Manas is the smallest Panda on this planet. So he loves writing on the wall. Today Manas is presented with a special wall which is infinitely long and which resembles a notebook with horizontal lines at a distance 10 units apart. Since he knows only 3 letters of the english alphabet, “O”, “N”, “I”, he starts writing these characters on this wall in any angle at any position. He writes “O” 677 times, “N” 733 times and “I” 779 times. We define a cut as the intersection of character with the horizontal lines on the wall. Find the expected number of cuts Manas will make.

The dimensions of the characters:
“I”: Line segment of length 1 unit.
“O”: Circle of radius 0.5 unit.
“N”: Smaller line segments have length 1 unit and longer line segment has a length 2 units.

If the answer is $p$, give the answer as $\lfloor p\times10^5\rfloor$

Note: A single character can make multiple cuts, for example, “O” can never make a single cut.

Hint - https://brilliant.org/wiki/linearity-of-expectation/