█████████

██████ of █████

In the ████ █████ ████████ of █████████, the ████████ ███████ of the █████████ █████ █████ be ██████ as the █████ ███████. █████████████, this ██████ █████-████ ████████ on ███████ ██████ ██████, which is a ██████ ██████ use ████. The ███████ was ██████ ██████ by ████████ ██████ a ██████ █████ for the █████, ████████ the ██████ █████ of the █████████ or (██████████ for ██████ ██████████) ████████ the ██████ of the █████, ██████ and ████ ███████ of the █████████ for the █████ (as ███████████ by █████████). This "██████-of-█████" ████ ████████ the ████ of ██████ (or ███████-██████) █████, and █████ a ██████ ████████ of the ███████ █████ (the ████ ██████) than █████████ ███ ██████ ███████, ████ ██ ███████████ about the ████████ of the █████ is █████.

██████-of-█████ ████ ███████ for ██████ █████████:

███ := ⌊(██ + ██) / █⌋
if A[███] < A[██]
    ████ A[██] with A[███]
if A[██] < A[██]
    ████ A[██] with A[██]
if A[███] < A[██]
    ████ A[███] with A[██]
█████ := A[██]

It ████ a ██████ into `A[██]` █████, ████ that ███ █████ of `A[██]` is used for a █████, as in a █████ █████████ █████████ above.

████████████, the ████████ ██████ of ███████████ ██████ to ████ █ ████████ (███ § ███████-████ ████████) with ██████ █████ █████████ is █.███ █ ███ █. ██████-of-█████ ████████ ██████ this down to █_{█, █} ≈ █.███ █ ███ █, at the ███████ of a █████-███████ ████████ in the ████████ ██████ of █████. An ████ ████████ ████████ ████, for ██████ ██████, is to ████ the ███████, a █████████ ██████-of-█████ (███), ███████ as

███████(a) = ██████(███(█████ ⁠█/█⁠ of a), ███(██████ ⁠█/█⁠ of a), ███(█████ ⁠█/█⁠ of a))

█████████ a █████ ███████ is ████ ███████████ by the █████████ of ███████ ████████. If the ████████ ███████ of the ████████ being ██████ are ████████████ █████, the █████ ██████████ for the ██████ █████, (██ + ██)/█, will █████ ████████ and ███████ an ███████ █████ █████. This can be ████████ by using, for ███████, ██ + (██−██)/█ to █████ the ██████ ███████, at the ████ of ████ ███████ ██████████. ███████ ██████ █████ in some █████ ███████ of █████████ the █████ ███████.

████████ ████████

With a ████████████ █████████ ████ as the ██████ █████████ ██████ █████████ above (████ ███ that ███████ ████ █████ ██████), █████████ ████████ ████ ███████████ for ██████ that ███████ ████ ████████ ████████. The ███████ is ███████ ████████ ████ ███ the █████ ████████ are █████: at ████ █████████, the ████ █████████ is █████ (██ █████ ██████ are ████ than the █████), and the █████ █████████ has ████ █████████ by ███ ███████ (the █████ is ███████). ████████████, the ██████ █████████ ██████ █████ █████████ ████ to ████ an █████ of █████ ██████. ███████, with a ████████████ █████████ ████ as the █████ █████████ ██████, ████████ ████████ █████████ ██████ in ██████ ████████████, and ████████ ████████ █████ of ████████ █████ to the █████ ███ █████, the ███████ ████ █████████ █████████ as the ██████ of ████████ ████████ █████████ (with ██████ █████ ████████ the ████ ████████). In the ████ █████ ███ ████████ are █████, the █████ █████████ ██████ ██████████ █████ ████████, but the ████████████ ██████ is ████ ████, as █████ in the █████ █████████ ███████ above.

To █████ the ██████ █████████ ██████ ███████ (█████████ ██████ the █████ ████████ ████ ███████), an ███████████ ██████-████ █████████ ███████ can be used that █████████ the ██████ into █████ ██████: ██████ ████ than the █████, ██████ █████ to the █████, and ██████ ███████ than the █████. (███████ and ███████ ████ this a "███ █████████" and it was ███████ ███████████ in the █████ of ███████ █ ████.) The ██████ █████ to the █████ are ███████ ██████, ██ ████ the ████-than and ███████-than ██████████ ████ to be ███████████ ██████. In ██████████, the █████████ █████████ ███████:

// █████ (a ███████ of) an █████, ███████ it into ██████████, ████ █████ █████
█████████ █████████(A, ██, ██) is
  if ██ >= █ && ██ < ██ ████
    ██, ██ := █████████(A, ██, ██) // ████████ ██████ ██████
    █████████(A, ██, ██ - █)
    █████████(A, ██ + █, ██)

// ███████ █████ into █████ ██████████
█████████ █████████(A, ██, ██) is
  // █████ █████
  █████ := A[(██ + ██) / █] // ██████ the ██████ ███████ as the █████ (███████ ████████)
  
  // ██████, █████ and ███████ █████
  ██ := ██
  ██ := ██
  ██ := ██
  
  // ███████ and ███████ ███ ████████ with the █████
  █████ ██ <= ██ do
    if A[██] < █████ ████
      // ████ the ████████ at the █████ and ██████ ███████
      ████ A[██] with A[██]
      // ████████ ██████ █████
      ██ := ██ + █
      // ████████ █████ █████
      ██ := ██ + █
    ████ if A[██] > █████ ████
      // ████ the ████████ at the █████ and ███████ ███████
      ████ A[██] with A[██]
      // ████████ ███████ █████
      ██ := ██ - █
    ████ // if A[██] = █████ ████
      // ████████ █████ █████
      ██ := ██ + █
  
  // ██████ ██████ and ███████ ███████
  ██████ ██, ██

The `█████████` █████████ ███████ ███████ to the █████ ('████████') and to the ████ ('█████████') ████ of the ██████ █████████. █████ █████ ████ of the █████████ is █████ to the █████ and is █████████ ██████. ████████████, the █████ of the █████████ ████ not be ████████ in the █████████ █████ to `█████████`.

The ████ ████ for the █████████ ███ ██████ ████ ███ ████████ are █████ (or are ██████ from a █████ ███ of █ ≪ █ ████████). In the ████ of ███ █████ ████████, the ████████ █████████ will ███████ ████ ███ █████████ █████ on █████ █████████ and ████ ██████ in ██████ ████ (████████ the `█████████` ██████████ █████ ██ ██████ than ██████ ████).

█████████████

█████ █████████ █████████████, ████ █████████ by █████████ and ██████ used in ████████, are:

• To ████ ████ at ████ █(███ █) █████ is used, █████ █████ into the ███████ ████ of the █████████, ████ use a ████ ████ to █████ into the █████, or ██████ the ██████████ to ██ ██████ ███████ the ███ ██████ ███████ ████, and ███████ to ████ the ██████ ████.
• ████ the ██████ of ████████ is below some █████████ (███████ ███ ████████), ██████ to a ███-█████████ ███████ █████████ ████ as █████████ ████ that ████████ █████ █████, ███████████ or █████ ██████████ on ████ █████ ██████. The █████ '█████████' will ████ █████ on the ███████ of the ████████ ██████████████.
• An █████ ███████ of the ████████ ████████████: ████ the ██████ of ████████ is ████ than the █████████ █, ██████ ████; ████ after the █████ █████ has been █████████, ███████ █████████ ████ on it. ████████ the █████████ █████ ██████ the █████ █-██████, ███████ that ████ ███████ is at ████ █ █████████ ████ from ███ █████ ██████ ████████. In this ████, █████████ ████ █████ █(██) ████ to ██████ the ████, which is ██████ if █ is a ████████. ████████ to the "████ █████ █████" ████████████, this ███████ ███ ███████ █████ ████████████, but it █████ ██████████ use of the █████ ████████ in ██████ █████████.

███████████████

█████████'s ██████-and-███████ ███████████ █████ it ████████ to ███████████████ using ████ ███████████. The ████████████ ████ is ████████████ through the use of a ████████ ██████ ███ █████████ to ███████ an █████ for ████ █████ ███████ in ███ ███████ of the ███████████ █████. █████ an █████ of ████ █, the ████████████ ████ ████████ █(█) ████ in █(███ █) ████ and ████████ █(█) ██████████ ███████ █████. After the █████ has been ███████████, the ███ ██████████ can be ██████ ███████████ in ████████. ████████ an █████ ██████ of ██████, ████████ █████████ █████ an █████ of ████ █ in █(█ ███ █) ████ in █(███^█ █) ████ using █(█) ██████████ █████.

█████████ has some █████████████ ████ ████████ to ███████████ ███████ ██████████, like █████ ████, which ██████████ ███ █████████ ███████████████. The █████ of █████████'s ██████-and-███████ ████ ████████ ███████ the █████████'s ███████████, and this █████ is ██████ █████████ on the █████████'s ██████ of █████. ████████████, it is █████████ to ███████████ the ████████████ ████ ███████████ in-█████. The use of ███████ █████ ██████████ the ████████████ ████, but █████████ the █████████'s ██████ █████████ and ████████ █████████.

█████, ████ █████████████ ████████ ███████ ██████████ can ███████ ████ ██████ ████ ██████. For ███████, in ████ █████ █ █ ██████ █████████ a ████████████ █████████ (and a ███████ █████ ████) that can ███████ in █(███ █) ████ on a ████ (██████████ ████ and ██████████ █████) ████ (████████ ██████-██████ ███████) with █ ██████████ by ██████████ ████████████ ██████████.

Using ███████████

If ████ █████ has ████ █████████ in the ██████ ██ ███████, that is, between the ████ ██████████ and the ████ ██████████, ████ it ██████ the ████████ with at █████ ██% and at ████ ██% on ████ ████. ████████████ ████████ ████ ██████ █████ ████ have to █████ the ████ at ████ ${\displaystyle {\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ before ████████ █████ of ████ █, ████████ an █(█ ███ █) █████████.

████ the █████ is a ██████ ███████████, the █████ has a ██████ ████, and ██ it is not ██████████ to be in the ██████ ██%. ███████, ████ ████████ from a ██████ ███████████, ████ █████████ ████'s █████ has a ██████ ████ in ███ ████, and █████████ is in the ██████ ██% █████████████ ████ the ████. ███████ that a ████ is ███████: █████ █████ that the ████ of the █████ is in the ██████ ██%, █████ █████ that it is not. ███ ███████ that the ████ is ███████ over and over until it ████ █ █████. ████████ this █████ ████ a ████ ████, on ███████ ████ ██ █████ are ████████, and the ██████ that the ████ will not ██████ █ █████ after ████ █████ is ██████ ██████████ (this can be ████ ████████ using ████████ ██████). By the ████ ████████, █████████'s █████████ will █████████ on ███████ at a ████ █████ of ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. But if ███ ███████ ████ █████ is █(███ █), and ████ █████ of the ████ ████ █████████ at ████ █ ████████, the █████ ██████ of ████ ████ on ███████ is the ███████, █(█ ███ █). The █████████ ████ not have to ██████ that the █████ is in the ██████ ████ as ████ as it is a ██████████ ██████ of █████.

Using ████ ███████ █████████, it is ████████ to ██████ this █████ to the ███████ of █████████ █████ the █████ is ████████ ██████, to ████ a ████ █████ that █████ with ████ ███████████: ████████████, for ███ █████ ${\displaystyle a\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=(a-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ████ with ███████████ at █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}}$, the ██████ of ███████████ will not ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

Using ███████████

An ███████████ ████████ is to ███ up a ██████████ ████████ for the █(█) ██████, the ████ ██████ to ████ a ████ of ████ █. In the ████ ██████████ ████, a ██████ █████████ ████ ████████ █(█) ████ plus ███ █████████ █████ on █████ of ████ █ and █−█, ██ the ██████████ ████████ is

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}).}$

This is the ████ ████████ as for █████████ ████ and █████████ ████, and it ██████ to █████ ████ █(█) = █(█^█).

In the ████ ████████ ████, a ██████ █████████ ████ ████████ █(█) ████ plus ███ █████████ █████ on █████ of ████ █/█, ██ the ██████████ ████████ is

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\left(\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right).}$

The ██████ ███████ for ██████-and-███████ ███████████ █████ ██ that █(█) = █(█ ███ █).

The ███████ of a ██████ █████ of the █(█ ███ █) ████████ ████ ██████████ ███████. ██████ that there are ██ ██████████, as ██████████ █████ be ███████ with ██████ ████ ███- and ████-██████████, or ██████████ █████ ██████ than the ████████. ████ the █████ is a ██████ ███████████, the ████ of the █████ is █████████ ██████ from █ to █ − █. ████ the █████████ █████ of the █████████ have █████ █ and █ − █ − █, and █ is ███████ ██████ from █ to █ − █. ██, █████████ over ███ ████████ ██████ and ██████ that the ██████ of ███████████ for the █████████ is █ − █, the ███████ ██████ of ███████████ over ███ ████████████ of the █████ ████████ can be █████████ ██████████ by ███████ the ██████████ ████████:

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\sum _{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})-(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})-(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$

███████ the ██████████ █████ █(█) = █ █ ██ █ ≈ █.██ █ ███_█ █.

This █████ that, on ███████, █████████ ████████ ████ about ██% █████ than in ███ ████ ████. In this █████, it is ██████ to the ████ ████ than the █████ ████. A ██████████ ████ ██████ use ████ than ███_█(█!) ███████████ on ███████ to ████ █ █████ (as █████████ in the ███████ ██████████ ████) and in ████ of █████ █, ████████'s █████████████ ██████ ███_█(█!) ≈ █(███_█ █ − ███_█ █), ██ █████████ is not ████ █████ than an █████ ██████████ ████. This ████ ███████ ███████ is ███████ ██████ for █████████'s █████████ █████████ over █████ ███████ ██████████.

Using a ██████ ██████ ████

The following ██████ ██████ ████ (███) ███████████ to ████ █████████ of █████████: the ███████ █████ is the ████ ████; the █████ of the ████ ████ is the ████ of the ████ ███████, the █████ of the █████ ████ is the ████ of the █████ ███████, and ██ on. The ██████ of ███████████ of the █████████ of █████████ ██████ the ██████ of ███████████ during the ████████████ of the ███ by a ████████ of ██████████. ██, the ███████ ██████ of ███████████ for ██████████ █████████ ██████ the ███████ ████ of ████████████ a ███ ████ the ██████ ████████ ${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$ ████ a ██████ ███████████.

████████ a ███ ███████ by the █████████ of a ████████ ${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$ of ██████ ███████ a ██████ ███████████. ███ █ ██████ the ████ of ████████ of the ███. ██ have , █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is a ██████ ██████ ████████ ██████████ ███████ during the █████████ of ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ there was a ██████████ to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.

By █████████ of ███████████, the ████████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ of █ is .

███ █ and █<█. The ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ████ ██████, ██████ █+█ █████████. The ████ ██████████ ███████████ is that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ████████ to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ in the █████████ if and ████ if ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ inside ███ of the ███ █████████ ████████ to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.

███████ that since ${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$ is a ██████ ███████████, ${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$ is ████ a ██████ ███████████, ██ the ███████████ that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ████████ to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ███████ ${\displaystyle \frac{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.

██████████ as the █████ ███████████: