Ornamentation Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⡈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣰⢯⡽⣆⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠄⣸⠃⣸⣇⠘⣆⠠⡹
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣶⠤⣀⠀⠀⠀⢸⡄⢛⡴⡒⠚⢢⡛⢠⡇⠀⠀⠀⣀⠤⣶⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⢿⡛⢉⣉⣩⣤⣬⣑⡪⢷⣄⠀⠀⢿⣸⢘⠉⠉⡃⣇⡿⠀⠀⣠⡾⢕⣊⣥⣤⣍⣉⡉⢛⡿⠁
⠀⠀⠀⠀⠀⠈⣿⡈⢧⠲⣤⣤⣨⠽⠶⢝⢦⠀⠈⢳⣆⢙⡛⣰⡞⠁⠀⡴⡫⠶⠽⣉⣤⡤⠖⡼⢁⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣇⠈⢷⣐⢳⠃⡞⡉⢢⠙⣷⠀⠀⠹⡜⢧⠏⠀⢀⣾⠋⡜⢉⢳⠘⡞⣂⡾⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠛⢍⣢⣝⡙⢦⡑⠒⠋⠰⢪⢷⡀⠀⢻⡟⠀⢀⡾⡕⠆⠑⠖⢊⡴⢋⣩⣔⡩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠓⠛⠓⠛⠦⠈⠁⠴⠛⠚⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⡤⣤⡤⣤⠖⢀⡀⠲⣤⢤⣤⢤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣊⠝⣪⣡⠞⡡⠴⢄⠰⢝⡾⠁⠀⣼⣧⠀⠈⢷⡫⠆⡠⠦⢌⠳⣬⣕⠫⣑⣦
⠀⠀⠀⠀⠀⠀⢸⡟⢠⡞⠩⡜⡄⢧⣁⠜⣠⡿⠀⠀⣰⢳⡞⣆⠀⠀⢿⣄⠣⣈⡴⢠⢣⠍⢳⡄⢻⡇
⠀⠀⠀⠀⠀⢀⣿⢁⡞⠴⠚⠛⣉⣒⠶⣪⠞⠀⢀⡼⠋⡬⣥⡹⢧⡀⠀⠳⣕⠶⣒⣉⠛⠓⠦⢳⡈⣿⡀
⠀⠀⠀⠀⢀⣾⣥⣈⣉⣉⠛⢋⡩⢕⡾⠋⠀⠀⣾⢹⠨⣀⣀⠅⡏⣷⠀⠀⠙⢷⡢⢍⡉⠉⣉⣉⣡⣬⣷⡀
⠀⠀⠀⠀⠈⠁⠈⠉⠉⠙⠛⠿⠒⠁⠀⠀⠀⢸⠃⣬⠳⡤⢤⠞⣥⠘⡇⠀⠀⠀⠈⠓⠿⠛⠋⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠹⡆⢹⡏⢰⠏⣘⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠹⣞⣳⠏⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡈⢁⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠔⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠞⢁⠒⠌⠃⠀⡴⠒⡆⠀⠀⠘⠤⣉⣀⡀⠀⠀⡀⡀⠀⠀⣀⣀⠤⢀⣀⣀⠄⠀⠸⡀⠋⡱⠀⡗
⠀⠀⠀⠀⠀⠀⡀⠓⠀⠁⠀⠑⡤⠁⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⡰⠫⡀⠀⠀⠀⠀⠀⠙⢲⠤⠀⢉⣤⠚⠁⠀⢀⠄⠀⣦
⠀⢰⠏⢉⡳⠀⠈⡡⠖⠂⠚⠀⠀⠀⠀⠀⣼⢠⠖⠀⠄⠀⠀⠀⠀⡇⠀⡧⠀⠀⠀⠔⢉⢳⠀⢧⠀⠀⠀⠉⠐⠲⠧⠔⠒⠁⠄⠀⢄
⠀⠈⠳⠤⠤⠰⠊⣀⢂⠀⠀⠀⢀⢀⠀⢠⠙⢎⣂⣁⠆⠀⠀⠀⠀⠙⠞⠁⠀⠀⠀⠣⣈⣁⡤⠋⢆⠀⠌⡢⠀⠀⠰⠠⢀⣀⣐⠣⠚
⠀⠀⠀⠀⠀⠀⠐⣶⠁⡀⠀⠀⠘⠦⠤⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⢸⡀⠀⠈
⠀⠀⠀⠀⠀⠙⠲⣿⡏⠁⠀⠀⠀⠀⡲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋
⠀⠀⠀⠀⣰⠄⠸⠀⠘⠂⠀⠀⠀⢠⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠀⠀⠀⠀⢀⢀⣤⠄⠀⠀⠀⢨⣅
⠀⠀⠀⢰⣝⠳⠆⠀⠀⠀⢘⠀⠀⠹⣿⡿⠃⠀⠀⡀⡀⠀⠀⠠⡆⢼⢦⠠⠀⠀⠀⠀⠀⡅⠂⠀⢀⣴⡾⢿⡦⢄⠀⠀⢘⡸⣗⠁
⠀⠀⠀⠀⢹⡟⠀⠀⡠⠲⠿⠗⢠⡀⠀⠀⠀⠀⠈⡙⠂⠀⠘⢪⣅⣁⡠⠖⡒⠂⠀⠀⠉⠀⠀⠀⢸⡉⣷⣎⣉⣿⠂⠀⠈
⠀⠀⠀⠐⠘⠁⠀⢸⢦⡵⣶⣚⠿⣧⠀⠀⠀⠀⢠⠧⡀⠀⠐⠠⢏⣼⣕⢿⡌⠂⠀⠀⠀⣀⠀⠀⠀⠻⠧⣼⠿⠎⠀⠀⠀⠟⠳
⠀⠀⠀⠈⠉⠈⠀⠸⣿⡟⠶⠿⣶⠟⠀⠀⠀⠀⢸⡫⠆⠀⠀⠐⠋⠁⠜⠀⠃⠀⠀⣀⣘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡚⠳⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⢐⡉⠄⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⡾⢵⣿⣴⣗⣼⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠂⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⣧⡒⠤⠤⠤⠤⣚⠃⠀⠀⠀⠀⠀⠘⢽⣟⣯⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣉⣉⣘⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⣥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⢀
⠀⠀⠙⠃⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠈⠛⠃⠰⠆⠠⣤⠄⢀⡀⢀⣤⠀⢠⡄⠀⠴⠆⠀⠛⠀⠀⠀⠙⠃⢤⡀⢀⡀⠀⠀⠀⣠⣤⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⣀⡰⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠟⠻⠟⣛⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣉⣫⣁⣡⣤⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⡉⠛⠛⠛⠿⠋⣉⡕⡞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⠿⠛⢋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠜⢦⡲⢔⠯⠁⠃⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⣶⣶⠟⠁⠀⠀⠀⠐⠛⠘⡀
⠀⠀⠀⠀⢀⣴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢠⣦⣌⣀⣉⣠⡥⠶⠃
⠀⠀⢀⠀⠈⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠩⠁⠤⠁⠂⢈⣤⠆
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠷⠶⠲⠶⠞⢋⢡⠄
⠀⢐⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢿⡿⠿⡟⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⠁⠐
⠀⠀⠁⣀⠀⠀⢀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢦⣀⣠⡀⢀⣄⣠⣶⠂
⠀⠀⠀⠀⠑⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⡀⢀
⠀⠀⠀⠀⠀⣀⣀⠀⡀⢤⠄⢄⠀⢄⠠⠠⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⣤⠔⠂⠛⠁⡉⠊⡁⠂⠀⠈⠀⠈⠈⠙⠛⠠⠒⠤⣀⣀
⠀⠀⠸⠉⠀⡑⠀⠑⢄⠀⠀⠠⡁⠄⠀⠀⠀⠠⡀⠈⠢⡑⠀⢀⠘⠀⠇⠐⠈⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠰⠄⠐⠈⠠⠀⠢⡀⠤⠀⢄⠀⠀⠢⡀⢀⠀⠢⡀⠀⠂⡀⢁⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⢀⡀⢀⠄⡀⠀⢀⡤⠀⠖⠠⠀⠀⠀⠀⠀⠀⡠
⠀⠀⢘⠀⠀⠀⠑⢤⠃⠀⠀⠀⠈⠻⠄⡑⢈⠢⣁⢀⠀⠀⠀⠈⠢⣁⠀⠀⢗⠀⠀⠀⠀⣢⠐⠁⠀⠀⠈⢂⡀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⢸⡃⠀⠀⠀⠂⠀⢸⣶⣤⡀⠀⠱⠊⠀⠀⠈⠈⠳⢄⠀⠀⠑⢬⠀⠀⠥⢀⠄⠀⠀⠅⠀⠀⢰⣦⣄⠈⠇⢀⣠⣴⡶⠀⠀⢘⡂⠐
⠀⠀⠀⡄⠀⠀⠀⠑⡀⠀⠙⢿⣷⣄⢀⣴⣾⡿⠋⠀⠀⡆⠑⢌⠂⡄⢸⡄⠈⠣⡄⠀⠈⠸⣄⠀⠀⠻⣿⣧⣠⣾⡿⠋⠀⠀⠀⡼
⠀⠀⠀⠓⠀⠀⠀⠀⠀⠢⡀⠀⠉⣻⡟⠋⠁⠀⠀⣠⠜⢌⠢⡀⠼⠂⢾⣿⢆⠄⠘⠒⠲⠤⡎⠕⠶⠆⠀⠙⣿⣦⡀⠀⡀⠄⠒
⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠀⠁⣴⣿⠇⠀⠀⠓⠉⢠⣠⣠⡴⠚⠀⠐⠈⣁⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡌⠀⠙⢿⣷⠀⠈⡖⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢁⠀⠀⠀⠀⢐⠀⠀⣿⠏⠀⠀⣹⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣄⡀⠀⠉⠀⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠡⣀⠀⠀⠀⠤⡁⠀⢡⠀⠀⠀⠀⠀⢸⠀⢀⠘⠁⠄⠠⠇⠀⠀⠀⠀⠀⢸⡇⠈⠑⠠⠒⠉⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠉⠂⠁⠈⢀⡟⠀⠀⠀⠀⠀⠀⢃⠰⣾⣿⢖⠄⢀⡠⠀⠀⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⠖⠁⡆⠀⠀⠐⠒⠠⢄⠀⠁⠤⢄⠀⡠⢊⡄⠀⠀⠀⠀⠐⠈⠢⡀⠀⠀⠀⠀⠀⢀⡤
⡀⠂⠁⠀⣀⣀⡀⠀⠀⠀⠉⠀⠉⠈⣁⣤⣶⣄⠀⣀⠀⠀⠀⣼⣆⠰⢡⣶⡆⢲⢰⣿⡮⢢⣄⣠⠐⢥⣾⣦⣍⡒⠢⠶⠀⠊⠁⠀⠈⣁⣀⡀
⠀⠀⠠⠀⡉⣉⠀⢀⠀⠀⠀⠠⢤⠍⡙⠻⠟⢩⠂⠈⠉⠁⠈⣿⢇⠜⢀⠉⡄⠉⢌⠋⠀⠀⠀⠀⠀⠀⠙⠛⠉⣁⠀⠀⠀⢀⡀⠠⣄⠉⠉
⠀⠀⠀⠀⠀⢁⠔⠁⠀⠀⠀⠀⠀⠀⠈⠐⡄⠀⠀⠀⠀⠐⠂⠐⠁⠔⣤⣶⡜⡄⠀⠙⠄⠀⠀⠀⠀⠀⡀⠐⠉⠈⠀⠀⠀⠀⠉⠑⢤⠢
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡠⠀⠒⠠⢀⠀⠀⢦⠀⠀⠀⠀⠀⢀⠞⠐⠉⠛⡡⠃⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆
⠀⠀⠀⡠⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠁⡀⢸⠁⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⢀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠠⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⣶⡀⠀⣊⠜⠀⠀⠠⡄⣀⠀⠀⠀⡀⢘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠎⠁⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡀⠈⠿⣿⡄⠀⠀⠒⠀⠢⠄⠁⠋⠳⠀⢠⣾⣦⢀⡥⠟⠛⠛⠒⢂⣄⠀⠁⠀⣠⣴⡿⠀⠀⢰⠄⠀⠀⠀⠀⠀⠂
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⣾⠿⣶⣦⡀⠀⠀⠈⢀⠀⠀⠈⡈⡿⡱⠏⠀⠀⠀⢀⠊⠉⠀⠁⣀⣼⡿⠛⠀⠀⡔⠃⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠄⠀⠀⠀⠀⣠⠀⠀⢀⣴⣿⠿⠃⠀⠈⠛⠻⠆⠀⠀⢠⠄⠀⠊⡃⢰⠂⠀⠀⠀⢠⠃⠀⢀⣴⣿⠟⠙⣿⣦⡀⠉⠀⢄⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠓⠀⠀⠀⠀⠐⡀⠀⠘⠉⠀⠀⠀⠐⠢⢀⠀⠀⢀⡔⠁⠔⠀⠘⠁⠸⠀⠀⠀⠀⠀⡀⠀⠈⠉⠁⠀⡀⠙⢿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⠀⠀⠀⠀⠊⠐⠠⠄⠀⢠⠄⠂⠀⠀⢊⠔⠡⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠠⠘⠁⠀⠀⠉⠁⠀⠀⡑⠀⠀⠀⠀⢈⡃
⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢦⠀⡀⣠⠴⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠀⠁⠀⠀⠙⠀⠀⠁⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠆⠀⠀⡄⢀⠀⣀⢀⡀⢀⢀⡠⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠙⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠠⢀⠀⡀⣀⠀⠀⠀⠠⠠⠀⠾
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡘⢡
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣛⡹⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣬⠑⠀⠀⣠⣿⣼⣇
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⢠⠿⠿⠁⠀⠀⡀⠀⠀⠀⢀⡡⠤⠀⠀⠀⠀⠐⣤⠇⠸⢿⠀⠂⠔⣿⣟⡠⠞⣷
⠀⠀⠀⠀⠀⠀⢸⡰⡆⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⣳⡜⠀⠀⢘⡁⢠⡦⠀⡀⠀⠸⡆⡾⠀⠣⠈⠠⣼⣿⠟⠁⠀⣠⡇
⠀⠀⠀⠀⠀⣴⡾⠀⠀⠀⡀⠀⠀⠚⡉⠀⠀⠤⡄⠀⡶⢰⡖⣠⡜⠃⠀⠁⠘⢇⣠⡴⠇⠽⢤⣀⠀⡇⠿⢃⣤⠶⠋⠁⣿⠀⢸⡀
⠀⠀⠠⠁⣿⣿⠟⢉⡁⢈⣯⡠⠰⡿⠇⠀⢀⣶⡇⢠⣧⣼⡅⠘⠀⣤⣼⡟⣴⣿⣁⣀⣀⣀⣤⡬⠷⠁⢴⠛⣵⠀⣀⠴⠀⢀⣎⢸⡄
⠀⠀⣇⢰⣏⡩⣶⢁⠀⡂⠀⡱⣤⠁⠸⠿⠤⠙⠁⡞⠁⠈⣧⠀⠀⠏⠙⠃⣾⣅⡀⣀⡀⣀⡄⡠⣾⣷⠈⢆⣿⠊⢉⠄⠀⢘⡁⢀⣙
⠀⠀⠸⡢⣿⣧⡜⢂⣉⠔⣤⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⠀⠀⢻⣯⣽⣯⣼⣧⠯⠻⢿⠇⠀⠀⠡⣔⠉⠀⠀⣫⡀⢀⣈⣇
⠀⠀⠀⠘⠻⢿⡿⠧⠁⠈⠔⠁⠀⠀⢀⣼⣤⣀⣀⠀⠀⠀⠀⡟⢃⠀⠀⢀⠀⠙⠶⣶⠶⠖⢒⡾⠋⠀⠀⠀⠀⠀⠀⣠⣾⣯⣥⣤⣤⣭⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣏⠉⢄⠀⠀⢰⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠂⠘⣧⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠌⡌⠐⠀⠆⠱⠈⠆⡆⠀⢘⠀⠠⠋⠰⠈⠀⠘⢠⠁⠚⠛⢠⢰⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡀⠄⠀⠀⠀⠀⠠⠂⠉⠙⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣰⡤⣰⣠⣦⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⢀⡠⠔⠀⠀⠀⠀⠐⠀⠀⠤⠉⠀⠀⠀⠀⠠⢀⡀⢀⡠⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢀⠴⢄⡀
⠀⠀⠀⠀⠃⠀⠅⠀⠈⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠈⠀⠑⠀⠌⠆
⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠁⠀⠄⠀⠀⠀⠀⠠⢀⠀⢁⡊
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠕⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡄
⠀⠀⠀⠀⢂⡀⠐⠀⣀⠀⠀⠀⠀⢀⡀⠍⠀⠀⠀⠀⠀⠀⠐⠉⠂⠀⠀⠈⢵
⠀⠀⠀⠐⠀⡀⠖⠂⡠⠀⠀⠀⠀⢀⠍⠲⢮⠀⠀⠀⠀⠀⠀⠀⠠⠄⡂⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠥⠴⠤⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠦⠑⠀⠀⠀⠀⠀⠀⠠⠤⠕⠋

⠀⠀⠀⠀⠀⠀⠶⠄⡀⠀⠀⠀⠀⠀⠀⠠⢤⣦⡀⠀⠀⠀⠀⠀⠀⢤⣦⣀⠀⠀⠀⠀⠀⡀⠰⠛⠢⣄
⠀⠀⠀⠀⡈⠀⠀⢀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠃⠊⠤⠱⠴⠀⠀⠀⠀⠀⡀⠀⡀⠀⡄
⠀⠀⠀⠀⠁⠈⠈⠁⡌⠄⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⢉⡠⡀⡙⢊⣈⠁⠀⠀⠀⡀⠄⠀⠀⠬⠆
⠀⠀⠀⠀⠀⠠⠬⠔⠀⠀⠀⠀⠀⠀⠈⠐⠚⠋⠁⠀⠀⠀⠀⠀⠐⠲⠶⠒⠉⠀⠀⠀⠀⠑⠢⠤⠒

⠀⠀⠀⠀⠀⢠⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂
⠀⠀⠀⣴⣤⡴⠱⣿⣿⣻⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠘⢦⣤⣆
⠀⠀⢸⣷⣾⣿⣿⣿⠿⠿⣿⣻⣾⡿⣻⣽⡯⠹⣿⣦⣭⣭⣉⣩⡉⢩⣉⣩⣭⣬⣬⣿⠍⣿⣯⡛⢿⣷⣿⡿⠿⠿⣿⣿⣿⣷⣿⠆
⠀⠀⢾⡟⠛⠋⠀⠀⠀⢰⣟⣿⣿⣷⣿⢽⡋⠁⠈⠉⠙⠛⠿⣿⣷⣾⣿⠟⠛⠋⠉⠀⠈⢹⡎⣿⣾⣿⣿⣿⡀⠀⠀⠀⠛⠛⣿⡇
⠀⠀⢸⢿⣗⠀⠀⠀⠀⢾⣿⢻⣿⣿⣿⢿⣝⡲⢤⣀⡀⠀⢀⢼⡏⣿⣷⡀⠀⢀⣠⡴⣞⣯⣾⣷⣿⣿⢯⣿⡷⠀⠀⠀⠀⣾⣿⡅
⠀⠀⢸⣿⣽⢿⣆⠀⠀⠉⠻⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣽⠟⢹⠞⢷⣭⣿⣿⣿⢿⣿⣿⣿⣵⣿⣯⡾⠟⠉⠀⠀⣷⡿⣫⣿⠃
⠀⠀⠀⣿⣿⣿⣭⣛⡷⣤⣤⣬⣿⣿⡿⣿⣿⣿⣿⣿⣾⣟⣷⣝⣷⣞⣷⣾⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣤⣤⣤⣿⣛⣵⣿⣿⡿
⠀⠀⠀⠸⡟⣟⣯⣽⣷⣾⠛⢻⣟⠛⣿⣾⣿⣯⣻⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣟⠛⣻⡟⢻⣷⣶⣯⣽⣛⢿⠇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⢠⣇⠿⢟⣹⣿⣿⡏⣛⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡋⣽⣿⣿⣏⡿⠿⣿⡀⠰⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠈⢿⣿⣿⣿⠋⠀⢰⡿⢿⣿⣥⣿⣿⡇⢮⣝⣿⣿⣿⣇⣸⣿⢿⣿⣫⡴⢻⣿⡿⣼⣿⡿⢻⡆⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⡟⠃⠀⡸⠞⢿⣼⣹⡇⢸⣿⡇⠶⢬⣿⣷⢻⡟⣿⣯⣿⣿⠵⠶⣸⣿⠃⣹⣿⣷⡟⠷⣆⠀⠘⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢷⣾⠓⠝⣷⣿⣿⣯⣷⣏⣽⢷⠲⠶⣿⣿⣿⣿⣿⢹⣿⡷⠶⢶⡿⣇⣻⣿⣹⣿⣷⣿⠩⢻⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣟⣵⣿⣾⣿⣿⣧⡞⢩⢩⣽⣿⢿⣿⣿⡼⣿⣭⢉⡍⣶⣿⣿⣿⣯⣿⣿⣻⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⡟⣽⣯⣾⣿⣷⣿⣧⠿⣫⡿⣣⣽⣷⣝⢿⣼⣷⣿⣿⣧⡽⣭⢿⣿⡟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣽⡞⣟⣉⠛⠻⢻⣿⣿⢿⢗⣺⠿⣿⣿⡟⠟⠋⣙⣿⣹⣣⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣹⡾⣧⣽⣯⡀⣴⣿⢿⡯⡙⢮⠕⣩⢿⡟⣿⣦⢀⣽⣧⣽⣿⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣻⣿⣶⣤⣿⠇⣼⣷⡮⢝⡫⣷⣿⡆⠹⣿⣤⣾⣿⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⣿⠏⠀⣼⣿⣯⣺⣺⣽⣿⡇⠀⠹⡿⣯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡀⠀⢸⣿⣏⣺⣒⣿⣿⡄⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢼⡿⣟⡺⢗⣿⣿⣆⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣏⡸⢇⣿⢿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣏⣲⣆⣿⡾⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⠼⢽⣿⣧⠘
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣿⣿⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣵⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢴⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⢰⣤⠤⢆⣄⣦⠀⠀⠀⠀⡀⣤⡶⠖⢛⠉⠉⠈⢐⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠅⢠⢋⣐⠶⣂⢺⣿⠏⠀⠀⠐⡩⠚⠁⠀⠀⠀⣀⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⡰⠟⢬⡷⠿⠃⣤⣦⡀⡈⢠⠎⠀⠄⠐⠂⠀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣢⣾⡿⢹⣿⠇⠙⡻⠏⣰⠁⠐⠲⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⡀⢖⡠⠀⠀⠀⠄⠐⢊⣿⠀⠀⠙⠀⡘⠀⢠⠃⠀⠀⠀⠀⠠⢂⡄⣧⡀
⠀⠀⠀⠀⠀⠐⠀⡠⢆⠳⠐⠌⠙⠧⡀⠀⠌⠁⠺⢻⡆⠀⠀⠰⠀⠀⡎⠀⠀⠀⣠⠖⢰⣦⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠃⠠⠀⢈⠀⠀⠀⢐⣀⣡⠒⣄⠙⡐⢚⣿⣦⣀⡆⠀⢰⣀⣠⠔⣪⣴⡶⠘⠻⡿
⠀⠀⠀⢰⣶⡄⠀⠧⡀⠀⠀⠉⠀⠀⠀⠳⠞⠛⠙⠢⠉⢿⣮⢛⣀⢵⠇⣨⣷⣮⡑⢰⣾⣇⠠⠐⠀⠂⢄
⠠⠾⣿⢿⣉⣁⠈⠄⠐⠁⡐⣂⣀⡄⠀⠀⠀⠀⠀⠀⠸⠿⢍⣨⡻⢹⣄⠙⣿⣻⣿⣷⠙⠛⠁⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠿⠿⣿⣷⠀⠀⠀⢠⢛⠃⢚⠃⠀⠂⠀⡀⠀⠀⠀⠝⠛⠛⠹⣷⠐⣿⣿⢻⠿⠀⠀⢠⣄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠙⠁⢀⣠⢠⠅⢾⡅⡭⠙⠀⠀⠀⠈⠂⠀⢀⠀⠀⠀⠀⠏⡦⠉⡄⠜⠀⠀⠀⢸⡿⢂⣄⠀⣠⣾⠆
⠀⠀⠀⠀⡀⢠⣐⣘⡾⠈⠀⠀⠘⠈⠻⠀⠀⠀⣀⡀⠀⢸⠀⠀⠀⠀⠸⡀⡊⡰⠁⠀⠀⣠⣴⡆⢿⡿⢐⠿⠟
⠀⠀⠀⠀⠐⠐⠀⠀⢠⠑⠺⡤⠀⠄⠃⠘⠀⠀⡄⠁⠀⠀⠀⠀⡀⠀⠂⣳⡱⣈⠂⠄⣌⣟⠫⠠⣢⣤⣁
⠀⠀⠀⠀⠀⠀⠀⢂⢀⠈⠀⠀⢀⠁⠧⢀⡄⠀⠠⠀⠀⠂⠐⠁⢀⠀⠨⠈⣄⠈⠲⠘⠻⣿⡷⠄⠻⠿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠈⢌⠀⣀⢀⠀⢀⠀⢤⡠⠀⠀⠀⢐⡀⠔⠀⡁⠂⣠⣴⣾⣶⢔⣠⡂⢀⠀⢸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠨⢄⠀⠐⠀⠀⠈⠛⠋⣡⠸⣿⡷⢰⣦⡌⣉⣭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⠰⠀⠘⠀⠀⠠⠐⠀⠀⣼⣿⠃⠄⠃⢺⣿⣧⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠐⢀⣴⣮⠟⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠀⠁⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠐⠄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠤⠔⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠲⡀⠀⠀⡔⠙⠀⠀⠐⠋⢦⠀⠀⠀⠔⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣀⠂⠰⡤⠀⠀⣀⠀⡀⠀⠀⢠⠖⠔⡠⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣮⠀⢁⡀⠀⠘⠞⠟⠗⠃⠀⠀⠈⠀⡴⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⡃⠀⠀⠀⢯⣢⣤⡀⠆⢀⣠⣞⡝⠀⠀⠀⠜⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⡬⠈⠣⠀⠐⠿⠟⣹⣼⡌⠻⠿⠀⠀⠜⠁⣤⢈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠣⠀⠀⢠⣀⡑⠂⢟⠛⡿⠐⢈⣀⡄⠀⠀⠜⢨⣍⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⢀⣀⠉⠧⠼⠘⠤⠞⠁⣀⡀⣀⢠⣾⣮⠱⣾⡆⢶⠎⣭⠕⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢭⡤⢆⠐⠂⠀⠀⠀⠐⠊⠀⠈⢡⣶⠙⠋⣤⣄⢰⡦⠰⠆⡮⠡⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣄⠀⠀⠀⠀⠀⠀⢫⠈⠀⠘⠀⠂⠈⠁⠀⠾⠀⢠⡶⣦⢙⡫⠤⣤⡛⠛⠿⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠒⢢⡀⠀⠀⠀⢈⡣⠀⠀⠀⠀⠁⠀⠛⠀⢶⡦⢩⣷⡭⣞⣷⢈⣭⡓⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⣀⡀⠀⠉⠚⠀⣀⠀⣋⠁⠀⠀⠀⢡⠀⣈⠁⠾⠆⠓⢈⣍⢁⣭⡁⠸⠿⢃⣤⡈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠐⠀⠀⣠⣄⣭⡄⠀⠀⠂⢘⡇⠸⢧⡀⠀⠀⠀⠀⢣⠈⠀⠀⢠⣶⡜⠛⠙⠛⠑⠿⠃⠘⢛⡃⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⡀⠄⠉⠀⠁⠄⢀⢠⡖⠘⢷⡻⠌⠉⠀⠀⠀⠀⠀⢣⠀⢠⣶⡍⢀⡒⢀⠀⠀⠀⠿⠃⠻⠿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣂⠀⠠⠀⣠⠶⠀⠀⠀⠀⣿⠀⠀⢠⣀⠀⠀⠀⠀⠱⢠⡍⢠⠈⣥⠈⠱⠖⠻⠗⠰⣟⡆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠤⠄⠀⣀⡀⠀⠀⠈⠧⣑⠦⠅⠀⠀⢶⠞⣀⠐⠳⠞⢠⠀⠿⢢⣶⡄⢾⡳⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠫⠅⠠⠍⠀⠀⠰⠈⢙⠀⢰⣦⠀⡠⡅⢠⡠⣄⣀⣮⡷⠒⣀⠀⠈⠀⠹⠷⢭⡾⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⣤⡀⠁⢄⠀⠸⢧⠘⠧⠸⢧⠀⢀⠛⠲⠵⠶⢂⢬⡉⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣄⢀⠛⣰⣆⡂⡀⠐⢰⠄⣤⠀⣀⣁⢨⡷⠴⠶⠶⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⠀⢸⣦⠉⢐⠁⠀⠛⠁⣿⠁⠋⠁⠀⣈⡴⠋⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣘⠄⣂⣐⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢮⣵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⣤⡙⠲⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣾⣶⣾⣿⣿⣿⣦⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣠⠞⠋⣠⣿⣿⣿⣝⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠛⢥⢀⣴⣿⣅⡽⢿⣭⣻⣛⣦⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣥⣬⣹⡿⡟⣋⣥⣾⣁⠾⠟⠋⢀⡷⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠛⣹⠟⠋⣠⣶⣷⣤⣀⣩⣷⣾⣿⣥⣴⢋⣀⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣤⠿⢻⡈⢁⢀⣰⣿⣿⣧⣄⣡⣱⣶⣤⡜⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣍⣀⡴⠂⢀⣤⣷⣼⣿⣿⣿⣿⣿⣏⠀⣹⣿⠛⡟⢯⣷⣦⣴⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣥⢶⣿⣿⣿⡿⠿⣿⣿⡟⣿⣷⣮⣄⣈⡉⠙⢲⡬⠁⠱⠚⣂⠲⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⣀⢨⠷⠛⠁⢀⣿⡏⢙⣟⣉⣀⣉⡻⣿⡭⠞⢫⣦⣶⣤⡾⢫⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢘⢉⡉⠀⠙⣆⠀⣴⡿⠛⢋⣩⡉⠻⣷⣤⡉⠁⠙⠷⣦⣠⣌⠉⠛⡛⢋⣋⣠⣤⣿
⠀⠀⠀⠀⡟⣸⣿⣶⠆⠀⠛⠾⢻⣿⢂⣵⡿⠱⢏⣀⣴⡿⢻⣷⡀⠈⠻⣿⣀⣀⢰⠋⢻⠻⣿⣶⣿⡾⠉⠁⠀⠁⠀⠀⢀
⠀⠀⠀⠀⣿⣿⣣⠏⠀⣀⣀⠀⠈⣹⣿⠏⢀⡀⣨⣿⣶⣏⢙⣿⣇⡀⠀⠹⣿⣿⣤⣭⣉⡀⠈⠛⠦⣄⡀⠀⢀⣠⣶⣸⣯
⠀⠀⠀⠰⠏⢀⣏⣦⢻⣿⣿⣷⠞⠋⢁⣴⣎⣿⣟⣿⣉⣉⢉⣿⡿⣧⣴⡆⢠⣌⣿⠷⣍⠉⣿⠶⢶⣴⣎⣛⢛⣿⡿⠿⣿⣀⡀
⠀⠀⠀⢰⡄⣼⠀⢻⣆⢿⣿⣿⠸⢶⡾⠛⣻⢾⣿⣿⣿⣿⠟⠛⠛⠛⣿⡇⣾⣿⣿⠁⡼⢃⣀⠀⠀⢘⡿⡿⡿⣿⠃⢰⠷⠦
⠀⠀⠀⢸⡇⠹⣖⢋⡟⠈⣁⣠⣴⣟⣶⣿⡿⠛⠻⣿⣿⠁⢀⣤⣤⣄⡟⠁⠻⢿⣯⣾⣷⠿⠛⢻⡆⢸⠤⣧⡼⢃⢄⡟
⠀⠀⡔⣿⣷⡀⠙⣟⣷⣿⣿⠉⠈⢿⣿⣿⠇⠀⠈⢧⢻⣤⡟⠁⠈⡿⠙⠓⠛⣾⣿⣿⣇⠀⡀⢸⣏⡾⣋⣩⣴⡯⠞⠶⠤
⠀⠀⠘⠻⠟⠑⣴⣙⡿⠋⠁⡀⢐⣿⣿⣷⣁⢀⡀⣿⡤⣿⣇⠠⠄⣿⢀⠀⠐⠷⣿⣅⢋⡀⢁⡜⢻⣯⣥⡾⠛⠛⢿⡶⠶⠐⠂
⠀⠀⠀⠀⣴⢶⠛⢟⠻⠿⣷⣪⡜⠉⣻⡉⠈⠑⠒⠋⠀⣏⢳⣥⣤⡾⠧⡠⡄⢶⣿⣾⣷⣬⣅⡴⢋⡈⠟⢂⡮⠄⠈
⠀⠀⠀⢰⣇⠘⣠⣈⣷⣄⣀⢩⣑⠛⠻⢷⣦⣄⣀⣤⣴⣿⣿⣿⣿⣄⣤⠋⣱⣤⣿⣿⡿⠿⠛⠋⠁⠀⠀⢸⣧⡄⠀⡀
⠀⠀⠀⢸⣣⡎⢰⣿⣿⠿⠋⢸⡯⣿⡆⠀⠀⠈⠋⠛⠛⠛⠛⢛⡛⡉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠿⠃⢀⠝
⠀⠀⠀⣯⡾⡇⠈⣻⢈⠀⠀⠸⠧⣿⣇⡞⢲⠀⡤⢠⡀⡄⢸⠈⠁⡧⣄⣤⠤⡤⢄⣺⢰⣶⣿⣼⠍⠃⣸⠋⢑⡏
⠀⠀⠀⡟⠀⣹⣦⠇⠙⠒⠦⢤⣄⣀⣀⠁⠘⠀⠓⠘⠳⡇⠘⠀⠀⠗⠚⠻⠀⠃⠘⠉⠈⢉⣁⣀⡤⠔⢳⣀⠞
⠀⠀⠀⢻⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡠⢄⣀⣀⣀⣀⣀⣀⣀⠴⠶⠶⠖⠙⠈⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⡿⠁⠈⢷⡀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠁⠀⢀⡄⠱⡄⢀⠔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠟⠀⠀⢸⡇⠈⡇⠀⠀⡗⠀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣛⠛⠉⠀⠀⠀⢸⡇⠀⣿⠀⢰⠇⡄⠠⡀⠦⡀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⠤⠀⢄⢀⠀⠀⠈⠏⠀⠀⠀⠸⡀⠓⠀⠧⠀⠇⠙⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡼⠁⠀⠀⣸⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⢸⠃⠄⠀⡀⠀⠉⠀⠀⢠⠀⠀⠈⠋⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠓⠃⢸⡇⢶⠀⠇⡄⣨⠰⣇⣸⠂⣶⢰⡄⡇⣰⢀⡄⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡴⠙⠃⠾⠈⠸⠇⠙⠂⡹⠻⠎⠛⠘⠸⠇⠉⠉⠧⠀⡽
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠂⠐⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠢⠄⠁⠀⠀⠀⠀⠀⢀⡀⠠⠀⠒⠒⠲⠠⠁⠀⠀⠀⡁
⠀⠀⠀⡠⠲⠄⠠⡆⡀⠀⠀⠰⠂⠀⠀⠀⠰⠀⠁⠀⠀⠉⠁⠊⠀⠂⢻⡉⠉⠑⣀⠀⠀⡀⣀⠘⠀⠀⠤⠀⠀⠠⠀⠀⠈⠣
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠐⠃⠀⠀⠀⠀⣀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠆⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡀⠀⠠⠀⠀⠀⠰⠄⠀⠀⠀⠚⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠐⠄⠤⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠊⢀⠀⠀⠁
⠀⠀⠀⠈⢄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠉⠁⠊⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠾⠛⠀⠀⢀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣐⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀


⠀⠠⠤⣄⣠⡀⢀⡀⢰⠄⡤⣀⣤⡀⣀⠀⠀⣀⡄⠀⠠⢀⢀⡀⣀⡤⢆⣤⢤⡴⢀⣦⣤⣥⣤⠒⣠⣶⣢⢦⡀⢀⠆⣀⣀⣁⣠⠂⠀⠠⠀⡀
⠀⠚⣿⡿⢋⡴⢋⣴⣿⣿⣿⣿⠇⢉⣴⣿⣿⣿⡿⣯⣾⢫⣎⣽⣿⣿⡿⠻⡟⡴⠟⢛⠟⠿⣭⣎⣿⣶⠿⣾⡷⢋⣾⡛⣟⡺⣽⣟⣿⢡⣾⡟⣸⣿⠤⠤⠄
⠀⢠⠍⠀⠃⠘⠋⢻⠁⠀⠄⠁⠁⠀⠉⠀⠈⠉⠁⠛⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠠⠀⠈⡄⠇⠉⠉⠋⠀⠃⠀⠁⠙⠁⠀⠁⠁⠈⠃⠉⠙⢋⠁⠠⡀
⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⢥⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡶
⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⠀⠀⠁⠀⠘⠀⠀⠀⠀⢰⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠊⠡⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣁⠒⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠠⢀⠁⠀⠀⠀⠈⢀⣀⣄⠰⡎⡄
⠀⠀⠀⠀⠀⠀⠀⢔⣤⡄⠀⠀⠀⠀⠀⠀⠀⢇⡨⠂⠀⣼⣠⣿⣸⠃⡇⢻⡁⠸⣆⣽⡖⡈⠒
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⢸⠏⢸⡇⠀⠙⣆⢻⡀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡤⠀⣀⡈⠁⠛⠒⠋⠈⠁⠀⠻⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣠⠂⠀⠀⢠⣟⣀⡾⢡⡾⠋⠀⢀⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠃⠘⠇⠀⢀⣾⠃⣶⣀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠴⢃⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠋⠁⠀⠀⠒⠃⠀⠙⠁⠉⠁⠐⣀⠀⠀⠀⠲⣬⠵⠋⠀⠀⠀⠀⠀⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠲⠦⣤⣀⡀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠛⢷⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡼⠚⡁⠀⠀⠀⠀⠸⡅⠀⢠⠄⠀⠀⠉⠙⠛⠻⠿⠖⠛⠃⠀⠈⠀⠀⠃⠀⠀⢨⣔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⡀⠀⠀⠀⢀⡀⠀⠄⠠⠀⠀⠀⠠⠀⠠⠠⠀⠀⣀⠀⠀⣶⠀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢻⡇⢠⣄⠀⠈⣿⠀⠀⡄⠀⠀⠑⣤⠀⠂⢰⡆⠀⣽⡇⠀⣿⠀⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⢸⡇⢀⣿⠀⠀⣿⠀⢸⣄⠀⠀⢠⣟⠀⢠⣿⡀⠀⢿⡦⠀⣿⡁⠀⠁⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⢸⣿⡀⠀⢿⡦⠜⠛⠉⠀⠈⠁⣀⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢧⡂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠸⣧⠀⠉⠀⠀⠠⠤⠤⠤⣀⠀⠂⣀⣼⣥⣤⣄⣀⣀⠀⠀⣿⡇⢠⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⢰⡆⠀⠀⢠⣤⠀⠀⠀⠹⠋⠁⢹⠀⠀⠀⠀⢩⣙⣷⠿⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⢸⡇⠀⠀⠘⠉⠀⠐⠂⢀⣤⣄⢸⠀⠀⢦⡶⢶⡿⣦⠀⠶⢶⡄⢠⣤⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠠⢂⠂⠒⠀⠀⠀⢸⣇⣄⡀⢴⡾⠻⢸⡇⠻⣦⡀⢸⠀⠀⢸⠀⢸⠀⢸⢠⡖⢛⡇⠘⢷⣅⠀⣀⡀⠒⠒⠋
⠀⠀⠀⠈⠀⠀⠀⢀⡁⠀⣶⡞⠀⠀⡀⢸⡏⠈⣧⢸⠁⠀⢸⡇⢀⣀⣿⠸⢦⠞⠺⠂⠘⠃⠚⠊⠛⠛⠓⠸⠦⠿⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠄⠙⠇⠀⠘⢷⣤⡤⠀⢸⡇⠀⠿⠼⠇⠀⠘⠁⣈⣉⣠⡤⠤⠒⢶⡂⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡊⠹⢋⠀⠀⠀⠠⠠⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠁⢠⠄⠐⠀⠀⠙⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⣀⡀⢀⣀⡴⠴⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠒⠀⠀⣴⠀⠀⠀⠀⠀⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠐⣹⣏⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⣺⡃⠀⠀⣼⣿⠄⠀⠀⠀⠀⠀⠀⠓⠀⢀⣼⣄
⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠜⣹⣏⠢⡀⠀⠀⢀⣿⣧⠀⠀⢀⢼⢤⠀⠀⣼⣿⡄⠀⠀⠀⣤⠀⠀⠀⢀⣤⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣠⢤⠤⠀⠀⢀⠴⣻⣟⢧⡀⠀⢀⣾⣿⣿⡆⠀⠠⢺⡣⠄⠈⣹⣿⡍⠀⠀⢰⡿⡆⠀⠀⣀⣴⣿⣿⣤⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠔⣻⣟⢦⡈⠀⣼⣿⣿⣿⣿⡄⠒⢹⡑⠆⠼⢿⣿⠛⠂⠀⣾⣩⣿⠀⢀⣠⣼⣿⣷⠤⠤
⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⢀⠼⠋⡟⢦⠉⣸⣿⣿⣿⣿⣿⣷⡐⢩⠙⠀⢠⣿⣿⣧⡀⣸⣿⡣⣿⣇⠉⢉⣽⣿⣿⡷⠒⠂
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠇⠀⠀⠉⠉⠉⢹⠉⠉⠉⠀⠸⠀⠀⠛⠉⡏⠉⠁⠛⠛⠛⠛⠛⠀⠛⠉⢹⠉⠛⠓

⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠐⠄⠃⠔
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠭⢹⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⢰⠄⠀⢀⠀⠀⠠⢠⠀⠀⠀⢀⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠐⠀⠀⠀⠀⠠⠉⠀⡀⠀⡄⠀⡀⠘⠀⠀⠘⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⢀⡈⡴⢶⡎⣀⠀⠠⠄⠀⠔⠁⠑⠄⠀⠁⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⡚⠣⡀⠀⠀⠀⠀⠢⠀⠠⠃⠀⠀⠀⠀⠁⠀⠀⠲⠀⣨⠡⡠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢴⣟⣳⠡⠠⠤⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⢀⠀⠀⣠⠐⠫⠁⠃⡄⠀⢠⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠠⢔⡀⠄⠀⠀⠤⠀⠌⢢⣀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠐⢨⢇⠜⡕⠂⠀⠀⣀⠀⠀⠈⠑⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⠄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⡱⠒⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠱⠎⡁⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣷⣶⠂⠀⠀⠀⠀⠀⠄⠀⡈⠴⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠁⠙⠻⢦⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠰⠀⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠶⠀⠀⠰⠄⢀⠈⠀⠀⠂⠀⠈⢀⠀⠰⠀⠀⠰⠆⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⢰⣷⡀⠀⠘⠀⠀⠀⠃⠀⠁⠘⠀⠀⢰⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠈⠁⠄⠀⠀⢾⣿⡇⠀⠀⠐⠄⢀⢁⠀⠔⠀⠀⠀⣿⣿⡆⠀⠈⠀⠉⠀⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠆⠄⠰⠐⠀⠆⠀⠆⠀⠀⠰⠰⠀⠀⠆⠂⠀⠆⠀⠂⠀⠀⠆⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⠀⠀⡀⢄⠠⢤⠉⠆⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠎⢁⠴⢀⠄⣀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠼⢀⡵⢘⡆⣹⠀⡅⠐⠁⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⢰⡁⢞⠱⣅⠘⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠈⠀⠁⠀⠀⢀⠆⠀⠀⢀⠀⠀⡆⢴⣶⠀⡆⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠀⠀⢀⠁⠁⢀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣀⠀⠃⠁⠀⠀⠈⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⢄⠀⠉⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠰⠘⠀⠀⠀⠀⠘⠃⢰⣶⠀⠛⠀⠐⠀⠀⠈⠐⠠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠆⠄⠄⠂⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠁⡀⢀⠀⣀⢿⡛⢀⠀⢠⣀⠀⢀⣀⢀⠤⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢫⡁⣦⠸⡆⣿⢸⡇⣿⠘⠃⠛⠰⣛⣬⡙⠀⡄⢉⠀⠖⠐⠦⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣥⠻⣆⢳⣼⡷⠟⠛⠛⠛⠁⠀⠀⠀⢴⣿⡍⠛⠀⣅⠈⠀⠐⠁⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣀⠳⣌⣳⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠘⠃⡀⠀⠀⠀⠈⣁⠘⢃
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢤⣍⣳⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠴⠀⠂⣀⠃⣈⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠏⠘⠲⢬⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⢶⣄⣁⡀⠃⠁⠀⠠
⠀⠀⠀⠀⠀⠀⣸⢠⣍⣛⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠄⠧⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⠰⠤⠬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⣛⡂⣤
⠀⠀⠀⠀⠀⠀⣿⠐⠒⣚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢭⣭⡅⣿⠁
⠀⠀⠀⠀⠀⠀⢹⠈⡉⠉⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠲⠲⠀⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠱⠄⡀⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡾⠍⠁⡴
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠚⣫⡼⢷⣀⡀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠤⠀⠀⣛⡀⠀⠪⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣾⠫⠄⣁⠉⠐⠄⠀⣿⡓⡇⡀⢁⠀⣮⠄⡀⠼⠁⠀⠑⠀⠀⠀⡀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠱⠄⠲⣤⡀⠀⠴⡏⠀⠠⠙⡷⢒⠀⠉⠴⣀⠂⠐⡔⠐⠀⠘⢄⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠂⠀⠉⠠⠐⠀⠀⣀⣀⡰⠟⠊⡖⠐⣀⠈⠃⠀⠁⠰⠃⠀⠀⢀⠀⡐
⠀⠀⠀⠀⠀⠀⠐⠂⠀⢴⡶⣤⡴⠧⠀⠂⠉⠀⠉⠙⠿⢔⣚⣳⠀⠈⠁⠴⠁⠙⡄⠀⠉⢐⡎⠀⠉⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⢘⣯⠀⠀⠆⡭⠈⢈⡡⡀⢀⡀⠀⠂⠔⠁⠀⠁⠪⠙⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠈⠀⠀⠀⠀⠂⠀⠈⠈⠀⠰⠀⢰⠀⠙

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⣷⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠡⢠
⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠉⠉⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠃⠀⠀⠀⠔⠈⠀⠀⠀⠀⠨⠤⠀⠀⠀⠀⡀⠀⠮⠌⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠛⠛⠛
⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢤⠈⣌⡁⣧⡀⣇⣀⠱⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠄⢀⠀⠀⠄⠀⢀⢠⡀⠠⡄⠀⠀⡄⠀⠀⡠⠀⠀⠀⣰⣿⠀⠀⠫⣶⠙
⠀⠀⠔⡃⠀⠀⠀⠀⠀⢀⠀⠐⠤⠀⠇⠳⠘⠒⠄⠂⠐⠅⠀⠳⠀⠇⠘⠐⠃⠐⠐⠒⠀⠀⠊⠟⠫⠀⠀⠀⣿
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⣀⠀⢠⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠿⠇⠀⠀⠀⠀⠈⣠⡄⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡆⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠁⠀⠀⠀⠈⠈⠄⠀⠘⠀⠀⠀⠈⠀⠀⠀⠁⠀⠠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣽⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⠀⢀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣀⠄⠀⢠⠀⠀⡠⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠠⠀⠂⢀
⠀⠀⠀⠀⠀⠄⣈⣁⠠⠀⠐⠀⠫⠛⠀⠒⠂⠀⠀⠴⢀⠀⣁⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⢘⡃
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠂⠠⠀⠀⢁⠀⠀⡾⠀⠀⠈⠀⠀⠈⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⢲⡄⠀⠀⢤⠄⠀⠐⠀⠁⠀⠀⠀⠄⠀⠂⠈⠀⠘⠀⠀⠁⠀⠀⠂⠀⢀⠀⠂
⠀⠀⠀⡀⠃⠀⠠⠀⠀⡀⠀⠠⠀⠀⠈⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠐
⠀⠀⢠⣻⠀⠀⠀⠀⠀⠁⠀⠑⡂⠀⠁⠀⠘⠀⠀⠀⡆⠀⠉⠀⠀⠀⠀⠀⡀⠢⡀⠴
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⡇⠀⠰⠀⠀⠀⠁⠵⠶⠐⢠⠘⠀⠀⠀⡀⢠⠀⠀⠐⠁⢀⡀
⠀⠀⠀⠀⠀⠁⠀⢃⠉⠁⠀⠈⠀⠌⢀⡀⠁⠀⠀⠐⠁⠀⠀⠀⠊⠀⠀⠰⢤⣀⠈⢁⡤⠞⠁
⠀⠀⠀⠀⠰⠆⠀⠂⠀⠐⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠐⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠚⢃⠀⠈⠓⠀⠠⡤⠒⠔⠀⠛⠒⠀⠋
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⣀⢀⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⢀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠒⠛⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠡⠀⠀⠐⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢒⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⣼⣟⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒
⠀⠀⠀⠀⢐⣻⠵⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⣭⡿⠿⣟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠗⠂
⠀⠀⠀⣠⣿⣓⣫⣭⠥⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢛⣋⣛⣉⣍⣁⡀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣊⣭⢄⣀
⠀⠀⠀⠴⠛⠉⠁⠀⠀⠀⠀⠉⠙⠒⠒⠂⠀⠀⠀⠀⠈⢋⡉⠉⠭⠤⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠤⠤⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⠙⠂
⠀⠀⠀⠀⠀⠀⣨⣠⣶⣾⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄
⠀⠀⠀⠀⠀⣘⣿⣿⣟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣠⠴⠂
⠀⠀⣀⣶⠶⠟⠋⠋⠉⠉⠉⠉⠁⠐⠒⠦⠤⠀⠀⠀⢠⠴⠞⠩⢭⣉⠈⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⢀⡁⠒⡈⠀⡀⢠⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢖⠒⠒⠂⢒⠐⢒⡶⠆⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⢀⠀⠀⠈⠉⠀⠒⠻⣑⠭⠀⢀⣀⠀⡀⠀⠉⡒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⠀⠀⠀⠀⠀⠀⠂⠀⠀⣴⠂⠀⠀⣰⠆⠀⠀⠉⠲⣄⠀⠀⢸⡗⠁⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠆⢀⠁⠀⣛⣛⣬⣬⣭⣭⣭⣥⣼⣒⡀⠤⢈⡃⠀⠜⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢠⡴⢓⣨⣴⠾⠋⠉⠉⠀⠀⠀⠀⠀⠉⡉⠛⠛⠻⣶⣮⣔⡠⡀⠀⠀⠰⠀⠘⠉⠙⢦
⠀⠀⠀⠀⠀⠀⡠⡁⠀⠀⠀⣠⠞⢃⢜⣥⣾⡟⠉⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣦⣕⠄⡀⢀⡀⠄
⠀⠀⠀⠀⢀⠌⠀⠉⠩⡍⠀⢀⢜⣵⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣔⢾⠟⠀⠱⢆
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⡤⣢⣾⣿⣿⡿⣤⣾⡿⠃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠹⣿⣿⣿⣧⡹⠿⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⡰⣱⣿⣿⣿⣿⣵⣿⡍⠀⠀⠀⠻⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢳⡀⠀⢿⣿⣿⣿⣷⡐⡀⢡
⠀⠀⢐⠀⠀⠀⠀⠀⠠⢱⣿⣿⣿⡿⣿⣿⣿⣷⣦⣶⡀⢀⣹⡆⠀⠀⢀⣤⠶⠚⠛⠉⢹⠿⠷⢶⣮⣇⡀⢸⣿⣿⣿⣿⣿⡘⠻
⠀⠀⡎⠀⠀⠠⡆⠀⢣⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣷⣿⣿⣧⣴⣾⡥⠄⠀⠀⠀⢠⣠⡤⠤⠈⢻⡟⢿⣿⣿⣿⣿⣿⣿⣧⢹
⠀⢠⠀⠀⠀⠉⠀⣤⢸⣿⣿⣿⣿⣷⣗⢹⣿⣿⣿⣿⣿⣿⡟⠛⢿⠃⢀⡤⢤⣷⡀⠙⠇⠀⠀⠀⢈⣉⡉⠻⠿⢿⣿⣿⣿⣿⡈
⠀⠸⠃⠀⣦⠀⢀⠇⣿⣿⣿⣿⣿⣿⣿⡿⣧⣿⣿⣿⣿⣿⣷⡀⠘⠛⠉⠀⠀⠙⣿⡄⠀⠀⡆⠀⠊⠐⠀⠄⠀⠈⠙⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡌⠁⣿⣿⣿⣿⠿⠿⠫⠟⠐⠈⢺⣿⣿⡏⠻⢿⣿⡇⠢⠄⣀⡴⣁⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠸⠀⡀⠀⠘⠁⢠⢻⣿⣿⣿⣢⡐⠀⠀⣠⣶⣿⣿⣿⠃⠀⠀⠈⠀⠀⡬⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⠀⠀⠀⠀⢘⣿⠃
⠀⠀⡆⢇⠀⠀⠀⠀⠸⣿⣿⡟⡼⠁⠀⠰⠿⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢤⣤⠖⠛⠛⠉⠙⠁⠀⠀⠀⠀⠀⣿⣰
⠀⠀⢐⠀⢷⡀⠀⢀⣠⣿⣿⠋⠄⠂⠀⠀⠀⣀⢸⣿⣿⣷⡄⠀⠀⢀⢰⣿⣿⣿⡋⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠈⠆⠀⢙⣴⣿⣿⣿⠟⠀⠀⠀⠉⠀⠀⠀⡀⢻⣇⢍⠟⣷⠀⡈⡀⠐⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣴⣾⡿⢟⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⣴⣿⡟⣡⠏⠐⠀⠳⠀⠀⠀⠀⢀⠀⢀⣋⣠⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⣾⡟⠟⠀⡉⠀⠁⠀⠀⠀⠀⠀⠰⠀⣠⣾⣿⣿⣿⣧⣴⣿⠃⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣦⠀⡆⠙⠀⠀⠀⠀⢠⡴⠂⠀⠀⠙⣿⣿⣽⣿⣿⣿⣶⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⢺⠀⠀⠀⠀⠀⠀⠀⠌⠐⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿

⠀⠀⠀⠀⣀⡄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣰⣷
⠀⠀⠀⢀⠛⢓⣚⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⣤⢀⣇⠉⢷
⠀⢠⠞⠤⠐⠉⠁⢳⠉⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠐⢲⣦⡌⣏⣠⣶⠒⢱
⠀⡄⢃⡄⢴⣼⣧⠮⠀⠀⠻⠀⠀⠀⠀⣶⠄⢤⡄⠀⠀⠀⠠⠂⢠⣤⡞⣟⢦⣤⠀⠛
⠀⢹⣮⢅⡚⢻⡟⠒⣴⣀⡇⠀⠀⣠⠈⠉⠉⣻⡇⠀⠀⠀⠘⢄⠉⢡⠘⡿⢀⣉⡁⠂⠀⠀⣌⣆⣾⡆
⠀⠀⠙⠏⠉⠀⢠⠀⠤⠈⠀⠀⢾⠳⡀⠠⠞⠋⠹⢲⡾⠄⠀⠀⠑⠒⠀⠁⠀⠉⠁⢀⠀⠈⠀⣸⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢰⠀⠈⣑⠀⢰⡆⢀⣸⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠤⠚⣁⣼⣶⣯⡀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⣙⡊⢱⡋⠀⠲⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢤⣁⠀⡽⠿⡟⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠁⠸⣁⡉⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⡃⠲⣿⠞⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠾⠿⠟⠋
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⠀⠀⠁⠇
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠂⡀⠀⠀⠀⣺⣆⣀⣤
⠀⠀⠀⣀⠤⠤⢚⠑⡀⠀⡆⠀⠀⢻⠀⠀⣗⣶⣲⣼⠆⠀⠀⠀⢀⣀⠀⠆⠀⠀⡼⠀⠀⢃⠀⠈⠉⠙⢊⠁
⠀⠀⢸⣯⣻⠗⠛⠋⡡⠀⢳⡀⠀⡜⠀⠀⢿⡉⠉⡹⠁⠀⠀⠆⡟⡳⣄⠖⠀⠀⢂⠀⠀⢼⠀⠀⠁⠀⠘⡄
⠀⠀⠀⠙⠧⠄⠤⠐⠁⠀⠀⠙⡜⠁⠀⠀⠀⠙⡎⠀⠀⠀⠐⠈⠲⡴⠀⠐⠀⠀⠨⠀⠠⡾⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⣽⠃
⠀⠀⠰⡖⠦⠽⢸⡿⠦⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⠤⣾⠼⣷⠤⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢦⠁⠀⢈⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣏⣇⠀⠀⡀
⠀⠀⠀⠀⢸⣤⣀⣤⣧⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣤⠘⡃⣍⠀⠀⠀⠒⠓⠄⠀⠀⠘⠭⡿⠉⠻⣿⠗⠁
⠀⠀⠀⣰⠛⠒⢒⣿⣿⣦⠀⠀⠀⠐⠃⡀⢡⣤⡆⠀⢸⡆⢸⣧⡧⠎⠀⡀⠀⠀⠤⣤⡆⠀⠀⢀⡇⠀⠀⣧
⠀⠀⠀⠉⠂⠀⢤⠄⠀⠋⠀⠀⠀⢤⣤⣤⣶⠟⠀⠀⠈⠙⠊⠁⠀⠀⠀⠐⢤⣤⣴⠿⠃⠀⠀⠀⠃⠀⠠⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⡷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣷⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⢏⡟⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⠸⡗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣴⣧⠗⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⡁⣔
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡙⠺⠿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡤⣀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⡿⢿⡿⠞⠿⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢝⠫⠖⣀⢚⣛⡀
⠀⠀⠀⠀⠀⠀⡈⠦⠤⠌⣀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡇⣉⣤⣾⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⡓⣻⡇⢌⠉⠻⣭⡄
⠀⠀⠀⠀⠀⣀⠛⠲⠀⠤⠁⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣷⡟⣿⣟⡻⣷⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢉⣵⡖⢹⣄⠻⠆⠖
⠀⠀⠀⠀⢠⠈⠁⠈⠘⠃⠁⠈⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣽⣿⣷⣿⣿⣿⣿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣋⣋⢉⣁⣠⠠⠀⢡⠚⠋
⠀⠀⠀⢀⡀⠙⠓⠶⠒⡄⠙⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⣻⣿⣿⣿⣿⣿⡿⣆⢀⡀⠀⠀⠀⠀⠀⠀⠈⠋⢶⢁⣉⠁⠐⠒⠳⠿⠓⢚⡁
⠀⠀⠀⢨⠇⠠⠄⠰⠶⠰⠆⠀⠀⠞⠀⡀⠀⠀⠀⠀⠀⠀⢤⣤⡤⣭⣿⠋⠵⣿⢩⣯⢹⣟⡟⢋⢠⠀⠀⠀⠀⠀⠀⣫⠖⣩⢿⣷⠞⣽⣄⠑⠎⠞⣁⢀⣀⡀
⠀⠀⠠⠀⠀⢠⢀⠀⠀⠀⠀⠐⠴⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢛⣷⣿⣶⣿⣸⣿⣶⣿⣻⡿⠉⠀⠀⠀⠀⠀⠰⠭⢙⠃⣘⡋⣀⡅⠉⢴⠒⣈⡄⠉
⠀⠀⢤⡀⠀⠀⠈⠁⠒⠀⠐⡀⠀⠄⠄⠂⡠⠀⠀⠀⠀⠘⢦⣢⡼⢟⣭⠟⢩⣿⡎⣿⣷⣿⣿⣤⣆⣤⡖⠀⠀⣈⣰⣠⡆⣀⡘⠉⠹⠗⠂⠀⠜⠣⣿
⠀⠰⢌⠀⠃⠒⠂⠰⠂⠀⠂⠉⠀⡀⠀⠀⠀⠓⠀⠀⠀⣀⣄⣈⣴⣿⣿⢿⣺⣿⣿⣉⣹⣿⠦⣟⡿⣍⠀⠀⠠⣌⣛⣻⡍⢩⣥⡀⣶⡇⢒⡶⣦⡀⣰⢶⣆⠠⠄
⠀⠀⠀⠀⠀⠉⠉⠐⠐⠒⠘⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣹⣿⣏⣤⣿⣿⠻⣿⣷⣲⣦⢼⡿⠒⠋⠀⠀⠀⠉⠋⠀⠃⠺⠞⠟⠃⠂⠀⠈⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠈⠙⠷⠜⠛⠛⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠤⢄⠀⠀⠀⠀⠀⠀⢰⠡⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣀⠀⢄
⠀⠀⠀⠀⠘⠀⣌⠂⠇⠠⡇⢹⠀⠀⠀⠑⠠⠤⠀⠀⠀⠠⢀⡠⠔⠒⠒⠂⠴⢆⡀⠐⠤⠤⠁⡘
⠀⢀⠤⢤⡀⠢⠄⣀⠀⡄⠘⠃⠀⠀⢀⠋⡀⠀⠀⠀⠀⠀⡎⠁⡄⠀⠀⢀⠠⢄⠙⡁⠀⠒⠠⠄⣀⡐⢁⡠⠇
⠀⠸⣄⠃⠀⡤⠊⡀⠀⠀⠀⠀⠀⠀⠿⡸⠄⢀⠆⠀⠀⠀⠳⡴⠃⠀⠀⢠⡀⠘⢁⠣⡀⠀⢀⠀⠀⢡⠀⠀⠀⠰⣨⠂
⠀⠀⠀⠀⠀⠀⣬⠂⠀⠀⠀⢧⣁⠘⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠈⠐⠚⠀⠀⢠⠀⠈⠋⠉
⠀⠀⠀⠀⠐⠲⣾⡞⠁⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋
⠀⠀⠀⢀⡇⠀⠁⠘⠂⠀⠀⢀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠄⣤⠄⠀⠀⠀⣽⡀⠀⠀⠀⠀⢀
⠀⠀⠀⢶⣝⡃⠀⠀⢀⣤⠀⠈⠻⠿⠃⠀⣠⡄⠀⢀⡀⡆⣸⠣⠒⠀⠀⠀⢀⠖⠃⠀⢰⣾⠻⣷⣢⡀⠀⢨⠹⠆
⠀⠀⠀⠈⡟⠀⢀⡄⣉⣉⣁⣦⠀⠀⠀⠀⠀⡈⠀⠀⡙⢦⢴⢞⡩⢍⠀⠀⠀⠀⠀⠀⢻⣼⠿⣤⣿⠁⠀⠀⣄⡀
⠀⠀⠀⠧⠀⠀⢸⣿⣿⣻⣿⣹⠄⠀⠀⠀⢺⣵⠀⠀⠉⡥⠞⡢⠹⡀⠀⠀⢠⣶⡄⠀⠀⠉⠙⠋⠁⠀⠀⣨⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠭⠿⠋⠀⠀⠀⠀⠘⠀⢄⠀⠀⠀⠀⠁⠀⠀⢀⣶⣳⣛⡿⢷⡀⠀⠀⠀⠀⠀⣾⣶⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢴⠀⠀⠀⠀⠀⠀⠀⢘⡤⣍⣉⣉⡩⠵⠀⠀⠀⠀⠀⠛⣿⣿⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⡈⠀⠀⠀⠀⠀⠀⠀⠘⢦⣘⣀⢙⣨⠃⠀⠀⠀⠀⠀⠀⢈⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⣶⣿⣾⣿⣿⣿⡿⣦⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠋⢸⢿⣿⣿⣷⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣌⡀⠀⣀⣰⣾⣿⣿⣿⣿⣧⣴⣶⡾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠙⣿⣿⠿⠻⢻⣿⣧⣄⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⠿⠂⢱⣿⣿⣿⣿⣿⡿⢿⣿⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣦⡈⢡⣶⣿⣿⣿⣿⣿⣿⣿⡶⢦⡙⠛⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⠿⣿⣷⣶⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠿⠟⠿⠛⠟⠛⣟⠛⣻⣿⣟⣻⣦⠉⣉⢹⣿⣿⣿⠿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡆⣠⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣿⣿⡃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⣾⠛⣟⣧⣴⣶⣾⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠟⣿⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⡟⠿⠻⣿⢹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣝⠻⢿⣿⣧⡔⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣿⣿⢏⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡘⠟⠛⢋⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣷⠙⠉⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠿⣿⣷⣤⣿⣿⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣇⡻⠿⢿⣿⣿⣾⣢⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠀⣹⣿⣿⣾⣿⣿⣿⡿⢿⣿⡿⠽⣿⣿⡋⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣶⣾⣾⣅⣀⣠⣍⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⣿⣿⡿⠛⠉⡛⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠃⠐⠠⣿⣿⣯⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣶⣶⣿⣿⣿⣿⣟⡡⣸⣿⣿⣿⣿⣿⣧⣰⡇⣀⣘⣿⣿⣿⣮⣅⠻⠿⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⣵⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢾⣿⡟⣿⣿⣿⢿⡿⣿⣿⠉⢻⣿⣿⣿⣯⠙⠻⢿⣿⣷⠎⠛⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠐⠻⠟⠀⠀⠙⠋⠀⠀⠉⠁⠙⠿⠗⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠰⠃⠇⠀⠀⠀⠀⡇⠄⢰⠀⠀⠀⠀⠀⠆⠇⠀⠆⠀⠀⠳⠀⠀⠀⠀⠧⠼⠀⠻⠀⠱




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡾⠃⣀⣤⡶⠶⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠟⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢦⣄⠀⠀⠀⣿⢠⣿⠞⡡⠖⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⠓⢄⠀⡟⣸⠇⠊⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠇⢈⣠⣤⣤⠶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣋⠩⣥⣤⣤⣄⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠙⠟⠉⠙⠋⠀⢀⣀⣴⣆⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠂⠄⠀⢿⠀⠀⢀⡶⠛⠓⣦⢀⡟⠉⢈⠙⠲⠀⠀⠁⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⣀⣀⠀⠱⡌⢃⠀⠈⠆⠄⠀⢸⠃⢇⠀⠈⠇⣠⠶⣔⡄⢠⠞⡩⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠁⠀⠃⢀⡇⠀⠳⠤⣀⡠⠴⠋⠀⠀⣉⣁⣀⠀⠀⣸⡇⠀⠰⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠄⠀⠀⠠⢿⣷⠶⠶⠛⠁⠀⠀⠀⠀⡴⠺⣆⢀⡴⠛⠛⠧⣄⠈⢁⡠⠤⡀⠈⠀⠀⣀⡤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠒⢄⣠⠚⠙⠃⠀⡹⠎⠀⡶⠀⠀⢹⠀⠉⢀⠂⡈⠂⡠⠚⠥⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⡀⠀⠀⣄⠶⠶⢶⢿⡇⠰⠁⠀⡉⠀⠀⠀⠈⠀⠀⠀⠁⠄⠤⠋⣠⣀⡀⠉⠁⠀⠙⢀⡶⠂⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⢀⠄⠢⢌⠀⠀⠀⡁⠀⠀⠀⠀⢻⡄⠁⡩⣄⡀⠀⣠⠞⠉⠉⠉⠒⣄⡐⠊⠁⣀⠈⠠⠀⠀⠀⠐⢷⣀⠂⡠⢇⡴
⠀⠀⠀⠀⠀⠀⠠⢀⡤⢈⡇⠀⠀⢩⢤⡀⠀⠀⢸⠃⠠⡿⠉⢙⡆⡇⠀⠀⢰⡂⠀⠸⠀⢀⡎⠉⠃⢀⠀⣴⠂⠀⠀⠩⢤⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠸⣆⠓⡀⣁⠀⡠⠇⠀⠀⠙⠀⠈⠀⠙⠶⠶⠞⠁⠀⢰⡄⠘⠛⠒⠚⠋⠀⠙⠓⠋⢀⠞⠁⠙⢦⣠
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠉⠈⠁⠈⠀⠠⠠⠃⠀⠐⢶⣶⣶⣄⣀⣤⠀⣠⣿⠇⠀⠀⠀⣠⢖⡵⠖⠲⢦⡀⠀⠤⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠜⣠⠤⠒⢒⣂⣤⠀⠀⢀⠐⣉⠤⢍⡙⢶⡍⠛⠛⠯⠙⠓⠛⠁⣀⠀⠀⢰⡷⠏⠀⠀⠀⢀⡗⠀⠔⠊⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡰⠊⣤⣤⣀⠀⠀⠀⢈⠁⠀⠀⠙⡆⢿⣾⠁⠀⠀⣄⠀⣠⣼⣿⣿⣷⡏⡀⠀⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠃⠀⠀⠐⠃⢘⠟⠋⣀⡘⠺⣷⡁⠀⠐⢦⣸⠇⠀⠔⠁⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠢⠤⠔⣪⠄⠀⠀⠀⠀⠀⣠⢼⣞⡡⢤⣀⠀⠀⠀⢸⠀⠀⠉⠙⡀⠈⠛⠶⣤⣄⣀⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠂⢁⣤⠀⠀⠀⠀⠉⡴⠋⠀⢀⠀⠀⠹⣆⠀⠈⠳⠤⠤⠞⠁⠀⠀⠀⣀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⡇⠀⢀⠀⣸⠁⠀⢰⡗⠉⠀⠀⣿⠀⠀⣠⡶⠾⠛⢿⡀⠀⢸⠋⠉⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠁⢠⠞⢰⣏⠀⠀⠈⠳⢦⡤⠞⠃⠀⠘⠁⠀⠀⠉⠆⠹⠀⠀⠀⠠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣑⡀⣤⡀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠠⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠯⠟⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣤⡀⢰⢄⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠦⣸⣡⣸⡤⠋⠉⢻⠉⢆
⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⢤⣄⡀⢇⠀⣶⠉⠀⠀⠙⢆⠀⠈⠀⠀⣱⣤⢤⣀⠀⠀⣀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠒⢤⡀⠈⢻⣉⢻⣤⣽⡄⠀⠀⠀⠈⠀⣄⣤⣴⠁⠀⠀⠚⠙⢿⣅⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣰⣿⣦⠋⠛⣿⡿⡟⢷⣴⡉⠑⢤⣀⡉⠉⢿⣦⣠⠖⠛⠋⠛⣿⠛⠙⣲⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣏⠀⠀⠀⡟⠀⣠⠞⠻⣆⢀⡀⣑⣟⡳⠺⠟⠿⣀⣰⠖⢴⣿⠖⠊⢉⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠙⠧⢀⣀⠁⠐⠁⠀⣴⠉⢹⡼⠧⣬⡱⡄⠀⠀⢸⠁⠀⠀⠉⠹⢾⣧⠀⡼⠋
⠀⠀⠀⠀⠀⠶⠿⢍⣿⠀⠀⢀⡀⠠⢠⡤⠦⢠⡖⠉⠉⣦⠾⡀⣀⡀⢱⣸⣆⣤⣎⠀⠐⠁⠀⠀⠀⣸⠊
⠀⠀⠀⠀⣀⣠⠔⢚⣿⡿⠿⣁⠈⡹⠓⠒⠂⠉⠁⢀⡴⠁⠸⣝⣈⡉⠻⠋⣭⣉⢿⡷⠖⠒⠉⠛⢿⣿⠍⠁⠒⢤⡀
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠙⠺⠤⢦⡠⠖⠒⠦⠋⠀⠀⠀⠈⠻⢤⣤⡤⠌⢙⣁⣧⠀⢀⡀⠀⠈⢻⣿⣷⠖⠚⠛⠲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠪⠿⢅⡀⠀⢹⡆⠀⢸⣿⣯⠛⢶⡒⠒⠚⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠤⢴⣾⣿⣿⡆⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠻⡎⠉⠑⠒⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠞⠁⢀⣀⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡼⢃⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⣿⠀⣸⡵⢋⠤⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠉⠓⢦⠀⢻⢀⡟⠔⠁⠀⠀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠸⠘⣁⣀⣠⡤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣉⢭⣤⣤⣤⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠻⠋⠉⠋⠁⢀⣀⣴⣦⡀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠃⢄⠘⣿⠀⠀⣴⠊⠉⠢⡀⡝⠁⢠⡉⠂⠤⠄⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⡤⢤⠀⠱⡈⢄⠀⠙⠀⠀⢀⠇⠣⣀⡀⠃⠴⠶⣦⠆⡴⠩⠐⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠁⣰⠃⠈⠑⠢⠄⢒⡉⠀⠀⣤⣤⡤⠀⢀⠼⠃⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠓⠀⠀⠐⠛⠛⠛⠛⡁⠀⠀⢀⣀⣼⠉⢻⢠⠞⢉⠉⠑⣆⠀⡠⠒⡂⣄⠀⢀⡤⠖⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⣀⣀⣀⣿⡿⢋⠉⠲⡎⠀⠀⠀⠔⠁⠀⠟⠀⠀⡸⠀⠀⠨⠤⠀⢠⡋⢐⡂⠒⠢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠣⠆⠀⠀⡔⠉⠉⠙⠙⣇⠁⠀⠔⠀⠀⠀⣀⠤⠤⠤⣀⠀⢉⠠⠒⠒⢄⠀⠀⠀⠀⣾⠁⡀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠊⠀⠉⢦⠀⠀⠢⠀⠀⠀⠀⢸⠀⢰⡼⠶⣄⢸⠁⠀⢠⡀⠀⢳⠂⠀⡠⠢⠀⠁⠀⣀⠀⠈⠳⣄⡊⢱⠏
⠀⠀⠀⠀⠀⠀⠀⠊⣡⠎⠠⡀⢸⠉⠇⠀⢀⠎⠀⠘⠇⠀⠋⠘⢄⣀⣰⠇⠀⢈⠀⠸⢧⣤⡤⠂⠸⠧⡴⠀⠠⠍⠥⣄⢀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠙⠒⠳⠎⠐⠁⢀⢐⠄⠀⢤⣀⣤⡄⠀⢀⠀⢀⣼⡇⠀⠀⠀⢀⢔⣠⠤⣄⡀⠃⣀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠆⣀⡠⠤⠄⣀⠀⠀⠀⠀⢒⣀⠒⢦⣝⠛⠿⢿⠛⠦⠿⠋⠀⠀⠀⢰⣳⠋⠀⠀⠀⢱⠀⣀⠔⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⢀⣍⡀⠀⠀⠈⠐⠁⠀⠉⢢⢹⣶⡖⠀⠀⣀⠀⢀⣹⣷⣶⣻⢃⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢻⠀⠀⠀⠈⠀⠀⠀⢸⣰⡟⠀⠀⠀⠋⢐⡿⠊⣁⠛⢼⣎⠀⠀⢦⣀⡷⠀⠤⠃⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡓⠤⠄⣪⠄⠀⠀⠀⠀⢀⡠⣶⣋⢤⣀⡀⠀⠀⢸⠀⠀⠉⢑⠀⠙⠳⢦⣄⣈⣀⣀⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠃⢀⣤⠀⠀⠀⠈⢁⠞⠁⠀⣀⠀⠙⢦⠀⠈⠳⠤⠤⢚⠀⠀⠀⢀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣈⡇⠀⣀⢀⡎⠀⠀⣮⠀⠀⠀⣸⠀⠀⣠⠶⠛⡛⢧⡀⠀⠟⠁⢙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠴⠋⣼⣇⠀⠀⠘⠳⠶⠚⠁⠀⠈⠀⠀⠀⠀⠂⠁⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣥⢰⣦⣤⣴⣦⣄⣀⡀⠀⠀⠀⠐⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠙⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣌⡵⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⣰⣿⣷⠞⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠟⠋⣠⣰⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣶⡟⢻⡅⡴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⢻⣴⣾⣣⡴⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣴⣌⢁⣠⠿⠟⠃⡠⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⣉⣠⣤⡤⠀⡟⠷⠛⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠃⠘⣱⣄⣽⣇⠈⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⣦⠋⠀⢀⣤⡞⠉⠹⠟⠔⠤⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣿⡿⠁⠄⣦⣀⣷⠤⠖⣀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡄⠴⠐⠾⠿⠁⣰⣠⡿⠛⠉⠀⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠄⣰⡖⢠⣄⣉⡅⠀⡰⢦⢀⡐⣠⠀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⡻⢉⣼⡟⠀⠀⠜⠁⠐⠀⠈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣴⠀⠀⠈⠀⣼⠟⠀⢀⡀⠂⠀⠀⠀⠈⠐⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘⣿⣾⠈⠀⠁⠀⠀⠀⠀⠀⠴⢠⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀⠀⡀⢠⠀⢻⢷⣧⡀⠀⠸⠖⠀⠀⡀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠄⠀⠜⢁⠀⠀⠘⣇⠀⡂⠀⠆⢃⡀⠔⠁⠀⢠⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠉⠲⠤⠒⠛⠂⠚⠒⠐⠚⠛⠉⢁⡠⠐⢉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠐⠀⠀⠂⢀⣰⡶⠀⠀⠈⠓⠧⡴⠋⠘⢃⠀⠀⠀⠀⠀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢀⢠⡦⢐⡐⠂⠓⢸⡿⠁⠀⠀⠐⣦⠀⠀⠄⡀⠀⠀⠂⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⣠⡾⠃⠀⠀⠞⣤⡀⣠⡄⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⣄⠀⠀⠀⡀⠈⠄⠀⠀⠌⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⡿⠀⠐⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈

⠀⣶⣶⣶⣦⣤⣤⣀⣀⣀⣀⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠓⠀⠲⣶⣦⣤⣤⣤⣤⣀⣀
⠀⣿⣿⣿⣿⣿⠋⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⡀⣀⡀
⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣽⣿⣿⣷⣦⣔⣤⢀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣶⣶⣶⣤⣤
⠀⣿⣿⠽⡏⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⣀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣽⣾⣷⣦⣄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡍⢀
⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⣿⢿⠿⠟⠻⠿⠛⠏⠋⠘⢈⣹⣿⣁⣠⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣠⣄⣠⣤⣤⢿⣿⣧⡀⣿⡿⣬⣿⣿⣯⣿⡋⢹⡏⠓⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⠀⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠃⠀⠀⠀⠈⢻⣿⣶⣤⣽⡿⢿⣛⣻⣿⡲⠶⠶⣾⢿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⣿⣿⠾⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⣿⠉⠉⠉⠀⠀⠀⠉⣁⣀⠀⠀⠀⠈⠻⣿⣿⠿⠿⠟⠁⢺
⠀⣿⣿⣶⡲⣶⣤⢀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣠⡤⣼⣿⡆⠀⠒⠁⣀⣀⣤⣤⣤⡄⡴⣾
⠀⣿⣿⣧⣤⡈⠻⣷⣤⣴⣬⣥⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠚⣻⣦⣤⣦⣀⣛⣴⣿⣿⡇⠀⠀⠀⠀⠀⣽⣿⣗⡱⢃⣿
⠀⣿⣿⣿⣿⣿⣷⣦⣤⣀⢿⣿⣿⣶⣿⣛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣻⣿⣽⣿⣭⣭⠾⣿⣿⣷⠀⠀⠀⠀⠀⣌⠻⣿⣧⣾⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⣿⣟⣩⣅⣦⢹⣿⡗⠀⠐⠦⠘⢃⠸⠀⠙⢾⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⡤⣶⣀⠀⠠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⢼⣿⡇⠄⠀⠑⠖⠀⠀⠀⠠⢼⠿⠿
⠀⢿⣿⠿⠿⠿⠿⠿⠿⠭⠠⠿⠿⠿⠗⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣿⣏⠀⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡈⢿⣿⣿⣶⣤⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⣷⣽⣿⣯⣴⢛⢀⡀⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣴⡾⠿⣿⣿⣗⠉⠉⠛⠛⠉⢩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣍⣯⠀⢀⢽⣿⡿⠦⠄⣁⣀⠀⠛⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⡄⠽⢻⣿⡷⣾⠟⠑⢰⣼⣿⣛⣤⡶⠯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⠓⠓⢓⡋⠰⢿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⣠⣄⠐⠏⣿⣿⡅⠀⠙⣿⣍⢁⣁⣈⣀⣤⢶⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠒⢿⡿⠿⢷⣶⣽⡳⢦⠾⠿⢏⣿⣿⣭⣻⠍⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢂⣀⣩⣿⠀⠀⢰⣟⣿⣿⣿⣿⣷⣿⡛⠙⠻⠏⠈⣤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠛⠿⠿⠲⣿⣭⣿⣿⣿⢿⣝⣿⣟⣶⡴⠾⣻⠿⢷⠶⡦
⠀⠀⠀⠀⠀⠀⠰⢽⣦⣶⣶⣾⣴⣶⡿⠟⢿⣿⢀⣟⣶⣿⣿⣿⠁⠀⠀⡸⣦⠴
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡤⡀⣉⡐⣤⣥⡼⣟⣯⣿⣏⣳⣮⣿⣷⣀⣈⣽⣧⣶⣯⣭⣀
⠀⠀⠀⠀⠙⠗⣶⣦⣄⣉⡉⢁⣭⣍⣛⣷⣿⣿⣿⣬⣋⠻⡟⣿⣯⣹⣿⡷⣶⣤⣬⣍⠙⠓
⠀⠀⠀⠀⠈⠀⠀⣈⠹⠙⢙⣿⢿⣿⠋⠉⠉⢿⣿⣷⣿⣟⣧⣸⣽⣿⠿⢿⣞⣂⣉⣉⡀
⠀⠀⠀⠀⢀⣠⣤⡤⠶⠚⠋⢀⣽⣿⠀⢠⢄⣹⣿⣿⣿⣿⣯⣀⣼⡁⣀⠀⣿⣿⠿⢿⣢⣦⣤⡀
⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⣶⣿⣍⣿⡿⣛⣿⠻⣿⡿⡏⣿⣏⠿⣼⡿⢶⠾⠻⡷⠄⡀⠈⠉⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠙⠋⠉⠀⣉⣽⠿⠛⠁⣰⠟⠈⣷⡜⢿⣆⠀⠛⢷⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⢹⡧⠀⠈⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠊⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⣈⣏⣹⣋⣏⣫⣙⣏⣙⣉⣋⣟⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣿⣿⣯⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣦⡀⠀⢀⣼⣿⣿⠗⣀⣀⣀⣀⠀⠀⠀⠰⠷⡞⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡅⠀⠀⠀⠈⢻⡄⣾⢟⣩⠖⠛⠉⠉⠉⠉⣹⡷⠂⠀⠐⡿⢀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣿⡇⣦⠀⠀⠀⠀⡧⢫⠞⠁⠀⣀⣤⠄⠀⣼⠏⣤⠀⠀⢀⡗⣉⠀⠀⣼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣇⣿⣧⢰⠀⠀⠃⠀⢀⢦⣾⣫⣤⡄⣴⠋⢠⣿⡆⢀⢈⡾⠃⠀⡰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠻⣿⡆⣇⠀⠀⣄⣾⣾⡿⠟⠁⠊⠀⠀⢸⣿⣿⣼⣨⣾⠁⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠂⠀⠈⢃⡿⠴⠚⣿⡏⠉⠀⠀⠀⠈⠙⠓⢮⣻⠇⣻⣿⣷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⡴⠦⣬⣶⣏⣀⣤⣾⡿⢁⡶⠒⠈⠡⢤⣀⣀⢰⣽⣾⡿⠀⠀⣴⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣀⠤⣬⣽⡿⢿⠟⢃⣤⣭⣍⠉⠉⢠⣛⡳⠦⣤⣤⣶⣾⣿⣿⣷⠟⣠⣤⣤⠸⣷⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣱⢟⣵⢸⠁⠀⠀⢸⣿⣿⡷⠀⠀⢈⣩⣤⢶⣿⡽⣿⡻⣿⣧⡿⠀⠀⢀⣿⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⡿⣿⡈⠀⠀⣸⠘⠿⣟⣥⠀⠀⢉⠛⠧⣽⣦⡀⠀⠈⠊⣿⡇⠀⡄⣾⢏⣴⡿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡏⢏⣿⣬⣁⣀⣠⠏⠀⣀⣭⠷⠾⢿⡜⣷⡀⠀⠙⠿⣧⠱⡄⡏⢠⣾⠱⠏⢚⣵⡾⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣉⣉⠁⠈⠳⢿⣿⣵⢋⡴⠞⢩⣶⠾⠿⢸⡇⣿⣷⠀⠀⢀⣈⠃⠚⣵⠛⣇⣀⣚⡛⠛⠛⠉⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣍⠉⠉⠉⠙⠓⢦⡀⠈⢀⡞⣴⣧⡞⠁⠀⠀⢸⡇⣿⣿⠀⣴⣿⣿⠇⡀⠻⣤⣿⡟⢷⣤⣴⣆⣀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⣿⡀⣤⡠⣀⠀⢀⠁⠀⠀⣸⣿⢋⠔⠀⠀⠀⣼⢇⣿⢃⣠⣿⠟⢡⣾⡇⣷⢬⡙⠛⠶⡀⠉⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⡸⣷⣿⣷⣌⢳⡌⣆⠀⠀⠿⣵⡿⠀⠀⢀⣼⣫⡾⣣⣿⡿⠉⡏⡿⠛⠈⠁⢀⡇⢸⣷⡍⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣙⢮⣟⣻⣿⣳⡿⢋⡴⠖⠶⣦⡙⣦⠖⠋⠚⢩⣌⣛⠋⠀⠀⣧⠀⠀⠀⣠⡞⣷⢈⢷⣍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⢯⡀⢌⣉⣛⡛⠃⣿⡀⠀⠀⢸⣧⢐⠚⠛⠻⠿⢓⣮⣝⢶⣄⠹⠷⠾⠟⠉⢸⣿⣯⡳⣮⣳⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⢟⡿⣫⣶⣿⣿⡟⣡⣆⠹⣿⣶⣶⣿⠇⣼⣿⠶⠦⠬⠭⠍⠙⠓⠹⣆⠀⠀⠀⠀⠀⠙⢿⣿⡎⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢫⡿⣁⣠⣤⠞⠩⠞⠁⣸⡷⢠⣭⣭⢡⡈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡴⣛⣤⣶⡟⠀⠀⠀⢀⠙⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡿⠋⠁⠀⠀⠀⣰⡿⢁⡿⠉⣿⢸⣿⣆⢀⢯⣝⣛⣛⣿⠍⠀⠾⠿⣟⣻⣃⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠻⠇⠀⠀⢀⣠⡾⣟⣵⢺⡇⠀⠸⠸⡿⣿⡌⡇⠿⠿⠛⠁⠀⠂⠉⠉⠉⢛⣿⡟⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⢸⣿⣿⡸⣇⠀⠀⠀⠃⢹⢧⡇⠐⢶⣤⣤⣤⣤⣴⣶⣾⠟⠋⠀⣠⡟⣴⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠙⢆⠀⠀⠀⠞⣾⠁⠀⠀⠛⠿⣦⣉⠉⠉⠀⠀⣀⡴⠋⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠳⣦⣠⣾⠃⠀⠀⠀⠀⠁⠒⠤⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠉⠉⠉
⠀⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⢀⣠⡤⠖⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⡡⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡉⠀⠈⠀⠈⠁⢀⠐⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⠠⡤⠄⠉⠢⡀⠂⠀⠑⠀⡤⠀⠀⠲⡄⠀⠀⠀⠜⠀⢀⣀⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠈⠀⢀⠳⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⡸⢿⠀⠀⠀⠀⢀⠋⢀⠀⣠⠄⠀⠙⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣜⢦⠀⠀⢰⡏⢀⣬⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠉⠀⠀⠀⠀⠉⠑⢦⡀⡘⢿⣦⣼⡷⠀⠀⠀⠀⠀⣀⠀⠀⡠⠀⢀⠀⠀⠀⠰⣇
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⢠⡆⣠⣆⣻⣿⡈⣹⡋⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠐
⠀⢳⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⢀⠀⠀⢻⠿⠿⢋⠼⢿⡿⠟⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡠⠒⠉⠀⠀⡔
⠀⠀⠙⢦⣀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠀⠴⣿⠀⠀⣾⣶⣿⡃⢠⣿⡇⠀⠀⠀⠀⠀⢀⡌⠀⣀⡠⠖⠚⠁⠀⠀⠀⠀⢠⠀⢀⡤
⠀⠀⠀⠀⢉⡑⡄⣳⡄⢀⠀⡀⠀⠀⠀⠀⠈⢆⠀⣈⠉⠹⣿⠿⣿⡇⠀⠀⠀⢀⣔⣡⣦⣤⡅⣠⡀⠆⠀⠀⣠⣴⡟⢲⢆⠞
⠠⡄⠀⠀⡌⢳⣴⠿⠛⠃⠀⢱⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣿⡇⢀⣤⠶⠟⠋⠉⠉⠉⣉⠀⣠⣼⣶⣾⣿⢿⠔⢀⠊
⠀⠀⠀⠀⠸⡈⢿⠀⠂⠀⠀⠀⡄⠀⢀⠔⠀⠀⠁⢠⡀⣦⡀⠀⠿⡷⠿⠤⣀⠀⠀⠾⠇⠀⢛⠛⠛⠁⣿⣿⡷⠀⠀⣸⠦⣤⠄
⠀⠀⠀⢠⠀⠰⠀⢦⢆⠀⠀⠀⡄⢀⠀⣠⣿⣄⡁⠺⣿⡿⠟⣦⣴⣿⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢿⡟⠥⠀⢀⠟
⠀⠀⠀⠀⠁⢠⡰⢼⣿⣦⠀⠀⠀⣀⣰⡿⠛⠁⠀⠀⣀⠀⣲⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢳⣶⣶⠁
⠀⠀⠀⠀⠀⠀⠉⠚⢿⡿⣷⣄⠃⢻⡟⢀⢀⡀⠀⠀⠻⢿⡿⢟⡈⢈⣦⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠙⢿⡋⠁
⠀⠀⠀⠂⠀⠀⠀⠀⢠⣷⠶⠋⠁⠀⠈⢠⡁⠀⠀⠀⠀⠀⠀⢛⣿⣾⠟⠀⠀⠀⣠⡆⠀⠀⠈⠀⠐⢆⡀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⠀⢿⡿⠃⠀⠀⠀⠀⠠⠀⠙⢦⣄⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⠁⢲⣶⣤⡀⠀⠀⠙⣀⠀⠀⠠⢴⠒⠋⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠀⢸⡟⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠔⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠻⣄⣀⣀⡈⢋⠀⠐⠁⠀⠀⠀⡠⠐⠁
⠠⠴⠆⠀⢀⣺⠏⢀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠈⠆⣼⠃⠀⣠⠐⣦⣠⡀⣴⡄⢠⡟⠁⡄⠀⠿⠋⢉⣠⠘⠛⠁⠀⢠⠂⠊
⠀⠀⠀⠀⢬⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠻⢿⣿⠙⠿⢿⡷⠋⠀⠊⠀⠴⠒⠉⣠⡀⠀⢀⠠⠀⠲⠲⠶
⠀⠀⠀⢠⡆⠀⠒⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠼⢀⣠⡶⠾⠛⢫⡁⠉⠙⠺⣄⠉⠀⠀⠀⢀⠤⠤⠿⢄⣃⡀
⠀⠀⠀⣨⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠄⠾⠏⢁⡘⢠⡄⣴⢉⣷⡄⠀⠀⠱⠆⠀⠈⠀⢀⣠
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠂⠀⠻⢿⡿⠇⠙⠿⠛⠀⠀⠀⠀⢀⠀⠙⠻⢯⣴⣄⡀
⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⡟⠛⠹⢲⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠈⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⠀⠀⠈⠀⢠⣶⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⡀⡿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⢂⣤⣶⠛⢿⣠⣧⣤⣿⠿⠿⠿⠿⣷⣄⠀⠙⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⢀⣰⣿⠿⠿⣦⠜⠛⢻⣿⠀⠀⠀⠀⠀⢸⣿⣿⣶⣧⡀⢠⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⡀⣈⠿⠚⠻⢿⡆⠀⠀⠀⠀⡼⠋⠉⠀⠙⣿⣾⣾⡿⢫⣍⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⢀⠴⠋⠈⣿⠟⠀⠻⡟⠀⠀⠀⠀⠙⣄⠀⣠⡞⠀⠀⠀⠀⠀⢹⣯⠙⣧⠾⣿⣧⠀⢸⡿⠿⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢀⣾⣿⣿⣿⣿⡏⠀⣠⣴⣶⣿⣿⣄⡀⠀⢀⣿⠀⠀⠀⡁⠀⠀⠀⠀⢁⣹⠫⠝⣇⡀⠀⠀⢀⣠⣾⣿⡿⣥⣤⣾⣿⠀⠀⠠⠀⠀⠹⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⣿⣿⣿⣿⣿⣇⡾⠿⢿⣿⡿⠛⣿⣿⡿⠿⠛⠲⢦⣼⣿⣶⣶⠾⠛⠉⠉⠳⡞⠙⠈⠉⠉⠻⣿⣿⠋⠀⠹⣿⣿⠛⡆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷
⠀⣼⣿⣿⡿⢿⣿⣿⣿⣿⣦⣤⠿⣧⢀⣼⣧⡀⠀⠀⠀⠤⢝⣿⣿⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⣿⠁⠀⠘⢦⡀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⢠⣿⣿⣿⡇⠀⠈⠙⢿⣿⣿⣤⣤⡿⠊⠻⣿⣿⣶⣤⣤⣶⣾⣿⣿⣷⣤⡀⠀⠀⣸⠏⣧⠀⠀⠀⣰⣿⣇⢀⣧⣤⣿⣦⣤⣠⣤⣷⣦⡀⢀⠀⢻⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣧⡤⠼⣄⡀⢿⡿⠋⠁⠀⠀⠀⠈⢿⡿⠁⠀⠀⠙⢿⣿⡇⠈⠛⢶⡂⢸⢰⣿⠿⠒⢿⣿⣿⣋⣁⡀⠀⠈⠙⢿⣿⡿⣿⡿⠋⣦⡑⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣟⠉⠀⠀⠀⠀⠉⠻⣧⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠙⣧⠀⠀⡀⢃⢸⣼⠁⠀⠀⢸⣿⡿⣬⣁⠀⠀⢀⣀⣴⣿⠀⢸⣷⣴⣿⣷⣀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣤⣀⣀⣈⣉⣽⣿⣦⡀⠀⠀⢀⠀⣾⠀⠀⠀⠀⠀⠀⣠⣿⣷⣦⣬⣾⣯⣿⣠⢀⡠⠟⠋⠀⠀⠉⢿⣿⡿⠋⠉⠙⢷⣻⣇⡀⣙⣿⣿⣿⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠈⠙⠲⣄⣨⠶⠿⣄⠀⣀⣠⣤⠊⣭⠤⠴⠶⠨⢽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⠀⠀⠙⢿⣿⣟⠛⠣⢤⣀⡀⠀⠉⢻
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣯⠐⢂⣽⠯⢁⡀⠀⠀⠀⠙⢿⣿⠿⠟⢻⣿⠻⣟⠷⣤⡀⠀⠀⢄⢸⠁⠀⠀⠀⠀⠀⠀⣼⣿⡌⠑⠄⠀⠙⣆⣀⣴⣾
⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⢪⢛⠋⢳⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢠⣿⠃⠈⠁⠈⠛⠶⣄⡼⠿⣤⣀⣀⣠⡤⠴⢾⣿⣿⣿⣄⡀⠀⠀⢹⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣿⡟⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⣼⣧⣤⣤⣶⣿⣿⠀⠀⠀⠀⠀⠀⡸⣄⠓⣸⡏⠁⠀⠀⠀⠀⠈⠻⣿⠿⠿⣷⣶⣾⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣟⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣾⣿⠿⠛⣩⠟⣿⣿⠀⠀⠀⠀⠀⣡⠞⠘⠛⠳⣄⠀⠀⠀⠀⠀⠀⡰⣇⣀⣴⠿⣿⣿⣿⣿⡟
⠀⠀⢿⣿⣿⣿⡛⠉⢻⣶⡴⠿⣭⣄⣀⣀⣀⣀⣀⣠⠿⣟⠉⠙⣿⠃⠀⠐⠁⢸⣟⠛⠧⣤⣤⣴⣿⡟⠀⠀⠀⠀⠈⣦⣄⡀⠀⠀⣰⣿⡏⠙⣷⣤⣼⣿⣿⡿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣀⣠⣿⡿⠛⠉⢉⣩⢿⣇⣀⣾⠛⣷⣿⠀⣀⣠⣴⣿⡄⠁⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠉⢀⢾⣿⣿⣿⣦⣾⣿⣿⣿⣿⠟⠋⠛⣦⣄⣀⣸⣿⣡⣄⠀⠀⢀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠒⠵⠋⣿⡟⠿⢿⣿⣿⣿⣿⡇⣀⡀⡀⢸⣿⠏⢉⣽⡛⢻⣿⠻⠏⣉⡀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣷⣄⣐⠐⠀⠀⠀⠈⠀⠀⠈⠛⢿⣿⣿⡁⣿⣾⡆⠑⠀⠘⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠛⣋⣿⣿⣦⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉

⠀⠀⡠⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠐⠉⠀⠹⠋⠑⠊⠁⠀⠀⢽⠋⠒⠂⠒⠒⠒⡿⠀⠩⠤⠄⠤⣲⡂⠀⠀⠒⠂⠀⢸⠬⠑⠚⠆
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢘⣃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡔⠈⠈⠁⢂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣖⣒⠩⢵⡀⠀⢀⠀⢘⢀⠀⡀⠀⡘⠀⠓⠀⢸⠀⠀⢀⢈⢀⡀⡀⠀⢀⣔⡒⠶⣄
⠀⠀⠀⠀⢓⡂⠭⡽⠁⠀⠀⠀⢈⠀⠄⠀⠀⠈⠂⠀⠒⠁⠀⠁⢔⡄⡈⠀⠀⠀⢸⡒⠨⢭⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠂⠀⠀⠀⠙⠋⠓⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⠉⠉⠉⠛⠛⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣦⡀
⠀⠀⠀⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠙⣦⡀
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠠⠬⠷⣄
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠻⢷⣶⣶⣾⠂
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⣼⡟
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⢀⣴⠶⠋⠀⠀⠀⠀⠲⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣠⠞⠉⠙⢦⣠⠞⠉⠑⢦⡀⠀⣀⣀⣤⣽⣷
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠠⠀⠀⠀⠀⣠⠟⠁⠀⠀⡼⠁⢠⣶⣤⠈⠁⠀⣤⣶⡄⢳⡀⠘⠻⠿⢿⣥⡀
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢶⡇⠀⠀⣴⠏⠀⠀⠀⢸⠇⠀⠈⠛⠁⠀⠀⠀⠈⠋⠀⠀⢷⠀⠀⠀⠀⠙⢿⣦
⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⢦⣴⣿⣶⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠘⢧⣀⠀⠀⠀⣀⡴⠛⠉⠀⣾⣿⠿⠾⠟⠛⠁⠀⠀⠀⠈⢧⡀⠀⠀⠀⣠⢦⡀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠻⢿⣿⣿
⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⢀⣈⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠚⠁⠀⠙⠲⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡿⠃
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⢿⣿⣛⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠓⠞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀
⠀⣠⣤⣤⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢫⡧⢤⠄⠀⠀⠀⠀⠀⠀⠀⣤⢬⣏⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡆
⠀⠘⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢧⡀⠀⠀⠀⠀⠀⠀⠀⡨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣽⡿⠃
⠀⠀⠀⠈⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠙⡄⠀⠀⠀⠀⠀⡞⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⢠⣶⠿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⠶⣸⠉⠙⠒⠃⠀⠀⠀⠀⠀⠓⠊⠉⣇⡴⡆⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠙⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣿
⠀⢠⣿⣋⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠋⠉
⠀⠈⠛⠛⠛⠛⠛⠛⠛⣿⣷⠆⢀⣠⣤⣤⣶⠶⠶⠶⣶⣤⣀⣀⣀⡀⠀⢀⡀⠀⢀⣤⣶⣶⣦⣄⠀⠀⢀⣀⣀⣠⣤⣦⣤⣶⣶⣶⣶⣶⣶⡶⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠿⠛⠋⠉⠛⠁⠀⠀⣀⣽⠉⠉⠉⠙⠿⣦⣿⡿⣿⠿⠃⠀⠀⠈⠻⣷⣶⡟⠋⠙⠛⠃⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠈⢹⡇⣿⠀⠀⠀⠀⠀⠀⠈⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠓⠒⠒⠚⠃⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢲⡂⢄⡀⡐⠃⠐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠘⠢⠈⠻⣴⣄⡃⠀⡖⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⢀⡀⠀⠀⢠⠄⠠⠀⠐⣠⡆⢹⣿⣶⣿⣀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠁⠠⠈⣇⠱⠂⠈⠙⠻⣷⠿⠟⠛⠻⡿⠭⡉⠉⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠤⠒⢷⡀⢠⠊⠀⠀⠀⠀⠀⠂⠀⠀⣀⣀⣀⠀⠀⠈⢦⠀⠀⠐⢄⡀⠀⡀⠠⣤⡖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠒⠒⢬⣿⡇⠀⠀⠀⠀⠲⠟⠀⠠⠂⠀⠈⠀⣁⡄⠀⢸⣆⠀⠀⠀⠙⣿⡁⢀⣀⣉⣉⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠗⠒⠛⠒⠛⣿⣿⠄⠀⠀⠀⣀⡀⠀⠂⢀⣰⢎⡉⠉⢣⡴⠀⠘⠀⢡⠀⠀⠀⠹⣿⣧⠤⡤⠠⠴⢿⠄
⠀⠀⠀⠀⠀⠀⠀⡠⢖⣁⡀⡴⠂⠠⠤⣄⡈⣷⡀⠀⢀⠀⠙⠇⠀⡇⢈⢥⠈⠉⠡⠆⠀⡇⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⠠⠒⠃⠄
⠀⠀⠀⠀⠈⠉⠉⠈⠁⢤⡄⠀⠀⢀⠀⠉⠐⢺⠗⠀⠼⡀⠀⠐⡀⠳⡽⠣⠀⢠⡀⠀⠀⣿⡤⠀⠏⠀⠀⠀⣰⡿⠚⠁⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠇⠀⠀⠀⠈⠳⠾⣦⣹⡆⢀⠈⢠⠱⣆⠀⠈⠀⢀⡤⠛⣠⡶⠄⠀⠀⠀⣿⡅⠀⠀⢈⣴⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡈⢙⣧⡈⠁⠺⣷⣝⡀⠀⢀⣫⠤⢾⣇⣀⡠⠀⢀⣴⣿⣏⣠⡴⠿⠿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢀⠸⠟⣿⠶⠦⠤⢈⠑⠐⠿⢥⣤⣾⣯⣁⠠⠶⠋⠀⢹⣟⠳⠒⠂⠐⠛⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠁⠀⠀⠀⠀⠙⠂⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠠⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢀⣀⣀⣠⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠩⠉⠀⡉⠉⢠⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⢾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡖⠀⠀⢁⢠⣾⡿⣤⣤⣶⡀⠀⠀⠀⢀⡀⢀⣠⠶⢶⣏⠈⠁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣠⣤⣶⠛⠁⠀⠈⠀⠀⢨⡿⠶⠶⣿⡟⢻⣿⠃⠀⠀⠈⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠘⠀⠀⠀⠀⣀⡴⠿⣔⠀⠀⠸⡄⠀⡿⠋⠑⠒⠲⠴⠬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠈⠐⢦⠀⠗⢴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠹⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⡞⣱⣜⢀⢠⠄⠠⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⣥⠓⡁⠀⠀⡄⠈⠁⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠃⠀⣸⣷⠀⠘⣿⣃⡄⠀⠈⡇⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢆⠐⡜⠿⠿⡣⡔⠈⠛⠓⠀⢠⡤⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⡉⠆⠀⡇⢱⠾⣿⡞⢱⣶⣴⡦⠤⢀⠀⡁⠀⣨⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⠈⠀⠑⢊⠔⠛⠥⢜⠛⠁⠀⠀⠘⢛⡰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠠⢀⣤⣸⠃⠀⠤⢀⠀⠈⠙⠛⠓⠤⠀⠈⠉⡑⠨⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⡀⡶⠒⠀⠀⠀⠀⠄⠊⠀⠆⠈⠉⣂⡄⠀⠀⠔⢫⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠘⠀⠇⠀⠀⠀⠀⠌⠀⠀⣤⠀⢶⠀⣾⠆⣿⣮⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡄⠀⠀⠀⠀⡘⢠⡌⢃⡀⣠⣄⣰⣶⡄⣬⡅⠻⠟⣠⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠌⠃⡀⠀⠀⢰⠃⠀⠀⠈⠁⠾⢡⣾⡍⡤⣟⠃⠾⢆⡉⣭⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡀⠀⣦⣀⡀⡜⢠⣶⡴⠿⠶⣿⣎⡉⢾⣽⠎⣷⠹⣮⡡⢖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠇⣤⣾⠤⠀⣹⠃⡉⢀⡄⠆⠀⠺⢟⡀⣴⣷⡎⡇⠘⠛⠪⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠌⢩⡳⠀⠟⣉⠄⠖⡐⣂⠀⠀⣙⠋⣠⣭⡀⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠈⢁⣜⢛⡀⠛⢶⡆⠛⢣⣬⡛⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢻⣝⡋⣴⣦⢰⣷⢌⣻⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠚⠁⠀⠑⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⢀⣠⡀⠀⣠⣤⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⣿⣿⣿⣤⣶⣾⣽⣿⣶⣾⠅⣂⡠⠼⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠟⠉⢶⣿⣷⣿⣟⣿⡿⢿⣯⣿⣿⣥⡟⢺⡤⣗⠒⠒⠐⠂⠛⣤
⠀⠀⠀⠀⠀⠀⠀⢰⢃⣜⣢⣼⡿⣯⢿⣿⣏⣹⣇⣿⡿⣟⢯⠻⣿⣿⣤⣿⣷⣶⣀⣤⣞⢿⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣼⣿⣿⣿⣿⣿⡿⠿⠉⠙⣿⣿⣜⡎⢃⠣⢸⣻⣿⢿⣽⣿⣷⣼⠘⡏⣷⡄
⠀⠀⠀⠀⠀⣴⣦⣜⣿⣿⣿⣿⣿⢛⣂⣇⠀⢀⠼⠛⢿⣿⣿⠛⠒⠓⢿⣿⣿⣿⣿⣻⣿⣧⣇⣲⣿
⠀⠀⠀⠀⠀⡯⣷⢻⢷⣿⣿⣿⡟⡛⠉⢙⠖⠉⠀⢀⠔⠉⢳⣄⠀⠀⠀⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⡗⣿⢼⢊⣿⣅⣝⢳⠄⠀⣠⠃⠀⠀⠸⠀⠀⢸⡿⠀⠀⠀⢿⡿⣾⣏⣿⣿⣯⣿⣿⣿⣿⠷
⠀⠀⠀⠀⣰⠖⠛⢾⣸⣿⣿⣯⣨⣶⣾⣯⠀⠀⣠⡃⠀⠀⠘⣇⢣⡀⠀⠀⠛⠻⣽⣷⢻⣯⣅⡼⣌⠙⡄
⠀⠀⠀⠀⣽⢂⠀⠀⠈⢯⣿⣿⣿⣽⡟⠁⠀⢰⣯⣤⣤⠄⣭⣿⣯⡵⠀⠀⠀⢰⡟⠃⠁⢺⡤⢶⠃⠀⠨⡂
⠀⠀⠀⠀⠘⡄⢰⡀⡀⠸⣷⣿⣿⡿⢟⣧⡀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⣀⣤⣾⣟⠀⢀⣉⣷⣤⣁⠀⢀⠇
⠀⠀⠀⠀⣤⠛⠋⠉⠃⣢⣼⣿⣿⣏⡙⠲⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣽⣿⣿⢿⣿⣿⣽⡏⠃
⠀⠀⠀⠀⠘⢶⡂⢀⣀⠯⣨⣿⣹⣿⣿⣏⣺⣿⣻⣷⣦⣀⠀⢀⣤⣺⣿⣟⢙⣿⡿⣿⣿⡿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠈⠱⣿⣾⣿⣿⣷⣿⢿⣿⣽⣁⣽⣿⣿⣿⣭⣵⣶⣾⣿⣿⣾⣯⣿⣿⣛⠄⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡟⠋⠉⠙⢿⣽⣻⣿⣿⣿⣿⡟⣠⠿⣿⣾⣿⣿⣿⣿⣿⡆⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⠀⣄⣘⢼⣹⣍⣿⣿⣿⣿⣿⣿⡽⡋⣟⣺⣿⣾⣽⡗⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⢿⣿⣿⣿⣝⡻⢭⣩⠿⠬⠤⣥⡽⢻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠛⠉⠹⡿⠿⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢤⠀⠀⠀⠀⠂
⠀⠀⢀⠨⠄⢠⠀⠀⠀⠆⠀⠀⠀⠄⠁⠈⠀⠀⠐⠀⠐⡂⠀⠂⠀⠀⡁⡀⠂⠀⠤⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠈⠀⠀⢀⠐⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠕⠀⠠
⠀⠀⠐⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⢒⣤⣰⢄⡤⢀⣂⣦⣤⣄⠄⣀⣠⣄⣀⢂⡀⣀⣠⣴⣤⣦⠖⣰⣶⣦⡤⣂⡴⣶⢦⢀⠂⣤⣬⣤⣆⣀⠠⣀⢀⡀
⠀⠹⠟⡵⢫⣤⡿⠛⠻⠯⠠⠾⠛⠿⡿⠿⢋⣾⠾⠟⠛⠉⠇⠚⠉⠍⠙⠾⠾⣿⠛⠟⠣⠺⡍⠯⠵⠿⠟⠾⣿⠼⠛⠒⠂
⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⢀⠀⠀⠀⠃⡀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠰⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣉⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣫⡟⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⢐⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣬⡻⣃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣏⣽⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣩⣤⣯⣀
⠀⠀⠀⠀⠀⠀⠀⢄⠳⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣏⣿⣿⣿⣿⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⣬⡍⣙⠿⣁⡀
⠀⠀⠀⠀⠀⠀⢠⠛⠓⠤⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣿⣿⡟⣿⣏⣙⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣦⠘⠱⢖⣭⠴
⠀⠀⠀⠀⠀⠀⣆⣉⠑⠡⠔⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣯⣰⣾⣿⣿⣟⣍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠥⣞⣠⣅⢠⣝⢲⡀
⠀⠀⠀⠀⠀⠶⠀⠄⢬⠁⠄⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣯⣺⣿⣦⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡴⢿⠃⠝⠂⠩⢍⣥⠄
⠀⠀⠀⠀⠪⠤⣄⢀⣀⠀⠤⠀⠊⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⢻⣿⣿⣿⣿⣿⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠦⣒⠂⠶⠒⣛⣩⣠⣿⣀⠴
⠀⠀⠀⢰⡇⢀⠀⢀⣀⣁⢀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣻⣷⣾⠟⣻⡿⣿⢻⣿⣷⡶⠂⠀⠀⠀⠀⠀⠠⢄⡠⢷⣴⣇⡴⣦⠠⢄⢤⣤⠚
⠀⠀⢀⠈⠩⠈⠁⠀⠀⢀⡁⢀⣀⠡⠐⠀⠀⠀⠀⠀⠀⠈⠻⣿⣼⣿⣡⣬⣽⢰⣿⣜⣿⣶⣴⠼⠀⠀⠀⠀⠀⢀⡞⠶⠏⠽⠏⠸⠛⠒⣉⡁⢖⠡⠞⠋
⠀⠀⡈⠳⠄⢉⠺⠄⢤⠀⠠⠀⠀⢀⠠⠘⡀⠀⠀⠀⠐⢆⠀⣄⣶⣟⣿⠟⢿⣿⢿⣿⣻⣿⣉⣄⢀⣀⠀⠀⠰⣮⣍⡘⠃⠾⠒⢻⣧⠀⢁⠴⢾⡇⠔⠚
⠀⢠⠙⠠⠤⠤⠄⢠⠀⠀⠐⠒⠀⠀⠀⠀⠱⠄⠀⠀⠀⠈⠙⣋⣴⣿⣵⣾⣿⣿⡞⢻⣿⣝⡻⣿⡛⠁⠀⢀⡚⠿⠾⠓⢓⡂⢀⣤⠄⢤⣤⡀⠈⣥⣤⠀⣀
⠀⠀⠘⠂⠀⠒⠀⠠⠠⠤⠲⠠⠔⠠⠀⠀⠀⠀⠀⠀⠘⠛⠿⡟⣿⣿⣉⣹⣿⢻⣿⣯⢯⣅⣸⣷⡭⠷⠀⠈⠉⠻⠟⠡⠋⣿⣼⠷⠢⠌⠈⠛⠄⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠋⠉⠻⢧⡼⠿⠿⠟⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣧⣄⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠠⠼⠧⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⢸
⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸
⣿⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣄⣀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾
⣿⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿
⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸
⣿⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢸
⣿⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠉⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠉⠲⠤⣄⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢰⠇⠇⢃⠀⠰⡆⠀⠳⢀⠈⡀⠀⠤⠀⠀⠀⠀⣇⠀⠀⢀⢆⠀⠰⠀⠀⠂⠀⢢⠀⢸⠀⠀⠆⠐⠀⠐⠴⠀⠐⡄⠀⠀⠀⢸
⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣾⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⠉⢩⣭⣭⡉⠈⠉⠙⠛⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢀⡀⠀⠀⠀⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠛⣛⣡⣼⡶⢶⣾⡶⠛⠓⠲⣦⣀⣀⠀⠀⠀⢙⣿⡿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⣶⣾⡿⠛⣿⡶⠶⣋⣷⡄⠀⢀⣤⣈⣿⣶⣤⣱⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣶⣶⣤⣄⡀⠙⠋⢼⣿⠇⢀⣾⠋⠙⠏⠛⠻⠇⢠⣿⣯⣉⡁⢹⣿⣿⣁⣀⣀⣴⣾⣿⣿⣿⡶⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣻⠁⠀⠸⣟⣀⣀⣀⣤⣦⣀⣈⡉⠉⠉⠁⢘⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠚⣿⠟⠛⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⣤⣄⣤⣼⣿⣛⣯⣁⣸⣏⢛⣱⣦⣤⣤⣿⡽⣿⣿⣿⣿⠏⠉⢉⣿⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠀⢄⠙⠻⢿⣿⣿⣿⣇⠀⠶⠟⢁⣙⡿⢋⣻⣛⠻⠿⢿⣿⣷⣄⠼⢿⣤⣿⣿⣿⢇⣀⡀⠷⠶⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢠⣶⣦⡀⠀⠙⠿⠋⢀⠀⠈⠁⠀⠚⠻⣿⣿⠿⣿⣿⣿⣿⣽⠛⣿⡭⠟⠻⡟⠋⠉⣅⠁⣴⡆⢈⣿⣿⣿⡛⠉⢠⣄⣀⠈⢻⣿⣿⣿⣿⣯⡀⣀⣴⣄
⠀⠀⠸⠳⣾⡿⣦⣀⠀⢀⡌⠁⠀⠀⢠⣴⠿⠋⢀⣴⣿⣧⣸⠀⢻⣤⠉⡀⠀⠀⣿⡆⢀⠙⣶⠛⢳⣾⣿⣿⣿⣧⡀⠛⠛⠋⣠⣼⡿⠟⠿⡿⢿⣿⡉⢹⣅⣠⡀
⠀⠀⢠⣀⣹⣿⡾⠛⠋⠉⢷⣶⣶⣶⣿⠋⠀⣴⡿⠃⢸⣿⣏⠀⠚⠁⠘⣿⠀⢸⡿⠃⠈⠁⡀⢠⣌⣿⣿⣏⠉⠛⢻⣶⣶⡾⠛⠁⠀⢀⣠⣴⡾⢿⣭⡄⠉⣿⠇
⠀⠀⠀⠉⠉⠀⠓⢀⠀⡀⠀⠀⠀⠉⠛⢻⣾⠋⠀⢀⣸⣿⣯⠄⢠⣀⣤⠙⡀⠘⠻⣄⠀⢠⣟⣾⣿⣿⣿⣄⡰⣆⣸⣿⣏⢁⣤⣤⡾⠛⢹⣿⣧⣀⣉⣹⣶⠁
⠀⠀⠀⠀⠀⠀⢤⡾⢿⣷⠀⢤⡀⣈⡀⢀⡁⠀⣠⣿⣿⢿⣿⣦⠉⣟⠁⡀⢹⡔⠛⣿⡤⢀⣿⠻⣿⡿⠟⠛⠛⠋⠙⢉⣍⠉⢉⣻⠀⣦⡼⠀⢋⣿⣿⢿⣟⡆
⠀⠀⢀⡄⠀⠀⠀⠀⠘⢛⣿⣶⣷⣬⡿⢿⣿⣿⣿⣿⣿⡌⣿⣿⣷⣿⣼⠷⠾⡷⣂⡏⣰⡿⠛⢁⣤⣴⣦⣄⠀⣠⣤⣾⣿⣌⠹⡿⠀⣻⣿⣾⣿⣽⣿⣾⣿⣿⡄
⠀⠀⡄⠀⠀⠀⡀⠀⣾⠛⠁⠀⠀⡴⠶⠾⠟⢀⡸⢿⣿⡤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⠁⠀⠦⣿⡿⢿⡍⢻⣿⡛⢷⣤⣤⣿⣇⠘⣿⣏⣻⡟⢿⣽⡃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣴⣤⣤⣤⡔⠂⠀⠀⢰⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠰⠉⢁⣨⠄⠀⣿⣧⠂⡙⣿⣿⣿⣾⣏⢙⢿⣥⡿⠹⡇
⠀⠀⠀⠀⠂⠘⢦⡘⣿⣄⡀⠀⠀⠀⢴⣦⣼⠿⠷⢶⣶⣶⣴⣿⣿⣿⡗⠒⠈⢉⣭⣭⣛⣿⠟⡩⠛⠋⠀⢠⠞⢃⡤⠀⣿⣿⣾⣧⠸⣯⣼⣿⣍⠀⠀⠉⣷⡆
⠀⠀⣀⣀⣀⠔⠛⠇⢨⡿⠛⢿⣷⣶⣾⣿⠁⠀⠀⠀⠁⢀⣼⣿⣿⣿⣷⣠⡿⢿⣿⡾⠛⠟⠂⠀⠀⡀⠀⠀⢠⣼⣀⡼⠟⠻⣧⣈⠂⢉⡉⢿⡇⣴⡀⡀⣿⣇⣀
⠀⢠⣶⣿⣥⣤⣴⣶⣿⠃⠀⠀⠀⢁⣴⣿⡇⠀⠀⠀⠀⣿⡿⠛⢛⣻⣿⣿⣶⣿⢯⣶⣾⣷⣤⣜⢻⣟⣙⣿⠁⢸⣿⣶⣶⡾⠛⢛⣻⡿⠃⠸⠿⢿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣎⣿⣿⣿⡇⠀⠀⠀⢾⣿⠃⣿⣿⠟⣽⣿⠟⢁⣼⣿⣿⣿⣿⣟⣿⣧⡈⣿⡗⠿⠿⠻⠋⣠⣾⠟⣉⣤⣾⣷⣦⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣶⠶⣶⣾⣿⣀⣿⣿⠀⣿⣧⡀⢻⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣁⣰⣧⡼⠿⣿⣿⣯⣭⣅⣤⣴⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⢻⣯⢻⣿⠀⣿⣿⣿⣿⣿⡷⢌⣻⣿⣿⣽⣿⣸⣿⣻⣿⣦⡁⠀⠛⢻⠿⣿⣿⣿⣿⣿⣿⣿⡛⡯⢹⣤⣿⣿⣿⣍⡙⣿⣌⡹⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡏⢰⣿⣿⣿⣿⣿⣧⠘⢻⣿⣿⣿⣿⠛⠻⢟⣫⢬⣷⣤⣤⣴⣄⡈⠉⠙⠿⠉⣷⣿⣿⡿⢋⣿⡇⢻⣿⣿⣷⣦⣉⣷⠃
⠀⠀⠀⠀⠀⣠⣴⣶⠛⠀⠨⢀⣿⣿⣿⣿⡟⠛⢿⣇⣻⣿⣿⣿⣿⣿⣶⣈⠁⠀⠉⣽⣿⣿⣿⣿⣿⣷⣤⣤⣬⣽⣿⡖⠛⠁⠀⠘⠋⠹⣧⣶⡿⠃
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣄⡈⢿⣿⣿⣿⣿⡷⠀⣿⡏⠉⢻⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⠿⣿⠟⣶⣶⠘⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣶⣾⣿⣿⣿⣿⣿⠶⠋⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣏⣽⣟⣻⣽⣿⣾⣿⣿⣿⡿⠗⠀⢁⣤⣿⡿⢿⣿⣶⡶
⠀⠀⠀⠀⠀⣼⠃⠰⠀⠀⠌⠉⢛⡿⠿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣿⡿⣿⣿⣿⣿⠿⠖⠚⠙⠛⠁⠀⠀⠀⠙⢿⣶⡀
⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⡟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⡇
⠀⠀⠀⠀⠀⣶⣠⠄⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣼⠃⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿⡿⠃
⠀⠀⠀⠀⠀⢻⣇⠀⠀⡀⠀⠀⠀⢢⠙⠄⠀⠀⠀⠀⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡃⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠛⢿⣤⣆⠀⠀⠀⠀⠤⠀⠀⠆⠀⠀⢿⡋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⣿⣷⣶⣤⣴⣦⣄⢘⣿⣇⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⣀⣄⣀⣄⣀⣀⣠⣀⣤⠜⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡛⠻⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡄⠀⢰⣿⡿⠿⣿⣿⣿⣿⣿⣿⠟⠋⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠉⠁⢀⠀⠸⢿⣿⡇⠀⠀⣯⣿⠆⡀⠈⠉⠉⠉⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⠀⠀⠀⠐⠛⢁⣀⣴⣾⡟⠀⠀⠀⠈⠛⠿⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣉⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠟⠛⠛⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣼⣿⣿⣿⣿⡿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣶⡀⣦⣀⢤⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⢀⣉⡽⣵⠬⣥⣉⠙⠀⠀⠀⠀⠀⠀⠀⣐⢶⣤⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠶⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠤⣩⣿⡞⢋⡛⠙⠣⠴⣩⡇⠀⠀⠀⠀⠀⢅⠀⢙⠟⠁⠂
⠀⠀⠀⠀⡰⡓⠢⠄⣀⠀⠀⠀⠀⠀⢠⠄⣠⣥⠀⠀⠀⠀⠘⠀⠑⠺⡧⠐⠊⠀⠀⡃⠀⠀⠠⠤⠄⠤⠤⠤⠥⠤⠆
⠀⠀⠀⠰⠃⠀⡠⠂⠀⠀⠀⠀⠀⠀⣀⡋⠐⢂⡠⠀⠀⠀⢀⣄⠀⠀⡏⠀⠀⢤⠠⠃⠀⠀⠐
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠐⠒⠪⢥⠄⠀⠀⠀⠉⠀⠐⡇⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠑⢄⡀⠀⠀⠃⠀⠀⠀⠀⠁⠒⠂⠉⣀⣙⣁⡀⠀⠀⠀⠀⠀⠀⠀⣀⢤⢀
⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⡀⠚⠞⢀⡃⠀⠀⠒⠒⢀⠀⠀⠀⠀⣠⡔⠓⠁⠤⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⢀⣀⠙⠉⠄⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠓⠛⠛⠒⠓⠚⡋
⠀⠀⠐⠲⠄⠀⠆⠀⢁⠀⣰⡄⠀⠀⠀⠼⡭⣄
⠀⠀⣠⣄⠀⢶⣀⣰⡇⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠
⠀⠀⠔⢀⣤⡆⠀⠈⡦⠌⢀⡄⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⠠⣠⡀⠀⢀⠀⠀⠄⡀⠀⠀⠐
⠀⠀⣔⠕⠀⡀⠀⠀⠀⢐⠄⠁⠀⠀⢀⠀⠀⠀⠀⢢
⠀⠀⠁⠀⠈⠃⠀⠀⠔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣘⠂⠀⠀⢠⠂⠀⠈⠀⠀⠠⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣀⣂
⠀⠀⡆⠊⣀⣆⠀⣀⡄⠈⠂⡀⠀⠀⠀⠠⠠⠄⠀⠊⠀⠀⠁⠀⠩⠂⠀⠐⠤⠁⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠼⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠸⠛⠉⠓⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣀⢹⠀⢰⣿⠇⠀⣠⡾⠁⣠⠤⢾⡇⢿⣷⣤⣀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢧⢸⡟⠀⢠⣿⣇⡞⠀⠀⠀⠀⠳⣯⣝⣛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣇⠀⠘⣿⣿⡇⠀⠀⢀⣀⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠦⠤⠄⠈⠳⣄⠘⢿⣇⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣵⣶⠾⠿⠟⠛⠛⠓⠈⠻⢦⣙⢦⡹⣏
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⢷⣵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠛⠛⠛⠛⠶⣤⡙⢿⡄⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣽⣟⠻⣿⠀⠀⠀⠀⠀⠀⠻⣎⢧⠀⢠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡟⠛⠛⢁⣿⠀⢺⡄⠀⠲⢿⣷⣦⡀⢹⡌⠀⣾⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠸⢿⡆⠈⣷⠀⠀⠀⠀⠉⢻⡀⡇⢸⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⣀⡶⢹⣴⡏⠀⠀⠀⠀⠀⠀⠃⡇⣸⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠟⠃⡼⠋⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⢋⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡼⠛⣩⣤⣴⡶⠾⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⣠⣧⡀
⠀⠀⠀⣠⣷⡄⠀⠀⠀⠀⠀⠀⠀⡐⣚⢛⠢⡀⠀⠀⣹⠀⠀⠀⠀⠀⣤⠀⠀⠘⠿⠿⠏⠀⠀⠸⣿⣸⠇
⠀⠀⠀⢿⣿⡿⠀⠀⠀⢀⠀⠀⠀⣉⣍⣩⣩⠅⠀⢰⣻⡇⠀⠀⢠⣟⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡀⠀⠀⠒⠒⠀⠀⠀⢠⢳⠇⠀⠀⠀⠻⠿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠖⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠶⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠃⠈⣍⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠶⠞⢣⡀⢀⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣁⢠⡀⠀⠁⣈⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠣⠆⠩⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠑⢄⠀⠠⡟⠰⠀⡘⠛⠳⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢁⡜⢀⢠⣩⠶⠊⡁⠄⢠⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠋⠀⠀⣡⠊⠀⠀⠰⡇⠳⢤⡴⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⣔⠢⣰⣿⠀⢠⠖⠉⠛⡄⠘⠤⠄⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⣄⣈⠤⣝⠨⠃⠈⠲⠃⠀⢸⡄⣀⠠⣞⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡏⠀⢀⠠⣎⠳⣄⡠⠀⢀⣠⠶⢤⣄⢀⡠⠥⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃⡆⠀⠁⠀⢈⣀⡀⢉⡉⠡⢔⣂⡀⠀⠉⢢⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⠇⠈⠶⡤⠄⢻⠀⠆⢀⠀⠀⡞⠁⣤⣡⠀⠀⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠑⣄⡷⢚⡽⠋⠀⠣⡀⠀⠁⠀⠰⡇⠀⣟⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⠷⢀⠀⠀⣴⢩⠁⠘⢇⣀⡀⢀⠙⠓⠖⢋⣠⣷⣤⣭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⢴⡌⠀⢰⠸⠆⠀⠠⠂⠩⠸⡇⠘⢀⡆⠀⠀⢑⣚⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠜⠀⠀⠛⠀⠘⡀⠀⠀⠘⠋⢀⡆⠼⠋⢋⠁⠀⡜⠀⣄⡁⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⡔⢋⠑⠀⠀⠀⡏⠂⢤⡤⠔⠊⡀⠀⠀⠀⠂⠢⠡⡀⠀⠀⠀⡤⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠐⣧⡈⠉⠀⢀⡔⠀⣠⡁⠘⠂⣠⢿⣄⠀⠈⠁⡠⠀⢠⠷⠛⠙⡀⠇⣁
⠀⢀⠀⠀⠀⠀⠀⠀⠒⠉⠈⠉⠉⠀⠈⠁⠀⠀⠀⡙⢀⡚⠡⠘⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠈⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠏⣴⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡇⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢷⠃⠄⠁
⠀⢀
⠀⠈
⠀⢉
⠀⠈

⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡄
⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠺⠿⡿⢟⣃⡀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣟⠂
⠀⠀⠀⢀⣿⣷⣿⣇⠀⠀⠀⠀⠀⠸⠿⠿⢿⠿⣟⣗⠀⠀⠀⠀⠀⠀⠀⠦⠉⠀⠄⠀⠀⠀⠀⠀⢘⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⡌⠀⠂⠠⠀⠈⠀⠀⠀⠀⠐⣻⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣏⠙
⠀⠀⢰⡿⠿⣿⣿⣿⣿⠀⠀⠀⢰⡾⣭⣽⣽⣷⠾⣿⠿⠇⠀⠀⠠⠀⠀⠀⠀⠀⠐⠡⠀⠀⠀⠠⢿⢿⣿⠿⡷⠀⠀⠀⠀⠠⠶⠿⠿⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣁⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠂⠀⠿⠆⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢈⣽⠛⢻⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠂⣴⡄⠀⢀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⡏⠙⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⡍⢁⡀⠉⠁⠀⠀⣴⣶⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢻⣿⡟⠛⠚⠛⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⡄⠀⢰⣼⣭⣦⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⣀⣤⣶⣶⣶⣾⣿
⠀⠀⢀⣴⣾⣶⣤⡀⠸⣿⠟⠛⠻⡇⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣿⣿⣿⣿⣿⣿⠦⣹⡀⢀⣀⣷⠁⠀⠈⣿⡿⠟⠁⠀⠀⠀⠀⢀⠔⠂⠐⠄⠀⠒⠒⠠⡀⠀⠙⠿⠁⡿⠟⣹⣿⣿⣿⡿⠁
⠀⠈⢿⣿⣿⣿⡿⠁⠀⢨⣿⠟⠛⠛⢿⣦⣴⣏⣠⣤⣶⣶⣦⡄⠀⢇⠀⠀⢀⢠⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠾⠿⠿⠿⠋⠁
⠀⠀⠀⠉⠉⠛⠛⢦⣤⣿⡇⠀⠀⠀⠀⣿⡇⠀⠘⣿⣿⣿⡿⠋⠐⠠⠀⢰⣼⠼⠰⣧⡎⢀⠡⠐⠢⠀⠀⠀⠠⢶⣶⣶⣤⣄⣀
⠀⠀⣠⣴⣶⣿⡿⠁⠀⠻⣷⣀⠀⢀⣰⣿⣥⣠⣼⣿⣿⣿⡇⠀⠀⣀⣲⡎⣴⣾⣷⣌⢰⡖⠂⠀⠀⠐⠀⠀⠈⠛⠿⠿⠿⠟⠋⠁
⠀⠀⣿⣿⣿⣿⣿⣄⣀⣴⠟⠛⠻⣿⠋⠀⠈⣧⡈⠉⠙⠛⠛⠂⠀⠀⠘⣀⢻⣿⣿⠟⣸⢷⣤⣤⣤⣾⣤⡀
⠀⠀⢿⣿⣿⣿⣿⠟⢁⣾⡀⠀⢀⡛⣤⣠⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠋⠝⢃⢬⣴⣾⠫⡑⠀⠉⢻⣿⣿⣷⡄
⠀⠀⠈⠙⠛⠋⠁⢀⣾⣿⣿⣶⣿⡇⢹⣿⣿⣿⣿⣿⣿⠀⠀⠠⠀⠀⢀⠂⠀⠂⠘⢹⣧⡀⠀⢀⠼⣦⣄⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡴⠋⠻⣿⣿⣿⠿⠃⠀⠀⠀⠀⠉⠁⠨⠀⠀⠀⢀⣿⣷⣶⠁⠀⢄⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⣿⣷
⠀⠀⠀⣠⠖⠲⢄⠘⡿⢿⣿⣿⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣿⣿⣿⠀⠀⠈⠻⣦⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋
⠀⠀⢸⠁⠀⠀⠀⠑⣿⠖⠊⡉⠓⢦⡀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⠀⠹⣷⠀⠙⣷⡉⠓⠶⣤⣤⣀⣈⣉⣭⡥⠆
⠀⠀⠘⠦⣄⣀⠀⡼⢁⣶⣿⣿⣿⣆⠙⡗⠚⠉⠉⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⣠⠀⠀⢻⡇⠀⠘⣧
⠀⠀⠀⣠⠤⠤⠛⡇⠸⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣤⠀⣸⠃⠀⠀⢻
⠀⠀⢸⠁⠀⠀⠀⠘⣄⠙⠻⠿⠛⢁⡼⢟⡒⠢⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠘⣄⠀⢀⡤⢊⠏⠙⠒⢲⣖⠉⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⢀⣀⡀
⠀⠀⠀⠈⠉⠉⠀⡎⠀⠀⠀⢸⠸⡄⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣋⢰⣆⡙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⢀⡜⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢃⣿⡿⣷⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣤⢌⡉⠉⠀⠀⠐⣼⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠸⡟⠱⣿⠃
⠀⠀⠀⠀⢀⣾⣿⣿⡿⢠⣾⠀⣿⣦⡘⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⣧⠈
⠀⠀⠀⠀⣼⡿⠟⠋⢠⣿⣿⣧⣿⣿⣿⡄⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⣾⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣿⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠻⡆⠀⠀⢰⠟⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣤⡔⢶⡟⢻⡶⢢⣤⠐⠛
⠀⠀⠀⠀⠀⡀⢀⡤⢤⡀⠀⢤⣤⠀⣸⠉⠓⠇⡘⠀⠀⢃⡸⠊⠉⣇⠀⣤⡦⠀⢀⡤⢤⡀⢀
⠀⠀⠀⠚⡴⣒⡟⠸⣉⡝⠀⠀⠀⢴⠓⣣⠀⠀⢹⣤⢄⡏⠀⢀⣜⠚⡦⠀⠀⠀⢫⣉⡇⢻⣒⢤⠓
⠀⠀⠈⣸⠼⢤⣿⡤⠂⢺⡁⣴⣄⢎⡁⢀⣉⠲⢎⣿⣿⡡⠖⣉⡀⢈⡱⣠⣦⠌⡗⠔⢤⣿⡤⠧⣇⠁
⠀⢠⡎⣠⠶⢤⠀⠙⣦⡀⠀⠙⠛⢠⣊⠁⠊⠑⠒⢹⡋⠒⠊⠑⠈⣑⡄⠛⠋⠁⢀⣴⠋⠀⡤⠶⣄⢱⡄
⠀⠘⢧⣑⣒⡼⠁⠀⠘⢷⣄⠀⠀⣏⢠⠉⣲⣶⡒⡿⢿⢒⣶⣖⠉⡄⣹⠀⠀⣠⡾⠃⠀⠈⢧⣒⣊⡼⠃
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠻⣦⡄⠈⢩⠎⢘⣫⠞⠁⠈⠳⣝⡃⠱⡍⠁⢠⣴⠟⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡛⢮⠉⠛⣻⠛⡉⠀⠀⠀⠀⠀⠀⢙⠛⣟⠛⠉⡵⢛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠦⠞⢀⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⡀⠳⠴⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠗⣌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢦⡘⢷⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣳⣿⣿⣄⠹⣆⠻⣮⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢏⣴⣿⡿⣇⠈⢦⡘⢷⣌⡪⡙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣻⠟⣡⡞⣽⡿⣡⡏⢧⣀⠙⣦⣙⢍⠪⣷⣍⠛⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣚⡵⡾⢋⣾⢟⣵⠏⣧⠀⠹⣷⢌⠻⣗⢷⣤⡉⠛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣡⢞⣵⡿⣫⣾⠏⣰⣏⠱⣄⠈⠳⡙⠮⣓⢬⡙⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠷⣫⣯⢞⡽⢃⣴⠋⡟⢷⣌⠳⣦⣈⠢⣈⠑⠻⢶⣤⡉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣾⠟⣡⠎⣰⡿⢃⡞⡷⣄⠹⣷⣌⡻⣗⠮⣓⢤⡀⠈⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣡⠞⣡⣾⠏⣴⡟⣰⡗⢌⢷⣄⡙⢿⡾⢷⣮⣙⠻⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠵⣫⠟⣡⢾⢞⡴⢹⡇⠀⠙⢿⣿⡲⢌⣓⢭⣙⠻⠶⣦⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡤⣚⡥⢚⡕⣡⠊⠀⢸⠃⠀⠀⠀⠈⠛⠷⣬⡉⠛⠻⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠋⢁⡴⣫⠞⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠗⠊⠁⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⡤⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡠⡄⠀⠀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⣡⢿⡈⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠃⠀⠀⠀⢩⠄⡠⠹⠄⠀⠀⠀⠀⠀⠨⠥⠀⠠⠬⠀⠀⠈⠁
⠀⠀⠀⠉⣺⠈⠒⠀⠀⠀⣠⣾⣿⡀⠀⠠⠂⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠉⢸⠿⣿⣿⠿⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠁⠂⠁⠀⡤⠀⠀⠀⢠⠄⠀⣼⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⣲⣆
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⣀⣀⣀⠀⠀⣴⣶⠀⠀⣤⣤⣤⣤⣤⡄⢀⣿⣿⠀⠀⠀⠀⠸⠂⣠⣤⣤⣌⠁
⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠈⠉⡧⠀⠀⠈⠀⠀⠀⠻⢿⣿⣿⣿⠀⣸⣿⣿⡇⠐⣞⣳⠂⠘⠋⣉⢉⠙⢧
⠀⠀⠈⣉⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠉⠉⠀⠀⠙⣀⠂
⠀⠀⠀⠈⠠⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⣠⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⢿⠿⠆⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠴⠿⢿⡇⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠆⠀⠈⠛⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢀⠃
⠀⠀⠐⠿⠾⠿⠂⠈⠀⣀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠘
⠀⠀⠀⠸⢆⡀⠀⠀⠀⠉⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠸⣶⣀⢀⡀⠀⢠⡄⠀⠀⣠⣶⣿⣿⡆
⠀⠀⠀⢰⡌⠃⠀⠀⣠⠀⣭⠀⠀⢀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠀⠀⠘⢷⣤⣴⣿⣿⣿⠟
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⠃⠀⠐⠀⠋⠙⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢄⡀⠀⠀⠀⡴⠲⠀⠀⠠⠔⢄⠀⠀⠀⢀⡠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⠁⣄⠈⠁⠀⠈⠀⠀⠀⠈⠃⣤⢈⠅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⣘⡂⡑⠉⠁⠀⢦⢻⣤⣟⡤⠀⠈⠁⢊⢔⣁⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢧⠙⠃⠀⢱⠤⡀⠀⠁⡁⠉⠀⢀⢤⡊⠀⠙⠃⡼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⠳⠄⢤⠀⠀⢳⣽⣷⢢⢣⡰⣾⣿⡎⠀⢀⡤⠈⠕⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⠂⠀⠁⠀⠈⣋⠡⣾⣿⣷⠈⣙⠁⠀⠊⠀⠐⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠂⠀⠀⠢⠤⣌⡉⢪⢉⡟⢉⣠⠤⠖⠀⡀⠐⡁⢶⢆⣀⠀⠠⢴⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⠤⢄⠈⠛⠞⠈⠗⠛⠀⡠⠤⣠⠄⢾⣾⣦⠸⠾⠃⠻⠃⠶⠎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠓⠶⠖⣦⢈⠁⠀⠀⠀⢈⡁⠀⠀⠐⢿⠆⠉⢡⣶⡄⠾⠇⠸⣃⠷⡐⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠈⠈⠃⠀⠁⠀⠻⠃⠀⢾⣻⡆⣉⠥⠤⣬⡉⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠒⠱⠓⢆⠀⠀⠀⠀⣉⡧⠁⠀⠀⠀⠀⠀⡛⠀⠰⣿⠆⣽⣶⢱⣿⣷⢈⣭⡙⠖⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡷⠀⣘⡀⠀⠈⠉⠃⠀⡠⠘⣫⠀⠀⠀⠀⢠⠀⢈⡁⠰⠷⠸⠇⣨⡋⢀⣍⠁⠸⠿⢏⣠⡈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠂⠒⠀⣀⣠⡔⣭⡍⢀⠀⠰⠀⢸⠁⢸⣇⠀⠀⠀⠀⠀⢣⠈⠁⠀⠀⣴⢦⠻⠟⠙⠟⠱⣿⠆⠘⠷⠋⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⢓⢀⣀⠙⠁⣋⡀⠂⠀⣰⠆⠻⣜⢦⡘⠋⠀⠀⠀⠀⠀⢣⠀⠀⣤⣝⠋⠀⠦⠀⠀⠀⠀⣿⠆⢾⣿⠆⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⠄⠀⢀⠀⢀⣬⡄⠁⠀⠀⢈⣷⠀⠀⣀⠀⠀⠀⠀⠀⠳⡀⡙⠋⡀⢙⡃⠛⢠⡄⢾⡶⢠⣶⣦⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⣀⡈⠁⠀⠀⠀⠀⠈⢻⣄⢤⣌⡋⠀⠀⣀⡴⠆⠐⠽⣤⠇⢈⢩⣦⢀⣤⡀⣴⢦⠉⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠦⠞⠭⠐⠈⠁⠀⡘⠻⠄⠀⣠⡀⠉⢓⠂⢅⢄⡀⠉⢱⣾⣣⠄⠉⠀⠓⠐⣶⣜⣛⣡⣭⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣀⠈⠁⠈⠁⠀⠠⠀⠁⠐⣷⠀⢿⡇⣴⡏⠃⠸⣮⣙⣂⣛⣫⠀⠿⠶⣄⡀⠀⠈⠉⠙⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠈⠹⣿⢃⣤⣙⠆⢀⡉⡃⠀⠁⠈⠓⠄⠰⣄⢈⣉⣈⠀⠛⢲⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢘⣧⠀⢒⡺⠿⠀⡐⢀⢠⡿⢸⢧⢀⡖⠖⠘⡯⢋⣩⢉⡴⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠈⠉⠀⡼⠟⠂⠰⠀⢂⠀⠁⠘⠋⠀⠀⠀⣠⠦⠟⠁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⢈⡀⠰⢂⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡤⠬⠒⣬⠬⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠠⣀⣤⡄
⠀⠀⠀⠀⠀⠀⣴⣶⣀⡄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣰⡬⣿⡇
⠀⠀⠀⠀⠀⠀⠟⠻⠶⠟⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢏⣤⡀⣸⡆⠀⠙⣗⠂
⠀⠀⠀⣴⠅⠛⢀⡴⠾⠃⣽⡔⠦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣄⣈⣉⡀⢽⡯⠀⣀⣉⣀⠳⡄
⠀⠀⠞⡍⠙⠛⠀⢀⣀⡀⢹⡅⠀⠈⢉⡀⠀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠿⠀⠈⠝⣻⠧⢤⣇⠼⢿⠻⠁⠀⣱
⠀⢠⠈⢃⣰⢀⣶⣤⣿⣤⣾⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢤⣦⡔⠠⣦⡀⠀⠀⠀⠀⠀⡦⠋⠀⢤⣶⣶⠚⡟⢢⣶⣤⠀⠘⢻⠀⠀⠀⠀⠄
⠀⠘⣾⣼⢓⠀⣤⢿⣿⡿⣤⠀⢠⠀⢲⡆⠀⠀⠀⠀⠀⠟⠛⠚⠿⣿⡦⠀⠀⠀⠀⠀⢳⡀⠴⠋⢙⠁⣺⣿⡊⠘⠙⡶⢠⠆⠀⠀⠀⡾⣄⣀⣤⡄
⠀⠀⠻⣿⣯⣴⣌⡐⠛⠂⠀⠹⠟⢦⡞⠀⠀⠀⣠⠞⠀⠂⠉⠀⣥⣽⣦⡀⠀⣄⠀⠀⠀⠹⣄⠀⠼⠀⠀⡇⠁⢴⣼⡥⠀⠀⠀⢀⣨⠷⠧⡽⠿⣧⡀
⠀⠀⠀⠙⠫⡈⠀⠀⠀⠰⠁⡰⠾⠉⠀⠀⠀⡼⣏⠻⡀⠀⠶⠻⠙⠉⠮⠟⣿⢻⠧⠀⠀⠀⠀⠉⠓⠣⠤⠐⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⢠⠇⠀⠀⠠⣑⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢰⡄⠀⠙⠾⣄⠀⢠⣧⠀⠀⠀⣿⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⣴⠶⠃⣘⣣⣴⡼⡃⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡀⠀⠰⢦⣰⣐⣷⣀⣰⠶⢛⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠉⡤⠘⠻⣺⣿⣿⣿⠵⣦⡼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣹⣇⢀⣿⡁⠀⠈⢛⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢉⠶⣄⠄⠀⣶⠏⠏⣧⠁⠁⠀⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠐⡉⠁⢨⡏⠈⠈⠁⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠀⠈⠛⠂⢵⣴⣿⣼⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⠄⠉⠾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣲⣽⣄⣠⣽⣿⢥⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠈⣅⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⡄⠀⠀⠀⢀⡼⠛⣧⠀⠀⠀⠀⠠⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡾⠁⠀⠘⣷⠴⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠰⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⢾⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠃⢠⡏⠀⠀⢀⠤⢀⠀⠈⣿⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠒⠉⠀⠀⠀⠈⠒⠘⣻⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⣀⡀⢴⡦⠙⠤⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⡇⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⣁⣀⠀⠀⠀⣀⣀⣀⣀⡀⢾⡹⠈⠐⠋⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⣀⣭⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢻⡏⠈⡻⡱⢇⠀⠀⠀⠀⠀⠀⢀⣀⣘⣧⣸⣟⣩⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣉⠁⠙⡫⢤⡀⠀⠀⠀⠀⣼⠄⣀⡸⠉⡟⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠉⠀⢰⡅⣀⠇⠀⠀⠀⠀⡟⠒⢠⡇⢸⣉⠒⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠝⠀⠀⠀⠣⠄⣼⣀⡎⠀⢈⡏⠻⢦⣀⡀
⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⣦⠀⢀⡠⢄⠉⠉⠉⠀⠀⠀⠉⠛⠶⣦⣤⣀⣀
⠀⠀⢠⣶⡛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠃⠖⠞⠧⠸⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡼⠛
⠀⠀⠀⠈⠉⠛⠶⢶⣤⣤⣤⣤⠋⠉⠉⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣿⠉⠙⠛⠓⠒⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠏⠉⢦⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠚⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⣀⠿⢷⣤⣀
⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡄⠛⠃⠀⠀⠀⠀⠉⠛⠿⢶⣤⣤⣀⣀⡀
⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⠀⠀⡖⠛⢲⡘⠟⢤⡄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⡟
⢤⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣇⣠⠿⡷⠀⠃⣤⠾⡅⠀⠀⠀⠘⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠉⠓⠶⠶⠤⣤⣤⠴⠶⠚⠛⠉⣿⠧⠞⠀⠀⠀⢀⡴⠃⠀⠙⢦⡀⠀⠀⠈⠻⣭⡛⠳⠶⢦⣤⣤⣤⣤⣤⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠃⠀⢀⣀⡤⢾⡇⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠙⢳⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⢈⡇⠀⠀⠀⠀⠀⠀⢿⠉⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣬⣇⣀⣀⣀⣀⣀⣀⣼⣦⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢸⢈⠉⢈⠁⢸⠀⠈⠀⡉⠀⢸⠀⢸⠀⢸⠀⢸⠀⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⢸⠀⠀⢸⠀⠸⠀⢰⠀⡇⠀⠈⠀⢸⠀⠸⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⠚⠚⠓⠚⠓⡟⠛⠛⠒⠛⠒⠛⢲⠛⠒⠛⠒⠛⢲⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢤⠤⠤⠤⠧⠤⠤⢤⠤⠤⠤⠼⠤⠤⠤⢤⠤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣸⡀⠀⠀⠀⢀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣨⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠶⣤⣤⣭⣭⣭⣭⣭⣬⣥⣭⣤⣤⣭⣥⣤⣤⠿

⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠁⡀⢐⢠⡀⠋⣨⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡷⠘⠛⡏⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡼⣦⣤⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢜⡮⠖⠀⡎⢈⣡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠐⣾⣧⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠂⡎⠀⠀⠀⠈⢅⠈⠀⠀⠐⣂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⢻⣹⣥⣤⡴⠀⠀⠀⠀⠀⠀⠧⠄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠸⠒⡅⠀⠀⠀⠀⠠⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠫⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⡈⠁⠀⢀⣦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣦⠀⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣶⣶⣶⡶⠾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠕⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠀⠀⡠⠔⠈⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠳⣄⠀⣰⠞⠛⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣊⠓⢦⡄⣰⢋⣤⠬⠵⠦⠀⠀⠀⠀⠀⠀⡌⠳⣄⣐⢠⡄⣤⢂⣪⠷⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣘⣼⣁⣠⣼⠇
⠀⠀⠀⠀⠀⠀⢠⠟⠚⠉⠒⠼⠻⣡⣶⣾⣿⢶⠂⠀⠀⠀⠀⠀⠈⠀⠂⡿⠛⠉⠉⢉⣷⢶⡈⠀⠀⠀⠀⠀⠀⠀⠾⠋⣹⣛⠯⢿⡟⢿⠋⢃⠸
⠀⠀⠀⠀⠀⠀⠰⡔⠿⠿⢟⡻⣤⡏⢽⣖⠂⠀⠀⠀⠀⠀⠀⠀⢠⡶⠎⢉⠓⠒⠛⠋⠁⢀⡹⡄⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢀⣸⣧⣼⠃⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢁⠇⠙⠲⣭⣛⣶⠶⠀⠀⠀⠀⠀⠘⢷⢠⢄⡀⡀⣀⠠⠐⠁⣬⡇⠡⠀⠀⠀⠀⠀⠀⠀⠘⣆⣩⣭⣿⣷⠾⠟⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠴⢬⢚⡵⠋⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢧⣄⣀⣀⣄⣠⣴⠞⡫⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠘⣷⠀⠀⢸⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⡍⣉⡡⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡤⠤⠟⠓⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠁⢠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢪⢀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⢀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⡀⠀⠠⠀⠀⠀⠈⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⢁⠀⠁⠉⠁⢀⠕⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠈⠂⠀⠀⠀⠀⠐⠁⠀⡀⠢⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠀⠀⠀⠂⢀⡄⠐⠠⠃⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢱⢃⢴⠤⠀⠀⠺⠕⢀⠀⠃⠀⠀⣀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢆⠰⠂⠀⠀⠀⠀⣣⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠴⠢⢀⡄⡠⠄⠀⢀⢀⠄⢀⠔⠙⠠⠤⠄⠁⠀⠀⠄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠔⠁⠄⠁⠂⡁⢐⠁⡀⠋⠀⠀⡰⠞⠣⠉⠀⠀⠀⠀⢈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡪⢠⠄⠠⡌⢠⠁⠁⠁⠉⠘⠄⠀⠐⠁⠀⠀⠀⠈⠀⠄⠀⠈⠆⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢈⠆⣉⠐⠀⠤⠀⠀⠀⢀⠄⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠒⠀⠠⠄⠒⠀⠤⡀⠀⢀⠀⢀⢖⡒⠀⢀⡒⠂⠀⠀⢀⠀⢀⡈⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣀⠀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠔⠁⠀⠀⠀⠤⠀⠀⠨⠀⣀⠀⠠⠃⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣉⠐⠠⡀⠀⠀⠀⠀⠀⡀⠀⠠⡈⠁⠁⠐⠂⠃⠀⠀⡀⠀⠀⠀⠀⣅⡄⠀⠤⠘⠡⠀⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠜⠋⡠⠊⠣⡄⡁⡐⢨⡄⣀⠊⠀⠠⠄⠰⠀⠀⠀⠐⠀⠀⠀⢀⠂⢈⠀⠀⠠⢀⡁⠀⢆⠄⢈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡣⡄⠀⠀⠀⠁⠈⠉⠁⠘⡀⠀⠀⡐⠀⢠⠀⢀⠁⠠⠄⠈⠑⠀⠀⠀⢠⡀⠀⠀⠟⠐⠄⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠛⢃⠴⠲⠲⠛⠠⠂⠠⠰⠏⢀⠀⠁⠀⠀⠴⠂⠀⠑⠂⠀⠀⣄⠀⠀⠀⡀⠘⠐⠁⠀⠀⠀⡄⠔
⠀⠀⠀⠀⠀⠢⠁⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠤⠀⠀⠀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠂⢀⡀⠁⡀⠀⠡⠐⠁⠄⠀⠂⠁⠀⠀⠀⠀⠁⠀⠀⠁⠠⠉⠢⠀⠀⠀⠬

⠀⠀⠀⠀⠂⠀⠁⠀⠛⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣸⡠⠗⠀⠀⡸
⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⣦⡔⠋
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷
⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣄⠀⠀⠀⠀⠀⣋⡃⠀⠀⠀⠀⠈⠟⠇⠀⠀⠀⠀⠀⢠⣤⠀⠀⠛⠋⠀⣀
⠀⠀⣩⡀⠀⠀⠀⠀⢀⢼⣿⣿⣾⣆⠀⠀⠀⢼⣿⣿⠦⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⣛
⠈⣵⣿⣷⣔⠂⠀⠀⠘⢻⣿⣿⡿⡟⠀⠀⣴⣿⣿⣿⣦⡀⠀⠰⣻⣿⣿⡿⠄⠀⠀⡰⡿⠹⣵⡀⠀⠀⢀⣿
⣾⣿⣿⣿⣷⡕⢀⡀⢠⢾⣿⣿⣿⣷⡀⢠⡟⡿⣿⣾⣿⢧⢀⡾⣿⣿⣿⣿⣦⡀⢀⣿⡇⢻⢮⠣⡀⠀⣼⣿⡆
⣾⣿⣿⣿⣿⣿⠊⢁⣾⣿⣻⣿⣿⣿⠷⣽⣿⣠⢻⣘⣿⣿⣧⣾⣿⣿⣿⣷⣄⢀⣾⣿⢁⢸⢆⢳⡞⢠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡓⠮⢀⣾⣿⣿⢿⣿⣾⠟⣟⢿⣧⣿⣿⡻⣿⣾⣿⣿⣿⣿⣿⣿⡔⡁⢸⠉⣆⠳⣌⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣝⢗⣞⣿⣿⣿⣿⣿⣿⡎⠈⠘⠟⠋⠏⣳⣿⣿⠿⢿⡿⠿⡿⢿⣞⠛⡞⠣⠽⠓⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡽⠿⣿⡿⠿⠿⣿⠛⢛⢛⠛⠀⣤⣶⣤⠈⢉⣥⣤⡄⢸⡇⢐⡡⢫⠜⣀⠿⡀⢸⠢⣿⣿⣿⣿⣿
⠿⠃⢸⠛⢿⡿⡷⠖⡂⠀⠀⣿⢰⣾⣿⣿⠂⢹⣦⡏⠀⢸⣿⣼⡏⠸⠇⠀⣶⣶⣦⠀⠀⠈⠊⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠛⠛⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⡇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣶⣶⣿⣿⣿⠏⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣌⣰⣿⣿⣿⣛⣤⡿⢿⠹⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⠛⠹⠫⣿⠉⠿⣿⣏⣹⣿⣥⢶⠟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣤⠂⢉⣽⣄⣻⣿⣿⡿⣿⣷⣯⣿⡽⢗⣖⠶
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣄⡀⠀⠀⢰⣾⠀⣼⡗⢛⣣⠘⡎⣿⣿⣿⣿⣿⣿⣛⠻⡿⢻⠛
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⢠⣿⣠⣿⡟⠉⠹⢤⣷⣿⣿⣿⣿⣏⠫⠏⠃⣀⠉
⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣷⣦⣶⣾⣿⣿⠟⠀⣿⡩⡿⢃⣽⣿⣿⣿⣿⣷⠶⣾⢧⣴⣿⡧⢤⠤
⠀⠀⠀⠀⠀⠀⠀⡽⢹⢿⣿⣿⣿⣿⣿⠟⠁⣠⠤⣭⣤⣾⢘⠉⣽⣿⣿⣿⣟⡿⠷⠫⠍⠉⠉⠻⠃
⠀⣠⣴⣿⣦⡀⠀⠀⠈⠉⣿⣿⣿⣿⣧⠀⡼⢿⣮⣁⢃⣽⣿⣾⣿⣿⣿⣿⣿⣶⣾⣾⣿⣖⢶⡖⠂
⠀⣿⣿⣿⣿⣿⡶⣷⠀⣀⡼⣿⣿⣿⣿⡠⢝⠾⠾⢿⣿⢿⣿⣿⣿⣿⣿⡟⠉⡝⠉⣵⠆⢀⣤⣤⣀⠀⢀
⠀⠘⠿⢿⣿⣿⣦⣸⣷⣿⢱⣿⣿⣿⣿⡗⠊⢹⠿⣦⣥⣤⣾⣿⣿⣿⣿⣷⣶⣷⢴⡷⢰⣿⣿⣿⣿⣦⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡌⠁⣸⣿⣿⣛⣿⣿⡿⠛⣻⠛⢻⣿⣿⣯⣄⠸⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣷⡟⣙⣵⣿⣹⣿⣿⣇⣀⣿⣀⣸⣿⣿⡯⠵⢂⠁⠀⣈⣡⣤⣾⣿⡟⠿⣿⣿⣿⣿⣷⡤
⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⢾⣿⣿⣿⣿⣿⣿⡿⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢽⠏⠂⠀⠎⢁⠉⣩⣿⡿⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⢺⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣏⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣼⡀⠀⣌⠑⡛⠛⢉⡉⠀⠀⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠈⣿⣿⣿⠀⠰⣿⣿⣿⣿⠿⠋⢿⢱⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣾⣷⣦⣽⣿⣷⣴⡟⣷⠀⠀⣸⣿⣿⣿⡿
⠀⠀⠀⠀⢸⣿⢿⣿⠀⠀⣿⡏⢻⣿⢠⢘⣿⡿⠟⢋⠟⠋⠉⣿⡿⢻⠛⣿⣿⣿⣿⡟⠉⠀⡜⠉⠁⠂⢲⠐⠀⢿⣿⡟⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣾⡿⠀⣠⣿⠀⢨⣿⡾⠇⠐⠀⠀⢸⡀⡀⢰⣉⣁⠈⣶⠀⠀⢱⡞⠃⠀⠀⡇⠀⠀⠄⠸⠀⠀⣼⣿⡇⣿⣿⣧
⠀⠀⠀⠀⠸⡿⣿⣧⡀⠈⣿⡇⠈⢻⣗⠀⠈⠀⠀⢸⡇⠀⢸⠁⠀⠀⠿⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠃⠀⠀⢀⣤⣿⠄⣈⣽⣧
⢀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣈⣁⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣙⣉⣁⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣉⡿⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢻⡗⢫⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣟⠨⡁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠯⠒⠁⠀⠀⠀⠀⠖⠠⡀⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⡖⣠⠂⠀⠀⠀⠀⠆⠀⠘⡄⡸⢁⡴⠒⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢼⡥⠦⠀⠀⢸⣿⣦⡈⠢⣀⣷⢁⠼⠤⠴⠊⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⢊⢥⠀⠀⠈⢿⣿⡇⠀⠀⡟⢁⣠⣤⠀⠀⠀⢀⠔⠒⡏⠀⡠⠔⠒⡩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢄⠀⠀⠶⡆⠀⠀⠀⠀⢈⣾⡧⢊⠀⠀⠀⢀⡉⢣⡀⠸⣰⣿⣿⡿⠀⢠⠚⡅⠀⢀⡷⠋⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢉⠢⡀⠘⡄⠀⢠⣄⠘⢌⣿⣰⠁⠀⠀⢨⠈⢢⠙⣆⣿⡿⠟⠁⢠⠃⠀⠃⢠⡮⠒⠉⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠺⢦⡸⠀⢙⠟⠀⡖⢿⡎⡅⠀⠀⠀⢑⡼⠖⠛⠁⠤⢀⣀⡎⠀⠀⣴⠋⢀⣀⢀⡞⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣀⠀⠀⠀⠙⡄⢀⠀⢀⣤⡽⣯⠚⡆⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠢⣴⠃⠉⠀⣠⠎⠀⢀⠔⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠤⠼⢆⠀⠈⡋⠁⢺⣏⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠤⣊⠁⠀⠀⠎⠀⡠⠃⢀⡤⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠘⣇⠀⡷⠊⠁⠸⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠠⣀⠀⢸⠀⠀⠑⠢⢤⣗⠛⠒⠒⠫⢀⣀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠠⢀⡉⠲⠤⡤⢀⡸⠋⠀⠀⠀⢀⣀⢤⠤⣤⢀⣀⣠⠁⠀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠙⡙⢏⠁⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠌⣐⣤⣠⠞⠁⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⡉⢠⠖⠉⠑⢢⠀⠀⠐⣀⠀⠀⠀⠀⠀⢃⡈⠑⠒⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠬⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠔⠓⠓⢄⠀⠀⠀⢃⠀⠀⠇⠉⠑⢄⠀⠀⣌⡀⠻⡉⠑⢦
⠀⠀⠀⠀⠀⣀⡤⠔⠒⠈⠹⡉⠁⠒⠬⢁⣀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡃⠀⠀⣸⢀⠜⡆⠀⠀⠀⠱⣴⢣⡈⠢⠈⠀⠊⠁
⠀⠀⢀⠴⠋⠀⠘⠦⣀⠀⠀⠙⢄⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢄⠀⠈⠉⠀⠀⡠⠋⠁⠀⢰⠀⠀⠀⠀⠸⠀⠙⠲⠃
⠀⡴⢁⠤⠐⠂⠙⠉⣉⣉⠭⠶⠶⠻⠦⢄⣀⡀⢵⡀⠀⠀⠀⠱⡀⠀⠀⠀⢀⡤⠚⢦⡀⢀⡠⠊⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡗⠀⠀⣀
⣸⣆⡁⠠⠄⣠⡔⠉⠁⠀⠀⠀⢀⠤⠂⠉⠀⠀⢀⡱⣄⠀⠀⠀⢘⠖⠤⠔⠊⢣⡀⠀⠈⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡘⠀⢀⣡⡟⠃
⠉⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣞⣁⣀⣀⣀⠤⠒⣉⣀⣫⣷⢖⠊⠁⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⢠⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣳⠞⣃⠢⠞⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣃⡀⠀⣤⡤⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣶⢻⢉⠙⠁⠀⢀⡠⠷⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣷⡛⡁⠆⠁⠀⢀⠔⠉⠀⠀⢈⡶⠤⢀⡠⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡞⢇⡅⠀⠀⠀⣰⣁⠠⠤⠒⢪⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠟⣉⡆⠀⠀⠀⢰⠁⠀⠀⢀⡔⢹⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣸⡟⠢⠈⠀⠀⠀⠀⡆⢀⡠⢔⠏⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣺⡟⢌⠊⠀⠀⠀⠀⠀⡏⠁⠀⡜⠀⠀⢠⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣻⡟⢚⠋⠀⠀⠀⠀⠀⠀⠇⠀⢰⠀⠀⢀⡸⠋
⠀⠀⠀⠀⠀⠀⠀⢈⠛⡝⠊⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡲⠚⠉⠉⠙⠣⡐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⣀⡰⠁⡔⠁⠀⠀⠀⠀⠀⠘⠄⠈⣂⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠓⠒⠒⠒⠤⠀⣘⠁⠰⡀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⡀⠀⠤⠀⠀⢤⣀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠻⠀⣧⠀⠢⡀⠀⠀⠀⡔⠁⢀⡔⠈⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠐⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠰⡐⡄⠑⠀⠀⡜⠀⡐⠈⠀⠐⠀⠀⠀⠀⠀⢀⡀⣸⢰
⠀⠀⠀⠀⠸⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⣰⡀⢣⠘⡄⠁⢠⠁⡴⢀⠎⠀⠁⠀⠀⣀⠔⠊⠁⠀⡀⢈⠁⠢⣀
⠀⠀⠀⠀⠀⠡⡀⠑⢄⡀⠄⠠⠄⡀⠀⠀⠀⡙⠋⠲⡀⢞⠀⣇⠌⣠⢤⠄⢀⠞⠁⡠⠔⠈⡸⠁⡜⠁⠑⠪⣦
⠀⠀⠀⠀⠀⠀⠈⡺⠗⠀⣀⣀⢀⠀⠐⡏⠀⡏⠑⠄⠙⠈⠖⠉⡩⡆⡄⠠⠃⡠⠊⠀⡠⠊⡠⠊⠀⠀⠀⠀⠘
⠀⠀⡠⢀⡠⠚⠋⠠⠔⠊⠁⣁⠄⠩⠤⣬⣄⠑⢄⣈⢀⣣⠄⠠⢀⠁⡷⠡⣔⡡⠐⣉⠤⠊⠀⠀⠀⠀⠀⠀⡘
⠀⠰⠀⠀⠀⡠⠀⠲⠤⣤⠖⢉⡠⠂⠁⠈⠉⣓⢦⠝⡯⢽⢲⣏⡡⠔⠓⢤⡌⠉⠻⠄⠀⢀⡀⠀⠀⠀⠀⡰⠁
⠀⠀⢡⠀⢊⠀⢀⠖⠵⠁⣀⣈⡉⠁⠉⠉⠁⣀⣼⣹⣦⡼⢽⣍⢁⣒⠐⠙⢦⠀⠀⢣⢀⡀⠀⠉⠒⡤⠊⠀⡠
⠀⢀⠎⠀⢀⠃⠁⢀⡤⢊⠔⠈⠃⠀⡴⢊⠋⠁⢁⠘⠚⠛⠃⣄⠠⠄⠀⠵⢤⠻⡀⠀⢣⣈⠑⠢⡀⢸⠤⠊
⡴⠅⠄⡠⠋⠢⠀⡐⢂⣊⡀⠀⠀⠀⠁⠨⢀⡘⣋⠀⠀⠘⠀⢹⡅⠀⠲⠆⠲⡒⠧⠢⡙⠄⠀⠀⠁⠠⡀
⠀⠀⠈⠀⠀⡘⢀⡀⠺⣘⠓⠚⢻⠿⡄⠘⠁⡀⢁⠀⠀⠈⢂⠘⠃⠀⠀⠀⠀⠈⢤⣀⠀⠈⠄⠀⠄⠀⠘⠢⡀
⠀⠀⠀⠀⠀⡧⢀⠿⠶⣵⠶⢛⣥⠶⣧⣒⡉⠯⢼⠶⣢⡀⠀⠆⡀⠀⠀⠀⠀⠀⠀⢆⠉⠢⢤⠀⠈⠢⡀⠐⠛
⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠉⠉⠒⠷⣺⣎⡏⠿⠁⠀⠘⠁⠀⠀⠀⠀⠀⢠⣮⣧⡀⠀⠀⠀⠀⠀⠓
⠀⠀⢠⡌⠉⠁⢈⣁⠐⠂⠠⠤⢀⡀⠀⠀⠀⠈⠁⢿⠃⠀⠀⠃⠀⠀⠀⢀⡀⡺⠒⠂⣤⢷⢄⡀
⠀⠀⠎⠀⠀⠀⠀⠀⠈⠉⠐⠂⠤⣈⡁⠢⢄⡀⠀⠀⡄⠀⢀⡀⣠⡔⡾⢽⡏⡋⢰⠗⠿⠃⠀⠈⠒⢤⡀
⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⢌⠐⠀⣻⡧⣼⢳⠎⣉⠓⡶⣤⠛⠛⠁⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⢀⣀⠄⡀⠀⠀⠑⢄⠘⠱⢦⡟⠲⠎⠛⠃⠀⠀⠀⠀⠀⢀⡠⠊⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⡰⠁⠀⠀⠑⡀⠀⠀⢀⡟⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢉⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡗⠒⠊⠁⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⣁⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠀⠀⠀⠹⣉⢉⣁⣠⡤⠒⠉⣠
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿