K Emojis & Symbols

⠀⡴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠓⣦⠀⠀⢀⡴⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢲⡄
⢸⡇⢸⠀⣏⠄⠛⡀⡉⠙⡭⠤⡰⠫⠊⢁⠹⡌⠁⠏⢁⠙⢍⢮⡇⢸⠀⠀⢸⡇⢾⢨⠇⠹⠈⠋⡻⠸⠻⣟⡉⠉⠥⢈⠉⠋⡩⢿⠀⡇
⠈⢧⡘⠚⠶⠤⢤⡚⢷⣡⣿⡨⠥⠅⢈⠱⡄⢀⡀⣠⠶⠝⠞⠚⢃⡼⠀⠀⠘⣧⡘⠒⠛⠶⢴⣉⠇⡀⡆⠀⡄⠩⢴⣤⠵⠟⠒⢊⣰⠇
⠀⠀⠉⠛⠛⠲⣆⠹⡖⡩⠀⠐⢀⣄⠂⡨⡐⢀⡟⢡⡖⠛⠛⠛⠉⠀⠀⠀⠀⠈⠉⢛⡿⢀⡞⠼⢠⠁⡃⠠⣀⠞⢋⣤⠖⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢹⠀⣧⡆⢈⠷⢆⣈⠊⠁⠘⣸⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠔⣃⣸⠠⣧⠔⢁⡴⠋
⠀⠀⠀⠀⠀⠀⢸⠂⡿⠄⡾⠰⠓⠨⢝⡑⡶⣹⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡰⢋⠀⢀⡞⠫⣠⠖⢁⡴⠋
⠀⠀⠀⠀⠀⠀⢸⡃⣧⡸⠡⠁⠀⠀⢀⢎⠔⢹⠀⣿⠀⠀⠀⠀⠀⢀⣴⠋⣠⣾⡡⠤⢠⠎⣨⠞⢁⡴⠋
⠀⠀⠀⠀⠀⠀⢸⡇⡿⠍⠁⢀⡒⠲⢧⠊⠀⢸⠀⣿⠀⠀⠀⠀⣰⠟⣡⠞⠅⡔⠀⠀⣿⡶⢃⡴⠋
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⡉⠢⡑⣶⢸⠀⣿⠀⠀⣠⠞⣡⠞⠁⠀⢠⣙⢲⡶⢋⡴⠋
⠀⠀⠀⠀⠀⠀⢸⠇⣇⠀⠀⠓⠄⢃⡈⠀⠹⣿⠀⣿⣠⠞⢁⠾⠟⠀⠀⠀⢨⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⢸⠅⣿⢄⠈⣉⣰⡉⠙⡈⢧⣺⠀⠟⢁⡔⢉⣖⣊⠁⣠⡶⠋⣴⠏
⠀⠀⠀⠀⠀⠀⢸⠂⡏⣤⣹⣄⠠⢤⣏⠑⣤⢸⢀⣴⡏⢹⡤⠄⢀⣜⣴⢙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠇⡷⠤⠉⣋⠉⣺⠌⡶⠬⡟⢛⠥⢴⠢⢔⠈⢙⠁⠿⢄⠘⡷⣄⠹⣆
⠀⠀⠀⠀⠀⠀⢸⡅⡇⠲⢳⠋⠡⠼⡞⢠⠞⢩⡏⠳⢆⢐⠧⠌⠙⢞⢷⠀⢑⡈⢌⢳⡈⢳⣄
⠀⠀⠀⠀⠀⠀⢸⠂⣟⠔⢉⣒⢲⠊⢉⠃⡴⣈⣍⣶⠞⢯⠑⡖⣒⡈⠢⡙⣤⡻⡌⢆⠙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡂⡟⠀⠈⣡⠄⡝⠉⠈⢡⣦⠞⣡⠶⣄⠻⣄⢌⠁⠀⠐⠡⢂⠹⣦⣑⠎⢱⣄⠻⣆
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠁⠀⠃⡠⢂⣿⢹⠀⣿⠀⠘⢷⡈⢦⡀⠀⠀⠸⣒⣩⠔⡞⠂⡆⢈⠷⡈⢳⡄
⠀⠀⠀⠀⠀⠀⢸⡃⣷⠀⣀⣀⡂⣥⡖⡁⠀⢸⠀⣿⠀⠀⠀⠙⣦⠙⢦⠀⠄⢯⡀⠀⢿⠉⢣⠠⡀⠙⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡃⡿⢣⠱⠀⠡⠀⠔⣌⢄⢸⠀⣿⠀⠀⠀⠀⠈⠳⣌⠻⣷⠲⠂⠉⠉⣧⡀⠣⣄⠀⠡⡱⣄⠻⣄
⠀⠀⠀⠀⠀⠀⢸⠅⣧⠌⢧⢡⡠⠄⢐⡊⣧⢹⠀⣿⠀⠀⠀⠀⠀⠀⠙⢧⡈⢧⡄⠐⠀⠀⡉⢢⢀⡉⠀⠑⡌⢧⡈⢳⡄
⠀⠀⠀⠀⠀⠀⢸⠂⡿⠆⠘⡤⠴⠛⣌⠁⢀⢻⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⣄⠠⡀⢌⡃⢸⠀⡏⢉⠜⣣⠙⢦⠙⢦⡀
⠀⠀⠀⠀⠀⠀⡾⢀⡟⡢⠌⣁⠐⠊⣈⠡⣢⠘⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⡇⠀⢩⠈⡄⡆⡈⡐⢁⠐⣀⣳⣌⠻⣤⣀
⢀⡴⠖⠒⠚⢋⣡⢞⡶⡫⣶⠢⠤⠄⠐⢨⠆⠈⠻⣄⡙⠓⠒⠶⢦⡀⠀⣠⠶⠖⠒⠛⢀⣽⢊⡙⢇⠀⠁⡠⠥⠀⢐⡡⠚⠺⢷⣤⣉⡛⠓⠲⢦
⣿⢰⡏⠩⡟⠡⣀⠊⡂⢡⠿⠈⠥⡑⢈⠙⢠⠂⠀⣄⠉⢉⠟⣷⠈⡇⠀⡏⢰⣏⠩⠛⠅⢠⢄⣈⣹⠘⠿⠍⣁⠈⠠⠄⠐⠆⠘⡍⠂⡝⠙⣙⡄
⢿⡘⠷⠴⠶⠤⠼⠤⠭⠥⠦⠤⠤⠬⠦⠵⠭⠴⠧⠬⠶⠵⠧⠞⢠⡇⠀⣧⠘⠶⠤⠼⠦⠤⠤⠤⠾⠶⠶⠶⠦⠬⠥⠶⠶⠶⠤⠵⠤⠧⠤⠴⢃
⣬⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⣤⣤⣬⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯
⣿⡟⢻⢿⡟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢀⣀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠉⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠙⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢻⡟⣻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣤⣀⣀⡀⠈⠙⣿⣿⠋⠁⢀⣀⣀⣠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⡴⠆⠀⠀⠈⠻⣿⣀⣰⣶⡟⢻⣶⣆⣀⣿⠟⠁⠀⠀⠰⢦⢸⡇⠀⡄
⠀⠀⠀⠀⢀⠀⢿⡇⠘⢶⡶⠀⠀⢀⣠⡄⠹⡿⠿⠿⠿⠿⠿⠿⢿⠏⢠⣄⡀⠀⠀⢶⡶⠃⢸⡿⠀⡀
⠀⠀⠀⠀⢿⡆⠘⠿⠷⠂⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠐⠾⠿⠃⢰⡿
⠀⠀⢰⣆⠨⠷⠾⠖⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠲⠿⠾⠁⣰⡆
⠀⢀⠈⢿⣤⣶⠆⠀⣰⠟⠀⠀⠀⢀⣤⠶⠚⠛⣻⣿⡏⠀⠀⠀⠘⢛⣿⠿⠛⠉⠀⠀⠻⣆⠀⠰⣶⣤⡿⠁⡀
⠀⢹⣧⢈⣥⡄⠀⣰⠏⠀⠀⠀⣴⡏⠀⠀⠀⢀⣿⡿⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠹⣇⠀⢠⣭⡁⣼⡏
⢠⣄⠹⠛⠋⠀⢀⡟⠀⠀⠀⠀⣿⣧⠀⠀⠀⣸⣿⠇⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠙⠛⠋⣠
⠈⠻⣧⣾⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣷⣾⠟
⢶⣦⣈⣴⡖⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢲⣦⣁⣴
⠀⠙⢻⢋⣤⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣤⡙⡟⠋
⠹⣿⣦⣾⢏⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⡹⣷⣴⣿
⠀⣤⣌⣇⣾⠇⠀⠈⢿⡄⠀⠀⢠⣤⠾⠿⠿⠤⡤⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠸⣷⣸⣡⣤
⠀⠙⠛⠛⡏⣼⡇⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⢠⣦⣴⠟⠁⠀⢸⣧⢹⠛⠛⠋
⠀⠀⠺⣿⡿⣿⢱⣷⢀⠀⠉⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠦⢴⣿⠟⠁⠀⡀⣾⡎⣿⢿⣿⠷
⠀⠀⠀⢀⣤⣼⣾⡟⣼⡇⣠⡀⠈⠙⠷⣦⣄⣀⡀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠁⢀⣄⢸⣧⢻⣷⣧⣤⡀
⠀⠀⠀⠀⠉⢉⣠⣽⣾⣇⢿⣇⢿⣆⢤⣄⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁⣠⡤⣰⣿⣼⡿⣸⣷⣯⣄⡉⠉
⠀⠀⠀⠀⠀⠈⠛⠋⣡⣼⡿⠿⣼⣿⣘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣃⣿⣧⠿⢿⣧⣌⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣾⡿⢃⣽⡿⠉⠙⠓⠶⣤⣤⠶⠚⠋⠉⢿⣯⡘⢿⣷⡀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢀⣴⡾⠋⠙⢷⣦⡀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠙⡗
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣄⢀⡤⠤⠒⠒⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣀
⠀⠀⠀⠀⠹⡏⠓⢄⠀⠘⢢⣼⣆⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣛⠻⣷⣯⢈⠄
⠀⠀⠀⠀⠶⡍⠂⠀⠀⠈⠉⠀⡠⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠊⠓⠶⠟⢸⡇
⠀⠀⠀⠀⠀⡇⣸⠃⣀⣙⣦⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⠄⠀⠀⣀⡴⠋
⠀⠀⠀⠀⢰⠇⢻⣜⢇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡴⠋⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢸⠀⢈⣻⣗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⣞⡕⠉⣓⠶⠖
⠀⠀⠀⠀⣿⠀⠸⢉⡙⠳⣄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⠋⣤⣾⣿⠖⠋
⠀⠀⠀⠀⣿⠀⠀⢸⣧⣶⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⠀⣠⣾⣻⣿⠃
⠀⠀⠀⠀⢿⠀⠀⠸⡏⢛⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣿⢣⣿⠃
⠀⠀⠀⠀⠸⡇⢸⣤⣴⠟⠁⡺⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣍⣠⠟⢁⣾⠋
⠀⠀⠀⠀⠀⣷⢀⣾⢟⠁⠀⠀⠀⠀⠀⠠⣄⢰⣧⠀⠀⣰⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⢸⣼⠃⢏⡀⣴⠆⠀⣤⡴⣖⣹⣿⡿⠀⠀⠈⠿⠵⠚⠉
⠀⠀⠀⠀⠀⠘⡉⠷⠀⠰⠛⠀⠀⠈⠁⣉⣉⣀⣈⡙⠓⠶⣄
⠀⠀⠀⠀⠀⢀⠇⣠⠖⠒⣦⢀⣠⣶⢟⣫⣭⣤⠍⠉⠲⠀⠘⢷⡀
⠀⠀⠀⠀⠀⢸⠀⠛⢦⣬⣷⣿⠟⠠⡈⢹⡿⠁⢰⡏⡽⡄⠀⠘⣷⡀
⠀⠀⠀⠀⠀⡈⠐⠏⠛⠛⠉⠈⠓⠊⠀⡾⠁⠀⠈⢷⣧⡀⢇⣘⣿⣷⡺⡉⢢⡀
⠀⠀⠀⠀⠀⠇⠀⣼⠁⣈⣹⣇⠀⢀⡼⠁⠀⠀⠀⠀⠙⠿⣦⣈⠈⢿⣿⠶⠾⠃
⠀⠀⠀⠀⢐⠀⣠⣿⣜⠇⠀⠉⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡙⠴⠀⣳
⠀⠀⠀⠀⢸⠀⠀⢈⣿⣗⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠹⢦⣭⣉⡀
⠀⠀⠀⠀⣿⠀⡇⠛⢉⡙⠳⣄⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣨⣿⢙⢿⣦⣄
⠀⠀⠀⠀⡇⠀⢹⠀⢸⣦⣾⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡁⠈⣧⠹⣿⣷⡀
⠀⠀⠀⠀⡇⠀⣸⠃⠸⡍⢙⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣽⣦⣿⡆⠘⣿⣿⢄
⠀⠀⠀⠀⣧⠀⠃⢸⣤⡶⡟⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⢿⡎⢆
⠀⠀⠀⠀⣇⣼⠀⢠⡿⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢧⡀⠈⢿⡌⣆
⠀⠀⠀⠀⡏⣇⠀⢸⠁⠇⡠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠙⠦⡈⢷⡸⡀
⠀⠀⠀⠀⢤⢸⣆⠘⠣⠀⠒⠋⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⡏⠙⠛⠎⢷⡡
⠀⠀⠀⠀⠘⣿⠟⠀⠀⠒⠶⢞⡋⢩⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⢦⣘⣠⣤⣷⣥
⠀⠀⠀⠀⢀⡝⠀⡀⠀⢠⣤⣀⣱⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠋⢻⡙⣷⡀⠀⠰⢶⣄
⠀⠀⠀⠀⣿⡤⢊⠀⠀⠶⠉⠽⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢠⣾⣧⠈⠻⣦⣀⣠⣿⠇
⠀⠀⠀⠀⠉⠀⠈⠁⠛⠓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠈⠉⠛⠉

⠀⠀⠀⠀⣀⣶⣷⣶⣶⣶⣦⣄⣠⠤⠤⢤⠠⢤⣠⣀⣰⣶⣶⣶⣶⣖⠀⣠⣤⣤⣂⣯⣥⣶⣖⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣄⡀
⠀⠀⠀⢰⡏⣿⣿⣿⣿⣿⣿⣟⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⢹⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠜⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⡿⠃
⠀⠀⠀⠀⠈⠙⠛⠛⠻⡿⣿⠙⢻⡿⠃⢸⢿⣿⢻⣿⡿⡿⠛⠋⠉⠁⠀⠀⠀⠁⠈⠹⣿⣿⡗⢸⣿⣿⣿⡿⢫⣶⡿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢻⡀⠀⡇⠀⠈⢿⣿⣾⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡝⢡⣿⣿⣿⠏⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⢸⢸⣿⣿⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣠⣿⣿⣿⣷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣴⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢨⢸⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⣀⣾⡟⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⢀⣴⡿⣩⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⢈⠀⣀⡀⣠⣾⣯⣾⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⡠⠙⢿⣿⣦⡹⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠙⢿⣿⣦⡻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠙⢿⣷⣄⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠙⢻⣿⣿⣷⡀⠀⠀⠀⠙⣿⣷⡝⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠈⠻⣿⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠀⠀⠀⠙⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠈⢻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠹⣿⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠘⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣤⣀⣀⡀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⣤⡀
⠀⠀⠀⢰⣿⣟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣦⠀⠀⣾⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠸⣿⣿⣶⣶⣶⣶⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢿⣯⣛⣛⣟⣿⣯⣭⣯⣭⣿⣿⣿⣭⣭⣭⣭⣽⣟⣛⣛⣛⣼⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣤⣌⣤⣄⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣠⣀⣤⣤⣄⣠⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠂⡔⣘⡦⠾⠁⠀⠀⠀⠀⠀⠀⢀⡀⢀⡴⡩⢆⣄⣒⡰⠒⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠰⡇⡆⠃⢧⠀⣀⠀⠀⠀⠀⠀⠁⠀⢀⡴⢫⢜⠕⠋⠀⠂⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠸⣇⢡⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠘⣴⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠈⣾⠿⡷⡀⠀⠀⠠⠂⢄⣰⡟⢚⠅⡾⠁⠀⢀
⠀⠀⠀⠀⠀⠀⢤⡄⠯⠀⡜⠪⢹⠂⠀⣠⢞⣉⡰⠟⠃⢧
⠀⠀⠀⠀⠀⠄⢸⡇⢲⣻⢸⢈⢸⣧⠞⣵⢥⠙⠇⠈⢫⡼
⠀⠀⠀⠀⠀⠀⢸⡇⢠⠁⣩⠔⡘⢥⠖⠀⣾⠀⠀⠀⠙⣦⡀⠐
⠀⠀⠀⠀⠠⠂⢰⡇⡄⠈⡅⠀⠁⠘⡄⣣⢌⠤⠶⠀⢶⡩⢷⡄⠐⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⢸⡇⠹⠂⡁⠀⠀⡰⣊⡴⠲⠜⢦⣌⢒⡢⡳⢿⣆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠦⣑⠔⣡⢚⡴⠋⠄⠀⠀⠊⠁⠈⢫⡧⣚⠮⢳⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡕⡦⢩⠨⠱⣆
⠀⠀⠀⠀⠔⠠⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⢰⣮⠜⠱⠿⠋⠉⠉⠶⠒⠀⠂
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣠⢴⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⠆⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣳⢄⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣟⣊⣡⣀⣑⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣲⣸⣖⣄⣀⣤⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⣢⠐⠶⣶⣶⢲⣶⣲⣶⣶⡶⡶⣖⣶⠀⠀⠀⠀⢀⣠⣴⠲⠒⣶⣶⣖⣚⣧⣭⣾⣿
⠀⠀⠀⠙⠻⣿⢾⣿⡄⢸⢻⣦⣿⣷⡾⠋⠁⠀⠀⢀⡴⠋⣣⡽⢺⡟⣩⡿⢿⣿⣿⢷⣿⡟
⠀⠀⠀⠀⠀⢸⣷⢿⣷⣼⡐⣯⣿⣿⡇⠀⠀⠀⣠⢋⣴⢿⢹⣇⣿⣀⣯⠸⢿⣿⣿⢸⡾⠁
⠀⠀⠀⠀⠀⢸⣟⣦⣿⣿⣿⣿⢻⣿⡇⠀⠀⣰⣷⣟⣿⣾⡿⠿⣿⣿⣟⣿⣻⣯⠷⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢸⣿⣹⢾⣿⣿⠧⢸⣿⡇⣸⣿⣿⠏
⠀⠀⠀⠀⠀⢸⡿⣼⣿⣿⣿⡰⢚⣿⣶⣿⣿⠋
⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢸⡇⣬⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⠛⠛⠿⠿⣶⣤⣀
⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠻⣿⣿⣷⣶⣶⣭⣟⣷⣤⡀
⠀⠀⠀⠀⠀⢸⣿⣟⣇⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣍⠙⠷⣟⠩⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣗⢿⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣷⡰⣾⢇⠴⠌⠻⣿⣄
⠀⠀⠀⠀⠀⢸⣿⣷⡞⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⡾⢛⠻⣆⢻⠿⣦
⠀⠀⠀⠀⠀⢸⣿⣿⣨⢮⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠿⠷⠃⣼⣋⡏⢷⡀
⠀⠀⠀⠀⢀⣸⣿⣿⣿⣍⢶⣭⡟⢿⣧⡀⠀⠀⠀⠀⠀⢀⡟⣿⣿⣦⣅⣠⣴⣟⣿⣿⣎⠳⡄
⠀⠀⠀⣴⣿⣿⣽⣿⣮⣿⣿⣮⣥⣭⣿⣿⣶⠀⠀⠀⣾⣿⣿⣟⣿⣷⣾⣽⣷⣿⣿⣿⣯⣷⣿⣿⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠉⠉⠻⢿⣿⣿⣿⣿⡿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣧⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠠⠀⠀⠀⢠⣤⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠾⢿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠈⠙⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡘⢿⣆⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠌⠻⣷⣿⣿⣿⣄⡀
⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠀⠈⠉⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈

⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠄⢦⣀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⡆⣄⠀⣰⣤⡀⢀⡀
⠀⠀⠙⠂⢉⣀⣄⣀⠶⠂⢀⠀⠀⢀⡀⠀⠐⠀⠺⠀⠋⠀⠄⠉⢀⡷⠋⠐⠀⠀⠀⠀⢀⡀⠀⣉⣉⠿⣉⡁⢻⣿⢠⣶⠀⣰⠀⠀⡀⠀⣀⠀⠠⣤⣀
⠀⠀⠉⠀⢼⣿⣿⣿⠋⠀⠀⠀⠀⣼⡏⠐⢀⠀⠋⠁⠙⠀⠰⣅⠀⠀⣣⠀⠀⠀⠀⠈⠉⠀⡀⠀⣈⠒⢉⡀⣈⡉⠸⡥⠀⢠⣄⠀⠀⠀⠀⠀⠀⠰⠟
⠀⠀⠀⠀⠀⠛⠽⢴⢲⣤⡤⠦⢸⡿⢇⣼⠃⠀⠀⢠⡎⠀⠀⠉⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠟⢛⡙⠨⠇⢴⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠻⠾⠻⢿⣕⡨⠻⣿⣿⠀⠘⠷⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡚⠋⢀⡄⠉⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠈⠁⣀⣤⣶⠾⠦⠤⠟⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣉⠿⢋⠰⠈⣋⡁⠉⢠⠻⠒⠆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠘⠟⠀⠀⢀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⢻⠃⠍⠁⣸⣿⣿⣠⡏⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡟⠠⠶⠤⠀⠀⠁⠻⠇⠀⢠⡀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠤⢛⡿⢋⠸⠀⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣶⣆⠀⠀⠂⠀⠀⢱⣹⣧⣀⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⡛⣿⠀⠁⠀⠀⠀⠸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣯⣵⣄⣠⡄⠀⠀⠀⠀⠀⠸⣿⣿⠻⣿⠏⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡸⠷⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠳⠀⡀⠀⠘⠿⠛⠈⠃⠀⠀⠀⠀⠀⠀⠿⠿⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠘⢠⡌⠁⣤⣾⣤⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⠼⠋⠉⠉⠙⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢶⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠟⣧
⠀⠀⠀⠀⠀⠀⢀⣘⣿⠛⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠊⡀⠤⢲⠖⢋⡙⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠈⣻⡅⠀⠀⣀⣿⣾⣿⣷⣦⠄⠀⠀⢀⣴⣚⣧⣤⢾⣷⡲⠿⢵⡞⠛⠧⠉⠄⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣿⣿⣿⠿⣻⣷⠆⠀⠀⢠⣌⡉⡹⠛⠉⠁⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠘⠻⣿⡿⠿⡏⠁⠀⠀⣤⡟⠁⠀⠀⠀⠀⢀⠰⠲⠚⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠁⠀⠀⠀⢶⣤⡿⠀⠀⠀⠙⠒⠂⠈⣴⣾⡄⠆⠀⠀⡄⠀⢀⠄⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠒⠷⢴⣦⣶⢄⣼⠗⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⠉⡱⠜⠛⠚⣿⠶⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⣀⣄⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⡼⠿⢀⢀⠀⠒⠒⠒⠿⢍⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣦⠀⠀⠀⠚⠿⠿⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠟⠉⠉⠀⡀⠀⣀⣀⠀⠀⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣿⠸⡦⢀⢀⡰⢛⢛⡩⠟⠛⣛⢠⡘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢰⠂⢈⠁⣨⣷⠌⢂⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲⣇⠈⠠⣈⡙⠋⡍⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠉⠶⠉⠤⠁⣈⠀⢋⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⠹⢀⣿⣦⡵
⠀⠀⠀⠀⠀⠀⠀⢐⠸⣗⠀⠀⠀⠀⠀⠙⠻⠌⣤⡄⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⢲⡞⠀⠀⠀⠘⠁⣠⡤⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⢻⣇⡀⠀⠀⠀⠀⠀⠀⢰⣦⣾⣄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣄⠀⠀⠀⠀⠀⠻⢷⠶⠶⢾⠛⢃⣠⣄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠙⢿⣷⣠⡀⢀⠰⣾⣥⢾⡽⢿⣿⣟⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠳⠂⠀⢀⣚⡄⣀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠚⣱⡿⠦⠠⠤⢤⣀⣈⣹⡿⠿⠇⠻⠿⠋⠀⢶⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠸⠂⠁⠀⠀⠈⠂⠉⠀⠀⠁⠀⠑⡀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⣰⠒⠒⠀⠀⠀⣠⡴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠂⠢⠲⠠⠄⠴⣢⡄
⠀⠀⠀⠀⠀⢉⡞⡹⢲⠆⣜⣽⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢫⠲⢼⡀⡀⠚⣠⠞⠁
⠀⠀⠀⠀⠀⣤⠗⠙⠀⠀⠀⠑⠂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⡵⠋⣌⢮⡑⣈⠗⠁
⠀⠀⠀⠀⠀⠖⣠⡄⠀⠀⠠⠄⢲⡇⠀⠀⠀⠀⠀⡠⢀⣴⣆⠿⣶⣤⠁⠎⡑⠁
⠀⠀⠀⠀⠀⠀⢘⣥⠄⢾⣷⡶⢰⡇⠀⠀⠀⢠⠆⠀⠀⠉⠑⠃⠛⠿⡣⠂
⠀⠀⠀⠀⠀⠶⢈⡄⠀⠀⠀⠇⣷⡃⠀⢀⡴⣡⣶⣶⣷⠀⠀⣶⢈⠜
⠀⠀⠀⠀⠀⠠⣿⠀⠀⠁⠀⢺⠋⣥⣤⢺⡿⣤⡝⠋⡀⠻⢂⠜⠁
⠀⠀⠀⠀⠀⢠⢋⡿⠅⠀⠀⣀⣠⣭⣄⣞⢠⣾⡤⠀⢲⡄⣇
⠀⠀⠀⠀⠀⠷⢸⡃⢰⡿⠆⣼⣿⣿⠟⠀⠀⠙⣠⠄⣀⡀⠈⢦⡀
⠀⠀⠀⠀⠀⡇⠿⠐⠟⠂⠀⠙⠋⠀⣀⣤⠀⠀⠐⢌⠙⠃⠀⠀⠱⣄
⠀⠀⠀⠀⠀⣇⣭⢰⣿⣿⣿⠅⢐⣾⡿⠾⠦⡉⢑⣎⠉⠳⠀⢤⣶⡌⢦
⠀⠀⠀⠀⠀⠇⣶⠸⠏⠉⠁⢠⡾⡿⠀⠀⠀⠘⢎⠛⠒⣀⣀⠆⣿⣿⠈⠱⣄
⠀⠀⠀⠀⠀⠟⣽⡿⣺⣾⣶⢀⡛⡇⠀⠀⠀⠀⠀⠣⡹⣴⣿⣿⣿⠿⠀⣠⡎⢦⡀
⠀⠀⠀⠀⠀⡷⣻⣥⣏⡼⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠱⣜⠟⠟⠁⠀⠀⣩⣴⠊⢷⡄
⠀⠀⠀⠀⠀⣧⡯⣏⣝⣶⣦⣟⡀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣷⣶⣿⡿⠛⠸⠃⢻⣄
⠀⠀⠀⠀⠀⣾⣾⣏⣿⣕⣿⡊⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠙⢁⣀⣘⣀⣸⣮⣷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⢄⣃⠄⠀⢤⣠⢞⠋⠃⠀⢀⡷⠀⠀⠄⠀⠀⠀⡀⠀⠂⠐⢆
⠀⠀⠀⠀⠀⠀⠀⡄⠉⠈⢠⣊⢂⣀⡀⣘⠃⠄⠀⠤⣏⠀⠀⠎⠀⠀⠀⢸⡃⠀⠀⠠⠦⠠⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠨⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖
⠀⠀⠀⠀⠀⠀⢰⡄⠤⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠳⠃⠘
⠀⠀⠀⠀⠀⠀⣀⠙⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⡁⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣱⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠻⠔⠀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣔⠗⠡⣥⠀⠤⠎
⠀⠀⠀⠀⠠⠦⣠⠂⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⡐⢀⠈⠱⠈⠂⡄
⠀⠀⠀⠀⠀⠀⠻⠄⢀⢂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⠉⢀⠀⠁
⠀⠀⠀⠀⠀⠀⣆⠀⠀⣘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⡆⠪⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠋⠈⠫⡠⡀⠀⠀⠀⠀⠀⠀⠐⠑⢟⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠝⠐⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢎⢄⠀⠀⠀⠀⠀⠀⠈⠈⠣⠀⡡⣀⣀
⠀⠀⠀⡀⠀⠐⣀⠄⠠⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣹⡥⡀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠉⠀⠑
⠀⠀⠀⠠⢀⣀⣫⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣅⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⢠⡀
⠀⠀⠀⠀⠀⠉⠉⢢⡁⢶⡤⢸⡿⠻⠟⠙⠯⠙⣿⢿⠼⠠⠀⠀⠀⠈⠃⠊⠉⠂⠩⢽⢿⣯⡿⡿⡟⠛⠆⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⣘⠈⠀⢀⣠⡀⠀⢀⡠⠒⠀⠠⠀⠀⠀⠀⠀⠀⠘⣉⠀⣈⡁⡉⠀⠀⡤⠤⠜⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠥⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄

⠀⠀⠀⠀⢀⣴⡆⣀⣤⣴⣶⠎⣥⣽⣭⣴⣢⠄⠀⠀⠈⢰⠶⡄⠀⠀⠐⣂⣤⣐⣚⣓⠚⠛⠛⠛⠒⠢⢴⡆
⠀⠀⠀⠀⠘⢿⣿⣿⣧⠀⣷⠤⣶⠤⣶⠮⡿⢷⢤⠤⢀⣬⣤⠀⣤⡶⠿⠿⠟⠉⠉⠉⠡⡶⠒⠺⣟⢷⡀⠙⡄
⠀⠀⠀⠀⢸⠰⣏⣿⠷⣾⣶⣶⣷⣿⣶⣿⣶⣶⢶⡶⢎⡠⠷⢷⣶⣾⣷⣾⣿⣶⣾⣿⣷⠶⠿⠷⢈⠀⠻⢆⠈⡄⠀⣴⠃⡤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⠀⠀⢻⣶⠌⣿⣿⣿⣿⣿⣿⡏⢸⡾⢶⣺⣶⣶⣞⣦⢹⣿⣿⡿⢟⣛⠵⠞⢃⣀⣗⠀⢀⡾⠀⣴⠆⣀⠙⡦⠀⠰⠂⠘⠃⢀⣀⠄
⠀⠀⠀⠀⠀⠘⣧⡈⠷⢼⢿⣿⣿⣿⣿⣿⣧⣸⣿⣾⣿⣿⢿⡟⣠⣿⡿⠋⠞⡁⠴⠶⠶⠂⣀⣈⡟⣋⣠⠴⠃⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠹⣿⠷⢾⣼⣿⣿⣿⣿⣿⣷⣟⢻⣿⠿⡿⣫⣾⠟⠡⠈⡄⠀⢤⡴⠂⠀⢀⡄⢏⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣰⡄⠹⣿⣼⢸⣿⣿⣿⣿⣿⣯⣹⣿⠏⣨⣾⢏⡵⢃⣶⣦⠧⣶⠀⠀⣾⢢⡌⡵⠈⡙⠏
⠀⠀⠀⠀⠀⢀⡀⠀⠛⡡⢸⣿⣿⣿⣿⣿⣿⠬⣫⣾⢟⡁⣿⣿⣿⠹⢿⣦⣤⠻⠗⢀⣱⠁⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠈⠑⣿⠇⢠⢸⣿⣿⣿⣿⣿⣧⣼⣿⣥⣬⣴⣤⣤⣶⣟⣋⡽⢿⡧⣾⣋⣉⡀
⠀⠀⠀⠀⠀⠘⠋⠋⣠⠸⢸⣿⣿⣿⣿⣿⡟⣫⣭⣭⣭⣭⣭⣛⢿⣿⣿⣿⣿⣍⢮⡿⡏⣿
⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⢀⣿⣿⣿⣿⣿⣟⢼⣿⣿⣿⣿⢿⣿⣆⢹⣿⣿⣿⣿⣯⡝⣡⡿
⠀⠀⠀⠀⠈⠿⠀⣀⡠⢘⢸⣿⣿⣿⣿⣿⣿⢠⣾⣿⣿⣿⣷⣿⣷⠈⣿⣿⣿⣿⣿⣷⠁⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸⣻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣆⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⣿⠇⣿⣿⣿⣿⣿⣿⣯⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠚⢹⣿⣿⣿⣿⣿⣿⢿⣿⡋⢹⢻⣿⣿⡇⣿⠀⣿⣿⣿⣿⣿⣿⣷⠘⠯⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡤⢻⣷⢸⣿⣿⣿⣿⣿⣿⣶⡾⣃⣼⣯⣙⣿⣃⣿⡆⣿⣿⣿⣿⣿⣿⡿⢠⡞⠂
⠀⠀⠀⠀⠠⣶⡄⠈⠉⢸⣿⣿⣿⣿⣿⠟⣫⣾⣿⣿⣏⣿⡟⢛⣿⡟⣿⣿⣿⣿⣟⣫⣾⠞⠃⠀⠁
⠀⠀⠀⠀⢀⠉⢿⣷⠀⡸⣿⣿⡿⢛⣵⢟⣼⡇⣤⣤⣼⣿⣁⣸⣿⣿⣿⣿⣿⡟⢰⠟⠟⣤
⠀⠀⠀⠀⢸⡧⣀⣤⣾⣵⠟⣫⣾⠣⣼⣵⠟⢻⣦⣿⣹⣾⢋⣵⠿⣿⢹⣿⡏⢁⡾⠀⠀⠀⢀⣤
⠀⠀⠀⠀⢻⠀⡏⣿⣿⣷⣿⡿⠶⠶⠶⣤⣄⣰⠏⣉⣽⡟⢂⠁⡀⠿⢸⣿⣷⣄⠀⠀⠀⣀⠘⠈⢁
⠀⠀⠀⠀⠸⠀⣵⣾⡿⠉⠀⠀⠀⢹⣦⢀⡼⣿⣩⣭⣵⢢⣏⠀⣿⠀⢸⣿⡇⣼⠇⠀⠀⠛⠀⠄
⠀⠀⠀⠀⠰⠂⢠⡟⠀⠀⠈⠀⣴⣿⢣⡞⡿⣻⢶⣿⠏⢸⡿⠀⠛⣷⠈⣿⣇⠿⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠆⠀⠃⠀⠀⣏⣰⠛⠘⣀⡟⢸⡿⠒⣿⠷⡸⢇⣿⠆⢻⣿⠀⣅⠠⢀⣤⡄⠑
⠀⠀⠀⠀⢐⠄⢻⠀⠘⠛⠂⠀⣸⠿⣴⡾⠋⠀⡎⠡⣌⠛⣠⠋⡸⠌⠀⠘⣿⠸⠏⠐⣿⣅⣀⣤⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣰⠁⠀⣿⢠⡶⢶⣀⡠⢼⣾⢧⣈⠁⠀⠀⠀⢻⣇⠐⠀⠹⣿⣿⣿⣿⡿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⡏⠀⠀⢿⣍⣴⣿⢁⣤⢾⣁⠀⠀⠙⢦⡀⠀⠀⠻⣦⡀⠀⠈⠙⠛⠋⠀⠀⣸⡇
⠀⠀⠀⠀⢸⠁⠀⠀⠈⢉⡻⠷⣤⣤⣤⣿⡿⠾⣍⡾⠏⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⠻⣦⣄⣀⠀⢀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⢰⡆⣻⢀⣠⡽⣅⣂⠀⠠⠀⡄⠀⠈⢳⠀⠀⢀⠁⠂⠉⠙⠿⠟⠋⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡞⠘⠋⢯⣙⣁⣠⡭⠛⠓⢢⡄⢀⠀⣹⠆⠀⠀⠁⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣬⠀⠂⠀⠈⠹⣏⠁⣴⠻⣷⣤⠿⠀⠀⡝⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠾⣧⡤⠀⢛⡆⠀⠘⣇⠀⠀⠂⠈⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣿⣧⣤⡀⣿⠀⠀⠀⣀⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡟⢫⠿⢷⠟⠶⠊⠛⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂
⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⠛⠻⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣄⣀⣠⣾⣿⣷⠀⠀⠀⠀⣴⣶⣦⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠉⠛⠛⠿⠿⢶⣤⡄⠀⠛⠛⠻⢇⣴⠟⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣠⠞⠁⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠔⠋⠉⠉⠙⠲⣼⣿⣡⠖⠛⠉⠛⠲⡄⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡏⠀⠀⠀⠀⠀⣶⠄⠀⣿⠀⠀⠀⠀⠺⠆⠀⡇⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢠⠟⣦⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠳⣤⣀⠀⢀⣀⡴⠋⠀⠈⠙⠲⠶⠞⠋⠀⣀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⢶⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠚⠉⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣷⡀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣤⣤⠤⠤⣤⣤⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⣀⣤⠞⠉⠛⠋⠁
⠀⠀⠀⠀⠹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⣀⣴⣿⣿⣋⣁
⠀⢀⣀⣤⣶⣿⣿⣿⠟⠛⠁⢿⠀⠀⠘⠿⢿⣷⣶⣶⣤⣤⣄⣀⡀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⡿⠛⠁⠀⠈⠉⠛⠓⠶⣤⣀
⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⠟⠉⠛⠛⠻⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣽⣿⣿
⣿⣿⣇⣈⣁⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣶⣶⣶⣶⠀⠀⠀⠀⣠⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠉⠉⠉⢹⣿⣿⣿⣿⠋⠉⠉⠉⠉⣽⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣷⡄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠀⠀⠀⠀⠘⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⣀⣀⣀⣼⣿⣿⣿⣿⣄⣀⣀⣀⣀⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣀⡤⠶⡻⢶⢤⢄⣤⡖⢟⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠶⠷⣷⣮⣳⡗⡐⡱⠡⢪⣞⢕⢹⡳⠲⢖⢶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣍⣿⠛⠽⣻⣴⣿⢵⡫⠉⠉⠉⢳⣛⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣌⣿⡄⢸⣺⠀⠀⣷⣥⡤⠔⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣎⣙⠷⢴⡿⣏⣰⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠽⣿⣶⣶⢭⡶⢻⣋⣭⣤⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣧⣼⣥⣮⣾⢿⣟⣿⡍⠝⡶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠝⣿⠛⠁⠁⠃⠀⠘⠆⠱⣄⠀⠁⠊⡜⡹⢲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠔⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠊⡰⠉⡹⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⡠⠰⠊⠀⠀⠀⢀⣀⣀⣸⣿⠝⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⢊⠜⢑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⡆⡇⠃⠀⠀⠀⡰⡫⢋⢅⣵⢵⠕⡫⣻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠔⡡⢎⡝⣦
⠀⠀⠀⠀⠀⣠⠚⠁⠀⠣⠉⠀⠀⠀⠀⢸⠋⣈⡵⠝⢳⡧⡪⣮⣏⣕⢉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⡴⢋⠔⣡⢷⡀
⠀⠀⠀⢠⠞⠁⠆⠢⠘⠀⠀⠀⠀⠀⠀⢿⡼⣿⣇⠀⢸⡪⡮⡟⠀⠙⢷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣡⠞⣡⢊⠝⡄
⠀⠀⡴⠁⢠⠺⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣕⢟⢷⠿⡪⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠞⡡⢋⠜⡼⡄
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣕⡩⡪⣞⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠊⡠⢂⠞⡰⣳
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣪⣾⣵⠟⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⢁⢞⣔⣽⡀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡄⠀⠀⡼⣊⣼⡇⠈⢿⣮⡪⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⡫⢪⢾⡅
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡱⡻⣦⡀⣿⣿⣿⠁⠀⣸⣯⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⡡⢊⠔⡵⡱⣻⠇
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣊⡿⢻⡿⣯⢞⢟⢟⣽⡻⣮⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⢊⠔⡡⢪⢎⡔⣩
⠸⡆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣏⢔⢵⠵⠦⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡫⢖⡡⢊⠔⡡⢊⠴⡏
⠀⠱⡀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⢋⠴⣋⠔⡡⢊⠔⣩⡾
⠀⠀⠱⡀⠰⢘⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⢀⠀⠀⠀⢀⠀⡀⢀⠀⡰⢃⠄⣁⡴⢩⠞⡡⢊⡴⣡⢞⣽⢭⠉⢩⠉⠉⣠⣤⡄
⠀⠀⠀⠘⢦⠈⠸⢈⢠⠠⢀⠀⡀⢀⢀⢀⠜⡰⢃⠜⡡⢊⠤⢊⠴⢊⠴⢁⠔⡠⢂⠞⡱⢡⢮⠎⡰⢁⠞⡰⢋⢜⡵⠟⠛⠒⠒⠒⠒⠒⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⢙⣦⣈⠘⠸⠸⠄⠃⠂⠂⠘⠐⠀⠃⠚⠐⠃⠐⠁⢘⣁⠚⠁⠊⠐⠡⢊⡔⡱⢃⠞⡰⢃⣎⣴⠷⠋⠉⠉⠉⠉⠉⠉⠩⠭⠭⠭⠭⠭⠉
⠀⠀⠀⠀⠀⠀⠁⠉⠉⢲⠦⣤⣤⡄⠒⣶⣶⣲⣶⡶⠾⢿⣿⣭⣤⣬⠭⢭⣉⣁⣰⣋⣞⣰⣧⠾⠶⠿⠭⠤⠤⠤⠤⠤⠬⠥⠤⠭⠭⠭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣒⣀⣀⣀⡭⠭⠍⠉⠭⠭⠍⠉⠉⠀⠂⠘⠉⠩⠿⠿⠿⣭⣭⣭⣽⠉⠉⠩⠭⠭⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿
⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⣼⠁
⠀⠹⣟⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⣠⡾⢻⠇
⠀⠀⢘⣦⡀⠉⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠁⠀⣀⡤⠞⠉⣰⣯⡦
⠀⠀⠘⢯⡙⠲⢤⣀⠀⠀⠈⠉⠉⠛⠒⠒⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶⠶⠚⢛⡖⢀⡤⠞⠉⠀⢀⣀⡤⠴⣒⣋⣭⠀⣠⡾⢋⡼⠁
⠀⠀⠀⢶⡿⣦⡀⠉⠉⣛⣒⡒⠶⠦⠤⣤⣤⣀⡀⠉⠓⢦⡀⠀⢠⣶⡿⠟⢋⣵⣿⣿⣾⣿⠿⠟⣿⣼⡵⠋⠀⣠⠴⠚⠉⠀⠀⠀⣀⠴⠋⠀⠁⣠⣞
⠀⠀⠀⠀⠻⣤⡉⠓⠀⠛⠬⣅⣀⡀⠀⠀⠀⠈⠉⠓⢦⡀⠙⢦⡻⣭⡀⢀⡙⣏⠋⠉⠁⠀⠀⠀⣿⡟⠀⣠⠟⠁⠀⠀⠀⠀⢈⣉⡭⠞⢀⡤⠞⣫⠟
⠀⠀⠀⠀⠀⢰⣿⢦⣄⡀⠐⠮⠭⣉⣀⣀⡀⠀⠀⠀⠀⠉⠢⡀⠹⣄⠙⠳⣝⣪⣳⣴⡄⢰⠀⢸⣿⠀⠞⠁⠀⠀⢀⣀⣉⡭⠽⠂⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠦⣭⣁⣀⠀⠘⠓⠒⠒⠒⠲⠆⣠⡶⢦⣌⣀⠙⡆⠀⠈⠙⣿⣿⣿⣄⣇⣠⣿⣿⡄⠀⠤⠔⠋⠀⠀⠀⣀⣺⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣭⣤⣄⣀⣀⡀⠈⠛⠻⠿⠿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⠿⣧⡀⠀⢀⣠⣶⣾⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⢲⣶⣤⠶⠟⠛⠩⢛⣿⣿⢿⡟⢹⣧⠹⣆⠈⠻⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⣠⡶⢶⡶⣻⡿⠟⢡⠟⠀⠈⡟⢧⠙⢦⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠘⠛⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠁⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⢿⠿⠏⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⠦⢤⡀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠳⣄⠀⢀⠜⠁⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⠤⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡱⡄⠀⠀⠄⠀⠀⢀⠀⢀⡜⠁⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣦⠤⠬⠷⠶⠥⣤⣿⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⣀⣀⣀⠀⠀⠈⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠖⠋⠉⠀⠟⡏⠉⠙⠒⢤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠀⠱⡀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⣿⠉⣟⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⣿⢠⡇⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢻⡷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠃⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⠇⣿⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢻⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠲⠤⣤⣤⣠⣤⡤⠴⠚⠧⠤⠤⠔⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⠤⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⣰⡀⠀⠀⣿⣦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠳⣧⠀⢸⣿⣿⠀⠸⣿⣿⠏⠀⣾⣿⡇⢀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡉⠉⠁⠀⠀⠉⠉⠀⠀⠉⠉⠀⢼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣶⣾⣾⣄⡀⠀⠀⠆⠀⠀⠈⠠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣦⠀⣧⡀⠀⠀⠀⠰⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⣏⣸⢿⣿⡿⠂⣀⣤⣽⣿⣇⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠁⠀⢟⠃⠀⠐⠴⢿⡉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠺⠄⠀⠘⠆⠀⠙

⣿⠟⠛⠛⠛⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⢹⡏⠉
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉
⠀⢠⣤⠤⣤⠤⢤⡄
⠀⢸⡇⠀⠁⣠⣿⡇⠀⣀⡄⠀⣤⢀⢄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢸⡇⠀⡀⠘⣿⡇⠀⠁⠋⠀⠉⠘⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠘⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂
⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠈⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠔⠂⠁⠐⠀⠀⠀⠐⠷⢢⣄⢂⣄⡱⢀⠚⠂⠀⠀⠀⠅⠀⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠋⠁⠛⠓⠰⠶⢀⣤
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠓⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀

⣶⣶⣶⣶⣶⣶⣶⣄⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣉⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⣀⣠⠤⠒⣦⣀⣀⣀⡤⠖⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠈⠻⣯⠥⠀⠀⠀⢿⠉⣽⠉⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⢳⡀⠀⠀⢸⣠⠇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⢀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢴⣶⡷⠞⠛⠛⠉⠉⠉⠉⢉⣩⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣛⣿⣯⡤⣤⡤⠤⢴⡶⠶⠛⠉⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⣭⡽⠋⡽⠀⢀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡟⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡸⠓⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠰⠃⢀⡄⡦⡀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠰⡀⠀⠓⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⡄⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⡉⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠱⠼⠘⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠶⠄⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢀⠀⢀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢘⣿⣿⣿⣿⣿⢀⣰⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡋⢛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⢘⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣭⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⢀⣿⣿⣿⣿⣿⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠀⠀⠀⠀⠀⠀⠐⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠆

⠀⠀⠀⠀⢠⡄
⠀⠀⢀⣤⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⠄
⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠤⠶⢿⡧⠛⠹⣶⡤⡀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⡟⠈⠀⠘⠛⠻⠟⠛⠉⠹⡀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⢸⢿⣿⣿⢿⣿⠿⣿⠀⠀⢧⣀⣹⡀⡀⠐⠂⢀⠂⢈⢄⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠸⡄⢹⠹⠘⢹⡀⠟⠀⠀⠄⠹⠅⠤⠑⡈⠁⠿⡙⠋⠐⠀⠀⠰⠾⠿⠛⢿⣿⣦⣀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠰⠟⠁⠀⠘⠓⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⡀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠
⠀⠀⠀⢀⣠⣼⣿⡆⠀⠀⠀⠀⠀⣸⣤⣦⣼⡆⠀⠀⠀⠀⠹⣿⣏⠀⣰⡏⠛⠇⠀⠀⠀⠀⠀⠀⣿⣶⣿⣷⣾⣿
⠀⠀⢴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⢰⣤⡀⠀⠀⠀⣿⢿⣿⣿⠿⣿
⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠉⠉⢹⡄⠀⠀⠀⠀⠀⠛⠿⣿⣭⠘⠛⠟⣿⡿⠋⠀⠀⠀⣿⠶⢿⠿⠾⡟
⠀⠀⠘⢛⣿⠿⠿⠷⠄⠀⠀⠀⢶⣿⣷⣶⣿⣷⠖⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⡿⠿⠀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⡀⣪⣷⠀⣶⣆⢀⣮⣔⢄⠀⠀⠀⢀⢐⣿⣷⣶⠶⠶⣾⣿⡂⡀⠀⠀⠀⣴⣾⣿⣧⣀⣴⣴⣦⣀⣼⣿⣷⣄
⠀⠐⠸⣿⡿⣿⣿⣿⣿⢿⣿⢪⠀⠀⠀⢠⡾⠿⠻⢿⣛⡿⠞⠿⢷⡄⠀⠀⠸⣿⣿⠿⢿⣥⡘⠛⡀⣽⠿⢿⣿⡿
⠀⠀⠀⠪⢀⣀⠘⠁⣀⠨⠑⠁⠀⠀⠀⠀⠑⠢⠤⢀⣉⡀⠤⠔⠊⠀⠀⠀⠀⠈⠻⠆⠀⠀⠈⠟⠀⠀⠀⠼⠋⠁

⣿⣿⣦⣀⣈⡧⢳⣟⠓⢧⠆⠉⣾⠻⣷⣿⣿⣿⣷⣽⣯⣯⠉⠀⠸⠏⠰⠀⠻⠈⠛⠈⠋⢿⣶⠼⠃⠀⡟⠀⢸
⣿⣿⣿⣿⣿⣶⠮⢍⡀⠈⠙⠆⠸⠛⠻⣚⣻⣿⣟⣝⡶⢿⣳⠉⠁⣯⣤⣀⠒⠀⠀⠀⠀⠈⡏⠀⠘⠠⡄⠔⢋
⣿⣿⠟⠛⣳⢾⣿⢸⢟⠖⠂⠀⠁⢸⡟⠯⠉⠛⠉⠉⠛⠃⠀⠰⠏⠛⡿⡻⡡⢀⠂⠄⠀⠢⠠⠀⢁⣠⡷⠖⠛
⣿⣿⣿⣿⣧⣼⡿⣛⣋⣴⠶⢀⣘⡓⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡞⠀⠋⠁⠰⠆⣠⠀⠑⢰⡄⠠⠀⠸⠁⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⠟⠘⠁⠀⠙⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡅⣿⢸⠃⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⣴⡶⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⣶⠞⡿⣵⣿⢿⡇⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣷⠀⠀⠀⠈⣅⡀⠀⠀⠀⠄⠈⠁⢄⠒⠋⠸⡆⠉⡟⠁⢀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢀⣄⢤⠋⠁⠃⠀⠀⠀⠀⠀⡽⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡴⣢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠴⠠⠄⠀⠀⣀⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣾⠁⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠀⠈⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⣰⣿⣅⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠏⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡶⡟⠃⣄⡀⠀⠀⠀⡶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠗⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⠿⠶⠀⣷⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⠏⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⢉⣶⣴⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⢤⣼⣿⣭⣿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠀⠀⠀⠀⠀⣨⠚⢻⣣⣾⠿⠅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⡠⠬⠍⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⣀⣀⣠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⢶⡏⢿⣿⣿⢿⠛⠋⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣶⡦⢯⣿⣷⣄⡀⠚⠟⠀⣰⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡌⠹⣿⣿⣿⣶⣶⣾⣿⣿⣿⠿⠯⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣆⠈⠙⢿⣿⣿⣿⣿⣿⣿⡲⣄⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⠏⠙⢻⣿⣶⣀⣀⣉⠙⢛⣻⣷⣹⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠟⠀⠠⠘⢋⣿⢿⣿⣿⣷⣿⣿⣳⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡿⢻⣿⣿⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠸⠛⢛⣿⠟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣧⣀⣐⣾⣂⠉⠀⠀⠀⠀⠀⠶⣤⣤
⠀⠀⠀⠀⠀⠀⡰⠂⣀⠀⠀⠀⠀⠀⠀⠰⠁⣼⣿⣯⣙⣛⣿⣬⣵⣦⣤⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⠿⠋⠁⠹⠡⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⣌⡽⠏⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢠⣿⠋
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⢀⡛⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣟⣀⣤⠄⣀⣀⠀⠀⠀⣀⣀⠽⣧
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣅⣀⠀⠀⢩⡏⣁⠀⢠⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⢀⡘⠛⠛⠛⠛⠛⠛⠒⠀⠀⠸⠷⠾⠿⠿⠿⠿⣷⡘⣆⠀⠀⠀⠀⣡⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠄⠀⠼⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠈⠁⠈⠙⠳⠾⠛⢓⡶⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣄⣀⣀⣀⣞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠲⠦⠤⠶⢦⠀⠀⠀⠀⠀⢀⣠⠼⠿⠿⠿⠿⠿⡿⠿⢤⡀⠀⠀⠀⠀⠐⣏⠉⠓⠚⠉⠙⢲⠆⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⣳⣤⣦⣤⣴⠃⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⢈⣦⣤⣤⣴⣴⡏⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠻⠛⠿⠛⠦⣀⡴⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢀⠜⠛⠻⠛⠛⠛⠻⣄
⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡴⠒⠛⠓⠲⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⡴⠃⠀⠀⠀⢀⡤⠶⠄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡴⠦⠄⠀⠀⠀⠀⠹⣄
⠀⠀⢰⠇⠀⠀⠀⠀⠸⣄⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⣸
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⠞⠁⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠓⠞⠁⠀⠀⠀⠀⣰⠃
⠀⠀⠚⡼⢦⣄⡀⠀⡀⠀⠀⠀⠀⠀⣀⣨⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣁⠀⠀⠀⠀⠀⠀⠀⣀⡤⢚⢁⢀
⠀⠀⠀⠀⠁⣠⠟⢉⡽⢋⡽⢛⡽⢛⡥⠋⡠⠋⣹⠗⡶⢲⡶⠒⡶⠒⢲⠖⢲⠖⢲⠿⢲⠟⡵⠋⡼⢫⠟⠲⢒⠖⡲⠋⡽⠣⠛⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠀⠈⠀⠈⠀⠀⠁⠞⠴⠋⠀⠚⠀⠐⠃⠐⠋⠐⠋⠐⠃⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡹⠋⠉⠋⡈⠜⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠉⢀⠼⢀⡈⠁⠀⡀⠠⠟⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣐⠀⠘⢁⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⣦⠈⠁⠀⠀⡇⠐⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣷⠭⢠⠞⠁⠆⡀⠀⡀⠀⠀⠔⠁⠀⠐⠁⠂⠴⠁⠀⡰⠒⢺⣁⡀⡅⠀⠄⡀⢛⡠⠂⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡀⠀⢹⣠⠞⠀⡠⢄⣀⠔⠀⠀⠰⠀⠀⠀⠀⠀⡠⠈⢤⠤⡄⢈⠞⡩⠕⠂⠉⠀⠁⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⢄⠨⠦⣾⠋⠐⠊⠀⢀⠀⠀⠀⠀⠀⠂⡴⠃⠀⠀⠀⡀⠁⠀⠼⡡⠊⠀⡀⠤⢤⠒⠂⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡄⢀⠀⣁⣀⢀⣈⠁⠀⠀⠀⡠⠔⢋⠄⠂⠀⡠⠁⠄⠀⠈⢑⡎⢀⠔⡡⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠲⠆⢼⡁⠙⡏⠉⢊⠑⠀⠊⠐⠈⣀⡠⠔⢊⡤⢀⠀⠠⠀⢸⠇⢌⠎⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠙⠤⡜⢬⢀⡌⠐⣾⣐⣊⠉⠉⣉⢍⠁⠠⠄⠈⡀⠂⢸⣴⡇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠃⣴⢾⠀⠀⡰⠠⡀⠉⠛⡀⠄⠁⢢⡈⠂⠷⠖⠄⠀⣀⠔⢠⣿⠄
⠀⠀⠀⠀⠀⠀⡐⠉⠀⢀⢈⠀⡴⠛⠈⠁⠢⡈⠂⢀⠠⣤⠋⠀⠙⠂⠤⣠⡤⠚⢁⠔⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢥⢾⠃⠊⠀⠠⠒⠢⡀⠈⠀⠃⠀⢨⠶⣆⡼⠦⠉⠀⠔⠈⣀⠔⠑⠹
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢀⠀⠀⠀⡰⡆⠀⠀⢠⡱⠤⡇⠜⣸⠡⠀⠀⠀⠀⠈⠖⠁⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢒⠊⠁⠤⡀⠀⣠⠇⠐⠀⢀⡀⠀⢉⠖⠋⠳⢶⣶⠴⡀⣀⡠⢀⠁⠀⠀⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢁⠔⠁⢀⠉⠀⠒⠋⡠⠠⠀⠈⢣⠑⠄⠈⡀⡄⠀⠀⠘⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡠⠊⠁⣀⣠⡡⠐⠊⠀⠈⠀⠀⠀⠀⠀⡆⠈⣆⠀⠌⢀⡀⠠⡉⢐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⠔⠁⠀⠀⠁⣀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠂⠳⠄⡈⠀⣠⢋⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢁⣠⡄⠒⠃⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⡞⠑⢢⠠⠱⡄⣀⠉⢀⡀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣉⡀⠀⠒⠤⣈⠠⠂⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⣁⠄⠀⠀⠀⡐⢄⣀⡀⠈⠀⠘⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠸⡛⠯⠈⠁⠂⣄⣀⣀⡠⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢀⠴⡀⠀⠈⠢⠈⠡⠔⠀⠀⠄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠤⡘⠢⣀⠀⠀⠀⠀⡠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣤⣏⠀⠀⠀⢠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠤⡤⠉⠉⠉⠁⠀⠀⠈⠁⠠⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⣤⣰⠉⠲⡆⣀⡀⠆⡤⠀⠀⢂⠄⡀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀⠀⠀⡄⠀⡀⢸⡤⠣⢽⠄⣶⡿⣠⣖⢋⣬⣩⡨⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣟⡛⠛⠛⠛⠛⠛⠻⠤⠒⠚⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⢴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠉⠻⢻⡟⠉⠉⠉⢹⠟⠉⠁⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠶⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠚⠛⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢑⡲⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠂⢬⣑⠲⠍⡛⠶⢦⣄⡀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠒⠚⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣒⠭⢔⡢⠍⠒⠦⠀⠀⠈⠙⠳⣤⠐⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠙⠲⢭⣒⠮⢅⠂⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠐⠒⠚⠛⠶⣤⣄⡀⠀⠀⠀⠀⣸⠇⠀⢀⣀⣠⣤⠴⠖⠛⠛⠛⠒⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⠶⠶⠲⠶⠲⠲⢲⡖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠸⠙⣮⢹⡶⠒⠲⠶⠶⠒⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠠⠴⠒⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠘⢾⣇⣀⣀⣤⣤⣤⣤⡤⠤⠶⠶⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⣀⣤⡤⠶⠚⠛⣻⣥⠶⠞⠛⠛⠛⠛⠛⣛⠛⠳⠶⠶⠶⠶⠶⠤⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣹⣦
⠀⣴⠞⠉⠁⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠩⠭⠭⠍⠐⠒⣒⣒⣒⣒⣒⣀⠉⠉⠉⠉⠉⢹⢯⣉
⣼⠃⠀⠀⠑⠢⠤⠀⠀⣿⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠦⠤⠤⠤⠤⠄⣀⣒⣒⣒⣒⠒⠒⠀⠀⠀⠀⡇⠀⠈⠙⠲⣤⣀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⡀⠤⠤⢤⣤⣬⣍⣉⣉⣉⣉⠉⠉⠉⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⣀⣤⣤⡽⠷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠶⠶⠶⠾⠿⠿⠿⠿⠿⢿⣿⣷⣦⣤⣂⣀⣀⣀⣀⣀⣀⣀⣈⣻⠉⠁⠀⡼
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⢀⣤⠴⠖⠒⠛⠉⣉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⡇
⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⣀⣁⣠⣤⠤⠤⠀⣀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣘⢿⣒⠠⠀⠀⠀⠀⠔⠒⢒⣚⣛⣩⣭⡭⠴⠶⠖⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣄⣠⣤⣶⣶⣿⢿⣷⡄⠀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣛⣻⣿⣿⣶⣶⣾⣿⣍⠉⠁⠀⣴⣿⠵⠞⠛⠉⠁⢀⣠⣬⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⡉⠉⠉⣴⣿⡛⠋⣹⣦⣤⣾⡿⢿⣿⣶⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⠘⢿⣿⠿⠿⠛⠋⠁⣰⠏⠀⠀⠀⣠⡿⠋⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣬⣿⣦⣀⡀⠀⠰⠏⠀⣀⣠⣾⣯⣴⠶⠛⢛⣛⣩⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠿⣯⣭⣭⣉⣉⣙⣛⡛⠛⣛⣭⣿⣿⠟⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠋⠉⠀⠘⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣀⣬⣷⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠛⠋⠙⣧⠀⠀⠙⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢻⡄⠀⠀⢸⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠿⠟⢿⡛⠉⠙⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠘⣷⠀⢀⣴⡟⠁
⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣤⡀⠀⣷⣀⣀⣠⣼⣷⠿⠋
⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⣿⠟⠛⠛⣿⡀
⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠹⡇
⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣶⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⡾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢈⢉⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣶⣠⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢸⣳⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣄⣠⣴⣤⣿⣽⣿⠃⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⡿⢣⠀⡔⡀⣾⡁⠀⠀⢀⣀⡈⢀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⡾⢧⡀⠀⠚⢫⣾⡿⠇⠀⠀⣸⠋⠋⡐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣀⠐⡿⣿⣿⣿⣿⣿⡆⠀⣶⣀⣆⢡⡵⢰⡆⣠⡄⠀⠀⠀⣾⡿⢿⣿⡟⣖⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣃⣼⣾⣿⣿⣿⣿⡴⢾⣿⣷⣾⣵⣿⡝⣿⣧⠀⠀⢈⣉⡡⣯⠈⣗⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣾⣿⣿⣿⣿⡷⣧⡰⣿⣿⣿⣿⣿⣿⣿⣙⠃⠺⣿⣟⣻⣟⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠿⠿⠍⠿⠿⠻⠟⠀⠈⠉⠛⠛⠿⠟⠛⠟⠿⠿⠙⠗⢈⠃⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣠⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣻⢿⣿⣿⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣇⣀⣀⣀⡀⢀⣀⡀⣀⣀⣀⣀⣀⠀⣀⣀⡀⣄⣈⠀⢹⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣹⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡗⢸⣿⣄⢸⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢀⡄⠀⢀⣿⠉⠘⠿⣿⡟⢹⣿⠂⠸⣿⢿⣿⣿⢿⣻⣿⣿⣽⠏⣻⡏⠀⠀⢸⡇⢹⡏⠙⣿⣿⠿⡿⠛⠛⠛⢹⣾⡄
⠀⠀⠈⠛⠷⠟⠁⢸⠃⠀⠀⢿⠈⣿⡇⠘⠛⢸⣿⣿⣿⣿⣿⣟⣿⣦⣼⡇⠀⠀⣸⡇⢸⣧⣾⣿⡷⠉⠁⠸⡇⠇⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠙⣟⠁⠀⡀⢺⠖⠛⡿⠻⠿⠿⢿⣿⣿⣿⡶⣶⣺⣷⢸⡏⢹⡟⡇⠀⠀⠀⡇⠠⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⣀⣠⣧⣀⣀⠃⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠸⠟⢸⣿⠸⠇⡧⢠⣤⣄⣧⠰⣆⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠃⠉⠉⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⠀⠈⠃⠈⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠁


⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠉⠉⠻⢿⠟⣿⣿⣿⣿⣿⡿⠿⠛⠉⠩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠊⠀⠀⠂⠀⠊⠰⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠘⠗⠀⠀⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢂⠈⠃⠀⠀⠀⠀⣏⣿⣿⣿⣿⠀⡆⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡁⠀⠀⠀⠀⢘⡀⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠊⠉⠀⠀⡰⠀⢦⡀⠀⠀⠀⠀⠁⠈⠻⣿⣿⣿⠱⡇⠀⠀⣠⠤⠾⠠⠴⠏⠉⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠠⠙⠋⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⢹⣠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣿⣿⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋
⠀⠀⣈⠀⠀⠀⠀⠀⠋⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⠃⠀⢀⠀⠀⠐⠁⠀⢀⣴⣿⣿⣿⠟⠁
⠀⠀⠠⣤⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⡠⠚⠉⠉⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⢠⣁⡠⠀⢀⠀⠐⠀⠁⠀⠁⠀⣶⣶⡄⠀⣾⣿⣿⣿⠋⠁⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢱⣦⠈⡡⠠⠀⣀⡀⠀⠀⢀⡘⠁⣠⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠠⠈⠊⠡⠀⠀⢻⡇⠀⠀⢡⡄⠀⠁⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠈⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠄⢤⠀⢶⠄⢿⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛
⠀⠐⠂⡄⠀⠀⠀⠀⠐⣧⠀⠀⠈⠳⣄⠈⡿
⠀⠐⠀⡁⢰⡄⡀⠀⠈⠉⠀⠀⠀⠀⠙⢿⣷⠟⣶⣄⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⢀⠙⠃⠀⣿⡀⣿⣿⣿⣿⣿⠋⠀⠘⠿⠿⠃⠀⠹⢶⣶⣦⣤⣤⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠲⠀⠀⠙⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢸⡿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢸⡿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠰⠶⢠⡄⠐⠀⠀⠾⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠘⢦⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⢿⣷⣶⣦⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⢀⣀⣀⠀⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⣾⣿⣿⣆⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⢀⡀⠀⡀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⡇⢸⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⠇⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⢠⣤⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⡇⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠙⠃⠘⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⢀⠀⠀⠀⠀⢈⡷⢤⣀⠀⠀⠀⠀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡜⣁⡤⠴⠾⠷⣤⣤⣴⢋⡴⣿⣫⣳⣄⠀⠀⣿⢸⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠶⢦⣤⣀⡀⠰⠿⢷⣓⣦⣠⢤⣴⣿⣿⣣⡆⠀⠀⠀⠀⠙⢯⠈⡇⠐⣼⡿⢍⡑⣄⣽⠾⠁⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠍⠀⠀⠀⠠⣀⣈⣿⣿⣦⠀⠀⠀⠁⠀⠀⢸⣿⡇⠛⠿⠃⠀⠀⠀⠀⠈⣇⣿⠐⣼⣿⡆⠘⣏⠀⣠⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠓⠀⠀⠀⠀⠈⠀⠀⢹⣿⣿⣧⡤⠚⠋⠉⠉⢹⡏⠉⢤⡀⠀⠀⠀⠀⠀⠀⣿⣌⢁⣿⣿⠃⠀⢿⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣄⡀⢀⣠⠀⠀⠀⠀⠀⣹⣿⠏⠀⠀⠀⠀⣀⡼⠃⠀⣀⣹⣿⣶⣦⣤⣀⣀⣈⠻⠿⢛⣁⣀⣤⣟⣈⣿⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⠉⠛⠻⣿⣦⣀⠀⠀⣿⠏⠀⠀⠀⣴⠟⠉⠷⣾⡋⠉⠁⠀⡽⢻⡟⠛⠻⣿⣿⡛⠛⠛⠿⠍⠉⠉⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣷⣼⠏⠀⠀⢀⣾⠃⠀⠀⠀⢸⣟⠂⢀⣰⠀⢸⡇⠀⠀⠙⢟⢮⠃⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠻⣶⡀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⣼⡟⠀⠀⠀⠀⣼⠉⠛⣿⣟⠀⣾⠁⠀⠀⠀⠸⡆⠀⠀⠀⢠⣷⡾⠃
⠀⠀⠀⢀⡄⠀⢸⡇⠀⠀⠀⠈⠻⣤⠀⠤⠊⢹⠃⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠇⠀⢀⣿⣿⢰⠇⠀⠀⠀⠀⢰⣧⣤⡶⠿⠛⠉
⠀⠀⠀⢸⣿⣦⣿⠁⠀⠀⠀⠀⠀⢫⠀⠀⠀⣸⣧⣤⣆⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡟⠀⠀⠀⠀⢀⡟⠉
⠀⠀⡠⣾⠋⠀⠙⠤⣼⠿⠷⠾⣦⣼⣇⠀⠀⣉⠻⣿⣿⣿⠏⠀⢀⡀⡀⡄⠀⣆⢸⡿⠈⠟⠀⠀⠀⢀⡤⠋
⠀⢰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡻⢿⣺⡃⠀⠋⠀⠀⣿⣿⣿⣿⣿⣾⣧⣧⣀⣀⣑⣒⣿⠟
⠀⡇⠀⢰⠀⠀⠀⠰⡀⠀⠀⠀⣸⠀⠀⢻⡇⠀⠙⠇⠀⠀⠀⣼⡿⠟⠻⢿⣥⣀⠀⠉⠙⠛⠉⡙⠁
⠀⡇⠀⢸⡇⢰⡀⠀⠹⣦⡀⢠⡟⠀⠀⠈⠁⠀⠀⢸⡂⠈⣿⠏⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠋⠁
⠀⢻⢆⢸⡇⠈⣿⡶⢦⣼⣿⣾⣇⠀⠀⠀⠀⣀⣴⠯⠄⠊⠁
⠀⡀⢠⣿⡇⠀⡟⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁
⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣌⠻⣿⡍⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠙⢿⣿⣮⡃⠙⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠛⠛⠛⠦⠀⠀⠀⠙⢿⣷⡀⠈⠆
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⡀⠀⠀⠀⠰⣿⠟⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⢸⣇⣽⠀⡇⠀⠀⡞⣇⢠⡏⠁⠁⣿⡜⠁⠀⠀⠀⣿⣿⣿⣾⠿⠿⠿⠆⠀⠀⠀⠀⠀⡔⠻⣟⣋⡿⠃⠀⠀⠀⠀⠀⢻⣿⣤
⠀⠀⠘⠧⠼⠀⠧⠤⠸⠉⠹⠌⠣⢤⠄⠿⠘⠆⠀⠀⠀⣽⣿⣿⣇⠀⣀⣀⣤⡀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣧
⣿⣿⣟⣻⣟⣿⠟⣿⣻⢻⣿⣿⢿⡟⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣏⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣿
⣿⣿⢵⡟⣽⡜⣶⢉⣿⢸⣧⣿⣼⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⠈⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⡟
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⡇⢿⡄⠀⠀⠹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⢰⠘⡇⣆⡀⢢⢸⠀⡆⣴⠘⡁⠠⣀⢶⠀⡄⠀⠀⣿⣿⣿⣧⢸⣿⡀⠀⠀⣰⣶⣾⣿⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣷⡄⠀⢿⣿⣯⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⡼⠻⣿⣶
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢿⣿⣿⣄⠀⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⢀⠞⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣦⣤⣤⣤⣶⣾⡿⠟⠁⠀⠀⠀⠃⠀⠀⠀⢳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣿⠻⠉⠙⠏⠉⠛⠏⠉⠟⠉⠹⠏⠉⠻⠋⠉⠛⠉⠉⠿⠉⠹⠏⠉⠻⠉⠉⠛⠉⠙⠟⠉⠹⠏⠉⠻⠉⠙⠛⠉⠹⠏⠉⢛⣿
⠀⠀⣇⡀⢺⠒⠓⠓⠂⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠚⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠚⠒⠐⠚⠚⠒⡗⠀⣸
⠀⠀⡏⠉⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠈⢹
⠀⠀⡿⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢿
⠀⠀⣧⠄⢹⠀⠀⠀⠀⠀⠀⠀⣾⢯⠉⠉⠉⡛⠯⢏⡝⠀⠀⠀⠀⠀⠀⢀⣴⣽⡉⠹⣍⠯⣟⡏⠉⠉⡯⠃⠀⠀⠀⠀⠀⡇⠠⣼
⠀⠀⣇⣀⢺⠀⠀⠀⠀⠀⠀⠀⣟⠂⠀⠀⠀⠞⣠⠞⣯⠀⠀⠀⠀⠀⣠⠞⡏⠀⢱⡰⠖⢦⡡⠄⣠⠋⠀⠀⠀⠀⠀⠀⠀⡗⢀⣸
⠀⠀⡏⠁⢸⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⡶⠄⠬⢄⡕⠀⠀⠀⢀⡴⠃⠀⠘⠆⠀⠁⠀⢸⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢹
⠀⠀⡿⠂⢸⠀⠀⠀⠀⠀⠀⠀⣾⢓⣩⡄⠥⠀⢀⣀⣾⠀⠀⣠⠿⠁⠀⠀⠀⠀⠀⡏⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢿
⠀⠀⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠸⢇⠀⠀⣀⣀⠈⠻⢀⣼⣻⡌⠀⠃⠉⢙⡀⢘⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣼
⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠖⠈⠁⠀⠈⠀⠉⡗⠋⠀⠑⢇⣀⢀⡀⣸⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⡟⠁⣸⠀⠀⠀⠀⠀⠀⠀⢯⡱⠄⠊⠉⠉⠉⢫⠃⠀⠀⣠⣾⣟⣟⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⢻
⠀⠀⡷⠆⢸⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡰⠒⠉⠉⠰⡷⠶⠒⣿⡖⣏⠀⡓⣿⡥⠴⠆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⢾
⠀⠀⣧⡄⢹⠀⠀⠀⠀⠀⠀⠀⢿⡜⠁⠀⡤⠒⠁⣘⡄⠀⠀⠈⢻⣧⣧⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣼
⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠂⢤⠎⠀⣠⠊⠉⡿⠂⢀⡤⡋⠀⠀⠀⢳⣄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⡟⠀⢰⠀⠀⠀⠀⠀⠀⠀⣯⢰⡇⠀⢨⠁⢀⡜⣷⠀⠙⣿⣄⢀⡄⣀⢸⡁⠉⢤⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻
⠀⠀⣷⠄⢸⠀⠀⠀⠀⠀⠀⠀⢿⡭⡛⠏⡅⠀⢈⠀⣿⠀⠀⠈⠳⣆⠀⢲⠀⠐⢄⡀⠈⠉⢵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣾
⠀⠀⣇⡀⢸⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠓⠐⣚⠀⢏⠀⠀⠀⠀⠙⢆⠀⠓⢄⠀⠁⠁⣖⠒⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣸
⠀⠀⡏⠉⢼⠀⠀⠀⠀⠀⠀⠀⣟⡀⠀⠀⠀⢢⠹⢶⣎⠀⠀⠀⠀⠀⠈⠳⣄⠀⠝⠰⠤⡟⢵⠂⠀⠙⣄⠀⠀⠀⠀⠀⠀⡧⠈⢹
⠀⠀⡟⠂⢸⠀⠀⠀⠀⠀⠀⠀⢿⣞⣀⣀⣀⣭⣗⣎⣻⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣔⣂⣖⣮⣇⣀⣀⣙⣗⡄⠀⠀⠀⠀⡇⠐⢻
⠀⠀⣷⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⣾
⠀⠀⣇⡀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢀⣸
⠀⠀⡏⠀⢸⠤⠤⡤⠄⠤⡤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⡤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠠⢤⢤⠤⠧⠈⢹
⠀⠀⣿⣥⣀⣰⣇⣀⣤⣀⣀⣦⣀⣰⣆⣀⣴⣄⣀⣦⣀⣀⣦⣀⣰⣆⣀⣷⣀⣀⣤⣀⣠⣦⣀⣰⣆⣀⣴⣀⣠⣤⣀⣸⣄⣀⣦⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⣀⣤⠀⢀⠔⠚⢩⠂⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠈⠁⠀⡁⠁⠀⠀⠀⢩⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣁⣀⡏⣠⣡⣴⡖⣓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠘⡄⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⣤⣬⣿⣛⣛⣉⣭⠽⠿⣕⠤⣀⠀⠀⠀⠀⠀⡠⠰⡄⠀⠀⠀⠰⠁⠀⠀⢀⠛⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠛⠀⠒⠐⠒⠖⢺⠒⠳⣟⠷⠀⠅⣈⠀⠀⠀⠀⡎⠀⠀⢡⠀⠀⠀⠆⢀⠀⠀⠌⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢐⡇⠘⣀⡀⠀⠈⠈⢣⢱⡀⠀⠱⠀⠀⢰⠀⠠⠀⢸⡀⠀⢀⡀⠐⡂⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡔⢉⣀⡀⠀⠀⠈⠳⡄⠐⠈⢣⡵⠀⠀⠑⢄⠘⡄⢔⠀⠀⡇⠀⠸⠀⠅⠒⠠⠀⠥⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢪⡀⡃⢸⠉⠑⣀⣁⠀⠀⠀⠀⠀⠀⠀⠈⡄⠠⢐⠀⠀⢰⠀⡠⠀⠭⠰⠆⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠘⠢⡈⠁⠘⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⣯⣄⠢⠀⢸⠰⢁⡒⡨⠋⡒⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡤⡄⠀⠀⡜⠒⢄⠙⡆⠀⠀⢀⡡⢂⠔⠠⠂⣀⠄⢹⣎⣀⣶⠥⠂⣔⡁⠤⠖⠂⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠘⢄⠘⠒⠀⠀⠀⠊⠀⡘⠀⠀⡠⠒⠡⢊⢔⠞⡡⠖⠉⠀⢀⠤⠒⠒⠒⢤⡎⠀⠀⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡂⠀⠀⠀⠈⠑⠒⡄⡐⠒⠀⠂⠁⠀⠀⣀⠄⡂⢑⠔⠋⠀⠀⠀⠀⠘⢔⠢⣀⡠⠾⠁⠂⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠡⠂⢀⠀⠀⠀⠉⠁⠀⠀⠀⡀⠔⡈⠔⣈⠔⠁⠀⠀⠀⠀⢀⠀⠑⠀⣽⠫⠭⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⣰⡥⠞⠚⠛⠛⠉⠁⠀⠋⠓⠒⠂⠈⠁⠀⠀⠀⠀⢠⠒⠀⣀⠴⣙⠲⠈⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⣠⠺⢅⡒⠠⠈⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⢀⡜⠭⣑⠂⠈⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈⢀⣤⠪⠌⠁⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠀⠀⠀⢀⡀⡀⠐⠁⠔⡡⠞⠁⠔⡀⠀⠠⠔⠺⠉⠂⠁⣀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⠄⣀⡀⠀⠨⠊⡠⠊⣠⠊⡀⠊⢡⠊⠐⡡⠀⢀⣀⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠉⠐⠒⠠⠾⣡⣊⣀⠔⡡⠊⢔⠐⠊⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠉⠐⠂⠤⠄⣀⡀⠀⠀⠀⠈⠈⠁⠐⠒⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡁⠄⠂⢀⡀⠀⠉⠑⠒⠠⠄⢄⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢁⠠⠐⠀⣀⠤⠒⢉⡠⠔⢀⡠⠄⢀⠉⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠤⠂⢁⠄⠂⣁⠄⢊⡡⠐⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠐⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⢀⡠⠀⢂⡀⠄⠒⡀⠄⢒⡀⠤⠐⣈⠠⠐⣀⠡⠐⢈⠡⠐⢂⠡⠀⢂⠨⠐⠂⠡⠄⠂⠀⠀⠂⠁⠐⠀⠡⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣄⣠⣤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢴⡖⠀⠲⠎⡱⠖⠀⢲⡦⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣤⠀⠉⠀⠰⠳⠀⠀⠈⠁⠀⠀⠖⠆⠀⠉⠀⣤⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⢈⡤⠀⠀⣀⣤⣶⢿⣿⣿⡿⣶⣤⣀⠀⠀⢤⡁⠰⣆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣄⠀⠀⠀⠐⣠⣾⣟⢿⠙⠰⠃⠘⠆⠋⡿⣻⣷⣄⠂⠀⠀⠀⣠⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⢠⡕⠆⣼⣿⣿⣿⠀⢣⡰⠀⠀⢄⡔⠀⣿⣿⣿⣧⠰⢊⡄⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠈⠀⠛⢿⡏⠸⠋⠀⢈⣵⡎⢱⣮⡁⠀⠙⠇⢹⡿⠋⠀⠁⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣣⣉⣥⣀⠀⠀⠀⣀⡠⠟⠰⣧⣼⠇⠻⢄⣀⠀⠀⠀⣀⣌⣉⣈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠻⣇⠀⠍⠵⣤⠀⠀⡍⠃⠀⣶⣾⣷⣶⠀⠘⢩⡀⠀⣤⠎⠩⠀⣸⠟⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⠠⡄⠀⠀⠀⠀⠈⠀⠀⠚⠏⡹⠓⠀⠀⠁⠀⠀⠀⠀⠠⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠈⣷⡈⣯⠉⢿⣿⡄⠀⠀⣤⠞⠳⣤⠀⠀⢰⣿⡿⠉⣽⢁⣾⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⢷⠈⠃⠀⠀⠀⣤⡜⠁⠀⠀⠈⢣⣄⠀⠀⠀⡘⠁⡾⢃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠻⣇⡚⠓⠀⠀⠀⣇⠀⡖⢱⠀⣸⠀⠀⠀⠚⢓⣘⠟⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣤⠼⠉⢲⠤⠀⠀⠹⣆⠑⠋⣰⠏⠀⠀⠤⡖⠉⢧⣤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣠⣀⣤⣤⠀⠠⠀⠀⠘⣧⣼⠃⠀⠀⠄⠀⣤⣤⣀⣤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠀⠰⢠⠀⠀⡐⠀⠁⢂⠀⠀⡄⠂⠀⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢻⡇⠐⠁⠀⣰⠁⢀⡀⠘⣇⠀⠈⠀⢪⡟⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⡜⠋⠇⣸⣇⠸⠙⢣⠀⠀⢁⣠⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⢿⠧⠀⠝⢷⣴⢼⡧⣦⡾⠫⠠⠼⡿⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠢⠀⣃⡄⠄⠉⠛⠛⠁⠠⢠⣌⠀⠐⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣃⣀⡴⢦⣀⣘⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⣄⠀⠀⠀⢀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⢠⡀⠸⠀⠀⠀⠀⢀⣸⠀⣀⠔⠋⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⢇⠦⠀⠀⠀⠳⡀⡇⠀⠀⢀⡄⠈⠛⠭⣀⢄⠀⠀⠐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢆⣰⠎⠍⠀⠙⣿⣟⣁⠈⠀⠀⠠⠓⡼⠦⠑⠎⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⣄⠉⢀⣤⣤⡶⣶⡁⠈⠙⠪⢲⡀⡀⡐⣰⣇⣠⣿⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⢷⣤⠃⣤⣄⠎⠀⠫⣄⣠⡀⠀⠑⣷⡼⠟⣫⡴⠞⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠢⢌⡓⠿⠵⣦⣤⣄⣀⠤⠼⠧⠤⠚⠛⠋⣁⣠⠖⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠂⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠴⠖⠋⠉⠉⠁⢠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠃⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⢀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⠤⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⠡⣄⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠒⠒⠀⠀⠐⠒⠒⠋⠉

⠀⠀⣒⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢀
⠀⠀⠈⣹⠆⠀⢀⣠⢴⡶⡶⠒⣶⠦⣄⡀⠈⠙⢾⣅⣀⡴⠶⠦⡄⠈⢳⡴⠚⠁⣀⠤⢶⣖⠛⠟⢛⣓⠲⣄⡀⠀⠺⡅
⠀⠀⣸⠃⢀⡴⡏⠙⠛⠓⢆⠀⠀⠁⠀⠉⠉⠙⠛⠛⢿⡀⠀⠀⢹⡄⠀⢃⠀⠈⠁⠀⠃⠈⠁⠈⠉⠉⠛⠛⡛⡇⠀⢳
⠀⢀⡇⠀⡼⠛⠀⠄⢀⠀⡄⡁⠀⠀⠀⠀⢰⠀⠁⢠⡀⠙⢦⡰⠋⠁⠀⠀⠀⠀⢠⠄⠀⠀⡀⢀⡀⠀⠀⠀⠀⢽⠀⢸⡆
⠀⠐⡇⠀⢰⡀⠒⠈⠀⠀⠀⣶⠀⠀⠀⠀⢨⠀⠀⡼⠹⣄⡜⠁⠀⠈⠀⠀⢈⠄⠁⢀⡴⠁⠀⣀⠀⠈⠀⠂⠀⠀⠀⢸⠇
⠀⠀⠃⠀⠈⠀⠀⠀⠚⠉⠉⣿⠀⠀⠀⠀⢸⠀⣰⠃⠀⡿⠀⠀⠐⠀⢀⡶⠋⢀⣴⣯⠖⠋⠉⠉⠙⠳⢄⠀⠘⠀⠀⠌
⠀⠀⠀⠤⠀⠀⠱⢤⣀⣀⣀⣿⣠⢤⡄⠀⢸⣶⠁⠀⢰⠁⠀⡀⠀⠑⠁⣠⠖⠁⡜⠛⠲⠤⢤⣤⣤⡤⠖⠃⠀⠀⠌
⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⡀⠀⣀⣠⠇⠀⢸⣹⠀⠀⡟⠀⠀⠇⠀⢸⡞⢻⠀⠠⡟⠶⢤⣀⣀⣀⠀⠀⣀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⢹⣿⠉⠀⠀⠀⢸⡏⠀⢀⡇⠀⠀⢀⠀⢸⡇⠸⡆⠀⢷⡀⠀⠀⠈⣯⢠⠞⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠰⣄⠀⣼⠏⣿⠀⠀⠀⠀⢸⠁⣠⠞⠁⢀⡄⠀⠀⢸⠃⠀⠹⣄⠀⠳⣄⡀⠀⢻⣏⠀⣠⠋
⠀⠀⣀⠀⠀⠀⠀⠈⠓⠶⣊⣻⠀⠀⠀⠀⠸⠟⠁⠀⠀⠈⠀⡀⠀⠈⠀⠀⠀⠈⠳⢤⣀⠉⠓⣲⠴⠊⠁⠀⠐⠢⢠⡀
⠀⠈⣯⣄⠀⠀⠀⠀⡀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠀⠀⠀⠀⠀⢀⡼⠛⠉⠀⢀⠀⠀⠁⠀⠀⣠⣭
⠀⠀⠘⡍⠙⠄⡀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠐⠀⠀⠠⣀⠀⠀⠀⠀⠁⢠⠀⠠⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⢀⠀⠏⢸⠁
⠀⠀⢰⡇⠀⣸⡡⠒⠀⢀⡀⢀⠀⠀⠀⢀⡀⠀⠠⣄⡸⠳⣄⠀⠀⠀⠀⠙⢤⣀⠀⠉⠑⠦⠄⣀⠀⠀⠢⣜⡇⠀⢸⡆
⠀⠀⢸⡇⠀⢿⠀⣠⣖⠻⡷⣿⠀⠀⠀⠀⢹⣆⠀⠘⣇⣠⢾⡳⣄⠀⠀⠀⠀⠙⢯⣿⣏⣸⣭⣯⠿⠦⣀⢈⡇⠀⢸⠃
⠀⠀⠀⣃⠀⠈⠛⡙⠞⠀⠋⠛⠀⠀⠀⠀⢸⠛⢧⠀⠸⡇⠀⠑⣌⠳⣄⠀⠀⠀⠀⠙⢧⣤⡹⠁⠈⠑⠈⠿⠁⢀⡿
⠀⠀⠀⠀⢳⣄⡀⠈⠑⠐⠚⠛⠀⠀⠀⠀⢘⠠⢾⠀⠀⡃⠀⠀⣸⠓⠈⣓⣀⠀⠀⠀⠀⠙⢠⡶⠖⠚⠁⠀⢰⡋⠀⣃
⠀⠀⠀⠀⢸⢩⢭⠓⡦⠠⠤⠄⠀⠀⠀⠀⢸⡇⢸⠀⠀⡃⠀⠀⢻⠀⠀⡿⠟⠷⡄⠀⠀⠀⠀⠻⣦⡴⣚⠉⢸⡇⠀⣿
⠀⠀⣆⠀⠈⡌⠀⡐⠃⠨⢗⡄⠀⠀⠀⠀⠘⣁⠆⠀⣀⠁⠀⠀⠸⡆⠀⠹⡉⢗⡊⢂⠀⠀⠀⠀⠈⠑⢦⣔⣰⠁⠀⡿
⠀⠀⢹⡄⡀⠙⢾⣉⠖⣾⠛⢶⣲⠖⣐⣶⠶⠟⣻⣷⠃⠀⠀⠀⠀⠙⣄⡀⠈⠲⣟⡻⢶⠶⠒⡖⠲⠶⢒⡾⠛⠛⢻⡇
⠀⠀⠀⡇⣸⣄⠀⠉⠛⠛⠓⠒⠒⠚⠉⠀⠀⠉⠀⠈⢧⡀⠀⠀⢀⡴⣉⣉⡁⠀⠀⠉⠛⠒⠚⠛⠒⠊⠁⠀⣠⡄⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢤⡀⠀⠀⠀⡀⠀⠀⠠⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠻⣾⣄⠀⣧⠀⢂⡀⠀⠀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⢸⣿⣷⣽⣶⣿⣾⡀⠰⣄⡀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣀⡴⣶⣾⣿⣿⡿⣿⠛⠙⠻⣶⣾⣿⣶⣶⣶⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠉⣾⢏⡟⣸⠑⠃⠉⣀⠀⠀⢆⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢸⣿⡾⠱⠇⢀⡀⠀⠀⠀⢀⣬⣄⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⢀⣀⢤⡤⠤⢠⠄⠤⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢰⣷⣤⣤⠖⠛⢋⠉⠉⠉⠉⠉
⠀⠀⠀⢀⣴⣦⣶⣿⣾⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠓⠈⠀⠀⢠⡍⠉⠀⠀⠀⣼⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡟⠁⠀⠀⢀⣤⣿⣷⣤⣴⣤⣼⠿⠛⠛⠛⠛⠛⢅
⠀⠀⠀⣿⡿⠋⠟⠿⠟⢻⡇⣇⠀⢸⡶⠖⠂⠀⠀⠀⣀⣤⣾⡟⠀⠀⠀⠀⣾⡿⢿⡏⡟⠋⠁⢂⢺⡆⠀⠀⠀⠀⡨⡇
⠀⠀⠀⡀⢁⠀⡀⣀⢰⢸⣇⢸⠀⠈⣧⣶⣤⣄⣐⣶⣿⣿⠏⠀⠀⠀⠀⠀⢿⣧⣼⡇⢳⣦⣀⣼⣾⣶⣶⣿⣿⣿⣿⡇
⠀⠀⢸⣧⣸⣼⣧⣿⣾⣿⣿⠸⡆⠀⢸⣿⣭⣷⣶⣶⣿⡟⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣾⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣇⠀⠀⣿⣿⠿⠿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡄⠀⢸⡇⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠠⣤⣄⢸⣇⢸⡇⠹⣿⡇⠀⠀⠀⠀⠀⠤
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢧⡀⠀⠿⠀⠀⢸⣯⣄⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣼⣧⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⠀⠀⠀⠀⠈⢸⣿⣿⣶⣤⣀⠀⠀⠀⠈⢹⡿⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠘⠈⠛⠿⠿⠿⠿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣴⠤⠶⠛⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢘⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠀⠀⠀⢈⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠀⠀⠀⠀⠀⠐⠀⡴⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠀⠀⠀⡧⠀⠀⠀⠀⠀⠸⢧⡇⠀⠀⠀⡇⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠀⡀⠀⠀⢰⠀⠲⠁⠀⠀⠼⠀⠀⠀⠀⢶⡄⠀⠈⡇⠀⠀⠁⠇⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⡄⡄⠀⠀⠘⠒⡆⠀⠀⠀⠀⠌⠀⠀⡠⢫⠗⠀⠀⠃⠀⢀⠄⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠆⠰⠁⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣹⠁⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠄⢶⠀⠀⠀⠀⡈⠀⠀⢠⠀⠂⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⡆⠈⣧
⠀⠀⠄⠂⠀⠀⢀⣧⠀⠂⠀⠀⠈⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⣠⣮⣤⡤⠤⠀⠀⠀⣼⠀⠀⠀⢡⠂⣹⡃⠀⠀⠀⣠⣄
⠀⠀⠀⠀⢇⣀⢈⡀⠀⡀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠈⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⢰⠆⡭⣿⠀⠀⠀⣟⠙⠁
⠀⠀⠀⢈⠼⣿⡿⢤⡦⣍⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡕⣿⡖⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⡐⢆⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠇⠀⠀⢸⡀⠀⠂⠀⣀⠤
⠀⠀⠀⠀⠀⠂⠡⢾⣿⡿⠀⠀⠀⠀⠀⠀⠀⡀⠦⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠀⠤
⠀⠀⠀⠀⠀⠀⠐⢃⡇⢿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡆⠀⠀⠀⠶⠖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠛⡀⠀⡀⠌⠀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢤⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡜⠠⠆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⢘⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡜⠀⡡⠀⠑⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠑⠀⢁⠀⠀⠀⠀⠀⠀⠀⠱⡧⠿⢿⡇⠀⠀⠰⢠⢸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⠋⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢤⠀⠋⠀⠘⡄⠂⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⣈⣀⠐⠄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡀⢀⡀⠁⠀⠐⠻⡆⠀⠀⠀⠀⠀⠀⠀⣠⠘⡄⠀⠀⠠⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠬⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢂⠠⡇⠀⠁⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠻⠇⠑⡀⠀⢠⠄⢠⡂⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⣈⠠⠄⠀⠈⢻⢢⡀⢻⡄⢷⡀⠀⠀⠀⠀⠰⣆⡀⠀⠸⣇⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠁⠀⢀⠀⠀⠀⠉⠙⢦⣽⣄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡂⢀⠄⠐⣿⣧⡄⠀⠈⠙⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡠⠔⢫⠆⠀⠹⡿⠱⠄⠀⠐⠂⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠠⢁⠜⡿⡕⠌⣟⣵⡚⣷⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨⠥⡾⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠁⠰⣯⡓
⠀⠘⠦⠅⠱⡀⠈⠀⠞⠓⠀⠄⠀⠀⠀⠀⠀⠖⠚⠀⠀⠀⠀⠀⠀⠀⢱⡀⡀⠄⠀⠀⠀⠀⠀⣡⡄⠀⠀⠀⣸⠀⠐⠶⠋⠠
⠀⠀⠀⠀⠀⠈⠓⠤⣀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠁⣤⡀⠀⠀⠙
⠀⠀⢀⠤⠄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⢈⡈⠀⣉⡈⡀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡂⠀⣰⠂⡄⠀⠀⠀⠀⠀⠀⠸⠔⡲⡛⠉⣻⠑⠜⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⣀⠀⠀⠀⠀⠀⠴⢊⠃
⠀⠀⠀⠀⠀⠀⠰⠘⠁⠁⠀⢈⣬⠤⢤⡀⠀⠀⠀⠀⢀⠎⠀⣔⣺⠆⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⢄⡈⠘⠁⢀⡀⠀⠀⢀⠀⣻⡅
⠀⠀⠀⠀⠀⢰⠉⣉⢽⡷⠚⠻⡇⢕⠶⠁⠀⠀⠀⠀⢸⠀⠠⢬⣽⠆⠀⠀⠀⠀⠀⠀⠀⢈⣉⡭⢶⠿⣤⣀⣈⠁⠂⠀⠸⠄⠈
⠀⠀⠀⠀⠀⠘⠊⣡⠋⠞⢰⣤⡑⠂⠡⠀⠀⠀⠀⠀⠾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠂⣀⣁⠄⢠⠏⣩⠉⡆
⠀⠀⠀⠀⠀⠀⢰⠁⠀⢼⣭⣽⡙⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⡀⢸⣽⡹⣯⠈⠂⠊⠉
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢤⣸⣹⡽⠀⢠⠀⢆⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠿⣄⠀⠀⡱⣯⣎⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠠
⣑⠄⠀⠀⠀⠀⢸⠁⠀⠀⠸⠙⠀⠀⣉⠀⠞⠀⠀⠀⠀⠀⣈⣉⠛⠀⠀⠀⠀⠀⠈⠑⠤⣀⠁⠀⢀⠆⢀⠂⠀⠀⠀⠀⢀⠠⠀⠉⣤
⠕⠠⡀⠀⠀⠀⠘⠓⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠰⠁⠰⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠄⠠⠎⠀⠀⠀⠀⠀⣂⠄⣶⡞⠉
⠆⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡜⡙⠑⣰
⣫⡷⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⣤⡰⠁⠀⠀⠀⠀⠤⢄⠀⠀⠀⠠⠀⠶⠒⡏⠄⠀⠀⠀⠀⠀⠀⠀⡤⠚⠀⠀⠀⠀⡇⠀⠛
⠉⢂⠀⠊⠁⠀⠀⢀⡀⠀⠀⠀⠠⠀⢀⡿⠉⣫⣤⠄⣀⠀⠲⢀⠀⠀⠀⢀⠁⢰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠸⡄
⠂⠁⠀⠀⠀⠀⢠⡤⠖⠔⠀⠀⢨⢀⠋⣿⡐⠘⣧⠿⢱⡧⠀⠌⠀⠀⠀⣬⠀⠙⠋⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⢹⣤
⠀⠀⠀⠀⠀⠀⠍⢠⣦⠀⠀⠀⠀⠘⠤⠇⠱⣀⠀⠀⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡤⠈⠠
⠀⠀⠀⠀⠀⠀⡄⠐⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡤⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⢀⠠⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⢠⢀⣦⢻⡕⢻⠆⠀⠘⣦⠀⢀⠈⠁⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢂⣤⣠⣤⡆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣷⡎⠈⢋⠓⢋⠀⢀⡴⠋⠁⠀⠀⠰⣾⡁⢸
⣻⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣨⠞⠍⣀⠸⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠆⠀⠙⡶⢷⣒⠒⠊⠁⠀⠀⠀⠀⠠⡐⢸⠀⠺
⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢮⣝⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠘⠤⣈⠢⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠎⠁⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡼⠀⠐⢦⡬⠇⢀⠈⡀⠀⠀⠀⠀⠀⠃⣤⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠐⠤⢠⣄⠼⠀⠀⠀⠀⠀⠐⠳⠀⠄⠈⠀⠀⠤⠀⠁⠀⠀⢀⠡⣴⡞⠙⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⠀⢈⡈
⠐⠤⠀⣰⠏⠑⣂⣄⠀⠀⠠⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⢱⠀⣼⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠟⢉⠹⠑⠊

⠀⠀⠀⢠⣤⣠⠔⠒⡒⢒⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⡀⢀
⠀⠀⠀⢈⢧⠙⠂⠀⠽⠞⢷⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⢩⡻⣿⠂⠂
⠀⠀⠀⠈⡇⢠⠄⠠⣄⠀⠊⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠁⠈⠉⣠⠏
⠀⠀⠀⠀⡇⢿⡰⡁⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡠⠚⠁⠀⠐⠊⠁
⠀⠀⠀⢠⡇⢈⣿⡢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⣞⠟⢑⡲⠖
⠀⠀⠀⣼⠃⠙⣩⠙⣦⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠊⣰⣾⡿⠊⠁
⠀⠀⠀⢸⡄⠀⣹⢾⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣠⣾⢻⡿⠁
⠀⠀⠀⠸⡇⢠⣉⣠⠞⡽⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢋⡿⢣⡿⠁
⠀⠀⠀⠀⢷⢈⣿⠗⠀⠁⠀⠀⠀⣀⢠⣆⠀⢉⡍⠉⠉⣠⠟⠁
⠀⠀⠀⠀⠸⣼⠱⣅⢤⠆⠀⣤⣶⣾⣿⡟⠀⠀⠹⠿⠚⠉
⠀⠀⠀⠀⠀⡍⠃⠀⠋⠀⠀⢈⣩⡭⠤⢬⣍⠙⢦⡀
⠀⠀⠀⠀⢀⠡⣞⠉⢟⣠⣾⠋⢵⣶⡟⢀⡤⡑⠀⢹⣆
⠀⠀⠀⠀⠸⠠⠬⠿⠟⠛⠥⠜⢠⠏⠀⠸⣼⡉⢠⠲⣿⣆⡶⢦
⠀⠀⠀⠀⠆⠀⡶⢀⣒⣆⠀⢀⠞⠀⠀⠀⠙⠻⣦⣉⠙⣿⡦⠴⠇
⠀⠀⠀⠀⠂⡤⣷⡹⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡙⢂⣰⠄
⠀⠀⠀⢠⠀⡀⣼⢿⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡻⣶⣤⣄
⠀⠀⠀⢸⠀⢧⠀⣖⣨⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠀⡝⣿⣦⡀
⠀⠀⠀⣿⠀⢸⠀⣟⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣑⣄⣿⠈⢿⣷⠄
⠀⠀⠀⣿⠀⠃⢦⣤⠞⠁⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣇⠀⢻⣏⢆
⠀⠀⠀⡿⣼⠀⣰⢟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢆⠀⢻⡌⡄
⠀⠀⠀⢁⢳⡀⢿⠘⢒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣑⣄⠻⡔⡀
⠀⠀⠀⠘⣬⡷⠀⢁⣀⡠⠾⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡺⣄⢨⢅⣹⣤
⠀⠀⠀⠀⡹⠁⠀⢀⣀⠈⣢⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠙⠻⠛⣿⢧⡀⠀⠠⣄⡀
⠀⠀⠀⣼⡧⢎⠀⠠⠞⠽⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣠⣿⡌⠻⣤⣀⣼⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡶⠾⠛⠁⠈⠙⢛⣛⣛⣻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠥⠶⢶⣦⣀⣴⠖⠻⠶⠛⠉⢉⣽⡿⠁⣀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠈⠁⠀⠀⠀⠀⠀⣰⣿⣿⡾⠟⠛⠋⠉⠉⠙⠛⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⡀⠀⣀⣀⣤⣴⣿⣿⠿⠶⠶⠶⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠿⠿⣿⡭⠾⠛⠙⠿⣷⣤⣀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⡀⠀⠀⠀⠀⠉⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⣤⣄⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢻⣿⡀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⠀⣿⣇⠙⢿⣷⡄⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢸⣿⡇⣿⣿⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢸⣿⡇⢿⣿⠀⠠⠿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣘⣿⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⢻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣿⠀⠀⣿⣿⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⢸⣿⡇⠀⢸⣿⡆⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⣿⣷⠀⠀⢿⣷⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⣸⣿⡆⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⠛⠋⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠀⠘⣿⣧⣄⣀⣈⣻⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠛⠛⠻⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⠶⠾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣟⠉⠁⠀⠀⠤⡀⣀⣀⢰⣶⡄⠀⠀⠠⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡄⠀⠀⠀⠀⠀⣆⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠙⠉⠙⠿⠆⠀⠀⠾⠃⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠟⠁⠀⠀⠀⠶⠀⢻⣆⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢄⠀⠀⠀⠀⢰⡿⢀
⠀⠀⠀⠀⢀⠴⠀⠀⠀⢿⠉⠁⢉⡀⡀⠀⠀⠀⠀⠀⢻⣦⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠘⢸⣧⡀⠀⢀⣸⡥⠞
⠀⠀⠀⠀⢹⡤⣀⡀⢀⣼⣴⡆⢻⣶⡔⠀⠀⠀⠨⠣⣯⢻⣿⣶⢪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣿⣿⣿⣿⣿⡇
⠀⠐⣦⠀⠈⠃⠀⠄⠚⠋⠘⠉⠉⠹⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣸⠀⠂⠀⢀⠠⢴⣤⣄⣒⣚⣉⠁⠀⢹⣿⣿⣿⣿⡇
⠀⠀⣿⣷⣶⣤⣤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡸⠁⠀⠯⠍⠲⡶⣞⠡⠀⠞⠙⠂⢰⣦⣬⣝⠂⢸⣿⣿⣿⣿⠇
⠀⠀⣿⡟⣾⠿⣿⠀⠀⠀⢀⣀⣀⣤⣴⣶⣶⣿⣿⡟⠁⠆⠀⠠⠈⠃⢀⣴⣾⣿⣶⡾⠿⠟⠛⠻⠿⣿⣌⣿⣿⣿⣿
⠀⠀⣿⣿⣷⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢤⡠⠁⢀⣴⣿⣿⡿⠋⠁⣠⣤⣶⣾⣿⣿⣿⣟⣦⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢠⣿⣽⡟⠁⢀⣴⣿⣿⣿⣷⣿⣿⡿⠿⠿⢿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠖⢰⣿⣿⠏⠀⣴⣿⣿⣿⣿⣿⠟⢋⣠⣴⣶⣶⣶⣶⣿⢿⠆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⣿⣿⣿⣧⡀⣈⣨⣁⢀⣀⣹⣿⣿⣿⠋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢻⣿⣿⣿⡁⣫⣙⡉⣸⣿⣿⣙⡙⢁⣸⣛⢉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⣿⣿⣷⡹⣿⣏⣿⣻⣿⡟⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠐⠙⠿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠃
⠀⠀⠀⠹⣟⣿⣿⣿⣿⣿⣻⡿⠽⠗⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠐⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⠋⠉⠉⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⣡⠄⡖⠖⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣀⣤⣤⣤⣤⣤⣦⣴⣸⠤⠴⠂⠈⠤⠦⠄⠀⠉⠈⠁
⠀⠀⠀⠀⠠⢤⡤⣾⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡈⠉⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠉⠉⠀⠈⠈⠈⠙⠻⠿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣻⣿⣿⣿⣿⣿⣿⢋⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢫⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠈⠻⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠿⠹⣿⡿⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⠿⣯⠙⢷⣄⠙⢿⣿⣷⣆⣀⣠⣤⣤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⣶⣦⣾⣿⣷⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣿⡯⠀⠀⠙⠟⢦⣍⡛⠻⠿⠿⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠿⠞⠙⣻⣿⣯⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣿⣿⣿⣝⡛⠷⢤⣌⣛⣿⢿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⢛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⡀⢀⠀⡀⠀⣀⢀⡀⢀⠀⠀⣠⠤⠤⣀⣀⣀⣀⣀⡤
⠀⠀⢘⠆⢸⡆⢸⠀⠈⢰⡇⢸⠀⠞⢁⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⣀⣀⡤⠈
⠀⠀⠟⠀⠈⠁⠟⠀⠇⠸⠀⠆⠀⠐⠤⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢸⣀⣈⡇
⠀⠀⠀⠀⠐⠒⠒⡂⠀⠀⠆⠐⠀⣀⠀⠰⠆⠀⠰⠄⢀⡀⠀⣠⠀⣤⢠⣄⢠⡄⣤⠈⣄⡀⠀⡀⡌⠀⠄⠉⠀⠀⠘⢠
⠀⢸⠀⢠⠴⠀⠀⠆⡄⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⡉⠀⠉⠉⢉⠉⡀⠉⠀⠀⡀⠀⡀⠀⠀⡄⠀⣀
⠀⠈⠀⠈⠠⣄⡤⢀⠁⠀⠂⠀⠀⠈⠀⠀⣁⠀⣤⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠠⠈⠍⠅⠠⠆⣀⠀⠛⠀⠠⠤⠇
⠀⠀⠀⠀⠀⡆⠒⢀⠠⠀⠀⠀⠀⠁⠀⠀⠉⠂⠉⠂⠐⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠚⠁
⠀⠀⠀⠀⣔⠀⠄⢂⠀⠀⠀⠀⠀⠀⠘⡆⢘⣇⢀⣀⡀⢀⣐⠋⢉⣉⣉⣙⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⢊⠀⠀⡁⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢀⡉⠋⣉⢱⡘⣦⢠⣦⡄⡴⠟⢀⣤⡄⣠⡄⠀⠀⠀⠀⠀⠀⠠⠰⠆
⠀⠀⠃⡀⠸⠀⠀⠠⠀⠀⢂⣀⢀⢰⠀⠹⡄⠀⢸⢸⡷⠠⣿⢸⠇⣿⢸⣿⡇⣇⠀⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠋
⠀⣺⡀⠀⠀⠆⠐⠠⠀⠀⢸⠀⡄⢸⠀⠀⢘⡆⢸⣈⡵⣄⣡⠞⢰⣋⣈⣿⣇⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⡀⡁⡄⠁⡀⠀⠈⠀⠉⠉⠉⣉⡀⣀⣠⡭⣤⣀⣀⣘⣡⣤⣀⢀⣀⣀⣙⣁⣀⡀⣁⣈⣀⠀⠁⢁⠀⠀⠀⠀⠀⠄⠠
⠀⠃⠀⠒⠲⠌⡇⠐⢂⠀⠄⠐⠈⢧⢻⠇⡆⣰⡆⠈⣿⡇⠀⣶⠌⢋⣤⡁⢴⣾⡇⡇⣏⢚⣻⡇⠂⠀⠀⠂⡀⠀⢀⡄
⠀⠀⣠⣤⢄⠀⠀⠀⠈⠓⠀⠀⠀⠈⡇⢸⡇⢿⡇⠀⣿⡇⠀⣔⢾⣷⡝⠿⢨⣿⡇⡇⢷⢻⠙⢁⣈⡀⠈⠀⢛⢩⢫⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⣷⣸⡷⣤⠴⢧⣙⣡⣄⣿⣈⣧⣉⣴⣬⣽⣧⣿⣿⣼⠐⡓⠛⠃⢠⠆⠘⠞⠚⠋
⠀⠀⠰⠃⠀⠀⢀⠀⠀⠈⠛⠛⠃⠀⠀⣉⣡⣤⣤⠀⠉⠀⠉⠉⠀⠹⠏⠀⠔⠂⢄⠀⠈⠈⠀⠸⣴⠀⠉⠀⠀⡀⠀⡶⠆
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠠⢀⡀⠁⠀⣄⠠⠈⠢⠐⣁⣤⣶⣤⣄⠀⠁⠀⠿⣿⠿⠀⠀⢸
⠀⠀⠄⡞⠁⠈⠈⠉⠉⠙⠂⠀⠀⠀⠄⠀⡤⠀⠀⠀⠈⠀⢅⡀⠒⠚⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠄⢈⠰⠀⠀⠈
⠀⠀⠀⠃⢠⠤⠀⠀⢶⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢤⢠⡄⠀⠀⠄⠀⡆⠉⠂⠠⠀⠀⠀⠒⠄⠂⠁
⠀⠀⠀⡄⠀⠐⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡁⠐⣆⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠁⠁⠀⠀⣄⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⡀⠈⠀⠀⠀⠀⠠⠁⢰⠆⠀⠠⠀⠀⠀⠧⠀⠁⠴⠶⠀⠰⠶⠄⠀⠃
⠀⠀⠂⠐⠀⠀⠀⠀⠈⠐⠀⠄⠀⠸⠀⢀⠀⠀⠠⠀⠀⠀⠰⠀⠀⡐⠀⢸⠀⡖⢲⡆⢰⡂⣤⠒⠖⢆⢠⡠⠀⠲⠖⢶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠘⠂⠀⠀⠀⠈⠈⠁⠈⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡤⠒⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣿⠏⠀⠀⢱⠀⠀⠀⠀⠀⠑⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⣿⣿⠀⠀⠉⠹⠀⠀⠀⠹⡆⠀⠐⠀⠀⠀⠸⡆⠓⢖⣠⣄⣤⠌⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠳⣀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣛⣿⠀⠀⣤⠀⣈⢄⢀⠀⠀⣃⣀⣅⣀⣠⣾⠛⠀⠈⠼⣿⣇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡏⠀⢀⣀⡠⠼⠻⠖⠲⠋⠉⠀⠀⠀⠄⠈⠉⠺⣠⡌⢿⣿⡇⣅⣈⣁⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡿⠭⢤⠜⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣆⠛⡀⠆⠀⣀⣈
⠀⠀⠀⠀⠀⠀⠀⢨⡟⠉⠙⡻⠃⠀⠀⣠⣶⡿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠹⣷⣽⡶⢁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⡸⠋⠉⠉⠁⢀⠀⢸⠇⣸⠇⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢹⣿⣿⢆⣂⠀⢅
⠀⠀⠀⠀⠀⠀⠠⠿⠄⣀⣀⡠⠴⡀⠘⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠋⣻⣦⠐⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠁⠀⠀⣿⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡿⠋⣄
⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠈⠀⠐⠀⢠⡄⢸⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡇⠈⢀⣼⠿⠿⢶⣤⣀⡀
⠀⠀⠀⠀⠘⠠⠤⠅⡀⠀⠀⠀⠀⠀⠰⡙⠶⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣰⣅⣰⢟⡇⢤⣍⡀⣿⣿⠋⠠
⠀⠀⠀⠀⠘⠀⠬⢽⠐⠠⠤⠀⠀⡀⠀⢷⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡠⣾⣿⣿⣿⣷⣮⣗⣶⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠡⠈⠉⠉⠁⢶⣤⣼⣿⣷⣄⠀⡀⠀⠀⠀⠀⡀⢺⣿⠟⣀⣾⠟⠻⢿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠧⢀⠀⠀⠀⠀⠘⠁⣰⡿⠵⢆⣀⠀⢈⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠠⣿⣿⡡⣘⣛⡎⣞⣿⠟⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣮⣭⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠙⠻⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣦⣴⣶⡶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣥⣶⣿⠿⢿⠷⠚⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⠋⠁⢀⣿⣷⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢀⣀⣀⣹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⡶⢶⣶⣶⣴⣶⣶⣶⣶⣤⣠⣶⣿⣤⡄⠙⠻⠿⣿⣥⣤⣀⣤⣤⣄⣠⣤⣤⣠⡶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠈⠙⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⣾⡏⠀⠀⠀⠀⠙⢦⣿⣿⣿⣿⣿⣿⣿⣿⣻⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡶⠀⠀⠀⠈⠹⢮⣹⣿⣿⣿⢋⡵⠋⠁⠀⣿⡆⠀⠀⠀⠀⠈⢱⠿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢢⣤⠀⠀⠀⠀⠸⣿⣛⣻⣛⣿⠿⢦⣀⣤⡤⠿⣆⠀⠀⠀⢀⡸⣧⡿⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠻⡛⢶⣾⣿⣿⣿⣿⠇⢠⣉⣀⣀⣀⣀⡀⠀⣠⣾⣷⣟⠷⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣭⣿⣷⠁⢰⣇⣿⣿⣿⣽⡇⠈⢻⣿⣿⣿⣿⣿⣿⣻⣾⣿⠟⢠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡦⠀⠙⢻⡟⠛⠀⢠⡇⣿⣿⣿⣿⡇⠀⣼⣿⡿⠋⢀⣿⣿⣿⣹⣿⠀⢸⠋⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣌⠀⠀⠾⣧⣿⡇⠀⢸⣟⣿⣿⣿⣿⡇⠀⠈⠿⢄⠰⣯⣿⣿⡿⠉⠇⣰⡿⠀⠀⠀⢠⡿⠟⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡙⢀⣿⣾⣿⠋⠀⠀⢸⡟⣿⣿⣿⣹⡇⠀⠀⢀⣼⣷⣿⣏⢿⡀⠀⠘⠋⣷⠀⠀⠀⢸⣀⠀⠀⣠⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣿⣿⣿⣿⠇⠀⠀⠀⢸⡇⣿⣿⣿⡻⣇⠀⣠⣻⣾⣿⣿⣿⣷⡛⣄⢀⣰⣿⠶⠛⠻⠟⠛⢣⣄⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠇⢿⡿⠷⠀⠀⠀⠀⢸⡿⣿⣿⣿⡟⣿⡈⠿⣿⣭⣾⣿⣿⣿⢿⣭⣿⡝⠃⠀⢰⣧⡀⠀⢀⣿⣧⡈⢿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⣄⠀⠄⠀⠀⣀⢸⣇⣿⣿⣿⢷⣿⣧⣀⠙⣧⠀⢱⣟⣷⣿⣿⣿⡿⠀⠀⠀⠹⠿⠿⣾⣿⠟⢷⣮⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⣿⣀⡜⠲⠾⠋⢸⣿⣿⣿⣿⣿⣿⣿⠛⢃⡷⣦⡶⠛⢷⣽⣿⣿⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢹⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢳⡏⠀⠘⣿⡟⠁⠀⠀⢹⣾⣿⣿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⢿⣿⣦⣄⣀⢸⣿⣿⣿⣿⣿⡟⣀⣰⡾⠋⠀⠀⢀⣰⠎⠙⢻⡿⢿⣿⣿⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⢠⡄⠀⡀⠈⠀⠈⠉⠻⢏⣍⣸⣿⣿⣿⣿⣿⡿⠟⠉⠀⣶⠑⢶⣾⠋⠀⠀⠀⠻⢏⣿⣿⣿⣯⡷⣄
⠀⠀⠀⠀⠀⠠⣤⣤⠛⠿⠆⠈⠁⠔⠁⠀⠀⠂⠀⠀⠀⠁⣸⣿⣿⣿⣿⣿⣇⡀⠀⠘⣿⣶⡾⠋⢀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣷⣽⣷⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠓⠠⠀⠉⠀⠀⠀⠀⠀⠀⢀⡠⢶⣏⣿⣾⣿⣿⣿⣿⣾⣿⣦⣤⠹⠟⠳⠶⠶⠋⠀⠀⠴⢿⣿⣿⣿⣿⣿⣿⣷⡌⠳⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠏⠁⠀⠉⣿⠿⠋⠛⠋⢛⣟⣉⣄⣘⠿⠀⠀⠀⠀⠀⠺⠿⠿⠟⠿⠿⠿⠟⠻⠛⠛⠛⠓⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠾⠛⢻⣿⡷⠦⢄⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢋⣁⣴⣾⡿⠟⠓⠶⠚⠛⠛⠛⠛⠿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢀⣤⣤⣤⣴⣾⣿⣾⣿⠿⠛⢁⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠈⠙⠻⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠛⠋⢉⣽⣿⣿⡿⣿⣦⣤⠶⠿⢷⣶⣛⠟⠋⠉⠉⠉⠙⠛⠿⠃⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣏⠁⣿⠟⠛⠀⠀⠚⢠⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡿⣿⣿⠟⢿⣦⠿⠀⣀⡀⢀⣤⡈⠻⣤⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢱⣿⡏⢀⡌⣠⠶⣾⠟⠋⠙⠿⣷⠆⢀⣀⡻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠸⣿⡄⢿⡀⣥⠐⣿⠀⢻⡇⠀⣿⠐⢦⡙⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠂⠀⠀⠠⠄⠀⢸⡇⢠⣿⡀⠸⠟⢀⣴⣹⣿⡏⢹⣿⠋⠁⠸⣷⣾⣿⣿⡟⠃⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢻⡇⠀⠸⠟⠿⠉⠻⣧⡼⠋⠙⠀⠀⠘⣿⣿⣿⣷⠀⣀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠂⣼⣦⣴⠿⠇⠈⢀⠘⠀⠣⡀⠀⠀⣶⠀⠈⠁⠀⠀⠀⠀⢠⣿⢿⣾⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠿⠟⢃⣀⠀⠘⢀⠻⡦⠉⠲⢀⣤⣴⠋⠀⠀⠀⠀⠀⢈⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠙⠿⣶⣌⣰⣦⣤⣄⣠⡈⠉⢰⡖⠀⠀⠀⣠⣾⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢿⣿⣥⣿⠋⠉⠀⢈⣀⣀⣿⡿⠻⣍⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠞⢉⣡⠶⢾⡏⠁⠀⠠⣶⣾⣿⠟⠋⠁⠀⢹⣷⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣜⠃⠀⠀⣤⣸⠟⠁⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠠⠀⠀⡸⠋⠀⠀⠀⠙⠟⠳⠟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⢦⠜⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠤⠀⠀⠀⣤⠀⠀⠀⠀⣠⠋⠀⠀⠛⢶⣆⠀⠀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⣡⠴⠆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢹⡄⠰⡆⠀⠀⠉⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠙⢿⣧⣤⡄⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠉⠉⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠐⠷⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣠⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠁⠀⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣤⣤⣤⣴⣶⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠤⠴⠶⠶⠒⡖⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣁⣀⣠⣤⡤⡤⠤⢤⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⡇⢸⠀⠁⠁⠀⢸⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸⠀⡇⠀⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸⢰⡇⡇⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸⢨⡇⡇⠀⢠⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠈⠀⡇⡇⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠀⠀⡇⡇⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢠⠀⡇⡇⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠃⢸⠀⡇⡇⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠃⢸⠀⡇⡀⠀⠘⡀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡀⠸⡀⢰⡇⠀⠰⡇⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣇⠀⡇⢸⡇⠀⠀⡇⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠷⠶⠶⠾⠰⠧⠼⠷⠤⠤⢧⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⠖⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠄⠒⠂⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠉⠉⠐⠒⠒⠦⠤⢤⠴⠒⠊⠉⠁⢀⣀⣀⣤⠤⡶⠚⠂⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⠒⠒⠤⠤⣤⣀⣀⣨⣤⡴⠒⠋⣫⣥⣤⣤⣤⣠⡇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢠⠗⠲⠶⣤⣆⠀⠈⠁⢹⢷⡀⢰⠃⠀⠀⠀⠀⠈⢳⡄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡏⠀⠀⠀⠀⠙⣆⠀⢰⠋⠀⡇⠈⡇⠀⠀⠀⠀⠀⠘⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⣇⢰⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡄⠀⡇⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣤⣀⣀⣾⣿⣿⠀⠀⠀⠀⣶⣶⣦⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠉⠉⠛⠛⠛⠿⠶⣶⡄⠀⠉⠙⠛⣢⡾⠋⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⠇⠀⠀⢠⡾⠋⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⠞⠉⠀⠀⠉⠑⢾⣿⡠⠊⠁⠀⠉⠢⡀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠘⠂⠀⣼⠀⠀⠀⠀⠙⠀⣸⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⡰⠉⠳⣄⣀⢀⣀⡴⠃⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⡀⠀⠙⠢⠤⠤⠴⠊⠀⠀⠀⠀⠉⠉⠁⠀⣰⠄⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠶⠶⠶⠒⠚⠋⠉⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣶⣾⣿⣶⠖⠛⠉⠉⠉⠉⠉⠉⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⢀⣠⠞⠻⠟⠋
⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣤⡤⠴⠒⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠀⠀⢸⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢀⣴⣾⠿⢯⣅⣀⡀
⠀⣀⣤⣶⣶⣿⣿⠿⠛⠉⠀⢻⠀⠀⠈⠛⠿⠿⢷⣶⣶⣦⣤⣤⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠛⠁⠀⠀⠀⠉⠉⠓⠶⢦⡀
⠈⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⡤⠞⠁⠀⠉⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿⠿⠿⢿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣬⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠰⢄⣐⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠈⠳⢄⡀⠀⠀⠈⠉⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⠖⠛⠒⠛⢅⠒⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⣳⢈⠓⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣠⢸⠁⠆⠁⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡖⠠⠤⣄⣀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠔⠂⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠙⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠰⢈⣀⣀⣓⣤⠞⠁⠀⠀⠀⡴⠛⡏⢽⠙⠀⠀⠀⠀⠀⠀⠀⢸⣤⠔⠂⠀⣀⠀⠀⠐⣈⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣙⢛⡿⠁⠀⠀⠀⠀⠀⠳⠤⣷⢾⡖⠶⡄⠀⠀⠀⠀⠀⠈⣿⢶⡶⠒⢀⡀⠀⢠⣈⡛⣋⣡⠄
⠀⠀⠀⠀⠀⠀⠀⢹⠶⣯⡞⠁⠀⠀⠀⠀⠀⠀⢤⡀⢸⠸⡇⣰⠃⠀⠀⠀⠀⠀⠀⢿⠖⠶⠒⢯⣄⣤⡤⢙⣷⢡⣬⡆
⠀⠀⠀⠀⠀⠀⠰⢶⣾⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠾⠟⠁⣠⠀⠀⠀⠀⠀⠀⢸⣇⣿⣷⣦⣄⣠⡄⣙⡿⣉⣉⠁
⠀⠀⠀⠀⣀⣀⠀⢆⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁⠀⢀⡀⠀⠀⠀⣿⣶⠛⣼⣶⡆⣶⠛⠋⣴⠯⠉⣀⡄
⠀⠀⠀⠈⣐⣈⠷⠲⠶⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣭⠤⠤⠒⠒⠊⠉⠀⠀⠀⠀⢰⡟⢀⣛⣪⣭⣭⠻⠹⠟⢛⠋⠘⠋⠁
⠀⠀⢀⠀⠋⠩⣶⠐⠂⣿⠀⠀⠀⢠⣤⣤⣤⣦⣤⣄⣀⣀⣀⣀⠀⣠⣄⣀⢀⠒⠛⠇⠀⢙⣉⣁⠙⣓⡐⢢⠉
⠀⠀⠈⢓⣒⠐⠓⠒⠀⢉⠁⠀⠀⣀⣽⠀⠀⠀⠀⢤⠄⠉⠉⠉⠉⠣⡌⠉⢈⡲⢷⡇⣀⣈⣉⡓⠒⠛⠒
⠀⢰⠋⠁⢀⡙⢢⡀⠀⠈⠓⠿⠃⠈⠱⣄⠀⠀⠀⠸⣧⠢⠀⠀⣠⠀⠈⠁⣼⡇⠨⡞⡅⠀⢀⡉⢦
⠀⠹⢷⣴⣾⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠓⡟⠋⠁⠚⠛⢋⡇⠀⠀⠀⠀⠀⠈⢷⣾⣾⣦⡾⠁
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⠾⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⡀
⠀⠀⠀⠀⠠⠼⠝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢄⢁⠀⠀⠀⠀⠀⠈⣈⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠦⠀⣠⣢⡀⢀⠄⠃⠀⠀⠀⠂⠀⣆⠀⠀⠈⠃⠀⠉
⠀⠀⠘⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⡴⢪⠿⠛⡹⠳⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠸⠶⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤
⠀⠀⠀⠄⡀⠀⢀⠀⢠⠄⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠠⠐⠂⠀⠀⡄⢲⠀⠀⠀⠀⠀⢀⡄⡀
⠀⠀⠀⠗⠘⠂⠀⠈⠁⠦⣠⢀⡀⠀⠠⠞⠀⠀⢀⠐⣄⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠌⢀⣽⠁⠀⠀⠀⠈
⠀⣤⣠⠀⠘⠀⠀⢀⠀⠀⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⢨⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠁
⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠂⠂⠀⡰⠀⠀⡈⠀⡤⣤⠃⠀⠙⠀⣦⣄⠀⠀⠀⠀⠐⠋⠉⠁⡀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠂⠀⠁⠈⠉⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣈⡀⠀⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠠
⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡘⠀⠀⢀⠄⠀⠀⠀⠄⠀⠀⡄⠀⠘⠀⠑⡌⠀⠐
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢉⢲⣿⡿⢠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢺⣤⡄⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠈⠁⠀⠫⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⣄⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠉⠉⠉⠁⠄
⠀⠀⠀⠁⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢰⡖
⠀⠀⠐⠊⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠂⠀⠂⠀⠀⡁⠀⠢⠖⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⣀⡀⠀⠠⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠶⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘