Petri dish Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⣐⠂⠭⠁⠀⠀⠐⠒⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠂⠀⠀⠀⠈⠩⠬⠍⠀⡒⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡂⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢅⠢⡀
⠀⠀⠀⠀⠀⢀⠔⢉⠔⠉⠀⠀⢀⠀⠀⠄⠄⠀⢀⡴⠒⢠⡄⣤⡄⣤⣀⡀⣀⡐⠢⣀⠤⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣄
⠀⠀⠀⠀⢠⠋⣰⢻⠀⠐⢀⣠⠤⠐⢂⠈⠉⠈⢈⡑⠶⢁⣄⠐⠋⠀⠈⠀⠠⠘⠋⢜⡲⠡⠀⠀⣠⡄⠀⠉⢲⣁⣢⡀⢀⡀⠀⠀⠀⠀⠙⡌⢢
⠀⠀⠀⠀⡆⠀⡿⣸⡴⠞⠡⠄⠀⠤⠌⠐⣋⣁⠈⠁⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠄⠀⠀⣤⣤⣁⠀⠴⠄⢑⢂⡀⠀⡀⡘⠀⡆
⠀⠀⠀⠀⢇⠀⢿⠁⠀⣰⠖⢳⡒⢶⣶⠾⡧⣹⠃⠀⢀⡠⡴⠦⣓⣓⣟⣿⣯⡿⠯⢯⡻⠾⣞⣴⠠⣤⣀⠀⠀⠳⠛⠀⠀⣀⡈⠙⠀⠑⠜⠁⡘⠃
⠀⠀⠀⠀⠈⠢⡀⠳⢄⠉⠖⠬⢲⢂⢴⠤⠒⠁⡐⡾⠕⡨⠛⠸⠏⠑⣊⠤⡴⣒⣒⢒⣲⣒⠺⠯⡉⢳⡌⢣⠀⠀⠲⠗⠀⠈⠀⢀⠀⠊⢀⠔⠁⢠
⠀⠀⠀⠀⢰⠁⠘⠢⢄⡉⠢⢄⡀⠀⠀⠠⠄⠀⠘⣧⢑⠑⠠⠤⣾⡤⠝⠛⠉⠁⠈⠀⠁⠈⠉⠓⠲⠲⠖⠃⠀⠀⠀⢀⡀⠀⠀⠀⢀⠔⠁⠤⠀⡒
⠀⠀⠀⠀⠸⣌⠀⠀⠀⠉⠒⠤⢈⡁⠒⠤⠄⣀⡀⠀⠋⠘⠊⠙⠀⠁⠀⢀⡀⠀⠰⠥⣝⣴⠇⠀⠀⣀⡀⠤⠐⠂⠉⠀⠀⡀⠄⠊⠀⠀⠀⠰⢠⣃⡀
⠀⠀⠀⠀⠀⠙⣄⠈⠢⡀⠀⠀⠀⠀⠉⠒⠂⠤⢀⡉⠃⠒⠒⠀⠠⠤⠤⠤⠬⠤⠤⠤⠀⠒⠂⠀⠉⠀⠀⠀⡀⠠⠐⠀⣄⢀⠒⠀⠠⠂⠁⠠⠏⡀
⠀⠀⠀⠀⠀⠀⠘⠣⣀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⡠⣀⠀⠀⠀⠀⡚⠸⢖⡀⢠⠀⢀⠤⠁⢀⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠈⠒⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠒⠞⢀⠤⠆⠂⡉⠀⣠⠔⠉⠀⢀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠤⣀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠤⠤⠀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠐⠂⠁⠀⠀⠂⡁⠤⠮⠁⢀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠓⠢⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠀⠀⠀⢀⣈⠤⠶⠉⠉⠥⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⠒⠒⠤⣤⣀⣀⣀⣀⡀⣀⡀⢠⠥⠤⠒⠒⠚⠐⠉⠉⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⡒⡒⠀⠀⠀⠤⠄⠀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠓⠶⢦⣤⣀
⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⣿⡀⠀⠀⢀⣀⣤⣤⡴⠶⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⠶⠶⠶⣤⣤⣀⣀⠀⠀⠀⣸⡇
⠀⠀⣏⣹⠶⢿⣍⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⠷⢿⣹⡇
⠀⠀⣟⠁⠀⠀⠈⠉⠙⠛⠛⠶⠶⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠛⠛⠛⠉⠁⠀⠀⠀⢹⡇
⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠈⠙⠛⠲⠶⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⡂⡭⠉⠭⠭⠍⠉⢀⠒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⢀⠄⢊⠴⠊⠋⡑⡜⡌⢆⠠⠀⠀⠀⠀⠉⠐⠢⢍⡂⢄⡀
⠀⠀⠀⠀⢀⠔⣁⠖⡘⠈⠀⠡⣐⣔⣌⡦⠦⠵⠵⣄⣀⡀⠀⠀⠀⠈⠒⢌⠒⢄
⠀⠀⠀⡔⢁⡔⢅⠑⣀⡤⠖⠋⠉⠁⠀⠀⠀⠐⠂⠀⠀⡀⠙⡒⠤⣀⠁⡀⠙⠢⡑⢦⡀
⠀⢀⠎⣰⢃⠐⣤⠗⠭⠲⢘⡢⠆⠠⠀⠀⠀⡔⠰⠤⠸⣀⠡⡸⠀⠐⠑⢄⡀⠀⠈⢂⠙⢌⠠
⢀⠂⡸⢁⣤⠟⠀⣈⣁⣹⠋⠍⡇⠀⠀⠀⠀⠀⠀⠁⡐⠸⠻⢠⠠⠀⣔⣒⢍⠢⡀⠀⠥⡈⢧⠠⠄
⡘⢰⠈⡾⠁⠒⠐⡀⠀⠀⠀⣩⡁⠐⡄⠀⡪⠄⠌⡂⠉⢀⠈⠇⢈⡅⢌⠉⠁⠀⠈⠢⡃⢡⠈⣇⠈⣁⠁
⡇⣞⡟⠀⠥⠀⠈⠁⠀⠀⠀⠁⠠⣼⠗⠀⠘⠿⠿⠊⠐⠆⠀⠡⠘⢡⡙⢁⠆⠤⡈⠀⠙⣄⠂⢸⡂⠐⠐
⡇⣿⠁⡀⣀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠠⢚⣁⡀⢤⢠⠬⣄⢋⡡⠒⠀⡔⢳⣉⣞⡸⠀⠀⠘⡇⢸⣒⡀
⣧⢹⠐⠒⠒⡂⠀⠀⠀⠢⠰⢹⡁⠀⠀⠸⢆⣊⡵⢋⡀⠴⢀⢔⡐⠤⡈⢀⠚⢉⡅⡄⠈⢠⠀⢾⡒⠂⠐
⠉⢂⠫⡁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⡖⣶⠀⡸⠀⠂⣠⠀⣗⠇⠢⡕⠀⠂⠁⢀⠊⡟⢸⠅
⢰⢀⠣⡙⢄⠀⣋⠁⠰⡇⠨⡃⠀⠘⣤⠡⠆⢠⣑⠉⣠⣿⡱⠈⠉⠀⠀⠄⠀⠂⠁⡰⢃⠌⡨⡯⠉
⠘⡀⢆⠘⠢⡱⠦⣠⠤⡀⠀⠊⠀⠀⠑⠉⡒⣓⠊⠘⠄⠁⢧⢪⡍⡩⡆⡄⢀⠤⢊⠰⣣⡿⡾⠥⠬⠤
⠀⠑⡈⢪⠀⣉⠓⠤⣉⠒⠤⣀⣤⣒⠂⢄⡀⠈⢀⡀⠀⠀⠠⣔⣐⡩⠖⢋⠡⢒⢩⠂⡟⡱⠯⠉⠩⠌
⠀⠀⠈⠢⡑⠠⡛⠀⠀⠉⠒⠢⠤⣉⣉⡉⠁⠐⠒⢒⣖⣀⣉⡩⠤⠒⡉⠅⠌⠢⣲⢋⡔⠁
⠀⠀⠀⠀⠈⠓⢌⡑⠢⣁⠠⠶⠄⠄⠀⡀⢈⠍⠉⠁⠀⠀⢰⡯⠛⠔⢈⠬⠬⣫⡔⣋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣈⠑⠂⠤⢁⣀⢠⡒⠁⡀⠀⢠⣋⣪⠮⢒⣋⡴⣻⡥⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠄⠀⢀⡌⣍⣀⠬⠵⠶⠚⠃⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⠻⣶⣾⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡈⠻⣶⡄⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠻⣦⡈⠻⣷⣄⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠈⠻⣦⡈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⣠⡾⠛⠻⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣾⠋⢀⣤⣤⣤⣾⣿⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠟⠛⠋⢨⣿⣷⠟⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⣰⡟⠁⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣰⣟⠀⠀⠀⠘⣷⣶⣶⣶⣶⣶⣶⠄⣤⢠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⣠⣴⠶⠟⠛⠉⢿⣦⣀⣠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠶⣦⣤⣴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠙⠻⢶⣦⣤⣄⣀⡈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠟⠋⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠷⠶⠶⠶⠶⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⣀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⣿⣯⢭⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠒⠒⠒⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠁⠐⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢀⣀⣠⠤⠄⠴⠔⠐⠒⠒⠂⠂⠀⠂⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⡵⢊⠀⠤⠔⠐⢈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⡿⠂⠁⢠⠒⠀⡩⠥⠚⠀⠀⠀⠀⡠⠀⠒⠀⢄⠀⠀⠀⡰⠂⡆⠀⠈⠀⡤⠠⠄⠤⣈⠀⠀⠀⠀⠀⢀⠀⡆
⠀⠀⠀⠀⢑⠑⢄⡀⠘⠤⣸⠄⠀⠀⠠⠒⠂⢉⠤⠊⠉⠈⠀⠀⢀⠠⠃⢀⠅⠀⠀⠀⠈⠉⠙⠢⡈⢑⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⢀⠀⠈⠀⠠⠀⡀⠀⠀⠀⣀⣁⡀⠀⠀⠀⠂⠀⠀⠣⠔⠒⠁⠀⠀⠀⢠⠁⡗⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢨⠀⠐⠀⠀⢰⠂⠤⣀⠉⠙⠒⠒⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢘⠊⢉⠀⠀⠀⠀⠠⠀⠀⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⣋⠠⠋⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠔⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠒⠂⠀⠤⠠⠠⠀⠄⠂⠒⠊⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠟⠛⠛⠉⣉⣉⣉⣉⡉⠛⠛⠻⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⢉⣠⣴⣶⡿⠿⠿⠛⠛⠛⠛⠿⠿⢿⣶⣦⣄⡉⠛⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⢁⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⡈⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⢀⣴⡿⠋⢠⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣦⠀⠀⠀⠀⠙⢿⣦⡀⠹⣿⣆
⠀⠀⠀⠀⠀⢀⣼⡿⢁⣴⡿⠋⠀⠀⣾⣧⡾⢃⣀⡀⠀⠀⠀⠀⠀⠀⢿⣇⢀⣽⠇⠀⠀⠀⠀⠀⠙⢿⣦⡈⢿⣷⡀
⠀⠀⠀⠀⢀⣾⡟⢀⣾⡟⠀⠀⠀⣠⡿⣿⠟⠛⠉⠀⣾⠛⠻⣶⡄⠀⣀⣿⢺⣏⡀⠀⣰⡾⠛⢻⣦⠀⢻⣷⡀⢻⣷⡀
⠀⠀⠀⠀⣼⡟⢀⣾⡟⠀⠀⠀⢠⣿⣰⡟⠀⠀⠀⠀⠻⣦⣤⣬⣻⠾⢛⡁⠀⠉⠻⠾⣛⣤⣤⡾⠃⠀⠀⢻⣷⡀⢻⣧
⠀⠀⠀⢰⣿⠁⣼⡿⠀⠀⠀⠀⣾⢻⡿⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⠀⢀⣤⣘⠋⠀⢸⡏⠁⠁⠀⠀⠀⠀⠀⢿⣧⠈⣿⡆
⠀⠀⠀⣼⡟⠀⣿⡇⠀⠀⠀⢸⣯⣼⠇⠀⠀⠀⠀⠀⢀⣤⣤⣴⠿⡀⢯⣐⣸⠇⠀⡸⣷⣤⣤⣄⠀⠀⠀⠀⢸⣿⡀⢻⣧
⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⣿⢋⣿⠀⠀⠀⠀⠀⠀⣿⠋⠀⣰⡟⠛⠷⣮⢡⡶⠟⠛⣷⡄⠀⢹⣧⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⣿⣾⣏⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⢠⡿⠸⣧⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⢿⣧⠈⣿⡇⠀⠀⠀⣿⡌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⡿
⠀⠀⠀⠸⣿⡀⢻⣷⠀⠀⠀⢸⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣿⠇
⠀⠀⠀⠀⢻⣧⠈⢿⣧⠀⠀⠈⣿⣸⣧⠀⠀⠀⠀⢠⣄⣺⣆⣀⣀⣀⣠⣤⡶⠶⠶⢶⣄⣠⡶⠀⠀⠀⠀⣼⡿⠁⣼⡟
⠀⠀⠀⠀⠈⢿⣧⠈⢿⣧⡀⠀⢹⡟⣿⡀⠀⠀⢶⣼⠟⠋⢉⣍⠉⠉⠉⠁⠀⠀⠀⠀⣹⡿⢶⡄⠀⠀⣼⡿⠁⣼⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣷⡈⠻⣷⣄⠘⣷⣼⠇⠀⠰⠶⢿⣄⠲⠈⣁⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣠⣾⠟⢁⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠈⠿⣷⣄⡀⠀⠀⠀⠰⠟⢻⡷⣶⣦⣤⣤⣴⡶⠶⠟⠛⠁⠀⠀⣠⣾⠟⠁⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡈⠛⢿⣶⣤⣀⠀⠀⠈⠁⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⢁⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⣈⠙⠻⠿⣷⣶⣶⣤⣤⣤⣤⣶⣶⣾⠿⠟⠋⣁⣤⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣦⣤⣤⣈⣉⣉⣉⣉⣀⣤⣤⣴⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣥⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢠⣤⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠷⠶⢦⣄
⠀⠀⠀⠀⠀⠀⣿⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠾⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣈⣉⣉⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣍⣉⣉⣁⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠶⠛⠛⠋⠉⠉⣭⣭⣅⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⣀⣬⣭⣭⣉⠉⠙⠛⠛⢶⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣬⣭⣭⣭⣥⣴⠶⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣲⣟⣉⡟⠉⠉⠉⠉⠓⠶⡧⠛⣉⣷⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣉⠿⣤⡌⠈⠁⠀⠀⠀⠀⠀⠀⣀⡘⢲⡋⠙⠚⠛⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣹⠟⣉⣆⣠⣀⡀⠀⠀⠐⢇⣀⡄⠀⣠⠀⠤⣄⡀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣠⢿⡋⠁⠀⡀⠀⠀⠀⣀⡄⢲⣤⣼⠋⠰⠚⢃⣴⠤⢋⡤⢂⠠⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣆⢣⢨⣉⣑⠲⡧⣀⣨⡿⠟⠉⣏⣨⠇⠀⠀⠀⠐⠙⠖⠉⣭⡙⠒⠂⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⡟⡿⠉⠉⢀⣄⠉⡉⠀⣀⣈⡄⠈⠛⠻⠓⢴⣧⠤⠀⡀⠀⠑⠒⣻⠗⠲⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⢰⡷⢇⠀⠙⠉⢉⡉⠀⠀⠉⢩⣀⣰⣤⣼⢲⠊⣠⠞⢳⠘⡄⣠⡆⢹⠦⠄⠀⠰⣄⣠⣿
⠀⠀⠀⠀⠀⠘⣷⡞⠰⣶⠲⠿⠿⢦⣄⣦⢸⡉⢉⡍⠛⢄⠻⠧⣠⠼⢧⣏⢈⡥⠞⠀⠀⠀⠀⠈⠹⣿
⠀⠀⠀⠀⠀⠀⢻⡷⢚⣉⣭⠟⠐⣿⣄⢈⣦⠟⠋⠣⢤⠼⠂⠀⠀⠘⢄⠙⠋⠓⠈⠉⠀⠀⠀⢸⢰⡟
⠀⠀⠀⠀⠀⠀⠈⢷⣤⡏⠀⠐⠶⠋⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⢉⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣀⠀⠀⡀⠀⠐⠊⠀⠀⠀⠈⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⣀⣠⠃⠀⠀⠈⠉⠀⠀⠀⠀⠰⠤⠴⠦⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣶⣤⠀⠨⡉⠓⠊⠀⠀⠀⠀⢀⠀⢸⣟⣉⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠓⠂⠤⠤⠤⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠙⣻⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠙⣻⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠾⠛⠛⣻⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⢀⣀⣠⣤⣼⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⣤⣤⣄⣀⡀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣟⣉⡉⠉⠛⠁⠰⣦⣤⠀⢛⡁⠀⡶⠀⠘⠛⠻⡆⠀⠉⣉⣙⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⡀⠈⠉⠛⠛⠛⢳⠶⠶⣶⠶⢾⣷⠶⠶⠶⠶⠶⠶⠞⠛⠛⠋⠉⠀⣀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣤⣙⣃⣀⣛⣻⣈⣉⣀⣀⣻⣀⣀⣀⣠⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡤⠀⢤⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⡉⣤⢠⠄⠖⣰⣠⡖⠶⢲⠤⠤⡬⢉⣒⠂⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⡠⡖⠛⡝⡱⢡⠂⠌⣰⠃⠊⠹⡀⠂⠈⠐⠁⠊⠌⡙⡑⢲⠤⣍⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⢴⢋⢜⠈⠈⠀⠀⠀⠀⢰⡃⢀⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠹⡲⣌⠑⢤⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠁⡴⠫⢁⠂⠂⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠠⡒⡂⠀⣠⠀⠀⢠⠤⣄⠁⠹⢦⡙⢆
⠀⠀⠀⠀⠀⡠⠁⡀⡰⡱⡡⠑⠉⠀⠀⣀⠀⠀⠀⠀⢀⡀⣤⣀⠄⠠⠄⠤⢠⠀⠀⠀⢀⢈⠀⠀⢺⡀⠸⠄⠀⠀⠹⣆⠹⡄
⠀⠀⠀⠀⡴⠁⢔⠄⠔⡔⠀⠈⠉⠁⠀⠀⠀⠀⡠⠊⠁⣠⢤⡤⣀⣀⣀⡤⠎⠀⠀⠀⢇⣀⡁⠀⠸⣄⣴⠀⠀⠤⠀⠈⢧⡘⢇
⠀⠀⠀⣰⠁⣌⢂⢊⠎⠀⠀⠀⠀⠀⣀⡠⠚⠉⠄⣠⠞⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⢄⠀⠀⢳⠘⡎⡀
⠀⠀⢀⠃⡴⡱⡡⠃⠀⠐⠗⠀⠀⢤⠊⠀⡰⠊⠉⠀⠀⠀⠺⠀⠀⠀⠚⠀⠀⣤⢤⡀⠀⠀⠀⠠⠄⠀⠀⠀⢧⡀⠘⡆⠀⠀⢃⢹⡠
⠀⠀⡘⢠⡖⡔⠀⠀⢎⣈⡁⠀⢀⡚⠀⠀⠇⢀⣤⠀⠤⠀⢀⠀⠀⠰⣒⠀⠀⣰⠀⡇⠀⠀⠀⠀⠐⠭⠂⠀⠀⢳⠀⢹⠀⠀⠘⠘⣧⠂
⠀⠀⠁⢈⢊⠄⠀⡀⠀⠀⠀⠀⢀⡇⠀⠀⠇⠀⠀⠀⢀⡴⣫⣭⡙⢦⡀⠀⡠⠋⣠⠂⠀⡴⠚⢉⣉⠆⠀⠀⠀⢸⠀⢈⡇⠀⠀⡃⣧⢂
⠀⠀⠀⣤⢊⠀⠘⠜⢠⡄⠀⢀⠜⠁⠀⡜⠀⠀⠀⠀⡸⢰⢃⠤⣍⠦⣉⣉⣠⠖⠁⠀⢸⡀⡰⠋⠀⠀⢠⠒⠒⠁⠀⣰⠀⠀⠀⡃⣿⢂⠄
⠀⠀⡆⣴⠡⠀⠀⠀⠀⠀⢠⠃⠠⣠⠎⠀⠀⠀⠀⠀⡇⢸⠈⠳⠬⡙⢦⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⠀⢺⠙⠚⠁⠀⠛⢀⠀⣏⠎⠔
⠀⠀⢡⢸⡔⠀⠀⠰⠀⠀⠈⠗⠋⠁⠀⠀⠛⠀⠀⠀⠹⣌⠓⠒⠚⣡⠞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢸⠀⠀⠐⠃⢰⡌⢰⢃⠌⠄
⠀⠀⠈⡆⢷⡀⠀⠀⢠⠤⠤⣄⠀⠀⠀⢀⡤⣄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⡜⠁⢱⠀⠀⡠⠰⡄⠀⡸⠀⣜⠀⢀⡀⢀⠃⠀⣮⢊⠌⡀
⠀⠀⠀⠘⡌⢧⠀⠀⠳⣴⣰⠼⠁⢀⡴⠃⣀⠜⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⢰⠃⢀⡼⠀⠀⠈⠒⠀⠀⢷⡠⡷⣄⢨⡤⢾⠆⣼⢣⢆⡼
⠀⠀⠀⠀⠘⢆⠱⣄⠀⠀⠀⠀⠀⡏⠀⡞⠁⠀⠀⠀⠁⢀⠄⠢⠉⠀⠀⠀⠀⠉⠉⠀⠀⠴⠀⠀⠀⡄⠘⠳⠿⠋⠸⣶⠇⣼⣳⢣⢞⡤
⠀⠀⠀⠀⠀⠀⠣⡈⠢⡀⠠⠀⠀⠹⡄⠙⠲⢤⣀⡀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡰⡛⢁⡜⡱⠡⢋⠎
⠀⠀⠀⠀⠀⠀⠀⠙⢢⡈⠲⣄⡠⠀⠈⠦⣄⣀⣀⡉⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡡⠀⡞⠁⣪⠊⣠⠞⠔⡰⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⡙⠢⣄⠀⠀⠀⠈⠉⠑⠦⣀⠙⠒⠦⢦⡄⠀⠀⠀⠀⠀⠀⣀⠀⡸⠉⣠⠞⢁⣴⢋⠎⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⡲⢄⡉⠒⠤⣀⡀⠀⠀⠈⠑⠒⠒⠋⠀⠀⠀⠥⠃⠀⢈⠀⢉⡤⠊⣀⠔⡱⢡⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢑⠦⡀⣉⠙⠒⠤⠤⢤⣀⡀⣀⢠⣤⠠⠦⠅⠐⠈⣀⠔⡨⢃⠜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠡⢋⠖⡲⠖⡤⢠⠤⡤⢤⠤⡤⢰⠖⡒⢉⠊⡔⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠐⠁⠊⠔⠁⠃⠈⠀⠁⠈

⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠶⠒⠒⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠒⢒⣠⡤⠤⢀⣀
⢀⡠⢔⡒⡭⡙⡩⡩⡠⡠⠢⢂⢊⠔⡴⡤⣀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠈⠥⢐⣂⠤⢀⡀
⢐⢪⠢⡱⡑⣜⣔⠴⠴⠓⠓⠛⠋⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⡈⠉⠉⠉⠁⠒⠒⠠⠤⠀⢀⠀⠀⠀⠀⠀⠈⠁⠘⠥
⡧⠧⠓⠋⠉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠤⣀⡀⠢⢢
⡠⠒⢒⠒⣉⡭⠟⠀⢀⠀⠀⠀⠈⣀⠤⠴⠰⢠⡀⠀⠀⠀⠀⡴⠚⣦⠀⠀⠉⠀⢀⡠⠄⣄⣀⡀⠒⠀⠀⠀⠈⠑⠢
⣄⠐⢰⠃⠀⠠⠀⠀⣨⣠⡠⠔⠋⣁⠴⠒⠒⠚⠃⠀⠀⠀⣰⠁⢰⡇⠀⠀⠀⠀⠚⠒⠦⢴⡄⢉⠳⢤⡀⠈
⠉⠛⠚⠁⠀⢀⠀⠈⠣⢤⠤⠴⠚⠀⠀⠀⠀⠀⠀⠠⡴⢚⠁⢂⡰⠃⠀⠀⠀⠁⢀⢄⡄⠀⢈⠑⢤⢬⠇⢀⠠⠒⢉
⡑⠒⠤⣀⡀⠀⠀⢀⣠⣠⣀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠓⠒⠚⠉⠠⠄⠀⠀⠀⢰⠃⢰⡃⠀⣀⡀⠤⠐⠈⡀⠤⠂⠁
⠈⡷⢢⢄⣈⡉⠉⠛⠒⠶⠶⠟⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠀⠄⠚⠓⠋⠉⣉⡠⠄⠐⠊⠁⠄⢀⠠⢊
⠠⢝⡒⠒⠚⠉⠉⠁⠒⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠐⠒⠒⣢⠶⡉⢩⠗⠀⠀⠁⣀⠠⠀⠀⡠⡌⢆
⠀⠀⠈⠑⠂⠤⢄⣀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠙⠦⠖⣊⡁⠤⠐⠊⠉⢀⠠⠣⢑⣡⢖⠡
⢄⡀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠒⠒⠒⠀⠀⠠⠤⠤⠤⠤⠤⠄⠀⠐⠒⠒⠈⠉⠀⠀⠂⠀⠀⢀⣊⣡⠔⡢⠋⠑⠁
⠀⠉⠓⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⢀⣀⢤⠖⠼⠋⠒⠁⠈
⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⠤⣤⢁⣉⣈⣈⣈⣈⣀⣀⣀⣀⢤⡤⡴⠒⠚⠙⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⠉⠁⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠫⠰⠤⠐⠁⠀⠀⠀⢀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⣥⠀⢀⠄⠈⣀⠀⠀⠂⠂⣂⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⡁⠤⠐⠈⢿⣇⡅⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⣁⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⣊⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠔⠲⠃⣷⠒⠒⠒⠒⠶⠲⠶⠤⢤⡤⣀⣀
⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠉⠙⠳⢤⡀
⠀⠀⣠⠞⢁⠀⠀⢀⣀⣁⣤⠄⣒⠀⠀⠭⠍⠭⠥⠬⠭⠭⠍⠀⢐⣒⡀⠤⢄⡀⠁⢠⠙⡓⣆
⠀⠠⡏⢈⣢⣖⡽⠝⠛⠋⢉⠤⠀⠄⠀⡀⠈⠁⣀⠀⠂⠐⠀⣀⢀⣀⠀⢈⢔⣬⣵⣦⣄⣧⣽⣤⣤⣤⢤⣶⣶⣶⣦⣤⣤⣀
⠀⠀⡿⣾⡽⢋⣐⠀⠀⠐⠂⠀⠠⠄⠂⠤⣲⡻⠡⠗⣀⠋⠀⠀⠷⠁⠊⠙⢻⢀⣄⠀⣡⣥⣽⣍⢨⡭⠿⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⢰⣏⠺⢿⣯⡥⠀⠔⠀⠁⠀⢠⠀⠀⠀⠰⠂⣈⠂⠈⠁⠁⡀⠒⠂⢠⠒⣢⣤⠤⠨⣾⣵⣤⡤⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠸⣌⢧⡀⠈⢛⢫⣔⣂⠈⠀⠄⠸⡀⢀⠄⢀⡀⠀⠀⠛⠀⠀⢀⠰⠞⠛⠉⠉⢀⡔⡱⠃
⠀⠀⠀⠘⢧⡍⠢⢤⠁⠙⠰⠶⠻⠀⠀⠙⡁⠘⠛⡛⠃⡀⠆⠀⠀⠋⠀⠐⠂⠄⠂⣡⣖⣁⡀
⠀⠀⠀⠀⠀⠈⠙⠲⢬⣑⡂⠠⠤⠄⠠⠀⣄⣀⢀⣠⢂⣀⣀⡀⠂⠤⢒⣛⠴⠞⠋⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣤⣥⠖⠛⠋⢃⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡴⠀⠀⠐⠖⠠⠀⠀⠀⡄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡤⠀⠀⢿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠄
⠤⠄⠀⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡤⠤⠤⣰⠰⠂⠀⠀⠀⠀⠀⠀⠀⠠⣂⡆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⢘⠀⠀⢴⡆⠀⠀⠀⢠⡾⠃⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠐⠓⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣀⠠⢄
⡤⠄⠂⡀⠀⠈⠓⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠌⡑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠋⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠄⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢏⠈⠐⠊⠁⢈⠂⠀⠀⠀⠈⠲⠐⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢀⡀⡀⠀⠀⠀⠅⡀⢀⠠⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠆⠐⠊⠀⢁⠐⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠀⠀⠀⠀⠠⠂⠰⠀⠀⡀⠀⠀⠨⠙⠀⠀⠘⠠⠰⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠊⠁⠀⠀⡀⠀⠄⠀⠀⠰⡿
⠛⠳⠢⣄⠀⠀⢈⠆⠀⠀⡆⡀⠐⠈⠐⠈⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠀⢙⡀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠐⡇⠀⠀⡮
⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠌⠀⠑⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠁⠆⠀⠧⡈
⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠁⠀⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⢀⠀⠀⡀⠀⠒⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⢿⣆⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠈⠀⢈⠀⠀⠀⠀⠐⠢⢀⠀⠘⢿⣷⣄⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠈⢻⣆⠀⠀⢀⠀⠀⠀⠦⠈⠁⠈⠁⢠⠀⢠⠚⠁⠀⠀⠁
⠀⠀⠘⠁⠀⠈⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠗⠀⠀⠈⠟⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⢴
⠀⠀⢠⠀⠠⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⢀⡀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡀⠀⠄
⠀⢠⠚⠀⢀⡄⢀⡀⠐⠀⠀⠀⠀⠀⠀⣼⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⠀⠄⠀⠀⠐
⠀⠈⠀⠀⠇⢤⣌⠁⠀⠈⠀⠀⠀⠴⢀⠏⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠈⠐⠡⠁
⠀⠀⠀⠀⢀⠀⠆⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠴⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠃⠀⠗⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠰⡀⠀⠀⡀⢀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠆⠀⣂⠔⢢⢀⠀⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠉⠀⠹⠀⠀⠀⠀⠀⠀⠀⢀⣩⠂⠤⡽⡓⠉⠁⠀⢴⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠫⠞⠀⠀⠀⠀⠀⠀⢼⡠⠇⠀⠀⢠⠛⠀⠀⠂⠂⠀⠀⡜⡙⠀⠀⢸⠀⠀⠀⠀⢉⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢭⠀⢁⡀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠒⠀⣾⡄⠀⠀⠃⠀⠀⢀⠄⠀⠀⠀⢸⣀⠠⠀⠀⡌⡤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣶⣀⣖⣤⢀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⢹⠉⣃⠀⠀⢰⠀⠀⠀⢀⡠⠖⢻⠿⠀⠀⠀⢘⠥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⡏⠀⠁⢄⢠⠂⡤⢠⠀⠀⠤⠀⣤⣤⠄⠘⠀⠀⠀⡾⠟⠀⠀⠐⠉⠀⠀⢸⠀⠀⠀⡛⡿
⠀⠀⠀⠀⠀⠀⠀⣞⠿⠑⠀⡠⠀⢈⠉⠀⠀⠡⠛⠓⣆⠀⠀⠀⠀⢨⢄⠐⠀⠀⠀⡀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢣⠄⠁⠈⢤⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠠⢀⠀⠈⠀⡆⢠⠜⣤⣤⡄⢰⠀⠀⠘⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⠁⠀⠀⢀⠰⣶⠄⠀⠶⠾⠶⢾⡣⠄
⠀⠀⠀⠀⣀⣀⠄⠀⢀⡀⠀⠆⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢬⠀⠀⠉⠉⠀⠛⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⣩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⠀⠊⠀⠀⠀⠨⣳
⠀⠀⠀⢀⣀⣀⣾⣆⠀⣀⠀⠀⠤⡦⣷⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠈⠀⠉
⠀⠀⠀⠈⠀⠀⣄⣀⣠⣶⣦⣿⠶⢦⣧⣤⠤⣤⣤⡤⠤⡤⡤⠄⠀⠀⢠⣼⡍⣁⣀⡀⣤⣀⡀⠀⣠⡤⠸⣦⣤⣤⣄⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠾⠿⠿⠲⠾⠗⠒⠒⠛⠀⠈⠓⠚⠛⠛⠉⠉⠃⠚⠛⠃⠈⠉⠙⠛⠉⠉⠉⠉⠉⠛⠉⠁⠁

⣿⢿⣿⠿⡿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⣄⡄⠀⠀⣤⢠⣤⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠔⠎⡛⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠂⠘⠀⠃⠇⠘⠂⠉⠈⠀⠀⠀⠀⠀⠁⠈⠁⠀⢀⡀⢸⣳⡠⠔⠁⠀⠀⢀⡜⠓⢤⡀⢰⠋⠀⠀⠠⠀⠠⠀⡇⠀⣰⣦⡁
⠀⠀⠸⢇⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⣼⣠⠏⠀⠀⠀⠐⠀⠈⠀⠀⠈⠀⠸⡆⢄⠀⢅⠀⣐⠼⠁⠀⡇⡜⠃⠀⠀⠀⣀
⠀⠀⠀⠘⡆⡜⠀⠀⠀⠀⣤⠀⡰⠂⠀⠀⠼⢾⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠒⠟⣶⠛⠛⠉⠁⠀⠀⠘⡇⣇⠀⢀⡰⢶⣝
⠀⠀⠛⢄⢻⡇⠀⠀⣠⡞⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⢉⠦⠤⠤⠴⢠⡤⣧⡄⢼⠆⠀⠀⢰⠉⠂⠌⣐⠀⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢳⣈⠉⢉⣀⠜⠋
⠀⠀⠀⠈⢢⡇⠀⠀⢈⣧⡀⠀⣸⡄⠀⠀⡠⡄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠘⣆⠌⠐⠀⢁⠂⠈⠂⡼⠀⣠⣤⣄⠀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢳⠀⠀⠁⠘⠛⠙⡍⠀⠀⠀⠉⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⣴⡽⠀⣀⡠⢤⠤⡬⠷⣤⠤⠤⠤⠖⠋⢀⢮⠞⠁⠀⡴⢹⢀⣤
⠀⠀⠀⠀⠀⢹⢠⠶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⡿⠋⠀⢸⠁⠠⠀⠀⠀⠄⠈⢦⠀⠀⠀⠀⢸⠘⠒⣦⡸⠁⠓⠊⡼⠀⣾⣿⡆
⠀⠀⠀⠰⢆⢸⡏⠀⠀⡠⠤⠤⣀⣀⠴⠊⠳⡀⠀⠀⠀⠀⣀⡠⣤⠄⣀⣀⣀⠘⣦⠈⡀⠀⠀⠄⠀⣘⠇⠀⠀⠀⠈⠓⠊⠡⡷⠒⡆⣸⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠈⢾⡇⠀⠘⣅⠀⠀⡼⠉⠓⢦⣸⠁⠰⠀⠖⠉⠃⠀⠀⢀⠠⠐⠉⠉⠉⢷⠚⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣵⠖⢲
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⡞⠁⠺⠇⢠⡏⢢⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⣤⣤⠀⢠⣤⡄⠀⣠⣤⡀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠠⠂⢼⠙⠲⢄⣠⠋⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣠⡇⠀⢸⢹⠀⠀⠀⡿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⡴⠞⠁⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣾⠀⢸⣿⡇⠀⢸⢸⠀⠀⠀⣙⠇⢸
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀⠠⠍⡇⠀⠀⢀⢏⣌⢧⠀⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⣧⠄⢾
⠀⠀⠀⠀⠠⠀⡷⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠀⡇⠀⠀⢸⢸⣸⢸⠀⠀⠘⠋⠀⠈⠛⠁⠀⠘⠛⠀⠀⠀⠿⠤⠼⠰⠆
⠀⠀⠀⠀⠀⠀⡧⡇⠀⠁⠀⠀⠀⠀⠀⠀⠐⡿⠷⢶⠂⠀⠀⢸⢰⡏⠙⢆⡇⠀⡆⠘⣆⣡⠞⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⠀⠀⠀⠀⠀⠀⢀⠇⠂⠘⡆⠀⠀⠀⠶⠁⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⢠⣾⡁⢀⣀⣠⠔⠛⠓⢤⣠⠎⠀⠈⠲⣤⡀
⠀⠀⠀⠀⠀⠀⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⢹⡀⠀⠀⠀⢀⠀⢀⠀⠀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠈⠛⠿⡀⠀⠀⠀⠈⠋⠀⠤⠆⠀⠈⠁
⠀⠀⠀⠀⢀⡞⠤⣈⣆⠀⠀⠀⠀⠀⠀⣸⠃⠠⣕⠀⠀⢧⠀⠀⠀⠉⠀⣿⠀⠀⠀⢰⡆⠀⢇⣤⣤⣀⣀⣀⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡞⠈⠘⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⠀⣤⡄⠀⢶⠀⠀⠀⠣⠤⠄⣀⣀⣀⣀⣤⠀⠀⢠⣤
⠀⠀⠀⠀⢣⣀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⠐⣿⠀⠀⠀⢸⢿⠀⣿⡇⠀⣿⠀⠀⡤⡄⠀⠀⠀⣶⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡀⠙⠿⢿⡿⢿⡿⠿⠿⠿⠿⠛⠀⠀⠀⢿⠀⠀⠀⢸⢸⠀⡇⡇⠀⣿⠀⠀⡇⡇⠀⠀⠀⢸⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢖⣢⣀⣀⣹⣷⣤⡤⠼⢷⣦⠤⠤⠄⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⢸⢸⠀⡇⡇⠀⡿⡆⠀⡇⠇⠀⠀⢸⢸⠀⠀⣷⡇⠀⠐⢶
⠀⠀⠀⢀⣤⣤⠔⠊⠉⡿⠃⠀⠐⠖⠁⠀⠺⠊⠀⠀⠀⠀⠀⢤⡄⠤⠤⢾⠤⠶⠶⠾⠾⠶⠷⠷⠶⠻⠗⠦⠗⡖⠒⠒⣼⠛⠒⠲⠟⠓⠿⠆⠙
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠘⠈⠀⠈⠉⠁⠀⠁⠀⠀⠈

⠉⠂⠀⠘⣇⢀⣌⢘⠠⠆⠀⠁⠸⠀⡀⠸⡄⠿⡾⠓⠀⢀⡴⡶⣶⡻⠃⠐⢿⠆⠀⠀⠀⠓⢀⠇⢀⠈⠉⢇⣤⠉⠙⢶⡞⠃⠠⠂⢨⡮⠨⡅⠀⠀⠉⠁⣠⣡⡀
⣌⠒⠂⠈⢡⠷⡄⢠⡄⠘⡁⠀⠄⢠⡀⠈⠀⠩⠐⠀⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠊⠀⠀⠹⠤⢦⡼⠓⠄⢀⠢⠂⠛⠃⠀⠀⣠⠐⢾⠙⣏
⠤⣱⢄⡄⢄⠐⢱⣤⣁⣠⠢⠀⠐⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⣀⡡⠀⠄⣴⠅⠠⣌⡰⠁
⠒⢯⡜⢔⠀⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⢀⢘⠇⠀⠀⠂
⡤⢄⠙⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄⡄⣠⠄⢠⢤⢀⡤⣄⢀⠤⡀⡠⢄⢀⠤⠀⢠⡀⢠⡀⡀⡄⣠⠄⣄⠀⣠⢠⠄⠀⠀⠀⠀⠀⠀⠈⠉⣀⠤⠔⢦⣀
⠧⠜⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠸⠱⠊⠄⠇⢧⡄⠸⠻⠸⢄⠼⠻⣤⠌⠜⠢⠰⣄⠦⠟⠳⠸⠑⠇⠇⢉⠗⠏⠖⠱⢨⡷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣶⢾⠏
⠀⠀⢐⡠⠒⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠠⢴⠏⠀⡀⠔⠟⠁⠀⣄⠀⡦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢖⡚⠺⡄⠘⠃⠁
⠀⠘⠛⠋⣥⠎⠀⠀⠀⢸⠇⠛⠛⣧⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢔⠿⢧⠄⠀⠐⠝⣁⡁⠷⠂⢆
⣠⠎⠀⠊⢀⠄⠠⠀⠙⠋⡠⠲⠒⠉⡦⡄⠈⣄⡠⠉⣀⠀⠀⢠⠖⡬⠀⠀⠀⠀⣇⡀⢤⠧⢀⣀⡄⠀⠰⢎⠙⠄⠜⢸⡶⠀⣄⡤⠂⡂⣯⡆⠀⠁⠴⡂⢿⠆⡕
⣷⣦⣤⣤⣷⣶⣾⣧⣤⣼⣧⣤⣴⣾⣶⣤⣤⣤⣷⣮⣤⣼⣦⣬⣿⣧⣤⣤⣤⣾⣷⣴⣦⣴⣿⣧⣤⣴⣷⣴⣧⣤⣴⣾⣧⣼⣧⣤⣴⣷⣿⣤⣤⣤⣬⣴⣶⣾⣦
⣿⣿⣇⣀⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠠⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡓⠃⡠⠀⠀⠈⠑⢄⢈⡀⠀⠀⠀⢄
⠀⠀⢀⡀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠢⠄⠀⠀⠀⠀⠲⡀⠀⠆⠀⠀⠀⠀⢁⡀⠀⠀⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢂⣀⠀⠀⠀⠐⠀⡀⠠⠶⠶⠶⢦⠄⠂⠀⠀⠀⠀⠠⠀⠀⠸⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠈⠀⠀⠿⠿⠇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉
⠀⠀⣠⠂⠀⠀⡀⠠⠀⠀⠀⠀⢠⡀⠰⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠠⡦⠀⠀⠀⠀⠈⠀⠀⢰⢀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠠⡀⠉⢂⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⡀⠄⠀⢀⠄⠀⠈⠁⠘⡆⠀⢶⣤⣄⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢀⡀⠀⢇⣀⡸⠀⠄⠀⡇⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⡤⠦⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠟⠁⠀⠐⠘⡆
⠀⠀⠀⠀⢠⠀⠱⠴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠃⠀⠈⠒⠆⠔⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠹⠤⣠⠖⠀⠀⠀⠀⠀⠀⠶⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⣠⠊⡠⠒⠂⣉⡁⠀⠀⠀⠉⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠑⠊⠀⠀⠀⠈⠉⠙⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⡶⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⣠⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡔⠁⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣂⠀⠀⠃⠀⠀⠙⠛⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠨⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢁⣄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡼⠀⠀⠀⠈⠀⠐⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⠧⣛⡫⡰⠀⣠⠁⡃⠸⠃⠀⠀⠀⠠⠜⢢⡑⠊⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⢣⣛⡫⡸⠀⣠⠁⠇⠺⠃⠀⠀⠀⠠⠜⢢⡑
⠀⡁⡉⢶⠀⠀⠀⠀⠀⢀⣧⡠⠤⠞⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠈⡉⡈⢶⠀⠀⠀⠀⠀⢀⣧⡤⠤⠞⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⢨⣶⣎⠀⡯⠄⠀⠀⣠⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⡡⡠⡍⢦⠀⠀⣉⡏⢨⣶⣎⠀⠧⠄⠀⠀⣠⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞⡡⡀⡍⢦⠀⠀⣉
⢤⣉⡡⢜⠑⠂⠀⠀⡏⠀⠀⡔⢉⡠⠤⣉⠆⠀⠀⠘⣌⢜⢋⠆⢃⠀⠀⠁⡱⢤⣉⡡⢜⠁⠂⠀⠀⡏⠀⠀⡔⢉⠠⠤⣉⡆⠀⠀⠘⡄⢜⢛⠆⣸⠀⠀⠁
⠃⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠁
⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⡀⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡄
⢂⠀⠀⢢⡏⢙⡦⠄⠀⠀⠠⢜⣶⣕⣢⠀⢉⣧⠀⠀⠀⢜⢀⣹⡆⠀⠀⠳⡌⢢⠀⠀⢢⡏⢹⡦⠄⠀⠀⠠⠜⣶⣗⣢⠀⢉⣧⠄⠀⠀⢜⢀⣙⡆⠀⠀⠳
⠤⠀⠀⠀⠹⠙⠈⠃⢀⠀⠀⠀⠊⠝⡦⣶⡿⠻⣦⠀⠀⠈⠑⠉⠀⠀⠀⠀⠘⠦⠂⠀⠀⠹⠙⠈⠃⠀⠀⠀⠀⠊⠕⡶⣶⡿⠻⣦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠠⡀⢨⠀⠀⠀⠀⠀⠁⠁⠈⠀⢹⢆⠀⠀⠀⠀⡄⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⢛⢆⠀⠀⠀⢀⡤⠂⢢
⢀⠂⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢠⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟⠀⠀⢀⠒⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢀⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟
⡎⡸⠀⠀⠁⠀⣰⢱⣶⡆⢸⡖⠊⠀⠀⢧⠰⡀⠀⠀⠀⠀⡌⠀⢠⠎⠀⠀⠀⡌⡼⠀⠀⠁⠀⣰⢱⣷⡆⢸⠖⠊⠀⠀⢧⠐⡀⠀⠀⠀⠀⡜⠀⢰⠎
⠷⠃⠀⠀⢀⡡⠘⡦⣄⣨⡶⢍⡁⠀⠀⠸⣄⡇⠀⢀⣀⣼⡀⣤⠂⠀⠀⠀⠀⠧⠃⠀⠀⢀⡡⠘⡦⣄⣠⡶⢍⡁⠀⠀⠸⣀⡇⠀⢀⣠⣼⡀⣠⠂
⠀⡀⠀⠈⠁⠀⠜⠀⠂⢃⠘⠀⠈⠂⠀⠀⠉⠀⠶⠡⢊⢊⠍⡅⠀⠀⠰⡀⡐⠀⣀⠀⠈⠁⠀⠞⠀⠆⢡⠘⠀⠈⠂⠀⠀⠉⠀⡶⢡⢊⢊⠍⠁⠀⠀⠰⡀
⡛⡥⠆⠀⠀⡠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⣡⢃⠃⡰⠀⠈⢱⢊⣅⠭⡛⡥⠆⠀⠀⠠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⠡⢋⠁⡰⠁⠈⢱⢊⢍
⢃⢙⠉⠀⠀⠢⠾⠁⠀⠀⡔⡽⣷⡖⠸⠀⢀⠇⠔⣡⡎⠐⠃⠀⠁⢹⡘⢝⡣⢃⢻⠉⠀⠀⠢⠶⠃⠀⠀⡔⡑⣷⡶⢱⠀⠀⠆⠔⣡⡎⠐⠃⠀⠁⢹⡘⢟
⠠⠎⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣪⠎⠀⠚⢠⠃⠈⠀⠀⠀⠀⠈⠀⠜⠲⡄⠠⠮⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣊⠎⠀⠚⢠⠂⠈⠀⠀⠀⠀⠈⠁⠜⠢
⠠⣂⡢⠙⡄⠂⠀⠀⠀⣴⠟⠊⠉⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤⡆⠠⣂⡢⠙⡄⠀⠀⠀⠀⣴⠟⠋⠋⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤
⠘⠿⠑⢠⢏⡁⠀⠀⡾⠁⠀⢀⠤⠄⠀⠤⡀⠀⠀⢠⠁⢪⣦⡃⡙⠄⠀⠖⢆⠘⠿⠗⢠⠍⣁⠀⠀⡾⠁⠀⢀⠤⠀⠀⠤⡀⠀⠀⢠⠁⢪⣦⠃⡹⠀⠀⠖
⡝⠒⢊⠱⠀⠀⠀⠀⠃⠀⠀⠣⠘⠈⠉⠓⠃⠀⠀⠀⠣⢑⣐⣡⠜⠀⠀⠀⠊⡙⠒⢂⠱⠀⠀⠀⠀⠃⠀⠀⠣⠚⠊⠉⠓⠁⠀⠀⠀⠣⢑⣐⣁⠞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠠
⡀⠀⠀⡙⡼⣴⣁⠀⠀⠀⠀⢲⡋⢍⡉⠓⠮⡔⠀⠀⠀⢠⠒⢢⡀⠀⠀⢆⠢⡀⠀⠀⡙⡼⣤⡁⠀⠀⠀⠀⢲⣋⣍⡉⠓⠪⡔⠀⠀⠀⢠⠒⢦⡀⠀⠀⣇
⠘⡀⠀⠘⢧⢴⠣⡅⠀⠀⠈⠐⡻⢗⢛⣄⣴⣿⡁⠀⠀⠱⢄⠾⠃⠀⠀⠈⢣⠘⡀⠀⠘⢧⢼⠣⡅⠀⠀⠈⠐⡻⢗⢛⣤⣴⣿⡁⠀⠀⠱⢴⠶⠃⠀⠀⠈
⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⡏⠟⠫⠈⠿⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⠏⠟⠫⠈⡿⡀⠀⠀⠀⠀⢀⡀⡀
⠀⡀⠀⠀⠀⠀⡈⢆⢸⠀⡠⠀⢀⠄⠀⠀⠀⠀⠐⢕⣄⠀⠀⡰⠋⠀⣴⠀⠀⠀⣀⠀⠀⠀⠀⡈⢆⢘⠀⡀⠀⢀⠄⠀⠀⠀⠀⠘⢕⣄⠀⠀⡰⠋⠀⣴
⠰⢠⠃⠀⠄⠀⢉⢞⣍⡙⢣⡊⡥⠀⠸⡌⢂⠀⠀⠀⠀⠀⠰⠁⠀⣠⠃⠀⠀⠰⢠⠃⠠⠄⡀⢙⢞⣍⡑⢣⣂⡥⠀⠘⡍⢂⠀⠀⠀⠀⠀⢰⠁⢀⡰⠃
⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣘⠧⠄⠀⠀⢸⠀⡆⠀⠀⠀⢠⠃⠀⡘⠁⠀⠀⠀⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣨⠧⠄⠀⠀⢹⠀⡆⠀⠀⠀⢠⠃⠀⡸⠁
⠉⠀⠀⠠⠔⠊⣠⠋⡓⠞⢫⠑⠢⡄⠀⠈⠧⠃⣀⠔⡪⡻⠮⠟⠀⠀⢀⠀⢀⠉⠀⠀⠠⠔⠊⣠⠋⡓⡞⢣⠑⠢⡀⠀⠈⠶⠃⣀⠔⡺⡻⠮⠟⠀⠀⢀
⣤⠆⡀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢋⠌⡘⡔⢁⠅⠠⢄⡠⠆⠢⣤⠆⡀⠀⠀⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢉⠌⡴⠕⢁⠆⠠⢄⡨⠆
⡆⢯⠥⠀⠀⡊⣹⠆⠀⠀⢀⢴⣖⢒⢢⠀⠀⡔⢁⠞⡰⢀⡎⠀⠄⢼⢰⣷⡌⡆⣯⠥⠀⠀⡉⣙⠆⠀⠀⢀⢴⣖⣒⢆⠀⠀⡔⢁⠎⡰⢀⡎⠀⠄⢼⢰⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣂⠉⠩⠍⢁⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠊⠁⠀⠀⠀⠀⠈⢂⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⢀⡀⢀⠀⠀⢀⠀⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠡⡀⠀⠀⠀⠀⡨⢀⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡱⢌⡒⠶⠄⣊⠥⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠤⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⠃⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢘⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠚⠂⠀⠈⠐⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠢⣀⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠠⡂⢰⠀⢀⢄⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⡀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠐⢄⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡋⠈⡐⡊⠉⠁⠀⠈⠀⠴⠄⠙⠊⠁⢙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠰⣁⡹⠀⠏⠀⠂⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢡⠀⠈⠀⠀⠀⡤⠀⠀⠀⠀⡤⢄⠀⠌⡌⠐⠀⠀⠀⠀⠀⠀⢀⠎⠀⠑⠤⡤⠊⠀⠒⠠⢄⡀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⡀⠀⠀⠀⠀⡠⠀⠀⠀⠑⢀⠌⠜⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠱⡀
⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⡄⠀⠈⠪⢕⠠⠀⡀⠦⠌⠀⠄⡊⠔⠁⠀⠀⠀⠀⠀⠀⠀⢰⢧⡀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠱
⠀⠀⠀⠀⠀⠘⠂⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠻⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡰⢀⣀⣆⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⢩⡍⣭⢩⣭⡍⡍⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀
⠀⠀⠀⠀⠠⠠⠉⠁⣀⠈⡜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠇⠄⠰⣰⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀⠀⠀⡠⠁⢀⠌
⠀⠀⠀⠠⠡⠁⢀⠀⠈⠀⠘⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠔⠁⠑⠤⡀⢠⠎⠁⠀⠀⠀⠀⠈⠢⠊⠀⡠⠊
⠀⠀⠠⠡⠁⠀⠉⠀⠀⠀⠀⠈⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⡇⠀⠀⢠⠊⠐⡀⠀⠀⣷⠊
⠀⠠⠡⠁⠀⠀⠀⠀⢞⡱⠀⠀⠐⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⢀⠀⠀⠙⠃⠀⠀⠈⠂⠊⠀⠀⠀⡅
⢀⢀⠁⠀⠛⠂⠀⠀⠀⠀⠀⡈⠂⠑⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⣧⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣅⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⠀⠀⢂⠀⠨⣀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠁⠀⠀⠰⠊⠁⠉⢡⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢠⠀⠌⠀⠂
⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠂⠀⠀⠐⠈⠀⠀⠘⣀⠀⠀⠔⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠂⢀⡀⠁
⠀⠀⠘⠀⡄⠐⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠒⠀⠐⢄⠀⠂⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠄⠁⠈⠂⠀⡃
⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠈⠀⠀⠉⠀⢀⢀⠤⠞⠀⠀⠀⠠⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⣤⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠘⠀⠄⠀⠀⠀⣠⣾⠟⠛⠫⠛⡛⡛⢉⣙⡻⢯⡀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠔⠐⠢⠀⠈⠀⢠⣿⠘⢸⡄⡄⣌⣳⣜⣈⣯⣩⣼⠿⡿⡏⠉⣿
⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠁⠒⠂⢀⠁⠀⠸⡿⠶⢾⠛⠻⡏⣭⣭⡩⡇⠒⢓⡐⢠⡀⢰⣽⠄
⠀⡠⠂⠀⠢⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣌⠌⠂⢦⣀⣝⣉⣷⣹⣌⢉⣣⣠⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠀⠄⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠙⠉⠋⠛⠛⠛⠉⠁⠀⠀⢀
⠀⠀⠁⠀⠁⢀⠀⠀⠀⠀⠀⢍⢈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⠱⠃⠚⠁⠀⠀⠀⠄
⠀⡊⠀⠀⠌⠀⠀⠀⢀⠀⠂⢀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠐⠠⠛⠁⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠰⠖⢲⢸⡣⢈⠄⠂
⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠘⠁⠁
⠀⢀⠂⢐⠈⠀⢃⠂⠀⠐⢈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠐⠁⠀⢀⠃⠀⠀⠀⠊⠐⠆⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠢⠀⠀⠀⠀⢄⠀⣀⢂⠐⠀⡜⡠⠐⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠄⠐
⠀⠈⠀⠡⠠⠐⠀⠊⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠐⠂⠐⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣀⠀⠀⡥⠀⠀⠀⠀⠤⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⡂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢠⡎⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢃⠀⠀⠊
⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⠂⠄
⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⡃⠀⠀⠀⡤⣖⡧⠀⣂⣀⠔⢒⠄⢀⣠⠀⠀⠀⢠⠀⢀⢢⣄⣐⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁
⠀⠀⡀⠀⠠⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠨⢰⡌⢇⠀⢀⣼⠀⢠⠔⠀⢠⡜⢸⢀⠇⢀⡠⠮⠂⠀⠀⡇⠀⠀⠙⠦⠀⠙⠁
⠀⠀⠃⠃⠉⠁⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠋⠁⠚⠁⠐⠚⠀⠙⠀⠋⠀⠀⠊⠁⠛⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠆⠀⠀⠁⠶⠦⠠⠶⠦⠼⠿⠧⠷⠄⠴⠶⠴⠄⠠⠶⠶⠦⠿⠇⠀⠘⠀⠀⣖⠀⠤⠀⢐⡀⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣀⠀⠀⠈⢠⡄⠀⠀⠈
⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠇⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠣⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠉⢀⣀⣀⡀⠊⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠓⣤⠤⠤⠤⠤⠶⢍⡀⠀⠀⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠃⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠓⢄⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⡤⠃⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢚⠦⣀⢀⠓⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢸⠀⠀⠁⠀⢱⠀⠑⠂⠔⠂⠤⠤⠤⠴⢂⠀⡖⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣂⣀⡀⢀⡤⠐⠒⢷⡦
⠀⠀⠀⠀⠀⠀⠘⠴⡀⢠⢧⡄⢆⠰⠤⣀⠀⡷⠶⡏⠁⢠⠀⣹⠹⣄⠀⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠳⡳⠈⠉⠀⠀⠘⠦⠤⠔⠣⢀⠌⠁⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠽⣝⠉⣝⢉⡎⡃⠀⢤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠛⢆⠈⣷⡱⣤⠜⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⠀⠀⠀⠀⠉⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⡦⠤⣀⠀⠀⣀⣰⠖⠉⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠤⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⡑
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠜⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⢸⠀⠀⣀⣀⠤⠄⠃⠀⠰⡤⠤⡴
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⡩⢷⠈⠉⠉⣹⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠀⠀⢀⠔⠊⢆⡀⠑⠒⢶⡁⠉⣉⠽⣄⠀⠀⠀⢀⠄⠀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⢋⠉⠉⣷⠀⠙⠤⠤⠋⠳⡀⠐⠁⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠑⠊⠁⢇⠀⠀⠀⠀⡰⠁⠃⠀⠀⠀⠀⢀⠇⠐
⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠤⠊⠀⠑⢄⡀⠀⠀⠀⡠⠊⠒⠒⠒⠉⠀⠀⠈⠢⠄⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⠀⢸⡉⡿⠀⣠⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⠀⠀⠙⠀⠀⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠃⠀⠀⠀⠈⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡴⠦⣄⣀⣀⡤⠖⠒⠒⠲⢤⣄⣀⣀⣀⡤⠖⠚⠳⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣙⠲⢤⣀⣀⠀⠀⠀⣀⣀⣤⠴⢚⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠬⣭⣭⣭⡭⠤⠴⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⠀⡀⠀⠒⠒⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠉⠁⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⣄⡀⠘⠛⠒⠢⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠸⠧⠀⠀⠛⠁⠅⠀⠀⠀⠀⠀⠀⠐⡞⠯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠂⠃⠈⠀⠀⡀⠈⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⡀⠒⠚⠀⠀⠀⠀⠀⠀⡑⠀⠈⢁⣒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢍⠉⣀⣀⣤
⠀⠀⠀⠀⠠⠀⠀⠀⣀⠄⠀⠂⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⢰⡏⡐⠀⢀⡁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠹⣭⠤⢤⣤⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠹⢦⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠘⣇⢀
⠀⠀⠀⡠⡿⢀⠋⠘⠓⠒⠛⠛⠛⠚⢛⠳⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠀⠀⠀⠀⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠈⠉⠉⠉⢾
⠀⠀⠀⠃⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢
⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠀⠐⠀⠀⠀⠀⠚⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠸⠇⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⣧⣀
⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⢸⣶⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⠗⠀⠀⠉⠉⠀⠀⠀⠀⠑⠄⣀
⠀⠀⠀⠀⢀⠻⡶⠄⠀⠀⠙⡿⠉⠀⠀⣀⣀⣉⣣⡀⠀⠀⠀⠀⠀⢀⠎⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⠖⢲⡶⣲⣦⣄⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠡⠌⠡⠈⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠘⢠⣦⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⢀⠿⠀⠀⠀⠀⠀⠈⠫⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣄⢀⡀⠀⠀⠀⠀⠀⠀⡎⠨⡆⠀⢀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⢙⡋⠉⠙⣯⠀⠀⠀⠀⠀⠀⠀⠓⠰⡛⣀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠇⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⢀⠔⢺⣼⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣀⠀⠒⠘⠀⢄⡀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠐⠿⠶⠶⠶⠶⠶⠶⠿⠖⠀⠀⠀⠀⠈⠀⠐⠂⢤⣄⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠉⣭⠙⠒⠒⠒⠒⢉⠙⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⠉⠉⠙⢢⣄⣀⣤⠬⣁⣀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢃⡼⠁⡏⠀⠀⡀⠈⢻⢶⣧⠀⠀⢀⣠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠋⠩⡀⠀⣸⣤⣀⣉⡰⠃⠸⣄⡤⠖⣉⡽⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠑⠦⣝⡋⠀⠀⠀⠀⠀⠀⢀⣀⣤⢚⡡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣞⠣⣄⠀⠀⠀⠀⢀⡎⠉⣿⣒⢒⣺⠋⡹⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠗⠀⠏⠑⠠⡔⠉⡇⢀⠂⠀⢀⠃⣞⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠳⠞⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⡘⢠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠒⠤⢀⡀⢴⢰⠃⠀⠀⠀⡇⠀⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡠⠴⠋⠀⠀⠀⠀⡆⡃⠀⠀⠀⠀⢠⠔⠋⠂⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡕⠀⠀⠀⣀⠴⠥⡀⠀⠀⠀⡠⠃⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡶⢄⣈⡷⠀⠀⠈⣢⠤⠒⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⠀⠈⢳⠧⠶⢊⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣰⠃⠀⠀⠀⣴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⡟⠀⢦⣀⣀⠀⠀⠀⣀⣀⠠⠜⢄⠀⠐⡠⠀⠀⠀⢢⠉⠉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⢧⣀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠈⠉⠒⠒⢲⠁⠀⠀⠀⠠⠀⢀⠀⠀⡇⠀⠀⢸⠀⠈⡇⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡞⠒⠦⢄⣀⠀⠀⠀⠀⠀⢱⠀⡠⠊⠀⠀⠑⢄⠀⠀⠌⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⠀⢀⠂⠀⠐⠒⠩⡉⠉⠉⠉⢣⡀⠀⠀⠀⠈⠉⠉⠙⣳⠃⠰⡀⠀⠀⠀⠀⠀⡆⢠⠂⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠸⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠊⠉⠁⠀⠈⢆⠀⠀⠀⠀⡰⢁⠆⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⢨⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⢀⠀⣀⡤⠶⠖⠛⠛⠉⠉⠉⡁⠒⠀⠄⡀⠀⠀⠄⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⠴⣯⢀⠀⠀⠀⠀⠀⠈⠐⠠⣀⠈⠑⠠⣀⠉⠒⢄⣀⣀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠠⠁⠀⠠⠊⢁⠈⠁⠀⠈⢦⡈⠐⠂⠄⠀⠀⠀⠀⠀⠙⠂⠄⡀⠁⠂⠤⢈⠐⠈⡂⠀⠀⠂
⠀⠀⠀⠀⠀⡄⠀⠀⡄⢠⠂⠀⢀⠄⠀⢀⡽⢦⣀⠀⠀⠉⠐⠠⠄⣀⠀⢀⠀⠉⠐⣂⣠⠼⠛⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠠⠊⠀⠠⠈⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⠐⠘⠛⣉⠴⠶⣭⣾
⠀⠀⠀⠀⠀⠁⠐⠢⡤⢄⠅⠠⠐⠋⠀⠀⠀⠀⢴⠋⡉⣒⡉⠉⠗⠚⠛⠓⠊⠉⠁⠠⠀⠠⠄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⠀⡀⠀⠀⡜⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠈⡄
⢀⠀⠠⠘⠀⠀⠔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⠄⠀⠘⠄⣀
⠣⢀⣀⡀⠤⠊⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠈⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠠⡁⣰⠂⠀⠤⣄⠺⠆⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠠⡱⠁⠈⠂⠄⣀⠀⠈⠙⠪⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢡⠛⠃⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⣞⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⢂⢅⢀⠐⢢⠀⢰⡈⠵⣶⠒⢄⠀⡰⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⡞⠉⠀⠀⠀⠀⡄⠱⠞⠹⠀⠀⠈⠳⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⠀⠀⠀⠀⣉⣉⢏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⣀⣀⣀⠡⣀⡀⠀⠀⢤⠄⠏⣥⠀⠀⠀⣀⣜⡀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢍⡀⠀⠀⠀⠉⠐⠒⠀⠀⠒⢒⠾⠯⡍⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡈⠑⠒⠤⣀⠀⠀⠀⠀⢀⠪⠁⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⡀⡿⠀⢔⠒⣽⠲⣤⣀⣲⠅⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢹⡇⠀⠀⠀⢸⠀⡆⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠀⢸⠀⡇⠀⡇⠀⠀⠀⠀⠀⢀⡆⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣶⣾⡽⠄⡀⠈⡀⠏⠀⡇⠀⡟⠀⠀⠀⣀⣀⣤⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠄⠠⠤⠴⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠡⠤⠤⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣇⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣽⣳⣒⣛⣯⠁⡏⢨⣭⣷⠶⠾⢽⡋⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡄⠀⠀⠀⣄⡘⠯⣂⠄⠀⣀⠀⢀⡰⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠺⡶⠿⠿⡷⠀⢠⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⠄⠤⣀⡤⠔⠢⡀⠀⠀⠘⡷⠤⠒⠉⠀⡀
⠀⠀⠀⠈⠁⡀⠀⡿⠀⠀⡇⢀⡀⠀⠀⠀⢀⡎⠉⠑⡍⠀⠀⠀⢀⣧⢠⡼⠵⢤⣀⣱⠀⠄⠊⠀⠀⢘⠉⢵⠈
⠀⠀⠀⠀⠀⠁⡰⠥⠀⠀⢣⠀⠁⡠⢤⣴⠟⠻⠀⢀⣼⠀⠀⠐⣅⠈⢲⡀⠀⣤⠑⣾⠉⠛⢆⠀⢠⢬⠉⢁⣤⡀
⠀⠀⠀⠀⠀⢠⠃⣠⣀⣠⣌⣆⠀⠣⡴⡅⠀⠀⠙⡿⠿⠀⠀⠀⢈⡉⢶⠬⠦⣄⣠⡏⣦⠤⠚⠀⡈⢊⡴⣋⠜⠁
⠀⠀⠀⠘⢁⣿⣿⣿⣿⣿⣿⣿⣆⠀⣷⠹⡄⠀⣐⣒⣒⡄⠀⠀⢀⣸⠈⢆⣀⡤⠛⠒⠊⠀⠀⠀⡤⣋⠜⢁⣀⡀
⠀⠀⠀⠀⢎⢻⣿⣿⣿⣿⣿⡿⢈⠀⢸⠖⠚⠚⠒⠒⠒⠚⣆⠀⠀⠙⠀⠀⠀⠀⣠⣴⠶⢒⡚⠿⣿⠁⠀⠀⢸⣏
⠀⠀⠀⠀⣈⠑⠒⠂⡒⠒⠒⠈⠁⠉⠘⠒⠦⠤⠤⠦⠆⠒⠃⠀⠀⣤⡆⠀⠀⡾⢋⠖⡒⠒⡌⢢⠙⡄⠀⠀⢸⣍⠁
⠀⠀⠀⠈⠚⠁⠀⠀⠻⠯⠀⠀⠀⠀⠀⠄⠀⠀⠀⠔⠒⠄⠴⠀⠀⠈⠁⠀⠀⡇⠸⣀⡛⠘⡜⡸⠀⡇⠀⡆⢸⠮
⠀⠀⠀⠀⢴⢀⡶⠚⢲⡀⠀⠓⠺⠰⠀⠀⠀⠀⠀⠊⠒⠤⠴⠂⠀⢠⣤⠀⣄⠹⣤⠈⢉⠉⠐⣡⠞⠀⠀⠧⠿⠁
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠀⠀⢠⠴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⣠⠞⠛⠳⡄⠀⢰⡆⠉⠂⣴⠶⠶⠄⠈⢀⡀⠀⢀⡄⠀⣠⠤⢤⡒⠀⢸⣂⣀⣀
⠀⠀⠀⠀⠐⣆⠀⠀⢀⡇⢰⡇⠀⠀⠀⠉⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⣾⢧⠀⢸⡇⢰⡇⠀⠈⠁⠀⢸⠉
⠀⠀⠀⠀⠀⡌⠛⠒⠋⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣟⠛⠛⠂⠀⡟⠈⣇⢹⠃⢺⢁⠀⠀⢀⡀⠸⠶⠖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢧⣀⣀⣠⠄⠀⣸⡇⠈⠁⣿⣤⣤⡄⠸⠃⠀⠘⠟⠀⠈⠦⠤⠖⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⡉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⢒⣤⣤⡄⢀⡴⣊⠥⢄⠉⢆⠲
⠀⠀⠀⠀⢠⣄⠈⠉⠀⠀⠠⡆⠀⠀⠘⠀⠈⢫⡂⢠⠛⠒⠠⢼⡀⠛⠑⠙⠀⠀⣀⠁⡀⡄⢠⣾⡔⠁⠀⢀⠃⣼⢠⣤
⠀⠀⠀⠀⠀⠁⢰⠭⡆⢰⠯⡆⠀⡟⡇⠀⠀⠀⡸⠡⠀⠀⠠⠀⠈⠟⢠⣄⣤⠀⠳⣄⢀⡗⠋⠀⠀⠀⢴⣧⡴⠃⢸⠏
⠀⠀⠀⠀⢶⣾⣯⡿⡽⠽⠯⡿⠿⠿⣿⠟⠀⠘⢇⠀⠀⠀⠀⠀⠀⡆⠈⠻⠃⠀⢂⡬⠛⠬⡀⠀⠀⠀⠔⠈⠀⢻⣮⡄
⠀⠀⠀⠀⢸⣿⠀⣶⡇⠀⣿⡇⢠⣿⣿⠀⠀⢀⡠⠣⡀⠀⠐⣂⣀⡇⠀⠀⠀⡰⠉⠀⠀⠀⠉⢦⠀⠀⠀⠀⣦⣠⠟⠁
⠀⠀⠀⠀⢸⣿⠀⣿⡇⠘⠿⠇⠀⠿⣿⡆⠀⡉⣀⢀⠙⠉⠀⠀⠀⠀⠐⠀⠙⠁⠀⠀⠀⠀⠀⠸⠟⠄⠀⠀⠸⠛⠋
⠀⠀⠀⠰⠿⠿⠿⠯⠿⠿⠯⠿⠽⠽⠽⠿⠃⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣫⠄⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⢛⡀⠀⠀⠀⢀⠀⣑⠠⠵⠕⠃⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⠁⠀⠀⠀⠀⠘⠘⢀⡀⠈⠁⠀⡄⠀⠈⠈⠀⠀⢸⠀⠀⠀⢠⢫
⠀⠀⠀⠀⠀⠀⠀⣰⣻⠀⡀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠿⠢⠀⠀⡀⠀⠀⠀⣀⢼⣆⠉⠁⢸⡑
⠀⠀⠀⠀⠀⠀⣰⠿⢹⠉⣃⡁⠅⢀⡀⠈⠠⢠⣤⠄⠈⠈⠀⡴⠇⠀⠰⠊⠀⢸⠀⠀⢒⡞
⠀⠀⠀⠀⠀⣰⡝⠃⠀⠀⠀⠁⠀⠀⠉⢣⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡴⠿⣶⣷⣴⣤⣤⡄⡆
⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠂⣖⠀⠐⠞⠁⠆⠀⠀⠀⠰⠀⠈⠃⠣⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠈⠁⠉⠀⠀⠘⠁⠉⠉⠉⢻⠆
⠀⠀⠠⠤⠜⠗⢠⣄⢠⣐⣛⠻⠅⠀⠀⢠⠀⠀⠀⠀⠠⠷⠆
⠀⠀⠀⠀⠈⠉⠛⠙⠻⠉⣹⣿⣯⢭⣿⠩⢥⡦⠄⢦⠽⠿⠶⠶⠮⠷⠖⠒⠺⠥⠟⠿⠷⠮⠥⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠉⠉⠉⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠄⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢰⡁⠀⠀⠀⠤⠠⠤⠐⠈⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠠⠸⠅⣀⠀⠀⠀⠀⠀⡀⣀⠀⠠⠤⠌⠂⣰⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠈⠠⣆⠀⣤⡄⠀⢀⡀⠀⣠⣄⠀⢀⠔⠈⠁⠀⠗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠌⠀⠩⠡⢀⠋⠈⠂⠈⠁⠐⠁⠀⠀⠒⠈⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇⠀⠀⠀⠀⠑⢄⠀⠀⠀⠂⠀⠀⠀⠀⢀⠜⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠀⠀⠃⠀⠀⠑⠠⣀⠀⠀⣀⠠⠔⢡⠁⠈⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠄⠠⠀⠠⠀⠠⠀⠀⠀⠃⠀⠀⠀⠐⡀⠀⠀⠀⠐⠠⠀⢐⠀⠀⡠⠃⠇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⢁⠀⠀⠀⠀⡑⢄⠸⠀⠎⠀⠰⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⢰⠒⠲⠲⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⢂⠀⠀⠀⠡⠀⠑⡇⠀⠀⡄⠀⠀⠀⠠⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡱⠶⡈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⢂⠀⢀⠀⡐⠀⠀⠀⢀⣆⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⢰⠀⠀⠀⢀⡀⡇⠀⠇⣀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⢡⠀⢲⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠉⠏⢸⠀⠠⠤⠰⠀⠀⠀⠀⠈⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⣀⢀⠀⠠⠀⠈⠢⡀
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠒⠒⠒⡀⠱⡀⠀⠈⢂
⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠒⠂⠐⠀⠁⠀⠀⠀⠑⢄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⣠⠄⠈⡁⠀⠘⠀⠾⠂⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣦⡠
⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣷⡀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⠷⠾⢓⣆⠀⠂
⠀⠀⠀⢠⡤⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⣦⠖⣾⣯⡉⠀⠀⡀⠀⣴⣷⣿⣼⣿⠗⠀⠀⡀⠀⠀⠀⠀⠀⠟⣷⢿⡏⠉⠂
⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⠐⣴⣷⣏⣩⡅⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⣄⠀⠀⠀⠀⠀⢤⠿⠙⠍⠋⠈⠀⠀⠀⠀⣠⣤⢰⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⡀⢰⡤⠀⡀⠀⠀⠀⠀⢺⡃⢰⡆⠀⠈⡀⠀⠀⠀⠻⠀⠀⡅⢻⠋
⠀⠀⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠁⠰⠆⠀⠀⠈⠁⠀⠙⣦⡀⣿⠀⠀⠀⠘⢶⡰⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠿⠿⠋⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢠
⠀⠀⠀⠰⠂⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢶⣴⣇⣀⠀⠀⠀⡀
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⣾⣭⣻⢻⡷⡔⠚⠁
⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠈⠀⠀⠐⣟⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⣼⣩⡄⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠁⣼
⠀⣀⠀⠀⠀⠰⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠐⢀⣠⣞⠁⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠘⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠿⠀⠀⠀⠀⠄⠉⠙⠛⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢈⠀⠀⠀⠀⠰⠦⠠⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⠈⢘⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠁⡄⠃⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣲⣾⣿⣞⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡚⢲⡄⠀⠀⠘⠟⢻⣿⠛⠃⠀⠀⠂⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠎⣰⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠉⠳⡖⠀⠀⢠⠆⠀⠈⠀⠂⠀⠀⠀⡀⠠⢥⣮⣿⣿⣷⡀⠀⠠⠄⠀⣇⠀⠉⢸⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⢠⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠻⠻⠟⠑⠦⠀⠀⠀⠉⠀⠀⡀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣴⠆⠁⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠒⠀⠀⠠⣤⠉⠀⠀⠄⠀⢨⠀⠀⡀⠀⢼⡴⠁⠀⣀⣀
⠀⠀⠀⠀⠁⠀⠀⡼⠀⠀⠀⠀⠀⣀⡴⠒⣫⡟⠁⠀⠀⠀⠀⢰⡀⣠⡔⠀⠀⠀⠛⠀⠀⠀⠀⠀⠗⠀⠞⠀⠀⠈⠁⠐⣴⠛⠃
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⣁⡴⠚⠁⠀⠀⠀⠀⠀⠐⠘⢿⣿⣆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⢄⣸⣿⣯⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣸⣧⠖⠚⠙⠋⠉⠁⠀⠀⠀⠀⠀⠙⠲⠦⠤⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢴⣶⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢰⡖⠤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡶⠋⠀⢀⢸⠀⡠⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⡴⠿⠛⠛⢛⠛⠛⠋⠈⡇⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡠⠖⠉⢰⡴⠚⠁⠀⠀⠀⠘⠾⠊⠀⡠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠐⡀⣰⠁⠀⠀⡠⡀
⠀⠀⠀⠀⡀⠄⢠⣤⠔⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠳⠿⠥⠀⠀⠶⠃⠸⠀⠀⠈⠣⣀⠀⠀⢀⣨⠔⠁⠀⠀⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⠋⠀⠀⠀⠀⠶⠂⠀⢠⠏⠂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⡤⡸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠿⠀⠀⠀⠀⠸⢦⣾⣥⢤⣄⠀⠀⢆⠠⢴⢀⢀⠎⠀⠉⠒⠢⢄⣀⠀⢀⣀⠀⠀⠀⠀⠙⣿⡤⣤
⠀⠀⠀⠀⠀⠀⠋⠀⢰⣖⡒⢤⡀⠀⣄⢠⠀⠀⠀⣾⢁⣀⣠⣟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠟⠢⠀⣠⠀⡮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠉⢹⠗⠋⡀⠐⠂⠂⠀⠀⠉⠛⢡⠏⢀⣽⠂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡿
⠀⠀⠀⠀⢀⠤⠐⠋⠁⢀⠏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⡿⠋⠉⢳⡄⠀⠀⠈⠢⡐⠀⠀⠠⢀⡸⠀⠀⠀⠀⢀⠀⣹⠧⢒⠆
⠀⠀⠀⢰⣿⣶⣤⣄⡀⠘⢄⠀⠀⡆⢀⠀⠀⢠⡄⠀⠀⠀⠸⣅⠀⠀⠚⠀⠀⠀⠀⠀⠘⡀⠒⠊⠉⠀⠀⠀⠀⠀⢺⡷⠛⠊⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡼⠀⠀⡏⠙⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡞⠙⡆⠀⠼⠁
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢄⣀⠀⢠⣤⡌⢀⡄⠀⠀⠀⠸⡿⠀⠀⠀⢀⣼⠙⡣
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠖⠛⠃⡀⣀⠀⠀⠀⣞⣽⣿⣿⣿⢶⠚⠁⠘⠀⠉⠀⠁⠀⠀⠀⠀⢿⠀⢀⣴⠟⠊⢹⡅
⠀⠀⠀⠀⠄⠸⣔⡽⠀⠀⠠⢀⣘⣧⣤⠤⠴⠞⠁⠀⠀⠀⠀⢹⢹⠁⣀⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠭⡟⠁⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢳⣏⠉⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠉⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⠹⣧⠀⠀⠂⢉⣻⣦⣤⡼⠀⠀⣀⡀⠀⠀⠀⠀⢃⢿⣿⠀⣿⠀⠀⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠸⣍⣀⠈⡧⠀⠀⠘⠉⠀⠃⠀⠀⠄⠸⡸⣿⡇⢻⡇⠘⠋⠉⠻⡁⢘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠧⡡⠃
⠀⠀⠀⠀⣀⡀⠀⠀⢈⡴⠒⠛⠻⣏⠃⠀⠀⠀⣀⡠⢠⡀⠀⠠⠀⡇⢿⣿⣘⣿⠀⠀⠀⠀⢸⢎⠀⠀⠀⠀⠑⠁⠈
⠀⠀⠀⠀⠛⠁⠀⠀⠾⠀⠀⠀⠀⣸⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢼⣟⡩⠋⠀⠀⠀⠰⠃⠀⠳⣄⠀⠀⣠⣐⣒⣒⢒⡄
⠀⠀⠀⠀⢞⣹⠀⢴⡦⠀⠀⠐⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⠆⠀⢀⡠⠖⠉⠀⠀⠈⡟⠛⠛⡟
⠀⠀⠀⠀⠀⣀⣶⠶⠦⢤⣤⡤⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⠙⠈⠂⠾⠃⠀⠀⢰⣹⠆⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⣀⣤⣤⣤⣤⣖⠚⠉⠉⠉⠉⠉⣷⠴⠶⠶⠶⠶⠚⠃⢀⠀⠀⢠⢊⣁⣀⣨⣌⣲
⠀⠀⠀⠀⡀⠸⣄⣀⣀⣠⠇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠸⢿⣿⣿⣿⣿⠟⠰⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠘⠒⠒⠒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⠠⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠒⠒⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠖⢲⠎⠀⠀⠀⢹⡤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢒⠒⠒⠒⣶⡒⠒⠒⠒⠒⠒⠒⠒⠺⣄⠀⠀⢀⡼⠓⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠰⡻⠆⢤⣄⠿⠛⣄⠀⠀⠀⠀⠀⠀⠀⠈⣷⠚⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠐⠂⠀⠀⡔⠂⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡈⠄⠠⡀⠐⣂⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠪⠴⠁⠈⣦⠟⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣤⣀⣀⣀⣀⣀⣠⣔⣁⣀⡀⠀⠀⠀⠀⢀⡽⠒⠿⡀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠞⠭⠭⠭⠭⠁⠸⣀⠀⣀⠛⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡈⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣄⣀⣠⠄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠨⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⠉⡆⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠵⡒⠁⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢦⣀⡼⠀⠀⠸⡯⠀⠁⠀⠀⢀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠓⠀⠀⠠⠄⠀⠈⠛⢇⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣼⠁⠀⠁⠀⠀⢸⠀⠀⠘⡏⡇⠀⢀⣤⡈⠀⠑⠀⠀⠀⡀⠀⠀⠀⢱⠀⣸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠘⠻⢤⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⢀⠊⠈⠁⠀⠀⠃⠀⠀⠙⠿⠿⠿⠋⠀⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡖⠀⠀⡀⠀⠹⡆⠀⠀⡇⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣⠀⠀⠅⠀⣠⠇⠀⠀⡇⠀⠀⠀⠀⠀⣸⠘⣦⠀⠀⠀⠀⡄⠀⠈⢩⠉⠉⡇⠀⠀⢠⡮⡀⠀⠀⢘
⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⠈⠟⠛⠟⠛⠏⠀⠀⠀⡇⠀⠀⠀⠀⠉⢻⠀⠉⠻⠉⠉⠋⠁⠀⠀⢸⠀⣗⡇⠀⡖⠉⠀⠀⢀
⠀⠀⣠⣤⣿⣀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣶⣶⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣷⣧⣤⣷⣤⣤⣤⣼⣤⣬⣤⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠂⠠⢄⣀⣀⠠⠤⠶⢀⠀⠤⡄⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠟⠒⠻⢤⣀⠀⣀⣐⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠰⢠⠏⢿⠁⠀⠉⠙⣶⣦⡀⠀⠀⣀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠊⢅⠀⢘⢦⣀⣁⡼⠁⢇⣠⠔⣉⢽⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡰⠀⠀⠀⠈⠑⠬⣙⡁⠀⠀⠀⢀⣀⢠⠤⠎⠡⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡾⣝⠢⣀⠀⠀⢀⡼⠀⡝⠭⠭⡟⣁⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⢈⢀⠃⠈⠐⠁⢰⠀⠃⠀⠰⢀⠇⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢱⡀⠀⠀⠀⡘⡠⠀⠀⢠⡆⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡜⠀⠈⠁⢉⠁⠁⠀⠀⠀⠃⡠⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢈⠄⠀⠀⢀⣠⡊⠀⠀⠀⢀⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⢄⡀⡯⠀⠀⠑⣄⠠⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠏⠀⠈⢳⠤⠖⡊⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠣⠄⠀⠀⠀⢠⠄⠒⠁⠤⠀⠤⠀⠀⠀⠳⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠤⢀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⢸⢄⡀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠀⠀⠀⡀⠀⠀⡈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠠⠀⠀⠉⠒⠒⠠⠐⢦⠀⠈⠉⠒⠒⠂⠤⢤⡄⠐⠁⠀⠀⠀⠈⠀⢀⠄⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠒⠉⠀⠨⡀⠀⠀⠀⢀⠂⠂⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⢠⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣟⣟⣿⣻⣛⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣛⣿⣟⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⣿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣶⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢰⢋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠠⠁⠠⠬⠐⢂⠀⠀⠀⠀⡦⠀⡐⠉⢂⢀⡀⠀⠀⠀⣀⣧⡵⠖
⠀⠀⠀⠀⠀⣥⠜⠁⢢⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠸⡀⠁⠐⠀⠂⢉⡜⠀⠀⠀⠈⢢⡠⣯⡟⣍⣈⠏⠀⠀⢼⠁⢈⡇
⠀⠀⢀⠀⡀⠀⠀⠰⢀⠀⠀⠘⡁⣤⠁⠠⡀⢀⠀⠀⠑⠤⡄⠀⡠⠎⠀⠀⠀⠀⠐⣁⣸⠨⢵⡋⠑⡀⢀⡴⠚⢯⠉
⠀⠀⠈⡉⠅⠀⠠⢂⠌⠀⠀⠀⠐⢄⠀⠀⠐⣄⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠄⠈⠉⠀⠀⠈⠉⠚
⠀⠀⠀⢰⣶⣿⣷⣷⣀⠀⠀⠀⠀⠈⠰⢤⡾⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠤⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠀⠑⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⡈⢀⠀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠃⠀⠐⠃⠀⠀⠀⠠⠘⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⡠⢊⠆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠉⡇⠠⠀⠀⠀⠀⠀⢻⣷⠄⠀⠠⠊⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡦⢄⠤⠖⠁⠀⠀⠀⠀⠀⠠⣠⣶⣶⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠢⠄⠄⠊
⠀⠀⠀⠀⠀⠠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡡⠀⠀⠀⠀⠈⢤⡐⢀⠆
⠀⠀⠀⠀⢠⠁⠏⠀⠀⠀⠄⢀⠴⠀⠀⠀⢠⠿⢿⠿⣿⣿⡿⠷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠂⠐⠔⠁⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠈⠒⢀⠸⠈⠂⠀⠀⠀⠀⠀⠀⢂⡀⠀⡰⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣈⠁⢈⣤⣤⡗⠀⠀⠀⠀⠀⢠⠊⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡍⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂
⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⡆⠀⠄⣀⠀⠀⠀⠀⠀⠀⡠⢐⣤⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠠⠐⠁⠀⠑⢩⠁⠀⠀⠀⠀⠀⠀⠈⢿⡇⣀⣀⠀⡄⠀⠀⠀⢰⡸⠏⠟⢀⢰⠀⠀⠀⠈⡀⣬⢢⠀⠀⡠⡂⠥⠀⠠⠁
⠀⠀⠀⡁⡄⠀⠐⠒⠄⠅⠀⠀⠀⠀⠀⣠⣴⡾⠛⠻⢿⠃⠀⠀⠀⠀⠀⠃⠈⠄⢉⡀⠂⠀⠀⠀⠐⠠⢙⢠⣌⠜⢁⠠
⠀⠀⠀⠑⠈⠀⠒⠨⠈⠀⠀⠀⠀⠀⠠⡈⠛⠃⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⣀⣰⠘⠋⠈⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠓⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⢦⣶⠛⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⠀⠀⠀⠙⠘⡀⠀⠀⠀⠁⠉⣦⠂⠆⣔⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠂⠀⠀⠀⠀⢎⣱⣿⠷⣶⠉⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⢻⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠄⠈⢋⣿⠢⠁⢄⠈⢸⣏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢠⣧⠘⠺⠅⠀⠀⠔⡀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡛⠃⠀⠐⠚⠻⠏⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⡟⠀⠀⠠⠀⡗
⠀⠀⠀⣀⠀⠐⠈⠀⠀⢀⣔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢄⡂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⡀
⠀⠀⢸⣿⠀⠀⠀⠀⣤⡼⠟⠒⠒⠀⠰⠂⠀⠀⠀⠀⢰⡀⠚⠀⠀⠀⠀⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡇
⠀⠀⢸⣿⡄⠀⠀⢤⡏⠁⡀⠀⠀⠀⠀⠘⠗⠁⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⠀⠀⡆⠀⠀⢂⣀⠃⢉⡽⡀
⠀⠀⢸⣿⡇⠀⠀⠈⠛⠚⣁⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣆⠀⠀⣤⣦⣞⡜⠁
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠿⠟⠻⢿⡿⠇⠀⠀⣽⠝⣸⣃⠄⠀⡀
⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⠄⠒⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⢬⠀⣴⠞⠶⣿⡿⣿⣶⠋⠀⣿⣿⠆⣸⠃
⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠀⠀⢰⡟⡰⠁⣄⡠⠄⠀⠀⠀⠀⠀⠀⢁⡂⠀⠈⠙⠻⠆⠠⣈⠋⣈⢫⣤⣤⣿⣿⣿⣇⣆
⠀⠀⠈⢿⣿⣿⣿⣄⣆⠀⢀⣤⣶⠀⠀⣿⣷⡇⠀⡀⣰⡷⠀⠀⠀⠀⣤⣦⣄⢀⠀⢀⡄⠀⠀⠀⢻⡿⠿⠿⣿⡿⠿⠿⢛⡠⠝⠁
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣧⣡⠍⠀⢸⣿⡇⣠⡘⢛⣻⣿⡀⡀⡄⠍⠁⠉⠻⠀⣣⡜⡂⠀⠀⠀⣾⡇⠀⠠⣶⡄⠒⠒⠁⠐⠀⣀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⢙⣇⣼⢻⡟⣀⣸⣿⠛⠉⠀⠀⠙⣯⠀⠀⠀⡀⠸⢿⣿⣷⣶⠄⡀⣿⣧⣾⣦⡛⠂⠀⠀⢠⡶⠋⢁
⠀⠀⠀⠀⠀⠉⣶⣿⣿⡏⠋⠻⢿⣷⣾⠃⠀⠈⣷⠀⠀⠀⠀⢰⣧⣤⣀⣤⡇⠀⣤⣷⠚⡛⠊⢳⣿⡿⠟⢻⣿⡆⠀⠀⡎⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⢀⢸⣿⣿⠈⣷⣤⠏⠀⠀⠀⠀⠈⢻⠿⢫⠥⠁⠀⠛⠉⠀⢛⣛⣤⣶⣷⠆⠀⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠈⠘⠛⢿⡈⠿⠿⠦⣀⣤⣤⣤⡤⠜⠀⠀⠀⠀⠤⠴⠶⠿⠿⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⡀
⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡁⢀⠀⣁⣠⢀⡅⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠤⠀⠤⠤⠤⠤⠜⡀⡀
⠀⠌⠀⡄⢠⠆⢀⡀⢠⠀⠀⢹⠁⠀⠉⠈⠀⠀⠀⠀⠈⡇⠀⠆⠰⠀⠠⠤⠄⠂⠁⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁
⠀⠉⠀⠁⠈⡏⢈⠀⠠⡀⠀⣸⠀⣀⠀⠀⡀⠀⠀⠤⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⡀⠠⣈⠃⠀⠀⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⢀⠀⠀⠠⠀⠂⣀⠐
⠀⠀⠀⠀⠠⠆⠀⠀⠀⢀⡀⠀⢁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠒⠂⡑⡄⡅⠀⠀⠀⠐⠠⡤⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣁⡒⠀⠠⠀⠒⠈⣀⠀⠐⠀⠀⠀⠀⠈⠀⠐⠄⠀⠀⠠⠄⠀⠆⡄⢀⠀⡆⠀⠑⠁⠀⠀⠀⢎⠀⠀⠀⣀⠘⠀⢀⡂⠶⡅
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠐⡱⠦⠤⠔⠊⠀⠀⠀⣇⢀⠙⣠⠀⢀⠠⠦⠀⢰⠀⠭⠃⢠⠠⡄⠀⠁⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⠁⠀⠀⠐⠀⠀⠀⠀⠘⢦⡀⠈⠁⠉⠁⢂⡠⠬⠀⠀⠉⠀⠋⠀⠠⡀⠀⠀⠐⠈⠐⠉⠐
⠀⠂⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠰⠀⠀⠀⠀⠀⠀⠉⡁⠒⠒⠊⠉⠀⢠⠀⠀⢰⠀⠑⠀⠠⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠔⠀⠈⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡊⠐⠀⠄⠀⠘⠀⠑⠁⠦⠀⠀⢀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠂⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣤⣄⡀⢀⣀⣀⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠈⠉⠉⠁⠁⠀⠀⠀⠈⠁⠀⠀⠀⡀⢸⣿⠀⠀⢸⠟⠉⢻⡇⣿⡇⢹⡇⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠍⠀⠁
⠀⠀⠀⠀⢨⠈⡅⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠃⢸⣿⠀⠀⢸⣆⣀⣸⡇⢸⣧⣾⠇⠀⠀⢀⣀⣀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠆⠺⠀⠆⡀⠠⡄⠀⠀⠀⠀⠱⡀⢀⠔⠀⢸⣿⠀⠀⢸⡇⠀⢸⡇⢸⡏⣹⡇⠀⠀⢸⠉⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠘⠃⠀⠘⠁⠘⠛⠛⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠂
⢀⠀⠐⠉⠀⠀⠀⡆⠀⠂⠀⠀⠀⢠⢀⠀⠀⣀⠀⠀⢸⡛⡟⣻⠻⢿⠛⢟⣿⢻⡇⠀⠀⠀⡄⠀⠆⠐⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠈
⠀⠉⠀⠀⠒⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣷⣷⢾⡾⣾⡷⣷⡿⡾⡇⠀⠀⠀⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠑⠀⠀⢸⠀⠠⠀⠀⠀⣀⠀⠀⠠⠀⠀⠐⢀⠀⠌⠐⢆⡃⠂⠀⠡⠠⢀⡐⠀⠀⠀⠀⠀⠠⡀⠠⠂
⠀⢀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠵⠀⠀⠀⠀⠊⢔⠀⠀⠀⠀⠀⠙⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠀⠀⠁⠀⠂⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠂
⠀⠀⢰⡆⢰⡆⠀⠀⢠⡾⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠐⠁⠊⠁⡐⠀⠀⠀⠉
⠀⠀⢸⣧⣼⡇⡶⣦⠸⣧⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠈⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⢸⡇⢀⡿⠀⣿⣸⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⡄⣡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠈⠛⠘⠁⠙⠛⠀⠙⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠛⠙⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⢠⡞⠲⣽⣍⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⣼⠀⢀⡬⣅⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⣸⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⣤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⣛⣉⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠋⠉⠀⠀⢀⣨⠿⠖⠒⠲⢦⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⣴⡆⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠹⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠘⠁⢠⡶⠛⠛⠒⠦⣏⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⡆
⠀⠀⠀⠀⢀⡤⠤⢤⣀⣠⢼⡇⠀⠀⠀⠀⠀⠀⣾⣤⣄⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢳⣔⣷⡆⠀⠀⠀⠀⡟⠀⣷⠀⠀⠀⠀⡏⠉⠙⡇
⠀⠀⠀⢰⡏⠀⠀⠀⠀⡏⣰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⢶⣄⠀⢹⡄⠀⠀⠀⠀⠀⢀⣿⠉⠀⠀⠀⢀⡼⠁⠀⣿⠀⠀⢀⣤⡇⠠⡞⠓⢦
⠀⠀⠀⢸⡇⠀⠀⠀⢼⠳⣏⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣧⠀⣻⣄⣀⣀⠀⠀⠈⢹⠷⠤⠤⢖⡯⠤⣄⠀⣿⠀⠀⣯⢠⡇⢠⠼⠧⣾⠁
⠀⠀⠀⠈⣧⠀⠀⠀⠈⠳⣝⡛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠘⣇⠀⠀⠀⠈⠙⢦⣤⠞⠀⠀⠀⠜⠀⢀⡼⢰⠇⠀⠀⠸⣼⡇⢸⠃⠲⡼⠃
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣉⣉⡉⠀⠀⢀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡟⠀⠀⠀⢀⣽⡇⠈⢹⣦⠞
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⡇⠀⠞⠓⠛⠉⡀⠀⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢠⡞⢹⡇⠀⢸⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⢦⣤⣤⠴⠋⠹⡄⢸⡧⠝⣦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣴⠋⠀⢸⡇⠀⣾⠳⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠰⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠷⠛⠁⠉⠀⠀⠀⣠⠞⠁⠀⢀⣴⠟⠁⠀⠀⠸⠦⠤⠟⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠀⠀⠀⠀⢀⡤⠞⠁⠀⣀⡴⠋⠁⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⡠⡾⠃⢸⡄⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⡾⠀⠀⢀⣠⠶⠋⠀⣀⡤⠚⠉⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⡏⠳⠶⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡷⠤⢰⠋⣷⠖⠒⠉⠁⠀⠀⣀⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⢥⡀⢣⠀⡼⠀⣼⣆⡠⠤⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢺⡀⢸⡀⠇⢠⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⣒⠒⠒⢒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠘⠀⣿⠀⠘⠀⠀⠀⠀⠀⠀⢫⠍⠉⢡⠝⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢹⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⣸⡀⠀⢸⡄⢠⡋⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠀⣴⠃⠀⠀⠀⠹⡇⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠷⠶⠖⠛⠒⠒⠒⠚⠒⠒⠓⠒⠒⠒⡾⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⡗⠚⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⣀⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⠶⠤⠤⠤⠤⠤⠤⠶⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⣠⡀⣀⠀⣀⡀⣠⢀⠀⡀⢀⣀⢠⠠⣀⢀⠀⣀⠀⢄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠁⠈⠀⠀⠁⠈⠈⠀⠀⠀⠁⠀⠈⠁⠁⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡆⢀⠀⡀⠀⡄⠘⣆⣘⣄⣸⣤⣧⣴⣥⣎⠎⡠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⢰⠸⡀⢠⠀⣇⢈⣆⣡⣤⣧⡼⠶⠷⣚⠛⠻⠉⡉⢩⠄⠀⠀⠀⠈⢝⢿⣴⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢱⠀⢇⣀⣱⣬⣦⡴⠶⢷⡛⠛⠋⠉⠉⠑⡀⢀⠦⢠⠄⠀⠀⠶⠀⠁⡄⠀⠀⠀⠀⣘⠃⠁⢹⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⣼⠞⠛⠩⠉⣅⠀⠀⣈⣙⡤⣄⡀⢀⢀⠁⠀⠁⠀⠀⠄⠀⠙⠀⢠⠄⠀⠤⠀⠀⢠⡀⠀⠠⠆⠀⣷⣒⠂⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣹⡞⡑⠙⠆⠀⠀⠀⠀⠀⠐⠢⣌⠁⠮⠋⡣⠑⠀⠘⡃⠀⠀⠁⠀⠀⠀⠀⠋⢀⡀⠀⣀⡀⠀⠖⠐⣼⡓⠤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠤⡤⣿⠀⠸⠃⠛⠀⠀⠀⠀⠀⢸⣀⣼⣧⠶⠠⠃⡜⠀⢀⠀⠠⠠⠀⠀⠀⠀⠖⠀⠆⠀⠲⠈⠠⣐⣥⢾⡓⠬⠁⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⡀⡠⡄⠉⢀⡄⠶⠀⠀⠀⠓⠀⠉⠤⠍⠙⠁⠤⠈⢐⡀⠫⠄⣀⣀⣀⣤⡤⣶⠶⡖⢛⠻⡙⠄⠣⠉⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⡨⢷⣜⠀⢃⠀⠀⠶⡀⠀⠀⠘⠀⣀⣒⣠⣤⣤⡴⠶⡖⠺⡟⢻⠉⠋⠃⠘⠀⠉⠀⠁⠈⣠⣴⡶⠶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢊⡝⢻⠶⡶⡷⢶⠶⡞⢻⠛⢏⠹⡉⢣⠸⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠘⠀⠃⠘⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⡶⠾⠋⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⢀⣼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣙⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠻⣄⣿⣿⣿⡿⢟⡃⠀⠀⠀⠀⣤⢤⣤⣤⣤⣤⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⣀⣉⣁⣼⢿⠟⠀⠀⠀⠀⠀⠐⠀⠙⠛⠛⠋⠉⠙⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢷⣶⣶⣦⣦⢸⣧⣾⣿⠀⠀⠀⠀⠀⠀⠀⠰⠄⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣾⡏⢻⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⠃⢸⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣴⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣿⣿⣿⡿⠁⠀⠈⣿⣿⣇⣀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣗⡂⣸⣿⣏⣼⠿⠿⣿⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠙⠃⠉⠉⠉⠀⠈⠉⠉⠉⣿⠁
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠙⠙⠛⠛⠛⠛⠛⠛⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣴⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⢠⡄⢤⣤⢤⣤⡄⣤⣤⢠⣄⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣇⣾⣿⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⠀⠀⠤
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⣿⡇⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⣿⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣗⣿⡿⠀⠀⠀⠀⠀⠀⢰⡆⠈⣿⠀⢻⠇⠘⡟⠀⠀⠀⠀⠀⢸⣿⣶⣶⣿⣠⣾⣿⣷⣄⣿⣿⡧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠉⠀⠈⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡡
⠀⠀⠀⠀⠀⠀⢠⡿⣟⠽⠋⢹⣿⣿⣿⠟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⡂
⠀⠀⠀⠀⠀⢀⡿⢊⠁⠀⢀⣿⣿⣿⠃⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⢀⡤⠒⠒⣀⠒⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠐⠻⠃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⡿⠀⠀⠀⠀⠀⠀⣼⣴⣿⣿⣿⣿⣷⣼⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣥⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠀⢰⡿⣛⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠸⣇⡁⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⡷
⠀⠀⠀⠀⠻⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣤⢠⣀⡄⣀⣠⢀⡀⡄⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠰⠇⠎⠼⠰⠡⠆⠮⠠⠠⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣴⣶⣿⣶⣦
⠀⠀⠀⣰⣋⡘⣘⣁⢋⡋⣘⢁⢀⢀⠈⠀⠐⠁⠀⠀⢀⡔⠄⠠⠁⠀⠀⠀⠉⠀⠠⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢰⠆⡴⠰⠤⠆⡶⠴⠠⠀⠄⠤⠠⣀⠁⠀⠀⠀⠈⠁⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠈⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢜⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂
⡒⠶⢶⠤⢄⠀⠀⠑⠊⠀⠀⠀⠀⠀⢀⠔⠂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠠
⠠⢀⠀⡇⠀⠀⠀⡠⢤⣶⣆⢀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡾⠀⠀⠀⠀⠱⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡸
⠀⢀⠆⠀⠀⠀⠀⠀⠉⢄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠙⠋⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠸⠀⠀⠠⠂⠀⠀⠀⠀⠑⠇⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠄⠉⠉⠉⢠⠁⠀⠀⠀⠈⠳⣤⣀⣀⢴⢣⠀⠀⠀⠀⠀⠠⠎⠉⠑⡄⠀⠀⠀⠀⠸
⢀⠇⠀⠀⠐⠄⣀⡀⠀⠀⢀⡀⠈⡀⠤⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡼⠶⣄⠀⠰⠋⠙⠳⡄⠀⠀⠈⠧⣀⡴⠁⠀⠀⠀⠀⠠⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢺⡀⢀⡸⠀⠘⢤⣀⠴⠃⠀⠀⠀⠀⠀⡶⠖⠢⡀
⠀⡠⠶⢤⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡞
⠀⣇⠀⣠⡦⣀⣀⢄⡀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠚⠁
⢀⣈⠉⠁⡸⠋⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠁⠈⢳⠄⣇⠀⠀⠀⢠⠆⠀⠀⠀⢀⠄⢤⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠀⠈⠀⠀⠀⠘⠀⠙⢄⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⣀⠠
⢤⠴⠋⠀⠈⠲⠤⠖⠃⠀⠀⠀⠀⠹⢄⣀⠇⠀⠀⠀⠀⢀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣⡀⠀⠀⠆⠻⠟⠀⠚⠂⣤⠄⠀⠀⠀⠀⠠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠁
⢀⣤⠆⢱⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠠⠉⠐
⠉⠀⠀⠀⢢⠀⠀⠘⢅⣀⡼⠓⠢⢼⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠄⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠾⢁⡤⠦⠠⣄⠀⠀⠀⡠⠄⢄⠀⠀⠀⡠⠲⠶⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⢄⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠈⡧⠀⠘⢅⣀⡼⠀⠀⠀⠈⡂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⠢⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠢⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠁
⠀⠀⠘⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢠⠋⠀⠀⠀⠉⢣⠀⠀⠀⠀⢠⠀⠲⡎⠉
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⡄⠀⠀⠘⢄⡀⠀⠀⣠⡎⠀⠀⠀⠀⠸⡀⡀⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣠⠃⠀⠀⠀⣸⣙⠉⠉⢱⠼⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⢴⠘⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⢱⠀⢣⡀⠀⣨⠃
⠀⠀⠀⠀⠀⢠⠒⠒⠄⠀⠀⠀⠀⠀⣇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠡⠀⢀⠌⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⡄⠀⠀⠠⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄

⠲⡎⠱⢠⡔⢤⡔
⣧⠍⠈⠀⠔⢲⣆⡀
⠛⠳⢄⡂⣰⠟
⠀⠀⠞⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣀⢀⣀⣤⠀⡀⠀⢀⡀⠀⣀⢀⣄⣄⢀⡀⠀⢀⢀⣄⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡿⣄⣿⢸⣧⠤⢸⡇⠀⢸⡇⠀⣿⢸⡧⠄⢸⡿⣆⣸⠀⣠⡟⠁⢠⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠃⠈⠟⠘⠇⠀⠘⠷⠦⠈⠳⠾⠃⠸⠷⠦⠸⠃⠈⠛⠐⠿⠶⠀⠟⠁⠙⠇
⠀⠀⠀⡀
⣰⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣢⡀
⠎⢳⣿⢲⡆⣠⠎⠀⠀⠀⠀⠀⠀⠙⠋
⠠⠈⢀⡁⢠⣿⡄⢀⡤
⠠⠄⠈⣀⠉⠉⣘⣡⠄

⡆⠠⡄⠀⠀⠴⣯⡅
⠀⠠⡄⠀⠑⢆⢀⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢲⠀⣄⠀⣴⣠⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⢅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⣤⣄⣹⡰⢿⡉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢁⡄⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠙⠃⠸⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⣠⣜⠓⠂⠀⠀⠀⠀⠐⠶⢤⣴⢧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠿⢹⡈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣷⣶⠾⣶⣶⠜⠀⠀⠀⠀⠀⠀⠠⣄⠈⢛⠀⢸⠃⢰⡆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠋⠁⠈⣦⡄
⠐⠾⠇⠀⠀⠀⠀⠀⠙⣹⣧⣤⣿⡛⠳⠆⠀⠀⠀⠀⣤⠀⣘⡶⠾⠛⠛⣟⠿⠃⢴⡎⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⡿⠟⢋⠀⠀⠀⠀⠠⣄⣩⠾⠇⠘⢗⠀⠀⠉⠀⠀⠰⠞⠛⣶⡞⠉⠀⣀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠀⣀⡀⠀⢨⡟⠘⠳⡄⠈⢀⠀⡿⠁⢀⠴⠃⠶⠟⢷⠖⠛⠁
⠀⠀⢀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢙⣋⠀⢈⡁⠈⠳⠈⠀⠰⠂⢀⣄⠰⠶⠿⢶⡗⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⣨⣄⣠⣃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋⠀⡈⣁⢀⡀⠀⠷⠀⡀⠀⠀⡀⠀⠠⣴⡇⠄⠀⠀⠀⠀⠀⠀⠀⣀⢰⡭⢱⡄⠀⠀⠀⠈⠷⠘
⢻⣌⠁⠈⠀⠿⠄⡶⢀⢀⡤⠚⠁⠀⠀⠀⢠⣤⠄⢿⡴⠟⠉⠀⠀⣠⠀⠀⢁⠐⠶⡉⠳⣶⡾⠷⠄⣠⠄⠀⠀⠀⠀⠀⠈⠳⠴⠛
⡀⠙⠀⢀⡔⢀⠘⣧⠈⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⣰⡆⠀⠉⠀⣤⠀⣧⠄⠀⣦⡸⠷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠲⠀⠈⠀⠀⠀⠀⢤⠿⡞⠁⠀⠀⠀⠀⠀⠀⠚⠋⠀⣘⡿⢅⣠⣜⣇⠀⢀⣼⣀⠴⢾⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠛
⢀⠤⠀⠀⠀⠉⠛⠰⠖⢀⡷⠄⠀⢤⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠉⢻⠛⡛⠙⠇⠀⠀⠻⠖⠀⠀⠀⠀⣿⢀⠤⢤⡄⢻⡁⠀⠀⠀⠀⠀⠘⢋⡰⠖
⠋⠠⠄⠸⡏⠐⣤⠔⠶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠁⠀⠀⠷⠀⠀⠐⢷⣆⡀⠀⠀⠀⠈⡷⢠
⡄⠦⠀⣤⠤⠦⡁⢠⠤⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢀⠁⠀⠀⠀⠀⠀⣠⠀⠠⢈⣡⡞⠃⠀⠈⠁
⠱⠶⢆⡻⠀⠄⠉⠲⠀⠈⠣⡤⠀⠀⢠⣄⠀⣱⣄⡄⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠳
⠇⠀⠘⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣁⢈⡁⠶⠈⠷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠈⠴
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠓⠻⡧⠌⣠⠀⠴⠒⢴⣧⣀⠀⠀⠠⠼⠃⠀⠀⠀⠀⠘⣭⠀⠀⠴⠀⠀⠀⠰⠆⠀⠀⠈⠀⠄⡴⠀⠀⠀⠋⠓
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣶⡀⠰⠂⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⠁⡴⢤⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠿⢧⠄⠐⡦⠀⣀⠀⢠⠿⠾
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⡬⠁⠐⠈⠁⢡⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠
⣰⢦⡗⢀⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣧⠸
⠉⠉⠁⠁⠩⠶⠒⢄⣰⠃⠀⠀⠀⠀⠀⣎⣷⠀⠀⠀⠀⠐⢢⡄⠀⣀⢨⡄⠈⠀⠉⠀⠙⣿⠶⣆⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁⠘⠆
⠀⠀⢌⠁⠀⠀⠈⠙⣃⣢⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠋⢠⡀⠁⠀⠐⡂⠀⠀⠁⠀⠉⣱⣖⠁⠀⠀⠀⠀⠀⠀⣀⡱⠀⠀⠈⠉⣻⡉⢁⡄
⠀⠀⠀⢀⠈⠋⠀⠀⡡⠙⡶⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠛⢀⠀⠀⣠⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡯⣤
⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣦⣤⣶⣤⣴⣶⣶⣶⣶⣾⣶⣤⣶⣶⣶⣶⣶⣶⣶⣴⣾⣷⣶⣷⣶⣿⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣦⣶⣿⣦⣶
⣿⣿⣿⠻⠍⠛⠟⠉⠙⠛⢻⡟⠏⣹⡿⢻⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⣀⣀⣀⣀⡬⠀⠀⠀⠀⠀⠀⢏⣉⣉⣉⣉⣉⡕⠀⠀⠀⠀⠀⠀⠸⣉⣉⣉⣉⣉⣹
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠠⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⢧⢤⠤⠤⠤⠤⢤⡀
⠀⠀⠘⠂⠀⡖⠆⠀⠐⠒⠐⡖⠒⠒⠒⠐⡖⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⡖⠒⠒⠒⡖⠖⠒⠁
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⡀
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⠇
⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⡇⠀⠀⠀⢷
⠀⠀⠀⠀⠸⡇⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⢸⣥⣤⣤⣤⢤⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢰⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⠇⠀⠀⢸⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⠢⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠊⠀⠀⠀⠸⢸
⠀⠀⢠⠀⠘⠚⠂⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄
⠀⠀⠀⠁⠈⠈⠁⠀⠈⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠈⠈

⠀⠀⠀⠀⡟⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⡇
⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣦⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⢀⠇⠀⠤⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠋⠛⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣇
⠀⢀⠞⠁⠀⢶⠆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⡁⠉⠈⠀⠀⠀⣠⣾⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠘⣆
⠀⣸⣤⣤⣄⡀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠦⢤⠴⠶⠤⣀⡼⣆
⠀⢸⣿⣿⣉⣿⣷⣶⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣤⡄⠈⠁⠀⣴⣦⠀⠘
⠀⠀⠙⢿⣿⣽⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣉⣁⣀⣀⣀⣙⣋⣀⣀
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠁⠉⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⢻
⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠍⠩⠍⠉⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⣿⣿⡗⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠙⠛⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣒⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⣶⢸
⠀⠀⠤⢤⣤⠄⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⡂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣧⣼⢸
⠀⠀⣠⣼⣿⣭⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡒⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⣷⢸
⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠤⠤⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠭⠕⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⡖⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⣴⠁⢘⣦⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠉⢳⡀
⠙⢦⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡤⣮⠽⠯⣵⢤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⡙⣄⣐⣿⣁⡀
⠀⠀⠙⡆⠰⠉⠺⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠰⣁⢀⡷⡇⠰⠆⣸⢮⡀⣨⠶⠀⠀⠀⠀⠀⠀⠠⠬⡦⠤⣽⠁⠀⣘⡄
⠀⠀⠀⠇⡇⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢟⡳⢞⡛⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⠦⠬⠟
⠀⠀⠀⠸⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠙⡄⣠⠋⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⡎

⠀⠀⠀⠀⠀⠈⡹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉
⡌⠛⠛⣱⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠄
⠀⠀⢀⠃⠀⠀⠀⢀⣀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⡸⠀⠀⠀⡎⠘⠛⠉⠐⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡇⠀⠀⠀⠡⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠
⠀⢸⠀⠀⠀⡀⠀⠑⢄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠃⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜
⠀⡇⠀⠀⠊⠀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⠈⠉⠁⡄⠀⠀⠀⠀⠱⢤⠤⠴⡟⡀⠀⠀⠀⠀⡜⠁⠈⡆⠀⠀⠀⢠⠃
⡜⠀⠀⠀⠒⠠⠤⠀⠀⡤⠠⠌⠒⠂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠚⠓⣄⠀⡏⠈⠙⡆⠀⠀⠘⠢⠾⠁⠀⠀⠀⠀⠢
⠀⠀⡀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠦⠤⠃⠀⠙⠒⠊⠀⠀⠀⠀⠀⡜⠉⠑⡄
⢰⠋⠈⣷⠀⠀⠀⠀⠈⠙⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠴⠃
⠀⠑⠒⢉⡞⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠉⠙⣦⢸⠀⠀⠀⢠⠂⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠂⠈⢄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠤⠔⠉⠈⠳⠤⠖⠁⠀⠀⠀⠘⢄⣠⠃⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠘⠛⠃⠓⠀⡤⠀⠀⠀⠀⠠⣶
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⣤
⡤⠞⠁⢆⠀⠀⢠⡔⠒⣄⢀⣀⡴⠛⠲⡄⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⠀⠀⠈⢂⠀⠈⠓⠒⠉⠀⠘⣄⠀⠀⣽⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⡀
⠀⠢⠀⠀⠀⠱⣀⡀⡀⠀⠀⠀⠈⠉⠉⠀⡞⠁⠀⠱⣄⡀⣞⠁⢘⠄⠀⠀⢢⠈⠀⢸
⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠙⠦⣄⠴⠁⠀⠀⠁⠁⠀⠀⠀⠸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠁⠈⡄⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⡀
⠀⠀⡇⠀⡀⠀⠐⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡞⠉⣢⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢰⠀⠀⠀⢀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠰⣄⡠⠇
⠀⠀⠰⡀⠁⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡎⠀⠀⠀⠈⡆⠀⠀⠀⠐⠒⠚⡄
⠀⠀⠀⠈⠂⠤⢀⣀⡀⠄⠊⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠀⠀⠑⢤⣤⠤⠞⣀⠀⠀⠀⠈⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡠⣧⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠀⠀⢀⠔⠛⢄⠀⡎⠉⠉⡆
⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⡏⠀⠈⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠠⠞⠀⠘⠒⠚⠁
⠀⠀⠀⠀⠘⡀⢀⡅⠀⠀⠀⠀⠉⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⣄⢴⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⣸⠀⠀⣙⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠴⠋⠀⣸⠉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠛⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠞⠋⠉⠀⠀⠀⡋⠥⠤⢤⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⢉⣤⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠈⠳⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠰⠋⠁⣠⠴⠒⠢⠄⡌⠀⠀⠀⠀⠀⠀⠀⠀⢷⢹⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣿⠀⠀⠀⠀⠀⠀⢰⣇⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢳⣤⣶⡄⠀⠀⠀⠀⣾⠀⣷⠀⠀⠀⠀⡖⠂⠒⡆
⠀⠀⠀⠀⢰⠃⠀⠀⠀⢹⢃⡾⠃⠀⠀⠀⠀⠀⠈⠀⠈⠉⠛⢦⣄⠀⠸⡇⠀⠀⠀⠀⠀⢀⣻⡛⠁⠀⠀⠀⣰⠃⠀⣿⠀⠀⢀⣀⡇⢠⡶⠓⢀
⠀⠀⠀⠀⢻⠀⠀⠀⠀⡾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⣄⠀⠀⠀⠀⠈⠙⡧⠤⡤⠴⣚⣡⡀⠀⣿⠀⠀⣏⢈⡇⢀⠽⠆⡼
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠙⢮⡛⠚⠛⠛⠛⠉⠉⠉⠙⠛⠒⠦⣄⠀⠈⢣⠀⠀⠀⠉⠑⠢⣀⠼⠁⠀⠀⠸⠁⠀⡸⢠⡇⠀⠀⠸⣼⡇⣸⠆⠀⡼
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠉⠳⢤⣀⡀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠉⠉⠀⠀⠀⣀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠈⢀⡞⠀⠀⠀⠀⣽⡇⠈⢱⣀⠄
⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢾⠀⠐⠃⠐⠋⢀⠀⠈⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⢀⡞⢁⠀⠀⢸⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠦⣀⣀⡤⠖⠙⡄⠀⣧⠜⢤⡀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡠⠋⠀⢸⠀⠀⠘⠢⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢳⠞⠁⠈⠀⠀⠀⣀⠔⠁⠀⠀⡠⠞⠁⠀⠀⠘⠦⠤⢂⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⣠⠖⠁⠀⢀⡤⠊⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣷⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣼⠃⠀⠀⣠⠴⠋⠁⣀⡤⠞⠉⠀⠀⠀⢀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢘⠘⠒⠒⠋⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠷⠠⢤⡏⢱⠖⠒⠋⠁⠀⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠤⠤⠤⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠧⡀⢸⠀⢰⠁⣼⠇⠠⠤⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⠇⠀⢀⠟⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢘⠛⠛⣓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠈⡄⠀⠀⠀⠀⠀⠓⠀⠈⢡⠞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⢠⡄⠀⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⣸⡄⠀⠸⡇⣰⣇⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠛⠓⠒⠚⠛⠛⠓⠛⠛⠛⠛⡿⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠀⠀⠀⠀⠄⠄⠀⠆⠄⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠂⢀⠀⠆⠄⠀⠂⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⢀
⠀⠖⠲⠀⢸⠀⠀⠀⠀⠀⢀⢀⣀⣄⣨⣀⣄⣸⣀⡇⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⢀⠤⠀⠀⠀⠀⠀⢛⡀⡀⠀⠀⡀⢀
⠀⣍⢈⡄⡜⣄⣸⠉⡄⠀⠈⠉⠉⠉⢉⠉⠉⢩⠀⠁⡇⠀⠖⠰⠠⠄⠐⠒⠈⠀⠀⠤⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈
⠀⠁⢀⠀⠸⠁⡜⠀⠣⠀⠠⠄⠠⠀⠈⠠⠀⠈⠤⠀⠇⠀⢀⠀⠠⠄⠀⠀⢀⠎⠀⠀⠀⠀⠀⠠⠠⠤⣏⡁⠀⠀⠌⠁⠐⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠈⠁⠀⢀⠈⠀⠀⠀⠀⠀⢀⡀⠂⢀⠀⠀⠈⠁⠸⠀⠀⡨⠀⠀⡆⠈⠣⠀⠁⠰
⠀⠀⠀⡀⠰⠈⠀⠂⠀⡤⠀⠠⠄⠀⠀⠀⠠⡀⠀⠀⠀⠂⠀⢁⠑⠘⠦⠀⠀⠀⠀⣠⠲⠆⠦⠀⡂⠀⠀⠀⠀⠀⠀⠊⢢
⠀⠀⢀⡉⡁⠒⠒⠂⠁⠠⠄⠈⠀⠀⠀⠀⠀⠀⠈⠡⠀⡀⠀⠂⠀⢠⠆⠀⢠⠐⢈⡅⠀⠀⠀⢘⠂⠀⡄⣤⣈⠀⠀⠗⠳⡆⠀⡀
⠀⠀⠀⠀⡆⢀⠤⡀⠀⠀⠀⠀⢠⠄⢐⠀⠀⠀⠂⠀⢈⡞⠓⠒⠈⠀⠀⠀⠘⡆⠈⠱⣦⢠⣄⠛⠁⢰⠃⠒⢇⡸⣐⠂⠀⠀⠀⠀⠀⢠⠰
⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⢀⣀⡒⠀⠀⠀⠀⠠⠋⠀⠀⡀⠀⠐⠀⠀⠀⠈⠢⣄⣐⠀⣀⣡⠔⠚⠀⠀⠀⣐⢁⠀⠐⡤⠀⠂⡀⠀⠁⠀⡁
⠀⠁⠀⠀⠀⠈⡆⠀⠂⢐⠀⠀⠠⠠⠀⠀⠀⠀⠀⠔⠈⠉⡉⠀⠜⠠⠀⠀⠀⠀⠀⠢⠉⠉⠁⠀⠀⠠⠀⠀⠘⠀⠈⠀⠐⢠⡀
⠀⠀⠀⠀⠀⠔⠀⠀⡀⠈⠠⠀⠠⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⢀⢀⠀⠀⡀⢦⠀⢄⠔⡙⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠔⡈⠁⠐⠀⠀⢀⡀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠄⠀⠀⠀⠀⠀⠘⠀⠀⠉⠉⠀⠙⠁⠀⢠⠀⠀⠀⠢⠒
⠀⠀⠂⠀⠀⣀⣀⣀⣈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⣰⣶⠶⣶⡆⣶⠶⣶⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠁⠠
⠀⠀⡀⠀⠄⠳⠄⠀⢸⠀⠀⠀⠀⢐⠀⣀⣀⡢⢸⣿⠀⠀⢿⡅⠀⢻⡇⣿⡀⣼⠇⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡁
⠀⠀⢧⠀⡝⢻⠀⠀⢸⠀⠀⠀⠀⢠⡀⠀⢠⠅⢸⣿⠀⠀⢸⡗⠒⢻⡇⣿⠿⣿⡄⠀⠀⡶⠶⠒⠒⢶
⠀⠀⠚⠁⠍⠈⠀⠂⢘⠃⠒⠀⠀⢀⠑⠐⠁⠀⠸⣿⣶⡆⣽⠇⠀⠸⠇⠿⣴⠿⠁⠀⠀⠃⠀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠀⠠⠀⠀⠃⠩⠁⠉⠀⠀⡂⠀⠀⢀⠀⠀⢠⡤⣤⣤⣶⣶⣶⣶⣶⣶⡄⠀⠀⢀⠀⢀⣐⡀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑
⠘⠒⠤⠠⠤⠔⠂⠁⠀⡀⠀⠀⠘⠉⠑⠒⠚⠀⠀⢸⣧⣧⣿⣦⣿⣤⣿⣧⣾⡇⠀⠀⠸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠉⠉⢉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠁
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠘⢘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⢀⠃⠄⠀⠀⠀⢀⢂⠀⣠⠀⠀⠀⠀⠀⣁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠖⠀⠀⠀⠀⠀⠁⡌⠀⠀⣑⡄⠂⠀⠐⠜⡡⠀⠀⠀⠀⠀⠂⠁⠀⠐⠁
⠀⠈⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⡐⠀⠀⢀⠈⠀⠈⠀⠀⠀⠀⠂⠑⠢⠁⡀⠀⠀⠀⠜⠁⠁⠀⠈⠀⠀⠄
⠀⠈⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠃⠠⠄⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠄⠠⠀⠠⠀⠀⠀⠘⠀⠀⠀⠀⠆⠀⠀⠡
⠀⠀⢠⡄⣴⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⡀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠆⠰⠀⢀⠠⢀⠒⠂⠐⠀⠀⠀⠉
⠀⠀⢸⣇⣿⢠⣶⡄⢸⡆⣿⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢂⠀⠱⠚⠀⠀⠁⠀⠀⡌⠀⠀⠘⠀⡀
⠀⠀⢸⡇⢹⠀⢰⡇⢸⣇⣿⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠂⠁⢁⢈⡀⡄⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠀⠂⠀⠐
⠀⠀⠘⠃⠘⠀⠛⠓⠈⠛⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠈
⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠨⠅⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⠀⠀⠀⠀⠀⢢⣔⢁⠀⠔⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠦⠤⢤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢐⠄⠈⠩⠩⠉⠉⠉⠀⠐⠀⠀⠈⠀⠰⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠱⢚⠃
⠀⠀⠀⠂⠀⠀⠀⠀⠉⢸⣳⠀⢿⠁⣼⠉⢧⢰⡇⠀⢰⠏⢳⡄⡞⠉⡃⠈⢧⣰⠃⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠂⣼⡀⢿⣤⡞⠘⣧⣄⠸⣄⡼⠃⢧⣀⡟⠁⢨⠇⠀⠀⠈⠐⠀⠐⠂
⠀⠀⠀⠀⢠⠀⠠⠐⠀⡀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠄⠀⠀⠈⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠄⢠⠀⢀⠀⡀⠀⠀⠠⡀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠈⠀⠀⠐⠄⠂⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠐⠀⠀⠐⠋⠀⠑⠂⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠋⠀⠀⠀⠀⣤⣖⣲⣴⣲⣰⣒⣦⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠶⠊⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⡟⡏⠙⢹⣩⢹⣿⢹⡇⠀⠀⠀⠀⠂⣾⣿⣿⡆⠀⠀⠀⠀⠈⢧⡚⠟⠂⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠠
⠀⠀⠀⢀⣎⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⡇⠻⠟⠸⠿⠘⠿⢸⡇⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⢷⣄⠀⠀⠀⠀⠀⠀⠃⠀⢨⡇⠀⢀
⠀⠀⠀⠸⠏⠻⠇⠿⠸⠇⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠀⠨⠇



⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⢀⣸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠉⢸⣿⣿⡎⢒⠂⠀⠀⠀⠀⠀⠂⠘⣿⣿⣿⠂⠐⠀⠀⠀⠀⢠⣾⢻⢯⣽⢿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠳⡀
⠀⠀⠀⠀⢰⡾⠿⠿⡁⠂⠃⠀⠀⠀⠀⠀⠀⠄⠻⠿⠟⠀⠀⠀⠀⠀⠀⠈⢿⣯⣾⣹⣾⠷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣷⢳
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉



⠀⠀⠀⢀⡴⠚⠉⢉⡓⢤⡀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠛⠢⣄⠀⠀⠀⠀⠀⣠⢖⠛⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⣆⠶⢆⡤⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⡀
⠀⠀⠀⡏⣀⣄⠀⠿⠟⠀⢳⠀⠀⠀⠀⣸⢁⣾⣿⣯⣠⠄⠘⡆⠀⠀⠀⢸⠁⠸⡅⢄⢠⠴⠚⡆⠀⠀⠀⠀⠀⠈⣓⡺⣅⠀⠀⠀⠀⠀⠀⠀⢿⠟⠛⢻⡿
⠀⠀⠈⡇⠻⠟⢀⣤⣶⡄⢸⠀⠀⠀⠀⢻⠀⣻⠿⣿⣿⡄⢀⡇⠀⠀⠀⢹⠀⠀⢸⠴⠋⠀⠀⡇⠀⠀⠀⠀⠘⣆⠣⠇⠘⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡾⠁
⠀⠀⠀⠙⢦⣀⠈⠻⣛⡵⠃⠀⠀⠀⠀⠈⠣⣄⠀⠟⢉⣠⠞⠀⠀⠀⠀⠈⠳⣄⡘⠦⢀⣠⠞⠁⠀⠀⠀⠀⠀⡼⠍⠙⣆⠀⠀⠀⠀⠀⠀⠈⢘⣻⣯⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⡤⠠⡄
⠀⢄⣀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⠖⠻⣗⣶⣾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢿⠁⠰⣆⡀⠈⡉⠀⢹⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠉⠉⠀⠀⢳⡬⠛⠉⠠⠘⣧⣧⡀⠀⠀⠀⠀⣠⡄⠀⠀⢠⢦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⡖⢤⡀⢀⣄⡈⠀⢀⠉⣏⠁⠀⠀⠰⣒⡋⡷⠖⠓⠚⣇⣩⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡛⣅⠀⣸⠎⠀⣸⡤⠚⠛⣂⣰⣧⡀⣤⡀⣴⠉⠉⠁⠀⠀⠀⠈⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠟⢦⣤⢀⠄⠛⠀⢀⣴⣧⠎⠀⠀⡱⠙⣯⠀⢀⡤⠜⡇⠀⡼⡂⠀⢬⠶⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠟⠣⢵⡖⠚⠋⠉⠛⠀⠀⠚⠊⡿⠁⣠⣄⡈⠙⠁⠀⠓⠚⠃⢸⡟⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠸⣅⠌⣱⡼⠀⡰⣩⠵⠆⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡤⢼⣢⠉⡼⡳⠦⣄⠀⢠⡄⠀⠀⠀⠘⠷⣍⣄⠄⢙⠁⣠⣰⠻⢥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠸⡏⠀⢊⡁⠙⠀⣀⠀⡑⣷⠎⠧⣀⡀⠀⠀⣴⡫⡸⡋⠉⠉⠉⠸⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠋⠁⣀⡜⢹⠀⢰⠙⢦⡄⠈⡺⣯⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡏⠀⠀⠉⠑⠋⠀⠀⠉⠁⡄⠠⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢈⡽⠀⠾⣁⢒⠄⠀⡔⢒⡦⠀⠀⣤⠿⡲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⣤⢠⡈⠚⠀⠀⠷⠁⠀⠃⠀⣿⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠚⣦⣄⠀⣊⣵⢶⡶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢣⡇⠉⠉⠉⡝⡤⠽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠊⠉⠉⠉⠉⠐⠢⣀
⠀⠀⠀⠀⠀⢀⠴⠊⢀⡀⠤⠄⠒⠂⠀⠐⠒⠠⢄⠀⠑⣄
⠀⠀⠀⠀⣠⠋⣠⠖⠉⠀⢀⠤⠀⠐⠀⠤⡀⠀⠀⠑⢄⠈⢆
⠀⠀⠀⢐⠃⡰⠁⠀⢠⠊⢀⡤⠒⠒⠒⢤⠈⠳⡀⠀⠀⠂⠈⡆
⠀⠀⠀⠘⠀⠃⠀⢠⠃⠀⡎⠀⠀⠀⠀⠀⢡⠀⢱⠀⠀⢀⠀⢰
⠀⠀⠀⢠⠀⢃⠀⠘⡄⠀⢇⠀⠀⠀⠀⠀⠎⠀⡘⠀⠀⠀⠀⠸
⠀⠀⠀⠘⡄⠈⠂⠀⠘⣄⠈⢢⣀⣠⠔⠋⢀⠔⠁⠀⠀⠀⠂⠀⡄
⠀⠀⠀⠀⠈⠢⡀⠈⠒⠚⢦⠀⠹⣀⠤⠒⠁⠀⠀⠀⠀⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠘⡄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⢆⡀⢀⣼⠛⠛⠛⢻⣀⠀⠀⠀⠀⣼⠛⠛⠛⢻⣄⠀⠀⠀⢀⣼⠛⠛⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠉⢸⠀⠀⠀⠈⠌⠉⠉⠉⠉⠀⠀⠀⠀⠀⡇⠉⠉⠉⠁⢀⠀⠀⠀⠀⡇
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠔⠃⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠺⠶⠶⠤⠼⠓⠀⠀⠀⠘⠺⠷⠶⠤⢼⠓⠀⠀⠀⠘⠻⠶⠶⠦⢼⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⡄⠒⠂⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣴⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠈⢧
⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⢿⠀⠀⠀⠀⠀⠀⠇⠀⠀⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⡼
⠀⡇⠀⠀⢀⡁⠀⠠⠄⣟⡁⠀⡀⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠀⠀⠀⠀⠀⠀⠐⣄
⠸⠉⣀⠤⡄⠿⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢂⠀⠄⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠤⠀⠝⢆
⠀⠀⠀⠀⠀⢀⠌⠀⢀⡀⠠⠀⠀⣀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢔⠀⠀⡀⠀⠄⠀⡀⠀⠂⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡃⠀⠀⠀⠀⠈⢁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠓⠶⣡⠀⣀⣀⠡⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠚⠀⠀⠀⠃⠀⠀⠀⠀⠀⠚⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⠉⠁⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⡉⠉⠉⡏⠉⠉⢹⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡁⠀⠀⠀⠀⠀⠁⠁⠀⠀⠇⠀⠀⠈⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⣏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠒⠒⠂⡇⠀⠀⠀⠀⠀⢸⠒⠒⢲⡇⠀⠀⠀⠀⠀⢸⡖⠒⠒⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠔⣖⣮⡂⢄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄⠀⣀⠇⠀⠀⠀⠀⠀⠈⡆⠀⡸⡇⠀⠀⠀⠀⠀⠸⡇⠀⢠⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣶⢣⡗⠉⠀⠳⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢸⣧⡝⠀⠀⡠⠈⠁⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⣆⣀⣉⣀⣉⣉⣉⣉⡇⠸⣀⣀⣈⣉⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣆⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⡇

⢀⠀⠠⠀⠂⡄⢀⠀⢀⠔⠒⠒⠤⢀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⣠⠠⣄⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠒⠂⡀
⠀⠈⠀⠀⠀⠈⠤⠄⠘⠂⠄⠤⣀⠀⠀⠈⡀⣀⣀⠀⡸⠀⠀⣌⠀⠀⠀⢃⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⢀⠇⠱⠄
⠠⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠦⠠⠄⡃⠀⠀⠀⣀⠀⠀⢠⠂⠀⠀⠀⠐⢶
⢀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠁⠄⠠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠤⢀⠀⠀⠈⠁⠉⠁⠂⠀⠐⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠈⠀⢈⠄⡀⡐⠀⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠨⠠⠀⠀⠀⠄⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⢀⠀⡀⠁⠀⠀⠈⠢⡀⠈⠓⢦⠀⠀⠀⡀
⠀⠁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠀⠀⠀⠀⠠⠀⢀⡴⠀⠇⠀⠰⠀⠁⠀⠀⠀⠂⠈
⠈⠤⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠤⠐⠁⢠⠞⠀⠀⠈⢀⡗⠀⠀⠀⠀⠀⢀⢠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠒⠈⠉⡁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⡶⣶⠶⠶⣾⣿⡟⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⡀⡀⠁⠠⠀⠀⣾⢹⢡⠀⠈⠰⠎⠦⢰⡶⠎⣻⣮⣼⠟⢿⡆
⠀⠀⢠⠀⠀⠀⠀⡀⠀⠘⣀⠸⠀⠠⠀⢸⣿⣀⣼⠦⣶⠗⢾⡒⢺⠛⣻⡏⠍⡈⠆⣼⡇⠀⠀⠈⠈⠀⠂⠐⠀⠀⠄
⠀⡀⠤⢄⠀⠀⠀⠀⠀⠄⢀⡀⠐⠂⠀⠈⢯⠀⡹⠀⡌⠘⠿⢿⡜⣇⠰⠶⠀⡓⢀⣿⡏⠀⠀⠀⠀⠀⠠⠀⠄⠀⡀
⢐⠀⠀⠀⢱⠀⢀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠓⠧⠶⠿⠾⠷⠾⠿⠿⠶⠶⠿⠿⠟⠋⠀⡀⠀⢢⠀⠀⠐
⠈⠢⠄⠤⠃⠀⠀⠀⡀⠁⡐⠒⡄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡐⣰⠈⠾⠄
⠀⠀⡄⢠⠊⠉⠁⠢⠀⠤⠈⠂⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠄⢠⠂
⠈⠒⠁⢂⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⠁⠑⠀⠀⠀⠘⠠⠜⠀⠀⡠⣤⣠⡔⢶⢰⡖⠢
⠀⠂⡀⠀⠑⠒⠂⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠝⠛⠀⠁
⠀⠠⠠⠔⢀⠀⠀⠆⡡⡀⡂⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⠢
⢄⠁⠊⠁⠈⠀⠈⠀⠀⠈⡢⠅⠀⢀⡤⠒⠉⢑⡄⠀⠀⡀⠒⢠⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⢈⠀⠀⠀⠀⠄⠀⠀⡀
⢂⡀⣀⠀⠀⠀⠀⠀⢀⠈⠐⠀⡰⢃⠤⠒⠂⠈⡀⠠⠂⠀⣀⠜⠀⠀⠈⠀⠀⠀⠀⠂⢠⠀⠔⠀⠀⠀⠈⠀⠄⠀⠂
⠀⠂⠂⡁⡉⠂⠊⠀⠁⠀⠁⠀⠈⠁⠀⠀⠀⠈⠒⠒⠂⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠀⠐⠀⠀⠀⠂
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠋⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⣠⣤⣶⠶⠶⠶⠶⠶⢶⣶⣤⣤⣀⣀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢀⣀⣠⣤⣤⣶⡶⠶⠶⠶⠶⢶⣦⣄⡀
⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⡟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠛⠻⢶⣦⣄⡀⣀⣤⣴⠾⠟⠋⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣤⣿⠿⠿⣯⣄⡀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠙⠻⢷⣤⣀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣀⣴⠿⠋⠀⣿⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠛⠿⣦⡀⠀⠀⠀⠀⠀⢿⡇⠈⠛⢷⣤⡀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⡾⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠻⣦⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⡿⠻⣷⣄
⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠙⢷⣦⡀⠀⣿⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣤⡾⠃⠀⠀⠀⠀⠀⣼⡇⠀⣠⣴⠟⠉⠀⠀⠈⠻⣷⣄
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⢻⣶⡶⣦⣄
⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿
⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠉⠛⢷⣦⣀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣾⣏
⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠈⠙⠻⣶⣤⣴⡾⠛⠉⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣀⣤⣴⠾⠟⠋⠙⠻⢶⣦⣄⡀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠹⣧⡀⠀⠀⠀⠀⢀⣤⣦⣤⡀⠀⠀⠀⣀⣀⣿⣷⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠈⠻⠷⣶⣤⣤⣿⠁⠀⠈⣿⠾⠿⠛⠛⠉⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠛⠛⠿⠶⢶⣶⣤⣤⣤⣤⣶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⡾⠋⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣄⣤⣴⠿⠋