Camera flash Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡟⠉⠉⠉⠉⠉⠉⣹⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣤⢴⣔⣴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣇⣀⣀⣀⣀⣀⣠⣨⣇⠀⠠⣀
⢀⠤⡾⠿⣿⣶⣶⣦⣤⣬⣿⡿⠷⢄⣀⣀⣤⣤⣄⣒⣒⢒⣒⣒⣒⣒⣾⣿⣿⣯⣿⣿⣯⣥⣤⠤⡀
⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⢑⡬⢉⣴⣶⡾⡭⢍⡛⠳⢦⣄⠀⠀⠀⢀⣠⡀⠀⠀⠬⠱⣰
⢸⡀⠸⠳⠀⠀⠀⠀⠀⠀⢠⡾⣩⠖⠉⠀⡼⡿⡫⢊⠕⡡⣪⣷⣤⡙⢿⣆⢀⠻⠴⠇⠀⡈⢑⡅⣿
⢸⠉⢩⣭⢭⢭⣉⣉⡉⣹⡕⣴⠏⠀⠀⢐⠬⡪⣐⢕⢨⢞⢫⠊⡠⣻⡈⣿⣗⣓⠒⠒⠒⢒⡒⡚⡟⡁
⢸⠓⢿⣿⣟⠭⣹⡯⣿⠗⢸⡏⠀⠀⠀⢐⢭⡪⠒⡱⡑⢕⠅⡪⡪⠊⣇⢸⣵⣟⣿⣺⣳⡪⡯⣷⡇⡅
⠘⠦⣏⡯⣗⣽⣺⣽⣾⡀⢸⡂⠀⠀⠨⣓⡵⢞⢅⡪⢂⠁⡪⢊⠔⢕⡇⢸⣽⣷⢽⣺⣺⠽⢽⣿⡇⠁
⢸⠈⣗⣯⣛⢽⣾⣿⣾⡟⡈⢯⡠⡶⢕⠨⡢⢑⡡⢒⠅⡪⡂⢐⢕⠟⠓⠿⠟⢿⣿⡾⣿⣟⣷⡿⣿⡆
⠌⠨⣷⢭⣺⣽⡾⣹⣝⡿⣮⣊⡻⢮⣑⠬⡒⢅⡪⢑⠅⡨⡊⢐⢽⣑⣞⣋⣗⣛⣃⡋⣛⣛⡛⣫⣿⠁
⢸⠀⡳⢿⢯⢳⣝⣯⣷⣯⣳⣽⡻⣦⣍⡓⠚⠷⠬⠶⠵⠚⢋⣡⣴⡽⣿⢭⣳⢻⢥⣯⣓⣇⡯⠿⣽
⠘⠯⠭⠅⢉⡉⣓⣛⣚⣛⡛⣛⣛⣛⢿⣿⣟⣷⣶⣶⠶⠾⠿⠿⠿⠿⠛⠉⠉⠉⠐⠂⠀⠀⠈⠉⠁

⠐⠀⠑⠅⠠⡪⡂⢐⢔⠄⡢⡂⣔⠄⠄⠀⡠⠂⢔⠔⡠⢂⠄⠠⢂⢀⠄⠠⡠⢀⢄⠀⠀⠀⠀⡀⡀⡀⡀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⡏⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⢛⢟⡛⡟⣛⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗⢶⠖⣚⠀⠀⠁⢾⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣤⠮⠄⡠⡐⡉⡏⢹⡟⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢻⡀⠀⣸⡁⠈⢻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⡤⠤⠤⠤⠤⠼⠧⠬⠭⢭⣿⠭⠭⠭⠽⠾⣇
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠉⠉⠓⠶⣄⡀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠒⠚⣇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠞⠁⠀⢀⣠⣤⣶⣤⣤⣀⠀⠀⠙⣆⠀⠀⠉⠉⠉⢉⣉⣉⣉⣉⣉⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣰⠃⠀⢀⣼⡿⠛⠛⢻⣿⣿⣿⣷⡄⠀⠈⢧⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⣿
⠀⠀⠀⠀⠀⠀⢸⠀⢀⡏⠀⠀⣾⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⢸⡆⠀⠀⣀⣘⣛⣛⣛⣛⣛⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠸⡇⠀⠀⣿⣿⣿⣶⠶⢾⣿⣿⣿⣿⣿⡇⠀⢠⡇⠀⠀⠉⢩⣭⣭⣭⣭⣭⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢷⠀⠀⢻⣿⣿⣇⠀⠀⣿⣿⣿⣿⡿⠁⠀⣸⠁⢀⣀⣀⣐⣒⣒⣒⣒⣒⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢧⡀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠀⠀⣰⠋⠀⠉⠉⠉⢩⣭⣭⣭⣭⣭⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⢦⡀⠀⠀⠉⠉⠉⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⣘⣛⣛⣛⣛⣛⣿
⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⢀⡐⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⡄
⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⢀⡾⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣰⠁⢂⠳⣤⣀⡀
⠀⠀⠀⠀⠘⡆⠈⠙⠓⠶⠋⠀⠀⣯⣠⡴⠖⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠉⣦⡀⠤⡤⠀⠀⠀⠈⠑⢢⡀⠀⠀⢀⡀⢀⡩⠟
⠀⢀⣀⣀⣀⣻⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⣉⠉⠀⠀⢠⢰⠛⠁⠀⠀⠀⠀⠀⡜⢀⡠⠶⢌⢰⡅
⠀⠘⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠶⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣤⣀⠘⣆⠀⠀⠀⠀⠀⠾⠛⠉⠀⠀⠀⠉⠃
⠀⠀⣘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠩⠭⠦⠴⠚⠋⠉⠑⢄⠀⠀⣦⡴⠋⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⢠⡀
⢾⡋⠉⠀⠀⠀⠀⠀⣀⠴⠞⠉⠉⠉⣉⣁⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡈⠈⡻⠃
⠀⠙⠲⣄⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠂⠋⠁⢈⠑⠄⠀⠃⠀⠀⠀⡰⠲⢶⠂⠀⠀⠀⠀⠀⠀⠀⠤⠂⠙
⠀⠀⣠⠎⠀⠀⠈⡇⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠘⠐⣀⠚⠃
⠀⢴⣇⣀⣀⣀⣀⡷⠀⠀⠀⠀⠀⠀⠈⠉⠁⠠⠀⠀⠀⠀⠀⡀⠈⠀⡀⠀⠇⠘⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡆
⠀⠀⠀⠀⠀⠀⣸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡄⠀⠚⠀⠙⢁⡼⠃⠀⣀⣀⣀⣀⣠⠃⢂⠹⣄⣀
⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⠀⠀⠀⠀⠢⠄⠀⠐⠂⠀⠀⠀⠁⠒⠒⠙⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⡈⠸⡄⠀⠀⠉⠢⢄⠀⠀⠀⠀⢀⡈⢙⡻
⠀⠀⠀⠀⠀⠀⠛⠋⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⢀⣀⠇⠀⠀⠀⠀⠀⠀⠀⣨⠖⠁⠀⠁⠛⠀⠀⠀⠀⡼⠁⠠⣤⡘⢅⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⣠⠄⠀⠀⣠⠤⠀⠒⠀⣉⠖⠈⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡴⠚⠉⠀⠈⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠀⠈⠙⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠇⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠀⠘⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠁⢀⠀⠀⠀⢃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠘⠀⠀⠀⠘⡀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⣰⡀⠀⠀⣀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣴⡿⣧⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠎⠻⠁⠛⢡⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠉⢛⡿⠧⠀⠀⠀⠀⠠⣭⣿⡿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠉⠉⠙⢿⣄⣠⣤⣶⡶⠿⣶⡄⠀⢤⣽⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⣤⣶⠾⠟⠛⠋⢉⣴⣶⣄⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠋⢉⣡⣴⣶⣶⣤⣄⡘⢿⣾⠟⠀⢻⣇
⠀⠀⠀⠀⠀⠀⣾⡟⠉⠀⠀⠀⠀⣰⡿⠋⠁⠶⢶⣦⣝⢿⣆⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠈⠻⠂⣿⡆⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠸⣿⢠⣤⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠻⣧⣙⠷⢶⡦⠀⣀⣼⠟⠀⠀⠀⠀⢀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠈⠛⠿⠶⠶⠿⠛⢁⣀⣤⣴⡶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣶⣶⠾⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠐⠠⠀⠀⠒⠄⠠⠄⠤⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠐⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠉⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠊⠀⠀⢢⠼⠿⠛⠛⠛⠒⠒⠚⠛⠛⠛⣷⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⢸⠀⠀⠀⠀⢀⢤⠔⠈⠀⠀⠀⣿⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠢⠵⠶⠶⢶⣶⡶⣦⡶⠶⠶⠿⠟⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⠀⠐⢠⠴⣷⣄⣽⠷⠶⡠⢀⡠⠐⠂
⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠱⡀⠁⠀⠀⠀⠀⢀⠀⠤⢤⠤⢀
⠀⠀⠀⠀⠀⢀⡋⠀⠤⠦⠿⠿⠤⠴⠧⠸⠛⠛⠂⠚⡀⠂⠀⠀⡀⠀⢈⡀⡳⠤⠤⢤⠤⠤⠚⠂⠀⠒⠒⠺⠦⠠⢄⡀
⠀⠀⠀⠀⡮⠥⠤⠤⠤⠤⠤⠤⠤⡤⠤⠀⠒⠒⠒⣚⠴⠒⣒⣀⣀⣀⠀⠀⠦⢄⡀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠐⠒⣂⢳
⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢨⣀⡹⠀⢀⠔⠉⠀⠀⢀⣠⢀⡦⢦⢤⣄⡉⠒⠬⣕⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸
⠀⠀⠀⢰⠳⠒⠒⠂⠀⠠⢄⠀⠀⠀⠀⡠⡡⠀⢀⣠⢞⣩⣴⠷⠲⠲⠲⠤⢭⣓⠦⣄⠙⢯⣶⣠⣀⣀⣀⣀⣀⡀⢠⣍⣀⡄
⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠈⡛⡋⠉⠙⠁⠀⣰⠫⡴⠏⠁⠀⠀⠀⠀⠀⠀⢀⡈⠳⣼⠑⣄⠹⣽⡏⡩⠉⠉⠉⢉⠙⠍⠫⡇
⠀⠀⠀⢸⠀⢀⠊⢀⠅⠈⠀⡯⣠⢂⠠⠀⣰⢏⡾⠠⠀⠀⠀⢀⠀⠀⠆⠐⢠⢤⡤⠺⣷⡸⡆⠘⣿⢄⠔⠔⢔⠑⠀⠐⣘⡇
⠀⠀⠀⢸⠀⠀⠈⡂⠁⠈⡀⢁⠈⠨⠀⢀⡟⣸⣂⠁⠀⠀⠀⠸⠀⠠⠀⠃⠀⢠⠙⠀⠰⣯⣰⠀⢽⡅⠀⠠⡀⠀⠊⠪⠞⡇
⠀⠀⠀⠘⡀⠀⠄⡂⠄⠨⢀⢘⠐⠰⠂⠸⣏⣼⡠⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠀⠀⠈⣬⣾⠀⠾⡧⡀⠊⢀⢔⠵⠪⠼⡇
⠀⠀⠀⠀⡇⠀⠠⠂⠅⡪⠐⢠⠀⠀⣷⠀⢻⡈⢧⡀⠀⠈⢀⠀⢀⢀⠀⠠⠀⠀⡀⠆⠐⣴⠇⢀⣛⡋⡨⢘⢕⢇⢔⠈⢸⠁
⠀⠀⠀⠀⢹⠀⠈⠂⠅⠢⢀⠀⡆⠀⠘⣷⡀⠳⣌⠱⣕⣁⠠⢁⢂⢀⢂⠀⢀⠐⣀⡴⢟⠍⠀⣽⡯⡪⡂⢑⠕⡡⡠⡀⡎
⠀⠀⠀⠀⠈⢆⠀⠂⢄⠈⡄⢆⡁⠨⡀⠈⠻⣦⡈⠛⠦⣍⣝⢗⢦⠦⢠⠤⢐⡽⣟⡵⠋⣰⣽⢗⠀⣊⠔⠡⡪⡪⠊⠨⠃
⠀⠀⠀⠀⠀⠈⠳⣒⣒⠒⢚⣛⠁⠂⠂⠀⠀⢀⣹⣗⣦⣄⣉⡓⠓⠓⠒⠒⠛⣉⡥⣴⣮⣯⠄⠥⠮⠴⠵⠦⠞⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠽⠻⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⢀⠄⡠⠀⠄⡠⢀⠄⠠⠀⢀⠀⡠⠀⠄⡠⡀⢀⠀⠀⡀⢀⢄⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠊⠀⠅⠠⠀⠐⠀⠂⠔⠠⠂⠐⠀⠀⠀⠡⠪⠐⠕⠠⠊⠐⠁⠊⠐⠁⠂⠊⠀⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⡇⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠐⠁⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⢀⣠⣤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⡀⠀⠀⡠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀⡊⢻⡟⠀⠀⠈⠉⠉
⠀⠀⠀⠀⢀⣀⣀⠀⢰⠿⠯⠭⠭⠭⣭⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠘⠾⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣞⡿⠀⠀⠐⠢⠄
⠀⣠⠤⠿⠽⠿⠿⠿⠼⠶⠶⢤⠤⠤⠽⠿⠿⠿⠧⠤⠤⠔⢒⣒⣶⣶⣖⣒⡒⠒⠒⠒⠒⠒⠒⠒⠒⡲⣺⣿⢾⢷⡷⡾⢴⠷⡿⣤⣤⣤⣤⢤⡀
⠀⡇⡞⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡽⣛⡭⠝⢚⣓⣛⣉⣙⣛⡛⠻⠿⢛⣫⣭⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠛⠛⡓⢦⢹⡀
⢀⡇⡇⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡥⡚⣱⡔⠋⠁⣔⡯⣪⣾⢏⡽⢙⡶⢤⣈⠙⠻⢿⢦⣤⡠⣀⠀⣰⡲⠷⣆⠀⠀⠠⡫⢒⠘⡆⡇
⢸⡇⡇⠰⠝⠝⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⡋⡵⠞⠃⠀⠀⣖⠵⡪⢛⠕⢋⡴⢋⠴⢋⢜⣵⣦⡀⠹⡼⣮⠥⢂⠹⣷⠾⠋⠀⠰⣊⠔⡡⡂⣇⣷
⢸⠛⡛⠒⢒⠒⣒⠒⡒⢒⠒⠒⠒⠒⡞⡴⣱⡾⠭⠀⠀⠀⢨⠕⣫⠞⣡⠔⡡⢚⡡⣺⢕⡥⡪⢊⡽⣆⠘⣟⣷⠥⠮⠴⠤⣤⣀⣘⣴⣫⣎⣆⣷⣿
⢸⢀⡁⡼⡭⢯⡽⣯⣗⣳⢾⣤⣧⣾⡹⣁⣾⠍⠀⠀⠀⠀⠔⣋⠴⣪⠔⣫⢔⡩⣊⠔⡩⢊⡴⣫⢎⠽⡄⢹⣿⡖⣾⣼⣰⣀⣆⠆⡰⢴⣴⣀⢿⢸
⢸⠘⠁⠽⡽⣭⣗⡷⢮⣼⣻⢾⣹⢣⠣⣼⣒⠀⠀⠀⠀⠀⣋⠴⣊⠕⡫⢖⠵⣊⠔⣩⠔⣡⠞⡱⢋⠜⡇⠈⡦⣯⣟⡷⢾⣩⣋⡏⡗⢺⠴⣿⣼⢸
⢸⢰⢈⡯⣽⣳⡥⣟⡧⢾⣹⢺⢼⢸⠀⣯⠖⠀⠀⠀⠀⣊⠕⣊⢔⡭⢊⠵⣊⠴⠊⡠⢞⡡⢊⠔⡡⢊⡇⠀⡟⡿⣧⣞⡽⢺⡥⣏⣽⣉⠟⣽⣿⢸
⢸⢘⠠⡗⣻⢼⣓⡯⣗⡻⢾⣹⢺⡼⡀⢱⣫⠄⠀⢀⡨⢔⡭⢚⡡⢚⡥⠊⣁⠴⢊⡴⢋⠔⡡⢊⡔⣩⢓⣰⣻⣏⡗⣯⣜⣹⠶⣧⣎⣼⣉⡖⣻⣼
⢸⡎⠐⣯⣝⢺⣥⡗⡯⢽⣻⢾⣻⢧⢣⡀⢳⣡⢖⡭⢚⡡⢖⡩⠖⣁⡤⢚⡡⢞⡡⢚⡡⢊⠔⣩⡞⠉⠋⡛⠞⠙⣻⢷⣯⡟⣻⠵⣯⣼⣩⡟⣿⣿
⢸⠁⢈⡗⣯⣽⢺⡭⣗⣮⡜⣫⡝⣮⢧⡑⢄⠙⢷⣊⡥⢖⣩⠴⢊⡥⢒⡩⠖⡩⠖⡡⢞⡡⢞⡽⡃⢒⠛⠚⣻⠗⡛⠻⠐⠟⠙⠚⠛⠾⠼⢋⣿⣿
⢸⢦⠰⣏⢵⣚⡯⣗⣹⢶⣹⢵⣋⡗⢾⣹⠾⣵⢤⡉⠺⢭⣖⣋⡥⢚⡥⠖⣫⠔⣫⣔⡫⢖⡑⢈⠷⣿⣻⡞⢿⣋⡿⡿⢳⡧⣾⣩⡟⣳⢺⡭⡿⡇
⢸⣘⣀⠽⢚⠯⢻⡩⢓⠦⢾⣻⢶⣟⡧⣾⣲⡭⣛⣺⣵⣦⢌⣉⣉⠛⠚⠛⠓⠛⠉⢁⣂⢤⣾⡽⣾⢺⡿⣻⣧⣞⣩⣟⣽⣻⡧⠴⠯⠟⣛⣓⣺⠁
⠘⠣⠭⣭⣉⣉⣉⣉⠉⠒⠛⠒⠛⠚⠛⠓⠛⠛⠧⠷⠷⢯⠷⡿⢻⡽⣯⣿⣽⣿⣯⣿⣞⣿⣽⠽⠽⠭⠭⠥⠬⠀⠒⠒⠒⠂⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⢀⠀⣀⢀⡄⢀⠀⡀⠀⡀⠀⠀⠀⠀⢀
⠒⠕⣪⠔⡩⢚⡡⢊⡵⣊⠔⣫⢔⡡⢒⡥⢊⠴⡪⢔⡠⢊⠔⣂⠔⣋⠔⡡⠖⢁⠔⢁⠔⣡⠔⢀⠄⡠⠂⡠⠂⡠⠀⡠⢀⡄⣠⠀⡤⣠⠄⡠⢀⠄⡠⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁⠐⠉⠚⠁⠊⠔⠡⠒⠡⠊⠡⠊⠰⠊⡠⠞⡡⠚⡡⠊⣠⠖⡥⢊⡴⢊⡴⢋⡴⢋⠔⠡⠊⡴⢋⠔⠡⠊⠔⠡⠊⠐⠁⠊⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠾⢷⢶⢶⢻⠶⢶⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡧⢤⡤⠴⠇⠁⠘⢩⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⣜⣀⠀⡀⠄⢽⠓⢿⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢼⡏⠁⢀⡜⠉⠺⣾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣘⡳⡒⣾⣗⣒⣒⣛⣦⣸
⠀⠀⠀⠀⠀⠀⠀⡼⠋⠉⠉⠉⠉⠉⣉⡭⠽⠿⠿⠿⠯⢭⣉⠉⠉⠉⠉⠉⠉⠉⠛⠉⣭⣭⣭⣭⣭⣷
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⣀⡀⠀⠀⠈⠙⢦⡀⠀⠀⠠⠶⠶⠶⠤⠶⠤⠤⠴⢼⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠋⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠇⠀⢀⣾⣿⠁⠀⠀⠙⣿⣿⣿⣿⣧⠀⠀⢹⡄⠀⠀⠉⠉⣉⣉⣉⣉⣉⣹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⣿⣿⣄⠀⢀⣰⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠤⠤⠤⠤⠤⠤⠤⢼⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⢸⣿⣿⣿⠟⠋⠻⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⣒⣒⣒⣒⣒⣺⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣇⠀⠀⠻⣿⣿⣦⣀⣠⣿⣿⣿⣿⠟⠀⠀⣸⠃⢠⣤⣤⣤⣭⣭⣭⣭⣭⣽⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢦⡀⠀⠉⠻⠿⣿⣿⣿⠿⠛⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠛⠛⣛⣛⣛⣛⣛⣻⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣭⣭⣭⣭⣽⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⣤⣤⡟⢸⠀⠀⠀⣠⢿⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡒⠒⢒⠒⣿⠻⣿⣿⣿⠁⢸⣄⣠⡼⠁⢸⣧⣦⡄⢀⣠⡤⢤⠾⠿⠥⠀⣠⣤⣦⣼⣿⣿⣤⣤⣀⣠⡤⠿⠶⠶⠦⠄
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣽⡝⠳⣍⣁⣸⡇⠘⢿⡏⠀⠈⣿⠟⠀⠀⣼⣿⠿⠟⢛⣿⠓⢒⣒⢒⠀⠉⠩⠉⠭⠍⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⣿⣿⣿⣿⡿⠞⠛⠻⣆⠀⠙⠿⡇⠀⠈⠁⠀⠀⠁⠀⢀⣀⠉⣤⡀⠀⡾⣁⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⠶⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⢸
⠀⠀⢠⣿⣿⣿⣿⣧⣤⣤⣀⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠉⢿⡀⢻⡇⠸⠧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸
⠀⠀⠰⣿⣿⣿⣿⡟⢷⣤⡀⠉⠉⠀⠀⠀⠀⠀⢠⣶⢶⡄⠹⣦⠞⢷⡀⢧⠀⠀⠀⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡀
⠀⠀⢰⣿⣿⣿⣿⡃⠀⣈⣻⡦⠀⠀⢰⡄⢶⣄⡘⣷⣄⣀⠀⠹⣆⡨⠷⢢⣄⣴⣿⣿⣶⣿⡿⠿⠿⠿⣿⣿⣟⣛⠋⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀⣀⡇
⠀⠀⢸⣿⣿⣿⠟⠛⠉⠁⠀⠀⣠⣴⡌⢿⡈⣏⣻⣮⡉⠛⠿⣾⠉⠀⠀⠈⠋⠈⠛⢿⣿⣿⣷⣿⣶⡿⢿⣆⣩⠭⠥⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠘⣿⣟⣿⣿⡟⠓⣶⠆⠛⢷⣰⡝⠘⣷⠘⣇⡸⠛⢷⣤⣿⠀⠀⠀⣤⣤⣶⣶⣶⣾⣿⣿⣿⠭⠚⣉⣤⣶⣶⣾⣷⣶⣾⣽⡻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣸⣿⢛⣧⡾⠋⠀⠀⠈⢿⡙⠀⠹⣧⣭⡄⠀⠀⠈⠀⠀⠀⠀⠈⢿⣧⣴⣿⣿⢟⠝⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣾⣋⣠⣤⣤⣶⠀⢨⠷⠂⠀⠉⠉⠀⠀⠀⠀⠀⢻⣷⣶⣤⣌⣻⣿⣿⡷⠃⣠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣆⢹⣿⣿⣿⡇
⠀⠀⠀⣵⣾⡛⢯⢹⣿⣿⣿⠇⠀⢀⣠⡆⠀⢀⣶⡀⠀⣼⣦⡀⠀⢿⣿⣿⣿⣿⣿⣿⡁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡬⣿⣿⡆⣿⣿⣿⠇
⠀⠀⠀⣯⣟⢿⡆⠾⣿⣿⡟⣠⣴⣿⣿⡇⢀⣾⣿⣷⠀⣿⣿⣿⣦⠘⣿⢿⣿⣿⣇⠁⢰⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⡧⢸⣿⣿
⠀⠀⠀⣿⣿⣿⣾⡆⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣋⣉⣽⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡇⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠹⢿⣿⣇⢿⣼⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣽⣿⡟⢰⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣾⣿⣿⣿⣿⠀⢻⣯⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⢡⣏⡁⠀⢸
⠀⠀⠀⣿⣿⣿⣿⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢻⣿⣿⣿⣿⣿⣿⠿⣿⠋⠁⢈⣿⣿⠟⣡⣿⣿⣇⡀⠞
⠀⠀⠀⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠟⠛⠛⠛⠛⠿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣤⣀⣾⣤⣶⡿⠛⡡⠘⠋⠉⠉
⠀⠀⠀⣿⣿⣿⣿⠀⠛⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠹⠿⠿⠗⠢⢌⡉⠛⠛⠛⢛⣉⠥⠐⠋
⠀⠀⠀⠈⠹⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠤⠤⠔⠒⠂⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣿⣿⡀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⣿⡻⣿⣿⣶⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠶⠶⢶⣤⡀⠀⠀⠶⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⣩⣴⣶⣿⣶⣶⣌⠻⣷⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠇⣼⣿⣿⣿⣿⣿⣿⣿⣷⠘⣷⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡄⢿⣿⣿⣿⣿⣿⣿⣿⡿⢡⡿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⠿⢿⣿⡿⠿⢋⣴⡿⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⣶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠿⢿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⢀⣿⡇⠀⢀
⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⡶⠶⠶⠖⠒⠒⠒⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠈⣿⡇⠀⠀⠙⢦⣀
⠀⣴⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠙⢿⣤⣀⠀⠀⠙⠳⢶⣤⣄⡀
⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠈⠉⠛⠒⠂⠀⠀⠈⠙⢿⣦
⣿⣿⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡿⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠐⠚⠋⠉⠁⠀⠀⠀⠀⠉⠙⠻⢿⣷⣦⣀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠇⠀⠀⠀⠀⠀⢰⣿⣇⣠⣤⣬⣭⣍⣛⡛⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢹⠀⠀⠀⠀⣀⣴⣿⣿⠿⠛⠛⠋⠉⠛⠛⠻⠿⣦⣍⠻⣿⣶⣄⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⢻⣿⣧⡀⠀⠀⠀⠀⠀⢻⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣴⣿⡟⠁⠀⠀⢀⣤⣶⠿⠿⠿⢿⣷⣶⣄⡀⠀⠀⠙⢧⡹⣿⣷⡀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣼⣿⡏⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠈⢳⢹⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿
⢸⣿⡟⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠈⠇⢿⣿⡄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢰⣿
⢿⣿⡇⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⢸⣿⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⣿
⠸⣿⣷⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⢀⠇⢸⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣤⣼⣿⠟
⠀⠹⣿⣧⠀⠀⠀⠹⣦⣄⡀⠀⠀⠀⢀⣠⣼⣿⡿⠋⠀⠀⢀⡞⢀⡟⠀⠐⠊⠁⠀⠀⠀⠒⠒⠒⠲⠶⠶⠾⠿⠿⠿⠟⠋
⠀⠀⠹⣿⣷⣄⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⣠⠟⠀⠈
⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣦⣤⣤⣤⣶⣶⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣤⣀⣼⢳⠀⠀⢠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢳⣶⡒⢲⠺⡟⢿⣿⡇⢸⣤⡴⠁⣾⣶⣄⣀⣤⠶⠾⠯⣀⣤⣶⣾⡿⠧⠤⠤⠤⠞⠒⠒⠂⠀⡀
⠀⠀⣠⣤⣤⣴⣶⣷⡌⠲⢴⡇⠈⠻⠀⠈⠏⠀⠀⠟⠛⠉⣼⠏⠀⠛⠀⠀⠀⣀⣀⣀⣈⣁⣠⣤⣤⣤
⠀⠀⣿⣿⣿⣯⣀⣀⣙⣄⠀⠁⠀⠀⠀⠀⣠⠔⢿⠘⣷⠰⣷⣷⣿⣿⣿⣿⣿⣿⣏⣯⣽⣿⣿⣿⣿⣿⠀⠀⠀⡄
⠀⠀⣿⣿⣿⡟⠳⣌⠉⠉⠀⠀⠀⠀⣴⠶⠈⢷⠞⢧⠸⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⠀⡀
⠀⠀⣿⣿⣿⣧⠤⠔⠛⠀⡀⢧⠸⡦⡙⠶⣤⣈⠷⠚⠉⠶⠾⣿⣿⣿⣻⣛⣻⡿⠿⢤⢀⣀⣀⣀⣤⣤⣤⣤⣶⡇
⠀⠀⣿⣿⣷⡶⠤⣤⠰⣎⢙⠚⣇⢻⡉⠶⣤⣹⠆⠀⢀⣠⣤⣬⣽⣿⣿⡟⠝⣋⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣽⡟⣧⠞⠁⠀⠘⣯⠂⠹⣮⡥⠀⠈⠁⣀⠀⠈⢻⣧⣾⣿⡿⠋⣠⢾⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⠁
⠀⠀⢟⣿⣿⠧⣶⣶⡾⠀⠚⠁⠀⠁⡀⠀⣄⠀⠸⣿⣷⣦⣿⣿⡟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣧⢻⣿⣿
⠀⠀⣼⣿⣎⢠⣿⣿⠃⣠⣾⡇⠀⣼⣧⠀⣿⣷⣄⢻⣿⣿⣿⡛⢁⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢹⣿⡌⣿⣿
⠀⠀⣿⣿⣷⡆⣿⣿⣿⣿⣿⣇⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⣿⣿
⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠀⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⡿⣿⣿⢸⣿⣿
⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣭⣿⣷⣿⣿⣿⡄⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⢃⡛⠛⠻
⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⠿⡟⠉⢉⣿⡿⣣⣾⣿⡀⠜
⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠛⠿⢿⣿⣦⡙⠿⣿⣷⣤⣷⡾⠟⡩⠂⠉
⠀⠀⠛⢿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠒⠀⠉⠉⠀⠁⠂⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠈⠑⠠⠤⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣁⣀⣀⣀⣀⡀⠀⠐⠆
⠀⠐⠫⠭⣭⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠰⣶⠋⠉⠉⠉⠉⠁⠀⠠⠮⣥⣍⡉⠉⠉⠛⠓⠲⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠉⠙⠲⢤⣄⠀⠀⠀⠀⠉⠙⣳⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠒⠒⠶⠤⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣠⠴⠋⢉⣠⠤⠄⠀⠤⠤⣤⣀
⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⠏⣴⠖⣩⡭⢭⣖⢦⡉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⡤⠤⠶⠖⠶⠶⢤⡀⠀⠀⠀⠀⠀⠐⣿⣄⠛⠾⠟⠀⠐⣋⣼⠟⠀⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠤⠖⠚⠋⣉⠠⠤⠖⠚⠛⠲⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠛⠛⢚⠛⠛⠉⠁⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠛⠁⠠⢄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢳⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣤⠶⠒⠒⠦⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡇⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⠏⠀⣠⣤⣦⣄⠈⠳⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⡏⠀⢸⡟⠉⠙⢿⡇⠀⢻⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⢸⡇⠀⠀⠸⡟⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠏⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡆⠀⠈⢧⠀⠀⢰⠇⠀⢸⡇⠘⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢷⣄⠀⠈⠣⣀⠎⠀⢀⣿⠀⠀⠀⠀⠀⠀⠠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠙⠓⠒⠒⠁⠀⣠⣿⠃⢀⠠⠴⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⣀⡤⠤⠤⢬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣤⣴⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣀⡀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠶⠶⠶⠖⠚⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠟⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡠⠄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⡰⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠋⠹⣄⡀
⠀⠀⠀⠘⡏⠉⠓⠦⠞⠁⠸⣇⡤⠴⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠑⣄⠀⣤⠀⠀⠀⠉⠢⡌⠁⠀⡀⢈⡹⠗
⠀⣤⠤⢤⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⡀⠀⠀⠄⡚⠁⠀⠀⠀⠀⣘⣠⠼⠂⢅⡇
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡛⠶⡄⢀⣀⠀⢄⠀⠀⠀⠃⣠⠒⠢⢽⡄⠀⠀⠀⠘⠋
⣠⠴⠚⠀⠀⠀⠀⢀⡤⠤⠤⠤⠀⠒⠒⠚⠁⠁⠉⠉⠀⠀⠀⠱⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠰⠳⢤⠄
⠈⠲⣄⡀⠀⢠⠒⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠒⠀⡀⠀⠀⠃⠀⠀⢠⠤⠤⠀⠀⠀⠀⠀⠀⢡⠀⠳
⠀⢀⡼⠁⠀⠘⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠃⡄⠘
⠀⠾⠤⠤⠤⢤⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠳⣀⠀⣀⠀⠀⠀⠀⠀⡰⠲⡄
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⣤⠀⠀⢸⠀⠀⠀⠀⠀⠒⢀⠉⠀⠀⡜⠁⠀⢤⡠⠄⠴⠁⠀⠙⠦⣤
⠀⠀⠀⠀⠀⠷⠺⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢀⣠⠔⠂⠸⠀⠀⠀⠈⡆⠀⡀⠠⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢠⠀⠀⢀⡀⠠⠄⢐⠤⠐⠚⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣬⠴⠒⠉⠑⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠁⠈⡃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠇⠀⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠀⢀⡠⠀⠈⡄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠠⠀⢀⠊⠀⢀⠀⠀⠄⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣀⣸⣿⣿⣿⣿⡿⠛⠉⠀⢀⠀⠈⠙⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣶⣿⣿⣿⣷⣆⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⠛⠿⠟⠛⠁⢀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠛⠛⢿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡋⠀⠀⠀⠀⠀⢙⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡂⠀⠀⠀⠀⠀⢐⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡼⣿⣿⣷⣢⣀⢀⣀⢤⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⢉⣉⣉⡉⠛⠻⢿⣦⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⣠⣴⣿⣿⣿⣿⣿⣿⣶⣄⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣉⠙⠛⠛⠛⢉⣡⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⠛⠒⠒⠛⠒⠀⣿⠀⣀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣿⠟⠟⠓⠒⠚⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠀⠀⠉⠉⠉⠉⠉⠩⠉⠉⢉⡉⠤⣥⣀⣀⠻⢿⣷⣿⣿⣿⣇⡰⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠐⠲⠛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⠗⠀⠀⠀⠀⠀⠀⣀⡀⠈⠛⢿⣦⡉⠉⠀⠀⠀⠀⠉⠀⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢠⡟⠜⠀⠀⡀⠀⠀⠀⠈⠙⢷⡀⠀⢻⣱⡄⠀⠀⠀⠀⠀⠀⢘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⢷⡆⠀⣸⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠘⣧⡀⠀⠀⠀⢀⣴⠇⠀⣸⣻⡇⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⢹⡽⣦⡀⠈⠛⠶⠴⠶⠟⠉⢀⣴⢿⡋⠁⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢦⣄⣀⣀⣀⣤⡴⠟⡵⠟⠁⠀⠀⠀⠀⠀⠀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠪⠬⠭⠷⠾⠛⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣛⣛⣛⣟⣒⣛⣛⣒⣚⢓⣒⣛⣛⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣾⣓⣒⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀⢀⠌⠀⠀⡀⢀⡀⠄⠂⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣄⣀⣀⣀⣀⣀⣀⡀⠀⠠⠄⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣀⣀⣸⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⣶⣾⣿⣶⣦⡀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⠛⠛⠋⠁⠀⣀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁






⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠛⠛⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣟⣉⣉⣉⣉⣉⣿⠀⢻⣤⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⣤⠀⣠⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡞⠛⠻⣦⣀⣀⣀⣀⣰⠏⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠹⣎⣹⣿⣶⣦⣤⣿⠳⢦⡾⠻⠟⣹⠏
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣍⠀⠀⠀⠀⠺⢧⣄⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⡿⠿⠿⠿⢿⣶⡦⣀⠀⠀⠀⠀⠀⠀⣴⣿⣁⠀⠀⠀⠀⠀⣲⣟⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠽⠋⣁⣤⣴⣶⣦⣤⣀⠙⠪⡳⣄⠀⠀⠀⠀⢀⡾⣫⣴⡆⣠⡀⢿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⣠⣾⡿⠛⠉⠉⠉⠛⢿⣷⣄⠙⣞⣆⠀⢀⣴⡿⠛⠉⠀⠻⠋⠻⣾⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⡟⠀⣠⡶⣛⠷⣄⠀⢹⣿⡆⠸⣿⡄⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⣿⠸⣿⠇⣿⠀⢨⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣧⠈⢿⣷⡀⠈⠻⠶⠞⠃⢀⣾⣿⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢦⡈⠻⣿⣶⣦⣤⣤⣶⣿⠟⠁⡴⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⡦⣄⡉⠉⠛⠋⢉⣠⢴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠠⠒⠤⠀⠄⠂⠄⠠⡀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⠠⣢⠤⠶⠶⠖⠟⠟⠒⠛⠛⠛⠛⣷⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⡏⠀⠀⠀⠀⠀⣀⠠⠒⠀⠀⠀⣾⡀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢧⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠀⠈⢜⣤⣤⣄⣤⣤⣤⣄⣄⣤⣄⣲⡿⠀⠀⡀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠄⠀⠤⢀⣨⣏⡁⣻⣧⣄⠀⡀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠉⠉⢉⠀⠈⢣⡈⠃
⠀⠀⠀⠀⠀⠀⠴⠛⠋⣉⣹⣛⣀⣀⣠⣐⣒⣶⣦⣀⠼⠀⠄⠁⠀⠁⠠⠠⠀⢷⣀⣀⣀⣀⣀⣠⣏⠀⣩⣭⣍⣳⡀
⠀⠀⠀⠀⢠⠒⢃⠀⠉⠉⠁⠀⠀⠀⠀⡀⢀⣀⣀⣀⣐⣈⣤⡡⠁⠁⠀⠀⣃⣂⣀⣁⢑⠁⠈⢀⠀⠀⠀⠀⡀⠀⣀⣈⣑⡲⣄
⠀⠀⠀⠀⡎⠄⠀⠀⠈⠉⠉⠉⠉⠝⠑⠄⠀⠀⢀⠔⠊⠀⢐⠀⠈⡀⡀⠐⠂⠬⢁⡒⠤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⡒⢰
⠀⠀⠀⠀⣅⣀⣀⡀⠀⠀⠀⠀⠀⠓⠘⠁⢀⠜⠄⠀⢄⣠⠴⣫⡜⣋⣙⣉⡛⠶⣤⣈⠙⠮⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⢠⠈⠀⠀⠀⠀⠈⠉⣦⣤⡤⠤⡴⠣⠁⢀⡶⣫⡴⠟⠋⠉⠈⠈⠈⠉⠙⠲⣬⡓⣦⡈⠪⣷⣷⠶⠶⠶⠶⠶⡤⡽⠷⣾
⠀⠀⠀⠸⠆⠀⢀⠁⡠⢀⠄⢰⠔⠀⠀⠂⠀⢠⠏⣼⠋⠀⠀⠀⠀⠀⠀⠀⢰⠰⠐⠀⢛⢆⠹⡄⠹⣷⡄⡡⡠⠀⢀⢔⢈⠈⢺⠄
⠀⠀⠀⢰⠀⠀⢂⠅⠪⢐⠠⢸⠨⠆⡄⠀⢀⡟⣰⠃⠁⠀⠀⠀⢐⠀⠀⠃⡀⠄⠻⣿⡡⠫⣿⠹⡀⠹⣯⢈⢀⢕⠕⠕⡑⡡⢰⡂
⠀⠀⠀⢸⠀⠀⢂⠅⡢⢐⠬⠀⡄⠁⡂⠀⣸⡇⣿⠠⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⢢⠀⠂⢹⠼⡇⠈⣿⠅⠁⡁⠠⢪⠈⡈⢨⠄
⠀⠀⠀⠀⡆⠀⡀⠅⡊⠐⡠⠀⠇⠁⢉⡀⢹⡧⣿⡂⠄⢀⠀⠀⡀⠀⠀⡀⠀⠄⠀⠘⠀⠀⠴⣺⠃⢸⣹⠇⡈⣠⢔⢕⢋⢐⢹
⠀⠀⠀⠀⢣⠀⢐⠅⢐⠅⡪⠀⠇⠀⠘⣧⠀⢫⡜⣧⣄⠔⡀⡀⡀⠠⢠⢠⠐⠀⡈⡄⠈⣀⣹⡏⢀⣭⡭⡠⢊⢔⢕⡑⠕⡁⡽
⠀⠀⠀⠀⠘⡄⠀⠨⢐⠁⡊⠔⢹⠀⡄⠙⣷⡈⠙⣦⡹⢦⣌⡐⡰⡡⠠⢣⠠⠡⢁⣠⡾⣫⠖⢀⣴⢟⠪⡪⢀⠕⡪⠪⠂⢈⡇
⠀⠀⠀⠀⠀⠡⡀⠈⠐⠄⠠⣘⣀⠀⠀⠀⠈⢻⣦⣄⠙⠳⢦⣋⡫⡳⢒⠰⠒⢊⡼⣫⠖⢁⡰⡶⢏⠅⡊⢔⡡⡪⢀⢔⢕⠜
⠀⠀⠀⠀⠀⠀⠙⠭⠭⠉⣉⣉⣁⣀⠂⠐⣀⣀⣊⣻⣽⣶⣤⢌⣉⡉⠙⣛⣙⢉⣁⢴⡶⠿⠾⠦⠱⠚⠒⠛⠛⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠠⠀⠀⠠⡀⠄⠀⠀⠄⠀⠀⠀⠄⡠⠀⠠⡀⠀⠠⠂⢄⠠⠀⢄⠠⡠⢀⠄⡠⢄⠄⡠⠀⢄⠄⡠⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠁⠈⠀⠐⠈⠂⠀⠈⠐⠕⠀⠐⠁⠨⠀⠡⠊⠔⠄⠪⠒⠕⠈⠂⠕⠊⠀⠐⠁⠊⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣄⣤⣠⣄⣐⣈⡙
⠀⠀⠓⠤⢤⡤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠉⠉⠉⠉⠁⠉⠀⠀⠰⠾⢤⣤⣈⠉⠉⠉⠛⠛⠲⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠉⠙⠛⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠤⠤⣤⣤⣀⣀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⢀⣠⠴⠚⠉⣁⣤⡤⠤⢤⣤⣀⡀
⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣴⠟⣡⡴⢒⣒⣒⡤⣌⡙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠸⣿⣰⣿⠉⢉⡿⠂⣿⡆⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣀⣤⠴⠖⠛⢉⣉⣡⣤⣄⡈⠉⠛⢦⡀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣭⣥⣤⣤⡶⠟⠋⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠀⠤⠐⠂⠈⠉⠉⠀⠀⠈⠙⢦⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠉⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⣤⠞⠛⠉⠉⠓⢦⣀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⡇⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⡟⠁⢀⣴⣶⣶⣤⡀⠙⣦⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡿⠀⠀⣿⠟⠉⠉⢿⣧⠀⠸⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣿⠀⠀⠀⠘⣿⠀⠀⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢻⡄⠀⠀⢀⡏⠀⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⡄⠀⠀⠹⣄⠀⡼⠁⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠈⠻⢦⣤⣀⡬⠛⠀⠀⣰⡿⠁⠀⠀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⠀⠀⢀⣀⣤⣾⠟⠡⠄⠒⠉⠀⠀⠀⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣠⠴⠖⠋⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣤⣀⣀⠀⠀⠀⣀⣧⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣯⣯⣽⣥⣮⣽⣯⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣷⣿⣷⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⣶⡀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⣸⣿⣇⢀⣠⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⡻⣿⣿⠙⣿⡿⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣿⠃⠈⠋⠀⠉⠰⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣄⠀⠈⠙⣻⡿⠦⠀⠀⠀⠀⠀⠀⣤⣼⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⠟⠛⠉⠙⢿⣧⡀⠀⣀⣀⣤⣴⣶⣶⣤⡀⠀⢀⣉⣻⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⣀⣠⣤⣿⣿⡿⠿⠛⢋⣉⡀⠈⢻⣷⠀⠈⠛⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣴⣶⣿⠿⠟⠛⠉⠁⠀⠀⠀⣼⡿⠻⣿⡄⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⡿⠟⠛⠋⠉⠁⣀⣴⣶⣾⣿⣷⣶⣤⣀⠙⢿⣿⠟⠁⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠉⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⢰⣶⣦⣬⡙⢿⣷⡄⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠈⠙⣿⣦⢹⣿⡄⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡇⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠸⣿⡄⣶⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠹⣿⣌⠻⢿⣶⣶⡆⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣤⣴⣶⣿⠟⠁⠀⠀⣀⣠⣤⣶⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣁⣤⣤⣶⣾⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⣀⣠⣤⣴⣶⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣶⣾⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣉⣉⣉⣉⣉⣉⣉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣰⠏⠀⢿⣤⣤⣤⣤⣤⡿⠀⠹⣶⢤⣄⣀⠀⠀⢠⣄⡀⠀⣴⣆⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠞⠉⠉⠹⠶⠶⠶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠾⠿⢿⣷⠾⡏⠙⠟⠉⠋⣴⠋
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠆⠀⠀⠀⠈⠙⣳⡦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⠿⠛⠋⠉⠉⠛⠻⢿⡦⡀⠀⠀⠀⠀⠘⠛⣶⠆⡀⠀⠀⢠⣬⠿⠄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠋⣠⣴⣿⡿⠿⠿⣿⣶⣄⠙⢾⢦⠀⠀⠀⣠⣾⡵⠞⢻⣴⢷⣘⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣰⣿⠏⠁⣀⣤⣄⡀⠙⣿⣧⠈⢯⣇⢀⡴⠛⠁⠀⠀⠀⠁⠀⠙⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⡏⠀⣾⢫⣶⡍⣷⠀⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⣿⣧⠀⠹⣮⣍⣵⠟⠀⣸⣿⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠘⢿⣷⣄⣀⣀⣀⣠⣾⡿⠋⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣳⣄⡙⠛⠿⠿⠿⠛⠋⣀⢔⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣶⣶⣾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠿⢿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⢀⣿⡇⠀⢀
⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⡶⠶⠶⠖⠒⠒⠒⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠈⣿⡇⠀⠀⠙⢦⣀
⠀⣴⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠙⢿⣤⣀⠀⠀⠙⠳⢶⣤⣄⡀
⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠈⠉⠛⠒⠂⠀⠀⠈⠙⢿⣦
⣿⣿⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡿⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠐⠚⠋⠉⠁⠀⠀⠀⠀⠉⠙⠻⢿⣷⣦⣀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠇⠀⠀⠀⠀⠀⢰⣿⣇⣠⣤⣬⣭⣍⣛⡛⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢹⠀⠀⠀⠀⣀⣴⣿⣿⠿⠛⠛⠋⠉⠛⠛⠻⠿⣦⣍⠻⣿⣶⣄⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⢻⣿⣧⡀⠀⠀⠀⠀⠀⢻⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣴⣿⡟⠁⠀⠀⢀⣤⣶⠿⠿⠿⢿⣷⣶⣄⡀⠀⠀⠙⢧⡹⣿⣷⡀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣼⣿⡏⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠈⢳⢹⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿
⢸⣿⡟⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠈⠇⢿⣿⡄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢰⣿
⢿⣿⡇⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⢸⣿⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⣿
⠸⣿⣷⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⢀⠇⢸⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣤⣼⣿⠟
⠀⠹⣿⣧⠀⠀⠀⠹⣦⣄⡀⠀⠀⠀⢀⣠⣼⣿⡿⠋⠀⠀⢀⡞⢀⡟⠀⠐⠊⠁⠀⠀⠀⠒⠒⠒⠲⠶⠶⠾⠿⠿⠿⠟⠋
⠀⠀⠹⣿⣷⣄⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⣠⠟⠀⠈
⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⣦⣤⣤⣤⣶⣶⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣙⣋⣙⡉⠁⢿⣠⣤⣄⣠⣤⣤⡤⠄⠤⠀⠀⣿⣛⣙⣋⣙⡙
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠁⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠒⠒⠙⠛⠛⠛⠛⠓⠛⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡤⠤⠟⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⣼⣶⠶⠶⠶⠶⠶⠶⢶⡆⠀⠀⠀⠀⠀⡀⠉⠻⢶⣄⠒⠂⠀⠀⠀⠂⠀⡗
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡞⠆⠀⠀⠀⠀⠀⠉⠳⣄⠀⢻⣤⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣻⡂⠀⣇⠀⠀⠀⠀⠀⣽⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢿⢷⠀⠙⢦⡀⢀⣀⣴⠏⢀⣼⡿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠘⢯⡳⣄⡀⠉⠉⠉⣀⣠⢞⡽⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠝⣿⣻⣭⠿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢺⣻⣳⣶⣖⣒⣲⣒⣒⣒⣖⣒⣲⣒⣒⣲⣖⣓⣒⣒⣒⣒⣶⣶⣒⣂⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣷⣻⣿⠿⠟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠘⡄⢀⣀⣤⣽⣿⣿⣿⣿
⠀⠀⠀⠀⣶⣾⠷⠻⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⢁⣸⣤⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠖⠋⢨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣭⣿⡗⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣴⢰⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢳⣿⢸⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣭⠭⠿⠿⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣿⡧⢼⠻⣿⢿⣾⣿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⠛⣛⡘⠹⠿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠘⠋⠁⢸⣶⣤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⠀⠀⠈⠙⠛⠾⢿⣿⣏⡟⠓⠲⢦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣟⣿⣿⡿⢿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠚⣶⣴⣎⣉⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡶⣿⡿⠀⠀⣿⣇⣘⣿⡏⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⣿⡇⠀⠀⣿⡿⠀⢻⣇⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢸⢋⣿⡏⢻⣿⡏⠀⠀⠸⣿⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠆⡏⢸⣿⠀⣸⡇⠀⠀⠀⠀⢹⣆⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⡏⠀⣿⡇⠀⠀⠀⠀⠀⢿⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣿⡇⠀⠀⠀⠀⠀⠘⣷⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡇⠀⡏⡗⠀⠀⠀⠀⠀⠀⠸⣇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣸⣿⠁⠀⡇⣿⡀⠀⠀⠀⠀⠀⠀⠿⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠆⣿⠀⠀⠁⡗⢐⠀⠀⠀⠀⠀⠀⠀⢇⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⠀⣿⠀⠀⠀⣧⣽⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⠇⢸⡿⠀⠀⠀⣷⣺⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣼⠀⢸⡇⠀⠀⠀⡧⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⡇⠀⣼⡇⠀⠀⠀⣗⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠁⠀⣿⠁⠀⡄⠀⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡏⠀⠀⣿⠀⠀⡇⠀⡇⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣼⡃⠀⢸⡟⠀⠀⠀⠀⡇⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣯⣿⣧⣄⣸⡇⠀⢸⠀⠀⡧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣡⠍⠙⠻⣿⡇⠀⣿⣄⣀⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣶⠞⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣁⡿⠀⠀⠀⣾⠃⠀⡿⠿⣿⣯⡉⣻⣧⣶⣶⡶⠶⠶⠿⠿⠒⠛⠛⠛⠙⣯⣤⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣿⠏⠀⠀⠀⠀⣿⠁⢰⡆⠀⡘⢡⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠸⠁⠌⣰⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠀⢽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⢱⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡦⠬⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣀⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢩⣍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠀⠀⠀⣀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠟⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡾⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠠⣾⣿⣿⣿⣷⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢷⠀⠀⢀⣴⣾⣿⠟⠃⠀⢠⠋⢸⣿⣿⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⢸⡿⢛⣿⣿⣿⡀⠀⠀⠚⢿⣿⣿⡿⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣀⡀⢹⣶⠀⠀⠀⠀⢠⣾⠀⠁⣾⣅⣸⠋⣷⠀⠀⡄⢸⣿⣷⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠋⠁⠈⠉⠀⠀⠀⠀⡘⣿⢀⡀⢿⡏⠉⢹⣯⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠃⠀⠀⢼⢘⣷⣌⣹⣿⣿⠏⠀⠰⢆⠀⠉⠛⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠒⠲⠶⠟⢸⣿⣿⣿⣟⣿⠀⠀⠀⠀⠈⠈⠁⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢶⣀⢾⣿⣿⣏⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⢸⠿⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⣀⣼⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢻⡟⠉⠉⠉⢹⡏⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣾⡇⠀⠀⠀⠸⣷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠏⡇⠀⠀⠀⢰⡏⣆⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡟⠀⡇⠀⠀⠀⢸⡇⢹⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣼⠁⠀⡇⠀⠀⠀⢸⡇⠈⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⡇⠀⠀⡇⠀⠀⠀⢸⡇⠀⠘⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣾⠁⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⢻⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣰⠃⠀⠀⠀⣟⠀⠀⠀⣸⠀⠀⠀⠸⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠀⠀⠀⢠⣿⡧⠀⢸⣿⡄⠀⠀⠀⣽⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⣿⡇⠀⢸⡟⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⣿⡿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣋⣹⣷⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣤⠖⠀⢀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⡃⢀⡤⢤⡄⠀⠀⠂⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⢰⠐⠤⠠⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠳⠄⣀⡴⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠔⠂⡡⠄⣀⡀⡤⠀⢊⠱⢄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣆⣼⡁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡄⢀⣴⠛⠻⢿⡥⣞⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠙⠳⢸⣧⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠈⣤⠀⣻⡗⢶⠋⡰⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠁⠚⠋⢸⠃⣌⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡌⠄⠐⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⢠⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⠆⠌⠀⠀⠀⠀⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⢉⡖⠀⠀⠀⠀⠈⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣹⠤⠒⠂⣦⣤⣀⣀⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠉⢀⢀⡔⢈⡟⠁⠀⠀⢀⡀⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⡻⢇⣤⠞⠙⠉⠡⠉⢉⠈⠹⡉⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠋⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢀⠀⠊⠉⣅⠀⠀⠀⠀⠀⠐⣀⣼⣠⠄⠸
⠀⠀⠀⢀⢠⡴⢦⠀⡀⠀⠀⠀⠀⠀⠀⠨⣀⣞⣛⣋⣥⣤⣤⡤⠤⠤⠴⡀
⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠆⠀⠄⠈⢄
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⢀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢦⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡐
⣿⣿⡿⠻⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣿⣤⣤⣦⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢸⣿⣿⣿⡟⢛⣛⣻⣯⡍⢉⣛⣛⡶⢦⣤⣤⣀⣀⣀⠀⠀⢀⠀⠀⢀⣀⣀⣀⡄⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⣿⣿⣿⢹⣿⣿⣿⠟⣿⣿⣶⣾⢿⣿⣭⣽⡿⣿⣏⣿⠸⡟⢹⣿⣿⡇⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⠻⡷⢸⣿⣿⡇⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⣼⣿⠀⣿⣿⣿⡿⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⡏⣧⢸⣿⠿⢇⣨⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⣼⣿⣤⣀⣤⣤⡼⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⣏⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣯⣼⡿⢿⣿⣿⣿⠻⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣀⣿⣿⣿⣇⢸⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⠻⣏⢸⡗⢨⣿⣿⡯⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⣿⣋⡿⣿⣿⣏⢸⣿⣿⣿⣀⣿⡿⣿⣧⣼⣿⢿⠿⠆⢿⠷⠿⠸⠇⢰⣿⣿⣇⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⢸⣿⣯⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣤⣤⣤⣤⣤⠀⣠⣀⢰⣶⣤⣾⣿⡏⢸⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠹⠿⠙⠃⠀⠿⠟⠛⠃⠒⠿⠛⠋⠉⠙⠉⠛⠛⠛⠻⠋⠀⠛⠛⢻⣿⣉⠵⠿⠋⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠀⠘⠠⠒⠦⢚⣀⢀⣂⡀⠀⠀⠀⢀⣠⣄⠀⣶⣿⣶⠶⠞⠛⠋⠉⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⣿⣿⣿⣿⣿⢱⣿⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣿⠋⣿⣿⣿⣼⣿⡟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢸⡇⠀⣿⡟⢻⣿⣿⡇⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⠀⠀⢻⣿⡀⢿⣿⡇⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣼⡏⠀⠀⠘⣿⠀⠘⣿⣧⣀⡈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⡿⠀⠀⠀⠀⣿⠀⠀⢻⣿⠁⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣼⠇⠀⠀⠀⠀⣿⡇⠀⠸⢿⡀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡟⠀⠀⠀⠀⠀⢻⣇⠀⠀⣼⣧⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⢇⣿⡆⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣸⡏⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣸⡏⣿⡀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢻⡇⢹⣇⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢦⠸⡇⠈⢿⡄⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠤⠄⣼⠀⢸⣷⣀⣠⣿⡇⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⣠⠟⠀⠀⢿⣿⣿⣿⣷⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣼⠀⠀⠀⠘⠿⣿⣿⣏⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢸⡇⠀⠀⠀⢳⣿⣿⣶⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⡇⠀⠀⠀⠀⠸⣿⠈⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⠀⠀⠀⠀⢹⡇⢸⡆⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡧⠀⠀⠀⠀⠀⠈⣿⡌⣧⠐⣦⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡃⣿⠀⠀⠀⠀⠀⠀⠙⣷⠹⣇⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⣻⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣄⣼⠀⠀⠀⠀⠀⠀⠀⠸⣿⡸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⢀⣿⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⣿⣷⡴⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠻⠃

⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠸⣀⣀⣸⠐⢁⣀⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⡠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡇
⠀⠀⠀⢠⠒⡸⠁⢸⠀⠙⠒⠤⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣧⣄⡀
⠀⠀⠀⢃⢠⠃⠀⠜⢀⠳⠀⠀⢠⠁⠀⠀⡸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡖
⠀⠀⠀⢀⠃⠀⠀⠣⠤⠜⠀⢠⠃⠀⠀⢰⢣⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⢀⠇⠀⠀⢠⠃⢠⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡀⠀⢀⠖⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⡠⠊⠒⠒⠊⠉⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣠⣁⣴⣦⣆⠀⠀⠀⠀⠒⠐⠂⠀⠀⠀⡠⠀⣀⠀⠘⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠤⡄⠂⣀⣤⣄⡀⠠⠀⢨⢎⠀⢸⠀⡈⣄⠁⠣⠄⠉⠑⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡯⠇⢸⡟⠀⠚⣯⣦⠀⠀⠐⢢⠠⠨⢀⡠⠄⠠⢄⡰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠂⠆⠘⢟⢾⣞⡵⠿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠂⢶⣻⣶⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣯⣽⣵⡶⢦⣤⣤⣀⣀⣐⣎⣉⠉⡉⢩⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡮⠽⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣐⣃⣀⣾⢎⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡽⠹⢛⡿⣏⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡞⠀⠀⣼⡇⠹⡄⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⠎⠀⠀⠀⣸⠇⠀⢁⠸⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣤⠏⠀⠀⠀⠀⢸⠀⠀⠰⠀⢿⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡤⠋⠀⠀⠀⠀⠑⠚⠀⠀⠀⢣⢼⡟⢶⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠟⡓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⢫⡉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡇⠀⠀⠻⣆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢻⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠳⡡⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆⠀⠀⠀⠀⠀⠙⢵⡄
⠀⠀⠀⠀⠀⢀⠴⡟⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠀⡀⠀⠀⣀⠤⠸⣯⣱⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠚⠘⠛⠐⠀⠉⠂⠑⠀⠀⠀⠐⠀⠂⠐⠀⠀⠀⠀⠐⠀⠔⠀⣾⢾⣄⠀⠀⠀⠐⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢬⠉⠠⠀⠀⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣈⠀⠀⣀⣄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣤⢤⡌⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠠⣤⠼⠛⠛⠓⢄⢠⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⠭⠥⠤⠤⠭⠁⠀⠀⠒⠲⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡊⠀⢀⠐⣩⣭⣉⠢⣤⡤⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡻⢉⠜⠉⠳⢩⡅⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣤⡜⢽⡃⠀⢀⡰⣰⡃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠲⠞⢞⠲⢍⣹⣥⠶⠗⠚⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠛⠛⢫⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⡴⠂⠀⠂⠒⠦⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢇⠠⡐⣌⣫⠗⠷⠖⠺⠇⠛⠳⠆⠶⠐⠴⣄⣆⣠⠤⠆⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣤⡟⠙⢝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⡀⠓⡐⠒⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⠮⠏⠿⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠃⠀⡇⠆⠈⡎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠀⠀⠇⡇⠀⠹⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠁⠀⠀⡇⡃⠀⠀⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡇⠀⠀⠀⠃⠁⠀⠀⠈⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠁⠀⠀⠀⡟⢳⠀⠀⠀⣃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡏⠀⠀⠀⠀⡇⢸⠀⠀⠀⢸⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠰⢻⡄⢀⠀⠀⢀⠀⡀⡇⢸⡀⠀⠀⡀⠀⡘⠶⢄⢀⠀⡀⡠⢀⣀⢄⡀⣀⢀⢀⡀⠀⠀⢸⣿
⠀⠀⠀⠁⠀⠙⠚⠁⠑⠨⢂⠅⢊⢔⡷⣯⠐⢁⡩⠊⠔⠛⠲⠟⠀⠈⠊⠐⠁⠁⠉⠈⠀⠁⠀⠈⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠦⠟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠒⠂⠉⠓⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣦⣄⠀⠀⠀⠀⠀⣈⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣧⡤⠶⣭⣍⠛⠶⣤⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⣰⣄⠙⠋⠀⢛⣛⣲⣤⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡇⠈⠙⣷⠿⠟⠋⢿⡇⠀⠀⠀⠀⠀⣀⣿⡿⠦⣀⣀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠂⠁⠀⠀⠉⢲⣶⣿⠀⠀⠀⣸⣇⡀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⣿⠋⠁⠀⠀⠀⠀⣰⠟⠿⣿⣽⣿⣋⣉⡩⢿⣿⣉⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⢁⣴⡿⠛⠀⠀⠀⠀⠀⢀⣿⣦⣰⡆⢛⠋⠁⢀⣀⣠⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⢀⣠⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⣾⠟⢨⡿⣶⡿⢶⣾⣟⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠲⠠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢠⣿⠁⣿⡇⣸⣿⣿⡀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢠⣿⠃⠀⣿⡇⣾⡟⢿⣇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⣿⠃⠀⠀⣿⠇⣿⡇⢸⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠃⠀⠀⠀⣿⠀⣿⡇⠀⣿⡆⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣼⠃⠀⠀⠀⠀⡿⠀⢿⣿⠀⣿⣇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣼⠃⠀⠀⠀⠀⠀⡇⠀⣼⣿⠀⢸⣿⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⣿⠸⠀⠸⣿⡆⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠃⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⠀⡄⠀⣿⣇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⡇⠀⢸⠹⡀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣷⠀⢸⡀⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣿⡄⢸⡇⢸⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢿⣧⠀⣿⠀⡇⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇⠀⣿⣤⣸⣿⠀⣿⡄⢸⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⣿⠁⢠⣿⢿⣎⠙⠇⡉⣷⡄⠇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣼⡿⠁⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⠀⠀⣿⠀⢸⣿⠀⠻⣷⡾⣧⠞⠀⢸⡀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⣿⠃⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⣀⣤⣿⡄⣼⣿⣄⠀⠈⠻⣿⠀⠀⠈⣧⠀⢸⣧
⠀⠀⠀⠀⠀⣾⣛⠁⠸⣿⣷⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣤⣀⣀⣼⠟⠀⠀⢀⣸⣆⠀⠀⣿⡆⠈⣿⡀
⠀⠀⠀⠀⣼⡇⠉⣀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⣻⣷⡀⢹⣷⠀⢿⣇
⠀⠀⠀⠀⣼⡿⢦⣽⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠉⠈⢿⣾⣿⡄⢸⣿⡀
⠀⠀⠀⢠⡉⠛⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⣿⡇
⠀⠀⠘⠿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢹⣿
⠀⠀⡀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠘⣿⡆
⣰⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⢿
⢧⣀⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢉⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠈⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠀⠸⣷⣄⠉⠛⠷⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⠻⣷⣄⠀⠀⠈⠉⠛⠻⠶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣠⡶⠛⠁⠀⢀⣠⣴⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡶⠟⣁⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⢻⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⢹⣿⣿⣿⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⣼⣿⣿⠟⢁⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣴⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣠⣾⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⢀⣠⣴⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣨⣿⣿⡿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠐⠒⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠁⡀⠭⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠠⠤⣤⠃⠀⠀⠐⢦⠀⠀⠀⢈⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠁⢸⠀⠀⠀⢹⡘⡇⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢢⡀⠀⢸⠀⠀⠀⠸⢡⡇⠀⠀⣿⣿⣿⣿⠙⠳⢦⣄⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⡆⣷⠀⠈⣄⠀⠀⠀⠋⠀⠀⢰⣿⣿⣿⡇⠀⠀⡼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠀⠀⠐⢡⠇⠀⠀⡟⢀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠀⠀⠰⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⡄
⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⡃⠑⠂⢠⣾⣿⣿⣿⣅⣀⡀⠸⠁⠆⢸⣿⣿⣿⣿⣯⣀⠤⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠸⠁⠀⠀⠀⣀⠘⣿⠟⣩⡿⣿⣿⣧⡄⠀⠀⡈⠉⣿⣿⣛⣭⣤⣴⣶⣶⣿⣇
⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠰⣂⡁⠀⠀⠀⠀⠐⢦⢸⠀⡇⢀⣿⣀⡠⠟⢸⣦⠀⠀⠰⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⠇⠀⢠⡤⣤⣤⣄⠀⣿⣿⠀⠀⠀⠀⠘⢸⣿⡄⠀⠈⣿⢻⠉⠙⣮⣷⠀⠀⢨⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⡿⠀⠀⠘⢿⠿⠋⠉⠀⠉⠁⠀⠀⠀⡀⠈⠼⠹⡇⢸⣄⠘⢧⣧⣴⣿⡿⠁⠂⢼⣄⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⠇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠡⠀⠀⠀⡇⢸⣿⣷⣶⣾⣿⣿⡇⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠛⡟⠉
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⡥⠴⠶⠒⠃⠸⣿⣷⣶⣶⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣀⣀⣠⣤⠀⢴⣶⣾⣶⡖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⢻⣦⠆⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠘⠛⢃⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⢴⣿⠟⠉⠀⠀⠀⠀⠀⣰⣒⣞⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣼⣛⠛⢛⣿⣿⣿⣿⢫⡎⢻⣷⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠘⠁⠀⣰⣶⣿⣿⠉⠉⠀⠀⠑⠌⠳⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⡶⠀⠀⣰⡏⣿⣿⣿⣀⣀⣤⣤⣶⡾⠷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠛⠛⠛⠛⠛⠉⠉
⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣷⣺⣯⣉⣯⣭⣙⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡵⠶⡻⠋⠉⠙⡗⣶⣿⣬⣽⠚⠵⣖⠒⡄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣂⣀⣀⣢⣤⣤⡐⣶⣦⢤⣤⢴⣾⣏⡤⡇⠀⠀⠀⠀⠙⠚⠛⠀⠀⠃⡧⠀⡗
⠀⠀⠀⢀⣮⠟⠛⠛⠛⠙⠉⡏⠉⣿⠙⠀⠊⠠⠈⡀⢁⠠⠂⢂⠇⠈⠀⠋⢰⠋⣿⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣏⠠⡇
⠀⠀⠀⠀⠻⢤⠀⠀⢠⠁⠸⡁⠀⡇⢠⠁⠀⠆⢀⠁⠈⠂⠐⢀⠃⢀⠀⠀⠁⡸⣿⠱⡇⠀⠀⠀⠀⠀⢀⣰⣶⣬⡅⡧⠀⣟⡒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠑⢦⡀⡐⢰⠀⢰⠁⡇⡄⠂⠀⠄⢀⠀⡈⠀⠀⠀⠄⢀⢀⠆⣰⡧⣰⣇⣀⠤⠤⠶⠚⢛⣭⡶⠶⡇⣗⢄⣿⣉⠷⣦⡀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠀⠇⠈⢀⠀⡀⡀⢀⠀⠀⠁⠀⠀⠀⠀⠈⡜⢠⣿⠾⡻⠁⠀⢀⠤⠒⠈⠁⠀⠀⢉⡇⡷⢁⢼⡕⣤⣾⣿⡅⠊⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⣠⣀⣀⣃⣰⣄⣤⣠⣄⣤⣤⣄⣆⣰⣇⣿⣤⡥⠄⠂⠁⠀⠀⠀⢀⠠⠔⠈⢹⡏⡷⢃⢸⣆⣷⠾⣿⣿⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠶⠤⠤⠤⠤⣤⠤⣤⣴⣤⣶⣤⠶⣶⣶⢶⣿⣿⣷⣦⡀⢀⠠⠐⠊⠁⠀⠀⠀⠰⣧⣿⠡⣸⡏⡥⣄⡇⢻⡇⢀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢞⢻⡄⠀⠀⡠⣪⣴⣿⠋⣠⢦⠴⡤⣴⡊⠕⡤⡙⠻⣹⡟⠿⣄⡀⠀⠀⠠⢀⣠⡴⢾⢷⣿⣾⣍⣹⣼⣹⣸⠜⡷⠟
⠀⢀⢠⣀⢴⢿⠯⠩⣙⢔⢜⡈⡇⠀⠎⣴⢻⣿⡇⢸⡝⣥⡻⣙⠎⠣⠀⠈⢈⠢⡝⣷⠀⠈⠙⠿⣶⣶⠋⠇⠀⠘⠸⣿⣿⣿⣽⣿⠏⠹⠠⣧⠔
⡞⠛⠛⠡⢚⠅⠈⠠⡢⡢⡠⣇⢹⡘⣼⡇⢸⣿⠀⢳⠞⠀⠁⠀⠀⠀⠀⠀⠀⠡⠙⢼⡆⠀⠀⠀⠈⠙⠷⣦⠀⢠⣤⠶⠻⠉⠈⠅⣠⣴⣾⡧⣺
⢛⡀⣀⢬⢕⢀⢄⠈⢈⣼⢞⢽⢘⣧⣟⡇⣈⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡗⠀⠀⠀⠀⠀⠀⢻⣿⠋⠈⠀⠄⣠⡶⠛⠩⣸⣸⠇⣼
⢸⡶⠣⢠⢎⠔⢕⣴⡟⣡⠔⣱⡆⣿⣿⡛⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣏⡀⠀⠀⠀⠀⠀⢸⣷⠈⣤⠖⠏⠡⣃⡤⠾⠷⠿⠒⠁
⠀⣷⡜⠡⡡⣠⢯⠋⡼⡫⡪⡜⣧⢸⣿⣾⠛⢿⣷⣌⠂⡀⠀⠀⠀⠀⠀⠀⣠⡢⠄⠀⣿⠀⡀⠀⠀⠀⠀⠘⣿⡿⠹⣠⠶⠛⠉
⠀⢹⡄⢆⡬⠥⢑⢠⢈⠤⠈⣢⣿⡘⣯⢿⢷⡈⢎⠻⢷⣄⠀⠀⠀⢀⠰⣈⠶⣭⠄⣿⢸⠎⠀⠀⠀⠀⠀⠀⣿⡷⠛⠁
⠀⠀⠳⠵⣼⣠⣂⡁⠐⢀⡴⡢⣪⣇⢿⢪⠳⡛⢦⡉⠢⢍⡛⠲⢤⡀⠁⠀⣥⣴⢡⣿⡾⠓⠁⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠾⢯⣿⣼⡄⠑⢌⠳⢯⣲⠤⣄⣉⣐⣒⣒⣠⣴⢆⡾⡸⢇⣿⣭⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡠⠤⠭⠦⢬⣙⣓⣲⣷⣶⣿⣛⡡⠮⠞⣁⣈⣻⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⠋⢛⠛⠛⠛⠚⢒⠖⢒⠶⢒⠖⠒⠖⠒⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠁⠁⠁⠑⠑⠡⠠⡑⡁⡁⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⡴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈⠐⠛⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⢀⠐⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠘⠛⢶⡇⠀⠀⠀⠰⣦⠀⠀⠈⠀⢨⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⢸⡇⠀⠀⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡘⣦⠀⠀⢹⠀⠀⠀⢀⡟⣸⠇⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠰⠋⠀⠀⢠⣿⣿⣿⣿⠁⠀⠀⢀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡾⠁⠀⢸⡷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⢠⣮⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⠂⡀⠀⠀⢀⣤⣾⣿⣿⡿⠋⠀⠀⢰⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠃⠀⠀⠁⢰⣿⣿⣿⣯⣥⣀⣀⠀⡐⠹⠀⣿⣿⣿⣿⣿⣿⠿⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢠⡄⢸⡿⠛⣩⣿⣿⣿⣿⣄⠀⠀⠀⡛⠿⣿⣿⣿⣭⠶⠖⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠈⢶⣶⡄⠀⠀⠀⠈⠀⢲⣸⡇⠸⠁⢰⣿⠀⢀⣿⢋⣿⠀⠀⠀⣇⠀⢿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠷⠀⡾⠿⠃⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢸⣿⢿⠻⠶⣌⢟⠀⠀⠀⡿⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡼⢹⡆⢸⡄⠘⣿⡸⡀⢠⣿⣿⡆⠀⠀⡇⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⠀⠀⠀⢸⡇⢸⣿⣦⣈⢻⣿⣿⣿⠋⠀⠈⠐⢦⡀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣈⣀⣠⣤⣼⠇⢸⣿⡿⢻⠿⠿⢿⣿⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠂⠀⠉⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⣖⠀⡻⣿⣿⣿⣿⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⣷⡁⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠃⠀⠛⠁⢡⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⣿⣿⣿⣷⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠛⣿⣿⣿⣿⣿⣟⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⣰⣆⣿⣿⡿⠿⠇⠛⠃⡜⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⣿⣿⠃⠀⠀⠀⠀⠘⢄⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠑⣌⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡰⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⢀⣼⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠾⢇⡰⠋