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Let {a1, a2,..., an} be an integer sequence of length n such that:
a1 = 6
for all 1 ≤ i &lt; n : φ(ai) &lt; φ(ai+1) &lt; ai &lt; ai+11
Let S(N) be the number of such sequences with an ≤ N.
For example, S(10) = 4: {6}, {6, 8}, {6, 8, 9} and {6, 10}.
We can verify that S(100) = 482073668 and S(10 000) mod 108 = 73808307.
Find S(20 000 000) mod 108.
1 φ denotes Euler's totient function.

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