阵列问题的公式在解决各类阵列问题时，我们通常采用一个综合性的数学模型来描述系统状态。该模型将阵列划分为多个独立单元，每个单元包含若干功能模块，各模块之间存在特定的连接关系。通过定义各单元间的耦合系数和传输效率，可以计算出整体系统的响应能力。公式表达为：总输出等于各单元输出之和，即 $Y = sum Y_i$，其中 $Y_i$ 代表第 $i$ 个单元的输出值，$Y$ 代表阵列的总输出值。这一公式揭示了阵列系统的整体性能由各部分贡献决定，且各部分之间存在相互影响。在实际应用中，该公式常被用于评估不同配置方案下的表现，帮助决策者选择最优策略。< p > < li > < br > < u > < / u > < li > < br > < u > 阵列问题的公式 < / u > < li > < br > < u > 该公式是分析阵列系统的基石，它通过线性叠加原理将复杂系统简化为可计算的数学结构。公式中的每一项都对应着阵列中的一个关键要素，如信号源、放大器和滤波器。通过代入具体数值，可以直观地看到各要素如何影响最终结果。这种分析方法不仅适用于硬件设计，也适用于软件算法优化。在实际操作中，该公式能够准确预测阵列在不同负载情况下的性能表现。 < / p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > 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> < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < 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> < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < 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> < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < 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> < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < 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> < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > 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> < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < 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< p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < p > < 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