Multi-messenger observations in the Einstein Telescope era: Binary neutron star and black hole–neutron star mergers

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Volume 704 (December 2025)

A&A, 704 (2025) A260

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Table 2.

Detection limits and predicted detection rates for NSNS and BHNS assuming different detector network configurations.

	GW ET	KN+GW			GRB afterglow+GW				GRB prompt+GW
		J	z	g	Radio	Optical	X-rays	VHE	Fermi
NSNS
Limit	12	21	24.4	26	0.01	26	10⁻¹³	CTA	3.09 × 10⁻⁷
ETΔ
Rate	$1 . 16_{- 0.85}^{+ 1.79} \times 10^{4}$ $1.16^{+1.79}_{-0.85}\times 10^4$	$2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$	$271_{- 200}^{+ 419}$ $271^{+419}_{-200}$	$2 . 54_{- 1.88}^{+ 3.93} \times 10^{3}$ $2.54^{+3.93}_{-1.88}\times 10^3$	$15_{- 11}^{+ 23}$ $15^{+23}_{-11}$	$15_{- 11}^{+ 23}$ $15^{+23}_{-11}$	$33_{- 24}^{+ 51}$ $33^{+51}_{-24}$	$0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$	$21_{- 13}^{+ 53}$ $21^{+53}_{-13}$
(ΔΩ_90% < 100 deg²)	( $130_{- 96}^{+ 202}$ $130^{+202}_{-96}$ )	( $1 . 8_{- 1.3}^{+ 2.8}$ $1.8^{+2.8}_{-1.3}$ )	( $42_{- 31}^{+ 65}$ $42^{+65}_{-31}$ )	( $104_{- 76}^{+ 160}$ $104^{+160}_{-76}$ )	( $2 . 8_{- 2.1}^{+ 4.4}$ $2.8^{+4.4}_{-2.1}$ )	( $1 . 2_{- 0.9}^{+ 1.8}$ $1.2^{+1.8}_{-0.9}$ )	( $1 . 7_{- 1.3}^{+ 2.7}$ $1.7^{+2.7}_{-1.3}$ )	( $0 . 01_{- 0.01}^{+ 0.02}$ $0.01^{+0.02}_{-0.01}$ )	( $1 . 3_{- 1.0}^{+ 2.1}$ $1.3^{+2.1}_{-1.0}$ )
(ΔΩ_90% < 10 deg²)	( $4 . 9_{- 3.6}^{+ 7.6}$ $4.9^{+7.6}_{-3.6}$ )	( $0 . 64_{- 0.47}^{+ 0.98}$ $0.64^{+0.98}_{-0.47}$ )	( $3 . 9_{- 2.9}^{+ 6.0}$ $3.9^{+6.0}_{-2.9}$ )	( $4 . 0_{- 3.0}^{+ 6.2}$ $4.0^{+6.2}_{-3.0}$ )	( $0 . 30_{- 0.22}^{+ 0.47}$ $0.30^{+0.47}_{-0.22}$ )	( $0 . 15_{- 0.11}^{+ 0.22}$ $0.15^{+0.22}_{-0.11}$ )	( $0 . 20_{- 0.15}^{+ 0.31}$ $0.20^{+0.31}_{-0.15}$ )	( $0 . 003_{- 0.002}^{+ 0.005}$ $0.003^{+0.005}_{-0.002}$ )	( $0 . 15_{- 0.11}^{+ 0.23}$ $0.15^{+0.23}_{-0.11}$ )
ET2L
Rate	$2 . 40_{- 1.77}^{+ 3.70} \times 10^{4}$ $2.40^{+3.70}_{-1.77}\times 10^4$	$2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$	$268_{- 198}^{+ 415}$ $268^{+415}_{-198}$	$2 . 89_{- 2.13}^{+ 4.47} \times 10^{3}$ $2.89^{+4.47}_{-2.13}\times 10^3$	$15_{- 11}^{+ 23}$ $15^{+23}_{-11}$	$20_{- 15}^{+ 31}$ $20^{+31}_{-15}$	$45_{- 33}^{+ 69}$ $45^{+69}_{-33}$	$0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$	$27_{- 17}^{+ 68}$ $27^{+68}_{-17}$
(ΔΩ_90% < 100 deg²)	( $412_{- 304}^{+ 636}$ $412^{+636}_{-304}$ )	( $2 . 0_{- 1.5}^{+ 3.2}$ $2.0^{+3.2}_{-1.5}$ )	( $125_{- 92}^{+ 193}$ $125^{+193}_{-92}$ )	( $283_{- 208}^{+ 437}$ $283^{+437}_{-208}$ )	( $6 . 6_{- 4.8}^{+ 10.1}$ $6.6^{+10.1}_{-4.8}$ )	( $4 . 0_{- 2.9}^{+ 6.1}$ $4.0^{+6.1}_{-2.9}$ )	( $5 . 7_{- 4.2}^{+ 8.8}$ $5.7^{+8.8}_{-4.2}$ )	( $0 . 02_{- 0.01}^{+ 0.03}$ $0.02^{+0.03}_{-0.01}$ )	( $3 . 9_{- 2.9}^{+ 6.1}$ $3.9^{+6.1}_{-2.9}$ )
(ΔΩ_90% < 10 deg²)	( $17_{- 13}^{+ 26}$ $17^{+26}_{-13}$ )	( $1 . 5_{- 1.1}^{+ 2.3}$ $1.5^{+2.3}_{-1.1}$ )	( $13_{- 10}^{+ 20}$ $13^{+20}_{-10}$ )	( $14_{- 10}^{+ 21}$ $14^{+21}_{-10}$ )	( $0 . 88_{- 0.64}^{+ 1.35}$ $0.88^{+1.35}_{-0.64}$ )	( $0 . 33_{- 0.24}^{+ 0.50}$ $0.33^{+0.50}_{-0.24}$ )	( $0 . 47_{- 0.35}^{+ 0.72}$ $0.47^{+0.72}_{-0.35}$ )	( $0 . 007_{- 0.005}^{+ 0.010}$ $0.007^{+0.010}_{-0.005}$ )	( $0 . 36_{- 0.27}^{+ 0.56}$ $0.36^{+0.56}_{-0.27}$ )
ETΔ+2CE
Rate	$6 . 70_{- 4.93}^{+ 10.34} \times 10^{4}$ $6.70^{+10.34}_{-4.93}\times 10^4$	$2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$	$278_{- 205}^{+ 430}$ $278^{+430}_{-205}$	$3 . 29_{- 2.43}^{+ 5.09} \times 10^{3}$ $3.29^{+5.09}_{-2.43}\times 10^3$	$16_{- 12}^{+ 25}$ $16^{+25}_{-12}$	$25_{- 18}^{+ 38}$ $25^{+38}_{-18}$	$65_{- 45}^{+ 100}$ $65^{+100}_{-45}$	$0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$	$37_{- 23}^{+ 100}$ $37^{+100}_{-23}$
(ΔΩ_90% < 100 deg²)	( $4 . 87_{- 3.60}^{+ 7.53} \times 10^{4}$ $4.87^{+7.53}_{-3.60}\times 10^4$ )	( $2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$ )	( $270_{- 200}^{+ 417}$ $270^{+417}_{-200}$ )	( $3 . 10_{- 2.28}^{+ 4.78} \times 10^{3}$ $3.10^{+4.78}_{-2.28}\times 10^3$ )	( $16_{- 12}^{+ 25}$ $16^{+25}_{-12}$ )	( $24_{- 18}^{+ 38}$ $24^{+38}_{-18}$ )	( $63_{- 46}^{+ 97}$ $63^{+97}_{-46}$ )	( $0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$ )	( $36_{- 27}^{+ 56}$ $36^{+56}_{-27}$ )
(ΔΩ_90% < 10 deg²)	( $3 . 68_{- 2.71}^{+ 5.68} \times 10^{3}$ $3.68^{+5.68}_{-2.71}\times 10^3$ )	( $2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$ )	( $251_{- 185}^{+ 388}$ $251^{+388}_{-185}$ )	( $1 . 98_{- 1.46}^{+ 3.05} \times 10^{3}$ $1.98^{+3.05}_{-1.46}\times 10^3$ )	( $13_{- 10}^{+ 20}$ $13^{+20}_{-10}$ )	( $11 . 5_{- 8.5}^{+ 17.8}$ $11.5^{+17.8}_{-8.5}$ )	( $20_{- 15}^{+ 31}$ $20^{+31}_{-15}$ )	( $0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$ )	( $13_{- 10}^{+ 20}$ $13^{+20}_{-10}$ )
ET2L+2CE
Rate	$7 . 81_{- 5.76}^{+ 12.06} \times 10^{4}$ $7.81^{+12.06}_{-5.76}\times 10^4$	$2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$	$278_{- 205}^{+ 430}$ $278^{+430}_{-205}$	$3 . 31_{- 2.44}^{+ 5.12} \times 10^{3}$ $3.31^{+5.12}_{-2.44}\times 10^3$	$16_{- 12}^{+ 25}$ $16^{+25}_{-12}$	$25_{- 19}^{+ 39}$ $25^{+39}_{-19}$	$68_{- 50}^{+ 100}$ $68^{+100}_{-50}$	$0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$	$38_{- 23}^{+ 100}$ $38^{+100}_{-23}$
(ΔΩ_90% < 100 deg²)	( $6 . 04_{- 4.45}^{+ 9.32} \times 10^{4}$ $6.04^{+9.32}_{-4.45}\times 10^4$ )	( $2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$ )	( $270_{- 200}^{+ 417}$ $270^{+417}_{-200}$ )	( $3 . 10_{- 2.28}^{+ 4.78} \times 10^{3}$ $3.10^{+4.78}_{-2.28}\times 10^3$ )	( $16_{- 12}^{+ 25}$ $16^{+25}_{-12}$ )	( $24_{- 18}^{+ 38}$ $24^{+38}_{-18}$ )	( $63_{- 46}^{+ 97}$ $63^{+97}_{-46}$ )	( $0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$ )	( $36_{- 27}^{+ 56}$ $36^{+56}_{-27}$ )
(ΔΩ_90% < 10 deg²)	( $4 . 98_{- 3.67}^{+ 7.69} \times 10^{3}$ $4.98^{+7.69}_{-3.67}\times 10^3$ )	( $2 . 4_{- 1.8}^{+ 3.8}$ $2.4^{+3.8}_{-1.8}$ )	( $251_{- 185}^{+ 388}$ $251^{+388}_{-185}$ )	( $1 . 98_{- 1.46}^{+ 3.05} \times 10^{3}$ $1.98^{+3.05}_{-1.46}\times 10^3$ )	( $13_{- 10}^{+ 20}$ $13^{+20}_{-10}$ )	( $11 . 5_{- 8.5}^{+ 17.8}$ $11.5^{+17.8}_{-8.5}$ )	( $20_{- 15}^{+ 31}$ $20^{+31}_{-15}$ )	( $0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$ )	( $13_{- 10}^{+ 20}$ $13^{+20}_{-10}$ )

BHNS
Limit	12	21	24.4	26	0.01	26	10⁻¹³	CTA	3.09 × 10⁻⁷
ETΔ
Rate	$1 . 39_{- 0.81}^{+ 1.41} \times 10^{4}$ $1.39^{+1.41}_{-0.81}\times 10^4$	$0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$	$4 . 2_{- 2.4}^{+ 4.2}$ $4.2^{+4.2}_{-2.4}$	$20_{- 11}^{+ 20}$ $20^{+20}_{-11}$	$0 . 21_{- 0.12}^{+ 0.21}$ $0.21^{+0.21}_{-0.12}$	$1 . 1_{- 0.6}^{+ 1.1}$ $1.1^{+1.1}_{-0.6}$	$1 . 4_{- 0.8}^{+ 1.4}$ $1.4^{+1.4}_{-0.8}$	$< 10^{- 3}$ ${<}10^{-3}$	$0 . 43_{- 0.24}^{+ 0.43}$ $0.43^{+0.43}_{-0.24}$
(ΔΩ_90% < 100 deg²)	( $94_{- 55}^{+ 95}$ $94^{+95}_{-55}$ )	( $0 . 04_{- 0.03}^{+ 0.04}$ $0.04^{+0.04}_{-0.03}$ )	( $0 . 8_{- 0.5}^{+ 0.8}$ $0.8^{+0.8}_{-0.5}$ )	( $2 . 6_{- 1.5}^{+ 2.6}$ $2.6^{+2.6}_{-1.5}$ )	( $0 . 08_{- 0.05}^{+ 0.08}$ $0.08^{+0.08}_{-0.05}$ )	( $0 . 10_{- 0.06}^{+ 0.11}$ $0.10^{+0.11}_{-0.06}$ )	( $0 . 14_{- 0.08}^{+ 0.14}$ $0.14^{+0.14}_{-0.08}$ )		( $0 . 06_{- 0.04}^{+ 0.06}$ $0.06^{+0.06}_{-0.04}$ )
(ΔΩ_90% < 10 deg²)	( $5 . 0_{- 2.9}^{+ 5.0}$ $5.0^{+5.0}_{-2.9}$ )	( $0 . 02_{- 0.01}^{+ 0.02}$ $0.02^{+0.02}_{-0.01}$ )	( $0 . 12_{- 0.07}^{+ 0.12}$ $0.12^{+0.12}_{-0.07}$ )	( $0 . 37_{- 0.21}^{+ 0.37}$ $0.37^{+0.37}_{-0.21}$ )	( $0 . 014_{- 0.008}^{+ 0.014}$ $0.014^{+0.014}_{-0.008}$ )	( $0 . 011_{- 0.007}^{+ 0.011}$ $0.011^{+0.011}_{-0.007}$ )	( $0 . 013_{- 0.008}^{+ 0.013}$ $0.013^{+0.013}_{-0.008}$ )		( $0 . 006_{- 0.004}^{+ 0.006}$ $0.006^{+0.006}_{-0.004}$ )
ET2L
Rate	$2 . 51_{- 1.46}^{+ 2.54} \times 10^{4}$ $2.51^{+2.54}_{-1.46}\times 10^4$	$0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$	$4 . 2_{- 2.4}^{+ 4.2}$ $4.2^{+4.2}_{-2.4}$	$20_{- 12}^{+ 20}$ $20^{+20}_{-12}$	$0 . 20_{- 0.12}^{+ 0.21}$ $0.20^{+0.21}_{-0.12}$	$1 . 6_{- 0.9}^{+ 1.6}$ $1.6^{+1.6}_{-0.9}$	$2 . 1_{- 1.2}^{+ 2.1}$ $2.1^{+2.1}_{-1.2}$	$< 10^{- 3}$ ${<}10^{-3}$	$0 . 47_{- 0.27}^{+ 0.47}$ $0.47^{+0.47}_{-0.27}$
(ΔΩ_90% < 100 deg²)	( $317_{- 184}^{+ 321}$ $317^{+321}_{-184}$ )	( $0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$ )	( $1 . 9_{- 1.1}^{+ 2.0}$ $1.9^{+2.0}_{-1.1}$ )	( $6 . 1_{- 3.6}^{+ 6.2}$ $6.1^{+6.2}_{-3.6}$ )	( $0 . 15_{- 0.09}^{+ 0.15}$ $0.15^{+0.15}_{-0.09}$ )	( $0 . 24_{- 0.14}^{+ 0.25}$ $0.24^{+0.25}_{-0.14}$ )	( $0 . 28_{- 0.17}^{+ 0.29}$ $0.28^{+0.29}_{-0.17}$ )		( $0 . 14_{- 0.08}^{+ 0.14}$ $0.14^{+0.14}_{-0.08}$ )
(ΔΩ_90% < 10 deg²)	( $13 . 9_{- 8.0}^{+ 14.1}$ $13.9^{+14.1}_{-8.0}$ )	( $0 . 04_{- 0.02}^{+ 0.04}$ $0.04^{+0.04}_{-0.02}$ )	( $0 . 38_{- 0.22}^{+ 0.38}$ $0.38^{+0.38}_{-0.22}$ )	( $0 . 45_{- 0.26}^{+ 0.45}$ $0.45^{+0.45}_{-0.26}$ )	( $0 . 04_{- 0.02}^{+ 0.04}$ $0.04^{+0.04}_{-0.02}$ )	( $0 . 03_{- 0.02}^{+ 0.03}$ $0.03^{+0.03}_{-0.02}$ )	( $0 . 03_{- 0.02}^{+ 0.03}$ $0.03^{+0.03}_{-0.02}$ )		( $0 . 02_{- 0.01}^{+ 0.02}$ $0.02^{+0.02}_{-0.01}$ )
ETΔ+2CE
Rate	$6 . 28_{- 3.64}^{+ 6.35} \times 10^{4}$ $6.28^{+6.35}_{-3.64}\times 10^4$	$0 . 06_{- 0.03}^{+ 0.05}$ $0.06^{+0.05}_{-0.03}$	$4 . 2_{- 2.4}^{+ 4.2}$ $4.2^{+4.2}_{-2.4}$	$20_{- 12}^{+ 21}$ $20^{+21}_{-12}$	$0 . 21_{- 0.12}^{+ 0.22}$ $0.21^{+0.22}_{-0.12}$	$2 . 8_{- 1.7}^{+ 2.9}$ $2.8^{+2.9}_{-1.7}$	$4 . 6_{- 2.7}^{+ 4.7}$ $4.6^{+4.7}_{-2.7}$	$< 10^{- 3}$ ${<}10^{-3}$	$0 . 64_{- 0.37}^{+ 0.65}$ $0.64^{+0.65}_{-0.37}$
(ΔΩ_90% < 100 deg²)	( $4 . 87_{- 2.82}^{+ 4.92} \times 10^{4}$ $4.87^{+4.92}_{-2.82}\times 10^4$ )	( $0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$ )	( $4 . 2_{- 2.4}^{+ 4.2}$ $4.2^{+4.2}_{-2.4}$ )	( $20_{- 11}^{+ 20}$ $20^{+20}_{-11}$ )	( $0 . 21_{- 0.12}^{+ 0.21}$ $0.21^{+0.21}_{-0.12}$ )	( $2 . 8_{- 1.6}^{+ 2.9}$ $2.8^{+2.9}_{-1.6}$ )	( $4 . 6_{- 2.6}^{+ 4.6}$ $4.6^{+4.6}_{-2.6}$ )		( $0 . 64_{- 0.37}^{+ 0.64}$ $0.64^{+0.64}_{-0.37}$ )
(ΔΩ_90% < 10 deg²)	( $4 . 66_{- 2.70}^{+ 4.71} \times 10^{3}$ $4.66^{+4.71}_{-2.70}\times 10^3$ )	( $0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$ )	( $4 . 2_{- 2.4}^{+ 4.2}$ $4.2^{+4.2}_{-2.4}$ )	( $19_{- 11}^{+ 19}$ $19^{+19}_{-11}$ )	( $0 . 20_{- 0.11}^{+ 0.20}$ $0.20^{+0.20}_{-0.11}$ )	( $0 . 86_{- 0.50}^{+ 0.87}$ $0.86^{+0.87}_{-0.50}$ )	( $1 . 0_{- 0.6}^{+ 1.0}$ $1.0^{+1.0}_{-0.6}$ )		( $0 . 35_{- 0.20}^{+ 0.36}$ $0.35^{+0.36}_{-0.20}$ )
ET2L+2CE
Rate	$7 . 15_{- 4.15}^{+ 7.24} \times 10^{4}$ $7.15^{+7.24}_{-4.15}\times 10^4$	$0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$	$4 . 2_{- 2.4}^{+ 4.2}$ $4.2^{+4.2}_{-2.4}$	$20_{- 12}^{+ 21}$ $20^{+21}_{-12}$	$0 . 23_{- 0.13}^{+ 0.23}$ $0.23^{+0.23}_{-0.13}$	$2 . 9_{- 1.7}^{+ 2.9}$ $2.9^{+2.9}_{-1.7}$	$4 . 6_{- 2.7}^{+ 4.7}$ $4.6^{+4.7}_{-2.7}$	< 10⁻³	$0 . 65_{- 0.37}^{+ 0.65}$ $0.65^{+0.65}_{-0.37}$
(ΔΩ_90% < 100 deg²)	( $5 . 82_{- 3.38}^{+ 5.89} \times 10^{4}$ $5.82^{+5.89}_{-3.38}\times 10^4$ )	( $0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$ )	( $4 . 2_{- 2.4}^{+ 4.2}$ $4.2^{+4.2}_{-2.4}$ )	( $20_{- 11}^{+ 20}$ $20^{+20}_{-11}$ )	( $0 . 21_{- 0.12}^{+ 0.21}$ $0.21^{+0.21}_{-0.12}$ )	( $2 . 8_{- 1.6}^{+ 2.9}$ $2.8^{+2.9}_{-1.6}$ )	( $4 . 6_{- 2.6}^{+ 4.6}$ $4.6^{+4.6}_{-2.6}$ )		( $0 . 64_{- 0.37}^{+ 0.64}$ $0.64^{+0.64}_{-0.37}$ )
(ΔΩ_90% < 10 deg²)	( $6 . 10_{- 3.54}^{+ 6.17} \times 10^{3}$ $6.10^{+6.17}_{-3.54}\times 10^3$ )	( $0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$ )	( $4 . 1_{- 2.4}^{+ 4.2}$ $4.1^{+4.2}_{-2.4}$ )	( $19_{- 11}^{+ 19}$ $19^{+19}_{-11}$ )	( $0 . 20_{- 0.12}^{+ 0.20}$ $0.20^{+0.20}_{-0.12}$ )	( $0 . 88_{- 0.51}^{+ 0.89}$ $0.88^{+0.89}_{-0.51}$ )	( $1 . 11_{- 0.65}^{+ 1.12}$ $1.11^{+1.12}_{-0.65}$ )		( $0 . 36_{- 0.21}^{+ 0.37}$ $0.36^{+0.37}_{-0.21}$ )

Notes. We report in parenthesis the detection rates assuming ΔΩ_90% < 100 deg² and ΔΩ_90% < 10 deg². The GW detection limits refer to the S/N_net threshold. Near infrared and optical limiting magnitudes are in the AB system; radio limiting flux densities are in mJy @ 1.4 GHz; X-ray limiting flux densities are in erg cm⁻² s⁻¹ keV⁻¹ @ 1 keV; gamma-ray limiting fluence is in erg cm⁻² (Fermi/GBM). Detection rates are in yr⁻¹. The reported errors, given at the 90% credible level, stem from the uncertainty on the overall merger rate, while systematic errors are not included.

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