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Statement
Goal
Monitoring trails (m-trails) can instantaneously detect single and dual link failures in optical communication networks. An m-trail is an optical light-path, i.e., a laser transmits a light beam on a given wavelength at the start nodeThe traversed links
At the photo detector for
Our task is to identify the failed links (at most two) from the alarm code vector for a given link code matrix.
Example:
M-trails:
The corresponding link code matrix:
m_0 m_1 m_2 l_0 1 0 0l_1 1 0 1l_2 1 1 0l_3 0 1 0l_4 1 1 1
Alarm code vector: 110
If there can be only single link failure, from the simultaneous failure of
Input
Line 1: An integer links for the number of optical links.
Line 2: An integer mtrails for the number of m-trails.
Line 3: An integer failures for the maximum number of failures.
Line 4: An mtrails-length strings containing zeros and ones for the alarm code vector.
Next links lines: An mtrails-length string containing zeros and ones for the link code matrix.
Line 2: An integer mtrails for the number of m-trails.
Line 3: An integer failures for the maximum number of failures.
Line 4: An mtrails-length strings containing zeros and ones for the alarm code vector.
Next links lines: An mtrails-length string containing zeros and ones for the link code matrix.
Output
Link identifier k of the single failed link l_k, or the identifiers of the dual failed links in ascending order separated with a space (links are numbered from 0 to links-1). If the failure cannot be unambiguously identified, return AMBIGUOUS .
Constraints
5 ≤ links ≤ 90
3 ≤ mtrails ≤ 20
1 ≤ failures ≤ 2
3 ≤ mtrails ≤ 20
1 ≤ failures ≤ 2
Example
Input
5 3 1 010 100 101 110 010 111
Output
3
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