⠄⢂⠐⡀⠂⠂⡂⢐⠐⡐⢐⠄⡂⢐⠄⡂⠄⠂⡀⠂⡀⠂⠐⡀⢂⠂⠠⢀⡢⣠⣐⡄⠄⠄⢀⠄⡀⠄⠄⢀⢺⢜⢵⢝⢮⡪⣳⢝⡞⣎⢯⢯⣳⢯⢿⣿⣿⣿⣿⣿
⣖⡲⢦⡓⣶⢺⡔⡶⣱⢲⠧⣞⡲⢞⡲⡞⣦⢳⢞⣲⢳⣞⣲⢳⢞⣲⢳⣞⣲⢳⣖⡳⢞⡶⣺⢴⢺⡴⢎⡖⣦⢓⡶⢲⢎⡖⡲⢆⠲⡀
⢧⡛⢶⡹⢦⣛⡼⣓⠧⣯⣝⡲⣝⣫⢵⣛⡼⣫⢞⡵⣫⠶⣭⣛⢮⡳⣏⠶⣭⢳⢮⡝⣯⡚⣥⣋⢷⢺⡹⣜⡎⣯⢺⣍⡞⡼⣱⢋⠖⡡
⣯⡹⢧⡝⣮⢵⣚⡭⣛⠶⣍⢷⡹⣎⢷⡹⣞⡵⣫⠞⡵⠛⠔⠉⠀⠁⠈⠃⠀⠉⠂⠙⠐⠁⢦⠡⢎⡡⡛⣼⡹⣎⡳⣜⠮⣕⢣⢍⡚⠄
⢧⣛⠮⡽⣜⢧⡻⡼⣭⢻⡜⣧⢻⡜⣧⢻⣜⠳⠣⢙⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⢣⢳⡜⣳⢭⡻⣌⢳⡊⡔⢡
⣧⢏⡿⣱⢏⡾⣱⢻⡜⣧⢻⡜⣧⢻⣜⡳⢮⠱⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⡭⢞⡵⣊⢗⡸⢄⠃
⣟⢮⡳⣝⢮⡳⣭⢳⡝⣮⢳⡝⣮⢳⢮⡝⣣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣯⠶⣩⢎⡔⢊⠅
⣟⢮⡳⣝⢮⡳⣭⢳⡝⣮⢳⡝⣮⣛⢮⣝⡂⠈⠐⠀⠀⢀⡀⣄⢠⡀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢫⡕⡎⡜⡨⠆
⣯⢞⡵⣫⢞⡵⣫⢷⡹⣎⢷⡹⢶⡹⣞⠄⠀⠀⠀⡀⢆⠣⡜⣬⢣⡝⣢⠳⣌⢯⡙⣎⠶⣰⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡱⢌⡱⠌
⣟⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⡝⣧⢻⡜⡀⠀⡀⠦⡙⣬⢳⡙⢦⠳⡜⣥⢛⡜⢦⡹⣌⠳⣥⢫⡜⢥⠂⠀⠀⠀⠀⠀⠀⠀⠀⡱⢊⡔⡃
⡟⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⡝⣮⢳⡽⠀⢆⡱⢊⡵⣊⢧⣙⠮⣝⠾⣜⡯⣞⡣⢗⣎⠳⣌⢧⠚⠦⡁⢄⠀⠀⠀⠀⠀⠀⠀⡕⢣⠜⡰
⡿⣜⢧⡻⣜⢧⡻⣜⢧⣛⢶⡹⢎⡷⠊⡜⢢⠕⣫⢖⣭⠲⣍⢻⣜⡻⣜⡳⣭⣛⠷⣎⡳⡜⢮⡙⠖⡤⢁⠎⡀⠀⠀⠀⠀⢠⡙⠦⡙⡄
⡿⣜⢧⡻⣜⢧⡻⣜⢧⣛⢾⠀⠀⠀⠀⠀⠁⠈⠀⠫⠞⠽⠎⠗⢮⢳⢭⡗⣧⣏⡟⣶⡹⣞⣣⠝⣎⡑⢎⡰⢀⠀⠀⠀⠀⢀⢇⢣⡑⠆
⣻⡜⣧⢻⡜⣧⢻⡜⣧⣛⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠛⠶⠹⢮⡵⣋⠖⡙⢆⠒⡩⠄⠀⠀⠀⣈⠎⣆⠱⢊
⣷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣞⡄⢰⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀⢈⠈⠁⠈⠐⠁⠎⠀⠀⠀⡔⢌⠢⢍⡂
⣧⢻⡜⣧⢻⡜⣧⣛⢧⡻⣼⡹⡄⠀⠤⣠⢠⠀⢀⡼⣱⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠉⣀⢀⡀⡀⣀⠤⢤⢢⠄⠀⡐⡈⢆⠣⡘
⣯⢳⡝⣮⢳⡝⣶⡹⣎⢷⣣⢟⡅⠳⢦⢤⡤⢒⡜⣾⣱⢳⡌⢒⡱⡘⢆⡣⠆⣠⢖⡮⢽⡩⢓⡌⡒⢌⠱⣌⠳⣏⢮⣹⠀⠐⡈⠆⢥⠃
⣏⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢮⡅⡙⣎⢳⣇⠣⡜⢣⡛⢾⡜⣣⢖⡴⢦⣖⡿⣱⢏⡜⣣⢑⢣⡐⡡⢎⡱⣎⠷⣍⢲⠅⠀⢂⠱⡈⢆⠱
⣟⢮⡳⣝⢮⡝⣧⢻⡜⣧⢻⡱⠆⡑⣎⠳⡌⢳⢩⠧⣹⢳⡾⣵⠪⣝⡻⣜⣳⢓⡮⡜⣥⢊⠦⡱⡑⢎⡵⣊⠷⣡⠋⠀⠀⠂⢆⠱⡈⢆
⣟⢮⡳⣝⢮⡝⣮⢳⡝⣮⢣⢇⠣⡘⣼⠳⣌⠡⣊⡱⣉⠷⣹⢎⡷⣌⢳⡝⣎⢧⣛⡜⢦⡙⡆⢧⡙⡼⡰⢍⠎⠁⠀⠀⠠⠑⡈⢆⡑⢂
⣟⢮⡳⣝⢮⡝⣮⢳⡝⣮⡓⣎⠱⢠⢫⠗⡌⣐⢩⠳⢍⡓⢦⣉⠾⣥⢻⡼⢭⡞⣵⡙⢦⠓⡜⢦⠑⡠⠁⠈⠀⠀⠀⠀⢂⠡⡘⠤⡘⢂
⣟⢮⡳⣝⢮⡝⣮⢳⡝⣶⡹⣌⡓⠢⠌⡫⢔⣠⢃⡞⣬⡹⢮⣝⡳⣍⢷⣙⢮⡝⢦⡹⢌⠳⡘⡄⢃⠐⠀⠀⠀⠀⠀⠐⠠⢡⠘⠤⡑⢂
⣟⢮⡳⣝⢮⡝⣮⢳⡝⣶⡹⢦⡍⡓⠤⠑⢪⡔⣫⢜⡲⣝⡳⣎⢷⡙⢦⡙⢦⡙⠦⡑⢎⡱⡑⢌⠂⠀⠀⠀⠀⠀⠀⠠⢁⠂⡍⠰⡁⠆
⣟⢮⡳⣝⢮⡝⣮⢳⡝⣶⡹⢆⠧⣉⠆⠐⠀⠙⠦⣋⠶⣩⠳⣍⠲⣍⢲⣉⢦⡹⡜⡱⢎⠴⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠡⢌⡑⢌⠂
⣟⢮⡳⣝⢮⡝⣮⢳⡝⣶⡹⢎⠳⠄⠊⠀⠀⠀⠀⠒⠰⢂⠳⢌⠳⣌⠳⡜⢢⠧⡹⣑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢃⠆⡘⢄⠃
⣟⢮⡳⣝⢮⡝⣮⢳⡝⠒⠉⠀⠀⠀⠀⠀⠀⠀⢦⠑⢦⡡⢎⡄⣣⢆⡳⣌⢧⣚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠌⡂
⡟⣮⢳⡝⣮⡝⡎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⢌⠲⣝⠦⡘⡵⣪⢗⡞⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡹⣎⢷⡹⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢜⠢⡙⢆⢧⡹⣜⢣⠯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡱⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⣪⠱⣉⠎⡶⡱⢎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡹⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣄⠳⣌⠚⡥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡳⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠲⣌⠳⣌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡳⢌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡈⡂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⠐⡠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄⡁⡂⡂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⢂⠂⡂⢄⢑⠀⠀⠀⠀⠐⠀⠂⠔⠠⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄⠄⠄⠄⠀⠀⠀⠀⠀⠀⡂⡂⠌⡐⡐⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠨⠐⡐⠨⠨⠐⡀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠅⠅⡊⠨⢈⠌⠨⢐⠀⠀⠀⠀⠀⠐⠠⡁⡂⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠅⡁⡂⠂⠅⡀⠀⠀
⠀⠀⠀⠀⠠⠨⠨⠠⠡⠡⢁⢂⠂⠅⡂⠌⠌⠀⠀⠀⠀⠀⠀⠠⡁⡂⠄⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠂⠅⠅⠌⡐⠀
⠀⠀⠀⠌⠌⠌⡐⡁⠅⢊⢐⠠⢁⠅⠂⠁⠀⠀⠀⠀⠀⠀⠀⠡⢐⠠⢁⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠨⢐⠁⠅⡂⠅
⠀⠀⢀⠔⠁⠅⡂⢄⢑⠐⡐⡈⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⠨⠐⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠢⠨⢈⢐⠨⢐⠠⢁
⠀⠌⠄⠌⠌⢂⠂⡂⠔⡈⠄⡂⠌⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡂⡂⠅⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⡑⡐⠨⠠⢁⠂⠌⡐⠈⠀
⠈⠠⠡⢁⢊⢐⢈⢐⠐⠠⡁⡂⠅⡐⡐⠠⠀⠀⠀⠀⠀⠀⠀⢐⢀⠂⠅⡐⡀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠅⠅⡂⡐⠡⠈⠀⠈⠀⠀⠀⠀
⠀⠀⠈⠀⠢⢐⠐⠀⠀⠀⠂⠄⠅⡂⠂⠅⡊⡀⠀⠀⠀⠀⠀⡐⠄⡡⢁⠂⠄⠀⠀⠀⠀⢀⠐⠄⠅⡡⢁⢂⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠐⠠⠡⢁⢂⢐⠡⢀⠀⠀⠀⢐⢐⢐⠠⢁⠂⠀⠀⢀⢐⠠⠡⠁⢅⢐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠐⡐⠠⠊⠄⡂⠄⠀⢂⠂⠔⡈⡐⠄⠀⡐⡐⠠⠊⢄⢑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠅⡡⢁⢂⠡⢁⠂⢌⢐⢐⢐⠠⢁⠂⠔⡁⠅⡂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠂⠌⡐⠨⢐⢀⠢⢐⠨⠐⠨⢐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⢁⠂⠅⡂⢂⠌⠄⡂⠅⡑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡁⡂⡂⠂⠅⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡂⡂⢂⠂⠅⠅⠅⡊⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡂⡂⠔⠠⠡⠨⢈⠄⠅⡂⠌⡐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠂⡂⠔⠠⢁⠅⠡⠊⠄⢌⠐⠄⠅⢂⢁⢂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠈⠔⡈⡐⠨⠈⠀⠌⠨⡈⠌⠄⠂⠁⠌⡐⡐⠠⠂⠌⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠅⡊⠨⢐⢐⠠⠁⠀⠀⠌⡂⠂⠅⠌⠂⠀⠀⠂⠂⠅⡡⠁⠅⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢑⠐⠀⠀⠀⠀⠀⢂⠂⠅⠅⡡⠁⠀⠀⠀⠈⠐⠠⠡⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡐⠨⡈⠔⠠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠅⡂⠌⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀