Bouquet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠅⣈⡰⠁⠀⢀⠀⢀⡀⠀⠠⡄⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡤⢀⡇⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⣡⠶⠜⡁⠀⡀⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣤⠀⠀⠀⢨⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⡃⣼⠂⣴⠀⡙⠄⣀⡁⠀⠂⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⢒⠀⢠⡀⢠⡖⠀⠠⠀⠀⢀⣸⣆⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠐⠱⠟⠀⠁⠒
⠀⠀⠀⣀⢠⡀⠀⢀⠠⢄⠀⠀⠙⠅⢿⡀⠀⢸⡇⢹⡌⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠐⠲⠂
⠀⠀⠀⠀⠘⠡⠒⣈⠣⣤⢑⠀⠀⣀⢸⡗⠁⠸⠇⠈⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠄
⠀⠀⠀⠀⠀⠨⠀⠀⠀⢙⣏⠀⠀⠉⢺⡇⣠⡀⠐⢹⡶⠃⠀⠀⠀⠀⠀⠀⠀⡀⠴⠾⡤⠛
⠀⠀⠀⢀⠇⠗⠚⠓⢀⣀⡁⠀⠀⠀⢹⡷⠼⠿⡧⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠄⠻⠷⣴⡆⠀⢰⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠉⠋⠛⣟⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠁⡀⠛⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡀⣂⠠⡦⡄⠘⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠒⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡘⠄⣽⠋⠁⣌⡃⢨⡀⠡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠠⣛⣡⣆⡶⠻⢿⡇⠛⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢈⣷⣈⠡⠌⠟⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⠇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣀⡀⢀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣠⠄⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠆⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠐⢀⣄⠀⡂⢀⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠘⠙⠀⠀⠈⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡴⠰⢀⢠⠅⢀⣻⡉⠑⠓⢄⣌⣀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠁⠺⢦⢁⡴⠀⠂⣁⣀⠈⣹⡯⣷⣦⣖⣀⠌⡛⣆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡄⠐⠦⢻⡦⠀⣀⣀⣆⠀⠙⠇⡛⣿⠝⢿⣟⣿⣼⢖⡙⣈
⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠀⣰⠟⠀⠁⢛⣦⣿⡍⠉⣷⠴⡆⠈⢺⡇⠆⠋⠻⠐⢿⠟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡭⠀⠀⣼⣻⣿⠿⠀⡀⡤⠀⢳⠀⠀⣟⠈⠳⢆⢠⠄⠀⠡⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⢀⠐⢁⡾⣿⣷⠌⡡⣧⠃⢄⠀⣇⠻⢆⠁⠸⠃⣤⣌⠀⣰⡁⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠡⠖⠀⠐⠉⢬⠳⡛⡀⢁⡤⠠⣮⠶⢉⣄⣀⡀⡟⠊⢵⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢲⣄⣠⡄⢸⡄⣿⡀⡘⠂⢀⠀⢠⠞⢿⣏⠀⢢⡄⠘⠂⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⢣⣀⠠⢻⣷⢀⠉⢹⠶⣎⠁⠡⡠⣾⣼⡋⠡⣶⣤⠲⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠤⢸⠉⢠⡊⣐⡈⠁⢠⢠⡇⡈⠃⠀⠈⢟⣇⠀⠘⢁⢹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⢑⡀⣞⣶⡙⢁⡶⠏⠈⢹⡁⠂⡁⢱⡞⡁⠀⠒⠀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⢹⠿⠈⢡⢡⣶⣦⣤⢸⣿⠦⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡄⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡷⠎⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠫⣿⠏⣷⠸⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠘⠃⠝⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠄⢀⠊⢀⠇⠀⠀⠀⡠⡞⣤⠀⠤⠀⢤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠐⢄⠈⣼⠢⠁⠠⡄⠀⡜⠠⠁⡆⠟⢸⠇⣤⠄⢀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⣀⠀⠀⠀⠀⠀⡀⢡⠀⠠⠐⠒⠢⣨⠓⠤⠤⡐⠁⡘⠀⠀⠀⠱⠄⠀⣀⡁⠄⣡⡆⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣈⠁⠒⠤⣀⠠⣀⠆⣀⣑⣒⠂⡏⠐⢄⣀⠸⢀⠁⠀⠃⢀⠄⠻⡀⠉⠠⢊⠜⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠔⠂⢹⠃⡀⠘⣀⣀⠸⡷⠌⣉⠀⣑⢘⠀⢈⣤⡀⠀⠀⢱⠔⢀⡊⠤⢀⠃⠀⠀⠀⡀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠘⢦⡀⢡⠓⠀⠀⣷⣌⠉⠉⠂⣘⡀⢸⣈⢻⡄⠀⠀⡤⠊⠀⠀⠈⠀⠀⠆⠎⠀⢰⠊⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⠁⢨⠷⠤⣱⠛⡆⡴⠞⢰⢶⣞⠛⠿⣹⠏⠁⠁⠈⠙⣲⠚⡅⠀⠀⣀⠜⠀⣸⢀⣶⢡⡎⣵⠯⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢆⠀⠀⠱⠸⠓⠶⠶⠒⡋⠞⠋⠀⣰⠅⢺⢧⡩⢾⣛⠶⣤⠠⣴⠞⠋⠈⠙⢦⡹⠁⡴⠈⠳⡎⠈⢦⣨⢤⠄⠡⠚
⠀⠀⠀⠀⠀⠀⠀⢐⠉⠢⡀⢣⠀⠂⠣⡀⠄⢄⣀⠨⣴⣹⣄⡉⢙⠇⣠⡧⣈⢀⡀⣨⠧⠸⠇⠻⢩⡄⠀⠀⢘⠁⣰⠀⠀⠀⢀⠐⠊⡕
⠀⠀⠀⠀⠀⢀⣀⡈⠢⡀⠈⢆⠑⣤⡤⠘⠟⢍⣍⠣⣧⢞⠉⠉⠉⠉⠹⢀⣀⡋⠀⢱⠤⣴⡆⣴⠊⠙⣶⠶⡞⠃⣤⣢⣄⡠⠿⠔⠋⠉⠉⠠
⠀⠀⠀⠀⠀⠘⢄⠀⠁⠢⢅⡰⠻⡌⣤⡉⠳⠊⠉⠘⢏⢰⢏⠠⡆⠀⠀⢺⠁⠈⢰⣇⣀⠭⠹⢿⣄⡜⢁⠜⡉⢉⢴⠏⠀⠱⡖⠓⠶⠐⠊⠁
⠀⠀⠀⠀⢀⠤⠀⠨⠉⣈⠋⠍⠑⢳⢄⡙⢽⡀⠀⠀⢸⠏⠀⠀⢸⢀⡴⢛⢳⡤⠞⡍⡷⠖⠒⠁⢙⣃⠗⠁⢀⡼⠙⠤⠠⠚⡇⠀⠀⠂
⠀⠀⠀⠀⠈⠒⠀⠐⣾⠋⠑⢊⠢⣀⡇⠈⡁⠴⠤⠊⠉⣤⣤⠒⢁⡌⢀⠞⠁⠈⠻⢿⣼⣒⣒⡒⢈⠛⡍⣩⠟⠛⠛⣅⡩⠁⠘⠒⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠎⢰⠈⢄⠀⢱⠀⠀⠸⣀⢀⡠⠓⡖⠁⠈⢲⢩⡠⠛⡘⢄⠀⢀⡟⠁⠀⠀⢹⣀⣨⠿⡤⠠⣔⣸⡉⠉⠳⣀⠅⠒⠉⣠⠤
⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⠀⠉⠁⠀⠀⠀⠀⢰⠁⠀⠛⢦⣠⡼⠦⢷⡄⠋⠉⢉⠀⠈⣄⣀⡀⠬⠀⠉⢲⡖⠈⠀⣀⠼⠃⠎⠙⢫⣉⣁⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⢀⡀⠨⠦⠤⠏⢙⠉⠂⢤⣜⠀⠀⣀⠌⠙⠁⠀⠙⢎⡈⠁⠢⣸⣈⠿⠘⠃⢺⢸⠀⡀⠘⡿⡁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡴⠀⡀⢀⠈⡄⠰⠃⠸⠃⢈⠟⠀⢐⢇⡀⠀⢈⠋⠁⠠⣽⡁⠀⠀⠺⡁⠈⠶⠈⢀⠃⠙⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⡚⠁⡾⠀⠇⡇⢠⢂⠔⣻⢟⠳⡙⢨⡉⠉⠭⠭⠤⢩⡿⠄⠐⠄⠐⠃⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠠⠚⠀⠛⢡⠊⡠⠙⠂⠑⢌⠢⡉⠒⣢⠶⠾⣽⣍⠢⠄⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡁⠜⠁⠘⡀⠀⠱⡄⠃⠘⠤⠐⠸⠇⠣⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠑⢄⠀⠘⡀⠀⠀⠀⡆⢠⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢁⠀⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣴⣸⡿⣿⣿⣷⡍⢉⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⠳⡌⠙⢿⣿⡿⠿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣩⠯⠉⡇⠀⠀⣠⣼⡋⣴⣶⣤⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢧⣤⣀⣾⣶⣾⣿⣦⣀⡀⠈⠙⠛⣷⠀⠀⠀⣠⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢻⣿⣿⣽⠟⢹⡇⢻⢿⠿⣷⡆⣈⡀⢀⡆⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣴⣼⡿⢿⣯⣾⣴⣷⡼⠃⠈⠛⠛⣿⠃⠸⠀⠀⠀⠀⠀⣵⢦⡀
⠀⠀⠀⣀⣾⣷⡈⠙⢷⡀⢀⡿⢃⣿⣻⡿⡛⠁⠆⠀⠀⠘⠂⣤⣿⡆⢠⠸⠀⢀⠀⢰⠇⠈⠐
⠀⠀⠀⠙⠿⡌⠛⣗⣾⠗⣈⣡⣍⢿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠈⠇⣵⠤⠦⣄⢉⡴⠁
⠀⠘⠉⢷⣤⣀⣀⣨⣽⣷⣿⣿⣿⣿⡿⠟⠻⢷⠀⠀⠀⠀⠀⠀⣻⢷⣟⣷⡌⡅⣀⠀⠀⠀⢀⡀
⠀⠀⡄⠉⣭⣭⡭⠖⣿⢿⡿⣿⣟⢯⡛⠳⡞⠀⠀⠀⠀⠀⢉⣫⣽⢻⡿⣿⣿⠳⠄⠀⠀⠀⠈
⠀⠀⠐⣶⣭⣡⠄⢊⡵⠋⣠⡉⣿⣄⠙⠂⠀⣂⢶⡄⢀⠀⠀⠀⢡⣿⠃⠛⠋⠓⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠉⠉⢰⣾⡶⣾⣿⣷⣬⣍⠠⣶⠿⣿⠇⢸⣿⣄⣀⠀⠋⠡⠤⠤⢀⣀⠀⢀⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠘⠷⠉⠘⢿⣃⠀⠀⠀⣿⠀⠈⠛⠿⣿⣟⣻⣶⣶⣾⣶⣶⣶⣬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⠻⣦⣠⣤⣥⡀⠀⠈⠀⠁⢀⣵⣿⣿⡿⢿⡿⢿⣿⣟⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠹⣦⣿⣥⣟⣳⣽⣶⠂⠀⠀⠛⣿⣿⣿⣿⣦⣻⣦⡙⢻⣍⣛⣿⣛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⢢⣤⣼⣿⣿⣿⣾⣧⣄⠀⠀⠀⠙⠛⠻⣿⣿⣿⣽⣻⣾⣥⣴⡮⠟⠿⠿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠋⡙⠻⠿⡎⠉⠓⠀⠀⠀⠀⢀⣤⣿⣿⣿⣷⣶⣾⣿⣷⣴⣾⣚⣓⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⠀⢀⡀⠘⢢⣤⣤⠀⠀⠀⠸⠉⠉⢹⢻⣿⣿⣯⣽⣿⣿⡟⣛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⡻⠃⠀⠀⠀⠀⠀⢠⠋⠀⠿⠟⠏⠳⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠤⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢠⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢲⠋⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢈⠀⠘⡿⠂⠀⠠⣀⠀⢀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣐⠛⠀⠐⠂⠀⢦⣃⡴⠃⢄⢍⡠⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠕⢢⠇⠠⠄⣨⢋⠡⡀⠀⡀⠁⡔⠂⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⠜⡥⠚⠉⠐⢾⡴⠾⠒⠺⡅⠀⢲⠊⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠠⠀⠀⠐⠀⠀⠀⠈⡴⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠻⡞⢁⣀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⠤⠚⠋⠀⢠⣐⣀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡵⠀⠒⢀⠈⠅⡄⣩⢥⡀⠈⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢲⠁⠀⠀⠀⡴⠋⠁⠀⠀⠙⠂⣀⣼⢴⣶⡦⢼⠖⠉⠀⠀⠀⠈⡄⠶⠃⠉⠁⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄⠀⠀⠐⠉⡡⠼⠁⠀⠀⠀⠀⢸⣟⠕⠁⠀⠀⠈⠑⡘⢖⠁⠀⠀⠀⣽⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⠀⢀⣀⢲⣀⡠⠊⠀⠀⣸⠋⠀⢊⡀⠢⠐⠀⠐⣼⣢⠔⠒⠋⢹⡏⠀⠂⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⣀⡀⠀⠀⠀⠀⣻⣶⡀⠀⠁⠁⠀⣠⣾⠟⠨⢀⣀⣀⡼⡁⠠⠀⢀⠀⠉⠓⠦⣤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣂⠴⠉⢡⢀⣀⠐⠁⠙⠿⢯⣶⣒⠿⠋⠁⠀⢤⣀⣀⣴⢇⡓⡢⢀⡄⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⠲⣼⠒⣅⠀⠀⡰⠚⢇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣆⠀⢀⡢⠛⠼⢇⢤⠖⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢄⠀⠘⠉⢈⣑⠇⠀⠀⢀⠀⠢⠤⠤⠔⠁⠀⠀⣀⡠⢤⠴⢺⡍⢿⣷⣄⣄⠘⠀⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠀⠀⠀⠐⠀⠁⠾⠀⠑⠀⠈⠀⠀⠀⣐⠀⠰⡯⢩⢩⠀⠸⠇⠈⠁⠘⣍⢄⠀⠈⠃⠀⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠇⠀⠀⠆⠀⠀⡠⠑⣦⣾⠀⠖⠡⠸⠀⢀⠈⠙⢟⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠀⠠⡄⠄⡀⠀⠉⠹⡀⠀⠀⠀⠐⠈⠀⠀⠨⢯⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀⡀⠀⢀⠀⢀⠀⠀⢀⠀⢀⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠒⠁⠀⠃⠀⠛⠂⠘⠙⠀⠘⠀⠑⠀⠀⠋⠂⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⡶⠀⠀⠀⠀⠀⠀⣴⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠱⠊⠀⠄⠀⠀⠁⠖⠂⠀⠀⠀⠀⠀⢶⣄⣿⣿⠁⡾⠟⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣰⠖⠁⠀⠀⠀⠀⠀⠈⠀⠀⣰⣾⣿⡟⠉⣥⣠⣶⠃⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣴⣞⠀⠀⠀⠀⡔⠃⠈⠋⠠⣵⠞⠩⢿⣧⣤⣙⠛⣡⣤⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠣⠀⠅⠀⠡⠀⠀⢀⡀⡆⠀⣠⣄⣤⣍⠁⣀⠉⢷⣼⣧⡶⢖⡀⢤⡦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠆⠀⠀⠀⠀⢀⠸⠷⠀⠀⣠⣿⣿⣿⡟⢈⡑⢢⠘⣫⠋⣁⣀⠈⠉⠛⠓⠙⢡⡞⠁⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⣄⠀⠀⠀⠀⠳⡟⠀⠀⠘⠿⣿⠿⠯⠠⡀⠌⢀⣰⡷⠀⠀⠁⠀⠀⠆⠀⣂⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⠺⢶⡆⠀⣤⠘⢅⡀⠀⡘⢡⡄⠓⠀⠘⡀⠉⠍⠀⢀⠔⠖⢸⡄⠀⡀⠉⣠⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡋⢉⣤⡾⠃⠲⣏⠃⣸⢟⣄⡀⠄⠀⠈⠆⠘⠅⢀⡤⠀⠨⠀⣾⣿⣇⠄⠀⠐⢋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠡⡎⠀⠀⡋⢭⠍⠺⠃⠀⢄⠘⢂⡽⣶⣦⣄⠀⢸⣧⠀⠀⣌⠻⠿⠃⠁⠀⣀⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢰⡾⠀⣘⠃⠀⢠⡀⠐⠂⠈⠒⢺⣿⣿⣿⣾⡇⠀⠻⡆⠤⣽⠏⠁⠔⠀⢀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠃⡁⠀⠂⠀⠈⠳⢿⡟⠛⠁⠀⠀⠙⠗⠂⠀⠀⢀⠀⠠⡄⠀⢠⣆⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢶⣎⠀⠀⠀⠈⢰⡀⠄⠀⠀⠀⠀⠀⢀⠀⢊⡰⢛⠃⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠀⠀⠀⠀⠉⡐⠀⠄⢠⣤⣀⠖⠼⠁⠉⠀⢨⠉⠀⠀⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣃⠰⠀⢀⣀⠀⠦⠨⠄⠀⢀⠀⠀⡀⠀⠀⣶⠞⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠶⠄⢈⣩⢻⠀⠀⠀⢻⡄⠉⢠⢙⢀⡂⠁⠀⠁⠀⠘⠣⢉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠉⠀⠀⡤⠋⠀⣤⠐⣆⡁⠀⠀⠀⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠜⣣⡄⠀⠙⠆
⠘⠀⠘⠂⠐⠊⠀⠊⠀⠃⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠃⠀⠛⠀⠛⠀⠀⠀⠛⠀⠙⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠈⡿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⢳⠖⠀⠉⠛⠁⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⡀⠀⠀⠀⠀⣍⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢯⢿⡀⠿⣇⢟⡈⢿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠞⠁⠀⠈⢛⠙⠋⡁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠂⢀⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠠⠀⡀⡆⢠⠀⠀⠀⠈⠀⠐⠋⢀⡠⡄⠀⠀⠀⠟⣁⡐⡑⠁⠐
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⠄⠈⢀⠀⢺⣡⠋⡶⢸⢁⠂⠄⠀⠀⢛⣶⡶⠀⠻⠃⠀⠉⠋⠀⠐⠇
⠀⠀⠀⠀⠀⠀⣀⠛⢇⡺⡿⠃⡗⠄⢸⢋⣴⣤⡆⠺⠃⢈⡀⠀⠀⠀⠀⠀⣤⠀⡔⠁⠖⢠⡀
⠀⠀⠀⠀⠀⢠⡤⢶⣾⣡⠆⣻⣷⣾⠘⠟⠣⠶⠀⠀⠀⡀⠅⠀⡀⠀⠀⠀⢩⡴⠄⠄⠈⠌
⠀⠀⠀⠀⠀⠰⠙⣊⠸⣛⣿⣾⢾⣾⢢⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⡄⣜⠧⣻⡛
⠀⠀⠀⠀⠀⠀⠴⠿⢑⣮⣟⣵⣋⡉⠀⠀⢲⠀⢀⠀⢰⡄⠀⠀⠰⣼⢟⡟⡻⡧⢋⠴⠂
⠀⠀⠀⠀⠀⠀⢀⢷⠾⣿⠿⣿⣡⣙⠗⣶⠾⠂⠶⣽⡺⡸⠞⠁⠈⠽⢶⣮⠙⠥⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⠉⠁⠠⠸⣆⠀⠀⣈⣳⡅⠀⠀⠀⣠⠂⠀⠂⠐⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠌⠓⠘⠄⠀⠀⠀⢹⠀⠀⠀⠄⠱⣶⠤⢿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⡖⠄⢻⠀⠀⠠⣀⣷⠙⢦⢸⡇⠀⠤⠄⠀⠀⠀⠀⠈⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢢⠈⠀⠀⠓⣾⠁⢀⡏⢾⡇⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠑⣤⣨⡒⣽⡄⠈⡧⠲⠿⠀⠈⠀⠀⠠⠄⠁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠃⠀⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⠀⢀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠂⢸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣠⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢁⡠⣄⠀⠀⡠⠤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠉⠉⢼⠛⠐⠲⠁⠀⠈⣖⣚⢀⠀⠀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣐⠁⠀⠀⠀⠀⠀⡇⠀⡐⠂⠀⢀⠉⠀⠑⣤⠄⠘⠂⠘⡆⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠒⢠⣄⠈⠢⡀⠀⠀⣠⠊⠁⠢⠈⠀⠀⠀⢆⠀⣰⠁⠀⠐⢠⠴⠁⠤⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣥⢀⠙⡤⢄⠀⠀⢀⢀⠀⣈⠁⠠⠬⠋⠒⠉⠎⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⣤⠀⠋⠉⠍⠲⡎⠀⠀⣁⠮⡰⠀⡖⠁⠀⠀⠀⠄⠀⠀⣅⠈⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⣉⠂⠀⠁⠶⠀⢻⢃⠺⠌⠀⠀⠙⡣⠀⠀⠀⠀⠀⠀⠀⠐⣥⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠀⠀⠀⠂⢀⠙⣗⠀⠈⠈⠠⠽⣀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠃⠴⠀⠘⠺⡴⠦⠉⠁⢀⠧⠰⣀⢤⠤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠑⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⢀⢀⡋⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣩⢦⢘⠨⣁⣀⣁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠈⠊⠈⡆⠠⠀⠘⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⢰⡀⢹⠸⠆⠀⠡⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⢧⢀⣧⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡴⡂⠉⠀⢀⣀⣀⠀⠀⢰⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢰⣄⠀⢿⣿⡧⠡⣷⡆⠺⠇⠸⠀⢀⠈⠁⡀⠠⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠄⠂⣠⡭⠅⠈⠻⢀⡾⠿⠃⣤⠄⠀⣠⠷⣦⣶⢏⣀⣤⠄⢀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠷⡶⢶⣶⣴⠀⣰⣦⣦⠁⠹⠣⣤⣿⣿⣿⣿⡿⠁⡆⠀⠄⠜⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣄⡤⠀⢈⠁⠀⠁⠀⠀⣄⣠⢻⣿⠲⠠⠀⠀⠒⠈⠻⢟⣿⡄⠊
⠀⠀⠀⠀⠀⠀⠰⣷⣽⢃⠀⠈⢊⢹⣽⣃⣀⣭⠿⢷⡠⣾⡾⠗⠒⠀⠀⠀⣀⡽⠁⡾⣶⠶⣦⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⠔⠚⡀⠓⣿⠱⡂⡈⠇⡲⣾⣤⡀⣦⠀⠀⠠⣿⣾⡄⢳⠈⣹⣯⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣴⡀⠍⢁⢴⣿⣿⣿⣇⣙⣃⣄⠀⠈⣻⠷⠉⣄⣙⠓
⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠸⠀⠌⠘⢉⠁⡄⠀⠙⣧⣿⠿⠿⣯⠿⣓⠤⠂⢻⣿⣿⣿⢿⠆⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡚⢈⣽⠏⠐⠈⠀⣡⣴⣾⣆⣾⣿⣾⠆⠀⣤⣤⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⡀⠚⠂⠀⡤⠇⠤⣀⡶⠺⠋⠉⠉⢛⡻⠿⡉⠀⠀⢿⣿⡃⠒⠀⠛⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢡⠠⣄⣀⣀⠉⠓⢡⡿⠀⠀⣴⣶⣦⣠⠤⣼⠃⠀⠃⠸⢿⡿⠀⠸⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⡀⠀⠈⠃⠀⠦⠈⠛⣿⣿⡿⢉⣷⣄⠇⠀⣂⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⠑⠀⡤⠘⢃⣠⠀⡀⠈⠁⠀⠀⡟⠈⠀⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠁⠠⠙⠿⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⠳⠦⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡀⢀⣂⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⡐⠿⠀⠀⠘⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠁⠘⢀⠐⢻⣎⡄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⢤⠄⢰⣅⡈⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠴⠼⠁⣊⣨⣶⣀⡀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢰⠀⣴⡀⠀⠀⠀⠀⢠⡠⠁⢎⠈⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢋⣀⠈⠛⠋⠀⢠⡄⠆⣠⣠⡟⢶⠄⢹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠿⢃⣤⡀⢄⡀⣹⣾⣿⡼⣿⣋⣴⣮⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠼⠟⠟⣿⣩⣿⣏⠙⢷⣿⣿⣿⡬⠀⠀⠀⠉⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣷⣶⣾⣦⠀⣹⣿⠟⠓⠀⣾⣿⣿⣿⡷⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣷⣾⣥⣿⠈⢳⣶⣿⣿⣿⣿⠃⠀⢉⠢⡀⣄⠈⠀⠀⠀⠄⣊⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡿⡿⠓⣿⠽⠿⢫⣍⠁⠀⠀⠁⠀⠀⠠⠐⠐⠀⡀⠄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣻⠟⠇⠁⠀⠙⣊⠋⠀⢾⡄⠀⠀⠀⠀⠀⠂⠂⠀⠁⠀⢀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠆⠀⠀⠀⠀⠙⠁⠛⠀⠀⠀⠀⢀⡸⢠⠀⢀⠆⠀⠀⠀⠑⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠌⢈⠅⠀⠀⡰⠀⠀⠐⣤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣞⡄⠄⠀⠀⡀⠀⡄
⠀⠀⠀⠀⡀⠀⡀⠤⣤⡀⠀⢠⡴⠠⣤⠆⢠⣄⠀⠬⠝⠥⠶⠖⡤⠒⠀⠨⢤⡀⠤⠤⠤⠤⣤⠀⠤⡀
⠀⠀⠀⠀⠈⠢⠉⠤⣈⡓⠀⢀⠹⡀⠈⢣⠀⠈⠉⠀⠀⠀⠀⠸⢣⠀⠀⠀⠐⠈⠀⠠⠄⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠈⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠤
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣇⣀
⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠚⠁⠂⠀⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣖⢈⡀⠈⢃⣤⣀⢑⣰⡀⠀⣠⣤⠀⠀⠀⣀⠤⠄⣄⢀⣄⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠉⠀⠀⠛⠟⠃⠀⠌⠉⠀⢀⡡⠚⡸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠓⠃⠀⠀⠶⠀⠀⣀⢠⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣴⠄⠀⠀⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠰⠆⠰⠖⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣡⠀⠀⠀⠀⠃⡄⠀⢀⣤⣤⣤⣀⠖⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⡆⢠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡄⠉⠀⠀⠀⠛⠀⠸⣿⣿⣿⣿⣿⡟⢠⣶⠞⠰⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣤⣤⣤⠀⠀⠈⠙⢻⢟⠆⠘⠃⠀⠈⠉⣧⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡾⠃⢰⡄⢾⠽⠉⠀⠀⠀⢀⣀⣾⡇⠀⠀⠐⢖⡐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⢼⡿⢇⠀⠀⣈⣿⡇⢀⣀⡀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣙⣦⣄⣽⣷⡇⢸⠦⣶⣼⡇
⠀⠀⠀⠀⠀⠀⠈⠲⠞⣦⣰⠀⠢⠀⣀⡔⠂⠀⠙⠁⠘⣿⣿⡿⠃⢷⠀⠾⠟⠃⠈⣂⠀⠀⡄⣠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠓⠇⠀⠀⠀⠀⠀⠈⢻⡁⢠⡸⠆⣴⣦⡆⠘⣥⢠⣶⣿⣅⠀⠀⠂
⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠚⣿⠀⠀⠀⠀⢀⣤⣬⣤⣄⢀⠄⠀⠀⠹⠀⠟⠿⠇⠀⠀⠸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠱⠟⠀⢶⣌⠙⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣀⣀⣠⣦⣤⠶⠘⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠟⢃⠀⢦⡀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢊⡁⠈⠷⣲⠿⠛⠻⠿⠉⠁⠀⠸⠀⢰⣼⣷⢾⠛⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣳⣶⣮⠀⠀⠀⠀⠀⠀⣦⠄⠁⠀⠚⠙⠃⢀⡴⠚⣁⡤⠔⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣭⣶⣤⣄⣠⡤⢾⣦⣤⣾⣧⠀⠙⢢⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣭⣿⣿⢿⣷⣾⣻⠛⠀⣀⠘⠻⡞⠉⢀⠀⠀⢀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡟⢻⣿⣿⢧⣽⡿⢿⣟⡏⢿⣦⠄⠁⣦⣼⣷⡂⠈⠀⠐⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠁⠀⣙⡀⠀⠻⣷⠀⢹⣷⠿⣿⠿⠟⠋⠘⠁⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣷⣤⣙⣶⠚⣷⠘⣿⠀⢠⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣥⠾⠟⠛⣿⠀⣿⠀⣿⠀⠻⢷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⡄⠈⡀⢻⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⣠⣴⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣒⠽⠛⠁⣀⣀⡠⠤⠤⠔⠋⢾⣵⠶⠾⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣺⣵⣮⣥⡖⠾⠭⠅⠒⢒⣉⣉⣩⠽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠾⢿⣶⢶⣬⠭⠝⠛⠉⠉⣉⣠⣤⡔⠒⠋⠉⢉⣁⡠⠤⠄⣒⠿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡆⡱⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠛⠋⠙⠻⡗⢜⢦⡴⣒⣯⣿⡫⢭⣽⣛⣶⣭⣭⡥⠶⠖⣚⣩⠤⣚⣩⣍⢹
⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠽⠶⣶⣾⠭⠽⠛⠋⠉⠁⠀⠀⢴⣖⡋⠭⢽⣎⢣⣻⡟⣛⣫⡿⢿⣿⣿⣟⣃⡴⠆⣒⡭⠕⣺⣽⣷⡟⢫⠁
⠀⠀⠀⠀⡏⢸⡆⢀⣤⣴⠒⠉⠁⠀⠀⠀⠀⣀⣤⣤⣴⣶⣾⢿⣖⣋⠭⠜⣆⣏⢿⣔⣥⠦⠶⠶⢻⣿⡿⠶⣻⣿⠶⣛⡭⠶⠛⠛⢻⡀⣄
⠀⠀⠀⠀⠙⢚⣴⠾⡅⠘⡧⢀⣠⣴⣶⣾⠿⠟⠛⣿⢿⠋⠉⠉⠀⣀⣠⠴⢺⣼⣾⣷⣂⣭⣿⠿⣋⡵⣖⠽⣋⠵⠋⠀⣀⠤⠔⠒⡞⠁
⠀⠀⠀⣠⣦⢿⣼⡤⠿⠾⣯⠭⠮⠭⠤⣤⣶⣾⣭⡧⠼⠶⠒⠚⠉⠁⠀⠒⡓⣿⡇⣿⡿⠟⣛⣩⠵⣊⡥⠾⡷⠖⠋⠉⠀⣀⣤⡴⠗⢲⡀
⠀⠀⢰⣓⣨⣽⣦⣉⣁⠤⠴⠶⢶⡒⠉⠉⠀⠀⠀⠀⣀⣀⣀⡐⣶⠊⠉⢥⣝⣹⡟⣿⡷⠛⠉⢀⡈⠭⢹⣇⣀⣠⠴⣚⣫⣭⣯⣴⠒⠊
⠀⠀⠀⠀⢠⣞⢵⠃⢸⡂⠀⢸⣤⣇⣠⣤⣶⠾⢟⣹⣀⣠⠤⣖⣪⣭⡿⠟⠛⢙⡇⣿⡷⠻⠿⠿⢛⣛⣫⣭⡶⠾⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⢀⢏⠊⢓⣺⡧⠿⠟⠛⣿⣫⣽⣒⠢⠭⠉⠐⠚⠉⠉⠀⣀⣠⢤⣤⣤⣿⣯⣷⣒⡺⠽⢛⣉⣉⣵⣮⠉
⠀⠀⠀⣴⢻⢩⣝⢹⣏⣂⣀⠤⢤⠋⣇⠀⠀⠀⢀⣀⣠⠤⠒⠒⠉⣡⣤⠤⢒⣺⣿⣿⣏⠥⠐⠊⠉
⠀⠀⠀⠹⠾⢚⡯⡝⠿⠧⠖⠒⣻⡤⢿⣒⣶⠛⠋⠁⠀⢀⡠⣔⡞⠁⠃⣨⠴⠿⠛⠋
⠀⠀⠀⠀⠀⠸⡄⢳⠀⢰⢲⢉⡴⡎⠉⢯⣸⣇⣴⡶⠏⠒⠉⡡⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠙⠚⠒⠉⠉⠉⠳⠷⡻⢡⠛⡄⠀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣄
⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⣠⣿⣿⣿⣆⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢯⠙⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠈⠋⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⢿⣿⣿⣿⣿⠛⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⣿⣆⡄⠈⢹⣿⡟⣿⣿⣿⠏⠉⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣥⣨⣅⢈⡁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠘⠟⠁⠿⠙⠿⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠄⠀⠀⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠛⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠶⢦⡴⢶⣖⣛⠛⠉⠙⠛⠛⠳⢦⣄⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⡆⠀⠀⠀⠀⠀⠉⢷⡀⢠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣩⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠙⢣⠠⢤⣤⣤⣄⡀⢻⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⡟⣹⠞⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣄⡀⢿⠀⠀⠙⠾⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣾⣥⠟⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠙⣻⣇⣀⡀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⠏⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⣤⡾⠋⣀⣠⣤⠖⠲⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⠉⠉⠉⠀⠀⠀⠈⠙⢦⡙⢦⡀⠀⣠⠄⠀⠀⠠⡄⢀⡼⣡⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⠻⣦⠱⣴⠃⠀⠀⠀⠀⢹⠏⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⢴⠤⣤⣤⣀⡀⠀⠀⠀⠀⠈⢳⡉⡄⠀⠀⠀⠀⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⠀⠀⢻⡜⡄⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⡀⠀⢿⣰⠀⠀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⡇
⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⣀⣀⠀⠀⠈⠀⠀⠀⠀⠈⢣⡀⠀⢇⢇⡀⠻⠒⠂⠀⠀⠀⠀⠀⠀⣠⡶⠊⠉⠀⠀⣿
⠀⠀⠀⠚⢏⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⢀⠀⠛⠒⢤⣀⠀⠈⢷⡀⠸⡘⢻⠆⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠉⠓⢿⣍⡉⠙⠳⣤⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠓⢦⠘⣧⠀⠇⢸⡄⠀⠀⠀⢀⣤⠋⠀⠀⠀⠀⣠⡄⠀⠀⢠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⡄⢸⠈⡃⠀⠀⣤⠎⠁⠀⠀⢀⢀⠞⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⠐⣦⣀⣀⠀⣤⣀⣰⡶⠛⠛⠉⠀⠙⠷⣄⡀⢳⠀⢰⡇⠀⠀⡀⠀⣸⠋⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡀⣿⠀⠀⠀⠹⣮⠃⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠉⠉⠙⠿⣄⣀⣀⣠⣉⡀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠙⠳⣄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠙⢦⣸⢦⣷⣤⠶⠞⠛⠛⠙⠛⠶⣄⠀⢀⣀⣀⣀⣀⠈⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠛⠉⠉⠉⠉⠉⠉⠛⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠞⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠁⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢤⣰⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣴⠤⣝⣋⠩⣙⣻⠇⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡇⠀⠀⠀⣴⠒⢦⣄⠀⠀⣰⣿⠀⣿⡀⠿⠃⢀⣼⢿⣔⢇⡦⠞⠁⠀⠀⠀⠀⠛⠷⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠻⣄⣀⣴⡟⠀⠀⠈⣳⡾⠃⠹⣧⣌⠙⠳⣤⡏⠁⠀⠹⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⢷⣄⠟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣀⠠⠤⠤⣀⣾⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⡴⠶⠤⠶⢤⡀⠀⠀⢀⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⡇⠀⢀⣴⠏⠀⣠⡴⢶⠉⠉⠀⢀⡿⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣠⡤⠤⠤⠚⠋⠁⢀⡼⠋⠀⠘⠳⢄⣀⡼⠃⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠷⢦⣄⣀⣀⣴⠞⠉⢩⠟⠁⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⣠⡶⣿⠖⠴⠶⠛⠛⡉⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠋⠉⡜⠁⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠷⣤⣀⣀⣀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠉⠉⠉⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣀⣀⣠⡶⠏⠥⠤⠤⢤⣬⡽⢶⣤⣀⣀⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠛⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠋⣠⣤⠀⠀⠀⠀⢈⠃⠀⠀⠀⡀⠙⢤⣼⣇⣀⣴⣴⣶⣶⣇⣴⣥⡷⠃⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠰⠂⠠⡀⠨⡤⡍⠀⠓⣥⡄⣈⠙⢿⣿⣿⣿⣿⣿⣿⣟⣿⢉⠐⢆⡀⣀⡴⠀⠀⠀⠀⠀⠶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠋⣴⣾⠓⣰⠿⢮⣇⠈⣤⣌⠙⢿⣿⡿⠿⢿⣿⣿⡾⣧⡼⢿⣧⡀⣸⣦⠔⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠄⠉⠑⣘⣫⢝⣿⣿⣀⡙⠋⠀⠀⠉⠀⠀⠀⠙⢿⣥⣿⣷⣾⣏⡠⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢡⢀⣠⢸⣲⡏⣿⣿⣿⣿⠇⠀⠀⣶⣿⣷⣶⣀⠈⠉⢿⣿⣿⣿⣯⠀⠶⠂⠄⠐⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡽⡿⡤⠀⠁⡾⠿⠻⠿⠟⠂⣄⢰⣿⣿⣿⣿⠃⠀⠀⢹⣿⡃⢳⡄⠚⠀⠀⢀⡀⠀⠘⠷⠄
⠀⠀⠀⠀⠀⠻⠟⠉⠀⠋⠀⠁⢴⡆⠀⠀⢈⣻⠛⣿⣦⡌⠉⠉⠙⠉⠉⢀⠄⣀⠿⢿⣿⣤⡀⠀⠀⠀⠀⠀⠈⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣻⠿⠂⠘⠿⣷⡄⣀⠀⢘⠒⠁⠀⠿⢿⠀⢻⡛⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⡆⠀⠸⠿⠀⢾⣿⡀⠀⠀⠀⠈⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠈⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢀⣀⣀⣀⣠⡦⣄⡤⢤⣠⠤⠤⠤⠤⡤⠶⠶⠲⠶⠶⢤⣀
⠀⠀⠀⠀⢠⣤⡤⣤⠶⠶⠚⠋⠀⠈⠉⢉⣉⠉⠉⠀⠹⢮⡳⣄⣠⠤⢤⣤⡄⠀⠀⠀⠀⠈⠉⠀⠘⠧⣄
⠀⠀⠀⠀⣼⠉⠳⣄⡀⠀⠀⠰⠛⠒⠛⠋⠁⠀⠀⣠⣄⣀⡹⣞⠳⡄⠀⠀⠀⠀⠴⢦⡤⠤⠶⠒⠒⠀⠙⠲⡄
⠀⠀⠀⠀⢯⠀⠀⠀⠛⢶⣆⠀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠉⠉⠉⠳⡝⢧⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠛⢧⡀
⠀⠀⠀⠀⢈⡇⢠⡄⠀⠀⠸⣦⡀⠉⠙⠋⠀⠰⠆⠀⣀⣠⣤⠤⠀⠙⢷⡙⢦⡀⠀⢀⣀⣀⡀⠀⠀⠈⠉⠛⠁⢠⣇
⠀⠀⠀⠀⣼⠀⠀⠙⣧⣀⠀⠈⠓⣆⠀⠀⡀⣀⣀⠘⠁⠀⠀⠀⠀⠀⠴⠛⢦⡙⢯⡉⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠃⢀⡀⠈⢻⣄⠉⠉⠀⠀⣤⡤⠤⠴⠶⠄⠀⠀⠘⠛⣖⠻⣶⠒⠚⠛⠋⠉⠉⠉⠁⢀⣀⣀⣀⣿
⠀⠀⠀⠀⢻⡀⠀⠀⣷⡀⠀⠈⢷⡀⠀⠈⠳⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡝⢧⣤⠶⢤⣤⠤⠤⠞⣉⣁⡀⠀⢸
⠀⠀⠀⢀⡟⢠⡖⠀⠈⠙⠦⠀⠀⠙⠧⠤⠀⠙⣦⠴⠒⠶⠶⠶⠦⠖⠋⠛⠉⠉⠉⢹⡧⣸⠀⠀⠀⠀⠀⠀⢀⣉⠉⠁⠀⣸
⠀⠀⠀⠈⣷⠈⠳⣄⠀⠀⢠⠄⠀⡄⠀⠀⠀⢠⡇⠀⢀⡀⠀⢀⣀⣀⣀⡄⠀⠀⢤⣼⠀⢸⡶⠲⠞⠛⠀⠈⠉⠉⠀⠀⠀⣻
⠀⠀⠀⠀⢿⠄⠀⠀⠀⡄⠀⠀⠀⠙⢦⡀⠀⠈⣷⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⣸⡇⠀⠀⠖⡴⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠙⠒⠀⢠⣄⠀⠉⠀⢀⡏⠀⢀⣤⣤⡄⠀⠀⠀⠳⠞⠛⠛⢻⢆⢹⠇⠀⠀⠀⢠⣄⣠⠴⠶⠤⠀⣹⠂
⠀⠀⠀⠀⠘⣦⠀⢸⣃⠀⠲⣦⠀⠹⢦⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢹⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢽
⠀⠀⠀⠀⠀⠘⢦⡀⠉⠓⠀⠀⡀⠀⠀⠉⠀⠀⣧⠀⠷⠆⠐⢦⡴⠳⠶⠴⠒⠚⠛⢻⡇⣸⠀⠀⠀⠀⣀⡀⣀⣄⡀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠀⠀⢧⡀⢰⡆⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡧⣿⠀⠀⠙⠛⠉⠉⠁⠀⠀⠘⠂⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠉⠈⠷⠀⠘⡆⠀⠀⠲⠂⠀⠀⠈⠉⠉⠋⠁⠀⢸⡇⣿⡤⣤⠴⠤⠶⠶⠒⠒⠃⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⡀⠀⠘⡧⠀⠲⠤⠶⠦⠶⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⢀⣄⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⣸⡇⠀⢀⣀⣄⣤⣀⣠⣤⣄⣠⣤⡴⠾⠷⠟⠋⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠤⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡁⠀⠃⠀⠀⠀⡄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠙⢆⢸⣄⡄⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⡀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠈⠀⠋⠉⠙⠈⠀⡀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠝⠦⣁⠂⠠⠈⠛⠁⠀⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠘⣆⠀⠀⢀⣀⣀⣠⣄⠀⠑⠊⠓⢢⡰⡴⣠⢜⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡓⠤⣄⡈⠘⠤⡀⢺⣴⣿⣿⣿⢿⡟⠣⡀⠉⠀⠀⠝⠹⡾⠋⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠉⠒⣤⠋⠁⠈⢻⠉⢧⠀⠑⠀⠈⠳⡄⠀⣰⢠⡁⠀⠀⠀⢄⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⢀⠀⠀⢸⠀⠈⡄⠀⠰⡄⢀⡀⢀⠀⠁⠀⣀⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⠂⠀⠐⠀⢀⠁⢈⠀⠀⠘⠀⣀⡘⠠⡴⠀⣉⢀⠂⢀⠔⠋⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠉⠀⠒⢲⠚⠉⠉⢀⡓⠁⣀⣤⡟⠛⠙⡇⠈⢈⡖⠛⠢⣀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⡀⠤⡰⡎⠁⠀⠀⠉⠀⠀⠀⠀⢠⠀⠸⠀⢀⠞⠉⠯⠙⠲⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠰⠀⡌⠀⠉⠳⢄⠀⢤⣸⣠⡇⡀⠁⠀⢀⡔⢡⠀⠀⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠈⠀⣁⠠⢤⣀⣀⣹⣟⣿⡿⣿⡤⠀⠀⠁⠀⠈⡗⠢⠀⠌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⡀⠂⠀⢸⠄⠀⢀⣀⠴⢿⣿⣿⣿⣿⣟⠃⠐⠒⠐⢂⡝⣆⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠁⠀⠀⠀⠀⠀⠀⠊⠉⠀⣠⠞⠙⢿⡿⡟⢦⡈⠑⠲⣤⡤⠁⠘⣇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣠⡞⠁⠀⡀⠀⠁⠱⠀⠑⢄⠀⢠⠏⢄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠳⣄⡴⠀⠀⠀⠀⠣⢀⡨⠁⠀⠀⠀⠁⠠⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠐⠋⠉⠀⠀⠀⠀⠀⠉⠈⠹⠋⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣶⡶⣿⣭⣍⣓⡲⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢒⣛⣊⠶⠖⠊⠁⠀⠈⠉⠛⠛⠱⢌⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠳⣿⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⡞⠀⠀⠀⠀⠀⠀⢰⠢⠶⡄⠸⠈⢳⡀⠀⠀⠈⢇⢟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣨⠞⢠⠓⠤⡄⣀⠀⣀⣫⠤⡠⠌⢥⣹⠁⠈⠉⢙⡆⠈⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⢹⠀⠱⣀⠊⠀⠰⠋⢁⠀⠙⢁⠀⠀⣹⣤⣀⣠⣾⠊⡳⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠾⢸⡔⠉⠉⠙⢄⠀⠦⢀⠀⡪⣷⣆⠂⠻⣄⡷⠀⠀⢈⣇⣇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠉⠳⣀⡆⡠⠀⠀⠀⢀⠐⠉⠙⠷⣷⡤⠄⠑⠀⢀⡤⠂⢴⡜
⠀⠀⠀⠀⠀⠀⠀⡴⠚⠀⠐⠈⢙⠟⠀⠀⠀⡠⠞⠠⠀⠀⠀⠸⠛⡆⠀⠀⠠⠀⠀⡈⢣
⠀⠀⠀⠀⠀⠀⢀⡗⢀⠄⠣⢀⠈⠢⠄⠂⠀⢧⣤⡶⠀⠒⢎⠁⠀⠡⣐⠀⢊⠰⡀⠑⠘⡄
⠀⠀⠀⠀⠀⠀⠘⡦⠀⢀⠀⠀⠂⠈⢄⠀⠀⠀⡀⠀⠀⠀⢀⠆⠀⠰⢊⠈⢣⠈⡇⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⢇⡠⢻⠈⠁⠙⠀⠢⠂⠤⠘⠁⠀⡠⢒⣧⡦⠀⠎⠉⠒⠀⠀⠃⡸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠇⠓⡙⠡⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣄⣀⣀⣄⣀⣠⠴⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣌⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣰⠉⣿⣿⣿⡿⣷⣄⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣿⣿⣿⣿⣤⠻⢷⣾⣻⣷⣤⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣟⠧⠿⠆⠀⠙⢿⣿⡿⠛⠛⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢉⣯⡍⠙⣿⠀⠀⠀⢀⣀⣾⡋⣠⣶⣦⣤⣉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣟⡁⠀⠀⢹⣦⣄⣴⣿⣏⡉⠉⠉⠉⠛⠿⣿⣷⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⠙⢿⣷⣶⣿⣿⣿⣿⣿⣿⠿⣦⣤⣄⣄⡀⠀⠈⢿⠇⠀⠀⣀⣰⡟⠀⠉⠷⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠈⣻⣿⣿⣷⡿⠋⠈⣿⠀⢻⠿⡿⠟⣛⣟⠀⣀⣀⠀⣰⠏⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⣆⣿⣿⣿⢿⣇⣼⡇⣻⣷⣼⠗⠀⠘⠿⠛⢿⣿⡟⢀⣇⠀⠀⠀⠀⠀⠀⠘⣧⢤⣄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠿⣿⣄⠀⠀⢀⣿⣿⠸⣷⢼⣿⣿⣿⡿⢛⠛⢉⠀⠈⢦⡀⠀⢈⣿⣇⠈⡅⢰⠀⠀⠀⠀⠀⣸⠃⠸⠛⣀⡀
⠀⠀⠀⠀⣴⣶⡿⢿⣦⣀⡀⢻⣇⠠⣼⡟⣩⣶⣿⣼⠟⣩⡄⠀⡸⠃⠀⠁⠀⠀⠀⠘⣿⣿⣿⠀⠷⠚⠁⠀⣼⠀⢠⡿⠁⠀⠈⠁⠉⠀⢀
⠀⠀⠀⠀⠈⠻⢿⡄⠉⢻⣉⣾⡿⢁⣠⣨⣦⡈⢿⡷⣿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣼⠷⠶⠶⣦⡀⢉⡴⠋
⠀⠀⠾⠛⣷⣆⡀⠈⠐⠢⠌⣛⠷⣸⣿⣿⣿⣧⣿⣿⣿⣿⢿⣷⡄⠀⠀⠀⠀⠀⠐⠂⠰⣾⣏⣵⡟⣶⣌⠛⡁⠐
⠀⠀⠀⠀⣼⠿⠿⠿⠶⠟⢋⣽⣯⣿⣿⣿⣿⣿⠳⣮⣤⣀⣡⡈⠁⠀⠀⠀⠀⠀⠠⣴⡶⢿⣤⣿⣿⣿⣷⣶⡁⠚⠁⠀⠀⠀⠰⠿⠂
⠀⠀⠰⡆⠀⢴⣾⣿⠶⠛⢉⡿⠟⣽⠛⣿⣿⣽⠳⣄⠉⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣾⣉⣿⡟⣿⣿⣇⠻⠃
⠀⠀⠀⠘⣷⣯⣄⣉⡤⠐⢋⣤⠞⠁⣠⠀⣻⣿⣄⠈⠛⠂⠀⠛⠐⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⠛⠳⠍⠳⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠛⠛⠛⢡⣤⣿⣥⣤⣶⣿⣧⡈⠛⠛⠀⣠⣴⣾⣿⣷⡌⢹⣿⣯⠀⠀⠤⠰⠿⠟⣁⡀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢋⣙⠿⣿⠛⣿⣿⡟⠀⠛⠋⠀⢸⡟⠀⠸⣿⣿⣶⣶⣤⣀⣀⣀⠉⣉⣉⡉⠛⠲⢀⡠⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⢤⡀⠹⣟⡤⠀⠀⠀⠀⣾⠇⠀⠀⠈⡻⠛⣿⡿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠙⢿⣷⣀⣀⣀⣤⡀⠀⠀⠀⠁⡐⠁⠀⢀⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠻⣦⣀⣿⡟⢻⣯⣭⡟⢷⣄⡤⠈⠀⠀⣤⣿⣿⣿⣿⣿⣶⣌⠻⣦⡈⠙⢿⣿⠿⠿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠻⠿⣏⣾⣧⣼⣿⣺⣿⠂⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣀⣹⡗⠰⢾⠿⣷⣤⣽⣷⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣌⡑⣢⣤⣴⣿⣿⣿⣿⣿⣿⣣⣦⠤⠀⠀⠀⠀⠈⠛⠙⠻⣿⣿⣷⣶⣭⣭⣿⣿⣶⣶⠿⠶⠛⠛⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡙⠛⠉⠿⢿⢿⣷⠸⠝⠻⠂⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡻⣯⣥⣤⣭⣭⣿⣿⡆⣶⣶⡷⠾⠖⣫⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠻⣤⠚⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠻⠿⠿⣿⣾⣟⣿⣿⡿⠿⣿⣿⣿⣿⣶⡿⠟⣋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠠⢦⠄⣀⣹⣿⣶⡶⠀⠀⠀⠀⢸⠃⠀⠀⢰⡏⢸⣿⣿⣿⣿⡿⠿⢿⣿⡯⠥⠖⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣏⢙⠟⠁⠀⠀⠀⠀⡀⠀⠀⢠⠟⠀⠸⡿⠿⠛⠏⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⠀⠀⠀⠀⠀⠐⠁⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢰⡆⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠘⠃⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⢀⣀⣤⣄⣀⢀⣠⡴⣦⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠶⠶⠶⢦⠶⣾⠙⢷⣬⢷⡖⠾⠏⠡⠄⠉⠉⠉⠁⠀⠉⠉⠉⠉⠛⠓⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠚⠋⠁⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈⠳⣄⡙⢦⡹⣦⣀⣀⡀⠀⠀⠐⠒⠚⠙⠿⠤⢤⡄⠀⠙⠓⠲⢶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠃⠀⠀⣠⠼⠏⠉⠀⠀⠈⠉⠀⠀⠀⠀⠈⢯⡉⢷⠘⣦⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠑⠒⣲⡀⠀⠀⠀⠉⠹⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣾⠛⠉⠉⠀⠀⣠⠶⠗⠀⠀⠀⢤⠤⠖⠒⠂⡠⠶⠶⠄⠀⠻⡌⢷⡬⣷⠢⠴⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⡄⠀⣼⠛
⠀⠀⠀⠀⢀⣠⠴⠛⣀⣠⠀⠀⠤⠴⠃⠀⠠⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⡮⢷⡈⣧⠀⠀⠀⠀⢀⠈⠉⠉⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢀⡴⠋⠀⠀⡾⠁⠀⠀⢠⣄⠀⠀⠀⠀⠉⠁⠀⠶⠉⠉⠀⠀⠀⠀⠀⠀⠘⠲⠚⢿⡈⣧⠸⡆⠀⠀⠈⠊⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⠀⠀⠀⢿⣄
⠀⠀⣹⠂⠀⢠⡊⠀⠀⠀⠀⠈⠉⠀⠀⠺⢦⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢹⡤⣽⠀⠤⠤⠤⠤⡠⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⢉⡷
⠀⠀⠈⡽⠃⠞⠁⠔⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠑⠒⠂⠀⣤⠄⣿⡈⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠞⠉⠀⠀⠀⠀⠀⠠⡾
⠀⠀⠀⣧⠀⢀⠀⠀⠀⠀⡷⠀⠀⠀⠠⣄⡠⢤⣀⣀⣠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢸⡍⣿⢸⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠴⠂⠀⠀⣰⠇
⠀⠀⣠⠟⠀⠙⠆⠀⠀⠘⠲⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⣀⣀⠀⣀⣀⡴⠂⠀⢸⡇⣿⣸⡷⠋⠓⠓⠊⠉⠉⠁⠀⠀⠒⠒⠒⠋⠀⠀⠀⣼⠃
⠀⠰⢯⣤⠄⠀⠀⣄⠀⠀⠀⠀⠀⢀⣀⣠⡀⣀⣀⣀⣀⡀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⢀⣾⡇⣿⢹⡇⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠞⠂⠀⠐⣯⠁
⠀⠀⠺⠷⣶⠀⠀⠀⠙⠙⠚⠁⠀⠀⠁⠀⠈⠁⠉⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠠⣄⡀⠀⣸⠓⣿⢸⡇⠒⠒⠊⣁⣀⣀⣀⣀⣠⠆⠀⠀⠀⣀⣠⣽⠆
⠀⠀⠀⠈⠛⢻⡂⠀⠀⠀⠓⠢⣄⣀⣀⡀⠀⣀⠄⠀⢀⢀⣀⣠⢄⡴⠒⠒⠀⠀⠀⠈⠁⡿⢀⡯⣼⠀⠀⠉⠚⢁⢀⣀⠀⠀⠀⠀⠀⣀⣀⣯
⠀⠀⠀⠀⠀⠀⠹⠦⣤⡀⠀⠀⠀⠈⠁⠈⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣼⣃⣼⣡⣯⣤⣤⡀⠀⠈⣈⠉⣀⣠⣄⡀⣸⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠶⢤⡄⠀⠀⣠⣤⣀⣠⡀⣠⣤⡴⠞⠛⠋⠉⠉⠉⠉⠀⠉⠁⠀⠀⠀⠈⠙⠲⣤⣯⠉⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠩⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⢀⠇⢨⡍⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢉⡄⠓⢄⠀⠣⠤⢴⠤⠬⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡆⢀⡖⢊⡴⡳⢤⠈⣆⡀⠀⠀⠸⢲⣽⣿⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣤⣤⡀⠈⠁⠘⡧⣦⢱⢁⠴⠃⣼⢉⠆⠀⠳⣿⡯⠊⠀⠀⢀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢳⢀⠸⣄⢀⡝⠀⢀⠤⣰⡏⠉⠘⠦⢾⠣⣀⠇⠀⠀⠇⠀⠀⠀⠀⢨⣿⣼⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣚⢾⣧⠈⢃⡀⢀⡧⢠⠟⢉⠗⠀⢀⠴⣦⠖⢦⠀⠀⣼⠀⢀⠀⢀⠼⢿⣿⣝⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢷⠿⠋⠲⣼⡇⡋⣠⠼⡁⢸⠀⠀⢈⠆⠾⠄⢏⢠⡀⣧⣴⣿⣔⡅⠀⠀⠈⠊⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢷⠜⠸⣠⣤⢾⡣⡈⢴⡢⢬⡙⡄⠀⢧⡠⢶⠦⠴⠉⢿⣿⣿⣟⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢧⣱⡥⢱⠘⢎⢯⠽⠁⠰⠀⡖⢄⢸⣠⠤⡄⢈⠟⠛⠋⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⡴⠁⠈⡵⠋⠱⣄⣽⣴⣟⡀⡇⠑⢌⣿⠧⠊⢀⠎⣀⣴⣾⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⡤⣀⣴⠋⠓⠛⣾⣧⢱⢻⣦⣷⡺⢢⠞⠋⡹⣯⢻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡴⡖⢢⠛⠿⢯⠘⡄⢹⠁⡴⠁⠀⠀⢧⠋⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠜⠓⠒⠒⢧⡇⣺⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃

⠀⢀⣴⣿⡏⠀⠙⠛⠻⠶⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢦⠈⡏⡇
⠀⠿⠿⠿⠿⠿⠗⠛⣛⣉⣉⣙⣛⠲⣍⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⡔⠷⢃⣴⠕⣡⠞
⣤⣤⣤⣴⣶⠶⠟⠛⠉⠉⠉⠉⠙⢳⣌⢳⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡕⠉⢁⡴⢚⡵⢁⣾⠷⠚
⣈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷⡀⠘⢧⠻⣄⠘⠋
⢦⡙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠞⣵⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣼⡇⠀⠈⢳⣍⠛⠶⠦⠴
⢼⣫⡾⠋⠀⠀⠀⠀⠀⣀⣀⣤⠞⢱⡏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠞⠋⠉⠀⠀⠀⠀⠙⠻⢿⣿⡿
⢋⣁⣀⡀⣀⣴⠟⢋⣭⠶⣲⠶⠶⠿⠃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡵⠖
⣟⡒⣎⠛⠋⣁⣴⠟⣱⠟⠉⠉⠙⠒⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏
⠀⠱⣌⠷⡾⠟⣡⡾⢋⡤⠴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣛⣶⣒⣒⣒⣒⠲⢶⣄⠐⢝⣲⠦
⠀⠀⠈⠓⠒⢚⠭⠊⠡⢤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣹⠗⣠⡿⠇⠀⠈⠙
⠿⠋⣩⠗⠊⣠⠂⠀⠀⠈⣇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢞⡡⠚⠁⢀⣀⣀⣤⡴
⡴⠛⠁⠀⢼⡃⠀⠀⠀⠀⠘⡄⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠯⠓⠚⠉⢀⣠⠞⣩⠵⢖⣒⣛
⣀⣀⡀⠀⠀⠙⢦⠀⠀⠀⠀⢱⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⣶⠾⠟⠛⠃⢸⢇⡾⠉⠁
⠒⢲⡽⡄⠀⠀⠈⡇⠀⠀⠀⢸⠀⢸⡝⢦⡀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⡀⠀⠀⢸⡇⢸⣿⣁⣴⡾⢿⣷⡸⡞⣷⣤⡤⠶
⠀⣰⢳⠁⠀⠀⡼⠁⠀⢀⠔⣋⠤⣚⡵⠟⠁⠀⠀⠀⠀⡴⢋⣴⡾⢷⣦⡙⠲⡶⢫⠀⣾⡿⣫⡶⣶⣒⠦⣕⣕⣶⣖⣺⡭
⠖⣱⠃⠀⣠⠞⠁⢀⠔⣡⣮⠟⠋⠁⠀⠀⠀⠀⠀⠀⠘⢧⡘⢿⣆⠀⠙⣿⣦⣠⠇⠀⣿⢱⡏⠀⠀⠈⠛⠶⢯⣕⡒⠲⣶
⣾⣷⠶⠾⠿⣶⣶⣿⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣷⣶⣿⣿⣿⣷⣾⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠸⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢘⠠⠀⠀⠄⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠴⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢀⡀⠀⠥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢈⢏⣤⠶⡉⠄⡄⢰⡄⠠⠆⠀⣀⣘⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⠴⠞⠀⠀⠂⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣌⣠⠉⣌⠀⢟⠉⣥⠄⡀⡤⠠⣁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠺⠷⠆⠀⢈⠀⠟⠀⠀⠀⠄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⠟⠐⢟⢒⣮⡛⣤⠴⠅⠈⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠒⠭⠁⣰⣆⠀⡾⠂⠁⢰⠀⣀⢀⣤⢣⣄⡴⠖⠀⠀⠀⠀⠀⠀⠊⠀⢁⠷⡁⠙⠘⠋⠀⠀⠈⠁
⠀⠀⠀⣀⠀⣄⠀⠀⣀⠰⢄⡀⠀⠈⠃⠹⣧⠀⠀⢹⡧⠉⡮⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠉⠔⠃⡈⢣⣤⠁⡀⠀⢀⡀⣿⠂⠁⠸⠏⠈⠑⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠷⠞⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢙⣿⠀⠀⠈⠱⣿⠀⣄⠀⠂⢹⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣧⡖⠓
⠀⠀⠀⠄⡸⠰⠆⠴⠆⠀⠄⡏⠁⠀⠀⠐⣿⣧⢽⣿⣇⢐⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠊
⠀⠀⠀⠀⠁⠀⠀⠐⠴⢈⣿⣧⣀⣤⠀⠀⣿⠀⠀⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠐⠋⠉⠉⠀⠒⠙⠵⠶⢶⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⢤⠀⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡑⠒⠀⠀⢠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⠀⠀⢀⣀⠀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠰⣦⣷⠈⠋⣷⢀⡄⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠁⠀⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⢕⣰⡞⠂⠈⣣⣄⡀⢇⡀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⢀⢪⣍⡼⣦⠟⢙⣻⠗⠈⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⣨⣿⣌⠳⠂⠛⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⡀⢀⡀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⡄⠰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠦⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠸⠀⢀⡀⠄⠀⠀⡾⡆⣐⡀⠺⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠿⡀⢀⣼⣿⣿⣇⠘⠛⠻⣯⣿⣿⣯⠤⡀⢸⣿⣯⣿⡀⠀⠀⠀⢀⣿⣿⣿⢟⣷⣿⣦⣴⣄⣠⡤⠀⢀⡄
⠀⠀⠈⢿⣟⠡⠀⠀⣀⢤⣀⠈⣿⣿⣯⣂⣼⣿⣿⡿⣿⡇⠄⠀⢤⣾⣋⣿⣿⣾⡾⢿⣿⣿⠙⠙⢿⣿⠍⠲⣭
⣶⣦⣄⠀⣯⣿⣦⠊⡁⠄⢀⣰⣿⠿⡟⢿⡏⠈⠁⠑⡿⡧⢀⣀⠀⢹⣿⣿⠿⠛⠈⣨⠉⣇⢹⠻⣾⡿⢂⡀⣻
⣿⡿⢻⣿⣿⣿⣿⣿⡿⣷⣾⣥⡴⢋⣧⢰⣇⠀⠀⠀⡼⠃⣈⢓⢈⠯⠉⠻⠘⢃⠀⠇⠀⡁⠈⢠⠋⢽⣌⣹⣺
⠀⠀⠐⡟⠻⡝⣾⣿⣧⢿⡌⠟⠳⢫⣽⡿⡟⠇⣠⡞⠀⢐⡔⣟⣁⡶⠔⣾⡿⣾⣗⢜⣠⣳⡀⣆⣁⡔⡚⣡⣉
⣦⢠⡒⣷⣄⢵⣸⣎⠹⢛⢉⠰⠆⠸⠷⡖⣛⡆⠦⣶⣶⣮⢩⡴⢈⡁⠀⠘⠀⠒⡿⠷⢿⣿⣿⣟⣿⠙⠃⠀⠙
⣀⢈⡷⠺⢷⣴⠿⠞⣲⣽⣤⠒⣀⢸⣦⣁⠿⠿⠧⠻⢿⣿⣏⠀⠛⣧⣿⣀⡶⠅⠀⢠⡄⣈⣽⣾⡇⠀⠀⢀⣄
⠛⠉⠀⠀⠀⠁⠀⠀⠁⠋⢻⣈⠻⡖⠆⠁⠀⠀⠀⠀⠀⠉⢻⣤⣴⣿⣿⣿⣿⠁⠐⣾⣿⣿⣿⡹⣇⠀⢐⡞⠉
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡯⠿⣿⡦⠀⠈⠀⠁⠀⣦⣠⡾⠿⠉⠉⠙⠛⢟⣯⣿⠟⢻⡟⠻⠽⠏⠀⡞⠀⣸
⠈⠓⢦⣀⠀⢸⣀⢁⡎⠻⡏⠲⠐⠺⡇⠀⠀⠀⠀⠀⣿⠁⣀⣀⡤⡉⠀⠀⣸⡟⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠏
⠀⡀⠀⠹⣿⣿⣿⠋⠁⠀⣡⠀⠶⠘⠳⡀⠀⠀⠀⡤⣣⡾⠋⠀⠀⢠⣄⡉⠉⠛⢦⣆⠄⠋⡾⢧⠀⠀⠠⣶⡀
⠾⠀⠀⠚⠛⠋⡏⠀⢀⣠⣿⠀⠀⠀⠴⡿⣦⡠⣼⢻⣻⣶⠞⠀⠀⠀⠈⠙⠀⠙⢀⡁⣠⣴⡆⠀⠀⡶⠶⣏
⠀⠀⠀⢀⣄⣰⡍⠒⠉⠁⠉⠦⣬⣦⡀⠀⠀⠘⢛⢴⣕⣑⣆⠀⠀⣀⡔⠀⡘⠀⠈⣿⡿⠁⠀⠀⣀⠀⠀⠀⠒
⣭⣿⣮⣩⣏⣿⢿⣦⣄⢀⡤⠊⠛⠀⠙⠻⠦⠀⡈⠎⢉⡡⣤⡤⢤⣿⣥⣴⣀⣠⣼⣿⠉⠃⣤⣾⣿⣿⣄⠀⠈
⣿⠋⠛⢻⡞⠁⠀⠙⣿⠿⠀⠀⡄⠀⠀⢀⣠⡤⠞⠢⣀⠀⠀⠀⠀⡀⠈⠙⠏⢏⢍⠡⢻⡀⣿⡿⠉⠙⢯⣷⠢
⠒⢠⣍⣁⣘⡀⣆⠐⠳⡆⡀⠀⠀⢠⣴⣿⠃⠀⠀⠀⠈⠙⢶⠔⠛⠀⠀⠀⠈⣿⢿⠿⣿⣷⣿⡀⠀⠖⣤⠛⠒
⠄⢙⠾⠏⢂⡙⣾⠇⣈⠁⠀⣈⠀⠰⣩⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣻⣾⠆⢀⠙⠻⠁⢦⡜⢈⠑⠎
⡘⠫⣌⣰⡦⣹⣟⠢⠤⠐⠂⢤⠈⢺⣿⣟⠁⠀⠀⠀⠀⢰⣿⠆⠀⠀⣤⠤⠚⢡⢿⣶⠶⢴⡀⠐⢺⣧⣼⡂⢀
⠒⠛⢻⡧⣶⡽⠋⢁⡔⠂⠀⣤⡔⢻⣿⣤⣀⣠⣿⡟⠉⠀⢩⡆⠀⢀⠀⣁⠐⠛⠀⠛⣛⣿⣿⠟⠉⠛⠋⠙⢏
⠀⠐⠛⠀⣁⠀⠊⢀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿⣴⣤⠤⣀⣷⡟⠻⣮⡁⠀⠀⠀⣀⣯⣿⡏⠠⡀⠀⠀⠀⢈
⠀⣠⠂⠊⣸⡄⠀⠀⡄⠀⠀⣀⣀⡼⠿⠿⠿⠿⢏⡹⣽⣦⣛⣍⣉⣶⠻⠛⠂⡄⠀⢱⡼⣻⠧⠚⠳⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⢶⠆⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢄⠈⣵⠀⠈⡉⣀⣀⡀⠀⢀⣠⠀⠀⠀⠀⢀⡀⠂
⠀⠀⠀⠀⠐⠛⢀⡄⢀⠀⣂⠠⠀⠤⠂⠀⠛⢿⣶⣾⣿⣿⣿⣷⣿⡿⠁⡤⠀⠀⣀⠘⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⣬⡿⢀⡴⢝⡅⠋⣀⡛⢿⣿⣿⢽⣿⣿⣧⣧⣰⢶⣎⠁⣰⣄⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠙⢁⢏⣓⣾⣿⣈⠛⠁⠀⠙⠁⠀⠈⠻⣟⣾⣷⣾⣏⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⢠⡄⣳⡏⣻⣿⣿⡷⠀⠀⣴⣾⣶⣦⡀⠉⢹⣿⣿⣿⠅⠐⠒⠀⠀⠉⠁⡀
⠀⠀⠀⠀⢀⣀⣠⠀⡨⢻⠷⠀⠀⠾⢛⢛⣛⡋⠠⣀⣿⣿⣿⡟⠁⠀⢨⣿⣇⠱⠄⠋⠀⠀⠄⢀⠘⠓
⠀⠀⠀⠀⠈⠋⠀⠀⠁⠀⠐⠛⢀⡀⣤⣿⠹⣿⣶⡀⠀⠈⢀⠀⠐⢠⣟⡛⣿⣧⣤⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⡭⠀⡈⢙⣷⠐⣠⣬⠁⠀⠈⠛⠀⠘⠍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣬⡄⠙⠟⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠠⣿⣆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⠀⡀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠰⠀⠀⢀⠀⠁⠀⠐⠃⡸⠀⠙⠄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⢐⣾⣿⡦⠄⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡞⠀⠁⢀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣦⡤⠂⠀⠀⡴⠻⢷⡟⠀⣰⠀⠀⠀⠚⠁
⠀⠀⠀⠀⢀⡀⣀⠀⢀⣼⣿⠛⠁⠀⠀⢲⣦⣤⠈⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠉⠀⠀⠄⠹⠋⢦⣼⠀⢀⡏⠁⠀⡘⠛⠹⠀⠀⠀⠀⣄⣴⣄⡀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⡞⠀⠀⡜⠀⠀⡌⠀⠀⣤⣾⣿⡏⠉⢳⡄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⢰⣿⠋⠈⠀⡀⠈⠋⠀⠀⠘⠳⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣀⠴⠆⠀⢁⡠⣀⡄⠁⠀⠀⠀⠆⠘⠋⠀⠀⠀⡀⢀⣾⡄⠀⣷⡄
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⡉⠚⠃⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⣤⠿⡙⠂
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠰⠀⢻⠆⠀⢸⣷⢠⡄⠀⢀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢸⠈⠙⠃⡀⢋⠀⠸⣇⢲⡿⠷⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢠⠙⢿⡀⠀⣏⡞⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠀⣷⡄⡟⢀⣶⣇⠀⠀⠀⠐⠂⣤⣁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⡄⣇⠉⡄⠸⣿⠋⡀⢀⣃⠀⠀⠛⠛⠋⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢳⣿⡁⢻⡀⠁⠀⠋⢀⠷⠟⣿⠏⣀⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢻⠁⢸⡁⠀⠀⣀⣼⣶⣶⠠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠸⡇⣸⣵⣧⣾⡿⢋⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⠓⠀⠀⣧⡟⣿⣩⣤⣶⣼⣿⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⢹⠇⣿⢀⢙⣿⣿⣿⣷⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⠛⢦⣀⠀⠀⣿⡰⣿⠏⠿⠿⣿⣹⡟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠻⣦⠀⣿⣷⡇⠀⠀⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⢀⣧⣤⡔⠒⠒⠂⠐⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⠟⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠁⠈⠂⠀⠀⠘⡀⠀⠀⠀⢀⣤⠤⠶⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠂⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠅
⠀⠀⡈⠀⠀⠀⠀⠠⠀⠀⠱⡀⠀⠖⢘⠋⠀⠰⠃⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠐⠀⠀⠰⠰⠀⠀⠀⠀⠀⠈⢦⡈⠙⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⢄⢀⠀⠀⡤
⠀⠀⠐⢄⠠⠀⡀⠄⢀⠀⠀⠀⠀⠉⠺⣤⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠨⠱⠽⡬
⠀⡆⡠⠒⠀⠀⢈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠁⠀⣁⠀⠀⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠖⠓⢦⠀⠀⠈⣼⡇⠁⠀⠈⡍⡏⠭⠀⢈⣽⢯
⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢤⣠⠜⠀⠀⠀⡨⢷⠄⠀⠠⡄⣧⡦⠀⠀⣙⣳
⠀⠠⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⠀⣦⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡿⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠋⠀⠀⠀⠸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⢀⡀⣀⠠⡴⠘⠀⠀⠀⠉⠁⠀⣠⢤⡄⠀⡀⣀⡀⣴⣡⢡⢦⣖⡞⡽⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠘⠁⠉⠀⠀⢀⡄⠀⠀⠀⠠⣮⣕⣋⡞⣼⢱⠟⣻⠣⠇⠛⢘⣼⠿⠥⠀⠀⠀⠤⠀⠀⢳⣶
⠀⠀⠀⠚⠀⠀⠇⠀⠀⠀⢠⡄⣶⠀⠟⠈⠁⠀⠀⠀⢠⣶⠞⠉⠁⠁⠀⠀⠛⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣀⢠⡄⠀⠀⠀⠈⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠿⠀⠛⠈⠁⠀⠀⠀⠀⠀⠧⣧⠇⠀⠀⠀⠀⠠⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣶⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠈⠀⠠⣤⠙⣿⡯⠆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉
⠀⠀⠀⢲⢀⠀⠆⠀⠀⠀⠀⠀⠿⠀⠿⠀⠀⠀⠀⠀⢀⠁⠀⠄⠀⠁⠀⠀⠐⠿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠸⣗⠢⣄⠀⣸⢀⠀⠀⠐⡀⠁
⠀⠀⠀⠀⠀⠀⠀⡘⣧⡘⡏⢣⠈⢣⡀⠲⠋⡁⠧⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⢴⠞⢻⠋⠑⠉⣦⠜⠋⣸⠇⢷⣿⢰⠀⠀⠠⠺⠆⠀⠀⣀⡀⠤⠀⠒⠀⠀⠈⠉⠁⢀⣈⣀⣀⣀
⠀⠀⠀⠀⠀⡎⠀⡾⠀⠀⢀⡿⣁⠞⠁⠀⢠⡽⠛⠃⠛⠛⡇⠀⢰⠊⢁⠀⠀⠀⠀⠀⠀⠐⠀⠤⠁⠀⠀⠀⡬
⠀⠀⠀⠀⠀⣧⢀⡽⡀⡤⢠⡆⡇⠀⠀⢀⣿⢁⠀⠑⢦⡀⡐⠀⠀⡄⠄⠁⡘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠇⡀
⢀⠀⠠⠄⠠⠱⠀⠀⢘⣀⡴⢷⡀⠐⠀⢸⠀⢌⠀⡀⠀⢻⠋⠀⠃⠘⠀⠈⢡⠘⠀⠁⠀⠀⠀⠀⠁⠒⠀⠀⠀⠁
⡎⠀⡁⣖⣤⠐⢈⠲⣏⠙⡑⡄⢱⡆⠀⠀⡴⠈⠀⢁⡤⠸⠃⠀⠀⠀⠀⠀⢸⠀⠀⢀⡗⠀⢠⣤⡼⠃⠈⠁⠀⠀⢄
⢄⠈⠙⠉⠓⠒⢤⣴⣘⢦⡹⣮⢀⠱⡆⠀⠰⡴⡄⠀⣅⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣞⠁⢀⣿⡟⠁
⠀⠙⢧⡀⠐⠀⠊⢽⣻⣧⡝⠪⡻⣷⡱⢅⡀⠘⢾⣤⠸⡀⢀⠀⠀⠀⠀⢀⠆⡀⢘⠏⣰⡾⠛⠉⠁⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠙⢦⡀⠀⠀⠁⠙⠛⠲⣌⣲⣿⣧⡳⣁⢄⠙⢿⣅⠀⠀⠀⠀⠀⡘⢐⣤⣾⠾⠟⠃⠉⠀⠀⢀⠀⢀⣀⠀⠁
⠀⠀⠀⠀⠀⠙⠓⡀⠶⠾⢛⠟⡿⠿⠻⣿⣦⣮⣷⣷⣶⣿⣶⣶⣶⡶⠿⠋⠛⡏⠁⠄⠀⠠⠀⠀⠀⣀⠟⠉⠁
⠀⠀⠀⠀⠀⠀⢤⡀⠡⠆⠀⠜⠁⠆⢙⠠⡐⠈⡀⢫⡆⠙⠈⠀⠀⠀⠀⢀⡔⢥⠔⣀⣀⡀⠀⠒⠈⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠐⠂⢻⣄⠘⠀⠀⠀⠁⣸⣤⣤⣤⡤⡤⠴⠚⠋⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⣀⡀⢀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢿⣔⡿⣷⣿⢾⣟⣍⢞⣿⠁⠀⠀⠠⠀⠀⣀⠀⠀⣷⠀⠀⠀⠠⠀⠀⠨⠁
⠀⠀⠀⠀⠈⠉⠆⠠⠀⠀⠀⠇⠀⠀⢿⣷⢹⣿⣇⡹⠏⡇⡀⠀⠀⠀⠀⠀⠀⠉⠀⢰⡇⠀⠐⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠈⠀⢌⣂⢀⠀⠀⣠⠈⣿⣿⡿⠙⠁⠀⠀⠈⠀⠀⠀⢀⣤⣼⣶⢐⣘⠁⠀⠀⠀⠀⣠⠔⡡⠴⠒⠊
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠓⢀⠀⢈⡿⣿⣿⣇⡰⢀⣨⣤⣤⣶⣤⣾⣿⣿⢿⡇⢈⣇⣥⣤⣄⣀⠞⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠙⢲⢤⢴⣶⣿⢷⣿⣼⣿⣿⣁⣿⠿⣿⣽⠿⠛⠩⢿⠞⠈⣿⣿⡿⠛⠝⣯⢿⣆⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠂⡀⠻⣿⣝⠻⣿⣾⣿⠀⠛⠛⡁⢠⡌⡄⢸⠇⣰⣿⣯⡷⢾⣬⣿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠂⠀⡹⣞⢷⣯⣿⣿⡇⠒⠘⢏⠂⠁⢠⠊⣰⡟⠋⣡⠚⠾⡡⠶⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠺⠄⠠⢄⣻⣬⢷⣸⡿⣿⠀⠛⠀⠀⠸⠆⠠⢍⠀⠒⠛⠁⣈⢁⣓⠊⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣁⡂⢺⣽⣿⣿⣷⣄⣾⡆⠀⢰⣄⣃⣐⠃⣀⡄⢀⣈⡉⢵⣄⣅⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠻⡇⢲⣼⣿⣿⣿⣦⣵⠞⠛⠉⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡘⢹⡏⣹⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡸⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⠠⠄⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⢀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢣⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠘⠁⠀⠀⠀⠀⡂⠀⡄⠀⠀⠀⠀⠀⢘⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣯⡶⣦⠊⠀⠀⠀⠠⠀⢐⠂⠀⠀⢀⢀⡴⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⢎⠍⢢⣴⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠴⢤⠂⠀⢜⣼⠇⠒⠱⠌⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡆⢀⠀⠀⢻⠀⠀⠀⡧⢄⢏⣻⣴⠾⡴⠆⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡁⠀⠀⠀⠀⠤⠌⠡⠀⠉⠻⠶⠃⠀⠠⠀⡙⣷⠂⣟⢴⠁⠁⠁⠀⠈⠉
⠀⠀⠀⠀⠘⠢⡤⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠳⣀⠠⢀⠶⣄⠄⠁⠈⢷⡅⠀⢁⠀⠆⡀⡀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠂⣀⢐⡈⠀⠢⠄⠀⡤⠦⡂⠀⣥⢢⣙⠢⠁⣌⡃⠀⠀⠀⠀⠚⠃⠴⠃⠀⠀⡧⠀⠈⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⢀⡀⠀⠘⠀⠀⣸⢠⣚⣯⣪⣿⣇⡭⣁⠀⠂⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⢀⢀⠀⠀⠀⠚⠋⠀⠉⠀⠈⢷⠊⡁⠨⢀⡷⡟⢻⢏⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣨⡟⡴⢤⡘⡄⠀⠀⡀⠲⠀⠠⢀⡀⠠⣯⣿⣿⡛⠀⠀⠀⢠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⢶⠐⢙⡿⢦⡄⠀⠀⠀⠀⡏⣀⢠⡙⡏⠓⢨⠛⠀⠀⠈⠈⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠄⠀⣢⡄⠀⠀⢀⡆⡅⠀⠉⠁⣸⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠻⢤⠀⠸⡻⠖⢩⠻⣧⣼⣴⣾⢀⠘⢃⠚⣿⢀⠠⠆⢀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣼⠿⡥⠛⣯⣡⠩⢁⠷⢀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⡹⠖⠀⢾⣯⠁⠘⣃⣠⠿⠄⠄⠚⠀⠈⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠷⠋⠉⠓⠂⠀⠀⠈⠀⠻⠋⠐⠀⠀⣀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢲⣤⠀⢺⡇⡀⠂⣿⡿⠇⠰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⡇⠋⢠⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⡇⢠⠋⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣙⣟⣉⠛⣻⡛⣻⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⣲⣿⣿⠀⠁⠈⠉⠀⠀⠀⠀⠀⠂
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⡟⠀⢄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢞⠟⠁⠀⠐⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠
⢠⠀⠁⠀⠀⡀⠀⠀⠀⣤⡒⠂⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⢁⡄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⠀⠈⢂⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⣠⣤⣴⣤⣄⣴⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢳⠀⠁⠁⠀⠀⠀⢀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣷⣶
⠓⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠄⠂⠀⠀⢹⡿⠃⠙⠉
⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠘⡁⠀⠂⠀⡐⢤⣄⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠈⠉⣺⣿⣿⣠⣿⣶⣾⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⠛⠛⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⣰⠁⠀⠶
⠀⠁⢰⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠤⠀⣲⠞⠛⠻⣇⠐⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⢠⠋⠁⠊⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⠶⢦⣤⡄
⠀⠁⠀⠀⡀⠀⠀⠀⠠⠤⣀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠉⢘⡄⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠆⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢹⣄⣸⣦⣶⣾⠋
⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠋⠀⠀⣠⣖⠀⠀⠀⠀⠀⠀⢈⣿⣿⡛⠉
⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⢄⡀⠀⠸⣿⣷⣤⡆⢠⣾⡿⠋⠄⠀⠀⠀⠐⠀⠈⠁⠀⠙⠦⣀⡒
⠁⠀⠀⠀⠀⠀⠀⢠⠀⠠⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣌⣙⠇⠀⡸⣿⠗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠔⠒⠊⠩⠛⠛⠛⡿⡿⢉⣤⢚⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠄⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⢃⠉⠀⠰⠀⠀⠀⣑⡴⢦⡀⠀⢀⡤⠒⠒⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⠀⠈⠉⠑⣘⠛⠊⠲⠎⠀⠀⠀⢱⠖⠚⠀⠀⠀⣀⠁⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⡠⠄⠠⢄⠘⠋⠉⠢⣀⣀⠀⠰⠄⠘⣄⠄⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠐⢧⠀⠀⠀⠀⠀⢀⡤⠆⢠⠐⠆⠀⠀⠐⢒⠀⠀⠀⡞⠉⠀⢀⠀⠀⡼⠀⠀⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠄⠀⢑⠤⢤⢤⡤⠞⠀⠀⠄⠓⠀⠀⠀⠀⣈⠃⠀⢶⣓⡐⢈⣄⢰⠊⠁⠀⠉⠀⢂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣀⠀⠀⠈⣶⢀⡀⡱⠒⢤⠀⠀⢂⡀⢠⠀⢤⠈⠀⠲⠐⠏⠈⠁⠘⠓⢲⣀⠀⠈⢀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠀⢠⡄⠐⠃⠉⠈⠙⣶⡞⠀⠀⠀⠁⢎⣱⠀⢰⡊⠁⠀⠀⠀⢀⡀⠀⠀⢸⡁⠙⢀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠒⢣⠄⠀⠂⣠⡄⠐⢳⠲⠀⢏⠛⠀⠁⠓⡽⡀⠀⠀⠀⠀⠠⠀⠂⠀⠀⣕⢀⠌⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠰⢇⢀⠀⠀⠀⢁⠈⠜⢲⣯⡀⠀⠠⠀⠀⠐⣥⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣀⡀⣀⡠⢰⠡⠾⠆⣀⠀⡀⢠⣹⠑⠲⡄⠀⠀⠀⠀⠀⢀⣀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢢⠈⠁⠚⠀⠀⠩⠱⠞⠓⠆⢀⠀⠀⠗⠈⢣⡔⠶⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠘⠋⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠧⢈⡀⠀⢀⠸⠒⠀⢀⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⣀⢈⡔⠺⠃⠀⠄⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⢀⠀⣰⠺⠹⠌⡆⠉⠆⠤⢴⠊⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡍⠀⠁⢃⢹⠀⣐⠀⠀⢣⠀⠀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠐⠇⠰⡎⡄⢇⠀⢂⠀⠀⢂⡀⢀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⢳⠐⠘⣆⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠸⠘⠺⠃⣱⠉⠒



⣿⠿⢿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢟⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⣰
⠀⢀⡴⠃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠈
⠀⣾⣇⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠠⠀⠠⣄⠀⠀⠀⠀⠠⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠘⠀⠀⡀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠘⠠⠀⠂⠐⠁⠀⡀⢀⠈⢁⠀⠙⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠀⠈⢐⠀⠀⠀⠃⢠⠀⠀⠀⠈⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠠⠀⠛⠀⠀⠐⠆
⠀⠀⠀⠀⢈⠁⠀⠄⠀⠀⠀⠀⠈⢁⣠⠈⢐⠀⠀⣬⠀⠀⠀⠀⠐⡊⠁⡆⠀⠀⠀⠀⢠⠀⠀⠓⠀⠀⠈⡀⠈⠀⡃⠀⠀⠂⠀⢠⠁
⠀⠀⠀⠀⠄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠈⠟⠀⡐⠀⠀⠖⠀⠀⠀⠀⠀⠀⡆⠐⠂⡀⠀⠀⡨⢤⠀⠹⠆⠀⠀⠄
⠀⠀⠀⡀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠁⠊⠈⠉⠀⠀⠆⠀⠀⠀⠃⠀⠀⢭⢀⡄⠀⢀⠀⠑
⠀⠀⢀⠀⡄⠈⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠠⠀⡄⠀⠀⠀⢰⠒⠀⢀⠀⠀⠀⠈⠀⠀⠀⢚⠀⠄⢀⠨⠀⠀⠀⠀⠂⠀⠀⠈
⠀⠦⠀⠠⠥⠤⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠖⢋⡴⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠈⡅⠀⠑⠀⣀⠘⠇⠀⠀⠀⠂⠀⠀⠀⠐⠀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⢀⠀⠀⠠⠀⠄⡃
⠀⠀⠐⠦⠈⢀⢺⡀⠹⠀⠀⠰⠀⠀⣁⠀⠉⠀⢌⡤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⢤⠀⠀⠘⠀⠀⠀⠈⠐⠀⠀⠀⠠⠄
⠀⠐⠡⠀⠀⠀⢈⣁⠁⢋⠀⠀⠀⠀⠀⠆⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠁⡛⠀⠶⠈⠁⠀⠈⠀⠀⣠
⠠⠄⢶⠀⠀⠀⠀⢱⣬⠋⠀⠀⠈⡀⠲⣤⠂⠀⠘⠀⠀⠀⠀⠀⠀⠐⠦⠀⢠⠄⡁⠀⠀⠀⠰⠶⠀⠛⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⢠⠉
⠀⠐⢠⡤⠀⠀⠀⠀⡀⠀⠊⠄⣠⢉⣠⢦⠆⠀⠀⠀⠀⡀⠀⠰⠇⠈⡴⠀⢈⣀⣁⠀⠀⠠⠄⢤⡀⠃⠀⠠⡼⢂⡐⠀⠀⠀⠀⢀⡤⠀⢀
⠀⡘⠲⡼⡄⠀⢀⡈⠁⠀⠀⠠⠈⠈⣉⢠⡄⠀⠂⠀⠀⠀⠀⠙⠀⠀⣇⠘⠢⢂⡇⠀⠊⠀⠈⢀⠀⡋⠠⠙⡁⠀⠁⠀⠨⠁⠆⡰⠄⠀⠤
⠀⠐⣀⠀⡰⠄⠀⡡⠀⠀⠖⠀⠀⠆⠀⠑⠈⡀⠀⠀⠀⠀⠀⠑⠆⠀⢍⡁⠳⠊⠁⠀⠀⠀⠒⠀⠉⠘⠀⢉⠀⠀⠀⠓⠃⠐⠄⣀⠀⢐⠃
⠀⠀⡩⢆⡀⠐⢄⠣⠄⢀⡤⠀⠀⡄⠀⠐⠦⠀⠀⠀⠀⠀⠀⠂⠴⠂⠏⠀⠀⠀⠀⠀⡀⠀⠀⠃⡀⠂⠀⠀⠀⢠⣤⠰⡎⠁⣀⡨⢤⡋
⢀⣆⢠⣥⣻⣾⣬⣗⣀⣀⣀⠛⠀⠀⠀⠀⠀⡀⠀⠒⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⢂⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢱⡀⠉⣀⠀⠐
⢨⣿⣿⣿⢿⣿⣿⣿⣶⣶⣤⠉⠀⠈⠳⠀⠀⢀⡀⠀⠈⠀⠀⢀⡀⠐⠄⠀⠀⠀⠀⠃⢠⠀⠘⠀⠀⠀⠀⠠⠀⠴⠂⠀⢤⣶⣶⡯⣯⣠⡂
⠀⠛⠟⠻⣾⣿⣿⣿⣯⣥⣴⡞⠁⠐⠐⠂⠀⠀⠀⣈⠁⠀⠦⡀⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠘⢦⠐⠶⠰⠀⠀⠀⠒⢶⣬⣿⣿⣿⣿⣝⠅
⠀⠰⢀⠴⠷⡫⠟⠻⣏⠛⣿⣿⣾⢂⣴⣦⡀⠻⠂⣀⠀⣠⠂⢁⣤⠀⠀⡀⢀⡀⠂⢤⠀⠈⣤⣠⡴⠃⠀⢠⣄⠺⣦⣬⣿⠿⣋⢛⡝⠃⢀
⠈⠀⢀⠀⠤⡀⠦⣱⡏⣾⡭⠿⢿⣿⣿⣿⣿⣶⣿⠁⢰⡇⣠⣌⣳⠾⢿⣗⣋⠄⣠⡐⠷⣆⢸⣿⣀⣴⠾⣏⢿⣿⣿⡟⠃⠹⠛⠠⠄⠁⠈
⠀⠀⠈⠀⠀⠀⠠⠌⠜⠋⠃⠀⢋⣝⠟⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣿⣿⣽⣿⡿⢓⣷⠾⠿⠿⢖⠋⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠘⡋⠹⠊⠙⣟⣹⠛⠉⠛⢻⡿⠟⡻⢘⣛⣛⡋⢿⠿⠟⡛⠏⠓⠉⠭⡄⠂⠤⠀⠄⢀⠀⠁⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠁⠘⠀⠀⠈⠀⠀⠀⠈⠁⠀⠋⠉⠓⠀⠈⠐⠀⠰
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢉⣉⣉⣉⠛⢦⣀⣹⣦⡀⠘⢿⡷⠀⠀⢻⡄⢻⣿⣷⣦⡙⣷⣀⠈⠻⠿⠋⢀⡾⢃⡾⢋⣡⣤⡉⢻⣆⠹⣧⢹⣇⠀⠀⠀⠈⢻⣧⠸⣆⠹⣇⢠⣿⠿
⢽⣷⣒⢺⣭⢖⡨⢉⡛⠿⠷⠦⠀⢀⣴⡿⠃⣸⣿⠟⠉⠛⠦⠭⠛⠲⣶⣖⣛⡵⠯⢚⣉⡉⠙⣿⡀⢿⡄⢻⣆⠻⣦⣄⣀⣀⣼⣿⠇⢘⡇⣻⢸⠏⣰
⢽⡺⠽⠭⣝⢿⣮⡳⣍⡳⠦⠴⠞⣛⣩⠴⠞⢋⣁⣠⣤⣶⣾⣿⣿⣿⡉⠁⢠⣶⠟⠋⠙⠻⢦⣘⠳⣌⠻⢦⣙⡓⠒⠒⠒⠒⣒⣒⣾⠭⣒⡵⣫⣾⠏
⠉⠀⠀⠀⠀⢱⡕⣝⢮⣙⣛⣻⡭⠵⠖⣚⣛⠙⠛⣿⣿⡟⠉⠉⠛⢿⣿⡄⢸⡇⢰⡿⠛⠛⠶⣬⡓⢮⡙⢦⡈⢻⣷⣆⠀⢿⣿⣿⠁⣼⢋⡴⠛⠁⢀
⠀⠀⠀⠀⠀⠀⠓⠬⣗⣊⣵⣒⣚⣛⣉⠙⠻⣷⡄⠘⢿⣷⣄⣀⣀⣠⣿⡇⢸⡇⢸⡇⠀⠀⠀⠀⠙⢷⡝⢦⢹⡄⢻⣿⣆⡀⠙⠿⣦⣹⢜⣧⣀⣚⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠳⢦⣈⡛⠶⢤⣬⣍⣉⣉⣉⣡⣤⣾⠟⢸⣧⠀⠀⠀⠀⠀⠀⠙⢮⡳⣝⠦⣙⣛⠛⠻⢿⠿⠿⠿⣶⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠶⠶⠶⠶⠶⠖⠒⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠉⠉⠓⠲⢯⣍⡓⠶⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⢁⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣴⣾⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠻⢿⣷⣶⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⣀⣤⠤⢖⣒⣛⣩⣭⣉⣙⠻⢦⣄⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⣠⡶⢋⣥⠖⢛⣩⡥⠶⠶⠶⠶⠬⣭⣓⠮⠭⣭⣭⣭⣭⡉⠉⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣖⣫⠭⢭⣝⠳⣆
⠀⣰⡟⢠⡿⠁⣼⡟⠁⢀⣴⣾⡿⠿⠷⢶⣬⣙⠳⣦⣄⠈⣿⠇⣼⠋⠀⠀⢀⡤⣤⢶⣶⣲⡶⣶⣶⡶⠶⢛⣫⣭⠿⠾⠦⠾⠿⠿⣷⣪⣗⢌⡳⣄⡀
⢀⣿⠁⢸⡇⠀⣿⣇⠀⢸⣿⣿⠀⠀⠀⠀⠈⠻⣷⡈⢿⠀⣿⡀⢿⣤⣀⡀⠈⠳⣇⢾⡩⡷⠖⢒⣚⣻⣥⠤⠖⠒⠊⠉⠉⠉⣉⣻⣷⣮⣑⠿⣿⢮⣽
⣾⣿⠀⠸⣿⡄⠘⣿⣆⠀⠹⣿⣷⣀⠀⠀⠀⣠⣿⠇⢸⣷⡈⠙⠷⣦⣍⡙⠳⢶⣬⣓⢄⡻⢬⡻⣿⣿⣦⣤⣶⡶⠶⢛⣛⣭⡭⠭⢭⣉⣛⡓⠀⠉⠓
⣉⣀⢀⣠⣿⣿⠀⠘⣿⣦⠀⠘⣿⣿⡿⠟⠛⠛⠿⢶⣄⡙⠻⢷⣤⣀⠙⠻⢷⣦⡌⠙⣷⠉⢢⡩⡳⣒⠤⣤⣤⡴⢚⣭⠖⠊⠭⠭⠉⠑⠺⣭⣕⡲⢤
⠛⠿⣿⣿⣿⣿⡆⠀⢸⣿⣇⠀⣿⠏⣤⣾⠿⠿⢷⣤⡈⢿⡆⢠⡿⢛⣡⠤⠾⢛⣡⠴⠋⠀⢠⡇⠳⣬⣙⠲⢤⣴⣿⠿⢛⡿⠷⣐⣋⣉⡿⠭⣟⣛⠂
⣀⣀⣀⣉⣙⣋⣀⣀⣀⣿⣿⣠⣏⣾⣋⣴⣾⣛⣳⣮⣻⣦⣻⣜⣧⣻⣰⣞⣉⣁⣀⣀⣀⣀⣸⣿⣦⣀⣉⣳⣦⣌⣻⣄⣻⣐⣿⣁⣀⣀⣈⣉⣓⣮⣍
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⢃⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢴⠂⡀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢱⡀⠀⠀⡀⠆⠀⠀⠀⠀⠒⢶⣄⠸⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠌⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⡲⡆⠀⣠⠄⠀⢁⠄⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠀⠀⠀⠈⠁⡀⢁⣦⡛⠀⠀⢲⣿⢴⠁⢐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠄⠊⠲⠰⠈⡃⠺⠻⣐⠛⡓⠖⢀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣄⠀⠀⠀⠿⣷⡍⢿⠿⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⣾⣿⣿⣶⡆⠀⠁⡘⠀⠀⠀⠀⠀⠀⠀⠠⠊⢹⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⢌⡀⠀⠿⠀⠀⠀⠀⠛⠛⠋⢩⠀⠀⠙⡧⠀⠀⠀⠀⠀⠀⠀⢷⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⢁⠿⡄⠀⣴⣴⣇⠀⠘⠂⠈⠀⠀⠀⠛⡅⢄⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⣰⠟⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠁



⣀⣀⡀⣀⢀⣀⣀⡀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⡀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣤⣤⣤⣤⡀⣳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣠⣿⣷⣸⣿⢹⣿⣽⢿⣏⣉⣀⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⡿⠿⢟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠛⣿⠛⢻⡟⠀⠉⠀⢰⣫⡿⢋⣤⣤⣉⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⣧⣄⣀⣸⣿⡛⠓⠙⠛⠻⣿⣿⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⠛⣿⣧⣴⣿⣿⣿⣿⣿⣿⣦⣤⣄⢀⡀⠉⠙⣿⠀⠀⠀⣀⣿⠆⠐⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⣿⣿⣿⣿⡿⢹⢿⡇⢹⠿⣿⠟⡛⣿⠀⣀⠀⢀⣶⠋⠀⠀⠀⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⡆⣿⢿⣿⣿⣠⣿⣸⣿⣼⡟⠀⠘⠻⠛⢿⣿⠇⣠⠇⠀⠀⠀⠀⠀⠘⣧⣤⡄
⠀⠀⠀⠀⠀⢠⣤⡀⠙⠿⣦⡀⠀⢀⣿⣿⢹⣧⣾⣿⣿⡿⠛⡛⢩⡀⠈⠣⣀⠀⢸⣿⡄⢻⠀⣇⠀⠀⠀⠀⢸⡏⠜⢋⠤⡀
⠀⠀⠀⠀⣶⣾⡻⣿⣦⣤⢙⣿⣀⡾⠟⠷⣾⣟⠻⣫⣴⠀⠸⠃⠀⠈⠀⠀⠀⠘⣿⡿⣷⠘⠋⠋⠀⠀⡃⢀⠟⠁⠀⠀⠀⠁
⠀⠀⢀⡀⠈⠛⢧⡄⠉⢧⣽⡝⢡⣤⣶⣷⡌⣿⣿⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡽⢛⠛⠷⣤⣀⠴⠋
⠀⠀⠋⠙⢿⣦⣀⣈⣉⣢⣌⣻⣶⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠈⠁⠙⣿⣴⣿⣻⣷⠌⣥⠀⡃⠀⠀⠀⢀⣀
⠀⠀⠀⠰⠚⣛⣛⣛⣋⣭⢾⣷⣿⣿⣿⣿⢿⡙⠷⣶⣦⡶⠁⠀⠀⠀⠀⠀⠙⠻⡟⢻⣿⣿⣿⣿⡿⢧⣭⡁⠀⠀⠀⠈⠉
⠀⠀⠈⢥⣄⠿⢻⠙⠋⣠⠟⣩⡞⠉⠻⣿⣮⠙⢦⡄⠙⢠⡄⣀⠀⠀⠀⠀⠀⠙⠛⢻⣾⡿⢹⣿⡻⣮⠁
⠀⠀⠀⠀⠿⣿⣷⡶⠀⣴⠾⠋⣀⣾⡆⠻⣿⡦⠀⠀⣀⣤⣤⣹⢧⣠⣄⠀⠀⡀⠀⣸⣿⠁⠀⠈⠁⠈⠁⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠿⣿⣿⢿⣦⣴⡆⠀⣿⠿⠛⣿⠏⢸⣿⣿⣄⣀⡁⠉⠀⠙⠶⠦⠤⠤⣤⡀⠀⣤⡾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠐⠿⣯⠏⠀⢿⣿⡁⠀⠉⠀⢸⣿⠀⠀⠛⢿⣿⣿⣿⠿⣿⣶⣶⣿⣷⣦⣴⣶⣶⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡈⢿⣷⡄⠀⠀⢈⡇⠀⠀⠀⠎⠉⠛⠉⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⣿⣿⢻⣏⣽⢦⣄⡀⠀⠁⠀⣠⣾⣿⣿⣿⣿⣌⠻⣧⡉⠻⣿⣿⠿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠹⢿⣿⡷⣿⣥⣿⣧⣿⠇⠀⠂⠀⠉⢉⣿⣿⣿⣿⣿⣷⣽⣿⣦⡈⣻⡦⠠⣿⣿⣯⣝⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠳⣦⣤⣴⣿⣿⣿⣿⣿⢿⣤⡄⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣶⣯⣛⣿⣿⣶⣶⣶⡶⠟⠻⠿⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡻⠟⡹⣿⣿⣿⡏⠛⠻⠆⠀⠀⠀⠀⠀⠈⣀⣸⣿⣿⣿⣯⣤⣹⣯⣿⣿⠆⢰⣶⡶⠶⠞⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠵⣶⠋⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⢸⠟⠻⠿⢿⣿⣟⣻⣿⣿⣿⡿⢛⣛⣁⠴⠖⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⠤⣄⣈⣿⣿⡷⠀⠀⠀⠀⠺⠀⠀⠀⡾⠁⣿⣿⣿⣿⡿⠿⠿⡿⠏⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡱⠟⠀⠀⠀⠀⢀⠀⠀⢀⡾⠀⠀⠿⠛⠉⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣣⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠘⡇⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠸⡇⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠈⠀⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠾⠿⠿⠷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⣼⣿⠀⣀⣤⣄⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠙⣷⣿⣿⣾⣿⣿⣿⣆⣿⠇⢀⣠⣤⣶⡶⠶⠿⠷⠶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠛⠉⠉⠉⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣤⣾⣿⣿⠋
⠀⠀⠀⠀⠀⢠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣶⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⢸⣿⣿⠿⢿⣿⣿⣿⡿⠋⣰⣿⠏⠻⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠉⠁⠀⣾⡿⠟⠁⠀⣼⣿⡟⠀⠀⠈⠛⢿⣷⣦⣄⡀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣀⣀⣀⣤⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉



⣿⣿⣶⣶⣶⡷⢾⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣷⣶⢶⠶⠾⠷⠾⢷⣶⠷⠶⣶⡾⠷⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣆⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⣿⣿⠓⠀⠀⡄⡄⠀⠀⠀⠀⠘⢆⢸⣰⣡⠎
⠀⠀⠀⠀⢀⢠⡀⣤⢠⠀⠀⠀⢯⣌⣥⠋⠀⠨⣷⣿⣧⡾⠤⠀⠀⠑⢾⣿⣿⣥⣄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⢙⣿⣿⣇⡀⠀⢀⢿⣿⡿⡀⢠⠞⣩⢿⢿⠙⢆⠀⠀⠐⡹⢻⠛⡆⠀⣀⣼⣿⣤⣾⣿⣿⣿⣿⣿⣿⣷⡤⣶⣶⣶⡶⣤⣾⣿⣿⣿⣿⡷⢄⣠⣴⣾
⠀⠀⠀⠀⠀⠐⣽⢻⠇⣠⣶⣤⡈⠉⢃⠠⣴⣤⡁⠘⠀⠇⠀⠀⠀⠀⠀⠀⡀⣠⠀⡹⢻⣿⣿⣿⠟⠛⠛⣡⣾⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⡄⣹⢿⣿⠀⢀⠀⠀⣠⣶⣾⣶⣶⣿⣿⣿⡆⣤⣼⣿⣿⣿⢿⣿⣹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠏⠙⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⣿⣿⣇⠀⣬⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣽⣿⣿⠜⠛⠛⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⢿⠿⣵⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⠉⢹⣿⣿⣿⢻⣿⣿⣿⣿⣿⣵⣿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⣿⣿⣽⣿⣿⠟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋
⠀⠀⠀⠀⠀⢰⣿⣿⣏⠉⢿⠄⠀⣿⣿⣿⣿⢻⣿⣿⣿⢿⣿⣿⣯⣾⣽⣿⣿⣿⡟⣿⣯⣿⣧⣿⣿⣿⣿⣦⠐⣿⣿⠄
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⠈⠻⣿⣿⣾⠟⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡴⠛⡿⣦
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⣽⠉⣿⠇⠀⠀⢠⣿⣀⠘⢛⣻⠿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣯⣷⣿⣿⣿⡿⣰⠋⢠⢶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿⣟⠋⠀⠀⠀⣼⢋⣿⠀⠈⠁⣾⣿⢿⣿⣿⣿⣫⣷⣿⣿⣿⣿⣿⡿⠟⠱⡟⢦⠈⣯⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣯⠀⣿⣿⣧⠀⠀⢠⣿⣾⣿⣧⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡝⡆⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡼⢿⣆⣽⠈⣷⠀⠀⢸⡇⣼⣻⣿⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⡏⠀⢸⡁
⠀⠀⠀⠀⠀⠀⢰⠃⢨⣟⣤⡄⣿⠀⢀⣯⡇⠀⡭⣻⡇⠘⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⡇⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠘⡆⠈⣩⠞⡷⠉⠇⠀⡇⠂⢀⡼⡏⠣⠀⠀⠙⣿⣯⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠣⠠⢻⡌⢧⡈⠃⠀⠀⠀⣾⢰⡇⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⠀⠀⠀⣠⠃⠀⣇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯⣿⣿⣻⣿⣧⢰⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠈
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠈⣇⡀⠀⠀⣤⡀⢳⡄⠀⣤⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⣰⣧⣴
⠀⠀⠀⠐⣿⣿⣿⣆⡀⣤⠁⣱⠀⠀⠘⢷⣆⢻⡄⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣸⠃⠀⢀⣼⣾⣆⠀⢺⢿⣟⠂
⠀⠀⠀⠘⢋⠇⠃⢐⣿⣿⣿⠁⠀⢤⣤⣄⣙⣧⢧⡿⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠿⣿⣆⠀⢡⣿⡿⡿⠆⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⢈⡏⠉⠀⠀⠀⠀⣨⣭⠷⣂⡀⠛⡆⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠁⠀⠀⠸⠀⠠⢄⣱⣸⢀
⠀⠀⠠⡀⢄⠀⠀⣴⣿⣿⣦⠀⠀⠀⠈⠁⠴⢛⣯⠷⢂⣡⡾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢐⡿⣿⣿⡿⡉
⠀⠀⠀⡘⣾⣾⠀⣿⣿⣿⣿⣷⠀⣄⣦⡤⠀⣨⣴⣿⣿⣿⠿⣋⡭⢩⣿⣿⣿⣿⣿⣶⣿⡆⣈⡿⡿⡿⢿⣿⣿⣿⣿⡀⠐⠉⡴⢉⠏⠇⠙⠄⠀⠀⠀⢀⣀⣴⣾
⣶⣶⣦⣬⡛⢩⣾⣿⣽⡻⣿⣿⢠⡿⢿⣟⢰⣿⣿⣿⡟⣁⣨⣭⣶⣿⣿⡟⠋⠉⢉⣩⣽⠿⠿⢿⣿⣿⣮⣿⣿⣿⣻⣷⣦⡄⠀⠘⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢹⣿⣇⣿⣽⣿⣿⣦⢻⣶⣿⣿⣿⣿⣿⠇⣿⡿⠉⢰⣿⣿⣇⣴⠿⣿⣿⣇⣠⣶⣶⡉⠙⠛⠛⣿⣾⣿⡿⢷⣿⣷⣶⣦⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢳⢯⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⣧⡴⠂⠀⠀⠀⠀⣤⣶⢺⡖⡟⠉⠀⠀⢀⠀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⣯⣼⠄⠀⠀⣀⢼⡎⣷⡼⢏⡽⠋⢀⣠⡴⣟⣹⣛⣿⣥⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⢠⣼⣋⣿⣵⡅⢀⣤⡟⢻⣤⡿⢉⣱⠟⣠⡶⣟⣹⡶⠻⣯⢼⣋⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⠠⡐⢤⡀⠀⠀⠀⣾⣧⣿⣥⣿⡶⢻⣥⠿⣏⣩⠶⢊⣡⡞⢻⣤⠿⣭⡽⣏⣷⡾⢿⣭⡟
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⢀⠀⢀⠢⣑⢮⡳⣝⠃⢀⡴⣫⣼⢿⢻⣥⡿⣞⣛⠶⢈⣡⡶⢻⣥⣿⣋⡱⢻⣩⣶⠿⣭⣿⠛⠁
⠀⠀⠁⠀⠀⠁⠀⠀⢀⠀⠌⠀⠀⠀⡀⢌⠢⣙⢦⣱⣬⠷⠙⣠⣾⣿⣿⣿⣷⣾⣿⣻⡶⣯⢍⡔⢻⣁⡾⣛⣿⠖⣯⣵⠿⢯⣩⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⡐⢬⡳⣜⣾⡷⠞⢃⣉⣀⣤⢾⣵⣟⠽⣛⣥⣽⣷⣾⣻⣿⣧⢿⣶⠿⣯⠙⣧⣿⡞⢿⣭⡿⠛
⠀⠀⠂⠀⢀⠀⠀⠀⡀⢤⡰⣝⣦⡙⠎⣁⣤⢶⡏⣿⣯⣿⣟⣫⣷⣿⣿⡿⣛⣽⢟⣥⣿⣯⣬⣿⡿⢿⡟⣿⣴⣛⡯⣤⡶⠂
⠀⠀⠀⠀⠆⠀⠀⠒⠙⠂⠙⣉⣡⡤⢴⡷⢸⡾⣷⠈⣿⣿⣫⣷⣿⣯⣷⣾⣿⣿⣿⣿⣿⠛⡿⢿⡿⢿⣿⣯⢭⣶⣿⣁⣀⣠⣄⣀
⠀⢰⣖⣒⠲⠤⠤⠤⣴⣬⣭⣶⣶⣿⢿⣧⣘⢧⣿⣌⠛⣿⣛⣿⣭⣭⣭⣭⣭⣭⣭⣘⣍⣻⡗⢿⢶⠷⣶⣧⣾⣶⣯⣭⣯⣼⣛⡤⠤
⠀⠀⣤⡭⢿⣿⣿⣿⣿⠿⢚⣫⡽⣶⣿⣿⣦⠼⣷⣿⣆⠙⣿⣒⡿⣿⣻⠿⠟⠋⠉⢉⢩⠉⢉⡛⠛⠟⠛⠓⠿⠾⠟⠿⢿⣷⡻⣤⡀
⠀⠀⠋⣉⣵⣿⣯⣵⣶⣿⣿⠿⠿⠿⣚⣛⣿⣷⠈⣻⣟⣷⣬⡿⢏⡁⢤⡲⣔⢦⡙⢮⡳⣌⠁⡉
⣾⣛⣯⣭⣭⡭⢶⣶⣶⣶⠶⢟⣻⡭⣿⡾⣫⠟⠓⠾⠿⠛⣁⣤⡲⣝⠦⡙⠊⠀⠈⠢⡙⠂⠁⠀⠠
⠭⠷⠶⢒⣻⠿⣛⣫⣵⣶⣿⡿⣫⣞⡵⠊⡡⣴⡶⡗⢦⡛⢍⠣⠙⠊⠀⠀⠀⡀⠂⠁⠀⠀⢀⠢⠁
⠀⣠⣞⣭⠶⢻⠿⣫⠟⢩⢏⣼⠿⠋⢀⡲⣝⢮⡓⠌⠂⠀⠀⠀⢀⠠⠔⠂⠁⠀⠀⠄⠢⠑
⠀⠟⠋⢁⠖⣡⠞⠁⢰⣯⡏⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⡴⣫⠞⠁⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⢸⡷⠃

⠀⠀⠀⠀⠀⣙⠘⠁⠀⢀⠜⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠀⣰⣶⣾⡃⠀⠈⠄
⠀⠀⠀⠀⣀⠈⠠⠆⠠⠎⢔⡃⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠡⠄⠐⠚⠁⠀⢸⡟⠁
⠀⠀⠀⢠⣿⣦⡄⠀⠀⠌⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠀⠜⠁
⠀⠀⠀⢸⠋⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾
⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠻
⣷⣶⣿⡃⠈⠑
⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡈⠣⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠬⢸
⠤⣿⣦⡶⠅⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⢀⡠
⢀⡿⠛⠃⠀⠈⠂⠀⡐⠊⡀⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠚⢿⣿⡍
⠉⠁⠀⠀⠀⢰⣤⣾⠂⠀⢢⠤⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠐⠊⠀⢹⡟⠁⠀⠀⠀⢀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣴⡆⢀⡀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠁⣴⢿⠟⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢚⣶⠿⡽⠀⠀⣠⠀⠀⠀⠀⢀⠐⠀⣜⡙⠟⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠂⠀⠚⣈⡇⢀⣨⣀⡄⠈⠀⢀⣉⣁⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠀⣴⣴⣧⣌⠉⠁⠀⣀⣿⣩⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠀⣻⣇⠸⢿⣽⣆⡀⠶⢛⣿⡠⠾⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⣿⣿⣏⣧⢸⡾⠿⠀⠐⢟⣉⣤⣰⠿⡿⣀
⠀⠀⠀⠀⠀⣶⠛⢾⡇⢀⠦⣤⠻⣯⢸⡿⠸⣷⣀⡔⠴⢾⠏⣿⠑⠲⣆⡈⠀⢠⠆
⠀⠀⠀⠠⠶⠟⠸⣿⡦⠈⣀⠈⠛⢋⣴⢳⠄⣹⢿⡀⠐⡿⠀⣿⠀⠀⢠⠀⠀⠀⣠⢠⠌
⠀⠀⠀⠀⠀⠀⠁⠈⢴⠋⠹⡆⠰⣿⡇⠾⡇⠀⠘⠻⠎⣠⠀⣿⠀⠀⢸⠤⠞⠊⠉⠀⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⣦⡟⢶⠀⢵⠀⠀⠐⠀⠈⢢⡿⣄⠰⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⣰⠞⠃⢨⣝⣡⠄⢿⡇⠈⡆⠀⣠⠆⠀⢸⡄⠛
⠀⠀⠀⠀⠀⠀⠉⢠⡌⠁⠀⠙⢍⣀⣈⢻⣦⣽⣿⠁⣤⠂⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⣀⠛⢀⡄⡀⠀⠀⢻⡀⠈⠇⣼⡟⠀⠈⡉⡟⠳⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⢈⡔⠉
⠀⢀⣠⡰⠷⠶⠘⠷⣤⡀⠇⢀⠲⠦⢿⣆⠀⣿⡀⠀⢸⡇⣿⣰⠆⠀⠀⠀⠙⣦⡤⠀⡀⠀⣀⡴⠋⣠⠖⠉⠀⣠⣤⠀⣀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠑⢿⠈⠃⠀⠘⢢⣟⠁⠐⢯⣿⣥⣿⠓⠿⢀⡐⢺⣿⠀⠔⠟⠛⠓⠂⠘⠁⠶⠘⠿⢏⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠆⢸⡀⢠⣿⡟⠋⢰⣏⠀⠉⠱⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠞⠀⠀⠉⠉⠉⠉⠉⣡⣤
⠀⠀⠀⢀⠀⠀⠐⠳⡄⠲⢄⡘⢇⠈⢃⡽⣿⠙⣧⢠⠃⠩⠓⠈⠀⠀⠀⠀⠀⠂⠠⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣉⡉⡀
⠀⠀⠈⠋⣑⠶⠶⠦⣈⠉⠈⠁⠨⢗⡸⢁⠈⠀⢹⡟⠃⠀⠀⠚⠛⠙⠻⠶⣄⡀⢀⣠⣤⣴⣦⠴⣶⣦⣤⡀⠀⠀⠀⠀⡘⠀⡀⠉⠉⠉⠲
⢀⣤⠶⠋⡹⢤⣦⡀⠀⠀⠀⠀⢀⡼⠀⢸⡆⠀⢸⡇⠀⠀⠀⠤⡀⠀⠀⢀⡽⠿⠛⠉⠁⠀⠛⠷⣦⣄⠉⠉⠙⠀⠀⠀⢠⠾⠁
⠋⣰⣆⠀⠀⠀⠀⠐⠢⠤⠐⠂⡹⠀⢇⠀⢠⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠐⠁
⢠⡏⠈⠀⠀⠀⠀⠀⠀⠀⢀⡺⡃⠀⠈⠷⠈⢂⣿⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣘⢁⡗⠀⠀⠀⠀⠈⢿⡇⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⡠⢊⡱⢹⠀⡧⠀⠀⠀⠀⠀⢰⡧⢀⡼⠃
⠀⠀⠀⠀⠀⠀⣤⠴⠋⣘⠀⡄⠸⣄⠀⠀⠀⠀⣸⡟⠘⠁
⠀⠀⠀⠀⠀⠘⠁⠀⠀⣿⠀⠹⣄⠉⠂⢀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⣷⡀⠘⠳⠀⠘⠃⠀⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⣹⠟⠤⡀⠀⠀⠀⢀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠃⢀⣰⠃⠀⠠⣀⣀⠀⣰⠂⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠦⠠⣥⣶⡟⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣦⡾⠗⠂⠺⠗⢾⣤⣀
⠀⠀⠀⠀⠀⠀⠄⠚⠁⠈⠀⠀⣀⣀⡶⣤⠄⠀⠀⡄⠀⠀⠈⠂
⠀⠀⠀⠀⣠⠶⠶⠒⠞⠓⠛⠛⣉⣿⠀⠻⠀⠀⠀⣈⠀⠒
⠀⠀⠀⡀⠡⠠⠦⠀⠂⠠⠲⠂⠝⢧⠀⠀⠀⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢚⠀⠈⠳⣄⠀⠀⠁⡀
⠀⠀⠀⠀⠀⣀⣤⡴⠖⠉⣠⠛⠀⠀⠀⠀⠙⠀⢀⡀
⠀⠀⠀⠀⠀⠊⠁⠀⢀⠘⠹⣄⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣤⠜⠃⠠⠀⠀⠒⢄⡀
⠀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⢀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡄⠈⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣿⣿⣿⣿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠜⠁
⠀⠀⠀⠀⠀⣀⣦⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⢀⠠⠊
⠀⠀⢀⠦⠀⠀⠀⠀⠒⠹⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⢀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠀⠈⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣀⡄⠀⠀⠀⠀⢀⡴⡀⠀⠀⠀⢉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠬⠀⡄⠀⢠⠀⠀⠑⠈⠉⠀⠀⠉⢡⡌⢀
⠒⠀⠀⠀⠀⠊⠊⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠄⠄⢀⠀⡀⣀⠖⠣⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠁⠀⠁⠈⠀⣄⠀⠰⠐⠠⠀⠤⠙⢆⠁⠈⡁⠀⠀⠀⡠
⠀⠀⠀⠀⠲⠀⠀⡈⠀⠀⢀⢦⠁⠀⠀⡉⠀⡤⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠈⠀⠁⠄⠀⠁⠂⡠⠐⠀⠁⠩
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣃⣘⣚⣀⣂⣰⣄⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠄⠀⡀⠀⠑⠄⢀⡀⠀⠀⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⢄⢦⠤⠤⡠⠚⠉⠑⣄⠤⠎⠁⠀⠈⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⢣⠀⠀⢁⡀⠀⠀⠴⠒⠢⡂⠀⠑⢀⠀⢅⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠲⡀⠀⠀⠂⠀⢀⠼⢀⠀⠇⠀⠀⠜⠀⠀⠀⡸⠛⠀⠰⠀⢀⠇⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠑⡤⠤⢤⡤⠊⠀⠠⠐⠀⠀⠀⠀⡉⠀⠰⣗⣄⠀⣁⡰⠈⠀⠈⠀⠲
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡀⠀⠀⢱⣀⣄⡕⠐⡆⠈⠂⡄⢠⠀⠦⠀⢀⠂⠊⠀⠁⠘⠃⠆⡀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣶⠀⠁⡀⠐⠘⢿⡁⠀⢀⣈⠣⡼⣀⡹⠀⠀⠀⠀⠠⠄⡀⠀⢦⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣀⠃⠀⠄⠰⠆⠨⣍⢉⠽⠌⠀⠀⠁⢳⠀⠀⠀⠀⠀⠀⠁⠀⠐⢥⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠐⠀⣠⢻⣃⠀⠈⠈⠀⠼⣇⡀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⢀⠐⠠⡆⠈⠙⣾⡠⠦⡝⠋⠀⣹⠤⢄⡠⣤⣀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠲⡀⠀⠀⠀⠱⡆⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⠀⠀⠀⠿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣀⢸⡒⠟⢀⠤⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⣰⠻⡙⡐⡌⠙⠒⠒⡏⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⡄⢀⠁⢳⢠⠆⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠈⡎⠌⣇⢫⠀⠀⠑⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠻⣹⠐⡜⢎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠂⠀⠂⠁⠀⠀⠀⠀⠀⠀⢈⣧⠄⡎⠊⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠓⣾⣿⠀⠐⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠆⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠃⠀⠚⠑⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣿⣿⣿⣥
⠀⠀⠘⠃⢻⠇⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⠷
⠀⠀⠀⠰⢄⠀⠀⠀⢠⣜⠈⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⠿⠿⠉
⠀⠰⠗⣀⠉⠀⠀⠀⠀⠉⠀⢉⣕⡄
⠀⠀⠈⠉⣶⡦⠀⠀⣤⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠠⠀⠀⠠⠀⠀⠙⠛⢁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠏⣙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⢆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣀⡙⠓
⢀⠀⠀⢊⣸⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠱⡌⣭⢥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⡿⣧⡀⠄
⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢟⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠻⡟⠉⠁
⠀⠀⢶⣿⠂⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⣰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢠⢿⣬⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢡⡴⣠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣌⣶⠎⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢹⡔⠋⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡴⣀⣸⣄⣠⠞⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠈⡻⣈⣣⡞⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡹⣌⠢⡀⢘⡿⢃⣠⡄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⢾⣤⡿⢹⣿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠴⣖⣄⡀⠀⠘⣤⡾⡛⠋⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠲⠽⣉⠻⠇⢾⠋⠉⢀⣴⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣛⡶⣦⡀⠀⢁⣾⡖⢠⡴⠟⠋⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢭⣿⡷⣤⣙⡿⠋⠀⢀⣶⣫⡽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⡀⠀⢢⠈⠁⠹⠀⠀⣰⣧⠮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠄⠂⠀⠁⠐⠀⠃⠀⠀⡀⠚⣉⣭⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣞⠿⠛⠆⠽⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⠘⠢⠦⣠⣙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠨⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡔⠀⣀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠈⠀⠐⠂⠃⠀⢀⠠⠄⠐⠤⠄⠈⠡⠂⠠⠀⠂⠀⠀⢠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠴⡤⠈⠁⠀⡀⠢⡀⠀⢠⡀⢈⠀⠀⠀⠰⠀⠀⠄⠐⠀⠁⠀⢤⠁⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠱⠄⡔⠀⢠⠀⢀⠤⠆⠀⢰⡈⢂⠈⠉⠀⠂⢀⠄⠈⠀⠀⠀⡀⠀⠀⡀⠁⠀⢀⣦⠠⠈⠂⠄⠐⠁⠀⠀⡅
⠀⠀⠀⠀⠐⠂⢰⠀⠀⠤⠬⠤⡀⢀⠒⠪⠀⠁⣐⡀⠁⣀⠤⠀⡠⠀⢈⡉⠈⠃⠀⣠⢀⠀⠈⠀⠐⠒⠗⠒⠀⢈
⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠰⠀⠁⢀⡀⣄⠀⠚⠙⡁⠀⠀⣐⣖⢈⠀⢄⠊⠑⠂⠙⠉⠃⢠⠀⠀⠀⠀⠶⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣔⡁⠔⠈⡂⢐⠀⠀⠀⠉⠀⠁⠀⠀⠈⣄⠀⠀⠀⠀⠀⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⢀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⢀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠸⠀⡄⠀⠀⠀⠀⡀⠐⠀⠐⠀⠀⠀⠐⠒⠂⠄⢀⡀⠀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢇⠀⠒⠀⠀⠐⠄⠀⠀⢀⠖⠀⠠⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠄⠀⠂

⠀⠀⠀⠀⠐⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄
⠀⠀⠀⠂⠠⠿⠔⣀⠀⠀⣤⠀⠠⠀⡴⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⡄⠀⠀⢀⠀⠠⠂⢧⠔⠠⠀⠁
⠀⠀⠀⠀⠀⠂⠒⠈⣀⠆⣉⠀⠀⠀⣵⡀⠀⠀⢫⠁⠀⠀⠀⠂⡀⢄⠀⠉⠁⠀⠀⢆⡀⠀⢀⡂⠠⡄⠲⢈⠉⠦⠠
⠀⠀⠀⠀⠀⠀⠐⠈⢐⠁⡤⠀⠀⠀⢠⣉⣰⠂⠉⢠⠀⢀⡴⠖⠠⠤⡀⠀⠀⠀⠀⠈⣟⠱⠮⠀⠀⠀⠈⢢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠚⠃⢙⡿⡀⠀⠀⠀⠈⠃⣠⣻⠂⣱⠛⠆⠓⠄⠀⡨⣑⣄⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠟⢳⠁⠹⠀⠀⠀⣤⢄⡈⠉⠁⠀⠀⠀⠀⠘⢸⠄⢘⡔⢉⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡴⠈⡉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠏⠀⡮⠀⠌⠑⠐⣔⠒⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠂⠊⠹⡌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡙
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⢻⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡆⣡⠜⠆
⠀⠀⠀⠈⠀⢀⠀⠁⠀⠀⠀⢦⡀⠀⠀⣿⡿⠃⣀⡶⠀⠀⠀⠀⠀⠰⡅⠙⢄⠥⠐⢻
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠻⣷⢠⠡⣧⠿⡏⢁⡴⠀⠀⢀⢰⡂⠑⠄⡸⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢀⣤⣶⡾⠛⠁⠀⠀⣠⡄⠙⠳⠠⠓⠒⠚⠃
⠀⠀⠀⠀⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠉⠀⠀⠀⠀⠀⠀⠡⠑⠺⢤⠋⠉⠛⠁⠀⠀⢈⠓
⠀⠀⠀⠀⢈⡘⠏⣤⡀⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠄⡘⠐⠃⠀⠀⠀⠀⠦⢤
⠀⠀⠀⠀⠈⣙⠛⣉⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢠⣴⠚⠀⠈⡀
⠀⠀⠀⠀⠀⢉⣹⣃⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣅⠜⠓⠃
⠀⠀⠀⠀⠛⢀⠏⠵⢞⠀⠀⠀⢦⢠⡄⡀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⢠⣬⠖⢻⡦⠤⠃
⠀⠀⠀⠀⢀⣙⠳⢒⣛⠃⠀⠀⠶⠞⢸⢃⡄⠀⠀⠀⠀⠘⠿⠾⣃⠀⠀⠀⢀⣀⡼⠓⢻⡤⠶⠂
⠀⠀⠀⢠⣬⣉⣉⣉⡉⠀⠀⠀⠀⠉⠥⠜⠴⣃⠀⠀⠀⣘⠦⣜⣟⠀⠀⠀⠈⠁⣽⠶⢻⡤⠤⠀⠀⠂
⠀⠀⠀⠺⠶⢤⣀⣭⠁⠀⠀⠀⠀⠀⣜⡛⣋⣉⠀⠀⠀⠈⠳⠶⠦⠀⠀⠀⠀⠉⠉⣙⣏⣀⡀
⠀⠀⠀⠸⡷⢔⣺⣄⠀⠀⠀⠀⠀⡐⠮⡭⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢹⣧
⠀⠀⠀⠈⠅⢨⠁⡲⠀⠀⠀⠀⠀⣝⣓⢒⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠈⠁⠋⠁⠀⠀⠀⠀⠀⠦⠬⡭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡒⠚⣫⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

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

⠐⢤⡄⠐⢮⡁⠪⣕⠪⢕⡂⢒⠀⠀⠑⠢⢍⣉⣉⡤⠖⣉⡉⠒⠤⣀⠀⠒⠠⠀⠀⠀⠄
⢣⢸⡠⢊⡩⠤⣤⡀⠙⠒⠬⠥⠂⠀⠨⡉⢐⠬⣭⡴⢋⠥⠍⡳⣶⡤⢅⣒⠀⠀⠀⠀⠀⠀⠂⢀⠀⢀⠀⢀⠀⠀⠀⢄⡠
⠁⠀⠀⠈⠂⠀⠞⠁⠐⠋⢑⣊⠄⠀⠈⠀⠀⠑⣄⡴⡡⠊⠁⠀⠀⠀⢠⡖⢠⠂⠀⠀⡂⠀⠀⠔⣉⠢⠑⠀⠅⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⠁⠀⠀⠀⠀⠀⣀⠄⠀⠀⠤⠠⠀⠠⣀⠳⣌⠳⡀⠀⠀⠀⠘⠐⡏⢣⠁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⣉⠁⠀⠀⠀⠉⠉⢀⣸⠀⠀⠀⠀⠑⡑⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡜⡿⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡆⠂⢸⠀⠀⠀⡜⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⡴⠀⢸⡀⠀⢠⡠⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢈⠁⠀⠘⠁⠀⠀⢀
⠀⡀⠀⠀⠀⠀⢈⠔⠂⣐⡶⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣤⡀⠀⠀⠀⠀⡎
⢸⢡⣄⡳⡂⠀⢀⠄⡪⢑⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⡀
⡼⠘⢧⠈⠁⠂⣂⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠢⡀⠰⠀⢣
⠓⠠⠤⡑⢄⠘⣯⠀⠀⠀⠀⠀⠀⠀⡠⢔⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⢬⡑⠈
⢀⢐⢝⠮⡢⢑⠢⠝⠂⠀⠁⠀⠀⠀⠊⠒⠈⠀⠈⠁⠀⠀⠀⠂⠠⢂⡀⠖⠈⠀⠀⠛⠅⠀⠇⡰⠠⠠⢀⠀⠀⠀⠀⠀⠢
⣒⠡⠀⠀⠊⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠐⠒⠲⠆⠀⠀⠀⠀⠈⠐⠡⠠⠧⠰⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠤⠍⣀⠀⠀⠀⠀⢄⡤⠴⠒⠒⠒⠦⢄⡀⠀⠙⠦⡀⢠⣤⠴⠂⠀⠀⠀⡀⣀⠲⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⠀⠘⣆⡀⠆⢠⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣄⠖⡃⠄⠀⠈⠋⠀⠋⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢋⠐⢀⠀⠄⠁⠀⠀⠀⠀⠀⢤⠸⠒⠀⡀⠄⠀⠀⠀⠀⠀⠔⢠⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠘⠀⠀⠀⠀⠀⡘⢀⠓⠛⠀⡅⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡨⡆⠀⢆⢀⢡⣟⡙⠀⠀⠀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠄⠃⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠈⣿⣥⠁⢀⡀⠀⢰⡎⠁⠀⡠⠀⠙⢀⡀⠀⠐⠀⠆⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⢀⡤⠐⡌⠑⠚⠗⡀⠀⡀⠀⠀⠸⠁⠠⠤⠀⠀⠘⠀⠁⠀⠀⠀⠀⠉⢂⡠⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠀⣸⣶⠋⠀⠀⠀⠈⠆⠸⠁⠠⠋⢋⢀⢀⠁⠀⠀⠀⠠⡠⠀⠁⠘⡘⢀⡼⠁⠰⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠔⠒⠊⠻⠿⠦⣀⠀⠀⢀⠘⢠⠀⠠⠁⢀⠔⠉⠳⣄⡄⠀⠀⠐⠀⠀⠂⢱⣘⠁⠤⠀⠐⢂⠘⠁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⢢⠂⡀⢀⠀⠀⠀⢈⣷⣤⣠⡥⠀⠀⠀⣾⠋⠁⠀⠖
⠀⠀⠀⠀⠀⠀⢆⠠⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⡰⠋⠉⠙⠻⣿⠿⣿⡂⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⢠⣄⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠰⠀⠀⠄⠠⠀⠠⣄⠰⠀⠀⠀⠀⠰⠏⠀⠈⠻⣆⠠⠀⠀⠁⠀⠀⠀⠤⢀⠵⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠈⣉⠙⢧⢁⡀⠀⠀⢰⠀⠀⠀⠀⠉⠀⠀⠀⠀⡆⢀⣥⣚⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠐⡤⠄⣀⡀⠀⠀⠠⠖⠛⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡈⢀⡺⠁⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⢼⢶⡄⠀⡤⡪⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠑⠳⣤⡗⠁
⠀⠀⠀⠀⠀⠄⡴⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⣷⠀⠀⡀
⠀⠀⠀⠀⠤⠀⡀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢽⡆⠀⠀⠂
⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⡀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠒⠀⢠⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⢦⣘⣧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢠⠦⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠠⡀⠀⠰⠺⠆⢠⡟⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⢠⠀⠀⠀⠀⡀⢸⠇⠐⣁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠤⡀⢀⠆⣀⠀⠄⠂⠀⢼⣊⣀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⣠⣫⠀⠀⠀⠀⠀⠐⠉⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠈⢂⣠⡶⠾⠷⢦⣤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⣀⢴⡿⠋⠀⠀⠀⠀⠙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠈⢇⢀⠀⠀⠀⠁⣶⠇⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠗⠳⠶⡶⠚⢉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⠂⠀⠀⠁⢐⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠤⢊⠀⠀⣠⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠀⠀⠙⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⢦⠢⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡴⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡀
⠀⠀⠀⠀⠀⣼⣿⣦⡀⣠⡾⣺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠈⠉⠛⢿⠋⢠⠇⠀⠀⠀⠀⠚⠀⠀⠊⠀⠀⠘⡿⠻⣣⣄⢀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⠳⡖⣰⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣴⡡⠊⠁⠈⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⠇⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⢤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⣸⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⣸⣷⠟⠃⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠⣾⢛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣴⡛⢇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡟⠹⣤⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣧⣾⣾⢟⠛⢹⠷⣶⡆⠀⠀⠀⠀⢸⡿⠛⠾⠗⠂
⠀⠀⠀⠀⠀⠀⢠⡷⠖⠛⠛⠏⠀⠀⠀⠀⠀⠀⠀⢾⣶⣦⣄⠈⣿⣿⣿⣏⢬⢙⠛⢊⣴⠋⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⡯⣹⢿⣿⣿⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠹⠿⠟⠛⠴⠁⠘⠋⣿⣍⣍⡉⠙⠃⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⢠⡤⠀⠐⠣⡤⠂⠀⡙⠉⠁⠀⠀⠀⡠⠀⠀⠀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡄⠀⠀⡻⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠻⠗⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡾⠣⠔⠊⠁⠀⠀⠀⢠⠄⠀⠀⢿⠶⠀⢀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⢄⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⡄⢁⠀⢢⠛⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡐⠢⢬⣤⣷⣭⢻⡜⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠯⠥⠉⠿⣿⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⡆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠙⢄⡿⢀⡀⠖⡹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠰⠀⣷⡏⣩⢠⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣵⠈⡿⢀⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢰⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢀⣀⠠⡃⣬⡜⠑⡂⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡋⠂⡞⢲⣣⡜⠟⣠⣿⢻⡌⠛⠉⣈⢠⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠘⠦⢽⡖⠫⠀⢾⠡⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡐⢣⠆⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠶⡍⠛⠠⢤⣌⣉⡕⢀⡿⡘⡟⢂⠌⠀⠀⠀⠀⠀⠀⠀⠰⢱⢆⣴⣼⣡⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢄⣰⢲⣤⡱⠀⠀⠀⠀⢆⡬⢆⡙⠶⢁⡸⠣⣈⢯⣙⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡷⠋⣡⢜⠰⠁⠀⠀⠈⡱⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠝⣡⡞⠁⠀⠀⠀⠀⢋⠐⠰⣏⠲⠊⠑⠷⣿⠞⠁⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⣿⠓⠘⠃⠘⠦⣀⢠⡗⢁⣿⠴
⠀⠀⠀⠀⢀⡸⢇⠀⠀⠈⠙⠙⢿⡀⠀⠀⠀⠈⢄⠰⢉⢆⠜⠀⠀⢸⠀⠀⠀⡠⠂⣐⢀⣁⠐⡦⠄⡰⠃⠀⠀⠀⢀⡂⡙⢮⠰⣇⣌⣻
⠀⠀⠀⢹⠈⠁⡄⣥⣀⡰⠂⠀⢀⡳⠀⢖⠰⠢⠞⡱⢤⡸⡂⢣⢆⣾⢺⡇⡰⢄⡁⢁⣸⡗⣠⡑⢦⠃⣉⡤⢀⠄⠈⠣⣽⣈⣶⣟⠷⠃
⠀⠀⠀⢸⣰⡄⣅⣳⠈⠰⣄⡺⡯⣟⡳⣌⣺⡳⢢⠇⠀⠑⡐⠌⡜⢋⣿⡥⡔⢫⠴⠂⠐⢏⣽⣼⣾⡫⣍⠴⠃⡌⢧⣀⡀⠈⡿⠋
⠀⠀⠀⠀⠘⢿⣼⣿⠟⠋⠀⣘⠑⠫⠶⢿⠟⠁⠁⠀⠀⢀⡌⠒⢾⠟⡿⠑⠂⡟⢄⠀⢠⣈⡪⢹⠀⠀⠀⠀⠀⡙⠄⣉⡲⣾⢧⣂⠤⡤
⠀⠀⠀⠀⠀⠀⠈⢇⠀⡀⡴⠤⣤⡄⡀⠀⠳⡄⠀⣀⣐⢺⡀⠀⠀⢸⡅⠀⠀⠇⡌⢾⠟⣸⡃⠘⠆⠀⠀⠀⠀⢛⢶⢸⡵⡷⠊⡤⡄⠃
⠀⠀⠀⠠⡤⠄⢇⠙⣿⢘⠧⡐⢄⡀⠈⠓⠶⢭⣺⣍⣩⡆⠀⠀⠀⢻⡄⠀⠀⡘⢻⣤⠟⠉⠁⡜⠀⠀⠀⠀⠀⠈⢳⣾⣙⣌⡉⠖⠁
⠀⠀⠀⠀⠘⢅⢊⡙⢯⡝⢶⡵⢄⡀⠘⠠⢄⠦⡙⢻⡏⠀⠀⠀⠀⣹⠀⠀⡘⢃⠝⢓⠒⣂⡠⠃⠀⠀⡀⠀⠀⠀⡼⠀⠁
⠀⠀⠀⠀⠀⠈⠑⠘⠣⠭⣾⠀⠀⠓⠄⠀⡀⠈⠑⣢⣜⣢⣀⠀⠀⣽⢀⡐⡴⢛⡡⢿⡈⠅⡑⠲⣀⠺⠑⡓⢆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⣀⠁⠒⠤⠕⠬⢹⡙⢶⣤⠞⣿⠕⠋⠀⠀⠀⠳⣈⣉⠢⣬⢲⡞⡇⣯⠇⡩⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡠⣩⢦⡅⢠⣒⡡⠆⢠⠀⠀⠀⡷⠟⠀⠀⠀⠚⠀⠀⠀⠉⠒⠉⠍⣼⣿⡉⣖⢓⣢⡎⣙⠊⢁⡝
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠂⢐⣺⣲⡀⠘⠛⢯⡑⠒⠈⠀⠀⠀⠗⡀⠀⠀⡌⠀⢱⠀⠀⠀⠀⠀⣠⡦⠏⡙⢉⡩⠤⠠⠄⠂⠉
⠀⠀⠀⠀⠀⠘⢆⡹⠖⣋⡠⣉⣉⣻⢯⡁⠐⣠⠀⠙⠳⡀⢀⠴⠀⡇⠁⠀⠀⡇⢸⠰⠄⠀⠀⢀⠼⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⠐⠉⠤⠬⠛⡴⠢⠘⠀⢴⠀⠙⣮⣴⣁⡇⣿⠀⠀⠹⡾⣦⠀⠀⣠⡶⠅⠂⠓⠒⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⢆⡀⠀⠀⢿⡁⡇⣿⠀⠀⠀⠘⣧⡀⣰⡥⠔⠉⠉⡠⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⢂⡴⢛⢦⣀⠉⠊⣦⠘⡍⠇⣿⠀⠀⢀⣠⠏⠘⠉⠀⠘⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠒⢠⢩⣯⣉⣳⣦⣉⠦⠱⣄⣿⣠⢶⡟⠛⠯⣍⣉⣉⢉⠉⠉⠓⠒⠢⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⠀⠀⠀⠀⠀⠈⠑⠶⣅⠿⡝⠂⠀⠉⠢⣉⠄⢙⠋⡉⣚⠁⠄⠉⢀⡤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⢅⡘⠠⢎⣹⣄⣆⣀⢘⡆⠀⠀⠀⠀⢩⢸⡇⠀⠠⠤⠤⠈⠓⠤⠤⠜⣄⡠⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠳⠟⠾⠶⠧⢾⡟⣷⣧⣷⠀⠸⠲⠖⠒⣈⢙⣟⡄⠀⠲⠶⠦⠘⠒⠀⠋⠉⣄⣀⣤⡄⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⠒⠚⣛⠟⠙⠚⠂⠞⣲⣟⡻⠽⣿⣹⣧⣽⣽⣿⣛⣛⡒⠒⣛⣛⣁⡀⠀⠉⠐⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣉⠁⠀⢈⠁⣠⣤⠬⠡⢤⣌⣁⣲⡉⠥⠤⠦⠬⠀⣉⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠁⠀⣠⠴⠦⠤⣤⣀⣀⡀⠂⠈⠉⢙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠥⠀⢀⡤⠖⢊⠟⢁⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⠤⣄⣀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢰⠛⠐⠲⠮⣤⠶⠟⠀⠀⠀⠀⠄⣀⡬⠖⠊⠉⠀⠀⠀⠀⡠⠐⣛⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⢐⡀⣠⡽⠛⠓⠦⣿⡀⢷⠀⠀⠠⢒⣉⡅⠈⠀⠀⠀⣀⠄⢀⡞⠁⣩⡌⡆⣧⠊⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⢘⣡⠟⠁⡒⠐⢀⠀⠈⠙⢾⣯⠛⠩⠁⣀⣿⣤⣀⣤⣊⣀⣤⣞⢀⢀⣇⢦⢃⠋⢱⠐⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣰⠃⠀⠁⢀⠀⠈⠀⠀⢀⡀⠬⠿⣭⣉⣉⣀⣤⡟⢀⣾⣁⡤⠿⠛⠒⠶⣎⢞⢄⡾⠘⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠀⠐⠒⠁⠉⢠⠖⠕⠈⠲⠶⠶⣹⡉⣰⣏⠴⠚⠉⡁⠠⠀⠀⠀⠀⠈⠻⡞⠓⡋⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⡙⢦⠀⠐⠀⢠⢃⠞⡞⡵⣛⣷⠀⣸⠟⠩⣑⢤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢱⡴⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠨⣉⠲⣵⣦⡀⣈⣼⢀⣶⠯⠴⣧⠷⡷⠞⣍⠀⠀⢨⢦⠀⠀⠀⠠⠀⠀⠀⠀⣸⠆⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠙⠲⠦⢭⣹⠟⠉⣠⡤⣶⠛⣄⢧⠻⡇⣄⡏⢹⠀⡖⠀⠀⠃⢀⡠⠔⢈⡀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣁⠀⢀⠮⠤⣞⢉⡠⠺⡀⢻⡝⠲⠷⣯⣤⡮⠤⣤⡤⠔⠊⠁⢀⣀⡤⠵⣛⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣘⠉⠀⠀⠳⠄⠛⠒⠒⠠⠤⠤⠤⣋⣠⠤⠖⠛⠉⠁⠀⠁⣀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣒⣲⣦⣤⣤⣌⣉⣙⡛⠒⠶⠶⠶⠦⢤⣤⠖⠚⠉⠁⠀⠁⣀⡠⠤⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣿⣿⣇⣬⣧⣠⡄⠒⠊⠉⠀⢠⠤⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣖⣻⣭⣿⣾⣿⣿⠿⠿⠿⠿⠿⠿⣼⣤⣭⣭⣓⣒⣲⢣⠀⠀⠶⠖⠒⢊⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣈⠀⠀⠲⠶⢆⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⠤⠄⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡖⣅⣢⠰⣍⢃⠄⠀⠀⠔⠀⠀⣀⠼⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠠⠀⠂⢈⠔⡊⠰⠑⡈⢂⡀⠤⠒⠉⡀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢀⣀⣀⣚⠁⢄⠉⢀⠀⠠⢀⠄⠾⡀⢀⣀⣀⣤⣤⡴⠖⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⢐⡋⠉⠉⢉⣀⠠⠐⡨⠢⠥⠎⡔⢨⡉⠉⠀⠤⡀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⠂⠉⢀⣀⡤⠖⠁⠀⠀⢠⠔⢌⠐⠂⠉⠓⠨⢦⡀⠀⠀⠙⠀⠀⢄⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡘⠀⣀⠤⠒⣉⠔⢁⡴⠊⠀⢀⠔⠁⠀⠀⣦⠀⠀⠐⠢⡀⠉⠋⡒⠠⠄⠄⣀⡈⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠳⠊⠀⢀⠜⢁⠔⠉⠀⠀⡔⠁⢠⠃⢸⠀⢸⡀⠀⠡⡀⠘⠆⠀⠀⠄⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠠⠋⠀⡠⠊⡸⠀⠀⡌⠀⡞⠀⢸⠱⡀⠀⠑⡄⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠀⢀⡇⠀⢀⠇⠀⣇⠀⡌⢂⠘⢦⡀⠈⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠔⠁⢇⠀⢸⠀⠀⠻⢠⠃⠘⡀⠀⠈⠒⠤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠘⢆⡀⢀⠤⣠⠇⠀⠀⢱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢆⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⢠⡀⠀⠠⢳⡀⠀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢆⢰⣆⣰⡅⠱⠒⣦⢦⣼⠃⢱⢯⠃⠌⢹⠛⠅⡸⢤⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⣧⣤⠉⢡⡁⢈⠁⠴⠇⠀⠚⡖⠀⠼⡤⠀⣏⠒⠈⡠⠞⢧⠔⠎⢈⣄⠀⠀⢀⡀⡀⢶
⠀⠀⠀⡗⠤⡠⠄⠀⠀⣏⠑⠁⢸⠄⢀⣧⠀⣠⣦⣀⠀⠰⢳⡠⢾⠠⠀⡏⠃⢀⡠⠾⡄⠒⡎⢀⡘⠀⢀⣤⠈⠥⢷
⡤⣀⢰⡞⠒⠇⠸⠲⠀⠸⡓⠂⠀⡸⢄⣜⡆⠀⠿⣤⡈⠠⠞⡦⠾⡶⢐⡘⠃⢈⠴⠺⡤⣾⣃⡬⠃⢠⡆⠈⠤⠴⡎
⡵⠬⠁⢸⠿⡒⠃⠀⠛⣂⡻⡁⠒⠀⠿⢄⣏⠂⠸⢳⣄⡁⠞⢳⢼⠓⢀⡛⠂⣀⠴⢾⣷⣥⣿⠃⠰⠆⠀⠆⠐⣯⠔
⠘⢦⠤⠤⠀⠟⢅⣉⢀⠉⢰⢽⣁⠘⠀⠛⣼⣁⠂⢻⣦⠁⠐⠓⣾⢛⣪⠱⠀⢁⠤⣾⡧⢴⡋⡐⠓⠀⠂⣚⠿⠀⢈
⠀⠀⠱⡂⠘⠀⡈⢡⡤⠀⠄⠨⢻⣅⡑⠠⠟⢯⡈⠘⣦⡈⠠⠚⣼⠋⡽⠷⠀⠁⡤⣮⠔⢾⡗⠆⠀⢁⣹⠃⡀⢉⠌
⠀⠀⠀⠈⠻⢀⣀⠀⠀⣶⠦⠄⠈⣿⣅⠁⠠⠯⣧⡘⣧⡀⠃⠚⢱⢀⣧⡀⠀⢀⡴⡥⠶⠞⠇⠀⣁⠽⠀⠂⠰
⠀⠀⠀⠀⠀⠈⠓⣤⠄⠄⠰⠷⡖⠄⢻⣄⡃⢰⠿⣄⣣⡁⠁⠰⠻⣉⣽⡄⠂⢠⢟⢰⠚⠇⢈⣡⠼⠀⣀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠱⣂⠒⠀⠾⠓⡆⢣⡀⠃⢠⠯⣽⣄⡈⠠⠾⣁⣅⡹⢸⠥⣾⠺⠆⠘⢀⢜⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡀⠂⠰⠓⣛⣏⣁⠃⠴⢿⢧⣄⢁⠚⠻⣉⠃⠷⠶⡟⠃⣈⣈⡽⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣈⠀⠉⢟⣧⡘⢀⡎⠆⢿⠀⣍⠁⣾⢰⢻⠁⢣⢈⡠⠞⠠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠁⠀⠐⠌⡆⣧⠐⣘⡇⠀⢀⣿⡈⠆⣤⢣⢣⢐⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡕⡌⢦⡸⡄⢱⡇⣇⢸⡏⠃⢰⢇⢃⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢌⢧⢹⣸⢇⢹⣼⠃⠀⠟⡬⢪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠻⡜⣱⣸⢸⡇⢰⡞⣰⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣇⢹⢸⠘⢁⢸⢣⢏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⢨⡄⣯⠈⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣼⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⢅⡞⡻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡾⢸⡇⢳⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣱⢇⡆⢻⡎⣷⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢿⢸⣿⣸⡧⠹⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠂⡿⠾⢿⡇⣇⢡⢛⠯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠐⠿⠀⠛⣷⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠲⡀⠀⠀⠀⢴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣖⠢⠿⣿⣿⡮⣿⣟⠳⣝⢤⣦⠀⣿⣿⣶⢀
⠀⠀⠀⠀⠀⠀⠀⣸⡶⢶⣏⣤⡾⠆⢴⣷⣶⣬⣿⡷⡌⠠⡙⣷⡙⠻⣿⡿⠀⠀⣀⣤⣦⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣣⣾⣿⢿⣷⣴⣷⣜⣻⣿⡻⢷⡜⢆⠀⢸⣧⠀⠙⣷⡆⣰⣿⣿⣿⣿⣿⣿⢿⠿⢷
⠀⠀⠀⠀⠀⠀⠀⣯⠈⡻⠿⢷⣭⢿⣿⣿⣿⣗⢻⡆⢻⣼⣧⣶⣿⡀⠀⣿⣿⣽⣿⣿⣯⣍⡀
⠀⠀⠀⠀⠀⢀⣴⣯⣼⣷⣶⣿⣥⣴⣿⣿⣿⣿⡗⣿⡎⣿⢹⡿⢿⡇⠀⣿⣿⡏⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢾⢿⠟⣭⣵⣾⣿⣿⣿⣿⣿⣿⡏⣄⢿⣿⣿⣞⣡⢾⣿⣆⣿⡏⠀⠀⠀⠈⠙⠻⠿⠿⠦
⠀⠀⠀⠀⠀⠘⣾⡌⡅⠈⣽⡿⣿⣿⣿⣿⡟⢀⡿⢸⡿⡛⢸⠟⣾⣿⣿⡇⠇
⣦⣄⣀⠀⠀⠸⢿⣇⣱⠟⣛⠛⠞⢛⣻⣿⣇⣾⣷⡿⣰⣤⢠⠏⣿⣿⣿⡿⠀⢀⣴⡆
⢻⣿⣿⣿⣦⣤⡈⠻⠿⢷⣄⣉⣻⣯⣿⡿⠟⡉⠛⣫⣿⡿⢋⣰⣿⡿⠋⣤⣴⣿⣿⠇⠀⠀⢀⣀⡀⣀⣤
⠘⢿⣿⣿⣿⣿⣿⣄⢀⣤⢉⣋⣙⣉⣩⣤⣢⣴⣿⡿⢿⣳⣿⠉⢸⡇⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠈⢻⣿⣿⣿⣿⣿⣾⣿⣷⡌⢛⣿⣇⠙⠙⠉⠁⣀⠸⣿⡟⣰⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⠇⠉⠉⠉⠓⢹⡄⠀⢹⣷⣼⡿⢃⣀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⢀⣴⣾⣿⣿⡿⠻⡟⠋⠀⣠⣴⣶⡆⠀⣷⢀⣼⣿⣋⣀⠻⣿⡟⢀⣿⣿⣿⠛⠛⠛⠉
⠀⠀⠸⣿⣿⣿⡟⢁⣀⠙⢦⢰⣿⣿⣿⠁⢀⣷⣾⣿⠿⠿⠿⡍⠉⠻⣯⣌⠙⠿⣿⣿⣷⣦
⠀⠀⠀⢿⣿⡿⠁⠘⣿⣷⣜⣟⡿⠛⠁⣄⣼⠟⠉⠀⣀⣀⣀⡄⠀⠀⣿⣿⣷⡀⠈⢻⣿⣿⡧
⠀⣄⡀⠀⠙⠷⠀⠀⠙⢿⣿⣿⣿⣇⢀⣿⣯⡄⣰⣿⣿⣿⠟⠀⠀⢀⣿⣿⣿⡇⠀⠀⠙⣿⡗
⠀⠘⣿⣷⣆⠀⠀⠀⣴⣿⣿⢿⣿⡟⣼⢏⣿⣇⣿⣋⣁⣀⠀⠀⠀⣾⣿⠿⠛⠁⢀⠀⠀⠈⠃
⠀⠀⠉⢿⣿⡆⢠⡄⠋⠁⠀⢠⣬⣾⣿⠟⣱⠟⢻⣧⣄⠉⢳⡴⢺⣿⣿⡿⢷⣦⡄⢱
⠀⠀⠀⣀⣉⣻⣾⡇⢀⠀⢰⡆⢻⣿⠇⣼⠋⠀⠈⣿⣿⣠⡎⠀⢼⣿⠋⠉⣠⣼⣿⣻⠠⣤⣤⣄
⠀⠀⣾⡿⢋⡀⠉⡙⠺⣇⣼⡷⢸⣿⣸⣧⣤⢤⡀⠨⣧⡿⡃⢀⡿⢞⠶⣾⣝⣻⡿⣿⣆⠙⠿⣿⣧
⠀⠀⡻⠁⣸⣿⡌⠙⠳⣿⣿⠁⣼⡟⠁⠀⢀⣴⣿⣿⣿⣦⡆⣿⠁⢿⣰⣿⣿⡿⣧⣝⠳⠀⠀⠈⠻⡇
⠀⠀⠉⠀⢻⣿⡿⠀⠀⠸⣷⣾⣿⠁⠀⢀⣿⣿⢿⠿⢿⣿⢇⣿⣿⡈⣿⢿⣿⡾⣿⢻⣥
⠀⠀⠀⠀⠈⢻⡇⠀⣠⣾⣿⣿⣧⣤⡀⠈⡿⠋⠀⢠⣼⣿⡿⣿⠙⣿⣿⡄⠹⠞⣡⣶⣅⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠋⢹⣿⠏⠈⠉⠛⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣌⣛⣩⡉⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣠⣿⠋⠀⢠⣿⠟⠆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⢹⣿⣿⣿⣧⡈⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠹⠁⠀⠠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠈⠀⠀⠸⣿⡿⠈⠻⢧⡀⠙⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠙⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⣴⠒⠒⠒⠂⢤⡄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢭⣭⠁⢀⡈⠁⠀⠀⠠⠄⠀⠉⠀⠀⡠⢤⠀⠉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡀⠠⠄⠳⣄⠈⠈⠀⠀⠒⠤⠀⠈⠉⠀⠀⠀⠀⣠⠠⣄⡀
⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠒⠠⣀⠀⠀⠀⠀⡌⢀⠀⡃⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⢰⠁⠊⠀⡸⠤⠤⠦⡤⠂⣼⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡁⠀⠀⢀⡔⠀⢻⡀⠀⠀⠀⡠⠚⠉⠉⠑⢄
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢮⡦⣾⡌⠉⠀⠀⠀⠐⠈⠀⠰⣯⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⣃⠀⠀⠘⣅⠀⠈⡷⠲⢤⡞⠀⠀⠀⠒⠂⢾
⠀⠀⠀⠀⠀⢻⠀⠀⠐⠈⠀⠀⠀⡀⠔⡦⢼⠲⠂⠀⠀⢀⡀⠀⠀⠐⠈⠳⡄⠀⠄⠀⡴⠉⠋⣉⠉⠉⠱⢄⣈⠁⠀⣤⠞⠄⣠⡛⠂⠠⠤⠠⠔⡼
⠀⠀⠀⠀⠀⠈⠢⡘⠒⠀⢀⣀⣥⠀⠌⠀⣮⠂⠀⢈⣀⠉⠁⠠⠀⠀⠀⠀⠈⠢⡀⢰⠃⠀⠀⠈⠙⢭⡙⠀⠙⠋⠑⢂⠀⠀⡶⢌⠀⢢⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⡯⠈⠉⠉⠁⠀⠀⢀⠾⠀⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠈⠦⡤⠀⠒⠚⣃⢀⣀⠀⠣⢤⠦⠳⢤⡀
⠀⠀⠀⠀⠀⠀⡸⠄⠂⠀⠀⠀⠀⢀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠁⠀⠈⢠⡀⠀⢂⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⠉⠩⠉⠉⠙⠉⠉⠀⠈⠇
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠢⢄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡀⠠⠄⠘⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠉⢢⡅⣀⣀⡀⢀⠀⠀⠀⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⢿⡀⣀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠐⠁⠈⠀⠙⡏
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠲⠠⠀⠀⠀⠲⠁⠀⠀⠦⠀⠀⠤⣰⠁
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠼⢦⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠒⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠙⢦⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠉⠚⠓⠒⠒⠒⠒⠋⠀⠂⠘⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠧⠼⠦⠐⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠄⠒⠒⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⠁⠤⠀⠂⠘⠂⠛⠪⠅⠐⠀⡠⢴⠀⢠⠂⣬⠛⣻⡏⠀⠀⣱⣾⠿⣿⣇⠈⠢
⣿⣷⡿⠟⢻⣿⠉⠀⠼⣛⣲⣦⠈⡀⢠⠙⠖⣆⡀⠀⣠⠿⢨⡖⢋⡁⠀⠀⠘⡇⠀⠀⠹⣿⣶⡿⡏⠁
⣿⣿⠀⠀⣸⣿⣧⡀⣴⣿⣼⣿⣦⣤⠞⠁⢨⣿⡟⣿⠃⠀⠀⠀⢹⣿⣶⣦⣶⣠⣄⠀⠀⠀⠀⠁⠀⠀⠒
⠁⠈⠢⣴⡿⠛⠛⠂⠀⠀⠘⢿⣿⡿⠇⠠⣬⣿⣿⣿⡆⠀⠀⢀⣼⠿⣾⣏⣼⣿⣿⣿⣷⡾⣯⣤⠴⣃
⣄⣀⠀⠙⡷⣭⡂⡰⠂⠛⠀⣸⣿⣿⣷⣿⠫⠟⠋⣻⡇⠀⠈⠙⢿⣾⣿⣿⡟⢍⠟⠟⠣⢦⣽⣿⡄⠈⢿
⣿⣿⣿⣴⣿⣿⣷⣶⣦⣠⡗⣛⡯⢹⠈⣏⠀⠀⠀⣡⡏⠹⡆⠠⡚⠿⡏⠥⠀⢰⠃⠘⠊⠃⡽⠺⡰⢢⣽
⠉⠁⢸⡿⢟⢿⣻⣿⣸⣏⢻⠿⡴⣛⣶⡿⣆⠀⣰⠁⠤⠡⡶⠀⣅⣠⣴⣄⣲⢈⠆⢰⡀⣨⠰⡩⠵⢋⠛
⣄⢀⠤⣧⠈⡀⣫⠛⡻⠟⠊⣤⠀⣿⡯⠴⡄⣌⣩⣤⣔⢓⡍⠙⠃⠀⠋⠩⢽⣯⣷⣷⣷⣿⣾⠷⠦⠉⠻
⠉⠘⣧⢽⣯⣬⡿⠷⣴⣧⡡⠄⠀⣧⡛⢸⣷⢦⢾⣿⣿⡋⠠⢾⣄⣆⢀⡜⠀⠀⣀⠉⢛⣭⡏⠀⠀⠀⢀
⠻⠋⠁⠀⠈⠃⠀⠘⠙⠛⣏⠺⣧⣮⠈⠀⠀⠀⠀⠀⠙⢻⣠⣼⣿⣿⣿⡗⠀⢤⣿⣿⢿⡻⣇⠀⠀⡜⠛
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⡻⢿⣧⡄⠐⠀⠀⠀⣤⣠⡾⠟⠉⠙⠻⠿⣗⣶⡯⠻⣿⠻⠟⠟⠀⡜⠀⣰
⠉⠲⢤⣀⠀⣼⡀⢠⡘⢿⡑⠆⠂⣿⠀⠀⠀⠀⠀⣿⠃⣀⣀⢤⠁⠀⠀⣿⡟⠀⠀⠁⠀⡂⠀⠀⠀⠀⠋
⠀⡀⠀⢻⣿⢿⡟⠉⠀⠀⡄⠰⠆⠛⢄⠀⠀⠀⡤⣣⡼⠋⠀⠀⢠⣜⠉⠙⠳⣴⡤⠈⣲⢷⠀⠀⠀⣾⡀
⠾⠀⠀⠚⠋⢙⠇⠀⣀⣼⡇⠀⠀⠰⠾⣷⠀⣠⠏⢝⢶⠊⠀⠀⠀⠈⠁⠈⠃⣈⣠⣴⡦⠀⠀⠷⠶⣇
⡁⠀⠀⣠⣄⣼⡁⠊⠁⠀⠙⢦⣵⣄⠀⠀⠀⢙⢸⣮⣴⡦⠀⠀⣠⡌⠀⠂⠀⣸⣿⡋⠀⠀⣀⣀⠀⠀⠙
⢶⡿⣧⣽⣮⡿⢻⣶⣄⡤⠂⠉⠁⠀⠙⠗⠢⢄⠋⠠⠤⠤⡖⠶⠿⣶⣶⣤⣴⣿⢏⠉⢰⣾⣿⣿⣆⡀
⠿⠁⣉⠹⣏⠀⠀⢹⠿⠃⠀⠠⠀⠀⢀⣤⠶⠚⠑⢤⣀⠀⠀⣠⠄⠀⠙⢟⣕⣄⣙⣇⢸⡿⠁⠈⠳⣿⡰
⠈⣸⢢⣤⠦⣜⣆⠈⢹⠠⠂⡀⠀⣶⣿⠇⠀⠀⠀⠀⠈⡻⠈⠉⠀⠀⠀⢸⣟⠛⠛⢿⣿⡇⠀⢉⠰⡍⡉
⢀⣨⠋⠁⠡⣌⡟⠠⠆⢀⠠⠤⢐⣱⣿⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣨⢿⣟⠀⡂⠉⠁⢹⡎⢠⡈⠃
⢂⣩⣦⠞⢃⣿⡧⡚⡃⠁⠐⠂⣨⣿⡿⠀⠀⣤⣤⡠⠸⠿⠀⠀⠀⠒⠞⢠⣿⣻⣯⣽⣧⣄⣸⣷⣾⣃⡴
⠁⣀⣼⠋⠟⠂⡠⠒⠀⠁⠘⢿⠀⣿⣷⣶⣴⣿⢋⠀⠀⠸⣆⣠⣄⢠⠆⠀⠀⠀⣩⢭⣿⠋⠀⠀⠀⠨⠱
⠀⠀⠀⡤⢠⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢿⣿⡉⡶⠿⠧⢹⣶⣄⠀⠀⠰⡚⣾⣏⢀⣦⠀⠀⠀⠐
⣠⣾⣀⢀⣾⡀⠀⠈⢢⢤⣰⣶⡞⠉⠉⠉⠈⠉⢺⠿⣿⡶⠳⡶⠏⠐⠤⣈⢠⡤⢟⣸⡋⢠⡈⠀⠢⢜
⢹⣿⠿⣿⠟⠑⠆⠀⠘⠀⠻⠅⣻⠀⠠⢦⣤⣀⠋⣸⠃⠀⠁⠀⡀⠀⠀⠠⡈⠛⠾⣿⠒⠤⠐⠂⡒⠢⣻
⡚⠁⠀⠸⠀⠘⠀⠘⠉⢀⡀⠀⠙⡀⠀⣼⡟⢿⠿⣿⣷⣄⠠⢶⡿⠤⠟⠀⢞⣀⡤⢀⢈⡠⠤⡌⢁⣾⡛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⣠⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡄⠀⠀⠀⠀⠐⣹⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⠦⠀⠀⠀⢀⠹⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡿⣟
⠀⠀⠀⠀⠀⠀⢰⡱⠠⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠃⠀⠀⠀⠀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣤⣦⡄⠀⠀⠰⣶⣟⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢹⣦⣶⠀⡀
⠀⠀⠀⠀⠀⣀⡀⠈⡉⠃⠀⠠⡀⠉⠳⠀⠀⠀⠀⢀⡀⣺⠷⠀⠀⠀⠀⠀⠀⡝⠛⠃⠈
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⡀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⣰⡔
⠀⠀⠀⠀⠁⠀⠂⠀⣀⣴⣴⣣⣤⡀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣄⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠐⢸⣾⠙⡞⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡖⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠈⠳⠌⠰⠁⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⢀⠘⡧⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠀⠂⠀⠀⠀⠀⠂⡰⠒⠀⡁⠁⠀⠀⢀⠀⠀⠈⠀⠀⠘⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠄⢈⣰⣋⠁⠀⠁⠀⠀⠀⠀⠠⡀⠐⠀⠠⠈⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢈⠧⠄⠀⠄⠀⢰⠁⠀⠠⠀⢈⢠⡀⠀⠀⠘⢀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠒⠀⢆⠈⢙⠡⢀⣠⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠤⣿⣇⠀⠀⠀⠀⠁⠉⠀⠀⠘⢀⠤⣀⠀⠀⠀⠂⠀⠀⠀⡀⡾⠁⠈⢀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠉⠲⡀⠀⠁⠠⠀⠁⠐⠁⠀⠈⢺⡄⢀⣀⠀⠀⠀⡿⠂⠈⣀⠀⠈
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠖⠒⠲⠾⣿⣿⡅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠠⠀⢄⡀⠁⠀⠀⠀⠸⠁⠈⠱⣆⠀⠀⠀⠀⠀⠀⠤⠠⠷⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠉⠳⡄⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⢰⣠⠤⡋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⢄⡀⠀⠀⠈⡀⠀⠀⠀⠰⠂⠠⠄⠀⠀⠒⠉⠙
⠀⠀⠀⠀⠀⠀⠂⠰⠉⠄⠀⠀⠀⠀⠀⠀⢀⠈⠙⢙⣆⢀⠢
⠀⠀⠀⠀⠀⢀⠈⠄⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣾⡅
⠀⠀⠀⢀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⠀⠀⠀⠐⠂

⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⣤⣀⣀⢀⡀⠀⢀⣤⣀⣀⣠⣤⣀⣴⣶⣾⣶⣤⣤⡐⢂⣀⠀⠀⢀⠀⠀⢀⠀⢀⣀⣀⣀⣀⣀⣄⣠⣤⣀⡀
⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠇

⢀⣤⡀⠀⢀⠀⠀⠀⢀⢀⠀⠀⣀⠀⠀⡄⠀⠀⠀⠀⣄⡀⡀⠀⢀⠀⠀⠀⠀⠀⠤⠀⣀⣀⣀⣤⣤⠀⢐⠀⠀⡀⠀⡀⡀
⠀⢻⣷⣿⣿⣷⣴⣿⣼⣿⣿⣾⣿⣷⣿⣷⣴⣾⣿⣦⣿⣿⣷⣼⣿⣷⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣼⣧⣦⣿⡿
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⢀⣤⣀⣄⣀⣀⣶⣤⣤⣄⣄⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣦⣿⣶⣶⣿⣷⣿⣾⣿⡆
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣃
⠀⠀⢀⡁⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢛⣴⠻⠏
⠀⠀⢨⣿⣾⣻⡇⣀⠀⣷⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⣅⢢⡄⡄
⠀⢠⣾⣿⣿⣿⣿⣿⣴⣿⣧⣄⣼⣤⣤⣥⣶⣶⣤⣤⣿⣄⡀⢀⣠⣴⣶⣴⣤⣠⣄⣀⣀⣀⣀⣀⣀⣀⣠⣶⣽⣯⣿⣾⡇
⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⣄
⠀⠈⠛⠋⠉⠉⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⢰⣶⣶⣦⣧⣤⣧⣤⣤⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⣀⣀⣀⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⡆
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⢀⣴⣶⣾⣿⣿⣷⣶⣦⣴⠀⠀⢀⠄⠀⣠⡀⠀⢀⣀⣀⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣶⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣤⣶⣶⣤⣄⣀⣤⣄⣀⣀⣠⣄⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣴⣾⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠀⠐⠉⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣴⠛⠃
⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣦⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠉⠀⠸⠄⠀⠀⠈⠀⠂⠀⠐⠒⠀⠀⠀⠀⠀⠈⢣⣼⡟⠐⢙⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣼⡇⠃⠚⣧
⠀⠀⠀⠀⡀⠉⢡⡄⠀⠰⠦⠀⠀⠁⠀⠀⠀⠀⠀⢈⠁⠄⠀⠀⠱⣿⣿⣄⢠⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣸⣿⠃⡟⢀⠀⠀⢻⡇
⠀⠀⠀⠁⠈⣤⢯⠙⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⢸⠀⠇⠈⡇
⠀⠀⡀⠀⠘⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⢸⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⠈⠀⠀⣄⠇
⠀⠀⠀⠳⢀⡀⢠⡖⠀⠣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⠺⣿⣿⡇⠰⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠆⠰⢠⡟
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣦⣬⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣿⠇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢀⡀⣠⡇
⠀⠀⠀⠀⢠⠐⠄⠀⠀⠠⠄⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡰⠘⣿⠟⡻⢒⣿⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡿⠋
⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠉⠁⠑⢦⡄⠃⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣇⡾⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⢀⠒⠒⠂⠀⠀⠀⠀⣰⣿⣷⣾⠇⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠲⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠢⡌⢉⡉⢁⡀⠙⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠈⠁⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⠘⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢃⠈⣶⣤⣄⣠⣿⣿⠀⠘⠂⡀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣿⠀⠀⠀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⢿⣿⣿⣷⣿⡄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢻⣿⣿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠁⠐⠀⠀⠀⡀⠀⣿⣿⡟⠁⢀⠙⠆⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢉⡓⠊⠀⠀⠀⠀⠀⣿⣟⡇⣠⣿⠖⠀⠆⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣆⠀⠷⣤⢛⣉⣩⣄⠁⡀⣀⣤⣄⣿⣉⣿⣿⠃
⠀⠀⠀⠀⠀⢠⣌⡛⣦⡤⠈⣽⠟⠠⠒⢴⣟⠛⣉⣠⣴⣿⢿⠓⣺⣿⣿⣿⠃⠀⠀⠀⠀⠀⣶⡀⠐
⠀⠀⠐⠀⣠⠄⠉⠽⠁⠐⠀⠀⠀⠴⠀⢀⡩⢞⡋⠙⢅⠙⠻⣿⣿⡟⠿⣇⠀⠀⠤⣀⣤⠟⠉⠘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⢀⡀⠈⠁⠀⢻⣿⣿⣷⣿⡇⠀⡀⢚⡁⢈⣷⣤⡬⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣄⡀⠠⡆⢀⡏⠀⢀⡾⠁⠀⠀⠀⠀⢿⣿⣿⡿⢁⡼⢋⡈⡉⡈⠉⠀⠀⠈
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠠⠭⠤⠣⣽⠖⣤⣿⣁⣀⡀⠀⠀⡀⣸⣿⣿⠆⣷⡷⠚⠶⠓⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠓⢴⣆⣝⠛⠛⢫⣀⣴⠞⠋⣸⣿⣿⣾⣟
⠀⠀⠀⠀⡀⠀⠈⠑⠂⠀⠴⠚⣿⢷⣾⡉⢿⣻⡦⣬⣛⠶⢦⣴⣿⣿⡿⢿⣿⢀⠀⠀⠀⠀⢀⣶⠀⠐⢂
⠀⠀⠀⠀⠈⠠⠀⠈⠀⠀⠀⠛⠛⠛⠻⣷⠞⢦⡷⣾⠹⣷⠀⢾⣿⣷⣶⡿⠇⠀⠰⣦⢀⣠⠞⠉⠙⠳
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠒⣴⣋⣀⠸⠧⢹⣶⣾⣶⣬⣿⣿⣿⡅⠀⠀⠀⣠⠟⠳⠲⣆⠀⠈⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠆⠀⠀⣤⣌⣩⣉⠁⠀⡀⣻⣿⣿⣿⣿⣬⢻⠇⣄⠀⣠⠏⡼⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⣠⠄⢈⣹⠷⠀⠒⡒⠛⠃⠠⢤⣐⠂⠈⠉⢹⣿⣿⣿⣿⣿⡆⣉⣿⣿⠿⠛⠾⢶⡆⣂⠀⠀⠀⠤
⠀⠀⠀⠀⢬⡄⣿⣁⠶⣀⢘⣛⠃⢀⡀⠶⣾⣍⠻⣿⣿⡜⠟⢹⣿⣿⣿⣿⣿⣿⠷⢤⣤⣌⣤⣾⡫⡄⢀⣤⠷⠂⢀
⠀⠀⢀⣶⠀⠛⠀⠙⠈⠁⠿⠟⢿⡺⣧⣰⣿⣿⣾⣿⣿⣿⣿⣷⣾⣯⡿⣿⣿⣷⣤⣔⣭⡛⠧⠈⢿⠀⠈⠑⠾⣯⣍⣀⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣯⠈⠻⠀⠀⠀⠘⠃⠉⠀⠈⠁⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣼⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠻⠛⠃⣤⣸⣦⠔⠲⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠙⠋⠙⠁⠘⠛⠈⠻⠚⠓⠻⠋⠉⠀⠀⠀⠛⠙⠓⠂⠐⠀⠀⠙⠛⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⢸⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⣈⠁⣤⠀⠀⢠⣆⣀⠠⠀⠀⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠧⠀⢀⠉⢑⠀⠀⢀⣀⠁⠀⠀⠀⠀⣠⠋⡤⠈⠘⠛⠢⣶⠟⣹⣏⠀⠀⣦⢠⣀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣦⣄⡀⣸⠷⠃⠀⠈⢢⠄⠀⢀⢀⡀⠒⠠⢀⣰⣤⠄⠀⠀⠛⠋⠁⢀⡱⠆⠈⠀⢥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠇⢀⠀⠀⢹⣧⣉⣿⡁⠀⡀⢢⣶⣾⣆⣠⣦⡁⠀⣾⠓⢿⡿⠟⢃⠤⡌⡗⢺⡗⠻⠆⠚⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣶⠈⠃⣀⣆⡀⠀⡀⢡⠖⠤⢜⣻⣦⣹⣇⢠⡓⠀⠘⠶⢿⢶⠶⠟⠶⠏⠙⢶⣇⡆⠀⣸⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠇⠀⠀⠱⠼⠼⠁⡿⢩⡗⢣⡞⡷⠛⠉⢳⡷⢕⣀⡀⣀⡀⠙⠋⢀⠀⡀⢀⡀⣿⣿⢫⣇⡞⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠃⠒⣄⢠⠀⠀⠀⠀⠀⢀⢄⠀⣀⣠⣅⠠⠴⠌⡈⠀⢀⠀⠀⠘⣿⣎⠙⢿⡿⠷⢿⣿⣞⡁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⣈⣳⡷⠠⠶⠀⣹⠇⠀⡽⣿⣿⣿⣖⠀⢈⠀⠀⠉⠑⠉⠁⠈⢻⣿⡇⢀⠀⠀⣿⣯⡷⠯⣀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⢤⡎⠉⠃⠀⠇⠀⢈⣢⠀⠀⢈⣛⠟⠉⠐⠇⠀⠀⠦⠀⠲⠀⠸⣋⣭⣦⡈⠀⠠⣿⣿⣆⠀⢠⠃⠴⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠈⠀⠈⣷⣶⢦⣠⠆⠀⠀⠀⢧⠀⠸⡀⠀⢀⠀⠘⠀⣀⠄⠚⠃⢀⠀⠀⠋⠙⣿⡿⠀⣈⣋⣁⣤⣤⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠦⣄⣼⣧⣀⣼⡟⠒⢀⡴⠂⠀⣸⣶⣿⣷⣾⣧⡖⣸⠃⠀⠀⡤⠶⠀⢀⣀⠰⣿⡁⠰⣏⢙⡍⡀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⣸⣉⠁⠀⠀⢠⡽⠞⠦⣄⠨⣿⣿⠛⠛⠛⣴⣧⣤⣆⡉⠁⠀⠀⢚⠁⠶⠻⢠⠀⠙⠛⢃⠈⡤⢈
⠀⠀⠀⠀⠀⠘⡆⠒⠀⠀⠳⣄⡄⣀⠀⢉⠅⠳⠛⠐⢲⠶⠤⣀⣽⣶⣇⠀⠈⠂⢸⣟⣹⣟⠛⠀⠀⢠⡹⣿⠿⣧⡼⠦⠀⠋
⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢦⠘⢴⣀⠀⠰⠀⢀⣤⢤⡷⣤⠀⠁⠉⣿⣿⣦⣄⣤⢾⣿⣿⡉⠀⠀⢴⠶⠷⣻⣄⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠔⠋⠉⣼⣾⢉⣀⠀⠛⣴⠄⠒⠐⠋⠊⣿⠿⣿⢧⢻⠿⡟⢗⠲⢮⡁⠁⠛⠿⠉⠈⠋⠚⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠁⠀⠀⠀⠈⠈⠠⠉⠀⠦⠍⠀⠀⠈⠄⠀⠏⠀⠘⢠⣏⠀⣠⣈⠷⠉⢁⡀⠀⠀⣀⠤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣤⠔⠛⠂⠀⠀⠀⠀⠊⠂⠀⠈⠀⠀⢃⠠⠌⣏⠀⣠⠏⣿⠎⠙⠧⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠠⢴⡶⠀⢰⠄⠀⣀⠄⠀⢀⡈⠀⡈⠉⠁⠙⡶⢿⠀⣠⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣄⡀⠈⠀⠀⡁⠢⠀⠋⢹⠶⠈⠃⠀⠒⠀⠐⠞⠉⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠈⠀⠀⠀⠀⠐⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠠⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠄⠀⠀⠀⣀⣄⢀⣀⣴⣤⣄⣀⣠⣤⣀
⠀⠀⠀⠀⠀⢀⣠⣴⣆⣀⣠⣤⡀⠀⢻⣿⡿⠃⢀⣀⡀⠀⠀⠀⢾⣿⣿⡟⠀⠀⢀⣸⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣴⣶⣿⢿⠋⠀⣠⣶⣤⡄⠈⣿⡀⠀⠘⢿⠟⠻⠀⣿⠳⠀⣻⠛⢛⠂⢀
⠀⠀⠀⠀⠐⢻⠙⡵⢿⣿⢇⠻⣿⠟⡻⣿⠙⢻⠋⡀⠐⢿⣿⣿⠛⠁⣿⣿⣿⣷⡦⠀⠹⣴⣿⣿⠠⣿⣿⣾⡿⢶⣿⠿
⠀⠀⠀⠀⠀⠀⠱⠈⢈⡋⠢⡑⠸⣷⣃⣀⠀⡀⢰⠅⢀⠀⢀⣿⡄⢀⣹⣭⣛⠫⡀⠀⠀⠸⣬⢇⠀⣨⢯⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⠂⢽⡿⣿⡖⠀⠎⠀⠀⠀⠻⡿⠗⣿⣿⣿⡿⠃⠈⢄⠀⠀⢸⢀⠶⡁⡎⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⢻⢻⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⢹⠃⠀⠀⠀⠀⠑⠄⣸⠃⠆⠘⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⣿⠇⠀⠀⣀⣀⠀⠀⠘⣠⠗⠁⠀⠀⠀⠀⠀⠀⢘⡏⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢹⠀⠀⢤⣿⡿⠀⣿⣿⡿⣷⣶⠆⠀⠀⠀⠀⠀⢸⡇⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢸⠀⠀⠀⠈⢆⠀⠀⢹⠀⢸⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠈⠢⣀⠎⡀⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠰⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⡀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠐⠶⠋⠁⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⣉⣉⣥⣀⣈⡉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣹⡧⢞⣋⣭⠤⢤⣤⣈⠙⠳⢤⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣰⣯⠖⠋⠁⠀⠀⠀⠀⠉⠓⢦⠀⢻⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣼⡿⠁⠀⠀⠠⢤⠀⠀⠀⠀⠀⠈⢷⠀⢿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠁⠀⠀⢸⣿⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⠶⠀⠀⣀⠙⠆⠀⢸⠇⡾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣿⠀⠀⠀⠘⣿⡀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢀⣞⡼⢁⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠳⣄⡀⠀⢻⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⡵⠋⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠈⠙⠲⢼⣇⣀⠀⠀⠀⠀⠙⣷⠦⣤⣤⣤⣤⣶⣿⠿⠟⠉⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠚⠓⠚⠛⠋⠉⠁⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢷⡀⠀⠉⠛⠲⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣀⣈⣳⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣟⣒⠛⠛⠛⠛⠉⠉⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠉⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⣤⡼⠃
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢲⣦⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⣯⠉⠉⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠖⠒⠚⠛⠋⢉⣡⠞⠉
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⡀⠀⠀⣀⣀⣀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⢀⡘⡀⠀⠀⠀⢃⡇⡌⠀⠀⠀⠀⠀⠀⡀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣆⢠⠀⠀⠀⠠⡜⣡⠁⢰⠐⣮⢮⠂⠀⠀⠎⢀⢂⡬⢞⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⠌⠋⡾⡇⢀⢠⢰⡜⢋⠘⢸⡙⣴⢃⠌⢤⡋⢀⢶⠌⣖⠕⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⣦⢙⡰⠗⡌⢈⢬⡹⡿⠐⡘⣣⡶⢁⢘⣬⠄⣾⢐⣟⡡⢂⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠠⡐⣄⠳⣍⣶⠉⢾⢇⡍⡸⢇⣼⠇⠿⣨⢅⠺⣯⡅⣿⠸⢟⡡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡓⣛⢱⡌⡈⡖⢶⡝⣴⠁⣾⡇⣿⣮⢛⣤⡜⠛⢸⢏⣫⢀⢵⡿⡫⠊⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢠⡉⠲⣚⡷⣠⢺⣍⠿⢀⠈⢰⣌⢱⣿⠇⠖⣼⡆⠿⠃⣫⣴⠞⣵⡵⠆⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠠⡠⣂⡀⡑⢆⠺⠾⣧⢙⢃⣻⠁⡻⢣⣿⡇⠚⣿⡧⢋⡀⣶⡙⣵⡾⠁⠟⢣⡆⠾⠃⣠⢛⡼⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣈⠒⢮⣞⣧⡙⢳⡺⡇⣉⢀⢻⣷⡝⣁⢠⣌⢵⣿⠁⣿⡧⣛⢱⠞⣼⡧⠿⠋⢾⣸⣞⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠱⢾⢽⡎⠻⡇⢿⡎⠃⣝⢱⣿⠈⣿⠎⡁⣶⡭⣾⢏⢠⣷⢩⡾⠋⣚⣿⠍⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⠛⢷⣇⣦⠹⣷⢁⢸⢠⡾⡀⠻⣃⢡⢋⡸⣻⡬⢘⣧⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⡐⢶⣿⠐⠠⡿⠘⡈⡇⡇⣾⠃⡏⢼⠟⢋⣸⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡍⢿⠐⡜⡄⠃⠃⠁⠘⢰⢁⡖⢡⠊⠀⠀⠀⠒⠲⢶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⢡⢀⠰⢸⠀⠀⠘⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡆⠌⠀⢸⠀⠀⡄⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣴⣼⣤⣤⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⠻⠻⠛⠟⡟⠛⡹⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠸⠀⠀⡀⠀⠇⠇⠇⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⡆⠀⡄⡇⠀⠀⠃⠂⢁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠁⠂⡇⡇⡇⠀⢸⢸⢰⠘⡈⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠠⠰⠂
⠀⠀⠀⠀⠀⠀⢴⡁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠆⠺⡆⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⣰⣧⡄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣸⠃⣴⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⣎⠙⠜⢐⠀⢔⣠⣤
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣤⣄⣀⠀⠀⠺⠾⡿⠛⠁⢠⡆⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⢄⢠⣷⣬⣶⠎⠉⡀⠈⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⢠⣿⡿⠃⠓⠾⡏⠁⠶⠈⢉⣤⠁⠀⢠⡾⠇⠀⠀⠀⠀⠀⣰⠆⡟⠁⠀⠀⣠⣧⣤⡄⡄⠰⣯⣼⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣣⡆⠤⠘⠋⠀⠁⠀⠺⣷⠇⡘⠛⠲⢾⡀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠻⠆⠂⠀⠀⣸⢋⣬⢠
⠀⠀⠀⠈⢀⠀⠀⠀⠰⠟⢀⣵⣆⠀⣈⣠⣴⡐⠃⢸⠀⠀⠀⠶⣸⠁⠀⠃⠀⠀⢀⡔⠲⠀⠀⠀⠀⠀⠀⢢⠀⠀⢠⡸⠇⣰⠿⣸⣿⣩⣀
⠀⠀⢠⠀⠀⡀⠀⣤⠆⢀⣿⠁⠀⠀⢿⣿⣿⣅⠀⠈⢠⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⣨⡁⣮⣶⣄⣶⡆⢿⣲⠀⠊⠀⣴⠃⣠⣭⣽⣿⣯
⠀⠀⠀⡝⠻⣟⡀⠁⢈⣰⡆⢲⣶⢀⣾⣿⠏⠰⠀⢰⡇⠈⢷⡀⠀⠀⠂⠀⠀⡧⠀⢘⣿⣦⣿⢿⣿⣷⣄⠀⠽⠹⠇⡒⠁⣀⣌⠉⣿⣾⣿
⠀⠀⠀⠀⠀⠙⠂⣴⡾⢃⠟⠀⣹⠾⣿⠛⠄⠐⡄⢸⠀⠀⠀⢿⡄⢠⡄⠀⠀⢂⠀⠉⣹⣿⣿⣿⢋⣿⣿⣷⡄⠀⣰⢳⡦⠛⠁⠈⢹⡇⠐
⠄⡓⢠⠄⠀⠀⣼⣟⠀⠸⠁⠀⠁⠲⣛⡀⢀⣀⣤⣿⡀⠀⣤⣶⡄⢻⢣⣾⠀⠈⢁⣼⣿⣿⣿⣿⠈⢸⢿⡏⣷⣴⣯⡟⠁⠀⡃⠀⣠⣶⣷
⠀⠀⣴⡶⢀⡀⠈⣹⡖⠒⣤⡠⠴⢻⠿⢿⣾⣷⣿⣿⠀⠀⠈⢑⣷⣨⠊⣿⡀⠘⠛⣷⣍⢻⡿⠋⣾⡿⠀⢀⣼⢛⣿⣟⣶⣿⣷⣿⣟⣉⣽
⠀⠀⠘⠕⢈⠉⢛⣿⡇⣼⣿⠃⢠⣿⠀⠀⠈⢻⠉⣿⠀⠀⠀⠈⣫⡴⠘⠛⣿⠆⠀⡅⠀⠀⠀⠀⠚⠁⠀⢚⣴⢿⣽⣾⣿⣿⣿⣿⣿⣽⡿