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Bobo has a string $s_1¡­s_n$ of length $n$ consisting of only digits $0,1$, and $2$, and he wants to pick some disjoint subsequences which equal to $2020$, as many as possible.

Formally, Bobo would like to find $k$ quadrangle $(a_1,b_1,c_1,d_1),¡­,(a_k,b_k,c_k,d_k)$ where

• $1¡Üa_i<b_i<c_i<d_i¡Ün$
• $s_{a_i}{s}_{b_i}{s}_{c_i}{s}_{d_i}=2020$
• { a i , b i , c i , d i } ¡É { a j , b j , c j , d j } = ? \{a_i, b_i, c_i, d_i\} \cap \{a_j, b_j, c_j, d_j\} = \emptyset {ai?,bi?,ci?,di?}¡É{aj?,bj?,cj?,dj?}=? for $iªÁ=j$

Find the maximum value of k k