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In the title compound, C10H18N2O4S2·2H2O, the two cysteine moieties (zwitterions), separated by the rigid butene-1,4-diyl chain, adopt different conformations. These are characterized by the fact that the first S atom is anti to the carboxyl group in one moiety while the second S atom is gauche to both the carboxyl and protonated amino groups in the other moiety. The cysteine moieties and water mol­ecules are linked by hydrogen bonds, forming a 14-membered ring within the ac plane and layer connections along the b axis, which bind the structure together in three dimensions.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536802013442/cv6127sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536802013442/cv6127Isup2.hkl
Contains datablock I

CCDC reference: 197461

Key indicators

  • Single-crystal X-ray study
  • T = 293 K
  • Mean [sigma](C-C) = 0.006 Å
  • R factor = 0.041
  • wR factor = 0.089
  • Data-to-parameter ratio = 11.9

checkCIF results

No syntax errors found

ADDSYM reports no extra symmetry

General Notes

REFLT_03 From the CIF: _diffrn_reflns_theta_max 25.02 From the CIF: _reflns_number_total 2338 Count of symmetry unique reflns 1491 Completeness (_total/calc) 156.81% TEST3: Check Friedels for noncentro structure Estimate of Friedel pairs measured 847 Fraction of Friedel pairs measured 0.568 Are heavy atom types Z>Si present yes Please check that the estimate of the number of Friedel pairs is correct. If it is not, please give the correct count in the _publ_section_exptl_refinement section of the submitted CIF.

Comment top

L-Cysteine is one of the essential amino acids in nature. Some of its derivatives present remarkable bioactivities, and they can be used as antioxidants, antibacterial agents (Rabinkov et al., 1998) and chemical precursors of antitumor medicines (Hakimelahi et al., 2002). Although the crystal structure of both L-cysteine (Kerr & Ashmore, 1973, 1975; Görbitz & Dalhus, 1996; Harding et al., 1968) and DL-cysteine (Luger & Weber, 1999) have been reported, structures of bis(L-cysteine) derivatives are rare in the literature (Bigoli et al., 1982).

In this paper, the structure of the title compound, trans-s,s'-(but-2-ene-1,4-diyl)bis(L-cysteine) dihydrate, (I), is reported. The molecular structure of (I) is illustrated in Fig. 1.

The molecule of (I) has a trans configuration. The distance between atoms C5 and C6 is 1.299 (5) Å, which is shorter than the distance of 1.34 (1) Å for a normal CC bond (Lide, 1992–1993) and the distance of 1.326 Å in trans-2,5-dimethyl-3-hexene-2,5-diol. The angles C4—C5—C6 and C5—C6—C7 are 125.6 (3) and 123.5 (3)°, respectively, which are slightly smaller than those of 127.4 and 124.9° in trans-2,5-dimethy-3-hexene-2,5-diol (Ruysink & Vos, 1974). The torsion angle C4—C5—C6—C7 is 177.7 (4)°, indicating that the butenediyl group is almost planar. The C—S bond lengths [C3—S2 = 1.794 (4), C4—S2 = 1.812 (4), C7—S1 = 1.820 (4) and C8—S1 = 1.80 (4) Å] are in the same magnitude compared with the value of 1.811 (3) Å in L-cysteine (Kerr & Ashmore, 1973). The bond angles C3—S2—C4 and C8—S1—C7 are 102.1 (2) and 100.4 (2)°, respectively, slightly larger than the value of 99.05° in dimethyl sulfide (Lide, 1992–1993).

The difference in the C—O bond lengths of the two carboxyl groups is obviously influenced by hydrogen-bond environment (Table 2). Atoms O1 and O4 are involved in more than one hydrogen bond (O6—H3···O1, O5—H2···O1 and O5—H1···O1; N2—H2b···O4 and O6—H4···O4), while atoms O2 and O3 only take part one hydrogen-bond interaction, which may explain why the C1—O1 [1.252 (5) Å] and C10—O4 [1.263 (4) Å] bond lengths are longer than those of C1—O2 [1.218 (6) Å] and C10—O3 [1.231 (5) Å].

The two cysteine moieties (zwitterions), separated by the rigid butene-1,4-diyl skeleton, adopt different conformations. Atom S1 is anti to the C10/O3/O4 carboxyl group, with a S1—C8—C9—C10 torsion angle of 178.4°. However, atom S2 is gauche with respect to both the C1/O1/O2 carboxyl and protonated amino groups; the corresponding torsion angles, S2—C3—C2—C1 and S2—C3—C2—N1, are 61.8 (4) and 57.8 (4)°, respectively. The difference is clearly illustrated by the Newman projection shown in Fig. 4.

The molecules are arranged in the crystal lattice parallel to the ac plane, in which two N—H groups of the protonated amino group and two C—O groups of the carboxyl group, as well as two water molecules, form a 14-membered ring via hydrogen bonds. Interestingly, these molecules are linked together through hydrogen bonds along the b axis to form a three-dimensional network with an infinite tunnel.

Besides overwhelming intermolecular hydrogen bonding, there exists one intramolecular hydrogen-bond interaction (N2—H2b···O4) in the S1/C8/C9/C10/N2 moiety. No such interaction is found in the other moiety, which may explain the conformational differences of the two zwitterion moieties.

Experimental top

Compound (I) was synthesized by a modified literature method (Kalopissis & Manousses, 1975). A solution of 5.35 g (0.0025 mol) of trans-1,4-dibromo-2-butene in 5 ml e thanol was added dropwise to a mixture of 0.88 g (0.005 mol) of L-cysteine hydrochloride monohydrate, 1 ml of 10 mol l−1 sodium hydroxide, 5 ml of water and 7.5 ml of ethanol. After that, the reaction mixture was stirred for 10 h at room temperature. The precipitate was filtered off and recrystallized from water. Needle-like colorless crystal were obtained (yield 68%; m.p. 513–515 K (decomposition)]; IR (KBr): 3479 (b), 3024 (b), 2924 (s), 1687 (w), 1613 (versus, b), 1483 (s), 1419 (s), 1393 (s), 1342 (s), 1303 (s), 1069 (w), 1045 (w), 966 (versus) cm−1; 1H NMR (D2O): δ 5.65 (2H, bs), 4.17 (2H, t), 3.23 (4H, bs), 3.14 (2H, d), 3.00 (2H, dd) p.p.m. 10 mg of (I) was dissolved in 10 ml hot distilled water and, after filtration, the solution was kept at room temperature for 10 d yielding colorless single crystals of (I) suitable for X-ray analysis.

Refinement top

The water atoms H1–H4 were located on a difference Fourier map and refined using constraints.

Computing details top

Data collection: SMART (Bruker, 1997); cell refinement: SMART); data reduction: SAINT (Bruker, 1997) and SHELXTL (Bruker, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.

Figures top
[Figure 1] Fig. 1. View of the molecular structure of (I), with 30% probability ellipsoids, H atoms are shown as small spheres of arbitrary radii.
[Figure 2] Fig. 2. The crystal cell structure of (I), with a 14-membered hydrogen bond.
[Figure 3] Fig. 3. A packing diagram for (I), viewed along the b axis.
[Figure 4] Fig. 4. The Newman projection of (I).
Trans-s,s'-2-butene-1,4-diylbis(L-cysteine) dihydrate top
Crystal data top
C10H22N2O6S2F(000) = 352
Mr = 330.42Dx = 1.453 Mg m3
Monoclinic, P21Mo Kα radiation, λ = 0.71073 Å
a = 11.672 (4) ÅCell parameters from 1870 reflections
b = 5.3982 (19) Åθ = 2.7–23.1°
c = 12.413 (4) ŵ = 0.38 mm1
β = 105.020 (5)°T = 293 K
V = 755.4 (4) Å3Prism, colourless
Z = 20.30 × 0.15 × 0.10 mm
Data collection top
Bruker CCD area-detector
diffractometer
2338 independent reflections
Radiation source: fine-focus sealed tube1894 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.032
ϕ and ω scansθmax = 25.0°, θmin = 2.1°
Absorption correction: multi-scan
(SADABS; Bruker, 1997)
h = 138
Tmin = 0.895, Tmax = 0.963k = 56
3157 measured reflectionsl = 1314
Refinement top
Refinement on F2H atoms treated by a mixture of independent and constrained refinement
Least-squares matrix: full w = 1/[σ2(Fo2) + (0.04P)2]
where P = (Fo2 + 2Fc2)/3
R[F2 > 2σ(F2)] = 0.041(Δ/σ)max = 0.026
wR(F2) = 0.089Δρmax = 0.22 e Å3
S = 1.03Δρmin = 0.29 e Å3
2338 reflectionsAbsolute structure: (Flack, 1983)
197 parametersAbsolute structure parameter: 0.06 (10)
5 restraints
Crystal data top
C10H22N2O6S2V = 755.4 (4) Å3
Mr = 330.42Z = 2
Monoclinic, P21Mo Kα radiation
a = 11.672 (4) ŵ = 0.38 mm1
b = 5.3982 (19) ÅT = 293 K
c = 12.413 (4) Å0.30 × 0.15 × 0.10 mm
β = 105.020 (5)°
Data collection top
Bruker CCD area-detector
diffractometer
2338 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 1997)
1894 reflections with I > 2σ(I)
Tmin = 0.895, Tmax = 0.963Rint = 0.032
3157 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.041H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.089Δρmax = 0.22 e Å3
S = 1.03Δρmin = 0.29 e Å3
2338 reflectionsAbsolute structure: (Flack, 1983)
197 parametersAbsolute structure parameter: 0.06 (10)
5 restraints
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
S10.98558 (8)0.4300 (2)1.10310 (7)0.0328 (3)
S20.45673 (9)0.1031 (2)0.85490 (8)0.0422 (3)
O10.6590 (3)0.2498 (7)0.6583 (2)0.0616 (10)
O20.5305 (3)0.0490 (7)0.5978 (3)0.0590 (9)
O30.8327 (3)0.1955 (6)1.2887 (2)0.0494 (8)
O41.0023 (2)0.1342 (5)1.4161 (2)0.0431 (8)
N10.3428 (3)0.2090 (7)0.5987 (2)0.0440 (9)
H1A0.28380.30310.60860.066*
H1B0.33980.06130.62980.066*
H1C0.33590.19020.52610.066*
N21.0210 (3)0.3356 (6)1.3602 (2)0.0344 (8)
H2B1.00070.35451.42400.052*
H2C1.02540.48341.32980.052*
H2D1.09130.26081.37350.052*
C10.5569 (4)0.1601 (10)0.6329 (3)0.0414 (12)
C20.4582 (3)0.3297 (8)0.6518 (3)0.0326 (9)
H2A0.46220.48920.61530.039*
C30.4690 (3)0.3735 (8)0.7745 (3)0.0369 (11)
H3A0.40790.49010.78110.044*
H3B0.54510.45080.80710.044*
C40.6099 (3)0.0045 (8)0.9034 (3)0.0387 (11)
H4A0.61310.15430.94060.046*
H4B0.64300.01660.83990.046*
C50.6824 (3)0.1883 (8)0.9819 (3)0.0348 (10)
H5A0.66770.20361.05170.042*
C60.7645 (3)0.3291 (8)0.9611 (3)0.0332 (10)
H6A0.78230.31200.89260.040*
C70.8319 (3)0.5170 (8)1.0413 (3)0.0357 (10)
H7A0.79250.54081.10040.043*
H7B0.83020.67381.00280.043*
C80.9649 (3)0.1480 (7)1.1733 (3)0.0282 (9)
H8A0.90370.05081.12330.034*
H8B1.03790.05311.18810.034*
C90.9306 (3)0.1825 (7)1.2825 (3)0.0266 (8)
H9A0.85390.26731.26740.032*
C100.9195 (3)0.0686 (9)1.3333 (3)0.0317 (9)
O50.2479 (3)0.2084 (8)0.3453 (3)0.0740 (11)
O60.7661 (3)0.2056 (7)0.4830 (3)0.0572 (9)
H40.8416 (16)0.266 (7)0.512 (3)0.038 (11)*
H30.728 (4)0.178 (12)0.539 (3)0.099*
H20.297 (3)0.345 (5)0.351 (4)0.063*
H10.277 (4)0.051 (4)0.340 (4)0.066*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.0318 (6)0.0388 (6)0.0288 (5)0.0032 (5)0.0096 (4)0.0045 (5)
S20.0360 (6)0.0594 (8)0.0322 (6)0.0110 (6)0.0109 (4)0.0029 (6)
O10.0337 (18)0.099 (3)0.058 (2)0.0064 (17)0.0206 (14)0.0044 (19)
O20.067 (2)0.052 (2)0.063 (2)0.0183 (19)0.0257 (16)0.009 (2)
O30.060 (2)0.045 (2)0.0472 (18)0.0201 (16)0.0211 (15)0.0082 (16)
O40.0511 (18)0.040 (2)0.0407 (16)0.0058 (14)0.0159 (14)0.0122 (14)
N10.040 (2)0.059 (3)0.0305 (17)0.0137 (18)0.0058 (15)0.0003 (18)
N20.052 (2)0.026 (2)0.0259 (17)0.0014 (16)0.0129 (15)0.0032 (15)
C10.042 (3)0.061 (4)0.026 (2)0.020 (3)0.0178 (19)0.013 (2)
C20.029 (2)0.037 (3)0.033 (2)0.0042 (18)0.0106 (17)0.0027 (19)
C30.035 (2)0.040 (3)0.035 (2)0.0093 (19)0.0090 (17)0.008 (2)
C40.048 (3)0.040 (3)0.028 (2)0.003 (2)0.0088 (18)0.001 (2)
C50.038 (2)0.043 (3)0.0222 (19)0.001 (2)0.0049 (16)0.001 (2)
C60.038 (2)0.038 (3)0.024 (2)0.006 (2)0.0082 (17)0.0041 (19)
C70.037 (2)0.034 (3)0.035 (2)0.0011 (18)0.0061 (17)0.0037 (19)
C80.034 (2)0.031 (3)0.0194 (18)0.0010 (18)0.0053 (15)0.0005 (18)
C90.027 (2)0.025 (2)0.0286 (19)0.0030 (16)0.0087 (15)0.0012 (17)
C100.040 (2)0.030 (2)0.033 (2)0.004 (2)0.0224 (18)0.002 (2)
O50.056 (2)0.064 (3)0.110 (3)0.0246 (19)0.037 (2)0.011 (3)
O60.043 (2)0.076 (3)0.0567 (19)0.0064 (18)0.0217 (15)0.0144 (19)
Geometric parameters (Å, º) top
S1—C81.801 (4)C3—H3B0.9700
S1—C71.821 (4)C4—C51.491 (5)
S2—C31.794 (4)C4—H4A0.9700
S2—C41.812 (4)C4—H4B0.9700
O1—C11.249 (5)C5—C61.301 (5)
O2—C11.220 (6)C5—H5A0.9300
O3—C101.229 (5)C6—C71.494 (5)
O4—C101.265 (4)C6—H6A0.9300
N1—C21.487 (5)C7—H7A0.9700
N1—H1A0.8900C7—H7B0.9700
N1—H1B0.8900C8—C91.522 (4)
N1—H1C0.8900C8—H8A0.9700
N2—C91.483 (5)C8—H8B0.9700
N2—H2B0.8900C9—C101.514 (6)
N2—H2C0.8900C9—H9A0.9800
N2—H2D0.8900O5—H20.93 (3)
C1—C21.536 (6)O5—H10.92 (3)
C2—C31.514 (5)O6—H40.92 (3)
C2—H2A0.9800O6—H30.93 (4)
C3—H3A0.9700
C8—S1—C7100.41 (18)C5—C4—H4B109.3
C3—S2—C4102.09 (18)S2—C4—H4B109.3
C2—N1—H1A109.5H4A—C4—H4B108.0
C2—N1—H1B109.5C6—C5—C4125.6 (3)
H1A—N1—H1B109.5C6—C5—H5A117.2
C2—N1—H1C109.5C4—C5—H5A117.2
H1A—N1—H1C109.5C5—C6—C7123.5 (3)
H1B—N1—H1C109.5C5—C6—H6A118.3
C9—N2—H2B109.5C7—C6—H6A118.3
C9—N2—H2C109.5C6—C7—S1113.4 (3)
H2B—N2—H2C109.5C6—C7—H7A108.9
C9—N2—H2D109.5S1—C7—H7A108.9
H2B—N2—H2D109.5C6—C7—H7B108.9
H2C—N2—H2D109.5S1—C7—H7B108.9
O2—C1—O1125.8 (4)H7A—C7—H7B107.7
O2—C1—C2118.4 (4)C9—C8—S1115.3 (3)
O1—C1—C2115.7 (5)C9—C8—H8A108.5
N1—C2—C3110.1 (3)S1—C8—H8A108.5
N1—C2—C1107.4 (4)C9—C8—H8B108.5
C3—C2—C1112.1 (3)S1—C8—H8B108.5
N1—C2—H2A109.0H8A—C8—H8B107.5
C3—C2—H2A109.0N2—C9—C10110.6 (3)
C1—C2—H2A109.0N2—C9—C8109.9 (3)
C2—C3—S2115.8 (3)C10—C9—C8109.4 (3)
C2—C3—H3A108.3N2—C9—H9A109.0
S2—C3—H3A108.3C10—C9—H9A109.0
C2—C3—H3B108.3C8—C9—H9A109.0
S2—C3—H3B108.3O3—C10—O4125.2 (4)
H3A—C3—H3B107.4O3—C10—C9117.4 (3)
C5—C4—S2111.4 (3)O4—C10—C9117.3 (4)
C5—C4—H4A109.3H2—O5—H1121 (4)
S2—C4—H4A109.3H4—O6—H3111 (4)
O2—C1—C2—N111.6 (5)C5—C6—C7—S1108.5 (4)
O1—C1—C2—N1170.3 (3)C8—S1—C7—C661.1 (3)
O2—C1—C2—C3109.5 (4)C7—S1—C8—C977.6 (3)
O1—C1—C2—C368.6 (5)S1—C8—C9—N256.9 (3)
N1—C2—C3—S257.6 (4)S1—C8—C9—C10178.5 (3)
C1—C2—C3—S261.9 (4)N2—C9—C10—O3165.9 (3)
C4—S2—C3—C291.0 (3)C8—C9—C10—O372.9 (4)
C3—S2—C4—C566.2 (3)N2—C9—C10—O416.4 (4)
S2—C4—C5—C6110.4 (4)C8—C9—C10—O4104.9 (4)
C4—C5—C6—C7177.8 (4)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1C···O50.892.223.053 (5)157
O6—H3···O10.93 (4)1.90 (3)2.787 (4)159 (6)
N2—H2D···O5i0.891.972.788 (5)152
N2—H2B···O4ii0.891.992.864 (4)165
O6—H4···O4iii0.92 (3)1.89 (3)2.805 (4)174 (4)
O5—H2···O2iv0.93 (3)2.03 (3)2.821 (5)142 (4)
O5—H2···O1iv0.93 (3)2.26 (2)3.122 (5)156 (4)
O5—H1···O1v0.92 (3)1.80 (2)2.709 (5)175 (5)
Symmetry codes: (i) x+1, y, z+1; (ii) x+2, y+1/2, z+3; (iii) x+2, y+1/2, z+2; (iv) x+1, y+1/2, z+1; (v) x+1, y1/2, z+1.

Experimental details

Crystal data
Chemical formulaC10H22N2O6S2
Mr330.42
Crystal system, space groupMonoclinic, P21
Temperature (K)293
a, b, c (Å)11.672 (4), 5.3982 (19), 12.413 (4)
β (°) 105.020 (5)
V3)755.4 (4)
Z2
Radiation typeMo Kα
µ (mm1)0.38
Crystal size (mm)0.30 × 0.15 × 0.10
Data collection
DiffractometerBruker CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Bruker, 1997)
Tmin, Tmax0.895, 0.963
No. of measured, independent and
observed [I > 2σ(I)] reflections
3157, 2338, 1894
Rint0.032
(sin θ/λ)max1)0.595
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.041, 0.089, 1.03
No. of reflections2338
No. of parameters197
No. of restraints5
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.22, 0.29
Absolute structure(Flack, 1983)
Absolute structure parameter0.06 (10)

Computer programs: SMART (Bruker, 1997), SMART), SAINT (Bruker, 1997) and SHELXTL (Bruker, 1997), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), SHELXTL.

Selected geometric parameters (Å, º) top
N1—C21.487 (5)C4—C51.491 (5)
N2—C91.483 (5)C6—C71.494 (5)
C1—C21.536 (6)C8—C91.522 (4)
C2—C31.514 (5)C9—C101.514 (6)
O2—C1—O1125.8 (4)C5—C6—C7123.5 (3)
O2—C1—C2118.4 (4)C9—C8—S1115.3 (3)
O1—C1—C2115.7 (5)N2—C9—C10110.6 (3)
N1—C2—C3110.1 (3)N2—C9—C8109.9 (3)
N1—C2—C1107.4 (4)C10—C9—C8109.4 (3)
C3—C2—C1112.1 (3)O3—C10—O4125.2 (4)
C2—C3—S2115.8 (3)O3—C10—C9117.4 (3)
C6—C5—C4125.6 (3)O4—C10—C9117.3 (4)
O2—C1—C2—N111.6 (5)C8—S1—C7—C661.1 (3)
O1—C1—C2—N1170.3 (3)C7—S1—C8—C977.6 (3)
O2—C1—C2—C3109.5 (4)S1—C8—C9—N256.9 (3)
O1—C1—C2—C368.6 (5)N2—C9—C10—O3165.9 (3)
C4—S2—C3—C291.0 (3)C8—C9—C10—O372.9 (4)
C3—S2—C4—C566.2 (3)N2—C9—C10—O416.4 (4)
S2—C4—C5—C6110.4 (4)C8—C9—C10—O4104.9 (4)
C5—C6—C7—S1108.5 (4)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1C···O50.892.223.053 (5)157
O6—H3···O10.93 (4)1.90 (3)2.787 (4)159 (6)
N2—H2D···O5i0.891.972.788 (5)152
N2—H2B···O4ii0.891.992.864 (4)165
O6—H4···O4iii0.92 (3)1.89 (3)2.805 (4)174 (4)
O5—H2···O2iv0.93 (3)2.03 (3)2.821 (5)142 (4)
O5—H2···O1iv0.93 (3)2.26 (2)3.122 (5)156 (4)
O5—H1···O1v0.92 (3)1.80 (2)2.709 (5)175 (5)
Symmetry codes: (i) x+1, y, z+1; (ii) x+2, y+1/2, z+3; (iii) x+2, y+1/2, z+2; (iv) x+1, y+1/2, z+1; (v) x+1, y1/2, z+1.
 

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