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. _ - 、 / ) _ -- 、 _ノ -  ̄`´、ー一'´ } { ,:'´ 、 / Ч , - _ ⌒ ,, }` ー--‐ ´ 乂__ヽノ_ - ´ { 、) /⌒Y _ゝ __ >r′ `ー ´ `´

⠀⠀ ,ー、_-ーーー-_,ー-、 / / \ / / ● ● ヽ ヽ_ ( ( ⊃ '-'ー′⊂⊃ ) ヽ 丶 `ヽ_ノ`(⌒)ーーーー<′ ヽ___ノ (_r / ̄ ̄~丶_)

. ∇ [> 〇 <] ( (:) ) [二二二] / \ / / o o \ ( 人○ ∀ ○人 )  ̄ (つ ノつ  ̄ し-O

⠀⠀ ⠀⣀⡤⣤⠶⠛⠉⠉ ⠀⠉⠉⠛⠲⣤⣤⣄ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳ ⡞⠀⠀⠹⣆⠀⠀ ⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⡽⠉⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀ ⠀⠀⢀⣠⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠦⡀ ⡴⠉⠀⠀⠀⠀⠀⡏⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠓⢤⣀ ⠀⠀⠀⠀⠀⠀⣀⡄⠬⠀⠘⠒⠦⠂⠀⠀⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲ ⠙⠤⣤⠤⠶⠋⠀⣈⡶⠴⠶⠤⣤⡀⠀⠀⠘⠘⠀⢀⡼⢦⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠏⠉⢦⠋⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠉⠉⢦⠀⠀⠈⠲⣄⡀⠀⠀⣠⠁ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣾⠀⠉⠆⠀⠀⠀⠘⡀⠀⢳⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠙⠤⠖⠓⠲⠤⢤⣸⡀⠀⣀⣤⠴⠚⠉⠀⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠔⠊⠉⢳ ⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠃⠀⠀⠀⠀⠀⢀⠜ ⠀⠀⠀⠀⡔⠚⠀⠀⠀⠀⠸⢆⣬⡖⠒⠒⠚⠁⠀ ⠀⠀⡠⠊⠀⡄⠲⠀⠲⡿⠀⣨⢙⣀⢀ ⡞⠁⠀⠀⢠⠳⠛⡡⠄⠒⠉⠀⠙⣅⡆⡃ ⠣⣀⣀⠔⠁⠀⠘⢲⣀⠀⠀⠀⡀⠗⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣨⠄⠒⠊⠀⠁

⠀⣠⠔⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡍⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⡸⠏⠑⢢⡴⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠷⣄⠀⣸⡤⣤⠏⠀⠀⠀⠀⠀⠈⠛⡖⠊⠳⠀⠀⠀ ⠀⠀⠀⠀⢈⡟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡴⣏⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠞⠙⠂⠀⠀⠀⠀⠀⢀⣄⡀⠁⣄⢹⡆⠀ ⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠻⠤⠤⣤⠀⠉⠀⠃⢀⣼⠀⢷⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⠶⢤⣤⣄⣀⣀⠀⠄⠀⢀⡡⠋⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣏⠀⠀⠀⢠⡯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠾⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠦⢄⡀⠀⠀⠀⠀ ⠀⠀⢠⢊⠘⠀⠀⠀⠀⠀⠀⠀⠃⠉⡄⠀⠀ ⠀⣠⢋⡏⠀⠿ ⢠⣀⢄⡦ ⠿⠀⠀⠙⣄⠀ ⢸⡇⠀⠳⢆⡀⠀ ⠀⣠⡾⠀⠀⢘⡄ ⠀⠳⣆⡶⠟⠙⠛⠛⠛⠛⠛⠁⠻⢶⣰⠾⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠾⠛⠋⠉⠁⠀⠀⠈⠉⠉⠛⠳⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠿⢉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡉⠹⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠃⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⢿⣄⠀⠀⠀ ⠀⠀⣠⡟⠁⠀⣿⠁⠀⠘⣟⠛⠛⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⢋⡟⠇⠀⠀⣿⡄⠀⠻⣦⡀⠀ ⠀⣸⠏⠀⠀⠀⢿⡄⠂⠀⣿⠀⠀⢹⠃⠀⣿⣠⡴⠦⣤⣻⠆⢠⡇⠀⣸⠃⠀⠀⠀⣿⠀⠀⠀⠘⣷⠀ ⢀⣿⠀⠀⠀⠀⠈⢿⣤⡀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠇⠀⣠⡾⠃⠀⠀⠀⠀⢹⡇ ⠈⣿⠀⠀⠀⠀⠀⠀⠈⢿⣷⣷⣆⣹⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣸⣇⣶⣿⡿⠉⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠹⣦⡀⠀⠀⠀⢀⣠⡾⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡟⠀ ⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄ ⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠻⢿⣶⡀⠀⠀⣠⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠙⣿⣀⣾⠟⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀ ⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀ ⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠐⣿⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣼⡿⠀⠀ ⠀⠀⠀⠘⣿⣤⡀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣠⣾⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⠀⠀⠀⠀⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⢹⣿⣿⠿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣝⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣋⠁⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠢⢊⢌⢅⢨⢅⠀⠀⠀⠀⣿⣤⣴⡿⠿⢿⣶⣶⠟⠀⠀⠀⠀⢑⢡⡊⢌⢕⠆⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡈⠔⠑⠑⠑⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⠑⠨⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣷⣶⣿⡿⠁⢸⣿⠀⠻⣿⣶⣶⣾⣷⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠻⢿⣷⣿⠁⠈⠀⠀⢀⣿⣿⣆⠀⠀⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢠⣦⠀⢈⣿⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣇⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣦⣤⣤⣾⣿⡇⠀⢀⣤⣄⣀⣀⣀⣤⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⣿⣄⠀⣽⡿⠋⠛⠻⣿⣅⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀

⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠉⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⢀⣴⡿⠛⠛⣻⣿⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡄⣰⣿⡿⠇⠐⣻⡟⠋⠁⢠⣶⠀⠀⠈⢿⣿⣶⣶⣤⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠛⠛⠻⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⢸⣟⠀⠀⠀⠈⠻⠷⣦⣴⠿⠁⠹⣯⠉⠛⠿⣿⡿⠛⠻⣿⣦⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠟⠛⠛⠛⠛⠛⠛⠛⠷⢶⣤⣄⡀⠀⠀⠀⣿⠇⠀⠀⠀⠙⠧⣀⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣤⣾⠟⠀⢀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣀⣄⣀⡈⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡲⣌⢧⡛⢷⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⢹⣷⣶⣶⣶⠶⠶⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣒⠹⠚⠁⣀⡀⣀⣽⡷⠖⠲⣤⣸⡇⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢶⣾⣿⣻⢟⣯⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⡖⢯⣛⠳⡶⣄⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣻⣧⣿⣿⣿⣟⣿⣿⣦⣤⣄⣀⣀⣈⣉⣳⣌⣻⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣛⣿⣛⣿⣿⠈⠉⢉⣩⣿⡿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣟⣿⣟⣿⣿⣿⣶⣾⠿⠟⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣤⣴⣶⡿⠿⠿⠛⠛⠛⠟⠛⠻⠶⢤⣤⣿⣟⣿⠟⠋⠁⠀⣀⣀⡀⠈⠉⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⣩⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣀⣴⠟⠋⠉⠙⢳⡄⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⢶⣦⣌⠃⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣶⣾⢿⣿⣽⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠙⢿⣦⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣠⣴⠟⠁⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠈⢿⣦⠀⠀⠀ ⢀⣴⣿⠟⠛⠋⠉⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⢸⣿⠀⠀⠀ ⣾⡿⠁⠀⠀⠀⠀⠀⠀⣼⡏⠀⣠⣤⣤⣶⣶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⢸⣿⣆⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⣦⣤⣀⡀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠉⢻⣷⡀ ⢻⣿⣄⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⣠⡇⠀⠀⠀⠀⠀⣿⣇⣀⣤⣤⣄⡀⠠⣦⠀⠀⠀⣀⣀⣉⣙⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⣠⣿⡇ ⠀⠙⢿⣶⣤⣀⣀⡀⣀⣀⣘⣿⣿⣧⣤⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠛⠛⠋⢠⡏⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣴⣶⡿⠟⠋⠀ ⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠀⠉⠙⠛⠿⠿⢶⣦⡤⠤⣦⣄⣀⣀⣀⣀⣀⣏⣀⣀⡀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠿⡿⣶⣶⣶⣦⢒⢛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⣿⣿⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡿⠁⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠉⠿⠿⠁⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀ ⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠤⠠⠐⢀⡀⠀⠀⠀⠀⠀⠋⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢁⠀⠀⣼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀ ⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢶⣤⣴⡾⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⠀⠜⣀⣴⠟⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣿⠃⠀⠀⢸⡟⠳⠶⠶⠶⢦⣶⣴⣶⣴⣶⣶⣿⠉⠀⠹⣷⣿⣿⣥⣄⡀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⢀⣿⠟⠉⠉⠉⠛⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣷⡀⠀⠀⣀⠀⠈⣿⡄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⠉⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⠏⠀⠀⣽⡇⠀⠀⠀⠈⠛⠿⠶⠶⠶⠶⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡾⠋⠀⠁⠀⠀⠀⠀⠀⢀⣾⠛⠉⠙⠓⠀⠀⢀⣴⠟⠛⠿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢶⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣠⡿⠁⠀⠀⠀⠀⢹⣇⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⣉⡉⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡾⠋⠀⣠⡾⠛⠛⠻⣷⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠖⠿⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⢷⣶⣿⣤⣤⣀⠀⠘⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⢷⣄⠀⠀⣠⣾⣇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣤⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡋⠀⠈⠻⣦⡀⠀⠀⠀ ⠀⢀⣴⠾⠋⠉⠁⠀⢀⣀⣀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠈⢿⡶⣤⡀ ⢠⡾⠁⠀⠀⠀⠀⠀⠈⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡷⠦⢤⡄⠀⠀⠀⠀⠙⢷⡄⠈⣧⠈⣿ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣋⣰⠟ ⢸⣆⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠁⠀ ⠀⠙⠷⣤⣄⣀⣀⣀⣀⣀⣻⣮⡉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⣤⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠛⠒⠒⠷⠴⠶⠤⠶⠤⠤⣤⣦⣤⣤⣤⣿⣦⣀⣀⣀⠀⢀⣀⣀⣀⣀⣤⣤⠶⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
そのほか
そのほか

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣿⣟⠛⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠛⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⣠⣶⡾⠿⠿⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠁⠀⠀⠀⠀⠙⢿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠈⣿⡆ ⠀⠀⢠⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⠀⠀⠀⠉⠛⠿⠟⠁⠀⠀⠀⣿⠇ ⠀⠀⣼⠙⠷⢾⡿⠃⣀⣀⣤⣤⣤⣤⡄⢀⣴⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀ ⠴⣾⣯⡀⣀⣘⣷⡈⠉⠁⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡆⠀⠀⠀⠈⢿⣧⣀⣀⣀⣀⣤⣶⡿⠋⠀⠀ ⠀⠀⠸⣷⡟⠉⠉⠋⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠁⢀⣀⣀⣀⣀⣸⣿⣛⣛⡛⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⢿⣛⡉⠉⢉⣩⣭⣟⣿⣏⣳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇⠀⠀⢀⡟⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢉⣉⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡾⠿⠿⠿⣶⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢾⣶⡿⠛⠉⣿⡇⠀⠀⠘⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⡿⠛⠛⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⣿⡇⠀⠀⠀⠀⠙⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠙⠿⠶⠾⠟⠁⠀⠀⣀⣽⠀⠀⠉⠉⠉⠉⠉⠉⣽⡟⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⢿⡿⠦⠤⣤⣤⣤⣤⣤⣤⣼⣿⣄⠀⠀⣠⣿⠃⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠁⠀⠀⢈⣿⣧⣠⣶⠿⠿⠿⢷⣶⣦⣄⣀⠀⣀⣀⣤⡴⣶⣟⣿⣏⡹⣷⢛⣐⣿⠀⠀⠀⣴⣾⣿⣿⣦⡀⠻⠿⣿⣾⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣼⡿⠹⣿⣇⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣟⠉⠁⠀⠙⢿⣿⠿⠟⠛⠛⢻⠄⠀⠸⣿⣿⣷⣿⣯⡽⠀⠀⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠈⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⣰⣶⠟⠁⠀⠀⠀⠀⠸⣶⣸⣿⣿⡿⢿⢿⣻⣯⣧⣠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣤⣤⣤⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠹⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢿⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠒⠶⣄ ⠀⠀⢀⡴⠋⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠉⠳⡀ ⠀⠟⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡙⡄ ⠘⡀⠙⠁⡏⠀⢰⣷⠀⠀⠀⠀⠀⠀⢠⣷⠀⠈⡆⠛⠁⣿ ⠀⠻⣤⣤⠀⠀⠈⠁⠀⣤⣀⣀⢰⠀⠀⠋⠀⠀⣯⣠⡴⠁ ⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣿⣿⣥⣤⣤⣤⣤⣄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣿⣿⢿⣿⣽⣽⣯⣷⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⣶⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠟⠛⠉⠁⠀⣿⣿⠀⠀⠀⣀⣄⣠⣀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⣠⣾⣿⣻⣾⠛⠃⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⣾⣿⣿⠿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣧⣀⢀⣀⣠⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣽⣿⣿⣻⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢿⡿⠁⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣟⣟⢿⣿⣿⣿⣿⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠿⠋⠀⢀⣼⣟⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣥⠀⠁⠛⢷⣯⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠁⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢿⣄⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠙⢿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣿⣿⣶⣶⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠩⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⣿⣽⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⠀⠀⠀⠹⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⠋⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡆⠀⠀⠀⠹⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⣴⣟⣿⠋⠀⠀⠀⠀⣿⣺⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣟⣟⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⠀⠀⠀⠀⠹⣟⣿⡆ ⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⠙⣿⣿⣆ ⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠘⣿⡿⣷ ⠀⠀⠀⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠉⢿⣻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣧ ⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡄ ⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿ ⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣀⠀⠀⠀⠀⣀⣾⠟⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿ ⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣿⣿⣷⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣽⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠁ ⠀⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣽⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣦⣴⣶⣾⣿⣿⣿⣿⣿⣯⣿⣯⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿ ⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⣿⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇ ⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⡟ ⠀⠀⠀⠻⣷⡿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⡿⠋ ⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠉⠙⠷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⡄⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⡞⡴⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀ ⣸⢠⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠉⠀⠀⠀⠀⠈⣦ ⡇⠾⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⢉⡟⠉⠉⠉⠉⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⣿⣰⠟⠛⢳⣄⠀⠀⠀⠀⠀⠙⢿⡞⠶⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⣟⣇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠷⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋ ⠀⠀⠀⠀⢿⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠃ ⠀⠀⠀⠀⠀⠻⣴⠃⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋ ⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⡟⢣⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠷⠀⠀⠀⠀⠸⡄⠉⠙⠛⠛⠛⠛⠉⠁⠀⡀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢷⣧⠃⠀⠀⠀⠀⡟⠁⠈⢿⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠒⠛⣉⡴ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣶⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿ ⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠀⠙⣦⣀⣀⣀⡀⢀⡀⢀⣀⣀⣀⣤⣤⣴⣲⡾⠽⠷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠂⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢀⣤⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢀⣤⠛⠿⠶⣤⣤⣄⣀⣀⣀⣀⣀⣄⣤⣤⡶⠾⣤⡀⣀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣠⣤⣤⣤⣄⣀⣄⣄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣥⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠉⠀⠀⠙⢿⣿⣶⣠⣤⣤⣀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⡿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⣀⣦⣦⣤⣴⣿⡿⠉⠀⠈⠙⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⠉⡉⠁⡁⡐⡁⢂⠢⡂⢐⡂⢐⡂⠄⢄⠢⠅⠌⠄⠉⠉⠙⠟⢟⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⠟⠻⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠋⡀⡀⢄⡂⡐⡅⢂⠔⠅⠅⡑⢊⡊⠡⠌⡡⠌⡁⠔⠅⢐⠆⠄⡄⠡⡂⠔⢂⡐⠠⠄⠜⠛⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢄⡡⠅⡨⡂⢄⡊⠡⠕⢂⠔⢅⠌⡑⢂⡢⢅⠌⡁⠔⢅⡐⠕⢂⠔⠅⡁⡄⢂⠌⡡⡊⠢⠅⡡⠌⠠⡠⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⢿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡇⠀⡑⡂⠅⡑⠢⢅⡢⠅⢄⡊⠆⡑⠊⡑⢂⡢⠕⠊⡁⠔⢅⡂⢄⡊⠆⡡⠅⡑⢂⠌⡡⡊⠢⠅⡑⠅⢌⠆⠂⣺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⢄⡢⠅⠌⡑⠢⢅⡢⠅⢄⡂⠌⡑⠊⡑⠢⡢⠕⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⠅⡄⠂⠐⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠠⡢⠅⠌⡑⠢⢅⡢⢅⢄⡂⠌⡑⠊⡑⠊⡡⠕⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⠅⡡⡂⢱⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⢂⡢⠅⠌⡑⠢⢅⡢⠕⢂⡂⠌⡑⠊⡑⠊⡑⠕⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡣⡐⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⢀⠄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⢅⡢⠅⠌⡑⠢⢅⡢⠕⠢⡂⠌⡑⠊⡑⠊⡁⠔⠊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⠅⡈⢐⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⡀⢻⣿⣿⣿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠄⢘⠅⣻⣿⣆⠀⠀⠀⠀⠀⣰⣿⣶⣀⣀⣶⣿⣿⠏⢄⡂⠢⢅⠌⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢌⡊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡃⢐⡂⠿⣿⣿⣦⣀⣠⣶⣿⡄⠀⠀⠀⠀⠀⣰⣿⡏⢈⡑⠂⢛⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡃⡂⡢⠌⡠⠨⢿⣿⣧⣤⡄⣠⣶⣿⡿⠿⣿⡿⠿⠛⠁⠐⠑⠌⠆⡑⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡊⡁⠔⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠂⡐⠔⡉⠟⢿⣿⡿⠿⣿⣿⣦⣤⢄⣤⣾⣿⡿⡀⠡⢌⠆⠆⢛⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠄⠡⠕⢂⡂⠐⢀⠙⠿⣿⣿⣿⠟⠋⠀⠠⠄⠠⠔⢁⡐⠢⢑⡢⠅⡑⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠅⢐⢅⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢊⡂⠄⡨⡑⠠⢄⢄⠄⠠⠛⠿⣿⣿⣿⠟⠓⠄⡑⢂⢌⠆⠢⠌⠽⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢐⡂⠔⠊⡡⡊⠢⠅⡡⠄⡀⢄⢄⡢⡢⢅⡐⡅⢂⠔⢅⡊⢂⠨⢅⡐⠕⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢂⡂⠌⡡⡃⡁⠔⡅⡑⠅⡁⢄⢄⢄⢄⡂⠡⢅⡊⠡⡊⠆⢐⢅⠀⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⠄⠌⡑⢂⠌⡡⡊⠢⠅⡑⠢⢅⡊⠂⡨⠕⢅⡢⠕⢂⠔⢅⡊⢂⠔⢅⡂⠔⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢂⡂⠌⡡⡊⡁⠌⡡⡂⢌⡢⠕⢂⠔⢂⠅⢐⡂⠢⠅⡁⢄⡊⢂⠌⠈⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⡐⢅⡊⠆⢌⡅⡌⠆⡡⠕⠢⢅⡊⠊⡁⠔⠢⡢⠕⢂⠔⠅⠊⢂⡐⢅⡂⠔⠊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠢⡂⠌⡡⡢⠅⠌⠡⠢⢂⡢⠕⢂⢄⡊⠢⠌⡑⢂⠡⡁⠂⠨⠢⠅⡂⠸⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡃⡐⢂⠨⠠⣺⣿⣿⣆⡐⡅⡑⠢⢅⡊⠊⡁⢌⡂⠢⠅⠂⠁⠐⠅⠡⢂⢄⡂⢌⡊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠊⡁⠌⠡⡂⠐⡂⢐⡢⠌⡡⠕⢂⢄⡊⠢⠅⡑⠢⣺⣿⣿⣆⠀⡌⠆⡀⢿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⠀⡑⢂⠀⣶⣿⣿⣿⡟⡁⢕⠌⠆⡡⡊⠊⡁⡄⠊⢁⣤⣶⣷⣶⠄⠐⠈⢄⡂⢄⡊⡑⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⢊⠆⠡⡠⣴⣷⣶⡤⠁⠢⠕⠕⢂⢄⡊⠢⢅⡃⠠⣿⣿⣿⣿⡦⠂⢅⡢⠐⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠠⠌⡡⠨⣰⣿⣿⣿⢿⠁⢄⡊⠢⠅⡡⡊⠆⡑⠅⢠⣿⣿⣿⣿⣿⣿⣆⠐⢄⡂⢄⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡊⠢⠅⣺⣿⣿⣿⣿⣿⣷⠄⠌⡑⢂⢄⡊⠢⠕⠪⡢⠀⣿⣿⣿⣿⡅⠡⠢⢅⡂⢿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠡⠌⡁⢀⣿⣿⣿⣿⡀⡂⠡⡊⠢⠅⡡⡂⠌⢐⠢⣻⣿⣿⣿⣿⣿⣿⣿⠅⡂⢂⢄⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⠔⢅⡐⡈⢸⣿⣿⣿⣿⣿⣿⣿⣧⠌⠕⢂⢄⡊⠢⢅⡊⡁⡌⢈⣿⣿⣿⣷⠁⡂⠄⠢⠈⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠀⠨⢂⠄⠠⣲⣿⣿⣿⠇⠄⢄⡂⠔⠢⠅⡡⡂⡄⠢⢘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡐⢂⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⠅⡁⢐⠅⢐⠨⢼⣿⣿⣿⣿⣿⣿⣿⣿⠄⡑⢂⢄⡊⠢⢅⡊⠡⡣⠅⢹⣿⣿⣿⣂⠁⢂⠄⡨⠈⢿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⢀⠄⠌⢑⡂⠀⣿⣿⣿⣟⡁⡢⢅⡂⠔⠢⠅⡡⡢⡃⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠕⢅⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⢅⡃⠔⢂⠌⠠⢺⣿⣿⣿⣿⣿⣿⣿⣿⠄⢅⠢⢅⡊⠢⢅⡂⠌⠡⡠⠰⣿⣿⣿⣿⠀⠌⠨⢅⡐⠘⢿⣿⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠠⡈⢐⡂⠨⠑⣡⣿⣿⣿⡗⡀⡂⠡⡂⢌⡢⠅⡡⡊⡑⠌⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⡂⠔⢅⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⢅⡂⠌⡑⠨⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡂⡂⢐⢅⡊⠢⢅⡂⢐⠢⢑⡪⢿⣿⣿⣿⡁⢌⡂⠨⠅⡈⡀⢿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡇⡠⡊⠂⡨⠅⠔⠂⣳⣿⣿⣿⡃⠂⡢⠅⡁⢄⡢⠅⡡⡊⡑⢊⠨⣿⣿⣿⣿⣿⣿⣿⠗⠠⡂⠔⢅⡢⠕⠢⢅⡢⠕⠊⡁⠌⡑⠊⡑⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⠌⡁⠔⠕⢂⠌⡡⡊⠢⢅⡂⠌⡑⢂⠌⠂⣻⣿⣿⣿⣿⣿⣿⡗⡀⢃⠔⠂⡨⡢⢅⡊⠢⡰⡇⠡⢜⣿⣿⣿⡆⢑⠆⢐⢅⡃⢂⡂⠻⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⣀⣿⣿⣿⡿⠁⡈⢅⠌⠊⡁⠔⢌⠆⣽⣿⣿⣿⠠⠨⠅⢌⡢⢅⡢⠅⡡⡢⡃⠢⡃⠄⠿⣿⣿⣿⡿⠋⢄⢘⠅⢐⢅⡢⠕⠢⢅⡢⡃⢔⠂⡐⡑⠢⡊⠊⡁⢄⡢⠕⢂⢄⡂⢄⡂⢌⠆⢐⢊⠅⡐⠡⡊⠢⢅⡂⠌⡑⢂⠔⠆⡀⠟⢿⣿⣿⣿⡟⠠⠪⠕⢂⠌⡡⡢⠕⢂⡰⢕⡪⠌⢱⣿⣿⣿⡇⠨⡂⠔⠢⢌⡢⡂⠄⠫⣿⣿⣿⣿⡀ ⠀⠀⠀⢠⣿⣿⣿⣿⠁⡌⠢⠕⢊⡊⡁⠔⡅⠄⣻⣿⣿⣿⠅⢁⡐⡅⠢⢅⡢⠅⡡⡊⡑⠊⡁⠔⠂⢁⡉⡁⢐⢌⡃⠢⠕⢂⢄⡢⡑⠢⠅⠨⠁⣰⣷⣾⣿⢄⠅⠨⡂⠡⠌⡡⠄⡠⢐⠢⡂⠄⡰⣿⣷⣾⣁⢌⠕⠢⢅⡂⠌⡑⢂⠔⡅⠡⠂⢈⡉⡁⢈⢄⡂⠔⠕⠂⡠⢌⡃⠡⡃⢸⡇⢸⡕⢡⣿⣿⣿⡇⠠⢐⡊⠢⢅⡊⡁⠔⡅⠩⣿⣿⣿⣿⡄ ⠀⠀⢠⣿⣿⣿⡿⠁⠨⠕⠢⠕⠂⡨⠅⠌⢑⠅⣝⣿⣿⣿⡆⠅⡡⡊⠢⢅⡢⠅⡡⡊⡑⠊⡁⠔⠊⠡⠌⠡⡊⠂⡨⡢⠕⢂⢄⡊⢑⡂⠐⠂⣼⣿⣿⣿⡿⠂⠑⠈⠁⡠⣤⣤⣤⣤⠤⠂⠁⠐⠍⣿⣿⣿⣿⡅⠂⡐⢅⡂⠌⡑⢂⠌⡑⢅⡊⠡⡂⠃⡨⢅⡂⠔⠕⠊⡑⠨⡢⢪⡕⢪⡕⢪⢕⣮⣿⣿⣿⠅⠡⢌⡃⠔⢅⡊⡁⢌⡂⢄⠈⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⡿⠀⡢⡢⠕⠢⠕⠊⡁⠔⠢⠕⠔⠐⣿⣿⣿⣷⡀⠨⠕⠢⢅⡢⠅⡡⡢⠕⠊⡁⠔⢂⡐⢂⡐⠕⢅⡊⠡⠕⢂⢄⠆⡡⠌⠄⠀⣻⣿⣿⣥⣀⣔⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣠⣼⣿⣿⡧⠠⡂⢄⡂⠌⡑⢂⠌⡁⢄⡂⢌⡂⠌⠡⢅⡂⠐⢑⠊⡅⢢⡜⢣⡜⢣⡜⡣⢥⣿⣿⣿⣿⠀⠢⢅⡂⠔⢅⡢⠅⢄⡂⠄⡀⠘⣿⣿⣿⣿ ⠀⣰⣿⣿⣿⡉⢌⠕⠂⡑⠢⠕⠊⡁⢌⡊⠆⡡⡀⢹⣿⣿⣿⣃⠐⠕⡢⢅⡢⠅⡡⡢⠕⠊⡁⠌⡡⡊⢂⡂⠔⢅⡢⢅⠌⡑⢂⠌⡁⠔⠂⡂⠸⢿⣿⣿⣿⣿⣿⣿⢿⡟⠫⠍⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⡿⢅⡂⢂⢄⡂⠌⡑⢂⠌⡁⢄⡂⢄⡂⢐⠢⢌⡣⢂⡰⢎⡱⢇⡪⢕⡪⢕⡪⢕⣺⣿⣿⣿⡃⠄⠂⠨⢅⡐⡅⠢⢅⢄⡂⢌⠆⠂⢝⣿⣿⣿⡆ ⠀⣿⣿⣿⣿⠀⠔⢂⠌⡑⠢⠕⠊⡁⢄⡂⠌⡡⡂⠐⣿⣿⣿⣿⣔⠈⠕⢅⡢⠅⡡⡢⠕⠊⡁⠌⡡⡊⢂⡂⠔⢅⡢⠕⠊⡑⢂⠌⡁⠔⠊⡁⠄⠐⠉⠛⠛⠏⠁⠀⠂⠢⠕⠢⡐⠌⢐⠄⠈⠋⠛⠛⠏⠁⢐⡊⠕⢂⢄⡂⠌⡑⢂⠌⡁⢄⡂⡄⠊⠁⡐⡆⢪⡣⢎⡑⢪⡕⢪⡕⢪⡕⡢⣴⣿⣿⣿⡏⠀⢂⡐⠢⢅⡢⠕⠢⠕⢂⡂⠔⢂⠌⠀⣿⣿⣿⣿ ⢸⣿⣿⣿⠁⡂⠡⠕⠅⡨⡢⠕⠊⡁⢄⡂⠌⡡⢅⢂⠌⣿⣿⣿⣿⣇⡀⢨⠅⠐⠡⡢⠕⠊⡁⠌⡡⡊⠢⡂⠔⢅⡢⠕⠊⡑⢂⠌⡁⠔⠊⡁⠔⠅⠌⡡⠌⡑⠢⠅⢐⡢⠕⠊⡁⡄⠆⢐⡢⠌⡡⠌⡑⠢⠌⡁⡄⠆⡡⡂⠌⡑⢂⠌⠢⢅⡂⡡⢢⡇⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡅⢨⣷⣿⣿⣿⡿⡂⠨⡂⠨⡢⢅⡢⠕⠢⠕⠢⡂⢄⠆⠡⡂⠫⣿⣿⣿⡄ ⢸⣿⣿⣿⠀⡃⠢⢅⠌⡡⡢⠕⠊⡁⢄⡂⠌⡡⠕⠂⡀⠈⣿⣿⣿⣿⣿⣄⠈⠌⡂⠡⠕⠊⡁⠌⡡⡊⠊⡁⠔⢅⡢⠕⠊⡑⢂⠌⡁⢌⡊⡁⠔⢅⠌⡁⠔⠕⠢⠕⢂⡢⠕⠊⡡⠅⡑⢂⡢⠅⡁⠔⠕⠢⠅⡡⢅⡐⡅⢂⡐⢂⠐⡈⢅⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⢪⡕⠪⣅⣖⣾⣿⣿⣿⡏⠀⠸⠌⡁⠔⡅⠡⡢⠕⠢⠕⠊⡁⠔⢅⢄⡂⢈⣿⣿⣿⡇ ⢿⣿⣿⡯⠀⡐⠢⠕⠊⡡⡢⠕⠊⡁⢄⡂⠌⡑⠕⢊⡢⡃⢈⠹⣿⣿⣿⣿⣾⣤⡂⠂⡐⡊⠅⠌⠡⠌⠨⠅⢐⢅⡢⠕⠊⡑⢂⠌⡁⢄⡊⡁⠔⠕⠊⡁⠔⠕⠢⠕⢂⡢⠕⠊⡁⠔⠕⢂⡢⡑⠅⢐⠕⠅⠐⠅⠡⡂⡁⡔⢡⡕⢣⡜⢣⡕⢪⡕⢣⡜⢣⡜⢣⡜⢓⠣⢘⢦⣬⣿⣿⣿⣿⣿⠋⡁⢄⡢⢅⡂⠌⡑⠢⠕⠕⠢⠕⠊⡁⠔⠅⡈⠄⠀⣿⣿⣿⣗ ⣽⣿⣿⣗⠀⠔⠢⠕⠊⡡⡢⠕⠊⡁⢄⡂⠌⡁⢄⡊⠡⡊⡂⡂⠈⠻⣿⣿⣿⣿⣿⣯⣧⣂⡀⠁⠐⠑⠂⡑⢂⠄⡂⡑⠊⡑⢂⠌⡁⢄⡢⠅⠐⢑⡊⡁⠔⠕⠢⠕⢂⡢⡃⠨⡢⠅⠄⠊⠃⡐⠕⠢⡂⠠⢕⡢⡬⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⢕⡪⠕⣂⣌⣧⣼⣿⣿⣿⣿⣿⡿⠛⢀⡊⠢⢅⡢⢅⡂⠌⡑⠢⠅⢐⡢⠕⠊⡁⠔⠅⡁⠐⠐⣿⣿⣿⡗ ⢸⣿⣿⣿⠀⠅⠔⠕⠊⡡⡢⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡃⠨⠅⡡⠄⢈⠫⢿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣂⣀⣂⡈⠁⠊⠊⠑⠂⠌⠅⢄⠢⠅⢂⢄⡊⠅⡐⡑⠂⠃⢄⣈⡂⡐⣑⡌⢎⡣⢕⡪⡕⢪⡕⢣⡜⢣⡎⢱⡎⢱⡎⠱⢪⢕⢎⢕⡜⢱⣃⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⡐⡂⠊⡑⠢⢅⡢⢅⡂⠌⡑⠢⠕⢂⡢⠕⠊⡁⠔⡅⠣⡅⠀⣿⣿⣿⡇ ⢸⣿⣿⣿⠄⡂⡐⠨⡊⠡⡢⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⠅⠌⡑⢂⡊⢑⡂⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣴⣤⣦⣢⣔⡖⢱⣖⡣⣴⢇⡕⢱⠮⡪⢕⢆⢨⡕⠃⡌⠡⣜⡃⣵⢇⣵⡱⣲⣵⣵⣶⣶⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢐⡁⠔⠅⡑⠢⡃⠔⢅⡢⢅⡂⠌⡑⠢⠕⢂⡢⠕⠊⡁⠌⡑⠊⡁⢔⣿⣿⣿⡇ ⠀⣿⣿⣿⣷⡀⡐⠨⠅⠌⡡⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⠅⠌⡑⠢⢌⠆⡄⢀⣿⣿⣿⣿⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠛⣿⣿⣿⣇⠈⢅⡁⠌⡑⠊⡁⠔⢅⡢⢅⡂⠌⡑⠢⠕⠢⡢⠕⠊⡁⠌⡑⠅⢀⣿⣿⣿⡿ ⠀⠺⣿⣿⣿⣗⠀⠁⢐⠅⡡⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⢅⠌⡑⠢⡑⠊⣁⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠝⠟⠿⠿⠿⠿⢿⣿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡂⠐⡢⠌⠨⢅⡐⡅⠢⢅⡂⠌⡑⠢⠕⠊⡡⡑⠨⢂⡐⡅⢀⣾⣿⣿⣿⠇ ⠀⠀⠻⣿⣿⣿⣾⠀⠂⢌⠕⠕⠊⡁⢄⡂⠌⡁⢄⡢⢅⡢⢃⠌⠡⠂⠢⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⠀⠈⢂⢄⡢⠕⠢⢅⡂⠌⡑⠢⠕⠊⡁⢐⠅⢈⠀⣐⣿⣿⣿⣿⠟ ⠀⠀⠀⠸⣿⣿⣿⣿⣧⣂⢀⠑⠊⢁⢄⡂⠈⡡⡐⡢⠅⠂⢁⣀⣮⣽⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣮⣅⣀⠠⠕⠢⢅⠆⠨⢕⠢⠃⠨⠂⠄⢀⣡⣾⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣧⣔⣀⣀⣀⣁⣀⣥⣗⣾⣷⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣕⣡⣁⣁⣈⣀⣀⣒⣼⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⢿⡿⢿⣿⡿⣿⡿⠟⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠿⡿⡿⣿⣿⣿⣿⡿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⡿⠿⢿⣿⣾⣶⣦⣤⣀ ⠀⠀⠀⠀⠀⣤⣾⠿⠋⠈⠄⡐⡂⠔⡂⠐⠆⠔⠄⡠⠉⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠿⠿⠿⠿⠿⢿⣷⣦⣄⡀ ⠀⠀⢀⣶⠿⢉⢄⢅⡢⠅⠂⡂⠅⢂⠨⠅⠂⡂⡂⠅⠅⢂⢂⠄⠉⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⡀⡄⢄⡡⠌⠁⡂⡈⢐⢂⡀⠉⠿⣿⣄ ⠀⢠⣿⠁⡐⠅⠅⢈⠅⠅⠂⠌⠄⠐⠡⠂⠅⠌⠅⠐⡂⠂⠅⠌⠐⠠⠉⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⡀⠅⠅⡂⠅⠅⠂⠅⠂⠅⠐⡂⠅⡂⠂⡂⢀⠙⣿⡀ ⢠⡿⠀⠅⠅⡂⠡⠡⠡⠁⡁⡂⡁⠠⠄⠢⡃⡂⠅⠄⡂⠡⠡⠄⡂⠠⠕⢂⠛⣷⠀⠀⠀⢀⣾⠛⠠⡁⡀⠄⠂⡄⠆⡀⡐⠢⠄⡂⡄⡂⠡⠄⠅⠅⠌⡁⠅⠀⣿⡄ ⣿⠁⡆⢊⠂⠁⠅⢈⠄⡂⡁⢁⡂⠠⠊⠈⡁⠁⠁⠌⠅⠅⡄⡈⢅⢄⡂⡂⡂⠙⣷⠀⣠⡿⢁⡊⡁⡈⢁⢃⠆⣿⠈⡁⠅⢂⠠⠂⠅⢊⡁⡂⡂⡃⠨⢅⡂⡈⠈⣿ ⣿⠀⠅⢂⠅⡂⠔⢂⠅⠅⠅⢊⠀⣿⠛⠛⠛⠛⠛⠟⠿⠿⣷⣦⣤⣁⠈⠢⠀⣄⣽⡗⣻⠀⠁⣁⣤⣤⣶⣾⠿⠿⣥⠁⠅⠆⠡⠂⠂⡂⠂⠅⠅⠆⠡⡊⡑⡁⡂⣿⡆ ⣿⠀⡑⠅⠅⠅⠄⡂⠅⠢⠅⠌⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣯⠁⠀⠀⠈⣿⠛⠉⠀⠀⠀⠀⠀⠀⠻⣦⠀⡂⠠⠂⡂⠡⠄⡂⡂⡄⠢⠅⡡⠄⠀⣿⠇ ⢻⣧⠂⡈⠅⡂⡈⠌⡁⠅⢅⡆⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣧⠈⡃⡀⡂⡁⠅⠁⠅⠁⡀⡨⢅⢅⠀⣿ ⠀⠛⣿⣄⠂⠢⠢⢂⡂⠢⠂⠂⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⠶⣿⠀⠀⠀⠀⣿⠛⠙⠉⠉⠉⣷⠀⠀⠀⠀⠈⡿⣤⠁⠇⠂⠈⡀⠄⠂⠅⡀⠑⢀⣾⠏ ⠀⠀⠀⠙⠿⡿⣷⣷⣶⣿⡿⠟⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣇⣀⡀⣠⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⣤⣀⣀⣀⣂⣀⣥⣮⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡾⠛⡀⠁⣧⣽⡁⡀⠋⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡉⠛⠛⠟⠛⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⡷⠛⡁⡐⠆⠁⣾⠛⠈⢿⣢⠑⠃⠠⠌⠙⠛⢷⣶⣄⡀⠀⠀⠀⠠⡯⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣧⣀⣀⣀⣤⡾⠟⢉⠀⢈⣁⣤⣶⠷⠿⠾⠟⠻⠛⠟⠻⠿⠿⣶⣤⣄⡀⠠⢄⡉⠛⠿⠷⠿⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⢀⡋⠉⢉⡄⠀⣀⣦⠿⠋⡁⠀⠀⡠⢂⡈⢁⡂⡊⠈⠅⡨⡅⢄⡀⠉⠛⠿⣦⣀⠢⠌⠡⠂⡂⡀⢹⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⡀⠐⡂⠅⢁⣴⠟⠃⠄⢐⡂⠌⠄⠄⠐⡈⠅⡂⢂⠅⠄⡂⢊⡃⡃⠂⡊⠐⠂⡀⠙⣿⣆⠀⡂⠅⠔⡀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⡁⠠⠢⠄⠛⠄⡂⡁⡂⢅⠄⠄⡂⡄⡂⡁⠠⠂⠅⠔⠆⡡⠅⡄⡂⡁⠡⠂⡂⠅⠄⠄⠙⣿⠀⡀⡌⡁⢽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡡⠡⡂⡃⡂⡃⡁⡈⡁⢅⡂⠂⠅⡁⡈⡁⠅⡂⡂⢂⡂⡊⡂⡈⡁⠅⡁⡂⠅⠄⡂⠨⢑⢄⡂⠅⡁⡃⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡿⠂⠂⢂⠅⠅⠐⠁⠌⠄⠂⡂⡂⠅⠄⡂⠅⠌⢁⠄⠅⡂⠅⠅⠄⠐⡑⠂⠅⠄⠨⠕⢊⠄⠄⢦⠈⢸⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⠟⡠⠄⠄⢅⠄⠐⡂⠐⠠⠂⡂⠅⡡⠄⡂⠡⠅⠌⡂⠅⡂⠡⠅⠄⡂⠄⠅⠅⡁⡁⠂⠅⠅⠅⠄⡄⢿⣾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡀⡈⠌⠆⠡⠀⣯⢫⢿⠀⠅⠂⡂⠅⢁⠅⡁⠅⡂⡈⠄⡊⡂⡁⠅⠂⢈⠄⢠⡿⡷⡄⠅⡂⠂⡂⢂⠀⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠌⠐⠆⠅⡰⡇⡣⢾⠀⠔⠔⠅⠔⠂⠅⠅⡂⠐⠡⠂⡂⢑⠆⡄⠂⡂⠅⣾⡺⡗⣻⠐⠪⡂⡂⠔⠅⢚⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢐⠄⡐⡂⡃⠢⠐⣧⣮⢟⠠⠅⠅⡂⡡⠄⢄⠅⠅⠔⠊⡂⠅⠄⡂⠅⠅⠌⠅⢚⣎⣜⡿⠠⠌⡂⡂⠄⠄⠐⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠨⠅⠡⠊⡁⠄⠄⠠⠄⠢⠄⡂⠂⠅⢊⡂⣮⠀⠊⣂⡂⠃⢿⠠⠣⠅⡂⡈⠌⠁⡈⠁⠄⡌⠡⠂⡂⡂⡡⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⡐⡐⠂⠄⡂⠄⠐⢂⠔⠢⡂⡂⠂⠔⠢⡉⠛⠋⢉⡉⠛⢋⡀⠅⠄⠄⠅⠄⠐⡂⡂⠂⠆⠡⠂⠅⠅⠂⣰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠠⠌⡊⡂⠅⠅⡁⠅⠄⡂⠅⠅⡂⠠⠅⠄⠄⡂⡂⠄⠅⠌⠢⠅⠢⠅⠅⠄⠅⠅⠄⡂⠠⠂⠄⠨⣀⣷⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣷⣀⠁⠈⠄⢈⠔⡅⡀⡂⡂⡂⢊⡁⠅⢂⡈⡁⡊⡁⡂⠢⡅⢅⡁⠌⠄⡂⡃⡀⠌⢃⠅⠂⣀⣲⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⢶⣤⣤⣁⣈⡁⠑⠂⠀⠐⠂⠊⠌⠑⠅⠅⠂⠂⠁⠈⠐⠐⡁⣀⣄⣤⣶⣾⡽⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⡀⡀⢈⡉⠋⠛⠛⠛⠛⠻⠟⠻⠟⠟⠻⠟⠛⠛⠛⠛⠛⠋⠙⠛⡮⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⢁⡄⠌⣦⡁⠌⡁⠅⠅⡑⠅⡨⡃⠂⠄⡂⠊⠅⡂⢅⡃⠅⠂⡠⡂⠂⠈⡀⡈⠛⣿⢶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠢⢊⠁⣴⠇⡂⢂⠄⠄⠄⠅⠐⡁⠅⠅⢂⡊⠄⡂⢂⠔⠂⡂⠐⣤⠁⠂⠂⠌⢈⠀⠀⣾⠉⠻⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠂⠐⢂⣁⡿⢐⠅⠅⡃⡂⡀⠅⠄⠅⠄⡂⠅⠌⠄⠅⠡⡅⡂⡁⠐⠈⠟⣶⣤⣤⣦⡶⠟⢁⠂⡠⡉⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠿⠿⠛⣗⠁⡃⡁⡨⡃⡂⡂⢂⡈⠄⠅⠁⢂⡂⡂⢂⡁⠅⠂⡂⡁⠅⠂⠄⠺⡆⠠⠄⠁⠂⡀⡀⢨⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡂⢑⡂⡂⠅⠔⠂⡂⠔⠂⡈⠅⠅⠂⡊⠆⠅⠄⠅⠐⠂⠔⠂⣿⠀⠠⠢⠀⡇⡃⡁⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠠⠂⠅⡄⡂⡀⠅⠄⠅⠄⠄⠐⡊⡂⡂⠔⠅⡃⡀⠅⠄⠂⠄⠆⢹⡆⣈⣤⡿⠁⡂⠄⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢁⢂⡂⡂⠂⡂⡂⢂⡈⠄⠅⡂⠨⠕⠅⡊⡡⡂⠆⠁⡂⢂⡁⡂⡑⣸⡏⢉⡁⠄⢅⢈⠀⣮⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠅⠐⡑⠅⠅⠄⡂⠂⡂⠔⠅⢑⡢⡂⡂⢑⠆⠄⡂⠅⠐⢂⠅⠁⣿⠀⠌⠄⠐⠈⡡⣷⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣷⠀⠔⠅⠅⠅⡂⡡⠄⡂⠄⡂⠢⢅⠡⠂⣈⣀⣁⣈⠂⠠⠢⠁⣮⣽⣶⣶⣶⣯⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠦⡊⠑⡁⠁⠅⠃⢕⡑⢅⡁⡁⠅⣺⡋⡉⠀⡡⠂⠨⠅⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡂⢄⡉⠛⢿⡿⣾⣶⣶⣶⣶⣶⣿⣆⠀⠄⠊⠢⠄⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠠⠅⠔⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠄⠌⢀⣾⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣈⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
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