Jag Emojis & Symbols

⠀⠀⠀⠀⣤⠀⠀⠀⠀⢦⣀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⢀⡈⠀⠘⢒⠤
⠀⠀⠀⠃⠀⠛⠁⠈⡂⠦⠀⠄⠉⠁⠒⢳⠤⣀⠀⠀⢀⣀⣀⣀⡀⣤⠤⠤⠤⣤⠰⠤⣄⡠⢤⣄⣀⡀
⠀⠀⢠⡤⠀⠀⡀⠀⠁⡌⠀⡴⠂⠀⡞⠀⣐⠋⠁⠋⠗⢸⣰⠘⡱⠆⠿⠝⠃⠚⡙⠠⢅⠼⠠⠎⣭⠸⠧⢄
⠀⠀⠀⠡⠀⠰⠿⢻⠛⠂⠖⠀⠠⠊⠄⠔⠄⠀⡈⠸⢉⡆⠀⣦⠐⢲⠘⠎⡽⢀⠰⠁⠚⡰⠶⢡⠅⢒⠂⠚⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⢌⠁⠓⠒⢀⣁⠐⠹⠀⠌⡀⠃⠀⢁⡘⠣⠖⡉⠐⠰⢘⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠄⠄⠄⠀⠀⠢⠈⢈⠉⡅⢐⡀⠶⠀⣌⠠⠀⠌⠐⢠⠅⢛⠈⡥⠈⡀⡞⠩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠂⠀⣂⡀⠚⢀⠉⣐⠂⡔⢀⠓⡀⢐⠃⠄⠀⡄⢀⣌⢁⡀⢶⢠⠰⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⡈⠁⠨⡤⡿⠃⢤⡉⢀⣡⠌⢡⣬⠠⠶⠒⠒⣶⣶⣆⢩⡁⣘⠃⡌⢸⠀⠋⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣁⡁⡿⠧⠶⠂⠀⠁⠀⠉⠀⠀⠀⠀⠀⢨⡴⠃⠿⡅⣉⠠⡦⢨⣁⠀⠤⢭⠀⡀⠀⠀⠀⢀⣴⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡀⣈⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠚⠠⢨⡧⠤⠖⢀⡘⠆⠀⠡⣼⠿⢲⣤⢰⣮⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⠤⢁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡂⣈⠀⠈⡄⠈⠀⠀⠀⠀⠈⠀⠿⠟⣼⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⡖⠀⣀⠇⠀⡠⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⠡⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠓⠛⠛⠁


⣿⢿⠿⠿⡿⡻⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠖⣐⡲⡖⢂⣐⢠⢤⢀⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠮⠀⢫⡟⢀⠀⣇⢵⢀⠛⠼⠣⠶⠈⠣⠛⣙⠳⢏⣶⡎⠷⣨⡽⣱⣄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿⠖⢚⣥⣤⠸⠎⣁⠰⢠⡤⣇⡖⡆⣼⠳⡜⣀⣏⠿⣳⠮⢈⠉⠥⠂⠀⡌⠉⢴⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠂⠰⣢⡘⢴⠴⠀⢺⣅⠓⢈⡃⠁⢶⢠⢠⡍⣰⢇⢴⡄⣅⢽⡾⠰⣷⠁⠈⠾⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢏⠥⣉⡤⣆⢾⡙⠂⡗⣤⢛⡚⢠⡎⡲⠲⠽⡨⣥⣂⣾⢄⣼⡀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠛⠁⡀⠀⠸⢓⡋⣾⣠⠂⠹⠃⡰⡄⠰⣎⠁⠚⡃⢿⡏⢥⢰⠦⣡⠈⠢⡀⣹⣋⢀⠇
⠀⠈⢀⣵⡀⠀⠀⠀⡠⠃⢰⠲⠁⠀⠀⣿⠁⣽⣃⠉⠸⢠⠑⠠⢤⡹⠂⡆⣁⣞⡬⠬⠰⢆⢌⡔⠡⠝⢗⢐⠏
⠀⠐⠞⠁⢸⡶⠒⠺⣷⡄⢈⠋⠀⠀⢀⢧⢦⣈⠋⡐⠷⣨⠀⠀⠀⠈⠘⠣⠼⡍⣀⠅⠚⢺⣠⡌⣁⡺⢚⢫
⠀⠀⠀⠐⠪⠀⣴⠢⠤⠛⠁⠀⠀⠐⠥⡀⠜⠻⡈⡉⣴⠈⠀⠀⠀⠀⠀⠀⠀⠰⡠⠜⡁⠀⠀⠘⢭⠷⣈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠂⠐⠤⡀⠐⠽⢠⡜⡀⠀⠀⠀⠀⠀⠀⠀⠁⡂⠰⡀⠀⡸⠂⡂⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠒⠋⠀⠬⣀⠐⠘⠲⠂⠠⢄⠀⠀⠀⢨⠤⠀⡠⣠⠓⡐⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠚⠀⠀⠀⢚⣀⠀⠀⢫⡀⢀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣞⡛⣟⡀⢴⣭⣼⡿⣿⣟⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣻⣿⣿⣭⣛⢿⣛⠲⣍⣛⠯⣭⣧⣜⠿⢷⣌⣙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⣄⣀⠀⠀⠀⠀⢀⣠⣶⠏⣭⣹⣿⣝⠶⠦⣌⡛⣣⣈⠻⢿⡉⢳⣦⡶⣏⢰⣦⡉⣌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⣻⣿⣶⣶⣶⣿⡿⡿⢘⢷⣞⡳⢿⣦⣁⣻⡷⢌⣛⣥⣾⣿⣿⣿⡇⠘⢧⠙⢿⡼⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⣧⡌⠻⣿⣿⣫⣿⡟⠱⡿⣿⣛⣿⣼⣯⣟⣛⢧⣿⣮⣻⣿⣿⣿⣿⠗⢀⠿⣸⣤⡛⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⢬⣍⠐⣿⢛⡯⣾⠫⣥⣿⣭⣥⢾⡿⢩⣟⢫⣧⣍⠭⢥⠹⣿⣿⠟⠣⣌⠻⣿⣬⣥⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠋⠽⠏⠹⢢⣭⡶⣿⠳⠔⡶⠿⢛⣏⠭⣽⡿⢛⢦⡻⠐⠘⠓⠀⣤⣾⣏⣮⣿⡟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣜⢥⠄⣡⣾⢩⡶⡂⢾⢧⡆⣷⡅⣺⢯⢉⡻⡥⠮⡑⠘⣋⣷⡐⠰⣦⡽⠟⠿⠟⣥⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢳⡎⣁⣩⡄⠘⣻⡇⣴⡦⣎⠲⠎⢥⣤⣤⣡⣌⢠⠷⡄⢗⣃⠶⣸⡿⠸⣿⢺⡿⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣜⡻⠝⣇⢠⣟⢚⣏⣣⣿⠀⢺⣾⣳⣰⣿⣉⣷⢶⣸⣏⠽⢲⠄⡇⢻⡇⡟⣣⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⡏⢯⣙⣷⢸⣍⣾⡶⣯⣿⣇⢘⡥⠿⢲⡾⣯⣿⣧⢻⡝⢰⣈⠀⠽⠃⠄⣰⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡑⣜⣦⣭⣿⢼⡏⠙⠟⠊⢿⠏⣾⣷⠶⣋⠴⢻⠉⣽⡇⣻⢄⠉⣠⠇⠁⣤⣽⣫⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣨⣊⠟⣿⠈⠀⠀⠀⠀⠀⢼⣷⣴⠾⢯⣲⣿⣯⡥⣀⠱⣫⠌⠾⠀⡶⣩⡅⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣍⣱⣿⠀⠀⠀⠀⠀⠀⢸⣿⣟⠧⢤⣼⢉⡋⣈⠁⢞⡑⠫⠖⠀⣠⢟⡘⠋⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⡏⠀⠀⠀⠀⠀⠀⢀⢉⡍⢋⣬⠱⠛⣙⠀⠶⣫⣴⡖⠈⣰⠿⠘⣃⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⢦⠡⣄⠀⠀⠀⠀⣀⡇⢚⡴⣫⠞⣠⢌⣉⣈⣚⠋⣁⡀⠋⣠⢖⠀⣿⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠆⠘⢿⣿⠟⠉⠉⠉⢻⢚⡽⠞⠓⢲⣿⣿⡟⠛⠀⣸⠿⠡⡿⠙⢫⡄⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣛⡁⠀⠀⠀⠀⣸⣥⣾⣮⣵⣋⣡⣄⣤⣴⠿⠁⢠⣴⠞⣟⢨⣶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣻⣿⣿⠛⢂⣁⡴⠋⠁⠘⢏⠉⠛⠋⢀⣠⣤⡿⢋⣴⡿⠳⣆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⢳⣷⠶⠾⠟⠛⠁⠚⠵⣣⣸⡿⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⣶⡷⠶⢟⠽⣿⣧⡼⢿
⣶⣶⣶⢶⢿⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠷⣾⣿⢿⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠉⠙⠛⠉⣭⣭⣍⡑⠲⣦⡤⠴⣏⠁⢀⡀⠙⢿⣷⡄
⠀⠀⠀⠀⢠⠊⠀⣭⣑⣒⠤⢄⣀⣠⡶⠿⢓⣤⡄⠈⠛⢋⡀⢀⠀⠉⠉⠀⠀⣦⣄⠀⠙⠂⠰⠬⠻⠞⢻⣿⡀
⠀⠀⠀⠠⡎⠀⣰⡾⠋⠙⢷⣦⣈⣉⠙⠒⠂⠐⠚⠛⠃⣀⣀⠈⢡⣴⣤⠀⠀⠀⠀⣦⣤⠘⠇⢰⡙⡄⢫⣍⠳⢄
⠀⠀⠀⢠⠃⢸⠇⠀⠀⠈⠻⣿⣿⣿⣷⣝⠛⠀⠀⠀⠀⠈⠉⠀⡄⢀⣀⠀⠛⠂⣀⡀⠀⠰⠟⠠⣦⠰⠲⢋⡀⠘⡁⣦⢀
⠀⠀⠀⠈⢇⡀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣷⣶⣤⡤⠀⠀⠀⠛⠟⠛⡀⠀⣉⠋⢤⣄⢶⣤⡈⢸⠒⢆⢩⣄⢻⣎⠀⢡
⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠈⠛⣛⢻⡿⠛⠛⠋⠁⠀⢀⡀⠛⠿⠂⠈⠉⠀⠈⠁⠀⠉⠈⠻⣿⡆⠾⢬⢐⠃⠸⣿⣠⣞⢀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠃⠉⠉⠁⠀⢠⡾⠂⠀⣀⠉⠀⠀⣈⠓⠶⢤⣤⣤⡶⠚⠛⣿⣷⣄⠁⠐⠀⠦⠐⢈⠛⠿⢸⣆⡓⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣯⣄⣤⡤⠄⠀⠞⠀⠁⠀⢾⡿⠁⣀⠈⠉⠀⡴⠶⠶⠄⠹⣄⠀⠁⣹⣿⣷⣀⠀⠁⠉⠈⠀⠀⠘⢧⣱⠇
⠀⠀⠀⠀⠀⠀⠴⡯⠀⠀⠀⠀⠀⠀⣀⡀⠀⠿⠿⠃⠀⠀⠞⠋⠀⢰⠶⠂⠉⠁⢠⡀⠀⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⣶
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣴⣾⡗⠀⠀⣀⡀⠶⢂⣴⡆⠘⠃⠀⠠⠖⢀⠀⣴⡦⠘⠛⠋⠰⠛⢡⠌⠁⠰⠀⠂⠀⠀⢂⠀⠀⡄⠀⠈⢦⡀
⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠙⠋⠀⠀⠸⠿⠋⠀⠈⠁⠀⠀⠀⢴⡶⠀⠋⠀⣀⣄⠀⠒⠃⡀⠐⠃⣀⣤⣡⣀⡀⠀⠀⠈⢦⣤⣼⣄⣀⣶⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⠇⠀⣠⡄⠀⢠⡿⣃⣤⣤⣤⡀⠰⠖⠘⠋⠁⠀⣀⠘⠋⢀⡀⠉⣭⣉⠉⠉⠑⠂⡄⠀⠉⢻⣿⡶⠃⣱
⠀⠀⠀⠀⠀⠈⡇⢀⡄⣤⡄⠀⣀⠀⠻⠛⣀⡀⠀⠀⡉⠛⠛⠛⠁⠀⠀⠀⣠⡶⠘⠋⠀⡖⠉⢀⣶⣌⡛⠓⠖⠠⠀⠀⠀⠀⣼⠟⠁⢈⡹
⠀⠀⠀⠀⠀⠀⠹⠾⡇⠈⠁⢸⡿⠀⢀⣌⡉⠀⠀⠘⣋⣀⡀⠀⣠⣾⡗⠀⠉⠀⢀⡄⠚⠁⢠⣿⣷⣌⡛⠓⠂⠆⢀⣀⣤⣾⣧⣀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⢿⡷⠀⢰⣿⠿⠛⢁⡀⠙⠁⠀⠀⠀⠀⠉⠁⠀⢠⣿⣿⣿⣿⣿⠛⢻⣿⣭⡭⠭⠿⠉⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⠀⠾⣃⡀⠀⠀⣴⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⣠⣿⡿⠋⠀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⣤⠀⠀⢰⡿⠇⠀⠀⠀⢰⣿⠇⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⡿⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⢧⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⣀⣀⠀⠀⠀⣿⡿⠋⣹⣿⣿⣿⣿⣃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⠶⣀⠴⢻⠖⠋⠁⠀⠀⠈⠾⡇⠀⢿⠁⢰⡿⠿⠿⢿⡉⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⠛⠿⣿⣶⣾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⢀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠿⠶⠶⠗⠒⠋⠁

⠀⠀⠀⢀⣤⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢠⡶⢒⠒⡶⠶⡆⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⢸⣿⣶⣾⣭⣿⣄⠁⠀⠀⣤⠂⢽⢶⣖⢀⠠⢒⣮⣗⠠⣀⢘⡶⢾⠕⣦⡤⠄⠀⢡⣾⣫⣷⣦⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣗⣻⣿⡇⠀⢠⡌⠅⡽⢆⡲⢒⡬⣤⣷⣧⠭⡐⠲⡐⠮⡁⠩⣌⠀⢠⣿⣟⣳⣿⣿⣿⡟
⠀⠀⠀⠀⠹⣿⣿⡟⠛⢿⡇⢠⣌⣤⠡⠴⢂⣴⠜⠀⣑⣏⣗⠁⠰⢤⣔⠶⡄⢡⣈⣤⠘⣿⠛⠻⣿⣿⠟⠁
⠀⠀⠀⠘⣿⣮⣿⠿⢋⠉⠖⠚⡁⠈⠊⢴⣬⠐⠚⡕⢈⣉⢧⠘⡟⠂⣨⡦⡘⢊⢈⡙⠐⠈⢉⠻⢿⣇⣿⡇
⠀⠀⠀⠀⠉⡛⠃⣤⠔⡀⠋⠘⠙⢵⣄⢸⡟⠘⣳⢇⡐⠁⠉⡑⢶⠃⢸⡿⣀⣴⡑⠑⠘⢂⠰⣤⡌⠛⠉
⠀⠀⠀⠀⠀⢱⡴⣡⠘⡁⠋⣀⣭⣤⣭⣁⠃⢀⠒⡋⡱⢐⢾⢙⡐⣂⠘⣁⣩⣥⣬⣄⡘⢂⠓⢠⣡⣼
⠀⠀⠀⠀⠀⢘⢁⣁⡖⠐⢦⠙⢯⡹⠷⢉⣷⡈⠷⠐⠀⠈⠁⠁⠰⠇⣸⣏⠸⠟⣸⢏⢥⠆⢰⢀⡃⣍
⠀⠀⠀⠀⠀⣸⢿⡇⡄⢿⢀⠚⠶⢍⠛⠛⢻⣷⣖⠀⠀⠀⠀⠀⠀⣰⣿⠛⠛⣫⠴⡟⣀⠾⠂⡜⣿⢨
⠀⠀⠀⠀⠀⢿⢐⠀⣶⢤⠎⠴⠸⢇⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠙⠋⢀⠀⡘⠛⠠⠡⢦⢶⡆⣂⢻
⠀⠀⠀⠀⠀⢀⢻⣅⡿⠀⠘⠧⢒⠤⣄⢉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢡⠤⢘⠰⠇⠠⢸⡇⣿⢀
⠀⠀⠀⠀⠀⢸⡆⢈⡁⠐⡇⠀⠳⠾⠈⠀⢸⢣⠦⠀⠀⠀⠀⠀⠀⠐⠣⠀⠈⠺⠾⠃⢸⠇⢀⣉⢠⡆
⠀⠀⠀⠀⠀⠈⢁⡀⣿⣧⠀⠛⠘⣶⣋⣀⠀⢿⣶⣶⢶⣶⣶⢶⣲⡾⠃⣀⣘⣳⡚⡘⠀⣰⣿⠇⡈⠁
⠀⠀⠀⠀⠀⠀⠘⣷⣬⠑⡌⠿⠆⣯⣅⣄⣈⣀⠉⠛⢇⣹⣰⠟⠉⣀⣁⣄⣤⣽⠂⠿⢂⡘⢩⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠦⣤⣛⡀⠷⣸⣯⣭⣥⠤⠄⠀⠀⢻⠁⠀⠠⠠⣤⣭⣭⣿⡼⠂⣈⣥⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣠⣿⣿⣿⣿⡇⣀⣠⣴⣿⣶⣤⣀⠈⣿⣿⣿⣿⣧⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠟⠿⢿⠗⠸⠿⠟⠟⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢠⣴⣈⢩⣾⠋⡒⣸⢃⣆⣴⢋⡜⣡⢦⢍⡕⠿⣤⡼⢈⣓⡻⠿⠓⢠⡀
⠀⠀⠀⠀⠀⠀⢀⢴⣯⣛⣱⠇⠾⣠⡄⢛⠃⠟⣨⣥⠘⠶⢰⣯⢆⡾⢹⢃⣤⠰⣏⠏⢹⣛⣟⡇⣶⣦⣄⢀⡤⣴⠿⠶⠀⡀
⠀⠀⠀⠀⠀⢀⢞⡙⢹⢉⡭⣾⢳⣏⡉⢹⠇⠾⣁⠚⡴⢶⢀⣭⠸⣧⢆⡞⢩⣤⢱⡈⣺⢶⣶⣶⡤⣸⢋⣷⣬⣑⡛⠉⣳⠂⠀⡀
⠀⠀⠀⠀⠀⣎⣼⢹⡏⢋⡴⡄⣶⢤⣙⠃⡾⢆⡛⢰⣇⡾⢸⢯⡆⣠⠘⠟⣉⣥⡈⡽⠕⣨⠐⢃⣄⣭⣤⠈⠨⠋⢁⣸⡕⢻⣇⢙⣇⢀
⠀⠀⠀⠀⠀⡋⢹⡎⠻⣋⡀⢡⠹⡆⣹⢂⡷⣈⠇⣬⡛⠃⠿⣨⢐⡏⠧⢼⠇⢨⣰⠖⠫⢦⡟⠜⡉⣁⠤⠘⡇⢻⢷⠙⣷⠒⢯⡭⣸⡰⡷
⠀⠀⠀⠀⢈⠻⠿⡸⢿⣞⢣⡼⡔⣧⠲⡘⠇⡮⢘⣇⠹⠸⣦⡍⢸⠁⡆⣻⠈⡼⠺⠆⢰⣠⠘⠎⠁⢠⡄⣰⠂⠀⠐⠺⣟⣲⠑⣍⠲⠬⠓
⠀⠀⠀⠀⢈⡿⣏⠻⣴⣽⣬⠡⣶⢨⢜⡃⡖⠢⢯⢁⢡⡓⢡⡟⣌⠋⣤⣘⠾⢳⠗⣴⠨⠵⢶⠈⠄⠈⠔⢀⠀⠺⢁⣰⡇⣡⣡⠈⢨⡓⠐
⠀⠀⠀⠀⡼⣣⡀⢸⢠⡝⡛⡁⣦⠹⠎⢡⣭⢸⡃⣧⠤⢁⡃⣰⡏⡋⡇⢻⢰⢇⢡⡯⡀⠂⡄⠘⠀⠇⣈⠂⢦⢻⡙⠕⠰⢲⢲⠓⡯⡬⠢
⠀⠀⠀⠠⠘⣿⣇⣈⡘⡟⣿⡏⣀⠶⡌⢇⢰⠸⠧⠙⣁⣖⠘⢻⣆⢏⡦⣰⠸⠌⠃⠀⡓⠗⣂⠌⠚⢴⣇⡜⣂⢶⠯⡄⠘⠀⠉⠈⢀⣙⡡
⠀⠀⠀⡺⠿⢠⣾⠁⠁⢡⠙⢠⡹⠆⣰⢞⢥⣷⠆⠘⠛⠛⣀⠃⢻⣃⣃⡢⠔⡇⡄⢛⠘⠂⣃⠀⢕⠘⣻⣄⡈⠉⠙⠇⠀⠀⠀⢀⡛⠈⠓
⠀⣤⣘⠻⣿⠈⠁⠀⠀⢿⡿⣿⡕⣦⡐⠿⣨⠻⠿⢏⣠⡅⠈⠀⠈⠛⠩⠤⢄⣃⠂⢑⣃⡁⢆⣀⠠⠀⠛⢻⡅⠁⠄⠀⠀⠀⠀⠀⠀⠐
⣴⡏⣿⡿⠂⠀⠀⠀⠈⢊⢡⣤⡘⠿⣯⡴⣍⠁⢒⣋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢨⡜⠒⠲⠲⡄⣈⠈⠄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣾⠟⠉⠀⠀⠀⠀⠀⠀⡿⡯⠛⣷⣶⡈⣦⠉⠻⠿⠝⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠴⠯⠒⣂⡱⠜⠳⠴⣶⢶⡀⠀⠀⢦⡤⠄⠂
⣅⠀⠀⠀⠀⠀⠀⠀⠀⢡⡴⣷⣌⡙⢻⡁⠺⠦⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠞⣰⢓⡩⠗⠌⠃⠀⠀⣬⣛⠂⡀
⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⢛⠠⠙⡋⠘⣛⠻⠮⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡌⣘⢍⡙⠀⠀⠀⠀⣀⡙⢩⠭⠽⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠘⢫⡾⠃⠀⠈⢄⠚⠠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢀⣉⢀⣩⠀⠀⠀⠀⠿⠿⡷⠶⠆⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠡⠀⠀⠀⠀⢤⡀⠰⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⡋⢨⡥⣜⠀⠀⠀⣶⠰⡶⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢃⠅⠆⠀⠀⠹⢦⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⡁⡴⢀⠀⠀⢋⠠⠐⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠙⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⢁⡀⠈⡅⠘⠰⠀⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢋⡁⢂⢂⠀⠀⠏⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣠⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢀⣤⣄⠒

⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⢠⢤⡶⢦⣦⡰⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⠀⠤⣔⣒⣦⣄⣀⠀⠀⢀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡷⠞⡲⢿⣿⢛⢮⡙⠊⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠋⠰⣟⠱⡯⣿⢛⢻⢞⣭⣴⡚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⢻⡏⠽⠌⠛⠏⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡐⠀⢴⠁⢊⠻⡽⠨⠃⠱⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣻⣥⠉⣜⣲⢋⠓⢯⣋⢲⣄⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠰⢆⠧⠯⠘⣣⣶⣙⠒⢟⡅⠎
⠀⠀⠀⠀⠀⠀⠀⠰⠎⢞⡆⠘⠐⠛⠀⣌⣴⠷⠉⡆⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣵⠗⡈⠦⣦⠀⠈⠁⠋⠀⡴⡖⠐⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢟⠃⠁⠀⠀⠀⠈⠁⠀⠒⡀⠚⢈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢃⡉⡀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠸⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣆⡀⠀⠙⠈⠛⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡄⠀⠀⠀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡈⢹⣏⡬⠉⡹⠛⢴⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣤⣤⡀⠲⢊⣣⡰⠥⡆⠀⠀⠀⢴⣣⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢍⡛⠦⡈⢰⠄⡸⢃⠃⠀⡄⠀⠛⢦⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⠁⡀⢀⡑⠘⡀⡄⠀⡃⠆⠠⠹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⣷⠘⣴⠀⣴⣄⡐⠉⠀⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢸⣿⠁⠹⢠⡟⠛⢃⡤⠙⠋⠀⠀⠀⣴⡶⢶⣄⣠⣴⣶⣦⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⠁⠀⠀⠈⠁⠀⠺⠁⠀⠀⠀⠀⣸⣿⣶⣿⣿⣷⡰⣿⣿⡁⣤⡿⠝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢿⢿⣿⡇⢻⣟⢳⣼⢛⢥⣿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣤⣤⣤⣤⡠⣠⡤⠄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣑⠗⣤⠵⢖⢛⡻⣯⠁⠿⠆⠹⢟⣥
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢯⣙⢛⡇⡝⢿⠛⣾⡿⣏⡙⣛⠟⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢈⡿⠡⠿⣮⣼⢮⣄⠒⣋⠌⠀⠐⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⡾⠠⠄⠔⢉⠐⢀⠀⠸⣏⣔⠄⡤⢣⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢⡗⣌⠦⣩⣬⣡⣧⣤⡀⠐⠴⠂
⠀⠀⠀⠀⠀⠀⢸⡁⠀⢀⣵⠲⣯⢨⣶⠄⠉⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢘⠛⡭⠈⡀⢊⠳⠆⠰⣦⣈
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠀⣙⣨⡇⢵⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡈⠊⣭⢉⡷⠄⠀⠶
⠀⠀⠀⠀⠀⠀⠤⢠⠀⠀⡈⠉⠲⣼⠯⢰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠿⢛⣿⡄⠘⠁
⠀⠀⠀⠀⠀⠀⠑⠀⢤⣼⣿⣿⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠂⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠦⢂⡖⠐⣶⢀⣶⡒⣦⣀⡠⠶⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡎⡝⠑⠫⡑⠸⠘⣌⠛⠦⡑⢤⡉⡋⠵⣊⢩⡉⠴⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⡘⠅⢢⠁⠼⠖⠃⠈⠈⠒⠃⠈⠀⠀⠁⢘⢀⣵⡆⢰⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢐⠐⡰⠌⠠⢀⠶⠸⠂⠐⢸⡗⢒⡦⠀⠤⡠⢯⠞⠿⢹⡧⠂⢤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡶⠈⢁⡀⠀⠰⢀⠤⠀⠔⡖⠈⠛⠉⠄⢻⠐⠁⢄⡐⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠤⠘⡠⢠⠀⠴⠠⠶⠀⠤⠀⠀⠀⠀⠀⢀⡀⡑⣀⠃⠀⠈⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣁⠠⠰⠄⠐⠀⠈⡆⠀⠐⠄⠀⠀⠘⡀⡂⠀⢉⡅⠀⠀⠐⠉⣤⠐⣚⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⢀⣠⢆⠃⠉⠀⠁⠀⠒⠀⠀⠀⠀⡁⠉⠠⠈⠙⠀⠀⠀⠘⠁⠆⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠛⡠⠀⢛⠈⠡⡴⢆⡀⡁⠠⠀⡌⠐⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣆⣠⡤⠰⠇⠙⢨⡷⣤⢀⡀⠈⡁⠃⠀⣀⠀⣁⠀⠀⠀⠐⠀⠆⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⣸⢣⣤⠀⠀⠀⠷⣄⠀⠀⠸⠟⠀⠉⠁⠀⠈⠠⡀⣁⠈⠂⠀⠀⠀⠀⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢸⣽⡿⣧⡙⠀⠀⢶⣀⠈⠻⠶⣶⠂⠀⠄⠐⠲⠈⠳⠀⠄⠀⠨⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡄⢿⠄⠀⠀⠀⢀⡙⠃⠀⠀⠀⠀⠀⠈⠐⠐⠂⠀⠀⠀⣄⠀⠠⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠷⡞⠛⣦⠀⠀⠀⡆⢃⠐⢂⠉⠀⡀⠉⠁⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡤⠀⠀⠀⠀⠀⣈⢠⠄⡀⠈⠃⠀⠂⠐⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠉⡶⠟⠀⠦⠀⠀⠀⠀⠘⠀⢀⡁⠀⠀⢃⠀⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠘⠈⡀⡈⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠁⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐



⠀⠀⡀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⠿⠻⣿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣼⣾⣾⣿⣿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡄⠀⠀⢠⠘⣿⣿⣜⣿⣿⣿⣿⣽⣿⡻⠛⠙⠃⠐⡀⠁⢀⠻⠞⠛⠓⢤⡤⢴⣶⠶⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄⢹⡇⣭⡇⠐⠀⠈⣿⣿⣿⣯⣻⣿⣙⣍⠑⠀⡥⠀⣃⠀⢁⣜⠻⢀⡲⠍⠉⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠙⣿⣇⣎⠁⡃⣄⣾⣿⣿⣿⣿⣿⣿⣷⠷⣶⣤⠰⠀⢁⡄⢀⠈⠀⠢⠀⠀⠲⠔⠾⡥⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⢠⡌⢿⣷⡿⣦⣐⣾⣻⣿⣿⣿⣿⣿⣿⣯⢻⣯⣿⣷⠂⠈⠱⣿⣶⡤⣤⡀⠈⡀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣉⢓⣵⡿⠇⠀⡀⠀⠋⠉⢈⡡⠀⣤⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⠿⣿⡿⣿⢿⣻⠿⠿⢿⠛⠛⢻⣟⢛⡻⠀⠙⣽⢇⡤⠀⡀⠐⠀⢀⡀⢄⡐⠋⠀⠀⢀⠠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠞⠠⢶⠈⣧⣠⠞⣫⡞⢧⠌⢥⠴⠋⢰⡾⣯⢉⣽⠿⠃⡀⢈⠀⠁⠀⠀⠀⠀⢠⣶⣤⢰⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡤⠤⠀⡔⠆⢹⢡⡄⢀⡆⠘⠀⢻⣘⠀⣿⠁⠀⠀⠐⠋⠀⠀⠀⠠⡤⠎⡈⠻⢠⡄⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣄⠀⢓⠛⡆⠡⠶⣬⠉⢥⠘⢁⡞⠀⠘⣷⠛⠻⠷⠖⠶⠶⢂⣴⣿⣿⡞⠀⣤⡛⠀⠀⠙⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠘⠖⠋⠀⢤⣸⠂⠈⠲⣎⠀⢀⢰⣉⠻⣿⣶⣦⣴⣿⣿⡏⠉⠉⠁⠺⡿⠛⠀⠀⢰⡆⠀⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠲⠀⠀⣴⠄⠠⢤⠀⠛⠸⠁⢉⠀⣾⢁⠹⣿⣏⢡⣉⠀⠀⠀⢠⣤⣀⡀⣴⣦⢈⡗⠀⡶⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣠⠀⢠⠼⠀⠀⠖⢣⠀⢤⡀⢻⣄⠉⠘⢷⣿⠻⢧⣶⣾⡿⠟⠛⠛⠁⠠⣿⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠢⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠎⢗⠸⢸⡆⠀⣦⠏⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⢻⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⢆⢠⠘⠀⣿⣆⠸⡆⠀⢿⡤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠋⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⢖⣐⠒⢶⠴⠦⣴⣤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣔⣂⠉⠡⠠⡔⠐⣾⣃⣖⠻⡈⡴⠙⠉⠸⢦⠰⠔⢊
⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⣀⣠⣤⠐⠞⢦⢃⣛⢂⠱⡝⣰⠂⠐⠀⠀⠀⠀⣴⠇⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢁⠈⡻⢿⣿⣦⡈⠁⢼⢋⡙⠳⢭⣼⡉⡥⠄⠀⠀⠉⠱⣿⣙⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠶⠉⠓⢦⣌⠙⢦⡘⢠⣽⠀⣤⡛⢠⡥⠰⠀⡷⠀⡀⠈⠉⣷⡌⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠁⡀⢡⠀⡙⠷⠸⡀⢠⡄⠀⠼⠁⣶⠀⣀⡘⣛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢻⡄⣄⠛⠆⠈⢃⣌⠃⢁⣰⠶⡀⠈⢥⡀⡍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣾⣧⠈⣼⡇⠀⢿⣿⣶⣌⢂⣀⢀⣀⣬⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⣼⣿⡿⢨⠜⡇⢀⣾⠻⠟⠋⢠⣤⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣥⣾⠟⠁⡠⠒⠁⠘⠏⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠎⠀⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⣄⢠⡠⢄⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⡀⡄⡀⡀⠀⠀⠀⡀⢠⣤⠤⣠⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣩⣻⢧⢁⡄⡇⠰⡝⡀⡣⠳⢄⣰⡧⢻⠈⡣⢖⡲⣧⠝⣊⠥⠵⠀⠄⠒⠡⠜⢰⣟⠿⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠜⣳⠣⢔⡋⣨⠝⣋⢕⢶⢳⢷⢏⢿⢤⣆⣓⡂⠆⠣⠸⠐⠀⢀⠆⡅⡁⠀⠀⠀⠈⠡⢡⠁⢀⠂⠎⣠⣄
⠀⠀⠀⠀⠀⠀⠀⡈⢂⠑⠰⠪⠄⠃⣛⠼⡂⠘⠫⠘⣌⠐⡏⢫⠙⡔⢪⠁⠦⢀⣂⠀⢦⠐⢰⡀⠀⠀⠀⠢⢀⡀⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠮⣰⡀⡔⠚⣸⠒⡀⠧⠌⠀⢰⠣⠠⠠⢐⡤⢂⠡⢥⠀⢈⡰⠔⠀⢂⠐⣎⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣤⡀⠀⠛
⠀⠀⠀⠀⠀⠀⢸⢩⣹⣅⣁⡧⢠⠄⣑⢒⣓⢨⢀⣌⠡⢥⢀⡑⡩⢘⠊⠨⠠⢄⣜⠀⣢⠖⠚⠀⡂⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⣐⢦⣻⢻⣝⠃⠄⠦⣭⡤⣭⣁⠘⠛⠀⠆⡂⣶⢱⡋⢶⣏⢐⣖⠇⡠⣌⠢⠀⠀⠠⠂
⠀⠀⠀⠀⠀⢀⡿⣿⠇⠘⠿⣿⣘⣄⣒⢹⣠⡝⠀⠀⠀⠂⠐⠋⠚⠃⠺⠉⠃⠿⠥⣄⠠⠁⠀⠀⠁
⠀⠀⠀⠀⠀⣸⣶⡏⠀⠀⢒⣤⠟⢻⡽⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠮⠪⢠⡁
⠀⠀⠀⠀⠠⣿⡛⠀⠀⠀⠈⠁⠙⠩⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠒⡀⡞⣚
⠀⠀⠀⣠⣝⠞⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠅⠁⣌⠂
⠀⠀⣠⣝⡿⠁⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢀⡀⠄
⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⣖⡖⢴⣚⢿⣈⢿⣗⡻⣛⣆⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⢬⠱⢏⣩⣸⣰⢰⡋⢫⡖⢪⢜⠳⠞⣨⣿⣛⣃⣤⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡾⢷⠷⢿⣌⡶⠮⣇⣹⠚⢇⣍⠻⠋⡏⣈⡾⢎⢃⢠⣓⣛⣝⢻⠦⡖⠷⡯⠥⡄
⠀⠀⠀⠀⠀⠀⣎⡾⡞⢚⣬⢸⢍⠳⣱⢌⠓⣞⡨⠸⣧⣉⠸⢎⣋⡙⡿⢸⠹⢋⣙⡌⠉⠛⢃⣾⠱⣆⣳⡀⡀⠀⣴
⠀⠀⠀⠀⠀⢀⣍⡿⣙⣭⡈⠜⡇⠷⡜⢸⢣⢍⢁⢧⣄⡏⢇⡟⢨⣴⠚⠣⢗⣋⠡⠄⢸⠸⠳⢹⡗⡯⣯⡤⡿⣛⡿
⠀⠀⠀⠀⠀⠐⣭⢿⣛⣧⠷⣋⠓⠱⣹⣃⡼⠪⣜⢳⡜⠧⠃⢇⣾⣍⡀⣶⡈⢄⠰⢂⠊⣀⠌⢹⠾⠆⠚⢽⢁⡀
⠀⠀⠀⠀⠀⣸⣏⠓⣏⡛⠓⣭⠸⠗⣙⢸⢝⡍⣓⠏⣼⠲⡛⣮⡄⢲⣏⠁⡍⠆⠀⡐⢣⡴⠒⡋⠬⠭⠒⠇⢠⡄
⠀⠀⠀⠀⠀⣘⠿⣤⣝⡟⡿⢨⠲⠜⡸⠚⠇⣡⣖⠋⢇⣯⡦⠎⠏⢃⡘⠛⡢⢈⢲⣧⠌⣰⣧⡄⠂⠋⠀⣌⣥⠳
⠀⠀⠀⠀⣬⣭⠺⠃⢀⣶⣡⡎⡣⢯⡷⣿⣥⠍⠉⠤⠈⠷⠶⠀⡟⠊⡯⠥⡆⠔⠀⣷⡦⠀⠈⠁⠀⠀⠰⢁⠉
⠀⠀⣤⡿⣦⠍⠀⠀⠀⠙⣭⡳⢿⣮⡝⠊⠭⡚⠃⠀⠀⠀⠈⠉⠀⢀⠶⢥⢥⠀⠁⠀⠙
⣼⣿⡿⠋⠁⠀⠀⠀⠀⡿⠟⢻⣶⣩⢈⠻⢿⠛⠀⠀⠀⠀⠀⠀⠀⠯⠞⠒⣌⠧⡓⠶⠷⣆⠀⠐⠤⠀⠂
⢾⣿⡷⠀⠀⠀⠀⠀⠀⣴⡟⢷⡌⢥⣼⣣⣌⠃⠀⠀⠀⠀⠀⠀⠀⠒⠑⢭⠼⡍⠁⠀⠐⢮⣥⠤⡄
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠟⠶⣡⠆⠐⢂⠥⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠲⠐⡆⠀⠀⠰⣶⣬⣭⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠩⢄⠀⠀⢤⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠪⡟⣨⠥⠂⠀⢰⡄⠦⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⡀⠙⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⢦⠔⠢⠄⠈⠑⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⡀⠁⠀⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⡀⢀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣆⣴⣦⣡⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣛⣛⣝⣛⣟⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣀⣄⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣾⣿⣿⣿⣷⡄⣀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⡌⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⣿⣿⣿⡿⣿⣿⣿⣿⠰⠀⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢶⣿⣿⠀⠐⣦⡿⢿⡏⢻⣉⣿⣿⣿⠀⢩⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⢿⣃⣾⣿⡷⠀⠰⣿⣿⣿⣿⣎⣿⣸⣿⣿⡄⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢶⣄⡀⣀⣤⢾⣿⣫⣾⡿⢳⣬⣛⢿⣍⠻⠀⠀⠈⢛⣹⣿⣿⣿⡿⣿⣿⡇⢀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢿⣾⣿⢿⡿⣿⣿⣻⣿⣬⣽⣾⡻⢿⣜⣿⣷⣀⠀⢀⠀⠧⣉⢿⡿⠷⣿⣿⡇⢨⡄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⣧⡼⣿⡾⣻⣿⣿⣿⣯⡿⢇⣼⣻⣟⣹⣿⡷⠻⢾⡆⢌⣉⠙⠒⠛⠻⠗⢨⣵⡘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡿⣣⣴⠏⣡⣶⠘⢿⣿⣿⣿⣿⣷⣶⣶⣯⠽⣿⣿⠺⣿⣶⠄⢠⣝⡓⠀⢤⡀⠆⡛⠛⢃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⣿⠟⣰⠟⠁⣼⣿⢳⣿⣶⣀⣽⣃⣍⢻⣿⣿⡿⢀⣿⣿⠐⣤⣿⣷⣦⣉⠛⠘⣷⣿⡀⢬⡍⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⣿⣿⣴⡏⠶⢠⣿⡏⡿⣿⣿⣿⣿⣽⣿⣦⣩⣥⣴⣿⣿⣶⣆⢿⣿⣿⣿⣿⡆⠀⢹⣿⣿⡄⠙⠂⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⢿⣿⣿⡟⢰⡆⠋⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢿⣿⣿⣿⣿⠦⣼⣿⣿⣿⣾⣷⡀⢷⡘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⣿⣿⣏⡀⣿⠀⠀⠀⣼⣿⣿⠾⣿⢯⣿⣿⣿⣿⢉⣈⣿⣿⣿⣿⣿⡦⢉⡛⠻⠟⠀⠈⠻⢿⣿⣿⣿⣷⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⡛⣹⢠⣋⢡⣿⣀⠀⣘⣿⡿⣿⣶⢿⣘⣿⣿⣿⣿⠐⠁⣴⣬⣩⣿⣯⣵⣿⣯⣄⢾⣿⣿⣷⡄⢿⣿⣧⡁⠀⣘⢧⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠂⠀⢉⣩⣾⠿⢀⣼⣿⠞⠋⣠⣾⣿⣿⣿⡟⠁⠀⠀⠙⢋⣀⠀⢿⣿⣿⣿⣿⡄⣿⣿⣿⡿⠀⠙⠋⠀⢸⡟⠀⠛⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠟⠛⢱⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⠂⠀⢰⣶⣿⡖⣿⣿⠇⣀⣉⣙⠿⠇⠀⠙⣿⣿⠇⠀⣴⣶⣶⣼⢇⣀⠈⠃⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠺⠟⣻⣟⣿⣿⣟⣿⠟⣿⣟⠉⠉⠻⣿⡆⠀⣀⣀⣀⡉⣼⣿⣿⣿⠇⠀⠲⣶⡄⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢈⣧⡛⢹⣿⣯⣼⢷⣌⠉⠾⢿⠶⠀⠸⢿⢿⣿⠿⠇⠻⣿⣿⣟⣀⠀⠀⢈⣁⣴⣦⡿⠿⣿⣿⣿⣿⣿⡇⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣼⣿⡇⠈⠻⢿⣿⣆⠙⠻⠷⢶⣦⣴⣶⠀⣾⡉⣰⣦⠘⢿⣿⣿⣿⡿⠂⣸⣿⣿⣿⠀⠀⢊⣿⣿⣿⣿⠆⢀⠃
⠀⠀⠀⠀⠀⢀⠎⠚⠀⠀⠀⠀⢀⣽⣾⣯⣬⡭⠖⣸⣿⠛⠻⠷⢶⡶⠀⣙⢻⣄⣿⣿⠙⢿⣿⡷⠙⠛⠋⠀⣀⡼⠿⠿⠿⠃⠰⣿⣿⣿⣿⠟⢀⡎
⠀⠀⠀⠀⠀⡾⣤⢞⣥⣤⣄⠀⣼⣿⠉⠋⠙⠻⠟⠛⣋⣠⣤⠔⠛⢙⣦⣿⣯⡉⠉⠛⠃⢀⣤⣶⠄⣀⣴⡾⠛⣀⣴⣶⣦⡀⢀⣀⡀⠈⠁⢀⠎
⠀⠀⠀⠀⢠⣄⣡⡾⢡⣶⣿⣿⣿⠃⠀⠶⠆⠸⠟⠀⠋⢁⣤⡴⠾⢛⣿⣿⣿⣿⣦⡀⢀⣼⠍⣰⣿⠋⠡⣶⣿⣿⣿⣿⣿⣵⣿⣿⠇⢀⡴⠋
⠀⠀⠀⠀⠀⢯⣻⣅⠘⠿⣿⡟⠁⢀⣄⣀⣠⣤⡴⠾⠟⢉⣡⡤⣾⣿⣿⣿⣿⣿⣿⣧⡄⠀⣤⣿⠁⠴⠶⡀⠘⣿⣿⣿⣿⠿⠥⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⠀⠀⠈⠱⢌⡀⣠⣤⠰⠿⢋⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⠇⠀⠀⣠⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⡆⠈⢻⡇⠐⠺⠗⠺⠘⣋⣨⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣾⣿⣷⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣿⣦⣤⣄⣂⣉⣉⡍⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣏⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⢫⣿⣿⣿⣿⢿⡅⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠞⢹⡟⢿⣍⡁⣭⢠⣏⠐⠢⢿⡿⠿⠟⣣⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠻⣦⣉⠁⠙⠂⠁⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⠙⠒⠀⢀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣄⡀⠀⠀⠀⣀⢐⣾⢩⣴⣶⠔⢞⢺⡋⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣄⠉⡗⠾⠃⠤⣤⣶⣾⡟⠻⡛⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆⠀⠘⠛⠈⠋⣸⡷⣀⣺⣧⠠⠶⡂⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠻⣿⣇⠀⠀⠀⣠⠄⢉⡌⠙⠟⢰⡶⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠛⠀⠀⣨⠉⣠⠉⠰⠀⠴⠶⠗⠠⣶⡇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢡⠆⠛⠀⠉⠀⢰⣿⠟⠀⢙⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣅⠴⢂⣄⢸⡿⡶⣚⣠⣀⠰⠖⢨⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢈⡇⠀⠙⢛⣄⡀⣶⡍⣿⣿⠘⣿⠄⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⢁⡄⣠⣤⣤⠾⣈⣛⣈⣛⠸⠇⠀⢸⣧⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢳⡟⠁⢸⡿⢃⣽⣏⢷⣈⢉⣷⠀⠀⠙⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠘⠃⠸⠃⢈⠛⠉⠀⠍⠉⢉⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⢻⡆⢀⠈⠘⠋⠸⠖⠠⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⡐⠃⣤⠄⠂⣸⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣷⣄⢈⣻⣟⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠈⠛⠈⠛⠁⠀⠀⠚⠀⡤⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠘⠧⣤⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⣱⣶⠆⠀⠞⢀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢴⣶⠋⠉⠀⠀⢼⡿⣀⠀⢣⡐⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠈⠛⠶⣤⣄⠀⠀⠀⠙⠀⠀⠹⣦⣀⣀⣀⣠⠤⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣃⡂⠀⠀⠀⠀⠙⣷⣦⣤⣤⣴⣿⣶⣄⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠀⣀⡀⠀⠐⠨⣛⡛⠛⠻⠿⠿⠛⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠰⣤⣄⠙⠋⠀⠀⠀⠀⠉⠑⠲⡄⠀⠀⠈⠉⠛⠛⠃⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠀⠙⠛⠃⠀⠛⠻⢶⠦⣤⣤⣤⠀⠀⠙⠦⢀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣴⣿⣷⣦⣀⣀⡀⠀⠀⠰⠶⠶⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠆⢀⣀⣤⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠷
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣤⣴⠶⠀⣼⡛⣿⣳⠶⡦⠠⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⡀⠀⢀
⠀⠀⠀⠀⠀⠛⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⡉⠉⣩⣥⡶⠶⠃⠈⣁⡍⠡⠆⣤⠌⠉⣉⡑⠶⡄⠀⠀⠀⢀⣠⠀⠀⠀⣡⣴⣶⣷⠀⠀⡟
⠀⠀⠀⠀⠀⠙⠀⠈⠻⣿⣦⣄⠀⠀⣶⡄⡀⢀⣿⣿⣿⠏⣠⣭⠟⠀⠰⡿⠃⣉⣠⠶⣌⢷⡄⢶⣏⠁⠆⠰⣿⠿⠶⠀⠀⡈⢠⣶⠆⣋⣩⠅⠀⣠⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠁⠈⠙⠿⢷⠆⠛⠁⣿⠀⠟⡉⠾⢋⡼⠃⣾⠟⣠⣤⠈⠻⠉⢘⡇⠸⠃⣠⠄⠀⠈⠻⠶⠁⡀⣠⣠⠀⠠⣥⣴⣿⣁⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠳⡀⠄⢀⠁⠐⣁⠀⠀⣀⣤⣶⣎⣁⠀⢨⡿⠣⠄⠘⠛⣧⡴⠆⠀⠿⠛⣦⠘⣃⠲⠆⠈⠛⠷⠠⣄⠙⢿⡀⠘⢾⣿⣿⠉⠻⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠷⢠⣶⣿⣷⡇⣸⡿⠛⠋⣻⡿⢰⡿⢃⣴⣶⠆⠾⡋⠀⢰⡶⢀⣛⣩⣬⣬⠛⣃⠘⠿⠀⢶⣄⣙⠆⢉⡢⡀⠉⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⣿⣿⠿⠇⠀⢂⣸⡏⠷⣠⡄⠈⠋⠁⣴⢾⣿⠆⠀⣄⠛⠁⢩⡜⣀⡶⠈⡁⠸⣷⠘⣇⣭⣰⣮⠳⠄⢷⢾⠆
⠀⠀⠀⠀⠀⠀⣠⡀⢰⣷⠄⣻⠷⠀⡄⠀⠋⣩⠄⣴⠿⠃⣰⣿⣤⡿⠘⣿⡀⠘⢿⣦⣀⠀⠓⠉⢷⡄⢀⣾⡟⠀⢏⠀⣛⠉⠀⣄⣬⣀⣄
⠀⠀⠀⠀⣠⠞⣿⠇⠘⠃⠀⠀⠀⠀⣼⡿⠁⢠⡀⢠⣤⡏⣀⣀⣤⢤⣄⣸⠁⠰⣬⠙⢣⣤⠛⠙⠚⠃⣈⠛⡺⠶⠾⠉⣉⠇⢉⡀⣹⣏⠘
⠀⢀⡤⢀⡁⢠⡿⠀⠀⣶⡄⠠⠀⢁⣨⡅⣴⣿⣿⠟⣃⠉⠉⠻⣄⣋⣩⣿⡇⠀⠀⠀⠀⠉⠀⠂⠐⠀⠃⠠⠉⢀⣿⠛⢁⣤⠋⢠⡌⠙⠋
⠀⣋⠀⣿⣧⡾⠃⢀⣷⠙⡁⠀⡀⣿⣿⠁⠀⠙⠛⠀⣿⡀⠙⠖⠀⠈⠉⠉⢱⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠈⣅⣸⠴⠁⡀⢲
⢘⣿⠀⠸⠟⠀⠀⠘⣯⣀⡇⠀⠁⠛⠁⣤⣶⡀⢀⡀⢹⣟⠶⠚⢃⡌⠰⠀⠈⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠲⣌⢁⣴⠀⠃⠈
⠛⠃⠀⠀⣀⠀⢻⡄⠀⣿⡁⠀⠁⢰⡆⠻⠟⠃⠘⠃⠀⠉⢶⠤⡶⠱⠚⠀⠠⡀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠈⣤⣀⡾
⠀⢼⣿⠆⢻⡇⠀⠁⠀⠈⠀⡀⠀⢿⡗⠀⠀⠀⢴⣦⡀⢀⣀⡀⢀⡀⢃⣀⡒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠱⡇
⡆⠈⢁⠀⢸⡇⠘⢷⣦⠀⢸⡇⡴⠈⠀⠀⠀⣶⣌⠙⢁⠀⠉⠁⠈⡰⠈⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⣀⣀⡀⠀⠀⠀⢀⣴
⠃⠀⣿⣷⠘⠃⣀⠀⠈⢣⡀⣧⠀⢀⠀⢾⣧⠙⢿⡆⠘⠇⠀⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⠀⠀⢰⣿⠟⠁⠀⠀⠠⠘⠁
⡿⠀⠈⠁⠀⠀⢻⡄⢠⡀⠃⠀⠀⠘⢷⠀⠙⠓⠀⠀⠈⠶⡆⠀⠀⢀⠆⡀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠡⠄⡠⠈⠀⠀⠀⠀⠤⠤
⠃⠀⣤⡄⢀⣀⠀⢳⣌⠃⠀⠰⣄⠀⡀⠀⠑⠆⠀⠀⣤⣤⣼⡀⠀⠀⢸⣥⣈⢀⠉⣈⠁⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠐
⠀⠘⣿⡏⠙⠿⢷⣄⠙⢷⣤⣤⣜⠁⠀⠠⣄⡠⢀⠀⠙⣿⣿⠷⠀⠘⣿⣿⣿⣿⣤⣉⠀⠁⠀⠀⠀⣠⣾⡷⠄⡀⠀⠀⠀⢺⡏
⢶⣄⡈⠉⠀⠀⠤⠉⢁⣀⠉⠛⠿⠶⠂⠀⠈⠙⠋⠀⡀⠤⠄⠰⠒⠒⠆⠈⢿⣿⣿⣿⣀⠄⠀⠀⢠⡍⠛⠀⠀⡈⠛⠲⠐⠋
⠀⠙⢷⡄⠻⣿⣶⣄⠘⠿⠷⠀⢤⣄⠀⠀⣴⣷⣦⣌⣛⡃⠀⠻⠾⣶⣤⠀⠛⠿⣷⡆⠉⠀⠀⠐⠃⠀⢉⠖⠀⠤
⠀⢦⠈⠁⣄⠈⠉⠉⠁⠀⠀⠀⠀⠙⢳⣤⡙⠿⣿⣿⣿⣿⣶⣶⣦⣄⣀⣀⣀⣀⡄
⠄⠀⠰⣦⠻⠷⠀⢲⣦⣄⢠⣤⣤⣄⡈⠙⠛⠃⠈⣉⣉⠛⠛⠛⠛⠉⢙⡛⠛⠛⠿⢿⣷⣤⣀
⠹⣶⣦⠉⠁⠀⠀⠀⣿⡏⠀⠉⠉⠙⠋⠀⠶⣶⣶⣿⠛⠠⣶⣶⣤⠄⣤⣴⣤⡄⣀⣀⣀⠀⠙
⣤⡈⠻⣷⣶⣤⣿⣷⡈⠻⣿⣶⣴⣿⣦⠀⢠⣤⣤⡀⠀⠘⠊⢉⡙⠂⠉⠁⣀⠀⠉⠙⠛⠛⠷⠶⠄
⣿⡿⠦⢀⡉⠙⠛⠿⠇⢀⣈⣉⣉⠛⠋⠀⠀⡹⢿⣿⣷⡀⠰⣿⣿⣷⠀⢸⣿⣦⣷⣾⣶⡦⢤⣤⣄⡀
⠈⠿⠀⠈⠻⣿⣶⣄⡀⠘⣿⣿⣿⠀⣷⢄⣿⣿⣦⠉⠉⢰⣤⣬⣛⣋⠀⠠⠙⠛⠻⠟⠛⠀⠀⠈⠙⠛⠓
⢸⣆⠘⢷⣤⡀⠈⣙⠻⢀⣈⡛⠛⢰⣶⣾⠿⡿⠇⠀⢠⣴⣯⣽⡛⠛⠀⠀⢀⠀⠀⢀⠀⠰⣿⣿⣷⠄
⣈⡻⣷⠀⠙⠻⢶⣬⣇⣀⠙⠿⣦⣄⠉⠉⢀⣤⣤⣄⠀⠉⠛⠿⠿⠀⠀⠛⠿⠿⠘⠿⣿⣶⡦⠀⢀⣀⣀⣀⣀
⢿⣿⣦⡀⠀⣀⡀⠈⠙⢿⣷⣄⠹⣿⣷⠀⠈⢻⣿⣿⠇⢀⡀⠀⠀⢀⡀⠀⢾⣷⣦⠀⠀⠀⠀⠀⠐⠛⠻⠿⠟⠻⠖
⣀⠉⠉⢁⡀⠻⣿⣷⣤⡀⠈⠁⢀⣄⡁⠀⠀⠀⠈⠁⠀⠻⣿⡿⣿⣿⣿⠆⠀⠉⠋⠀⠀⠀⠀⣴⣶⣶⣶⡄⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠘⠓⠀⠈⠻⠦⠈⠛⠻⠿⠆⠀⠻⣿⣿⣄⠀⠸⢿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠈⢉⣭⣉⡁⠀⠀⠠⡶⠶⢿⣟⡀⠀⠰⠆⠀⢺⣿⣷⠀⢠⣶⣤
⣰⣶⣦⣄⡀⠀⠻⣦⡀⠀⣤⣤⣀⠀⠙⢿⣿⣶⡀⠉⠛⠃⠀⠀⠀⣤⣴⣶⣶⡄⠈⠙⠿⠛⣀⣤⣈⡙⠋⠁⠀⠀⠀⢴⣶⡿⠟⠁⠀⠲⠆⠀⢈⣙⡉⠀⠈⠛⠋
⠙⠿⠻⠿⠿⠂⠀⠘⣿⣦⡀⠙⠻⢿⣶⣄⠈⠉⠁⠀⠀⠀⠀⣴⣶⣌⡛⠛⠛⠁⠀⠀⠀⠀⠛⠛⠻⠋⠀⠀⠀⢀⣀⣠⣥⣦⠀⠀⠀⠀⢀⣴⣿⣿⣿⡆
⢰⣦⣤⣀⠀⠀⠀⠀⠀⠙⠻⢶⣄⠲⣬⣍⠀⠀⢰⣶⣦⣤⣀⠈⠻⢿⣿⡦⠀⢶⣿⣿⡿⠂⠀⠀⣀⣀⡀⠀⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁
⠹⣿⣿⣿⣿⣦⣄⠀⠀⠐⣦⣤⣤⣀⡀⠉⠀⠀⠻⢿⡿⠿⠿⢿⣶⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠛⠛⠁⠀⠈⠉⠙⠋⢁⣀⣀⠀⠀⠀⠀⠈⠛⠋
⠀⢤⣭⣉⡛⠛⠛⢃⠀⠀⠈⠙⠿⣿⣿⣷⣆⠀⠀⢠⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠙⠛⠿⡿⢿⣿⣷⣄⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣦⣦⣤⣤⣤⣴⣶⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣟⣭⣿⣻⣿⣽⡟⣿⣿⣛⣉⠉⠀⠀⠀⠀⠀⠠⢾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣴⢞⣻⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠙⠛⠿⠯⣭⡉⠀⠀⠀⠘⠃⢼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⣱⠟⢻⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⣽⢿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠀⠀⠐⣿⣽⣷⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠧⠀⠂⠀⠀⠀⠀⠹⣻⣧⣙⣿⣟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⣹⠀⠀⠀⢀⣴⡖⣻⣿⣷⣶⣶⣶⣿⣿⣧⡾⠀⠀⠀⠀⠀⠀⠀⠀⠩⡟⣿⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡤⠖⠁⠀⢀⡴⠋⢀⡰⣿⣽⣙⠿⠟⠲⣻⣿⣏⠻⠢⠄⠀⡀⠀⠀⠀⠀⣠⡇⡈⣻⣻⡡⣿⠂
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠀⠀⢀⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⢡⠀⠀⠀⠀⠀⠀⠹⣦⣉⣠⣤⠟
⠀⠀⠀⠀⠀⢸⣿⣿⣇⣠⣴⢧⣤⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣆
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⡞⠡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠗⡧⠄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⣻⣿⣿⣿⠿⠿⠟⢿⣿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣯⣉⣛⣷⡦⡤⠄⠀⠀⠀⠀⡼⠁⣸⣿⡿⠋⠀⠀⠀⠀⠉⢿⡿⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢤⡤⠞⢀⠒⠉⠘⠃⠀⠀⠀⠀⠀⠀⠈⡁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⣰⡾⢷⢶⣤⣄⡀⠀⠀⢀⣠⣤⣶⣿⡛⠙⣳⠄⠠⣞⠋⢛⣿⣶⣤⣄⡀⠀⠀⢀⣀⣤⡶⡶⢷⣆
⠀⠀⠀⢻⡄⠀⠉⠢⣍⠛⠳⠞⠛⡉⠔⣂⠀⢛⣀⠈⡀⢀⠁⣀⡛⠀⣐⠢⢉⠛⠳⠞⠛⣩⠔⠉⠀⢠⡟
⠀⠀⠀⠘⣷⡀⠀⠠⢾⠁⠼⠥⠘⣡⠈⢱⡆⡉⢁⠘⠥⠬⠃⡈⢉⢰⡎⠁⣌⠃⠬⠧⠈⡷⠄⠀⢀⣾⠃
⠀⠀⠀⠀⠘⣷⡀⠀⢉⠃⠔⡀⡻⠇⠸⠟⣀⠉⠻⠄⣄⣠⠠⠟⠉⣀⠛⠇⠸⢟⢀⠢⠘⡉⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠘⢷⡀⠘⠁⠞⠜⠱⣶⡖⠂⢌⡀⠀⠒⠊⠑⠒⠀⢀⡡⠐⢲⣶⢎⠣⠳⠈⠃⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠈⣿⠘⢃⣶⠄⣉⢀⡁⠀⠈⠛⠒⠀⠀⠀⠀⠒⠛⠁⠀⢈⡀⣉⠠⣶⡘⠃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠘⠈⠁⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠉⠁⠃⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣴⣇⠀⠋⠀⢀⠑⠂⠀⠸⡀⠈⠉⠉⠁⢀⠇⠀⠐⠊⡀⠀⠙⠀⣼⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡻⢧⡀⠀⠢⣅⡀⠀⠀⠈⢆⠀⠀⡰⠁⠀⠀⢀⣨⠔⠀⢀⡼⢟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⠃⠃⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⠀⡚⠘⣣⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠰⡖⠆⠐⠒⠉⠡⠌⠉⠒⠂⠰⣶⠆⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠙⣆⡀⠀⠀⠀⠀⠀⠀⢀⣰⠃⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣹⣿⣄⠀⠀⠀⠀⣰⣿⣇⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⡟⠈⠉⠈⠀⠉⠁⢻⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⠀⠀⠀⠀⠀⠀⠘⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢷⣤⡀⢀⠀⢀⣤⡾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⣾⢟⣨⢻⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣼⢿⢶⣽⠻⣀⢊⣓⡙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣏⣭⡀⢶⠗⡄⡀⠐⢙⣁⣘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⢿⡽⡏⠞⣭⡜⢠⠒⠄⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠻⣮⣥⣛⡌⠶⢐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡌⣭⣛⣷⣽⣷⢓⣈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣶⡕⢸⣮⣡⡤⣾⠰⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⣴⣶⠩⢿⡗⡒⢛⠳⠆⡙⠎⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⣽⣦⠸⢆⠾⠢⠶⠈⠿⢳⣿⣤⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢻⣭⠷⠼⠜⣧⡄⠾⢇⡿⢪⡴⡿⣴⣏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⢋⡛⣥⠺⣃⣣⡎⠸⠇⣹⢟⣸⣷⢾⢶⠎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣛⣙⠣⠾⣽⢃⣍⡙⡃⢂⢩⡌⣮⢹⣖⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣬⡏⣭⣔⡞⣭⡌⡑⢠⠉⡍⣾⣳⡏⢂⢎⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢾⢮⣟⢓⠰⡎⣍⣾⣵⡇⢺⡶⡓⠅⣋⣬⣉⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢺⢞⣉⡿⠿⠋⡂⢼⠍⡿⠂⣿⣍⠶⡛⠱⢬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠿⣹⠏⣭⡩⢷⣏⡛⣘⢋⡿⣀⠇⣨⠭⣻⠹⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡙⡟⣍⢻⢩⣼⣒⠎⠃⣩⠮⡄⣿⠀⠠⢐⡳⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣋⣏⠱⢉⡕⢇⠿⣡⠛⣶⣛⡸⠃⠀⠀⠥⣐⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢠⣄⣰⢘⠣⢜⣃⡛⣤⠛⣁⠠⢄⡀⠢⠎⠽⡂⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢾⡇⡎⢁⡘⣐⠎⢿⢧⠻⢵⡀⡄⠱⠇⠈⠓⠶⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠾⣲⠀⠓⠉⠈⠀⠀⠀⠀⠀⠀⣴⣆⣝⣓⡱⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⠧⡆⠀⠀⠀⠀⠀⠀⠀⠀⣟⢾⣽⠑⠛⠳⣩⣔⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⠶⢥⣀⠀⠀⠀⠀⠀⠀⢯⣿⣷⠀⠀⠀⣭⣛⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⣛⣽⣴⠀⠀⠀⠀⠀⠈⠊⠉⠀⣠⠘⣧⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠷⠞⣞⣭⣶⠝⣶⢰⡆⣔⢮⣟⢋⡬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠫⠿⠗⠿⠋⠽⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠉⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠄⣀⣤⠆⠀⠰⠶⠀⡀⢠⡀⠀⠀⠀⡀⠈⠀⠉⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡄⠉⠀⡀⠘⠛⢣⡤⠉⠠⠡⢤⡄⠐⠻⢿⢿⣷⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢲⣤⣄⠀⠁⠘⠑⢏⡉⢚⣥⠶⣀⡘⠀⢑⠘⠦⠀⡠⠀⠘⠛⢏⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⠺⣟⠉⠉⠈⠁⠀⠶⣉⣤⠀⢀⡈⠙⣋⣤⠀⠀⢂⣰⠀⠀⢻⠂⠉⣧
⠀⠀⠀⠀⠀⠀⠀⢴⠞⠁⢱⠀⠃⠀⠀⠀⠐⠋⠀⠉⣉⡀⣠⢀⡠⢩⡄⢳⡈⡁⢁⠈⠀⣪⢃⠙⣿
⠀⠀⠀⠀⠀⠀⠀⣶⠄⢠⠀⠉⠀⠀⣤⠀⠀⢠⠆⢘⡋⠀⠁⠉⠁⠘⠃⠈⠙⠛⠆⠰⠛⠁⠈⠉⠜⢦
⠀⠀⠀⠀⠀⠀⠀⠛⠀⡿⠀⠀⠀⠘⠏⠀⠀⠀⢠⣬⠁⠒⣶⢀⡀⢦⡄⠈⠃⠂⠄⠀⠀⠜⠁⠀⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⡿⠀⠀⣴⣷⠆⠘⠃⢈⡁⠈⠢⠀⣼⠷⠀⠀⠀⠀⠀⠀⠀⢘⢂⡿⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⡀⢰⣆⢠⡌⠁⢠⠀⡄⠙⡵⠖⢀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣸⠛⠚⠋⠀⠁⣠⣄⠀⡀⠀⠤⠀⡀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢆⠂⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠶⠀⠉⠋⠀⠁⠙⠀⠅⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠸⢿⡆⠙⠛⠛⠀⠀⣄⠲⠀⠀⠀⠀⠀⠀⢠⡀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⣿⡆⠀⢀⣀⣀⠈⠓⠀⠀⠀⢠⡈⠁⠂⠐⠀⠀⠙⠿⢛⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠇⠀⠁⠀⠈⠙⣿⣶⡄⠀⠀⢿⠶⢤⣀⢁⡉⡘⠀⠀⠀⠀⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠈⠑⠶⢶⣄⡀⠱⠦⠼⠶⠶⡄⠀⠀⢀⣠⣦⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠙⠋⠀⠀⠀⠁⠀⠀⠠⠛⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⡄⠁⠀⠀⡀⠤⠀⠘
⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⡇⢀⣤⣆⠀⠀⢀⣰⣄⠠⡔⣆⣤
⠀⠀⠀⠀⠀⠀⢸⡿⠀⢠⠛⠘⢻⣿⣦⣠⠟⠋⢙⠂⢹⣿⣆
⠀⠀⠀⠀⠀⠀⢨⡗⠀⠈⠲⡄⠀⠉⠈⠃⠀⠀⣿⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠘⠃⢰⣆⢀⠙⠀⢀⣀⢀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⣘⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠿⠇⠙⠈⠻⠇⠉⠙
⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⣶⡄⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢰⡧⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠸⠟⠀⠁⠁⠀⠀⠀⠀⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⢄⣀⣄⢤⣀⣀⡀⢀⡀⠀⠀⢀⠀⡀⢀⣐⠂⢒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢚⡩⠆⠰⠘⠠⠦⡞⠞⠷⡚⡽⢨⠹⣐⢁⠱⠲⣒⢯⣩⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢛⡱⠎⡃⠾⡚⣈⢑⡗⠨⠁⡆⠔⡈⠂⣥⠈⠁⡁⣂⢠⠘⠃⢁⡤⠠⠀⠢⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣮⠃⡎⣰⡎⣿⠰⠆⡜⢱⠦⠁⠲⠠⠃⡄⠀⠡⢀⢐⠀⠂⠈⡉⢓⠁⠀⠀⠐
⠀⣠⣀⠀⠀⠀⠀⠀⡀⠉⠂⢒⡖⡶⠷⠰⠌⢿⡞⢡⠈⣥⠀⡁⢂⡌⢀⢐⢀⠰⠂⠌⢡⠀⠀⠀⢀⠆⠀⠩⠂
⣘⣛⣿⠀⠀⠀⠀⢀⠑⠀⢟⣬⠓⢠⠦⣇⢢⢸⣷⢈⠣⠄⣶⢙⠀⢄⠢⢨⠄⠆⡹⣠⠜⣆⠀⠀⠀⠀⠠
⢿⠏⣝⣡⡄⠀⢰⠹⠃⣩⠨⠡⠁⠦⠔⠦⣜⠲⡌⠐⠄⢦⠁⢠⠊⢀⡓⠆⢠⠐⡈⠠⠁⡀⠀⠀⠁⣤⣠⣦
⠀⠘⡿⢡⡶⣿⠳⠄⢨⡙⠆⠙⠂⠸⠞⢓⡠⠤⠀⠀⠀⠀⠀⠀⠀⠛⠱⡞⢀⡐⠠⠤⢄⡀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠈⠁⠀⠚⠀⠑⡉⠀⠀⠀⠐⢌⣬⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣕⢈⠁⣘⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠐⠒⡍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠼⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠠⠁

⠀⠀⠀⠀⠀⠀⡀⣤⣶⢾⢶⣶⠖⠎⣶⠖⡴⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⣠⣾⢿⣻⣛⡅⣿⣅⡂⣴⡿⣾⢃⡭⣶⣍⢻⡶⣦⣤⡴⣢⡤⣴⢲⣫⣄⡿⠿⠢⠜⣙⠾⣃⢯⡗⡸⢟⣷⣄
⠀⠀⠀⢀⠘⣡⣿⡝⡿⠟⣮⡿⣲⡽⠹⠆⠖⡂⢷⢨⡍⣷⣻⠾⣘⠳⢞⣱⢳⡏⣽⣯⡛⠧⠏⡿⡾⣩⣭⠺⠽⢣⣵⡌⢳⡄
⠀⠀⠀⠾⠴⠃⠀⢼⢒⣞⣛⠑⠋⢇⣣⣨⡬⠄⣎⠛⣵⣎⡽⣈⣽⢃⣓⣭⢩⣔⡓⢞⢱⡟⣶⣙⡁⡧⠞⣴⡓⠴⣯⢘⣛⣷
⠀⠀⠀⠀⠐⠒⣤⣼⣟⠿⠚⢤⠢⣿⢨⣼⠄⢀⠈⣬⠄⢽⠦⣍⠋⡘⡲⠃⣮⣐⡃⢈⡜⣓⢳⣡⠄⠚⣷⢉⡁⣾⣃⡧⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠲⠬⠁⠀⠀⠀⠈⠻⡀⣞⠡⢂⡼⠉⣸⠘⠗⣉⢸⡩⢻⡔⢇⠶⣤⠘⠨⠿⣗⣣⣬⠻⢣⡉⣷⡘⣼⠖⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠁⢜⡐⣌⠋⠑⣸⡈⣥⠩⣄⠧⡸⢤⠛⡔⣿⠋⢤⣼⢁⣬⠅⡾⣻⡟⣋⣾⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠓⠴⢤⠩⢈⣇⡦⢢⣄⣶⢈⡖⢷⣐⣆⣹⣇⢣⠄⡺⢘⡦⡸⣳⢫⣟⣫⣟⣙⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢃⡤⢿⡎⠬⢩⡿⠋⠉⠉⠉⠉⠉⠉⠉⠁⢁⠾⢈⠳⠘⠣⢤⡿⡘⢻⣿⠻⣏⡌⣛⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡍⠰⣦⢓⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢳⣇⣶⠋⣾⣻⠘⢿⣯⢋⡀⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⢸⣧⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣈⣸⡇⢺⣌⣻⣄⣀⠱⣿⣿⢃⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⢡⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠛⣁⣿⠈⠏⢛⣛⣁⣼⠟⠑⢿⣵⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⢀⠤⠀⠜⠠⡼⠁⣀⠀⠀⠀⠀⠀⢀⠄⠀⢤⣀⣤⣄⠀⡀⡨⣨⠎⡞⡀⠀⢀⡉⠉⢀⣠⡀⠠⢔⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠦⣅⣶⣤⣏⡰⣁⣜⣶⣷⡤⣾⣻⣶⡨⣿⣾⣀⣟⢶⡿⠆⠈⠛⣁⠱⣥⠿⢟⣥⢚⣯⣤⣴⢆⣉⠵⡅⣺⡿⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠚⠉⠉⠉⠉⠉⠁⠀⠀⠁⠐⠂⠀⠉⠙⠉⠋⠈⠦⠾⠏⠿⠷⠇⠈⠹⠷⣔⠒⠚⠀⠛⠶⠛⠓⠺⠷⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠷⣶⡄⠈⣶⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠈⠀⢀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡷⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⠟⢿⣦⡀⣀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠙⠻⣿⣿⣿⣿⣿⣿⣧⢹⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⡀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠘⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⣷⣾⣿⣿⣿⣛⠋⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣿⣿⢹⡿⠋⢀⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠿⡎⢰⣷⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡍⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡘⡿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡃⠀⠃

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⢀⡀⠀⢀⡀⠀⠀⠀⣀⠀⣴⡲⣦⡄⣠⢄⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠿⣄⠤⡀⢤⣘⣩⣿⣭⣛⡳⣦⣹⠟⠁⢀⠄⠀⢿⡟⣟⣈⡻⢬⡓⣭⡙⠫⣬⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⣟⣋⣼⡣⣽⣎⣜⡵⢆⡁⠀⣠⠄⠀⠦⣬⢓⣦⠸⣿⣶⢬⣒⣷⠜⢾
⠀⠀⠀⠀⠀⠀⠀⠠⣞⡌⣻⠇⠖⡆⠯⢙⠇⡀⠆⢐⢀⠀⠀⠀⡀⢳⠾⣹⢦⣶⢡⣮⠛⢠⡞⠦
⠀⠀⠀⠀⠀⠀⢀⣞⣽⡬⠉⡝⣚⡛⡹⠸⣍⣋⢷⡔⡒⣦⡤⠀⠓⢟⢃⠢⣖⢿⡓⢠⠘⡈⣣⠇
⠀⠀⠀⠀⠀⠀⠀⣾⢫⣛⡄⠽⠑⡞⠅⢀⠭⢥⢷⡜⣴⠁⣴⠰⠇⡙⠿⠠⢉⡈⣁⢨⡣⠰⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠷⠉⡆⠀⠀⠀⠀⠼⠓⢋⣤⢃⢩⠆⠳⠰⠐⠯⡄⠇⢨⠅⣿⠐⢃⣼⠂⡒
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠩⢶⡤⢠⠆⢠⣶⠶⠀⠁⠀⠛⠩⡄⠻⣃⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠖⡠⢤⠌⠉⣟⠀⠰⠂⠸⠇⠈⡁⢻⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢨⡿⠘⠁⠀⠈⡙⢛⣰⢒⣤⠀⣲⡾⠀⣠⠁⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⠢⡐⠾⠹⡚⠋⢀⠐⠋⣼⠟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣀⡀⠁⢀⡈⠀⣄⡋⢀⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⠶⣦⠅⠀⣁⣤⣭⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠦⠤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠎⠓⠖⠒⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⢠⠀⠠⣈⢔⡈⠇⠌⢓⢔⡁⠂⣤⣈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⣰⡾⠂⠀⢍⡘⠣⠼⠈⠸⠅⢐⠀⠀⠉⠹⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⠉⠀⠊⠁⣼⡆⡀⠂⠄⠜⡇⠉⡄⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠿⢳⡔⠒⠶⠃⢋⡾⢦⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⢮⣷⡀⠐⠁⠀⠀⢸⠖⠣⠶⠰⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⡘⢩⡁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⠀⠙⣐⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠖⢀⠠
⠀⠀⠀⡀⠀⢀⡀⠠⢀⡠⠀⡀⠀⢀⠀⡀⢂⢀⠴⠂⠀⠘⡄⡄⢨⣵⠈⠀⠰⣤⣤⣴⡶⠆⠀⠁⠰⠇⣀⠈
⠀⠲⠀⡄⢀⣠⠓⢈⡃⣁⠘⠀⢠⠌⠨⢓⠀⡤⢌⢀⠡⠀⠐⡙⡈⠋⠱⠶⠒⠂⠙⡟⠐⠒⢨⡦⠾⠁⠀⢂
⠀⢀⠶⣂⠠⠀⠞⠈⠃⢈⡘⠂⠉⠈⡋⢈⠴⢎⠐⡀⡁⠜⠀⢠⠅⡙⡆⢀⣹⡇⠸⠛⠳⠘⠛⠈⣠⠐⠐⠈⠀⡀
⠀⠀⡀⢈⡀⢘⠃⠐⠦⠙⠃⠱⠞⢓⡀⢌⡒⠖⡀⢲⢂⠁⡂⠥⠔⠐⡈⡀⣙⠷⡄⠀⠀⠀⠟⢙⠁⠀⠀⢐⠄⠁
⠀⠀⣷⠀⢧⠀⠩⣦⠘⠀⢦⠓⡠⠙⠛⡸⠎⠣⢍⠠⢍⠐⣒⣀⢫⣈⣡⣄⠌⢀⡘⢾⣄⠀⠀⠀⠔⣤⠆⠉
⠀⠀⠈⠀⠀⠁⣷⠈⠀⢻⣦⠁⡷⠂⣼⠇⠂⢋⡭⣈⡉⠤⠘⢉⡃⠴⡅⢄⢮⢀⠉⡄⠉⠈⠳⠀⠄⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠉⠈⠉⠀⠋⠉⠀⠛⠁⠐⠂⠀⠃⠀⠒⠂⠀⠀⠁⠀⠀⠀⠠⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠤⠐⠿⠗⠂⠐⣾⣇⡀⠒⠂⠰⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣊⠀⠀⠀⠠⡿⠿⢂⡌⢛⣉⢡⡦⢸⣛⡀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢿⣿⠿⠧⠴⠀⣴⣾⣷⠄⣛⠀⠴⠆⠩⣴⠄⠈⠉⠁⠘⠛⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠛⠛⠋⠾⠟⠃⣶⣿⣆⡉⠉⠁⠻⠟⠀⠲⠄⣤⣀⠀⠀⠀⠀⢀⣜⠁⠾⠷⠄
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠀⠛⠀⠾⠿⢷⣤⡄⠀⠺⠿⢛⣠⣟⠀⠰⠆⠀⠀⠙⠛⠃⠄⠀⠀⠀⠉⠺⠖⣂
⠀⠀⢀⣤⣶⠗⠀⢨⡵⠆⢾⣶⠀⡿⢂⣠⣤⡝⢡⣴⣤⡀⠻⠿⢿⡁⣷⣿⣶⣴⠶⢿⣿⣶⡀⠖⠤⠖⠀⢠⠹⣧⣴⣄
⠀⠀⠛⠉⠁⣠⣄⠙⣥⣤⠆⣤⣤⣄⠈⠛⠉⢰⠜⠛⣫⡁⣠⣤⣌⠁⠩⠿⢧⣘⢦⣛⣩⣿⣿⣦⣛⡤⠀⠀⠀⢿⣟⡟
⠀⠀⢀⡴⠂⠉⠻⠃⠀⠀⣨⡋⠉⠉⢡⠘⣿⡦⠐⠿⠛⠁⠙⣛⣭⡀⠃⣴⣶⡌⠁⠀⠉⠙⠻⣿⣿⡄⠀⠀⠀⠈⠛⠃
⠀⠀⠺⡧⢀⣀⣰⡗⢀⣤⢻⣷⢀⣤⣾⠃⣄⣀⠀⠀⠀⠀⣈⠛⢉⣱⡆⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⣶⣦⣀
⠀⠀⠀⠀⠛⠛⠋⠀⠸⠏⢀⣩⣤⣉⠀⠐⢿⠟⠀⠀⠀⠀⠈⠛⠘⠋⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠠⠀⢻⡿⢿⣿⣿⣿⠟⣄
⠀⠀⢰⣿⡗⠸⢿⣶⡄⢀⡻⠟⠛⢋⣤⡀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠦⣤⣐⣦⠟⠣⡄⡀⠉⠛⠿⣎⣠⣾⡋
⠀⠀⣾⣷⡀⠀⠀⣽⠁⢿⡇⠀⣀⡸⠟⣡⣤⡄⠚⠀⠀⢠⣤⣤⣄⢠⣤⡴⢶⠿⠿⠟⠀⣺⣿⣤⡙⠳⠤⢡⡍⣀⠀⢼⣿⡯⠅
⠀⠀⠈⠻⠇⠰⠾⠏⠀⢀⡘⠿⠿⠗⠀⠛⠟⢁⣠⣄⠰⣿⣿⣿⣿⣿⠿⠶⣠⡴⣖⣠⣄⣹⣿⣿⣩⡝⢃⠒⡐⣀⣦⣾⡥⣘
⠀⢾⣿⣶⡄⠀⠀⣠⣾⠛⠿⣿⠆⠀⠀⠀⠰⣿⣿⣿⣶⣿⠏⠈⠉⠀⠀⠀⠁⠈⠹⠞⠋⠃⣉⠿⣿⣷⣾⣶⣿⣿⣿⣿⣿⠁
⠀⠀⠈⠻⡇⠀⢠⡍⠁⠀⢀⣾⠀⣠⣶⣤⣀⣠⣍⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠛⠛⠛⠉⠉⠉
⠀⠀⣴⣾⠿⠀⠘⣷⣾⣿⡿⠟⢰⣿⣿⣿⣿⡏⣩⡄
⠀⠀⠉⠀⢰⣶⣶⠀⠉⣁⣀⣀⡀⠉⠉⢙⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡿⢀⣾⡟⠉⠻⣿⣧⠀⢺⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣉⡀⠀⢀⣠⣯⠀⠀⢙⣋⣤⡻⠿⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠿⠟⠁⣶⣿⣿⣿⣿⠇⣰⣾⣿⣿⣷⠀⣴⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⠉⠀⠀⠙⢿⣿⠟⠁⢸⣿⣿⣿⡟⠛⠛⠛⠖⠛⠗⠰⠄⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⡆⠐⣶⡤⠤⠖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢺⣏⡿⠓⠀⠈⠀⠠⠱⢏⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡗⢘⠋⠀⠠⢈⠀⠁⠠⣶⣮⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⢶⠁⢆⠘⠀⠄⠈⠂⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢄⠉⠀⠘⠃⢃⡀⢤⠁⡠⠄⣤⣤⠀⠀⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠱⢌⡀⠀⢠⡄⠲⡆⣀⣉⣤⣾⣿⣿⡞⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡐⠃⣤⠁⠶⣈⣠⣤⡄⠀⢹⣿⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢉⣀⠀⢭⠈⠉⠁⠀⠻⡆⠰⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠙⠓⠐⠳⣢⣀⡀⣤⡴⠃⠀⠀⢠⣝⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠂⠑⠂⠄⠀⠀⠈⢁⠈⠄⠈⡀⠐⠀⡟⢻⣾⡷⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠳⠚⠚⠀⠀⠀⠀⢂⣋⠰⠆⠉⡘⠿⠫⡝⢠⠿⠹⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡛⢠⡄⠀⠀⠀⠃⣨⠁⠘⠣⣀⠴⣇⢰⡄⡆⠂⣄⡍⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⢠⡄⠀⠀⠀⠀⡄⠀⠸⠟⣡⠆⡄⠾⠸⡏⢰⠎⠡⠾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⢦⡄⠀⠂⠀⠀⠀⠰⢃⠐⣡⠘⢰⢸⠃⣄⢻⠘⠰⠆⣨⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣃⠀⠀⠂⠀⠀⠀⠩⡄⢩⣤⣠⣧⠘⢃⡄⣾⣧⣰⣏⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣰⠍⢈⣄⣤⠔⠀⠐⠂⠾⢈⢈⣻⢡⣾⣏⢃⣛⠫⣾⣏⣿⣿⣟⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⢀⡮⠉⢻⣷⣤⠷⢰⠆⢏⠘⣼⣿⣟⠀⣷⢿⡜⣿⣽⣿⣯⣾⣹⣿⡽⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣁⡚⠑⣿⡟⠲⣤⡠⠈⣾⣽⣿⠟⣀⡋⠚⣵⣾⣿⣿⣿⠞⣿⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⡅⣍⣿⡃⠖⣠⠄⠛⣿⣿⣷⠾⠿⣟⣾⣿⣿⣿⣿⣿⣾⣷⣟⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢰⡞⢌⠲⠈⢓⢀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠿⠻⠾⣯⡿⠊⠁⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠟⠦⠿⠶⠸⠶⠖⠚⠛⠛⠛⠛⠛⠛⠛⠿⠧⠤⠀⠉⣙⣻⣿⣿⡿⠟⠋⠉⠉⠋⠛⠻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠷⢶⣤⣄⣀⠀⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣖⢠⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡏⠰⡄⠓⡌⡐⢂⠦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰⠂⠀⠀⠤⢀⠂⠘⠒⠂⣉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠁⠀⢀⢈⡀⡃⡀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠠⢠⠺⡨⡵⡎⢡⠂⣨⠄⠀⠀⠀⠐⣶⡄
⠀⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⢀⡤⠀⢙⡦⠀⠀⠃⠘⡃⠑⡍⠃⠀⢸⠠⠀⡄⠀⡶⢛⠋⢀⠦
⠀⠀⠀⠀⠀⢀⣤⡘⣿⢰⡿⣴⡇⠀⠶⠀⢄⡃⠀⠀⠀⣺⠄⠀⡄⠀⡀⢤⠄⠀⡀⠀⡀⣿⡁⠀⣁⢀
⠀⠀⠀⠀⣆⠸⡿⢿⣮⠟⠓⠋⢸⡇⣠⢀⣴⠑⠂⢡⡬⣌⠀⠐⠀⠈⠀⠀⣠⢤⠄⠁⠂⠉⡧⠀⠤⡼⠀⢀⠒⡦
⠀⠀⠀⠐⠁⣠⡶⢈⡁⠀⠀⠐⠈⡀⠉⠀⠀⡂⠂⠤⠓⠐⣧⠀⠀⠀⠠⠛⠒⠆⠆⠐⢘⠊⠏⠀⠶⠾⢄⡄⠂⣠⡀⢀
⠀⠀⠀⠀⡀⠛⢃⡛⠇⠀⠀⠴⠀⡇⠀⢰⠠⠉⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⠀⠉⢆⢁⠈⠀⡐⠂⠀⡄⠟⣡⡄
⠀⠀⠀⠀⠉⢘⡋⢁⠾⣤⠤⠇⠀⠀⠃⡀⡁⠀⠠⡄⢬⣁⠈⢲⣤⣶⠂⣈⠤⠀⠀⠈⢐⠀⢺⠌⣘⣙⡣⠥⠊⠀⠙
⠀⠀⠀⠀⠀⠈⠁⡤⢠⠄⣆⠐⣦⠀⡀⠛⢀⡘⢀⡐⢓⡂⠀⠀⢹⡇⠀⠀⠈⠂⠂⣠⢹⠶⣌⢓⢉⡠⡄⠆⠚⠿⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠴⠍⠐⠙⢇⡘⠠⡈⠰⠢⠄⠸⣿⣆⣷⣶⣶⣧⣸⣿⣶⡾⠣⢩⡄⢎⢨⠡⡱⢄⣓⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢁⡃⣡⠘⢫⢿⣿⠻⣿⣿⠟⣿⣿⡟⠐⠧⢼⠂⢏⠈⢁⠘⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣴⣃⠺⢈⡟⢷⣾⣷⡾⢋⣽⡇⠀⠃⠤⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠆⠱⡂⠶⠐⡆⢤⠔⣿⣿⣀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠂⠦⠘⠀⢀⢸⣿⣿⠶⠶⠦⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠠⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠴⢦⣤⣴⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡖⠲⠶⢒⣒⣂⠠⣤⣀⣠⡒⠛⠛⠻⣶⡄
⠀⠀⠀⢠⠂⢠⣤⣂⠤⢀⣤⡶⠟⣬⡅⠙⠋⡀⢀⠉⠉⠁⠰⣤⠀⠓⠀⠼⠳⢟⣿⡄
⠀⠀⠀⡆⢠⠟⠁⢉⣷⣦⣤⡉⣅⠀⠉⠉⠠⣤⠈⠶⠶⠀⣀⠀⠲⠖⣉⡐⡀⢈⣦⠙⣀⡀
⠀⠀⠀⡄⠈⠀⠀⠀⠹⣿⣿⣿⣶⣦⣤⣀⣀⠀⠈⠰⣶⡤⠀⠰⠶⣀⢉⣀⠛⣭⡅⠂⠰⣼⠂⠄
⠀⠀⠀⠈⠲⢤⡀⠀⠀⠈⠻⡿⣿⠟⠛⠛⠁⢀⡐⠶⠆⠘⠂⠉⠃⠉⠃⠻⣷⠡⣎⠙⠃⢿⣄⡞
⠀⠀⠀⠀⠀⠨⠇⣀⡈⠋⠉⠉⢀⠠⠞⠀⣠⡈⠀⣠⠙⠲⠶⠶⠖⠛⢻⢷⣦⠀⠀⡒⡀⡝⠛⣸⢬⣂
⠀⠀⠀⠀⠀⣠⠞⠛⠓⠒⠒⠀⠈⣠⣤⠘⠛⣠⠖⠀⣀⡛⠭⠃⠈⠢⠤⠜⠛⠳⠄⠀⠀⠀⠀⠈⠳⣏
⠀⠀⠀⠀⢀⠌⠀⠀⣤⣤⠀⠉⠀⢨⢁⣤⠀⠆⠀⢨⠁⠀⣤⡨⠷⠆⡤⢂⡐⠀⠄⠄⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⣸⠀⠀⠈⠛⢁⠀⠺⠟⠀⠈⡁⠀⠀⠶⠆⠈⢀⣡⠀⠒⢂⡐⠊⣠⣬⣤⣀⠀⠀⠢⣤⣥⣀⣶⡃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠃⣠⡖⠀⠸⠫⣶⣶⡦⠀⠃⠈⢁⢀⡤⠈⢠⠄⡸⢦⣄⡉⠉⠐⠀⠈⣿⡾⢁⠇
⠀⠀⠀⠀⠘⣤⡆⠻⠂⣴⠀⠉⠲⠂⠀⠴⠀⠀⠀⣠⣤⠀⠟⠁⠀⡴⠀⣰⣟⠶⢤⡁⡈⠀⢀⣴⡏⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠱⠀⠀⠉⠀⠻⣷⠀⢰⣾⠿⢃⠀⠛⠁⠀⠀⠘⠃⠀⣼⣿⣿⣿⡖⢲⣖⣝⠛⡿⢛⠋
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⣀⡄⠰⠂⢚⣥⠀⠀⡶⠀⠀⠀⣼⣿⣿⣿⡿⣠⣿⠟⠁⢀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣰⡀⠀⠛⠁⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⢀⡄⠀⢴⠤⠒⠛⠛⢢⣴⠀⡟⠁⡾⣿⣿⡟⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠈⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠛⠿⣶⣶⠷⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢀⡀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠛⠛⣻⣿⣛⡻⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⣀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣬⡉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢰⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣷⡄⢀⣤⣄⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⠋⠉⢹⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⢰⣿⠁⠀⠀⢸⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⣿⡇⠀⠀⢠⠇⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⢻⣧⣀⡴⠋⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣤⣴⣾⣏⠉⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⡿⠇⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀
⠶⠁⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠙⢋⡘⠠⡠⠑⣂⠰⠝⠐⠄⣀⠠⣄⡐⡄
⠃⠼⣬⣀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡘⢹⠙⡁⠖⠆⠘⠢⠍⠊⠁⠀⠄⠈⡄⠡⡐⠈⠀⠴⠂⠁⠙⠋⠁
⠉⡤⠉⣬⡇⡤⢋⢜⣱⡴⠐⣆⣖⢘⣘⣭⢑⠚⡁⡄⠒⡀⠔⠀⠀⠀⠀⠀⠤⢸⠏⠘⣀⠀⡀⡧⢀
⣭⢡⡞⡰⢘⢋⢬⢘⠵⢆⠩⡮⠰⡌⣅⠨⠬⢜⠉⠀⠀⠀⠀⠉⠀⡀⢀⠘⢌⣡⠀⠉⠀⠉⢀⠁⠠
⢼⢇⣥⢆⡩⠶⢛⠸⢉⡙⢡⠐⠃⡶⣽⠸⢰⡌⠄⠀⠠⠐⢦⡔⠈⣙⠂⠀⠀⠈⠀⠀⠀⠀⠘⠃⠐⠀⠄
⣥⢌⠱⡬⠇⣴⣉⡇⣉⠏⠶⢸⡄⠇⣀⢢⣄⢐⢂⡀⠀⠳⠰⠐⠈⣜⠀⠂
⡅⢼⠃⠰⣾⢨⡤⠰⠇⠘⠶⠉⣴⣄⠱⠀⢈⢋⠂⠐⡒⠀⠀⡀⠀⠘⢽⡐⠀⠐⢦⡀⠀⡠⠀⣀
⣴⠄⣾⢣⠍⣶⣀⠇⡐⠋⠸⠀⣨⡛⠰⠇⡍⡢⠶⣡⠄⠄⢄⡓⠀⣙⡊⣬⢻⣄⠀⢹⡂⠀⣀
⡄⣰⢂⡙⢰⡦⣠⠠⣿⠀⣻⡄⢸⡇⠰⠦⠐⠀⢃⡅⠆⡩⠴⠀⠂⢉⠙⣄⣨⡉⠀⠉⠁⠈⢡⠈
⣤⠐⣈⣁⠰⢖⣘⠃⣄⠀⣤⢤⠈⠁⠶⢀⣹⣍⡁⣬⢋⣐⠔⠈⣀⠜⠠⣌⠛⠃⠄⠰⠀⠀⠂
⠈⠁⠁⠀⠀⠈⠛⠀⠤⠀⠐⠒⠀⡉⠡⠆⣨⣶⠞⢒⠃⣩⠤⢉⡀⢒⡓⠰⠄⠀⠀⠀⠂⠈⠀⣰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣆⢨⣶⢿⡍⠷⢈⣀⠤⡤⠀⣂⡐⢀⡄⠑⠀⠀⠀⡀⢰⠈⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠬⢀⣴⣶⣮⠻⠀⣴⠄⣩⡁⣴⠆⢈⣤⠁⠊⡁⢀⠒⣉⠨⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠰⢦⡘⢿⡦⠉⣐⡶⠆⢈⣴⠀⢛⡃⣘⡂⠁⢴⠀⠀⠂⠂⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠢⠙⠃⢰⠞⣉⠲⢏⡁⠬⢆⡰⢆⢈⠋⠒⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠏⢠⠊⡁⠉⠈⠀⢐⠕⠨⠉⠋⠉⠉⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠈⠀⠀⠀⠘

⠀⠀⠀⠀⢀⠀⠾⠃⠐⢖⠂⢠⠀⠠⣤⣄⢠⣤⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⢀⣤⡀⡤⣀⣤⣄⡠⢤⣄⡀
⢀⠒⡄⠸⠘⠈⠀⠙⠀⠡⠀⢿⠀⢷⡦⣝⡚⣂⣏⡶⣿⣰⡤⣤⠄⠄⡴⡐⣲⢋⣿⠹⡎⣽⢨⡙⢷⣊⠷⣾⢻⣶⣉⠛⢦⣤⣄
⠀⠀⠐⢆⠈⡀⠐⠔⢺⡔⢧⡂⡀⠲⡱⣤⠿⣇⣍⠁⡇⡮⠷⢉⠙⠞⣨⢰⡇⣦⠇⠶⠰⡑⢣⣙⠓⠹⣧⡍⢷⠞⡿⣾⢆⣉⠿⣷⡀
⠀⠀⡦⠞⠆⠀⠀⠀⡞⠋⠈⠓⠈⠀⢁⠐⠳⠲⢦⠛⡁⢡⡤⣬⠞⢻⠘⣋⠴⣶⢠⠎⣷⠐⡊⠉⡷⠳⢜⠋⠶⡆⣗⢾⣘⢵⠆⢙⣗⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠪⠀⢸⢀⡼⠈⣐⢊⢇⠓⣬⣅⡍⠌⣋⠰⠃⢰⠋⣌⢛⣥⠏⢽⠊⠘⢣⡼⠉⠾⣡⡉⠚⠉⣿⢸⠇⣿⡌
⠀⠀⠀⠀⠀⠲⡶⠚⠀⠀⠀⡂⢀⠂⠬⢐⣒⠆⡙⡛⢣⠈⢧⣄⠳⠟⣀⠓⣉⡰⢬⠙⢛⡐⣋⣀⡼⣠⠴⠞⣦⡌⠙⠗⡰⢼⣇⢶⡌⣻
⠀⠀⠀⠀⠀⡤⠶⠦⢠⣤⢀⡀⢘⠈⠊⠅⢯⢏⣁⠳⠈⡄⢦⠀⡆⡖⣙⠸⠉⢳⡄⣞⢉⡵⠈⡥⠆⣥⡆⠞⣀⣥⠙⣾⠇⠀⣘⣤⢸⣿
⠀⠀⠀⠀⠀⠙⠶⠞⠒⠃⠈⠱⠛⢠⡚⢪⡁⣎⡐⠲⡑⠃⠖⡰⢃⠧⣘⠆⣛⠰⢃⣭⢃⠰⠶⢃⠛⡤⡴⣟⠋⣜⣁⡀⣀⠀⠵⠁⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡑⣀⣡⣉⡁⡉⢉⣦⡀⣇⠮⢵⢩⣔⣯⢸⢎⠧⣈⡷⡖⠻⠖⣾⢶⣎⠶⣸⣹⠏⠁⠂⡸⢿⡿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⡭⠘⣬⠳⠾⣧⡷⠸⣃⠏⣶⠹⣨⠆⣻⡪⠿⣏⠱⣦⣡⢾⡆⡸⠿⡶⢹⣹⣇⠂⣾⡷⢆⣼⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢿⡲⠯⠉⣦⣡⣶⠟⣩⣌⡿⠿⢐⣿⣿⠘⡿⡧⠈⣿⢈⠹⡿⠢⣦⡾⡏⠛⠗⢿⠐⣸⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠘⠗⠾⢣⣌⣀⡐⠀⠉⠉⠙⠉⠓⠉⠋⠈⠁⠀⠀⠀⣿⠷⣰⣶⠸⢷⠀⠀⠘⢫⠤⣝⣃⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢷⡜⢿⡤⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡦⣤⡍⣶⣼⠀⠀⠀⠈⢀⡼⢣⣽⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⢎⣫⣥⠴⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⣴⡞⠹⢀⠀⠀⠀⠈⢁⣾⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠺⠋⠉⠴⢖⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡌⠠⠞⠀⠀⠀⠀⠀⠀⠉⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⢚⠀⣛⠎⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠻⢋⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡔⠉⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⡥⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢋⣀⣈⠀⠠⠀⠰⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣴⡾⠃⠀⠀⠀⠀⠀⠀⢈⣴⣤⣿⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣤⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣇⠿⠀⠈⠁⠐⢦⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣟⢸⠁⠀⢈⠀⠁⠰⡶⣅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⢢⢀⡐⠀⡁⠀⠀⠀⠺⠂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡈⠆⠀⠀⠀⣒⠘⠦⢊⣤⣶⣄⡀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠡⢁⡒⣠⠘⢁⡘⠀⢻⣿⠞⠛⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣁⠈⢘⠀⠋⠉⠹⢦⠰⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠌⠛⠒⠓⡢⣠⠰⡶⠃⠀⠀⢬⣱⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣉⣐⠀⠀⠀⠀⢀⠀⠄⠄⣸⢩⢿⠟⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡊⡅⠆⠀⠀⢀⠀⠄⢈⡁⠀⣈⠋⠂⡘⢛⡬⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡕⠆⡉⠀⠀⠀⢀⠃⢠⡶⢣⠙⢸⢁⡗⣄⠚⣙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⡁⠀⠀⠀⠀⠀⢆⠰⣁⢾⡰⠆⡁⠗⠆⡦⢩⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣹⠀⠀⠂⠀⠀⠩⠄⣡⣄⣦⢘⢣⣰⣶⣰⣮⣿⣟⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡖⢠⣤⣖⠃⢀⠓⠋⡀⠸⣦⣿⠯⣩⡍⣷⣷⣿⡟⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠏⢠⢹⣿⢋⠘⠉⢥⡼⣿⣷⠀⠟⡿⣹⣿⣿⣿⣷⣟⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣂⢺⡯⢠⢉⡉⢾⣿⣟⣥⣿⢦⣼⣿⣿⣿⣯⣬⣽⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢭⢏⠢⡜⠖⢸⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠟⡻⢶⡿⠛⠁⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠚⠛⠒⠓⠛⠙⠛⠛⠛⠋⠉⠉⠛⠂⠀⢠⣬⣿⣿⣟⣋⡁⠉⠉⠉⠙⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠲⣦⣤⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠎⠙⠛⠉⠁⠠⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠒⠒⠒⠺⠇
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⣀
⠀⠀⠀⠀⡀⢤⠴⢧⠤⠤⢤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠐⠒⠚⠓⠀⠉⠀⠉⠐⠓⠦⣄
⠀⣠⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣦⡘⠛⠿⠿⠿⠟⠛⣡⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞
⠀⠉⠘⠓⣢⣤⣤⡄⠀⠀⠀⣀⠀⠀⠀⣠⣔⣢⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣡⡒⢄⡀⠠⣤⠤⠤⠐⠾⡇⠈⢹⡄
⠀⠀⠀⠀⣿⣤⠋⠀⠀⠈⠉⠉⠉⢉⡾⣯⠚⠁⠀⠒⠒⠂⢰⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⢎⡹⠀⠀⠀⠀⠀⠀⠈⠑⣾⡏⡄
⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⣎⠻⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⢡⠛⣄⠀⠀⠀⠀⠀⠀⠈⢠⢇⡀
⠀⠀⠚⠀⡄⠀⠀⠀⠀⠀⠀⠀⣷⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡀⠀⠀⠀⠀⠀⠀⢺⠀⢣
⠀⠀⢷⢀⡇⠀⠀⠀⠀⠀⠀⣴⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡇⠀⠀⠀⠀⠀⠀⢨⣠⠆
⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡈⠃⠀⠀⠀⠀⠀⢀⡙
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠇⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢋⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⠋⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠛⢿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠃⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠙⠻⣶⣦⣀⣀⠀⠀⠀⠀⣀⣀⣠⣶⠿⠋⠁⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠈⠉⠉⢻⡟⠛⠛⢿⠉⠉⠀⠀⠀⠀⢀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠂⢤⡤⠄⠀⣸⠀⠀⠀⣿⠃⠠⣤⡤⠐⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⡀⠀⠀⠀⠀⢹⠁⠀⠀⢻⠁⠀⠀⠀⠀⣼⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣟⠁⠀⠈⠉⠙⠋⢻⡇⠀⠀⢹⣋⡉⠉⠉⠁⠈⢻⡄⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⡿⠛⢦⡀⠀⠀⠀⠘⣃⠀⠀⢻⠉⢃⠀⠀⣠⠔⠿⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⣀⠁⠀⠀⠙⢢⡄⢀⡼⠛⠷⣤⠆⠀⠘⣷⢾⣁⠀⢐⡇⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢀⣽⣀⣀⡀⠴⠧⣤⡼⠳⠦⠀⠀⠀⠀⢰⠆⠀⠀⠈⠛⠛⠦⠄⣀⡀⠀⠀⠷⡀
⠀⠀⠀⠀⠀⢀⡮⠁⠀⠀⠀⠘⠁⠈⠉⠈⠁⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠻⡄
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⣀⣀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠁⠈⠙⠿⢲⡤⠤⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠐⠒⢶⡶⠶⠶⠶⠶⣶⠶⢶⣶⠶⠷⠶⢶⡶⠒⠒⢉⡴⢦⣤⣄⣈⣽⠋⢻⡷⠒⠒⠒⠒⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⡸⠦⠤⠤⣾⠀⣄⣀⣀⣘⠛⠁⠀⢛⣋⣉⣥⠀⣇⢀⠀⢼⣆⢨⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣄⢀⣶⣄⠈⠛⠁⠀⠁⠙⣷⢤⣤⣾⠉⠀⠉⠚⠃⠀⠀⠀⠈⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣼⣿⠖⠺⣿⠉⢹⡿⠳⣄⠀⠀⠀⣾⠇⣸⣇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⢙⣁⣀⠤⠴⡿⠄⢀⣭⠀⠀⢠⡏⢠⠛⠻⣧⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣗⠚⣉⡁⣤⠤⣶⠦⠤⣤⣏⠀⠀⡶⠀⣻⠀⠄⠈⣦⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣉⣉⣀⡀⢰⡏⠀⠀⣸⣧⡄⠸⣄⢰⡋⢹⡷⠀⠀⣦⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡘⣿⠛⠋⠁⠀⠛⠃⠉⠛⠋⠀⠙⣂⠀⠙⠃⠙⡇⠀⠀⢀⠛⠀⠉⠛⠋⠀⠀⠀⠀⠀⠉⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣦
⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄
⠀⠀⠀⠀⠀⣰⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⢠⡇⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠙⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⡇⠀⠀⠀⠙⣤⡀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠈⢁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠧⠤⠤⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠤⢚⣿⣿⣿⡿⠟⣛⣛⣯⣭⠉⣿⡟⢩⣽⣿⣛⡛⠛⢿⡿⠿⣿⡓⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⣠⣿⣷⠈⠉⠉⠉⠉⠁⠀⠀⠀⠉⠃⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣡⠤⢀⣀⣀⢀⣀⠠⣦⣉⠷⠋⠱⠞⣡⡤⠄⣀⣀⣀⠀⢠⢤⣜⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣴⢶⡞⠿⡗⢦⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠠⢽⡀⠠⢘⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠆⠘⠛⠆⠀⣾⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣄⠀⠀⠀⠠⣄⣺⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠳⢭⢿⣷⡆⠤⠤⣿⣿⣿⡲⢂⣤⣴⣂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣄⠸⠶⢾⢻⣿⣶⣾⣿⣽⣿⣷⡉⠎⣿⣧⣆⡹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠲⠉⣧⣖⠪⢚⣿⣿⣾⣘⢿⣿⣿⣥⣗⣵⠿⣿⡿⣯⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣅⢠⢀⠉⡁⠉⠀⠀⢀⠁⡟⣿⣿⢠⡄⢃⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣼⣦⠠⣄⢻⣄⡄⢀⡤⡃⣯⣿⣿⡎⣑⡆⠳⣿⣯⣿⡟⡛⣛⠻⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢀⢳⣽⣿⣿⡾⣿⠛⡁⢆⣛⣶⣿⣿⣿⣵⠯⠵⢷⡿⠿⠿⠷⠿⠿⠷⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣞⣥⣦⣶⢟⣋⣻⣴⣷⣿⣿⣵⣴⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠁⠀⢍⠉⣫⣀⡛⠟⠻⣟⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢿⣿⣟⢟⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⢤⣾⡻⠿⣽⡯⢉⠙⣏⢛⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡠⢗⢆⣿⡗⢸⢠⢭⠕⢾⢻⣝⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣿⣿⣍⣕⣁⡠⠙⣧⠍⢒⡆⢞⠔⢿⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢿⣿⢿⡯⢰⣏⢰⡗⡛⠮⢻⣾⣓⣿⡇⠀⠐⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣿⣿⡿⠢⠁⣻⡁⢼⡧⡱⡅⡆⣿⣿⣿⣧⢻⡷⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡷⣦⣄⣿⡉⣹⣿⣷⣿⣿⣿⠸⣷⢒⣻⣷⣲⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⢿⣿⢗⣝⣸⡉⠁⢸⣿⣿⠆⢻⠥⡻⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢧⡤⢾⡟⡝⣌⣾⠀⠀⢸⢟⢻⡀⢸⣯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡱⣱⡃⠀⠀⢸⣷⣶⡅⣸⣏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⣓⣲⣧⣉⠄⠀⠘⠛⣛⢰⠿⡾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⣿⠿⠛⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣺⡾⣞⣀

⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣴⠖⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⢲⣶⠶⢿⡍⣡⡛⣸⢿⢳⣶⠾⢻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣴⣷⡼⢣⣏⠷⣪⣴⢛⣃⡿⣥⡜⢃⣄⣀⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢨⣯⣾⣭⣁⣛⣉⢴⣿⢿⣇⣛⡙⠹⣿⣟⣷⢛⡯⢟⣋⣷⢠⡠⣄⣀⣐⢂⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣭⣭⣍⡁⢵⡛⡛⣻⠾⣁⣬⣤⣍⣱⠿⠸⡿⣬⡌⣽⠧⡘⢧⡼⠡⡶⠿⣉⢚⣰⠖⢴⠖⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣏⠿⣿⣿⡀⠁⠁⠁⢰⡿⠿⠟⣴⠷⠿⠣⣭⣌⡘⣧⣞⠁⣟⠉⣻⠑⠶⢋⣟⣁⣟⠈⠓⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⡇⠀⢈⠃⠀⠀⠀⠘⠃⡀⠜⣃⠋⢿⣅⠢⢶⣬⣫⠦⣛⠉⣿⣏⠰⣏⠛⣣⠈⣿⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠷⣀⣒⠀⠀⠀⠀⠀⢀⠀⠉⠁⠙⠯⠺⠶⣃⠯⢠⡵⣶⠉⣿⠳⣤⠔⢉⡋⢻⠶⣍⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡀⠙⠶⣶⡶⠋⣀⢾⠀⠀⠲⣳⡙⢭⠆⣰⢲⡌⢒⣁⣤⡀⢶⠋⣥⠙⠶⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣺⢀⢀⣸⣄⡀⣼⣿⡀⠀⠀⠀⢰⣏⡷⠛⢰⢇⣘⣇⣀⣻⠀⠛⢁⡟⠳⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣉⠉⣉⣉⣹⠃⠈⠃⠀⠀⣤⣄⢴⠏⢙⣍⢩⠹⡟⠋⣾⠓⣌⠳⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠈⠉⠁⠀⠀⠀⠐⡜⠷⣩⠘⠟⢘⣥⡼⣦⢜⣧⣌⠲⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠸⢯⣼⠃⢊⡀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⣴⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⣿⣿⣿⣿⣿⢟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠛⠛⠋⠉⠉⠉⠙⠋⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠠⠤⢤⠤⠔⠠⠶⠒⣶⣶⡶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡻⠤⠈⠀⠣⣐⢶⣫⠄⡈⠞⡿⠝⠲⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣖⠇⠒⠂⡿⠚⠋⠉⢻⡟⠳⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⢀⡠⢤⣤⠶⣶⣦⡤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠺⠁⠘⡬⣝⣿⡈⠀⣈⠈⢰⡟⠋⠁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢪⢍⠆⠈⠓⢀⡄⡉⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⢲⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠁⢀⠡⠀⣄⠀⠠⠤⡆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢤⠀⡀
⠀⠀⠀⠀⠀⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢴⠏⠀⠀⡀⠰⠜⣦⠲⡟⣶⡄
⠀⠀⠀⣴⣄⡶⠈⢌⣑⠆⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⣰⣡⣃⣌⣀⣤⡔⣾⠟⠈⠠⠛⠋⠀⡀
⠀⠀⠀⠐⠟⠃⠀⣁⡈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣼⠯⠈⢛⣹⣽⠮⢷⡊⡦⢂⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠈⣛⣼⣏⣬⡛⡎⠉⠀⠀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠐⠻⠫⠅⠀⠂⠀⠀⠀⠀⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⢀⠄⠀⠀⣀⠐⠈⠀⠀⠀⠀⠀⠀⠁⠒⣅⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣦⣤⣄⣠⣶⣶⣶⣄
⠀⠀⠀⠐⠁⠀⠀⠀⠨⠆⠀⠀⠀⢀⠀⠀⠸⠀⠀⠀⠌⢂⠀⠀⠀⢠⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⡇
⠀⠀⠀⡇⠀⠀⠚⠀⠀⠀⠀⠀⠀⠜⠂⠒⠂⠒⠒⠀⠤⢈⡔⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡆⢹⣿⠃
⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⠀⠀⢄⢘⠀⠀⠀⠀⣿⣿⡏⣿⣿⣿⣿⣿⣿⠉⠁⢀⠀⠀⠀⠀⠐⢡⠘⠁
⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⠀⠀⠀⠘⠑⠀⠀⠀⠈⢙⠀⠀⠀⠀⠘⠿⣇⢿⣿⣿⣿⡿⠃⠀⠠⣿⡆⠀⠀⠘⠿⢾
⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠀⠀⠀⠈⠀⠁⠀⠔⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢀⡀⠀⠀⢀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⡀⠀⠀⠀⠀⠐⠂⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⣈⠣⡀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣒⠖⠲⡒⠒⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡀⠀⠀⠀⠀⡈⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣿⣦⡀⣱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⣿⣿⣿⣿⣿⠣⢌⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠒⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⠘⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡌⢸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⠲⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣫⣵⠶⠿⠛⠛⠛⠛⠛⠛⠷⢦⣍⡻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⣥⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣩⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢟⣵⠛⣁⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠙⣆⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣭⣶⡿⠿⠿⠿⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢿⣿⣿⣦⡀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠘⣿⣿⢻⣿⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡝⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢿⡇⠀⠀⠀⢹⣷⣼⣿⡇⠿⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢮⣛⡛⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠟⣭⠄⠀⠀⠀⠀⠀⠈⣿⣯⣹⡿⠚⠛⢳⣝⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡷⢸⣧⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠉⠀⢺⣿⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⡣⡎⢠⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⣿⣿⠀⣶⣿⣿⣿⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡇⠈⣾⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡅⣿⠀⠉⠋⠈⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡸⠂⠈⢠⡟⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡆⢸⠀⠀⠀⠀⢋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠁⠀⢀⡾⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢷⣼⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠟⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⣿⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⡇⠀⠀⠀⠀⢀⡀⣿⠤⠤⠤⣤⠶⠖⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠛⠒⠒⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⡀⢹⢸⣇⠀⠀⠀⠐⢏⠁⠀⠀⠀⠀⠀⠀⠀⠱⡌⠳⣄⠀⠀⠀⢀⠤⠤⠚⠛⠛⠛⠛⢻⣶⢽⡇
⠀⠀⠀⠀⠀⣠⠾⣫⣽⣶⣶⢮⣍⡻⣇⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠙⢦⡔⠚⢻⡄⠀⠤⠤⠤⠤⠄⢸⣿⢸⡇
⠀⠀⠀⠀⣴⢫⡞⢡⠞⠀⠲⢀⡉⢻⣦⢠⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠳⣄⠀⠛⠆⣼⡄⠀⠀⠀⠀⠀⠀⢸⡿⣸
⠀⠀⠀⢰⡏⣾⠀⢈⠀⠀⠀⠀⢳⠀⣿⡌⣷⣌⢻⣆⡀⠀⠀⠀⠀⠀⠀⢶⡋⠁⠀⠀⠹⢦⡀⠀⠀⠳⡄⠀⠀⠀⠀⢀⣾⣧⡝⣦
⠀⠀⠀⠸⣇⢿⠀⠘⣄⠀⠀⢀⡌⠀⣿⢣⡟⠈⣣⠝⣿⣦⣀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢷⠀⠙⠦⠤⣀⣀⣀⣀⣀⡤⠛⢀⣼⠟⣼⠁
⠀⠀⠀⠀⠹⣎⠷⣄⡈⣛⡿⠋⣡⡾⢋⡾⠁⢰⡋⣾⣿⣿⣿⣷⣦⣤⣄⣀⣀⣹⣦⠀⠸⣇⡀⠀⠀⠀⠉⠉⠉⠉⠀⢠⠏⠙⢷⡝⣧
⠀⠀⠀⠀⠀⢈⣷⠎⣙⣿⣰⣿⠻⡆⣿⠀⠀⠈⠛⠶⢮⣍⡛⢻⣿⣿⣿⣿⣿⣿⠙⠀⠸⣇⠙⠂⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢻⡌⢧
⠀⠀⠀⠀⠀⡟⣵⠟⠋⢙⡄⣟⠀⢿⡹⣄⠀⣀⣠⣤⠖⣫⣴⣿⣿⣿⣿⣿⣿⣿⣾⠄⠀⢹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢻⡜⣧
⠀⠀⠀⠀⠀⣷⣸⡧⠚⢛⠄⢛⠀⠈⢻⡌⢛⣭⣷⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠘⠃⠸⠂⠀⠀⠈⢿⡸⣇
⠀⠀⠀⠀⠀⢳⡙⣷⠞⢛⡆⢠⠀⠀⢸⣇⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡹⡆⠲⣀⠀⠈⠳⠶⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣧⢹⡀
⠀⠀⠀⠀⠀⢸⡄⢿⡤⠛⣹⡷⠂⠀⠀⢀⠉⠙⠻⠏⠀⠀⠉⠛⠿⠿⠟⠛⠁⢰⡆⠳⣄⣀⣀⡄⠈⡀⠀⠈⠉⠙⠓⠶⠶⡇⠀⠀⠀⣼⣿⡇⢷
⠀⠀⠀⠀⠀⠀⠹⣮⡛⠶⠿⣿⠉⠐⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣼⢿⣿⣿⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡇⣿⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣠⡞⠁⣀⣠⠞⠁⣾⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢻⡆⠀⡴⠃⠀⠀⠀⠀⠀⣠⠟⡌⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⡁⠀⠀⣿⣿⣿⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠻⠿⠷⠶⣶⣶⣶⡖⠚⠁⣰⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢰⣿⣿⣿⣿⡇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢹⡇⣾⣿⣿⣿⠀⠄⠀⠈⠁⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⣿⣿⣿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⣋⣾⣿⣿⣿⣿⠐⠶⠀⠀⠀⣤⠇⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢳⣾⢿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢩⣶⣿⣿⣿⣿⣿⣿⣅⣼⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠖⠀⠀⠀⠛⠀⠀⠐⠒⢛⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⢿⣿⣿⣿⡿⢟⣭⢸⣇⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣝⣛⣭⠶⠛⠳⣮⡻⢦⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⢸⣿⣿⣿⣿⡿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣝⡓⠶⣤⣤⣄⣀⣀⡀⠀⠀⠙⠒⠀⠠⠤⠤⠤⠒⠊⠁⣀⣀⣠⣼⣿⣿⣿⣿⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠭⢭⣍⣛⣛⣛⣛⣛⣛⣒⣒⣚⣛⣛⣛⣛⣫⡭⢭⡜⣿⣿⠟⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠻⣮⣡⠞⠁

⠀⠀⠀⠀⠀⠀⠀⢨⡥⢀⢀⡴⢶⡿⣶⢦⣄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣷⠌⠒⠜⡩⢌⢊⡩⡞⡷⠹⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠃⢨⠕⣢⣒⣸⠁⡒⠴⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠄⢝⣳⡶⢚⠷⣽⡂⠃⠘⢦⡹⠥
⠀⠀⠀⠀⠀⡠⠁⢰⢜⡉⢣⠍⠟⢠⠓⠀⠀⠑⠾⠉
⠀⠀⠀⠀⠀⠘⠀⢶⡌⠁⡆⠀⡄⠀⠀⣄⠀⡀⠀⠀⠀⢀⣄⢸⢄⡰
⠀⠀⠀⠀⠘⢧⣁⠀⢦⡠⣴⢎⣻⣄⣀⣨⣷⡀⠠⠄⠢⣄⠁⣶⠠⢶⢘⢠⡀
⠀⠀⠀⠀⢁⠤⡉⠓⢄⠀⠀⠌⠂⢙⡤⠈⡁⠥⣂⠀⠄⠨⣙⢳⣇⡇⣭⠆
⠀⠀⠀⢈⡃⠐⣤⡐⠄⠙⠒⠚⠛⠁⢀⠈⠴⠋⣉⢀⠃⡀⢘⢣⣨⠖⣡⠦⠡
⠀⠀⠀⠤⠡⠬⣄⢬⠰⡄⠆⠠⠐⡴⣡⢄⠴⢖⡠⡁⠁⡅⠀⠇⠣⣬⣁⡳⠂
⠀⠀⠀⠀⠉⠀⢠⡑⠀⣝⠠⠀⢁⡀⠀⠰⠈⠋⠈⢢⢁⢄⡀⠘⣛⣋⣋⣹
⠀⠀⠴⣐⡁⡡⢀⠁⠀⠉⠆⠘⠀⠀⠑⠨⠃⣝⢘⠏⣃⢨⠀⠀⢛⢋⣇⢡⣀⣀⣀⢀⣀⡀⣀⡀⣀
⠀⠀⠱⡥⠒⠘⠀⠀⠀⡀⡠⠄⡀⢁⠀⠀⢰⢧⡮⣻⡋⣯⣤⣄⣸⡾⠖⠷⠹⠏⠿⠼⠿⠃⠿⠋⠷⠹⠂
⠀⠀⠀⠀⠰⠀⠰⢄⣠⠙⠃⠰⠤⠀⠂
⠀⠀⠀⠀⠀⣘⣧⢨⠁
⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⡄⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣅⣽⣷⠄⠭⠠⠬⢀⠀⡄⠀⠀⠀⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⡛⢢⠀⠀⠀⣠⣸⠥⠐⠂⠄⢀⠃⠀⠌⢎⣫⠨⡱⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂⠊⠀⠀⠀⠀⠼⠄⠧⣈⡳⢆⣎⠳⡆⢒⢘⡁⢲⡌⢙⠀⡓⢹⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡀⠐⣈⡥⠺⣦⡋⠽⢮⢘⡃⣚⡀⣧⢨⠈⣤⢃⡰⠇⠌⡅⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢠⡈⣂⢱⡠⡌⠷⡂⢽⡃⣛⠊⢡⣮⢀⣷⠰⡖⣂⣸⠉⢼⠡⠛⣊⡀
⠒⠦⡀⠀⠀⠀⠀⠀⠂⡀⠠⠄⢬⠸⠆⠳⠘⣥⡌⢁⠮⠣⠖⣬⣅⣩⣷⠈⠧⠘⢋⣤⡴⠟⠑⠀⠒⡈⠐⠐⠆
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠀⠀⠀⠲⣈⣘⠻⣧⣤⣿⣿⠿⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠁⠠⣀⡤
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣩⣅⢠⣄⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠛⠐⠊⠛⠘⢡⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⢠⠀⠠⣈⢔⡈⠇⠌⢓⢔⡁⠂⣥⣈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⣠⡾⠂⠀⢍⡘⠣⠼⠈⠸⠅⠐⠀⠀⠉⠹⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⠉⠀⠊⠁⣼⠆⡀⠂⠄⠜⡇⠉⡄⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠿⢳⡔⠒⠲⠃⢋⡾⢦⠔⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⢮⣷⡀⠐⠁⠀⠀⢸⠖⠣⠶⠰⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⡘⢉⡁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡀⠀⠙⣐⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠖⢀⠠
⠀⠀⠀⡀⠀⢀⡀⠠⢀⡠⠀⡀⠀⢀⠀⡀⢂⢀⠔⠂⠀⠘⣄⡄⢨⣵⠈⠀⠰⣤⣤⣴⡶⠆⠀⠁⠸⠃⣀⠈
⠀⠲⠀⡄⢀⣠⠓⢈⡃⣁⠘⠀⢠⠌⠨⢓⠀⡤⢌⢀⠡⠀⠐⡙⡘⠋⠰⣦⣒⣀⠙⣏⠀⠠⣩⠆⠾⠁⠀⠂
⠀⢐⠶⣂⠠⠀⠞⠈⠃⢈⡘⠂⠉⠈⡋⢈⠴⢎⠐⠀⡁⠜⠀⢠⠅⡙⡆⢂⣉⠃⠘⠛⠓⠈⠛⠀⣀⠐⠐⠈⠀⡀
⠀⠀⡀⠈⡀⢘⠃⠀⠶⠙⠃⠱⠞⢓⡀⢌⡒⠖⡂⢲⢂⠁⣂⠥⠔⠐⡈⡀⣙⠷⡄⠀⠀⠀⠟⢙⠁⠀⠀⢐⠄⠁
⠀⠀⣷⠀⢧⠀⠉⣦⠘⠀⢦⠓⡠⠙⠛⡸⠎⠣⢍⠠⠍⠐⣒⣀⢩⣈⣡⣄⠌⢀⡘⢾⣄⠀⠀⠀⠔⣤⠆⠉
⠀⠀⠈⠀⠀⠁⣷⠉⠀⢻⣦⠁⡶⠂⣼⠇⠂⢋⡭⣈⡉⠤⠘⢉⡃⠴⡅⢄⠮⢀⠉⡄⠉⠘⠳⠀⠄⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠉⠈⠉⠀⠋⠉⠀⠛⠁⠐⠂⠀⠃⠀⠒⠂⠀⠀⠑⠀⠀⠀⠀⠠⠄

⠀⠀⠀⢀⡤⠒⠚⠉⠉⠙⠒⠲⢤⡀
⠀⢀⡜⠁⠀⠀⠀⢀⡤⢤⡀⠀⠐⠈⢣⡀
⠀⢸⠀⠀⠀⠁⣰⠃⠀⠀⠙⢦⠀⠈⠆⢻⡀
⠀⢸⠀⠀⠓⠒⠉⠙⡄⠀⠀⠘⡆⠀⠀⠀⢧
⠀⠘⢆⠀⠀⠀⠀⣀⠟⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠈⠙⠊⠉⠉⠀⠀⠀⠀⢀⡇⠀⡀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡂⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⡠⠖⠋⠓⢦⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢱⠀⠀⠀⠈⠧⠐⠒⠒⠉⠋⠀⠈⠉⠉⢙⠒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠫⠭⠍⠉⠀⠀⢀⠀⠀⠀⠀⠀⢀⠔⠐⠀⠀⠀⠀⠀⢀⠀⠈⠈⠓⢤
⠀⠀⠀⠠⠖⠒⠊⠀⠀⠁⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠱⣄
⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠔⠣
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⡀
⠀⠀⣀⠞⠀⠀⠀⠠⠠⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡
⠀⠀⠣⠶⣈⣩⡅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⢤⡚⢢⡀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⡖⠚⢀⠀⠀⠙⢯⠁⠒⠒⠒⠒⠒⠒⠒⠹⠁⠀⠱⠀⢀⠼⠀⠙⣆⠀⠀⠘⡆⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⣀⣤⡴⢥⣤⠀⠀⣔⠁⠀⠀⢀⢸⡆⠀⠃⠘⣉⣁⣀⣀⣀⣀⠈⠑⠀⠄⠠⣄⣀
⡠⣀⣠⠖⠉⠒⠤⠤⠔⠀⠂⠤⠇⠄⠈⠀⠠⠞⠒⠒⠒⠒⠶⠶⠒⠋⢀⣠⣴⣆⠀⢀⠀⡥⢀⣈⣉⡡⠤⠻⠀⠀⠠⠇⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⣀⡀⠉
⢧⠄⠒⠒⠉⠁⠒⠒⠒⠀⠒⠀⢖⣦⣦⠤⠜⠈⠁⠂⠉⠑⢲⠄⡠⠚⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡤⢂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⡰⠉⢀⣀⡀⠈⠄⠀⠀⠀⠀⠘⠀⢀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⠁⢀⠔⢀⡆⠀⠀⠀⢀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⡄⠈⠉⠁⠀⠀⢀⡀⠃⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠈⠑⠂⠀⠀⠂⠁⠀⢀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⣄⣀⣀⡦⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⣉⣀⣀⡀⠀⠀⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⠋⠙⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⠀⠀⠙⠛⠛⠉⠹⡟⠛⠛⠋⠁⢀⣾⣿⠟⢩⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⣠⣿⡿⠁⠀⣾⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠚⢧⡀⠀⠰⣄⠀⠀⠀⠐⢲⡾⠉⠁⠀⠀⢠⣿⡿⠁⠀⣼⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⡄⠈⠳⡄⠀⢸⣿⣶⣤⣤⣾⣅⡀⠀⠀⠀⣾⣿⠁⢀⣼⣣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣹⣶⣾⠉⠁⣸⣿⣿⣿⣿⣷⣦⣄⣿⣿⢠⢞⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠻⣿⡟⠧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⣇⠀⢸⣿⣿⡿⠛⠁⠀⠀⠀⣀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⠟⠉⠀⠀⠀⠀⠀⣄⠙⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡀⠀⠀⠀⠀⠀⠀⠲⣌⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢷⣄⣴⣿⣿⣋⣿⣶⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⠛⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⢸⡃⠈⡷⠴⡏⠀⢹⠀⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⠀⠙⠛⠁⠀⠉⠛⠉⢀⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⡀⠀⠀⠀⠀⠀⢀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠈⡟⠒⠶⠶⠶⠚⡏⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⣻⠇⠀⢻⠉⣻⠿⡏⢹⠃⠀⢿⡳⠤⣄⣀⡤⠖⠚⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢴⡃⠀⠀⠈⣇⢳⣶⢋⡏⠀⠀⠀⣹⠄⣰⠋⠳⡄⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⢦⣀⠀⢹⡞⠘⣿⠀⠀⣠⠞⠁⢠⡇⣾⠁⢿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⢷⢰⢇⡴⠋⠁⠀⠀⠘⡇⠉⠀⢸⡄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠇⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣤⣤⠴⠞⠙⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⠟⠛⢷⣆⠀⠀⠀⠉⠉⠉⠉⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⢶⣶⠾⣿⡀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠁⠀⠀⠀⠀⠀⣸⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡉⣹⡇⠀⠀⠀⠀⢐⣿⣩⣿⣉⣙⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣩⡿⢻⡇⠀⠀⠀⠀⣼⡏⠉⠉⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠃⠀⠀⢰⣿⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⠛⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢰⡿⠙⢷⣄⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢿⡇⠀⠀⢹⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢻⡿⠁⠀⠀⢸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⣼⠏⢠⡿⠁⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠿⣶⡿⠀⠀⠀⠀⠀⠸⠷⠾⠃⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣼⠏



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⢀⠀⠄⠀⠀⠀⢂⠀⠀⠀⠄⠠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠴⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⡅⠱⠀⠀⠀⠀⠀⠀⠙⢟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢹⡄⠓⠂⣀⠀⠀⠀⠀⠀⢷⠨⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠤⣿⡈⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠋⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢈⡬⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠐⠂⠀⢠⠀⠀⠰⣿⠀⠖⠀⠀⠀⢠⠀⠀⠀⣼⠀⠀⣁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠷⡾⠄⢀⠇⠀⠐⢰⡇⣀⡀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⢩⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⢛⠛⠛⠓⠒⠚⠓⠒⠃⣼⠀⡍⠀⠀⠀⢀⡇⠀⡌⢸⡇⠀⠁⠸⠂⢻
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣯⣭⣵⣶⣅⣀⣤⣨⡥⠴⠖⠚⠋⠻⣿⣿⣿⣿⡿⢾⣷⣶⣷⣿⣯⡉⠝⠀⢡⢸⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⡟⣿⣿⣂⠀⠀⠀⠀⠀⠈⢻⣷⣯⠿⠚⠻⣾⣿⢿⣿⣿⣦⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠻⣇⠈⠁⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⣌⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣼⣿⣿⣿⣿⣿⣿⡟⠁⠉⠛⠶⣽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⠉⢉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣦⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⣰⣿⠿⠛⢻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⢀⡠⠴⠒⠉⠁⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢰⡇⠀⠀⠀⢀⢀⣀⣀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⣠⢤⣿⣿⣿⣿⣿⡷⣤
⠀⠀⢀⣀⣤⣤⣤⠀⢀⣾⠏⠀⠀⠀⠀⠀⠳⢤⣴⣾⣿⡿⣿⣿⡇⡜⣈⡧⠀⠀⣀⣤⡖⠋⢠⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠡⡉⠻⡿⠴⣊⡏⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡝⡓⢸⣿⣿⣭⢤⣴⣺⡽⠛⠉⠀⣴⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⢳⡀⣠⢞⠟⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠷⠃⣏⠉⠉⠉⢩⣾⠉⠁⠀⠀⣠⣾⣿⡿⡿⠿⠿⢿⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⡴⢻⣿⣿⠟⠁⠀⠀⠘⡄⠀⠀⣾⡏⠀⠀⠀⠘⠋⠉⠉⠀⠀⠠⢀⠀⢠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡿⠛⠁⠀⠀⠀⠀⠀⣷⠀⠴⢿⣇⠀⠀⠔⢉⢀⣦⣔⠶⠋⠚⠂⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢻⡄⢆⠤⠊⠈⠀⢠⡄⢀⠆⡀⢐⣤⣤⡴⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠜⠀⡏⠐⠘⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣽⣷⣦⣴⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣇⢱⡀⣀⣔⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⣐⢂⡓⡜⠒⡠⠙⣿⣼⣁⠈⠠⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡶⢂⣻⠼⠧⢰⣛⢳⠋⠁⡀⠈⢛⠣⢠⠰⣼⡌⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡝⡶⠻⢭⠲⠐⠋⠕⣪⠃⠀⠠⠙⠼⣵⢖⡘⠿⡻⠎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡹⣵⠺⠕⠲⡏⡨⢺⢃⡳⡂⠀⡆⡒⢲⠐⣭⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⢘⢣⡴⢾⣁⠌⡀⠸⢩⠅⢓⣘⡔⠳⠌⣴⣿⣷⣄⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⡳⣨⣅⢲⡞⠧⠦⡋⠀⢶⢼⠊⣪⡤⠀⠀⠈⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢷⡆⣆⡽⣠⣶⡝⣐⠦⠈⡓⢪⢌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⡹⢶⠍⡕⣼⢾⠇⠳⡾⠈⢨⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⡍⠹⡬⡓⢞⣰⣞⣷⡝⡑⢬⡉⢬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⠀⢆⣃⣼⠼⣍⡝⣩⡌⡙⠥⢬⡻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣅⠶⠞⢠⡗⢨⠙⡬⢤⢹⣵⣿⠸⡍⠉⠋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣩⢶⢫⠗⢨⠩⣼⣧⡟⣸⡇⣾⠜⠟⠴⠶⣍⣓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣹⣸⢷⣝⣮⠶⢋⠶⡆⣩⡇⢿⠼⡏⣧⣊⡊⢝⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠞⡰⣚⡆⣛⡞⣴⠏⣹⡱⣶⡆⣟⠦⣧⣺⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡟⡚⣽⣴⣒⣭⣾⣫⡗⢹⣇⣾⣌⣳⢳⡇⢭⡑⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣃⣼⢮⣡⠖⢺⡕⣿⠎⣭⡶⡎⣛⣥⢴⣪⣝⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡿⣐⢟⡙⣥⢲⠰⣢⠉⣷⣶⢩⢻⣤⡛⠾⠃⠸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢿⠏⠡⡮⢴⡴⣼⢻⡎⣡⣾⡌⢹⣹⠆⠀⠸⡦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆⡾⢡⣡⠆⠜⠁⠀⠀⢰⣄⠖⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⣮⢽⣷⡄⠀⢀⣰⣶⠸⣊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢛⡕⣯⣫⣏⢵⠅⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠒⠛
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⢀⢖⠀⠀⢹⡿⢀⠌⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢠⠠⣤⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⠉
⣀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠞⢎⢂⠰⢰⠂⠀⠀⢀⢠⠀⠠⠠⣰⡐⢤⡸⣜⡝⣖⣁⣊⡔⣺⣼⢲⡡⢐⢀⢆⡀⠄⢠⢠⠠⣄⢘⡗⠃
⠹⠶⣢⣤⠀⠰⡀⠀⠀⠀⠈⠀⢀⢑⠎⣂⢓⡪⣓⣌⢸⡨⢌⠪⢺⠙⣠⢢⢡⡕⣮⡵⢎⠢⡸⡽⣯⣹⡰⢚⡌⠑⠛⠀⠋⠀⠁
⠀⠈⠛⠉⠀⠀⠀⠠⠀⠀⠀⢀⡄⢯⠳⢢⡴⢁⢣⠸⢠⠥⢂⣃⢌⡈⣄⢚⡐⣒⣣⡿⠨⣑⣻⠣⢦⣍⣖⣋⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠮⢄⡗⣲⠸⡐⢔⢨⠃⣘⢆⣫⡘⣗⢘⣆⢚⢸⡜⢍⠡⠒⡔⣚⢣⣵⣨⣾⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠠⡸⠽⣻⠑⣧⣬⠱⣎⠚⢐⡁⠔⣀⠗⣤⡋⢼⠙⠳⠛⢶⠘⡭⢱⣅⢗⡌⢧⢡⡔⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠅⢅⠣⢫⠻⠏⢩⡉⢷⡐⢻⡄⢻⡯⠻⠆⠛⠁⠛⠈⠀⠀⠀⠀⠙⣞⣱⢞⣧⣵⠿⠋⢑⠆⢠⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠦⢤⣝⡓⠀⠀⠀⠀⠈⢿⡌⠻⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣛⠴⣀⠀⠙⢉⢠⢠⡮⠄
⠀⠀⠀⠀⠀⠀⡀⡌⣍⠛⠂⠀⠀⠀⠀⠀⠀⠀⠊⡺⠛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢙⣛⣄⠀⠀⠀⠀⠉⠤⠁⠐⡀
⠀⡀⠀⠀⢀⠠⣙⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠍⢺⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡀⠀⠀⠤⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠓⠘⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠠⣤⠷⠎

⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣉⡉⠉⣉⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⣿
⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠛⠃⠀⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠃⣠⠶⠲⣦⡈⢻⡄⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠟⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⡀⠀⣸⠇⢸⡇⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠛⠉⢠⡟⠁⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⡀⠘⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠿⠛⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡟⠀⣾⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⣿
⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⣿
⣿⣿⠀⠻⠿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⣿
⣿⣿⠷⢶⣶⡶⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⢶⣿⠆
⣿⣿⠀⠘⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⠟⠁
⣿⣿⠀⡄⠸⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠋
⣿⣿⠀⣿⡄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡷⠋
⣿⣿⣴⣿⣷⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡁⢿⠻⣿⣿⣿⣿⣿⣿⡿⡇⠸⢿⣿⣿⣿⣿⣿⣿⢿⡿⢧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣶⡈⠉⠛⠛⠛⠋⠀⡇⢸⠂⠉⠛⠛⠛⠉⢁⢨⣶⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡙⠇⠀⠀⠀⠀⢶⣀⠃⠈⣀⡶⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣹⣟⣟⣉⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣄⠀⠀⠁⠙⠛⠛⠻⠟⠛⠛⠃⠘⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⢦⡀⠀⠀⠈⢹⠿⠿⠋⠁⠀⠀⣠⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢮⣿⣦⣆⡀⠀⠀⠀⠀⢰⣦⢞⠕⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠛⠿⢿⣶⣶⠶⠞⠫⠐⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣼⣷⣻⣆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡏⢷⡀⠀⠀⢀⣾⣿⣿⣿⣻⣆⠀⠸⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠾⠿⠿⠿⠿⡷⠛⠂⠰⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⣀⣀⢀⠀⡀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠰⡄⠇⡰⢄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡿⠁⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠊⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠠⡀⡆⢠⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠈⠀⠘⡶⠁⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠇⡠⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡀⡇⢠⡀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢰⠂⠐⠂⠁⠬⠐⠀⠁⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⠂⠀⠱⣶⠃⠈⠂⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠂⠀⠀⡨⠠⠞⠀⠆⠇⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠦⠀⠅⠀⠔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠈⡌⡔⠀⡤⠤⠤⢤⣀⠀⠀⠈⠀⢳⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣃⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠭⠭⣙⣒⠀⠸⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠭⢝⣒⣂⠀⠰⠿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣊⣩⣍⣙⣓⣒⠦⠥⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣛⣛⣒⣒⣒⠭⠭⣓⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣒⣒⣒⣒⣒⡦⠭⢭⣒⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠉⠙⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⣉⣀⣉⣉⣉⣉⣓⣒⣤⣼⣤⣤⣐⣀⣀⣀⣀⣀⣀⣀⣈⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⡰⠶⠶⠶⠶⠆⣶⣶⣶⠶⠄⠀⠀⠀⠀⣠⣤⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣛⣋⣭⣵⣶⡿⠇⠀⠀⣰⡿⣫⣵⡖⡲⣶⣭⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢟⣛⣭⣵⣶⡾⠿⢟⡻⣿⡅⣶⣾⡇⠀⢸⡟⣼⡟⣭⣶⣶⣮⡻⣷⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢟⣛⣯⣭⡶⠾⠿⠿⣧⣿⣷⢹⣿⡇⠀⢿⡇⡿⢘⣛⣛⣛⣛⣓⢹⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣫⣵⣾⠿⠿⢿⣶⣝⢿⡎⣿⡇⠀⠘⣷⡹⣶⣿⣿⣿⣿⣷⠞⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣱⣿⡟⡴⣫⣝⢲⡹⣿⣧⢻⣸⡇⠀⠀⠘⢿⣮⣝⣛⣛⣋⣵⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡏⣧⠻⠿⣹⢇⣿⣿⢸⣧⠃⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡸⣿⣿⣎⢿⡿⣣⣿⣿⡟⣼⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⡻⢿⣷⣴⡿⠟⣫⣾⣧⢻⡇⠀⠀⠀⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣶⣶⢰⣿⣿⣿⣿⡜⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣛⣛⣭⣽⡇⣿⣿⢺⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢟⣛⣭⣽⣿⣦⡱⢿⡿⣿⣿⣿⣿⠇⠀⣀⣀⣀⡀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠿⠿⠶⠶⠆⠀⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡶⡄⡀⢉⠀⠆⣤⣀⣀⡀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢀⡊⢠⣿⣷⣼⡃⠚⠀⠈⠻⢟⢹⢧⡞⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⡟⢱⣿⣿⠁⣿⣛⠧⠀⠀⠀⢀⣎⢸⡆⢉⡘⠿⡁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢁⠀⡛⠙⢣⣿⡟⠿⣧⠙⠻⠂⠀⠠⢐⡉⣩⠀⠶⢠⣍⣨⣡⣴⢸⠣⡀
⠀⠀⠀⠀⠀⢀⡌⠛⠿⢘⡋⢾⠜⠋⢱⠄⠀⠀⠀⢀⠉⠞⢨⡤⠅⡒⠒⢀⡨⡍⣙⠿⠈⠰⠹
⠀⠀⠀⠀⣠⠈⣵⡸⠐⣛⢠⡶⠀⠀⢠⠀⢀⡀⡄⢘⡁⡿⣨⠁⣈⠛⢊⡄⡁⢀⣿⡆⠀⠈⠂
⠀⠀⠀⠀⠿⣤⡈⣱⠿⢁⡉⠃⠀⠀⡆⠚⠙⠡⢦⢙⣥⡄⢫⢘⡀⠇⠄⣈⠑⣮⠉⠉⠀⠀⠀⠀⢃
⠀⠀⠀⠀⢠⢎⠀⣴⠀⢨⡅⠀⡄⠀⡄⡀⠀⣶⡌⢈⣉⡱⠶⠆⠐⡀⢃⡉⣃⠐⡃⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⢀⡘⡁⠛⠀⢲⡄⠀⡄⠀⠀⠁⢀⣤⡀⣈⣍⠁⠀⣘⠇⠿⢈⡁⠉⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠙⠃⠉⢠⡄⠁⠀⢠⡶⠀⠀⢀⣍⠀⠉⠿⠖⠈⠛⠀⣻⠎⢡⠁⡂⠠⣤⣉⣀⡀⠐⣦⣤⣤⢢
⠀⠀⠀⠀⠀⣿⠀⢠⣤⠀⠀⠀⣤⠀⣀⡄⠘⠛⢀⣠⣿⡟⠲⠀⣤⡛⠀⠀⢨⣥⣘⣳⠶⠠⠤⠤⠈⠙⠔⠁
⠀⠀⠀⠀⠀⠻⣦⢈⡅⠀⠀⠰⠟⠀⢘⡵⠶⠟⠀⠉⠉⠁⢤⣍⡉⠁⠀⢸⣟⢿⡿⠯⣽⣟⡛⠢⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⡶⠀⢀⡤⠀⢀⡀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠲⣿⣯⡉⠿⠿⠶⠒⠈⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠇⠀⠛⣿⠀⠀⣠⡔⠈⠀⠀⠀⠀⠀⠀⠉⠛⠿⠃⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠿


⠀⢀⡀⢀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣴⣶⣶⣦⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣏⣻⡿⠟⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣫⣟⡀⢁⣀⠁⣬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢀⣄⡀⣀⣀⣀⣠⣤⡤⣶⠿⡏⢝⣥⣿⣿⡦⠯⣼⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⣭⡟⣾⣝⢯⡿⣰⣯⣥⣻⡯⡞⣇⢛⣶⢿⡛⠵⢛⡝⠻⠿⢃⢀
⠀⠀⠀⠀⢀⣠⡿⣿⣏⢷⣻⡸⢆⣷⢨⢧⡔⣏⠑⣂⠟⣿⢈⣽⠏⣹⢾⣟⣭⢵⢆⠍⢸⡖⢑⢆
⠀⢀⣤⣶⣿⣭⣻⣿⣲⣺⣻⡇⣭⢏⡚⢿⣌⡇⡄⢿⠇⣵⡆⢿⣃⡍⣾⣿⣯⢰⡶⣻⠼⣾⣿⠋⡎⡶⣠⣀⡀
⠀⣿⣿⣿⠗⢛⣯⣽⠷⣯⣯⣝⣻⣆⣷⣜⣿⡙⢷⡟⢷⣴⣿⣼⠻⠷⠷⣿⣷⣿⣌⢥⢚⣷⠹⡞⢵⢧⢷⣷⣷⣃⡄⢀
⠀⠙⢿⣿⣣⣶⡿⠼⣧⣥⣍⣤⣉⣁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠛⠛⠹⠦⠹⢾⣤⣁⡢⠜⠙⡛⢮⣼⣼⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠾⠾⠾⠃






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡴⠚⢹⡏⠓⢦⡀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠙⡏⠉⠀⠀⠀⠀⠉⣹⠋⠉⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢦⣀⣰⡆⣀⡴⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⢹⡏⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠞⢧⠀⠀⠀⢀⡾⠱⠶⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⣀⣤⠴⠶⠒⠊⢳⡄⣠⠞⠐⠒⠶⠦⣤⣀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠐⢧⣀⡀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢀⣀⡼⠂⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣈⡉⠙⠛⠛⠒⠒⠒⠒⠛⠛⠋⢉⣁⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠁⠈⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⣄⣀⣈⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠚⠃⠉⠉⠉⠉⠙⠳⢆⣤⡠⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⡄⠀⡦⢘⡇⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⡩⠒⠙⢦⡀⠘⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡇⠀⡷⣾⠀⠀⠀⠀⢠⠃⢀⣤⠀⠀⠀⠀⠠⠤⣄⠀⠀⠀⣎⣀⣤⡄⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡀⠀⠀⢀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢄⠀⢧⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠈⡇⠀⠀⢸⠀⠀⠀⢰⣶⡀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠁⠀⢻⡀⠀⢸⠀⠀⠀⠸⠿⠃⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠍⠁⠀⠈⣧⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠂⠀⠀⠀⠀⠀⢠⠃⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠙⣦⠀⠀⠀⣀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣔⡒⢶⣶⣤⡄⢹⡄⠀⠈⠓⢦⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣶⣿⣿⣿⡶⠚⣷⡗⠂⣄⠀⠀⠀⠀⠈⠙⠲⠦⢤⠤⠤⠤⠶⠚⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠜⠛⠿⠿⠿⠧⠤⠿⠛⠀⠈⢧⡀⠶⠶⠶⠶⠶⠶⣾⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡧⠀⠀⠀⠀⠀⠀⠗⠀⠈⠛⠲⠤⣄⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⡛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣲⡄⢈⠹⣦⢸⠁⡛⠀⣩⡝⠀⢤⠀⣀⠀⠀⠀⠀⡴⠊⠈⢠⣤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠀⠠⡄⢻⠄⢙⡆⢘⠆⠠⠄⡚⠠⠌⢩⡅⠠⡖⠀⠶⡀⠀⠀⣀⡄⢀⠤⢠⣿⣿⣧⢄
⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠐⠀⠈⡀⠱⠆⣐⡰⠱⣡⡘⠀⣉⣱⠠⢈⡴⠶⠶⠀⢀⡉⠀⠀⠀⣤⣤⣼⣿⣿⠿⠃⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⢀⣤⣷⠋⢙⡃⠦⣭⠑⠠⠍⠀⢸⡇⢠⣀⡲⣇⢻⠀⠷⠈⢧⠀⠀⠀⠚⣿⣿⣿⣯⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡂⡏⠀⠨⡔⢂⡜⣈⠰⡄⠀⣸⡇⠀⠋⠒⠈⠈⠠⠄⡦⣼⠁⠸⠾⢷⣾⣿⡿⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢶⣦⠈⠁⠢⠉⠃⠒⠐⢢⠈⠉⣱⡿⢛⠟⢶⣶⣄⠀⠸⠆⢀⡀⢠⣀⠈⠙⠇⣠⡞
⠀⠀⠀⠀⠀⠀⠀⡈⣄⠹⢄⣈⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⡴⢿⣦⣀⠀⠊⡀⡁⠛⠀⢶⢘⡇⣀⠈⠻⠘⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⠀⠀⡆⠀⠀⢀⠄⠴⠀⠀⠀⠘⠃⠀⠀⠀⢀⡀⠑⠘⠃⢶⣴⣜⠃⠙⠃⢀⠾⠟⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠄⠂⠀⠁⠀⠀⠈⠀⢀⡀⠀⠀⠌⠁⣀⠀⠀⠠⢀⡔⠲⠆⢶⢂⡙⠿⢠⣿⠹⢠⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⢡⡀⠂⠀⠁⠢⠄⠠⡘⠁⣐⠟⢩⣄⡌⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠃⣈⠁⠐⠈⡁⢠⢤⡠⠄⠁⠰⠀⢈⠻⠿⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⣦⣦⡄⣅⣤⣶⣶⣾⡿⠀⠀⠀⣀⢁⡜⡆⠚⠀⠡⢠⣶⠂⠀⣼⢇⣄⡘⠃⡄⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⢫⣿⣿⡿⠉⠁⠀⠀⠘⠋⣉⣈⣤⡤⠘⣤⢃⣘⣉⣼⡇⢀⣾⠈⠛⠀⣐⠇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠙⡟⠀⠀⢁⢛⢘⠚⣋⣉⣨⡴⡆⠀⠁⠚⠿⠿⠓⠰⣾⣻⡿⠠⣿⣿⢡⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠄⠀⠀⣠⡷⣄⣀⠀⠈⠨⣯⣯⢷⣶⣶⣶⣤⣄⣙⠛⠿⠿⣶⣦⣌⠀⠘⢿⡃⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠿⠿⠟⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣤⣀⡀⠀⠀⣼⣗⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠁⣤⡀⠀⠀⠀⠀⣀⣤⣾⠿⢿⣿⡿⠿⠿⠿⠿⠋⠀⠈⠻⣿⣷⠀⠈⠛⠋⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢠⡆⠀⠛⠀⠀⢰⣾⠉⠉⢽⣷⣦⣬⠁⠼⠿⠂⢠⣴⣤⣾⠙⠛⠉⠀⠀⠀⣤⡄⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠏⠘⠁⠀⣶⡆⢠⡈⠿⣷⠄⠀⢉⢙⣁⠀⠀⠀⠀⠈⢉⡉⢀⣤⣴⣷⣾⠄⠒⠛⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠆⠀⠈⠀⠈⠁⠀⠀⠀⠀⠈⠻⠿⠾⠷⠾⠀⠀⠉⠀⠿⠟⠛⠛⠛⠀⠴⠖⠀⠠⠤

⠀⠀⠀⠀⢀⣠⣴⠶⠿⠛⠛⠻⠷⢶⣦⣄
⠀⠀⢀⣴⠟⠉⢀⣠⣤⣤⣶⣤⣤⣀⠀⠙⠿⣦⡀
⠀⣠⡟⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠙⠳⣦⠀⠙⢷⡄
⢰⡟⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠈⣿⡀
⣿⠃⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢹⡇
⣿⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⢹⣇⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣾⠃
⠈⢿⣄⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⣼⠏
⠀⠀⠻⣧⡀⠀⠈⠙⠛⠿⠶⠿⠛⠋⠀⠀⣠⡾⠋
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠿⠿⠿⠷⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⣀⣀⣀⣀⣀⡀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⣠⡶⠟⠋⠉⠉⠉⠉⠛⠷⣦⡀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠖⠠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣶⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⢻⡆⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠈⠛⠷⢶⣦⣤⣤⣶⠾⠛⠉⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⢠⣤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠛⠐⠶⠶⠆⢠⣄⡈⠻⣦⣀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢼⡟⠋
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⡤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣴⣶⡷⠶⢶⣶⣦⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⢿⣿⣿⠓⠒⠀⠀⠈⠉⠛⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠻⠃⠀⠨⠽⢶⡆⣤⠠⠿⠿⠿⢓⣴⡮⠞⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠆⠀⠀⠀⠀⠀⠬⠇⠂⠀⠀⠀⠠⡫⠋⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⡞⠉⠁⢿⣶⠀⠀⠀⠠⠠⠔⠡⠀⠀⠀⣿⠃⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⢰⠁⠀⡆⠈⢿⣦⠀⠀⠀⣹⣦⣄⡀⠀⠀⢩⣘⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⡀⠀⠘⣤⠀⢰⠀⢠⣿⣿⢿⣿⣿⣿⡿⠋⠉⢉⡉⠛⡙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢱⠀⠸⡁⠀⠘⣆⠏⣼⣿⣤⣿⣿⠟⠀⠀⠀⢄⡈⢢⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡇⠀⠙⣄⠀⢻⣼⣿⣿⣿⠟⠁⠀⠀⠀⠐⢤⣹⣿⡄
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠆⢸⡿⠛⠋⢁⠀⠀⢀⣀⣤⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠴⠊⠁⠀⠀⢠⠈⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡴⢦⣫⢻⢽⡪⠿⣇⠾⢢⡶⣶⢠⣀⡀
⠀⠀⣠⡿⠟⡶⣖⠖⡻⠙⣾⠟⡟⠨⠽⡎⠮⠏⡎⣧⢓⡛⢿⢮⢵⣶⣶⣀⡀
⠀⡘⣆⣻⣿⣡⢛⠚⣋⣙⡞⡚⠙⠋⡏⢫⢩⠙⡉⡭⠜⡘⡇⣘⡚⠳⡾⣛⢳⡆⡀
⠀⢑⣾⠞⢿⣷⡿⡇⠧⠞⡥⠛⣀⢒⠇⠡⠣⠙⡠⢑⠣⣅⠜⣩⠵⢳⠲⢛⠲⢧⣇⡆⠀⠀⠀⠀⠀⠀⣺⡇⣀
⣜⡞⠀⠀⠉⡟⡀⠀⠡⠈⡈⡾⢨⠌⠣⣀⣥⡡⠅⣧⢋⠾⡇⢦⡘⢣⡹⠯⠟⠀⣝⡍⡳⢀⡀⠀⠈⠋⢹⣿⡛
⠕⠱⠮⣠⣄⠀⠀⠜⢯⢁⣫⢒⣑⠄⣁⡄⢤⢚⠇⣖⣱⡧⡙⣫⡿⡬⣔⠆⡀⠀⠀⢩⣑⡾⠱⠇⠴⢲⡝⢶⡅
⠘⢚⠀⠈⠈⠁⠀⠀⠀⡄⣊⢭⣋⠄⣩⣼⠰⢂⡧⠶⣣⡜⣥⣯⠱⠶⣴⢚⠁⠀⠀⠀⠈⠐⠃⠿⠘⠏⠁⠁
⠀⣯⡓⠠⡀⠀⠄⠀⠠⣔⠷⢖⠚⡭⠛⠋⠀⠀⠀⠀⢡⠾⣦⣴⡲⠇⣡⠆
⠀⢈⣹⡠⣍⣒⡚⠐⠁⢩⣫⠝⡛⠇⠀⠀⠀⠀⠀⠀⢀⣶⣤⡜⢱⡵⢆⡶
⠀⠈⠥⠔⠷⢶⠀⠀⠀⠀⡗⣃⠙⠃⠀⠀⠀⠀⠀⠀⠀⢤⣈⡱⢒⣡⠶⠤
⠀⠀⠐⠈⠰⠲⠀⠀⠀⠀⡓⢌⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠂⠀⠒
⠀⠀⠀⠚⠱⠈⠆⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⡠
⠀⠀⠀⡐⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠋⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣻⣷⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣙⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣿⣿⢿⣿⠾⠟⠋⢿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣶⣶⣙⣻⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⠿⠟⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣿⣿⣿⣿⡿⢿⠿⣿⣿⢿⣉⢛⠻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢹⡆⣿⣿⣷⣾⣿⣿⣻⣿⠿⣿⣿⣷⣯⡴⠀⢠⡽⣿⣿⣿⣦⣹⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⡿⠙⣩⠷⠀⠉⣽⣿⡏⠙⢿⣿⣿⡟⠁⠀⣿⣿⡈⠙⠷⣾⡉⠀⠀⠉⢿⣿⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⣿⣿⠿⠛⠛⠋⢙⣋⣉⣠⣤⢁⣀⣀⣀⡛⠿⠿⣄⠀⣿⣿⡀⠀⠀⢛⣋⣡⣤⣤⡤⠤⢤⣤⣄⣀⠉⠉⣙⣻⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣷⢸⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⣦⣄⣀⣉⣉⣀⡠⠞⣡⣾⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⡜⣿⣿⣽⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣿⡇⢼⣿⣿⣿⠿⠿⣿⣿⣿⣿⡟⢻⣿⣧⣿⣿⣿⣿⣿⡇⢸⣿⣯⣀⣼⣯⢻⡟⠀⢸⣿⣿⠟⠃⣸⣿⣿⠟
⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣼⣿⣿⣿⣿⣯⡾⠃⠀⣰⣿⣿⡇⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡸⣿⣿⣿⣂⠀⠘⠿⣿⣿⡿⠿⠛⣩⣟⠁⠀⠀⠄⠹⣧⠉⠉⠛⠋⠉⠁⠀⣠⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣏⡹⣿⣿⣶⣤⡄⠀⠀⠀⣠⡼⠻⣇⣤⡄⣀⢠⣤⡼⠷⣄⡀⠀⠀⠀⢾⣿⣿⠿⣡⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⡷⠹⣾⣭⣭⣤⡤⠶⠒⠋⠁⠀⠀⠀⠙⢧⣿⣼⠃⠀⠀⠀⠙⠛⢶⣶⣾⣷⣶⣋⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⢿⣿⣿⣿⡆⠀⠒⠀⠂⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⠠⠍⣠⣿⣿⣿⡿⣟⣾⣿⣾⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣷⣂⣱⡶⠊⠁⠀⠀⢠⣿⣧⡀⠀⠀⠀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⡿⣿⣿⣿⡿⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣷⣄⠁⠈⠙⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠻⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣷⣦⣤⣤⣴⣦⣤⣶⣿⣿⣿⣿⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠛⣿⣿⡿⠛⠿⠋⢈⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠋⠁

⠀⠀⠀⠀⢀⣀⣠⡴⣖⢚⢏⣻⠶⠤⡤⣤⠤⢀⠴⢢⡴⠖⡒⡒⢒⡒⡶⡢⣤⢤⣤⣀
⠀⣀⢸⠚⠈⠁⠀⠈⠀⠱⠈⢛⣿⣷⣘⣹⡈⡹⠤⢂⡟⠏⠥⠫⣞⢾⡌⢂⡿⠧⣲⣻⣽⢦⡀
⣰⠁⢀⠀⠀⢀⠰⠀⢠⠄⠀⢀⡠⣮⢟⡾⣫⢋⡕⠬⢦⣝⢱⢰⡘⠿⢐⣇⡏⢿⣸⣝⢿⠱⣝⣦
⡗⠂⠈⠀⠀⠀⠀⣦⢀⠈⠓⢰⢺⡇⣛⣶⡿⣧⡶⣘⠁⠧⠒⢊⣉⣸⣇⣓⡤⠍⢨⢼⣫⣧⠈⠳⣵⡄
⠡⠄⡔⠀⠀⠀⠀⠘⡦⠤⣀⣔⠜⠛⠜⣫⢵⡚⡖⠶⠀⠒⠐⠉⠙⡌⢡⡕⣷⡾⣺⢭⣧⣟⡵⣤⡈⢻⣢⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡣⢤⡸⠀⠀⠀⠀⠐⢿⢷⢦⠀⠀⠀⠀⠀⠀⠈⠣⣀⡖⢨⠟⡷⠧⣟⣶⢸⠈⡇⠙⢷⣆⡀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⢀⢪⣚⠞⠁⠀⠀⠀⠀⠀⠸⠩⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡾⣀⠇⠀⠀⠀⣹⢁⠇⠀⠀⠙⠷⣶⣤⣰⡾⠋
⠀⠀⠀⠠⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠠⢂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⡠⠤⢚⡤⠂⠀⠀⡀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⣣⡴⠎⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠈⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⢀⡀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢒⣤⡴⣧⣤⣤⣤⣤⣤⣤⣤⣾⡧⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⢰⡅⣀⣀⣤⡄⠀⠀⠈⢉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠸⢄⣘⣿⡷⠃⠀⠠⢄⣀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⢸⠇⠀⠲⠖⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠸⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⢀⡇⠀⠀⠀⠀⢀⣤⠴⠶⠶⠶⠷⠶⠶⠶⠶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠉⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣼⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⣨⡟⢻⣏⠉⢹⡇⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠁⢹⡏⠙⢧⣈⡇⡤⠀⠀⠀⠀⢰⡏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡻⡇⠀⢀⠸⡇⠀⠀⢹⡟⠀⠀⠀⠀⠀⠈⢣⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡸⠁⡇⠀⠸⠀⡇⠀⠀⣾⠀⠀⠀⠀⢀⠀⠀⢸⠀⠸⡀
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⠇⠀⡇⠀⡄⠀⡇⠀⢰⠁⠀⠀⠀⠀⠸⠀⠀⠈⣇⠀⣿
⠀⠀⢀⣀⣹⣿⠿⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣿⠀⠀⡇⠀⠇⠀⡇⠀⡜⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⠀⢸⡆
⠀⣴⣶⣿⡇⢉⣀⣀⠘⣆⢰⠛⢦⡀⠀⠀⠀⠀⣠⠖⠉⠁⠀⣠⢺⡇⠀⠀⡇⢀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠈⣧
⣷⢿⡟⠁⠀⠻⣄⡈⠓⢾⡿⠀⠠⡈⠳⡶⠖⠋⠁⠀⢀⡴⠊⠁⣼⠁⠀⠀⡇⢸⠀⠀⡇⣸⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⠀⠀⢸
⠙⢦⡀⠀⠀⠀⢠⡙⠆⣼⠃⠀⢀⡇⠀⢇⡀⣠⡴⠖⠉⠀⠀⠀⡿⠀⠀⠀⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠘⡄
⠀⠀⠹⣦⠀⠖⣩⠁⠀⢥⣤⡴⣏⠑⢦⣜⠉⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⡏⠀⠀⠀⣇
⠀⠀⠀⠈⢣⡄⠁⠀⠀⠀⠀⡤⠈⠙⢦⣈⠑⠦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠻⣄⠠⢄⠀⠈⠀⠀⠀⠀⢻⡟⠃⠸⠷⠀⠀⢠⡏⠀⠀⠀⠀⡟⢧⣄⠀⢸⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡜⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠈⠙⡟⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⡇⠠⢤⣀⣀⡞⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⠀⠀⢨⡉⠛⠳⠦⢤⣼⣇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⠃⠀⠀⠀⠈⠓⠶⢀⣀⠀⠀⠉⠛⠛⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡇⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣸⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⠴⠖⠚⢙⡇⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠤⠤⠤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠏⠀⠉⠙⠛⠓⠶⠶⠦⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠶⠶⠶⠖⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠶⠖⠀⠉⠉⠁⠀⠀⠀⣠⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠶⠶⠶⠶⠶⠶⠒⠚⠛⠋⠀⢘⣧⡿⠷⠶⠶⠶⢀⣤⡤⠤⠤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠒⠒⠉⣉⣉⠁⢀⣠⣤⡤⠶⠚⠉⠹⣤⣤⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢖⣠⡿⢁⡉⢋⡐⠦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⠖⣂⣰⠖⡞⠩⠄⢽⠄⢠⣬⡄⠰⠗⠈⠶⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣧⣼⣿⣷⣶⠒⠲⢇⢈⣢⡾⠿⠀⠘⣛⠀⣟⡓⢀⣉⣥⠂⠛⣢⠄⢀⣨⣻⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠉⣣⠍⠘⠇⣠⠞⣛⠀⣭⡓⢠⣭⠐⠆⢱⡐⢍⣙⣷⠞⠁⠀⠚⣁⣼⣇⠿⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡈⠁⠐⣠⠀⢋⠈⣰⡏⠀⠶⠠⡌⣅⠰⡌⢠⣜⠋⠉⠘⠰⡌⢶⣶⣿⣿⡿⠛⣟⣀⠘⠛⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⡀⢊⡗⡘⢠⢀⠯⠐⠠⠈⣣⠁⡄⠤⣄⡀⢱⡄⣿⠆⢢⡉⣶⣶⣿⣿⣿⠏⡏⠛⠀⢴⠄⣄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⡘⡸⠱⠈⠀⢨⠁⠁⠜⠐⣿⠒⠂⠛⢨⡱⠄⣀⡄⠰⠂⠉⠀⢄⠈⢟⠉⢻⠗⠀⢶⠆⣀⠻⠎⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣿⣻⣦⢰⠆⠀⠃⠈⠰⡰⠶⢇⣼⣶⢦⣄⣀⡀⢀⠀⢠⡜⠇⠶⠀⠁⠊⢀⣟⡺⠇⠀⠀⠿⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣙⠦⡶⠘⠀⢸⠄⠀⠀⠂⢠⣿⣇⣉⡼⣫⣉⣍⡛⢠⣦⢡⡄⢠⣶⠘⠀⠸⡿⠃⠤⠰⠶⠀⣰⡆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠱⡇⠈⠀⠟⠀⠀⡄⣰⣏⠁⠀⠱⢒⣙⠶⠎⡡⠆⢡⡌⠡⣤⡀⠘⢣⠈⡟⢡⣄⠀⣀⠀⠉⢁⡀⢶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂⠈⠀⠀⠀⠀⠀⠀⠈⢸⡏⠠⠂⠀⠄⡤⠶⡌⢂⡀⠌⠑⠒⠉⠁⠺⠎⠉⣷⠈⠋⠀⣋⠐⠀⠸⠟⡈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⡰⠤⠀⠙⠆⠀⠘⡂⠀⠈⠀⡬⠁⠰⢈⠁⠈⠋⢠⡄⢠⣷⣁⠾⠂⠟⢣⣶⠀⠄⣠⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⣀⠀⠀⡀⠀⣠⠀⠀⠀⢀⠫⠔⠀⠒⠀⠂⠀⢃⡀⠀⠒⠚⣡⠈⣄⣼⣏⠀⠁⠀⠂⠈⣡⣄⠀⠉⠀⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠘⠻⣿⣩⣿⠿⠋⢀⣉⣁⠤⠒⣹⣶⣵⣆⢐⠓⣘⡀⠻⣮⣤⠍⢛⣽⣽⣯⢉⢠⣾⣷⠸⣿⡿⠀⣦⠀⠙⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠘⣿⠁⠀⠀⠤⠤⠴⣲⣿⣿⣿⣿⣽⣿⣷⣞⣹⣛⡽⠱⢶⣽⣿⣿⠿⠧⠀⠉⠃⣈⠀⢠⣴⠁⢿⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠸⣿⣷⣦⣄⡈⣈⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⡛⡃⢻⠛⣠⣤⣴⣶⠄⠉⠐⠛⢁⣴⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣹⣿⣿⣿⡇⢹⣿⣿⣿⢋⣾⣿⣿⣿⣿⣿⣽⣧⣼⣿⣿⣯⣤⡿⠃⣉⠉⠁⣠⣤⣴⢈⣈⠁⣶⣷⢈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠿⠿⠛⠿⠿⣿⣿⣵⡿⢻⣿⣿⣿⣿⣿⡿⠿⠋⣹⠿⢿⡆⠀⠂⢹⣤⣄⠙⠋⠁⣾⡇⢀⠛⠁⠚⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢾⣿⣥⡿⢧⠘⠿⢿⢿⣷⣷⠷⠉⡣⣦⣷⡆⠶⣿⠛⠋⠀⠿⠇⢀⣴⡆⢀⠠⡿⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⠛⠿⣉⠿⢀⡥⠽⠗⣛⢁⣦⣄⠘⠉⢩⠘⠸⡷⠈⠉⣀⣀⡀⣀⢿⠗⠀⢴⡿⠛⢰⣿⠇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡘⠃⣉⠀⢻⡇⠛⠀⠁⠘⠛⠿⠆⢱⠀⠀⠐⢂⠀⢺⡿⠿⠏⠀⢰⣶⠀⠂⣢⣶⡬⡷⣚⠂⠫⡍⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠉⢡⣦⢉⠐⠿⠆⠳⠎⠻⣷⡌⡀⠺⠚⠿⣴⡦⠀⣀⣠⣤⣶⠖⠋⢨⢽⡒⠋⠉⠥⠠⠅⠈⢀⡃⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠸⠇⣀⠠⡿⢟⡘⠿⠃⣄⠢⡄⠋⣶⣄⣀⠉⠀⠘⠟⠉⠀⠀⠀⣀⠄⢠⠡⠀⠶⠐⠀⢘⡛⣤⢳⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡄⣿⡆⢀⡈⠹⠿⠆⣉⠁⣄⠠⠈⠋⠉⠰⡆⠀⠀⠘⠀⠀⢨⡏⠀⢠⠀⠁⠰⠂⠒⠀⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣈⣰⣿⢁⡀⢾⡷⢉⡡⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠔⠀⠀⠆⠀⠒⠂⠈⠁⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡃⢃⠈⣿⠇⡀⠀⠀⢡⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢤⣧⣀⠁⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⢸⣷⠀⡘⠇⠀⠛⢠⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠢⢈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠛⢄⠀⠀⠈⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⢴⡁⠀⠀⠀⠈⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠑⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠤⠄⠠⠄⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠰⠁⡠⠐⠢⡀⠙⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢃⠀⢠⡀⣀⠄⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠢⢀⣈⣁⡠⠊⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⠐⠠⣤⠀⠀⠤⠔⠚⠣⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣙⠳⣤⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠠⠄⠤⠄⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣭⠆⠀⠈⢩⠋⠝⣋⡛⢍⢫⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⢁⢠⠸⡘⢅⠸⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⢀⠔⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡜⢠⣤⡄⠊⠀⡈⢆⠢⢍⣒⣒⡡⠊⠳⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢄⠁
⠀⠀⠀⠀⠀⠀⡜⠠⠁⠀⠀⢀⠀⠘⡌⢆⠀⠀⠉⠢⡀⠀⠈⠢⡀⠀⢀⠊⠀⠀⠀⢠⠊⠉⠑⡄⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡼⠠⠁⠀⠀⠀⠑⠃⠀⠘⡌⢆⠀⠀⠀⠈⠦⡀⠀⠈⢦⡌⠀⠀⠀⠀⠐⢄⣀⡠⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⡰⢡⠃⠀⢠⡆⠀⠀⠀⠀⠀⠘⡜⡆⠀⠀⠀⠀⠈⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣦⠀⠀⠀⠀⠀⠈⢢⡇⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⣀⡠⠤⠿⠐⠒⠺⠄
⠀⠀⡰⢁⠂⠀⠀⠀⠀⠀⠀⡔⠉⡆⠀⠀⠀⠱⡘⣄⠀⣀⣀⡀⠤⢤⣗⠒⠦⠭⠙⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢰⢃⠂⠀⢠⢢⠀⠀⠀⠀⠈⠛⠁⠀⡠⠠⡀⠱⡘⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⢠⢃⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠁⠀⠡⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⣣⣤⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣍⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠌⠛⠛⠛⠻⠿⠿⠷⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⣀⡀⠒⠂⣠⣤⠿⠿⠿⣷⣄⠀⠀⠀⠀⠣⡀⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠴⠉⠀⢀⣶⠏⠉⠀⠀⠀⠈⠹⣷⡀⠀⠀⠀⠉⣄⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣶⡀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠛⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠔⠛⠻⠟⠉⠙⠛⢻⡆⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠻⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣠⣤⣾⣤⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣰⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠉⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠁⠀⠀⠀⢀⠈⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠐⠁⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⣀⠀⠰⠶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠁⢠⣤⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠘⠁⠀⢰⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣘⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠈⠀⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣀⣀⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠙⠉
⠀⠀⠀⠀⠀⠀⢀⡿⢷⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠛⠛⠠⣤⡀⠀⠀⠀⣤⣤⣶⡆⠀⢤⣤⣤⣤⠀⣠⡾⠋⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠶⠛⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢳⡆⠀⠰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⠿⣄
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠘⠀⠀⠀⠀⠈⠁⢰⣿⣿⣷⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⡿⠀⢠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠏⠀⣀⠀⠀⠀⣿
⠀⠀⠀⢴⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠉⠉⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠁⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⢉⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⢀⡀⠤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠁
⠀⠀⠀⠀⠙⢿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⠃⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃
⠀⠀⠀⠀⢰⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠛⠛⢠⠀⠀⠀⠀⠄⠀⠀⠀⣠⣤⡿
⠀⠀⠀⠀⠀⠀⠙⠛⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠗⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⣼⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⣴⠟⠁⠀⠀⣠⡶⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣴⠟⠁⠀⢠⡴⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⣾⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣦⠉⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⣿⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡀
⠀⣴⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠙⣤⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠉⢷⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠙⢳⣤⡀⠀⠈⠛⢦⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠡⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⣆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣤⠐⠛⠓⠚⠛⠛⢤
⠀⠀⠀⠀⠀⣀⠾⠃⠈⠁⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠉⠉⠁⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⢠⡌⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠘⠇⣀⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣴⣦⣤⣀⣠⡟⠛⠀⠛⠛⠁⠀⠘⢻⣤⣤⣤⣤⣤⣤⣤⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠂⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠓⠢⠄⣀⠀⠀⢸
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠘⠂
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣤⣀⠀⠉⠉⣿⣿⣶⣴⣤⣤⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⢹⣿⣿⣿⣿⣿⡏⠔⠈⠙⡄⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠛⢿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣮⣴⡇⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠱⠟⠀⠀⢸⠉⠉⠉⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⢸⣿⣿⣿⣿⣿⡄⠘⡏⠀⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠈⠙⠻⢾⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⡛⠁⠀⢹⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠈⠙⢦⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠂⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⣀⣀⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⢻⣟⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⠈⠡⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠧⠤⡤⣼⣈⣷⢦⠦⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡴⢦⣬⠶⣾⠶⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠋⠀⠀⠉⠀⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡵⠀⠀⠀⠜⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣠⠄⠀⡠⠚⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⡛⠉⢹⠉⢳⡤⠊⠀⡸⠀⠈⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣄⡀⠀⠀⠀⡜⠀⡀⢸⠠⣿⡿⠦⢠⠇⠀⠀⣇⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣾⠇⡰⠦⠾⣄⠔⠁⢸⣷⣾⣧⠐⡎⠀⠇⠀⢸⠀⢀⠀⢠⡄⠂⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⠀⣿⠀⠀⠀⠀⠀⢸⣿⡟⣻⡜⠀⠀⠈⠛⠋⠉⡿⠀⢸⡇⠀⡀⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⠀⢿⡆⠀⠀⠀⠀⠸⣋⣼⣿⠁⠀⠀⠀⠀⢀⣼⢁⣀⣾⡀⠀⢷⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⢸⣷⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⡞⣿⢛⣋⡟⠀⠀⢸⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡏⢠⡞⠀⣿⠀⢸⡟⡆⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⡠⠻⡭⡤⠤⢸⡇⢀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⣿⠀⠈⠁⢹⡀⠀⠀⠀⡜⠀⠀⠀⢀⡄⠀⠀⢠⠄⠀⣼⣷⠈⢇⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣠⣤⣄⡀⣿⠀⠀⠀⠀⢳⠀⠀⡜⠀⠀⠀⣠⡞⠀⠀⢠⡟⠀⠀⣿⣿⠀⠘⢧⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣅⠀⢤⣬⡁⣿⡀⠀⠀⣤⠘⣧⡼⠁⠀⢠⣾⠋⠀⣀⠀⡞⠀⠀⢸⣿⣯⣤⡶⠦⣅⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡉⠓⠀⠀⠀⣿⡇⢸⠀⠉⠀⣹⠁⣀⢶⡿⠁⠀⠀⠛⠀⢰⠀⠀⣿⣿⣇⣀⡰⠖⠋⢡⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠛⠛⢀⣿⡇⢸⠀⠀⠀⢣⠞⠡⠋⣀⣀⣄⠀⠀⠀⢸⠆⢸⣿⡿⢋⡉⠀⢠⠾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡀⠀⠘⣶⣿⠐⠚⠛⠉⠁⣤⠀⠀⢠⠟⠀⣿⠟⠀⠉⠁⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⡏⣇⠀⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣶⡴⠋⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡄⠀⠀⠐⢾⣿⣄⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣿⠁⠀⠀⠔⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡇⠀⠀⠀⢸⣿⠉⠉⠀⢰⡧⡤⠀⠀⠀⠀⢠⣤⠀⡀⠚⠿⠿⣦⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢷⣶⠟⢿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠞⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⢸⣁⢿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⢸⡷⢿⣇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⡿⣦⣿⣤⣤⣄⣼⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠀⠆⢸⢹⡉⠉⡹⢿⠉⠉⣭⡿⠋⠉⠉⠉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⠸⡇⠀⣷⠘⡆⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣘⠂⢳⠀⣿⠀⢣⠀⠀⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣦⣾⣧⣤⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⢀⡞⠻⣿⠶⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣆
⠀⠀⢸⡇⠒⠛⣧⡈⠛⢶⣴⠶⠛⠋⠻⡏⣽⢡⡍⣽⠏⠛⠳⣦⣤⣤⠶⢛⣩⢴⡓⢂⠏
⠀⠀⠀⣧⠈⣡⠭⢿⡶⠻⢟⣡⠀⠀⠘⠷⣼⢸⡇⣶⠀⠀⣬⣝⠛⣻⣶⣟⡓⠂⢀⠎
⠀⠀⠀⠘⣧⠀⣠⠞⣤⠐⢋⣥⡶⠀⠰⡷⣠⣌⣵⣧⠀⢴⣶⡍⠰⢏⣅⠈⠙⢶⡏
⠀⠀⠀⠀⠘⡿⣁⠈⢡⡾⠈⠁⢠⡴⠀⢀⣭⠉⣈⡀⢶⡀⠀⠀⣶⡌⠿⠀⠀⡾
⠀⠀⠀⠀⢸⢻⡿⢰⡷⢠⣶⠀⠈⠀⡴⠟⠁⠀⠻⠿⠀⢀⣔⢾⣿⠓⡶⣤⣰⠃
⠀⠀⠀⠀⢸⡈⠀⠈⠀⣈⣡⣤⣤⣄⠀⠀⠀⠀⠀⢀⡔⠉⠉⠛⠛⠉⠀⠀⢿⡄
⠀⠀⠀⠀⠈⣧⡤⠒⠉⠻⣤⣿⡣⠼⣧⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣀⠘⣇
⠀⠀⠀⠀⢠⡏⣶⡆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠤⠀⠹⡇⠀⠀⠀⠀⠀⠘⠛⠀⢹⡄
⠀⠀⠀⠀⡾⠀⠈⢀⣤⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⠰⠟⠀⠀⠈⣧
⠀⠀⠀⢸⠇⣠⡀⠈⠋⠀⣴⡆⠀⣠⣾⠃⠀⠀⠀⢀⣻⣦⠀⠰⠟⠀⠀⠰⠿⠃⠹⡆
⠀⠀⠀⣾⠀⢛⡀⠀⠀⠀⠈⢁⠔⠁⣿⣤⡀⠤⠀⢄⣸⡇⠱⣄⠀⠀⠀⠀⠠⣿⠀⢳⡀
⠀⠀⠀⢿⠀⢘⠿⠆⡀⠀⢠⠏⠀⢸⣧⣤⣤⣤⣤⣤⣍⣷⠀⠈⢣⡀⣠⣴⠂⠀⣠⡜⡇
⠀⠀⠀⠸⣆⠿⠇⠘⢿⠆⡞⠀⢀⡘⠛⠻⣿⣿⣿⠟⠻⠋⠠⠦⠀⣷⣚⣁⣶⡘⠛⢹⠗⠂⠠⢀⡀
⠀⠀⠀⠀⠈⠳⣦⣾⣿⣎⣯⠥⠍⢡⠖⠀⢿⣿⡟⠀⣀⠚⢂⡉⠁⢸⠸⠿⠋⢀⡽⠛⠤⡀⠀⠀⠀⠈⠉
⠀⠀⢀⠄⠂⠁⠀⠚⠉⡳⠿⣶⣉⠉⠁⣀⡴⠛⢧⡀⠉⠀⠀⠀⣩⠿⠶⠶⠚⠉⠀⠀⠀⠈⠂
⠀⠁⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠀⠉⠛⢻⡟⠋⠁⠀⠀⠀⠈⠀⠂
⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠓⠶⠶⠶⠤⠤⠤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣾⡿⣷⣷⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣩⡖⠋⠁⠀⠘⣧⢳⡀
⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠒⠙⠛⠃⠒⣂⠤⠤⣄⣹⣼⡇
⠀⠀⢰⣿⡏⢹⠿⣦⠀⠀⠀⠀⠀⠀⠀⠺⠤⣀⣀⠀⡠⢤⢄⠊⠙⠳⣤⡀⠀⠉⠉⢢⣀
⠀⠀⢸⣿⣇⠛⠀⠘⢷⡀⠀⠀⠀⠀⡠⠀⠈⠁⠀⠀⢰⣶⠀⠇⠀⠀⠘⠉⠑⡶⣶⠒⠚⠃
⠀⠀⠈⣿⣷⠀⠀⣶⢈⣷⡀⠀⠀⠺⢤⣀⣤⣤⣤⢤⣸⡁⠀⠀⠀⠀⠀⣀⡠⠋⣸⣿⣶⠶
⠀⠀⠀⠹⣿⣧⢠⡇⡀⠸⣇⠀⠀⠀⠀⠀⠀⡇⠀⠂⠙⠤⣤⠖⠀⠀⠀⠀⠀⣸⣿⣿⠁⣠⠞⠃⣠⣄
⠀⠀⠀⠀⠹⣿⣿⣡⠀⢸⣿⠀⠀⠀⠀⠀⠀⠉⠐⠂⠂⠚⢣⣀⠀⡠⠔⠁⣼⣿⣿⡷⠀⠘⢀⡈⠘⠉⢪⣦⣄⡀
⠀⠀⠀⠀⠀⠈⠻⣿⣧⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠦⣄⣼⣿⠿⣿⢳⠀⠐⡿⣿⠢⣤⡈⠉⠈⣙⣢
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⣾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡦⣤⠖⠆⠀⠀⠀⠀⠀⡰⠛⣿⣿⡿⣿⣾⣤⠤⡷⠺⠀⠐⡖⣶⠖⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣲⣡⡆⠸⣿⣿⣿⡖⢚⣣⡎⠉⣸⡆⢺⠭⠀⠀⠤⠄⠀⠀⣀⣀⣀⡎⠀⠉⢙⠛⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠉⠀⢰⣿⣿⣿⠋⠈⠋⣠⠞⠉⡇⣴⣶⠀⠀⢴⢠⠀⠀⠠⡤⠄⠀⢨⡯⠏⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠤⠠⠊⠀⠀⠀⡇⠀⠉⠀⠀⠈⠈⠀⠀⠀⠉⠁⠀⠈⠉⠁⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣶⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠋⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠌⢤⣄⣀⡀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⡖⠒⠓⣷⣶⣾⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣠⣾⣿⣿⣧⡀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠛⠻⣿⣧⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠻⠿⠿⠿⠟⠛⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠁⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣼⢄⠀⠀⠘⡄⢱⢀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣪⠗⢋⣿⣯⡺⣼⠆⣹⠅⠀⠺⣿⣿⠏⣳⠂⢿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣟⣤⣦⢀⣾⣿⣿⢷⣿⣤⣈⠀⢀⠀⠈⠑⢂⡟⣹⠃⣿⡐⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠰⣾⣹⣿⠁⣾⣿⣿⡀⢫⢟⣍⠛⠤⠀⠀⠀⢀⣈⡄⢼⠇⠠⣄⠛⢃⣌⠰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢁⠀⠐⠏⠘⠃⣼⣿⠻⠿⢷⡈⠚⠻⠆⠀⠀⠤⠚⡈⢈⣁⠠⠶⢃⣤⡁⣘⣡⣦⡂⡞⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠟⣼⠀⠿⢃⣴⡄⠿⠙⣡⠀⠈⠀⠀⠀⠀⠘⢣⡶⢈⡁⡉⢡⡶⢶⠂⠀⠙⠋⠻⢿⡇⠛⣴⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠾⣣⢤⡄⣤⡾⠀⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⢰⡆⢠⡆⠘⠋⠁⢴⣦⠴⠘⢃⠩⠉⣶⡈⠀⠂⢆⡀⠁
⠀⠀⠀⠀⠀⣰⡄⠐⢣⠞⣡⣠⠆⣾⡟⠁⠀⠀⠺⢀⢀⣤⠰⠃⢠⡤⠸⢃⡾⢂⡰⢆⠉⠰⢟⣤⢁⢼⡿⣿⡀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠹⣠⣦⠀⣸⠿⠆⣠⡈⠁⠀⠀⢰⡇⠉⠈⠉⠰⣆⠈⣤⣶⠎⡥⢈⣥⠘⠁⠂⣀⡀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⡴⠁⠀⣴⠀⠀⣫⡅⠀⣤⠀⢠⠀⣀⠀⢰⣦⠉⢀⣉⡉⢴⡶⠆⠐⠆⠘⢃⡈⠙⢃⠐⢃⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠿⠂⢀⡁⠀⠀⡉⠀⠈⠘⠏⠀⠈⣉⠀⠘⠛⠛⠀⠀⠰⣷⢘⣷⠘⠃⠹⢃⡚⠅⠂⠀⠀⠀⣀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠰⡇⣴⡆⣄⠀⠀⠻⠆⠀⠛⠀⠀⠀⠀⠀⠿⠟⠀⠾⢿⣆⡀⢠⣶⡄⠨⣅⠸⡇⠰⢊⠄⠀⠀⢠⠆⠀⠀⠀⣀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⠐⠷⠀⠀⠀⠐⠟⠃⠀⠀⠀⣴⡆⠀⠀⢛⣛⡁⠀⠈⠁⢠⡿⠀⠐⡆⣨⠄⠘⠻⠢⠦⢤⠄⠄⠹⣿⣾⡷⢈⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣴⠀⠀⠀⠀⣶⡄⠀⣀⡄⠀⠛⠃⢀⣠⣾⡿⠛⠳⠀⢴⣜⠃⠀⠀⠀⣤⣤⣌⣛⠶⠒⠲⠶⠶⠄⠀⢙⠔⠁
⠀⠀⠀⠀⠀⠀⢸⣷⡄⠈⡋⠀⠀⠀⢰⡿⠁⠀⢛⣡⣤⣶⠆⠀⠉⠩⠝⢁⣀⡙⠋⡉⠀⠀⠘⡿⠿⣾⣯⣍⣛⣟⡓⠖⠂⠒⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⡅⠀⠀⣀⣤⠀⠀⠀⡈⠁⠀⠁⠀⠀⠀⠀⠀⠀⢹⣿⣗⠀⠀⠀⣌⣹⣷⡛⠂⢤⣿⣏⣙⡃⠤⠖⠡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⠀⣠⣾⡇⠀⢠⣶⣄⠀⠀⠀⠀⢀⡸⠟⠋⠉⠈⠉⠈⠙⠻⢿⣦⣭⣍⠉⠁⢀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠀⠀⠉⣿⡏⠀⠀⢠⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿