀⠀⠘⣇⠀⢸⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⣿⠀⡿⠀⠀⣿⠀⢸⡏
⠀⠀⠀⠀⣿⠀⣷⠀⣧⠀⣿⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠈⡇⣼⠀⠀⠀⣿⠀⡇⠀⢠⡏⠀⣼⠇
⠀⠀⠀⠀⢹⡆⢻⠀⢸⡀⢸⡄⠀⠀⢻⡀⠘⡄⠀⠀⠀⠀⡇⣿⠀⠀⠀⡟⢸⡇⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢸⡇⠸⡇⠘⡇⠸⡇⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⡇⣿⠀⠀⢰⡇⢸⡇⠀⣼⠁⢰⡏
⠀⠀⠀⠀⠀⣿⠀⢷⠀⢿⠀⣿⠀⠀⠈⣇⠀⡇⠀⠀⠀⠀⡇⣿⠀⠀⢸⡇⢸⠀⠀⡿⠀⢸⡇
⠀⠀⠀⠀⠀⢿⡄⢸⡀⢸⡆⢸⡄⠀⠀⣿⠀⡇⠀⠀⠀⢠⡇⣿⠀⠀⢸⠀⣼⠀⢰⡇⠀⣿⠁
⠀⠀⠀⠀⠀⢸⣇⠈⡇⠈⡇⠘⡇⠀⠀⣿⠀⢿⠀⠀⠀⢸⠁⣿⠀⠀⣾⠀⣿⠀⢸⠁⢠⡿
⠀⠀⠀⠀⠀⠀⣿⡀⢻⣀⡿⠀⢻⡀⢀⡟⠀⠈⢷⣄⣠⡟⠀⠸⣆⣴⠇⠀⢸⣦⡟⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⠀⠙⠛⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠶⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠸⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡾⠃⠀⠀⠀⢴⣿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⣶⡶⠶⠶⠿⠷⠶⠶⠶⠶⠿⠛⠛⠛⢻⣿⡃⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⣴⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠚⠻⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢿⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠂⣀⣠⣴⠶⠟⠋⠁⠀⠈⣷⡀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⣤⣤⣤⠤⠶⠞⠛⠙⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣼⠇⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠈⠻⣧⠀⠀⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⡇⠀⠀⠀⠀⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⢸⡇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⢸⡇⠀⠀⠠⣴⠶⣾⣿⣷⠆⠀⠀⠀⠀⠰⣿⣿⠿⠷⠦⠄⠀⠀⠀⣾⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⡇⠀⠀⠀⠀⠲⠛⠋⠁⠀⣴⠆⢀⡀⠀⠀⠙⢶⡄⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⢠⣾⠛⢹⣿⢰⡾⢷⣶⢦⠀⠀⠀⠀⠀⠀⠀⣈⣉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠫⣄⠀⠀⠀⠀⣾⠃⢰⡟⢛⣿⠀⢠⡷⢸⣷⡆⠀⠀⠀⠀⣰⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢹⡀⠈⠛⠛⠁⠀⠛⢵⣿⣿⡇⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠗⠈⠻⣦⡀⣸⡇⠀⠀⠀⠀⠀⠀⢈⣫⣿⣧⡴⠟⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⢀⣤⡿⠋⠀⠠⣤⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⢀⣠⡾⠟⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢰⣟⣤⡾⣿⣿⠟⠋⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡿⢋⣼⠟⠁⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⡂⣿⡃⠀⠀⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⣠⠤⠤⠤⠤⠤⢤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⡇⠀⠰⣯⡵⠶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⢔⣒⣪⡉⡇⢸⠀⢰⡇⠀⠀⠀⣠⠔⣋⠭⠭⠽⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⢰⡚⢳⠀⠀⠀⠀⠉⡠⢀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢰⢒⠭⠽⠖⢶⡎⠉⠉⠃⠀⡇⡇⢸⠀⢸⡇⣀⠴⠊⣡⠞⠁⡀⢐⠐⡀⠀⠀⠀⠀⠀⠀⢸
⠀⣇⡔⠉⠉⠉⠙⣆⠀⠀⠀⠐⡀⠀⠂⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢸⠸⢀⣠⣄⢸⡇⠀⠀⠂⠀⡇⡇⢸⠀⢸⡟⢁⡴⠊⠀⠀⠠⠄⠠⠀⠡⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡷⠶⠶⠶⠶⢾⠀⠀⠐⠰⠒⠲⠦⠤⠤⠤⢺⡇⠀⡇⠀⠀⣀⡤⢚⠁⠈⠁⢸⣧⠄⠀⠀⠀⡇⡇⢸⠀⢸⡗⠋⠀⠀⠀⠀⠐⠀⢐⣀⡤⠶⠤⠤⠤⠤⠤⢾
⠀⣿⡇⠀⠀⠀⠀⢸⠀⠀⢀⡻⢭⡉⠉⠉⠙⠉⢹⡇⠀⡇⠀⠉⠀⢸⣸⠀⡀⠀⢸⡟⠀⠀⠀⠀⡇⡇⢸⠀⢸⡇⠀⢀⢤⠀⠀⡡⠐⠃⢀⡯⣍⡉⠉⠛⠛⠋⢹
⠀⣿⡇⠀⠀⠀⠀⢸⢠⣚⠭⢒⡉⠁⠀⠀⠀⠀⣸⡇⠀⡇⠀⠀⢀⣨⢖⠉⠁⠀⢸⡇⠀⠀⠀⠀⡇⡇⢸⠀⢸⡇⠀⠈⠉⠀⢀⠇⠰⣊⠭⢒⡉⠀⠀⠀⠀⠀⣸
⠀⣯⡗⠒⠒⠒⠒⢻⣸⠴⣚⡭⠔⣀⠀⢀⡤⠚⢹⡇⠀⡇⠛⠋⠉⢰⡸⠤⠤⣄⣼⣇⣀⡁⠀⠀⡇⡇⢸⠀⢸⡇⠀⢔⠑⡆⠘⠄⡮⠴⣚⡭⠔⡀⠀⢀⡤⠚⢹
⠀⡏⠓⠒⠒⠒⠒⠊⠙⠯⢥⣒⣫⠵⠚⠉⠀⠀⢸⠇⠀⡇⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠤⠬⠭⣍⣁⡇⢸⠀⠸⡇⠀⠈⠉⠀⠀⠈⠑⠯⣥⣒⣩⠵⠚⠉⠀⠀⢸
⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠋
⠀⣠⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⡤⠤⠤⠤⠤⠤⣄⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⡇⠀⠀⢀⠔⠊⠉⠉⠉⠀⠈⠉⠑⢦⡀⠀⠀⢸⡆⠀⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⡀⢸
⠀⡇⠀⢠⠋⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠹⡄⠀⢸⡇⠀⡇⢀⡔⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⣏⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⣷⢸
⠀⡇⠀⣼⠀⢀⠟⠦⣼⠙⠦⡯⠑⢄⡀⠀⢷⠀⢸⡇⠀⡇⡞⠉⠉⠙⠛⠲⢤⣀⣀⠀⠀⠀⣀⠤⠤⣀⢸⠀⢸⡇⠙⠲⠶⠋⠀⢘⣽⢣⡶⡖⡆⠀⠓⠶⠞⠁⢸
⠀⡇⠀⢻⢠⡏⠀⣥⠀⠀⠀⠀⣥⠀⠉⡆⡘⠀⢸⡇⠀⣇⡇⠐⠠⠀⠀⢀⡀⠀⠉⠉⠉⢹⠁⠀⠀⢸⣾⠀⢸⡇⡴⠋⠉⢳⡀⣈⠉⠀⠀⠁⡁⢠⠞⠉⠙⣆⢸
⠀⡇⠀⣎⠙⢳⠒⠛⠉⠉⠉⠉⠛⠒⡖⠋⢹⠀⢸⡇⠀⡇⡇⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⢸⠀⢸⡇⡇⠀⠀⢸⠃⠻⠛⠛⠛⠛⠟⢸⡄⠀⠀⡿⢸
⠀⡇⠀⠈⠲⣼⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠃⠀⢸⡇⠀⡇⢹⡀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢸⢀⡠⠚⠀⢸⠀⢸⡇⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⢸
⠀⡇⠀⠀⠀⠘⠲⢤⣈⡉⢉⣉⣠⠴⠋⠀⠀⠀⢸⡇⠀⡇⠀⠳⢤⣉⠀⠐⠂⣀⣉⡤⠴⠚⠉⠀⠀⠀⢸⠀⢸⡇⢿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⢸
⠀⡇⠀⠀⠀⣀⣠⣴⠃⠉⠉⠘⢧⣄⣀⡀⠀⠀⢸⠇⠀⡇⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡇⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⢸
⠀⠉⠒⠒⠚⠒⠒⠚⠓⠒⠒⠚⠓⠒⠒⠛⠒⠒⠋⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧
⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⡄⣤⡤⢀⣴⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠰⣦⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣛⣸⣆⣛⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣭⢹⡿⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⠶⠏⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡿⠁⠀⠀⢠⡶⠟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠛⠉⠉⠙⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⠀⠀⠸⣧⠀⠀⠀⠉⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣤⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣾⣇⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣬⢻⡏⢭⣝⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⡇⠉⠉⠈⢿⡆⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⠗⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠻⠶⠆⢀⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⣘⢁⡒⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⡎⠄⣈⣄⠠⠂⢹⣊⠔⣁⠠⠄⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠚⢫⡡⠤⠄⠀⠉⠒⠴⠉⣀⠔⠉⢀⠜⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠦⣀⠀⠀⠀⠀⣀⠔⠁⠀⠉⠀⠀⠀⢈⡩⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⡀⠀⠈⢆⠀⠀⠤⢤⣄⠀⠀⠀⠀⠀⠯⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⠈⠑⠁⠠⠨⠦⠠⠀⣈⣁⣀⡀⣀⠄⢊⡰⢠⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠐⠂⠙⠊⠂⠄⣀⠀⠀⠀⡘⠀⠀⠉⠉⠐⠉⠀⢸⠠⠀⠑⢲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠖⠁⠀⠀⠀⠈⠆⢠⡉⠉⠀⠐⠁⠤⣀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠘⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⠀⠀⠀⠀⠀⡸⠉⠙⠳⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⡒⠲⣏⠀⠀⠀⡹⠓⠀⠀⠉⠉⠉⠉⢉⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢻⣄⡠⠂⠣⡀⠀⠀⠀⠀⠀⠘⢁⢓⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠒⠀⠀⠀⣇⡘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠛⣦⠋⠈⢑⡆⠀⠀⠀⠀⠀⠘⠧⣤⡶⠟⠛⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⡄
⠀⠀⢀⣀⡤⡤⠖⠒⠒⠒⠒⠶⢤⣤⣄⡀⠀⠀⠀⢈⣧⣀⡤⠟⠀⢠⠞⠀⠀⠀⠀⠀⠀⢀⣼⠭⢽⣆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⣱⢄⡽
⠀⢰⡏⠀⡧⡇⠀⠀⠀⠀⠀⢠⣷⡇⢀⡿⠀⠀⣰⢋⡴⠁⢀⣀⣀⣸⠀⠀⠀⠀⠀⠀⢀⡯⠤⠶⠶⠾⡇⠐⠊⠈⢀⠀⠀⠀⠀⢠⠞⠁⠘⠤⢞⡽⠋
⠀⠀⠙⠦⣷⡃⠀⠀⠀⠀⠀⢸⣲⠗⠉⠀⠀⠀⡿⣫⢖⣾⠉⠀⠈⠙⢦⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠃⠉⠀⠀⠀⠀⣠⠇⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠉⠛⠲⠤⠴⠚⠉⠁⠀⠀⠀⠀⠀⢿⣱⣻⡇⠀⠀⠀⠀⣺⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣴⣾⡵⠋⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⠶⡤⠤⠞⠁⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢠⣶⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⣄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⢙⠒⣦⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣠⠌⢹⡀⠾⠆⢠⣤⠀⠀⠀⠀⠀⠀⢠⣺⠏⠀⠐⠶⠿⠆⠀⠈⢿⢦
⠀⠀⣿⣿⣿⣿⣿⣿⡧⠀⠋⢀⡞⣆⠉⣀⠸⠗⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⣏⢹⡄⣴⡌⠉⠀⠀⠀⠀⠀⢠⠋⡏⠒⠒⠒⠒⠒⠒⠒⠒⢸⡟⡇
⠀⠀⠹⣿⣿⣿⣿⣿⡃⠀⠀⠀⠳⢼⠈⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⠀⠀⠈⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠛⠒⠲⠶⠶⠶⠶⠶⠶⠚⠀⢹
⠀⠀⠀⠘⢿⣿⣿⣿⣿⡏⠀⠀⣤⠞⠀⣤⠦⠤⣤⠀⠀⠀⠻⣿⣿⣿⠟⠟⣧⣀⣀⣾⠁⢠⣾⠉⠉⢹⠀⠀⠀⠀⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠉⠁⢰⣷⣶⣶⣷⠀⢾⣏⠀⠀⢻⠀⠀⠀⠀⠈⢻⡿⠀⠸⠿⠿⠿⠿⠀⠘⢻⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠛⠒⠒⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢭⣭⣭⣭⣹⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⢶⡄⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⢀⡴⠒⠛⠉⠉⠀⠀⠀⠀⢧⠀⠀⢶⡞⠉⠁⠉⠓⡖⠀⢀⣴⣶⣤⡀⠀⢠⡤⠤⠤⠤⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼
⠀⠀⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⡄⠈⠀⠈⠀⡿⠀⣿⣯⣿⣽⣿⠂⢸⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⠀⠀⢀⡤⠶⠒⠒⠒⠶⠦⢄⠀⣷⠀⠀⠀⠀⣿
⠀⠀⢸⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠙⢢⡤⠴⠚⠃⠀⠘⠿⠿⠿⠋⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇⢸⣸⡆⠀⢼⣤⣤⣤⣤⣤⣤⣤⣼⠄⢹⠀⠀⠀⠀⡇
⠀⠀⠈⡇⢧⠀⢾⣿⣧⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢠⡖⠛⠒⢶⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⣼⡿⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⢹⠀⠸⣄⣀⣀⣰⠇
⠀⠀⠀⠸⡜⣆⢈⣁⣠⡤⣤⣶⣾⠿⠋⠀⠀⠀⠀⢸⡄⠁⠉⣠⠏⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡿⠚⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⣿⣿⣸⣸
⠀⠀⠀⠀⠙⠾⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠸⠛⡛⠀⠀⠀⠀⠀⠀⠀⢺⠛⡃⠀⠀⠀⠀⢠⡏⢷⠀⠀⠀⢰⠋⣇⠀⠀⠀⢀⡤⠤⠤⠤⠤⢤⠤⠤⠤⢤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣄
⠀⠀⠔⠛⠑⡄⢀⠀⠀⠀⠀⢀⠐⠛⠢⠀⠀⠀⢠⠟⠀⢸⣀⣀⣀⡼⠀⠸⡄⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⣰⠋⣠⢿⠀⠀⠀⣀⣀⣀⣀⣠⣶⠿⠋⠉⣮⢳⡄
⠀⠀⠀⠀⢸⠐⠿⠒⠒⠒⠿⠃⡀⠀⢸⠀⠀⠀⡏⠀⢠⠀⣠⠀⣀⢠⡄⠀⣿⠀⠀⢸⡇⠀⠀⠀⣠⢼⠀⠀⠀⠀⠁⢸⠀⠀⣸⢁⣠⡞⡽⠋⠁⢀⣤⣪⢵⡏
⠀⠠⣶⣶⣾⡆⠀⠀⠀⠀⠀⢰⣿⣶⣾⠀⠀⠀⡇⠀⠈⢀⠉⠀⢁⡈⠁⠀⢼⠀⢀⣸⡧⠴⢒⡩⢆⣸⠀⠀⠀⠀⠀⢸⠀⣰⠃⡜⠀⠙⢿⣲⠞⢿⣁⡵⠀⣧
⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⡇⠀⠀⠓⠃⠊⠘⠀⠀⠀⢸⠀⠀⢸⣆⣊⣡⣔⣋⣸⣀⣀⣀⣀⣀⣸⠀⢿⠒⠒⠒⠒⠚⠛⠒⠚⠓⠒⠒⡿
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞⠀⠀⠠⠴⠋⠁⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠁⠀⠐⠤⠀⠀⠀⠈⢂⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠞⠉⠈⠑⠤⠤⠤⠒⠉⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⡈⠀⣸⠀⠠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢰⠀⣼⡿⠀⠀⠀⠀⠠⠀⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⢀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢠
⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⢀⡀⠀⡀⠀⠀⠈⠉⠐⠦⣀⠀⠀⠀⠀⠄⠠⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⢊⣤⣤⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠐⠀⣆
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢆⠉⠻⡿⠿⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⡀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡄⠀⠀⠀⠀⠈⢦⠀⠀⠀⠉⢄
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠴⠟⠁⠨⠆⠀⠀⠀⠀⢈⠆⠀⠀⠠⠂⢀
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐⠄⡀⠀⠀⠀⠀⠉⠀⠀⠘⢆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠸⡀⠀⠀⠈⠂⡀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠡⠀⠀⠀⠀⠐⡆⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⠀⠂⡤⢀⠀⠀⠀⠀⠀⠘⠛⡓⠀⠀⢀⠄⠀⠀⠠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⢀⡜⠀⠀⠀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠦⢄⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⢀⠀⠰⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡈
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠑⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠈⠳⢆⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤
⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣰⣿⠘⠀⠀⠀⡔⠒⠐⠂⠠⠄⠠⠀⠊⠀⠀⠁⢀⠀⠔⠊
⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠟⠁⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠀⣀⢠⠄⠈⠀⠀⠀⠀⠀⠀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠑⠂⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠌⠁⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢇⠀⠻⣿⣿⣝⠂⠀⠄⡹
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⡉⢉⡁⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⡤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⡄⠀⠀⠀⢱⡞⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⣆⠀⣀⢚⣇⠘⠄⣤⠆⠀⢀⡄⢤⠀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢢⠀⠀⠀⣔⡵⠖⢚⠘⣏⠁⠀⠉⠈⠹⡗⠢⠤⣬⣰⠇⣡⡷⡻⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣜⠦⡀⠔⡁⠤⡀⠀⠐⠄⢀⠀⠀⠠⠁⣧⠀⠀⠀⠉⠪⢞⢀⢇⣄⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡰⡀⡈⠃⠀⠸⠤⢴⣇⠀⠀⠀⢠⠔⠒⠠⡈⠙⢓⠀⠀⢀⡠⣞⠽⢧⣄⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡎⢉⡙⢄⡈⢉⠏⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠱⣄⠒⣢⠇⠀⠀⠀⢀⡁⡸⠇⠄⠀⡝⠤⢴⣆⣤⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠯⣙⠢⠄⠀⠀⠀⠀⠀⠈⡅⣢⠤⠤⣈⢿⡁⠆⠀⠀⢀⠁⣄⠈⠆⢁⠜⡰⠄⡇⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⣎⡉⣶⣲⠀⠉⠀⢀⣀⠀⠀⠀⠀⢰⡃⣠⡄⢌⠇⠈⠙⠀⠐⠮⠶⡽⠎⠀⠡⢪⡞⠲⣽⠚⠶⠞⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢐⡋⠀⠀⠀⡇⢈⣡⡶⣦⡄⠀⠉⠓⢢⠫⠀⡤⠂⠤⡀⠈⠁⠐⢒⣢⡶⡷⣤⣦⢶⣶⡶⠾⠯⣄⡜
⠀⠀⠀⠀⠀⢀⢄⠀⠀⠈⣃⡀⠄⠀⠑⠘⠁⠀⡂⠀⠀⠀⠀⠨⠀⠚⣄⡖⣀⡇⠀⢀⢔⡨⠊⢈⣤⡵⠒⠋⢢⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⢀⠽⠝⠻⢴⠒⠒⠀⠀⠀⠀⣠⢂⣤⡄⠀⠀⠀⠆⣠⠈⢑⠝⠊⣈⡵⠛⠢⣕⠍⡩⢉⣹⠶⠊
⠀⠀⠀⠀⠀⠈⠉⠀⡠⢄⡸⠀⠀⢀⠤⠠⢺⠕⢩⠂⠄⠀⡠⠒⡁⢻⠤⡢⠅⠘⠩⢳⣔⣂⠥⢊⢔⠝⠍⣲⣶⡊⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠋⢱⡐⣇⠠⢐⠃⠀⢈⢃⡴⠀⢱⣌⡲⠞⢁⠠⡪⣓⣌⠕⠭⣁⠔⢁⠡⡪⣸⡠⢄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⡾⠓⢌⠉⠁⠠⠐⠪⡯⢒⣈⠕⣊⢅⡢⠕⣍⠦⡋⢦⣉⠲⠁⠣⢤⣗⢴⠉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⠃⡀⣊⠶⡂⢓⠤⢕⡁⠅⣂⠥⡂⠡⡀⡎⠔⡪⢐⠱⢙⠗⢡⢅⣣⠜⠑⣵⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣪⠞⠁⠀⢈⣶⣌⣐⡆⣠⠤⢅⡂⢔⢿⢇⠠⢒⡡⡪⠵⣐⢜⣏⠁⠀⠀⠈⢇⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠃⠀⢠⠤⢺⠃⠀⡸⣰⠓⠌⣁⣊⢱⡛⠆⡱⢥⡟⠂⠛⠋⠈⠞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠋⠀⠰⡱⠃⠀⠀⢸⢏⠀⠈⠉⠀⠸⢗⢢⠀⠀⠀⢘⠈⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⡇⠀⠀⠐⠯⠦⠁⠀⠀⠀⠛⠭⠞⠀⠀⠀⠈⠒⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠄⣀⠤⠂⣀⠤⢂⡠⢔⡀⠔⣂⠤⢂⡠⠒⡉⠔⢊⠡⢒⡡⢒⡡⢒⡡⢒⡥⡪⢒⠕⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⠠⠒⠩⠔⠊⠥⠒⠡⠔⠈⠔⠊⡡⠐⠁⠔⠊⠠⠂⠡⠒⠡⠒⠁⠒⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣾⣯⠉⠛⢷⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠋⠁⠀⠀⠊⢷⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⡀⠀⠀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⡁⠀⠀⠀⠀⣸⠁⡞
⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣤⠏⡸⠁
⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⢠⠞⠋⣰⠃
⠀⠀⠀⠀⠘⠿⠟⠀⢀⣀⣤⣤⣤⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠌⠉⠁⠀⠐⠜⠀⠀⠀⠀⠀⠀⠰⢄⣀⠀⠀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡿⠀⠀⠀⠀⢠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢸⡇⠀⠀⠀⢠⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⢠⣿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣷⠀⠀⣼⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⢸⡇⠀⠈⣿⡀⠀⣿⡇⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⢸⣿⠀⠀⢻⣇⠀⢹⣧⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣿⠀⠀⠈⣿⡄⠀⠈⣿⡄⠈⢿⣆⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢸⣿⠀⠀⠀⢹⣧⠀⠀⠘⣿⡄⠈⢿⣆⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⣿⡀⠀⠀⠀⢻⣧⠀⠀⠘⣿⡄⠀⠻⣷⡀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢹⣧⠀⠀⠀⠀⢻⣧⠀⠀⠘⣿⡄⠀⠙⣿⡄⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢻⣧⠀⠀⠀⠀⢻⣧⠀⠀⠘⣿⡀⠀⠘⣿⡀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠹⣷⡀⠀⠀⠀⢻⣇⠀⠀⢹⣧⠀⠀⢹⣧⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠘⢿⣆⠀⠀⠈⣿⡄⠀⠀⣿⡀⠀⠘⣿⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⢻⣧⠀⠀⢸⣷⠀⠀⣿⡇⠀⢀⣿⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢿⡇⠀⠀⣿⡀⠀⣿⠃⠀⢸⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢸⣿⠀⠀⣿⡇⢰⣿⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⠀⠀⣿⡇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⠃⠀⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠋⠀⠀⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡿⢣⣶⢠⡄⠀⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠀⢠⡾⣏⣷⡀⠀⠀⠀⠀⣴⣾⣿⡶⠀⠀⠀⠀⠀⣰⣿⣯⣷
⠀⠀⠀⣦⣭⠡⡿⠃⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠈⠻⠧⠟⠁⠀⠀⠀⠀⢾⡿⣿⠿⠃⠀⠀⠀⠀⠘⠾⠽⠟


⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⢀⢀⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⡀
⠀⠀⢰⡏⢸⡇⢸⡇⠀⠀⠀⠀⠐⢨⣀⢂⠀⠀⠀⠀⠀⢀⡄⠙⠗⠀⠀⠀⠀⠐⣯⠉⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠘⠗⢼⠗⠋⠀⠀⠀⠀⠀⠉⠤⠂⠬⠀⠀⠀⠀⠀⠘⠻⠂⠘⠃⠀⠀⠀⠀⠙⠷⠙⠻⡧⠀⠀⠀⠀⠑⠐⠐⠻⡦


⠀⠀⠀⣀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⢠⣬⣿⣿⣥⡄⠀⠀⠀⠀⢰⡙⢉⡆⠀⠀⠀⠀⠀⣾⠻⣄⡙⣧⠀⠀⠀⠀⢴⢿⡿⣦⠀⠀⠀⠀⠈⡛⠛⠶⣤⡄
⠀⠀⠀⠶⢹⡟⠆⠀⠀⠀⠀⠀⠩⠺⠐⠃⠀⠀⠀⠀⠀⠹⢦⣬⡿⠋⠀⠀⠀⠀⠈⠻⠛⠃⠀⠀⠀⠀⠀⠻⠶⠶⢦⡄


⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢀⠀⠀⠀⠀⠀⢀⡀⡆⣀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢸⣶⣿⣻⡵⠀⠀⠀⠀⠀⣿⡇⢠⣶⡀⠀⠀⠀⠀⡁⠺⡷⢈⠀⠀⠀⠀⠠⠬⠁⠈⠥⠄⠀⠀⠀⠀⢼⢈⠠⢽
⠀⠀⠀⠙⠛⢿⠙⠀⠀⠀⠀⠀⠈⠁⠸⣿⠃⠀⠀⠀⠀⠀⠂⠐⠻⡷⠀⠀⠀⠀⠰⠋⡎⠳⠀⠀⠀⠀⠀⠈⠛⠐⠁


⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⣠⣤⣧⡀⠀⠀⠀⠀⠀⠀⠘⡃⠀⡀⠀⠀⠀⠀⣀⡀⢇⡤⠀⠀⠀⠀⠀⢀⡤⢶⠶⡄
⠀⠀⠛⠶⠶⠶⠞⠃⠀⠀⠀⠀⢺⣏⡿⠓⠀⠀⠀⠀⠀⠀⠿⡽⠊⠋⠀⠀⠀⠀⢨⡅⣴⠰⠄⠀⠀⠀⠀⢯⣽⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢛⣒⠒⠢⣀⠀⠀⢀⠰⣄⣰⣄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⢃⣤⣿⣿⣿⣿⣿⣦⣥⡜⠂⠙⠃⠈⠃⠙⠷⢄⠔⢒⣊⣡⣴⣆⠢⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠈⡇⣲⣿⣿⢋⠄⢉⢀⢀⢹⣿⣆⡆⣆⡄⣆⡄⡆⡄⡀⠉⢻⣿⣿⣿⣿⣌⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢻⡿⠋⠀⠠⡠⣻⣿⣿⣗⢿⣿⣿⣿⣿⣿⣾⣽⣿⣱⣾⣿⠐⢌⣿⣿⡧⡀
⠀⠀⠀⠀⠀⣄⢠⡀⠀⠣⠊⠀⡀⣑⣽⡿⠟⠉⠀⠀⠀⠙⠿⢿⠿⠿⠛⠉⢻⣿⣾⡕⡴⡀⠻⣿⡿⠀⠀⣰
⠀⠀⠀⠀⢠⡸⡓⠿⣢⡤⣄⣵⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⠀⠙⢿⣾⡵⣣⠘⣿⠔⣷⠟⡀
⠀⠀⠀⠀⢀⢳⠿⠀⠛⢛⣿⣜⣿⣿⣿⡿⠀⠀⠀⠀⠀⣠⡄⠀⣿⣧⠀⠈⣀⣴⣦⡀⢻⣻⣷⣣⠘⡄⣨⢼⠁
⠀⠀⠀⠀⠈⠻⣄⠀⠀⢻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⢿⣿⣄⠘⣿⣦⠘⠿⠛⣿⣷⠀⢷⣻⣷⡃⣱⠰⡷⠃
⠀⠀⠀⠀⠀⠀⠘⠀⢰⣿⣿⡿⠿⠋⠁⠀⠀⠶⣿⣷⣶⣤⣌⣿⣷⣌⠻⣿⣶⣾⣿⡟⠀⣸⣿⢿⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣿⡇⠀⢀⣤⠀⠀⠀⠈⠻⣿⣿⡿⢿⣿⣿⣷⡄⠉⣻⠙⡆⠀⠊⠉⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠶⣿⠿⠟⠁⠐⠿⣿⣧⠀⠀⠀⠀⠈⢻⣿⣦⡀⠉⠛⢡⣶⡻⡷⠈⣰⡇⠀⠬⣿⣽⠛⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠈⠻⣷⡄⠀⠀⣾⣦⡻⡿⣫⠄⣏⣹⠉⠁⣔⣽⢿⠁⠨⢭⣿⡏⣟⠂
⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⠉⠛⠻⣷⡄⠀⠘⣿⣦⣾⣿⠟⣁⣦⡙⠾⠃⠀⠀⠀⢘⣷⣇⢐⠭⣿⣿⠋⠁
⠀⠀⠀⠀⠐⠿⣿⣆⠸⣿⡄⠀⠀⢻⣷⠀⠀⠘⠿⣫⢤⣷⠿⠋⠠⣬⣿⡒⢆⠀⠀⣘⣿⢢⣽⣿⣿⡁
⠀⣠⣶⣦⣤⣄⣘⣿⣧⡙⢿⣷⣄⣸⣿⠀⢀⣤⣯⠿⢞⡉⠀⣲⣟⡺⠧⠒⢁⢠⣢⣿⣿⣿⣿⣿⣿⡇
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⡙⠻⢛⡁⠞⣍⠒⠃⣰⣿⡇⣀⡀⣠⢠⡲⣮⣦⣷⣿⡿⠛⣿⣿⣿⣿⠇
⠀⠀⠀⠈⢻⣷⣄⠉⠛⠿⠿⡋⡤⡿⡏⠈⠁⠀⠀⠹⣿⣷⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠹⣿⡷⠀⢰⣎⠳⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⠟⠻⠿⠟⠿⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣾⢠⣤⡀⣠⣄⠀⢀⡼⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠔⠒⠢⢄⡀⠙⠾⠏⠘⠀⠇⠧⠼⠀⡀⠀⡀⠁⠀⠀⠀⠸⢻⣤
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠈⠉⠒⢒⣤⣤⠀⠀⠀⠀⡟⠶⣷⢠⠶⣤⠀⢀⡾⢹
⠀⠀⠀⠀⡼⠀⠀⣤⡀⠀⠀⠀⢀⣴⡿⣿⣿⠀⠀⠀⠀⠿⠀⠛⠹⣭⡵⠆⠙
⠀⠀⠀⠀⠳⣄⠀⠛⣿⣿⣷⣴⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⣬⣷⣦⡘⣿⣿⣿⣿⣿⣿⡟⠻⢿⣟⣶⣦⣀⣀⣴⠏⢁⣀⠀⠀⢰⠊⣜⣰⣋⠉⣉⠝⠁
⠀⠀⠀⠀⠀⠻⠿⣿⡿⣯⣿⣿⣿⣿⣟⠿⣶⣐⠋⢘⠓⠿⣥⣄⠀⣠⠈⢻⡻⣼⠚⠉⠀⠈⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢹⣿⣿⣏⠻⢄⡟⠁⠀⡴⢷⡀⣠⣝⡸⠏⠀⢀⡆⣿⠂⠐⢻⠉⣉⣽⡄
⠀⠀⠀⠀⠀⠀⠐⣯⢹⡆⠀⡋⠹⠏⠀⣸⠁⠀⠀⣇⠈⢧⡀⠀⢀⡺⠔⠋⠀⢸⡆⠀⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠿⠚⢁⠐⠻⠜⢢⡶⣿⡂⠀⠀⢻⣆⠀⠉⠋⠉⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⣸⣟⢡⢛⣿⡄⠀⠀⠉⢷⣤⡀⠀⠀⠀⣶⡾⢏⣀⠢⣄⣴⣉⣈⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠘⢿⠸⣿⡁⠀⠀⠀⠈⠛⢿⣷⠞⣯⠿⠈⣟⢛⢦⣀⣈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅⣸⡆⠘⠻⢧⣦⣤⢴⣴⡞⠉⢻⠁⠀⠀⠘⠢⠭⢻⡍⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡄⡀⡇⠀⢳⡀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⢚⡷⠀⠀⠑⠾⠃⢀⣼⡎⠦⠬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠋⠀⠀⠀⠀⠀⠀⠏⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈

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