Glottometrics 7, 2004, 68-88

Symmetry of Japanese Kanji Lexical Productivity
on the Left- and Right-hand Sides
Katsuo Tamaoka (Hiroshima, Japan)1
Gabriel Altmann (Lüdenscheid, Germany)
Abstract: Japanese kanji combine with other kanji to produce various two-kanji compound words.
First, the present study examined whether the extent of left-hand and right-hand productivity of theJapanese 1,945 basic kanji abides by an ‘honest’ distribution. The result showed that kanji compound building (or kanji lexical productivity) was depicted by a birth-and-death process
leading to the negative binomial and/or the Waring distribution. Second, the study investigated whether these basic kanji display symmetry on the left- and right-side lexical productivity.
Analysis of these kanji suggested that although each kanji displayed symmetry in lexical
productivity, there is no tendency among the basic kanji to produce their compound words
to the same extent on the left or the right side on the whole.
Key words: Japanese kanji, kanji lexical productivity, birth-and-death process, symmetry

1. Two-kanji compound words in a Japanese Dictionary
In the written Japanese, kanji, which adopted Chinese characters for expressing various
words, often combine with another kanji to produce a new meaning. In this sense, the unitof kanji refers to ‘morpheme’, the smallest unit of meanings. Yokosawa and Umeda (1988)
reported that approximately 70 percent of 51,962 words listed in a particular Japanese dictionary were composed of two kanji or two morpheme combinations. In 1981, the Ministryof Education, Science, Sports and Culture, Government of Japan (hereafter simply called
the ‘Japanese Ministry of Education’ except in quotes) published a list of the 1,945 BasicJapanese Kanji (for detailed information, see Kato, 1989; Yasunaga, 1981). This list established a standard for kanji usage in printed and written Japanese texts (Ministry of Education, Science, Sports and Culture, Government of Japan, 1987, 1998). The National Institute for Japanese Language (1976) conducted a survey on the frequency of kanji in print,
and found that 2,000 kanji encompassed 99.6 percent of all kanji used in three major
Japanese newspapers, Asahi, Mainichi and Yomiuri) published during the year 1966. Although the 1,945 Basic Japanese Kanji and the 2,000 kanji mentioned above were not
identical, it is roughly estimated that these basic kanji cover approximately 99 percent of
all kanji used in Japanese newspapers. Combining this figure with 70 percent of two-kanji
compound words in a dictionary, 1,945 kanji will provide us a reasonable estimate on
Japanese kanji and their productivity.

1

Address correspondence to: Katsuo Tamaoka, International Student Center, Hiroshima University 1-1, 1chome, Higashihiroshima, Japan 739-8524. E-mail: ktamaoka@hiroshima-u.ac.jp

Symmetry of Japanese kanji lexical productivity
2. Counting of kanji lexical productivity and purpose of the present study
As Yokosawa and Umeda (1988) pointed out, the majority of lexical items in a Japanesedictionary are words consisting of two kanji units. The number of lexical productivity issimple counting (i.e., type frequency, not token frequency) of all possible two kanji combinations. Interestingly, various complex compound words are often constructed by two
kanji compound words such as 経済政策 (/keizai seisaku/2, ‘economic policy’), 宇宙遊泳(/utjuR juRei/, ‘space walk’), and 冷凍食品 (/reitoR sjokuhiN/, ‘frozen food’). Furthermore, the word ‘frozen food’ can be combined with another two-kanji compound word 貯
蔵 (/tjo zoR/, ‘storage’) to make a six-kanji compound word, 冷凍食品貯蔵 (/reitoR
sjokuhiN tjozoR/, ‘storage of frozen food’) consisting of three two-kanji compound words.
Thus, two-kanji compound words are a sensible unit to count how many words each kanji
can produce.
A single kanji can produce two-kanji compound words in two ways, produced by the
combination of kanji placed on the left-hand and right-hand side positions of two-kanji
compound words. For example, the kanji 学 /gaku/ meaning ‘to learn’ or ‘learning’ is combined with another kanji on the right-hand side position such as in 学校 (/gaQ koR/,‘school’), 学生 (/gaku sei/, ‘student’) and 学者 (/gaku sja/, ‘scholar’). Combinations withother kanji on the left-hand side position are also possible such as in 入学 (/njuR gaku/,‘school admission’), 文学 (/bun gaku/, ‘literature’) and 私学 (/si gaku/, ‘private school’).
Kanji productivity of two-kanji compound words refers to the unit of one kanji combinedwith another kanji to create two-kanji compound words. Therefore, the concept of this term
could be understood as a linguistic concept of kanji ‘lexical productivity’ (details see,Hayashi, 1987; Nomoto, 1989; Nomura, 1988, 1989), which can be calculated by the leftside, right-side and both sides together. The present paper investigated two questions: (1)how two-kanji compound words were produced by a single kanji on the left-hand and theright-hand sides, and (2) how symmetric they are on both sides.

3. Kanji lexical productivity
The present study used a lexical corpus of 341,771 words that was established fromnewspapers containing 287,792,797 words by Amano and Kondo (2000), all of which weretaken from the Asahi Newspaper printed from 1985 to 1998. At present, this is the largest
and the most up-to-date word corpus created from calculating the word frequency of occurrence in Japanese written texts. For counting kanji lexical productivity, the programming
language of MacJPerl 5.15r4J for Macintosh was used to run a calculation procedure.
Type frequency counts of kanji lexical productivity on the left-hand, right-hand and bothsides were arranged for all the 1,945 basic kanji. The beginning 10 kanji of the raw data
are presented in Table 1.

2

The pronunciation in this paper is transcribed using Japanese phonemic symbols which indicate three
special sounds in Japanese: /N/ for nasal, /Q/ for geminate and /R/ for long vowel.

69

Katsuo Tamaoka, Gabriel Altmann

70

Table 1
The first ten kanji and their lexical productivity on the left- and right-hand sides
No. Kanji

In phonemes

Left-hand side

Right-hand side

Both sides together

1

亜

/a/

3

13

16

2

哀

/ai/

1

19

20

3

愛

/ai/

28

55

83

4

悪

/aku/

35

80

115

5

握

/aku/

4

4

8

6

圧

/atu/

42

21

63

7

扱

/atu/

1

1

2

8

安

/aN/

24

40

64

9

案

/aN/

49

6

55

暗
/aN/
10
5
40
Note: A common kanji pronunciations are used to arrange kanji in this table.

45

Each of the chosen kanji develops its own individual left and right lexical productivity.
For example, the eighth kanji 安 (/aN/, ‘rest’, ‘relax’, ‘cheap’, ‘peaceful’, etc.) produced 24
two-kanji compound words by adding kanji on the left-hand side while producing 40 compounds by adding kanji on the right-hand side. The total lexical productivity becomes 64.
By counting the number of kanji with x compounds, the results presented in Table 2 forkanji on the left-hand side and in Table 3 for kanji on the right-hand side. Two-stepinvestigation is conducted using data of kanji lexical productivity in the present study. The
first step is to conjecture the mechanism generating the distribution of compounds. The
second step is the eventual modification of the result. This second step must be madebecause the basic kanji were taken from a ready list, not at random from the dictionary.
Thus the bias can be quite systematic.
Table 2Distribution of productivity of the 1,945 basic kanji on the left-hand side
x
0
1
2
3
4
5
6
7
8

fx
108
135
109
128
82
84
84
61
73

X
35
37
38
39
40
41
42
43
44

fx
10
14
16
5
9
13
6
8
10

x
71
72
73
75
76
77
78
79
80

fx
2
1
1
5
1
3
2
2
2

x
112
114
116
117
118
120
121
122
123

fx
1
1
1
1
4
2
2
1
1

Symmetry of Japanese kanji lexical productivity
9
67
45
9
82
4
126
10
59
46
8
83
2
127
11
53
47
5
84
2
128
12
48
48
8
85
2
129
13
49
49
6
86
1
130
14
36
50
5
87
1
131
15
37
51
2
88
1
132
16
37
52
7
89
2
135
17
39
53
9
91
1
136
18
33
54
3
92
1
138
19
29
55
6
93
2
140
20
17
56
2
94
1
142
21
34
57
5
96
2
146
22
28
58
3
97
1
148
23
15
59
5
98
1
151
24
17
60
3
99
1
153
25
22
61
3
100
1
162
26
21
62
3
101
1
170
27
19
63
3
102
1
171
28
16
64
6
103
1
180
29
13
65
6
104
1
213
30
16
66
3
106
4
246
31
15
67
8
108
1
268
32
13
68
3
109
2
33
8
69
3
110
1
34
11
70
3
111
1
Note: x = number of compounds, fx = number of kanji producing x compounds.

71
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Table 3Distribution of productivity of the 1,945 basic kanji on the right-hand side

x
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14

fx
72
91
115
121
90
93
92
87
80
61
78
51
57
49
51

X
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47

fx
17
16
7
13
13
13
7
11
11
15
9
12
4
6
10

x
67
68
69
70
71
72
73
74
75
76
77
78
79
80
82

fx
3
1
2
4
4
5
3
1
3
2
6
1
3
4
1

x
111
114
116
118
119
120
126
127
132
135
137
138
145
146
148

fx
2
1
1
1
1
1
1
1
1
2
2
3
1
1
1

Katsuo Tamaoka, Gabriel Altmann

72
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

34
45
32
35
31
29
22
21
18
22
11
21
15
17
12
14
15
15

48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
66

5
7
8
5
6
4
8
4
2
4
1
6
3
5
4
5
3
1

83
86
87
88
90
91
92
95
96
97
99
101
103
104
106
107
109
110

2
1
3
1
2
1
1
2
1
4
1
1
2
1
3
1
1
1

149
151
154
156
157
158
160
163
170
179
194
195
293
350
399

1
1
2
1
1
1
1
1
1
1
1
1
1
1
1

Note: x = number of compounds, fx = number of kanji producing x compounds.

4. A birth-and-death process of kanji compound words
Lexical productivity in languages, consisting of two kanji in the present study, always
faces to the birth of new forms (e.g., compounds) and their death. The process of the birthand death has two general features in languages. First, this process is incessant in any
language since newly-formed words are influenced steadily by various linguistic environments. As a result, some newly-produced words die immediately, some live longer, andsome survive for a very long time. Second, this process is, nevertheless, in steady state andis balanced by language self-regulation (Köhler 1986). Thus, having these two features
together, lexical productivity is consistently modeled in the manner of an incessant steadystate birth-and-death process (Altmann 1985; Wimmer, Altmann 1995).
Considering fx the number of kanji building exactly x compounds, Px is the relative
number corresponding to fx, or the probability in the model. A kanji leaves class x if either
a compound “dies” (the kanji goes in class x-1) or a new compound arises (it goes to classx+1). A kanji enters class x if in class x-1 a new compound is born or in the class x+1 acompound dies. Let the birth ratio be λx and the death ratio µx. Then, considering theprobability of birth or death of two or more compounds at a time as zero, the process canbe written in form of simple equations:(1)

λ0P0 = µ1P1
(λx + µx)Px = λx-1Px-1 + µx+1Px+1 , x = 1,2,…

The equation (1) can be solved stepwise but the solution is known as(2)

Px = P0λ0λ1...λx−1.
µ1µ 2 ...µ x

Symmetry of Japanese kanji lexical productivity
Using simple linear functions for the rates, namely
λx = a+bx (a = constant birth coefficient, b = coefficient of assertion against x
rivals)µx = cx(c = death coefficient) .
The equation (3) is obtained by substituting them in (2)(3)

Px = P0

a(a + b)(a + 2b)...[a + ( x − 1)b].
x !c xThe rest is simple manipulation. Factoring out b and requiring c > b (because of
convergence), and substituting
b/c = q (0 < q < 1)
a/b = rthe equation (4) is obtained:(4)

Px = P0

 r + x − 1 x
r (r + 1)...(r + x − 1) x
q = P0 
q .
x
x!



Since P0 is the normalizing constant following from ΣPx = 1, we obtain at last (with p = 1q)(5)

 r + x − 1 r x
Px = 
 p q , x = 0,1,2,…
 x 

representing the usual negative binomial distribution, symbolized as NB(r,p). Now fitting
this distribution to the data, it can be seen easily that it is not adequate because of thepossible bias. The data can even be smoothed by pooling the empirical classes but werather seek a modified model. The model can be found in different ways. The study will
present two of them.

4.1. Fitting the mixed negative binomial distribution for kanji lexical productivity
on the left-hand side
Since the kanji are taken from the ready list which may contain different classes of kanji –whatever kinds of classes may be concerned – it is, in the first step possible to add to theequation (5) a second component with different parameters and mixing the components indifferent proportions, say α and 1-α. Considering this specification, we obtain from theequation (5) the model in the form(6)

 r + x − 2  r x−1
 r + x − 2  r x−1α+−
Px =α 
p
q
(1
)
 1 1
 x − 1  p2 q2 , x = 1, 2,3,...
x
1
−





73

Katsuo Tamaoka, Gabriel Altmann

74

where p1, p2, r and α are coefficients interpreted above. In our case k = 1.2269, p1 = 0.1159,
p2 = 0.0270, α = 0.672. As can be seen, the Chi-square is 121.52 which with 143 DF
signalizes a very good fit, P = 0.90. The last theoretical value (at x = 268) was computed
as 1–

∑

267
x =0

Px . The graphical representation displaying it can be found in Fig. 1. The ob-served and theoretical values are shown together with class pooling NPx > 1 in Table A of
the Appendix.

Fig 1. Fitting the mixed negative binomial distribution to left-hand kanji
compounding

4.2. Fitting the Waring distribution for kanji lexical productivity on the left-hand side
Another method is the randomization of the parameter p yielding a compound distribution.
One of the many possibilities is, symbolically(7)

NB(r,p) ∧ beta(b,1)
pwhere beta(b,1) is the beta distribution with parameters b and 1, that is(8)

f ( p) =p b−1, 0 < p <1, q = 1 − p .
B (b,1)

Multiplying (5) by (8) and integrating the product according to p ∈ <0,1>, one obtains theWaring distribution, introduced in linguistics by G. Herdan, yielding
(9)

Px =

b
r ( x), x = 0,1, 2,...
b + r (b + r + 1)( x )However, this distribution can be obtained directly from the birth-and-death process with

Symmetry of Japanese kanji lexical productivity
birth-rate λx = r+x and death-rate µx = b+r+x. This distribution holds equally well for thedata in Table 2: Parameters: b = 3.4961, r = 53.6656, DF =136, Chi-square = 124.70, DF= 136, P = 0.75. Thus, one can derive the Waring distribution either directly form thebirth-and-death process or indirectly by randomisation. Assuming that more extended
examination could conceal some surprise, we preliminarily adhere to the negative binomial
distribution.

Fig. 2. Fitting the Waring distribution to left-hand kanji compounding

4.3. Kanji lexical productivity on the right-hand side
For the right-hand compounding in Table 3, the mixed negative binomial yields a X2 =134.56, DF = 136, P = 0.52, the fitting is shown graphically in Fig. 3. The Waring
distribution (with parameters b = 3.4224, r = 50.9697) is somewhat weaker (X2 = 162.19,
DF = 137, P = 0.07) but still acceptable. Different pooling of data can improve the fitting(up to P = 0.11). In Figure 4, one finds the fitting of (6) displayed graphically.

Fig. 3. Fitting the mixed negative binomial d. to right-hand kanji compounding

75

76

Katsuo Tamaoka, Gabriel Altmann

It must be remarked that the pooling of theoretical values has been performed so thateach class contained at least NPx > 1.00. The empirical values were pooled a posteriori but
the computation was made for each frequency class explicitly.

Fig. 4. Fitting the Waring distribution to right-hand kanji compounding

5. Symmetry of kanji lexical productivity
Looking at Table 1, one would intuitively say that left-hand and right-hand side compounding is not symmetrical. In order to test the symmetry (a), one can use for individual
kanji the binomial test setting p = 1/2, n = total compounding, and compute the probabilityof, say, the left-hand or the more extreme x. (b) For the whole table one can use the Bowker-test for symmetry (Bowker 1948), leaving out all kanji for which xleft = xright or simply
perform the test for homogeneity of two sides. (c) Making a quadratic contingency table ofthe data in Table 1, one can test the marginal homogeneity using Stuart´s test (Stuart
1955).
But if one constructs a two-dimensional distribution with X = left-hand, Y = right-handcompounding, one obtains an enormous matrix which is neither well processable nor very
interesting because the great majority of cells is empty. Thus, pooling is necessary. However, in that case, some differences between left and right compounding (within the pooling interval) disappear and the problem of symmetry gets a new face. Problem (a) is
eliminated, problem (b) changes thoroughly, problem (c) will display greater homogeneity,
but a new aspect arises, namely (d) the possibility to test whether the diagonal of the contingency matrix is preferred; that is, whether there is a tendency to make left-hand andright-hand compounding similar or not. Using test (a), one gets a result concerning individual kanjis, test (b) ignores the diagonal, but test (d) can show whether there is a tendency
to make the productivity on the two sides of kanji similar (not identical).

5.1. The compounding symmetry of individual kanji
In Table 1, kanji No. 1 has 16 compound words out of which it is 3 times on the left side(i.e., it is progressive) and 13 times on the right side (i.e., it is regressive) of the com-

Symmetry of Japanese kanji lexical productivity
pounds. One can ask whether this ratio is random or whether there is a tendency to build
compounds of a special kind. If there is no tendency, the probability that the compounding
part will stay right or left is p = 0.5. One finds n (here 16) compounds. What is theprobability that exactly x compounds will be progressive (regressive respectively)? Since
there are merely two possibilities, the compounds are distributed binomially; thus,
(10)

n
n
Px =   p x q n− x =   (1/ 2) n
 x
 x

in this case. However, we need the sum of all probabilities being smaller than 0.025 orgreater than 0.975; that is, we seek a number k1 for which P(X ≤ k1) ≤ 0.025 and a number
k2 for which P(X ≥ k2) ≤ 0.025. These can be computed by means of the criteria
(11)

n
P ( X ≤ k1 ) = ∑   (1/ 2) n ≤ 0.025
x =0  x 

(12)

n
n
P( X ≥ k2 ) = ∑   (1/ 2)n ≤ 0.025 .
x =k2  x 

k1

Thus, we obtain a kind of confidence interval [k1; k2] within which the basic kanji issymmetric, and below or above the interval there is a significant tendency to constructprogressive or regressive compounds.
For our example, we have n = 16. Computing the probabilities from 0 according to (11)we see that k1 = 4 and according to (3) k2 = 12 because the sum of the probabilities from x= 0 to x = 3 is smaller than 0.025, and that from 13 to 16 is smaller than 0.025, i.e. ourinterval is [4; 12]. Since kanji No.1 has 13 regressive compounds, it lies outside of theinterval and can be classified as a compositionally regressive kanji.
Consider kanji No. 6 with n = 63 compounds. The interval is [24; 39]; since the numbers
in Table 1 lie outside this interval and the left-hand side productivity is greater, this kanji
has a progressive compounding. However kanji No. 8 with n = 64 and interval [24; 40] lies
still in the interval and can be classified as symmetric. The other values are shown in thelast column of Table 4. All intervals for n = 6 to 400 are in the Appendix, Table C.
An asymptotic test for symmetry of individual kanji can be performed as follows: Let
the number of left-hand side compounds be nL, that of right-hand side ones nR and nL + nR
= n. Then, under the hypothesis of equality of both sides, the expected value is n/2. The
asymptotic Chi-square criterion is

(13)

n
n
n
n
( nL − ) 2 ( nR − ) 2 ( nL − ) 2 ( n − nL − ) 2
2 +
2 =
2 +
2
X2 =
n
n
n
n
2
2
2
2
(nL − nR ) 2=
nL + nR

77

Katsuo Tamaoka, Gabriel Altmann

78

which is distributed as a chi-square with 1 degree of freedom. At the α = 0.05 level it must
be greater than 3.84 in order to be significant. For example, let nL = 2 and n = 10, then (13)yields(2 − 8)2
= 3.6
X =
2+8
2

which is not significant, but for nL = 1, we obtain (1-9)2/10 = 6.4 which is significant. In
most cases this test yields the same results as the exact (binomial) test. Instead of nL one
can insert nR. The interpretation is the same.
All the 1,945 kanji were tested for symmetry. There were 227 kanji (11.67% of the total)
with less than 5 of the total kanji lexical productivity putting both the left-hand and righthand sides together. Excluding these kanji for symmetry, 902 kanji (46.38%) were judged
to be symmetric represented by ‘S’ in Table 4 for the examples of ten kanji. When the lefthand side productivity was greater than the right-hand side, a kanji was judged as progressively asymmetric presented by ‘P’. 403 kanji (20.72%) fell into this category. When theright-hand side productivity was greater than the left-hand side, a kanji was judged as
regressively asymmetric presented by ‘R’. 413 kanji (21.23%) were counted in thiscategory. Simply looking at the percentages, a set of the whole 1,945 basic kanji seems todisplay symmetric pattern of lexical productivity, being 20.72% for progressive, 46.38%
for symmetry and 21.23% for regressive. The next section investigates the pattern of the
1,945 basic kanji.
Table 4
Symmetric classification of the first ten kanji in lexical productivity
In
No. Kanji phonemes

Left-handside

Right-handsideBoth sides
togetherClassification

1

亜

/a/

3

13

16

R

2

哀

/ai/

1

19

20

R

3

愛

/ai/

28

55

83

R

4

悪

/aku/

35

80

115

R

5

握

/aku/

4

4

8

S

6

圧

/atu/

42

21

63

P

7

扱

/atu/

1

1

2

S

8

安

/aN/

24

40

64

S

9

案

/aN/

49

6

55

P

10

暗

/aN/

5

40

45

R

Symmetry of Japanese kanji lexical productivity

79

5.2. The symmetry of the entire compounding of 1,945 basic kanji
In order to ascertain whether the whole field of basic kanji displays symmetric compounding, one simply builds the sum of (13) which is identical with Bowker´s test forsymmetry in a contingency table, i.e.
(14)(nL ,i − nR ,i )2X =∑nL ,i + nR ,i
i =1
2

K

where K is the number of comparisons (here 1945). The number of degrees of freedom is
DF = (K – number of cases where nL and nR are equal).
An asymptotically equivalent test can be derived using information statistics, namely
K

(15)

2

2 I = 2∑∑ nij ln
i =1 j =1

nijni / 2K

2K

i =1 j =1

i =1= 2 N ln 2 + 2∑∑ nij ln nij − 2∑ ni ln ni

where N is the total sum of all frequencies, i is the identification number (ID in Table 4), j= 1,2 are the indices for left and right kanji respectively, ni = ni1 + ni2 (i.e. the marginal sum
for the ith kanji) and 0 ln 0 = 0 by definition.
Using criterion (14) we obtain X2 = 16,720.30 with 1,859 degree of freedom for the
1,945 kanji and using criterion (15) we obtain 2I = 2(76,485)ln 2 + 2(138,221.6192 +138,093.1164) – 2(319,903.0166) = 18,854.1622. Then subtracting 1 for each zero in thetable (complete Table 4 where there are 374 zeros) we obtain 2I = 18,483.16 with 1,944
degree of freedom. Though the difference between the test results seems to be great, bothof them indicated the same result 3 . The kanji productivity of compounds according toposition before or behind the kanji is extremely significant, suggesting an ‘asymmetric’
pattern of kanji lexical productivity on both sides. Consequently, although individual kanji
may display symmetry, there is no such symmetric tendency in the whole 1,945 basic kanji.

6. Summary
The present paper investigated the symmetry of the Japanese 1,945 basic kanji when
producing two-kanji compound words. The results indicated the following two findings.
First, construction of kanji compounds (or kanji lexical productivity) was represented by abirth-and-death process leading to the negative binomial and/or the Waring distribution.
Second, although about a half of individual kanji displayed symmetry in lexical productivity on the left-hand and right-hand sides, there is no tendency on the whole for basic
kanji to produce their compound words to the same extent on the left or the right side. Insummary, lexical productivity of two-kanji compound words was highly asymmetricamong the 1,945 basic kanji.

3

However, it is to be noted that this is not identical with the test for homogeneity for the left- and right-handproduction.

80

Katsuo Tamaoka, Gabriel Altmann

References4
Altmann, G. (1985). Die Entstehung diatopischer Varianten. Ein stochastisches Modell.
Zeitschrift für Sprachwissenschaft 4, 139-155.
Amano, N., & Kondo, K. (2000). Nihongo-no goi tokusei [Lexical properties ofJapanese]. Tokyo: Sanseido.
Bowker, A. H. (1948). A test for symmetry in contingency tables. Jouranal of theAmerican Statistical Association 43, 572-574.
Hayashi, S. (1987). Kanji, goi, bunshoo no kenkyuu e [Studies of kanji, words andsentences]. Tokyo: Meiji Shoin.
Ministry of Education, Science, Sports and Culture, Government of Japan (1987).
Shoogakkoo shidoosho - Kokugohen [The Japanese language - the course of
study at elementary school]. Osaka: Osaka Shoseki.
Ministry of Education, Science, Sports and Culture, Government of Japan (1998).
Monbushoo kokuji - Shoogakkoo gakushuu shidoo yooryoo [The announcement of
the elementary school course of study by the Ministry of Education, Science andCulture, Government of Japan.]. Tokyo: Gyosei.
Nomoto, K. (1989). Miraishakai to kanji [Kanji in the future society]. In K. Sato (ed.),Kanji kooza Vol. 11 - Kanji to kokugo mondai [Kanji lecture series Vol. 11 – Kanji
and problems of national language] (pp. 210-228). Tokyo: Meiji Shoin.
Nomura, M. (1988). Niji kango no koozoo [Structure of two-kanji compound words].
Nihongogaku [Study on the Japanese language], 7(5), 44-55.
Nomura, M. (1989). Kanji no zoogo ryoku [Productivity of kanji]. In K. Sato (ed.), Kanjikooza Vol. 1 - Kanji towa [Kanji lecture series Vol. 1 - What is kanji?] (pp. 193217). Tokyo: Meiji Shoin.
Kato, M. (1989). Kakushu kanji seigenan oyobi gen ‘Jooyoo Kanji’ wo meguru shojikooichiranhyoo [A proposal for the restriction of usage of various kanji and a list of
information regarding the present ‘Jooyoo Kanji’]. In K. Sato (ed.), Kanji koozaVol. 11 - Kanji to kokugo mondai [Kanji lecture series Vol. 11 – Kanji andproblems of the national language] (pp. 210-228). Tokyo: Meiji Shoin.
Köhler, R. (1986). Zur linguistischen Synergetik. Struktur und Dynamik der Lexik.
Bochum: Brockmeyer.
National Institute for Japanese Language (1976). Gendai Shinbun no Kanji [Japanese
kanji characters in modern newspapers]. Tokyo: National Language ResearchInstitute.
Stuart, A. (1955). A test for homogeneity of the marginal distribution in a two-way
classification. Biometrika 12, 412-416.
Tamaoka, K., Kirsner, K., Yanase, Y., Miyaoka, Y., Kawakami, M. (2002) A Webaccessible database of characteristics of the 1,945 basic Japanese kanji. Behavior
Research Methods, Instruments & Computers 34(2), 260-275.
Wimmer, G., Altmann, G. (1995). A model for morphological productivity. J. of
Quantitative Linguistics 2, 212-216.
Yasunaga, M. (1981). Jooyoo kanjihyoo ga umarerumade [A background history of the
Jooyoo Kanji List]. Gengo Seikatsu, 355, 24-31.
4In this paper, including references, an alphabetic description of Japanese names follows the commonly used
Hepburn style. As the Hepburn style does not distinguish between long and short vowels (for example,
the proper name of ‘Kondo’ is pronounced /koNdoR/ with a long vowel at the end), this paper uses thespelling of ‘Kondo’, not ‘Kondoo’. However, to represent precise sounds, Japanese titles of research papers
which include long vowels are shown by repeating the same vowels twice, such as ‘oo’.

Symmetry of Japanese kanji lexical productivity

81

Yokosawa, K., & Umeda, M. (1988). Processes in human Kanji-word recognition.
Proceedings of the 1988 IEEE international conference on systems, man, andcybernetics (pp. 377-380). August 8-12, 1988, Beijing and Shenyang, China.

Appendixes
Table A
Observed and computed values of the formula (6) for kanji lexical productivity(frequency counts of two-kanji compounds) on the left-hand with class pooling
X[i] F[i] NP[i]0 108 99.8942
1 135 109.1996
2 109 108.4107
3 128 104.0518
4
82 98.1938
584 91.7526
6
84 85.1954
7
61 78.7763
8
73 72.6353
967 66.8469
10
59 61.4462
11
53 56.4438
12
48 51.8353
13
49 47.6072
14
36 43.7403
15
37 40.2123
16
37 36.9996
17
39 34.0784
18
33 31.4251
19
29 29.0171
20
17 26.8330
21
34 24.8526
22
28 23.0571
23
15 21.4292
24
17 19.9530
25
22 18.6137
26
21 17.3981
27
19 16.2939
28
16 15.2902
29
13 14.3770
30
16 13.5451
31
15 12.7865
32
13 12.0937
33
8 11.4602
34
11 10.8800
35
10 10.3476
36
14 9.8584
37
14 9.4079
38
16 8.9923
39
5 8.6081
40
9 8.2522
41
13 7.9218
42
6 7.6144
43
8 7.3278

44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88

10
9
8
5
8
6
5
2
7
9
3
6
2
5
3
5
3
3
3
3
6
6
3
8
3
3
3
2
1
1
0
5
1
3
2
2
2
0
4
2
2
2
1
1
1

7.06006.8092
6.57386.3523
6.14365.94635.75965.58245.41415.25375.10084.95464.81474.68054.55174.42794.30874.19394.08303.97603.87253.77233.67533.58133.49023.40173.31583.23233.1512
3.07232.99552.92092.84822.77742.70842.64122.57582.51202.44982.38922.33012.2725
2.21632.16142.1080

89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133

2
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
4
0
1
2
1
1
1
0
1
0
1
1
4
0
2
2
1
1
0
0
1
1
1
1
1
2
1
0

2.05582.00491.95531.90691.85961.8135
1.76851.72471.68181.64011.5993
1.55961.52081.48291.44601.40991.37481.34041.30701.2743
1.2425
1.21141.18111.1515
1.1226
1.0945
1.06701.0402
1.01410.9886
0.96370.93950.91580.89280.87030.84830.82690.80600.78570.76580.74640.72760.7091
0.6912
0.6737

82

Katsuo Tamaoka, Gabriel Altmann
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178

0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0

0.65660.64000.62370.60790.59240.57740.56270.54840.53450.52090.50760.4947
0.48210.46980.45780.44610.43470.4236
0.41280.40230.39200.38200.37220.36270.35340.34430.33550.32690.31850.31040.30240.29470.28710.27970.27250.26550.25870.25210.2456
0.23930.23310.22710.22130.21560.2100

179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223

0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0

0.2046
0.19940.19420.18920.18430.17960.17490.17040.16600.16170.1576
0.15350.14950.14570.14190.13820.13470.13120.12780.12450.12130.11810.11510.11210.10920.10630.10360.10090.09830.0957
0.09330.09080.08850.08620.08390.08180.07960.07760.0756
0.0736
0.07170.06980.06800.06620.0645

224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1

0.06280.06120.0596
0.0581
0.0566
0.0551
0.0536
0.05220.05090.0496
0.04830.04700.04580.0446
0.04340.04230.04120.04010.03910.03810.03710.03610.03520.03420.03330.03250.03160.03080.03000.02920.02840.02770.02700.02630.02560.02490.02430.02360.02300.02240.02180.02130.02070.02020.7476

Symmetry of Japanese kanji lexical productivity

X[i] F[i] NP[i]072 70.0911
1
91 94.3658
2 115 103.6675
3 121 105.3928
4
90 102.8910
593 98.0122
6
92 91.8696
7
87 85.1598
880 78.3235
961 71.6374
1078 65.2700
11
51 59.3174
12
57 53.8274
13
49 48.8154
14
51 44.2755
15
34 40.1885
1645 36.5269
17
32 33.2588
18
35 30.3507
19
31 27.7686
20
29 25.4797
21
22 23.4529
22
21 21.6591
23
18 20.0716
24
22 18.6662
25
11 17.4210
26
21 16.3162
27
15 15.3343
28
17 14.4599
29
12 13.6792
30
14 12.9801
31
15 12.3521
32
15 11.7858
33
17 11.2733
34
16 10.8074
35
7 10.3820
36 13 9.9920
37
13 9.6326
38
13 9.2999
39
7 8.9906
40
11 8.7016
41
11 8.4305
42
15 8.1751
43
9 7.9334
44
12 7.7040
45
4 7.4854
46
6 7.2764
47
10 7.0762
48
5 6.8837
49
7 6.6982
50
8 6.5192
51
5 6.3460

52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104

6
4
8
4
2
4
1
6
3
5
4
5
3
0
1
3
1
2
2
4
5
3
1
3
2
6
1
3
4
0
1
2
0
0
1
3
1
0
2
1
1
0
0
2
1
1
0
1
0
1
0
2
1

6.17836.01565.85765.70405.55455.40895.26705.12884.99394.86244.73404.60874.48644.36704.25044.13664.02553.91703.8112
3.70783.60703.50853.41253.31883.22733.1381
3.05122.96632.88362.80302.72442.64782.57322.50042.42952.36052.29332.22782.16402.10192.04151.98261.9254
1.86961.8154
1.7626
1.7113
1.6613
1.61271.56551.51951.47481.4314

105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157

83

0
3
1
0
1
1
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
1
1

1.3891
1.34811.3082
1.26941.2317
1.19501.1594
1.12481.0912
1.05851.02680.99590.96600.93690.90870.88130.85460.82880.80370.77930.75560.73260.71030.68870.66770.64730.62750.60830.5896
0.57150.55400.53700.52040.50440.48890.47380.45910.44500.43120.41780.40490.39230.38010.36830.35690.34580.33500.32450.31440.3046
0.29510.28590.2769

84

Katsuo Tamaoka, Gabriel Altmann
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214

1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0.26820.25980.25170.24380.23610.22870.22150.21450.20780.20120.19490.18870.18280.17700.17140.16600.16070.15570.15070.14590.14130.13680.13250.12830.12420.12020.11640.11270.10910.10560.10230.09900.09590.09280.08980.08700.08420.08150.07890.07630.07390.07150.06920.06700.06490.06280.06080.05880.05690.0551
0.05330.05160.04990.04830.04680.04530.0438

215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0.04240.04100.03970.03840.03720.03600.03480.03370.0326
0.03150.03050.02950.02860.0276
0.02670.02590.02500.02420.02340.02270.02190.02120.02050.01990.01920.01860.01800.01740.01680.01630.01580.01520.01480.01430.01380.01340.01290.01250.01210.01170.01130.01090.01060.01020.00990.00960.00930.00900.00870.00840.00810.00780.00760.00730.00710.00690.0066

272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0.00640.00620.00600.00580.00560.00540.00530.00510.00490.00480.00460.00440.00430.00420.00400.00390.00380.00360.00350.00340.00330.00320.00310.00300.00290.00280.00270.00260.00250.00240.00240.00230.00220.00210.00210.00200.00190.00190.00180.00170.00170.00160.00160.00150.00150.00140.00140.00130.00130.00120.00120.00120.00110.00110.00100.00100.0010Symmetry of Japanese kanji lexical productivity
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0

0.00090.00090.00090.00090.00080.00080.00080.00070.00070.00070.00070.00070.00060.00060.00060.00060.00060.00050.00050.00050.00050.00050.00050.0004

353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399

0.00040.00040.00040.00040.00040.00040.00030.00030.00030.00030.00030.00030.00030.00030.00030.00030.00020.00020.00020.00020.00020.00020.00020.0002

85
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1

0.00020.00020.00020.00020.00020.00020.00020.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.00010.0026

Table CThe intervals for the symmetry of compound buildingn k1 k2
6, [1, 5]
7, [1, 6]8, [1, 7]
9, [2, 7]
10, [2, 8]
11, [2, 9]
12, [3, 9]
13, [3, 10]
14, [3, 11]
15, [4, 11]
16, [4, 12]
17, [5, 12]
18, [5, 13]
19, [5, 14]
20, [6, 14]
21, [6, 15]
22, [6, 16]
23, [7, 16]
24, [7, 17]25, [8, 17]
26, [8, 18]
27, [8, 19]
28, [9, 19]
29, [9, 20]
30, [10, 20]
31, [10, 21]
32, [10, 22]
33, [11, 22]34, [11, 23]
35, [12, 23]
36, [12, 24]
37, [13, 24]
38, [13, 25]
39, [13, 26]
40, [14, 26]
41, [14, 27]
42, [15, 27]
43, [15, 28]
44, [16, 28]
45, [16, 29]
46, [16, 30]
47, [17, 30]
48, [17, 31]
49, [18, 31]
50, [18, 32]
51, [19, 32]
52, [19, 33]
53, [19, 34]
54, [20, 34]
55, [20, 35]
56, [21, 35]
57, [21, 36]
58, [22, 36]
59, [22, 37]
60, [22, 38]
61, [23, 38]
62, [23, 39]

63, [24, 39]
64, [24, 40]
65, [25, 40]
66, [25, 41]
67, [26, 41]
68, [26, 42]
69, [26, 43]
70, [27, 43]
71, [27, 44]
72, [28, 44]73, [28, 45]
74, [29, 45]
75, [29, 46]
76, [29, 47]
77, [30, 47]
78, [30, 48]
79, [31, 48]
80, [31, 49]
81, [32, 49]
82, [32, 50]
83, [33, 50]
84, [33, 51]
85, [33, 52]
86, [34, 52]
87, [34, 53]
88, [35, 53]
89, [35, 54]
90, [36, 54]
91, [36, 55]

92, [37, 55]
93, [37, 56]
94, [38, 56]
95, [38, 57]
96, [38, 58]
97, [39, 58]
98, [39, 59]
99, [40, 59]
100, [40, 60]
101, [41, 60]
102, [41, 61]
103, [42, 61]
104, [42, 62]
105, [42, 63]
106, [43, 63]
107, [43, 64]
108, [44, 64]
109, [44, 65]
110, [45, 65]
111, [45, 66]
112, [46, 66]
113, [46, 67]
114, [47, 67]
115, [47, 68]
116, [47, 69]
117, [48, 69]
118, [48, 70]
119, [49, 70]
120, [49, 71]

86
121, [50, 71]
122, [50, 72]
123, [51, 72]
124, [51, 73]
125, [52, 73]
126, [52, 74]
127, [52, 75]
128, [53, 75]
129, [53, 76]
130, [54, 76]
131, [54, 77]
132, [55, 77]
133, [55, 78]
134, [56, 78]
135, [56, 79]
136, [57, 79]
137, [57, 80]
138, [58, 80]
139, [58, 81]
140, [58, 82]
141, [59, 82]
142, [59, 83]
143, [60, 83]
144, [60, 84]
145, [61, 84]
146, [61, 85]
147, [62, 85]
148, [62, 86]
149, [63, 86]
150, [63, 87]
151, [63, 88]
152, [64, 88]
153, [64, 89]
154, [65, 89]
155, [65, 90]
156, [66, 90]
157, [66, 91]
158, [67, 91]
159, [67, 92]
160, [68, 92]
161, [68, 93]
162, [69, 93]
163, [69, 94]
164, [69, 95]
165, [70, 95]
166, [70, 96]167, [71, 96]
168, [71, 97]
169, [72, 97]
170, [72, 98]
171, [73, 98]
172, [73, 99]
173, [74, 99]
174, [74, 100]
175, [75, 100]
176, [75, 101]
177, [75, 102]

Katsuo Tamaoka, Gabriel Altmann
178, [76, 102]
179, [76, 103]
180, [77, 103]
181, [77, 104]
182, [78, 104]
183, [78, 105]
184, [79, 105]
185, [79, 106]
186, [80, 106]
187, [80, 107]
188, [81, 107]
189, [81, 108]
190, [82, 108]
191, [82, 109]
192, [82, 110]
193, [83, 110]
194, [83, 111]
195, [84, 111]
196, [84, 112]
197, [85, 112]
198, [85, 113]
199, [86, 113]
200, [86, 114]
201, [87, 114]
202, [87, 115]
203, [88, 115]
204, [88, 116]
205, [88, 117]
206, [89, 117]
207, [89, 118]
208, [90, 118]
209, [90, 119]
210, [91, 119]
211, [91, 120]
212, [92, 120]
213, [92, 121]
214, [93, 121]
215, [93, 122]
216, [94, 122]
217, [94, 123]
218, [95, 123]
219, [95, 124]
220, [95, 125]
221, [96, 125]
222, [96, 126]
223, [97, 126]
224, [97, 127]
225, [98, 127]
226, [98, 128]
227, [99, 128]
228, [99, 129]
229, [100, 129]
230, [100, 130]
231, [101, 130]
232, [101, 131]
233, [102, 131]
234, [102, 132]

235, [102, 133]
236, [103, 133]
237, [103, 134]
238, [104, 134]
239, [104, 135]
240, [105, 135]
241, [105, 136]
242, [106, 136]
243, [106, 137]
244, [107, 137]
245, [107, 138]
246, [108, 138]
247, [108, 139]
248, [109, 139]
249, [109, 140]
250, [110, 140]
251, [110, 141]
252, [110, 142]
253, [111, 142]
254, [111, 143]
255, [112, 143]
256, [112, 144]
257, [113, 144]
258, [113, 145]
259, [114, 145]
260, [114, 146]
261, [115, 146]
262, [115, 147]
263, [116, 147]
264, [116, 148]
265, [117, 148]
266, [117, 149]
267, [118, 149]
268, [118, 150]
269, [118, 151]
270, [119, 151]
271, [119, 152]
272, [120, 152]
273, [120, 153]
274, [121, 153]
275, [121, 154]
276, [122, 154]
277, [122, 155]
278, [123, 155]
279, [123, 156]
280, [124, 156]
281, [124, 157]
282, [125, 157]
283, [125, 158]
284, [125, 159]
285, [126, 159]
286, [126, 160]
287, [127, 160]
288, [127, 161]
289, [128, 161]
290, [128, 162]
291, [129, 162]

292, [129, 163]
293, [130, 163]
294, [130, 164]
295, [131, 164]
296, [131, 165]
297, [132, 165]
298, [132, 166]
299, [133, 166]
300, [133, 167]
301, [134, 167]
302, [134, 168]
303, [134, 169]
304, [135, 169]
305, [135, 170]
306, [136, 170]
307, [136, 171]308, [137, 171]309, [137, 172]
310, [138, 172]
311, [138, 173]
312, [139, 173]
313, [139, 174]
314, [140, 174]
315, [140, 175]
316, [141, 175]
317, [141, 176]
318, [142, 176]
319, [142, 177]
320, [142, 178]
321, [143, 178]
322, [143, 179]
323, [144, 179]
324, [144, 180]
325, [145, 180]
326, [145, 181]
327, [146, 181]
328, [146, 182]
329, [147, 182]
330, [147, 183]
331, [148, 183]
332, [148, 184]
333, [149, 184]
334, [149, 185]
335, [150, 185]
336, [150, 186]
337, [151, 186]
338, [151, 187]
339, [151, 188]
340, [152, 188]
341, [152, 189]
342, [153, 189]
343, [153, 190]
344, [154, 190]
345, [154, 191]
346, [155, 191]
347, [155, 192]
348, [156, 192]

Symmetry of Japanese kanji lexical productivity
349, [156, 193]
350, [157, 193]
351, [157, 194]
352, [158, 194]
353, [158, 195]
354, [159, 195]
355, [159, 196]
356, [160, 196]
357, [160, 197]
358, [160, 198]
359, [161, 198]
360, [161, 199]
361, [162, 199]

362, [162, 200]
363, [163, 200]
364, [163, 201]
365, [164, 201]
366, [164, 202]
367, [165, 202]
368, [165, 203]
369, [166, 203]
370, [166, 204]
371, [167, 204]
372, [167, 205]
373, [168, 205]
374, [168, 206]

375, [169, 206]
376, [169, 207]
377, [169, 208]
378, [170, 208]
379, [170, 209]
380, [171, 209]
381, [171, 210]
382, [172, 210]
383, [172, 211]
384, [173, 211]
385, [173, 212]
386, [174, 212]
387, [174, 213]

87
388, [175, 213]
389, [175, 214]
390, [176, 214]
391, [176, 215]
392, [177, 215]
393, [177, 216]
394, [178, 216]
395, [178, 217]
396, [179, 217]
397, [179, 218]
398, [179, 219]
399, [180, 219]
400, [180, 220]