Aztec headdress Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⣉⡀⣀⢠⠤⠤⣄⠀⡠⠬⢉⠉⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⠀⠀⢀⡤⠂⠁⢀⣄⠐⠊⠽⠀⢃⣰⡉⢠⢤⢧⣥⢤⣤⣦⣌⡀⠀⠀⠀⠠⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠆⣤⠞⠋⢸⠀⠘⡡⣊⣠⢷⢓⠙⣹⡸⡇⠀⠐⠄⣐⠀⣄⠤⠹⠉⠀⠒⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠒⢯⣉⡑⠿⢄⡀⢸⣇⠤⣛⠉⠧⠍⠘⣀⠑⣀⣁⡀⠀⢠⠀⢀⠀⠀⡛⠆⣂⠀⠊⠥⠍⠁⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠈⡁⠀⢀⡀⠀⠉⢴⢁⠆⣸⠀⢸⣱⣼⣀⣥⣧⣼⣀⡼⠯⠦⠦⠐⠳⢾⡿⢭⣉⠈⠉⠉⠉⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠒⠐⠢⡉⣷⠀⢉⡋⠿⡯⠈⠓⢶⡉⡔⠉⠐⠋⡄⣀⠀⡀⢸⠽⢡⠇⠀⠀⡀⡀⠐⠄⢁⡄⠀⠈⠒⠤⣀
⠀⠀⠀⢀⣤⠤⢶⣅⠀⠀⠂⢤⣤⡤⠾⣤⣀⣐⡆⠐⠂⣠⠈⣠⢊⣼⠁⢤⣦⣬⡀⣀⣀⣀⣬⣰⣦⣬⣤⣤⣀⣠⣥⣏⣑⠀⠈⠳⢤⡀
⠀⠀⠚⠋⠀⠀⠀⠡⣸⣧⠀⣸⠷⣄⠆⠙⢫⡝⠇⠀⢟⢫⡄⠧⠚⣡⠢⡀⠀⠀⢀⠴⡄⠀⠀⠠⣀⠀⠀⠀⠉⠉⠛⠂⠤⣈⠉⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠁⠀⠀⠻⣿⣀⢹⡇⡆⠀⣞⡇⢸⣥⣤⠖⠉⠓⠎⠁⡀⠘⣄⠀⠀⠐⢀⠀⢀⣀⠂⠁⠀⠀⠈⠑⢦⡀
⠀⠀⢠⣖⣶⠤⠤⠔⡀⢀⡀⠤⠀⠀⠠⡌⢿⡸⣝⠇⠀⡀⠀⠘⠀⠀⠢⣀⠀⣰⠢⡀⠈⢳⠶⠠⢀⡘⠒⠊⠀⢀⡰⠆⠡⠄⠀⠀⡽⠆
⠀⠀⠘⠉⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠠⣼⡾⢷⡙⠀⣀⢇⠀⡏⢉⣨⡤⠟⠕⡤⣃⠜⠀⠃⠬⠂⠀⠀⢁⠲⢤⣧⣀⡀⠀⢠⡄⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡤⢛⠑⢤⡽⣆⠈⠆⡰⠉⢢⡩⠓⢄⠁⠛⡸⠃⠆⠤⢀⡘⡍⠶⠓⠣⠂⠀⠈⠙⠻⣙⠲⠤⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⢧⡼⢨⣄⡯⢂⣔⠛⡒⣤⡤⠅⢠⢳⣎⠀⠦⡐⢢⠀⡙⠳⢦⣄⣀⣈⡡⠷⠀⣔⠡⡗⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⣶⡖⢈⡿⠒⢏⠑⢬⣉⣰⠰⢄⠀⣩⠋⠑⢄⠈⢁⠌⡠⠢⣄⠈⠻⣏⠓⠤⣀⠀⠑⣊⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡜⢛⠛⡧⠱⣷⡆⠡⠀⠡⠀⠦⠤⠶⡁⠀⢀⣤⡘⢣⡀⠈⠒⡁⢀⠪⡀⠑⡄⠀⠁⠢⣽⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢶⣎⡞⣴⢋⡆⢰⠄⠹⡤⢀⢡⠀⢱⡂⢠⠀⠑⣴⠁⠑⠤⠊⡉⢦⣜⠀⠈⠠⡠⠀⣸⢆⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢴⣁⡔⠦⠙⠻⢳⠎⣀⠀⢃⠀⢹⠜⠀⡆⠀⡿⡇⠀⠎⡈⣷⣄⠀⠘⢮⡤⠛⣇⠢⢔⠁⠘⠯⠛⢆
⠀⠀⣤⡤⠔⠒⢉⣠⡴⢟⠿⣤⣞⠓⣠⡄⠸⠁⠘⡀⠀⣷⡢⢀⠀⠁⠐⣄⣀⡀⠀⢂⠑⢄⠣⠀⠀⡸⠆⠀⠁⠲⢞⠠⣊⣆
⠀⠀⢧⠰⠶⠛⣋⡅⠒⠁⠈⠽⠟⠻⣿⣀⠃⠀⠀⠡⠀⠸⣇⢸⠀⠀⠀⢡⡠⠁⣠⠼⡄⠀⠠⡑⠢⣑⠶⠀⠀⠀⠀⠑⢬⢚⡄
⠀⠀⠈⠣⡀⠑⠢⠀⠀⠀⠀⠄⠊⠁⡐⠁⠀⠀⠀⠀⠣⡀⠹⡈⠀⢸⠀⠀⠇⠀⠑⠒⠆⠀⠀⠈⢆⠀⢀⠷⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠈⠐⠤⠤⠀⠀⠠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⣇⠈⡄⠀⠘⡖⠦⠀⠀⠀⠀⠀⠀⠱⡖⠠⠀⠀⠀⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠐⡄⠀⠹⡅⣴⡇⠀⠀⠀⠀⠀⢰⣸⡆⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢦⠀⠹⣌⡇⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⣼⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠒⠈⡁⢄⠠⢀⠂⢈⡡⢑⣀⣀⡐⠀⠀⠈⠐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⢇⣠⠞⡅⠀⠘⠂⣰⡅⠶⣺⠆⠉⠍⠏⠉⡛⡛⠓⠀⢄⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣖⠚⣼⡁⠀⣅⡀⠗⢿⡳⠄⠀⠃⠃⠈⢉⣉⣀⠉⢩⡐⡄⠈⠷⠙⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⠀⠀⠁⢫⠈⠁⡌⠀⣯⣇⣨⣿⣁⣠⠭⠧⠤⠺⢶⡧⣌⠉⠉⠉⠁⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠐⠍⣳⠀⠙⠿⣏⠑⢢⡟⡜⢁⠚⢅⣀⣀⠠⠯⠀⢀⣀⣀⠀⠤⠁⢀⡈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢮⠀⡀⠠⣤⡴⢿⣄⣐⡆⢐⣀⢠⠄⣼⠰⠖⠾⠀⠀⠀⠼⢴⠦⠤⣤⣤⣤⡾⠭⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⢼⣇⣠⠟⢴⣈⡙⣭⡅⠸⢽⠄⡊⠡⢀⡀⢀⡠⠂⠀⠀⠐⠀⠀⠀⠀⢈⠁⠐⢄⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢾⢰⠀⠸⠆⠓⠶⠋⠀⠉⠂⠄⣰⠀⠀⠐⠂⠠⠄⠀⠀⠄⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣀⡔⠤⠁⠒⠒⠡⡲⠐⠈⠉⠒⣼⣎⠯⠀⡴⠀⡄⠠⠑⣆⠘⡕⠀⢠⠻⡐⠢⠌⡀⢀⠒⠉⠐⠂⠀⢸⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣸⠏⣙⣆⠐⠇⠰⠒⠺⠋⠀⢭⠲⢄⡀⠉⠠⢀⣤⠜⠉⠓⠶⣄⢨⡀⠸⡀⢡⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⢁⣀⢈⠉⡆⢠⠦⣈⣁⡀⠡⡤⠁⠌⠌⠘⠳⣭⣀⠀⡐⢠⡄⡨⢃⠌⠀⠠⡀⠇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠠⡅⢚⡿⠴⠃⣑⢊⡩⡀⠑⠟⠢⡈⠂⡀⠁⢄⠙⢿⡞⠌⡀⠁⠨⠂⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⡏⢲⣆⠀⠈⠉⠠⠤⠎⠀⢀⣌⠲⡀⠉⠂⠃⣀⡉⢆⠈⠑⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⣦⣆⡾⡓⠸⠀⢧⡄⠀⠐⡆⠄⠈⣦⠉⠡⠔⣉⢦⡄⠈⠡⡔⢀⢦⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣤⠛⢈⡉⠻⢠⠀⠃⠈⡇⠀⠀⠹⠁⠐⠄⠷⣄⠀⢳⠄⠻⠒⠶⡀⠺⢃⢇⠀⠀⠀⠈⢲⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⣁⡤⢞⠏⢳⣮⣡⡶⠘⠀⠐⠀⢹⠖⠀⠀⠰⠄⣀⠀⠂⠀⡀⠀⠠⠆⠀⠈⠲⢁⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢅⠒⠀⠒⠊⣁⠝⠳⠂⠀⠀⢃⠈⣆⠀⠀⠀⢰⠀⣄⢙⠀⠈⠌⠀⠛⠂⠀⠀⠈⠺⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠉⣀⠔⠁⠀⠀⠀⠀⠂⠀⣄⠀⠀⠘⣀⠀⠈⠀⠀⠀⠁⠐⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠀⠀⠀⠡⠈⢠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣤⠀⠁⠹⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⣡⡴⠶⠚⠛⠛⠲⠶⣤⡉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢞⣋⢿⡄⣷⢰⣚⣫⡭⣭⣛⣖⢸⠇⣼⢏⣛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣹⠾⢊⣡⢼⣮⠿⠼⠀⠿⠼⢯⡾⣤⣙⠺⢾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⢚⡍⣧⠧⠗⠚⠛⠛⡛⠓⠚⠧⢧⡏⡝⢲⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣬⣟⣩⠴⠚⠻⠍⠉⠉⠉⠉⠿⠓⠲⢬⣙⣯⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡞⣉⢻⣿⣴⣁⣈⠲⠤⠀⠠⠴⢃⣀⣱⣼⣿⢋⡹⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⢸⣏⡿⢿⣿⣿⣾⠀⢸⣾⣿⡿⠿⡏⡇⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠛⣸⣧⣙⠂⠀⠁⢁⣶⣆⠁⠁⠀⢊⣡⣿⡘⢣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⠹⡇⢹⣽⢳⣦⠔⠻⠞⠾⠃⢤⣶⣻⡽⠀⡟⢹⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⢀⡇⠀⣿⡏⡧⡀⠀⠀⠀⠀⡰⡏⣿⡇⠀⡇⢸⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢧⣴⢿⡇⠿⢛⣯⠭⢭⣛⠻⠇⣿⢷⣤⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠳⢮⣁⣀⣀⣽⠖⠛⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣀⠻⣷⣬⣿⡦⣦⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣤⣝⣿⣍⡛⠿⣿⣷⣌⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣶⠶⠿⠿⣿⣿⣿⣶⡈⠻⣿⣦⠙⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣍⣙⣶⣶⣤⣈⠉⠙⠻⣦⣄⠹⣷⣌⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⣦⣭⣿⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⡶⠞⣛⡛⣛⣛⣛⣿⣯⣭⣭⢉⣴⣾⣿⣿⣿⣿⣿⣾⣛⣖⣶⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⣿⣿⣿⣿⣿⣿⣿⣾⣤⣓⣶⣤⣀⣀⢾⣿⣾⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣏⣍
⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣽⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⡁
⠀⠀⠀⠀⠉⠉⢉⣉⣭⣽⣿⣿⣿⣿⡿⠟⠛⢉⣩⣤⣶⣪⣿⣿⣿⣯⣻⣿⡿⣿⣿⣿⣿⢟⣫⣭⣷⣿⣿⡁⠀⢹⡇⡇
⠀⠀⠀⢀⣠⣶⣿⣿⢿⣿⡿⠟⠋⡉⢁⣤⣾⣿⣿⣿⠋⣹⣿⣿⣯⣿⡟⠁⣼⣿⠉⣻⡿⠿⠛⢋⣉⣉⣉⢣
⠀⠀⠀⠈⠉⠀⣠⣴⠟⣁⣤⣴⣿⣿⣿⣿⡿⠛⠌⣠⣿⣿⣿⡿⢻⠏⣠⢾⣿⣿⣿⢻⠀⠀⠀⠀⠐⠶⠏⠳⡄
⠀⠀⠀⢀⣴⣿⣿⡷⠿⠛⣩⣾⣿⣿⣿⣿⡿⢊⣾⡿⠟⣩⣴⣾⣿⡾⣣⢾⣿⣿⣿⡄⠛⣳⣲⣦⣤⣄⡀⠀⠘⡄
⠀⠀⠐⠛⠋⠉⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⡑⢋⣡⣶⣿⡿⡿⠟⣩⠞⢡⣿⣿⣿⣿⣿⣤⣿⣵⠄⠉⠉⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⠏⢀⣤⠞⢉⣰⣿⡿⢡⣿⣿⣿⣇⠀⠀⠀⠀⠘⠁⠀⢰⠆
⠀⠀⠀⠀⠀⢰⣿⠿⠟⢫⣾⣿⣿⢿⡿⢿⣿⠟⠉⣀⣴⣿⠏⢠⣿⣿⣿⠃⣼⣿⣿⣿⣿⣟⠶⣤⣄⣀⣀⣀⣸⠆
⠀⠀⠀⠀⠐⠛⠁⠀⣰⣿⣿⠟⠁⢉⣴⣟⣥⣴⠞⣩⡟⢁⣾⣿⣿⣿⡟⢠⡏⣿⣿⠙⢿⠙⢿⣾⣽⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⣴⣿⠿⠛⠉⠀⣴⣿⡴⢛⣿⣿⣿⣿⠁⡿⠀⢻⣿⣦⣤⣤⡴⠋⠙⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⡿⠋⠀⣾⣿⣿⠏⣾⣼⠃⠀⠸⠏⠙⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⢸⣿⣿⠋⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣹⣩⣙⣻⣋⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⣼⣾⣧⣧⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⢸⣿⣇⠀⠀⣯⣿⣿⣽⠀⠀⣸⣿⡇⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣳⡄⢻⣿⣦⠘⠟⢯⣄⠀⣤⣴⢾⣤⠀⣰⡽⠻⠃⣴⣿⡟⢠⣞⡷
⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⠘⣿⣿⢾⡟⢳⡶⣶⣿⢉⡆⠙⢿⣼⠋⢰⡉⣿⣶⢶⡜⢻⡷⣿⣿⠃⣠⢶⠄
⠀⠀⠀⠀⠀⠀⣀⠀⢻⣿⣶⢼⣉⣺⠛⣿⢇⣿⣀⣻⣻⣦⣼⣹⣶⣟⣟⣀⣿⡰⣿⠛⣷⣉⡧⣶⣿⡟⠀⣀
⠀⠀⠀⠀⠀⠘⢯⣿⣄⣻⠋⣾⠛⣟⠳⡿⣮⣧⣿⣿⡟⣟⢻⡟⡿⢻⣿⣿⣼⣵⢿⠞⣻⠛⣷⠙⣟⣤⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠈⢿⡿⢴⡟⢿⠳⡿⣲⣷⡿⢻⣧⣳⣿⣾⡿⣷⣷⣿⣞⣹⡿⢿⣿⣞⢻⠞⡿⢻⡧⢿⡿⠁
⠀⠀⠀⠻⣽⣷⣤⢄⡰⡾⠷⢼⠷⣿⣿⡙⣿⣾⣿⡟⢿⣏⣿⣏⣿⡿⢿⣿⣷⣿⢋⣿⣿⠾⡷⠾⢷⢆⡠⣤⣾⣯⠟
⠀⠀⠀⠀⠙⢿⡟⢺⣇⢹⣦⣼⣿⣯⡱⣿⡿⢿⣦⣿⣾⣿⢿⡿⣿⣷⣿⣴⡿⣿⣿⢎⣽⣿⣧⣴⡏⣸⡗⢻⡿⠋
⠀⠀⣿⣿⣦⡦⢠⡿⣋⠉⣧⣿⡛⢾⡟⣟⢻⣾⡿⢟⢻⢸⡞⢳⢇⡞⡻⢿⣷⡟⣻⢻⡶⢛⣿⣼⠉⣹⢿⡄⢶⣶⣿⣷
⠀⢀⣀⠙⢿⡏⣹⣧⣽⡟⣿⠿⣽⡿⣟⣻⣿⡟⢳⠸⡜⣯⣇⣸⣽⢣⢇⡞⢻⣿⣟⣻⢿⣯⠿⣿⢻⣯⣼⣏⢹⡿⠋⣀⡀
⠀⠿⣿⣿⣯⢽⣏⢻⡶⣿⡿⣷⣾⣟⣻⣿⢯⡘⣇⣷⣷⣿⣿⣿⣿⣾⣾⣼⢃⡽⣿⣛⣻⣷⣾⢿⣿⢶⡟⣹⡯⣽⣿⣿⠿
⠀⠀⠈⠙⠃⢼⡟⠉⢹⣿⠷⣾⣿⣛⣿⡿⢦⡹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⢏⡴⢿⣿⣛⣿⣷⠾⣿⡎⠉⢻⡧⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠲⠏⢸⣿⣿⠷⣮⣹⣿⣿⡿⠛⠋⠙⠛⢿⣿⣿⣯⣵⠾⣿⣿⡇⠹⠖⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡏⠀⠀⠀⠀⠀⠀⢹⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡟⠀⠀⠀⠀⠀⠀⢻⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⢀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⢀⠀⠀⠀⠀⡀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⠀⠆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠆⠀⠀⠈⠀⡀⡆⠀⠸⠠⠀⠆⠀⢰⢀⠀⠁⠀⠀⠠⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢄⠀⠀⠠⠘⠀⠢⠀⠘⠃⠀⢀⡄⢤⢠⠄⠀⢠⡀⠀⠐⠃⠀⡔⠀⠁⠄⠀⠀⡠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠆⠐⢄⠀⢠⠈⠀⠰⡀⠀⠙⡄⠱⠀⢸⠀⠐⠆⢠⠃⠀⢀⡆⠀⠁⡤⠀⡠⠂⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⢌⠹⣄⡐⠀⠰⢤⡀⠀⠆⠈⡇⠀⢂⠀⡅⢨⠀⠘⠀⡐⠀⢸⠁⠰⠀⢀⡤⠆⠀⢂⣠⠇⡡⢘
⠀⠀⠀⠀⠀⠀⠎⡙⠰⣄⠀⠄⠑⣦⡲⠀⠁⡄⠀⠀⠘⡀⠈⡌⠁⠸⠀⠈⢠⠁⢀⠃⠠⠀⢠⠈⠀⠖⡵⠊⠠⠀⣠⠆⠋⠑
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠉⠦⣤⠄⠈⢀⣆⠈⢠⠈⠆⠰⠀⢠⡄⢰⠀⠀⡆⠀⠆⠰⠉⡔⠁⣰⡀⠃⠠⣴⠴⠉⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠐⢤⠀⠚⣤⣀⠘⡂⡀⠢⠘⡄⢣⢈⡆⢰⠀⢰⡇⡌⢠⢃⠔⢀⠜⠃⢀⣤⠓⠀⠤⠂⠀⠖
⠀⠀⠠⠉⢉⠐⠒⠀⣤⣀⣀⠀⠁⠦⡀⠹⣠⡈⢛⣆⠰⠘⣄⠀⣿⣼⣀⣾⢀⣠⠇⠆⣰⡛⠁⣔⠏⢀⡴⠈⠀⣀⣀⣤⠀⠒⠂⡉⠉⠄
⠀⠀⠀⠁⠤⠀⡉⠀⢄⡀⠈⠐⠢⡀⠁⢦⡈⠳⣆⢫⣷⡤⢿⡉⣭⠸⠅⣬⢉⡿⠤⣿⡍⣰⠞⢁⡴⠊⢀⠔⠂⠉⢀⡤⠀⠈⠀⠤⠊
⠀⠠⠤⠀⠤⠌⠧⡤⢤⣈⠈⠒⠤⣀⠈⠠⠙⢦⡬⢷⡀⢷⡘⣧⢹⡐⢀⡏⣼⢃⡞⢀⡾⢥⡴⠋⠄⠉⣁⠤⠒⠉⣁⡤⢠⡼⠡⠄⠀⠤⠄
⠀⠱⠤⠤⠴⠦⢤⠤⣀⢀⢁⠉⠠⠮⢁⠲⢴⡐⠳⣄⢻⡌⣧⣹⡾⠷⠾⢷⣏⣼⢁⡟⣠⡞⢂⡦⠖⡊⠥⠐⠉⡈⡀⣠⠤⡤⠴⠦⠬⠤⠌
⠀⠂⠈⠒⠐⠀⠤⡄⢀⡈⠉⠙⠒⠤⣤⣵⠊⠹⣦⡙⣶⡿⢙⣤⣶⣶⣶⣶⣤⡋⢿⣴⢋⣴⠏⠑⣮⣤⠤⠖⠊⠉⢁⠀⢤⡤⠀⠀⠒⢁⠐
⠀⠀⠈⠁⠲⢀⠀⠀⠁⠈⠉⠐⠲⠤⢬⣟⠙⠷⣮⣻⢏⣵⢿⡿⣿⣞⣳⣻⢿⡿⣮⡹⣟⣥⠾⠋⣻⡤⡤⠖⠂⠉⠁⠈⠀⠀⠀⠖⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠠⢀⣀⡀⠀⠊⠛⠶⣮⣛⣾⢯⣿⣿⡿⠿⠿⢿⣿⣿⡽⣷⣛⣵⠾⠛⠑⠀⢀⣀⠀⠄⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣯⡿⠋⠁⠀⠀⠀⠀⠈⠙⢿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠀⠉⠉⢉⣉⣉⡉⠉⣉⣁⡒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣆⠀⠀⣀⠤⠒⠉⣀⠀⡔⣲⠆⠋⢡⠚⣸⣰⣖⣁⣰⣁⣖⣚⣀⣀⣀⣀⣉⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡴⢸⣴⠞⠉⡆⠀⡎⡜⢀⣷⢷⠒⡿⡹⡇⢸⠸⡼⡏⠀⡏⣏⢿⠓⠒⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢾⣙⣒⣺⣧⣀⠁⣇⡠⢞⠛⣿⠿⠼⠂⠑⢒⣃⡈⠉⣉⣁⣀⠉⢩⣟⡒⡆⠘⠾⢯⠟⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⡏⠀⠀⠀⠈⠙⢣⡊⡽⢠⠇⠰⣩⣝⣄⣯⣿⣹⣀⣵⠿⠼⠤⠼⢷⢾⡿⣍⡉⠉⠉⠉⠉⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢍⣙⡆⠈⡙⠻⣿⡉⠕⣢⡝⢥⠋⢐⠚⡭⣀⣀⡀⢸⣯⣃⠇⢀⣀⣀⡀⠲⠌⣁⡆⡀⠉⠢⢄
⠀⠀⠀⠀⢀⡠⠤⢾⡁⠀⡑⠢⣤⣤⠴⣯⣅⣀⣲⠉⠶⢈⡘⣅⠜⣼⠧⢧⣶⣼⣀⣀⣀⣀⣇⣾⣆⣥⣀⣀⣀⣸⣽⣏⣗⠀⠉⠢⡀
⠀⠀⡠⠚⠁⠀⠀⠈⢇⣿⡆⢀⡿⢶⡵⣈⡻⣯⢿⠉⢹⡿⣇⢰⠚⣩⠒⢄⠀⠀⢀⡴⡦⠀⠀⠸⣄⠀⠀⠀⠉⠉⡟⠒⢤⡈⠉⠑⠊⠷⡄
⢀⠞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣀⠈⢳⣷⣼⡿⣰⠈⢼⣷⢸⡭⣤⠖⠉⠑⠺⠥⣀⠸⣄⠀⠀⠸⢤⠀⣀⣰⠒⠁⠀⠀⠈⠳⢄
⡜⠀⡠⠤⣒⡒⠤⠶⢒⠠⣤⡪⠔⠒⠪⢦⡹⣇⢧⡿⠀⢠⠀⢸⠀⠈⡳⣄⠀⣴⡢⣄⠉⡱⡶⠤⢀⡘⠒⠁⠀⣠⠔⠊⠹⡀⠀⢀⠷⡄
⣷⠟⠊⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⢴⣿⠿⢯⠆⢠⡿⠄⣼⠭⣭⡥⠚⡝⡶⢍⡎⠀⠓⠬⢃⡀⠈⣉⡲⠶⢧⣄⣀⠀⢢⠀⠀⡇⠘⢆
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⢚⢍⡲⡾⢷⡝⡝⣰⠁⠵⡜⡝⢦⡈⢛⠔⢉⠖⠤⢤⣎⠬⠟⠑⠒⢃⡀⠈⠙⢫⣍⠒⠬⢓⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣦⡸⠶⢇⣧⡼⢊⡴⢍⣏⢲⣶⠞⠠⣻⣯⡀⠣⢜⡣⢀⠜⡙⠲⣤⣤⣎⠾⠟⠠⢏⠸⡑⠄⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⣹⣿⣁⣽⢛⠫⡌⠲⣬⠼⢨⠧⡀⡨⠋⠈⠢⣀⡠⠋⣜⠓⡦⡘⢻⢮⡑⠢⢄⡀⢉⡥⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡸⢉⡉⡹⡈⢿⡿⠈⢆⠘⢆⠛⠒⠛⢄⠀⣠⡶⠌⢳⣄⠀⢉⠞⣴⠵⡄⡱⡄⠀⠈⠒⢏⡰⠂⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢛⢿⣾⣱⢏⡷⢡⢧⠀⢶⣶⡜⡄⠈⣏⣹⠀⢈⠿⡁⠈⠒⢁⢄⠳⣧⡀⠈⢒⠝⢀⣞⢆⠀⠀⠀⠈⠢⡀⠂
⠀⠀⠀⠀⠀⠀⣀⡠⠔⢳⣴⣹⠀⣩⡚⢟⡰⣇⠘⡄⠈⣏⡀⢡⠀⠛⢣⠀⠚⠂⠻⡦⡀⠈⡷⠚⠉⢎⠑⠫⣀⠈⢊⠜⣧⠀⠀⠀⠀⠈⠻
⠀⠀⢠⠒⠂⢉⣀⣤⠶⣛⠝⣻⣾⣝⣱⡶⢈⠃⠀⢡⠀⢹⡾⢸⠀⢸⠀⢶⠢⡤⠀⢡⠈⠢⡱⣀⠠⣞⣆⠀⠈⠙⠧⡺⡺⣆
⠀⠀⠀⢣⡘⠯⣁⠶⠮⠤⠄⠚⠋⡩⠛⢷⠊⠀⠀⠀⢆⠀⢷⡦⡆⢸⠀⠘⡞⠀⣔⠊⡆⠀⠘⢮⠑⠞⠛⡄⠀⠀⠀⠈⢾⣹⡄
⠀⠀⠀⠀⠑⢄⡈⠉⠒⠒⠒⠊⠉⣀⠔⠁⠀⠀⠀⠀⠈⢢⡈⢇⡇⠘⡀⠀⢱⣀⠀⠈⡇⠀⠀⠀⠱⡄⡖⢳⠀⠀⠀⠀⠀⠱⣷
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠻⠀⢣⠀⠀⢣⠝⠀⡇⠀⠀⠀⠀⠘⡏⢸⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣣⡀⠈⢢⠻⡇⠀⠀⠀⠀⠀⠸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠱⡇⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⣤⣀⣑⠒⠤⣄⣀⣀⣀⣀⡤⠔⢒⣊⣀⣬⣽⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣖⣏⣈⣁⣈⢙⣛⢿⣿⣌⠻⣿⣿⣿⣿⠟⣡⣿⠿⣛⡋⣁⣉⣡⣥⣦⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠭⠍⣛⣛⣛⠛⠻⣶⣮⣛⣷⣼⣿⣿⣧⣾⣛⣷⡾⠟⠛⣛⣛⣋⠩⠭⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠷⢖⡾⠿⢛⣿⣟⣛⡛⣶⣾⠿⣅⠀⠈⠁⢀⡽⠿⣷⣞⢛⣻⡻⣟⠛⠷⣷⠶⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣩⣤⠾⣿⣿⣛⣛⣻⢃⣿⣿⣶⡀⠀⠀⢠⣾⣿⣿⢹⣟⣛⣛⣿⡿⢦⣤⣉⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣟⣩⣿⢷⣿⣿⣿⣿⠟⠛⠛⣿⠿⡿⢳⠂⢰⠻⣿⢟⡟⠛⠛⣿⣿⣿⣿⣷⣾⣿⣉⡻⠛
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⢿⣌⢻⡉⠀⢹⣿⣿⣿⠰⡏⢉⣷⣾⢂⣴⣆⢸⣷⣏⡉⣵⢀⣷⣿⣿⡁⠀⢙⠟⣴⠷⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠢⢿⡄⠑⣤⣿⣿⣧⡾⢤⠉⠁⣼⣸⡸⣌⣨⢸⣩⣇⠈⢉⡌⣧⣿⣿⣇⡴⠃⣸⡯⠊⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢷⣌⠛⣾⣟⣝⣙⣿⢃⣰⣶⣻⣿⣿⣿⡆⣺⣟⣤⣟⣷⣶⣆⠙⣟⣛⣝⢞⣿⢋⣤⡿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⣏⢦⣾⣿⢿⣿⣿⣦⣧⡿⣛⣿⣿⣿⣿⣿⣽⣿⡿⠟⣩⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣷⣷⣖⣟⣥⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⡯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⢶⣿⣿⣾⣿⣿⡿⣻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣻⣿⣿⣿⡶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⣤⢴⣿⣿⣿⣿⣿⣿⣟⣿⣆⣸⠛⣻⡿⠀⢻⣿⡟⢿⣁⣾⣟⣿⣿⣿⣿⣿⣿⣷⢦⣌⡳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣯⡿⢟⡿⢻⣿⣿⣿⣿⣿⣇⢺⣿⣿⣼⠟⢷⣶⣾⡟⢿⣾⣿⣿⠇⢻⣿⣿⣿⣿⣿⡛⣿⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡞⢠⣿⣿⣿⣯⣾⣿⣥⡾⣿⣿⣿⣶⣶⣻⣳⣶⣾⣿⣿⣿⣧⣼⣿⣯⣿⣿⣿⣷⡈⢧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡥⣿⡏⣼⣿⣿⣿⢿⣿⣶⠿⣿⣿⣿⣯⡍⣭⣿⣿⣿⣿⣷⣾⣿⡿⣿⣿⣿⡆⢿⣧⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣟⠀⣿⣿⣫⣴⡿⠛⣿⣧⣉⡙⠛⣿⣛⣻⡟⣿⣯⣿⣿⡿⠛⣴⣮⣹⣿⣗⠈⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢡⡇⣨⣿⣟⠍⣿⣴⣿⡞⣩⣻⣿⣷⣾⡟⢻⣾⣿⣿⣿⣝⣿⣿⣬⡟⠩⣿⣿⡄⢹⠘⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣷⣳⣿⠛⢾⣿⣿⣿⢫⣛⢂⠞⣫⡼⣿⣿⣿⡞⠛⠧⣷⣻⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡿⢻⣟⣯⢿⣿⣿⣾⣿⣹⠿⠿⣿⡾⣶⡿⠿⢿⣻⡿⣷⣿⣷⣮⣿⣿⠹⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⠸⢋⠵⣋⣭⣭⣿⡾⣿⣄⣴⡎⣷⣞⢰⣤⣸⣿⣿⣿⣭⣭⡙⢮⠙⠂⠈⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠎⣞⡽⣻⠭⢍⢻⣎⠹⣿⡅⠃⢁⢼⣿⠙⣼⠟⡭⢭⡻⣟⣆⢣⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡿⡷⣏⢾⣷⣾⢇⢤⣿⣿⣧⣺⣿⣿⢰⡻⣶⣾⠇⣿⣿⣸⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢷⣷⣟⣳⣶⣟⣡⣾⣿⣿⡁⢹⣿⣿⣷⣝⣳⣶⣾⣵⣿⣞⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⡽⠿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⠟⣽⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠈⢿⠏⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⣀⡀⢈⠉⡁⢀⠐⡒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⣠⡔⠈⡀⡄⠀⡜⣀⣰⡥⠤⠦⠥⠦⡶⣥⠤⠤⠤⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠀⢥⣟⠡⢸⠀⡡⢶⣪⡩⠀⠎⠂⠀⠉⠂⠐⠐⡆⠄⠈⣳⢢⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡋⠀⣉⠀⠚⡁⠐⡜⠑⣠⣢⢰⣦⣀⣨⠏⠇⠤⠿⢶⢆⠀⠉⠀⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠐⠨⠇⢈⠙⠻⢀⠑⠯⢊⠉⢉⡆⠀⢄⠐⠓⠂⡠⠄⠄⠐⠈⠀⠄⣁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠈⠓⣤⡀⢹⣞⣉⠷⡶⡦⠨⠵⠆⡂⢞⠈⠉⠙⠀⣀⠒⠃⡛⠘⠒⠒⠶⠾⢒⠂⠄⠀⣄⡀
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠙⠃⠉⠈⠑⣷⡘⡇⡄⢹⡃⢐⣨⠔⠓⠲⢉⠈⢆⠀⠈⢄⠀⣀⠒⠀⠀⠁⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠈⣀⡀⠐⠀⠀⠒⢀⠤⠀⠒⠒⠎⣧⠟⠅⢠⠀⣁⡀⠐⣄⠰⡂⡀⠙⢖⠀⠌⣀⠀⠠⠒⠉⠆⠀⢸⠢
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠿⢉⣳⡐⠝⢀⠃⠒⠋⠐⠽⠰⢄⣈⠈⢄⣠⠖⠉⠛⠲⢦⡼⢀⠸⡀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣅⠮⢆⣅⡅⣠⠓⡠⣥⠄⢐⣆⡁⢆⡢⢉⠓⠦⣄⣀⡡⠆⠠⠩⠂⠀⠐⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢤⣽⣥⢟⣙⢉⠲⡥⢠⠣⡠⠋⠈⠢⡀⠀⢎⡢⠈⠻⢍⠂⠄⡈⠅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⢦⢶⠘⡄⢛⣀⢂⠐⡌⢉⠑⢤⠘⢛⠈⠢⣄⠂⠢⣑⠌⢢⠀⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡴⠊⢙⠻⠮⡄⢀⠈⢟⠀⠀⠙⠆⠀⠄⢷⠀⠐⡧⠘⢗⠠⢌⠐⢓⢧⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⢰⢂⣈⡤⠴⠚⠙⣷⣭⣴⠂⠃⠀⠆⠸⡆⠁⢠⠘⡖⠠⠀⡀⠀⡁⣀⢜⡂⠀⠘⠃⠺⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠨⢁⣀⣀⠡⠐⢉⠋⠀⠀⠐⠀⠻⢀⠈⠀⠘⠀⠊⢤⠀⠈⠢⠁⢉⡄⠀⠀⠈⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠂⠹⠄⠂⠀⢓⡢⢸⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣄⠈⢀⠻⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠑⣄⠀⢑⡄⢠⠊⠀⣠⠚⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠑⠀⠀⠈⡆⠀⠀⠀⠀⢰⠁⠀⠀⠋⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠂⢁⠀⠀⡆⠀⠙⠀⢨⠁⠀⠋⠀⢰⠀⠀⡈⠐⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⡄⠀⠐⡄⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠆⠀⢠⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠠⠀⢤⡈⢀⠀⠀⢠⡀⠀⠰⠄⠀⠃⠀⠸⡆⠀⠃⠀⢘⠀⠠⠆⠀⢀⡄⠀⠀⡀⠁⣤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠹⠀⠀⡆⠀⣇⠀⠰⡇⢠⡆⠀⣸⠀⢰⠀⠀⠎⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠒⠒⠖⠄⠐⠀⠀⠀⠱⡀⠀⢡⡀⢸⡆⢸⡆⠀⡇⢈⠀⢰⡇⢰⡏⢀⡌⠀⢀⠎⠀⠀⠀⠂⠠⠰⠒⠒
⠀⠀⠀⠀⠀⠐⢀⠀⠁⠈⠲⡄⠀⠑⣄⠀⢷⡀⠻⣄⣻⣜⣧⣿⣠⣟⣰⠟⢠⡟⠀⣠⠊⠀⢠⠞⠁⠀⠀⡀⠂
⠀⠀⠰⠒⠒⠂⠌⠁⢄⡀⠀⠈⢢⡀⠘⣧⣈⢹⠷⠋⡅⢺⢸⣇⡗⣨⠙⠾⡏⣁⣼⠃⢀⡔⠁⠀⢀⡠⠊⠡⠐⠒⠒⡂
⠀⠀⠀⠑⠂⣀⠀⠀⠀⠙⠢⡀⠀⠙⣷⣤⣽⢻⡈⣧⢻⣸⣾⣿⣇⡇⣼⢡⠟⣏⣤⣾⠋⠀⢀⠔⠋⠀⠀⠀⣀⠐⠊
⠀⣀⠤⠤⠀⠀⠀⠂⢤⡀⠀⠈⠛⣤⣤⣝⠙⣮⢷⣸⡾⣿⣿⣿⣿⢳⣧⡟⣴⠋⣫⣤⣴⠟⠁⠀⢀⡤⠐⠈⢀⠀⠠⠤⣀
⠀⠁⠀⣀⡀⠀⠀⠂⠀⠉⠲⠶⣤⣤⣩⣌⢷⣜⣿⣿⣿⣿⢜⡽⣿⣿⣿⣿⣣⡞⣠⣍⣤⣤⠶⠞⠉⠀⠀⠀⠀⢀⣀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠒⠠⢀⣀⣀⣉⣉⢥⣙⢷⣿⣿⣃⡟⣿⡳⢞⣿⢻⣘⣿⣿⡾⣋⡨⣉⣉⣈⣀⡀⠤⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠙⠻⢿⣿⡯⠅⠉⠁⠉⠉⠨⣽⣿⡿⠟⠋⠀⠈⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡍⠀⠀⠀⠀⠀⠀⠀⠈⢻⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠐⢀⠀⠀⠀⠀⣀⠂⠀⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠒⠒⠒⠈⠉⠉⢉⣉⡉⠉⠁⠒⠒⠒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⣀⠤⠒⠉⠁⢀⠤⢴⡀⢒⢉⡩⠆⠋⢠⠐⠃⢀⡋⣩⠭⠇⠀⠀⠀⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡘⡀⣠⡴⠻⡄⠀⡤⢊⠇⠘⣜⣍⠤⠼⠾⡖⠈⡋⠋⢹⡟⠉⡟⠛⢻⠿⠍⣉⡉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠥⢎⣇⣿⠉⠠⠀⡇⠀⢑⣽⢶⣺⡹⢱⠀⢇⣓⡩⠀⠳⠌⠥⠗⠀⠳⠼⠩⣇⣀⠀⢨⠻⣶⢤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠉⠙⢶⠴⠂⠛⠒⠤⣀⡷⢒⠭⡄⢸⠓⢊⠩⢤⠀⢠⢄⠠⡄⠀⡖⣖⠲⠀⠀⡯⡖⡌⣄⣀⣉⠓⠯⠀⣈⣑⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⠀⢧⣀⣀⣀⣀⣀⡀⠰⣅⡸⢀⡏⠀⢸⣼⠦⠦⠼⢮⢧⣧⢤⠗⠓⠚⠃⠚⠙⡟⣿⡓⡦⠤⣀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠉⠓⢄⣹⠇⠀⢸⠑⠿⠧⠤⢚⡱⣎⢳⣋⡉⡉⢑⡆⣀⣀⣀⠸⠬⠾⠸⠀⣀⣀⣀⣀⠀⠓⠬⢤⠇⣀⡀⠉⠢⣄
⠀⠀⠀⠀⠀⣀⠤⠤⢾⡁⠀⠈⠐⢤⣄⣤⡴⠧⣍⣁⠀⠏⠀⠶⠀⡂⢃⡰⢃⡾⢠⣧⣶⣬⣀⣀⣀⣀⣀⣇⣠⡇⣸⣄⣀⣀⣀⣸⣰⣯⣹⠀⠀⠙⠢⡀
⠀⠀⠀⡤⠊⠁⠀⠀⠀⢇⢼⣧⠀⠀⣿⣔⣲⠈⠳⣭⠽⡏⠉⢹⡻⡱⠘⡤⠊⣕⠢⡀⠀⠀⠀⣀⠤⡄⠀⠀⢸⣀⠀⠀⠀⠉⠉⠙⡳⠲⢤⡉⠉⠐⠒⠬⢦⣀
⠀⣠⠊⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠁⠈⠑⢮⣽⣈⢳⡇⣠⠸⢑⢯⠀⣗⢊⣁⡤⠚⠢⢴⡚⠁⠈⢳⠀⠀⠀⢸⣀⠀⠀⠀⠠⠠⠃⠀⠀⠈⠓⢄⠀⠀⠀⠉
⢰⠃⠀⠀⣀⣀⠀⠠⠀⣀⣀⠀⢀⠄⣀⣀⣐⠄⠹⣞⢹⢣⡿⠀⠈⠉⠀⡏⠉⠻⣄⠀⠀⠀⣌⠉⠒⠢⢧⣀⡀⠀⠸⣄⡠⠃⠁⠀⢀⡠⢒⠄⠀⠀⠑⣄
⣌⡠⣒⠭⠔⠒⠈⠉⠉⠑⠢⢽⠗⠉⠀⠀⠀⠙⣗⣹⢎⡞⡆⠀⣸⠠⢀⡇⠠⠴⠌⣳⢤⡘⡢⠙⡆⢠⡃⠣⡌⠑⠂⠤⢄⣀⠀⠏⠃⠀⠈⢑⠀⠀⠘⡄⠳⡀
⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⢉⣿⣋⠙⣾⢀⡔⡅⠂⡸⢗⠒⡾⣋⠁⢯⣺⡓⢮⣀⠀⠈⠉⢠⠤⣀⣰⠦⢎⡝⠓⠶⣦⡤⢀⡇⠀⢈⡇⠀⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⢋⠔⢬⠹⠓⢫⢎⠎⣰⣃⠀⠱⠜⡌⠳⣄⢈⠔⢁⡜⠉⠒⠤⢧⡖⠚⠀⠉⠉⡠⢄⡀⠀⠉⡶⢌⠑⠒⠭⣉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢾⡘⠷⠞⣰⣧⡼⢁⣔⠥⣹⡙⡷⡖⠃⠰⣩⣿⣄⠈⠢⣉⠷⢀⠞⡸⠛⢶⣤⣴⣣⠒⠟⠀⠮⡀⢯⠑⠄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⣈⣿⣋⣠⡿⠛⠫⡈⠳⣤⣥⡥⠸⢦⠀⣨⠎⠀⠑⢄⠀⡠⠋⣔⠑⢢⢀⠎⡳⣌⠑⠢⢄⡀⠈⣋⠄⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠏⡙⠉⣇⠙⣿⣵⠈⢆⠈⢦⠀⠧⠤⠻⡅⠀⠀⣠⣦⡙⢧⡀⠈⠑⡡⢃⢔⡥⡈⢳⡀⠀⠈⠒⢬⡂⣠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣾⣱⢋⡞⡹⡜⣸⡄⠘⣤⢄⡈⡆⠀⢳⠒⢦⠀⠈⣦⠊⠈⠢⠤⠊⡙⢦⣔⠁⠈⠲⠴⡡⠁⡸⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⡠⢶⠙⠫⣛⢵⡟⣰⠁⢡⠀⠹⡧⠇⢸⠀⠈⡷⡇⠀⢰⢁⣳⣄⠀⠀⠪⣾⣠⠝⣗⠢⣠⠞⠀⠸⣹⢎⣆⠀⠀⠀⠀⠀⠑⢌⡄
⠀⠀⠀⠀⢀⣀⠤⠔⠊⠉⣠⡿⢧⣎⣠⢾⠆⣁⠪⢽⠂⠘⡄⠀⢳⣒⡄⡆⠀⡇⠱⡀⠀⠀⠈⠱⠑⢄⠠⡏⠁⠀⠘⡄⠀⠙⠢⣀⡔⢃⢜⢆⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⢏⠁⣀⣤⠴⠶⢛⡩⠒⠱⣏⣟⣮⣼⡻⢀⠎⠀⠀⢱⠀⠘⡟⠃⠃⠀⠁⠀⢫⠉⡕⠀⠀⣇⠀⠑⢌⢦⢄⠫⣼⡄⠀⠀⠀⠑⢌⠺⡻⡆
⠀⠀⠀⠈⢆⠉⠢⢄⡛⠃⠒⠒⠂⠉⣁⠔⠋⢹⠊⠀⠀⠀⠀⢧⠀⠹⡥⢸⠀⢰⠀⠈⡞⠀⠴⣉⣸⠀⠀⠈⠳⡀⠑⠉⢱⠀⠀⠀⠀⠀⠙⢄⢿⡀
⠀⠀⠀⠀⠀⠳⢄⠀⠈⠉⠓⠀⠛⠉⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠣⡀⠱⡘⡀⢸⠀⠀⠸⣀⠀⠀⠈⡇⠀⠀⠀⠘⢆⠰⡊⡇⠀⠀⠀⠀⠀⠀⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠇⠀⢆⠀⠀⢫⡩⠃⢀⠇⠀⠀⠀⠀⠀⢻⠁⢸⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡈⢆⠀⠀⢣⠰⢾⠀⠀⠀⠀⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠱⣸⠀⠀⠀⠀⠀⠀⠀⢸⡎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⢢⠀⠘⠀⢠⠀⠰⡄⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠢⠼⠀⠀⢀⠀⢠⠀⠐⠢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠁⢤⡠⠄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠰⠄⠀⠀⠀⠄⠀⠲⡄⠀⢀⠀⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⡙⠀⠀⣤⠀⠀⠀⠄⠀⠸⢦⠈⠂⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢀⠀⠀⠀⠀⠁⠀⢀⣀⠀⠀⠈⠃⢀⠀⠙⠳⠄⠀⡄⠀⠈⠄⣩⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠐⠀⠐⠂⠒⠀⠹⠶⠤⣄⣀⠈⠀⡄⠀⠀⢣⡼⠀⠀⠒⠂⠀⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠐⠀⢀⢀⠀⠉⠙⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠂⠀⣀⠀⣀⣀⡈⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠠⠀⠀⠘⠃⠀⠀⠁⠉⠁⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣦⡆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠖⠁⠀⠀⠈⠀⠈⢀⠀⠒⠀⠀⠀⠀⠀⠂⢴⠆⢼⣩⠀⠾⠡⣙⡆⠰⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠬⠟⠁⠂⠈⠉⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠔⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⠤⠀⠀⠀⠀⢈⡀⠐⠁⠀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠚⠪⠏⠀⠀⠠⠊⠀⢠⡌⠛⠁⡀⠒⠨⠍⠈⠀⠀⠀⢠⣚⡋⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡀⠀⠀⣀⠐⠋⠸⠀⠆⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⡈⠤⠀⠁⠁⠀⠀⢰⣰⠂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠈⠠⠀⠀⠀⠋⠀⠀⠈⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⠀⠤⠁⠀⠘⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠂⡀⠉⢉⠉⡉⠉⡀⢐⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⢀⣤⠂⢁⠠⠀⢢⠅⣠⣰⠁⠴⠮⠥⠼⠴⣬⡄⠀⠠⠤⠵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠀⡄⠈⠾⣔⢿⡁⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠁⢀⠂⡎⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠐⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠈⡛⠿⠇⠔⠠⡣⡘⠓⠂⠀⠀⠀⠀⠅⠄⢀⣀⣀⠘⠬⠠⢀
⠀⠀⠀⠀⠀⠐⠄⢀⠀⢲⡤⡞⢷⣬⣼⠀⣃⣤⢡⠀⠔⠀⠀⠀⠤⠄⠤⠧⠾⠰⠤⠤⢤⣷⡦
⠀⡠⠀⠀⠀⠀⠀⠻⠇⠜⠉⠪⣴⠝⣾⢀⠘⣽⡀⠀⠀⡀⠀⣠⠔⠙⡄⠀⠁⡆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠂
⠘⠀⠀⠀⠀⠀⠠⠀⣀⡀⠠⠀⡈⢷⡹⡾⠀⡉⠁⠀⠉⢀⠀⣠⢍⠐⠺⡤⢀⠈⠤⠀⠁⣀⠔⠂
⡶⠓⠀⠀⠀⠀⠀⠁⠉⠀⠀⡀⢼⡾⢿⡀⣠⠇⠀⠀⣠⠄⢑⠢⢣⠃⠐⠩⢂⠈⢀⡲⠴⢄⣀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢨⢉⠲⠳⠈⠀⠀⠀⠀⠀⠄⠀⠈⠙⠐⠠⣵⡘⠉⠀⠠⠀⠈⠀⠀⠀⠠⢑⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⢈⠉⠘⡌⠔⠀⠀⢈⢩⠁⠀⠃⠀⠀⠀⠀⠀⠉⠑⢦⠀⠀⠀⠀⠠⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈⢀⡀⢀⠘⠍⠤⠴⢎⠀⢀⣄⠂⡀⠀⠀⠀⠀⠁⡀⠀⠀⢼⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡲⣶⣣⢯⠄⠴⠈⢦⡄⠂⠘⣆⠂⠀⠶⡀⠑⢂⢄⢲⣄⠀⢒⠅⣠⣂⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣳⣎⠁⣠⡈⠛⢪⠀⠄⠘⣅⡈⠀⠉⠄⠈⠐⠛⠠⡀⠑⠂⠙⠈⠁⢀⡀⠉⢧⠀⠀⠀⠀⠳
⠀⠀⠂⢠⡤⢖⡛⠙⠀⢸⠷⢼⣇⠀⠀⠀⠀⢻⡁⠀⠀⠈⣁⠀⢀⠄⠀⠀⠤⡀⠠⡀⠀⠉⠂⠘⢆
⠀⠀⠀⠀⠈⠂⠈⠉⠀⠀⠂⠀⠋⠀⠀⠀⠀⡀⠁⠀⠐⠀⠩⠀⠑⢰⠀⠀⠑⠄⢀⠁⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈⠄⠳⠈⠀⠀⢃⠔⢸⠀⠀⠀⠈⠚⢸⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⣄⠀⢂⠻⠀⠀⠀⠀⠈⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠰⠐⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠂⢠⠧⠀⠰⠀⠈⠀⠖⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢡⡀⠀⠂⡀⠀⡞⠀⠀⠀⠃⠀⣄⠂⠀⢠⠇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⣄⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⣿⠂⡀⠀⢈⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⣀⠀⠀⠀⠀⠀⣦⡄⠠⠀⠀⢉⠀⠿⠀⡉⠀⠈⠀⢠⡴⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠊⠁⠀⠀⠀⠀⠙⠀⠻⣄⠰⠧⠀⠉⣁⣠⣤⣶⣤⣀⡉⠁⠀⠽⠀⡴⠛⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⢀⣠⠄⠀⠀⡹⠀⠉⠙⢿⣾⠁⠀⠘⣮⠟⠃⠁⠀⣏⠀⠀⢠⣆⡀⠀⠀⠀⠀⣄⣀⠀⡀
⠀⠀⠀⠀⣠⣤⣀⡉⠟⠉⠁⠶⠾⠄⠒⠒⠉⡀⠀⠀⠉⡀⠰⣄⣠⡇⠀⠀⠀⣯⡀⣠⠂⡀⠁⠀⠀⠀⠀⠒⠂⠈⠒⠖⠈⠙⠻⣁⡀⣤⣀
⠀⠀⠀⠀⠁⠀⠘⠀⣀⡴⠚⠁⢻⡔⠒⠉⠀⢳⣀⡀⠐⢿⣇⣀⣹⣿⣿⣬⣿⣿⣥⣀⣻⠗⠂⢁⣀⡟⠀⠉⠐⢠⡅⠈⠓⣤⣀⠄⠃
⠀⠀⠀⠀⠀⠀⣠⣾⣉⡿⢾⡀⣰⠟⠀⡠⠀⣚⣿⣦⣴⣾⣿⣿⣿⣿⣿⣾⡿⢿⣿⣿⣿⣴⣦⣰⣟⣓⠠⠀⠈⢻⣆⢞⡶⣿⣈⣷⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣌⣥⡙⠆⠈⢠⣶⣿⣿⣿⠿⠛⠛⠉⠉⠁⠉⠁⠀⠀⠉⠉⠉⠉⢽⣿⡿⣿⣦⣄⡀⠼⣫⣏⣥⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⠻⠶⣄⠀⣽⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣟⣤⠀⣤⢾⠛⠛⢿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⣸⠟⠿⠃⣠⠶⣶⠀⠘⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠁⢠⡶⢶⣄⠙⢿⣻⡆
⠀⠀⠀⢀⣀⣰⣋⣘⣠⣾⡇⠀⠊⠁⣀⡆⣿⡏⢠⣤⠒⢲⢦⣤⣄⠀⠀⠀⠀⠀⣠⣤⡴⠒⠂⣤⡀⢹⣧⢰⡀⠈⠓⠀⣹⣷⣖⣛⣁⣀⣀⡀
⠀⠀⠀⠀⠈⠉⠋⠙⠏⣻⣽⣶⣴⣦⡈⠧⠿⠇⠸⣧⠀⠀⠀⠀⣹⡦⠄⠀⠀⣾⣏⠀⠀⠀⢄⣿⠁⡸⠷⠼⢁⣶⣶⣶⣿⣟⠿⠋⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡷⠛⣠⠶⢛⣛⣿⡆⠉⠒⠚⠀⠾⠟⠁⠀⠀⠀⠈⠻⠗⠂⠓⠛⠉⢸⣟⡛⠳⠦⣌⠛⠵⠉⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢠⢼⡗⢠⣾⣹⣿⣿⣿⡿⣿⣄⣀⣠⣤⣄⡀⠀⢠⣤⡄⠀⢀⣠⣤⣄⣀⣴⣿⣿⣿⣿⣿⣏⣷⡄⠠⠢⡄
⠀⠀⠀⠀⢀⠈⠓⠛⢣⡖⢀⣾⣿⢃⣾⣿⠿⠛⠿⣿⣿⣫⠁⠈⠁⠀⢿⣿⡷⠀⠈⠁⢈⣿⣿⣿⠿⠻⢿⣿⣿⡽⣿⢱⡀⢠⠼⡁⠂⠈
⠀⠀⠀⠀⠈⠀⠐⠉⣹⠇⢨⠛⢿⢸⠻⡏⠀⠀⠀⣸⣿⣼⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢈⣿⣿⡇⠀⠀⠆⣹⣿⣇⡿⢿⡇⢸⣍⠁
⠀⠀⠀⠀⠀⡀⢀⠴⠁⡆⢸⡄⠸⣷⠉⢛⠢⢤⣶⠻⣿⡟⣷⡄⠂⠀⠠⠀⠀⠀⠀⣠⣾⢿⣿⣿⣦⣴⣾⣿⣿⣿⠇⣰⡇⠈⠈⢆⡀
⠀⠀⠀⠀⠀⣠⡿⠀⠂⠱⠀⠛⠂⠀⠘⠀⠤⠏⠉⠗⢉⡴⠃⠇⠀⠂⠀⠀⠀⠐⠂⢹⠿⣆⠛⠿⠿⣿⢿⠽⠛⡁⠔⢹⠁⠂⠀⠈⣿⡀
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠠⢀⣔⠛⢁⣾⠀⠀⠀⠀⡼⠀⠀⠀⢀⣷⡙⠛⣶⣤⠄⠤⠀⠎⡁⡀⠂⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠙⠻⠦⠔⣠⢭⡠⠶⢥⣘⠳⠄⠀⠀⢁⣀⣠⣴⠊⢡⣿⠾⣴⣧⣴⡶⠷⠞⠋⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⣤⡧⢀⠀⠀⠘⠻⣻⡄⠀⠂⣨⣟⣤⡾⣿⠁⠀⠀⠀⣤⡿⣦⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠊⠀⠀⠀⠀⠈⢿⣆⠁⠉⢠⡄⡰⠁⢠⡅⠀⡞⠿⠁⠽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣋⡰⠃⠀⠘⠁⠀⢁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢷⠟⠛⡛⠙⠂⢠⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣄⡄⠃⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡜⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⡻⣇⣠⢻⡀⠀⠀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣄⠀⠀⠸⢈⠂⠀⠀⢃⣎⡇⡌⠃⠀⢰⡅⠇⠀⠀⣠⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢗⣄⠀⠃⡸⡄⠀⠀⠈⡕⠀⢐⣈⣼⢱⡀⡀⠀⢪⠉⠀⠀⢀⢇⠘⠀⢠⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠢⡄⠈⠃⢵⢄⠀⡀⡯⠀⢐⠚⡇⠁⠀⠠⡇⠘⠇⢀⠈⢸⠃⡂⠀⢼⢀⠀⣠⡫⠘⠀⢠⡔⡆
⠀⠀⠀⠀⠀⠀⠀⢀⢄⣀⠀⠆⢸⢠⠀⢀⣦⠐⠆⠸⡀⠶⡀⠰⡌⠓⢀⠁⡘⠀⠈⢁⠂⠀⠴⣀⠃⠰⠂⣮⠀⠀⡄⡏⠰⠀⣀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠉⡄⡀⢀⣰⠄⠣⡘⢠⣈⢢⡘⢀⠁⠂⠰⢈⠘⡀⠣⠀⢠⠄⠐⠈⡐⢋⡔⢁⡄⢃⠜⠠⣆⡁⢀⢰⠉⡜
⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠁⣳⠙⢄⠁⢄⠁⢦⠑⠄⢁⠈⡐⢄⠠⠊⢠⠀⡂⠀⡘⠄⡠⢀⠀⡈⠠⠊⡴⢈⡠⠊⡠⢋⣞⠈⠀⠀⢀⡤⢠
⠀⠀⠀⠀⠀⠘⠆⠛⠲⠀⠈⠀⠃⠌⠀⢦⡘⠀⠃⠠⢁⢢⡱⠈⠇⡎⢨⠀⡇⠀⣆⠸⠁⢎⡔⡈⠄⠘⠐⢃⡴⢀⡡⠘⢀⠁⠀⠖⠟⠰⠊
⠀⠀⢀⣀⠀⠀⠀⠀⡄⠃⢀⠑⠐⠀⢘⠂⠕⠐⢐⡐⢜⡀⢋⠆⠐⢰⠀⠀⠂⠀⠇⠂⡰⡘⢀⡠⠂⡂⠂⠊⠐⠃⠐⠆⠋⡠⠟⢠⠀⠀⠀⢀⣀⡀
⠀⠀⠘⢭⠙⡂⠄⠀⠈⠀⠀⢁⠐⠄⠂⢀⡣⡅⠲⢠⠀⢷⠀⠈⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⡾⠂⡄⠖⢸⢘⡀⠐⠠⠂⡉⠀⠀⠀⠀⠠⢐⠋⡭⠃
⠀⡀⣀⡀⠁⠀⡸⢣⠄⣁⡘⠦⡈⠀⠓⢥⠙⢂⣂⡈⠑⠀⡀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠚⢁⣐⡐⠋⡬⢚⠁⢁⠴⠃⢈⢠⡾⢇⠁⠈⢀⣀⢀
⠀⠛⢬⠘⠔⣂⡘⠂⠤⢬⣁⠓⢈⢠⠂⢁⠑⠤⠠⠀⠀⠀⠀⠀⢀⠐⡐⣄⣠⢂⠀⡀⠀⠀⠀⠀⠀⠥⠤⠊⡈⠐⡀⡁⠒⣀⡥⠤⠐⢃⡒⠨⠃⡥⠛
⠀⠀⠀⠀⠀⠔⡙⠂⠴⠂⠤⠠⠄⠬⡢⠤⡁⠑⠀⠀⠀⠀⢡⣱⡬⣁⣭⣶⣮⣭⣉⢥⢆⡈⠀⠀⠀⠀⣚⢀⠤⢌⠥⠠⠆⢤⠔⠦⠐⢉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠈⡂⠂⣀⠀⠀⠀⠀⠀⠀⡘⠦⣩⣾⣿⣿⣿⣿⣿⣿⣷⣍⠴⢃⠀⠀⠀⠀⠀⠀⣀⢜⢐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⣈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣅⡀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡠⣿⣿⡿⠋⠉⠀⠀⠉⠛⢿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢚⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠁⠀⠘⡣⡀⠀⠀⠀⠀⢀⡘⠂⠀⠈⠰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠑⡄⠈⢡⡀⣠⠉⠀⡔⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠓⠀⠀⠙⡇⠀⠁⠁⠀⡏⠀⠐⠐⠃⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠙⠀⢁⠀⠰⠆⠀⠁⠀⠈⠀⠀⠃⠀⡶⠀⢀⠁⠘⠁⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⡄⠀⠰⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠂⠀⡰⠁⠀⡄⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠰⠂⣄⠈⢀⠀⠀⢠⡀⠀⢡⠀⠀⠀⠀⢸⠀⠈⠀⠀⠂⠀⢠⠀⠀⣠⠀⠀⢀⠀⢀⠄⠲
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠈⢄⠀⠀⠱⠀⠠⡄⠐⡇⠀⢸⠆⢰⠀⠀⡖⠀⡄⠀⠰⠁⠀⢀⠌⠀⠀⢀
⠀⠀⠀⠀⠒⠐⠂⢄⠑⠀⠀⠈⠳⠀⠀⢢⠀⢱⡄⢻⡀⢠⡄⢁⠀⣸⠃⣴⠁⢠⠂⠀⠰⠋⠀⠀⠐⠁⠄⠒⠐⠂
⠀⠀⠀⠀⠀⠐⢀⠀⠀⠈⠢⡄⠀⠱⣄⠈⢷⡀⢿⣌⣳⣼⣇⣯⣴⣋⣼⠇⣰⠏⢀⡰⠁⠀⡤⠊⠀⠀⢀
⠀⠀⠐⠚⠒⠂⠌⠑⢄⠀⠀⠉⢄⡀⠹⣧⣈⣻⢶⠩⡅⣦⢸⢠⠃⡭⢱⢾⢋⣠⡿⠁⣀⠌⠀⠀⣀⠔⠉⠄⠒⠒⠐
⠀⠀⠀⠐⠠⣀⠀⠀⠀⠙⠦⡀⠀⠙⣦⣄⡿⢵⡸⡆⣷⢽⣼⣼⢸⢃⡏⣰⠽⣇⣤⡞⠁⠀⡠⠞⠁⠀⠀⢀⡠⠐
⠀⡀⠤⠄⠀⠀⠁⠂⢤⡀⠀⠈⢻⣦⣤⣝⢹⣜⣧⣻⣼⣿⣟⣿⡿⣼⣱⢏⡾⢙⣥⣤⣾⠋⠀⠀⣠⠄⠂⠀⠀⠄⠤⠄⡀
⠀⠁⠀⠀⡀⠀⠀⠀⠀⠉⠲⠶⣤⣤⣭⣘⢷⣽⣿⣿⣿⡷⢩⣽⣿⣿⣿⣿⣴⢏⣨⣥⣤⡴⠶⠊⠁⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠒⠤⣀⣀⣀⣉⣩⢦⣙⢷⣿⣟⣫⡻⣟⠲⣺⡟⣇⣛⣿⣷⣟⣡⢬⣉⣁⣀⣀⠠⠔⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠙⠻⢿⣿⡿⢈⣉⢰⢉⣁⠽⣿⣿⠿⠛⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠬⡋⢤⣶⣮⢹⢩⣶⣦⠌⡫⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢤⠤⡖⠺⠒⡤⢤⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠸⠀⡇⢀⠀⡇⠸⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠸⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠐⢀⠀⠀⠀⢀⠐⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠢⡀⠌⢣⡀⢀⡞⠑⢀⠔⠂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡁⠹⠆⠀⠀⠳⡄⠈⠁⠈⠁⢠⠞⠀⠀⠰⠏⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢆⠐⠀⠈⢠⠀⠀⠣⠀⠰⠂⠀⠼⠀⠀⡄⠁⠀⠂⡰⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⣄⠐⡀⠀⠪⡃⠀⠈⠄⠀⠀⠀⠞⠀⠀⠀⠀⠠⠁⠀⢘⠔⠀⠀⠂⢠⠖⠊⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠡⠀⠀⠢⢛⠀⠀⠑⡀⠀⢠⠀⠀⢠⡄⠀⡄⠀⠀⡄⠀⢀⠊⠀⠀⡛⠔⠀⠀⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢃⠈⠓⢄⠰⠀⠀⠈⢣⡀⠀⢉⠀⢰⡀⠀⢸⡇⠀⡁⠀⠀⡆⠀⡉⠀⢀⡜⠁⠀⠀⠆⡠⠚⠁⠈
⠀⠀⠀⠀⠀⣀⣀⠀⠂⣀⠀⠁⠱⣄⠀⠀⢃⠀⠸⡄⠈⣧⠀⠘⡃⢰⠃⠀⣼⠁⢠⠇⠀⡘⠀⠀⣠⠎⠈⠀⣀⠐⠀⣀⣀
⠀⠀⠀⠀⠈⠀⠈⠁⠢⠉⢄⠀⠁⠈⢇⠀⠈⢦⡀⢿⣂⢹⡅⢀⡇⣠⠄⢨⡏⣰⡿⢀⡴⠁⠀⡸⠁⠈⠀⡠⠁⠔⠈⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠄⠙⣆⠀⠈⢢⣀⠘⣧⣈⠻⣦⡿⢮⢧⡿⡴⢯⣴⡟⣁⣼⠁⣀⡔⠁⠀⡰⠋⠠⠀⠀⡠⠈
⠀⠀⠐⡉⠉⠁⠂⠀⠑⢄⡀⠀⠈⠳⣄⡀⢻⣦⣌⡿⣛⠑⡆⣿⢸⡇⡏⣰⠊⣛⢟⣡⣴⠞⢀⣠⠞⠁⠀⣀⡤⠊⠀⠐⠈⠋⢉⠂
⠀⠀⠀⠈⠒⢠⡀⠀⠀⠀⠙⠢⣀⠀⠈⢷⣦⣬⠏⢧⠸⡇⣷⣸⣾⣷⣇⡟⣸⠇⡼⠹⣥⣴⡾⠁⠀⣀⠔⠋⠀⠀⠀⢀⡤⠒⠁
⠀⢀⠠⠤⠄⡀⠈⠑⠂⣄⠀⠀⠈⡛⣶⣤⣸⡋⣷⡜⣧⢿⣸⡿⣿⣿⣿⢧⣟⣼⢣⡞⢙⣇⣤⣶⠛⠁⠀⠀⣠⠐⠊⠁⣀⠠⢤⠤⡀
⠀⠁⢀⡀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣠⣀⣉⣇⠻⣮⣻⣿⣿⣿⣷⢝⣫⣿⣿⣽⣷⣟⣴⠏⣘⣉⣁⣤⣴⠖⠋⠁⠀⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠈⠁⠒⠀⠦⣀⠀⠀⡀⠊⠙⣃⡘⢷⣾⣿⠿⢸⢿⣟⢮⡵⣿⢿⡹⢿⣿⣵⡿⣃⣘⠋⠑⢀⠀⢀⣀⠴⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠻⢷⣿⣿⣿⣛⠁⠛⢣⡞⠛⢘⣻⣿⣿⣿⠿⠛⠀⠙⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣛⡟⢁⣈⣓⢺⡗⣚⣁⡈⠻⣛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⠂⠉⢛⣛⣹⣏⣛⡛⠉⠘⠯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡇⠈⠁⢸⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⡇⢰⡆⢸⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠁⠘⠃⠈⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠩⠠⠀⠀⠀⠀⠄⠍⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤⠍⠉⠥⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣺⠀⠈⠉⢩⠀⠀⣾⣦⢤⠄⢀⡆⠀⢨⠉⠉⠀⢸⣒⡤
⠀⠀⠀⠀⠀⠀⠀⢴⣻⢞⣋⣭⠈⠀⣟⡧⢄⠰⠀⣿⠀⠸⠗⠐⢀⠤⣞⡟⠈⢸⣭⣛⢾⣳⡄
⠀⠀⠀⠀⢀⢀⣵⠛⠵⠎⢁⡼⡕⢄⣠⣽⣶⠌⠣⣌⠀⢀⡤⠞⢤⣾⣥⣂⠀⣽⣄⠩⢶⠝⢓⣅
⠀⠀⠀⡀⣠⠟⠵⣇⡀⠀⣉⡲⢢⠟⣋⣥⣾⠃⡈⣹⠀⠨⡋⡀⢻⣯⢍⠛⢧⠲⢊⡩⠀⢠⣶⡝⢧⡀
⠀⠀⠐⣴⢋⢾⡄⣼⣣⠰⡿⢋⠕⣿⡤⡘⢧⠶⠂⣷⠘⢰⣇⠰⣦⠟⣠⣾⡗⢉⠻⣷⢂⠻⣄⡴⢆⢳⡄
⠀⠀⣸⢣⡿⠟⣴⣾⣌⠖⣱⣿⢦⢑⣴⣿⣷⡹⡏⢰⡟⣳⡌⡿⣱⣿⣷⣔⢡⣾⢷⡝⢌⣽⢶⡝⠿⣧⢻⡀
⠀⢰⡇⣜⡴⠀⢻⣿⠏⣼⣿⣯⠟⣭⡻⢿⠟⣵⣯⣌⠛⠋⣬⣷⡜⠿⠿⣛⡝⢯⣿⣽⡌⢿⣿⠃⠰⣜⡄⣷
⠀⣾⢸⣟⣷⡜⠻⡟⣸⣿⣓⠏⢞⣤⣙⢊⣾⢇⢉⣨⣓⣺⣄⢁⣿⣏⠚⣡⣜⠎⣟⣻⣿⡘⠿⠗⣴⣟⣛⢸⡆
⠄⡏⣀⣈⡿⠐⣂⠃⣿⡯⣽⢠⠺⣧⡿⠀⠙⠮⠉⠙⠋⠙⠉⠭⠞⠁⠘⣯⣽⢇⢸⡭⣿⡇⢃⡰⠨⣏⢀⡈⡇
⠒⡇⣉⠀⠀⢸⣿⠘⣿⣟⣧⡴⠤⢤⣰⣶⠀⢰⣄⠉⠁⠩⢁⣰⠀⢰⣶⣠⡤⠼⣄⣟⣿⣗⢸⣿⠀⠀⢈⡁⡷
⠀⣇⠉⢈⡷⢰⡌⡺⡟⢛⣩⣾⣿⣮⣺⣿⣆⠀⠼⡗⢪⡳⡺⠄⢀⣾⣿⢫⣾⣾⣮⣙⠛⡇⣊⢵⠴⣏⠉⢁⡇
⠀⢿⢨⠈⠁⠀⢈⢠⠰⣿⡮⠿⡿⢟⠬⠝⣋⠉⢠⣘⣀⣘⣠⠀⠩⡛⠿⢜⠿⡿⠯⣾⣷⠡⣘⡀⠀⠉⠹⢸⠇
⠀⠘⣇⠀⠀⠄⠂⢁⡀⡉⢲⣾⢿⡿⣀⣿⡙⠗⠸⣿⡿⣿⡿⠀⠺⣹⡗⡰⢿⢿⣶⠊⡁⣄⡁⠃⠄⠀⢀⡟
⠀⠀⢹⡜⢦⡀⡎⢬⠙⢧⡲⣿⡿⢁⣬⡉⡤⢀⠐⣤⣿⣯⡄⢀⡠⣜⣩⣅⠘⢿⡷⣠⠝⢋⠄⡆⢀⡎⣼⠁
⠀⠀⠀⠻⣌⢄⠘⢈⡷⠼⣷⣮⡻⣍⠛⢟⢛⣬⣵⠻⣟⣻⠳⣬⣄⠛⡟⢋⡵⣋⣾⡿⠤⣞⠘⢁⢎⡼⠃
⠀⠀⠀⠐⠙⢾⡲⡟⠀⠀⡨⠱⠌⠶⠀⠈⢳⠛⢟⡸⣟⣫⢘⡿⢻⠊⠀⠰⠎⠴⢈⣅⡀⠈⡶⣺⠟⠁
⠀⠀⠀⠀⠈⠈⡻⣤⡺⣅⣢⡜⢀⡀⠒⡄⠛⡗⣨⢰⣿⣷⢮⡔⠟⠃⡄⠂⢄⡘⣡⣰⠼⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠪⠙⢦⣝⠈⠉⠂⣴⡏⠁⠒⠬⣄⠁⠉⡬⠵⠇⠘⣏⡤⠚⠉⢘⣥⠞⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢬⣝⣃⠙⠶⠀⠼⡀⠸⠧⠠⠗⢃⣘⣭⠴⠚⠩⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢒⢣⡒⠚⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢀⢀⣦⡸⣧⡿⢦⠀⢀⣉⣲⣒⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣘⢾⣿⣿⣷⣥⣶⣿⡇⠀⢷⢼⣌⣈⠲⢄⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣶⣿⣿⠟⢋⣥⡴⣶⡶⢶⡶⣬⣁⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣻⣶⣝⠿⣿⡟⠛⠿⣧⣾⣿⣿⣤⡶⢿⠏⠁⠉⠯⡝⠦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⡾⣧⡀⠀⠀⠹⠟⡉⠀⢀⡞⠀⢠⠀⠀⠀⠱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠿⢿⣟⣀⣿⣿⢳⣤⣀⣿⠃⣀⣸⡇⢠⢎⣼⣷⣄⠀⣻⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡄⠀⠹⣿⣿⣿⣿⣿⣿⣻⡁⢼⣇⡹⢦⡿⣋⣨⠀⣽⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⣽⣷⠶⠾⠻⣿⡿⣿⣿⣥⡖⣻⣿⣇⣹⡑⢛⣯⠺⢼⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢛⣻⣿⣷⣶⣾⣿⣤⣿⣿⣿⣵⣿⣶⣶⣦⣤⣬⣥⣐⡘⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠋⠟⠙⠻⠙⠿⠟⠁⠹⢯⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣺⣿⣿⣿⣿⣄⣿⠀⢾⣦⡀⠀⠀⣤⣤⣀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠿⠿⠋⢀⣿⡏⢷⠀⣀⣤⣤⣅⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⡶⢿⣿⣿⣡⣸⡾⡄⠛⠳⠶⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣤⣄⣀⣀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡟⠁⠀⠈⠁⠻⣧⣼⣿⣿⣿⣿⣿⣿⠟⣿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠄⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⣾⣅⣀⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣠⡶⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣇⠈⢻⠟⠛⣿⣿⣿⠻⢿⣿⣿⣿⣧⡀⠹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⠧⣿⣧⣀⠈⣿⣿⣦⣨⣿⡀⢹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢻⣷⣿⡏⣥⢢⡽⡟⣿⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠹⣿⣛⣧⡋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢖⣛⣭⣭⠿⠶⠾⠿⣟⣯⣿⣓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡫⠖⠋⠉⠉⢳⡘⡆⠀⠀⢠⡿⠱⢉⠀⠈⠳⢯⣓⢤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢀⣼⠃⠻⣤⣤⡾⠃⠰⣘⣀⢀⡜⠀⠈⠳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡼⡿⠗⠚⠑⢛⡼⣛⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠍⣛⠷⡁⠈⢿⢦⡳⡄

⠀⠀⠀⠀⠀⢀⡞⡞⠀⠀⠀⠀⠠⣪⣴⢶⣶⣶⣤⡀⠀⠀⢀⣠⡴⠶⠶⢶⣬⣕⡉⠀⠀⠀⢳⠹⡄
⠀⠀⠀⠆⠀⡾⡼⠀⠀⠀⢠⠀⠀⡀⠀⠀⠒⣠⠉⠹⡦⢤⡟⠁⠠⠄⠒⠂⣀⡈⢻⢠⡀⠀⠀⢣⢻⡀
⠀⠀⠐⠀⢸⢷⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠁⠀⠈⠃⠘⡃⠀⠀⠀⠀⠙⠊⠁⠸⢸⡇⠀⠀⠘⡎⣇⠀⠂
⠀⠀⠀⠀⢸⢸⡃⠀⠀⠠⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡧⠀⠀⠀⠀⠀⠀⠀⣠⣯⠿⠀⣀⠀⣇⣿⠀⠃
⠀⠀⠀⠀⢸⢸⢃⢠⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠃⠀⠀⠈⠓⠒⠉⠀⢱⠫⣭⣭⣿⡯⣿
⠀⠀⢰⠀⠘⡀⣼⣿⡁⣀⡾⠃⠀⠀⠀⠀⠒⠒⠒⠛⠿⠿⠿⢓⣒⡊⠀⠀⠀⠀⠀⠸⠶⢤⣾⣿⡇⡇⠀⡇
⠀⠀⠘⡄⠀⠁⢻⣿⠀⠀⠀⠀⠀⠀⣠⡾⣟⣛⣛⣛⣛⣛⣟⣋⣙⣛⠿⣆⠂⠀⠀⠀⠀⠀⢾⡿⢰⠀⢸⠇
⠀⠀⠀⢻⡀⠀⠈⢿⡆⠀⢀⡀⠀⠀⠙⠉⠈⠙⣎⠁⠓⠂⠀⢀⠎⠁⠀⢋⠄⠀⠀⣄⡀⠁⡹⠁⠁⢀⡟
⠀⠀⠀⠀⢷⡀⠀⠈⢻⠻⡛⢳⣤⡀⠀⠈⠙⠒⠛⠀⠀⠀⠀⢸⠛⠛⠀⠁⠀⠀⣼⠋⣍⡉⠁⠁⢀⡾⠁
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠑⢳⣄⣰⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡀⡴⠊⠡⡼⠋⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠁⠠⢠⣀⡨⠙⠛⠛⣆⡀⠀⣀⠟⠖⠂⢺⠰⣰⠖⠀⠀⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠉⢐⠂⠢⠴⠀⠬⠍⠡⠰⠶⠊⡀⠈⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣄⣀⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣶⣶⣶⣶⣶⣾⣿⡿⠿⠛⠋⠁

⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠘⠀⠀⠀⣀⠅⡀⣆⠀⠀⡂⢀⠥⡀⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠄
⢀⣤⣀⣟⡀⠁⠠⢰⡃⡆⠀⠀⡇⢹⠀⠀⠁⢀⣗⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠂
⠸⠗⠂⢻⢹⡶⣦⣦⡱⡇⠀⠀⣶⢨⣦⣶⢶⡉⡟⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣁⠄⠒⠐⠿⠀⠒⢠⣈
⠀⢀⣀⢈⣻⣅⠈⣅⠒⢷⠉⢑⡞⢂⣎⠀⣨⣟⡀⣀⠀⠀⠀⠀⠀⠀⢤⣟⡤⠀⡜⠀⠀⠠⠐⠄⠀⠀⢣⠀⢤⣻⠤
⠠⠞⠀⢠⢩⡶⠼⢤⡍⢎⠁⢈⡜⣡⠴⠤⢾⡁⠔⠈⠳⠄⠀⠀⠀⠀⢐⡀⢴⢸⣬⣕⣤⢈⠀⡀⣤⣲⣴⡇⠮⢀⡂
⠀⠀⠀⢀⠈⡏⣦⠸⠽⠤⢀⡀⠬⢯⠁⡞⢻⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⣾⠀⡄⠀⠩⡄⠀⢠⠍⠁⢠⠀⣷⢈⣀
⠀⠀⠀⠀⢰⠀⢻⡄⣅⠤⠼⠶⠄⡄⢰⠇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠎⣠⡩⠖⠈⠶⠈⠲⢍⣆⢁⣈⠁
⠀⠀⠀⠠⡈⠀⠒⠃⠐⠓⠹⠣⠒⠅⠚⢂⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣁⠈⠑⠀⠘⠁⠀⠰⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢨⠈⢁⣙⡀⠀⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠬⠶⠾⡟⠛⣿⡛⢻⠷⠶⠥
⠀⠀⢠⠀⡤⠀⢀⠀⠀⠸⠿⠇⠀⠀⡂⠀⢄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠜⠀⠀⣀⣭⢀⠐⠀⠂⠀⠠⡀
⠀⠀⢀⣅⢰⣶⣧⣄⠀⠀⠀⠀⠀⣀⣼⡶⡇⣠⣁⠀⠀⠀⠀⠀⢈⠀⣻⠖⠄⠀⠀⠘⠛⠀⠀⠀⠀⠶⣟⠀⡀
⠀⠀⠙⡄⠀⠙⠝⡊⠀⠠⠀⠀⠀⠑⠪⠊⠀⢠⠟⠀⠀⠀⢠⡱⠀⠠⢃⡀⠴⡶⡀⢀⠀⠀⢂⡶⡶⠐⡜⠆⢀⢞⡀
⠀⢀⣴⠛⠉⡂⢀⡁⠑⢤⠀⡤⠎⠘⡀⢔⠋⠛⣢⡀⠀⠀⠀⠺⠘⡄⣀⢉⢩⣥⣛⠛⠀⠚⣛⣬⣭⡍⣈⢠⠂⠕
⠀⣄⠀⠡⠊⡐⠀⢠⠂⠀⢛⠀⠀⣀⠄⢂⠐⠌⠀⣠⠀⠀⠀⠁⠈⠀⠈⠃⢸⠓⢕⠡⣤⢤⡪⠘⡷⠈⠁⠀⠁⠀⠁
⠀⢐⢤⣇⢰⠄⢠⡿⠀⠀⠉⢀⠀⠻⡄⠀⡆⣸⡦⡒⠀⠀⠀⠀⠀⠐⠸⡄⠈⡄⠄⠄⠚⠤⡠⢤⡂⢀⠗⠂
⠀⠈⠈⠨⡀⠒⠀⠀⠉⠁⣂⠘⠁⠃⠀⠐⢂⠅⠁⠁⠀⠀⠀⠀⠀⠀⠀⠃⡩⠀⠉⠱⠀⠞⠈⠀⢬⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣻⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠔⡕⠁⢄
⠀⠀⠀⠀⠀⠀⠈⢀⠆⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠀⡀⡠⢀⠀⠈⠠⠀⠐⠀⠀⣀⡀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠓⠇⠠⠦⡈⠃⡀⠒⠀⠐⠀⠀⡈⠀⠄⠀⠈⠁⠀⠀⠂⠀⢨⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠄⠀⠀⠐⠀⠀⠀⠀⠡⣄⠑⠀⣀⠀⢐⠀⠀⠨⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠡⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠠⢌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⠀⠀⠈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠑⠀⠀⠄
⠀⠀⠀⠀⠄⡀⢠⢀⠠⠀⠀⠄⠀⠀⠈⠐⠀⠀⢈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⣤⠀⠁⠀⠀⢀⠀⡀⢈⠀⣦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠰⠂⠆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⠀⠀⡙⡟⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠄⠈⡡⢀⠀⠀⠀⠀⠀⠄⠮⠐⠃⠠⠤⠔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠉⠂⢀⠄⠤⠄⠤⢠⠐⠠⠀⠭⠕⡠
⠀⠀⠀⠀⠀⠀⠑⠄⢀⠀⠀⠈⠀⠀⠀⠂⠀⠃⠀⠁⠐⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠂⠄⠂⠀⠐⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⣄⠀⠀⢀⣤⠶⣶⣶⠶⣤⡀⠀⠀⣠⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⠲⣏⠛⢦⣞⣁⣖⣇⣸⣲⣌⣻⡴⠛⣹⠖⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠲⣵⡢⢄⢙⠶⣉⠳⡤⠤⠤⢤⠞⣉⠶⡋⡡⠔⣮⠖⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣶⣄⡉⠲⢯⡄⢸⠀⡧⠤⠤⢼⠀⡇⢀⡽⠖⢋⣠⢶⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠾⠶⢾⡟⢓⣚⣛⣛⣋⣉⠙⠋⣉⣛⣛⣛⣓⡚⢻⡷⢶⠷⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣉⣉⣏⣉⣹⠂⡏⠉⠉⠹⠉⣏⣗⣺⣹⠉⠏⠉⠉⣹⠸⣏⣉⣹⣉⣉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣤⢀⡤⠤⠼⠦⠤⠤⠤⠤⠤⢤⡤⢤⡤⠤⠤⠤⠤⠤⠴⠧⠤⢤⡀⣤⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣀⣺⡇⣞⡿⠛⢁⡈⠛⢿⣻⢸⠛⠙⡇⣟⡿⠋⢁⡈⠛⢿⣷⢸⣗⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⡶⢾⡇⣿⠁⢸⢻⣿⡧⠈⡇⣼⠀⠀⣧⢹⠁⣼⢻⣿⡆⠈⣿⢸⡷⢶⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢼⠃⣟⣧⡈⠛⠛⢁⣼⠃⡗⠀⠀⢺⠸⣧⡈⠛⠛⢁⣼⣿⢸⡧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠀⡭⡭⢩⣤⠤⣭⠭⣾⣃⣐⣒⢸⣷⢭⣭⠤⣤⡍⢭⢥⠈⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡇⢸⣧⠤⠿⣦⣬⣭⣭⣭⣭⣥⣴⠷⠤⣼⡇⢸⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢦⣇⠘⢯⣦⣤⡤⠤⠶⠶⠶⠶⠤⢤⣤⣴⡽⠃⣸⡰⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣾⢳⢦⡏⢠⠶⣶⢲⠶⠶⡖⣶⠶⡄⢹⡴⡞⣷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣚⠧⣼⠀⠚⡶⣒⣒⢶⠓⠀⣧⠼⣓⣃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡿⠤⠠⡇⡏⢹⢸⠀⠀⢿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⢧⣭⣭⡼⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣴⣔⢀⠀⠀⠀⠀⠀⢀⡀⠀⢠⢖⢂⠰⠀⣀⠀⠀⠀⠀⠄⡀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠰⡼⠿⠛⠹⡽⣧⡀⣬⠁⠀⠋⠉⠲⣼⠆⡤⡴⠊⠈⠃⠀⡀⠚⢤⡀⠠⣂⡀⠀⠀⢰⠝⢗⢿⣉⠈⣶⠤⠄
⠀⠀⠀⠀⠀⠤⠒⠻⠿⠍⠀⠀⠀⠀⠀⣸⠾⣺⡁⠀⠀⠀⠀⠿⠓⢠⣥⠉⠹⠃⠀⠀⢀⠀⠈⠉⠉⠈⢄
⠀⠀⠀⠐⠀⢹⣄⣂⠀⠀⠀⠀⠀⠀⢀⣿⠋⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢴⢶⠦⣀⡄⠀⠀⣀⠠⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠢⠈⢻⠀⠀⠀⠀⠀⠀⠰⠾⢮⠜⠧
⠀⠀⣶⣀⣠⣴⠶⠁⠀⠉⠀⠀⠀⠀⡬⡉⠟⢀⠀⠀⠀⠀⠀⠂⠐⡠⠒⢀⠂⠐⠆⠀⠀⠀⡐⠋⠸⠋
⠀⠐⡧⡭⢽⢏⠀⠀⠀⠀⠀⠀⠀⣚⠓⠓⠛⢛⡌⠀⠀⠀⠀⢀⠈⠔⢠⣾⣆⡀⠀⠀⠀⠀⠅⠤
⠀⠀⠐⠀⠰⠯⠄⠷⠄⠀⠀⠀⠀⠛⠂⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠠⡄⠠⠲⠟⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⣿⠆⠀⡰⠃⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⢂⠀⠀⡀⠪⠄⠩⠀⠹⠂⢤
⠀⠌⢁⠀⠀⣰⠊⠄⠈⠈⠡⠂⠀⠇⠀⠀⠐⠀⠁⠀⠀⠀⠀⠲⢶⢷⢶⡶⠀⠀⠀⠀⠁⠀⠈⠉⠈
⠀⡘⠫⠀⠐⠐⠠⠄⠃⠆⠀⠀⠀⠀⠀⢀⣠⡧⣄⡀⠀⣶⣖⠘⣨⢙⣨⡘⣔⣶⡆⠀⠀⠀⠀⠂⠀⠰⠀⠐
⠀⠐⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣈⣁⡁⠰⠚⠁⠀⠿⠿⠘⠉⠀⠀⠙⠐⠿⠇⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠄⢀⣴⣼⡤⠀⠀⠀⠀⠀⠀⠀⣾⠻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠤⡀⠈⠉⢡⢂
⠀⠀⠀⠀⠀⠠⡀⠙⠩⠆⠁⠀⠀⣴⢂⠀⠀⠈⠀⠾⠀⣰⢶⡄⠘⠀⠄⠂⡠⠀⣬⠄⠀⢰⣯⡼⠂⠘⢶⡷⠃
⠀⠄⠀⣀⢀⢀⠁⠀⡠⠀⠀⠈⠈⠁⡈⡠⠀⠀⡀⢀⠀⠻⠾⠶⠖⡇⠘⠻⠉⠄⠺⠂⠀⠀⠊⣡⣤⣤⡀
⠀⠀⠘⠆⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠺⢿⣿⢪⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠒⠀⢈⠉⣍⠉⡉⢉⡀⠒⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡡⠀⣠⡔⠊⢁⢤⠐⣢⠇⣸⣴⡉⡴⠶⣤⠶⢶⠦⣶⠒⠒⠒⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡞⠬⢿⡏⠡⢘⠀⢡⣧⣴⣟⡃⠹⡿⠇⠰⠙⠛⠀⠒⢳⡇⡄⠨⢿⣲⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⠋⠉⠉⠐⠺⡋⢱⢠⠏⠡⣔⡆⢐⣖⣆⣸⣿⣯⠄⢾⣿⣶⣖⠀⠉⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠐⠫⢹⠆⢸⠛⢿⡉⠖⢽⢧⠚⠒⢺⢉⡁⡀⠹⠿⠇⢀⣀⣀⠐⠪⠥⢇⣈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠻⡆⣤⠀⢶⣶⡛⣦⣤⣼⠀⣣⡄⢧⢫⣾⠰⠾⠿⠀⠀⠠⠰⠾⠶⠶⠤⠤⣾⣿⠺⠤⢈⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠙⠿⠤⠞⠙⢷⣬⢻⣷⠀⠻⣿⠸⠍⢂⡱⢄⣠⠔⠙⡄⠀⠙⣆⠀⠀⢀⠤⠀⠁⠢⡀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣀⢠⡤⢤⣄⣀⣠⡀⠀⢢⡹⣏⢧⡇⠈⠙⠈⠉⠻⣀⠀⣠⢉⠒⢺⣄⣀⠈⠧⠖⠁⣀⠔⢒⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠟⠋⠀⠀⠀⠀⠘⠉⠀⠀⡠⣽⡿⣯⠆⣼⡇⣸⢂⣭⠼⡳⣼⣋⠃⠚⠹⢂⠉⢐⣢⡴⣅⣀⠀⡆⠀⡇⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡷⡩⡐⠾⢿⡿⢠⡋⠳⠭⠃⣌⢋⠎⡑⠂⠤⣭⠵⠋⠓⣀⡀⠉⢫⣑⠢⢷⡒⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠧⣛⡫⢷⣞⡴⣃⠽⠿⢟⠁⠾⡷⢄⠑⠝⡠⢉⡋⠳⣦⡴⠙⠁⠣⣪⠀⡀⠈⢲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⠿⢶⠻⣤⡔⠌⠻⡋⠍⢡⡜⠀⢀⣑⢶⠁⠣⢝⠆⣈⠳⡌⠑⠠⣐⡂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣵⣳⣳⠈⡆⠹⣤⡘⡄⢱⡄⡄⠘⣦⠉⠫⠔⣑⢦⡊⠘⠫⡵⠋⣆⠀⠈⠑⢅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣦⣖⠎⣛⠝⠧⡆⢸⠀⢻⣁⢠⠀⡻⡄⠘⠢⠷⢄⠈⡻⠔⠻⡐⠶⡁⠘⡟⢦⠀⠀⠀⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢂⣉⡤⢶⠏⢿⣾⣭⣾⠂⠃⠀⢇⠈⣿⠁⠀⡇⠘⡒⠆⠀⣇⠐⢔⢄⡰⣳⡀⠈⠙⢄⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠫⢄⡚⠁⠐⠈⡡⠊⡹⠃⠀⠀⠈⢄⠘⡟⠀⠁⠀⢻⠀⠛⢼⠀⠀⠱⡌⠋⣱⠀⠀⠀⠙⢯⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡈⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠢⡈⠧⠘⡀⠀⢗⡲⢀⠀⠀⠀⠈⢾⠍⡀⠀⠀⠀⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢤⣄⠈⢶⠺⠁⠀⠀⠀⠀⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠰⣆⡂⠻⠇⠒⠦⢀⡀⢶⣄⠰⣦⡀⠶⡀⠖⢤⠓⠄⢦⠠⡆
⠀⠀⠀⣤⣂⣉⣁⣉⠉⠀⠀⠀⠀⠢⣉⠲⢧⡁⠈⡂⠢⡈⢌⡌⢧⠘⡆⢀
⠀⠀⢀⡦⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠑⠄⠙⢆⠘⣆⠳⡜⣧⣸⡆⢋⢸⡇⢃
⠀⢀⣨⡍⠚⠓⠒⠒⠂⠠⢄⣀⠀⠉⠠⠀⠂⠀⢠⡷⡜⢷⡹⣜⣇⣧⢸⣈⣇⡈
⠀⠀⠷⠟⣉⣉⣉⣉⡓⠒⠀⠀⡉⠀⠤⡀⣑⠎⠙⡶⢊⢦⡻⣾⣿⢿⠿⢿⣿⡃
⠀⠒⠈⢁⣀⣠⣤⣤⣀⠀⠁⠀⠀⠀⠠⣬⡉⣿⡶⣥⣿⢻⣯⢻⣿⠙⣻⢿⣿⠆
⣤⣖⣉⡩⠥⣤⡴⠶⠒⠒⠠⣤⢄⡰⠏⣡⠟⢳⣝⢯⣉⣷⠶⣼⣟⣇⣿⡏⠻
⠀⠀⠀⠴⠪⣥⠖⢂⡈⠀⠀⢾⠟⣠⡞⠁⣴⢟⣵⣿⢿⡷⡶⡷⢍⣤⣯⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣄
⠀⠀⠀⢀⡞⡡⠂⠁⠐⠀⣉⣽⡾⢋⣠⠞⣡⣾⣿⡿⢦⣷⣶⠛⣾⣿⢿⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣒⡒⢲⣶⣦⡤⣄⡘⢿⣷⡌⣿⡇
⠀⠀⠀⠈⢠⣡⠆⡠⢀⠀⣡⠾⡇⡿⠃⣰⡋⠀⠀⠀⠈⠿⠮⣿⣿⣍⣛⢛⣷⡅⠀⠀⠀⠀⠀⠀⡼⠡⢻⢋⡁⠀⡛⢿⢻⣦⠳⡄⠛⣻⠋⣧
⠀⠀⠀⠀⠀⣦⠌⣔⠏⡔⢁⡼⢛⣷⣾⡵⠛⠖⠀⠀⠀⡠⠥⠼⠛⠛⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⢟⢀⣎⣅⣀⡐⠉⡀⢿⠃⢂⠀⠈⣷⡇⣃
⠀⠀⠀⠀⠀⠰⣞⡽⣸⢀⣾⢃⢾⣿⣼⠣⢀⠿⣀⠀⠨⢄⠀⠠⣤⣌⠈⠀⠀⠀⠀⠀⣤⣀⠀⠀⣧⡟⠀⠉⣿⠊⣅⡀⣈⢏⡄⣘⠀⠘⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠙⣥⢧⡸⡣⣠⢿⣾⠣⢁⠎⢀⡁⡎⠁⡆⢠⠀⠀⠄⢀⡡⠀⠀⠀⢐⣿⡋⢻⣿⣿⣇⠄⣀⠡⡒⠍⠩⠵⣫⡄⠉⠴⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⣵⣿⢛⢅⣰⢥⢒⣧⣷⣍⣩⣴⡂⠀⠀⠠⣌⠃⠀⠀⠰⡿⠉⠹⡟⢿⣿⠙⠄⢿⠄⡹⠋⠁⠀⠈⠓⢿⠀⢀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⢠⢩⣞⠻⣃⢴⣻⡽⣛⡯⢷⡇⠉⠈⠁⢇⠀⢂⡐⠁⠀⠀⠀⠀⣀⣀⣤⢥⡿⠿⠒⠲⢾⡎⣠⣤⡶⠾⠃⠀⠘⠖⠦⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠬⠭⣿⢞⣻⣞⣯⡛⣯⣷⡾⢃⢰⣶⠀⣤⡄⠰⣿⠃⠀⠈⠉⠉⠀⣹⣿⡼⠀⠀⢀⣿⣿⡁⢟⢀⣠⣴⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠠⠚⣭⢞⡽⢽⣶⣟⣻⣿⢧⣟⣻⠛⣺⣿⢠⣌⡁⣠⠤⠤⠖⠒⠋⠉⠉⠓⠦⢿⣿⡞⠿⢘⣌⠢⡑⠄⣈⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣡⠎⠀⠘⡤⣬⢽⣿⠖⠚⣿⣷⣽⣇⣘⣿⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⡼⢻⡝⣧⠄⠈⣻⣽⣼⣏⠃⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⣠⡰⠗⠋⢠⡄⢲⣸⣯⣡⡆⣿⣱⢠⢳⠆⠤⣤⣤⠊⢩⢶⠐⠍⢷⣱⠛⣇⣿⠐⠂⠠⠮⣿⡆⢟⠚⢧⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢐⣷⢢⡄⣠⠀⡆⢸⣄⣧⣾⣿⠀⠀⠉⠙⠛⠋⢶⠦⢠⣿⣵⣄⡀⢘⢇⣴⣾⡍⠹⠿⣿⣶⠂⠀⣤⣷⡜⣤⣱⢤⠄⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠈⢉⡟⠁⣍⠈⠉⡀⠸⣱⠮⡏⠴⢄⠶⢄⠠⠒⠤⢧⠀⣏⣿⣿⣻⡋⠿⢿⣿⡏⣿⣴⣻⡹⣏⣴⠈⠺⣷⣁⠳⣌⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⢶⠶⢶⡶⠖⡎⣯⣹⡇⣶⣶⢒⣸⣿⣉⣏⡟⡄⠀⠈⢻⣍⢿⢟⡻⡿⠛⠛⢀⣜⣷⢼⣟⠊⠀⠉⣧⡳⠡⢉⢛⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⢙⡉⠉⠛⡋⠉⠉⠙⡏⠉⠩⣍⢹⣅⡀⠀⠀⠀⠀⣶⣂⣿⠞⠷⡥⠀⠀⠀⣉⠘⣧⢻⣀⣯⡳⢀⣷⠐⢿⠛⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡒⣂⣢⢱⠾⢷⣴⡇⠀⠵⠻⠋⢪⣝⡆⠀⠀⠀⣷⣶⣂⣴⣠⣿⠀⠀⠀⢀⣌⣻⢸⣏⣷⠀⠠⢻⣇⠈⣓⢶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣴⡎⠋⢬⣯⡗⣶⣶⣍⠀⠠⡿⠀⠀⢀⡀⣀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣞⣇⢙⣄⣄⡠⢿⡀⡘⡏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠵⣛⣛⣓⡩⠭⠭⢤⣶⣶⣦⣄⡀⢴⣿⡿⠿⠓⠶⢢⣤⡴⠾⢿⣶⣄⢔⠉⣉⣄⣐⣈⣉⣉⣍⣓⣛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡩⠐⠉⠈⠉⠉⠉⠁⠉⠀⠀⠬⢼⢋⡾⡫⠀⢀⡀⠀⠀⠀⠈⠙⠛⠛⢿⡇⠠⠊⠁⢀⣀⡀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣇⠀⣾⡍⠙⡆⠀⠀⠀⠀⠀⠀⢘⡸⣿⡀⠀⠻⣄⠹⡄⠀⠀⠀⠀⠀⠀⣆⠰⣀⠀⣸⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⣮⣲⣛⣈⣠⠇⠀⠀⠀⠀⠀⠀⠀⠱⠝⣍⣒⣂⣹⣳⠃⠀⠀⠀⠀⠀⠀⠘⠿⠶⣭⡭⠶⠈

⠀⠀⠀⠀⠀⠀⠠⡫⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢋⠀⢀⠠⠄
⠀⠀⠀⠀⠀⢀⠀⠄⠉⠉⠚⡅⠈⠠⠀⢀⣀⠂⠀⠀⠀⠀⠊⠀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠰⢟⠐⡥⡌⠢⢀⠠⠤⠠⠬⠨⢉⠒⢀⡀⠀⠐⠓⠁⠈⠄⠐⠐⡂⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣩⢀⠈⠀⠀⠄⠀⠀⠈⠐⢂⡐⠢⠀⠀⠀⠀⠅⠀⢈⡂⠠⠀⠠⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠰⠀⠂⡀⠀⠀⠀⡙⢀⠀⠙⠂⠘⠀⠀⠀⠀⠁⠂⠀⣀⠂⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⠀⠀⠐⢀⠀⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠁⢀⠴⢄
⠀⠀⠀⠀⠤⠀⢠⠀⠀⡀⠠⡅⠀⠒⠀⠀⣤⠀⡄⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡀⠀⢀⠆⠈
⠀⠀⠀⠀⠀⡉⠉⡅⣂⣀⢀⠒⠀⠀⢀⠀⠄⡀⠀⢰⠀⡁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⡐⢌⠀⡀
⠀⠀⠀⠀⢠⠀⠀⡁⠈⡙⠚⠃⠀⠀⠀⠀⣘⢀⡃⠐⢤⠯⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠤⠀⠀⠠⣧⣤⡇⢠⠈⡀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠐⠀⠋⡀⢸⡀⠉⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠼⠃⡤⢀⡀⠀⠀⠈⠁⠋⠀⢀⢘⠉⢩⢜
⠀⠀⠀⠀⠀⠁⣀⠐⠀⢀⠈⠠⡄⠀⡽⠉⠻⢠⡙⠸⡍⢐⡒⠚⡊⢐⢂
⠀⠀⠀⠀⠀⢀⠁⡐⠂⡄⢀⡀⠀⢀⠀⠈⠀⠈⠄⠀⢀⢈⡀⠀⠘⠚
⠀⠀⡌⠠⠄⠀⢀⠀⠠⠀⠀⠀⠈⠈⠘⠀⠙⠀⠉⠀⠉⠀⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡍⠀⠤
⠀⠀⠀⠀⠄⢀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠂⠐⠈
⠀⠀⠀⠰⠀⠤⠀⠤⠀⠰⠀⠀⠆⠀⠠⠀⠰⠀⠀⠇⠀⠰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣾⣷⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡆⣾⢿⣿⣿⢸⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠿⣿⣟⣇⣿⣷⣾⣿⣸⣻⡿⠿⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡙⠀⠀⠠⡀⣿⢿⣿⡿⣿⣿⡿⣿⢀⠄⠀⠀⢋⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⢶⡤⣴⢷⡄⠄⠙⢿⣿⠋⠠⢀⡾⣦⢴⡶⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣝⡆⣘⣾⣙⢻⣷⣬⡶⠊⠑⢶⣥⣾⡟⣋⣷⣃⣰⣣⢈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⢊⣙⠻⣿⣿⣼⣸⡇⠀⠠⠀⠀⠄⠀⢨⣇⣧⣿⣿⠟⣛⡑⡴⣿
⠀⠀⠀⠀⠠⢤⣄⣀⣀⡀⠀⠪⣿⠿⣿⡏⢉⠷⡇⢠⡤⠠⢤⡌⠳⣆⣰⠞⢱⡤⠤⢤⡄⢸⠾⡉⢹⣿⢿⣿⠑⠀⢀⣀⣀⣠⡤⠄
⠀⠀⠀⠀⠰⣼⣿⣿⣿⣷⡀⢘⣿⣶⣿⡞⠜⣁⣁⠸⣧⣀⣠⡟⣦⡏⢹⣴⢻⣄⣀⣼⠇⢉⣈⠫⢷⣿⣷⣟⡣⢀⣾⣿⣿⣿⣣⠄
⠀⠀⠀⠀⠀⣽⣾⣿⣿⣿⣧⣾⣿⣸⣿⡗⡦⣦⠈⠚⢃⢭⣭⢛⣋⡀⢀⣙⡛⣯⡭⠘⠳⠀⣤⢶⢺⣿⣇⣿⣷⣼⣿⣿⣿⣳⣿
⠀⠀⠀⠀⠀⣿⣿⣟⢿⣿⡝⣿⣿⣯⣯⡇⢽⣨⣽⣦⣴⠋⠉⠈⠻⡥⢬⠟⠀⠉⠙⣧⣴⣿⣥⡯⢸⣽⣿⣿⣿⢫⣿⣿⣳⣿⣾
⠀⠀⠀⠀⠀⢹⡿⣿⣜⣿⣿⡝⢿⣿⣯⡇⠜⢿⣿⣿⣟⣳⣦⡤⣄⠁⠊⡠⢴⣴⣞⣻⣿⣿⡿⠣⢸⣿⣿⡷⢱⣟⣿⣿⣿⢿⡏
⠀⠀⠀⠀⠀⢸⣿⣾⣿⡞⣷⣹⡾⣷⣾⡇⡆⢉⢿⣿⣿⡿⣿⣳⠾⣭⣭⠷⣞⣿⠿⣿⣿⡿⡉⢰⢸⣷⣾⣷⣟⣾⣱⣿⣵⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣞⣿⣿⢿⣏⣧⡛⠎⡌⠉⢋⡜⠙⠋⠀⠈⠁⠀⠙⠋⢣⡙⠉⢦⠰⢋⣼⣹⡿⣿⣿⣳⣿⣿⡿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣟⣿⠀⡿⢿⣭⣜⢅⠸⢾⡇⠀⠀⠀⢦⡴⠀⠀⠀⢸⡷⠗⡨⣣⣭⡿⢻⠀⣿⣻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣼⣄⡳⠘⢟⡹⢿⣹⠇⣷⡄⠀⠐⢒⡒⠀⠀⢠⣿⠹⣟⠿⢏⡻⠃⡞⣠⣷⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣾⠻⡿⣾⣿⣷⡶⣾⣷⣾⣶⣦⡋⢑⣴⣾⣿⡾⣷⢾⣷⣿⣷⣿⠟⣷⣿⣿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣿⡇⢿⣿⣾⡇⠛⢻⣶⣴⡶⣽⠋⠙⢯⢷⣶⣶⡟⠛⢸⣧⣿⡿⢰⣿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣧⣈⠛⠿⠻⡖⢘⡿⡨⣿⣧⡷⢮⣶⣿⢅⢿⡋⢲⠟⠷⠛⣁⣼⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣿⣷⣦⣄⣿⣿⣤⣼⠁⣐⠁⠈⣆⠈⣧⣤⣿⣿⣠⣴⣾⡿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣭⣿⣿⣽⣿⣶⣭⣽⣳⣾⣯⣭⣶⢿⣭⣿⣿⣭⠏⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣩⣝⣻⣍⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠏⠛⠉

⠀⠀⠀⠀⠀⢠⠀⢀⢀⡀⢀⣄⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣀⠀⠀⠀⠀⠀⣀⣄⣤⡄
⠀⠀⠀⠤⢀⣲⣿⠤⠔⠣⠜⠦⠤⣿⣖⡀⠤⠀⠀⠀⠀⠀⠀⠐⠤⣅⣼⡧⢷⣀⠀⣀⣾⢼⣧⣨⠥
⠀⠀⢸⢐⣊⡗⡷⢀⡉⠀⠀⢉⡀⢾⢺⣑⣂⡇⠀⠀⠀⠀⠀⠔⣞⠯⠿⣷⣇⣂⠀⣕⣹⣾⠿⠽⣳⠢
⠀⠀⢈⠄⣺⣗⠘⡆⠁⠠⠀⠈⢐⠃⣺⣟⠠⣁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⠙⡿⠋⠉⠀⠀⠀⠠
⠀⢦⣈⡯⣽⢹⠥⢶⡧⠀⠀⢼⡶⠬⡋⣯⢽⣋⡴⠀⠀⠀⠀⠀⠨⠄⣤⣤⣀⣀⣿⣀⣀⣤⣤⠤⠅
⠀⠸⠾⠔⣿⠈⠲⡄⢢⠀⠀⠔⢀⠖⠁⣿⠢⠷⠇⠀⠀⠀⠀⠀⢘⡒⠒⠁⠹⢉⣀⡙⠟⠈⠒⢒⡁
⠀⠀⠀⠀⠉⠠⣀⠢⡈⠃⠘⢡⠜⣀⠄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠁⣔⡴⠮⣤⠷⢦⣢⠈⢾⠁
⠀⠀⠀⠀⠀⠀⠅⠂⠻⠘⠋⠞⠰⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠟⢛⠿⣿⠿⡛⠻⣃⡀
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠃⠘⠀⠀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠺⡆⢈⠂⠤⢐⡅⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣱⠛⠬⠙⠛⠊⠄⠓⡮⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠓⠉
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣔⠠⡄⢈⣭⣵⣦⣰⣶⣖⣰⣮⣍⣃⢂⠄⢢⠄⠀⠀⠀⠀⠀⢖⣦⣢⡆⣄⠀⢀⡤⣦⣂⣒⠆
⠀⢀⢺⡿⣿⢰⣶⣶⠛⠛⣛⠛⠛⣷⣶⡆⣼⣷⡗⡀⠀⠀⠀⠐⢑⣯⡏⢥⡄⠠⠛⠃⠀⣤⠝⣭⣎⠐
⠀⠀⡝⠲⠋⠛⣡⡈⠁⠰⠀⠄⠈⢁⣌⠛⠉⡖⢫⠀⠀⢠⡔⣾⣝⡄⠉⣚⠁⠀⠀⢀⡀⣑⠋⢀⣹⣽⡖
⠀⠀⠀⠁⣯⠀⠍⠙⠁⡴⠀⢢⡈⠋⠩⠀⢸⠆⠁⠀⠀⠀⠷⣾⠟⠉⠙⠛⡋⠀⠀⠀⢘⡟⠛⠉⠙⢿⡾
⠀⠀⠀⠀⠉⠀⣦⡀⠈⠁⠀⠈⠁⢀⢴⠀⠉⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠉⠦⠀⠠⡊⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠠⡍⢃⡭⢭⣿⡭⢭⡜⢹⠬⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡇⢻⠀⠙⣭⠙⠁⢸⠁⡏⠈
⠀⠀⠀⠀⠀⠀⠘⠂⢹⣷⢤⣾⣏⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⢄⡛⠉⠙⣃⠾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠛⠊⠉⠁⠛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠐⠀⡀
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣴⡧⣺⣯⣶⡿⣃⣠⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣿⡿⢋⣴⣿⡿⠟⣉⣽⣿⣥⣶⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⣡⣾⠿⠋⣰⣾⣿⣿⡿⠿⠷⢶⣶⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢏⣴⡿⢁⣤⡾⠛⠉⢉⣀⣶⣶⣾⣉⣥⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⡤⠴⠿⣿⣿⣿⣾⣿⣥⡶⠶⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠂
⠀⠀⣠⠖⠒⠉⠁⠀⠶⣶⣶⡶⢦⣤⣉⣙⣻⣶⣮⢩⣭⣽⣿⣛⣛⣛⣛⢛⣛⠷⣶⣤⣤⣤⣄⣀⣀
⠀⠀⡿⠛⠛⢶⡶⠦⠄⠀⠉⠁⠈⠉⠉⠻⢿⣾⣿⣾⣿⣇⣀⣀⣤⣶⣻⣬⣶⣿⣿⣿⣿⣿⣿⣿⣋⣙⠁
⠀⠀⠀⠀⠀⠀⠻⣷⣶⣤⣄⣀⡀⠈⠓⠲⢦⣽⣷⣿⣿⡏⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣷⣭⣍⣛⠛⠶⢤⣀⣦⣍⠻⣏⣟⣿⣿⣿⣱⣦⣭⣉⠛⠛⠿⢿⣿⣿⣿⣿⣯⣭⣉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⢋⣉⠉⠙⠛⠷⢍⣰⠚⢻⣿⡌⠙⣏⣯⣿⣿⣿⡍⠻⣿⣿⣿⣶⣄⡈⠉⠛⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⡰⠛⣯⠭⠉⠀⠀⠀⢸⢛⣿⣿⣿⣦⡉⢷⠛⣿⣿⣿⣶⡜⢀⢻⣿⣿⣿⣾⣷⣦⣄⡙⠳⣦⣍⠈⠉⠉
⠀⠀⠀⠀⢀⡎⠀⠀⣀⣀⣤⣤⣶⠒⠃⣸⣿⣿⣿⢮⡻⣮⣿⣦⣍⡛⠿⣿⣦⠢⣾⣿⣿⣿⣿⣿⣝⠻⢷⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠘⢠⠀⠂⠛⠋⠉⣹⣻⣇⣼⣿⣿⣿⣿⣧⠹⣌⠛⢿⣿⣿⣷⣬⣙⡳⢚⣿⣿⣿⣿⣿⣿⣶⣄⠀⠉⠙⠛⠿⠦
⠀⠀⠀⠀⠀⡦⠄⠀⢳⠀⠀⠈⠉⠀⣿⣿⣿⣿⢻⣿⣧⡈⠳⣤⣀⠈⢻⣿⣿⣿⣾⣥⣻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⣀⣀⣤⢾⣿⢻⣿⣿⠀⢻⣿⠳⣧⠈⢿⣷⣄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡙⠿⣿⣿⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣏⠁⠀⣼⠃⢸⣿⡇⠀⠀⠙⠀⠈⢷⣄⠙⣿⡻⢦⣄⣙⢷⣌⠛⠙⢿⣿⣿⣄⠀⠙⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠙⢷⣜⣿⡄⠉⠛⠿⣿⣷⣄⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⠉⠛⠂⠀⠀⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢀⣠⣿⠀⢹⣇⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢺⣏⠉⠛⠋⠉⠀⠀⠀⠈⠉⠛⠋⢉⣿⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠛⠛⠶⠶⠶⣤⣤⡟⠀⠀⢀⣿⠃⠀⠀⣠⡴⠶⢶⣤⡀⠀⠀⢻⡇⠀⠀⠀⢿⣤⣤⠶⠶⠶⠛⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠇⠀⠀⣾⠋⠀⠀⠀⠈⢻⡄⠀⠀⠿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢿⣤⣄⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣤⣿⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠙⢷⣄⣀⣠⣴⠟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠧⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠾⣧⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⠟⠳⢶⣤⠀⢠⡴⠾⠛⠷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢳⣄⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⣿⣤⡀⠀⠀⠀⠀⢀⣠⣼⡇⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⢿⣤⣤⣤⠿⠈⠙⠳⣦⣤⠶⠛⠉⠸⣧⣤⣤⣼⠇⠈⠛⠶⣤⣴⠞⠋⠁⠿⣤⣤⣤⠿⠀⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⢀
⣿⡟⡋⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠤⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⢀⢀⠴⡀⠐⠤⠚⠦⠐⡆⠄⡄⣀⡀
⠀⠀⢱⣭⢉⡁⠈⢉⠀⡊⢈⠁⠼⠠⢴⠀⠁⠀⠀⡔⢢⣀⣀⡄⢢⠀⠉⠀⠓⠈⠼⠐⣲⣀⠤⡄
⠀⠀⢠⣭⡉⠞⢪⢤⢗⣂⠥⡀⠠⢝⠅⠀⢴⣁⡈⠈⣟⢕⡈⡯⠁⠨⣀⡱⠀⢀⢄⣠⣦⠬⠤⠭⠍⠡⠤⢤⡦
⠀⠀⠀⣤⣤⠤⠴⠦⠔⠾⠇⠃⠐⣥⠀⡀⣆⡀⠀⢊⡙⠒⠺⠓⠀⡲⠌⠀⡠⢊⠤⣄⠠⡀
⠀⠀⠀⠉⠉⢉⡉⠀⠀⠀⠀⢤⡊⢥⡒⠔⠒⢌⠢⢄⠀⠀⢀⡙⠇⡀⢔⢬⠪⠚⣢⢄⠑⢥⠲⢦
⠀⠀⠀⠀⠀⢈⣑⡒⢠⣀⠒⠔⠋⠁⠀⠀⠀⠀⠈⠂⠭⠉⠉⢧⡘⠌⠂⣁⠲⠈⠉⠀⠑⠠⠷
⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠉⠛⢻⣿⣷⣿⢿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⡿⣛⣵⣴⣦⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⠿⠟⣷⣿⣿⣿⣿⣦⣀⡀⠀⠀⢽⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣿⣿⠅⠒⠄⣶⣍⡻⢿⣿⣿⣿⣿⡄⠀⠀⠹⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⣿⣿⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢼⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣧⠀⠀⠐⡟⢡⡿⣻⣿⣿⣿⣿⣿⠶⣄⣀⡲⢿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠆⠀⢘⢆⡾⣱⣿⣿⣿⠻⣿⢿⠑⠈⠹⣙⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣏⡿⠃⡭⡸⣿⣿⡿⠋⠙⣿⡝⠧⡄⣰⡀⣻⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡞⣹⡇⢠⡶⠐⠻⣿⣿⣧⣶⢹⣼⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣹⣿⣿⣿⠟⠁⢹⣿⠜⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡟⠉⠀⠘⣸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⠯⠀⠀⠀⠀⠿⠼⠻⠿⠿⠿⡿⠿⠿⠿⡿⡿⠿⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠟⠻⣷⣶⣤⣄⡀⠀⠀⠀⣀⣠⣴⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠻⡏⠙⢿⣆⢀⡴⠋⠁⠀⠈⠉⠛⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢹⡇⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡾⠛⠛⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣤⡴⠾⠋⠉⠉⠻⢦⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠈⠙⣄
⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣄
⠀⠀⠀⣠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠙⠛⠿⠶⣤⡀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿
⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣁⣀⣀⡀⠀⣀⣴⣿⠃⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⠦⣤⣄
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⣿⠁⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⢠⣿⣧⣄
⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠁⠀⡹
⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣤⣤⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⠀⢹⣿⡏⠁⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⡿⣿⣷⣿⣿⣿⣄⡀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⡿⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⢸
⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⢰⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⣿
⢹⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⣧⡈⠙⢿⣿⣶⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⣴⠿⠻⠿⠁⠀⠀⣿
⠈⢿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡈⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣍⣷⠶⠀⠀⠀⠀⢠⣿
⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢻⣿⣿⣿⡌⠻⣿⡙⠛⠛⠿⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⢿⡟⣿⡉⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣇⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠒⠒⠓⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠓⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣾⠏⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡉⠃⠀⠉⠿⠁⢀⡞⠉⠉⣹⡅⠛⢐⣧⡿⢋⡿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿