chore(i8n,learn): processed translations

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---
id: 5900f50c1000cf542c51001e
title: 问题415泰坦尼克号集
title: 'Problem 415: Titanic sets'
challengeType: 5
videoUrl: ''
forumTopicId: 302084
dashedName: problem-415-titanic-sets
---
# --description--
如果存在一条直线恰好经过S中的两个点则一组晶格点S称为钛酸组。
A set of lattice points S is called a titanic set if there exists a line passing through exactly two points in S.
泰坦尼克集的示例是S = {000102112010},其中 通过0120的通道不会通过S中的任何其他点。
An example of a titanic set is S = {(0, 0), (0, 1), (0, 2), (1, 1), (2, 0), (1, 0)}, where the line passing through (0, 1) and (2, 0) does not pass through any other point in S.
另一方面,集合{00112244}不是泰坦尼克号集合,因为穿过集合中任意两点的线也经过 通过其他两个。
On the other hand, the set {(0, 0), (1, 1), (2, 2), (4, 4)} is not a titanic set since the line passing through any two points in the set also passes through the other two.
对于任何正整数N令TN为每个点xy都满足0≤xy≤N的钛酸集合S的数量。 可以验证T1= 11T2= 494T4= 33554178T111mod 108 = 13500401和T105mod 108 = 63259062
For any positive integer N, let T(N) be the number of titanic sets S whose every point (x, y) satisfies 0 ≤ x, y ≤ N. It can be verified that T(1) = 11, T(2) = 494, T(4) = 33554178, T(111) mod 108 = 13500401 and T(105) mod 108 = 63259062.
找出T1011mod 108
Find T(1011) mod 108.
# --hints--
`euler415()`应该返回55859742
`euler415()` should return 55859742.
```js
assert.strictEqual(euler415(), 55859742);