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4 changes: 3 additions & 1 deletion docs/assets/js/mathjax.js
Original file line number Diff line number Diff line change
@@ -1,9 +1,11 @@
window.MathJax = {
loader: {load: ['[tex]/colortbl']},
tex: {
inlineMath: [["\\(", "\\)"]],
displayMath: [["\\[", "\\]"]],
processEscapes: true,
processEnvironments: true
processEnvironments: true,
packages: {'[+]': ['colortbl']},
},
options: {
ignoreHtmlClass: ".*|",
Expand Down
206 changes: 181 additions & 25 deletions docs/fundamentals/ideas/congeneric_decomposition.md
Original file line number Diff line number Diff line change
Expand Up @@ -11,35 +11,191 @@ This reversible process preserves the order of the sequence and allows the origi

The concept of Cogeneric decomposition can be demonstrated using an example:

Let's assume there is a symbolic sequence `INTELLIGENCE IS THE ABILITY TO ADAPT TO CHANGE` congeneric decomposition
Let's assume there is a symbolic sequence `INTELLIGENCE IS THE ABILITY TO ADAPT` congeneric decomposition
could be presented by the following table, where each row is a congeneric sequence and `-` is an empty position in a congeneric sequence.

| I | N | T | E | L | L | I | G | E | N | C | E |    | I | S |    | T | H | E |    | A | B | I | L | I | T | Y |    | T | O |    | A | D | A | P | T |    | T | O |    | C | H | A | N | G | E |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| I | - | - | - | - | - | I | - | - | - | - | - | - | I | - | - | - | - | - | - | - | - | I | - | I | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| - | N | - | - | - | - | - | - | - | N | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | N | - | - |
| - | - | T | - | - | - | - | - | - | - | - | - | - | - | - | - | T | - | - | - | - | - | - | - | - | T | - | - | T | - | - | - | - | - | - | T | - | T | - | - | - | - | - | - | - | - |
| - | - | - | E | - | - | - | - | E | - | - | E | - | - | - | - | - | - | E | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | E |
| - | - | - | - | L | L | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | L | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| - | - | - | - | - | - | - | G | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | G | - |
| - | - | - | - | - | - | - | - | - | - | C | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | C | - | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - |    | - | - |    | - | - | - |    | - | - | - | - | - | - | - |    | - | - |    | - | - | - | - | - |    | - | - |    | - | - | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | S | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | H | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | H | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | A | - | - | - | - | - | - | - | - | - | - | A | - | A | - | - | - | - | - | - | - | - | A | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | B | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | Y | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | O | - | - | - | - | - | - | - | - | O | - | - | - | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | D | - | - | - | - | - | - | - | - | - | - | - | - | - |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | P | - | - | - | - | - | - | - | - | - | - | - |


Congeneric sequence for `I`

<!-- \begin{equation}
\scriptsize
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\cellcolor{#ff7f0e}I & \cellcolor{#ffbb78}N & \cellcolor{#2ca02c}T & \cellcolor{#98df8a}E & \cellcolor{#d62728}L & \cellcolor{#d62728}L & \cellcolor{#ff7f0e}I & \cellcolor{#ff9896}G & \cellcolor{#98df8a}E & \cellcolor{#ffbb78}N & \cellcolor{#9467bd}C & \cellcolor{#98df8a}E & \cellcolor{#c5b0d5}\text{ } & \cellcolor{#ff7f0e}I & \cellcolor{#8c564b}S & \cellcolor{#c5b0d5}\text{ } & \cellcolor{#2ca02c}T & \cellcolor{#c49c94}H & \cellcolor{#98df8a}E & \cellcolor{#c5b0d5}\text{ } & \cellcolor{#e377c2}A & \cellcolor{#f7b6d2}B & \cellcolor{#ff7f0e}I & \cellcolor{#d62728}L & \cellcolor{#ff7f0e}I & \cellcolor{#2ca02c}T & \cellcolor{#bcbd22}Y & \cellcolor{#c5b0d5}\text{ } & \cellcolor{#2ca02c}T & \cellcolor{#dbdb8d}O & \cellcolor{#c5b0d5}\text{ } & \cellcolor{#e377c2}A & \cellcolor{#17becf}D & \cellcolor{#e377c2}A & \cellcolor{#9edae5}P & \cellcolor{#2ca02c}T \\
\hline
\cellcolor{#ff7f0e}I & - & - & - & - & - & \cellcolor{#ff7f0e}I & - & - & - & - & - & - & \cellcolor{#ff7f0e}I & - & - & - & - & - & - & - & - & \cellcolor{#ff7f0e}I & - & \cellcolor{#ff7f0e}I & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & \cellcolor{#ffbb78}N & - & - & - & - & - & - & - & \cellcolor{#ffbb78}N & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & \cellcolor{#2ca02c}T & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#2ca02c}T & - & - & - & - & - & - & - & - & \cellcolor{#2ca02c}T & - & - & \cellcolor{#2ca02c}T & - & - & - & - & - &- & \cellcolor{#2ca02c}T \\
\hline
- & - & - & \cellcolor{#98df8a}E & - & - & - & - & \cellcolor{#98df8a}E & - & - & \cellcolor{#98df8a}E & - & - & - & - & - & - & \cellcolor{#98df8a}E & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & \cellcolor{#d62728}L & \cellcolor{#d62728}L & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#d62728}L & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & \cellcolor{#ff9896}G & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & \cellcolor{#9467bd}C & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#c5b0d5}\text{ } & - & - & \cellcolor{#c5b0d5}\text{ } & - & - & - & \cellcolor{#c5b0d5}\text{ } & - & - & - & - & - & - & - & \cellcolor{#c5b0d5}\text{ } & - & - & \cellcolor{#c5b0d5}\text{ } & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#8c564b}S & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#c49c94}H & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#e377c2}A & - & - & - & - & - & - & - & - & - & - & \cellcolor{#e377c2}A & - & \cellcolor{#e377c2}A & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#f7b6d2}B & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#bcbd22}Y & - & - & - & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#dbdb8d}O & - & - & - & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#17becf}D & - & - & - \\
\hline
- & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \cellcolor{#9edae5}P & - \\
\hline
\end{array}
\end{equation}
-->



``` mermaid
block-beta
columns 36
seq1["I"] seq2["N"] seq3["T"] seq4["E"] seq5["L"] seq6["L"] seq7["I"] seq8["G"] seq9["E"] seq10["N"]
seq11["C"] seq12["E"] seq13[" "] seq14["I"] seq15["S"] seq16[" "] seq17["T"] seq18["H"] seq19["E"] seq20[" "]
seq21["A"] seq22["B"] seq23["I"] seq24["L"] seq25["I"] seq26["T"] seq27["Y"] seq28[" "] seq29["T"] seq30["O"]
seq31[" "] seq32["A"] seq33["D"] seq34["A"] seq35["P"] seq36["T"]

space:36

i1["I"] i2["-"] i3["-"] i4["-"] i5["-"] i6["-"] i7["I"] i8["-"] i9["-"] i10["-"]
i11["-"] i12["-"] i13["-"] i14["I"] i15["-"] i16["-"] i17["-"] i18["-"] i19["-"] i20["-"]
i21["-"] i22["-"] i23["I"] i24["-"] i25["I"] i26["-"] i27["-"] i28["-"] i29["-"] i30["-"]
i31["-"] i32["-"] i33["-"] i34["-"] i35["-"] i36["-"]

n1["-"] n2["N"] n3["-"] n4["-"] n5["-"] n6["-"] n7["-"] n8["-"] n9["-"] n10["N"]
n11["-"] n12["-"] n13["-"] n14["-"] n15["-"] n16["-"] n17["-"] n18["-"] n19["-"] n20["-"]
n21["-"] n22["-"] n23["-"] n24["-"] n25["-"] n26["-"] n27["-"] n28["-"] n29["-"] n30["-"]
n31["-"] n32["-"] n33["-"] n34["-"] n35["-"] n36["-"]

t1["-"] t2["-"] t3["T"] t4["-"] t5["-"] t6["-"] t7["-"] t8["-"] t9["-"] t10["-"]
t11["-"] t12["-"] t13["-"] t14["-"] t15["-"] t16["-"] t17["T"] t18["-"] t19["-"] t20["-"]
t21["-"] t22["-"] t23["-"] t24["-"] t25["-"] t26["T"] t27["-"] t28["-"] t29["T"] t30["-"]
t31["-"] t32["-"] t33["-"] t34["-"] t35["-"] t36["T"]

e1["-"] e2["-"] e3["-"] e4["E"] e5["-"] e6["-"] e7["-"] e8["-"] e9["E"] e10["-"]
e11["-"] e12["E"] e13["-"] e14["-"] e15["-"] e16["-"] e17["-"] e18["-"] e19["E"] e20["-"]
e21["-"] e22["-"] e23["-"] e24["-"] e25["-"] e26["-"] e27["-"] e28["-"] e29["-"] e30["-"]
e31["-"] e32["-"] e33["-"] e34["-"] e35["-"] e36["-"]

l1["-"] l2["-"] l3["-"] l4["-"] l5["L"] l6["L"] l7["-"] l8["-"] l9["-"] l10["-"]
l11["-"] l12["-"] l13["-"] l14["-"] l15["-"] l16["-"] l17["-"] l18["-"] l19["-"] l20["-"]
l21["-"] l22["-"] l23["-"] l24["L"] l25["-"] l26["-"] l27["-"] l28["-"] l29["-"] l30["-"]
l31["-"] l32["-"] l33["-"] l34["-"] l35["-"] l36["-"]

g1["-"] g2["-"] g3["-"] g4["-"] g5["-"] g6["-"] g7["-"] g8["G"] g9["-"] g10["-"]
g11["-"] g12["-"] g13["-"] g14["-"] g15["-"] g16["-"] g17["-"] g18["-"] g19["-"] g20["-"]
g21["-"] g22["-"] g23["-"] g24["-"] g25["-"] g26["-"] g27["-"] g28["-"] g29["-"] g30["-"]
g31["-"] g32["-"] g33["-"] g34["-"] g35["-"] g36["-"]

c1["-"] c2["-"] c3["-"] c4["-"] c5["-"] c6["-"] c7["-"] c8["-"] c9["-"] c10["-"]
c11["C"] c12["-"] c13["-"] c14["-"] c15["-"] c16["-"] c17["-"] c18["-"] c19["-"] c20["-"]
c21["-"] c22["-"] c23["-"] c24["-"] c25["-"] c26["-"] c27["-"] c28["-"] c29["-"] c30["-"]
c31["-"] c32["-"] c33["-"] c34["-"] c35["-"] c36["-"]

sp1["-"] sp2["-"] sp3["-"] sp4["-"] sp5["-"] sp6["-"] sp7["-"] sp8["-"] sp9["-"] sp10["-"]
sp11["-"] sp12["-"] sp13[" "] sp14["-"] sp15["-"] sp16[" "] sp17["-"] sp18["-"] sp19["-"] sp20[" "]
sp21["-"] sp22["-"] sp23["-"] sp24["-"] sp25["-"] sp26["-"] sp27["-"] sp28[" "] sp29["-"] sp30["-"]
sp31[" "] sp32["-"] sp33["-"] sp34["-"] sp35["-"] sp36["-"]

s1["-"] s2["-"] s3["-"] s4["-"] s5["-"] s6["-"] s7["-"] s8["-"] s9["-"] s10["-"]
s11["-"] s12["-"] s13["-"] s14["-"] s15["S"] s16["-"] s17["-"] s18["-"] s19["-"] s20["-"]
s21["-"] s22["-"] s23["-"] s24["-"] s25["-"] s26["-"] s27["-"] s28["-"] s29["-"] s30["-"]
s31["-"] s32["-"] s33["-"] s34["-"] s35["-"] s36["-"]

h1["-"] h2["-"] h3["-"] h4["-"] h5["-"] h6["-"] h7["-"] h8["-"] h9["-"] h10["-"]
h11["-"] h12["-"] h13["-"] h14["-"] h15["-"] h16["-"] h17["-"] h18["H"] h19["-"] h20["-"]
h21["-"] h22["-"] h23["-"] h24["-"] h25["-"] h26["-"] h27["-"] h28["-"] h29["-"] h30["-"]
h31["-"] h32["-"] h33["-"] h34["-"] h35["-"] h36["-"]

a1["-"] a2["-"] a3["-"] a4["-"] a5["-"] a6["-"] a7["-"] a8["-"] a9["-"] a10["-"]
a11["-"] a12["-"] a13["-"] a14["-"] a15["-"] a16["-"] a17["-"] a18["-"] a19["-"] a20["-"]
a21["A"] a22["-"] a23["-"] a24["-"] a25["-"] a26["-"] a27["-"] a28["-"] a29["-"] a30["-"]
a31["-"] a32["A"] a33["-"] a34["A"] a35["-"] a36["-"]

b1["-"] b2["-"] b3["-"] b4["-"] b5["-"] b6["-"] b7["-"] b8["-"] b9["-"] b10["-"]
b11["-"] b12["-"] b13["-"] b14["-"] b15["-"] b16["-"] b17["-"] b18["-"] b19["-"] b20["-"]
b21["-"] b22["B"] b23["-"] b24["-"] b25["-"] b26["-"] b27["-"] b28["-"] b29["-"] b30["-"]
b31["-"] b32["-"] b33["-"] b34["-"] b35["-"] b36["-"]

y1["-"] y2["-"] y3["-"] y4["-"] y5["-"] y6["-"] y7["-"] y8["-"] y9["-"] y10["-"]
y11["-"] y12["-"] y13["-"] y14["-"] y15["-"] y16["-"] y17["-"] y18["-"] y19["-"] y20["-"]
y21["-"] y22["-"] y23["-"] y24["-"] y25["-"] y26["-"] y27["Y"] y28["-"] y29["-"] y30["-"]
y31["-"] y32["-"] y33["-"] y34["-"] y35["-"] y36["-"]

o1["-"] o2["-"] o3["-"] o4["-"] o5["-"] o6["-"] o7["-"] o8["-"] o9["-"] o10["-"]
o11["-"] o12["-"] o13["-"] o14["-"] o15["-"] o16["-"] o17["-"] o18["-"] o19["-"] o20["-"]
o21["-"] o22["-"] o23["-"] o24["-"] o25["-"] o26["-"] o27["-"] o28["-"] o29["-"] o30["O"]
o31["-"] o32["-"] o33["-"] o34["-"] o35["-"] o36["-"]

d1["-"] d2["-"] d3["-"] d4["-"] d5["-"] d6["-"] d7["-"] d8["-"] d9["-"] d10["-"]
d11["-"] d12["-"] d13["-"] d14["-"] d15["-"] d16["-"] d17["-"] d18["-"] d19["-"] d20["-"]
d21["-"] d22["-"] d23["-"] d24["-"] d25["-"] d26["-"] d27["-"] d28["-"] d29["-"] d30["-"]
d31["-"] d32["-"] d33["D"] d34["-"] d35["-"] d36["-"]

p1["-"] p2["-"] p3["-"] p4["-"] p5["-"] p6["-"] p7["-"] p8["-"] p9["-"] p10["-"]
p11["-"] p12["-"] p13["-"] p14["-"] p15["-"] p16["-"] p17["-"] p18["-"] p19["-"] p20["-"]
p21["-"] p22["-"] p23["-"] p24["-"] p25["-"] p26["-"] p27["-"] p28["-"] p29["-"] p30["-"]
p31["-"] p32["-"] p33["-"] p34["-"] p35["P"] p36["-"]

classDef c1 fill:#ff7f0e,color:#fff;
classDef c2 fill:#ffbb78,color:#000;
classDef c3 fill:#2ca02c,color:#fff;
classDef c4 fill:#98df8a,color:#000;
classDef c5 fill:#d62728,color:#fff;
classDef c6 fill:#ff9896,color:#000;
classDef c7 fill:#9467bd,color:#fff;
classDef c8 fill:#c5b0d5,color:#000;
classDef c9 fill:#8c564b,color:#fff;
classDef c10 fill:#c49c94,color:#000;
classDef c11 fill:#e377c2,color:#fff;
classDef c12 fill:#f7b6d2,color:#000;
classDef c13 fill:#bcbd22,color:#fff;
classDef c14 fill:#dbdb8d,color:#000;
classDef c15 fill:#17becf,color:#fff;
classDef c16 fill:#9edae5,color:#000;

class seq1,seq7,seq14,seq23,seq25,i1,i7,i14,i23,i25 c1
class seq2,seq10,n2,n10 c2
class seq3,seq17,seq26,seq29,seq36,t3,t17,t26,t29,t36 c3
class seq4,seq9,seq12,seq19,e4,e9,e12,e19 c4
class seq5,seq6,seq24,l5,l6,l24 c5
class seq8,g8 c6
class seq11,c11 c7
class seq13,seq16,seq20,seq28,seq31,sp13,sp16,sp20,sp28,sp31 c8
class seq15,s15 c9
class seq18,h18 c10
class seq21,seq32,seq34,a21,a32,a34 c11
class seq22,b22 c12
class seq27,y27 c13
class seq30,o30 c14
class seq33,d33 c15
class seq35,p35 c16
```
I - - - - - I - - - - - - I - - - - - - - - I - I - - - - - - - - - - - - - - - - - - - - -

Congeneric sequence for `E`
``` mermaid
block-beta
columns 36
e1["-"] e2["-"] e3["-"] e4["E"] e5["-"] e6["-"] e7["-"] e8["-"] e9["E"] e10["-"]
e11["-"] e12["E"] e13["-"] e14["-"] e15["-"] e16["-"] e17["-"] e18["-"] e19["E"] e20["-"]
e21["-"] e22["-"] e23["-"] e24["-"] e25["-"] e26["-"] e27["-"] e28["-"] e29["-"] e30["-"]
e31["-"] e32["-"] e33["-"] e34["-"] e35["-"] e36["-"]
```
could be a part of multiple symbol sequences that have the same order of `I` element.


could be a part of multiple symbol sequences that have the same order of `E` element.

While keeping the main idea, the congeneric decomposition could be applied, with a flavor, to any type of special case symbolic sequences, such as Order.

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10 changes: 10 additions & 0 deletions docs/fundamentals/ideas/interval_as_a_basic_information_unit.md
Original file line number Diff line number Diff line change
Expand Up @@ -13,6 +13,11 @@ block-beta
columns 12
s1["A"] s2["C"] s3["T"] s4["A"] s5["C"] s6["G"] s7["A"] s8["A"] s9["A"] s10["T"] s11["A"] s12["A"]
i1["3"]:3 i2["3"]:3 i3["1"]:1 i4["1"]:1 i5["2"]:2 i6["1"]:1 i7["1"]:1

classDef c3 fill:#2ca02c,color:#fff;
classDef c4 fill:#98df8a,color:#000;
class s1,s4,s7,s8,s9,s11,s12 c3
class i1,i2,i3,i4,i5,i6,i7 c4
```

In general, a sequence does not necessarily end with the same symbol it begins with.
Expand All @@ -26,6 +31,11 @@ block-beta
s1["A"] s2["C"] s3["T"] s4["A"] s5["C"] s6["G"] s7["A"] s8["A"] s9["A"] s10["T"] s11["A"] s12["A"] space s13["T"] s14["C"]
space i1["3"]:3 i2["9"]:10
s12 --> s13

classDef c3 fill:#2ca02c,color:#fff;
classDef c4 fill:#98df8a,color:#000;
class s2,s5,s14 c3
class i1,i2 c4
```

The circular pattern preserves both the statistical properties and the order of elements.
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