⠀⠀⢀⣀⠤⠿⢤⢖⡆
⡔⢩⠂⠀⠒⠗⠈⠀⠉⠢⠄⣀⠠⠤⠄⠒⢖⡒⢒⠂⠤⢄
⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠈⡨⢀⠡⡪⠢⡀
⠈⠒⠀⠤⠤⣄⡆⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢕⠱
⠀⠀⠀⠀⠀⠈⢳⣐⡐⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠑⢤⢁⠀⠆⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⡀⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⡷⠢⠤⠤⠤⠤⢬⢈⡇⢠⣈⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⡇⠀⠀⠀⠀⠀⠈⢪⢀⣺⡅⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠶⡿⠤⠚⠁⠀⠀⠀⢀⣠⡤⢺⣥⠟⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠒⠒⠒⠒⠂⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⣀⠤⠐⠒⠒⠒⠒⠒⠒⠂⠄⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⠄⣀⣀⣀⣀⣀⣀⡀⣀⡀⠄⠘⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣦⣤⡀⠀⠀⠀⢀⣠⣶⠾⠟⠛⠋⠉⠉⠉⠉⠛⠛⠿⢷⣦⣀⠀⠀⠀⣠⣴⣶⣦⡀⠀⠀
⠀⠀⣾⡟⠉⠙⠿⣷⣤⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠾⠟⠛⠉⠀ ⢹⣷⠀⠀
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡟⠀⠀
⠀⠀⠀⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠀⠀⠀
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀
⠀⠀⠀⢀⣿⠃⠀⠀⢀⣤⣶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢶⣦⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀
⠀⠀⠀⢸⡿⠀⠀⠀⠈⣩⣤⣄⠀⠀⠐⢦⡴⠶⢦⣤⡶⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡆⠀⠀
⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⠀⠀
⠀⣠⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣧⠀
⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀ ⠀⢻⡇
⠈⠿⣾⣤⣴⣾⣿⣿⣿⣷⣦⣀⡀⠀⣀⣤⣶⣿⣿⣿⣷⣤⣀⢀⢀⣠⣾⣿⣿⣿⣿⡷⣦⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠋⠛⠋⠉⠛⠛⠛⠛⠋⠉⠙⠛⠋⠁⠉⠉⠛⠛⠋⠁⠈⠉⠉⠁⠀⠈⠉⠉⠀⠀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢖⡀⠀⠀⠀⠀⠀⠀⣠⠲⣍⠶⣢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⠎⠁⠀⠀⠀⠀⣠⠞⡥⠛⠈⠳⣣⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⡎⠉⠀⠀⠀⠀⣠⠞⣥⠻⠜⣯⣘⢳⡥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⢳⠀⠀⠀⠀⣠⠞⣥⠛⠀⢀⡼⢦⡹⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⢳⢊⡗⢦⠤⣄⡞⣥⠛⠀⢀⡴⣫⠜⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⡬⣅⢪⠼⣩⢞⡲⠙⠀⢀⡴⢫⡖⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠡⢳⣍⢮⠳⣍⠎⠁⢀⡴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⣈⡼⢣⠞⡼⠙⠀⢀⡴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⣈⢶⡱⢭⡫⠝⠀⢠⢴⣋⡞⡅⠀⠀⠀⠀⣀⠶⣩⢖⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⣈⢶⡙⡦⢏⠇⠁⢀⡴⣫⢖⡣⡞⣥⢀⡀⡠⣜⡬⢳⢣⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⣈⢶⡙⣦⢛⠕⠁⢀⡴⣫⢞⡱⣎⠵⣙⠦⣏⡼⡱⢞⡼⡍⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⣈⢶⡙⣦⢛⠔⠁⢀⡴⣫⢼⡱⢎⡳⣜⢣⡝⣚⢦⠳⣭⠓⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⣈⢶⡙⡦⠛⠀⠂⢀⡴⢫⢞⡱⢎⡕⢮⣔⢫⠞⣼⢩⢞⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⣈⠶⠙⠂⠁⠀⠠⠐⢠⠞⣭⠳⣍⠮⣑⣎⢳⡬⣋⢾⣡⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⢌⠱⠈⠂⠁⢀⠠⠐⠈⠀⠄⢠⢏⡞⡥⢫⢔⣣⠽⣌⠷⣸⠭⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠶⣩⢞⡱⣎⡳⠌⠁⡀⠠⠀⠂⠈⠀⡀⠄⠂⠈⢠⢞⢣⢎⡱⣣⠞⣥⣛⢬⡳⡃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⢩⡞⣱⠎⠃⠀⢀⠀⠄⠀⠄⠐⠀⠁⠠⠀⢀⠐⢠⢏⡚⣬⠲⣝⢲⡛⡴⢭⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠞⡦⢏⡼⠁⠀⠀⠌⠀⠀⠄⠈⠀⠀⠀⠈⢀⠐⠀⢠⢣⢎⡵⢎⡽⢬⢧⣹⡙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣛⠼⡭⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⢈⢖⣣⠞⣼⢩⢞⡱⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⡹⢎⡅⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢠⠞⣎⡖⡻⣌⢧⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣱⢋⡶⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢡⢞⡹⢦⡝⣱⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣣⠯⣜⢣⠀⠂⢀⠀⠀⠀⠀⠀⢀⠐⠈⣠⢏⣎⢗⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⢫⢼⡩⢗⣤⣀⠠⠈⢀⠐⠈⢀⣠⠶⣍⡞⡜⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠣⢝⡺⢴⣩⢳⣙⡖⢮⣙⢏⡶⣙⢦⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠒⠣⠳⢎⡼⢣⠝⠎⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀