Luck Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⢸⣿⠀⣾⢋⣤⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⢹⡇⠀⠰⠂⠀⠀⡿⠀⠃⠈⠉⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⢀⠀⠟⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⡀⠀⣠⡶⢶⣿⠁⠀⠠⠄⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⣠⡾⢉⠇⣰⡿⢠⠇⣴⡟⢠⣿⠇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣧⡼⣾⡏⢻⡾⢾⡟⣠⢿⡿⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⣤⣴⣶⡄⣼⡏⢀⡞⢠⣿⣠⠏⠀⠸⡷⠋⣾⡇⠀⢀⡾⠁⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠉⠉⢁⡼⠃⠹⠷⢋⣠⣬⡿⠷⠦⣄⠀⠀⠀⣿⡇⢀⡾⠁⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡶⠛⠉⠀⣴⠂⠀⡼⠀⠀⠀⠘⠳⠛⡁⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠸⣿⣄⠀⢀⣠⡾⠋⡀⠀⣼⠏⠀⠀⠀⢰⡏⣠⠞⣱⠆⢀⣾⠀⣰⠟⣹⠇⠀⠀⠛⣥⣴⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠈⠛⠛⠛⠁⠀⠀⠁⢸⡏⠀⠀⠀⢀⣿⢿⡅⢠⣿⡴⢻⡏⣸⣿⠞⠁⣠⠄⣀⠀⠰⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠀⠀⠀⠀⣠⣴⡾⠿⠿⠿⣷⣄⠀⠀⣼⡇⠀⡟⠀⠉⢀⣾⠷⣿⠁⠀⣰⠏⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠗⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠈⠛⠀⠀⣿⠀⡼⠁⢀⡴⢻⡟⠀⠻⣶⠾⠋⠀⠀⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠻⠟⠁⣠⠏⠀⣾⠁⢠⣶⡆⠀⠀⠀⢰⡿⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡀⠀⢠⡏⢀⣼⠃⢠⡞⣯⡀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠛⢁⡀⠀⠉⠀⢁⣀⣠⣿⠃⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⣠⡞⢹⠄⠀⣴⠋⡷⠀⢀⣾⠟⢩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⣿⢃⣾⣿⠀⣜⣠⣾⢿⣴⣃⣠⣿⠁⣠⢿⡟⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⢀⣼⠇⣼⡇⠘⡿⠉⢸⡇⣴⠋⠉⢸⣇⡴⠃⢸⡇⠀⣠⡟⠀⠀⠛⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣀⣀⣀⣤⣿⣿⠀⣿⣠⡞⠁⠀⠸⠟⠁⠀⠀⠀⠉⠀⠀⣼⠛⠞⠋⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⢁⣾⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡆⣸⠇⢀⣤⠄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢠⣦⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⣼⠀⣰⡇⢀⣾⠃⠀⣴⣿⣾⠿⠋⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⣼⢇⣼⣿⠀⣼⠇⣠⢞⣿⣿⡁⠀⠀⠀⢀⣾⠃⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣾⡿⠀⠀⠀⢀⣀⡀⣿⠟⢸⣧⡾⠻⠶⠃⣸⠇⠘⢷⣤⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⣿⠷⠶⠿⠿⠟⠛⠁⠀⠀⠀⢉⡀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠀⠀⢀⡾⢹⡇⠙⠀⠀⠀⠰⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣏⠆⢾⣋⣉⣛⣋⣩⣉⣉⣋⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢁⣤⣤⣶⣶⠦⡄⣼⣿⠋⢱⡆⣠⣾⡿⣀⠀⣰⣿⠏⢠⣿⡟
⠀⠀⠀⠀⠀⠀⢠⣿⡟⢼⣿⠟⣻⣿⠃⠀⢸⣿⠃⢀⣿⢰⣿⠏⢠⣿⢰⣿⠏⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣴⣿⠃⠀⠀⢿⡟⢀⣼⠃⣿⡿⠀⣾⠇⢸⣿⣠⡟⢹⣿⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠘⣿⣇⣠⣾⠟⠁⠀⠀⠀⠈⠛⠚⠁⠀⢿⣧⡼⠋⠀⠀⠉⢡⣾⡆⠙⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⢀⣾⣿⠀⢀⣀⠀⠀⣤⣾⣿⣧⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⣾⣿⡏⣠⣿⡟⢀⣾⡿⠫⣿⡟⣠⣾⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢸⣿⣟⣴⣿⣿⠁⣼⣿⠁⠀⠈⠀⣼⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⢈⠻⠛⠁⣿⡇⠀⢿⣇⣠⡴⠂⢠⡿⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣠⠏⠀⠀⠀⠘⠓⠚⠁⠈⠉⠀⠀⠘⠃⠀⠹⣿⣧⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⣂⡄⡀⡔⠒⡀⠀⢀⠀⡤⠔⠒⠠⡀⠀⠀⢀⠀⡤⠔⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡈⠀⡨⣜⢰⢅⠃⡰⢁⠊⠅⡄⠂⠄⠑⠀⡰⢡⠊⠁⡄⠢⡀⠱⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠡⡀⡁⡘⢹⠁⢀⠃⡌⠀⠃⡈⣒⠽⠀⢠⠁⡀⠀⢆⡈⣒⢽⠀⠇⠀⠀⢀⠠⠤⢤⣃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠊⠀⠀⠆⢘⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⠇⠀⠀⠀⠀⢸⠀⡀⢀⢊⠔⠁⡑⣦⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠇⠀⠀⠀⠸⠀⠠⠀⠀⠀⠀⡘⠀⠿⠀⢠⠀⠀⠀⠀⡌⠀⠃⠁⢌⠀⠀⠇⠁⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⢀⠄⠄⠀⢣⠀⠑⠤⠤⠊⠀⡔⠀⢣⠀⠑⠤⠄⠊⠀⡌⠀⡀⠐⡀⠀⠈⢻⠧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠤⠊⠀⠀⠀⠑⠠⠀⠠⠄⠊⠀⠀⠀⠑⠠⠀⠠⠔⠊⠀⠀⠑⠢⠄⠁⠩⠊⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠀⢈⠀⢡⠀⠠⠪⢪⢢⠀⠀⠀⡠⡊⠥⢈⠑⢄⠀⠈⡀⡅⢀⠆⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢤⠀⠀⠈⡄⢸⠀⢀⢠⠌⡘⠀⠀⠌⠔⠀⠄⡂⠂⢘⠀⠀⢠⢠⡌⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠈⠀⠀⠀⠀⡈⠀⠈⠎⢀⠁⠀⡘⠘⠀⠀⠈⠢⠤⠊⠀⠀⢠⠌⡞⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠆⠁⠀⠌⠀⡌⢣⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⡡⡆⠃⠈⢢⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠧⠊⢀⠌⠈⠀⠆⠁⠰⠀⠀⠀⠀⠀⠠⠀⢰⠀⡇⠀⠀⠀⢃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡇⣗⠂⠠⠤⠤⢲⡆⠀⠀⢀⠌⠀⠀⠀⢰⠐⠄⠑⠄⣀⠀⢠⠖⠀⠠⣀⡣⠁⠀⠈⢌⠒⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠜⠀⠈⠁⠒⠂⠁⠑⠤⠐⠁⠀⠀⠀⠐⠊⠀⠀⠑⠒⠒⠂⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⢛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣖⡒⠶⠶⣤⣀⣾⢁⠀⡀⠀⠀⢉⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡒⠂⠨⣀⡢⢍⡻⣿⣆⠞⡴⢀⠀⠀⠔⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠠⠀⣀⡒⠭⣓⠯⣺⢎⡞⠐⢁⠄⡀⠐⡿⠀⣀⣤⣤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⠀⠀⠬⣕⡪⢝⠊⢳⠀⠀⠀⠈⣠⡾⣡⠞⡙⠀⠁⠐⠀⠋⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣤⣤⣙⢦⣤⣙⡒⠍⠀⠀⢠⡆⡔⠀⣠⠏⡴⠏⠰⢁⠄⡠⢀⠀⠀⠀⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠁⠀⠂⠈⢢⡙⢷⣮⡙⠺⣄⡀⢀⢸⡏⡴⡴⢃⠞⠁⠀⠀⢈⠜⡡⢃⢎⡄⡀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⠢⣈⠢⠁⠀⠀⠉⡳⢤⡙⠦⣙⣏⣞⡵⠳⢂⣞⡰⠤⠤⣞⢼⣱⢿⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠐⠬⣑⠮⣑⠀⠀⠠⣑⣊⣑⣉⣓⣻⣿⣿⣖⠻⡛⠉⠀⠀⢤⡲⢝⠮⡓⢍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣦⣽⣶⣹⢦⢟⢀⠀⠁⠉⠱⢫⠞⢩⠿⡽⢍⡓⢦⣀⢀⠢⡑⢌⠢⡑⢌⠢⠁⢈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⡵⡱⢣⢣⢎⠄⡄⡀⣴⠋⣰⢏⠜⣷⠒⠝⢦⣌⠳⣵⡘⠂⠁⠉⠀⠀⡐⣌⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⠰⢡⢣⠏⡎⡜⣰⡼⢡⢞⠁⠀⠀⠺⣏⠣⠀⠈⠳⣮⡙⠦⣷⣼⣤⣦⠽⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⢀⠁⠀⠈⠀⠀⢠⣟⣵⠟⣩⢖⡄⡠⠀⣐⢀⠀⣀⠒⠤⢉⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⣴⣠⣥⡷⠞⠉⣾⠅⢈⠔⣫⢞⠔⡱⣯⡢⣕⠢⣉⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠰⡷⠂⠀⢊⠵⣫⢎⢜⣵⢝⠮⡑⠀⠀⠀⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⣿⡥⢀⠁⢊⠔⠁⣾⠿⣧⠁⠀⠀⠀⣈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡟⠀⠀⠀⠀⠀⠘⢶⣥⣔⣡⡴⠞⠁⠀⠈⠛⠶⠾⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⢟⣻⣙⣯⣍⠛⠛⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⠋⠃⠀⠘⠛⣛⠛⠋⠀⠀⠀⣠⣄⡙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⣿⣷⠄⣀⣴⣾⠿⠿⠿⠿⠿⣷⣦⣈⠻⣿⣆⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣯⣿⣿⢁⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣊⠁⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠚⣿⣿⣿⣻⣿⢯⡍⢉⣉⡉⠛⠒⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡄⠀⠀⣿⣿⣷⣺⣇⣻⡆⣏⠀⣹⢰⠟⠳⡄⣠⣌⡉⠓⠶⢤⣀⡀⠀⣿⣯⣺⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣸⡿⠛⣿⣿⣷⣤⡤⣌⣉⣁⡘⠦⠾⢡⡏⣀⡗⠀⢠⠆⠈⠙⠳⢿⣟⣺⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣋⡀⠙⣿⠁⢠⣿⣟⡺⠿⢠⣿⡏⠉⠉⠛⠓⠦⣌⣉⡀⠠⢯⡀⢠⡟⢀⡆⢈⡙⠧⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⡴⠋⠀⢸⣿⡒⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⢤⣘⠲⠟⣴⠋⠙⠆⣈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⣾⣿⢭⣀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⣌⡓⠃⡾⣷⠒⠂⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣹⣿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠧⣿⡟⢳⣤⣙⠀⠀⣰⠏⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⢾⣿⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠋⠁⠀⢠⣿⠃⠙⢳⡞⠁⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⢣⣅⠀⣠⣿⠃⠀⢀⣾⣤⣤⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣤⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⣲⣿⠏⣴⣿⠁⠀⠀⢸⡟⣫⡃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠁⠀⠉⠀⠀⠀⠀⠀⢀⣴⣿⡿⠍⠈⠻⢃⣾⡿⠁⠀⠀⠀⠀⣿⠋⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣯⡀⠀⠰⣿⣿⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠈⡇⠀⠀⢸⠀⠀⢸⠀⠀⣰⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠘⡆⠀⡄⢡⠀⢀⠈⢰⠀⡆⠰⠀⠇⠀⠀⢠⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠘⢆⠀⢦⠐⠀⠱⠈⠀⠸⠀⠸⠀⠁⠇⣠⣤⠚⠠⠃⢀⠀⣠⠎
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠢⡀⠑⣄⠂⠀⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⡟⢠⡇⠁⡰⢃⠜⠁⡀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠑⠦⣀⠈⠢⡈⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⣀⣿⡷⠛⠀⠈⠀⠀⡀⠊⡠⢚⡁⠀⠀⠀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⢌⡑⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡇⠀⠀⠀⠀⢰⠏⠀⡠⢸⡟⠠⠖⠋
⠀⠀⠀⠀⠀⠉⠓⠢⠄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣇⠀⠀⠀⣠⠟⠀⠉⠀⢸⡇⡠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡞⢹⣿⢻⠟⢦⣠⠼⠋⠀⠀⠀⠂⢸⡇⠀⠂⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣤⠀⠀⢠⣶⣤⠞⣹⣿⠀⣿⠘⠻⠟⢰⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠒⠒⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣿⡄⠀⣾⣿⠈⡇⠸⢿⠴⠋⠀⠀⠀⢸⣧⠀⣀⠀⠀⠀⠀⠀⢸⠇⣀⣈⠁
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⣿⡇⢰⣿⣷⣼⢿⣿⣰⡇⠀⠀⠀⠀⢀⣠⡀⢸⣿⣼⣿⠃⠀⠀⠀⡆⢠⡀⠠⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠈⢿⣧⡞⠘⣿⣇⠀⢬⡉⠀⠀⠀⠀⠀⣾⡟⠷⣸⣿⣿⡃⠀⠀⠀⢸⡇⠘⠃⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⣿⠀⢸⣷⠀⣶⡄⢰⡀⣿⡇⢀⡟⣿⡏⢿⡄⠀⠀⡾⠠⢄⣀⠁⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⢠⡏⢸⣿⡆⢸⣿⠀⢿⣇⢸⡇⣼⠛⠊⠀⠈⠋⠀⠻⣆⣼⢃⠀⠀⠌⣉
⠀⠀⠀⠀⠀⠀⣀⡤⠒⡡⠖⠁⡾⢀⠈⣿⡇⠸⣿⡇⣼⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠈⠙⠲⠄
⠀⠀⠀⠀⠀⠊⠁⠀⠈⢀⡤⢰⡇⠀⢠⣿⠁⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡑⢦⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢸⡇⠆⣼⠃⠀⢠⠈⠛⠁⠀⠀⠀⠀⢀⠀⠀⢠⠀⢀⠱⡄⠘⢦⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠛⠚⠁⡰⢀⠇⠀⠀⡆⠀⠀⡆⠀⠀⡆⠀⡄⢧⠀⢣⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣰⠁⠀⠀⡜⠀⠁⢸⠀⠃⠀⡇⠁⠀⢱⡀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢰⠇⠀⠀⢸⠀⠀⠀⢷⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠒⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠉⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⢠⡾⠛⣷⠀⠁⠀⠀⢠⣿⠇⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⡀⠀⠀⠀⣾⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⣿⠃⠀⡟⠀⣀⠀⢀⣾⣿⣴⣾⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣿⠁⢀⣠⡀⠀⠀⣿⣇⣼⠁⠀⠀⢀⣼⣿⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠤⠀⠀⠀⠀⢀⣿⡏⠀⣠⡿⠃⢠⡟⢁⡟⠀⠀⢻⣿⡁⠀⢀⡴⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣥⡾⠛⠁⢀⣿⣡⠞⠁⠀⢠⡾⣿⣧⣴⠏⠀⣿⣿⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢠⣿⡟⠙⢳⣄⣀⣼⡿⠁⠀⢀⣴⠋⢀⣿⣿⠁⠀⢸⣿⡟⠀⠰⠂⠀⠀⢰⡆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠙⠿⣷⣦⣤⠆⣸⣿⠇⠀⠀⣿⠁⢸⣧⣀⣴⠟⠁⣠⡿⢻⣿⠀⠀⣼⣿⡇⠀⠀⠀⠀⢠⡿⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣿⠀⠀⠙⢋⣁⠀⣴⠏⠀⣼⣿⠀⠀⢿⣿⡇⠀⠀⠀⣴⡿⠁⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣿⣿⠀⠀⣼⠇⠀⠀⢀⣾⠏⣼⠃⠀⢀⣿⡏⠀⠀⠘⣿⣧⣤⣴⣾⠟⠀⠀⠉⠴⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⠀⢻⣿⣀⣼⠟⠀⡤⣄⡼⠁⢰⡏⠀⢀⣾⠟⠀⠀⡀⠀⠈⠙⢛⣿⠃⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠛⠛⠉⠀⣼⣳⢯⣧⠀⠈⠷⠶⠟⠉⠀⠀⠀⠁⠀⠀⠀⣼⡏⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠗⠀⠀⠀⢰⡏⠀⠛⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢰⣿⠁⣠⠏⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣠⡄⠀⠀⢀⣿⠇⠀⠀⠀⢿⠃⠀⠀⠀⠉⠀⠀⠀⢠⣾⠟⠙⢃⣿⡏⣰⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣿⠀⢠⣿⠋⠀⠀⣹⡛⢳⡻⠟⠁⠀⢰⡆⠀⠀⢠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠾⠇⠀⢀⡾⠀⢠⣿⡇⢀⣾⡏⠀⣠⣾⣻⣻⡛⠁⠀⠀⠀⠀⠀⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⣾⠇⢠⢿⣿⢀⣾⣿⠁⣴⠏⢸⣿⡟⢿⣦⣀⠀⠀⢀⣠⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⣰⣿⣠⡟⢸⣿⡾⠁⠻⠟⠁⠀⢸⣿⠁⠀⠙⠻⠿⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⢀⣤⣶⠿⠛⣿⠟⠀⠈⠛⠁⠀⠐⠟⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣠⣾⠿⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠸⠂⠀⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⢠⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⡠⠒⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡤⠀⡠⢀⠤⠀⣀⠄⣢⠄⢀⡠⠂⡾⠁⠀⠀⣼⠁⣠⠄⠀⣠⠄⢀⡤⡰⠄⣰⣏⠤⣶⠄
⠀⠀⠀⠀⠀⠻⢷⣤⣀⠠⢴⡞⠁⢾⡤⠜⠓⠸⠧⠤⠛⠂⠻⠖⠈⠃⠀⠀⣰⠇⠐⠿⠖⠈⠻⠄⠺⠧⠄⠸⠋⠐⠮⠅
⠀⠀⠀⠀⠤⠤⠤⠤⠤⣤⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢀⠤⠒⠚⠛⠓⠒⠶⢤⣄⡀⠀⢀⣾⠋
⠀⠀⠀⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⠿⢧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢀⣀⣀⣠⡤⠶⠛⠉⠀⠀⠀⠈⠉⠛⠓⠲⠶⠒⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠶⣄⡔⠋⠙⢦⡴⠊⠉⠙⠶⠁⠀⠀⣾⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠈⠀⢀⣤⣌⠀⢠⡶⣄⠀⢠⡶⡄⠀⣴⠿⣶⡿⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⠆⠁⠀⢠⣿⠋⢹⡄⠹⣿⣸⣠⡾⣧⣇⣼⡏⠀⣿⡇⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣾⡇⢀⢸⣧⢾⣏⡝⠸⣇⡜⠉⠹⠔⠁⢿⡇⠀⣼⠃⠀⣠⠟⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣷⠀⠘⠛⢁⣼⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠾⠋⠀⢊⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢁⡟⠀⠀⠀⡞⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣼⣿⠞⠀⠀⠀⠀⠳⠋⠀⠀⠀⠀⣠⣤⡀⠀⢰⡿⣠⠖⣳⠄⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣀⣤⣿⡇⠀⠀⠀⢀⡄⠀⠀⣼⠀⠀⣼⡏⠘⠃⢀⣿⣿⣡⠾⠋⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢤⠀⠈⠉⠉⠁⣿⡇⠀⠀⠀⢸⡇⠀⣼⣿⠀⢠⣿⠀⠀⢠⠎⣿⢿⣧⡀⠀⠀⠀⠀⠀⢀⣾⠏⢠⡄
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⡆⠀⢻⡇⠀⠀⡰⢻⣇⡼⠸⣷⣠⠏⠻⣦⠴⠋⠀⠿⠀⠙⠿⣶⣦⣤⣤⣶⠿⠋⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⠻⠶⠞⠁⠈⠉⠀⠀⢈⡁⠀⠀⠀⣤⠀⠀⠀⣠⣷⡀⠀⠈⠉⠉⠀⠀⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣤⠞⠷⣤⣠⣤⠞⠙⠶⠶⠚⠉⠓⠒⠚⠉⠈⠙⠶⢦⣤⣤⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⢤⣀⠈⠐⠤⣀⣼⠁
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠠⠃⢀⣀⠀⠀⡞⠀⠀⠹⡆⠀⠀⠀⣿⠈⠁
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠢⠤⠀⠀⠀⢰⡁⠈⣧⠀⢷⡄⠀⠀⡇⢀⡔⠛⣿⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣠⡄⠀⠀⠀⢸⣷⢠⡟⠀⣾⡛⠶⣴⠗⠺⣧⡼⠻⣆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢘⣿⣀⣀⠔⠁⣉⣉⡀⠀⠘⠳⠒⠁⠀⠀⠀⣠⠀⠉⠓⠦⠄⠊
⠀⠀⡠⠒⠉⠉⠉⠉⠉⠉⢹⡏⠁⠀⢠⠏⠀⠀⢹⠀⠀⠀⠀⣠⠤⡀⢰⡇⠰⣦
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢄⣿⣀⢀⠀⠊⠀⣄⠀⣼⠃⠀⠀⣸⣇⡴⠃⠀⠀⡠⠔⠒⢦⡀
⠀⠸⣆⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢸⣏⠀⠀⢸⠇⢰⣏⠀⣿⣆⣀⠔⠹⠏⠉⠓⡶⣮⣀⣀⣀⡼⠁
⠀⠀⠙⠳⠦⠤⠤⠖⠋⠀⠀⠀⠀⠀⢿⣄⣀⠾⠧⠜⠛⠊⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⡀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⢠⣄⠀⠀⠀⠀⢀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠋⢀⣀⡙⢛⣗⡒⢒⣺⡏⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣰⣗⣿⣙⡿⣿⣓⡷⣏⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⣏⣀⣍⠀⠈⠁⠀⣼⢦⠁⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣿⠁⢋⡙⣷⠶⣶⢾⡟⣁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣟⠀⢸⣇⣏⣾⡉⢹⡷⣏⠀⢛
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⢮⣍⣉⠈⠉⠈⠁⠹⣧⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⡤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣛⣻⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⣀⣀⣤⣤⠤⣤⣤⣀⣀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠉⠉⠁⠀⠀⢌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⣡⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡞⠁⠀⠀⠀⠀⠀⠀⣰⢲⡔⡄⠑⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⢀⡠⢂⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡇⠀⠀⠱⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⣀⡀⠀⠀⠎⣰⡟⠁⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⢀⡄⢸⣇⡠⠤⢄⣀⣀⡀⠀⢐⢠⡀
⠀⠀⠀⠀⠀⠀⣼⠇⠀⢈⣉⠓⠀⢠⡿⠀⠀⠀⠿⠀⠀⣀⣀⢤⠀⢀⣐⡒⡄⠀⠀⠀⢀⣇⡾⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡑⢝⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⣉⡉⠁⣼⡇⠀⠀⠀⠀⠀⣸⠧⣌⣧⣀⣿⢧⣹⡇⣀⡴⠚⠉⣿⠃⢀⣀⠐⠚⠋⣁⡀⠀⠀⠀⠀⠤⠀⠀⠈⢻⡜⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⡠⠀⣿⡀⠈⠉⠉⢳⡆⢿⠀⢠⡏⠈⣏⠀⣸⠏⢹⡁⠀⣰⢿⣠⣟⡽⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠚⠀⠀⠘⣧⡀⠀⠀⣸⡇⠈⠑⠩⠄⠀⢙⠚⡩⠀⠈⢑⣊⠅⠀⠉⠻⠤⠄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠪⣙⠒⣚⠏⠀⣠⠖⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⢀⠄⠀⠀⣀⣠⣄⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣾⢸⠇⠀⠀⠀⠀⠀⠀⠻⠟⠃⠀⠀⢀⡿
⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠲⣄⡀⠀⠀⣿⠀⣠⠟⠁⠀⠀⣸⠃⠀⣾⣷⢠⡟⠉⠓⠀⣿⡿⢖⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⢀⠄⠀⠉⠓⠒⢿⡛⠁⠀⠀⠀⣴⢿⠀⠀⢷⡿⢸⣇⠀⠀⢀⣿⣏⠁⠀⢀⣄⡀⠀⠀⠀⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠘⣧⠈⢆⠀⠀⠀⠀⠀⠀⠃⠆⠀⠘⣎⠳⢤⣀⣠⠼⠋⠈⠓⠤⠚⠓⠋⢉⡓⠚⠍⠃⠈⠙⠢⢿⡞⠁⢠⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡙⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠋⠀⠈⠳⣄⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⣌⣉⠉⠛⠛⠋⢉⣩⠴⠂⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡢⢊⣴⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣄⣀⣀⣀⣀⣀⣀⠤⠖⠋⡡⢞⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠐⠁

⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⠁⠐⠊⠉⠑⠸⢍⢱⠀⠀⠀⠀⢠⠤⢄⡼⠀⠈⠦⡤⠔⠛⡆⠀⠀⠀⠀⢇⢢⠈⠉⠙⠛⠋⠉⠉⢡⠂⡅
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡹⠒⢄⠀⠀⡗⠀⡸⠁⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⣺⠀⠀⠀⠀⠀⠀⠀⠘⡋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⠒⠺⠀⢀⠇⠀⣇⠀⠀⠀⠂⠀⠀⠀⡟⠉⢹⠀⢰⠋⣈⡇⠀⠀⠀⠀⠀⠀⣮⡈⢱
⠀⢀⡰⠃⠀⠀⠀⢀⠀⠀⠀⠀⢠⠃⠀⠘⡀⠀⠈⠀⠠⢀⣀⣀⡀⠴⠃⠀⢸⠀⠀⢻⡀⠘⡀⠀⠀⠂⠀⡸⠀⣨⠃
⠀⣦⣀⡔⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠁⣀⡠⠃⠀⠀⠀⢳⠄⠈⠀⠈⠐⠊⠀⢴⠃
⠀⢇⠈⢩⡤⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠘⡄⢢⡶⠆⠀⠀⠀⡀⠀⠠⣸⠀⠀⠀⠀⢻⠀⠠⡀⠀⠀⢀⠄⠀⢸⠀⠀⠀⠀⠀⢣⠀⠓⡀⠀⠀⡰⠃⢠⠃
⠀⠀⠘⠢⠤⠒⠉⠉⠉⠳⠤⠴⠃⠀⠀⠀⠀⠀⠣⠤⠕⠒⠒⠮⠤⠔⠁⠀⠀⠀⠀⠀⠈⠦⠤⠎⠉⠙⠦⠤⠎
⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢈⡾⠷⠀⠾⢶⡡⠀⠀⠀⠀⠀⠠⠒⠢⠤⠠⠔⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠑⠒⠶⠒⠊⢠
⠀⠀⣎⣡⠃⠀⠈⠈⠀⠀⠙⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠤⡀⠀⢀⠤⠀⢃
⠀⠀⡈⠋⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠸⠀⠀⠄⠀⠀⠀⠀⠘⡧⠈⢂⠀⠀⡊⠈⠑⠁⢁⠀⠀⠀⠐⠀⢠⣊⡉⡆
⠀⢠⠁⠁⠀⠀⠀⢀⠀⠀⠀⢈⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⡠⠃⠀⡈⡠⠤⡏⢀⣴⣿⣷⣿⣦⡀⢀⠐⠺⢁⣀⡇
⠀⠀⢢⠄⠀⠀⡨⠶⣏⠀⠀⠀⡃⠀⢀⠊⠀⠁⠀⢀⠠⠀⠈⠁⢀⠜⠀⠃⡄⢰⡏⣷⡆⠀⣴⡎⢷⡒⡆⢀⠬⠻⠁
⠀⠀⠘⠀⠀⢰⢁⣽⡏⠹⠉⠈⠇⠀⠘⡤⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠄⣼⣗⠮⠄⠀⠨⠔⣸⣧⢰⠂⠰⠎⠄
⠀⠀⠰⡀⠀⢴⠾⠷⢅⠆⠀⢀⠇⠀⠀⢃⠀⣀⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠸⣮⣿⡞⠛⣿⣿⣷⠩⣿⣆⣦⠈
⠀⠀⠀⠈⠁⠈⠁⠀⠉⠀⠉⠁⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠊⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠠⢤⣀⠁⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠄⠀⠀⢀⣀⠀⠐⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠲⢿⣭⣗⢾⣿⠃⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢳⡸⠖⣫⣩⠅⠀⠁⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣄⡀⠀⠃⢉⣯⠇⠀⠀⠀⠀⢰⠋⠀⠀⠙⠞⠁⠀⠈⢢⡀⠀⠀⠀⠈⢧⠁⠸⠀⠀⣀⣄⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡿⠻⢩⠄⠀⠸⡿⠀⠀⠀⠀⠀⢃⠀⠀⠀⠒⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡆⠀⠀⢿⠟⠘⣧⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠼⡗⠀⣼⠀⠀⢸⡇⠀⣀⠤⠀⣀⠈⢆⠀⠀⠀⠀⠀⠀⢀⡐⣀⠠⠄⠠⢄⠀⢳⢀⠀⠘⣴⠑⠌⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡗⠀⠆⠂⠀⠀⣸⠀⡞⠁⠀⠀⠀⠈⠚⢧⢌⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠃⢸⠈⠀⠀⡇⠀⡤⡄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⢰⣿⠀⢧⡀⠀⠀⠐⠂⠀⠀⠲⣵⠤⠮⠋⠀⣀⣀⣐⣒⣀⣠⠆⢸⡄⠀⠀⠁⠠⡇⢿⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣃⠄⠀⠂⠀⢸⣿⠀⡰⠋⠀⠀⠀⠀⠀⠀⡠⡲⠒⡖⣄⠀⠀⠀⠀⠀⠀⠙⡆⠀⡇⠀⠀⢀⡠⠀⠚⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡝⢠⠄⡀⠀⠸⣿⠀⢁⠀⡀⢀⠀⠀⣠⡾⠋⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⢀⠇⢰⢣⠀⠀⠈⠃⣠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠇⠀⠀⠹⡄⠀⠑⠲⠤⠔⠊⡝⠀⠀⠀⠀⠀⠀⠀⢫⡙⠓⠒⠒⠉⠀⣼⡸⠀⠀⡮⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⣷⠀⠀⠐⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⠀⠈⠀⠆⡇⠀⠀⢀⠀⡆⠀⠀⠀⠀⣰⢣⡇⠀⢠⠁⠀⢀⡄⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⣐⠂⠀⡀⠀⠀⠀⠳⡀⠀⠀⠀⠰⣀⠀⠀⣂⣧⣀⠂⢀⡼⠁⠀⠀⠀⣰⠣⠁⡆⢀⢶⡄⢠⠀⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢫⠑⠞⠐⣆⠀⠀⠈⢿⣄⡀⣀⣀⣀⠉⠉⠉⠀⠈⢉⣉⣀⣀⡀⣠⠞⠁⠀⠀⢃⣾⠀⠁⢀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⣀⠤⢐⢚⣧⠀⠀⣢⠠⠄⠚⠓⠓⠂⠈⠉⡀⠀⢀⣀⣀⡀⠀⠀⠀⣤⣀⠀⢀⣀⠉⠉⠒⠒⠲⠺⠤⠤⣠⠂⠀⢠⣟⠳⠶⣄⡀
⠀⠀⢀⡴⠋⢀⢲⡀⡸⢟⠃⠁⢀⣀⠀⢠⣶⢶⡄⢸⡟⢻⡄⠈⣿⠹⡇⠀⠀⠀⢹⠉⠀⢈⡟⢹⡟⢠⡿⣶⠂⣤⣄⣀⠈⠉⠛⠶⣤⣴⠄⠈⠳⣄
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠀⠀⠀⣿⠙⣃⠈⣧⠈⣷⠘⣇⣈⣇⢀⣿⣤⡇⠀⠀⢀⣾⣤⡆⢸⣇⣼⠁⣾⠀⡈⠀⣾⣡⠟⠃⠀⠀⠀⢀⡟⢀⡴⠋
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠹⣄⣽⡀⠹⣶⠿⠀⠙⠛⠋⢀⣉⣉⣁⣀⣀⣀⣉⣉⣁⡈⠙⠋⠀⠻⠿⠃⣾⡇⣸⡇⠀⠀⠀⢀⠞⢀⠏
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠙⢉⣁⢤⣴⢶⡒⠋⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⢲⢦⣤⣄⣀⠉⠁⠀⢀⢀⡎⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠶⠒⠙⠶⠴⠒⠋⠉⠀⠀⠈⠓⠮⣤⣠⡀⢀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀⢠⣔⡮⠟⠋⠀⠀⠀⠉⠙⠛⠻⠋⠑⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠲⠶⠶⠶⠶⠒⠒⠋⠉⠁


⣿⢿⠿⠿⣿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⢀⠀⢀⣠⠀⠀⠀⢰⡆⠀⠀⢀⠀⠀⠈⠃⠀⠀⢰⡄⠀⠀⠸⡵
⠀⠀⠈⠀⠀⠘⡾⠛⠃⠠⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠒⠀⠀⠸⠀⠀⠀⠠
⠀⠀⠠⣢⠀⠀⢣⡤⠀⠀⠃⡀⠀⠀⠀⠀⡘⢗⢄⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠣⡣⡀⠀⠀⠀⠀⡘⠌⠂⠄⣀⠚⠁⠈⠓⠩⠐⠛⠁⠐⠚⠛⠱⡶⠒⠋
⠀⠀⠀⠀⠑⠪⢀⣐⡂⠞⠀⠄⠀⠀⡈⠀⠀⠀⠀⠀⠁⠀⡀⠀⢀⠄⠀⠁⠀⠀⠀⠤⠂⠀⢀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢇⢀⠀⠀⠀⠀⣠⠄⠀⠀⡘⠁⠀⠀⠀⢀⡠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣑⠂⢐⡲⠃⠀⠑⠬⠤⠶⠊⠩⣰⣤⠤⠇⢀⠀⠀⠀⠠⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣐⡲⠦⠙⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠍⠚⠰⡐⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠉⠉⠲⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⢰⡇⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⣀⠤⢄⠀⠀⠀⠀⠘⢄⡀⠀⠀⢠⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡀⠀⠀⢀⡾⠃⢀⡴⠀⠀⠀⠀⠀⠀⠀⢀⡠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠁⠀⠀⢠⣿⠁⠀⠀⡀⠀⣠⡀⢀⡴⣷⢠⡟⢰⡿⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠐⠀⣼⠇⠀⠀⣾⡇⡾⠑⠇⣾⠁⠈⠈⠃⢸⡇⠀⠀⣰⠊⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⢪⡿⠀⠓⠂⣀⡈⢁⠔⠈⠀⠈⠣⠜⣰⠇⠈⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡠⣾⠏⡩⢀⡾⢁⠁⣌⢀⡀⠀⠀⠀⢀⣿⢢⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡟⠀⠀⣼⠃⠂⣀⠈⣉⠀⣰⠋⠂⣼⣏⠜⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠋⠀⠀⢰⡟⠁⣰⡏⣼⡇⣰⡏⢀⢘⡿⢸⡆⠀⠉⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣿⠁⠐⠙⠃⠻⠈⠘⠃⠁⠈⢀⠀⠻⢦⣀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡀⠔⠁⠀⠿⠈⠀⠀⠀⠀⠀⠀⡀⠄⢈⡠⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠈⠉⠁⢠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⠛⠋⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⢀⣤⣤⡤⠄⣼⣿⠋⣇⠀⣰⡟⢹⡷⠀⢠⣾⠟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢀⡿⠃⢸⣿⡏⢀⡟⠀⡟⢀⣾⡃⢠⡟⢁⣴⣿⣿⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣠⡿⠁⠀⠘⣿⣥⠞⠁⠀⠳⣾⠟⠁⠸⠿⠟⢰⣿⣗⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⢀⡀⠀⠀⣀⠀⠀⢀⣠⣄⠀⢀⣶⡗⣠⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⣿⣿⣤⣾⣿⢇⣶⡟⠛⠛⠁⣼⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⢿⣿⡏⣿⠃⢸⣿⣠⣴⠖⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠶⠖⠛⠃⠀⠉⠀⠛⠀⠀⠉⠁⠁⢀⣿⡟⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢰⣢⣾⣷⣒⠀⠀⠀⣾⣿⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⣿⡳⠀⠘⠀⠰⣿⠇⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠔⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣿⣇⣀⣏⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⡇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⠇⠀⠀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣏⣌⠥⠀⠈⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠈⠀⢸⣿⣿⡿⠿⠿⠛⠛⠉⠁⠀⣀⣠⡤⠀⠀⠀⢀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣀⣤⣤⣶⣾⣿⣿⡿⢃⣗⠀⠄⢼⡄⢃⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⢀⣄⣾⠀⠈⠁⣤⡀⣀⡭⠴⣙⡻⣿⣿⡿⡟⢿⠿⣿⡟⠋⠁⢸⣿⠀⠂⣿⡇⢠⡄⠈⠑
⠀⠀⠀⠀⠀⠀⢀⣿⡀⣼⠿⠓⠁⡠⠟⠪⠴⠀⠩⠈⢁⣄⢂⡡⠈⠉⠉⢠⠀⢀⡄⠁⠊⠲⠄⢄⣠⠈⠙⠛⠻⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠸⡟⠁⠡⠀⠀⢊⠑⢠⡆⡀⠠⣀⠀⠈⠁⠀⠀⡠⠐⠈⠀⡄⢸⣇⠀⠀⠀⠀⠀⠘⠩⢂⠀⠀⡉
⠀⠀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠸⡧⠓⠀⡀⠀⠀⠀⣸⡆⣀⠄⠀⣰⣷⣾⠿⠄⠲⢂⠀⠂⠀⠄⢸⠀⠀⠇
⠀⠀⠃⠠⠀⠀⠤⠈⠐⠒⠀⠾⢿⣿⠿⠆⠀⠈⠉⠀⠚⠃⠾⢧⠈⣉⠈⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠁⠲⠄⠀⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠒⢂⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠒⣄⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢰⡏⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣿⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢠⡾⠁⠀⡕⠀⠀⠀⠀⠀⠈⠉⠉⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⠘⠀⠀⣰⡟⠀⠀⠉⠀⠀⠀⠀⢀⡤⡄⢀⡾⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⠄⢪⣿⠁⠀⢀⣾⢢⡾⢹⣠⣾⠁⠗⠸⠇⢸⡇⠀⠀⢀⡴⡄⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇⠀⠠⢺⡟⢸⣇⠀⠀⠓⠊⡠⠄⠒⠸⣇⠢⢠⡟⡀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⣁⣿⠓⡄⢀⣴⢫⠂⡞⠀⠀⠀⠀⠈⠁⣾⡇⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣹⠏⠈⠁⣼⢃⠋⠀⠳⠞⠁⢠⠤⠄⢸⡿⣹⠇⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣰⠏⠀⠀⢸⡿⠀⢠⡆⣰⡆⢠⡟⠀⢠⣿⢻⡁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣿⠁⠠⣿⠑⣿⡀⢻⡃⠔⠘⠃⠈⣧⡀⠐⠀⠁⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⡠⠊⢸⣏⠔⠀⠀⠀⠉⠀⠀⠀⢀⠠⠐⠀⠀⠙⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠐⠊⠀⠀⢈⠅⠀⠀⠀⠀⠀⠠⠤⠆⢁⡴⠎⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠐⠀⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⣷⣦⡀⠀⠀⢀⣴⣿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠋⠀⠀⠀⠹⣿⡄⢠⣿⠏⠀⠀⠀⠙⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠋⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠙⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣴⣤⡀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠰⣶⣄⠀⠀⣿⣿⠀⠀⣠⣶⠆⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⢀⣾⣿⠻⣿⣶⣿⣷⠀⠀⠘⠋⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠁⣠⣾⠟⠁⠀⠀⢀⣠⣴⡿⠃⠀⠀⣾⣿⣿⣿⠟⢻⣿⡀
⠀⠀⠀⢠⣾⣿⠟⠃⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠘⢿⣷⣶⣦⣄⠈⠁⠀⠀⠈⠁⣠⣴⣶⣾⡿⠟⠋⠀⠀⠀⠀⢘⣿⡆⠀⠀⠈⠻⣿⣶⡀
⠀⠀⠀⠀⠙⠻⣿⡆⢀⣤⣌⣿⣧⠀⠀⠀⢀⣴⣾⡿⠟⠛⠋⠁⣠⣄⠀⠀⣠⣄⠈⠙⠛⠻⠿⣷⣦⣀⠀⠀⠀⣾⣿⣥⣤⡀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⢿⣿⡿⠛⠛⠛⠋⠀⠀⢰⣿⠋⠁⠀⠀⠀⣠⣾⠟⠁⣠⣄⠈⠻⣷⣆⡀⠀⠀⠈⠙⣿⣆⠀⠀⠙⠛⠋⠻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⣿⣿⡀⠀⠀⠀⠈⠛⠁⠀⢀⣿⣿⡀⠀⠈⠛⠃⠀⠀⠀⢀⣿⣿⣀⡀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠻⣿⣶⣦⠀⠀⠀⠀⠀⣼⡿⢿⣧⠀⠀⠀⠀⠀⣴⣶⣿⠟⠙⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⣀⣼⡿⠁⠈⢿⣧⣀⠀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⣰⣾⠿⠛⠻⠿⠆⠀⠀⣠⣾⡿⠛⠛⢿⣷⣄⠀⠀⣰⣿⠿⠛⠻⢿⣷⡀⠀⢸⣿⠛⠻⢿⣦⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⣼⡿⠁⠀⠀⠀⠀⢰⣿⠃⠀⠀⣤⣤⣤⡄⢀⣿⡏⠀⠀⠀⠀⢹⣿⡄⢸⣿⠃⠀⠀⠀⠀⢻⣷⠀⢸⣿⠀⠀⠘⣿⡇⠀⠀⠀⠀⠈⢿⣧
⠀⢰⣿⠃⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠉⣹⣿⠇⠀⢿⣧⡀⠀⠀⢀⣼⡿⠁⠘⣿⣆⠀⠀⠀⢀⣾⡟⠀⢸⣿⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠘⣿⡆
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣾⠿⠋⠀⠀⠈⠻⠿⣷⣾⡿⠟⠁⠀⠀⠈⠻⢿⣷⣾⠿⠋⠀⠀⠸⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⣾⡆⠀⠀⢰⣷⡀⠀⠀⣠⣶⣿⣿⣶⣄⠀⢰⣿⠄⣀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠇⠀⣾⡿⠁⠀⠀⠈⠁⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠆⠀⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⡀⠀⢻⣷⣤⣤⣾⡿⠀⠀⠙⢿⣶⣤⣤⣶⡷⠀⢸⣿⡍⠻⣿⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠺⠗⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣿⡿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠛⠛⠛⣷⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣏⣀⣀⣀⣀⣠⡴⠟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠹⣯⣭⣭⣭⣭⣥⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢰⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⣿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣴⣾⣯⣀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠳⣦⣀⣿⠀⣿
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠋⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢹⡄⠀⢠⡾⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏⠀⠀⠀⠀⣿⢿⣦⠀⣴⢾⡆⠀⣴⠿⣿⡄⠀⢠⡿⢷⣶⢶⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⢀⣸⡇⠀⠀⣼⣷⠞⠁⢀⣟⢀⣾⠁⠀⣼⠇⣼⠇⣼⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠘⢷⣤⠾⠋⠙⠃⠀⠀⠹⣧⣤⡶⠻⣿⠿⢿⡴⠖⠿⠀⠟⠀⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⣠⣤⡶⠶⠟⠛⠛⠛⠛⠛⠷⠶⣶⣤⣄⡀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠾⠛⠛⠷⠶⠶⣦⣤⣀
⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⣼⠏⠀⠀⠀⣀⣠⠴⠖⠛⠛⠋⠉⠙⠛⠓⠶⢤⠄⠀⠈⣿⠀⠀⢀⡤⠶⠚⠛⠋⠉⠙⠛⠛⠲⠦⣤⣀⠀⠀⠙⣷⡀
⣿⡀⠀⠀⠛⠉⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⢻⡆⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠛⠶⡄⠈⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⡇⠀⠐⠛⠉⠉⠁⠀⠀⠀⠉⠉⠛⠓⠶⠀⠀⠀⠀⠀⢸
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠤⠶⠖⠛⠛⠛⠓⠲⠶⢤⣤⣀⠀⠀⠀⠀⠀⢠⡿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠙⠓⠆⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠋⠉⠉⠉⠉⠉⠙⠛⠒⠶⠄⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⣷⠀⠀⠀⠀⢀⣤⠶⠚⠛⠉⠉⠛⠛⠲⠤⠀⠀⣿⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢤⡄⠀⢠⡿
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣀⠀⣿⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⣿⠀⠀⢀⣤⠶⢛⣉⣥⡤⠶⠶⠶⠦⠬⣭⣻⡿⣿⣿⣯⠭⠥⠤⠤⠤⣤⣤⣄⣉⡛⠳⢦⣄⠀⠀⣾⠃
⠀⠀⠀⠀⢹⣇⡴⢋⡴⢞⣯⠵⢚⣛⣩⣭⣭⣿⣿⣿⣿⣇⣸⣷⣖⣒⣚⣒⣒⡒⠶⠦⣤⣈⡉⠛⢶⣍⠻⣶⡿
⠀⠀⠀⠀⠀⢻⡶⣫⡶⣫⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⢦⣌⡙⠳⢦⣈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢻⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣴⠟⠋
⣶⣶⠶⠶⠶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣶⣶⠤⣶⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⣿⣿⣿⢽⣿⣿⣟⢿⣮⣿⡷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⣫⣾⣿⣷⣻⣿⣿⣛⢿⣿⡟⠟⣭⡽⣿⣿⣦⣄
⠀⠀⠀⠀⠀⢀⢼⢟⣿⣯⡹⣟⣯⣿⣍⣵⣿⣿⣿⣿⠻⢟⣿⣿⣽⣿⡿⢺⣯⣶⣄
⠀⠀⠀⠀⢰⣿⣷⡿⣻⣿⢷⣾⣟⣻⣿⣎⣽⣾⣭⢿⣧⣿⢿⣛⣛⢋⣷⣾⣿⣽⣿⣤
⠀⠀⠀⠀⣽⣿⢛⡾⣛⣻⢮⣿⠿⠿⣧⣿⡿⣿⣿⣏⣷⢾⠿⣿⣿⣷⣻⠟⣘⣛⣷⣿⣦⡀
⠀⠀⠀⢸⣟⣿⡹⣿⣻⣿⢞⣿⢿⣿⣮⢰⣿⣿⣿⣿⣾⣿⣿⡼⣿⣇⣿⣓⢾⠿⣯⣥⣽⣛⡀
⠀⠀⠀⢨⣿⣯⣭⢻⣿⣿⡿⣽⣿⣿⣿⣯⣾⣿⡟⣻⣟⢿⣿⣷⣿⣿⣿⣿⣹⡝⣿⣿⡾⣿⣽⡆
⠀⠀⠀⠘⢟⡿⣿⢞⣿⣛⡿⣼⢿⣿⣿⣿⣷⣿⠿⣿⢿⡟⣿⣽⣿⣽⣿⣬⣿⠿⠿⣼⣾⣳⡴⡄
⠀⠀⠀⠀⠘⣟⡧⣿⡷⣟⡿⣽⣿⣏⣿⢿⣿⣿⣿⡿⣿⢻⣿⢿⣟⣛⣿⡞⠿⠀⢠⡝⢛⣞⠳⣜⠄
⠀⠀⠀⠀⠀⠈⣷⡾⣷⢿⣷⣿⣿⣟⣿⣟⣿⣿⣻⢷⣭⠟⣿⣿⡋⣾⡼⠁⠀⠾⡷⠽⣾⣯⢱⠹⡄
⠀⠀⠀⠀⠀⠀⠈⢿⡻⣿⣻⣟⣿⣿⡾⠿⠋⢊⡵⣮⢷⣮⠓⣿⣽⠜⠀⢀⣶⢻⣿⣾⣿⢿⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⣿⢿⣿⣟⣻⢣⣀⢇⢾⣫⡗⠀⠀⠈⠁⠀⢀⣜⣿⣟⣹⣟⣿⢘⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⣿⢿⡝⡾⣿⣿⣼⣻⠟⣁⠀⠀⣤⣤⣤⣤⠹⣿⣿⣿⡇⢹⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣵⣿⣧⣝⣯⢿⣿⣦⣿⣿⣷⡿⢿⣿⢏⣾⣷⣹⣿⡇⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢱⣻⣿⠿⣛⣿⣶⡿⣯⣿⣿⣟⣾⣿⣿⣏⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠽⣮⢿⣿⣿⡷⣿⣿⣿⣿⡻⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠉⠛⠋⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠟⢯⣽⣭⣷⡌⠉⠙⠛⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⠁⠉⠀⢈⣉⣭⣍⣁⣀⠀⠀⣶⣦⡙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣿⡿⢃⣤⣾⠿⠛⠋⠙⠛⠛⠿⢶⣤⡙⣿⠆⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣾⠿⠿⣾⣿⣥⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⢹⣿⣶⣻⡿⢝⡗⣠⠶⢦⡀⣉⣙⠛⠲⠦⢄⣀⠀⠀⠀⠀⢻⣿⣆⣠⡀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡀⣸⣿⣿⣿⣿⠞⠃⠻⣤⠼⢹⡃⢨⡇⡾⠲⡄⠈⠙⠓⠦⣤⣸⣿⣖⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⣷⡿⠁⢹⣿⣛⣿⡟⣳⡶⠶⢦⣭⣉⡘⠧⠴⠃⢀⡾⠀⢀⡄⠉⠛⠶⣿⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠳⢦⡄⣨⠏⠀⣿⣟⠊⠙⠁⣿⡇⠀⠀⠀⠈⠉⠓⠶⠦⣬⣓⠆⢾⣁⡾⣡⠶⣌⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⢠⣿⡷⠄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣍⡀⢧⣤⢈⣴⣂⡌⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⠯⣷⡆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣷⣤⣘⠹⡇⠀⠀⣸⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣙⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡳⠉⠛⢠⣿⠛⢦⣀⡞⠁⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣓⠀⠀⣠⣿⠃⠀⢠⡏⢀⣀⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣀⣀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣵⣿⠇⣴⡿⠃⠀⠀⣿⢿⠻⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣠⣼⣿⡛⠹⣿⢋⣼⡿⠃⠀⠀⠀⢻⡾⠛⠲⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣓⠀⠀⢴⣿⣏⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣆⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣧⣾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢀⡿⠁⠀⢀⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⡇⠀⠀⠀⠀⣼⠇⣿⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢳⣹⣾⠁⠀⣠⣾⣿⣿⣿⣟⣛⡻⠷⢦⣤⣀⣀⣀⣠⡾⠟⣿⠀⣿⣇⠀⠀⠀⠀⣿⢿⡿⠀⠀⠀⢀⣼⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡔⢯⣿⠃⠀⠀⠻⢿⣿⠏⠉⠉⠉⠙⠻⢶⣾⣍⣉⣛⣋⣮⣼⠏⠀⠘⣿⣦⣀⠀⢠⣿⣼⡇⢀⣀⣴⠟⢁⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠉⠉⣉⣭⣍⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣯⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠰⠍⣿⠁⢀⣀⡀⠀⣠⣾⣿⠀⢸⣿⣿⠿⣷⡀⠀⠸⣿⣿⠿⣷⡄⠀⢠⣾⣟⣿⣦⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠐⣰⡿⠀⠈⢿⣿⣿⢿⣿⣿⢠⡿⢿⡿⢦⣼⣧⣤⣾⣿⡿⢦⣼⣧⣤⣿⣽⠟⠙⣿⢣⣿⠃⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠹⣹⡇⠀⠀⠀⠈⠀⣼⣿⠇⣿⢁⡿⠁⠀⢸⡇⣾⣃⣾⠃⠀⢸⡟⣼⣿⡟⠀⠀⣿⢈⣿⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣼⣇⠀⠀⠀⠀⣴⣿⠏⠐⣿⣾⠃⠀⠀⣾⠃⣿⣾⠇⠀⠀⣼⠇⣿⢽⡇⠀⣸⣟⢹⡇⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣤⣴⣾⡿⠋⠀⠀⢿⣿⡀⢀⣼⠏⠀⢻⣿⡀⢀⣼⠏⠀⣿⣿⣷⣴⡟⢻⣿⣇⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠙⠛⠿⠿⠛⠋⣠⣶⣶⣦⠈⠛⠿⠛⠁⠀⠀⠈⠛⠿⠛⠁⠀⠀⠘⠻⢛⡋⠀⠀⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⢀⣼⣏⣽⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⡹⢷⣶⣼⣿⣿⣷⠾⣋⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣿⢰⡿⠀⠀⢀⣴⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⠏⠀⢸⡿⣷⠀⠀⢀⣿⢻⡷⠀⢀⣴⣿⠟⢹⣷⠀⢰⣿⣼⡇⠀⣴⡟⠁⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢼⡟⠀⢀⣿⢱⡿⠀⢀⣾⠿⣾⠃⢠⡟⣿⠏⢠⣿⡿⠀⣾⡇⣾⢣⡾⢋⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢣⣿⠁⠀⣼⢯⣾⠃⢀⣾⣿⣾⠏⢀⣿⢡⡿⠀⠈⠻⠃⢠⣿⣈⢻⣿⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣿⣿⣿⠃⠀⢰⣿⣿⣇⣴⠟⣿⣯⡟⠀⢸⣯⣼⡇⠀⠀⠀⢀⣾⡋⣥⣾⡛⠋⠁⢀⣠⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⣰⣿⡟⠋⠉⢩⣿⣿⣿⣿⣿⣶⣤⣙⠿⠛⠁⢸⣿⣿⣁⣴⠾⣿⣿⣇⣠⣤⣶⣿⠉⢱⡿⠘⢿⣿⣿⣿⠟⣠⡾⢻⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣄⣀⣴⠟⣩⡿⠋⠀⠈⠙⠻⢿⣿⣷⣶⣤⣙⡛⠋⠁⠀⠈⠛⠛⠛⠉⠀⢿⣧⣾⠃⠀⠀⠈⣉⣥⡾⠟⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣛⠻⠶⠶⣶⣦⣤⣤⣤⣤⣬⣥⣤⣶⠶⠟⣫⠑⢃⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢶⣦⣤⣔⣎⣀⣠⣼⣸⣡⣼⣵⣾⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⡧⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠛⠁⠀⠀⡠⠐⠊⠉⠙⠳⢦⡀⠀⠀⠀⠀⣸⣏⣚⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢐⡄⠀⢹⡄⠀⠀⠛⠛⣮⢩⣬⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⡋⠸⠇⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⠴⠀⠄⠁⠀⠀⡷⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠘⣃⠘⠆⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡃⢄⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢛⣐⠓⠉
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠔⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒
⠀⣠⠔⣊⡍⠋⠢⣄⣀⠤⠤⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣴⠄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⡇⣉⠤⢒⣧⢄⠛⡉⠀⠠⠆⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡄⠀⠈⠛⠛
⠀⢡⡄⣀⠱⢆⡘⣄⡅⣠⠤⠀⣖⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⢼⠧⠒⠱⡔⠱⠄⠑⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢶⣶⣆⣻⠏⣀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⣟⠛⠋
⠀⠀⢀⠠⠤⠄⠀⠀⠀⣠⠖⠲⠄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⠋⠀⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠄
⠀⠀⡇⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠉⠙⠂⠀⠀⡖⠉⠰⢿⣿⡀
⡐⠞⠁⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡐⢄⠂⡔⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠴⠋⠻⣦⡀
⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢌⣠⣱⠲⢮⠲⠵⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⠻⣄
⠀⣤⠲⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠲⠁⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠸⣷⠀⠀⠀⣴⣦⣿⡶⠀⠀⠀⠀⢀⢹
⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢻⡆⠀⠀⢸⣿⡿⣿⠃⠀⠀⠀⢈⢘
⠀⠀⢰⠋⠀⠀⢀⡄⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠻⣄⠀⠀⠈⠁⠃⠀⠀⠀⠀⠈⢸
⠀⠀⠈⠓⠀⢐⡫⠀⠌⠓⠄⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠰⠙⠳⣤⣄⣀⡀⠀⠀⠀⠛⡠⠃
⠀⠀⠀⠀⠰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠯⠀⠀⠀⠀⠘⠀⠠⠄⠀⠈⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡷⢿⣿⣿⣷⣶⣶⣦⡿⠏⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⢾⣫⢻⡇⠸⡿⡿⠿⠻⡆⠈⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣡⣶⣶⠶⣬⣿⣿⣄⣄⠘⠛⠟⠁⢀⣼⣿⣿⣷⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡭⠙⢻⣿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣍⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠀⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣽⣿⣿⣷⡀⠀⠘⠻⣿⣿⣿⣿⣿⡟⣿⣮⣹⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⢃⠘⠙⣿⣿⣿⣤⣤⣤⣤⡈⢉⣩⣽⣿⢸⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠿⠗⠀⠠⠄⠛⢋⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⣯⡽⣯⣿⣿⣛⣵⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠃⢰⣿⣿⣿⣿⣿⡯⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⢸⠁⢀⣴⠟⠃⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢠⠚⢿⣿⣄⣈⣙⣿⣏⠎⠀⠀⠀⠀⠀⠈⠐⠻⢷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⡀⠀⠀⠂⠀⠐⠀⠀⠀⠀⡎⢠⣿⣿⣿⡘⠿⠿⣻⣤⣓⣶⣦⣄⡀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⣷⡆⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⠷⣿⠟⡄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣅⡄⣹⠿⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣯⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣶⡌⠁⠀⠀⠧⢀⠀⠀⡀⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣁⣤⣴⠖⢢⣤⣤⠀⣀⠀⠀⢤⣅⡰⢟⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣅⣀⠀⠀⠀⠀⣩⡏⢁⡀⠀⢠⡟⣿⣿⣿⣷⡀⠅⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⣄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⢷⣦⠄⠀⠈⢈⣷⣄⣽⣿⣿⣿⣿⣿⣷⡀⢦⡀⠀⠀⠀⠀⠀⢸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄⣀⡀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣎⣛⠀⠀⠀⠀⢠⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠐⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣷⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣵⠟⠁⢰⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢯⡗⠀⠙⠉⠀⣆⣉⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠙⠛⠁⢀⡀⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣄⠀⣀⠀⠀⠀⢀⣤⣤⠀⣾⡇
⠀⠀⠀⠀⠀⢰⢋⣠⣤⣤⣠⣾⢟⣄⣾⢟⡀⣠⠞⣻⡟⠀⠀⠀⣼⣿⢸⡿⢠⣿⢠⡿⢻⡟⣰⣟⣀⣄
⠀⠀⠀⠀⢠⣿⠈⠛⣿⠇⢸⡏⡼⢹⡏⣸⢻⣇⣼⣿⠇⢠⡆⢰⣿⠃⢿⡷⣿⡇⢿⡇⣀⢈⣿⡟⠋⠁
⠀⠀⠀⠀⠈⠻⠷⠚⠁⠀⠈⠉⣡⡌⠓⠃⠈⠛⠃⠈⠓⠉⠀⢸⡏⣠⠆⠀⠹⠇⠈⠉⠁⢸⠘⠿⣄⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡿⠧⢀⣴⡆⠀⠀⣴⡆⢠⣄⢈⣩⣥⠀⣰⡄⢀⣤⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢸⡿⠀⢠⡿⢁⡞⠀⢸⡟⣵⣿⢇⣾⠟⢱⢠⡿⢁⣾⠃⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⠧⠚⠁⠀⣙⠋⣸⡟⠸⣏⡰⠃⠺⠷⠛⣿⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⣠⡿⠁⣱⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠁⠀⠈⠉⠁

⠷⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⠓⠒⠚⠛⠛⠛⠓⢦⡀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠋⢀⣴⡿⠋⢀⣤⣴⠶⠶⠟⢶⡄⠸⣷
⠒⠛⠛⠛⠒⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢠⣾⠋⠀⢀⡿⠉⢀⣤⡀⠀⠈⣿⠀⢿⡄
⣤⣤⣤⠴⠶⠦⠤⢤⣤⣀⠀⢠⠶⡄⢠⣦⣤⣄⣠⣴⠿⠁⠀⠀⣼⠃⢠⠏⠀⣧⠀⠀⣿⠀⠘⣷⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡇⠀⡇⠈⠉⢉⣀⣠⣤⠶⠾⠋⠀⡿⠀⠀⣿⠀⠀⢿⣄⡀⠈⠛⠛⠿⠶⣶
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠀⠘⠚⠃⠀⠳⠒⠛⠉⢉⣀⣤⣤⡀⠀⢰⡇⠀⠀⢸⡆⠀⠀⠈⠉⠛⠛⢶⣄
⠀⠀⠀⢀⡴⠋⠉⠉⠀⠀⠀⣀⣠⣤⣤⠴⠶⠚⠋⠉⠁⠀⢨⡇⠀⣸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⢸⠀⠀⢠⡶⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣟⠀⠀⠀⣠⡿⣀⡴⠛⠛⠓⢦⡀⠹⣧⡀
⠀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠃⠀⠙⣛⣛⣛⠋⢰⡏⠀⠀⠀⠀⠀⠹⡀⠈⠙
⠀⠀⠀⣿⠀⠀⡿⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠚⠋⢁⣀⣤⡴⠶⠛⠛⠉⠉⠉⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⢠⡇⠀⠀⠀⠀⢀⡟⢠⡄⢀⡴⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡟⢈⠓⢦⡀⠀⠀⠀⠀⣿
⠀⠀⢰⡟⠀⢸⡇⠀⠀⠀⢀⡾⠁⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⣼⣧⠀⢱⠀⠀⠀⠀⣿
⠳⠶⠿⠃⠀⠘⣧⣤⠴⠖⠋⢀⣴⠟⢷⡀⠙⠳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣼⠃⣿⠀⠈⡇⠀⠀⠀⣿
⣄⡀⠀⠀⠀⢤⣤⣤⣤⣤⠾⠋⠁⠀⠀⠙⠶⣤⣈⠉⠉⠉⠛⠛⠋⠁⠀⣀⡼⠃⠀⣿⠀⠀⡇⠀⠀⠀⢿
⠈⠉⠛⠲⣄⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡥⠞⣻⠆⣀⣤⡶⠛⠉⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢨
⠀⢠⠀⠀⠈⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⡞⠁⣰⢫⢴⣺⠵⠚⠉⠁⠀⠀⠀⠀⠀⠀⣿⡄⠀⣷⠀⠀⠀⡀
⣷⠸⣇⠀⣠⡿⠀⠀⢸⠇⠀⠀⠀⠀⢸⠇⣼⢗⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⠳⣄⡤⠁
⣿⡀⠈⠛⠛⠁⠀⢠⣟⣀⣀⣀⠀⠀⢸⢰⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⡀
⠘⣷⣤⣤⣤⣤⣤⣬⣉⡉⠁⠉⠙⢦⣸⢰⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢦⣤⣀
⠀⠀⠀⣠⡤⠤⣤⣀⡈⠙⠳⣄⠀⠀⢹⣀⡇⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠉
⣧⠀⢸⠃⠀⠀⠀⠈⠉⢳⡄⠙⡆⠀⢸⡟⠇⠛⠉⠉⠉⠙⠛⠛⠛⠛⠷⠶⠞⠛⠋⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛
⣿⠀⣿⠀⠀⣶⠛⣦⠀⠀⡇⠀⣿
⠏⠀⡟⠀⢸⡏⠀⢸⡀⢀⡇⠀⣿⠀⢠⡞⢳⡄⠀⢀⡶⢶⡄⠀⠀⢰⠶⢦⡄⠀⠀⢀⡾⢷⡄⠀⠀⣠⣤⡀
⠀⢀⠇⠀⢸⡇⢰⡈⠙⠛⠃⢠⡟⠀⣾⠀⢸⡇⠀⢸⡇⢸⡇⠀⠀⣿⠀⠈⣿⠀⠀⢸⡇⠀⢿⡄⠀⣿⠋⢿⡄
⣠⣎⣀⣀⣠⣿⣈⣷⣦⣤⣶⣏⣀⣼⣏⣀⣨⣧⣀⣼⣇⣀⣿⣄⣠⣿⣄⣀⣿⣆⣀⣼⣇⣀⣸⣧⣀⣿⣄⣈⣿
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠂⠀⠀⠀⠰⠷⠁⠀⠀⠀⡀⠀⠀⠀⢰⠲⡀
⠰⠀⠀⠀⣴⢠⡤⣲⡂⡀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠃⠁
⠀⠀⠀⠀⠀⠟⠉⠉⠀⠐⡀⠀⠀⠀⠠⠀⠀⠀⢀⡂⠀⠀⠀⠉⠀⠀⠀⡘⠁⠀⠀⠀⠀⠂
⢠⠰⠀⠀⠈⢣⡤⠄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠘⢧⠣⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⢣⠱⡀⠀⠀⠉⠁⠀⠀⠘⢎⠀⠄⢀⣀⣠⡴⠃⠈⠳⢌⣒⣐⠰⠛⠁⠰⠬⠝⣒⣒⣒⣲⠶⠊
⠀⠀⠳⣈⠢⢄⠀⢀⣀⢠⠃⠀⠉⠐⠒⠒⡏⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠈⠑⠂⡠⠄⠒⠁⠀⠊⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠁⠀⢀⡤⡲⢄⣠⠎⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⠀⠀⡠
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠆⠴⠀⠀⢠⡷⠃⠀⠀⣠⠖⠀⡖⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠊⠀⠀⠸⢡⠃⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠑⠜⠐⠀⠀⢀⠞⠂⠀⠛⠀⠀⢀⠃⠋⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣀⠀⠀⠀⢀⣠⠊⢆⡑⠄⣀⡀⣀⣀⠔⡏⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠒⢪⠥⢶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠧⢀⣉⣁⡉⠴⠃⠀⠀⠈⠒⠀⠂⠚⠁⠰⠦⠏⡂⠒⠃⠀⣀⡀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⣀⣒⣂⠭⠕⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠢⠄⠉⠁⢧⠑⢄⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣦⣠⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⣀⡤⠶⠒⠛⠛⠛⠛⠒⠶⠤⠀⠀⣿⠀⠀⠤⠶⠒⠛⠛⠛⠛⠒⠶⢤⣀⡀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁⠀⠀⠠⠤⠶⠶⠶⠦⢤⣄⡀⠀⢸⡄⠀⢀⣠⡤⠤⠤⠤⣤⣄⣀⠀⠈⠙⠲⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡤⠶⠖⠒⠲⠶⠤⣤⣀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣀⣀⣀⣀⠀⠈⠉⠛⠂⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠉⠀⠀⠀⠀⠉⠉⠉⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⢤⣄⠀⠀⣸⠀⠀⠴⠒⠚⠛⠛⠓⠒⠶⠤⣄⣀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠋⠁⣀⣠⣤⣤⣤⣄⣀⠀⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⠴⢛⣉⡥⢴⣶⡶⠬⣭⣻⡿⣿⡿⠭⠭⠥⠤⠤⢬⣭⣙⡛⠶⣄⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢞⡵⣺⠽⣚⣯⡭⠿⠿⠿⠿⢿⣧⣽⣿⣯⣭⣯⣿⣛⣒⠶⢬⣉⡓⢮⣛⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢞⣵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣌⡙⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠂⠀⠀⠀⠰⠷⠁⠀⠀⠀⡀⠀⠀⠀⢰⠲⡀
⠰⠀⠀⠀⣴⢠⡤⣲⡂⡀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠃⠁
⠀⠀⠀⠀⠀⠟⠉⠉⠀⠐⡀⠀⠀⠀⠠⠀⠀⠀⢀⡂⠀⠀⠀⠉⠀⠀⠀⡘⠁⠀⠀⠀⠀⠂
⢠⠰⠀⠀⠈⢣⡤⠄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠘⢧⠣⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⢣⠱⡀⠀⠀⠉⠁⠀⠀⠘⢎⠀⠄⢀⣀⣠⡴⠃⠈⠳⢌⣒⣐⠰⠛⠁⠰⠬⠝⣒⣒⣒⣲⠶⠊
⠀⠀⠳⣈⠢⢄⠀⢀⣀⢠⠃⠀⠉⠐⠒⠒⡏⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠈⠑⠂⡠⠄⠒⠁⠀⠊⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠁⠀⢀⡤⡲⢄⣠⠎⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⠀⠀⡠
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠆⠴⠀⠀⢠⡷⠃⠀⠀⣠⠖⠀⡖⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠊⠀⠀⠸⢡⠃⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠑⠜⠐⠀⠀⢀⠞⠂⠀⠛⠀⠀⢀⠃⠋⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣀⠀⠀⠀⢀⣠⠊⢆⡑⠄⣀⡀⣀⣀⠔⡏⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠒⢪⠥⢶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠧⢀⣉⣁⡉⠴⠃⠀⠀⠈⠒⠀⠂⠚⠁⠰⠦⠏⡂⠒⠃⠀⣀⡀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⣀⣒⣂⠭⠕⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠢⠄⠉⠁⢧⠑⢄⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡢⠀⠀⠀⠀⠀⢀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠙⠶⡟⠠⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⡄
⠀⠀⠀⠀⠸⣷⡀⢀⢲⢴⡷⣧⣵⣄⣷⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡐⡆⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣰⣿⣷⠈⠉⢙⣟⠁⢤⣠⠶⠚⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣙⡂⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⡀
⠀⠀⠀⠀⣿⣿⣿⣇⢷⢞⣩⠈⣻⡛⠒⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍
⠀⠀⠀⠀⣿⢿⢸⣷⢿⣽⣿⣄⠻⢷⡿⢿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠙⣧⠈⠛⠛⣻⣋⢻⢶⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣌⠁⠄⠀⠀⠀⠈⢰⠘⡦⣄⠀⣁⡭
⠀⠀⠀⠀⠀⣽⣧⣀⠀⠻⡙⠁⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣁⠀⠁⢀⠀⠀⣨⣴⠀⣻⡆⢀⠆⣼
⠀⠀⠀⣠⣾⣿⢾⣟⠳⡶⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⢠⣤⣾⣿⣿⡗⠹⢁⣾⠗⢋⡠
⠀⠀⢸⣿⣿⣿⣆⠈⢹⣶⣿⡄⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⡀⢀⣀⡀⠀⠙⠿⠟⠛⠐⠏⡁⠈⠉
⠀⠀⢸⣿⣿⣿⣿⣷⡘⢻⣿⡀⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠋⠉⣀⣤⣄⣤⣠⣴⠶⢚⡀⠀⡐
⠀⠀⢸⣿⣿⣿⣿⣿⣷⣼⣿⣷⣼⣿⣿⣿⣿⣿⣿⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠙⢳⣿⣿⣦⣄⢉⠛⠿⠃⠒⢈⢀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠃⠀⠂⠙⠛⠿⠟⠛⠓⠒⠂⠐⠂⠀⠛
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⣠⠖⠋⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠚⠲⣴⠋⠉⠳⠞⠉⠈⠙⠃⣀⢠⡇⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠻⠀⠀⣰⡶⣆⢠⣟⢳⠀⣼⢹⢀⣾⠛⣿⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠉⠀⠀⢸⡟⠀⣿⢀⣿⢲⢺⢏⡿⢺⣇⠀⣿⠀⢠⡆⠀⢠⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠘⠗⠀⣿⠃⠛⠃⠈⠋⠀⠀⠀⠀⠹⣧⡾⠁⢐⣫⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⠃⠀⠀⡎⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠒⠋
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣼⡷⠃⠀⠀⠀⠛⠁⡀⠀⢀⣴⣦⠀⢠⣿⡴⢊⡗⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠘⢷⣶⡶⣿⠃⠀⠀⢀⡆⠀⢰⡇⠀⣾⠃⠈⢀⣾⣿⡖⠋⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠸⣄⣀⣀⠀⣿⡀⠀⠀⣼⡇⡠⢻⡃⣰⢿⡀⣠⠎⢸⠏⢿⣦⣀⡀⢀⣠⣼⠟⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⢧⣤⠞⠈⠓⠁⠈⠛⠁⠈⠉⡁⠀⠈⢀⣄⠈⠙⠛⠛⠋⠁⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⡴⠲⣄⣀⡴⠛⠶⠴⠞⠙⠶⠖⠋⠉⠳⠦⣤⣤⡤⠞⠋





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⣿⠀⣾⢃⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠁⢹⡇⠀⠲⠀⠀⠿⠘⠃⠉⠁⠀⠀⠀⣾⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⣀⠘⠁⠀⠀⢀⣠⡀⠀⣠⢤⠀⣰⠞⣿⠇⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠁⠀⠀⠀⣰⣾⢁⣧⣾⣇⣎⣼⠏⣼⡟⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣀⣀⡀⣸⡏⢙⠏⣿⢁⡟⢹⣯⡞⣿⠇⠀⢠⠇⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⠋⣩⠏⠻⡷⢋⣀⣿⣯⣤⡀⠉⠀⣿⠀⣠⠏⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⠀⠀⠀⢀⡴⠋⠀⣠⠞⠋⠁⣰⠂⢠⠇⠀⠀⠘⠛⣋⠀⠀⠀⣠⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡘⣿⣄⣠⡴⠋⠠⠀⣼⠃⠀⠀⢰⣏⡴⢫⡞⣠⣾⢀⡾⣩⠇⠀⠀⠩⢶⡛⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣌⠉⠀⠉⠁⣀⣤⣤⣤⣇⠀⠀⠀⣿⠙⡆⠸⠟⢹⣇⣾⠋⠁⣰⠁⠂⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣩⡄⠀⠀⣠⣾⠟⠉⠁⠉⠙⠷⠀⢸⡇⣰⠇⢀⣤⣿⠉⣿⣤⡾⠁⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢀⣼⠟⠁⠀⠀⠀⠀⠐⠂⠀⠸⠷⠋⣠⠋⢰⡇⢠⣤⠄⠀⠀⢠⡟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠉⠀⢀⡀⠀⢤⠀⠠⡇⣠⠟⠀⣞⣧⡀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠉⢡⣤⠀⠀⢀⣤⣤⡿⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠰⠶⢿⡆⣴⡟⢠⢃⣴⡏⡸⠀⣴⠟⢡⣿⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢠⡟⣼⠏⢳⠞⢹⡏⣽⠓⢻⣏⡰⠋⣿⠀⢀⡞⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣴⣿⠃⣿⣠⠏⠀⠸⠟⠁⠀⠀⠉⠀⢠⡟⠶⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣸⡟⠀⠈⠁⠀⠀⡀⢀⡀⠀⣴⠿⢆⡿⣠⣴⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠂⠀⢠⣿⠃⠀⠀⠀⠀⣼⢁⣾⠁⣾⠃⣠⣾⡿⠛⠁⠀⠀⣼⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⡏⠀⠀⠀⠀⢸⣧⢻⣏⣼⣧⡔⢱⡟⢷⣄⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣿⣧⡶⠶⠾⠟⠈⠁⠈⢛⠀⠀⠀⠘⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⢀⡾⢹⡈⠃⠀⠀⢴⡦
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠀⠀⢸⡧⢰⠟⣤⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⢨⡗⠀⠙⠀⠈⠇⠈⠀⠀⠀⠀⣀⣸⠃⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⡤⠈⠀⠀⠀⣠⢶⡄⣠⡖⡆⣠⠟⣹⡏⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⢀⡾⣯⣸⣶⠿⣼⣴⡏⣴⡿⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣤⣤⣶⡄⣾⢇⡼⢱⣏⡜⠁⠸⠞⢹⡇⠀⣰⠃⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡴⠁⠘⣋⡴⠞⢛⠓⢲⠀⠀⠸⣇⣴⠋⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡸⣿⡀⠀⢀⣤⠟⠀⢠⡞⠁⠀⢠⡟⣠⢞⡄⢀⡄⢈⡴⣦⠀⠀⠴⣋⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠙⠳⠶⠋⠁⠀⠀⡟⠀⠀⠀⣾⢿⡁⣾⡱⣻⢣⣿⠔⢁⡄⢀⠀⢽⡦
⠀⠀⠀⠀⠀⠀⠐⠻⢛⠃⠀⠀⣠⣴⠿⠛⠻⢷⣄⠀⢸⡏⢸⠇⠉⣠⡿⢻⡇⢀⡾⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠴⠟⠀⢀⣾⠟⠁⠀⠀⠀⢠⠉⠀⢿⣥⠏⢠⠞⣹⠃⢈⡛⠋⠀⠀⣾⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠠⠀⠀⠀⠀⡀⠁⢰⠃⢠⠏⢀⣷⡃⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⡀⠈⠒⢋⡀⠈⠉⢁⣀⣼⠏⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣶⡄⣠⡞⢹⠀⣰⡏⡟⢀⣴⠋⣹⡟
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣇⠀⠀⠀⠀⠀⢀⡾⣰⠟⢧⠾⢺⠏⡿⠗⣾⢃⡜⢹⠃⠀⡴⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀⣀⣠⣿⠃⣿⣠⠎⠀⢿⠞⠀⠀⠙⠋⠀⣼⠦⠞⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⢡⡿⠀⠈⠁⠀⠀⠀⢀⠀⢀⡶⡶⣸⢇⣠⠆⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⠆⠀⠀⣿⠃⠀⠀⠀⢀⡾⢠⡟⢠⡟⠀⣴⣿⠟⠋⠀⠀⣰⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣸⡟⠀⠀⠀⠀⣸⡷⢻⣃⣾⣥⠊⣿⠻⣆⡀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⠷⠶⠶⠿⠛⠈⠀⠘⣋⠀⠀⠀⠁⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⢰⠏⣷⠘⠀⠀⠰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⣀⣤⣾⠟⠋⠁⠀⠀⠀⢀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⣶⡿⠛⠉⠀⠀⠀⠀⣀⣤⣴⠾⠗⠀⠀⠀⠀⣀
⣠⣶⠿⠛⠉⠀⠀⠀⠀⣀⣤⡾⠟⠋⠁⠀⠀⠀⠀⣀⣤⣤⡀⢀⣤⣝⡛⠷⢶⣤⣤⣶⠿⠛⠉⠀⠀⠀⠀⣀⣴⡾⠛
⠋⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠹⣧⠘⡏⠉⠛⢷⣦⠀⠁⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁
⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⢿⡄⢹⣤⠶⠛⠁⠀⠀⠀⠀⢀⣴⡾⠟⠁
⣴⡾⠛⠉⠀⠀⠀⢀⣠⣤⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠁⠀⠀⢀⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⣀⣀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⢀⣤⣾⠟⢻⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟
⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠛⠉⠀⠀⢀⣤⣾⠿⠋⠁⠀⢸⠁⠀⠀⡿⠀⠀⠀⠀⠀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠋⠁⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠸⡆⠀⢀⡇⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⣤⡀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⣇⠀⢸⣇⣤⡾⠋⠁⠀⠀⠀⢀⣤⡾⠛
⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⢀⣠⡾⢿⡇⢰⡏⠻⣦⠀⠈⢿⣦⠀⠀⠀⠀⠀⢿⠀⠸⠟⠉⠀⠀⠀⠀⣠⣾⠟⠁
⣠⡶⠟⠋⠀⠀⠀⠀⣀⣴⠟⠁⠀⢸⡇⠸⡇⠀⠈⢷⡄⠀⠻⣧⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⣴⠾⠋
⠉⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⢼⡇⠀⣿⠀⠀⠀⠙⢦⣀⠙⢷⡴⠟⠁⠀⠀⠀⢀⣴⠿⠋⠁
⠀⢀⣠⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡇⠀⠀⢀⣠⠾⠋⠁⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠴⠶⠾⠃⠀⣇⣴⠾⠛⠁⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠁
⠒⠛⠛⠉⠉⠉⠉⣁⣀⣤⣤⣤⣤⣤⣄⠀⠉⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠁
⣤⠶⠶⠶⠟⠛⠛⠋⠉⠁⠀⣠⡴⠟⠁⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⢀⣴⠟⠋⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟
⠀⠀⢀⣤⡶⠋⠁⠀⠀⢀⣤⠾⠋⠁⠀⠀⣿⠋⠛⠻⠶⣦⣤⣀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠁
⣤⡶⠟⠁⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⢀
⠁⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⣠⣴⠟
⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⣠⣴⠾⠋
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠘⣇⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠸⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⢄⡀⠀⠀⠀⠀⣀⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠉⠉⠑⡍⠉⠁⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠒⠉⠀⠀⠀⠰⠿⠭⢉⣺⢡⠉⢒⠊⠑⠦⠤⣄⠀⠀⢼⠠⠖⠉⢒⠊⢡⢻⣊⠩⠽⠷⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡸⠀⡎⠀⠀⡜⠀⢸⠀⠀⢸⠘⡄⠀⠈⡆⠸⡸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠇⢠⠁⠀⢀⠃⠀⢷⠋⢺⡇⠀⢃⠀⠀⢡⠀⠇⢧⡀
⠀⠀⠉⠑⢄⠀⠀⠀⠀⠀⢄⣼⢸⠀⡸⠀⠀⢸⠀⢸⡿⠀⠸⣿⠀⢸⠀⠀⠸⡀⢸⢸⣄⠄⠀⠀⠀⠀⢀⠔⠉⠁
⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⡠⡏⠊⠀⠇⠀⠀⡇⠀⡜⠇⠀⠀⡟⡄⠀⡇⠀⠀⠇⠈⠊⡧⡠⠤⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⣀⣀⠀⠀⡹⠀⠀⠀⠸⡁⠀⢀⣀⡠⠤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣡⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠘⠻⣶⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠠⠤⠶⢦⣤⡀⠀⠀⠀⠀⠠⠴⠖⢶⡆⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⢠⣿⠃⠀⠀⠊⠁⡉⠙⢿⣆⠀⠀⠀⠀⢀⣤⡄⠀⢻⣷⠀⠀⠀⠀⣠⣤⡴⠆⠀⢀⣾⡟⠁⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⢀⡄⠀⣼⠟⠀⠀⠀⣴⡿⠃⠀⢈⣿⣠⡆⠀⣰⣿⠋⠀⠀⣸⣿⠀⠀⢠⣾⡟⢁⣤⡆⠀⢸⣿⠠⠀⣨⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠀⠀⣡⣤⡶⠀⢰⣿⠁⠀⢀⣾⡟⠀⠀⠀⠻⠷⢀⣠⣾⠟⠁⠀⠀⠙⣁⣴⡿⠋⠀⠠⣈⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⣾⡇⠀⣠⣿⠏⠀⢰⣿⠁⠀⠀⠌⣉⣥⡾⠟⠋⠀⠀⠀⡀⠐⠚⠛⠉⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠻⠃⣰⣿⢃⡄⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠉⢁⣾⠇⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⠃⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⠏⠀⠀⠀⠀⠀⠠⠿⠋⣼⡏⠀⠀⠀⠀⠀⢀⣴⣦⠀⣠⣾⡧⢀⣀⣴⠟⠉⢉⣤⣾⣯⠾⣿⣛⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠐⢟⣿⢃⡴⠋⣿⣧⠞⠹⣧⣤⠞⠋⠀⠋⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣤⣴⠶⣶⣶⣦⠘⢿⡟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠖⠛⢋⣉⣥⠴⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠟⠛⢋⣁⣤⣶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠛⠉⢀⣤⡶⠾⣟⣛⣭⠤⠶⠶⠶⠂⠀⠀⠐⠂⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⢠⣾⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⡞⡷⠀⠀⠀⠀⠀⣀⡀⢰⣴⡟⢀⡼⣿⠀⠀⠋
⠀⠀⠀⠀⠀⣴⠟⠉⢹⡇⣾⣸⢃⡄⢠⠶⡆⣼⡡⢃⣾⠇⠙⠻⠴⠟⠀⠈⠁
⠀⠀⠀⠀⣼⠇⢠⡴⠟⠀⣿⣿⣿⢁⣿⣞⡵⠿⠷⠋⠉
⠀⠀⠀⠀⣿⠀⠀⠀⣀⡴⡿⠙⠿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠙⠷⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠉⣼⣯⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠹⡄⠀⠀⣠⣷⡄⠙⣦⡀⣸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠌⠂⠐⠀⠈⠙⢧⣾⣦⣨⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣝⠃⠀⣰⠀⣴⣤⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⡀⢰⡇⢰⣭⣟⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣟⣽⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣿⣿⣿⣿⡇⠹⠀⠀⣀⣴⡄⠸⡄⠀⢩⣴⣿⡄⠈⠢⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣇⢠⣶⣿⢟⣿⣭⡀⢻⡀⣠⣿⣿⡇⠀⠀⠐⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⠿⠶⠶⠚⠻⡀⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠌⠢⢀⣀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠗⢁⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⠀⠀⡀⣠⡿⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦
⠀⠀⠀⠀⠀⠈⠲⠶⡉⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠓⣄⣀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⡀⠄⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠁

⣿⣿⣿⣿⡁⠀⠀⠄⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⡐⠀⠀⢈⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠘⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠄⠀⠀⠀⣸⣿⣿⣿
⡿⢿⡿⠛⠅⠀⠀⠀⠀⠠⠛⠉⠉⠀⠉⠀⠉⠉⠛⠊⠀⠀⠀⠀⠈⠟⠿⡻⢿⠿⢿⢟⠟⠙⠄⠀⠀⠀⠀⠙⠉⠉⠀⠈⠀⠉⠙⠛⠀⠀⠀⠀⠀⠊⠻⡿⡿
⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠋⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⢠⣴⣵⣺⣽⣷⣦⣀⡤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣔⣴⣾⣿⣷⣴⣦⣈⡀⠀⠀⠀⠀⣀⡀
⣷⣿⣿⣿⣷⣂⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢄⣾⣿⣿⣿
⣿⣿⣿⣿⣿⡕⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠡⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⢺⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⡖⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠘⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢻⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢏⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⣽⣿⣿⣿⣿
⠉⠙⠛⠻⠏⠃⠀⠀⠀⠨⢻⣿⣿⣿⣿⣿⡿⣿⠟⠅⠀⠀⠀⠈⠿⠿⠛⠋⠉⠉⠙⠛⠻⠏⠂⠀⠀⠀⠸⠛⣿⣿⣿⣿⣿⡿⡿⠟⠇⠀⠀⠀⠐⠽⠟⠛⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠭⠕⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠨⠭⠕⠋⠈
⡦⣴⢦⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣢⢴⣦⣕⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣣
⣿⣿⣿⣿⣿⠀⠀⠀⠀⢬⣾⣶⣶⣦⣤⣴⣶⣶⣿⣤⠀⠀⠀⠀⢵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⣷⣶⣶⣦⣤⣴⣶⣶⣿⢆⠀⠀⠀⠀⢵⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⠂⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⠀⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠀⠀⠀⠐⣿⣿⣿
⣿⣿⣿⣿⡆⠀⠀⠁⠜⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠀⠀⠀⢰⣿⣿⣿
⣿⣿⣿⣿⢿⠀⠀⠀⠀⢙⣿⡿⠿⠟⠛⠻⠿⠿⣿⠟⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠛⣿⠿⠿⠟⠛⠻⠿⢿⡿⠋⠀⠀⠀⠀⠾⣿⣿⣿
⠗⡛⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢟⠳⠟⣛⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⢛
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣒⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⣂⡢⡄⢀
⣀⣠⣤⣴⣔⠅⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠠⢶⣦⣤⣤⣄⣀⣠⣤⣴⣖⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⣦⣦⣤⣄
⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡠⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢰⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡌⡆⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠼⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠂⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡐⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣯⡓⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠨⣿⣿⣿⣿
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠊⠻⡻⢿⣿⣯⢟⠗⠃⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠛⡿⢿⣛⡻⠿⠟⠁⠀⠀⠀⠀⠀⠈⠁
⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⣾⣾⣷⣤⣠⠀⠀⠀⠀⡀⣠⣄⣀⠀⡀⡀⣀⣀⢄⡀⠀⠀⠀⠐⣔⣶⣿⣿⣾⣷⣾⣿⣦⣠⠀⠀⠀⠀⠠⣤⣀⣀⢀⢀⠀⣀⣠⣄⠀⠀⠀⠀⠀⢄⣼⣵⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⠅⠀⠀⠂⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⡄⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⠀⠀⠀⢨⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠉⠉⠉⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠈⠓⠦⣀⡀⢰⡟⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡴⠉⠀⠈⠻⣦⠀⠀⠀⠀⠉⣿⡗⠒⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡠⠤⣤⡀⠀⢰⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠙⠲⠤⠤⠒⠊⠀⠀⡾⢀⠀⠈⣷⠀⢨⢷⡴⠀⠀⠀⢸⠃⠀⣴⠛⠉⣿⡇⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢹⣿⣀⣀⣿⠔⠁⣾⡿⢦⣄⣀⣿⣠⠴⣿⡀⣰⠿⣿⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⢻⣷⠀⠀⠀⠀⢠⠞⢿⣦⠜⠁⠀⠀⢿⣧⡀⢈⡽⠃⠀⠀⠻⠟⠋⠀⠹⣷⣄⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢸⣿⣀⣀⡤⠖⠁⢀⣠⠤⣤⡀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠉⠛⠓⠒⠋
⠀⢀⡤⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⠉⠀⠀⠀⣴⠏⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣸⡇⢀⢤⣄
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣸⡏⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⣠⡞⠁⠈⡇⠀⣿⡷⠁⣸⠇⠀⠀⠀⠀⠀⢀⣀⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠑⢲⣿⣅⣠⠤⠔⢊⠀⠀⢠⣶⠀⠀⣿⠁⠀⠀⠁⢰⣿⣧⡾⠋⠀⠀⠀⢀⠴⠚⠉⠉⠹
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠃⠀⢸⡇⠀⢀⣿⣇⠀⢀⡰⠋⢿⡏⠉⠙⠻⢶⣴⣁⡀⠀⠀⠀⣠
⠈⠻⣷⣄⣀⠀⠀⢀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢀⣿⡀⢀⡾⣿⡤⠞⠈⠙⠛⠉⠀⠀⠀⠀⠀⢀⡴⠃⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢦⠤⠊⠙⠛⢋⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣶⣶⣶⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⣾⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢰⠋⠀⢠⡟⠉⢳⢤⣶⠆⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⡀⣀⠘⠄⠤⠊⠣⣠⠜⠹⢇⡴⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⠴⠋⠀⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣰⣿⣀⣀⣀⣠⣤⣤⡤⠴⠂⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢫⣿⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣠⡿⠃⣸⡇⠀⡀⠀⠀⠀⢀⣠⠄⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⡇⠘⡇⠀⠀⡻⣾⠀⠀⠀⢸⣇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠱⠄⡠⠆⠈⠳⠴⠂⠀⣿⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠒⠋⠀⠀⠉⠉⠉⠓⠂⠛⠛⠛⠋⠙⠛⠉⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣖⣲⣶⣶⣶⣶⡄⢀⣶⣶⣾⣯⣴⣶⣶⣶⣶⣶⣶⣶⣶⠆⡼⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⡿⢿⣏⣭⣭⣿⠟⢻⡿⠿⠛⠛⠀⠈⠁⠚⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡝⢻⣿⢿⣿⡇⠰⣿⣿⣿⣿⠋⠁⢀⣠⠄⢀⣀⠀⠀⠀⣠⣶⣶⣄⣠⣄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢣⣴⢶⢶⣄⢷⣄⠙⠿⠃⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠸⣿⣿⣿⠟⠀⣻⡷⠀⣸⣷⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⢀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢹⠏⠁⠀⠀⣛⣥⡶⢰⠂⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⢠⣶⣤⣾⣿⡿⠙⠘⢀⣼⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣯⠈⠻⣯⣿⣿⠿⠛⠛⠻⣶⠳⠶⢾⣿⣧⣀⠀⠀⠀⠀⠘⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡼⠋⣠⠀⣹⡟⠁⢂⣀⡀⠈⠉⠀⠀⠠⠉⠛⠿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡀⢻⣾⠟⠁⢆⠀⠈⠁⠁⠀⠀⠀⠀⠁⠸⠗⡄⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣙⣡⡮⠨⠀⠈⢀⠀⠀⠀⠁⠀⠀⠀⠐⠀⣀⡐⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⣦⣤⠀⠀⠑⠂⢀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠠⢸⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣼⡇⠀⢿⣿⠓⢄⠀⠀⠊⠻⠷⣤⣤⡤⠠⣾⣷⣆⠀⠀⠙⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡇⠀⢸⣿⡔⣆⢀⢀⣀⠀⠀⠀⠀⠀⣤⣼⣿⡘⠂⢠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣠⣼⣿⣥⣬⣿⣿⡛⠱⣤⣤⣠⣶⣿⢩⣿⣧⠄⠁⣬⠸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡟⣿⣽⢻⣿⣿⣿⣿⣿⣥⣌⣉⣁⡿⠿⣿⣿⣿⢻⡄⣢⠽⠺⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠙⠛⠿⠒⠛⠁⣿⡟⣿⣟⡉⠀⢈⣿⣿⣿⣿⣿⢻⡇⠀⠂⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⣖⣲⡆⢀⣇⢀⡳⠄⠀⢀⣀⠈⠉⠉⠉⠋⠸⠇⡰⣤⣨⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠉⠉⢡⠊⠉⠁⠉⠀⠀⠉⠉⣻⠀⠀⠈⠀⠀⢈⡟⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠀⢠⡀⢽⣷⣶⣶⣶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠙⠛⠏⠉⠏⠱⠄