In today's Function-as-a-Service offerings, a programmer is usually responsible for configuring function memory for its successful execution, which allocates proportional function resources such as CPU and network. However, right-sizing the function memory force developers to speculate performance and make ad-hoc configuration decisions. Recent research has highlighted that a function's input characteristics, such as input size, type and number of inputs, significantly impact its resource demand, run-time performance and costs with fluctuating workloads. This correlation further makes memory configuration a non-trivial task. On that account, an input-aware function memory allocator not only improves developer productivity by completely hiding resource-related decisions but also drives an opportunity to reduce resource wastage and offer a finer-grained cost-optimised pricing scheme. Therefore, we present MemFigLess, a serverless solution that estimates the memory requirement of a serverless function with input-awareness. The framework executes function profiling in an offline stage and trains a multi-output Random Forest Regression model on the collected metrics to invoke input-aware optimal configurations. We evaluate our work with the state-of-the-art approaches on AWS Lambda service to find that MemFigLess is able to capture the input-aware resource relationships and allocate upto 82% less resources and save up to 87% run-time costs.