A. Chord

Vasya 正在学习音乐。 他已经学到了许多有趣的知识。例如，他知道共有 12 个音符：_C_、_C#_、_D_、_D#_、_E_、_F_、_F#_、_G_、_G#_、_A_、_B_、_H_。他还知道这些音符是循环重复的：_H_ 之后是 _C_，_C_ 之前是 _H_。我们将乐谱开头的 _C_ 和 _H_ 之后的 _C_ 视为相同，并将它们等同看待。音符之间的距离以全音为单位度量：相邻两个音符之间恰好是一个半音，即 0.5 全音。距离从最低音到最高音计算，即 _C_ 到 _E_ 的距离是 4 个半音，而 _E_ 到 _C_ 的距离是 8 个半音。 Vasya 也知道和弦是什么。和弦是不少于三个音符的无序集合。但目前 Vasya 只处理三和弦，即恰好由三个音符组成的和弦。他已能区分两种三和弦——大三和弦与小三和弦。 定义大三和弦：设该和弦由音符 #cf_span[X]、#cf_span[Y] 和 #cf_span[Z] 组成。如果能将这些音符排序，使得 #cf_span[X] 与 #cf_span[Y] 之间的距离为 4 个半音，且 #cf_span[Y] 与 #cf_span[Z] 之间的距离为 3 个半音，则该和弦为大三和弦。此时，#cf_span[X] 与 #cf_span[Z] 之间的距离为 7 个半音。 小三和弦的区别在于：#cf_span[X] 与 #cf_span[Y] 之间的距离应为 3 个半音，而 #cf_span[Y] 与 #cf_span[Z] 之间的距离为 4 个半音。 例如，和弦 "_C E G_" 是大三和弦：_C_ 与 _E_ 之间是 4 个半音，_E_ 与 _G_ 之间是 3 个半音。而三音组 "_C# B F_" 是小三和弦，因为若将音符排序为 "_B C# F_"，则 _B_ 与 _C#_ 之间是 3 个半音，_C#_ 与 _F_ 之间是 4 个半音。 帮助 Vasya 判断老师给他的三和弦类型。 仅一行，包含三个用空格分隔的音符，使用上述记号。 如果和弦是大三和弦，输出 "_major_"；如果是小三和弦，输出 "_minor_"；如果老师给的和弦既不是大三也不是小三，则输出 "_strange_"。Vasya 向你保证答案总是明确的，即不存在同时是大三和弦和小三和弦的和弦。 ## Input 仅一行，包含三个用空格分隔的音符，使用上述记号。 ## Output 如果和弦是大三和弦，输出 "_major_"；如果是小三和弦，输出 "_minor_"；如果老师给的和弦既不是大三也不是小三，则输出 "_strange_"。Vasya 向你保证答案总是明确的，即不存在同时是大三和弦和小三和弦的和弦。 [samples]

Let the 12 musical notes be represented as elements of $\mathbb{Z}_{12}$, where: $$ \begin{aligned} &\text{C} \mapsto 0, \quad \text{C\#} \mapsto 1, \quad \text{D} \mapsto 2, \quad \text{D\#} \mapsto 3, \quad \text{E} \mapsto 4, \quad \text{F} \mapsto 5, \\ &\text{F\#} \mapsto 6, \quad \text{G} \mapsto 7, \quad \text{G\#} \mapsto 8, \quad \text{A} \mapsto 9, \quad \text{B} \mapsto 10, \quad \text{H} \mapsto 11. \end{aligned} $$ Given three notes $a, b, c \in \mathbb{Z}_{12}$, define the set $S = \{a, b, c\}$. Let $x_0 < x_1 < x_2$ be the sorted representatives of $S$ in the cyclic order modulo 12, considering the circular nature: the distances are computed as the minimal clockwise steps. Define the three pairwise clockwise distances between consecutive notes (in sorted cyclic order): $$ d_1 = (x_1 - x_0) \mod 12, \quad d_2 = (x_2 - x_1) \mod 12, \quad d_3 = (x_0 + 12 - x_2) \mod 12. $$ Since the chord is a triad, exactly one of the three cyclic orderings yields a valid sequence of two adjacent intervals summing to 7 semitones (the third interval being 5 semitones, completing the circle). But for triads, we only consider the two intervals forming the stack (i.e., skip the wrap-around). Actually, since the chord is unordered and we are to find *any* permutation of the three notes such that the two consecutive intervals are (4,3) for major or (3,4) for minor, we can do the following: Let $T = \{a, b, c\}$. For each of the 6 permutations $(p_1, p_2, p_3)$ of $T$, compute: $$ d_1 = (p_2 - p_1) \mod 12, \quad d_2 = (p_3 - p_2) \mod 12. $$ If $d_1 = 4$ and $d_2 = 3$, then it is a **major** triad. If $d_1 = 3$ and $d_2 = 4$, then it is a **minor** triad. If no permutation satisfies either, output **strange**. Note: The third interval $d_3 = (p_1 - p_3) \mod 12$ is always $12 - d_1 - d_2$, and we do not need to check it. **Formal Statement:** Let $S \subset \mathbb{Z}_{12}$ with $|S| = 3$. Let $\mathcal{P}$ be the set of all ordered triples $(x, y, z)$ formed by permuting the elements of $S$. Define: $$ \text{major} \iff \exists (x, y, z) \in \mathcal{P} \text{ such that } (y - x) \mod 12 = 4 \text{ and } (z - y) \mod 12 = 3 \\ \text{minor} \iff \exists (x, y, z) \in \mathcal{P} \text{ such that } (y - x) \mod 12 = 3 \text{ and } (z - y) \mod 12 = 4 $$ Output: - "major" if major condition holds, - "minor" if minor condition holds, - "strange" otherwise.